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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_124.107', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.10452846326765347, 0.9945218953682733], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.5, -0.8660254037844386], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.9781476007338057, 0.20791169081775934], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9781476007338057, 0.20791169081775934], 'algebraic': True, 'analytic_conductor': 13.325650674533502, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '124.107', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 124, 'conductor_radical': 62, 'conjugate': 'dirichlet_L_124.51', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 'a^20', 0, 'a^31', 0, 'a^14', 0, 'a^41', 0, 'a^2', 0, 'a^27', 0, 'a^4', 0, 'a^43', 0, 'a^8', 0, 'a^39', 0, 'a^10', 0, 'a^21', 0, 'a^18', 0, 0, 0, 'a^18', 0, 'a^21', 0, 'a^10', 0, 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'root_analytic_conductor': 13.325650674533502, 'root_angle': 0.34670626381758723, 'root_number': '-0.570917848852004054695087403209+0.821007192332807917945584079434*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.346706263818', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.916965758420237123417286670056+0.425270695573018763925820208529*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.73273326545', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.74889121114', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.68750841932', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 13.325650674533502, 'bad_primes': [2, 31], 'central_character': '124.107', 'conductor': 124, 'conductor_radical': 62, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/124/107'], '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': '1-124-124.107-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-124-124.107-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.325650674533502, 'root_angle': 0.34670626381758723, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73273326545', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_124.107', 'Lhash_array': ['dirichlet_L_124.107'], 'factors': ['1-124-124.107-r1-0-0'], 'label': '1-124-124.107-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/124/107'}
Lfunction data - 1-124-124.107-r1-0-0