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lfunc_lfunctions • Show schema
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{'Lhash': '906091375228039251466294212849', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.8161602025381944, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.7015621187164243, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.5887375530780297, 0.0], 'a8': [0.0, 0.0], 'a9': [0.2984378812835757, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.574213792682123, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 13], 'central_character': '3328.1', 'coefficient_field': 'CDF', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.8161602025381944, 0], [3.0, 0]], [[1.0, 0], [2.7015621187164243, 0], [5.0, 0]], [[1.0, 0], [2.5887375530780297, 0], [7.0, 0]], [[1.0, 0], [-0.7725773505398351, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.7015621187164244, 0], [17.0, 0]], [[1.0, 0], [-4.404897755616224, 0], [19.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 18, 'label': '2-3328-1.1-c1-0-18', 'leading_term': '1.67707870571071899528601845308', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3328/2/a/bl/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.677078705710719, 1.6691509321621396, 1.6452971965425294, 1.6053133473689927, 1.5488823205185043, 1.4756073761937563, 1.3850557156843073, 1.2768099366911763, 1.1505245098481516, 1.0059844005218375, 0.8431630770606593, 0.6622773841743476, 0.4638370633886572, 0.24868702723156277, 0.018040810676099025, -0.22649608179266795, -0.4829139442622108, -0.7487985104268301, -1.0213429802344163, -1.2973726969059136, -1.573382479559284, -1.8455863397469312, -2.109979013783403, -2.3624084283621345, -2.5986578895697128, 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'5.72078407464534970419689778267000', '6.46789628696237233813542082865077', '7.56675516850914238339108997509963', '7.70086041899519495422255706409438', '8.719522514270146021917910750997919'], 'prelabel': '2-3328-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.15501831157583, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71478006247534251599436837326', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.34833689272783114998014315397', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17836463439786396408546822860', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.574213792682123, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3328/2/a/bl/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': '2-3328-1.1-c1-0-18', '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': '2-3328-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.15501831157583, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71478006247534251599436837326', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '906091375228039251466294212849', 'Lhash_array': ['906091375228039251466294212849'], 'factors': ['2-3328-1.1-c1-0-18'], 'label': '2-3328-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3328/2/a/bl/1/3'}