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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2183.319', 'a10': [-0.7960930657056438, 0.6051742151937651], 'a2': [-0.48428315338761946, 0.8749113254181496], 'a3': [-0.9895865165556373, -0.14393931447411912], 'a4': [-0.5309396546898868, -0.8474096312160865], 'a5': [0.9150082349740122, 0.4034351619898085], 'a6': [0.6051742151937651, -0.7960930657056438], 'a7': [0.19730334902640007, -0.9803424852891802], 'a8': [0.9985334138511238, -0.054138908585417526], 'a9': [0.9585629474974413, 0.2848808096116999], 'algebraic': True, 'analytic_conductor': 10.137809379757133, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]], [59, [1]]], 'bad_primes': [37, 59], 'central_character': '2183.319', 'coeff_info': ['x^348 - 1', '0.999837010564641 + 0.0180541492505604*I', '\\\\zeta_{348}'], 'conductor': 2183, 'conductor_radical': 2183, 'conjugate': 'dirichlet_L_2183.917', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^115', 'a^182', 'a^230', 'a^23', 'a^297', 'a^272', 'a^345', 'a^16', 'a^138', 'a^120', 'a^64', 'a^245', 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-0.26036510075285524, 'root_number': '-0.0650798213159467045723410859776-0.997880061358821042628894385928*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.260365100753', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(348)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.562332915328624973522694375559+0.136499873377961793670153231562*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.153225576881', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.39551403074', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.10047802256', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 10.137809379757133, 'bad_primes': [37, 59], 'central_character': '2183.319', 'conductor': 2183, 'conductor_radical': 2183, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2183/319'], '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': '1-2183-2183.319-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': '1-2183-2183.319-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.137809379757133, 'root_angle': -0.26036510075285524, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.153225576881', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2183.319', 'Lhash_array': ['dirichlet_L_2183.319'], 'factors': ['1-2183-2183.319-r0-0-0'], 'label': '1-2183-2183.319-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2183/319'}
Lfunction data - 1-2183-2183.319-r0-0-0