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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4003.785', 'a10': [-0.9837448439320028, -0.17957194111887165], 'a2': [0.19730334902640007, -0.9803424852891802], 'a3': [0.5907027951645512, 0.8068892165500704], 'a4': [-0.9221427769259332, -0.3868497110808392], 'a5': [-0.018054149250560442, -0.9998370105646412], 'a6': [0.907575419670957, -0.4198891015602646], 'a7': [0.9585629474974413, -0.2848808096116999], 'a8': [-0.5611870653623824, 0.8276889981568906], 'a9': [-0.3021404155695727, 0.9532634312085227], 'algebraic': True, 'analytic_conductor': 18.589853846618325, 'analytic_normalization': 0, 'bad_lfactors': [[4003, [1]]], 'bad_primes': [4003], 'central_character': '4003.785', 'coeff_info': ['x^87 - 1', '0.997393231517950 + 0.0721577558006161*I', '\\\\zeta_{87}'], 'conductor': 4003, 'conductor_radical': 4003, 'conjugate': 'dirichlet_L_4003.2412', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^68', 'a^13', 'a^49', 'a^65', 'a^81', 'a^83', 'a^30', 'a^26', 'a^46', 'a^69', 'a^62', 'a^60', 'a^64', 'a^78', 'a^11', 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'193.85498306445626404641273568473', '194.59043588710063429204198915756', '195.18818609487941011658319388394', '195.5916515663289035989288113500', '196.07912464661036957033591557720', '196.869973560966037682892349158945', '197.220867888354106818153594563147', '197.95988608902207453489295661027', '198.55004672774634163168724733500', '199.01798364747971083715054466648', '199.615077636832129872741476317523', '199.87887884563576240883863177230'], 'prelabel': '1-4003-4003.785-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.589853846618325, 'root_angle': -0.586258101751779, 'root_number': '-0.267683337384802593031974527268-0.963506943870428962085941402522*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(87)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28420021034980662790251486376-0.784485212523222690233281202520*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.794749744656', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.31434406249', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.54609229552', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.589853846618325, 'bad_primes': [4003], 'central_character': '4003.785', 'conductor': 4003, 'conductor_radical': 4003, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4003/785'], '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': '1-4003-4003.785-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': '1-4003-4003.785-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.589853846618325, 'root_angle': -0.2931290508758895, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.794749744656', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4003.785', 'Lhash_array': ['dirichlet_L_4003.785'], 'label': '1-4003-4003.785-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4003/785'}
Lfunction data - 1-4003-4003.785-r0-0-0