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lfunc_lfunctions • Show schema
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{'Lhash': '2831707098106816807311496716826', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.4142135623730951, 1.0], 'a4': [0.0, 0.0], 'a5': [-1.7320508075688772, -1.4142135623730951], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, -2.8284271247461903], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.4142135623730951, -1.0]]], [5, [[1.0, 0], [1.7320508075688772, 1.4142135623730951]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.239', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '387620423402007189670493864533', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.4142135623730951, -1.0]], [[1.0, 0], [1.7320508075688772, 1.4142135623730951]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [4.898979485566356, 0], [11.0, 0]], [[1.0, 0], [0, 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[[1.0, 0], [2.0, 0], [109.0, 0]], [[1.0, 0], [3.4641016151377544, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-240-60.59-c1-0-8', '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/240/2/o/b/239/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.35979455083172135, 0.4964872087661623, 0.6343099407573122, 0.7759210695335176, 0.921769135562633, 1.069953452232005, 1.2162987514302337, 1.3545715731758965, 1.4767958588453636, 1.5736599554338915, 1.635026584506183, 1.6505587506963693, 1.6104633041838161, 1.5063357431307451, 1.3320690757311449, 1.0847690909475534, 0.7656005684360376, 0.38047601089606753, -0.05950741493844608, -0.5379738930010777, -1.0335953573398193, -1.520890626761655, -1.9715135396429104, -2.3560009347087276, 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'8.206512529521974946875474537125398', '9.796055159475602554161942082646366', '10.89201704853482193869461871278867', '11.42134135491692517718233535634200', '12.29842972763067572273573034575784'], 'prelabel': '2-240-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': 0.6887062822268756, 'root_number': '-0.5587172127311096 + 0.8293582315248218*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.344353141113', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.23382302473330799143475228313', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.04350852873106186643099601937', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.33574215362576482465350029422', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '60.59', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/o/b/239/3'], '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': '2-240-60.59-c1-0-8', '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': '2-240-60.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': 0.3443531411134378, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.23382302473330799143475228313', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2831707098106816807311496716826', 'Lhash_array': ['2831707098106816807311496716826'], 'label': '2-240-60.59-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/o/b/239/3'}