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lfunc_lfunctions • Show schema
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{'Lhash': '1137294035302976238638719127719', 'a10': [-1.753037948264605, 1.3881130904736199], 'a2': [0.5, -0.8660254037844386], 'a3': [0, 0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-2.078660173808184, -0.8241188517584884], 'a6': [0, 0], 'a7': [0.8375341598073038, 2.5096885326980067], 'a8': [-1.0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [2.078660173808184, 0.8241188517584884]]], [7, [[1.0, 0], [-0.8375341598073038, -2.5096885326980067]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1890.1529', 'coefficient_field': 'CDF', 'conductor': 1890, 'conductor_radical': 210, 'conjugate': '1000428603816301066124887729185', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.078660173808184, 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[-3.6058848715758582, 6.245575803813362], [-56.5, -97.86087062764156]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 23, 'label': '2-1890-315.59-c1-0-23', 'leading_term': '1.682708175088306347292749638630927770863785880004748668', '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/1890/2/r/b/1529/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.6827081750883064, 1.7130107175583464, 1.7295089045892929, 1.7313458460984543, 1.7173858547668204, 1.6862462259291469, 1.6363497512263416, 1.5659946432910565, 1.4734378792559362, 1.3569877623112492, 1.2151016341282244, 1.0464849982669824, 0.850188702160395, 0.6257011801795077, 0.3730330372141225, 0.09279144594275765, -0.21375803659278664, -0.5446445207727086, -0.8971618725028614, -1.2678578379700531, 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'4.39399460547639949152916324132345', '5.17526517335176905136251201667446', '6.45383794648058849715966910255601', '6.90768903041808041634694367845841', '7.76192440370881229274153248022980', '8.265466878652907883816445647034233', '9.111138655561655096144274652216266'], 'prelabel': '2-1890-315.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': 0.3171691403199594, 'root_number': '0.543314458845200722003334269599243784083671034230865055 + 0.839529272157765021270065656405379135699083803365923687*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1585845701599797', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.897166802191563192832336880967', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.75166336921238299399195505540', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.72865397756122005154523610433', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.091725982022, 'bad_primes': [2, 3, 5, 7], 'central_character': '315.59', 'conductor': 1890, 'conductor_radical': 210, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1890/2/r/b/1529/4'], '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': '2-1890-315.59-c1-0-23', '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': '2-1890-315.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.884807071402903, 'root_angle': 0.1585845701599797, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.897166802191563192832336880967', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1137294035302976238638719127719', 'Lhash_array': ['1137294035302976238638719127719'], 'label': '2-1890-315.59-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1890/2/r/b/1529/4'}