Properties

Label 1152.2.w.a.1007.1
Level $1152$
Weight $2$
Character 1152.1007
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 1007.1
Character \(\chi\) \(=\) 1152.1007
Dual form 1152.2.w.a.143.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.32268 - 3.19322i) q^{5} +(2.32913 + 2.32913i) q^{7} +O(q^{10})\) \(q+(-1.32268 - 3.19322i) q^{5} +(2.32913 + 2.32913i) q^{7} +(1.47061 + 3.55036i) q^{11} +(4.49745 + 1.86291i) q^{13} -4.93452 q^{17} +(1.98599 - 4.79460i) q^{19} +(1.08935 + 1.08935i) q^{23} +(-4.91167 + 4.91167i) q^{25} +(3.43073 + 1.42105i) q^{29} +8.82364i q^{31} +(4.35675 - 10.5181i) q^{35} +(1.94208 - 0.804437i) q^{37} +(5.87486 - 5.87486i) q^{41} +(2.44320 - 1.01201i) q^{43} +1.61865i q^{47} +3.84969i q^{49} +(5.62320 - 2.32921i) q^{53} +(9.39195 - 9.39195i) q^{55} +(7.67495 - 3.17907i) q^{59} +(3.16892 - 7.65045i) q^{61} -16.8254i q^{65} +(-3.31324 - 1.37239i) q^{67} +(2.13686 - 2.13686i) q^{71} +(-1.81541 - 1.81541i) q^{73} +(-4.84401 + 11.6945i) q^{77} -1.42339 q^{79} +(1.04174 + 0.431504i) q^{83} +(6.52678 + 15.7570i) q^{85} +(0.708782 + 0.708782i) q^{89} +(6.13620 + 14.8141i) q^{91} -17.9370 q^{95} +12.2142 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{8}\right)\)

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
\(5\) −1.32268 3.19322i −0.591519 1.42805i −0.882035 0.471183i \(-0.843827\pi\)
0.290517 0.956870i \(-0.406173\pi\)
\(6\) 0 0
\(7\) 2.32913 + 2.32913i 0.880328 + 0.880328i 0.993568 0.113239i \(-0.0361227\pi\)
−0.113239 + 0.993568i \(0.536123\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.47061 + 3.55036i 0.443405 + 1.07047i 0.974746 + 0.223316i \(0.0716881\pi\)
−0.531341 + 0.847158i \(0.678312\pi\)
\(12\) 0 0
\(13\) 4.49745 + 1.86291i 1.24737 + 0.516677i 0.906010 0.423256i \(-0.139113\pi\)
0.341358 + 0.939933i \(0.389113\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.93452 −1.19680 −0.598399 0.801199i \(-0.704196\pi\)
−0.598399 + 0.801199i \(0.704196\pi\)
\(18\) 0 0
\(19\) 1.98599 4.79460i 0.455617 1.09996i −0.514538 0.857468i \(-0.672036\pi\)
0.970154 0.242488i \(-0.0779635\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.08935 + 1.08935i 0.227144 + 0.227144i 0.811499 0.584354i \(-0.198652\pi\)
−0.584354 + 0.811499i \(0.698652\pi\)
\(24\) 0 0
\(25\) −4.91167 + 4.91167i −0.982334 + 0.982334i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.43073 + 1.42105i 0.637070 + 0.263883i 0.677754 0.735289i \(-0.262954\pi\)
−0.0406838 + 0.999172i \(0.512954\pi\)
\(30\) 0 0
\(31\) 8.82364i 1.58477i 0.610019 + 0.792387i \(0.291162\pi\)
−0.610019 + 0.792387i \(0.708838\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.35675 10.5181i 0.736425 1.77789i
\(36\) 0 0
\(37\) 1.94208 0.804437i 0.319276 0.132249i −0.217289 0.976107i \(-0.569721\pi\)
0.536565 + 0.843859i \(0.319721\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.87486 5.87486i 0.917498 0.917498i −0.0793485 0.996847i \(-0.525284\pi\)
0.996847 + 0.0793485i \(0.0252840\pi\)
\(42\) 0 0
\(43\) 2.44320 1.01201i 0.372585 0.154330i −0.188530 0.982067i \(-0.560372\pi\)
0.561115 + 0.827738i \(0.310372\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.61865i 0.236105i 0.993007 + 0.118052i \(0.0376651\pi\)
−0.993007 + 0.118052i \(0.962335\pi\)
\(48\) 0 0
\(49\) 3.84969i 0.549956i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.62320 2.32921i 0.772407 0.319941i 0.0385598 0.999256i \(-0.487723\pi\)
0.733847 + 0.679315i \(0.237723\pi\)
\(54\) 0 0
\(55\) 9.39195 9.39195i 1.26641 1.26641i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7.67495 3.17907i 0.999193 0.413879i 0.177692 0.984086i \(-0.443137\pi\)
0.821501 + 0.570207i \(0.193137\pi\)
\(60\) 0 0
\(61\) 3.16892 7.65045i 0.405738 0.979539i −0.580508 0.814255i \(-0.697146\pi\)
0.986246 0.165284i \(-0.0528542\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 16.8254i 2.08693i
\(66\) 0 0
\(67\) −3.31324 1.37239i −0.404777 0.167664i 0.171000 0.985271i \(-0.445300\pi\)
−0.575777 + 0.817607i \(0.695300\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.13686 2.13686i 0.253599 0.253599i −0.568846 0.822444i \(-0.692610\pi\)
0.822444 + 0.568846i \(0.192610\pi\)
\(72\) 0 0
\(73\) −1.81541 1.81541i −0.212478 0.212478i 0.592841 0.805319i \(-0.298006\pi\)
−0.805319 + 0.592841i \(0.798006\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.84401 + 11.6945i −0.552027 + 1.33271i
\(78\) 0 0
\(79\) −1.42339 −0.160144 −0.0800721 0.996789i \(-0.525515\pi\)
−0.0800721 + 0.996789i \(0.525515\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.04174 + 0.431504i 0.114346 + 0.0473637i 0.439123 0.898427i \(-0.355289\pi\)
−0.324777 + 0.945791i \(0.605289\pi\)
\(84\) 0 0
\(85\) 6.52678 + 15.7570i 0.707928 + 1.70909i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.708782 + 0.708782i 0.0751308 + 0.0751308i 0.743674 0.668543i \(-0.233082\pi\)
−0.668543 + 0.743674i \(0.733082\pi\)
\(90\) 0 0
\(91\) 6.13620 + 14.8141i 0.643248 + 1.55294i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −17.9370 −1.84030
\(96\) 0 0
\(97\) 12.2142 1.24016 0.620082 0.784537i \(-0.287099\pi\)
0.620082 + 0.784537i \(0.287099\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.13564 + 14.8127i 0.610519 + 1.47392i 0.862432 + 0.506173i \(0.168940\pi\)
−0.251913 + 0.967750i \(0.581060\pi\)
\(102\) 0 0
\(103\) 9.45184 + 9.45184i 0.931318 + 0.931318i 0.997788 0.0664707i \(-0.0211739\pi\)
−0.0664707 + 0.997788i \(0.521174\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.93527 9.50057i −0.380436 0.918455i −0.991881 0.127168i \(-0.959411\pi\)
0.611445 0.791287i \(-0.290589\pi\)
\(108\) 0 0
\(109\) −10.8399 4.49003i −1.03827 0.430067i −0.202582 0.979265i \(-0.564933\pi\)
−0.835692 + 0.549198i \(0.814933\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.42620 −0.886742 −0.443371 0.896338i \(-0.646218\pi\)
−0.443371 + 0.896338i \(0.646218\pi\)
\(114\) 0 0
\(115\) 2.03767 4.91937i 0.190014 0.458734i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −11.4931 11.4931i −1.05357 1.05357i
\(120\) 0 0
\(121\) −2.66419 + 2.66419i −0.242199 + 0.242199i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.21449 + 2.57413i 0.555841 + 0.230237i
\(126\) 0 0
\(127\) 6.69360i 0.593961i −0.954884 0.296980i \(-0.904020\pi\)
0.954884 0.296980i \(-0.0959796\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.25325 + 12.6825i −0.458979 + 1.10807i 0.509833 + 0.860273i \(0.329707\pi\)
−0.968811 + 0.247799i \(0.920293\pi\)
\(132\) 0 0
\(133\) 15.7929 6.54162i 1.36941 0.567230i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.46480 + 3.46480i −0.296018 + 0.296018i −0.839452 0.543434i \(-0.817124\pi\)
0.543434 + 0.839452i \(0.317124\pi\)
\(138\) 0 0
\(139\) −15.2400 + 6.31262i −1.29264 + 0.535429i −0.919771 0.392455i \(-0.871626\pi\)
−0.372869 + 0.927884i \(0.621626\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 18.7072i 1.56437i
\(144\) 0 0
\(145\) 12.8347i 1.06586i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.66511 3.58921i 0.709873 0.294039i 0.00162119 0.999999i \(-0.499484\pi\)
0.708252 + 0.705959i \(0.249484\pi\)
\(150\) 0 0
\(151\) −16.6619 + 16.6619i −1.35592 + 1.35592i −0.477045 + 0.878879i \(0.658292\pi\)
−0.878879 + 0.477045i \(0.841708\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 28.1759 11.6708i 2.26314 0.937423i
\(156\) 0 0
\(157\) 3.37611 8.15066i 0.269443 0.650493i −0.730014 0.683432i \(-0.760487\pi\)
0.999457 + 0.0329386i \(0.0104866\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.07445i 0.399923i
\(162\) 0 0
\(163\) −14.2435 5.89984i −1.11564 0.462112i −0.252761 0.967529i \(-0.581339\pi\)
−0.862875 + 0.505417i \(0.831339\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.0550 + 10.0550i −0.778080 + 0.778080i −0.979504 0.201424i \(-0.935443\pi\)
0.201424 + 0.979504i \(0.435443\pi\)
\(168\) 0 0
\(169\) 7.56426 + 7.56426i 0.581866 + 0.581866i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.57483 + 8.63040i −0.271789 + 0.656157i −0.999560 0.0296634i \(-0.990556\pi\)
0.727771 + 0.685820i \(0.240556\pi\)
\(174\) 0 0
\(175\) −22.8798 −1.72955
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −6.36855 2.63794i −0.476008 0.197169i 0.131763 0.991281i \(-0.457936\pi\)
−0.607771 + 0.794112i \(0.707936\pi\)
\(180\) 0 0
\(181\) −2.04004 4.92510i −0.151635 0.366080i 0.829748 0.558138i \(-0.188484\pi\)
−0.981384 + 0.192058i \(0.938484\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.13749 5.13749i −0.377716 0.377716i
\(186\) 0 0
\(187\) −7.25674 17.5193i −0.530665 1.28114i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.91926 0.717732 0.358866 0.933389i \(-0.383163\pi\)
0.358866 + 0.933389i \(0.383163\pi\)
\(192\) 0 0
\(193\) −20.8089 −1.49785 −0.748927 0.662653i \(-0.769431\pi\)
−0.748927 + 0.662653i \(0.769431\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −2.99573 7.23234i −0.213437 0.515283i 0.780510 0.625143i \(-0.214960\pi\)
−0.993947 + 0.109861i \(0.964960\pi\)
\(198\) 0 0
\(199\) 16.3928 + 16.3928i 1.16205 + 1.16205i 0.984026 + 0.178027i \(0.0569713\pi\)
0.178027 + 0.984026i \(0.443029\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.68079 + 11.3004i 0.328527 + 0.793134i
\(204\) 0 0
\(205\) −26.5303 10.9892i −1.85295 0.767519i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 19.9431 1.37950
\(210\) 0 0
\(211\) 9.39938 22.6921i 0.647080 1.56219i −0.169861 0.985468i \(-0.554332\pi\)
0.816941 0.576721i \(-0.195668\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.46314 6.46314i −0.440782 0.440782i
\(216\) 0 0
\(217\) −20.5514 + 20.5514i −1.39512 + 1.39512i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −22.1928 9.19255i −1.49285 0.618358i
\(222\) 0 0
\(223\) 13.0361i 0.872961i −0.899714 0.436480i \(-0.856225\pi\)
0.899714 0.436480i \(-0.143775\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.970105 + 2.34204i −0.0643882 + 0.155447i −0.952798 0.303603i \(-0.901810\pi\)
0.888410 + 0.459050i \(0.151810\pi\)
\(228\) 0 0
\(229\) 10.5855 4.38467i 0.699512 0.289747i −0.00444500 0.999990i \(-0.501415\pi\)
0.703957 + 0.710243i \(0.251415\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −15.0433 + 15.0433i −0.985522 + 0.985522i −0.999897 0.0143751i \(-0.995424\pi\)
0.0143751 + 0.999897i \(0.495424\pi\)
\(234\) 0 0
\(235\) 5.16872 2.14095i 0.337170 0.139660i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 10.1723i 0.657989i 0.944332 + 0.328995i \(0.106710\pi\)
−0.944332 + 0.328995i \(0.893290\pi\)
\(240\) 0 0
\(241\) 20.6542i 1.33045i −0.746642 0.665227i \(-0.768335\pi\)
0.746642 0.665227i \(-0.231665\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 12.2929 5.09190i 0.785366 0.325309i
\(246\) 0 0
\(247\) 17.8638 17.8638i 1.13664 1.13664i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −18.5479 + 7.68280i −1.17073 + 0.484934i −0.881435 0.472304i \(-0.843422\pi\)
−0.289299 + 0.957239i \(0.593422\pi\)
\(252\) 0 0
\(253\) −2.26557 + 5.46957i −0.142435 + 0.343869i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.80823i 0.487064i −0.969893 0.243532i \(-0.921694\pi\)
0.969893 0.243532i \(-0.0783061\pi\)
\(258\) 0 0
\(259\) 6.39700 + 2.64972i 0.397490 + 0.164646i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 19.5761 19.5761i 1.20711 1.20711i 0.235158 0.971957i \(-0.424439\pi\)
0.971957 0.235158i \(-0.0755606\pi\)
\(264\) 0 0
\(265\) −14.8754 14.8754i −0.913786 0.913786i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.69145 4.08353i 0.103130 0.248977i −0.863889 0.503682i \(-0.831978\pi\)
0.967019 + 0.254705i \(0.0819783\pi\)
\(270\) 0 0
\(271\) −6.31185 −0.383418 −0.191709 0.981452i \(-0.561403\pi\)
−0.191709 + 0.981452i \(0.561403\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −24.6613 10.2151i −1.48713 0.615991i
\(276\) 0 0
\(277\) 7.53180 + 18.1834i 0.452542 + 1.09253i 0.971352 + 0.237644i \(0.0763751\pi\)
−0.518810 + 0.854889i \(0.673625\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 16.2957 + 16.2957i 0.972118 + 0.972118i 0.999622 0.0275040i \(-0.00875591\pi\)
−0.0275040 + 0.999622i \(0.508756\pi\)
\(282\) 0 0
\(283\) 3.93995 + 9.51187i 0.234206 + 0.565422i 0.996664 0.0816150i \(-0.0260078\pi\)
−0.762458 + 0.647037i \(0.776008\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 27.3666 1.61540
\(288\) 0 0
\(289\) 7.34950 0.432324
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5.02532 + 12.1322i 0.293582 + 0.708770i 1.00000 0.000974464i \(0.000310182\pi\)
−0.706417 + 0.707795i \(0.749690\pi\)
\(294\) 0 0
\(295\) −20.3029 20.3029i −1.18208 1.18208i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.86993 + 6.92862i 0.165972 + 0.400693i
\(300\) 0 0
\(301\) 8.04764 + 3.33344i 0.463858 + 0.192136i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −28.6210 −1.63884
\(306\) 0 0
\(307\) 5.19514 12.5422i 0.296502 0.715820i −0.703485 0.710710i \(-0.748374\pi\)
0.999987 0.00510930i \(-0.00162635\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.27753 + 5.27753i 0.299261 + 0.299261i 0.840725 0.541463i \(-0.182129\pi\)
−0.541463 + 0.840725i \(0.682129\pi\)
\(312\) 0 0
\(313\) −18.5402 + 18.5402i −1.04795 + 1.04795i −0.0491617 + 0.998791i \(0.515655\pi\)
−0.998791 + 0.0491617i \(0.984345\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.2977 4.67965i −0.634540 0.262835i 0.0421404 0.999112i \(-0.486582\pi\)
−0.676681 + 0.736276i \(0.736582\pi\)
\(318\) 0 0
\(319\) 14.2701i 0.798973i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −9.79989 + 23.6590i −0.545281 + 1.31642i
\(324\) 0 0
\(325\) −31.2400 + 12.9400i −1.73288 + 0.717783i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.77005 + 3.77005i −0.207850 + 0.207850i
\(330\) 0 0
\(331\) −26.3575 + 10.9176i −1.44874 + 0.600087i −0.961899 0.273405i \(-0.911850\pi\)
−0.486839 + 0.873492i \(0.661850\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.3952i 0.677219i
\(336\) 0 0
\(337\) 8.96574i 0.488395i −0.969726 0.244197i \(-0.921475\pi\)
0.969726 0.244197i \(-0.0785245\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −31.3271 + 12.9761i −1.69646 + 0.702696i
\(342\) 0 0
\(343\) 7.33747 7.33747i 0.396186 0.396186i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.0344829 + 0.0142833i −0.00185114 + 0.000766767i −0.383609 0.923496i \(-0.625319\pi\)
0.381758 + 0.924262i \(0.375319\pi\)
\(348\) 0 0
\(349\) −1.36920 + 3.30553i −0.0732914 + 0.176941i −0.956280 0.292454i \(-0.905528\pi\)
0.882988 + 0.469395i \(0.155528\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.2214i 0.544031i −0.962293 0.272016i \(-0.912310\pi\)
0.962293 0.272016i \(-0.0876902\pi\)
\(354\) 0 0
\(355\) −9.64984 3.99710i −0.512161 0.212144i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −21.7022 + 21.7022i −1.14540 + 1.14540i −0.157953 + 0.987447i \(0.550489\pi\)
−0.987447 + 0.157953i \(0.949511\pi\)
\(360\) 0 0
\(361\) −5.60898 5.60898i −0.295210 0.295210i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.39581 + 8.19821i −0.177745 + 0.429114i
\(366\) 0 0
\(367\) 2.68336 0.140070 0.0700350 0.997545i \(-0.477689\pi\)
0.0700350 + 0.997545i \(0.477689\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 18.5222 + 7.67215i 0.961625 + 0.398318i
\(372\) 0 0
\(373\) −3.60763 8.70959i −0.186796 0.450965i 0.802543 0.596594i \(-0.203480\pi\)
−0.989339 + 0.145628i \(0.953480\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.7822 + 12.7822i 0.658318 + 0.658318i
\(378\) 0 0
\(379\) 7.30210 + 17.6288i 0.375083 + 0.905532i 0.992872 + 0.119187i \(0.0380289\pi\)
−0.617788 + 0.786344i \(0.711971\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −17.7992 −0.909497 −0.454748 0.890620i \(-0.650271\pi\)
−0.454748 + 0.890620i \(0.650271\pi\)
\(384\) 0 0
\(385\) 43.7502 2.22971
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −10.4216 25.1599i −0.528396 1.27566i −0.932574 0.360979i \(-0.882442\pi\)
0.404178 0.914680i \(-0.367558\pi\)
\(390\) 0 0
\(391\) −5.37540 5.37540i −0.271846 0.271846i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.88269 + 4.54521i 0.0947284 + 0.228695i
\(396\) 0 0
\(397\) −6.35478 2.63224i −0.318938 0.132108i 0.217471 0.976067i \(-0.430219\pi\)
−0.536408 + 0.843959i \(0.680219\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14.1764 −0.707935 −0.353968 0.935258i \(-0.615168\pi\)
−0.353968 + 0.935258i \(0.615168\pi\)
\(402\) 0 0
\(403\) −16.4376 + 39.6839i −0.818816 + 1.97680i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.71208 + 5.71208i 0.283137 + 0.283137i
\(408\) 0 0
\(409\) 23.0001 23.0001i 1.13728 1.13728i 0.148347 0.988935i \(-0.452605\pi\)
0.988935 0.148347i \(-0.0473951\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 25.2804 + 10.4715i 1.24397 + 0.515268i
\(414\) 0 0
\(415\) 3.89725i 0.191309i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.33096 8.04166i 0.162728 0.392861i −0.821392 0.570364i \(-0.806802\pi\)
0.984120 + 0.177503i \(0.0568021\pi\)
\(420\) 0 0
\(421\) −6.91049 + 2.86242i −0.336797 + 0.139506i −0.544671 0.838650i \(-0.683346\pi\)
0.207874 + 0.978156i \(0.433346\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 24.2367 24.2367i 1.17565 1.17565i
\(426\) 0 0
\(427\) 25.1997 10.4381i 1.21950 0.505133i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 18.8488i 0.907917i −0.891023 0.453958i \(-0.850011\pi\)
0.891023 0.453958i \(-0.149989\pi\)
\(432\) 0 0
\(433\) 32.1408i 1.54459i 0.635264 + 0.772295i \(0.280891\pi\)
−0.635264 + 0.772295i \(0.719109\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.38640 3.05955i 0.353339 0.146358i
\(438\) 0 0
\(439\) 19.4979 19.4979i 0.930584 0.930584i −0.0671583 0.997742i \(-0.521393\pi\)
0.997742 + 0.0671583i \(0.0213933\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.4270 + 5.14742i −0.590424 + 0.244561i −0.657833 0.753164i \(-0.728527\pi\)
0.0674092 + 0.997725i \(0.478527\pi\)
\(444\) 0 0
\(445\) 1.32581 3.20079i 0.0628494 0.151732i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 16.8751i 0.796387i 0.917301 + 0.398194i \(0.130363\pi\)
−0.917301 + 0.398194i \(0.869637\pi\)
\(450\) 0 0
\(451\) 29.4975 + 12.2182i 1.38898 + 0.575335i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 39.1885 39.1885i 1.83719 1.83719i
\(456\) 0 0
\(457\) 19.1686 + 19.1686i 0.896670 + 0.896670i 0.995140 0.0984696i \(-0.0313947\pi\)
−0.0984696 + 0.995140i \(0.531395\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.32718 15.2752i 0.294686 0.711436i −0.705311 0.708898i \(-0.749192\pi\)
0.999997 0.00253708i \(-0.000807579\pi\)
\(462\) 0 0
\(463\) −32.5710 −1.51370 −0.756852 0.653587i \(-0.773263\pi\)
−0.756852 + 0.653587i \(0.773263\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.84384 2.42060i −0.270420 0.112012i 0.243353 0.969938i \(-0.421753\pi\)
−0.513773 + 0.857926i \(0.671753\pi\)
\(468\) 0 0
\(469\) −4.52050 10.9134i −0.208737 0.503936i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.18598 + 7.18598i 0.330412 + 0.330412i
\(474\) 0 0
\(475\) 13.7950 + 33.3040i 0.632956 + 1.52809i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.92963 −0.362314 −0.181157 0.983454i \(-0.557984\pi\)
−0.181157 + 0.983454i \(0.557984\pi\)
\(480\) 0 0
\(481\) 10.2330 0.466585
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.1554 39.0027i −0.733581 1.77102i
\(486\) 0 0
\(487\) −10.7904 10.7904i −0.488961 0.488961i 0.419017 0.907978i \(-0.362375\pi\)
−0.907978 + 0.419017i \(0.862375\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.68219 4.06116i −0.0759160 0.183277i 0.881366 0.472435i \(-0.156625\pi\)
−0.957282 + 0.289158i \(0.906625\pi\)
\(492\) 0 0
\(493\) −16.9290 7.01222i −0.762443 0.315814i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.95405 0.446500
\(498\) 0 0
\(499\) 15.0645 36.3690i 0.674380 1.62810i −0.0997053 0.995017i \(-0.531790\pi\)
0.774086 0.633081i \(-0.218210\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.41533 + 8.41533i 0.375221 + 0.375221i 0.869375 0.494153i \(-0.164522\pi\)
−0.494153 + 0.869375i \(0.664522\pi\)
\(504\) 0 0
\(505\) 39.1849 39.1849i 1.74371 1.74371i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −16.2989 6.75122i −0.722436 0.299243i −0.00899639 0.999960i \(-0.502864\pi\)
−0.713440 + 0.700717i \(0.752864\pi\)
\(510\) 0 0
\(511\) 8.45666i 0.374100i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 17.6801 42.6836i 0.779079 1.88086i
\(516\) 0 0
\(517\) −5.74680 + 2.38040i −0.252744 + 0.104690i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.7934 17.7934i 0.779542 0.779542i −0.200211 0.979753i \(-0.564163\pi\)
0.979753 + 0.200211i \(0.0641628\pi\)
\(522\) 0 0
\(523\) −10.5763 + 4.38083i −0.462468 + 0.191560i −0.601737 0.798694i \(-0.705525\pi\)
0.139270 + 0.990254i \(0.455525\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 43.5405i 1.89665i
\(528\) 0 0
\(529\) 20.6267i 0.896811i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 37.3662 15.4776i 1.61851 0.670408i
\(534\) 0 0
\(535\) −25.1324 + 25.1324i −1.08657 + 1.08657i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −13.6678 + 5.66139i −0.588714 + 0.243853i
\(540\) 0 0
\(541\) −0.161261 + 0.389318i −0.00693315 + 0.0167381i −0.927308 0.374299i \(-0.877883\pi\)
0.920375 + 0.391037i \(0.127883\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 40.5531i 1.73710i
\(546\) 0 0
\(547\) −2.37145 0.982285i −0.101396 0.0419995i 0.331409 0.943487i \(-0.392476\pi\)
−0.432805 + 0.901488i \(0.642476\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 13.6268 13.6268i 0.580519 0.580519i
\(552\) 0 0
\(553\) −3.31527 3.31527i −0.140980 0.140980i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.975580 2.35526i 0.0413366 0.0997955i −0.901863 0.432023i \(-0.857800\pi\)
0.943199 + 0.332227i \(0.107800\pi\)
\(558\) 0 0
\(559\) 12.8735 0.544489
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.62858 3.98829i −0.405796 0.168086i 0.170443 0.985368i \(-0.445480\pi\)
−0.576239 + 0.817281i \(0.695480\pi\)
\(564\) 0 0
\(565\) 12.4678 + 30.1000i 0.524525 + 1.26631i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.8578 + 18.8578i 0.790559 + 0.790559i 0.981585 0.191026i \(-0.0611814\pi\)
−0.191026 + 0.981585i \(0.561181\pi\)
\(570\) 0 0
\(571\) −2.27949 5.50317i −0.0953936 0.230300i 0.868979 0.494850i \(-0.164777\pi\)
−0.964372 + 0.264549i \(0.914777\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −10.7010 −0.446263
\(576\) 0 0
\(577\) −2.80878 −0.116931 −0.0584655 0.998289i \(-0.518621\pi\)
−0.0584655 + 0.998289i \(0.518621\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.42132 + 3.43138i 0.0589665 + 0.142358i
\(582\) 0 0
\(583\) 16.5390 + 16.5390i 0.684977 + 0.684977i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 10.2932 + 24.8501i 0.424848 + 1.02567i 0.980898 + 0.194524i \(0.0623162\pi\)
−0.556050 + 0.831149i \(0.687684\pi\)
\(588\) 0 0
\(589\) 42.3058 + 17.5236i 1.74318 + 0.722049i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 40.3079 1.65525 0.827624 0.561283i \(-0.189692\pi\)
0.827624 + 0.561283i \(0.189692\pi\)
\(594\) 0 0
\(595\) −21.4985 + 51.9019i −0.881351 + 2.12777i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −12.4557 12.4557i −0.508926 0.508926i 0.405271 0.914197i \(-0.367177\pi\)
−0.914197 + 0.405271i \(0.867177\pi\)
\(600\) 0 0
\(601\) 6.85263 6.85263i 0.279525 0.279525i −0.553395 0.832919i \(-0.686668\pi\)
0.832919 + 0.553395i \(0.186668\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 12.0312 + 4.98349i 0.489139 + 0.202608i
\(606\) 0 0
\(607\) 5.54311i 0.224988i 0.993652 + 0.112494i \(0.0358839\pi\)
−0.993652 + 0.112494i \(0.964116\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −3.01540 + 7.27981i −0.121990 + 0.294510i
\(612\) 0 0
\(613\) 1.34403 0.556714i 0.0542847 0.0224855i −0.355376 0.934723i \(-0.615647\pi\)
0.409661 + 0.912238i \(0.365647\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −27.3420 + 27.3420i −1.10075 + 1.10075i −0.106429 + 0.994320i \(0.533942\pi\)
−0.994320 + 0.106429i \(0.966058\pi\)
\(618\) 0 0
\(619\) 27.2304 11.2792i 1.09448 0.453350i 0.238916 0.971040i \(-0.423208\pi\)
0.855568 + 0.517690i \(0.173208\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.30169i 0.132280i
\(624\) 0 0
\(625\) 11.4818i 0.459270i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.58325 + 3.96951i −0.382109 + 0.158275i
\(630\) 0 0
\(631\) 6.25063 6.25063i 0.248834 0.248834i −0.571658 0.820492i \(-0.693700\pi\)
0.820492 + 0.571658i \(0.193700\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −21.3741 + 8.85346i −0.848207 + 0.351339i
\(636\) 0 0
\(637\) −7.17161 + 17.3138i −0.284150 + 0.685998i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 13.6953i 0.540934i 0.962729 + 0.270467i \(0.0871781\pi\)
−0.962729 + 0.270467i \(0.912822\pi\)
\(642\) 0 0
\(643\) −17.4338 7.22130i −0.687520 0.284780i 0.0114464 0.999934i \(-0.496356\pi\)
−0.698967 + 0.715154i \(0.746356\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.78525 2.78525i 0.109500 0.109500i −0.650234 0.759734i \(-0.725329\pi\)
0.759734 + 0.650234i \(0.225329\pi\)
\(648\) 0 0
\(649\) 22.5737 + 22.5737i 0.886094 + 0.886094i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.42546 + 8.26978i −0.134048 + 0.323622i −0.976623 0.214957i \(-0.931039\pi\)
0.842575 + 0.538579i \(0.181039\pi\)
\(654\) 0 0
\(655\) 47.4463 1.85388
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −44.7390 18.5315i −1.74278 0.721885i −0.998542 0.0539756i \(-0.982811\pi\)
−0.744243 0.667909i \(-0.767189\pi\)
\(660\) 0 0
\(661\) −5.04994 12.1916i −0.196420 0.474200i 0.794727 0.606967i \(-0.207614\pi\)
−0.991147 + 0.132767i \(0.957614\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −41.7777 41.7777i −1.62007 1.62007i
\(666\) 0 0
\(667\) 2.18923 + 5.28526i 0.0847672 + 0.204646i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 31.8221 1.22848
\(672\) 0 0
\(673\) −38.7728 −1.49458 −0.747291 0.664497i \(-0.768646\pi\)
−0.747291 + 0.664497i \(0.768646\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.27320 7.90221i −0.125799 0.303706i 0.848415 0.529332i \(-0.177557\pi\)
−0.974214 + 0.225626i \(0.927557\pi\)
\(678\) 0 0
\(679\) 28.4485 + 28.4485i 1.09175 + 1.09175i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −19.5003 47.0778i −0.746157 1.80138i −0.578769 0.815491i \(-0.696467\pi\)
−0.167388 0.985891i \(-0.553533\pi\)
\(684\) 0 0
\(685\) 15.6467 + 6.48108i 0.597830 + 0.247629i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 29.6292 1.12878
\(690\) 0 0
\(691\) −5.45976 + 13.1810i −0.207699 + 0.501430i −0.993060 0.117608i \(-0.962477\pi\)
0.785361 + 0.619038i \(0.212477\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 40.3152 + 40.3152i 1.52924 + 1.52924i
\(696\) 0 0
\(697\) −28.9896 + 28.9896i −1.09806 + 1.09806i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6.06309 2.51141i −0.229000 0.0948547i 0.265233 0.964184i \(-0.414551\pi\)
−0.494233 + 0.869330i \(0.664551\pi\)
\(702\) 0 0
\(703\) 10.9091i 0.411445i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.2101 + 48.7915i −0.760079 + 1.83499i
\(708\) 0 0
\(709\) 17.0266 7.05266i 0.639448 0.264868i −0.0393132 0.999227i \(-0.512517\pi\)
0.678762 + 0.734359i \(0.262517\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −9.61199 + 9.61199i −0.359972 + 0.359972i
\(714\) 0 0
\(715\) 59.7362 24.7435i 2.23401 0.925356i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 40.0842i 1.49489i −0.664324 0.747445i \(-0.731281\pi\)
0.664324 0.747445i \(-0.268719\pi\)
\(720\) 0 0
\(721\) 44.0291i 1.63973i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −23.8303 + 9.87085i −0.885036 + 0.366594i
\(726\) 0 0
\(727\) −17.6896 + 17.6896i −0.656073 + 0.656073i −0.954448 0.298376i \(-0.903555\pi\)
0.298376 + 0.954448i \(0.403555\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.0560 + 4.99378i −0.445909 + 0.184701i
\(732\) 0 0
\(733\) −2.68410 + 6.47999i −0.0991395 + 0.239344i −0.965666 0.259787i \(-0.916348\pi\)
0.866526 + 0.499131i \(0.166348\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.7814i 0.507646i
\(738\) 0 0
\(739\) 8.93406 + 3.70061i 0.328645 + 0.136129i 0.540904 0.841084i \(-0.318082\pi\)
−0.212259 + 0.977213i \(0.568082\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −32.3436 + 32.3436i −1.18657 + 1.18657i −0.208565 + 0.978009i \(0.566879\pi\)
−0.978009 + 0.208565i \(0.933121\pi\)
\(744\) 0 0
\(745\) −22.9223 22.9223i −0.839807 0.839807i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12.9623 31.2938i 0.473633 1.14345i
\(750\) 0 0
\(751\) 34.4295 1.25635 0.628175 0.778072i \(-0.283802\pi\)
0.628175 + 0.778072i \(0.283802\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 75.2433 + 31.1668i 2.73839 + 1.13428i
\(756\) 0 0
\(757\) 2.48272 + 5.99382i 0.0902361 + 0.217849i 0.962554 0.271090i \(-0.0873840\pi\)
−0.872318 + 0.488939i \(0.837384\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −4.40886 4.40886i −0.159821 0.159821i 0.622666 0.782488i \(-0.286049\pi\)
−0.782488 + 0.622666i \(0.786049\pi\)
\(762\) 0 0
\(763\) −14.7897 35.7054i −0.535422 1.29262i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 40.4400 1.46020
\(768\) 0 0
\(769\) −16.9600 −0.611592 −0.305796 0.952097i \(-0.598923\pi\)
−0.305796 + 0.952097i \(0.598923\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 12.5028 + 30.1845i 0.449695 + 1.08566i 0.972436 + 0.233169i \(0.0749096\pi\)
−0.522741 + 0.852492i \(0.675090\pi\)
\(774\) 0 0
\(775\) −43.3388 43.3388i −1.55678 1.55678i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16.5002 39.8350i −0.591180 1.42724i
\(780\) 0 0
\(781\) 10.7291 + 4.44414i 0.383917 + 0.159024i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −30.4924 −1.08832
\(786\) 0 0
\(787\) −0.0428254 + 0.103390i −0.00152656 + 0.00368545i −0.924641 0.380840i \(-0.875635\pi\)
0.923114 + 0.384525i \(0.125635\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −21.9548 21.9548i −0.780624 0.780624i
\(792\) 0 0
\(793\) 28.5041 28.5041i 1.01221 1.01221i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −32.6670 13.5311i −1.15712 0.479297i −0.280208 0.959939i \(-0.590403\pi\)
−0.876917 + 0.480642i \(0.840403\pi\)
\(798\) 0 0
\(799\) 7.98728i 0.282569i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.77560 9.11512i 0.133238 0.321665i
\(804\) 0 0
\(805\) 16.2039 6.71186i 0.571111