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lfunc_lfunctions • Show schema
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{'Lhash': '1952937386664419665710114318502', 'a10': [2.611992088484409, 0.0], 'a2': [2.611992088484409, 0.0], 'a3': [0.49230382614145496, 0.0], 'a4': [4.822502670305145, 0.0], 'a5': [1.0, 0.0], 'a6': [1.2858936990120844, 0.0], 'a7': [3.4710990416270184, 0.0], 'a8': [7.372354644563155, 0.0], 'a9': [-2.757636942766484, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.059936411544086, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [73, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 11, 73], 'central_character': '4015.1', 'coefficient_field': 'CDF', 'conductor': 4015, 'conductor_radical': 4015, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.611992088484409, 0], [2.0, 0]], [[1.0, 0], [-0.49230382614145496, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.4710990416270184, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.6986808692815519, 0], [13.0, 0]], [[1.0, 0], 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'4.87939007442420308118889335977324', '5.43185446663838081540266789916285', '5.73865344907480685476372432032461', '6.78800958411912719886075285839586', '7.61605187740950412096744014271785', '8.097527791371719315593830721241575'], 'prelabel': '2-4015-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.662149451537295, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54059595468405124647464467684', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.18622396018091752165090325237', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.28822347927592567070381431097', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.059936411544086, 'bad_primes': [5, 11, 73], 'central_character': '1.1', 'conductor': 4015, 'conductor_radical': 4015, 'degree': 2, 'index': 193, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4015/2/a/h/1/35'], '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': '2-4015-1.1-c1-0-193', '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': '2-4015-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.662149451537295, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54059595468405124647464467684', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1952937386664419665710114318502', 'Lhash_array': ['1952937386664419665710114318502'], 'label': '2-4015-1.1-c1-0-193', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4015/2/a/h/1/35'}