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lfunc_lfunctions • Show schema
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{'Lhash': '1270753263261310075187017341412,1729304594428942309436459547658', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -82, 'a6': 0, 'a7': 98, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26136.183442385598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -98, 2401]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.1', 'coefficient_field': '1.1.1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, 82, 4826, 256250, 9765625], [1, -98, 2401], [1, -340, 338582, -54757340, 25937424601], [1, -910, 424866, -337876630, 137858491849], [1, 3216, 5412958, 4566260112, 2015993900449], [1, -674, 4367142, -1668890726, 6131066257801], [1, 1104, 11388910, 7105722672, 41426511213649], [1, 8064, 52795702, 165401905536, 420707233300201], [1, -6212, 51691038, -177844286012, 819628286980801], [1, 8512, 104326950, 590255761984, 4808584372417849], [1, 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'2.17011482081177402574975964839097', '2.44900018590490422955780581196449', '3.58853481527506547326383037837849', '3.65515025034331237826678027192183', '4.27542748156182842835518704917532', '4.28189411681381673905601221169651', '5.11106346973371617143128620697320', '5.48658832419772704847951516642163', '6.24719227751406570541971007090596', '6.48140196088266776150910194410515', '6.99776912218785861485492708788294', '7.30992995182567865005322322296145', '7.86306698847164462236556414465513', '8.337453001800300570429596163726766', '8.555462264747417879930574420369698', '8.788583736632121018759224213150307'], 'prelabel': '4-1008e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c5e2-0', 'trace_hash': 197697958404883351, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00244756956887179034387628849', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.36418078776407011893637310241', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.17011482081177402574975964839', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 26136.183442385598, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -82, 0, 98, 0, 0, 0, 340, 0, 910, 0, 0, 0, -3216, 0, 674, 0, 0, 0, -1104, 0, 1898, 0, 0, 0, -8064, 0, 6212, 0, 0, 0, -8036, 0, -8512, 0, 0, 0, 1304, 0, 10004, 0, 0, 0, -12748, 0, 7203, 0, 0, 0, 11220, 0, -27880, 0, 0, 0, -12018, 0, 102738, 0, 0, 0, -74620, 0, -24136, 0, 0, 0, 89720, 0, -55588, 0, 0, 0, 33320, 0, -48824, 0, 0, 0, 35782, 0, 263712, 0, 0, 0, 18300, 0, 89180, 0, 0, 0, -55268, 0, -69984, 0, 0, 0], 'euler11': [1, -340, 338582, -54757340, 25937424601], 'euler13': [1, -910, 424866, -337876630, 137858491849], 'euler17': [1, 3216, 5412958, 4566260112, 2015993900449], 'euler19': [1, -674, 4367142, -1668890726, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 1104, 11388910, 7105722672, 41426511213649], 'euler29': [1, 8064, 52795702, 165401905536, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -6212, 51691038, -177844286012, 819628286980801], 'euler37': [1, 8512, 104326950, 590255761984, 4808584372417849], 'euler41': [1, -1304, 73546526, -151076486104, 13422659310152401], 'euler43': [1, -10004, 99339510, -1470672463772, 21611482313284249], 'euler47': [1, 12748, 323438270, 2923690149236, 52599132235830049], 'euler5': [1, 82, 4826, 256250, 9765625], 'euler53': [1, -11220, 664373806, -4692153431460, 174887470365513049], 'euler59': [1, 12018, -285266426, 8591960225382, 511116753300641401], 'euler61': [1, -102738, 4326026138, -86772134772138, 713342911662882601], 'euler67': [1, 24136, 1542084918, 32586619582552, 1822837804551761449], 'euler7': [1, -98, 2401, 0, 0], 'euler71': [1, -89720, 4576356302, -161875457371720, 3255243551009881201], 'euler73': [1, 55588, 3902743302, 115237903711684, 4297625829703557649], 'euler79': [1, 48824, 5430110622, 150234201624776, 9468276082626847201], 'euler83': [1, -35782, 4098945062, -140946752287826, 15516041187205853449], 'euler89': [1, -18300, 3539716918, -102188287916700, 31181719929966183601], 'euler97': [1, 69984, 18325482398, 600976420545888, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 82, 4826, 256250, 9765625], [1, -98, 2401, 0, 0], [1, -340, 338582, -54757340, 25937424601], [1, -910, 424866, -337876630, 137858491849], [1, 3216, 5412958, 4566260112, 2015993900449], [1, -674, 4367142, -1668890726, 6131066257801], [1, 1104, 11388910, 7105722672, 41426511213649], [1, 8064, 52795702, 165401905536, 420707233300201], [1, -6212, 51691038, -177844286012, 819628286980801], [1, 8512, 104326950, 590255761984, 4808584372417849], [1, -1304, 73546526, -151076486104, 13422659310152401], [1, -10004, 99339510, -1470672463772, 21611482313284249], [1, 12748, 323438270, 2923690149236, 52599132235830049], [1, -11220, 664373806, -4692153431460, 174887470365513049], [1, 12018, -285266426, 8591960225382, 511116753300641401], [1, -102738, 4326026138, -86772134772138, 713342911662882601], [1, 24136, 1542084918, 32586619582552, 1822837804551761449], [1, -89720, 4576356302, -161875457371720, 3255243551009881201], [1, 55588, 3902743302, 115237903711684, 4297625829703557649], [1, 48824, 5430110622, 150234201624776, 9468276082626847201], [1, -35782, 4098945062, -140946752287826, 15516041187205853449], [1, -18300, 3539716918, -102188287916700, 31181719929966183601], [1, 69984, 18325482398, 600976420545888, 73742412689492826049]], 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/6/a/bd'], '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': '4-1008e2-1.1-c5e2-0-15', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'prelabel': '4-1008e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 197697958404883351, 'z1': {'__RealLiteral__': 0, 'data': '1.00244756956887179034387628849', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1270753263261310075187017341412,1729304594428942309436459547658', 'Lhash_array': ['1270753263261310075187017341412', '1729304594428942309436459547658'], 'factors': ['2-1008-1.1-c5-0-42', '2-1008-1.1-c5-0-64'], 'label': '4-1008e2-1.1-c5e2-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/6/a/bd'}