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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_287.97', 'a10': [0.8090169943749475, -0.5877852522924731], 'a2': [0.9510565162951535, 0.30901699437494745], 'a3': [-0.7071067811865476, 0.7071067811865476], 'a4': [0.8090169943749475, 0.5877852522924731], 'a5': [0.5877852522924731, -0.8090169943749475], 'a6': [-0.8910065241883679, 0.4539904997395468], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.5877852522924731, 0.8090169943749475], 'a9': [2.9010907910729803e-30, -1.0], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.97', 'coeff_info': ['x^40 - 1', '0.987688340595138 + 0.156434465040231*I', '\\\\zeta_{40}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.216', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^15', 'a^4', 'a^34', 'a^17', 0, 'a^6', 'a^30', 'a^36', 'a^31', 'a^19', 'a^7', 0, 'a^9', 'a^8', 'a^1', 'a^32', 'a^33', 'a^38', 0, 'a^33', 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'196.71699395069433953706048258826', '197.4482152861771510976745721339', '197.84790716237532418793583213226', '198.775710592932925216767428435802', '199.59109141188312531851736878953'], 'prelabel': '1-287-287.97-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.11857285077305126, 'root_number': '0.735077601323224656445063458047+0.677982979161641187589478612761*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.118572850773', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(40)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.60451468731202744511055280089+0.461170322241469065192613519048*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.46610208172', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.31517522894', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.25274630176', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.97', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/97'], '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': '1-287-287.97-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': '1-287-287.97-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': 0.11857285077305126, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46610208172', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_287.97', 'Lhash_array': ['dirichlet_L_287.97'], 'factors': ['1-287-287.97-r0-0-0'], 'label': '1-287-287.97-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/97'}
Lfunction data - 1-287-287.97-r0-0-0