Properties

Label 128.4.g.a.49.3
Level $128$
Weight $4$
Character 128.49
Analytic conductor $7.552$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 128.g (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.55224448073\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(11\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 49.3
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-5.53310 + 2.29188i) q^{3} +(4.22177 - 10.1923i) q^{5} +(11.6451 + 11.6451i) q^{7} +(6.27055 - 6.27055i) q^{9} +O(q^{10})\) \(q+(-5.53310 + 2.29188i) q^{3} +(4.22177 - 10.1923i) q^{5} +(11.6451 + 11.6451i) q^{7} +(6.27055 - 6.27055i) q^{9} +(-27.7531 - 11.4957i) q^{11} +(15.9612 + 38.5338i) q^{13} +66.0706i q^{15} +131.437i q^{17} +(13.7982 + 33.3119i) q^{19} +(-91.1226 - 37.7442i) q^{21} +(-128.594 + 128.594i) q^{23} +(2.32952 + 2.32952i) q^{25} +(41.5567 - 100.327i) q^{27} +(-192.157 + 79.5938i) q^{29} +215.350 q^{31} +179.908 q^{33} +(167.853 - 69.5268i) q^{35} +(-9.39705 + 22.6865i) q^{37} +(-176.630 - 176.630i) q^{39} +(257.295 - 257.295i) q^{41} +(81.5685 + 33.7868i) q^{43} +(-37.4383 - 90.3840i) q^{45} +113.432i q^{47} -71.7841i q^{49} +(-301.238 - 727.254i) q^{51} +(-11.8996 - 4.92896i) q^{53} +(-234.335 + 234.335i) q^{55} +(-152.694 - 152.694i) q^{57} +(-210.637 + 508.522i) q^{59} +(-251.800 + 104.299i) q^{61} +146.042 q^{63} +460.131 q^{65} +(418.173 - 173.213i) q^{67} +(416.801 - 1006.25i) q^{69} +(28.0923 + 28.0923i) q^{71} +(-333.018 + 333.018i) q^{73} +(-18.2285 - 7.55047i) q^{75} +(-189.319 - 457.056i) q^{77} +38.8621i q^{79} +889.794i q^{81} +(-229.913 - 555.060i) q^{83} +(1339.64 + 554.897i) q^{85} +(880.801 - 880.801i) q^{87} +(-872.568 - 872.568i) q^{89} +(-262.859 + 634.599i) q^{91} +(-1191.55 + 493.557i) q^{93} +397.776 q^{95} -51.1346 q^{97} +(-246.112 + 101.943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(1\)

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
\(3\) −5.53310 + 2.29188i −1.06485 + 0.441073i −0.845169 0.534499i \(-0.820500\pi\)
−0.219676 + 0.975573i \(0.570500\pi\)
\(4\) 0 0
\(5\) 4.22177 10.1923i 0.377607 0.911624i −0.614807 0.788678i \(-0.710766\pi\)
0.992413 0.122946i \(-0.0392341\pi\)
\(6\) 0 0
\(7\) 11.6451 + 11.6451i 0.628775 + 0.628775i 0.947760 0.318985i \(-0.103342\pi\)
−0.318985 + 0.947760i \(0.603342\pi\)
\(8\) 0 0
\(9\) 6.27055 6.27055i 0.232243 0.232243i
\(10\) 0 0
\(11\) −27.7531 11.4957i −0.760717 0.315099i −0.0316109 0.999500i \(-0.510064\pi\)
−0.729106 + 0.684401i \(0.760064\pi\)
\(12\) 0 0
\(13\) 15.9612 + 38.5338i 0.340527 + 0.822104i 0.997663 + 0.0683319i \(0.0217677\pi\)
−0.657136 + 0.753772i \(0.728232\pi\)
\(14\) 0 0
\(15\) 66.0706i 1.13729i
\(16\) 0 0
\(17\) 131.437i 1.87518i 0.347736 + 0.937592i \(0.386951\pi\)
−0.347736 + 0.937592i \(0.613049\pi\)
\(18\) 0 0
\(19\) 13.7982 + 33.3119i 0.166607 + 0.402224i 0.985028 0.172394i \(-0.0551503\pi\)
−0.818421 + 0.574619i \(0.805150\pi\)
\(20\) 0 0
\(21\) −91.1226 37.7442i −0.946884 0.392212i
\(22\) 0 0
\(23\) −128.594 + 128.594i −1.16582 + 1.16582i −0.182634 + 0.983181i \(0.558462\pi\)
−0.983181 + 0.182634i \(0.941538\pi\)
\(24\) 0 0
\(25\) 2.32952 + 2.32952i 0.0186362 + 0.0186362i
\(26\) 0 0
\(27\) 41.5567 100.327i 0.296207 0.715106i
\(28\) 0 0
\(29\) −192.157 + 79.5938i −1.23043 + 0.509662i −0.900712 0.434416i \(-0.856955\pi\)
−0.329721 + 0.944078i \(0.606955\pi\)
\(30\) 0 0
\(31\) 215.350 1.24768 0.623839 0.781553i \(-0.285572\pi\)
0.623839 + 0.781553i \(0.285572\pi\)
\(32\) 0 0
\(33\) 179.908 0.949027
\(34\) 0 0
\(35\) 167.853 69.5268i 0.810636 0.335777i
\(36\) 0 0
\(37\) −9.39705 + 22.6865i −0.0417531 + 0.100801i −0.943380 0.331713i \(-0.892373\pi\)
0.901627 + 0.432514i \(0.142373\pi\)
\(38\) 0 0
\(39\) −176.630 176.630i −0.725216 0.725216i
\(40\) 0 0
\(41\) 257.295 257.295i 0.980067 0.980067i −0.0197381 0.999805i \(-0.506283\pi\)
0.999805 + 0.0197381i \(0.00628325\pi\)
\(42\) 0 0
\(43\) 81.5685 + 33.7868i 0.289281 + 0.119824i 0.522605 0.852575i \(-0.324960\pi\)
−0.233324 + 0.972399i \(0.574960\pi\)
\(44\) 0 0
\(45\) −37.4383 90.3840i −0.124022 0.299414i
\(46\) 0 0
\(47\) 113.432i 0.352037i 0.984387 + 0.176018i \(0.0563218\pi\)
−0.984387 + 0.176018i \(0.943678\pi\)
\(48\) 0 0
\(49\) 71.7841i 0.209283i
\(50\) 0 0
\(51\) −301.238 727.254i −0.827094 1.99678i
\(52\) 0 0
\(53\) −11.8996 4.92896i −0.0308402 0.0127744i 0.367210 0.930138i \(-0.380313\pi\)
−0.398050 + 0.917364i \(0.630313\pi\)
\(54\) 0 0
\(55\) −234.335 + 234.335i −0.574504 + 0.574504i
\(56\) 0 0
\(57\) −152.694 152.694i −0.354821 0.354821i
\(58\) 0 0
\(59\) −210.637 + 508.522i −0.464789 + 1.12210i 0.501619 + 0.865088i \(0.332738\pi\)
−0.966408 + 0.257011i \(0.917262\pi\)
\(60\) 0 0
\(61\) −251.800 + 104.299i −0.528519 + 0.218920i −0.630954 0.775820i \(-0.717336\pi\)
0.102436 + 0.994740i \(0.467336\pi\)
\(62\) 0 0
\(63\) 146.042 0.292057
\(64\) 0 0
\(65\) 460.131 0.878034
\(66\) 0 0
\(67\) 418.173 173.213i 0.762507 0.315841i 0.0326737 0.999466i \(-0.489598\pi\)
0.729833 + 0.683625i \(0.239598\pi\)
\(68\) 0 0
\(69\) 416.801 1006.25i 0.727203 1.75562i
\(70\) 0 0
\(71\) 28.0923 + 28.0923i 0.0469569 + 0.0469569i 0.730195 0.683238i \(-0.239429\pi\)
−0.683238 + 0.730195i \(0.739429\pi\)
\(72\) 0 0
\(73\) −333.018 + 333.018i −0.533928 + 0.533928i −0.921739 0.387811i \(-0.873231\pi\)
0.387811 + 0.921739i \(0.373231\pi\)
\(74\) 0 0
\(75\) −18.2285 7.55047i −0.0280645 0.0116247i
\(76\) 0 0
\(77\) −189.319 457.056i −0.280193 0.676446i
\(78\) 0 0
\(79\) 38.8621i 0.0553460i 0.999617 + 0.0276730i \(0.00880971\pi\)
−0.999617 + 0.0276730i \(0.991190\pi\)
\(80\) 0 0
\(81\) 889.794i 1.22057i
\(82\) 0 0
\(83\) −229.913 555.060i −0.304051 0.734045i −0.999875 0.0158320i \(-0.994960\pi\)
0.695823 0.718213i \(-0.255040\pi\)
\(84\) 0 0
\(85\) 1339.64 + 554.897i 1.70946 + 0.708083i
\(86\) 0 0
\(87\) 880.801 880.801i 1.08542 1.08542i
\(88\) 0 0
\(89\) −872.568 872.568i −1.03924 1.03924i −0.999198 0.0400377i \(-0.987252\pi\)
−0.0400377 0.999198i \(-0.512748\pi\)
\(90\) 0 0
\(91\) −262.859 + 634.599i −0.302804 + 0.731033i
\(92\) 0 0
\(93\) −1191.55 + 493.557i −1.32858 + 0.550317i
\(94\) 0 0
\(95\) 397.776 0.429589
\(96\) 0 0
\(97\) −51.1346 −0.0535251 −0.0267625 0.999642i \(-0.508520\pi\)
−0.0267625 + 0.999642i \(0.508520\pi\)
\(98\) 0 0
\(99\) −246.112 + 101.943i −0.249850 + 0.103491i
\(100\) 0 0
\(101\) −153.885 + 371.512i −0.151606 + 0.366008i −0.981376 0.192096i \(-0.938471\pi\)
0.829770 + 0.558105i \(0.188471\pi\)
\(102\) 0 0
\(103\) −601.189 601.189i −0.575115 0.575115i 0.358438 0.933553i \(-0.383309\pi\)
−0.933553 + 0.358438i \(0.883309\pi\)
\(104\) 0 0
\(105\) −769.398 + 769.398i −0.715100 + 0.715100i
\(106\) 0 0
\(107\) 825.321 + 341.859i 0.745671 + 0.308867i 0.722974 0.690875i \(-0.242775\pi\)
0.0226969 + 0.999742i \(0.492775\pi\)
\(108\) 0 0
\(109\) 790.968 + 1909.57i 0.695055 + 1.67801i 0.734338 + 0.678784i \(0.237493\pi\)
−0.0392828 + 0.999228i \(0.512507\pi\)
\(110\) 0 0
\(111\) 147.064i 0.125754i
\(112\) 0 0
\(113\) 717.104i 0.596987i −0.954412 0.298493i \(-0.903516\pi\)
0.954412 0.298493i \(-0.0964841\pi\)
\(114\) 0 0
\(115\) 767.770 + 1853.56i 0.622565 + 1.50300i
\(116\) 0 0
\(117\) 341.714 + 141.543i 0.270013 + 0.111843i
\(118\) 0 0
\(119\) −1530.59 + 1530.59i −1.17907 + 1.17907i
\(120\) 0 0
\(121\) −303.075 303.075i −0.227705 0.227705i
\(122\) 0 0
\(123\) −833.948 + 2013.33i −0.611338 + 1.47590i
\(124\) 0 0
\(125\) 1307.61 541.630i 0.935650 0.387559i
\(126\) 0 0
\(127\) 713.424 0.498474 0.249237 0.968443i \(-0.419820\pi\)
0.249237 + 0.968443i \(0.419820\pi\)
\(128\) 0 0
\(129\) −528.762 −0.360890
\(130\) 0 0
\(131\) −918.787 + 380.574i −0.612784 + 0.253824i −0.667419 0.744683i \(-0.732601\pi\)
0.0546341 + 0.998506i \(0.482601\pi\)
\(132\) 0 0
\(133\) −227.238 + 548.601i −0.148151 + 0.357667i
\(134\) 0 0
\(135\) −847.113 847.113i −0.540058 0.540058i
\(136\) 0 0
\(137\) 1589.55 1589.55i 0.991274 0.991274i −0.00868786 0.999962i \(-0.502765\pi\)
0.999962 + 0.00868786i \(0.00276547\pi\)
\(138\) 0 0
\(139\) −828.901 343.342i −0.505802 0.209510i 0.115166 0.993346i \(-0.463260\pi\)
−0.620967 + 0.783836i \(0.713260\pi\)
\(140\) 0 0
\(141\) −259.972 627.629i −0.155274 0.374865i
\(142\) 0 0
\(143\) 1252.92i 0.732688i
\(144\) 0 0
\(145\) 2294.54i 1.31414i
\(146\) 0 0
\(147\) 164.521 + 397.188i 0.0923092 + 0.222854i
\(148\) 0 0
\(149\) −1399.70 579.774i −0.769582 0.318771i −0.0368792 0.999320i \(-0.511742\pi\)
−0.732703 + 0.680548i \(0.761742\pi\)
\(150\) 0 0
\(151\) 521.322 521.322i 0.280958 0.280958i −0.552533 0.833491i \(-0.686339\pi\)
0.833491 + 0.552533i \(0.186339\pi\)
\(152\) 0 0
\(153\) 824.183 + 824.183i 0.435498 + 0.435498i
\(154\) 0 0
\(155\) 909.159 2194.90i 0.471131 1.13741i
\(156\) 0 0
\(157\) 1501.66 622.009i 0.763348 0.316189i 0.0331736 0.999450i \(-0.489439\pi\)
0.730175 + 0.683260i \(0.239439\pi\)
\(158\) 0 0
\(159\) 77.1380 0.0384745
\(160\) 0 0
\(161\) −2994.98 −1.46607
\(162\) 0 0
\(163\) 1676.94 694.610i 0.805815 0.333779i 0.0585321 0.998286i \(-0.481358\pi\)
0.747283 + 0.664506i \(0.231358\pi\)
\(164\) 0 0
\(165\) 759.529 1833.67i 0.358359 0.865156i
\(166\) 0 0
\(167\) 664.730 + 664.730i 0.308014 + 0.308014i 0.844139 0.536125i \(-0.180112\pi\)
−0.536125 + 0.844139i \(0.680112\pi\)
\(168\) 0 0
\(169\) 323.421 323.421i 0.147210 0.147210i
\(170\) 0 0
\(171\) 295.406 + 122.361i 0.132107 + 0.0547205i
\(172\) 0 0
\(173\) 190.687 + 460.359i 0.0838016 + 0.202315i 0.960226 0.279225i \(-0.0900776\pi\)
−0.876424 + 0.481540i \(0.840078\pi\)
\(174\) 0 0
\(175\) 54.2549i 0.0234359i
\(176\) 0 0
\(177\) 3296.45i 1.39987i
\(178\) 0 0
\(179\) −1230.51 2970.71i −0.513814 1.24046i −0.941648 0.336599i \(-0.890723\pi\)
0.427835 0.903857i \(-0.359277\pi\)
\(180\) 0 0
\(181\) −1720.96 712.847i −0.706731 0.292738i 0.000220198 1.00000i \(-0.499930\pi\)
−0.706951 + 0.707262i \(0.749930\pi\)
\(182\) 0 0
\(183\) 1154.19 1154.19i 0.466231 0.466231i
\(184\) 0 0
\(185\) 191.554 + 191.554i 0.0761263 + 0.0761263i
\(186\) 0 0
\(187\) 1510.96 3647.79i 0.590869 1.42648i
\(188\) 0 0
\(189\) 1652.24 684.381i 0.635889 0.263394i
\(190\) 0 0
\(191\) 454.987 0.172365 0.0861825 0.996279i \(-0.472533\pi\)
0.0861825 + 0.996279i \(0.472533\pi\)
\(192\) 0 0
\(193\) 3199.61 1.19333 0.596666 0.802490i \(-0.296492\pi\)
0.596666 + 0.802490i \(0.296492\pi\)
\(194\) 0 0
\(195\) −2545.95 + 1054.57i −0.934971 + 0.387278i
\(196\) 0 0
\(197\) −1023.92 + 2471.95i −0.370309 + 0.894006i 0.623388 + 0.781912i \(0.285756\pi\)
−0.993698 + 0.112093i \(0.964244\pi\)
\(198\) 0 0
\(199\) 2332.44 + 2332.44i 0.830867 + 0.830867i 0.987635 0.156768i \(-0.0501077\pi\)
−0.156768 + 0.987635i \(0.550108\pi\)
\(200\) 0 0
\(201\) −1916.81 + 1916.81i −0.672643 + 0.672643i
\(202\) 0 0
\(203\) −3164.56 1310.80i −1.09413 0.453203i
\(204\) 0 0
\(205\) −1536.18 3708.66i −0.523372 1.26353i
\(206\) 0 0
\(207\) 1612.71i 0.541504i
\(208\) 0 0
\(209\) 1083.13i 0.358476i
\(210\) 0 0
\(211\) 2070.04 + 4997.52i 0.675390 + 1.63054i 0.772311 + 0.635245i \(0.219101\pi\)
−0.0969206 + 0.995292i \(0.530899\pi\)
\(212\) 0 0
\(213\) −219.822 91.0531i −0.0707133 0.0292904i
\(214\) 0 0
\(215\) 688.727 688.727i 0.218469 0.218469i
\(216\) 0 0
\(217\) 2507.77 + 2507.77i 0.784509 + 0.784509i
\(218\) 0 0
\(219\) 1079.38 2605.86i 0.333049 0.804052i
\(220\) 0 0
\(221\) −5064.76 + 2097.89i −1.54160 + 0.638550i
\(222\) 0 0
\(223\) −6620.99 −1.98822 −0.994112 0.108357i \(-0.965441\pi\)
−0.994112 + 0.108357i \(0.965441\pi\)
\(224\) 0 0
\(225\) 29.2148 0.00865623
\(226\) 0 0
\(227\) 1044.31 432.568i 0.305345 0.126478i −0.224750 0.974417i \(-0.572156\pi\)
0.530095 + 0.847939i \(0.322156\pi\)
\(228\) 0 0
\(229\) −986.462 + 2381.53i −0.284660 + 0.687231i −0.999933 0.0116150i \(-0.996303\pi\)
0.715272 + 0.698846i \(0.246303\pi\)
\(230\) 0 0
\(231\) 2095.04 + 2095.04i 0.596725 + 0.596725i
\(232\) 0 0
\(233\) 978.403 978.403i 0.275096 0.275096i −0.556052 0.831148i \(-0.687684\pi\)
0.831148 + 0.556052i \(0.187684\pi\)
\(234\) 0 0
\(235\) 1156.13 + 478.883i 0.320925 + 0.132931i
\(236\) 0 0
\(237\) −89.0675 215.028i −0.0244116 0.0589349i
\(238\) 0 0
\(239\) 706.309i 0.191160i 0.995422 + 0.0955801i \(0.0304706\pi\)
−0.995422 + 0.0955801i \(0.969529\pi\)
\(240\) 0 0
\(241\) 1700.85i 0.454611i −0.973824 0.227305i \(-0.927008\pi\)
0.973824 0.227305i \(-0.0729916\pi\)
\(242\) 0 0
\(243\) −917.274 2214.50i −0.242153 0.584609i
\(244\) 0 0
\(245\) −731.642 303.056i −0.190787 0.0790267i
\(246\) 0 0
\(247\) −1063.40 + 1063.40i −0.273936 + 0.273936i
\(248\) 0 0
\(249\) 2544.27 + 2544.27i 0.647535 + 0.647535i
\(250\) 0 0
\(251\) 436.343 1053.43i 0.109728 0.264907i −0.859472 0.511184i \(-0.829207\pi\)
0.969200 + 0.246277i \(0.0792072\pi\)
\(252\) 0 0
\(253\) 5047.17 2090.61i 1.25420 0.519508i
\(254\) 0 0
\(255\) −8684.12 −2.13263
\(256\) 0 0
\(257\) 7006.16 1.70052 0.850258 0.526366i \(-0.176446\pi\)
0.850258 + 0.526366i \(0.176446\pi\)
\(258\) 0 0
\(259\) −373.616 + 154.757i −0.0896345 + 0.0371278i
\(260\) 0 0
\(261\) −705.831 + 1704.03i −0.167394 + 0.404125i
\(262\) 0 0
\(263\) 361.548 + 361.548i 0.0847681 + 0.0847681i 0.748219 0.663451i \(-0.230909\pi\)
−0.663451 + 0.748219i \(0.730909\pi\)
\(264\) 0 0
\(265\) −100.474 + 100.474i −0.0232909 + 0.0232909i
\(266\) 0 0
\(267\) 6827.83 + 2828.18i 1.56500 + 0.648246i
\(268\) 0 0
\(269\) 45.5340 + 109.929i 0.0103207 + 0.0249163i 0.928956 0.370190i \(-0.120708\pi\)
−0.918635 + 0.395107i \(0.870708\pi\)
\(270\) 0 0
\(271\) 3443.94i 0.771972i 0.922505 + 0.385986i \(0.126139\pi\)
−0.922505 + 0.385986i \(0.873861\pi\)
\(272\) 0 0
\(273\) 4113.74i 0.911996i
\(274\) 0 0
\(275\) −37.8720 91.4310i −0.00830460 0.0200491i
\(276\) 0 0
\(277\) −2101.15 870.326i −0.455762 0.188783i 0.142979 0.989726i \(-0.454332\pi\)
−0.598741 + 0.800943i \(0.704332\pi\)
\(278\) 0 0
\(279\) 1350.36 1350.36i 0.289764 0.289764i
\(280\) 0 0
\(281\) 2252.56 + 2252.56i 0.478207 + 0.478207i 0.904558 0.426351i \(-0.140201\pi\)
−0.426351 + 0.904558i \(0.640201\pi\)
\(282\) 0 0
\(283\) −2659.18 + 6419.84i −0.558559 + 1.34848i 0.352349 + 0.935869i \(0.385383\pi\)
−0.910907 + 0.412611i \(0.864617\pi\)
\(284\) 0 0
\(285\) −2200.93 + 911.657i −0.457446 + 0.189480i
\(286\) 0 0
\(287\) 5992.45 1.23248
\(288\) 0 0
\(289\) −12362.7 −2.51632
\(290\) 0 0
\(291\) 282.933 117.195i 0.0569959 0.0236085i
\(292\) 0 0
\(293\) −1751.78 + 4229.17i −0.349284 + 0.843245i 0.647421 + 0.762132i \(0.275847\pi\)
−0.996705 + 0.0811131i \(0.974153\pi\)
\(294\) 0 0
\(295\) 4293.73 + 4293.73i 0.847425 + 0.847425i
\(296\) 0 0
\(297\) −2306.65 + 2306.65i −0.450659 + 0.450659i
\(298\) 0 0
\(299\) −7007.74 2902.70i −1.35541 0.561430i
\(300\) 0 0
\(301\) 556.422 + 1343.32i 0.106550 + 0.257235i
\(302\) 0 0
\(303\) 2408.30i 0.456612i
\(304\) 0 0
\(305\) 3006.73i 0.564476i
\(306\) 0 0
\(307\) 172.273 + 415.904i 0.0320265 + 0.0773189i 0.939084 0.343689i \(-0.111677\pi\)
−0.907057 + 0.421008i \(0.861677\pi\)
\(308\) 0 0
\(309\) 4704.29 + 1948.58i 0.866077 + 0.358741i
\(310\) 0 0
\(311\) −1586.57 + 1586.57i −0.289279 + 0.289279i −0.836795 0.547516i \(-0.815574\pi\)
0.547516 + 0.836795i \(0.315574\pi\)
\(312\) 0 0
\(313\) 1221.66 + 1221.66i 0.220615 + 0.220615i 0.808757 0.588143i \(-0.200141\pi\)
−0.588143 + 0.808757i \(0.700141\pi\)
\(314\) 0 0
\(315\) 616.557 1488.50i 0.110283 0.266246i
\(316\) 0 0
\(317\) 1676.17 694.291i 0.296981 0.123013i −0.229218 0.973375i \(-0.573617\pi\)
0.526199 + 0.850362i \(0.323617\pi\)
\(318\) 0 0
\(319\) 6247.93 1.09661
\(320\) 0 0
\(321\) −5350.08 −0.930257
\(322\) 0 0
\(323\) −4378.41 + 1813.60i −0.754245 + 0.312419i
\(324\) 0 0
\(325\) −52.5833 + 126.947i −0.00897475 + 0.0216670i
\(326\) 0 0
\(327\) −8753.01 8753.01i −1.48025 1.48025i
\(328\) 0 0
\(329\) −1320.92 + 1320.92i −0.221352 + 0.221352i
\(330\) 0 0
\(331\) −1687.62 699.037i −0.280242 0.116080i 0.238135 0.971232i \(-0.423464\pi\)
−0.518378 + 0.855152i \(0.673464\pi\)
\(332\) 0 0
\(333\) 83.3322 + 201.182i 0.0137134 + 0.0331072i
\(334\) 0 0
\(335\) 4993.39i 0.814383i
\(336\) 0 0
\(337\) 7042.63i 1.13839i 0.822203 + 0.569194i \(0.192745\pi\)
−0.822203 + 0.569194i \(0.807255\pi\)
\(338\) 0 0
\(339\) 1643.52 + 3967.81i 0.263315 + 0.635699i
\(340\) 0 0
\(341\) −5976.63 2475.60i −0.949129 0.393142i
\(342\) 0 0
\(343\) 4830.20 4830.20i 0.760367 0.760367i
\(344\) 0 0
\(345\) −8496.30 8496.30i −1.32587 1.32587i
\(346\) 0 0
\(347\) 1762.67 4255.46i 0.272695 0.658343i −0.726902 0.686741i \(-0.759041\pi\)
0.999597 + 0.0283982i \(0.00904065\pi\)
\(348\) 0 0
\(349\) 10776.6 4463.83i 1.65289 0.684651i 0.655392 0.755289i \(-0.272503\pi\)
0.997502 + 0.0706374i \(0.0225033\pi\)
\(350\) 0 0
\(351\) 4529.26 0.688758
\(352\) 0 0
\(353\) 9544.92 1.43916 0.719582 0.694407i \(-0.244333\pi\)
0.719582 + 0.694407i \(0.244333\pi\)
\(354\) 0 0
\(355\) 404.923 167.725i 0.0605383 0.0250758i
\(356\) 0 0
\(357\) 4960.98 11976.9i 0.735471 1.77558i
\(358\) 0 0
\(359\) 5623.45 + 5623.45i 0.826725 + 0.826725i 0.987062 0.160338i \(-0.0512583\pi\)
−0.160338 + 0.987062i \(0.551258\pi\)
\(360\) 0 0
\(361\) 3930.76 3930.76i 0.573080 0.573080i
\(362\) 0 0
\(363\) 2371.55 + 982.330i 0.342904 + 0.142036i
\(364\) 0 0
\(365\) 1988.28 + 4800.13i 0.285127 + 0.688356i
\(366\) 0 0
\(367\) 5141.87i 0.731344i −0.930744 0.365672i \(-0.880839\pi\)
0.930744 0.365672i \(-0.119161\pi\)
\(368\) 0 0
\(369\) 3226.77i 0.455227i
\(370\) 0 0
\(371\) −81.1732 195.969i −0.0113593 0.0274238i
\(372\) 0 0
\(373\) 5767.56 + 2389.00i 0.800625 + 0.331630i 0.745207 0.666833i \(-0.232351\pi\)
0.0554183 + 0.998463i \(0.482351\pi\)
\(374\) 0 0
\(375\) −5993.78 + 5993.78i −0.825380 + 0.825380i
\(376\) 0 0
\(377\) −6134.10 6134.10i −0.837991 0.837991i
\(378\) 0 0
\(379\) 961.979 2322.42i 0.130379 0.314762i −0.845187 0.534471i \(-0.820511\pi\)
0.975565 + 0.219709i \(0.0705108\pi\)
\(380\) 0 0
\(381\) −3947.45 + 1635.09i −0.530798 + 0.219864i
\(382\) 0 0
\(383\) 2634.68 0.351503 0.175752 0.984435i \(-0.443764\pi\)
0.175752 + 0.984435i \(0.443764\pi\)
\(384\) 0 0
\(385\) −5457.70 −0.722467
\(386\) 0 0
\(387\) 723.341 299.618i 0.0950116 0.0393551i
\(388\) 0 0
\(389\) 4066.54 9817.49i 0.530030 1.27961i −0.401473 0.915871i \(-0.631502\pi\)
0.931503 0.363734i \(-0.118498\pi\)
\(390\) 0 0
\(391\) −16902.0 16902.0i −2.18612 2.18612i
\(392\) 0 0
\(393\) 4211.51 4211.51i 0.540566 0.540566i
\(394\) 0 0
\(395\) 396.093 + 164.067i 0.0504547 + 0.0208990i
\(396\) 0 0
\(397\) −1600.83 3864.76i −0.202377 0.488581i 0.789809 0.613353i \(-0.210180\pi\)
−0.992185 + 0.124773i \(0.960180\pi\)
\(398\) 0 0
\(399\) 3556.26i 0.446205i
\(400\) 0 0
\(401\) 2096.79i 0.261119i −0.991440 0.130560i \(-0.958323\pi\)
0.991440 0.130560i \(-0.0416774\pi\)
\(402\) 0 0
\(403\) 3437.25 + 8298.25i 0.424867 + 1.02572i
\(404\) 0 0
\(405\) 9069.01 + 3756.51i 1.11270 + 0.460895i
\(406\) 0 0
\(407\) 521.595 521.595i 0.0635246 0.0635246i
\(408\) 0 0
\(409\) −2541.72 2541.72i −0.307286 0.307286i 0.536570 0.843856i \(-0.319720\pi\)
−0.843856 + 0.536570i \(0.819720\pi\)
\(410\) 0 0
\(411\) −5152.08 + 12438.2i −0.618329 + 1.49278i
\(412\) 0 0
\(413\) −8374.66 + 3468.90i −0.997796 + 0.413301i
\(414\) 0 0
\(415\) −6627.96 −0.783985
\(416\) 0 0
\(417\) 5373.29 0.631010
\(418\) 0 0
\(419\) 10221.3 4233.80i 1.19175 0.493639i 0.303425 0.952855i \(-0.401870\pi\)
0.888324 + 0.459217i \(0.151870\pi\)
\(420\) 0 0
\(421\) −1917.63 + 4629.56i −0.221994 + 0.535940i −0.995161 0.0982623i \(-0.968672\pi\)
0.773167 + 0.634203i \(0.218672\pi\)
\(422\) 0 0
\(423\) 711.280 + 711.280i 0.0817580 + 0.0817580i
\(424\) 0 0
\(425\) −306.185 + 306.185i −0.0349462 + 0.0349462i
\(426\) 0 0
\(427\) −4146.80 1717.66i −0.469971 0.194668i
\(428\) 0 0
\(429\) 2871.54 + 6932.52i 0.323169 + 0.780199i
\(430\) 0 0
\(431\) 12541.7i 1.40165i 0.713331 + 0.700827i \(0.247186\pi\)
−0.713331 + 0.700827i \(0.752814\pi\)
\(432\) 0 0
\(433\) 5467.10i 0.606772i 0.952868 + 0.303386i \(0.0981171\pi\)
−0.952868 + 0.303386i \(0.901883\pi\)
\(434\) 0 0
\(435\) −5258.81 12695.9i −0.579634 1.39936i
\(436\) 0 0
\(437\) −6058.08 2509.34i −0.663152 0.274687i
\(438\) 0 0
\(439\) 6912.86 6912.86i 0.751556 0.751556i −0.223214 0.974770i \(-0.571655\pi\)
0.974770 + 0.223214i \(0.0716548\pi\)
\(440\) 0 0
\(441\) −450.126 450.126i −0.0486045 0.0486045i
\(442\) 0 0
\(443\) −5145.53 + 12422.4i −0.551854 + 1.33229i 0.364230 + 0.931309i \(0.381332\pi\)
−0.916084 + 0.400985i \(0.868668\pi\)
\(444\) 0 0
\(445\) −12577.2 + 5209.66i −1.33981 + 0.554969i
\(446\) 0 0
\(447\) 9073.44 0.960088
\(448\) 0 0
\(449\) 4228.21 0.444413 0.222207 0.975000i \(-0.428674\pi\)
0.222207 + 0.975000i \(0.428674\pi\)
\(450\) 0 0
\(451\) −10098.5 + 4182.95i −1.05437 + 0.436735i
\(452\) 0 0
\(453\) −1689.72 + 4079.34i −0.175253 + 0.423099i
\(454\) 0 0
\(455\) 5358.26 + 5358.26i 0.552086 + 0.552086i
\(456\) 0 0
\(457\) −1932.67 + 1932.67i −0.197826 + 0.197826i −0.799067 0.601242i \(-0.794673\pi\)
0.601242 + 0.799067i \(0.294673\pi\)
\(458\) 0 0
\(459\) 13186.6 + 5462.08i 1.34096 + 0.555443i
\(460\) 0 0
\(461\) 5203.91 + 12563.3i 0.525749 + 1.26927i 0.934285 + 0.356527i \(0.116039\pi\)
−0.408536 + 0.912742i \(0.633961\pi\)
\(462\) 0 0
\(463\) 6800.09i 0.682564i −0.939961 0.341282i \(-0.889139\pi\)
0.939961 0.341282i \(-0.110861\pi\)
\(464\) 0 0
\(465\) 14228.3i 1.41897i
\(466\) 0 0
\(467\) −3594.92 8678.90i −0.356216 0.859982i −0.995825 0.0912813i \(-0.970904\pi\)
0.639609 0.768700i \(-0.279096\pi\)
\(468\) 0 0
\(469\) 6886.74 + 2852.58i 0.678038 + 0.280853i
\(470\) 0 0
\(471\) −6883.27 + 6883.27i −0.673385 + 0.673385i
\(472\) 0 0
\(473\) −1875.38 1875.38i −0.182304 0.182304i
\(474\) 0 0
\(475\) −45.4574 + 109.744i −0.00439101 + 0.0106008i
\(476\) 0 0
\(477\) −105.524 + 43.7095i −0.0101292 + 0.00419564i
\(478\) 0 0
\(479\) 6129.80 0.584714 0.292357 0.956309i \(-0.405561\pi\)
0.292357 + 0.956309i \(0.405561\pi\)
\(480\) 0 0
\(481\) −1024.18 −0.0970869
\(482\) 0 0
\(483\) 16571.5 6864.15i 1.56114 0.646645i
\(484\) 0 0
\(485\) −215.879 + 521.177i −0.0202114 + 0.0487947i
\(486\) 0 0
\(487\) 5985.06 + 5985.06i 0.556897 + 0.556897i 0.928423 0.371526i \(-0.121165\pi\)
−0.371526 + 0.928423i \(0.621165\pi\)
\(488\) 0 0
\(489\) −7686.69 + 7686.69i −0.710847 + 0.710847i
\(490\) 0 0
\(491\) 4495.22 + 1861.98i 0.413170 + 0.171141i 0.579579 0.814916i \(-0.303217\pi\)
−0.166409 + 0.986057i \(0.553217\pi\)
\(492\) 0 0
\(493\) −10461.6 25256.5i −0.955711 2.30729i
\(494\) 0 0
\(495\) 2938.82i 0.266849i
\(496\) 0 0
\(497\) 654.274i 0.0590507i
\(498\) 0 0
\(499\) −6391.46 15430.3i −0.573389 1.38428i −0.898653 0.438659i \(-0.855453\pi\)
0.325265 0.945623i \(-0.394547\pi\)
\(500\) 0 0
\(501\) −5201.50 2154.53i −0.463844 0.192131i
\(502\) 0 0
\(503\) −13536.2 + 13536.2i −1.19990 + 1.19990i −0.225706 + 0.974196i \(0.572469\pi\)
−0.974196 + 0.225706i \(0.927531\pi\)
\(504\) 0 0
\(505\) 3136.88 + 3136.88i 0.276415 + 0.276415i
\(506\) 0 0
\(507\) −1048.28 + 2530.76i −0.0918257 + 0.221687i
\(508\) 0 0
\(509\) −6936.01 + 2872.99i −0.603995 + 0.250183i −0.663659 0.748036i \(-0.730997\pi\)
0.0596637 + 0.998219i \(0.480997\pi\)
\(510\) 0 0
\(511\) −7756.03 −0.671442
\(512\) 0 0
\(513\) 3915.48 0.336983
\(514\) 0 0
\(515\) −8665.56 + 3589.39i −0.741456 + 0.307121i
\(516\) 0 0
\(517\) 1303.98 3148.09i 0.110926 0.267800i
\(518\) 0 0
\(519\) −2110.18 2110.18i −0.178471 0.178471i
\(520\) 0 0
\(521\) −513.751 + 513.751i −0.0432012 + 0.0432012i −0.728377 0.685176i \(-0.759725\pi\)
0.685176 + 0.728377i \(0.259725\pi\)
\(522\) 0 0
\(523\) −10786.8 4468.04i −0.901861 0.373563i −0.116926 0.993141i \(-0.537304\pi\)
−0.784936 + 0.619577i \(0.787304\pi\)
\(524\) 0 0
\(525\) −124.346 300.198i −0.0103370 0.0249556i
\(526\) 0 0
\(527\) 28304.9i 2.33963i
\(528\) 0 0
\(529\) 20905.9i 1.71825i
\(530\) 0 0
\(531\) 1867.90 + 4509.52i 0.152656 + 0.368543i
\(532\) 0 0
\(533\) 14021.3 + 5807.81i 1.13946 + 0.471978i
\(534\) 0 0
\(535\) 6968.63 6968.63i 0.563141 0.563141i
\(536\) 0 0
\(537\) 13617.1 + 13617.1i 1.09426 + 1.09426i
\(538\) 0 0
\(539\) −825.210 + 1992.23i −0.0659449 + 0.159205i
\(540\) 0 0
\(541\) 1012.42 419.356i 0.0804568 0.0333263i −0.342092 0.939666i \(-0.611135\pi\)
0.422549 + 0.906340i \(0.361135\pi\)
\(542\) 0 0
\(543\) 11156.0 0.881678
\(544\) 0 0
\(545\) 22802.1 1.79217
\(546\) 0 0
\(547\) 16637.9 6891.62i 1.30052 0.538692i 0.378415 0.925636i \(-0.376469\pi\)
0.922103 + 0.386944i \(0.126469\pi\)
\(548\) 0 0
\(549\) −924.912 + 2232.94i −0.0719022 + 0.173587i
\(550\) 0 0
\(551\) −5302.84 5302.84i −0.409997 0.409997i
\(552\) 0 0
\(553\) −452.553 + 452.553i −0.0348002 + 0.0348002i
\(554\) 0 0
\(555\) −1498.91 620.869i −0.114640 0.0474854i
\(556\) 0 0
\(557\) −5219.38 12600.7i −0.397041 0.958543i −0.988364 0.152108i \(-0.951394\pi\)
0.591323 0.806435i \(-0.298606\pi\)
\(558\) 0 0
\(559\) 3682.42i 0.278622i
\(560\) 0 0
\(561\) 23646.5i 1.77960i
\(562\) 0 0
\(563\) −7201.62 17386.3i −0.539098 1.30150i −0.925353 0.379106i \(-0.876232\pi\)
0.386255 0.922392i \(-0.373768\pi\)
\(564\) 0 0
\(565\) −7308.92 3027.45i −0.544227 0.225426i
\(566\) 0 0
\(567\) −10361.7 + 10361.7i −0.767463 + 0.767463i
\(568\) 0 0
\(569\) −2337.98 2337.98i −0.172255 0.172255i 0.615714 0.787969i \(-0.288868\pi\)
−0.787969 + 0.615714i \(0.788868\pi\)
\(570\) 0 0
\(571\) 6423.07 15506.7i 0.470748 1.13649i −0.493086 0.869981i \(-0.664131\pi\)
0.963834 0.266505i \(-0.0858688\pi\)
\(572\) 0 0
\(573\) −2517.49 + 1042.78i −0.183542 + 0.0760256i
\(574\) 0 0
\(575\) −599.126 −0.0434526
\(576\) 0 0
\(577\) −15420.1 −1.11256 −0.556279 0.830995i \(-0.687772\pi\)
−0.556279 + 0.830995i \(0.687772\pi\)
\(578\) 0 0
\(579\) −17703.8 + 7333.13i −1.27071 + 0.526347i
\(580\) 0 0
\(581\) 3786.36 9141.08i 0.270369 0.652730i
\(582\) 0 0
\(583\) 273.588 + 273.588i 0.0194354 + 0.0194354i
\(584\) 0 0
\(585\) 2885.28 2885.28i 0.203917 0.203917i
\(586\) 0 0
\(587\) 4807.28 + 1991.24i 0.338020 + 0.140013i 0.545236 0.838283i \(-0.316440\pi\)
−0.207216 + 0.978295i \(0.566440\pi\)
\(588\) 0 0
\(589\) 2971.45 + 7173.71i 0.207872 + 0.501846i
\(590\) 0 0
\(591\) 16024.2i 1.11531i
\(592\) 0 0
\(593\) 7386.71i 0.511528i −0.966739 0.255764i \(-0.917673\pi\)
0.966739 0.255764i \(-0.0823269\pi\)
\(594\) 0 0
\(595\) 9138.40 + 22062.0i 0.629643 + 1.52009i
\(596\) 0 0
\(597\) −18251.3 7559.95i −1.25122 0.518271i
\(598\) 0 0
\(599\) 14260.6 14260.6i 0.972744 0.972744i −0.0268941 0.999638i \(-0.508562\pi\)
0.999638 + 0.0268941i \(0.00856169\pi\)
\(600\) 0 0
\(601\) −849.123 849.123i −0.0576314 0.0576314i 0.677704 0.735335i \(-0.262975\pi\)
−0.735335 + 0.677704i \(0.762975\pi\)
\(602\) 0 0
\(603\) 1536.04 3708.32i 0.103735 0.250438i
\(604\) 0 0
\(605\) −4368.53 + 1809.50i −0.293564 + 0.121598i
\(606\) 0 0
\(607\) −24362.0 −1.62904 −0.814518 0.580139i \(-0.802998\pi\)
−0.814518 + 0.580139i \(0.802998\pi\)
\(608\) 0 0
\(609\) 20514.0 1.36497
\(610\) 0 0
\(611\) −4370.96 + 1810.51i −0.289411 + 0.119878i
\(612\) 0 0
\(613\) −2098.82 + 5066.99i −0.138288 + 0.333856i −0.977818 0.209457i \(-0.932830\pi\)
0.839530 + 0.543313i \(0.182830\pi\)
\(614\) 0 0
\(615\) 16999.6 + 16999.6i 1.11462 + 1.11462i
\(616\) 0 0
\(617\) 18585.0 18585.0i 1.21265 1.21265i 0.242493 0.970153i \(-0.422035\pi\)
0.970153 0.242493i \(-0.0779652\pi\)
\(618\) 0 0
\(619\) −5415.72 2243.27i −0.351658 0.145662i 0.199860 0.979824i \(-0.435951\pi\)
−0.551518 + 0.834163i \(0.685951\pi\)
\(620\) 0 0
\(621\) 7557.48 + 18245.4i 0.488360 + 1.17900i
\(622\) 0 0
\(623\) 20322.2i 1.30689i
\(624\) 0 0
\(625\) 15202.3i 0.972950i
\(626\) 0 0
\(627\) 2482.41 + 5993.06i 0.158114 + 0.381722i
\(628\) 0 0
\(629\) −2981.84 1235.12i −0.189020 0.0782949i
\(630\) 0 0
\(631\) −9326.18 + 9326.18i −0.588382 + 0.588382i −0.937193 0.348811i \(-0.886586\pi\)
0.348811 + 0.937193i \(0.386586\pi\)
\(632\) 0 0
\(633\) −22907.5 22907.5i −1.43837 1.43837i
\(634\) 0 0
\(635\) 3011.92 7271.41i 0.188227 0.454421i
\(636\) 0 0
\(637\) 2766.11 1145.76i 0.172052 0.0712664i
\(638\) 0 0
\(639\) 352.309 0.0218108
\(640\) 0 0
\(641\) −24698.6 −1.52189 −0.760947 0.648814i \(-0.775265\pi\)
−0.760947 + 0.648814i \(0.775265\pi\)
\(642\) 0 0
\(643\) 15953.0 6607.95i 0.978422 0.405276i 0.164581 0.986364i \(-0.447373\pi\)
0.813841 + 0.581088i \(0.197373\pi\)
\(644\) 0 0
\(645\) −2232.31 + 5389.28i −0.136275 + 0.328996i
\(646\) 0 0
\(647\) −15582.9 15582.9i −0.946874 0.946874i 0.0517843 0.998658i \(-0.483509\pi\)
−0.998658 + 0.0517843i \(0.983509\pi\)
\(648\) 0 0
\(649\) 11691.6 11691.6i 0.707145 0.707145i
\(650\) 0 0
\(651\) −19623.2 8128.21i −1.18141 0.489354i
\(652\) 0 0
\(653\) 6341.65 + 15310.1i 0.380043 + 0.917504i 0.991956 + 0.126580i \(0.0403999\pi\)
−0.611914 + 0.790924i \(0.709600\pi\)
\(654\) 0 0
\(655\) 10971.2i 0.654474i
\(656\) 0 0
\(657\) 4176.41i 0.248002i
\(658\) 0 0
\(659\) 7357.67 + 17763.0i 0.434923 + 1.05000i 0.977679 + 0.210106i \(0.0673810\pi\)
−0.542756 + 0.839891i \(0.682619\pi\)
\(660\) 0 0
\(661\) −8796.41 3643.59i −0.517611 0.214401i 0.108556 0.994090i \(-0.465377\pi\)
−0.626167 + 0.779689i \(0.715377\pi\)
\(662\) 0 0
\(663\) 23215.7 23215.7i 1.35991 1.35991i
\(664\) 0 0
\(665\) 4632.14 + 4632.14i 0.270115 + 0.270115i
\(666\) 0 0
\(667\) 14474.9 34945.5i 0.840286 2.02863i
\(668\) 0 0
\(669\) 36634.6 15174.5i 2.11715 0.876953i
\(670\) 0 0
\(671\) 8187.22 0.471034
\(672\) 0 0
\(673\) −18778.9 −1.07559 −0.537795 0.843076i \(-0.680743\pi\)
−0.537795 + 0.843076i \(0.680743\pi\)
\(674\) 0 0
\(675\) 330.520 136.906i 0.0188470 0.00780668i
\(676\) 0 0
\(677\) 2171.42 5242.27i 0.123271 0.297603i −0.850182 0.526489i \(-0.823508\pi\)
0.973453 + 0.228886i \(0.0735083\pi\)
\(678\) 0 0
\(679\) −595.467 595.467i −0.0336552 0.0336552i
\(680\) 0 0
\(681\) −4786.88 + 4786.88i −0.269359 + 0.269359i
\(682\) 0 0
\(683\) 25821.4 + 10695.6i 1.44660 + 0.599202i 0.961389 0.275195i \(-0.0887423\pi\)
0.485212 + 0.874396i \(0.338742\pi\)
\(684\) 0 0
\(685\) −9490.40 22911.9i −0.529357 1.27798i
\(686\) 0 0
\(687\) 15438.1i 0.857351i
\(688\) 0 0
\(689\) 537.207i 0.0297039i
\(690\) 0 0
\(691\) 4070.96 + 9828.16i 0.224120 + 0.541072i 0.995442 0.0953726i \(-0.0304042\pi\)
−0.771322 + 0.636445i \(0.780404\pi\)
\(692\) 0 0
\(693\) −4053.13 1678.86i −0.222173 0.0920269i
\(694\) 0 0
\(695\) −6998.86 + 6998.86i −0.381988 + 0.381988i
\(696\) 0 0
\(697\) 33818.1 + 33818.1i 1.83781 + 1.83781i
\(698\) 0 0
\(699\) −3171.21 + 7655.98i −0.171597 + 0.414272i
\(700\) 0 0
\(701\) 1993.12 825.577i 0.107388 0.0444816i −0.328343 0.944559i \(-0.606490\pi\)
0.435731 + 0.900077i \(0.356490\pi\)
\(702\) 0 0
\(703\) −885.392 −0.0475010
\(704\) 0 0
\(705\) −7494.50 −0.400368
\(706\) 0 0
\(707\) −6118.30 + 2534.28i −0.325463 + 0.134811i
\(708\) 0 0
\(709\) −8011.74 + 19342.1i −0.424383 + 1.02455i 0.556657 + 0.830742i \(0.312084\pi\)
−0.981040 + 0.193808i \(0.937916\pi\)
\(710\) 0 0
\(711\) 243.687 + 243.687i 0.0128537 + 0.0128537i
\(712\) 0 0
\(713\) −27692.8 + 27692.8i −1.45456 + 1.45456i
\(714\) 0 0
\(715\) −12770.1 5289.54i −0.667935 0.276668i
\(716\) 0 0
\(717\) −1618.78 3908.07i −0.0843157 0.203556i
\(718\) 0 0
\(719\) 29047.6i 1.50667i −0.657639 0.753334i \(-0.728445\pi\)
0.657639 0.753334i \(-0.271555\pi\)
\(720\) 0 0
\(721\) 14001.8i 0.723237i
\(722\) 0 0
\(723\) 3898.15 + 9410.96i 0.200517 + 0.484090i
\(724\) 0 0
\(725\) −633.048 262.217i −0.0324287 0.0134324i
\(726\) 0 0
\(727\) 12248.6 12248.6i 0.624862 0.624862i −0.321909 0.946771i \(-0.604324\pi\)
0.946771 + 0.321909i \(0.104324\pi\)
\(728\) 0 0
\(729\) −6837.10 6837.10i −0.347361 0.347361i
\(730\) 0 0
\(731\) −4440.83 + 10721.1i −0.224692 + 0.542455i
\(732\) 0 0
\(733\) 17288.6 7161.19i 0.871174 0.360852i 0.0981066 0.995176i \(-0.468721\pi\)
0.773067 + 0.634324i \(0.218721\pi\)
\(734\) 0 0
\(735\) 4742.82 0.238016
\(736\) 0 0
\(737\) −13596.8 −0.679573
\(738\) 0 0
\(739\) −31548.5 + 13067.8i −1.57041 + 0.650483i −0.986857 0.161595i \(-0.948336\pi\)
−0.583548 + 0.812079i \(0.698336\pi\)
\(740\) 0 0
\(741\) 3446.69 8321.05i 0.170874 0.412526i
\(742\) 0 0
\(743\) 19385.2 + 19385.2i 0.957163 + 0.957163i 0.999119 0.0419563i \(-0.0133590\pi\)
−0.0419563 + 0.999119i \(0.513359\pi\)
\(744\) 0 0
\(745\) −11818.4 + 11818.4i −0.581199 + 0.581199i
\(746\) 0 0
\(747\) −4922.22 2038.85i −0.241090 0.0998629i
\(748\) 0 0
\(749\) 5629.95 + 13591.9i 0.274651 + 0.663067i
\(750\) 0 0
\(751\) 32864.8i 1.59688i 0.602078 + 0.798438i \(0.294340\pi\)
−0.602078 + 0.798438i \(0.705660\pi\)
\(752\) 0 0
\(753\) 6828.75i 0.330483i
\(754\) 0 0
\(755\) −3112.55 7514.36i −0.150036 0.362219i
\(756\) 0 0
\(757\) 29982.4 + 12419.1i 1.43954 + 0.596275i 0.959686 0.281076i \(-0.0906912\pi\)
0.479850 + 0.877351i \(0.340691\pi\)
\(758\) 0 0
\(759\) −23135.1 + 23135.1i −1.10639 + 1.10639i
\(760\) 0 0
\(761\) 11824.8 + 11824.8i 0.563270 + 0.563270i 0.930235 0.366965i \(-0.119603\pi\)
−0.366965 + 0.930235i \(0.619603\pi\)
\(762\) 0 0
\(763\) −13026.2 + 31448.0i −0.618059 + 1.49213i
\(764\) 0 0
\(765\) 11879.8 4920.77i 0.561457 0.232563i
\(766\) 0 0
\(767\) −22957.3 −1.08076
\(768\) 0 0
\(769\) −6754.02 −0.316718 −0.158359 0.987382i \(-0.550620\pi\)
−0.158359 + 0.987382i \(0.550620\pi\)
\(770\) 0 0
\(771\) −38765.8 + 16057.3i −1.81079 + 0.750052i
\(772\) 0 0
\(773\) −8503.04 + 20528.2i −0.395644 + 0.955170i 0.593042 + 0.805172i \(0.297927\pi\)
−0.988686 + 0.149998i \(0.952073\pi\)
\(774\) 0 0
\(775\) 501.662 + 501.662i 0.0232519 + 0.0232519i
\(776\) 0 0
\(777\) 1712.57 1712.57i 0.0790708 0.0790708i
\(778\) 0 0
\(779\) 12121.2 + 5020.76i 0.557493 + 0.230921i
\(780\) 0 0
\(781\) −456.708 1102.59i −0.0209248 0.0505170i
\(782\) 0 0
\(783\) 22586.1i 1.03086i
\(784\) 0 0
\(785\) 17931.3i 0.815282i
\(786\) 0 0