Properties

Label 432.2.be.b.47.6
Level $432$
Weight $2$
Character 432.47
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 47.6
Character \(\chi\) \(=\) 432.47
Dual form 432.2.be.b.239.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50778 + 0.852402i) q^{3} +(-2.12767 + 0.375166i) q^{5} +(-2.50142 + 2.98107i) q^{7} +(1.54682 + 2.57047i) q^{9} +O(q^{10})\) \(q+(1.50778 + 0.852402i) q^{3} +(-2.12767 + 0.375166i) q^{5} +(-2.50142 + 2.98107i) q^{7} +(1.54682 + 2.57047i) q^{9} +(-0.0357619 + 0.202816i) q^{11} +(-2.01394 - 0.733014i) q^{13} +(-3.52786 - 1.24796i) q^{15} +(-5.87137 + 3.38984i) q^{17} +(6.56062 + 3.78777i) q^{19} +(-6.31267 + 2.36260i) q^{21} +(3.99143 - 3.34921i) q^{23} +(-0.312223 + 0.113640i) q^{25} +(0.141195 + 5.19423i) q^{27} +(-0.709501 - 1.94934i) q^{29} +(1.02516 + 1.22174i) q^{31} +(-0.226802 + 0.275319i) q^{33} +(4.20380 - 7.28120i) q^{35} +(3.90071 + 6.75622i) q^{37} +(-2.41176 - 2.82191i) q^{39} +(4.12650 - 11.3375i) q^{41} +(6.15496 + 1.08528i) q^{43} +(-4.25549 - 4.88881i) q^{45} +(-3.44521 - 2.89087i) q^{47} +(-1.41417 - 8.02017i) q^{49} +(-11.7423 + 0.106374i) q^{51} +6.89537i q^{53} -0.444942i q^{55} +(6.66329 + 11.3034i) q^{57} +(-0.0937549 - 0.531710i) q^{59} +(0.695271 + 0.583402i) q^{61} +(-11.5320 - 1.81864i) q^{63} +(4.56001 + 0.804052i) q^{65} +(-1.77754 + 4.88376i) q^{67} +(8.87308 - 1.64758i) q^{69} +(5.04889 + 8.74494i) q^{71} +(1.46358 - 2.53500i) q^{73} +(-0.567631 - 0.0947951i) q^{75} +(-0.515154 - 0.613936i) q^{77} +(1.25749 + 3.45493i) q^{79} +(-4.21468 + 7.95213i) q^{81} +(10.0574 - 3.66058i) q^{83} +(11.2206 - 9.41520i) q^{85} +(0.591846 - 3.54396i) q^{87} +(-9.79768 - 5.65669i) q^{89} +(7.22287 - 4.17013i) q^{91} +(0.504309 + 2.71597i) q^{93} +(-15.3799 - 5.59782i) q^{95} +(1.67663 - 9.50863i) q^{97} +(-0.576651 + 0.221795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\)

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
\(3\) 1.50778 + 0.852402i 0.870519 + 0.492134i
\(4\) 0 0
\(5\) −2.12767 + 0.375166i −0.951524 + 0.167779i −0.627802 0.778373i \(-0.716045\pi\)
−0.323722 + 0.946152i \(0.604934\pi\)
\(6\) 0 0
\(7\) −2.50142 + 2.98107i −0.945447 + 1.12674i 0.0463507 + 0.998925i \(0.485241\pi\)
−0.991798 + 0.127815i \(0.959204\pi\)
\(8\) 0 0
\(9\) 1.54682 + 2.57047i 0.515607 + 0.856825i
\(10\) 0 0
\(11\) −0.0357619 + 0.202816i −0.0107826 + 0.0611513i −0.989724 0.142989i \(-0.954329\pi\)
0.978942 + 0.204140i \(0.0654398\pi\)
\(12\) 0 0
\(13\) −2.01394 0.733014i −0.558566 0.203302i 0.0472822 0.998882i \(-0.484944\pi\)
−0.605848 + 0.795580i \(0.707166\pi\)
\(14\) 0 0
\(15\) −3.52786 1.24796i −0.910890 0.322223i
\(16\) 0 0
\(17\) −5.87137 + 3.38984i −1.42402 + 0.822156i −0.996639 0.0819176i \(-0.973896\pi\)
−0.427377 + 0.904074i \(0.640562\pi\)
\(18\) 0 0
\(19\) 6.56062 + 3.78777i 1.50511 + 0.868975i 0.999982 + 0.00592975i \(0.00188751\pi\)
0.505127 + 0.863045i \(0.331446\pi\)
\(20\) 0 0
\(21\) −6.31267 + 2.36260i −1.37754 + 0.515562i
\(22\) 0 0
\(23\) 3.99143 3.34921i 0.832271 0.698358i −0.123540 0.992340i \(-0.539425\pi\)
0.955811 + 0.293982i \(0.0949804\pi\)
\(24\) 0 0
\(25\) −0.312223 + 0.113640i −0.0624446 + 0.0227280i
\(26\) 0 0
\(27\) 0.141195 + 5.19423i 0.0271730 + 0.999631i
\(28\) 0 0
\(29\) −0.709501 1.94934i −0.131751 0.361983i 0.856222 0.516608i \(-0.172805\pi\)
−0.987973 + 0.154625i \(0.950583\pi\)
\(30\) 0 0
\(31\) 1.02516 + 1.22174i 0.184125 + 0.219431i 0.850209 0.526445i \(-0.176475\pi\)
−0.666084 + 0.745876i \(0.732031\pi\)
\(32\) 0 0
\(33\) −0.226802 + 0.275319i −0.0394811 + 0.0479269i
\(34\) 0 0
\(35\) 4.20380 7.28120i 0.710572 1.23075i
\(36\) 0 0
\(37\) 3.90071 + 6.75622i 0.641272 + 1.11072i 0.985149 + 0.171701i \(0.0549264\pi\)
−0.343877 + 0.939015i \(0.611740\pi\)
\(38\) 0 0
\(39\) −2.41176 2.82191i −0.386191 0.451868i
\(40\) 0 0
\(41\) 4.12650 11.3375i 0.644452 1.77062i 0.00718287 0.999974i \(-0.497714\pi\)
0.637269 0.770642i \(-0.280064\pi\)
\(42\) 0 0
\(43\) 6.15496 + 1.08528i 0.938622 + 0.165504i 0.621973 0.783038i \(-0.286331\pi\)
0.316649 + 0.948543i \(0.397442\pi\)
\(44\) 0 0
\(45\) −4.25549 4.88881i −0.634370 0.728781i
\(46\) 0 0
\(47\) −3.44521 2.89087i −0.502535 0.421677i 0.355958 0.934502i \(-0.384155\pi\)
−0.858493 + 0.512825i \(0.828599\pi\)
\(48\) 0 0
\(49\) −1.41417 8.02017i −0.202025 1.14574i
\(50\) 0 0
\(51\) −11.7423 + 0.106374i −1.64424 + 0.0148953i
\(52\) 0 0
\(53\) 6.89537i 0.947152i 0.880753 + 0.473576i \(0.157037\pi\)
−0.880753 + 0.473576i \(0.842963\pi\)
\(54\) 0 0
\(55\) 0.444942i 0.0599960i
\(56\) 0 0
\(57\) 6.66329 + 11.3034i 0.882574 + 1.49718i
\(58\) 0 0
\(59\) −0.0937549 0.531710i −0.0122058 0.0692228i 0.978096 0.208152i \(-0.0667450\pi\)
−0.990302 + 0.138930i \(0.955634\pi\)
\(60\) 0 0
\(61\) 0.695271 + 0.583402i 0.0890203 + 0.0746969i 0.686212 0.727402i \(-0.259272\pi\)
−0.597191 + 0.802099i \(0.703717\pi\)
\(62\) 0 0
\(63\) −11.5320 1.81864i −1.45290 0.229127i
\(64\) 0 0
\(65\) 4.56001 + 0.804052i 0.565599 + 0.0997304i
\(66\) 0 0
\(67\) −1.77754 + 4.88376i −0.217161 + 0.596646i −0.999662 0.0260040i \(-0.991722\pi\)
0.782500 + 0.622650i \(0.213944\pi\)
\(68\) 0 0
\(69\) 8.87308 1.64758i 1.06819 0.198345i
\(70\) 0 0
\(71\) 5.04889 + 8.74494i 0.599193 + 1.03783i 0.992940 + 0.118614i \(0.0378452\pi\)
−0.393747 + 0.919219i \(0.628821\pi\)
\(72\) 0 0
\(73\) 1.46358 2.53500i 0.171299 0.296699i −0.767575 0.640959i \(-0.778537\pi\)
0.938874 + 0.344260i \(0.111870\pi\)
\(74\) 0 0
\(75\) −0.567631 0.0947951i −0.0655444 0.0109460i
\(76\) 0 0
\(77\) −0.515154 0.613936i −0.0587072 0.0699645i
\(78\) 0 0
\(79\) 1.25749 + 3.45493i 0.141479 + 0.388710i 0.990113 0.140270i \(-0.0447969\pi\)
−0.848634 + 0.528980i \(0.822575\pi\)
\(80\) 0 0
\(81\) −4.21468 + 7.95213i −0.468298 + 0.883571i
\(82\) 0 0
\(83\) 10.0574 3.66058i 1.10394 0.401800i 0.275171 0.961395i \(-0.411265\pi\)
0.828766 + 0.559595i \(0.189043\pi\)
\(84\) 0 0
\(85\) 11.2206 9.41520i 1.21704 1.02122i
\(86\) 0 0
\(87\) 0.591846 3.54396i 0.0634525 0.379953i
\(88\) 0 0
\(89\) −9.79768 5.65669i −1.03855 0.599608i −0.119129 0.992879i \(-0.538010\pi\)
−0.919423 + 0.393270i \(0.871344\pi\)
\(90\) 0 0
\(91\) 7.22287 4.17013i 0.757163 0.437148i
\(92\) 0 0
\(93\) 0.504309 + 2.71597i 0.0522944 + 0.281633i
\(94\) 0 0
\(95\) −15.3799 5.59782i −1.57794 0.574324i
\(96\) 0 0
\(97\) 1.67663 9.50863i 0.170236 0.965455i −0.773265 0.634084i \(-0.781378\pi\)
0.943500 0.331372i \(-0.107511\pi\)
\(98\) 0 0
\(99\) −0.576651 + 0.221795i −0.0579556 + 0.0222912i
\(100\) 0 0
\(101\) 5.78270 6.89155i 0.575400 0.685735i −0.397330 0.917676i \(-0.630063\pi\)
0.972730 + 0.231941i \(0.0745076\pi\)
\(102\) 0 0
\(103\) −5.36511 + 0.946015i −0.528640 + 0.0932136i −0.431597 0.902067i \(-0.642050\pi\)
−0.0970435 + 0.995280i \(0.530939\pi\)
\(104\) 0 0
\(105\) 12.5449 7.39514i 1.22426 0.721692i
\(106\) 0 0
\(107\) 1.67182 0.161621 0.0808106 0.996729i \(-0.474249\pi\)
0.0808106 + 0.996729i \(0.474249\pi\)
\(108\) 0 0
\(109\) 15.6614 1.50009 0.750043 0.661389i \(-0.230033\pi\)
0.750043 + 0.661389i \(0.230033\pi\)
\(110\) 0 0
\(111\) 0.122405 + 13.5119i 0.0116181 + 1.28249i
\(112\) 0 0
\(113\) −18.6094 + 3.28135i −1.75063 + 0.308683i −0.954890 0.296958i \(-0.904028\pi\)
−0.795738 + 0.605641i \(0.792917\pi\)
\(114\) 0 0
\(115\) −7.23595 + 8.62347i −0.674755 + 0.804142i
\(116\) 0 0
\(117\) −1.23101 6.31062i −0.113807 0.583417i
\(118\) 0 0
\(119\) 4.58140 25.9824i 0.419976 2.38180i
\(120\) 0 0
\(121\) 10.2968 + 3.74772i 0.936069 + 0.340701i
\(122\) 0 0
\(123\) 15.8860 13.5770i 1.43239 1.22420i
\(124\) 0 0
\(125\) 9.97689 5.76016i 0.892360 0.515205i
\(126\) 0 0
\(127\) −13.2182 7.63155i −1.17293 0.677191i −0.218561 0.975823i \(-0.570136\pi\)
−0.954368 + 0.298633i \(0.903470\pi\)
\(128\) 0 0
\(129\) 8.35524 + 6.88287i 0.735638 + 0.606003i
\(130\) 0 0
\(131\) −6.54614 + 5.49286i −0.571939 + 0.479914i −0.882289 0.470709i \(-0.843998\pi\)
0.310350 + 0.950622i \(0.399554\pi\)
\(132\) 0 0
\(133\) −27.7025 + 10.0829i −2.40211 + 0.874297i
\(134\) 0 0
\(135\) −2.24912 10.9987i −0.193573 0.946614i
\(136\) 0 0
\(137\) 3.62113 + 9.94898i 0.309374 + 0.849999i 0.992779 + 0.119959i \(0.0382763\pi\)
−0.683405 + 0.730040i \(0.739501\pi\)
\(138\) 0 0
\(139\) −3.73633 4.45278i −0.316911 0.377680i 0.583948 0.811791i \(-0.301507\pi\)
−0.900859 + 0.434111i \(0.857063\pi\)
\(140\) 0 0
\(141\) −2.73044 7.29551i −0.229945 0.614393i
\(142\) 0 0
\(143\) 0.220689 0.382245i 0.0184550 0.0319649i
\(144\) 0 0
\(145\) 2.24091 + 3.88137i 0.186098 + 0.322331i
\(146\) 0 0
\(147\) 4.70414 13.2981i 0.387991 1.09681i
\(148\) 0 0
\(149\) 2.99214 8.22085i 0.245126 0.673478i −0.754722 0.656045i \(-0.772228\pi\)
0.999848 0.0174333i \(-0.00554947\pi\)
\(150\) 0 0
\(151\) 21.7992 + 3.84379i 1.77400 + 0.312803i 0.962445 0.271478i \(-0.0875125\pi\)
0.811551 + 0.584282i \(0.198624\pi\)
\(152\) 0 0
\(153\) −17.7955 9.84873i −1.43868 0.796223i
\(154\) 0 0
\(155\) −2.63957 2.21486i −0.212015 0.177902i
\(156\) 0 0
\(157\) −0.835627 4.73908i −0.0666903 0.378220i −0.999825 0.0186933i \(-0.994049\pi\)
0.933135 0.359526i \(-0.117062\pi\)
\(158\) 0 0
\(159\) −5.87763 + 10.3967i −0.466126 + 0.824514i
\(160\) 0 0
\(161\) 20.2765i 1.59801i
\(162\) 0 0
\(163\) 0.859928i 0.0673547i −0.999433 0.0336774i \(-0.989278\pi\)
0.999433 0.0336774i \(-0.0107219\pi\)
\(164\) 0 0
\(165\) 0.379270 0.670877i 0.0295261 0.0522277i
\(166\) 0 0
\(167\) 2.13490 + 12.1076i 0.165203 + 0.936915i 0.948854 + 0.315714i \(0.102244\pi\)
−0.783651 + 0.621201i \(0.786645\pi\)
\(168\) 0 0
\(169\) −6.43994 5.40375i −0.495380 0.415673i
\(170\) 0 0
\(171\) 0.411729 + 22.7229i 0.0314857 + 1.73766i
\(172\) 0 0
\(173\) 18.9738 + 3.34560i 1.44255 + 0.254361i 0.839509 0.543346i \(-0.182843\pi\)
0.603045 + 0.797707i \(0.293954\pi\)
\(174\) 0 0
\(175\) 0.442231 1.21502i 0.0334295 0.0918469i
\(176\) 0 0
\(177\) 0.311869 0.881621i 0.0234415 0.0662667i
\(178\) 0 0
\(179\) 6.93879 + 12.0183i 0.518629 + 0.898292i 0.999766 + 0.0216464i \(0.00689082\pi\)
−0.481136 + 0.876646i \(0.659776\pi\)
\(180\) 0 0
\(181\) −12.0771 + 20.9182i −0.897687 + 1.55484i −0.0672441 + 0.997737i \(0.521421\pi\)
−0.830443 + 0.557103i \(0.811913\pi\)
\(182\) 0 0
\(183\) 0.551026 + 1.47229i 0.0407330 + 0.108835i
\(184\) 0 0
\(185\) −10.8341 12.9116i −0.796541 0.949281i
\(186\) 0 0
\(187\) −0.477541 1.31203i −0.0349213 0.0959454i
\(188\) 0 0
\(189\) −15.8376 12.5720i −1.15201 0.914481i
\(190\) 0 0
\(191\) −6.84293 + 2.49062i −0.495137 + 0.180215i −0.577505 0.816387i \(-0.695974\pi\)
0.0823686 + 0.996602i \(0.473752\pi\)
\(192\) 0 0
\(193\) 7.46660 6.26522i 0.537458 0.450981i −0.333210 0.942853i \(-0.608132\pi\)
0.870667 + 0.491872i \(0.163687\pi\)
\(194\) 0 0
\(195\) 6.19013 + 5.09929i 0.443284 + 0.365168i
\(196\) 0 0
\(197\) −5.00953 2.89226i −0.356914 0.206065i 0.310812 0.950471i \(-0.399399\pi\)
−0.667726 + 0.744407i \(0.732732\pi\)
\(198\) 0 0
\(199\) 3.57936 2.06654i 0.253734 0.146493i −0.367739 0.929929i \(-0.619868\pi\)
0.621473 + 0.783436i \(0.286535\pi\)
\(200\) 0 0
\(201\) −6.84307 + 5.84847i −0.482673 + 0.412519i
\(202\) 0 0
\(203\) 7.58588 + 2.76104i 0.532425 + 0.193787i
\(204\) 0 0
\(205\) −4.52641 + 25.6706i −0.316138 + 1.79291i
\(206\) 0 0
\(207\) 14.7831 + 5.07924i 1.02750 + 0.353032i
\(208\) 0 0
\(209\) −1.00284 + 1.19514i −0.0693680 + 0.0826695i
\(210\) 0 0
\(211\) −9.16208 + 1.61552i −0.630744 + 0.111217i −0.479875 0.877337i \(-0.659318\pi\)
−0.150868 + 0.988554i \(0.548207\pi\)
\(212\) 0 0
\(213\) 0.158435 + 17.4892i 0.0108558 + 1.19834i
\(214\) 0 0
\(215\) −13.5029 −0.920890
\(216\) 0 0
\(217\) −6.20646 −0.421322
\(218\) 0 0
\(219\) 4.36760 2.57467i 0.295135 0.173980i
\(220\) 0 0
\(221\) 14.3094 2.52313i 0.962553 0.169724i
\(222\) 0 0
\(223\) 0.613674 0.731349i 0.0410947 0.0489747i −0.745106 0.666946i \(-0.767601\pi\)
0.786200 + 0.617972i \(0.212045\pi\)
\(224\) 0 0
\(225\) −0.775062 0.626781i −0.0516708 0.0417854i
\(226\) 0 0
\(227\) −4.84335 + 27.4680i −0.321465 + 1.82312i 0.211972 + 0.977276i \(0.432011\pi\)
−0.533436 + 0.845840i \(0.679100\pi\)
\(228\) 0 0
\(229\) −11.0424 4.01909i −0.729700 0.265589i −0.0496624 0.998766i \(-0.515815\pi\)
−0.680038 + 0.733177i \(0.738037\pi\)
\(230\) 0 0
\(231\) −0.253420 1.36480i −0.0166738 0.0897973i
\(232\) 0 0
\(233\) −12.8253 + 7.40471i −0.840216 + 0.485099i −0.857337 0.514755i \(-0.827883\pi\)
0.0171219 + 0.999853i \(0.494550\pi\)
\(234\) 0 0
\(235\) 8.41483 + 4.85831i 0.548923 + 0.316921i
\(236\) 0 0
\(237\) −1.04896 + 6.28118i −0.0681375 + 0.408006i
\(238\) 0 0
\(239\) −18.1559 + 15.2346i −1.17441 + 0.985446i −0.174409 + 0.984673i \(0.555801\pi\)
−1.00000 0.000772466i \(0.999754\pi\)
\(240\) 0 0
\(241\) −7.90441 + 2.87697i −0.509168 + 0.185322i −0.583813 0.811888i \(-0.698440\pi\)
0.0746451 + 0.997210i \(0.476218\pi\)
\(242\) 0 0
\(243\) −13.1332 + 8.39749i −0.842498 + 0.538700i
\(244\) 0 0
\(245\) 6.01779 + 16.5338i 0.384463 + 1.05630i
\(246\) 0 0
\(247\) −10.4362 12.4374i −0.664039 0.791371i
\(248\) 0 0
\(249\) 18.2846 + 3.05355i 1.15874 + 0.193511i
\(250\) 0 0
\(251\) 7.92565 13.7276i 0.500263 0.866481i −0.499737 0.866177i \(-0.666570\pi\)
1.00000 0.000303448i \(-9.65905e-5\pi\)
\(252\) 0 0
\(253\) 0.536531 + 0.929300i 0.0337314 + 0.0584246i
\(254\) 0 0
\(255\) 24.9438 4.63162i 1.56204 0.290044i
\(256\) 0 0
\(257\) −3.10717 + 8.53688i −0.193820 + 0.532516i −0.998092 0.0617455i \(-0.980333\pi\)
0.804272 + 0.594261i \(0.202555\pi\)
\(258\) 0 0
\(259\) −29.8981 5.27184i −1.85778 0.327576i
\(260\) 0 0
\(261\) 3.91325 4.83904i 0.242224 0.299529i
\(262\) 0 0
\(263\) 14.0506 + 11.7898i 0.866396 + 0.726993i 0.963336 0.268297i \(-0.0864610\pi\)
−0.0969397 + 0.995290i \(0.530905\pi\)
\(264\) 0 0
\(265\) −2.58691 14.6711i −0.158913 0.901238i
\(266\) 0 0
\(267\) −9.95101 16.8806i −0.608992 1.03308i
\(268\) 0 0
\(269\) 15.0367i 0.916806i 0.888745 + 0.458403i \(0.151578\pi\)
−0.888745 + 0.458403i \(0.848422\pi\)
\(270\) 0 0
\(271\) 17.2892i 1.05025i −0.851027 0.525123i \(-0.824019\pi\)
0.851027 0.525123i \(-0.175981\pi\)
\(272\) 0 0
\(273\) 14.4452 0.130859i 0.874261 0.00791996i
\(274\) 0 0
\(275\) −0.0118823 0.0673878i −0.000716528 0.00406363i
\(276\) 0 0
\(277\) −9.22261 7.73869i −0.554133 0.464973i 0.322205 0.946670i \(-0.395576\pi\)
−0.876338 + 0.481697i \(0.840020\pi\)
\(278\) 0 0
\(279\) −1.55471 + 4.52497i −0.0930781 + 0.270903i
\(280\) 0 0
\(281\) 7.09306 + 1.25070i 0.423137 + 0.0746104i 0.381162 0.924508i \(-0.375524\pi\)
0.0419746 + 0.999119i \(0.486635\pi\)
\(282\) 0 0
\(283\) 10.6550 29.2743i 0.633373 1.74018i −0.0382310 0.999269i \(-0.512172\pi\)
0.671604 0.740910i \(-0.265605\pi\)
\(284\) 0 0
\(285\) −18.4179 21.5502i −1.09099 1.27652i
\(286\) 0 0
\(287\) 23.4757 + 40.6612i 1.38573 + 2.40015i
\(288\) 0 0
\(289\) 14.4820 25.0835i 0.851881 1.47550i
\(290\) 0 0
\(291\) 10.6332 12.9078i 0.623327 0.756668i
\(292\) 0 0
\(293\) −14.3668 17.1217i −0.839316 1.00026i −0.999912 0.0132378i \(-0.995786\pi\)
0.160596 0.987020i \(-0.448658\pi\)
\(294\) 0 0
\(295\) 0.398959 + 1.09613i 0.0232283 + 0.0638193i
\(296\) 0 0
\(297\) −1.05852 0.157119i −0.0614217 0.00911698i
\(298\) 0 0
\(299\) −10.4935 + 3.81933i −0.606856 + 0.220877i
\(300\) 0 0
\(301\) −18.6314 + 15.6336i −1.07390 + 0.901107i
\(302\) 0 0
\(303\) 14.5934 5.46179i 0.838371 0.313771i
\(304\) 0 0
\(305\) −1.69818 0.980446i −0.0972376 0.0561402i
\(306\) 0 0
\(307\) 8.17802 4.72158i 0.466744 0.269475i −0.248132 0.968726i \(-0.579817\pi\)
0.714876 + 0.699252i \(0.246483\pi\)
\(308\) 0 0
\(309\) −8.89582 3.14685i −0.506065 0.179018i
\(310\) 0 0
\(311\) 11.0789 + 4.03239i 0.628227 + 0.228656i 0.636460 0.771310i \(-0.280398\pi\)
−0.00823228 + 0.999966i \(0.502620\pi\)
\(312\) 0 0
\(313\) −1.74976 + 9.92336i −0.0989020 + 0.560901i 0.894580 + 0.446909i \(0.147475\pi\)
−0.993482 + 0.113993i \(0.963636\pi\)
\(314\) 0 0
\(315\) 25.2187 0.456951i 1.42091 0.0257463i
\(316\) 0 0
\(317\) 9.34365 11.1353i 0.524792 0.625422i −0.436915 0.899503i \(-0.643929\pi\)
0.961707 + 0.274080i \(0.0883734\pi\)
\(318\) 0 0
\(319\) 0.420730 0.0741861i 0.0235564 0.00415362i
\(320\) 0 0
\(321\) 2.52075 + 1.42506i 0.140694 + 0.0795394i
\(322\) 0 0
\(323\) −51.3597 −2.85773
\(324\) 0 0
\(325\) 0.712098 0.0395001
\(326\) 0 0
\(327\) 23.6140 + 13.3498i 1.30585 + 0.738244i
\(328\) 0 0
\(329\) 17.2358 3.03914i 0.950241 0.167553i
\(330\) 0 0
\(331\) −6.36795 + 7.58902i −0.350014 + 0.417130i −0.912113 0.409940i \(-0.865550\pi\)
0.562099 + 0.827070i \(0.309994\pi\)
\(332\) 0 0
\(333\) −11.3330 + 20.4773i −0.621045 + 1.12215i
\(334\) 0 0
\(335\) 1.94981 11.0579i 0.106529 0.604158i
\(336\) 0 0
\(337\) −15.9688 5.81216i −0.869874 0.316608i −0.131758 0.991282i \(-0.542062\pi\)
−0.738116 + 0.674674i \(0.764284\pi\)
\(338\) 0 0
\(339\) −30.8560 10.9152i −1.67587 0.592830i
\(340\) 0 0
\(341\) −0.284450 + 0.164227i −0.0154039 + 0.00889342i
\(342\) 0 0
\(343\) 3.85511 + 2.22575i 0.208156 + 0.120179i
\(344\) 0 0
\(345\) −18.2609 + 6.83438i −0.983134 + 0.367951i
\(346\) 0 0
\(347\) 4.11669 3.45432i 0.220996 0.185437i −0.525568 0.850752i \(-0.676147\pi\)
0.746563 + 0.665314i \(0.231703\pi\)
\(348\) 0 0
\(349\) 16.9030 6.15220i 0.904799 0.329320i 0.152625 0.988284i \(-0.451227\pi\)
0.752174 + 0.658964i \(0.229005\pi\)
\(350\) 0 0
\(351\) 3.52309 10.5644i 0.188049 0.563884i
\(352\) 0 0
\(353\) −2.47242 6.79292i −0.131594 0.361551i 0.856343 0.516407i \(-0.172731\pi\)
−0.987937 + 0.154856i \(0.950509\pi\)
\(354\) 0 0
\(355\) −14.0232 16.7122i −0.744274 0.886991i
\(356\) 0 0
\(357\) 29.0552 35.2706i 1.53776 1.86672i
\(358\) 0 0
\(359\) 10.4680 18.1311i 0.552481 0.956925i −0.445614 0.895225i \(-0.647015\pi\)
0.998095 0.0616998i \(-0.0196521\pi\)
\(360\) 0 0
\(361\) 19.1945 + 33.2458i 1.01024 + 1.74978i
\(362\) 0 0
\(363\) 12.3307 + 14.4277i 0.647195 + 0.757259i
\(364\) 0 0
\(365\) −2.16298 + 5.94273i −0.113215 + 0.311057i
\(366\) 0 0
\(367\) −10.0472 1.77160i −0.524461 0.0924766i −0.0948516 0.995491i \(-0.530238\pi\)
−0.429609 + 0.903015i \(0.641349\pi\)
\(368\) 0 0
\(369\) 35.5257 6.92998i 1.84939 0.360760i
\(370\) 0 0
\(371\) −20.5556 17.2482i −1.06719 0.895482i
\(372\) 0 0
\(373\) 2.55154 + 14.4705i 0.132114 + 0.749254i 0.976826 + 0.214034i \(0.0686603\pi\)
−0.844712 + 0.535220i \(0.820229\pi\)
\(374\) 0 0
\(375\) 19.9530 0.180755i 1.03037 0.00933413i
\(376\) 0 0
\(377\) 4.44593i 0.228977i
\(378\) 0 0
\(379\) 1.47535i 0.0757834i −0.999282 0.0378917i \(-0.987936\pi\)
0.999282 0.0378917i \(-0.0120642\pi\)
\(380\) 0 0
\(381\) −13.4251 22.7740i −0.687788 1.16675i
\(382\) 0 0
\(383\) −3.50484 19.8770i −0.179089 1.01567i −0.933317 0.359053i \(-0.883100\pi\)
0.754228 0.656613i \(-0.228011\pi\)
\(384\) 0 0
\(385\) 1.32641 + 1.11299i 0.0675999 + 0.0567231i
\(386\) 0 0
\(387\) 6.73092 + 17.4999i 0.342152 + 0.889570i
\(388\) 0 0
\(389\) 12.1450 + 2.14149i 0.615777 + 0.108578i 0.472832 0.881153i \(-0.343232\pi\)
0.142945 + 0.989731i \(0.454343\pi\)
\(390\) 0 0
\(391\) −12.0819 + 33.1947i −0.611008 + 1.67873i
\(392\) 0 0
\(393\) −14.5523 + 2.70211i −0.734066 + 0.136303i
\(394\) 0 0
\(395\) −3.97170 6.87919i −0.199838 0.346130i
\(396\) 0 0
\(397\) −8.83157 + 15.2967i −0.443244 + 0.767720i −0.997928 0.0643404i \(-0.979506\pi\)
0.554684 + 0.832061i \(0.312839\pi\)
\(398\) 0 0
\(399\) −50.3640 8.41085i −2.52135 0.421069i
\(400\) 0 0
\(401\) 9.13835 + 10.8907i 0.456347 + 0.543853i 0.944330 0.329000i \(-0.106712\pi\)
−0.487983 + 0.872853i \(0.662267\pi\)
\(402\) 0 0
\(403\) −1.16906 3.21197i −0.0582351 0.160000i
\(404\) 0 0
\(405\) 5.98409 18.5007i 0.297352 0.919309i
\(406\) 0 0
\(407\) −1.50977 + 0.549510i −0.0748363 + 0.0272382i
\(408\) 0 0
\(409\) 14.7136 12.3461i 0.727539 0.610477i −0.201921 0.979402i \(-0.564718\pi\)
0.929459 + 0.368925i \(0.120274\pi\)
\(410\) 0 0
\(411\) −3.02065 + 18.0876i −0.148997 + 0.892194i
\(412\) 0 0
\(413\) 1.81959 + 1.05054i 0.0895361 + 0.0516937i
\(414\) 0 0
\(415\) −20.0254 + 11.5617i −0.983009 + 0.567541i
\(416\) 0 0
\(417\) −1.83801 9.89868i −0.0900079 0.484741i
\(418\) 0 0
\(419\) −5.36997 1.95451i −0.262340 0.0954840i 0.207502 0.978235i \(-0.433467\pi\)
−0.469842 + 0.882751i \(0.655689\pi\)
\(420\) 0 0
\(421\) 4.99357 28.3200i 0.243372 1.38023i −0.580872 0.813995i \(-0.697288\pi\)
0.824244 0.566235i \(-0.191601\pi\)
\(422\) 0 0
\(423\) 2.10179 13.3275i 0.102193 0.648005i
\(424\) 0 0
\(425\) 1.44796 1.72561i 0.0702361 0.0837042i
\(426\) 0 0
\(427\) −3.47833 + 0.613323i −0.168328 + 0.0296808i
\(428\) 0 0
\(429\) 0.658578 0.388227i 0.0317964 0.0187438i
\(430\) 0 0
\(431\) 14.3077 0.689176 0.344588 0.938754i \(-0.388019\pi\)
0.344588 + 0.938754i \(0.388019\pi\)
\(432\) 0 0
\(433\) 2.66463 0.128054 0.0640269 0.997948i \(-0.479606\pi\)
0.0640269 + 0.997948i \(0.479606\pi\)
\(434\) 0 0
\(435\) 0.0703202 + 7.76243i 0.00337159 + 0.372180i
\(436\) 0 0
\(437\) 38.8723 6.85423i 1.85951 0.327882i
\(438\) 0 0
\(439\) 24.2181 28.8620i 1.15587 1.37751i 0.242609 0.970124i \(-0.421997\pi\)
0.913257 0.407383i \(-0.133559\pi\)
\(440\) 0 0
\(441\) 18.4282 16.0409i 0.877533 0.763851i
\(442\) 0 0
\(443\) −3.46327 + 19.6412i −0.164545 + 0.933179i 0.784988 + 0.619511i \(0.212669\pi\)
−0.949533 + 0.313668i \(0.898442\pi\)
\(444\) 0 0
\(445\) 22.9685 + 8.35983i 1.08881 + 0.396294i
\(446\) 0 0
\(447\) 11.5190 9.84475i 0.544828 0.465641i
\(448\) 0 0
\(449\) 24.0203 13.8682i 1.13359 0.654479i 0.188755 0.982024i \(-0.439555\pi\)
0.944835 + 0.327546i \(0.106222\pi\)
\(450\) 0 0
\(451\) 2.15185 + 1.24237i 0.101327 + 0.0585009i
\(452\) 0 0
\(453\) 29.5921 + 24.3773i 1.39036 + 1.14535i
\(454\) 0 0
\(455\) −13.8034 + 11.5824i −0.647114 + 0.542993i
\(456\) 0 0
\(457\) −0.0182308 + 0.00663549i −0.000852803 + 0.000310395i −0.342447 0.939537i \(-0.611256\pi\)
0.341594 + 0.939848i \(0.389033\pi\)
\(458\) 0 0
\(459\) −18.4366 30.0186i −0.860547 1.40115i
\(460\) 0 0
\(461\) −7.58160 20.8303i −0.353110 0.970163i −0.981365 0.192155i \(-0.938452\pi\)
0.628254 0.778008i \(-0.283770\pi\)
\(462\) 0 0
\(463\) 26.6835 + 31.8001i 1.24009 + 1.47788i 0.822018 + 0.569461i \(0.192848\pi\)
0.418068 + 0.908416i \(0.362707\pi\)
\(464\) 0 0
\(465\) −2.09194 5.58950i −0.0970116 0.259207i
\(466\) 0 0
\(467\) 11.4135 19.7688i 0.528154 0.914789i −0.471307 0.881969i \(-0.656218\pi\)
0.999461 0.0328204i \(-0.0104489\pi\)
\(468\) 0 0
\(469\) −10.1125 17.5153i −0.466950 0.808782i
\(470\) 0 0
\(471\) 2.77965 7.85779i 0.128080 0.362068i
\(472\) 0 0
\(473\) −0.440226 + 1.20951i −0.0202416 + 0.0556134i
\(474\) 0 0
\(475\) −2.47882 0.437082i −0.113736 0.0200547i
\(476\) 0 0
\(477\) −17.7244 + 10.6659i −0.811543 + 0.488358i
\(478\) 0 0
\(479\) −2.42704 2.03652i −0.110894 0.0930512i 0.585655 0.810561i \(-0.300838\pi\)
−0.696549 + 0.717510i \(0.745282\pi\)
\(480\) 0 0
\(481\) −2.90338 16.4659i −0.132383 0.750780i
\(482\) 0 0
\(483\) −17.2837 + 30.5726i −0.786438 + 1.39110i
\(484\) 0 0
\(485\) 20.8603i 0.947216i
\(486\) 0 0
\(487\) 26.6585i 1.20801i −0.796980 0.604005i \(-0.793571\pi\)
0.796980 0.604005i \(-0.206429\pi\)
\(488\) 0 0
\(489\) 0.733004 1.29658i 0.0331476 0.0586336i
\(490\) 0 0
\(491\) 0.111406 + 0.631817i 0.00502770 + 0.0285135i 0.987218 0.159373i \(-0.0509473\pi\)
−0.982191 + 0.187887i \(0.939836\pi\)
\(492\) 0 0
\(493\) 10.7737 + 9.04019i 0.485222 + 0.407150i
\(494\) 0 0
\(495\) 1.14371 0.688247i 0.0514061 0.0309344i
\(496\) 0 0
\(497\) −38.6987 6.82363i −1.73587 0.306081i
\(498\) 0 0
\(499\) 0.174102 0.478340i 0.00779386 0.0214134i −0.935735 0.352705i \(-0.885262\pi\)
0.943529 + 0.331291i \(0.107484\pi\)
\(500\) 0 0
\(501\) −7.10159 + 20.0755i −0.317276 + 0.896905i
\(502\) 0 0
\(503\) 17.3187 + 29.9969i 0.772203 + 1.33750i 0.936353 + 0.351060i \(0.114179\pi\)
−0.164150 + 0.986435i \(0.552488\pi\)
\(504\) 0 0
\(505\) −9.71821 + 16.8324i −0.432455 + 0.749034i
\(506\) 0 0
\(507\) −5.10386 13.6371i −0.226671 0.605645i
\(508\) 0 0
\(509\) −6.71875 8.00710i −0.297804 0.354908i 0.596306 0.802757i \(-0.296635\pi\)
−0.894109 + 0.447849i \(0.852190\pi\)
\(510\) 0 0
\(511\) 3.89599 + 10.7041i 0.172348 + 0.473523i
\(512\) 0 0
\(513\) −18.7483 + 34.6122i −0.827756 + 1.52817i
\(514\) 0 0
\(515\) 11.0603 4.02562i 0.487375 0.177390i
\(516\) 0 0
\(517\) 0.709522 0.595360i 0.0312048 0.0261839i
\(518\) 0 0
\(519\) 25.7566 + 21.2178i 1.13059 + 0.931357i
\(520\) 0 0
\(521\) −18.6891 10.7902i −0.818785 0.472726i 0.0312124 0.999513i \(-0.490063\pi\)
−0.849997 + 0.526787i \(0.823397\pi\)
\(522\) 0 0
\(523\) −2.21284 + 1.27758i −0.0967607 + 0.0558648i −0.547600 0.836741i \(-0.684458\pi\)
0.450839 + 0.892605i \(0.351125\pi\)
\(524\) 0 0
\(525\) 1.70247 1.45503i 0.0743021 0.0635027i
\(526\) 0 0
\(527\) −10.1606 3.69816i −0.442603 0.161094i
\(528\) 0 0
\(529\) 0.720415 4.08568i 0.0313224 0.177638i
\(530\) 0 0
\(531\) 1.22173 1.06346i 0.0530184 0.0461501i
\(532\) 0 0
\(533\) −16.6211 + 19.8082i −0.719938 + 0.857988i
\(534\) 0 0
\(535\) −3.55709 + 0.627211i −0.153786 + 0.0271167i
\(536\) 0 0
\(537\) 0.217740 + 24.0357i 0.00939618 + 1.03722i
\(538\) 0 0
\(539\) 1.67719 0.0722418
\(540\) 0 0
\(541\) −11.9264 −0.512754 −0.256377 0.966577i \(-0.582529\pi\)
−0.256377 + 0.966577i \(0.582529\pi\)
\(542\) 0 0
\(543\) −36.0405 + 21.2456i −1.54664 + 0.911735i
\(544\) 0 0
\(545\) −33.3223 + 5.87561i −1.42737 + 0.251684i
\(546\) 0 0
\(547\) 13.7484 16.3847i 0.587838 0.700558i −0.387351 0.921932i \(-0.626610\pi\)
0.975189 + 0.221374i \(0.0710543\pi\)
\(548\) 0 0
\(549\) −0.424159 + 2.68960i −0.0181027 + 0.114789i
\(550\) 0 0
\(551\) 2.72889 15.4763i 0.116255 0.659313i
\(552\) 0 0
\(553\) −13.4449 4.89355i −0.571736 0.208095i
\(554\) 0 0
\(555\) −5.32964 28.7030i −0.226231 1.21837i
\(556\) 0 0
\(557\) 23.2042 13.3970i 0.983196 0.567648i 0.0799622 0.996798i \(-0.474520\pi\)
0.903233 + 0.429150i \(0.141187\pi\)
\(558\) 0 0
\(559\) −11.6002 6.69737i −0.490635 0.283268i
\(560\) 0 0
\(561\) 0.398351 2.38532i 0.0168184 0.100708i
\(562\) 0 0
\(563\) 22.0741 18.5223i 0.930311 0.780624i −0.0455620 0.998962i \(-0.514508\pi\)
0.975873 + 0.218338i \(0.0700634\pi\)
\(564\) 0 0
\(565\) 38.3637 13.9633i 1.61397 0.587439i
\(566\) 0 0
\(567\) −13.1632 32.4559i −0.552803 1.36302i
\(568\) 0 0
\(569\) −9.21939 25.3301i −0.386497 1.06189i −0.968567 0.248753i \(-0.919979\pi\)
0.582070 0.813138i \(-0.302243\pi\)
\(570\) 0 0
\(571\) 2.01830 + 2.40531i 0.0844631 + 0.100659i 0.806621 0.591069i \(-0.201294\pi\)
−0.722158 + 0.691728i \(0.756850\pi\)
\(572\) 0 0
\(573\) −12.4407 2.07761i −0.519716 0.0867932i
\(574\) 0 0
\(575\) −0.865612 + 1.49928i −0.0360985 + 0.0625245i
\(576\) 0 0
\(577\) −19.8980 34.4644i −0.828366 1.43477i −0.899319 0.437292i \(-0.855937\pi\)
0.0709533 0.997480i \(-0.477396\pi\)
\(578\) 0 0
\(579\) 16.5985 3.08205i 0.689811 0.128086i
\(580\) 0 0
\(581\) −14.2452 + 39.1383i −0.590990 + 1.62373i
\(582\) 0 0
\(583\) −1.39849 0.246592i −0.0579196 0.0102128i
\(584\) 0 0
\(585\) 4.98672 + 12.9651i 0.206176 + 0.536041i
\(586\) 0 0
\(587\) 12.9410 + 10.8588i 0.534132 + 0.448190i 0.869525 0.493888i \(-0.164425\pi\)
−0.335394 + 0.942078i \(0.608869\pi\)
\(588\) 0 0
\(589\) 2.09802 + 11.8985i 0.0864474 + 0.490268i
\(590\) 0 0
\(591\) −5.08793 8.63103i −0.209289 0.355033i
\(592\) 0 0
\(593\) 0.0610029i 0.00250509i −0.999999 0.00125254i \(-0.999601\pi\)
0.999999 0.00125254i \(-0.000398697\pi\)
\(594\) 0 0
\(595\) 57.0008i 2.33680i
\(596\) 0 0
\(597\) 7.15842 0.0648484i 0.292975 0.00265407i
\(598\) 0 0
\(599\) −4.17873 23.6987i −0.170738 0.968304i −0.942949 0.332938i \(-0.891960\pi\)
0.772211 0.635366i \(-0.219151\pi\)
\(600\) 0 0
\(601\) −18.4133 15.4506i −0.751095 0.630244i 0.184697 0.982795i \(-0.440870\pi\)
−0.935792 + 0.352552i \(0.885314\pi\)
\(602\) 0 0
\(603\) −15.3031 + 2.98518i −0.623191 + 0.121566i
\(604\) 0 0
\(605\) −23.3142 4.11091i −0.947855 0.167132i
\(606\) 0 0
\(607\) −0.920929 + 2.53023i −0.0373794 + 0.102699i −0.956978 0.290160i \(-0.906292\pi\)
0.919599 + 0.392859i \(0.128514\pi\)
\(608\) 0 0
\(609\) 9.08436 + 10.6293i 0.368117 + 0.430720i
\(610\) 0 0
\(611\) 4.81939 + 8.34743i 0.194972 + 0.337701i
\(612\) 0 0
\(613\) 13.5649 23.4951i 0.547880 0.948957i −0.450539 0.892757i \(-0.648768\pi\)
0.998420 0.0562001i \(-0.0178985\pi\)
\(614\) 0 0
\(615\) −28.7065 + 34.8473i −1.15756 + 1.40518i
\(616\) 0 0
\(617\) 21.5765 + 25.7138i 0.868635 + 1.03520i 0.999043 + 0.0437387i \(0.0139269\pi\)
−0.130408 + 0.991460i \(0.541629\pi\)
\(618\) 0 0
\(619\) 15.2455 + 41.8867i 0.612769 + 1.68357i 0.724022 + 0.689776i \(0.242291\pi\)
−0.111254 + 0.993792i \(0.535487\pi\)
\(620\) 0 0
\(621\) 17.9601 + 20.2595i 0.720715 + 0.812987i
\(622\) 0 0
\(623\) 41.3711 15.0579i 1.65750 0.603280i
\(624\) 0 0
\(625\) −17.7939 + 14.9309i −0.711756 + 0.597235i
\(626\) 0 0
\(627\) −2.53081 + 0.947188i −0.101071 + 0.0378270i
\(628\) 0 0
\(629\) −45.8050 26.4455i −1.82636 1.05445i
\(630\) 0 0
\(631\) 22.8750 13.2069i 0.910640 0.525758i 0.0300027 0.999550i \(-0.490448\pi\)
0.880637 + 0.473792i \(0.157115\pi\)
\(632\) 0 0
\(633\) −15.1915 5.37392i −0.603808 0.213594i
\(634\) 0 0
\(635\) 30.9872 + 11.2784i 1.22969 + 0.447570i
\(636\) 0 0
\(637\) −3.03084 + 17.1888i −0.120086 + 0.681043i
\(638\) 0 0
\(639\) −14.6689 + 26.5049i −0.580293 + 1.04852i
\(640\) 0 0
\(641\) −11.6135 + 13.8404i −0.458704 + 0.546663i −0.944974 0.327146i \(-0.893913\pi\)
0.486269 + 0.873809i \(0.338357\pi\)
\(642\) 0 0
\(643\) 42.9848 7.57937i 1.69515 0.298901i 0.759156 0.650908i \(-0.225612\pi\)
0.935997 + 0.352007i \(0.114501\pi\)
\(644\) 0 0
\(645\) −20.3594 11.5099i −0.801652 0.453201i
\(646\) 0 0
\(647\) −44.0779 −1.73288 −0.866441 0.499279i \(-0.833598\pi\)
−0.866441 + 0.499279i \(0.833598\pi\)
\(648\) 0 0
\(649\) 0.111192 0.00436468
\(650\) 0 0
\(651\) −9.35800 5.29040i −0.366769 0.207347i
\(652\) 0 0
\(653\) −14.7422 + 2.59945i −0.576906 + 0.101724i −0.454486 0.890754i \(-0.650177\pi\)
−0.122421 + 0.992478i \(0.539066\pi\)
\(654\) 0 0
\(655\) 11.8673 14.1429i 0.463694 0.552609i
\(656\) 0 0
\(657\) 8.78005 0.159091i 0.342542 0.00620672i
\(658\) 0 0
\(659\) 2.62215 14.8709i 0.102144 0.579290i −0.890178 0.455613i \(-0.849420\pi\)
0.992323 0.123677i \(-0.0394687\pi\)
\(660\) 0 0
\(661\) 18.1294 + 6.59856i 0.705152 + 0.256654i 0.669609 0.742714i \(-0.266462\pi\)
0.0355431 + 0.999368i \(0.488684\pi\)
\(662\) 0 0
\(663\) 23.7262 + 8.39301i 0.921448 + 0.325957i
\(664\) 0 0
\(665\) 55.1591 31.8461i 2.13898 1.23494i
\(666\) 0 0
\(667\) −9.36067 5.40438i −0.362446 0.209259i
\(668\) 0 0
\(669\) 1.54869 0.579618i 0.0598759 0.0224093i
\(670\) 0 0
\(671\) −0.143187 + 0.120148i −0.00552769 + 0.00463828i
\(672\) 0 0
\(673\) 10.3140 3.75400i 0.397576 0.144706i −0.135491 0.990779i \(-0.543261\pi\)
0.533068 + 0.846073i \(0.321039\pi\)
\(674\) 0 0
\(675\) −0.634356 1.60571i −0.0244164 0.0618039i
\(676\) 0 0
\(677\) 10.9926 + 30.2020i 0.422481 + 1.16076i 0.950283 + 0.311388i \(0.100794\pi\)
−0.527802 + 0.849367i \(0.676984\pi\)
\(678\) 0 0
\(679\) 24.1520 + 28.7832i 0.926868 + 1.10460i
\(680\) 0 0
\(681\) −30.7165 + 37.2873i −1.17706 + 1.42885i
\(682\) 0 0
\(683\) 16.0306 27.7658i 0.613394 1.06243i −0.377270 0.926103i \(-0.623137\pi\)
0.990664 0.136327i \(-0.0435297\pi\)
\(684\) 0 0
\(685\) −11.4371 19.8097i −0.436989 0.756888i
\(686\) 0 0
\(687\) −13.2236 15.4725i −0.504513 0.590311i
\(688\) 0 0
\(689\) 5.05440 13.8869i 0.192557 0.529047i
\(690\) 0 0
\(691\) −4.37408 0.771269i −0.166398 0.0293405i 0.0898284 0.995957i \(-0.471368\pi\)
−0.256226 + 0.966617i \(0.582479\pi\)
\(692\) 0 0
\(693\) 0.781257 2.27384i 0.0296775 0.0863761i
\(694\) 0 0
\(695\) 9.62021 + 8.07232i 0.364915 + 0.306200i
\(696\) 0 0
\(697\) 14.2040 + 80.5547i 0.538013 + 3.05123i
\(698\) 0 0
\(699\) −25.6496 + 0.232361i −0.970158 + 0.00878870i
\(700\) 0 0
\(701\) 27.5938i 1.04220i −0.853495 0.521101i \(-0.825522\pi\)
0.853495 0.521101i \(-0.174478\pi\)
\(702\) 0 0
\(703\) 59.1000i 2.22900i
\(704\) 0 0
\(705\) 8.54652 + 14.4981i 0.321880 + 0.546030i
\(706\) 0 0
\(707\) 6.07928 + 34.4773i 0.228635 + 1.29665i
\(708\) 0 0
\(709\) 7.46960 + 6.26774i 0.280527 + 0.235390i 0.772184 0.635399i \(-0.219164\pi\)
−0.491657 + 0.870789i \(0.663609\pi\)
\(710\) 0 0
\(711\) −6.93570 + 8.57652i −0.260109 + 0.321644i
\(712\) 0 0
\(713\) 8.18373 + 1.44301i 0.306483 + 0.0540412i
\(714\) 0 0
\(715\) −0.326149 + 0.896087i −0.0121973 + 0.0335118i
\(716\) 0 0
\(717\) −40.3612 + 7.49438i −1.50732 + 0.279883i
\(718\) 0 0
\(719\) −16.5609 28.6843i −0.617616 1.06974i −0.989920 0.141631i \(-0.954765\pi\)
0.372304 0.928111i \(-0.378568\pi\)
\(720\) 0 0
\(721\) 10.6003 18.3602i 0.394774 0.683769i
\(722\) 0 0
\(723\) −14.3705 2.39989i −0.534444 0.0892527i
\(724\) 0 0
\(725\) 0.443045 + 0.528001i 0.0164543 + 0.0196095i
\(726\) 0 0
\(727\) −3.52972 9.69783i −0.130910 0.359673i 0.856869 0.515535i \(-0.172407\pi\)
−0.987779 + 0.155862i \(0.950184\pi\)
\(728\) 0 0
\(729\) −26.9601 + 1.46680i −0.998523 + 0.0543260i
\(730\) 0 0
\(731\) −39.8170 + 14.4922i −1.47268 + 0.536013i
\(732\) 0 0
\(733\) −18.0067 + 15.1094i −0.665091 + 0.558078i −0.911608 0.411061i \(-0.865158\pi\)
0.246517 + 0.969138i \(0.420714\pi\)
\(734\) 0 0
\(735\) −5.01987 + 30.0589i −0.185161 + 1.10874i
\(736\) 0 0
\(737\) −0.926936 0.535166i −0.0341441 0.0197131i
\(738\) 0 0
\(739\) −18.0525 + 10.4226i −0.664073 + 0.383403i −0.793827 0.608143i \(-0.791915\pi\)
0.129754 + 0.991546i \(0.458581\pi\)
\(740\) 0 0
\(741\) −5.13388 27.6487i −0.188598 1.01570i
\(742\) 0 0
\(743\) −17.7561 6.46269i −0.651408 0.237093i −0.00488550 0.999988i \(-0.501555\pi\)
−0.646522 + 0.762895i \(0.723777\pi\)
\(744\) 0 0
\(745\) −3.28212 + 18.6138i −0.120247 + 0.681957i
\(746\) 0 0
\(747\) 24.9664 + 20.1899i 0.913471 + 0.738710i
\(748\) 0 0
\(749\) −4.18193 + 4.98383i −0.152804 + 0.182105i
\(750\) 0 0
\(751\) −0.970086 + 0.171052i −0.0353989 + 0.00624179i −0.191320 0.981528i \(-0.561277\pi\)
0.155921 + 0.987770i \(0.450166\pi\)
\(752\) 0 0
\(753\) 23.6516 13.9425i 0.861913 0.508091i
\(754\) 0 0
\(755\) −47.8237 −1.74048
\(756\) 0 0
\(757\) 1.04898 0.0381259 0.0190630 0.999818i \(-0.493932\pi\)
0.0190630 + 0.999818i \(0.493932\pi\)
\(758\) 0 0
\(759\) 0.0168364 + 1.85852i 0.000611124 + 0.0674601i
\(760\) 0 0
\(761\) −45.5984 + 8.04023i −1.65294 + 0.291458i −0.920899 0.389801i \(-0.872544\pi\)
−0.732043 + 0.681259i \(0.761433\pi\)
\(762\) 0 0
\(763\) −39.1756 + 46.6877i −1.41825 + 1.69021i
\(764\) 0 0
\(765\) 41.5578 + 14.2786i 1.50253 + 0.516245i
\(766\) 0 0
\(767\) −0.200935 + 1.13956i −0.00725532 + 0.0411470i
\(768\) 0 0
\(769\) 7.85772 + 2.85997i 0.283356 + 0.103133i 0.479789 0.877384i \(-0.340713\pi\)
−0.196432 + 0.980517i \(0.562936\pi\)
\(770\) 0 0
\(771\) −11.9618 + 10.2232i −0.430793 + 0.368180i
\(772\) 0 0
\(773\) −18.6959 + 10.7941i −0.672445 + 0.388236i −0.797003 0.603976i \(-0.793582\pi\)
0.124557 + 0.992212i \(0.460249\pi\)
\(774\) 0 0
\(775\) −0.458918 0.264956i −0.0164848 0.00951751i
\(776\) 0 0
\(777\) −40.5861 33.4340i −1.45602 1.19944i
\(778\) 0 0
\(779\) 70.0162 58.7506i 2.50859 2.10496i
\(780\) 0 0
\(781\) −1.95417 + 0.711260i −0.0699257 + 0.0254509i
\(782\) 0 0
\(783\) 10.0251 3.96055i 0.358269 0.141539i
\(784\) 0 0
\(785\) 3.55588 + 9.76971i 0.126915 + 0.348696i
\(786\) 0 0
\(787\) 0.551585 + 0.657353i 0.0196619 + 0.0234321i 0.775786 0.630996i \(-0.217354\pi\)
−0.756124 + 0.654428i \(0.772909\pi\)
\(788\) 0 0
\(789\) 11.1356 + 29.7533i 0.396436 + 1.05924i
\(790\) 0 0
\(791\) 36.7680 63.6841i 1.30732 2.26435i
\(792\) 0 0
\(793\) −0.972592 1.68458i −0.0345378 0.0598212i
\(794\) 0 0
\(795\) 8.60516 24.3259i 0.305194 0.862751i