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lfunc_lfunctions • Show schema
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{'Lhash': '780984972679020132534529501549', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 2.449489742783178], 'a4': [0.0, 0.0], 'a5': [-0.22474487139158905, 2.224744871391589], 'a6': [0.0, 0.0], 'a7': [0.0, 1.0], 'a8': [0.0, 0.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.471622513191703, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.22474487139158905, -2.224744871391589]]], [7, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '560.449', 'coefficient_field': 'CDF', 'conductor': 560, 'conductor_radical': 70, 'conjugate': '3326299547875236416878812385061', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.449489742783178], [-3.0, 0]], [[1.0, 0], [0.22474487139158905, -2.224744871391589]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, -0.4494897427831781], [-13.0, 0]], [[1.0, 0], 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0], [-2.898979485566356, 0], [109.0, 0]], [[1.0, 0], [0, 0.20204102886728761], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-560-5.4-c1-0-1', '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/560/2/g/e/449/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.08728305416285, 0.8548242714296002, 0.632171848700706, 0.41425370829635655, 0.19831079769330343, -0.015053793764804098, -0.2214241451822787, -0.4126779646435051, -0.5775656752574435, -0.7026898797384649, -0.7738303720360281, -0.7775559969665843, -0.7030368161840435, -0.5439271889528094, -0.30014458563594254, 0.020668105740847934, 0.4022271020055085, 0.8194602348925029, 1.2393066481899668, 1.6225662791291895, 1.9267932859997259, 2.110095418187067, 2.135558848575322, 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'5.61574650205583044526235799683684', '6.99415327141256090395497325091842', '7.68414523634273407074751041423784', '8.213501166713106520238873691060275', '9.379112251077911053384122580331010', '10.30938474347751412150041228463601'], 'prelabel': '2-560-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.114621127576215, 'root_angle': -0.9679528915755126, 'root_number': '-0.9949361530051241 - 0.10050896200520834*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.483976445788', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61608851251157899507562863377', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86767772322833534227136792854', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30188167355794241111823405207', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.471622513191703, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 560, 'conductor_radical': 70, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/560/2/g/e/449/3'], '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': '2-560-5.4-c1-0-1', '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': '2-560-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.114621127576215, 'root_angle': -0.4839764457877563, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61608851251157899507562863377', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '780984972679020132534529501549', 'Lhash_array': ['780984972679020132534529501549'], 'label': '2-560-5.4-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/560/2/g/e/449/3'}