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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_547.296', 'a10': [-0.970941817426052, -0.23931566428755777], 'a2': [0.7994427634035012, -0.6007422642379789], 'a3': [1.0, 0.0], 'a4': [0.27821746391645263, -0.9605181116313724], 'a5': [-0.6324453755953773, -0.7746049618276546], 'a6': [0.7994427634035012, -0.6007422642379789], 'a7': [-0.9199794436588242, 0.3919666098600751], 'a8': [-0.3546048870425356, -0.9350162426854148], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 2.540257320534655, 'analytic_normalization': 0, 'bad_lfactors': [[547, [1]]], 'bad_primes': [547], 'central_character': '547.296', 'coeff_info': ['x^39 - 1', '0.987050262637913 + 0.160411280857760*I', '\\\\zeta_{39}'], 'conductor': 547, 'conductor_radical': 547, 'conjugate': 'dirichlet_L_547.231', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^35', 'a^0', 'a^31', 'a^25', 'a^35', 'a^17', 'a^27', 'a^0', 'a^21', 'a^32', 'a^31', 'a^26', 'a^13', 'a^25', 'a^23', 'a^20', 'a^35', 'a^16', 'a^17', 'a^17', 'a^28', 'a^37', 'a^27', 'a^11', 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'199.112065847220365854822549433376', '199.586756741765986956028926071378'], 'prelabel': '1-547-547.296-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.3954544198910597, 'root_number': '-0.791901764158315609471150046105-0.610648504397535950566271819252*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.395454419891', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(39)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.33813235290605199455831499177-1.09495658985146497613410015903*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.75263057651', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.22680947494', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.17925291983', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.540257320534655, 'bad_primes': [547], 'central_character': '547.296', 'conductor': 547, 'conductor_radical': 547, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/547/296'], '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': '1-547-547.296-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': '1-547-547.296-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': -0.3954544198910597, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75263057651', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_547.296', 'Lhash_array': ['dirichlet_L_547.296'], 'factors': ['1-547-547.296-r0-0-0'], 'label': '1-547-547.296-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/547/296'}
Lfunction data - 1-547-547.296-r0-0-0