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lfunc_lfunctions • Show schema
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{'Lhash': '4037328669953835035480435408485', 'a10': [0.22474487139158905, 2.224744871391589], 'a2': [0.0, -1.0], 'a3': [0.0, -2.449489742783178], 'a4': [-1.0, 0.0], 'a5': [-2.224744871391589, 0.22474487139158905], 'a6': [-2.449489742783178, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 1.0], 'a9': [-3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.9126696990427408, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [2.224744871391589, -0.22474487139158905]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5, 7], 'central_character': '490.99', 'coefficient_field': 'CDF', 'conductor': 490, 'conductor_radical': 70, 'conjugate': '185746016413970948663743727614', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 2.449489742783178], [-3.0, 0]], [[1.0, 0], [2.224744871391589, -0.22474487139158905]], [[1.0, 0], [0, 0]], [[1.0, 0], [4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, 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'7.931335787965834452649465330584498', '8.899527850273962194991611529882414', '9.830570585529713895969043715605056', '10.67293811695615672360656784281594', '11.21019923032026601338348259802913'], 'prelabel': '2-490-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9780469405559467, 'root_angle': -0.5320471084244875, 'root_number': '-0.10050896200520838 - 0.9949361530051241*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.266023554212', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.18489074925452591269683327485', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.98861477662556925968682259245', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.13906010295543071750474090957', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.9126696990427408, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 490, 'conductor_radical': 70, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/490/2/c/e/99/1'], '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': '2-490-5.4-c1-0-19', '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': '2-490-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9780469405559467, 'root_angle': -0.2660235542122438, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.18489074925452591269683327485', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4037328669953835035480435408485', 'Lhash_array': ['4037328669953835035480435408485'], 'label': '2-490-5.4-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/490/2/c/e/99/1'}