Properties

Label 108.4.i.a.13.4
Level 108
Weight 4
Character 108.13
Analytic conductor 6.372
Analytic rank 0
Dimension 54
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 108.i (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.37220628062\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(9\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 13.4
Character \(\chi\) \(=\) 108.13
Dual form 108.4.i.a.25.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.716497 - 5.14652i) q^{3} +(7.52940 + 6.31792i) q^{5} +(24.9076 + 9.06562i) q^{7} +(-25.9733 + 7.37493i) q^{9} +O(q^{10})\) \(q+(-0.716497 - 5.14652i) q^{3} +(7.52940 + 6.31792i) q^{5} +(24.9076 + 9.06562i) q^{7} +(-25.9733 + 7.37493i) q^{9} +(17.0456 - 14.3030i) q^{11} +(13.5975 - 77.1153i) q^{13} +(27.1205 - 43.2769i) q^{15} +(32.2518 - 55.8618i) q^{17} +(35.2151 + 60.9943i) q^{19} +(28.8101 - 134.683i) q^{21} +(-112.980 + 41.1215i) q^{23} +(-4.93023 - 27.9607i) q^{25} +(56.5650 + 128.388i) q^{27} +(30.3150 + 171.925i) q^{29} +(139.932 - 50.9312i) q^{31} +(-85.8237 - 77.4776i) q^{33} +(130.263 + 225.623i) q^{35} +(144.919 - 251.008i) q^{37} +(-406.617 - 14.7269i) q^{39} +(-76.1146 + 431.667i) q^{41} +(-76.4782 + 64.1728i) q^{43} +(-242.157 - 108.568i) q^{45} +(-290.224 - 105.633i) q^{47} +(275.449 + 231.129i) q^{49} +(-310.602 - 125.960i) q^{51} -533.670 q^{53} +218.708 q^{55} +(288.677 - 224.937i) q^{57} +(320.392 + 268.841i) q^{59} +(-87.3117 - 31.7789i) q^{61} +(-713.789 - 51.7720i) q^{63} +(589.589 - 494.724i) q^{65} +(-80.8767 + 458.675i) q^{67} +(292.583 + 551.992i) q^{69} +(-451.994 + 782.877i) q^{71} +(-86.0801 - 149.095i) q^{73} +(-140.368 + 45.4073i) q^{75} +(554.231 - 201.723i) q^{77} +(-27.8206 - 157.779i) q^{79} +(620.221 - 383.102i) q^{81} +(103.082 + 584.607i) q^{83} +(595.767 - 216.841i) q^{85} +(863.095 - 279.201i) q^{87} +(-818.257 - 1417.26i) q^{89} +(1037.78 - 1797.48i) q^{91} +(-362.379 - 683.672i) q^{93} +(-120.209 + 681.737i) q^{95} +(-323.876 + 271.765i) q^{97} +(-337.247 + 497.205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54q + 12q^{5} - 48q^{9} + O(q^{10}) \) \( 54q + 12q^{5} - 48q^{9} - 87q^{11} + 234q^{15} + 204q^{17} - 12q^{21} + 96q^{23} - 216q^{25} + 27q^{27} + 318q^{29} - 54q^{31} + 63q^{33} + 6q^{35} + 66q^{39} + 867q^{41} - 513q^{43} - 306q^{45} - 1548q^{47} + 594q^{49} - 1368q^{51} - 1068q^{53} - 1269q^{57} - 1218q^{59} - 54q^{61} + 30q^{63} + 96q^{65} - 2997q^{67} + 1476q^{69} - 120q^{71} - 216q^{73} + 732q^{75} + 3480q^{77} + 2808q^{79} + 3348q^{81} + 4464q^{83} + 2160q^{85} + 4824q^{87} + 4029q^{89} + 270q^{91} + 1164q^{93} - 1650q^{95} - 3483q^{97} - 5076q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\) \(1\)

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
\(3\) −0.716497 5.14652i −0.137890 0.990448i
\(4\) 0 0
\(5\) 7.52940 + 6.31792i 0.673450 + 0.565092i 0.914084 0.405524i \(-0.132911\pi\)
−0.240634 + 0.970616i \(0.577355\pi\)
\(6\) 0 0
\(7\) 24.9076 + 9.06562i 1.34488 + 0.489497i 0.911347 0.411639i \(-0.135044\pi\)
0.433536 + 0.901136i \(0.357266\pi\)
\(8\) 0 0
\(9\) −25.9733 + 7.37493i −0.961973 + 0.273146i
\(10\) 0 0
\(11\) 17.0456 14.3030i 0.467223 0.392046i −0.378558 0.925578i \(-0.623580\pi\)
0.845780 + 0.533531i \(0.179135\pi\)
\(12\) 0 0
\(13\) 13.5975 77.1153i 0.290098 1.64522i −0.396389 0.918083i \(-0.629737\pi\)
0.686487 0.727142i \(-0.259152\pi\)
\(14\) 0 0
\(15\) 27.1205 43.2769i 0.466832 0.744937i
\(16\) 0 0
\(17\) 32.2518 55.8618i 0.460130 0.796969i −0.538837 0.842410i \(-0.681136\pi\)
0.998967 + 0.0454411i \(0.0144693\pi\)
\(18\) 0 0
\(19\) 35.2151 + 60.9943i 0.425205 + 0.736477i 0.996440 0.0843100i \(-0.0268686\pi\)
−0.571234 + 0.820787i \(0.693535\pi\)
\(20\) 0 0
\(21\) 28.8101 134.683i 0.299375 1.39953i
\(22\) 0 0
\(23\) −112.980 + 41.1215i −1.02426 + 0.372801i −0.798894 0.601472i \(-0.794581\pi\)
−0.225369 + 0.974274i \(0.572359\pi\)
\(24\) 0 0
\(25\) −4.93023 27.9607i −0.0394419 0.223686i
\(26\) 0 0
\(27\) 56.5650 + 128.388i 0.403183 + 0.915119i
\(28\) 0 0
\(29\) 30.3150 + 171.925i 0.194116 + 1.10089i 0.913672 + 0.406452i \(0.133234\pi\)
−0.719556 + 0.694434i \(0.755655\pi\)
\(30\) 0 0
\(31\) 139.932 50.9312i 0.810728 0.295081i 0.0968036 0.995304i \(-0.469138\pi\)
0.713925 + 0.700223i \(0.246916\pi\)
\(32\) 0 0
\(33\) −85.8237 77.4776i −0.452727 0.408700i
\(34\) 0 0
\(35\) 130.263 + 225.623i 0.629100 + 1.08963i
\(36\) 0 0
\(37\) 144.919 251.008i 0.643908 1.11528i −0.340644 0.940192i \(-0.610645\pi\)
0.984553 0.175090i \(-0.0560215\pi\)
\(38\) 0 0
\(39\) −406.617 14.7269i −1.66951 0.0604664i
\(40\) 0 0
\(41\) −76.1146 + 431.667i −0.289929 + 1.64427i 0.397197 + 0.917733i \(0.369983\pi\)
−0.687126 + 0.726538i \(0.741128\pi\)
\(42\) 0 0
\(43\) −76.4782 + 64.1728i −0.271228 + 0.227588i −0.768249 0.640151i \(-0.778872\pi\)
0.497021 + 0.867739i \(0.334427\pi\)
\(44\) 0 0
\(45\) −242.157 108.568i −0.802193 0.359653i
\(46\) 0 0
\(47\) −290.224 105.633i −0.900712 0.327832i −0.150174 0.988660i \(-0.547983\pi\)
−0.750538 + 0.660827i \(0.770206\pi\)
\(48\) 0 0
\(49\) 275.449 + 231.129i 0.803057 + 0.673845i
\(50\) 0 0
\(51\) −310.602 125.960i −0.852804 0.345841i
\(52\) 0 0
\(53\) −533.670 −1.38312 −0.691558 0.722321i \(-0.743075\pi\)
−0.691558 + 0.722321i \(0.743075\pi\)
\(54\) 0 0
\(55\) 218.708 0.536193
\(56\) 0 0
\(57\) 288.677 224.937i 0.670810 0.522696i
\(58\) 0 0
\(59\) 320.392 + 268.841i 0.706975 + 0.593222i 0.923748 0.383000i \(-0.125109\pi\)
−0.216774 + 0.976222i \(0.569553\pi\)
\(60\) 0 0
\(61\) −87.3117 31.7789i −0.183264 0.0667027i 0.248758 0.968566i \(-0.419978\pi\)
−0.432022 + 0.901863i \(0.642200\pi\)
\(62\) 0 0
\(63\) −713.789 51.7720i −1.42744 0.103534i
\(64\) 0 0
\(65\) 589.589 494.724i 1.12507 0.944045i
\(66\) 0 0
\(67\) −80.8767 + 458.675i −0.147473 + 0.836359i 0.817876 + 0.575395i \(0.195152\pi\)
−0.965349 + 0.260964i \(0.915960\pi\)
\(68\) 0 0
\(69\) 292.583 + 551.992i 0.510475 + 0.963073i
\(70\) 0 0
\(71\) −451.994 + 782.877i −0.755519 + 1.30860i 0.189597 + 0.981862i \(0.439282\pi\)
−0.945116 + 0.326735i \(0.894051\pi\)
\(72\) 0 0
\(73\) −86.0801 149.095i −0.138012 0.239045i 0.788732 0.614738i \(-0.210738\pi\)
−0.926744 + 0.375693i \(0.877405\pi\)
\(74\) 0 0
\(75\) −140.368 + 45.4073i −0.216111 + 0.0699091i
\(76\) 0 0
\(77\) 554.231 201.723i 0.820265 0.298552i
\(78\) 0 0
\(79\) −27.8206 157.779i −0.0396211 0.224702i 0.958567 0.284866i \(-0.0919490\pi\)
−0.998189 + 0.0601633i \(0.980838\pi\)
\(80\) 0 0
\(81\) 620.221 383.102i 0.850783 0.525517i
\(82\) 0 0
\(83\) 103.082 + 584.607i 0.136322 + 0.773120i 0.973930 + 0.226849i \(0.0728423\pi\)
−0.837608 + 0.546272i \(0.816047\pi\)
\(84\) 0 0
\(85\) 595.767 216.841i 0.760235 0.276703i
\(86\) 0 0
\(87\) 863.095 279.201i 1.06360 0.344063i
\(88\) 0 0
\(89\) −818.257 1417.26i −0.974551 1.68797i −0.681408 0.731904i \(-0.738632\pi\)
−0.293143 0.956068i \(-0.594701\pi\)
\(90\) 0 0
\(91\) 1037.78 1797.48i 1.19548 2.07063i
\(92\) 0 0
\(93\) −362.379 683.672i −0.404053 0.762295i
\(94\) 0 0
\(95\) −120.209 + 681.737i −0.129823 + 0.736260i
\(96\) 0 0
\(97\) −323.876 + 271.765i −0.339017 + 0.284469i −0.796362 0.604820i \(-0.793245\pi\)
0.457345 + 0.889289i \(0.348800\pi\)
\(98\) 0 0
\(99\) −337.247 + 497.205i −0.342370 + 0.504758i
\(100\) 0 0
\(101\) 743.112 + 270.471i 0.732103 + 0.266464i 0.681055 0.732233i \(-0.261522\pi\)
0.0510481 + 0.998696i \(0.483744\pi\)
\(102\) 0 0
\(103\) 696.301 + 584.266i 0.666103 + 0.558927i 0.911909 0.410392i \(-0.134608\pi\)
−0.245806 + 0.969319i \(0.579053\pi\)
\(104\) 0 0
\(105\) 1067.84 832.060i 0.992478 0.773340i
\(106\) 0 0
\(107\) 225.538 0.203772 0.101886 0.994796i \(-0.467512\pi\)
0.101886 + 0.994796i \(0.467512\pi\)
\(108\) 0 0
\(109\) −1916.33 −1.68396 −0.841979 0.539510i \(-0.818610\pi\)
−0.841979 + 0.539510i \(0.818610\pi\)
\(110\) 0 0
\(111\) −1395.65 565.984i −1.19342 0.483971i
\(112\) 0 0
\(113\) −496.602 416.698i −0.413419 0.346900i 0.412234 0.911078i \(-0.364749\pi\)
−0.825653 + 0.564178i \(0.809193\pi\)
\(114\) 0 0
\(115\) −1110.48 404.180i −0.900456 0.327739i
\(116\) 0 0
\(117\) 215.548 + 2103.22i 0.170320 + 1.66190i
\(118\) 0 0
\(119\) 1309.74 1099.00i 1.00894 0.846597i
\(120\) 0 0
\(121\) −145.148 + 823.172i −0.109051 + 0.618462i
\(122\) 0 0
\(123\) 2276.12 + 82.4366i 1.66854 + 0.0604313i
\(124\) 0 0
\(125\) 753.840 1305.69i 0.539404 0.934275i
\(126\) 0 0
\(127\) −180.673 312.934i −0.126237 0.218649i 0.795979 0.605324i \(-0.206957\pi\)
−0.922216 + 0.386676i \(0.873623\pi\)
\(128\) 0 0
\(129\) 385.063 + 347.617i 0.262813 + 0.237255i
\(130\) 0 0
\(131\) −659.456 + 240.022i −0.439824 + 0.160083i −0.552434 0.833556i \(-0.686301\pi\)
0.112611 + 0.993639i \(0.464079\pi\)
\(132\) 0 0
\(133\) 324.171 + 1838.47i 0.211348 + 1.19861i
\(134\) 0 0
\(135\) −385.243 + 1324.06i −0.245603 + 0.844122i
\(136\) 0 0
\(137\) −490.451 2781.48i −0.305854 1.73459i −0.619456 0.785031i \(-0.712647\pi\)
0.313602 0.949555i \(-0.398464\pi\)
\(138\) 0 0
\(139\) −928.816 + 338.061i −0.566771 + 0.206288i −0.609482 0.792800i \(-0.708623\pi\)
0.0427113 + 0.999087i \(0.486400\pi\)
\(140\) 0 0
\(141\) −335.696 + 1569.33i −0.200502 + 0.937313i
\(142\) 0 0
\(143\) −871.200 1508.96i −0.509464 0.882418i
\(144\) 0 0
\(145\) −857.954 + 1486.02i −0.491374 + 0.851085i
\(146\) 0 0
\(147\) 992.150 1583.20i 0.556674 0.888302i
\(148\) 0 0
\(149\) −339.478 + 1925.27i −0.186652 + 1.05855i 0.737163 + 0.675715i \(0.236165\pi\)
−0.923815 + 0.382840i \(0.874946\pi\)
\(150\) 0 0
\(151\) −2176.29 + 1826.12i −1.17287 + 0.984156i −1.00000 0.000788384i \(-0.999749\pi\)
−0.172872 + 0.984944i \(0.555305\pi\)
\(152\) 0 0
\(153\) −425.708 + 1688.77i −0.224944 + 0.892345i
\(154\) 0 0
\(155\) 1375.38 + 500.599i 0.712733 + 0.259413i
\(156\) 0 0
\(157\) 544.235 + 456.668i 0.276654 + 0.232140i 0.770548 0.637382i \(-0.219983\pi\)
−0.493894 + 0.869522i \(0.664427\pi\)
\(158\) 0 0
\(159\) 382.373 + 2746.54i 0.190718 + 1.36990i
\(160\) 0 0
\(161\) −3186.86 −1.56000
\(162\) 0 0
\(163\) 1340.84 0.644311 0.322156 0.946687i \(-0.395593\pi\)
0.322156 + 0.946687i \(0.395593\pi\)
\(164\) 0 0
\(165\) −156.704 1125.59i −0.0739357 0.531071i
\(166\) 0 0
\(167\) 1287.33 + 1080.20i 0.596508 + 0.500530i 0.890321 0.455333i \(-0.150480\pi\)
−0.293813 + 0.955863i \(0.594924\pi\)
\(168\) 0 0
\(169\) −3697.37 1345.73i −1.68292 0.612531i
\(170\) 0 0
\(171\) −1364.48 1324.51i −0.610201 0.592328i
\(172\) 0 0
\(173\) −118.475 + 99.4124i −0.0520664 + 0.0436889i −0.668450 0.743758i \(-0.733042\pi\)
0.616383 + 0.787446i \(0.288597\pi\)
\(174\) 0 0
\(175\) 130.681 741.130i 0.0564490 0.320138i
\(176\) 0 0
\(177\) 1154.03 1841.53i 0.490071 0.782021i
\(178\) 0 0
\(179\) −426.813 + 739.262i −0.178221 + 0.308687i −0.941271 0.337652i \(-0.890367\pi\)
0.763050 + 0.646339i \(0.223701\pi\)
\(180\) 0 0
\(181\) −985.862 1707.56i −0.404854 0.701228i 0.589451 0.807804i \(-0.299344\pi\)
−0.994304 + 0.106577i \(0.966011\pi\)
\(182\) 0 0
\(183\) −100.992 + 472.121i −0.0407953 + 0.190711i
\(184\) 0 0
\(185\) 2677.00 974.349i 1.06388 0.387219i
\(186\) 0 0
\(187\) −249.238 1413.50i −0.0974656 0.552755i
\(188\) 0 0
\(189\) 244.983 + 3710.62i 0.0942850 + 1.42809i
\(190\) 0 0
\(191\) −887.225 5031.70i −0.336112 1.90618i −0.415970 0.909378i \(-0.636558\pi\)
0.0798581 0.996806i \(-0.474553\pi\)
\(192\) 0 0
\(193\) 456.904 166.299i 0.170408 0.0620233i −0.255408 0.966833i \(-0.582210\pi\)
0.425815 + 0.904810i \(0.359987\pi\)
\(194\) 0 0
\(195\) −2968.54 2679.86i −1.09016 0.984147i
\(196\) 0 0
\(197\) 1019.37 + 1765.60i 0.368665 + 0.638546i 0.989357 0.145508i \(-0.0464817\pi\)
−0.620692 + 0.784054i \(0.713148\pi\)
\(198\) 0 0
\(199\) 2237.59 3875.62i 0.797079 1.38058i −0.124432 0.992228i \(-0.539711\pi\)
0.921511 0.388353i \(-0.126956\pi\)
\(200\) 0 0
\(201\) 2418.53 + 87.5942i 0.848705 + 0.0307384i
\(202\) 0 0
\(203\) −803.533 + 4557.06i −0.277817 + 1.57558i
\(204\) 0 0
\(205\) −3300.34 + 2769.31i −1.12442 + 0.943498i
\(206\) 0 0
\(207\) 2631.20 1901.28i 0.883484 0.638397i
\(208\) 0 0
\(209\) 1472.66 + 536.006i 0.487399 + 0.177399i
\(210\) 0 0
\(211\) 3003.60 + 2520.32i 0.979983 + 0.822304i 0.984087 0.177688i \(-0.0568618\pi\)
−0.00410365 + 0.999992i \(0.501306\pi\)
\(212\) 0 0
\(213\) 4352.94 + 1765.27i 1.40028 + 0.567860i
\(214\) 0 0
\(215\) −981.273 −0.311266
\(216\) 0 0
\(217\) 3947.10 1.23478
\(218\) 0 0
\(219\) −705.644 + 549.839i −0.217731 + 0.169656i
\(220\) 0 0
\(221\) −3869.25 3246.69i −1.17771 0.988217i
\(222\) 0 0
\(223\) 1464.87 + 533.169i 0.439888 + 0.160106i 0.552464 0.833537i \(-0.313688\pi\)
−0.112576 + 0.993643i \(0.535910\pi\)
\(224\) 0 0
\(225\) 334.263 + 689.871i 0.0990408 + 0.204406i
\(226\) 0 0
\(227\) −195.605 + 164.132i −0.0571927 + 0.0479904i −0.670936 0.741515i \(-0.734107\pi\)
0.613743 + 0.789506i \(0.289663\pi\)
\(228\) 0 0
\(229\) −897.549 + 5090.25i −0.259003 + 1.46888i 0.526581 + 0.850125i \(0.323474\pi\)
−0.785584 + 0.618755i \(0.787637\pi\)
\(230\) 0 0
\(231\) −1435.28 2707.82i −0.408807 0.771263i
\(232\) 0 0
\(233\) 2015.27 3490.54i 0.566629 0.981430i −0.430268 0.902701i \(-0.641581\pi\)
0.996896 0.0787281i \(-0.0250859\pi\)
\(234\) 0 0
\(235\) −1517.83 2628.96i −0.421329 0.729764i
\(236\) 0 0
\(237\) −792.077 + 256.227i −0.217092 + 0.0702268i
\(238\) 0 0
\(239\) 5365.88 1953.02i 1.45226 0.528579i 0.509037 0.860745i \(-0.330002\pi\)
0.943221 + 0.332166i \(0.107779\pi\)
\(240\) 0 0
\(241\) −438.520 2486.97i −0.117210 0.664730i −0.985632 0.168905i \(-0.945977\pi\)
0.868422 0.495825i \(-0.165134\pi\)
\(242\) 0 0
\(243\) −2416.03 2917.49i −0.637812 0.770192i
\(244\) 0 0
\(245\) 613.710 + 3480.52i 0.160035 + 0.907602i
\(246\) 0 0
\(247\) 5182.43 1886.25i 1.33502 0.485908i
\(248\) 0 0
\(249\) 2934.83 949.383i 0.746938 0.241625i
\(250\) 0 0
\(251\) −289.705 501.784i −0.0728526 0.126184i 0.827298 0.561764i \(-0.189877\pi\)
−0.900150 + 0.435579i \(0.856544\pi\)
\(252\) 0 0
\(253\) −1337.66 + 2316.90i −0.332403 + 0.575740i
\(254\) 0 0
\(255\) −1542.84 2910.76i −0.378889 0.714819i
\(256\) 0 0
\(257\) −614.801 + 3486.71i −0.149223 + 0.846284i 0.814657 + 0.579944i \(0.196925\pi\)
−0.963879 + 0.266340i \(0.914186\pi\)
\(258\) 0 0
\(259\) 5885.13 4938.21i 1.41191 1.18473i
\(260\) 0 0
\(261\) −2055.32 4241.88i −0.487436 1.00600i
\(262\) 0 0
\(263\) 2173.81 + 791.204i 0.509670 + 0.185505i 0.584038 0.811726i \(-0.301472\pi\)
−0.0743683 + 0.997231i \(0.523694\pi\)
\(264\) 0 0
\(265\) −4018.21 3371.68i −0.931460 0.781587i
\(266\) 0 0
\(267\) −6707.69 + 5226.64i −1.53747 + 1.19800i
\(268\) 0 0
\(269\) −595.561 −0.134989 −0.0674944 0.997720i \(-0.521500\pi\)
−0.0674944 + 0.997720i \(0.521500\pi\)
\(270\) 0 0
\(271\) −498.234 −0.111681 −0.0558406 0.998440i \(-0.517784\pi\)
−0.0558406 + 0.998440i \(0.517784\pi\)
\(272\) 0 0
\(273\) −9994.35 4053.05i −2.21570 0.898541i
\(274\) 0 0
\(275\) −483.961 406.091i −0.106123 0.0890481i
\(276\) 0 0
\(277\) 8126.82 + 2957.92i 1.76279 + 0.641604i 0.999987 0.00502614i \(-0.00159988\pi\)
0.762804 + 0.646630i \(0.223822\pi\)
\(278\) 0 0
\(279\) −3258.88 + 2354.84i −0.699298 + 0.505307i
\(280\) 0 0
\(281\) −1183.18 + 992.805i −0.251183 + 0.210768i −0.759682 0.650295i \(-0.774645\pi\)
0.508498 + 0.861063i \(0.330201\pi\)
\(282\) 0 0
\(283\) 1007.68 5714.81i 0.211661 1.20039i −0.674946 0.737867i \(-0.735833\pi\)
0.886607 0.462523i \(-0.153056\pi\)
\(284\) 0 0
\(285\) 3594.70 + 130.193i 0.747128 + 0.0270595i
\(286\) 0 0
\(287\) −5809.16 + 10061.8i −1.19479 + 2.06943i
\(288\) 0 0
\(289\) 376.139 + 651.493i 0.0765600 + 0.132606i
\(290\) 0 0
\(291\) 1630.70 + 1472.12i 0.328499 + 0.296553i
\(292\) 0 0
\(293\) −3902.90 + 1420.54i −0.778191 + 0.283238i −0.700418 0.713733i \(-0.747003\pi\)
−0.0777730 + 0.996971i \(0.524781\pi\)
\(294\) 0 0
\(295\) 713.846 + 4048.42i 0.140887 + 0.799011i
\(296\) 0 0
\(297\) 2800.51 + 1379.40i 0.547146 + 0.269498i
\(298\) 0 0
\(299\) 1634.84 + 9271.66i 0.316206 + 1.79329i
\(300\) 0 0
\(301\) −2486.65 + 905.067i −0.476174 + 0.173313i
\(302\) 0 0
\(303\) 859.544 4018.23i 0.162969 0.761852i
\(304\) 0 0
\(305\) −456.629 790.904i −0.0857261 0.148482i
\(306\) 0 0
\(307\) −3125.08 + 5412.80i −0.580970 + 1.00627i 0.414395 + 0.910097i \(0.363993\pi\)
−0.995365 + 0.0961718i \(0.969340\pi\)
\(308\) 0 0
\(309\) 2508.04 4002.15i 0.461739 0.736810i
\(310\) 0 0
\(311\) −893.683 + 5068.33i −0.162946 + 0.924111i 0.788212 + 0.615404i \(0.211007\pi\)
−0.951157 + 0.308707i \(0.900104\pi\)
\(312\) 0 0
\(313\) 4309.20 3615.85i 0.778180 0.652971i −0.164610 0.986359i \(-0.552636\pi\)
0.942790 + 0.333388i \(0.108192\pi\)
\(314\) 0 0
\(315\) −5047.31 4899.47i −0.902806 0.876362i
\(316\) 0 0
\(317\) −2826.93 1028.92i −0.500872 0.182302i 0.0792143 0.996858i \(-0.474759\pi\)
−0.580086 + 0.814555i \(0.696981\pi\)
\(318\) 0 0
\(319\) 2975.78 + 2496.98i 0.522294 + 0.438257i
\(320\) 0 0
\(321\) −161.597 1160.73i −0.0280981 0.201825i
\(322\) 0 0
\(323\) 4543.01 0.782599
\(324\) 0 0
\(325\) −2223.24 −0.379456
\(326\) 0 0
\(327\) 1373.05 + 9862.44i 0.232201 + 1.66787i
\(328\) 0 0
\(329\) −6271.14 5262.11i −1.05088 0.881792i
\(330\) 0 0
\(331\) −4837.44 1760.69i −0.803293 0.292375i −0.0924426 0.995718i \(-0.529467\pi\)
−0.710850 + 0.703343i \(0.751690\pi\)
\(332\) 0 0
\(333\) −1912.87 + 7588.26i −0.314788 + 1.24875i
\(334\) 0 0
\(335\) −3506.82 + 2942.57i −0.571935 + 0.479910i
\(336\) 0 0
\(337\) 935.450 5305.20i 0.151208 0.857545i −0.810963 0.585098i \(-0.801056\pi\)
0.962171 0.272447i \(-0.0878328\pi\)
\(338\) 0 0
\(339\) −1788.73 + 2854.33i −0.286580 + 0.457304i
\(340\) 0 0
\(341\) 1656.77 2869.60i 0.263105 0.455712i
\(342\) 0 0
\(343\) 219.637 + 380.422i 0.0345751 + 0.0598859i
\(344\) 0 0
\(345\) −1284.47 + 6004.68i −0.200445 + 0.937047i
\(346\) 0 0
\(347\) 9458.09 3442.46i 1.46322 0.532568i 0.516969 0.856004i \(-0.327060\pi\)
0.946250 + 0.323436i \(0.104838\pi\)
\(348\) 0 0
\(349\) 197.712 + 1121.28i 0.0303246 + 0.171979i 0.996209 0.0869952i \(-0.0277265\pi\)
−0.965884 + 0.258975i \(0.916615\pi\)
\(350\) 0 0
\(351\) 10669.8 2616.27i 1.62254 0.397852i
\(352\) 0 0
\(353\) 910.038 + 5161.08i 0.137214 + 0.778177i 0.973293 + 0.229568i \(0.0737314\pi\)
−0.836079 + 0.548609i \(0.815158\pi\)
\(354\) 0 0
\(355\) −8349.40 + 3038.93i −1.24828 + 0.454337i
\(356\) 0 0
\(357\) −6594.44 5953.15i −0.977632 0.882560i
\(358\) 0 0
\(359\) 324.335 + 561.764i 0.0476817 + 0.0825871i 0.888881 0.458138i \(-0.151483\pi\)
−0.841200 + 0.540725i \(0.818150\pi\)
\(360\) 0 0
\(361\) 949.293 1644.22i 0.138401 0.239718i
\(362\) 0 0
\(363\) 4340.47 + 157.203i 0.627591 + 0.0227301i
\(364\) 0 0
\(365\) 293.839 1666.44i 0.0421376 0.238974i
\(366\) 0 0
\(367\) −4084.64 + 3427.42i −0.580971 + 0.487493i −0.885266 0.465085i \(-0.846024\pi\)
0.304295 + 0.952578i \(0.401579\pi\)
\(368\) 0 0
\(369\) −1206.57 11773.2i −0.170221 1.66094i
\(370\) 0 0
\(371\) −13292.4 4838.04i −1.86013 0.677032i
\(372\) 0 0
\(373\) −5635.34 4728.61i −0.782270 0.656403i 0.161549 0.986865i \(-0.448351\pi\)
−0.943819 + 0.330462i \(0.892795\pi\)
\(374\) 0 0
\(375\) −7259.88 2944.13i −0.999729 0.405424i
\(376\) 0 0
\(377\) 13670.3 1.86752
\(378\) 0 0
\(379\) 12285.0 1.66501 0.832507 0.554015i \(-0.186905\pi\)
0.832507 + 0.554015i \(0.186905\pi\)
\(380\) 0 0
\(381\) −1481.07 + 1154.05i −0.199153 + 0.155181i
\(382\) 0 0
\(383\) −9861.87 8275.10i −1.31571 1.10401i −0.987195 0.159517i \(-0.949006\pi\)
−0.328518 0.944498i \(-0.606549\pi\)
\(384\) 0 0
\(385\) 5447.50 + 1982.73i 0.721117 + 0.262465i
\(386\) 0 0
\(387\) 1513.12 2230.80i 0.198750 0.293018i
\(388\) 0 0
\(389\) 3905.60 3277.18i 0.509053 0.427146i −0.351743 0.936097i \(-0.614411\pi\)
0.860796 + 0.508951i \(0.169966\pi\)
\(390\) 0 0
\(391\) −1346.70 + 7637.53i −0.174183 + 0.987843i
\(392\) 0 0
\(393\) 1707.78 + 3221.92i 0.219201 + 0.413549i
\(394\) 0 0
\(395\) 787.359 1363.75i 0.100295 0.173715i
\(396\) 0 0
\(397\) 3842.87 + 6656.05i 0.485814 + 0.841455i 0.999867 0.0163035i \(-0.00518981\pi\)
−0.514053 + 0.857759i \(0.671856\pi\)
\(398\) 0 0
\(399\) 9229.44 2985.61i 1.15802 0.374605i
\(400\) 0 0
\(401\) 10580.7 3851.08i 1.31765 0.479585i 0.414944 0.909847i \(-0.363801\pi\)
0.902704 + 0.430262i \(0.141579\pi\)
\(402\) 0 0
\(403\) −2024.84 11483.4i −0.250284 1.41943i
\(404\) 0 0
\(405\) 7090.30 + 1033.98i 0.869925 + 0.126861i
\(406\) 0 0
\(407\) −1119.92 6351.37i −0.136394 0.773527i
\(408\) 0 0
\(409\) 9890.09 3599.70i 1.19568 0.435192i 0.333966 0.942585i \(-0.391613\pi\)
0.861715 + 0.507393i \(0.169391\pi\)
\(410\) 0 0
\(411\) −13963.6 + 4517.04i −1.67584 + 0.542115i
\(412\) 0 0
\(413\) 5542.98 + 9600.73i 0.660417 + 1.14388i
\(414\) 0 0
\(415\) −2917.35 + 5053.01i −0.345078 + 0.597692i
\(416\) 0 0
\(417\) 2405.33 + 4537.95i 0.282469 + 0.532912i
\(418\) 0 0
\(419\) −605.417 + 3433.49i −0.0705884 + 0.400327i 0.928957 + 0.370187i \(0.120706\pi\)
−0.999546 + 0.0301399i \(0.990405\pi\)
\(420\) 0 0
\(421\) 6215.42 5215.36i 0.719527 0.603755i −0.207727 0.978187i \(-0.566607\pi\)
0.927255 + 0.374432i \(0.122162\pi\)
\(422\) 0 0
\(423\) 8317.09 + 603.249i 0.956006 + 0.0693403i
\(424\) 0 0
\(425\) −1720.95 626.373i −0.196419 0.0714907i
\(426\) 0 0
\(427\) −1886.63 1583.07i −0.213818 0.179415i
\(428\) 0 0
\(429\) −7141.69 + 5564.81i −0.803739 + 0.626274i
\(430\) 0 0
\(431\) −3793.19 −0.423925 −0.211962 0.977278i \(-0.567985\pi\)
−0.211962 + 0.977278i \(0.567985\pi\)
\(432\) 0 0
\(433\) −13262.0 −1.47190 −0.735948 0.677038i \(-0.763263\pi\)
−0.735948 + 0.677038i \(0.763263\pi\)
\(434\) 0 0
\(435\) 8262.55 + 3350.75i 0.910710 + 0.369324i
\(436\) 0 0
\(437\) −6486.79 5443.07i −0.710081 0.595829i
\(438\) 0 0
\(439\) −9674.73 3521.31i −1.05182 0.382832i −0.242471 0.970159i \(-0.577958\pi\)
−0.809350 + 0.587327i \(0.800180\pi\)
\(440\) 0 0
\(441\) −8858.86 3971.75i −0.956577 0.428869i
\(442\) 0 0
\(443\) 6433.59 5398.43i 0.689998 0.578977i −0.228910 0.973447i \(-0.573516\pi\)
0.918909 + 0.394470i \(0.129072\pi\)
\(444\) 0 0
\(445\) 2793.16 15840.8i 0.297547 1.68748i
\(446\) 0 0
\(447\) 10151.7 + 367.674i 1.07418 + 0.0389047i
\(448\) 0 0
\(449\) 5426.60 9399.15i 0.570373 0.987914i −0.426155 0.904650i \(-0.640132\pi\)
0.996528 0.0832641i \(-0.0265345\pi\)
\(450\) 0 0
\(451\) 4876.71 + 8446.71i 0.509169 + 0.881907i
\(452\) 0 0
\(453\) 10957.5 + 9891.88i 1.13648 + 1.02596i
\(454\) 0 0
\(455\) 19170.2 6977.38i 1.97519 0.718911i
\(456\) 0 0
\(457\) 2521.85 + 14302.1i 0.258134 + 1.46395i 0.787899 + 0.615805i \(0.211169\pi\)
−0.529765 + 0.848144i \(0.677720\pi\)
\(458\) 0 0
\(459\) 8996.29 + 980.917i 0.914839 + 0.0997501i
\(460\) 0 0
\(461\) −1197.28 6790.14i −0.120961 0.686005i −0.983625 0.180227i \(-0.942317\pi\)
0.862664 0.505778i \(-0.168794\pi\)
\(462\) 0 0
\(463\) −16976.9 + 6179.10i −1.70407 + 0.620231i −0.996279 0.0861899i \(-0.972531\pi\)
−0.707792 + 0.706421i \(0.750309\pi\)
\(464\) 0 0
\(465\) 1590.88 7437.12i 0.158657 0.741695i
\(466\) 0 0
\(467\) 4432.93 + 7678.07i 0.439254 + 0.760811i 0.997632 0.0687761i \(-0.0219094\pi\)
−0.558378 + 0.829587i \(0.688576\pi\)
\(468\) 0 0
\(469\) −6172.61 + 10691.3i −0.607729 + 1.05262i
\(470\) 0 0
\(471\) 1960.30 3128.12i 0.191775 0.306021i
\(472\) 0 0
\(473\) −385.756 + 2187.73i −0.0374991 + 0.212668i
\(474\) 0 0
\(475\) 1531.83 1285.36i 0.147969 0.124160i
\(476\) 0 0
\(477\) 13861.1 3935.78i 1.33052 0.377792i
\(478\) 0 0
\(479\) −13232.7 4816.31i −1.26225 0.459422i −0.377727 0.925917i \(-0.623294\pi\)
−0.884524 + 0.466495i \(0.845516\pi\)
\(480\) 0 0
\(481\) −17386.0 14588.6i −1.64809 1.38291i
\(482\) 0 0
\(483\) 2283.38 + 16401.2i 0.215108 + 1.54510i
\(484\) 0 0
\(485\) −4155.58 −0.389062
\(486\) 0 0
\(487\) −19389.4 −1.80414 −0.902072 0.431586i \(-0.857954\pi\)
−0.902072 + 0.431586i \(0.857954\pi\)
\(488\) 0 0
\(489\) −960.709 6900.66i −0.0888441 0.638157i
\(490\) 0 0
\(491\) −13194.3 11071.3i −1.21273 1.01760i −0.999173 0.0406697i \(-0.987051\pi\)
−0.213556 0.976931i \(-0.568505\pi\)
\(492\) 0 0
\(493\) 10581.8 + 3851.45i 0.966691 + 0.351847i
\(494\) 0 0
\(495\) −5680.57 + 1612.96i −0.515803 + 0.146459i
\(496\) 0 0
\(497\) −18355.3 + 15402.0i −1.65664 + 1.39009i
\(498\) 0 0
\(499\) −2323.05 + 13174.7i −0.208405 + 1.18192i 0.683585 + 0.729871i \(0.260420\pi\)
−0.891991 + 0.452054i \(0.850691\pi\)
\(500\) 0 0
\(501\) 4636.90 7399.24i 0.413496 0.659828i
\(502\) 0 0
\(503\) 6922.31 11989.8i 0.613620 1.06282i −0.377005 0.926211i \(-0.623046\pi\)
0.990625 0.136609i \(-0.0436205\pi\)
\(504\) 0 0
\(505\) 3886.38 + 6731.40i 0.342458 + 0.593155i
\(506\) 0 0
\(507\) −4276.67 + 19992.8i −0.374623 + 1.75130i
\(508\) 0 0
\(509\) −14055.9 + 5115.94i −1.22400 + 0.445501i −0.871540 0.490324i \(-0.836878\pi\)
−0.352464 + 0.935825i \(0.614656\pi\)
\(510\) 0 0
\(511\) −792.407 4493.96i −0.0685989 0.389044i
\(512\) 0 0
\(513\) −5838.98 + 7971.33i −0.502529 + 0.686048i
\(514\) 0 0
\(515\) 1551.39 + 8798.34i 0.132742 + 0.752818i
\(516\) 0 0
\(517\) −6457.91 + 2350.49i −0.549359 + 0.199950i
\(518\) 0 0
\(519\) 596.514 + 538.505i 0.0504510 + 0.0455448i
\(520\) 0 0
\(521\) −3924.43 6797.31i −0.330004 0.571584i 0.652508 0.757782i \(-0.273717\pi\)
−0.982512 + 0.186198i \(0.940384\pi\)
\(522\) 0 0
\(523\) 7321.97 12682.0i 0.612175 1.06032i −0.378698 0.925520i \(-0.623628\pi\)
0.990873 0.134798i \(-0.0430385\pi\)
\(524\) 0 0
\(525\) −3907.87 141.535i −0.324864 0.0117659i
\(526\) 0 0
\(527\) 1667.96 9459.49i 0.137870 0.781901i
\(528\) 0 0
\(529\) 1753.12 1471.05i 0.144088 0.120905i
\(530\) 0 0
\(531\) −10304.3 4619.81i −0.842126 0.377556i
\(532\) 0 0
\(533\) 32253.2 + 11739.2i 2.62109 + 0.953998i
\(534\) 0 0
\(535\) 1698.17 + 1424.93i 0.137230 + 0.115150i
\(536\) 0 0
\(537\) 4110.43 + 1666.92i 0.330313 + 0.133953i
\(538\) 0 0
\(539\) 8001.03 0.639385
\(540\) 0 0
\(541\) −12240.4 −0.972745 −0.486372 0.873752i \(-0.661680\pi\)
−0.486372 + 0.873752i \(0.661680\pi\)
\(542\) 0 0
\(543\) −8081.64 + 6297.22i −0.638704 + 0.497679i
\(544\) 0 0
\(545\) −14428.8 12107.2i −1.13406 0.951591i
\(546\) 0 0
\(547\) 13010.6 + 4735.49i 1.01699 + 0.370155i 0.796114 0.605146i \(-0.206885\pi\)
0.220879 + 0.975301i \(0.429108\pi\)
\(548\) 0 0
\(549\) 2502.14 + 181.483i 0.194515 + 0.0141084i
\(550\) 0 0
\(551\) −9418.91 + 7903.41i −0.728238 + 0.611064i
\(552\) 0 0
\(553\) 737.416 4182.09i 0.0567054 0.321593i
\(554\) 0 0
\(555\) −6932.57 13079.1i −0.530218 1.00032i
\(556\) 0 0
\(557\) −2049.36 + 3549.59i −0.155896 + 0.270020i −0.933385 0.358877i \(-0.883160\pi\)
0.777489 + 0.628897i \(0.216493\pi\)
\(558\) 0 0
\(559\) 3908.79 + 6770.22i 0.295750 + 0.512254i
\(560\) 0 0
\(561\) −7096.01 + 2295.47i −0.534035 + 0.172754i
\(562\) 0 0
\(563\) 19726.1 7179.71i 1.47665 0.537458i 0.526755 0.850017i \(-0.323408\pi\)
0.949898 + 0.312559i \(0.101186\pi\)
\(564\) 0 0
\(565\) −1106.45 6274.97i −0.0823869 0.467239i
\(566\) 0 0
\(567\) 18921.3 3919.46i 1.40144 0.290303i
\(568\) 0 0
\(569\) 3207.06 + 18188.1i 0.236286 + 1.34005i 0.839888 + 0.542760i \(0.182621\pi\)
−0.603602 + 0.797286i \(0.706268\pi\)
\(570\) 0 0
\(571\) 8850.02 3221.15i 0.648620 0.236078i 0.00330448 0.999995i \(-0.498948\pi\)
0.645315 + 0.763916i \(0.276726\pi\)
\(572\) 0 0
\(573\) −25260.0 + 8171.32i −1.84163 + 0.595745i
\(574\) 0 0
\(575\) 1706.81 + 2956.28i 0.123789 + 0.214409i
\(576\) 0 0
\(577\) −6534.09 + 11317.4i −0.471435 + 0.816549i −0.999466 0.0326762i \(-0.989597\pi\)
0.528031 + 0.849225i \(0.322930\pi\)
\(578\) 0 0
\(579\) −1183.23 2232.31i −0.0849283 0.160227i
\(580\) 0 0
\(581\) −2732.30 + 15495.7i −0.195103 + 1.10649i
\(582\) 0 0
\(583\) −9096.74 + 7633.07i −0.646223 + 0.542246i
\(584\) 0 0
\(585\) −11665.0 + 17197.8i −0.824424 + 1.21545i
\(586\) 0 0
\(587\) −2383.29 867.448i −0.167579 0.0609939i 0.256868 0.966446i \(-0.417309\pi\)
−0.424447 + 0.905453i \(0.639532\pi\)
\(588\) 0 0
\(589\) 8034.24 + 6741.53i 0.562046 + 0.471613i
\(590\) 0 0
\(591\) 8356.30 6511.24i 0.581611 0.453192i
\(592\) 0 0
\(593\) 8431.98 0.583912 0.291956 0.956432i \(-0.405694\pi\)
0.291956 + 0.956432i \(0.405694\pi\)
\(594\) 0 0
\(595\) 16804.9 1.15787
\(596\) 0 0
\(597\) −21549.2 8738.93i −1.47730 0.599097i
\(598\) 0 0
\(599\) −285.369 239.453i −0.0194655 0.0163335i 0.633003 0.774149i \(-0.281822\pi\)
−0.652468 + 0.757816i \(0.726267\pi\)
\(600\) 0 0
\(601\) 3783.87 + 1377.22i 0.256818 + 0.0934740i 0.467221 0.884141i \(-0.345255\pi\)
−0.210403 + 0.977615i \(0.567478\pi\)
\(602\) 0 0
\(603\) −1282.06 12509.7i −0.0865831 0.844836i
\(604\) 0 0
\(605\) −6293.61 + 5280.96i −0.422928 + 0.354879i
\(606\) 0 0
\(607\) −240.592 + 1364.47i −0.0160879 + 0.0912388i −0.991795 0.127842i \(-0.959195\pi\)
0.975707 + 0.219081i \(0.0703060\pi\)
\(608\) 0 0
\(609\) 24028.7 + 870.273i 1.59884 + 0.0579068i
\(610\) 0 0
\(611\) −12092.2 + 20944.3i −0.800652 + 1.38677i
\(612\) 0 0
\(613\) −6625.82 11476.3i −0.436565 0.756153i 0.560857 0.827913i \(-0.310472\pi\)
−0.997422 + 0.0717601i \(0.977138\pi\)
\(614\) 0 0
\(615\) 16617.0 + 15001.0i 1.08953 + 0.983577i
\(616\) 0 0
\(617\) 5742.14 2089.97i 0.374667 0.136368i −0.147821 0.989014i \(-0.547226\pi\)
0.522489 + 0.852646i \(0.325004\pi\)
\(618\) 0 0
\(619\) 158.970 + 901.563i 0.0103224 + 0.0585410i 0.989534 0.144301i \(-0.0460933\pi\)
−0.979211 + 0.202842i \(0.934982\pi\)
\(620\) 0 0
\(621\) −11670.2 12179.3i −0.754122 0.787016i
\(622\) 0 0
\(623\) −7532.44 42718.6i −0.484399 2.74716i
\(624\) 0 0
\(625\) 10590.2 3854.53i 0.677774 0.246690i
\(626\) 0 0
\(627\) 1703.40 7963.14i 0.108497 0.507204i
\(628\) 0 0
\(629\) −9347.83 16190.9i −0.592563 1.02635i
\(630\) 0 0
\(631\) 3125.11 5412.85i 0.197161 0.341493i −0.750446 0.660932i \(-0.770161\pi\)
0.947607 + 0.319439i \(0.103495\pi\)
\(632\) 0 0
\(633\) 10818.8 17263.9i 0.679319 1.08401i
\(634\) 0 0
\(635\) 616.735 3497.68i 0.0385423 0.218585i
\(636\) 0 0
\(637\) 21569.0 18098.5i 1.34159 1.12573i
\(638\) 0 0
\(639\) 5966.10 23667.3i 0.369351 1.46520i
\(640\) 0 0
\(641\) 7732.55 + 2814.42i 0.476470 + 0.173421i 0.569081 0.822281i \(-0.307299\pi\)
−0.0926108 + 0.995702i \(0.529521\pi\)
\(642\) 0 0
\(643\) −1394.39 1170.03i −0.0855201 0.0717599i 0.599025 0.800730i \(-0.295555\pi\)
−0.684545 + 0.728970i \(0.739999\pi\)
\(644\) 0 0
\(645\) 703.080 + 5050.14i 0.0429205 + 0.308293i
\(646\) 0 0
\(647\) −14438.2 −0.877318 −0.438659 0.898654i \(-0.644546\pi\)
−0.438659 + 0.898654i \(0.644546\pi\)
\(648\) 0 0
\(649\) 9306.51 0.562885
\(650\) 0 0
\(651\) −2828.08 20313.8i −0.170263 1.22298i
\(652\) 0 0
\(653\) 15367.0 + 12894.4i 0.920914 + 0.772739i 0.974164 0.225842i \(-0.0725134\pi\)
−0.0532495 + 0.998581i \(0.516958\pi\)
\(654\) 0 0
\(655\) −6481.75 2359.16i −0.386661 0.140733i
\(656\) 0 0
\(657\) 3335.35 + 3237.65i 0.198058 + 0.192257i
\(658\) 0 0
\(659\) 14421.1 12100.7i 0.852451 0.715291i −0.107877 0.994164i \(-0.534405\pi\)
0.960328 + 0.278873i \(0.0899608\pi\)
\(660\) 0 0
\(661\) 387.406 2197.09i 0.0227963 0.129284i −0.971286 0.237916i \(-0.923536\pi\)
0.994082 + 0.108632i \(0.0346469\pi\)
\(662\) 0 0
\(663\) −13936.8 + 22239.4i −0.816382 + 1.30273i
\(664\) 0 0
\(665\) −9174.47 + 15890.6i −0.534993 + 0.926636i
\(666\) 0 0
\(667\) −10494.8 18177.6i −0.609237 1.05523i
\(668\) 0 0
\(669\) 1694.39 7920.99i 0.0979206 0.457763i
\(670\) 0 0
\(671\) −1942.82 + 707.127i −0.111776 + 0.0406831i
\(672\) 0 0
\(673\) −2561.47 14526.8i −0.146712 0.832048i −0.965976 0.258631i \(-0.916729\pi\)
0.819264 0.573417i \(-0.194382\pi\)
\(674\) 0 0
\(675\) 3310.94 2214.58i 0.188797 0.126280i
\(676\) 0 0
\(677\) 666.714 + 3781.13i 0.0378492 + 0.214654i 0.997867 0.0652871i \(-0.0207963\pi\)
−0.960017 + 0.279941i \(0.909685\pi\)
\(678\) 0 0
\(679\) −10530.7 + 3832.86i −0.595185 + 0.216630i
\(680\) 0 0
\(681\) 984.857 + 889.083i 0.0554182 + 0.0500290i
\(682\) 0 0
\(683\) 6452.62 + 11176.3i 0.361497 + 0.626132i 0.988207 0.153121i \(-0.0489323\pi\)
−0.626710 + 0.779252i \(0.715599\pi\)
\(684\) 0 0
\(685\) 13880.4 24041.5i 0.774222 1.34099i
\(686\) 0 0
\(687\) 26840.2 + 972.098i 1.49056 + 0.0539852i
\(688\) 0 0
\(689\) −7256.57 + 41154.1i −0.401239 + 2.27554i
\(690\) 0 0
\(691\) −5853.56 + 4911.72i −0.322257 + 0.270406i −0.789536 0.613704i \(-0.789679\pi\)
0.467279 + 0.884110i \(0.345234\pi\)
\(692\) 0 0
\(693\) −12907.5 + 9326.83i −0.707525 + 0.511251i
\(694\) 0 0
\(695\) −9129.27 3322.78i −0.498263 0.181353i
\(696\) 0 0
\(697\) 21658.9 + 18174.0i 1.17703 + 0.987644i
\(698\) 0 0
\(699\) −19408.1 7870.63i −1.05019 0.425887i
\(700\) 0 0
\(701\) 16562.4 0.892373 0.446187 0.894940i \(-0.352782\pi\)
0.446187 + 0.894940i \(0.352782\pi\)
\(702\) 0 0
\(703\) 20413.4 1.09517
\(704\) 0 0
\(705\) −12442.5 + 9695.18i −0.664695 + 0.517932i
\(706\) 0 0
\(707\) 16057.1 + 13473.5i 0.854159 + 0.716725i
\(708\) 0 0
\(709\) 866.193 + 315.268i 0.0458823 + 0.0166998i 0.364859 0.931063i \(-0.381117\pi\)
−0.318977 + 0.947762i \(0.603339\pi\)
\(710\) 0 0
\(711\) 1886.20 + 3892.85i 0.0994908 + 0.205335i
\(712\) 0 0
\(713\) −13715.2 + 11508.4i −0.720392 + 0.604481i
\(714\) 0 0
\(715\) 2973.89 16865.8i 0.155548 0.882159i
\(716\) 0 0
\(717\) −13895.9 26216.2i −0.723781 1.36550i
\(718\) 0 0
\(719\) 1108.55 1920.06i 0.0574992 0.0995915i −0.835843 0.548969i \(-0.815021\pi\)
0.893342 + 0.449377i \(0.148354\pi\)
\(720\) 0 0
\(721\) 12046.4 + 20865.0i 0.622237 + 1.07775i
\(722\) 0 0
\(723\) −12485.0 + 4038.76i −0.642218 + 0.207750i
\(724\) 0 0
\(725\) 4657.69 1695.26i 0.238596 0.0868420i
\(726\) 0 0
\(727\) 2305.90 + 13077.4i 0.117636 + 0.667145i 0.985411 + 0.170189i \(0.0544378\pi\)
−0.867776 + 0.496956i \(0.834451\pi\)
\(728\) 0 0
\(729\) −13283.8 + 14524.5i −0.674887 + 0.737921i
\(730\) 0 0
\(731\) 1118.25 + 6341.90i 0.0565799 + 0.320880i
\(732\) 0 0
\(733\) 18468.5 6721.99i 0.930628 0.338721i 0.168169 0.985758i \(-0.446214\pi\)
0.762458 + 0.647037i \(0.223992\pi\)
\(734\) 0 0
\(735\) 17472.8 5652.25i 0.876865 0.283655i
\(736\) 0 0
\(737\) 5181.82 + 8975.18i 0.258989 + 0.448582i
\(738\) 0 0
\(739\) 6917.27 11981.1i 0.344325 0.596388i −0.640906 0.767619i \(-0.721441\pi\)
0.985231 + 0.171231i \(0.0547746\pi\)
\(740\) 0 0
\(741\) −13420.8 25320.0i −0.665352 1.25527i
\(742\) 0 0
\(743\) −3872.43 + 21961.6i −0.191206 + 1.08438i 0.726514 + 0.687152i \(0.241139\pi\)
−0.917720 + 0.397229i \(0.869972\pi\)
\(744\) 0 0
\(745\) −14719.8 + 12351.4i −0.723881 + 0.607408i
\(746\) 0 0
\(747\) −6988.82 14423.9i −0.342312 0.706485i
\(748\) 0 0
\(749\) 5617.60 + 2044.64i 0.274049 + 0.0997457i
\(750\) 0 0
\(751\) 18445.2 + 15477.4i 0.896238 + 0.752033i 0.969451 0.245283i \(-0.0788810\pi\)
−0.0732136 + 0.997316i \(0.523325\pi\)
\(752\) 0 0
\(753\) −2374.87 + 1850.50i −0.114933 + 0.0895563i
\(754\) 0 0
\(755\) −27923.4 −1.34601
\(756\) 0 0
\(757\) 15873.5 0.762132 0.381066 0.924548i \(-0.375557\pi\)
0.381066 + 0.924548i \(0.375557\pi\)
\(758\) 0 0
\(759\) 12882.4 + 5224.25i 0.616075 + 0.249839i
\(760\) 0 0
\(761\) −21981.7 18444.8i −1.04709 0.878613i −0.0543053 0.998524i \(-0.517294\pi\)
−0.992785 + 0.119912i \(0.961739\pi\)
\(762\) 0 0
\(763\) −47731.2 17372.7i −2.26473 0.824293i
\(764\) 0 0
\(765\) −13874.8 + 10025.8i −0.655746 + 0.473836i
\(766\) 0 0
\(767\) 25088.3 21051.6i 1.18108 0.991040i
\(768\) 0 0
\(769\) −2217.08 + 12573.7i −0.103966 + 0.589620i 0.887662 + 0.460495i \(0.152328\pi\)
−0.991628 + 0.129125i \(0.958783\pi\)
\(770\) 0 0
\(771\) 18384.9 + 665.865i 0.858776 + 0.0311032i
\(772\) 0 0
\(773\) 3017.93 5227.21i 0.140424 0.243221i −0.787233 0.616656i \(-0.788487\pi\)
0.927656 + 0.373435i \(0.121820\pi\)
\(774\) 0 0
\(775\) −2113.97 3661.51i −0.0979821 0.169710i
\(776\) 0 0
\(777\) −29631.3 26749.7i −1.36810 1.23506i
\(778\) 0 0
\(779\) −29009.7 + 10558.7i −1.33425 + 0.485626i
\(780\) 0 0
\(781\) 3492.95 + 19809.5i 0.160035 + 0.907605i
\(782\) 0 0