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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_967.125', 'a10': [0.5112232110728013, 0.8594479789146136], 'a2': [0.5278952305728325, 0.8493094992630519], 'a3': [-0.08769569505720053, -0.9961473109276733], 'a4': [-0.442653251076912, 0.8966928678823315], 'a5': [0.9998096274980727, 0.019511759586594398], 'a6': [0.7997432346737522, -0.6003422012432275], 'a7': [0.2603893779468603, 0.965503688160976], 'a8': [-0.9952443106549532, 0.0974102772244637], 'a9': [-0.984618930136869, 0.1747156616223271], 'algebraic': True, 'analytic_conductor': 103.91858227640239, 'analytic_normalization': 0, 'bad_lfactors': [[967, [1]]], 'bad_primes': [967], 'central_character': '967.125', 'coeff_info': ['x^322 - 1', '0.999809627498073 + 0.0195117595865944*I', '\\\\zeta_{322}'], 'conductor': 967, 'conductor_radical': 967, 'conjugate': 'dirichlet_L_967.557', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^52', 'a^237', 'a^104', 'a^1', 'a^289', 'a^67', 'a^156', 'a^152', 'a^53', 'a^244', 'a^19', 'a^239', 'a^119', 'a^238', 'a^208', 'a^176', 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[1, 'a^270'], [1, 'a^126'], [1, 'a^103'], [1, 'a^36'], [1, 'a^97'], [1, 'a^184'], [1, 'a^116']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-967-967.125-r1-0-0', 'leading_term': '-0.0514642026454000952811072188863+0.408858131302348510023575870406*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/967/125', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [-0.41208437932779646, -2.204599981162931, -3.1482393616057665, -2.698367330021827, -0.9203859663899948, 1.3094463657189663, 2.686039428983672, 2.373866727076347, 0.7687424909883571, -0.6195941628520657, -0.2753262691031619, 2.0228254977431277, 4.853252753073721, 6.207656387316648, 5.1463930543163, 2.583989252991713, 0.4339616156653036, -0.11800390620977692, 0.4519595531446971, 0.7738173475121457, 0.20497833290501358, 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'186.40967435104151782703346678870', '186.66002927564147462858646033968', '187.76807428518675519535377128082', '188.62319066545521830350114975323', '188.9216208860455275593166536649', '189.4064275651453516414223574349', '189.92161897618918994904026633231', '190.3199029588446997249643703800', '191.17736051374568623083044591039', '192.01125703183099394926845271189', '192.64731099583674887086713401542', '193.4127753490906453593305170087', '193.88154383212546343768689742026', '194.54185290821407571030491035680', '195.17631174991717962057078036735', '195.618509469038686800204914448081', '196.3677483129658942843700940248', '196.79616862926181900327895832913', '197.18811243851561176608789660817', '197.647696750428355178317611768097', '198.61611847930965046141962089498', '199.26889669720150332342068014603', '199.79547493688582657601531586752'], 'prelabel': '1-967-967.125-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': -0.9202859871087377, 'root_number': '-0.968806206840606422002911424932-0.247819558524173241683515913028*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.460142993554', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(322)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.14729579380843711921529090737+0.303259112274363092252797308136*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.37648535637', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.64267796516', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.17841777864', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 103.91858227640239, 'bad_primes': [967], 'central_character': '967.125', 'conductor': 967, 'conductor_radical': 967, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/967/125'], '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': '1-967-967.125-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': '1-967-967.125-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 103.91858227640239, 'root_angle': -0.46014299355436883, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37648535637', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_967.125', 'Lhash_array': ['dirichlet_L_967.125'], 'label': '1-967-967.125-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/967/125'}
Lfunction data - 1-967-967.125-r1-0-0