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lfunc_lfunctions • Show schema
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{'Lhash': '813449773971977908785818875447', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 17, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 101.95530048991984, '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': 1728, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 125], [1, -17, 343], [1, 0, 1331], [1, 89, 2197], [1, 0, 4913], [1, 107, 6859], [1, 0, 12167], [1, 0, 24389], [1, -308, 29791], [1, -433, 50653], [1, 0, 68921], [1, -520, 79507], [1, 0, 103823], [1, 0, 148877], [1, 0, 205379], [1, -901, 226981], [1, 1007, 300763], [1, 0, 357911], [1, 271, 389017], [1, -503, 493039], [1, 0, 571787], [1, 0, 704969], [1, -1853, 912673], [1, 0, 1030301], [1, 19, 1092727], [1, 0, 1225043], [1, -646, 1295029], [1, 0, 1442897]], 'euler_factors_factorization': [[1], [1], 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10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1728/4/a/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.919323602860528, 1.9051973309118135, 1.8629822336831947, 1.7931687392121647, 1.696571752008754, 1.5743267691307952, 1.4278841109695908, 1.259000956733289, 1.0697308160558048, 0.8624100304287905, 0.6396408841218303, 0.40427091587595326, 0.1593680609117662, -0.09180868231808026, -0.3458432756581378, -0.5992014557913683, -0.8482743052404519, -1.0894263925509498, -1.319048128429714, -1.5336118102386653, -1.72973064970543, -1.9042199036124776, -2.0541590603904054, -2.1769538828853796, -2.270396974967267, -2.332725432777796, -2.362674065634489, -2.359522631761718, -2.3231355343217377, -2.2539924670656344, -2.153208588756722, -2.0225429426726236, -1.864394022069453, -1.6817816132527215, -1.478314322182231, -1.2581425042081393, -1.0258966639770548, -0.7866117666968828, -0.545638294376238, 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'root_analytic_conductor': 10.097291740358889, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'trace_hash': 979053122975154024, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.64169872504736194092209789466', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05012142655228164502731962092', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69126841543013924088549871818', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 101.95530048991984, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, -89, 0, 0, 0, 0, 0, -107, 0, 0, 0, 0, 0, -125, 0, 0, 0, 0, 0, 308, 0, 0, 0, 0, 0, 433, 0, 0, 0, 0, 0, 520, 0, 0, 0, 0, 0, -54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 901, 0, 0, 0, 0, 0, -1007, 0, 0, 0, 0, 0, -271, 0, 0, 0, 0, 0, 503, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1513, 0, 0, 0, 0, 0, 1853, 0, 0, 0], 'euler11': [1, 0, 1331], 'euler13': [1, 89, 2197], 'euler17': [1, 0, 4913], 'euler19': [1, 107, 6859], 'euler2': [1, 0, 0], 'euler23': [1, 0, 12167], 'euler29': [1, 0, 24389], 'euler3': [1, 0, 0], 'euler31': [1, -308, 29791], 'euler37': [1, -433, 50653], 'euler41': [1, 0, 68921], 'euler43': [1, -520, 79507], 'euler47': [1, 0, 103823], 'euler5': [1, 0, 125], 'euler53': [1, 0, 148877], 'euler59': [1, 0, 205379], 'euler61': [1, -901, 226981], 'euler67': [1, 1007, 300763], 'euler7': [1, -17, 343], 'euler71': [1, 0, 357911], 'euler73': [1, 271, 389017], 'euler79': [1, -503, 493039], 'euler83': [1, 0, 571787], 'euler89': [1, 0, 704969], 'euler97': [1, -1853, 912673], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 125], [1, -17, 343], [1, 0, 1331], [1, 89, 2197], [1, 0, 4913], [1, 107, 6859], [1, 0, 12167], [1, 0, 24389], [1, -308, 29791], [1, -433, 50653], [1, 0, 68921], [1, -520, 79507], [1, 0, 103823], [1, 0, 148877], [1, 0, 205379], [1, -901, 226981], [1, 1007, 300763], [1, 0, 357911], [1, 271, 389017], [1, -503, 493039], [1, 0, 571787], [1, 0, 704969], [1, -1853, 912673]], 'index': 21, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1728/4/a/q/1/1', 'ModularForm/GL2/Q/holomorphic/1728/4/a/q'], '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': '2-12e3-1.1-c3-0-21', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-12e3-1.1-c3-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.097291740358889, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'trace_hash': 979053122975154024, 'z1': {'__RealLiteral__': 0, 'data': '0.64169872504736194092209789466', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21243979
{'Lhash': '813449773971977908785818875447', 'Lhash_array': ['813449773971977908785818875447'], 'label': '2-12e3-1.1-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/4/a/q'}
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id: 24592100
{'Lhash': '813449773971977908785818875447', 'Lhash_array': ['813449773971977908785818875447'], 'label': '2-12e3-1.1-c3-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/4/a/q/1/1'}