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lfunc_lfunctions • Show schema
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{'Lhash': '1770378423514004920017341428823', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-19.524174696260022, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [35.048349392520045, 0.0], 'a8': [0.0, 0.0], 'a9': [138.19339757008018, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.07676396259613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '200.1', 'coefficient_field': 'CDF', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [19.524174696260022, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-35.048349392520045, 0], [16807.0, 0]], [[1.0, 0], [426.0076686214605, 0], [161051.0, 0]], [[1.0, 0], [-1103.2570842055213, 0], [371293.0, 0]], [[1.0, 0], [-109.38679514016037, 0], [1419857.0, 0]], [[1.0, 0], [-495.9263070793414, 0], [2476099.0, 0]], [[1.0, 0], 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'4.95155947663365623047543729956411', '5.70652502886651365904248202647090', '6.72447644073990467713234609752646', '7.997269832550830833557662419788244', '9.094743527295853053285596360663679', '10.67716164538473569843465991134596', '10.89166894643321559551063461473148'], 'prelabel': '2-200-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.663635225064917, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.39658232575700573302213261371', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.36095711603878397734376682983', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.95155947663365623047543729956', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.07676396259613, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/6/a/e/1/1'], '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': '2-200-1.1-c5-0-14', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-200-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.663635225064917, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.39658232575700573302213261371', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1770378423514004920017341428823', 'Lhash_array': ['1770378423514004920017341428823'], 'label': '2-200-1.1-c5-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/6/a/e/1/1'}