Properties

Label 441.4.e.y.361.2
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.5922408960000.19
Defining polynomial: \(x^{8} - 4 x^{7} - 54 x^{6} + 176 x^{5} + 1307 x^{4} - 2912 x^{3} - 15314 x^{2} + 16800 x + 86044\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: no (minimal twist has level 49)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(-4.23824 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.y.226.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.76556 - 3.05805i) q^{2} +(-2.23444 + 3.87016i) q^{4} +(1.03865 + 1.79899i) q^{5} -12.4689 q^{8} +O(q^{10})\) \(q+(-1.76556 - 3.05805i) q^{2} +(-2.23444 + 3.87016i) q^{4} +(1.03865 + 1.79899i) q^{5} -12.4689 q^{8} +(3.66760 - 6.35247i) q^{10} +(24.5934 - 42.5970i) q^{11} +44.8559 q^{13} +(39.8901 + 69.0916i) q^{16} +(-13.2589 + 22.9652i) q^{17} +(38.8675 + 67.3205i) q^{19} -9.28317 q^{20} -173.685 q^{22} +(27.8755 + 48.2818i) q^{23} +(60.3424 - 104.516i) q^{25} +(-79.1960 - 137.171i) q^{26} -121.436 q^{29} +(152.776 - 264.616i) q^{31} +(90.9815 - 157.585i) q^{32} +93.6380 q^{34} +(-38.5934 - 66.8457i) q^{37} +(137.246 - 237.717i) q^{38} +(-12.9508 - 22.4314i) q^{40} +248.720 q^{41} -147.179 q^{43} +(109.905 + 190.360i) q^{44} +(98.4319 - 170.489i) q^{46} +(-134.925 - 233.698i) q^{47} -426.154 q^{50} +(-100.228 + 173.599i) q^{52} +(-70.5603 + 122.214i) q^{53} +102.176 q^{55} +(214.403 + 371.356i) q^{58} +(212.417 - 367.917i) q^{59} +(-293.998 - 509.220i) q^{61} -1078.95 q^{62} -4.29373 q^{64} +(46.5895 + 80.6954i) q^{65} +(89.8171 - 155.568i) q^{67} +(-59.2525 - 102.628i) q^{68} -674.872 q^{71} +(118.744 - 205.671i) q^{73} +(-136.278 + 236.041i) q^{74} -347.388 q^{76} +(-247.926 - 429.421i) q^{79} +(-82.8636 + 143.524i) q^{80} +(-439.131 - 760.598i) q^{82} -24.4406 q^{83} -55.0855 q^{85} +(259.854 + 450.080i) q^{86} +(-306.652 + 531.136i) q^{88} +(-536.144 - 928.628i) q^{89} -249.144 q^{92} +(-476.439 + 825.216i) q^{94} +(-80.7393 + 139.845i) q^{95} -1667.43 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 34q^{4} - 132q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 34q^{4} - 132q^{8} + 100q^{11} + 174q^{16} - 680q^{22} + 352q^{23} + 128q^{25} - 520q^{29} - 30q^{32} - 212q^{37} + 1080q^{43} + 460q^{44} - 696q^{46} - 2732q^{50} + 16q^{53} + 780q^{58} - 3356q^{64} - 756q^{65} + 1944q^{67} - 4496q^{71} - 284q^{74} + 1048q^{79} - 6568q^{85} + 4820q^{86} - 1260q^{88} - 7024q^{92} + 2192q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76556 3.05805i −0.624221 1.08118i −0.988691 0.149968i \(-0.952083\pi\)
0.364470 0.931215i \(-0.381250\pi\)
\(3\) 0 0
\(4\) −2.23444 + 3.87016i −0.279304 + 0.483769i
\(5\) 1.03865 + 1.79899i 0.0928996 + 0.160907i 0.908730 0.417384i \(-0.137053\pi\)
−0.815830 + 0.578291i \(0.803720\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −12.4689 −0.551051
\(9\) 0 0
\(10\) 3.66760 6.35247i 0.115980 0.200883i
\(11\) 24.5934 42.5970i 0.674108 1.16759i −0.302621 0.953111i \(-0.597862\pi\)
0.976729 0.214478i \(-0.0688050\pi\)
\(12\) 0 0
\(13\) 44.8559 0.956983 0.478492 0.878092i \(-0.341184\pi\)
0.478492 + 0.878092i \(0.341184\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 39.8901 + 69.0916i 0.623282 + 1.07956i
\(17\) −13.2589 + 22.9652i −0.189163 + 0.327639i −0.944971 0.327153i \(-0.893911\pi\)
0.755809 + 0.654793i \(0.227244\pi\)
\(18\) 0 0
\(19\) 38.8675 + 67.3205i 0.469306 + 0.812862i 0.999384 0.0350869i \(-0.0111708\pi\)
−0.530078 + 0.847949i \(0.677837\pi\)
\(20\) −9.28317 −0.103789
\(21\) 0 0
\(22\) −173.685 −1.68317
\(23\) 27.8755 + 48.2818i 0.252715 + 0.437715i 0.964272 0.264913i \(-0.0853432\pi\)
−0.711558 + 0.702628i \(0.752010\pi\)
\(24\) 0 0
\(25\) 60.3424 104.516i 0.482739 0.836129i
\(26\) −79.1960 137.171i −0.597369 1.03467i
\(27\) 0 0
\(28\) 0 0
\(29\) −121.436 −0.777588 −0.388794 0.921325i \(-0.627108\pi\)
−0.388794 + 0.921325i \(0.627108\pi\)
\(30\) 0 0
\(31\) 152.776 264.616i 0.885143 1.53311i 0.0395940 0.999216i \(-0.487394\pi\)
0.845549 0.533897i \(-0.179273\pi\)
\(32\) 90.9815 157.585i 0.502607 0.870540i
\(33\) 0 0
\(34\) 93.6380 0.472317
\(35\) 0 0
\(36\) 0 0
\(37\) −38.5934 66.8457i −0.171479 0.297010i 0.767458 0.641099i \(-0.221521\pi\)
−0.938937 + 0.344089i \(0.888188\pi\)
\(38\) 137.246 237.717i 0.585902 1.01481i
\(39\) 0 0
\(40\) −12.9508 22.4314i −0.0511924 0.0886679i
\(41\) 248.720 0.947403 0.473702 0.880685i \(-0.342917\pi\)
0.473702 + 0.880685i \(0.342917\pi\)
\(42\) 0 0
\(43\) −147.179 −0.521967 −0.260984 0.965343i \(-0.584047\pi\)
−0.260984 + 0.965343i \(0.584047\pi\)
\(44\) 109.905 + 190.360i 0.376563 + 0.652226i
\(45\) 0 0
\(46\) 98.4319 170.489i 0.315500 0.546462i
\(47\) −134.925 233.698i −0.418742 0.725283i 0.577071 0.816694i \(-0.304196\pi\)
−0.995813 + 0.0914112i \(0.970862\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −426.154 −1.20534
\(51\) 0 0
\(52\) −100.228 + 173.599i −0.267290 + 0.462959i
\(53\) −70.5603 + 122.214i −0.182872 + 0.316743i −0.942857 0.333197i \(-0.891873\pi\)
0.759986 + 0.649940i \(0.225206\pi\)
\(54\) 0 0
\(55\) 102.176 0.250497
\(56\) 0 0
\(57\) 0 0
\(58\) 214.403 + 371.356i 0.485387 + 0.840715i
\(59\) 212.417 367.917i 0.468717 0.811842i −0.530643 0.847595i \(-0.678050\pi\)
0.999361 + 0.0357532i \(0.0113830\pi\)
\(60\) 0 0
\(61\) −293.998 509.220i −0.617092 1.06883i −0.990014 0.140972i \(-0.954977\pi\)
0.372922 0.927863i \(-0.378356\pi\)
\(62\) −1078.95 −2.21010
\(63\) 0 0
\(64\) −4.29373 −0.00838618
\(65\) 46.5895 + 80.6954i 0.0889033 + 0.153985i
\(66\) 0 0
\(67\) 89.8171 155.568i 0.163775 0.283666i −0.772445 0.635082i \(-0.780966\pi\)
0.936219 + 0.351416i \(0.114300\pi\)
\(68\) −59.2525 102.628i −0.105668 0.183022i
\(69\) 0 0
\(70\) 0 0
\(71\) −674.872 −1.12806 −0.564032 0.825753i \(-0.690750\pi\)
−0.564032 + 0.825753i \(0.690750\pi\)
\(72\) 0 0
\(73\) 118.744 205.671i 0.190383 0.329754i −0.754994 0.655732i \(-0.772360\pi\)
0.945377 + 0.325978i \(0.105694\pi\)
\(74\) −136.278 + 236.041i −0.214081 + 0.370800i
\(75\) 0 0
\(76\) −347.388 −0.524317
\(77\) 0 0
\(78\) 0 0
\(79\) −247.926 429.421i −0.353087 0.611564i 0.633702 0.773578i \(-0.281535\pi\)
−0.986789 + 0.162013i \(0.948201\pi\)
\(80\) −82.8636 + 143.524i −0.115805 + 0.200581i
\(81\) 0 0
\(82\) −439.131 760.598i −0.591389 1.02432i
\(83\) −24.4406 −0.0323217 −0.0161609 0.999869i \(-0.505144\pi\)
−0.0161609 + 0.999869i \(0.505144\pi\)
\(84\) 0 0
\(85\) −55.0855 −0.0702925
\(86\) 259.854 + 450.080i 0.325823 + 0.564342i
\(87\) 0 0
\(88\) −306.652 + 531.136i −0.371468 + 0.643402i
\(89\) −536.144 928.628i −0.638552 1.10600i −0.985751 0.168213i \(-0.946200\pi\)
0.347199 0.937792i \(-0.387133\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −249.144 −0.282337
\(93\) 0 0
\(94\) −476.439 + 825.216i −0.522776 + 0.905474i
\(95\) −80.7393 + 139.845i −0.0871966 + 0.151029i
\(96\) 0 0
\(97\) −1667.43 −1.74538 −0.872690 0.488275i \(-0.837626\pi\)
−0.872690 + 0.488275i \(0.837626\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 269.662 + 467.069i 0.269662 + 0.467069i
\(101\) 38.5593 66.7867i 0.0379881 0.0657973i −0.846406 0.532538i \(-0.821238\pi\)
0.884394 + 0.466740i \(0.154572\pi\)
\(102\) 0 0
\(103\) 82.3463 + 142.628i 0.0787749 + 0.136442i 0.902722 0.430225i \(-0.141566\pi\)
−0.823947 + 0.566667i \(0.808232\pi\)
\(104\) −559.302 −0.527347
\(105\) 0 0
\(106\) 498.315 0.456610
\(107\) 511.311 + 885.617i 0.461966 + 0.800148i 0.999059 0.0433749i \(-0.0138110\pi\)
−0.537093 + 0.843523i \(0.680478\pi\)
\(108\) 0 0
\(109\) −681.259 + 1179.97i −0.598649 + 1.03689i 0.394372 + 0.918951i \(0.370962\pi\)
−0.993021 + 0.117940i \(0.962371\pi\)
\(110\) −180.398 312.458i −0.156366 0.270833i
\(111\) 0 0
\(112\) 0 0
\(113\) 1538.41 1.28072 0.640360 0.768075i \(-0.278785\pi\)
0.640360 + 0.768075i \(0.278785\pi\)
\(114\) 0 0
\(115\) −57.9057 + 100.296i −0.0469542 + 0.0813270i
\(116\) 271.340 469.975i 0.217184 0.376174i
\(117\) 0 0
\(118\) −1500.14 −1.17033
\(119\) 0 0
\(120\) 0 0
\(121\) −544.169 942.529i −0.408842 0.708136i
\(122\) −1038.15 + 1798.12i −0.770404 + 1.33438i
\(123\) 0 0
\(124\) 682.738 + 1182.54i 0.494449 + 0.856411i
\(125\) 510.360 0.365184
\(126\) 0 0
\(127\) −170.358 −0.119030 −0.0595151 0.998227i \(-0.518955\pi\)
−0.0595151 + 0.998227i \(0.518955\pi\)
\(128\) −720.271 1247.55i −0.497372 0.861473i
\(129\) 0 0
\(130\) 164.514 284.946i 0.110991 0.192242i
\(131\) 375.968 + 651.195i 0.250751 + 0.434314i 0.963733 0.266869i \(-0.0859890\pi\)
−0.712981 + 0.701183i \(0.752656\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −634.312 −0.408927
\(135\) 0 0
\(136\) 165.324 286.350i 0.104238 0.180546i
\(137\) 259.311 449.140i 0.161711 0.280092i −0.773771 0.633465i \(-0.781632\pi\)
0.935483 + 0.353373i \(0.114965\pi\)
\(138\) 0 0
\(139\) 2975.72 1.81581 0.907905 0.419177i \(-0.137681\pi\)
0.907905 + 0.419177i \(0.137681\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1191.53 + 2063.79i 0.704161 + 1.21964i
\(143\) 1103.16 1910.73i 0.645110 1.11736i
\(144\) 0 0
\(145\) −126.129 218.462i −0.0722376 0.125119i
\(146\) −838.604 −0.475365
\(147\) 0 0
\(148\) 344.938 0.191579
\(149\) −1358.97 2353.80i −0.747188 1.29417i −0.949165 0.314778i \(-0.898070\pi\)
0.201977 0.979390i \(-0.435263\pi\)
\(150\) 0 0
\(151\) −353.825 + 612.843i −0.190688 + 0.330281i −0.945478 0.325685i \(-0.894405\pi\)
0.754791 + 0.655966i \(0.227738\pi\)
\(152\) −484.634 839.410i −0.258612 0.447929i
\(153\) 0 0
\(154\) 0 0
\(155\) 634.724 0.328918
\(156\) 0 0
\(157\) 1558.96 2700.19i 0.792473 1.37260i −0.131958 0.991255i \(-0.542126\pi\)
0.924431 0.381349i \(-0.124540\pi\)
\(158\) −875.459 + 1516.34i −0.440809 + 0.763503i
\(159\) 0 0
\(160\) 377.991 0.186768
\(161\) 0 0
\(162\) 0 0
\(163\) −904.387 1566.44i −0.434583 0.752720i 0.562678 0.826676i \(-0.309771\pi\)
−0.997262 + 0.0739557i \(0.976438\pi\)
\(164\) −555.749 + 962.585i −0.264614 + 0.458325i
\(165\) 0 0
\(166\) 43.1514 + 74.7404i 0.0201759 + 0.0349457i
\(167\) 3147.38 1.45839 0.729197 0.684303i \(-0.239894\pi\)
0.729197 + 0.684303i \(0.239894\pi\)
\(168\) 0 0
\(169\) −184.949 −0.0841827
\(170\) 97.2570 + 168.454i 0.0438781 + 0.0759991i
\(171\) 0 0
\(172\) 328.862 569.606i 0.145788 0.252512i
\(173\) 1642.18 + 2844.34i 0.721691 + 1.25001i 0.960322 + 0.278895i \(0.0899681\pi\)
−0.238631 + 0.971110i \(0.576699\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3924.13 1.68064
\(177\) 0 0
\(178\) −1893.19 + 3279.11i −0.797196 + 1.38078i
\(179\) 1399.41 2423.85i 0.584341 1.01211i −0.410616 0.911808i \(-0.634686\pi\)
0.994957 0.100300i \(-0.0319802\pi\)
\(180\) 0 0
\(181\) 3723.04 1.52890 0.764451 0.644682i \(-0.223010\pi\)
0.764451 + 0.644682i \(0.223010\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −347.576 602.019i −0.139259 0.241203i
\(185\) 80.1699 138.858i 0.0318606 0.0551842i
\(186\) 0 0
\(187\) 652.164 + 1129.58i 0.255032 + 0.441728i
\(188\) 1205.93 0.467826
\(189\) 0 0
\(190\) 570.202 0.217720
\(191\) 479.825 + 831.081i 0.181774 + 0.314842i 0.942485 0.334249i \(-0.108483\pi\)
−0.760710 + 0.649091i \(0.775149\pi\)
\(192\) 0 0
\(193\) 1895.12 3282.45i 0.706808 1.22423i −0.259227 0.965816i \(-0.583468\pi\)
0.966035 0.258411i \(-0.0831988\pi\)
\(194\) 2943.95 + 5099.08i 1.08950 + 1.88707i
\(195\) 0 0
\(196\) 0 0
\(197\) −5117.99 −1.85097 −0.925487 0.378779i \(-0.876344\pi\)
−0.925487 + 0.378779i \(0.876344\pi\)
\(198\) 0 0
\(199\) 432.427 748.986i 0.154040 0.266805i −0.778669 0.627435i \(-0.784105\pi\)
0.932709 + 0.360630i \(0.117438\pi\)
\(200\) −752.402 + 1303.20i −0.266014 + 0.460750i
\(201\) 0 0
\(202\) −272.316 −0.0948519
\(203\) 0 0
\(204\) 0 0
\(205\) 258.333 + 447.445i 0.0880134 + 0.152444i
\(206\) 290.775 503.637i 0.0983460 0.170340i
\(207\) 0 0
\(208\) 1789.30 + 3099.17i 0.596471 + 1.03312i
\(209\) 3823.53 1.26545
\(210\) 0 0
\(211\) −1344.61 −0.438707 −0.219353 0.975645i \(-0.570395\pi\)
−0.219353 + 0.975645i \(0.570395\pi\)
\(212\) −315.325 546.159i −0.102154 0.176936i
\(213\) 0 0
\(214\) 1805.51 3127.23i 0.576738 0.998939i
\(215\) −152.867 264.774i −0.0484905 0.0839881i
\(216\) 0 0
\(217\) 0 0
\(218\) 4811.23 1.49476
\(219\) 0 0
\(220\) −228.305 + 395.435i −0.0699650 + 0.121183i
\(221\) −594.741 + 1030.12i −0.181026 + 0.313545i
\(222\) 0 0
\(223\) 864.916 0.259727 0.129863 0.991532i \(-0.458546\pi\)
0.129863 + 0.991532i \(0.458546\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2716.16 4704.53i −0.799452 1.38469i
\(227\) −857.672 + 1485.53i −0.250774 + 0.434353i −0.963739 0.266846i \(-0.914018\pi\)
0.712965 + 0.701200i \(0.247352\pi\)
\(228\) 0 0
\(229\) 522.729 + 905.394i 0.150842 + 0.261267i 0.931537 0.363646i \(-0.118468\pi\)
−0.780695 + 0.624912i \(0.785135\pi\)
\(230\) 408.945 0.117239
\(231\) 0 0
\(232\) 1514.17 0.428491
\(233\) 724.335 + 1254.58i 0.203660 + 0.352749i 0.949705 0.313146i \(-0.101383\pi\)
−0.746045 + 0.665895i \(0.768050\pi\)
\(234\) 0 0
\(235\) 280.280 485.459i 0.0778019 0.134757i
\(236\) 949.263 + 1644.17i 0.261830 + 0.453502i
\(237\) 0 0
\(238\) 0 0
\(239\) 3153.12 0.853383 0.426691 0.904397i \(-0.359679\pi\)
0.426691 + 0.904397i \(0.359679\pi\)
\(240\) 0 0
\(241\) 190.506 329.966i 0.0509194 0.0881950i −0.839442 0.543449i \(-0.817118\pi\)
0.890362 + 0.455254i \(0.150451\pi\)
\(242\) −1921.53 + 3328.19i −0.510416 + 0.884067i
\(243\) 0 0
\(244\) 2627.68 0.689426
\(245\) 0 0
\(246\) 0 0
\(247\) 1743.44 + 3019.72i 0.449118 + 0.777895i
\(248\) −1904.95 + 3299.47i −0.487759 + 0.844824i
\(249\) 0 0
\(250\) −901.074 1560.71i −0.227956 0.394831i
\(251\) −3776.23 −0.949617 −0.474808 0.880089i \(-0.657483\pi\)
−0.474808 + 0.880089i \(0.657483\pi\)
\(252\) 0 0
\(253\) 2742.21 0.681428
\(254\) 300.778 + 520.963i 0.0743012 + 0.128693i
\(255\) 0 0
\(256\) −2560.55 + 4435.00i −0.625133 + 1.08276i
\(257\) 2129.21 + 3687.90i 0.516795 + 0.895116i 0.999810 + 0.0195034i \(0.00620851\pi\)
−0.483014 + 0.875612i \(0.660458\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −416.405 −0.0993244
\(261\) 0 0
\(262\) 1327.59 2299.45i 0.313049 0.542216i
\(263\) 2099.41 3636.29i 0.492226 0.852560i −0.507734 0.861514i \(-0.669517\pi\)
0.999960 + 0.00895400i \(0.00285018\pi\)
\(264\) 0 0
\(265\) −293.150 −0.0679548
\(266\) 0 0
\(267\) 0 0
\(268\) 401.381 + 695.212i 0.0914860 + 0.158458i
\(269\) 1870.29 3239.44i 0.423917 0.734247i −0.572401 0.819974i \(-0.693988\pi\)
0.996319 + 0.0857271i \(0.0273213\pi\)
\(270\) 0 0
\(271\) −2178.15 3772.66i −0.488240 0.845656i 0.511669 0.859183i \(-0.329028\pi\)
−0.999909 + 0.0135265i \(0.995694\pi\)
\(272\) −2115.60 −0.471607
\(273\) 0 0
\(274\) −1831.32 −0.403775
\(275\) −2968.05 5140.81i −0.650837 1.12728i
\(276\) 0 0
\(277\) 672.152 1164.20i 0.145797 0.252527i −0.783873 0.620921i \(-0.786759\pi\)
0.929670 + 0.368394i \(0.120092\pi\)
\(278\) −5253.83 9099.90i −1.13347 1.96322i
\(279\) 0 0
\(280\) 0 0
\(281\) −4205.54 −0.892817 −0.446408 0.894829i \(-0.647297\pi\)
−0.446408 + 0.894829i \(0.647297\pi\)
\(282\) 0 0
\(283\) −2376.02 + 4115.38i −0.499079 + 0.864431i −0.999999 0.00106280i \(-0.999662\pi\)
0.500920 + 0.865494i \(0.332995\pi\)
\(284\) 1507.96 2611.86i 0.315073 0.545723i
\(285\) 0 0
\(286\) −7790.79 −1.61077
\(287\) 0 0
\(288\) 0 0
\(289\) 2104.90 + 3645.80i 0.428435 + 0.742071i
\(290\) −445.378 + 771.418i −0.0901845 + 0.156204i
\(291\) 0 0
\(292\) 530.654 + 919.119i 0.106350 + 0.184203i
\(293\) 4961.17 0.989196 0.494598 0.869122i \(-0.335315\pi\)
0.494598 + 0.869122i \(0.335315\pi\)
\(294\) 0 0
\(295\) 882.506 0.174174
\(296\) 481.216 + 833.490i 0.0944936 + 0.163668i
\(297\) 0 0
\(298\) −4798.69 + 8311.58i −0.932822 + 1.61569i
\(299\) 1250.38 + 2165.72i 0.241844 + 0.418886i
\(300\) 0 0
\(301\) 0 0
\(302\) 2498.80 0.476126
\(303\) 0 0
\(304\) −3100.85 + 5370.84i −0.585020 + 1.01329i
\(305\) 610.722 1057.80i 0.114655 0.198589i
\(306\) 0 0
\(307\) −4234.00 −0.787124 −0.393562 0.919298i \(-0.628757\pi\)
−0.393562 + 0.919298i \(0.628757\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1120.65 1941.02i −0.205317 0.355620i
\(311\) −342.350 + 592.968i −0.0624209 + 0.108116i −0.895547 0.444967i \(-0.853215\pi\)
0.833126 + 0.553083i \(0.186549\pi\)
\(312\) 0 0
\(313\) 2972.04 + 5147.72i 0.536707 + 0.929604i 0.999079 + 0.0429180i \(0.0136654\pi\)
−0.462371 + 0.886686i \(0.653001\pi\)
\(314\) −11009.8 −1.97872
\(315\) 0 0
\(316\) 2215.90 0.394475
\(317\) −1411.95 2445.56i −0.250166 0.433301i 0.713405 0.700752i \(-0.247152\pi\)
−0.963571 + 0.267451i \(0.913819\pi\)
\(318\) 0 0
\(319\) −2986.52 + 5172.80i −0.524178 + 0.907904i
\(320\) −4.45967 7.72438i −0.000779073 0.00134939i
\(321\) 0 0
\(322\) 0 0
\(323\) −2061.37 −0.355101
\(324\) 0 0
\(325\) 2706.71 4688.16i 0.461974 0.800162i
\(326\) −3193.51 + 5531.32i −0.542552 + 0.939728i
\(327\) 0 0
\(328\) −3101.26 −0.522068
\(329\) 0 0
\(330\) 0 0
\(331\) 1406.48 + 2436.10i 0.233557 + 0.404533i 0.958852 0.283905i \(-0.0916301\pi\)
−0.725295 + 0.688438i \(0.758297\pi\)
\(332\) 54.6109 94.5888i 0.00902760 0.0156363i
\(333\) 0 0
\(334\) −5556.91 9624.85i −0.910361 1.57679i
\(335\) 373.154 0.0608584
\(336\) 0 0
\(337\) 4260.10 0.688612 0.344306 0.938857i \(-0.388114\pi\)
0.344306 + 0.938857i \(0.388114\pi\)
\(338\) 326.540 + 565.584i 0.0525486 + 0.0910169i
\(339\) 0 0
\(340\) 123.085 213.190i 0.0196330 0.0340054i
\(341\) −7514.58 13015.6i −1.19336 2.06697i
\(342\) 0 0
\(343\) 0 0
\(344\) 1835.16 0.287631
\(345\) 0 0
\(346\) 5798.74 10043.7i 0.900990 1.56056i
\(347\) 18.0292 31.2275i 0.00278922 0.00483106i −0.864627 0.502414i \(-0.832445\pi\)
0.867417 + 0.497583i \(0.165779\pi\)
\(348\) 0 0
\(349\) −242.692 −0.0372236 −0.0186118 0.999827i \(-0.505925\pi\)
−0.0186118 + 0.999827i \(0.505925\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4475.09 7751.08i −0.677622 1.17368i
\(353\) −54.9949 + 95.2539i −0.00829201 + 0.0143622i −0.870142 0.492802i \(-0.835973\pi\)
0.861850 + 0.507164i \(0.169306\pi\)
\(354\) 0 0
\(355\) −700.955 1214.09i −0.104797 0.181513i
\(356\) 4791.92 0.713402
\(357\) 0 0
\(358\) −9883.01 −1.45903
\(359\) 6202.23 + 10742.6i 0.911814 + 1.57931i 0.811500 + 0.584352i \(0.198651\pi\)
0.100314 + 0.994956i \(0.468015\pi\)
\(360\) 0 0
\(361\) 408.136 706.913i 0.0595038 0.103064i
\(362\) −6573.26 11385.2i −0.954373 1.65302i
\(363\) 0 0
\(364\) 0 0
\(365\) 493.335 0.0707461
\(366\) 0 0
\(367\) −6929.81 + 12002.8i −0.985649 + 1.70719i −0.346634 + 0.938001i \(0.612675\pi\)
−0.639015 + 0.769194i \(0.720658\pi\)
\(368\) −2223.91 + 3851.93i −0.315025 + 0.545640i
\(369\) 0 0
\(370\) −566.181 −0.0795523
\(371\) 0 0
\(372\) 0 0
\(373\) −2449.03 4241.85i −0.339963 0.588832i 0.644463 0.764636i \(-0.277081\pi\)
−0.984425 + 0.175803i \(0.943748\pi\)
\(374\) 2302.88 3988.70i 0.318393 0.551472i
\(375\) 0 0
\(376\) 1682.37 + 2913.94i 0.230748 + 0.399668i
\(377\) −5447.11 −0.744139
\(378\) 0 0
\(379\) −9806.25 −1.32906 −0.664530 0.747262i \(-0.731368\pi\)
−0.664530 + 0.747262i \(0.731368\pi\)
\(380\) −360.814 624.948i −0.0487088 0.0843662i
\(381\) 0 0
\(382\) 1694.32 2934.65i 0.226935 0.393063i
\(383\) 5364.84 + 9292.18i 0.715746 + 1.23971i 0.962671 + 0.270673i \(0.0872463\pi\)
−0.246926 + 0.969034i \(0.579420\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −13383.8 −1.76482
\(387\) 0 0
\(388\) 3725.76 6453.21i 0.487492 0.844361i
\(389\) 2632.03 4558.80i 0.343057 0.594191i −0.641942 0.766753i \(-0.721871\pi\)
0.984999 + 0.172562i \(0.0552044\pi\)
\(390\) 0 0
\(391\) −1478.40 −0.191217
\(392\) 0 0
\(393\) 0 0
\(394\) 9036.15 + 15651.1i 1.15542 + 2.00124i
\(395\) 515.016 892.034i 0.0656032 0.113628i
\(396\) 0 0
\(397\) −607.450 1052.13i −0.0767935 0.133010i 0.825071 0.565029i \(-0.191135\pi\)
−0.901865 + 0.432018i \(0.857802\pi\)
\(398\) −3053.91 −0.384620
\(399\) 0 0
\(400\) 9628.26 1.20353
\(401\) 1147.73 + 1987.92i 0.142929 + 0.247561i 0.928599 0.371086i \(-0.121014\pi\)
−0.785669 + 0.618647i \(0.787681\pi\)
\(402\) 0 0
\(403\) 6852.92 11869.6i 0.847067 1.46716i
\(404\) 172.317 + 298.461i 0.0212205 + 0.0367550i
\(405\) 0 0
\(406\) 0 0
\(407\) −3796.57 −0.462381
\(408\) 0 0
\(409\) −2323.27 + 4024.03i −0.280876 + 0.486492i −0.971601 0.236626i \(-0.923958\pi\)
0.690724 + 0.723118i \(0.257292\pi\)
\(410\) 912.206 1579.99i 0.109880 0.190317i
\(411\) 0 0
\(412\) −735.990 −0.0880087
\(413\) 0 0
\(414\) 0 0
\(415\) −25.3852 43.9684i −0.00300267 0.00520078i
\(416\) 4081.06 7068.60i 0.480986 0.833093i
\(417\) 0 0
\(418\) −6750.69 11692.5i −0.789922 1.36818i
\(419\) −7541.24 −0.879269 −0.439634 0.898177i \(-0.644892\pi\)
−0.439634 + 0.898177i \(0.644892\pi\)
\(420\) 0 0
\(421\) −6243.63 −0.722794 −0.361397 0.932412i \(-0.617700\pi\)
−0.361397 + 0.932412i \(0.617700\pi\)
\(422\) 2374.00 + 4111.90i 0.273850 + 0.474322i
\(423\) 0 0
\(424\) 879.808 1523.87i 0.100772 0.174542i
\(425\) 1600.15 + 2771.55i 0.182632 + 0.316329i
\(426\) 0 0
\(427\) 0 0
\(428\) −4569.97 −0.516116
\(429\) 0 0
\(430\) −539.794 + 934.951i −0.0605376 + 0.104854i
\(431\) 5732.90 9929.68i 0.640706 1.10974i −0.344570 0.938761i \(-0.611975\pi\)
0.985275 0.170974i \(-0.0546915\pi\)
\(432\) 0 0
\(433\) 5156.40 0.572289 0.286144 0.958187i \(-0.407626\pi\)
0.286144 + 0.958187i \(0.407626\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3044.46 5273.16i −0.334411 0.579216i
\(437\) −2166.90 + 3753.18i −0.237201 + 0.410844i
\(438\) 0 0
\(439\) 2532.12 + 4385.77i 0.275289 + 0.476814i 0.970208 0.242274i \(-0.0778932\pi\)
−0.694919 + 0.719088i \(0.744560\pi\)
\(440\) −1274.01 −0.138037
\(441\) 0 0
\(442\) 4200.22 0.452000
\(443\) 6351.82 + 11001.7i 0.681228 + 1.17992i 0.974606 + 0.223925i \(0.0718871\pi\)
−0.293378 + 0.955996i \(0.594780\pi\)
\(444\) 0 0
\(445\) 1113.73 1929.04i 0.118642 0.205495i
\(446\) −1527.06 2644.95i −0.162127 0.280812i
\(447\) 0 0
\(448\) 0 0
\(449\) −13942.2 −1.46542 −0.732709 0.680542i \(-0.761744\pi\)
−0.732709 + 0.680542i \(0.761744\pi\)
\(450\) 0 0
\(451\) 6116.87 10594.7i 0.638652 1.10618i
\(452\) −3437.48 + 5953.88i −0.357711 + 0.619573i
\(453\) 0 0
\(454\) 6057.10 0.626154
\(455\) 0 0
\(456\) 0 0
\(457\) 7607.01 + 13175.7i 0.778646 + 1.34865i 0.932722 + 0.360595i \(0.117426\pi\)
−0.154077 + 0.988059i \(0.549240\pi\)
\(458\) 1845.82 3197.06i 0.188318 0.326177i
\(459\) 0 0
\(460\) −258.773 448.208i −0.0262290 0.0454300i
\(461\) 11430.2 1.15479 0.577394 0.816465i \(-0.304070\pi\)
0.577394 + 0.816465i \(0.304070\pi\)
\(462\) 0 0
\(463\) −9347.88 −0.938300 −0.469150 0.883119i \(-0.655440\pi\)
−0.469150 + 0.883119i \(0.655440\pi\)
\(464\) −4844.08 8390.20i −0.484657 0.839451i
\(465\) 0 0
\(466\) 2557.72 4430.10i 0.254258 0.440387i
\(467\) 1815.42 + 3144.40i 0.179888 + 0.311575i 0.941842 0.336056i \(-0.109093\pi\)
−0.761954 + 0.647631i \(0.775760\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1979.41 −0.194262
\(471\) 0 0
\(472\) −2648.60 + 4587.51i −0.258287 + 0.447367i
\(473\) −3619.63 + 6269.38i −0.351862 + 0.609443i
\(474\) 0 0
\(475\) 9381.43 0.906210
\(476\) 0 0
\(477\) 0 0
\(478\) −5567.04 9642.39i −0.532700 0.922663i
\(479\) 3260.62 5647.57i 0.311027 0.538714i −0.667558 0.744557i \(-0.732661\pi\)
0.978585 + 0.205844i \(0.0659939\pi\)
\(480\) 0 0
\(481\) −1731.14 2998.42i −0.164102 0.284234i
\(482\) −1345.40 −0.127140
\(483\) 0 0
\(484\) 4863.65 0.456766
\(485\) −1731.87 2999.69i −0.162145 0.280843i
\(486\) 0 0
\(487\) 1833.14 3175.10i 0.170570 0.295436i −0.768049 0.640391i \(-0.778772\pi\)
0.938619 + 0.344955i \(0.112106\pi\)
\(488\) 3665.83 + 6349.40i 0.340049 + 0.588983i
\(489\) 0 0
\(490\) 0 0
\(491\) 12470.7 1.14623 0.573113 0.819476i \(-0.305736\pi\)
0.573113 + 0.819476i \(0.305736\pi\)
\(492\) 0 0
\(493\) 1610.11 2788.79i 0.147091 0.254768i
\(494\) 6156.30 10663.0i 0.560698 0.971158i
\(495\) 0 0
\(496\) 24377.0 2.20678
\(497\) 0 0
\(498\) 0 0
\(499\) 1151.97 + 1995.26i 0.103345 + 0.178998i 0.913061 0.407824i \(-0.133712\pi\)
−0.809716 + 0.586822i \(0.800379\pi\)
\(500\) −1140.37 + 1975.17i −0.101998 + 0.176665i
\(501\) 0 0
\(502\) 6667.18 + 11547.9i 0.592771 + 1.02671i
\(503\) 10520.4 0.932570 0.466285 0.884635i \(-0.345592\pi\)
0.466285 + 0.884635i \(0.345592\pi\)
\(504\) 0 0
\(505\) 160.198 0.0141163
\(506\) −4841.55 8385.81i −0.425362 0.736748i
\(507\) 0 0
\(508\) 380.654 659.312i 0.0332457 0.0575832i
\(509\) −4831.11 8367.73i −0.420698 0.728670i 0.575310 0.817935i \(-0.304881\pi\)
−0.996008 + 0.0892655i \(0.971548\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 6558.89 0.566142
\(513\) 0 0
\(514\) 7518.51 13022.4i 0.645189 1.11750i
\(515\) −171.058 + 296.281i −0.0146363 + 0.0253508i
\(516\) 0 0
\(517\) −13273.1 −1.12911
\(518\) 0 0
\(519\) 0 0
\(520\) −580.919 1006.18i −0.0489903 0.0848537i
\(521\) 4303.90 7454.58i 0.361914 0.626854i −0.626361 0.779533i \(-0.715457\pi\)
0.988276 + 0.152679i \(0.0487899\pi\)
\(522\) 0 0
\(523\) 5241.36 + 9078.30i 0.438219 + 0.759018i 0.997552 0.0699250i \(-0.0222760\pi\)
−0.559333 + 0.828943i \(0.688943\pi\)
\(524\) −3360.30 −0.280144
\(525\) 0 0
\(526\) −14826.6 −1.22903
\(527\) 4051.30 + 7017.06i 0.334872 + 0.580015i
\(528\) 0 0
\(529\) 4529.41 7845.18i 0.372270 0.644791i
\(530\) 517.574 + 896.465i 0.0424189 + 0.0734716i
\(531\) 0 0
\(532\) 0 0
\(533\) 11156.6 0.906649
\(534\) 0 0
\(535\) −1062.15 + 1839.69i −0.0858328 + 0.148667i
\(536\) −1119.92 + 1939.75i −0.0902483 + 0.156315i
\(537\) 0 0
\(538\) −13208.5 −1.05847
\(539\) 0 0
\(540\) 0 0
\(541\) −10361.3 17946.3i −0.823416 1.42620i −0.903124 0.429380i \(-0.858732\pi\)
0.0797082 0.996818i \(-0.474601\pi\)
\(542\) −7691.32 + 13321.8i −0.609540 + 1.05575i
\(543\) 0 0
\(544\) 2412.64 + 4178.81i 0.190149 + 0.329347i
\(545\) −2830.35 −0.222457
\(546\) 0 0
\(547\) −4175.09 −0.326351 −0.163176 0.986597i \(-0.552174\pi\)
−0.163176 + 0.986597i \(0.552174\pi\)
\(548\) 1158.83 + 2007.15i 0.0903334 + 0.156462i
\(549\) 0 0
\(550\) −10480.6 + 18152.9i −0.812532 + 1.40735i
\(551\) −4719.91 8175.12i −0.364927 0.632072i
\(552\) 0 0
\(553\) 0 0
\(554\) −4746.91 −0.364038
\(555\) 0 0
\(556\) −6649.06 + 11516.5i −0.507164 + 0.878433i
\(557\) −5080.87 + 8800.33i −0.386505 + 0.669447i −0.991977 0.126420i \(-0.959651\pi\)
0.605472 + 0.795867i \(0.292985\pi\)
\(558\) 0 0
\(559\) −6601.85 −0.499514
\(560\) 0 0
\(561\) 0 0
\(562\) 7425.15 + 12860.7i 0.557315 + 0.965298i
\(563\) −8552.22 + 14812.9i −0.640201 + 1.10886i 0.345187 + 0.938534i \(0.387816\pi\)
−0.985388 + 0.170326i \(0.945518\pi\)
\(564\) 0 0
\(565\) 1597.87 + 2767.59i 0.118978 + 0.206076i
\(566\) 16780.0 1.24614
\(567\) 0 0
\(568\) 8414.89 0.621621
\(569\) −9128.79 15811.5i −0.672581 1.16495i −0.977170 0.212461i \(-0.931852\pi\)
0.304588 0.952484i \(-0.401481\pi\)
\(570\) 0 0
\(571\) −6815.25 + 11804.4i −0.499491 + 0.865143i −1.00000 0.000587868i \(-0.999813\pi\)
0.500509 + 0.865731i \(0.333146\pi\)
\(572\) 4929.87 + 8538.79i 0.360364 + 0.624169i
\(573\) 0 0
\(574\) 0 0
\(575\) 6728.30 0.487981
\(576\) 0 0
\(577\) −2221.04 + 3846.96i −0.160248 + 0.277558i −0.934958 0.354759i \(-0.884563\pi\)
0.774709 + 0.632317i \(0.217896\pi\)
\(578\) 7432.68 12873.8i 0.534877 0.926433i
\(579\) 0 0
\(580\) 1127.31 0.0807052
\(581\) 0 0
\(582\) 0 0
\(583\) 3470.63 + 6011.32i 0.246551 + 0.427038i
\(584\) −1480.61 + 2564.49i −0.104911 + 0.181711i
\(585\) 0 0
\(586\) −8759.26 15171.5i −0.617477 1.06950i
\(587\) −3103.38 −0.218211 −0.109106 0.994030i \(-0.534799\pi\)
−0.109106 + 0.994030i \(0.534799\pi\)
\(588\) 0 0
\(589\) 23752.1 1.66161
\(590\) −1558.12 2698.74i −0.108723 0.188314i
\(591\) 0 0
\(592\) 3078.99 5332.96i 0.213759 0.370242i
\(593\) 2968.86 + 5142.21i 0.205592 + 0.356096i 0.950321 0.311271i \(-0.100755\pi\)
−0.744729 + 0.667367i \(0.767421\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 12146.1 0.834772
\(597\) 0 0
\(598\) 4415.25 7647.44i 0.301928 0.522955i
\(599\) −1300.16 + 2251.95i −0.0886866 + 0.153610i −0.906956 0.421225i \(-0.861600\pi\)
0.818270 + 0.574835i \(0.194934\pi\)
\(600\) 0 0
\(601\) −13881.4 −0.942156 −0.471078 0.882092i \(-0.656135\pi\)
−0.471078 + 0.882092i \(0.656135\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1581.20 2738.71i −0.106520 0.184498i
\(605\) 1130.40 1957.91i 0.0759626 0.131571i
\(606\) 0 0
\(607\) 6142.28 + 10638.7i 0.410721 + 0.711389i 0.994969 0.100186i \(-0.0319438\pi\)
−0.584248 + 0.811575i \(0.698610\pi\)
\(608\) 14144.9 0.943505
\(609\) 0 0
\(610\) −4313.07 −0.286281
\(611\) −6052.20 10482.7i −0.400729 0.694084i
\(612\) 0 0
\(613\) −11031.0 + 19106.2i −0.726815 + 1.25888i 0.231408 + 0.972857i \(0.425667\pi\)
−0.958223 + 0.286023i \(0.907666\pi\)
\(614\) 7475.40 + 12947.8i 0.491340 + 0.851025i
\(615\) 0 0
\(616\) 0 0
\(617\) 12182.2 0.794871 0.397436 0.917630i \(-0.369900\pi\)
0.397436 + 0.917630i \(0.369900\pi\)
\(618\) 0 0
\(619\) −11624.3 + 20133.9i −0.754799 + 1.30735i 0.190675 + 0.981653i \(0.438932\pi\)
−0.945474 + 0.325698i \(0.894401\pi\)
\(620\) −1418.25 + 2456.48i −0.0918682 + 0.159120i
\(621\) 0 0
\(622\) 2417.76 0.155858
\(623\) 0 0
\(624\) 0 0
\(625\) −7012.72 12146.4i −0.448814 0.777368i
\(626\) 10494.6 18177.3i 0.670048 1.16056i
\(627\) 0 0
\(628\) 6966.78 + 12066.8i 0.442683 + 0.766749i
\(629\) 2046.83 0.129749
\(630\) 0 0
\(631\) 19184.4 1.21033 0.605165 0.796100i \(-0.293107\pi\)
0.605165 + 0.796100i \(0.293107\pi\)
\(632\) 3091.36 + 5354.39i 0.194569 + 0.337004i
\(633\) 0 0
\(634\) −4985.76 + 8635.59i −0.312318 + 0.540951i
\(635\) −176.942 306.473i −0.0110579 0.0191528i
\(636\) 0 0
\(637\) 0 0
\(638\) 21091.6 1.30881
\(639\) 0 0
\(640\) 1496.22 2591.53i 0.0924113 0.160061i
\(641\) −9716.68 + 16829.8i −0.598730 + 1.03703i 0.394279 + 0.918991i \(0.370994\pi\)
−0.993009 + 0.118040i \(0.962339\pi\)
\(642\) 0 0
\(643\) 5777.47 0.354341 0.177170 0.984180i \(-0.443306\pi\)
0.177170 + 0.984180i \(0.443306\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3639.48 + 6303.76i 0.221661 + 0.383929i
\(647\) −14615.7 + 25315.2i −0.888106 + 1.53824i −0.0459932 + 0.998942i \(0.514645\pi\)
−0.842112 + 0.539302i \(0.818688\pi\)
\(648\) 0 0
\(649\) −10448.1 18096.6i −0.631932 1.09454i
\(650\) −19115.5 −1.15349
\(651\) 0 0
\(652\) 8083.18 0.485524
\(653\) −3546.63 6142.95i −0.212543 0.368135i 0.739967 0.672643i \(-0.234841\pi\)
−0.952510 + 0.304508i \(0.901508\pi\)
\(654\) 0 0
\(655\) −780.997 + 1352.73i −0.0465894 + 0.0806952i
\(656\) 9921.46 + 17184.5i 0.590500 + 1.02278i
\(657\) 0 0
\(658\) 0 0
\(659\) −19014.2 −1.12396 −0.561980 0.827151i \(-0.689960\pi\)
−0.561980 + 0.827151i \(0.689960\pi\)
\(660\) 0 0
\(661\) 10529.2 18237.1i 0.619573 1.07313i −0.369990 0.929036i \(-0.620639\pi\)
0.989564 0.144097i \(-0.0460277\pi\)
\(662\) 4966.48 8602.19i 0.291583 0.505036i
\(663\) 0 0
\(664\) 304.746 0.0178109
\(665\) 0 0
\(666\) 0 0
\(667\) −3385.08 5863.13i −0.196508 0.340362i
\(668\) −7032.63 + 12180.9i −0.407336 + 0.705527i
\(669\) 0 0
\(670\) −658.827 1141.12i −0.0379891 0.0657991i
\(671\) −28921.6 −1.66395
\(672\) 0 0
\(673\) 9634.87 0.551853 0.275926 0.961179i \(-0.411015\pi\)
0.275926 + 0.961179i \(0.411015\pi\)
\(674\) −7521.48 13027.6i −0.429846 0.744516i
\(675\) 0 0
\(676\) 413.257 715.783i 0.0235126 0.0407250i
\(677\) 4185.66 + 7249.77i 0.237619 + 0.411568i 0.960030 0.279895i \(-0.0902998\pi\)
−0.722412 + 0.691463i \(0.756966\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 686.854 0.0387348
\(681\) 0 0
\(682\) −26534.9 + 45959.9i −1.48985 + 2.58049i
\(683\) −6034.42 + 10451.9i −0.338069 + 0.585552i −0.984069 0.177785i \(-0.943107\pi\)
0.646001 + 0.763337i \(0.276440\pi\)
\(684\) 0 0
\(685\) 1077.33 0.0600917
\(686\) 0 0
\(687\) 0 0
\(688\) −5870.98 10168.8i −0.325333 0.563493i
\(689\) −3165.05 + 5482.02i −0.175005 + 0.303118i
\(690\) 0 0
\(691\) −1490.64 2581.87i −0.0820648 0.142140i 0.822072 0.569384i \(-0.192818\pi\)
−0.904137 + 0.427243i \(0.859485\pi\)
\(692\) −14677.4 −0.806286
\(693\) 0 0
\(694\) −127.327 −0.00696435
\(695\) 3090.73 + 5353.30i 0.168688 + 0.292176i
\(696\) 0 0
\(697\) −3297.76 + 5711.89i −0.179213 + 0.310407i
\(698\) 428.489 + 742.165i 0.0232357 + 0.0402455i
\(699\) 0 0
\(700\) 0 0
\(701\) 28978.0 1.56132 0.780660 0.624956i \(-0.214883\pi\)
0.780660 + 0.624956i \(0.214883\pi\)
\(702\) 0 0
\(703\) 3000.06 5196.25i 0.160952 0.278777i
\(704\) −105.597 + 182.900i −0.00565319 + 0.00979161i
\(705\) 0 0
\(706\) 388.388 0.0207042
\(707\) 0 0
\(708\) 0 0
\(709\) 8186.22 + 14178.9i 0.433625 + 0.751060i 0.997182 0.0750169i \(-0.0239011\pi\)
−0.563558 + 0.826077i \(0.690568\pi\)
\(710\) −2475.16 + 4287.10i −0.130833 + 0.226609i
\(711\) 0 0
\(712\) 6685.11 + 11578.9i 0.351875 + 0.609465i
\(713\) 17034.9 0.894755
\(714\) 0 0
\(715\) 4583.18 0.239722
\(716\) 6253.79 + 10831.9i 0.326418 + 0.565373i
\(717\) 0 0
\(718\) 21900.9 37933.4i 1.13835 1.97168i
\(719\) 11505.3 + 19927.7i 0.596765 + 1.03363i 0.993295 + 0.115605i \(0.0368808\pi\)
−0.396530 + 0.918022i \(0.629786\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −2882.36 −0.148574
\(723\) 0 0
\(724\) −8318.89 + 14408.7i −0.427029 + 0.739636i
\(725\) −7327.73 + 12692.0i −0.375372 + 0.650164i
\(726\) 0 0
\(727\) −24636.8 −1.25685 −0.628423 0.777872i \(-0.716299\pi\)
−0.628423 + 0.777872i \(0.716299\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −871.015 1508.64i −0.0441612 0.0764895i
\(731\) 1951.44 3379.99i 0.0987367 0.171017i
\(732\) 0 0
\(733\) −3452.38 5979.70i −0.173965 0.301317i 0.765837 0.643034i \(-0.222325\pi\)
−0.939803 + 0.341718i \(0.888991\pi\)
\(734\) 48940.1 2.46105
\(735\) 0 0
\(736\) 10144.6 0.508065
\(737\) −4417.81 7651.88i −0.220804 0.382443i
\(738\) 0 0
\(739\) 4617.44 7997.65i 0.229845 0.398103i −0.727917 0.685665i \(-0.759511\pi\)
0.957762 + 0.287562i \(0.0928448\pi\)
\(740\) 358.269 + 620.540i 0.0177976 + 0.0308264i
\(741\) 0 0
\(742\) 0 0
\(743\) −20216.9 −0.998232 −0.499116 0.866535i \(-0.666342\pi\)
−0.499116 + 0.866535i \(0.666342\pi\)
\(744\) 0 0
\(745\) 2822.98 4889.55i 0.138827 0.240455i
\(746\) −8647.84 + 14978.5i −0.424424 + 0.735123i
\(747\) 0 0
\(748\) −5828.88 −0.284926
\(749\) 0 0
\(750\) 0 0
\(751\) −12027.5 20832.2i −0.584405 1.01222i −0.994949 0.100378i \(-0.967995\pi\)
0.410544 0.911841i \(-0.365339\pi\)
\(752\) 10764.4 18644.4i 0.521989 0.904112i
\(753\) 0 0
\(754\) 9617.23 + 16657.5i 0.464508 + 0.804551i
\(755\) −1470.00 −0.0708593
\(756\) 0 0
\(757\) −30328.2 −1.45614 −0.728069 0.685504i \(-0.759582\pi\)
−0.728069 + 0.685504i \(0.759582\pi\)
\(758\) 17313.6 + 29988.0i 0.829627 + 1.43696i
\(759\) 0 0
\(760\) 1006.73 1743.70i 0.0480498 0.0832248i
\(761\) −16917.1 29301.2i −0.805839 1.39575i −0.915723 0.401810i \(-0.868381\pi\)
0.109884 0.993944i \(-0.464952\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4288.55 −0.203082
\(765\) 0 0
\(766\) 18943.9 32811.9i 0.893567 1.54770i
\(767\) 9528.14 16503.2i 0.448555 0.776919i
\(768\) 0 0
\(769\) 31738.1 1.48830 0.744151 0.668011i \(-0.232854\pi\)
0.744151 + 0.668011i \(0.232854\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8469.06 + 14668.8i 0.394829 + 0.683864i
\(773\) 13747.1 23810.7i 0.639650 1.10791i −0.345860 0.938286i \(-0.612413\pi\)
0.985510 0.169619i \(-0.0542538\pi\)
\(774\) 0 0
\(775\) −18437.8 31935.2i −0.854587 1.48019i
\(776\) 20791.0 0.961794
\(777\) 0 0
\(778\) −18588.0 −0.856573
\(779\) 9667.12 + 16743.9i 0.444622 + 0.770108i
\(780\) 0 0
\(781\) −16597.4 + 28747.5i −0.760436 + 1.31711i
\(782\) 2610.21 + 4521.01i 0.119362 + 0.206740i
\(783\) 0 0
\(784\) 0 0
\(785\) 6476.84 0.294482
\(786\) 0 0
\(787\) 234.178 405.608i 0.0106068 0.0183715i −0.860673 0.509158i \(-0.829957\pi\)
0.871280 + 0.490786i \(0.163290\pi\)
\(788\) 11435.8 19807.4i 0.516985 0.895445i
\(789\) 0 0
\(790\) −3637.18 −0.163804
\(791\)