Properties

Label 108.3.f.c.91.7
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 91.7
Root \(1.84233 - 0.778342i\) 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.19.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.84233 - 0.778342i) q^{2} +(2.78837 - 2.86793i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(7.23844 - 4.17912i) q^{7} +(2.90487 - 7.45397i) q^{8} +O(q^{10})\) \(q+(1.84233 - 0.778342i) q^{2} +(2.78837 - 2.86793i) q^{4} +(-1.10093 + 1.90686i) q^{5} +(7.23844 - 4.17912i) q^{7} +(2.90487 - 7.45397i) q^{8} +(-0.544081 + 4.36996i) q^{10} +(4.54769 - 2.62561i) q^{11} +(-7.37788 + 12.7789i) q^{13} +(10.0828 - 13.3333i) q^{14} +(-0.450004 - 15.9937i) q^{16} -28.2789 q^{17} +19.1376i q^{19} +(2.39894 + 8.47440i) q^{20} +(6.33472 - 8.37689i) q^{22} +(-3.16702 - 1.82848i) q^{23} +(10.0759 + 17.4520i) q^{25} +(-3.64618 + 29.2854i) q^{26} +(8.19805 - 32.4122i) q^{28} +(12.3355 + 21.3657i) q^{29} +(-32.9674 - 19.0338i) q^{31} +(-13.2776 - 29.1154i) q^{32} +(-52.0991 + 22.0106i) q^{34} +18.4036i q^{35} -4.21977 q^{37} +(14.8956 + 35.2578i) q^{38} +(11.0156 + 13.7454i) q^{40} +(9.92483 - 17.1903i) q^{41} +(20.1894 - 11.6564i) q^{43} +(5.15057 - 20.3636i) q^{44} +(-7.25787 - 0.903640i) q^{46} +(-25.8538 + 14.9267i) q^{47} +(10.4300 - 18.0654i) q^{49} +(32.1468 + 24.3099i) q^{50} +(16.0766 + 56.7914i) q^{52} +32.1118 q^{53} +11.5624i q^{55} +(-10.1243 - 66.0950i) q^{56} +(39.3559 + 29.7615i) q^{58} +(7.96159 + 4.59663i) q^{59} +(-40.8215 - 70.7049i) q^{61} +(-75.5517 - 9.40656i) q^{62} +(-47.1234 - 43.3057i) q^{64} +(-16.2450 - 28.1372i) q^{65} +(6.86179 + 3.96166i) q^{67} +(-78.8519 + 81.1017i) q^{68} +(14.3243 + 33.9055i) q^{70} -62.9286i q^{71} +33.3218 q^{73} +(-7.77421 + 3.28442i) q^{74} +(54.8852 + 53.3626i) q^{76} +(21.9454 - 38.0106i) q^{77} +(53.7133 - 31.0114i) q^{79} +(30.9931 + 16.7497i) q^{80} +(4.90489 - 39.3951i) q^{82} +(103.056 - 59.4995i) q^{83} +(31.1329 - 53.9238i) q^{85} +(28.1230 - 37.1892i) q^{86} +(-6.36077 - 41.5254i) q^{88} +107.361 q^{89} +123.332i q^{91} +(-14.0747 + 3.98430i) q^{92} +(-36.0132 + 47.6231i) q^{94} +(-36.4927 - 21.0690i) q^{95} +(1.78621 + 3.09380i) q^{97} +(5.15457 - 41.4005i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84233 0.778342i 0.921166 0.389171i
\(3\) 0 0
\(4\) 2.78837 2.86793i 0.697092 0.716982i
\(5\) −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 0.115917 0.993259i \(-0.463019\pi\)
0.918146 + 0.396242i \(0.129686\pi\)
\(8\) 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 \(-0.589948\pi\)
0.692261 + 0.721648i \(0.256615\pi\)
\(12\) 0 0
\(13\) −7.37788 + 12.7789i −0.567529 + 0.982990i 0.429280 + 0.903171i \(0.358767\pi\)
−0.996809 + 0.0798182i \(0.974566\pi\)
\(14\) 10.0828 13.3333i 0.720202 0.952379i
\(15\) 0 0
\(16\) −0.450004 15.9937i −0.0281253 0.999604i
\(17\) −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 \(0.832001\pi\)
\(20\) 2.39894 + 8.47440i 0.119947 + 0.423720i
\(21\) 0 0
\(22\) 6.33472 8.37689i 0.287942 0.380768i
\(23\) −3.16702 1.82848i −0.137696 0.0794990i 0.429569 0.903034i \(-0.358665\pi\)
−0.567266 + 0.823535i \(0.691999\pi\)
\(24\) 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 −0.137077 0.990560i \(-0.543771\pi\)
−0.926389 + 0.376568i \(0.877104\pi\)
\(32\) −13.2776 29.1154i −0.414925 0.909856i
\(33\) 0 0
\(34\) −52.0991 + 22.0106i −1.53233 + 0.647372i
\(35\) 18.4036i 0.525817i
\(36\) 0 0
\(37\) −4.21977 −0.114048 −0.0570239 0.998373i \(-0.518161\pi\)
−0.0570239 + 0.998373i \(0.518161\pi\)
\(38\) 14.8956 + 35.2578i 0.391989 + 0.927836i
\(39\) 0 0
\(40\) 11.0156 + 13.7454i 0.275391 + 0.343636i
\(41\) 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 −0.246518 0.969138i \(-0.579286\pi\)
0.716039 + 0.698060i \(0.245953\pi\)
\(44\) 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 \(-0.769540\pi\)
0.199073 + 0.979985i \(0.436207\pi\)
\(48\) 0 0
\(49\) 10.4300 18.0654i 0.212858 0.368681i
\(50\) 32.1468 + 24.3099i 0.642937 + 0.486198i
\(51\) 0 0
\(52\) 16.0766 + 56.7914i 0.309165 + 1.09214i
\(53\) 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
\(56\) −10.1243 66.0950i −0.180791 1.18027i
\(57\) 0 0
\(58\) 39.3559 + 29.7615i 0.678550 + 0.513129i
\(59\) 7.96159 + 4.59663i 0.134942 + 0.0779089i 0.565951 0.824439i \(-0.308509\pi\)
−0.431009 + 0.902348i \(0.641842\pi\)
\(60\) 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 0.550333 0.834946i \(-0.314501\pi\)
−0.447918 + 0.894075i \(0.647834\pi\)
\(68\) −78.8519 + 81.1017i −1.15959 + 1.19267i
\(69\) 0 0
\(70\) 14.3243 + 33.9055i 0.204633 + 0.484364i
\(71\) 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 \(0.426706\pi\)
\(74\) −7.77421 + 3.28442i −0.105057 + 0.0443841i
\(75\) 0 0
\(76\) 54.8852 + 53.3626i 0.722173 + 0.702140i
\(77\) 21.9454 38.0106i 0.285006 0.493644i
\(78\) 0 0
\(79\) 53.7133 31.0114i 0.679916 0.392549i −0.119908 0.992785i \(-0.538260\pi\)
0.799823 + 0.600236i \(0.204927\pi\)
\(80\) 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 \(-0.412245\pi\)
0.969428 + 0.245376i \(0.0789114\pi\)
\(84\) 0 0
\(85\) 31.1329 53.9238i 0.366270 0.634398i
\(86\) 28.1230 37.1892i 0.327011 0.432432i
\(87\) 0 0
\(88\) −6.36077 41.5254i −0.0722815 0.471879i
\(89\) 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
\(92\) −14.0747 + 3.98430i −0.152986 + 0.0433076i
\(93\) 0 0
\(94\) −36.0132 + 47.6231i −0.383120 + 0.506629i
\(95\) −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 −0.160294 0.987069i \(-0.551244\pi\)
−0.934974 + 0.354716i \(0.884578\pi\)
\(104\) 73.8215 + 92.1155i 0.709822 + 0.885726i
\(105\) 0 0
\(106\) 59.1606 24.9940i 0.558119 0.235792i
\(107\) 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 \(0.537280\pi\)
\(110\) 8.99949 + 21.3018i 0.0818136 + 0.193652i
\(111\) 0 0
\(112\) −70.0968 113.889i −0.625864 1.01686i
\(113\) −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
\(122\) −130.239 98.4888i −1.06754 0.807285i
\(123\) 0 0
\(124\) −146.513 + 41.4751i −1.18156 + 0.334476i
\(125\) −99.4176 −0.795341
\(126\) 0 0
\(127\) 147.428i 1.16085i −0.814314 0.580425i \(-0.802886\pi\)
0.814314 0.580425i \(-0.197114\pi\)
\(128\) −120.524 43.1052i −0.941591 0.336760i
\(129\) 0 0
\(130\) −51.8290 39.1938i −0.398684 0.301491i
\(131\) 112.889 + 65.1766i 0.861750 + 0.497532i 0.864598 0.502464i \(-0.167573\pi\)
−0.00284803 + 0.999996i \(0.500907\pi\)
\(132\) 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 0.767293 0.641297i \(-0.221603\pi\)
−0.171733 + 0.985144i \(0.554937\pi\)
\(140\) 52.7801 + 51.3160i 0.377001 + 0.366543i
\(141\) 0 0
\(142\) −48.9799 115.935i −0.344929 0.816445i
\(143\) 77.4857i 0.541858i
\(144\) 0 0
\(145\) −54.3218 −0.374633
\(146\) 61.3898 25.9358i 0.420478 0.177642i
\(147\) 0 0
\(148\) −11.7663 + 12.1020i −0.0795018 + 0.0817701i
\(149\) −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 −0.770768 0.637116i \(-0.780127\pi\)
0.166375 + 0.986063i \(0.446794\pi\)
\(152\) 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 \(0.926587\pi\)
\(158\) 74.8203 98.9406i 0.473546 0.626206i
\(159\) 0 0
\(160\) 70.1366 + 6.73536i 0.438353 + 0.0420960i
\(161\) −30.5657 −0.189849
\(162\) 0 0
\(163\) 33.7439i 0.207018i 0.994629 + 0.103509i \(0.0330071\pi\)
−0.994629 + 0.103509i \(0.966993\pi\)
\(164\) −21.6265 76.3966i −0.131869 0.465833i
\(165\) 0 0
\(166\) 143.553 189.831i 0.864775 1.14356i
\(167\) −131.565 75.9589i −0.787812 0.454843i 0.0513797 0.998679i \(-0.483638\pi\)
−0.839192 + 0.543836i \(0.816971\pi\)
\(168\) 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
\(176\) −44.0396 71.5526i −0.250225 0.406549i
\(177\) 0 0
\(178\) 197.795 83.5636i 1.11121 0.469458i
\(179\) 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 \(0.330199\pi\)
\(182\) 95.9945 + 227.219i 0.527443 + 1.24845i
\(183\) 0 0
\(184\) −22.8292 + 18.2954i −0.124072 + 0.0994313i
\(185\) 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 \(-0.440497\pi\)
0.943862 + 0.330339i \(0.107163\pi\)
\(192\) 0 0
\(193\) 125.086 216.656i 0.648115 1.12257i −0.335457 0.942055i \(-0.608891\pi\)
0.983573 0.180513i \(-0.0577758\pi\)
\(194\) 5.69882 + 4.30953i 0.0293754 + 0.0222141i
\(195\) 0 0
\(196\) −22.7273 80.2855i −0.115956 0.409620i
\(197\) −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 \(-0.283087\pi\)
\(200\) 159.356 24.4098i 0.796781 0.122049i
\(201\) 0 0
\(202\) −24.0780 18.2081i −0.119198 0.0901392i
\(203\) 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 \(0.0499261\pi\)
0.629140 + 0.777292i \(0.283407\pi\)
\(212\) 89.5395 92.0943i 0.422356 0.434407i
\(213\) 0 0
\(214\) 39.9082 + 94.4624i 0.186487 + 0.441413i
\(215\) 51.3311i 0.238750i
\(216\) 0 0
\(217\) −318.177 −1.46626
\(218\) −46.9310 + 19.8272i −0.215280 + 0.0909506i
\(219\) 0 0
\(220\) 33.1601 + 32.2402i 0.150728 + 0.146546i
\(221\) 208.638 361.372i 0.944064 1.63517i
\(222\) 0 0
\(223\) −89.4002 + 51.6152i −0.400898 + 0.231458i −0.686871 0.726779i \(-0.741016\pi\)
0.285974 + 0.958238i \(0.407683\pi\)
\(224\) −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 \(-0.767273\pi\)
0.206049 + 0.978542i \(0.433939\pi\)
\(228\) 0 0
\(229\) 105.572 182.856i 0.461012 0.798496i −0.538000 0.842945i \(-0.680820\pi\)
0.999012 + 0.0444490i \(0.0141532\pi\)
\(230\) 9.71349 12.8449i 0.0422326 0.0558474i
\(231\) 0 0
\(232\) 195.092 29.8838i 0.840916 0.128810i
\(233\) 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
\(236\) 35.3826 10.0162i 0.149926 0.0424414i
\(237\) 0 0
\(238\) −285.131 + 377.051i −1.19803 + 1.58425i
\(239\) −339.349 195.923i −1.41987 0.819762i −0.423583 0.905857i \(-0.639228\pi\)
−0.996287 + 0.0860949i \(0.972561\pi\)
\(240\) 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
\(248\) −237.643 + 190.448i −0.958239 + 0.767935i
\(249\) 0 0
\(250\) −183.160 + 77.3809i −0.732641 + 0.309524i
\(251\) 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
\(254\) −114.749 271.611i −0.451769 1.06933i
\(255\) 0 0
\(256\) −255.595 + 14.3944i −0.998418 + 0.0562283i
\(257\) 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 −0.718089 0.695951i \(-0.754983\pi\)
0.243667 + 0.969859i \(0.421650\pi\)
\(264\) 0 0
\(265\) −35.3527 + 61.2327i −0.133406 + 0.231067i
\(266\) 255.167 + 192.961i 0.959275 + 0.725417i
\(267\) 0 0
\(268\) 30.4949 8.63255i 0.113787 0.0322110i
\(269\) 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 \(0.979154\pi\)
\(272\) 12.7256 + 452.283i 0.0467854 + 1.66281i
\(273\) 0 0
\(274\) −159.261 120.435i −0.581245 0.439545i
\(275\) 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 0.0613442 0.998117i \(-0.480461\pi\)
−0.833722 + 0.552184i \(0.813795\pi\)
\(284\) −180.474 175.468i −0.635474 0.617845i
\(285\) 0 0
\(286\) 60.3103 + 142.754i 0.210875 + 0.499141i
\(287\) 165.908i 0.578077i
\(288\) 0 0
\(289\) 510.695 1.76711
\(290\) −100.079 + 42.2809i −0.345099 + 0.145796i
\(291\) 0 0
\(292\) 92.9135 95.5646i 0.318197 0.327276i
\(293\) −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
\(302\) −127.126 + 168.108i −0.420946 + 0.556650i
\(303\) 0 0
\(304\) 306.080 8.61199i 1.00684 0.0283289i
\(305\) 179.766 0.589396
\(306\) 0 0
\(307\) 136.830i 0.445701i 0.974853 + 0.222850i \(0.0715361\pi\)
−0.974853 + 0.222850i \(0.928464\pi\)
\(308\) −47.8197 168.926i −0.155259 0.548460i
\(309\) 0 0
\(310\) 101.114 133.711i 0.326174 0.431324i
\(311\) 371.260 + 214.347i 1.19376 + 0.689219i 0.959158 0.282871i \(-0.0912869\pi\)
0.234605 + 0.972091i \(0.424620\pi\)
\(312\) 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
\(320\) 134.457 42.1814i 0.420179 0.131817i
\(321\) 0 0
\(322\) −56.3121 + 23.7906i −0.174882 + 0.0738837i
\(323\) 541.189i 1.67551i
\(324\) 0 0
\(325\) −297.356 −0.914941
\(326\) 26.2643 + 62.1675i 0.0805654 + 0.190698i
\(327\) 0 0
\(328\) −99.3057 123.915i −0.302761 0.377790i
\(329\) −124.761 + 216.092i −0.379213 + 0.656816i
\(330\) 0 0
\(331\) −73.1501 + 42.2332i −0.220997 + 0.127593i −0.606412 0.795151i \(-0.707392\pi\)
0.385415 + 0.922743i \(0.374058\pi\)
\(332\) 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 \(0.896994\pi\)
\(338\) −77.7396 58.7877i −0.229999 0.173928i
\(339\) 0 0
\(340\) −67.8395 239.646i −0.199528 0.704842i
\(341\) −199.901 −0.586219
\(342\) 0 0
\(343\) 235.200i 0.685714i
\(344\) −28.2386 184.352i −0.0820889 0.535906i
\(345\) 0 0
\(346\) 189.514 + 143.313i 0.547729 + 0.414200i
\(347\) −424.751 245.230i −1.22407 0.706715i −0.258284 0.966069i \(-0.583157\pi\)
−0.965782 + 0.259354i \(0.916490\pi\)
\(348\) 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
\(356\) 299.362 307.904i 0.840905 0.864898i
\(357\) 0 0
\(358\) −169.826 401.977i −0.474374 1.12284i
\(359\) 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
\(362\) 339.133 143.276i 0.936832 0.395789i
\(363\) 0 0
\(364\) 353.707 + 343.895i 0.971724 + 0.944768i
\(365\) −36.6848 + 63.5400i −0.100506 + 0.174082i
\(366\) 0 0
\(367\) 466.176 269.147i 1.27023 0.733370i 0.295203 0.955435i \(-0.404613\pi\)
0.975032 + 0.222064i \(0.0712795\pi\)
\(368\) −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 \(0.231075\pi\)
\(374\) −179.139 + 236.889i −0.478981 + 0.633393i
\(375\) 0 0
\(376\) 36.1613 + 236.074i 0.0961737 + 0.627857i
\(377\) −364.039 −0.965621
\(378\) 0 0
\(379\) 184.361i 0.486442i −0.969971 0.243221i \(-0.921796\pi\)
0.969971 0.243221i \(-0.0782040\pi\)
\(380\) −162.179 + 45.9100i −0.426788 + 0.120816i
\(381\) 0 0
\(382\) 300.565 397.460i 0.786818 1.04047i
\(383\) 180.514 + 104.220i 0.471315 + 0.272114i 0.716790 0.697289i \(-0.245611\pi\)
−0.245475 + 0.969403i \(0.578944\pi\)
\(384\) 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
\(392\) −104.361 130.223i −0.266227 0.332201i
\(393\) 0 0
\(394\) −471.036 + 199.002i −1.19552 + 0.505081i
\(395\) 136.565i 0.345734i
\(396\) 0 0
\(397\) −246.672 −0.621341 −0.310670 0.950518i \(-0.600553\pi\)
−0.310670 + 0.950518i \(0.600553\pi\)
\(398\) −240.593 569.483i −0.604506 1.43086i
\(399\) 0 0
\(400\) 274.588 169.005i 0.686469 0.422511i
\(401\) −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 \(0.0631067\pi\)
\(410\) 69.7210 + 52.7240i 0.170051 + 0.128595i
\(411\) 0 0
\(412\) −501.358 + 141.925i −1.21689 + 0.344479i
\(413\) 76.8394 0.186052
\(414\) 0 0
\(415\) 262.018i 0.631369i
\(416\) 470.022 + 45.1372i 1.12986 + 0.108503i
\(417\) 0 0
\(418\) 160.313 + 121.231i 0.383525 + 0.290027i
\(419\) 340.246 + 196.441i 0.812043 + 0.468833i 0.847665 0.530532i \(-0.178008\pi\)
−0.0356217 + 0.999365i \(0.511341\pi\)
\(420\) 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
\(428\) 147.048 + 142.969i 0.343570 + 0.334039i
\(429\) 0 0
\(430\) 39.9532 + 94.5690i 0.0929144 + 0.219928i
\(431\) 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 \(0.429374\pi\)
\(434\) −586.188 + 247.651i −1.35066 + 0.570624i
\(435\) 0 0
\(436\) −71.0300 + 73.0567i −0.162913 + 0.167561i
\(437\) 34.9926 60.6090i 0.0800747 0.138693i
\(438\) 0 0
\(439\) −379.279 + 218.977i −0.863962 + 0.498809i −0.865337 0.501190i \(-0.832896\pi\)
0.00137479 + 0.999999i \(0.499562\pi\)
\(440\) 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 \(0.723402\pi\)
−0.984157 + 0.177297i \(0.943265\pi\)
\(444\) 0 0
\(445\) −118.196 + 204.722i −0.265610 + 0.460050i
\(446\) −124.530 + 164.676i −0.279216 + 0.369229i
\(447\) 0 0
\(448\) −522.080 116.531i −1.16536 0.260114i
\(449\) 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
\(452\) 165.939 + 586.189i 0.367122 + 1.29688i
\(453\) 0 0
\(454\) −170.233 + 225.112i −0.374962 + 0.495841i
\(455\) −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 0.528477 0.848948i \(-0.322763\pi\)
−0.470972 + 0.882148i \(0.656097\pi\)
\(464\) 336.165 206.904i 0.724494 0.445915i
\(465\) 0 0
\(466\) 516.054 218.021i 1.10741 0.467856i
\(467\) 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
\(470\) −51.1626 121.102i −0.108857 0.257663i
\(471\) 0 0
\(472\) 57.3905 45.9929i 0.121590 0.0974426i
\(473\) 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 \(-0.425326\pi\)
0.958528 + 0.284999i \(0.0919932\pi\)
\(480\) 0 0
\(481\) 31.1329 53.9238i 0.0647254 0.112108i
\(482\) −75.5456 57.1286i −0.156734 0.118524i
\(483\) 0 0
\(484\) 101.787 + 359.570i 0.210305 + 0.742912i
\(485\) −7.86593 −0.0162184
\(486\) 0 0
\(487\) 715.589i 1.46938i 0.678402 + 0.734691i \(0.262673\pi\)
−0.678402 + 0.734691i \(0.737327\pi\)
\(488\) −645.614 + 98.8937i −1.32298 + 0.202651i
\(489\) 0 0
\(490\) 73.2702 + 55.4079i 0.149531 + 0.113077i
\(491\) −574.179 331.502i −1.16941 0.675157i −0.215866 0.976423i \(-0.569258\pi\)
−0.953540 + 0.301266i \(0.902591\pi\)
\(492\) 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 \(-0.511415\pi\)
−0.883396 + 0.468627i \(0.844749\pi\)
\(500\) −277.213 + 285.122i −0.554426 + 0.570245i
\(501\) 0 0
\(502\) 303.099 + 717.434i 0.603783 + 1.42915i
\(503\) 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
\(506\) −35.3791 + 14.9469i −0.0699192 + 0.0295392i
\(507\) 0 0
\(508\) −422.812 411.083i −0.832308 0.809219i
\(509\) 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
\(518\) −42.5472 + 56.2634i −0.0821374 + 0.108617i
\(519\) 0 0
\(520\) −256.923 + 39.3549i −0.494083 + 0.0756826i
\(521\) 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 \(0.990707\pi\)
\(524\) 501.699 142.022i 0.957440 0.271034i
\(525\) 0 0
\(526\) −173.803 + 229.834i −0.330425 + 0.436946i
\(527\) 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
\(536\) 49.4627 39.6395i 0.0922811 0.0739543i
\(537\) 0 0
\(538\) 133.406 56.3607i 0.247966 0.104760i
\(539\) 109.541i 0.203230i
\(540\) 0 0
\(541\) 526.091 0.972442 0.486221 0.873836i \(-0.338375\pi\)
0.486221 + 0.873836i \(0.338375\pi\)
\(542\) 27.6074 + 65.3466i 0.0509361 + 0.120566i
\(543\) 0 0
\(544\) 375.476 + 823.350i 0.690213 + 1.51351i
\(545\) 28.0446 48.5747i 0.0514580 0.0891279i
\(546\) 0 0
\(547\) 823.276 475.318i 1.50507 0.868955i 0.505092 0.863066i \(-0.331459\pi\)
0.999983 0.00588962i \(-0.00187474\pi\)
\(548\) −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
\(554\) −532.558 402.728i −0.961297 0.726946i
\(555\) 0 0
\(556\) 367.901 104.146i 0.661692 0.187313i
\(557\) −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
\(560\) 294.341 8.28169i 0.525609 0.0147887i
\(561\) 0 0
\(562\) 65.5271 + 49.5525i 0.116596 + 0.0881718i
\(563\) −925.131 534.125i −1.64322 0.948712i −0.979680 0.200569i \(-0.935721\pi\)
−0.663538 0.748143i \(1.26905\pi\)
\(564\) 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 0.271756 0.962366i \(-0.412396\pi\)
−0.697556 + 0.716531i \(0.745729\pi\)
\(572\) 222.223 + 216.059i 0.388502 + 0.377725i
\(573\) 0 0
\(574\) −129.133 305.658i −0.224971 0.532505i
\(575\) 73.6944i 0.128164i
\(576\) 0 0
\(577\) −552.228 −0.957068 −0.478534 0.878069i \(-0.658832\pi\)
−0.478534 + 0.878069i \(0.658832\pi\)
\(578\) 940.869 397.495i 1.62780 0.687708i
\(579\) 0 0
\(580\) −151.469 + 155.791i −0.261154 + 0.268605i
\(581\) 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 \(-0.711104\pi\)
0.374628 + 0.927175i \(0.377770\pi\)
\(588\) 0 0
\(589\) 364.260 630.917i 0.618438 1.07117i
\(590\) −24.4188 + 32.2909i −0.0413879 + 0.0547304i
\(591\) 0 0
\(592\) 1.89891 + 67.4895i 0.00320762 + 0.114003i
\(593\) 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
\(596\) 74.8238 + 264.319i 0.125543 + 0.443488i
\(597\) 0 0
\(598\) 65.0952 86.0804i 0.108855 0.143947i
\(599\) 398.849 + 230.275i 0.665857 + 0.384433i 0.794505 0.607257i \(-0.207730\pi\)
−0.128648 + 0.991690i \(0.541064\pi\)
\(600\) 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 0.972829 0.231524i \(-0.0743712\pi\)
0.285909 + 0.958257i \(0.407705\pi\)
\(608\) 557.198 254.101i 0.916444 0.417929i
\(609\) 0 0
\(610\) 331.188 139.919i 0.542931 0.229376i
\(611\) 440.510i 0.720966i
\(612\) 0 0
\(613\) 19.4869 0.0317895 0.0158947 0.999874i \(-0.494940\pi\)
0.0158947 + 0.999874i \(0.494940\pi\)
\(614\) 106.501 + 252.086i 0.173454 + 0.410564i
\(615\) 0 0
\(616\) −219.582 273.997i −0.356464 0.444800i
\(617\) 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 −0.764284 0.644880i \(-0.776907\pi\)
0.176340 + 0.984329i \(0.443574\pi\)
\(620\) 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
\(626\) 19.1014 + 14.4448i 0.0305135 + 0.0230747i
\(627\) 0 0
\(628\) 234.250 + 827.502i 0.373010 + 1.31768i
\(629\) 119.330 0.189714
\(630\) 0 0
\(631\) 483.230i 0.765816i −0.923787 0.382908i \(-0.874923\pi\)
0.923787 0.382908i \(-0.125077\pi\)
\(632\) −75.1279 490.462i −0.118873 0.776047i
\(633\) 0 0
\(634\) 75.0607 + 56.7619i 0.118392 + 0.0895299i
\(635\) 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 0.809472 0.587159i \(-0.199754\pi\)
−0.103759 + 0.994602i \(0.533087\pi\)
\(644\) −85.2284 + 87.6602i −0.132342 + 0.136118i
\(645\) 0 0
\(646\) −421.230 997.050i −0.652059 1.54342i
\(647\) 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
\(650\) −547.828 + 231.445i −0.842813 + 0.356069i
\(651\) 0 0
\(652\) 96.7752 + 94.0906i 0.148428 + 0.144311i
\(653\) −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 −0.530918 0.847423i \(-0.678153\pi\)
0.468432 + 0.883500i \(0.344819\pi\)
\(660\) 0 0
\(661\) −24.8421 + 43.0278i −0.0375826 + 0.0650950i −0.884205 0.467099i \(-0.845299\pi\)
0.846622 + 0.532194i \(0.178632\pi\)
\(662\) −101.895 + 134.743i −0.153920 + 0.203540i
\(663\) 0 0
\(664\) −144.143 941.016i −0.217083 1.41719i
\(665\) −352.200 −0.529624
\(666\) 0 0
\(667\) 90.2207i 0.135263i
\(668\) −584.695 + 165.516i −0.875292 + 0.247779i
\(669\) 0 0
\(670\) −21.0457 + 27.8303i −0.0314114 + 0.0415377i
\(671\) −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
\(680\) −311.510 388.706i −0.458102 0.571626i
\(681\) 0 0
\(682\) −368.283 + 155.591i −0.540005 + 0.228139i
\(683\) 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
\(686\) 183.066 + 433.316i 0.266860 + 0.631656i
\(687\) 0 0
\(688\) −195.513 317.657i −0.284176 0.461711i
\(689\) −236.917 + 410.352i −0.343856 + 0.595577i
\(690\) 0 0
\(691\) −800.188 + 461.988i −1.15801 + 0.668580i −0.950827 0.309722i \(-0.899764\pi\)
−0.207187 + 0.978301i \(0.566431\pi\)
\(692\) 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
\(698\) 596.526 + 451.102i 0.854622 + 0.646277i
\(699\) 0 0
\(700\) 648.262 183.511i 0.926089 0.262159i
\(701\) −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
\(704\) −328.006 73.2129i −0.465918 0.103996i
\(705\) 0 0
\(706\) −947.650 716.626i −1.34228 1.01505i
\(707\) −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
\(716\) −625.751 608.392i −0.873954 0.849710i
\(717\) 0 0
\(718\) 319.815 + 757.001i 0.445425 + 1.05432i
\(719\) 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
\(722\) −9.66652 + 4.08388i −0.0133885 + 0.00565634i
\(723\) 0 0
\(724\) 513.278 527.923i 0.708947 0.729175i
\(725\) −248.583 + 430.559i −0.342873 + 0.593874i
\(726\) 0 0
\(727\) −1041.96 + 601.573i −1.43323 + 0.827473i −0.997365 0.0725411i \(-0.976889\pi\)
−0.435860 + 0.900014i \(0.643556\pi\)
\(728\) 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 \(0.921310\pi\)
\(734\) 649.363 858.702i 0.884690 1.16989i
\(735\) 0 0
\(736\) −11.1865 + 116.487i −0.0151990 + 0.158270i
\(737\) 41.6070 0.0564546
\(738\) 0 0
\(739\) 259.300i 0.350879i −0.984490 0.175439i \(-0.943865\pi\)
0.984490 0.175439i \(-0.0561346\pi\)
\(740\) −10.1230 35.7600i −0.0136797 0.0483243i
\(741\) 0 0
\(742\) 323.778 428.156i 0.436358 0.577030i
\(743\) 100.270 + 57.8907i 0.134953 + 0.0779149i 0.565956 0.824435i \(-0.308507\pi\)
−0.431004 + 0.902350i \(0.641840\pi\)
\(744\) 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 \(-0.196103\pi\)
−0.0923438 + 0.995727i \(0.529436\pi\)
\(752\) 250.367 + 406.781i 0.332935 + 0.540932i
\(753\) 0 0
\(754\) −670.681 + 283.347i −0.889497 + 0.375792i
\(755\) 232.035i 0.307331i
\(756\) 0 0
\(757\) 49.5546 0.0654618 0.0327309 0.999464i \(-0.489580\pi\)
0.0327309 + 0.999464i \(0.489580\pi\)
\(758\) −143.496 339.655i −0.189309 0.448093i
\(759\) 0 0
\(760\) −263.055 + 210.812i −0.346124 + 0.277385i
\(761\) 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 \(0.127832\pi\)
\(770\) 154.165 + 116.582i 0.200214 + 0.151405i
\(771\) 0 0
\(772\) −272.566 962.854i −0.353065 1.24722i
\(773\) 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
\(776\) 28.2498 4.32725i 0.0364044 0.00557635i
\(777\) 0 0
\(778\) 481.483 + 364.105i 0.618873 + 0.468001i
\(779\) 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