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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_539.10', 'a10': [-0.9888308262251285, -0.14904226617617444], 'a2': [-0.9555728057861407, -0.2947551744109042], 'a3': [-0.36534102436639504, 0.9308737486442042], 'a4': [0.8262387743159949, 0.5633200580636221], 'a5': [0.9888308262251285, -0.14904226617617444], 'a6': [0.6234898018587335, -0.7818314824680298], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.6234898018587335, -0.7818314824680298], 'a9': [-0.7330518718298263, -0.6801727377709194], 'algebraic': True, 'analytic_conductor': 2.503105476724276, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [11, [1]]], 'bad_primes': [7, 11], 'central_character': '539.10', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 539, 'conductor_radical': 77, 'conjugate': 'dirichlet_L_539.54', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^23', 'a^13', 'a^4', 'a^41', 'a^36', 0, 'a^27', 'a^26', 'a^22', 0, 'a^17', 'a^30', 0, 'a^12', 'a^8', 'a^10', 'a^7', 'a^14', 'a^3', 0, 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'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': 0.11054421768707484, 'root_number': '0.768329121733127771161393808887+0.640054966933934922079835502627*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.110544217687', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.743550657773808894815469614572+0.129094330191064366524867014448*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.03692764242', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.40602573753', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.40237101351', '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': '539.10', 'conductor': 539, 'conductor_radical': 77, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/539/10'], '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': '1-539-539.10-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': '1-539-539.10-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.503105476724276, 'root_angle': 0.11054421768707484, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.03692764242', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_539.10', 'Lhash_array': ['dirichlet_L_539.10'], 'factors': ['1-539-539.10-r0-0-0'], 'label': '1-539-539.10-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/539/10'}