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lfunc_lfunctions • Show schema
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{'Lhash': '2000830983638110369647080566334', 'a10': -80, 'a2': 8, 'a3': 27, 'a4': 64, 'a5': -10, 'a6': 216, 'a7': -343, 'a8': 512, 'a9': 729, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 170.56222391433056, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -8]], [3, [1, -27]], [7, [1, 343]], [13, [1, -2197]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.1', 'coefficient_field': '1.1.1.1', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, -8], [1, -27], [1, 10, 78125], [1, 343], [1, -1508, 19487171], [1, -2197], [1, 1042, 410338673], [1, 9068, 893871739], [1, 98988, 3404825447], [1, 213642, 17249876309], [1, 22048, 27512614111], [1, -418246, 94931877133], [1, 76414, 194754273881], [1, 177524, 271818611107], [1, -631916, 506623120463], [1, 982354, 1174711139837], [1, 596384, 2488651484819], [1, -1863406, 3142742836021], [1, 1845652, 6060711605323], [1, -1632280, 9095120158391], [1, 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'positive_zeros': ['1.57837734094700720670726401601774', '2.49219681664845626921846534962585', '3.69569971310356149828961154530120', '4.20721176332782513868914523472295', '5.62869530701833990314981776335755', '6.34969379181831723846537577132834', '7.43956525317654958554676863649349', '8.194205921707959177733702930532310', '9.323215567299887563768310128727532'], 'prelabel': '2-546-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.059947316675155, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 232368339943961002, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57837734094700720670726401602', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49219681664845626921846534963', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69569971310356149828961154530', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 170.56222391433056, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 8, 27, 64, -10, 216, -343, 512, 729, -80, 1508, 1728, 2197, -2744, -270, 4096, -1042, 5832, -9068, -640, -9261, 12064, -98988, 13824, -78025, 17576, 19683, -21952, -213642, -2160, -22048, 32768, 40716, -8336, 3430, 46656, 418246, -72544, 59319, -5120, -76414, -74088, -177524, 96512, -7290, -791904, 631916, 110592, 117649, -624200, -28134, 140608, -982354, 157464, -15080, -175616, -244836, -1709136, -596384, -17280, 1863406, -176384, -250047, 262144, -21970, 325728, -1845652, -66688, -2672676, 27440, 1632280, 373248, 216650, 3345968, -2106675, -580352, -517244, 474552, -6460168, -40960, 531441, -611312, 3592152, -592704, 10420, -1420192, -5768334, 772096, -9482662, -58320, -753571, -6335232, -595296, 5055328, 90680, 884736, 840226, 941192, 1099332, -4993600], 'euler11': [1, -1508, 19487171], 'euler13': [1, -2197, 0], 'euler17': [1, 1042, 410338673], 'euler19': [1, 9068, 893871739], 'euler2': [1, -8, 0], 'euler23': [1, 98988, 3404825447], 'euler29': [1, 213642, 17249876309], 'euler3': [1, -27, 0], 'euler31': [1, 22048, 27512614111], 'euler37': [1, -418246, 94931877133], 'euler41': [1, 76414, 194754273881], 'euler43': [1, 177524, 271818611107], 'euler47': [1, -631916, 506623120463], 'euler5': [1, 10, 78125], 'euler53': [1, 982354, 1174711139837], 'euler59': [1, 596384, 2488651484819], 'euler61': [1, -1863406, 3142742836021], 'euler67': [1, 1845652, 6060711605323], 'euler7': [1, 343, 0], 'euler71': [1, -1632280, 9095120158391], 'euler73': [1, -216650, 11047398519097], 'euler79': [1, 6460168, 19203908986159], 'euler83': [1, -3592152, 27136050989627], 'euler89': [1, 9482662, 44231334895529], 'euler97': [1, -840226, 80798284478113], 'euler_factors': [[1, -8, 0], [1, -27, 0], [1, 10, 78125], [1, 343, 0], [1, -1508, 19487171], [1, -2197, 0], [1, 1042, 410338673], [1, 9068, 893871739], [1, 98988, 3404825447], [1, 213642, 17249876309], [1, 22048, 27512614111], [1, -418246, 94931877133], [1, 76414, 194754273881], [1, 177524, 271818611107], [1, -631916, 506623120463], [1, 982354, 1174711139837], [1, 596384, 2488651484819], [1, -1863406, 3142742836021], [1, 1845652, 6060711605323], [1, -1632280, 9095120158391], [1, -216650, 11047398519097], [1, 6460168, 19203908986159], [1, -3592152, 27136050989627], [1, 9482662, 44231334895529], [1, -840226, 80798284478113]], 'index': 78, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/8/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/546/8/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-546-1.1-c7-0-78', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-546-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 13.059947316675155, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 232368339943961002, 'z1': {'__RealLiteral__': 0, 'data': '1.57837734094700720670726401602', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20865686
{'Lhash': '2000830983638110369647080566334', 'Lhash_array': ['2000830983638110369647080566334'], 'label': '2-546-1.1-c7-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/8/a/c'}
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id: 24594018
{'Lhash': '2000830983638110369647080566334', 'Lhash_array': ['2000830983638110369647080566334'], 'label': '2-546-1.1-c7-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/8/a/c/1/1'}