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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_317.156', 'a10': [0.6410936375922202, -0.767462668693908], 'a2': [-0.0992537989080616, 0.9950621505224274], 'a3': [0.36886392452400785, 0.929483407697387], 'a4': [-0.9802973668046362, -0.19752739717795267], 'a5': [-0.8273040325430573, -0.5617544283207708], 'a6': [-0.9615049043274204, 0.27478777075102534], 'a7': [-0.25561663244047467, 0.9667782254580372], 'a8': [0.2938502743379209, -0.9558514614057608], 'a9': [-0.7278788103694941, 0.6857057950864132], 'algebraic': True, 'analytic_conductor': 1.4721418109862625, 'analytic_normalization': 0, 'bad_lfactors': [[317, [1]]], 'bad_primes': [317], 'central_character': '317.156', 'coeff_info': ['x^79 - 1', '0.996838839014696 + 0.0794501669717144*I', '\\\\zeta_{79}'], 'conductor': 317, 'conductor_radical': 317, 'conjugate': 'dirichlet_L_317.63', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^21', 'a^15', 'a^42', 'a^47', 'a^36', 'a^23', 'a^63', 'a^30', 'a^68', 'a^44', 'a^57', 'a^48', 'a^44', 'a^62', 'a^5', 'a^72', 'a^51', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-317-317.156-r0-0-0', 'leading_term': '0.0775805297385210752969976676138-0.0440354691989595514876276848710*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/317/156', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.08920684470421456, -0.5496491069063932, -1.7457951825583087, -3.4770223870579535, -5.268981705181983, -6.413465345094587, -6.295583172785241, -4.742593094950882, -2.211923851121002, 0.33923695087935796, 1.899170497991621, 1.9459601515278013, 0.7591687313395754, -0.7387049819481742, -1.5624147731989506, -1.3117382777926418, -0.43642411906081313, 0.10543925098243326, -0.41095181630560745, -1.8709015422218855, -3.3344634026272058, -3.712215009014691, -2.6145397478352863, -0.6988787974188915, 0.8061851109957244, 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'191.705270386086100350001548526184', '192.051057859027029535563417075559', '193.1454832599429853902018436860', '193.946502465187875925452432224303', '194.22706510144196799936491529696', '195.37750310635069724277567210245', '196.02407074198863480217925101479', '196.563817497855120311465860682649', '196.94041423656790749547094174556', '198.035194393239666175433499774580', '198.63273696244825483791620010752', '199.02386499991921898940786189908', '199.65963270734102870296576190132'], 'prelabel': '1-317-317.156-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4721418109862625, 'root_angle': -0.32866298839774627, 'root_number': '0.512652328822824924827238010685-0.858596290320738684255128048323*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.164331494199', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(79)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.475202435174803447817237173609+0.368183447632560436581807262704*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0563029913644', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '2.76587766614', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.90231940466', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4721418109862625, 'bad_primes': [317], 'central_character': '317.156', 'conductor': 317, 'conductor_radical': 317, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/317/156'], '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': '1-317-317.156-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': '1-317-317.156-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4721418109862625, 'root_angle': -0.16433149419887313, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0563029913644', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_317.156', 'Lhash_array': ['dirichlet_L_317.156'], 'label': '1-317-317.156-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/317/156'}