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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4033.2153', 'a10': [0.9396926207859084, -0.3420201433256687], 'a2': [-0.17364817766693036, -0.984807753012208], 'a3': [0.17364817766693036, 0.984807753012208], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [0.9396926207859084, -0.3420201433256687], 'a7': [0.17364817766693036, 0.984807753012208], 'a8': [0.5, 0.8660254037844386], 'a9': [-0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 18.729173260907245, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [109, [1]]], 'bad_primes': [37, 109], 'central_character': '4033.2153', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 4033, 'conductor_radical': 4033, 'conjugate': 'dirichlet_L_4033.3383', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^4', 'a^8', 'a^4', 'a^17', 'a^4', 'a^3', 'a^8', 'a^17', 'a^1', 'a^12', 'a^1', 'a^17', 'a^8', 'a^16', 'a^1', 'a^3', 'a^17', 'a^12', 'a^8', 'a^14', 'a^9', 'a^7', 'a^8', 'a^14', 'a^12', 'a^12', 'a^14', 'a^3', 'a^4', 'a^11', 'a^5', 'a^14', 'a^8', 'a^16', 0, 'a^12', 'a^5', 'a^7', 'a^5', 'a^3', 'a^6', 'a^9', 'a^12', 'a^4', 'a^7', 'a^2', 'a^8', 'a^3', 'a^5', 'a^9', 'a^15', 'a^7', 'a^5', 'a^7', 'a^3', 'a^9', 'a^17', 'a^16', 'a^4', 'a^17', 'a^12', 'a^6', 'a^5', 'a^0', 'a^3', 'a^9', 'a^13', 'a^3', 'a^14', 'a^11', 'a^16', 0, 'a^12', 'a^7', 'a^5', 'a^0', 'a^3', 'a^2', 'a^16', 'a^0', 'a^6', 'a^16', 'a^5', 'a^1', 'a^0', 'a^4', 'a^0', 'a^7', 'a^5', 'a^17', 'a^8', 'a^2', 'a^3', 'a^15', 'a^2', 'a^3', 'a^9', 'a^16'], 'euler_factors': [[1, 'a^13'], [1, 'a^4'], [1, 'a^4'], [1, 'a^4'], [1, 'a^1'], [1, 'a^1'], [1, 'a^1'], [1, 'a^17'], [1, 'a^9'], [1, 'a^14'], [1, 'a^4'], [0], [1, 'a^5'], [1, 'a^6'], [1, 'a^7'], [1, 'a^15'], [1, 'a^17'], [1, 'a^4'], [1, 'a^3'], [1, 'a^14'], [1, 'a^16'], [1, 'a^3'], [1, 'a^6'], [1, 'a^0'], [1, 'a^2'], [1, 'a^15']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4033-4033.2153-r0-0-0', 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'195.68077588939103353838978439060', '196.65647671361783684403423168345', '197.00144711501917709720924527073', '197.87687827469958636441133555694', '198.19474557999723377874219010946', '198.60733367901386321831985421960', '199.21905103428914452954226587373', '199.54934588719350704804949587301'], 'prelabel': '1-4033-4033.2153-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.6556499747248469, 'root_number': '-0.469733447843004031376396400970+0.882808296278146567862178890386*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.04529534796551940400841599051+0.374849157078907227852408822970*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.30538334056', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.12988918671', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.95700519731', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.729173260907245, 'bad_primes': [37, 109], 'central_character': '4033.2153', 'conductor': 4033, 'conductor_radical': 4033, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4033/2153'], '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': '1-4033-4033.2153-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': '1-4033-4033.2153-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.729173260907245, 'root_angle': 0.32782498736242344, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.30538334056', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4033.2153', 'Lhash_array': ['dirichlet_L_4033.2153'], 'label': '1-4033-4033.2153-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4033/2153'}
Lfunction data - 1-4033-4033.2153-r0-0-0