Properties

Label 108.3.k.a.41.4
Level 108
Weight 3
Character 108.41
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
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 41.4
Character \(\chi\) \(=\) 108.41
Dual form 108.3.k.a.29.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0634556 + 2.99933i) q^{3} +(5.64904 - 6.73227i) q^{5} +(4.05297 + 1.47516i) q^{7} +(-8.99195 + 0.380648i) q^{9} +O(q^{10})\) \(q+(0.0634556 + 2.99933i) q^{3} +(5.64904 - 6.73227i) q^{5} +(4.05297 + 1.47516i) q^{7} +(-8.99195 + 0.380648i) q^{9} +(12.6606 + 15.0883i) q^{11} +(-1.31536 + 7.45976i) q^{13} +(20.5507 + 16.5161i) q^{15} +(-3.16520 - 1.82743i) q^{17} +(-16.8333 - 29.1562i) q^{19} +(-4.16730 + 12.2498i) q^{21} +(1.05125 + 2.88830i) q^{23} +(-9.07052 - 51.4415i) q^{25} +(-1.71228 - 26.9457i) q^{27} +(23.9443 - 4.22203i) q^{29} +(-27.1255 + 9.87288i) q^{31} +(-44.4514 + 38.9307i) q^{33} +(32.8265 - 18.9524i) q^{35} +(-14.9004 + 25.8083i) q^{37} +(-22.4577 - 3.47182i) q^{39} +(-22.6547 - 3.99463i) q^{41} +(-6.85241 + 5.74986i) q^{43} +(-48.2333 + 62.6865i) q^{45} +(3.60489 - 9.90435i) q^{47} +(-23.2857 - 19.5391i) q^{49} +(5.28021 - 9.60944i) q^{51} -70.8948i q^{53} +173.099 q^{55} +(86.3808 - 52.3388i) q^{57} +(-43.8902 + 52.3064i) q^{59} +(-99.7950 - 36.3224i) q^{61} +(-37.0056 - 11.7218i) q^{63} +(42.7906 + 50.9958i) q^{65} +(-4.27685 + 24.2552i) q^{67} +(-8.59625 + 3.33634i) q^{69} +(29.9139 + 17.2708i) q^{71} +(20.9190 + 36.2328i) q^{73} +(153.714 - 30.4697i) q^{75} +(29.0553 + 79.8287i) q^{77} +(8.78445 + 49.8191i) q^{79} +(80.7102 - 6.84554i) q^{81} +(-30.9208 + 5.45218i) q^{83} +(-30.1831 + 10.9857i) q^{85} +(14.1827 + 71.5490i) q^{87} +(40.0231 - 23.1073i) q^{89} +(-16.3354 + 28.2938i) q^{91} +(-31.3333 - 80.7318i) q^{93} +(-291.379 - 51.3780i) q^{95} +(84.8132 - 71.1668i) q^{97} +(-119.587 - 130.854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 0
\(3\) 0.0634556 + 2.99933i 0.0211519 + 0.999776i
\(4\) 0 0
\(5\) 5.64904 6.73227i 1.12981 1.34645i 0.199404 0.979917i \(-0.436099\pi\)
0.930404 0.366536i \(-0.119456\pi\)
\(6\) 0 0
\(7\) 4.05297 + 1.47516i 0.578995 + 0.210737i 0.614882 0.788619i \(-0.289204\pi\)
−0.0358873 + 0.999356i \(0.511426\pi\)
\(8\) 0 0
\(9\) −8.99195 + 0.380648i −0.999105 + 0.0422943i
\(10\) 0 0
\(11\) 12.6606 + 15.0883i 1.15096 + 1.37166i 0.916742 + 0.399479i \(0.130809\pi\)
0.234219 + 0.972184i \(0.424747\pi\)
\(12\) 0 0
\(13\) −1.31536 + 7.45976i −0.101181 + 0.573828i 0.891496 + 0.453029i \(0.149657\pi\)
−0.992677 + 0.120799i \(0.961454\pi\)
\(14\) 0 0
\(15\) 20.5507 + 16.5161i 1.37005 + 1.10108i
\(16\) 0 0
\(17\) −3.16520 1.82743i −0.186188 0.107496i 0.404009 0.914755i \(-0.367617\pi\)
−0.590197 + 0.807259i \(0.700950\pi\)
\(18\) 0 0
\(19\) −16.8333 29.1562i −0.885964 1.53453i −0.844605 0.535391i \(-0.820164\pi\)
−0.0413596 0.999144i \(-0.513169\pi\)
\(20\) 0 0
\(21\) −4.16730 + 12.2498i −0.198443 + 0.583323i
\(22\) 0 0
\(23\) 1.05125 + 2.88830i 0.0457067 + 0.125578i 0.960446 0.278467i \(-0.0898262\pi\)
−0.914739 + 0.404045i \(0.867604\pi\)
\(24\) 0 0
\(25\) −9.07052 51.4415i −0.362821 2.05766i
\(26\) 0 0
\(27\) −1.71228 26.9457i −0.0634178 0.997987i
\(28\) 0 0
\(29\) 23.9443 4.22203i 0.825667 0.145587i 0.255179 0.966894i \(-0.417865\pi\)
0.570487 + 0.821306i \(0.306754\pi\)
\(30\) 0 0
\(31\) −27.1255 + 9.87288i −0.875016 + 0.318480i −0.740197 0.672390i \(-0.765268\pi\)
−0.134820 + 0.990870i \(0.543045\pi\)
\(32\) 0 0
\(33\) −44.4514 + 38.9307i −1.34701 + 1.17972i
\(34\) 0 0
\(35\) 32.8265 18.9524i 0.937901 0.541497i
\(36\) 0 0
\(37\) −14.9004 + 25.8083i −0.402714 + 0.697522i −0.994052 0.108902i \(-0.965267\pi\)
0.591338 + 0.806424i \(0.298600\pi\)
\(38\) 0 0
\(39\) −22.4577 3.47182i −0.575839 0.0890211i
\(40\) 0 0
\(41\) −22.6547 3.99463i −0.552552 0.0974299i −0.109601 0.993976i \(-0.534957\pi\)
−0.442951 + 0.896546i \(0.646069\pi\)
\(42\) 0 0
\(43\) −6.85241 + 5.74986i −0.159358 + 0.133718i −0.718980 0.695031i \(-0.755391\pi\)
0.559622 + 0.828748i \(0.310946\pi\)
\(44\) 0 0
\(45\) −48.2333 + 62.6865i −1.07185 + 1.39303i
\(46\) 0 0
\(47\) 3.60489 9.90435i 0.0766997 0.210731i −0.895417 0.445229i \(-0.853122\pi\)
0.972117 + 0.234498i \(0.0753446\pi\)
\(48\) 0 0
\(49\) −23.2857 19.5391i −0.475219 0.398756i
\(50\) 0 0
\(51\) 5.28021 9.60944i 0.103534 0.188420i
\(52\) 0 0
\(53\) 70.8948i 1.33764i −0.743426 0.668818i \(-0.766800\pi\)
0.743426 0.668818i \(-0.233200\pi\)
\(54\) 0 0
\(55\) 173.099 3.14725
\(56\) 0 0
\(57\) 86.3808 52.3388i 1.51545 0.918224i
\(58\) 0 0
\(59\) −43.8902 + 52.3064i −0.743903 + 0.886549i −0.996717 0.0809663i \(-0.974199\pi\)
0.252814 + 0.967515i \(0.418644\pi\)
\(60\) 0 0
\(61\) −99.7950 36.3224i −1.63598 0.595449i −0.649653 0.760231i \(-0.725086\pi\)
−0.986330 + 0.164781i \(0.947308\pi\)
\(62\) 0 0
\(63\) −37.0056 11.7218i −0.587390 0.186060i
\(64\) 0 0
\(65\) 42.7906 + 50.9958i 0.658317 + 0.784551i
\(66\) 0 0
\(67\) −4.27685 + 24.2552i −0.0638336 + 0.362018i 0.936113 + 0.351699i \(0.114396\pi\)
−0.999947 + 0.0103194i \(0.996715\pi\)
\(68\) 0 0
\(69\) −8.59625 + 3.33634i −0.124583 + 0.0483527i
\(70\) 0 0
\(71\) 29.9139 + 17.2708i 0.421323 + 0.243251i 0.695643 0.718387i \(-0.255119\pi\)
−0.274320 + 0.961638i \(0.588453\pi\)
\(72\) 0 0
\(73\) 20.9190 + 36.2328i 0.286562 + 0.496340i 0.972987 0.230861i \(-0.0741542\pi\)
−0.686425 + 0.727201i \(0.740821\pi\)
\(74\) 0 0
\(75\) 153.714 30.4697i 2.04953 0.406263i
\(76\) 0 0
\(77\) 29.0553 + 79.8287i 0.377341 + 1.03674i
\(78\) 0 0
\(79\) 8.78445 + 49.8191i 0.111196 + 0.630621i 0.988564 + 0.150804i \(0.0481861\pi\)
−0.877368 + 0.479818i \(0.840703\pi\)
\(80\) 0 0
\(81\) 80.7102 6.84554i 0.996422 0.0845129i
\(82\) 0 0
\(83\) −30.9208 + 5.45218i −0.372540 + 0.0656889i −0.356784 0.934187i \(-0.616127\pi\)
−0.0157564 + 0.999876i \(0.505016\pi\)
\(84\) 0 0
\(85\) −30.1831 + 10.9857i −0.355095 + 0.129244i
\(86\) 0 0
\(87\) 14.1827 + 71.5490i 0.163019 + 0.822403i
\(88\) 0 0
\(89\) 40.0231 23.1073i 0.449697 0.259633i −0.258005 0.966144i \(-0.583065\pi\)
0.707702 + 0.706511i \(0.249732\pi\)
\(90\) 0 0
\(91\) −16.3354 + 28.2938i −0.179510 + 0.310921i
\(92\) 0 0
\(93\) −31.3333 80.7318i −0.336917 0.868084i
\(94\) 0 0
\(95\) −291.379 51.3780i −3.06715 0.540821i
\(96\) 0 0
\(97\) 84.8132 71.1668i 0.874363 0.733678i −0.0906489 0.995883i \(-0.528894\pi\)
0.965012 + 0.262205i \(0.0844497\pi\)
\(98\) 0 0
\(99\) −119.587 130.854i −1.20795 1.32176i
\(100\) 0 0
\(101\) −27.7555 + 76.2576i −0.274807 + 0.755026i 0.723123 + 0.690719i \(0.242706\pi\)
−0.997930 + 0.0643070i \(0.979516\pi\)
\(102\) 0 0
\(103\) 120.693 + 101.273i 1.17177 + 0.983234i 0.999998 0.00190171i \(-0.000605335\pi\)
0.171775 + 0.985136i \(0.445050\pi\)
\(104\) 0 0
\(105\) 58.9275 + 97.2549i 0.561214 + 0.926237i
\(106\) 0 0
\(107\) 60.6265i 0.566603i −0.959031 0.283301i \(-0.908570\pi\)
0.959031 0.283301i \(-0.0914297\pi\)
\(108\) 0 0
\(109\) 13.0119 0.119375 0.0596876 0.998217i \(-0.480990\pi\)
0.0596876 + 0.998217i \(0.480990\pi\)
\(110\) 0 0
\(111\) −78.3531 43.0536i −0.705884 0.387870i
\(112\) 0 0
\(113\) 72.3782 86.2570i 0.640515 0.763336i −0.343936 0.938993i \(-0.611760\pi\)
0.984452 + 0.175657i \(0.0562048\pi\)
\(114\) 0 0
\(115\) 25.3834 + 9.23879i 0.220725 + 0.0803373i
\(116\) 0 0
\(117\) 8.98807 67.5785i 0.0768211 0.577594i
\(118\) 0 0
\(119\) −10.1327 12.0757i −0.0851487 0.101476i
\(120\) 0 0
\(121\) −46.3548 + 262.891i −0.383098 + 2.17265i
\(122\) 0 0
\(123\) 10.5436 68.2022i 0.0857206 0.554490i
\(124\) 0 0
\(125\) −207.284 119.676i −1.65827 0.957405i
\(126\) 0 0
\(127\) 28.4023 + 49.1942i 0.223640 + 0.387356i 0.955911 0.293658i \(-0.0948726\pi\)
−0.732270 + 0.681014i \(0.761539\pi\)
\(128\) 0 0
\(129\) −17.6805 20.1878i −0.137058 0.156494i
\(130\) 0 0
\(131\) 4.65602 + 12.7923i 0.0355421 + 0.0976511i 0.956194 0.292733i \(-0.0945646\pi\)
−0.920652 + 0.390384i \(0.872342\pi\)
\(132\) 0 0
\(133\) −25.2149 143.001i −0.189586 1.07519i
\(134\) 0 0
\(135\) −191.078 140.690i −1.41539 1.04215i
\(136\) 0 0
\(137\) 176.617 31.1423i 1.28917 0.227316i 0.513302 0.858208i \(-0.328422\pi\)
0.775871 + 0.630892i \(0.217311\pi\)
\(138\) 0 0
\(139\) −108.775 + 39.5907i −0.782551 + 0.284825i −0.702236 0.711944i \(-0.747815\pi\)
−0.0803153 + 0.996770i \(0.525593\pi\)
\(140\) 0 0
\(141\) 29.9351 + 10.1838i 0.212306 + 0.0722252i
\(142\) 0 0
\(143\) −129.208 + 74.5984i −0.903554 + 0.521667i
\(144\) 0 0
\(145\) 106.839 185.050i 0.736819 1.27621i
\(146\) 0 0
\(147\) 57.1265 71.0815i 0.388615 0.483547i
\(148\) 0 0
\(149\) −77.5851 13.6804i −0.520706 0.0918145i −0.0928828 0.995677i \(-0.529608\pi\)
−0.427823 + 0.903863i \(0.640719\pi\)
\(150\) 0 0
\(151\) −31.2173 + 26.1944i −0.206737 + 0.173473i −0.740277 0.672302i \(-0.765306\pi\)
0.533540 + 0.845775i \(0.320861\pi\)
\(152\) 0 0
\(153\) 29.1569 + 15.2273i 0.190568 + 0.0995250i
\(154\) 0 0
\(155\) −86.7663 + 238.388i −0.559783 + 1.53799i
\(156\) 0 0
\(157\) −140.499 117.893i −0.894901 0.750911i 0.0742864 0.997237i \(-0.476332\pi\)
−0.969187 + 0.246326i \(0.920777\pi\)
\(158\) 0 0
\(159\) 212.637 4.49867i 1.33734 0.0282935i
\(160\) 0 0
\(161\) 13.2569i 0.0823413i
\(162\) 0 0
\(163\) −225.642 −1.38431 −0.692154 0.721750i \(-0.743338\pi\)
−0.692154 + 0.721750i \(0.743338\pi\)
\(164\) 0 0
\(165\) 10.9841 + 519.179i 0.0665701 + 3.14654i
\(166\) 0 0
\(167\) 119.618 142.556i 0.716278 0.853627i −0.277986 0.960585i \(-0.589667\pi\)
0.994263 + 0.106959i \(0.0341112\pi\)
\(168\) 0 0
\(169\) 104.890 + 38.1769i 0.620652 + 0.225899i
\(170\) 0 0
\(171\) 162.463 + 255.763i 0.950073 + 1.49569i
\(172\) 0 0
\(173\) 89.4213 + 106.568i 0.516886 + 0.616001i 0.959841 0.280543i \(-0.0905145\pi\)
−0.442956 + 0.896544i \(0.646070\pi\)
\(174\) 0 0
\(175\) 39.1219 221.871i 0.223553 1.26783i
\(176\) 0 0
\(177\) −159.669 128.322i −0.902085 0.724984i
\(178\) 0 0
\(179\) 125.967 + 72.7273i 0.703728 + 0.406298i 0.808735 0.588174i \(-0.200153\pi\)
−0.105006 + 0.994472i \(0.533486\pi\)
\(180\) 0 0
\(181\) 125.541 + 217.444i 0.693599 + 1.20135i 0.970651 + 0.240494i \(0.0773094\pi\)
−0.277052 + 0.960855i \(0.589357\pi\)
\(182\) 0 0
\(183\) 102.610 301.623i 0.560712 1.64821i
\(184\) 0 0
\(185\) 89.5752 + 246.106i 0.484190 + 1.33030i
\(186\) 0 0
\(187\) −12.5005 70.8938i −0.0668475 0.379111i
\(188\) 0 0
\(189\) 32.8093 111.736i 0.173594 0.591194i
\(190\) 0 0
\(191\) −28.3584 + 5.00035i −0.148473 + 0.0261798i −0.247391 0.968916i \(-0.579573\pi\)
0.0989175 + 0.995096i \(0.468462\pi\)
\(192\) 0 0
\(193\) 84.8880 30.8967i 0.439834 0.160087i −0.112605 0.993640i \(-0.535919\pi\)
0.552439 + 0.833553i \(0.313697\pi\)
\(194\) 0 0
\(195\) −150.238 + 131.579i −0.770451 + 0.674764i
\(196\) 0 0
\(197\) 246.767 142.471i 1.25263 0.723204i 0.280996 0.959709i \(-0.409335\pi\)
0.971630 + 0.236505i \(0.0760020\pi\)
\(198\) 0 0
\(199\) 78.3479 135.703i 0.393708 0.681922i −0.599227 0.800579i \(-0.704525\pi\)
0.992935 + 0.118657i \(0.0378588\pi\)
\(200\) 0 0
\(201\) −73.0208 11.2886i −0.363288 0.0561620i
\(202\) 0 0
\(203\) 103.274 + 18.2099i 0.508738 + 0.0897042i
\(204\) 0 0
\(205\) −154.870 + 129.951i −0.755463 + 0.633909i
\(206\) 0 0
\(207\) −10.5523 25.5713i −0.0509771 0.123533i
\(208\) 0 0
\(209\) 226.797 623.120i 1.08515 2.98143i
\(210\) 0 0
\(211\) 142.593 + 119.650i 0.675795 + 0.567060i 0.914774 0.403965i \(-0.132368\pi\)
−0.238979 + 0.971025i \(0.576813\pi\)
\(212\) 0 0
\(213\) −49.9027 + 90.8177i −0.234285 + 0.426374i
\(214\) 0 0
\(215\) 78.6134i 0.365644i
\(216\) 0 0
\(217\) −124.503 −0.573746
\(218\) 0 0
\(219\) −107.347 + 65.0422i −0.490168 + 0.296996i
\(220\) 0 0
\(221\) 17.7956 21.2079i 0.0805229 0.0959634i
\(222\) 0 0
\(223\) −50.7592 18.4748i −0.227620 0.0828468i 0.225693 0.974199i \(-0.427536\pi\)
−0.453312 + 0.891352i \(0.649758\pi\)
\(224\) 0 0
\(225\) 101.143 + 459.107i 0.449524 + 2.04047i
\(226\) 0 0
\(227\) −184.955 220.421i −0.814781 0.971018i 0.185150 0.982710i \(-0.440723\pi\)
−0.999932 + 0.0116918i \(0.996278\pi\)
\(228\) 0 0
\(229\) 38.3441 217.460i 0.167441 0.949608i −0.779070 0.626937i \(-0.784308\pi\)
0.946511 0.322671i \(-0.104581\pi\)
\(230\) 0 0
\(231\) −237.589 + 92.2119i −1.02852 + 0.399186i
\(232\) 0 0
\(233\) 351.012 + 202.657i 1.50649 + 0.869772i 0.999972 + 0.00754192i \(0.00240069\pi\)
0.506517 + 0.862230i \(0.330933\pi\)
\(234\) 0 0
\(235\) −46.3145 80.2191i −0.197083 0.341358i
\(236\) 0 0
\(237\) −148.866 + 29.5087i −0.628128 + 0.124509i
\(238\) 0 0
\(239\) 113.967 + 313.121i 0.476848 + 1.31013i 0.912154 + 0.409847i \(0.134418\pi\)
−0.435306 + 0.900283i \(0.643360\pi\)
\(240\) 0 0
\(241\) 5.43972 + 30.8502i 0.0225714 + 0.128009i 0.994011 0.109277i \(-0.0348534\pi\)
−0.971440 + 0.237286i \(0.923742\pi\)
\(242\) 0 0
\(243\) 25.6535 + 241.642i 0.105570 + 0.994412i
\(244\) 0 0
\(245\) −263.084 + 46.3889i −1.07381 + 0.189342i
\(246\) 0 0
\(247\) 239.640 87.2218i 0.970202 0.353125i
\(248\) 0 0
\(249\) −18.3150 92.3958i −0.0735541 0.371068i
\(250\) 0 0
\(251\) 86.8677 50.1531i 0.346086 0.199813i −0.316874 0.948468i \(-0.602633\pi\)
0.662960 + 0.748655i \(0.269300\pi\)
\(252\) 0 0
\(253\) −30.2700 + 52.4292i −0.119644 + 0.207230i
\(254\) 0 0
\(255\) −34.8652 89.8319i −0.136726 0.352282i
\(256\) 0 0
\(257\) −389.385 68.6591i −1.51512 0.267156i −0.646605 0.762825i \(-0.723812\pi\)
−0.868512 + 0.495669i \(0.834923\pi\)
\(258\) 0 0
\(259\) −98.4623 + 82.6197i −0.380163 + 0.318995i
\(260\) 0 0
\(261\) −213.699 + 47.0787i −0.818770 + 0.180378i
\(262\) 0 0
\(263\) −107.565 + 295.532i −0.408992 + 1.12370i 0.548729 + 0.836000i \(0.315112\pi\)
−0.957721 + 0.287697i \(0.907110\pi\)
\(264\) 0 0
\(265\) −477.282 400.487i −1.80107 1.51127i
\(266\) 0 0
\(267\) 71.8461 + 118.576i 0.269087 + 0.444105i
\(268\) 0 0
\(269\) 182.669i 0.679069i 0.940594 + 0.339534i \(0.110269\pi\)
−0.940594 + 0.339534i \(0.889731\pi\)
\(270\) 0 0
\(271\) −461.198 −1.70184 −0.850919 0.525297i \(-0.823954\pi\)
−0.850919 + 0.525297i \(0.823954\pi\)
\(272\) 0 0
\(273\) −85.8989 47.1999i −0.314648 0.172893i
\(274\) 0 0
\(275\) 661.326 788.138i 2.40482 2.86596i
\(276\) 0 0
\(277\) −148.424 54.0220i −0.535827 0.195025i 0.0599111 0.998204i \(-0.480918\pi\)
−0.595738 + 0.803179i \(0.703141\pi\)
\(278\) 0 0
\(279\) 240.153 99.1017i 0.860764 0.355203i
\(280\) 0 0
\(281\) −131.821 157.098i −0.469113 0.559067i 0.478665 0.877998i \(-0.341121\pi\)
−0.947778 + 0.318930i \(0.896676\pi\)
\(282\) 0 0
\(283\) 70.6906 400.906i 0.249790 1.41663i −0.559310 0.828959i \(-0.688934\pi\)
0.809100 0.587671i \(-0.199955\pi\)
\(284\) 0 0
\(285\) 135.610 877.202i 0.475824 3.07790i
\(286\) 0 0
\(287\) −85.9258 49.6093i −0.299393 0.172855i
\(288\) 0 0
\(289\) −137.821 238.713i −0.476889 0.825996i
\(290\) 0 0
\(291\) 218.834 + 249.867i 0.752008 + 0.858649i
\(292\) 0 0
\(293\) 146.516 + 402.550i 0.500055 + 1.37389i 0.891221 + 0.453570i \(0.149850\pi\)
−0.391166 + 0.920320i \(0.627928\pi\)
\(294\) 0 0
\(295\) 104.202 + 590.962i 0.353229 + 2.00326i
\(296\) 0 0
\(297\) 384.885 366.983i 1.29591 1.23563i
\(298\) 0 0
\(299\) −22.9288 + 4.04297i −0.0766849 + 0.0135216i
\(300\) 0 0
\(301\) −36.2545 + 13.1956i −0.120447 + 0.0438391i
\(302\) 0 0
\(303\) −230.483 78.4089i −0.760670 0.258775i
\(304\) 0 0
\(305\) −808.278 + 466.660i −2.65009 + 1.53003i
\(306\) 0 0
\(307\) −50.5433 + 87.5435i −0.164636 + 0.285158i −0.936526 0.350598i \(-0.885978\pi\)
0.771890 + 0.635756i \(0.219312\pi\)
\(308\) 0 0
\(309\) −296.093 + 368.423i −0.958229 + 1.19231i
\(310\) 0 0
\(311\) 7.38442 + 1.30207i 0.0237441 + 0.00418673i 0.185508 0.982643i \(-0.440607\pi\)
−0.161764 + 0.986830i \(0.551718\pi\)
\(312\) 0 0
\(313\) 353.344 296.491i 1.12889 0.947254i 0.129875 0.991530i \(-0.458543\pi\)
0.999019 + 0.0442760i \(0.0140981\pi\)
\(314\) 0 0
\(315\) −287.960 + 182.914i −0.914159 + 0.580681i
\(316\) 0 0
\(317\) 22.7695 62.5587i 0.0718281 0.197346i −0.898584 0.438802i \(-0.855403\pi\)
0.970412 + 0.241456i \(0.0776250\pi\)
\(318\) 0 0
\(319\) 366.852 + 307.826i 1.15001 + 0.964971i
\(320\) 0 0
\(321\) 181.839 3.84709i 0.566476 0.0119847i
\(322\) 0 0
\(323\) 123.047i 0.380950i
\(324\) 0 0
\(325\) 395.672 1.21745
\(326\) 0 0
\(327\) 0.825677 + 39.0269i 0.00252501 + 0.119348i
\(328\) 0 0
\(329\) 29.2210 34.8242i 0.0888175 0.105849i
\(330\) 0 0
\(331\) 250.644 + 91.2269i 0.757233 + 0.275610i 0.691646 0.722237i \(-0.256886\pi\)
0.0655866 + 0.997847i \(0.479108\pi\)
\(332\) 0 0
\(333\) 124.160 237.739i 0.372853 0.713930i
\(334\) 0 0
\(335\) 139.133 + 165.812i 0.415321 + 0.494960i
\(336\) 0 0
\(337\) −94.3310 + 534.978i −0.279914 + 1.58747i 0.442993 + 0.896525i \(0.353917\pi\)
−0.722907 + 0.690945i \(0.757194\pi\)
\(338\) 0 0
\(339\) 263.306 + 211.613i 0.776714 + 0.624226i
\(340\) 0 0
\(341\) −492.390 284.281i −1.44396 0.833669i
\(342\) 0 0
\(343\) −171.223 296.568i −0.499194 0.864629i
\(344\) 0 0
\(345\) −26.0995 + 76.7194i −0.0756506 + 0.222375i
\(346\) 0 0
\(347\) −142.664 391.967i −0.411136 1.12959i −0.956588 0.291445i \(-0.905864\pi\)
0.545452 0.838142i \(-0.316358\pi\)
\(348\) 0 0
\(349\) 76.3391 + 432.940i 0.218737 + 1.24052i 0.874304 + 0.485380i \(0.161319\pi\)
−0.655567 + 0.755137i \(0.727570\pi\)
\(350\) 0 0
\(351\) 203.260 + 22.6700i 0.579089 + 0.0645868i
\(352\) 0 0
\(353\) −11.4788 + 2.02403i −0.0325180 + 0.00573380i −0.189883 0.981807i \(-0.560811\pi\)
0.157366 + 0.987540i \(0.449700\pi\)
\(354\) 0 0
\(355\) 285.257 103.825i 0.803540 0.292465i
\(356\) 0 0
\(357\) 35.5760 31.1576i 0.0996526 0.0872761i
\(358\) 0 0
\(359\) 192.363 111.061i 0.535831 0.309362i −0.207557 0.978223i \(-0.566551\pi\)
0.743387 + 0.668861i \(0.233218\pi\)
\(360\) 0 0
\(361\) −386.221 + 668.955i −1.06986 + 1.85306i
\(362\) 0 0
\(363\) −791.439 122.351i −2.18027 0.337056i
\(364\) 0 0
\(365\) 362.101 + 63.8483i 0.992059 + 0.174927i
\(366\) 0 0
\(367\) 185.653 155.782i 0.505868 0.424473i −0.353805 0.935319i \(-0.615112\pi\)
0.859672 + 0.510846i \(0.170668\pi\)
\(368\) 0 0
\(369\) 205.230 + 27.2960i 0.556179 + 0.0739729i
\(370\) 0 0
\(371\) 104.581 287.334i 0.281890 0.774485i
\(372\) 0 0
\(373\) 445.391 + 373.728i 1.19408 + 1.00195i 0.999779 + 0.0210080i \(0.00668756\pi\)
0.194299 + 0.980942i \(0.437757\pi\)
\(374\) 0 0
\(375\) 345.793 629.308i 0.922115 1.67815i
\(376\) 0 0
\(377\) 184.172i 0.488521i
\(378\) 0 0
\(379\) −225.207 −0.594213 −0.297107 0.954844i \(-0.596022\pi\)
−0.297107 + 0.954844i \(0.596022\pi\)
\(380\) 0 0
\(381\) −145.747 + 88.3095i −0.382539 + 0.231783i
\(382\) 0 0
\(383\) 25.3855 30.2532i 0.0662806 0.0789902i −0.731885 0.681428i \(-0.761359\pi\)
0.798166 + 0.602438i \(0.205804\pi\)
\(384\) 0 0
\(385\) 701.562 + 255.348i 1.82224 + 0.663241i
\(386\) 0 0
\(387\) 59.4278 54.3108i 0.153560 0.140338i
\(388\) 0 0
\(389\) −143.473 170.984i −0.368824 0.439548i 0.549429 0.835540i \(-0.314845\pi\)
−0.918254 + 0.395992i \(0.870401\pi\)
\(390\) 0 0
\(391\) 1.95073 11.0631i 0.00498908 0.0282945i
\(392\) 0 0
\(393\) −38.0729 + 14.7767i −0.0968775 + 0.0375997i
\(394\) 0 0
\(395\) 385.019 + 222.291i 0.974732 + 0.562762i
\(396\) 0 0
\(397\) −81.7197 141.543i −0.205843 0.356531i 0.744558 0.667558i \(-0.232660\pi\)
−0.950401 + 0.311027i \(0.899327\pi\)
\(398\) 0 0
\(399\) 427.306 84.7019i 1.07094 0.212286i
\(400\) 0 0
\(401\) 98.9356 + 271.823i 0.246722 + 0.677864i 0.999801 + 0.0199338i \(0.00634555\pi\)
−0.753079 + 0.657930i \(0.771432\pi\)
\(402\) 0 0
\(403\) −37.9696 215.336i −0.0942173 0.534333i
\(404\) 0 0
\(405\) 409.849 582.033i 1.01197 1.43712i
\(406\) 0 0
\(407\) −578.051 + 101.926i −1.42027 + 0.250433i
\(408\) 0 0
\(409\) −85.1579 + 30.9950i −0.208210 + 0.0757823i −0.444020 0.896017i \(-0.646448\pi\)
0.235810 + 0.971799i \(0.424226\pi\)
\(410\) 0 0
\(411\) 104.613 + 527.756i 0.254534 + 1.28408i
\(412\) 0 0
\(413\) −255.046 + 147.251i −0.617544 + 0.356539i
\(414\) 0 0
\(415\) −137.968 + 238.967i −0.332452 + 0.575824i
\(416\) 0 0
\(417\) −125.648 323.739i −0.301314 0.776352i
\(418\) 0 0
\(419\) −636.775 112.281i −1.51975 0.267973i −0.649415 0.760434i \(-0.724986\pi\)
−0.870334 + 0.492462i \(0.836097\pi\)
\(420\) 0 0
\(421\) −94.6516 + 79.4221i −0.224826 + 0.188651i −0.748242 0.663426i \(-0.769102\pi\)
0.523416 + 0.852077i \(0.324657\pi\)
\(422\) 0 0
\(423\) −28.6449 + 90.4315i −0.0677184 + 0.213786i
\(424\) 0 0
\(425\) −65.2957 + 179.398i −0.153637 + 0.422114i
\(426\) 0 0
\(427\) −350.884 294.427i −0.821743 0.689524i
\(428\) 0 0
\(429\) −231.944 382.804i −0.540662 0.892317i
\(430\) 0 0
\(431\) 679.383i 1.57629i 0.615487 + 0.788147i \(0.288959\pi\)
−0.615487 + 0.788147i \(0.711041\pi\)
\(432\) 0 0
\(433\) 738.981 1.70665 0.853327 0.521376i \(-0.174581\pi\)
0.853327 + 0.521376i \(0.174581\pi\)
\(434\) 0 0
\(435\) 561.805 + 308.702i 1.29151 + 0.709660i
\(436\) 0 0
\(437\) 66.5156 79.2702i 0.152210 0.181396i
\(438\) 0 0
\(439\) −294.308 107.120i −0.670407 0.244008i −0.0156837 0.999877i \(-0.504992\pi\)
−0.654723 + 0.755869i \(0.727215\pi\)
\(440\) 0 0
\(441\) 216.822 + 166.831i 0.491659 + 0.378300i
\(442\) 0 0
\(443\) −316.952 377.729i −0.715467 0.852661i 0.278715 0.960374i \(-0.410092\pi\)
−0.994182 + 0.107713i \(0.965647\pi\)
\(444\) 0 0
\(445\) 70.5273 399.980i 0.158488 0.898832i
\(446\) 0 0
\(447\) 36.1087 233.571i 0.0807800 0.522531i
\(448\) 0 0
\(449\) −403.766 233.114i −0.899255 0.519185i −0.0222969 0.999751i \(-0.507098\pi\)
−0.876959 + 0.480566i \(0.840431\pi\)
\(450\) 0 0
\(451\) −226.549 392.394i −0.502326 0.870054i
\(452\) 0 0
\(453\) −80.5466 91.9688i −0.177807 0.203022i
\(454\) 0 0
\(455\) 98.2018 + 269.807i 0.215828 + 0.592983i
\(456\) 0 0
\(457\) −65.2077 369.811i −0.142687 0.809216i −0.969196 0.246292i \(-0.920788\pi\)
0.826509 0.562923i \(-0.190323\pi\)
\(458\) 0 0
\(459\) −43.8216 + 88.4175i −0.0954718 + 0.192631i
\(460\) 0 0
\(461\) −116.143 + 20.4791i −0.251937 + 0.0444232i −0.298190 0.954507i \(-0.596383\pi\)
0.0462535 + 0.998930i \(0.485272\pi\)
\(462\) 0 0
\(463\) 82.8187 30.1435i 0.178874 0.0651048i −0.251030 0.967979i \(-0.580769\pi\)
0.429905 + 0.902874i \(0.358547\pi\)
\(464\) 0 0
\(465\) −720.511 245.114i −1.54949 0.527126i
\(466\) 0 0
\(467\) 288.366 166.488i 0.617486 0.356506i −0.158403 0.987374i \(-0.550635\pi\)
0.775890 + 0.630869i \(0.217301\pi\)
\(468\) 0 0
\(469\) −53.1143 + 91.9966i −0.113250 + 0.196155i
\(470\) 0 0
\(471\) 344.684 428.885i 0.731814 0.910584i
\(472\) 0 0
\(473\) −173.511 30.5947i −0.366831 0.0646822i
\(474\) 0 0
\(475\) −1347.15 + 1130.39i −2.83610 + 2.37977i
\(476\) 0 0
\(477\) 26.9860 + 637.482i 0.0565744 + 1.33644i
\(478\) 0 0
\(479\) −143.904 + 395.374i −0.300427 + 0.825416i 0.693999 + 0.719976i \(0.255847\pi\)
−0.994426 + 0.105440i \(0.966375\pi\)
\(480\) 0 0
\(481\) −172.924 145.101i −0.359510 0.301665i
\(482\) 0 0
\(483\) −39.7619 + 0.841227i −0.0823228 + 0.00174167i
\(484\) 0 0
\(485\) 973.009i 2.00620i
\(486\) 0 0
\(487\) 212.098 0.435519 0.217760 0.976002i \(-0.430125\pi\)
0.217760 + 0.976002i \(0.430125\pi\)
\(488\) 0 0
\(489\) −14.3183 676.775i −0.0292807 1.38400i
\(490\) 0 0
\(491\) −173.315 + 206.549i −0.352983 + 0.420669i −0.913094 0.407748i \(-0.866314\pi\)
0.560111 + 0.828418i \(0.310758\pi\)
\(492\) 0 0
\(493\) −83.5041 30.3930i −0.169380 0.0616491i
\(494\) 0 0
\(495\) −1556.49 + 65.8897i −3.14443 + 0.133110i
\(496\) 0 0
\(497\) 95.7630 + 114.126i 0.192682 + 0.229629i
\(498\) 0 0
\(499\) 61.6379 349.566i 0.123523 0.700533i −0.858651 0.512560i \(-0.828697\pi\)
0.982174 0.187973i \(-0.0601918\pi\)
\(500\) 0 0
\(501\) 435.162 + 349.729i 0.868586 + 0.698062i
\(502\) 0 0
\(503\) 410.636 + 237.081i 0.816374 + 0.471333i 0.849164 0.528129i \(-0.177106\pi\)
−0.0327908 + 0.999462i \(0.510439\pi\)
\(504\) 0 0
\(505\) 356.595 + 617.640i 0.706128 + 1.22305i
\(506\) 0 0
\(507\) −107.849 + 317.023i −0.212720 + 0.625291i
\(508\) 0 0
\(509\) −28.2600 77.6437i −0.0555206 0.152542i 0.908832 0.417163i \(-0.136975\pi\)
−0.964353 + 0.264621i \(0.914753\pi\)
\(510\) 0 0
\(511\) 31.3349 + 177.709i 0.0613208 + 0.347768i
\(512\) 0 0
\(513\) −756.808 + 503.508i −1.47526 + 0.981498i
\(514\) 0 0
\(515\) 1363.60 240.439i 2.64776 0.466871i
\(516\) 0 0
\(517\) 195.080 71.0032i 0.377330 0.137337i
\(518\) 0 0
\(519\) −313.959 + 274.966i −0.604930 + 0.529800i
\(520\) 0 0
\(521\) 489.450 282.584i 0.939444 0.542388i 0.0496582 0.998766i \(-0.484187\pi\)
0.889786 + 0.456378i \(0.150853\pi\)
\(522\) 0 0
\(523\) 340.114 589.095i 0.650314 1.12638i −0.332733 0.943021i \(-0.607971\pi\)
0.983047 0.183356i \(-0.0586960\pi\)
\(524\) 0 0
\(525\) 667.947 + 103.260i 1.27228 + 0.196686i
\(526\) 0 0
\(527\) 103.900 + 18.3203i 0.197153 + 0.0347634i
\(528\) 0 0
\(529\) 398.000 333.962i 0.752364 0.631308i
\(530\) 0 0
\(531\) 374.748 487.043i 0.705741 0.917218i
\(532\) 0 0
\(533\) 59.5979 163.744i 0.111816 0.307212i
\(534\) 0 0
\(535\) −408.154 342.482i −0.762904 0.640153i
\(536\) 0 0
\(537\) −210.140 + 382.433i −0.391322 + 0.712165i
\(538\) 0 0
\(539\) 598.718i 1.11079i
\(540\) 0 0
\(541\) 53.2254 0.0983833 0.0491916 0.998789i \(-0.484335\pi\)
0.0491916 + 0.998789i \(0.484335\pi\)
\(542\) 0 0
\(543\) −644.220 + 390.338i −1.18641 + 0.718855i
\(544\) 0 0
\(545\) 73.5047 87.5995i 0.134871 0.160733i
\(546\) 0 0
\(547\) −128.793 46.8768i −0.235453 0.0856981i 0.221599 0.975138i \(-0.428873\pi\)
−0.457052 + 0.889440i \(0.651095\pi\)
\(548\) 0 0
\(549\) 911.177 + 288.622i 1.65970 + 0.525724i
\(550\) 0 0
\(551\) −526.161 627.054i −0.954920 1.13803i
\(552\) 0 0
\(553\) −37.8880 + 214.873i −0.0685135 + 0.388560i
\(554\) 0 0
\(555\) −732.468 + 284.282i −1.31976 + 0.512220i
\(556\) 0 0
\(557\) 519.540 + 299.956i 0.932746 + 0.538521i 0.887679 0.460463i \(-0.152317\pi\)
0.0450671 + 0.998984i \(0.485650\pi\)
\(558\) 0 0
\(559\) −33.8792 58.6805i −0.0606068 0.104974i
\(560\) 0 0
\(561\) 211.841 41.9917i 0.377612 0.0748515i
\(562\) 0 0
\(563\) 75.8301 + 208.342i 0.134689 + 0.370056i 0.988641 0.150296i \(-0.0480228\pi\)
−0.853952 + 0.520352i \(0.825801\pi\)
\(564\) 0 0
\(565\) −171.838 974.539i −0.304137 1.72485i
\(566\) 0 0
\(567\) 337.214 + 91.3156i 0.594734 + 0.161050i
\(568\) 0 0
\(569\) −121.585 + 21.4387i −0.213681 + 0.0376778i −0.279464 0.960156i \(-0.590157\pi\)
0.0657826 + 0.997834i \(0.479046\pi\)
\(570\) 0 0
\(571\) −704.732 + 256.501i −1.23421 + 0.449215i −0.875036 0.484057i \(-0.839163\pi\)
−0.359171 + 0.933272i \(0.616940\pi\)
\(572\) 0 0
\(573\) −16.7972 84.7388i −0.0293145 0.147886i
\(574\) 0 0
\(575\) 139.043 80.2765i 0.241814 0.139611i
\(576\) 0 0
\(577\) −15.9521 + 27.6299i −0.0276467 + 0.0478855i −0.879518 0.475866i \(-0.842135\pi\)
0.851871 + 0.523752i \(0.175468\pi\)
\(578\) 0 0
\(579\) 98.0560 + 252.647i 0.169354 + 0.436350i
\(580\) 0 0
\(581\) −133.364 23.5157i −0.229542 0.0404745i
\(582\) 0 0
\(583\) 1069.68 897.569i 1.83479 1.53957i
\(584\) 0 0
\(585\) −404.182 442.264i −0.690910 0.756006i
\(586\) 0 0
\(587\) −43.4593 + 119.403i −0.0740363 + 0.203413i −0.971190 0.238304i \(-0.923408\pi\)
0.897154 + 0.441717i \(0.145631\pi\)
\(588\) 0 0
\(589\) 744.468 + 624.683i 1.26395 + 1.06058i
\(590\) 0 0
\(591\) 442.977 + 731.096i 0.749538 + 1.23705i
\(592\) 0 0
\(593\) 606.986i 1.02359i 0.859109 + 0.511793i \(0.171019\pi\)
−0.859109 + 0.511793i \(0.828981\pi\)
\(594\) 0 0
\(595\) −138.537 −0.232835
\(596\) 0 0
\(597\) 411.988 + 226.380i 0.690097 + 0.379196i
\(598\) 0 0
\(599\) −168.791 + 201.157i −0.281787 + 0.335821i −0.888309 0.459246i \(-0.848120\pi\)
0.606522 + 0.795067i \(0.292564\pi\)
\(600\) 0 0
\(601\) −998.384 363.382i −1.66120 0.604629i −0.670653 0.741771i \(-0.733986\pi\)
−0.990551 + 0.137142i \(0.956208\pi\)
\(602\) 0 0
\(603\) 29.2245 219.730i 0.0484652 0.364394i
\(604\) 0 0
\(605\) 1507.99 + 1797.16i 2.49255 + 2.97051i
\(606\) 0 0
\(607\) −180.588 + 1024.16i −0.297509 + 1.68725i 0.359320 + 0.933215i \(0.383009\pi\)
−0.656828 + 0.754040i \(0.728102\pi\)
\(608\) 0 0
\(609\) −48.0643 + 310.907i −0.0789233 + 0.510521i
\(610\) 0 0
\(611\) 69.1423 + 39.9193i 0.113163 + 0.0653344i
\(612\) 0 0
\(613\) 244.419 + 423.347i 0.398726 + 0.690614i 0.993569 0.113228i \(-0.0361190\pi\)
−0.594843 + 0.803842i \(0.702786\pi\)
\(614\) 0 0
\(615\) −399.594 456.260i −0.649746 0.741886i
\(616\) 0 0
\(617\) 122.120 + 335.523i 0.197926 + 0.543797i 0.998459 0.0554913i \(-0.0176725\pi\)
−0.800533 + 0.599288i \(0.795450\pi\)
\(618\) 0 0
\(619\) −53.2686 302.101i −0.0860559 0.488047i −0.997124 0.0757908i \(-0.975852\pi\)
0.911068 0.412257i \(-0.135259\pi\)
\(620\) 0 0
\(621\) 76.0271 33.2723i 0.122427 0.0535786i
\(622\) 0 0
\(623\) 196.299 34.6128i 0.315087 0.0555583i
\(624\) 0 0
\(625\) −749.523 + 272.804i −1.19924 + 0.436486i
\(626\) 0 0
\(627\) 1883.33 + 640.699i 3.00372 + 1.02185i
\(628\) 0 0
\(629\) 94.3257 54.4590i 0.149961 0.0865803i
\(630\) 0 0
\(631\) 403.300 698.535i 0.639144 1.10703i −0.346477 0.938058i \(-0.612622\pi\)
0.985621 0.168971i \(-0.0540444\pi\)
\(632\) 0 0
\(633\) −349.820 + 435.275i −0.552638 + 0.687638i
\(634\) 0 0
\(635\) 491.634 + 86.6884i 0.774227 + 0.136517i
\(636\) 0 0
\(637\) 176.386 148.005i 0.276901 0.232347i
\(638\) 0 0
\(639\) −275.559 143.912i −0.431234 0.225214i
\(640\) 0 0
\(641\) 196.557 540.037i 0.306642 0.842492i −0.686664 0.726975i \(-0.740925\pi\)
0.993306 0.115516i \(-0.0368523\pi\)
\(642\) 0 0
\(643\) −499.279 418.945i −0.776484 0.651548i 0.165876 0.986147i \(-0.446955\pi\)
−0.942361 + 0.334599i \(0.891399\pi\)
\(644\) 0 0
\(645\) −235.788 + 4.98846i −0.365562 + 0.00773405i
\(646\) 0 0
\(647\) 653.900i 1.01066i −0.862925 0.505332i \(-0.831370\pi\)
0.862925 0.505332i \(-0.168630\pi\)
\(648\) 0 0
\(649\) −1344.89 −2.07225
\(650\) 0 0
\(651\) −7.90040 373.425i −0.0121358 0.573617i
\(652\) 0 0
\(653\) −691.419 + 824.001i −1.05883 + 1.26187i −0.0949693 + 0.995480i \(0.530275\pi\)
−0.963865 + 0.266390i \(0.914169\pi\)
\(654\) 0 0
\(655\) 112.423 + 40.9187i 0.171638 + 0.0624713i
\(656\) 0 0
\(657\) −201.895 317.841i −0.307298 0.483776i
\(658\) 0 0
\(659\) 624.556 + 744.317i 0.947733 + 1.12946i 0.991459 + 0.130421i \(0.0416329\pi\)
−0.0437255 + 0.999044i \(0.513923\pi\)
\(660\) 0 0
\(661\) −9.91401 + 56.2251i −0.0149985 + 0.0850607i −0.991388 0.130956i \(-0.958195\pi\)
0.976390 + 0.216017i \(0.0693065\pi\)
\(662\) 0 0
\(663\) 64.7387 + 52.0290i 0.0976452 + 0.0784751i
\(664\) 0 0
\(665\) −1105.16 638.064i −1.66189 0.959494i
\(666\) 0 0
\(667\) 37.3661 + 64.7200i 0.0560211 + 0.0970314i
\(668\) 0 0
\(669\) 52.1912 153.416i 0.0780137 0.229321i
\(670\) 0 0
\(671\) −715.419 1965.60i −1.06620 2.92936i
\(672\) 0 0
\(673\) −57.6515 326.958i −0.0856634 0.485821i −0.997211 0.0746277i \(-0.976223\pi\)
0.911548 0.411194i \(-0.134888\pi\)
\(674\) 0 0
\(675\) −1370.59 + 332.493i −2.03051 + 0.492583i
\(676\) 0 0
\(677\) 389.350 68.6529i 0.575111 0.101408i 0.121475 0.992595i \(-0.461238\pi\)
0.453636 + 0.891187i \(0.350127\pi\)
\(678\) 0 0
\(679\) 448.727 163.323i 0.660865 0.240535i
\(680\) 0 0
\(681\) 649.379 568.729i 0.953567 0.835138i
\(682\) 0 0
\(683\) 74.8054 43.1889i 0.109525 0.0632341i −0.444237 0.895909i \(-0.646525\pi\)
0.553762 + 0.832675i \(0.313192\pi\)
\(684\) 0 0
\(685\) 788.057 1364.95i 1.15045 1.99263i
\(686\) 0 0
\(687\) 654.668 + 101.207i 0.952937 + 0.147318i
\(688\) 0 0
\(689\) 528.858 + 93.2519i 0.767573 + 0.135344i
\(690\) 0 0
\(691\) 460.719 386.589i 0.666742 0.559463i −0.245357 0.969433i \(-0.578905\pi\)
0.912099 + 0.409970i \(0.134461\pi\)
\(692\) 0 0
\(693\) −291.650 706.755i −0.420851 1.01985i
\(694\) 0 0
\(695\) −347.937 + 955.949i −0.500629 + 1.37547i
\(696\) 0 0
\(697\) 64.4066 + 54.0436i 0.0924055 + 0.0775374i
\(698\) 0 0
\(699\) −585.561 + 1065.66i −0.837712 + 1.52455i
\(700\) 0 0
\(701\) 839.245i 1.19721i −0.801044 0.598606i \(-0.795722\pi\)
0.801044 0.598606i \(-0.204278\pi\)
\(702\) 0 0
\(703\) 1003.29 1.42716
\(704\) 0 0
\(705\) 237.665 144.003i 0.337113 0.204259i
\(706\) 0 0
\(707\) −224.984 + 268.126i −0.318224 + 0.379244i
\(708\) 0 0
\(709\) −500.860 182.298i −0.706432 0.257120i −0.0362774 0.999342i \(-0.511550\pi\)
−0.670155 + 0.742222i \(0.733772\pi\)
\(710\) 0 0
\(711\) −97.9529 444.627i −0.137768 0.625354i
\(712\) 0 0
\(713\) −57.0317 67.9677i −0.0799883 0.0953263i
\(714\) 0 0
\(715\) −227.686 + 1291.27i −0.318442 + 1.80598i
\(716\) 0 0
\(717\) −931.921 + 361.693i −1.29975 + 0.504453i
\(718\) 0 0
\(719\) −903.864 521.846i −1.25711 0.725794i −0.284600 0.958646i \(-0.591861\pi\)
−0.972512 + 0.232852i \(0.925194\pi\)
\(720\) 0 0
\(721\) 339.769 + 588.497i 0.471247 + 0.816224i
\(722\) 0 0
\(723\) −92.1846 + 18.2731i −0.127503 + 0.0252740i
\(724\) 0 0
\(725\) −434.375 1193.44i −0.599138 1.64612i
\(726\) 0 0
\(727\) 144.189 + 817.738i 0.198335 + 1.12481i 0.907589 + 0.419859i \(0.137921\pi\)
−0.709255 + 0.704952i \(0.750968\pi\)
\(728\) 0 0
\(729\) −723.136 + 92.2770i −0.991956 + 0.126580i
\(730\) 0 0
\(731\) 32.1967 5.67715i 0.0440448 0.00776628i
\(732\) 0 0
\(733\) −948.261 + 345.139i −1.29367 + 0.470858i −0.894930 0.446206i \(-0.852775\pi\)
−0.398741 + 0.917064i \(0.630553\pi\)
\(734\) 0 0
\(735\) −155.830 786.133i −0.212013 1.06957i
\(736\) 0 0
\(737\) −420.117 + 242.555i −0.570037 + 0.329111i
\(738\) 0 0
\(739\) −397.795 + 689.001i −0.538288 + 0.932342i 0.460708 + 0.887552i \(0.347595\pi\)
−0.998996 + 0.0447908i \(0.985738\pi\)
\(740\) 0 0
\(741\) 276.813 + 713.224i 0.373567 + 0.962515i
\(742\) 0 0
\(743\) 82.1407 + 14.4836i 0.110553 + 0.0194934i 0.228651 0.973509i \(-0.426569\pi\)
−0.118098 + 0.993002i \(0.537680\pi\)
\(744\) 0 0
\(745\) −530.381 + 445.043i −0.711921 + 0.597373i
\(746\) 0 0
\(747\) 275.963 60.7957i 0.369429 0.0813865i
\(748\) 0 0
\(749\) 89.4337 245.717i 0.119404 0.328060i
\(750\) 0 0
\(751\) 378.125 + 317.285i 0.503496 + 0.422483i 0.858833 0.512255i \(-0.171190\pi\)
−0.355338 + 0.934738i \(0.615634\pi\)
\(752\) 0 0
\(753\) 155.938 + 257.362i 0.207089 + 0.341783i
\(754\) 0 0
\(755\) 358.137i 0.474353i
\(756\) 0 0
\(757\) −488.264 −0.644998 −0.322499 0.946570i \(-0.604523\pi\)
−0.322499 + 0.946570i \(0.604523\pi\)
\(758\) 0 0
\(759\) −159.173 87.4628i −0.209714 0.115234i
\(760\) 0 0
\(761\) −54.9049 + 65.4331i −0.0721483 + 0.0859830i −0.800911 0.598783i \(-0.795651\pi\)
0.728763 + 0.684766i \(0.240096\pi\)
\(762\) 0 0
\(763\) 52.7367 + 19.1946i 0.0691176 + 0.0251567i
\(764\) 0 0
\(765\) 267.223 110.272i 0.349311 0.144147i
\(766\) 0 0
\(767\) −332.462 396.212i −0.433457 0.516574i
\(768\) 0 0
\(769\) 158.722 900.158i 0.206401 1.17056i −0.688819 0.724933i \(-0.741871\pi\)
0.895220 0.445624i \(-0.147018\pi\)
\(770\) 0 0
\(771\) 181.223 1172.25i 0.235049 1.52043i
\(772\) 0 0
\(773\) 1171.92 + 676.608i 1.51607 + 0.875301i 0.999822 + 0.0188590i \(0.00600335\pi\)
0.516243 + 0.856442i \(0.327330\pi\)
\(774\) 0 0
\(775\) 753.918 + 1305.82i 0.972798 + 1.68494i
\(776\) 0 0
\(777\) −254.052 290.078i −0.326965 0.373331i
\(778\) 0 0
\(779\) 264.885 + 727.766i 0.340032 + 0.934230i
\(780\) 0 0
\(781\) 118.141 + 670.009i 0.151268 + 0.857886i
\(782\) 0 0
\(783\) −154.765 637.966i −0.197656 0.814772i
\(784\)