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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': -3, 'Lhash': '1005447061264035202', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 997.427341728218, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [37, [1, -1]], [211, [1, 1]]], 'bad_primes': [2, 37, 211], 'central_character': '124912.1', 'coefficient_field': '1.1.1.1', 'conductor': 124912, 'conductor_radical': 15614, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, -2, 5], [1, -2, 7], [1, 1, 11], [1, 0, 13], [1, -2, 17], [1, 8, 19], [1, 3, 23], [1, -7, 29], [1, -7, 31], [1, -1], [1, -12, 41], [1, 8, 43], [1, 0, 47], [1, -6, 53], [1, -2, 59], [1, -7, 61], [1, 6, 67], [1, 1, 71], [1, -11, 73], [1, 8, 79], [1, 9, 83], [1, -15, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-124912-1.1-c1-0-1', 'leading_term': '2.58255399797', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/124912/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.582553997972398, 1.800467022542375, -0.1023826875586896, -1.846095697177188, -1.973247562613797, -0.2353834108738385, 1.776950275077976, 2.098200802767297, 0.721121545275741, -0.2454100851090668, 0.5908254197959087, 1.617236760893699, 0.1966999034328295, -3.13435305025411, -4.467694560782574, -1.671908378453355, 2.121714447325321, 2.485578102394085, -0.06407430925057074, -1.057542300623877, 0.9216100635171091, 2.282878943579214, 0.7040838665243048, -1.024839914047633, -0.2805200652641364, 0.4952305037559178, -1.370640173118285, -2.731322247037784, 0.5820638451811514, 5.56124822075858, 5.757358538912832, 1.674405515010045, -0.4190178034889008, 0.7412736219089023, 0.5887529316871988, -1.349313230926688, -0.4313425925746079, 3.128783291648711, 3.453490644444885, -0.0925952132066002, -1.60165729105955, 0.07131053375425671, -0.2430292997803574, -2.846004753642573, -2.394025532331466, 0.5965395714813277, 0.2002590407860528, -2.596982842720731, -1.545251777915468, 1.683006515756672, 0.3299545685504023, -3.5038611580356, -2.685611578650987, 0.7962468683386459, 0.409797251128372, -1.769683430895428, -0.7052458893863364, 0.781719377804495, -0.4287894874997467, -0.2207866686752489, 2.239153032020734, 0.5423129294794228, -4.628677550820207, -4.358112696077108, 0.7141433930797141, 0.877332492842306, -3.497953404058496, -3.719914429811339, -0.4226317497833243, 0.1874946639823269, -0.08572103044441791, 1.599144706216737, 1.221330110386419, -0.9185661726586652, 1.633857242278319, 6.122614758138868, 4.103458639923484, -0.6899665611638024, -0.1595825511299499, 0.9913359231436379, -2.905844664987022, -4.834281145899016, -0.680301841484543, 1.818888042483409, 0.09114086170908467, -0.2193497018534081, -0.1549658052413192, -2.624869645849717, -1.804387345157558, 3.513303115803814, 4.072109332487008, -0.4919812887772465, -0.9345263402338321, 1.178011239704966, -0.7738603167253265, -1.597823886653563, 2.489484130946389, 3.072223370666113, -1.38030848720058, -1.774091354051035, 1.09153597446504, 0.2425096618684409, -0.9070512812247945, 0.7462145469774873, -0.1396486663566773, -1.741617050188232, 2.082040048508124, 4.681999492312823, 0.2000930730075624, -1.937655468663393, 2.026741892455407, 2.492785138937129, -0.5637467463920143, 0.4027800785602892, 1.367503442153326, -1.444519725773507, -0.9249127712848915, 2.487072711250644, 1.01494951911615, -1.50537116404822, -0.1857744424374365], 'positive_zeros': ['0.4877730261733812', '1.275956443528768', '2.135042167957868', '2.381139595332902', '3.016791887556796', '3.848397235340960', '4.493635680616574', '4.906128612020470', '5.575422765513549', '6.047764943112848', '6.353715153160693', '6.971889140169486', '7.885416616169087', '8.122960373719819', '8.575631540110907', '9.033317373134854', '9.743444493878057', '10.23857704403717', '10.46981781572563', '11.19027543180866', '11.51821383801559', '12.10518060422156', '12.52049643676298', '13.17826132810694', '13.54013622087184', '14.07850106932741', '14.43247853767815', '14.77456800519458', '15.27740457057970', '15.95926084930774', '16.30470140932993', '17.05021191448289', '17.30630283516559', '17.52062084698287', '18.11877987813278', '18.40726909432986', '19.19750286418460', '19.51547906472346', '19.84165801030544'], 'prelabel': '2-124912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.582073106878497, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1005447061264035202, 'z1': {'__RealLiteral__': 0, 'data': '0.4877730261733812', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.275956443528768', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.135042167957868', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 997.427341728218, 'bad_primes': [2, 37, 211], 'central_character': '1.1', 'conductor': 124912, 'conductor_radical': 15614, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 2, 0, -3, 0, -1, 0, 0, 0, 0, 0, 2, 0, -8, 0, 0, 0, -3, 0, -1, 0, 0, 0, 7, 0, 7, 0, 0, 0, 4, 0, 1, 0, 0, 0, 12, 0, -8, 0, -6, 0, 0, 0, -3, 0, 0, 0, 6, 0, -2, 0, 0, 0, 2, 0, 7, 0, -6, 0, 0, 0, -6, 0, 0, 0, -1, 0, 11, 0, 0, 0, -2, 0, -8, 0, 9, 0, -9, 0, 4, 0, 0, 0, 15, 0, 0, 0, 0, 0, -16, 0, -2, 0, 3, 0], 'euler11': [1, 1, 11], 'euler13': [1, 0, 13], 'euler17': [1, -2, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, -7, 29], 'euler3': [1, 0, 3], 'euler31': [1, -7, 31], 'euler37': [1, -1, 0], 'euler41': [1, -12, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -2, 59], 'euler61': [1, -7, 61], 'euler67': [1, 6, 67], 'euler7': [1, -2, 7], 'euler71': [1, 1, 71], 'euler73': [1, -11, 73], 'euler79': [1, 8, 79], 'euler83': [1, 9, 83], 'euler89': [1, -15, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, -2, 5], [1, -2, 7], [1, 1, 11], [1, 0, 13], [1, -2, 17], [1, 8, 19], [1, 3, 23], [1, -7, 29], [1, -7, 31], [1, -1, 0], [1, -12, 41], [1, 8, 43], [1, 0, 47], [1, -6, 53], [1, -2, 59], [1, -7, 61], [1, 6, 67], [1, 1, 71], [1, -11, 73], [1, 8, 79], [1, 9, 83], [1, -15, 89], [1, 2, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/124912/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-124912-1.1-c1-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-124912-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 31.582073106878497, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1005447061264035202, 'z1': {'__RealLiteral__': 0, 'data': '0.4877730261733812', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1005447061264035202', 'Lhash_array': ['1005447061264035202'], 'label': '2-124912-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/124912/c'}