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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1001.2', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.5877852522924731, -0.8090169943749475], 'a3': [-0.9781476007338057, 0.20791169081775934], 'a4': [-0.30901699437494745, -0.9510565162951535], 'a5': [0.4067366430758002, -0.9135454576426009], 'a6': [-0.4067366430758002, 0.9135454576426009], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.9510565162951535, -0.30901699437494745], 'a9': [0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 4.648624456773655, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]], [13, [1]]], 'bad_primes': [7, 11, 13], 'central_character': '1001.2', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1001, 'conductor_radical': 1001, 'conjugate': 'dirichlet_L_1001.501', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^51', 'a^28', 'a^42', 'a^49', 'a^19', 0, 'a^33', 'a^56', 'a^40', 0, 'a^10', 0, 0, 'a^17', 'a^24', 'a^24', 'a^47', 'a^23', 'a^31', 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0.5382987845512371, 'root_number': '-0.120029086032266543708637602512+0.992770375518054404691077158939*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.269149392276', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.646147317779297873966661111882-0.471592558551334422974445446883*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0686557648823', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.40112537295', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.13815118594', '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': '1001.2', 'conductor': 1001, 'conductor_radical': 1001, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1001/2'], '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': '1-1001-1001.2-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': '1-1001-1001.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.648624456773655, 'root_angle': 0.26914939227561857, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0686557648823', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1001.2', 'Lhash_array': ['dirichlet_L_1001.2'], 'label': '1-1001-1001.2-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1001/2'}