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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': -2, 'Lhash': '1600004477358453206080218410252', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.57942739416335, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -1]]], 'bad_primes': [2, 7], 'central_character': '1404928.1', 'coefficient_field': '1.1.1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, 2, 0, 9], [1, 0, 8, 0, 25], [1, -1], [1, -6, 30, -66, 121], [1, 0, 4, 0, 169], [1, 0, -22, 0, 289], [1, 0, -14, 0, 361], [1, -10, 70, -230, 529], [1, 14, 106, 406, 841], [1, 0, -46, 0, 961], [1, 2, 26, 74, 1369], [1, 0, -46, 0, 1681], [1, -2, 62, -86, 1849], [1, 0, -82, 0, 2209], [1, 8, 86, 424, 2809], [1, 0, 10, 0, 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2.541728579198039, 2.169614168325253, 1.591810054820108, 0.8843030236002738], 'positive_zeros': ['1.26218098036666128375643352070171', '1.68105390643200857934875531675901', '2.40213773909164008819186977900291', '3.21711526668262135430254399682641', '3.53419929117187714366368404909159', '4.10105863210729616019051460617106', '4.48764415928674941661971002365807', '5.17733604323633274017674967504657', '5.52643091712039831522349668780846', '6.04367171022473139435736811593356', '6.32695677493953297295543975626388', '6.92812750941875009988582899305016', '7.37489765847668238354813168060444', '7.58320343069701196961183081394209'], 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1334494067788609326, 'z1': {'__RealLiteral__': 0, 'data': '1.26218098036666128375643352070171', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.68105390643200857934875531675901', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.40213773909164008819186977900291', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.57942739416335, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 1404928, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, -8, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -24, 0, 0, 0, 8, 0, 0, 0, 0, 0, 6, 0, -4, 0, -5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0], 'euler11': [1, -6, 30, -66, 121], 'euler13': [1, 0, 4, 0, 169], 'euler17': [1, 0, -22, 0, 289], 'euler19': [1, 0, -14, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -10, 70, -230, 529], 'euler29': [1, 14, 106, 406, 841], 'euler3': [1, 0, 2, 0, 9], 'euler31': [1, 0, -46, 0, 961], 'euler37': [1, 2, 26, 74, 1369], 'euler41': [1, 0, -46, 0, 1681], 'euler43': [1, -2, 62, -86, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, 8, 0, 25], 'euler53': [1, 8, 86, 424, 2809], 'euler59': [1, 0, 10, 0, 3481], 'euler61': [1, 0, 48, 0, 3721], 'euler67': [1, 24, 262, 1608, 4489], 'euler7': [1, -1, 0, 0, 0], 'euler71': [1, -8, 142, -568, 5041], 'euler73': [1, 0, -26, 0, 5329], 'euler79': [1, 4, 158, 316, 6241], 'euler83': [1, 0, 34, 0, 6889], 'euler89': [1, 0, 38, 0, 7921], 'euler97': [1, 0, -6, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 2, 0, 9], [1, 0, 8, 0, 25], [1, -1, 0, 0, 0], [1, -6, 30, -66, 121], [1, 0, 4, 0, 169], [1, 0, -22, 0, 289], [1, 0, -14, 0, 361], [1, -10, 70, -230, 529], [1, 14, 106, 406, 841], [1, 0, -46, 0, 961], [1, 2, 26, 74, 1369], [1, 0, -46, 0, 1681], [1, -2, 62, -86, 1849], [1, 0, -82, 0, 2209], [1, 8, 86, 424, 2809], [1, 0, 10, 0, 3481], [1, 0, 48, 0, 3721], [1, 24, 262, 1608, 4489], [1, -8, 142, -568, 5041], [1, 0, -26, 0, 5329], [1, 4, 158, 316, 6241], [1, 0, 34, 0, 6889], [1, 0, 38, 0, 7921], [1, 0, -6, 0, 9409]], 'index': 35, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.7.1/28672.6/i', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/i', 'EllipticCurve/2.0.7.1/28672.8/i', 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/i'], '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': '4-112e3-1.1-c1e2-0-35', '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': 1, 'prelabel': '4-112e3-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.076465650952455, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1334494067788609326, 'z1': {'__RealLiteral__': 0, 'data': '1.26218098036666128375643352070171', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9621203
{'Lhash': '1600004477358453206080218410252', 'Lhash_array': ['1600004477358453206080218410252'], 'label': '4-112e3-1.1-c1e2-0-35', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.8/i'}
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id: 9620932
{'Lhash': '1600004477358453206080218410252', 'Lhash_array': ['1600004477358453206080218410252'], 'label': '4-112e3-1.1-c1e2-0-35', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.8/i'}
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id: 9620453
{'Lhash': '1600004477358453206080218410252', 'Lhash_array': ['1600004477358453206080218410252'], 'label': '4-112e3-1.1-c1e2-0-35', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.7.1/28672.6/i'}
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id: 9619973
{'Lhash': '1600004477358453206080218410252', 'Lhash_array': ['1600004477358453206080218410252'], 'label': '4-112e3-1.1-c1e2-0-35', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.7.1/28672.6/i'}