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lfunc_lfunctions • Show schema
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{'Lhash': '195821296485434003159402398896,1497345646267439371197962832984', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -4, 'a6': 0, 'a7': 6, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10394.883297989847, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1728.1', 'coefficient_field': '1.1.1.1', 'conductor': 2985984, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 4, 74, 500, 15625], [1, -6, -25, -2058, 117649], [1, -52, 1718, -69212, 1771561], [1, 26, 3843, 57122, 4826809], [1, -188, 18482, -923644, 24137569], [1, 74, 3567, 507566, 47045881], [1, 148, 25310, 1800716, 148035889], [1, 288, 57994, 7024032, 594823321], [1, -248, 63438, -7388168, 887503681], [1, 342, 112547, 17323326, 2565726409], [1, 0, -46478, 0, 4750104241], [1, 256, 172518, 20353792, 6321363049], [1, 132, 211822, 13704636, 10779215329], [1, 952, 489050, 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'5.67554976613937624703579401705167', '5.86420357352723047894603606616432', '6.45449177217074427172400006372972', '6.59264484946358436920412706657847', '7.45288748471507346510946204860032', '7.53888082995470534991793904964235', '8.037734608372937347590407404933557', '8.146562049973368067210063741889027', '8.797001251532814768053227947355703', '9.210981706177144223936553175815533'], 'prelabel': '4-12e6-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.097291740358889, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e2-0', 'trace_hash': 1578469274424507988, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15447576520705160532441018235', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.18119744194327315900281415741', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.59435355266943973355241035071', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10394.883297989847, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 2985984, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -4, 0, 6, 0, 0, 0, 52, 0, -26, 0, 0, 0, 188, 0, -74, 0, 0, 0, -148, 0, -58, 0, 0, 0, -288, 0, 248, 0, 0, 0, -24, 0, -342, 0, 0, 0, 0, 0, -256, 0, 0, 0, -132, 0, 61, 0, 0, 0, -952, 0, -208, 0, 0, 0, -1004, 0, 34, 0, 0, 0, 104, 0, -866, 0, 0, 0, -776, 0, 1874, 0, 0, 0, 312, 0, -182, 0, 0, 0, -1336, 0, -752, 0, 0, 0, 876, 0, -156, 0, 0, 0, 296, 0, -38, 0, 0, 0], 'euler11': [1, -52, 1718, -69212, 1771561], 'euler13': [1, 26, 3843, 57122, 4826809], 'euler17': [1, -188, 18482, -923644, 24137569], 'euler19': [1, 74, 3567, 507566, 47045881], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 148, 25310, 1800716, 148035889], 'euler29': [1, 288, 57994, 7024032, 594823321], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, -248, 63438, -7388168, 887503681], 'euler37': [1, 342, 112547, 17323326, 2565726409], 'euler41': [1, 0, -46478, 0, 4750104241], 'euler43': [1, 256, 172518, 20353792, 6321363049], 'euler47': [1, 132, 211822, 13704636, 10779215329], 'euler5': [1, 4, 74, 500, 15625], 'euler53': [1, 952, 489050, 141730904, 22164361129], 'euler59': [1, 1004, 583382, 206200516, 42180533641], 'euler61': [1, -34, 246171, -7717354, 51520374361], 'euler67': [1, 866, 742935, 260460758, 90458382169], 'euler7': [1, -6, -25, -2058, 117649], 'euler71': [1, 776, 704366, 277738936, 128100283921], 'euler73': [1, -1874, 1630083, -729017858, 151334226289], 'euler79': [1, 182, 872679, 89733098, 243087455521], 'euler83': [1, 1336, 1208918, 763907432, 326940373369], 'euler89': [1, -876, 1522402, -617552844, 496981290961], 'euler97': [1, 38, 431787, 34681574, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 4, 74, 500, 15625], [1, -6, -25, -2058, 117649], [1, -52, 1718, -69212, 1771561], [1, 26, 3843, 57122, 4826809], [1, -188, 18482, -923644, 24137569], [1, 74, 3567, 507566, 47045881], [1, 148, 25310, 1800716, 148035889], [1, 288, 57994, 7024032, 594823321], [1, -248, 63438, -7388168, 887503681], [1, 342, 112547, 17323326, 2565726409], [1, 0, -46478, 0, 4750104241], [1, 256, 172518, 20353792, 6321363049], [1, 132, 211822, 13704636, 10779215329], [1, 952, 489050, 141730904, 22164361129], [1, 1004, 583382, 206200516, 42180533641], [1, -34, 246171, -7717354, 51520374361], [1, 866, 742935, 260460758, 90458382169], [1, 776, 704366, 277738936, 128100283921], [1, -1874, 1630083, -729017858, 151334226289], [1, 182, 872679, 89733098, 243087455521], [1, 1336, 1208918, 763907432, 326940373369], [1, -876, 1522402, -617552844, 496981290961], [1, 38, 431787, 34681574, 832972004929]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/4/a/bj'], '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': '4-12e6-1.1-c3e2-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-12e6-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 10.097291740358889, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1578469274424507988, 'z1': {'__RealLiteral__': 0, 'data': '0.15447576520705160532441018235', 'prec': 103}}
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{'Lhash': '195821296485434003159402398896,1497345646267439371197962832984', 'Lhash_array': ['195821296485434003159402398896', '1497345646267439371197962832984'], 'label': '4-12e6-1.1-c3e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/4/a/bj'}