Properties

Label 108.3.k.a.5.3
Level 108
Weight 3
Character 108.5
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 108.5
Dual form 108.3.k.a.65.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.727525 - 2.91045i) q^{3} +(0.0686711 + 0.188672i) q^{5} +(-1.47862 - 8.38565i) q^{7} +(-7.94141 + 4.23485i) q^{9} +O(q^{10})\) \(q+(-0.727525 - 2.91045i) q^{3} +(0.0686711 + 0.188672i) q^{5} +(-1.47862 - 8.38565i) q^{7} +(-7.94141 + 4.23485i) q^{9} +(2.58315 - 7.09715i) q^{11} +(-12.5592 - 10.5384i) q^{13} +(0.499161 - 0.337127i) q^{15} +(5.21882 + 3.01309i) q^{17} +(-0.189946 - 0.328995i) q^{19} +(-23.3303 + 10.4042i) q^{21} +(27.6819 + 4.88107i) q^{23} +(19.1202 - 16.0438i) q^{25} +(18.1029 + 20.0321i) q^{27} +(26.6332 + 31.7402i) q^{29} +(2.35612 - 13.3622i) q^{31} +(-22.5352 - 2.35477i) q^{33} +(1.48060 - 0.854825i) q^{35} +(-2.26190 + 3.91773i) q^{37} +(-21.5344 + 44.2199i) q^{39} +(-49.3383 + 58.7991i) q^{41} +(1.63966 + 0.596788i) q^{43} +(-1.34434 - 1.20751i) q^{45} +(75.3795 - 13.2914i) q^{47} +(-22.0879 + 8.03934i) q^{49} +(4.97261 - 17.3812i) q^{51} -85.8739i q^{53} +1.51642 q^{55} +(-0.819334 + 0.792179i) q^{57} +(6.23410 + 17.1281i) q^{59} +(-6.51665 - 36.9578i) q^{61} +(47.2543 + 60.3322i) q^{63} +(1.12585 - 3.09326i) q^{65} +(-53.9204 - 45.2446i) q^{67} +(-5.93319 - 84.1179i) q^{69} +(-38.9179 - 22.4692i) q^{71} +(51.2495 + 88.7667i) q^{73} +(-60.6050 - 43.9762i) q^{75} +(-63.3337 - 11.1674i) q^{77} +(64.7058 - 54.2946i) q^{79} +(45.1321 - 67.2614i) q^{81} +(-44.2042 - 52.6805i) q^{83} +(-0.210104 + 1.19156i) q^{85} +(73.0020 - 100.606i) q^{87} +(-119.245 + 68.8461i) q^{89} +(-69.8014 + 120.900i) q^{91} +(-40.6042 + 2.86398i) q^{93} +(0.0490285 - 0.0584299i) q^{95} +(112.916 + 41.0979i) q^{97} +(9.54147 + 67.3007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.727525 2.91045i −0.242508 0.970149i
\(4\) 0 0
\(5\) 0.0686711 + 0.188672i 0.0137342 + 0.0377344i 0.946370 0.323084i \(-0.104720\pi\)
−0.932636 + 0.360818i \(0.882497\pi\)
\(6\) 0 0
\(7\) −1.47862 8.38565i −0.211231 1.19795i −0.887328 0.461138i \(-0.847441\pi\)
0.676098 0.736812i \(-0.263670\pi\)
\(8\) 0 0
\(9\) −7.94141 + 4.23485i −0.882379 + 0.470539i
\(10\) 0 0
\(11\) 2.58315 7.09715i 0.234832 0.645195i −0.765167 0.643832i \(-0.777344\pi\)
0.999999 0.00136376i \(-0.000434100\pi\)
\(12\) 0 0
\(13\) −12.5592 10.5384i −0.966094 0.810649i 0.0158399 0.999875i \(-0.494958\pi\)
−0.981934 + 0.189226i \(0.939402\pi\)
\(14\) 0 0
\(15\) 0.499161 0.337127i 0.0332774 0.0224752i
\(16\) 0 0
\(17\) 5.21882 + 3.01309i 0.306990 + 0.177241i 0.645579 0.763694i \(-0.276616\pi\)
−0.338589 + 0.940934i \(0.609950\pi\)
\(18\) 0 0
\(19\) −0.189946 0.328995i −0.00999714 0.0173155i 0.860984 0.508633i \(-0.169849\pi\)
−0.870981 + 0.491317i \(0.836516\pi\)
\(20\) 0 0
\(21\) −23.3303 + 10.4042i −1.11097 + 0.495438i
\(22\) 0 0
\(23\) 27.6819 + 4.88107i 1.20356 + 0.212220i 0.739238 0.673445i \(-0.235186\pi\)
0.464324 + 0.885665i \(0.346297\pi\)
\(24\) 0 0
\(25\) 19.1202 16.0438i 0.764809 0.641751i
\(26\) 0 0
\(27\) 18.1029 + 20.0321i 0.670477 + 0.741930i
\(28\) 0 0
\(29\) 26.6332 + 31.7402i 0.918387 + 1.09449i 0.995241 + 0.0974484i \(0.0310681\pi\)
−0.0768538 + 0.997042i \(0.524487\pi\)
\(30\) 0 0
\(31\) 2.35612 13.3622i 0.0760038 0.431039i −0.922934 0.384959i \(-0.874216\pi\)
0.998938 0.0460807i \(-0.0146731\pi\)
\(32\) 0 0
\(33\) −22.5352 2.35477i −0.682885 0.0713568i
\(34\) 0 0
\(35\) 1.48060 0.854825i 0.0423029 0.0244236i
\(36\) 0 0
\(37\) −2.26190 + 3.91773i −0.0611325 + 0.105885i −0.894972 0.446122i \(-0.852805\pi\)
0.833839 + 0.552007i \(0.186138\pi\)
\(38\) 0 0
\(39\) −21.5344 + 44.2199i −0.552165 + 1.13384i
\(40\) 0 0
\(41\) −49.3383 + 58.7991i −1.20337 + 1.43412i −0.332156 + 0.943225i \(0.607776\pi\)
−0.871217 + 0.490899i \(0.836668\pi\)
\(42\) 0 0
\(43\) 1.63966 + 0.596788i 0.0381317 + 0.0138788i 0.361016 0.932560i \(-0.382430\pi\)
−0.322884 + 0.946439i \(0.604652\pi\)
\(44\) 0 0
\(45\) −1.34434 1.20751i −0.0298743 0.0268336i
\(46\) 0 0
\(47\) 75.3795 13.2914i 1.60382 0.282797i 0.701112 0.713051i \(-0.252687\pi\)
0.902708 + 0.430255i \(0.141576\pi\)
\(48\) 0 0
\(49\) −22.0879 + 8.03934i −0.450773 + 0.164068i
\(50\) 0 0
\(51\) 4.97261 17.3812i 0.0975022 0.340808i
\(52\) 0 0
\(53\) 85.8739i 1.62026i −0.586249 0.810131i \(-0.699396\pi\)
0.586249 0.810131i \(-0.300604\pi\)
\(54\) 0 0
\(55\) 1.51642 0.0275713
\(56\) 0 0
\(57\) −0.819334 + 0.792179i −0.0143743 + 0.0138979i
\(58\) 0 0
\(59\) 6.23410 + 17.1281i 0.105663 + 0.290306i 0.981246 0.192762i \(-0.0617446\pi\)
−0.875583 + 0.483068i \(0.839522\pi\)
\(60\) 0 0
\(61\) −6.51665 36.9578i −0.106830 0.605865i −0.990473 0.137704i \(-0.956028\pi\)
0.883643 0.468161i \(-0.155083\pi\)
\(62\) 0 0
\(63\) 47.2543 + 60.3322i 0.750068 + 0.957654i
\(64\) 0 0
\(65\) 1.12585 3.09326i 0.0173208 0.0475886i
\(66\) 0 0
\(67\) −53.9204 45.2446i −0.804783 0.675293i 0.144574 0.989494i \(-0.453819\pi\)
−0.949356 + 0.314201i \(0.898263\pi\)
\(68\) 0 0
\(69\) −5.93319 84.1179i −0.0859883 1.21910i
\(70\) 0 0
\(71\) −38.9179 22.4692i −0.548139 0.316468i 0.200232 0.979748i \(-0.435830\pi\)
−0.748371 + 0.663280i \(0.769164\pi\)
\(72\) 0 0
\(73\) 51.2495 + 88.7667i 0.702047 + 1.21598i 0.967747 + 0.251926i \(0.0810639\pi\)
−0.265699 + 0.964056i \(0.585603\pi\)
\(74\) 0 0
\(75\) −60.6050 43.9762i −0.808067 0.586349i
\(76\) 0 0
\(77\) −63.3337 11.1674i −0.822516 0.145032i
\(78\) 0 0
\(79\) 64.7058 54.2946i 0.819060 0.687273i −0.133692 0.991023i \(-0.542683\pi\)
0.952752 + 0.303750i \(0.0982387\pi\)
\(80\) 0 0
\(81\) 45.1321 67.2614i 0.557187 0.830387i
\(82\) 0 0
\(83\) −44.2042 52.6805i −0.532580 0.634704i 0.430927 0.902387i \(-0.358187\pi\)
−0.963507 + 0.267682i \(0.913742\pi\)
\(84\) 0 0
\(85\) −0.210104 + 1.19156i −0.00247181 + 0.0140183i
\(86\) 0 0
\(87\) 73.0020 100.606i 0.839103 1.15640i
\(88\) 0 0
\(89\) −119.245 + 68.8461i −1.33983 + 0.773551i −0.986782 0.162054i \(-0.948188\pi\)
−0.353048 + 0.935605i \(0.614855\pi\)
\(90\) 0 0
\(91\) −69.8014 + 120.900i −0.767048 + 1.32857i
\(92\) 0 0
\(93\) −40.6042 + 2.86398i −0.436604 + 0.0307955i
\(94\) 0 0
\(95\) 0.0490285 0.0584299i 0.000516090 0.000615052i
\(96\) 0 0
\(97\) 112.916 + 41.0979i 1.16408 + 0.423690i 0.850553 0.525889i \(-0.176267\pi\)
0.313526 + 0.949580i \(0.398490\pi\)
\(98\) 0 0
\(99\) 9.54147 + 67.3007i 0.0963785 + 0.679805i
\(100\) 0 0
\(101\) 13.1189 2.31321i 0.129890 0.0229031i −0.108325 0.994116i \(-0.534549\pi\)
0.238215 + 0.971212i \(0.423438\pi\)
\(102\) 0 0
\(103\) −183.161 + 66.6652i −1.77826 + 0.647235i −0.778454 + 0.627702i \(0.783996\pi\)
−0.999809 + 0.0195327i \(0.993782\pi\)
\(104\) 0 0
\(105\) −3.56510 3.68731i −0.0339533 0.0351172i
\(106\) 0 0
\(107\) 155.702i 1.45516i −0.686024 0.727579i \(-0.740645\pi\)
0.686024 0.727579i \(-0.259355\pi\)
\(108\) 0 0
\(109\) 70.1664 0.643729 0.321864 0.946786i \(-0.395691\pi\)
0.321864 + 0.946786i \(0.395691\pi\)
\(110\) 0 0
\(111\) 13.0479 + 3.73291i 0.117549 + 0.0336298i
\(112\) 0 0
\(113\) 35.8589 + 98.5216i 0.317336 + 0.871873i 0.991123 + 0.132947i \(0.0424441\pi\)
−0.673787 + 0.738925i \(0.735334\pi\)
\(114\) 0 0
\(115\) 0.980025 + 5.55800i 0.00852196 + 0.0483304i
\(116\) 0 0
\(117\) 144.367 + 30.5037i 1.23390 + 0.260716i
\(118\) 0 0
\(119\) 17.5501 48.2184i 0.147480 0.405197i
\(120\) 0 0
\(121\) 48.9945 + 41.1113i 0.404913 + 0.339763i
\(122\) 0 0
\(123\) 207.026 + 100.819i 1.68314 + 0.819664i
\(124\) 0 0
\(125\) 8.68705 + 5.01547i 0.0694964 + 0.0401238i
\(126\) 0 0
\(127\) 77.8451 + 134.832i 0.612954 + 1.06167i 0.990740 + 0.135774i \(0.0433521\pi\)
−0.377786 + 0.925893i \(0.623315\pi\)
\(128\) 0 0
\(129\) 0.544026 5.20633i 0.00421726 0.0403592i
\(130\) 0 0
\(131\) −140.642 24.7989i −1.07360 0.189305i −0.391216 0.920299i \(-0.627945\pi\)
−0.682383 + 0.730994i \(0.739057\pi\)
\(132\) 0 0
\(133\) −2.47798 + 2.07928i −0.0186315 + 0.0156336i
\(134\) 0 0
\(135\) −2.53636 + 4.79114i −0.0187878 + 0.0354899i
\(136\) 0 0
\(137\) 123.444 + 147.114i 0.901048 + 1.07383i 0.996919 + 0.0784331i \(0.0249917\pi\)
−0.0958717 + 0.995394i \(0.530564\pi\)
\(138\) 0 0
\(139\) −12.4043 + 70.3485i −0.0892398 + 0.506104i 0.907121 + 0.420870i \(0.138275\pi\)
−0.996361 + 0.0852345i \(0.972836\pi\)
\(140\) 0 0
\(141\) −93.5245 209.718i −0.663295 1.48736i
\(142\) 0 0
\(143\) −107.235 + 61.9123i −0.749897 + 0.432953i
\(144\) 0 0
\(145\) −4.15957 + 7.20458i −0.0286867 + 0.0496868i
\(146\) 0 0
\(147\) 39.4676 + 58.4369i 0.268487 + 0.397530i
\(148\) 0 0
\(149\) −64.1576 + 76.4600i −0.430588 + 0.513155i −0.937092 0.349083i \(-0.886493\pi\)
0.506504 + 0.862238i \(0.330938\pi\)
\(150\) 0 0
\(151\) −91.0224 33.1295i −0.602797 0.219400i 0.0225513 0.999746i \(-0.492821\pi\)
−0.625349 + 0.780345i \(0.715043\pi\)
\(152\) 0 0
\(153\) −54.2048 1.82727i −0.354280 0.0119429i
\(154\) 0 0
\(155\) 2.68288 0.473063i 0.0173089 0.00305202i
\(156\) 0 0
\(157\) 225.856 82.2049i 1.43857 0.523598i 0.499198 0.866488i \(-0.333628\pi\)
0.939376 + 0.342890i \(0.111406\pi\)
\(158\) 0 0
\(159\) −249.931 + 62.4754i −1.57190 + 0.392927i
\(160\) 0 0
\(161\) 239.348i 1.48663i
\(162\) 0 0
\(163\) −58.5417 −0.359152 −0.179576 0.983744i \(-0.557473\pi\)
−0.179576 + 0.983744i \(0.557473\pi\)
\(164\) 0 0
\(165\) −1.10324 4.41347i −0.00668628 0.0267483i
\(166\) 0 0
\(167\) 22.4027 + 61.5510i 0.134148 + 0.368569i 0.988519 0.151094i \(-0.0482797\pi\)
−0.854371 + 0.519663i \(0.826057\pi\)
\(168\) 0 0
\(169\) 17.3288 + 98.2765i 0.102537 + 0.581518i
\(170\) 0 0
\(171\) 2.90168 + 1.80830i 0.0169689 + 0.0105748i
\(172\) 0 0
\(173\) 25.8686 71.0734i 0.149530 0.410829i −0.842201 0.539163i \(-0.818741\pi\)
0.991731 + 0.128334i \(0.0409629\pi\)
\(174\) 0 0
\(175\) −162.809 136.613i −0.930337 0.780646i
\(176\) 0 0
\(177\) 45.3148 30.6051i 0.256016 0.172910i
\(178\) 0 0
\(179\) 259.614 + 149.888i 1.45035 + 0.837363i 0.998501 0.0547292i \(-0.0174296\pi\)
0.451854 + 0.892092i \(0.350763\pi\)
\(180\) 0 0
\(181\) −148.560 257.314i −0.820774 1.42162i −0.905107 0.425184i \(-0.860209\pi\)
0.0843330 0.996438i \(-0.473124\pi\)
\(182\) 0 0
\(183\) −102.823 + 45.8541i −0.561872 + 0.250569i
\(184\) 0 0
\(185\) −0.894495 0.157724i −0.00483511 0.000852560i
\(186\) 0 0
\(187\) 34.8654 29.2555i 0.186446 0.156447i
\(188\) 0 0
\(189\) 141.215 181.424i 0.747170 0.959917i
\(190\) 0 0
\(191\) −52.6139 62.7028i −0.275466 0.328287i 0.610519 0.792001i \(-0.290961\pi\)
−0.885985 + 0.463714i \(0.846516\pi\)
\(192\) 0 0
\(193\) 20.4421 115.933i 0.105918 0.600688i −0.884932 0.465720i \(-0.845796\pi\)
0.990850 0.134968i \(-0.0430933\pi\)
\(194\) 0 0
\(195\) −9.82186 1.02632i −0.0503685 0.00526317i
\(196\) 0 0
\(197\) −69.8603 + 40.3339i −0.354621 + 0.204740i −0.666719 0.745310i \(-0.732302\pi\)
0.312098 + 0.950050i \(0.398968\pi\)
\(198\) 0 0
\(199\) 87.9561 152.345i 0.441991 0.765550i −0.555846 0.831285i \(-0.687606\pi\)
0.997837 + 0.0657347i \(0.0209391\pi\)
\(200\) 0 0
\(201\) −92.4536 + 189.849i −0.459968 + 0.944524i
\(202\) 0 0
\(203\) 226.782 270.268i 1.11715 1.33137i
\(204\) 0 0
\(205\) −14.4819 5.27097i −0.0706432 0.0257120i
\(206\) 0 0
\(207\) −240.504 + 78.4661i −1.16186 + 0.379063i
\(208\) 0 0
\(209\) −2.82559 + 0.498227i −0.0135196 + 0.00238386i
\(210\) 0 0
\(211\) −34.0107 + 12.3789i −0.161188 + 0.0586678i −0.421354 0.906896i \(-0.638445\pi\)
0.260166 + 0.965564i \(0.416223\pi\)
\(212\) 0 0
\(213\) −37.0818 + 129.615i −0.174093 + 0.608523i
\(214\) 0 0
\(215\) 0.350341i 0.00162949i
\(216\) 0 0
\(217\) −115.535 −0.532418
\(218\) 0 0
\(219\) 221.065 213.739i 1.00943 0.975976i
\(220\) 0 0
\(221\) −33.7911 92.8403i −0.152901 0.420092i
\(222\) 0 0
\(223\) −70.0960 397.534i −0.314332 1.78266i −0.575942 0.817490i \(-0.695365\pi\)
0.261611 0.965174i \(-0.415746\pi\)
\(224\) 0 0
\(225\) −83.8987 + 208.382i −0.372883 + 0.926140i
\(226\) 0 0
\(227\) −59.9958 + 164.837i −0.264299 + 0.726155i 0.734567 + 0.678536i \(0.237385\pi\)
−0.998866 + 0.0476187i \(0.984837\pi\)
\(228\) 0 0
\(229\) 102.807 + 86.2654i 0.448939 + 0.376705i 0.839042 0.544066i \(-0.183116\pi\)
−0.390103 + 0.920771i \(0.627561\pi\)
\(230\) 0 0
\(231\) 13.5746 + 192.454i 0.0587645 + 0.833135i
\(232\) 0 0
\(233\) 342.572 + 197.784i 1.47027 + 0.848858i 0.999443 0.0333693i \(-0.0106237\pi\)
0.470823 + 0.882228i \(0.343957\pi\)
\(234\) 0 0
\(235\) 7.68412 + 13.3093i 0.0326984 + 0.0566352i
\(236\) 0 0
\(237\) −205.097 148.822i −0.865386 0.627941i
\(238\) 0 0
\(239\) 442.556 + 78.0346i 1.85170 + 0.326504i 0.985030 0.172380i \(-0.0551458\pi\)
0.866668 + 0.498885i \(0.166257\pi\)
\(240\) 0 0
\(241\) −174.607 + 146.513i −0.724511 + 0.607937i −0.928629 0.371009i \(-0.879012\pi\)
0.204118 + 0.978946i \(0.434567\pi\)
\(242\) 0 0
\(243\) −228.595 82.4204i −0.940722 0.339179i
\(244\) 0 0
\(245\) −3.03360 3.61530i −0.0123820 0.0147563i
\(246\) 0 0
\(247\) −1.08153 + 6.13365i −0.00437866 + 0.0248326i
\(248\) 0 0
\(249\) −121.164 + 166.980i −0.486603 + 0.670603i
\(250\) 0 0
\(251\) −307.522 + 177.548i −1.22519 + 0.707362i −0.966019 0.258471i \(-0.916781\pi\)
−0.259167 + 0.965832i \(0.583448\pi\)
\(252\) 0 0
\(253\) 106.148 183.854i 0.419558 0.726697i
\(254\) 0 0
\(255\) 3.62083 0.255392i 0.0141993 0.00100154i
\(256\) 0 0
\(257\) −122.816 + 146.366i −0.477883 + 0.569519i −0.950093 0.311968i \(-0.899012\pi\)
0.472210 + 0.881486i \(0.343456\pi\)
\(258\) 0 0
\(259\) 36.1972 + 13.1747i 0.139758 + 0.0508676i
\(260\) 0 0
\(261\) −345.920 139.275i −1.32537 0.533620i
\(262\) 0 0
\(263\) −59.8335 + 10.5503i −0.227504 + 0.0401150i −0.286238 0.958159i \(-0.592405\pi\)
0.0587341 + 0.998274i \(0.481294\pi\)
\(264\) 0 0
\(265\) 16.2020 5.89705i 0.0611397 0.0222530i
\(266\) 0 0
\(267\) 287.127 + 296.969i 1.07538 + 1.11224i
\(268\) 0 0
\(269\) 1.02338i 0.00380438i −0.999998 0.00190219i \(-0.999395\pi\)
0.999998 0.00190219i \(-0.000605486\pi\)
\(270\) 0 0
\(271\) 264.552 0.976205 0.488102 0.872786i \(-0.337689\pi\)
0.488102 + 0.872786i \(0.337689\pi\)
\(272\) 0 0
\(273\) 402.654 + 115.196i 1.47492 + 0.421963i
\(274\) 0 0
\(275\) −64.4747 177.143i −0.234453 0.644155i
\(276\) 0 0
\(277\) 63.0965 + 357.838i 0.227785 + 1.29183i 0.857288 + 0.514837i \(0.172147\pi\)
−0.629503 + 0.776998i \(0.716742\pi\)
\(278\) 0 0
\(279\) 37.8760 + 116.093i 0.135756 + 0.416103i
\(280\) 0 0
\(281\) −64.8213 + 178.095i −0.230681 + 0.633790i −0.999987 0.00509010i \(-0.998380\pi\)
0.769306 + 0.638880i \(0.220602\pi\)
\(282\) 0 0
\(283\) 219.711 + 184.359i 0.776364 + 0.651447i 0.942330 0.334685i \(-0.108630\pi\)
−0.165966 + 0.986131i \(0.553074\pi\)
\(284\) 0 0
\(285\) −0.205727 0.100186i −0.000721848 0.000351529i
\(286\) 0 0
\(287\) 566.021 + 326.792i 1.97220 + 1.13865i
\(288\) 0 0
\(289\) −126.343 218.832i −0.437172 0.757203i
\(290\) 0 0
\(291\) 37.4644 358.535i 0.128744 1.23208i
\(292\) 0 0
\(293\) 197.305 + 34.7903i 0.673397 + 0.118738i 0.499883 0.866093i \(-0.333376\pi\)
0.173515 + 0.984831i \(0.444488\pi\)
\(294\) 0 0
\(295\) −2.80348 + 2.35240i −0.00950334 + 0.00797425i
\(296\) 0 0
\(297\) 188.933 76.7329i 0.636139 0.258360i
\(298\) 0 0
\(299\) −296.225 353.027i −0.990717 1.18069i
\(300\) 0 0
\(301\) 2.58003 14.6321i 0.00857152 0.0486115i
\(302\) 0 0
\(303\) −16.2768 36.4989i −0.0537189 0.120459i
\(304\) 0 0
\(305\) 6.52540 3.76744i 0.0213948 0.0123523i
\(306\) 0 0
\(307\) −87.7799 + 152.039i −0.285928 + 0.495242i −0.972834 0.231505i \(-0.925635\pi\)
0.686906 + 0.726746i \(0.258968\pi\)
\(308\) 0 0
\(309\) 327.280 + 484.580i 1.05916 + 1.56822i
\(310\) 0 0
\(311\) 92.2362 109.923i 0.296579 0.353450i −0.597091 0.802174i \(-0.703677\pi\)
0.893670 + 0.448724i \(0.148121\pi\)
\(312\) 0 0
\(313\) −469.902 171.030i −1.50128 0.546422i −0.544891 0.838507i \(-0.683429\pi\)
−0.956392 + 0.292085i \(0.905651\pi\)
\(314\) 0 0
\(315\) −8.13801 + 13.0586i −0.0258350 + 0.0414560i
\(316\) 0 0
\(317\) −159.214 + 28.0736i −0.502251 + 0.0885604i −0.419033 0.907971i \(-0.637631\pi\)
−0.0832179 + 0.996531i \(0.526520\pi\)
\(318\) 0 0
\(319\) 294.063 107.030i 0.921827 0.335518i
\(320\) 0 0
\(321\) −453.162 + 113.277i −1.41172 + 0.352888i
\(322\) 0 0
\(323\) 2.28929i 0.00708759i
\(324\) 0 0
\(325\) −409.211 −1.25911
\(326\) 0 0
\(327\) −51.0478 204.216i −0.156110 0.624513i
\(328\) 0 0
\(329\) −222.915 612.453i −0.677553 1.86156i
\(330\) 0 0
\(331\) 79.9019 + 453.146i 0.241396 + 1.36902i 0.828717 + 0.559668i \(0.189072\pi\)
−0.587321 + 0.809354i \(0.699817\pi\)
\(332\) 0 0
\(333\) 1.37172 40.6912i 0.00411927 0.122196i
\(334\) 0 0
\(335\) 4.83363 13.2803i 0.0144287 0.0396426i
\(336\) 0 0
\(337\) 262.855 + 220.561i 0.779984 + 0.654484i 0.943245 0.332099i \(-0.107757\pi\)
−0.163261 + 0.986583i \(0.552201\pi\)
\(338\) 0 0
\(339\) 260.654 176.042i 0.768890 0.519299i
\(340\) 0 0
\(341\) −88.7474 51.2384i −0.260256 0.150259i
\(342\) 0 0
\(343\) −108.543 188.002i −0.316453 0.548112i
\(344\) 0 0
\(345\) 15.4633 6.89589i 0.0448211 0.0199881i
\(346\) 0 0
\(347\) −270.540 47.7035i −0.779653 0.137474i −0.230362 0.973105i \(-0.573991\pi\)
−0.549291 + 0.835631i \(0.685102\pi\)
\(348\) 0 0
\(349\) −377.022 + 316.359i −1.08029 + 0.906473i −0.995945 0.0899629i \(-0.971325\pi\)
−0.0843479 + 0.996436i \(0.526881\pi\)
\(350\) 0 0
\(351\) −16.2509 442.364i −0.0462987 1.26030i
\(352\) 0 0
\(353\) 71.2407 + 84.9014i 0.201815 + 0.240514i 0.857454 0.514561i \(-0.172045\pi\)
−0.655639 + 0.755075i \(0.727601\pi\)
\(354\) 0 0
\(355\) 1.56679 8.88570i 0.00441349 0.0250302i
\(356\) 0 0
\(357\) −153.105 15.9985i −0.428867 0.0448136i
\(358\) 0 0
\(359\) −480.926 + 277.663i −1.33963 + 0.773433i −0.986752 0.162237i \(-0.948129\pi\)
−0.352874 + 0.935671i \(0.614796\pi\)
\(360\) 0 0
\(361\) 180.428 312.510i 0.499800 0.865679i
\(362\) 0 0
\(363\) 84.0075 172.505i 0.231426 0.475222i
\(364\) 0 0
\(365\) −13.2284 + 15.7650i −0.0362423 + 0.0431919i
\(366\) 0 0
\(367\) 374.715 + 136.385i 1.02102 + 0.371622i 0.797656 0.603113i \(-0.206073\pi\)
0.223367 + 0.974734i \(0.428295\pi\)
\(368\) 0 0
\(369\) 142.811 675.888i 0.387021 1.83167i
\(370\) 0 0
\(371\) −720.108 + 126.975i −1.94099 + 0.342249i
\(372\) 0 0
\(373\) 189.416 68.9418i 0.507818 0.184830i −0.0753893 0.997154i \(-0.524020\pi\)
0.583207 + 0.812324i \(0.301798\pi\)
\(374\) 0 0
\(375\) 8.27722 28.9321i 0.0220726 0.0771523i
\(376\) 0 0
\(377\) 679.305i 1.80187i
\(378\) 0 0
\(379\) 135.501 0.357522 0.178761 0.983892i \(-0.442791\pi\)
0.178761 + 0.983892i \(0.442791\pi\)
\(380\) 0 0
\(381\) 335.786 324.658i 0.881329 0.852120i
\(382\) 0 0
\(383\) 82.3154 + 226.160i 0.214923 + 0.590495i 0.999566 0.0294519i \(-0.00937620\pi\)
−0.784643 + 0.619947i \(0.787154\pi\)
\(384\) 0 0
\(385\) −2.24221 12.7162i −0.00582392 0.0330291i
\(386\) 0 0
\(387\) −15.5486 + 2.20438i −0.0401771 + 0.00569606i
\(388\) 0 0
\(389\) 34.2832 94.1925i 0.0881317 0.242140i −0.887795 0.460240i \(-0.847764\pi\)
0.975927 + 0.218100i \(0.0699857\pi\)
\(390\) 0 0
\(391\) 129.760 + 108.882i 0.331867 + 0.278469i
\(392\) 0 0
\(393\) 30.1443 + 427.372i 0.0767031 + 1.08746i
\(394\) 0 0
\(395\) 14.6873 + 8.47971i 0.0371830 + 0.0214676i
\(396\) 0 0
\(397\) −31.5616 54.6663i −0.0795003 0.137699i 0.823534 0.567267i \(-0.191999\pi\)
−0.903034 + 0.429568i \(0.858666\pi\)
\(398\) 0 0
\(399\) 7.85442 + 5.69932i 0.0196853 + 0.0142840i
\(400\) 0 0
\(401\) −382.225 67.3965i −0.953178 0.168071i −0.324630 0.945841i \(-0.605240\pi\)
−0.628549 + 0.777770i \(0.716351\pi\)
\(402\) 0 0
\(403\) −170.408 + 142.989i −0.422848 + 0.354812i
\(404\) 0 0
\(405\) 15.7896 + 3.89627i 0.0389867 + 0.00962042i
\(406\) 0 0
\(407\) 21.9619 + 26.1732i 0.0539604 + 0.0643075i
\(408\) 0 0
\(409\) −90.7835 + 514.859i −0.221965 + 1.25882i 0.646439 + 0.762966i \(0.276258\pi\)
−0.868404 + 0.495858i \(0.834854\pi\)
\(410\) 0 0
\(411\) 338.360 466.305i 0.823261 1.13456i
\(412\) 0 0
\(413\) 134.412 77.6028i 0.325453 0.187900i
\(414\) 0 0
\(415\) 6.90379 11.9577i 0.0166356 0.0288138i
\(416\) 0 0
\(417\) 213.770 15.0781i 0.512638 0.0361585i
\(418\) 0 0
\(419\) 324.985 387.301i 0.775619 0.924347i −0.223107 0.974794i \(-0.571620\pi\)
0.998727 + 0.0504466i \(0.0160645\pi\)
\(420\) 0 0
\(421\) −61.4522 22.3668i −0.145967 0.0531277i 0.268003 0.963418i \(-0.413636\pi\)
−0.413971 + 0.910290i \(0.635858\pi\)
\(422\) 0 0
\(423\) −542.333 + 424.774i −1.28211 + 1.00419i
\(424\) 0 0
\(425\) 148.126 26.1187i 0.348533 0.0614557i
\(426\) 0 0
\(427\) −300.279 + 109.293i −0.703230 + 0.255955i
\(428\) 0 0
\(429\) 258.209 + 267.060i 0.601885 + 0.622517i
\(430\) 0 0
\(431\) 449.973i 1.04402i 0.852939 + 0.522010i \(0.174818\pi\)
−0.852939 + 0.522010i \(0.825182\pi\)
\(432\) 0 0
\(433\) 57.6415 0.133121 0.0665606 0.997782i \(-0.478797\pi\)
0.0665606 + 0.997782i \(0.478797\pi\)
\(434\) 0 0
\(435\) 23.9948 + 6.86469i 0.0551604 + 0.0157809i
\(436\) 0 0
\(437\) −3.65221 10.0344i −0.00835746 0.0229619i
\(438\) 0 0
\(439\) −40.0913 227.369i −0.0913241 0.517925i −0.995812 0.0914252i \(-0.970858\pi\)
0.904488 0.426499i \(-0.140253\pi\)
\(440\) 0 0
\(441\) 141.364 157.383i 0.320553 0.356877i
\(442\) 0 0
\(443\) 97.4032 267.613i 0.219872 0.604093i −0.779890 0.625917i \(-0.784725\pi\)
0.999762 + 0.0218237i \(0.00694726\pi\)
\(444\) 0 0
\(445\) −21.1780 17.7705i −0.0475910 0.0399336i
\(446\) 0 0
\(447\) 269.209 + 131.101i 0.602258 + 0.293290i
\(448\) 0 0
\(449\) 249.959 + 144.314i 0.556701 + 0.321412i 0.751821 0.659368i \(-0.229176\pi\)
−0.195119 + 0.980780i \(0.562509\pi\)
\(450\) 0 0
\(451\) 289.858 + 502.048i 0.642700 + 1.11319i
\(452\) 0 0
\(453\) −30.2005 + 289.019i −0.0666677 + 0.638010i
\(454\) 0 0
\(455\) −27.6037 4.86728i −0.0606675 0.0106973i
\(456\) 0 0
\(457\) 57.0131 47.8396i 0.124755 0.104682i −0.578276 0.815842i \(-0.696274\pi\)
0.703031 + 0.711160i \(0.251830\pi\)
\(458\) 0 0
\(459\) 34.1172 + 159.090i 0.0743294 + 0.346601i
\(460\) 0 0
\(461\) −81.2197 96.7939i −0.176182 0.209965i 0.670726 0.741705i \(-0.265983\pi\)
−0.846907 + 0.531740i \(0.821538\pi\)
\(462\) 0 0
\(463\) 7.85137 44.5273i 0.0169576 0.0961713i −0.975154 0.221527i \(-0.928896\pi\)
0.992112 + 0.125355i \(0.0400071\pi\)
\(464\) 0 0
\(465\) −3.32869 7.46421i −0.00715846 0.0160521i
\(466\) 0 0
\(467\) −395.495 + 228.339i −0.846884 + 0.488949i −0.859598 0.510970i \(-0.829286\pi\)
0.0127140 + 0.999919i \(0.495953\pi\)
\(468\) 0 0
\(469\) −299.678 + 519.057i −0.638972 + 1.10673i
\(470\) 0 0
\(471\) −403.569 597.536i −0.856835 1.26865i
\(472\) 0 0
\(473\) 8.47099 10.0953i 0.0179091 0.0213432i
\(474\) 0 0
\(475\) −8.91013 3.24302i −0.0187582 0.00682742i
\(476\) 0 0
\(477\) 363.663 + 681.960i 0.762396 + 1.42969i
\(478\) 0 0
\(479\) −370.216 + 65.2790i −0.772893 + 0.136282i −0.546166 0.837677i \(-0.683913\pi\)
−0.226726 + 0.973959i \(0.572802\pi\)
\(480\) 0 0
\(481\) 69.6945 25.3667i 0.144895 0.0527375i
\(482\) 0 0
\(483\) −696.610 + 174.132i −1.44226 + 0.360521i
\(484\) 0 0
\(485\) 24.1263i 0.0497449i
\(486\) 0 0
\(487\) 51.3988 0.105542 0.0527708 0.998607i \(-0.483195\pi\)
0.0527708 + 0.998607i \(0.483195\pi\)
\(488\) 0 0
\(489\) 42.5906 + 170.383i 0.0870973 + 0.348431i
\(490\) 0 0
\(491\) 254.558 + 699.393i 0.518449 + 1.42443i 0.872229 + 0.489098i \(0.162674\pi\)
−0.353780 + 0.935329i \(0.615104\pi\)
\(492\) 0 0
\(493\) 43.3579 + 245.895i 0.0879471 + 0.498773i
\(494\) 0 0
\(495\) −12.0425 + 6.42182i −0.0243284 + 0.0129734i
\(496\) 0 0
\(497\) −130.875 + 359.575i −0.263329 + 0.723491i
\(498\) 0 0
\(499\) −292.343 245.305i −0.585858 0.491593i 0.301007 0.953622i \(-0.402677\pi\)
−0.886865 + 0.462029i \(0.847122\pi\)
\(500\) 0 0
\(501\) 162.842 109.982i 0.325035 0.219525i
\(502\) 0 0
\(503\) 169.431 + 97.8211i 0.336841 + 0.194475i 0.658874 0.752253i \(-0.271033\pi\)
−0.322033 + 0.946728i \(0.604366\pi\)
\(504\) 0 0
\(505\) 1.33733 + 2.31632i 0.00264817 + 0.00458677i
\(506\) 0 0
\(507\) 273.422 121.933i 0.539293 0.240499i
\(508\) 0 0
\(509\) 429.935 + 75.8091i 0.844666 + 0.148937i 0.579203 0.815184i \(-0.303364\pi\)
0.265463 + 0.964121i \(0.414475\pi\)
\(510\) 0 0
\(511\) 668.588 561.012i 1.30839 1.09787i
\(512\) 0 0
\(513\) 3.15191 9.76078i 0.00614408 0.0190269i
\(514\) 0 0
\(515\) −25.1557 29.9794i −0.0488461 0.0582125i
\(516\) 0 0
\(517\) 100.385 569.314i 0.194169 1.10119i
\(518\) 0 0
\(519\) −225.676 23.5816i −0.434828 0.0454365i
\(520\) 0 0
\(521\) 253.777 146.518i 0.487097 0.281226i −0.236272 0.971687i \(-0.575926\pi\)
0.723369 + 0.690461i \(0.242592\pi\)
\(522\) 0 0
\(523\) 166.756 288.830i 0.318845 0.552256i −0.661402 0.750032i \(-0.730038\pi\)
0.980247 + 0.197775i \(0.0633716\pi\)
\(524\) 0 0
\(525\) −279.157 + 573.236i −0.531728 + 1.09188i
\(526\) 0 0
\(527\) 52.5577 62.6358i 0.0997300 0.118854i
\(528\) 0 0
\(529\) 245.367 + 89.3062i 0.463831 + 0.168821i
\(530\) 0 0
\(531\) −122.042 109.620i −0.229835 0.206442i
\(532\) 0 0
\(533\) 1239.30 218.522i 2.32514 0.409985i
\(534\) 0 0
\(535\) 29.3766 10.6922i 0.0549096 0.0199855i
\(536\) 0 0
\(537\) 247.366 864.639i 0.460644 1.61013i
\(538\) 0 0
\(539\) 177.528i 0.329365i
\(540\) 0 0
\(541\) −51.1409 −0.0945304 −0.0472652 0.998882i \(-0.515051\pi\)
−0.0472652 + 0.998882i \(0.515051\pi\)
\(542\) 0 0
\(543\) −640.817 + 619.578i −1.18014 + 1.14103i
\(544\) 0 0
\(545\) 4.81840 + 13.2385i 0.00884110 + 0.0242907i
\(546\) 0 0
\(547\) −78.2579 443.823i −0.143068 0.811376i −0.968898 0.247459i \(-0.920405\pi\)
0.825831 0.563918i \(-0.190707\pi\)
\(548\) 0 0
\(549\) 208.262 + 265.900i 0.379348 + 0.484335i
\(550\) 0 0
\(551\) 5.38353 14.7911i 0.00977047 0.0268441i
\(552\) 0 0
\(553\) −550.970 462.319i −0.996330 0.836020i
\(554\) 0 0
\(555\) 0.191721 + 2.71813i 0.000345443 + 0.00489753i
\(556\) 0 0
\(557\) −255.303 147.399i −0.458354 0.264631i 0.252998 0.967467i \(-0.418583\pi\)
−0.711352 + 0.702836i \(0.751917\pi\)
\(558\) 0 0
\(559\) −14.3037 24.7747i −0.0255880 0.0443196i
\(560\) 0 0
\(561\) −110.512 80.1897i −0.196991 0.142941i
\(562\) 0 0
\(563\) −570.607 100.613i −1.01351 0.178709i −0.357861 0.933775i \(-0.616494\pi\)
−0.655650 + 0.755065i \(0.727605\pi\)
\(564\) 0 0
\(565\) −16.1258 + 13.5312i −0.0285413 + 0.0239490i
\(566\) 0 0
\(567\) −630.763 279.009i −1.11246 0.492079i
\(568\) 0 0
\(569\) 134.264 + 160.010i 0.235965 + 0.281212i 0.871012 0.491261i \(-0.163464\pi\)
−0.635047 + 0.772473i \(0.719019\pi\)
\(570\) 0 0
\(571\) −83.0575 + 471.043i −0.145460 + 0.824943i 0.821537 + 0.570155i \(0.193117\pi\)
−0.966997 + 0.254788i \(0.917994\pi\)
\(572\) 0 0
\(573\) −144.215 + 198.748i −0.251685 + 0.346855i
\(574\) 0 0
\(575\) 607.596 350.795i 1.05669 0.610079i
\(576\) 0 0
\(577\) 94.3702 163.454i 0.163553 0.283282i −0.772587 0.634908i \(-0.781038\pi\)
0.936141 + 0.351626i \(0.114371\pi\)
\(578\) 0 0
\(579\) −352.288 + 24.8484i −0.608443 + 0.0429161i
\(580\) 0 0
\(581\) −376.399 + 448.575i −0.647847 + 0.772074i
\(582\) 0 0
\(583\) −609.460 221.825i −1.04539 0.380489i
\(584\) 0 0
\(585\) 4.15861 + 29.3327i 0.00710873 + 0.0501414i
\(586\) 0 0
\(587\) 563.429 99.3478i 0.959846 0.169247i 0.328290 0.944577i \(-0.393528\pi\)
0.631556 + 0.775330i \(0.282417\pi\)
\(588\) 0 0
\(589\) −4.84364 + 1.76294i −0.00822350 + 0.00299311i
\(590\) 0 0
\(591\) 168.215 + 173.981i 0.284627 + 0.294384i
\(592\) 0 0
\(593\) 1075.40i 1.81349i −0.421682 0.906744i \(-0.638560\pi\)
0.421682 0.906744i \(-0.361440\pi\)
\(594\) 0 0
\(595\) 10.3027 0.0173154
\(596\) 0 0
\(597\) −507.381 145.157i −0.849885 0.243145i
\(598\) 0 0
\(599\) 145.620 + 400.088i 0.243106 + 0.667927i 0.999898 + 0.0142721i \(0.00454310\pi\)
−0.756793 + 0.653655i \(0.773235\pi\)
\(600\) 0 0
\(601\) −128.421 728.311i −0.213679 1.21183i −0.883185 0.469026i \(-0.844605\pi\)
0.669506 0.742807i \(-0.266506\pi\)
\(602\) 0 0
\(603\) 619.809 + 130.961i 1.02788 + 0.217183i
\(604\) 0 0
\(605\) −4.39205 + 12.0671i −0.00725959 + 0.0199455i
\(606\) 0 0
\(607\) −379.228 318.210i −0.624758 0.524235i 0.274537 0.961577i \(-0.411475\pi\)
−0.899295 + 0.437342i \(0.855920\pi\)
\(608\) 0 0
\(609\) −951.592 463.411i −1.56255 0.760937i
\(610\) 0 0
\(611\) −1086.78 627.452i −1.77869 1.02693i
\(612\) 0 0
\(613\) −521.519 903.298i −0.850766 1.47357i −0.880518 0.474012i \(-0.842805\pi\)
0.0297525 0.999557i \(-0.490528\pi\)
\(614\) 0 0
\(615\) −4.80496 + 45.9835i −0.00781294 + 0.0747699i
\(616\) 0 0
\(617\) 154.839 + 27.3024i 0.250955 + 0.0442502i 0.297711 0.954656i \(-0.403777\pi\)
−0.0467552 + 0.998906i \(0.514888\pi\)
\(618\) 0 0
\(619\) 207.387 174.018i 0.335035 0.281128i −0.459713 0.888068i \(-0.652048\pi\)
0.794748 + 0.606940i \(0.207603\pi\)
\(620\) 0 0
\(621\) 403.344 + 642.889i 0.649508 + 1.03525i
\(622\) 0 0
\(623\) 753.636 + 898.149i 1.20969 + 1.44165i
\(624\) 0 0
\(625\) 108.005 612.529i 0.172809 0.980046i
\(626\) 0 0
\(627\) 3.50575 + 7.86125i 0.00559131 + 0.0125379i
\(628\) 0 0
\(629\) −23.6090 + 13.6306i −0.0375341 + 0.0216703i
\(630\) 0 0
\(631\) −226.092 + 391.603i −0.358308 + 0.620608i −0.987678 0.156498i \(-0.949980\pi\)
0.629370 + 0.777106i \(0.283313\pi\)
\(632\) 0 0
\(633\) 60.7718 + 89.9805i 0.0960060 + 0.142149i
\(634\) 0 0
\(635\) −20.0933 + 23.9462i −0.0316430 + 0.0377106i
\(636\) 0 0
\(637\) 362.129 + 131.804i 0.568491 + 0.206914i
\(638\) 0 0
\(639\) 404.217 + 13.6263i 0.632577 + 0.0213245i
\(640\) 0 0
\(641\) 682.172 120.285i 1.06423 0.187653i 0.385998 0.922500i \(-0.373857\pi\)
0.678233 + 0.734847i \(0.262746\pi\)
\(642\) 0 0
\(643\) −738.955 + 268.958i −1.14923 + 0.418286i −0.845239 0.534389i \(-0.820542\pi\)
−0.303992 + 0.952675i \(0.598319\pi\)
\(644\) 0 0
\(645\) 1.01965 0.254882i 0.00158085 0.000395166i
\(646\) 0 0
\(647\) 62.1427i 0.0960475i −0.998846 0.0480237i \(-0.984708\pi\)
0.998846 0.0480237i \(-0.0152923\pi\)
\(648\) 0 0
\(649\) 137.664 0.212117
\(650\) 0 0
\(651\) 84.0544 + 336.258i 0.129116 + 0.516525i
\(652\) 0 0
\(653\) 101.323 + 278.384i 0.155166 + 0.426315i 0.992780 0.119947i \(-0.0382725\pi\)
−0.837614 + 0.546262i \(0.816050\pi\)
\(654\) 0 0
\(655\) −4.97914 28.2381i −0.00760174 0.0431116i
\(656\) 0 0
\(657\) −782.906 487.899i −1.19164 0.742617i
\(658\) 0 0
\(659\) 94.7068 260.205i 0.143713 0.394848i −0.846863 0.531811i \(-0.821512\pi\)
0.990576 + 0.136963i \(0.0437340\pi\)
\(660\) 0 0
\(661\) 489.455 + 410.702i 0.740477 + 0.621334i 0.932966 0.359965i \(-0.117212\pi\)
−0.192489 + 0.981299i \(0.561656\pi\)
\(662\) 0 0
\(663\) −245.623 + 165.891i −0.370472 + 0.250212i
\(664\) 0 0
\(665\) −0.562467 0.324741i −0.000845815 0.000488332i
\(666\) 0 0
\(667\) 582.332 + 1008.63i 0.873062 + 1.51219i
\(668\) 0 0
\(669\) −1106.01 + 493.227i −1.65322 + 0.737260i
\(670\) 0 0
\(671\) −279.128 49.2179i −0.415989 0.0733500i
\(672\) 0 0
\(673\) 361.710 303.510i 0.537459 0.450981i −0.333209 0.942853i \(-0.608132\pi\)
0.870668 + 0.491872i \(0.163687\pi\)
\(674\) 0 0
\(675\) 667.522 + 92.5801i 0.988922 + 0.137156i
\(676\) 0 0
\(677\) −198.994 237.152i −0.293935 0.350298i 0.598785 0.800910i \(-0.295650\pi\)
−0.892720 + 0.450612i \(0.851206\pi\)
\(678\) 0 0
\(679\) 177.674 1007.64i 0.261670 1.48401i
\(680\) 0 0
\(681\) 523.399 + 54.6916i 0.768574 + 0.0803107i
\(682\) 0 0
\(683\) 654.635 377.954i 0.958470 0.553373i 0.0627681 0.998028i \(-0.480007\pi\)
0.895702 + 0.444655i \(0.146674\pi\)
\(684\) 0 0
\(685\) −19.2794 + 33.3929i −0.0281451 + 0.0487487i
\(686\) 0 0
\(687\) 176.276 361.975i 0.256588 0.526892i
\(688\) 0 0
\(689\) −904.976 + 1078.51i −1.31346 + 1.56533i
\(690\) 0 0
\(691\) 711.871 + 259.100i 1.03020 + 0.374963i 0.801158 0.598452i \(-0.204217\pi\)
0.229045 + 0.973416i \(0.426440\pi\)
\(692\) 0 0
\(693\) 550.252 179.523i 0.794014 0.259052i
\(694\) 0 0
\(695\) −14.1246 + 2.49055i −0.0203232 + 0.00358353i
\(696\) 0 0
\(697\) −434.654 + 158.201i −0.623608 + 0.226975i
\(698\) 0 0
\(699\) 326.410 1140.93i 0.466968 1.63223i
\(700\) 0 0
\(701\) 1368.47i 1.95217i 0.217397 + 0.976083i \(0.430243\pi\)
−0.217397 + 0.976083i \(0.569757\pi\)
\(702\) 0 0
\(703\) 1.71855 0.00244460
\(704\) 0 0
\(705\) 33.1456 32.0471i 0.0470150 0.0454568i
\(706\) 0 0
\(707\) −38.7956 106.590i −0.0548736 0.150764i
\(708\) 0 0
\(709\) 70.8018 + 401.537i 0.0998615 + 0.566343i 0.993149 + 0.116857i \(0.0372818\pi\)
−0.893287 + 0.449486i \(0.851607\pi\)
\(710\) 0 0
\(711\) −283.926 + 705.195i −0.399333 + 0.991835i
\(712\) 0 0
\(713\) 130.444 358.391i 0.182951 0.502653i
\(714\) 0 0
\(715\) −19.0451 15.9807i −0.0266365 0.0223507i
\(716\) 0 0
\(717\) −94.8550 1344.81i −0.132294 1.87560i
\(718\) 0 0
\(719\) −214.968 124.112i −0.298982 0.172617i 0.343004 0.939334i \(-0.388556\pi\)
−0.641985 + 0.766717i \(0.721889\pi\)
\(720\) 0 0
\(721\) 829.856 + 1437.35i 1.15098 + 1.99355i
\(722\) 0 0
\(723\) 553.449 + 401.593i 0.765490 + 0.555454i
\(724\) 0 0
\(725\) 1018.47 + 179.583i 1.40478 + 0.247701i
\(726\) 0 0
\(727\) 229.792 192.819i 0.316083 0.265225i −0.470918 0.882177i \(-0.656077\pi\)
0.787001 + 0.616952i \(0.211633\pi\)
\(728\) 0 0
\(729\) −73.5714 + 725.278i −0.100921 + 0.994894i
\(730\) 0 0
\(731\) 6.75893 + 8.05498i 0.00924615 + 0.0110191i
\(732\) 0 0
\(733\) −132.659 + 752.346i −0.180981 + 1.02639i 0.750031 + 0.661403i \(0.230039\pi\)
−0.931011 + 0.364990i \(0.881072\pi\)
\(734\) 0 0
\(735\) −8.31513 + 11.4594i −0.0113131 + 0.0155910i
\(736\) 0 0
\(737\) −460.393 + 265.808i −0.624685 + 0.360662i
\(738\) 0 0
\(739\) −437.913 + 758.487i −0.592575 + 1.02637i 0.401309 + 0.915943i \(0.368555\pi\)
−0.993884 + 0.110427i \(0.964778\pi\)
\(740\) 0 0
\(741\) 18.6385 1.31465i 0.0251532 0.00177416i
\(742\) 0 0
\(743\) 57.9224 69.0292i 0.0779574 0.0929060i −0.725656 0.688058i \(-0.758464\pi\)
0.803613 + 0.595152i \(0.202908\pi\)
\(744\) 0 0
\(745\) −18.8317 6.85416i −0.0252774 0.00920022i
\(746\) 0 0
\(747\) 574.137 + 231.160i 0.768591 + 0.309450i
\(748\) 0 0
\(749\) −1305.66 + 230.223i −1.74321 + 0.307374i
\(750\) 0 0
\(751\) −423.400 + 154.105i −0.563782 + 0.205200i −0.608159 0.793815i \(-0.708092\pi\)
0.0443772 + 0.999015i \(0.485870\pi\)
\(752\) 0 0
\(753\) 740.473 + 765.856i 0.983364 + 1.01707i
\(754\) 0 0
\(755\) 19.4484i 0.0257595i
\(756\) 0 0
\(757\) 67.0196 0.0885332 0.0442666 0.999020i \(-0.485905\pi\)
0.0442666 + 0.999020i \(0.485905\pi\)
\(758\) 0 0
\(759\) −612.324 175.181i −0.806751 0.230804i
\(760\) 0 0
\(761\) −309.817 851.216i −0.407119 1.11855i −0.958698 0.284427i \(-0.908197\pi\)
0.551579 0.834123i \(-0.314026\pi\)
\(762\) 0 0
\(763\) −103.749 588.391i −0.135975 0.771155i
\(764\) 0 0
\(765\) −3.37755 10.3524i −0.00441509 0.0135326i
\(766\) 0 0
\(767\) 102.207 280.813i 0.133256 0.366118i
\(768\) 0 0
\(769\) −706.730 593.017i −0.919024 0.771153i 0.0547901 0.998498i \(-0.482551\pi\)
−0.973814 + 0.227345i \(0.926995\pi\)
\(770\) 0 0
\(771\) 515.343 + 250.964i 0.668409 + 0.325505i
\(772\) 0 0
\(773\) −1317.32 760.554i −1.70416 0.983900i −0.941443 0.337172i \(-0.890530\pi\)
−0.762721 0.646728i \(-0.776137\pi\)
\(774\) 0 0
\(775\) −169.331 293.290i −0.218491 0.378438i
\(776\) 0 0
\(777\) 12.0099 114.935i 0.0154568 0.147922i
\(778\) 0 0
\(779\) 28.7162 + 5.06344i 0.0368629 + 0.00649993i
\(780\) 0 0
\(781\) −259.998 + 218.164i −0.332904 + 0.279340i
\(782\) 0 0
\(783\) −153.686 + 1108.11i −0.196279 + 1.41521i
\(784\)