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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_37.17', 'a10': [-0.5, -0.8660254037844386], 'a2': [0.3420201433256687, 0.9396926207859084], 'a3': [0.9396926207859084, 0.3420201433256687], 'a4': [-0.766044443118978, 0.6427876096865394], 'a5': [-0.984807753012208, 0.17364817766693036], 'a6': [-7.040766286173228e-31, 1.0], 'a7': [0.17364817766693036, 0.984807753012208], 'a8': [-0.8660254037844386, -0.5], 'a9': [0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 3.976202217401126, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]]], 'bad_primes': [37], 'central_character': '37.17', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 37, 'conductor_radical': 37, 'conjugate': 'dirichlet_L_37.24', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^7', 'a^2', 'a^14', 'a^17', 'a^9', 'a^8', 'a^21', 'a^4', 'a^24', 'a^30', 'a^16', 'a^5', 'a^15', 'a^19', 'a^28', 'a^13', 'a^11', 'a^29', 'a^31', 'a^10', 'a^1', 'a^33', 'a^23', 'a^34', 'a^12', 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0.3648876207464408, 'root_number': '-0.660782047327984307620957990905+0.750577834690738457157794267540*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.364887620746', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.01514751503346877625876631712+0.981830712123945458086104370653*I']], 'z1': {'__RealLiteral__': 0, 'data': '3.21010262275', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.5752448088', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '6.63584535569', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.976202217401126, 'bad_primes': [37], 'central_character': '37.17', 'conductor': 37, 'conductor_radical': 37, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/37/17'], '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': '1-37-37.17-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': '1-37-37.17-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.976202217401126, 'root_angle': 0.3648876207464408, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.21010262275', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_37.17', 'Lhash_array': ['dirichlet_L_37.17'], 'factors': ['1-37-37.17-r1-0-0'], 'label': '1-37-37.17-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/37/17'}
Lfunction data - 1-37-37.17-r1-0-0