Nonlift and nonlift candidate paramodular cusp forms

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Fourier coefficients	Proof of at most one nonlift	Proof/conjecture of existence, integrality, congruences
277	277	277
349	349	349
353	353	353
389	389	389
461	461	461
523	523	523
587-	587	587-
587+	587	587+

Proof of no nonlifts

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Proof level	raw data file
3 proof	raw file
5 proof	raw file
7 proof	raw file
11 proof	raw file
13 proof	raw file
17 proof	raw file
19 proof	raw file
23 proof	raw file
29 proof	raw file
31 proof	raw file
37 proof	raw file
41 proof	raw file
43 proof	raw file
47 proof	raw file
53 proof	raw file
59 proof	raw file
61 proof	raw file
67 proof	raw file
71 proof	raw file
73 proof	raw file
79 proof	raw file
83 proof	raw file
89 proof	raw file
97 proof	raw file
101 proof	raw file
103 proof	raw file
107 proof	raw file
109 proof	raw file
113 proof	raw file
127 proof	raw file
131 proof	raw file
137 proof	raw file
139 proof	raw file
149 proof	raw file
151 proof	raw file
157 proof	raw file
163 proof	raw file
167 proof	raw file
173 proof	raw file
179 proof	raw file
181 proof	raw file
191 proof	raw file
193 proof	raw file
197 proof	raw file
199 proof	raw file
211 proof	raw file
223 proof	raw file
227 proof	raw file
229 proof	raw file
233 proof	raw file
239 proof	raw file
241 proof	raw file
251 proof	raw file
257 proof	raw file
263 proof	raw file
269 proof	raw file
271 proof	raw file
277 (see above table)
281 proof	raw file
283 proof	raw file
293 proof	raw file
307 proof	raw file
311 proof	raw file
313 proof	raw file
317 proof	raw file
331 proof	raw file
337 proof	raw file
347 proof	raw file
349 (see above table)
353 (see above table)
359 proof	raw file
367 proof	raw file
373 proof	raw file
379 proof	raw file
383 proof	raw file
389 (see above table)
397 proof	raw file
401 proof	raw file
409 proof	raw file
419 proof	raw file
421 proof	raw file
431 proof	raw file
433 proof	raw file
439 proof	raw file
443 proof	raw file
449 proof	raw file
457 proof	raw file
461 (see above table)
463 proof	raw file
467 proof	raw file
479 proof	raw file
487 proof	raw file
491 proof	raw file
499 is special, read appendix of paper
503 proof	raw file
509 proof	raw file
521 proof	raw file
523 (see above table)
541 proof	raw file
547 proof	raw file
557 proof	raw file
563 proof	raw file
569 proof	raw file
571 proof	raw file
577 proof	raw file
587 (see above table)
593 proof	raw file
599 proof	raw file