Properties

Label 576.2.bb.e.241.2
Level $576$
Weight $2$
Character 576.241
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 241.2
Character \(\chi\) \(=\) 576.241
Dual form 576.2.bb.e.337.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.71768 - 0.222657i) q^{3} +(-0.798307 + 2.97932i) q^{5} +(1.78208 + 1.02889i) q^{7} +(2.90085 + 0.764906i) q^{9} +O(q^{10})\) \(q+(-1.71768 - 0.222657i) q^{3} +(-0.798307 + 2.97932i) q^{5} +(1.78208 + 1.02889i) q^{7} +(2.90085 + 0.764906i) q^{9} +(0.446347 - 0.119598i) q^{11} +(-5.67550 - 1.52075i) q^{13} +(2.03460 - 4.93977i) q^{15} +0.0443921 q^{17} +(1.10726 - 1.10726i) q^{19} +(-2.83196 - 2.16409i) q^{21} +(-7.89263 + 4.55681i) q^{23} +(-3.90893 - 2.25682i) q^{25} +(-4.81242 - 1.95976i) q^{27} +(1.86402 + 6.95662i) q^{29} +(-0.542236 - 0.939180i) q^{31} +(-0.793310 + 0.106049i) q^{33} +(-4.48803 + 4.48803i) q^{35} +(-0.769054 - 0.769054i) q^{37} +(9.41009 + 3.87585i) q^{39} +(-5.77193 + 3.33242i) q^{41} +(-11.0600 + 2.96351i) q^{43} +(-4.59467 + 8.03193i) q^{45} +(1.22453 - 2.12095i) q^{47} +(-1.38279 - 2.39506i) q^{49} +(-0.0762514 - 0.00988420i) q^{51} +(2.44801 + 2.44801i) q^{53} +1.42529i q^{55} +(-2.14846 + 1.65538i) q^{57} +(0.962265 - 3.59122i) q^{59} +(0.318210 + 1.18758i) q^{61} +(4.38255 + 4.34777i) q^{63} +(9.06158 - 15.6951i) q^{65} +(5.52723 + 1.48102i) q^{67} +(14.5716 - 6.06980i) q^{69} +6.88571i q^{71} -13.1963i q^{73} +(6.21180 + 4.74685i) q^{75} +(0.918480 + 0.246106i) q^{77} +(-3.46441 + 6.00054i) q^{79} +(7.82984 + 4.43775i) q^{81} +(-0.157584 - 0.588112i) q^{83} +(-0.0354385 + 0.132258i) q^{85} +(-1.65285 - 12.3643i) q^{87} -5.30004i q^{89} +(-8.54954 - 8.54954i) q^{91} +(0.722273 + 1.73394i) q^{93} +(2.41495 + 4.18282i) q^{95} +(-5.88304 + 10.1897i) q^{97} +(1.38627 - 0.00552307i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.71768 0.222657i −0.991703 0.128551i
\(4\) 0 0
\(5\) −0.798307 + 2.97932i −0.357014 + 1.33239i 0.520918 + 0.853607i \(0.325590\pi\)
−0.877932 + 0.478786i \(0.841077\pi\)
\(6\) 0 0
\(7\) 1.78208 + 1.02889i 0.673564 + 0.388882i 0.797426 0.603417i \(-0.206195\pi\)
−0.123862 + 0.992299i \(0.539528\pi\)
\(8\) 0 0
\(9\) 2.90085 + 0.764906i 0.966949 + 0.254969i
\(10\) 0 0
\(11\) 0.446347 0.119598i 0.134579 0.0360602i −0.190901 0.981609i \(-0.561141\pi\)
0.325480 + 0.945549i \(0.394474\pi\)
\(12\) 0 0
\(13\) −5.67550 1.52075i −1.57410 0.421779i −0.637008 0.770857i \(-0.719828\pi\)
−0.937094 + 0.349078i \(0.886495\pi\)
\(14\) 0 0
\(15\) 2.03460 4.93977i 0.525332 1.27544i
\(16\) 0 0
\(17\) 0.0443921 0.0107667 0.00538333 0.999986i \(-0.498286\pi\)
0.00538333 + 0.999986i \(0.498286\pi\)
\(18\) 0 0
\(19\) 1.10726 1.10726i 0.254023 0.254023i −0.568595 0.822618i \(-0.692513\pi\)
0.822618 + 0.568595i \(0.192513\pi\)
\(20\) 0 0
\(21\) −2.83196 2.16409i −0.617984 0.472243i
\(22\) 0 0
\(23\) −7.89263 + 4.55681i −1.64573 + 0.950161i −0.666984 + 0.745072i \(0.732415\pi\)
−0.978743 + 0.205089i \(0.934252\pi\)
\(24\) 0 0
\(25\) −3.90893 2.25682i −0.781786 0.451364i
\(26\) 0 0
\(27\) −4.81242 1.95976i −0.926150 0.377155i
\(28\) 0 0
\(29\) 1.86402 + 6.95662i 0.346140 + 1.29181i 0.891275 + 0.453464i \(0.149812\pi\)
−0.545134 + 0.838349i \(0.683521\pi\)
\(30\) 0 0
\(31\) −0.542236 0.939180i −0.0973884 0.168682i 0.813214 0.581964i \(-0.197716\pi\)
−0.910603 + 0.413282i \(0.864382\pi\)
\(32\) 0 0
\(33\) −0.793310 + 0.106049i −0.138098 + 0.0184608i
\(34\) 0 0
\(35\) −4.48803 + 4.48803i −0.758615 + 0.758615i
\(36\) 0 0
\(37\) −0.769054 0.769054i −0.126432 0.126432i 0.641060 0.767491i \(-0.278495\pi\)
−0.767491 + 0.641060i \(0.778495\pi\)
\(38\) 0 0
\(39\) 9.41009 + 3.87585i 1.50682 + 0.620632i
\(40\) 0 0
\(41\) −5.77193 + 3.33242i −0.901423 + 0.520437i −0.877662 0.479281i \(-0.840898\pi\)
−0.0237617 + 0.999718i \(0.507564\pi\)
\(42\) 0 0
\(43\) −11.0600 + 2.96351i −1.68663 + 0.451932i −0.969517 0.245023i \(-0.921204\pi\)
−0.717115 + 0.696955i \(0.754538\pi\)
\(44\) 0 0
\(45\) −4.59467 + 8.03193i −0.684932 + 1.19733i
\(46\) 0 0
\(47\) 1.22453 2.12095i 0.178617 0.309373i −0.762790 0.646646i \(-0.776171\pi\)
0.941407 + 0.337273i \(0.109504\pi\)
\(48\) 0 0
\(49\) −1.38279 2.39506i −0.197541 0.342151i
\(50\) 0 0
\(51\) −0.0762514 0.00988420i −0.0106773 0.00138406i
\(52\) 0 0
\(53\) 2.44801 + 2.44801i 0.336260 + 0.336260i 0.854958 0.518698i \(-0.173583\pi\)
−0.518698 + 0.854958i \(0.673583\pi\)
\(54\) 0 0
\(55\) 1.42529i 0.192186i
\(56\) 0 0
\(57\) −2.14846 + 1.65538i −0.284570 + 0.219260i
\(58\) 0 0
\(59\) 0.962265 3.59122i 0.125276 0.467537i −0.874573 0.484894i \(-0.838858\pi\)
0.999849 + 0.0173563i \(0.00552495\pi\)
\(60\) 0 0
\(61\) 0.318210 + 1.18758i 0.0407426 + 0.152054i 0.983301 0.181989i \(-0.0582536\pi\)
−0.942558 + 0.334043i \(0.891587\pi\)
\(62\) 0 0
\(63\) 4.38255 + 4.34777i 0.552149 + 0.547767i
\(64\) 0 0
\(65\) 9.06158 15.6951i 1.12395 1.94674i
\(66\) 0 0
\(67\) 5.52723 + 1.48102i 0.675258 + 0.180935i 0.580122 0.814529i \(-0.303005\pi\)
0.0951361 + 0.995464i \(0.469671\pi\)
\(68\) 0 0
\(69\) 14.5716 6.06980i 1.75422 0.730718i
\(70\) 0 0
\(71\) 6.88571i 0.817184i 0.912717 + 0.408592i \(0.133980\pi\)
−0.912717 + 0.408592i \(0.866020\pi\)
\(72\) 0 0
\(73\) 13.1963i 1.54451i −0.635312 0.772255i \(-0.719129\pi\)
0.635312 0.772255i \(-0.280871\pi\)
\(74\) 0 0
\(75\) 6.21180 + 4.74685i 0.717276 + 0.548119i
\(76\) 0 0
\(77\) 0.918480 + 0.246106i 0.104670 + 0.0280464i
\(78\) 0 0
\(79\) −3.46441 + 6.00054i −0.389777 + 0.675113i −0.992419 0.122898i \(-0.960781\pi\)
0.602643 + 0.798011i \(0.294115\pi\)
\(80\) 0 0
\(81\) 7.82984 + 4.43775i 0.869982 + 0.493084i
\(82\) 0 0
\(83\) −0.157584 0.588112i −0.0172971 0.0645537i 0.956738 0.290951i \(-0.0939718\pi\)
−0.974035 + 0.226398i \(0.927305\pi\)
\(84\) 0 0
\(85\) −0.0354385 + 0.132258i −0.00384385 + 0.0143454i
\(86\) 0 0
\(87\) −1.65285 12.3643i −0.177205 1.32559i
\(88\) 0 0
\(89\) 5.30004i 0.561803i −0.959737 0.280902i \(-0.909367\pi\)
0.959737 0.280902i \(-0.0906335\pi\)
\(90\) 0 0
\(91\) −8.54954 8.54954i −0.896235 0.896235i
\(92\) 0 0
\(93\) 0.722273 + 1.73394i 0.0748962 + 0.179802i
\(94\) 0 0
\(95\) 2.41495 + 4.18282i 0.247769 + 0.429148i
\(96\) 0 0
\(97\) −5.88304 + 10.1897i −0.597333 + 1.03461i 0.395880 + 0.918302i \(0.370439\pi\)
−0.993213 + 0.116309i \(0.962894\pi\)
\(98\) 0 0
\(99\) 1.38627 0.00552307i 0.139325 0.000555089i
\(100\) 0 0
\(101\) −5.65271 + 1.51464i −0.562466 + 0.150712i −0.528839 0.848722i \(-0.677372\pi\)
−0.0336269 + 0.999434i \(0.510706\pi\)
\(102\) 0 0
\(103\) 1.13680 0.656334i 0.112013 0.0646705i −0.442947 0.896548i \(-0.646067\pi\)
0.554960 + 0.831877i \(0.312734\pi\)
\(104\) 0 0
\(105\) 8.70829 6.70971i 0.849842 0.654800i
\(106\) 0 0
\(107\) 2.92966 + 2.92966i 0.283221 + 0.283221i 0.834392 0.551171i \(-0.185819\pi\)
−0.551171 + 0.834392i \(0.685819\pi\)
\(108\) 0 0
\(109\) 11.5193 11.5193i 1.10335 1.10335i 0.109344 0.994004i \(-0.465125\pi\)
0.994004 0.109344i \(-0.0348750\pi\)
\(110\) 0 0
\(111\) 1.14975 + 1.49222i 0.109130 + 0.141636i
\(112\) 0 0
\(113\) 3.79250 + 6.56880i 0.356768 + 0.617941i 0.987419 0.158126i \(-0.0505452\pi\)
−0.630651 + 0.776067i \(0.717212\pi\)
\(114\) 0 0
\(115\) −7.27547 27.1524i −0.678441 2.53198i
\(116\) 0 0
\(117\) −15.3005 8.75268i −1.41454 0.809186i
\(118\) 0 0
\(119\) 0.0791104 + 0.0456744i 0.00725204 + 0.00418696i
\(120\) 0 0
\(121\) −9.34136 + 5.39324i −0.849214 + 0.490294i
\(122\) 0 0
\(123\) 10.6563 4.43888i 0.960847 0.400240i
\(124\) 0 0
\(125\) −1.06075 + 1.06075i −0.0948761 + 0.0948761i
\(126\) 0 0
\(127\) 10.6374 0.943915 0.471958 0.881621i \(-0.343548\pi\)
0.471958 + 0.881621i \(0.343548\pi\)
\(128\) 0 0
\(129\) 19.6574 2.62779i 1.73073 0.231364i
\(130\) 0 0
\(131\) 18.5982 + 4.98338i 1.62493 + 0.435400i 0.952446 0.304708i \(-0.0985589\pi\)
0.672488 + 0.740108i \(0.265226\pi\)
\(132\) 0 0
\(133\) 3.11247 0.833985i 0.269886 0.0723157i
\(134\) 0 0
\(135\) 9.68053 12.7732i 0.833167 1.09935i
\(136\) 0 0
\(137\) 8.30213 + 4.79324i 0.709299 + 0.409514i 0.810802 0.585321i \(-0.199032\pi\)
−0.101502 + 0.994835i \(0.532365\pi\)
\(138\) 0 0
\(139\) 1.82598 6.81465i 0.154878 0.578011i −0.844238 0.535968i \(-0.819947\pi\)
0.999116 0.0420428i \(-0.0133866\pi\)
\(140\) 0 0
\(141\) −2.57560 + 3.37047i −0.216905 + 0.283845i
\(142\) 0 0
\(143\) −2.71512 −0.227050
\(144\) 0 0
\(145\) −22.2141 −1.84478
\(146\) 0 0
\(147\) 1.84191 + 4.42183i 0.151918 + 0.364707i
\(148\) 0 0
\(149\) −5.22476 + 19.4991i −0.428029 + 1.59743i 0.329189 + 0.944264i \(0.393225\pi\)
−0.757218 + 0.653162i \(0.773442\pi\)
\(150\) 0 0
\(151\) 3.86699 + 2.23261i 0.314691 + 0.181687i 0.649024 0.760768i \(-0.275178\pi\)
−0.334333 + 0.942455i \(0.608511\pi\)
\(152\) 0 0
\(153\) 0.128775 + 0.0339558i 0.0104108 + 0.00274516i
\(154\) 0 0
\(155\) 3.23099 0.865741i 0.259519 0.0695380i
\(156\) 0 0
\(157\) 15.9143 + 4.26421i 1.27010 + 0.340321i 0.830068 0.557662i \(-0.188302\pi\)
0.440029 + 0.897984i \(0.354968\pi\)
\(158\) 0 0
\(159\) −3.65983 4.74996i −0.290243 0.376696i
\(160\) 0 0
\(161\) −18.7538 −1.47800
\(162\) 0 0
\(163\) −5.24124 + 5.24124i −0.410525 + 0.410525i −0.881922 0.471396i \(-0.843750\pi\)
0.471396 + 0.881922i \(0.343750\pi\)
\(164\) 0 0
\(165\) 0.317350 2.44819i 0.0247056 0.190591i
\(166\) 0 0
\(167\) −11.2974 + 6.52257i −0.874220 + 0.504731i −0.868748 0.495254i \(-0.835075\pi\)
−0.00547195 + 0.999985i \(0.501742\pi\)
\(168\) 0 0
\(169\) 18.6403 + 10.7620i 1.43387 + 0.827847i
\(170\) 0 0
\(171\) 4.05894 2.36504i 0.310395 0.180859i
\(172\) 0 0
\(173\) −0.371831 1.38769i −0.0282698 0.105504i 0.950349 0.311185i \(-0.100726\pi\)
−0.978619 + 0.205681i \(0.934059\pi\)
\(174\) 0 0
\(175\) −4.64402 8.04369i −0.351055 0.608046i
\(176\) 0 0
\(177\) −2.45247 + 5.95432i −0.184339 + 0.447554i
\(178\) 0 0
\(179\) 2.50772 2.50772i 0.187436 0.187436i −0.607151 0.794587i \(-0.707688\pi\)
0.794587 + 0.607151i \(0.207688\pi\)
\(180\) 0 0
\(181\) 10.8795 + 10.8795i 0.808666 + 0.808666i 0.984432 0.175766i \(-0.0562403\pi\)
−0.175766 + 0.984432i \(0.556240\pi\)
\(182\) 0 0
\(183\) −0.282161 2.11073i −0.0208580 0.156029i
\(184\) 0 0
\(185\) 2.90520 1.67732i 0.213594 0.123319i
\(186\) 0 0
\(187\) 0.0198143 0.00530922i 0.00144896 0.000388248i
\(188\) 0 0
\(189\) −6.55976 8.44387i −0.477152 0.614201i
\(190\) 0 0
\(191\) 6.59227 11.4182i 0.477000 0.826188i −0.522653 0.852546i \(-0.675057\pi\)
0.999653 + 0.0263575i \(0.00839081\pi\)
\(192\) 0 0
\(193\) 8.71808 + 15.1002i 0.627541 + 1.08693i 0.988044 + 0.154175i \(0.0492718\pi\)
−0.360503 + 0.932758i \(0.617395\pi\)
\(194\) 0 0
\(195\) −19.0595 + 24.9416i −1.36488 + 1.78610i
\(196\) 0 0
\(197\) −8.36275 8.36275i −0.595822 0.595822i 0.343376 0.939198i \(-0.388429\pi\)
−0.939198 + 0.343376i \(0.888429\pi\)
\(198\) 0 0
\(199\) 15.6420i 1.10883i 0.832240 + 0.554416i \(0.187058\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(200\) 0 0
\(201\) −9.16425 3.77459i −0.646396 0.266239i
\(202\) 0 0
\(203\) −3.83573 + 14.3151i −0.269216 + 1.00473i
\(204\) 0 0
\(205\) −5.32059 19.8567i −0.371606 1.38685i
\(206\) 0 0
\(207\) −26.3809 + 7.18150i −1.83360 + 0.499149i
\(208\) 0 0
\(209\) 0.361796 0.626649i 0.0250259 0.0433462i
\(210\) 0 0
\(211\) 18.6925 + 5.00865i 1.28685 + 0.344810i 0.836462 0.548024i \(-0.184620\pi\)
0.450386 + 0.892834i \(0.351287\pi\)
\(212\) 0 0
\(213\) 1.53315 11.8275i 0.105050 0.810404i
\(214\) 0 0
\(215\) 35.3170i 2.40860i
\(216\) 0 0
\(217\) 2.23159i 0.151491i
\(218\) 0 0
\(219\) −2.93825 + 22.6670i −0.198548 + 1.53170i
\(220\) 0 0
\(221\) −0.251948 0.0675091i −0.0169478 0.00454116i
\(222\) 0 0
\(223\) 2.07790 3.59904i 0.139147 0.241009i −0.788027 0.615641i \(-0.788897\pi\)
0.927174 + 0.374631i \(0.122231\pi\)
\(224\) 0 0
\(225\) −9.61296 9.53666i −0.640864 0.635778i
\(226\) 0 0
\(227\) 1.66928 + 6.22983i 0.110794 + 0.413488i 0.998938 0.0460768i \(-0.0146719\pi\)
−0.888144 + 0.459565i \(0.848005\pi\)
\(228\) 0 0
\(229\) 2.51329 9.37974i 0.166083 0.619831i −0.831816 0.555051i \(-0.812699\pi\)
0.997900 0.0647799i \(-0.0206345\pi\)
\(230\) 0 0
\(231\) −1.52286 0.627237i −0.100197 0.0412692i
\(232\) 0 0
\(233\) 22.2096i 1.45500i 0.686108 + 0.727499i \(0.259318\pi\)
−0.686108 + 0.727499i \(0.740682\pi\)
\(234\) 0 0
\(235\) 5.34145 + 5.34145i 0.348438 + 0.348438i
\(236\) 0 0
\(237\) 7.28681 9.53563i 0.473329 0.619406i
\(238\) 0 0
\(239\) 4.02723 + 6.97537i 0.260500 + 0.451199i 0.966375 0.257137i \(-0.0827792\pi\)
−0.705875 + 0.708337i \(0.749446\pi\)
\(240\) 0 0
\(241\) 5.07653 8.79280i 0.327008 0.566394i −0.654909 0.755708i \(-0.727293\pi\)
0.981917 + 0.189314i \(0.0606263\pi\)
\(242\) 0 0
\(243\) −12.4611 9.36600i −0.799377 0.600829i
\(244\) 0 0
\(245\) 8.23954 2.20778i 0.526405 0.141050i
\(246\) 0 0
\(247\) −7.96812 + 4.60040i −0.507000 + 0.292716i
\(248\) 0 0
\(249\) 0.139732 + 1.04528i 0.00885516 + 0.0662417i
\(250\) 0 0
\(251\) −11.0682 11.0682i −0.698617 0.698617i 0.265495 0.964112i \(-0.414465\pi\)
−0.964112 + 0.265495i \(0.914465\pi\)
\(252\) 0 0
\(253\) −2.97786 + 2.97786i −0.187217 + 0.187217i
\(254\) 0 0
\(255\) 0.0903202 0.219287i 0.00565607 0.0137323i
\(256\) 0 0
\(257\) −10.3807 17.9800i −0.647533 1.12156i −0.983710 0.179761i \(-0.942467\pi\)
0.336177 0.941799i \(-0.390866\pi\)
\(258\) 0 0
\(259\) −0.579249 2.16179i −0.0359928 0.134327i
\(260\) 0 0
\(261\) 0.0860808 + 21.6059i 0.00532827 + 1.33737i
\(262\) 0 0
\(263\) −9.13436 5.27373i −0.563249 0.325192i 0.191200 0.981551i \(-0.438762\pi\)
−0.754448 + 0.656359i \(0.772096\pi\)
\(264\) 0 0
\(265\) −9.24767 + 5.33914i −0.568080 + 0.327981i
\(266\) 0 0
\(267\) −1.18009 + 9.10377i −0.0722203 + 0.557142i
\(268\) 0 0
\(269\) −0.529850 + 0.529850i −0.0323055 + 0.0323055i −0.723075 0.690770i \(-0.757272\pi\)
0.690770 + 0.723075i \(0.257272\pi\)
\(270\) 0 0
\(271\) −14.3682 −0.872804 −0.436402 0.899752i \(-0.643747\pi\)
−0.436402 + 0.899752i \(0.643747\pi\)
\(272\) 0 0
\(273\) 12.7818 + 16.5890i 0.773587 + 1.00401i
\(274\) 0 0
\(275\) −2.01465 0.539824i −0.121488 0.0325526i
\(276\) 0 0
\(277\) −8.19567 + 2.19602i −0.492430 + 0.131946i −0.496485 0.868046i \(-0.665376\pi\)
0.00405455 + 0.999992i \(0.498709\pi\)
\(278\) 0 0
\(279\) −0.854559 3.13918i −0.0511611 0.187938i
\(280\) 0 0
\(281\) −6.21827 3.59012i −0.370951 0.214169i 0.302923 0.953015i \(-0.402038\pi\)
−0.673874 + 0.738847i \(0.735371\pi\)
\(282\) 0 0
\(283\) −3.98753 + 14.8817i −0.237034 + 0.884623i 0.740187 + 0.672401i \(0.234737\pi\)
−0.977221 + 0.212222i \(0.931930\pi\)
\(284\) 0 0
\(285\) −3.21678 7.72245i −0.190546 0.457438i
\(286\) 0 0
\(287\) −13.7147 −0.809555
\(288\) 0 0
\(289\) −16.9980 −0.999884
\(290\) 0 0
\(291\) 12.3740 16.1928i 0.725377 0.949239i
\(292\) 0 0
\(293\) 4.11281 15.3492i 0.240273 0.896711i −0.735428 0.677603i \(-0.763019\pi\)
0.975701 0.219108i \(-0.0703146\pi\)
\(294\) 0 0
\(295\) 9.93122 + 5.73379i 0.578218 + 0.333834i
\(296\) 0 0
\(297\) −2.38239 0.299175i −0.138240 0.0173599i
\(298\) 0 0
\(299\) 51.7244 13.8595i 2.99130 0.801517i
\(300\) 0 0
\(301\) −22.7589 6.09824i −1.31180 0.351496i
\(302\) 0 0
\(303\) 10.0468 1.34305i 0.577173 0.0771563i
\(304\) 0 0
\(305\) −3.79220 −0.217141
\(306\) 0 0
\(307\) −7.37130 + 7.37130i −0.420702 + 0.420702i −0.885446 0.464743i \(-0.846147\pi\)
0.464743 + 0.885446i \(0.346147\pi\)
\(308\) 0 0
\(309\) −2.09880 + 0.874254i −0.119397 + 0.0497346i
\(310\) 0 0
\(311\) −6.23360 + 3.59897i −0.353475 + 0.204079i −0.666215 0.745760i \(-0.732087\pi\)
0.312740 + 0.949839i \(0.398753\pi\)
\(312\) 0 0
\(313\) 9.23161 + 5.32987i 0.521801 + 0.301262i 0.737671 0.675160i \(-0.235925\pi\)
−0.215870 + 0.976422i \(0.569259\pi\)
\(314\) 0 0
\(315\) −16.4520 + 9.58617i −0.926966 + 0.540119i
\(316\) 0 0
\(317\) −3.89052 14.5196i −0.218513 0.815503i −0.984900 0.173123i \(-0.944614\pi\)
0.766387 0.642379i \(-0.222053\pi\)
\(318\) 0 0
\(319\) 1.66400 + 2.88213i 0.0931662 + 0.161369i
\(320\) 0 0
\(321\) −4.37991 5.68453i −0.244463 0.317280i
\(322\) 0 0
\(323\) 0.0491536 0.0491536i 0.00273498 0.00273498i
\(324\) 0 0
\(325\) 18.7531 + 18.7531i 1.04023 + 1.04023i
\(326\) 0 0
\(327\) −22.3513 + 17.2216i −1.23603 + 0.952357i
\(328\) 0 0
\(329\) 4.36444 2.51981i 0.240619 0.138922i
\(330\) 0 0
\(331\) 24.3818 6.53309i 1.34015 0.359091i 0.483658 0.875257i \(-0.339308\pi\)
0.856488 + 0.516166i \(0.172641\pi\)
\(332\) 0 0
\(333\) −1.64265 2.81916i −0.0900169 0.154489i
\(334\) 0 0
\(335\) −8.82485 + 15.2851i −0.482153 + 0.835113i
\(336\) 0 0
\(337\) 1.80217 + 3.12146i 0.0981707 + 0.170037i 0.910928 0.412566i \(-0.135368\pi\)
−0.812757 + 0.582603i \(0.802034\pi\)
\(338\) 0 0
\(339\) −5.05171 12.1275i −0.274371 0.658677i
\(340\) 0 0
\(341\) −0.354350 0.354350i −0.0191891 0.0191891i
\(342\) 0 0
\(343\) 20.0953i 1.08505i
\(344\) 0 0
\(345\) 6.45126 + 48.2591i 0.347324 + 2.59818i
\(346\) 0 0
\(347\) 4.13293 15.4243i 0.221867 0.828020i −0.761768 0.647850i \(-0.775669\pi\)
0.983635 0.180170i \(-0.0576648\pi\)
\(348\) 0 0
\(349\) 4.05477 + 15.1326i 0.217047 + 0.810029i 0.985436 + 0.170047i \(0.0543918\pi\)
−0.768389 + 0.639983i \(0.778942\pi\)
\(350\) 0 0
\(351\) 24.3326 + 18.4411i 1.29878 + 0.984312i
\(352\) 0 0
\(353\) 2.05577 3.56070i 0.109418 0.189517i −0.806117 0.591756i \(-0.798435\pi\)
0.915534 + 0.402239i \(0.131768\pi\)
\(354\) 0 0
\(355\) −20.5147 5.49691i −1.08881 0.291746i
\(356\) 0 0
\(357\) −0.125717 0.0960684i −0.00665363 0.00508448i
\(358\) 0 0
\(359\) 20.1902i 1.06560i 0.846242 + 0.532800i \(0.178860\pi\)
−0.846242 + 0.532800i \(0.821140\pi\)
\(360\) 0 0
\(361\) 16.5479i 0.870945i
\(362\) 0 0
\(363\) 17.2463 7.18394i 0.905196 0.377059i
\(364\) 0 0
\(365\) 39.3160 + 10.5347i 2.05789 + 0.551411i
\(366\) 0 0
\(367\) −11.2398 + 19.4679i −0.586714 + 1.01622i 0.407946 + 0.913006i \(0.366245\pi\)
−0.994659 + 0.103212i \(0.967088\pi\)
\(368\) 0 0
\(369\) −19.2925 + 5.25187i −1.00433 + 0.273402i
\(370\) 0 0
\(371\) 1.84383 + 6.88128i 0.0957270 + 0.357258i
\(372\) 0 0
\(373\) 6.87405 25.6543i 0.355925 1.32833i −0.523392 0.852092i \(-0.675334\pi\)
0.879317 0.476237i \(-0.158000\pi\)
\(374\) 0 0
\(375\) 2.05821 1.58584i 0.106285 0.0818925i
\(376\) 0 0
\(377\) 42.3171i 2.17944i
\(378\) 0 0
\(379\) 6.62881 + 6.62881i 0.340499 + 0.340499i 0.856555 0.516056i \(-0.172600\pi\)
−0.516056 + 0.856555i \(0.672600\pi\)
\(380\) 0 0
\(381\) −18.2716 2.36848i −0.936083 0.121341i
\(382\) 0 0
\(383\) −1.98902 3.44509i −0.101634 0.176036i 0.810724 0.585429i \(-0.199074\pi\)
−0.912358 + 0.409393i \(0.865741\pi\)
\(384\) 0 0
\(385\) −1.46646 + 2.53998i −0.0747376 + 0.129449i
\(386\) 0 0
\(387\) −34.3502 + 0.136856i −1.74612 + 0.00695676i
\(388\) 0 0
\(389\) −4.54738 + 1.21847i −0.230561 + 0.0617787i −0.372250 0.928133i \(-0.621414\pi\)
0.141688 + 0.989911i \(0.454747\pi\)
\(390\) 0 0
\(391\) −0.350370 + 0.202286i −0.0177190 + 0.0102301i
\(392\) 0 0
\(393\) −30.8362 12.7009i −1.55548 0.640674i
\(394\) 0 0
\(395\) −15.1119 15.1119i −0.760360 0.760360i
\(396\) 0 0
\(397\) −18.1361 + 18.1361i −0.910223 + 0.910223i −0.996289 0.0860661i \(-0.972570\pi\)
0.0860661 + 0.996289i \(0.472570\pi\)
\(398\) 0 0
\(399\) −5.53193 + 0.739506i −0.276943 + 0.0370216i
\(400\) 0 0
\(401\) −2.47526 4.28727i −0.123608 0.214096i 0.797580 0.603214i \(-0.206113\pi\)
−0.921188 + 0.389118i \(0.872780\pi\)
\(402\) 0 0
\(403\) 1.64921 + 6.15492i 0.0821528 + 0.306599i
\(404\) 0 0
\(405\) −19.4721 + 19.7849i −0.967576 + 0.983120i
\(406\) 0 0
\(407\) −0.435242 0.251287i −0.0215742 0.0124558i
\(408\) 0 0
\(409\) 12.4390 7.18164i 0.615067 0.355109i −0.159879 0.987137i \(-0.551110\pi\)
0.774946 + 0.632027i \(0.217777\pi\)
\(410\) 0 0
\(411\) −13.1932 10.0818i −0.650771 0.497297i
\(412\) 0 0
\(413\) 5.40979 5.40979i 0.266199 0.266199i
\(414\) 0 0
\(415\) 1.87798 0.0921862
\(416\) 0 0
\(417\) −4.65378 + 11.2988i −0.227896 + 0.553305i
\(418\) 0 0
\(419\) −24.4257 6.54483i −1.19327 0.319736i −0.393093 0.919499i \(-0.628595\pi\)
−0.800178 + 0.599763i \(0.795262\pi\)
\(420\) 0 0
\(421\) −4.96853 + 1.33131i −0.242151 + 0.0648842i −0.377853 0.925865i \(-0.623338\pi\)
0.135702 + 0.990750i \(0.456671\pi\)
\(422\) 0 0
\(423\) 5.17452 5.21591i 0.251594 0.253606i
\(424\) 0 0
\(425\) −0.173526 0.100185i −0.00841723 0.00485969i
\(426\) 0 0
\(427\) −0.654803 + 2.44376i −0.0316882 + 0.118262i
\(428\) 0 0
\(429\) 4.66371 + 0.604540i 0.225166 + 0.0291875i
\(430\) 0 0
\(431\) −20.0912 −0.967760 −0.483880 0.875134i \(-0.660773\pi\)
−0.483880 + 0.875134i \(0.660773\pi\)
\(432\) 0 0
\(433\) 21.8262 1.04890 0.524449 0.851442i \(-0.324271\pi\)
0.524449 + 0.851442i \(0.324271\pi\)
\(434\) 0 0
\(435\) 38.1567 + 4.94611i 1.82947 + 0.237148i
\(436\) 0 0
\(437\) −3.69362 + 13.7848i −0.176690 + 0.659415i
\(438\) 0 0
\(439\) 25.7554 + 14.8699i 1.22924 + 0.709700i 0.966870 0.255268i \(-0.0821636\pi\)
0.262367 + 0.964968i \(0.415497\pi\)
\(440\) 0 0
\(441\) −2.17926 8.00541i −0.103774 0.381210i
\(442\) 0 0
\(443\) −33.8185 + 9.06164i −1.60677 + 0.430532i −0.947077 0.321007i \(-0.895979\pi\)
−0.659689 + 0.751539i \(0.729312\pi\)
\(444\) 0 0
\(445\) 15.7905 + 4.23106i 0.748543 + 0.200571i
\(446\) 0 0
\(447\) 13.3161 32.3298i 0.629828 1.52915i
\(448\) 0 0
\(449\) 27.6805 1.30633 0.653163 0.757217i \(-0.273442\pi\)
0.653163 + 0.757217i \(0.273442\pi\)
\(450\) 0 0
\(451\) −2.17773 + 2.17773i −0.102545 + 0.102545i
\(452\) 0 0
\(453\) −6.14514 4.69591i −0.288724 0.220633i
\(454\) 0 0
\(455\) 32.2970 18.6467i 1.51411 0.874169i
\(456\) 0 0
\(457\) −13.8114 7.97402i −0.646070 0.373009i 0.140879 0.990027i \(-0.455007\pi\)
−0.786949 + 0.617018i \(0.788341\pi\)
\(458\) 0 0
\(459\) −0.213633 0.0869977i −0.00997155 0.00406071i
\(460\) 0 0
\(461\) 4.87059 + 18.1773i 0.226846 + 0.846600i 0.981657 + 0.190658i \(0.0610620\pi\)
−0.754811 + 0.655943i \(0.772271\pi\)
\(462\) 0 0
\(463\) −6.07529 10.5227i −0.282343 0.489032i 0.689619 0.724173i \(-0.257778\pi\)
−0.971961 + 0.235141i \(0.924445\pi\)
\(464\) 0 0
\(465\) −5.74257 + 0.767664i −0.266305 + 0.0355996i
\(466\) 0 0
\(467\) 15.9698 15.9698i 0.738992 0.738992i −0.233391 0.972383i \(-0.574982\pi\)
0.972383 + 0.233391i \(0.0749822\pi\)
\(468\) 0 0
\(469\) 8.32618 + 8.32618i 0.384467 + 0.384467i
\(470\) 0 0
\(471\) −26.3862 10.8680i −1.21581 0.500770i
\(472\) 0 0
\(473\) −4.58216 + 2.64551i −0.210688 + 0.121641i
\(474\) 0 0
\(475\) −6.82710 + 1.82931i −0.313249 + 0.0839347i
\(476\) 0 0
\(477\) 5.22881 + 8.97380i 0.239411 + 0.410882i
\(478\) 0 0
\(479\) 9.27240 16.0603i 0.423667 0.733813i −0.572628 0.819815i \(-0.694076\pi\)
0.996295 + 0.0860026i \(0.0274094\pi\)
\(480\) 0 0
\(481\) 3.19523 + 5.53430i 0.145690 + 0.252343i
\(482\) 0 0
\(483\) 32.2130 + 4.17565i 1.46574 + 0.189999i
\(484\) 0 0
\(485\) −25.6620 25.6620i −1.16525 1.16525i
\(486\) 0 0
\(487\) 6.58835i 0.298547i −0.988796 0.149273i \(-0.952307\pi\)
0.988796 0.149273i \(-0.0476934\pi\)
\(488\) 0 0
\(489\) 10.1698 7.83577i 0.459893 0.354346i
\(490\) 0 0
\(491\) −1.30320 + 4.86361i −0.0588126 + 0.219491i −0.989077 0.147397i \(-0.952910\pi\)
0.930265 + 0.366889i \(0.119577\pi\)
\(492\) 0 0
\(493\) 0.0827478 + 0.308819i 0.00372678 + 0.0139085i
\(494\) 0 0
\(495\) −1.09021 + 4.13454i −0.0490013 + 0.185834i
\(496\) 0 0
\(497\) −7.08461 + 12.2709i −0.317788 + 0.550425i
\(498\) 0 0
\(499\) 20.9744 + 5.62008i 0.938944 + 0.251589i 0.695664 0.718367i \(-0.255110\pi\)
0.243279 + 0.969956i \(0.421777\pi\)
\(500\) 0 0
\(501\) 20.8576 8.68824i 0.931851 0.388162i
\(502\) 0 0
\(503\) 9.04140i 0.403136i 0.979475 + 0.201568i \(0.0646037\pi\)
−0.979475 + 0.201568i \(0.935396\pi\)
\(504\) 0 0
\(505\) 18.0504i 0.803232i
\(506\) 0 0
\(507\) −29.6219 22.6361i −1.31556 1.00530i
\(508\) 0 0
\(509\) −14.1941 3.80331i −0.629144 0.168579i −0.0698626 0.997557i \(-0.522256\pi\)
−0.559281 + 0.828978i \(0.688923\pi\)
\(510\) 0 0
\(511\) 13.5775 23.5169i 0.600633 1.04033i
\(512\) 0 0
\(513\) −7.49856 + 3.15864i −0.331070 + 0.139457i
\(514\) 0 0
\(515\) 1.04791 + 3.91086i 0.0461765 + 0.172333i
\(516\) 0 0
\(517\) 0.292904 1.09313i 0.0128819 0.0480760i
\(518\) 0 0
\(519\) 0.329708 + 2.46640i 0.0144726 + 0.108263i
\(520\) 0 0
\(521\) 7.25761i 0.317962i −0.987282 0.158981i \(-0.949179\pi\)
0.987282 0.158981i \(-0.0508208\pi\)
\(522\) 0 0
\(523\) 19.0736 + 19.0736i 0.834028 + 0.834028i 0.988065 0.154037i \(-0.0492274\pi\)
−0.154037 + 0.988065i \(0.549227\pi\)
\(524\) 0 0
\(525\) 6.18597 + 14.8505i 0.269978 + 0.648129i
\(526\) 0 0
\(527\) −0.0240710 0.0416922i −0.00104855 0.00181614i
\(528\) 0 0
\(529\) 30.0291 52.0119i 1.30561 2.26139i
\(530\) 0 0
\(531\) 5.53833 9.68155i 0.240343 0.420143i
\(532\) 0 0
\(533\) 37.8264 10.1355i 1.63844 0.439019i
\(534\) 0 0
\(535\) −11.0672 + 6.38963i −0.478476 + 0.276248i
\(536\) 0 0
\(537\) −4.86582 + 3.74910i −0.209976 + 0.161786i
\(538\) 0 0
\(539\) −0.903648 0.903648i −0.0389229 0.0389229i
\(540\) 0 0
\(541\) 12.1246 12.1246i 0.521279 0.521279i −0.396679 0.917957i \(-0.629837\pi\)
0.917957 + 0.396679i \(0.129837\pi\)
\(542\) 0 0
\(543\) −16.2651 21.1099i −0.698001 0.905911i
\(544\) 0 0
\(545\) 25.1237 + 43.5156i 1.07618 + 1.86400i
\(546\) 0 0
\(547\) 9.94693 + 37.1224i 0.425300 + 1.58724i 0.763267 + 0.646083i \(0.223594\pi\)
−0.337967 + 0.941158i \(0.609739\pi\)
\(548\) 0 0
\(549\) 0.0146950 + 3.68838i 0.000627167 + 0.157416i
\(550\) 0 0
\(551\) 9.76675 + 5.63884i 0.416078 + 0.240223i
\(552\) 0 0
\(553\) −12.3477 + 7.12897i −0.525079 + 0.303155i
\(554\) 0 0
\(555\) −5.36367 + 2.23423i −0.227675 + 0.0948379i
\(556\) 0 0
\(557\) −7.00897 + 7.00897i −0.296979 + 0.296979i −0.839830 0.542850i \(-0.817345\pi\)
0.542850 + 0.839830i \(0.317345\pi\)
\(558\) 0 0
\(559\) 67.2778 2.84555
\(560\) 0 0
\(561\) −0.0352167 + 0.00470776i −0.00148685 + 0.000198762i
\(562\) 0 0
\(563\) 6.06076 + 1.62398i 0.255430 + 0.0684424i 0.384262 0.923224i \(-0.374456\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(564\) 0 0
\(565\) −22.5981 + 6.05515i −0.950711 + 0.254742i
\(566\) 0 0
\(567\) 9.38748 + 15.9644i 0.394237 + 0.670444i
\(568\) 0 0
\(569\) 5.33529 + 3.08033i 0.223667 + 0.129134i 0.607647 0.794207i \(-0.292113\pi\)
−0.383980 + 0.923341i \(0.625447\pi\)
\(570\) 0 0
\(571\) 4.83727 18.0529i 0.202433 0.755491i −0.787783 0.615952i \(-0.788771\pi\)
0.990217 0.139539i \(-0.0445620\pi\)
\(572\) 0 0
\(573\) −13.8657 + 18.1449i −0.579250 + 0.758015i
\(574\) 0 0
\(575\) 41.1357 1.71548
\(576\) 0 0
\(577\) 11.2964 0.470277 0.235138 0.971962i \(-0.424446\pi\)
0.235138 + 0.971962i \(0.424446\pi\)
\(578\) 0 0
\(579\) −11.6127 27.8784i −0.482608 1.15859i
\(580\) 0 0
\(581\) 0.324272 1.21020i 0.0134531 0.0502076i
\(582\) 0 0
\(583\) 1.38544 + 0.799884i 0.0573790 + 0.0331278i
\(584\) 0 0
\(585\) 38.2916 38.5979i 1.58316 1.59583i
\(586\) 0 0
\(587\) −37.0905 + 9.93836i −1.53089 + 0.410200i −0.923309 0.384059i \(-0.874526\pi\)
−0.607579 + 0.794259i \(0.707859\pi\)
\(588\) 0 0
\(589\) −1.64031 0.439521i −0.0675879 0.0181101i
\(590\) 0 0
\(591\) 12.5025 + 16.2266i 0.514285 + 0.667471i
\(592\) 0 0
\(593\) 7.39166 0.303539 0.151770 0.988416i \(-0.451503\pi\)
0.151770 + 0.988416i \(0.451503\pi\)
\(594\) 0 0
\(595\) −0.199233 + 0.199233i −0.00816776 + 0.00816776i
\(596\) 0 0
\(597\) 3.48280 26.8679i 0.142541 1.09963i
\(598\) 0 0
\(599\) 22.9017 13.2223i 0.935739 0.540249i 0.0471171 0.998889i \(-0.484997\pi\)
0.888622 + 0.458640i \(0.151663\pi\)
\(600\) 0 0
\(601\) 33.6284 + 19.4154i 1.37173 + 0.791970i 0.991146 0.132775i \(-0.0423887\pi\)
0.380587 + 0.924745i \(0.375722\pi\)
\(602\) 0 0
\(603\) 14.9008 + 8.52401i 0.606808 + 0.347125i
\(604\) 0 0
\(605\) −8.61091 32.1364i −0.350083 1.30653i
\(606\) 0 0
\(607\) −1.86964 3.23831i −0.0758863 0.131439i 0.825585 0.564278i \(-0.190845\pi\)
−0.901471 + 0.432839i \(0.857512\pi\)
\(608\) 0 0
\(609\) 9.77592 23.7348i 0.396140 0.961782i
\(610\) 0 0
\(611\) −10.1753 + 10.1753i −0.411648 + 0.411648i
\(612\) 0 0
\(613\) −4.21378 4.21378i −0.170193 0.170193i 0.616871 0.787064i \(-0.288400\pi\)
−0.787064 + 0.616871i \(0.788400\pi\)
\(614\) 0 0
\(615\) 4.71784 + 35.2921i 0.190242 + 1.42312i
\(616\) 0 0
\(617\) 19.3833 11.1910i 0.780343 0.450531i −0.0562088 0.998419i \(-0.517901\pi\)
0.836552 + 0.547888i \(0.184568\pi\)
\(618\) 0 0
\(619\) −15.3149 + 4.10361i −0.615557 + 0.164938i −0.553107 0.833110i \(-0.686558\pi\)
−0.0624496 + 0.998048i \(0.519891\pi\)
\(620\) 0 0
\(621\) 46.9129 6.46164i 1.88255 0.259297i
\(622\) 0 0
\(623\) 5.45314 9.44511i 0.218475 0.378410i
\(624\) 0 0
\(625\) −13.5976 23.5518i −0.543905 0.942071i
\(626\) 0 0
\(627\) −0.760977 + 0.995826i −0.0303905 + 0.0397694i
\(628\) 0 0
\(629\) −0.0341399 0.0341399i −0.00136125 0.00136125i
\(630\) 0 0
\(631\) 38.2887i 1.52425i −0.647429 0.762125i \(-0.724156\pi\)
0.647429 0.762125i \(-0.275844\pi\)
\(632\) 0 0
\(633\) −30.9926 12.7653i −1.23185 0.507374i
\(634\) 0 0
\(635\) −8.49189 + 31.6922i −0.336990 + 1.25767i
\(636\) 0 0
\(637\) 4.20574 + 15.6960i 0.166638 + 0.621900i
\(638\) 0 0
\(639\) −5.26692 + 19.9744i −0.208356 + 0.790175i
\(640\) 0 0
\(641\) −8.82135 + 15.2790i −0.348422 + 0.603485i −0.985969 0.166926i \(-0.946616\pi\)
0.637547 + 0.770412i \(0.279949\pi\)
\(642\) 0 0
\(643\) 27.9805 + 7.49737i 1.10345 + 0.295667i 0.764167 0.645019i \(-0.223150\pi\)
0.339278 + 0.940686i \(0.389817\pi\)
\(644\) 0 0
\(645\) −7.86358 + 60.6634i −0.309628 + 2.38862i
\(646\) 0 0
\(647\) 5.73725i 0.225555i 0.993620 + 0.112777i \(0.0359747\pi\)
−0.993620 + 0.112777i \(0.964025\pi\)
\(648\) 0 0
\(649\) 1.71802i 0.0674380i
\(650\) 0 0
\(651\) −0.496880 + 3.83317i −0.0194742 + 0.150234i
\(652\) 0 0
\(653\) −37.5980 10.0743i −1.47132 0.394239i −0.567938 0.823072i \(-0.692259\pi\)
−0.903384 + 0.428832i \(0.858925\pi\)
\(654\) 0 0
\(655\) −29.6942 + 51.4318i −1.16025 + 2.00961i
\(656\) 0 0
\(657\) 10.0939 38.2805i 0.393802 1.49346i
\(658\) 0 0
\(659\) −10.2644 38.3072i −0.399844 1.49224i −0.813371 0.581745i \(-0.802370\pi\)
0.413528 0.910492i \(-0.364297\pi\)
\(660\) 0 0
\(661\) −1.47348 + 5.49909i −0.0573116 + 0.213890i −0.988643 0.150283i \(-0.951982\pi\)
0.931331 + 0.364173i \(0.118648\pi\)
\(662\) 0 0
\(663\) 0.417734 + 0.172057i 0.0162234 + 0.00668214i
\(664\) 0 0
\(665\) 9.93883i 0.385411i
\(666\) 0 0
\(667\) −46.4121 46.4121i −1.79708 1.79708i
\(668\) 0 0
\(669\) −4.37052 + 5.71933i −0.168974 + 0.221122i
\(670\) 0 0
\(671\) 0.284064 + 0.492013i 0.0109662 + 0.0189940i
\(672\) 0 0
\(673\) −2.23206 + 3.86604i −0.0860396 + 0.149025i −0.905834 0.423633i \(-0.860754\pi\)
0.819794 + 0.572658i \(0.194088\pi\)
\(674\) 0 0
\(675\) 14.3886 + 18.5213i 0.553817 + 0.712886i
\(676\) 0 0
\(677\) −8.06369 + 2.16066i −0.309913 + 0.0830409i −0.410423 0.911895i \(-0.634619\pi\)
0.100511 + 0.994936i \(0.467952\pi\)
\(678\) 0 0
\(679\) −20.9681 + 12.1060i −0.804683 + 0.464584i
\(680\) 0 0
\(681\) −1.48017 11.0725i −0.0567203 0.424300i
\(682\) 0 0
\(683\) −3.00972 3.00972i −0.115164 0.115164i 0.647177 0.762340i \(-0.275950\pi\)
−0.762340 + 0.647177i \(0.775950\pi\)
\(684\) 0 0
\(685\) −20.9082 + 20.9082i −0.798863 + 0.798863i
\(686\) 0 0
\(687\) −6.40550 + 15.5518i −0.244385 + 0.593338i
\(688\) 0 0
\(689\) −10.1709 17.6165i −0.387480 0.671135i
\(690\) 0 0
\(691\) −7.65924 28.5847i −0.291371 1.08741i −0.944057 0.329783i \(-0.893024\pi\)
0.652686 0.757629i \(-0.273642\pi\)
\(692\) 0 0
\(693\) 2.47612 + 1.41647i 0.0940601 + 0.0538071i
\(694\) 0 0
\(695\) 18.8453 + 10.8804i 0.714844 + 0.412715i
\(696\) 0 0
\(697\) −0.256228 + 0.147933i −0.00970532 + 0.00560337i
\(698\) 0 0
\(699\) 4.94511 38.1490i 0.187041 1.44293i
\(700\) 0 0
\(701\) −1.29990 + 1.29990i −0.0490966 + 0.0490966i −0.731229 0.682132i \(-0.761053\pi\)
0.682132 + 0.731229i \(0.261053\pi\)
\(702\) 0 0
\(703\) −1.70309 −0.0642331
\(704\) 0 0
\(705\) −7.98559 10.3642i −0.300755 0.390339i
\(706\) 0 0
\(707\) −11.6320 3.11678i −0.437466 0.117219i
\(708\) 0 0
\(709\) −36.6010 + 9.80720i −1.37458 + 0.368317i −0.869149 0.494551i \(-0.835333\pi\)
−0.505429 + 0.862868i \(0.668666\pi\)
\(710\) 0 0
\(711\) −14.6396 + 14.7567i −0.549027 + 0.553419i
\(712\) 0 0
\(713\) 8.55933 + 4.94173i 0.320550 + 0.185069i
\(714\) 0 0
\(715\) 2.16750 8.08922i 0.0810599 0.302520i
\(716\) 0 0
\(717\) −5.36438 12.8782i −0.200337 0.480943i
\(718\) 0 0
\(719\) −5.11125 −0.190617 −0.0953087 0.995448i \(-0.530384\pi\)
−0.0953087 + 0.995448i \(0.530384\pi\)
\(720\) 0 0
\(721\) 2.70117 0.100597
\(722\) 0 0
\(723\) −10.6776 + 13.9729i −0.397105 + 0.519658i
\(724\) 0 0
\(725\) 8.41353 31.3997i 0.312471 1.16616i
\(726\) 0 0
\(727\) −18.6355 10.7592i −0.691154 0.399038i 0.112890 0.993607i \(-0.463989\pi\)
−0.804044 + 0.594570i \(0.797322\pi\)
\(728\) 0 0
\(729\) 19.3187 + 18.8623i 0.715508 + 0.698605i
\(730\) 0 0
\(731\) −0.490976 + 0.131557i −0.0181594 + 0.00486580i
\(732\) 0 0
\(733\) 2.98220 + 0.799079i 0.110150 + 0.0295147i 0.313473 0.949597i \(-0.398507\pi\)
−0.203323 + 0.979112i \(0.565174\pi\)
\(734\) 0 0
\(735\) −14.6445 + 1.95767i −0.540169 + 0.0722096i
\(736\) 0 0
\(737\) 2.64419 0.0973999
\(738\) 0 0
\(739\) −23.9990 + 23.9990i −0.882818 + 0.882818i −0.993820 0.111002i \(-0.964594\pi\)
0.111002 + 0.993820i \(0.464594\pi\)
\(740\) 0 0
\(741\) 14.7110 6.12786i 0.540422 0.225112i
\(742\) 0 0
\(743\) 14.4499 8.34266i 0.530116 0.306062i −0.210948 0.977497i \(-0.567655\pi\)
0.741064 + 0.671435i \(0.234322\pi\)
\(744\) 0 0
\(745\) −53.9230 31.1325i −1.97559 1.14061i
\(746\) 0 0
\(747\) −0.00727726 1.82656i −0.000266261 0.0668304i
\(748\) 0 0
\(749\) 2.20661 + 8.23519i 0.0806278 + 0.300907i
\(750\) 0 0
\(751\) −17.1635 29.7281i −0.626305 1.08479i −0.988287 0.152607i \(-0.951233\pi\)
0.361982 0.932185i \(-0.382100\pi\)
\(752\) 0 0
\(753\) 16.5472 + 21.4760i 0.603012 + 0.782628i
\(754\) 0 0
\(755\) −9.73869 + 9.73869i −0.354427 + 0.354427i
\(756\) 0 0
\(757\) −24.0162 24.0162i −0.872884 0.872884i 0.119902 0.992786i \(-0.461742\pi\)
−0.992786 + 0.119902i \(0.961742\pi\)
\(758\) 0 0
\(759\) 5.77806 4.45198i 0.209730 0.161596i
\(760\) 0 0
\(761\) −13.2713 + 7.66221i −0.481086 + 0.277755i −0.720869 0.693072i \(-0.756257\pi\)
0.239783 + 0.970826i \(0.422924\pi\)
\(762\) 0 0
\(763\) 32.3804 8.67629i 1.17225 0.314103i
\(764\) 0 0
\(765\) −0.203967 + 0.356554i −0.00737444 + 0.0128912i
\(766\) 0 0
\(767\) −10.9227 + 18.9186i −0.394395 + 0.683112i
\(768\) 0 0
\(769\) 20.6394 + 35.7485i 0.744276 + 1.28912i 0.950532 + 0.310626i \(0.100539\pi\)
−0.206256 + 0.978498i \(0.566128\pi\)
\(770\) 0 0
\(771\) 13.8274 + 33.1952i 0.497983 + 1.19550i
\(772\) 0 0
\(773\) 36.3711 + 36.3711i 1.30818 + 1.30818i 0.922730 + 0.385448i \(0.125953\pi\)
0.385448 + 0.922730i \(0.374047\pi\)
\(774\) 0 0
\(775\) 4.89492i 0.175831i
\(776\) 0 0
\(777\) 0.513628 + 3.84223i 0.0184263 + 0.137839i
\(778\) 0 0
\(779\) −2.70117 + 10.0809i −0.0967793 + 0.361185i
\(780\) 0 0
\(781\) 0.823519 + 3.07342i 0.0294678 + 0.109975i
\(782\) 0 0
\(783\) 4.66284 37.1312i 0.166636 1.32696i
\(784\) 0 0
\(785\) −25.4089 + 44.0096i −0.906883 + 1.57077i
\(786\) 0 0
\(787\) −29.8060 7.98650i −1.06247 0.284688i −0.315074 0.949067i \(-0.602029\pi\)
−0.747396 + 0.664379i \(0.768696\pi\)
\(788\) 0 0
\(789\) 14.5157 + 11.0924i 0.516772 + 0.394900i
\(790\) 0 0
\(791\) 15.6082i 0.554963i
\(792\) 0 0
\(793\) 7.22401i 0.256532i
\(794\) 0 0
\(795\) 17.0733 7.11188i 0.605528 0.252232i
\(796\) 0 0
\(797\)