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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1660434836536046581', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, -1], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, 8, 23], [1, 2, 29], [1, 4, 31], [1, -2, 37], [1, -10, 41], [1, 4, 43], [1, -8, 47], [1, -10, 53], [1, -4, 59], [1, -10, 61], [1, 0, 67], [1, 8, 71], [1, -6, 73], [1, -4, 79], [1, -8, 83], [1, 6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 113, 'label': '2-369600-1.1-c1-0-113', 'leading_term': '1.84197385855', '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/369600/fj', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.841973858549005, 1.074084781422714, -0.5010837189196568, -1.1786414811833, 0.05210571126124486, 1.83784815503127, 1.58528397800632, -0.9133184117940197, -2.378172715343597, -0.3794933930479191, 2.421242247146874, 1.440576044029659, -2.750698311669581, -4.669444199731948, -2.191492822063145, 0.3817243087264921, 0.0209412674235596, 0.1265795895150217, 3.574134888828886, 6.301633014118605, 4.062391774977857, 0.2682315670333327, -0.1282521903495556, 0.8307900534485574, -0.4639390515734299, -1.443188780999541, 0.4292713845897393, 1.010802380189475, -2.077999292675694, -3.244017196434926, 0.1286793483762989, 1.653618050769307, -0.9525565699122525, -0.6147792301553168, 3.958911342349684, 4.437702065574627, -0.1153282746054778, -1.051731127879111, 2.082400740913915, 1.58643256556638, -1.56503518703675, -1.124270676550176, 0.0609992392746794, -2.25468620080484, -2.923633301716292, 0.5418085300323481, 1.465630986130451, -1.04216280122119, -0.6760921817976363, 0.933641663716025, -0.9758597831770879, -1.838843320773846, 0.7220993857159032, -0.4458592291389994, -4.710841107933735, -3.191110896050348, 0.737451645131659, -1.422263804333197, -3.756406219946948, -0.4610001043563393, 0.0517574374948028, -4.317485141762621, -3.548900051347183, 1.367786958167453, 1.407232085677314, -0.373977039556093, 0.7724728602179944, 0.1238180888092652, -1.401102329357414, 1.634670589704718, 3.638202720411996, 0.4651866923114026, -0.2453042666465732, 1.787668400694982, -0.5182727866786446, -2.532722178444254, 0.07850808975889766, -0.4959371098344164, -3.312629347525249, 0.2489493249623357, 3.356771666265585, -0.859280001656895, -1.973962512070755, 2.258653940297002, 1.033190794147352, -2.40513673869032, -0.3258069005900334, 0.2854410646383208, -2.52558486500582, -1.163672694882894, 0.5279619241005823, -2.031819741098391, -1.751909247701104, 0.8972819834010173, 0.005804895209754504, 0.4600592370500918, 2.334883260563109, -1.325017794298201, -3.179670392725561, 2.448521006629784, 3.756511995825102, -0.3067590692057444, 0.8273202710000775, 2.223253240104863, -0.1658985387730889, 2.648627991420044, 6.022460205854052, 1.149081939496943, -1.115867206686252, 3.401447687347749, 3.084088865673067, -0.2672001051297547, 0.001076046790583135, -0.6682987213951181, 0.0334172939189006, 5.295117967506646, 5.308423131291337, 0.4401731603012183, 0.4006273788748924, 0.693835890078723, -1.184385280168794], 'positive_zeros': ['0.4190202364084392', '0.9932505133006185', '1.667530169223928', '2.278764764357326', '2.842965264844857', '3.686312390353985', '4.005118273410482', '4.231592417858205', '5.281089948856194', '5.526141943642593', '5.940772431233222', '6.454008913189203', '6.852011266491535', '7.491515204158108', '7.916808884395699', '8.290073826303489', '8.993006283971392', '9.338718721466425', '9.864295580873586', '10.40865371476638', '10.51801777206253', '11.21245943203319', '11.64409801364863', '12.07417498633249', '12.40988358787530', '12.92668859198661', '13.22152547683289', '13.92393929834197', '14.15900541542533', '14.78343991696253', '15.00397555256169', '15.66851696784089', '16.15086185937948', '16.37042074393981', '16.76333450243035', '17.15119403369468', '17.78813888587613', '18.02826919140428', '18.46637983555624', '18.99210845782576', '19.20979801079610', '19.73911343451280'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1660434836536046581, 'z1': {'__RealLiteral__': 0, 'data': '0.4190202364084392', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.9932505133006185', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.667530169223928', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 2, 0, 0, 0, 6, 0, -4, 0, 1, 0, -8, 0, 0, 0, -1, 0, -2, 0, -4, 0, -1, 0, 0, 0, 2, 0, -2, 0, 10, 0, -4, 0, 0, 0, 8, 0, 1, 0, -6, 0, 10, 0, 0, 0, 4, 0, 4, 0, 10, 0, -1, 0, 0, 0, 0, 0, 8, 0, -8, 0, 6, 0, 0, 0, -1, 0, 4, 0, 1, 0, 8, 0, 0, 0, 2, 0, -6, 0, -2, 0, 4, 0, 0, 0, -14, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -10, 53], 'euler59': [1, -4, 59], 'euler61': [1, -10, 61], 'euler67': [1, 0, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -6, 73], 'euler79': [1, -4, 79], 'euler83': [1, -8, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, 8, 23], [1, 2, 29], [1, 4, 31], [1, -2, 37], [1, -10, 41], [1, 4, 43], [1, -8, 47], [1, -10, 53], [1, -4, 59], [1, -10, 61], [1, 0, 67], [1, 8, 71], [1, -6, 73], [1, -4, 79], [1, -8, 83], [1, 6, 89], [1, 14, 97]], 'index': 113, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/fj'], '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': '2-369600-1.1-c1-0-113', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1660434836536046581, 'z1': {'__RealLiteral__': 0, 'data': '0.4190202364084392', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1660434836536046581', 'Lhash_array': ['1660434836536046581'], 'label': '2-369600-1.1-c1-0-113', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/fj'}