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lfunc_lfunctions • Show schema
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{'Lhash': '1077914641112011166796065802048,1829654354720492160131892596977,2198902924753626687239859009179,2916821802276990479378050053650', 'a10': 4, 'a2': 2, 'a3': 0, 'a4': 1, 'a5': 2, 'a6': 0, 'a7': 2, 'a8': -2, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 82.99952890949935, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 3, -2, 1]], [3, [1]], [7, [1, -2, 3, -2, 1]]], 'bad_primes': [2, 3, 7], 'central_character': '378.1', 'coefficient_field': '1.1.1.1', 'conductor': 20415837456, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1, -2, 3, -2, 1], [1], [1, -2, -1, 10, -20, 50, -25, -250, 625], [1, -2, 3, -2, 1], [1, -4, -10, -16, 379, -176, -1210, -5324, 14641], [1, 0, -2, 0, -165, 0, -338, 0, 28561], [1, 8, 92, 440, 2566, 7480, 26588, 39304, 83521], [1, -20, 214, -1520, 7771, -28880, 77254, -137180, 130321], [1, 2, -43, 2, 1588, 46, -22747, 24334, 279841], [1, 4, -22, -80, 139, -2320, -18502, 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'0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 461998097967843364, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.850324719538603196320751462879', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.44334279050637367970325691865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.73462855171427635585311649090', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 82.99952890949935, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 20415837456, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 2, 0, 1, 2, 0, 2, -2, 0, 4, 4, 0, 0, 4, 0, -4, -8, 0, 20, 2, 0, 8, -2, 0, 5, 0, 0, 2, -4, 0, -12, -2, 0, -16, 4, 0, 8, 40, 0, -4, 0, 0, -4, 4, 0, -4, 0, 0, 1, 10, 0, 0, 24, 0, 8, -4, 0, -8, -4, 0, -18, -24, 0, 3, 0, 0, 16, -8, 0, 8, -20, 0, -8, 16, 0, 20, 8, 0, -6, -8, 0, 0, 4, 0, -16, -8, 0, -8, 48, 0, 0, -2, 0, 0, 40, 0, 4, 2, 0, 5], 'euler11': [1, -4, -10, -16, 379, -176, -1210, -5324, 14641], 'euler13': [1, 0, -2, 0, -165, 0, -338, 0, 28561], 'euler17': [1, 8, 92, 440, 2566, 7480, 26588, 39304, 83521], 'euler19': [1, -20, 214, -1520, 7771, -28880, 77254, -137180, 130321], 'euler2': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler23': [1, 2, -43, 2, 1588, 46, -22747, 24334, 279841], 'euler29': [1, 4, -22, -80, 139, -2320, -18502, 97556, 707281], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 12, 46, 432, 4179, 13392, 44206, 357492, 923521], 'euler37': [1, -8, -20, -152, 4246, -5624, -27380, -405224, 1874161], 'euler41': [1, 0, 14, 0, -1485, 0, 23534, 0, 2825761], 'euler43': [1, 4, -50, -80, 1819, -3440, -92450, 318028, 3418801], 'euler47': [1, 0, 2, 0, -2205, 0, 4418, 0, 4879681], 'euler5': [1, -2, -1, 10, -20, 50, -25, -250, 625], 'euler53': [1, -24, 380, -4104, 34806, -217512, 1067420, -3573048, 7890481], 'euler59': [1, 4, -106, 16, 10459, 944, -368986, 821516, 12117361], 'euler61': [1, 18, 127, 1350, 15324, 82350, 472567, 4085658, 13845841], 'euler67': [1, -16, 82, -640, 8635, -42880, 368098, -4812208, 20151121], 'euler7': [1, -2, 3, -2, 1, 0, 0, 0, 0], 'euler71': [1, 20, 386, 4280, 44731, 303880, 1945826, 7158220, 25411681], 'euler73': [1, 8, 268, 1592, 28870, 116216, 1428172, 3112136, 28398241], 'euler79': [1, 6, -107, -90, 11364, -7110, -667787, 2958234, 38950081], 'euler83': [1, -4, -154, -16, 20683, -1328, -1060906, -2287148, 47458321], 'euler89': [1, -48, 1172, -18576, 207174, -1653264, 9283412, -33838512, 62742241], 'euler97': [1, -4, -158, 80, 19315, 7760, -1486622, -3650692, 88529281], 'euler_factors': [[1, -2, 3, -2, 1, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, -1, 10, -20, 50, -25, -250, 625], [1, -2, 3, -2, 1, 0, 0, 0, 0], [1, -4, -10, -16, 379, -176, -1210, -5324, 14641], [1, 0, -2, 0, -165, 0, -338, 0, 28561], [1, 8, 92, 440, 2566, 7480, 26588, 39304, 83521], [1, -20, 214, -1520, 7771, -28880, 77254, -137180, 130321], [1, 2, -43, 2, 1588, 46, -22747, 24334, 279841], [1, 4, -22, -80, 139, -2320, -18502, 97556, 707281], [1, 12, 46, 432, 4179, 13392, 44206, 357492, 923521], [1, -8, -20, -152, 4246, -5624, -27380, -405224, 1874161], [1, 0, 14, 0, -1485, 0, 23534, 0, 2825761], [1, 4, -50, -80, 1819, -3440, -92450, 318028, 3418801], [1, 0, 2, 0, -2205, 0, 4418, 0, 4879681], [1, -24, 380, -4104, 34806, -217512, 1067420, -3573048, 7890481], [1, 4, -106, 16, 10459, 944, -368986, 821516, 12117361], [1, 18, 127, 1350, 15324, 82350, 472567, 4085658, 13845841], [1, -16, 82, -640, 8635, -42880, 368098, -4812208, 20151121], [1, 20, 386, 4280, 44731, 303880, 1945826, 7158220, 25411681], [1, 8, 268, 1592, 28870, 116216, 1428172, 3112136, 28398241], [1, 6, -107, -90, 11364, -7110, -667787, 2958234, 38950081], [1, -4, -154, -16, 20683, -1328, -1060906, -2287148, 47458321], [1, -48, 1172, -18576, 207174, -1653264, 9283412, -33838512, 62742241], [1, -4, -158, 80, 19315, 7760, -1486622, -3650692, 88529281]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/f/d'], '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': '8-378e4-1.1-c1e4-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-378e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 461998097967843364, 'z1': {'__RealLiteral__': 0, 'data': '0.850324719538603196320751462879', 'prec': 107}}
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{'Lhash': '1077914641112011166796065802048,1829654354720492160131892596977,2198902924753626687239859009179,2916821802276990479378050053650', 'Lhash_array': ['1077914641112011166796065802048', '1829654354720492160131892596977', '2198902924753626687239859009179', '2916821802276990479378050053650'], 'label': '8-378e4-1.1-c1e4-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/f/d'}