Properties

Label 108.3.f.c.91.1
Level 108
Weight 3
Character 108.91
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 91.1
Root \(-1.59523 + 1.20633i\) of \(x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + 28672 x^{2} - 49152 x + 65536\)
Character \(\chi\) \(=\) 108.91
Dual form 108.3.f.c.19.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.59523 + 1.20633i) q^{2} +(1.08951 - 3.84876i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(-7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +O(q^{10})\) \(q+(-1.59523 + 1.20633i) q^{2} +(1.08951 - 3.84876i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(-7.23844 + 4.17912i) q^{7} +(2.90487 + 7.45397i) q^{8} +(-0.544081 - 4.36996i) q^{10} +(-4.54769 + 2.62561i) q^{11} +(-7.37788 + 12.7789i) q^{13} +(6.50556 - 15.3986i) q^{14} +(-13.6259 - 8.38655i) q^{16} -28.2789 q^{17} -19.1376i q^{19} +(6.13957 + 6.31475i) q^{20} +(4.08724 - 9.67448i) q^{22} +(3.16702 + 1.82848i) q^{23} +(10.0759 + 17.4520i) q^{25} +(-3.64618 - 29.2854i) q^{26} +(8.19805 + 32.4122i) q^{28} +(12.3355 + 21.3657i) q^{29} +(32.9674 + 19.0338i) q^{31} +(31.8535 - 3.05895i) q^{32} +(45.1113 - 34.1138i) q^{34} -18.4036i q^{35} -4.21977 q^{37} +(23.0863 + 30.5288i) q^{38} +(-17.4117 - 2.66709i) q^{40} +(9.92483 - 17.1903i) q^{41} +(-20.1894 + 11.6564i) q^{43} +(5.15057 + 20.3636i) q^{44} +(-7.25787 + 0.903640i) q^{46} +(25.8538 - 14.9267i) q^{47} +(10.4300 - 18.0654i) q^{49} +(-37.1264 - 15.6850i) q^{50} +(41.1445 + 42.3184i) q^{52} +32.1118 q^{53} -11.5624i q^{55} +(-52.1778 - 41.8154i) q^{56} +(-45.4521 - 19.2025i) q^{58} +(-7.96159 - 4.59663i) q^{59} +(-40.8215 - 70.7049i) q^{61} +(-75.5517 + 9.40656i) q^{62} +(-47.1234 + 43.3057i) q^{64} +(-16.2450 - 28.1372i) q^{65} +(-6.86179 - 3.96166i) q^{67} +(-30.8102 + 108.839i) q^{68} +(22.2009 + 29.3579i) q^{70} +62.9286i q^{71} +33.3218 q^{73} +(6.73149 - 5.09045i) q^{74} +(-73.6560 - 20.8506i) q^{76} +(21.9454 - 38.0106i) q^{77} +(-53.7133 + 31.0114i) q^{79} +(30.9931 - 16.7497i) q^{80} +(4.90489 + 39.3951i) q^{82} +(-103.056 + 59.4995i) q^{83} +(31.1329 - 53.9238i) q^{85} +(18.1453 - 42.9498i) q^{86} +(-32.7816 - 26.2713i) q^{88} +107.361 q^{89} -123.332i q^{91} +(10.4879 - 10.1969i) q^{92} +(-23.2362 + 54.9999i) q^{94} +(36.4927 + 21.0690i) q^{95} +(1.78621 + 3.09380i) q^{97} +(5.15457 + 41.4005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59523 + 1.20633i −0.797615 + 0.603167i
\(3\) 0 0
\(4\) 1.08951 3.84876i 0.272378 0.962190i
\(5\) −1.10093 + 1.90686i −0.220185 + 0.381372i −0.954864 0.297043i \(-0.903999\pi\)
0.734679 + 0.678415i \(0.237333\pi\)
\(6\) 0 0
\(7\) −7.23844 + 4.17912i −1.03406 + 0.597017i −0.918146 0.396242i \(-0.870314\pi\)
−0.115917 + 0.993259i \(0.536981\pi\)
\(8\) 2.90487 + 7.45397i 0.363109 + 0.931747i
\(9\) 0 0
\(10\) −0.544081 4.36996i −0.0544081 0.436996i
\(11\) −4.54769 + 2.62561i −0.413426 + 0.238692i −0.692261 0.721648i \(-0.743385\pi\)
0.278835 + 0.960339i \(0.410052\pi\)
\(12\) 0 0
\(13\) −7.37788 + 12.7789i −0.567529 + 0.982990i 0.429280 + 0.903171i \(0.358767\pi\)
−0.996809 + 0.0798182i \(0.974566\pi\)
\(14\) 6.50556 15.3986i 0.464683 1.09990i
\(15\) 0 0
\(16\) −13.6259 8.38655i −0.851620 0.524159i
\(17\) −28.2789 −1.66346 −0.831732 0.555178i \(-0.812650\pi\)
−0.831732 + 0.555178i \(0.812650\pi\)
\(18\) 0 0
\(19\) 19.1376i 1.00724i −0.863925 0.503620i \(-0.832001\pi\)
0.863925 0.503620i \(-0.167999\pi\)
\(20\) 6.13957 + 6.31475i 0.306979 + 0.315737i
\(21\) 0 0
\(22\) 4.08724 9.67448i 0.185784 0.439749i
\(23\) 3.16702 + 1.82848i 0.137696 + 0.0794990i 0.567266 0.823535i \(-0.308001\pi\)
−0.429569 + 0.903034i \(0.641335\pi\)
\(24\) 0 0
\(25\) 10.0759 + 17.4520i 0.403037 + 0.698081i
\(26\) −3.64618 29.2854i −0.140238 1.12636i
\(27\) 0 0
\(28\) 8.19805 + 32.4122i 0.292787 + 1.15758i
\(29\) 12.3355 + 21.3657i 0.425362 + 0.736748i 0.996454 0.0841375i \(-0.0268135\pi\)
−0.571092 + 0.820886i \(0.693480\pi\)
\(30\) 0 0
\(31\) 32.9674 + 19.0338i 1.06347 + 0.613992i 0.926389 0.376568i \(-0.122896\pi\)
0.137077 + 0.990560i \(0.456229\pi\)
\(32\) 31.8535 3.05895i 0.995421 0.0955923i
\(33\) 0 0
\(34\) 45.1113 34.1138i 1.32680 1.00335i
\(35\) 18.4036i 0.525817i
\(36\) 0 0
\(37\) −4.21977 −0.114048 −0.0570239 0.998373i \(-0.518161\pi\)
−0.0570239 + 0.998373i \(0.518161\pi\)
\(38\) 23.0863 + 30.5288i 0.607535 + 0.803390i
\(39\) 0 0
\(40\) −17.4117 2.66709i −0.435293 0.0666773i
\(41\) 9.92483 17.1903i 0.242069 0.419276i −0.719235 0.694767i \(-0.755507\pi\)
0.961303 + 0.275492i \(0.0888406\pi\)
\(42\) 0 0
\(43\) −20.1894 + 11.6564i −0.469521 + 0.271078i −0.716039 0.698060i \(-0.754047\pi\)
0.246518 + 0.969138i \(0.420714\pi\)
\(44\) 5.15057 + 20.3636i 0.117058 + 0.462809i
\(45\) 0 0
\(46\) −7.25787 + 0.903640i −0.157780 + 0.0196444i
\(47\) 25.8538 14.9267i 0.550082 0.317590i −0.199073 0.979985i \(-0.563793\pi\)
0.749155 + 0.662395i \(0.230460\pi\)
\(48\) 0 0
\(49\) 10.4300 18.0654i 0.212858 0.368681i
\(50\) −37.1264 15.6850i −0.742528 0.313701i
\(51\) 0 0
\(52\) 41.1445 + 42.3184i 0.791240 + 0.813816i
\(53\) 32.1118 0.605883 0.302942 0.953009i \(-0.402031\pi\)
0.302942 + 0.953009i \(0.402031\pi\)
\(54\) 0 0
\(55\) 11.5624i 0.210225i
\(56\) −52.1778 41.8154i −0.931746 0.746703i
\(57\) 0 0
\(58\) −45.4521 19.2025i −0.783657 0.331077i
\(59\) −7.96159 4.59663i −0.134942 0.0779089i 0.431009 0.902348i \(-0.358158\pi\)
−0.565951 + 0.824439i \(0.691491\pi\)
\(60\) 0 0
\(61\) −40.8215 70.7049i −0.669205 1.15910i −0.978127 0.208009i \(-0.933302\pi\)
0.308922 0.951087i \(-0.400032\pi\)
\(62\) −75.5517 + 9.40656i −1.21858 + 0.151719i
\(63\) 0 0
\(64\) −47.1234 + 43.3057i −0.736304 + 0.676651i
\(65\) −16.2450 28.1372i −0.249923 0.432879i
\(66\) 0 0
\(67\) −6.86179 3.96166i −0.102415 0.0591292i 0.447918 0.894075i \(-0.352166\pi\)
−0.550333 + 0.834946i \(0.685499\pi\)
\(68\) −30.8102 + 108.839i −0.453091 + 1.60057i
\(69\) 0 0
\(70\) 22.2009 + 29.3579i 0.317155 + 0.419399i
\(71\) 62.9286i 0.886318i 0.896443 + 0.443159i \(0.146142\pi\)
−0.896443 + 0.443159i \(0.853858\pi\)
\(72\) 0 0
\(73\) 33.3218 0.456463 0.228232 0.973607i \(-0.426706\pi\)
0.228232 + 0.973607i \(0.426706\pi\)
\(74\) 6.73149 5.09045i 0.0909661 0.0687899i
\(75\) 0 0
\(76\) −73.6560 20.8506i −0.969157 0.274351i
\(77\) 21.9454 38.0106i 0.285006 0.493644i
\(78\) 0 0
\(79\) −53.7133 + 31.0114i −0.679916 + 0.392549i −0.799823 0.600236i \(-0.795073\pi\)
0.119908 + 0.992785i \(0.461740\pi\)
\(80\) 30.9931 16.7497i 0.387414 0.209372i
\(81\) 0 0
\(82\) 4.90489 + 39.3951i 0.0598157 + 0.480429i
\(83\) −103.056 + 59.4995i −1.24164 + 0.716861i −0.969428 0.245376i \(-0.921089\pi\)
−0.272212 + 0.962237i \(0.587755\pi\)
\(84\) 0 0
\(85\) 31.1329 53.9238i 0.366270 0.634398i
\(86\) 18.1453 42.9498i 0.210992 0.499416i
\(87\) 0 0
\(88\) −32.7816 26.2713i −0.372519 0.298537i
\(89\) 107.361 1.20630 0.603152 0.797626i \(-0.293911\pi\)
0.603152 + 0.797626i \(0.293911\pi\)
\(90\) 0 0
\(91\) 123.332i 1.35530i
\(92\) 10.4879 10.1969i 0.113999 0.110836i
\(93\) 0 0
\(94\) −23.2362 + 54.9999i −0.247193 + 0.585106i
\(95\) 36.4927 + 21.0690i 0.384133 + 0.221779i
\(96\) 0 0
\(97\) 1.78621 + 3.09380i 0.0184145 + 0.0318949i 0.875086 0.483968i \(-0.160805\pi\)
−0.856671 + 0.515863i \(0.827471\pi\)
\(98\) 5.15457 + 41.4005i 0.0525976 + 0.422454i
\(99\) 0 0
\(100\) 78.1465 19.7656i 0.781465 0.197656i
\(101\) −7.54688 13.0716i −0.0747216 0.129422i 0.826244 0.563313i \(-0.190473\pi\)
−0.900965 + 0.433891i \(0.857140\pi\)
\(102\) 0 0
\(103\) 112.813 + 65.1324i 1.09527 + 0.632353i 0.934974 0.354716i \(-0.115422\pi\)
0.160294 + 0.987069i \(0.448756\pi\)
\(104\) −116.685 17.8736i −1.12197 0.171861i
\(105\) 0 0
\(106\) −51.2257 + 38.7376i −0.483261 + 0.365449i
\(107\) 51.2733i 0.479190i −0.970873 0.239595i \(-0.922985\pi\)
0.970873 0.239595i \(-0.0770146\pi\)
\(108\) 0 0
\(109\) −25.4737 −0.233704 −0.116852 0.993149i \(-0.537280\pi\)
−0.116852 + 0.993149i \(0.537280\pi\)
\(110\) 13.9481 + 18.4447i 0.126801 + 0.167679i
\(111\) 0 0
\(112\) 133.679 + 3.76124i 1.19356 + 0.0335825i
\(113\) −76.1529 + 131.901i −0.673919 + 1.16726i 0.302864 + 0.953034i \(0.402057\pi\)
−0.976783 + 0.214229i \(0.931276\pi\)
\(114\) 0 0
\(115\) −6.97330 + 4.02603i −0.0606374 + 0.0350090i
\(116\) 95.6712 24.1982i 0.824751 0.208605i
\(117\) 0 0
\(118\) 18.2456 2.27167i 0.154624 0.0192514i
\(119\) 204.695 118.181i 1.72013 0.993116i
\(120\) 0 0
\(121\) −46.7124 + 80.9082i −0.386053 + 0.668663i
\(122\) 150.413 + 63.5461i 1.23290 + 0.520870i
\(123\) 0 0
\(124\) 109.175 106.146i 0.880443 0.856019i
\(125\) −99.4176 −0.795341
\(126\) 0 0
\(127\) 147.428i 1.16085i 0.814314 + 0.580425i \(0.197114\pi\)
−0.814314 + 0.580425i \(0.802886\pi\)
\(128\) 22.9316 125.929i 0.179153 0.983821i
\(129\) 0 0
\(130\) 59.8573 + 25.2883i 0.460441 + 0.194525i
\(131\) −112.889 65.1766i −0.861750 0.497532i 0.00284803 0.999996i \(-0.499093\pi\)
−0.864598 + 0.502464i \(0.832427\pi\)
\(132\) 0 0
\(133\) 79.9782 + 138.526i 0.601340 + 1.04155i
\(134\) 15.7252 1.95787i 0.117352 0.0146109i
\(135\) 0 0
\(136\) −82.1465 210.790i −0.604018 1.54993i
\(137\) −49.9179 86.4604i −0.364364 0.631098i 0.624310 0.781177i \(-0.285380\pi\)
−0.988674 + 0.150079i \(0.952047\pi\)
\(138\) 0 0
\(139\) −82.7828 47.7947i −0.595560 0.343847i 0.171733 0.985144i \(-0.445063\pi\)
−0.767293 + 0.641297i \(0.778397\pi\)
\(140\) −70.8310 20.0509i −0.505936 0.143221i
\(141\) 0 0
\(142\) −75.9129 100.385i −0.534598 0.706940i
\(143\) 77.4857i 0.541858i
\(144\) 0 0
\(145\) −54.3218 −0.374633
\(146\) −53.1560 + 40.1973i −0.364082 + 0.275324i
\(147\) 0 0
\(148\) −4.59749 + 16.2409i −0.0310641 + 0.109736i
\(149\) −34.3382 + 59.4755i −0.230458 + 0.399164i −0.957943 0.286959i \(-0.907356\pi\)
0.727485 + 0.686123i \(0.240689\pi\)
\(150\) 0 0
\(151\) 91.2633 52.6909i 0.604393 0.348946i −0.166375 0.986063i \(-0.553206\pi\)
0.770768 + 0.637116i \(0.219873\pi\)
\(152\) 142.651 55.5922i 0.938493 0.365738i
\(153\) 0 0
\(154\) 10.8455 + 87.1092i 0.0704255 + 0.565644i
\(155\) −72.5894 + 41.9095i −0.468319 + 0.270384i
\(156\) 0 0
\(157\) −107.502 + 186.200i −0.684729 + 1.18598i 0.288794 + 0.957391i \(0.406746\pi\)
−0.973522 + 0.228593i \(0.926587\pi\)
\(158\) 48.2749 114.267i 0.305538 0.723206i
\(159\) 0 0
\(160\) −29.2353 + 64.1077i −0.182721 + 0.400673i
\(161\) −30.5657 −0.189849
\(162\) 0 0
\(163\) 33.7439i 0.207018i −0.994629 0.103509i \(-0.966993\pi\)
0.994629 0.103509i \(-0.0330071\pi\)
\(164\) −55.3481 56.9273i −0.337489 0.347118i
\(165\) 0 0
\(166\) 92.6219 219.236i 0.557963 1.32070i
\(167\) 131.565 + 75.9589i 0.787812 + 0.454843i 0.839192 0.543836i \(-0.183029\pi\)
−0.0513797 + 0.998679i \(0.516362\pi\)
\(168\) 0 0
\(169\) −24.3663 42.2036i −0.144179 0.249726i
\(170\) 15.3860 + 123.578i 0.0905060 + 0.726927i
\(171\) 0 0
\(172\) 22.8659 + 90.4040i 0.132941 + 0.525605i
\(173\) 59.4003 + 102.884i 0.343354 + 0.594707i 0.985053 0.172249i \(-0.0551035\pi\)
−0.641699 + 0.766957i \(0.721770\pi\)
\(174\) 0 0
\(175\) −145.868 84.2170i −0.833532 0.481240i
\(176\) 83.9862 + 2.36307i 0.477194 + 0.0134265i
\(177\) 0 0
\(178\) −171.265 + 129.513i −0.962166 + 0.727603i
\(179\) 218.189i 1.21894i 0.792811 + 0.609468i \(0.208617\pi\)
−0.792811 + 0.609468i \(0.791383\pi\)
\(180\) 0 0
\(181\) 184.078 1.01701 0.508503 0.861060i \(-0.330199\pi\)
0.508503 + 0.861060i \(0.330199\pi\)
\(182\) 148.780 + 196.743i 0.817472 + 1.08101i
\(183\) 0 0
\(184\) −4.42965 + 28.9183i −0.0240742 + 0.157165i
\(185\) 4.64565 8.04650i 0.0251116 0.0434946i
\(186\) 0 0
\(187\) 128.603 74.2492i 0.687719 0.397055i
\(188\) −29.2813 115.768i −0.155752 0.615788i
\(189\) 0 0
\(190\) −83.6305 + 10.4124i −0.440160 + 0.0548021i
\(191\) −215.775 + 124.578i −1.12971 + 0.652239i −0.943862 0.330339i \(-0.892837\pi\)
−0.185849 + 0.982578i \(0.559503\pi\)
\(192\) 0 0
\(193\) 125.086 216.656i 0.648115 1.12257i −0.335457 0.942055i \(-0.608891\pi\)
0.983573 0.180513i \(-0.0577758\pi\)
\(194\) −6.58158 2.78056i −0.0339256 0.0143328i
\(195\) 0 0
\(196\) −58.1656 59.8252i −0.296763 0.305231i
\(197\) −255.674 −1.29784 −0.648919 0.760858i \(-0.724779\pi\)
−0.648919 + 0.760858i \(0.724779\pi\)
\(198\) 0 0
\(199\) 309.110i 1.55332i 0.629921 + 0.776659i \(0.283087\pi\)
−0.629921 + 0.776659i \(0.716913\pi\)
\(200\) −100.818 + 125.802i −0.504088 + 0.629008i
\(201\) 0 0
\(202\) 27.8077 + 11.7481i 0.137662 + 0.0581589i
\(203\) −178.580 103.103i −0.879702 0.507896i
\(204\) 0 0
\(205\) 21.8530 + 37.8505i 0.106600 + 0.184636i
\(206\) −258.533 + 32.1887i −1.25502 + 0.156256i
\(207\) 0 0
\(208\) 207.701 112.249i 0.998563 0.539658i
\(209\) 50.2478 + 87.0317i 0.240420 + 0.416420i
\(210\) 0 0
\(211\) −341.158 196.968i −1.61686 0.933497i −0.987725 0.156205i \(-0.950074\pi\)
−0.629140 0.777292i \(1.28341\pi\)
\(212\) 34.9862 123.591i 0.165029 0.582975i
\(213\) 0 0
\(214\) 61.8528 + 81.7927i 0.289032 + 0.382209i
\(215\) 51.3311i 0.238750i
\(216\) 0 0
\(217\) −318.177 −1.46626
\(218\) 40.6364 30.7298i 0.186405 0.140962i
\(219\) 0 0
\(220\) −44.5009 12.5974i −0.202277 0.0572608i
\(221\) 208.638 361.372i 0.944064 1.63517i
\(222\) 0 0
\(223\) 89.4002 51.6152i 0.400898 0.231458i −0.285974 0.958238i \(-0.592317\pi\)
0.686871 + 0.726779i \(0.258984\pi\)
\(224\) −217.786 + 155.261i −0.972258 + 0.693131i
\(225\) 0 0
\(226\) −37.6350 302.278i −0.166527 1.33751i
\(227\) 122.210 70.5578i 0.538369 0.310828i −0.206049 0.978542i \(-0.566061\pi\)
0.744418 + 0.667714i \(0.232727\pi\)
\(228\) 0 0
\(229\) 105.572 182.856i 0.461012 0.798496i −0.538000 0.842945i \(-0.680820\pi\)
0.999012 + 0.0444490i \(0.0141532\pi\)
\(230\) 6.26726 14.8346i 0.0272490 0.0644982i
\(231\) 0 0
\(232\) −123.426 + 154.013i −0.532010 + 0.663849i
\(233\) 280.109 1.20219 0.601093 0.799179i \(-0.294732\pi\)
0.601093 + 0.799179i \(0.294732\pi\)
\(234\) 0 0
\(235\) 65.7328i 0.279714i
\(236\) −26.3656 + 25.6342i −0.111719 + 0.108619i
\(237\) 0 0
\(238\) −183.970 + 435.456i −0.772983 + 1.82965i
\(239\) 339.349 + 195.923i 1.41987 + 0.819762i 0.996287 0.0860949i \(-0.0274388\pi\)
0.423583 + 0.905857i \(0.360772\pi\)
\(240\) 0 0
\(241\) −23.6786 41.0125i −0.0982514 0.170176i 0.812710 0.582669i \(-0.197992\pi\)
−0.910961 + 0.412493i \(0.864658\pi\)
\(242\) −23.0854 185.418i −0.0953943 0.766190i
\(243\) 0 0
\(244\) −316.602 + 80.0783i −1.29755 + 0.328190i
\(245\) 22.9654 + 39.7772i 0.0937363 + 0.162356i
\(246\) 0 0
\(247\) 244.557 + 141.195i 0.990107 + 0.571639i
\(248\) −46.1110 + 301.029i −0.185931 + 1.21383i
\(249\) 0 0
\(250\) 158.594 119.931i 0.634376 0.479724i
\(251\) 389.416i 1.55146i −0.631065 0.775730i \(-0.717382\pi\)
0.631065 0.775730i \(-0.282618\pi\)
\(252\) 0 0
\(253\) −19.2035 −0.0759030
\(254\) −177.847 235.181i −0.700187 0.925911i
\(255\) 0 0
\(256\) 115.332 + 228.549i 0.450514 + 0.892769i
\(257\) 32.5409 56.3625i 0.126618 0.219310i −0.795746 0.605631i \(-0.792921\pi\)
0.922364 + 0.386321i \(0.126254\pi\)
\(258\) 0 0
\(259\) 30.5445 17.6349i 0.117933 0.0680884i
\(260\) −125.992 + 31.8673i −0.484586 + 0.122567i
\(261\) 0 0
\(262\) 258.709 32.2105i 0.987439 0.122941i
\(263\) 124.773 72.0378i 0.474423 0.273908i −0.243667 0.969859i \(-0.578350\pi\)
0.718089 + 0.695951i \(0.245017\pi\)
\(264\) 0 0
\(265\) −35.3527 + 61.2327i −0.133406 + 0.231067i
\(266\) −294.693 124.501i −1.10787 0.468048i
\(267\) 0 0
\(268\) −22.7235 + 22.0931i −0.0847891 + 0.0824370i
\(269\) 72.4113 0.269187 0.134593 0.990901i \(-0.457027\pi\)
0.134593 + 0.990901i \(0.457027\pi\)
\(270\) 0 0
\(271\) 35.4695i 0.130884i −0.997856 0.0654419i \(-0.979154\pi\)
0.997856 0.0654419i \(-0.0208457\pi\)
\(272\) 385.326 + 237.162i 1.41664 + 0.871920i
\(273\) 0 0
\(274\) 183.931 + 77.7064i 0.671280 + 0.283600i
\(275\) −91.6443 52.9109i −0.333252 0.192403i
\(276\) 0 0
\(277\) −166.922 289.118i −0.602607 1.04375i −0.992425 0.122854i \(-0.960795\pi\)
0.389818 0.920892i \(-0.372538\pi\)
\(278\) 189.714 23.6203i 0.682424 0.0849651i
\(279\) 0 0
\(280\) 137.180 53.4600i 0.489928 0.190929i
\(281\) 20.5385 + 35.5737i 0.0730906 + 0.126597i 0.900254 0.435364i \(-0.143380\pi\)
−0.827164 + 0.561961i \(0.810047\pi\)
\(282\) 0 0
\(283\) 218.583 + 126.199i 0.772378 + 0.445933i 0.833722 0.552184i \(-0.186205\pi\)
−0.0613442 + 0.998117i \(0.519539\pi\)
\(284\) 242.197 + 68.5615i 0.852806 + 0.241414i
\(285\) 0 0
\(286\) 93.4737 + 123.607i 0.326831 + 0.432194i
\(287\) 165.908i 0.578077i
\(288\) 0 0
\(289\) 510.695 1.76711
\(290\) 86.6558 65.5303i 0.298813 0.225967i
\(291\) 0 0
\(292\) 36.3046 128.248i 0.124331 0.439205i
\(293\) −20.3415 + 35.2325i −0.0694248 + 0.120247i −0.898648 0.438670i \(-0.855450\pi\)
0.829223 + 0.558917i \(0.188783\pi\)
\(294\) 0 0
\(295\) 17.5302 10.1211i 0.0594245 0.0343088i
\(296\) −12.2579 31.4540i −0.0414117 0.106264i
\(297\) 0 0
\(298\) −16.9701 136.300i −0.0569465 0.457384i
\(299\) −46.7317 + 26.9806i −0.156293 + 0.0902361i
\(300\) 0 0
\(301\) 97.4266 168.748i 0.323677 0.560624i
\(302\) −82.0231 + 194.148i −0.271600 + 0.642875i
\(303\) 0 0
\(304\) −160.498 + 260.767i −0.527955 + 0.857787i
\(305\) 179.766 0.589396
\(306\) 0 0
\(307\) 136.830i 0.445701i −0.974853 0.222850i \(-0.928464\pi\)
0.974853 0.222850i \(-0.0715361\pi\)
\(308\) −122.384 125.876i −0.397351 0.408688i
\(309\) 0 0
\(310\) 65.2398 154.422i 0.210451 0.498137i
\(311\) −371.260 214.347i −1.19376 0.689219i −0.234605 0.972091i \(-0.575380\pi\)
−0.959158 + 0.282871i \(0.908713\pi\)
\(312\) 0 0
\(313\) 5.98705 + 10.3699i 0.0191280 + 0.0331306i 0.875431 0.483343i \(-0.160578\pi\)
−0.856303 + 0.516474i \(0.827244\pi\)
\(314\) −53.1281 426.715i −0.169198 1.35896i
\(315\) 0 0
\(316\) 60.8341 + 240.517i 0.192513 + 0.761130i
\(317\) 23.5266 + 40.7493i 0.0742164 + 0.128547i 0.900745 0.434348i \(-0.143021\pi\)
−0.826529 + 0.562894i \(0.809688\pi\)
\(318\) 0 0
\(319\) −112.196 64.7763i −0.351711 0.203061i
\(320\) −30.6984 137.534i −0.0959324 0.429794i
\(321\) 0 0
\(322\) 48.7593 36.8725i 0.151426 0.114511i
\(323\) 541.189i 1.67551i
\(324\) 0 0
\(325\) −297.356 −0.914941
\(326\) 40.7065 + 53.8293i 0.124867 + 0.165121i
\(327\) 0 0
\(328\) 156.966 + 24.0438i 0.478556 + 0.0733042i
\(329\) −124.761 + 216.092i −0.379213 + 0.656816i
\(330\) 0 0
\(331\) 73.1501 42.2332i 0.220997 0.127593i −0.385415 0.922743i \(-0.625942\pi\)
0.606412 + 0.795151i \(0.292608\pi\)
\(332\) 116.718 + 461.464i 0.351561 + 1.38995i
\(333\) 0 0
\(334\) −301.508 + 37.5392i −0.902717 + 0.112393i
\(335\) 15.1086 8.72297i 0.0451004 0.0260387i
\(336\) 0 0
\(337\) −252.558 + 437.443i −0.749430 + 1.29805i 0.198667 + 0.980067i \(0.436339\pi\)
−0.948096 + 0.317983i \(0.896994\pi\)
\(338\) 89.7815 + 37.9306i 0.265626 + 0.112221i
\(339\) 0 0
\(340\) −173.620 178.574i −0.510648 0.525217i
\(341\) −199.901 −0.586219
\(342\) 0 0
\(343\) 235.200i 0.685714i
\(344\) −145.534 116.631i −0.423064 0.339044i
\(345\) 0 0
\(346\) −218.870 92.4675i −0.632572 0.267247i
\(347\) 424.751 + 245.230i 1.22407 + 0.706715i 0.965782 0.259354i \(-0.0835097\pi\)
0.258284 + 0.966069i \(0.416843\pi\)
\(348\) 0 0
\(349\) 186.972 + 323.845i 0.535736 + 0.927923i 0.999127 + 0.0417686i \(0.0132992\pi\)
−0.463391 + 0.886154i \(0.653367\pi\)
\(350\) 334.287 41.6203i 0.955105 0.118915i
\(351\) 0 0
\(352\) −136.828 + 97.5458i −0.388716 + 0.277119i
\(353\) −297.026 514.465i −0.841434 1.45741i −0.888682 0.458523i \(-0.848379\pi\)
0.0472483 0.998883i \(-0.484955\pi\)
\(354\) 0 0
\(355\) −119.996 69.2796i −0.338016 0.195154i
\(356\) 116.971 413.207i 0.328571 1.16069i
\(357\) 0 0
\(358\) −263.209 348.062i −0.735222 0.972241i
\(359\) 410.893i 1.14455i −0.820062 0.572274i \(-0.806061\pi\)
0.820062 0.572274i \(-0.193939\pi\)
\(360\) 0 0
\(361\) −5.24690 −0.0145343
\(362\) −293.647 + 222.060i −0.811180 + 0.613425i
\(363\) 0 0
\(364\) −474.676 134.372i −1.30405 0.369154i
\(365\) −36.6848 + 63.5400i −0.100506 + 0.174082i
\(366\) 0 0
\(367\) −466.176 + 269.147i −1.27023 + 0.733370i −0.975032 0.222064i \(-0.928721\pi\)
−0.295203 + 0.955435i \(0.595387\pi\)
\(368\) −27.8189 51.4750i −0.0755948 0.139878i
\(369\) 0 0
\(370\) 2.29590 + 18.4402i 0.00620512 + 0.0498384i
\(371\) −232.440 + 134.199i −0.626522 + 0.361722i
\(372\) 0 0
\(373\) −74.9606 + 129.836i −0.200967 + 0.348085i −0.948840 0.315757i \(-0.897742\pi\)
0.747873 + 0.663841i \(0.231075\pi\)
\(374\) −115.583 + 273.583i −0.309044 + 0.731506i
\(375\) 0 0
\(376\) 186.365 + 149.354i 0.495653 + 0.397217i
\(377\) −364.039 −0.965621
\(378\) 0 0
\(379\) 184.361i 0.486442i 0.969971 + 0.243221i \(0.0782040\pi\)
−0.969971 + 0.243221i \(0.921796\pi\)
\(380\) 120.849 117.497i 0.318024 0.309201i
\(381\) 0 0
\(382\) 193.928 459.027i 0.507665 1.20164i
\(383\) −180.514 104.220i −0.471315 0.272114i 0.245475 0.969403i \(-0.421056\pi\)
−0.716790 + 0.697289i \(0.754389\pi\)
\(384\) 0 0
\(385\) 48.3206 + 83.6937i 0.125508 + 0.217386i
\(386\) 61.8181 + 496.511i 0.160150 + 1.28630i
\(387\) 0 0
\(388\) 13.8534 3.50395i 0.0357047 0.00903080i
\(389\) 150.914 + 261.390i 0.387953 + 0.671954i 0.992174 0.124863i \(-0.0398491\pi\)
−0.604221 + 0.796816i \(0.706516\pi\)
\(390\) 0 0
\(391\) −89.5597 51.7073i −0.229053 0.132244i
\(392\) 164.957 + 25.2677i 0.420808 + 0.0644585i
\(393\) 0 0
\(394\) 407.859 308.428i 1.03517 0.782813i
\(395\) 136.565i 0.345734i
\(396\) 0 0
\(397\) −246.672 −0.621341 −0.310670 0.950518i \(-0.600553\pi\)
−0.310670 + 0.950518i \(0.600553\pi\)
\(398\) −372.890 493.102i −0.936911 1.23895i
\(399\) 0 0
\(400\) 9.06842 322.302i 0.0226711 0.805755i
\(401\) −377.516 + 653.877i −0.941437 + 1.63062i −0.178703 + 0.983903i \(0.557190\pi\)
−0.762734 + 0.646713i \(0.776143\pi\)
\(402\) 0 0
\(403\) −486.460 + 280.858i −1.20710 + 0.696917i
\(404\) −58.5318 + 14.8045i −0.144881 + 0.0366447i
\(405\) 0 0
\(406\) 409.252 50.9539i 1.00801 0.125502i
\(407\) 19.1902 11.0794i 0.0471503 0.0272222i
\(408\) 0 0
\(409\) 130.730 226.432i 0.319634 0.553622i −0.660778 0.750582i \(-0.729773\pi\)
0.980412 + 0.196959i \(0.0631067\pi\)
\(410\) −80.5209 34.0182i −0.196392 0.0829712i
\(411\) 0 0
\(412\) 373.590 363.226i 0.906771 0.881617i
\(413\) 76.8394 0.186052
\(414\) 0 0
\(415\) 262.018i 0.631369i
\(416\) −195.921 + 429.620i −0.470964 + 1.03274i
\(417\) 0 0
\(418\) −185.146 78.2199i −0.442933 0.187129i
\(419\) −340.246 196.441i −0.812043 0.468833i 0.0356217 0.999365i \(-0.488659\pi\)
−0.847665 + 0.530532i \(0.821992\pi\)
\(420\) 0 0
\(421\) 102.451 + 177.450i 0.243351 + 0.421496i 0.961667 0.274221i \(-0.0884200\pi\)
−0.718316 + 0.695717i \(0.755087\pi\)
\(422\) 781.835 97.3423i 1.85269 0.230669i
\(423\) 0 0
\(424\) 93.2807 + 239.361i 0.220002 + 0.564530i
\(425\) −284.936 493.524i −0.670438 1.16123i
\(426\) 0 0
\(427\) 590.968 + 341.196i 1.38400 + 0.799053i
\(428\) −197.339 55.8629i −0.461072 0.130521i
\(429\) 0 0
\(430\) 61.9225 + 81.8850i 0.144006 + 0.190430i
\(431\) 462.725i 1.07361i 0.843707 + 0.536803i \(0.180368\pi\)
−0.843707 + 0.536803i \(0.819632\pi\)
\(432\) 0 0
\(433\) 190.574 0.440126 0.220063 0.975486i \(-0.429374\pi\)
0.220063 + 0.975486i \(0.429374\pi\)
\(434\) 507.566 383.828i 1.16951 0.884397i
\(435\) 0 0
\(436\) −27.7539 + 98.0421i −0.0636558 + 0.224867i
\(437\) 34.9926 60.6090i 0.0800747 0.138693i
\(438\) 0 0
\(439\) 379.279 218.977i 0.863962 0.498809i −0.00137479 0.999999i \(-0.500438\pi\)
0.865337 + 0.501190i \(0.167104\pi\)
\(440\) 86.1858 33.5873i 0.195877 0.0763347i
\(441\) 0 0
\(442\) 103.110 + 828.159i 0.233280 + 1.87366i
\(443\) 721.993 416.843i 1.62978 0.940954i 0.645623 0.763657i \(-0.276598\pi\)
0.984157 0.177297i \(-0.0567354\pi\)
\(444\) 0 0
\(445\) −118.196 + 204.722i −0.265610 + 0.460050i
\(446\) −80.3486 + 190.185i −0.180154 + 0.426423i
\(447\) 0 0
\(448\) 160.121 510.400i 0.357413 1.13929i
\(449\) 480.789 1.07080 0.535399 0.844599i \(-0.320161\pi\)
0.535399 + 0.844599i \(0.320161\pi\)
\(450\) 0 0
\(451\) 104.235i 0.231119i
\(452\) 424.685 + 436.802i 0.939568 + 0.966376i
\(453\) 0 0
\(454\) −109.836 + 259.982i −0.241930 + 0.572647i
\(455\) 235.177 + 135.779i 0.516872 + 0.298416i
\(456\) 0 0
\(457\) 109.313 + 189.336i 0.239197 + 0.414302i 0.960484 0.278334i \(-0.0897824\pi\)
−0.721287 + 0.692636i \(0.756449\pi\)
\(458\) 52.1739 + 419.051i 0.113917 + 0.914959i
\(459\) 0 0
\(460\) 7.89775 + 31.2250i 0.0171690 + 0.0678804i
\(461\) 358.474 + 620.894i 0.777600 + 1.34684i 0.933322 + 0.359042i \(0.116896\pi\)
−0.155722 + 0.987801i \(0.549770\pi\)
\(462\) 0 0
\(463\) −26.6250 15.3719i −0.0575053 0.0332007i 0.470972 0.882148i \(-0.343903\pi\)
−0.528477 + 0.848948i \(0.677237\pi\)
\(464\) 11.1021 394.580i 0.0239268 0.850387i
\(465\) 0 0
\(466\) −446.838 + 337.905i −0.958881 + 0.725119i
\(467\) 458.639i 0.982096i −0.871133 0.491048i \(-0.836614\pi\)
0.871133 0.491048i \(-0.163386\pi\)
\(468\) 0 0
\(469\) 66.2249 0.141204
\(470\) −79.2958 104.859i −0.168714 0.223104i
\(471\) 0 0
\(472\) 11.1357 72.6981i 0.0235927 0.154021i
\(473\) 61.2101 106.019i 0.129408 0.224142i
\(474\) 0 0
\(475\) 333.989 192.829i 0.703135 0.405955i
\(476\) −231.832 916.582i −0.487041 1.92559i
\(477\) 0 0
\(478\) −777.688 + 96.8260i −1.62696 + 0.202565i
\(479\) −570.477 + 329.365i −1.19098 + 0.687610i −0.958528 0.284999i \(-0.908007\pi\)
−0.232448 + 0.972609i \(0.574674\pi\)
\(480\) 0 0
\(481\) 31.1329 53.9238i 0.0647254 0.112108i
\(482\) 87.2476 + 36.8601i 0.181012 + 0.0764732i
\(483\) 0 0
\(484\) 260.503 + 267.935i 0.538228 + 0.553585i
\(485\) −7.86593 −0.0162184
\(486\) 0 0
\(487\) 715.589i 1.46938i −0.678402 0.734691i \(-0.737327\pi\)
0.678402 0.734691i \(-0.262673\pi\)
\(488\) 408.451 509.671i 0.836990 1.04441i
\(489\) 0 0
\(490\) −84.6198 35.7499i −0.172693 0.0729589i
\(491\) 574.179 + 331.502i 1.16941 + 0.675157i 0.953540 0.301266i \(-0.0974091\pi\)
0.215866 + 0.976423i \(0.430742\pi\)
\(492\) 0 0
\(493\) −348.834 604.198i −0.707574 1.22555i
\(494\) −560.452 + 69.7790i −1.13452 + 0.141253i
\(495\) 0 0
\(496\) −289.584 535.836i −0.583839 1.08031i
\(497\) −262.986 455.505i −0.529147 0.916509i
\(498\) 0 0
\(499\) 458.706 + 264.834i 0.919251 + 0.530730i 0.883396 0.468627i \(-0.155251\pi\)
0.0358546 + 0.999357i \(0.488585\pi\)
\(500\) −108.317 + 382.635i −0.216634 + 0.765269i
\(501\) 0 0
\(502\) 469.766 + 621.208i 0.935790 + 1.23747i
\(503\) 68.3537i 0.135892i −0.997689 0.0679460i \(-0.978355\pi\)
0.997689 0.0679460i \(-0.0216446\pi\)
\(504\) 0 0
\(505\) 33.2342 0.0658103
\(506\) 30.6339 23.1658i 0.0605413 0.0457822i
\(507\) 0 0
\(508\) 567.415 + 160.625i 1.11696 + 0.316190i
\(509\) 400.473 693.640i 0.786784 1.36275i −0.141143 0.989989i \(-0.545078\pi\)
0.927927 0.372761i \(-0.121589\pi\)
\(510\) 0 0
\(511\) −241.198 + 139.256i −0.472012 + 0.272516i
\(512\) −459.687 225.460i −0.897826 0.440351i
\(513\) 0 0
\(514\) 16.0818 + 129.166i 0.0312876 + 0.251297i
\(515\) −248.396 + 143.412i −0.482323 + 0.278469i
\(516\) 0 0
\(517\) −78.3834 + 135.764i −0.151612 + 0.262600i
\(518\) −27.4520 + 64.9786i −0.0529961 + 0.125441i
\(519\) 0 0
\(520\) 162.544 202.825i 0.312585 0.390047i
\(521\) 208.227 0.399668 0.199834 0.979830i \(-0.435960\pi\)
0.199834 + 0.979830i \(0.435960\pi\)
\(522\) 0 0
\(523\) 30.5350i 0.0583843i −0.999574 0.0291921i \(-0.990707\pi\)
0.999574 0.0291921i \(-0.00929347\pi\)
\(524\) −373.844 + 363.473i −0.713442 + 0.693651i
\(525\) 0 0
\(526\) −112.140 + 265.435i −0.213194 + 0.504629i
\(527\) −932.283 538.254i −1.76904 1.02135i
\(528\) 0 0
\(529\) −257.813 446.546i −0.487360 0.844132i
\(530\) −17.4714 140.327i −0.0329650 0.264769i
\(531\) 0 0
\(532\) 620.292 156.891i 1.16596 0.294907i
\(533\) 146.448 + 253.656i 0.274762 + 0.475903i
\(534\) 0 0
\(535\) 97.7710 + 56.4481i 0.182749 + 0.105510i
\(536\) 9.59747 62.6557i 0.0179057 0.116895i
\(537\) 0 0
\(538\) −115.513 + 87.3522i −0.214707 + 0.162365i
\(539\) 109.541i 0.203230i
\(540\) 0 0
\(541\) 526.091 0.972442 0.486221 0.873836i \(-0.338375\pi\)
0.486221 + 0.873836i \(0.338375\pi\)
\(542\) 42.7881 + 56.5820i 0.0789448 + 0.104395i
\(543\) 0 0
\(544\) −900.780 + 86.5038i −1.65585 + 0.159014i
\(545\) 28.0446 48.5747i 0.0514580 0.0891279i
\(546\) 0 0
\(547\) −823.276 + 475.318i −1.50507 + 0.868955i −0.505092 + 0.863066i \(0.668541\pi\)
−0.999983 + 0.00588962i \(0.998125\pi\)
\(548\) −387.151 + 97.9224i −0.706481 + 0.178691i
\(549\) 0 0
\(550\) 210.022 26.1487i 0.381858 0.0475432i
\(551\) 408.888 236.071i 0.742083 0.428442i
\(552\) 0 0
\(553\) 259.201 448.949i 0.468717 0.811842i
\(554\) 615.052 + 259.845i 1.11020 + 0.469034i
\(555\) 0 0
\(556\) −274.143 + 266.538i −0.493063 + 0.479385i
\(557\) −978.257 −1.75630 −0.878148 0.478390i \(-0.841221\pi\)
−0.878148 + 0.478390i \(0.841221\pi\)
\(558\) 0 0
\(559\) 343.997i 0.615379i
\(560\) −154.343 + 250.766i −0.275612 + 0.447796i
\(561\) 0 0
\(562\) −75.6773 31.9719i −0.134657 0.0568895i
\(563\) 925.131 + 534.125i 1.64322 + 0.948712i 0.979680 + 0.200569i \(0.0642792\pi\)
0.663538 + 0.748143i \(0.269054\pi\)
\(564\) 0 0
\(565\) −167.677 290.426i −0.296774 0.514028i
\(566\) −500.928 + 62.3680i −0.885032 + 0.110191i
\(567\) 0 0
\(568\) −469.068 + 182.799i −0.825824 + 0.321830i
\(569\) 481.775 + 834.459i 0.846705 + 1.46654i 0.884132 + 0.467237i \(0.154750\pi\)
−0.0374271 + 0.999299i \(0.511916\pi\)
\(570\) 0 0
\(571\) 243.132 + 140.372i 0.425800 + 0.245836i 0.697556 0.716531i \(-0.254271\pi\)
−0.271756 + 0.962366i \(0.587604\pi\)
\(572\) −298.224 84.4217i −0.521370 0.147590i
\(573\) 0 0
\(574\) −200.141 264.661i −0.348677 0.461083i
\(575\) 73.6944i 0.128164i
\(576\) 0 0
\(577\) −552.228 −0.957068 −0.478534 0.878069i \(-0.658832\pi\)
−0.478534 + 0.878069i \(0.658832\pi\)
\(578\) −814.676 + 616.069i −1.40947 + 1.06586i
\(579\) 0 0
\(580\) −59.1843 + 209.072i −0.102042 + 0.360469i
\(581\) 497.311 861.367i 0.855956 1.48256i
\(582\) 0 0
\(583\) −146.034 + 84.3130i −0.250488 + 0.144619i
\(584\) 96.7956 + 248.380i 0.165746 + 0.425308i
\(585\) 0 0
\(586\) −10.0528 80.7425i −0.0171550 0.137786i
\(587\) 141.476 81.6811i 0.241015 0.139150i −0.374628 0.927175i \(-0.622230\pi\)
0.615643 + 0.788025i \(0.288896\pi\)
\(588\) 0 0
\(589\) 364.260 630.917i 0.618438 1.07117i
\(590\) −15.7553 + 37.2928i −0.0267039 + 0.0632081i
\(591\) 0 0
\(592\) 57.4982 + 35.3893i 0.0971253 + 0.0597792i
\(593\) 818.460 1.38020 0.690101 0.723713i \(-0.257566\pi\)
0.690101 + 0.723713i \(0.257566\pi\)
\(594\) 0 0
\(595\) 520.433i 0.874677i
\(596\) 191.495 + 196.959i 0.321300 + 0.330468i
\(597\) 0 0
\(598\) 42.0002 99.4143i 0.0702345 0.166245i
\(599\) −398.849 230.275i −0.665857 0.384433i 0.128648 0.991690i \(-0.458936\pi\)
−0.794505 + 0.607257i \(0.792270\pi\)
\(600\) 0 0
\(601\) 162.324 + 281.153i 0.270090 + 0.467809i 0.968885 0.247513i \(-0.0796132\pi\)
−0.698795 + 0.715322i \(0.746280\pi\)
\(602\) 48.1486 + 386.721i 0.0799811 + 0.642393i
\(603\) 0 0
\(604\) −103.362 408.658i −0.171129 0.676587i
\(605\) −102.854 178.148i −0.170006 0.294459i
\(606\) 0 0
\(607\) −764.054 441.127i −1.25874 0.726733i −0.285909 0.958257i \(-0.592295\pi\)
−0.972829 + 0.231524i \(0.925629\pi\)
\(608\) −58.5409 609.598i −0.0962845 1.00263i
\(609\) 0 0
\(610\) −286.767 + 216.858i −0.470111 + 0.355504i
\(611\) 440.510i 0.720966i
\(612\) 0 0
\(613\) 19.4869 0.0317895 0.0158947 0.999874i \(-0.494940\pi\)
0.0158947 + 0.999874i \(0.494940\pi\)
\(614\) 165.063 + 218.275i 0.268832 + 0.355497i
\(615\) 0 0
\(616\) 347.079 + 53.1648i 0.563440 + 0.0863065i
\(617\) 48.3314 83.7124i 0.0783329 0.135677i −0.824198 0.566302i \(-0.808374\pi\)
0.902531 + 0.430625i \(0.141707\pi\)
\(618\) 0 0
\(619\) 363.937 210.119i 0.587944 0.339449i −0.176340 0.984329i \(-0.556426\pi\)
0.764284 + 0.644880i \(0.223093\pi\)
\(620\) 82.2126 + 325.040i 0.132601 + 0.524258i
\(621\) 0 0
\(622\) 850.820 105.931i 1.36788 0.170307i
\(623\) −777.127 + 448.674i −1.24739 + 0.720184i
\(624\) 0 0
\(625\) −142.447 + 246.725i −0.227915 + 0.394760i
\(626\) −22.0603 9.31995i −0.0352401 0.0148881i
\(627\) 0 0
\(628\) 599.512 + 616.618i 0.954638 + 0.981875i
\(629\) 119.330 0.189714
\(630\) 0 0
\(631\) 483.230i 0.765816i 0.923787 + 0.382908i \(0.125077\pi\)
−0.923787 + 0.382908i \(0.874923\pi\)
\(632\) −387.188 310.294i −0.612640 0.490971i
\(633\) 0 0
\(634\) −86.6876 36.6235i −0.136731 0.0577658i
\(635\) −281.124 162.307i −0.442715 0.255602i
\(636\) 0 0
\(637\) 153.903 + 266.568i 0.241606 + 0.418475i
\(638\) 257.120 32.0127i 0.403010 0.0501767i
\(639\) 0 0
\(640\) 214.883 + 182.366i 0.335755 + 0.284947i
\(641\) 45.2967 + 78.4562i 0.0706657 + 0.122397i 0.899193 0.437552i \(-0.144154\pi\)
−0.828528 + 0.559948i \(0.810821\pi\)
\(642\) 0 0
\(643\) −453.773 261.986i −0.705713 0.407444i 0.103759 0.994602i \(-0.466913\pi\)
−0.809472 + 0.587159i \(0.800246\pi\)
\(644\) −33.3017 + 117.640i −0.0517107 + 0.182671i
\(645\) 0 0
\(646\) −652.855 863.321i −1.01061 1.33641i
\(647\) 31.3018i 0.0483799i 0.999707 + 0.0241900i \(0.00770066\pi\)
−0.999707 + 0.0241900i \(0.992299\pi\)
\(648\) 0 0
\(649\) 48.2758 0.0743848
\(650\) 474.351 358.711i 0.729771 0.551863i
\(651\) 0 0
\(652\) −129.872 36.7645i −0.199191 0.0563872i
\(653\) −445.115 + 770.961i −0.681646 + 1.18065i 0.292833 + 0.956164i \(0.405402\pi\)
−0.974478 + 0.224481i \(0.927931\pi\)
\(654\) 0 0
\(655\) 248.565 143.509i 0.379489 0.219098i
\(656\) −279.402 + 150.999i −0.425918 + 0.230181i
\(657\) 0 0
\(658\) −61.6574 495.221i −0.0937042 0.752615i
\(659\) 41.1783 23.7743i 0.0624860 0.0360763i −0.468432 0.883500i \(-0.655181\pi\)
0.530918 + 0.847423i \(0.321847\pi\)
\(660\) 0 0
\(661\) −24.8421 + 43.0278i −0.0375826 + 0.0650950i −0.884205 0.467099i \(-0.845299\pi\)
0.846622 + 0.532194i \(0.178632\pi\)
\(662\) −65.7437 + 155.615i −0.0993108 + 0.235068i
\(663\) 0 0
\(664\) −742.872 595.339i −1.11878 0.896595i
\(665\) −352.200 −0.529624
\(666\) 0 0
\(667\) 90.2207i 0.135263i
\(668\) 435.689 423.603i 0.652229 0.634136i
\(669\) 0 0
\(670\) −13.5789 + 32.1412i −0.0202670 + 0.0479720i
\(671\) 371.287 + 214.362i 0.553333 + 0.319467i
\(672\) 0 0
\(673\) −16.4365 28.4688i −0.0244227 0.0423013i 0.853556 0.521002i \(-0.174441\pi\)
−0.877978 + 0.478700i \(0.841108\pi\)
\(674\) −124.815 1002.49i −0.185185 1.48738i
\(675\) 0 0
\(676\) −188.979 + 47.7986i −0.279555 + 0.0707079i
\(677\) −457.417 792.269i −0.675653 1.17026i −0.976278 0.216522i \(-0.930529\pi\)
0.300625 0.953742i \(-0.402805\pi\)
\(678\) 0 0
\(679\) −25.8587 14.9296i −0.0380836 0.0219876i
\(680\) 492.384 + 75.4223i 0.724094 + 0.110915i
\(681\) 0 0
\(682\) 318.888 241.147i 0.467577 0.353588i
\(683\) 870.646i 1.27474i −0.770559 0.637369i \(-0.780023\pi\)
0.770559 0.637369i \(-0.219977\pi\)
\(684\) 0 0
\(685\) 219.824 0.320910
\(686\) 283.730 + 375.198i 0.413600 + 0.546936i
\(687\) 0 0
\(688\) 372.856 + 10.4908i 0.541942 + 0.0152483i
\(689\) −236.917 + 410.352i −0.343856 + 0.595577i
\(690\) 0 0
\(691\) 800.188 461.988i 1.15801 0.668580i 0.207187 0.978301i \(-0.433569\pi\)
0.950827 + 0.309722i \(0.100236\pi\)
\(692\) 460.695 116.524i 0.665744 0.168387i
\(693\) 0 0
\(694\) −973.405 + 121.194i −1.40260 + 0.174631i
\(695\) 182.275 105.237i 0.262267 0.151420i
\(696\) 0 0
\(697\) −280.663 + 486.123i −0.402673 + 0.697450i
\(698\) −688.929 291.056i −0.987004 0.416986i
\(699\) 0 0
\(700\) −483.056 + 469.656i −0.690080 + 0.670937i
\(701\) −1191.44 −1.69963 −0.849815 0.527082i \(-0.823286\pi\)
−0.849815 + 0.527082i \(0.823286\pi\)
\(702\) 0 0
\(703\) 80.7561i 0.114874i
\(704\) 100.599 320.668i 0.142896 0.455495i
\(705\) 0 0
\(706\) 1094.44 + 462.376i 1.55020 + 0.654923i
\(707\) 109.255 + 63.0786i 0.154534 + 0.0892201i
\(708\) 0 0
\(709\) 655.954 + 1136.15i 0.925182 + 1.60246i 0.791268 + 0.611469i \(0.209421\pi\)
0.133914 + 0.990993i \(0.457246\pi\)
\(710\) 274.995 34.2383i 0.387317 0.0482229i
\(711\) 0 0
\(712\) 311.870 + 800.266i 0.438020 + 1.12397i
\(713\) 69.6056 + 120.560i 0.0976236 + 0.169089i
\(714\) 0 0
\(715\) 147.754 + 85.3059i 0.206649 + 0.119309i
\(716\) 839.759 + 237.720i 1.17285 + 0.332011i
\(717\) 0 0
\(718\) 495.674 + 655.468i 0.690354 + 0.912909i
\(719\) 245.763i 0.341813i 0.985287 + 0.170906i \(0.0546695\pi\)
−0.985287 + 0.170906i \(0.945330\pi\)
\(720\) 0 0
\(721\) −1088.78 −1.51010
\(722\) 8.37001 6.32952i 0.0115928 0.00876664i
\(723\) 0 0
\(724\) 200.556 708.473i 0.277011 0.978554i
\(725\) −248.583 + 430.559i −0.342873 + 0.593874i
\(726\) 0 0
\(727\) 1041.96 601.573i 1.43323 0.827473i 0.435860 0.900014i \(-0.356444\pi\)
0.997365 + 0.0725411i \(0.0231108\pi\)
\(728\) 919.314 358.264i 1.26279 0.492121i
\(729\) 0 0
\(730\) −18.1298 145.615i −0.0248353 0.199473i
\(731\) 570.934 329.629i 0.781032 0.450929i
\(732\) 0 0
\(733\) −510.693 + 884.546i −0.696716 + 1.20675i 0.272883 + 0.962047i \(0.412023\pi\)
−0.969599 + 0.244700i \(0.921310\pi\)
\(734\) 418.977 991.716i 0.570813 1.35111i
\(735\) 0 0
\(736\) 106.474 + 48.5556i 0.144665 + 0.0659723i
\(737\) 41.6070 0.0564546
\(738\) 0 0
\(739\) 259.300i 0.350879i 0.984490 + 0.175439i \(0.0561346\pi\)
−0.984490 + 0.175439i \(0.943865\pi\)
\(740\) −25.9076 26.6467i −0.0350102 0.0360091i
\(741\) 0 0
\(742\) 208.905 494.478i 0.281544 0.666412i
\(743\) −100.270 57.8907i −0.134953 0.0779149i 0.431004 0.902350i \(-0.358160\pi\)
−0.565956 + 0.824435i \(0.691493\pi\)
\(744\) 0 0
\(745\) −75.6076 130.956i −0.101487 0.175780i
\(746\) −37.0458 297.545i −0.0496593 0.398854i
\(747\) 0 0
\(748\) −145.652 575.859i −0.194723 0.769866i
\(749\) 214.277 + 371.139i 0.286084 + 0.495513i
\(750\) 0 0
\(751\) −543.581 313.837i −0.723809 0.417891i 0.0923438 0.995727i \(-0.470564\pi\)
−0.816153 + 0.577836i \(0.803897\pi\)
\(752\) −477.466 13.4342i −0.634928 0.0178646i
\(753\) 0 0
\(754\) 580.726 439.153i 0.770194 0.582431i
\(755\) 232.035i 0.307331i
\(756\) 0 0
\(757\) 49.5546 0.0654618 0.0327309 0.999464i \(-0.489580\pi\)
0.0327309 + 0.999464i \(0.489580\pi\)
\(758\) −222.402 294.099i −0.293406 0.387993i
\(759\) 0 0
\(760\) −51.0416 + 333.218i −0.0671601 + 0.438445i
\(761\) 13.0738 22.6446i 0.0171798 0.0297563i −0.857308 0.514804i \(-0.827865\pi\)
0.874488 + 0.485048i \(0.161198\pi\)
\(762\) 0 0
\(763\) 184.390 106.458i 0.241664 0.139525i
\(764\) 244.380 + 966.195i 0.319869 + 1.26465i
\(765\) 0 0
\(766\) 413.684 51.5057i 0.540058 0.0672398i
\(767\) 117.479 67.8267i 0.153167 0.0884312i
\(768\) 0 0
\(769\) 93.5875 162.098i 0.121700 0.210791i −0.798738 0.601679i \(-0.794499\pi\)
0.920438 + 0.390888i \(0.127832\pi\)
\(770\) −178.045 75.2199i −0.231227 0.0976881i
\(771\) 0 0
\(772\) −697.573 717.476i −0.903592 0.929373i
\(773\) 877.069 1.13463 0.567315 0.823501i \(-0.307982\pi\)
0.567315 + 0.823501i \(0.307982\pi\)
\(774\) 0 0
\(775\) 767.131i 0.989847i
\(776\) −17.8724 + 22.3015i −0.0230315 + 0.0287390i
\(777\) 0 0
\(778\) −556.066 234.925i −0.714737 0.301960i
\(779\) −328.981 189.937i −0.422312 0.243822i
\(780\) 0 0
\(781\) −165.226 286.179i −0.211557 0.366427i
\(782\) 205.245 25.5539i 0.262461 0.0326777i