Properties

Label 441.2.e.g.226.2
Level $441$
Weight $2$
Character 441.226
Analytic conductor $3.521$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.2.e.g.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(1.70711 - 2.95680i) q^{5} +1.58579 q^{8} +O(q^{10})\) \(q+(0.207107 - 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(1.70711 - 2.95680i) q^{5} +1.58579 q^{8} +(-0.707107 - 1.22474i) q^{10} +(-1.00000 - 1.73205i) q^{11} +2.58579 q^{13} +(-1.50000 + 2.59808i) q^{16} +(-1.12132 - 1.94218i) q^{17} +(1.41421 - 2.44949i) q^{19} +6.24264 q^{20} -0.828427 q^{22} +(-3.82843 + 6.63103i) q^{23} +(-3.32843 - 5.76500i) q^{25} +(0.535534 - 0.927572i) q^{26} +6.82843 q^{29} +(0.585786 + 1.01461i) q^{31} +(2.20711 + 3.82282i) q^{32} -0.928932 q^{34} +(2.00000 - 3.46410i) q^{37} +(-0.585786 - 1.01461i) q^{38} +(2.70711 - 4.68885i) q^{40} -6.24264 q^{41} +5.65685 q^{43} +(1.82843 - 3.16693i) q^{44} +(1.58579 + 2.74666i) q^{46} +(-1.41421 + 2.44949i) q^{47} -2.75736 q^{50} +(2.36396 + 4.09450i) q^{52} +(-1.00000 - 1.73205i) q^{53} -6.82843 q^{55} +(1.41421 - 2.44949i) q^{58} +(-0.585786 - 1.01461i) q^{59} +(-6.12132 + 10.6024i) q^{61} +0.485281 q^{62} -4.17157 q^{64} +(4.41421 - 7.64564i) q^{65} +(2.82843 + 4.89898i) q^{67} +(2.05025 - 3.55114i) q^{68} -9.31371 q^{71} +(-6.94975 - 12.0373i) q^{73} +(-0.828427 - 1.43488i) q^{74} +5.17157 q^{76} +(-6.82843 + 11.8272i) q^{79} +(5.12132 + 8.87039i) q^{80} +(-1.29289 + 2.23936i) q^{82} -7.31371 q^{83} -7.65685 q^{85} +(1.17157 - 2.02922i) q^{86} +(-1.58579 - 2.74666i) q^{88} +(-7.12132 + 12.3345i) q^{89} -14.0000 q^{92} +(0.585786 + 1.01461i) q^{94} +(-4.82843 - 8.36308i) q^{95} +2.58579 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} + 4q^{5} + 12q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} + 4q^{5} + 12q^{8} - 4q^{11} + 16q^{13} - 6q^{16} + 4q^{17} + 8q^{20} + 8q^{22} - 4q^{23} - 2q^{25} - 12q^{26} + 16q^{29} + 8q^{31} + 6q^{32} - 32q^{34} + 8q^{37} - 8q^{38} + 8q^{40} - 8q^{41} - 4q^{44} + 12q^{46} - 28q^{50} - 16q^{52} - 4q^{53} - 16q^{55} - 8q^{59} - 16q^{61} - 32q^{62} - 28q^{64} + 12q^{65} + 28q^{68} + 8q^{71} - 8q^{73} + 8q^{74} + 32q^{76} - 16q^{79} + 12q^{80} - 8q^{82} + 16q^{83} - 8q^{85} + 16q^{86} - 12q^{88} - 20q^{89} - 56q^{92} + 8q^{94} - 8q^{95} + 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.207107 0.358719i 0.146447 0.253653i −0.783465 0.621436i \(-0.786550\pi\)
0.929912 + 0.367783i \(0.119883\pi\)
\(3\) 0 0
\(4\) 0.914214 + 1.58346i 0.457107 + 0.791732i
\(5\) 1.70711 2.95680i 0.763441 1.32232i −0.177625 0.984098i \(-0.556842\pi\)
0.941067 0.338221i \(-0.109825\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.58579 0.560660
\(9\) 0 0
\(10\) −0.707107 1.22474i −0.223607 0.387298i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) 2.58579 0.717168 0.358584 0.933497i \(-0.383260\pi\)
0.358584 + 0.933497i \(0.383260\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) −1.12132 1.94218i −0.271960 0.471049i 0.697404 0.716679i \(-0.254339\pi\)
−0.969364 + 0.245630i \(0.921005\pi\)
\(18\) 0 0
\(19\) 1.41421 2.44949i 0.324443 0.561951i −0.656957 0.753928i \(-0.728157\pi\)
0.981399 + 0.191977i \(0.0614899\pi\)
\(20\) 6.24264 1.39590
\(21\) 0 0
\(22\) −0.828427 −0.176621
\(23\) −3.82843 + 6.63103i −0.798282 + 1.38267i 0.122452 + 0.992474i \(0.460924\pi\)
−0.920734 + 0.390191i \(0.872409\pi\)
\(24\) 0 0
\(25\) −3.32843 5.76500i −0.665685 1.15300i
\(26\) 0.535534 0.927572i 0.105027 0.181912i
\(27\) 0 0
\(28\) 0 0
\(29\) 6.82843 1.26801 0.634004 0.773330i \(-0.281410\pi\)
0.634004 + 0.773330i \(0.281410\pi\)
\(30\) 0 0
\(31\) 0.585786 + 1.01461i 0.105210 + 0.182230i 0.913824 0.406110i \(-0.133115\pi\)
−0.808614 + 0.588340i \(0.799782\pi\)
\(32\) 2.20711 + 3.82282i 0.390165 + 0.675786i
\(33\) 0 0
\(34\) −0.928932 −0.159311
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −0.585786 1.01461i −0.0950271 0.164592i
\(39\) 0 0
\(40\) 2.70711 4.68885i 0.428031 0.741372i
\(41\) −6.24264 −0.974937 −0.487468 0.873141i \(-0.662080\pi\)
−0.487468 + 0.873141i \(0.662080\pi\)
\(42\) 0 0
\(43\) 5.65685 0.862662 0.431331 0.902194i \(-0.358044\pi\)
0.431331 + 0.902194i \(0.358044\pi\)
\(44\) 1.82843 3.16693i 0.275646 0.477432i
\(45\) 0 0
\(46\) 1.58579 + 2.74666i 0.233811 + 0.404973i
\(47\) −1.41421 + 2.44949i −0.206284 + 0.357295i −0.950541 0.310599i \(-0.899470\pi\)
0.744257 + 0.667893i \(0.232804\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.75736 −0.389949
\(51\) 0 0
\(52\) 2.36396 + 4.09450i 0.327822 + 0.567805i
\(53\) −1.00000 1.73205i −0.137361 0.237915i 0.789136 0.614218i \(-0.210529\pi\)
−0.926497 + 0.376303i \(0.877195\pi\)
\(54\) 0 0
\(55\) −6.82843 −0.920745
\(56\) 0 0
\(57\) 0 0
\(58\) 1.41421 2.44949i 0.185695 0.321634i
\(59\) −0.585786 1.01461i −0.0762629 0.132091i 0.825372 0.564589i \(-0.190965\pi\)
−0.901635 + 0.432498i \(0.857632\pi\)
\(60\) 0 0
\(61\) −6.12132 + 10.6024i −0.783755 + 1.35750i 0.145985 + 0.989287i \(0.453365\pi\)
−0.929740 + 0.368216i \(0.879969\pi\)
\(62\) 0.485281 0.0616308
\(63\) 0 0
\(64\) −4.17157 −0.521447
\(65\) 4.41421 7.64564i 0.547516 0.948325i
\(66\) 0 0
\(67\) 2.82843 + 4.89898i 0.345547 + 0.598506i 0.985453 0.169948i \(-0.0543599\pi\)
−0.639906 + 0.768453i \(0.721027\pi\)
\(68\) 2.05025 3.55114i 0.248630 0.430639i
\(69\) 0 0
\(70\) 0 0
\(71\) −9.31371 −1.10533 −0.552667 0.833402i \(-0.686390\pi\)
−0.552667 + 0.833402i \(0.686390\pi\)
\(72\) 0 0
\(73\) −6.94975 12.0373i −0.813406 1.40886i −0.910467 0.413583i \(-0.864277\pi\)
0.0970601 0.995279i \(-0.469056\pi\)
\(74\) −0.828427 1.43488i −0.0963027 0.166801i
\(75\) 0 0
\(76\) 5.17157 0.593220
\(77\) 0 0
\(78\) 0 0
\(79\) −6.82843 + 11.8272i −0.768258 + 1.33066i 0.170249 + 0.985401i \(0.445543\pi\)
−0.938507 + 0.345261i \(0.887790\pi\)
\(80\) 5.12132 + 8.87039i 0.572581 + 0.991739i
\(81\) 0 0
\(82\) −1.29289 + 2.23936i −0.142776 + 0.247296i
\(83\) −7.31371 −0.802784 −0.401392 0.915906i \(-0.631473\pi\)
−0.401392 + 0.915906i \(0.631473\pi\)
\(84\) 0 0
\(85\) −7.65685 −0.830502
\(86\) 1.17157 2.02922i 0.126334 0.218817i
\(87\) 0 0
\(88\) −1.58579 2.74666i −0.169045 0.292795i
\(89\) −7.12132 + 12.3345i −0.754858 + 1.30745i 0.190586 + 0.981670i \(0.438961\pi\)
−0.945445 + 0.325783i \(0.894372\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −14.0000 −1.45960
\(93\) 0 0
\(94\) 0.585786 + 1.01461i 0.0604193 + 0.104649i
\(95\) −4.82843 8.36308i −0.495386 0.858034i
\(96\) 0 0
\(97\) 2.58579 0.262547 0.131273 0.991346i \(-0.458093\pi\)
0.131273 + 0.991346i \(0.458093\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 6.08579 10.5409i 0.608579 1.05409i
\(101\) 1.46447 + 2.53653i 0.145720 + 0.252394i 0.929641 0.368466i \(-0.120117\pi\)
−0.783921 + 0.620860i \(0.786784\pi\)
\(102\) 0 0
\(103\) −2.24264 + 3.88437i −0.220974 + 0.382738i −0.955104 0.296271i \(-0.904257\pi\)
0.734130 + 0.679009i \(0.237590\pi\)
\(104\) 4.10051 0.402088
\(105\) 0 0
\(106\) −0.828427 −0.0804640
\(107\) −0.171573 + 0.297173i −0.0165866 + 0.0287288i −0.874200 0.485567i \(-0.838613\pi\)
0.857613 + 0.514296i \(0.171947\pi\)
\(108\) 0 0
\(109\) 2.82843 + 4.89898i 0.270914 + 0.469237i 0.969096 0.246683i \(-0.0793407\pi\)
−0.698182 + 0.715920i \(0.746007\pi\)
\(110\) −1.41421 + 2.44949i −0.134840 + 0.233550i
\(111\) 0 0
\(112\) 0 0
\(113\) 5.31371 0.499872 0.249936 0.968262i \(-0.419590\pi\)
0.249936 + 0.968262i \(0.419590\pi\)
\(114\) 0 0
\(115\) 13.0711 + 22.6398i 1.21888 + 2.11117i
\(116\) 6.24264 + 10.8126i 0.579615 + 1.00392i
\(117\) 0 0
\(118\) −0.485281 −0.0446738
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 2.53553 + 4.39167i 0.229556 + 0.397603i
\(123\) 0 0
\(124\) −1.07107 + 1.85514i −0.0961847 + 0.166597i
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) −1.65685 −0.147022 −0.0735110 0.997294i \(-0.523420\pi\)
−0.0735110 + 0.997294i \(0.523420\pi\)
\(128\) −5.27817 + 9.14207i −0.466529 + 0.808052i
\(129\) 0 0
\(130\) −1.82843 3.16693i −0.160364 0.277758i
\(131\) −7.65685 + 13.2621i −0.668982 + 1.15871i 0.309207 + 0.950995i \(0.399937\pi\)
−0.978189 + 0.207717i \(0.933397\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.34315 0.202417
\(135\) 0 0
\(136\) −1.77817 3.07989i −0.152477 0.264098i
\(137\) 7.07107 + 12.2474i 0.604122 + 1.04637i 0.992190 + 0.124739i \(0.0398094\pi\)
−0.388067 + 0.921631i \(0.626857\pi\)
\(138\) 0 0
\(139\) −17.6569 −1.49763 −0.748817 0.662776i \(-0.769378\pi\)
−0.748817 + 0.662776i \(0.769378\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.92893 + 3.34101i −0.161872 + 0.280371i
\(143\) −2.58579 4.47871i −0.216234 0.374529i
\(144\) 0 0
\(145\) 11.6569 20.1903i 0.968049 1.67671i
\(146\) −5.75736 −0.476482
\(147\) 0 0
\(148\) 7.31371 0.601183
\(149\) 8.65685 14.9941i 0.709197 1.22837i −0.255958 0.966688i \(-0.582391\pi\)
0.965155 0.261678i \(-0.0842757\pi\)
\(150\) 0 0
\(151\) −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i \(-0.329040\pi\)
−0.999909 + 0.0134886i \(0.995706\pi\)
\(152\) 2.24264 3.88437i 0.181902 0.315064i
\(153\) 0 0
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −5.87868 10.1822i −0.469170 0.812626i 0.530209 0.847867i \(-0.322113\pi\)
−0.999379 + 0.0352411i \(0.988780\pi\)
\(158\) 2.82843 + 4.89898i 0.225018 + 0.389742i
\(159\) 0 0
\(160\) 15.0711 1.19147
\(161\) 0 0
\(162\) 0 0
\(163\) 5.65685 9.79796i 0.443079 0.767435i −0.554837 0.831959i \(-0.687219\pi\)
0.997916 + 0.0645236i \(0.0205528\pi\)
\(164\) −5.70711 9.88500i −0.445650 0.771889i
\(165\) 0 0
\(166\) −1.51472 + 2.62357i −0.117565 + 0.203628i
\(167\) 19.7990 1.53209 0.766046 0.642786i \(-0.222221\pi\)
0.766046 + 0.642786i \(0.222221\pi\)
\(168\) 0 0
\(169\) −6.31371 −0.485670
\(170\) −1.58579 + 2.74666i −0.121624 + 0.210659i
\(171\) 0 0
\(172\) 5.17157 + 8.95743i 0.394329 + 0.682997i
\(173\) 10.5355 18.2481i 0.801002 1.38738i −0.117956 0.993019i \(-0.537634\pi\)
0.918957 0.394357i \(-0.129033\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) 2.94975 + 5.10911i 0.221093 + 0.382944i
\(179\) −9.82843 17.0233i −0.734611 1.27238i −0.954894 0.296948i \(-0.904031\pi\)
0.220283 0.975436i \(-0.429302\pi\)
\(180\) 0 0
\(181\) −2.58579 −0.192200 −0.0961000 0.995372i \(-0.530637\pi\)
−0.0961000 + 0.995372i \(0.530637\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.07107 + 10.5154i −0.447565 + 0.775205i
\(185\) −6.82843 11.8272i −0.502036 0.869552i
\(186\) 0 0
\(187\) −2.24264 + 3.88437i −0.163998 + 0.284053i
\(188\) −5.17157 −0.377176
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) −2.65685 4.60181i −0.191245 0.331245i 0.754418 0.656394i \(-0.227919\pi\)
−0.945663 + 0.325149i \(0.894586\pi\)
\(194\) 0.535534 0.927572i 0.0384491 0.0665958i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) −10.8284 18.7554i −0.767607 1.32953i −0.938857 0.344307i \(-0.888114\pi\)
0.171250 0.985228i \(-0.445219\pi\)
\(200\) −5.27817 9.14207i −0.373223 0.646442i
\(201\) 0 0
\(202\) 1.21320 0.0853607
\(203\) 0 0
\(204\) 0 0
\(205\) −10.6569 + 18.4582i −0.744307 + 1.28918i
\(206\) 0.928932 + 1.60896i 0.0647218 + 0.112101i
\(207\) 0 0
\(208\) −3.87868 + 6.71807i −0.268938 + 0.465814i
\(209\) −5.65685 −0.391293
\(210\) 0 0
\(211\) 12.9706 0.892930 0.446465 0.894801i \(-0.352683\pi\)
0.446465 + 0.894801i \(0.352683\pi\)
\(212\) 1.82843 3.16693i 0.125577 0.217506i
\(213\) 0 0
\(214\) 0.0710678 + 0.123093i 0.00485810 + 0.00841447i
\(215\) 9.65685 16.7262i 0.658592 1.14071i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.34315 0.158698
\(219\) 0 0
\(220\) −6.24264 10.8126i −0.420879 0.728983i
\(221\) −2.89949 5.02207i −0.195041 0.337821i
\(222\) 0 0
\(223\) 24.9706 1.67215 0.836076 0.548613i \(-0.184844\pi\)
0.836076 + 0.548613i \(0.184844\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1.10051 1.90613i 0.0732045 0.126794i
\(227\) 11.8995 + 20.6105i 0.789797 + 1.36797i 0.926091 + 0.377300i \(0.123148\pi\)
−0.136294 + 0.990668i \(0.543519\pi\)
\(228\) 0 0
\(229\) 0.121320 0.210133i 0.00801707 0.0138860i −0.861989 0.506927i \(-0.830781\pi\)
0.870006 + 0.493041i \(0.164115\pi\)
\(230\) 10.8284 0.714005
\(231\) 0 0
\(232\) 10.8284 0.710921
\(233\) −3.07107 + 5.31925i −0.201192 + 0.348475i −0.948913 0.315538i \(-0.897815\pi\)
0.747721 + 0.664014i \(0.231148\pi\)
\(234\) 0 0
\(235\) 4.82843 + 8.36308i 0.314972 + 0.545547i
\(236\) 1.07107 1.85514i 0.0697206 0.120760i
\(237\) 0 0
\(238\) 0 0
\(239\) 15.6569 1.01276 0.506379 0.862311i \(-0.330984\pi\)
0.506379 + 0.862311i \(0.330984\pi\)
\(240\) 0 0
\(241\) 8.12132 + 14.0665i 0.523140 + 0.906105i 0.999637 + 0.0269294i \(0.00857294\pi\)
−0.476497 + 0.879176i \(0.658094\pi\)
\(242\) −1.44975 2.51104i −0.0931933 0.161416i
\(243\) 0 0
\(244\) −22.3848 −1.43304
\(245\) 0 0
\(246\) 0 0
\(247\) 3.65685 6.33386i 0.232680 0.403014i
\(248\) 0.928932 + 1.60896i 0.0589873 + 0.102169i
\(249\) 0 0
\(250\) −1.17157 + 2.02922i −0.0740968 + 0.128339i
\(251\) 12.4853 0.788064 0.394032 0.919097i \(-0.371080\pi\)
0.394032 + 0.919097i \(0.371080\pi\)
\(252\) 0 0
\(253\) 15.3137 0.962765
\(254\) −0.343146 + 0.594346i −0.0215309 + 0.0372926i
\(255\) 0 0
\(256\) −1.98528 3.43861i −0.124080 0.214913i
\(257\) 11.6066 20.1032i 0.724000 1.25400i −0.235384 0.971902i \(-0.575635\pi\)
0.959384 0.282102i \(-0.0910318\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 16.1421 1.00109
\(261\) 0 0
\(262\) 3.17157 + 5.49333i 0.195940 + 0.339379i
\(263\) 2.65685 + 4.60181i 0.163829 + 0.283760i 0.936239 0.351365i \(-0.114282\pi\)
−0.772410 + 0.635124i \(0.780949\pi\)
\(264\) 0 0
\(265\) −6.82843 −0.419467
\(266\) 0 0
\(267\) 0 0
\(268\) −5.17157 + 8.95743i −0.315904 + 0.547162i
\(269\) −7.36396 12.7548i −0.448989 0.777671i 0.549332 0.835604i \(-0.314882\pi\)
−0.998320 + 0.0579332i \(0.981549\pi\)
\(270\) 0 0
\(271\) 5.07107 8.78335i 0.308045 0.533550i −0.669889 0.742461i \(-0.733658\pi\)
0.977935 + 0.208911i \(0.0669918\pi\)
\(272\) 6.72792 0.407940
\(273\) 0 0
\(274\) 5.85786 0.353887
\(275\) −6.65685 + 11.5300i −0.401423 + 0.695286i
\(276\) 0 0
\(277\) 4.65685 + 8.06591i 0.279803 + 0.484633i 0.971336 0.237712i \(-0.0763974\pi\)
−0.691532 + 0.722345i \(0.743064\pi\)
\(278\) −3.65685 + 6.33386i −0.219324 + 0.379880i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.485281 −0.0289495 −0.0144747 0.999895i \(-0.504608\pi\)
−0.0144747 + 0.999895i \(0.504608\pi\)
\(282\) 0 0
\(283\) 4.24264 + 7.34847i 0.252199 + 0.436821i 0.964131 0.265427i \(-0.0855130\pi\)
−0.711932 + 0.702248i \(0.752180\pi\)
\(284\) −8.51472 14.7479i −0.505256 0.875128i
\(285\) 0 0
\(286\) −2.14214 −0.126667
\(287\) 0 0
\(288\) 0 0
\(289\) 5.98528 10.3668i 0.352075 0.609812i
\(290\) −4.82843 8.36308i −0.283535 0.491097i
\(291\) 0 0
\(292\) 12.7071 22.0094i 0.743627 1.28800i
\(293\) −16.5858 −0.968952 −0.484476 0.874805i \(-0.660990\pi\)
−0.484476 + 0.874805i \(0.660990\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 3.17157 5.49333i 0.184344 0.319293i
\(297\) 0 0
\(298\) −3.58579 6.21076i −0.207719 0.359780i
\(299\) −9.89949 + 17.1464i −0.572503 + 0.991604i
\(300\) 0 0
\(301\) 0 0
\(302\) −4.97056 −0.286024
\(303\) 0 0
\(304\) 4.24264 + 7.34847i 0.243332 + 0.421464i
\(305\) 20.8995 + 36.1990i 1.19670 + 2.07275i
\(306\) 0 0
\(307\) 30.1421 1.72030 0.860151 0.510039i \(-0.170369\pi\)
0.860151 + 0.510039i \(0.170369\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.828427 1.43488i 0.0470515 0.0814956i
\(311\) 3.07107 + 5.31925i 0.174144 + 0.301627i 0.939865 0.341547i \(-0.110951\pi\)
−0.765721 + 0.643173i \(0.777617\pi\)
\(312\) 0 0
\(313\) −0.949747 + 1.64501i −0.0536829 + 0.0929815i −0.891618 0.452788i \(-0.850429\pi\)
0.837935 + 0.545770i \(0.183763\pi\)
\(314\) −4.87006 −0.274833
\(315\) 0 0
\(316\) −24.9706 −1.40470
\(317\) 5.00000 8.66025i 0.280828 0.486408i −0.690761 0.723083i \(-0.742724\pi\)
0.971589 + 0.236675i \(0.0760576\pi\)
\(318\) 0 0
\(319\) −6.82843 11.8272i −0.382319 0.662195i
\(320\) −7.12132 + 12.3345i −0.398094 + 0.689519i
\(321\) 0 0
\(322\) 0 0
\(323\) −6.34315 −0.352942
\(324\) 0 0
\(325\) −8.60660 14.9071i −0.477408 0.826896i
\(326\) −2.34315 4.05845i −0.129775 0.224777i
\(327\) 0 0
\(328\) −9.89949 −0.546608
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) −6.68629 11.5810i −0.366958 0.635590i
\(333\) 0 0
\(334\) 4.10051 7.10228i 0.224370 0.388620i
\(335\) 19.3137 1.05522
\(336\) 0 0
\(337\) −29.6569 −1.61551 −0.807756 0.589517i \(-0.799318\pi\)
−0.807756 + 0.589517i \(0.799318\pi\)
\(338\) −1.30761 + 2.26485i −0.0711247 + 0.123192i
\(339\) 0 0
\(340\) −7.00000 12.1244i −0.379628 0.657536i
\(341\) 1.17157 2.02922i 0.0634442 0.109889i
\(342\) 0 0
\(343\) 0 0
\(344\) 8.97056 0.483660
\(345\) 0 0
\(346\) −4.36396 7.55860i −0.234608 0.406353i
\(347\) 16.6569 + 28.8505i 0.894187 + 1.54878i 0.834808 + 0.550541i \(0.185579\pi\)
0.0593789 + 0.998236i \(0.481088\pi\)
\(348\) 0 0
\(349\) −9.89949 −0.529908 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.41421 7.64564i 0.235278 0.407514i
\(353\) −7.36396 12.7548i −0.391944 0.678867i 0.600762 0.799428i \(-0.294864\pi\)
−0.992706 + 0.120561i \(0.961531\pi\)
\(354\) 0 0
\(355\) −15.8995 + 27.5387i −0.843858 + 1.46160i
\(356\) −26.0416 −1.38020
\(357\) 0 0
\(358\) −8.14214 −0.430325
\(359\) −0.171573 + 0.297173i −0.00905527 + 0.0156842i −0.870518 0.492137i \(-0.836216\pi\)
0.861462 + 0.507822i \(0.169549\pi\)
\(360\) 0 0
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) −0.535534 + 0.927572i −0.0281470 + 0.0487521i
\(363\) 0 0
\(364\) 0 0
\(365\) −47.4558 −2.48395
\(366\) 0 0
\(367\) 1.65685 + 2.86976i 0.0864871 + 0.149800i 0.906024 0.423226i \(-0.139103\pi\)
−0.819537 + 0.573027i \(0.805769\pi\)
\(368\) −11.4853 19.8931i −0.598712 1.03700i
\(369\) 0 0
\(370\) −5.65685 −0.294086
\(371\) 0 0
\(372\) 0 0
\(373\) 5.34315 9.25460i 0.276658 0.479185i −0.693894 0.720077i \(-0.744107\pi\)
0.970552 + 0.240892i \(0.0774399\pi\)
\(374\) 0.928932 + 1.60896i 0.0480339 + 0.0831972i
\(375\) 0 0
\(376\) −2.24264 + 3.88437i −0.115655 + 0.200321i
\(377\) 17.6569 0.909374
\(378\) 0 0
\(379\) 8.68629 0.446185 0.223092 0.974797i \(-0.428385\pi\)
0.223092 + 0.974797i \(0.428385\pi\)
\(380\) 8.82843 15.2913i 0.452889 0.784426i
\(381\) 0 0
\(382\) 3.72792 + 6.45695i 0.190737 + 0.330366i
\(383\) −9.17157 + 15.8856i −0.468645 + 0.811718i −0.999358 0.0358343i \(-0.988591\pi\)
0.530712 + 0.847552i \(0.321924\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.20101 −0.112028
\(387\) 0 0
\(388\) 2.36396 + 4.09450i 0.120012 + 0.207867i
\(389\) −9.07107 15.7116i −0.459921 0.796607i 0.539035 0.842283i \(-0.318789\pi\)
−0.998956 + 0.0456762i \(0.985456\pi\)
\(390\) 0 0
\(391\) 17.1716 0.868404
\(392\) 0 0
\(393\) 0 0
\(394\) −0.414214 + 0.717439i −0.0208678 + 0.0361441i
\(395\) 23.3137 + 40.3805i 1.17304 + 2.03176i
\(396\) 0 0
\(397\) 1.19239 2.06528i 0.0598442 0.103653i −0.834551 0.550931i \(-0.814273\pi\)
0.894395 + 0.447277i \(0.147606\pi\)
\(398\) −8.97056 −0.449654
\(399\) 0 0
\(400\) 19.9706 0.998528
\(401\) −3.07107 + 5.31925i −0.153362 + 0.265630i −0.932461 0.361270i \(-0.882343\pi\)
0.779100 + 0.626900i \(0.215677\pi\)
\(402\) 0 0
\(403\) 1.51472 + 2.62357i 0.0754535 + 0.130689i
\(404\) −2.67767 + 4.63786i −0.133219 + 0.230742i
\(405\) 0 0
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) 10.7071 + 18.5453i 0.529432 + 0.917004i 0.999411 + 0.0343258i \(0.0109284\pi\)
−0.469978 + 0.882678i \(0.655738\pi\)
\(410\) 4.41421 + 7.64564i 0.218002 + 0.377591i
\(411\) 0 0
\(412\) −8.20101 −0.404035
\(413\) 0 0
\(414\) 0 0
\(415\) −12.4853 + 21.6251i −0.612878 + 1.06154i
\(416\) 5.70711 + 9.88500i 0.279814 + 0.484652i
\(417\) 0 0
\(418\) −1.17157 + 2.02922i −0.0573035 + 0.0992526i
\(419\) −33.1716 −1.62054 −0.810269 0.586059i \(-0.800679\pi\)
−0.810269 + 0.586059i \(0.800679\pi\)
\(420\) 0 0
\(421\) 16.6274 0.810371 0.405185 0.914235i \(-0.367207\pi\)
0.405185 + 0.914235i \(0.367207\pi\)
\(422\) 2.68629 4.65279i 0.130767 0.226494i
\(423\) 0 0
\(424\) −1.58579 2.74666i −0.0770126 0.133390i
\(425\) −7.46447 + 12.9288i −0.362080 + 0.627141i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.627417 −0.0303273
\(429\) 0 0
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) −13.4853 23.3572i −0.649563 1.12508i −0.983227 0.182384i \(-0.941618\pi\)
0.333664 0.942692i \(-0.391715\pi\)
\(432\) 0 0
\(433\) −20.2426 −0.972799 −0.486400 0.873736i \(-0.661690\pi\)
−0.486400 + 0.873736i \(0.661690\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −5.17157 + 8.95743i −0.247673 + 0.428983i
\(437\) 10.8284 + 18.7554i 0.517994 + 0.897192i
\(438\) 0 0
\(439\) −6.34315 + 10.9867i −0.302742 + 0.524364i −0.976756 0.214354i \(-0.931235\pi\)
0.674014 + 0.738718i \(0.264569\pi\)
\(440\) −10.8284 −0.516225
\(441\) 0 0
\(442\) −2.40202 −0.114252
\(443\) 17.4853 30.2854i 0.830751 1.43890i −0.0666929 0.997774i \(-0.521245\pi\)
0.897444 0.441129i \(-0.145422\pi\)
\(444\) 0 0
\(445\) 24.3137 + 42.1126i 1.15258 + 1.99633i
\(446\) 5.17157 8.95743i 0.244881 0.424146i
\(447\) 0 0
\(448\) 0 0
\(449\) 5.31371 0.250769 0.125385 0.992108i \(-0.459983\pi\)
0.125385 + 0.992108i \(0.459983\pi\)
\(450\) 0 0
\(451\) 6.24264 + 10.8126i 0.293954 + 0.509144i
\(452\) 4.85786 + 8.41407i 0.228495 + 0.395764i
\(453\) 0 0
\(454\) 9.85786 0.462652
\(455\) 0 0
\(456\) 0 0
\(457\) 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) −0.0502525 0.0870399i −0.00234815 0.00406711i
\(459\) 0 0
\(460\) −23.8995 + 41.3951i −1.11432 + 1.93006i
\(461\) 16.5858 0.772477 0.386239 0.922399i \(-0.373774\pi\)
0.386239 + 0.922399i \(0.373774\pi\)
\(462\) 0 0
\(463\) −26.6274 −1.23748 −0.618741 0.785595i \(-0.712357\pi\)
−0.618741 + 0.785595i \(0.712357\pi\)
\(464\) −10.2426 + 17.7408i −0.475503 + 0.823595i
\(465\) 0 0
\(466\) 1.27208 + 2.20330i 0.0589279 + 0.102066i
\(467\) 0.100505 0.174080i 0.00465082 0.00805546i −0.863691 0.504022i \(-0.831853\pi\)
0.868341 + 0.495967i \(0.165186\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 4.00000 0.184506
\(471\) 0 0
\(472\) −0.928932 1.60896i −0.0427576 0.0740583i
\(473\) −5.65685 9.79796i −0.260102 0.450511i
\(474\) 0 0
\(475\) −18.8284 −0.863907
\(476\) 0 0
\(477\) 0 0
\(478\) 3.24264 5.61642i 0.148315 0.256889i
\(479\) 0.928932 + 1.60896i 0.0424440 + 0.0735152i 0.886467 0.462792i \(-0.153152\pi\)
−0.844023 + 0.536307i \(0.819819\pi\)
\(480\) 0 0
\(481\) 5.17157 8.95743i 0.235803 0.408424i
\(482\) 6.72792 0.306448
\(483\) 0 0
\(484\) 12.7990 0.581772
\(485\) 4.41421 7.64564i 0.200439 0.347171i
\(486\) 0 0
\(487\) −13.3137 23.0600i −0.603302 1.04495i −0.992317 0.123718i \(-0.960518\pi\)
0.389016 0.921231i \(-0.372815\pi\)
\(488\) −9.70711 + 16.8132i −0.439420 + 0.761098i
\(489\) 0 0
\(490\) 0 0
\(491\) −5.02944 −0.226975 −0.113488 0.993539i \(-0.536202\pi\)
−0.113488 + 0.993539i \(0.536202\pi\)
\(492\) 0 0
\(493\) −7.65685 13.2621i −0.344847 0.597293i
\(494\) −1.51472 2.62357i −0.0681504 0.118040i
\(495\) 0 0
\(496\) −3.51472 −0.157816
\(497\) 0 0
\(498\) 0 0
\(499\) −1.65685 + 2.86976i −0.0741710 + 0.128468i −0.900725 0.434389i \(-0.856964\pi\)
0.826554 + 0.562857i \(0.190298\pi\)
\(500\) −5.17157 8.95743i −0.231280 0.400588i
\(501\) 0 0
\(502\) 2.58579 4.47871i 0.115409 0.199895i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 3.17157 5.49333i 0.140994 0.244208i
\(507\) 0 0
\(508\) −1.51472 2.62357i −0.0672048 0.116402i
\(509\) 2.77817 4.81194i 0.123140 0.213285i −0.797864 0.602837i \(-0.794037\pi\)
0.921005 + 0.389552i \(0.127370\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.7574 −1.00574
\(513\) 0 0
\(514\) −4.80761 8.32703i −0.212055 0.367289i
\(515\) 7.65685 + 13.2621i 0.337401 + 0.584396i
\(516\) 0 0
\(517\) 5.65685 0.248788
\(518\) 0 0
\(519\) 0 0
\(520\) 7.00000 12.1244i 0.306970 0.531688i
\(521\) −17.7071 30.6696i −0.775762 1.34366i −0.934365 0.356317i \(-0.884032\pi\)
0.158603 0.987343i \(-0.449301\pi\)
\(522\) 0 0
\(523\) 12.8284 22.2195i 0.560948 0.971590i −0.436466 0.899721i \(-0.643770\pi\)
0.997414 0.0718696i \(-0.0228966\pi\)
\(524\) −28.0000 −1.22319
\(525\) 0 0
\(526\) 2.20101 0.0959686
\(527\) 1.31371 2.27541i 0.0572260 0.0991184i
\(528\) 0 0
\(529\) −17.8137 30.8542i −0.774509 1.34149i
\(530\) −1.41421 + 2.44949i −0.0614295 + 0.106399i
\(531\) 0 0
\(532\) 0 0
\(533\) −16.1421 −0.699194
\(534\) 0 0
\(535\) 0.585786 + 1.01461i 0.0253258 + 0.0438655i
\(536\) 4.48528 + 7.76874i 0.193735 + 0.335558i
\(537\) 0 0
\(538\) −6.10051 −0.263011
\(539\) 0 0
\(540\) 0 0
\(541\) −8.65685 + 14.9941i −0.372187 + 0.644647i −0.989902 0.141755i \(-0.954725\pi\)
0.617715 + 0.786402i \(0.288059\pi\)
\(542\) −2.10051 3.63818i −0.0902244 0.156273i
\(543\) 0 0
\(544\) 4.94975 8.57321i 0.212219 0.367574i
\(545\) 19.3137 0.827308
\(546\) 0 0
\(547\) −36.9706 −1.58075 −0.790374 0.612625i \(-0.790114\pi\)
−0.790374 + 0.612625i \(0.790114\pi\)
\(548\) −12.9289 + 22.3936i −0.552297 + 0.956606i
\(549\) 0 0
\(550\) 2.75736 + 4.77589i 0.117574 + 0.203644i
\(551\) 9.65685 16.7262i 0.411396 0.712558i
\(552\) 0 0
\(553\) 0 0
\(554\) 3.85786 0.163905
\(555\) 0 0
\(556\) −16.1421 27.9590i −0.684579 1.18573i
\(557\) 13.0000 + 22.5167i 0.550828 + 0.954062i 0.998215 + 0.0597213i \(0.0190212\pi\)
−0.447387 + 0.894340i \(0.647645\pi\)
\(558\) 0 0
\(559\) 14.6274 0.618674
\(560\) 0 0
\(561\) 0 0
\(562\) −0.100505 + 0.174080i −0.00423955 + 0.00734312i
\(563\) −0.585786 1.01461i −0.0246880 0.0427608i 0.853417 0.521228i \(-0.174526\pi\)
−0.878105 + 0.478467i \(0.841193\pi\)
\(564\) 0 0
\(565\) 9.07107 15.7116i 0.381623 0.660990i
\(566\) 3.51472 0.147735
\(567\) 0 0
\(568\) −14.7696 −0.619717
\(569\) −8.24264 + 14.2767i −0.345549 + 0.598509i −0.985453 0.169946i \(-0.945641\pi\)
0.639904 + 0.768455i \(0.278974\pi\)
\(570\) 0 0
\(571\) −11.1716 19.3497i −0.467516 0.809761i 0.531795 0.846873i \(-0.321518\pi\)
−0.999311 + 0.0371118i \(0.988184\pi\)
\(572\) 4.72792 8.18900i 0.197684 0.342399i
\(573\) 0 0
\(574\) 0 0
\(575\) 50.9706 2.12562
\(576\) 0 0
\(577\) 16.9497 + 29.3578i 0.705627 + 1.22218i 0.966465 + 0.256799i \(0.0826680\pi\)
−0.260837 + 0.965383i \(0.583999\pi\)
\(578\) −2.47918 4.29407i −0.103120 0.178610i
\(579\) 0 0
\(580\) 42.6274 1.77001
\(581\) 0 0
\(582\) 0 0
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) −11.0208 19.0886i −0.456045 0.789892i
\(585\) 0 0
\(586\) −3.43503 + 5.94964i −0.141900 + 0.245778i
\(587\) 22.8284 0.942230 0.471115 0.882072i \(-0.343852\pi\)
0.471115 + 0.882072i \(0.343852\pi\)
\(588\) 0 0
\(589\) 3.31371 0.136539
\(590\) −0.828427 + 1.43488i −0.0341058 + 0.0590730i
\(591\) 0 0
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) −3.46447 + 6.00063i −0.142269 + 0.246416i −0.928351 0.371706i \(-0.878773\pi\)
0.786082 + 0.618122i \(0.212106\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 31.6569 1.29672
\(597\) 0 0
\(598\) 4.10051 + 7.10228i 0.167682 + 0.290434i
\(599\) −1.00000 1.73205i −0.0408589 0.0707697i 0.844873 0.534967i \(-0.179676\pi\)
−0.885732 + 0.464198i \(0.846343\pi\)
\(600\) 0 0
\(601\) −15.0711 −0.614762 −0.307381 0.951587i \(-0.599453\pi\)
−0.307381 + 0.951587i \(0.599453\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 10.9706 19.0016i 0.446386 0.773163i
\(605\) −11.9497 20.6976i −0.485826 0.841476i
\(606\) 0 0
\(607\) 9.17157 15.8856i 0.372263 0.644778i −0.617651 0.786453i \(-0.711915\pi\)
0.989913 + 0.141675i \(0.0452487\pi\)
\(608\) 12.4853 0.506345
\(609\) 0 0
\(610\) 17.3137 0.701012
\(611\) −3.65685 + 6.33386i −0.147940 + 0.256240i
\(612\) 0 0
\(613\) −2.34315 4.05845i −0.0946388 0.163919i 0.814819 0.579715i \(-0.196836\pi\)
−0.909458 + 0.415796i \(0.863503\pi\)
\(614\) 6.24264 10.8126i 0.251932 0.436360i
\(615\) 0 0
\(616\) 0 0
\(617\) 24.4853 0.985740 0.492870 0.870103i \(-0.335948\pi\)
0.492870 + 0.870103i \(0.335948\pi\)
\(618\) 0 0
\(619\) −14.4853 25.0892i −0.582213 1.00842i −0.995217 0.0976926i \(-0.968854\pi\)
0.413004 0.910729i \(-0.364480\pi\)
\(620\) 3.65685 + 6.33386i 0.146863 + 0.254374i
\(621\) 0 0
\(622\) 2.54416 0.102011
\(623\) 0 0
\(624\) 0 0
\(625\) 6.98528 12.0989i 0.279411 0.483954i
\(626\) 0.393398 + 0.681386i 0.0157234 + 0.0272337i
\(627\) 0 0
\(628\) 10.7487 18.6174i 0.428921 0.742914i
\(629\) −8.97056 −0.357680
\(630\) 0 0
\(631\) 23.3137 0.928104 0.464052 0.885808i \(-0.346395\pi\)
0.464052 + 0.885808i \(0.346395\pi\)
\(632\) −10.8284 + 18.7554i −0.430732 + 0.746049i
\(633\) 0 0
\(634\) −2.07107 3.58719i −0.0822526 0.142466i
\(635\) −2.82843 + 4.89898i −0.112243 + 0.194410i
\(636\) 0 0
\(637\) 0 0
\(638\) −5.65685 −0.223957
\(639\) 0 0
\(640\) 18.0208 + 31.2130i 0.712335 + 1.23380i
\(641\) −5.41421 9.37769i −0.213849 0.370397i 0.739067 0.673632i \(-0.235267\pi\)
−0.952916 + 0.303235i \(0.901933\pi\)
\(642\) 0 0
\(643\) −34.4264 −1.35764 −0.678822 0.734302i \(-0.737509\pi\)
−0.678822 + 0.734302i \(0.737509\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −1.31371 + 2.27541i −0.0516872 + 0.0895248i
\(647\) 13.4142 + 23.2341i 0.527367 + 0.913427i 0.999491 + 0.0318946i \(0.0101541\pi\)
−0.472124 + 0.881532i \(0.656513\pi\)
\(648\) 0 0
\(649\) −1.17157 + 2.02922i −0.0459883 + 0.0796540i
\(650\) −7.12994 −0.279659
\(651\) 0 0
\(652\) 20.6863 0.810138
\(653\) 18.2426 31.5972i 0.713890 1.23649i −0.249497 0.968376i \(-0.580265\pi\)
0.963386 0.268118i \(-0.0864016\pi\)
\(654\) 0 0
\(655\) 26.1421 + 45.2795i 1.02146 + 1.76922i
\(656\) 9.36396 16.2189i 0.365601 0.633240i
\(657\) 0 0
\(658\) 0 0
\(659\) −9.31371 −0.362811 −0.181405 0.983408i \(-0.558065\pi\)
−0.181405 + 0.983408i \(0.558065\pi\)
\(660\) 0 0
\(661\) 11.7782 + 20.4004i 0.458118 + 0.793483i 0.998862 0.0477040i \(-0.0151904\pi\)
−0.540744 + 0.841187i \(0.681857\pi\)
\(662\) −0.828427 1.43488i −0.0321977 0.0557681i
\(663\) 0 0
\(664\) −11.5980 −0.450089
\(665\) 0 0
\(666\) 0 0
\(667\) −26.1421 + 45.2795i −1.01223 + 1.75323i
\(668\) 18.1005 + 31.3510i 0.700330 + 1.21301i
\(669\) 0 0
\(670\) 4.00000 6.92820i 0.154533 0.267660i
\(671\) 24.4853 0.945244
\(672\) 0 0
\(673\) 23.3137 0.898677 0.449339 0.893361i \(-0.351660\pi\)
0.449339 + 0.893361i \(0.351660\pi\)
\(674\) −6.14214 + 10.6385i −0.236586 + 0.409779i
\(675\) 0 0
\(676\) −5.77208 9.99753i −0.222003 0.384520i
\(677\) 15.7071 27.2055i 0.603673 1.04559i −0.388587 0.921412i \(-0.627037\pi\)
0.992260 0.124180i \(-0.0396301\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −12.1421 −0.465630
\(681\) 0 0
\(682\) −0.485281 0.840532i −0.0185824 0.0321856i
\(683\) −9.82843 17.0233i −0.376074 0.651380i 0.614413 0.788985i \(-0.289393\pi\)
−0.990487 + 0.137605i \(0.956060\pi\)
\(684\) 0 0
\(685\) 48.2843 1.84485
\(686\) 0 0
\(687\) 0 0
\(688\) −8.48528 + 14.6969i −0.323498 + 0.560316i
\(689\) −2.58579 4.47871i −0.0985106 0.170625i
\(690\) 0 0
\(691\) 0.343146 0.594346i 0.0130539 0.0226100i −0.859425 0.511262i \(-0.829178\pi\)
0.872479 + 0.488652i \(0.162511\pi\)
\(692\) 38.5269 1.46457
\(693\) 0 0
\(694\) 13.7990 0.523802
\(695\) −30.1421 + 52.2077i −1.14336 + 1.98035i
\(696\) 0 0
\(697\) 7.00000 + 12.1244i 0.265144 + 0.459243i
\(698\) −2.05025 + 3.55114i −0.0776032 + 0.134413i
\(699\) 0 0
\(700\) 0 0
\(701\) 17.1716 0.648561 0.324281 0.945961i \(-0.394878\pi\)
0.324281 + 0.945961i \(0.394878\pi\)
\(702\) 0 0
\(703\) −5.65685 9.79796i −0.213352 0.369537i
\(704\) 4.17157 + 7.22538i 0.157222 + 0.272317i
\(705\) 0 0
\(706\) −6.10051 −0.229596
\(707\) 0 0
\(708\) 0 0
\(709\) 18.1421 31.4231i 0.681342 1.18012i −0.293229 0.956042i \(-0.594730\pi\)
0.974571 0.224077i \(-0.0719368\pi\)
\(710\) 6.58579 + 11.4069i 0.247160 + 0.428094i
\(711\) 0 0
\(712\) −11.2929 + 19.5599i −0.423219 + 0.733037i
\(713\) −8.97056 −0.335950
\(714\) 0 0
\(715\) −17.6569 −0.660329
\(716\) 17.9706 31.1259i 0.671591 1.16323i
\(717\) 0 0
\(718\) 0.0710678 + 0.123093i 0.00265223 + 0.00459379i
\(719\) 20.9706 36.3221i 0.782070 1.35459i −0.148664 0.988888i \(-0.547497\pi\)
0.930734 0.365697i \(-0.119169\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 4.55635 0.169570
\(723\) 0 0
\(724\) −2.36396 4.09450i −0.0878559 0.152171i
\(725\) −22.7279 39.3659i −0.844094 1.46201i
\(726\) 0 0
\(727\) 12.4853 0.463053 0.231527 0.972829i \(-0.425628\pi\)
0.231527 + 0.972829i \(0.425628\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −9.82843 + 17.0233i −0.363766 + 0.630062i
\(731\) −6.34315 10.9867i −0.234610 0.406356i
\(732\) 0 0
\(733\) −24.8492 + 43.0402i −0.917828 + 1.58972i −0.115120 + 0.993352i \(0.536725\pi\)
−0.802708 + 0.596373i \(0.796608\pi\)
\(734\) 1.37258 0.0506630
\(735\) 0 0
\(736\) −33.7990 −1.24585
\(737\) 5.65685 9.79796i 0.208373 0.360912i
\(738\) 0 0
\(739\) −2.34315 4.05845i −0.0861940 0.149292i 0.819705 0.572785i \(-0.194137\pi\)
−0.905899 + 0.423493i \(0.860804\pi\)
\(740\) 12.4853 21.6251i 0.458968 0.794956i
\(741\) 0 0
\(742\) 0 0
\(743\) 50.9706 1.86993 0.934964 0.354742i \(-0.115431\pi\)
0.934964 + 0.354742i \(0.115431\pi\)
\(744\) 0 0
\(745\) −29.5563 51.1931i −1.08286 1.87557i
\(746\) −2.21320 3.83338i −0.0810311 0.140350i
\(747\) 0 0
\(748\) −8.20101 −0.299859
\(749\) 0 0
\(750\) 0 0
\(751\) −6.82843 + 11.8272i −0.249173 + 0.431580i −0.963297 0.268440i \(-0.913492\pi\)
0.714124 + 0.700020i \(0.246825\pi\)
\(752\) −4.24264 7.34847i −0.154713 0.267971i
\(753\) 0 0
\(754\) 3.65685 6.33386i 0.133175 0.230665i
\(755\) −40.9706 −1.49107
\(756\) 0 0
\(757\) 26.3431 0.957458 0.478729 0.877963i \(-0.341098\pi\)
0.478729 + 0.877963i \(0.341098\pi\)
\(758\) 1.79899 3.11594i 0.0653423 0.113176i
\(759\) 0 0
\(760\) −7.65685 13.2621i −0.277743 0.481065i
\(761\) −9.26346 + 16.0448i −0.335800 + 0.581623i −0.983638 0.180155i \(-0.942340\pi\)
0.647838 + 0.761778i \(0.275673\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −32.9117 −1.19070
\(765\) 0 0
\(766\) 3.79899 + 6.58004i 0.137263 + 0.237747i
\(767\) −1.51472 2.62357i −0.0546933 0.0947316i
\(768\) 0 0
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4.85786 8.41407i 0.174838 0.302829i
\(773\) −4.77817 8.27604i −0.171859 0.297669i 0.767211 0.641395i \(-0.221644\pi\)
−0.939070 + 0.343727i \(0.888311\pi\)
\(774\) 0 0
\(775\) 3.89949 6.75412i 0.140074 0.242615i
\(776\) 4.10051 0.147200
\(777\) 0 0
\(778\) −7.51472 −0.269416
\(779\) −8.82843 + 15.2913i −0.316311 + 0.547867i
\(780\) 0 0
\(781\) 9.31371 + 16.1318i 0.333271 + 0.577242i
\(782\) 3.55635 6.15978i 0.127175 0.220273i
\(783\) 0 0
\(784\) 0 0
\(785\) −40.1421 −1.43273
\(786\) 0 0
\(787\) −12.3431 21.3790i −0.439986 0.762077i 0.557702 0.830041i \(-0.311683\pi\)
−0.997688 + 0.0679637i \(0.978350\pi\)
\(788\) −1.82843 3.16693i −0.0651350 0.112817i
\(789\) 0 0
\(790\) 19.3137 0.687151
\(791\) 0 0
\(792\) 0 0
\(793\) −15.8284 + 27.4156i −0.562084 + 0.973558i
\(794\) −0.493903