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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1001.228', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.9510565162951535, -0.30901699437494745], 'a3': [-0.10452846326765347, -0.9945218953682733], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [0.20791169081775934, -0.9781476007338057], 'a6': [-0.20791169081775934, 0.9781476007338057], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, -0.8090169943749475], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.228', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.821', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^33', 'a^44', 'a^6', 'a^47', 'a^17', 0, 'a^39', 'a^28', 'a^20', 0, 'a^50', 0, 0, 'a^31', 'a^12', 'a^12', 'a^1', 'a^49', 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'-0.527408281086907354232054075776+0.849611973221278068864921526719*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.338418081929', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.440829371777328663162517601358-0.359023585081356104150263663510*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.192502120183', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.34496504968', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.00860819126', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.648624456773655, 'bad_primes': [7, 11, 13], 'central_character': '1001.228', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/228'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-1001-1001.228-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1001-1001.228-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.3384180819287249, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.192502120183', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1001.228', 'Lhash_array': ['dirichlet_L_1001.228'], 'label': '1-1001-1001.228-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/228'}