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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5041.19', 'a10': [0.9121690539814163, 0.4098141248891355], 'a2': [-0.5530053906499306, 0.8331776748762041], 'a3': [-0.9987847707987818, 0.049284699658463146], 'a4': [-0.3883700758242352, -0.9215034911514323], 'a5': [-0.16298642432921462, -0.986628311718439], 'a6': [0.5112704508823714, -0.8594198776235843], 'a7': [0.8723801589522876, -0.48882804570358], 'a8': [0.9825468816457794, 0.18601512134274137], 'a9': [0.9951420367591501, -0.09844961490452983], 'algebraic': True, 'analytic_conductor': 23.41030558101498, 'analytic_normalization': 0, 'bad_lfactors': [[71, [1]]], 'bad_primes': [71], 'central_character': '5041.19', 'coeff_info': ['x^2485 - 1', '0.999996803485171 + 0.00252844209755057*I', '\\\\zeta_{2485}'], 'conductor': 5041, 'conductor_radical': 71, 'conjugate': 'dirichlet_L_5041.796', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^853', 'a^1223', 'a^1706', 'a^1799', 'a^2076', 'a^2283', 'a^74', 'a^2446', 'a^167', 'a^213', 'a^444', 'a^2342', 'a^651', 'a^537', 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'199.54360882097412247212632152714', '199.90698340965602268920228564702'], 'prelabel': '1-71e2-5041.19-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.41030558101498, 'root_angle': 0.00019837333862328903, 'root_number': '0.999999223223121418649207196489+0.00124641612384483477004360175591*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2485)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.666119918525197529138440262618+0.0778784326657519160536820429322*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.588269453081', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.39635661262', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.78429476326', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 23.41030558101498, 'bad_primes': [71], 'central_character': '5041.19', 'conductor': 5041, 'conductor_radical': 71, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5041/19'], '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': '1-71e2-5041.19-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': '1-71e2-5041.19-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 23.41030558101498, 'root_angle': 0.00019837333862328903, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.588269453081', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5041.19', 'Lhash_array': ['dirichlet_L_5041.19'], 'factors': ['1-71e2-5041.19-r0-0-0'], 'label': '1-71e2-5041.19-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5041/19'}
Lfunction data - 1-71e2-5041.19-r0-0-0