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lfunc_lfunctions • Show schema
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{'Lhash': '2154445151089437190005480339261,3392201983318784990809002423501', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -6, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.216044621806596, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]], [67, [1, 11, 67]]], 'bad_primes': [2, 3, 67], 'central_character': '804.1', 'coefficient_field': '1.1.1.1', 'conductor': 646416, 'conductor_radical': 402, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, 0, 10, 0, 25], [1, 6, 19, 42, 49], [1, 0, -11, 0, 121], [1, 9, 40, 117, 169], [1, 0, 17, 0, 289], [1, -8, 45, -152, 361], [1, 0, 23, 0, 529], [1, 0, 29, 0, 841], [1, -3, 34, -93, 961], [1, 10, 63, 370, 1369], [1, 0, -41, 0, 1681], [1, 0, -83, 0, 1849], [1, 0, 47, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, -118, 0, 3481], [1, 27, 304, 1647, 3721], [1, 11, 67], [1, 0, 71, 0, 5041], [1, 7, -24, 511, 5329], [1, 21, 226, 1659, 6241], [1, 0, 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'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 1426916578634273174, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69955755213743297015120101622', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67597552725336831600453735092', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98916828815000323641775569873', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 41.216044621806596, 'bad_primes': [2, 3, 67], 'central_character': '1.1', 'conductor': 646416, 'conductor_radical': 402, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, -6, 0, -3, 0, 0, 0, -9, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -27, 0, 18, 0, 0, 0, -11, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, -21, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, -33, 0, 0, 0], 'euler11': [1, 0, -11, 0, 121], 'euler13': [1, 9, 40, 117, 169], 'euler17': [1, 0, 17, 0, 289], 'euler19': [1, -8, 45, -152, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 23, 0, 529], 'euler29': [1, 0, 29, 0, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, -3, 34, -93, 961], 'euler37': [1, 10, 63, 370, 1369], 'euler41': [1, 0, -41, 0, 1681], 'euler43': [1, 0, -83, 0, 1849], 'euler47': [1, 0, 47, 0, 2209], 'euler5': [1, 0, 10, 0, 25], 'euler53': [1, 0, 106, 0, 2809], 'euler59': [1, 0, -118, 0, 3481], 'euler61': [1, 27, 304, 1647, 3721], 'euler67': [1, 11, 67, 0, 0], 'euler7': [1, 6, 19, 42, 49], 'euler71': [1, 0, 71, 0, 5041], 'euler73': [1, 7, -24, 511, 5329], 'euler79': [1, 21, 226, 1659, 6241], 'euler83': [1, 0, 83, 0, 6889], 'euler89': [1, 0, -178, 0, 7921], 'euler97': [1, 33, 460, 3201, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, 0, 10, 0, 25], [1, 6, 19, 42, 49], [1, 0, -11, 0, 121], [1, 9, 40, 117, 169], [1, 0, 17, 0, 289], [1, -8, 45, -152, 361], [1, 0, 23, 0, 529], [1, 0, 29, 0, 841], [1, -3, 34, -93, 961], [1, 10, 63, 370, 1369], [1, 0, -41, 0, 1681], [1, 0, -83, 0, 1849], [1, 0, 47, 0, 2209], [1, 0, 106, 0, 2809], [1, 0, -118, 0, 3481], [1, 27, 304, 1647, 3721], [1, 11, 67, 0, 0], [1, 0, 71, 0, 5041], [1, 7, -24, 511, 5329], [1, 21, 226, 1659, 6241], [1, 0, 83, 0, 6889], [1, 0, -178, 0, 7921], [1, 33, 460, 3201, 9409]], 'index': 14, 'instance_types': ['ECNF', 'ECNF', 'CMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/71824.3/CMb', 'EllipticCurve/2.0.3.1/71824.1/CMb', 'ModularForm/GL2/Q/holomorphic/804/2/o/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-804e2-1.1-c1e2-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-804e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.533766430141292, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1426916578634273174, 'z1': {'__RealLiteral__': 0, 'data': '1.69955755213743297015120101622', 'prec': 103}}
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lfunc_instances • Show schema
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id: 15058663
{'Lhash': '2154445151089437190005480339261,3392201983318784990809002423501', 'Lhash_array': ['2154445151089437190005480339261', '3392201983318784990809002423501'], 'label': '4-804e2-1.1-c1e2-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/804/2/o/a'}
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id: 9796541
{'Lhash': '_2154445151089437190005480339261', 'Lhash_array': ['_2154445151089437190005480339261'], 'label': '4-804e2-1.1-c1e2-0-14', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/71824.1/CMb'}
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id: 9796543
{'Lhash': '_2154445151089437190005480339261', 'Lhash_array': ['_2154445151089437190005480339261'], 'label': '4-804e2-1.1-c1e2-0-14', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/71824.3/CMb'}