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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.10', 'a10': [-0.9763439220543082, 0.21622337030860211], 'a2': [-0.773958037050753, -0.6332368884426628], 'a3': [-0.11931882848395176, 0.9928559901462132], 'a4': [0.19802208623090942, 0.9801975583344198], 'a5': [0.6187286111767809, -0.7856048025001195], 'a6': [0.7210608041484818, -0.6928717895258435], 'a7': [-0.31608614686174, -0.948730492691206], 'a8': [0.46743646674681383, -0.8840266678982341], 'a9': [-0.9715260343384347, -0.2369328271950402], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.10', 'coeff_info': ['x^1182 - 1', '0.999985871574519 + 0.00531569857584313*I', '\\\\zeta_{1182}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.473', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^720', 'a^318', 'a^258', 'a^1012', 'a^1038', 'a^826', 'a^978', 'a^636', 'a^550', 'a^603', 'a^576', 'a^208', 'a^364', 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21.961383672410207, 'root_angle': -0.48472629785305515, 'root_number': '-0.995398652453445503515041266252-0.0958202624389268195335541147530*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(1182)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.616732069720693563542109691041-0.166415569448586490478520094098*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.169462469006', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.03133246956', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.09926337804', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.10', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/10'], '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': '1-4729-4729.10-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': '1-4729-4729.10-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.48472629785305515, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.169462469006', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.10', 'Lhash_array': ['dirichlet_L_4729.10'], 'factors': ['1-4729-4729.10-r0-0-0'], 'label': '1-4729-4729.10-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/10'}
Lfunction data - 1-4729-4729.10-r0-0-0