Properties

Label 69.7.d.a.22.11
Level $69$
Weight $7$
Character 69.22
Analytic conductor $15.874$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 69.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.8737317698\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.11
Character \(\chi\) \(=\) 69.22
Dual form 69.7.d.a.22.12

$q$-expansion

\(f(q)\) \(=\) \(q-3.69366 q^{2} +15.5885 q^{3} -50.3569 q^{4} -218.943i q^{5} -57.5785 q^{6} -261.444i q^{7} +422.396 q^{8} +243.000 q^{9} +O(q^{10})\) \(q-3.69366 q^{2} +15.5885 q^{3} -50.3569 q^{4} -218.943i q^{5} -57.5785 q^{6} -261.444i q^{7} +422.396 q^{8} +243.000 q^{9} +808.702i q^{10} +1771.61i q^{11} -784.986 q^{12} -2889.11 q^{13} +965.685i q^{14} -3412.99i q^{15} +1662.65 q^{16} -559.041i q^{17} -897.560 q^{18} -1593.98i q^{19} +11025.3i q^{20} -4075.50i q^{21} -6543.74i q^{22} +(-11698.6 - 3343.37i) q^{23} +6584.50 q^{24} -32311.1 q^{25} +10671.4 q^{26} +3788.00 q^{27} +13165.5i q^{28} -19917.0 q^{29} +12606.4i q^{30} +14468.1 q^{31} -33174.6 q^{32} +27616.7i q^{33} +2064.91i q^{34} -57241.3 q^{35} -12236.7 q^{36} +63378.4i q^{37} +5887.61i q^{38} -45036.8 q^{39} -92480.7i q^{40} +4348.78 q^{41} +15053.5i q^{42} +26412.8i q^{43} -89212.9i q^{44} -53203.2i q^{45} +(43210.8 + 12349.3i) q^{46} -155401. q^{47} +25918.2 q^{48} +49296.2 q^{49} +119346. q^{50} -8714.59i q^{51} +145487. q^{52} +119055. i q^{53} -13991.6 q^{54} +387883. q^{55} -110433. i q^{56} -24847.6i q^{57} +73566.8 q^{58} +235457. q^{59} +171867. i q^{60} -210647. i q^{61} -53440.1 q^{62} -63530.8i q^{63} +16126.0 q^{64} +632551. i q^{65} -102007. i q^{66} -494703. i q^{67} +28151.5i q^{68} +(-182363. - 52118.0i) q^{69} +211430. q^{70} -508838. q^{71} +102642. q^{72} -39370.7 q^{73} -234098. i q^{74} -503681. q^{75} +80267.6i q^{76} +463177. q^{77} +166351. q^{78} -150541. i q^{79} -364027. i q^{80} +59049.0 q^{81} -16062.9 q^{82} +226820. i q^{83} +205230. i q^{84} -122398. q^{85} -97560.0i q^{86} -310476. q^{87} +748322. i q^{88} -576409. i q^{89} +196515. i q^{90} +755340. i q^{91} +(589106. + 168362. i) q^{92} +225535. q^{93} +573999. q^{94} -348990. q^{95} -517141. q^{96} +973550. i q^{97} -182083. q^{98} +430502. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + O(q^{10}) \) \( 24q - 20q^{2} + 816q^{4} - 324q^{6} - 940q^{8} + 5832q^{9} + 384q^{13} + 29544q^{16} - 4860q^{18} + 29336q^{23} - 39204q^{24} - 61272q^{25} + 10088q^{26} + 64672q^{29} + 9696q^{31} - 319620q^{32} - 225744q^{35} + 198288q^{36} - 11664q^{39} + 135280q^{41} + 233232q^{46} - 74336q^{47} + 552096q^{48} - 722136q^{49} + 619324q^{50} + 1059720q^{52} - 78732q^{54} - 1019328q^{55} - 694344q^{58} + 1057648q^{59} - 488776q^{62} - 273888q^{64} - 23328q^{69} + 2785512q^{70} - 255392q^{71} - 228420q^{72} - 322560q^{73} - 365472q^{75} - 1002960q^{77} - 171072q^{78} + 1417176q^{81} - 5732712q^{82} - 2704704q^{85} + 611712q^{87} - 1611444q^{92} + 2484432q^{93} - 147720q^{94} - 1672656q^{95} - 1818612q^{96} + 9104212q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.69366 −0.461708 −0.230854 0.972988i \(-0.574152\pi\)
−0.230854 + 0.972988i \(0.574152\pi\)
\(3\) 15.5885 0.577350
\(4\) −50.3569 −0.786826
\(5\) 218.943i 1.75155i −0.482723 0.875773i \(-0.660352\pi\)
0.482723 0.875773i \(-0.339648\pi\)
\(6\) −57.5785 −0.266567
\(7\) 261.444i 0.762227i −0.924528 0.381113i \(-0.875541\pi\)
0.924528 0.381113i \(-0.124459\pi\)
\(8\) 422.396 0.824991
\(9\) 243.000 0.333333
\(10\) 808.702i 0.808702i
\(11\) 1771.61i 1.33104i 0.746380 + 0.665520i \(0.231790\pi\)
−0.746380 + 0.665520i \(0.768210\pi\)
\(12\) −784.986 −0.454274
\(13\) −2889.11 −1.31503 −0.657513 0.753444i \(-0.728391\pi\)
−0.657513 + 0.753444i \(0.728391\pi\)
\(14\) 965.685i 0.351926i
\(15\) 3412.99i 1.01126i
\(16\) 1662.65 0.405921
\(17\) 559.041i 0.113788i −0.998380 0.0568940i \(-0.981880\pi\)
0.998380 0.0568940i \(-0.0181197\pi\)
\(18\) −897.560 −0.153903
\(19\) 1593.98i 0.232392i −0.993226 0.116196i \(-0.962930\pi\)
0.993226 0.116196i \(-0.0370701\pi\)
\(20\) 11025.3i 1.37816i
\(21\) 4075.50i 0.440072i
\(22\) 6543.74i 0.614552i
\(23\) −11698.6 3343.37i −0.961504 0.274790i
\(24\) 6584.50 0.476309
\(25\) −32311.1 −2.06791
\(26\) 10671.4 0.607157
\(27\) 3788.00 0.192450
\(28\) 13165.5i 0.599740i
\(29\) −19917.0 −0.816640 −0.408320 0.912839i \(-0.633885\pi\)
−0.408320 + 0.912839i \(0.633885\pi\)
\(30\) 12606.4i 0.466904i
\(31\) 14468.1 0.485652 0.242826 0.970070i \(-0.421926\pi\)
0.242826 + 0.970070i \(0.421926\pi\)
\(32\) −33174.6 −1.01241
\(33\) 27616.7i 0.768476i
\(34\) 2064.91i 0.0525368i
\(35\) −57241.3 −1.33507
\(36\) −12236.7 −0.262275
\(37\) 63378.4i 1.25123i 0.780133 + 0.625613i \(0.215151\pi\)
−0.780133 + 0.625613i \(0.784849\pi\)
\(38\) 5887.61i 0.107297i
\(39\) −45036.8 −0.759230
\(40\) 92480.7i 1.44501i
\(41\) 4348.78 0.0630981 0.0315491 0.999502i \(-0.489956\pi\)
0.0315491 + 0.999502i \(0.489956\pi\)
\(42\) 15053.5i 0.203185i
\(43\) 26412.8i 0.332207i 0.986108 + 0.166104i \(0.0531186\pi\)
−0.986108 + 0.166104i \(0.946881\pi\)
\(44\) 89212.9i 1.04730i
\(45\) 53203.2i 0.583849i
\(46\) 43210.8 + 12349.3i 0.443934 + 0.126873i
\(47\) −155401. −1.49679 −0.748394 0.663254i \(-0.769175\pi\)
−0.748394 + 0.663254i \(0.769175\pi\)
\(48\) 25918.2 0.234359
\(49\) 49296.2 0.419011
\(50\) 119346. 0.954772
\(51\) 8714.59i 0.0656956i
\(52\) 145487. 1.03470
\(53\) 119055.i 0.799690i 0.916583 + 0.399845i \(0.130936\pi\)
−0.916583 + 0.399845i \(0.869064\pi\)
\(54\) −13991.6 −0.0888557
\(55\) 387883. 2.33138
\(56\) 110433.i 0.628830i
\(57\) 24847.6i 0.134172i
\(58\) 73566.8 0.377049
\(59\) 235457. 1.14645 0.573226 0.819398i \(-0.305692\pi\)
0.573226 + 0.819398i \(0.305692\pi\)
\(60\) 171867.i 0.795682i
\(61\) 210647.i 0.928036i −0.885826 0.464018i \(-0.846407\pi\)
0.885826 0.464018i \(-0.153593\pi\)
\(62\) −53440.1 −0.224229
\(63\) 63530.8i 0.254076i
\(64\) 16126.0 0.0615157
\(65\) 632551.i 2.30333i
\(66\) 102007.i 0.354811i
\(67\) 494703.i 1.64483i −0.568891 0.822413i \(-0.692627\pi\)
0.568891 0.822413i \(-0.307373\pi\)
\(68\) 28151.5i 0.0895314i
\(69\) −182363. 52118.0i −0.555125 0.158650i
\(70\) 211430. 0.616414
\(71\) −508838. −1.42169 −0.710844 0.703350i \(-0.751687\pi\)
−0.710844 + 0.703350i \(0.751687\pi\)
\(72\) 102642. 0.274997
\(73\) −39370.7 −0.101206 −0.0506028 0.998719i \(-0.516114\pi\)
−0.0506028 + 0.998719i \(0.516114\pi\)
\(74\) 234098.i 0.577701i
\(75\) −503681. −1.19391
\(76\) 80267.6i 0.182852i
\(77\) 463177. 1.01455
\(78\) 166351. 0.350542
\(79\) 150541.i 0.305333i −0.988278 0.152667i \(-0.951214\pi\)
0.988278 0.152667i \(-0.0487861\pi\)
\(80\) 364027.i 0.710989i
\(81\) 59049.0 0.111111
\(82\) −16062.9 −0.0291329
\(83\) 226820.i 0.396686i 0.980133 + 0.198343i \(0.0635560\pi\)
−0.980133 + 0.198343i \(0.936444\pi\)
\(84\) 205230.i 0.346260i
\(85\) −122398. −0.199305
\(86\) 97560.0i 0.153383i
\(87\) −310476. −0.471488
\(88\) 748322.i 1.09810i
\(89\) 576409.i 0.817637i −0.912616 0.408819i \(-0.865941\pi\)
0.912616 0.408819i \(-0.134059\pi\)
\(90\) 196515.i 0.269567i
\(91\) 755340.i 1.00235i
\(92\) 589106. + 168362.i 0.756536 + 0.216212i
\(93\) 225535. 0.280391
\(94\) 573999. 0.691079
\(95\) −348990. −0.407045
\(96\) −517141. −0.584514
\(97\) 973550.i 1.06670i 0.845894 + 0.533351i \(0.179068\pi\)
−0.845894 + 0.533351i \(0.820932\pi\)
\(98\) −182083. −0.193460
\(99\) 430502.i 0.443680i
\(100\) 1.62709e6 1.62709
\(101\) −1.22771e6 −1.19160 −0.595801 0.803132i \(-0.703165\pi\)
−0.595801 + 0.803132i \(0.703165\pi\)
\(102\) 32188.7i 0.0303322i
\(103\) 1.71152e6i 1.56628i −0.621842 0.783142i \(-0.713616\pi\)
0.621842 0.783142i \(-0.286384\pi\)
\(104\) −1.22035e6 −1.08488
\(105\) −892304. −0.770806
\(106\) 439751.i 0.369223i
\(107\) 2.25275e6i 1.83891i −0.393190 0.919457i \(-0.628629\pi\)
0.393190 0.919457i \(-0.371371\pi\)
\(108\) −190752. −0.151425
\(109\) 1.94287e6i 1.50025i −0.661293 0.750127i \(-0.729992\pi\)
0.661293 0.750127i \(-0.270008\pi\)
\(110\) −1.43271e6 −1.07642
\(111\) 987971.i 0.722396i
\(112\) 434690.i 0.309404i
\(113\) 2.07914e6i 1.44095i 0.693481 + 0.720475i \(0.256076\pi\)
−0.693481 + 0.720475i \(0.743924\pi\)
\(114\) 91778.7i 0.0619480i
\(115\) −732009. + 2.56133e6i −0.481308 + 1.68412i
\(116\) 1.00296e6 0.642554
\(117\) −702054. −0.438342
\(118\) −869699. −0.529325
\(119\) −146158. −0.0867323
\(120\) 1.44163e6i 0.834277i
\(121\) −1.36706e6 −0.771668
\(122\) 778057.i 0.428481i
\(123\) 67790.8 0.0364297
\(124\) −728566. −0.382124
\(125\) 3.65332e6i 1.87050i
\(126\) 234661.i 0.117309i
\(127\) 3.21735e6 1.57068 0.785339 0.619066i \(-0.212489\pi\)
0.785339 + 0.619066i \(0.212489\pi\)
\(128\) 2.06361e6 0.984006
\(129\) 411735.i 0.191800i
\(130\) 2.33643e6i 1.06346i
\(131\) −1.76389e6 −0.784618 −0.392309 0.919834i \(-0.628324\pi\)
−0.392309 + 0.919834i \(0.628324\pi\)
\(132\) 1.39069e6i 0.604657i
\(133\) −416735. −0.177135
\(134\) 1.82727e6i 0.759429i
\(135\) 829356.i 0.337085i
\(136\) 236136.i 0.0938742i
\(137\) 2.12948e6i 0.828154i 0.910242 + 0.414077i \(0.135896\pi\)
−0.910242 + 0.414077i \(0.864104\pi\)
\(138\) 673589. + 192506.i 0.256305 + 0.0732500i
\(139\) 132686. 0.0494060 0.0247030 0.999695i \(-0.492136\pi\)
0.0247030 + 0.999695i \(0.492136\pi\)
\(140\) 2.88249e6 1.05047
\(141\) −2.42246e6 −0.864171
\(142\) 1.87947e6 0.656404
\(143\) 5.11839e6i 1.75035i
\(144\) 404025. 0.135307
\(145\) 4.36070e6i 1.43038i
\(146\) 145422. 0.0467274
\(147\) 768451. 0.241916
\(148\) 3.19154e6i 0.984498i
\(149\) 5.17537e6i 1.56453i −0.622949 0.782263i \(-0.714065\pi\)
0.622949 0.782263i \(-0.285935\pi\)
\(150\) 1.86043e6 0.551238
\(151\) 1.40318e6 0.407550 0.203775 0.979018i \(-0.434679\pi\)
0.203775 + 0.979018i \(0.434679\pi\)
\(152\) 673288.i 0.191721i
\(153\) 135847.i 0.0379294i
\(154\) −1.71082e6 −0.468428
\(155\) 3.16768e6i 0.850642i
\(156\) 2.26791e6 0.597382
\(157\) 4.35430e6i 1.12517i −0.826739 0.562586i \(-0.809806\pi\)
0.826739 0.562586i \(-0.190194\pi\)
\(158\) 556048.i 0.140975i
\(159\) 1.85589e6i 0.461701i
\(160\) 7.26335e6i 1.77328i
\(161\) −874104. + 3.05853e6i −0.209452 + 0.732884i
\(162\) −218107. −0.0513009
\(163\) −6.04372e6 −1.39554 −0.697769 0.716323i \(-0.745824\pi\)
−0.697769 + 0.716323i \(0.745824\pi\)
\(164\) −218991. −0.0496472
\(165\) 6.04650e6 1.34602
\(166\) 837796.i 0.183153i
\(167\) 5.03976e6 1.08208 0.541041 0.840996i \(-0.318030\pi\)
0.541041 + 0.840996i \(0.318030\pi\)
\(168\) 1.72147e6i 0.363055i
\(169\) 3.52015e6 0.729291
\(170\) 452098. 0.0920207
\(171\) 387336.i 0.0774640i
\(172\) 1.33007e6i 0.261389i
\(173\) −2.13405e6 −0.412161 −0.206080 0.978535i \(-0.566071\pi\)
−0.206080 + 0.978535i \(0.566071\pi\)
\(174\) 1.14679e6 0.217689
\(175\) 8.44755e6i 1.57622i
\(176\) 2.94558e6i 0.540297i
\(177\) 3.67041e6 0.661904
\(178\) 2.12906e6i 0.377509i
\(179\) −5.58887e6 −0.974463 −0.487231 0.873273i \(-0.661993\pi\)
−0.487231 + 0.873273i \(0.661993\pi\)
\(180\) 2.67915e6i 0.459387i
\(181\) 4.82682e6i 0.814001i −0.913428 0.407001i \(-0.866575\pi\)
0.913428 0.407001i \(-0.133425\pi\)
\(182\) 2.78997e6i 0.462791i
\(183\) 3.28365e6i 0.535802i
\(184\) −4.94145e6 1.41223e6i −0.793233 0.226699i
\(185\) 1.38763e7 2.19158
\(186\) −833049. −0.129459
\(187\) 990405. 0.151457
\(188\) 7.82551e6 1.17771
\(189\) 990348.i 0.146691i
\(190\) 1.28905e6 0.187936
\(191\) 7.07156e6i 1.01488i −0.861687 0.507440i \(-0.830592\pi\)
0.861687 0.507440i \(-0.169408\pi\)
\(192\) 251379. 0.0355161
\(193\) −1.35096e7 −1.87919 −0.939597 0.342284i \(-0.888800\pi\)
−0.939597 + 0.342284i \(0.888800\pi\)
\(194\) 3.59597e6i 0.492505i
\(195\) 9.86050e6i 1.32983i
\(196\) −2.48240e6 −0.329688
\(197\) −6.44400e6 −0.842862 −0.421431 0.906860i \(-0.638472\pi\)
−0.421431 + 0.906860i \(0.638472\pi\)
\(198\) 1.59013e6i 0.204851i
\(199\) 1.20114e6i 0.152417i −0.997092 0.0762084i \(-0.975719\pi\)
0.997092 0.0762084i \(-0.0242814\pi\)
\(200\) −1.36481e7 −1.70601
\(201\) 7.71166e6i 0.949641i
\(202\) 4.53474e6 0.550172
\(203\) 5.20719e6i 0.622465i
\(204\) 438839.i 0.0516910i
\(205\) 952137.i 0.110519i
\(206\) 6.32178e6i 0.723166i
\(207\) −2.84277e6 812439.i −0.320501 0.0915967i
\(208\) −4.80359e6 −0.533796
\(209\) 2.82391e6 0.309323
\(210\) 3.29587e6 0.355887
\(211\) 5.47137e6 0.582437 0.291218 0.956657i \(-0.405939\pi\)
0.291218 + 0.956657i \(0.405939\pi\)
\(212\) 5.99526e6i 0.629217i
\(213\) −7.93199e6 −0.820812
\(214\) 8.32089e6i 0.849041i
\(215\) 5.78290e6 0.581876
\(216\) 1.60003e6 0.158770
\(217\) 3.78258e6i 0.370177i
\(218\) 7.17632e6i 0.692679i
\(219\) −613728. −0.0584311
\(220\) −1.95326e7 −1.83439
\(221\) 1.61513e6i 0.149634i
\(222\) 3.64923e6i 0.333536i
\(223\) −1.00870e7 −0.909590 −0.454795 0.890596i \(-0.650287\pi\)
−0.454795 + 0.890596i \(0.650287\pi\)
\(224\) 8.67329e6i 0.771684i
\(225\) −7.85161e6 −0.689304
\(226\) 7.67965e6i 0.665298i
\(227\) 1.98153e7i 1.69404i 0.531560 + 0.847021i \(0.321606\pi\)
−0.531560 + 0.847021i \(0.678394\pi\)
\(228\) 1.25125e6i 0.105570i
\(229\) 7.97432e6i 0.664029i −0.943274 0.332015i \(-0.892272\pi\)
0.943274 0.332015i \(-0.107728\pi\)
\(230\) 2.70379e6 9.46070e6i 0.222223 0.777571i
\(231\) 7.22022e6 0.585753
\(232\) −8.41287e6 −0.673721
\(233\) 5.30042e6 0.419028 0.209514 0.977806i \(-0.432812\pi\)
0.209514 + 0.977806i \(0.432812\pi\)
\(234\) 2.59315e6 0.202386
\(235\) 3.40240e7i 2.62169i
\(236\) −1.18569e7 −0.902058
\(237\) 2.34670e6i 0.176284i
\(238\) 539857. 0.0400450
\(239\) −6.35315e6 −0.465366 −0.232683 0.972553i \(-0.574751\pi\)
−0.232683 + 0.972553i \(0.574751\pi\)
\(240\) 5.67461e6i 0.410490i
\(241\) 9.34983e6i 0.667964i −0.942580 0.333982i \(-0.891608\pi\)
0.942580 0.333982i \(-0.108392\pi\)
\(242\) 5.04945e6 0.356285
\(243\) 920483. 0.0641500
\(244\) 1.06075e7i 0.730203i
\(245\) 1.07931e7i 0.733916i
\(246\) −250396. −0.0168199
\(247\) 4.60517e6i 0.305601i
\(248\) 6.11125e6 0.400659
\(249\) 3.53577e6i 0.229027i
\(250\) 1.34941e7i 0.863624i
\(251\) 2.94710e6i 0.186369i 0.995649 + 0.0931847i \(0.0297047\pi\)
−0.995649 + 0.0931847i \(0.970295\pi\)
\(252\) 3.19921e6i 0.199913i
\(253\) 5.92317e6 2.07254e7i 0.365757 1.27980i
\(254\) −1.18838e7 −0.725194
\(255\) −1.90800e6 −0.115069
\(256\) −8.65434e6 −0.515839
\(257\) 593358. 0.0349556 0.0174778 0.999847i \(-0.494436\pi\)
0.0174778 + 0.999847i \(0.494436\pi\)
\(258\) 1.52081e6i 0.0885555i
\(259\) 1.65699e7 0.953718
\(260\) 3.18533e7i 1.81232i
\(261\) −4.83984e6 −0.272213
\(262\) 6.51522e6 0.362264
\(263\) 8.55513e6i 0.470283i 0.971961 + 0.235142i \(0.0755554\pi\)
−0.971961 + 0.235142i \(0.924445\pi\)
\(264\) 1.16652e7i 0.633986i
\(265\) 2.60664e7 1.40069
\(266\) 1.53928e6 0.0817847
\(267\) 8.98532e6i 0.472063i
\(268\) 2.49117e7i 1.29419i
\(269\) 2.39465e7 1.23023 0.615114 0.788439i \(-0.289110\pi\)
0.615114 + 0.788439i \(0.289110\pi\)
\(270\) 3.06336e6i 0.155635i
\(271\) −8.20740e6 −0.412380 −0.206190 0.978512i \(-0.566106\pi\)
−0.206190 + 0.978512i \(0.566106\pi\)
\(272\) 929491.i 0.0461890i
\(273\) 1.17746e7i 0.578705i
\(274\) 7.86557e6i 0.382365i
\(275\) 5.72429e7i 2.75248i
\(276\) 9.18325e6 + 2.62450e6i 0.436787 + 0.124830i
\(277\) 2.22467e7 1.04671 0.523356 0.852114i \(-0.324680\pi\)
0.523356 + 0.852114i \(0.324680\pi\)
\(278\) −490096. −0.0228111
\(279\) 3.51574e6 0.161884
\(280\) −2.41785e7 −1.10143
\(281\) 7.91487e6i 0.356718i 0.983965 + 0.178359i \(0.0570788\pi\)
−0.983965 + 0.178359i \(0.942921\pi\)
\(282\) 8.94776e6 0.398994
\(283\) 1.78585e6i 0.0787928i 0.999224 + 0.0393964i \(0.0125435\pi\)
−0.999224 + 0.0393964i \(0.987456\pi\)
\(284\) 2.56235e7 1.11862
\(285\) −5.44022e6 −0.235008
\(286\) 1.89056e7i 0.808151i
\(287\) 1.13696e6i 0.0480951i
\(288\) −8.06143e6 −0.337469
\(289\) 2.38250e7 0.987052
\(290\) 1.61070e7i 0.660419i
\(291\) 1.51761e7i 0.615861i
\(292\) 1.98258e6 0.0796312
\(293\) 4.56796e7i 1.81602i 0.418953 + 0.908008i \(0.362397\pi\)
−0.418953 + 0.908008i \(0.637603\pi\)
\(294\) −2.83840e6 −0.111694
\(295\) 5.15517e7i 2.00806i
\(296\) 2.67708e7i 1.03225i
\(297\) 6.71087e6i 0.256159i
\(298\) 1.91161e7i 0.722354i
\(299\) 3.37986e7 + 9.65937e6i 1.26440 + 0.361356i
\(300\) 2.53638e7 0.939400
\(301\) 6.90546e6 0.253217
\(302\) −5.18286e6 −0.188169
\(303\) −1.91381e7 −0.687972
\(304\) 2.65023e6i 0.0943328i
\(305\) −4.61196e7 −1.62550
\(306\) 501773.i 0.0175123i
\(307\) 5.19187e7 1.79436 0.897178 0.441670i \(-0.145614\pi\)
0.897178 + 0.441670i \(0.145614\pi\)
\(308\) −2.33242e7 −0.798278
\(309\) 2.66800e7i 0.904295i
\(310\) 1.17004e7i 0.392748i
\(311\) −3.85711e7 −1.28227 −0.641137 0.767426i \(-0.721537\pi\)
−0.641137 + 0.767426i \(0.721537\pi\)
\(312\) −1.90233e7 −0.626358
\(313\) 5.22230e7i 1.70306i −0.524309 0.851528i \(-0.675676\pi\)
0.524309 0.851528i \(-0.324324\pi\)
\(314\) 1.60833e7i 0.519501i
\(315\) −1.39096e7 −0.445025
\(316\) 7.58078e6i 0.240244i
\(317\) 4.17049e7 1.30921 0.654605 0.755972i \(-0.272835\pi\)
0.654605 + 0.755972i \(0.272835\pi\)
\(318\) 6.85504e6i 0.213171i
\(319\) 3.52853e7i 1.08698i
\(320\) 3.53067e6i 0.107747i
\(321\) 3.51169e7i 1.06170i
\(322\) 3.22864e6 1.12972e7i 0.0967058 0.338378i
\(323\) −891098. −0.0264434
\(324\) −2.97352e6 −0.0874251
\(325\) 9.33505e7 2.71936
\(326\) 2.23235e7 0.644330
\(327\) 3.02864e7i 0.866173i
\(328\) 1.83691e6 0.0520554
\(329\) 4.06286e7i 1.14089i
\(330\) −2.23337e7 −0.621469
\(331\) −4.94227e7 −1.36283 −0.681417 0.731896i \(-0.738636\pi\)
−0.681417 + 0.731896i \(0.738636\pi\)
\(332\) 1.14219e7i 0.312123i
\(333\) 1.54010e7i 0.417076i
\(334\) −1.86152e7 −0.499606
\(335\) −1.08312e8 −2.88099
\(336\) 6.77615e6i 0.178634i
\(337\) 7.33390e7i 1.91622i 0.286402 + 0.958110i \(0.407541\pi\)
−0.286402 + 0.958110i \(0.592459\pi\)
\(338\) −1.30022e7 −0.336719
\(339\) 3.24106e7i 0.831933i
\(340\) 6.16359e6 0.156818
\(341\) 2.56318e7i 0.646423i
\(342\) 1.43069e6i 0.0357657i
\(343\) 4.36468e7i 1.08161i
\(344\) 1.11567e7i 0.274068i
\(345\) −1.14109e7 + 3.99272e7i −0.277883 + 0.972326i
\(346\) 7.88246e6 0.190298
\(347\) −7.00163e7 −1.67576 −0.837878 0.545857i \(-0.816204\pi\)
−0.837878 + 0.545857i \(0.816204\pi\)
\(348\) 1.56346e7 0.370979
\(349\) −4.25755e6 −0.100157 −0.0500787 0.998745i \(-0.515947\pi\)
−0.0500787 + 0.998745i \(0.515947\pi\)
\(350\) 3.12024e7i 0.727752i
\(351\) −1.09439e7 −0.253077
\(352\) 5.87726e7i 1.34756i
\(353\) −2.44696e7 −0.556292 −0.278146 0.960539i \(-0.589720\pi\)
−0.278146 + 0.960539i \(0.589720\pi\)
\(354\) −1.35573e7 −0.305606
\(355\) 1.11407e8i 2.49015i
\(356\) 2.90261e7i 0.643338i
\(357\) −2.27837e6 −0.0500749
\(358\) 2.06434e7 0.449917
\(359\) 4.27662e7i 0.924310i −0.886799 0.462155i \(-0.847076\pi\)
0.886799 0.462155i \(-0.152924\pi\)
\(360\) 2.24728e7i 0.481670i
\(361\) 4.45051e7 0.945994
\(362\) 1.78286e7i 0.375831i
\(363\) −2.13103e7 −0.445523
\(364\) 3.80365e7i 0.788673i
\(365\) 8.61995e6i 0.177266i
\(366\) 1.21287e7i 0.247384i
\(367\) 3.81457e7i 0.771699i 0.922562 + 0.385849i \(0.126092\pi\)
−0.922562 + 0.385849i \(0.873908\pi\)
\(368\) −1.94507e7 5.55887e6i −0.390295 0.111543i
\(369\) 1.05675e6 0.0210327
\(370\) −5.12543e7 −1.01187
\(371\) 3.11263e7 0.609545
\(372\) −1.13572e7 −0.220619
\(373\) 8.90738e7i 1.71642i 0.513299 + 0.858210i \(0.328423\pi\)
−0.513299 + 0.858210i \(0.671577\pi\)
\(374\) −3.65822e6 −0.0699286
\(375\) 5.69496e7i 1.07993i
\(376\) −6.56407e7 −1.23484
\(377\) 5.75425e7 1.07390
\(378\) 3.65801e6i 0.0677282i
\(379\) 6.77299e7i 1.24412i −0.782969 0.622061i \(-0.786296\pi\)
0.782969 0.622061i \(-0.213704\pi\)
\(380\) 1.75741e7 0.320274
\(381\) 5.01535e7 0.906831
\(382\) 2.61199e7i 0.468578i
\(383\) 2.59319e7i 0.461570i −0.973005 0.230785i \(-0.925871\pi\)
0.973005 0.230785i \(-0.0741294\pi\)
\(384\) 3.21685e7 0.568116
\(385\) 1.01410e8i 1.77704i
\(386\) 4.99000e7 0.867638
\(387\) 6.41831e6i 0.110736i
\(388\) 4.90249e7i 0.839309i
\(389\) 3.18918e7i 0.541788i −0.962609 0.270894i \(-0.912681\pi\)
0.962609 0.270894i \(-0.0873193\pi\)
\(390\) 3.64213e7i 0.613991i
\(391\) −1.86908e6 + 6.54001e6i −0.0312678 + 0.109408i
\(392\) 2.08225e7 0.345680
\(393\) −2.74964e7 −0.452999
\(394\) 2.38019e7 0.389156
\(395\) −3.29600e7 −0.534805
\(396\) 2.16787e7i 0.349099i
\(397\) −6.02801e7 −0.963391 −0.481696 0.876339i \(-0.659979\pi\)
−0.481696 + 0.876339i \(0.659979\pi\)
\(398\) 4.43659e6i 0.0703720i
\(399\) −6.49626e6 −0.102269
\(400\) −5.37222e7 −0.839410
\(401\) 8.25668e7i 1.28048i −0.768176 0.640239i \(-0.778835\pi\)
0.768176 0.640239i \(-0.221165\pi\)
\(402\) 2.84842e7i 0.438457i
\(403\) −4.17998e7 −0.638645
\(404\) 6.18236e7 0.937583
\(405\) 1.29284e7i 0.194616i
\(406\) 1.92336e7i 0.287397i
\(407\) −1.12282e8 −1.66543
\(408\) 3.68100e6i 0.0541983i
\(409\) 1.28874e8 1.88363 0.941816 0.336129i \(-0.109118\pi\)
0.941816 + 0.336129i \(0.109118\pi\)
\(410\) 3.51687e6i 0.0510276i
\(411\) 3.31953e7i 0.478135i
\(412\) 8.61869e7i 1.23239i
\(413\) 6.15588e7i 0.873856i
\(414\) 1.05002e7 + 3.00088e6i 0.147978 + 0.0422909i
\(415\) 4.96607e7 0.694814
\(416\) 9.58451e7 1.33134
\(417\) 2.06837e6 0.0285246
\(418\) −1.04306e7 −0.142817
\(419\) 3.80324e7i 0.517025i 0.966008 + 0.258513i \(0.0832323\pi\)
−0.966008 + 0.258513i \(0.916768\pi\)
\(420\) 4.49336e7 0.606490
\(421\) 2.33866e7i 0.313416i 0.987645 + 0.156708i \(0.0500882\pi\)
−0.987645 + 0.156708i \(0.949912\pi\)
\(422\) −2.02094e7 −0.268916
\(423\) −3.77624e7 −0.498929
\(424\) 5.02885e7i 0.659738i
\(425\) 1.80633e7i 0.235304i
\(426\) 2.92981e7 0.378975
\(427\) −5.50722e7 −0.707374
\(428\) 1.13441e8i 1.44691i
\(429\) 7.97878e7i 1.01057i
\(430\) −2.13601e7 −0.268657
\(431\) 3.70034e7i 0.462179i −0.972932 0.231090i \(-0.925771\pi\)
0.972932 0.231090i \(-0.0742290\pi\)
\(432\) 6.29812e6 0.0781195
\(433\) 1.05066e8i 1.29419i 0.762408 + 0.647096i \(0.224017\pi\)
−0.762408 + 0.647096i \(0.775983\pi\)
\(434\) 1.39716e7i 0.170914i
\(435\) 6.79766e7i 0.825832i
\(436\) 9.78370e7i 1.18044i
\(437\) −5.32925e6 + 1.86473e7i −0.0638590 + 0.223446i
\(438\) 2.26691e6 0.0269781
\(439\) −4.23482e7 −0.500543 −0.250271 0.968176i \(-0.580520\pi\)
−0.250271 + 0.968176i \(0.580520\pi\)
\(440\) 1.63840e8 1.92337
\(441\) 1.19790e7 0.139670
\(442\) 5.96575e6i 0.0690873i
\(443\) −7.62775e7 −0.877375 −0.438688 0.898640i \(-0.644557\pi\)
−0.438688 + 0.898640i \(0.644557\pi\)
\(444\) 4.97511e7i 0.568400i
\(445\) −1.26201e8 −1.43213
\(446\) 3.72578e7 0.419965
\(447\) 8.06760e7i 0.903279i
\(448\) 4.21603e6i 0.0468889i
\(449\) −2.09418e7 −0.231353 −0.115676 0.993287i \(-0.536904\pi\)
−0.115676 + 0.993287i \(0.536904\pi\)
\(450\) 2.90012e7 0.318257
\(451\) 7.70437e6i 0.0839861i
\(452\) 1.04699e8i 1.13378i
\(453\) 2.18734e7 0.235299
\(454\) 7.31912e7i 0.782152i
\(455\) 1.65377e8 1.75566
\(456\) 1.04955e7i 0.110690i
\(457\) 1.44360e8i 1.51251i −0.654274 0.756257i \(-0.727026\pi\)
0.654274 0.756257i \(-0.272974\pi\)
\(458\) 2.94544e7i 0.306587i
\(459\) 2.11764e6i 0.0218985i
\(460\) 3.68617e7 1.28981e8i 0.378705 1.32511i
\(461\) 5.85463e7 0.597581 0.298790 0.954319i \(-0.403417\pi\)
0.298790 + 0.954319i \(0.403417\pi\)
\(462\) −2.66691e7 −0.270447
\(463\) −3.56162e7 −0.358843 −0.179422 0.983772i \(-0.557423\pi\)
−0.179422 + 0.983772i \(0.557423\pi\)
\(464\) −3.31151e7 −0.331492
\(465\) 4.93793e7i 0.491118i
\(466\) −1.95780e7 −0.193468
\(467\) 9.94961e7i 0.976912i 0.872589 + 0.488456i \(0.162440\pi\)
−0.872589 + 0.488456i \(0.837560\pi\)
\(468\) 3.53532e7 0.344899
\(469\) −1.29337e8 −1.25373
\(470\) 1.25673e8i 1.21046i
\(471\) 6.78768e7i 0.649619i
\(472\) 9.94560e7 0.945813
\(473\) −4.67933e7 −0.442181
\(474\) 8.66793e6i 0.0813918i
\(475\) 5.15032e7i 0.480566i
\(476\) 7.36004e6 0.0682432
\(477\) 2.89305e7i 0.266563i
\(478\) 2.34664e7 0.214863
\(479\) 1.73205e8i 1.57599i 0.615679 + 0.787997i \(0.288882\pi\)
−0.615679 + 0.787997i \(0.711118\pi\)
\(480\) 1.13224e8i 1.02380i
\(481\) 1.83107e8i 1.64539i
\(482\) 3.45351e7i 0.308404i
\(483\) −1.36259e7 + 4.76778e7i −0.120927 + 0.423131i
\(484\) 6.88407e7 0.607168
\(485\) 2.13152e8 1.86838
\(486\) −3.39995e6 −0.0296186
\(487\) 4.78345e7 0.414147 0.207073 0.978325i \(-0.433606\pi\)
0.207073 + 0.978325i \(0.433606\pi\)
\(488\) 8.89762e7i 0.765622i
\(489\) −9.42123e7 −0.805714
\(490\) 3.98659e7i 0.338855i
\(491\) 1.10447e8 0.933059 0.466530 0.884506i \(-0.345504\pi\)
0.466530 + 0.884506i \(0.345504\pi\)
\(492\) −3.41373e6 −0.0286638
\(493\) 1.11344e7i 0.0929240i
\(494\) 1.70099e7i 0.141098i
\(495\) 9.42556e7 0.777126
\(496\) 2.40554e7 0.197136
\(497\) 1.33032e8i 1.08365i
\(498\) 1.30600e7i 0.105743i
\(499\) 3.75153e7 0.301930 0.150965 0.988539i \(-0.451762\pi\)
0.150965 + 0.988539i \(0.451762\pi\)
\(500\) 1.83970e8i 1.47176i
\(501\) 7.85621e7 0.624741
\(502\) 1.08856e7i 0.0860482i
\(503\) 101609.i 0.000798411i −1.00000 0.000399205i \(-0.999873\pi\)
1.00000 0.000399205i \(-0.000127071\pi\)
\(504\) 2.68351e7i 0.209610i
\(505\) 2.68799e8i 2.08715i
\(506\) −2.18782e7 + 7.65528e7i −0.168873 + 0.590894i
\(507\) 5.48737e7 0.421056
\(508\) −1.62016e8 −1.23585
\(509\) 9.08093e7 0.688616 0.344308 0.938857i \(-0.388114\pi\)
0.344308 + 0.938857i \(0.388114\pi\)
\(510\) 7.04751e6 0.0531282
\(511\) 1.02932e7i 0.0771416i
\(512\) −1.00105e8 −0.745839
\(513\) 6.03797e6i 0.0447238i
\(514\) −2.19166e6 −0.0161393
\(515\) −3.74726e8 −2.74342
\(516\) 2.07337e7i 0.150913i
\(517\) 2.75311e8i 1.99228i
\(518\) −6.12036e7 −0.440339
\(519\) −3.32666e7 −0.237961
\(520\) 2.67187e8i 1.90022i
\(521\) 1.52672e8i 1.07956i −0.841806 0.539779i \(-0.818508\pi\)
0.841806 0.539779i \(-0.181492\pi\)
\(522\) 1.78767e7 0.125683
\(523\) 1.29320e8i 0.903982i 0.892023 + 0.451991i \(0.149286\pi\)
−0.892023 + 0.451991i \(0.850714\pi\)
\(524\) 8.88241e7 0.617358
\(525\) 1.31684e8i 0.910030i
\(526\) 3.15998e7i 0.217133i
\(527\) 8.08824e6i 0.0552614i
\(528\) 4.59170e7i 0.311941i
\(529\) 1.25680e8 + 7.82257e7i 0.848981 + 0.528424i
\(530\) −9.62805e7 −0.646711
\(531\) 5.72161e7 0.382150
\(532\) 2.09855e7 0.139375
\(533\) −1.25641e7 −0.0829756
\(534\) 3.31888e7i 0.217955i
\(535\) −4.93224e8 −3.22094
\(536\) 2.08960e8i 1.35697i
\(537\) −8.71219e7 −0.562606
\(538\) −8.84503e7 −0.568005
\(539\) 8.73338e7i 0.557720i
\(540\) 4.17638e7i 0.265227i
\(541\) 3.69700e7 0.233484 0.116742 0.993162i \(-0.462755\pi\)
0.116742 + 0.993162i \(0.462755\pi\)
\(542\) 3.03153e7 0.190399
\(543\) 7.52426e7i 0.469964i
\(544\) 1.85460e7i 0.115200i
\(545\) −4.25379e8 −2.62777
\(546\) 4.34913e7i 0.267193i
\(547\) −1.45850e8 −0.891140 −0.445570 0.895247i \(-0.646999\pi\)
−0.445570 + 0.895247i \(0.646999\pi\)
\(548\) 1.07234e8i 0.651613i
\(549\) 5.11871e7i 0.309345i
\(550\) 2.11436e8i 1.27084i
\(551\) 3.17473e7i 0.189781i
\(552\) −7.70295e7 2.20144e7i −0.457973 0.130885i
\(553\) −3.93580e7 −0.232733
\(554\) −8.21719e7 −0.483275
\(555\) 2.16310e8 1.26531
\(556\) −6.68164e6 −0.0388739
\(557\) 1.78399e8i 1.03235i −0.856483 0.516175i \(-0.827355\pi\)
0.856483 0.516175i \(-0.172645\pi\)
\(558\) −1.29860e7 −0.0747431
\(559\) 7.63095e7i 0.436861i
\(560\) −9.51725e7 −0.541935
\(561\) 1.54389e7 0.0874435
\(562\) 2.92349e7i 0.164699i
\(563\) 1.68361e8i 0.943442i 0.881748 + 0.471721i \(0.156367\pi\)
−0.881748 + 0.471721i \(0.843633\pi\)
\(564\) 1.21988e8 0.679952
\(565\) 4.55214e8 2.52389
\(566\) 6.59634e6i 0.0363792i
\(567\) 1.54380e7i 0.0846918i
\(568\) −2.14931e8 −1.17288
\(569\) 1.19163e8i 0.646852i −0.946253 0.323426i \(-0.895165\pi\)
0.946253 0.323426i \(-0.104835\pi\)
\(570\) 2.00943e7 0.108505
\(571\) 2.59509e7i 0.139394i −0.997568 0.0696970i \(-0.977797\pi\)
0.997568 0.0696970i \(-0.0222032\pi\)
\(572\) 2.57746e8i 1.37722i
\(573\) 1.10235e8i 0.585942i
\(574\) 4.19956e6i 0.0222059i
\(575\) 3.77996e8 + 1.08028e8i 1.98831 + 0.568242i
\(576\) 3.91861e6 0.0205052
\(577\) 8.32275e7 0.433251 0.216625 0.976255i \(-0.430495\pi\)
0.216625 + 0.976255i \(0.430495\pi\)
\(578\) −8.80017e7 −0.455730
\(579\) −2.10594e8 −1.08495
\(580\) 2.19591e8i 1.12546i
\(581\) 5.93007e7 0.302365
\(582\) 5.60556e7i 0.284348i
\(583\) −2.10920e8 −1.06442
\(584\) −1.66300e7 −0.0834937
\(585\) 1.53710e8i 0.767776i
\(586\) 1.68725e8i 0.838468i
\(587\) −6.50290e6 −0.0321509 −0.0160754 0.999871i \(-0.505117\pi\)
−0.0160754 + 0.999871i \(0.505117\pi\)
\(588\) −3.86968e7 −0.190346
\(589\) 2.30617e7i 0.112862i
\(590\) 1.90415e8i 0.927138i
\(591\) −1.00452e8 −0.486627
\(592\) 1.05376e8i 0.507899i
\(593\) 7.43776e7 0.356680 0.178340 0.983969i \(-0.442927\pi\)
0.178340 + 0.983969i \(0.442927\pi\)
\(594\) 2.47877e7i 0.118270i
\(595\) 3.20002e7i 0.151916i
\(596\) 2.60615e8i 1.23101i
\(597\) 1.87238e7i 0.0879978i
\(598\) −1.24841e8 3.56784e7i −0.583784 0.166841i
\(599\) 1.01274e8 0.471213 0.235606 0.971849i \(-0.424292\pi\)
0.235606 + 0.971849i \(0.424292\pi\)
\(600\) −2.12753e8 −0.984966
\(601\) 2.15901e8 0.994561 0.497281 0.867590i \(-0.334332\pi\)
0.497281 + 0.867590i \(0.334332\pi\)
\(602\) −2.55064e7 −0.116912
\(603\) 1.20213e8i 0.548275i
\(604\) −7.06595e7 −0.320671
\(605\) 2.99308e8i 1.35161i
\(606\) 7.06896e7 0.317642
\(607\) 3.76162e8 1.68193 0.840966 0.541088i \(-0.181987\pi\)
0.840966 + 0.541088i \(0.181987\pi\)
\(608\) 5.28795e7i 0.235275i
\(609\) 8.11720e7i 0.359380i
\(610\) 1.70350e8 0.750505
\(611\) 4.48971e8 1.96831
\(612\) 6.84083e6i 0.0298438i
\(613\) 2.12207e8i 0.921250i −0.887595 0.460625i \(-0.847625\pi\)
0.887595 0.460625i \(-0.152375\pi\)
\(614\) −1.91770e8 −0.828468
\(615\) 1.48423e7i 0.0638083i
\(616\) 1.95644e8 0.836998
\(617\) 2.28882e8i 0.974443i −0.873278 0.487222i \(-0.838010\pi\)
0.873278 0.487222i \(-0.161990\pi\)
\(618\) 9.85468e7i 0.417520i
\(619\) 2.46253e8i 1.03827i −0.854693 0.519133i \(-0.826255\pi\)
0.854693 0.519133i \(-0.173745\pi\)
\(620\) 1.59515e8i 0.669307i
\(621\) −4.43143e7 1.26647e7i −0.185042 0.0528834i
\(622\) 1.42469e8 0.592036
\(623\) −1.50698e8 −0.623225
\(624\) −7.48805e7 −0.308187
\(625\) 2.95008e8 1.20835
\(626\) 1.92894e8i 0.786314i
\(627\) 4.40204e7 0.178588
\(628\) 2.19269e8i 0.885315i
\(629\) 3.54311e7 0.142375
\(630\) 5.13775e7 0.205471
\(631\) 7.39331e7i 0.294273i 0.989116 + 0.147137i \(0.0470057\pi\)
−0.989116 + 0.147137i \(0.952994\pi\)
\(632\) 6.35879e7i 0.251897i
\(633\) 8.52903e7 0.336270
\(634\) −1.54044e8 −0.604472
\(635\) 7.04417e8i 2.75111i
\(636\) 9.34569e7i 0.363279i
\(637\) −1.42422e8 −0.551010
\(638\) 1.30332e8i 0.501868i
\(639\) −1.23648e8 −0.473896
\(640\) 4.51814e8i 1.72353i
\(641\) 4.71156e8i 1.78892i −0.447149 0.894460i \(-0.647561\pi\)
0.447149 0.894460i \(-0.352439\pi\)
\(642\) 1.29710e8i 0.490194i
\(643\) 4.36101e8i 1.64042i −0.572065 0.820208i \(-0.693857\pi\)
0.572065 0.820208i \(-0.306143\pi\)
\(644\) 4.40171e7 1.54018e8i 0.164803 0.576652i
\(645\) 9.01466e7 0.335946
\(646\) 3.29141e6 0.0122091
\(647\) 2.21024e8 0.816067 0.408034 0.912967i \(-0.366215\pi\)
0.408034 + 0.912967i \(0.366215\pi\)
\(648\) 2.49420e7 0.0916657
\(649\) 4.17139e8i 1.52597i
\(650\) −3.44805e8 −1.25555
\(651\) 5.89647e7i 0.213722i
\(652\) 3.04343e8 1.09805
\(653\) −1.19383e8 −0.428749 −0.214374 0.976752i \(-0.568771\pi\)
−0.214374 + 0.976752i \(0.568771\pi\)
\(654\) 1.11868e8i 0.399919i
\(655\) 3.86192e8i 1.37429i
\(656\) 7.23052e6 0.0256129
\(657\) −9.56708e6 −0.0337352
\(658\) 1.50068e8i 0.526758i
\(659\) 3.11263e8i 1.08760i 0.839213 + 0.543802i \(0.183016\pi\)
−0.839213 + 0.543802i \(0.816984\pi\)
\(660\) −3.04483e8 −1.05908
\(661\) 1.51166e8i 0.523421i 0.965146 + 0.261710i \(0.0842865\pi\)
−0.965146 + 0.261710i \(0.915714\pi\)
\(662\) 1.82551e8 0.629231
\(663\) 2.51774e7i 0.0863913i
\(664\) 9.58078e7i 0.327263i
\(665\) 9.12413e7i 0.310261i
\(666\) 5.68859e7i 0.192567i
\(667\) 2.33002e8 + 6.65901e7i 0.785203 + 0.224405i
\(668\) −2.53787e8 −0.851411
\(669\) −1.57240e8 −0.525152
\(670\) 4.00067e8 1.33017
\(671\) 3.73184e8 1.23525
\(672\) 1.35203e8i 0.445532i
\(673\) 4.67833e6 0.0153478 0.00767389 0.999971i \(-0.497557\pi\)
0.00767389 + 0.999971i \(0.497557\pi\)
\(674\) 2.70889e8i 0.884733i
\(675\) −1.22394e8 −0.397970
\(676\) −1.77264e8 −0.573825
\(677\) 1.72661e8i 0.556454i 0.960515 + 0.278227i \(0.0897468\pi\)
−0.960515 + 0.278227i \(0.910253\pi\)
\(678\) 1.19714e8i 0.384110i
\(679\) 2.54529e8 0.813069
\(680\) −5.17005e7 −0.164425
\(681\) 3.08891e8i 0.978056i
\(682\) 9.46753e7i 0.298458i
\(683\) −4.96528e8 −1.55841 −0.779205 0.626769i \(-0.784377\pi\)
−0.779205 + 0.626769i \(0.784377\pi\)
\(684\) 1.95050e7i 0.0609507i
\(685\) 4.66235e8 1.45055
\(686\) 1.61216e8i 0.499387i
\(687\) 1.24307e8i 0.383377i
\(688\) 4.39153e7i 0.134850i
\(689\) 3.43964e8i 1.05161i
\(690\) 4.21480e7 1.47478e8i 0.128301 0.448931i
\(691\) 3.22850e8 0.978512 0.489256 0.872140i \(-0.337268\pi\)
0.489256 + 0.872140i \(0.337268\pi\)
\(692\) 1.07464e8 0.324299
\(693\) 1.12552e8 0.338185
\(694\) 2.58617e8 0.773710
\(695\) 2.90506e7i 0.0865369i
\(696\) −1.31144e8 −0.388973
\(697\) 2.43115e6i 0.00717981i
\(698\) 1.57259e7 0.0462435
\(699\) 8.26254e7 0.241926
\(700\) 4.25392e8i 1.24021i
\(701\) 7.25912e7i 0.210732i 0.994434 + 0.105366i \(0.0336014\pi\)
−0.994434 + 0.105366i \(0.966399\pi\)
\(702\) 4.04232e7 0.116847
\(703\) 1.01024e8 0.290775
\(704\) 2.85690e7i 0.0818798i
\(705\) 5.30382e8i 1.51364i
\(706\) 9.03824e7 0.256844
\(707\) 3.20977e8i 0.908271i
\(708\) −1.84830e8 −0.520803
\(709\) 3.61431e8i 1.01411i 0.861912 + 0.507057i \(0.169267\pi\)
−0.861912 + 0.507057i \(0.830733\pi\)
\(710\) 4.11498e8i 1.14972i
\(711\) 3.65815e7i 0.101778i
\(712\) 2.43473e8i 0.674544i
\(713\) −1.69256e8 4.83721e7i −0.466957 0.133452i
\(714\) 8.41554e6 0.0231200
\(715\) −1.12064e9 −3.06582
\(716\) 2.81438e8 0.766733
\(717\) −9.90357e7 −0.268679
\(718\) 1.57964e8i 0.426761i
\(719\) −3.68121e8 −0.990384 −0.495192 0.868784i \(-0.664902\pi\)
−0.495192 + 0.868784i \(0.664902\pi\)
\(720\) 8.84585e7i 0.236996i
\(721\) −4.47467e8 −1.19386
\(722\) −1.64387e8 −0.436773
\(723\) 1.45749e8i 0.385649i
\(724\) 2.43063e8i 0.640478i
\(725\) 6.43542e8 1.68874
\(726\) 7.87131e7 0.205701
\(727\) 4.93322e8i 1.28389i −0.766751 0.641944i \(-0.778128\pi\)
0.766751 0.641944i \(-0.221872\pi\)
\(728\) 3.19052e8i 0.826928i
\(729\) 1.43489e7 0.0370370
\(730\) 3.18392e7i 0.0818452i
\(731\) 1.47658e7 0.0378012
\(732\) 1.65355e8i 0.421583i
\(733\) 6.84962e8i 1.73922i 0.493738 + 0.869611i \(0.335630\pi\)
−0.493738 + 0.869611i \(0.664370\pi\)
\(734\) 1.40897e8i 0.356299i
\(735\) 1.68247e8i 0.423727i
\(736\) 3.88097e8 + 1.10915e8i 0.973435 + 0.278200i
\(737\) 8.76423e8 2.18933
\(738\) −3.90329e6 −0.00971096
\(739\) −2.60679e8 −0.645911 −0.322956 0.946414i \(-0.604676\pi\)
−0.322956 + 0.946414i \(0.604676\pi\)
\(740\) −6.98766e8 −1.72439
\(741\) 7.17875e7i 0.176439i
\(742\) −1.14970e8 −0.281432
\(743\) 6.77473e7i 0.165168i 0.996584 + 0.0825839i \(0.0263172\pi\)
−0.996584 + 0.0825839i \(0.973683\pi\)
\(744\) 9.52649e7 0.231320
\(745\) −1.13311e9 −2.74034
\(746\) 3.29008e8i 0.792484i
\(747\) 5.51173e7i 0.132229i
\(748\) −4.98737e7 −0.119170
\(749\) −5.88967e8 −1.40167
\(750\) 2.10353e8i 0.498613i
\(751\) 1.58709e8i 0.374698i 0.982293 + 0.187349i \(0.0599896\pi\)
−0.982293 + 0.187349i \(0.940010\pi\)
\(752\) −2.58378e8 −0.607578
\(753\) 4.59408e7i 0.107600i
\(754\) −2.12543e8 −0.495829
\(755\) 3.07216e8i 0.713843i
\(756\) 4.98708e7i 0.115420i
\(757\) 4.53416e8i 1.04522i −0.852571 0.522612i \(-0.824958\pi\)
0.852571 0.522612i \(-0.175042\pi\)
\(758\) 2.50171e8i 0.574421i
\(759\) 9.23330e7 3.23078e8i 0.211170 0.738893i
\(760\) −1.47412e8 −0.335809
\(761\) 1.89469e8 0.429917 0.214958 0.976623i \(-0.431038\pi\)
0.214958 + 0.976623i \(0.431038\pi\)
\(762\) −1.85250e8 −0.418691
\(763\) −5.07952e8 −1.14353
\(764\) 3.56101e8i 0.798534i
\(765\) −2.97428e7 −0.0664350
\(766\) 9.57836e7i 0.213110i
\(767\) −6.80261e8 −1.50761
\(768\) −1.34908e8 −0.297820
\(769\) 4.26727e8i 0.938363i −0.883102 0.469182i \(-0.844549\pi\)
0.883102 0.469182i \(-0.155451\pi\)
\(770\) 3.74573e8i 0.820472i
\(771\) 9.24953e6 0.0201816
\(772\) 6.80303e8 1.47860
\(773\) 3.03849e8i 0.657839i 0.944358 + 0.328919i \(0.106684\pi\)
−0.944358 + 0.328919i \(0.893316\pi\)
\(774\) 2.37071e7i 0.0511276i
\(775\) −4.67480e8 −1.00429
\(776\) 4.11223e8i 0.880020i
\(777\) 2.58299e8 0.550630
\(778\) 1.17797e8i 0.250148i
\(779\) 6.93186e6i 0.0146635i
\(780\) 4.96544e8i 1.04634i
\(781\) 9.01464e8i 1.89232i
\(782\) 6.90376e6 2.41566e7i 0.0144366 0.0505144i
\(783\) −7.54457e7 −0.157163
\(784\) 8.19624e7 0.170085