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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': -3, 'A8': -1, 'A9': 1, 'Lhash': '501039690598178405', 'a10': [-0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [-1.1338934190276817, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1514.107353047115, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [11, [1, 1]], [13, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 11, 13, 17], 'central_character': '189618.1', 'coefficient_field': '1.1.1.1', 'conductor': 189618, 'conductor_radical': 14586, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -1, 5], [1, 3, 7], [1, 1], [1], [1, -1], [1, 0, 19], [1, -1, 23], [1, 3, 29], [1, -2, 31], [1, -2, 37], [1, -9, 41], [1, 13, 43], [1, 2, 47], [1, 0, 53], [1, -3, 59], [1, 3, 61], [1, -3, 67], [1, 0, 71], [1, 1, 73], [1, 14, 79], [1, -14, 83], [1, -18, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-189618-1.1-c1-0-4', 'leading_term': '0.728873314271', '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/189618/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.7288733142707771, 0.2713593334145361, -0.6611989076599004, -0.9881464859885494, 0.05784074487085527, 1.747024725475054, 2.169959725614996, 0.5309390010324752, -1.245240587639838, -0.522973921170854, 2.21001774984714, 3.296334280153879, 0.9771570608546618, -1.328840258888071, 0.4281623337544593, 4.179857615848855, 3.72954600907005, -1.867851372957965, -5.791260187229393, -3.068567670140335, 1.963355261096948, 2.461443238104158, -0.6540251093951192, -1.553650599514835, 0.3496128448637463, 0.8091603910601745, -0.3730381873703766, 0.577283881621681, 3.007915945661193, 2.50824687513154, 0.0003098238508056952, 0.6764180190346172, 3.639992176960464, 2.835895244324629, -1.355267561814497, -2.363911796149808, 0.5087061813682593, 1.58216533266048, -0.03253926712523923, -0.2475525021437045, 0.5844897646064737, -0.4932941570099698, -1.191867205312075, 0.977222114299306, 1.768093379434077, -1.315863061177019, -2.717759964951052, -0.2915812904300229, -0.4605060688097105, -4.243356672544757, -4.142103980077883, -0.14362730791108, 0.1806086000302422, -1.207040162981715, 2.587923205788129, 5.37640671950468, -1.318842089286973, -8.1913550017474, -3.938536880485476, 2.630961461591459, 0.1138999748974272, -4.343634492712423, -2.041207698162258, 0.9848607973630223, -0.1959382007347603, -0.4192008962445138, 1.260278491640357, 0.4601347777838555, -0.6381032453386322, 0.989484875565323, 1.245121913604348, -0.7145979818557715, -0.04119258342378929, 1.597937970465645, -0.05387680194220529, -1.079987626793338, 0.744418242767366, 0.03108772114315135, -2.13637595341746, 0.09113528544542505, 1.8396200728256, -1.793976895494679, -2.295376509809826, 3.294015241229747, 4.241062133367524, 0.04104843212051676, 0.503653355343534, 2.227230157912253, -1.513897001637755, -2.749110267367802, 1.930615966446572, 2.399553764131146, -0.8627926671179574, 0.6951739938530487, 1.262644178901315, -4.328035668410663, -5.222284714446526, 0.6621160016062637, 1.153724293350375, -2.475507347274173, -0.7674735494312933, 1.448120483310734, -0.6387656957949349, -0.4671537658805557, 1.542407523355845, -0.1409730382797654, -0.7870435223722538, 1.564186033920513, -0.08314766991139096, -3.056396370477456, -0.4961314269617196, 1.837918176677744, 0.07544085393592807, 0.4059286212672457, 2.041465274433753, 0.5699609289511653, -0.2398028777860773, -0.001596813568761076, -1.905938141535873, -1.229490958492996, 1.477721180950729], 'positive_zeros': ['0.3249071780500154', '0.9911005130197885', '1.809904843653614', '2.304224670503584', '3.078139212225379', '3.469843728353699', '4.176046674717635', '4.889781646428310', '5.446539501067803', '5.955262958949695', '6.408008847328063', '6.680285245073043', '7.500049486789970', '7.674034159944294', '8.416945673323705', '8.957928705567018', '9.494515229763162', '9.809391183068650', '10.17564417185493', '10.65774196143770', '11.15905201710227', '11.78542933624724', '11.95267003207790', '12.76215035519499', '13.02163547496275', '13.37127289027122', '13.96549615419330', '14.62081496118463', '15.00484502510924', '15.62626695281997', '15.97292733744580', '16.31099062831424', '16.81068229738645', '17.12690824146421', '17.65016446819556', '18.00466112790923', '18.49453500762125', '18.90185666060427', '19.25293734624975', '19.74379845518661'], 'prelabel': '2-189618-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.91153239140185, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 501039690598178405, 'z1': {'__RealLiteral__': 0, 'data': '0.3249071780500154', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9911005130197885', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.809904843653614', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1514.107353047115, 'bad_primes': [2, 3, 11, 13, 17], 'central_character': '1.1', 'conductor': 189618, 'conductor_radical': 14586, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 1, 1, -3, -1, 1, -1, -1, -1, 0, 3, -1, 1, 1, -1, 0, 1, 3, 1, 1, 1, -4, 0, -1, -3, -3, 1, 2, -1, 1, -1, -3, 1, 2, 0, 0, -1, 9, -3, -13, -1, 1, -1, -2, -1, 2, 4, -1, 0, 0, 1, -1, 3, 0, 3, 3, -1, -3, -2, -3, 1, 0, -1, 3, 1, -1, 3, 0, -1, -1, -2, 4, 0, 3, 0, -14, 1, 1, -9, 14, 3, 1, 13, 3, 1, 18, -1, 0, 1, -2, 2, 0, 1, 8, -2, -1, -4], 'euler11': [1, 1, 0], 'euler13': [1, 0, 0], 'euler17': [1, -1, 0], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, -1, 23], 'euler29': [1, 3, 29], 'euler3': [1, 1, 0], 'euler31': [1, -2, 31], 'euler37': [1, -2, 37], 'euler41': [1, -9, 41], 'euler43': [1, 13, 43], 'euler47': [1, 2, 47], 'euler5': [1, -1, 5], 'euler53': [1, 0, 53], 'euler59': [1, -3, 59], 'euler61': [1, 3, 61], 'euler67': [1, -3, 67], 'euler7': [1, 3, 7], 'euler71': [1, 0, 71], 'euler73': [1, 1, 73], 'euler79': [1, 14, 79], 'euler83': [1, -14, 83], 'euler89': [1, -18, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -1, 5], [1, 3, 7], [1, 1, 0], [1, 0, 0], [1, -1, 0], [1, 0, 19], [1, -1, 23], [1, 3, 29], [1, -2, 31], [1, -2, 37], [1, -9, 41], [1, 13, 43], [1, 2, 47], [1, 0, 53], [1, -3, 59], [1, 3, 61], [1, -3, 67], [1, 0, 71], [1, 1, 73], [1, 14, 79], [1, -14, 83], [1, -18, 89], [1, -8, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/189618/h'], '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': '2-189618-1.1-c1-0-4', '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': '2-189618-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 38.91153239140185, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 501039690598178405, 'z1': {'__RealLiteral__': 0, 'data': '0.3249071780500154', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '501039690598178405', 'Lhash_array': ['501039690598178405'], 'label': '2-189618-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/189618/h'}