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lfunc_lfunctions • Show schema
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{'Lhash': '1622722726921639826291984334934', 'a10': [3.590276766380157, 0.0], 'a2': [-1.0, 0.0], 'a3': [2.1116129669786914, 0.0], 'a4': [1.0, 0.0], 'a5': [-3.590276766380157, 0.0], 'a6': [-2.1116129669786914, 0.0], 'a7': [-1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.4589093223125522, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.35639318155513, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7, 19], 'central_character': '5054.1', 'coefficient_field': 'CDF', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [-2.1116129669786914, 0], [3.0, 0]], [[1.0, 0], [3.590276766380157, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.242980411046296, 0], [11.0, 0]], [[1.0, 0], [-0.6139408680264412, 0], [13.0, 0]], [[1.0, 0], [4.697126940053138, 0], [17.0, 0]], [[1.0, 0], [0, 0]], 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'5.95801872946194430510069494408674', '6.85924983936196814105581671345625', '7.37466306218266279955618555298297', '7.943804175276135854389858633263038'], 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28010251928211353701233256848', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55611680922922566712144181291', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20542517492370352127111250131', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.35639318155513, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5054, 'conductor_radical': 266, 'degree': 2, 'index': 115, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5054/2/a/bb/1/5'], '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': '2-5054-1.1-c1-0-115', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-5054-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.352668193881617, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28010251928211353701233256848', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1622722726921639826291984334934', 'Lhash_array': ['1622722726921639826291984334934'], 'label': '2-5054-1.1-c1-0-115', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5054/2/a/bb/1/5'}