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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4729.633', 'a10': [-0.36604781432377465, 0.9305960442795721], 'a2': [-0.5363652715952123, -0.8439859568894462], 'a3': [0.2601024648601949, 0.9655810208230333], 'a4': [-0.4246245908531884, 0.9053695139791059], 'a5': [-0.589074657562223, -0.8080786148747842], 'a6': [0.6754268926062935, -0.7374269541752637], 'a7': [-0.7937576660606797, 0.608234138773797], 'a8': [0.9918730395931648, -0.12723157362941068], 'a9': [-0.8646934155473022, 0.5023000070765883], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.633', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2301', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^260', 'a^82', 'a^126', 'a^256', 'a^342', 'a^156', 'a^386', 'a^164', 'a^122', 'a^267', 'a^208', 'a^294', 'a^22', 'a^338', 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{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(394)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.610853745379272404833005113354-0.119668150450594916206966757332*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.248484640985', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.18764577368', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.58050291199', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.633', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/633'], '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': '1-4729-4729.633-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': '1-4729-4729.633-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.31322798184844614, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.248484640985', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4729.633', 'Lhash_array': ['dirichlet_L_4729.633'], 'factors': ['1-4729-4729.633-r0-0-0'], 'label': '1-4729-4729.633-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/633'}