Properties

Label 128.4.g.a.49.8
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 49.8
Character \(\chi\) \(=\) 128.49
Dual form 128.4.g.a.81.8

$q$-expansion

\(f(q)\) \(=\) \(q+(2.66269 - 1.10292i) q^{3} +(-5.50788 + 13.2972i) q^{5} +(6.48055 + 6.48055i) q^{7} +(-13.2184 + 13.2184i) q^{9} +O(q^{10})\) \(q+(2.66269 - 1.10292i) q^{3} +(-5.50788 + 13.2972i) q^{5} +(6.48055 + 6.48055i) q^{7} +(-13.2184 + 13.2184i) q^{9} +(-49.3605 - 20.4458i) q^{11} +(21.4409 + 51.7628i) q^{13} +41.4811i q^{15} +3.73808i q^{17} +(36.7064 + 88.6171i) q^{19} +(24.4033 + 10.1082i) q^{21} +(45.4559 - 45.4559i) q^{23} +(-58.0905 - 58.0905i) q^{25} +(-50.3966 + 121.668i) q^{27} +(51.9617 - 21.5233i) q^{29} +73.5204 q^{31} -153.982 q^{33} +(-121.867 + 50.4791i) q^{35} +(-165.530 + 399.624i) q^{37} +(114.181 + 114.181i) q^{39} +(334.781 - 334.781i) q^{41} +(-328.962 - 136.261i) q^{43} +(-102.962 - 248.573i) q^{45} -185.755i q^{47} -259.005i q^{49} +(4.12282 + 9.95337i) q^{51} +(412.832 + 171.001i) q^{53} +(543.744 - 543.744i) q^{55} +(195.476 + 195.476i) q^{57} +(214.856 - 518.709i) q^{59} +(85.1187 - 35.2573i) q^{61} -171.325 q^{63} -806.394 q^{65} +(252.042 - 104.399i) q^{67} +(70.9008 - 171.170i) q^{69} +(-430.147 - 430.147i) q^{71} +(41.8371 - 41.8371i) q^{73} +(-218.746 - 90.6077i) q^{75} +(-187.383 - 452.383i) q^{77} +1211.19i q^{79} -125.180i q^{81} +(290.920 + 702.342i) q^{83} +(-49.7061 - 20.5889i) q^{85} +(114.620 - 114.620i) q^{87} +(365.332 + 365.332i) q^{89} +(-196.503 + 474.400i) q^{91} +(195.762 - 81.0874i) q^{93} -1380.53 q^{95} +508.891 q^{97} +(922.727 - 382.206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

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
\(3\) 2.66269 1.10292i 0.512435 0.212258i −0.111455 0.993769i \(-0.535551\pi\)
0.623890 + 0.781512i \(0.285551\pi\)
\(4\) 0 0
\(5\) −5.50788 + 13.2972i −0.492640 + 1.18934i 0.460732 + 0.887539i \(0.347587\pi\)
−0.953372 + 0.301798i \(0.902413\pi\)
\(6\) 0 0
\(7\) 6.48055 + 6.48055i 0.349917 + 0.349917i 0.860079 0.510162i \(-0.170414\pi\)
−0.510162 + 0.860079i \(0.670414\pi\)
\(8\) 0 0
\(9\) −13.2184 + 13.2184i −0.489570 + 0.489570i
\(10\) 0 0
\(11\) −49.3605 20.4458i −1.35298 0.560422i −0.415858 0.909430i \(-0.636519\pi\)
−0.937120 + 0.349008i \(0.886519\pi\)
\(12\) 0 0
\(13\) 21.4409 + 51.7628i 0.457433 + 1.10434i 0.969433 + 0.245355i \(0.0789045\pi\)
−0.512001 + 0.858985i \(0.671096\pi\)
\(14\) 0 0
\(15\) 41.4811i 0.714025i
\(16\) 0 0
\(17\) 3.73808i 0.0533305i 0.999644 + 0.0266653i \(0.00848882\pi\)
−0.999644 + 0.0266653i \(0.991511\pi\)
\(18\) 0 0
\(19\) 36.7064 + 88.6171i 0.443212 + 1.07001i 0.974815 + 0.223015i \(0.0715899\pi\)
−0.531603 + 0.846994i \(0.678410\pi\)
\(20\) 0 0
\(21\) 24.4033 + 10.1082i 0.253582 + 0.105037i
\(22\) 0 0
\(23\) 45.4559 45.4559i 0.412097 0.412097i −0.470372 0.882468i \(-0.655880\pi\)
0.882468 + 0.470372i \(0.155880\pi\)
\(24\) 0 0
\(25\) −58.0905 58.0905i −0.464724 0.464724i
\(26\) 0 0
\(27\) −50.3966 + 121.668i −0.359216 + 0.867223i
\(28\) 0 0
\(29\) 51.9617 21.5233i 0.332726 0.137820i −0.210065 0.977687i \(-0.567368\pi\)
0.542791 + 0.839868i \(0.317368\pi\)
\(30\) 0 0
\(31\) 73.5204 0.425957 0.212978 0.977057i \(-0.431684\pi\)
0.212978 + 0.977057i \(0.431684\pi\)
\(32\) 0 0
\(33\) −153.982 −0.812267
\(34\) 0 0
\(35\) −121.867 + 50.4791i −0.588552 + 0.243786i
\(36\) 0 0
\(37\) −165.530 + 399.624i −0.735485 + 1.77562i −0.112109 + 0.993696i \(0.535760\pi\)
−0.623376 + 0.781922i \(0.714240\pi\)
\(38\) 0 0
\(39\) 114.181 + 114.181i 0.468809 + 0.468809i
\(40\) 0 0
\(41\) 334.781 334.781i 1.27522 1.27522i 0.331906 0.943312i \(-0.392308\pi\)
0.943312 0.331906i \(-0.107692\pi\)
\(42\) 0 0
\(43\) −328.962 136.261i −1.16666 0.483245i −0.286570 0.958059i \(-0.592515\pi\)
−0.880086 + 0.474814i \(0.842515\pi\)
\(44\) 0 0
\(45\) −102.962 248.573i −0.341083 0.823446i
\(46\) 0 0
\(47\) 185.755i 0.576492i −0.957556 0.288246i \(-0.906928\pi\)
0.957556 0.288246i \(-0.0930721\pi\)
\(48\) 0 0
\(49\) 259.005i 0.755116i
\(50\) 0 0
\(51\) 4.12282 + 9.95337i 0.0113198 + 0.0273284i
\(52\) 0 0
\(53\) 412.832 + 171.001i 1.06994 + 0.443184i 0.846970 0.531641i \(-0.178424\pi\)
0.222971 + 0.974825i \(0.428424\pi\)
\(54\) 0 0
\(55\) 543.744 543.744i 1.33306 1.33306i
\(56\) 0 0
\(57\) 195.476 + 195.476i 0.454235 + 0.454235i
\(58\) 0 0
\(59\) 214.856 518.709i 0.474100 1.14458i −0.488235 0.872712i \(-0.662359\pi\)
0.962335 0.271867i \(-0.0876410\pi\)
\(60\) 0 0
\(61\) 85.1187 35.2573i 0.178661 0.0740038i −0.291560 0.956553i \(-0.594174\pi\)
0.470221 + 0.882549i \(0.344174\pi\)
\(62\) 0 0
\(63\) −171.325 −0.342618
\(64\) 0 0
\(65\) −806.394 −1.53878
\(66\) 0 0
\(67\) 252.042 104.399i 0.459579 0.190364i −0.140868 0.990028i \(-0.544989\pi\)
0.600447 + 0.799665i \(0.294989\pi\)
\(68\) 0 0
\(69\) 70.9008 171.170i 0.123702 0.298643i
\(70\) 0 0
\(71\) −430.147 430.147i −0.719001 0.719001i 0.249400 0.968401i \(-0.419767\pi\)
−0.968401 + 0.249400i \(0.919767\pi\)
\(72\) 0 0
\(73\) 41.8371 41.8371i 0.0670775 0.0670775i −0.672772 0.739850i \(-0.734897\pi\)
0.739850 + 0.672772i \(0.234897\pi\)
\(74\) 0 0
\(75\) −218.746 90.6077i −0.336782 0.139500i
\(76\) 0 0
\(77\) −187.383 452.383i −0.277329 0.669531i
\(78\) 0 0
\(79\) 1211.19i 1.72493i 0.506119 + 0.862464i \(0.331080\pi\)
−0.506119 + 0.862464i \(0.668920\pi\)
\(80\) 0 0
\(81\) 125.180i 0.171715i
\(82\) 0 0
\(83\) 290.920 + 702.342i 0.384730 + 0.928820i 0.991037 + 0.133589i \(0.0426504\pi\)
−0.606307 + 0.795231i \(0.707350\pi\)
\(84\) 0 0
\(85\) −49.7061 20.5889i −0.0634280 0.0262727i
\(86\) 0 0
\(87\) 114.620 114.620i 0.141247 0.141247i
\(88\) 0 0
\(89\) 365.332 + 365.332i 0.435113 + 0.435113i 0.890363 0.455250i \(-0.150450\pi\)
−0.455250 + 0.890363i \(0.650450\pi\)
\(90\) 0 0
\(91\) −196.503 + 474.400i −0.226364 + 0.546491i
\(92\) 0 0
\(93\) 195.762 81.0874i 0.218275 0.0904126i
\(94\) 0 0
\(95\) −1380.53 −1.49095
\(96\) 0 0
\(97\) 508.891 0.532681 0.266340 0.963879i \(-0.414185\pi\)
0.266340 + 0.963879i \(0.414185\pi\)
\(98\) 0 0
\(99\) 922.727 382.206i 0.936743 0.388012i
\(100\) 0 0
\(101\) −184.802 + 446.152i −0.182065 + 0.439543i −0.988392 0.151927i \(-0.951452\pi\)
0.806327 + 0.591470i \(0.201452\pi\)
\(102\) 0 0
\(103\) 610.875 + 610.875i 0.584382 + 0.584382i 0.936104 0.351722i \(-0.114404\pi\)
−0.351722 + 0.936104i \(0.614404\pi\)
\(104\) 0 0
\(105\) −268.821 + 268.821i −0.249849 + 0.249849i
\(106\) 0 0
\(107\) −603.347 249.914i −0.545119 0.225796i 0.0930915 0.995658i \(-0.470325\pi\)
−0.638211 + 0.769862i \(0.720325\pi\)
\(108\) 0 0
\(109\) −271.916 656.462i −0.238943 0.576860i 0.758231 0.651986i \(-0.226064\pi\)
−0.997174 + 0.0751265i \(0.976064\pi\)
\(110\) 0 0
\(111\) 1246.64i 1.06600i
\(112\) 0 0
\(113\) 1651.29i 1.37469i 0.726329 + 0.687347i \(0.241225\pi\)
−0.726329 + 0.687347i \(0.758775\pi\)
\(114\) 0 0
\(115\) 354.071 + 854.803i 0.287107 + 0.693137i
\(116\) 0 0
\(117\) −967.635 400.807i −0.764597 0.316707i
\(118\) 0 0
\(119\) −24.2248 + 24.2248i −0.0186612 + 0.0186612i
\(120\) 0 0
\(121\) 1077.27 + 1077.27i 0.809369 + 0.809369i
\(122\) 0 0
\(123\) 522.180 1260.66i 0.382792 0.924142i
\(124\) 0 0
\(125\) −569.754 + 236.000i −0.407683 + 0.168868i
\(126\) 0 0
\(127\) −313.499 −0.219044 −0.109522 0.993984i \(-0.534932\pi\)
−0.109522 + 0.993984i \(0.534932\pi\)
\(128\) 0 0
\(129\) −1026.21 −0.700408
\(130\) 0 0
\(131\) −516.522 + 213.951i −0.344494 + 0.142694i −0.548221 0.836334i \(-0.684695\pi\)
0.203726 + 0.979028i \(0.434695\pi\)
\(132\) 0 0
\(133\) −336.410 + 812.166i −0.219327 + 0.529501i
\(134\) 0 0
\(135\) −1340.27 1340.27i −0.854458 0.854458i
\(136\) 0 0
\(137\) 544.876 544.876i 0.339795 0.339795i −0.516495 0.856290i \(-0.672764\pi\)
0.856290 + 0.516495i \(0.172764\pi\)
\(138\) 0 0
\(139\) 2149.49 + 890.348i 1.31164 + 0.543297i 0.925361 0.379086i \(-0.123762\pi\)
0.386275 + 0.922384i \(0.373762\pi\)
\(140\) 0 0
\(141\) −204.873 494.608i −0.122365 0.295415i
\(142\) 0 0
\(143\) 2993.41i 1.75050i
\(144\) 0 0
\(145\) 809.493i 0.463619i
\(146\) 0 0
\(147\) −285.662 689.650i −0.160279 0.386948i
\(148\) 0 0
\(149\) 1483.83 + 614.624i 0.815841 + 0.337932i 0.751282 0.659982i \(-0.229436\pi\)
0.0645591 + 0.997914i \(0.479436\pi\)
\(150\) 0 0
\(151\) −2047.66 + 2047.66i −1.10355 + 1.10355i −0.109572 + 0.993979i \(0.534948\pi\)
−0.993979 + 0.109572i \(0.965052\pi\)
\(152\) 0 0
\(153\) −49.4115 49.4115i −0.0261090 0.0261090i
\(154\) 0 0
\(155\) −404.942 + 977.616i −0.209843 + 0.506606i
\(156\) 0 0
\(157\) 1545.54 640.184i 0.785653 0.325428i 0.0464585 0.998920i \(-0.485206\pi\)
0.739194 + 0.673492i \(0.235206\pi\)
\(158\) 0 0
\(159\) 1287.85 0.642345
\(160\) 0 0
\(161\) 589.159 0.288399
\(162\) 0 0
\(163\) 1275.93 528.509i 0.613121 0.253963i −0.0544412 0.998517i \(-0.517338\pi\)
0.667562 + 0.744554i \(0.267338\pi\)
\(164\) 0 0
\(165\) 848.114 2047.53i 0.400155 0.966060i
\(166\) 0 0
\(167\) 1744.38 + 1744.38i 0.808287 + 0.808287i 0.984375 0.176088i \(-0.0563442\pi\)
−0.176088 + 0.984375i \(0.556344\pi\)
\(168\) 0 0
\(169\) −666.164 + 666.164i −0.303215 + 0.303215i
\(170\) 0 0
\(171\) −1656.58 686.176i −0.740828 0.306861i
\(172\) 0 0
\(173\) −286.418 691.473i −0.125872 0.303883i 0.848364 0.529414i \(-0.177588\pi\)
−0.974236 + 0.225531i \(0.927588\pi\)
\(174\) 0 0
\(175\) 752.916i 0.325229i
\(176\) 0 0
\(177\) 1618.13i 0.687154i
\(178\) 0 0
\(179\) −944.647 2280.58i −0.394448 0.952282i −0.988958 0.148194i \(-0.952654\pi\)
0.594510 0.804088i \(-0.297346\pi\)
\(180\) 0 0
\(181\) −1523.13 630.902i −0.625489 0.259086i 0.0473461 0.998879i \(-0.484924\pi\)
−0.672835 + 0.739793i \(0.734924\pi\)
\(182\) 0 0
\(183\) 187.759 187.759i 0.0758444 0.0758444i
\(184\) 0 0
\(185\) −4402.17 4402.17i −1.74948 1.74948i
\(186\) 0 0
\(187\) 76.4281 184.514i 0.0298876 0.0721550i
\(188\) 0 0
\(189\) −1115.07 + 461.879i −0.429152 + 0.177760i
\(190\) 0 0
\(191\) 1792.15 0.678931 0.339465 0.940619i \(-0.389754\pi\)
0.339465 + 0.940619i \(0.389754\pi\)
\(192\) 0 0
\(193\) 3221.65 1.20155 0.600776 0.799417i \(-0.294858\pi\)
0.600776 + 0.799417i \(0.294858\pi\)
\(194\) 0 0
\(195\) −2147.18 + 889.391i −0.788527 + 0.326618i
\(196\) 0 0
\(197\) 365.826 883.183i 0.132305 0.319412i −0.843819 0.536628i \(-0.819698\pi\)
0.976123 + 0.217216i \(0.0696977\pi\)
\(198\) 0 0
\(199\) −198.562 198.562i −0.0707321 0.0707321i 0.670856 0.741588i \(-0.265927\pi\)
−0.741588 + 0.670856i \(0.765927\pi\)
\(200\) 0 0
\(201\) 555.965 555.965i 0.195098 0.195098i
\(202\) 0 0
\(203\) 476.223 + 197.258i 0.164652 + 0.0682010i
\(204\) 0 0
\(205\) 2607.71 + 6295.58i 0.888442 + 2.14489i
\(206\) 0 0
\(207\) 1201.71i 0.403500i
\(208\) 0 0
\(209\) 5124.68i 1.69608i
\(210\) 0 0
\(211\) −87.1014 210.281i −0.0284185 0.0686084i 0.909033 0.416724i \(-0.136822\pi\)
−0.937452 + 0.348115i \(0.886822\pi\)
\(212\) 0 0
\(213\) −1619.77 670.930i −0.521055 0.215828i
\(214\) 0 0
\(215\) 3623.77 3623.77i 1.14948 1.14948i
\(216\) 0 0
\(217\) 476.453 + 476.453i 0.149049 + 0.149049i
\(218\) 0 0
\(219\) 65.2562 157.542i 0.0201352 0.0486106i
\(220\) 0 0
\(221\) −193.494 + 80.1477i −0.0588950 + 0.0243951i
\(222\) 0 0
\(223\) 2508.49 0.753278 0.376639 0.926360i \(-0.377080\pi\)
0.376639 + 0.926360i \(0.377080\pi\)
\(224\) 0 0
\(225\) 1535.73 0.455030
\(226\) 0 0
\(227\) −2537.71 + 1051.15i −0.741998 + 0.307345i −0.721472 0.692444i \(-0.756534\pi\)
−0.0205258 + 0.999789i \(0.506534\pi\)
\(228\) 0 0
\(229\) 697.363 1683.58i 0.201236 0.485826i −0.790755 0.612132i \(-0.790312\pi\)
0.991991 + 0.126306i \(0.0403120\pi\)
\(230\) 0 0
\(231\) −997.888 997.888i −0.284226 0.284226i
\(232\) 0 0
\(233\) −2051.84 + 2051.84i −0.576911 + 0.576911i −0.934051 0.357140i \(-0.883752\pi\)
0.357140 + 0.934051i \(0.383752\pi\)
\(234\) 0 0
\(235\) 2470.02 + 1023.12i 0.685644 + 0.284003i
\(236\) 0 0
\(237\) 1335.85 + 3225.02i 0.366129 + 0.883914i
\(238\) 0 0
\(239\) 2551.88i 0.690659i −0.938482 0.345329i \(-0.887767\pi\)
0.938482 0.345329i \(-0.112233\pi\)
\(240\) 0 0
\(241\) 2268.42i 0.606314i 0.952941 + 0.303157i \(0.0980407\pi\)
−0.952941 + 0.303157i \(0.901959\pi\)
\(242\) 0 0
\(243\) −1498.77 3618.35i −0.395663 0.955216i
\(244\) 0 0
\(245\) 3444.04 + 1426.57i 0.898088 + 0.372000i
\(246\) 0 0
\(247\) −3800.05 + 3800.05i −0.978914 + 0.978914i
\(248\) 0 0
\(249\) 1549.26 + 1549.26i 0.394298 + 0.394298i
\(250\) 0 0
\(251\) −2808.05 + 6779.23i −0.706145 + 1.70479i 0.00326968 + 0.999995i \(0.498959\pi\)
−0.709415 + 0.704791i \(0.751041\pi\)
\(252\) 0 0
\(253\) −3173.11 + 1314.35i −0.788505 + 0.326610i
\(254\) 0 0
\(255\) −155.060 −0.0380793
\(256\) 0 0
\(257\) −2117.45 −0.513942 −0.256971 0.966419i \(-0.582724\pi\)
−0.256971 + 0.966419i \(0.582724\pi\)
\(258\) 0 0
\(259\) −3662.51 + 1517.06i −0.878677 + 0.363960i
\(260\) 0 0
\(261\) −402.348 + 971.354i −0.0954203 + 0.230365i
\(262\) 0 0
\(263\) −632.092 632.092i −0.148200 0.148200i 0.629114 0.777313i \(-0.283418\pi\)
−0.777313 + 0.629114i \(0.783418\pi\)
\(264\) 0 0
\(265\) −4547.66 + 4547.66i −1.05419 + 1.05419i
\(266\) 0 0
\(267\) 1375.70 + 569.833i 0.315323 + 0.130611i
\(268\) 0 0
\(269\) 835.101 + 2016.11i 0.189283 + 0.456968i 0.989822 0.142312i \(-0.0454535\pi\)
−0.800539 + 0.599280i \(0.795454\pi\)
\(270\) 0 0
\(271\) 2528.01i 0.566663i −0.959022 0.283331i \(-0.908560\pi\)
0.959022 0.283331i \(-0.0914396\pi\)
\(272\) 0 0
\(273\) 1479.91i 0.328088i
\(274\) 0 0
\(275\) 1679.67 + 4055.08i 0.368320 + 0.889202i
\(276\) 0 0
\(277\) −1743.13 722.029i −0.378103 0.156616i 0.185534 0.982638i \(-0.440598\pi\)
−0.563637 + 0.826022i \(0.690598\pi\)
\(278\) 0 0
\(279\) −971.822 + 971.822i −0.208536 + 0.208536i
\(280\) 0 0
\(281\) −3983.45 3983.45i −0.845667 0.845667i 0.143922 0.989589i \(-0.454029\pi\)
−0.989589 + 0.143922i \(0.954029\pi\)
\(282\) 0 0
\(283\) 580.183 1400.69i 0.121867 0.294213i −0.851159 0.524907i \(-0.824100\pi\)
0.973026 + 0.230695i \(0.0740999\pi\)
\(284\) 0 0
\(285\) −3675.94 + 1522.62i −0.764013 + 0.316465i
\(286\) 0 0
\(287\) 4339.13 0.892441
\(288\) 0 0
\(289\) 4899.03 0.997156
\(290\) 0 0
\(291\) 1355.02 561.267i 0.272964 0.113066i
\(292\) 0 0
\(293\) −797.079 + 1924.32i −0.158928 + 0.383686i −0.983206 0.182499i \(-0.941581\pi\)
0.824278 + 0.566185i \(0.191581\pi\)
\(294\) 0 0
\(295\) 5713.98 + 5713.98i 1.12773 + 1.12773i
\(296\) 0 0
\(297\) 4975.20 4975.20i 0.972021 0.972021i
\(298\) 0 0
\(299\) 3327.54 + 1378.31i 0.643601 + 0.266588i
\(300\) 0 0
\(301\) −1248.81 3014.90i −0.239137 0.577328i
\(302\) 0 0
\(303\) 1391.79i 0.263882i
\(304\) 0 0
\(305\) 1326.03i 0.248946i
\(306\) 0 0
\(307\) −2999.31 7240.97i −0.557588 1.34614i −0.911670 0.410923i \(-0.865206\pi\)
0.354082 0.935215i \(-0.384794\pi\)
\(308\) 0 0
\(309\) 2300.32 + 952.824i 0.423498 + 0.175418i
\(310\) 0 0
\(311\) −5951.01 + 5951.01i −1.08505 + 1.08505i −0.0890208 + 0.996030i \(0.528374\pi\)
−0.996030 + 0.0890208i \(0.971626\pi\)
\(312\) 0 0
\(313\) 2649.88 + 2649.88i 0.478531 + 0.478531i 0.904661 0.426131i \(-0.140124\pi\)
−0.426131 + 0.904661i \(0.640124\pi\)
\(314\) 0 0
\(315\) 943.638 2278.14i 0.168787 0.407488i
\(316\) 0 0
\(317\) 5107.96 2115.79i 0.905021 0.374872i 0.118873 0.992910i \(-0.462072\pi\)
0.786149 + 0.618038i \(0.212072\pi\)
\(318\) 0 0
\(319\) −3004.92 −0.527408
\(320\) 0 0
\(321\) −1882.16 −0.327265
\(322\) 0 0
\(323\) −331.258 + 137.212i −0.0570641 + 0.0236367i
\(324\) 0 0
\(325\) 1761.42 4252.43i 0.300633 0.725793i
\(326\) 0 0
\(327\) −1448.05 1448.05i −0.244886 0.244886i
\(328\) 0 0
\(329\) 1203.79 1203.79i 0.201724 0.201724i
\(330\) 0 0
\(331\) −2534.49 1049.82i −0.420870 0.174330i 0.162189 0.986760i \(-0.448145\pi\)
−0.583059 + 0.812430i \(0.698145\pi\)
\(332\) 0 0
\(333\) −3094.35 7470.43i −0.509218 1.22936i
\(334\) 0 0
\(335\) 3926.47i 0.640376i
\(336\) 0 0
\(337\) 3412.65i 0.551629i −0.961211 0.275814i \(-0.911053\pi\)
0.961211 0.275814i \(-0.0889475\pi\)
\(338\) 0 0
\(339\) 1821.25 + 4396.88i 0.291789 + 0.704442i
\(340\) 0 0
\(341\) −3629.01 1503.18i −0.576310 0.238715i
\(342\) 0 0
\(343\) 3901.32 3901.32i 0.614145 0.614145i
\(344\) 0 0
\(345\) 1885.56 + 1885.56i 0.294247 + 0.294247i
\(346\) 0 0
\(347\) 1608.37 3882.95i 0.248824 0.600714i −0.749281 0.662252i \(-0.769601\pi\)
0.998105 + 0.0615384i \(0.0196007\pi\)
\(348\) 0 0
\(349\) 5617.33 2326.78i 0.861573 0.356875i 0.0922505 0.995736i \(-0.470594\pi\)
0.769323 + 0.638861i \(0.220594\pi\)
\(350\) 0 0
\(351\) −7378.43 −1.12203
\(352\) 0 0
\(353\) −8007.64 −1.20738 −0.603688 0.797221i \(-0.706303\pi\)
−0.603688 + 0.797221i \(0.706303\pi\)
\(354\) 0 0
\(355\) 8088.95 3350.55i 1.20934 0.500927i
\(356\) 0 0
\(357\) −37.7852 + 91.2214i −0.00560169 + 0.0135237i
\(358\) 0 0
\(359\) −7420.49 7420.49i −1.09092 1.09092i −0.995431 0.0954845i \(-0.969560\pi\)
−0.0954845 0.995431i \(-0.530440\pi\)
\(360\) 0 0
\(361\) −1655.59 + 1655.59i −0.241375 + 0.241375i
\(362\) 0 0
\(363\) 4056.58 + 1680.29i 0.586544 + 0.242954i
\(364\) 0 0
\(365\) 325.882 + 786.750i 0.0467328 + 0.112823i
\(366\) 0 0
\(367\) 4739.58i 0.674126i −0.941482 0.337063i \(-0.890566\pi\)
0.941482 0.337063i \(-0.109434\pi\)
\(368\) 0 0
\(369\) 8850.53i 1.24862i
\(370\) 0 0
\(371\) 1567.20 + 3783.56i 0.219313 + 0.529468i
\(372\) 0 0
\(373\) −6348.63 2629.69i −0.881285 0.365040i −0.104290 0.994547i \(-0.533257\pi\)
−0.776995 + 0.629507i \(0.783257\pi\)
\(374\) 0 0
\(375\) −1256.79 + 1256.79i −0.173068 + 0.173068i
\(376\) 0 0
\(377\) 2228.21 + 2228.21i 0.304399 + 0.304399i
\(378\) 0 0
\(379\) 2437.33 5884.23i 0.330335 0.797500i −0.668230 0.743955i \(-0.732948\pi\)
0.998565 0.0535452i \(-0.0170521\pi\)
\(380\) 0 0
\(381\) −834.752 + 345.765i −0.112246 + 0.0464937i
\(382\) 0 0
\(383\) −205.714 −0.0274451 −0.0137226 0.999906i \(-0.504368\pi\)
−0.0137226 + 0.999906i \(0.504368\pi\)
\(384\) 0 0
\(385\) 7047.52 0.932921
\(386\) 0 0
\(387\) 6149.49 2547.20i 0.807743 0.334578i
\(388\) 0 0
\(389\) 736.006 1776.88i 0.0959305 0.231597i −0.868629 0.495464i \(-0.834998\pi\)
0.964559 + 0.263867i \(0.0849981\pi\)
\(390\) 0 0
\(391\) 169.918 + 169.918i 0.0219773 + 0.0219773i
\(392\) 0 0
\(393\) −1139.37 + 1139.37i −0.146243 + 0.146243i
\(394\) 0 0
\(395\) −16105.4 6671.08i −2.05152 0.849768i
\(396\) 0 0
\(397\) −1882.80 4545.49i −0.238023 0.574638i 0.759055 0.651026i \(-0.225661\pi\)
−0.997078 + 0.0763880i \(0.975661\pi\)
\(398\) 0 0
\(399\) 2533.58i 0.317889i
\(400\) 0 0
\(401\) 6670.63i 0.830712i 0.909659 + 0.415356i \(0.136343\pi\)
−0.909659 + 0.415356i \(0.863657\pi\)
\(402\) 0 0
\(403\) 1576.34 + 3805.62i 0.194846 + 0.470401i
\(404\) 0 0
\(405\) 1664.54 + 689.476i 0.204227 + 0.0845935i
\(406\) 0 0
\(407\) 16341.3 16341.3i 1.99019 1.99019i
\(408\) 0 0
\(409\) −2441.40 2441.40i −0.295158 0.295158i 0.543956 0.839114i \(-0.316926\pi\)
−0.839114 + 0.543956i \(0.816926\pi\)
\(410\) 0 0
\(411\) 849.880 2051.79i 0.101999 0.246247i
\(412\) 0 0
\(413\) 4753.91 1969.13i 0.566403 0.234612i
\(414\) 0 0
\(415\) −10941.5 −1.29421
\(416\) 0 0
\(417\) 6705.42 0.787448
\(418\) 0 0
\(419\) 15396.0 6377.25i 1.79510 0.743554i 0.806838 0.590772i \(-0.201177\pi\)
0.988260 0.152782i \(-0.0488231\pi\)
\(420\) 0 0
\(421\) −1566.59 + 3782.09i −0.181356 + 0.437833i −0.988247 0.152868i \(-0.951149\pi\)
0.806890 + 0.590702i \(0.201149\pi\)
\(422\) 0 0
\(423\) 2455.38 + 2455.38i 0.282233 + 0.282233i
\(424\) 0 0
\(425\) 217.147 217.147i 0.0247840 0.0247840i
\(426\) 0 0
\(427\) 780.103 + 323.129i 0.0884117 + 0.0366213i
\(428\) 0 0
\(429\) −3301.50 7970.54i −0.371557 0.897019i
\(430\) 0 0
\(431\) 8391.23i 0.937799i 0.883252 + 0.468899i \(0.155349\pi\)
−0.883252 + 0.468899i \(0.844651\pi\)
\(432\) 0 0
\(433\) 14275.6i 1.58439i −0.610270 0.792193i \(-0.708939\pi\)
0.610270 0.792193i \(-0.291061\pi\)
\(434\) 0 0
\(435\) 892.809 + 2155.43i 0.0984067 + 0.237575i
\(436\) 0 0
\(437\) 5696.70 + 2359.65i 0.623593 + 0.258301i
\(438\) 0 0
\(439\) −11181.1 + 11181.1i −1.21559 + 1.21559i −0.246429 + 0.969161i \(0.579257\pi\)
−0.969161 + 0.246429i \(0.920743\pi\)
\(440\) 0 0
\(441\) 3423.63 + 3423.63i 0.369682 + 0.369682i
\(442\) 0 0
\(443\) −4372.54 + 10556.2i −0.468952 + 1.13215i 0.495670 + 0.868511i \(0.334923\pi\)
−0.964622 + 0.263639i \(0.915077\pi\)
\(444\) 0 0
\(445\) −6870.09 + 2845.68i −0.731850 + 0.303142i
\(446\) 0 0
\(447\) 4628.87 0.489794
\(448\) 0 0
\(449\) −9965.25 −1.04741 −0.523707 0.851898i \(-0.675451\pi\)
−0.523707 + 0.851898i \(0.675451\pi\)
\(450\) 0 0
\(451\) −23369.8 + 9680.09i −2.44000 + 1.01068i
\(452\) 0 0
\(453\) −3193.88 + 7710.70i −0.331261 + 0.799736i
\(454\) 0 0
\(455\) −5225.88 5225.88i −0.538446 0.538446i
\(456\) 0 0
\(457\) 11250.2 11250.2i 1.15155 1.15155i 0.165312 0.986241i \(-0.447137\pi\)
0.986241 0.165312i \(-0.0528632\pi\)
\(458\) 0 0
\(459\) −454.805 188.387i −0.0462495 0.0191572i
\(460\) 0 0
\(461\) 567.298 + 1369.58i 0.0573139 + 0.138368i 0.949942 0.312425i \(-0.101141\pi\)
−0.892629 + 0.450793i \(0.851141\pi\)
\(462\) 0 0
\(463\) 1601.42i 0.160744i 0.996765 + 0.0803720i \(0.0256108\pi\)
−0.996765 + 0.0803720i \(0.974389\pi\)
\(464\) 0 0
\(465\) 3049.71i 0.304144i
\(466\) 0 0
\(467\) 4458.09 + 10762.8i 0.441747 + 1.06647i 0.975335 + 0.220728i \(0.0708433\pi\)
−0.533588 + 0.845744i \(0.679157\pi\)
\(468\) 0 0
\(469\) 2309.93 + 956.805i 0.227426 + 0.0942029i
\(470\) 0 0
\(471\) 3409.22 3409.22i 0.333522 0.333522i
\(472\) 0 0
\(473\) 13451.8 + 13451.8i 1.30764 + 1.30764i
\(474\) 0 0
\(475\) 3015.52 7280.10i 0.291287 0.703229i
\(476\) 0 0
\(477\) −7717.33 + 3196.62i −0.740781 + 0.306841i
\(478\) 0 0
\(479\) 3203.43 0.305571 0.152785 0.988259i \(-0.451176\pi\)
0.152785 + 0.988259i \(0.451176\pi\)
\(480\) 0 0
\(481\) −24234.8 −2.29732
\(482\) 0 0
\(483\) 1568.75 649.797i 0.147786 0.0612149i
\(484\) 0 0
\(485\) −2802.91 + 6766.82i −0.262420 + 0.633537i
\(486\) 0 0
\(487\) 12622.9 + 12622.9i 1.17454 + 1.17454i 0.981116 + 0.193422i \(0.0619586\pi\)
0.193422 + 0.981116i \(0.438041\pi\)
\(488\) 0 0
\(489\) 2814.51 2814.51i 0.260279 0.260279i
\(490\) 0 0
\(491\) −2183.75 904.539i −0.200716 0.0831391i 0.280061 0.959982i \(-0.409645\pi\)
−0.480777 + 0.876843i \(0.659645\pi\)
\(492\) 0 0
\(493\) 80.4558 + 194.237i 0.00734999 + 0.0177444i
\(494\) 0 0
\(495\) 14374.8i 1.30525i
\(496\) 0 0
\(497\) 5575.18i 0.503181i
\(498\) 0 0
\(499\) −3796.86 9166.43i −0.340623 0.822336i −0.997653 0.0684718i \(-0.978188\pi\)
0.657030 0.753864i \(-0.271812\pi\)
\(500\) 0 0
\(501\) 6568.65 + 2720.82i 0.585760 + 0.242630i
\(502\) 0 0
\(503\) 5777.19 5777.19i 0.512112 0.512112i −0.403061 0.915173i \(-0.632054\pi\)
0.915173 + 0.403061i \(0.132054\pi\)
\(504\) 0 0
\(505\) −4914.71 4914.71i −0.433073 0.433073i
\(506\) 0 0
\(507\) −1039.06 + 2508.52i −0.0910184 + 0.219738i
\(508\) 0 0
\(509\) 10526.2 4360.11i 0.916636 0.379683i 0.126043 0.992025i \(-0.459772\pi\)
0.790593 + 0.612342i \(0.209772\pi\)
\(510\) 0 0
\(511\) 542.255 0.0469431
\(512\) 0 0
\(513\) −12631.8 −1.08715
\(514\) 0 0
\(515\) −11487.6 + 4758.30i −0.982917 + 0.407138i
\(516\) 0 0
\(517\) −3797.90 + 9168.95i −0.323079 + 0.779981i
\(518\) 0 0
\(519\) −1525.28 1525.28i −0.129003 0.129003i
\(520\) 0 0
\(521\) −3790.76 + 3790.76i −0.318764 + 0.318764i −0.848292 0.529528i \(-0.822369\pi\)
0.529528 + 0.848292i \(0.322369\pi\)
\(522\) 0 0
\(523\) 10160.9 + 4208.78i 0.849531 + 0.351887i 0.764604 0.644500i \(-0.222934\pi\)
0.0849264 + 0.996387i \(0.472934\pi\)
\(524\) 0 0
\(525\) −830.409 2004.78i −0.0690324 0.166659i
\(526\) 0 0
\(527\) 274.826i 0.0227165i
\(528\) 0 0
\(529\) 8034.51i 0.660353i
\(530\) 0 0
\(531\) 4016.45 + 9696.56i 0.328247 + 0.792457i
\(532\) 0 0
\(533\) 24507.2 + 10151.2i 1.99160 + 0.824948i
\(534\) 0 0
\(535\) 6646.33 6646.33i 0.537095 0.537095i
\(536\) 0 0
\(537\) −5030.61 5030.61i −0.404258 0.404258i
\(538\) 0 0
\(539\) −5295.56 + 12784.6i −0.423184 + 1.02166i
\(540\) 0 0
\(541\) 870.092 360.404i 0.0691463 0.0286413i −0.347842 0.937553i \(-0.613086\pi\)
0.416989 + 0.908912i \(0.363086\pi\)
\(542\) 0 0
\(543\) −4751.47 −0.375516
\(544\) 0 0
\(545\) 10226.8 0.803794
\(546\) 0 0
\(547\) −1669.92 + 691.704i −0.130531 + 0.0540679i −0.446993 0.894537i \(-0.647505\pi\)
0.316462 + 0.948605i \(0.397505\pi\)
\(548\) 0 0
\(549\) −659.087 + 1591.18i −0.0512371 + 0.123697i
\(550\) 0 0
\(551\) 3814.66 + 3814.66i 0.294936 + 0.294936i
\(552\) 0 0
\(553\) −7849.17 + 7849.17i −0.603581 + 0.603581i
\(554\) 0 0
\(555\) −16576.9 6866.36i −1.26784 0.525155i
\(556\) 0 0
\(557\) 4440.93 + 10721.4i 0.337825 + 0.815581i 0.997924 + 0.0644026i \(0.0205142\pi\)
−0.660099 + 0.751178i \(0.729486\pi\)
\(558\) 0 0
\(559\) 19949.5i 1.50944i
\(560\) 0 0
\(561\) 575.598i 0.0433186i
\(562\) 0 0
\(563\) −4527.75 10931.0i −0.338938 0.818268i −0.997818 0.0660203i \(-0.978970\pi\)
0.658881 0.752247i \(-0.271030\pi\)
\(564\) 0 0
\(565\) −21957.5 9095.11i −1.63498 0.677229i
\(566\) 0 0
\(567\) 811.235 811.235i 0.0600859 0.0600859i
\(568\) 0 0
\(569\) −10557.5 10557.5i −0.777844 0.777844i 0.201620 0.979464i \(-0.435379\pi\)
−0.979464 + 0.201620i \(0.935379\pi\)
\(570\) 0 0
\(571\) 4454.66 10754.5i 0.326483 0.788199i −0.672366 0.740219i \(-0.734722\pi\)
0.998848 0.0479798i \(-0.0152783\pi\)
\(572\) 0 0
\(573\) 4771.96 1976.61i 0.347908 0.144108i
\(574\) 0 0
\(575\) −5281.11 −0.383022
\(576\) 0 0
\(577\) 17387.0 1.25447 0.627234 0.778831i \(-0.284187\pi\)
0.627234 + 0.778831i \(0.284187\pi\)
\(578\) 0 0
\(579\) 8578.27 3553.24i 0.615718 0.255039i
\(580\) 0 0
\(581\) −2666.25 + 6436.89i −0.190386 + 0.459633i
\(582\) 0 0
\(583\) −16881.4 16881.4i −1.19924 1.19924i
\(584\) 0 0
\(585\) 10659.2 10659.2i 0.753342 0.753342i
\(586\) 0 0
\(587\) −7009.84 2903.57i −0.492891 0.204162i 0.122372 0.992484i \(-0.460950\pi\)
−0.615263 + 0.788322i \(0.710950\pi\)
\(588\) 0 0
\(589\) 2698.67 + 6515.17i 0.188789 + 0.455777i
\(590\) 0 0
\(591\) 2755.12i 0.191761i
\(592\) 0 0
\(593\) 10833.0i 0.750181i −0.926988 0.375091i \(-0.877612\pi\)
0.926988 0.375091i \(-0.122388\pi\)
\(594\) 0 0
\(595\) −188.695 455.550i −0.0130013 0.0313878i
\(596\) 0 0
\(597\) −747.708 309.711i −0.0512590 0.0212322i
\(598\) 0 0
\(599\) 3185.59 3185.59i 0.217295 0.217295i −0.590063 0.807358i \(-0.700897\pi\)
0.807358 + 0.590063i \(0.200897\pi\)
\(600\) 0 0
\(601\) 2409.29 + 2409.29i 0.163522 + 0.163522i 0.784125 0.620603i \(-0.213112\pi\)
−0.620603 + 0.784125i \(0.713112\pi\)
\(602\) 0 0
\(603\) −1951.60 + 4711.57i −0.131800 + 0.318193i
\(604\) 0 0
\(605\) −20258.2 + 8391.20i −1.36134 + 0.563886i
\(606\) 0 0
\(607\) 28227.6 1.88752 0.943759 0.330636i \(-0.107263\pi\)
0.943759 + 0.330636i \(0.107263\pi\)
\(608\) 0 0
\(609\) 1485.60 0.0988496
\(610\) 0 0
\(611\) 9615.19 3982.74i 0.636643 0.263706i
\(612\) 0 0
\(613\) 9916.41 23940.3i 0.653377 1.57739i −0.154470 0.987998i \(-0.549367\pi\)
0.807846 0.589393i \(-0.200633\pi\)
\(614\) 0 0
\(615\) 13887.1 + 13887.1i 0.910538 + 0.910538i
\(616\) 0 0
\(617\) 10610.2 10610.2i 0.692304 0.692304i −0.270435 0.962738i \(-0.587167\pi\)
0.962738 + 0.270435i \(0.0871674\pi\)
\(618\) 0 0
\(619\) 2228.33 + 923.005i 0.144692 + 0.0599333i 0.453854 0.891076i \(-0.350049\pi\)
−0.309162 + 0.951009i \(0.600049\pi\)
\(620\) 0 0
\(621\) 3239.71 + 7821.36i 0.209348 + 0.505411i
\(622\) 0 0
\(623\) 4735.10i 0.304507i
\(624\) 0 0
\(625\) 19145.0i 1.22528i
\(626\) 0 0
\(627\) −5652.13 13645.4i −0.360007 0.869133i
\(628\) 0 0
\(629\) −1493.83 618.765i −0.0946946 0.0392238i
\(630\) 0 0
\(631\) −4628.63 + 4628.63i −0.292017 + 0.292017i −0.837877 0.545860i \(-0.816203\pi\)
0.545860 + 0.837877i \(0.316203\pi\)
\(632\) 0 0
\(633\) −463.848 463.848i −0.0291253 0.0291253i
\(634\) 0 0
\(635\) 1726.72 4168.66i 0.107910 0.260517i
\(636\) 0 0
\(637\) 13406.8 5553.29i 0.833905 0.345415i
\(638\) 0 0
\(639\) 11371.7 0.704003
\(640\) 0 0
\(641\) 6544.85 0.403286 0.201643 0.979459i \(-0.435372\pi\)
0.201643 + 0.979459i \(0.435372\pi\)
\(642\) 0 0
\(643\) −12954.9 + 5366.09i −0.794543 + 0.329110i −0.742768 0.669548i \(-0.766488\pi\)
−0.0517744 + 0.998659i \(0.516488\pi\)
\(644\) 0 0
\(645\) 5652.24 13645.7i 0.345049 0.833022i
\(646\) 0 0
\(647\) −6054.03 6054.03i −0.367865 0.367865i 0.498833 0.866698i \(-0.333762\pi\)
−0.866698 + 0.498833i \(0.833762\pi\)
\(648\) 0 0
\(649\) −21210.8 + 21210.8i −1.28289 + 1.28289i
\(650\) 0 0
\(651\) 1794.14 + 743.156i 0.108015 + 0.0447413i
\(652\) 0 0
\(653\) −5840.08 14099.2i −0.349985 0.844937i −0.996621 0.0821390i \(-0.973825\pi\)
0.646636 0.762798i \(-0.276175\pi\)
\(654\) 0 0
\(655\) 8046.71i 0.480017i
\(656\) 0 0
\(657\) 1106.04i 0.0656783i
\(658\) 0 0
\(659\) 7839.56 + 18926.4i 0.463408 + 1.11877i 0.966989 + 0.254818i \(0.0820157\pi\)
−0.503581 + 0.863948i \(0.667984\pi\)
\(660\) 0 0
\(661\) −29468.7 12206.3i −1.73404 0.718262i −0.999199 0.0400217i \(-0.987257\pi\)
−0.734840 0.678241i \(-0.762743\pi\)
\(662\) 0 0
\(663\) −426.817 + 426.817i −0.0250018 + 0.0250018i
\(664\) 0 0
\(665\) −8946.62 8946.62i −0.521707 0.521707i
\(666\) 0 0
\(667\) 1383.61 3340.33i 0.0803202 0.193910i
\(668\) 0 0
\(669\) 6679.34 2766.67i 0.386006 0.159889i
\(670\) 0 0
\(671\) −4922.36 −0.283198
\(672\) 0 0
\(673\) 17972.6 1.02941 0.514704 0.857368i \(-0.327902\pi\)
0.514704 + 0.857368i \(0.327902\pi\)
\(674\) 0 0
\(675\) 9995.31 4140.19i 0.569955 0.236083i
\(676\) 0 0
\(677\) −1779.19 + 4295.35i −0.101004 + 0.243846i −0.966301 0.257414i \(-0.917130\pi\)
0.865297 + 0.501259i \(0.167130\pi\)
\(678\) 0 0
\(679\) 3297.89 + 3297.89i 0.186394 + 0.186394i
\(680\) 0 0
\(681\) −5597.79 + 5597.79i −0.314989 + 0.314989i
\(682\) 0 0
\(683\) 7660.17 + 3172.95i 0.429149 + 0.177759i 0.586793 0.809737i \(-0.300390\pi\)
−0.157645 + 0.987496i \(0.550390\pi\)
\(684\) 0 0
\(685\) 4244.21 + 10246.4i 0.236734 + 0.571527i
\(686\) 0 0
\(687\) 5252.00i 0.291668i
\(688\) 0 0
\(689\) 25035.8i 1.38431i
\(690\) 0 0
\(691\) −3344.80 8075.06i −0.184142 0.444558i 0.804670 0.593722i \(-0.202342\pi\)
−0.988813 + 0.149163i \(0.952342\pi\)
\(692\) 0 0
\(693\) 8456.69 + 3502.87i 0.463554 + 0.192010i
\(694\) 0 0
\(695\) −23678.3 + 23678.3i −1.29233 + 1.29233i
\(696\) 0 0
\(697\) 1251.44 + 1251.44i 0.0680080 + 0.0680080i
\(698\) 0 0
\(699\) −3200.39 + 7726.43i −0.173176 + 0.418084i
\(700\) 0 0
\(701\) −11050.1 + 4577.09i −0.595371 + 0.246611i −0.659960 0.751301i \(-0.729427\pi\)
0.0645882 + 0.997912i \(0.479427\pi\)
\(702\) 0 0
\(703\) −41489.6 −2.22590
\(704\) 0 0
\(705\) 7705.32 0.411630
\(706\) 0 0
\(707\) −4088.94 + 1693.69i −0.217511 + 0.0900960i
\(708\) 0 0
\(709\) 10279.5 24817.0i 0.544508 1.31456i −0.377005 0.926211i \(-0.623046\pi\)
0.921513 0.388347i \(-0.126954\pi\)
\(710\) 0 0
\(711\) −16010.0 16010.0i −0.844473 0.844473i
\(712\) 0 0
\(713\) 3341.94 3341.94i 0.175535 0.175535i
\(714\) 0 0
\(715\) 39804.0 + 16487.4i 2.08194 + 0.862367i
\(716\) 0 0
\(717\) −2814.53 6794.87i −0.146598 0.353918i
\(718\) 0 0
\(719\) 8782.64i 0.455546i −0.973714 0.227773i \(-0.926856\pi\)
0.973714 0.227773i \(-0.0731444\pi\)
\(720\) 0 0
\(721\) 7917.62i 0.408970i
\(722\) 0 0
\(723\) 2501.89 + 6040.10i 0.128695 + 0.310697i
\(724\) 0 0
\(725\) −4268.78 1768.19i −0.218674 0.0905776i
\(726\) 0 0
\(727\) −19402.1 + 19402.1i −0.989798 + 0.989798i −0.999948 0.0101501i \(-0.996769\pi\)
0.0101501 + 0.999948i \(0.496769\pi\)
\(728\) 0 0
\(729\) −5591.61 5591.61i −0.284083 0.284083i
\(730\) 0 0
\(731\) 509.353 1229.69i 0.0257717 0.0622184i
\(732\) 0 0
\(733\) 12567.1 5205.47i 0.633256 0.262303i −0.0428799 0.999080i \(-0.513653\pi\)
0.676136 + 0.736777i \(0.263653\pi\)
\(734\) 0 0
\(735\) 10743.8 0.539172
\(736\) 0 0
\(737\) −14575.4 −0.728484
\(738\) 0 0
\(739\) 9220.93 3819.43i 0.458995 0.190122i −0.141191 0.989982i \(-0.545093\pi\)
0.600186 + 0.799860i \(0.295093\pi\)
\(740\) 0 0
\(741\) −5927.21 + 14309.5i −0.293848 + 0.709412i
\(742\) 0 0
\(743\) 22825.1 + 22825.1i 1.12702 + 1.12702i 0.990660 + 0.136355i \(0.0435389\pi\)
0.136355 + 0.990660i \(0.456461\pi\)
\(744\) 0 0
\(745\) −16345.5 + 16345.5i −0.803831 + 0.803831i
\(746\) 0 0
\(747\) −13129.3 5438.35i −0.643075 0.266370i
\(748\) 0 0
\(749\) −2290.44 5529.60i −0.111737 0.269756i
\(750\) 0 0
\(751\) 16863.5i 0.819384i −0.912224 0.409692i \(-0.865636\pi\)
0.912224 0.409692i \(-0.134364\pi\)
\(752\) 0 0
\(753\) 21148.1i 1.02348i
\(754\) 0 0
\(755\) −15949.9 38506.4i −0.768842 1.85615i
\(756\) 0 0
\(757\) 13042.4 + 5402.33i 0.626200 + 0.259381i 0.673138 0.739517i \(-0.264946\pi\)
−0.0469375 + 0.998898i \(0.514946\pi\)
\(758\) 0 0
\(759\) −6999.40 + 6999.40i −0.334733 + 0.334733i
\(760\) 0 0
\(761\) 14227.7 + 14227.7i 0.677732 + 0.677732i 0.959487 0.281754i \(-0.0909163\pi\)
−0.281754 + 0.959487i \(0.590916\pi\)
\(762\) 0 0
\(763\) 2492.07 6016.40i 0.118243 0.285463i
\(764\) 0 0
\(765\) 929.187 384.882i 0.0439148 0.0181901i
\(766\) 0 0
\(767\) 31456.5 1.48087
\(768\) 0 0
\(769\) 22350.4 1.04808 0.524041 0.851693i \(-0.324424\pi\)
0.524041 + 0.851693i \(0.324424\pi\)
\(770\) 0 0
\(771\) −5638.12 + 2335.39i −0.263362 + 0.109088i
\(772\) 0 0
\(773\) 4110.34 9923.25i 0.191253 0.461726i −0.798943 0.601406i \(-0.794607\pi\)
0.990197 + 0.139680i \(0.0446074\pi\)
\(774\) 0 0
\(775\) −4270.84 4270.84i −0.197952 0.197952i
\(776\) 0 0
\(777\) −8078.94 + 8078.94i −0.373012 + 0.373012i
\(778\) 0 0
\(779\) 41955.9 + 17378.7i 1.92969 + 0.799302i
\(780\) 0 0
\(781\) 12437.6 + 30027.0i 0.569849 + 1.37574i
\(782\) 0 0
\(783\) 7406.78i 0.338055i
\(784\) 0 0
\(785\) 24077.4i 1.09473i
\(786\) 0 0