Properties

Label 108.4.i.a.25.4
Level 108
Weight 4
Character 108.25
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 25.4
Character \(\chi\) \(=\) 108.25
Dual form 108.4.i.a.13.4

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(1\)

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 −0.240634 0.970616i \(-0.577355\pi\)
0.914084 + 0.405524i \(0.132911\pi\)
\(6\) 0 0
\(7\) 24.9076 9.06562i 1.34488 0.489497i 0.433536 0.901136i \(-0.357266\pi\)
0.911347 + 0.411639i \(0.135044\pi\)
\(8\) 0 0
\(9\) −25.9733 7.37493i −0.961973 0.273146i
\(10\) 0 0
\(11\) 17.0456 + 14.3030i 0.467223 + 0.392046i 0.845780 0.533531i \(-0.179135\pi\)
−0.378558 + 0.925578i \(0.623580\pi\)
\(12\) 0 0
\(13\) 13.5975 + 77.1153i 0.290098 + 1.64522i 0.686487 + 0.727142i \(0.259152\pi\)
−0.396389 + 0.918083i \(0.629737\pi\)
\(14\) 0 0
\(15\) 27.1205 + 43.2769i 0.466832 + 0.744937i
\(16\) 0 0
\(17\) 32.2518 + 55.8618i 0.460130 + 0.796969i 0.998967 0.0454411i \(-0.0144693\pi\)
−0.538837 + 0.842410i \(0.681136\pi\)
\(18\) 0 0
\(19\) 35.2151 60.9943i 0.425205 0.736477i −0.571234 0.820787i \(-0.693535\pi\)
0.996440 + 0.0843100i \(0.0268686\pi\)
\(20\) 0 0
\(21\) 28.8101 + 134.683i 0.299375 + 1.39953i
\(22\) 0 0
\(23\) −112.980 41.1215i −1.02426 0.372801i −0.225369 0.974274i \(-0.572359\pi\)
−0.798894 + 0.601472i \(0.794581\pi\)
\(24\) 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 −0.719556 0.694434i \(-0.755655\pi\)
0.913672 0.406452i \(-0.133234\pi\)
\(30\) 0 0
\(31\) 139.932 + 50.9312i 0.810728 + 0.295081i 0.713925 0.700223i \(-0.246916\pi\)
0.0968036 + 0.995304i \(0.469138\pi\)
\(32\) 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 0.984553 + 0.175090i \(0.0560215\pi\)
−0.340644 + 0.940192i \(0.610645\pi\)
\(38\) 0 0
\(39\) −406.617 + 14.7269i −1.66951 + 0.0604664i
\(40\) 0 0
\(41\) −76.1146 431.667i −0.289929 1.64427i −0.687126 0.726538i \(-0.741128\pi\)
0.397197 0.917733i \(-0.369983\pi\)
\(42\) 0 0
\(43\) −76.4782 64.1728i −0.271228 0.227588i 0.497021 0.867739i \(-0.334427\pi\)
−0.768249 + 0.640151i \(0.778872\pi\)
\(44\) 0 0
\(45\) −242.157 + 108.568i −0.802193 + 0.359653i
\(46\) 0 0
\(47\) −290.224 + 105.633i −0.900712 + 0.327832i −0.750538 0.660827i \(-0.770206\pi\)
−0.150174 + 0.988660i \(0.547983\pi\)
\(48\) 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 −0.216774 0.976222i \(-0.569553\pi\)
0.923748 + 0.383000i \(0.125109\pi\)
\(60\) 0 0
\(61\) −87.3117 + 31.7789i −0.183264 + 0.0667027i −0.432022 0.901863i \(-0.642200\pi\)
0.248758 + 0.968566i \(0.419978\pi\)
\(62\) 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 −0.965349 0.260964i \(-0.915960\pi\)
0.817876 0.575395i \(-0.195152\pi\)
\(68\) 0 0
\(69\) 292.583 551.992i 0.510475 0.963073i
\(70\) 0 0
\(71\) −451.994 782.877i −0.755519 1.30860i −0.945116 0.326735i \(-0.894051\pi\)
0.189597 0.981862i \(-0.439282\pi\)
\(72\) 0 0
\(73\) −86.0801 + 149.095i −0.138012 + 0.239045i −0.926744 0.375693i \(-0.877405\pi\)
0.788732 + 0.614738i \(0.210738\pi\)
\(74\) 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 −0.998189 0.0601633i \(-0.980838\pi\)
0.958567 + 0.284866i \(0.0919490\pi\)
\(80\) 0 0
\(81\) 620.221 + 383.102i 0.850783 + 0.525517i
\(82\) 0 0
\(83\) 103.082 584.607i 0.136322 0.773120i −0.837608 0.546272i \(-0.816047\pi\)
0.973930 0.226849i \(-0.0728423\pi\)
\(84\) 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 −0.293143 + 0.956068i \(0.594701\pi\)
−0.681408 + 0.731904i \(0.738632\pi\)
\(90\) 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 0.457345 0.889289i \(-0.348800\pi\)
−0.796362 + 0.604820i \(0.793245\pi\)
\(98\) 0 0
\(99\) −337.247 497.205i −0.342370 0.504758i
\(100\) 0 0
\(101\) 743.112 270.471i 0.732103 0.266464i 0.0510481 0.998696i \(-0.483744\pi\)
0.681055 + 0.732233i \(0.261522\pi\)
\(102\) 0 0
\(103\) 696.301 584.266i 0.666103 0.558927i −0.245806 0.969319i \(-0.579053\pi\)
0.911909 + 0.410392i \(0.134608\pi\)
\(104\) 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 −0.825653 0.564178i \(-0.809193\pi\)
0.412234 + 0.911078i \(0.364749\pi\)
\(114\) 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 −0.922216 0.386676i \(-0.873623\pi\)
0.795979 + 0.605324i \(0.206957\pi\)
\(128\) 0 0
\(129\) 385.063 347.617i 0.262813 0.237255i
\(130\) 0 0
\(131\) −659.456 240.022i −0.439824 0.160083i 0.112611 0.993639i \(-0.464079\pi\)
−0.552434 + 0.833556i \(0.686301\pi\)
\(132\) 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 0.313602 + 0.949555i \(0.398464\pi\)
−0.619456 + 0.785031i \(0.712647\pi\)
\(138\) 0 0
\(139\) −928.816 338.061i −0.566771 0.206288i 0.0427113 0.999087i \(-0.486400\pi\)
−0.609482 + 0.792800i \(0.708623\pi\)
\(140\) 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 −0.923815 0.382840i \(-0.874946\pi\)
0.737163 0.675715i \(-0.236165\pi\)
\(150\) 0 0
\(151\) −2176.29 1826.12i −1.17287 0.984156i −0.172872 0.984944i \(-0.555305\pi\)
−1.00000 0.000788384i \(0.999749\pi\)
\(152\) 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 −0.493894 0.869522i \(-0.664427\pi\)
0.770548 + 0.637382i \(0.219983\pi\)
\(158\) 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 −0.293813 0.955863i \(-0.594924\pi\)
0.890321 + 0.455333i \(0.150480\pi\)
\(168\) 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 0.616383 0.787446i \(-0.288597\pi\)
−0.668450 + 0.743758i \(0.733042\pi\)
\(174\) 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 0.763050 0.646339i \(-0.223701\pi\)
−0.941271 + 0.337652i \(0.890367\pi\)
\(180\) 0 0
\(181\) −985.862 + 1707.56i −0.404854 + 0.701228i −0.994304 0.106577i \(-0.966011\pi\)
0.589451 + 0.807804i \(0.299344\pi\)
\(182\) 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 0.0798581 + 0.996806i \(0.474553\pi\)
−0.415970 + 0.909378i \(0.636558\pi\)
\(192\) 0 0
\(193\) 456.904 + 166.299i 0.170408 + 0.0620233i 0.425815 0.904810i \(-0.359987\pi\)
−0.255408 + 0.966833i \(0.582210\pi\)
\(194\) 0 0
\(195\) −2968.54 + 2679.86i −1.09016 + 0.984147i
\(196\) 0 0
\(197\) 1019.37 1765.60i 0.368665 0.638546i −0.620692 0.784054i \(-0.713148\pi\)
0.989357 + 0.145508i \(0.0464817\pi\)
\(198\) 0 0
\(199\) 2237.59 + 3875.62i 0.797079 + 1.38058i 0.921511 + 0.388353i \(0.126956\pi\)
−0.124432 + 0.992228i \(0.539711\pi\)
\(200\) 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 −0.00410365 0.999992i \(-0.501306\pi\)
0.984087 + 0.177688i \(0.0568618\pi\)
\(212\) 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 −0.112576 0.993643i \(-0.535910\pi\)
0.552464 + 0.833537i \(0.313688\pi\)
\(224\) 0 0
\(225\) 334.263 689.871i 0.0990408 0.204406i
\(226\) 0 0
\(227\) −195.605 164.132i −0.0571927 0.0479904i 0.613743 0.789506i \(-0.289663\pi\)
−0.670936 + 0.741515i \(0.734107\pi\)
\(228\) 0 0
\(229\) −897.549 5090.25i −0.259003 1.46888i −0.785584 0.618755i \(-0.787637\pi\)
0.526581 0.850125i \(-0.323474\pi\)
\(230\) 0 0
\(231\) −1435.28 + 2707.82i −0.408807 + 0.771263i
\(232\) 0 0
\(233\) 2015.27 + 3490.54i 0.566629 + 0.981430i 0.996896 + 0.0787281i \(0.0250859\pi\)
−0.430268 + 0.902701i \(0.641581\pi\)
\(234\) 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 0.943221 0.332166i \(-0.107779\pi\)
0.509037 + 0.860745i \(0.330002\pi\)
\(240\) 0 0
\(241\) −438.520 + 2486.97i −0.117210 + 0.664730i 0.868422 + 0.495825i \(0.165134\pi\)
−0.985632 + 0.168905i \(0.945977\pi\)
\(242\) 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 −0.900150 0.435579i \(-0.856544\pi\)
0.827298 + 0.561764i \(0.189877\pi\)
\(252\) 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 −0.963879 0.266340i \(-0.914186\pi\)
0.814657 0.579944i \(-0.196925\pi\)
\(258\) 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 −0.0743683 0.997231i \(-0.523694\pi\)
0.584038 + 0.811726i \(0.301472\pi\)
\(264\) 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 0.762804 0.646630i \(-0.223822\pi\)
0.999987 + 0.00502614i \(0.00159988\pi\)
\(278\) 0 0
\(279\) −3258.88 2354.84i −0.699298 0.505307i
\(280\) 0 0
\(281\) −1183.18 992.805i −0.251183 0.210768i 0.508498 0.861063i \(-0.330201\pi\)
−0.759682 + 0.650295i \(0.774645\pi\)
\(282\) 0 0
\(283\) 1007.68 + 5714.81i 0.211661 + 1.20039i 0.886607 + 0.462523i \(0.153056\pi\)
−0.674946 + 0.737867i \(0.735833\pi\)
\(284\) 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 −0.0777730 0.996971i \(-0.524781\pi\)
−0.700418 + 0.713733i \(0.747003\pi\)
\(294\) 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 −0.995365 0.0961718i \(-0.969340\pi\)
0.414395 0.910097i \(-0.363993\pi\)
\(308\) 0 0
\(309\) 2508.04 + 4002.15i 0.461739 + 0.736810i
\(310\) 0 0
\(311\) −893.683 5068.33i −0.162946 0.924111i −0.951157 0.308707i \(-0.900104\pi\)
0.788212 0.615404i \(-0.211007\pi\)
\(312\) 0 0
\(313\) 4309.20 + 3615.85i 0.778180 + 0.652971i 0.942790 0.333388i \(-0.108192\pi\)
−0.164610 + 0.986359i \(0.552636\pi\)
\(314\) 0 0
\(315\) −5047.31 + 4899.47i −0.902806 + 0.876362i
\(316\) 0 0
\(317\) −2826.93 + 1028.92i −0.500872 + 0.182302i −0.580086 0.814555i \(-0.696981\pi\)
0.0792143 + 0.996858i \(0.474759\pi\)
\(318\) 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 −0.710850 0.703343i \(-0.751690\pi\)
−0.0924426 + 0.995718i \(0.529467\pi\)
\(332\) 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 0.962171 + 0.272447i \(0.0878328\pi\)
−0.810963 + 0.585098i \(0.801056\pi\)
\(338\) 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 0.946250 0.323436i \(-0.104838\pi\)
0.516969 + 0.856004i \(0.327060\pi\)
\(348\) 0 0
\(349\) 197.712 1121.28i 0.0303246 0.171979i −0.965884 0.258975i \(-0.916615\pi\)
0.996209 + 0.0869952i \(0.0277265\pi\)
\(350\) 0 0
\(351\) 10669.8 + 2616.27i 1.62254 + 0.397852i
\(352\) 0 0
\(353\) 910.038 5161.08i 0.137214 0.778177i −0.836079 0.548609i \(-0.815158\pi\)
0.973293 0.229568i \(-0.0737314\pi\)
\(354\) 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 −0.841200 0.540725i \(-0.818150\pi\)
0.888881 + 0.458138i \(0.151483\pi\)
\(360\) 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 0.304295 0.952578i \(-0.401579\pi\)
−0.885266 + 0.465085i \(0.846024\pi\)
\(368\) 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 −0.943819 0.330462i \(-0.892795\pi\)
0.161549 + 0.986865i \(0.448351\pi\)
\(374\) 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 −0.328518 + 0.944498i \(0.606549\pi\)
−0.987195 + 0.159517i \(0.949006\pi\)
\(384\) 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 0.860796 0.508951i \(-0.169966\pi\)
−0.351743 + 0.936097i \(0.614411\pi\)
\(390\) 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 −0.514053 0.857759i \(-0.671856\pi\)
0.999867 + 0.0163035i \(0.00518981\pi\)
\(398\) 0 0
\(399\) 9229.44 + 2985.61i 1.15802 + 0.374605i
\(400\) 0 0
\(401\) 10580.7 + 3851.08i 1.31765 + 0.479585i 0.902704 0.430262i \(-0.141579\pi\)
0.414944 + 0.909847i \(0.363801\pi\)
\(402\) 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 0.861715 0.507393i \(-0.169391\pi\)
0.333966 + 0.942585i \(0.391613\pi\)
\(410\) 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 −0.999546 0.0301399i \(-0.990405\pi\)
0.928957 0.370187i \(-0.120706\pi\)
\(420\) 0 0
\(421\) 6215.42 + 5215.36i 0.719527 + 0.603755i 0.927255 0.374432i \(-0.122162\pi\)
−0.207727 + 0.978187i \(0.566607\pi\)
\(422\) 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 −0.809350 0.587327i \(-0.800180\pi\)
−0.242471 + 0.970159i \(0.577958\pi\)
\(440\) 0 0
\(441\) −8858.86 + 3971.75i −0.956577 + 0.428869i
\(442\) 0 0
\(443\) 6433.59 + 5398.43i 0.689998 + 0.578977i 0.918909 0.394470i \(-0.129072\pi\)
−0.228910 + 0.973447i \(0.573516\pi\)
\(444\) 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 0.996528 + 0.0832641i \(0.0265345\pi\)
−0.426155 + 0.904650i \(0.640132\pi\)
\(450\) 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 −0.529765 0.848144i \(-0.677720\pi\)
0.787899 0.615805i \(-0.211169\pi\)
\(458\) 0 0
\(459\) 8996.29 980.917i 0.914839 0.0997501i
\(460\) 0 0
\(461\) −1197.28 + 6790.14i −0.120961 + 0.686005i 0.862664 + 0.505778i \(0.168794\pi\)
−0.983625 + 0.180227i \(0.942317\pi\)
\(462\) 0 0
\(463\) −16976.9 6179.10i −1.70407 0.620231i −0.707792 0.706421i \(-0.750309\pi\)
−0.996279 + 0.0861899i \(0.972531\pi\)
\(464\) 0 0
\(465\) 1590.88 + 7437.12i 0.158657 + 0.741695i
\(466\) 0 0
\(467\) 4432.93 7678.07i 0.439254 0.760811i −0.558378 0.829587i \(-0.688576\pi\)
0.997632 + 0.0687761i \(0.0219094\pi\)
\(468\) 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 −0.884524 0.466495i \(-0.845516\pi\)
−0.377727 + 0.925917i \(0.623294\pi\)
\(480\) 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 −0.213556 + 0.976931i \(0.568505\pi\)
−0.999173 + 0.0406697i \(0.987051\pi\)
\(492\) 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 −0.891991 0.452054i \(-0.850691\pi\)
0.683585 0.729871i \(-0.260420\pi\)
\(500\) 0 0
\(501\) 4636.90 + 7399.24i 0.413496 + 0.659828i
\(502\) 0 0
\(503\) 6922.31 + 11989.8i 0.613620 + 1.06282i 0.990625 + 0.136609i \(0.0436205\pi\)
−0.377005 + 0.926211i \(0.623046\pi\)
\(504\) 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 −0.352464 0.935825i \(-0.614656\pi\)
−0.871540 + 0.490324i \(0.836878\pi\)
\(510\) 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 −0.982512 0.186198i \(-0.940384\pi\)
0.652508 + 0.757782i \(0.273717\pi\)
\(522\) 0 0
\(523\) 7321.97 + 12682.0i 0.612175 + 1.06032i 0.990873 + 0.134798i \(0.0430385\pi\)
−0.378698 + 0.925520i \(0.623628\pi\)
\(524\) 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 0.220879 0.975301i \(-0.429108\pi\)
0.796114 + 0.605146i \(0.206885\pi\)
\(548\) 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 0.777489 0.628897i \(-0.216493\pi\)
−0.933385 + 0.358877i \(0.883160\pi\)
\(558\) 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 0.949898 0.312559i \(-0.101186\pi\)
0.526755 + 0.850017i \(0.323408\pi\)
\(564\) 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 −0.603602 0.797286i \(-0.706268\pi\)
0.839888 0.542760i \(-0.182621\pi\)
\(570\) 0 0
\(571\) 8850.02 + 3221.15i 0.648620 + 0.236078i 0.645315 0.763916i \(-0.276726\pi\)
0.00330448 + 0.999995i \(0.498948\pi\)
\(572\) 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 0.528031 0.849225i \(-0.322930\pi\)
−0.999466 + 0.0326762i \(0.989597\pi\)
\(578\) 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 −0.424447 0.905453i \(-0.639532\pi\)
0.256868 + 0.966446i \(0.417309\pi\)
\(588\) 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 −0.652468 0.757816i \(-0.726267\pi\)
0.633003 + 0.774149i \(0.281822\pi\)
\(600\) 0 0
\(601\) 3783.87 1377.22i 0.256818 0.0934740i −0.210403 0.977615i \(-0.567478\pi\)
0.467221 + 0.884141i \(0.345255\pi\)
\(602\) 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 0.975707 0.219081i \(-0.0703060\pi\)
−0.991795 + 0.127842i \(0.959195\pi\)
\(608\) 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 −0.997422 0.0717601i \(-0.977138\pi\)
0.560857 + 0.827913i \(0.310472\pi\)
\(614\) 0 0
\(615\) 16617.0 15001.0i 1.08953 0.983577i
\(616\) 0 0
\(617\) 5742.14 + 2089.97i 0.374667 + 0.136368i 0.522489 0.852646i \(-0.325004\pi\)
−0.147821 + 0.989014i \(0.547226\pi\)
\(618\) 0 0
\(619\) 158.970 901.563i 0.0103224 0.0585410i −0.979211 0.202842i \(-0.934982\pi\)
0.989534 + 0.144301i \(0.0460933\pi\)
\(620\) 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 0.947607 0.319439i \(-0.103495\pi\)
−0.750446 + 0.660932i \(0.770161\pi\)
\(632\) 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 −0.0926108 0.995702i \(-0.529521\pi\)
0.569081 + 0.822281i \(0.307299\pi\)
\(642\) 0 0
\(643\) −1394.39 + 1170.03i −0.0855201 + 0.0717599i −0.684545 0.728970i \(-0.739999\pi\)
0.599025 + 0.800730i \(0.295555\pi\)
\(644\) 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 −0.0532495 0.998581i \(-0.516958\pi\)
0.974164 + 0.225842i \(0.0725134\pi\)
\(654\) 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 0.960328 0.278873i \(-0.0899608\pi\)
−0.107877 + 0.994164i \(0.534405\pi\)
\(660\) 0 0
\(661\) 387.406 + 2197.09i 0.0227963 + 0.129284i 0.994082 0.108632i \(-0.0346469\pi\)
−0.971286 + 0.237916i \(0.923536\pi\)
\(662\) 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 0.819264 + 0.573417i \(0.194382\pi\)
−0.965976 + 0.258631i \(0.916729\pi\)
\(674\) 0 0
\(675\) 3310.94 + 2214.58i 0.188797 + 0.126280i
\(676\) 0 0
\(677\) 666.714 3781.13i 0.0378492 0.214654i −0.960017 0.279941i \(-0.909685\pi\)
0.997867 + 0.0652871i \(0.0207963\pi\)
\(678\) 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 −0.626710 0.779252i \(-0.715599\pi\)
0.988207 + 0.153121i \(0.0489323\pi\)
\(684\) 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 0.467279 0.884110i \(-0.345234\pi\)
−0.789536 + 0.613704i \(0.789679\pi\)
\(692\) 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 −0.318977 0.947762i \(-0.603339\pi\)
0.364859 + 0.931063i \(0.381117\pi\)
\(710\) 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 0.893342 0.449377i \(-0.148354\pi\)
−0.835843 + 0.548969i \(0.815021\pi\)
\(720\) 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 −0.867776 0.496956i \(-0.834451\pi\)
0.985411 0.170189i \(-0.0544378\pi\)
\(728\) 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 0.762458 0.647037i \(-0.223992\pi\)
0.168169 + 0.985758i \(0.446214\pi\)
\(734\) 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 0.985231 0.171231i \(-0.0547746\pi\)
−0.640906 + 0.767619i \(0.721441\pi\)
\(740\) 0 0
\(741\) −13420.8 + 25320.0i −0.665352 + 1.25527i
\(742\) 0 0
\(743\) −3872.43 21961.6i −0.191206 1.08438i −0.917720 0.397229i \(-0.869972\pi\)
0.726514 0.687152i \(-0.241139\pi\)
\(744\) 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 −0.0732136 0.997316i \(-0.523325\pi\)
0.969451 + 0.245283i \(0.0788810\pi\)
\(752\) 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 −0.992785 0.119912i \(-0.961739\pi\)
−0.0543053 + 0.998524i \(0.517294\pi\)
\(762\) 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 −0.991628 0.129125i \(-0.958783\pi\)
0.887662 0.460495i \(-0.152328\pi\)
\(770\) 0 0
\(771\) 18384.9 665.865i 0.858776 0.0311032i
\(772\) 0 0
\(773\) 3017.93 + 5227.21i 0.140424 + 0.243221i 0.927656 0.373435i \(-0.121820\pi\)
−0.787233 + 0.616656i \(0.788487\pi\)
\(774\) 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