Properties

Label 324.3.o.a.5.16
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.16
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.16

$q$-expansion

\(f(q)\) \(=\) \(q+(2.91181 - 0.722057i) q^{3} +(-2.43946 + 1.81611i) q^{5} +(-7.41916 + 4.87966i) q^{7} +(7.95727 - 4.20498i) q^{9} +O(q^{10})\) \(q+(2.91181 - 0.722057i) q^{3} +(-2.43946 + 1.81611i) q^{5} +(-7.41916 + 4.87966i) q^{7} +(7.95727 - 4.20498i) q^{9} +(-2.42099 + 20.7129i) q^{11} +(0.0230612 + 0.0770297i) q^{13} +(-5.79191 + 7.04960i) q^{15} +(10.3358 + 1.82248i) q^{17} +(4.67439 + 26.5098i) q^{19} +(-18.0798 + 19.5657i) q^{21} +(3.75889 - 5.71512i) q^{23} +(-4.51737 + 15.0891i) q^{25} +(20.1338 - 17.9897i) q^{27} +(6.47304 - 6.10700i) q^{29} +(2.04297 - 35.0765i) q^{31} +(7.90643 + 62.0602i) q^{33} +(9.23675 - 25.3778i) q^{35} +(-44.6777 + 16.2614i) q^{37} +(0.122770 + 0.207644i) q^{39} +(15.1306 - 63.8412i) q^{41} +(2.90157 + 6.72659i) q^{43} +(-11.7747 + 24.7092i) q^{45} +(3.18730 - 0.185639i) q^{47} +(11.8250 - 27.4134i) q^{49} +(31.4119 - 2.15632i) q^{51} +(64.8390 + 37.4348i) q^{53} +(-31.7111 - 54.9252i) q^{55} +(32.7525 + 73.8163i) q^{57} +(8.93375 + 76.4331i) q^{59} +(-72.0716 - 36.1957i) q^{61} +(-38.5174 + 70.0262i) q^{63} +(-0.196151 - 0.146029i) q^{65} +(-42.7276 + 45.2886i) q^{67} +(6.81854 - 19.3555i) q^{69} +(14.0684 - 16.7661i) q^{71} +(-82.0962 + 68.8869i) q^{73} +(-2.25856 + 47.1983i) q^{75} +(-83.1103 - 165.486i) q^{77} +(107.327 - 25.4369i) q^{79} +(45.6363 - 66.9203i) q^{81} +(-8.85205 - 37.3497i) q^{83} +(-28.5236 + 14.3251i) q^{85} +(14.4387 - 22.4563i) q^{87} +(34.5784 + 41.2090i) q^{89} +(-0.546974 - 0.458965i) q^{91} +(-19.3785 - 103.611i) q^{93} +(-59.5477 - 56.1804i) q^{95} +(59.3556 - 79.7285i) q^{97} +(67.8330 + 174.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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
\(3\) 2.91181 0.722057i 0.970603 0.240686i
\(4\) 0 0
\(5\) −2.43946 + 1.81611i −0.487892 + 0.363222i −0.812818 0.582517i \(-0.802068\pi\)
0.324926 + 0.945739i \(0.394660\pi\)
\(6\) 0 0
\(7\) −7.41916 + 4.87966i −1.05988 + 0.697094i −0.954764 0.297365i \(-0.903892\pi\)
−0.105117 + 0.994460i \(0.533522\pi\)
\(8\) 0 0
\(9\) 7.95727 4.20498i 0.884141 0.467220i
\(10\) 0 0
\(11\) −2.42099 + 20.7129i −0.220090 + 1.88299i 0.206351 + 0.978478i \(0.433841\pi\)
−0.426441 + 0.904515i \(0.640233\pi\)
\(12\) 0 0
\(13\) 0.0230612 + 0.0770297i 0.00177394 + 0.00592536i 0.958872 0.283839i \(-0.0916082\pi\)
−0.957098 + 0.289765i \(0.906423\pi\)
\(14\) 0 0
\(15\) −5.79191 + 7.04960i −0.386127 + 0.469973i
\(16\) 0 0
\(17\) 10.3358 + 1.82248i 0.607989 + 0.107205i 0.469163 0.883112i \(-0.344556\pi\)
0.138827 + 0.990317i \(0.455667\pi\)
\(18\) 0 0
\(19\) 4.67439 + 26.5098i 0.246021 + 1.39525i 0.818110 + 0.575062i \(0.195022\pi\)
−0.572089 + 0.820191i \(0.693867\pi\)
\(20\) 0 0
\(21\) −18.0798 + 19.5657i −0.860943 + 0.931700i
\(22\) 0 0
\(23\) 3.75889 5.71512i 0.163430 0.248483i −0.744483 0.667641i \(-0.767304\pi\)
0.907913 + 0.419158i \(0.137675\pi\)
\(24\) 0 0
\(25\) −4.51737 + 15.0891i −0.180695 + 0.603563i
\(26\) 0 0
\(27\) 20.1338 17.9897i 0.745697 0.666285i
\(28\) 0 0
\(29\) 6.47304 6.10700i 0.223208 0.210586i −0.566512 0.824054i \(-0.691707\pi\)
0.789720 + 0.613468i \(0.210226\pi\)
\(30\) 0 0
\(31\) 2.04297 35.0765i 0.0659024 1.13150i −0.789573 0.613656i \(-0.789698\pi\)
0.855475 0.517843i \(-0.173265\pi\)
\(32\) 0 0
\(33\) 7.90643 + 62.0602i 0.239589 + 1.88061i
\(34\) 0 0
\(35\) 9.23675 25.3778i 0.263907 0.725079i
\(36\) 0 0
\(37\) −44.6777 + 16.2614i −1.20751 + 0.439496i −0.865838 0.500324i \(-0.833214\pi\)
−0.341668 + 0.939821i \(0.610992\pi\)
\(38\) 0 0
\(39\) 0.122770 + 0.207644i 0.00314794 + 0.00532422i
\(40\) 0 0
\(41\) 15.1306 63.8412i 0.369040 1.55710i −0.399153 0.916884i \(-0.630696\pi\)
0.768193 0.640218i \(-0.221156\pi\)
\(42\) 0 0
\(43\) 2.90157 + 6.72659i 0.0674784 + 0.156432i 0.948618 0.316424i \(-0.102482\pi\)
−0.881140 + 0.472856i \(0.843223\pi\)
\(44\) 0 0
\(45\) −11.7747 + 24.7092i −0.261661 + 0.549093i
\(46\) 0 0
\(47\) 3.18730 0.185639i 0.0678149 0.00394977i −0.0242038 0.999707i \(-0.507705\pi\)
0.0920187 + 0.995757i \(0.470668\pi\)
\(48\) 0 0
\(49\) 11.8250 27.4134i 0.241326 0.559458i
\(50\) 0 0
\(51\) 31.4119 2.15632i 0.615919 0.0422808i
\(52\) 0 0
\(53\) 64.8390 + 37.4348i 1.22338 + 0.706318i 0.965637 0.259896i \(-0.0836883\pi\)
0.257742 + 0.966214i \(0.417022\pi\)
\(54\) 0 0
\(55\) −31.7111 54.9252i −0.576565 0.998639i
\(56\) 0 0
\(57\) 32.7525 + 73.8163i 0.574606 + 1.29502i
\(58\) 0 0
\(59\) 8.93375 + 76.4331i 0.151419 + 1.29548i 0.828676 + 0.559729i \(0.189095\pi\)
−0.677256 + 0.735747i \(0.736831\pi\)
\(60\) 0 0
\(61\) −72.0716 36.1957i −1.18150 0.593372i −0.254004 0.967203i \(-0.581748\pi\)
−0.927497 + 0.373831i \(0.878044\pi\)
\(62\) 0 0
\(63\) −38.5174 + 70.0262i −0.611387 + 1.11153i
\(64\) 0 0
\(65\) −0.196151 0.146029i −0.00301771 0.00224660i
\(66\) 0 0
\(67\) −42.7276 + 45.2886i −0.637725 + 0.675949i −0.962948 0.269688i \(-0.913079\pi\)
0.325222 + 0.945638i \(0.394561\pi\)
\(68\) 0 0
\(69\) 6.81854 19.3555i 0.0988194 0.280514i
\(70\) 0 0
\(71\) 14.0684 16.7661i 0.198147 0.236142i −0.657817 0.753178i \(-0.728520\pi\)
0.855964 + 0.517036i \(0.172965\pi\)
\(72\) 0 0
\(73\) −82.0962 + 68.8869i −1.12461 + 0.943656i −0.998828 0.0484025i \(-0.984587\pi\)
−0.125777 + 0.992058i \(0.540143\pi\)
\(74\) 0 0
\(75\) −2.25856 + 47.1983i −0.0301142 + 0.629311i
\(76\) 0 0
\(77\) −83.1103 165.486i −1.07935 2.14917i
\(78\) 0 0
\(79\) 107.327 25.4369i 1.35857 0.321986i 0.514162 0.857693i \(-0.328103\pi\)
0.844404 + 0.535707i \(0.179955\pi\)
\(80\) 0 0
\(81\) 45.6363 66.9203i 0.563411 0.826177i
\(82\) 0 0
\(83\) −8.85205 37.3497i −0.106651 0.449997i −1.00000 0.000632419i \(-0.999799\pi\)
0.893349 0.449364i \(-0.148349\pi\)
\(84\) 0 0
\(85\) −28.5236 + 14.3251i −0.335572 + 0.168531i
\(86\) 0 0
\(87\) 14.4387 22.4563i 0.165962 0.258119i
\(88\) 0 0
\(89\) 34.5784 + 41.2090i 0.388522 + 0.463022i 0.924485 0.381219i \(-0.124496\pi\)
−0.535963 + 0.844242i \(0.680051\pi\)
\(90\) 0 0
\(91\) −0.546974 0.458965i −0.00601070 0.00504358i
\(92\) 0 0
\(93\) −19.3785 103.611i −0.208371 1.11410i
\(94\) 0 0
\(95\) −59.5477 56.1804i −0.626818 0.591373i
\(96\) 0 0
\(97\) 59.3556 79.7285i 0.611914 0.821943i −0.382886 0.923796i \(-0.625070\pi\)
0.994799 + 0.101853i \(0.0324771\pi\)
\(98\) 0 0
\(99\) 67.8330 + 174.999i 0.685182 + 1.76766i
\(100\) 0 0
\(101\) 81.7947 162.867i 0.809848 1.61254i 0.0195568 0.999809i \(-0.493774\pi\)
0.790291 0.612731i \(-0.209929\pi\)
\(102\) 0 0
\(103\) −16.5283 + 1.93188i −0.160469 + 0.0187561i −0.195948 0.980614i \(-0.562778\pi\)
0.0354791 + 0.999370i \(0.488704\pi\)
\(104\) 0 0
\(105\) 8.57148 80.5647i 0.0816331 0.767282i
\(106\) 0 0
\(107\) 79.4796 45.8876i 0.742800 0.428856i −0.0802866 0.996772i \(-0.525584\pi\)
0.823086 + 0.567916i \(0.192250\pi\)
\(108\) 0 0
\(109\) 19.8962 34.4612i 0.182534 0.316158i −0.760209 0.649679i \(-0.774903\pi\)
0.942743 + 0.333521i \(0.108237\pi\)
\(110\) 0 0
\(111\) −118.351 + 79.6098i −1.06623 + 0.717206i
\(112\) 0 0
\(113\) 5.52388 + 2.38277i 0.0488839 + 0.0210865i 0.420381 0.907348i \(-0.361896\pi\)
−0.371497 + 0.928434i \(0.621156\pi\)
\(114\) 0 0
\(115\) 1.20962 + 20.7684i 0.0105184 + 0.180594i
\(116\) 0 0
\(117\) 0.507413 + 0.515974i 0.00433686 + 0.00441004i
\(118\) 0 0
\(119\) −85.5762 + 36.9140i −0.719128 + 0.310201i
\(120\) 0 0
\(121\) −305.426 72.3872i −2.52418 0.598242i
\(122\) 0 0
\(123\) −2.03941 196.819i −0.0165805 1.60015i
\(124\) 0 0
\(125\) −42.3877 116.459i −0.339102 0.931675i
\(126\) 0 0
\(127\) 171.294 + 62.3461i 1.34877 + 0.490914i 0.912565 0.408931i \(-0.134098\pi\)
0.436209 + 0.899845i \(0.356321\pi\)
\(128\) 0 0
\(129\) 13.3058 + 17.4915i 0.103146 + 0.135593i
\(130\) 0 0
\(131\) 165.863 + 9.66044i 1.26613 + 0.0737438i 0.678025 0.735039i \(-0.262836\pi\)
0.588107 + 0.808783i \(0.299873\pi\)
\(132\) 0 0
\(133\) −164.039 173.871i −1.23338 1.30730i
\(134\) 0 0
\(135\) −16.4443 + 80.4504i −0.121810 + 0.595929i
\(136\) 0 0
\(137\) 23.7141 + 7.09952i 0.173095 + 0.0518213i 0.372178 0.928161i \(-0.378611\pi\)
−0.199083 + 0.979983i \(0.563796\pi\)
\(138\) 0 0
\(139\) 41.4410 + 27.2562i 0.298136 + 0.196087i 0.689760 0.724038i \(-0.257716\pi\)
−0.391624 + 0.920126i \(0.628086\pi\)
\(140\) 0 0
\(141\) 9.14676 2.84196i 0.0648707 0.0201557i
\(142\) 0 0
\(143\) −1.65134 + 0.291176i −0.0115478 + 0.00203620i
\(144\) 0 0
\(145\) −4.69974 + 26.6535i −0.0324120 + 0.183817i
\(146\) 0 0
\(147\) 14.6381 88.3610i 0.0995789 0.601095i
\(148\) 0 0
\(149\) 63.0855 18.8866i 0.423393 0.126755i −0.0680167 0.997684i \(-0.521667\pi\)
0.491409 + 0.870929i \(0.336482\pi\)
\(150\) 0 0
\(151\) −20.4515 2.39044i −0.135440 0.0158307i 0.0481025 0.998842i \(-0.484683\pi\)
−0.183543 + 0.983012i \(0.558757\pi\)
\(152\) 0 0
\(153\) 89.9084 28.9599i 0.587636 0.189281i
\(154\) 0 0
\(155\) 58.7190 + 89.2780i 0.378833 + 0.575987i
\(156\) 0 0
\(157\) −102.386 137.528i −0.652138 0.875973i 0.345920 0.938264i \(-0.387567\pi\)
−0.998058 + 0.0622909i \(0.980159\pi\)
\(158\) 0 0
\(159\) 215.829 + 62.1857i 1.35742 + 0.391105i
\(160\) 0 0
\(161\) 60.7435i 0.377289i
\(162\) 0 0
\(163\) −274.915 −1.68660 −0.843299 0.537445i \(-0.819389\pi\)
−0.843299 + 0.537445i \(0.819389\pi\)
\(164\) 0 0
\(165\) −131.996 137.034i −0.799973 0.830512i
\(166\) 0 0
\(167\) 81.2537 60.4911i 0.486549 0.362222i −0.325757 0.945453i \(-0.605619\pi\)
0.812306 + 0.583231i \(0.198212\pi\)
\(168\) 0 0
\(169\) 141.192 92.8635i 0.835456 0.549488i
\(170\) 0 0
\(171\) 148.669 + 191.290i 0.869408 + 1.11865i
\(172\) 0 0
\(173\) −12.3842 + 105.954i −0.0715850 + 0.612449i 0.909061 + 0.416662i \(0.136800\pi\)
−0.980646 + 0.195787i \(0.937274\pi\)
\(174\) 0 0
\(175\) −40.1145 133.992i −0.229225 0.765666i
\(176\) 0 0
\(177\) 81.2024 + 216.108i 0.458771 + 1.22095i
\(178\) 0 0
\(179\) 126.982 + 22.3903i 0.709395 + 0.125086i 0.516692 0.856171i \(-0.327163\pi\)
0.192704 + 0.981257i \(0.438274\pi\)
\(180\) 0 0
\(181\) 43.4947 + 246.671i 0.240302 + 1.36282i 0.831154 + 0.556043i \(0.187681\pi\)
−0.590851 + 0.806780i \(0.701208\pi\)
\(182\) 0 0
\(183\) −235.994 53.3552i −1.28958 0.291559i
\(184\) 0 0
\(185\) 79.4571 120.809i 0.429498 0.653020i
\(186\) 0 0
\(187\) −62.7719 + 209.673i −0.335679 + 1.12124i
\(188\) 0 0
\(189\) −61.5924 + 231.715i −0.325886 + 1.22600i
\(190\) 0 0
\(191\) −243.521 + 229.750i −1.27498 + 1.20288i −0.307040 + 0.951697i \(0.599338\pi\)
−0.967939 + 0.251184i \(0.919180\pi\)
\(192\) 0 0
\(193\) −8.70777 + 149.507i −0.0451180 + 0.774645i 0.897550 + 0.440913i \(0.145345\pi\)
−0.942668 + 0.333732i \(0.891692\pi\)
\(194\) 0 0
\(195\) −0.676597 0.283577i −0.00346973 0.00145424i
\(196\) 0 0
\(197\) −50.4984 + 138.743i −0.256337 + 0.704280i 0.743049 + 0.669237i \(0.233379\pi\)
−0.999386 + 0.0350430i \(0.988843\pi\)
\(198\) 0 0
\(199\) 191.241 69.6060i 0.961009 0.349779i 0.186580 0.982440i \(-0.440260\pi\)
0.774429 + 0.632661i \(0.218037\pi\)
\(200\) 0 0
\(201\) −91.7137 + 162.724i −0.456287 + 0.809570i
\(202\) 0 0
\(203\) −18.2245 + 76.8951i −0.0897757 + 0.378793i
\(204\) 0 0
\(205\) 79.0321 + 183.217i 0.385522 + 0.893741i
\(206\) 0 0
\(207\) 5.87855 61.2828i 0.0283988 0.296052i
\(208\) 0 0
\(209\) −560.413 + 32.6403i −2.68140 + 0.156174i
\(210\) 0 0
\(211\) 11.7056 27.1366i 0.0554768 0.128610i −0.888223 0.459412i \(-0.848060\pi\)
0.943700 + 0.330802i \(0.107319\pi\)
\(212\) 0 0
\(213\) 28.8585 58.9778i 0.135486 0.276891i
\(214\) 0 0
\(215\) −19.2945 11.1397i −0.0897419 0.0518125i
\(216\) 0 0
\(217\) 156.004 + 270.207i 0.718914 + 1.24519i
\(218\) 0 0
\(219\) −189.308 + 259.864i −0.864421 + 1.18659i
\(220\) 0 0
\(221\) 0.0979708 + 0.838194i 0.000443307 + 0.00379273i
\(222\) 0 0
\(223\) 274.849 + 138.034i 1.23251 + 0.618988i 0.941267 0.337663i \(-0.109636\pi\)
0.291238 + 0.956650i \(0.405933\pi\)
\(224\) 0 0
\(225\) 27.5034 + 139.063i 0.122237 + 0.618059i
\(226\) 0 0
\(227\) 197.836 + 147.284i 0.871526 + 0.648827i 0.937115 0.349019i \(-0.113485\pi\)
−0.0655892 + 0.997847i \(0.520893\pi\)
\(228\) 0 0
\(229\) 140.537 148.960i 0.613698 0.650482i −0.343759 0.939058i \(-0.611700\pi\)
0.957457 + 0.288576i \(0.0931817\pi\)
\(230\) 0 0
\(231\) −361.492 421.854i −1.56490 1.82621i
\(232\) 0 0
\(233\) 279.036 332.542i 1.19758 1.42722i 0.320244 0.947335i \(-0.396235\pi\)
0.877333 0.479882i \(-0.159321\pi\)
\(234\) 0 0
\(235\) −7.43815 + 6.24135i −0.0316517 + 0.0265589i
\(236\) 0 0
\(237\) 294.148 151.563i 1.24113 0.639508i
\(238\) 0 0
\(239\) 2.78756 + 5.55049i 0.0116634 + 0.0232238i 0.899389 0.437149i \(-0.144012\pi\)
−0.887725 + 0.460373i \(0.847716\pi\)
\(240\) 0 0
\(241\) 412.616 97.7918i 1.71210 0.405775i 0.746413 0.665483i \(-0.231774\pi\)
0.965687 + 0.259708i \(0.0836263\pi\)
\(242\) 0 0
\(243\) 84.5638 227.811i 0.347999 0.937495i
\(244\) 0 0
\(245\) 20.9392 + 88.3494i 0.0854661 + 0.360610i
\(246\) 0 0
\(247\) −1.93425 + 0.971415i −0.00783096 + 0.00393285i
\(248\) 0 0
\(249\) −52.7441 102.364i −0.211824 0.411099i
\(250\) 0 0
\(251\) 49.1366 + 58.5587i 0.195763 + 0.233302i 0.854992 0.518640i \(-0.173562\pi\)
−0.659229 + 0.751942i \(0.729117\pi\)
\(252\) 0 0
\(253\) 109.277 + 91.6939i 0.431923 + 0.362426i
\(254\) 0 0
\(255\) −72.7119 + 62.3077i −0.285145 + 0.244344i
\(256\) 0 0
\(257\) −216.519 204.275i −0.842485 0.794844i 0.138207 0.990403i \(-0.455866\pi\)
−0.980692 + 0.195560i \(0.937348\pi\)
\(258\) 0 0
\(259\) 252.121 338.658i 0.973442 1.30756i
\(260\) 0 0
\(261\) 25.8279 75.8141i 0.0989575 0.290475i
\(262\) 0 0
\(263\) −166.554 + 331.637i −0.633287 + 1.26098i 0.316652 + 0.948542i \(0.397441\pi\)
−0.949939 + 0.312436i \(0.898855\pi\)
\(264\) 0 0
\(265\) −226.158 + 26.4341i −0.853427 + 0.0997513i
\(266\) 0 0
\(267\) 130.441 + 95.0251i 0.488543 + 0.355899i
\(268\) 0 0
\(269\) −219.330 + 126.630i −0.815353 + 0.470745i −0.848812 0.528696i \(-0.822681\pi\)
0.0334580 + 0.999440i \(0.489348\pi\)
\(270\) 0 0
\(271\) −101.699 + 176.148i −0.375274 + 0.649994i −0.990368 0.138460i \(-0.955785\pi\)
0.615094 + 0.788454i \(0.289118\pi\)
\(272\) 0 0
\(273\) −1.92408 0.941474i −0.00704792 0.00344862i
\(274\) 0 0
\(275\) −301.603 130.099i −1.09674 0.473086i
\(276\) 0 0
\(277\) 24.0503 + 412.927i 0.0868240 + 1.49071i 0.707539 + 0.706675i \(0.249806\pi\)
−0.620715 + 0.784037i \(0.713157\pi\)
\(278\) 0 0
\(279\) −131.240 287.704i −0.470393 1.03120i
\(280\) 0 0
\(281\) −17.9684 + 7.75081i −0.0639444 + 0.0275829i −0.427812 0.903868i \(-0.640715\pi\)
0.363867 + 0.931451i \(0.381456\pi\)
\(282\) 0 0
\(283\) 129.951 + 30.7990i 0.459191 + 0.108830i 0.453700 0.891155i \(-0.350104\pi\)
0.00549123 + 0.999985i \(0.498252\pi\)
\(284\) 0 0
\(285\) −213.957 120.590i −0.750727 0.423122i
\(286\) 0 0
\(287\) 199.267 + 547.481i 0.694309 + 1.90760i
\(288\) 0 0
\(289\) −168.064 61.1701i −0.581535 0.211661i
\(290\) 0 0
\(291\) 115.264 275.012i 0.396096 0.945059i
\(292\) 0 0
\(293\) −323.762 18.8570i −1.10499 0.0643583i −0.504066 0.863665i \(-0.668163\pi\)
−0.600923 + 0.799307i \(0.705200\pi\)
\(294\) 0 0
\(295\) −160.605 170.231i −0.544422 0.577054i
\(296\) 0 0
\(297\) 323.876 + 460.583i 1.09049 + 1.55079i
\(298\) 0 0
\(299\) 0.526918 + 0.157749i 0.00176227 + 0.000527589i
\(300\) 0 0
\(301\) −54.3507 35.7470i −0.180567 0.118761i
\(302\) 0 0
\(303\) 120.572 533.297i 0.397926 1.76006i
\(304\) 0 0
\(305\) 241.551 42.5920i 0.791971 0.139646i
\(306\) 0 0
\(307\) −0.218569 + 1.23957i −0.000711951 + 0.00403767i −0.985162 0.171629i \(-0.945097\pi\)
0.984450 + 0.175667i \(0.0562081\pi\)
\(308\) 0 0
\(309\) −46.7323 + 17.5596i −0.151237 + 0.0568273i
\(310\) 0 0
\(311\) −527.369 + 157.884i −1.69572 + 0.507666i −0.981371 0.192122i \(-0.938463\pi\)
−0.714351 + 0.699788i \(0.753278\pi\)
\(312\) 0 0
\(313\) −70.2959 8.21642i −0.224588 0.0262505i 0.00305475 0.999995i \(-0.499028\pi\)
−0.227642 + 0.973745i \(0.573102\pi\)
\(314\) 0 0
\(315\) −33.2137 240.778i −0.105440 0.764375i
\(316\) 0 0
\(317\) 152.323 + 231.596i 0.480515 + 0.730587i 0.991656 0.128910i \(-0.0411477\pi\)
−0.511142 + 0.859496i \(0.670777\pi\)
\(318\) 0 0
\(319\) 110.823 + 148.861i 0.347406 + 0.466648i
\(320\) 0 0
\(321\) 198.296 191.005i 0.617744 0.595030i
\(322\) 0 0
\(323\) 282.520i 0.874673i
\(324\) 0 0
\(325\) −1.26648 −0.00389687
\(326\) 0 0
\(327\) 33.0510 114.711i 0.101073 0.350797i
\(328\) 0 0
\(329\) −22.7412 + 16.9302i −0.0691223 + 0.0514596i
\(330\) 0 0
\(331\) 536.492 352.856i 1.62082 1.06603i 0.676790 0.736176i \(-0.263370\pi\)
0.944032 0.329855i \(-0.107000\pi\)
\(332\) 0 0
\(333\) −287.134 + 317.265i −0.862264 + 0.952748i
\(334\) 0 0
\(335\) 21.9831 188.078i 0.0656213 0.561426i
\(336\) 0 0
\(337\) −110.936 370.553i −0.329188 1.09956i −0.949122 0.314910i \(-0.898026\pi\)
0.619934 0.784654i \(-0.287160\pi\)
\(338\) 0 0
\(339\) 17.8050 + 2.94962i 0.0525221 + 0.00870094i
\(340\) 0 0
\(341\) 721.591 + 127.236i 2.11610 + 0.373126i
\(342\) 0 0
\(343\) −29.5215 167.425i −0.0860685 0.488119i
\(344\) 0 0
\(345\) 18.5181 + 59.6001i 0.0536757 + 0.172754i
\(346\) 0 0
\(347\) 295.912 449.913i 0.852774 1.29658i −0.100643 0.994923i \(-0.532090\pi\)
0.953417 0.301657i \(-0.0975397\pi\)
\(348\) 0 0
\(349\) 70.4626 235.362i 0.201899 0.674388i −0.795736 0.605644i \(-0.792916\pi\)
0.997634 0.0687443i \(-0.0218993\pi\)
\(350\) 0 0
\(351\) 1.85005 + 1.13604i 0.00527080 + 0.00323658i
\(352\) 0 0
\(353\) −16.5575 + 15.6212i −0.0469051 + 0.0442527i −0.709337 0.704869i \(-0.751006\pi\)
0.662432 + 0.749122i \(0.269524\pi\)
\(354\) 0 0
\(355\) −3.87027 + 66.4500i −0.0109022 + 0.187183i
\(356\) 0 0
\(357\) −222.528 + 169.277i −0.623327 + 0.474166i
\(358\) 0 0
\(359\) 22.9795 63.1356i 0.0640097 0.175865i −0.903565 0.428452i \(-0.859059\pi\)
0.967574 + 0.252587i \(0.0812813\pi\)
\(360\) 0 0
\(361\) −341.691 + 124.365i −0.946513 + 0.344502i
\(362\) 0 0
\(363\) −941.609 + 9.75683i −2.59397 + 0.0268783i
\(364\) 0 0
\(365\) 75.1642 317.143i 0.205929 0.868884i
\(366\) 0 0
\(367\) 17.0893 + 39.6175i 0.0465649 + 0.107950i 0.939911 0.341420i \(-0.110908\pi\)
−0.893346 + 0.449370i \(0.851649\pi\)
\(368\) 0 0
\(369\) −148.053 571.626i −0.401226 1.54912i
\(370\) 0 0
\(371\) −663.721 + 38.6573i −1.78901 + 0.104198i
\(372\) 0 0
\(373\) 139.989 324.532i 0.375307 0.870059i −0.620969 0.783835i \(-0.713261\pi\)
0.996276 0.0862236i \(-0.0274799\pi\)
\(374\) 0 0
\(375\) −207.515 308.501i −0.553374 0.822669i
\(376\) 0 0
\(377\) 0.619697 + 0.357782i 0.00164376 + 0.000949024i
\(378\) 0 0
\(379\) 113.603 + 196.767i 0.299745 + 0.519174i 0.976078 0.217423i \(-0.0697650\pi\)
−0.676332 + 0.736597i \(0.736432\pi\)
\(380\) 0 0
\(381\) 543.794 + 57.8556i 1.42728 + 0.151852i
\(382\) 0 0
\(383\) 16.0122 + 136.993i 0.0418073 + 0.357684i 0.997908 + 0.0646466i \(0.0205920\pi\)
−0.956101 + 0.293038i \(0.905334\pi\)
\(384\) 0 0
\(385\) 503.286 + 252.760i 1.30724 + 0.656518i
\(386\) 0 0
\(387\) 51.3738 + 41.3243i 0.132749 + 0.106781i
\(388\) 0 0
\(389\) 397.470 + 295.905i 1.02177 + 0.760682i 0.971255 0.238041i \(-0.0765052\pi\)
0.0505184 + 0.998723i \(0.483913\pi\)
\(390\) 0 0
\(391\) 49.2669 52.2199i 0.126002 0.133555i
\(392\) 0 0
\(393\) 489.938 91.6333i 1.24666 0.233164i
\(394\) 0 0
\(395\) −215.623 + 256.970i −0.545881 + 0.650556i
\(396\) 0 0
\(397\) −159.386 + 133.741i −0.401477 + 0.336879i −0.821064 0.570836i \(-0.806619\pi\)
0.419587 + 0.907715i \(0.362175\pi\)
\(398\) 0 0
\(399\) −603.195 387.834i −1.51177 0.972016i
\(400\) 0 0
\(401\) 15.2202 + 30.3058i 0.0379555 + 0.0755756i 0.911811 0.410610i \(-0.134684\pi\)
−0.873856 + 0.486186i \(0.838388\pi\)
\(402\) 0 0
\(403\) 2.74905 0.651536i 0.00682145 0.00161671i
\(404\) 0 0
\(405\) 10.2069 + 246.130i 0.0252023 + 0.607728i
\(406\) 0 0
\(407\) −228.656 964.775i −0.561808 2.37046i
\(408\) 0 0
\(409\) −320.127 + 160.774i −0.782706 + 0.393090i −0.794827 0.606837i \(-0.792438\pi\)
0.0121201 + 0.999927i \(0.496142\pi\)
\(410\) 0 0
\(411\) 74.1771 + 3.54957i 0.180479 + 0.00863642i
\(412\) 0 0
\(413\) −439.249 523.476i −1.06356 1.26750i
\(414\) 0 0
\(415\) 89.4254 + 75.0369i 0.215483 + 0.180812i
\(416\) 0 0
\(417\) 140.349 + 49.4420i 0.336568 + 0.118566i
\(418\) 0 0
\(419\) 182.230 + 171.925i 0.434916 + 0.410322i 0.872314 0.488946i \(-0.162618\pi\)
−0.437398 + 0.899268i \(0.644100\pi\)
\(420\) 0 0
\(421\) −415.811 + 558.531i −0.987674 + 1.32668i −0.0428560 + 0.999081i \(0.513646\pi\)
−0.944818 + 0.327595i \(0.893762\pi\)
\(422\) 0 0
\(423\) 24.5816 14.8797i 0.0581125 0.0351766i
\(424\) 0 0
\(425\) −74.1903 + 147.725i −0.174566 + 0.347589i
\(426\) 0 0
\(427\) 711.333 83.1430i 1.66589 0.194714i
\(428\) 0 0
\(429\) −4.59815 + 2.04021i −0.0107183 + 0.00475574i
\(430\) 0 0
\(431\) −179.342 + 103.543i −0.416107 + 0.240239i −0.693410 0.720543i \(-0.743893\pi\)
0.277303 + 0.960782i \(0.410559\pi\)
\(432\) 0 0
\(433\) −50.2497 + 87.0351i −0.116050 + 0.201005i −0.918199 0.396119i \(-0.870357\pi\)
0.802149 + 0.597124i \(0.203690\pi\)
\(434\) 0 0
\(435\) 5.56062 + 81.0035i 0.0127830 + 0.186215i
\(436\) 0 0
\(437\) 169.077 + 72.9328i 0.386904 + 0.166894i
\(438\) 0 0
\(439\) −35.4378 608.444i −0.0807240 1.38598i −0.758962 0.651135i \(-0.774293\pi\)
0.678238 0.734842i \(-0.262744\pi\)
\(440\) 0 0
\(441\) −21.1783 267.860i −0.0480233 0.607392i
\(442\) 0 0
\(443\) −259.615 + 111.987i −0.586038 + 0.252792i −0.668390 0.743811i \(-0.733016\pi\)
0.0823517 + 0.996603i \(0.473757\pi\)
\(444\) 0 0
\(445\) −159.193 37.7294i −0.357737 0.0847851i
\(446\) 0 0
\(447\) 170.056 100.545i 0.380438 0.224934i
\(448\) 0 0
\(449\) −55.7332 153.126i −0.124127 0.341037i 0.862028 0.506860i \(-0.169194\pi\)
−0.986155 + 0.165823i \(0.946972\pi\)
\(450\) 0 0
\(451\) 1285.71 + 467.959i 2.85079 + 1.03760i
\(452\) 0 0
\(453\) −61.2769 + 7.80665i −0.135269 + 0.0172332i
\(454\) 0 0
\(455\) 2.16785 + 0.126263i 0.00476451 + 0.000277501i
\(456\) 0 0
\(457\) −378.480 401.165i −0.828183 0.877823i 0.165933 0.986137i \(-0.446936\pi\)
−0.994117 + 0.108314i \(0.965455\pi\)
\(458\) 0 0
\(459\) 240.885 149.245i 0.524805 0.325152i
\(460\) 0 0
\(461\) 15.4251 + 4.61796i 0.0334600 + 0.0100173i 0.303490 0.952835i \(-0.401848\pi\)
−0.270029 + 0.962852i \(0.587033\pi\)
\(462\) 0 0
\(463\) −249.740 164.257i −0.539396 0.354766i 0.250394 0.968144i \(-0.419440\pi\)
−0.789790 + 0.613378i \(0.789810\pi\)
\(464\) 0 0
\(465\) 235.442 + 217.562i 0.506328 + 0.467875i
\(466\) 0 0
\(467\) −297.637 + 52.4814i −0.637338 + 0.112380i −0.482975 0.875634i \(-0.660444\pi\)
−0.154363 + 0.988014i \(0.549333\pi\)
\(468\) 0 0
\(469\) 96.0100 544.500i 0.204712 1.16098i
\(470\) 0 0
\(471\) −397.430 326.526i −0.843801 0.693262i
\(472\) 0 0
\(473\) −146.352 + 43.8150i −0.309413 + 0.0926320i
\(474\) 0 0
\(475\) −421.125 49.2224i −0.886578 0.103626i
\(476\) 0 0
\(477\) 673.355 + 25.2321i 1.41164 + 0.0528974i
\(478\) 0 0
\(479\) 323.349 + 491.628i 0.675050 + 1.02636i 0.996831 + 0.0795496i \(0.0253482\pi\)
−0.321781 + 0.946814i \(0.604281\pi\)
\(480\) 0 0
\(481\) −2.28293 3.06651i −0.00474622 0.00637527i
\(482\) 0 0
\(483\) 43.8602 + 176.873i 0.0908079 + 0.366198i
\(484\) 0 0
\(485\) 302.291i 0.623280i
\(486\) 0 0
\(487\) −459.023 −0.942553 −0.471277 0.881985i \(-0.656207\pi\)
−0.471277 + 0.881985i \(0.656207\pi\)
\(488\) 0 0
\(489\) −800.501 + 198.504i −1.63702 + 0.405939i
\(490\) 0 0
\(491\) 167.248 124.512i 0.340627 0.253588i −0.413229 0.910627i \(-0.635599\pi\)
0.753856 + 0.657040i \(0.228192\pi\)
\(492\) 0 0
\(493\) 78.0341 51.3238i 0.158284 0.104105i
\(494\) 0 0
\(495\) −483.293 303.710i −0.976349 0.613555i
\(496\) 0 0
\(497\) −22.5631 + 193.039i −0.0453985 + 0.388409i
\(498\) 0 0
\(499\) −45.1916 150.951i −0.0905644 0.302506i 0.900692 0.434459i \(-0.143060\pi\)
−0.991256 + 0.131953i \(0.957875\pi\)
\(500\) 0 0
\(501\) 192.917 234.808i 0.385064 0.468679i
\(502\) 0 0
\(503\) −476.114 83.9517i −0.946549 0.166902i −0.320993 0.947082i \(-0.604017\pi\)
−0.625556 + 0.780180i \(0.715128\pi\)
\(504\) 0 0
\(505\) 96.2489 + 545.855i 0.190592 + 1.08090i
\(506\) 0 0
\(507\) 344.072 372.349i 0.678642 0.734417i
\(508\) 0 0
\(509\) −148.199 + 225.326i −0.291158 + 0.442684i −0.951214 0.308532i \(-0.900162\pi\)
0.660056 + 0.751216i \(0.270533\pi\)
\(510\) 0 0
\(511\) 272.940 911.685i 0.534130 1.78412i
\(512\) 0 0
\(513\) 571.017 + 449.653i 1.11309 + 0.876516i
\(514\) 0 0
\(515\) 36.8116 34.7300i 0.0714788 0.0674368i
\(516\) 0 0
\(517\) −3.87130 + 66.4677i −0.00748802 + 0.128564i
\(518\) 0 0
\(519\) 40.4441 + 317.459i 0.0779270 + 0.611674i
\(520\) 0 0
\(521\) 351.711 966.317i 0.675068 1.85474i 0.185838 0.982580i \(-0.440500\pi\)
0.489230 0.872155i \(-0.337278\pi\)
\(522\) 0 0
\(523\) 212.328 77.2811i 0.405981 0.147765i −0.130954 0.991388i \(-0.541804\pi\)
0.536935 + 0.843623i \(0.319582\pi\)
\(524\) 0 0
\(525\) −213.555 361.193i −0.406772 0.687987i
\(526\) 0 0
\(527\) 85.0421 358.821i 0.161370 0.680875i
\(528\) 0 0
\(529\) 190.993 + 442.771i 0.361045 + 0.836997i
\(530\) 0 0
\(531\) 392.488 + 570.633i 0.739149 + 1.07464i
\(532\) 0 0
\(533\) 5.26660 0.306745i 0.00988105 0.000575506i
\(534\) 0 0
\(535\) −110.550 + 256.285i −0.206636 + 0.479037i
\(536\) 0 0
\(537\) 385.914 26.4917i 0.718648 0.0493328i
\(538\) 0 0
\(539\) 539.184 + 311.298i 1.00034 + 0.577547i
\(540\) 0 0
\(541\) 196.601 + 340.523i 0.363403 + 0.629433i 0.988519 0.151100i \(-0.0482814\pi\)
−0.625115 + 0.780532i \(0.714948\pi\)
\(542\) 0 0
\(543\) 304.759 + 686.853i 0.561250 + 1.26492i
\(544\) 0 0
\(545\) 14.0494 + 120.200i 0.0257787 + 0.220551i
\(546\) 0 0
\(547\) −334.294 167.889i −0.611141 0.306927i 0.116176 0.993229i \(-0.462936\pi\)
−0.727317 + 0.686302i \(0.759233\pi\)
\(548\) 0 0
\(549\) −725.695 + 15.0407i −1.32185 + 0.0273966i
\(550\) 0 0
\(551\) 192.153 + 143.053i 0.348735 + 0.259624i
\(552\) 0 0
\(553\) −672.151 + 712.439i −1.21546 + 1.28832i
\(554\) 0 0
\(555\) 144.133 409.144i 0.259700 0.737197i
\(556\) 0 0
\(557\) 58.4418 69.6482i 0.104922 0.125042i −0.711028 0.703164i \(-0.751770\pi\)
0.815950 + 0.578122i \(0.196214\pi\)
\(558\) 0 0
\(559\) −0.451234 + 0.378630i −0.000807217 + 0.000677335i
\(560\) 0 0
\(561\) −31.3842 + 655.852i −0.0559434 + 1.16908i
\(562\) 0 0
\(563\) 89.4036 + 178.017i 0.158799 + 0.316194i 0.958936 0.283623i \(-0.0915364\pi\)
−0.800137 + 0.599817i \(0.795240\pi\)
\(564\) 0 0
\(565\) −17.8027 + 4.21931i −0.0315091 + 0.00746780i
\(566\) 0 0
\(567\) −12.0342 + 719.182i −0.0212244 + 1.26840i
\(568\) 0 0
\(569\) −138.915 586.130i −0.244140 1.03011i −0.947622 0.319393i \(-0.896521\pi\)
0.703483 0.710712i \(-0.251627\pi\)
\(570\) 0 0
\(571\) −496.773 + 249.489i −0.870004 + 0.436933i −0.827039 0.562144i \(-0.809977\pi\)
−0.0429650 + 0.999077i \(0.513680\pi\)
\(572\) 0 0
\(573\) −543.194 + 844.825i −0.947983 + 1.47439i
\(574\) 0 0
\(575\) 69.2555 + 82.5355i 0.120444 + 0.143540i
\(576\) 0 0
\(577\) −24.3144 20.4022i −0.0421393 0.0353591i 0.621475 0.783434i \(-0.286534\pi\)
−0.663614 + 0.748075i \(0.730978\pi\)
\(578\) 0 0
\(579\) 82.5968 + 441.622i 0.142654 + 0.762732i
\(580\) 0 0
\(581\) 247.929 + 233.909i 0.426728 + 0.402597i
\(582\) 0 0
\(583\) −932.360 + 1252.38i −1.59925 + 2.14816i
\(584\) 0 0
\(585\) −2.17488 0.337181i −0.00371774 0.000576378i
\(586\) 0 0
\(587\) 247.321 492.457i 0.421331 0.838939i −0.578400 0.815753i \(-0.696323\pi\)
0.999731 0.0231859i \(-0.00738095\pi\)
\(588\) 0 0
\(589\) 939.421 109.803i 1.59494 0.186422i
\(590\) 0 0
\(591\) −46.8613 + 440.457i −0.0792915 + 0.745273i
\(592\) 0 0
\(593\) −25.0711 + 14.4748i −0.0422785 + 0.0244095i −0.520990 0.853563i \(-0.674437\pi\)
0.478712 + 0.877972i \(0.341104\pi\)
\(594\) 0 0
\(595\) 141.720 245.466i 0.238185 0.412548i
\(596\) 0 0
\(597\) 506.597 340.766i 0.848572 0.570797i
\(598\) 0 0
\(599\) 825.405 + 356.045i 1.37797 + 0.594399i 0.950809 0.309776i \(-0.100254\pi\)
0.427162 + 0.904175i \(0.359513\pi\)
\(600\) 0 0
\(601\) 7.12981 + 122.414i 0.0118632 + 0.203684i 0.999032 + 0.0440005i \(0.0140103\pi\)
−0.987168 + 0.159684i \(0.948953\pi\)
\(602\) 0 0
\(603\) −149.557 + 540.042i −0.248022 + 0.895593i
\(604\) 0 0
\(605\) 876.537 378.101i 1.44882 0.624961i
\(606\) 0 0
\(607\) −600.125 142.232i −0.988674 0.234320i −0.295698 0.955281i \(-0.595552\pi\)
−0.692975 + 0.720961i \(0.743700\pi\)
\(608\) 0 0
\(609\) 2.45641 + 237.063i 0.00403352 + 0.389266i
\(610\) 0 0
\(611\) 0.0878026 + 0.241236i 0.000143703 + 0.000394821i
\(612\) 0 0
\(613\) −769.627 280.121i −1.25551 0.456968i −0.373250 0.927731i \(-0.621756\pi\)
−0.882260 + 0.470763i \(0.843979\pi\)
\(614\) 0 0
\(615\) 362.419 + 476.427i 0.589300 + 0.774679i
\(616\) 0 0
\(617\) −483.861 28.1817i −0.784215 0.0456753i −0.338636 0.940918i \(-0.609965\pi\)
−0.445580 + 0.895242i \(0.647002\pi\)
\(618\) 0 0
\(619\) 544.835 + 577.491i 0.880185 + 0.932942i 0.998194 0.0600707i \(-0.0191326\pi\)
−0.118009 + 0.993013i \(0.537651\pi\)
\(620\) 0 0
\(621\) −27.1324 182.688i −0.0436915 0.294184i
\(622\) 0 0
\(623\) −457.629 137.005i −0.734557 0.219912i
\(624\) 0 0
\(625\) −14.0834 9.26280i −0.0225334 0.0148205i
\(626\) 0 0
\(627\) −1608.25 + 499.692i −2.56499 + 0.796957i
\(628\) 0 0
\(629\) −491.417 + 86.6500i −0.781267 + 0.137758i
\(630\) 0 0
\(631\) 140.847 798.782i 0.223212 1.26590i −0.642861 0.765983i \(-0.722253\pi\)
0.866074 0.499917i \(-0.166636\pi\)
\(632\) 0 0
\(633\) 14.4903 87.4688i 0.0228915 0.138181i
\(634\) 0 0
\(635\) −531.093 + 158.999i −0.836367 + 0.250392i
\(636\) 0 0
\(637\) 2.38435 + 0.278690i 0.00374309 + 0.000437504i
\(638\) 0 0
\(639\) 41.4451 192.570i 0.0648593 0.301361i
\(640\) 0 0
\(641\) 338.923 + 515.307i 0.528740 + 0.803911i 0.996813 0.0797796i \(-0.0254216\pi\)
−0.468072 + 0.883690i \(0.655051\pi\)
\(642\) 0 0
\(643\) 37.4032 + 50.2412i 0.0581698 + 0.0781356i 0.830256 0.557382i \(-0.188194\pi\)
−0.772086 + 0.635518i \(0.780787\pi\)
\(644\) 0 0
\(645\) −64.2254 18.5049i −0.0995742 0.0286898i
\(646\) 0 0
\(647\) 724.898i 1.12040i 0.828358 + 0.560200i \(0.189276\pi\)
−0.828358 + 0.560200i \(0.810724\pi\)
\(648\) 0 0
\(649\) −1604.78 −2.47270
\(650\) 0 0
\(651\) 649.360 + 674.148i 0.997480 + 1.03556i
\(652\) 0 0
\(653\) 156.855 116.774i 0.240207 0.178827i −0.470323 0.882494i \(-0.655863\pi\)
0.710530 + 0.703667i \(0.248455\pi\)
\(654\) 0 0
\(655\) −422.161 + 277.660i −0.644521 + 0.423908i
\(656\) 0 0
\(657\) −363.593 + 893.364i −0.553415 + 1.35976i
\(658\) 0 0
\(659\) −8.27044 + 70.7581i −0.0125500 + 0.107372i −0.998061 0.0622372i \(-0.980176\pi\)
0.985511 + 0.169609i \(0.0542505\pi\)
\(660\) 0 0
\(661\) −40.3837 134.891i −0.0610949 0.204071i 0.921993 0.387207i \(-0.126560\pi\)
−0.983088 + 0.183136i \(0.941375\pi\)
\(662\) 0 0
\(663\) 0.890496 + 2.36992i 0.00134313 + 0.00357454i
\(664\) 0 0
\(665\) 715.936 + 126.239i 1.07660 + 0.189833i
\(666\) 0 0
\(667\) −10.5708 59.9497i −0.0158482 0.0898796i
\(668\) 0 0
\(669\) 899.976 + 203.473i 1.34526 + 0.304145i
\(670\) 0 0
\(671\) 924.204 1405.18i 1.37735 2.09416i
\(672\) 0 0
\(673\) 260.002 868.466i 0.386332 1.29044i −0.514954 0.857218i \(-0.672191\pi\)
0.901287 0.433223i \(-0.142624\pi\)
\(674\) 0 0
\(675\) 180.496 + 385.067i 0.267402 + 0.570470i
\(676\) 0 0
\(677\) 884.193 834.193i 1.30605 1.23219i 0.350774 0.936460i \(-0.385919\pi\)
0.955272 0.295730i \(-0.0955629\pi\)
\(678\) 0 0
\(679\) −51.3214 + 881.154i −0.0755838 + 1.29772i
\(680\) 0 0
\(681\) 682.409 + 286.013i 1.00207 + 0.419990i
\(682\) 0 0
\(683\) 164.977 453.270i 0.241547 0.663646i −0.758382 0.651810i \(-0.774010\pi\)
0.999930 0.0118365i \(-0.00376775\pi\)
\(684\) 0 0
\(685\) −70.7430 + 25.7483i −0.103274 + 0.0375888i
\(686\) 0 0
\(687\) 301.659 535.220i 0.439096 0.779069i
\(688\) 0 0
\(689\) −1.38833 + 5.85783i −0.00201499 + 0.00850193i
\(690\) 0 0
\(691\) −165.577 383.850i −0.239619 0.555500i 0.755391 0.655275i \(-0.227447\pi\)
−0.995010 + 0.0997747i \(0.968188\pi\)
\(692\) 0 0
\(693\) −1357.20 967.341i −1.95844 1.39587i
\(694\) 0 0
\(695\) −150.594 + 8.77109i −0.216682 + 0.0126203i
\(696\) 0 0
\(697\) 272.737 632.276i 0.391301 0.907139i
\(698\) 0 0
\(699\) 572.384 1169.78i 0.818862 1.67350i
\(700\) 0 0
\(701\) 183.116 + 105.722i 0.261221 + 0.150816i 0.624891 0.780712i \(-0.285143\pi\)
−0.363670 + 0.931528i \(0.618477\pi\)
\(702\) 0 0
\(703\) −639.927 1108.39i −0.910280 1.57665i
\(704\) 0 0
\(705\) −17.1519 + 23.5444i −0.0243289 + 0.0333963i
\(706\) 0 0
\(707\) 187.886 + 1607.46i 0.265750 + 2.27364i
\(708\) 0 0
\(709\) 659.235 + 331.080i 0.929809 + 0.466968i 0.848188 0.529696i \(-0.177694\pi\)
0.0816215 + 0.996663i \(0.473990\pi\)
\(710\) 0 0
\(711\) 747.066 653.715i 1.05073 0.919431i
\(712\) 0 0
\(713\) −192.787 143.525i −0.270388 0.201297i
\(714\) 0 0
\(715\) 3.49958 3.70933i 0.00489451 0.00518788i
\(716\) 0 0
\(717\) 12.1246 + 14.1492i 0.0169102 + 0.0197339i
\(718\) 0 0
\(719\) 282.615 336.808i 0.393067 0.468439i −0.532826 0.846225i \(-0.678870\pi\)
0.925893 + 0.377786i \(0.123314\pi\)
\(720\) 0 0
\(721\) 113.199 94.9854i 0.157003 0.131741i
\(722\) 0 0
\(723\) 1130.85 582.683i 1.56411 0.805924i
\(724\) 0 0
\(725\) 62.9079 + 125.260i 0.0867695 + 0.172772i
\(726\) 0 0
\(727\) −1249.98 + 296.251i −1.71937 + 0.407498i −0.967712 0.252058i \(-0.918892\pi\)
−0.751655 + 0.659556i \(0.770744\pi\)
\(728\) 0 0
\(729\) 81.7411 724.403i 0.112128 0.993694i
\(730\) 0 0
\(731\) 17.7310 + 74.8129i 0.0242558 + 0.102343i
\(732\) 0 0
\(733\) 500.968 251.595i 0.683448 0.343241i −0.0729651 0.997334i \(-0.523246\pi\)
0.756413 + 0.654094i \(0.226950\pi\)
\(734\) 0 0
\(735\) 124.764 + 242.137i 0.169747 + 0.329439i
\(736\) 0 0
\(737\) −834.617 994.657i −1.13245 1.34960i
\(738\) 0 0
\(739\) −1009.75 847.278i −1.36637 1.14652i −0.973958 0.226730i \(-0.927197\pi\)
−0.392411 0.919790i \(-0.628359\pi\)
\(740\) 0 0
\(741\) −4.93074 + 4.22521i −0.00665417 + 0.00570204i
\(742\) 0 0
\(743\) −826.046 779.334i −1.11177 1.04890i −0.998467 0.0553417i \(-0.982375\pi\)
−0.113304 0.993560i \(-0.536143\pi\)
\(744\) 0 0
\(745\) −119.594 + 160.643i −0.160529 + 0.215629i
\(746\) 0 0
\(747\) −227.493 259.979i −0.304542 0.348031i
\(748\) 0 0
\(749\) −365.756 + 728.281i −0.488326 + 0.972337i
\(750\) 0 0
\(751\) −476.853 + 55.7361i −0.634957 + 0.0742158i −0.427481 0.904024i \(-0.640599\pi\)
−0.207476 + 0.978240i \(0.566525\pi\)
\(752\) 0 0
\(753\) 185.359 + 135.032i 0.246161 + 0.179326i
\(754\) 0 0
\(755\) 54.2319 31.3108i 0.0718304 0.0414713i
\(756\) 0 0
\(757\) 12.0101 20.8020i 0.0158653 0.0274796i −0.857984 0.513677i \(-0.828283\pi\)
0.873849 + 0.486197i \(0.161616\pi\)
\(758\) 0 0
\(759\) 384.401 + 188.091i 0.506457 + 0.247815i
\(760\) 0 0
\(761\) −1185.46 511.359i −1.55777 0.671956i −0.569128 0.822249i \(-0.692719\pi\)
−0.988641 + 0.150293i \(0.951978\pi\)
\(762\) 0 0
\(763\) 20.5459 + 352.760i 0.0269278 + 0.462333i
\(764\) 0 0
\(765\) −166.733 + 233.930i −0.217952 + 0.305791i
\(766\) 0 0
\(767\) −5.68160 + 2.45080i −0.00740756 + 0.00319531i
\(768\) 0 0
\(769\) −455.866 108.042i −0.592804 0.140497i −0.0767459 0.997051i \(-0.524453\pi\)
−0.516058 + 0.856554i \(0.672601\pi\)
\(770\) 0 0
\(771\) −777.959 438.471i −1.00903 0.568704i
\(772\) 0 0
\(773\) −136.310 374.507i −0.176338 0.484486i 0.819763 0.572703i \(-0.194105\pi\)
−0.996101 + 0.0882174i \(0.971883\pi\)
\(774\) 0 0
\(775\) 520.043 + 189.280i 0.671023 + 0.244233i
\(776\) 0 0
\(777\) 489.600 1168.15i 0.630115 1.50341i
\(778\) 0 0
\(779\) 1763.15 + 102.692i 2.26334 + 0.131825i
\(780\) 0 0
\(781\) 313.215 + 331.989i 0.401044 + 0.425082i
\(782\) 0 0
\(783\) 20.4639 239.405i 0.0261353 0.305754i
\(784\) 0 0
\(785\) 499.531 + 149.550i 0.636346 + 0.190509i
\(786\) 0 0
\(787\) 1088.62 + 715.998i 1.38325 + 0.909781i 0.999904 0.0138221i \(-0.00439984\pi\)
0.383350 + 0.923603i \(0.374770\pi\)
\(788\) 0 0
\(789\) −245.514 + 1085.93i −0.311171 + 1.37633i
\(790\) 0 0
\(791\) −52.6097 + 9.27651i −0.0665104 + 0.0117276i
\(792\) 0 0
\(793\) 1.12609 6.38637i 0.00142004 0.00805343i
\(794\) 0 0
\(795\) −639.442 + 240.270i −0.804330 + 0.302226i
\(796\) 0