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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_37.19', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.984807753012208, -0.17364817766693036], 'a3': [-0.17364817766693036, 0.984807753012208], 'a4': [0.9396926207859084, -0.3420201433256687], 'a5': [-0.6427876096865394, 0.766044443118978], 'a6': [-7.040766286173228e-31, 1.0], 'a7': [0.766044443118978, 0.6427876096865394], 'a8': [0.8660254037844386, -0.5], 'a9': [-0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 3.976202217401126, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]]], 'bad_primes': [37], 'central_character': '37.19', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 37, 'conductor_radical': 37, 'conjugate': 'dirichlet_L_37.2', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 'a^10', 'a^34', 'a^13', 'a^9', 'a^4', 'a^33', 'a^20', 'a^12', 'a^6', 'a^8', 'a^25', 'a^3', 'a^23', 'a^32', 'a^29', 'a^19', 'a^1', 'a^11', 'a^14', 'a^5', 'a^21', 'a^7', 'a^26', 'a^24', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.164375791612', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.65325576836885655776002342451+0.551607898922910805875537715934*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.81510137789', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.32047230628', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.63871109018', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.976202217401126, 'bad_primes': [37], 'central_character': '37.19', 'conductor': 37, 'conductor_radical': 37, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/37/19'], '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': '1-37-37.19-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-37-37.19-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.976202217401126, 'root_angle': 0.16437579161174218, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.81510137789', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_37.19', 'Lhash_array': ['dirichlet_L_37.19'], 'label': '1-37-37.19-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/37/19'}
Lfunction data - 1-37-37.19-r1-0-0