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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_539.307', 'a10': [-0.2225209339563144, -0.9749279121818236], 'a2': [0.9009688679024191, -0.4338837391175581], 'a3': [0.2225209339563144, -0.9749279121818236], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [0.2225209339563144, -0.9749279121818236], 'a6': [-0.2225209339563144, -0.9749279121818236], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.2225209339563144, -0.9749279121818236], 'a9': [-0.9009688679024191, -0.4338837391175581], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.307', 'coeff_info': ['x^14 - 1', '0.900968867902419 + 0.433883739117558*I', '\\\\zeta_{14}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.230', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^11', 'a^12', 'a^11', 'a^10', 0, 'a^11', 'a^8', 'a^10', 0, 'a^9', 'a^6', 0, 'a^8', 'a^10', 'a^2', 'a^7', 'a^0', 'a^9', 0, 0, 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'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.8673469387755103, 'root_number': '-0.914412623015812481321662155277-0.404783343122393817155922992987*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.433673469388', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(14)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.23802012273754638970696203109-1.37569621525762812398135912872*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.949569524024', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.87774194622', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.87783297801', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.503105476724276, 'bad_primes': [7, 11], 'central_character': '539.307', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/307'], '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': '1-539-539.307-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': '1-539-539.307-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': -0.43367346938775514, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.949569524024', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_539.307', 'Lhash_array': ['dirichlet_L_539.307'], 'label': '1-539-539.307-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/307'}