Properties

Label 441.2.bg.a.395.13
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 395.13
Character \(\chi\) \(=\) 441.395
Dual form 441.2.bg.a.278.13

$q$-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 0.698402 0.715705i \(-0.253895\pi\)
0.0251617 + 0.999683i \(0.491990\pi\)
\(3\) 0 0
\(4\) −0.580301 0.538441i −0.290151 0.269220i
\(5\) 1.00842 + 0.687530i 0.450980 + 0.307473i 0.767426 0.641138i \(-0.221537\pi\)
−0.316446 + 0.948610i \(0.602490\pi\)
\(6\) 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 0.998235 0.0593840i \(-0.0189136\pi\)
−0.971390 + 0.237489i \(0.923676\pi\)
\(12\) 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 0.595664 0.803234i \(-0.296889\pi\)
0.0396825 + 0.999212i \(0.487365\pi\)
\(18\) 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 \(0.166413\pi\)
−0.434601 + 0.900623i \(0.643111\pi\)
\(24\) 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 0.0411199 0.999154i \(-0.486907\pi\)
0.470565 + 0.882366i \(0.344050\pi\)
\(30\) 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 −0.780412 0.625266i \(-0.784991\pi\)
0.00227370 + 0.999997i \(0.499276\pi\)
\(42\) 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 −0.804664 0.593731i \(-0.797654\pi\)
0.993700 + 0.112075i \(0.0357496\pi\)
\(48\) 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 \(0.575102\pi\)
−0.952108 + 0.305763i \(0.901088\pi\)
\(54\) 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 −0.642546 0.766248i \(-0.722122\pi\)
0.478531 + 0.878070i \(0.341169\pi\)
\(60\) 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 −0.203652 0.979043i \(-0.565281\pi\)
−0.608275 + 0.793726i \(0.708138\pi\)
\(72\) 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 −0.954155 0.299314i \(-0.903242\pi\)
0.504129 + 0.863628i \(0.331814\pi\)
\(84\) 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 −0.0266252 0.999645i \(-0.508476\pi\)
−0.320093 + 0.947386i \(0.603714\pi\)
\(90\) 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 \(-0.820771\pi\)
0.915735 0.401784i \(-0.131610\pi\)
\(102\) 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 \(0.166065\pi\)
−0.975347 + 0.220676i \(0.929174\pi\)
\(108\) 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 0.273169 0.961966i \(-0.411928\pi\)
−0.877062 + 0.480378i \(0.840500\pi\)
\(114\) 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 \(-0.961102\pi\)
0.963289 0.268468i \(-0.0865173\pi\)
\(132\) 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 0.458817 0.888531i \(-0.348273\pi\)
−0.994735 + 0.102484i \(0.967321\pi\)
\(138\) 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 0.703557 0.710639i \(-0.251594\pi\)
0.0323867 + 0.999475i \(0.489689\pi\)
\(150\) 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 \(0.0828580\pi\)
−0.758945 + 0.651155i \(0.774285\pi\)
\(168\) 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 0.803776 0.594932i \(-0.202821\pi\)
0.999248 + 0.0387726i \(0.0123448\pi\)
\(174\) 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 \(0.339360\pi\)
−0.892593 + 0.450864i \(0.851116\pi\)
\(180\) 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 \(0.516018\pi\)
−0.911319 + 0.411701i \(0.864935\pi\)
\(192\) 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 \(-0.879415\pi\)
0.929098 0.369833i \(-0.120585\pi\)
\(198\) 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 \(-0.640487\pi\)
0.996620 0.0821526i \(-0.0261795\pi\)
\(228\) 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 0.427994 0.903782i \(-0.359221\pi\)
−0.933239 + 0.359257i \(0.883030\pi\)
\(234\) 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 \(0.335007\pi\)
−0.988033 + 0.154240i \(0.950707\pi\)
\(240\) 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 0.479360 0.877618i \(-0.340869\pi\)
−0.387274 + 0.921965i \(0.626583\pi\)
\(252\) 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 \(-0.377494\pi\)
0.952314 0.305120i \(-0.0986965\pi\)
\(258\) 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 0.132159 0.991229i \(-0.457809\pi\)
−0.792349 + 0.610067i \(0.791142\pi\)
\(264\) 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 0.766769 0.641923i \(-0.221863\pi\)
−0.998700 + 0.0509729i \(0.983768\pi\)
\(270\) 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 −0.854365 0.519673i \(-0.826054\pi\)
0.316529 + 0.948583i \(0.397482\pi\)
\(282\) 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 \(-0.187796\pi\)
0.830952 + 0.556344i \(0.187796\pi\)
\(294\) 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 −0.718457 0.695572i \(-0.755151\pi\)
−0.985446 + 0.169987i \(0.945627\pi\)
\(312\) 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 \(-0.880045\pi\)
0.560963 0.827841i \(-0.310431\pi\)
\(318\) 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 \(-0.431550\pi\)
0.958289 0.285801i \(-0.0922596\pi\)
\(348\) 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 −0.919891 0.392174i \(-0.871723\pi\)
0.0289908 + 0.999580i \(0.490771\pi\)
\(354\) 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 −0.333890 0.942612i \(-0.608361\pi\)
−0.189672 + 0.981848i \(0.560742\pi\)
\(360\) 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 −0.787719 0.616035i \(-0.788738\pi\)
−0.934302 + 0.356482i \(0.883976\pi\)
\(384\) 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 0.114578 0.993414i \(-0.463448\pi\)
−0.0347621 + 0.999396i \(0.511067\pi\)
\(390\) 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 \(-0.822177\pi\)
0.966531 0.256548i \(-0.0825852\pi\)
\(402\) 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 −0.984693 0.174299i \(-0.944234\pi\)
0.962803 + 0.270205i \(0.0870914\pi\)
\(420\) 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 \(-0.861608\pi\)
−0.0607346 0.998154i \(-0.519344\pi\)
\(432\) 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 −0.0371671 0.999309i \(-0.511833\pi\)
−0.706948 + 0.707265i \(0.749929\pi\)
\(444\) 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 0.975174 0.221438i \(-0.0710752\pi\)
−0.781139 + 0.624357i \(0.785361\pi\)
\(450\) 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 \(0.107562\pi\)
−0.706176 + 0.708036i \(0.749581\pi\)
\(462\) 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 −0.0173621 0.999849i \(-0.505527\pi\)
0.548890 + 0.835895i \(0.315051\pi\)
\(468\) 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 0.126056 0.992023i \(-0.459768\pi\)
0.412860 + 0.910794i \(0.364530\pi\)
\(480\) 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 \(0.215036\pi\)
−0.780360 + 0.625331i \(0.784964\pi\)
\(492\) 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 0.682684 0.730714i \(-0.260813\pi\)
−0.864305 + 0.502969i \(0.832241\pi\)
\(504\) 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 \(-0.741947\pi\)
−0.283171 0.959069i \(-0.591387\pi\)
\(510\) 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 −0.729548 0.683930i \(-0.760269\pi\)
0.957074 + 0.289842i \(0.0936028\pi\)
\(522\) 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 −0.304815 0.952411i \(-0.598595\pi\)
−0.977220 + 0.212228i \(0.931928\pi\)
\(558\) 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 \(-0.880177\pi\)
0.431686 0.902024i \(-0.357919\pi\)
\(564\) 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 −0.389405 0.921067i \(-0.627319\pi\)
0.602965 + 0.797768i \(0.293986\pi\)
\(570\) 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 \(-0.161160\pi\)
0.874545 + 0.484944i \(0.161160\pi\)
\(588\) 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 0.998800 0.0489669i \(-0.0155929\pi\)
0.319321 + 0.947647i \(0.396545\pi\)
\(594\) 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 \(0.206584\pi\)
−0.583143 + 0.812369i \(0.698177\pi\)
\(600\) 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 −0.231248 0.972895i \(-0.574281\pi\)
0.213776 + 0.976883i \(0.431424\pi\)
\(618\) 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 −0.356011 0.934482i \(-0.615863\pi\)
0.958474 + 0.285182i \(0.0920539\pi\)
\(642\) 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 −0.978446 0.206503i \(-0.933792\pi\)
−0.165238 + 0.986254i \(0.552839\pi\)
\(648\) 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 0.533386 0.845872i \(-0.320919\pi\)
0.653499 + 0.756927i \(0.273300\pi\)
\(654\) 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 0.983668 0.179990i \(-0.0576065\pi\)
0.808160 + 0.588963i \(0.200464\pi\)
\(660\) 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 −0.739140 0.673551i \(-0.764768\pi\)
−0.904835 + 0.425762i \(0.860006\pi\)
\(678\) 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 0.724125 0.689669i \(-0.242244\pi\)
0.613248 + 0.789891i \(0.289863\pi\)
\(684\) 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 0.828991 0.559262i \(-0.188916\pi\)
−0.360773 + 0.932654i \(0.617487\pi\)
\(702\) 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 \(0.169423\pi\)
−0.776404 + 0.630235i \(0.782958\pi\)
\(720\) 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 \(0.184606\pi\)
−0.0931076 + 0.995656i \(0.529680\pi\)
\(744\) 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 −0.619297 0.785157i \(-0.712582\pi\)
−0.0693930 + 0.997589i \(0.522106\pi\)
\(762\) 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 −0.0542795 0.998526i \(-0.517286\pi\)
0.242453 + 0.970163i \(0.422048\pi\)
\(774\) 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 \(0.693771\pi\)