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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1588.1035', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9029265382866212, -0.4297949120891716], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9341478602651068, 0.35688622159187183], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.7761464642917568, -0.6305526670845225], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.6305526670845225, -0.7761464642917568], 'algebraic': True, 'analytic_conductor': 7.374640996360204, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [397, [1]]], 'bad_primes': [2, 397], 'central_character': '1588.1035', 'coeff_info': ['x^396 - 1', '0.999874127673875 + 0.0158659638348079*I', '\\\\zeta_{396}'], 'conductor': 1588, 'conductor_radical': 794, 'conjugate': 'dirichlet_L_1588.1163', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^368', 0, 'a^175', 0, 'a^353', 0, 'a^340', 0, 'a^542', 0, 'a^251', 0, 'a^543', 0, 'a^111', 0, 'a^422', 0, 'a^325', 0, 'a^212', 0, 'a^350', 0, 'a^312', 0, 'a^32', 0, 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'196.59338205488796260847241919876', '197.598430829960845642778349376821', '197.930714473105881485000550955263', '198.60450853815593527135995800932', '198.98479299411590678242046120978', '199.36841354980192627672054080296'], 'prelabel': '1-1588-1588.1035-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.374640996360204, 'root_angle': -0.18517961353558085, 'root_number': '0.396111910436813271217778653220-0.918202240473251089669734913545*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.185179613536', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(396)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.24333968505874071736452062512-0.294569162566318495987532540408*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.664899437986', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.91559659777', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.69483605276', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 7.374640996360204, 'bad_primes': [2, 397], 'central_character': '1588.1035', 'conductor': 1588, 'conductor_radical': 794, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1588/1035'], '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': '1-1588-1588.1035-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': '1-1588-1588.1035-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.374640996360204, 'root_angle': -0.18517961353558085, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.664899437986', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1588.1035', 'Lhash_array': ['dirichlet_L_1588.1035'], 'factors': ['1-1588-1588.1035-r0-0-0'], 'label': '1-1588-1588.1035-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1588/1035'}
Lfunction data - 1-1588-1588.1035-r0-0-0