Properties

Label 441.4.e.y.226.2
Level $441$
Weight $4$
Character 441.226
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 226.2
Root \(-4.23824 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.y.361.2

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76556 + 3.05805i −0.624221 + 1.08118i 0.364470 + 0.931215i \(0.381250\pi\)
−0.988691 + 0.149968i \(0.952083\pi\)
\(3\) 0 0
\(4\) −2.23444 3.87016i −0.279304 0.483769i
\(5\) 1.03865 1.79899i 0.0928996 0.160907i −0.815830 0.578291i \(-0.803720\pi\)
0.908730 + 0.417384i \(0.137053\pi\)
\(6\) 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 0.976729 + 0.214478i \(0.0688050\pi\)
−0.302621 + 0.953111i \(0.597862\pi\)
\(12\) 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 0.755809 0.654793i \(-0.227244\pi\)
−0.944971 + 0.327153i \(0.893911\pi\)
\(18\) 0 0
\(19\) 38.8675 67.3205i 0.469306 0.812862i −0.530078 0.847949i \(-0.677837\pi\)
0.999384 + 0.0350869i \(0.0111708\pi\)
\(20\) −9.28317 −0.103789
\(21\) 0 0
\(22\) −173.685 −1.68317
\(23\) 27.8755 48.2818i 0.252715 0.437715i −0.711558 0.702628i \(-0.752010\pi\)
0.964272 + 0.264913i \(0.0853432\pi\)
\(24\) 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 0.845549 + 0.533897i \(0.179273\pi\)
0.0395940 + 0.999216i \(0.487394\pi\)
\(32\) 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 −0.938937 0.344089i \(-0.888188\pi\)
0.767458 + 0.641099i \(0.221521\pi\)
\(38\) 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 −0.995813 0.0914112i \(-0.970862\pi\)
0.577071 + 0.816694i \(0.304196\pi\)
\(48\) 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 0.759986 0.649940i \(-0.225206\pi\)
−0.942857 + 0.333197i \(0.891873\pi\)
\(54\) 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 0.999361 0.0357532i \(-0.0113830\pi\)
−0.530643 + 0.847595i \(0.678050\pi\)
\(60\) 0 0
\(61\) −293.998 + 509.220i −0.617092 + 1.06883i 0.372922 + 0.927863i \(0.378356\pi\)
−0.990014 + 0.140972i \(0.954977\pi\)
\(62\) −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 0.936219 0.351416i \(-0.114300\pi\)
−0.772445 + 0.635082i \(0.780966\pi\)
\(68\) −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 0.945377 0.325978i \(-0.105694\pi\)
−0.754994 + 0.655732i \(0.772360\pi\)
\(74\) −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 −0.986789 0.162013i \(-0.948201\pi\)
0.633702 + 0.773578i \(0.281535\pi\)
\(80\) −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 0.347199 + 0.937792i \(0.387133\pi\)
−0.985751 + 0.168213i \(0.946200\pi\)
\(90\) 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 0.884394 0.466740i \(-0.154572\pi\)
−0.846406 + 0.532538i \(0.821238\pi\)
\(102\) 0 0
\(103\) 82.3463 142.628i 0.0787749 0.136442i −0.823947 0.566667i \(-0.808232\pi\)
0.902722 + 0.430225i \(0.141566\pi\)
\(104\) −559.302 −0.527347
\(105\) 0 0
\(106\) 498.315 0.456610
\(107\) 511.311 885.617i 0.461966 0.800148i −0.537093 0.843523i \(-0.680478\pi\)
0.999059 + 0.0433749i \(0.0138110\pi\)
\(108\) 0 0
\(109\) −681.259 1179.97i −0.598649 1.03689i −0.993021 0.117940i \(-0.962371\pi\)
0.394372 0.918951i \(-0.370962\pi\)
\(110\) −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 −0.712981 0.701183i \(-0.752656\pi\)
0.963733 + 0.266869i \(0.0859890\pi\)
\(132\) 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 0.935483 0.353373i \(-0.114965\pi\)
−0.773771 + 0.633465i \(0.781632\pi\)
\(138\) 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 0.201977 + 0.979390i \(0.435263\pi\)
−0.949165 + 0.314778i \(0.898070\pi\)
\(150\) 0 0
\(151\) −353.825 612.843i −0.190688 0.330281i 0.754791 0.655966i \(-0.227738\pi\)
−0.945478 + 0.325685i \(0.894405\pi\)
\(152\) −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 0.924431 + 0.381349i \(0.124540\pi\)
−0.131958 + 0.991255i \(0.542126\pi\)
\(158\) −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 −0.997262 0.0739557i \(-0.976438\pi\)
0.562678 + 0.826676i \(0.309771\pi\)
\(164\) −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 −0.238631 0.971110i \(-0.576699\pi\)
0.960322 0.278895i \(-0.0899681\pi\)
\(174\) 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 0.994957 + 0.100300i \(0.0319802\pi\)
−0.410616 + 0.911808i \(0.634686\pi\)
\(180\) 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 −0.760710 0.649091i \(-0.775149\pi\)
0.942485 + 0.334249i \(0.108483\pi\)
\(192\) 0 0
\(193\) 1895.12 + 3282.45i 0.706808 + 1.22423i 0.966035 + 0.258411i \(0.0831988\pi\)
−0.259227 + 0.965816i \(0.583468\pi\)
\(194\) 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 0.932709 0.360630i \(-0.117438\pi\)
−0.778669 + 0.627435i \(0.784105\pi\)
\(200\) −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 0.712965 0.701200i \(-0.247352\pi\)
−0.963739 + 0.266846i \(0.914018\pi\)
\(228\) 0 0
\(229\) 522.729 905.394i 0.150842 0.261267i −0.780695 0.624912i \(-0.785135\pi\)
0.931537 + 0.363646i \(0.118468\pi\)
\(230\) 408.945 0.117239
\(231\) 0 0
\(232\) 1514.17 0.428491
\(233\) 724.335 1254.58i 0.203660 0.352749i −0.746045 0.665895i \(-0.768050\pi\)
0.949705 + 0.313146i \(0.101383\pi\)
\(234\) 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 0.890362 0.455254i \(-0.150451\pi\)
−0.839442 + 0.543449i \(0.817118\pi\)
\(242\) −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 −0.483014 0.875612i \(-0.660458\pi\)
0.999810 0.0195034i \(-0.00620851\pi\)
\(258\) 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 0.999960 0.00895400i \(-0.00285018\pi\)
−0.507734 + 0.861514i \(0.669517\pi\)
\(264\) 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 0.996319 0.0857271i \(-0.0273213\pi\)
−0.572401 + 0.819974i \(0.693988\pi\)
\(270\) 0 0
\(271\) −2178.15 + 3772.66i −0.488240 + 0.845656i −0.999909 0.0135265i \(-0.995694\pi\)
0.511669 + 0.859183i \(0.329028\pi\)
\(272\) −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 0.929670 0.368394i \(-0.120092\pi\)
−0.783873 + 0.620921i \(0.786759\pi\)
\(278\) −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 0.500920 0.865494i \(-0.332995\pi\)
−0.999999 + 0.00106280i \(0.999662\pi\)
\(284\) 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 0.833126 0.553083i \(-0.186549\pi\)
−0.895547 + 0.444967i \(0.853215\pi\)
\(312\) 0 0
\(313\) 2972.04 5147.72i 0.536707 0.929604i −0.462371 0.886686i \(-0.653001\pi\)
0.999079 0.0429180i \(-0.0136654\pi\)
\(314\) −11009.8 −1.97872
\(315\) 0 0
\(316\) 2215.90 0.394475
\(317\) −1411.95 + 2445.56i −0.250166 + 0.433301i −0.963571 0.267451i \(-0.913819\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(318\) 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 −0.725295 0.688438i \(-0.758297\pi\)
0.958852 + 0.283905i \(0.0916301\pi\)
\(332\) 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 0.867417 0.497583i \(-0.165779\pi\)
−0.864627 + 0.502414i \(0.832445\pi\)
\(348\) 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 0.861850 0.507164i \(-0.169306\pi\)
−0.870142 + 0.492802i \(0.835973\pi\)
\(354\) 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 0.100314 0.994956i \(-0.468015\pi\)
0.811500 0.584352i \(-0.198651\pi\)
\(360\) 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 −0.639015 0.769194i \(-0.720658\pi\)
−0.346634 0.938001i \(-0.612675\pi\)
\(368\) −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 −0.984425 0.175803i \(-0.943748\pi\)
0.644463 + 0.764636i \(0.277081\pi\)
\(374\) 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 −0.246926 0.969034i \(-0.579420\pi\)
0.962671 0.270673i \(-0.0872463\pi\)
\(384\) 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 0.984999 0.172562i \(-0.0552044\pi\)
−0.641942 + 0.766753i \(0.721871\pi\)
\(390\) 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 −0.901865 0.432018i \(-0.857802\pi\)
0.825071 + 0.565029i \(0.191135\pi\)
\(398\) −3053.91 −0.384620
\(399\) 0 0
\(400\) 9628.26 1.20353
\(401\) 1147.73 1987.92i 0.142929 0.247561i −0.785669 0.618647i \(-0.787681\pi\)
0.928599 + 0.371086i \(0.121014\pi\)
\(402\) 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 0.690724 0.723118i \(-0.257292\pi\)
−0.971601 + 0.236626i \(0.923958\pi\)
\(410\) 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 0.985275 + 0.170974i \(0.0546915\pi\)
−0.344570 + 0.938761i \(0.611975\pi\)
\(432\) 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 −0.694919 0.719088i \(-0.744560\pi\)
0.970208 + 0.242274i \(0.0778932\pi\)
\(440\) −1274.01 −0.138037
\(441\) 0 0
\(442\) 4200.22 0.452000
\(443\) 6351.82 11001.7i 0.681228 1.17992i −0.293378 0.955996i \(-0.594780\pi\)
0.974606 0.223925i \(-0.0718871\pi\)
\(444\) 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 −0.154077 0.988059i \(-0.549240\pi\)
0.932722 0.360595i \(-0.117426\pi\)
\(458\) 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 −0.761954 0.647631i \(-0.775760\pi\)
0.941842 + 0.336056i \(0.109093\pi\)
\(468\) 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 0.978585 0.205844i \(-0.0659939\pi\)
−0.667558 + 0.744557i \(0.732661\pi\)
\(480\) 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 0.938619 0.344955i \(-0.112106\pi\)
−0.768049 + 0.640391i \(0.778772\pi\)
\(488\) 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 −0.809716 0.586822i \(-0.800379\pi\)
0.913061 + 0.407824i \(0.133712\pi\)
\(500\) −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 −0.996008 0.0892655i \(-0.971548\pi\)
0.575310 + 0.817935i \(0.304881\pi\)
\(510\) 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 0.988276 0.152679i \(-0.0487899\pi\)
−0.626361 + 0.779533i \(0.715457\pi\)
\(522\) 0 0
\(523\) 5241.36 9078.30i 0.438219 0.759018i −0.559333 0.828943i \(-0.688943\pi\)
0.997552 + 0.0699250i \(0.0222760\pi\)
\(524\) −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 0.0797082 + 0.996818i \(0.474601\pi\)
−0.903124 + 0.429380i \(0.858732\pi\)
\(542\) −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 0.605472 0.795867i \(-0.292985\pi\)
−0.991977 + 0.126420i \(0.959651\pi\)
\(558\) 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 −0.985388 0.170326i \(-0.945518\pi\)
0.345187 0.938534i \(-0.387816\pi\)
\(564\) 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 0.304588 + 0.952484i \(0.401481\pi\)
−0.977170 + 0.212461i \(0.931852\pi\)
\(570\) 0 0
\(571\) −6815.25 11804.4i −0.499491 0.865143i 0.500509 0.865731i \(-0.333146\pi\)
−1.00000 0.000587868i \(0.999813\pi\)
\(572\) 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 0.774709 0.632317i \(-0.217896\pi\)
−0.934958 + 0.354759i \(0.884563\pi\)
\(578\) 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 −0.744729 0.667367i \(-0.767421\pi\)
0.950321 + 0.311271i \(0.100755\pi\)
\(594\) 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 0.818270 0.574835i \(-0.194934\pi\)
−0.906956 + 0.421225i \(0.861600\pi\)
\(600\) 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 −0.584248 0.811575i \(-0.698610\pi\)
0.994969 + 0.100186i \(0.0319438\pi\)
\(608\) 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 −0.958223 0.286023i \(-0.907666\pi\)
0.231408 0.972857i \(-0.425667\pi\)
\(614\) 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 −0.945474 0.325698i \(-0.894401\pi\)
0.190675 0.981653i \(-0.438932\pi\)
\(620\) −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 −0.993009 0.118040i \(-0.962339\pi\)
0.394279 0.918991i \(-0.370994\pi\)
\(642\) 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 −0.842112 0.539302i \(-0.818688\pi\)
−0.0459932 0.998942i \(-0.514645\pi\)
\(648\) 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 −0.952510 0.304508i \(-0.901508\pi\)
0.739967 + 0.672643i \(0.234841\pi\)
\(654\) 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 0.989564 + 0.144097i \(0.0460277\pi\)
−0.369990 + 0.929036i \(0.620639\pi\)
\(662\) 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 −0.722412 0.691463i \(-0.756966\pi\)
0.960030 + 0.279895i \(0.0902998\pi\)
\(678\) 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 0.646001 0.763337i \(-0.276440\pi\)
−0.984069 + 0.177785i \(0.943107\pi\)
\(684\) 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 −0.904137 0.427243i \(-0.859485\pi\)
0.822072 + 0.569384i \(0.192818\pi\)
\(692\) −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 −0.563558 0.826077i \(-0.690568\pi\)
0.997182 + 0.0750169i \(0.0239011\pi\)
\(710\) −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 −0.396530 0.918022i \(-0.629786\pi\)
0.993295 0.115605i \(-0.0368808\pi\)
\(720\) 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 −0.939803 0.341718i \(-0.888991\pi\)
0.765837 + 0.643034i \(0.222325\pi\)
\(734\) 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 0.957762 0.287562i \(-0.0928448\pi\)
−0.727917 + 0.685665i \(0.759511\pi\)
\(740\) 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 0.410544 + 0.911841i \(0.365339\pi\)
−0.994949 + 0.100378i \(0.967995\pi\)
\(752\) 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 0.109884 + 0.993944i \(0.464952\pi\)
−0.915723 + 0.401810i \(0.868381\pi\)
\(762\) 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 0.985510 + 0.169619i \(0.0542538\pi\)
−0.345860 + 0.938286i \(0.612413\pi\)
\(774\) 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 0.871280 0.490786i \(-0.163290\pi\)
−0.860673 + 0.509158i \(0.829957\pi\)
\(788\) 11435.8 + 19807.4i 0.516985 + 0.895445i
\(789\) 0 0
\(790\) −3637.18 −0.163804
\(791\)