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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4729.1037', 'a10': [0.9817453282554334, 0.1902001851961016], 'a2': [0.2754670247744354, -0.961310521247906], 'a3': [0.9444462754567683, -0.3286658375551652], 'a4': [-0.8482358365238412, -0.5296186983450447], 'a5': [0.08759702548841304, 0.9961559923654439], 'a6': [-0.055786122057162574, -0.9984427417663084], 'a7': [-0.1666639201255505, 0.9860137614295168], 'a8': [-0.7427890291629893, 0.6695255470518686], 'a9': [0.7839575344483235, -0.6208144522977099], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.1037', 'coeff_info': ['x^788 - 1', '0.999968211136237 + 0.00797350092461664*I', '\\\\zeta_{788}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2686', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^626', 'a^746', 'a^464', 'a^186', 'a^584', 'a^218', 'a^302', 'a^704', 'a^24', 'a^17', 'a^422', 'a^32', 'a^56', 'a^144', 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'0.846976303063962802624456250321-0.531630644383957831685605240246*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(788)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.69468148422494424404203841538-0.555251044249034006053208212145*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.0251980174', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.89364954794', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.38369257918', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.1037', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/1037'], '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': '1-4729-4729.1037-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': '1-4729-4729.1037-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.08921027012455118, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.0251980174', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4729.1037', 'Lhash_array': ['dirichlet_L_4729.1037'], 'factors': ['1-4729-4729.1037-r0-0-0'], 'label': '1-4729-4729.1037-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/1037'}
Lfunction data - 1-4729-4729.1037-r0-0-0