Properties

Label 128.4.g.a.81.3
Level $128$
Weight $4$
Character 128.81
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 81.3
Character \(\chi\) \(=\) 128.81
Dual form 128.4.g.a.49.3

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\)

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 −0.219676 0.975573i \(-0.570500\pi\)
−0.845169 + 0.534499i \(0.820500\pi\)
\(4\) 0 0
\(5\) 4.22177 + 10.1923i 0.377607 + 0.911624i 0.992413 + 0.122946i \(0.0392341\pi\)
−0.614807 + 0.788678i \(0.710766\pi\)
\(6\) 0 0
\(7\) 11.6451 11.6451i 0.628775 0.628775i −0.318985 0.947760i \(-0.603342\pi\)
0.947760 + 0.318985i \(0.103342\pi\)
\(8\) 0 0
\(9\) 6.27055 + 6.27055i 0.232243 + 0.232243i
\(10\) 0 0
\(11\) −27.7531 + 11.4957i −0.760717 + 0.315099i −0.729106 0.684401i \(-0.760064\pi\)
−0.0316109 + 0.999500i \(0.510064\pi\)
\(12\) 0 0
\(13\) 15.9612 38.5338i 0.340527 0.822104i −0.657136 0.753772i \(-0.728232\pi\)
0.997663 0.0683319i \(-0.0217677\pi\)
\(14\) 0 0
\(15\) 66.0706i 1.13729i
\(16\) 0 0
\(17\) 131.437i 1.87518i −0.347736 0.937592i \(-0.613049\pi\)
0.347736 0.937592i \(-0.386951\pi\)
\(18\) 0 0
\(19\) 13.7982 33.3119i 0.166607 0.402224i −0.818421 0.574619i \(-0.805150\pi\)
0.985028 + 0.172394i \(0.0551503\pi\)
\(20\) 0 0
\(21\) −91.1226 + 37.7442i −0.946884 + 0.392212i
\(22\) 0 0
\(23\) −128.594 128.594i −1.16582 1.16582i −0.983181 0.182634i \(-0.941538\pi\)
−0.182634 0.983181i \(-0.558462\pi\)
\(24\) 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 −0.329721 0.944078i \(-0.606955\pi\)
−0.900712 + 0.434416i \(0.856955\pi\)
\(30\) 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 0.901627 0.432514i \(-0.142373\pi\)
−0.943380 + 0.331713i \(0.892373\pi\)
\(38\) 0 0
\(39\) −176.630 + 176.630i −0.725216 + 0.725216i
\(40\) 0 0
\(41\) 257.295 + 257.295i 0.980067 + 0.980067i 0.999805 0.0197381i \(-0.00628325\pi\)
−0.0197381 + 0.999805i \(0.506283\pi\)
\(42\) 0 0
\(43\) 81.5685 33.7868i 0.289281 0.119824i −0.233324 0.972399i \(-0.574960\pi\)
0.522605 + 0.852575i \(0.324960\pi\)
\(44\) 0 0
\(45\) −37.4383 + 90.3840i −0.124022 + 0.299414i
\(46\) 0 0
\(47\) 113.432i 0.352037i −0.984387 0.176018i \(-0.943678\pi\)
0.984387 0.176018i \(-0.0563218\pi\)
\(48\) 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 −0.398050 0.917364i \(-0.630313\pi\)
0.367210 + 0.930138i \(0.380313\pi\)
\(54\) 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 −0.966408 0.257011i \(-0.917262\pi\)
0.501619 0.865088i \(-0.332738\pi\)
\(60\) 0 0
\(61\) −251.800 104.299i −0.528519 0.218920i 0.102436 0.994740i \(-0.467336\pi\)
−0.630954 + 0.775820i \(0.717336\pi\)
\(62\) 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 0.729833 0.683625i \(-0.239598\pi\)
0.0326737 + 0.999466i \(0.489598\pi\)
\(68\) 0 0
\(69\) 416.801 + 1006.25i 0.727203 + 1.75562i
\(70\) 0 0
\(71\) 28.0923 28.0923i 0.0469569 0.0469569i −0.683238 0.730195i \(-0.739429\pi\)
0.730195 + 0.683238i \(0.239429\pi\)
\(72\) 0 0
\(73\) −333.018 333.018i −0.533928 0.533928i 0.387811 0.921739i \(-0.373231\pi\)
−0.921739 + 0.387811i \(0.873231\pi\)
\(74\) 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 \(-0.991190\pi\)
0.999617 0.0276730i \(-0.00880971\pi\)
\(80\) 0 0
\(81\) 889.794i 1.22057i
\(82\) 0 0
\(83\) −229.913 + 555.060i −0.304051 + 0.734045i 0.695823 + 0.718213i \(0.255040\pi\)
−0.999875 + 0.0158320i \(0.994960\pi\)
\(84\) 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 −0.0400377 + 0.999198i \(0.512748\pi\)
−0.999198 + 0.0400377i \(0.987252\pi\)
\(90\) 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 0.829770 0.558105i \(-0.188471\pi\)
−0.981376 + 0.192096i \(0.938471\pi\)
\(102\) 0 0
\(103\) −601.189 + 601.189i −0.575115 + 0.575115i −0.933553 0.358438i \(-0.883309\pi\)
0.358438 + 0.933553i \(0.383309\pi\)
\(104\) 0 0
\(105\) −769.398 769.398i −0.715100 0.715100i
\(106\) 0 0
\(107\) 825.321 341.859i 0.745671 0.308867i 0.0226969 0.999742i \(-0.492775\pi\)
0.722974 + 0.690875i \(0.242775\pi\)
\(108\) 0 0
\(109\) 790.968 1909.57i 0.695055 1.67801i −0.0392828 0.999228i \(-0.512507\pi\)
0.734338 0.678784i \(-0.237493\pi\)
\(110\) 0 0
\(111\) 147.064i 0.125754i
\(112\) 0 0
\(113\) 717.104i 0.596987i 0.954412 + 0.298493i \(0.0964841\pi\)
−0.954412 + 0.298493i \(0.903516\pi\)
\(114\) 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 0.0546341 0.998506i \(-0.482601\pi\)
−0.667419 + 0.744683i \(0.732601\pi\)
\(132\) 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 0.999962 0.00868786i \(-0.00276547\pi\)
−0.00868786 + 0.999962i \(0.502765\pi\)
\(138\) 0 0
\(139\) −828.901 + 343.342i −0.505802 + 0.209510i −0.620967 0.783836i \(-0.713260\pi\)
0.115166 + 0.993346i \(0.463260\pi\)
\(140\) 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 −0.732703 0.680548i \(-0.761742\pi\)
−0.0368792 + 0.999320i \(0.511742\pi\)
\(150\) 0 0
\(151\) 521.322 + 521.322i 0.280958 + 0.280958i 0.833491 0.552533i \(-0.186339\pi\)
−0.552533 + 0.833491i \(0.686339\pi\)
\(152\) 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 0.730175 0.683260i \(-0.239439\pi\)
0.0331736 + 0.999450i \(0.489439\pi\)
\(158\) 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 0.747283 0.664506i \(-0.231358\pi\)
0.0585321 + 0.998286i \(0.481358\pi\)
\(164\) 0 0
\(165\) 759.529 + 1833.67i 0.358359 + 0.865156i
\(166\) 0 0
\(167\) 664.730 664.730i 0.308014 0.308014i −0.536125 0.844139i \(-0.680112\pi\)
0.844139 + 0.536125i \(0.180112\pi\)
\(168\) 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 −0.876424 0.481540i \(-0.840078\pi\)
0.960226 + 0.279225i \(0.0900776\pi\)
\(174\) 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 0.427835 + 0.903857i \(0.359277\pi\)
−0.941648 + 0.336599i \(0.890723\pi\)
\(180\) 0 0
\(181\) −1720.96 + 712.847i −0.706731 + 0.292738i −0.706951 0.707262i \(-0.749930\pi\)
0.000220198 1.00000i \(0.499930\pi\)
\(182\) 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 −0.993698 0.112093i \(-0.964244\pi\)
0.623388 0.781912i \(-0.285756\pi\)
\(198\) 0 0
\(199\) 2332.44 2332.44i 0.830867 0.830867i −0.156768 0.987635i \(-0.550108\pi\)
0.987635 + 0.156768i \(0.0501077\pi\)
\(200\) 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 −0.0969206 0.995292i \(-0.530899\pi\)
0.772311 0.635245i \(-0.219101\pi\)
\(212\) 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 0.530095 0.847939i \(-0.322156\pi\)
−0.224750 + 0.974417i \(0.572156\pi\)
\(228\) 0 0
\(229\) −986.462 2381.53i −0.284660 0.687231i 0.715272 0.698846i \(-0.246303\pi\)
−0.999933 + 0.0116150i \(0.996303\pi\)
\(230\) 0 0
\(231\) 2095.04 2095.04i 0.596725 0.596725i
\(232\) 0 0
\(233\) 978.403 + 978.403i 0.275096 + 0.275096i 0.831148 0.556052i \(-0.187684\pi\)
−0.556052 + 0.831148i \(0.687684\pi\)
\(234\) 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 \(-0.969529\pi\)
0.995422 0.0955801i \(-0.0304706\pi\)
\(240\) 0 0
\(241\) 1700.85i 0.454611i 0.973824 + 0.227305i \(0.0729916\pi\)
−0.973824 + 0.227305i \(0.927008\pi\)
\(242\) 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 0.969200 0.246277i \(-0.0792072\pi\)
−0.859472 + 0.511184i \(0.829207\pi\)
\(252\) 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 −0.663451 0.748219i \(-0.730909\pi\)
0.748219 + 0.663451i \(0.230909\pi\)
\(264\) 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 −0.918635 0.395107i \(-0.870708\pi\)
0.928956 + 0.370190i \(0.120708\pi\)
\(270\) 0 0
\(271\) 3443.94i 0.771972i −0.922505 0.385986i \(-0.873861\pi\)
0.922505 0.385986i \(-0.126139\pi\)
\(272\) 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 −0.598741 0.800943i \(-0.704332\pi\)
0.142979 + 0.989726i \(0.454332\pi\)
\(278\) 0 0
\(279\) 1350.36 + 1350.36i 0.289764 + 0.289764i
\(280\) 0 0
\(281\) 2252.56 2252.56i 0.478207 0.478207i −0.426351 0.904558i \(-0.640201\pi\)
0.904558 + 0.426351i \(0.140201\pi\)
\(282\) 0 0
\(283\) −2659.18 6419.84i −0.558559 1.34848i −0.910907 0.412611i \(-0.864617\pi\)
0.352349 0.935869i \(-0.385383\pi\)
\(284\) 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 −0.996705 0.0811131i \(-0.974153\pi\)
0.647421 0.762132i \(-0.275847\pi\)
\(294\) 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 −0.907057 0.421008i \(-0.861677\pi\)
0.939084 + 0.343689i \(0.111677\pi\)
\(308\) 0 0
\(309\) 4704.29 1948.58i 0.866077 0.358741i
\(310\) 0 0
\(311\) −1586.57 1586.57i −0.289279 0.289279i 0.547516 0.836795i \(-0.315574\pi\)
−0.836795 + 0.547516i \(0.815574\pi\)
\(312\) 0 0
\(313\) 1221.66 1221.66i 0.220615 0.220615i −0.588143 0.808757i \(-0.700141\pi\)
0.808757 + 0.588143i \(0.200141\pi\)
\(314\) 0 0
\(315\) 616.557 + 1488.50i 0.110283 + 0.266246i
\(316\) 0 0
\(317\) 1676.17 + 694.291i 0.296981 + 0.123013i 0.526199 0.850362i \(-0.323617\pi\)
−0.229218 + 0.973375i \(0.573617\pi\)
\(318\) 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 −0.518378 0.855152i \(-0.673464\pi\)
0.238135 + 0.971232i \(0.423464\pi\)
\(332\) 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 \(-0.807255\pi\)
0.822203 0.569194i \(-0.192745\pi\)
\(338\) 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 0.999597 0.0283982i \(-0.00904065\pi\)
−0.726902 + 0.686741i \(0.759041\pi\)
\(348\) 0 0
\(349\) 10776.6 + 4463.83i 1.65289 + 0.684651i 0.997502 0.0706374i \(-0.0225033\pi\)
0.655392 + 0.755289i \(0.272503\pi\)
\(350\) 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 −0.160338 0.987062i \(-0.551258\pi\)
0.987062 + 0.160338i \(0.0512583\pi\)
\(360\) 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 \(0.119161\pi\)
−0.930744 + 0.365672i \(0.880839\pi\)
\(368\) 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 0.0554183 0.998463i \(-0.482351\pi\)
0.745207 + 0.666833i \(0.232351\pi\)
\(374\) 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 0.975565 0.219709i \(-0.0705108\pi\)
−0.845187 + 0.534471i \(0.820511\pi\)
\(380\) 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 0.931503 + 0.363734i \(0.118498\pi\)
−0.401473 + 0.915871i \(0.631502\pi\)
\(390\) 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 −0.992185 0.124773i \(-0.960180\pi\)
0.789809 + 0.613353i \(0.210180\pi\)
\(398\) 0 0
\(399\) 3556.26i 0.446205i
\(400\) 0 0
\(401\) 2096.79i 0.261119i 0.991440 + 0.130560i \(0.0416774\pi\)
−0.991440 + 0.130560i \(0.958323\pi\)
\(402\) 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 −0.843856 0.536570i \(-0.819720\pi\)
0.536570 + 0.843856i \(0.319720\pi\)
\(410\) 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 0.888324 0.459217i \(-0.151870\pi\)
0.303425 + 0.952855i \(0.401870\pi\)
\(420\) 0 0
\(421\) −1917.63 4629.56i −0.221994 0.535940i 0.773167 0.634203i \(-0.218672\pi\)
−0.995161 + 0.0982623i \(0.968672\pi\)
\(422\) 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 \(-0.752814\pi\)
0.713331 0.700827i \(-0.247186\pi\)
\(432\) 0 0
\(433\) 5467.10i 0.606772i −0.952868 0.303386i \(-0.901883\pi\)
0.952868 0.303386i \(-0.0981171\pi\)
\(434\) 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 0.974770 0.223214i \(-0.0716548\pi\)
−0.223214 + 0.974770i \(0.571655\pi\)
\(440\) 0 0
\(441\) −450.126 + 450.126i −0.0486045 + 0.0486045i
\(442\) 0 0
\(443\) −5145.53 12422.4i −0.551854 1.33229i −0.916084 0.400985i \(-0.868668\pi\)
0.364230 0.931309i \(-0.381332\pi\)
\(444\) 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 0.601242 0.799067i \(-0.294673\pi\)
−0.799067 + 0.601242i \(0.794673\pi\)
\(458\) 0 0
\(459\) 13186.6 5462.08i 1.34096 0.555443i
\(460\) 0 0
\(461\) 5203.91 12563.3i 0.525749 1.26927i −0.408536 0.912742i \(-0.633961\pi\)
0.934285 0.356527i \(-0.116039\pi\)
\(462\) 0 0
\(463\) 6800.09i 0.682564i 0.939961 + 0.341282i \(0.110861\pi\)
−0.939961 + 0.341282i \(0.889139\pi\)
\(464\) 0 0
\(465\) 14228.3i 1.41897i
\(466\) 0 0
\(467\) −3594.92 + 8678.90i −0.356216 + 0.859982i 0.639609 + 0.768700i \(0.279096\pi\)
−0.995825 + 0.0912813i \(0.970904\pi\)
\(468\) 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 −0.371526 0.928423i \(-0.621165\pi\)
0.928423 + 0.371526i \(0.121165\pi\)
\(488\) 0 0
\(489\) −7686.69 7686.69i −0.710847 0.710847i
\(490\) 0 0
\(491\) 4495.22 1861.98i 0.413170 0.171141i −0.166409 0.986057i \(-0.553217\pi\)
0.579579 + 0.814916i \(0.303217\pi\)
\(492\) 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 0.325265 + 0.945623i \(0.394547\pi\)
−0.898653 + 0.438659i \(0.855453\pi\)
\(500\) 0 0
\(501\) −5201.50 + 2154.53i −0.463844 + 0.192131i
\(502\) 0 0
\(503\) −13536.2 13536.2i −1.19990 1.19990i −0.974196 0.225706i \(-0.927531\pi\)
−0.225706 0.974196i \(-0.572469\pi\)
\(504\) 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 0.0596637 0.998219i \(-0.480997\pi\)
−0.663659 + 0.748036i \(0.730997\pi\)
\(510\) 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 0.685176 0.728377i \(-0.259725\pi\)
−0.728377 + 0.685176i \(0.759725\pi\)
\(522\) 0 0
\(523\) −10786.8 + 4468.04i −0.901861 + 0.373563i −0.784936 0.619577i \(-0.787304\pi\)
−0.116926 + 0.993141i \(0.537304\pi\)
\(524\) 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 0.422549 0.906340i \(-0.361135\pi\)
−0.342092 + 0.939666i \(0.611135\pi\)
\(542\) 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 0.922103 0.386944i \(-0.126469\pi\)
0.378415 + 0.925636i \(0.376469\pi\)
\(548\) 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 0.591323 + 0.806435i \(0.298606\pi\)
−0.988364 + 0.152108i \(0.951394\pi\)
\(558\) 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 0.386255 + 0.922392i \(0.373768\pi\)
−0.925353 + 0.379106i \(0.876232\pi\)
\(564\) 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 −0.787969 0.615714i \(-0.788868\pi\)
0.615714 + 0.787969i \(0.288868\pi\)
\(570\) 0 0
\(571\) 6423.07 + 15506.7i 0.470748 + 1.13649i 0.963834 + 0.266505i \(0.0858688\pi\)
−0.493086 + 0.869981i \(0.664131\pi\)
\(572\) 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 −0.207216 0.978295i \(-0.566440\pi\)
0.545236 + 0.838283i \(0.316440\pi\)
\(588\) 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 \(0.0823269\pi\)
−0.966739 + 0.255764i \(0.917673\pi\)
\(594\) 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 0.999638 0.0268941i \(-0.00856169\pi\)
−0.0268941 + 0.999638i \(0.508562\pi\)
\(600\) 0 0
\(601\) −849.123 + 849.123i −0.0576314 + 0.0576314i −0.735335 0.677704i \(-0.762975\pi\)
0.677704 + 0.735335i \(0.262975\pi\)
\(602\) 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 0.839530 0.543313i \(-0.182830\pi\)
−0.977818 + 0.209457i \(0.932830\pi\)
\(614\) 0 0
\(615\) 16999.6 16999.6i 1.11462 1.11462i
\(616\) 0 0
\(617\) 18585.0 + 18585.0i 1.21265 + 1.21265i 0.970153 + 0.242493i \(0.0779652\pi\)
0.242493 + 0.970153i \(0.422035\pi\)
\(618\) 0 0
\(619\) −5415.72 + 2243.27i −0.351658 + 0.145662i −0.551518 0.834163i \(-0.685951\pi\)
0.199860 + 0.979824i \(0.435951\pi\)
\(620\) 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 0.348811 0.937193i \(-0.386586\pi\)
−0.937193 + 0.348811i \(0.886586\pi\)
\(632\) 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 0.813841 0.581088i \(-0.197373\pi\)
0.164581 + 0.986364i \(0.447373\pi\)
\(644\) 0 0
\(645\) −2232.31 5389.28i −0.136275 0.328996i
\(646\) 0 0
\(647\) −15582.9 + 15582.9i −0.946874 + 0.946874i −0.998658 0.0517843i \(-0.983509\pi\)
0.0517843 + 0.998658i \(0.483509\pi\)
\(648\) 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 −0.611914 0.790924i \(-0.709600\pi\)
0.991956 0.126580i \(-0.0403999\pi\)
\(654\) 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 −0.542756 0.839891i \(-0.682619\pi\)
0.977679 0.210106i \(-0.0673810\pi\)
\(660\) 0 0
\(661\) −8796.41 + 3643.59i −0.517611 + 0.214401i −0.626167 0.779689i \(-0.715377\pi\)
0.108556 + 0.994090i \(0.465377\pi\)
\(662\) 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 0.973453 0.228886i \(-0.0735083\pi\)
−0.850182 + 0.526489i \(0.823508\pi\)
\(678\) 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 0.485212 0.874396i \(-0.338742\pi\)
0.961389 + 0.275195i \(0.0887423\pi\)
\(684\) 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 −0.771322 0.636445i \(-0.780404\pi\)
0.995442 + 0.0953726i \(0.0304042\pi\)
\(692\) 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 0.435731 0.900077i \(-0.356490\pi\)
−0.328343 + 0.944559i \(0.606490\pi\)
\(702\) 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 −0.981040 0.193808i \(-0.937916\pi\)
0.556657 0.830742i \(-0.312084\pi\)
\(710\) 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 \(0.271555\pi\)
−0.657639 + 0.753334i \(0.728445\pi\)
\(720\) 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 0.946771 0.321909i \(-0.104324\pi\)
−0.321909 + 0.946771i \(0.604324\pi\)
\(728\) 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 0.773067 0.634324i \(-0.218721\pi\)
0.0981066 + 0.995176i \(0.468721\pi\)
\(734\) 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 −0.583548 0.812079i \(-0.698336\pi\)
−0.986857 + 0.161595i \(0.948336\pi\)
\(740\) 0 0
\(741\) 3446.69 + 8321.05i 0.170874 + 0.412526i
\(742\) 0 0
\(743\) 19385.2 19385.2i 0.957163 0.957163i −0.0419563 0.999119i \(-0.513359\pi\)
0.999119 + 0.0419563i \(0.0133590\pi\)
\(744\) 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 \(-0.705660\pi\)
0.602078 0.798438i \(-0.294340\pi\)
\(752\) 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 0.479850 0.877351i \(-0.340691\pi\)
0.959686 + 0.281076i \(0.0906912\pi\)
\(758\) 0 0
\(759\) −23135.1 23135.1i −1.10639 1.10639i
\(760\) 0 0
\(761\) 11824.8 11824.8i 0.563270 0.563270i −0.366965 0.930235i \(-0.619603\pi\)
0.930235 + 0.366965i \(0.119603\pi\)
\(762\) 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 −0.988686 0.149998i \(-0.952073\pi\)
0.593042 0.805172i \(-0.297927\pi\)
\(774\) 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
\(787\) 7710.78 18615.5i 0.349250 0.843164i −0.647459 0.762100i \(-0.724168\pi\)
0.996709 0.0810635i \(-0.0258317\pi\)
\(788\) 0 0
\(789\) −2829.11 + 1171.86i −0.127654 + 0.0528760i
\(790\) 0 0
\(791\) 8350.74 + 8350.74i 0.375371 + 0.375371i
\(792\) 0 0
\(793\) −8038.06 + 8038.06i −0.359949 + 0.359949i
\(794\) 0 0
\(795\) 325.659 + 786.211i 0.0145282 + 0.0350742i
\(796\) 0 0
\(797\)