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lfunc_lfunctions • Show schema
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{'Lhash': '2399114316966278158147159760786', 'a10': [0, 0], 'a2': [0, -2.350829680058364], 'a3': [0, -1.0], 'a4': [-3.52640018464331, 0], 'a5': [0, 0], 'a6': [-2.350829680058364, 0], 'a7': [0, -3.4818865932569945], 'a8': [0, 3.588306857706061], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.97195037899008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 5], 'central_character': '1875.1249', 'coefficient_field': 'CDF', 'conductor': 1875, 'conductor_radical': 15, 'conjugate': '732802038880826455205290974163', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 2.350829680058364], [-2.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.4818865932569945], [-7.0, 0]], [[1.0, 0], [-2.931106981809192, 0], [11.0, 0]], [[1.0, 0], [0, 1.8757468279208576], [-13.0, 0]], [[1.0, 0], [0, 6.785661275834891], [-17.0, 0]], [[1.0, 0], 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'4.30821141409471308587377285498295', '5.40768283080380680877516764787987', '5.75832344750539465595124176420769', '6.55412641020028438447572335799823', '7.36568648387603289243279737561506', '8.408735596333760692838364775341806', '8.773846293104457161919988397572266', '9.412814721342810807090832148537585'], 'prelabel': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': -0.5, 'root_number': '0.e-56 - 1.00000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.89256749181070762889954472761', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.49821182585391797262680654246', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.30821141409471308587377285498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.97195037899008, 'bad_primes': [3, 5], 'central_character': '5.4', 'conductor': 1875, 'conductor_radical': 15, 'degree': 2, 'index': 72, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1875/2/b/h/1249/2'], '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': '2-1875-5.4-c1-0-72', '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': '2-1875-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8693604612377586, 'root_angle': -0.25, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89256749181070762889954472761', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2399114316966278158147159760786', 'Lhash_array': ['2399114316966278158147159760786'], 'label': '2-1875-5.4-c1-0-72', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1875/2/b/h/1249/2'}