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lfunc_lfunctions • Show schema
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{'Lhash': '1480750251278910797709101581191', 'a10': [0, 0], 'a2': [0, 0], 'a3': [92856.06846863042, 0], 'a4': [0, 0], 'a5': [-9765625.0, 0], 'a6': [0, 0], 'a7': [-995099637.3531928, 0], 'a8': [0, 0], 'a9': [-1838103751.549019, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 223.5818754296497, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 14}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [9765625.0, 0]]]], 'bad_primes': [2, 5], 'central_character': '80.1', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-92856.06846863042, 0], [10460353203.0, 0]], [[1.0, 0], [9765625.0, 0]], [[1.0, 0], [995099637.3531928, 0], [558545864083284030, 0]], [[1.0, 0], [-81123862081.75052, 0], [7400249944258161000000, 0]], [[1.0, 0], [-392945074669.29407, 0], [247064529073450400000000, 0]], [[1.0, 0], [5412584585141.165, 0], [69091933913008730000000000, 0]], [[1.0, 0], 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'9.023102844831899818387884075420321', '9.648041893593141542157386948277039'], 'prelabel': '2-80-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.952654460986173, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16810598363012226569409661041', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61845682994694176176364519863', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.38927565098459266813178159751', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 223.5818754296497, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 80, 'conductor_radical': 10, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/80/22/a/i/1/4'], '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': '2-80-1.1-c21-0-31', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [21], 'order_of_vanishing': 1, 'prelabel': '2-80-1.1-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.952654460986173, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16810598363012226569409661041', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1480750251278910797709101581191', 'Lhash_array': ['1480750251278910797709101581191'], 'factors': ['2-80-1.1-c21-0-31'], 'label': '2-80-1.1-c21-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/80/22/a/i/1/4'}