Properties

Label 864.2.w.a.107.4
Level $864$
Weight $2$
Character 864.107
Analytic conductor $6.899$
Analytic rank $0$
Dimension $128$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 864.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.89907473464\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 107.4
Character \(\chi\) \(=\) 864.107
Dual form 864.2.w.a.323.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36834 + 0.357292i) q^{2} +(1.74468 - 0.977791i) q^{4} +(0.202568 + 0.0839066i) q^{5} +(-0.0119413 + 0.0119413i) q^{7} +(-2.03796 + 1.96131i) q^{8} +O(q^{10})\) \(q+(-1.36834 + 0.357292i) q^{2} +(1.74468 - 0.977791i) q^{4} +(0.202568 + 0.0839066i) q^{5} +(-0.0119413 + 0.0119413i) q^{7} +(-2.03796 + 1.96131i) q^{8} +(-0.307161 - 0.0424363i) q^{10} +(-3.46699 - 1.43608i) q^{11} +(1.44858 + 3.49717i) q^{13} +(0.0120732 - 0.0206062i) q^{14} +(2.08785 - 3.41187i) q^{16} -1.93975 q^{17} +(-2.32957 + 0.964939i) q^{19} +(0.435461 - 0.0516790i) q^{20} +(5.25711 + 0.726304i) q^{22} +(-4.79172 + 4.79172i) q^{23} +(-3.50154 - 3.50154i) q^{25} +(-3.23165 - 4.26774i) q^{26} +(-0.00915771 + 0.0325099i) q^{28} +(1.79276 + 4.32810i) q^{29} -0.213195i q^{31} +(-1.63784 + 5.41456i) q^{32} +(2.65423 - 0.693057i) q^{34} +(-0.00342088 + 0.00141698i) q^{35} +(1.04659 - 2.52670i) q^{37} +(2.84287 - 2.15270i) q^{38} +(-0.577392 + 0.226301i) q^{40} +(2.21601 + 2.21601i) q^{41} +(-1.38417 + 3.34169i) q^{43} +(-7.45299 + 0.884495i) q^{44} +(4.84464 - 8.26873i) q^{46} -2.42072i q^{47} +6.99971i q^{49} +(6.04235 + 3.54021i) q^{50} +(5.94681 + 4.68506i) q^{52} +(-1.24746 + 3.01163i) q^{53} +(-0.581807 - 0.581807i) q^{55} +(0.000915288 - 0.0477564i) q^{56} +(-3.99949 - 5.28175i) q^{58} +(1.49224 - 3.60257i) q^{59} +(-3.46424 + 1.43494i) q^{61} +(0.0761730 + 0.291723i) q^{62} +(0.306539 - 7.99412i) q^{64} +0.829962i q^{65} +(3.85824 + 9.31462i) q^{67} +(-3.38425 + 1.89667i) q^{68} +(0.00417464 - 0.00316115i) q^{70} +(-8.45626 - 8.45626i) q^{71} +(-11.0555 + 11.0555i) q^{73} +(-0.529321 + 3.83131i) q^{74} +(-3.12085 + 3.96135i) q^{76} +(0.0585490 - 0.0242518i) q^{77} -15.3461 q^{79} +(0.709211 - 0.515953i) q^{80} +(-3.82400 - 2.24048i) q^{82} +(1.25116 + 3.02056i) q^{83} +(-0.392932 - 0.162758i) q^{85} +(0.700054 - 5.06711i) q^{86} +(9.88217 - 3.87318i) q^{88} +(-1.44269 + 1.44269i) q^{89} +(-0.0590587 - 0.0244629i) q^{91} +(-3.67474 + 13.0453i) q^{92} +(0.864905 + 3.31236i) q^{94} -0.552862 q^{95} -11.8857 q^{97} +(-2.50094 - 9.57796i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128 q+O(q^{10}) \) Copy content Toggle raw display \( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(353\) \(703\)
\(\chi(n)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36834 + 0.357292i −0.967559 + 0.252644i
\(3\) 0 0
\(4\) 1.74468 0.977791i 0.872342 0.488896i
\(5\) 0.202568 + 0.0839066i 0.0905913 + 0.0375242i 0.427519 0.904006i \(-0.359388\pi\)
−0.336928 + 0.941531i \(0.609388\pi\)
\(6\) 0 0
\(7\) −0.0119413 + 0.0119413i −0.00451339 + 0.00451339i −0.709360 0.704846i \(-0.751016\pi\)
0.704846 + 0.709360i \(0.251016\pi\)
\(8\) −2.03796 + 1.96131i −0.720527 + 0.693427i
\(9\) 0 0
\(10\) −0.307161 0.0424363i −0.0971327 0.0134195i
\(11\) −3.46699 1.43608i −1.04534 0.432993i −0.207112 0.978317i \(-0.566407\pi\)
−0.838225 + 0.545324i \(0.816407\pi\)
\(12\) 0 0
\(13\) 1.44858 + 3.49717i 0.401763 + 0.969941i 0.987238 + 0.159251i \(0.0509079\pi\)
−0.585475 + 0.810690i \(0.699092\pi\)
\(14\) 0.0120732 0.0206062i 0.00322669 0.00550725i
\(15\) 0 0
\(16\) 2.08785 3.41187i 0.521962 0.852969i
\(17\) −1.93975 −0.470458 −0.235229 0.971940i \(-0.575584\pi\)
−0.235229 + 0.971940i \(0.575584\pi\)
\(18\) 0 0
\(19\) −2.32957 + 0.964939i −0.534440 + 0.221372i −0.633546 0.773705i \(-0.718401\pi\)
0.0991068 + 0.995077i \(0.468401\pi\)
\(20\) 0.435461 0.0516790i 0.0973720 0.0115558i
\(21\) 0 0
\(22\) 5.25711 + 0.726304i 1.12082 + 0.154849i
\(23\) −4.79172 + 4.79172i −0.999143 + 0.999143i −1.00000 0.000856866i \(-0.999727\pi\)
0.000856866 1.00000i \(0.499727\pi\)
\(24\) 0 0
\(25\) −3.50154 3.50154i −0.700308 0.700308i
\(26\) −3.23165 4.26774i −0.633779 0.836973i
\(27\) 0 0
\(28\) −0.00915771 + 0.0325099i −0.00173064 + 0.00614380i
\(29\) 1.79276 + 4.32810i 0.332906 + 0.803707i 0.998359 + 0.0572669i \(0.0182386\pi\)
−0.665453 + 0.746440i \(0.731761\pi\)
\(30\) 0 0
\(31\) 0.213195i 0.0382910i −0.999817 0.0191455i \(-0.993905\pi\)
0.999817 0.0191455i \(-0.00609458\pi\)
\(32\) −1.63784 + 5.41456i −0.289532 + 0.957168i
\(33\) 0 0
\(34\) 2.65423 0.693057i 0.455196 0.118858i
\(35\) −0.00342088 + 0.00141698i −0.000578235 + 0.000239513i
\(36\) 0 0
\(37\) 1.04659 2.52670i 0.172059 0.415386i −0.814202 0.580581i \(-0.802825\pi\)
0.986261 + 0.165195i \(0.0528253\pi\)
\(38\) 2.84287 2.15270i 0.461174 0.349214i
\(39\) 0 0
\(40\) −0.577392 + 0.226301i −0.0912937 + 0.0357813i
\(41\) 2.21601 + 2.21601i 0.346082 + 0.346082i 0.858648 0.512566i \(-0.171305\pi\)
−0.512566 + 0.858648i \(0.671305\pi\)
\(42\) 0 0
\(43\) −1.38417 + 3.34169i −0.211085 + 0.509603i −0.993590 0.113040i \(-0.963941\pi\)
0.782506 + 0.622643i \(0.213941\pi\)
\(44\) −7.45299 + 0.884495i −1.12358 + 0.133343i
\(45\) 0 0
\(46\) 4.84464 8.26873i 0.714303 1.21916i
\(47\) 2.42072i 0.353099i −0.984292 0.176549i \(-0.943506\pi\)
0.984292 0.176549i \(-0.0564935\pi\)
\(48\) 0 0
\(49\) 6.99971i 0.999959i
\(50\) 6.04235 + 3.54021i 0.854518 + 0.500661i
\(51\) 0 0
\(52\) 5.94681 + 4.68506i 0.824675 + 0.649701i
\(53\) −1.24746 + 3.01163i −0.171352 + 0.413679i −0.986104 0.166130i \(-0.946873\pi\)
0.814752 + 0.579809i \(0.196873\pi\)
\(54\) 0 0
\(55\) −0.581807 0.581807i −0.0784508 0.0784508i
\(56\) 0.000915288 0.0477564i 0.000122310 0.00638172i
\(57\) 0 0
\(58\) −3.99949 5.28175i −0.525158 0.693528i
\(59\) 1.49224 3.60257i 0.194272 0.469015i −0.796485 0.604658i \(-0.793310\pi\)
0.990758 + 0.135643i \(0.0433099\pi\)
\(60\) 0 0
\(61\) −3.46424 + 1.43494i −0.443551 + 0.183725i −0.593270 0.805004i \(-0.702163\pi\)
0.149719 + 0.988729i \(0.452163\pi\)
\(62\) 0.0761730 + 0.291723i 0.00967398 + 0.0370488i
\(63\) 0 0
\(64\) 0.306539 7.99412i 0.0383174 0.999266i
\(65\) 0.829962i 0.102944i
\(66\) 0 0
\(67\) 3.85824 + 9.31462i 0.471359 + 1.13796i 0.963563 + 0.267482i \(0.0861916\pi\)
−0.492203 + 0.870480i \(0.663808\pi\)
\(68\) −3.38425 + 1.89667i −0.410401 + 0.230005i
\(69\) 0 0
\(70\) 0.00417464 0.00316115i 0.000498965 0.000377830i
\(71\) −8.45626 8.45626i −1.00357 1.00357i −0.999994 0.00357951i \(-0.998861\pi\)
−0.00357951 0.999994i \(-0.501139\pi\)
\(72\) 0 0
\(73\) −11.0555 + 11.0555i −1.29394 + 1.29394i −0.361618 + 0.932326i \(0.617776\pi\)
−0.932326 + 0.361618i \(0.882224\pi\)
\(74\) −0.529321 + 3.83131i −0.0615323 + 0.445381i
\(75\) 0 0
\(76\) −3.12085 + 3.96135i −0.357987 + 0.454398i
\(77\) 0.0585490 0.0242518i 0.00667228 0.00276375i
\(78\) 0 0
\(79\) −15.3461 −1.72658 −0.863288 0.504712i \(-0.831599\pi\)
−0.863288 + 0.504712i \(0.831599\pi\)
\(80\) 0.709211 0.515953i 0.0792922 0.0576854i
\(81\) 0 0
\(82\) −3.82400 2.24048i −0.422290 0.247420i
\(83\) 1.25116 + 3.02056i 0.137332 + 0.331549i 0.977551 0.210698i \(-0.0675736\pi\)
−0.840219 + 0.542247i \(0.817574\pi\)
\(84\) 0 0
\(85\) −0.392932 0.162758i −0.0426194 0.0176536i
\(86\) 0.700054 5.06711i 0.0754888 0.546400i
\(87\) 0 0
\(88\) 9.88217 3.87318i 1.05344 0.412882i
\(89\) −1.44269 + 1.44269i −0.152925 + 0.152925i −0.779423 0.626498i \(-0.784488\pi\)
0.626498 + 0.779423i \(0.284488\pi\)
\(90\) 0 0
\(91\) −0.0590587 0.0244629i −0.00619103 0.00256441i
\(92\) −3.67474 + 13.0453i −0.383118 + 1.36007i
\(93\) 0 0
\(94\) 0.864905 + 3.31236i 0.0892081 + 0.341644i
\(95\) −0.552862 −0.0567224
\(96\) 0 0
\(97\) −11.8857 −1.20681 −0.603404 0.797436i \(-0.706189\pi\)
−0.603404 + 0.797436i \(0.706189\pi\)
\(98\) −2.50094 9.57796i −0.252633 0.967520i
\(99\) 0 0
\(100\) −9.53286 2.68531i −0.953286 0.268531i
\(101\) 9.63369 + 3.99041i 0.958588 + 0.397060i 0.806452 0.591299i \(-0.201385\pi\)
0.152136 + 0.988360i \(0.451385\pi\)
\(102\) 0 0
\(103\) 1.67304 1.67304i 0.164850 0.164850i −0.619861 0.784711i \(-0.712811\pi\)
0.784711 + 0.619861i \(0.212811\pi\)
\(104\) −9.81117 4.28598i −0.962065 0.420275i
\(105\) 0 0
\(106\) 0.630910 4.56663i 0.0612794 0.443550i
\(107\) −14.0152 5.80527i −1.35490 0.561217i −0.417246 0.908794i \(-0.637005\pi\)
−0.937651 + 0.347577i \(0.887005\pi\)
\(108\) 0 0
\(109\) −2.85189 6.88507i −0.273161 0.659470i 0.726454 0.687215i \(-0.241167\pi\)
−0.999615 + 0.0277456i \(0.991167\pi\)
\(110\) 1.00398 + 0.588232i 0.0957259 + 0.0560857i
\(111\) 0 0
\(112\) 0.0158106 + 0.0656739i 0.00149396 + 0.00620560i
\(113\) 14.2128 1.33703 0.668514 0.743700i \(-0.266931\pi\)
0.668514 + 0.743700i \(0.266931\pi\)
\(114\) 0 0
\(115\) −1.37271 + 0.568594i −0.128006 + 0.0530217i
\(116\) 7.35977 + 5.79822i 0.683337 + 0.538351i
\(117\) 0 0
\(118\) −0.754707 + 5.46269i −0.0694764 + 0.502882i
\(119\) 0.0231631 0.0231631i 0.00212336 0.00212336i
\(120\) 0 0
\(121\) 2.17955 + 2.17955i 0.198141 + 0.198141i
\(122\) 4.22755 3.20122i 0.382745 0.289825i
\(123\) 0 0
\(124\) −0.208461 0.371959i −0.0187203 0.0334029i
\(125\) −0.835032 2.01595i −0.0746875 0.180312i
\(126\) 0 0
\(127\) 0.594874i 0.0527865i 0.999652 + 0.0263933i \(0.00840222\pi\)
−0.999652 + 0.0263933i \(0.991598\pi\)
\(128\) 2.43679 + 11.0482i 0.215384 + 0.976529i
\(129\) 0 0
\(130\) −0.296539 1.13567i −0.0260082 0.0996045i
\(131\) −11.9207 + 4.93770i −1.04151 + 0.431409i −0.836855 0.547424i \(-0.815608\pi\)
−0.204658 + 0.978833i \(0.565608\pi\)
\(132\) 0 0
\(133\) 0.0162955 0.0393407i 0.00141300 0.00341127i
\(134\) −8.60741 11.3670i −0.743567 0.981960i
\(135\) 0 0
\(136\) 3.95313 3.80445i 0.338978 0.326229i
\(137\) 10.8258 + 10.8258i 0.924915 + 0.924915i 0.997372 0.0724568i \(-0.0230840\pi\)
−0.0724568 + 0.997372i \(0.523084\pi\)
\(138\) 0 0
\(139\) −3.55148 + 8.57403i −0.301232 + 0.727239i 0.698698 + 0.715417i \(0.253763\pi\)
−0.999930 + 0.0118224i \(0.996237\pi\)
\(140\) −0.00458286 + 0.00581709i −0.000387322 + 0.000491634i
\(141\) 0 0
\(142\) 14.5924 + 8.54964i 1.22456 + 0.717470i
\(143\) 14.2049i 1.18788i
\(144\) 0 0
\(145\) 1.02716i 0.0853009i
\(146\) 11.1776 19.0776i 0.925061 1.57888i
\(147\) 0 0
\(148\) −0.644608 5.43164i −0.0529865 0.446478i
\(149\) 4.25928 10.2828i 0.348933 0.842400i −0.647813 0.761799i \(-0.724316\pi\)
0.996746 0.0806006i \(-0.0256838\pi\)
\(150\) 0 0
\(151\) −9.71514 9.71514i −0.790607 0.790607i 0.190986 0.981593i \(-0.438831\pi\)
−0.981593 + 0.190986i \(0.938831\pi\)
\(152\) 2.85502 6.53551i 0.231573 0.530100i
\(153\) 0 0
\(154\) −0.0714497 + 0.0541037i −0.00575758 + 0.00435980i
\(155\) 0.0178885 0.0431866i 0.00143684 0.00346883i
\(156\) 0 0
\(157\) 11.4671 4.74982i 0.915172 0.379077i 0.125138 0.992139i \(-0.460063\pi\)
0.790034 + 0.613063i \(0.210063\pi\)
\(158\) 20.9987 5.48305i 1.67056 0.436208i
\(159\) 0 0
\(160\) −0.786092 + 0.959393i −0.0621461 + 0.0758467i
\(161\) 0.114439i 0.00901904i
\(162\) 0 0
\(163\) 3.79553 + 9.16322i 0.297289 + 0.717719i 0.999981 + 0.00622432i \(0.00198128\pi\)
−0.702692 + 0.711494i \(0.748019\pi\)
\(164\) 6.03302 + 1.69944i 0.471100 + 0.132704i
\(165\) 0 0
\(166\) −2.79122 3.68611i −0.216641 0.286097i
\(167\) 8.08092 + 8.08092i 0.625320 + 0.625320i 0.946887 0.321567i \(-0.104209\pi\)
−0.321567 + 0.946887i \(0.604209\pi\)
\(168\) 0 0
\(169\) −0.939459 + 0.939459i −0.0722661 + 0.0722661i
\(170\) 0.595815 + 0.0823157i 0.0456969 + 0.00631333i
\(171\) 0 0
\(172\) 0.852529 + 7.18363i 0.0650047 + 0.547747i
\(173\) −1.73554 + 0.718885i −0.131951 + 0.0546558i −0.447682 0.894193i \(-0.647750\pi\)
0.315731 + 0.948849i \(0.397750\pi\)
\(174\) 0 0
\(175\) 0.0836259 0.00632153
\(176\) −12.1383 + 8.83063i −0.914956 + 0.665634i
\(177\) 0 0
\(178\) 1.45862 2.48954i 0.109328 0.186599i
\(179\) −2.93125 7.07665i −0.219092 0.528934i 0.775672 0.631136i \(-0.217411\pi\)
−0.994764 + 0.102202i \(0.967411\pi\)
\(180\) 0 0
\(181\) 20.2266 + 8.37811i 1.50343 + 0.622740i 0.974189 0.225733i \(-0.0724777\pi\)
0.529239 + 0.848473i \(0.322478\pi\)
\(182\) 0.0895525 + 0.0123723i 0.00663808 + 0.000917094i
\(183\) 0 0
\(184\) 0.367280 19.1634i 0.0270762 1.41274i
\(185\) 0.424013 0.424013i 0.0311741 0.0311741i
\(186\) 0 0
\(187\) 6.72510 + 2.78563i 0.491788 + 0.203705i
\(188\) −2.36696 4.22340i −0.172628 0.308023i
\(189\) 0 0
\(190\) 0.756500 0.197533i 0.0548823 0.0143306i
\(191\) 2.52579 0.182760 0.0913800 0.995816i \(-0.470872\pi\)
0.0913800 + 0.995816i \(0.470872\pi\)
\(192\) 0 0
\(193\) −6.18898 −0.445492 −0.222746 0.974876i \(-0.571502\pi\)
−0.222746 + 0.974876i \(0.571502\pi\)
\(194\) 16.2636 4.24666i 1.16766 0.304892i
\(195\) 0 0
\(196\) 6.84426 + 12.2123i 0.488876 + 0.872307i
\(197\) 22.6357 + 9.37602i 1.61273 + 0.668014i 0.993142 0.116915i \(-0.0373005\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(198\) 0 0
\(199\) −1.71266 + 1.71266i −0.121407 + 0.121407i −0.765200 0.643793i \(-0.777360\pi\)
0.643793 + 0.765200i \(0.277360\pi\)
\(200\) 14.0036 + 0.268389i 0.990203 + 0.0189780i
\(201\) 0 0
\(202\) −14.6079 2.01817i −1.02781 0.141998i
\(203\) −0.0730909 0.0302753i −0.00512998 0.00212491i
\(204\) 0 0
\(205\) 0.262955 + 0.634830i 0.0183656 + 0.0443385i
\(206\) −1.69152 + 2.88705i −0.117854 + 0.201150i
\(207\) 0 0
\(208\) 14.9563 + 2.35921i 1.03703 + 0.163582i
\(209\) 9.46232 0.654522
\(210\) 0 0
\(211\) 8.84986 3.66573i 0.609249 0.252359i −0.0566581 0.998394i \(-0.518045\pi\)
0.665908 + 0.746034i \(0.268045\pi\)
\(212\) 0.768324 + 6.47410i 0.0527687 + 0.444643i
\(213\) 0 0
\(214\) 21.2516 + 2.93605i 1.45273 + 0.200704i
\(215\) −0.560780 + 0.560780i −0.0382449 + 0.0382449i
\(216\) 0 0
\(217\) 0.00254583 + 0.00254583i 0.000172822 + 0.000172822i
\(218\) 6.36232 + 8.40213i 0.430911 + 0.569064i
\(219\) 0 0
\(220\) −1.58395 0.446184i −0.106790 0.0300817i
\(221\) −2.80988 6.78364i −0.189013 0.456317i
\(222\) 0 0
\(223\) 25.7423i 1.72383i −0.507049 0.861917i \(-0.669264\pi\)
0.507049 0.861917i \(-0.330736\pi\)
\(224\) −0.0450989 0.0842149i −0.00301330 0.00562684i
\(225\) 0 0
\(226\) −19.4479 + 5.07812i −1.29365 + 0.337792i
\(227\) 20.1573 8.34944i 1.33789 0.554172i 0.404994 0.914319i \(-0.367274\pi\)
0.932895 + 0.360147i \(0.117274\pi\)
\(228\) 0 0
\(229\) 2.08085 5.02362i 0.137507 0.331970i −0.840093 0.542442i \(-0.817500\pi\)
0.977600 + 0.210471i \(0.0674999\pi\)
\(230\) 1.67517 1.26849i 0.110457 0.0836414i
\(231\) 0 0
\(232\) −12.1423 5.30433i −0.797180 0.348246i
\(233\) 11.8444 + 11.8444i 0.775951 + 0.775951i 0.979140 0.203188i \(-0.0651304\pi\)
−0.203188 + 0.979140i \(0.565130\pi\)
\(234\) 0 0
\(235\) 0.203114 0.490362i 0.0132497 0.0319877i
\(236\) −0.919085 7.74445i −0.0598273 0.504121i
\(237\) 0 0
\(238\) −0.0234189 + 0.0399709i −0.00151802 + 0.00259093i
\(239\) 10.0203i 0.648161i −0.946030 0.324080i \(-0.894945\pi\)
0.946030 0.324080i \(-0.105055\pi\)
\(240\) 0 0
\(241\) 2.24829i 0.144825i 0.997375 + 0.0724124i \(0.0230698\pi\)
−0.997375 + 0.0724124i \(0.976930\pi\)
\(242\) −3.76109 2.20362i −0.241772 0.141654i
\(243\) 0 0
\(244\) −4.64094 + 5.89081i −0.297106 + 0.377121i
\(245\) −0.587322 + 1.41792i −0.0375226 + 0.0905876i
\(246\) 0 0
\(247\) −6.74912 6.74912i −0.429436 0.429436i
\(248\) 0.418142 + 0.434483i 0.0265520 + 0.0275897i
\(249\) 0 0
\(250\) 1.86289 + 2.46014i 0.117819 + 0.155593i
\(251\) 7.33649 17.7119i 0.463075 1.11796i −0.504053 0.863673i \(-0.668158\pi\)
0.967128 0.254290i \(-0.0818418\pi\)
\(252\) 0 0
\(253\) 23.4941 9.73159i 1.47706 0.611820i
\(254\) −0.212544 0.813988i −0.0133362 0.0510741i
\(255\) 0 0
\(256\) −7.28177 14.2470i −0.455111 0.890435i
\(257\) 26.7917i 1.67122i −0.549325 0.835609i \(-0.685115\pi\)
0.549325 0.835609i \(-0.314885\pi\)
\(258\) 0 0
\(259\) 0.0176744 + 0.0426697i 0.00109823 + 0.00265137i
\(260\) 0.811529 + 1.44802i 0.0503289 + 0.0898025i
\(261\) 0 0
\(262\) 14.5473 11.0156i 0.898733 0.680546i
\(263\) −17.1686 17.1686i −1.05866 1.05866i −0.998169 0.0604905i \(-0.980734\pi\)
−0.0604905 0.998169i \(-0.519266\pi\)
\(264\) 0 0
\(265\) −0.505391 + 0.505391i −0.0310459 + 0.0310459i
\(266\) −0.00824153 + 0.0596535i −0.000505321 + 0.00365759i
\(267\) 0 0
\(268\) 15.8392 + 12.4785i 0.967531 + 0.762247i
\(269\) −20.0795 + 8.31721i −1.22427 + 0.507109i −0.898765 0.438431i \(-0.855534\pi\)
−0.325505 + 0.945540i \(0.605534\pi\)
\(270\) 0 0
\(271\) 27.7852 1.68783 0.843915 0.536476i \(-0.180245\pi\)
0.843915 + 0.536476i \(0.180245\pi\)
\(272\) −4.04990 + 6.61818i −0.245562 + 0.401286i
\(273\) 0 0
\(274\) −18.6814 10.9454i −1.12858 0.661236i
\(275\) 7.11134 + 17.1683i 0.428830 + 1.03529i
\(276\) 0 0
\(277\) −14.1201 5.84875i −0.848396 0.351417i −0.0842374 0.996446i \(-0.526845\pi\)
−0.764158 + 0.645029i \(0.776845\pi\)
\(278\) 1.79618 13.0011i 0.107728 0.779752i
\(279\) 0 0
\(280\) 0.00419249 0.00959715i 0.000250549 0.000573539i
\(281\) −17.2705 + 17.2705i −1.03027 + 1.03027i −0.0307455 + 0.999527i \(0.509788\pi\)
−0.999527 + 0.0307455i \(0.990212\pi\)
\(282\) 0 0
\(283\) 26.6752 + 11.0492i 1.58568 + 0.656808i 0.989300 0.145897i \(-0.0466067\pi\)
0.596376 + 0.802705i \(0.296607\pi\)
\(284\) −23.0220 6.48505i −1.36610 0.384817i
\(285\) 0 0
\(286\) 5.07531 + 19.4371i 0.300109 + 1.14934i
\(287\) −0.0529240 −0.00312401
\(288\) 0 0
\(289\) −13.2374 −0.778669
\(290\) −0.366996 1.40550i −0.0215507 0.0825337i
\(291\) 0 0
\(292\) −8.47837 + 30.0982i −0.496159 + 1.76137i
\(293\) 25.5733 + 10.5928i 1.49401 + 0.618838i 0.972185 0.234215i \(-0.0752520\pi\)
0.521823 + 0.853054i \(0.325252\pi\)
\(294\) 0 0
\(295\) 0.604559 0.604559i 0.0351988 0.0351988i
\(296\) 2.82272 + 7.20199i 0.164067 + 0.418607i
\(297\) 0 0
\(298\) −2.15416 + 15.5921i −0.124787 + 0.903228i
\(299\) −23.6987 9.81630i −1.37053 0.567691i
\(300\) 0 0
\(301\) −0.0233753 0.0564330i −0.00134733 0.00325274i
\(302\) 16.7647 + 9.82243i 0.964701 + 0.565217i
\(303\) 0 0
\(304\) −1.57154 + 9.96284i −0.0901339 + 0.571408i
\(305\) −0.822146 −0.0470760
\(306\) 0 0
\(307\) −1.03022 + 0.426730i −0.0587976 + 0.0243548i −0.411888 0.911234i \(-0.635131\pi\)
0.353091 + 0.935589i \(0.385131\pi\)
\(308\) 0.0784364 0.0995604i 0.00446933 0.00567298i
\(309\) 0 0
\(310\) −0.00904721 + 0.0654852i −0.000513847 + 0.00371931i
\(311\) −23.9114 + 23.9114i −1.35589 + 1.35589i −0.476971 + 0.878919i \(0.658265\pi\)
−0.878919 + 0.476971i \(0.841735\pi\)
\(312\) 0 0
\(313\) −4.43744 4.43744i −0.250819 0.250819i 0.570487 0.821306i \(-0.306754\pi\)
−0.821306 + 0.570487i \(0.806754\pi\)
\(314\) −13.9937 + 10.5964i −0.789712 + 0.597991i
\(315\) 0 0
\(316\) −26.7742 + 15.0053i −1.50616 + 0.844115i
\(317\) 2.38033 + 5.74662i 0.133693 + 0.322763i 0.976522 0.215419i \(-0.0691116\pi\)
−0.842829 + 0.538181i \(0.819112\pi\)
\(318\) 0 0
\(319\) 17.5800i 0.984291i
\(320\) 0.732855 1.59364i 0.0409678 0.0890870i
\(321\) 0 0
\(322\) 0.0408881 + 0.156591i 0.00227860 + 0.00872646i
\(323\) 4.51878 1.87174i 0.251432 0.104146i
\(324\) 0 0
\(325\) 7.17324 17.3177i 0.397900 0.960616i
\(326\) −8.46750 11.1822i −0.468972 0.619327i
\(327\) 0 0
\(328\) −8.86240 0.169854i −0.489344 0.00937864i
\(329\) 0.0289066 + 0.0289066i 0.00159367 + 0.00159367i
\(330\) 0 0
\(331\) −6.95616 + 16.7937i −0.382345 + 0.923063i 0.609166 + 0.793043i \(0.291504\pi\)
−0.991511 + 0.130021i \(0.958496\pi\)
\(332\) 5.13635 + 4.04655i 0.281894 + 0.222083i
\(333\) 0 0
\(334\) −13.9447 8.17016i −0.763018 0.447051i
\(335\) 2.21058i 0.120777i
\(336\) 0 0
\(337\) 19.6482i 1.07030i −0.844756 0.535152i \(-0.820254\pi\)
0.844756 0.535152i \(-0.179746\pi\)
\(338\) 0.949834 1.62116i 0.0516641 0.0881793i
\(339\) 0 0
\(340\) −0.844685 + 0.100244i −0.0458095 + 0.00543651i
\(341\) −0.306165 + 0.739147i −0.0165797 + 0.0400270i
\(342\) 0 0
\(343\) −0.167175 0.167175i −0.00902659 0.00902659i
\(344\) −3.73320 9.52501i −0.201281 0.513554i
\(345\) 0 0
\(346\) 2.11795 1.60377i 0.113862 0.0862193i
\(347\) −6.02247 + 14.5395i −0.323303 + 0.780523i 0.675755 + 0.737126i \(0.263818\pi\)
−0.999058 + 0.0433963i \(0.986182\pi\)
\(348\) 0 0
\(349\) 10.4951 4.34720i 0.561788 0.232700i −0.0836734 0.996493i \(-0.526665\pi\)
0.645461 + 0.763793i \(0.276665\pi\)
\(350\) −0.114428 + 0.0298789i −0.00611645 + 0.00159709i
\(351\) 0 0
\(352\) 13.4541 16.4202i 0.717106 0.875198i
\(353\) 30.0234i 1.59798i −0.601342 0.798992i \(-0.705367\pi\)
0.601342 0.798992i \(-0.294633\pi\)
\(354\) 0 0
\(355\) −1.00343 2.42251i −0.0532568 0.128573i
\(356\) −1.10639 + 3.92769i −0.0586385 + 0.208167i
\(357\) 0 0
\(358\) 6.53936 + 8.63593i 0.345616 + 0.456423i
\(359\) 10.5864 + 10.5864i 0.558730 + 0.558730i 0.928946 0.370216i \(-0.120716\pi\)
−0.370216 + 0.928946i \(0.620716\pi\)
\(360\) 0 0
\(361\) −8.93925 + 8.93925i −0.470487 + 0.470487i
\(362\) −30.6701 4.23728i −1.61199 0.222707i
\(363\) 0 0
\(364\) −0.126958 + 0.0150670i −0.00665443 + 0.000789725i
\(365\) −3.16711 + 1.31186i −0.165774 + 0.0686660i
\(366\) 0 0
\(367\) −3.82385 −0.199604 −0.0998018 0.995007i \(-0.531821\pi\)
−0.0998018 + 0.995007i \(0.531821\pi\)
\(368\) 6.34436 + 26.3531i 0.330722 + 1.37375i
\(369\) 0 0
\(370\) −0.428696 + 0.731689i −0.0222868 + 0.0380387i
\(371\) −0.0210665 0.0508591i −0.00109372 0.00264047i
\(372\) 0 0
\(373\) 23.5062 + 9.73660i 1.21711 + 0.504142i 0.896489 0.443067i \(-0.146110\pi\)
0.320617 + 0.947209i \(0.396110\pi\)
\(374\) −10.1975 1.40885i −0.527299 0.0728498i
\(375\) 0 0
\(376\) 4.74778 + 4.93333i 0.244848 + 0.254417i
\(377\) −12.5392 + 12.5392i −0.645799 + 0.645799i
\(378\) 0 0
\(379\) −2.96668 1.22884i −0.152388 0.0631212i 0.305186 0.952293i \(-0.401281\pi\)
−0.457574 + 0.889172i \(0.651281\pi\)
\(380\) −0.964569 + 0.540583i −0.0494814 + 0.0277313i
\(381\) 0 0
\(382\) −3.45613 + 0.902446i −0.176831 + 0.0461731i
\(383\) 4.97811 0.254369 0.127185 0.991879i \(-0.459406\pi\)
0.127185 + 0.991879i \(0.459406\pi\)
\(384\) 0 0
\(385\) 0.0138951 0.000708158
\(386\) 8.46860 2.21127i 0.431040 0.112551i
\(387\) 0 0
\(388\) −20.7368 + 11.6217i −1.05275 + 0.590003i
\(389\) −8.47226 3.50933i −0.429561 0.177930i 0.157418 0.987532i \(-0.449683\pi\)
−0.586979 + 0.809602i \(0.699683\pi\)
\(390\) 0 0
\(391\) 9.29474 9.29474i 0.470055 0.470055i
\(392\) −13.7286 14.2651i −0.693399 0.720497i
\(393\) 0 0
\(394\) −34.3232 4.74198i −1.72918 0.238897i
\(395\) −3.10864 1.28764i −0.156413 0.0647883i
\(396\) 0 0
\(397\) −1.22095 2.94765i −0.0612780 0.147938i 0.890275 0.455424i \(-0.150512\pi\)
−0.951553 + 0.307486i \(0.900512\pi\)
\(398\) 1.73157 2.95541i 0.0867958 0.148141i
\(399\) 0 0
\(400\) −19.2575 + 4.63613i −0.962875 + 0.231806i
\(401\) −27.8490 −1.39071 −0.695356 0.718665i \(-0.744753\pi\)
−0.695356 + 0.718665i \(0.744753\pi\)
\(402\) 0 0
\(403\) 0.745581 0.308830i 0.0371400 0.0153839i
\(404\) 20.7095 2.45774i 1.03034 0.122277i
\(405\) 0 0
\(406\) 0.110830 + 0.0153119i 0.00550040 + 0.000759917i
\(407\) −7.25705 + 7.25705i −0.359719 + 0.359719i
\(408\) 0 0
\(409\) −0.776560 0.776560i −0.0383984 0.0383984i 0.687647 0.726045i \(-0.258644\pi\)
−0.726045 + 0.687647i \(0.758644\pi\)
\(410\) −0.586631 0.774709i −0.0289716 0.0382602i
\(411\) 0 0
\(412\) 1.28305 4.55482i 0.0632111 0.224400i
\(413\) 0.0252002 + 0.0608387i 0.00124002 + 0.00299368i
\(414\) 0 0
\(415\) 0.716849i 0.0351888i
\(416\) −21.3082 + 2.11559i −1.04472 + 0.103725i
\(417\) 0 0
\(418\) −12.9476 + 3.38081i −0.633289 + 0.165361i
\(419\) −6.17161 + 2.55636i −0.301503 + 0.124887i −0.528306 0.849054i \(-0.677173\pi\)
0.226803 + 0.973941i \(0.427173\pi\)
\(420\) 0 0
\(421\) 4.54054 10.9618i 0.221293 0.534248i −0.773773 0.633462i \(-0.781633\pi\)
0.995066 + 0.0992148i \(0.0316331\pi\)
\(422\) −10.7998 + 8.17794i −0.525728 + 0.398096i
\(423\) 0 0
\(424\) −3.36447 8.58423i −0.163393 0.416887i
\(425\) 6.79211 + 6.79211i 0.329466 + 0.329466i
\(426\) 0 0
\(427\) 0.0242326 0.0585026i 0.00117270 0.00283114i
\(428\) −30.1284 + 3.57553i −1.45631 + 0.172830i
\(429\) 0 0
\(430\) 0.566973 0.967697i 0.0273418 0.0466665i
\(431\) 14.2802i 0.687851i −0.938997 0.343925i \(-0.888243\pi\)
0.938997 0.343925i \(-0.111757\pi\)
\(432\) 0 0
\(433\) 36.5612i 1.75702i 0.477723 + 0.878510i \(0.341462\pi\)
−0.477723 + 0.878510i \(0.658538\pi\)
\(434\) −0.00439316 0.00257395i −0.000210878 0.000123553i
\(435\) 0 0
\(436\) −11.7078 9.22372i −0.560702 0.441736i
\(437\) 6.53892 15.7864i 0.312799 0.755164i
\(438\) 0 0
\(439\) −19.9584 19.9584i −0.952563 0.952563i 0.0463616 0.998925i \(-0.485237\pi\)
−0.998925 + 0.0463616i \(0.985237\pi\)
\(440\) 2.32680 + 0.0445948i 0.110926 + 0.00212598i
\(441\) 0 0
\(442\) 6.26859 + 8.27835i 0.298167 + 0.393761i
\(443\) 1.86847 4.51089i 0.0887737 0.214319i −0.873257 0.487260i \(-0.837996\pi\)
0.962031 + 0.272941i \(0.0879965\pi\)
\(444\) 0 0
\(445\) −0.413294 + 0.171192i −0.0195920 + 0.00811528i
\(446\) 9.19753 + 35.2241i 0.435516 + 1.66791i
\(447\) 0 0
\(448\) 0.0917998 + 0.0991208i 0.00433713 + 0.00468302i
\(449\) 18.5243i 0.874217i 0.899409 + 0.437109i \(0.143997\pi\)
−0.899409 + 0.437109i \(0.856003\pi\)
\(450\) 0 0
\(451\) −4.50053 10.8652i −0.211921 0.511624i
\(452\) 24.7969 13.8971i 1.16635 0.653667i
\(453\) 0 0
\(454\) −24.5988 + 18.6269i −1.15448 + 0.874204i
\(455\) −0.00991083 0.00991083i −0.000464627 0.000464627i
\(456\) 0 0
\(457\) 4.31755 4.31755i 0.201967 0.201967i −0.598876 0.800842i \(-0.704386\pi\)
0.800842 + 0.598876i \(0.204386\pi\)
\(458\) −1.05240 + 7.61748i −0.0491756 + 0.355941i
\(459\) 0 0
\(460\) −1.83898 + 2.33424i −0.0857427 + 0.108834i
\(461\) −8.85130 + 3.66633i −0.412246 + 0.170758i −0.579161 0.815213i \(-0.696620\pi\)
0.166915 + 0.985971i \(0.446620\pi\)
\(462\) 0 0
\(463\) −30.4291 −1.41416 −0.707080 0.707134i \(-0.749988\pi\)
−0.707080 + 0.707134i \(0.749988\pi\)
\(464\) 18.5099 + 2.91975i 0.859301 + 0.135546i
\(465\) 0 0
\(466\) −20.4390 11.9752i −0.946818 0.554740i
\(467\) 11.8108 + 28.5138i 0.546539 + 1.31946i 0.920038 + 0.391830i \(0.128158\pi\)
−0.373499 + 0.927631i \(0.621842\pi\)
\(468\) 0 0
\(469\) −0.157301 0.0651563i −0.00726349 0.00300864i
\(470\) −0.102726 + 0.743551i −0.00473842 + 0.0342974i
\(471\) 0 0
\(472\) 4.02465 + 10.2686i 0.185249 + 0.472652i
\(473\) 9.59784 9.59784i 0.441309 0.441309i
\(474\) 0 0
\(475\) 11.5359 + 4.77831i 0.529301 + 0.219244i
\(476\) 0.0177637 0.0630611i 0.000814196 0.00289040i
\(477\) 0 0
\(478\) 3.58018 + 13.7112i 0.163754 + 0.627134i
\(479\) 33.1421 1.51430 0.757151 0.653240i \(-0.226591\pi\)
0.757151 + 0.653240i \(0.226591\pi\)
\(480\) 0 0
\(481\) 10.3524 0.472027
\(482\) −0.803295 3.07641i −0.0365891 0.140127i
\(483\) 0 0
\(484\) 5.93377 + 1.67148i 0.269717 + 0.0759764i
\(485\) −2.40766 0.997286i −0.109326 0.0452844i
\(486\) 0 0
\(487\) 8.33714 8.33714i 0.377792 0.377792i −0.492513 0.870305i \(-0.663922\pi\)
0.870305 + 0.492513i \(0.163922\pi\)
\(488\) 4.24562 9.71878i 0.192190 0.439949i
\(489\) 0 0
\(490\) 0.297042 2.15004i 0.0134190 0.0971288i
\(491\) −9.27696 3.84264i −0.418664 0.173416i 0.163399 0.986560i \(-0.447754\pi\)
−0.582063 + 0.813144i \(0.697754\pi\)
\(492\) 0 0
\(493\) −3.47750 8.39542i −0.156619 0.378111i
\(494\) 11.6465 + 6.82365i 0.523999 + 0.307011i
\(495\) 0 0
\(496\) −0.727396 0.445120i −0.0326610 0.0199865i
\(497\) 0.201957 0.00905903
\(498\) 0 0
\(499\) 10.2993 4.26612i 0.461061 0.190978i −0.140048 0.990145i \(-0.544726\pi\)
0.601109 + 0.799167i \(0.294726\pi\)
\(500\) −3.42804 2.70070i −0.153307 0.120779i
\(501\) 0 0
\(502\) −3.71048 + 26.8570i −0.165607 + 1.19869i
\(503\) −17.7557 + 17.7557i −0.791687 + 0.791687i −0.981768 0.190082i \(-0.939125\pi\)
0.190082 + 0.981768i \(0.439125\pi\)
\(504\) 0 0
\(505\) 1.61666 + 1.61666i 0.0719404 + 0.0719404i
\(506\) −28.6708 + 21.7103i −1.27457 + 0.965142i
\(507\) 0 0
\(508\) 0.581663 + 1.03787i 0.0258071 + 0.0460479i
\(509\) −16.3316 39.4279i −0.723884 1.74761i −0.661971 0.749530i \(-0.730280\pi\)
−0.0619134 0.998082i \(-0.519720\pi\)
\(510\) 0 0
\(511\) 0.264033i 0.0116801i
\(512\) 15.0542 + 16.8929i 0.665309 + 0.746568i
\(513\) 0 0
\(514\) 9.57245 + 36.6600i 0.422223 + 1.61700i
\(515\) 0.479285 0.198526i 0.0211198 0.00874811i
\(516\) 0 0
\(517\) −3.47634 + 8.39262i −0.152889 + 0.369107i
\(518\) −0.0394301 0.0520716i −0.00173246 0.00228790i
\(519\) 0 0
\(520\) −1.62781 1.69143i −0.0713842 0.0741740i
\(521\) 2.59199 + 2.59199i 0.113557 + 0.113557i 0.761602 0.648045i \(-0.224413\pi\)
−0.648045 + 0.761602i \(0.724413\pi\)
\(522\) 0 0
\(523\) 6.55437 15.8236i 0.286602 0.691919i −0.713358 0.700800i \(-0.752827\pi\)
0.999961 + 0.00888020i \(0.00282669\pi\)
\(524\) −15.9698 + 20.2707i −0.697642 + 0.885528i
\(525\) 0 0
\(526\) 29.6266 + 17.3582i 1.29178 + 0.756852i
\(527\) 0.413546i 0.0180143i
\(528\) 0 0
\(529\) 22.9212i 0.996573i
\(530\) 0.510973 0.872117i 0.0221952 0.0378823i
\(531\) 0 0
\(532\) −0.0100366 0.0845707i −0.000435140 0.00366661i
\(533\) −4.53970 + 10.9598i −0.196636 + 0.474722i
\(534\) 0 0
\(535\) −2.35193 2.35193i −0.101683 0.101683i
\(536\) −26.1318 11.4156i −1.12872 0.493079i
\(537\) 0 0
\(538\) 24.5039 18.5550i 1.05644 0.799962i
\(539\) 10.0521 24.2680i 0.432975 1.04529i
\(540\) 0 0
\(541\) 31.3688 12.9934i 1.34865 0.558628i 0.412733 0.910852i \(-0.364574\pi\)
0.935916 + 0.352224i \(0.114574\pi\)
\(542\) −38.0195 + 9.92743i −1.63308 + 0.426420i
\(543\) 0 0
\(544\) 3.17700 10.5029i 0.136213 0.450308i
\(545\) 1.63399i 0.0699924i
\(546\) 0 0
\(547\) 16.7932 + 40.5423i 0.718024 + 1.73346i 0.678903 + 0.734228i \(0.262456\pi\)
0.0391202 + 0.999235i \(0.487544\pi\)
\(548\) 29.4731 + 8.30228i 1.25903 + 0.354656i
\(549\) 0 0
\(550\) −15.8648 20.9512i −0.676477 0.893360i
\(551\) −8.35270 8.35270i −0.355837 0.355837i
\(552\) 0 0
\(553\) 0.183253 0.183253i 0.00779271 0.00779271i
\(554\) 21.4108 + 2.95804i 0.909657 + 0.125675i
\(555\) 0 0
\(556\) 2.18740 + 18.4316i 0.0927663 + 0.781673i
\(557\) −23.9875 + 9.93595i −1.01638 + 0.421000i −0.827780 0.561053i \(-0.810396\pi\)
−0.188604 + 0.982053i \(0.560396\pi\)
\(558\) 0 0
\(559\) −13.6916 −0.579091
\(560\) −0.00230775 + 0.0146301i −9.75200e−5 + 0.000618233i
\(561\) 0 0
\(562\) 17.4612 29.8025i 0.736558 1.25714i
\(563\) 15.7397 + 37.9991i 0.663350 + 1.60147i 0.792519 + 0.609847i \(0.208769\pi\)
−0.129169 + 0.991623i \(0.541231\pi\)
\(564\) 0 0
\(565\) 2.87906 + 1.19255i 0.121123 + 0.0501708i
\(566\) −40.4484 5.58822i −1.70017 0.234890i
\(567\) 0 0
\(568\) 33.8188 + 0.648163i 1.41901 + 0.0271963i
\(569\) −26.5263 + 26.5263i −1.11204 + 1.11204i −0.119168 + 0.992874i \(0.538023\pi\)
−0.992874 + 0.119168i \(0.961977\pi\)
\(570\) 0 0
\(571\) 4.44812 + 1.84247i 0.186148 + 0.0771050i 0.473811 0.880627i \(-0.342878\pi\)
−0.287663 + 0.957732i \(0.592878\pi\)
\(572\) −13.8895 24.7831i −0.580747 1.03624i
\(573\) 0 0
\(574\) 0.0724178 0.0189093i 0.00302266 0.000789260i
\(575\) 33.5568 1.39942
\(576\) 0 0
\(577\) −27.0428 −1.12581 −0.562903 0.826523i \(-0.690315\pi\)
−0.562903 + 0.826523i \(0.690315\pi\)
\(578\) 18.1132 4.72961i 0.753408 0.196726i
\(579\) 0 0
\(580\) 1.00435 + 1.79207i 0.0417032 + 0.0744116i
\(581\) −0.0510098 0.0211290i −0.00211624 0.000876577i
\(582\) 0 0
\(583\) 8.64986 8.64986i 0.358240 0.358240i
\(584\) 0.847389 44.2137i 0.0350652 1.82958i
\(585\) 0 0
\(586\) −38.7776 5.35738i −1.60189 0.221311i
\(587\) −24.7371 10.2464i −1.02101 0.422915i −0.191549 0.981483i \(-0.561351\pi\)
−0.829459 + 0.558568i \(0.811351\pi\)
\(588\) 0 0
\(589\) 0.205721 + 0.496653i 0.00847657 + 0.0204642i
\(590\) −0.611236 + 1.04324i −0.0251642 + 0.0429497i
\(591\) 0 0
\(592\) −6.43565 8.84620i −0.264503 0.363577i
\(593\) 14.7443 0.605477 0.302738 0.953074i \(-0.402099\pi\)
0.302738 + 0.953074i \(0.402099\pi\)
\(594\) 0 0
\(595\) 0.00663566 0.00274858i 0.000272035 0.000112681i
\(596\) −2.62334 22.1049i −0.107456 0.905453i
\(597\) 0 0
\(598\) 35.9350 + 4.96466i 1.46949 + 0.203020i
\(599\) −3.57851 + 3.57851i −0.146214 + 0.146214i −0.776424 0.630210i \(-0.782969\pi\)
0.630210 + 0.776424i \(0.282969\pi\)
\(600\) 0 0
\(601\) −2.91144 2.91144i −0.118760 0.118760i 0.645229 0.763989i \(-0.276762\pi\)
−0.763989 + 0.645229i \(0.776762\pi\)
\(602\) 0.0521483 + 0.0688675i 0.00212541 + 0.00280683i
\(603\) 0 0
\(604\) −26.4492 7.45048i −1.07620 0.303156i
\(605\) 0.258629 + 0.624386i 0.0105148 + 0.0253849i
\(606\) 0 0
\(607\) 4.29692i 0.174406i 0.996191 + 0.0872032i \(0.0277929\pi\)
−0.996191 + 0.0872032i \(0.972207\pi\)
\(608\) −1.40925 14.1940i −0.0571527 0.575643i
\(609\) 0 0
\(610\) 1.12497 0.293746i 0.0455488 0.0118934i
\(611\) 8.46568 3.50660i 0.342485 0.141862i
\(612\) 0 0
\(613\) 15.8444 38.2518i 0.639949 1.54497i −0.186797 0.982399i \(-0.559811\pi\)
0.826746 0.562575i \(-0.190189\pi\)
\(614\) 1.25722 0.951998i 0.0507371 0.0384195i
\(615\) 0 0
\(616\) −0.0717551 + 0.164257i −0.00289110 + 0.00661810i
\(617\) −16.9817 16.9817i −0.683659 0.683659i 0.277163 0.960823i \(-0.410606\pi\)
−0.960823 + 0.277163i \(0.910606\pi\)
\(618\) 0 0
\(619\) 5.89007 14.2199i 0.236742 0.571545i −0.760200 0.649689i \(-0.774899\pi\)
0.996942 + 0.0781434i \(0.0248992\pi\)
\(620\) −0.0110177 0.0928383i −0.000442483 0.00372847i
\(621\) 0 0
\(622\) 24.1754 41.2621i 0.969347 1.65446i
\(623\) 0.0344552i 0.00138042i
\(624\) 0 0
\(625\) 24.2812i 0.971248i
\(626\) 7.65737 + 4.48645i 0.306050 + 0.179314i
\(627\) 0 0
\(628\) 15.3621 19.4993i 0.613014 0.778108i
\(629\) −2.03013 + 4.90116i −0.0809464 + 0.195422i
\(630\) 0 0
\(631\) 23.5566 + 23.5566i 0.937772 + 0.937772i 0.998174 0.0604020i \(-0.0192383\pi\)
−0.0604020 + 0.998174i \(0.519238\pi\)
\(632\) 31.2748 30.0985i 1.24404 1.19725i
\(633\) 0 0
\(634\) −5.31031 7.01284i −0.210900 0.278515i
\(635\) −0.0499139 + 0.120503i −0.00198077 + 0.00478200i
\(636\) 0 0
\(637\) −24.4792 + 10.1396i −0.969902 + 0.401746i
\(638\) 6.28120 + 24.0553i 0.248675 + 0.952360i
\(639\) 0 0
\(640\) −0.433398 + 2.44247i −0.0171315 + 0.0965472i
\(641\) 32.1521i 1.26993i −0.772540 0.634966i \(-0.781014\pi\)
0.772540 0.634966i \(-0.218986\pi\)
\(642\) 0 0
\(643\) 17.0638 + 41.1958i 0.672932 + 1.62460i 0.776603 + 0.629991i \(0.216941\pi\)
−0.103670 + 0.994612i \(0.533059\pi\)
\(644\) −0.111897 0.199660i −0.00440937 0.00786769i
\(645\) 0 0
\(646\) −5.51445 + 4.17569i −0.216963 + 0.164290i
\(647\) 10.0224 + 10.0224i 0.394023 + 0.394023i 0.876119 0.482096i \(-0.160124\pi\)
−0.482096 + 0.876119i \(0.660124\pi\)
\(648\) 0 0
\(649\) −10.3471 + 10.3471i −0.406161 + 0.406161i
\(650\) −3.62791 + 26.2594i −0.142298 + 1.02998i
\(651\) 0 0
\(652\) 15.5817 + 12.2757i 0.610227 + 0.480753i
\(653\) −32.9549 + 13.6503i −1.28962 + 0.534179i −0.918873 0.394553i \(-0.870899\pi\)
−0.370750 + 0.928733i \(0.620899\pi\)
\(654\) 0 0
\(655\) −2.82906 −0.110540
\(656\) 12.1874 2.93405i 0.475839 0.114555i
\(657\) 0 0
\(658\) −0.0498820 0.0292258i −0.00194460 0.00113934i
\(659\) 12.1112 + 29.2389i 0.471784 + 1.13899i 0.963374 + 0.268161i \(0.0864159\pi\)
−0.491590 + 0.870827i \(0.663584\pi\)
\(660\) 0 0
\(661\) −1.46878 0.608388i −0.0571289 0.0236636i 0.353936 0.935270i \(-0.384843\pi\)
−0.411065 + 0.911606i \(0.634843\pi\)
\(662\) 3.51812 25.4648i 0.136736 0.989716i
\(663\) 0 0
\(664\) −8.47405 3.70186i −0.328857 0.143660i
\(665\) 0.00660189 0.00660189i 0.000256010 0.000256010i
\(666\) 0 0
\(667\) −29.3294 12.1486i −1.13564 0.470397i
\(668\) 22.0001 + 6.19721i 0.851210 + 0.239777i
\(669\) 0 0
\(670\) −0.789823 3.02482i −0.0305135 0.116859i
\(671\) 14.0712 0.543212
\(672\) 0 0
\(673\) 18.9627 0.730957 0.365478 0.930820i \(-0.380905\pi\)
0.365478 + 0.930820i \(0.380905\pi\)
\(674\) 7.02014 + 26.8853i 0.270406 + 1.03558i
\(675\) 0 0
\(676\) −0.720465 + 2.55765i −0.0277102 + 0.0983713i
\(677\) −30.8482 12.7778i −1.18559 0.491089i −0.299276 0.954166i \(-0.596745\pi\)
−0.886318 + 0.463077i \(0.846745\pi\)
\(678\) 0 0
\(679\) 0.141930 0.141930i 0.00544679 0.00544679i
\(680\) 1.12000 0.438967i 0.0429499 0.0168336i
\(681\) 0 0
\(682\) 0.154845 1.12079i 0.00592931 0.0429173i
\(683\) 23.3005 + 9.65139i 0.891570 + 0.369300i 0.780973 0.624565i \(-0.214724\pi\)
0.110597 + 0.993865i \(0.464724\pi\)
\(684\) 0 0
\(685\) 1.28461 + 3.10133i 0.0490826 + 0.118496i
\(686\) 0.288482 + 0.169021i 0.0110143 + 0.00645325i
\(687\) 0 0
\(688\) 8.51148 + 11.6996i 0.324497 + 0.446042i
\(689\) −12.3392 −0.470087
\(690\) 0 0
\(691\) 17.6321 7.30344i 0.670756 0.277836i −0.0212009 0.999775i \(-0.506749\pi\)
0.691957 + 0.721939i \(0.256749\pi\)
\(692\) −2.32506 + 2.95123i −0.0883854 + 0.112189i
\(693\) 0 0
\(694\) 3.04590 22.0467i 0.115621 0.836883i
\(695\) −1.43883 + 1.43883i −0.0545781 + 0.0545781i
\(696\) 0 0
\(697\) −4.29850 4.29850i −0.162817 0.162817i
\(698\) −12.8075 + 9.69823i −0.484773 + 0.367083i
\(699\) 0 0
\(700\) 0.145901 0.0817687i 0.00551453 0.00309057i
\(701\) 3.99504 + 9.64488i 0.150891 + 0.364282i 0.981192 0.193032i \(-0.0618321\pi\)
−0.830302 + 0.557314i \(0.811832\pi\)
\(702\) 0 0
\(703\) 6.89601i 0.260088i
\(704\) −12.5429 + 27.2754i −0.472730 + 1.02798i
\(705\) 0 0
\(706\) 10.7271 + 41.0821i 0.403721 + 1.54614i
\(707\) −0.162689 + 0.0673882i −0.00611857 + 0.00253439i
\(708\) 0 0
\(709\) −13.5796 + 32.7841i −0.509994 + 1.23123i 0.433893 + 0.900965i \(0.357140\pi\)
−0.943887 + 0.330270i \(0.892860\pi\)
\(710\) 2.23858 + 2.95628i 0.0840123 + 0.110947i
\(711\) 0 0
\(712\) 0.110581 5.76970i 0.00414418 0.216229i
\(713\) 1.02157 + 1.02157i 0.0382582 + 0.0382582i
\(714\) 0 0
\(715\) 1.19189 2.87747i 0.0445741 0.107611i
\(716\) −12.0336 9.48038i −0.449716 0.354299i
\(717\) 0 0
\(718\) −18.2682 10.7033i −0.681764 0.399445i
\(719\) 33.9773i 1.26714i −0.773686 0.633570i \(-0.781589\pi\)
0.773686 0.633570i \(-0.218411\pi\)
\(720\) 0 0
\(721\) 0.0399566i 0.00148806i
\(722\) 9.03797 15.4258i 0.336358 0.574089i
\(723\) 0 0
\(724\) 43.4810 5.16018i 1.61596 0.191776i
\(725\) 8.87759 21.4324i 0.329706 0.795980i
\(726\) 0 0
\(727\) −6.66650 6.66650i −0.247247 0.247247i 0.572593 0.819840i \(-0.305938\pi\)
−0.819840 + 0.572593i \(0.805938\pi\)
\(728\) 0.168338 0.0659780i 0.00623904 0.00244531i
\(729\) 0 0
\(730\) 3.86496 2.92665i 0.143048 0.108320i
\(731\) 2.68495 6.48204i 0.0993065 0.239747i
\(732\) 0 0
\(733\) −20.4629 + 8.47602i −0.755815 + 0.313069i −0.727112 0.686519i \(-0.759138\pi\)
−0.0287034 + 0.999588i \(0.509138\pi\)
\(734\) 5.23232 1.36623i 0.193128 0.0504286i
\(735\) 0 0
\(736\) −18.0970 33.7931i −0.667063 1.24563i
\(737\) 37.8345i 1.39365i
\(738\) 0 0
\(739\) −14.5912 35.2264i −0.536748 1.29582i −0.926981 0.375108i \(-0.877606\pi\)
0.390234 0.920716i \(-0.372394\pi\)
\(740\) 0.325173 1.15437i 0.0119536 0.0424353i
\(741\) 0 0
\(742\) 0.0469976 + 0.0620654i 0.00172534 + 0.00227849i
\(743\) 30.0108 + 30.0108i 1.10099 + 1.10099i 0.994292 + 0.106696i \(0.0340272\pi\)
0.106696 + 0.994292i \(0.465973\pi\)
\(744\) 0 0
\(745\) 1.72559 1.72559i 0.0632207 0.0632207i
\(746\) −35.6432 4.92434i −1.30499 0.180293i
\(747\) 0 0
\(748\) 14.4569 1.71570i 0.528598 0.0627322i
\(749\) 0.236682 0.0980368i 0.00864817 0.00358219i
\(750\) 0 0
\(751\) 36.3413 1.32611 0.663056 0.748570i \(-0.269259\pi\)
0.663056 + 0.748570i \(0.269259\pi\)
\(752\) −8.25920 5.05410i −0.301182 0.184304i
\(753\) 0 0
\(754\) 12.6776 21.6379i 0.461692 0.788006i
\(755\) −1.15282 2.78314i −0.0419553 0.101289i
\(756\) 0 0
\(757\) −20.0419 8.30162i −0.728435 0.301728i −0.0125261 0.999922i \(-0.503987\pi\)
−0.715909 + 0.698194i \(0.753987\pi\)
\(758\) 4.49847 + 0.621493i 0.163392 + 0.0225736i
\(759\) 0 0
\(760\) 1.12671 1.08433i 0.0408700 0.0393329i
\(761\) 29.5308 29.5308i 1.07049 1.07049i 0.0731706 0.997319i \(-0.476688\pi\)
0.997319 0.0731706i \(-0.0233118\pi\)
\(762\) 0 0
\(763\) 0.116272 + 0.0481614i 0.00420933 + 0.00174356i
\(764\) 4.40671 2.46970i 0.159429 0.0893505i
\(765\) 0 0
\(766\) −6.81172 + 1.77864i −0.246118 + 0.0642648i
\(767\) 14.7604 0.532969
\(768\) 0 0
\(769\) −4.12972 −0.148922 −0.0744608 0.997224i \(-0.523724\pi\)
−0.0744608 + 0.997224i \(0.523724\pi\)
\(770\) −0.0190131 + 0.00496460i −0.000685185 + 0.000178912i
\(771\) 0 0
\(772\) −10.7978 + 6.05153i −0.388622 + 0.217799i
\(773\) 40.0041 + 16.5702i 1.43885 + 0.595990i 0.959519 0.281645i \(-0.0908800\pi\)
0.479329 + 0.877635i \(0.340880\pi\)
\(774\) 0 0
\(775\) −0.746512 + 0.746512i −0.0268155 + 0.0268155i
\(776\) 24.2225 23.3115i 0.869537 0.836833i
\(777\) 0 0
\(778\) 12.8468 + 1.77486i 0.460579 + 0.0636319i
\(779\) −7.30065 3.02403i −0.261573 0.108347i
\(780\) 0 0
\(781\) 17.1740 + 41.4616i 0.614532 + 1.48361i
\(782\) −9.39738 + 16.0393i −0.336050 + 0.573563i
\(783\) 0 0
\(784\) 23.8821 + 14.6144i 0.852934 + 0.521941i
\(785\) 2.72141 0.0971311
\(786\) 0 0
\(787\) −35.6785 + 14.7785i −1.27180 + 0.526797i −0.913511 0.406813i \(-0.866640\pi\)
−0.358290 + 0.933610i \(0.616640\pi\)
\(788\) 48.6600