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lfunc_lfunctions • Show schema
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{'Lhash': '1258905676944014819914711253565', 'a10': [0.0, 0.0], 'a2': [2.3512191641457623, 0.0], 'a3': [-0.22924739181652393, 0.0], 'a4': [3.528231557846298, 0.0], 'a5': [0.0, 0.0], 'a6': [-0.5390108609694435, 0.0], 'a7': [2.0664686492911906, 0.0], 'a8': [3.593207326060549, 0.0], 'a9': [-2.947445633345321, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 57.69191546037511, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 17], 'central_character': '7225.1', 'coefficient_field': 'CDF', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.3512191641457623, 0], [2.0, 0]], [[1.0, 0], [0.22924739181652393, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.0664686492911906, 0], [7.0, 0]], [[1.0, 0], [0.6359503589022711, 0], [11.0, 0]], [[1.0, 0], [-0.3756977040479234, 0], [13.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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[[1.0, 0], [-7.121866907457632, 0], [109.0, 0]], [[1.0, 0], [-14.788171245990167, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 212, 'label': '2-85e2-1.1-c1-0-212', 'leading_term': '5.9146507005453452060798526366603', '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/7225/2/a/bw/1/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [5.914650700545345, 5.901739713493536, 5.862896534991312, 5.797800939205489, 5.705953332684725, 5.586723759971969, 5.439416390443851, 5.263345831781447, 5.057921148094517, 4.822733294351263, 4.55764177505415, 4.262856633810398, 3.93901231438029, 3.587230441198031, 3.209169099793589, 2.8070567228545227, 2.383709189143725, 1.9425292155757863, 1.4874875708155435, 1.0230860689838586, 0.5543027221134829, 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'3.37223310757804134123025196626476', '4.64644514220091974278773428885494', '5.16534740608627812367836963664343', '5.35333215353343017477588181677673', '6.50546037080160374505893924056530', '6.77970331241132914629666165551208', '7.85994386268815612003922432792233'], 'prelabel': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.993101471901926181675802169792', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.17367670721986284632213628972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13952986660679044008866627567', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 57.69191546037511, 'bad_primes': [5, 17], 'central_character': '1.1', 'conductor': 7225, 'conductor_radical': 85, 'degree': 2, 'index': 212, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7225/2/a/bw/1/14'], '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': '2-85e2-1.1-c1-0-212', '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': '2-85e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.595519433216869, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.993101471901926181675802169792', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1258905676944014819914711253565', 'Lhash_array': ['1258905676944014819914711253565'], 'label': '2-85e2-1.1-c1-0-212', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7225/2/a/bw/1/14'}