Properties

Label 324.3.o.a.5.7
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.7
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.40095 - 2.65280i) q^{3} +(1.05662 - 0.786622i) q^{5} +(-3.63828 + 2.39294i) q^{7} +(-5.07467 + 7.43288i) q^{9} +O(q^{10})\) \(q+(-1.40095 - 2.65280i) q^{3} +(1.05662 - 0.786622i) q^{5} +(-3.63828 + 2.39294i) q^{7} +(-5.07467 + 7.43288i) q^{9} +(0.102829 - 0.879762i) q^{11} +(-5.05132 - 16.8726i) q^{13} +(-3.56702 - 1.70097i) q^{15} +(-25.3507 - 4.47002i) q^{17} +(1.99904 + 11.3371i) q^{19} +(11.4450 + 6.29924i) q^{21} +(-22.2073 + 33.7646i) q^{23} +(-6.67242 + 22.2874i) q^{25} +(26.8273 + 3.04895i) q^{27} +(26.3326 - 24.8435i) q^{29} +(-2.94284 + 50.5267i) q^{31} +(-2.47789 + 0.959719i) q^{33} +(-1.96194 + 5.39037i) q^{35} +(-52.9367 + 19.2674i) q^{37} +(-37.6829 + 37.0378i) q^{39} +(10.9812 - 46.3332i) q^{41} +(-16.1115 - 37.3508i) q^{43} +(0.484891 + 11.8456i) q^{45} +(-11.3117 + 0.658832i) q^{47} +(-11.8969 + 27.5802i) q^{49} +(23.6571 + 73.5126i) q^{51} +(-19.9552 - 11.5211i) q^{53} +(-0.583389 - 1.01046i) q^{55} +(27.2745 - 21.1858i) q^{57} +(-1.62732 - 13.9226i) q^{59} +(-41.2423 - 20.7127i) q^{61} +(0.676659 - 39.1863i) q^{63} +(-18.6097 - 13.8544i) q^{65} +(-42.5466 + 45.0968i) q^{67} +(120.682 + 11.6089i) q^{69} +(80.7693 - 96.2571i) q^{71} +(59.5008 - 49.9271i) q^{73} +(68.4717 - 13.5230i) q^{75} +(1.73109 + 3.44689i) q^{77} +(-35.6596 + 8.45149i) q^{79} +(-29.4955 - 75.4388i) q^{81} +(-1.52870 - 6.45010i) q^{83} +(-30.3022 + 15.2184i) q^{85} +(-102.795 - 35.0504i) q^{87} +(-73.1252 - 87.1472i) q^{89} +(58.7531 + 49.2997i) q^{91} +(138.160 - 62.9787i) q^{93} +(11.0302 + 10.4065i) q^{95} +(-59.2463 + 79.5816i) q^{97} +(6.01734 + 5.22882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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
\(3\) −1.40095 2.65280i −0.466984 0.884266i
\(4\) 0 0
\(5\) 1.05662 0.786622i 0.211323 0.157324i −0.486293 0.873796i \(-0.661651\pi\)
0.697617 + 0.716471i \(0.254244\pi\)
\(6\) 0 0
\(7\) −3.63828 + 2.39294i −0.519755 + 0.341848i −0.782127 0.623119i \(-0.785865\pi\)
0.262373 + 0.964967i \(0.415495\pi\)
\(8\) 0 0
\(9\) −5.07467 + 7.43288i −0.563852 + 0.825876i
\(10\) 0 0
\(11\) 0.102829 0.879762i 0.00934813 0.0799784i −0.987759 0.155988i \(-0.950144\pi\)
0.997107 + 0.0760096i \(0.0242180\pi\)
\(12\) 0 0
\(13\) −5.05132 16.8726i −0.388563 1.29789i −0.898990 0.437970i \(-0.855698\pi\)
0.510427 0.859921i \(-0.329487\pi\)
\(14\) 0 0
\(15\) −3.56702 1.70097i −0.237801 0.113398i
\(16\) 0 0
\(17\) −25.3507 4.47002i −1.49122 0.262942i −0.632168 0.774831i \(-0.717835\pi\)
−0.859052 + 0.511889i \(0.828946\pi\)
\(18\) 0 0
\(19\) 1.99904 + 11.3371i 0.105212 + 0.596689i 0.991135 + 0.132857i \(0.0424150\pi\)
−0.885923 + 0.463833i \(0.846474\pi\)
\(20\) 0 0
\(21\) 11.4450 + 6.29924i 0.545002 + 0.299964i
\(22\) 0 0
\(23\) −22.2073 + 33.7646i −0.965535 + 1.46802i −0.0836858 + 0.996492i \(0.526669\pi\)
−0.881849 + 0.471532i \(0.843701\pi\)
\(24\) 0 0
\(25\) −6.67242 + 22.2874i −0.266897 + 0.891497i
\(26\) 0 0
\(27\) 26.8273 + 3.04895i 0.993604 + 0.112924i
\(28\) 0 0
\(29\) 26.3326 24.8435i 0.908019 0.856672i −0.0821393 0.996621i \(-0.526175\pi\)
0.990159 + 0.139949i \(0.0446938\pi\)
\(30\) 0 0
\(31\) −2.94284 + 50.5267i −0.0949305 + 1.62989i 0.529147 + 0.848530i \(0.322512\pi\)
−0.624077 + 0.781363i \(0.714525\pi\)
\(32\) 0 0
\(33\) −2.47789 + 0.959719i −0.0750876 + 0.0290824i
\(34\) 0 0
\(35\) −1.96194 + 5.39037i −0.0560553 + 0.154011i
\(36\) 0 0
\(37\) −52.9367 + 19.2674i −1.43072 + 0.520740i −0.937138 0.348958i \(-0.886536\pi\)
−0.493584 + 0.869698i \(0.664313\pi\)
\(38\) 0 0
\(39\) −37.6829 + 37.0378i −0.966228 + 0.949687i
\(40\) 0 0
\(41\) 10.9812 46.3332i 0.267833 1.13008i −0.658262 0.752789i \(-0.728708\pi\)
0.926096 0.377289i \(-0.123144\pi\)
\(42\) 0 0
\(43\) −16.1115 37.3508i −0.374687 0.868622i −0.996352 0.0853389i \(-0.972803\pi\)
0.621665 0.783283i \(-0.286457\pi\)
\(44\) 0 0
\(45\) 0.484891 + 11.8456i 0.0107754 + 0.263235i
\(46\) 0 0
\(47\) −11.3117 + 0.658832i −0.240674 + 0.0140177i −0.178058 0.984020i \(-0.556982\pi\)
−0.0626164 + 0.998038i \(0.519944\pi\)
\(48\) 0 0
\(49\) −11.8969 + 27.5802i −0.242795 + 0.562862i
\(50\) 0 0
\(51\) 23.6571 + 73.5126i 0.463865 + 1.44142i
\(52\) 0 0
\(53\) −19.9552 11.5211i −0.376513 0.217380i 0.299787 0.954006i \(-0.403084\pi\)
−0.676300 + 0.736626i \(0.736418\pi\)
\(54\) 0 0
\(55\) −0.583389 1.01046i −0.0106071 0.0183720i
\(56\) 0 0
\(57\) 27.2745 21.1858i 0.478500 0.371680i
\(58\) 0 0
\(59\) −1.62732 13.9226i −0.0275817 0.235976i −0.999996 0.00271729i \(-0.999135\pi\)
0.972415 0.233259i \(-0.0749390\pi\)
\(60\) 0 0
\(61\) −41.2423 20.7127i −0.676103 0.339552i 0.0773963 0.997000i \(-0.475339\pi\)
−0.753499 + 0.657449i \(0.771636\pi\)
\(62\) 0 0
\(63\) 0.676659 39.1863i 0.0107406 0.622005i
\(64\) 0 0
\(65\) −18.6097 13.8544i −0.286302 0.213144i
\(66\) 0 0
\(67\) −42.5466 + 45.0968i −0.635024 + 0.673086i −0.962346 0.271827i \(-0.912372\pi\)
0.327322 + 0.944913i \(0.393854\pi\)
\(68\) 0 0
\(69\) 120.682 + 11.6089i 1.74901 + 0.168246i
\(70\) 0 0
\(71\) 80.7693 96.2571i 1.13760 1.35573i 0.211978 0.977274i \(-0.432009\pi\)
0.925618 0.378460i \(-0.123546\pi\)
\(72\) 0 0
\(73\) 59.5008 49.9271i 0.815080 0.683933i −0.136735 0.990608i \(-0.543661\pi\)
0.951814 + 0.306675i \(0.0992164\pi\)
\(74\) 0 0
\(75\) 68.4717 13.5230i 0.912957 0.180307i
\(76\) 0 0
\(77\) 1.73109 + 3.44689i 0.0224817 + 0.0447648i
\(78\) 0 0
\(79\) −35.6596 + 8.45149i −0.451388 + 0.106981i −0.450021 0.893018i \(-0.648583\pi\)
−0.00136724 + 0.999999i \(0.500435\pi\)
\(80\) 0 0
\(81\) −29.4955 75.4388i −0.364142 0.931343i
\(82\) 0 0
\(83\) −1.52870 6.45010i −0.0184181 0.0777121i 0.963060 0.269288i \(-0.0867883\pi\)
−0.981478 + 0.191576i \(0.938640\pi\)
\(84\) 0 0
\(85\) −30.3022 + 15.2184i −0.356497 + 0.179039i
\(86\) 0 0
\(87\) −102.795 35.0504i −1.18156 0.402878i
\(88\) 0 0
\(89\) −73.1252 87.1472i −0.821631 0.979182i 0.178357 0.983966i \(-0.442922\pi\)
−0.999989 + 0.00478390i \(0.998477\pi\)
\(90\) 0 0
\(91\) 58.7531 + 49.2997i 0.645639 + 0.541755i
\(92\) 0 0
\(93\) 138.160 62.9787i 1.48559 0.677190i
\(94\) 0 0
\(95\) 11.0302 + 10.4065i 0.116108 + 0.109542i
\(96\) 0 0
\(97\) −59.2463 + 79.5816i −0.610786 + 0.820429i −0.994687 0.102946i \(-0.967173\pi\)
0.383900 + 0.923374i \(0.374581\pi\)
\(98\) 0 0
\(99\) 6.01734 + 5.22882i 0.0607813 + 0.0528164i
\(100\) 0 0
\(101\) 67.2080 133.822i 0.665426 1.32497i −0.267030 0.963688i \(-0.586042\pi\)
0.932456 0.361284i \(-0.117662\pi\)
\(102\) 0 0
\(103\) 85.7742 10.0256i 0.832759 0.0973356i 0.310980 0.950416i \(-0.399343\pi\)
0.521779 + 0.853081i \(0.325269\pi\)
\(104\) 0 0
\(105\) 17.0481 2.34704i 0.162363 0.0223527i
\(106\) 0 0
\(107\) −54.0083 + 31.1817i −0.504751 + 0.291418i −0.730673 0.682727i \(-0.760794\pi\)
0.225923 + 0.974145i \(0.427460\pi\)
\(108\) 0 0
\(109\) 33.2197 57.5383i 0.304768 0.527874i −0.672442 0.740150i \(-0.734754\pi\)
0.977210 + 0.212276i \(0.0680877\pi\)
\(110\) 0 0
\(111\) 125.274 + 113.438i 1.12860 + 1.02196i
\(112\) 0 0
\(113\) −93.8943 40.5021i −0.830923 0.358425i −0.0622450 0.998061i \(-0.519826\pi\)
−0.768678 + 0.639636i \(0.779085\pi\)
\(114\) 0 0
\(115\) 3.09534 + 53.1450i 0.0269160 + 0.462130i
\(116\) 0 0
\(117\) 151.046 + 48.0769i 1.29099 + 0.410913i
\(118\) 0 0
\(119\) 102.930 44.3995i 0.864955 0.373105i
\(120\) 0 0
\(121\) 116.975 + 27.7236i 0.966736 + 0.229121i
\(122\) 0 0
\(123\) −138.297 + 35.7798i −1.12436 + 0.290892i
\(124\) 0 0
\(125\) 21.7450 + 59.7438i 0.173960 + 0.477950i
\(126\) 0 0
\(127\) −201.479 73.3322i −1.58645 0.577419i −0.609853 0.792515i \(-0.708771\pi\)
−0.976593 + 0.215096i \(0.930994\pi\)
\(128\) 0 0
\(129\) −76.5125 + 95.0673i −0.593120 + 0.736956i
\(130\) 0 0
\(131\) 68.9240 + 4.01437i 0.526137 + 0.0306440i 0.319158 0.947701i \(-0.396600\pi\)
0.206979 + 0.978345i \(0.433637\pi\)
\(132\) 0 0
\(133\) −34.4020 36.4640i −0.258662 0.274166i
\(134\) 0 0
\(135\) 30.7446 17.8814i 0.227737 0.132455i
\(136\) 0 0
\(137\) 73.1173 + 21.8899i 0.533703 + 0.159780i 0.542303 0.840183i \(-0.317552\pi\)
−0.00860018 + 0.999963i \(0.502738\pi\)
\(138\) 0 0
\(139\) −83.1785 54.7074i −0.598407 0.393578i 0.213860 0.976864i \(-0.431396\pi\)
−0.812267 + 0.583286i \(0.801767\pi\)
\(140\) 0 0
\(141\) 17.5949 + 29.0847i 0.124786 + 0.206274i
\(142\) 0 0
\(143\) −15.3633 + 2.70896i −0.107436 + 0.0189438i
\(144\) 0 0
\(145\) 8.28099 46.9638i 0.0571103 0.323889i
\(146\) 0 0
\(147\) 89.8318 7.07838i 0.611101 0.0481522i
\(148\) 0 0
\(149\) 34.6895 10.3854i 0.232816 0.0697004i −0.168270 0.985741i \(-0.553818\pi\)
0.401086 + 0.916041i \(0.368633\pi\)
\(150\) 0 0
\(151\) −79.1363 9.24970i −0.524081 0.0612563i −0.150061 0.988677i \(-0.547947\pi\)
−0.374020 + 0.927420i \(0.622021\pi\)
\(152\) 0 0
\(153\) 161.872 165.745i 1.05798 1.08330i
\(154\) 0 0
\(155\) 36.6360 + 55.7023i 0.236361 + 0.359369i
\(156\) 0 0
\(157\) 130.675 + 175.528i 0.832328 + 1.11801i 0.991416 + 0.130746i \(0.0417373\pi\)
−0.159088 + 0.987264i \(0.550855\pi\)
\(158\) 0 0
\(159\) −2.60697 + 69.0776i −0.0163960 + 0.434450i
\(160\) 0 0
\(161\) 175.986i 1.09308i
\(162\) 0 0
\(163\) 22.9884 0.141033 0.0705166 0.997511i \(-0.477535\pi\)
0.0705166 + 0.997511i \(0.477535\pi\)
\(164\) 0 0
\(165\) −1.86324 + 2.96322i −0.0112924 + 0.0179589i
\(166\) 0 0
\(167\) −108.837 + 81.0259i −0.651716 + 0.485185i −0.871520 0.490359i \(-0.836866\pi\)
0.219804 + 0.975544i \(0.429458\pi\)
\(168\) 0 0
\(169\) −117.971 + 77.5905i −0.698051 + 0.459116i
\(170\) 0 0
\(171\) −94.4118 42.6734i −0.552116 0.249552i
\(172\) 0 0
\(173\) 8.78992 75.2026i 0.0508088 0.434697i −0.943761 0.330628i \(-0.892740\pi\)
0.994570 0.104069i \(-0.0331864\pi\)
\(174\) 0 0
\(175\) −29.0562 97.0546i −0.166036 0.554598i
\(176\) 0 0
\(177\) −34.6541 + 23.8218i −0.195786 + 0.134587i
\(178\) 0 0
\(179\) −285.704 50.3772i −1.59611 0.281437i −0.696310 0.717741i \(-0.745176\pi\)
−0.899799 + 0.436304i \(0.856287\pi\)
\(180\) 0 0
\(181\) 4.79250 + 27.1796i 0.0264779 + 0.150163i 0.995180 0.0980610i \(-0.0312640\pi\)
−0.968703 + 0.248225i \(0.920153\pi\)
\(182\) 0 0
\(183\) 2.83199 + 138.425i 0.0154753 + 0.756420i
\(184\) 0 0
\(185\) −40.7777 + 61.9995i −0.220420 + 0.335132i
\(186\) 0 0
\(187\) −6.53936 + 21.8430i −0.0349698 + 0.116807i
\(188\) 0 0
\(189\) −104.901 + 53.1031i −0.555033 + 0.280969i
\(190\) 0 0
\(191\) −74.4869 + 70.2748i −0.389984 + 0.367931i −0.856115 0.516785i \(-0.827129\pi\)
0.466132 + 0.884715i \(0.345647\pi\)
\(192\) 0 0
\(193\) −5.02042 + 86.1973i −0.0260125 + 0.446618i 0.960006 + 0.279980i \(0.0903280\pi\)
−0.986018 + 0.166637i \(0.946709\pi\)
\(194\) 0 0
\(195\) −10.6816 + 68.7770i −0.0547775 + 0.352702i
\(196\) 0 0
\(197\) 123.605 339.602i 0.627437 1.72387i −0.0605704 0.998164i \(-0.519292\pi\)
0.688007 0.725704i \(-0.258486\pi\)
\(198\) 0 0
\(199\) 325.194 118.361i 1.63414 0.594778i 0.648138 0.761523i \(-0.275548\pi\)
0.986000 + 0.166745i \(0.0533257\pi\)
\(200\) 0 0
\(201\) 179.238 + 49.6891i 0.891733 + 0.247210i
\(202\) 0 0
\(203\) −36.3564 + 153.400i −0.179096 + 0.755664i
\(204\) 0 0
\(205\) −24.8438 57.5945i −0.121189 0.280949i
\(206\) 0 0
\(207\) −138.273 336.408i −0.667987 1.62516i
\(208\) 0 0
\(209\) 10.1795 0.592889i 0.0487058 0.00283679i
\(210\) 0 0
\(211\) −126.593 + 293.475i −0.599966 + 1.39088i 0.299588 + 0.954069i \(0.403151\pi\)
−0.899554 + 0.436810i \(0.856108\pi\)
\(212\) 0 0
\(213\) −368.505 79.4130i −1.73007 0.372831i
\(214\) 0 0
\(215\) −46.4047 26.7917i −0.215836 0.124613i
\(216\) 0 0
\(217\) −110.200 190.872i −0.507835 0.879596i
\(218\) 0 0
\(219\) −215.804 87.8981i −0.985408 0.401361i
\(220\) 0 0
\(221\) 52.6339 + 450.312i 0.238162 + 2.03761i
\(222\) 0 0
\(223\) −33.4852 16.8169i −0.150158 0.0754121i 0.372133 0.928179i \(-0.378626\pi\)
−0.522291 + 0.852767i \(0.674923\pi\)
\(224\) 0 0
\(225\) −131.800 162.697i −0.585776 0.723096i
\(226\) 0 0
\(227\) 115.242 + 85.7943i 0.507673 + 0.377948i 0.820305 0.571926i \(-0.193803\pi\)
−0.312633 + 0.949874i \(0.601211\pi\)
\(228\) 0 0
\(229\) −99.4039 + 105.362i −0.434078 + 0.460096i −0.907076 0.420968i \(-0.861691\pi\)
0.472997 + 0.881064i \(0.343172\pi\)
\(230\) 0 0
\(231\) 6.71872 9.42116i 0.0290854 0.0407843i
\(232\) 0 0
\(233\) −109.199 + 130.139i −0.468666 + 0.558535i −0.947659 0.319284i \(-0.896558\pi\)
0.478993 + 0.877819i \(0.341002\pi\)
\(234\) 0 0
\(235\) −11.4339 + 9.59417i −0.0486548 + 0.0408262i
\(236\) 0 0
\(237\) 72.3775 + 82.7577i 0.305390 + 0.349188i
\(238\) 0 0
\(239\) 138.792 + 276.358i 0.580720 + 1.15631i 0.971768 + 0.235938i \(0.0758162\pi\)
−0.391048 + 0.920370i \(0.627887\pi\)
\(240\) 0 0
\(241\) −209.721 + 49.7048i −0.870211 + 0.206244i −0.641381 0.767222i \(-0.721638\pi\)
−0.228830 + 0.973466i \(0.573490\pi\)
\(242\) 0 0
\(243\) −158.802 + 183.932i −0.653507 + 0.756921i
\(244\) 0 0
\(245\) 9.12470 + 38.5001i 0.0372437 + 0.157143i
\(246\) 0 0
\(247\) 181.188 90.9962i 0.733556 0.368406i
\(248\) 0 0
\(249\) −14.9692 + 13.0916i −0.0601172 + 0.0525768i
\(250\) 0 0
\(251\) 164.515 + 196.062i 0.655440 + 0.781123i 0.986724 0.162408i \(-0.0519262\pi\)
−0.331284 + 0.943531i \(0.607482\pi\)
\(252\) 0 0
\(253\) 27.4212 + 23.0091i 0.108384 + 0.0909452i
\(254\) 0 0
\(255\) 82.8232 + 59.0655i 0.324797 + 0.231629i
\(256\) 0 0
\(257\) −91.5983 86.4186i −0.356414 0.336259i 0.487120 0.873335i \(-0.338047\pi\)
−0.843534 + 0.537076i \(0.819529\pi\)
\(258\) 0 0
\(259\) 146.493 196.774i 0.565611 0.759747i
\(260\) 0 0
\(261\) 51.0298 + 321.799i 0.195516 + 1.23295i
\(262\) 0 0
\(263\) 53.9252 107.374i 0.205039 0.408266i −0.767486 0.641066i \(-0.778493\pi\)
0.972525 + 0.232800i \(0.0747888\pi\)
\(264\) 0 0
\(265\) −30.1477 + 3.52377i −0.113765 + 0.0132972i
\(266\) 0 0
\(267\) −128.739 + 316.075i −0.482168 + 1.18380i
\(268\) 0 0
\(269\) −400.114 + 231.006i −1.48741 + 0.858757i −0.999897 0.0143575i \(-0.995430\pi\)
−0.487514 + 0.873115i \(0.662096\pi\)
\(270\) 0 0
\(271\) 231.413 400.819i 0.853923 1.47904i −0.0237184 0.999719i \(-0.507551\pi\)
0.877641 0.479319i \(-0.159116\pi\)
\(272\) 0 0
\(273\) 48.4719 224.927i 0.177553 0.823907i
\(274\) 0 0
\(275\) 18.9215 + 8.16194i 0.0688055 + 0.0296798i
\(276\) 0 0
\(277\) −3.49796 60.0577i −0.0126280 0.216815i −0.998719 0.0506064i \(-0.983885\pi\)
0.986091 0.166208i \(-0.0531524\pi\)
\(278\) 0 0
\(279\) −360.625 278.280i −1.29256 0.997419i
\(280\) 0 0
\(281\) −163.242 + 70.4158i −0.580933 + 0.250590i −0.666206 0.745767i \(-0.732083\pi\)
0.0852730 + 0.996358i \(0.472824\pi\)
\(282\) 0 0
\(283\) 328.753 + 77.9159i 1.16167 + 0.275321i 0.765858 0.643010i \(-0.222314\pi\)
0.395814 + 0.918331i \(0.370463\pi\)
\(284\) 0 0
\(285\) 12.1535 43.8400i 0.0426438 0.153824i
\(286\) 0 0
\(287\) 70.9198 + 194.850i 0.247107 + 0.678922i
\(288\) 0 0
\(289\) 351.108 + 127.793i 1.21491 + 0.442189i
\(290\) 0 0
\(291\) 294.115 + 45.6784i 1.01070 + 0.156971i
\(292\) 0 0
\(293\) −104.095 6.06285i −0.355274 0.0206923i −0.120420 0.992723i \(-0.538424\pi\)
−0.234854 + 0.972031i \(0.575461\pi\)
\(294\) 0 0
\(295\) −12.6713 13.4308i −0.0429535 0.0455281i
\(296\) 0 0
\(297\) 5.44099 23.2881i 0.0183198 0.0784112i
\(298\) 0 0
\(299\) 681.871 + 204.139i 2.28051 + 0.682739i
\(300\) 0 0
\(301\) 147.996 + 97.3387i 0.491682 + 0.323384i
\(302\) 0 0
\(303\) −449.158 + 9.18918i −1.48237 + 0.0303273i
\(304\) 0 0
\(305\) −59.8703 + 10.5568i −0.196296 + 0.0346123i
\(306\) 0 0
\(307\) −18.8221 + 106.746i −0.0613099 + 0.347706i 0.938686 + 0.344774i \(0.112044\pi\)
−0.999996 + 0.00293187i \(0.999067\pi\)
\(308\) 0 0
\(309\) −146.761 213.496i −0.474956 0.690926i
\(310\) 0 0
\(311\) −93.2358 + 27.9130i −0.299793 + 0.0897523i −0.433167 0.901314i \(-0.642604\pi\)
0.133374 + 0.991066i \(0.457419\pi\)
\(312\) 0 0
\(313\) −440.061 51.4357i −1.40595 0.164331i −0.620958 0.783844i \(-0.713256\pi\)
−0.784987 + 0.619512i \(0.787330\pi\)
\(314\) 0 0
\(315\) −30.1098 41.9372i −0.0955868 0.133134i
\(316\) 0 0
\(317\) −20.9355 31.8308i −0.0660425 0.100413i 0.800957 0.598722i \(-0.204325\pi\)
−0.866999 + 0.498310i \(0.833954\pi\)
\(318\) 0 0
\(319\) −19.1486 25.7210i −0.0600270 0.0806302i
\(320\) 0 0
\(321\) 158.382 + 99.5890i 0.493401 + 0.310246i
\(322\) 0 0
\(323\) 296.340i 0.917460i
\(324\) 0 0
\(325\) 409.751 1.26077
\(326\) 0 0
\(327\) −199.177 7.51687i −0.609103 0.0229874i
\(328\) 0 0
\(329\) 39.5786 29.4652i 0.120300 0.0895599i
\(330\) 0 0
\(331\) −97.9061 + 64.3938i −0.295789 + 0.194543i −0.688726 0.725022i \(-0.741829\pi\)
0.392937 + 0.919565i \(0.371459\pi\)
\(332\) 0 0
\(333\) 125.424 491.248i 0.376649 1.47522i
\(334\) 0 0
\(335\) −9.48135 + 81.1181i −0.0283025 + 0.242144i
\(336\) 0 0
\(337\) 103.067 + 344.268i 0.305837 + 1.02157i 0.963378 + 0.268147i \(0.0864114\pi\)
−0.657541 + 0.753419i \(0.728403\pi\)
\(338\) 0 0
\(339\) 24.0977 + 305.824i 0.0710846 + 0.902136i
\(340\) 0 0
\(341\) 44.1489 + 7.78463i 0.129469 + 0.0228288i
\(342\) 0 0
\(343\) −59.7662 338.951i −0.174246 0.988195i
\(344\) 0 0
\(345\) 136.646 82.6649i 0.396077 0.239608i
\(346\) 0 0
\(347\) −180.008 + 273.688i −0.518754 + 0.788727i −0.995935 0.0900779i \(-0.971288\pi\)
0.477181 + 0.878805i \(0.341659\pi\)
\(348\) 0 0
\(349\) 99.7425 333.163i 0.285795 0.954623i −0.687715 0.725980i \(-0.741386\pi\)
0.973511 0.228642i \(-0.0734285\pi\)
\(350\) 0 0
\(351\) −84.0696 468.047i −0.239514 1.33347i
\(352\) 0 0
\(353\) 384.472 362.731i 1.08916 1.02757i 0.0896547 0.995973i \(-0.471424\pi\)
0.999501 0.0315924i \(-0.0100578\pi\)
\(354\) 0 0
\(355\) 9.62424 165.242i 0.0271105 0.465470i
\(356\) 0 0
\(357\) −261.982 210.850i −0.733844 0.590616i
\(358\) 0 0
\(359\) 9.34524 25.6758i 0.0260313 0.0715204i −0.925996 0.377533i \(-0.876773\pi\)
0.952028 + 0.306012i \(0.0989948\pi\)
\(360\) 0 0
\(361\) 214.695 78.1427i 0.594724 0.216462i
\(362\) 0 0
\(363\) −90.3313 349.150i −0.248847 0.961847i
\(364\) 0 0
\(365\) 23.5958 99.5585i 0.0646460 0.272763i
\(366\) 0 0
\(367\) −105.196 243.873i −0.286639 0.664503i 0.712677 0.701492i \(-0.247483\pi\)
−0.999316 + 0.0369892i \(0.988223\pi\)
\(368\) 0 0
\(369\) 288.663 + 316.747i 0.782286 + 0.858394i
\(370\) 0 0
\(371\) 100.172 5.83435i 0.270005 0.0157260i
\(372\) 0 0
\(373\) 45.3015 105.021i 0.121452 0.281557i −0.846634 0.532175i \(-0.821375\pi\)
0.968086 + 0.250619i \(0.0806340\pi\)
\(374\) 0 0
\(375\) 128.025 141.383i 0.341399 0.377022i
\(376\) 0 0
\(377\) −552.188 318.806i −1.46469 0.845639i
\(378\) 0 0
\(379\) −295.427 511.695i −0.779491 1.35012i −0.932236 0.361852i \(-0.882145\pi\)
0.152745 0.988266i \(-0.451189\pi\)
\(380\) 0 0
\(381\) 87.7263 + 637.217i 0.230253 + 1.67248i
\(382\) 0 0
\(383\) −2.46582 21.0964i −0.00643817 0.0550821i 0.989637 0.143589i \(-0.0458644\pi\)
−0.996076 + 0.0885072i \(0.971790\pi\)
\(384\) 0 0
\(385\) 4.54050 + 2.28033i 0.0117935 + 0.00592292i
\(386\) 0 0
\(387\) 359.385 + 69.7874i 0.928642 + 0.180329i
\(388\) 0 0
\(389\) 249.617 + 185.833i 0.641689 + 0.477720i 0.868151 0.496300i \(-0.165308\pi\)
−0.226462 + 0.974020i \(0.572716\pi\)
\(390\) 0 0
\(391\) 713.900 756.689i 1.82583 1.93527i
\(392\) 0 0
\(393\) −85.9099 188.465i −0.218600 0.479556i
\(394\) 0 0
\(395\) −31.0305 + 36.9807i −0.0785581 + 0.0936219i
\(396\) 0 0
\(397\) −103.559 + 86.8961i −0.260853 + 0.218882i −0.763829 0.645419i \(-0.776683\pi\)
0.502976 + 0.864301i \(0.332239\pi\)
\(398\) 0 0
\(399\) −48.5361 + 142.346i −0.121644 + 0.356757i
\(400\) 0 0
\(401\) 312.153 + 621.547i 0.778435 + 1.54999i 0.834145 + 0.551545i \(0.185962\pi\)
−0.0557095 + 0.998447i \(0.517742\pi\)
\(402\) 0 0
\(403\) 867.381 205.573i 2.15231 0.510107i
\(404\) 0 0
\(405\) −90.5073 56.5081i −0.223475 0.139526i
\(406\) 0 0
\(407\) 11.5073 + 48.5530i 0.0282734 + 0.119295i
\(408\) 0 0
\(409\) −608.719 + 305.710i −1.48831 + 0.747457i −0.992646 0.121057i \(-0.961372\pi\)
−0.495665 + 0.868514i \(0.665075\pi\)
\(410\) 0 0
\(411\) −44.3644 224.632i −0.107943 0.546550i
\(412\) 0 0
\(413\) 39.2366 + 46.7603i 0.0950038 + 0.113221i
\(414\) 0 0
\(415\) −6.68905 5.61278i −0.0161182 0.0135248i
\(416\) 0 0
\(417\) −28.5985 + 297.298i −0.0685815 + 0.712945i
\(418\) 0 0
\(419\) 445.414 + 420.227i 1.06304 + 1.00293i 0.999988 + 0.00491779i \(0.00156539\pi\)
0.0630536 + 0.998010i \(0.479916\pi\)
\(420\) 0 0
\(421\) −17.1951 + 23.0970i −0.0408435 + 0.0548623i −0.822076 0.569378i \(-0.807184\pi\)
0.781232 + 0.624240i \(0.214591\pi\)
\(422\) 0 0
\(423\) 52.5061 87.4219i 0.124128 0.206671i
\(424\) 0 0
\(425\) 268.776 535.177i 0.632414 1.25924i
\(426\) 0 0
\(427\) 199.615 23.3317i 0.467483 0.0546409i
\(428\) 0 0
\(429\) 28.7095 + 36.9606i 0.0669220 + 0.0861551i
\(430\) 0 0
\(431\) 476.994 275.393i 1.10671 0.638962i 0.168738 0.985661i \(-0.446031\pi\)
0.937976 + 0.346699i \(0.112698\pi\)
\(432\) 0 0
\(433\) −201.537 + 349.073i −0.465444 + 0.806173i −0.999221 0.0394524i \(-0.987439\pi\)
0.533778 + 0.845625i \(0.320772\pi\)
\(434\) 0 0
\(435\) −136.187 + 43.8263i −0.313073 + 0.100750i
\(436\) 0 0
\(437\) −427.185 184.270i −0.977541 0.421670i
\(438\) 0 0
\(439\) 14.6584 + 251.674i 0.0333903 + 0.573290i 0.972966 + 0.230949i \(0.0741829\pi\)
−0.939576 + 0.342342i \(0.888780\pi\)
\(440\) 0 0
\(441\) −144.628 228.389i −0.327954 0.517889i
\(442\) 0 0
\(443\) −633.762 + 273.378i −1.43061 + 0.617107i −0.963650 0.267169i \(-0.913912\pi\)
−0.466965 + 0.884276i \(0.654653\pi\)
\(444\) 0 0
\(445\) −145.817 34.5593i −0.327679 0.0776614i
\(446\) 0 0
\(447\) −76.1486 77.4749i −0.170355 0.173322i
\(448\) 0 0
\(449\) −41.8244 114.912i −0.0931502 0.255928i 0.884364 0.466798i \(-0.154593\pi\)
−0.977514 + 0.210870i \(0.932370\pi\)
\(450\) 0 0
\(451\) −39.6330 14.4252i −0.0878781 0.0319850i
\(452\) 0 0
\(453\) 86.3285 + 222.891i 0.190571 + 0.492033i
\(454\) 0 0
\(455\) 100.860 + 5.87442i 0.221670 + 0.0129108i
\(456\) 0 0
\(457\) 495.145 + 524.823i 1.08347 + 1.14841i 0.988233 + 0.152954i \(0.0488785\pi\)
0.0952342 + 0.995455i \(0.469640\pi\)
\(458\) 0 0
\(459\) −666.463 197.212i −1.45199 0.429655i
\(460\) 0 0
\(461\) −36.0803 10.8017i −0.0782652 0.0234311i 0.247431 0.968905i \(-0.420414\pi\)
−0.325696 + 0.945474i \(0.605599\pi\)
\(462\) 0 0
\(463\) −165.199 108.653i −0.356800 0.234671i 0.358435 0.933555i \(-0.383310\pi\)
−0.715236 + 0.698883i \(0.753681\pi\)
\(464\) 0 0
\(465\) 96.4416 175.224i 0.207401 0.376826i
\(466\) 0 0
\(467\) 225.643 39.7870i 0.483176 0.0851969i 0.0732458 0.997314i \(-0.476664\pi\)
0.409930 + 0.912117i \(0.365553\pi\)
\(468\) 0 0
\(469\) 46.8829 265.886i 0.0999635 0.566921i
\(470\) 0 0
\(471\) 282.569 592.561i 0.599935 1.25809i
\(472\) 0 0
\(473\) −34.5165 + 10.3336i −0.0729736 + 0.0218469i
\(474\) 0 0
\(475\) −266.013 31.0925i −0.560028 0.0654578i
\(476\) 0 0
\(477\) 186.901 89.8586i 0.391826 0.188383i
\(478\) 0 0
\(479\) −38.2991 58.2309i −0.0799564 0.121568i 0.793296 0.608837i \(-0.208364\pi\)
−0.873252 + 0.487269i \(0.837993\pi\)
\(480\) 0 0
\(481\) 592.491 + 795.853i 1.23179 + 1.65458i
\(482\) 0 0
\(483\) −466.854 + 246.547i −0.966572 + 0.510450i
\(484\) 0 0
\(485\) 130.692i 0.269467i
\(486\) 0 0
\(487\) 67.9011 0.139427 0.0697137 0.997567i \(-0.477791\pi\)
0.0697137 + 0.997567i \(0.477791\pi\)
\(488\) 0 0
\(489\) −32.2057 60.9836i −0.0658603 0.124711i
\(490\) 0 0
\(491\) −618.995 + 460.825i −1.26068 + 0.938544i −0.999641 0.0267840i \(-0.991473\pi\)
−0.261042 + 0.965328i \(0.584066\pi\)
\(492\) 0 0
\(493\) −778.601 + 512.094i −1.57931 + 1.03873i
\(494\) 0 0
\(495\) 10.4711 + 0.791483i 0.0211538 + 0.00159896i
\(496\) 0 0
\(497\) −63.5245 + 543.487i −0.127816 + 1.09353i
\(498\) 0 0
\(499\) 79.2466 + 264.702i 0.158811 + 0.530465i 0.999946 0.0103593i \(-0.00329754\pi\)
−0.841136 + 0.540824i \(0.818112\pi\)
\(500\) 0 0
\(501\) 367.420 + 175.208i 0.733374 + 0.349717i
\(502\) 0 0
\(503\) 367.059 + 64.7224i 0.729739 + 0.128673i 0.526160 0.850386i \(-0.323631\pi\)
0.203579 + 0.979058i \(0.434742\pi\)
\(504\) 0 0
\(505\) −34.2544 194.266i −0.0678304 0.384685i
\(506\) 0 0
\(507\) 371.103 + 204.252i 0.731959 + 0.402863i
\(508\) 0 0
\(509\) 261.971 398.307i 0.514677 0.782529i −0.480870 0.876792i \(-0.659679\pi\)
0.995547 + 0.0942631i \(0.0300495\pi\)
\(510\) 0 0
\(511\) −97.0084 + 324.031i −0.189840 + 0.634111i
\(512\) 0 0
\(513\) 19.0625 + 310.239i 0.0371588 + 0.604754i
\(514\) 0 0
\(515\) 82.7442 78.0651i 0.160668 0.151583i
\(516\) 0 0
\(517\) −0.583561 + 10.0194i −0.00112874 + 0.0193798i
\(518\) 0 0
\(519\) −211.811 + 82.0373i −0.408115 + 0.158068i
\(520\) 0 0
\(521\) −169.007 + 464.342i −0.324389 + 0.891251i 0.665115 + 0.746741i \(0.268383\pi\)
−0.989503 + 0.144510i \(0.953840\pi\)
\(522\) 0 0
\(523\) 82.6741 30.0909i 0.158077 0.0575352i −0.261770 0.965130i \(-0.584306\pi\)
0.419846 + 0.907595i \(0.362084\pi\)
\(524\) 0 0
\(525\) −216.760 + 213.049i −0.412876 + 0.405808i
\(526\) 0 0
\(527\) 300.458 1267.73i 0.570130 2.40557i
\(528\) 0 0
\(529\) −437.355 1013.90i −0.826758 1.91664i
\(530\) 0 0
\(531\) 111.743 + 58.5569i 0.210439 + 0.110277i
\(532\) 0 0
\(533\) −837.230 + 48.7631i −1.57079 + 0.0914880i
\(534\) 0 0
\(535\) −32.5379 + 75.4313i −0.0608185 + 0.140993i
\(536\) 0 0
\(537\) 266.616 + 828.490i 0.496492 + 1.54281i
\(538\) 0 0
\(539\) 23.0407 + 13.3025i 0.0427471 + 0.0246800i
\(540\) 0 0
\(541\) 138.642 + 240.135i 0.256270 + 0.443873i 0.965240 0.261366i \(-0.0841730\pi\)
−0.708970 + 0.705239i \(0.750840\pi\)
\(542\) 0 0
\(543\) 65.3879 50.7908i 0.120420 0.0935374i
\(544\) 0 0
\(545\) −10.1603 86.9273i −0.0186428 0.159500i
\(546\) 0 0
\(547\) −410.687 206.255i −0.750799 0.377065i 0.0318795 0.999492i \(-0.489851\pi\)
−0.782678 + 0.622426i \(0.786147\pi\)
\(548\) 0 0
\(549\) 363.246 201.439i 0.661650 0.366920i
\(550\) 0 0
\(551\) 334.293 + 248.872i 0.606702 + 0.451673i
\(552\) 0 0
\(553\) 109.516 116.080i 0.198040 0.209910i
\(554\) 0 0
\(555\) 221.600 + 21.3167i 0.399278 + 0.0384084i
\(556\) 0 0
\(557\) −608.359 + 725.014i −1.09221 + 1.30164i −0.142052 + 0.989859i \(0.545370\pi\)
−0.950154 + 0.311781i \(0.899074\pi\)
\(558\) 0 0
\(559\) −548.819 + 460.514i −0.981787 + 0.823817i
\(560\) 0 0
\(561\) 67.1063 13.2534i 0.119619 0.0236245i
\(562\) 0 0
\(563\) −165.897 330.328i −0.294666 0.586728i 0.696774 0.717290i \(-0.254618\pi\)
−0.991440 + 0.130563i \(0.958322\pi\)
\(564\) 0 0
\(565\) −131.070 + 31.0642i −0.231983 + 0.0549809i
\(566\) 0 0
\(567\) 287.833 + 203.887i 0.507643 + 0.359589i
\(568\) 0 0
\(569\) −97.9687 413.363i −0.172177 0.726472i −0.988793 0.149291i \(-0.952301\pi\)
0.816616 0.577181i \(-0.195847\pi\)
\(570\) 0 0
\(571\) −183.309 + 92.0614i −0.321032 + 0.161228i −0.602016 0.798484i \(-0.705636\pi\)
0.280984 + 0.959713i \(0.409339\pi\)
\(572\) 0 0
\(573\) 290.777 + 99.1471i 0.507465 + 0.173032i
\(574\) 0 0
\(575\) −604.349 720.235i −1.05104 1.25258i
\(576\) 0 0
\(577\) 355.484 + 298.287i 0.616091 + 0.516962i 0.896572 0.442898i \(-0.146050\pi\)
−0.280481 + 0.959860i \(0.590494\pi\)
\(578\) 0 0
\(579\) 235.697 107.440i 0.407076 0.185561i
\(580\) 0 0
\(581\) 20.9965 + 19.8092i 0.0361386 + 0.0340950i
\(582\) 0 0
\(583\) −12.1878 + 16.3711i −0.0209054 + 0.0280808i
\(584\) 0 0
\(585\) 197.416 68.0171i 0.337463 0.116268i
\(586\) 0 0
\(587\) 64.0060 127.446i 0.109039 0.217115i −0.832495 0.554033i \(-0.813088\pi\)
0.941534 + 0.336918i \(0.109384\pi\)
\(588\) 0 0
\(589\) −578.709 + 67.6414i −0.982528 + 0.114841i
\(590\) 0 0
\(591\) −1074.06 + 147.867i −1.81736 + 0.250198i
\(592\) 0 0
\(593\) −73.1016 + 42.2053i −0.123274 + 0.0711724i −0.560369 0.828243i \(-0.689341\pi\)
0.437095 + 0.899415i \(0.356007\pi\)
\(594\) 0 0
\(595\) 73.8316 127.880i 0.124087 0.214924i
\(596\) 0 0
\(597\) −769.568 696.855i −1.28906 1.16726i
\(598\) 0 0
\(599\) −912.280 393.519i −1.52301 0.656960i −0.540188 0.841544i \(-0.681647\pi\)
−0.982817 + 0.184584i \(0.940906\pi\)
\(600\) 0 0
\(601\) 64.4266 + 1106.16i 0.107199 + 1.84054i 0.440543 + 0.897732i \(0.354786\pi\)
−0.333344 + 0.942805i \(0.608177\pi\)
\(602\) 0 0
\(603\) −119.289 545.095i −0.197826 0.903972i
\(604\) 0 0
\(605\) 145.406 62.7219i 0.240340 0.103673i
\(606\) 0 0
\(607\) −686.367 162.672i −1.13075 0.267993i −0.377684 0.925935i \(-0.623279\pi\)
−0.753069 + 0.657941i \(0.771427\pi\)
\(608\) 0 0
\(609\) 457.872 118.460i 0.751843 0.194515i
\(610\) 0 0
\(611\) 68.2552 + 187.530i 0.111711 + 0.306922i
\(612\) 0 0
\(613\) −1102.34 401.218i −1.79827 0.654516i −0.998532 0.0541655i \(-0.982750\pi\)
−0.799737 0.600351i \(-0.795028\pi\)
\(614\) 0 0
\(615\) −117.981 + 146.593i −0.191840 + 0.238362i
\(616\) 0 0
\(617\) 200.561 + 11.6813i 0.325058 + 0.0189324i 0.219898 0.975523i \(-0.429428\pi\)
0.105160 + 0.994455i \(0.466465\pi\)
\(618\) 0 0
\(619\) −256.698 272.084i −0.414698 0.439554i 0.486027 0.873944i \(-0.338446\pi\)
−0.900725 + 0.434390i \(0.856964\pi\)
\(620\) 0 0
\(621\) −698.708 + 838.103i −1.12513 + 1.34960i
\(622\) 0 0
\(623\) 474.588 + 142.082i 0.761778 + 0.228061i
\(624\) 0 0
\(625\) −415.964 273.584i −0.665543 0.437734i
\(626\) 0 0
\(627\) −15.8338 26.1736i −0.0252533 0.0417441i
\(628\) 0 0
\(629\) 1428.11 251.814i 2.27045 0.400341i
\(630\) 0 0
\(631\) −122.780 + 696.320i −0.194580 + 1.10352i 0.718435 + 0.695594i \(0.244859\pi\)
−0.913015 + 0.407925i \(0.866252\pi\)
\(632\) 0 0
\(633\) 955.881 75.3195i 1.51008 0.118988i
\(634\) 0 0
\(635\) −270.570 + 81.0035i −0.426095 + 0.127565i
\(636\) 0 0
\(637\) 525.445 + 61.4157i 0.824874 + 0.0964140i
\(638\) 0 0
\(639\) 305.591 + 1088.82i 0.478232 + 1.70395i
\(640\) 0 0
\(641\) −591.063 898.668i −0.922096 1.40198i −0.915640 0.401999i \(-0.868315\pi\)
−0.00645568 0.999979i \(-0.502055\pi\)
\(642\) 0 0
\(643\) −102.096 137.138i −0.158780 0.213279i 0.715613 0.698497i \(-0.246147\pi\)
−0.874393 + 0.485218i \(0.838740\pi\)
\(644\) 0 0
\(645\) −6.06236 + 160.636i −0.00939901 + 0.249048i
\(646\) 0 0
\(647\) 56.2609i 0.0869565i 0.999054 + 0.0434783i \(0.0138439\pi\)
−0.999054 + 0.0434783i \(0.986156\pi\)
\(648\) 0 0
\(649\) −12.4159 −0.0191308
\(650\) 0 0
\(651\) −351.961 + 559.742i −0.540646 + 0.859819i
\(652\) 0 0
\(653\) 980.248 729.767i 1.50115 1.11756i 0.539948 0.841698i \(-0.318444\pi\)
0.961197 0.275863i \(-0.0889636\pi\)
\(654\) 0 0
\(655\) 75.9841 49.9755i 0.116006 0.0762985i
\(656\) 0 0
\(657\) 69.1556 + 695.626i 0.105260 + 1.05879i
\(658\) 0 0
\(659\) −37.2683 + 318.851i −0.0565528 + 0.483840i 0.935050 + 0.354517i \(0.115355\pi\)
−0.991602 + 0.129323i \(0.958720\pi\)
\(660\) 0 0
\(661\) −190.640 636.781i −0.288411 0.963360i −0.972293 0.233767i \(-0.924895\pi\)
0.683881 0.729593i \(-0.260291\pi\)
\(662\) 0 0
\(663\) 1120.85 770.492i 1.69057 1.16213i
\(664\) 0 0
\(665\) −65.0332 11.4671i −0.0977942 0.0172438i
\(666\) 0 0
\(667\) 254.054 + 1440.81i 0.380891 + 2.16014i
\(668\) 0 0
\(669\) 2.29933 + 112.389i 0.00343697 + 0.167996i
\(670\) 0 0
\(671\) −22.4631 + 34.1535i −0.0334771 + 0.0508995i
\(672\) 0 0
\(673\) 145.600 486.339i 0.216345 0.722643i −0.779065 0.626943i \(-0.784306\pi\)
0.995410 0.0957002i \(-0.0305090\pi\)
\(674\) 0 0
\(675\) −246.956 + 577.567i −0.365861 + 0.855655i
\(676\) 0 0
\(677\) −149.815 + 141.343i −0.221292 + 0.208778i −0.788902 0.614520i \(-0.789350\pi\)
0.567609 + 0.823298i \(0.307868\pi\)
\(678\) 0 0
\(679\) 25.1211 431.313i 0.0369972 0.635218i
\(680\) 0 0
\(681\) 66.1467 425.907i 0.0971317 0.625413i
\(682\) 0 0
\(683\) 400.942 1101.58i 0.587030 1.61285i −0.188873 0.982001i \(-0.560484\pi\)
0.775904 0.630851i \(-0.217294\pi\)
\(684\) 0 0
\(685\) 94.4761 34.3865i 0.137921 0.0501992i
\(686\) 0 0
\(687\) 418.764 + 116.091i 0.609555 + 0.168983i
\(688\) 0 0
\(689\) −93.5911 + 394.892i −0.135836 + 0.573138i
\(690\) 0 0
\(691\) 400.083 + 927.497i 0.578991 + 1.34225i 0.916162 + 0.400809i \(0.131271\pi\)
−0.337170 + 0.941444i \(0.609470\pi\)
\(692\) 0 0
\(693\) −34.4050 4.62480i −0.0496465 0.00667360i
\(694\) 0 0
\(695\) −130.922 + 7.62533i −0.188377 + 0.0109717i
\(696\) 0 0
\(697\) −485.491 + 1125.49i −0.696544 + 1.61477i
\(698\) 0 0
\(699\) 498.214 + 107.366i 0.712753 + 0.153599i
\(700\) 0 0
\(701\) −827.278 477.629i −1.18014 0.681354i −0.224093 0.974568i \(-0.571942\pi\)
−0.956047 + 0.293214i \(0.905275\pi\)
\(702\) 0 0
\(703\) −324.259 561.633i −0.461250 0.798908i
\(704\) 0 0
\(705\) 41.4697 + 16.8908i 0.0588223 + 0.0239586i
\(706\) 0 0
\(707\) 75.7062 + 647.708i 0.107081 + 0.916135i
\(708\) 0 0
\(709\) 105.679 + 53.0742i 0.149054 + 0.0748578i 0.521763 0.853091i \(-0.325275\pi\)
−0.372709 + 0.927948i \(0.621571\pi\)
\(710\) 0 0
\(711\) 118.142 307.942i 0.166163 0.433112i
\(712\) 0 0
\(713\) −1640.66 1221.42i −2.30106 1.71308i
\(714\) 0 0
\(715\) −14.1022 + 14.9474i −0.0197233 + 0.0209055i
\(716\) 0 0
\(717\) 538.680 755.351i 0.751297 1.05349i
\(718\) 0 0
\(719\) −217.523 + 259.234i −0.302536 + 0.360548i −0.895798 0.444461i \(-0.853395\pi\)
0.593262 + 0.805009i \(0.297840\pi\)
\(720\) 0 0
\(721\) −288.080 + 241.728i −0.399557 + 0.335268i
\(722\) 0 0
\(723\) 425.666 + 486.713i 0.588749 + 0.673186i
\(724\) 0 0
\(725\) 377.996 + 752.651i 0.521373 + 1.03814i
\(726\) 0 0
\(727\) 640.773 151.866i 0.881393 0.208894i 0.235089 0.971974i \(-0.424462\pi\)
0.646304 + 0.763080i \(0.276314\pi\)
\(728\) 0 0
\(729\) 710.408 + 163.590i 0.974496 + 0.224404i
\(730\) 0 0
\(731\) 241.481 + 1018.89i 0.330343 + 1.39383i
\(732\) 0 0
\(733\) −464.043 + 233.051i −0.633074 + 0.317942i −0.736238 0.676723i \(-0.763400\pi\)
0.103164 + 0.994664i \(0.467103\pi\)
\(734\) 0 0
\(735\) 89.3498 78.1428i 0.121564 0.106317i
\(736\) 0 0
\(737\) 35.2994 + 42.0682i 0.0478960 + 0.0570803i
\(738\) 0 0
\(739\) 614.828 + 515.902i 0.831973 + 0.698108i 0.955743 0.294203i \(-0.0950540\pi\)
−0.123770 + 0.992311i \(0.539498\pi\)
\(740\) 0 0
\(741\) −495.231 353.175i −0.668327 0.476619i
\(742\) 0 0
\(743\) −771.921 728.270i −1.03892 0.980175i −0.0391061 0.999235i \(-0.512451\pi\)
−0.999818 + 0.0190604i \(0.993933\pi\)
\(744\) 0 0
\(745\) 28.4842 38.2609i 0.0382338 0.0513569i
\(746\) 0 0
\(747\) 55.7005 + 21.3695i 0.0745656 + 0.0286070i
\(748\) 0 0
\(749\) 121.882 242.686i 0.162726 0.324014i
\(750\) 0 0
\(751\) 22.6115 2.64290i 0.0301085 0.00351918i −0.101025 0.994884i \(-0.532212\pi\)
0.131134 + 0.991365i \(0.458138\pi\)
\(752\) 0 0
\(753\) 289.634 711.099i 0.384640 0.944355i
\(754\) 0 0
\(755\) −90.8928 + 52.4770i −0.120388 + 0.0695059i
\(756\) 0 0
\(757\) 687.048 1190.00i 0.907593 1.57200i 0.0901938 0.995924i \(-0.471251\pi\)
0.817399 0.576072i \(-0.195415\pi\)
\(758\) 0 0
\(759\) 22.6228 104.978i 0.0298060 0.138310i
\(760\) 0 0
\(761\) −554.457 239.169i −0.728590 0.314283i −0.000721465 1.00000i \(-0.500230\pi\)
−0.727869 + 0.685717i \(0.759489\pi\)
\(762\) 0 0
\(763\) 16.8226 + 288.833i 0.0220480 + 0.378549i
\(764\) 0 0
\(765\) 40.6575 302.461i 0.0531471 0.395374i
\(766\) 0 0
\(767\) −226.690 + 97.7846i −0.295554 + 0.127490i
\(768\) 0 0
\(769\) 1320.13 + 312.876i 1.71668 + 0.406861i 0.966967 0.254900i \(-0.0820426\pi\)
0.749715 + 0.661761i \(0.230191\pi\)
\(770\) 0 0
\(771\) −100.926 + 364.060i −0.130903 + 0.472192i
\(772\) 0 0
\(773\) 228.966 + 629.080i 0.296205 + 0.813816i 0.995125 + 0.0986170i \(0.0314419\pi\)
−0.698921 + 0.715199i \(0.746336\pi\)
\(774\) 0 0
\(775\) −1106.47 402.723i −1.42771 0.519643i
\(776\) 0 0
\(777\) −727.233 112.945i −0.935949 0.145360i
\(778\) 0 0
\(779\) 547.236 + 31.8729i 0.702485 + 0.0409151i
\(780\) 0 0
\(781\) −76.3779 80.9559i −0.0977950 0.103657i
\(782\) 0 0
\(783\) 782.178 586.197i 0.998950 0.748655i
\(784\) 0 0
\(785\) 276.148 + 82.6733i 0.351781 + 0.105316i
\(786\) 0 0
\(787\) −701.183 461.175i −0.890957 0.585991i 0.0194019 0.999812i \(-0.493824\pi\)
−0.910359 + 0.413820i \(0.864194\pi\)
\(788\) 0 0
\(789\) −360.388 + 7.37305i −0.456765 + 0.00934481i
\(790\) 0 0
\(791\) 438.533 77.3252i 0.554403 0.0977563i
\(792\) 0 0
\(793\) −141.148 + 800.490i −0.177992 + 1.00945i
\(794\) 0 0
\(795\) 51.5834 + 75.0392i 0.0648848 + 0.0943890i