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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_3549.3461', 'a10': [0.970941817426052, -0.23931566428755777], 'a2': [0.99675730813421, 0.08046656871672588], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9870502626379128, 0.16041128085776024], 'a5': [0.9485364419471455, -0.3166679938014725], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [0.970941817426052, 0.23931566428755777], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 16.481486710379325, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [7, [1]], [13, [1]]], 'bad_primes': [3, 7, 13], 'central_character': '3549.3461', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 3549, 'conductor_radical': 273, 'conjugate': 'dirichlet_L_3549.3428', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1', 0, 'a^2', 'a^74', 0, 0, 'a^3', 0, 'a^75', 'a^51', 0, 0, 0, 0, 'a^4', 'a^68', 0, 'a^39', 'a^76', 0, 'a^52', 'a^13', 0, 'a^70', 0, 0, 0, 'a^53', 0, 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'199.683964018300125906151411194009'], 'prelabel': '1-3549-3549.3461-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.481486710379325, 'root_angle': -0.19831287101242334, 'root_number': '0.812121037738724405192802469516-0.583489005947993308417886201137*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.34035286070134040070335174835-0.251694285396454431229448951330*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.859360926533', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.8918359852', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.62468617744', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 16.481486710379325, 'bad_primes': [3, 7, 13], 'central_character': '3549.3461', 'conductor': 3549, 'conductor_radical': 273, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3549/3461'], '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': '1-3549-3549.3461-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': '1-3549-3549.3461-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 16.481486710379325, 'root_angle': -0.09915643550621167, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.859360926533', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_3549.3461', 'Lhash_array': ['dirichlet_L_3549.3461'], 'label': '1-3549-3549.3461-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3549/3461'}
Lfunction data - 1-3549-3549.3461-r0-0-0