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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -4, 'A4': -4, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 6, 'Lhash': '248433140460278545,1800720059813796826', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-2.309401076758503, 0], 'a4': [-2.0, 0], 'a5': [-0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.7013771528442, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [1, 2, 11]], [101, [1, 0, -1]]], 'bad_primes': [11, 101], 'central_character': '1234321.1', 'coefficient_field': '1.1.1.1', 'conductor': 1234321, 'conductor_radical': 1111, 'degree': 4, 'euler_factors': [[1, 0, 4, 0, 4], [1, 4, 10, 12, 9], [1, 2, 11, 10, 25], [1, 0, 10, 0, 49], [1, 2, 11], [1, 0, 25, 0, 169], [1, 0, 25, 0, 289], [1, 0, 13, 0, 361], [1, -2, 47, -46, 529], [1, 0, 42, 0, 841], [1, 18, 143, 558, 961], [1, 4, 78, 148, 1369], [1, 0, 18, 0, 1681], [1, 0, 22, 0, 1849], [1, -14, 143, -658, 2209], 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-3.2797587519460776, -3.0991611826441625, -2.7294724894096865, -2.225831216879868, -1.6578491245840912], 'positive_zeros': ['0.845638584611923894041993845992612', '1.85866097915362029590487734312538', '3.14223806423963647907216241484547', '3.72933468340090913789145872057212', '3.91187178475190732797803079947649', '4.70898772624388144319899057533448', '5.05190011683367889598807367642284', '5.17330498735283860298501426044468', '5.66222777548012373876842190686851', '6.16055116457811093791815485098464', '6.33628735398302806971209845546055', '7.27123391412294223311092606979238', '7.74187934910278185224762610895640'], 'prelabel': '4-1111e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.97848613637268, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 2049153200274075371, 'z1': {'__RealLiteral__': 0, 'data': '0.845638584611923894041993845992612', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '1.85866097915362029590487734312538', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '3.14223806423963647907216241484547', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.7013771528442, 'bad_primes': [11, 101], 'central_character': '1.1', 'conductor': 1234321, 'conductor_radical': 1111, 'degree': 4, 'dirichlet_coefficients': [1, 0, -4, -4, -2, 0, 0, 0, 6, 0, -2, 16, 0, 0, 8, 12, 0, 0, 0, 8, 0, 0, 2, 0, -7, 0, 4, 0, 0, 0, -18, 0, 8, 0, 0, -24, -4, 0, 0, 0, 0, 0, 0, 8, -12, 0, 14, -48, -10, 0, 0, 0, -4, 0, 4, 0, 0, 0, -28, -32, 0, 0, 0, -32, 0, 0, 4, 0, -8, 0, 26, 0, 0, 0, 28, 0, 0, 0, 0, -24, -37, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, -8, 72, 0, 0, 0, 4, 0, -12, 28], 'euler11': [1, 2, 11, 0, 0], 'euler13': [1, 0, 25, 0, 169], 'euler17': [1, 0, 25, 0, 289], 'euler19': [1, 0, 13, 0, 361], 'euler2': [1, 0, 4, 0, 4], 'euler23': [1, -2, 47, -46, 529], 'euler29': [1, 0, 42, 0, 841], 'euler3': [1, 4, 10, 12, 9], 'euler31': [1, 18, 143, 558, 961], 'euler37': [1, 4, 78, 148, 1369], 'euler41': [1, 0, 18, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, -14, 143, -658, 2209], 'euler5': [1, 2, 11, 10, 25], 'euler53': [1, 4, 110, 212, 2809], 'euler59': [1, 28, 314, 1652, 3481], 'euler61': [1, 0, 106, 0, 3721], 'euler67': [1, -4, 138, -268, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, -26, 311, -1846, 5041], 'euler73': [1, 0, 82, 0, 5329], 'euler79': [1, 0, 77, 0, 6241], 'euler83': [1, 0, 150, 0, 6889], 'euler89': [1, -28, 374, -2492, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 4, 0, 4], [1, 4, 10, 12, 9], [1, 2, 11, 10, 25], [1, 0, 10, 0, 49], [1, 2, 11, 0, 0], [1, 0, 25, 0, 169], [1, 0, 25, 0, 289], [1, 0, 13, 0, 361], [1, -2, 47, -46, 529], [1, 0, 42, 0, 841], [1, 18, 143, 558, 961], [1, 4, 78, 148, 1369], [1, 0, 18, 0, 1681], [1, 0, 22, 0, 1849], [1, -14, 143, -658, 2209], [1, 4, 110, 212, 2809], [1, 28, 314, 1652, 3481], [1, 0, 106, 0, 3721], [1, -4, 138, -268, 4489], [1, -26, 311, -1846, 5041], [1, 0, 82, 0, 5329], [1, 0, 77, 0, 6241], [1, 0, 150, 0, 6889], [1, -28, 374, -2492, 7921], [1, -4, 198, -388, 9409]], 'index': 0, 'instance_types': ['ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.11.1/10201.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/10201.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, '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': '4-1111e2-1.1-c1e2-0-0', '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': '4-1111e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.97848613637268, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 2049153200274075371, 'z1': {'__RealLiteral__': 0, 'data': '0.845638584611923894041993845992612', 'prec': 117}}
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lfunc_instances • Show schema
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id: 9888384
{'Lhash': '248433140460278545,1800720059813796826', 'Lhash_array': ['248433140460278545', '1800720059813796826'], 'label': '4-1111e2-1.1-c1e2-0-0', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.11.1/10201.1/a'}
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id: 9888409
{'Lhash': '248433140460278545,1800720059813796826', 'Lhash_array': ['248433140460278545', '1800720059813796826'], 'label': '4-1111e2-1.1-c1e2-0-0', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.11.1/10201.1/a'}