Properties

Label 108.3.k.a.41.6
Level 108
Weight 3
Character 108.41
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 41.6
Character \(\chi\) \(=\) 108.41
Dual form 108.3.k.a.29.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.88785 - 0.812609i) q^{3} +(0.980262 - 1.16823i) q^{5} +(3.23920 + 1.17897i) q^{7} +(7.67933 - 4.69338i) q^{9} +O(q^{10})\) \(q+(2.88785 - 0.812609i) q^{3} +(0.980262 - 1.16823i) q^{5} +(3.23920 + 1.17897i) q^{7} +(7.67933 - 4.69338i) q^{9} +(-3.21124 - 3.82701i) q^{11} +(-0.778815 + 4.41688i) q^{13} +(1.88153 - 4.17024i) q^{15} +(-3.57252 - 2.06259i) q^{17} +(6.75637 + 11.7024i) q^{19} +(10.3124 + 0.772492i) q^{21} +(-5.79885 - 15.9322i) q^{23} +(3.93735 + 22.3298i) q^{25} +(18.3629 - 19.7941i) q^{27} +(-47.1200 + 8.30853i) q^{29} +(-14.3439 + 5.22075i) q^{31} +(-12.3834 - 8.44233i) q^{33} +(4.55258 - 2.62843i) q^{35} +(-32.3836 + 56.0901i) q^{37} +(1.34010 + 13.3882i) q^{39} +(-55.4020 - 9.76887i) q^{41} +(22.7258 - 19.0692i) q^{43} +(2.04481 - 13.5720i) q^{45} +(-7.04255 + 19.3493i) q^{47} +(-28.4337 - 23.8587i) q^{49} +(-11.9930 - 3.05340i) q^{51} +19.8596i q^{53} -7.61868 q^{55} +(29.0208 + 28.3044i) q^{57} +(63.6903 - 75.9031i) q^{59} +(77.5488 + 28.2255i) q^{61} +(30.4083 - 6.14908i) q^{63} +(4.39650 + 5.23954i) q^{65} +(11.2495 - 63.7992i) q^{67} +(-29.6928 - 41.2976i) q^{69} +(109.778 + 63.3803i) q^{71} +(18.0346 + 31.2369i) q^{73} +(29.5159 + 61.2857i) q^{75} +(-5.88991 - 16.1824i) q^{77} +(-14.4798 - 82.1188i) q^{79} +(36.9443 - 72.0841i) q^{81} +(-16.5506 + 2.91831i) q^{83} +(-5.91159 + 2.15164i) q^{85} +(-129.324 + 62.2839i) q^{87} +(66.0425 - 38.1296i) q^{89} +(-7.73012 + 13.3890i) q^{91} +(-37.1806 + 26.7327i) q^{93} +(20.2941 + 3.57840i) q^{95} +(82.1613 - 68.9415i) q^{97} +(-42.6218 - 14.3173i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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
\(3\) 2.88785 0.812609i 0.962616 0.270870i
\(4\) 0 0
\(5\) 0.980262 1.16823i 0.196052 0.233646i −0.659058 0.752092i \(-0.729045\pi\)
0.855110 + 0.518446i \(0.173489\pi\)
\(6\) 0 0
\(7\) 3.23920 + 1.17897i 0.462743 + 0.168425i 0.562862 0.826551i \(-0.309700\pi\)
−0.100119 + 0.994975i \(0.531922\pi\)
\(8\) 0 0
\(9\) 7.67933 4.69338i 0.853259 0.521487i
\(10\) 0 0
\(11\) −3.21124 3.82701i −0.291931 0.347910i 0.600067 0.799950i \(-0.295141\pi\)
−0.891997 + 0.452040i \(0.850696\pi\)
\(12\) 0 0
\(13\) −0.778815 + 4.41688i −0.0599089 + 0.339760i −0.999999 0.00116503i \(-0.999629\pi\)
0.940090 + 0.340925i \(0.110740\pi\)
\(14\) 0 0
\(15\) 1.88153 4.17024i 0.125436 0.278016i
\(16\) 0 0
\(17\) −3.57252 2.06259i −0.210148 0.121329i 0.391232 0.920292i \(-0.372049\pi\)
−0.601380 + 0.798963i \(0.705382\pi\)
\(18\) 0 0
\(19\) 6.75637 + 11.7024i 0.355599 + 0.615915i 0.987220 0.159362i \(-0.0509437\pi\)
−0.631622 + 0.775277i \(0.717610\pi\)
\(20\) 0 0
\(21\) 10.3124 + 0.772492i 0.491065 + 0.0367853i
\(22\) 0 0
\(23\) −5.79885 15.9322i −0.252124 0.692705i −0.999596 0.0284118i \(-0.990955\pi\)
0.747472 0.664293i \(-0.231267\pi\)
\(24\) 0 0
\(25\) 3.93735 + 22.3298i 0.157494 + 0.893194i
\(26\) 0 0
\(27\) 18.3629 19.7941i 0.680106 0.733114i
\(28\) 0 0
\(29\) −47.1200 + 8.30853i −1.62483 + 0.286501i −0.910562 0.413373i \(-0.864351\pi\)
−0.714267 + 0.699874i \(0.753240\pi\)
\(30\) 0 0
\(31\) −14.3439 + 5.22075i −0.462706 + 0.168411i −0.562845 0.826562i \(-0.690293\pi\)
0.100139 + 0.994973i \(0.468071\pi\)
\(32\) 0 0
\(33\) −12.3834 8.44233i −0.375255 0.255828i
\(34\) 0 0
\(35\) 4.55258 2.62843i 0.130074 0.0750981i
\(36\) 0 0
\(37\) −32.3836 + 56.0901i −0.875233 + 1.51595i −0.0187185 + 0.999825i \(0.505959\pi\)
−0.856514 + 0.516123i \(0.827375\pi\)
\(38\) 0 0
\(39\) 1.34010 + 13.3882i 0.0343614 + 0.343286i
\(40\) 0 0
\(41\) −55.4020 9.76887i −1.35127 0.238265i −0.549297 0.835627i \(-0.685104\pi\)
−0.801972 + 0.597362i \(0.796216\pi\)
\(42\) 0 0
\(43\) 22.7258 19.0692i 0.528507 0.443470i −0.339079 0.940758i \(-0.610115\pi\)
0.867585 + 0.497288i \(0.165671\pi\)
\(44\) 0 0
\(45\) 2.04481 13.5720i 0.0454402 0.301600i
\(46\) 0 0
\(47\) −7.04255 + 19.3493i −0.149842 + 0.411686i −0.991791 0.127870i \(-0.959186\pi\)
0.841949 + 0.539557i \(0.181408\pi\)
\(48\) 0 0
\(49\) −28.4337 23.8587i −0.580280 0.486913i
\(50\) 0 0
\(51\) −11.9930 3.05340i −0.235156 0.0598706i
\(52\) 0 0
\(53\) 19.8596i 0.374710i 0.982292 + 0.187355i \(0.0599915\pi\)
−0.982292 + 0.187355i \(0.940009\pi\)
\(54\) 0 0
\(55\) −7.61868 −0.138522
\(56\) 0 0
\(57\) 29.0208 + 28.3044i 0.509138 + 0.496569i
\(58\) 0 0
\(59\) 63.6903 75.9031i 1.07950 1.28649i 0.123746 0.992314i \(-0.460509\pi\)
0.955750 0.294179i \(-0.0950463\pi\)
\(60\) 0 0
\(61\) 77.5488 + 28.2255i 1.27129 + 0.462713i 0.887543 0.460725i \(-0.152411\pi\)
0.383749 + 0.923437i \(0.374633\pi\)
\(62\) 0 0
\(63\) 30.4083 6.14908i 0.482671 0.0976044i
\(64\) 0 0
\(65\) 4.39650 + 5.23954i 0.0676384 + 0.0806083i
\(66\) 0 0
\(67\) 11.2495 63.7992i 0.167903 0.952226i −0.778117 0.628119i \(-0.783825\pi\)
0.946020 0.324107i \(-0.105064\pi\)
\(68\) 0 0
\(69\) −29.6928 41.2976i −0.430331 0.598516i
\(70\) 0 0
\(71\) 109.778 + 63.3803i 1.54617 + 0.892680i 0.998429 + 0.0560292i \(0.0178440\pi\)
0.547737 + 0.836650i \(0.315489\pi\)
\(72\) 0 0
\(73\) 18.0346 + 31.2369i 0.247049 + 0.427902i 0.962706 0.270550i \(-0.0872057\pi\)
−0.715656 + 0.698453i \(0.753872\pi\)
\(74\) 0 0
\(75\) 29.5159 + 61.2857i 0.393545 + 0.817142i
\(76\) 0 0
\(77\) −5.88991 16.1824i −0.0764924 0.210161i
\(78\) 0 0
\(79\) −14.4798 82.1188i −0.183288 1.03948i −0.928135 0.372243i \(-0.878589\pi\)
0.744847 0.667235i \(-0.232522\pi\)
\(80\) 0 0
\(81\) 36.9443 72.0841i 0.456103 0.889927i
\(82\) 0 0
\(83\) −16.5506 + 2.91831i −0.199404 + 0.0351604i −0.272458 0.962168i \(-0.587837\pi\)
0.0730538 + 0.997328i \(0.476726\pi\)
\(84\) 0 0
\(85\) −5.91159 + 2.15164i −0.0695481 + 0.0253135i
\(86\) 0 0
\(87\) −129.324 + 62.2839i −1.48648 + 0.715907i
\(88\) 0 0
\(89\) 66.0425 38.1296i 0.742050 0.428423i −0.0807640 0.996733i \(-0.525736\pi\)
0.822814 + 0.568310i \(0.192403\pi\)
\(90\) 0 0
\(91\) −7.73012 + 13.3890i −0.0849464 + 0.147132i
\(92\) 0 0
\(93\) −37.1806 + 26.7327i −0.399791 + 0.287448i
\(94\) 0 0
\(95\) 20.2941 + 3.57840i 0.213622 + 0.0376674i
\(96\) 0 0
\(97\) 82.1613 68.9415i 0.847023 0.710737i −0.112109 0.993696i \(-0.535761\pi\)
0.959132 + 0.282959i \(0.0913161\pi\)
\(98\) 0 0
\(99\) −42.6218 14.3173i −0.430523 0.144619i
\(100\) 0 0
\(101\) −38.6196 + 106.106i −0.382372 + 1.05056i 0.587982 + 0.808874i \(0.299922\pi\)
−0.970355 + 0.241685i \(0.922300\pi\)
\(102\) 0 0
\(103\) −110.992 93.1334i −1.07759 0.904208i −0.0818743 0.996643i \(-0.526091\pi\)
−0.995719 + 0.0924347i \(0.970535\pi\)
\(104\) 0 0
\(105\) 11.0113 11.2900i 0.104869 0.107524i
\(106\) 0 0
\(107\) 90.9102i 0.849628i 0.905281 + 0.424814i \(0.139661\pi\)
−0.905281 + 0.424814i \(0.860339\pi\)
\(108\) 0 0
\(109\) −44.2294 −0.405774 −0.202887 0.979202i \(-0.565032\pi\)
−0.202887 + 0.979202i \(0.565032\pi\)
\(110\) 0 0
\(111\) −47.9397 + 188.295i −0.431889 + 1.69635i
\(112\) 0 0
\(113\) 92.3757 110.089i 0.817484 0.974240i −0.182476 0.983210i \(-0.558411\pi\)
0.999960 + 0.00897066i \(0.00285549\pi\)
\(114\) 0 0
\(115\) −24.2969 8.84335i −0.211277 0.0768987i
\(116\) 0 0
\(117\) 14.7493 + 37.5740i 0.126063 + 0.321145i
\(118\) 0 0
\(119\) −9.14036 10.8931i −0.0768098 0.0915383i
\(120\) 0 0
\(121\) 16.6775 94.5829i 0.137831 0.781677i
\(122\) 0 0
\(123\) −167.931 + 16.8091i −1.36529 + 0.136660i
\(124\) 0 0
\(125\) 62.9637 + 36.3521i 0.503709 + 0.290817i
\(126\) 0 0
\(127\) −18.8346 32.6225i −0.148304 0.256870i 0.782297 0.622906i \(-0.214048\pi\)
−0.930601 + 0.366036i \(0.880715\pi\)
\(128\) 0 0
\(129\) 50.1328 73.5361i 0.388626 0.570047i
\(130\) 0 0
\(131\) 52.3965 + 143.958i 0.399973 + 1.09892i 0.962297 + 0.272001i \(0.0876853\pi\)
−0.562324 + 0.826917i \(0.690093\pi\)
\(132\) 0 0
\(133\) 8.08846 + 45.8720i 0.0608155 + 0.344902i
\(134\) 0 0
\(135\) −5.12362 40.8555i −0.0379527 0.302633i
\(136\) 0 0
\(137\) −58.4666 + 10.3092i −0.426764 + 0.0752499i −0.382905 0.923788i \(-0.625076\pi\)
−0.0438588 + 0.999038i \(0.513965\pi\)
\(138\) 0 0
\(139\) −56.3970 + 20.5268i −0.405734 + 0.147675i −0.536822 0.843696i \(-0.680375\pi\)
0.131088 + 0.991371i \(0.458153\pi\)
\(140\) 0 0
\(141\) −4.61445 + 61.6006i −0.0327266 + 0.436883i
\(142\) 0 0
\(143\) 19.4044 11.2031i 0.135695 0.0783436i
\(144\) 0 0
\(145\) −36.4837 + 63.1916i −0.251612 + 0.435804i
\(146\) 0 0
\(147\) −101.500 45.7949i −0.690477 0.311530i
\(148\) 0 0
\(149\) −264.707 46.6751i −1.77656 0.313255i −0.813304 0.581839i \(-0.802333\pi\)
−0.963256 + 0.268584i \(0.913444\pi\)
\(150\) 0 0
\(151\) 9.35126 7.84664i 0.0619289 0.0519645i −0.611298 0.791401i \(-0.709352\pi\)
0.673227 + 0.739436i \(0.264908\pi\)
\(152\) 0 0
\(153\) −37.1151 + 0.927838i −0.242582 + 0.00606430i
\(154\) 0 0
\(155\) −7.96173 + 21.8747i −0.0513660 + 0.141127i
\(156\) 0 0
\(157\) −34.5963 29.0297i −0.220359 0.184903i 0.525925 0.850531i \(-0.323719\pi\)
−0.746284 + 0.665628i \(0.768164\pi\)
\(158\) 0 0
\(159\) 16.1381 + 57.3516i 0.101498 + 0.360702i
\(160\) 0 0
\(161\) 58.4443i 0.363008i
\(162\) 0 0
\(163\) 5.88721 0.0361178 0.0180589 0.999837i \(-0.494251\pi\)
0.0180589 + 0.999837i \(0.494251\pi\)
\(164\) 0 0
\(165\) −22.0016 + 6.19101i −0.133343 + 0.0375213i
\(166\) 0 0
\(167\) 143.168 170.621i 0.857294 1.02168i −0.142198 0.989838i \(-0.545417\pi\)
0.999493 0.0318455i \(-0.0101384\pi\)
\(168\) 0 0
\(169\) 139.906 + 50.9215i 0.827845 + 0.301311i
\(170\) 0 0
\(171\) 106.808 + 58.1563i 0.624609 + 0.340095i
\(172\) 0 0
\(173\) 16.4944 + 19.6573i 0.0953434 + 0.113626i 0.811607 0.584204i \(-0.198593\pi\)
−0.716263 + 0.697830i \(0.754149\pi\)
\(174\) 0 0
\(175\) −13.5724 + 76.9729i −0.0775566 + 0.439845i
\(176\) 0 0
\(177\) 122.248 270.952i 0.690668 1.53080i
\(178\) 0 0
\(179\) −67.7828 39.1344i −0.378675 0.218628i 0.298567 0.954389i \(-0.403492\pi\)
−0.677242 + 0.735761i \(0.736825\pi\)
\(180\) 0 0
\(181\) 72.1634 + 124.991i 0.398693 + 0.690557i 0.993565 0.113264i \(-0.0361306\pi\)
−0.594872 + 0.803821i \(0.702797\pi\)
\(182\) 0 0
\(183\) 246.885 + 18.4940i 1.34910 + 0.101060i
\(184\) 0 0
\(185\) 33.7817 + 92.8145i 0.182604 + 0.501700i
\(186\) 0 0
\(187\) 3.57865 + 20.2955i 0.0191372 + 0.108532i
\(188\) 0 0
\(189\) 82.8177 42.4676i 0.438189 0.224697i
\(190\) 0 0
\(191\) 109.649 19.3342i 0.574081 0.101226i 0.120932 0.992661i \(-0.461412\pi\)
0.453149 + 0.891435i \(0.350301\pi\)
\(192\) 0 0
\(193\) 90.9049 33.0867i 0.471010 0.171434i −0.0955998 0.995420i \(-0.530477\pi\)
0.566610 + 0.823986i \(0.308255\pi\)
\(194\) 0 0
\(195\) 16.9541 + 11.5584i 0.0869441 + 0.0592737i
\(196\) 0 0
\(197\) 12.0311 6.94615i 0.0610715 0.0352596i −0.469153 0.883117i \(-0.655441\pi\)
0.530225 + 0.847857i \(0.322108\pi\)
\(198\) 0 0
\(199\) 77.7745 134.709i 0.390827 0.676932i −0.601732 0.798698i \(-0.705522\pi\)
0.992559 + 0.121766i \(0.0388558\pi\)
\(200\) 0 0
\(201\) −19.3569 193.384i −0.0963028 0.962108i
\(202\) 0 0
\(203\) −162.427 28.6402i −0.800132 0.141085i
\(204\) 0 0
\(205\) −65.7208 + 55.1463i −0.320589 + 0.269006i
\(206\) 0 0
\(207\) −119.307 95.1325i −0.576363 0.459577i
\(208\) 0 0
\(209\) 23.0888 63.4358i 0.110473 0.303521i
\(210\) 0 0
\(211\) 285.417 + 239.493i 1.35269 + 1.13504i 0.978167 + 0.207821i \(0.0666370\pi\)
0.374520 + 0.927219i \(0.377807\pi\)
\(212\) 0 0
\(213\) 368.525 + 93.8261i 1.73016 + 0.440498i
\(214\) 0 0
\(215\) 45.2418i 0.210427i
\(216\) 0 0
\(217\) −52.6179 −0.242479
\(218\) 0 0
\(219\) 77.4646 + 75.5522i 0.353719 + 0.344987i
\(220\) 0 0
\(221\) 11.8926 14.1730i 0.0538125 0.0641313i
\(222\) 0 0
\(223\) −256.023 93.1848i −1.14809 0.417869i −0.303259 0.952908i \(-0.598075\pi\)
−0.844827 + 0.535039i \(0.820297\pi\)
\(224\) 0 0
\(225\) 135.039 + 152.999i 0.600172 + 0.679995i
\(226\) 0 0
\(227\) −186.342 222.073i −0.820888 0.978296i 0.179097 0.983831i \(-0.442682\pi\)
−0.999985 + 0.00553531i \(0.998238\pi\)
\(228\) 0 0
\(229\) −24.8927 + 141.173i −0.108702 + 0.616478i 0.880975 + 0.473162i \(0.156888\pi\)
−0.989677 + 0.143316i \(0.954224\pi\)
\(230\) 0 0
\(231\) −30.1591 41.9461i −0.130559 0.181585i
\(232\) 0 0
\(233\) −244.086 140.923i −1.04758 0.604819i −0.125607 0.992080i \(-0.540088\pi\)
−0.921970 + 0.387261i \(0.873421\pi\)
\(234\) 0 0
\(235\) 15.7009 + 27.1947i 0.0668122 + 0.115722i
\(236\) 0 0
\(237\) −108.546 225.380i −0.457999 0.950971i
\(238\) 0 0
\(239\) 132.471 + 363.961i 0.554271 + 1.52285i 0.827823 + 0.560990i \(0.189579\pi\)
−0.273551 + 0.961857i \(0.588198\pi\)
\(240\) 0 0
\(241\) 33.2184 + 188.391i 0.137836 + 0.781705i 0.972843 + 0.231466i \(0.0743522\pi\)
−0.835007 + 0.550239i \(0.814537\pi\)
\(242\) 0 0
\(243\) 48.1135 238.189i 0.197998 0.980202i
\(244\) 0 0
\(245\) −55.7450 + 9.82935i −0.227531 + 0.0401198i
\(246\) 0 0
\(247\) −56.9500 + 20.7281i −0.230567 + 0.0839195i
\(248\) 0 0
\(249\) −45.4240 + 21.8768i −0.182426 + 0.0878585i
\(250\) 0 0
\(251\) −377.425 + 217.906i −1.50368 + 0.868153i −0.503693 + 0.863882i \(0.668026\pi\)
−0.999991 + 0.00427006i \(0.998641\pi\)
\(252\) 0 0
\(253\) −42.3512 + 73.3543i −0.167396 + 0.289938i
\(254\) 0 0
\(255\) −15.3233 + 11.0174i −0.0600915 + 0.0432056i
\(256\) 0 0
\(257\) −412.498 72.7345i −1.60505 0.283014i −0.701880 0.712295i \(-0.747656\pi\)
−0.903171 + 0.429281i \(0.858767\pi\)
\(258\) 0 0
\(259\) −171.026 + 143.508i −0.660331 + 0.554084i
\(260\) 0 0
\(261\) −322.855 + 284.956i −1.23699 + 1.09179i
\(262\) 0 0
\(263\) 113.154 310.887i 0.430242 1.18208i −0.515423 0.856936i \(-0.672365\pi\)
0.945665 0.325144i \(-0.105413\pi\)
\(264\) 0 0
\(265\) 23.2006 + 19.4676i 0.0875496 + 0.0734628i
\(266\) 0 0
\(267\) 159.736 163.779i 0.598263 0.613406i
\(268\) 0 0
\(269\) 136.569i 0.507690i −0.967245 0.253845i \(-0.918305\pi\)
0.967245 0.253845i \(-0.0816953\pi\)
\(270\) 0 0
\(271\) 170.355 0.628615 0.314307 0.949321i \(-0.398228\pi\)
0.314307 + 0.949321i \(0.398228\pi\)
\(272\) 0 0
\(273\) −11.4434 + 44.9469i −0.0419173 + 0.164641i
\(274\) 0 0
\(275\) 72.8127 86.7748i 0.264773 0.315545i
\(276\) 0 0
\(277\) −125.607 45.7173i −0.453456 0.165044i 0.105188 0.994452i \(-0.466456\pi\)
−0.558643 + 0.829408i \(0.688678\pi\)
\(278\) 0 0
\(279\) −85.6486 + 107.413i −0.306984 + 0.384994i
\(280\) 0 0
\(281\) 291.841 + 347.803i 1.03858 + 1.23773i 0.970764 + 0.240034i \(0.0771587\pi\)
0.0678161 + 0.997698i \(0.478397\pi\)
\(282\) 0 0
\(283\) −67.6428 + 383.621i −0.239020 + 1.35555i 0.594959 + 0.803756i \(0.297168\pi\)
−0.833979 + 0.551796i \(0.813943\pi\)
\(284\) 0 0
\(285\) 61.5141 6.15730i 0.215839 0.0216045i
\(286\) 0 0
\(287\) −167.941 96.9608i −0.585161 0.337843i
\(288\) 0 0
\(289\) −135.991 235.544i −0.470559 0.815031i
\(290\) 0 0
\(291\) 181.247 265.857i 0.622841 0.913600i
\(292\) 0 0
\(293\) 116.307 + 319.550i 0.396951 + 1.09061i 0.963762 + 0.266765i \(0.0859548\pi\)
−0.566811 + 0.823848i \(0.691823\pi\)
\(294\) 0 0
\(295\) −26.2392 148.810i −0.0889465 0.504440i
\(296\) 0 0
\(297\) −134.720 6.71133i −0.453601 0.0225971i
\(298\) 0 0
\(299\) 74.8869 13.2046i 0.250458 0.0441625i
\(300\) 0 0
\(301\) 96.0954 34.9759i 0.319254 0.116199i
\(302\) 0 0
\(303\) −25.3045 + 337.802i −0.0835132 + 1.11486i
\(304\) 0 0
\(305\) 108.992 62.9266i 0.357351 0.206317i
\(306\) 0 0
\(307\) 232.919 403.428i 0.758695 1.31410i −0.184822 0.982772i \(-0.559171\pi\)
0.943516 0.331326i \(-0.107496\pi\)
\(308\) 0 0
\(309\) −396.209 178.762i −1.28223 0.578518i
\(310\) 0 0
\(311\) 82.0156 + 14.4616i 0.263716 + 0.0465002i 0.303942 0.952690i \(-0.401697\pi\)
−0.0402268 + 0.999191i \(0.512808\pi\)
\(312\) 0 0
\(313\) −213.260 + 178.947i −0.681343 + 0.571714i −0.916398 0.400268i \(-0.868917\pi\)
0.235056 + 0.971982i \(0.424473\pi\)
\(314\) 0 0
\(315\) 22.6245 41.5516i 0.0718240 0.131910i
\(316\) 0 0
\(317\) 56.6181 155.557i 0.178606 0.490716i −0.817792 0.575513i \(-0.804802\pi\)
0.996398 + 0.0847979i \(0.0270245\pi\)
\(318\) 0 0
\(319\) 183.110 + 153.648i 0.574014 + 0.481655i
\(320\) 0 0
\(321\) 73.8744 + 262.535i 0.230138 + 0.817866i
\(322\) 0 0
\(323\) 55.7426i 0.172578i
\(324\) 0 0
\(325\) −101.695 −0.312907
\(326\) 0 0
\(327\) −127.728 + 35.9412i −0.390605 + 0.109912i
\(328\) 0 0
\(329\) −45.6245 + 54.3732i −0.138676 + 0.165268i
\(330\) 0 0
\(331\) −10.7745 3.92161i −0.0325515 0.0118478i 0.325693 0.945476i \(-0.394402\pi\)
−0.358245 + 0.933628i \(0.616625\pi\)
\(332\) 0 0
\(333\) 14.5675 + 582.723i 0.0437461 + 1.74992i
\(334\) 0 0
\(335\) −63.5047 75.6819i −0.189566 0.225916i
\(336\) 0 0
\(337\) 70.1777 397.997i 0.208242 1.18100i −0.684013 0.729470i \(-0.739767\pi\)
0.892255 0.451531i \(-0.149122\pi\)
\(338\) 0 0
\(339\) 177.308 392.986i 0.523032 1.15925i
\(340\) 0 0
\(341\) 66.0415 + 38.1291i 0.193670 + 0.111815i
\(342\) 0 0
\(343\) −148.427 257.084i −0.432733 0.749515i
\(344\) 0 0
\(345\) −77.3519 5.79437i −0.224208 0.0167953i
\(346\) 0 0
\(347\) 182.542 + 501.529i 0.526057 + 1.44533i 0.863676 + 0.504047i \(0.168156\pi\)
−0.337620 + 0.941283i \(0.609622\pi\)
\(348\) 0 0
\(349\) −40.5969 230.237i −0.116324 0.659704i −0.986086 0.166234i \(-0.946839\pi\)
0.869763 0.493470i \(-0.164272\pi\)
\(350\) 0 0
\(351\) 73.1268 + 96.5225i 0.208338 + 0.274993i
\(352\) 0 0
\(353\) 486.656 85.8106i 1.37863 0.243090i 0.565297 0.824888i \(-0.308762\pi\)
0.813333 + 0.581798i \(0.197651\pi\)
\(354\) 0 0
\(355\) 181.654 66.1166i 0.511701 0.186244i
\(356\) 0 0
\(357\) −35.2478 24.0300i −0.0987333 0.0673108i
\(358\) 0 0
\(359\) 46.1066 26.6196i 0.128431 0.0741494i −0.434408 0.900716i \(-0.643042\pi\)
0.562839 + 0.826567i \(0.309709\pi\)
\(360\) 0 0
\(361\) 89.2028 154.504i 0.247099 0.427988i
\(362\) 0 0
\(363\) −28.6967 286.693i −0.0790544 0.789789i
\(364\) 0 0
\(365\) 54.1705 + 9.55172i 0.148412 + 0.0261691i
\(366\) 0 0
\(367\) −51.6382 + 43.3296i −0.140704 + 0.118064i −0.710423 0.703775i \(-0.751496\pi\)
0.569719 + 0.821839i \(0.307052\pi\)
\(368\) 0 0
\(369\) −471.300 + 185.004i −1.27724 + 0.501367i
\(370\) 0 0
\(371\) −23.4140 + 64.3293i −0.0631104 + 0.173394i
\(372\) 0 0
\(373\) −138.334 116.076i −0.370868 0.311195i 0.438237 0.898860i \(-0.355603\pi\)
−0.809105 + 0.587664i \(0.800048\pi\)
\(374\) 0 0
\(375\) 211.370 + 53.8145i 0.563652 + 0.143505i
\(376\) 0 0
\(377\) 214.594i 0.569216i
\(378\) 0 0
\(379\) 609.218 1.60743 0.803717 0.595011i \(-0.202852\pi\)
0.803717 + 0.595011i \(0.202852\pi\)
\(380\) 0 0
\(381\) −80.9007 78.9036i −0.212338 0.207096i
\(382\) 0 0
\(383\) 220.984 263.359i 0.576983 0.687622i −0.396065 0.918222i \(-0.629625\pi\)
0.973048 + 0.230601i \(0.0740691\pi\)
\(384\) 0 0
\(385\) −24.6785 8.98222i −0.0640999 0.0233304i
\(386\) 0 0
\(387\) 85.0199 253.099i 0.219690 0.654004i
\(388\) 0 0
\(389\) 314.120 + 374.354i 0.807507 + 0.962349i 0.999820 0.0189843i \(-0.00604325\pi\)
−0.192313 + 0.981334i \(0.561599\pi\)
\(390\) 0 0
\(391\) −12.1452 + 68.8788i −0.0310619 + 0.176161i
\(392\) 0 0
\(393\) 268.295 + 373.152i 0.682684 + 0.949495i
\(394\) 0 0
\(395\) −110.128 63.5822i −0.278804 0.160968i
\(396\) 0 0
\(397\) −185.104 320.610i −0.466258 0.807582i 0.533000 0.846115i \(-0.321065\pi\)
−0.999257 + 0.0385336i \(0.987731\pi\)
\(398\) 0 0
\(399\) 60.6342 + 125.898i 0.151965 + 0.315535i
\(400\) 0 0
\(401\) 182.815 + 502.279i 0.455897 + 1.25257i 0.928514 + 0.371298i \(0.121087\pi\)
−0.472617 + 0.881268i \(0.656691\pi\)
\(402\) 0 0
\(403\) −11.8882 67.4213i −0.0294992 0.167298i
\(404\) 0 0
\(405\) −47.9957 113.821i −0.118508 0.281039i
\(406\) 0 0
\(407\) 318.649 56.1863i 0.782920 0.138050i
\(408\) 0 0
\(409\) 137.720 50.1258i 0.336723 0.122557i −0.168125 0.985766i \(-0.553771\pi\)
0.504847 + 0.863209i \(0.331549\pi\)
\(410\) 0 0
\(411\) −160.465 + 77.2820i −0.390427 + 0.188034i
\(412\) 0 0
\(413\) 295.793 170.776i 0.716207 0.413502i
\(414\) 0 0
\(415\) −12.8146 + 22.1956i −0.0308786 + 0.0534833i
\(416\) 0 0
\(417\) −146.186 + 105.107i −0.350565 + 0.252055i
\(418\) 0 0
\(419\) −197.145 34.7619i −0.470512 0.0829640i −0.0666354 0.997777i \(-0.521226\pi\)
−0.403877 + 0.914813i \(0.632338\pi\)
\(420\) 0 0
\(421\) 337.985 283.603i 0.802815 0.673641i −0.146067 0.989275i \(-0.546661\pi\)
0.948881 + 0.315633i \(0.102217\pi\)
\(422\) 0 0
\(423\) 36.7313 + 181.643i 0.0868353 + 0.429416i
\(424\) 0 0
\(425\) 31.9911 87.8950i 0.0752733 0.206812i
\(426\) 0 0
\(427\) 217.919 + 182.856i 0.510349 + 0.428234i
\(428\) 0 0
\(429\) 46.9332 48.1211i 0.109401 0.112170i
\(430\) 0 0
\(431\) 474.920i 1.10190i 0.834537 + 0.550951i \(0.185735\pi\)
−0.834537 + 0.550951i \(0.814265\pi\)
\(432\) 0 0
\(433\) −540.928 −1.24926 −0.624628 0.780922i \(-0.714749\pi\)
−0.624628 + 0.780922i \(0.714749\pi\)
\(434\) 0 0
\(435\) −54.0093 + 212.135i −0.124159 + 0.487666i
\(436\) 0 0
\(437\) 147.266 175.504i 0.336992 0.401612i
\(438\) 0 0
\(439\) −615.853 224.152i −1.40285 0.510597i −0.473831 0.880616i \(-0.657129\pi\)
−0.929024 + 0.370019i \(0.879351\pi\)
\(440\) 0 0
\(441\) −330.330 49.7688i −0.749048 0.112855i
\(442\) 0 0
\(443\) −461.210 549.649i −1.04111 1.24074i −0.969957 0.243277i \(-0.921777\pi\)
−0.0711502 0.997466i \(-0.522667\pi\)
\(444\) 0 0
\(445\) 20.1947 114.530i 0.0453814 0.257371i
\(446\) 0 0
\(447\) −802.363 + 80.3131i −1.79500 + 0.179671i
\(448\) 0 0
\(449\) 118.270 + 68.2833i 0.263408 + 0.152079i 0.625888 0.779913i \(-0.284737\pi\)
−0.362480 + 0.931991i \(0.618070\pi\)
\(450\) 0 0
\(451\) 140.524 + 243.394i 0.311582 + 0.539676i
\(452\) 0 0
\(453\) 20.6288 30.2588i 0.0455381 0.0667965i
\(454\) 0 0
\(455\) 8.06386 + 22.1553i 0.0177228 + 0.0486929i
\(456\) 0 0
\(457\) 43.5634 + 247.060i 0.0953247 + 0.540613i 0.994647 + 0.103327i \(0.0329490\pi\)
−0.899323 + 0.437286i \(0.855940\pi\)
\(458\) 0 0
\(459\) −106.429 + 32.8395i −0.231871 + 0.0715458i
\(460\) 0 0
\(461\) −227.426 + 40.1013i −0.493331 + 0.0869876i −0.414779 0.909922i \(-0.636141\pi\)
−0.0785527 + 0.996910i \(0.525030\pi\)
\(462\) 0 0
\(463\) −418.337 + 152.262i −0.903535 + 0.328860i −0.751669 0.659541i \(-0.770751\pi\)
−0.151867 + 0.988401i \(0.548528\pi\)
\(464\) 0 0
\(465\) −5.21672 + 69.6405i −0.0112188 + 0.149765i
\(466\) 0 0
\(467\) −515.922 + 297.868i −1.10476 + 0.637833i −0.937467 0.348075i \(-0.886836\pi\)
−0.167292 + 0.985907i \(0.553502\pi\)
\(468\) 0 0
\(469\) 111.657 193.395i 0.238074 0.412357i
\(470\) 0 0
\(471\) −123.499 55.7202i −0.262205 0.118302i
\(472\) 0 0
\(473\) −145.956 25.7360i −0.308575 0.0544100i
\(474\) 0 0
\(475\) −234.710 + 196.945i −0.494127 + 0.414622i
\(476\) 0 0
\(477\) 93.2088 + 152.509i 0.195406 + 0.319725i
\(478\) 0 0
\(479\) −112.035 + 307.814i −0.233894 + 0.642618i −1.00000 9.59229e-5i \(-0.999969\pi\)
0.766106 + 0.642714i \(0.222192\pi\)
\(480\) 0 0
\(481\) −222.522 186.718i −0.462624 0.388188i
\(482\) 0 0
\(483\) −47.4924 168.778i −0.0983279 0.349437i
\(484\) 0 0
\(485\) 163.564i 0.337245i
\(486\) 0 0
\(487\) −39.4271 −0.0809592 −0.0404796 0.999180i \(-0.512889\pi\)
−0.0404796 + 0.999180i \(0.512889\pi\)
\(488\) 0 0
\(489\) 17.0014 4.78400i 0.0347676 0.00978322i
\(490\) 0 0
\(491\) −209.908 + 250.158i −0.427510 + 0.509487i −0.936202 0.351462i \(-0.885685\pi\)
0.508692 + 0.860949i \(0.330129\pi\)
\(492\) 0 0
\(493\) 185.474 + 67.5071i 0.376216 + 0.136931i
\(494\) 0 0
\(495\) −58.5064 + 35.7574i −0.118195 + 0.0722371i
\(496\) 0 0
\(497\) 280.869 + 334.726i 0.565128 + 0.673494i
\(498\) 0 0
\(499\) −77.0969 + 437.238i −0.154503 + 0.876229i 0.804736 + 0.593633i \(0.202307\pi\)
−0.959239 + 0.282596i \(0.908804\pi\)
\(500\) 0 0
\(501\) 274.800 609.068i 0.548502 1.21570i
\(502\) 0 0
\(503\) −248.594 143.526i −0.494223 0.285340i 0.232102 0.972692i \(-0.425440\pi\)
−0.726325 + 0.687352i \(0.758773\pi\)
\(504\) 0 0
\(505\) 86.0996 + 149.129i 0.170494 + 0.295305i
\(506\) 0 0
\(507\) 445.406 + 33.3650i 0.878513 + 0.0658087i
\(508\) 0 0
\(509\) −278.163 764.247i −0.546489 1.50147i −0.838418 0.545027i \(-0.816519\pi\)
0.291929 0.956440i \(-0.405703\pi\)
\(510\) 0 0
\(511\) 21.5903 + 122.445i 0.0422511 + 0.239618i
\(512\) 0 0
\(513\) 355.704 + 81.1532i 0.693380 + 0.158193i
\(514\) 0 0
\(515\) −217.603 + 38.3692i −0.422530 + 0.0745034i
\(516\) 0 0
\(517\) 96.6650 35.1832i 0.186973 0.0680526i
\(518\) 0 0
\(519\) 63.6070 + 43.3637i 0.122557 + 0.0835524i
\(520\) 0 0
\(521\) −17.1141 + 9.88086i −0.0328486 + 0.0189652i −0.516334 0.856387i \(-0.672704\pi\)
0.483486 + 0.875352i \(0.339370\pi\)
\(522\) 0 0
\(523\) −342.155 + 592.630i −0.654216 + 1.13313i 0.327874 + 0.944721i \(0.393668\pi\)
−0.982090 + 0.188413i \(0.939666\pi\)
\(524\) 0 0
\(525\) 23.3538 + 233.315i 0.0444835 + 0.444410i
\(526\) 0 0
\(527\) 62.0121 + 10.9344i 0.117670 + 0.0207484i
\(528\) 0 0
\(529\) 185.029 155.258i 0.349771 0.293493i
\(530\) 0 0
\(531\) 132.857 881.808i 0.250201 1.66066i
\(532\) 0 0
\(533\) 86.2959 237.096i 0.161906 0.444833i
\(534\) 0 0
\(535\) 106.204 + 89.1159i 0.198512 + 0.166572i
\(536\) 0 0
\(537\) −227.548 57.9334i −0.423738 0.107883i
\(538\) 0 0
\(539\) 185.432i 0.344030i
\(540\) 0 0
\(541\) 283.876 0.524724 0.262362 0.964970i \(-0.415499\pi\)
0.262362 + 0.964970i \(0.415499\pi\)
\(542\) 0 0
\(543\) 309.966 + 302.314i 0.570839 + 0.556747i
\(544\) 0 0
\(545\) −43.3564 + 51.6702i −0.0795531 + 0.0948077i
\(546\) 0 0
\(547\) 681.270 + 247.962i 1.24547 + 0.453312i 0.878867 0.477067i \(-0.158300\pi\)
0.366598 + 0.930379i \(0.380522\pi\)
\(548\) 0 0
\(549\) 727.996 147.213i 1.32604 0.268148i
\(550\) 0 0
\(551\) −415.590 495.281i −0.754247 0.898877i
\(552\) 0 0
\(553\) 49.9130 283.071i 0.0902585 0.511882i
\(554\) 0 0
\(555\) 172.978 + 240.583i 0.311673 + 0.433483i
\(556\) 0 0
\(557\) 637.275 + 367.931i 1.14412 + 0.660558i 0.947448 0.319911i \(-0.103653\pi\)
0.196672 + 0.980469i \(0.436986\pi\)
\(558\) 0 0
\(559\) 66.5272 + 115.228i 0.119011 + 0.206133i
\(560\) 0 0
\(561\) 26.8269 + 55.7024i 0.0478198 + 0.0992912i
\(562\) 0 0
\(563\) −264.958 727.966i −0.470618 1.29301i −0.917256 0.398298i \(-0.869601\pi\)
0.446638 0.894715i \(-0.352621\pi\)
\(564\) 0 0
\(565\) −38.0571 215.832i −0.0673576 0.382004i
\(566\) 0 0
\(567\) 204.655 189.938i 0.360944 0.334989i
\(568\) 0 0
\(569\) −649.361 + 114.500i −1.14123 + 0.201230i −0.712144 0.702033i \(-0.752276\pi\)
−0.429087 + 0.903263i \(0.641165\pi\)
\(570\) 0 0
\(571\) 96.2986 35.0498i 0.168649 0.0613832i −0.256316 0.966593i \(-0.582509\pi\)
0.424965 + 0.905210i \(0.360286\pi\)
\(572\) 0 0
\(573\) 300.940 144.936i 0.525200 0.252943i
\(574\) 0 0
\(575\) 332.932 192.218i 0.579012 0.334292i
\(576\) 0 0
\(577\) −474.467 + 821.801i −0.822300 + 1.42426i 0.0816661 + 0.996660i \(0.473976\pi\)
−0.903966 + 0.427605i \(0.859357\pi\)
\(578\) 0 0
\(579\) 235.633 169.419i 0.406966 0.292607i
\(580\) 0 0
\(581\) −57.0512 10.0597i −0.0981948 0.0173144i
\(582\) 0 0
\(583\) 76.0029 63.7740i 0.130365 0.109389i
\(584\) 0 0
\(585\) 58.3533 + 19.6017i 0.0997492 + 0.0335073i
\(586\) 0 0
\(587\) −286.142 + 786.168i −0.487465 + 1.33930i 0.415504 + 0.909591i \(0.363605\pi\)
−0.902968 + 0.429707i \(0.858617\pi\)
\(588\) 0 0
\(589\) −158.008 132.584i −0.268265 0.225101i
\(590\) 0 0
\(591\) 29.0994 29.8360i 0.0492376 0.0504839i
\(592\) 0 0
\(593\) 485.118i 0.818075i −0.912518 0.409037i \(-0.865865\pi\)
0.912518 0.409037i \(-0.134135\pi\)
\(594\) 0 0
\(595\) −21.6856 −0.0364463
\(596\) 0 0
\(597\) 115.135 452.221i 0.192856 0.757488i
\(598\) 0 0
\(599\) 190.110 226.565i 0.317380 0.378238i −0.583643 0.812010i \(-0.698373\pi\)
0.901023 + 0.433772i \(0.142818\pi\)
\(600\) 0 0
\(601\) 642.355 + 233.798i 1.06881 + 0.389015i 0.815732 0.578431i \(-0.196335\pi\)
0.253079 + 0.967446i \(0.418557\pi\)
\(602\) 0 0
\(603\) −213.045 542.733i −0.353308 0.900055i
\(604\) 0 0
\(605\) −94.1463 112.199i −0.155614 0.185453i
\(606\) 0 0
\(607\) 27.7719 157.502i 0.0457527 0.259476i −0.953348 0.301873i \(-0.902388\pi\)
0.999101 + 0.0423966i \(0.0134993\pi\)
\(608\) 0 0
\(609\) −492.337 + 49.2808i −0.808436 + 0.0809209i
\(610\) 0 0
\(611\) −79.9785 46.1756i −0.130898 0.0755739i
\(612\) 0 0
\(613\) 370.587 + 641.875i 0.604546 + 1.04711i 0.992123 + 0.125268i \(0.0399790\pi\)
−0.387577 + 0.921838i \(0.626688\pi\)
\(614\) 0 0
\(615\) −144.979 + 212.659i −0.235739 + 0.345788i
\(616\) 0 0
\(617\) −33.9467 93.2678i −0.0550189 0.151163i 0.909139 0.416494i \(-0.136741\pi\)
−0.964158 + 0.265330i \(0.914519\pi\)
\(618\) 0 0
\(619\) 67.3069 + 381.716i 0.108735 + 0.616666i 0.989663 + 0.143415i \(0.0458085\pi\)
−0.880928 + 0.473251i \(0.843080\pi\)
\(620\) 0 0
\(621\) −421.847 177.778i −0.679302 0.286277i
\(622\) 0 0
\(623\) 258.879 45.6473i 0.415536 0.0732701i
\(624\) 0 0
\(625\) −428.484 + 155.955i −0.685574 + 0.249529i
\(626\) 0 0
\(627\) 15.1283 201.955i 0.0241281 0.322098i
\(628\) 0 0
\(629\) 231.382 133.589i 0.367857 0.212382i
\(630\) 0 0
\(631\) 116.257 201.363i 0.184243 0.319118i −0.759078 0.650999i \(-0.774350\pi\)
0.943321 + 0.331882i \(0.107683\pi\)
\(632\) 0 0
\(633\) 1018.86 + 459.688i 1.60957 + 0.726205i
\(634\) 0 0
\(635\) −56.5734 9.97542i −0.0890920 0.0157093i
\(636\) 0 0
\(637\) 127.526 107.007i 0.200198 0.167986i
\(638\) 0 0
\(639\) 1140.49 28.5110i 1.78480 0.0446181i
\(640\) 0 0
\(641\) −23.5131 + 64.6018i −0.0366819 + 0.100783i −0.956681 0.291137i \(-0.905967\pi\)
0.920000 + 0.391919i \(0.128189\pi\)
\(642\) 0 0
\(643\) −659.704 553.557i −1.02598 0.860898i −0.0356111 0.999366i \(-0.511338\pi\)
−0.990367 + 0.138468i \(0.955782\pi\)
\(644\) 0 0
\(645\) −36.7639 130.651i −0.0569982 0.202560i
\(646\) 0 0
\(647\) 175.249i 0.270864i 0.990787 + 0.135432i \(0.0432422\pi\)
−0.990787 + 0.135432i \(0.956758\pi\)
\(648\) 0 0
\(649\) −495.006 −0.762722
\(650\) 0 0
\(651\) −151.952 + 42.7577i −0.233414 + 0.0656801i
\(652\) 0 0
\(653\) 231.306 275.659i 0.354220 0.422143i −0.559282 0.828978i \(-0.688923\pi\)
0.913502 + 0.406835i \(0.133367\pi\)
\(654\) 0 0
\(655\) 219.539 + 79.9056i 0.335174 + 0.121993i
\(656\) 0 0
\(657\) 285.100 + 155.235i 0.433943 + 0.236279i
\(658\) 0 0
\(659\) −19.8517 23.6583i −0.0301240 0.0359004i 0.750772 0.660561i \(-0.229682\pi\)
−0.780896 + 0.624661i \(0.785237\pi\)
\(660\) 0 0
\(661\) 39.3517 223.174i 0.0595335 0.337631i −0.940464 0.339894i \(-0.889609\pi\)
0.999997 + 0.00226216i \(0.000720070\pi\)
\(662\) 0 0
\(663\) 22.8268 50.5935i 0.0344296 0.0763100i
\(664\) 0 0
\(665\) 61.5179 + 35.5174i 0.0925081 + 0.0534096i
\(666\) 0 0
\(667\) 405.615 + 702.546i 0.608119 + 1.05329i
\(668\) 0 0
\(669\) −815.079 61.0569i −1.21835 0.0912660i
\(670\) 0 0
\(671\) −141.009 387.418i −0.210147 0.577375i
\(672\) 0 0
\(673\) 101.271 + 574.339i 0.150478 + 0.853401i 0.962805 + 0.270199i \(0.0870894\pi\)
−0.812327 + 0.583202i \(0.801799\pi\)
\(674\) 0 0
\(675\) 514.300 + 332.104i 0.761925 + 0.492006i
\(676\) 0 0
\(677\) −1292.96 + 227.984i −1.90984 + 0.336756i −0.997375 0.0724045i \(-0.976933\pi\)
−0.912462 + 0.409160i \(0.865822\pi\)
\(678\) 0 0
\(679\) 347.417 126.449i 0.511660 0.186229i
\(680\) 0 0
\(681\) −718.585 489.891i −1.05519 0.719370i
\(682\) 0 0
\(683\) 201.799 116.509i 0.295460 0.170584i −0.344941 0.938624i \(-0.612101\pi\)
0.640402 + 0.768040i \(0.278768\pi\)
\(684\) 0 0
\(685\) −45.2690 + 78.4083i −0.0660862 + 0.114465i
\(686\) 0 0
\(687\) 42.8325 + 427.916i 0.0623471 + 0.622876i
\(688\) 0 0
\(689\) −87.7176 15.4670i −0.127312 0.0224485i
\(690\) 0 0
\(691\) 641.761 538.502i 0.928743 0.779308i −0.0468483 0.998902i \(-0.514918\pi\)
0.975591 + 0.219594i \(0.0704733\pi\)
\(692\) 0 0
\(693\) −121.181 96.6265i −0.174864 0.139432i
\(694\) 0 0
\(695\) −31.3038 + 86.0064i −0.0450414 + 0.123750i
\(696\) 0 0
\(697\) 177.776 + 149.171i 0.255058 + 0.214019i
\(698\) 0 0
\(699\) −819.397 208.618i −1.17224 0.298452i
\(700\) 0 0
\(701\) 855.750i 1.22076i 0.792111 + 0.610378i \(0.208982\pi\)
−0.792111 + 0.610378i \(0.791018\pi\)
\(702\) 0 0
\(703\) −875.183 −1.24493
\(704\) 0 0
\(705\) 67.4403 + 65.7755i 0.0956600 + 0.0932985i
\(706\) 0 0
\(707\) −250.193 + 298.169i −0.353880 + 0.421738i
\(708\) 0 0
\(709\) −115.321 41.9735i −0.162653 0.0592010i 0.259410 0.965767i \(-0.416472\pi\)
−0.422064 + 0.906566i \(0.638694\pi\)
\(710\) 0 0
\(711\) −496.610 562.659i −0.698466 0.791362i
\(712\) 0 0
\(713\) 166.356 + 198.255i 0.233319 + 0.278058i
\(714\) 0 0
\(715\) 5.93355 33.6508i 0.00829867 0.0470641i
\(716\) 0 0
\(717\) 678.313 + 943.416i 0.946043 + 1.31578i
\(718\) 0 0
\(719\) 675.931 + 390.249i 0.940099 + 0.542766i 0.889991 0.455978i \(-0.150710\pi\)
0.0501075 + 0.998744i \(0.484044\pi\)
\(720\) 0 0
\(721\) −249.724 432.535i −0.346358 0.599909i
\(722\) 0 0
\(723\) 249.018 + 517.051i 0.344423 + 0.715146i
\(724\) 0 0
\(725\) −371.057 1019.47i −0.511802 1.40616i
\(726\) 0 0
\(727\) −136.489 774.066i −0.187742 1.06474i −0.922381 0.386281i \(-0.873759\pi\)
0.734639 0.678458i \(-0.237352\pi\)
\(728\) 0 0
\(729\) −54.6101 726.952i −0.0749109 0.997190i
\(730\) 0 0
\(731\) −120.520 + 21.2510i −0.164870 + 0.0290711i
\(732\) 0 0
\(733\) −1059.68 + 385.691i −1.44567 + 0.526181i −0.941379 0.337352i \(-0.890469\pi\)
−0.504292 + 0.863533i \(0.668247\pi\)
\(734\) 0 0
\(735\) −152.996 + 73.6846i −0.208157 + 0.100251i
\(736\) 0 0
\(737\) −280.285 + 161.822i −0.380305 + 0.219569i
\(738\) 0 0
\(739\) 57.1510 98.9885i 0.0773357 0.133949i −0.824764 0.565477i \(-0.808692\pi\)
0.902100 + 0.431528i \(0.142025\pi\)
\(740\) 0 0
\(741\) −147.619 + 106.138i −0.199216 + 0.143236i
\(742\) 0 0
\(743\) 1136.32 + 200.363i 1.52936 + 0.269668i 0.874105 0.485738i \(-0.161449\pi\)
0.655258 + 0.755405i \(0.272560\pi\)
\(744\) 0 0
\(745\) −314.010 + 263.486i −0.421490 + 0.353672i
\(746\) 0 0
\(747\) −113.401 + 100.089i −0.151808 + 0.133988i
\(748\) 0 0
\(749\) −107.181 + 294.477i −0.143098 + 0.393160i
\(750\) 0 0
\(751\) −747.335 627.088i −0.995120 0.835004i −0.00881873 0.999961i \(-0.502807\pi\)
−0.986301 + 0.164957i \(0.947252\pi\)
\(752\) 0 0
\(753\) −912.873 + 935.979i −1.21231 + 1.24300i
\(754\) 0 0
\(755\) 18.6162i 0.0246572i
\(756\) 0 0
\(757\) 886.690 1.17132 0.585661 0.810556i \(-0.300835\pi\)
0.585661 + 0.810556i \(0.300835\pi\)
\(758\) 0 0
\(759\) −62.6953 + 246.251i −0.0826025 + 0.324442i
\(760\) 0 0
\(761\) −553.370 + 659.480i −0.727161 + 0.866597i −0.995306 0.0967819i \(-0.969145\pi\)
0.268145 + 0.963379i \(0.413590\pi\)
\(762\) 0 0
\(763\) −143.268 52.1453i −0.187769 0.0683424i
\(764\) 0 0
\(765\) −35.2986 + 44.2685i −0.0461420 + 0.0578674i
\(766\) 0 0
\(767\) 285.652 + 340.427i 0.372428 + 0.443842i
\(768\) 0 0
\(769\) 44.1099 250.159i 0.0573600 0.325305i −0.942603 0.333916i \(-0.891630\pi\)
0.999963 + 0.00861097i \(0.00274099\pi\)
\(770\) 0 0
\(771\) −1250.34 + 125.153i −1.62171 + 0.162326i
\(772\) 0 0
\(773\) 45.5630 + 26.3058i 0.0589430 + 0.0340308i 0.529182 0.848508i \(-0.322499\pi\)
−0.470239 + 0.882539i \(0.655832\pi\)
\(774\) 0 0
\(775\) −173.056 299.741i −0.223297 0.386763i
\(776\) 0 0
\(777\) −377.281 + 553.405i −0.485561 + 0.712233i
\(778\) 0 0
\(779\) −259.998 714.338i −0.333758 0.916993i
\(780\) 0 0
\(781\) −109.966 623.649i −0.140802 0.798527i
\(782\) 0 0
\(783\) −700.799 + 1085.27i −0.895018 + 1.38604i
\(784\)