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lfunc_lfunctions • Show schema
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{'Lhash': '1728171975064766726696768532966,1888626844458264144656608338212,2128738666216129546810272422240,2182256921729971518797731787462,2371560048268254574788757769869', 'a10': 0, 'a2': 0, 'a3': 5, 'a4': 0, 'a5': 1, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': 15, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33575624.512262076, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -5, 10, -10, 5, -1]], [167, [1, -5, 10, -10, 5, -1]]], 'bad_primes': [2, 3, 167], 'central_character': '4008.1', 'coefficient_field': '1.1.1.1', 'conductor': 1034281042001952768, 'conductor_radical': 1002, 'degree': 10, 'euler_factors': [[1], [1, -5, 10, -10, 5, -1], [1, -1, 12, -8, 74, -25, 370, -200, 1500, -625, 3125], [1, 4, 30, 99, 402, 989, 2814, 4851, 10290, 9604, 16807], [1, 3, 36, 102, 630, 1573, 6930, 12342, 47916, 43923, 161051], [1, 14, 126, 790, 3937, 15593, 51181, 133510, 276822, 399854, 371293], [1, 13, 119, 830, 4589, 20715, 78013, 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'6.95888008256943049152738482332208', '6.98961624480005355431184544251716', '7.29277993791635236163254716537020', '7.45195054559887099906628410927304', '7.47735732787606476935940622164667', '7.53995561550556969801664198757885', '7.953145877951037384210336873301575', '8.075383220738574985636441804588894', '8.158558821950084021051116666907729', '8.268656831514387994751446830303973', '8.275707890780732237982267029327065'], 'prelabel': '10-4008e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.657211427030918, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e5-0', 'trace_hash': 456773196300895914, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36328730862717572190691733952', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.48986388214404931652563979471', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.67927871121022525576417319446', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33575624.512262076, 'bad_primes': [2, 3, 167], 'central_character': '1.1', 'conductor': 1034281042001952768, 'conductor_radical': 1002, 'degree': 10, 'dirichlet_coefficients': [1, 0, 5, 0, 1, 0, -4, 0, 15, 0, -3, 0, -14, 0, 5, 0, -13, 0, -2, 0, -20, 0, -5, 0, -11, 0, 35, 0, 13, 0, 2, 0, -15, 0, -4, 0, -5, 0, -70, 0, -20, 0, -20, 0, 15, 0, 1, 0, -14, 0, -65, 0, -3, 0, -3, 0, -10, 0, -1, 0, -34, 0, -60, 0, -14, 0, -16, 0, -25, 0, -5, 0, -12, 0, -55, 0, 12, 0, -20, 0, 70, 0, -15, 0, -13, 0, 65, 0, -48, 0, 56, 0, 10, 0, -2, 0, -21, 0, -45, 0], 'euler11': [1, 3, 36, 102, 630, 1573, 6930, 12342, 47916, 43923, 161051], 'euler13': [1, 14, 126, 790, 3937, 15593, 51181, 133510, 276822, 399854, 371293], 'euler17': [1, 13, 119, 830, 4589, 20715, 78013, 239870, 584647, 1085773, 1419857], 'euler19': [1, 2, 82, 108, 2829, 2651, 53751, 38988, 562438, 260642, 2476099], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 5, 78, 386, 2904, 12749, 66792, 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161051], [1, 14, 126, 790, 3937, 15593, 51181, 133510, 276822, 399854, 371293], [1, 13, 119, 830, 4589, 20715, 78013, 239870, 584647, 1085773, 1419857], [1, 2, 82, 108, 2829, 2651, 53751, 38988, 562438, 260642, 2476099], [1, 5, 78, 386, 2904, 12749, 66792, 204194, 949026, 1399205, 6436343], [1, -13, 158, -1100, 7688, -39579, 222952, -925100, 3853462, -9194653, 20511149], [1, -2, 105, -215, 5580, -8789, 172980, -206615, 3128055, -1847042, 28629151], [1, 5, 114, 372, 5706, 14757, 211122, 509268, 5774442, 9370805, 69343957], [1, 20, 219, 1955, 16226, 114713, 665266, 3286355, 15093699, 56515220, 115856201], [1, 20, 293, 3203, 28482, 201705, 1224726, 5922347, 23295551, 68376020, 147008443], [1, -1, 80, 105, 5053, -627, 237491, 231945, 8305840, -4879681, 229345007], [1, 3, 174, 423, 15171, 27597, 804063, 1188207, 25904598, 23671443, 418195493], [1, 1, 94, -389, -829, -52407, -48911, -1354109, 19305626, 12117361, 714924299], [1, 34, 606, 7646, 77597, 659411, 4733417, 28450766, 137550486, 470758594, 844596301], [1, 16, 232, 2478, 23361, 190905, 1565187, 11123742, 69777016, 322417936, 1350125107], [1, 5, 215, 595, 19727, 33999, 1400617, 2999395, 76950865, 127058405, 1804229351], [1, 12, 262, 1656, 24261, 111631, 1771053, 8824824, 101922454, 340778892, 2073071593], [1, 20, 363, 4417, 51806, 475675, 4092674, 27566497, 178973157, 779001620, 3077056399], [1, 15, 214, 1165, 7325, -3901, 607975, 8025685, 122362418, 711874815, 3939040643], [1, 48, 1306, 24216, 335755, 3585017, 29882195, 191814936, 920689514, 3011627568, 5584059449], [1, 21, 593, 8159, 124997, 1187307, 12124709, 76768031, 541215089, 1859114901, 8587340257]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4008/2/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': '10-4008e5-1.1-c1e5-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 5, 'prelabel': '10-4008e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.657211427030918, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 456773196300895914, 'z1': {'__RealLiteral__': 0, 'data': '1.36328730862717572190691733952', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1728171975064766726696768532966,1888626844458264144656608338212,2128738666216129546810272422240,2182256921729971518797731787462,2371560048268254574788757769869', 'Lhash_array': ['1728171975064766726696768532966', '1888626844458264144656608338212', '2128738666216129546810272422240', '2182256921729971518797731787462', '2371560048268254574788757769869'], 'label': '10-4008e5-1.1-c1e5-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4008/2/a/f'}