Properties

Label 441.2.bg.a.395.6
Level $441$
Weight $2$
Character 441.395
Analytic conductor $3.521$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.bg (of order \(42\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 395.6
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.02327 - 0.401605i) q^{2} +(-0.580301 - 0.538441i) q^{4} +(-1.00842 - 0.687530i) q^{5} +(2.62056 - 0.364218i) q^{7} +(1.33147 + 2.76483i) q^{8} +O(q^{10})\) \(q+(-1.02327 - 0.401605i) q^{2} +(-0.580301 - 0.538441i) q^{4} +(-1.00842 - 0.687530i) q^{5} +(2.62056 - 0.364218i) q^{7} +(1.33147 + 2.76483i) q^{8} +(0.755775 + 1.10852i) q^{10} +(-0.0890350 - 0.590708i) q^{11} +(2.95451 - 2.35614i) q^{13} +(-2.82782 - 0.679737i) q^{14} +(-0.133773 - 1.78508i) q^{16} +(-2.61960 - 0.808039i) q^{17} +(0.127290 - 0.0734907i) q^{19} +(0.214994 + 0.941949i) q^{20} +(-0.146125 + 0.640213i) q^{22} +(-2.07095 - 6.71384i) q^{23} +(-1.28249 - 3.26773i) q^{25} +(-3.96951 + 1.22443i) q^{26} +(-1.71682 - 1.19966i) q^{28} +(-2.75551 + 0.628926i) q^{29} +(-4.54912 - 2.62644i) q^{31} +(1.22903 - 3.98443i) q^{32} +(2.35605 + 1.87889i) q^{34} +(-2.89304 - 1.43443i) q^{35} +(-0.323554 + 0.300214i) q^{37} +(-0.159766 + 0.0240809i) q^{38} +(0.558218 - 3.70353i) q^{40} +(4.98252 - 2.39945i) q^{41} +(1.07470 + 0.517549i) q^{43} +(-0.266394 + 0.390729i) q^{44} +(-0.577170 + 7.70180i) q^{46} +(-1.29597 + 3.30207i) q^{47} +(6.73469 - 1.90891i) q^{49} +3.85884i q^{50} +(-2.98315 - 0.223556i) q^{52} +(8.63323 - 9.30441i) q^{53} +(-0.316345 + 0.656897i) q^{55} +(4.49620 + 6.76045i) q^{56} +(3.07222 + 0.463062i) q^{58} +(1.25982 - 0.858928i) q^{59} +(-9.59443 - 10.3403i) q^{61} +(3.60020 + 4.51451i) q^{62} +(-5.09001 + 6.38267i) q^{64} +(-4.59931 + 0.344671i) q^{65} +(-1.69535 + 2.93644i) q^{67} +(1.08507 + 1.87940i) q^{68} +(2.38430 + 2.62968i) q^{70} +(6.84143 + 1.56151i) q^{71} +(-14.5201 + 5.69870i) q^{73} +(0.451652 - 0.177260i) q^{74} +(-0.113437 - 0.0258912i) q^{76} +(-0.448468 - 1.51556i) q^{77} +(5.62817 + 9.74827i) q^{79} +(-1.09240 + 1.89208i) q^{80} +(-6.06211 + 0.454292i) q^{82} +(4.09993 - 5.14115i) q^{83} +(2.08611 + 2.61590i) q^{85} +(-0.891863 - 0.961200i) q^{86} +(1.51466 - 1.03268i) q^{88} +(3.27093 + 0.493014i) q^{89} +(6.88433 - 7.25051i) q^{91} +(-2.41323 + 5.01113i) q^{92} +(2.65226 - 2.85845i) q^{94} +(-0.178888 - 0.0134058i) q^{95} +12.1414i q^{97} +(-7.65806 - 0.751350i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q - 16q^{4} + 2q^{7} + O(q^{10}) \) \( 216q - 16q^{4} + 2q^{7} + 12q^{10} + 12q^{16} - 6q^{19} + 44q^{22} + 26q^{25} + 84q^{28} - 6q^{31} - 112q^{34} + 60q^{37} - 304q^{40} + 20q^{43} - 20q^{46} - 86q^{49} - 168q^{52} - 84q^{55} - 120q^{58} - 2q^{61} + 32q^{64} + 22q^{67} - 136q^{70} - 6q^{73} + 84q^{76} + 2q^{79} - 104q^{82} + 96q^{85} - 12q^{88} + 58q^{91} + 52q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{42}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02327 0.401605i −0.723564 0.283978i −0.0251617 0.999683i \(-0.508010\pi\)
−0.698402 + 0.715705i \(0.746105\pi\)
\(3\) 0 0
\(4\) −0.580301 0.538441i −0.290151 0.269220i
\(5\) −1.00842 0.687530i −0.450980 0.307473i 0.316446 0.948610i \(-0.397510\pi\)
−0.767426 + 0.641138i \(0.778463\pi\)
\(6\) 0 0
\(7\) 2.62056 0.364218i 0.990479 0.137661i
\(8\) 1.33147 + 2.76483i 0.470746 + 0.977514i
\(9\) 0 0
\(10\) 0.755775 + 1.10852i 0.238997 + 0.350544i
\(11\) −0.0890350 0.590708i −0.0268450 0.178105i 0.971390 0.237489i \(-0.0763245\pi\)
−0.998235 + 0.0593840i \(0.981086\pi\)
\(12\) 0 0
\(13\) 2.95451 2.35614i 0.819434 0.653477i −0.121302 0.992616i \(-0.538707\pi\)
0.940736 + 0.339139i \(0.110136\pi\)
\(14\) −2.82782 0.679737i −0.755768 0.181667i
\(15\) 0 0
\(16\) −0.133773 1.78508i −0.0334433 0.446270i
\(17\) −2.61960 0.808039i −0.635346 0.195978i −0.0396825 0.999212i \(-0.512635\pi\)
−0.595664 + 0.803234i \(0.703111\pi\)
\(18\) 0 0
\(19\) 0.127290 0.0734907i 0.0292022 0.0168599i −0.485328 0.874332i \(-0.661300\pi\)
0.514530 + 0.857472i \(0.327966\pi\)
\(20\) 0.214994 + 0.941949i 0.0480741 + 0.210626i
\(21\) 0 0
\(22\) −0.146125 + 0.640213i −0.0311539 + 0.136494i
\(23\) −2.07095 6.71384i −0.431822 1.39993i −0.866423 0.499310i \(-0.833587\pi\)
0.434601 0.900623i \(-0.356889\pi\)
\(24\) 0 0
\(25\) −1.28249 3.26773i −0.256498 0.653546i
\(26\) −3.96951 + 1.22443i −0.778486 + 0.240131i
\(27\) 0 0
\(28\) −1.71682 1.19966i −0.324449 0.226715i
\(29\) −2.75551 + 0.628926i −0.511684 + 0.116789i −0.470565 0.882366i \(-0.655950\pi\)
−0.0411199 + 0.999154i \(0.513093\pi\)
\(30\) 0 0
\(31\) −4.54912 2.62644i −0.817046 0.471722i 0.0323508 0.999477i \(-0.489701\pi\)
−0.849397 + 0.527755i \(0.823034\pi\)
\(32\) 1.22903 3.98443i 0.217265 0.704355i
\(33\) 0 0
\(34\) 2.35605 + 1.87889i 0.404060 + 0.322227i
\(35\) −2.89304 1.43443i −0.489013 0.242463i
\(36\) 0 0
\(37\) −0.323554 + 0.300214i −0.0531919 + 0.0493549i −0.706321 0.707892i \(-0.749646\pi\)
0.653129 + 0.757247i \(0.273456\pi\)
\(38\) −0.159766 + 0.0240809i −0.0259175 + 0.00390644i
\(39\) 0 0
\(40\) 0.558218 3.70353i 0.0882620 0.585580i
\(41\) 4.98252 2.39945i 0.778138 0.374732i −0.00227370 0.999997i \(-0.500724\pi\)
0.780412 + 0.625266i \(0.215009\pi\)
\(42\) 0 0
\(43\) 1.07470 + 0.517549i 0.163890 + 0.0789254i 0.514031 0.857772i \(-0.328152\pi\)
−0.350140 + 0.936697i \(0.613866\pi\)
\(44\) −0.266394 + 0.390729i −0.0401605 + 0.0589046i
\(45\) 0 0
\(46\) −0.577170 + 7.70180i −0.0850991 + 1.13557i
\(47\) −1.29597 + 3.30207i −0.189036 + 0.481656i −0.993700 0.112075i \(-0.964250\pi\)
0.804664 + 0.593731i \(0.202346\pi\)
\(48\) 0 0
\(49\) 6.73469 1.90891i 0.962099 0.272702i
\(50\) 3.85884i 0.545722i
\(51\) 0 0
\(52\) −2.98315 0.223556i −0.413689 0.0310017i
\(53\) 8.63323 9.30441i 1.18586 1.27806i 0.233757 0.972295i \(-0.424898\pi\)
0.952108 0.305763i \(-0.0989117\pi\)
\(54\) 0 0
\(55\) −0.316345 + 0.656897i −0.0426559 + 0.0885760i
\(56\) 4.49620 + 6.76045i 0.600830 + 0.903403i
\(57\) 0 0
\(58\) 3.07222 + 0.463062i 0.403402 + 0.0608030i
\(59\) 1.25982 0.858928i 0.164014 0.111823i −0.478531 0.878070i \(-0.658831\pi\)
0.642546 + 0.766248i \(0.277878\pi\)
\(60\) 0 0
\(61\) −9.59443 10.3403i −1.22844 1.32394i −0.929114 0.369793i \(-0.879428\pi\)
−0.299327 0.954151i \(-0.596762\pi\)
\(62\) 3.60020 + 4.51451i 0.457226 + 0.573344i
\(63\) 0 0
\(64\) −5.09001 + 6.38267i −0.636251 + 0.797833i
\(65\) −4.59931 + 0.344671i −0.570474 + 0.0427511i
\(66\) 0 0
\(67\) −1.69535 + 2.93644i −0.207120 + 0.358743i −0.950806 0.309786i \(-0.899742\pi\)
0.743686 + 0.668529i \(0.233076\pi\)
\(68\) 1.08507 + 1.87940i 0.131585 + 0.227911i
\(69\) 0 0
\(70\) 2.38430 + 2.62968i 0.284978 + 0.314306i
\(71\) 6.84143 + 1.56151i 0.811928 + 0.185317i 0.608275 0.793726i \(-0.291862\pi\)
0.203652 + 0.979043i \(0.434719\pi\)
\(72\) 0 0
\(73\) −14.5201 + 5.69870i −1.69944 + 0.666982i −0.998912 0.0466388i \(-0.985149\pi\)
−0.700532 + 0.713621i \(0.747054\pi\)
\(74\) 0.451652 0.177260i 0.0525034 0.0206061i
\(75\) 0 0
\(76\) −0.113437 0.0258912i −0.0130121 0.00296992i
\(77\) −0.448468 1.51556i −0.0511077 0.172714i
\(78\) 0 0
\(79\) 5.62817 + 9.74827i 0.633218 + 1.09677i 0.986890 + 0.161396i \(0.0515998\pi\)
−0.353671 + 0.935370i \(0.615067\pi\)
\(80\) −1.09240 + 1.89208i −0.122134 + 0.211542i
\(81\) 0 0
\(82\) −6.06211 + 0.454292i −0.669448 + 0.0501682i
\(83\) 4.09993 5.14115i 0.450025 0.564314i −0.504129 0.863628i \(-0.668186\pi\)
0.954155 + 0.299314i \(0.0967579\pi\)
\(84\) 0 0
\(85\) 2.08611 + 2.61590i 0.226270 + 0.283734i
\(86\) −0.891863 0.961200i −0.0961721 0.103649i
\(87\) 0 0
\(88\) 1.51466 1.03268i 0.161463 0.110084i
\(89\) 3.27093 + 0.493014i 0.346718 + 0.0522594i 0.320093 0.947386i \(-0.396286\pi\)
0.0266252 + 0.999645i \(0.491524\pi\)
\(90\) 0 0
\(91\) 6.88433 7.25051i 0.721674 0.760060i
\(92\) −2.41323 + 5.01113i −0.251597 + 0.522447i
\(93\) 0 0
\(94\) 2.65226 2.85845i 0.273559 0.294827i
\(95\) −0.178888 0.0134058i −0.0183536 0.00137541i
\(96\) 0 0
\(97\) 12.1414i 1.23277i 0.787444 + 0.616387i \(0.211404\pi\)
−0.787444 + 0.616387i \(0.788596\pi\)
\(98\) −7.65806 0.751350i −0.773581 0.0758978i
\(99\) 0 0
\(100\) −1.01525 + 2.58681i −0.101525 + 0.258681i
\(101\) −0.704604 + 9.40229i −0.0701108 + 0.935563i 0.845624 + 0.533779i \(0.179229\pi\)
−0.915735 + 0.401784i \(0.868390\pi\)
\(102\) 0 0
\(103\) 10.0187 14.6947i 0.987173 1.44792i 0.0953964 0.995439i \(-0.469588\pi\)
0.891776 0.452477i \(-0.149459\pi\)
\(104\) 10.4482 + 5.03157i 1.02453 + 0.493386i
\(105\) 0 0
\(106\) −12.5709 + 6.05380i −1.22099 + 0.587998i
\(107\) 1.12107 7.43778i 0.108377 0.719038i −0.866970 0.498361i \(-0.833935\pi\)
0.975347 0.220676i \(-0.0708265\pi\)
\(108\) 0 0
\(109\) 8.76053 1.32044i 0.839107 0.126475i 0.284592 0.958649i \(-0.408142\pi\)
0.554515 + 0.832174i \(0.312904\pi\)
\(110\) 0.587521 0.545140i 0.0560179 0.0519770i
\(111\) 0 0
\(112\) −1.00072 4.62919i −0.0945590 0.437417i
\(113\) 6.41946 + 5.11935i 0.603892 + 0.481588i 0.877062 0.480378i \(-0.159500\pi\)
−0.273169 + 0.961966i \(0.588072\pi\)
\(114\) 0 0
\(115\) −2.52758 + 8.19422i −0.235698 + 0.764115i
\(116\) 1.93766 + 1.11871i 0.179907 + 0.103870i
\(117\) 0 0
\(118\) −1.63409 + 0.372970i −0.150430 + 0.0343346i
\(119\) −7.15912 1.16341i −0.656276 0.106650i
\(120\) 0 0
\(121\) 10.1703 3.13712i 0.924572 0.285193i
\(122\) 5.66499 + 14.4342i 0.512884 + 1.30681i
\(123\) 0 0
\(124\) 1.22568 + 3.97355i 0.110069 + 0.356836i
\(125\) −2.31130 + 10.1265i −0.206729 + 0.905739i
\(126\) 0 0
\(127\) 2.71555 + 11.8976i 0.240966 + 1.05574i 0.940140 + 0.340789i \(0.110694\pi\)
−0.699174 + 0.714952i \(0.746449\pi\)
\(128\) 0.549691 0.317364i 0.0485863 0.0280513i
\(129\) 0 0
\(130\) 4.84478 + 1.49442i 0.424915 + 0.131069i
\(131\) 0.334827 + 4.46795i 0.0292539 + 0.390367i 0.992543 + 0.121899i \(0.0388983\pi\)
−0.963289 + 0.268468i \(0.913483\pi\)
\(132\) 0 0
\(133\) 0.306804 0.238948i 0.0266032 0.0207194i
\(134\) 2.91410 2.32392i 0.251740 0.200756i
\(135\) 0 0
\(136\) −1.25383 8.31861i −0.107515 0.713315i
\(137\) 6.27275 + 9.20044i 0.535917 + 0.786046i 0.994735 0.102484i \(-0.0326791\pi\)
−0.458817 + 0.888531i \(0.651727\pi\)
\(138\) 0 0
\(139\) 0.284202 + 0.590152i 0.0241057 + 0.0500560i 0.912674 0.408688i \(-0.134014\pi\)
−0.888568 + 0.458744i \(0.848299\pi\)
\(140\) 0.906479 + 2.39013i 0.0766115 + 0.202003i
\(141\) 0 0
\(142\) −6.37354 4.34541i −0.534856 0.364659i
\(143\) −1.65485 1.53548i −0.138385 0.128403i
\(144\) 0 0
\(145\) 3.21111 + 1.26027i 0.266669 + 0.104660i
\(146\) 17.1466 1.41906
\(147\) 0 0
\(148\) 0.349406 0.0287210
\(149\) −8.98334 3.52570i −0.735944 0.288837i −0.0323867 0.999475i \(-0.510311\pi\)
−0.703557 + 0.710639i \(0.748406\pi\)
\(150\) 0 0
\(151\) −0.969253 0.899335i −0.0788767 0.0731868i 0.639749 0.768584i \(-0.279038\pi\)
−0.718626 + 0.695397i \(0.755229\pi\)
\(152\) 0.372671 + 0.254083i 0.0302276 + 0.0206088i
\(153\) 0 0
\(154\) −0.149751 + 1.73094i −0.0120673 + 0.139483i
\(155\) 2.78168 + 5.77621i 0.223430 + 0.463956i
\(156\) 0 0
\(157\) −0.669063 0.981335i −0.0533970 0.0783190i 0.798612 0.601847i \(-0.205568\pi\)
−0.852009 + 0.523527i \(0.824616\pi\)
\(158\) −1.84420 12.2355i −0.146717 0.973400i
\(159\) 0 0
\(160\) −3.97880 + 3.17299i −0.314552 + 0.250847i
\(161\) −7.87234 16.8398i −0.620428 1.32716i
\(162\) 0 0
\(163\) 1.18522 + 15.8157i 0.0928336 + 1.23878i 0.827936 + 0.560823i \(0.189515\pi\)
−0.735102 + 0.677956i \(0.762866\pi\)
\(164\) −4.18332 1.29038i −0.326663 0.100762i
\(165\) 0 0
\(166\) −6.26006 + 3.61425i −0.485875 + 0.280520i
\(167\) −2.67976 11.7408i −0.207366 0.908531i −0.966311 0.257376i \(-0.917142\pi\)
0.758945 0.651155i \(-0.225715\pi\)
\(168\) 0 0
\(169\) 0.284950 1.24845i 0.0219192 0.0960344i
\(170\) −1.08410 3.51457i −0.0831468 0.269555i
\(171\) 0 0
\(172\) −0.344981 0.878997i −0.0263045 0.0670229i
\(173\) −23.7151 + 7.31513i −1.80302 + 0.556159i −0.999248 0.0387726i \(-0.987655\pi\)
−0.803776 + 0.594932i \(0.797179\pi\)
\(174\) 0 0
\(175\) −4.55101 8.09618i −0.344024 0.612014i
\(176\) −1.04255 + 0.237955i −0.0785852 + 0.0179366i
\(177\) 0 0
\(178\) −3.14906 1.81811i −0.236032 0.136273i
\(179\) 5.47310 17.7434i 0.409079 1.32620i −0.483514 0.875337i \(-0.660640\pi\)
0.892593 0.450864i \(-0.148884\pi\)
\(180\) 0 0
\(181\) −8.94857 7.13625i −0.665142 0.530433i 0.231698 0.972788i \(-0.425572\pi\)
−0.896840 + 0.442355i \(0.854143\pi\)
\(182\) −9.95640 + 4.65447i −0.738017 + 0.345012i
\(183\) 0 0
\(184\) 15.8052 14.6651i 1.16517 1.08112i
\(185\) 0.532684 0.0802893i 0.0391637 0.00590298i
\(186\) 0 0
\(187\) −0.244080 + 1.61936i −0.0178489 + 0.118420i
\(188\) 2.53002 1.21839i 0.184521 0.0888605i
\(189\) 0 0
\(190\) 0.177668 + 0.0855604i 0.0128894 + 0.00620721i
\(191\) 13.2898 19.4926i 0.961618 1.41043i 0.0502992 0.998734i \(-0.483982\pi\)
0.911319 0.411701i \(-0.135065\pi\)
\(192\) 0 0
\(193\) 0.357297 4.76780i 0.0257188 0.343193i −0.969469 0.245212i \(-0.921142\pi\)
0.995188 0.0979813i \(-0.0312386\pi\)
\(194\) 4.87605 12.4240i 0.350080 0.891990i
\(195\) 0 0
\(196\) −4.93598 2.51849i −0.352570 0.179892i
\(197\) 10.3817i 0.739667i 0.929098 + 0.369833i \(0.120585\pi\)
−0.929098 + 0.369833i \(0.879415\pi\)
\(198\) 0 0
\(199\) 3.02679 + 0.226826i 0.214563 + 0.0160793i 0.181578 0.983377i \(-0.441880\pi\)
0.0329853 + 0.999456i \(0.489499\pi\)
\(200\) 7.32711 7.89674i 0.518105 0.558384i
\(201\) 0 0
\(202\) 4.49702 9.33815i 0.316409 0.657030i
\(203\) −6.99191 + 2.65174i −0.490736 + 0.186116i
\(204\) 0 0
\(205\) −6.67417 1.00597i −0.466144 0.0702599i
\(206\) −16.1534 + 11.0132i −1.12546 + 0.767325i
\(207\) 0 0
\(208\) −4.60114 4.95885i −0.319032 0.343834i
\(209\) −0.0547448 0.0686478i −0.00378677 0.00474846i
\(210\) 0 0
\(211\) 8.83991 11.0849i 0.608564 0.763115i −0.378121 0.925756i \(-0.623430\pi\)
0.986685 + 0.162641i \(0.0520012\pi\)
\(212\) −10.0197 + 0.750876i −0.688159 + 0.0515704i
\(213\) 0 0
\(214\) −4.13421 + 7.16066i −0.282609 + 0.489493i
\(215\) −0.727921 1.26080i −0.0496438 0.0859856i
\(216\) 0 0
\(217\) −12.8778 5.22587i −0.874205 0.354755i
\(218\) −9.49472 2.16711i −0.643063 0.146775i
\(219\) 0 0
\(220\) 0.537275 0.210865i 0.0362231 0.0142165i
\(221\) −9.64349 + 3.78479i −0.648691 + 0.254593i
\(222\) 0 0
\(223\) 20.8492 + 4.75870i 1.39617 + 0.318666i 0.853418 0.521228i \(-0.174526\pi\)
0.542750 + 0.839894i \(0.317383\pi\)
\(224\) 1.76956 10.8891i 0.118234 0.727558i
\(225\) 0 0
\(226\) −4.51291 7.81659i −0.300194 0.519952i
\(227\) −8.57972 + 14.8605i −0.569456 + 0.986327i 0.427164 + 0.904174i \(0.359513\pi\)
−0.996620 + 0.0821526i \(0.973821\pi\)
\(228\) 0 0
\(229\) −13.6062 + 1.01964i −0.899122 + 0.0673799i −0.516266 0.856428i \(-0.672678\pi\)
−0.382856 + 0.923808i \(0.625059\pi\)
\(230\) 5.87725 7.36984i 0.387534 0.485953i
\(231\) 0 0
\(232\) −5.40774 6.78110i −0.355036 0.445201i
\(233\) 7.71223 + 8.31180i 0.505245 + 0.544524i 0.933239 0.359257i \(-0.116970\pi\)
−0.427994 + 0.903782i \(0.640779\pi\)
\(234\) 0 0
\(235\) 3.57715 2.43886i 0.233348 0.159094i
\(236\) −1.19355 0.179899i −0.0776938 0.0117104i
\(237\) 0 0
\(238\) 6.85851 + 4.06563i 0.444571 + 0.263536i
\(239\) 7.61533 15.8134i 0.492595 1.02288i −0.495439 0.868643i \(-0.664993\pi\)
0.988033 0.154240i \(-0.0492930\pi\)
\(240\) 0 0
\(241\) 3.98556 4.29542i 0.256733 0.276692i −0.591512 0.806296i \(-0.701469\pi\)
0.848245 + 0.529604i \(0.177659\pi\)
\(242\) −11.6669 0.874312i −0.749975 0.0562029i
\(243\) 0 0
\(244\) 11.1665i 0.714864i
\(245\) −8.10384 2.70532i −0.517735 0.172836i
\(246\) 0 0
\(247\) 0.202924 0.517042i 0.0129117 0.0328986i
\(248\) 1.20462 16.0745i 0.0764935 1.02073i
\(249\) 0 0
\(250\) 6.43194 9.43393i 0.406792 0.596654i
\(251\) −1.45893 0.702581i −0.0920865 0.0443465i 0.387274 0.921965i \(-0.373417\pi\)
−0.479360 + 0.877618i \(0.659131\pi\)
\(252\) 0 0
\(253\) −3.78154 + 1.82109i −0.237743 + 0.114491i
\(254\) 1.99939 13.2651i 0.125453 0.832325i
\(255\) 0 0
\(256\) 15.4552 2.32949i 0.965948 0.145593i
\(257\) −21.2854 + 19.7500i −1.32775 + 1.23197i −0.375433 + 0.926849i \(0.622506\pi\)
−0.952314 + 0.305120i \(0.901303\pi\)
\(258\) 0 0
\(259\) −0.738549 + 0.904573i −0.0458912 + 0.0562074i
\(260\) 2.85457 + 2.27644i 0.177033 + 0.141179i
\(261\) 0 0
\(262\) 1.45173 4.70641i 0.0896884 0.290763i
\(263\) 10.7065 + 6.18139i 0.660190 + 0.381161i 0.792349 0.610067i \(-0.208858\pi\)
−0.132159 + 0.991229i \(0.542191\pi\)
\(264\) 0 0
\(265\) −15.1030 + 3.44716i −0.927769 + 0.211757i
\(266\) −0.409907 + 0.121295i −0.0251330 + 0.00743709i
\(267\) 0 0
\(268\) 2.56491 0.791171i 0.156677 0.0483284i
\(269\) 3.80395 + 9.69230i 0.231931 + 0.590950i 0.998700 0.0509729i \(-0.0162322\pi\)
−0.766769 + 0.641923i \(0.778137\pi\)
\(270\) 0 0
\(271\) 5.16634 + 16.7489i 0.313833 + 1.01742i 0.965825 + 0.259195i \(0.0834572\pi\)
−0.651992 + 0.758225i \(0.726067\pi\)
\(272\) −1.09198 + 4.78429i −0.0662111 + 0.290090i
\(273\) 0 0
\(274\) −2.72380 11.9337i −0.164551 0.720944i
\(275\) −1.81609 + 1.04852i −0.109514 + 0.0632281i
\(276\) 0 0
\(277\) 8.46264 + 2.61038i 0.508471 + 0.156842i 0.538367 0.842711i \(-0.319041\pi\)
−0.0298962 + 0.999553i \(0.509518\pi\)
\(278\) −0.0538085 0.718024i −0.00322722 0.0430642i
\(279\) 0 0
\(280\) 0.113952 9.90865i 0.00680991 0.592155i
\(281\) 9.01577 7.18984i 0.537836 0.428910i −0.316529 0.948583i \(-0.602518\pi\)
0.854365 + 0.519673i \(0.173946\pi\)
\(282\) 0 0
\(283\) 0.320975 + 2.12953i 0.0190800 + 0.126587i 0.996343 0.0854430i \(-0.0272305\pi\)
−0.977263 + 0.212030i \(0.931992\pi\)
\(284\) −3.12931 4.58985i −0.185690 0.272357i
\(285\) 0 0
\(286\) 1.07671 + 2.23581i 0.0636671 + 0.132206i
\(287\) 12.1831 8.10264i 0.719144 0.478283i
\(288\) 0 0
\(289\) −7.83669 5.34296i −0.460982 0.314292i
\(290\) −2.77972 2.57920i −0.163231 0.151456i
\(291\) 0 0
\(292\) 11.4944 + 4.51123i 0.672660 + 0.264000i
\(293\) −28.4472 −1.66190 −0.830952 0.556344i \(-0.812204\pi\)
−0.830952 + 0.556344i \(0.812204\pi\)
\(294\) 0 0
\(295\) −1.86096 −0.108349
\(296\) −1.26084 0.494844i −0.0732849 0.0287622i
\(297\) 0 0
\(298\) 7.77648 + 7.21551i 0.450479 + 0.417984i
\(299\) −21.9374 14.9567i −1.26867 0.864967i
\(300\) 0 0
\(301\) 3.00482 + 0.964843i 0.173195 + 0.0556126i
\(302\) 0.630633 + 1.30952i 0.0362889 + 0.0753546i
\(303\) 0 0
\(304\) −0.148215 0.217391i −0.00850069 0.0124682i
\(305\) 2.56594 + 17.0239i 0.146925 + 0.974784i
\(306\) 0 0
\(307\) −19.3774 + 15.4529i −1.10592 + 0.881946i −0.993737 0.111741i \(-0.964357\pi\)
−0.112187 + 0.993687i \(0.535786\pi\)
\(308\) −0.555793 + 1.12095i −0.0316692 + 0.0638723i
\(309\) 0 0
\(310\) −0.526659 7.02778i −0.0299122 0.399151i
\(311\) 30.0487 + 9.26878i 1.70390 + 0.525584i 0.985446 0.169987i \(-0.0543726\pi\)
0.718457 + 0.695572i \(0.244849\pi\)
\(312\) 0 0
\(313\) 13.3170 7.68856i 0.752720 0.434583i −0.0739557 0.997262i \(-0.523562\pi\)
0.826676 + 0.562678i \(0.190229\pi\)
\(314\) 0.290525 + 1.27287i 0.0163953 + 0.0718324i
\(315\) 0 0
\(316\) 1.98284 8.68737i 0.111543 0.488703i
\(317\) 6.56746 + 21.2912i 0.368865 + 1.19583i 0.929829 + 0.367992i \(0.119955\pi\)
−0.560963 + 0.827841i \(0.689569\pi\)
\(318\) 0 0
\(319\) 0.616848 + 1.57170i 0.0345369 + 0.0879985i
\(320\) 9.52114 2.93688i 0.532248 0.164177i
\(321\) 0 0
\(322\) 1.29262 + 20.3933i 0.0720351 + 1.13647i
\(323\) −0.392831 + 0.0896611i −0.0218577 + 0.00498888i
\(324\) 0 0
\(325\) −11.4884 6.63281i −0.637260 0.367922i
\(326\) 5.13885 16.6597i 0.284615 0.922698i
\(327\) 0 0
\(328\) 13.2681 + 10.5810i 0.732610 + 0.584237i
\(329\) −2.19349 + 9.12529i −0.120931 + 0.503094i
\(330\) 0 0
\(331\) 21.9476 20.3644i 1.20635 1.11933i 0.216635 0.976253i \(-0.430492\pi\)
0.989712 0.143074i \(-0.0456986\pi\)
\(332\) −5.14740 + 0.775845i −0.282500 + 0.0425800i
\(333\) 0 0
\(334\) −1.97304 + 13.0903i −0.107960 + 0.716268i
\(335\) 3.72852 1.79556i 0.203711 0.0981019i
\(336\) 0 0
\(337\) −7.76079 3.73740i −0.422757 0.203589i 0.210395 0.977616i \(-0.432525\pi\)
−0.633152 + 0.774027i \(0.718239\pi\)
\(338\) −0.792965 + 1.16307i −0.0431316 + 0.0632624i
\(339\) 0 0
\(340\) 0.197935 2.64125i 0.0107345 0.143242i
\(341\) −1.14643 + 2.92105i −0.0620825 + 0.158184i
\(342\) 0 0
\(343\) 16.9534 7.45531i 0.915398 0.402549i
\(344\) 3.66046i 0.197359i
\(345\) 0 0
\(346\) 27.2048 + 2.03872i 1.46254 + 0.109602i
\(347\) −21.8259 + 23.5228i −1.17168 + 1.26277i −0.213389 + 0.976967i \(0.568450\pi\)
−0.958289 + 0.285801i \(0.907740\pi\)
\(348\) 0 0
\(349\) 3.66405 7.60847i 0.196132 0.407272i −0.779588 0.626292i \(-0.784572\pi\)
0.975720 + 0.219020i \(0.0702860\pi\)
\(350\) 1.40546 + 10.1123i 0.0751248 + 0.540526i
\(351\) 0 0
\(352\) −2.46306 0.371247i −0.131282 0.0197875i
\(353\) 16.7385 11.4121i 0.890900 0.607405i −0.0289908 0.999580i \(-0.509229\pi\)
0.919891 + 0.392174i \(0.128277\pi\)
\(354\) 0 0
\(355\) −5.82545 6.27835i −0.309183 0.333220i
\(356\) −1.63267 2.04730i −0.0865312 0.108507i
\(357\) 0 0
\(358\) −12.7263 + 15.9583i −0.672606 + 0.843422i
\(359\) 9.92008 0.743407i 0.523562 0.0392355i 0.189672 0.981848i \(-0.439258\pi\)
0.333890 + 0.942612i \(0.391639\pi\)
\(360\) 0 0
\(361\) −9.48920 + 16.4358i −0.499431 + 0.865041i
\(362\) 6.29088 + 10.8961i 0.330642 + 0.572688i
\(363\) 0 0
\(364\) −7.89895 + 0.500674i −0.414018 + 0.0262424i
\(365\) 18.5604 + 4.23628i 0.971493 + 0.221737i
\(366\) 0 0
\(367\) −7.78931 + 3.05708i −0.406599 + 0.159578i −0.559821 0.828613i \(-0.689130\pi\)
0.153222 + 0.988192i \(0.451035\pi\)
\(368\) −11.7077 + 4.59494i −0.610306 + 0.239528i
\(369\) 0 0
\(370\) −0.577327 0.131771i −0.0300138 0.00685045i
\(371\) 19.2351 27.5271i 0.998635 1.42914i
\(372\) 0 0
\(373\) 5.90695 + 10.2311i 0.305850 + 0.529748i 0.977450 0.211166i \(-0.0677260\pi\)
−0.671600 + 0.740914i \(0.734393\pi\)
\(374\) 0.900105 1.55903i 0.0465433 0.0806154i
\(375\) 0 0
\(376\) −10.8552 + 0.813484i −0.559813 + 0.0419522i
\(377\) −6.65933 + 8.35054i −0.342973 + 0.430075i
\(378\) 0 0
\(379\) 2.27986 + 2.85885i 0.117108 + 0.146849i 0.836930 0.547309i \(-0.184348\pi\)
−0.719822 + 0.694159i \(0.755777\pi\)
\(380\) 0.0965910 + 0.104100i 0.00495501 + 0.00534023i
\(381\) 0 0
\(382\) −21.4275 + 14.6090i −1.09632 + 0.747462i
\(383\) 33.7006 + 5.07955i 1.72202 + 0.259553i 0.934302 0.356482i \(-0.116024\pi\)
0.787719 + 0.616035i \(0.211262\pi\)
\(384\) 0 0
\(385\) −0.589748 + 1.83666i −0.0300563 + 0.0936047i
\(386\) −2.28039 + 4.73527i −0.116069 + 0.241019i
\(387\) 0 0
\(388\) 6.53743 7.04567i 0.331888 0.357690i
\(389\) −1.57422 0.117972i −0.0798162 0.00598139i 0.0347621 0.999396i \(-0.488933\pi\)
−0.114578 + 0.993414i \(0.536552\pi\)
\(390\) 0 0
\(391\) 19.2610i 0.974070i
\(392\) 14.2448 + 16.0786i 0.719473 + 0.812091i
\(393\) 0 0
\(394\) 4.16936 10.6233i 0.210049 0.535196i
\(395\) 1.02667 13.6999i 0.0516571 0.689317i
\(396\) 0 0
\(397\) −16.7864 + 24.6211i −0.842486 + 1.23570i 0.127330 + 0.991860i \(0.459359\pi\)
−0.969816 + 0.243839i \(0.921593\pi\)
\(398\) −3.00614 1.44768i −0.150684 0.0725656i
\(399\) 0 0
\(400\) −5.66159 + 2.72648i −0.283080 + 0.136324i
\(401\) −2.37414 + 15.7514i −0.118559 + 0.786588i 0.847972 + 0.530040i \(0.177823\pi\)
−0.966531 + 0.256548i \(0.917415\pi\)
\(402\) 0 0
\(403\) −19.6287 + 2.95855i −0.977774 + 0.147376i
\(404\) 5.47146 5.07677i 0.272215 0.252579i
\(405\) 0 0
\(406\) 8.21959 + 0.0945271i 0.407931 + 0.00469130i
\(407\) 0.206146 + 0.164396i 0.0102183 + 0.00814882i
\(408\) 0 0
\(409\) −3.27118 + 10.6049i −0.161749 + 0.524379i −0.999774 0.0212535i \(-0.993234\pi\)
0.838025 + 0.545632i \(0.183710\pi\)
\(410\) 6.42550 + 3.70976i 0.317333 + 0.183212i
\(411\) 0 0
\(412\) −13.7261 + 3.13290i −0.676237 + 0.154347i
\(413\) 2.98859 2.70972i 0.147059 0.133337i
\(414\) 0 0
\(415\) −7.66915 + 2.36562i −0.376464 + 0.116124i
\(416\) −5.75670 14.6678i −0.282245 0.719149i
\(417\) 0 0
\(418\) 0.0284496 + 0.0922313i 0.00139151 + 0.00451118i
\(419\) 0.448076 1.96315i 0.0218900 0.0959062i −0.962803 0.270205i \(-0.912909\pi\)
0.984693 + 0.174299i \(0.0557658\pi\)
\(420\) 0 0
\(421\) −2.65745 11.6431i −0.129516 0.567448i −0.997488 0.0708345i \(-0.977434\pi\)
0.867972 0.496614i \(-0.165423\pi\)
\(422\) −13.4974 + 7.79273i −0.657043 + 0.379344i
\(423\) 0 0
\(424\) 37.2199 + 11.4808i 1.80756 + 0.557558i
\(425\) 0.719154 + 9.59644i 0.0348841 + 0.465496i
\(426\) 0 0
\(427\) −28.9089 23.6030i −1.39900 1.14223i
\(428\) −4.65536 + 3.71253i −0.225025 + 0.179452i
\(429\) 0 0
\(430\) 0.238520 + 1.58248i 0.0115025 + 0.0763138i
\(431\) 20.0900 + 29.4666i 0.967701 + 1.41936i 0.906966 + 0.421203i \(0.138392\pi\)
0.0607346 + 0.998154i \(0.480656\pi\)
\(432\) 0 0
\(433\) −15.3199 31.8121i −0.736228 1.52879i −0.845024 0.534728i \(-0.820414\pi\)
0.108797 0.994064i \(-0.465300\pi\)
\(434\) 11.0788 + 10.5193i 0.531801 + 0.504943i
\(435\) 0 0
\(436\) −5.79472 3.95078i −0.277517 0.189208i
\(437\) −0.757014 0.702407i −0.0362129 0.0336007i
\(438\) 0 0
\(439\) 22.5761 + 8.86048i 1.07750 + 0.422887i 0.836685 0.547684i \(-0.184490\pi\)
0.240814 + 0.970571i \(0.422586\pi\)
\(440\) −2.23741 −0.106664
\(441\) 0 0
\(442\) 11.3879 0.541668
\(443\) 15.6618 + 6.14681i 0.744115 + 0.292044i 0.706948 0.707265i \(-0.250071\pi\)
0.0371671 + 0.999309i \(0.488167\pi\)
\(444\) 0 0
\(445\) −2.95952 2.74603i −0.140295 0.130174i
\(446\) −19.4234 13.2426i −0.919723 0.627056i
\(447\) 0 0
\(448\) −11.0140 + 18.5800i −0.520363 + 0.877825i
\(449\) −4.11154 8.53770i −0.194036 0.402919i 0.781139 0.624357i \(-0.214639\pi\)
−0.975174 + 0.221438i \(0.928925\pi\)
\(450\) 0 0
\(451\) −1.86099 2.72958i −0.0876308 0.128531i
\(452\) −0.968754 6.42727i −0.0455664 0.302313i
\(453\) 0 0
\(454\) 14.7475 11.7607i 0.692133 0.551958i
\(455\) −11.9272 + 2.57838i −0.559158 + 0.120876i
\(456\) 0 0
\(457\) 1.35220 + 18.0438i 0.0632531 + 0.844054i 0.935124 + 0.354319i \(0.115287\pi\)
−0.871871 + 0.489735i \(0.837094\pi\)
\(458\) 14.3323 + 4.42094i 0.669707 + 0.206577i
\(459\) 0 0
\(460\) 5.87886 3.39416i 0.274103 0.158254i
\(461\) −5.09445 22.3202i −0.237272 1.03956i −0.943448 0.331520i \(-0.892438\pi\)
0.706176 0.708036i \(-0.250419\pi\)
\(462\) 0 0
\(463\) −0.225238 + 0.986834i −0.0104677 + 0.0458621i −0.979892 0.199528i \(-0.936059\pi\)
0.969424 + 0.245390i \(0.0789161\pi\)
\(464\) 1.49130 + 4.83466i 0.0692317 + 0.224444i
\(465\) 0 0
\(466\) −4.55365 11.6025i −0.210944 0.537477i
\(467\) −11.4864 + 3.54309i −0.531528 + 0.163955i −0.548890 0.835895i \(-0.684949\pi\)
0.0173621 + 0.999849i \(0.494473\pi\)
\(468\) 0 0
\(469\) −3.37327 + 8.31259i −0.155763 + 0.383840i
\(470\) −4.63987 + 1.05902i −0.214021 + 0.0488489i
\(471\) 0 0
\(472\) 4.05219 + 2.33953i 0.186517 + 0.107686i
\(473\) 0.210034 0.680915i 0.00965739 0.0313085i
\(474\) 0 0
\(475\) −0.403395 0.321697i −0.0185090 0.0147605i
\(476\) 3.52802 + 4.52989i 0.161706 + 0.207627i
\(477\) 0 0
\(478\) −14.1433 + 13.1231i −0.646900 + 0.600236i
\(479\) −11.7948 + 1.77777i −0.538917 + 0.0812286i −0.412860 0.910794i \(-0.635470\pi\)
−0.126056 + 0.992023i \(0.540232\pi\)
\(480\) 0 0
\(481\) −0.248596 + 1.64932i −0.0113350 + 0.0752027i
\(482\) −5.80339 + 2.79476i −0.264337 + 0.127298i
\(483\) 0 0
\(484\) −7.59099 3.65563i −0.345045 0.166165i
\(485\) 8.34758 12.2437i 0.379044 0.555956i
\(486\) 0 0
\(487\) 2.35956 31.4861i 0.106922 1.42677i −0.643314 0.765602i \(-0.722441\pi\)
0.750236 0.661170i \(-0.229940\pi\)
\(488\) 15.8145 40.2948i 0.715890 1.82406i
\(489\) 0 0
\(490\) 7.20598 + 6.02282i 0.325533 + 0.272083i
\(491\) 27.7128i 1.25066i −0.780360 0.625331i \(-0.784964\pi\)
0.780360 0.625331i \(-0.215036\pi\)
\(492\) 0 0
\(493\) 7.72651 + 0.579022i 0.347985 + 0.0260778i
\(494\) −0.415293 + 0.447580i −0.0186849 + 0.0201376i
\(495\) 0 0
\(496\) −4.07985 + 8.47189i −0.183190 + 0.380399i
\(497\) 18.4971 + 1.60027i 0.829709 + 0.0717818i
\(498\) 0 0
\(499\) −15.6910 2.36504i −0.702427 0.105874i −0.211889 0.977294i \(-0.567962\pi\)
−0.490538 + 0.871420i \(0.663200\pi\)
\(500\) 6.79376 4.63191i 0.303826 0.207145i
\(501\) 0 0
\(502\) 1.21072 + 1.30485i 0.0540371 + 0.0582381i
\(503\) 4.07333 + 5.10779i 0.181621 + 0.227745i 0.864305 0.502969i \(-0.167759\pi\)
−0.682684 + 0.730714i \(0.739187\pi\)
\(504\) 0 0
\(505\) 7.17490 8.99703i 0.319279 0.400363i
\(506\) 4.60091 0.344790i 0.204535 0.0153278i
\(507\) 0 0
\(508\) 4.83031 8.36635i 0.214311 0.371197i
\(509\) 21.9330 + 37.9891i 0.972164 + 1.68384i 0.688993 + 0.724768i \(0.258053\pi\)
0.283171 + 0.959069i \(0.408613\pi\)
\(510\) 0 0
\(511\) −35.9751 + 20.2223i −1.59145 + 0.894580i
\(512\) −17.9880 4.10565i −0.794967 0.181446i
\(513\) 0 0
\(514\) 29.7125 11.6613i 1.31056 0.514358i
\(515\) −20.2062 + 7.93033i −0.890389 + 0.349452i
\(516\) 0 0
\(517\) 2.06595 + 0.471539i 0.0908602 + 0.0207382i
\(518\) 1.11902 0.629021i 0.0491669 0.0276376i
\(519\) 0 0
\(520\) −7.07680 12.2574i −0.310338 0.537521i
\(521\) −5.19339 + 8.99522i −0.227527 + 0.394088i −0.957074 0.289842i \(-0.906397\pi\)
0.729548 + 0.683930i \(0.239731\pi\)
\(522\) 0 0
\(523\) −17.4606 + 1.30849i −0.763501 + 0.0572165i −0.450788 0.892631i \(-0.648857\pi\)
−0.312713 + 0.949848i \(0.601238\pi\)
\(524\) 2.21143 2.77304i 0.0966066 0.121141i
\(525\) 0 0
\(526\) −8.47319 10.6250i −0.369449 0.463274i
\(527\) 9.79460 + 10.5561i 0.426660 + 0.459830i
\(528\) 0 0
\(529\) −21.7834 + 14.8516i −0.947103 + 0.645724i
\(530\) 16.8389 + 2.53805i 0.731435 + 0.110246i
\(531\) 0 0
\(532\) −0.306698 0.0265338i −0.0132970 0.00115039i
\(533\) 9.06744 18.8287i 0.392754 0.815563i
\(534\) 0 0
\(535\) −6.24420 + 6.72965i −0.269960 + 0.290948i
\(536\) −10.3760 0.777577i −0.448177 0.0335862i
\(537\) 0 0
\(538\) 11.4456i 0.493453i
\(539\) −1.72723 3.80828i −0.0743972 0.164034i
\(540\) 0 0
\(541\) −6.58030 + 16.7663i −0.282909 + 0.720841i 0.716813 + 0.697266i \(0.245600\pi\)
−0.999722 + 0.0235754i \(0.992495\pi\)
\(542\) 1.43985 19.2135i 0.0618469 0.825290i
\(543\) 0 0
\(544\) −6.43915 + 9.44450i −0.276076 + 0.404930i
\(545\) −9.74214 4.69157i −0.417308 0.200965i
\(546\) 0 0
\(547\) 23.9587 11.5379i 1.02440 0.493325i 0.155251 0.987875i \(-0.450381\pi\)
0.869149 + 0.494550i \(0.164667\pi\)
\(548\) 1.31381 8.71653i 0.0561230 0.372352i
\(549\) 0 0
\(550\) 2.27945 0.343571i 0.0971960 0.0146499i
\(551\) −0.304527 + 0.282560i −0.0129733 + 0.0120374i
\(552\) 0 0
\(553\) 18.2995 + 23.4961i 0.778172 + 0.999155i
\(554\) −7.61125 6.06977i −0.323371 0.257880i
\(555\) 0 0
\(556\) 0.152839 0.495492i 0.00648182 0.0210135i
\(557\) 30.2571 + 17.4690i 1.28204 + 0.740184i 0.977220 0.212228i \(-0.0680719\pi\)
0.304815 + 0.952411i \(0.401405\pi\)
\(558\) 0 0
\(559\) 4.39463 1.00305i 0.185873 0.0424244i
\(560\) −2.17356 + 5.35620i −0.0918497 + 0.226341i
\(561\) 0 0
\(562\) −12.1131 + 3.73639i −0.510959 + 0.157610i
\(563\) 11.8233 + 30.1254i 0.498294 + 1.26963i 0.929981 + 0.367609i \(0.119823\pi\)
−0.431686 + 0.902024i \(0.642081\pi\)
\(564\) 0 0
\(565\) −2.95382 9.57603i −0.124268 0.402867i
\(566\) 0.526785 2.30800i 0.0221424 0.0970123i
\(567\) 0 0
\(568\) 4.79185 + 20.9945i 0.201061 + 0.880908i
\(569\) −5.09419 + 2.94113i −0.213560 + 0.123299i −0.602965 0.797768i \(-0.706014\pi\)
0.389405 + 0.921067i \(0.372681\pi\)
\(570\) 0 0
\(571\) −9.47090 2.92138i −0.396345 0.122256i 0.0901746 0.995926i \(-0.471257\pi\)
−0.486519 + 0.873670i \(0.661734\pi\)
\(572\) 0.133548 + 1.78208i 0.00558393 + 0.0745123i
\(573\) 0 0
\(574\) −15.7207 + 3.39843i −0.656168 + 0.141848i
\(575\) −19.2831 + 15.3777i −0.804159 + 0.641295i
\(576\) 0 0
\(577\) −1.86601 12.3801i −0.0776829 0.515392i −0.993503 0.113804i \(-0.963696\pi\)
0.915820 0.401588i \(-0.131542\pi\)
\(578\) 5.87332 + 8.61457i 0.244298 + 0.358319i
\(579\) 0 0
\(580\) −1.18483 2.46033i −0.0491975 0.102160i
\(581\) 8.87162 14.9660i 0.368057 0.620893i
\(582\) 0 0
\(583\) −6.26485 4.27130i −0.259464 0.176899i
\(584\) −35.0889 32.5578i −1.45199 1.34725i
\(585\) 0 0
\(586\) 29.1093 + 11.4246i 1.20249 + 0.471944i
\(587\) −42.3771 −1.74909 −0.874545 0.484944i \(-0.838840\pi\)
−0.874545 + 0.484944i \(0.838840\pi\)
\(588\) 0 0
\(589\) −0.772074 −0.0318127
\(590\) 1.90427 + 0.747373i 0.0783978 + 0.0307689i
\(591\) 0 0
\(592\) 0.579189 + 0.537408i 0.0238045 + 0.0220874i
\(593\) −32.0983 21.8843i −1.31812 0.898680i −0.319321 0.947647i \(-0.603455\pi\)
−0.998800 + 0.0489669i \(0.984407\pi\)
\(594\) 0 0
\(595\) 6.41953 + 6.09532i 0.263175 + 0.249884i
\(596\) 3.31466 + 6.88296i 0.135774 + 0.281937i
\(597\) 0 0
\(598\) 16.4413 + 24.1150i 0.672335 + 0.986134i
\(599\) −5.22634 34.6745i −0.213543 1.41676i −0.796686 0.604393i \(-0.793416\pi\)
0.583143 0.812369i \(-0.301823\pi\)
\(600\) 0 0
\(601\) 27.7268 22.1114i 1.13100 0.901941i 0.134958 0.990851i \(-0.456910\pi\)
0.996040 + 0.0889104i \(0.0283385\pi\)
\(602\) −2.68727 2.19405i −0.109525 0.0894228i
\(603\) 0 0
\(604\) 0.0782198 + 1.04377i 0.00318272 + 0.0424704i
\(605\) −12.4128 3.82884i −0.504652 0.155665i
\(606\) 0 0
\(607\) 7.36201 4.25046i 0.298815 0.172521i −0.343095 0.939301i \(-0.611475\pi\)
0.641910 + 0.766780i \(0.278142\pi\)
\(608\) −0.136375 0.597499i −0.00553075 0.0242318i
\(609\) 0 0
\(610\) 4.21122 18.4506i 0.170507 0.747042i
\(611\) 3.95120 + 12.8095i 0.159849 + 0.518216i
\(612\) 0 0
\(613\) −16.1317 41.1030i −0.651555 1.66013i −0.747102 0.664709i \(-0.768555\pi\)
0.0955474 0.995425i \(-0.469540\pi\)
\(614\) 26.0343 8.03053i 1.05066 0.324086i
\(615\) 0 0
\(616\) 3.59314 3.25786i 0.144772 0.131263i
\(617\) 0.434012 0.0990604i 0.0174727 0.00398802i −0.213776 0.976883i \(-0.568576\pi\)
0.231248 + 0.972895i \(0.425719\pi\)
\(618\) 0 0
\(619\) 29.1881 + 16.8517i 1.17317 + 0.677328i 0.954424 0.298454i \(-0.0964710\pi\)
0.218743 + 0.975782i \(0.429804\pi\)
\(620\) 1.49594 4.84971i 0.0600783 0.194769i
\(621\) 0 0
\(622\) −27.0256 21.5522i −1.08363 0.864165i
\(623\) 8.75125 + 0.100641i 0.350611 + 0.00403211i
\(624\) 0 0
\(625\) −3.57347 + 3.31569i −0.142939 + 0.132628i
\(626\) −16.7147 + 2.51933i −0.668053 + 0.100693i
\(627\) 0 0
\(628\) −0.140133 + 0.929720i −0.00559191 + 0.0370999i
\(629\) 1.09017 0.524996i 0.0434677 0.0209330i
\(630\) 0 0
\(631\) 35.6887 + 17.1868i 1.42075 + 0.684195i 0.977252 0.212082i \(-0.0680244\pi\)
0.443494 + 0.896277i \(0.353739\pi\)
\(632\) −19.4585 + 28.5404i −0.774019 + 1.13528i
\(633\) 0 0
\(634\) 1.83034 24.4243i 0.0726923 0.970011i
\(635\) 5.44154 13.8648i 0.215941 0.550208i
\(636\) 0 0
\(637\) 15.4001 21.5078i 0.610172 0.852170i
\(638\) 1.85601i 0.0734802i
\(639\) 0 0
\(640\) −0.772517 0.0578921i −0.0305364 0.00228839i
\(641\) −15.2531 + 16.4390i −0.602463 + 0.649300i −0.958474 0.285182i \(-0.907946\pi\)
0.356011 + 0.934482i \(0.384137\pi\)
\(642\) 0 0
\(643\) 17.6815 36.7159i 0.697289 1.44794i −0.187654 0.982235i \(-0.560088\pi\)
0.884943 0.465700i \(-0.154197\pi\)
\(644\) −4.49889 + 14.0109i −0.177281 + 0.552108i
\(645\) 0 0
\(646\) 0.437982 + 0.0660152i 0.0172322 + 0.00259733i
\(647\) 29.0910 19.8339i 1.14368 0.779750i 0.165238 0.986254i \(-0.447161\pi\)
0.978446 + 0.206503i \(0.0662085\pi\)
\(648\) 0 0
\(649\) −0.619543 0.667709i −0.0243192 0.0262099i
\(650\) 9.09198 + 11.4010i 0.356617 + 0.447183i
\(651\) 0 0
\(652\) 7.82802 9.81602i 0.306569 0.384425i
\(653\) −30.3295 + 2.27288i −1.18688 + 0.0889447i −0.653499 0.756927i \(-0.726700\pi\)
−0.533386 + 0.845872i \(0.679081\pi\)
\(654\) 0 0
\(655\) 2.73420 4.73578i 0.106834 0.185042i
\(656\) −4.94974 8.57320i −0.193255 0.334727i
\(657\) 0 0
\(658\) 5.90931 8.45676i 0.230369 0.329679i
\(659\) −45.9980 10.4987i −1.79183 0.408973i −0.808160 0.588963i \(-0.799536\pi\)
−0.983668 + 0.179990i \(0.942394\pi\)
\(660\) 0 0
\(661\) −6.83240 + 2.68152i −0.265749 + 0.104299i −0.494475 0.869192i \(-0.664640\pi\)
0.228725 + 0.973491i \(0.426544\pi\)
\(662\) −30.6368 + 12.0241i −1.19073 + 0.467328i
\(663\) 0 0
\(664\) 19.6733 + 4.49030i 0.763472 + 0.174258i
\(665\) −0.473671 + 0.0300235i −0.0183682 + 0.00116426i
\(666\) 0 0
\(667\) 9.92901 + 17.1976i 0.384453 + 0.665892i
\(668\) −4.76666 + 8.25610i −0.184428 + 0.319438i
\(669\) 0 0
\(670\) −4.53640 + 0.339956i −0.175256 + 0.0131337i
\(671\) −5.25388 + 6.58816i −0.202824 + 0.254333i
\(672\) 0 0
\(673\) 13.7235 + 17.2087i 0.529001 + 0.663346i 0.972493 0.232932i \(-0.0748320\pi\)
−0.443492 + 0.896278i \(0.646261\pi\)
\(674\) 6.44045 + 6.94116i 0.248077 + 0.267363i
\(675\) 0 0
\(676\) −0.837572 + 0.571047i −0.0322143 + 0.0219633i
\(677\) 42.7750 + 6.44729i 1.64398 + 0.247789i 0.904835 0.425762i \(-0.139994\pi\)
0.739140 + 0.673551i \(0.235232\pi\)
\(678\) 0 0
\(679\) 4.42212 + 31.8173i 0.169705 + 1.22104i
\(680\) −4.45491 + 9.25071i −0.170838 + 0.354749i
\(681\) 0 0
\(682\) 2.34622 2.52862i 0.0898413 0.0968259i
\(683\) −34.9513 2.61923i −1.33737 0.100222i −0.613248 0.789891i \(-0.710137\pi\)
−0.724125 + 0.689669i \(0.757756\pi\)
\(684\) 0 0
\(685\) 13.5906i 0.519271i
\(686\) −20.3421 + 0.820244i −0.776664 + 0.0313171i
\(687\) 0 0
\(688\) 0.780099 1.98766i 0.0297410 0.0757788i
\(689\) 3.58445 47.8311i 0.136556 1.82222i
\(690\) 0 0
\(691\) 20.4381 29.9772i 0.777502 1.14039i −0.209205 0.977872i \(-0.567087\pi\)
0.986706 0.162514i \(-0.0519602\pi\)
\(692\) 17.7007 + 8.52419i 0.672878 + 0.324041i
\(693\) 0 0
\(694\) 31.7808 15.3048i 1.20638 0.580963i
\(695\) 0.119152 0.790519i 0.00451968 0.0299861i
\(696\) 0 0
\(697\) −14.9910 + 2.25954i −0.567826 + 0.0855860i
\(698\) −6.80492 + 6.31405i −0.257570 + 0.238990i
\(699\) 0 0
\(700\) −1.71836 + 7.14867i −0.0649479 + 0.270194i
\(701\) −12.3967 9.88606i −0.468218 0.373391i 0.360773 0.932654i \(-0.382513\pi\)
−0.828991 + 0.559262i \(0.811084\pi\)
\(702\) 0 0
\(703\) −0.0191221 + 0.0619923i −0.000721203 + 0.00233808i
\(704\) 4.22348 + 2.43843i 0.159179 + 0.0919018i
\(705\) 0 0
\(706\) −21.7112 + 4.95545i −0.817113 + 0.186501i
\(707\) 1.57802 + 24.8959i 0.0593477 + 0.936307i
\(708\) 0 0
\(709\) 19.9754 6.16161i 0.750193 0.231404i 0.104000 0.994577i \(-0.466836\pi\)
0.646194 + 0.763173i \(0.276360\pi\)
\(710\) 3.43962 + 8.76400i 0.129087 + 0.328907i
\(711\) 0 0
\(712\) 2.99205 + 9.69999i 0.112132 + 0.363523i
\(713\) −8.21249 + 35.9813i −0.307560 + 1.34751i
\(714\) 0 0
\(715\) 0.613099 + 2.68616i 0.0229286 + 0.100457i
\(716\) −12.7298 + 7.34955i −0.475735 + 0.274666i
\(717\) 0 0
\(718\) −10.4495 3.22325i −0.389972 0.120291i
\(719\) −2.28617 30.5069i −0.0852599 1.13771i −0.861664 0.507479i \(-0.830577\pi\)
0.776404 0.630235i \(-0.217042\pi\)
\(720\) 0 0
\(721\) 20.9026 42.1575i 0.778452 1.57003i
\(722\) 16.3107 13.0074i 0.607023 0.484085i
\(723\) 0 0
\(724\) 1.35042 + 8.95945i 0.0501879 + 0.332975i
\(725\) 5.58907 + 8.19765i 0.207573 + 0.304453i
\(726\) 0 0
\(727\) −5.02146 10.4272i −0.186236 0.386722i 0.786857 0.617135i \(-0.211707\pi\)
−0.973093 + 0.230413i \(0.925992\pi\)
\(728\) 29.2127 + 9.38014i 1.08269 + 0.347651i
\(729\) 0 0
\(730\) −17.2910 11.7888i −0.639969 0.436324i
\(731\) −2.39709 2.22417i −0.0886594 0.0822639i
\(732\) 0 0
\(733\) 8.21013 + 3.22224i 0.303248 + 0.119016i 0.512086 0.858934i \(-0.328873\pi\)
−0.208838 + 0.977950i \(0.566968\pi\)
\(734\) 9.19834 0.339517
\(735\) 0 0
\(736\) −29.2961 −1.07987
\(737\) 1.88552 + 0.740013i 0.0694541 + 0.0272587i
\(738\) 0 0
\(739\) 6.75975 + 6.27213i 0.248661 + 0.230724i 0.794649 0.607069i \(-0.207655\pi\)
−0.545988 + 0.837793i \(0.683845\pi\)
\(740\) −0.352348 0.240227i −0.0129526 0.00883092i
\(741\) 0 0
\(742\) −30.7378 + 20.4429i −1.12842 + 0.750482i
\(743\) −20.2631 42.0767i −0.743379 1.54364i −0.836487 0.547987i \(-0.815394\pi\)
0.0931076 0.995656i \(-0.470320\pi\)
\(744\) 0 0
\(745\) 6.63496 + 9.73170i 0.243086 + 0.356542i
\(746\) −1.93555 12.8415i −0.0708654 0.470161i
\(747\) 0 0
\(748\) 1.01357 0.808296i 0.0370598 0.0295542i
\(749\) 0.228848 19.8995i 0.00836194 0.727111i
\(750\) 0 0
\(751\) 3.43092 + 45.7824i 0.125196 + 1.67062i 0.607271 + 0.794495i \(0.292264\pi\)
−0.482075 + 0.876130i \(0.660117\pi\)
\(752\) 6.06782 + 1.87168i 0.221271 + 0.0682530i
\(753\) 0 0
\(754\) 10.1679 5.87046i 0.370295 0.213790i
\(755\) 0.359095 + 1.57330i 0.0130688 + 0.0572582i
\(756\) 0 0
\(757\) −3.22626 + 14.1352i −0.117261 + 0.513752i 0.881848 + 0.471534i \(0.156300\pi\)
−0.999108 + 0.0422180i \(0.986558\pi\)
\(758\) −1.18479 3.84099i −0.0430335 0.139511i
\(759\) 0 0
\(760\) −0.201120 0.512445i −0.00729538 0.0185883i
\(761\) 18.9984 5.86022i 0.688690 0.212433i 0.0693930 0.997589i \(-0.477894\pi\)
0.619297 + 0.785157i \(0.287418\pi\)
\(762\) 0 0
\(763\) 22.4766 6.65103i 0.813707 0.240783i
\(764\) −18.2077 + 4.15579i −0.658732 + 0.150351i
\(765\) 0 0
\(766\) −32.4450 18.7321i −1.17228 0.676819i
\(767\) 1.69838 5.50602i 0.0613250 0.198811i
\(768\) 0 0
\(769\) −9.19228 7.33060i −0.331482 0.264348i 0.443578 0.896236i \(-0.353709\pi\)
−0.775060 + 0.631888i \(0.782280\pi\)
\(770\) 1.34109 1.64256i 0.0483294 0.0591937i
\(771\) 0 0
\(772\) −2.77452 + 2.57437i −0.0998570 + 0.0926537i
\(773\) −5.23175 + 0.788560i −0.188173 + 0.0283625i −0.242453 0.970163i \(-0.577952\pi\)
0.0542795 + 0.998526i \(0.482714\pi\)
\(774\) 0 0
\(775\) −2.74828 + 18.2337i −0.0987212 + 0.654973i
\(776\) −33.5689 + 16.1659i −1.20505 + 0.580323i
\(777\) 0 0
\(778\) 1.56348 + 0.752933i 0.0560535 + 0.0269939i
\(779\) 0.457885 0.671594i 0.0164054 0.0240623i
\(780\) 0 0
\(781\) 0.313271 4.18032i 0.0112097 0.149583i
\(782\) 7.73531 19.7093i 0.276614 0.704802i
\(783\) 0 0
\(784\) −4.30848 11.7666i −0.153874 0.420236i
\(785\) 1.44960i 0.0517384i
\(786\) 0 0
\(787\) −28.4751 2.13391i −1.01503 0.0760658i −0.443186 0.896430i \(-0.646152\pi\)
−0.571842 + 0.820364i \(0.693771\pi\)
\(788\)