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lfunc_lfunctions • Show schema
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{'Lhash': '2935559329553279090709200282816', 'a10': [0.0, 0.0], 'a2': [0.9009688679024191, -0.4338837391175581], 'a3': [0.4338837391175581, -1.900968867902419], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [0.0, 0.0], 'a6': [-0.4338837391175581, -1.900968867902419], 'a7': [0.9749279121818236, 0.2225209339563144], 'a8': [0.2225209339563144, -0.9749279121818236], 'a9': [-2.524458669761153, -1.215715221585588], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9009688679024191, 0.4338837391175581]]], [7, [[1.0, 0], [-0.9749279121818236, -0.2225209339563144]]], [17, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1835', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1460529803666098830530852286780', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 3, 'label': '2-3332-3332.1835-c0-0-3', 'leading_term': '2.58842919041986141853741596348', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/be/c/1835/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [2.5884291904198613, 2.755196609736867, 2.9579502475157513, 3.198846111854441, 3.4778864508699265, 3.793154134172648, 4.14116756650724, 4.5172343264978725, 4.915738964922464, 5.330352096087763, 5.7541767413956, 6.179856782806359, 6.599670331687534, 7.005624885943847, 7.3895649940248775, 7.743298063321479, 8.058740101582963, 8.328080336913438, 8.543961550149858, 8.69967136147559, 8.789338507686383, 8.808127256928957, 8.752422505540963, 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'5.10883514961152540407019229825171', '5.64132575359613991663494613237657', '6.86196347446419068078581255035187', '7.956049579301469208973203934569735', '8.105874494272073648341098889914717', '9.216942959544971842643543627452907'], 'prelabel': '2-3332-3332.1835-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.8775510204081634, 'root_number': '-0.92691675734602176302483849969967 + 0.37526700487937413388755922567427*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4387755102040816', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.31574799004138625653225051349', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99783523918738259681014161286', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00354548623843837463063398171', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.1835', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/be/c/1835/2'], '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': '2-3332-3332.1835-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-3332.1835-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.4387755102040817, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.31574799004138625653225051349', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2935559329553279090709200282816', 'Lhash_array': ['2935559329553279090709200282816'], 'label': '2-3332-3332.1835-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/be/c/1835/2'}