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lfunc_lfunctions • Show schema
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{'Lhash': '1157732875977539353648970421101', 'a10': [0.0, 0.0], 'a2': [-1.1223335080217338, 0.0], 'a3': [1.0, 0.0], 'a4': [-0.7403674967716287, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.1223335080217338, 0.0], 'a7': [1.1137344694780558, 0.0], 'a8': [3.0756062659204395, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.1223335080217338, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.1137344694780558, 0], [7.0, 0]], [[1.0, 0], [-3.6700757289417525, 0], [11.0, 0]], [[1.0, 0], [4.052041740191858, 0], [13.0, 0]], [[1.0, 0], [-2.122333508021734, 0], [17.0, 0]], [[1.0, 0], [4.060640778735536, 0], [19.0, 0]], 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[109.0, 0]], [[1.0, 0], [-4.835201797416873, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 20, 'label': '2-1875-1.1-c1-0-20', 'leading_term': '1.3595530105457319077877545883609', '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/1875/2/a/h/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.3595530105457319, 1.3545439844828342, 1.3394313049644346, 1.3139675934415285, 1.277771211273768, 1.2303697077149973, 1.1712559531985198, 1.0999530585381694, 1.0160839666117407, 0.9194417501360033, 0.8100570315582488, 0.688259429866185, 0.5547304335489932, 0.41054554024519824, 0.2572038731135232, 0.09664379239138143, -0.06875670504788303, -0.23619573318903392, -0.40248004765935724, -0.5640746490671189, -0.7171693406472331, -0.8577616507307333, 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'4.84035549041700819034464343802866', '6.26097941179739414795313788089702', '7.15547093356250528323766880126041', '7.890133502046111237129512442470105', '8.480472240547853023398991941349850', '9.317496466483100998466286388742156'], 'prelabel': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.913290204547767087296950666723', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.01194103234678130750228730253', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24397678861649761029938054500', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/a/h/1/2'], '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': '2-1875-1.1-c1-0-20', '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': '2-1875-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.913290204547767087296950666723', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1157732875977539353648970421101', 'Lhash_array': ['1157732875977539353648970421101'], 'label': '2-1875-1.1-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/a/h/1/2'}