Properties

Label 128.4.g.a.17.8
Level $128$
Weight $4$
Character 128.17
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 17.8
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.20185 - 2.90153i) q^{3} +(-3.98512 + 1.65069i) q^{5} +(-22.4050 + 22.4050i) q^{7} +(12.1174 + 12.1174i) q^{9} +O(q^{10})\) \(q+(1.20185 - 2.90153i) q^{3} +(-3.98512 + 1.65069i) q^{5} +(-22.4050 + 22.4050i) q^{7} +(12.1174 + 12.1174i) q^{9} +(16.5161 + 39.8735i) q^{11} +(17.9201 + 7.42277i) q^{13} +13.5469i q^{15} -45.9852i q^{17} +(25.0023 + 10.3563i) q^{19} +(38.0813 + 91.9364i) q^{21} +(40.3415 + 40.3415i) q^{23} +(-75.2319 + 75.2319i) q^{25} +(128.064 - 53.0458i) q^{27} +(-88.6955 + 214.130i) q^{29} -260.478 q^{31} +135.544 q^{33} +(52.3029 - 126.270i) q^{35} +(70.4470 - 29.1801i) q^{37} +(43.0748 - 43.0748i) q^{39} +(-251.246 - 251.246i) q^{41} +(95.7143 + 231.075i) q^{43} +(-68.2916 - 28.2873i) q^{45} -15.5684i q^{47} -660.968i q^{49} +(-133.428 - 55.2676i) q^{51} +(171.815 + 414.797i) q^{53} +(-131.638 - 131.638i) q^{55} +(60.0981 - 60.0981i) q^{57} +(-53.3294 + 22.0897i) q^{59} +(297.690 - 718.686i) q^{61} -542.983 q^{63} -83.6667 q^{65} +(377.382 - 911.080i) q^{67} +(165.537 - 68.5675i) q^{69} +(359.297 - 359.297i) q^{71} +(605.446 + 605.446i) q^{73} +(127.870 + 308.706i) q^{75} +(-1263.41 - 523.321i) q^{77} +380.220i q^{79} +27.3544i q^{81} +(-235.183 - 97.4158i) q^{83} +(75.9074 + 183.257i) q^{85} +(514.706 + 514.706i) q^{87} +(-949.793 + 949.793i) q^{89} +(-567.808 + 235.194i) q^{91} +(-313.056 + 755.785i) q^{93} -116.732 q^{95} +663.589 q^{97} +(-283.031 + 683.298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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
\(3\) 1.20185 2.90153i 0.231297 0.558400i −0.765033 0.643991i \(-0.777278\pi\)
0.996330 + 0.0855902i \(0.0272776\pi\)
\(4\) 0 0
\(5\) −3.98512 + 1.65069i −0.356440 + 0.147642i −0.553716 0.832706i \(-0.686791\pi\)
0.197276 + 0.980348i \(0.436791\pi\)
\(6\) 0 0
\(7\) −22.4050 + 22.4050i −1.20976 + 1.20976i −0.238651 + 0.971105i \(0.576705\pi\)
−0.971105 + 0.238651i \(0.923295\pi\)
\(8\) 0 0
\(9\) 12.1174 + 12.1174i 0.448794 + 0.448794i
\(10\) 0 0
\(11\) 16.5161 + 39.8735i 0.452709 + 1.09294i 0.971288 + 0.237907i \(0.0764614\pi\)
−0.518578 + 0.855030i \(0.673539\pi\)
\(12\) 0 0
\(13\) 17.9201 + 7.42277i 0.382320 + 0.158362i 0.565562 0.824706i \(-0.308659\pi\)
−0.183242 + 0.983068i \(0.558659\pi\)
\(14\) 0 0
\(15\) 13.5469i 0.233185i
\(16\) 0 0
\(17\) 45.9852i 0.656062i −0.944667 0.328031i \(-0.893615\pi\)
0.944667 0.328031i \(-0.106385\pi\)
\(18\) 0 0
\(19\) 25.0023 + 10.3563i 0.301890 + 0.125047i 0.528486 0.848942i \(-0.322760\pi\)
−0.226596 + 0.973989i \(0.572760\pi\)
\(20\) 0 0
\(21\) 38.0813 + 91.9364i 0.395715 + 0.955341i
\(22\) 0 0
\(23\) 40.3415 + 40.3415i 0.365729 + 0.365729i 0.865917 0.500188i \(-0.166736\pi\)
−0.500188 + 0.865917i \(0.666736\pi\)
\(24\) 0 0
\(25\) −75.2319 + 75.2319i −0.601856 + 0.601856i
\(26\) 0 0
\(27\) 128.064 53.0458i 0.912812 0.378099i
\(28\) 0 0
\(29\) −88.6955 + 214.130i −0.567943 + 1.37113i 0.335344 + 0.942096i \(0.391148\pi\)
−0.903286 + 0.429039i \(0.858852\pi\)
\(30\) 0 0
\(31\) −260.478 −1.50913 −0.754567 0.656223i \(-0.772153\pi\)
−0.754567 + 0.656223i \(0.772153\pi\)
\(32\) 0 0
\(33\) 135.544 0.715007
\(34\) 0 0
\(35\) 52.3029 126.270i 0.252594 0.609817i
\(36\) 0 0
\(37\) 70.4470 29.1801i 0.313011 0.129654i −0.220647 0.975354i \(-0.570817\pi\)
0.533658 + 0.845700i \(0.320817\pi\)
\(38\) 0 0
\(39\) 43.0748 43.0748i 0.176859 0.176859i
\(40\) 0 0
\(41\) −251.246 251.246i −0.957026 0.957026i 0.0420884 0.999114i \(-0.486599\pi\)
−0.999114 + 0.0420884i \(0.986599\pi\)
\(42\) 0 0
\(43\) 95.7143 + 231.075i 0.339449 + 0.819501i 0.997769 + 0.0667635i \(0.0212673\pi\)
−0.658320 + 0.752738i \(0.728733\pi\)
\(44\) 0 0
\(45\) −68.2916 28.2873i −0.226229 0.0937072i
\(46\) 0 0
\(47\) 15.5684i 0.0483167i −0.999708 0.0241584i \(-0.992309\pi\)
0.999708 0.0241584i \(-0.00769059\pi\)
\(48\) 0 0
\(49\) 660.968i 1.92702i
\(50\) 0 0
\(51\) −133.428 55.2676i −0.366345 0.151745i
\(52\) 0 0
\(53\) 171.815 + 414.797i 0.445294 + 1.07503i 0.974065 + 0.226270i \(0.0726531\pi\)
−0.528771 + 0.848765i \(0.677347\pi\)
\(54\) 0 0
\(55\) −131.638 131.638i −0.322728 0.322728i
\(56\) 0 0
\(57\) 60.0981 60.0981i 0.139652 0.139652i
\(58\) 0 0
\(59\) −53.3294 + 22.0897i −0.117676 + 0.0487431i −0.440745 0.897633i \(-0.645286\pi\)
0.323069 + 0.946376i \(0.395286\pi\)
\(60\) 0 0
\(61\) 297.690 718.686i 0.624840 1.50850i −0.221118 0.975247i \(-0.570971\pi\)
0.845958 0.533250i \(-0.179029\pi\)
\(62\) 0 0
\(63\) −542.983 −1.08586
\(64\) 0 0
\(65\) −83.6667 −0.159655
\(66\) 0 0
\(67\) 377.382 911.080i 0.688127 1.66128i −0.0603949 0.998175i \(-0.519236\pi\)
0.748522 0.663110i \(-0.230764\pi\)
\(68\) 0 0
\(69\) 165.537 68.5675i 0.288815 0.119631i
\(70\) 0 0
\(71\) 359.297 359.297i 0.600574 0.600574i −0.339891 0.940465i \(-0.610390\pi\)
0.940465 + 0.339891i \(0.110390\pi\)
\(72\) 0 0
\(73\) 605.446 + 605.446i 0.970714 + 0.970714i 0.999583 0.0288694i \(-0.00919069\pi\)
−0.0288694 + 0.999583i \(0.509191\pi\)
\(74\) 0 0
\(75\) 127.870 + 308.706i 0.196869 + 0.475284i
\(76\) 0 0
\(77\) −1263.41 523.321i −1.86986 0.774520i
\(78\) 0 0
\(79\) 380.220i 0.541494i 0.962650 + 0.270747i \(0.0872707\pi\)
−0.962650 + 0.270747i \(0.912729\pi\)
\(80\) 0 0
\(81\) 27.3544i 0.0375232i
\(82\) 0 0
\(83\) −235.183 97.4158i −0.311020 0.128829i 0.221713 0.975112i \(-0.428835\pi\)
−0.532733 + 0.846283i \(0.678835\pi\)
\(84\) 0 0
\(85\) 75.9074 + 183.257i 0.0968625 + 0.233847i
\(86\) 0 0
\(87\) 514.706 + 514.706i 0.634279 + 0.634279i
\(88\) 0 0
\(89\) −949.793 + 949.793i −1.13121 + 1.13121i −0.141237 + 0.989976i \(0.545108\pi\)
−0.989976 + 0.141237i \(0.954892\pi\)
\(90\) 0 0
\(91\) −567.808 + 235.194i −0.654093 + 0.270934i
\(92\) 0 0
\(93\) −313.056 + 755.785i −0.349058 + 0.842701i
\(94\) 0 0
\(95\) −116.732 −0.126068
\(96\) 0 0
\(97\) 663.589 0.694611 0.347305 0.937752i \(-0.387097\pi\)
0.347305 + 0.937752i \(0.387097\pi\)
\(98\) 0 0
\(99\) −283.031 + 683.298i −0.287331 + 0.693677i
\(100\) 0 0
\(101\) 937.978 388.523i 0.924082 0.382767i 0.130651 0.991428i \(-0.458293\pi\)
0.793430 + 0.608661i \(0.208293\pi\)
\(102\) 0 0
\(103\) 954.756 954.756i 0.913348 0.913348i −0.0831859 0.996534i \(-0.526510\pi\)
0.996534 + 0.0831859i \(0.0265095\pi\)
\(104\) 0 0
\(105\) −303.517 303.517i −0.282098 0.282098i
\(106\) 0 0
\(107\) 172.355 + 416.102i 0.155721 + 0.375945i 0.982416 0.186706i \(-0.0597813\pi\)
−0.826694 + 0.562651i \(0.809781\pi\)
\(108\) 0 0
\(109\) 253.241 + 104.896i 0.222533 + 0.0921761i 0.491164 0.871067i \(-0.336571\pi\)
−0.268632 + 0.963243i \(0.586571\pi\)
\(110\) 0 0
\(111\) 239.475i 0.204774i
\(112\) 0 0
\(113\) 1164.80i 0.969690i 0.874600 + 0.484845i \(0.161124\pi\)
−0.874600 + 0.484845i \(0.838876\pi\)
\(114\) 0 0
\(115\) −227.357 94.1743i −0.184358 0.0763635i
\(116\) 0 0
\(117\) 127.201 + 307.091i 0.100511 + 0.242655i
\(118\) 0 0
\(119\) 1030.30 + 1030.30i 0.793675 + 0.793675i
\(120\) 0 0
\(121\) −375.954 + 375.954i −0.282459 + 0.282459i
\(122\) 0 0
\(123\) −1030.96 + 427.038i −0.755760 + 0.313046i
\(124\) 0 0
\(125\) 381.960 922.133i 0.273308 0.659825i
\(126\) 0 0
\(127\) 624.520 0.436356 0.218178 0.975909i \(-0.429989\pi\)
0.218178 + 0.975909i \(0.429989\pi\)
\(128\) 0 0
\(129\) 785.506 0.536123
\(130\) 0 0
\(131\) −370.999 + 895.672i −0.247438 + 0.597368i −0.997985 0.0634490i \(-0.979790\pi\)
0.750547 + 0.660817i \(0.229790\pi\)
\(132\) 0 0
\(133\) −792.208 + 328.143i −0.516490 + 0.213937i
\(134\) 0 0
\(135\) −422.788 + 422.788i −0.269539 + 0.269539i
\(136\) 0 0
\(137\) 1408.41 + 1408.41i 0.878308 + 0.878308i 0.993360 0.115051i \(-0.0367032\pi\)
−0.115051 + 0.993360i \(0.536703\pi\)
\(138\) 0 0
\(139\) 127.491 + 307.790i 0.0777958 + 0.187816i 0.957992 0.286794i \(-0.0925894\pi\)
−0.880197 + 0.474609i \(0.842589\pi\)
\(140\) 0 0
\(141\) −45.1722 18.7110i −0.0269801 0.0111755i
\(142\) 0 0
\(143\) 837.134i 0.489543i
\(144\) 0 0
\(145\) 999.742i 0.572580i
\(146\) 0 0
\(147\) −1917.82 794.387i −1.07605 0.445714i
\(148\) 0 0
\(149\) −765.994 1849.27i −0.421159 1.01677i −0.982006 0.188849i \(-0.939524\pi\)
0.560847 0.827919i \(-0.310476\pi\)
\(150\) 0 0
\(151\) −773.796 773.796i −0.417024 0.417024i 0.467153 0.884177i \(-0.345280\pi\)
−0.884177 + 0.467153i \(0.845280\pi\)
\(152\) 0 0
\(153\) 557.223 557.223i 0.294437 0.294437i
\(154\) 0 0
\(155\) 1038.04 429.968i 0.537916 0.222812i
\(156\) 0 0
\(157\) 640.806 1547.04i 0.325745 0.786417i −0.673154 0.739502i \(-0.735061\pi\)
0.998899 0.0469150i \(-0.0149390\pi\)
\(158\) 0 0
\(159\) 1410.04 0.703295
\(160\) 0 0
\(161\) −1807.70 −0.884887
\(162\) 0 0
\(163\) 636.715 1537.17i 0.305959 0.738651i −0.693869 0.720102i \(-0.744095\pi\)
0.999828 0.0185496i \(-0.00590487\pi\)
\(164\) 0 0
\(165\) −540.160 + 223.742i −0.254857 + 0.105565i
\(166\) 0 0
\(167\) −1241.93 + 1241.93i −0.575469 + 0.575469i −0.933651 0.358183i \(-0.883396\pi\)
0.358183 + 0.933651i \(0.383396\pi\)
\(168\) 0 0
\(169\) −1287.48 1287.48i −0.586017 0.586017i
\(170\) 0 0
\(171\) 177.472 + 428.455i 0.0793661 + 0.191607i
\(172\) 0 0
\(173\) 1247.56 + 516.757i 0.548268 + 0.227100i 0.639583 0.768722i \(-0.279107\pi\)
−0.0913149 + 0.995822i \(0.529107\pi\)
\(174\) 0 0
\(175\) 3371.14i 1.45620i
\(176\) 0 0
\(177\) 181.286i 0.0769845i
\(178\) 0 0
\(179\) 985.168 + 408.070i 0.411368 + 0.170394i 0.578763 0.815496i \(-0.303536\pi\)
−0.167395 + 0.985890i \(0.553536\pi\)
\(180\) 0 0
\(181\) −120.962 292.028i −0.0496742 0.119924i 0.897095 0.441839i \(-0.145674\pi\)
−0.946769 + 0.321914i \(0.895674\pi\)
\(182\) 0 0
\(183\) −1727.51 1727.51i −0.697822 0.697822i
\(184\) 0 0
\(185\) −232.573 + 232.573i −0.0924274 + 0.0924274i
\(186\) 0 0
\(187\) 1833.59 759.499i 0.717035 0.297006i
\(188\) 0 0
\(189\) −1680.78 + 4057.76i −0.646872 + 1.56169i
\(190\) 0 0
\(191\) −584.594 −0.221465 −0.110732 0.993850i \(-0.535320\pi\)
−0.110732 + 0.993850i \(0.535320\pi\)
\(192\) 0 0
\(193\) 660.360 0.246289 0.123145 0.992389i \(-0.460702\pi\)
0.123145 + 0.992389i \(0.460702\pi\)
\(194\) 0 0
\(195\) −100.555 + 242.762i −0.0369277 + 0.0891514i
\(196\) 0 0
\(197\) −827.877 + 342.918i −0.299410 + 0.124020i −0.527331 0.849660i \(-0.676807\pi\)
0.227921 + 0.973680i \(0.426807\pi\)
\(198\) 0 0
\(199\) 153.764 153.764i 0.0547742 0.0547742i −0.679189 0.733963i \(-0.737668\pi\)
0.733963 + 0.679189i \(0.237668\pi\)
\(200\) 0 0
\(201\) −2189.97 2189.97i −0.768500 0.768500i
\(202\) 0 0
\(203\) −2810.36 6784.80i −0.971667 2.34581i
\(204\) 0 0
\(205\) 1415.98 + 586.516i 0.482420 + 0.199825i
\(206\) 0 0
\(207\) 977.671i 0.328274i
\(208\) 0 0
\(209\) 1167.97i 0.386557i
\(210\) 0 0
\(211\) 5199.68 + 2153.78i 1.69650 + 0.702712i 0.999891 0.0147412i \(-0.00469245\pi\)
0.696606 + 0.717454i \(0.254692\pi\)
\(212\) 0 0
\(213\) −610.690 1474.34i −0.196450 0.474272i
\(214\) 0 0
\(215\) −762.866 762.866i −0.241986 0.241986i
\(216\) 0 0
\(217\) 5836.00 5836.00i 1.82568 1.82568i
\(218\) 0 0
\(219\) 2484.38 1029.06i 0.766570 0.317524i
\(220\) 0 0
\(221\) 341.338 824.062i 0.103895 0.250825i
\(222\) 0 0
\(223\) −998.982 −0.299986 −0.149993 0.988687i \(-0.547925\pi\)
−0.149993 + 0.988687i \(0.547925\pi\)
\(224\) 0 0
\(225\) −1823.24 −0.540218
\(226\) 0 0
\(227\) −1393.39 + 3363.95i −0.407413 + 0.983583i 0.578402 + 0.815752i \(0.303676\pi\)
−0.985816 + 0.167831i \(0.946324\pi\)
\(228\) 0 0
\(229\) 941.495 389.980i 0.271684 0.112535i −0.242682 0.970106i \(-0.578027\pi\)
0.514366 + 0.857571i \(0.328027\pi\)
\(230\) 0 0
\(231\) −3036.87 + 3036.87i −0.864984 + 0.864984i
\(232\) 0 0
\(233\) 540.109 + 540.109i 0.151861 + 0.151861i 0.778949 0.627088i \(-0.215753\pi\)
−0.627088 + 0.778949i \(0.715753\pi\)
\(234\) 0 0
\(235\) 25.6986 + 62.0420i 0.00713359 + 0.0172220i
\(236\) 0 0
\(237\) 1103.22 + 456.969i 0.302371 + 0.125246i
\(238\) 0 0
\(239\) 2875.66i 0.778287i 0.921177 + 0.389144i \(0.127229\pi\)
−0.921177 + 0.389144i \(0.872771\pi\)
\(240\) 0 0
\(241\) 179.902i 0.0480851i −0.999711 0.0240425i \(-0.992346\pi\)
0.999711 0.0240425i \(-0.00765371\pi\)
\(242\) 0 0
\(243\) 3537.10 + 1465.11i 0.933765 + 0.386778i
\(244\) 0 0
\(245\) 1091.05 + 2634.04i 0.284510 + 0.686867i
\(246\) 0 0
\(247\) 371.172 + 371.172i 0.0956158 + 0.0956158i
\(248\) 0 0
\(249\) −565.311 + 565.311i −0.143876 + 0.143876i
\(250\) 0 0
\(251\) −5834.77 + 2416.84i −1.46728 + 0.607767i −0.966237 0.257655i \(-0.917050\pi\)
−0.501043 + 0.865422i \(0.667050\pi\)
\(252\) 0 0
\(253\) −942.270 + 2274.84i −0.234150 + 0.565288i
\(254\) 0 0
\(255\) 622.955 0.152984
\(256\) 0 0
\(257\) −5382.92 −1.30653 −0.653263 0.757131i \(-0.726600\pi\)
−0.653263 + 0.757131i \(0.726600\pi\)
\(258\) 0 0
\(259\) −924.585 + 2232.15i −0.221818 + 0.535516i
\(260\) 0 0
\(261\) −3669.47 + 1519.94i −0.870247 + 0.360468i
\(262\) 0 0
\(263\) −1725.28 + 1725.28i −0.404508 + 0.404508i −0.879818 0.475311i \(-0.842336\pi\)
0.475311 + 0.879818i \(0.342336\pi\)
\(264\) 0 0
\(265\) −1369.40 1369.40i −0.317441 0.317441i
\(266\) 0 0
\(267\) 1614.34 + 3897.37i 0.370023 + 0.893315i
\(268\) 0 0
\(269\) 7959.26 + 3296.83i 1.80403 + 0.747255i 0.984776 + 0.173826i \(0.0556130\pi\)
0.819256 + 0.573428i \(0.194387\pi\)
\(270\) 0 0
\(271\) 1049.81i 0.235320i 0.993054 + 0.117660i \(0.0375393\pi\)
−0.993054 + 0.117660i \(0.962461\pi\)
\(272\) 0 0
\(273\) 1930.18i 0.427912i
\(274\) 0 0
\(275\) −4242.30 1757.22i −0.930256 0.385325i
\(276\) 0 0
\(277\) 1433.09 + 3459.78i 0.310852 + 0.750463i 0.999674 + 0.0255326i \(0.00812818\pi\)
−0.688822 + 0.724931i \(0.741872\pi\)
\(278\) 0 0
\(279\) −3156.32 3156.32i −0.677291 0.677291i
\(280\) 0 0
\(281\) 1634.94 1634.94i 0.347089 0.347089i −0.511935 0.859024i \(-0.671071\pi\)
0.859024 + 0.511935i \(0.171071\pi\)
\(282\) 0 0
\(283\) 4367.76 1809.19i 0.917443 0.380017i 0.126542 0.991961i \(-0.459612\pi\)
0.790901 + 0.611944i \(0.209612\pi\)
\(284\) 0 0
\(285\) −140.295 + 338.702i −0.0291591 + 0.0703963i
\(286\) 0 0
\(287\) 11258.3 2.31553
\(288\) 0 0
\(289\) 2798.36 0.569582
\(290\) 0 0
\(291\) 797.537 1925.43i 0.160661 0.387871i
\(292\) 0 0
\(293\) −440.173 + 182.326i −0.0877651 + 0.0363535i −0.426134 0.904660i \(-0.640125\pi\)
0.338369 + 0.941014i \(0.390125\pi\)
\(294\) 0 0
\(295\) 176.061 176.061i 0.0347480 0.0347480i
\(296\) 0 0
\(297\) 4230.25 + 4230.25i 0.826477 + 0.826477i
\(298\) 0 0
\(299\) 423.480 + 1022.37i 0.0819079 + 0.197743i
\(300\) 0 0
\(301\) −7321.71 3032.75i −1.40205 0.580747i
\(302\) 0 0
\(303\) 3188.52i 0.604540i
\(304\) 0 0
\(305\) 3355.44i 0.629942i
\(306\) 0 0
\(307\) −20.2214 8.37598i −0.00375927 0.00155714i 0.380803 0.924656i \(-0.375648\pi\)
−0.384562 + 0.923099i \(0.625648\pi\)
\(308\) 0 0
\(309\) −1622.78 3917.73i −0.298759 0.721269i
\(310\) 0 0
\(311\) 390.934 + 390.934i 0.0712791 + 0.0712791i 0.741848 0.670568i \(-0.233950\pi\)
−0.670568 + 0.741848i \(0.733950\pi\)
\(312\) 0 0
\(313\) −3353.24 + 3353.24i −0.605548 + 0.605548i −0.941779 0.336231i \(-0.890848\pi\)
0.336231 + 0.941779i \(0.390848\pi\)
\(314\) 0 0
\(315\) 2163.85 896.296i 0.387045 0.160319i
\(316\) 0 0
\(317\) 1362.73 3289.92i 0.241447 0.582904i −0.755980 0.654594i \(-0.772839\pi\)
0.997427 + 0.0716906i \(0.0228394\pi\)
\(318\) 0 0
\(319\) −10003.0 −1.75568
\(320\) 0 0
\(321\) 1414.48 0.245946
\(322\) 0 0
\(323\) 476.236 1149.73i 0.0820386 0.198059i
\(324\) 0 0
\(325\) −1906.60 + 789.738i −0.325412 + 0.134790i
\(326\) 0 0
\(327\) 608.717 608.717i 0.102942 0.102942i
\(328\) 0 0
\(329\) 348.810 + 348.810i 0.0584514 + 0.0584514i
\(330\) 0 0
\(331\) −3035.45 7328.23i −0.504059 1.21691i −0.947255 0.320481i \(-0.896155\pi\)
0.443196 0.896425i \(-0.353845\pi\)
\(332\) 0 0
\(333\) 1207.23 + 500.049i 0.198665 + 0.0822899i
\(334\) 0 0
\(335\) 4253.70i 0.693745i
\(336\) 0 0
\(337\) 2973.12i 0.480582i 0.970701 + 0.240291i \(0.0772429\pi\)
−0.970701 + 0.240291i \(0.922757\pi\)
\(338\) 0 0
\(339\) 3379.70 + 1399.92i 0.541475 + 0.224286i
\(340\) 0 0
\(341\) −4302.09 10386.2i −0.683200 1.64939i
\(342\) 0 0
\(343\) 7124.07 + 7124.07i 1.12147 + 1.12147i
\(344\) 0 0
\(345\) −546.500 + 546.500i −0.0852828 + 0.0852828i
\(346\) 0 0
\(347\) −1239.20 + 513.294i −0.191711 + 0.0794094i −0.476474 0.879189i \(-0.658085\pi\)
0.284762 + 0.958598i \(0.408085\pi\)
\(348\) 0 0
\(349\) 618.263 1492.62i 0.0948276 0.228934i −0.869347 0.494202i \(-0.835460\pi\)
0.964175 + 0.265268i \(0.0854604\pi\)
\(350\) 0 0
\(351\) 2688.67 0.408862
\(352\) 0 0
\(353\) 2669.91 0.402563 0.201282 0.979533i \(-0.435489\pi\)
0.201282 + 0.979533i \(0.435489\pi\)
\(354\) 0 0
\(355\) −838.754 + 2024.93i −0.125398 + 0.302739i
\(356\) 0 0
\(357\) 4227.72 1751.18i 0.626763 0.259614i
\(358\) 0 0
\(359\) 6834.40 6834.40i 1.00475 1.00475i 0.00476246 0.999989i \(-0.498484\pi\)
0.999989 0.00476246i \(-0.00151595\pi\)
\(360\) 0 0
\(361\) −4332.19 4332.19i −0.631606 0.631606i
\(362\) 0 0
\(363\) 639.000 + 1542.68i 0.0923934 + 0.223057i
\(364\) 0 0
\(365\) −3412.18 1413.37i −0.489320 0.202683i
\(366\) 0 0
\(367\) 12688.1i 1.80467i −0.431034 0.902336i \(-0.641851\pi\)
0.431034 0.902336i \(-0.358149\pi\)
\(368\) 0 0
\(369\) 6088.92i 0.859015i
\(370\) 0 0
\(371\) −13143.0 5444.03i −1.83923 0.761832i
\(372\) 0 0
\(373\) 921.648 + 2225.05i 0.127939 + 0.308871i 0.974850 0.222863i \(-0.0715404\pi\)
−0.846911 + 0.531735i \(0.821540\pi\)
\(374\) 0 0
\(375\) −2216.54 2216.54i −0.305231 0.305231i
\(376\) 0 0
\(377\) −3178.87 + 3178.87i −0.434271 + 0.434271i
\(378\) 0 0
\(379\) −13206.6 + 5470.36i −1.78992 + 0.741407i −0.799955 + 0.600060i \(0.795143\pi\)
−0.989960 + 0.141348i \(0.954857\pi\)
\(380\) 0 0
\(381\) 750.582 1812.06i 0.100928 0.243661i
\(382\) 0 0
\(383\) −1489.39 −0.198706 −0.0993529 0.995052i \(-0.531677\pi\)
−0.0993529 + 0.995052i \(0.531677\pi\)
\(384\) 0 0
\(385\) 5898.68 0.780843
\(386\) 0 0
\(387\) −1640.22 + 3959.85i −0.215445 + 0.520130i
\(388\) 0 0
\(389\) 11998.3 4969.86i 1.56385 0.647768i 0.578097 0.815968i \(-0.303795\pi\)
0.985753 + 0.168200i \(0.0537954\pi\)
\(390\) 0 0
\(391\) 1855.11 1855.11i 0.239941 0.239941i
\(392\) 0 0
\(393\) 2152.93 + 2152.93i 0.276339 + 0.276339i
\(394\) 0 0
\(395\) −627.625 1515.22i −0.0799475 0.193010i
\(396\) 0 0
\(397\) −8675.83 3593.64i −1.09679 0.454307i −0.240423 0.970668i \(-0.577286\pi\)
−0.856371 + 0.516361i \(0.827286\pi\)
\(398\) 0 0
\(399\) 2693.00i 0.337891i
\(400\) 0 0
\(401\) 3772.26i 0.469769i −0.972023 0.234885i \(-0.924529\pi\)
0.972023 0.234885i \(-0.0754713\pi\)
\(402\) 0 0
\(403\) −4667.80 1933.47i −0.576972 0.238990i
\(404\) 0 0
\(405\) −45.1537 109.011i −0.00554001 0.0133748i
\(406\) 0 0
\(407\) 2327.03 + 2327.03i 0.283406 + 0.283406i
\(408\) 0 0
\(409\) −9020.80 + 9020.80i −1.09059 + 1.09059i −0.0951210 + 0.995466i \(0.530324\pi\)
−0.995466 + 0.0951210i \(0.969676\pi\)
\(410\) 0 0
\(411\) 5779.24 2393.84i 0.693598 0.287298i
\(412\) 0 0
\(413\) 699.924 1689.77i 0.0833922 0.201327i
\(414\) 0 0
\(415\) 1098.03 0.129880
\(416\) 0 0
\(417\) 1046.29 0.122870
\(418\) 0 0
\(419\) 3925.38 9476.72i 0.457679 1.10494i −0.511655 0.859191i \(-0.670968\pi\)
0.969335 0.245745i \(-0.0790325\pi\)
\(420\) 0 0
\(421\) −4298.89 + 1780.66i −0.497660 + 0.206138i −0.617372 0.786671i \(-0.711803\pi\)
0.119712 + 0.992809i \(0.461803\pi\)
\(422\) 0 0
\(423\) 188.649 188.649i 0.0216843 0.0216843i
\(424\) 0 0
\(425\) 3459.56 + 3459.56i 0.394855 + 0.394855i
\(426\) 0 0
\(427\) 9432.43 + 22771.9i 1.06901 + 2.58082i
\(428\) 0 0
\(429\) 2428.97 + 1006.11i 0.273361 + 0.113230i
\(430\) 0 0
\(431\) 2281.76i 0.255008i 0.991838 + 0.127504i \(0.0406966\pi\)
−0.991838 + 0.127504i \(0.959303\pi\)
\(432\) 0 0
\(433\) 8491.53i 0.942441i −0.882016 0.471220i \(-0.843814\pi\)
0.882016 0.471220i \(-0.156186\pi\)
\(434\) 0 0
\(435\) −2900.78 1201.54i −0.319729 0.132436i
\(436\) 0 0
\(437\) 590.840 + 1426.41i 0.0646767 + 0.156143i
\(438\) 0 0
\(439\) 3417.05 + 3417.05i 0.371496 + 0.371496i 0.868022 0.496526i \(-0.165391\pi\)
−0.496526 + 0.868022i \(0.665391\pi\)
\(440\) 0 0
\(441\) 8009.24 8009.24i 0.864835 0.864835i
\(442\) 0 0
\(443\) 984.558 407.817i 0.105593 0.0437381i −0.329261 0.944239i \(-0.606800\pi\)
0.434855 + 0.900501i \(0.356800\pi\)
\(444\) 0 0
\(445\) 2217.23 5352.86i 0.236195 0.570224i
\(446\) 0 0
\(447\) −6286.34 −0.665176
\(448\) 0 0
\(449\) −6407.14 −0.673434 −0.336717 0.941606i \(-0.609317\pi\)
−0.336717 + 0.941606i \(0.609317\pi\)
\(450\) 0 0
\(451\) 5868.44 14167.7i 0.612714 1.47922i
\(452\) 0 0
\(453\) −3175.18 + 1315.20i −0.329323 + 0.136410i
\(454\) 0 0
\(455\) 1874.55 1874.55i 0.193144 0.193144i
\(456\) 0 0
\(457\) 6405.90 + 6405.90i 0.655701 + 0.655701i 0.954360 0.298659i \(-0.0965393\pi\)
−0.298659 + 0.954360i \(0.596539\pi\)
\(458\) 0 0
\(459\) −2439.32 5889.05i −0.248057 0.598861i
\(460\) 0 0
\(461\) −11209.2 4642.99i −1.13246 0.469080i −0.263843 0.964566i \(-0.584990\pi\)
−0.868616 + 0.495486i \(0.834990\pi\)
\(462\) 0 0
\(463\) 10213.2i 1.02515i 0.858642 + 0.512576i \(0.171309\pi\)
−0.858642 + 0.512576i \(0.828691\pi\)
\(464\) 0 0
\(465\) 3528.65i 0.351908i
\(466\) 0 0
\(467\) 8301.10 + 3438.43i 0.822546 + 0.340710i 0.753948 0.656935i \(-0.228147\pi\)
0.0685986 + 0.997644i \(0.478147\pi\)
\(468\) 0 0
\(469\) 11957.5 + 28868.0i 1.17728 + 2.84222i
\(470\) 0 0
\(471\) −3718.64 3718.64i −0.363792 0.363792i
\(472\) 0 0
\(473\) −7632.93 + 7632.93i −0.741992 + 0.741992i
\(474\) 0 0
\(475\) −2660.09 + 1101.85i −0.256954 + 0.106434i
\(476\) 0 0
\(477\) −2944.33 + 7108.24i −0.282624 + 0.682314i
\(478\) 0 0
\(479\) 1983.62 0.189215 0.0946075 0.995515i \(-0.469840\pi\)
0.0946075 + 0.995515i \(0.469840\pi\)
\(480\) 0 0
\(481\) 1479.02 0.140203
\(482\) 0 0
\(483\) −2172.59 + 5245.10i −0.204672 + 0.494121i
\(484\) 0 0
\(485\) −2644.48 + 1095.38i −0.247587 + 0.102554i
\(486\) 0 0
\(487\) 2241.43 2241.43i 0.208561 0.208561i −0.595095 0.803655i \(-0.702886\pi\)
0.803655 + 0.595095i \(0.202886\pi\)
\(488\) 0 0
\(489\) −3694.90 3694.90i −0.341696 0.341696i
\(490\) 0 0
\(491\) 1553.51 + 3750.50i 0.142788 + 0.344720i 0.979053 0.203605i \(-0.0652657\pi\)
−0.836265 + 0.548325i \(0.815266\pi\)
\(492\) 0 0
\(493\) 9846.81 + 4078.68i 0.899550 + 0.372606i
\(494\) 0 0
\(495\) 3190.22i 0.289677i
\(496\) 0 0
\(497\) 16100.1i 1.45310i
\(498\) 0 0
\(499\) 8740.71 + 3620.52i 0.784144 + 0.324803i 0.738587 0.674159i \(-0.235494\pi\)
0.0455575 + 0.998962i \(0.485494\pi\)
\(500\) 0 0
\(501\) 2110.88 + 5096.11i 0.188238 + 0.454446i
\(502\) 0 0
\(503\) 3856.31 + 3856.31i 0.341838 + 0.341838i 0.857058 0.515220i \(-0.172290\pi\)
−0.515220 + 0.857058i \(0.672290\pi\)
\(504\) 0 0
\(505\) −3096.62 + 3096.62i −0.272867 + 0.272867i
\(506\) 0 0
\(507\) −5283.03 + 2188.30i −0.462776 + 0.191688i
\(508\) 0 0
\(509\) −776.546 + 1874.75i −0.0676224 + 0.163255i −0.954078 0.299559i \(-0.903160\pi\)
0.886455 + 0.462814i \(0.153160\pi\)
\(510\) 0 0
\(511\) −27130.0 −2.34865
\(512\) 0 0
\(513\) 3751.24 0.322849
\(514\) 0 0
\(515\) −2228.81 + 5380.82i −0.190705 + 0.460403i
\(516\) 0 0
\(517\) 620.767 257.130i 0.0528071 0.0218734i
\(518\) 0 0
\(519\) 2998.78 2998.78i 0.253626 0.253626i
\(520\) 0 0
\(521\) −4528.26 4528.26i −0.380780 0.380780i 0.490603 0.871383i \(-0.336777\pi\)
−0.871383 + 0.490603i \(0.836777\pi\)
\(522\) 0 0
\(523\) 1376.98 + 3324.33i 0.115127 + 0.277940i 0.970931 0.239359i \(-0.0769373\pi\)
−0.855804 + 0.517300i \(0.826937\pi\)
\(524\) 0 0
\(525\) −9781.48 4051.62i −0.813141 0.336814i
\(526\) 0 0
\(527\) 11978.1i 0.990086i
\(528\) 0 0
\(529\) 8912.13i 0.732484i
\(530\) 0 0
\(531\) −913.887 378.544i −0.0746880 0.0309368i
\(532\) 0 0
\(533\) −2637.43 6367.31i −0.214333 0.517446i
\(534\) 0 0
\(535\) −1373.71 1373.71i −0.111011 0.111011i
\(536\) 0 0
\(537\) 2368.06 2368.06i 0.190296 0.190296i
\(538\) 0 0
\(539\) 26355.1 10916.6i 2.10611 0.872380i
\(540\) 0 0
\(541\) −3507.90 + 8468.82i −0.278773 + 0.673018i −0.999802 0.0198866i \(-0.993669\pi\)
0.721029 + 0.692905i \(0.243669\pi\)
\(542\) 0 0
\(543\) −992.708 −0.0784552
\(544\) 0 0
\(545\) −1182.35 −0.0929287
\(546\) 0 0
\(547\) 2578.26 6224.46i 0.201532 0.486542i −0.790510 0.612450i \(-0.790184\pi\)
0.992042 + 0.125907i \(0.0401842\pi\)
\(548\) 0 0
\(549\) 12315.9 5101.40i 0.957429 0.396580i
\(550\) 0 0
\(551\) −4435.17 + 4435.17i −0.342912 + 0.342912i
\(552\) 0 0
\(553\) −8518.82 8518.82i −0.655076 0.655076i
\(554\) 0 0
\(555\) 395.299 + 954.335i 0.0302333 + 0.0729897i
\(556\) 0 0
\(557\) 8187.07 + 3391.19i 0.622796 + 0.257970i 0.671689 0.740834i \(-0.265569\pi\)
−0.0488930 + 0.998804i \(0.515569\pi\)
\(558\) 0 0
\(559\) 4851.36i 0.367067i
\(560\) 0 0
\(561\) 6233.04i 0.469089i
\(562\) 0 0
\(563\) 5205.06 + 2156.00i 0.389639 + 0.161394i 0.568898 0.822408i \(-0.307370\pi\)
−0.179259 + 0.983802i \(0.557370\pi\)
\(564\) 0 0
\(565\) −1922.72 4641.86i −0.143167 0.345636i
\(566\) 0 0
\(567\) −612.876 612.876i −0.0453939 0.0453939i
\(568\) 0 0
\(569\) 13921.3 13921.3i 1.02568 1.02568i 0.0260140 0.999662i \(-0.491719\pi\)
0.999662 0.0260140i \(-0.00828146\pi\)
\(570\) 0 0
\(571\) −18276.2 + 7570.27i −1.33947 + 0.554826i −0.933341 0.358990i \(-0.883121\pi\)
−0.406128 + 0.913816i \(0.633121\pi\)
\(572\) 0 0
\(573\) −702.597 + 1696.22i −0.0512241 + 0.123666i
\(574\) 0 0
\(575\) −6069.93 −0.440232
\(576\) 0 0
\(577\) 24309.7 1.75394 0.876972 0.480542i \(-0.159560\pi\)
0.876972 + 0.480542i \(0.159560\pi\)
\(578\) 0 0
\(579\) 793.657 1916.06i 0.0569659 0.137528i
\(580\) 0 0
\(581\) 7451.87 3086.66i 0.532109 0.220407i
\(582\) 0 0
\(583\) −13701.7 + 13701.7i −0.973356 + 0.973356i
\(584\) 0 0
\(585\) −1013.83 1013.83i −0.0716522 0.0716522i
\(586\) 0 0
\(587\) −6035.14 14570.1i −0.424356 1.02449i −0.981048 0.193767i \(-0.937929\pi\)
0.556691 0.830719i \(-0.312071\pi\)
\(588\) 0 0
\(589\) −6512.53 2697.58i −0.455593 0.188713i
\(590\) 0 0
\(591\) 2814.25i 0.195876i
\(592\) 0 0
\(593\) 14290.4i 0.989608i −0.869005 0.494804i \(-0.835240\pi\)
0.869005 0.494804i \(-0.164760\pi\)
\(594\) 0 0
\(595\) −5806.57 2405.16i −0.400078 0.165718i
\(596\) 0 0
\(597\) −261.350 630.954i −0.0179168 0.0432550i
\(598\) 0 0
\(599\) −2752.47 2752.47i −0.187751 0.187751i 0.606972 0.794723i \(-0.292384\pi\)
−0.794723 + 0.606972i \(0.792384\pi\)
\(600\) 0 0
\(601\) −10680.0 + 10680.0i −0.724871 + 0.724871i −0.969593 0.244722i \(-0.921303\pi\)
0.244722 + 0.969593i \(0.421303\pi\)
\(602\) 0 0
\(603\) 15612.9 6467.06i 1.05440 0.436748i
\(604\) 0 0
\(605\) 877.637 2118.80i 0.0589769 0.142383i
\(606\) 0 0
\(607\) 13933.7 0.931719 0.465859 0.884859i \(-0.345745\pi\)
0.465859 + 0.884859i \(0.345745\pi\)
\(608\) 0 0
\(609\) −23064.0 −1.53464
\(610\) 0 0
\(611\) 115.561 278.988i 0.00765153 0.0184724i
\(612\) 0 0
\(613\) −20129.3 + 8337.81i −1.32629 + 0.549366i −0.929594 0.368586i \(-0.879842\pi\)
−0.396692 + 0.917952i \(0.629842\pi\)
\(614\) 0 0
\(615\) 3403.59 3403.59i 0.223164 0.223164i
\(616\) 0 0
\(617\) 4886.46 + 4886.46i 0.318836 + 0.318836i 0.848320 0.529484i \(-0.177615\pi\)
−0.529484 + 0.848320i \(0.677615\pi\)
\(618\) 0 0
\(619\) 7135.77 + 17227.3i 0.463345 + 1.11861i 0.967015 + 0.254718i \(0.0819827\pi\)
−0.503670 + 0.863896i \(0.668017\pi\)
\(620\) 0 0
\(621\) 7306.23 + 3026.34i 0.472124 + 0.195560i
\(622\) 0 0
\(623\) 42560.2i 2.73698i
\(624\) 0 0
\(625\) 8993.94i 0.575612i
\(626\) 0 0
\(627\) 3388.91 + 1403.73i 0.215853 + 0.0894094i
\(628\) 0 0
\(629\) −1341.85 3239.52i −0.0850608 0.205355i
\(630\) 0 0
\(631\) −9484.77 9484.77i −0.598388 0.598388i 0.341496 0.939883i \(-0.389067\pi\)
−0.939883 + 0.341496i \(0.889067\pi\)
\(632\) 0 0
\(633\) 12498.5 12498.5i 0.784790 0.784790i
\(634\) 0 0
\(635\) −2488.79 + 1030.89i −0.155535 + 0.0644245i
\(636\) 0 0
\(637\) 4906.21 11844.6i 0.305167 0.736737i
\(638\) 0 0
\(639\) 8707.53 0.539068
\(640\) 0 0
\(641\) −26621.4 −1.64038 −0.820189 0.572092i \(-0.806132\pi\)
−0.820189 + 0.572092i \(0.806132\pi\)
\(642\) 0 0
\(643\) 3206.34 7740.79i 0.196650 0.474754i −0.794539 0.607213i \(-0.792287\pi\)
0.991188 + 0.132459i \(0.0422873\pi\)
\(644\) 0 0
\(645\) −3130.33 + 1296.63i −0.191096 + 0.0791545i
\(646\) 0 0
\(647\) 11415.8 11415.8i 0.693664 0.693664i −0.269373 0.963036i \(-0.586816\pi\)
0.963036 + 0.269373i \(0.0868163\pi\)
\(648\) 0 0
\(649\) −1761.59 1761.59i −0.106546 0.106546i
\(650\) 0 0
\(651\) −9919.33 23947.4i −0.597188 1.44174i
\(652\) 0 0
\(653\) 24638.3 + 10205.5i 1.47652 + 0.611596i 0.968336 0.249650i \(-0.0803156\pi\)
0.508188 + 0.861246i \(0.330316\pi\)
\(654\) 0 0
\(655\) 4181.76i 0.249458i
\(656\) 0 0
\(657\) 14672.9i 0.871301i
\(658\) 0 0
\(659\) −13287.3 5503.77i −0.785430 0.325336i −0.0463255 0.998926i \(-0.514751\pi\)
−0.739105 + 0.673591i \(0.764751\pi\)
\(660\) 0 0
\(661\) −1075.25 2595.89i −0.0632716 0.152751i 0.889081 0.457749i \(-0.151344\pi\)
−0.952353 + 0.304998i \(0.901344\pi\)
\(662\) 0 0
\(663\) −1980.81 1980.81i −0.116030 0.116030i
\(664\) 0 0
\(665\) 2615.38 2615.38i 0.152511 0.152511i
\(666\) 0 0
\(667\) −12216.4 + 5060.20i −0.709177 + 0.293751i
\(668\) 0 0
\(669\) −1200.63 + 2898.58i −0.0693858 + 0.167512i
\(670\) 0 0
\(671\) 33573.2 1.93156
\(672\) 0 0
\(673\) 2416.06 0.138384 0.0691920 0.997603i \(-0.477958\pi\)
0.0691920 + 0.997603i \(0.477958\pi\)
\(674\) 0 0
\(675\) −5643.76 + 13625.2i −0.321820 + 0.776942i
\(676\) 0 0
\(677\) −10314.0 + 4272.22i −0.585526 + 0.242533i −0.655724 0.755000i \(-0.727637\pi\)
0.0701988 + 0.997533i \(0.477637\pi\)
\(678\) 0 0
\(679\) −14867.7 + 14867.7i −0.840310 + 0.840310i
\(680\) 0 0
\(681\) 8085.96 + 8085.96i 0.455000 + 0.455000i
\(682\) 0 0
\(683\) −3410.41 8233.45i −0.191062 0.461265i 0.799098 0.601200i \(-0.205311\pi\)
−0.990161 + 0.139935i \(0.955311\pi\)
\(684\) 0 0
\(685\) −7937.51 3287.83i −0.442740 0.183389i
\(686\) 0 0
\(687\) 3200.48i 0.177738i
\(688\) 0 0
\(689\) 8708.57i 0.481524i
\(690\) 0 0
\(691\) 3706.50 + 1535.28i 0.204055 + 0.0845224i 0.482370 0.875967i \(-0.339776\pi\)
−0.278315 + 0.960490i \(0.589776\pi\)
\(692\) 0 0
\(693\) −8967.98 21650.6i −0.491580 1.18678i
\(694\) 0 0
\(695\) −1016.13 1016.13i −0.0554591 0.0554591i
\(696\) 0 0
\(697\) −11553.6 + 11553.6i −0.627868 + 0.627868i
\(698\) 0 0
\(699\) 2216.27 918.011i 0.119924 0.0496743i
\(700\) 0 0
\(701\) −6159.04 + 14869.2i −0.331846 + 0.801146i 0.666600 + 0.745415i \(0.267749\pi\)
−0.998446 + 0.0557306i \(0.982251\pi\)
\(702\) 0 0
\(703\) 2063.53 0.110708
\(704\) 0 0
\(705\) 210.903 0.0112668
\(706\) 0 0
\(707\) −12310.5 + 29720.2i −0.654859 + 1.58097i
\(708\) 0 0
\(709\) −1554.84 + 644.034i −0.0823598 + 0.0341145i −0.423483 0.905904i \(-0.639193\pi\)
0.341123 + 0.940019i \(0.389193\pi\)
\(710\) 0 0
\(711\) −4607.29 + 4607.29i −0.243020 + 0.243020i
\(712\) 0 0
\(713\) −10508.0 10508.0i −0.551935 0.551935i
\(714\) 0 0
\(715\) −1381.85 3336.08i −0.0722773 0.174493i
\(716\) 0 0
\(717\) 8343.81 + 3456.12i 0.434596 + 0.180016i
\(718\) 0 0
\(719\) 33535.5i 1.73945i 0.493540 + 0.869723i \(0.335703\pi\)
−0.493540 + 0.869723i \(0.664297\pi\)
\(720\) 0 0
\(721\) 42782.6i 2.20986i
\(722\) 0 0
\(723\) −521.991 216.216i −0.0268507 0.0111219i
\(724\) 0 0
\(725\) −9436.67 22782.1i −0.483406 1.16704i
\(726\) 0 0
\(727\) 15842.6 + 15842.6i 0.808210 + 0.808210i 0.984363 0.176153i \(-0.0563654\pi\)
−0.176153 + 0.984363i \(0.556365\pi\)
\(728\) 0 0
\(729\) 7979.90 7979.90i 0.405421 0.405421i
\(730\) 0 0
\(731\) 10626.0 4401.44i 0.537644 0.222699i
\(732\) 0 0
\(733\) 10693.1 25815.3i 0.538823 1.30083i −0.386722 0.922196i \(-0.626393\pi\)
0.925545 0.378638i \(-0.123607\pi\)
\(734\) 0 0
\(735\) 8954.03 0.449353
\(736\) 0 0
\(737\) 42560.8 2.12720
\(738\) 0 0
\(739\) 2894.05 6986.86i 0.144059 0.347789i −0.835337 0.549738i \(-0.814728\pi\)
0.979396 + 0.201949i \(0.0647276\pi\)
\(740\) 0 0
\(741\) 1523.06 630.873i 0.0755075 0.0312762i
\(742\) 0 0
\(743\) −15149.2 + 15149.2i −0.748009 + 0.748009i −0.974105 0.226096i \(-0.927404\pi\)
0.226096 + 0.974105i \(0.427404\pi\)
\(744\) 0 0
\(745\) 6105.16 + 6105.16i 0.300236 + 0.300236i
\(746\) 0 0
\(747\) −1669.38 4030.24i −0.0817664 0.197401i
\(748\) 0 0
\(749\) −13184.4 5461.15i −0.643187 0.266417i
\(750\) 0 0
\(751\) 23633.7i 1.14834i −0.818735 0.574171i \(-0.805324\pi\)
0.818735 0.574171i \(-0.194676\pi\)
\(752\) 0 0
\(753\) 19834.5i 0.959905i
\(754\) 0 0
\(755\) 4360.97 + 1806.37i 0.210214 + 0.0870736i
\(756\) 0 0
\(757\) −8369.97 20206.9i −0.401865 0.970188i −0.987213 0.159406i \(-0.949042\pi\)
0.585348 0.810782i \(-0.300958\pi\)
\(758\) 0 0
\(759\) 5468.05 + 5468.05i 0.261499 + 0.261499i
\(760\) 0 0
\(761\) 4475.11 4475.11i 0.213170 0.213170i −0.592442 0.805613i \(-0.701836\pi\)
0.805613 + 0.592442i \(0.201836\pi\)
\(762\) 0 0
\(763\) −8024.05 + 3323.67i −0.380721 + 0.157700i
\(764\) 0 0
\(765\) −1300.80 + 3140.41i −0.0614778 + 0.148420i
\(766\) 0 0
\(767\) −1119.64 −0.0527089
\(768\) 0 0
\(769\) −6556.87 −0.307473 −0.153736 0.988112i \(-0.549131\pi\)
−0.153736 + 0.988112i \(0.549131\pi\)
\(770\) 0 0
\(771\) −6469.48 + 15618.7i −0.302195 + 0.729564i
\(772\) 0 0
\(773\) 16437.5 6808.62i 0.764832 0.316804i 0.0340547 0.999420i \(-0.489158\pi\)
0.730777 + 0.682616i \(0.239158\pi\)
\(774\) 0 0
\(775\) 19596.2 19596.2i 0.908281 0.908281i
\(776\) 0 0
\(777\) 5365.43 + 5365.43i 0.247727 + 0.247727i
\(778\) 0 0
\(779\) −3679.74 8883.69i −0.169243 0.408590i
\(780\) 0 0
\(781\) 20260.6 + 8392.23i 0.928275 + 0.384504i
\(782\) 0 0
\(783\) 32127.2i 1.46633i
\(784\) 0 0
\(785\) 7222.93i 0.328404i
\(786\) 0 0