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  • lfunc_lfunctions • Show schema
    {'Lhash': '835458838018239026432759427314', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.449489742783178, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.4142135623730951, -1.7320508075688772], 'a6': [0.0, 0.0], 'a7': [0.0, 1.4142135623730951], 'a8': [0.0, 0.0], 'a9': [3.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.5552128646809735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.4142135623730951, 1.7320508075688772]]]], 'bad_primes': [2, 5], 'central_character': '320.289', 'coefficient_field': 'CDF', 'conductor': 320, 'conductor_radical': 10, 'conjugate': '1697004516120209414313838472424', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.449489742783178, 0], [3.0, 0]], [[1.0, 0], [1.4142135623730951, 1.7320508075688772]], [[1.0, 0], [0, -1.4142135623730951], [-7.0, 0]], [[1.0, 0], [0, -2.0], [-11.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [13.0, 0]], [[1.0, 0], [0, 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'6.57771911182382030034896459962378', '7.34995260832987264352652700660696', '8.598163691516383065625469503059461', '9.994985523808342936963889936037445', '10.91752135931185007087567807877431', '11.45160167584911197455789172559244'], 'prelabel': '2-320-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.598503320197044, 'root_angle': -0.15064311245442294, 'root_number': '0.5845113909070773 - 0.8113855026433945*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.150643112454', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.65906081523396271103566142236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21517462654926945323503370272', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.44542507118119795734508654157', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 2.5552128646809735, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 320, 'conductor_radical': 10, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/320/2/f/b/289/1'], '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': '2-320-40.29-c1-0-2', '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': '2-320-40.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.598503320197044, 'root_angle': -0.15064311245442294, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.65906081523396271103566142236', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '835458838018239026432759427314', 'Lhash_array': ['835458838018239026432759427314'], 'factors': ['2-320-40.29-c1-0-2'], 'label': '2-320-40.29-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/320/2/f/b/289/1'}