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lfunc_lfunctions • Show schema
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{'Lhash': '1800991096383167303082965266119', 'a10': 960, 'a2': 8, 'a3': 0, 'a4': 64, 'a5': 120, 'a6': 0, 'a7': 377, 'a8': 512, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.868791376142582, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -8]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '54.1', 'coefficient_field': '1.1.1.1', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1, -8], [1], [1, -120, 78125], [1, -377, 823543], [1, -600, 19487171], [1, -5369, 62748517], [1, -12168, 410338673], [1, -16211, 893871739], [1, -106392, 3404825447], [1, -177216, 17249876309], [1, 268060, 27512614111], [1, -114959, 94931877133], [1, 112128, 194754273881], [1, 115048, 271818611107], [1, -561336, 506623120463], [1, 1787760, 1174711139837], [1, 1786344, 2488651484819], [1, 1306837, 3142742836021], [1, 2013817, 6060711605323], [1, 4060944, 9095120158391], [1, 3850639, 11047398519097], [1, 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'positive_zeros': ['1.42073146658780787921852952738646', '3.22013881846311690052507274075433', '4.88279479120442117985688092903918', '6.12058908911325826341898168948183', '7.56692515506943755919618262672812', '9.121085939868488568377273578416847', '10.59619386209118130026424453878151', '11.65172943096396841762973300616571', '12.88681696965334178388850609695622', '13.86867928058926597482648858992633'], 'prelabel': '2-54-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.107163422137301, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c7-0', 'trace_hash': 1590183144751372177, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.42073146658780787921852952739', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.22013881846311690052507274075', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.88279479120442117985688092904', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.868791376142582, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 8, 0, 64, 120, 0, 377, 512, 0, 960, 600, 0, 5369, 3016, 0, 4096, 12168, 0, 16211, 7680, 0, 4800, 106392, 0, -63725, 42952, 0, 24128, 177216, 0, -268060, 32768, 0, 97344, 45240, 0, 114959, 129688, 0, 61440, -112128, 0, -115048, 38400, 0, 851136, 561336, 0, -681414, -509800, 0, 343616, -1787760, 0, 72000, 193024, 0, 1417728, -1786344, 0, -1306837, -2144480, 0, 262144, 644280, 0, -2013817, 778752, 0, 361920, -4060944, 0, -3850639, 919672, 0, 1037504, 226200, 0, 1037231, 491520, 0, -897024, 9203568, 0, 1460160, -920384, 0, 307200, -1289304, 0, 2024113, 6809088, 0, 4490688, 1945320, 0, 8555885, -5451312, 0, -4078400], 'euler11': [1, -600, 19487171], 'euler13': [1, -5369, 62748517], 'euler17': [1, -12168, 410338673], 'euler19': [1, -16211, 893871739], 'euler2': [1, -8, 0], 'euler23': [1, -106392, 3404825447], 'euler29': [1, -177216, 17249876309], 'euler3': [1, 0, 0], 'euler31': [1, 268060, 27512614111], 'euler37': [1, -114959, 94931877133], 'euler41': [1, 112128, 194754273881], 'euler43': [1, 115048, 271818611107], 'euler47': [1, -561336, 506623120463], 'euler5': [1, -120, 78125], 'euler53': [1, 1787760, 1174711139837], 'euler59': [1, 1786344, 2488651484819], 'euler61': [1, 1306837, 3142742836021], 'euler67': [1, 2013817, 6060711605323], 'euler7': [1, -377, 823543], 'euler71': [1, 4060944, 9095120158391], 'euler73': [1, 3850639, 11047398519097], 'euler79': [1, -1037231, 19203908986159], 'euler83': [1, -9203568, 27136050989627], 'euler89': [1, 1289304, 44231334895529], 'euler97': [1, -8555885, 80798284478113], 'euler_factors': [[1, -8, 0], [1, 0, 0], [1, -120, 78125], [1, -377, 823543], [1, -600, 19487171], [1, -5369, 62748517], [1, -12168, 410338673], [1, -16211, 893871739], [1, -106392, 3404825447], [1, -177216, 17249876309], [1, 268060, 27512614111], [1, -114959, 94931877133], [1, 112128, 194754273881], [1, 115048, 271818611107], [1, -561336, 506623120463], [1, 1787760, 1174711139837], [1, 1786344, 2488651484819], [1, 1306837, 3142742836021], [1, 2013817, 6060711605323], [1, 4060944, 9095120158391], [1, 3850639, 11047398519097], [1, -1037231, 19203908986159], [1, -9203568, 27136050989627], [1, 1289304, 44231334895529], [1, -8555885, 80798284478113]], 'index': 4, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/54/8/a/f/1/1', 'ModularForm/GL2/Q/holomorphic/54/8/a/f'], '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': '2-54-1.1-c7-0-4', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-54-1.1-c7-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.107163422137301, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'trace_hash': 1590183144751372177, 'z1': {'__RealLiteral__': 0, 'data': '1.42073146658780787921852952739', 'prec': 103}}
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lfunc_instances • Show schema
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id: 16281934
{'Lhash': '1800991096383167303082965266119', 'Lhash_array': ['1800991096383167303082965266119'], 'label': '2-54-1.1-c7-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/8/a/f'}
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id: 24555880
{'Lhash': '1800991096383167303082965266119', 'Lhash_array': ['1800991096383167303082965266119'], 'label': '2-54-1.1-c7-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/8/a/f/1/1'}