Properties

Label 128.4.g.a.17.2
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 17.2
Character \(\chi\) \(=\) 128.17
Dual form 128.4.g.a.113.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.92731 + 7.06715i) q^{3} +(13.5234 - 5.60159i) q^{5} +(23.0737 - 23.0737i) q^{7} +(-22.2836 - 22.2836i) q^{9} +O(q^{10})\) \(q+(-2.92731 + 7.06715i) q^{3} +(13.5234 - 5.60159i) q^{5} +(23.0737 - 23.0737i) q^{7} +(-22.2836 - 22.2836i) q^{9} +(7.41078 + 17.8912i) q^{11} +(14.8121 + 6.13537i) q^{13} +111.970i q^{15} +27.7996i q^{17} +(82.2959 + 34.0881i) q^{19} +(95.5216 + 230.610i) q^{21} +(-39.2456 - 39.2456i) q^{23} +(63.1173 - 63.1173i) q^{25} +(31.8994 - 13.2132i) q^{27} +(5.57538 - 13.4602i) q^{29} -155.853 q^{31} -148.133 q^{33} +(182.787 - 441.286i) q^{35} +(188.743 - 78.1798i) q^{37} +(-86.7192 + 86.7192i) q^{39} +(113.814 + 113.814i) q^{41} +(24.6509 + 59.5126i) q^{43} +(-426.174 - 176.527i) q^{45} +217.464i q^{47} -721.795i q^{49} +(-196.464 - 81.3779i) q^{51} +(-35.7808 - 86.3826i) q^{53} +(200.438 + 200.438i) q^{55} +(-481.811 + 481.811i) q^{57} +(116.586 - 48.2914i) q^{59} +(-197.015 + 475.636i) q^{61} -1028.33 q^{63} +234.678 q^{65} +(-144.765 + 349.494i) q^{67} +(392.239 - 162.471i) q^{69} +(523.475 - 523.475i) q^{71} +(-718.521 - 718.521i) q^{73} +(261.296 + 630.823i) q^{75} +(583.811 + 241.822i) q^{77} -958.779i q^{79} -586.755i q^{81} +(-1241.90 - 514.414i) q^{83} +(155.722 + 375.946i) q^{85} +(78.8041 + 78.8041i) q^{87} +(-808.016 + 808.016i) q^{89} +(483.336 - 200.204i) q^{91} +(456.231 - 1101.44i) q^{93} +1303.87 q^{95} +1399.29 q^{97} +(233.541 - 563.819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + O(q^{10}) \) \( 44q + 4q^{3} - 4q^{5} + 4q^{7} - 4q^{9} + 4q^{11} - 4q^{13} + 4q^{19} - 4q^{21} - 324q^{23} - 4q^{25} + 268q^{27} - 4q^{29} + 752q^{31} - 8q^{33} + 460q^{35} - 4q^{37} - 596q^{39} - 4q^{41} - 804q^{43} + 104q^{45} + 1384q^{51} + 748q^{53} + 292q^{55} - 4q^{57} - 1372q^{59} - 1828q^{61} - 2512q^{63} - 8q^{65} - 2036q^{67} - 1060q^{69} - 220q^{71} - 4q^{73} + 1712q^{75} + 1900q^{77} - 2436q^{83} + 496q^{85} + 1292q^{87} - 4q^{89} + 3604q^{91} - 112q^{93} + 6088q^{95} - 8q^{97} + 5424q^{99} + O(q^{100}) \)

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
\(3\) −2.92731 + 7.06715i −0.563361 + 1.36007i 0.343702 + 0.939079i \(0.388319\pi\)
−0.907063 + 0.420995i \(0.861681\pi\)
\(4\) 0 0
\(5\) 13.5234 5.60159i 1.20957 0.501022i 0.315493 0.948928i \(-0.397830\pi\)
0.894081 + 0.447906i \(0.147830\pi\)
\(6\) 0 0
\(7\) 23.0737 23.0737i 1.24586 1.24586i 0.288335 0.957530i \(-0.406898\pi\)
0.957530 0.288335i \(-0.0931017\pi\)
\(8\) 0 0
\(9\) −22.2836 22.2836i −0.825318 0.825318i
\(10\) 0 0
\(11\) 7.41078 + 17.8912i 0.203130 + 0.490400i 0.992312 0.123760i \(-0.0394951\pi\)
−0.789182 + 0.614159i \(0.789495\pi\)
\(12\) 0 0
\(13\) 14.8121 + 6.13537i 0.316010 + 0.130896i 0.535051 0.844820i \(-0.320293\pi\)
−0.219040 + 0.975716i \(0.570293\pi\)
\(14\) 0 0
\(15\) 111.970i 1.92737i
\(16\) 0 0
\(17\) 27.7996i 0.396611i 0.980140 + 0.198305i \(0.0635438\pi\)
−0.980140 + 0.198305i \(0.936456\pi\)
\(18\) 0 0
\(19\) 82.2959 + 34.0881i 0.993683 + 0.411597i 0.819477 0.573112i \(-0.194264\pi\)
0.174206 + 0.984709i \(0.444264\pi\)
\(20\) 0 0
\(21\) 95.5216 + 230.610i 0.992596 + 2.39634i
\(22\) 0 0
\(23\) −39.2456 39.2456i −0.355795 0.355795i 0.506466 0.862260i \(-0.330952\pi\)
−0.862260 + 0.506466i \(0.830952\pi\)
\(24\) 0 0
\(25\) 63.1173 63.1173i 0.504938 0.504938i
\(26\) 0 0
\(27\) 31.8994 13.2132i 0.227372 0.0941805i
\(28\) 0 0
\(29\) 5.57538 13.4602i 0.0357008 0.0861892i −0.905024 0.425362i \(-0.860147\pi\)
0.940724 + 0.339172i \(0.110147\pi\)
\(30\) 0 0
\(31\) −155.853 −0.902970 −0.451485 0.892279i \(-0.649106\pi\)
−0.451485 + 0.892279i \(0.649106\pi\)
\(32\) 0 0
\(33\) −148.133 −0.781416
\(34\) 0 0
\(35\) 182.787 441.286i 0.882760 2.13117i
\(36\) 0 0
\(37\) 188.743 78.1798i 0.838625 0.347370i 0.0783139 0.996929i \(-0.475046\pi\)
0.760311 + 0.649559i \(0.225046\pi\)
\(38\) 0 0
\(39\) −86.7192 + 86.7192i −0.356056 + 0.356056i
\(40\) 0 0
\(41\) 113.814 + 113.814i 0.433530 + 0.433530i 0.889827 0.456297i \(-0.150825\pi\)
−0.456297 + 0.889827i \(0.650825\pi\)
\(42\) 0 0
\(43\) 24.6509 + 59.5126i 0.0874240 + 0.211060i 0.961545 0.274649i \(-0.0885615\pi\)
−0.874121 + 0.485709i \(0.838562\pi\)
\(44\) 0 0
\(45\) −426.174 176.527i −1.41179 0.584781i
\(46\) 0 0
\(47\) 217.464i 0.674902i 0.941343 + 0.337451i \(0.109565\pi\)
−0.941343 + 0.337451i \(0.890435\pi\)
\(48\) 0 0
\(49\) 721.795i 2.10436i
\(50\) 0 0
\(51\) −196.464 81.3779i −0.539420 0.223435i
\(52\) 0 0
\(53\) −35.7808 86.3826i −0.0927335 0.223879i 0.870706 0.491803i \(-0.163662\pi\)
−0.963440 + 0.267925i \(0.913662\pi\)
\(54\) 0 0
\(55\) 200.438 + 200.438i 0.491402 + 0.491402i
\(56\) 0 0
\(57\) −481.811 + 481.811i −1.11960 + 1.11960i
\(58\) 0 0
\(59\) 116.586 48.2914i 0.257257 0.106559i −0.250328 0.968161i \(-0.580538\pi\)
0.507585 + 0.861602i \(0.330538\pi\)
\(60\) 0 0
\(61\) −197.015 + 475.636i −0.413528 + 0.998344i 0.570655 + 0.821190i \(0.306689\pi\)
−0.984183 + 0.177155i \(0.943311\pi\)
\(62\) 0 0
\(63\) −1028.33 −2.05647
\(64\) 0 0
\(65\) 234.678 0.447819
\(66\) 0 0
\(67\) −144.765 + 349.494i −0.263968 + 0.637276i −0.999177 0.0405648i \(-0.987084\pi\)
0.735208 + 0.677841i \(0.237084\pi\)
\(68\) 0 0
\(69\) 392.239 162.471i 0.684348 0.283466i
\(70\) 0 0
\(71\) 523.475 523.475i 0.875001 0.875001i −0.118011 0.993012i \(-0.537652\pi\)
0.993012 + 0.118011i \(0.0376519\pi\)
\(72\) 0 0
\(73\) −718.521 718.521i −1.15201 1.15201i −0.986150 0.165856i \(-0.946961\pi\)
−0.165856 0.986150i \(-0.553039\pi\)
\(74\) 0 0
\(75\) 261.296 + 630.823i 0.402291 + 0.971216i
\(76\) 0 0
\(77\) 583.811 + 241.822i 0.864045 + 0.357899i
\(78\) 0 0
\(79\) 958.779i 1.36546i −0.730673 0.682728i \(-0.760793\pi\)
0.730673 0.682728i \(-0.239207\pi\)
\(80\) 0 0
\(81\) 586.755i 0.804876i
\(82\) 0 0
\(83\) −1241.90 514.414i −1.64237 0.680292i −0.645836 0.763476i \(-0.723491\pi\)
−0.996534 + 0.0831842i \(0.973491\pi\)
\(84\) 0 0
\(85\) 155.722 + 375.946i 0.198711 + 0.479730i
\(86\) 0 0
\(87\) 78.8041 + 78.8041i 0.0971113 + 0.0971113i
\(88\) 0 0
\(89\) −808.016 + 808.016i −0.962354 + 0.962354i −0.999317 0.0369622i \(-0.988232\pi\)
0.0369622 + 0.999317i \(0.488232\pi\)
\(90\) 0 0
\(91\) 483.336 200.204i 0.556785 0.230628i
\(92\) 0 0
\(93\) 456.231 1101.44i 0.508698 1.22811i
\(94\) 0 0
\(95\) 1303.87 1.40815
\(96\) 0 0
\(97\) 1399.29 1.46471 0.732354 0.680924i \(-0.238422\pi\)
0.732354 + 0.680924i \(0.238422\pi\)
\(98\) 0 0
\(99\) 233.541 563.819i 0.237089 0.572383i
\(100\) 0 0
\(101\) −1024.11 + 424.200i −1.00894 + 0.417916i −0.825067 0.565035i \(-0.808863\pi\)
−0.183871 + 0.982950i \(0.558863\pi\)
\(102\) 0 0
\(103\) 483.862 483.862i 0.462877 0.462877i −0.436720 0.899597i \(-0.643860\pi\)
0.899597 + 0.436720i \(0.143860\pi\)
\(104\) 0 0
\(105\) 2583.56 + 2583.56i 2.40124 + 2.40124i
\(106\) 0 0
\(107\) 682.420 + 1647.51i 0.616561 + 1.48851i 0.855673 + 0.517517i \(0.173144\pi\)
−0.239112 + 0.970992i \(0.576856\pi\)
\(108\) 0 0
\(109\) −1813.85 751.322i −1.59390 0.660217i −0.603367 0.797463i \(-0.706175\pi\)
−0.990537 + 0.137247i \(0.956175\pi\)
\(110\) 0 0
\(111\) 1562.73i 1.33629i
\(112\) 0 0
\(113\) 1392.34i 1.15912i 0.814931 + 0.579558i \(0.196775\pi\)
−0.814931 + 0.579558i \(0.803225\pi\)
\(114\) 0 0
\(115\) −750.574 310.898i −0.608621 0.252099i
\(116\) 0 0
\(117\) −193.349 466.785i −0.152778 0.368840i
\(118\) 0 0
\(119\) 641.440 + 641.440i 0.494123 + 0.494123i
\(120\) 0 0
\(121\) 675.984 675.984i 0.507877 0.507877i
\(122\) 0 0
\(123\) −1137.51 + 471.171i −0.833867 + 0.345399i
\(124\) 0 0
\(125\) −200.193 + 483.310i −0.143247 + 0.345828i
\(126\) 0 0
\(127\) −909.845 −0.635714 −0.317857 0.948139i \(-0.602963\pi\)
−0.317857 + 0.948139i \(0.602963\pi\)
\(128\) 0 0
\(129\) −492.746 −0.336309
\(130\) 0 0
\(131\) −375.465 + 906.452i −0.250416 + 0.604558i −0.998238 0.0593418i \(-0.981100\pi\)
0.747822 + 0.663900i \(0.231100\pi\)
\(132\) 0 0
\(133\) 2685.41 1112.34i 1.75079 0.725201i
\(134\) 0 0
\(135\) 357.375 357.375i 0.227837 0.227837i
\(136\) 0 0
\(137\) −821.434 821.434i −0.512262 0.512262i 0.402957 0.915219i \(-0.367982\pi\)
−0.915219 + 0.402957i \(0.867982\pi\)
\(138\) 0 0
\(139\) −673.401 1625.73i −0.410915 0.992036i −0.984893 0.173165i \(-0.944600\pi\)
0.573978 0.818871i \(-0.305400\pi\)
\(140\) 0 0
\(141\) −1536.85 636.584i −0.917916 0.380213i
\(142\) 0 0
\(143\) 310.474i 0.181560i
\(144\) 0 0
\(145\) 213.259i 0.122139i
\(146\) 0 0
\(147\) 5101.03 + 2112.92i 2.86208 + 1.18551i
\(148\) 0 0
\(149\) 247.105 + 596.564i 0.135863 + 0.328003i 0.977138 0.212604i \(-0.0681946\pi\)
−0.841275 + 0.540607i \(0.818195\pi\)
\(150\) 0 0
\(151\) −373.703 373.703i −0.201401 0.201401i 0.599199 0.800600i \(-0.295486\pi\)
−0.800600 + 0.599199i \(0.795486\pi\)
\(152\) 0 0
\(153\) 619.474 619.474i 0.327330 0.327330i
\(154\) 0 0
\(155\) −2107.67 + 873.027i −1.09221 + 0.452408i
\(156\) 0 0
\(157\) −186.690 + 450.709i −0.0949011 + 0.229112i −0.964200 0.265174i \(-0.914570\pi\)
0.869299 + 0.494286i \(0.164570\pi\)
\(158\) 0 0
\(159\) 715.220 0.356734
\(160\) 0 0
\(161\) −1811.09 −0.886544
\(162\) 0 0
\(163\) 495.962 1197.36i 0.238324 0.575364i −0.758786 0.651340i \(-0.774207\pi\)
0.997110 + 0.0759758i \(0.0242072\pi\)
\(164\) 0 0
\(165\) −2003.27 + 829.783i −0.945180 + 0.391506i
\(166\) 0 0
\(167\) 644.684 644.684i 0.298725 0.298725i −0.541789 0.840514i \(-0.682253\pi\)
0.840514 + 0.541789i \(0.182253\pi\)
\(168\) 0 0
\(169\) −1371.76 1371.76i −0.624378 0.624378i
\(170\) 0 0
\(171\) −1074.24 2593.45i −0.480406 1.15980i
\(172\) 0 0
\(173\) 2383.01 + 987.076i 1.04727 + 0.433792i 0.838915 0.544262i \(-0.183190\pi\)
0.208351 + 0.978054i \(0.433190\pi\)
\(174\) 0 0
\(175\) 2912.70i 1.25817i
\(176\) 0 0
\(177\) 965.293i 0.409920i
\(178\) 0 0
\(179\) −3184.86 1319.21i −1.32987 0.550852i −0.399254 0.916840i \(-0.630731\pi\)
−0.930619 + 0.365988i \(0.880731\pi\)
\(180\) 0 0
\(181\) −820.433 1980.70i −0.336919 0.813394i −0.998008 0.0630866i \(-0.979906\pi\)
0.661089 0.750307i \(-0.270094\pi\)
\(182\) 0 0
\(183\) −2784.67 2784.67i −1.12486 1.12486i
\(184\) 0 0
\(185\) 2114.52 2114.52i 0.840339 0.840339i
\(186\) 0 0
\(187\) −497.368 + 206.016i −0.194498 + 0.0805637i
\(188\) 0 0
\(189\) 431.161 1040.92i 0.165938 0.400611i
\(190\) 0 0
\(191\) 330.108 0.125056 0.0625282 0.998043i \(-0.480084\pi\)
0.0625282 + 0.998043i \(0.480084\pi\)
\(192\) 0 0
\(193\) −914.905 −0.341224 −0.170612 0.985338i \(-0.554575\pi\)
−0.170612 + 0.985338i \(0.554575\pi\)
\(194\) 0 0
\(195\) −686.976 + 1658.51i −0.252284 + 0.609068i
\(196\) 0 0
\(197\) −41.3093 + 17.1109i −0.0149399 + 0.00618832i −0.390141 0.920755i \(-0.627574\pi\)
0.375201 + 0.926943i \(0.377574\pi\)
\(198\) 0 0
\(199\) −2946.98 + 2946.98i −1.04978 + 1.04978i −0.0510831 + 0.998694i \(0.516267\pi\)
−0.998694 + 0.0510831i \(0.983733\pi\)
\(200\) 0 0
\(201\) −2046.16 2046.16i −0.718033 0.718033i
\(202\) 0 0
\(203\) −181.931 439.221i −0.0629018 0.151858i
\(204\) 0 0
\(205\) 2176.69 + 901.616i 0.741594 + 0.307178i
\(206\) 0 0
\(207\) 1749.07i 0.587288i
\(208\) 0 0
\(209\) 1724.99i 0.570910i
\(210\) 0 0
\(211\) −1661.58 688.250i −0.542124 0.224555i 0.0947802 0.995498i \(-0.469785\pi\)
−0.636904 + 0.770943i \(0.719785\pi\)
\(212\) 0 0
\(213\) 2167.10 + 5231.85i 0.697124 + 1.68301i
\(214\) 0 0
\(215\) 666.731 + 666.731i 0.211492 + 0.211492i
\(216\) 0 0
\(217\) −3596.12 + 3596.12i −1.12498 + 1.12498i
\(218\) 0 0
\(219\) 7181.22 2974.56i 2.21581 0.917818i
\(220\) 0 0
\(221\) −170.561 + 411.770i −0.0519147 + 0.125333i
\(222\) 0 0
\(223\) 2657.54 0.798035 0.399018 0.916943i \(-0.369351\pi\)
0.399018 + 0.916943i \(0.369351\pi\)
\(224\) 0 0
\(225\) −2812.96 −0.833470
\(226\) 0 0
\(227\) −833.769 + 2012.90i −0.243785 + 0.588549i −0.997653 0.0684772i \(-0.978186\pi\)
0.753868 + 0.657026i \(0.228186\pi\)
\(228\) 0 0
\(229\) −5607.23 + 2322.59i −1.61806 + 0.670224i −0.993820 0.111006i \(-0.964593\pi\)
−0.624244 + 0.781230i \(0.714593\pi\)
\(230\) 0 0
\(231\) −3417.99 + 3417.99i −0.973538 + 0.973538i
\(232\) 0 0
\(233\) 132.710 + 132.710i 0.0373138 + 0.0373138i 0.725518 0.688204i \(-0.241600\pi\)
−0.688204 + 0.725518i \(0.741600\pi\)
\(234\) 0 0
\(235\) 1218.14 + 2940.86i 0.338140 + 0.816343i
\(236\) 0 0
\(237\) 6775.83 + 2806.64i 1.85712 + 0.769245i
\(238\) 0 0
\(239\) 138.825i 0.0375727i 0.999824 + 0.0187863i \(0.00598023\pi\)
−0.999824 + 0.0187863i \(0.994020\pi\)
\(240\) 0 0
\(241\) 4825.11i 1.28968i −0.764318 0.644839i \(-0.776924\pi\)
0.764318 0.644839i \(-0.223076\pi\)
\(242\) 0 0
\(243\) 5007.97 + 2074.37i 1.32206 + 0.547616i
\(244\) 0 0
\(245\) −4043.20 9761.15i −1.05433 2.54537i
\(246\) 0 0
\(247\) 1009.83 + 1009.83i 0.260138 + 0.260138i
\(248\) 0 0
\(249\) 7270.88 7270.88i 1.85049 1.85049i
\(250\) 0 0
\(251\) 3296.58 1365.49i 0.828996 0.343381i 0.0724909 0.997369i \(-0.476905\pi\)
0.756505 + 0.653988i \(0.226905\pi\)
\(252\) 0 0
\(253\) 411.311 992.992i 0.102209 0.246754i
\(254\) 0 0
\(255\) −3112.71 −0.764414
\(256\) 0 0
\(257\) 6601.51 1.60230 0.801149 0.598465i \(-0.204222\pi\)
0.801149 + 0.598465i \(0.204222\pi\)
\(258\) 0 0
\(259\) 2551.10 6158.90i 0.612038 1.47759i
\(260\) 0 0
\(261\) −424.180 + 175.701i −0.100598 + 0.0416691i
\(262\) 0 0
\(263\) −4812.19 + 4812.19i −1.12826 + 1.12826i −0.137799 + 0.990460i \(0.544003\pi\)
−0.990460 + 0.137799i \(0.955997\pi\)
\(264\) 0 0
\(265\) −967.760 967.760i −0.224336 0.224336i
\(266\) 0 0
\(267\) −3345.06 8075.69i −0.766720 1.85103i
\(268\) 0 0
\(269\) 952.102 + 394.374i 0.215802 + 0.0893880i 0.487965 0.872863i \(-0.337739\pi\)
−0.272164 + 0.962251i \(0.587739\pi\)
\(270\) 0 0
\(271\) 134.675i 0.0301880i −0.999886 0.0150940i \(-0.995195\pi\)
0.999886 0.0150940i \(-0.00480475\pi\)
\(272\) 0 0
\(273\) 4001.87i 0.887195i
\(274\) 0 0
\(275\) 1596.99 + 661.496i 0.350190 + 0.145053i
\(276\) 0 0
\(277\) 196.577 + 474.579i 0.0426396 + 0.102941i 0.943764 0.330619i \(-0.107257\pi\)
−0.901125 + 0.433560i \(0.857257\pi\)
\(278\) 0 0
\(279\) 3472.97 + 3472.97i 0.745238 + 0.745238i
\(280\) 0 0
\(281\) −5752.69 + 5752.69i −1.22127 + 1.22127i −0.254087 + 0.967181i \(0.581775\pi\)
−0.967181 + 0.254087i \(0.918225\pi\)
\(282\) 0 0
\(283\) 30.6153 12.6813i 0.00643071 0.00266369i −0.379466 0.925206i \(-0.623892\pi\)
0.385896 + 0.922542i \(0.373892\pi\)
\(284\) 0 0
\(285\) −3816.84 + 9214.66i −0.793298 + 1.91519i
\(286\) 0 0
\(287\) 5252.22 1.08024
\(288\) 0 0
\(289\) 4140.18 0.842700
\(290\) 0 0
\(291\) −4096.16 + 9889.01i −0.825159 + 1.99211i
\(292\) 0 0
\(293\) 6083.38 2519.82i 1.21295 0.502421i 0.317790 0.948161i \(-0.397059\pi\)
0.895163 + 0.445740i \(0.147059\pi\)
\(294\) 0 0
\(295\) 1306.13 1306.13i 0.257783 0.257783i
\(296\) 0 0
\(297\) 472.799 + 472.799i 0.0923722 + 0.0923722i
\(298\) 0 0
\(299\) −340.523 822.096i −0.0658628 0.159007i
\(300\) 0 0
\(301\) 1941.97 + 804.390i 0.371871 + 0.154034i
\(302\) 0 0
\(303\) 8479.30i 1.60767i
\(304\) 0 0
\(305\) 7535.84i 1.41476i
\(306\) 0 0
\(307\) 5493.47 + 2275.47i 1.02127 + 0.423022i 0.829553 0.558428i \(-0.188595\pi\)
0.191714 + 0.981451i \(0.438595\pi\)
\(308\) 0 0
\(309\) 2003.11 + 4835.94i 0.368780 + 0.890314i
\(310\) 0 0
\(311\) 640.062 + 640.062i 0.116703 + 0.116703i 0.763047 0.646344i \(-0.223703\pi\)
−0.646344 + 0.763047i \(0.723703\pi\)
\(312\) 0 0
\(313\) 571.963 571.963i 0.103288 0.103288i −0.653574 0.756862i \(-0.726731\pi\)
0.756862 + 0.653574i \(0.226731\pi\)
\(314\) 0 0
\(315\) −13906.6 + 5760.29i −2.48745 + 1.03034i
\(316\) 0 0
\(317\) 1686.24 4070.95i 0.298766 0.721284i −0.701200 0.712965i \(-0.747352\pi\)
0.999965 0.00831921i \(-0.00264812\pi\)
\(318\) 0 0
\(319\) 282.136 0.0495191
\(320\) 0 0
\(321\) −13640.8 −2.37183
\(322\) 0 0
\(323\) −947.634 + 2287.79i −0.163244 + 0.394106i
\(324\) 0 0
\(325\) 1322.15 547.651i 0.225660 0.0934715i
\(326\) 0 0
\(327\) 10619.4 10619.4i 1.79589 1.79589i
\(328\) 0 0
\(329\) 5017.70 + 5017.70i 0.840836 + 0.840836i
\(330\) 0 0
\(331\) 2604.99 + 6288.99i 0.432577 + 1.04433i 0.978453 + 0.206467i \(0.0661968\pi\)
−0.545877 + 0.837866i \(0.683803\pi\)
\(332\) 0 0
\(333\) −5948.00 2463.74i −0.978823 0.405442i
\(334\) 0 0
\(335\) 5537.28i 0.903086i
\(336\) 0 0
\(337\) 5051.39i 0.816518i −0.912866 0.408259i \(-0.866136\pi\)
0.912866 0.408259i \(-0.133864\pi\)
\(338\) 0 0
\(339\) −9839.85 4075.80i −1.57648 0.653000i
\(340\) 0 0
\(341\) −1154.99 2788.40i −0.183421 0.442817i
\(342\) 0 0
\(343\) −8740.21 8740.21i −1.37588 1.37588i
\(344\) 0 0
\(345\) 4394.32 4394.32i 0.685746 0.685746i
\(346\) 0 0
\(347\) −1548.08 + 641.238i −0.239497 + 0.0992030i −0.499204 0.866485i \(-0.666374\pi\)
0.259707 + 0.965688i \(0.416374\pi\)
\(348\) 0 0
\(349\) 3012.90 7273.78i 0.462111 1.11563i −0.505418 0.862875i \(-0.668662\pi\)
0.967529 0.252760i \(-0.0813383\pi\)
\(350\) 0 0
\(351\) 553.564 0.0841797
\(352\) 0 0
\(353\) −3877.72 −0.584675 −0.292337 0.956315i \(-0.594433\pi\)
−0.292337 + 0.956315i \(0.594433\pi\)
\(354\) 0 0
\(355\) 4146.89 10011.5i 0.619983 1.49677i
\(356\) 0 0
\(357\) −6410.84 + 2655.46i −0.950414 + 0.393674i
\(358\) 0 0
\(359\) 80.3532 80.3532i 0.0118130 0.0118130i −0.701176 0.712989i \(-0.747341\pi\)
0.712989 + 0.701176i \(0.247341\pi\)
\(360\) 0 0
\(361\) 760.577 + 760.577i 0.110887 + 0.110887i
\(362\) 0 0
\(363\) 2798.47 + 6756.09i 0.404632 + 0.976867i
\(364\) 0 0
\(365\) −13741.7 5692.01i −1.97062 0.816256i
\(366\) 0 0
\(367\) 2569.61i 0.365484i −0.983161 0.182742i \(-0.941503\pi\)
0.983161 0.182742i \(-0.0584973\pi\)
\(368\) 0 0
\(369\) 5072.36i 0.715601i
\(370\) 0 0
\(371\) −2818.77 1167.57i −0.394456 0.163389i
\(372\) 0 0
\(373\) 3461.88 + 8357.71i 0.480561 + 1.16018i 0.959343 + 0.282243i \(0.0910785\pi\)
−0.478782 + 0.877934i \(0.658922\pi\)
\(374\) 0 0
\(375\) −2829.60 2829.60i −0.389652 0.389652i
\(376\) 0 0
\(377\) 165.166 165.166i 0.0225636 0.0225636i
\(378\) 0 0
\(379\) −200.232 + 82.9388i −0.0271378 + 0.0112408i −0.396211 0.918159i \(-0.629675\pi\)
0.369073 + 0.929400i \(0.379675\pi\)
\(380\) 0 0
\(381\) 2663.40 6430.01i 0.358136 0.864618i
\(382\) 0 0
\(383\) 4511.40 0.601885 0.300942 0.953642i \(-0.402699\pi\)
0.300942 + 0.953642i \(0.402699\pi\)
\(384\) 0 0
\(385\) 9249.73 1.22444
\(386\) 0 0
\(387\) 776.844 1875.47i 0.102039 0.246345i
\(388\) 0 0
\(389\) 4993.23 2068.26i 0.650814 0.269576i −0.0327533 0.999463i \(-0.510428\pi\)
0.683567 + 0.729887i \(0.260428\pi\)
\(390\) 0 0
\(391\) 1091.01 1091.01i 0.141112 0.141112i
\(392\) 0 0
\(393\) −5306.93 5306.93i −0.681169 0.681169i
\(394\) 0 0
\(395\) −5370.69 12966.0i −0.684123 1.65162i
\(396\) 0 0
\(397\) −7615.39 3154.40i −0.962734 0.398778i −0.154732 0.987957i \(-0.549451\pi\)
−0.808003 + 0.589179i \(0.799451\pi\)
\(398\) 0 0
\(399\) 22234.4i 2.78975i
\(400\) 0 0
\(401\) 5161.80i 0.642813i 0.946941 + 0.321407i \(0.104156\pi\)
−0.946941 + 0.321407i \(0.895844\pi\)
\(402\) 0 0
\(403\) −2308.51 956.218i −0.285348 0.118195i
\(404\) 0 0
\(405\) −3286.76 7934.94i −0.403260 0.973557i
\(406\) 0 0
\(407\) 2797.46 + 2797.46i 0.340700 + 0.340700i
\(408\) 0 0
\(409\) 554.377 554.377i 0.0670225 0.0670225i −0.672801 0.739823i \(-0.734909\pi\)
0.739823 + 0.672801i \(0.234909\pi\)
\(410\) 0 0
\(411\) 8209.79 3400.61i 0.985302 0.408125i
\(412\) 0 0
\(413\) 1575.81 3804.33i 0.187749 0.453266i
\(414\) 0 0
\(415\) −19676.4 −2.32741
\(416\) 0 0
\(417\) 13460.6 1.58074
\(418\) 0 0
\(419\) −1812.51 + 4375.80i −0.211330 + 0.510195i −0.993628 0.112709i \(-0.964047\pi\)
0.782298 + 0.622904i \(0.214047\pi\)
\(420\) 0 0
\(421\) −4077.46 + 1688.94i −0.472026 + 0.195520i −0.605999 0.795465i \(-0.707226\pi\)
0.133973 + 0.990985i \(0.457226\pi\)
\(422\) 0 0
\(423\) 4845.88 4845.88i 0.557008 0.557008i
\(424\) 0 0
\(425\) 1754.63 + 1754.63i 0.200264 + 0.200264i
\(426\) 0 0
\(427\) 6428.84 + 15520.6i 0.728602 + 1.75900i
\(428\) 0 0
\(429\) −2194.17 908.853i −0.246936 0.102284i
\(430\) 0 0
\(431\) 17343.8i 1.93833i −0.246418 0.969164i \(-0.579254\pi\)
0.246418 0.969164i \(-0.420746\pi\)
\(432\) 0 0
\(433\) 10223.8i 1.13469i 0.823479 + 0.567347i \(0.192030\pi\)
−0.823479 + 0.567347i \(0.807970\pi\)
\(434\) 0 0
\(435\) 1507.13 + 624.274i 0.166118 + 0.0688084i
\(436\) 0 0
\(437\) −1891.95 4567.56i −0.207103 0.499991i
\(438\) 0 0
\(439\) 12436.5 + 12436.5i 1.35208 + 1.35208i 0.883335 + 0.468742i \(0.155293\pi\)
0.468742 + 0.883335i \(0.344707\pi\)
\(440\) 0 0
\(441\) −16084.2 + 16084.2i −1.73676 + 1.73676i
\(442\) 0 0
\(443\) −9677.23 + 4008.44i −1.03788 + 0.429902i −0.835549 0.549416i \(-0.814850\pi\)
−0.202327 + 0.979318i \(0.564850\pi\)
\(444\) 0 0
\(445\) −6400.98 + 15453.3i −0.681878 + 1.64620i
\(446\) 0 0
\(447\) −4939.36 −0.522648
\(448\) 0 0
\(449\) −2416.16 −0.253954 −0.126977 0.991906i \(-0.540527\pi\)
−0.126977 + 0.991906i \(0.540527\pi\)
\(450\) 0 0
\(451\) −1192.82 + 2879.71i −0.124540 + 0.300666i
\(452\) 0 0
\(453\) 3734.96 1547.07i 0.387381 0.160458i
\(454\) 0 0
\(455\) 5414.91 5414.91i 0.557922 0.557922i
\(456\) 0 0
\(457\) 6285.99 + 6285.99i 0.643427 + 0.643427i 0.951396 0.307969i \(-0.0996493\pi\)
−0.307969 + 0.951396i \(0.599649\pi\)
\(458\) 0 0
\(459\) 367.320 + 886.789i 0.0373530 + 0.0901782i
\(460\) 0 0
\(461\) 8841.89 + 3662.43i 0.893292 + 0.370014i 0.781637 0.623733i \(-0.214385\pi\)
0.111655 + 0.993747i \(0.464385\pi\)
\(462\) 0 0
\(463\) 7744.43i 0.777353i 0.921374 + 0.388676i \(0.127068\pi\)
−0.921374 + 0.388676i \(0.872932\pi\)
\(464\) 0 0
\(465\) 17450.9i 1.74035i
\(466\) 0 0
\(467\) −7032.30 2912.87i −0.696822 0.288633i 0.00601716 0.999982i \(-0.498085\pi\)
−0.702839 + 0.711349i \(0.748085\pi\)
\(468\) 0 0
\(469\) 4723.86 + 11404.4i 0.465091 + 1.12283i
\(470\) 0 0
\(471\) −2638.73 2638.73i −0.258145 0.258145i
\(472\) 0 0
\(473\) −882.070 + 882.070i −0.0857455 + 0.0857455i
\(474\) 0 0
\(475\) 7345.84 3042.75i 0.709580 0.293918i
\(476\) 0 0
\(477\) −1127.59 + 2722.24i −0.108236 + 0.261306i
\(478\) 0 0
\(479\) 19364.6 1.84716 0.923580 0.383405i \(-0.125249\pi\)
0.923580 + 0.383405i \(0.125249\pi\)
\(480\) 0 0
\(481\) 3275.34 0.310484
\(482\) 0 0
\(483\) 5301.61 12799.2i 0.499444 1.20577i
\(484\) 0 0
\(485\) 18923.3 7838.27i 1.77167 0.733850i
\(486\) 0 0
\(487\) −2799.10 + 2799.10i −0.260450 + 0.260450i −0.825237 0.564787i \(-0.808958\pi\)
0.564787 + 0.825237i \(0.308958\pi\)
\(488\) 0 0
\(489\) 7010.08 + 7010.08i 0.648276 + 0.648276i
\(490\) 0 0
\(491\) 935.299 + 2258.01i 0.0859663 + 0.207541i 0.961016 0.276491i \(-0.0891717\pi\)
−0.875050 + 0.484032i \(0.839172\pi\)
\(492\) 0 0
\(493\) 374.186 + 154.993i 0.0341836 + 0.0141593i
\(494\) 0 0
\(495\) 8932.98i 0.811126i
\(496\) 0 0
\(497\) 24157.1i 2.18027i
\(498\) 0 0
\(499\) 552.418 + 228.819i 0.0495583 + 0.0205277i 0.407325 0.913283i \(-0.366462\pi\)
−0.357767 + 0.933811i \(0.616462\pi\)
\(500\) 0 0
\(501\) 2668.89 + 6443.27i 0.237998 + 0.574579i
\(502\) 0 0
\(503\) 254.724 + 254.724i 0.0225797 + 0.0225797i 0.718307 0.695727i \(-0.244918\pi\)
−0.695727 + 0.718307i \(0.744918\pi\)
\(504\) 0 0
\(505\) −11473.3 + 11473.3i −1.01100 + 1.01100i
\(506\) 0 0
\(507\) 13710.0 5678.86i 1.20095 0.497450i
\(508\) 0 0
\(509\) −5370.63 + 12965.8i −0.467680 + 1.12908i 0.497494 + 0.867468i \(0.334254\pi\)
−0.965173 + 0.261611i \(0.915746\pi\)
\(510\) 0 0
\(511\) −33157.9 −2.87049
\(512\) 0 0
\(513\) 3075.60 0.264700
\(514\) 0 0
\(515\) 3833.08 9253.88i 0.327972 0.791796i
\(516\) 0 0
\(517\) −3890.69 + 1611.58i −0.330972 + 0.137093i
\(518\) 0 0
\(519\) −13951.6 + 13951.6i −1.17998 + 1.17998i
\(520\) 0 0
\(521\) 2418.86 + 2418.86i 0.203402 + 0.203402i 0.801456 0.598054i \(-0.204059\pi\)
−0.598054 + 0.801456i \(0.704059\pi\)
\(522\) 0 0
\(523\) 3061.70 + 7391.60i 0.255982 + 0.617996i 0.998665 0.0516471i \(-0.0164471\pi\)
−0.742683 + 0.669643i \(0.766447\pi\)
\(524\) 0 0
\(525\) 20584.5 + 8526.38i 1.71120 + 0.708804i
\(526\) 0 0
\(527\) 4332.65i 0.358128i
\(528\) 0 0
\(529\) 9086.56i 0.746820i
\(530\) 0 0
\(531\) −3674.06 1521.84i −0.300264 0.124374i
\(532\) 0 0
\(533\) 987.531 + 2384.11i 0.0802528 + 0.193747i
\(534\) 0 0
\(535\) 18457.3 + 18457.3i 1.49155 + 1.49155i
\(536\) 0 0
\(537\) 18646.1 18646.1i 1.49840 1.49840i
\(538\) 0 0
\(539\) 12913.8 5349.06i 1.03198 0.427459i
\(540\) 0 0
\(541\) 4520.94 10914.5i 0.359280 0.867379i −0.636121 0.771589i \(-0.719462\pi\)
0.995402 0.0957899i \(-0.0305377\pi\)
\(542\) 0 0
\(543\) 16399.6 1.29608
\(544\) 0 0
\(545\) −28738.1 −2.25873
\(546\) 0 0
\(547\) −4726.46 + 11410.7i −0.369450 + 0.891930i 0.624391 + 0.781112i \(0.285347\pi\)
−0.993841 + 0.110818i \(0.964653\pi\)
\(548\) 0 0
\(549\) 14989.1 6208.68i 1.16524 0.482660i
\(550\) 0 0
\(551\) 917.662 917.662i 0.0709505 0.0709505i
\(552\) 0 0
\(553\) −22122.6 22122.6i −1.70117 1.70117i
\(554\) 0 0
\(555\) 8753.78 + 21133.5i 0.669509 + 1.61634i
\(556\) 0 0
\(557\) −2303.67 954.213i −0.175242 0.0725876i 0.293337 0.956009i \(-0.405234\pi\)
−0.468579 + 0.883421i \(0.655234\pi\)
\(558\) 0 0
\(559\) 1032.75i 0.0781407i
\(560\) 0 0
\(561\) 4118.04i 0.309918i
\(562\) 0 0
\(563\) 2533.84 + 1049.55i 0.189677 + 0.0785670i 0.475501 0.879715i \(-0.342267\pi\)
−0.285823 + 0.958282i \(0.592267\pi\)
\(564\) 0 0
\(565\) 7799.30 + 18829.2i 0.580742 + 1.40204i
\(566\) 0 0
\(567\) −13538.6 13538.6i −1.00277 1.00277i
\(568\) 0 0
\(569\) −10461.9 + 10461.9i −0.770801 + 0.770801i −0.978247 0.207445i \(-0.933485\pi\)
0.207445 + 0.978247i \(0.433485\pi\)
\(570\) 0 0
\(571\) −21510.2 + 8909.80i −1.57648 + 0.653001i −0.987852 0.155400i \(-0.950333\pi\)
−0.588632 + 0.808401i \(0.700333\pi\)
\(572\) 0 0
\(573\) −966.329 + 2332.92i −0.0704519 + 0.170086i
\(574\) 0 0
\(575\) −4954.16 −0.359309
\(576\) 0 0
\(577\) 8321.88 0.600424 0.300212 0.953873i \(-0.402943\pi\)
0.300212 + 0.953873i \(0.402943\pi\)
\(578\) 0 0
\(579\) 2678.21 6465.77i 0.192232 0.464090i
\(580\) 0 0
\(581\) −40524.8 + 16785.9i −2.89372 + 1.19862i
\(582\) 0 0
\(583\) 1280.32 1280.32i 0.0909530 0.0909530i
\(584\) 0 0
\(585\) −5229.48 5229.48i −0.369594 0.369594i
\(586\) 0 0
\(587\) −7994.94 19301.5i −0.562158 1.35717i −0.908037 0.418890i \(-0.862419\pi\)
0.345880 0.938279i \(-0.387581\pi\)
\(588\) 0 0
\(589\) −12826.1 5312.74i −0.897266 0.371660i
\(590\) 0 0
\(591\) 342.028i 0.0238057i
\(592\) 0 0
\(593\) 17757.1i 1.22968i 0.788654 + 0.614838i \(0.210778\pi\)
−0.788654 + 0.614838i \(0.789222\pi\)
\(594\) 0 0
\(595\) 12267.6 + 5081.39i 0.845245 + 0.350112i
\(596\) 0 0
\(597\) −12200.0 29453.5i −0.836371 2.01918i
\(598\) 0 0
\(599\) −17544.2 17544.2i −1.19672 1.19672i −0.975143 0.221578i \(-0.928879\pi\)
−0.221578 0.975143i \(-0.571121\pi\)
\(600\) 0 0
\(601\) 16.0607 16.0607i 0.00109006 0.00109006i −0.706562 0.707652i \(-0.749755\pi\)
0.707652 + 0.706562i \(0.249755\pi\)
\(602\) 0 0
\(603\) 11013.9 4562.10i 0.743814 0.308098i
\(604\) 0 0
\(605\) 5355.04 12928.2i 0.359857 0.868771i
\(606\) 0 0
\(607\) 15461.8 1.03390 0.516950 0.856016i \(-0.327067\pi\)
0.516950 + 0.856016i \(0.327067\pi\)
\(608\) 0 0
\(609\) 3636.61 0.241975
\(610\) 0 0
\(611\) −1334.22 + 3221.10i −0.0883418 + 0.213276i
\(612\) 0 0
\(613\) 13837.1 5731.53i 0.911708 0.377642i 0.122998 0.992407i \(-0.460749\pi\)
0.788710 + 0.614765i \(0.210749\pi\)
\(614\) 0 0
\(615\) −12743.7 + 12743.7i −0.835571 + 0.835571i
\(616\) 0 0
\(617\) 6349.72 + 6349.72i 0.414312 + 0.414312i 0.883238 0.468926i \(-0.155359\pi\)
−0.468926 + 0.883238i \(0.655359\pi\)
\(618\) 0 0
\(619\) −7640.34 18445.4i −0.496109 1.19771i −0.951563 0.307453i \(-0.900523\pi\)
0.455455 0.890259i \(-0.349477\pi\)
\(620\) 0 0
\(621\) −1770.47 733.353i −0.114407 0.0473888i
\(622\) 0 0
\(623\) 37287.9i 2.39793i
\(624\) 0 0
\(625\) 18815.1i 1.20417i
\(626\) 0 0
\(627\) −12190.8 5049.59i −0.776480 0.321628i
\(628\) 0 0
\(629\) 2173.37 + 5246.97i 0.137771 + 0.332608i
\(630\) 0 0
\(631\) 3471.86 + 3471.86i 0.219037 + 0.219037i 0.808093 0.589055i \(-0.200500\pi\)
−0.589055 + 0.808093i \(0.700500\pi\)
\(632\) 0 0
\(633\) 9727.94 9727.94i 0.610823 0.610823i
\(634\) 0 0
\(635\) −12304.2 + 5096.58i −0.768943 + 0.318506i
\(636\) 0 0
\(637\) 4428.48 10691.3i 0.275452 0.664999i
\(638\) 0 0
\(639\) −23329.8 −1.44431
\(640\) 0 0
\(641\) 7666.55 0.472403 0.236202 0.971704i \(-0.424097\pi\)
0.236202 + 0.971704i \(0.424097\pi\)
\(642\) 0 0
\(643\) 3146.10 7595.36i 0.192955 0.465835i −0.797560 0.603240i \(-0.793876\pi\)
0.990515 + 0.137405i \(0.0438761\pi\)
\(644\) 0 0
\(645\) −6663.62 + 2760.16i −0.406790 + 0.168498i
\(646\) 0 0
\(647\) 10868.8 10868.8i 0.660428 0.660428i −0.295053 0.955481i \(-0.595337\pi\)
0.955481 + 0.295053i \(0.0953372\pi\)
\(648\) 0 0
\(649\) 1727.98 + 1727.98i 0.104513 + 0.104513i
\(650\) 0 0
\(651\) −14887.4 35941.3i −0.896285 2.16382i
\(652\) 0 0
\(653\) −2635.05 1091.47i −0.157914 0.0654099i 0.302327 0.953204i \(-0.402237\pi\)
−0.460240 + 0.887794i \(0.652237\pi\)
\(654\) 0 0
\(655\) 14361.6i 0.856721i
\(656\) 0 0
\(657\) 32022.4i 1.90154i
\(658\) 0 0
\(659\) 19323.7 + 8004.13i 1.14225 + 0.473136i 0.871928 0.489633i \(-0.162869\pi\)
0.270323 + 0.962770i \(0.412869\pi\)
\(660\) 0 0
\(661\) 67.1965 + 162.227i 0.00395407 + 0.00954598i 0.925844 0.377905i \(-0.123356\pi\)
−0.921890 + 0.387451i \(0.873356\pi\)
\(662\) 0 0
\(663\) −2410.76 2410.76i −0.141216 0.141216i
\(664\) 0 0
\(665\) 30085.2 30085.2i 1.75437 1.75437i
\(666\) 0 0
\(667\) −747.061 + 309.443i −0.0433678 + 0.0179635i
\(668\) 0 0
\(669\) −7779.43 + 18781.2i −0.449582 + 1.08539i
\(670\) 0 0
\(671\) −9969.74 −0.573588
\(672\) 0 0
\(673\) 3444.70 0.197301 0.0986503 0.995122i \(-0.468547\pi\)
0.0986503 + 0.995122i \(0.468547\pi\)
\(674\) 0 0
\(675\) 1179.42 2847.38i 0.0672534 0.162364i
\(676\) 0 0
\(677\) −4665.73 + 1932.61i −0.264872 + 0.109714i −0.511167 0.859481i \(-0.670787\pi\)
0.246295 + 0.969195i \(0.420787\pi\)
\(678\) 0 0
\(679\) 32286.9 32286.9i 1.82483 1.82483i
\(680\) 0 0
\(681\) −11784.7 11784.7i −0.663131 0.663131i
\(682\) 0 0
\(683\) −537.141 1296.77i −0.0300924 0.0726496i 0.908119 0.418712i \(-0.137518\pi\)
−0.938211 + 0.346063i \(0.887518\pi\)
\(684\) 0 0
\(685\) −15710.0 6507.27i −0.876272 0.362964i
\(686\) 0 0
\(687\) 46426.1i 2.57826i
\(688\) 0 0
\(689\) 1499.04i 0.0828864i
\(690\) 0 0
\(691\) −10591.5 4387.14i −0.583097 0.241526i 0.0715810 0.997435i \(-0.477196\pi\)
−0.654678 + 0.755908i \(0.727196\pi\)
\(692\) 0 0
\(693\) −7620.73 18398.1i −0.417731 1.00849i
\(694\) 0 0
\(695\) −18213.4 18213.4i −0.994063 0.994063i
\(696\) 0 0
\(697\) −3163.97 + 3163.97i −0.171943 + 0.171943i
\(698\) 0 0
\(699\) −1326.36 + 549.398i −0.0717706 + 0.0297284i
\(700\) 0 0
\(701\) 2339.32 5647.61i 0.126041 0.304290i −0.848245 0.529604i \(-0.822341\pi\)
0.974286 + 0.225314i \(0.0723406\pi\)
\(702\) 0 0
\(703\) 18197.8 0.976304
\(704\) 0 0
\(705\) −24349.4 −1.30078
\(706\) 0 0
\(707\) −13842.2 + 33417.9i −0.736334 + 1.77767i
\(708\) 0 0
\(709\) 13955.2 5780.42i 0.739207 0.306189i 0.0188776 0.999822i \(-0.493991\pi\)
0.720329 + 0.693632i \(0.243991\pi\)
\(710\) 0 0
\(711\) −21365.0 + 21365.0i −1.12694 + 1.12694i
\(712\) 0 0
\(713\) 6116.56 + 6116.56i 0.321272 + 0.321272i
\(714\) 0 0
\(715\) 1739.15 + 4198.68i 0.0909657 + 0.219611i
\(716\) 0 0
\(717\) −981.100 406.385i −0.0511016 0.0211670i
\(718\) 0 0
\(719\) 153.579i 0.00796595i −0.999992 0.00398298i \(-0.998732\pi\)
0.999992 0.00398298i \(-0.00126782\pi\)
\(720\) 0 0
\(721\) 22329.0i 1.15336i
\(722\) 0 0
\(723\) 34099.7 + 14124.6i 1.75406 + 0.726554i
\(724\) 0 0
\(725\) −497.666 1201.47i −0.0254936 0.0615469i
\(726\) 0 0
\(727\) 5550.98 + 5550.98i 0.283184 + 0.283184i 0.834377 0.551194i \(-0.185827\pi\)
−0.551194 + 0.834377i \(0.685827\pi\)
\(728\) 0 0
\(729\) −18117.5 + 18117.5i −0.920464 + 0.920464i
\(730\) 0 0
\(731\) −1654.43 + 685.286i −0.0837088 + 0.0346733i
\(732\) 0 0
\(733\) −827.485 + 1997.73i −0.0416969 + 0.100665i −0.943356 0.331782i \(-0.892350\pi\)
0.901659 + 0.432448i \(0.142350\pi\)
\(734\) 0 0
\(735\) 80819.2 4.05587
\(736\) 0 0
\(737\) −7325.69 −0.366140
\(738\) 0 0
\(739\) 1375.10 3319.78i 0.0684489 0.165250i −0.885953 0.463775i \(-0.846495\pi\)
0.954402 + 0.298525i \(0.0964946\pi\)
\(740\) 0 0
\(741\) −10092.7 + 4180.54i −0.500358 + 0.207255i
\(742\) 0 0
\(743\) −22288.2 + 22288.2i −1.10051 + 1.10051i −0.106156 + 0.994349i \(0.533854\pi\)
−0.994349 + 0.106156i \(0.966146\pi\)
\(744\) 0 0
\(745\) 6683.41 + 6683.41i 0.328673 + 0.328673i
\(746\) 0 0
\(747\) 16211.1 + 39137.1i 0.794021 + 1.91694i
\(748\) 0 0
\(749\) 53760.1 + 22268.2i 2.62263 + 1.08633i
\(750\) 0 0
\(751\) 24467.3i 1.18885i −0.804151 0.594424i \(-0.797380\pi\)
0.804151 0.594424i \(-0.202620\pi\)
\(752\) 0 0
\(753\) 27294.6i 1.32094i
\(754\) 0 0
\(755\) −7147.08 2960.42i −0.344515 0.142703i
\(756\) 0 0
\(757\) 13698.7 + 33071.6i 0.657712 + 1.58786i 0.801328 + 0.598225i \(0.204127\pi\)
−0.143616 + 0.989633i \(0.545873\pi\)
\(758\) 0 0
\(759\) 5813.59 + 5813.59i 0.278024 + 0.278024i
\(760\) 0 0
\(761\) 23068.9 23068.9i 1.09888 1.09888i 0.104338 0.994542i \(-0.466728\pi\)
0.994542 0.104338i \(-0.0332725\pi\)
\(762\) 0 0
\(763\) −59188.2 + 24516.5i −2.80833 + 1.16325i
\(764\) 0 0
\(765\) 4907.38 11847.5i 0.231930 0.559929i
\(766\) 0 0
\(767\) 2023.17 0.0952441
\(768\) 0 0
\(769\) −22615.1 −1.06050 −0.530249 0.847842i \(-0.677902\pi\)
−0.530249 + 0.847842i \(0.677902\pi\)
\(770\) 0 0
\(771\) −19324.7 + 46653.8i −0.902672 + 2.17924i
\(772\) 0 0
\(773\) −5061.63 + 2096.60i −0.235516 + 0.0975541i −0.497320 0.867567i \(-0.665683\pi\)
0.261804 + 0.965121i \(0.415683\pi\)
\(774\) 0 0
\(775\) −9837.04 + 9837.04i −0.455944 + 0.455944i
\(776\) 0 0
\(777\) 36058.0 + 36058.0i 1.66483 + 1.66483i
\(778\) 0 0
\(779\) 5486.72 + 13246.1i 0.252352 + 0.609231i
\(780\) 0 0
\(781\) 13245.0 + 5486.24i 0.606840 + 0.251361i
\(782\) 0 0
\(783\) 503.039i 0.0229593i
\(784\) 0 0
\(785\) 7140.90i 0.324675i
\(786\) 0 0
\(787\) 4514.92