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lfunc_lfunctions • Show schema
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{'Lhash': '290552252934787405777531192216', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-2.0, 0.0], 'a5': [1.5804909718503342, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.0825392597499204, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.934196333374636, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]], [29, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 23, 29], 'central_character': '6003.1', 'coefficient_field': 'CDF', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.5804909718503342, 0], [5.0, 0]], [[1.0, 0], [3.0825392597499204, 0], [7.0, 0]], [[1.0, 0], [6.03290741410963, 0], [11.0, 0]], [[1.0, 0], [2.3698771825093754, 0], [13.0, 0]], [[1.0, 0], [6.8500171107545285, 0], [17.0, 0]], [[1.0, 0], [5.137355033513983, 0], [19.0, 0]], [[1.0, 0], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-6003-1.1-c1-0-7', 'leading_term': '0.22219073349536913667385486996500', '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/6003/2/a/g/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.22219073349536914, 0.21128164615556905, 0.1785515956433263, 0.12400044583081381, 0.04765478351070873, -0.050393957612624274, -0.16994009617291603, -0.3106065276354295, -0.471783701392887, -0.652568811655732, -0.8517091478190318, -1.067553244944154, -1.2980130421931122, -1.5405397488750718, -1.7921155715475554, -2.0492628931728825, -2.3080719259193425, -2.564247284052551, -2.8131733403118258, -3.0499976364110135, -3.269731017021742, -3.4673625523729816, -3.6379867178730505, -3.776939724950447, -3.8799413644594414, 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'5.14444525214121841935959792255256', '5.94445650812570695734063225536938', '6.52327438063131279540874851582014', '7.40063941119786158411405988870735', '8.243149818900987459298404711194156'], 'prelabel': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.22920531326414077689182805904', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.09100152541022055736364075259', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.67007398277643549023008782042', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.934196333374636, 'bad_primes': [3, 23, 29], 'central_character': '1.1', 'conductor': 6003, 'conductor_radical': 2001, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6003/2/a/g/1/3'], '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': '2-6003-1.1-c1-0-7', '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': '2-6003-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.923452630976444, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.22920531326414077689182805904', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '290552252934787405777531192216', 'Lhash_array': ['290552252934787405777531192216'], 'label': '2-6003-1.1-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6003/2/a/g/1/3'}