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lfunc_lfunctions • Show schema
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{'Lhash': '2448920676775627744597670026281', 'a10': -6, 'a2': -2, 'a3': 0, 'a4': 2, 'a5': 3, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [1]], [13, [1, -1]]], 'bad_primes': [7, 13], 'central_character': '637.1', 'coefficient_field': '1.1.1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, 0, 3], [1, -3, 5], [1], [1, 6, 11], [1, -1], [1, 4, 17], [1, 5, 19], [1, -3, 23], [1, 5, 29], [1, -3, 31], [1, 4, 37], [1, -6, 41], [1, 1, 43], [1, 7, 47], [1, 9, 53], [1, 8, 59], [1, -10, 61], [1, 6, 67], [1, 8, 71], [1, -13, 73], [1, -3, 79], [1, 15, 83], [1, 3, 89], [1, 7, 97], [1, -14, 101], [1, -4, 103], [1, 4, 107], [1, 2, 109], [1, 3, 113]], 'euler_factors_factorization': [[[[1, 2, 2], 1]], [[[1, 0, 3], 1]], [[[1, -3, 5], 1]], [1], [[[1, 6, 11], 1]], [[[1, -1], 1]], [[[1, 4, 17], 1]], 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-0.36691365556414707, 0.06295265539867384, -0.8558621735923625, -2.7076135884764283, -4.783522414897842, -6.299909060103752, -6.640082437526721], 'positive_zeros': ['1.93185778189567456463072050240519', '2.72528535271701611265854270606411', '4.82450768688560173606084932648164', '5.78821104763479917640596143352955', '6.67298853468060181727432085852270', '7.85318737682082614131812951370636', '8.568760068955747319631158439107772', '9.232409444628192264737671791785220', '10.06879161414549558260575138606938'], 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 47762176379386545, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93185778189567456463072050241', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72528535271701611265854270606', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.82450768688560173606084932648', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '1.1', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, 3, 0, 0, 0, -3, -6, -6, 0, 1, 0, 0, -4, -4, 6, -5, 6, 0, 12, 3, 0, 4, -2, 0, 0, -5, 0, 3, 8, 0, 8, 0, -6, -4, 10, 0, 0, 6, 0, -1, -12, -9, -6, -7, 0, 0, -8, 0, 2, -9, 0, -18, 0, 0, 10, -8, 0, 10, -6, 0, -8, 3, 0, -6, -8, 0, 0, -8, 0, 13, 8, 0, -10, 0, 0, 3, -12, 9, -12, -15, 0, -12, 2, 0, 0, -3, 18, 0, 6, 0, 14, -15, 0, -7, 0, 18, 8], 'euler11': [1, 6, 11], 'euler13': [1, -1, 0], 'euler17': [1, 4, 17], 'euler19': [1, 5, 19], 'euler2': [1, 2, 2], 'euler23': [1, -3, 23], 'euler29': [1, 5, 29], 'euler3': [1, 0, 3], 'euler31': [1, -3, 31], 'euler37': [1, 4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 1, 43], 'euler47': [1, 7, 47], 'euler5': [1, -3, 5], 'euler53': [1, 9, 53], 'euler59': [1, 8, 59], 'euler61': [1, -10, 61], 'euler67': [1, 6, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, -13, 73], 'euler79': [1, -3, 79], 'euler83': [1, 15, 83], 'euler89': [1, 3, 89], 'euler97': [1, 7, 97], 'euler_factors': [[1, 2, 2], [1, 0, 3], [1, -3, 5], [1, 0, 0], [1, 6, 11], [1, -1, 0], [1, 4, 17], [1, 5, 19], [1, -3, 23], [1, 5, 29], [1, -3, 31], [1, 4, 37], [1, -6, 41], [1, 1, 43], [1, 7, 47], [1, 9, 53], [1, 8, 59], [1, -10, 61], [1, 6, 67], [1, 8, 71], [1, -13, 73], [1, -3, 79], [1, 15, 83], [1, 3, 89], [1, 7, 97]], 'index': 24, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/637/a', 'ModularForm/GL2/Q/holomorphic/637/2/a/a/1/1', 'ModularForm/GL2/Q/holomorphic/637/2/a/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-637-1.1-c1-0-24', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-637-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 47762176379386545, 'z1': {'__RealLiteral__': 0, 'data': '1.93185778189567456463072050241', 'prec': 103}}
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lfunc_instances • Show schema
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id: 12488845
{'Lhash': '2448920676775627744597670026281', 'Lhash_array': ['2448920676775627744597670026281'], 'label': '2-637-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/a'}
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id: 24550001
{'Lhash': '2448920676775627744597670026281', 'Lhash_array': ['2448920676775627744597670026281'], 'label': '2-637-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/a/a/1/1'}
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id: 36933
{'Lhash': '47762176379386545', 'Lhash_array': ['47762176379386545'], 'label': '2-637-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/637/a'}