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lfunc_lfunctions • Show schema
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{'Lhash': '2442049038313404637513132999520', 'a10': [-0.4755255399989674, 0.27983687849532224], 'a2': [-1.4141647742045491, 0.011746974035739082], 'a3': [1.7061709674439542, 0.29829621159404834], 'a4': [1.9997240172020074, -0.03322431376967532], 'a5': [0.3378793522235315, -0.19507473495987226], 'a6': [-2.4163109587822915, -0.4017976486598739], 'a7': [1.3952565872118234, -2.2479455188776294], 'a8': [-2.8275489781066834, 0.07047536028890983], 'a9': [2.8220387402972773, 1.017888671840568], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.341486753957511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.4141647742045491, -0.011746974035739082]]], [3, [[1.0, 0], [-1.7061709674439542, -0.29829621159404834]]], [7, [[1.0, 0], [-1.3952565872118234, 2.2479455188776294]]]], 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'coefficient_field': 'CDF', 'conductor': 168, 'conductor_radical': 42, 'conjugate': 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'5.36022266642475431296745702088809', '6.92123407146629599660262085647086', '7.85844270857429233932795764971498', '8.778348099808517027107949063350455', '9.489254138092792408271890476989950', '10.57748919066392090166762848974256', '11.75364154098709137659619536270356', '12.64752905990941372931315448083452'], 'prelabel': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.016966901029850275, 'root_number': '0.9985797265348735 + 0.053277854250498476*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00848345051493', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92643701495801372284142810891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14808553724927076822090342786', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36022266642475431296745702089', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.341486753957511, 'bad_primes': [2, 3, 7], 'central_character': '168.101', 'conductor': 168, 'conductor_radical': 42, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-168-168.101-c1-0-13', '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': '2-168-168.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1582256921505028, 'root_angle': 0.008483450514925137, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92643701495801372284142810891', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2442049038313404637513132999520', 'Lhash_array': ['2442049038313404637513132999520'], 'label': '2-168-168.101-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/168/2/ba/c/101/1'}