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lfunc_lfunctions • Show schema
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{'Lhash': '606947676404633511217673487270', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.1512133034013585, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.3722813232690143, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.847069993022323, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 19], 'central_character': '2736.1', 'coefficient_field': 'CDF', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.1512133034013585, 0], [5.0, 0]], [[1.0, 0], [3.3722813232690143, 0], [7.0, 0]], [[1.0, 0], [4.7028548744147995, 0], [11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [2.1512133034013585, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [6.854068177816158, 0], [23.0, 0]], [[1.0, 0], 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[0]], 'group': 'GL2', 'index': 0, 'label': '2-2736-1.1-c1-0-0', 'leading_term': '0.67182685252359005782688145674564', '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/2736/2/a/bf/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.6718268525235901, 0.6645245253572524, 0.6425682155045593, 0.6058155249182275, 0.5540474023834073, 0.48699439427943697, 0.4043711902062378, 0.3059175332361192, 0.19144334458861398, 0.06087585325093333, -0.08569340816040152, -0.24796371964872152, -0.42538417075472607, -0.6171180800093979, -0.8220141566786306, -1.0385855172969132, -1.2649974782187097, -1.4990648651803795, -1.7382594036560595, -1.9797275710531954, -2.220319096179194, -2.4566260778198976, -2.685032460324942, -2.9017733502151217, -3.103003387062378, -3.284873099614635, 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'5.91481280872669157378273828486670', '6.49794453748563139172271638054977', '7.36396442346700714759525199173079', '8.188085705404294572356566101304090', '8.542703413663872604287355756967136'], 'prelabel': '2-2736-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.47879729343034893960514321785', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.33466469563871227316883924625', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.17966453059115101880052687183', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.847069993022323, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 2736, 'conductor_radical': 114, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2736/2/a/bf/1/2'], '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': '2-2736-1.1-c1-0-0', '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': '2-2736-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.67408493643647, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47879729343034893960514321785', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '606947676404633511217673487270', 'Lhash_array': ['606947676404633511217673487270'], 'label': '2-2736-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2736/2/a/bf/1/2'}