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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1400.947', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.20791169081775934, 0.9781476007338057], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9135454576426009, -0.4067366430758002], 'algebraic': True, 'analytic_conductor': 6.501572666816301, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '1400.947', 'coeff_info': ['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}'], 'conductor': 1400, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_1400.683', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^17', 0, 0, 0, 0, 0, 'a^34', 0, 'a^56', 0, 'a^39', 0, 0, 0, 'a^23', 0, 'a^58', 0, 0, 0, 'a^31', 0, 0, 0, 'a^51', 0, 'a^72', 0, 'a^38', 0, 'a^13', 0, 0, 0, 'a^49', 0, 'a^56', 0, 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6.501572666816301, 'root_angle': -0.2998270469460539, 'root_number': '0.588224743306987388735829305237-0.808697503001850992619552295720*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.149913523473', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(60)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.870745226802201463172709435118+0.0985797325293938926333328118212*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.37258143769', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.87857059729', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.12617645133', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.501572666816301, 'bad_primes': [2, 5, 7], 'central_character': '1400.947', 'conductor': 1400, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1400/947'], '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': '1-1400-1400.947-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': '1-1400-1400.947-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.501572666816301, 'root_angle': -0.14991352347302694, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.37258143769', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1400.947', 'Lhash_array': ['dirichlet_L_1400.947'], 'label': '1-1400-1400.947-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1400/947'}