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lfunc_lfunctions • Show schema
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{'Lhash': '1679796976431626197373924657684', 'a10': 0, 'a2': 1, 'a3': 1, 'a4': 1, 'a5': 0, 'a6': 1, 'a7': 3, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.570828394149682, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '1950.1', 'coefficient_field': '1.1.1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1], [1, -3, 7], [1, 3, 11], [1, -1], [1, -3, 17], [1, 0, 19], [1, -4, 23], [1, -5, 29], [1, 3, 31], [1, 12, 37], [1, -2, 41], [1, -4, 43], [1, -3, 47], [1, -9, 53], [1, -15, 59], [1, 3, 61], [1, 7, 67], [1, 8, 71], [1, 16, 73], [1, 0, 79], [1, 1, 83], [1, 0, 89], [1, 2, 97], [1, 3, 101], [1, 6, 103], [1, 2, 107], [1, -10, 109], [1, -14, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [[[1, -1], 1]], [1], [[[1, -3, 7], 1]], [[[1, 3, 11], 1]], [[[1, 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1.8276911935868205, 2.02788622980334, 2.1405986495281004, 2.16174040859792, 2.0919559055711825, 1.9365298739435814, 1.7050539422078002, 1.4108703567392915, 1.070323160870237, 0.701857352908663, 0.3250146493099538, -0.04061999207686465, -0.37646429490638184], 'positive_zeros': ['1.32512616341537127516841939290187', '2.41024263072843413513774850848243', '3.29845174761783363418427055474720', '4.29885874464191948579845964702947', '5.12549501155078775052077320989201', '5.70721380824909254302815531777102', '7.00227519035662633790722146485840', '7.55697011933255808289536752219811', '8.372178951472568303607979391931074', '8.933816175732799236793232920480599'], 'prelabel': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1466124542247377910, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.32512616341537127516841939290', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41024263072843413513774850848', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.29845174761783363418427055475', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.570828394149682, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 1950, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 3, 1, 1, 0, -3, 1, 1, 3, 0, 1, 3, 1, 0, 0, 3, -3, 4, 1, 0, 1, 1, 3, 5, 0, -3, 1, -3, 3, 0, 1, -12, 0, 1, 0, 2, 3, 4, -3, 0, 4, 3, 1, 2, 0, 3, 1, 9, 1, 0, 3, 0, 5, 15, 0, -3, -3, 3, 1, 0, -3, -7, 3, 4, 0, -8, 1, -16, -12, 0, 0, -9, 1, 0, 0, 1, 2, -1, 3, 0, 4, 5, -3, 0, 0, 3, 4, -3, 3, 0, 1, -2, 2, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, -1, 0], 'euler17': [1, -3, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -5, 29], 'euler3': [1, -1, 0], 'euler31': [1, 3, 31], 'euler37': [1, 12, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 0], 'euler53': [1, -9, 53], 'euler59': [1, -15, 59], 'euler61': [1, 3, 61], 'euler67': [1, 7, 67], 'euler7': [1, -3, 7], 'euler71': [1, 8, 71], 'euler73': [1, 16, 73], 'euler79': [1, 0, 79], 'euler83': [1, 1, 83], 'euler89': [1, 0, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, 0, 0], [1, -3, 7], [1, 3, 11], [1, -1, 0], [1, -3, 17], [1, 0, 19], [1, -4, 23], [1, -5, 29], [1, 3, 31], [1, 12, 37], [1, -2, 41], [1, -4, 43], [1, -3, 47], [1, -9, 53], [1, -15, 59], [1, 3, 61], [1, 7, 67], [1, 8, 71], [1, 16, 73], [1, 0, 79], [1, 1, 83], [1, 0, 89], [1, 2, 97]], 'index': 21, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1950/bb', 'ModularForm/GL2/Q/holomorphic/1950/2/a/bb/1/1', 'ModularForm/GL2/Q/holomorphic/1950/2/a/bb'], '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': '2-1950-1.1-c1-0-21', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1950-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.9459888993951417, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1466124542247377910, 'z1': {'__RealLiteral__': 0, 'data': '1.32512616341537127516841939290', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20574082
{'Lhash': '1679796976431626197373924657684', 'Lhash_array': ['1679796976431626197373924657684'], 'label': '2-1950-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/bb'}
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id: 24555228
{'Lhash': '1679796976431626197373924657684', 'Lhash_array': ['1679796976431626197373924657684'], 'label': '2-1950-1.1-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1950/2/a/bb/1/1'}
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id: 100791
{'Lhash': '1466124542247377910', 'Lhash_array': ['1466124542247377910'], 'label': '2-1950-1.1-c1-0-21', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1950/bb'}