Properties

Label 432.2.be.a.239.2
Level $432$
Weight $2$
Character 432.239
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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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 239.2
Character \(\chi\) \(=\) 432.239
Dual form 432.2.be.a.47.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.991247 - 1.42036i) q^{3} +(-3.85028 - 0.678908i) q^{5} +(1.90230 + 2.26708i) q^{7} +(-1.03486 + 2.81586i) q^{9} +O(q^{10})\) \(q+(-0.991247 - 1.42036i) q^{3} +(-3.85028 - 0.678908i) q^{5} +(1.90230 + 2.26708i) q^{7} +(-1.03486 + 2.81586i) q^{9} +(0.560068 + 3.17630i) q^{11} +(1.43878 - 0.523674i) q^{13} +(2.85228 + 6.14175i) q^{15} +(-2.60029 - 1.50128i) q^{17} +(4.90409 - 2.83138i) q^{19} +(1.33442 - 4.94920i) q^{21} +(6.11794 + 5.13356i) q^{23} +(9.66525 + 3.51786i) q^{25} +(5.02534 - 1.32134i) q^{27} +(-1.57709 + 4.33301i) q^{29} +(-6.11407 + 7.28646i) q^{31} +(3.95634 - 3.94400i) q^{33} +(-5.78526 - 10.0204i) q^{35} +(-2.24428 + 3.88720i) q^{37} +(-2.17000 - 1.52450i) q^{39} +(0.210120 + 0.577300i) q^{41} +(-3.35455 + 0.591498i) q^{43} +(5.89620 - 10.1393i) q^{45} +(-0.982922 + 0.824769i) q^{47} +(-0.305345 + 1.73170i) q^{49} +(0.445172 + 5.18150i) q^{51} +5.01133i q^{53} -12.6099i q^{55} +(-8.88275 - 4.15899i) q^{57} +(-0.0386715 + 0.219317i) q^{59} +(-10.2571 + 8.60675i) q^{61} +(-8.35239 + 3.01052i) q^{63} +(-5.89524 + 1.03949i) q^{65} +(1.16511 + 3.20112i) q^{67} +(1.22713 - 13.7783i) q^{69} +(4.12205 - 7.13960i) q^{71} +(3.87009 + 6.70320i) q^{73} +(-4.58401 - 17.2152i) q^{75} +(-6.13551 + 7.31202i) q^{77} +(-1.28358 + 3.52662i) q^{79} +(-6.85814 - 5.82803i) q^{81} +(11.3755 + 4.14034i) q^{83} +(8.99262 + 7.54571i) q^{85} +(7.71773 - 2.05505i) q^{87} +(0.527753 - 0.304698i) q^{89} +(3.92421 + 2.26565i) q^{91} +(16.4100 + 1.46151i) q^{93} +(-20.8044 + 7.57217i) q^{95} +(-3.21509 - 18.2337i) q^{97} +(-9.52362 - 1.70995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 6 q^{5} - 12 q^{9} + O(q^{10}) \) \( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97} + O(q^{100}) \)

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
\(3\) −0.991247 1.42036i −0.572297 0.820047i
\(4\) 0 0
\(5\) −3.85028 0.678908i −1.72190 0.303617i −0.776640 0.629945i \(-0.783077\pi\)
−0.945256 + 0.326328i \(0.894188\pi\)
\(6\) 0 0
\(7\) 1.90230 + 2.26708i 0.719004 + 0.856875i 0.994534 0.104417i \(-0.0332978\pi\)
−0.275530 + 0.961293i \(0.588853\pi\)
\(8\) 0 0
\(9\) −1.03486 + 2.81586i −0.344953 + 0.938620i
\(10\) 0 0
\(11\) 0.560068 + 3.17630i 0.168867 + 0.957692i 0.944987 + 0.327107i \(0.106074\pi\)
−0.776120 + 0.630585i \(0.782815\pi\)
\(12\) 0 0
\(13\) 1.43878 0.523674i 0.399046 0.145241i −0.134698 0.990887i \(-0.543007\pi\)
0.533745 + 0.845646i \(0.320784\pi\)
\(14\) 0 0
\(15\) 2.85228 + 6.14175i 0.736456 + 1.58579i
\(16\) 0 0
\(17\) −2.60029 1.50128i −0.630664 0.364114i 0.150345 0.988634i \(-0.451962\pi\)
−0.781009 + 0.624520i \(0.785295\pi\)
\(18\) 0 0
\(19\) 4.90409 2.83138i 1.12508 0.649563i 0.182384 0.983227i \(-0.441619\pi\)
0.942692 + 0.333665i \(0.108285\pi\)
\(20\) 0 0
\(21\) 1.33442 4.94920i 0.291194 1.08000i
\(22\) 0 0
\(23\) 6.11794 + 5.13356i 1.27568 + 1.07042i 0.993824 + 0.110965i \(0.0353941\pi\)
0.281855 + 0.959457i \(0.409050\pi\)
\(24\) 0 0
\(25\) 9.66525 + 3.51786i 1.93305 + 0.703573i
\(26\) 0 0
\(27\) 5.02534 1.32134i 0.967127 0.254292i
\(28\) 0 0
\(29\) −1.57709 + 4.33301i −0.292858 + 0.804621i 0.702788 + 0.711400i \(0.251938\pi\)
−0.995645 + 0.0932208i \(0.970284\pi\)
\(30\) 0 0
\(31\) −6.11407 + 7.28646i −1.09812 + 1.30869i −0.150740 + 0.988573i \(0.548166\pi\)
−0.947379 + 0.320114i \(0.896279\pi\)
\(32\) 0 0
\(33\) 3.95634 3.94400i 0.688710 0.686563i
\(34\) 0 0
\(35\) −5.78526 10.0204i −0.977888 1.69375i
\(36\) 0 0
\(37\) −2.24428 + 3.88720i −0.368957 + 0.639052i −0.989403 0.145197i \(-0.953618\pi\)
0.620446 + 0.784249i \(0.286952\pi\)
\(38\) 0 0
\(39\) −2.17000 1.52450i −0.347477 0.244116i
\(40\) 0 0
\(41\) 0.210120 + 0.577300i 0.0328152 + 0.0901591i 0.955018 0.296547i \(-0.0958351\pi\)
−0.922203 + 0.386706i \(0.873613\pi\)
\(42\) 0 0
\(43\) −3.35455 + 0.591498i −0.511565 + 0.0902026i −0.423471 0.905910i \(-0.639189\pi\)
−0.0880934 + 0.996112i \(0.528077\pi\)
\(44\) 0 0
\(45\) 5.89620 10.1393i 0.878953 1.51147i
\(46\) 0 0
\(47\) −0.982922 + 0.824769i −0.143374 + 0.120305i −0.711654 0.702530i \(-0.752054\pi\)
0.568280 + 0.822835i \(0.307609\pi\)
\(48\) 0 0
\(49\) −0.305345 + 1.73170i −0.0436207 + 0.247385i
\(50\) 0 0
\(51\) 0.445172 + 5.18150i 0.0623366 + 0.725555i
\(52\) 0 0
\(53\) 5.01133i 0.688359i 0.938904 + 0.344179i \(0.111843\pi\)
−0.938904 + 0.344179i \(0.888157\pi\)
\(54\) 0 0
\(55\) 12.6099i 1.70032i
\(56\) 0 0
\(57\) −8.88275 4.15899i −1.17655 0.550872i
\(58\) 0 0
\(59\) −0.0386715 + 0.219317i −0.00503460 + 0.0285526i −0.987222 0.159354i \(-0.949059\pi\)
0.982187 + 0.187906i \(0.0601701\pi\)
\(60\) 0 0
\(61\) −10.2571 + 8.60675i −1.31329 + 1.10198i −0.325609 + 0.945504i \(0.605569\pi\)
−0.987682 + 0.156477i \(0.949986\pi\)
\(62\) 0 0
\(63\) −8.35239 + 3.01052i −1.05230 + 0.379290i
\(64\) 0 0
\(65\) −5.89524 + 1.03949i −0.731214 + 0.128933i
\(66\) 0 0
\(67\) 1.16511 + 3.20112i 0.142341 + 0.391079i 0.990293 0.138994i \(-0.0443868\pi\)
−0.847952 + 0.530073i \(0.822165\pi\)
\(68\) 0 0
\(69\) 1.22713 13.7783i 0.147729 1.65872i
\(70\) 0 0
\(71\) 4.12205 7.13960i 0.489197 0.847315i −0.510725 0.859744i \(-0.670623\pi\)
0.999923 + 0.0124293i \(0.00395647\pi\)
\(72\) 0 0
\(73\) 3.87009 + 6.70320i 0.452960 + 0.784550i 0.998568 0.0534906i \(-0.0170347\pi\)
−0.545608 + 0.838040i \(0.683701\pi\)
\(74\) 0 0
\(75\) −4.58401 17.2152i −0.529316 1.98784i
\(76\) 0 0
\(77\) −6.13551 + 7.31202i −0.699206 + 0.833282i
\(78\) 0 0
\(79\) −1.28358 + 3.52662i −0.144414 + 0.396775i −0.990719 0.135923i \(-0.956600\pi\)
0.846305 + 0.532699i \(0.178822\pi\)
\(80\) 0 0
\(81\) −6.85814 5.82803i −0.762015 0.647559i
\(82\) 0 0
\(83\) 11.3755 + 4.14034i 1.24862 + 0.454462i 0.879936 0.475092i \(-0.157585\pi\)
0.368687 + 0.929553i \(0.379807\pi\)
\(84\) 0 0
\(85\) 8.99262 + 7.54571i 0.975387 + 0.818447i
\(86\) 0 0
\(87\) 7.71773 2.05505i 0.827428 0.220325i
\(88\) 0 0
\(89\) 0.527753 0.304698i 0.0559417 0.0322980i −0.471768 0.881723i \(-0.656384\pi\)
0.527710 + 0.849425i \(0.323051\pi\)
\(90\) 0 0
\(91\) 3.92421 + 2.26565i 0.411369 + 0.237504i
\(92\) 0 0
\(93\) 16.4100 + 1.46151i 1.70163 + 0.151551i
\(94\) 0 0
\(95\) −20.8044 + 7.57217i −2.13448 + 0.776888i
\(96\) 0 0
\(97\) −3.21509 18.2337i −0.326443 1.85135i −0.499336 0.866409i \(-0.666422\pi\)
0.172893 0.984941i \(-0.444689\pi\)
\(98\) 0 0
\(99\) −9.52362 1.70995i −0.957160 0.171856i
\(100\) 0 0
\(101\) −5.45656 6.50288i −0.542948 0.647061i 0.422898 0.906177i \(-0.361013\pi\)
−0.965846 + 0.259117i \(0.916569\pi\)
\(102\) 0 0
\(103\) 8.08845 + 1.42621i 0.796978 + 0.140529i 0.557287 0.830320i \(-0.311843\pi\)
0.239692 + 0.970849i \(0.422954\pi\)
\(104\) 0 0
\(105\) −8.49793 + 18.1498i −0.829313 + 1.77124i
\(106\) 0 0
\(107\) −15.6604 −1.51395 −0.756974 0.653445i \(-0.773323\pi\)
−0.756974 + 0.653445i \(0.773323\pi\)
\(108\) 0 0
\(109\) 9.01637 0.863611 0.431806 0.901967i \(-0.357877\pi\)
0.431806 + 0.901967i \(0.357877\pi\)
\(110\) 0 0
\(111\) 7.74587 0.665492i 0.735205 0.0631657i
\(112\) 0 0
\(113\) 6.84827 + 1.20753i 0.644231 + 0.113595i 0.486212 0.873841i \(-0.338378\pi\)
0.158019 + 0.987436i \(0.449489\pi\)
\(114\) 0 0
\(115\) −20.0706 23.9192i −1.87159 2.23047i
\(116\) 0 0
\(117\) −0.0143422 + 4.59334i −0.00132593 + 0.424654i
\(118\) 0 0
\(119\) −1.54303 8.75097i −0.141449 0.802200i
\(120\) 0 0
\(121\) 0.561386 0.204328i 0.0510351 0.0185753i
\(122\) 0 0
\(123\) 0.611694 0.870694i 0.0551546 0.0785078i
\(124\) 0 0
\(125\) −17.8962 10.3324i −1.60069 0.924156i
\(126\) 0 0
\(127\) 8.87022 5.12122i 0.787105 0.454435i −0.0518375 0.998656i \(-0.516508\pi\)
0.838942 + 0.544220i \(0.183174\pi\)
\(128\) 0 0
\(129\) 4.16533 + 4.17836i 0.366737 + 0.367884i
\(130\) 0 0
\(131\) −0.436664 0.366404i −0.0381515 0.0320129i 0.623513 0.781813i \(-0.285705\pi\)
−0.661664 + 0.749800i \(0.730149\pi\)
\(132\) 0 0
\(133\) 15.7480 + 5.73182i 1.36553 + 0.497011i
\(134\) 0 0
\(135\) −20.2460 + 1.67579i −1.74250 + 0.144229i
\(136\) 0 0
\(137\) 2.42588 6.66504i 0.207257 0.569433i −0.791893 0.610659i \(-0.790904\pi\)
0.999150 + 0.0412269i \(0.0131267\pi\)
\(138\) 0 0
\(139\) 1.82538 2.17540i 0.154827 0.184515i −0.683055 0.730367i \(-0.739349\pi\)
0.837882 + 0.545851i \(0.183794\pi\)
\(140\) 0 0
\(141\) 2.14579 + 0.578555i 0.180708 + 0.0487231i
\(142\) 0 0
\(143\) 2.46916 + 4.27672i 0.206482 + 0.357637i
\(144\) 0 0
\(145\) 9.01394 15.6126i 0.748567 1.29656i
\(146\) 0 0
\(147\) 2.76231 1.28284i 0.227831 0.105807i
\(148\) 0 0
\(149\) −2.77050 7.61188i −0.226968 0.623590i 0.772973 0.634439i \(-0.218769\pi\)
−0.999941 + 0.0108491i \(0.996547\pi\)
\(150\) 0 0
\(151\) −18.5383 + 3.26880i −1.50862 + 0.266011i −0.865950 0.500130i \(-0.833285\pi\)
−0.642672 + 0.766141i \(0.722174\pi\)
\(152\) 0 0
\(153\) 6.91833 5.76845i 0.559314 0.466352i
\(154\) 0 0
\(155\) 28.4877 23.9040i 2.28819 1.92002i
\(156\) 0 0
\(157\) −1.04493 + 5.92610i −0.0833945 + 0.472954i 0.914297 + 0.405045i \(0.132744\pi\)
−0.997691 + 0.0679094i \(0.978367\pi\)
\(158\) 0 0
\(159\) 7.11790 4.96746i 0.564486 0.393945i
\(160\) 0 0
\(161\) 23.6355i 1.86273i
\(162\) 0 0
\(163\) 16.4440i 1.28800i 0.765028 + 0.643998i \(0.222725\pi\)
−0.765028 + 0.643998i \(0.777275\pi\)
\(164\) 0 0
\(165\) −17.9106 + 12.4995i −1.39434 + 0.973086i
\(166\) 0 0
\(167\) −2.56815 + 14.5647i −0.198729 + 1.12705i 0.708278 + 0.705934i \(0.249472\pi\)
−0.907007 + 0.421115i \(0.861639\pi\)
\(168\) 0 0
\(169\) −8.16272 + 6.84933i −0.627901 + 0.526872i
\(170\) 0 0
\(171\) 2.89773 + 16.7393i 0.221595 + 1.28009i
\(172\) 0 0
\(173\) 2.00249 0.353093i 0.152246 0.0268451i −0.0970054 0.995284i \(-0.530926\pi\)
0.249252 + 0.968439i \(0.419815\pi\)
\(174\) 0 0
\(175\) 10.4110 + 28.6039i 0.786996 + 2.16225i
\(176\) 0 0
\(177\) 0.349843 0.162470i 0.0262958 0.0122120i
\(178\) 0 0
\(179\) −0.253380 + 0.438867i −0.0189385 + 0.0328024i −0.875339 0.483509i \(-0.839362\pi\)
0.856401 + 0.516312i \(0.172695\pi\)
\(180\) 0 0
\(181\) −4.56085 7.89962i −0.339005 0.587174i 0.645241 0.763979i \(-0.276757\pi\)
−0.984246 + 0.176805i \(0.943424\pi\)
\(182\) 0 0
\(183\) 22.3921 + 6.03742i 1.65527 + 0.446299i
\(184\) 0 0
\(185\) 11.2801 13.4431i 0.829332 0.988359i
\(186\) 0 0
\(187\) 3.31218 9.10015i 0.242211 0.665469i
\(188\) 0 0
\(189\) 12.5553 + 8.87925i 0.913265 + 0.645870i
\(190\) 0 0
\(191\) 12.4556 + 4.53348i 0.901259 + 0.328031i 0.750757 0.660578i \(-0.229689\pi\)
0.150502 + 0.988610i \(0.451911\pi\)
\(192\) 0 0
\(193\) −15.8300 13.2829i −1.13947 0.956126i −0.140045 0.990145i \(-0.544725\pi\)
−0.999421 + 0.0340192i \(0.989169\pi\)
\(194\) 0 0
\(195\) 7.32009 + 7.34298i 0.524202 + 0.525842i
\(196\) 0 0
\(197\) 21.7739 12.5711i 1.55132 0.895657i 0.553289 0.832989i \(-0.313373\pi\)
0.998034 0.0626676i \(-0.0199608\pi\)
\(198\) 0 0
\(199\) 0.870852 + 0.502786i 0.0617330 + 0.0356416i 0.530549 0.847654i \(-0.321986\pi\)
−0.468816 + 0.883296i \(0.655319\pi\)
\(200\) 0 0
\(201\) 3.39184 4.82798i 0.239242 0.340540i
\(202\) 0 0
\(203\) −12.8234 + 4.66733i −0.900025 + 0.327582i
\(204\) 0 0
\(205\) −0.417087 2.36542i −0.0291306 0.165208i
\(206\) 0 0
\(207\) −20.7866 + 11.9148i −1.44477 + 0.828133i
\(208\) 0 0
\(209\) 11.7399 + 13.9911i 0.812069 + 0.967786i
\(210\) 0 0
\(211\) 11.1122 + 1.95939i 0.764998 + 0.134890i 0.542514 0.840046i \(-0.317472\pi\)
0.222484 + 0.974936i \(0.428583\pi\)
\(212\) 0 0
\(213\) −14.2268 + 1.22231i −0.974803 + 0.0837510i
\(214\) 0 0
\(215\) 13.3175 0.908248
\(216\) 0 0
\(217\) −28.1498 −1.91093
\(218\) 0 0
\(219\) 5.68475 12.1415i 0.384140 0.820444i
\(220\) 0 0
\(221\) −4.52744 0.798310i −0.304549 0.0537001i
\(222\) 0 0
\(223\) 2.04837 + 2.44115i 0.137169 + 0.163471i 0.830256 0.557383i \(-0.188194\pi\)
−0.693087 + 0.720854i \(0.743750\pi\)
\(224\) 0 0
\(225\) −19.9080 + 23.5755i −1.32720 + 1.57170i
\(226\) 0 0
\(227\) 2.84631 + 16.1423i 0.188917 + 1.07140i 0.920819 + 0.389990i \(0.127521\pi\)
−0.731903 + 0.681409i \(0.761367\pi\)
\(228\) 0 0
\(229\) −7.62322 + 2.77463i −0.503757 + 0.183352i −0.581383 0.813630i \(-0.697488\pi\)
0.0776261 + 0.996983i \(0.475266\pi\)
\(230\) 0 0
\(231\) 16.4675 + 1.46663i 1.08348 + 0.0964972i
\(232\) 0 0
\(233\) 5.45161 + 3.14749i 0.357147 + 0.206199i 0.667829 0.744315i \(-0.267224\pi\)
−0.310682 + 0.950514i \(0.600557\pi\)
\(234\) 0 0
\(235\) 4.34446 2.50828i 0.283402 0.163622i
\(236\) 0 0
\(237\) 6.28142 1.67260i 0.408022 0.108647i
\(238\) 0 0
\(239\) −8.17874 6.86278i −0.529039 0.443916i 0.338730 0.940883i \(-0.390003\pi\)
−0.867769 + 0.496967i \(0.834447\pi\)
\(240\) 0 0
\(241\) −17.5678 6.39416i −1.13164 0.411884i −0.292754 0.956188i \(-0.594572\pi\)
−0.838888 + 0.544304i \(0.816794\pi\)
\(242\) 0 0
\(243\) −1.47980 + 15.5181i −0.0949292 + 0.995484i
\(244\) 0 0
\(245\) 2.35132 6.46021i 0.150220 0.412727i
\(246\) 0 0
\(247\) 5.57320 6.64188i 0.354614 0.422613i
\(248\) 0 0
\(249\) −5.39515 20.2614i −0.341904 1.28402i
\(250\) 0 0
\(251\) −6.86771 11.8952i −0.433486 0.750820i 0.563685 0.825990i \(-0.309383\pi\)
−0.997171 + 0.0751704i \(0.976050\pi\)
\(252\) 0 0
\(253\) −12.8793 + 22.3076i −0.809714 + 1.40247i
\(254\) 0 0
\(255\) 1.80372 20.2524i 0.112954 1.26826i
\(256\) 0 0
\(257\) 9.34803 + 25.6835i 0.583114 + 1.60209i 0.782827 + 0.622239i \(0.213777\pi\)
−0.199713 + 0.979854i \(0.564001\pi\)
\(258\) 0 0
\(259\) −13.0819 + 2.30669i −0.812869 + 0.143331i
\(260\) 0 0
\(261\) −10.5691 8.92491i −0.654211 0.552438i
\(262\) 0 0
\(263\) −6.99737 + 5.87149i −0.431476 + 0.362051i −0.832508 0.554012i \(-0.813096\pi\)
0.401032 + 0.916064i \(0.368652\pi\)
\(264\) 0 0
\(265\) 3.40223 19.2950i 0.208997 1.18528i
\(266\) 0 0
\(267\) −0.955916 0.447569i −0.0585011 0.0273908i
\(268\) 0 0
\(269\) 1.49499i 0.0911509i 0.998961 + 0.0455754i \(0.0145121\pi\)
−0.998961 + 0.0455754i \(0.985488\pi\)
\(270\) 0 0
\(271\) 24.4160i 1.48317i −0.670861 0.741583i \(-0.734075\pi\)
0.670861 0.741583i \(-0.265925\pi\)
\(272\) 0 0
\(273\) −0.671828 7.81962i −0.0406609 0.473265i
\(274\) 0 0
\(275\) −5.76061 + 32.6700i −0.347378 + 1.97008i
\(276\) 0 0
\(277\) 5.49016 4.60679i 0.329872 0.276795i −0.462776 0.886475i \(-0.653147\pi\)
0.792648 + 0.609680i \(0.208702\pi\)
\(278\) 0 0
\(279\) −14.1905 24.7568i −0.849561 1.48215i
\(280\) 0 0
\(281\) 25.8279 4.55416i 1.54076 0.271678i 0.662209 0.749319i \(-0.269619\pi\)
0.878555 + 0.477641i \(0.158508\pi\)
\(282\) 0 0
\(283\) 4.65241 + 12.7824i 0.276557 + 0.759834i 0.997747 + 0.0670962i \(0.0213734\pi\)
−0.721190 + 0.692738i \(0.756404\pi\)
\(284\) 0 0
\(285\) 31.3775 + 22.0438i 1.85864 + 1.30576i
\(286\) 0 0
\(287\) −0.909072 + 1.57456i −0.0536608 + 0.0929433i
\(288\) 0 0
\(289\) −3.99231 6.91489i −0.234842 0.406758i
\(290\) 0 0
\(291\) −22.7115 + 22.6407i −1.33137 + 1.32722i
\(292\) 0 0
\(293\) 5.19618 6.19256i 0.303564 0.361773i −0.592600 0.805497i \(-0.701898\pi\)
0.896164 + 0.443724i \(0.146343\pi\)
\(294\) 0 0
\(295\) 0.297792 0.818177i 0.0173381 0.0476361i
\(296\) 0 0
\(297\) 7.01152 + 15.2220i 0.406849 + 0.883268i
\(298\) 0 0
\(299\) 11.4907 + 4.18227i 0.664524 + 0.241867i
\(300\) 0 0
\(301\) −7.72236 6.47983i −0.445109 0.373491i
\(302\) 0 0
\(303\) −3.82764 + 14.1963i −0.219892 + 0.815554i
\(304\) 0 0
\(305\) 45.3360 26.1747i 2.59593 1.49876i
\(306\) 0 0
\(307\) 21.6044 + 12.4733i 1.23303 + 0.711890i 0.967660 0.252257i \(-0.0811730\pi\)
0.265369 + 0.964147i \(0.414506\pi\)
\(308\) 0 0
\(309\) −5.99191 12.9023i −0.340868 0.733983i
\(310\) 0 0
\(311\) 27.1209 9.87120i 1.53788 0.559744i 0.572348 0.820011i \(-0.306033\pi\)
0.965537 + 0.260267i \(0.0838106\pi\)
\(312\) 0 0
\(313\) 0.406391 + 2.30476i 0.0229706 + 0.130273i 0.994137 0.108132i \(-0.0344868\pi\)
−0.971166 + 0.238404i \(0.923376\pi\)
\(314\) 0 0
\(315\) 34.2029 5.92084i 1.92711 0.333601i
\(316\) 0 0
\(317\) 5.49865 + 6.55303i 0.308835 + 0.368055i 0.898029 0.439937i \(-0.144999\pi\)
−0.589194 + 0.807992i \(0.700555\pi\)
\(318\) 0 0
\(319\) −14.6462 2.58253i −0.820033 0.144594i
\(320\) 0 0
\(321\) 15.5233 + 22.2434i 0.866427 + 1.24151i
\(322\) 0 0
\(323\) −17.0028 −0.946060
\(324\) 0 0
\(325\) 15.7484 0.873564
\(326\) 0 0
\(327\) −8.93745 12.8065i −0.494242 0.708202i
\(328\) 0 0
\(329\) −3.73963 0.659398i −0.206173 0.0363538i
\(330\) 0 0
\(331\) 6.63073 + 7.90220i 0.364458 + 0.434344i 0.916845 0.399244i \(-0.130727\pi\)
−0.552387 + 0.833588i \(0.686283\pi\)
\(332\) 0 0
\(333\) −8.62331 10.3423i −0.472554 0.566753i
\(334\) 0 0
\(335\) −2.31274 13.1162i −0.126359 0.716615i
\(336\) 0 0
\(337\) 5.42698 1.97526i 0.295626 0.107599i −0.189949 0.981794i \(-0.560832\pi\)
0.485576 + 0.874195i \(0.338610\pi\)
\(338\) 0 0
\(339\) −5.07319 10.9240i −0.275538 0.593309i
\(340\) 0 0
\(341\) −26.5683 15.3392i −1.43876 0.830666i
\(342\) 0 0
\(343\) 13.4340 7.75614i 0.725369 0.418792i
\(344\) 0 0
\(345\) −14.0790 + 52.2173i −0.757987 + 2.81128i
\(346\) 0 0
\(347\) 4.31009 + 3.61659i 0.231378 + 0.194149i 0.751104 0.660184i \(-0.229522\pi\)
−0.519726 + 0.854333i \(0.673966\pi\)
\(348\) 0 0
\(349\) −16.8949 6.14924i −0.904363 0.329161i −0.152363 0.988325i \(-0.548688\pi\)
−0.752000 + 0.659163i \(0.770911\pi\)
\(350\) 0 0
\(351\) 6.53842 4.53276i 0.348995 0.241941i
\(352\) 0 0
\(353\) −5.25148 + 14.4283i −0.279508 + 0.767942i 0.717911 + 0.696135i \(0.245099\pi\)
−0.997419 + 0.0718066i \(0.977124\pi\)
\(354\) 0 0
\(355\) −20.7182 + 24.6909i −1.09961 + 1.31046i
\(356\) 0 0
\(357\) −10.9000 + 10.8660i −0.576890 + 0.575092i
\(358\) 0 0
\(359\) −16.4899 28.5614i −0.870305 1.50741i −0.861682 0.507449i \(-0.830589\pi\)
−0.00862297 0.999963i \(-0.502745\pi\)
\(360\) 0 0
\(361\) 6.53341 11.3162i 0.343864 0.595589i
\(362\) 0 0
\(363\) −0.846692 0.594832i −0.0444398 0.0312206i
\(364\) 0 0
\(365\) −10.3501 28.4366i −0.541748 1.48844i
\(366\) 0 0
\(367\) −1.19429 + 0.210586i −0.0623416 + 0.0109925i −0.204732 0.978818i \(-0.565632\pi\)
0.142390 + 0.989811i \(0.454521\pi\)
\(368\) 0 0
\(369\) −1.84304 0.00575468i −0.0959449 0.000299577i
\(370\) 0 0
\(371\) −11.3611 + 9.53307i −0.589837 + 0.494932i
\(372\) 0 0
\(373\) 1.14523 6.49494i 0.0592979 0.336295i −0.940698 0.339246i \(-0.889828\pi\)
0.999996 + 0.00295067i \(0.000939230\pi\)
\(374\) 0 0
\(375\) 3.06384 + 35.6610i 0.158216 + 1.84153i
\(376\) 0 0
\(377\) 7.06014i 0.363616i
\(378\) 0 0
\(379\) 23.0138i 1.18214i −0.806620 0.591070i \(-0.798706\pi\)
0.806620 0.591070i \(-0.201294\pi\)
\(380\) 0 0
\(381\) −16.0666 7.52253i −0.823116 0.385391i
\(382\) 0 0
\(383\) 3.25873 18.4812i 0.166513 0.944344i −0.780977 0.624560i \(-0.785278\pi\)
0.947490 0.319784i \(-0.103610\pi\)
\(384\) 0 0
\(385\) 28.5876 23.9878i 1.45696 1.22253i
\(386\) 0 0
\(387\) 1.80591 10.0581i 0.0917995 0.511280i
\(388\) 0 0
\(389\) −26.3690 + 4.64957i −1.33696 + 0.235743i −0.795996 0.605301i \(-0.793053\pi\)
−0.540967 + 0.841044i \(0.681942\pi\)
\(390\) 0 0
\(391\) −8.20153 22.5335i −0.414769 1.13957i
\(392\) 0 0
\(393\) −0.0875852 + 0.983418i −0.00441809 + 0.0496069i
\(394\) 0 0
\(395\) 7.33640 12.7070i 0.369134 0.639359i
\(396\) 0 0
\(397\) −9.33339 16.1659i −0.468429 0.811343i 0.530920 0.847422i \(-0.321847\pi\)
−0.999349 + 0.0360788i \(0.988513\pi\)
\(398\) 0 0
\(399\) −7.46894 28.0496i −0.373915 1.40423i
\(400\) 0 0
\(401\) −10.2927 + 12.2664i −0.513994 + 0.612554i −0.959150 0.282899i \(-0.908704\pi\)
0.445156 + 0.895453i \(0.353148\pi\)
\(402\) 0 0
\(403\) −4.98108 + 13.6854i −0.248125 + 0.681719i
\(404\) 0 0
\(405\) 22.4490 + 27.0956i 1.11550 + 1.34639i
\(406\) 0 0
\(407\) −13.6039 4.95141i −0.674319 0.245432i
\(408\) 0 0
\(409\) 12.0693 + 10.1274i 0.596791 + 0.500767i 0.890412 0.455155i \(-0.150416\pi\)
−0.293622 + 0.955922i \(0.594861\pi\)
\(410\) 0 0
\(411\) −11.8714 + 3.16108i −0.585573 + 0.155925i
\(412\) 0 0
\(413\) −0.570774 + 0.329537i −0.0280860 + 0.0162154i
\(414\) 0 0
\(415\) −40.9879 23.6644i −2.01202 1.16164i
\(416\) 0 0
\(417\) −4.89926 0.436338i −0.239918 0.0213676i
\(418\) 0 0
\(419\) 15.8780 5.77912i 0.775691 0.282329i 0.0763166 0.997084i \(-0.475684\pi\)
0.699375 + 0.714755i \(0.253462\pi\)
\(420\) 0 0
\(421\) 4.75431 + 26.9630i 0.231711 + 1.31410i 0.849431 + 0.527700i \(0.176945\pi\)
−0.617720 + 0.786398i \(0.711944\pi\)
\(422\) 0 0
\(423\) −1.30525 3.62129i −0.0634635 0.176073i
\(424\) 0 0
\(425\) −19.8512 23.6577i −0.962925 1.14757i
\(426\) 0 0
\(427\) −39.0244 6.88105i −1.88852 0.332997i
\(428\) 0 0
\(429\) 3.62694 7.74639i 0.175110 0.373999i
\(430\) 0 0
\(431\) 6.64210 0.319939 0.159969 0.987122i \(-0.448860\pi\)
0.159969 + 0.987122i \(0.448860\pi\)
\(432\) 0 0
\(433\) −7.60807 −0.365621 −0.182810 0.983148i \(-0.558519\pi\)
−0.182810 + 0.983148i \(0.558519\pi\)
\(434\) 0 0
\(435\) −31.1106 + 2.67289i −1.49164 + 0.128155i
\(436\) 0 0
\(437\) 44.5380 + 7.85325i 2.13054 + 0.375672i
\(438\) 0 0
\(439\) −1.70790 2.03539i −0.0815135 0.0971440i 0.723746 0.690066i \(-0.242419\pi\)
−0.805260 + 0.592922i \(0.797974\pi\)
\(440\) 0 0
\(441\) −4.56022 2.65187i −0.217154 0.126279i
\(442\) 0 0
\(443\) 1.28130 + 7.26659i 0.0608762 + 0.345246i 0.999999 + 0.00166347i \(0.000529499\pi\)
−0.939122 + 0.343583i \(0.888359\pi\)
\(444\) 0 0
\(445\) −2.23886 + 0.814878i −0.106132 + 0.0386289i
\(446\) 0 0
\(447\) −8.06538 + 11.4804i −0.381479 + 0.543003i
\(448\) 0 0
\(449\) −28.2078 16.2858i −1.33121 0.768573i −0.345723 0.938337i \(-0.612366\pi\)
−0.985485 + 0.169764i \(0.945700\pi\)
\(450\) 0 0
\(451\) −1.71600 + 0.990733i −0.0808032 + 0.0466518i
\(452\) 0 0
\(453\) 23.0189 + 23.0909i 1.08152 + 1.08490i
\(454\) 0 0
\(455\) −13.5711 11.3875i −0.636225 0.533856i
\(456\) 0 0
\(457\) −24.9862 9.09423i −1.16880 0.425410i −0.316570 0.948569i \(-0.602531\pi\)
−0.852235 + 0.523159i \(0.824753\pi\)
\(458\) 0 0
\(459\) −15.0511 4.10857i −0.702524 0.191772i
\(460\) 0 0
\(461\) 6.89899 18.9548i 0.321318 0.882814i −0.668909 0.743345i \(-0.733238\pi\)
0.990226 0.139469i \(-0.0445395\pi\)
\(462\) 0 0
\(463\) 5.25098 6.25787i 0.244034 0.290828i −0.630099 0.776514i \(-0.716986\pi\)
0.874133 + 0.485686i \(0.161430\pi\)
\(464\) 0 0
\(465\) −62.1907 16.7681i −2.88403 0.777600i
\(466\) 0 0
\(467\) −6.73312 11.6621i −0.311571 0.539658i 0.667131 0.744940i \(-0.267522\pi\)
−0.978703 + 0.205283i \(0.934189\pi\)
\(468\) 0 0
\(469\) −5.04079 + 8.73091i −0.232762 + 0.403156i
\(470\) 0 0
\(471\) 9.45299 4.39005i 0.435571 0.202283i
\(472\) 0 0
\(473\) −3.75756 10.3238i −0.172773 0.474689i
\(474\) 0 0
\(475\) 57.3597 10.1141i 2.63184 0.464065i
\(476\) 0 0
\(477\) −14.1112 5.18601i −0.646107 0.237451i
\(478\) 0 0
\(479\) −25.8908 + 21.7250i −1.18298 + 0.992641i −0.183028 + 0.983108i \(0.558590\pi\)
−0.999955 + 0.00953287i \(0.996966\pi\)
\(480\) 0 0
\(481\) −1.19340 + 6.76810i −0.0544143 + 0.308599i
\(482\) 0 0
\(483\) 33.5709 23.4286i 1.52753 1.06604i
\(484\) 0 0
\(485\) 72.3874i 3.28694i
\(486\) 0 0
\(487\) 15.6103i 0.707368i 0.935365 + 0.353684i \(0.115071\pi\)
−0.935365 + 0.353684i \(0.884929\pi\)
\(488\) 0 0
\(489\) 23.3565 16.3001i 1.05622 0.737116i
\(490\) 0 0
\(491\) −3.17929 + 18.0307i −0.143479 + 0.813712i 0.825096 + 0.564992i \(0.191121\pi\)
−0.968575 + 0.248720i \(0.919990\pi\)
\(492\) 0 0
\(493\) 10.6060 8.89946i 0.477669 0.400812i
\(494\) 0 0
\(495\) 35.5077 + 13.0494i 1.59595 + 0.586529i
\(496\) 0 0
\(497\) 24.0274 4.23668i 1.07778 0.190041i
\(498\) 0 0
\(499\) −9.65791 26.5349i −0.432348 1.18787i −0.944368 0.328892i \(-0.893325\pi\)
0.512020 0.858973i \(-0.328897\pi\)
\(500\) 0 0
\(501\) 23.2328 10.7895i 1.03796 0.482039i
\(502\) 0 0
\(503\) −0.320624 + 0.555338i −0.0142959 + 0.0247613i −0.873085 0.487568i \(-0.837884\pi\)
0.858789 + 0.512330i \(0.171217\pi\)
\(504\) 0 0
\(505\) 16.5944 + 28.7424i 0.738442 + 1.27902i
\(506\) 0 0
\(507\) 17.8198 + 4.80463i 0.791405 + 0.213381i
\(508\) 0 0
\(509\) −8.99662 + 10.7218i −0.398768 + 0.475233i −0.927644 0.373466i \(-0.878169\pi\)
0.528876 + 0.848699i \(0.322614\pi\)
\(510\) 0 0
\(511\) −7.83458 + 21.5253i −0.346581 + 0.952224i
\(512\) 0 0
\(513\) 20.9035 20.7086i 0.922913 0.914308i
\(514\) 0 0
\(515\) −30.1745 10.9826i −1.32965 0.483952i
\(516\) 0 0
\(517\) −3.17022 2.66013i −0.139426 0.116992i
\(518\) 0 0
\(519\) −2.48648 2.49426i −0.109144 0.109486i
\(520\) 0 0
\(521\) 4.55944 2.63240i 0.199753 0.115327i −0.396787 0.917911i \(-0.629875\pi\)
0.596540 + 0.802583i \(0.296542\pi\)
\(522\) 0 0
\(523\) 8.39941 + 4.84940i 0.367280 + 0.212049i 0.672270 0.740306i \(-0.265320\pi\)
−0.304989 + 0.952356i \(0.598653\pi\)
\(524\) 0 0
\(525\) 30.3081 43.1409i 1.32275 1.88283i
\(526\) 0 0
\(527\) 26.8374 9.76802i 1.16906 0.425502i
\(528\) 0 0
\(529\) 7.08184 + 40.1631i 0.307906 + 1.74622i
\(530\) 0 0
\(531\) −0.577547 0.335856i −0.0250634 0.0145749i
\(532\) 0 0
\(533\) 0.604634 + 0.720575i 0.0261896 + 0.0312116i
\(534\) 0 0
\(535\) 60.2969 + 10.6320i 2.60686 + 0.459660i
\(536\) 0 0
\(537\) 0.874512 0.0751343i 0.0377380 0.00324229i
\(538\) 0 0
\(539\) −5.67141 −0.244285
\(540\) 0 0
\(541\) 23.0789 0.992241 0.496121 0.868254i \(-0.334757\pi\)
0.496121 + 0.868254i \(0.334757\pi\)
\(542\) 0 0
\(543\) −6.69940 + 14.3085i −0.287499 + 0.614038i
\(544\) 0 0
\(545\) −34.7155 6.12128i −1.48705 0.262207i
\(546\) 0 0
\(547\) 10.3472 + 12.3313i 0.442414 + 0.527249i 0.940461 0.339901i \(-0.110394\pi\)
−0.498047 + 0.867150i \(0.665949\pi\)
\(548\) 0 0
\(549\) −13.6207 37.7894i −0.581319 1.61281i
\(550\) 0 0
\(551\) 4.53422 + 25.7148i 0.193164 + 1.09549i
\(552\) 0 0
\(553\) −10.4369 + 3.79871i −0.443821 + 0.161538i
\(554\) 0 0
\(555\) −30.2755 2.69640i −1.28512 0.114456i
\(556\) 0 0
\(557\) 0.287981 + 0.166266i 0.0122022 + 0.00704492i 0.506089 0.862481i \(-0.331091\pi\)
−0.493887 + 0.869526i \(0.664424\pi\)
\(558\) 0 0
\(559\) −4.51672 + 2.60773i −0.191037 + 0.110295i
\(560\) 0 0
\(561\) −16.2087 + 4.31600i −0.684332 + 0.182222i
\(562\) 0 0
\(563\) 23.2634 + 19.5203i 0.980435 + 0.822682i 0.984155 0.177311i \(-0.0567398\pi\)
−0.00372038 + 0.999993i \(0.501184\pi\)
\(564\) 0 0
\(565\) −25.5479 9.29868i −1.07481 0.391199i
\(566\) 0 0
\(567\) 0.166329 26.6346i 0.00698515 1.11855i
\(568\) 0 0
\(569\) −3.31656 + 9.11217i −0.139037 + 0.382002i −0.989595 0.143880i \(-0.954042\pi\)
0.850558 + 0.525881i \(0.176264\pi\)
\(570\) 0 0
\(571\) −13.1651 + 15.6896i −0.550944 + 0.656590i −0.967604 0.252473i \(-0.918756\pi\)
0.416660 + 0.909063i \(0.363201\pi\)
\(572\) 0 0
\(573\) −5.90744 22.1853i −0.246787 0.926806i
\(574\) 0 0
\(575\) 41.0723 + 71.1393i 1.71283 + 2.96671i
\(576\) 0 0
\(577\) 19.3818 33.5702i 0.806873 1.39755i −0.108146 0.994135i \(-0.534491\pi\)
0.915019 0.403410i \(-0.132175\pi\)
\(578\) 0 0
\(579\) −3.17515 + 35.6510i −0.131955 + 1.48160i
\(580\) 0 0
\(581\) 12.2532 + 33.6654i 0.508348 + 1.39667i
\(582\) 0 0
\(583\) −15.9175 + 2.80668i −0.659235 + 0.116241i
\(584\) 0 0
\(585\) 3.17367 17.6759i 0.131215 0.730808i
\(586\) 0 0
\(587\) 32.0219 26.8696i 1.32169 1.10903i 0.335742 0.941954i \(-0.391013\pi\)
0.985945 0.167073i \(-0.0534315\pi\)
\(588\) 0 0
\(589\) −9.35322 + 53.0447i −0.385393 + 2.18567i
\(590\) 0 0
\(591\) −39.4389 18.4657i −1.62230 0.759576i
\(592\) 0 0
\(593\) 16.1880i 0.664760i 0.943146 + 0.332380i \(0.107852\pi\)
−0.943146 + 0.332380i \(0.892148\pi\)
\(594\) 0 0
\(595\) 34.7412i 1.42425i
\(596\) 0 0
\(597\) −0.149090 1.73531i −0.00610187 0.0710215i
\(598\) 0 0
\(599\) 6.02017 34.1421i 0.245977 1.39501i −0.572234 0.820090i \(-0.693923\pi\)
0.818212 0.574917i \(-0.194966\pi\)
\(600\) 0 0
\(601\) −2.59895 + 2.18078i −0.106013 + 0.0889558i −0.694254 0.719730i \(-0.744265\pi\)
0.588240 + 0.808686i \(0.299821\pi\)
\(602\) 0 0
\(603\) −10.2196 0.0319096i −0.416176 0.00129946i
\(604\) 0 0
\(605\) −2.30021 + 0.405589i −0.0935169 + 0.0164896i
\(606\) 0 0
\(607\) −0.0868318 0.238568i −0.00352439 0.00968319i 0.937918 0.346857i \(-0.112751\pi\)
−0.941442 + 0.337174i \(0.890529\pi\)
\(608\) 0 0
\(609\) 19.3404 + 13.5874i 0.783715 + 0.550588i
\(610\) 0 0
\(611\) −0.982300 + 1.70139i −0.0397396 + 0.0688310i
\(612\) 0 0
\(613\) −0.676216 1.17124i −0.0273121 0.0473059i 0.852046 0.523466i \(-0.175361\pi\)
−0.879358 + 0.476161i \(0.842028\pi\)
\(614\) 0 0
\(615\) −2.94631 + 2.93713i −0.118807 + 0.118436i
\(616\) 0 0
\(617\) 23.9230 28.5104i 0.963105 1.14778i −0.0258648 0.999665i \(-0.508234\pi\)
0.988970 0.148118i \(-0.0473216\pi\)
\(618\) 0 0
\(619\) 14.9951 41.1988i 0.602705 1.65592i −0.143063 0.989714i \(-0.545695\pi\)
0.745768 0.666206i \(-0.232083\pi\)
\(620\) 0 0
\(621\) 37.5279 + 17.7140i 1.50594 + 0.710839i
\(622\) 0 0
\(623\) 1.69472 + 0.616829i 0.0678976 + 0.0247127i
\(624\) 0 0
\(625\) 22.4947 + 18.8753i 0.899788 + 0.755012i
\(626\) 0 0
\(627\) 8.23527 30.5436i 0.328885 1.21980i
\(628\) 0 0
\(629\) 11.6716 6.73858i 0.465376 0.268685i
\(630\) 0 0
\(631\) 15.7443 + 9.08996i 0.626770 + 0.361866i 0.779500 0.626402i \(-0.215473\pi\)
−0.152730 + 0.988268i \(0.548807\pi\)
\(632\) 0 0
\(633\) −8.23194 17.7256i −0.327190 0.704531i
\(634\) 0 0
\(635\) −37.6296 + 13.6961i −1.49329 + 0.543512i
\(636\) 0 0
\(637\) 0.467519 + 2.65143i 0.0185238 + 0.105054i
\(638\) 0 0
\(639\) 15.8384 + 18.9956i 0.626557 + 0.751454i
\(640\) 0 0
\(641\) 15.1322 + 18.0338i 0.597685 + 0.712293i 0.977063 0.212949i \(-0.0683067\pi\)
−0.379379 + 0.925241i \(0.623862\pi\)
\(642\) 0 0
\(643\) −18.8082 3.31639i −0.741722 0.130786i −0.209996 0.977702i \(-0.567345\pi\)
−0.531726 + 0.846917i \(0.678456\pi\)
\(644\) 0 0
\(645\) −13.2010 18.9157i −0.519788 0.744806i
\(646\) 0 0
\(647\) −4.40584 −0.173211 −0.0866057 0.996243i \(-0.527602\pi\)
−0.0866057 + 0.996243i \(0.527602\pi\)
\(648\) 0 0
\(649\) −0.718276 −0.0281948
\(650\) 0 0
\(651\) 27.9034 + 39.9829i 1.09362 + 1.56705i
\(652\) 0 0
\(653\) −17.9597 3.16677i −0.702816 0.123925i −0.189191 0.981940i \(-0.560587\pi\)
−0.513625 + 0.858015i \(0.671698\pi\)
\(654\) 0 0
\(655\) 1.43252 + 1.70721i 0.0559733 + 0.0667063i
\(656\) 0 0
\(657\) −22.8803 + 3.96078i −0.892644 + 0.154525i
\(658\) 0 0
\(659\) −6.46263 36.6514i −0.251748 1.42773i −0.804284 0.594246i \(-0.797451\pi\)
0.552536 0.833489i \(-0.313660\pi\)
\(660\) 0 0
\(661\) 8.82083 3.21052i 0.343090 0.124875i −0.164727 0.986339i \(-0.552674\pi\)
0.507818 + 0.861464i \(0.330452\pi\)
\(662\) 0 0
\(663\) 3.35392 + 7.22193i 0.130256 + 0.280476i
\(664\) 0 0
\(665\) −56.7429 32.7605i −2.20040 1.27040i
\(666\) 0 0
\(667\) −31.8923 + 18.4130i −1.23488 + 0.712956i
\(668\) 0 0
\(669\) 1.43688 5.32920i 0.0555528 0.206039i
\(670\) 0 0
\(671\) −33.0824 27.7594i −1.27713 1.07164i
\(672\) 0 0
\(673\) 19.1849 + 6.98275i 0.739525 + 0.269165i 0.684191 0.729303i \(-0.260155\pi\)
0.0553340 + 0.998468i \(0.482378\pi\)
\(674\) 0 0
\(675\) 53.2195 + 4.90737i 2.04842 + 0.188885i
\(676\) 0 0
\(677\) −11.4047 + 31.3341i −0.438317 + 1.20427i 0.502269 + 0.864711i \(0.332499\pi\)
−0.940586 + 0.339555i \(0.889724\pi\)
\(678\) 0 0
\(679\) 35.2211 41.9749i 1.35166 1.61085i
\(680\) 0 0
\(681\) 20.1064 20.0438i 0.770481 0.768079i
\(682\) 0 0
\(683\) 22.7613 + 39.4237i 0.870937 + 1.50851i 0.861029 + 0.508556i \(0.169821\pi\)
0.00990835 + 0.999951i \(0.496846\pi\)
\(684\) 0 0
\(685\) −13.8652 + 24.0153i −0.529763 + 0.917577i
\(686\) 0 0
\(687\) 11.4975 + 8.07740i 0.438656 + 0.308172i
\(688\) 0 0
\(689\) 2.62430 + 7.21021i 0.0999779 + 0.274687i
\(690\) 0 0
\(691\) −5.27547 + 0.930207i −0.200688 + 0.0353867i −0.273089 0.961989i \(-0.588045\pi\)
0.0724003 + 0.997376i \(0.476934\pi\)
\(692\) 0 0
\(693\) −14.2402 24.8436i −0.540942 0.943732i
\(694\) 0 0
\(695\) −8.50512 + 7.13664i −0.322618 + 0.270708i
\(696\) 0 0
\(697\) 0.320315 1.81660i 0.0121328 0.0688086i
\(698\) 0 0
\(699\) −0.933320 10.8632i −0.0353014 0.410884i
\(700\) 0 0
\(701\) 21.2531i 0.802717i −0.915921 0.401358i \(-0.868538\pi\)
0.915921 0.401358i \(-0.131462\pi\)
\(702\) 0 0
\(703\) 25.4176i 0.958642i
\(704\) 0 0
\(705\) −7.86910 3.68439i −0.296367 0.138762i
\(706\) 0 0
\(707\) 4.36249 24.7409i 0.164068 0.930478i
\(708\) 0 0
\(709\) 36.3373 30.4906i 1.36468 1.14510i 0.390170 0.920743i \(-0.372416\pi\)
0.974507 0.224358i \(-0.0720284\pi\)
\(710\) 0 0
\(711\) −8.60213 7.26394i −0.322605 0.272419i
\(712\) 0 0
\(713\) −74.8110 + 13.1912i −2.80170 + 0.494014i
\(714\) 0 0
\(715\) −6.60347 18.1429i −0.246956 0.678505i
\(716\) 0 0
\(717\) −1.64048 + 18.4195i −0.0612647 + 0.687889i
\(718\) 0 0
\(719\) −18.7915 + 32.5479i −0.700806 + 1.21383i 0.267378 + 0.963592i \(0.413843\pi\)
−0.968184 + 0.250240i \(0.919490\pi\)
\(720\) 0 0
\(721\) 12.1534 + 21.0502i 0.452615 + 0.783952i
\(722\) 0 0
\(723\) 8.33202 + 31.2908i 0.309871 + 1.16372i
\(724\) 0 0
\(725\) −30.4859 + 36.3317i −1.13222 + 1.34933i
\(726\) 0 0
\(727\) −7.85023 + 21.5683i −0.291149 + 0.799925i 0.704750 + 0.709456i \(0.251059\pi\)
−0.995899 + 0.0904698i \(0.971163\pi\)
\(728\) 0 0
\(729\) 23.5081 13.2804i 0.870671 0.491866i
\(730\) 0 0
\(731\) 9.61083 + 3.49806i 0.355469 + 0.129380i
\(732\) 0 0
\(733\) −4.21278 3.53494i −0.155603 0.130566i 0.561663 0.827366i \(-0.310162\pi\)
−0.717265 + 0.696800i \(0.754606\pi\)
\(734\) 0 0
\(735\) −11.5066 + 3.06393i −0.424426 + 0.113015i
\(736\) 0 0
\(737\) −9.51519 + 5.49360i −0.350497 + 0.202359i
\(738\) 0 0
\(739\) −2.63042 1.51867i −0.0967614 0.0558652i 0.450838 0.892606i \(-0.351125\pi\)
−0.547600 + 0.836740i \(0.684458\pi\)
\(740\) 0 0
\(741\) −14.9583 1.33222i −0.549507 0.0489402i
\(742\) 0 0
\(743\) 7.90477 2.87710i 0.289998 0.105551i −0.192925 0.981214i \(-0.561797\pi\)
0.482923 + 0.875663i \(0.339575\pi\)
\(744\) 0 0
\(745\) 5.49942 + 31.1888i 0.201483 + 1.14267i
\(746\) 0 0
\(747\) −23.4307 + 27.7472i −0.857283 + 1.01522i
\(748\) 0 0
\(749\) −29.7908 35.5033i −1.08853 1.29726i
\(750\) 0 0
\(751\) 36.4856 + 6.43340i 1.33138 + 0.234758i 0.793658 0.608364i \(-0.208174\pi\)
0.537722 + 0.843122i \(0.319285\pi\)
\(752\) 0 0
\(753\) −10.0879 + 21.5457i −0.367624 + 0.785170i
\(754\) 0 0
\(755\) 73.5967 2.67846
\(756\) 0 0
\(757\) −4.63964 −0.168630 −0.0843152 0.996439i \(-0.526870\pi\)
−0.0843152 + 0.996439i \(0.526870\pi\)
\(758\) 0 0
\(759\) 44.4514 3.81908i 1.61348 0.138624i
\(760\) 0 0
\(761\) −28.9212 5.09959i −1.04839 0.184860i −0.377191 0.926135i \(-0.623110\pi\)
−0.671201 + 0.741276i \(0.734221\pi\)
\(762\) 0 0
\(763\) 17.1519 + 20.4408i 0.620940 + 0.740007i
\(764\) 0 0
\(765\) −30.5537 + 17.5132i −1.10467 + 0.633192i
\(766\) 0 0
\(767\) 0.0592107 + 0.335801i 0.00213798 + 0.0121251i
\(768\) 0 0
\(769\) 43.0305 15.6618i 1.55172 0.564780i 0.582900 0.812544i \(-0.301918\pi\)
0.968821 + 0.247764i \(0.0796956\pi\)
\(770\) 0 0
\(771\) 27.2137 38.7363i 0.980077 1.39505i
\(772\) 0 0
\(773\) −7.09568 4.09670i −0.255214 0.147348i 0.366935 0.930246i \(-0.380407\pi\)
−0.622149 + 0.782899i \(0.713740\pi\)
\(774\) 0 0
\(775\) −84.7268 + 48.9170i −3.04348 + 1.75715i
\(776\) 0 0
\(777\) 16.2437 + 16.2945i 0.582740 + 0.584563i
\(778\) 0 0
\(779\) 2.66500 + 2.23620i 0.0954836 + 0.0801203i
\(780\) 0 0
\(781\) 24.9862 + 9.09422i 0.894075 + 0.325417i
\(782\) 0 0
\(783\) −2.20002 + 23.8588i −0.0786222 + 0.852642i
\(784\) 0 0
\(785\) 8.04654 22.1077i 0.287193 0.789058i
\(786\) 0 0
\(787\) 25.8770 30.8390i 0.922415 1.09929i −0.0723778 0.997377i \(-0.523059\pi\)
0.994793 0.101915i \(-0.0324968\pi\)
\(788\) 0 0
\(789\) 15.2758 + 4.11870i 0.543832 + 0.146630i
\(790\) 0 0
\(791\) 10.2899 + 17.8227i 0.365867 + 0.633701i
\(792\) 0 0
\(793\) −10.2506 + 17.7546i −0.364011 + 0.630486i
\(794\) 0 0
\(795\) −30.7783 + 14.2937i −1.09159 + 0.506946i
\(796\)