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lfunc_lfunctions • Show schema
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{'Lhash': '1607411993967717763722196381560', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 2.813606502648331], 'a4': [0.0, 0.0], 'a5': [0.28916854644830997, 0.0], 'a6': [0.0, 0.0], 'a7': [4.387986555425315, 0.0], 'a8': [0.0, 0.0], 'a9': [-4.916381551744972, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.810734151149071, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-2.564826912853306, -2.102775049096641]]]], 'bad_primes': [2, 11], 'central_character': '352.351', 'coefficient_field': 'CDF', 'conductor': 352, 'conductor_radical': 22, 'conjugate': '2694634948451820962714457381801', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.813606502648331], [-3.0, 0]], [[1.0, 0], [-0.28916854644830997, 0], [5.0, 0]], [[1.0, 0], [-4.387986555425315, 0], [7.0, 0]], [[1.0, 0], [-2.564826912853306, -2.102775049096641]], [[1.0, 0], [0, -1.5595594306791252], [-13.0, 0]], 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'5.68121311991338657963387941031429', '6.39017323270040025468311826485328', '7.69147402806712418928191971745162', '8.087876182012918181236422964528538', '9.005302229633835186785331931142931', '10.68617484013368774936382982957125', '11.43464949725883986384560834662648'], 'prelabel': '2-352-44.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': -0.5314075773415784, 'root_number': '-0.09850978834636598 - 0.9951360819505813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.265703788671', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26802448062448540270173985493', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.21352439853079373817864203079', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13446783422625853316052787695', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.810734151149071, 'bad_primes': [2, 11], 'central_character': '44.43', 'conductor': 352, 'conductor_radical': 22, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/352/2/e/a/351/12'], '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': '2-352-44.43-c1-0-3', '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': '2-352-44.43-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6765244260520247, 'root_angle': -0.2657037886707892, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.26802448062448540270173985493', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1607411993967717763722196381560', 'Lhash_array': ['1607411993967717763722196381560'], 'label': '2-352-44.43-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/352/2/e/a/351/12'}