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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.120', 'a10': [0.951657690100178, -0.30716061087514734], 'a2': [-0.9646517542300513, -0.26352797396269845], 'a3': [-0.5112232110728013, -0.8594479789146136], 'a4': [0.8611060138782306, 0.5084254447436167], 'a5': [-0.8370728467165828, 0.5470914450892065], 'a6': [0.2666637827547935, 0.9637896175861744], 'a7': [-0.465830365995821, 0.884874041949587], 'a8': [-0.6966830995013129, -0.7173790203715493], 'a9': [-0.477301656920828, 0.878739511061516], 'algebraic': True, 'analytic_conductor': 4.490729120579545, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.120', 'coeff_info': ['x^483 - 1', '0.999915388507649 + 0.0130082983359933*I', '\\\\zeta_{483}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.137', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^262', 'a^321', 'a^41', 'a^197', 'a^100', 'a^158', 'a^303', 'a^159', 'a^459', 'a^90', 'a^362', 'a^71', 'a^420', 'a^35', 'a^82', 'a^57', 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'187.48763460182382372498998910483', '187.83044599970892701327989370666', '188.16688410278712690229923711804', '189.15836492870597627402537894052', '189.88342660680315527449292996870', '190.14482052643652316006571901392', '190.47871300334102277321817555929', '191.078477782527661240213925111612', '191.82357224697646425280161163065', '192.48543104626331553219525021363', '193.13527831923810342664929474449', '193.74788382811183987983969843230', '194.31538841098118062650694417953', '195.15338045525132755530505096873', '195.42549776812454963483334345394', '196.42191308596506094519234698513', '196.750297680777474671151182137664', '197.39805137851295697316516412218', '198.378950996885560545386575114521', '198.746959349194336727351496833548', '199.2589869520110137948449501961', '199.97276081764743832169706090872'], 'prelabel': '1-967-967.120-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.5785235756787859, 'root_number': '-0.244194625785983020226939798185+0.969726242161798835075086000948*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.289261787839', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(483)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.496012857667863578940999656901+0.0515665877990253273569152333493*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2128175178', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.21695347984', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.08305444053', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.490729120579545, 'bad_primes': [967], 'central_character': '967.120', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/120'], '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': '1-967-967.120-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': '1-967-967.120-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.490729120579545, 'root_angle': 0.28926178783939294, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2128175178', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.120', 'Lhash_array': ['dirichlet_L_967.120'], 'label': '1-967-967.120-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/120'}
Lfunction data - 1-967-967.120-r0-0-0