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lfunc_lfunctions • Show schema
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{'Lhash': '863461223956955073716915879697', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.4860015917157687, 0.0], 'a4': [0.0, 0.0], 'a5': [-59.87223893176025, 0.0], 'a6': [0.0, 0.0], 'a7': [-145.0711707830647, 0.0], 'a8': [0.0, 0.0], 'a9': [-230.8477929025551, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.2275522870846, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [121.0, 0]]]], 'bad_primes': [2, 11], 'central_character': '176.1', 'coefficient_field': 'CDF', 'conductor': 176, 'conductor_radical': 22, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.4860015917157687, 0], [243.0, 0]], [[1.0, 0], [59.87223893176025, 0], [3125.0, 0]], [[1.0, 0], [145.0711707830647, 0], [16807.0, 0]], [[1.0, 0], [121.0, 0]], [[1.0, 0], [-615.7715006796145, 0], [371293.0, 0]], [[1.0, 0], [-1840.676074046081, 0], [1419857.0, 0]], [[1.0, 0], [366.63346459772106, 0], [2476099.0, 0]], 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['0.68115080275392638450641550872985', '3.00324836445701566840171319838056', '3.68868556020357652724600750104619', '5.40429490645093890308204859268367', '6.59162039441687536518210681964191', '7.81582666584048064888033322354186', '8.642790166111257396934610847869406', '9.744956639385253730499668237129582', '10.95772089600745345903165405349262', '11.77237765668583924635433281482027'], 'prelabel': '2-176-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.312960783507121, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68115080275392638450641550873', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00324836445701566840171319838', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68868556020357652724600750105', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.2275522870846, 'bad_primes': [2, 11], 'central_character': '1.1', 'conductor': 176, 'conductor_radical': 22, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/176/6/a/i/1/3'], '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': '2-176-1.1-c5-0-3', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-176-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.312960783507121, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.68115080275392638450641550873', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '863461223956955073716915879697', 'Lhash_array': ['863461223956955073716915879697'], 'label': '2-176-1.1-c5-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/176/6/a/i/1/3'}