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lfunc_lfunctions • Show schema
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{'Lhash': '2787302351486141422227536482503', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '162.1', 'coefficient_field': '1.1.1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 0, 5], [1, -2, 7], [1, 3, 11], [1, -2, 13], [1, 3, 17], [1, 1, 19], [1, 6, 23], [1, -6, 29], [1, 4, 31], [1, 4, 37], [1, -9, 41], [1, 1, 43], [1, 6, 47], [1, -12, 53], [1, -3, 59], [1, -8, 61], [1, -5, 67], [1, 12, 71], [1, -11, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, -5, 97], [1, 0, 101], [1, -14, 103], [1, -3, 107], [1, 16, 109], [1, -6, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 0, 5], 1]], [[[1, -2, 7], 1]], [[[1, 3, 11], 1]], [[[1, -2, 13], 1]], [[[1, 3, 17], 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0.8264436468237323, 1.2582431727506886, 1.4361273807157762, 1.247531818352823, 0.6840827315088145, -0.15269186397359927, -1.0767348981115286], 'positive_zeros': ['2.19879385611801234222671009190633', '3.94847330019587176084970982030586', '5.13805326110939411578475614906574', '6.25936593777468405983226275094273', '7.63671497466111343831458484772724', '8.543319215757720981308384286559420', '10.11405722912123694469504278058588', '11.04396588795957112420276163217655', '11.89683285365062918010959055989694', '12.99772192968520356227401533433942'], 'prelabel': '2-162-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 18950087430636185, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.19879385611801234222671009191', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.94847330019587176084970982031', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.13805326110939411578475614907', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 2, 1, 0, 0, -3, 0, 2, 2, 0, 1, -3, 0, -1, 0, 0, -3, -6, 0, -5, 2, 0, 2, 6, 0, -4, 1, 0, -3, 0, 0, -4, -1, 0, 0, 9, 0, -1, -3, 0, -6, -6, 0, -3, -5, 0, 2, 12, 0, 0, 2, 0, 6, 3, 0, 8, -4, 0, 1, 0, 0, 5, -3, 0, 0, -12, 0, 11, -4, 0, -1, -6, 0, -4, 0, 0, 9, 12, 0, 0, -1, 0, -3, 6, 0, 4, -6, 0, -6, 0, 0, 5, -3, 0, -5], 'euler11': [1, 3, 11], 'euler13': [1, -2, 13], 'euler17': [1, 3, 17], 'euler19': [1, 1, 19], 'euler2': [1, -1, 0], 'euler23': [1, 6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 4, 37], 'euler41': [1, -9, 41], 'euler43': [1, 1, 43], 'euler47': [1, 6, 47], 'euler5': [1, 0, 5], 'euler53': [1, -12, 53], 'euler59': [1, -3, 59], 'euler61': [1, -8, 61], 'euler67': [1, -5, 67], 'euler7': [1, -2, 7], 'euler71': [1, 12, 71], 'euler73': [1, -11, 73], 'euler79': [1, 4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -5, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 5], [1, -2, 7], [1, 3, 11], [1, -2, 13], [1, 3, 17], [1, 1, 19], [1, 6, 23], [1, -6, 29], [1, 4, 31], [1, 4, 37], [1, -9, 41], [1, 1, 43], [1, 6, 47], [1, -12, 53], [1, -3, 59], [1, -8, 61], [1, -5, 67], [1, 12, 71], [1, -11, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, -5, 97]], 'index': 1, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/162/c', 'ModularForm/GL2/Q/holomorphic/162/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/162/2/a/c'], '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': '2-162-1.1-c1-0-1', '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': '2-162-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 18950087430636185, 'z1': {'__RealLiteral__': 0, 'data': '2.19879385611801234222671009191', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9995301
{'Lhash': '2787302351486141422227536482503', 'Lhash_array': ['2787302351486141422227536482503'], 'label': '2-162-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/a/c'}
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id: 24547505
{'Lhash': '2787302351486141422227536482503', 'Lhash_array': ['2787302351486141422227536482503'], 'label': '2-162-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/a/c/1/1'}
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id: 21831
{'Lhash': '18950087430636185', 'Lhash_array': ['18950087430636185'], 'label': '2-162-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/162/c'}