Properties

Label 108.3.k.a.29.4
Level 108
Weight 3
Character 108.29
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 29.4
Character \(\chi\) \(=\) 108.29
Dual form 108.3.k.a.41.4

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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 0.930404 + 0.366536i \(0.119456\pi\)
0.199404 + 0.979917i \(0.436099\pi\)
\(6\) 0 0
\(7\) 4.05297 1.47516i 0.578995 0.210737i −0.0358873 0.999356i \(-0.511426\pi\)
0.614882 + 0.788619i \(0.289204\pi\)
\(8\) 0 0
\(9\) −8.99195 0.380648i −0.999105 0.0422943i
\(10\) 0 0
\(11\) 12.6606 15.0883i 1.15096 1.37166i 0.234219 0.972184i \(-0.424747\pi\)
0.916742 0.399479i \(-0.130809\pi\)
\(12\) 0 0
\(13\) −1.31536 7.45976i −0.101181 0.573828i −0.992677 0.120799i \(-0.961454\pi\)
0.891496 0.453029i \(-0.149657\pi\)
\(14\) 0 0
\(15\) 20.5507 16.5161i 1.37005 1.10108i
\(16\) 0 0
\(17\) −3.16520 + 1.82743i −0.186188 + 0.107496i −0.590197 0.807259i \(-0.700950\pi\)
0.404009 + 0.914755i \(0.367617\pi\)
\(18\) 0 0
\(19\) −16.8333 + 29.1562i −0.885964 + 1.53453i −0.0413596 + 0.999144i \(0.513169\pi\)
−0.844605 + 0.535391i \(0.820164\pi\)
\(20\) 0 0
\(21\) −4.16730 12.2498i −0.198443 0.583323i
\(22\) 0 0
\(23\) 1.05125 2.88830i 0.0457067 0.125578i −0.914739 0.404045i \(-0.867604\pi\)
0.960446 + 0.278467i \(0.0898262\pi\)
\(24\) 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 0.570487 0.821306i \(-0.306754\pi\)
0.255179 + 0.966894i \(0.417865\pi\)
\(30\) 0 0
\(31\) −27.1255 9.87288i −0.875016 0.318480i −0.134820 0.990870i \(-0.543045\pi\)
−0.740197 + 0.672390i \(0.765268\pi\)
\(32\) 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 0.591338 0.806424i \(-0.298600\pi\)
−0.994052 + 0.108902i \(0.965267\pi\)
\(38\) 0 0
\(39\) −22.4577 + 3.47182i −0.575839 + 0.0890211i
\(40\) 0 0
\(41\) −22.6547 + 3.99463i −0.552552 + 0.0974299i −0.442951 0.896546i \(-0.646069\pi\)
−0.109601 + 0.993976i \(0.534957\pi\)
\(42\) 0 0
\(43\) −6.85241 5.74986i −0.159358 0.133718i 0.559622 0.828748i \(-0.310946\pi\)
−0.718980 + 0.695031i \(0.755391\pi\)
\(44\) 0 0
\(45\) −48.2333 62.6865i −1.07185 1.39303i
\(46\) 0 0
\(47\) 3.60489 + 9.90435i 0.0766997 + 0.210731i 0.972117 0.234498i \(-0.0753446\pi\)
−0.895417 + 0.445229i \(0.853122\pi\)
\(48\) 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 \(0.233200\pi\)
−0.743426 + 0.668818i \(0.766800\pi\)
\(54\) 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 0.252814 0.967515i \(-0.418644\pi\)
−0.996717 + 0.0809663i \(0.974199\pi\)
\(60\) 0 0
\(61\) −99.7950 + 36.3224i −1.63598 + 0.595449i −0.986330 0.164781i \(-0.947308\pi\)
−0.649653 + 0.760231i \(0.725086\pi\)
\(62\) 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 −0.999947 0.0103194i \(-0.996715\pi\)
0.936113 0.351699i \(-0.114396\pi\)
\(68\) 0 0
\(69\) −8.59625 3.33634i −0.124583 0.0483527i
\(70\) 0 0
\(71\) 29.9139 17.2708i 0.421323 0.243251i −0.274320 0.961638i \(-0.588453\pi\)
0.695643 + 0.718387i \(0.255119\pi\)
\(72\) 0 0
\(73\) 20.9190 36.2328i 0.286562 0.496340i −0.686425 0.727201i \(-0.740821\pi\)
0.972987 + 0.230861i \(0.0741542\pi\)
\(74\) 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 −0.877368 0.479818i \(-0.840703\pi\)
0.988564 0.150804i \(-0.0481861\pi\)
\(80\) 0 0
\(81\) 80.7102 + 6.84554i 0.996422 + 0.0845129i
\(82\) 0 0
\(83\) −30.9208 5.45218i −0.372540 0.0656889i −0.0157564 0.999876i \(-0.505016\pi\)
−0.356784 + 0.934187i \(0.616127\pi\)
\(84\) 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 0.707702 0.706511i \(-0.249732\pi\)
−0.258005 + 0.966144i \(0.583065\pi\)
\(90\) 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 0.965012 0.262205i \(-0.0844497\pi\)
−0.0906489 + 0.995883i \(0.528894\pi\)
\(98\) 0 0
\(99\) −119.587 + 130.854i −1.20795 + 1.32176i
\(100\) 0 0
\(101\) −27.7555 76.2576i −0.274807 0.755026i −0.997930 0.0643070i \(-0.979516\pi\)
0.723123 0.690719i \(-0.242706\pi\)
\(102\) 0 0
\(103\) 120.693 101.273i 1.17177 0.983234i 0.171775 0.985136i \(-0.445050\pi\)
0.999998 + 0.00190171i \(0.000605335\pi\)
\(104\) 0 0
\(105\) 58.9275 97.2549i 0.561214 0.926237i
\(106\) 0 0
\(107\) 60.6265i 0.566603i 0.959031 + 0.283301i \(0.0914297\pi\)
−0.959031 + 0.283301i \(0.908570\pi\)
\(108\) 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 0.984452 0.175657i \(-0.0562048\pi\)
−0.343936 + 0.938993i \(0.611760\pi\)
\(114\) 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 −0.732270 0.681014i \(-0.761539\pi\)
0.955911 + 0.293658i \(0.0948726\pi\)
\(128\) 0 0
\(129\) −17.6805 + 20.1878i −0.137058 + 0.156494i
\(130\) 0 0
\(131\) 4.65602 12.7923i 0.0355421 0.0976511i −0.920652 0.390384i \(-0.872342\pi\)
0.956194 + 0.292733i \(0.0945646\pi\)
\(132\) 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 0.775871 0.630892i \(-0.217311\pi\)
0.513302 + 0.858208i \(0.328422\pi\)
\(138\) 0 0
\(139\) −108.775 39.5907i −0.782551 0.284825i −0.0803153 0.996770i \(-0.525593\pi\)
−0.702236 + 0.711944i \(0.747815\pi\)
\(140\) 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 −0.427823 0.903863i \(-0.640719\pi\)
−0.0928828 + 0.995677i \(0.529608\pi\)
\(150\) 0 0
\(151\) −31.2173 26.1944i −0.206737 0.173473i 0.533540 0.845775i \(-0.320861\pi\)
−0.740277 + 0.672302i \(0.765306\pi\)
\(152\) 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 −0.969187 0.246326i \(-0.920777\pi\)
0.0742864 + 0.997237i \(0.476332\pi\)
\(158\) 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 0.994263 0.106959i \(-0.0341112\pi\)
−0.277986 + 0.960585i \(0.589667\pi\)
\(168\) 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 −0.442956 0.896544i \(-0.646070\pi\)
0.959841 + 0.280543i \(0.0905145\pi\)
\(174\) 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 −0.105006 0.994472i \(-0.533486\pi\)
0.808735 + 0.588174i \(0.200153\pi\)
\(180\) 0 0
\(181\) 125.541 217.444i 0.693599 1.20135i −0.277052 0.960855i \(-0.589357\pi\)
0.970651 0.240494i \(-0.0773094\pi\)
\(182\) 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 0.0989175 0.995096i \(-0.468462\pi\)
−0.247391 + 0.968916i \(0.579573\pi\)
\(192\) 0 0
\(193\) 84.8880 + 30.8967i 0.439834 + 0.160087i 0.552439 0.833553i \(-0.313697\pi\)
−0.112605 + 0.993640i \(0.535919\pi\)
\(194\) 0 0
\(195\) −150.238 131.579i −0.770451 0.674764i
\(196\) 0 0
\(197\) 246.767 + 142.471i 1.25263 + 0.723204i 0.971630 0.236505i \(-0.0760020\pi\)
0.280996 + 0.959709i \(0.409335\pi\)
\(198\) 0 0
\(199\) 78.3479 + 135.703i 0.393708 + 0.681922i 0.992935 0.118657i \(-0.0378588\pi\)
−0.599227 + 0.800579i \(0.704525\pi\)
\(200\) 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 −0.238979 0.971025i \(-0.576813\pi\)
0.914774 + 0.403965i \(0.132368\pi\)
\(212\) 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 −0.453312 0.891352i \(-0.649758\pi\)
0.225693 + 0.974199i \(0.427536\pi\)
\(224\) 0 0
\(225\) 101.143 459.107i 0.449524 2.04047i
\(226\) 0 0
\(227\) −184.955 + 220.421i −0.814781 + 0.971018i −0.999932 0.0116918i \(-0.996278\pi\)
0.185150 + 0.982710i \(0.440723\pi\)
\(228\) 0 0
\(229\) 38.3441 + 217.460i 0.167441 + 0.949608i 0.946511 + 0.322671i \(0.104581\pi\)
−0.779070 + 0.626937i \(0.784308\pi\)
\(230\) 0 0
\(231\) −237.589 92.2119i −1.02852 0.399186i
\(232\) 0 0
\(233\) 351.012 202.657i 1.50649 0.869772i 0.506517 0.862230i \(-0.330933\pi\)
0.999972 0.00754192i \(-0.00240069\pi\)
\(234\) 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 −0.435306 0.900283i \(-0.643360\pi\)
0.912154 0.409847i \(-0.134418\pi\)
\(240\) 0 0
\(241\) 5.43972 30.8502i 0.0225714 0.128009i −0.971440 0.237286i \(-0.923742\pi\)
0.994011 + 0.109277i \(0.0348534\pi\)
\(242\) 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 0.662960 0.748655i \(-0.269300\pi\)
−0.316874 + 0.948468i \(0.602633\pi\)
\(252\) 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 −0.868512 0.495669i \(-0.834923\pi\)
−0.646605 + 0.762825i \(0.723812\pi\)
\(258\) 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 −0.957721 0.287697i \(-0.907110\pi\)
0.548729 0.836000i \(-0.315112\pi\)
\(264\) 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 \(-0.889731\pi\)
0.940594 0.339534i \(-0.110269\pi\)
\(270\) 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 −0.595738 0.803179i \(-0.703141\pi\)
0.0599111 + 0.998204i \(0.480918\pi\)
\(278\) 0 0
\(279\) 240.153 + 99.1017i 0.860764 + 0.355203i
\(280\) 0 0
\(281\) −131.821 + 157.098i −0.469113 + 0.559067i −0.947778 0.318930i \(-0.896676\pi\)
0.478665 + 0.877998i \(0.341121\pi\)
\(282\) 0 0
\(283\) 70.6906 + 400.906i 0.249790 + 1.41663i 0.809100 + 0.587671i \(0.199955\pi\)
−0.559310 + 0.828959i \(0.688934\pi\)
\(284\) 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 −0.391166 0.920320i \(-0.627928\pi\)
0.891221 0.453570i \(-0.149850\pi\)
\(294\) 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 0.771890 0.635756i \(-0.219312\pi\)
−0.936526 + 0.350598i \(0.885978\pi\)
\(308\) 0 0
\(309\) −296.093 368.423i −0.958229 1.19231i
\(310\) 0 0
\(311\) 7.38442 1.30207i 0.0237441 0.00418673i −0.161764 0.986830i \(-0.551718\pi\)
0.185508 + 0.982643i \(0.440607\pi\)
\(312\) 0 0
\(313\) 353.344 + 296.491i 1.12889 + 0.947254i 0.999019 0.0442760i \(-0.0140981\pi\)
0.129875 + 0.991530i \(0.458543\pi\)
\(314\) 0 0
\(315\) −287.960 182.914i −0.914159 0.580681i
\(316\) 0 0
\(317\) 22.7695 + 62.5587i 0.0718281 + 0.197346i 0.970412 0.241456i \(-0.0776250\pi\)
−0.898584 + 0.438802i \(0.855403\pi\)
\(318\) 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 0.0655866 0.997847i \(-0.479108\pi\)
0.691646 + 0.722237i \(0.256886\pi\)
\(332\) 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 −0.722907 0.690945i \(-0.757194\pi\)
0.442993 0.896525i \(-0.353917\pi\)
\(338\) 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 0.545452 + 0.838142i \(0.316358\pi\)
−0.956588 + 0.291445i \(0.905864\pi\)
\(348\) 0 0
\(349\) 76.3391 432.940i 0.218737 1.24052i −0.655567 0.755137i \(-0.727570\pi\)
0.874304 0.485380i \(-0.161319\pi\)
\(350\) 0 0
\(351\) 203.260 22.6700i 0.579089 0.0645868i
\(352\) 0 0
\(353\) −11.4788 2.02403i −0.0325180 0.00573380i 0.157366 0.987540i \(-0.449700\pi\)
−0.189883 + 0.981807i \(0.560811\pi\)
\(354\) 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 0.743387 0.668861i \(-0.233218\pi\)
−0.207557 + 0.978223i \(0.566551\pi\)
\(360\) 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 0.859672 0.510846i \(-0.170668\pi\)
−0.353805 + 0.935319i \(0.615112\pi\)
\(368\) 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 0.194299 0.980942i \(-0.437757\pi\)
0.999779 0.0210080i \(-0.00668756\pi\)
\(374\) 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 0.798166 0.602438i \(-0.205804\pi\)
−0.731885 + 0.681428i \(0.761359\pi\)
\(384\) 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 −0.918254 0.395992i \(-0.870401\pi\)
0.549429 + 0.835540i \(0.314845\pi\)
\(390\) 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 −0.950401 0.311027i \(-0.899327\pi\)
0.744558 + 0.667558i \(0.232660\pi\)
\(398\) 0 0
\(399\) 427.306 + 84.7019i 1.07094 + 0.212286i
\(400\) 0 0
\(401\) 98.9356 271.823i 0.246722 0.677864i −0.753079 0.657930i \(-0.771432\pi\)
0.999801 0.0199338i \(-0.00634555\pi\)
\(402\) 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 0.235810 0.971799i \(-0.424226\pi\)
−0.444020 + 0.896017i \(0.646448\pi\)
\(410\) 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 −0.870334 0.492462i \(-0.836097\pi\)
−0.649415 + 0.760434i \(0.724986\pi\)
\(420\) 0 0
\(421\) −94.6516 79.4221i −0.224826 0.188651i 0.523416 0.852077i \(-0.324657\pi\)
−0.748242 + 0.663426i \(0.769102\pi\)
\(422\) 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 \(-0.711041\pi\)
0.615487 0.788147i \(-0.288959\pi\)
\(432\) 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 −0.654723 0.755869i \(-0.727215\pi\)
−0.0156837 + 0.999877i \(0.504992\pi\)
\(440\) 0 0
\(441\) 216.822 166.831i 0.491659 0.378300i
\(442\) 0 0
\(443\) −316.952 + 377.729i −0.715467 + 0.852661i −0.994182 0.107713i \(-0.965647\pi\)
0.278715 + 0.960374i \(0.410092\pi\)
\(444\) 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 −0.876959 0.480566i \(-0.840431\pi\)
−0.0222969 + 0.999751i \(0.507098\pi\)
\(450\) 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 0.826509 + 0.562923i \(0.190323\pi\)
−0.969196 + 0.246292i \(0.920788\pi\)
\(458\) 0 0
\(459\) −43.8216 88.4175i −0.0954718 0.192631i
\(460\) 0 0
\(461\) −116.143 20.4791i −0.251937 0.0444232i 0.0462535 0.998930i \(-0.485272\pi\)
−0.298190 + 0.954507i \(0.596383\pi\)
\(462\) 0 0
\(463\) 82.8187 + 30.1435i 0.178874 + 0.0651048i 0.429905 0.902874i \(-0.358547\pi\)
−0.251030 + 0.967979i \(0.580769\pi\)
\(464\) 0 0
\(465\) −720.511 + 245.114i −1.54949 + 0.527126i
\(466\) 0 0
\(467\) 288.366 + 166.488i 0.617486 + 0.356506i 0.775890 0.630869i \(-0.217301\pi\)
−0.158403 + 0.987374i \(0.550635\pi\)
\(468\) 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 −0.994426 0.105440i \(-0.966375\pi\)
0.693999 0.719976i \(-0.255847\pi\)
\(480\) 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 0.560111 0.828418i \(-0.310758\pi\)
−0.913094 + 0.407748i \(0.866314\pi\)
\(492\) 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 0.982174 + 0.187973i \(0.0601918\pi\)
−0.858651 + 0.512560i \(0.828697\pi\)
\(500\) 0 0
\(501\) 435.162 349.729i 0.868586 0.698062i
\(502\) 0 0
\(503\) 410.636 237.081i 0.816374 0.471333i −0.0327908 0.999462i \(-0.510439\pi\)
0.849164 + 0.528129i \(0.177106\pi\)
\(504\) 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 −0.964353 0.264621i \(-0.914753\pi\)
0.908832 + 0.417163i \(0.136975\pi\)
\(510\) 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 0.889786 0.456378i \(-0.150853\pi\)
0.0496582 + 0.998766i \(0.484187\pi\)
\(522\) 0 0
\(523\) 340.114 + 589.095i 0.650314 + 1.12638i 0.983047 + 0.183356i \(0.0586960\pi\)
−0.332733 + 0.943021i \(0.607971\pi\)
\(524\) 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 −0.457052 0.889440i \(-0.651095\pi\)
0.221599 + 0.975138i \(0.428873\pi\)
\(548\) 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 0.0450671 0.998984i \(-0.485650\pi\)
0.887679 + 0.460463i \(0.152317\pi\)
\(558\) 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 −0.853952 0.520352i \(-0.825801\pi\)
0.988641 + 0.150296i \(0.0480228\pi\)
\(564\) 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 0.0657826 0.997834i \(-0.479046\pi\)
−0.279464 + 0.960156i \(0.590157\pi\)
\(570\) 0 0
\(571\) −704.732 256.501i −1.23421 0.449215i −0.359171 0.933272i \(-0.616940\pi\)
−0.875036 + 0.484057i \(0.839163\pi\)
\(572\) 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 0.851871 0.523752i \(-0.175468\pi\)
−0.879518 + 0.475866i \(0.842135\pi\)
\(578\) 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 0.897154 0.441717i \(-0.145631\pi\)
−0.971190 + 0.238304i \(0.923408\pi\)
\(588\) 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 \(-0.828981\pi\)
0.859109 0.511793i \(-0.171019\pi\)
\(594\) 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 0.606522 0.795067i \(-0.292564\pi\)
−0.888309 + 0.459246i \(0.848120\pi\)
\(600\) 0 0
\(601\) −998.384 + 363.382i −1.66120 + 0.604629i −0.990551 0.137142i \(-0.956208\pi\)
−0.670653 + 0.741771i \(0.733986\pi\)
\(602\) 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 −0.656828 0.754040i \(-0.728102\pi\)
0.359320 0.933215i \(-0.383009\pi\)
\(608\) 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 −0.594843 0.803842i \(-0.702786\pi\)
0.993569 + 0.113228i \(0.0361190\pi\)
\(614\) 0 0
\(615\) −399.594 + 456.260i −0.649746 + 0.741886i
\(616\) 0 0
\(617\) 122.120 335.523i 0.197926 0.543797i −0.800533 0.599288i \(-0.795450\pi\)
0.998459 + 0.0554913i \(0.0176725\pi\)
\(618\) 0 0
\(619\) −53.2686 + 302.101i −0.0860559 + 0.488047i 0.911068 + 0.412257i \(0.135259\pi\)
−0.997124 + 0.0757908i \(0.975852\pi\)
\(620\) 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 0.985621 + 0.168971i \(0.0540444\pi\)
−0.346477 + 0.938058i \(0.612622\pi\)
\(632\) 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 0.993306 + 0.115516i \(0.0368523\pi\)
−0.686664 + 0.726975i \(0.740925\pi\)
\(642\) 0 0
\(643\) −499.279 + 418.945i −0.776484 + 0.651548i −0.942361 0.334599i \(-0.891399\pi\)
0.165876 + 0.986147i \(0.446955\pi\)
\(644\) 0 0
\(645\) −235.788 4.98846i −0.365562 0.00773405i
\(646\) 0 0
\(647\) 653.900i 1.01066i 0.862925 + 0.505332i \(0.168630\pi\)
−0.862925 + 0.505332i \(0.831370\pi\)
\(648\) 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 −0.963865 0.266390i \(-0.914169\pi\)
−0.0949693 0.995480i \(-0.530275\pi\)
\(654\) 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 −0.0437255 0.999044i \(-0.513923\pi\)
0.991459 0.130421i \(-0.0416329\pi\)
\(660\) 0 0
\(661\) −9.91401 56.2251i −0.0149985 0.0850607i 0.976390 0.216017i \(-0.0693065\pi\)
−0.991388 + 0.130956i \(0.958195\pi\)
\(662\) 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 0.911548 + 0.411194i \(0.134888\pi\)
−0.997211 + 0.0746277i \(0.976223\pi\)
\(674\) 0 0
\(675\) −1370.59 332.493i −2.03051 0.492583i
\(676\) 0 0
\(677\) 389.350 + 68.6529i 0.575111 + 0.101408i 0.453636 0.891187i \(-0.350127\pi\)
0.121475 + 0.992595i \(0.461238\pi\)
\(678\) 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 0.553762 0.832675i \(-0.313192\pi\)
−0.444237 + 0.895909i \(0.646525\pi\)
\(684\) 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 0.912099 0.409970i \(-0.134461\pi\)
−0.245357 + 0.969433i \(0.578905\pi\)
\(692\) 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 \(0.204278\pi\)
−0.801044 + 0.598606i \(0.795722\pi\)
\(702\) 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 −0.670155 0.742222i \(-0.733772\pi\)
−0.0362774 + 0.999342i \(0.511550\pi\)
\(710\) 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 −0.972512 0.232852i \(-0.925194\pi\)
−0.284600 + 0.958646i \(0.591861\pi\)
\(720\) 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 −0.709255 0.704952i \(-0.750968\pi\)
0.907589 0.419859i \(-0.137921\pi\)
\(728\) 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 −0.398741 0.917064i \(-0.630553\pi\)
−0.894930 + 0.446206i \(0.852775\pi\)
\(734\) 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 −0.998996 0.0447908i \(-0.985738\pi\)
0.460708 0.887552i \(-0.347595\pi\)
\(740\) 0 0
\(741\) 276.813 713.224i 0.373567 0.962515i
\(742\) 0 0
\(743\) 82.1407 14.4836i 0.110553 0.0194934i −0.118098 0.993002i \(-0.537680\pi\)
0.228651 + 0.973509i \(0.426569\pi\)
\(744\) 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 −0.355338 0.934738i \(-0.615634\pi\)
0.858833 + 0.512255i \(0.171190\pi\)
\(752\) 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 0.728763 0.684766i \(-0.240096\pi\)
−0.800911 + 0.598783i \(0.795651\pi\)
\(762\) 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 0.895220 + 0.445624i \(0.147018\pi\)
−0.688819 + 0.724933i \(0.741871\pi\)
\(770\) 0 0
\(771\) 181.223 + 1172.25i 0.235049 + 1.52043i
\(772\) 0 0
\(773\) 1171.92 676.608i 1.51607 0.875301i 0.516243 0.856442i \(-0.327330\pi\)
0.999822 0.0188590i \(-0.00600335\pi\)
\(774\) 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
\(784\)