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lfunc_lfunctions • Show schema
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{'Lhash': '1793503083573933978399311001293', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.3271911668031888, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 61.70839068204551, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '7728.1', 'coefficient_field': 'CDF', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.3271911668031888, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.743009893649977, 0], [11.0, 0]], [[1.0, 0], [5.070201060453166, 0], [13.0, 0]], [[1.0, 0], [-3.3835083949559803, 0], [17.0, 0]], [[1.0, 0], [-3.743009893649977, 0], [19.0, 0]], [[1.0, 0], [-1.0, 0]], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 114, 'label': '2-7728-1.1-c1-0-114', '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': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/7728/2/a/cb/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-1.1449375765127335e-60, 0.23840517390994156, 0.47553024943686073, 0.7100493643894561, 0.9405486486290308, 1.1654907614064571, 1.3831889889954725, 1.591793031663448, 1.7892878643234893, 1.9735062876059715, 2.142155056466068, 2.292853824789025, 2.4231856001074075, 2.530756968648276, 2.613266021351166, 2.668575673437561, 2.694789909024364, 2.6903303853814364, 2.6540107896556346, 2.585106349390536, 2.483415955954939, 2.349314468867997, 2.1837929323696508, 1.9884846571671824, 1.7656754030660664, 1.5182962434836504, 1.2498980996425582, 0.9646073967744364, 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'6.00035724978743530936790746270398', '7.09528812815843418153476615235367', '7.48458646483744408839370175005189'], 'prelabel': '2-7728-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.855468839098371, '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': '1.41482446602480954712250837880', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49217517576195735640266702170', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.86020545742159243800374438650', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 61.70839068204551, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 7728, 'conductor_radical': 966, 'degree': 2, 'index': 114, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7728/2/a/cb/1/4'], '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': '2-7728-1.1-c1-0-114', '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': '2-7728-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.855468839098371, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.41482446602480954712250837880', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1793503083573933978399311001293', 'Lhash_array': ['1793503083573933978399311001293'], 'label': '2-7728-1.1-c1-0-114', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7728/2/a/cb/1/4'}