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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1800.1021', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 8.359164857335244, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1021', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1800, 'conductor_radical': 30, 'conjugate': 'dirichlet_L_1800.781', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 0, 0, 'a^10', 0, 0, 0, 'a^43', 0, 'a^17', 0, 0, 0, 'a^24', 0, 'a^39', 0, 0, 0, 'a^8', 0, 0, 0, 0, 0, 'a^31', 0, 'a^14', 0, 0, 0, 0, 0, 'a^27', 0, 0, 0, 'a^2', 0, 'a^25', 0, 0, 0, 'a^16', 0, 'a^20', 0, 0, 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'198.73181508573786278270952865616', '198.96230623420684865251078375371', '199.6399651079530815861106240937'], 'prelabel': '1-1800-1800.1021-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.359164857335244, 'root_angle': -0.3155555555555556, 'root_number': '-0.400349032556894953956424370080-0.916362729562239596984676420834*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.315555555556', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.762903478974745463912261643535+0.0473085556851472275428654897075*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.137982810643', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.75208999333', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.65190237416', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.359164857335244, 'bad_primes': [2, 3, 5], 'central_character': '1800.1021', 'conductor': 1800, 'conductor_radical': 30, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1800/1021'], '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': '1-1800-1800.1021-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': '1-1800-1800.1021-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.359164857335244, 'root_angle': -0.3155555555555556, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.137982810643', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1800.1021', 'Lhash_array': ['dirichlet_L_1800.1021'], 'factors': ['1-1800-1800.1021-r0-0-0'], 'label': '1-1800-1800.1021-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1800/1021'}
Lfunction data - 1-1800-1800.1021-r0-0-0