Properties

Label 1728.3.q.g.449.1
Level $1728$
Weight $3$
Character 1728.449
Analytic conductor $47.085$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1728.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(47.0845896815\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 449.1
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 1728.449
Dual form 1728.3.q.g.1601.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.05842 - 1.18843i) q^{5} +(4.05842 + 7.02939i) q^{7} +O(q^{10})\) \(q+(-2.05842 - 1.18843i) q^{5} +(4.05842 + 7.02939i) q^{7} +(-17.6168 + 10.1711i) q^{11} +(3.05842 - 5.29734i) q^{13} +17.9653i q^{17} -9.11684 q^{19} +(-29.0584 - 16.7769i) q^{23} +(-9.67527 - 16.7581i) q^{25} +(14.4090 - 8.31901i) q^{29} +(11.1753 - 19.3561i) q^{31} -19.2926i q^{35} +50.4674 q^{37} +(-29.9674 - 17.3017i) q^{41} +(11.5000 + 19.9186i) q^{43} +(33.1753 - 19.1537i) q^{47} +(-8.44158 + 14.6212i) q^{49} -19.0149i q^{53} +48.3505 q^{55} +(-2.96738 - 1.71322i) q^{59} +(-23.1753 - 40.1407i) q^{61} +(-12.5910 + 7.26944i) q^{65} +(-3.14947 + 5.45504i) q^{67} -35.9306i q^{71} +47.3505 q^{73} +(-142.993 - 82.5571i) q^{77} +(42.2921 + 73.2521i) q^{79} +(-33.1753 + 19.1537i) q^{83} +(21.3505 - 36.9802i) q^{85} -143.723i q^{89} +49.6495 q^{91} +(18.7663 + 10.8347i) q^{95} +(-40.3832 - 69.9457i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 9 q^{5} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 9 q^{5} - q^{7} - 36 q^{11} - 5 q^{13} - 2 q^{19} - 99 q^{23} + 13 q^{25} - 63 q^{29} - 7 q^{31} + 64 q^{37} + 18 q^{41} + 46 q^{43} + 81 q^{47} - 51 q^{49} + 90 q^{55} + 126 q^{59} - 41 q^{61} - 171 q^{65} - 116 q^{67} + 86 q^{73} - 279 q^{77} + 83 q^{79} - 81 q^{83} - 18 q^{85} + 302 q^{91} + 144 q^{95} - 196 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.05842 1.18843i −0.411684 0.237686i 0.279829 0.960050i \(-0.409722\pi\)
−0.691513 + 0.722364i \(0.743056\pi\)
\(6\) 0 0
\(7\) 4.05842 + 7.02939i 0.579775 + 1.00420i 0.995505 + 0.0947110i \(0.0301927\pi\)
−0.415730 + 0.909488i \(0.636474\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −17.6168 + 10.1711i −1.60153 + 0.924645i −0.610350 + 0.792132i \(0.708971\pi\)
−0.991181 + 0.132513i \(0.957695\pi\)
\(12\) 0 0
\(13\) 3.05842 5.29734i 0.235263 0.407488i −0.724086 0.689710i \(-0.757738\pi\)
0.959349 + 0.282222i \(0.0910714\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 17.9653i 1.05678i 0.849001 + 0.528392i \(0.177205\pi\)
−0.849001 + 0.528392i \(0.822795\pi\)
\(18\) 0 0
\(19\) −9.11684 −0.479834 −0.239917 0.970793i \(-0.577120\pi\)
−0.239917 + 0.970793i \(0.577120\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −29.0584 16.7769i −1.26341 0.729430i −0.289677 0.957124i \(-0.593548\pi\)
−0.973733 + 0.227695i \(0.926881\pi\)
\(24\) 0 0
\(25\) −9.67527 16.7581i −0.387011 0.670322i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 14.4090 8.31901i 0.496860 0.286863i −0.230556 0.973059i \(-0.574054\pi\)
0.727416 + 0.686197i \(0.240721\pi\)
\(30\) 0 0
\(31\) 11.1753 19.3561i 0.360492 0.624391i −0.627549 0.778577i \(-0.715942\pi\)
0.988042 + 0.154185i \(0.0492753\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 19.2926i 0.551217i
\(36\) 0 0
\(37\) 50.4674 1.36398 0.681992 0.731360i \(-0.261114\pi\)
0.681992 + 0.731360i \(0.261114\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −29.9674 17.3017i −0.730912 0.421992i 0.0878440 0.996134i \(-0.472002\pi\)
−0.818756 + 0.574142i \(0.805336\pi\)
\(42\) 0 0
\(43\) 11.5000 + 19.9186i 0.267442 + 0.463223i 0.968200 0.250176i \(-0.0804883\pi\)
−0.700759 + 0.713398i \(0.747155\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 33.1753 19.1537i 0.705857 0.407527i −0.103668 0.994612i \(-0.533058\pi\)
0.809525 + 0.587085i \(0.199725\pi\)
\(48\) 0 0
\(49\) −8.44158 + 14.6212i −0.172277 + 0.298393i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 19.0149i 0.358771i −0.983779 0.179386i \(-0.942589\pi\)
0.983779 0.179386i \(-0.0574110\pi\)
\(54\) 0 0
\(55\) 48.3505 0.879101
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.96738 1.71322i −0.0502945 0.0290375i 0.474642 0.880179i \(-0.342578\pi\)
−0.524936 + 0.851141i \(0.675911\pi\)
\(60\) 0 0
\(61\) −23.1753 40.1407i −0.379922 0.658045i 0.611128 0.791532i \(-0.290716\pi\)
−0.991051 + 0.133487i \(0.957383\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −12.5910 + 7.26944i −0.193708 + 0.111838i
\(66\) 0 0
\(67\) −3.14947 + 5.45504i −0.0470070 + 0.0814185i −0.888572 0.458738i \(-0.848302\pi\)
0.841565 + 0.540157i \(0.181635\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 35.9306i 0.506065i −0.967458 0.253033i \(-0.918572\pi\)
0.967458 0.253033i \(-0.0814280\pi\)
\(72\) 0 0
\(73\) 47.3505 0.648637 0.324319 0.945948i \(-0.394865\pi\)
0.324319 + 0.945948i \(0.394865\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −142.993 82.5571i −1.85705 1.07217i
\(78\) 0 0
\(79\) 42.2921 + 73.2521i 0.535343 + 0.927242i 0.999147 + 0.0413035i \(0.0131510\pi\)
−0.463803 + 0.885938i \(0.653516\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −33.1753 + 19.1537i −0.399702 + 0.230768i −0.686355 0.727266i \(-0.740791\pi\)
0.286653 + 0.958034i \(0.407457\pi\)
\(84\) 0 0
\(85\) 21.3505 36.9802i 0.251183 0.435061i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 143.723i 1.61486i −0.589963 0.807430i \(-0.700858\pi\)
0.589963 0.807430i \(-0.299142\pi\)
\(90\) 0 0
\(91\) 49.6495 0.545599
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 18.7663 + 10.8347i 0.197540 + 0.114050i
\(96\) 0 0
\(97\) −40.3832 69.9457i −0.416321 0.721089i 0.579245 0.815154i \(-0.303347\pi\)
−0.995566 + 0.0940641i \(0.970014\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 105.942 61.1654i 1.04893 0.605598i 0.126578 0.991957i \(-0.459601\pi\)
0.922349 + 0.386359i \(0.126267\pi\)
\(102\) 0 0
\(103\) −36.8247 + 63.7823i −0.357522 + 0.619246i −0.987546 0.157330i \(-0.949712\pi\)
0.630024 + 0.776575i \(0.283045\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 72.9108i 0.681410i −0.940170 0.340705i \(-0.889334\pi\)
0.940170 0.340705i \(-0.110666\pi\)
\(108\) 0 0
\(109\) −31.2989 −0.287146 −0.143573 0.989640i \(-0.545859\pi\)
−0.143573 + 0.989640i \(0.545859\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −16.2269 9.36858i −0.143601 0.0829078i 0.426478 0.904498i \(-0.359754\pi\)
−0.570079 + 0.821590i \(0.693087\pi\)
\(114\) 0 0
\(115\) 39.8763 + 69.0678i 0.346751 + 0.600590i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −126.285 + 72.9108i −1.06122 + 0.612696i
\(120\) 0 0
\(121\) 146.402 253.576i 1.20993 2.09567i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 105.415i 0.843320i
\(126\) 0 0
\(127\) −126.103 −0.992939 −0.496469 0.868054i \(-0.665370\pi\)
−0.496469 + 0.868054i \(0.665370\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 140.694 + 81.2299i 1.07400 + 0.620075i 0.929272 0.369396i \(-0.120435\pi\)
0.144730 + 0.989471i \(0.453769\pi\)
\(132\) 0 0
\(133\) −37.0000 64.0859i −0.278195 0.481849i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −90.3832 + 52.1827i −0.659731 + 0.380896i −0.792174 0.610295i \(-0.791051\pi\)
0.132443 + 0.991191i \(0.457718\pi\)
\(138\) 0 0
\(139\) 30.6168 53.0299i 0.220265 0.381510i −0.734623 0.678475i \(-0.762641\pi\)
0.954888 + 0.296965i \(0.0959744\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 124.430i 0.870139i
\(144\) 0 0
\(145\) −39.5463 −0.272733
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −128.344 74.0993i −0.861367 0.497311i 0.00310272 0.999995i \(-0.499012\pi\)
−0.864470 + 0.502685i \(0.832346\pi\)
\(150\) 0 0
\(151\) −127.526 220.881i −0.844542 1.46279i −0.886019 0.463650i \(-0.846540\pi\)
0.0414769 0.999139i \(-0.486794\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −46.0068 + 26.5621i −0.296818 + 0.171368i
\(156\) 0 0
\(157\) 146.227 253.272i 0.931381 1.61320i 0.150418 0.988622i \(-0.451938\pi\)
0.780963 0.624577i \(-0.214729\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 272.351i 1.69162i
\(162\) 0 0
\(163\) −93.5326 −0.573820 −0.286910 0.957958i \(-0.592628\pi\)
−0.286910 + 0.957958i \(0.592628\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 97.2269 + 56.1340i 0.582197 + 0.336131i 0.762006 0.647570i \(-0.224215\pi\)
−0.179809 + 0.983702i \(0.557548\pi\)
\(168\) 0 0
\(169\) 65.7921 + 113.955i 0.389302 + 0.674292i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −205.227 + 118.488i −1.18628 + 0.684900i −0.957460 0.288568i \(-0.906821\pi\)
−0.228823 + 0.973468i \(0.573488\pi\)
\(174\) 0 0
\(175\) 78.5326 136.022i 0.448758 0.777271i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 234.599i 1.31061i −0.755366 0.655304i \(-0.772541\pi\)
0.755366 0.655304i \(-0.227459\pi\)
\(180\) 0 0
\(181\) −221.636 −1.22451 −0.612254 0.790661i \(-0.709737\pi\)
−0.612254 + 0.790661i \(0.709737\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −103.883 59.9770i −0.561531 0.324200i
\(186\) 0 0
\(187\) −182.727 316.492i −0.977149 1.69247i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 130.162 75.1488i 0.681474 0.393449i −0.118936 0.992902i \(-0.537948\pi\)
0.800410 + 0.599452i \(0.204615\pi\)
\(192\) 0 0
\(193\) 24.5000 42.4352i 0.126943 0.219872i −0.795548 0.605891i \(-0.792817\pi\)
0.922491 + 0.386019i \(0.126150\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 276.827i 1.40521i −0.711579 0.702606i \(-0.752020\pi\)
0.711579 0.702606i \(-0.247980\pi\)
\(198\) 0 0
\(199\) −198.935 −0.999672 −0.499836 0.866120i \(-0.666606\pi\)
−0.499836 + 0.866120i \(0.666606\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 116.955 + 67.5241i 0.576134 + 0.332631i
\(204\) 0 0
\(205\) 41.1237 + 71.2283i 0.200603 + 0.347455i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 160.610 92.7282i 0.768469 0.443676i
\(210\) 0 0
\(211\) 47.0068 81.4182i 0.222781 0.385868i −0.732870 0.680368i \(-0.761820\pi\)
0.955651 + 0.294500i \(0.0951531\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 54.6678i 0.254269i
\(216\) 0 0
\(217\) 181.416 0.836017
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 95.1684 + 54.9455i 0.430626 + 0.248622i
\(222\) 0 0
\(223\) 77.8763 + 134.886i 0.349221 + 0.604869i 0.986111 0.166086i \(-0.0531128\pi\)
−0.636890 + 0.770955i \(0.719780\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −138.448 + 79.9332i −0.609905 + 0.352129i −0.772928 0.634493i \(-0.781209\pi\)
0.163023 + 0.986622i \(0.447875\pi\)
\(228\) 0 0
\(229\) −19.1237 + 33.1232i −0.0835095 + 0.144643i −0.904755 0.425932i \(-0.859946\pi\)
0.821246 + 0.570575i \(0.193280\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 157.490i 0.675921i 0.941160 + 0.337960i \(0.109737\pi\)
−0.941160 + 0.337960i \(0.890263\pi\)
\(234\) 0 0
\(235\) −91.0516 −0.387454
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 62.4742 + 36.0695i 0.261398 + 0.150918i 0.624972 0.780647i \(-0.285110\pi\)
−0.363574 + 0.931565i \(0.618444\pi\)
\(240\) 0 0
\(241\) −113.370 196.362i −0.470413 0.814779i 0.529015 0.848613i \(-0.322562\pi\)
−0.999427 + 0.0338337i \(0.989228\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 34.7527 20.0645i 0.141848 0.0818957i
\(246\) 0 0
\(247\) −27.8832 + 48.2950i −0.112887 + 0.195526i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 222.931i 0.888171i 0.895985 + 0.444085i \(0.146471\pi\)
−0.895985 + 0.444085i \(0.853529\pi\)
\(252\) 0 0
\(253\) 682.557 2.69785
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −92.2011 53.2323i −0.358759 0.207130i 0.309777 0.950809i \(-0.399746\pi\)
−0.668536 + 0.743680i \(0.733079\pi\)
\(258\) 0 0
\(259\) 204.818 + 354.755i 0.790803 + 1.36971i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −155.344 + 89.6877i −0.590660 + 0.341018i −0.765359 0.643604i \(-0.777438\pi\)
0.174698 + 0.984622i \(0.444105\pi\)
\(264\) 0 0
\(265\) −22.5979 + 39.1407i −0.0852750 + 0.147701i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 416.351i 1.54777i −0.633324 0.773887i \(-0.718310\pi\)
0.633324 0.773887i \(-0.281690\pi\)
\(270\) 0 0
\(271\) 396.907 1.46460 0.732302 0.680980i \(-0.238446\pi\)
0.732302 + 0.680980i \(0.238446\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 340.895 + 196.816i 1.23962 + 0.715695i
\(276\) 0 0
\(277\) −57.7731 100.066i −0.208567 0.361249i 0.742696 0.669629i \(-0.233547\pi\)
−0.951263 + 0.308379i \(0.900213\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −422.564 + 243.967i −1.50379 + 0.868211i −0.503795 + 0.863823i \(0.668063\pi\)
−0.999990 + 0.00438786i \(0.998603\pi\)
\(282\) 0 0
\(283\) −169.825 + 294.145i −0.600087 + 1.03938i 0.392720 + 0.919658i \(0.371534\pi\)
−0.992807 + 0.119724i \(0.961799\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 280.870i 0.978641i
\(288\) 0 0
\(289\) −33.7527 −0.116791
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 122.409 + 70.6728i 0.417778 + 0.241204i 0.694126 0.719853i \(-0.255791\pi\)
−0.276348 + 0.961058i \(0.589124\pi\)
\(294\) 0 0
\(295\) 4.07207 + 7.05304i 0.0138036 + 0.0239086i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −177.746 + 102.622i −0.594468 + 0.343216i
\(300\) 0 0
\(301\) −93.3437 + 161.676i −0.310112 + 0.537130i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 110.169i 0.361209i
\(306\) 0 0
\(307\) 120.649 0.392995 0.196498 0.980504i \(-0.437043\pi\)
0.196498 + 0.980504i \(0.437043\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 119.254 + 68.8514i 0.383454 + 0.221387i 0.679320 0.733842i \(-0.262275\pi\)
−0.295866 + 0.955229i \(0.595608\pi\)
\(312\) 0 0
\(313\) −129.266 223.896i −0.412991 0.715322i 0.582224 0.813029i \(-0.302183\pi\)
−0.995215 + 0.0977064i \(0.968849\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.7079 + 9.64630i −0.0527063 + 0.0304300i −0.526122 0.850409i \(-0.676354\pi\)
0.473415 + 0.880839i \(0.343021\pi\)
\(318\) 0 0
\(319\) −169.227 + 293.110i −0.530492 + 0.918839i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 163.787i 0.507081i
\(324\) 0 0
\(325\) −118.364 −0.364197
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 269.278 + 155.468i 0.818476 + 0.472547i
\(330\) 0 0
\(331\) −98.3953 170.426i −0.297267 0.514881i 0.678243 0.734838i \(-0.262742\pi\)
−0.975510 + 0.219957i \(0.929408\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.9659 7.48585i 0.0387041 0.0223458i
\(336\) 0 0
\(337\) −158.720 + 274.911i −0.470979 + 0.815760i −0.999449 0.0331921i \(-0.989433\pi\)
0.528470 + 0.848952i \(0.322766\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 454.659i 1.33331i
\(342\) 0 0
\(343\) 260.687 0.760022
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −537.407 310.272i −1.54872 0.894157i −0.998240 0.0593116i \(-0.981109\pi\)
−0.550485 0.834845i \(-0.685557\pi\)
\(348\) 0 0
\(349\) −189.512 328.245i −0.543015 0.940529i −0.998729 0.0504030i \(-0.983949\pi\)
0.455714 0.890126i \(-0.349384\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 213.514 123.272i 0.604855 0.349213i −0.166094 0.986110i \(-0.553116\pi\)
0.770949 + 0.636897i \(0.219782\pi\)
\(354\) 0 0
\(355\) −42.7011 + 73.9604i −0.120285 + 0.208339i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 572.791i 1.59552i −0.602976 0.797759i \(-0.706019\pi\)
0.602976 0.797759i \(-0.293981\pi\)
\(360\) 0 0
\(361\) −277.883 −0.769759
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −97.4674 56.2728i −0.267034 0.154172i
\(366\) 0 0
\(367\) 93.9279 + 162.688i 0.255934 + 0.443291i 0.965149 0.261701i \(-0.0842836\pi\)
−0.709214 + 0.704993i \(0.750950\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 133.663 77.1704i 0.360278 0.208007i
\(372\) 0 0
\(373\) 75.0584 130.005i 0.201229 0.348539i −0.747696 0.664042i \(-0.768840\pi\)
0.948925 + 0.315503i \(0.102173\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 101.772i 0.269953i
\(378\) 0 0
\(379\) 26.6222 0.0702432 0.0351216 0.999383i \(-0.488818\pi\)
0.0351216 + 0.999383i \(0.488818\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 444.966 + 256.901i 1.16179 + 0.670760i 0.951733 0.306929i \(-0.0993013\pi\)
0.210058 + 0.977689i \(0.432635\pi\)
\(384\) 0 0
\(385\) 196.227 + 339.875i 0.509680 + 0.882792i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −22.1616 + 12.7950i −0.0569707 + 0.0328921i −0.528215 0.849111i \(-0.677138\pi\)
0.471244 + 0.882003i \(0.343805\pi\)
\(390\) 0 0
\(391\) 301.402 522.044i 0.770849 1.33515i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 201.045i 0.508975i
\(396\) 0 0
\(397\) −388.804 −0.979356 −0.489678 0.871903i \(-0.662886\pi\)
−0.489678 + 0.871903i \(0.662886\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 34.0842 + 19.6785i 0.0849981 + 0.0490736i 0.541897 0.840445i \(-0.317706\pi\)
−0.456899 + 0.889519i \(0.651040\pi\)
\(402\) 0 0
\(403\) −68.3574 118.398i −0.169621 0.293793i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −889.076 + 513.308i −2.18446 + 1.26120i
\(408\) 0 0
\(409\) −86.7200 + 150.204i −0.212029 + 0.367246i −0.952350 0.305009i \(-0.901341\pi\)
0.740320 + 0.672255i \(0.234674\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 27.8118i 0.0673409i
\(414\) 0 0
\(415\) 91.0516 0.219401
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 115.031 + 66.4132i 0.274537 + 0.158504i 0.630948 0.775825i \(-0.282666\pi\)
−0.356411 + 0.934329i \(0.616000\pi\)
\(420\) 0 0
\(421\) 317.447 + 549.834i 0.754031 + 1.30602i 0.945855 + 0.324590i \(0.105226\pi\)
−0.191824 + 0.981429i \(0.561440\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 301.064 173.819i 0.708385 0.408986i
\(426\) 0 0
\(427\) 188.110 325.816i 0.440539 0.763035i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 602.424i 1.39774i −0.715251 0.698868i \(-0.753687\pi\)
0.715251 0.698868i \(-0.246313\pi\)
\(432\) 0 0
\(433\) 266.155 0.614676 0.307338 0.951600i \(-0.400562\pi\)
0.307338 + 0.951600i \(0.400562\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 264.921 + 152.952i 0.606227 + 0.350005i
\(438\) 0 0
\(439\) −250.330 433.584i −0.570228 0.987664i −0.996542 0.0830886i \(-0.973522\pi\)
0.426314 0.904575i \(-0.359812\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −261.098 + 150.745i −0.589386 + 0.340282i −0.764855 0.644203i \(-0.777189\pi\)
0.175469 + 0.984485i \(0.443856\pi\)
\(444\) 0 0
\(445\) −170.804 + 295.842i −0.383830 + 0.664813i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 565.321i 1.25907i 0.776973 + 0.629534i \(0.216754\pi\)
−0.776973 + 0.629534i \(0.783246\pi\)
\(450\) 0 0
\(451\) 703.907 1.56077
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −102.200 59.0049i −0.224614 0.129681i
\(456\) 0 0
\(457\) −26.1495 45.2922i −0.0572198 0.0991077i 0.835997 0.548735i \(-0.184890\pi\)
−0.893216 + 0.449627i \(0.851557\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 166.357 96.0465i 0.360862 0.208344i −0.308597 0.951193i \(-0.599859\pi\)
0.669459 + 0.742849i \(0.266526\pi\)
\(462\) 0 0
\(463\) −283.110 + 490.361i −0.611469 + 1.05909i 0.379524 + 0.925182i \(0.376088\pi\)
−0.990993 + 0.133913i \(0.957246\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 174.405i 0.373459i −0.982411 0.186729i \(-0.940211\pi\)
0.982411 0.186729i \(-0.0597888\pi\)
\(468\) 0 0
\(469\) −51.1275 −0.109014
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −405.187 233.935i −0.856633 0.494577i
\(474\) 0 0
\(475\) 88.2079 + 152.781i 0.185701 + 0.321643i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −473.784 + 273.539i −0.989110 + 0.571063i −0.905008 0.425394i \(-0.860135\pi\)
−0.0841020 + 0.996457i \(0.526802\pi\)
\(480\) 0 0
\(481\) 154.351 267.343i 0.320895 0.555807i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 191.970i 0.395815i
\(486\) 0 0
\(487\) −769.945 −1.58100 −0.790498 0.612464i \(-0.790178\pi\)
−0.790498 + 0.612464i \(0.790178\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −154.916 89.4407i −0.315511 0.182160i 0.333879 0.942616i \(-0.391642\pi\)
−0.649390 + 0.760456i \(0.724976\pi\)
\(492\) 0 0
\(493\) 149.454 + 258.861i 0.303152 + 0.525074i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 252.571 145.822i 0.508190 0.293404i
\(498\) 0 0
\(499\) −192.655 + 333.688i −0.386082 + 0.668713i −0.991919 0.126876i \(-0.959505\pi\)
0.605837 + 0.795589i \(0.292838\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 67.6630i 0.134519i 0.997736 + 0.0672594i \(0.0214255\pi\)
−0.997736 + 0.0672594i \(0.978574\pi\)
\(504\) 0 0
\(505\) −290.763 −0.575769
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 523.292 + 302.123i 1.02808 + 0.593562i 0.916434 0.400187i \(-0.131055\pi\)
0.111645 + 0.993748i \(0.464388\pi\)
\(510\) 0 0
\(511\) 192.168 + 332.846i 0.376063 + 0.651361i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 151.602 87.5273i 0.294372 0.169956i
\(516\) 0 0
\(517\) −389.629 + 674.857i −0.753634 + 1.30533i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 273.678i 0.525294i 0.964892 + 0.262647i \(0.0845954\pi\)
−0.964892 + 0.262647i \(0.915405\pi\)
\(522\) 0 0
\(523\) −687.402 −1.31434 −0.657172 0.753740i \(-0.728248\pi\)
−0.657172 + 0.753740i \(0.728248\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 347.739 + 200.767i 0.659846 + 0.380962i
\(528\) 0 0
\(529\) 298.428 + 516.892i 0.564136 + 0.977112i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −183.306 + 105.832i −0.343913 + 0.198558i
\(534\) 0 0
\(535\) −86.6495 + 150.081i −0.161962 + 0.280526i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 343.440i 0.637180i
\(540\) 0 0
\(541\) −664.543 −1.22836 −0.614180 0.789166i \(-0.710513\pi\)
−0.614180 + 0.789166i \(0.710513\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 64.4264 + 37.1966i 0.118214 + 0.0682507i
\(546\) 0 0
\(547\) 259.603 + 449.646i 0.474594 + 0.822022i 0.999577 0.0290914i \(-0.00926138\pi\)
−0.524982 + 0.851113i \(0.675928\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −131.364 + 75.8431i −0.238410 + 0.137646i
\(552\) 0 0
\(553\) −343.278 + 594.576i −0.620757 + 1.07518i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 422.648i 0.758794i 0.925234 + 0.379397i \(0.123869\pi\)
−0.925234 + 0.379397i \(0.876131\pi\)
\(558\) 0 0
\(559\) 140.687 0.251677
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 798.799 + 461.187i 1.41883 + 0.819159i 0.996196 0.0871428i \(-0.0277737\pi\)
0.422630 + 0.906302i \(0.361107\pi\)
\(564\) 0 0
\(565\) 22.2678 + 38.5690i 0.0394121 + 0.0682637i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 914.445 527.955i 1.60711 0.927865i 0.617097 0.786887i \(-0.288309\pi\)
0.990013 0.140978i \(-0.0450247\pi\)
\(570\) 0 0
\(571\) 401.524 695.460i 0.703195 1.21797i −0.264144 0.964483i \(-0.585089\pi\)
0.967339 0.253486i \(-0.0815772\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 649.283i 1.12919i
\(576\) 0 0
\(577\) −96.6495 −0.167503 −0.0837517 0.996487i \(-0.526690\pi\)
−0.0837517 + 0.996487i \(0.526690\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −269.278 155.468i −0.463474 0.267587i
\(582\) 0 0
\(583\) 193.402 + 334.982i 0.331736 + 0.574584i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −870.497 + 502.582i −1.48296 + 0.856187i −0.999813 0.0193528i \(-0.993839\pi\)
−0.483146 + 0.875540i \(0.660506\pi\)
\(588\) 0 0
\(589\) −101.883 + 176.467i −0.172976 + 0.299604i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 752.444i 1.26888i 0.772973 + 0.634439i \(0.218769\pi\)
−0.772973 + 0.634439i \(0.781231\pi\)
\(594\) 0 0
\(595\) 346.598 0.582517
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 24.0857 + 13.9059i 0.0402099 + 0.0232152i 0.519970 0.854184i \(-0.325943\pi\)
−0.479760 + 0.877400i \(0.659276\pi\)
\(600\) 0 0
\(601\) 475.356 + 823.340i 0.790942 + 1.36995i 0.925385 + 0.379030i \(0.123742\pi\)
−0.134443 + 0.990921i \(0.542925\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −602.715 + 347.978i −0.996223 + 0.575169i
\(606\) 0 0
\(607\) 161.306 279.390i 0.265743 0.460280i −0.702015 0.712162i \(-0.747716\pi\)
0.967758 + 0.251882i \(0.0810495\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 234.321i 0.383504i
\(612\) 0 0
\(613\) −138.206 −0.225459 −0.112730 0.993626i \(-0.535959\pi\)
−0.112730 + 0.993626i \(0.535959\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 682.084 + 393.802i 1.10548 + 0.638252i 0.937656 0.347564i \(-0.112991\pi\)
0.167829 + 0.985816i \(0.446324\pi\)
\(618\) 0 0
\(619\) −121.747 210.873i −0.196684 0.340667i 0.750767 0.660567i \(-0.229684\pi\)
−0.947451 + 0.319900i \(0.896351\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1010.28 583.287i 1.62164 0.936255i
\(624\) 0 0
\(625\) −116.603 + 201.963i −0.186565 + 0.323140i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 906.662i 1.44143i
\(630\) 0 0
\(631\) 111.924 0.177376 0.0886879 0.996059i \(-0.471733\pi\)
0.0886879 + 0.996059i \(0.471733\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 259.574 + 149.865i 0.408777 + 0.236008i
\(636\) 0 0
\(637\) 51.6358 + 89.4359i 0.0810609 + 0.140402i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −632.095 + 364.940i −0.986107 + 0.569329i −0.904108 0.427303i \(-0.859464\pi\)
−0.0819990 + 0.996632i \(0.526130\pi\)
\(642\) 0 0
\(643\) −288.500 + 499.697i −0.448678 + 0.777133i −0.998300 0.0582801i \(-0.981438\pi\)
0.549622 + 0.835413i \(0.314772\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 129.029i 0.199426i 0.995016 + 0.0997130i \(0.0317925\pi\)
−0.995016 + 0.0997130i \(0.968208\pi\)
\(648\) 0 0
\(649\) 69.7011 0.107398
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1026.62 + 592.717i 1.57215 + 0.907682i 0.995905 + 0.0904070i \(0.0288168\pi\)
0.576247 + 0.817275i \(0.304517\pi\)
\(654\) 0 0
\(655\) −193.072 334.411i −0.294767 0.510551i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 947.808 547.217i 1.43825 0.830375i 0.440524 0.897741i \(-0.354793\pi\)
0.997728 + 0.0673658i \(0.0214595\pi\)
\(660\) 0 0
\(661\) 604.876 1047.68i 0.915093 1.58499i 0.108327 0.994115i \(-0.465451\pi\)
0.806765 0.590872i \(-0.201216\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 175.888i 0.264493i
\(666\) 0 0
\(667\) −558.269 −0.836984
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 816.550 + 471.435i 1.21692 + 0.702586i
\(672\) 0 0
\(673\) −508.615 880.948i −0.755743 1.30899i −0.945004 0.327059i \(-0.893942\pi\)
0.189260 0.981927i \(-0.439391\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 689.890 398.308i 1.01904 0.588343i 0.105214 0.994450i \(-0.466447\pi\)
0.913826 + 0.406107i \(0.133114\pi\)
\(678\) 0 0
\(679\) 327.784 567.738i 0.482745 0.836139i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 400.485i 0.586361i −0.956057 0.293181i \(-0.905286\pi\)
0.956057 0.293181i \(-0.0947138\pi\)
\(684\) 0 0
\(685\) 248.062 0.362135
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −100.728 58.1556i −0.146195 0.0844057i
\(690\) 0 0
\(691\) −216.423 374.855i −0.313202 0.542482i 0.665852 0.746084i \(-0.268068\pi\)
−0.979054 + 0.203602i \(0.934735\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −126.045 + 72.7720i −0.181359 + 0.104708i
\(696\) 0 0
\(697\) 310.830 538.373i 0.445954 0.772415i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 65.4412i 0.0933541i −0.998910 0.0466770i \(-0.985137\pi\)
0.998910 0.0466770i \(-0.0148632\pi\)
\(702\) 0 0
\(703\) −460.103 −0.654485
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 859.911 + 496.470i 1.21628 + 0.702221i
\(708\) 0 0
\(709\) 100.461 + 174.003i 0.141693 + 0.245420i 0.928134 0.372245i \(-0.121412\pi\)
−0.786441 + 0.617665i \(0.788079\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −649.471 + 374.972i −0.910899 + 0.525908i
\(714\) 0 0
\(715\) 147.876 256.129i 0.206820 0.358223i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1062.98i 1.47841i −0.673478 0.739207i \(-0.735200\pi\)
0.673478 0.739207i \(-0.264800\pi\)
\(720\) 0 0
\(721\) −597.801 −0.829128
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −278.821 160.977i −0.384581 0.222038i
\(726\) 0 0
\(727\) −495.629 858.455i −0.681746 1.18082i −0.974448 0.224614i \(-0.927888\pi\)
0.292702 0.956204i \(-0.405446\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −357.844 + 206.601i −0.489526 + 0.282628i
\(732\) 0 0
\(733\) −590.134 + 1022.14i −0.805095 + 1.39446i 0.111133 + 0.993806i \(0.464552\pi\)
−0.916227 + 0.400659i \(0.868781\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 128.134i 0.173859i
\(738\) 0 0
\(739\) −599.351 −0.811029 −0.405515 0.914089i \(-0.632908\pi\)
−0.405515 + 0.914089i \(0.632908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −287.083 165.747i −0.386383 0.223078i 0.294209 0.955741i \(-0.404944\pi\)
−0.680592 + 0.732663i \(0.738277\pi\)
\(744\) 0 0
\(745\) 176.124 + 305.055i 0.236408 + 0.409470i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 512.519 295.903i 0.684271 0.395064i
\(750\) 0 0
\(751\) −76.0448 + 131.713i −0.101258 + 0.175384i −0.912203 0.409738i \(-0.865620\pi\)
0.810945 + 0.585122i \(0.198953\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 606.222i 0.802943i
\(756\) 0 0
\(757\) 1179.61 1.55827 0.779134 0.626858i \(-0.215659\pi\)
0.779134 + 0.626858i \(0.215659\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1162.58 + 671.214i 1.52770 + 0.882016i 0.999458 + 0.0329205i \(0.0104808\pi\)
0.528239 + 0.849096i \(0.322853\pi\)
\(762\) 0 0
\(763\) −127.024 220.013i −0.166480 0.288352i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −18.1510 + 10.4795i −0.0236649 + 0.0136629i
\(768\) 0 0
\(769\) −548.512 + 950.051i −0.713280 + 1.23544i 0.250339 + 0.968158i \(0.419458\pi\)
−0.963619 + 0.267279i \(0.913876\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1181.39i 1.52832i −0.645028 0.764159i \(-0.723154\pi\)
0.645028 0.764159i \(-0.276846\pi\)
\(774\) 0 0
\(775\) −432.495 −0.558058
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 273.208 + 157.737i 0.350716 + 0.202486i
\(780\) 0 0
\(781\) 365.454 + 632.984i 0.467931 + 0.810479i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −601.993 + 347.561i −0.766870 + 0.442753i
\(786\) 0 0
\(787\) −18.0311 + 31.2308i −0.0229112 + 0.0396834i −0.877254 0.480027i \(-0.840627\pi\)
0.854342 + 0.519710i \(0.173960\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 152.087i 0.192271i
\(792\) 0 0
\(793\) −283.519 −0.357527
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −115.618 66.7523i −0.145067 0.0837544i 0.425710 0.904860i \(-0.360024\pi\)
−0.570777 + 0.821105i \(0.693358\pi\)
\(798\) 0 0
\(799\) 344.103