Properties

Label 108.3.f.c.19.1
Level 108
Weight 3
Character 108.19
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 19.1
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 \(\chi\) \(=\) 108.19
Dual form 108.3.f.c.91.1

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 0.734679 0.678415i \(-0.237333\pi\)
−0.954864 + 0.297043i \(0.903999\pi\)
\(6\) 0 0
\(7\) −7.23844 4.17912i −1.03406 0.597017i −0.115917 0.993259i \(-0.536981\pi\)
−0.918146 + 0.396242i \(0.870314\pi\)
\(8\) 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 0.278835 0.960339i \(-0.410052\pi\)
−0.692261 + 0.721648i \(0.743385\pi\)
\(12\) 0 0
\(13\) −7.37788 12.7789i −0.567529 0.982990i −0.996809 0.0798182i \(-0.974566\pi\)
0.429280 0.903171i \(-0.358767\pi\)
\(14\) 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 \(0.167999\pi\)
−0.863925 + 0.503620i \(0.832001\pi\)
\(20\) 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 −0.429569 0.903034i \(-0.641335\pi\)
0.567266 + 0.823535i \(0.308001\pi\)
\(24\) 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 −0.571092 0.820886i \(-0.693480\pi\)
0.996454 + 0.0841375i \(0.0268135\pi\)
\(30\) 0 0
\(31\) 32.9674 19.0338i 1.06347 0.613992i 0.137077 0.990560i \(-0.456229\pi\)
0.926389 + 0.376568i \(0.122896\pi\)
\(32\) 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 0.961303 0.275492i \(-0.0888406\pi\)
−0.719235 + 0.694767i \(0.755507\pi\)
\(42\) 0 0
\(43\) −20.1894 11.6564i −0.469521 0.271078i 0.246518 0.969138i \(-0.420714\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(44\) 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 0.749155 0.662395i \(-0.230460\pi\)
−0.199073 + 0.979985i \(0.563793\pi\)
\(48\) 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 −0.565951 0.824439i \(-0.691491\pi\)
0.431009 + 0.902348i \(0.358158\pi\)
\(60\) 0 0
\(61\) −40.8215 + 70.7049i −0.669205 + 1.15910i 0.308922 + 0.951087i \(0.400032\pi\)
−0.978127 + 0.208009i \(0.933302\pi\)
\(62\) −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 −0.550333 0.834946i \(-0.685499\pi\)
0.447918 + 0.894075i \(0.352166\pi\)
\(68\) −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 \(-0.853858\pi\)
0.896443 0.443159i \(-0.146142\pi\)
\(72\) 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 0.119908 0.992785i \(-0.461740\pi\)
−0.799823 + 0.600236i \(0.795073\pi\)
\(80\) 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 −0.272212 0.962237i \(-0.587755\pi\)
−0.969428 + 0.245376i \(0.921089\pi\)
\(84\) 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 −0.856671 0.515863i \(-0.827471\pi\)
0.875086 + 0.483968i \(0.160805\pi\)
\(98\) 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 −0.900965 0.433891i \(-0.857140\pi\)
0.826244 + 0.563313i \(0.190473\pi\)
\(102\) 0 0
\(103\) 112.813 65.1324i 1.09527 0.632353i 0.160294 0.987069i \(-0.448756\pi\)
0.934974 + 0.354716i \(0.115422\pi\)
\(104\) −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 \(0.0770146\pi\)
−0.970873 + 0.239595i \(0.922985\pi\)
\(108\) 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 −0.976783 0.214229i \(-0.931276\pi\)
0.302864 0.953034i \(-0.402057\pi\)
\(114\) 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 \(-0.802886\pi\)
0.814314 0.580425i \(-0.197114\pi\)
\(128\) 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 −0.864598 0.502464i \(-0.832427\pi\)
0.00284803 + 0.999996i \(0.499093\pi\)
\(132\) 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 −0.988674 0.150079i \(-0.952047\pi\)
0.624310 + 0.781177i \(0.285380\pi\)
\(138\) 0 0
\(139\) −82.7828 + 47.7947i −0.595560 + 0.343847i −0.767293 0.641297i \(-0.778397\pi\)
0.171733 + 0.985144i \(0.445063\pi\)
\(140\) −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 0.727485 0.686123i \(-0.240689\pi\)
−0.957943 + 0.286959i \(0.907356\pi\)
\(150\) 0 0
\(151\) 91.2633 + 52.6909i 0.604393 + 0.348946i 0.770768 0.637116i \(-0.219873\pi\)
−0.166375 + 0.986063i \(0.553206\pi\)
\(152\) 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 −0.973522 0.228593i \(-0.926587\pi\)
0.288794 0.957391i \(-0.406746\pi\)
\(158\) 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 \(0.0330071\pi\)
−0.994629 + 0.103509i \(0.966993\pi\)
\(164\) −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 −0.0513797 0.998679i \(-0.516362\pi\)
0.839192 + 0.543836i \(0.183029\pi\)
\(168\) 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 −0.641699 0.766957i \(-0.721770\pi\)
0.985053 + 0.172249i \(0.0551035\pi\)
\(174\) 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 \(-0.791383\pi\)
0.792811 0.609468i \(-0.208617\pi\)
\(180\) 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 −0.185849 0.982578i \(-0.559503\pi\)
−0.943862 + 0.330339i \(0.892837\pi\)
\(192\) 0 0
\(193\) 125.086 + 216.656i 0.648115 + 1.12257i 0.983573 + 0.180513i \(0.0577758\pi\)
−0.335457 + 0.942055i \(0.608891\pi\)
\(194\) −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 \(-0.716913\pi\)
0.629921 0.776659i \(-0.283087\pi\)
\(200\) −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 −0.629140 + 0.777292i \(0.716593\pi\)
−0.987725 + 0.156205i \(0.950074\pi\)
\(212\) 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 0.686871 0.726779i \(-0.258984\pi\)
−0.285974 + 0.958238i \(0.592317\pi\)
\(224\) −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 0.744418 0.667714i \(-0.232727\pi\)
−0.206049 + 0.978542i \(0.566061\pi\)
\(228\) 0 0
\(229\) 105.572 + 182.856i 0.461012 + 0.798496i 0.999012 0.0444490i \(-0.0141532\pi\)
−0.538000 + 0.842945i \(0.680820\pi\)
\(230\) 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 0.423583 0.905857i \(-0.360772\pi\)
0.996287 + 0.0860949i \(0.0274388\pi\)
\(240\) 0 0
\(241\) −23.6786 + 41.0125i −0.0982514 + 0.170176i −0.910961 0.412493i \(-0.864658\pi\)
0.812710 + 0.582669i \(0.197992\pi\)
\(242\) −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 \(0.282618\pi\)
−0.631065 + 0.775730i \(0.717382\pi\)
\(252\) 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 0.922364 0.386321i \(-0.126254\pi\)
−0.795746 + 0.605631i \(0.792921\pi\)
\(258\) 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 0.718089 0.695951i \(-0.245017\pi\)
−0.243667 + 0.969859i \(0.578350\pi\)
\(264\) 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 \(0.0208457\pi\)
−0.997856 + 0.0654419i \(0.979154\pi\)
\(272\) 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 0.389818 + 0.920892i \(0.372538\pi\)
−0.992425 + 0.122854i \(0.960795\pi\)
\(278\) 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 −0.827164 0.561961i \(-0.810047\pi\)
0.900254 + 0.435364i \(0.143380\pi\)
\(282\) 0 0
\(283\) 218.583 126.199i 0.772378 0.445933i −0.0613442 0.998117i \(-0.519539\pi\)
0.833722 + 0.552184i \(0.186205\pi\)
\(284\) 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 0.829223 0.558917i \(-0.188783\pi\)
−0.898648 + 0.438670i \(0.855450\pi\)
\(294\) 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 \(0.0715361\pi\)
−0.974853 + 0.222850i \(0.928464\pi\)
\(308\) −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 −0.959158 0.282871i \(-0.908713\pi\)
−0.234605 + 0.972091i \(0.575380\pi\)
\(312\) 0 0
\(313\) 5.98705 10.3699i 0.0191280 0.0331306i −0.856303 0.516474i \(-0.827244\pi\)
0.875431 + 0.483343i \(0.160578\pi\)
\(314\) −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 −0.826529 0.562894i \(-0.809688\pi\)
0.900745 + 0.434348i \(0.143021\pi\)
\(318\) 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 0.606412 0.795151i \(-0.292608\pi\)
−0.385415 + 0.922743i \(0.625942\pi\)
\(332\) 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 −0.948096 0.317983i \(-0.896994\pi\)
0.198667 0.980067i \(-0.436339\pi\)
\(338\) 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 0.258284 0.966069i \(-0.416843\pi\)
0.965782 + 0.259354i \(0.0835097\pi\)
\(348\) 0 0
\(349\) 186.972 323.845i 0.535736 0.927923i −0.463391 0.886154i \(-0.653367\pi\)
0.999127 0.0417686i \(-0.0132992\pi\)
\(350\) 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 0.0472483 + 0.998883i \(0.484955\pi\)
−0.888682 + 0.458523i \(0.848379\pi\)
\(354\) 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 \(0.193939\pi\)
−0.820062 + 0.572274i \(0.806061\pi\)
\(360\) 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 −0.295203 0.955435i \(-0.595387\pi\)
−0.975032 + 0.222064i \(0.928721\pi\)
\(368\) −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 0.747873 0.663841i \(-0.231075\pi\)
−0.948840 + 0.315757i \(0.897742\pi\)
\(374\) −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 \(-0.921796\pi\)
0.969971 0.243221i \(-0.0782040\pi\)
\(380\) 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 −0.716790 0.697289i \(-0.754389\pi\)
0.245475 + 0.969403i \(0.421056\pi\)
\(384\) 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 −0.604221 0.796816i \(-0.706516\pi\)
0.992174 + 0.124863i \(0.0398491\pi\)
\(390\) 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 −0.762734 0.646713i \(-0.776143\pi\)
−0.178703 0.983903i \(-0.557190\pi\)
\(402\) 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 0.980412 0.196959i \(-0.0631067\pi\)
−0.660778 + 0.750582i \(0.729773\pi\)
\(410\) −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 −0.847665 0.530532i \(-0.821992\pi\)
0.0356217 + 0.999365i \(0.488659\pi\)
\(420\) 0 0
\(421\) 102.451 177.450i 0.243351 0.421496i −0.718316 0.695717i \(-0.755087\pi\)
0.961667 + 0.274221i \(0.0884200\pi\)
\(422\) 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 \(-0.819632\pi\)
0.843707 0.536803i \(-0.180368\pi\)
\(432\) 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 0.865337 0.501190i \(-0.167104\pi\)
−0.00137479 + 0.999999i \(0.500438\pi\)
\(440\) 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 0.984157 + 0.177297i \(0.0567354\pi\)
0.645623 + 0.763657i \(0.276598\pi\)
\(444\) 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 −0.721287 0.692636i \(-0.756449\pi\)
0.960484 + 0.278334i \(0.0897824\pi\)
\(458\) 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 −0.155722 0.987801i \(-0.549770\pi\)
0.933322 0.359042i \(-0.116896\pi\)
\(462\) 0 0
\(463\) −26.6250 + 15.3719i −0.0575053 + 0.0332007i −0.528477 0.848948i \(-0.677237\pi\)
0.470972 + 0.882148i \(0.343903\pi\)
\(464\) 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 \(0.163386\pi\)
−0.871133 + 0.491048i \(0.836614\pi\)
\(468\) 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 −0.232448 0.972609i \(-0.574674\pi\)
−0.958528 + 0.284999i \(0.908007\pi\)
\(480\) 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 \(0.262673\pi\)
−0.678402 + 0.734691i \(0.737327\pi\)
\(488\) 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 0.215866 0.976423i \(-0.430742\pi\)
0.953540 + 0.301266i \(0.0974091\pi\)
\(492\) 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 0.0358546 0.999357i \(-0.488585\pi\)
0.883396 + 0.468627i \(0.155251\pi\)
\(500\) −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 \(0.0216446\pi\)
−0.997689 + 0.0679460i \(0.978355\pi\)
\(504\) 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 0.927927 + 0.372761i \(0.121589\pi\)
−0.141143 + 0.989989i \(0.545078\pi\)
\(510\) 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 \(0.00929347\pi\)
−0.999574 + 0.0291921i \(0.990707\pi\)
\(524\) −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 −0.999983 0.00588962i \(-0.998125\pi\)
−0.505092 0.863066i \(1.33146\pi\)
\(548\) −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 0.663538 0.748143i \(-0.269054\pi\)
0.979680 0.200569i \(-0.0642792\pi\)
\(564\) 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 −0.0374271 0.999299i \(-0.511916\pi\)
0.884132 0.467237i \(-0.154750\pi\)
\(570\) 0 0
\(571\) 243.132 140.372i 0.425800 0.245836i −0.271756 0.962366i \(-0.587604\pi\)
0.697556 + 0.716531i \(0.254271\pi\)
\(572\) −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 0.615643 0.788025i \(-0.288896\pi\)
−0.374628 + 0.927175i \(0.622230\pi\)
\(588\) 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 −0.794505 0.607257i \(-0.792270\pi\)
0.128648 + 0.991690i \(0.458936\pi\)
\(600\) 0 0
\(601\) 162.324 281.153i 0.270090 0.467809i −0.698795 0.715322i \(-0.746280\pi\)
0.968885 + 0.247513i \(0.0796132\pi\)
\(602\) 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 −0.972829 0.231524i \(-0.925629\pi\)
−0.285909 + 0.958257i \(0.592295\pi\)
\(608\) −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 0.902531 0.430625i \(-0.141707\pi\)
−0.824198 + 0.566302i \(0.808374\pi\)
\(618\) 0 0
\(619\) 363.937 + 210.119i 0.587944 + 0.339449i 0.764284 0.644880i \(-0.223093\pi\)
−0.176340 + 0.984329i \(0.556426\pi\)
\(620\) 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 \(-0.874923\pi\)
0.923787 0.382908i \(-0.125077\pi\)
\(632\) −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 −0.828528 0.559948i \(-0.810821\pi\)
0.899193 + 0.437552i \(0.144154\pi\)
\(642\) 0 0
\(643\) −453.773 + 261.986i −0.705713 + 0.407444i −0.809472 0.587159i \(-0.800246\pi\)
0.103759 + 0.994602i \(0.466913\pi\)
\(644\) −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 \(-0.992299\pi\)
0.999707 0.0241900i \(-0.00770066\pi\)
\(648\) 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 −0.974478 0.224481i \(-0.927931\pi\)
0.292833 0.956164i \(-0.405402\pi\)
\(654\) 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 0.530918 0.847423i \(-0.321847\pi\)
−0.468432 + 0.883500i \(0.655181\pi\)
\(660\) 0 0
\(661\) −24.8421 43.0278i −0.0375826 0.0650950i 0.846622 0.532194i \(-0.178632\pi\)
−0.884205 + 0.467099i \(0.845299\pi\)
\(662\) −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 −0.877978 0.478700i \(-0.841108\pi\)
0.853556 + 0.521002i \(0.174441\pi\)
\(674\) −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 0.300625 + 0.953742i \(0.402805\pi\)
−0.976278 + 0.216522i \(0.930529\pi\)
\(678\) 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 \(0.219977\pi\)
−0.770559 + 0.637369i \(0.780023\pi\)
\(684\) 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 0.950827 0.309722i \(-0.100236\pi\)
0.207187 + 0.978301i \(0.433569\pi\)
\(692\) 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 0.133914 0.990993i \(-0.457246\pi\)
0.791268 0.611469i \(-0.209421\pi\)
\(710\) 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 \(-0.945330\pi\)
0.985287 0.170906i \(-0.0546695\pi\)
\(720\) 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 0.997365 0.0725411i \(-0.0231108\pi\)
0.435860 + 0.900014i \(0.356444\pi\)
\(728\) 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 −0.969599 0.244700i \(-0.921310\pi\)
0.272883 0.962047i \(-0.412023\pi\)
\(734\) 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 \(-0.943865\pi\)
0.984490 0.175439i \(-0.0561346\pi\)
\(740\) −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 −0.565956 0.824435i \(-0.691493\pi\)
0.431004 + 0.902350i \(0.358160\pi\)
\(744\) 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 −0.816153 0.577836i \(-0.803897\pi\)
0.0923438 + 0.995727i \(0.470564\pi\)
\(752\) −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 0.874488 0.485048i \(-0.161198\pi\)
−0.857308 + 0.514804i \(0.827865\pi\)
\(762\) 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 0.920438 0.390888i \(-0.127832\pi\)
−0.798738 + 0.601679i \(0.794499\pi\)
\(770\) −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