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lfunc_lfunctions • Show schema
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{'Lhash': '2319571554861968228912161793516', 'a10': [0.0, 0.0], 'a2': [0.3826834323650898, -0.9238795325112867], 'a3': [0.541196100146197, 0.541196100146197], 'a4': [-0.7071067811865476, -0.7071067811865476], 'a5': [0.0, 0.0], 'a6': [0.7071067811865476, -0.2928932188134525], 'a7': [0.0, 0.0], 'a8': [-0.9238795325112867, 0.3826834323650898], 'a9': [0.0, -0.41421356237309503], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9482235240027046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.3826834323650898, 0.9238795325112867]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.1443', 'coefficient_field': 'CDF', 'conductor': 1900, 'conductor_radical': 190, 'conjugate': '1201758978675783495902575416688', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.3826834323650898, 0.9238795325112867]], [[1.0, 0], [-0.541196100146197, -0.541196100146197], [0, 1.0]], 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'4.18349282811218865180569265000274', '4.62328336452092402814194591423029', '5.80631318650078260808157781363528', '6.55966938591925544238696870225843', '7.44932511482799549510543305668012', '7.71249890605844308698971627927966', '8.779650969188698369497979499097202', '9.199301876710615110911715381614189'], 'prelabel': '2-1900-380.303-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9737676950909311, 'root_angle': 0.5737918088252166, 'root_number': '-0.22975292054736118352393736938184 + 0.97324898946773016378805774830813*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2868959044126083', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82981931649332210426262911042', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82521972678388321272019008533', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.18349282811218865180569265000', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9482235240027046, 'bad_primes': [2, 5, 19], 'central_character': '380.303', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/1/j/a/1443/3'], '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': '2-1900-380.303-c0-0-7', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1900-380.303-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9737676950909311, 'root_angle': 0.2868959044126083, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82981931649332210426262911042', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2319571554861968228912161793516', 'Lhash_array': ['2319571554861968228912161793516'], 'label': '2-1900-380.303-c0-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/1/j/a/1443/3'}