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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_289.186', 'a10': [0.8502171357296141, 0.5264321628773558], 'a2': [-0.2736629900720829, -0.961825643172819], 'a3': [-0.092268359463302, -0.9957341762950345], 'a4': [-0.8502171357296141, 0.5264321628773558], 'a5': [-0.7390089172206591, 0.6736956436465572], 'a6': [-0.9324722294043558, 0.3612416661871529], 'a7': [0.9829730996839018, -0.18374951781657034], 'a8': [0.7390089172206591, 0.6736956436465572], 'a9': [-0.9829730996839018, 0.18374951781657034], 'algebraic': True, 'analytic_conductor': 1.3421103576499365, 'analytic_normalization': 0, 'bad_lfactors': [[17, [1]]], 'bad_primes': [17], 'central_character': '289.186', 'coeff_info': ['x^34 - 1', '0.982973099683902 + 0.183749517816570*I', '\\\\zeta_{34}'], 'conductor': 289, 'conductor_radical': 17, 'conjugate': 'dirichlet_L_289.101', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^24', 'a^25', 'a^14', 'a^13', 'a^15', 'a^33', 'a^4', 'a^16', 'a^3', 'a^31', 'a^5', 'a^4', 'a^23', 'a^4', 'a^28', 0, 'a^6', 'a^10', 'a^27', 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'194.469765105882097943492067660145', '194.93236716748453589373854825181', '195.34926479022289143743732891594', '195.87570536568308218361018725178', '197.18755105368665455623097556962', '197.91403010018367980850339099189', '198.33237692851018612696507811998', '199.37436348643795607794004906925', '199.82970271197642187280230700704'], 'prelabel': '1-17e2-289.186-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3421103576499365, 'root_angle': -0.2750865051903114, 'root_number': '-0.156971278314055687788196626117-0.987603168172546553901410873294*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.27508650519', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(34)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.710231464120733163589372206497-0.512318573651429553201181015720*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.00437048117', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.0744680763', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.40159551178', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 1.3421103576499365, 'bad_primes': [17], 'central_character': '289.186', 'conductor': 289, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/289/186'], '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': '1-17e2-289.186-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': '1-17e2-289.186-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3421103576499365, 'root_angle': -0.2750865051903114, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00437048117', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_289.186', 'Lhash_array': ['dirichlet_L_289.186'], 'factors': ['1-17e2-289.186-r0-0-0'], 'label': '1-17e2-289.186-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/289/186'}
Lfunction data - 1-17e2-289.186-r0-0-0