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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1183.502', 'a10': [-0.8451900855437947, 0.5344658261278011], 'a2': [0.16041128085776024, 0.9870502626379128], 'a3': [0.99675730813421, -0.08046656871672588], 'a4': [-0.9485364419471455, 0.3166679938014725], 'a5': [0.3919666098600751, 0.9199794436588242], 'a6': [0.23931566428755777, 0.970941817426052], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.46472317204376856, -0.8854560256532099], 'a9': [0.9870502626379128, -0.16041128085776024], 'algebraic': True, 'analytic_conductor': 5.493828903459774, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [13, [1]]], 'bad_primes': [7, 13], 'central_character': '1183.502', 'coeff_info': ['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}'], 'conductor': 1183, 'conductor_radical': 91, 'conjugate': 'dirichlet_L_1183.304', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 'a^154', 'a^70', 'a^29', 'a^33', 0, 'a^105', 'a^152', 'a^64', 'a^121', 'a^68', 0, 0, 'a^27', 'a^140', 'a^40', 'a^31', 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5.493828903459774, 'root_angle': 0.37233197791252337, 'root_number': '-0.695154273002055550070387230428+0.718860582259859079394395536336*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.372331977913', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(156)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.17390358426431995527778078359+0.987447381793694150261155973568*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.42417424999', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.6854165167', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.57285581785', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 5.493828903459774, 'bad_primes': [7, 13], 'central_character': '1183.502', 'conductor': 1183, 'conductor_radical': 91, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1183/502'], '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': '1-1183-1183.502-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': '1-1183-1183.502-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.493828903459774, 'root_angle': 0.37233197791252337, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.42417424999', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1183.502', 'Lhash_array': ['dirichlet_L_1183.502'], 'factors': ['1-1183-1183.502-r0-0-0'], 'label': '1-1183-1183.502-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1183/502'}
Lfunction data - 1-1183-1183.502-r0-0-0