Properties

Label 108.3.k.a.29.6
Level 108
Weight 3
Character 108.29
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 29.6
Character \(\chi\) \(=\) 108.29
Dual form 108.3.k.a.41.6

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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 0.855110 0.518446i \(-0.173489\pi\)
−0.659058 + 0.752092i \(0.729045\pi\)
\(6\) 0 0
\(7\) 3.23920 1.17897i 0.462743 0.168425i −0.100119 0.994975i \(-0.531922\pi\)
0.562862 + 0.826551i \(0.309700\pi\)
\(8\) 0 0
\(9\) 7.67933 + 4.69338i 0.853259 + 0.521487i
\(10\) 0 0
\(11\) −3.21124 + 3.82701i −0.291931 + 0.347910i −0.891997 0.452040i \(-0.850696\pi\)
0.600067 + 0.799950i \(0.295141\pi\)
\(12\) 0 0
\(13\) −0.778815 4.41688i −0.0599089 0.339760i 0.940090 0.340925i \(-0.110740\pi\)
−0.999999 + 0.00116503i \(0.999629\pi\)
\(14\) 0 0
\(15\) 1.88153 + 4.17024i 0.125436 + 0.278016i
\(16\) 0 0
\(17\) −3.57252 + 2.06259i −0.210148 + 0.121329i −0.601380 0.798963i \(-0.705382\pi\)
0.391232 + 0.920292i \(0.372049\pi\)
\(18\) 0 0
\(19\) 6.75637 11.7024i 0.355599 0.615915i −0.631622 0.775277i \(-0.717610\pi\)
0.987220 + 0.159362i \(0.0509437\pi\)
\(20\) 0 0
\(21\) 10.3124 0.772492i 0.491065 0.0367853i
\(22\) 0 0
\(23\) −5.79885 + 15.9322i −0.252124 + 0.692705i 0.747472 + 0.664293i \(0.231267\pi\)
−0.999596 + 0.0284118i \(0.990955\pi\)
\(24\) 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 −0.714267 0.699874i \(-0.753240\pi\)
−0.910562 + 0.413373i \(0.864351\pi\)
\(30\) 0 0
\(31\) −14.3439 5.22075i −0.462706 0.168411i 0.100139 0.994973i \(-0.468071\pi\)
−0.562845 + 0.826562i \(0.690293\pi\)
\(32\) 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 −0.856514 0.516123i \(-0.827375\pi\)
−0.0187185 0.999825i \(-0.505959\pi\)
\(38\) 0 0
\(39\) 1.34010 13.3882i 0.0343614 0.343286i
\(40\) 0 0
\(41\) −55.4020 + 9.76887i −1.35127 + 0.238265i −0.801972 0.597362i \(-0.796216\pi\)
−0.549297 + 0.835627i \(0.685104\pi\)
\(42\) 0 0
\(43\) 22.7258 + 19.0692i 0.528507 + 0.443470i 0.867585 0.497288i \(-0.165671\pi\)
−0.339079 + 0.940758i \(0.610115\pi\)
\(44\) 0 0
\(45\) 2.04481 + 13.5720i 0.0454402 + 0.301600i
\(46\) 0 0
\(47\) −7.04255 19.3493i −0.149842 0.411686i 0.841949 0.539557i \(-0.181408\pi\)
−0.991791 + 0.127870i \(0.959186\pi\)
\(48\) 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 \(-0.940009\pi\)
0.982292 0.187355i \(-0.0599915\pi\)
\(54\) 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 0.955750 + 0.294179i \(0.0950463\pi\)
0.123746 + 0.992314i \(0.460509\pi\)
\(60\) 0 0
\(61\) 77.5488 28.2255i 1.27129 0.462713i 0.383749 0.923437i \(-0.374633\pi\)
0.887543 + 0.460725i \(0.152411\pi\)
\(62\) 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 0.946020 + 0.324107i \(0.105064\pi\)
−0.778117 + 0.628119i \(0.783825\pi\)
\(68\) 0 0
\(69\) −29.6928 + 41.2976i −0.430331 + 0.598516i
\(70\) 0 0
\(71\) 109.778 63.3803i 1.54617 0.892680i 0.547737 0.836650i \(-0.315489\pi\)
0.998429 0.0560292i \(-0.0178440\pi\)
\(72\) 0 0
\(73\) 18.0346 31.2369i 0.247049 0.427902i −0.715656 0.698453i \(-0.753872\pi\)
0.962706 + 0.270550i \(0.0872057\pi\)
\(74\) 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 0.744847 + 0.667235i \(0.232522\pi\)
−0.928135 + 0.372243i \(0.878589\pi\)
\(80\) 0 0
\(81\) 36.9443 + 72.0841i 0.456103 + 0.889927i
\(82\) 0 0
\(83\) −16.5506 2.91831i −0.199404 0.0351604i 0.0730538 0.997328i \(-0.476726\pi\)
−0.272458 + 0.962168i \(0.587837\pi\)
\(84\) 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 0.822814 0.568310i \(-0.192403\pi\)
−0.0807640 + 0.996733i \(0.525736\pi\)
\(90\) 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 0.959132 0.282959i \(-0.0913161\pi\)
−0.112109 + 0.993696i \(0.535761\pi\)
\(98\) 0 0
\(99\) −42.6218 + 14.3173i −0.430523 + 0.144619i
\(100\) 0 0
\(101\) −38.6196 106.106i −0.382372 1.05056i −0.970355 0.241685i \(-0.922300\pi\)
0.587982 0.808874i \(-0.299922\pi\)
\(102\) 0 0
\(103\) −110.992 + 93.1334i −1.07759 + 0.904208i −0.995719 0.0924347i \(-0.970535\pi\)
−0.0818743 + 0.996643i \(0.526091\pi\)
\(104\) 0 0
\(105\) 11.0113 + 11.2900i 0.104869 + 0.107524i
\(106\) 0 0
\(107\) 90.9102i 0.849628i −0.905281 0.424814i \(-0.860339\pi\)
0.905281 0.424814i \(-0.139661\pi\)
\(108\) 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 0.999960 0.00897066i \(-0.00285549\pi\)
−0.182476 + 0.983210i \(0.558411\pi\)
\(114\) 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 −0.930601 0.366036i \(-0.880715\pi\)
0.782297 + 0.622906i \(0.214048\pi\)
\(128\) 0 0
\(129\) 50.1328 + 73.5361i 0.388626 + 0.570047i
\(130\) 0 0
\(131\) 52.3965 143.958i 0.399973 1.09892i −0.562324 0.826917i \(-0.690093\pi\)
0.962297 0.272001i \(-0.0876853\pi\)
\(132\) 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 −0.0438588 0.999038i \(-0.513965\pi\)
−0.382905 + 0.923788i \(0.625076\pi\)
\(138\) 0 0
\(139\) −56.3970 20.5268i −0.405734 0.147675i 0.131088 0.991371i \(-0.458153\pi\)
−0.536822 + 0.843696i \(0.680375\pi\)
\(140\) 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 −0.963256 0.268584i \(-0.913444\pi\)
−0.813304 + 0.581839i \(0.802333\pi\)
\(150\) 0 0
\(151\) 9.35126 + 7.84664i 0.0619289 + 0.0519645i 0.673227 0.739436i \(-0.264908\pi\)
−0.611298 + 0.791401i \(0.709352\pi\)
\(152\) 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 −0.746284 0.665628i \(-0.768164\pi\)
0.525925 + 0.850531i \(0.323719\pi\)
\(158\) 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 0.999493 + 0.0318455i \(0.0101384\pi\)
−0.142198 + 0.989838i \(0.545417\pi\)
\(168\) 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 −0.716263 0.697830i \(-0.754149\pi\)
0.811607 + 0.584204i \(0.198593\pi\)
\(174\) 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 −0.677242 0.735761i \(-0.736825\pi\)
0.298567 + 0.954389i \(0.403492\pi\)
\(180\) 0 0
\(181\) 72.1634 124.991i 0.398693 0.690557i −0.594872 0.803821i \(-0.702797\pi\)
0.993565 + 0.113264i \(0.0361306\pi\)
\(182\) 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 0.453149 0.891435i \(-0.350301\pi\)
0.120932 + 0.992661i \(0.461412\pi\)
\(192\) 0 0
\(193\) 90.9049 + 33.0867i 0.471010 + 0.171434i 0.566610 0.823986i \(-0.308255\pi\)
−0.0955998 + 0.995420i \(0.530477\pi\)
\(194\) 0 0
\(195\) 16.9541 11.5584i 0.0869441 0.0592737i
\(196\) 0 0
\(197\) 12.0311 + 6.94615i 0.0610715 + 0.0352596i 0.530225 0.847857i \(-0.322108\pi\)
−0.469153 + 0.883117i \(0.655441\pi\)
\(198\) 0 0
\(199\) 77.7745 + 134.709i 0.390827 + 0.676932i 0.992559 0.121766i \(-0.0388558\pi\)
−0.601732 + 0.798698i \(0.705522\pi\)
\(200\) 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 0.374520 0.927219i \(-0.377807\pi\)
0.978167 0.207821i \(-0.0666370\pi\)
\(212\) 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 −0.844827 0.535039i \(-0.820297\pi\)
−0.303259 + 0.952908i \(0.598075\pi\)
\(224\) 0 0
\(225\) 135.039 152.999i 0.600172 0.679995i
\(226\) 0 0
\(227\) −186.342 + 222.073i −0.820888 + 0.978296i −0.999985 0.00553531i \(-0.998238\pi\)
0.179097 + 0.983831i \(0.442682\pi\)
\(228\) 0 0
\(229\) −24.8927 141.173i −0.108702 0.616478i −0.989677 0.143316i \(-0.954224\pi\)
0.880975 0.473162i \(-0.156888\pi\)
\(230\) 0 0
\(231\) −30.1591 + 41.9461i −0.130559 + 0.181585i
\(232\) 0 0
\(233\) −244.086 + 140.923i −1.04758 + 0.604819i −0.921970 0.387261i \(-0.873421\pi\)
−0.125607 + 0.992080i \(0.540088\pi\)
\(234\) 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 −0.273551 0.961857i \(-0.588198\pi\)
0.827823 0.560990i \(-0.189579\pi\)
\(240\) 0 0
\(241\) 33.2184 188.391i 0.137836 0.781705i −0.835007 0.550239i \(-0.814537\pi\)
0.972843 0.231466i \(-0.0743522\pi\)
\(242\) 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 −0.999991 0.00427006i \(-0.998641\pi\)
−0.503693 0.863882i \(-0.668026\pi\)
\(252\) 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 −0.903171 0.429281i \(-0.858767\pi\)
−0.701880 + 0.712295i \(0.747656\pi\)
\(258\) 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 0.945665 + 0.325144i \(0.105413\pi\)
−0.515423 + 0.856936i \(0.672365\pi\)
\(264\) 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 \(0.0816953\pi\)
−0.967245 + 0.253845i \(0.918305\pi\)
\(270\) 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 −0.558643 0.829408i \(-0.688678\pi\)
0.105188 + 0.994452i \(0.466456\pi\)
\(278\) 0 0
\(279\) −85.6486 107.413i −0.306984 0.384994i
\(280\) 0 0
\(281\) 291.841 347.803i 1.03858 1.23773i 0.0678161 0.997698i \(-0.478397\pi\)
0.970764 0.240034i \(-0.0771587\pi\)
\(282\) 0 0
\(283\) −67.6428 383.621i −0.239020 1.35555i −0.833979 0.551796i \(-0.813943\pi\)
0.594959 0.803756i \(-0.297168\pi\)
\(284\) 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 −0.566811 0.823848i \(-0.691823\pi\)
0.963762 0.266765i \(-0.0859548\pi\)
\(294\) 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 0.943516 + 0.331326i \(0.107496\pi\)
−0.184822 + 0.982772i \(0.559171\pi\)
\(308\) 0 0
\(309\) −396.209 + 178.762i −1.28223 + 0.578518i
\(310\) 0 0
\(311\) 82.0156 14.4616i 0.263716 0.0465002i −0.0402268 0.999191i \(-0.512808\pi\)
0.303942 + 0.952690i \(0.401697\pi\)
\(312\) 0 0
\(313\) −213.260 178.947i −0.681343 0.571714i 0.235056 0.971982i \(-0.424473\pi\)
−0.916398 + 0.400268i \(0.868917\pi\)
\(314\) 0 0
\(315\) 22.6245 + 41.5516i 0.0718240 + 0.131910i
\(316\) 0 0
\(317\) 56.6181 + 155.557i 0.178606 + 0.490716i 0.996398 0.0847979i \(-0.0270245\pi\)
−0.817792 + 0.575513i \(0.804802\pi\)
\(318\) 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 −0.358245 0.933628i \(-0.616625\pi\)
0.325693 + 0.945476i \(0.394402\pi\)
\(332\) 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 0.892255 + 0.451531i \(0.149122\pi\)
−0.684013 + 0.729470i \(0.739767\pi\)
\(338\) 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 −0.337620 0.941283i \(-0.609622\pi\)
0.863676 0.504047i \(-0.168156\pi\)
\(348\) 0 0
\(349\) −40.5969 + 230.237i −0.116324 + 0.659704i 0.869763 + 0.493470i \(0.164272\pi\)
−0.986086 + 0.166234i \(0.946839\pi\)
\(350\) 0 0
\(351\) 73.1268 96.5225i 0.208338 0.274993i
\(352\) 0 0
\(353\) 486.656 + 85.8106i 1.37863 + 0.243090i 0.813333 0.581798i \(-0.197651\pi\)
0.565297 + 0.824888i \(0.308762\pi\)
\(354\) 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 0.562839 0.826567i \(-0.309709\pi\)
−0.434408 + 0.900716i \(0.643042\pi\)
\(360\) 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 0.569719 0.821839i \(-0.307052\pi\)
−0.710423 + 0.703775i \(0.751496\pi\)
\(368\) 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 −0.809105 0.587664i \(-0.800048\pi\)
0.438237 + 0.898860i \(0.355603\pi\)
\(374\) 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 0.973048 0.230601i \(-0.0740691\pi\)
−0.396065 + 0.918222i \(0.629625\pi\)
\(384\) 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 −0.192313 0.981334i \(-0.561599\pi\)
0.999820 + 0.0189843i \(0.00604325\pi\)
\(390\) 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 −0.999257 0.0385336i \(-0.987731\pi\)
0.533000 + 0.846115i \(0.321065\pi\)
\(398\) 0 0
\(399\) 60.6342 125.898i 0.151965 0.315535i
\(400\) 0 0
\(401\) 182.815 502.279i 0.455897 1.25257i −0.472617 0.881268i \(-0.656691\pi\)
0.928514 0.371298i \(-0.121087\pi\)
\(402\) 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 0.504847 0.863209i \(-0.331549\pi\)
−0.168125 + 0.985766i \(0.553771\pi\)
\(410\) 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 −0.403877 0.914813i \(-0.632338\pi\)
−0.0666354 + 0.997777i \(0.521226\pi\)
\(420\) 0 0
\(421\) 337.985 + 283.603i 0.802815 + 0.673641i 0.948881 0.315633i \(-0.102217\pi\)
−0.146067 + 0.989275i \(0.546661\pi\)
\(422\) 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 \(-0.814265\pi\)
0.834537 0.550951i \(-0.185735\pi\)
\(432\) 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 −0.929024 0.370019i \(-0.879351\pi\)
−0.473831 + 0.880616i \(0.657129\pi\)
\(440\) 0 0
\(441\) −330.330 + 49.7688i −0.749048 + 0.112855i
\(442\) 0 0
\(443\) −461.210 + 549.649i −1.04111 + 1.24074i −0.0711502 + 0.997466i \(0.522667\pi\)
−0.969957 + 0.243277i \(0.921777\pi\)
\(444\) 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 −0.362480 0.931991i \(-0.618070\pi\)
0.625888 + 0.779913i \(0.284737\pi\)
\(450\) 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 −0.899323 0.437286i \(-0.855940\pi\)
0.994647 0.103327i \(-0.0329490\pi\)
\(458\) 0 0
\(459\) −106.429 32.8395i −0.231871 0.0715458i
\(460\) 0 0
\(461\) −227.426 40.1013i −0.493331 0.0869876i −0.0785527 0.996910i \(-0.525030\pi\)
−0.414779 + 0.909922i \(0.636141\pi\)
\(462\) 0 0
\(463\) −418.337 152.262i −0.903535 0.328860i −0.151867 0.988401i \(-0.548528\pi\)
−0.751669 + 0.659541i \(0.770751\pi\)
\(464\) 0 0
\(465\) −5.21672 69.6405i −0.0112188 0.149765i
\(466\) 0 0
\(467\) −515.922 297.868i −1.10476 0.637833i −0.167292 0.985907i \(-0.553502\pi\)
−0.937467 + 0.348075i \(0.886836\pi\)
\(468\) 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 0.766106 0.642714i \(-0.222192\pi\)
−1.00000 9.59229e-5i \(0.999969\pi\)
\(480\) 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 0.508692 0.860949i \(-0.330129\pi\)
−0.936202 + 0.351462i \(0.885685\pi\)
\(492\) 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 −0.959239 0.282596i \(-0.908804\pi\)
0.804736 0.593633i \(-0.202307\pi\)
\(500\) 0 0
\(501\) 274.800 + 609.068i 0.548502 + 1.21570i
\(502\) 0 0
\(503\) −248.594 + 143.526i −0.494223 + 0.285340i −0.726325 0.687352i \(-0.758773\pi\)
0.232102 + 0.972692i \(0.425440\pi\)
\(504\) 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 0.291929 + 0.956440i \(0.405703\pi\)
−0.838418 + 0.545027i \(0.816519\pi\)
\(510\) 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 0.483486 0.875352i \(-0.339370\pi\)
−0.516334 + 0.856387i \(0.672704\pi\)
\(522\) 0 0
\(523\) −342.155 592.630i −0.654216 1.13313i −0.982090 0.188413i \(-0.939666\pi\)
0.327874 0.944721i \(-0.393668\pi\)
\(524\) 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 0.366598 0.930379i \(-0.380522\pi\)
0.878867 + 0.477067i \(0.158300\pi\)
\(548\) 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 0.196672 0.980469i \(-0.436986\pi\)
0.947448 + 0.319911i \(0.103653\pi\)
\(558\) 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 0.446638 + 0.894715i \(0.352621\pi\)
−0.917256 + 0.398298i \(0.869601\pi\)
\(564\) 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 −0.429087 0.903263i \(-0.641165\pi\)
−0.712144 + 0.702033i \(0.752276\pi\)
\(570\) 0 0
\(571\) 96.2986 + 35.0498i 0.168649 + 0.0613832i 0.424965 0.905210i \(-0.360286\pi\)
−0.256316 + 0.966593i \(0.582509\pi\)
\(572\) 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 −0.903966 0.427605i \(-0.859357\pi\)
0.0816661 0.996660i \(-0.473976\pi\)
\(578\) 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 −0.902968 0.429707i \(-0.858617\pi\)
0.415504 0.909591i \(-0.363605\pi\)
\(588\) 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 \(0.134135\pi\)
−0.912518 + 0.409037i \(0.865865\pi\)
\(594\) 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 0.901023 0.433772i \(-0.142818\pi\)
−0.583643 + 0.812010i \(0.698373\pi\)
\(600\) 0 0
\(601\) 642.355 233.798i 1.06881 0.389015i 0.253079 0.967446i \(-0.418557\pi\)
0.815732 + 0.578431i \(0.196335\pi\)
\(602\) 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 0.999101 0.0423966i \(-0.0134993\pi\)
−0.953348 + 0.301873i \(0.902388\pi\)
\(608\) 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 −0.387577 0.921838i \(-0.626688\pi\)
0.992123 0.125268i \(-0.0399790\pi\)
\(614\) 0 0
\(615\) −144.979 212.659i −0.235739 0.345788i
\(616\) 0 0
\(617\) −33.9467 + 93.2678i −0.0550189 + 0.151163i −0.964158 0.265330i \(-0.914519\pi\)
0.909139 + 0.416494i \(0.136741\pi\)
\(618\) 0 0
\(619\) 67.3069 381.716i 0.108735 0.616666i −0.880928 0.473251i \(-0.843080\pi\)
0.989663 0.143415i \(-0.0458085\pi\)
\(620\) 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 0.943321 0.331882i \(-0.107683\pi\)
−0.759078 + 0.650999i \(0.774350\pi\)
\(632\) 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 0.920000 0.391919i \(-0.128189\pi\)
−0.956681 + 0.291137i \(0.905967\pi\)
\(642\) 0 0
\(643\) −659.704 + 553.557i −1.02598 + 0.860898i −0.990367 0.138468i \(-0.955782\pi\)
−0.0356111 + 0.999366i \(0.511338\pi\)
\(644\) 0 0
\(645\) −36.7639 + 130.651i −0.0569982 + 0.202560i
\(646\) 0 0
\(647\) 175.249i 0.270864i −0.990787 0.135432i \(-0.956758\pi\)
0.990787 0.135432i \(-0.0432422\pi\)
\(648\) 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 0.913502 0.406835i \(-0.133367\pi\)
−0.559282 + 0.828978i \(0.688923\pi\)
\(654\) 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 −0.780896 0.624661i \(-0.785237\pi\)
0.750772 + 0.660561i \(0.229682\pi\)
\(660\) 0 0
\(661\) 39.3517 + 223.174i 0.0595335 + 0.337631i 0.999997 0.00226216i \(-0.000720070\pi\)
−0.940464 + 0.339894i \(0.889609\pi\)
\(662\) 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 −0.812327 0.583202i \(-0.801799\pi\)
0.962805 0.270199i \(-0.0870894\pi\)
\(674\) 0 0
\(675\) 514.300 332.104i 0.761925 0.492006i
\(676\) 0 0
\(677\) −1292.96 227.984i −1.90984 0.336756i −0.912462 0.409160i \(-0.865822\pi\)
−0.997375 + 0.0724045i \(0.976933\pi\)
\(678\) 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 0.640402 0.768040i \(-0.278768\pi\)
−0.344941 + 0.938624i \(0.612101\pi\)
\(684\) 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 0.975591 0.219594i \(-0.0704733\pi\)
−0.0468483 + 0.998902i \(0.514918\pi\)
\(692\) 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 \(-0.791018\pi\)
0.792111 0.610378i \(-0.208982\pi\)
\(702\) 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 −0.422064 0.906566i \(-0.638694\pi\)
0.259410 + 0.965767i \(0.416472\pi\)
\(710\) 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 0.0501075 0.998744i \(-0.484044\pi\)
0.889991 + 0.455978i \(0.150710\pi\)
\(720\) 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 0.734639 + 0.678458i \(0.237352\pi\)
−0.922381 + 0.386281i \(0.873759\pi\)
\(728\) 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 −0.504292 0.863533i \(-0.668247\pi\)
−0.941379 + 0.337352i \(0.890469\pi\)
\(734\) 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 0.902100 0.431528i \(-0.142025\pi\)
−0.824764 + 0.565477i \(0.808692\pi\)
\(740\) 0 0
\(741\) −147.619 106.138i −0.199216 0.143236i
\(742\) 0 0
\(743\) 1136.32 200.363i 1.52936 0.269668i 0.655258 0.755405i \(-0.272560\pi\)
0.874105 + 0.485738i \(0.161449\pi\)
\(744\) 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 −0.986301 0.164957i \(-0.947252\pi\)
−0.00881873 + 0.999961i \(0.502807\pi\)
\(752\) 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 0.268145 0.963379i \(-0.413590\pi\)
−0.995306 + 0.0967819i \(0.969145\pi\)
\(762\) 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 0.999963 0.00861097i \(-0.00274099\pi\)
−0.942603 + 0.333916i \(0.891630\pi\)
\(770\) 0 0
\(771\) −1250.34 125.153i −1.62171 0.162326i
\(772\) 0 0
\(773\) 45.5630 26.3058i 0.0589430 0.0340308i −0.470239 0.882539i \(-0.655832\pi\)
0.529182 + 0.848508i \(0.322499\pi\)
\(774\) 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
\(784\)