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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_57.32', 'a10': [-0.17364817766693036, -0.984807753012208], 'a2': [0.17364817766693036, -0.984807753012208], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.9396926207859084, -0.3420201433256687], 'a5': [0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.5, -0.8660254037844386], 'a8': [-0.5, 0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.2647068871489494, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '57.32', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 57, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_57.41', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 0, 'a^10', 'a^17', 0, 'a^12', 'a^6', 0, 'a^13', 'a^15', 0, 'a^7', 'a^8', 0, 'a^2', 'a^5', 0, 0, 'a^9', 0, 'a^11', 'a^1', 0, 'a^16', 'a^3', 0, 'a^4', 'a^4', 0, 'a^3', 'a^16', 0, 'a^1', 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'197.566690237788885757068755921200', '198.76155366717367965238405897673', '199.82002673504626881743503757183'], 'prelabel': '1-57-57.32-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2647068871489494, 'root_angle': -0.5557633174735626, 'root_number': '-0.174290927917683321782628136101-0.984694202504306875268706413996*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.277881658737', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.866723483394178433975844525127-0.618793193876971096882185801861*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.47556277978', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.31946694305', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.88174169297', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.2647068871489494, 'bad_primes': [3, 19], 'central_character': '57.32', 'conductor': 57, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/57/32'], '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': '1-57-57.32-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': '1-57-57.32-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2647068871489494, 'root_angle': -0.2778816587367813, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47556277978', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_57.32', 'Lhash_array': ['dirichlet_L_57.32'], 'label': '1-57-57.32-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/57/32'}
Lfunction data - 1-57-57.32-r0-0-0