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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1441.1124', 'a10': [0.7155989607441211, -0.698511365248937], 'a2': [-0.7485107481711011, 0.6631226582407952], 'a3': [-0.2627073781985869, 0.9648755533435515], 'a4': [0.12053668025532305, -0.992708874098054], 'a5': [-0.9988322268323266, 0.048313379525507065], 'a6': [-0.44319154559924134, -0.8964269372957038], 'a7': [0.9895063994510511, 0.14448904956922132], 'a8': [0.5680647467311558, 0.8229838658936564], 'a9': [-0.8619696668800493, -0.5069598538135904], 'algebraic': True, 'analytic_conductor': 6.691975866344493, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [131, [1]]], 'bad_primes': [11, 131], 'central_character': '1441.1124', 'coeff_info': ['x^130 - 1', '0.998832226832327 + 0.0483133795255071*I', '\\\\zeta_{130}'], 'conductor': 1441, 'conductor_radical': 1441, 'conjugate': 'dirichlet_L_1441.50', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^50', 'a^38', 'a^100', 'a^64', 'a^88', 'a^3', 'a^20', 'a^76', 'a^114', 0, 'a^8', 'a^29', 'a^53', 'a^102', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-1441-1441.1124-r0-0-0', 'leading_term': '0.114498269788421606851503230453+0.779512547832081429358358906515*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1441/1124', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.7878766819827862, 1.2433450553808085, 1.4066549115965974, 0.581744433871762, -1.2763535834721513, -3.0964614310499936, -3.247292389780587, -0.85858642859476, 3.1315315013844685, 6.31704225345021, 6.596680129735099, 3.9823087663306764, 0.7017368782935539, -0.7312391243294445, 0.2202932092068379, 1.7604840799749308, 1.7571680804760672, 0.05596628340876249, -1.3925943266093994, -0.7953278494621493, 1.3367287858799097, 2.655229477176373, 1.6119277607208744, -0.7684909760861982, -2.1003311526783284, 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'2.26016150284', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.84393122667', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.691975866344493, 'bad_primes': [11, 131], 'central_character': '1441.1124', 'conductor': 1441, 'conductor_radical': 1441, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1441/1124'], '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': '1-1441-1441.1124-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': '1-1441-1441.1124-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.691975866344493, 'root_angle': 0.45357718692079363, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.04982776696', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1441.1124', 'Lhash_array': ['dirichlet_L_1441.1124'], 'label': '1-1441-1441.1124-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1441/1124'}