Properties

Label 432.2.be.a.47.5
Level $432$
Weight $2$
Character 432.47
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 47.5
Character \(\chi\) \(=\) 432.47
Dual form 432.2.be.a.239.5

$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

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

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
\(3\) 0.991247 1.42036i 0.572297 0.820047i
\(4\) 0 0
\(5\) −3.85028 + 0.678908i −1.72190 + 0.303617i −0.945256 0.326328i \(-0.894188\pi\)
−0.776640 + 0.629945i \(0.783077\pi\)
\(6\) 0 0
\(7\) −1.90230 + 2.26708i −0.719004 + 0.856875i −0.994534 0.104417i \(-0.966702\pi\)
0.275530 + 0.961293i \(0.411147\pi\)
\(8\) 0 0
\(9\) −1.03486 2.81586i −0.344953 0.938620i
\(10\) 0 0
\(11\) −0.560068 + 3.17630i −0.168867 + 0.957692i 0.776120 + 0.630585i \(0.217185\pi\)
−0.944987 + 0.327107i \(0.893926\pi\)
\(12\) 0 0
\(13\) 1.43878 + 0.523674i 0.399046 + 0.145241i 0.533745 0.845646i \(-0.320784\pi\)
−0.134698 + 0.990887i \(0.543007\pi\)
\(14\) 0 0
\(15\) −2.85228 + 6.14175i −0.736456 + 1.58579i
\(16\) 0 0
\(17\) −2.60029 + 1.50128i −0.630664 + 0.364114i −0.781009 0.624520i \(-0.785295\pi\)
0.150345 + 0.988634i \(0.451962\pi\)
\(18\) 0 0
\(19\) −4.90409 2.83138i −1.12508 0.649563i −0.182384 0.983227i \(-0.558381\pi\)
−0.942692 + 0.333665i \(0.891715\pi\)
\(20\) 0 0
\(21\) 1.33442 + 4.94920i 0.291194 + 1.08000i
\(22\) 0 0
\(23\) −6.11794 + 5.13356i −1.27568 + 1.07042i −0.281855 + 0.959457i \(0.590950\pi\)
−0.993824 + 0.110965i \(0.964606\pi\)
\(24\) 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 −0.995645 0.0932208i \(-0.970284\pi\)
0.702788 0.711400i \(-0.251938\pi\)
\(30\) 0 0
\(31\) 6.11407 + 7.28646i 1.09812 + 1.30869i 0.947379 + 0.320114i \(0.103721\pi\)
0.150740 + 0.988573i \(0.451834\pi\)
\(32\) 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 0.620446 0.784249i \(-0.286952\pi\)
−0.989403 + 0.145197i \(0.953618\pi\)
\(38\) 0 0
\(39\) 2.17000 1.52450i 0.347477 0.244116i
\(40\) 0 0
\(41\) 0.210120 0.577300i 0.0328152 0.0901591i −0.922203 0.386706i \(-0.873613\pi\)
0.955018 + 0.296547i \(0.0958351\pi\)
\(42\) 0 0
\(43\) 3.35455 + 0.591498i 0.511565 + 0.0902026i 0.423471 0.905910i \(-0.360811\pi\)
0.0880934 + 0.996112i \(0.471923\pi\)
\(44\) 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 \(-0.247946\pi\)
−0.568280 + 0.822835i \(0.692391\pi\)
\(48\) 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 \(-0.888157\pi\)
0.938904 0.344179i \(-0.111843\pi\)
\(54\) 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 \(-0.0509410\pi\)
−0.982187 + 0.187906i \(0.939830\pi\)
\(60\) 0 0
\(61\) −10.2571 8.60675i −1.31329 1.10198i −0.987682 0.156477i \(-0.949986\pi\)
−0.325609 0.945504i \(-0.605569\pi\)
\(62\) 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 \(-0.955613\pi\)
0.847952 + 0.530073i \(0.177835\pi\)
\(68\) 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 \(-0.329377\pi\)
−0.999923 + 0.0124293i \(0.996044\pi\)
\(72\) 0 0
\(73\) 3.87009 6.70320i 0.452960 0.784550i −0.545608 0.838040i \(-0.683701\pi\)
0.998568 + 0.0534906i \(0.0170347\pi\)
\(74\) 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 \(-0.0434001\pi\)
−0.846305 + 0.532699i \(0.821178\pi\)
\(80\) 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 \(-0.842415\pi\)
−0.368687 + 0.929553i \(0.620193\pi\)
\(84\) 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 0.527710 0.849425i \(-0.323051\pi\)
−0.471768 + 0.881723i \(0.656384\pi\)
\(90\) 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 0.172893 + 0.984941i \(0.444689\pi\)
−0.499336 + 0.866409i \(0.666422\pi\)
\(98\) 0 0
\(99\) 9.52362 1.70995i 0.957160 0.171856i
\(100\) 0 0
\(101\) −5.45656 + 6.50288i −0.542948 + 0.647061i −0.965846 0.259117i \(-0.916569\pi\)
0.422898 + 0.906177i \(0.361013\pi\)
\(102\) 0 0
\(103\) −8.08845 + 1.42621i −0.796978 + 0.140529i −0.557287 0.830320i \(-0.688157\pi\)
−0.239692 + 0.970849i \(0.577046\pi\)
\(104\) 0 0
\(105\) −8.49793 18.1498i −0.829313 1.77124i
\(106\) 0 0
\(107\) 15.6604 1.51395 0.756974 0.653445i \(-0.226677\pi\)
0.756974 + 0.653445i \(0.226677\pi\)
\(108\) 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 0.158019 0.987436i \(-0.449489\pi\)
0.486212 + 0.873841i \(0.338378\pi\)
\(114\) 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 \(-0.483492\pi\)
−0.838942 + 0.544220i \(0.816826\pi\)
\(128\) 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 \(-0.714295\pi\)
0.661664 + 0.749800i \(0.269851\pi\)
\(132\) 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 0.999150 0.0412269i \(-0.0131267\pi\)
−0.791893 + 0.610659i \(0.790904\pi\)
\(138\) 0 0
\(139\) −1.82538 2.17540i −0.154827 0.184515i 0.683055 0.730367i \(-0.260651\pi\)
−0.837882 + 0.545851i \(0.816206\pi\)
\(140\) 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 −0.999941 0.0108491i \(-0.996547\pi\)
0.772973 + 0.634439i \(0.218769\pi\)
\(150\) 0 0
\(151\) 18.5383 + 3.26880i 1.50862 + 0.266011i 0.865950 0.500130i \(-0.166715\pi\)
0.642672 + 0.766141i \(0.277826\pi\)
\(152\) 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 −0.997691 0.0679094i \(-0.978367\pi\)
0.914297 0.405045i \(-0.132744\pi\)
\(158\) 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 0.907007 + 0.421115i \(0.138361\pi\)
−0.708278 + 0.705934i \(0.750528\pi\)
\(168\) 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 0.249252 0.968439i \(-0.419815\pi\)
−0.0970054 + 0.995284i \(0.530926\pi\)
\(174\) 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 \(-0.160638\pi\)
−0.856401 + 0.516312i \(0.827305\pi\)
\(180\) 0 0
\(181\) −4.56085 + 7.89962i −0.339005 + 0.587174i −0.984246 0.176805i \(-0.943424\pi\)
0.645241 + 0.763979i \(0.276757\pi\)
\(182\) 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 \(-0.770311\pi\)
−0.150502 + 0.988610i \(0.548089\pi\)
\(192\) 0 0
\(193\) −15.8300 + 13.2829i −1.13947 + 0.956126i −0.999421 0.0340192i \(-0.989169\pi\)
−0.140045 + 0.990145i \(0.544725\pi\)
\(194\) 0 0
\(195\) −7.32009 + 7.34298i −0.524202 + 0.525842i
\(196\) 0 0
\(197\) 21.7739 + 12.5711i 1.55132 + 0.895657i 0.998034 + 0.0626676i \(0.0199608\pi\)
0.553289 + 0.832989i \(0.313373\pi\)
\(198\) 0 0
\(199\) −0.870852 + 0.502786i −0.0617330 + 0.0356416i −0.530549 0.847654i \(-0.678014\pi\)
0.468816 + 0.883296i \(0.344681\pi\)
\(200\) 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 \(-0.682528\pi\)
−0.222484 + 0.974936i \(0.571417\pi\)
\(212\) 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 \(-0.811806\pi\)
0.693087 + 0.720854i \(0.256250\pi\)
\(224\) 0 0
\(225\) −19.9080 23.5755i −1.32720 1.57170i
\(226\) 0 0
\(227\) −2.84631 + 16.1423i −0.188917 + 1.07140i 0.731903 + 0.681409i \(0.238633\pi\)
−0.920819 + 0.389990i \(0.872479\pi\)
\(228\) 0 0
\(229\) −7.62322 2.77463i −0.503757 0.183352i 0.0776261 0.996983i \(-0.475266\pi\)
−0.581383 + 0.813630i \(0.697488\pi\)
\(230\) 0 0
\(231\) −16.4675 + 1.46663i −1.08348 + 0.0964972i
\(232\) 0 0
\(233\) 5.45161 3.14749i 0.357147 0.206199i −0.310682 0.950514i \(-0.600557\pi\)
0.667829 + 0.744315i \(0.267224\pi\)
\(234\) 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 \(-0.609997\pi\)
0.867769 + 0.496967i \(0.165553\pi\)
\(240\) 0 0
\(241\) −17.5678 + 6.39416i −1.13164 + 0.411884i −0.838888 0.544304i \(-0.816794\pi\)
−0.292754 + 0.956188i \(0.594572\pi\)
\(242\) 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 \(-0.690617\pi\)
0.997171 + 0.0751704i \(0.0239501\pi\)
\(252\) 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 −0.199713 0.979854i \(-0.564001\pi\)
0.782827 0.622239i \(-0.213777\pi\)
\(258\) 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 \(-0.186904\pi\)
−0.401032 + 0.916064i \(0.631348\pi\)
\(264\) 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 \(-0.985488\pi\)
0.998961 0.0455754i \(-0.0145121\pi\)
\(270\) 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 0.792648 0.609680i \(-0.208702\pi\)
−0.462776 + 0.886475i \(0.653147\pi\)
\(278\) 0 0
\(279\) 14.1905 24.7568i 0.849561 1.48215i
\(280\) 0 0
\(281\) 25.8279 + 4.55416i 1.54076 + 0.271678i 0.878555 0.477641i \(-0.158508\pi\)
0.662209 + 0.749319i \(0.269619\pi\)
\(282\) 0 0
\(283\) −4.65241 + 12.7824i −0.276557 + 0.759834i 0.721190 + 0.692738i \(0.243596\pi\)
−0.997747 + 0.0670962i \(0.978627\pi\)
\(284\) 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 0.896164 0.443724i \(-0.146343\pi\)
−0.592600 + 0.805497i \(0.701898\pi\)
\(294\) 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 \(-0.918827\pi\)
−0.265369 + 0.964147i \(0.585494\pi\)
\(308\) 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 \(-0.693967\pi\)
−0.965537 + 0.260267i \(0.916189\pi\)
\(312\) 0 0
\(313\) 0.406391 2.30476i 0.0229706 0.130273i −0.971166 0.238404i \(-0.923376\pi\)
0.994137 + 0.108132i \(0.0344868\pi\)
\(314\) 0 0
\(315\) −34.2029 5.92084i −1.92711 0.333601i
\(316\) 0 0
\(317\) 5.49865 6.55303i 0.308835 0.368055i −0.589194 0.807992i \(-0.700555\pi\)
0.898029 + 0.439937i \(0.144999\pi\)
\(318\) 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 \(-0.869273\pi\)
0.552387 + 0.833588i \(0.313717\pi\)
\(332\) 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 0.485576 0.874195i \(-0.338610\pi\)
−0.189949 + 0.981794i \(0.560832\pi\)
\(338\) 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 \(-0.770478\pi\)
0.519726 + 0.854333i \(0.326034\pi\)
\(348\) 0 0
\(349\) −16.8949 + 6.14924i −0.904363 + 0.329161i −0.752000 0.659163i \(-0.770911\pi\)
−0.152363 + 0.988325i \(0.548688\pi\)
\(350\) 0 0
\(351\) −6.53842 4.53276i −0.348995 0.241941i
\(352\) 0 0
\(353\) −5.25148 14.4283i −0.279508 0.767942i −0.997419 0.0718066i \(-0.977124\pi\)
0.717911 0.696135i \(-0.245099\pi\)
\(354\) 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 0.00862297 0.999963i \(-0.497255\pi\)
0.861682 0.507449i \(-0.169411\pi\)
\(360\) 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 \(-0.434368\pi\)
−0.142390 + 0.989811i \(0.545479\pi\)
\(368\) 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 0.999996 0.00295067i \(-0.000939230\pi\)
−0.940698 + 0.339246i \(0.889828\pi\)
\(374\) 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 −0.947490 0.319784i \(-0.896390\pi\)
0.780977 0.624560i \(-0.214722\pi\)
\(384\) 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 −0.540967 0.841044i \(-0.681942\pi\)
−0.795996 + 0.605301i \(0.793053\pi\)
\(390\) 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 −0.999349 0.0360788i \(-0.988513\pi\)
0.530920 + 0.847422i \(0.321847\pi\)
\(398\) 0 0
\(399\) 7.46894 28.0496i 0.373915 1.40423i
\(400\) 0 0
\(401\) −10.2927 12.2664i −0.513994 0.612554i 0.445156 0.895453i \(-0.353148\pi\)
−0.959150 + 0.282899i \(0.908704\pi\)
\(402\) 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 −0.293622 0.955922i \(-0.594861\pi\)
0.890412 + 0.455155i \(0.150416\pi\)
\(410\) 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 \(-0.524316\pi\)
−0.699375 + 0.714755i \(0.746538\pi\)
\(420\) 0 0
\(421\) 4.75431 26.9630i 0.231711 1.31410i −0.617720 0.786398i \(-0.711944\pi\)
0.849431 0.527700i \(-0.176945\pi\)
\(422\) 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 \(-0.551140\pi\)
−0.159969 + 0.987122i \(0.551140\pi\)
\(432\) 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 \(-0.757581\pi\)
0.805260 + 0.592922i \(0.202026\pi\)
\(440\) 0 0
\(441\) −4.56022 + 2.65187i −0.217154 + 0.126279i
\(442\) 0 0
\(443\) −1.28130 + 7.26659i −0.0608762 + 0.345246i 0.939122 + 0.343583i \(0.111641\pi\)
−0.999999 + 0.00166347i \(0.999471\pi\)
\(444\) 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 −0.985485 0.169764i \(-0.945700\pi\)
−0.345723 + 0.938337i \(0.612366\pi\)
\(450\) 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 −0.852235 0.523159i \(-0.824753\pi\)
−0.316570 + 0.948569i \(0.602531\pi\)
\(458\) 0 0
\(459\) 15.0511 4.10857i 0.702524 0.191772i
\(460\) 0 0
\(461\) 6.89899 + 18.9548i 0.321318 + 0.882814i 0.990226 + 0.139469i \(0.0445395\pi\)
−0.668909 + 0.743345i \(0.733238\pi\)
\(462\) 0 0
\(463\) −5.25098 6.25787i −0.244034 0.290828i 0.630099 0.776514i \(-0.283014\pi\)
−0.874133 + 0.485686i \(0.838570\pi\)
\(464\) 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 \(-0.732478\pi\)
0.978703 + 0.205283i \(0.0658113\pi\)
\(468\) 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 0.999955 + 0.00953287i \(0.00303445\pi\)
0.183028 + 0.983108i \(0.441410\pi\)
\(480\) 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 0.968575 + 0.248720i \(0.0800098\pi\)
−0.825096 + 0.564992i \(0.808879\pi\)
\(492\) 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 −0.512020 0.858973i \(-0.671103\pi\)
0.944368 0.328892i \(-0.106675\pi\)
\(500\) 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 \(-0.162116\pi\)
−0.858789 + 0.512330i \(0.828783\pi\)
\(504\) 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 0.528876 0.848699i \(-0.322614\pi\)
−0.927644 + 0.373466i \(0.878169\pi\)
\(510\) 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 0.596540 0.802583i \(-0.296542\pi\)
−0.396787 + 0.917911i \(0.629875\pi\)
\(522\) 0 0
\(523\) −8.39941 + 4.84940i −0.367280 + 0.212049i −0.672270 0.740306i \(-0.734680\pi\)
0.304989 + 0.952356i \(0.401347\pi\)
\(524\) 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 \(-0.889606\pi\)
0.498047 + 0.867150i \(0.334051\pi\)
\(548\) 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 −0.493887 0.869526i \(-0.664424\pi\)
0.506089 + 0.862481i \(0.331091\pi\)
\(558\) 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 \(-0.943260\pi\)
0.00372038 + 0.999993i \(0.498816\pi\)
\(564\) 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 0.850558 0.525881i \(-0.176264\pi\)
−0.989595 + 0.143880i \(0.954042\pi\)
\(570\) 0 0
\(571\) 13.1651 + 15.6896i 0.550944 + 0.656590i 0.967604 0.252473i \(-0.0812438\pi\)
−0.416660 + 0.909063i \(0.636799\pi\)
\(572\) 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 0.915019 + 0.403410i \(0.132175\pi\)
−0.108146 + 0.994135i \(0.534491\pi\)
\(578\) 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 −0.985945 0.167073i \(-0.946568\pi\)
−0.335742 0.941954i \(-0.608987\pi\)
\(588\) 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 \(-0.892148\pi\)
0.943146 0.332380i \(-0.107852\pi\)
\(594\) 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 −0.818212 0.574917i \(-0.805034\pi\)
0.572234 0.820090i \(-0.306077\pi\)
\(600\) 0 0
\(601\) −2.59895 2.18078i −0.106013 0.0889558i 0.588240 0.808686i \(-0.299821\pi\)
−0.694254 + 0.719730i \(0.744265\pi\)
\(602\) 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 \(-0.887249\pi\)
0.941442 + 0.337174i \(0.109471\pi\)
\(608\) 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 −0.879358 0.476161i \(-0.842028\pi\)
0.852046 + 0.523466i \(0.175361\pi\)
\(614\) 0 0
\(615\) 2.94631 + 2.93713i 0.118807 + 0.118436i
\(616\) 0 0
\(617\) 23.9230 + 28.5104i 0.963105 + 1.14778i 0.988970 + 0.148118i \(0.0473216\pi\)
−0.0258648 + 0.999665i \(0.508234\pi\)
\(618\) 0 0
\(619\) −14.9951 41.1988i −0.602705 1.65592i −0.745768 0.666206i \(-0.767917\pi\)
0.143063 0.989714i \(-0.454305\pi\)
\(620\) 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 \(-0.784527\pi\)
0.152730 + 0.988268i \(0.451193\pi\)
\(632\) 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 −0.379379 0.925241i \(-0.623862\pi\)
0.977063 + 0.212949i \(0.0683067\pi\)
\(642\) 0 0
\(643\) 18.8082 3.31639i 0.741722 0.130786i 0.209996 0.977702i \(-0.432655\pi\)
0.531726 + 0.846917i \(0.321544\pi\)
\(644\) 0 0
\(645\) −13.2010 + 18.9157i −0.519788 + 0.744806i
\(646\) 0 0
\(647\) 4.40584 0.173211 0.0866057 0.996243i \(-0.472398\pi\)
0.0866057 + 0.996243i \(0.472398\pi\)
\(648\) 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 −0.513625 0.858015i \(-0.671698\pi\)
−0.189191 + 0.981940i \(0.560587\pi\)
\(654\) 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 −0.552536 0.833489i \(-0.686340\pi\)
0.804284 0.594246i \(-0.202549\pi\)
\(660\) 0 0
\(661\) 8.82083 + 3.21052i 0.343090 + 0.124875i 0.507818 0.861464i \(-0.330452\pi\)
−0.164727 + 0.986339i \(0.552674\pi\)
\(662\) 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 0.0553340 0.998468i \(-0.482378\pi\)
0.684191 + 0.729303i \(0.260155\pi\)
\(674\) 0 0
\(675\) −53.2195 + 4.90737i −2.04842 + 0.188885i
\(676\) 0 0
\(677\) −11.4047 31.3341i −0.438317 1.20427i −0.940586 0.339555i \(-0.889724\pi\)
0.502269 0.864711i \(-0.332499\pi\)
\(678\) 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 −0.00990835 + 0.999951i \(0.503154\pi\)
−0.861029 + 0.508556i \(0.830179\pi\)
\(684\) 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 \(-0.411955\pi\)
−0.0724003 + 0.997376i \(0.523066\pi\)
\(692\) 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 \(0.131462\pi\)
−0.915921 + 0.401358i \(0.868538\pi\)
\(702\) 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 0.974507 + 0.224358i \(0.0720284\pi\)
0.390170 + 0.920743i \(0.372416\pi\)
\(710\) 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 0.968184 + 0.250240i \(0.0805095\pi\)
−0.267378 + 0.963592i \(0.586157\pi\)
\(720\) 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 0.995899 + 0.0904698i \(0.0288369\pi\)
−0.704750 + 0.709456i \(0.748941\pi\)
\(728\) 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 −0.717265 0.696800i \(-0.754606\pi\)
0.561663 + 0.827366i \(0.310162\pi\)
\(734\) 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 \(-0.648875\pi\)
0.547600 + 0.836740i \(0.315542\pi\)
\(740\) 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 \(-0.438203\pi\)
−0.482923 + 0.875663i \(0.660425\pi\)
\(744\) 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 \(-0.791826\pi\)
−0.537722 + 0.843122i \(0.680715\pi\)
\(752\) 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 −0.671201 0.741276i \(-0.734221\pi\)
−0.377191 + 0.926135i \(0.623110\pi\)
\(762\) 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 0.968821 0.247764i \(-0.0796956\pi\)
0.582900 + 0.812544i \(0.301918\pi\)
\(770\) 0 0
\(771\) −27.2137 38.7363i −0.980077 1.39505i
\(772\) 0 0
\(773\) −7.09568 + 4.09670i −0.255214 + 0.147348i −0.622149 0.782899i \(-0.713740\pi\)
0.366935 + 0.930246i \(0.380407\pi\)
\(774\) 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 −0.994793 0.101915i \(-0.967503\pi\)
0.0723778 0.997377i \(-0.476941\pi\)
\(788\) 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
\(796\)