Properties

Label 432.2.be.b.239.4
Level $432$
Weight $2$
Character 432.239
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 239.4
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.b.47.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.721706 - 1.57453i) q^{3} +(0.976679 + 0.172215i) q^{5} +(3.12803 + 3.72784i) q^{7} +(-1.95828 - 2.27269i) q^{9} +O(q^{10})\) \(q+(0.721706 - 1.57453i) q^{3} +(0.976679 + 0.172215i) q^{5} +(3.12803 + 3.72784i) q^{7} +(-1.95828 - 2.27269i) q^{9} +(0.961816 + 5.45473i) q^{11} +(2.65607 - 0.966729i) q^{13} +(0.976032 - 1.41352i) q^{15} +(-0.517267 - 0.298644i) q^{17} +(0.141252 - 0.0815519i) q^{19} +(8.12712 - 2.23477i) q^{21} +(-5.35924 - 4.49693i) q^{23} +(-3.77422 - 1.37370i) q^{25} +(-4.99172 + 1.44316i) q^{27} +(0.610528 - 1.67741i) q^{29} +(3.26328 - 3.88903i) q^{31} +(9.28277 + 2.42230i) q^{33} +(2.41309 + 4.17960i) q^{35} +(0.726277 - 1.25795i) q^{37} +(0.394755 - 4.87975i) q^{39} +(-3.84382 - 10.5608i) q^{41} +(6.11082 - 1.07750i) q^{43} +(-1.52122 - 2.55694i) q^{45} +(-6.37666 + 5.35065i) q^{47} +(-2.89670 + 16.4280i) q^{49} +(-0.843539 + 0.598919i) q^{51} -8.40465i q^{53} +5.49316i q^{55} +(-0.0264635 - 0.281262i) q^{57} +(-1.35597 + 7.69008i) q^{59} +(-3.16592 + 2.65652i) q^{61} +(2.34667 - 14.4092i) q^{63} +(2.76061 - 0.486770i) q^{65} +(2.02334 + 5.55908i) q^{67} +(-10.9483 + 5.19281i) q^{69} +(1.86491 - 3.23013i) q^{71} +(3.05997 + 5.30003i) q^{73} +(-4.88681 + 4.95121i) q^{75} +(-17.3258 + 20.6481i) q^{77} +(4.05391 - 11.1380i) q^{79} +(-1.33026 + 8.90115i) q^{81} +(-9.04948 - 3.29374i) q^{83} +(-0.453773 - 0.380761i) q^{85} +(-2.20051 - 2.17189i) q^{87} +(-1.45033 + 0.837348i) q^{89} +(11.9121 + 6.87744i) q^{91} +(-3.76826 - 7.94486i) q^{93} +(0.152002 - 0.0553244i) q^{95} +(-2.34010 - 13.2714i) q^{97} +(10.5134 - 12.8678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\)

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
\(3\) 0.721706 1.57453i 0.416677 0.909055i
\(4\) 0 0
\(5\) 0.976679 + 0.172215i 0.436784 + 0.0770169i 0.387717 0.921779i \(-0.373264\pi\)
0.0490676 + 0.998795i \(0.484375\pi\)
\(6\) 0 0
\(7\) 3.12803 + 3.72784i 1.18229 + 1.40899i 0.891990 + 0.452055i \(0.149309\pi\)
0.290295 + 0.956937i \(0.406247\pi\)
\(8\) 0 0
\(9\) −1.95828 2.27269i −0.652761 0.757564i
\(10\) 0 0
\(11\) 0.961816 + 5.45473i 0.289998 + 1.64466i 0.686864 + 0.726786i \(0.258987\pi\)
−0.396866 + 0.917877i \(0.629902\pi\)
\(12\) 0 0
\(13\) 2.65607 0.966729i 0.736661 0.268123i 0.0536791 0.998558i \(-0.482905\pi\)
0.682981 + 0.730436i \(0.260683\pi\)
\(14\) 0 0
\(15\) 0.976032 1.41352i 0.252010 0.364970i
\(16\) 0 0
\(17\) −0.517267 0.298644i −0.125456 0.0724319i 0.435959 0.899967i \(-0.356409\pi\)
−0.561415 + 0.827535i \(0.689743\pi\)
\(18\) 0 0
\(19\) 0.141252 0.0815519i 0.0324055 0.0187093i −0.483710 0.875228i \(-0.660711\pi\)
0.516115 + 0.856519i \(0.327378\pi\)
\(20\) 0 0
\(21\) 8.12712 2.23477i 1.77348 0.487667i
\(22\) 0 0
\(23\) −5.35924 4.49693i −1.11748 0.937675i −0.119004 0.992894i \(-0.537970\pi\)
−0.998474 + 0.0552184i \(0.982415\pi\)
\(24\) 0 0
\(25\) −3.77422 1.37370i −0.754844 0.274741i
\(26\) 0 0
\(27\) −4.99172 + 1.44316i −0.960658 + 0.277736i
\(28\) 0 0
\(29\) 0.610528 1.67741i 0.113372 0.311488i −0.870010 0.493034i \(-0.835888\pi\)
0.983382 + 0.181546i \(0.0581101\pi\)
\(30\) 0 0
\(31\) 3.26328 3.88903i 0.586102 0.698490i −0.388750 0.921343i \(-0.627093\pi\)
0.974852 + 0.222854i \(0.0715373\pi\)
\(32\) 0 0
\(33\) 9.28277 + 2.42230i 1.61592 + 0.421668i
\(34\) 0 0
\(35\) 2.41309 + 4.17960i 0.407887 + 0.706482i
\(36\) 0 0
\(37\) 0.726277 1.25795i 0.119399 0.206806i −0.800131 0.599826i \(-0.795236\pi\)
0.919530 + 0.393020i \(0.128570\pi\)
\(38\) 0 0
\(39\) 0.394755 4.87975i 0.0632114 0.781385i
\(40\) 0 0
\(41\) −3.84382 10.5608i −0.600304 1.64932i −0.750658 0.660691i \(-0.770264\pi\)
0.150354 0.988632i \(-0.451959\pi\)
\(42\) 0 0
\(43\) 6.11082 1.07750i 0.931892 0.164318i 0.312964 0.949765i \(-0.398678\pi\)
0.618928 + 0.785447i \(0.287567\pi\)
\(44\) 0 0
\(45\) −1.52122 2.55694i −0.226770 0.381166i
\(46\) 0 0
\(47\) −6.37666 + 5.35065i −0.930131 + 0.780473i −0.975841 0.218482i \(-0.929890\pi\)
0.0457098 + 0.998955i \(0.485445\pi\)
\(48\) 0 0
\(49\) −2.89670 + 16.4280i −0.413814 + 2.34685i
\(50\) 0 0
\(51\) −0.843539 + 0.598919i −0.118119 + 0.0838654i
\(52\) 0 0
\(53\) 8.40465i 1.15447i −0.816579 0.577234i \(-0.804132\pi\)
0.816579 0.577234i \(-0.195868\pi\)
\(54\) 0 0
\(55\) 5.49316i 0.740697i
\(56\) 0 0
\(57\) −0.0264635 0.281262i −0.00350517 0.0372541i
\(58\) 0 0
\(59\) −1.35597 + 7.69008i −0.176532 + 1.00116i 0.759828 + 0.650124i \(0.225283\pi\)
−0.936361 + 0.351040i \(0.885828\pi\)
\(60\) 0 0
\(61\) −3.16592 + 2.65652i −0.405354 + 0.340133i −0.822559 0.568680i \(-0.807454\pi\)
0.417204 + 0.908813i \(0.363010\pi\)
\(62\) 0 0
\(63\) 2.34667 14.4092i 0.295653 1.81539i
\(64\) 0 0
\(65\) 2.76061 0.486770i 0.342412 0.0603764i
\(66\) 0 0
\(67\) 2.02334 + 5.55908i 0.247190 + 0.679150i 0.999786 + 0.0206675i \(0.00657914\pi\)
−0.752596 + 0.658483i \(0.771199\pi\)
\(68\) 0 0
\(69\) −10.9483 + 5.19281i −1.31803 + 0.625141i
\(70\) 0 0
\(71\) 1.86491 3.23013i 0.221325 0.383345i −0.733886 0.679273i \(-0.762295\pi\)
0.955210 + 0.295927i \(0.0956287\pi\)
\(72\) 0 0
\(73\) 3.05997 + 5.30003i 0.358143 + 0.620321i 0.987651 0.156673i \(-0.0500768\pi\)
−0.629508 + 0.776994i \(0.716743\pi\)
\(74\) 0 0
\(75\) −4.88681 + 4.95121i −0.564280 + 0.571716i
\(76\) 0 0
\(77\) −17.3258 + 20.6481i −1.97446 + 2.35306i
\(78\) 0 0
\(79\) 4.05391 11.1380i 0.456100 1.25312i −0.472266 0.881456i \(-0.656564\pi\)
0.928366 0.371668i \(-0.121214\pi\)
\(80\) 0 0
\(81\) −1.33026 + 8.90115i −0.147807 + 0.989016i
\(82\) 0 0
\(83\) −9.04948 3.29374i −0.993309 0.361535i −0.206308 0.978487i \(-0.566145\pi\)
−0.787001 + 0.616952i \(0.788367\pi\)
\(84\) 0 0
\(85\) −0.453773 0.380761i −0.0492186 0.0412993i
\(86\) 0 0
\(87\) −2.20051 2.17189i −0.235920 0.232851i
\(88\) 0 0
\(89\) −1.45033 + 0.837348i −0.153735 + 0.0887587i −0.574894 0.818228i \(-0.694957\pi\)
0.421159 + 0.906987i \(0.361623\pi\)
\(90\) 0 0
\(91\) 11.9121 + 6.87744i 1.24873 + 0.720952i
\(92\) 0 0
\(93\) −3.76826 7.94486i −0.390750 0.823844i
\(94\) 0 0
\(95\) 0.152002 0.0553244i 0.0155951 0.00567616i
\(96\) 0 0
\(97\) −2.34010 13.2714i −0.237601 1.34750i −0.837066 0.547102i \(-0.815731\pi\)
0.599465 0.800401i \(-0.295380\pi\)
\(98\) 0 0
\(99\) 10.5134 12.8678i 1.05664 1.29326i
\(100\) 0 0
\(101\) 8.98820 + 10.7117i 0.894360 + 1.06586i 0.997463 + 0.0711857i \(0.0226783\pi\)
−0.103103 + 0.994671i \(0.532877\pi\)
\(102\) 0 0
\(103\) −5.43335 0.958047i −0.535364 0.0943991i −0.100572 0.994930i \(-0.532067\pi\)
−0.434792 + 0.900531i \(0.643178\pi\)
\(104\) 0 0
\(105\) 8.32245 0.783045i 0.812188 0.0764173i
\(106\) 0 0
\(107\) −11.3996 −1.10204 −0.551021 0.834491i \(-0.685762\pi\)
−0.551021 + 0.834491i \(0.685762\pi\)
\(108\) 0 0
\(109\) 10.4472 1.00066 0.500329 0.865835i \(-0.333212\pi\)
0.500329 + 0.865835i \(0.333212\pi\)
\(110\) 0 0
\(111\) −1.45652 2.05141i −0.138247 0.194712i
\(112\) 0 0
\(113\) −3.27678 0.577786i −0.308254 0.0543535i 0.0173814 0.999849i \(-0.494467\pi\)
−0.325635 + 0.945495i \(0.605578\pi\)
\(114\) 0 0
\(115\) −4.45982 5.31500i −0.415880 0.495627i
\(116\) 0 0
\(117\) −7.39841 4.14330i −0.683983 0.383048i
\(118\) 0 0
\(119\) −0.504729 2.86246i −0.0462684 0.262401i
\(120\) 0 0
\(121\) −18.4923 + 6.73066i −1.68112 + 0.611878i
\(122\) 0 0
\(123\) −19.4024 1.56959i −1.74946 0.141525i
\(124\) 0 0
\(125\) −7.74402 4.47101i −0.692646 0.399899i
\(126\) 0 0
\(127\) 3.80947 2.19940i 0.338036 0.195165i −0.321367 0.946955i \(-0.604142\pi\)
0.659403 + 0.751790i \(0.270809\pi\)
\(128\) 0 0
\(129\) 2.71366 10.3993i 0.238924 0.915608i
\(130\) 0 0
\(131\) −1.04355 0.875644i −0.0911755 0.0765053i 0.596061 0.802939i \(-0.296732\pi\)
−0.687236 + 0.726434i \(0.741176\pi\)
\(132\) 0 0
\(133\) 0.745854 + 0.271469i 0.0646737 + 0.0235393i
\(134\) 0 0
\(135\) −5.12385 + 0.549852i −0.440990 + 0.0473238i
\(136\) 0 0
\(137\) −1.38622 + 3.80861i −0.118433 + 0.325391i −0.984718 0.174159i \(-0.944279\pi\)
0.866285 + 0.499551i \(0.166501\pi\)
\(138\) 0 0
\(139\) −10.0544 + 11.9823i −0.852801 + 1.01633i 0.146830 + 0.989162i \(0.453093\pi\)
−0.999631 + 0.0271664i \(0.991352\pi\)
\(140\) 0 0
\(141\) 3.82269 + 13.9018i 0.321928 + 1.17075i
\(142\) 0 0
\(143\) 7.82789 + 13.5583i 0.654601 + 1.13380i
\(144\) 0 0
\(145\) 0.885166 1.53315i 0.0735090 0.127321i
\(146\) 0 0
\(147\) 23.7758 + 16.4171i 1.96099 + 1.35406i
\(148\) 0 0
\(149\) 2.36175 + 6.48884i 0.193482 + 0.531587i 0.998060 0.0622599i \(-0.0198308\pi\)
−0.804578 + 0.593847i \(0.797609\pi\)
\(150\) 0 0
\(151\) −5.40054 + 0.952262i −0.439490 + 0.0774940i −0.389015 0.921231i \(-0.627185\pi\)
−0.0504750 + 0.998725i \(0.516074\pi\)
\(152\) 0 0
\(153\) 0.334228 + 1.76042i 0.0270208 + 0.142321i
\(154\) 0 0
\(155\) 3.85693 3.23635i 0.309796 0.259949i
\(156\) 0 0
\(157\) 0.626364 3.55229i 0.0499893 0.283503i −0.949558 0.313592i \(-0.898468\pi\)
0.999547 + 0.0300883i \(0.00957885\pi\)
\(158\) 0 0
\(159\) −13.2334 6.06568i −1.04947 0.481040i
\(160\) 0 0
\(161\) 34.0449i 2.68312i
\(162\) 0 0
\(163\) 5.07293i 0.397343i 0.980066 + 0.198671i \(0.0636627\pi\)
−0.980066 + 0.198671i \(0.936337\pi\)
\(164\) 0 0
\(165\) 8.64914 + 3.96444i 0.673334 + 0.308631i
\(166\) 0 0
\(167\) 1.81056 10.2682i 0.140105 0.794576i −0.831062 0.556179i \(-0.812267\pi\)
0.971168 0.238397i \(-0.0766220\pi\)
\(168\) 0 0
\(169\) −3.83845 + 3.22084i −0.295265 + 0.247757i
\(170\) 0 0
\(171\) −0.461954 0.161321i −0.0353265 0.0123365i
\(172\) 0 0
\(173\) 19.5905 3.45433i 1.48944 0.262628i 0.631094 0.775707i \(-0.282606\pi\)
0.858341 + 0.513079i \(0.171495\pi\)
\(174\) 0 0
\(175\) −6.68493 18.3667i −0.505333 1.38839i
\(176\) 0 0
\(177\) 11.1296 + 7.68499i 0.836555 + 0.577639i
\(178\) 0 0
\(179\) 7.51483 13.0161i 0.561685 0.972866i −0.435665 0.900109i \(-0.643487\pi\)
0.997350 0.0727573i \(-0.0231798\pi\)
\(180\) 0 0
\(181\) 2.08688 + 3.61458i 0.155116 + 0.268669i 0.933101 0.359613i \(-0.117091\pi\)
−0.777985 + 0.628283i \(0.783758\pi\)
\(182\) 0 0
\(183\) 1.89791 + 6.90206i 0.140297 + 0.510215i
\(184\) 0 0
\(185\) 0.925978 1.10354i 0.0680792 0.0811337i
\(186\) 0 0
\(187\) 1.13151 3.10879i 0.0827440 0.227337i
\(188\) 0 0
\(189\) −20.9941 14.0941i −1.52710 1.02520i
\(190\) 0 0
\(191\) 22.5495 + 8.20734i 1.63162 + 0.593862i 0.985546 0.169409i \(-0.0541860\pi\)
0.646078 + 0.763272i \(0.276408\pi\)
\(192\) 0 0
\(193\) 6.52079 + 5.47159i 0.469377 + 0.393854i 0.846567 0.532282i \(-0.178665\pi\)
−0.377191 + 0.926136i \(0.623110\pi\)
\(194\) 0 0
\(195\) 1.22591 4.69797i 0.0877896 0.336428i
\(196\) 0 0
\(197\) 3.63484 2.09858i 0.258972 0.149517i −0.364894 0.931049i \(-0.618895\pi\)
0.623865 + 0.781532i \(0.285561\pi\)
\(198\) 0 0
\(199\) −4.58250 2.64571i −0.324845 0.187549i 0.328705 0.944433i \(-0.393388\pi\)
−0.653550 + 0.756883i \(0.726721\pi\)
\(200\) 0 0
\(201\) 10.2132 + 0.826213i 0.720383 + 0.0582765i
\(202\) 0 0
\(203\) 8.16288 2.97105i 0.572922 0.208527i
\(204\) 0 0
\(205\) −1.93545 10.9765i −0.135178 0.766632i
\(206\) 0 0
\(207\) 0.274751 + 20.9862i 0.0190965 + 1.45864i
\(208\) 0 0
\(209\) 0.580702 + 0.692054i 0.0401680 + 0.0478704i
\(210\) 0 0
\(211\) −11.1463 1.96540i −0.767344 0.135303i −0.223744 0.974648i \(-0.571828\pi\)
−0.543600 + 0.839345i \(0.682939\pi\)
\(212\) 0 0
\(213\) −3.74001 5.26756i −0.256261 0.360927i
\(214\) 0 0
\(215\) 6.15388 0.419691
\(216\) 0 0
\(217\) 24.7053 1.67711
\(218\) 0 0
\(219\) 10.5534 0.992956i 0.713136 0.0670977i
\(220\) 0 0
\(221\) −1.66260 0.293162i −0.111839 0.0197202i
\(222\) 0 0
\(223\) 11.2504 + 13.4077i 0.753380 + 0.897843i 0.997410 0.0719243i \(-0.0229140\pi\)
−0.244030 + 0.969768i \(0.578470\pi\)
\(224\) 0 0
\(225\) 4.26898 + 11.2677i 0.284599 + 0.751182i
\(226\) 0 0
\(227\) 0.724677 + 4.10985i 0.0480985 + 0.272780i 0.999367 0.0355847i \(-0.0113294\pi\)
−0.951268 + 0.308365i \(0.900218\pi\)
\(228\) 0 0
\(229\) −1.78302 + 0.648967i −0.117825 + 0.0428849i −0.400260 0.916402i \(-0.631080\pi\)
0.282435 + 0.959287i \(0.408858\pi\)
\(230\) 0 0
\(231\) 20.0069 + 42.1818i 1.31635 + 2.77536i
\(232\) 0 0
\(233\) 15.7256 + 9.07917i 1.03022 + 0.594796i 0.917047 0.398779i \(-0.130566\pi\)
0.113171 + 0.993576i \(0.463899\pi\)
\(234\) 0 0
\(235\) −7.14941 + 4.12772i −0.466376 + 0.269262i
\(236\) 0 0
\(237\) −14.6114 14.4214i −0.949112 0.936768i
\(238\) 0 0
\(239\) −13.3664 11.2158i −0.864602 0.725487i 0.0983526 0.995152i \(-0.468643\pi\)
−0.962954 + 0.269665i \(0.913087\pi\)
\(240\) 0 0
\(241\) −25.1799 9.16473i −1.62198 0.590352i −0.638222 0.769853i \(-0.720330\pi\)
−0.983758 + 0.179500i \(0.942552\pi\)
\(242\) 0 0
\(243\) 13.0551 + 8.51854i 0.837482 + 0.546465i
\(244\) 0 0
\(245\) −5.65828 + 15.5460i −0.361495 + 0.993198i
\(246\) 0 0
\(247\) 0.296336 0.353160i 0.0188554 0.0224710i
\(248\) 0 0
\(249\) −11.7171 + 11.8716i −0.742544 + 0.752329i
\(250\) 0 0
\(251\) 9.18578 + 15.9102i 0.579801 + 1.00425i 0.995502 + 0.0947437i \(0.0302032\pi\)
−0.415700 + 0.909502i \(0.636464\pi\)
\(252\) 0 0
\(253\) 19.3749 33.5584i 1.21809 2.10980i
\(254\) 0 0
\(255\) −0.927009 + 0.439682i −0.0580516 + 0.0275339i
\(256\) 0 0
\(257\) 7.13045 + 19.5908i 0.444786 + 1.22204i 0.936310 + 0.351174i \(0.114218\pi\)
−0.491525 + 0.870864i \(0.663560\pi\)
\(258\) 0 0
\(259\) 6.96126 1.22746i 0.432551 0.0762705i
\(260\) 0 0
\(261\) −5.00783 + 1.89730i −0.309977 + 0.117440i
\(262\) 0 0
\(263\) −20.5295 + 17.2263i −1.26590 + 1.06222i −0.270878 + 0.962614i \(0.587314\pi\)
−0.995027 + 0.0996068i \(0.968242\pi\)
\(264\) 0 0
\(265\) 1.44741 8.20865i 0.0889135 0.504253i
\(266\) 0 0
\(267\) 0.271718 + 2.88790i 0.0166289 + 0.176737i
\(268\) 0 0
\(269\) 6.10651i 0.372321i 0.982519 + 0.186160i \(0.0596044\pi\)
−0.982519 + 0.186160i \(0.940396\pi\)
\(270\) 0 0
\(271\) 5.24989i 0.318908i 0.987205 + 0.159454i \(0.0509734\pi\)
−0.987205 + 0.159454i \(0.949027\pi\)
\(272\) 0 0
\(273\) 19.4257 13.7924i 1.17570 0.834756i
\(274\) 0 0
\(275\) 3.86307 21.9086i 0.232952 1.32114i
\(276\) 0 0
\(277\) 21.8063 18.2977i 1.31022 1.09940i 0.321934 0.946762i \(-0.395667\pi\)
0.988282 0.152640i \(-0.0487775\pi\)
\(278\) 0 0
\(279\) −15.2290 + 0.199378i −0.911735 + 0.0119364i
\(280\) 0 0
\(281\) 2.99467 0.528040i 0.178647 0.0315002i −0.0836090 0.996499i \(-0.526645\pi\)
0.262256 + 0.964998i \(0.415534\pi\)
\(282\) 0 0
\(283\) −5.13245 14.1013i −0.305092 0.838235i −0.993595 0.113001i \(-0.963954\pi\)
0.688502 0.725234i \(-0.258268\pi\)
\(284\) 0 0
\(285\) 0.0225912 0.279260i 0.00133819 0.0165419i
\(286\) 0 0
\(287\) 27.3455 47.3638i 1.61415 2.79579i
\(288\) 0 0
\(289\) −8.32162 14.4135i −0.489507 0.847851i
\(290\) 0 0
\(291\) −22.5850 5.89346i −1.32396 0.345481i
\(292\) 0 0
\(293\) 12.3270 14.6907i 0.720150 0.858241i −0.274495 0.961588i \(-0.588511\pi\)
0.994645 + 0.103347i \(0.0329552\pi\)
\(294\) 0 0
\(295\) −2.64869 + 7.27723i −0.154213 + 0.423696i
\(296\) 0 0
\(297\) −12.6731 25.8404i −0.735370 1.49941i
\(298\) 0 0
\(299\) −18.5818 6.76323i −1.07461 0.391127i
\(300\) 0 0
\(301\) 23.1316 + 19.4097i 1.33328 + 1.11876i
\(302\) 0 0
\(303\) 23.3528 6.42147i 1.34158 0.368904i
\(304\) 0 0
\(305\) −3.54958 + 2.04935i −0.203248 + 0.117346i
\(306\) 0 0
\(307\) −13.9719 8.06666i −0.797416 0.460388i 0.0451507 0.998980i \(-0.485623\pi\)
−0.842567 + 0.538592i \(0.818957\pi\)
\(308\) 0 0
\(309\) −5.42975 + 7.86354i −0.308888 + 0.447341i
\(310\) 0 0
\(311\) −17.9054 + 6.51704i −1.01532 + 0.369548i −0.795475 0.605986i \(-0.792779\pi\)
−0.219849 + 0.975534i \(0.570556\pi\)
\(312\) 0 0
\(313\) 1.68661 + 9.56523i 0.0953328 + 0.540659i 0.994645 + 0.103352i \(0.0329567\pi\)
−0.899312 + 0.437307i \(0.855932\pi\)
\(314\) 0 0
\(315\) 4.77343 13.6691i 0.268952 0.770164i
\(316\) 0 0
\(317\) 12.4921 + 14.8875i 0.701628 + 0.836167i 0.992710 0.120531i \(-0.0384596\pi\)
−0.291082 + 0.956698i \(0.594015\pi\)
\(318\) 0 0
\(319\) 9.73704 + 1.71690i 0.545170 + 0.0961281i
\(320\) 0 0
\(321\) −8.22716 + 17.9490i −0.459195 + 1.00182i
\(322\) 0 0
\(323\) −0.0974201 −0.00542060
\(324\) 0 0
\(325\) −11.3526 −0.629728
\(326\) 0 0
\(327\) 7.53979 16.4494i 0.416951 0.909653i
\(328\) 0 0
\(329\) −39.8928 7.03417i −2.19936 0.387807i
\(330\) 0 0
\(331\) −21.1483 25.2035i −1.16241 1.38531i −0.908395 0.418113i \(-0.862692\pi\)
−0.254020 0.967199i \(-0.581753\pi\)
\(332\) 0 0
\(333\) −4.28119 + 0.812814i −0.234608 + 0.0445420i
\(334\) 0 0
\(335\) 1.01880 + 5.77789i 0.0556629 + 0.315680i
\(336\) 0 0
\(337\) −3.50899 + 1.27717i −0.191147 + 0.0695717i −0.435820 0.900034i \(-0.643542\pi\)
0.244673 + 0.969606i \(0.421319\pi\)
\(338\) 0 0
\(339\) −3.27461 + 4.74240i −0.177853 + 0.257572i
\(340\) 0 0
\(341\) 24.3522 + 14.0598i 1.31875 + 0.761380i
\(342\) 0 0
\(343\) −40.8012 + 23.5566i −2.20306 + 1.27193i
\(344\) 0 0
\(345\) −11.5873 + 3.18624i −0.623839 + 0.171542i
\(346\) 0 0
\(347\) 17.2766 + 14.4968i 0.927456 + 0.778228i 0.975359 0.220624i \(-0.0708093\pi\)
−0.0479028 + 0.998852i \(0.515254\pi\)
\(348\) 0 0
\(349\) −7.89430 2.87329i −0.422572 0.153804i 0.121977 0.992533i \(-0.461077\pi\)
−0.544548 + 0.838729i \(0.683299\pi\)
\(350\) 0 0
\(351\) −11.8632 + 8.65877i −0.633211 + 0.462171i
\(352\) 0 0
\(353\) 9.50025 26.1017i 0.505648 1.38926i −0.380039 0.924971i \(-0.624089\pi\)
0.885686 0.464285i \(-0.153688\pi\)
\(354\) 0 0
\(355\) 2.37770 2.83363i 0.126195 0.150394i
\(356\) 0 0
\(357\) −4.87129 1.27114i −0.257816 0.0672760i
\(358\) 0 0
\(359\) 11.1197 + 19.2599i 0.586877 + 1.01650i 0.994639 + 0.103412i \(0.0329759\pi\)
−0.407762 + 0.913088i \(0.633691\pi\)
\(360\) 0 0
\(361\) −9.48670 + 16.4314i −0.499300 + 0.864813i
\(362\) 0 0
\(363\) −2.74840 + 33.9743i −0.144254 + 1.78319i
\(364\) 0 0
\(365\) 2.07587 + 5.70340i 0.108656 + 0.298530i
\(366\) 0 0
\(367\) −6.99817 + 1.23397i −0.365302 + 0.0644125i −0.353286 0.935515i \(-0.614936\pi\)
−0.0120154 + 0.999928i \(0.503825\pi\)
\(368\) 0 0
\(369\) −16.4742 + 29.4169i −0.857613 + 1.53138i
\(370\) 0 0
\(371\) 31.3312 26.2900i 1.62664 1.36491i
\(372\) 0 0
\(373\) −3.08072 + 17.4716i −0.159514 + 0.904646i 0.795029 + 0.606571i \(0.207456\pi\)
−0.954543 + 0.298075i \(0.903656\pi\)
\(374\) 0 0
\(375\) −12.6286 + 8.96642i −0.652140 + 0.463024i
\(376\) 0 0
\(377\) 5.04554i 0.259858i
\(378\) 0 0
\(379\) 0.696553i 0.0357795i −0.999840 0.0178898i \(-0.994305\pi\)
0.999840 0.0178898i \(-0.00569479\pi\)
\(380\) 0 0
\(381\) −0.713701 7.58544i −0.0365640 0.388614i
\(382\) 0 0
\(383\) 2.97272 16.8591i 0.151899 0.861462i −0.809667 0.586889i \(-0.800352\pi\)
0.961566 0.274573i \(-0.0885365\pi\)
\(384\) 0 0
\(385\) −20.4776 + 17.1828i −1.04364 + 0.875715i
\(386\) 0 0
\(387\) −14.4156 11.7780i −0.732784 0.598708i
\(388\) 0 0
\(389\) −16.9672 + 2.99177i −0.860269 + 0.151689i −0.586344 0.810062i \(-0.699433\pi\)
−0.273925 + 0.961751i \(0.588322\pi\)
\(390\) 0 0
\(391\) 1.42917 + 3.92662i 0.0722764 + 0.198578i
\(392\) 0 0
\(393\) −2.13186 + 1.01114i −0.107538 + 0.0510055i
\(394\) 0 0
\(395\) 5.87750 10.1801i 0.295729 0.512218i
\(396\) 0 0
\(397\) 4.24458 + 7.35182i 0.213029 + 0.368977i 0.952661 0.304034i \(-0.0983337\pi\)
−0.739632 + 0.673012i \(0.765000\pi\)
\(398\) 0 0
\(399\) 0.965722 0.978448i 0.0483466 0.0489837i
\(400\) 0 0
\(401\) 6.54824 7.80389i 0.327004 0.389708i −0.577346 0.816499i \(-0.695912\pi\)
0.904350 + 0.426792i \(0.140356\pi\)
\(402\) 0 0
\(403\) 4.90786 13.4842i 0.244478 0.671697i
\(404\) 0 0
\(405\) −2.83215 + 8.46447i −0.140731 + 0.420603i
\(406\) 0 0
\(407\) 7.56031 + 2.75173i 0.374751 + 0.136398i
\(408\) 0 0
\(409\) −18.6107 15.6162i −0.920238 0.772171i 0.0538011 0.998552i \(-0.482866\pi\)
−0.974039 + 0.226380i \(0.927311\pi\)
\(410\) 0 0
\(411\) 4.99632 + 4.93134i 0.246450 + 0.243245i
\(412\) 0 0
\(413\) −32.9089 + 19.0000i −1.61934 + 0.934928i
\(414\) 0 0
\(415\) −8.27121 4.77538i −0.406018 0.234414i
\(416\) 0 0
\(417\) 11.6102 + 24.4786i 0.568556 + 1.19872i
\(418\) 0 0
\(419\) −0.0629252 + 0.0229029i −0.00307410 + 0.00111888i −0.343557 0.939132i \(-0.611632\pi\)
0.340483 + 0.940251i \(0.389410\pi\)
\(420\) 0 0
\(421\) −4.84853 27.4974i −0.236303 1.34014i −0.839853 0.542814i \(-0.817359\pi\)
0.603550 0.797325i \(-0.293752\pi\)
\(422\) 0 0
\(423\) 24.6477 + 4.01410i 1.19841 + 0.195172i
\(424\) 0 0
\(425\) 1.54203 + 1.83772i 0.0747995 + 0.0891425i
\(426\) 0 0
\(427\) −19.8062 3.49237i −0.958489 0.169007i
\(428\) 0 0
\(429\) 26.9974 2.54014i 1.30345 0.122639i
\(430\) 0 0
\(431\) −28.9982 −1.39679 −0.698397 0.715710i \(-0.746103\pi\)
−0.698397 + 0.715710i \(0.746103\pi\)
\(432\) 0 0
\(433\) −25.6912 −1.23464 −0.617320 0.786712i \(-0.711782\pi\)
−0.617320 + 0.786712i \(0.711782\pi\)
\(434\) 0 0
\(435\) −1.77516 2.50020i −0.0851126 0.119876i
\(436\) 0 0
\(437\) −1.12374 0.198145i −0.0537556 0.00947857i
\(438\) 0 0
\(439\) 8.68012 + 10.3446i 0.414280 + 0.493719i 0.932319 0.361638i \(-0.117782\pi\)
−0.518039 + 0.855357i \(0.673338\pi\)
\(440\) 0 0
\(441\) 43.0083 25.5873i 2.04801 1.21844i
\(442\) 0 0
\(443\) −1.24107 7.03844i −0.0589649 0.334406i 0.941027 0.338330i \(-0.109862\pi\)
−0.999992 + 0.00392386i \(0.998751\pi\)
\(444\) 0 0
\(445\) −1.56071 + 0.568052i −0.0739848 + 0.0269283i
\(446\) 0 0
\(447\) 11.9214 + 0.964397i 0.563861 + 0.0456144i
\(448\) 0 0
\(449\) −18.7841 10.8450i −0.886477 0.511807i −0.0136882 0.999906i \(-0.504357\pi\)
−0.872788 + 0.488099i \(0.837691\pi\)
\(450\) 0 0
\(451\) 53.9093 31.1246i 2.53849 1.46560i
\(452\) 0 0
\(453\) −2.39824 + 9.19057i −0.112679 + 0.431810i
\(454\) 0 0
\(455\) 10.4499 + 8.76849i 0.489898 + 0.411073i
\(456\) 0 0
\(457\) 34.0401 + 12.3896i 1.59233 + 0.579561i 0.977838 0.209363i \(-0.0671390\pi\)
0.614492 + 0.788923i \(0.289361\pi\)
\(458\) 0 0
\(459\) 3.01304 + 0.744252i 0.140637 + 0.0347387i
\(460\) 0 0
\(461\) −4.10359 + 11.2745i −0.191123 + 0.525107i −0.997830 0.0658453i \(-0.979026\pi\)
0.806707 + 0.590952i \(0.201248\pi\)
\(462\) 0 0
\(463\) 0.669388 0.797745i 0.0311091 0.0370744i −0.750266 0.661137i \(-0.770074\pi\)
0.781375 + 0.624062i \(0.214519\pi\)
\(464\) 0 0
\(465\) −2.31215 8.40853i −0.107224 0.389936i
\(466\) 0 0
\(467\) −2.21810 3.84186i −0.102641 0.177780i 0.810131 0.586249i \(-0.199396\pi\)
−0.912772 + 0.408469i \(0.866063\pi\)
\(468\) 0 0
\(469\) −14.3943 + 24.9317i −0.664668 + 1.15124i
\(470\) 0 0
\(471\) −5.14113 3.54993i −0.236891 0.163572i
\(472\) 0 0
\(473\) 11.7550 + 32.2965i 0.540494 + 1.48500i
\(474\) 0 0
\(475\) −0.645144 + 0.113756i −0.0296013 + 0.00521950i
\(476\) 0 0
\(477\) −19.1012 + 16.4587i −0.874583 + 0.753591i
\(478\) 0 0
\(479\) −12.7569 + 10.7043i −0.582876 + 0.489091i −0.885890 0.463895i \(-0.846452\pi\)
0.303014 + 0.952986i \(0.402007\pi\)
\(480\) 0 0
\(481\) 0.712945 4.04331i 0.0325075 0.184359i
\(482\) 0 0
\(483\) −53.6048 24.5704i −2.43910 1.11799i
\(484\) 0 0
\(485\) 13.3649i 0.606867i
\(486\) 0 0
\(487\) 15.4161i 0.698570i −0.937016 0.349285i \(-0.886424\pi\)
0.937016 0.349285i \(-0.113576\pi\)
\(488\) 0 0
\(489\) 7.98748 + 3.66117i 0.361206 + 0.165564i
\(490\) 0 0
\(491\) −1.16739 + 6.62060i −0.0526836 + 0.298784i −0.999753 0.0222468i \(-0.992918\pi\)
0.947069 + 0.321030i \(0.104029\pi\)
\(492\) 0 0
\(493\) −0.816756 + 0.685340i −0.0367848 + 0.0308661i
\(494\) 0 0
\(495\) 12.4843 10.7572i 0.561126 0.483498i
\(496\) 0 0
\(497\) 17.8749 3.15183i 0.801799 0.141379i
\(498\) 0 0
\(499\) 11.8160 + 32.4641i 0.528956 + 1.45329i 0.860302 + 0.509785i \(0.170275\pi\)
−0.331346 + 0.943509i \(0.607503\pi\)
\(500\) 0 0
\(501\) −14.8609 10.2614i −0.663935 0.458445i
\(502\) 0 0
\(503\) −7.55590 + 13.0872i −0.336901 + 0.583530i −0.983848 0.179005i \(-0.942712\pi\)
0.646947 + 0.762535i \(0.276045\pi\)
\(504\) 0 0
\(505\) 6.93387 + 12.0098i 0.308553 + 0.534430i
\(506\) 0 0
\(507\) 2.30108 + 8.36825i 0.102194 + 0.371647i
\(508\) 0 0
\(509\) −5.27599 + 6.28768i −0.233854 + 0.278696i −0.870191 0.492715i \(-0.836004\pi\)
0.636337 + 0.771411i \(0.280449\pi\)
\(510\) 0 0
\(511\) −10.1860 + 27.9858i −0.450601 + 1.23802i
\(512\) 0 0
\(513\) −0.587399 + 0.610934i −0.0259343 + 0.0269734i
\(514\) 0 0
\(515\) −5.14165 1.87141i −0.226568 0.0824641i
\(516\) 0 0
\(517\) −35.3195 29.6366i −1.55335 1.30342i
\(518\) 0 0
\(519\) 8.69961 33.3388i 0.381870 1.46341i
\(520\) 0 0
\(521\) −2.45686 + 1.41847i −0.107637 + 0.0621444i −0.552852 0.833279i \(-0.686461\pi\)
0.445215 + 0.895424i \(0.353127\pi\)
\(522\) 0 0
\(523\) 26.4086 + 15.2470i 1.15477 + 0.666705i 0.950044 0.312116i \(-0.101038\pi\)
0.204722 + 0.978820i \(0.434371\pi\)
\(524\) 0 0
\(525\) −33.7434 2.72973i −1.47268 0.119135i
\(526\) 0 0
\(527\) −2.84942 + 1.03710i −0.124123 + 0.0451770i
\(528\) 0 0
\(529\) 4.50510 + 25.5497i 0.195874 + 1.11086i
\(530\) 0 0
\(531\) 20.1326 11.9776i 0.873679 0.519786i
\(532\) 0 0
\(533\) −20.4189 24.3343i −0.884441 1.05404i
\(534\) 0 0
\(535\) −11.1338 1.96318i −0.481355 0.0848758i
\(536\) 0 0
\(537\) −15.0707 21.2261i −0.650348 0.915973i
\(538\) 0 0
\(539\) −92.3962 −3.97979
\(540\) 0 0
\(541\) 35.3176 1.51842 0.759212 0.650844i \(-0.225585\pi\)
0.759212 + 0.650844i \(0.225585\pi\)
\(542\) 0 0
\(543\) 7.19737 0.677188i 0.308869 0.0290609i
\(544\) 0 0
\(545\) 10.2035 + 1.79916i 0.437072 + 0.0770676i
\(546\) 0 0
\(547\) −13.0568 15.5605i −0.558270 0.665320i 0.410909 0.911676i \(-0.365211\pi\)
−0.969179 + 0.246356i \(0.920767\pi\)
\(548\) 0 0
\(549\) 12.2372 + 1.99294i 0.522272 + 0.0850567i
\(550\) 0 0
\(551\) −0.0505578 0.286728i −0.00215384 0.0122150i
\(552\) 0 0
\(553\) 54.2015 19.7277i 2.30488 0.838909i
\(554\) 0 0
\(555\) −1.06927 2.25441i −0.0453879 0.0956943i
\(556\) 0 0
\(557\) 26.5321 + 15.3183i 1.12420 + 0.649059i 0.942471 0.334289i \(-0.108496\pi\)
0.181733 + 0.983348i \(0.441830\pi\)
\(558\) 0 0
\(559\) 15.1891 8.76943i 0.642431 0.370908i
\(560\) 0 0
\(561\) −4.07827 4.02522i −0.172185 0.169945i
\(562\) 0 0
\(563\) 15.2500 + 12.7963i 0.642712 + 0.539299i 0.904850 0.425731i \(-0.139983\pi\)
−0.262138 + 0.965030i \(0.584428\pi\)
\(564\) 0 0
\(565\) −3.10086 1.12862i −0.130454 0.0474815i
\(566\) 0 0
\(567\) −37.3432 + 22.8841i −1.56827 + 0.961040i
\(568\) 0 0
\(569\) −2.77000 + 7.61051i −0.116124 + 0.319049i −0.984115 0.177531i \(-0.943189\pi\)
0.867991 + 0.496580i \(0.165411\pi\)
\(570\) 0 0
\(571\) −13.7051 + 16.3331i −0.573540 + 0.683518i −0.972353 0.233514i \(-0.924978\pi\)
0.398814 + 0.917032i \(0.369422\pi\)
\(572\) 0 0
\(573\) 29.1968 29.5815i 1.21971 1.23579i
\(574\) 0 0
\(575\) 14.0495 + 24.3344i 0.585904 + 1.01482i
\(576\) 0 0
\(577\) 0.0682767 0.118259i 0.00284239 0.00492317i −0.864601 0.502460i \(-0.832429\pi\)
0.867443 + 0.497536i \(0.165762\pi\)
\(578\) 0 0
\(579\) 13.3213 6.31829i 0.553613 0.262579i
\(580\) 0 0
\(581\) −16.0285 44.0380i −0.664975 1.82700i
\(582\) 0 0
\(583\) 45.8451 8.08372i 1.89871 0.334794i
\(584\) 0 0
\(585\) −6.51233 5.32079i −0.269252 0.219987i
\(586\) 0 0
\(587\) 21.3306 17.8985i 0.880407 0.738749i −0.0858556 0.996308i \(-0.527362\pi\)
0.966263 + 0.257558i \(0.0829179\pi\)
\(588\) 0 0
\(589\) 0.143788 0.815460i 0.00592466 0.0336004i
\(590\) 0 0
\(591\) −0.680984 7.23771i −0.0280119 0.297720i
\(592\) 0 0
\(593\) 16.6379i 0.683238i −0.939839 0.341619i \(-0.889025\pi\)
0.939839 0.341619i \(-0.110975\pi\)
\(594\) 0 0
\(595\) 2.88263i 0.118176i
\(596\) 0 0
\(597\) −7.47297 + 5.30586i −0.305848 + 0.217154i
\(598\) 0 0
\(599\) −4.24539 + 24.0768i −0.173462 + 0.983752i 0.766442 + 0.642314i \(0.222025\pi\)
−0.939904 + 0.341439i \(0.889086\pi\)
\(600\) 0 0
\(601\) 30.7637 25.8138i 1.25488 1.05297i 0.258671 0.965965i \(-0.416715\pi\)
0.996208 0.0870032i \(-0.0277290\pi\)
\(602\) 0 0
\(603\) 8.67181 15.4847i 0.353144 0.630585i
\(604\) 0 0
\(605\) −19.2202 + 3.38904i −0.781413 + 0.137784i
\(606\) 0 0
\(607\) 5.65409 + 15.5345i 0.229493 + 0.630526i 0.999976 0.00693444i \(-0.00220732\pi\)
−0.770483 + 0.637460i \(0.779985\pi\)
\(608\) 0 0
\(609\) 1.21320 14.9969i 0.0491613 0.607706i
\(610\) 0 0
\(611\) −11.7642 + 20.3762i −0.475929 + 0.824333i
\(612\) 0 0
\(613\) −1.00864 1.74701i −0.0407385 0.0705611i 0.844937 0.534865i \(-0.179638\pi\)
−0.885676 + 0.464304i \(0.846304\pi\)
\(614\) 0 0
\(615\) −18.6796 4.87437i −0.753236 0.196554i
\(616\) 0 0
\(617\) 20.7709 24.7538i 0.836204 0.996549i −0.163746 0.986503i \(-0.552358\pi\)
0.999950 0.0100465i \(-0.00319796\pi\)
\(618\) 0 0
\(619\) −4.84499 + 13.3115i −0.194737 + 0.535035i −0.998177 0.0603502i \(-0.980778\pi\)
0.803441 + 0.595385i \(0.203000\pi\)
\(620\) 0 0
\(621\) 33.2416 + 14.7132i 1.33394 + 0.590421i
\(622\) 0 0
\(623\) −7.65818 2.78735i −0.306818 0.111673i
\(624\) 0 0
\(625\) 8.59041 + 7.20821i 0.343616 + 0.288328i
\(626\) 0 0
\(627\) 1.50875 0.414873i 0.0602538 0.0165684i
\(628\) 0 0
\(629\) −0.751359 + 0.433797i −0.0299586 + 0.0172966i
\(630\) 0 0
\(631\) 13.0965 + 7.56128i 0.521365 + 0.301010i 0.737493 0.675355i \(-0.236010\pi\)
−0.216128 + 0.976365i \(0.569343\pi\)
\(632\) 0 0
\(633\) −11.1389 + 16.1318i −0.442733 + 0.641180i
\(634\) 0 0
\(635\) 4.09940 1.49206i 0.162680 0.0592106i
\(636\) 0 0
\(637\) 8.18759 + 46.4341i 0.324404 + 1.83979i
\(638\) 0 0
\(639\) −10.9931 + 2.08712i −0.434881 + 0.0825653i
\(640\) 0 0
\(641\) 2.66991 + 3.18187i 0.105455 + 0.125676i 0.816190 0.577783i \(-0.196082\pi\)
−0.710735 + 0.703460i \(0.751638\pi\)
\(642\) 0 0
\(643\) 43.0780 + 7.59582i 1.69883 + 0.299550i 0.937286 0.348561i \(-0.113329\pi\)
0.761546 + 0.648111i \(0.224441\pi\)
\(644\) 0 0
\(645\) 4.44129 9.68946i 0.174876 0.381522i
\(646\) 0 0
\(647\) 12.1823 0.478936 0.239468 0.970904i \(-0.423027\pi\)
0.239468 + 0.970904i \(0.423027\pi\)
\(648\) 0 0
\(649\) −43.2515 −1.69777
\(650\) 0 0
\(651\) 17.8300 38.8992i 0.698812 1.52458i
\(652\) 0 0
\(653\) 36.7762 + 6.48464i 1.43916 + 0.253763i 0.838135 0.545463i \(-0.183646\pi\)
0.601030 + 0.799227i \(0.294757\pi\)
\(654\) 0 0
\(655\) −0.868416 1.03494i −0.0339318 0.0404384i
\(656\) 0 0
\(657\) 6.05305 17.3333i 0.236152 0.676238i
\(658\) 0 0
\(659\) −1.48344 8.41298i −0.0577865 0.327723i 0.942186 0.335089i \(-0.108766\pi\)
−0.999973 + 0.00736587i \(0.997655\pi\)
\(660\) 0 0
\(661\) 0.439161 0.159841i 0.0170814 0.00621711i −0.333465 0.942762i \(-0.608218\pi\)
0.350547 + 0.936545i \(0.385996\pi\)
\(662\) 0 0
\(663\) −1.66150 + 2.40624i −0.0645274 + 0.0934507i
\(664\) 0 0
\(665\) 0.681709 + 0.393585i 0.0264355 + 0.0152626i
\(666\) 0 0
\(667\) −10.8152 + 6.24415i −0.418765 + 0.241774i
\(668\) 0 0
\(669\) 29.2302 8.03764i 1.13010 0.310753i
\(670\) 0 0
\(671\) −17.5356 14.7141i −0.676956 0.568033i
\(672\) 0 0
\(673\) 4.43038 + 1.61253i 0.170779 + 0.0621584i 0.425994 0.904726i \(-0.359924\pi\)
−0.255216 + 0.966884i \(0.582147\pi\)
\(674\) 0 0
\(675\) 20.8223 + 1.41036i 0.801452 + 0.0542846i
\(676\) 0 0
\(677\) 9.86735 27.1103i 0.379233 1.04193i −0.592442 0.805613i \(-0.701836\pi\)
0.971675 0.236321i \(-0.0759417\pi\)
\(678\) 0 0
\(679\) 42.1537 50.2368i 1.61771 1.92791i
\(680\) 0 0
\(681\) 6.99407 + 1.82507i 0.268014 + 0.0699370i
\(682\) 0 0
\(683\) 22.0332 + 38.1626i 0.843076 + 1.46025i 0.887282 + 0.461228i \(0.152591\pi\)
−0.0442060 + 0.999022i \(0.514076\pi\)
\(684\) 0 0
\(685\) −2.00979 + 3.48106i −0.0767902 + 0.133004i
\(686\) 0 0
\(687\) −0.265000 + 3.27578i −0.0101104 + 0.124979i
\(688\) 0 0
\(689\) −8.12502 22.3233i −0.309539 0.850451i
\(690\) 0 0
\(691\) −41.2765 + 7.27817i −1.57023 + 0.276875i −0.889944 0.456069i \(-0.849257\pi\)
−0.680289 + 0.732944i \(0.738146\pi\)
\(692\) 0 0
\(693\) 80.8555 1.05856i 3.07144 0.0402114i
\(694\) 0 0
\(695\) −11.8834 + 9.97138i −0.450764 + 0.378236i
\(696\) 0 0
\(697\) −1.16564 + 6.61070i −0.0441519 + 0.250398i
\(698\) 0 0
\(699\) 25.6447 18.2079i 0.969970 0.688686i
\(700\) 0 0
\(701\) 0.277648i 0.0104866i 0.999986 + 0.00524332i \(0.00166901\pi\)
−0.999986 + 0.00524332i \(0.998331\pi\)
\(702\) 0 0
\(703\) 0.236917i 0.00893550i
\(704\) 0 0
\(705\) 1.33944 + 14.2360i 0.0504461 + 0.536157i
\(706\) 0 0
\(707\) −11.8162 + 67.0132i −0.444395 + 2.52029i
\(708\) 0 0
\(709\) −26.9969 + 22.6531i −1.01389 + 0.850754i −0.988847 0.148933i \(-0.952416\pi\)
−0.0250415 + 0.999686i \(0.507972\pi\)
\(710\) 0 0
\(711\) −33.2520 + 12.5981i −1.24705 + 0.472465i
\(712\) 0 0
\(713\) −34.9774 + 6.16746i −1.30991 + 0.230973i
\(714\) 0 0
\(715\) 5.31040 + 14.5902i 0.198598 + 0.545642i
\(716\) 0 0
\(717\) −27.3061 + 12.9513i −1.01977 + 0.483677i
\(718\) 0 0
\(719\) 25.5033 44.1730i 0.951113 1.64738i 0.208091 0.978109i \(-0.433275\pi\)
0.743022 0.669267i \(-0.233392\pi\)
\(720\) 0 0
\(721\) −13.4243 23.2515i −0.499945 0.865931i
\(722\) 0 0
\(723\) −32.6026 + 33.0322i −1.21250 + 1.22848i
\(724\) 0 0
\(725\) −4.60853 + 5.49224i −0.171157 + 0.203977i
\(726\) 0 0
\(727\) 3.74866 10.2994i 0.139030 0.381982i −0.850564 0.525872i \(-0.823739\pi\)
0.989594 + 0.143890i \(0.0459612\pi\)
\(728\) 0 0
\(729\) 22.8346 14.4077i 0.845726 0.533618i
\(730\) 0 0
\(731\) −3.48272 1.26761i −0.128813 0.0468841i
\(732\) 0 0
\(733\) −5.12425 4.29976i −0.189269 0.158815i 0.543230 0.839584i \(-0.317201\pi\)
−0.732498 + 0.680769i \(0.761646\pi\)
\(734\) 0 0
\(735\) 20.3940 + 20.1288i 0.752245 + 0.742461i
\(736\) 0 0
\(737\) −28.3772 + 16.3836i −1.04529 + 0.603497i
\(738\) 0 0
\(739\) 14.5944 + 8.42609i 0.536864 + 0.309959i 0.743807 0.668394i \(-0.233018\pi\)
−0.206943 + 0.978353i \(0.566351\pi\)
\(740\) 0 0
\(741\) −0.342193 0.721468i −0.0125708 0.0265038i
\(742\) 0 0
\(743\) 10.5585 3.84299i 0.387355 0.140986i −0.140999 0.990010i \(-0.545031\pi\)
0.528354 + 0.849024i \(0.322809\pi\)
\(744\) 0 0
\(745\) 1.18919 + 6.74425i 0.0435687 + 0.247090i
\(746\) 0 0
\(747\) 10.2358 + 27.0168i 0.374507 + 0.988491i
\(748\) 0 0
\(749\) −35.6584 42.4960i −1.30293 1.55277i
\(750\) 0 0
\(751\) 46.3569 + 8.17398i 1.69159 + 0.298273i 0.934744 0.355322i \(-0.115629\pi\)
0.756844 + 0.653595i \(0.226740\pi\)
\(752\) 0 0
\(753\) 31.6806 2.98077i 1.15450 0.108625i
\(754\) 0 0
\(755\) −5.43859 −0.197931
\(756\) 0 0
\(757\) −34.8478 −1.26656 −0.633282 0.773921i \(-0.718292\pi\)
−0.633282 + 0.773921i \(0.718292\pi\)
\(758\) 0 0
\(759\) −38.8557 54.7257i −1.41037 1.98642i
\(760\) 0 0
\(761\) 8.01971 + 1.41409i 0.290714 + 0.0512608i 0.317103 0.948391i \(-0.397290\pi\)
−0.0263892 + 0.999652i \(0.508401\pi\)
\(762\) 0 0
\(763\) 32.6791 + 38.9455i 1.18306 + 1.40992i
\(764\) 0 0
\(765\) 0.0232635 + 1.77692i 0.000841093 + 0.0642448i
\(766\) 0 0
\(767\) 3.83268 + 21.7362i 0.138390 + 0.784850i
\(768\) 0 0
\(769\) −33.8466 + 12.3191i −1.22054 + 0.444240i −0.870347 0.492438i \(-0.836106\pi\)
−0.350191 + 0.936678i \(0.613883\pi\)
\(770\) 0 0
\(771\) 35.9923 + 2.91166i 1.29623 + 0.104861i
\(772\) 0 0
\(773\) 22.6182 + 13.0586i 0.813521 + 0.469687i 0.848177 0.529713i \(-0.177700\pi\)
−0.0346560 + 0.999399i \(0.511034\pi\)
\(774\) 0 0
\(775\) −17.6587 + 10.1953i −0.634319 + 0.366224i
\(776\) 0 0
\(777\) 3.09131 11.8466i 0.110900 0.424993i
\(778\) 0 0
\(779\) −1.40420 1.17827i −0.0503108 0.0422158i
\(780\) 0 0
\(781\) 19.4132 + 7.06581i 0.694657 + 0.252835i
\(782\) 0 0
\(783\) −0.626818 + 9.25427i −0.0224006 + 0.330721i
\(784\) 0 0
\(785\) 1.22351 3.36157i 0.0436690 0.119980i
\(786\) 0 0
\(787\) −6.45027 + 7.68713i −0.229927 + 0.274017i −0.868656 0.495415i \(-0.835016\pi\)
0.638729 + 0.769432i \(0.279460\pi\)
\(788\) 0 0
\(789\) 12.3071 + 44.7567i 0.438143 + 1.59338i
\(790\) 0 0
\(791\) −8.09599 14.0227i −0.287860 0.498589i
\(792\) 0 0
\(793\) −5.84076 + 10.1165i −0.207411 + 0.359247i
\(794\) 0 0
\(795\) −11.8802 8.20321i −0.421346 0.290938i