Properties

Label 43.11.b.b.42.16
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.16
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.19

$q$-expansion

\(f(q)\) \(=\) \(q-5.51570i q^{2} -292.852i q^{3} +993.577 q^{4} +3204.10i q^{5} -1615.28 q^{6} -16511.8i q^{7} -11128.3i q^{8} -26713.4 q^{9} +O(q^{10})\) \(q-5.51570i q^{2} -292.852i q^{3} +993.577 q^{4} +3204.10i q^{5} -1615.28 q^{6} -16511.8i q^{7} -11128.3i q^{8} -26713.4 q^{9} +17672.9 q^{10} +31573.6 q^{11} -290971. i q^{12} +240071. q^{13} -91074.0 q^{14} +938328. q^{15} +956042. q^{16} +1.02720e6 q^{17} +147343. i q^{18} -1.67184e6i q^{19} +3.18352e6i q^{20} -4.83551e6 q^{21} -174150. i q^{22} -6.08630e6 q^{23} -3.25896e6 q^{24} -500648. q^{25} -1.32416e6i q^{26} -9.46955e6i q^{27} -1.64057e7i q^{28} -1.23237e7i q^{29} -5.17554e6i q^{30} -5.08085e6 q^{31} -1.66687e7i q^{32} -9.24639e6i q^{33} -5.66573e6i q^{34} +5.29054e7 q^{35} -2.65418e7 q^{36} -2.30677e7i q^{37} -9.22138e6 q^{38} -7.03054e7i q^{39} +3.56564e7 q^{40} -7.74946e7 q^{41} +2.66712e7i q^{42} +(2.90004e7 - 1.44120e8i) q^{43} +3.13708e7 q^{44} -8.55925e7i q^{45} +3.35702e7i q^{46} -2.22341e8 q^{47} -2.79979e8i q^{48} +9.83663e6 q^{49} +2.76142e6i q^{50} -3.00818e8i q^{51} +2.38529e8 q^{52} -1.87870e8 q^{53} -5.22312e7 q^{54} +1.01165e8i q^{55} -1.83749e8 q^{56} -4.89603e8 q^{57} -6.79736e7 q^{58} -5.73654e8 q^{59} +9.32302e8 q^{60} -4.87066e7i q^{61} +2.80245e7i q^{62} +4.41086e8i q^{63} +8.87048e8 q^{64} +7.69213e8i q^{65} -5.10003e7 q^{66} +6.11603e8 q^{67} +1.02060e9 q^{68} +1.78239e9i q^{69} -2.91810e8i q^{70} +2.16541e9i q^{71} +2.97276e8i q^{72} -5.90470e8i q^{73} -1.27234e8 q^{74} +1.46616e8i q^{75} -1.66110e9i q^{76} -5.21336e8i q^{77} -3.87783e8 q^{78} +3.70326e9 q^{79} +3.06326e9i q^{80} -4.35058e9 q^{81} +4.27437e8i q^{82} +4.86372e9 q^{83} -4.80445e9 q^{84} +3.29126e9i q^{85} +(-7.94920e8 - 1.59958e8i) q^{86} -3.60901e9 q^{87} -3.51362e8i q^{88} +6.61537e9i q^{89} -4.72102e8 q^{90} -3.96400e9i q^{91} -6.04721e9 q^{92} +1.48794e9i q^{93} +1.22637e9i q^{94} +5.35675e9 q^{95} -4.88146e9 q^{96} +3.91240e9 q^{97} -5.42559e7i q^{98} -8.43438e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.51570i 0.172366i −0.996279 0.0861828i \(-0.972533\pi\)
0.996279 0.0861828i \(-0.0274669\pi\)
\(3\) 292.852i 1.20515i −0.798061 0.602577i \(-0.794141\pi\)
0.798061 0.602577i \(-0.205859\pi\)
\(4\) 993.577 0.970290
\(5\) 3204.10i 1.02531i 0.858594 + 0.512656i \(0.171339\pi\)
−0.858594 + 0.512656i \(0.828661\pi\)
\(6\) −1615.28 −0.207727
\(7\) 16511.8i 0.982434i −0.871037 0.491217i \(-0.836552\pi\)
0.871037 0.491217i \(-0.163448\pi\)
\(8\) 11128.3i 0.339610i
\(9\) −26713.4 −0.452394
\(10\) 17672.9 0.176729
\(11\) 31573.6 0.196047 0.0980235 0.995184i \(-0.468748\pi\)
0.0980235 + 0.995184i \(0.468748\pi\)
\(12\) 290971.i 1.16935i
\(13\) 240071. 0.646582 0.323291 0.946300i \(-0.395211\pi\)
0.323291 + 0.946300i \(0.395211\pi\)
\(14\) −91074.0 −0.169338
\(15\) 938328. 1.23566
\(16\) 956042. 0.911753
\(17\) 1.02720e6 0.723454 0.361727 0.932284i \(-0.382187\pi\)
0.361727 + 0.932284i \(0.382187\pi\)
\(18\) 147343.i 0.0779771i
\(19\) 1.67184e6i 0.675192i −0.941291 0.337596i \(-0.890386\pi\)
0.941291 0.337596i \(-0.109614\pi\)
\(20\) 3.18352e6i 0.994851i
\(21\) −4.83551e6 −1.18398
\(22\) 174150.i 0.0337918i
\(23\) −6.08630e6 −0.945615 −0.472807 0.881166i \(-0.656759\pi\)
−0.472807 + 0.881166i \(0.656759\pi\)
\(24\) −3.25896e6 −0.409282
\(25\) −500648. −0.0512663
\(26\) 1.32416e6i 0.111448i
\(27\) 9.46955e6i 0.659949i
\(28\) 1.64057e7i 0.953246i
\(29\) 1.23237e7i 0.600828i −0.953809 0.300414i \(-0.902875\pi\)
0.953809 0.300414i \(-0.0971248\pi\)
\(30\) 5.17554e6i 0.212985i
\(31\) −5.08085e6 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(32\) 1.66687e7i 0.496765i
\(33\) 9.24639e6i 0.236267i
\(34\) 5.66573e6i 0.124699i
\(35\) 5.29054e7 1.00730
\(36\) −2.65418e7 −0.438953
\(37\) 2.30677e7i 0.332656i −0.986071 0.166328i \(-0.946809\pi\)
0.986071 0.166328i \(-0.0531910\pi\)
\(38\) −9.22138e6 −0.116380
\(39\) 7.03054e7i 0.779230i
\(40\) 3.56564e7 0.348207
\(41\) −7.74946e7 −0.668886 −0.334443 0.942416i \(-0.608548\pi\)
−0.334443 + 0.942416i \(0.608548\pi\)
\(42\) 2.66712e7i 0.204078i
\(43\) 2.90004e7 1.44120e8i 0.197270 0.980349i
\(44\) 3.13708e7 0.190223
\(45\) 8.55925e7i 0.463845i
\(46\) 3.35702e7i 0.162991i
\(47\) −2.22341e8 −0.969460 −0.484730 0.874664i \(-0.661082\pi\)
−0.484730 + 0.874664i \(0.661082\pi\)
\(48\) 2.79979e8i 1.09880i
\(49\) 9.83663e6 0.0348230
\(50\) 2.76142e6i 0.00883655i
\(51\) 3.00818e8i 0.871873i
\(52\) 2.38529e8 0.627372
\(53\) −1.87870e8 −0.449240 −0.224620 0.974446i \(-0.572114\pi\)
−0.224620 + 0.974446i \(0.572114\pi\)
\(54\) −5.22312e7 −0.113753
\(55\) 1.01165e8i 0.201010i
\(56\) −1.83749e8 −0.333645
\(57\) −4.89603e8 −0.813710
\(58\) −6.79736e7 −0.103562
\(59\) −5.73654e8 −0.802398 −0.401199 0.915991i \(-0.631406\pi\)
−0.401199 + 0.915991i \(0.631406\pi\)
\(60\) 9.32302e8 1.19895
\(61\) 4.87066e7i 0.0576685i −0.999584 0.0288343i \(-0.990820\pi\)
0.999584 0.0288343i \(-0.00917950\pi\)
\(62\) 2.80245e7i 0.0305900i
\(63\) 4.41086e8i 0.444447i
\(64\) 8.87048e8 0.826128
\(65\) 7.69213e8i 0.662948i
\(66\) −5.10003e7 −0.0407243
\(67\) 6.11603e8 0.452997 0.226499 0.974012i \(-0.427272\pi\)
0.226499 + 0.974012i \(0.427272\pi\)
\(68\) 1.02060e9 0.701960
\(69\) 1.78239e9i 1.13961i
\(70\) 2.91810e8i 0.173624i
\(71\) 2.16541e9i 1.20019i 0.799930 + 0.600094i \(0.204870\pi\)
−0.799930 + 0.600094i \(0.795130\pi\)
\(72\) 2.97276e8i 0.153638i
\(73\) 5.90470e8i 0.284828i −0.989807 0.142414i \(-0.954514\pi\)
0.989807 0.142414i \(-0.0454865\pi\)
\(74\) −1.27234e8 −0.0573384
\(75\) 1.46616e8i 0.0617838i
\(76\) 1.66110e9i 0.655132i
\(77\) 5.21336e8i 0.192603i
\(78\) −3.87783e8 −0.134312
\(79\) 3.70326e9 1.20351 0.601753 0.798682i \(-0.294469\pi\)
0.601753 + 0.798682i \(0.294469\pi\)
\(80\) 3.06326e9i 0.934832i
\(81\) −4.35058e9 −1.24773
\(82\) 4.27437e8i 0.115293i
\(83\) 4.86372e9 1.23475 0.617374 0.786670i \(-0.288196\pi\)
0.617374 + 0.786670i \(0.288196\pi\)
\(84\) −4.80445e9 −1.14881
\(85\) 3.29126e9i 0.741767i
\(86\) −7.94920e8 1.59958e8i −0.168978 0.0340026i
\(87\) −3.60901e9 −0.724089
\(88\) 3.51362e8i 0.0665796i
\(89\) 6.61537e9i 1.18469i 0.805685 + 0.592345i \(0.201798\pi\)
−0.805685 + 0.592345i \(0.798202\pi\)
\(90\) −4.72102e8 −0.0799510
\(91\) 3.96400e9i 0.635224i
\(92\) −6.04721e9 −0.917521
\(93\) 1.48794e9i 0.213880i
\(94\) 1.22637e9i 0.167102i
\(95\) 5.35675e9 0.692283
\(96\) −4.88146e9 −0.598678
\(97\) 3.91240e9 0.455601 0.227800 0.973708i \(-0.426847\pi\)
0.227800 + 0.973708i \(0.426847\pi\)
\(98\) 5.42559e7i 0.00600228i
\(99\) −8.43438e8 −0.0886905
\(100\) −4.97432e8 −0.0497432
\(101\) 3.04443e9 0.289667 0.144834 0.989456i \(-0.453735\pi\)
0.144834 + 0.989456i \(0.453735\pi\)
\(102\) −1.65922e9 −0.150281
\(103\) 1.78627e10 1.54085 0.770424 0.637532i \(-0.220045\pi\)
0.770424 + 0.637532i \(0.220045\pi\)
\(104\) 2.67160e9i 0.219586i
\(105\) 1.54935e10i 1.21395i
\(106\) 1.03624e9i 0.0774336i
\(107\) 2.44008e10 1.73974 0.869871 0.493279i \(-0.164202\pi\)
0.869871 + 0.493279i \(0.164202\pi\)
\(108\) 9.40873e9i 0.640342i
\(109\) −1.37165e10 −0.891478 −0.445739 0.895163i \(-0.647059\pi\)
−0.445739 + 0.895163i \(0.647059\pi\)
\(110\) 5.57996e8 0.0346471
\(111\) −6.75541e9 −0.400901
\(112\) 1.57860e10i 0.895737i
\(113\) 6.06915e9i 0.329409i −0.986343 0.164705i \(-0.947333\pi\)
0.986343 0.164705i \(-0.0526671\pi\)
\(114\) 2.70050e9i 0.140256i
\(115\) 1.95011e10i 0.969551i
\(116\) 1.22445e10i 0.582977i
\(117\) −6.41312e9 −0.292509
\(118\) 3.16410e9i 0.138306i
\(119\) 1.69609e10i 0.710746i
\(120\) 1.04420e10i 0.419642i
\(121\) −2.49405e10 −0.961566
\(122\) −2.68651e8 −0.00994007
\(123\) 2.26944e10i 0.806110i
\(124\) −5.04822e9 −0.172199
\(125\) 2.96859e10i 0.972749i
\(126\) 2.43290e9 0.0766074
\(127\) −3.99008e10 −1.20771 −0.603855 0.797094i \(-0.706369\pi\)
−0.603855 + 0.797094i \(0.706369\pi\)
\(128\) 2.19614e10i 0.639161i
\(129\) −4.22057e10 8.49283e9i −1.18147 0.237741i
\(130\) 4.24275e9 0.114269
\(131\) 4.31876e10i 1.11944i 0.828680 + 0.559722i \(0.189092\pi\)
−0.828680 + 0.559722i \(0.810908\pi\)
\(132\) 9.18700e9i 0.229247i
\(133\) −2.76051e10 −0.663332
\(134\) 3.37342e9i 0.0780811i
\(135\) 3.03414e10 0.676654
\(136\) 1.14311e10i 0.245692i
\(137\) 7.78479e9i 0.161304i 0.996742 + 0.0806518i \(0.0257002\pi\)
−0.996742 + 0.0806518i \(0.974300\pi\)
\(138\) 9.83111e9 0.196430
\(139\) 7.64081e10 1.47253 0.736267 0.676691i \(-0.236587\pi\)
0.736267 + 0.676691i \(0.236587\pi\)
\(140\) 5.25656e10 0.977376
\(141\) 6.51130e10i 1.16835i
\(142\) 1.19438e10 0.206871
\(143\) 7.57991e9 0.126760
\(144\) −2.55391e10 −0.412471
\(145\) 3.94863e10 0.616036
\(146\) −3.25685e9 −0.0490946
\(147\) 2.88068e9i 0.0419670i
\(148\) 2.29195e10i 0.322772i
\(149\) 6.05305e10i 0.824220i −0.911134 0.412110i \(-0.864792\pi\)
0.911134 0.412110i \(-0.135208\pi\)
\(150\) 8.08689e8 0.0106494
\(151\) 4.49709e10i 0.572858i 0.958101 + 0.286429i \(0.0924683\pi\)
−0.958101 + 0.286429i \(0.907532\pi\)
\(152\) −1.86048e10 −0.229302
\(153\) −2.74401e10 −0.327286
\(154\) −2.87553e9 −0.0331982
\(155\) 1.62796e10i 0.181964i
\(156\) 6.98538e10i 0.756079i
\(157\) 1.13946e11i 1.19454i 0.802040 + 0.597270i \(0.203748\pi\)
−0.802040 + 0.597270i \(0.796252\pi\)
\(158\) 2.04260e10i 0.207443i
\(159\) 5.50182e10i 0.541403i
\(160\) 5.34081e10 0.509340
\(161\) 1.00496e11i 0.929004i
\(162\) 2.39965e10i 0.215066i
\(163\) 1.77980e11i 1.54680i 0.633919 + 0.773399i \(0.281445\pi\)
−0.633919 + 0.773399i \(0.718555\pi\)
\(164\) −7.69968e10 −0.649013
\(165\) 2.96264e10 0.242247
\(166\) 2.68268e10i 0.212828i
\(167\) 1.04020e11 0.800820 0.400410 0.916336i \(-0.368868\pi\)
0.400410 + 0.916336i \(0.368868\pi\)
\(168\) 5.38112e10i 0.402093i
\(169\) −8.02243e10 −0.581932
\(170\) 1.81536e10 0.127855
\(171\) 4.46606e10i 0.305453i
\(172\) 2.88141e10 1.43194e11i 0.191409 0.951223i
\(173\) 1.68634e10 0.108822 0.0544109 0.998519i \(-0.482672\pi\)
0.0544109 + 0.998519i \(0.482672\pi\)
\(174\) 1.99062e10i 0.124808i
\(175\) 8.26658e9i 0.0503658i
\(176\) 3.01857e10 0.178746
\(177\) 1.67996e11i 0.967012i
\(178\) 3.64884e10 0.204200
\(179\) 3.41248e10i 0.185697i −0.995680 0.0928484i \(-0.970403\pi\)
0.995680 0.0928484i \(-0.0295972\pi\)
\(180\) 8.50427e10i 0.450064i
\(181\) −2.40858e11 −1.23985 −0.619924 0.784662i \(-0.712836\pi\)
−0.619924 + 0.784662i \(0.712836\pi\)
\(182\) −2.18642e10 −0.109491
\(183\) −1.42638e10 −0.0694994
\(184\) 6.77305e10i 0.321140i
\(185\) 7.39111e10 0.341076
\(186\) 8.20702e9 0.0368656
\(187\) 3.24324e10 0.141831
\(188\) −2.20913e11 −0.940658
\(189\) −1.56359e11 −0.648357
\(190\) 2.95462e10i 0.119326i
\(191\) 1.22618e11i 0.482376i −0.970478 0.241188i \(-0.922463\pi\)
0.970478 0.241188i \(-0.0775370\pi\)
\(192\) 2.59774e11i 0.995610i
\(193\) 3.39835e10 0.126906 0.0634530 0.997985i \(-0.479789\pi\)
0.0634530 + 0.997985i \(0.479789\pi\)
\(194\) 2.15796e10i 0.0785299i
\(195\) 2.25266e11 0.798954
\(196\) 9.77345e9 0.0337884
\(197\) −4.27539e10 −0.144094 −0.0720468 0.997401i \(-0.522953\pi\)
−0.0720468 + 0.997401i \(0.522953\pi\)
\(198\) 4.65215e9i 0.0152872i
\(199\) 3.23926e11i 1.03796i −0.854787 0.518979i \(-0.826312\pi\)
0.854787 0.518979i \(-0.173688\pi\)
\(200\) 5.57138e9i 0.0174106i
\(201\) 1.79109e11i 0.545931i
\(202\) 1.67922e10i 0.0499287i
\(203\) −2.03486e11 −0.590274
\(204\) 2.98886e11i 0.845970i
\(205\) 2.48300e11i 0.685817i
\(206\) 9.85250e10i 0.265589i
\(207\) 1.62586e11 0.427790
\(208\) 2.29518e11 0.589523
\(209\) 5.27860e10i 0.132369i
\(210\) −8.54573e10 −0.209244
\(211\) 2.63888e11i 0.630967i 0.948931 + 0.315484i \(0.102167\pi\)
−0.948931 + 0.315484i \(0.897833\pi\)
\(212\) −1.86664e11 −0.435894
\(213\) 6.34146e11 1.44641
\(214\) 1.34587e11i 0.299872i
\(215\) 4.61774e11 + 9.29203e10i 1.00516 + 0.202264i
\(216\) −1.05380e11 −0.224126
\(217\) 8.38939e10i 0.174354i
\(218\) 7.56560e10i 0.153660i
\(219\) −1.72920e11 −0.343262
\(220\) 1.00515e11i 0.195038i
\(221\) 2.46602e11 0.467772
\(222\) 3.72608e10i 0.0691015i
\(223\) 5.14534e11i 0.933018i −0.884516 0.466509i \(-0.845512\pi\)
0.884516 0.466509i \(-0.154488\pi\)
\(224\) −2.75229e11 −0.488039
\(225\) 1.33740e10 0.0231926
\(226\) −3.34756e10 −0.0567788
\(227\) 1.64053e11i 0.272179i 0.990697 + 0.136089i \(0.0434534\pi\)
−0.990697 + 0.136089i \(0.956547\pi\)
\(228\) −4.86458e11 −0.789534
\(229\) −1.09291e12 −1.73543 −0.867716 0.497060i \(-0.834413\pi\)
−0.867716 + 0.497060i \(0.834413\pi\)
\(230\) −1.07562e11 −0.167117
\(231\) −1.52674e11 −0.232117
\(232\) −1.37142e11 −0.204047
\(233\) 1.28928e12i 1.87744i 0.344680 + 0.938720i \(0.387987\pi\)
−0.344680 + 0.938720i \(0.612013\pi\)
\(234\) 3.53728e10i 0.0504186i
\(235\) 7.12403e11i 0.994000i
\(236\) −5.69969e11 −0.778559
\(237\) 1.08451e12i 1.45041i
\(238\) −9.35513e10 −0.122508
\(239\) 5.08555e11 0.652152 0.326076 0.945344i \(-0.394273\pi\)
0.326076 + 0.945344i \(0.394273\pi\)
\(240\) 8.97082e11 1.12662
\(241\) 1.38456e12i 1.70304i 0.524318 + 0.851522i \(0.324320\pi\)
−0.524318 + 0.851522i \(0.675680\pi\)
\(242\) 1.37564e11i 0.165741i
\(243\) 7.14909e11i 0.843761i
\(244\) 4.83938e10i 0.0559552i
\(245\) 3.15176e10i 0.0357044i
\(246\) 1.25176e11 0.138946
\(247\) 4.01361e11i 0.436567i
\(248\) 5.65415e10i 0.0602711i
\(249\) 1.42435e12i 1.48806i
\(250\) 1.63739e11 0.167668
\(251\) −4.19781e10 −0.0421361 −0.0210680 0.999778i \(-0.506707\pi\)
−0.0210680 + 0.999778i \(0.506707\pi\)
\(252\) 4.38253e11i 0.431243i
\(253\) −1.92166e11 −0.185385
\(254\) 2.20081e11i 0.208168i
\(255\) 9.63852e11 0.893943
\(256\) 7.87205e11 0.715958
\(257\) 5.14381e11i 0.458795i 0.973333 + 0.229398i \(0.0736756\pi\)
−0.973333 + 0.229398i \(0.926324\pi\)
\(258\) −4.68439e10 + 2.32794e11i −0.0409784 + 0.203645i
\(259\) −3.80888e11 −0.326812
\(260\) 7.64272e11i 0.643252i
\(261\) 3.29207e11i 0.271811i
\(262\) 2.38210e11 0.192954
\(263\) 2.20947e12i 1.75594i 0.478719 + 0.877968i \(0.341101\pi\)
−0.478719 + 0.877968i \(0.658899\pi\)
\(264\) −1.02897e11 −0.0802386
\(265\) 6.01956e11i 0.460612i
\(266\) 1.52261e11i 0.114336i
\(267\) 1.93733e12 1.42773
\(268\) 6.07674e11 0.439539
\(269\) −5.98549e11 −0.424950 −0.212475 0.977166i \(-0.568152\pi\)
−0.212475 + 0.977166i \(0.568152\pi\)
\(270\) 1.67354e11i 0.116632i
\(271\) −8.02913e11 −0.549315 −0.274658 0.961542i \(-0.588565\pi\)
−0.274658 + 0.961542i \(0.588565\pi\)
\(272\) 9.82048e11 0.659612
\(273\) −1.16087e12 −0.765542
\(274\) 4.29386e10 0.0278032
\(275\) −1.58072e10 −0.0100506
\(276\) 1.77094e12i 1.10575i
\(277\) 3.55023e11i 0.217700i 0.994058 + 0.108850i \(0.0347168\pi\)
−0.994058 + 0.108850i \(0.965283\pi\)
\(278\) 4.21444e11i 0.253814i
\(279\) 1.35727e11 0.0802869
\(280\) 5.88750e11i 0.342090i
\(281\) 9.07881e11 0.518200 0.259100 0.965851i \(-0.416574\pi\)
0.259100 + 0.965851i \(0.416574\pi\)
\(282\) 3.59144e11 0.201383
\(283\) −1.06931e12 −0.589074 −0.294537 0.955640i \(-0.595165\pi\)
−0.294537 + 0.955640i \(0.595165\pi\)
\(284\) 2.15150e12i 1.16453i
\(285\) 1.56874e12i 0.834307i
\(286\) 4.18085e10i 0.0218491i
\(287\) 1.27957e12i 0.657136i
\(288\) 4.45277e11i 0.224733i
\(289\) −9.60851e11 −0.476614
\(290\) 2.17795e11i 0.106183i
\(291\) 1.14575e12i 0.549069i
\(292\) 5.86677e11i 0.276366i
\(293\) −3.17887e12 −1.47209 −0.736046 0.676932i \(-0.763309\pi\)
−0.736046 + 0.676932i \(0.763309\pi\)
\(294\) −1.58890e10 −0.00723367
\(295\) 1.83805e12i 0.822709i
\(296\) −2.56705e11 −0.112973
\(297\) 2.98988e11i 0.129381i
\(298\) −3.33868e11 −0.142067
\(299\) −1.46115e12 −0.611417
\(300\) 1.45674e11i 0.0599482i
\(301\) −2.37967e12 4.78848e11i −0.963129 0.193805i
\(302\) 2.48046e11 0.0987411
\(303\) 8.91569e11i 0.349093i
\(304\) 1.59835e12i 0.615608i
\(305\) 1.56061e11 0.0591283
\(306\) 1.51351e11i 0.0564129i
\(307\) −1.42283e11 −0.0521749 −0.0260875 0.999660i \(-0.508305\pi\)
−0.0260875 + 0.999660i \(0.508305\pi\)
\(308\) 5.17987e11i 0.186881i
\(309\) 5.23112e12i 1.85696i
\(310\) −8.97932e10 −0.0313643
\(311\) 2.92237e12 1.00446 0.502231 0.864733i \(-0.332513\pi\)
0.502231 + 0.864733i \(0.332513\pi\)
\(312\) −7.82383e11 −0.264634
\(313\) 3.24566e11i 0.108039i 0.998540 + 0.0540195i \(0.0172033\pi\)
−0.998540 + 0.0540195i \(0.982797\pi\)
\(314\) 6.28492e11 0.205898
\(315\) −1.41328e12 −0.455697
\(316\) 3.67947e12 1.16775
\(317\) 5.95423e12 1.86007 0.930034 0.367473i \(-0.119777\pi\)
0.930034 + 0.367473i \(0.119777\pi\)
\(318\) 3.03464e11 0.0933193
\(319\) 3.89102e11i 0.117791i
\(320\) 2.84219e12i 0.847039i
\(321\) 7.14582e12i 2.09666i
\(322\) 5.54304e11 0.160128
\(323\) 1.71732e12i 0.488470i
\(324\) −4.32263e12 −1.21066
\(325\) −1.20191e11 −0.0331479
\(326\) 9.81685e11 0.266615
\(327\) 4.01690e12i 1.07437i
\(328\) 8.62386e11i 0.227160i
\(329\) 3.67124e12i 0.952431i
\(330\) 1.63410e11i 0.0417551i
\(331\) 4.61496e12i 1.16152i −0.814073 0.580762i \(-0.802755\pi\)
0.814073 0.580762i \(-0.197245\pi\)
\(332\) 4.83248e12 1.19806
\(333\) 6.16216e11i 0.150491i
\(334\) 5.73743e11i 0.138034i
\(335\) 1.95964e12i 0.464464i
\(336\) −4.62295e12 −1.07950
\(337\) 5.38665e12 1.23928 0.619640 0.784886i \(-0.287279\pi\)
0.619640 + 0.784886i \(0.287279\pi\)
\(338\) 4.42493e11i 0.100305i
\(339\) −1.77737e12 −0.396989
\(340\) 3.27012e12i 0.719729i
\(341\) −1.60421e11 −0.0347927
\(342\) 2.46334e11 0.0526495
\(343\) 4.82659e12i 1.01665i
\(344\) −1.60381e12 3.22727e11i −0.332937 0.0669950i
\(345\) −5.71095e12 −1.16846
\(346\) 9.30137e10i 0.0187571i
\(347\) 8.09633e12i 1.60931i −0.593740 0.804657i \(-0.702349\pi\)
0.593740 0.804657i \(-0.297651\pi\)
\(348\) −3.58583e12 −0.702577
\(349\) 5.38376e12i 1.03982i 0.854221 + 0.519910i \(0.174035\pi\)
−0.854221 + 0.519910i \(0.825965\pi\)
\(350\) 4.55960e10 0.00868133
\(351\) 2.27337e12i 0.426711i
\(352\) 5.26289e11i 0.0973893i
\(353\) 4.06273e12 0.741215 0.370608 0.928790i \(-0.379149\pi\)
0.370608 + 0.928790i \(0.379149\pi\)
\(354\) 9.26614e11 0.166680
\(355\) −6.93820e12 −1.23057
\(356\) 6.57288e12i 1.14949i
\(357\) −4.96704e12 −0.856558
\(358\) −1.88222e11 −0.0320078
\(359\) −7.21622e12 −1.21015 −0.605073 0.796170i \(-0.706856\pi\)
−0.605073 + 0.796170i \(0.706856\pi\)
\(360\) −9.52503e11 −0.157527
\(361\) 3.33601e12 0.544116
\(362\) 1.32850e12i 0.213707i
\(363\) 7.30389e12i 1.15883i
\(364\) 3.93854e12i 0.616351i
\(365\) 1.89192e12 0.292038
\(366\) 7.86750e10i 0.0119793i
\(367\) 1.20158e13 1.80477 0.902385 0.430931i \(-0.141815\pi\)
0.902385 + 0.430931i \(0.141815\pi\)
\(368\) −5.81876e12 −0.862167
\(369\) 2.07014e12 0.302600
\(370\) 4.07672e11i 0.0587898i
\(371\) 3.10207e12i 0.441349i
\(372\) 1.47838e12i 0.207526i
\(373\) 5.46051e12i 0.756291i −0.925746 0.378146i \(-0.876562\pi\)
0.925746 0.378146i \(-0.123438\pi\)
\(374\) 1.78887e11i 0.0244468i
\(375\) 8.69359e12 1.17231
\(376\) 2.47429e12i 0.329239i
\(377\) 2.95856e12i 0.388484i
\(378\) 8.62429e11i 0.111754i
\(379\) 2.08400e12 0.266503 0.133251 0.991082i \(-0.457458\pi\)
0.133251 + 0.991082i \(0.457458\pi\)
\(380\) 5.32235e12 0.671715
\(381\) 1.16850e13i 1.45547i
\(382\) −6.76321e11 −0.0831450
\(383\) 6.42552e12i 0.779676i 0.920883 + 0.389838i \(0.127469\pi\)
−0.920883 + 0.389838i \(0.872531\pi\)
\(384\) −6.43145e12 −0.770287
\(385\) 1.67041e12 0.197479
\(386\) 1.87443e11i 0.0218742i
\(387\) −7.74700e11 + 3.84993e12i −0.0892439 + 0.443504i
\(388\) 3.88727e12 0.442065
\(389\) 6.24207e12i 0.700779i 0.936604 + 0.350389i \(0.113951\pi\)
−0.936604 + 0.350389i \(0.886049\pi\)
\(390\) 1.24250e12i 0.137712i
\(391\) −6.25186e12 −0.684109
\(392\) 1.09465e11i 0.0118262i
\(393\) 1.26476e13 1.34910
\(394\) 2.35818e11i 0.0248368i
\(395\) 1.18656e13i 1.23397i
\(396\) −8.38020e11 −0.0860555
\(397\) −3.04685e12 −0.308958 −0.154479 0.987996i \(-0.549370\pi\)
−0.154479 + 0.987996i \(0.549370\pi\)
\(398\) −1.78668e12 −0.178908
\(399\) 8.08421e12i 0.799416i
\(400\) −4.78641e11 −0.0467422
\(401\) −5.06144e12 −0.488149 −0.244074 0.969757i \(-0.578484\pi\)
−0.244074 + 0.969757i \(0.578484\pi\)
\(402\) −9.87912e11 −0.0940997
\(403\) −1.21977e12 −0.114750
\(404\) 3.02488e12 0.281061
\(405\) 1.39397e13i 1.27932i
\(406\) 1.12237e12i 0.101743i
\(407\) 7.28328e11i 0.0652161i
\(408\) −3.34761e12 −0.296097
\(409\) 9.21342e12i 0.805016i −0.915416 0.402508i \(-0.868139\pi\)
0.915416 0.402508i \(-0.131861\pi\)
\(410\) −1.36955e12 −0.118211
\(411\) 2.27979e12 0.194396
\(412\) 1.77479e13 1.49507
\(413\) 9.47204e12i 0.788303i
\(414\) 8.96774e11i 0.0737363i
\(415\) 1.55839e13i 1.26600i
\(416\) 4.00167e12i 0.321199i
\(417\) 2.23763e13i 1.77463i
\(418\) −2.91152e11 −0.0228159
\(419\) 1.86619e13i 1.44506i 0.691339 + 0.722531i \(0.257021\pi\)
−0.691339 + 0.722531i \(0.742979\pi\)
\(420\) 1.53940e13i 1.17789i
\(421\) 8.57888e12i 0.648665i −0.945943 0.324332i \(-0.894860\pi\)
0.945943 0.324332i \(-0.105140\pi\)
\(422\) 1.45552e12 0.108757
\(423\) 5.93948e12 0.438578
\(424\) 2.09069e12i 0.152567i
\(425\) −5.14266e11 −0.0370889
\(426\) 3.49776e12i 0.249311i
\(427\) −8.04232e11 −0.0566555
\(428\) 2.42441e13 1.68805
\(429\) 2.21979e12i 0.152766i
\(430\) 5.12520e11 2.54701e12i 0.0348633 0.173256i
\(431\) −2.69197e13 −1.81002 −0.905010 0.425390i \(-0.860137\pi\)
−0.905010 + 0.425390i \(0.860137\pi\)
\(432\) 9.05329e12i 0.601711i
\(433\) 1.86409e13i 1.22469i −0.790590 0.612346i \(-0.790226\pi\)
0.790590 0.612346i \(-0.209774\pi\)
\(434\) 4.62733e11 0.0300526
\(435\) 1.15636e13i 0.742418i
\(436\) −1.36284e13 −0.864992
\(437\) 1.01753e13i 0.638471i
\(438\) 9.53776e11i 0.0591665i
\(439\) −1.34913e13 −0.827428 −0.413714 0.910407i \(-0.635769\pi\)
−0.413714 + 0.910407i \(0.635769\pi\)
\(440\) 1.12580e12 0.0682649
\(441\) −2.62770e11 −0.0157537
\(442\) 1.36018e12i 0.0806278i
\(443\) −1.26659e13 −0.742367 −0.371184 0.928559i \(-0.621048\pi\)
−0.371184 + 0.928559i \(0.621048\pi\)
\(444\) −6.71202e12 −0.388990
\(445\) −2.11963e13 −1.21468
\(446\) −2.83802e12 −0.160820
\(447\) −1.77265e13 −0.993311
\(448\) 1.46467e13i 0.811616i
\(449\) 2.11844e13i 1.16087i 0.814306 + 0.580436i \(0.197118\pi\)
−0.814306 + 0.580436i \(0.802882\pi\)
\(450\) 7.37670e10i 0.00399760i
\(451\) −2.44678e12 −0.131133
\(452\) 6.03017e12i 0.319623i
\(453\) 1.31698e13 0.690382
\(454\) 9.04866e11 0.0469143
\(455\) 1.27011e13 0.651303
\(456\) 5.44847e12i 0.276344i
\(457\) 1.61516e13i 0.810277i 0.914255 + 0.405138i \(0.132777\pi\)
−0.914255 + 0.405138i \(0.867223\pi\)
\(458\) 6.02817e12i 0.299129i
\(459\) 9.72714e12i 0.477443i
\(460\) 1.93759e13i 0.940746i
\(461\) 4.88602e11 0.0234666 0.0117333 0.999931i \(-0.496265\pi\)
0.0117333 + 0.999931i \(0.496265\pi\)
\(462\) 8.42105e11i 0.0400089i
\(463\) 2.11110e13i 0.992210i −0.868263 0.496105i \(-0.834763\pi\)
0.868263 0.496105i \(-0.165237\pi\)
\(464\) 1.17819e13i 0.547807i
\(465\) −4.76751e12 −0.219294
\(466\) 7.11126e12 0.323606
\(467\) 2.80571e13i 1.26316i 0.775311 + 0.631580i \(0.217593\pi\)
−0.775311 + 0.631580i \(0.782407\pi\)
\(468\) −6.37193e12 −0.283819
\(469\) 1.00986e13i 0.445040i
\(470\) −3.92940e12 −0.171331
\(471\) 3.33693e13 1.43960
\(472\) 6.38382e12i 0.272503i
\(473\) 9.15647e11 4.55037e12i 0.0386743 0.192195i
\(474\) −5.98181e12 −0.250001
\(475\) 8.37004e11i 0.0346146i
\(476\) 1.68520e13i 0.689630i
\(477\) 5.01866e12 0.203234
\(478\) 2.80504e12i 0.112409i
\(479\) 2.61293e13 1.03622 0.518108 0.855315i \(-0.326636\pi\)
0.518108 + 0.855315i \(0.326636\pi\)
\(480\) 1.56407e13i 0.613832i
\(481\) 5.53788e12i 0.215089i
\(482\) 7.63681e12 0.293546
\(483\) 2.94304e13 1.11959
\(484\) −2.47803e13 −0.932998
\(485\) 1.25357e13i 0.467133i
\(486\) 3.94322e12 0.145435
\(487\) −2.80825e13 −1.02516 −0.512579 0.858640i \(-0.671310\pi\)
−0.512579 + 0.858640i \(0.671310\pi\)
\(488\) −5.42024e11 −0.0195848
\(489\) 5.21219e13 1.86413
\(490\) 1.73841e11 0.00615422
\(491\) 2.65400e13i 0.930024i −0.885304 0.465012i \(-0.846050\pi\)
0.885304 0.465012i \(-0.153950\pi\)
\(492\) 2.25487e13i 0.782160i
\(493\) 1.26589e13i 0.434671i
\(494\) −2.21379e12 −0.0752491
\(495\) 2.70246e12i 0.0909355i
\(496\) −4.85751e12 −0.161810
\(497\) 3.57548e13 1.17910
\(498\) −7.85630e12 −0.256490
\(499\) 5.01516e13i 1.62100i 0.585741 + 0.810499i \(0.300804\pi\)
−0.585741 + 0.810499i \(0.699196\pi\)
\(500\) 2.94953e13i 0.943848i
\(501\) 3.04625e13i 0.965110i
\(502\) 2.31538e11i 0.00726281i
\(503\) 4.15535e13i 1.29053i −0.763959 0.645264i \(-0.776747\pi\)
0.763959 0.645264i \(-0.223253\pi\)
\(504\) 4.90855e12 0.150939
\(505\) 9.75467e12i 0.297000i
\(506\) 1.05993e12i 0.0319540i
\(507\) 2.34939e13i 0.701318i
\(508\) −3.96445e13 −1.17183
\(509\) −1.85803e13 −0.543831 −0.271916 0.962321i \(-0.587657\pi\)
−0.271916 + 0.962321i \(0.587657\pi\)
\(510\) 5.31632e12i 0.154085i
\(511\) −9.74970e12 −0.279825
\(512\) 2.68305e13i 0.762568i
\(513\) −1.58316e13 −0.445592
\(514\) 2.83717e12 0.0790805
\(515\) 5.72338e13i 1.57985i
\(516\) −4.19347e13 8.43828e12i −1.14637 0.230678i
\(517\) −7.02010e12 −0.190060
\(518\) 2.10086e12i 0.0563312i
\(519\) 4.93850e12i 0.131147i
\(520\) 8.56007e12 0.225144
\(521\) 4.29356e13i 1.11848i 0.829005 + 0.559241i \(0.188907\pi\)
−0.829005 + 0.559241i \(0.811093\pi\)
\(522\) 1.81581e12 0.0468508
\(523\) 5.43272e13i 1.38838i 0.719791 + 0.694191i \(0.244238\pi\)
−0.719791 + 0.694191i \(0.755762\pi\)
\(524\) 4.29102e13i 1.08619i
\(525\) 2.42089e12 0.0606985
\(526\) 1.21868e13 0.302663
\(527\) −5.21906e12 −0.128392
\(528\) 8.83994e12i 0.215417i
\(529\) −4.38346e12 −0.105813
\(530\) −3.32021e12 −0.0793937
\(531\) 1.53242e13 0.363000
\(532\) −2.74278e13 −0.643624
\(533\) −1.86042e13 −0.432489
\(534\) 1.06857e13i 0.246092i
\(535\) 7.81826e13i 1.78378i
\(536\) 6.80613e12i 0.153842i
\(537\) −9.99351e12 −0.223793
\(538\) 3.30141e12i 0.0732468i
\(539\) 3.10577e11 0.00682694
\(540\) 3.01465e13 0.656551
\(541\) 2.25829e13 0.487297 0.243648 0.969864i \(-0.421656\pi\)
0.243648 + 0.969864i \(0.421656\pi\)
\(542\) 4.42862e12i 0.0946831i
\(543\) 7.05358e13i 1.49421i
\(544\) 1.71221e13i 0.359387i
\(545\) 4.39490e13i 0.914043i
\(546\) 6.40299e12i 0.131953i
\(547\) 3.55882e13 0.726724 0.363362 0.931648i \(-0.381629\pi\)
0.363362 + 0.931648i \(0.381629\pi\)
\(548\) 7.73479e12i 0.156511i
\(549\) 1.30112e12i 0.0260889i
\(550\) 8.71880e10i 0.00173238i
\(551\) −2.06032e13 −0.405674
\(552\) 1.98350e13 0.387023
\(553\) 6.11473e13i 1.18237i
\(554\) 1.95820e12 0.0375240
\(555\) 2.16450e13i 0.411049i
\(556\) 7.59173e13 1.42878
\(557\) −8.95325e13 −1.66995 −0.834977 0.550285i \(-0.814519\pi\)
−0.834977 + 0.550285i \(0.814519\pi\)
\(558\) 7.48629e11i 0.0138387i
\(559\) 6.96216e12 3.45990e13i 0.127551 0.633876i
\(560\) 5.05798e13 0.918411
\(561\) 9.49791e12i 0.170928i
\(562\) 5.00760e12i 0.0893198i
\(563\) −3.15967e13 −0.558598 −0.279299 0.960204i \(-0.590102\pi\)
−0.279299 + 0.960204i \(0.590102\pi\)
\(564\) 6.46948e13i 1.13364i
\(565\) 1.94462e13 0.337748
\(566\) 5.89797e12i 0.101536i
\(567\) 7.18358e13i 1.22582i
\(568\) 2.40975e13 0.407596
\(569\) 5.74761e13 0.963665 0.481832 0.876263i \(-0.339971\pi\)
0.481832 + 0.876263i \(0.339971\pi\)
\(570\) −8.65268e12 −0.143806
\(571\) 4.22519e13i 0.696090i −0.937478 0.348045i \(-0.886846\pi\)
0.937478 0.348045i \(-0.113154\pi\)
\(572\) 7.53122e12 0.122994
\(573\) −3.59088e13 −0.581337
\(574\) 7.05774e12 0.113268
\(575\) 3.04709e12 0.0484782
\(576\) −2.36961e13 −0.373735
\(577\) 8.04729e13i 1.25826i −0.777300 0.629131i \(-0.783411\pi\)
0.777300 0.629131i \(-0.216589\pi\)
\(578\) 5.29976e12i 0.0821518i
\(579\) 9.95215e12i 0.152941i
\(580\) 3.92327e13 0.597734
\(581\) 8.03087e13i 1.21306i
\(582\) −6.31964e12 −0.0946405
\(583\) −5.93174e12 −0.0880723
\(584\) −6.57095e12 −0.0967306
\(585\) 2.05483e13i 0.299914i
\(586\) 1.75337e13i 0.253738i
\(587\) 1.08267e14i 1.55348i −0.629822 0.776739i \(-0.716872\pi\)
0.629822 0.776739i \(-0.283128\pi\)
\(588\) 2.86218e12i 0.0407202i
\(589\) 8.49438e12i 0.119827i
\(590\) −1.01381e13 −0.141807
\(591\) 1.25206e13i 0.173655i
\(592\) 2.20537e13i 0.303300i
\(593\) 1.10196e14i 1.50278i −0.659861 0.751388i \(-0.729385\pi\)
0.659861 0.751388i \(-0.270615\pi\)
\(594\) −1.64913e12 −0.0223009
\(595\) 5.43445e13 0.728737
\(596\) 6.01417e13i 0.799732i
\(597\) −9.48623e13 −1.25090
\(598\) 8.05924e12i 0.105387i
\(599\) −2.01917e13 −0.261841 −0.130921 0.991393i \(-0.541793\pi\)
−0.130921 + 0.991393i \(0.541793\pi\)
\(600\) 1.63159e12 0.0209824
\(601\) 6.69262e13i 0.853539i 0.904360 + 0.426770i \(0.140348\pi\)
−0.904360 + 0.426770i \(0.859652\pi\)
\(602\) −2.64118e12 + 1.31255e13i −0.0334053 + 0.166010i
\(603\) −1.63380e13 −0.204933
\(604\) 4.46821e13i 0.555839i
\(605\) 7.99120e13i 0.985905i
\(606\) −4.91762e12 −0.0601717
\(607\) 1.38942e14i 1.68613i 0.537815 + 0.843063i \(0.319250\pi\)
−0.537815 + 0.843063i \(0.680750\pi\)
\(608\) −2.78674e13 −0.335412
\(609\) 5.95912e13i 0.711370i
\(610\) 8.60785e11i 0.0101917i
\(611\) −5.33776e13 −0.626835
\(612\) −2.72638e13 −0.317563
\(613\) −5.52303e13 −0.638080 −0.319040 0.947741i \(-0.603360\pi\)
−0.319040 + 0.947741i \(0.603360\pi\)
\(614\) 7.84791e11i 0.00899316i
\(615\) −7.27153e13 −0.826514
\(616\) −5.80160e12 −0.0654101
\(617\) −6.03257e13 −0.674647 −0.337324 0.941389i \(-0.609522\pi\)
−0.337324 + 0.941389i \(0.609522\pi\)
\(618\) −2.88533e13 −0.320076
\(619\) 1.44434e14 1.58934 0.794671 0.607041i \(-0.207644\pi\)
0.794671 + 0.607041i \(0.207644\pi\)
\(620\) 1.61750e13i 0.176557i
\(621\) 5.76345e13i 0.624058i
\(622\) 1.61189e13i 0.173135i
\(623\) 1.09232e14 1.16388
\(624\) 6.72149e13i 0.710465i
\(625\) −1.00006e14 −1.04864
\(626\) 1.79021e12 0.0186222
\(627\) −1.54585e13 −0.159525
\(628\) 1.13214e14i 1.15905i
\(629\) 2.36951e13i 0.240661i
\(630\) 7.79525e12i 0.0785466i
\(631\) 1.75437e14i 1.75378i −0.480692 0.876890i \(-0.659614\pi\)
0.480692 0.876890i \(-0.340386\pi\)
\(632\) 4.12111e13i 0.408723i
\(633\) 7.72801e13 0.760412
\(634\) 3.28417e13i 0.320612i
\(635\) 1.27846e14i 1.23828i
\(636\) 5.46649e13i 0.525318i
\(637\) 2.36149e12 0.0225159
\(638\) −2.14617e12 −0.0203030
\(639\) 5.78455e13i 0.542957i
\(640\) 7.03666e13 0.655340
\(641\) 1.42208e14i 1.31412i −0.753838 0.657060i \(-0.771800\pi\)
0.753838 0.657060i \(-0.228200\pi\)
\(642\) −3.94142e13 −0.361391
\(643\) 1.12154e14 1.02037 0.510186 0.860064i \(-0.329577\pi\)
0.510186 + 0.860064i \(0.329577\pi\)
\(644\) 9.98501e13i 0.901404i
\(645\) 2.72119e13 1.35232e14i 0.243759 1.21138i
\(646\) −9.47221e12 −0.0841955
\(647\) 9.56448e13i 0.843607i 0.906687 + 0.421803i \(0.138603\pi\)
−0.906687 + 0.421803i \(0.861397\pi\)
\(648\) 4.84147e13i 0.423743i
\(649\) −1.81123e13 −0.157308
\(650\) 6.62938e11i 0.00571355i
\(651\) 2.45685e13 0.210123
\(652\) 1.76837e14i 1.50084i
\(653\) 7.62193e13i 0.641947i 0.947088 + 0.320974i \(0.104010\pi\)
−0.947088 + 0.320974i \(0.895990\pi\)
\(654\) 2.21560e13 0.185184
\(655\) −1.38377e14 −1.14778
\(656\) −7.40881e13 −0.609858
\(657\) 1.57735e13i 0.128855i
\(658\) 2.02495e13 0.164166
\(659\) 1.91006e14 1.53681 0.768403 0.639967i \(-0.221052\pi\)
0.768403 + 0.639967i \(0.221052\pi\)
\(660\) 2.94361e13 0.235050
\(661\) −1.55645e13 −0.123347 −0.0616733 0.998096i \(-0.519644\pi\)
−0.0616733 + 0.998096i \(0.519644\pi\)
\(662\) −2.54548e13 −0.200207
\(663\) 7.22178e13i 0.563737i
\(664\) 5.41252e13i 0.419333i
\(665\) 8.84495e13i 0.680122i
\(666\) 3.39886e12 0.0259395
\(667\) 7.50055e13i 0.568152i
\(668\) 1.03352e14 0.777027
\(669\) −1.50682e14 −1.12443
\(670\) 1.08088e13 0.0800576
\(671\) 1.53784e12i 0.0113057i
\(672\) 8.06015e13i 0.588162i
\(673\) 5.98762e13i 0.433690i 0.976206 + 0.216845i \(0.0695766\pi\)
−0.976206 + 0.216845i \(0.930423\pi\)
\(674\) 2.97111e13i 0.213609i
\(675\) 4.74091e12i 0.0338332i
\(676\) −7.97090e13 −0.564643
\(677\) 9.73601e12i 0.0684601i 0.999414 + 0.0342301i \(0.0108979\pi\)
−0.999414 + 0.0342301i \(0.989102\pi\)
\(678\) 9.80341e12i 0.0684272i
\(679\) 6.46006e13i 0.447598i
\(680\) 3.66263e13 0.251912
\(681\) 4.80432e13 0.328017
\(682\) 8.84832e11i 0.00599707i
\(683\) 7.39029e13 0.497231 0.248615 0.968602i \(-0.420025\pi\)
0.248615 + 0.968602i \(0.420025\pi\)
\(684\) 4.43737e13i 0.296378i
\(685\) −2.49433e13 −0.165387
\(686\) −2.66220e13 −0.175235
\(687\) 3.20062e14i 2.09146i
\(688\) 2.77256e13 1.37784e14i 0.179862 0.893836i
\(689\) −4.51022e13 −0.290471
\(690\) 3.14999e13i 0.201402i
\(691\) 2.93000e14i 1.85985i 0.367751 + 0.929924i \(0.380128\pi\)
−0.367751 + 0.929924i \(0.619872\pi\)
\(692\) 1.67551e13 0.105589
\(693\) 1.39267e13i 0.0871326i
\(694\) −4.46569e13 −0.277390
\(695\) 2.44819e14i 1.50981i
\(696\) 4.01624e13i 0.245908i
\(697\) −7.96025e13 −0.483908
\(698\) 2.96952e13 0.179229
\(699\) 3.77567e14 2.26260
\(700\) 8.21349e12i 0.0488694i
\(701\) 4.69230e13 0.277201 0.138601 0.990348i \(-0.455740\pi\)
0.138601 + 0.990348i \(0.455740\pi\)
\(702\) −1.25392e13 −0.0735503
\(703\) −3.85655e13 −0.224606
\(704\) 2.80073e13 0.161960
\(705\) −2.08629e14 −1.19792
\(706\) 2.24088e13i 0.127760i
\(707\) 5.02690e13i 0.284579i
\(708\) 1.66917e14i 0.938283i
\(709\) −9.97058e13 −0.556531 −0.278265 0.960504i \(-0.589759\pi\)
−0.278265 + 0.960504i \(0.589759\pi\)
\(710\) 3.82690e13i 0.212107i
\(711\) −9.89266e13 −0.544459
\(712\) 7.36182e13 0.402333
\(713\) 3.09236e13 0.167819
\(714\) 2.73967e13i 0.147641i
\(715\) 2.42868e13i 0.129969i
\(716\) 3.39056e13i 0.180180i
\(717\) 1.48932e14i 0.785943i
\(718\) 3.98025e13i 0.208588i
\(719\) −1.78844e14 −0.930741 −0.465371 0.885116i \(-0.654079\pi\)
−0.465371 + 0.885116i \(0.654079\pi\)
\(720\) 8.18300e13i 0.422912i
\(721\) 2.94944e14i 1.51378i
\(722\) 1.84004e13i 0.0937869i
\(723\) 4.05471e14 2.05243
\(724\) −2.39311e14 −1.20301
\(725\) 6.16982e12i 0.0308022i
\(726\) 4.02861e13 0.199743
\(727\) 2.91641e14i 1.43607i 0.696005 + 0.718037i \(0.254959\pi\)
−0.696005 + 0.718037i \(0.745041\pi\)
\(728\) −4.41128e13 −0.215729
\(729\) −4.75347e13 −0.230873
\(730\) 1.04353e13i 0.0503373i
\(731\) 2.97893e13 1.48040e14i 0.142716 0.709238i
\(732\) −1.41722e13 −0.0674346
\(733\) 2.10681e14i 0.995648i 0.867278 + 0.497824i \(0.165867\pi\)
−0.867278 + 0.497824i \(0.834133\pi\)
\(734\) 6.62755e13i 0.311080i
\(735\) 9.22999e12 0.0430293
\(736\) 1.01451e14i 0.469748i
\(737\) 1.93105e13 0.0888087
\(738\) 1.14183e13i 0.0521578i
\(739\) 5.50708e13i 0.249862i −0.992165 0.124931i \(-0.960129\pi\)
0.992165 0.124931i \(-0.0398709\pi\)
\(740\) 7.34364e13 0.330943
\(741\) −1.17539e14 −0.526130
\(742\) 1.71101e13 0.0760734
\(743\) 5.59921e13i 0.247276i 0.992327 + 0.123638i \(0.0394562\pi\)
−0.992327 + 0.123638i \(0.960544\pi\)
\(744\) 1.65583e13 0.0726359
\(745\) 1.93946e14 0.845083
\(746\) −3.01185e13 −0.130359
\(747\) −1.29927e14 −0.558593
\(748\) 3.22241e13 0.137617
\(749\) 4.02900e14i 1.70918i
\(750\) 4.79512e13i 0.202066i
\(751\) 2.89087e14i 1.21012i −0.796179 0.605061i \(-0.793149\pi\)
0.796179 0.605061i \(-0.206851\pi\)
\(752\) −2.12567e14 −0.883908
\(753\) 1.22934e13i 0.0507804i
\(754\) −1.63185e13 −0.0669613
\(755\) −1.44092e14 −0.587359
\(756\) −1.55355e14 −0.629094
\(757\) 1.01995e14i 0.410297i −0.978731 0.205149i \(-0.934232\pi\)
0.978731 0.205149i \(-0.0657678\pi\)
\(758\) 1.14947e13i 0.0459359i
\(759\) 5.62763e13i 0.223417i
\(760\) 5.96118e13i 0.235106i
\(761\) 1.48371e14i 0.581335i −0.956824 0.290667i \(-0.906123\pi\)
0.956824 0.290667i \(-0.0938773\pi\)
\(762\) 6.44511e13 0.250874
\(763\) 2.26484e14i 0.875818i
\(764\) 1.21830e14i 0.468045i
\(765\) 8.79207e13i 0.335571i
\(766\) 3.54412e13 0.134389
\(767\) −1.37718e14 −0.518816
\(768\) 2.30535e14i 0.862839i
\(769\) 4.82893e14 1.79564 0.897820 0.440362i \(-0.145150\pi\)
0.897820 + 0.440362i \(0.145150\pi\)
\(770\) 9.21349e12i 0.0340385i
\(771\) 1.50637e14 0.552919
\(772\) 3.37653e13 0.123136
\(773\) 4.77918e13i 0.173163i −0.996245 0.0865817i \(-0.972406\pi\)
0.996245 0.0865817i \(-0.0275943\pi\)
\(774\) 2.12350e13 + 4.27301e12i 0.0764448 + 0.0153826i
\(775\) 2.54372e12 0.00909831
\(776\) 4.35385e13i 0.154727i
\(777\) 1.11544e14i 0.393859i
\(778\) 3.44294e13 0.120790
\(779\) 1.29559e14i 0.451626i