Properties

Label 336.4.h.b.239.13
Level $336$
Weight $4$
Character 336.239
Analytic conductor $19.825$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 336.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(19.8246417619\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 239.13
Character \(\chi\) \(=\) 336.239
Dual form 336.4.h.b.239.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.13969 - 5.06963i) q^{3} +14.6453i q^{5} -7.00000i q^{7} +(-24.4022 - 11.5556i) q^{9} +O(q^{10})\) \(q+(1.13969 - 5.06963i) q^{3} +14.6453i q^{5} -7.00000i q^{7} +(-24.4022 - 11.5556i) q^{9} +13.9027 q^{11} -45.4743 q^{13} +(74.2459 + 16.6910i) q^{15} +120.873i q^{17} +34.9253i q^{19} +(-35.4874 - 7.97783i) q^{21} -151.440 q^{23} -89.4834 q^{25} +(-86.3935 + 110.540i) q^{27} -224.601i q^{29} +44.2927i q^{31} +(15.8448 - 70.4815i) q^{33} +102.517 q^{35} -224.904 q^{37} +(-51.8266 + 230.538i) q^{39} +459.995i q^{41} +497.722i q^{43} +(169.235 - 357.377i) q^{45} +134.391 q^{47} -49.0000 q^{49} +(612.781 + 137.758i) q^{51} +282.447i q^{53} +203.608i q^{55} +(177.058 + 39.8040i) q^{57} +48.3707 q^{59} -343.594 q^{61} +(-80.8892 + 170.816i) q^{63} -665.982i q^{65} +678.793i q^{67} +(-172.594 + 767.743i) q^{69} +820.561 q^{71} +370.525 q^{73} +(-101.983 + 453.647i) q^{75} -97.3188i q^{77} -986.876i q^{79} +(461.936 + 563.965i) q^{81} -484.889 q^{83} -1770.22 q^{85} +(-1138.64 - 255.976i) q^{87} -980.557i q^{89} +318.320i q^{91} +(224.548 + 50.4800i) q^{93} -511.490 q^{95} -488.599 q^{97} +(-339.256 - 160.654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 136 q^{9} + O(q^{10}) \) \( 24 q - 136 q^{9} + 96 q^{13} - 112 q^{21} + 168 q^{25} - 320 q^{33} - 864 q^{37} + 592 q^{45} - 1176 q^{49} - 1120 q^{57} - 2304 q^{61} + 1168 q^{69} + 3312 q^{73} - 968 q^{81} - 5808 q^{85} + 1776 q^{93} + 6480 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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
\(3\) 1.13969 5.06963i 0.219333 0.975650i
\(4\) 0 0
\(5\) 14.6453i 1.30991i 0.755667 + 0.654956i \(0.227313\pi\)
−0.755667 + 0.654956i \(0.772687\pi\)
\(6\) 0 0
\(7\) 7.00000i 0.377964i
\(8\) 0 0
\(9\) −24.4022 11.5556i −0.903786 0.427985i
\(10\) 0 0
\(11\) 13.9027 0.381075 0.190537 0.981680i \(-0.438977\pi\)
0.190537 + 0.981680i \(0.438977\pi\)
\(12\) 0 0
\(13\) −45.4743 −0.970176 −0.485088 0.874465i \(-0.661213\pi\)
−0.485088 + 0.874465i \(0.661213\pi\)
\(14\) 0 0
\(15\) 74.2459 + 16.6910i 1.27801 + 0.287307i
\(16\) 0 0
\(17\) 120.873i 1.72447i 0.506506 + 0.862236i \(0.330937\pi\)
−0.506506 + 0.862236i \(0.669063\pi\)
\(18\) 0 0
\(19\) 34.9253i 0.421706i 0.977518 + 0.210853i \(0.0676242\pi\)
−0.977518 + 0.210853i \(0.932376\pi\)
\(20\) 0 0
\(21\) −35.4874 7.97783i −0.368761 0.0829002i
\(22\) 0 0
\(23\) −151.440 −1.37293 −0.686465 0.727163i \(-0.740838\pi\)
−0.686465 + 0.727163i \(0.740838\pi\)
\(24\) 0 0
\(25\) −89.4834 −0.715867
\(26\) 0 0
\(27\) −86.3935 + 110.540i −0.615794 + 0.787907i
\(28\) 0 0
\(29\) 224.601i 1.43819i −0.694913 0.719093i \(-0.744557\pi\)
0.694913 0.719093i \(-0.255443\pi\)
\(30\) 0 0
\(31\) 44.2927i 0.256620i 0.991734 + 0.128310i \(0.0409552\pi\)
−0.991734 + 0.128310i \(0.959045\pi\)
\(32\) 0 0
\(33\) 15.8448 70.4815i 0.0835824 0.371795i
\(34\) 0 0
\(35\) 102.517 0.495100
\(36\) 0 0
\(37\) −224.904 −0.999299 −0.499649 0.866228i \(-0.666538\pi\)
−0.499649 + 0.866228i \(0.666538\pi\)
\(38\) 0 0
\(39\) −51.8266 + 230.538i −0.212792 + 0.946553i
\(40\) 0 0
\(41\) 459.995i 1.75217i 0.482153 + 0.876087i \(0.339855\pi\)
−0.482153 + 0.876087i \(0.660145\pi\)
\(42\) 0 0
\(43\) 497.722i 1.76516i 0.470161 + 0.882581i \(0.344196\pi\)
−0.470161 + 0.882581i \(0.655804\pi\)
\(44\) 0 0
\(45\) 169.235 357.377i 0.560623 1.18388i
\(46\) 0 0
\(47\) 134.391 0.417085 0.208543 0.978013i \(-0.433128\pi\)
0.208543 + 0.978013i \(0.433128\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) 612.781 + 137.758i 1.68248 + 0.378234i
\(52\) 0 0
\(53\) 282.447i 0.732020i 0.930611 + 0.366010i \(0.119276\pi\)
−0.930611 + 0.366010i \(0.880724\pi\)
\(54\) 0 0
\(55\) 203.608i 0.499174i
\(56\) 0 0
\(57\) 177.058 + 39.8040i 0.411438 + 0.0924942i
\(58\) 0 0
\(59\) 48.3707 0.106734 0.0533672 0.998575i \(-0.483005\pi\)
0.0533672 + 0.998575i \(0.483005\pi\)
\(60\) 0 0
\(61\) −343.594 −0.721192 −0.360596 0.932722i \(-0.617427\pi\)
−0.360596 + 0.932722i \(0.617427\pi\)
\(62\) 0 0
\(63\) −80.8892 + 170.816i −0.161763 + 0.341599i
\(64\) 0 0
\(65\) 665.982i 1.27084i
\(66\) 0 0
\(67\) 678.793i 1.23773i 0.785498 + 0.618864i \(0.212407\pi\)
−0.785498 + 0.618864i \(0.787593\pi\)
\(68\) 0 0
\(69\) −172.594 + 767.743i −0.301129 + 1.33950i
\(70\) 0 0
\(71\) 820.561 1.37159 0.685794 0.727796i \(-0.259455\pi\)
0.685794 + 0.727796i \(0.259455\pi\)
\(72\) 0 0
\(73\) 370.525 0.594064 0.297032 0.954868i \(-0.404003\pi\)
0.297032 + 0.954868i \(0.404003\pi\)
\(74\) 0 0
\(75\) −101.983 + 453.647i −0.157014 + 0.698436i
\(76\) 0 0
\(77\) 97.3188i 0.144033i
\(78\) 0 0
\(79\) 986.876i 1.40547i −0.711451 0.702736i \(-0.751962\pi\)
0.711451 0.702736i \(-0.248038\pi\)
\(80\) 0 0
\(81\) 461.936 + 563.965i 0.633657 + 0.773614i
\(82\) 0 0
\(83\) −484.889 −0.641247 −0.320624 0.947207i \(-0.603892\pi\)
−0.320624 + 0.947207i \(0.603892\pi\)
\(84\) 0 0
\(85\) −1770.22 −2.25891
\(86\) 0 0
\(87\) −1138.64 255.976i −1.40317 0.315442i
\(88\) 0 0
\(89\) 980.557i 1.16785i −0.811807 0.583926i \(-0.801516\pi\)
0.811807 0.583926i \(-0.198484\pi\)
\(90\) 0 0
\(91\) 318.320i 0.366692i
\(92\) 0 0
\(93\) 224.548 + 50.4800i 0.250371 + 0.0562852i
\(94\) 0 0
\(95\) −511.490 −0.552398
\(96\) 0 0
\(97\) −488.599 −0.511440 −0.255720 0.966751i \(-0.582313\pi\)
−0.255720 + 0.966751i \(0.582313\pi\)
\(98\) 0 0
\(99\) −339.256 160.654i −0.344410 0.163094i
\(100\) 0 0
\(101\) 171.807i 0.169262i 0.996412 + 0.0846309i \(0.0269711\pi\)
−0.996412 + 0.0846309i \(0.973029\pi\)
\(102\) 0 0
\(103\) 1178.61i 1.12750i −0.825946 0.563749i \(-0.809358\pi\)
0.825946 0.563749i \(-0.190642\pi\)
\(104\) 0 0
\(105\) 116.837 519.722i 0.108592 0.483044i
\(106\) 0 0
\(107\) −401.039 −0.362336 −0.181168 0.983452i \(-0.557988\pi\)
−0.181168 + 0.983452i \(0.557988\pi\)
\(108\) 0 0
\(109\) −866.058 −0.761039 −0.380520 0.924773i \(-0.624255\pi\)
−0.380520 + 0.924773i \(0.624255\pi\)
\(110\) 0 0
\(111\) −256.321 + 1140.18i −0.219180 + 0.974966i
\(112\) 0 0
\(113\) 419.806i 0.349487i 0.984614 + 0.174744i \(0.0559096\pi\)
−0.984614 + 0.174744i \(0.944090\pi\)
\(114\) 0 0
\(115\) 2217.87i 1.79842i
\(116\) 0 0
\(117\) 1109.67 + 525.483i 0.876832 + 0.415221i
\(118\) 0 0
\(119\) 846.112 0.651789
\(120\) 0 0
\(121\) −1137.72 −0.854782
\(122\) 0 0
\(123\) 2332.00 + 524.251i 1.70951 + 0.384310i
\(124\) 0 0
\(125\) 520.150i 0.372189i
\(126\) 0 0
\(127\) 204.993i 0.143230i −0.997432 0.0716151i \(-0.977185\pi\)
0.997432 0.0716151i \(-0.0228153\pi\)
\(128\) 0 0
\(129\) 2523.27 + 567.249i 1.72218 + 0.387159i
\(130\) 0 0
\(131\) −44.9236 −0.0299618 −0.0149809 0.999888i \(-0.504769\pi\)
−0.0149809 + 0.999888i \(0.504769\pi\)
\(132\) 0 0
\(133\) 244.477 0.159390
\(134\) 0 0
\(135\) −1618.89 1265.25i −1.03209 0.806636i
\(136\) 0 0
\(137\) 729.133i 0.454701i −0.973813 0.227350i \(-0.926994\pi\)
0.973813 0.227350i \(-0.0730063\pi\)
\(138\) 0 0
\(139\) 1890.32i 1.15349i −0.816926 0.576743i \(-0.804323\pi\)
0.816926 0.576743i \(-0.195677\pi\)
\(140\) 0 0
\(141\) 153.165 681.314i 0.0914807 0.406929i
\(142\) 0 0
\(143\) −632.215 −0.369709
\(144\) 0 0
\(145\) 3289.34 1.88390
\(146\) 0 0
\(147\) −55.8448 + 248.412i −0.0313333 + 0.139379i
\(148\) 0 0
\(149\) 734.918i 0.404073i 0.979378 + 0.202036i \(0.0647559\pi\)
−0.979378 + 0.202036i \(0.935244\pi\)
\(150\) 0 0
\(151\) 990.698i 0.533920i −0.963708 0.266960i \(-0.913981\pi\)
0.963708 0.266960i \(-0.0860191\pi\)
\(152\) 0 0
\(153\) 1396.76 2949.57i 0.738049 1.55855i
\(154\) 0 0
\(155\) −648.678 −0.336149
\(156\) 0 0
\(157\) 1520.81 0.773080 0.386540 0.922273i \(-0.373670\pi\)
0.386540 + 0.922273i \(0.373670\pi\)
\(158\) 0 0
\(159\) 1431.90 + 321.902i 0.714195 + 0.160556i
\(160\) 0 0
\(161\) 1060.08i 0.518919i
\(162\) 0 0
\(163\) 3135.82i 1.50685i −0.657535 0.753424i \(-0.728401\pi\)
0.657535 0.753424i \(-0.271599\pi\)
\(164\) 0 0
\(165\) 1032.22 + 232.050i 0.487019 + 0.109485i
\(166\) 0 0
\(167\) 4075.35 1.88839 0.944193 0.329394i \(-0.106844\pi\)
0.944193 + 0.329394i \(0.106844\pi\)
\(168\) 0 0
\(169\) −129.091 −0.0587578
\(170\) 0 0
\(171\) 403.583 852.255i 0.180484 0.381132i
\(172\) 0 0
\(173\) 721.361i 0.317018i −0.987358 0.158509i \(-0.949331\pi\)
0.987358 0.158509i \(-0.0506687\pi\)
\(174\) 0 0
\(175\) 626.384i 0.270572i
\(176\) 0 0
\(177\) 55.1276 245.222i 0.0234104 0.104135i
\(178\) 0 0
\(179\) −4087.07 −1.70660 −0.853301 0.521418i \(-0.825403\pi\)
−0.853301 + 0.521418i \(0.825403\pi\)
\(180\) 0 0
\(181\) −3549.84 −1.45778 −0.728889 0.684632i \(-0.759963\pi\)
−0.728889 + 0.684632i \(0.759963\pi\)
\(182\) 0 0
\(183\) −391.591 + 1741.89i −0.158182 + 0.703631i
\(184\) 0 0
\(185\) 3293.78i 1.30899i
\(186\) 0 0
\(187\) 1680.46i 0.657152i
\(188\) 0 0
\(189\) 773.782 + 604.755i 0.297801 + 0.232748i
\(190\) 0 0
\(191\) −1269.54 −0.480945 −0.240473 0.970656i \(-0.577302\pi\)
−0.240473 + 0.970656i \(0.577302\pi\)
\(192\) 0 0
\(193\) 1979.22 0.738172 0.369086 0.929395i \(-0.379671\pi\)
0.369086 + 0.929395i \(0.379671\pi\)
\(194\) 0 0
\(195\) −3376.28 759.013i −1.23990 0.278739i
\(196\) 0 0
\(197\) 4655.85i 1.68384i 0.539606 + 0.841918i \(0.318573\pi\)
−0.539606 + 0.841918i \(0.681427\pi\)
\(198\) 0 0
\(199\) 166.378i 0.0592676i −0.999561 0.0296338i \(-0.990566\pi\)
0.999561 0.0296338i \(-0.00943411\pi\)
\(200\) 0 0
\(201\) 3441.23 + 773.613i 1.20759 + 0.271475i
\(202\) 0 0
\(203\) −1572.21 −0.543584
\(204\) 0 0
\(205\) −6736.74 −2.29519
\(206\) 0 0
\(207\) 3695.47 + 1749.98i 1.24083 + 0.587594i
\(208\) 0 0
\(209\) 485.556i 0.160701i
\(210\) 0 0
\(211\) 1923.89i 0.627707i −0.949471 0.313853i \(-0.898380\pi\)
0.949471 0.313853i \(-0.101620\pi\)
\(212\) 0 0
\(213\) 935.185 4159.94i 0.300835 1.33819i
\(214\) 0 0
\(215\) −7289.27 −2.31220
\(216\) 0 0
\(217\) 310.049 0.0969931
\(218\) 0 0
\(219\) 422.283 1878.42i 0.130298 0.579598i
\(220\) 0 0
\(221\) 5496.62i 1.67304i
\(222\) 0 0
\(223\) 3286.15i 0.986803i −0.869802 0.493402i \(-0.835753\pi\)
0.869802 0.493402i \(-0.164247\pi\)
\(224\) 0 0
\(225\) 2183.59 + 1034.03i 0.646990 + 0.306380i
\(226\) 0 0
\(227\) 4610.89 1.34817 0.674087 0.738652i \(-0.264537\pi\)
0.674087 + 0.738652i \(0.264537\pi\)
\(228\) 0 0
\(229\) −5100.93 −1.47196 −0.735980 0.677003i \(-0.763278\pi\)
−0.735980 + 0.677003i \(0.763278\pi\)
\(230\) 0 0
\(231\) −493.370 110.913i −0.140525 0.0315912i
\(232\) 0 0
\(233\) 6943.92i 1.95241i 0.216853 + 0.976204i \(0.430421\pi\)
−0.216853 + 0.976204i \(0.569579\pi\)
\(234\) 0 0
\(235\) 1968.20i 0.546345i
\(236\) 0 0
\(237\) −5003.09 1124.73i −1.37125 0.308267i
\(238\) 0 0
\(239\) 3416.16 0.924572 0.462286 0.886731i \(-0.347029\pi\)
0.462286 + 0.886731i \(0.347029\pi\)
\(240\) 0 0
\(241\) 3724.80 0.995584 0.497792 0.867296i \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(242\) 0 0
\(243\) 3385.55 1699.10i 0.893759 0.448548i
\(244\) 0 0
\(245\) 717.617i 0.187130i
\(246\) 0 0
\(247\) 1588.20i 0.409129i
\(248\) 0 0
\(249\) −552.624 + 2458.21i −0.140647 + 0.625633i
\(250\) 0 0
\(251\) 4455.29 1.12038 0.560189 0.828365i \(-0.310728\pi\)
0.560189 + 0.828365i \(0.310728\pi\)
\(252\) 0 0
\(253\) −2105.42 −0.523188
\(254\) 0 0
\(255\) −2017.50 + 8974.34i −0.495453 + 2.20390i
\(256\) 0 0
\(257\) 1067.17i 0.259020i 0.991578 + 0.129510i \(0.0413405\pi\)
−0.991578 + 0.129510i \(0.958660\pi\)
\(258\) 0 0
\(259\) 1574.33i 0.377699i
\(260\) 0 0
\(261\) −2595.40 + 5480.77i −0.615523 + 1.29981i
\(262\) 0 0
\(263\) 2881.25 0.675533 0.337767 0.941230i \(-0.390329\pi\)
0.337767 + 0.941230i \(0.390329\pi\)
\(264\) 0 0
\(265\) −4136.51 −0.958881
\(266\) 0 0
\(267\) −4971.05 1117.53i −1.13941 0.256149i
\(268\) 0 0
\(269\) 5561.17i 1.26049i 0.776398 + 0.630243i \(0.217045\pi\)
−0.776398 + 0.630243i \(0.782955\pi\)
\(270\) 0 0
\(271\) 5418.65i 1.21461i 0.794468 + 0.607306i \(0.207750\pi\)
−0.794468 + 0.607306i \(0.792250\pi\)
\(272\) 0 0
\(273\) 1613.76 + 362.786i 0.357763 + 0.0804278i
\(274\) 0 0
\(275\) −1244.06 −0.272799
\(276\) 0 0
\(277\) 3291.26 0.713908 0.356954 0.934122i \(-0.383815\pi\)
0.356954 + 0.934122i \(0.383815\pi\)
\(278\) 0 0
\(279\) 511.829 1080.84i 0.109829 0.231929i
\(280\) 0 0
\(281\) 6394.15i 1.35745i −0.734393 0.678724i \(-0.762533\pi\)
0.734393 0.678724i \(-0.237467\pi\)
\(282\) 0 0
\(283\) 9183.66i 1.92902i 0.264050 + 0.964509i \(0.414942\pi\)
−0.264050 + 0.964509i \(0.585058\pi\)
\(284\) 0 0
\(285\) −582.940 + 2593.06i −0.121159 + 0.538947i
\(286\) 0 0
\(287\) 3219.96 0.662260
\(288\) 0 0
\(289\) −9697.30 −1.97381
\(290\) 0 0
\(291\) −556.851 + 2477.01i −0.112176 + 0.498987i
\(292\) 0 0
\(293\) 3914.97i 0.780598i −0.920688 0.390299i \(-0.872372\pi\)
0.920688 0.390299i \(-0.127628\pi\)
\(294\) 0 0
\(295\) 708.402i 0.139813i
\(296\) 0 0
\(297\) −1201.10 + 1536.81i −0.234663 + 0.300251i
\(298\) 0 0
\(299\) 6886.61 1.33198
\(300\) 0 0
\(301\) 3484.06 0.667168
\(302\) 0 0
\(303\) 870.998 + 195.807i 0.165140 + 0.0371248i
\(304\) 0 0
\(305\) 5032.02i 0.944698i
\(306\) 0 0
\(307\) 1579.23i 0.293588i 0.989167 + 0.146794i \(0.0468955\pi\)
−0.989167 + 0.146794i \(0.953104\pi\)
\(308\) 0 0
\(309\) −5975.14 1343.26i −1.10004 0.247298i
\(310\) 0 0
\(311\) 515.431 0.0939788 0.0469894 0.998895i \(-0.485037\pi\)
0.0469894 + 0.998895i \(0.485037\pi\)
\(312\) 0 0
\(313\) 10135.1 1.83026 0.915129 0.403161i \(-0.132089\pi\)
0.915129 + 0.403161i \(0.132089\pi\)
\(314\) 0 0
\(315\) −2501.64 1184.64i −0.447464 0.211895i
\(316\) 0 0
\(317\) 7471.40i 1.32377i −0.749604 0.661886i \(-0.769756\pi\)
0.749604 0.661886i \(-0.230244\pi\)
\(318\) 0 0
\(319\) 3122.56i 0.548056i
\(320\) 0 0
\(321\) −457.060 + 2033.12i −0.0794723 + 0.353513i
\(322\) 0 0
\(323\) −4221.53 −0.727221
\(324\) 0 0
\(325\) 4069.19 0.694517
\(326\) 0 0
\(327\) −987.037 + 4390.59i −0.166921 + 0.742508i
\(328\) 0 0
\(329\) 940.740i 0.157643i
\(330\) 0 0
\(331\) 6725.92i 1.11689i 0.829542 + 0.558444i \(0.188601\pi\)
−0.829542 + 0.558444i \(0.811399\pi\)
\(332\) 0 0
\(333\) 5488.16 + 2598.90i 0.903152 + 0.427685i
\(334\) 0 0
\(335\) −9941.09 −1.62131
\(336\) 0 0
\(337\) −75.0546 −0.0121320 −0.00606600 0.999982i \(-0.501931\pi\)
−0.00606600 + 0.999982i \(0.501931\pi\)
\(338\) 0 0
\(339\) 2128.26 + 478.449i 0.340977 + 0.0766542i
\(340\) 0 0
\(341\) 615.788i 0.0977912i
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) −11243.8 2527.69i −1.75462 0.394453i
\(346\) 0 0
\(347\) −4435.86 −0.686252 −0.343126 0.939289i \(-0.611486\pi\)
−0.343126 + 0.939289i \(0.611486\pi\)
\(348\) 0 0
\(349\) 2611.13 0.400489 0.200245 0.979746i \(-0.435826\pi\)
0.200245 + 0.979746i \(0.435826\pi\)
\(350\) 0 0
\(351\) 3928.68 5026.74i 0.597429 0.764409i
\(352\) 0 0
\(353\) 916.862i 0.138243i 0.997608 + 0.0691213i \(0.0220196\pi\)
−0.997608 + 0.0691213i \(0.977980\pi\)
\(354\) 0 0
\(355\) 12017.3i 1.79666i
\(356\) 0 0
\(357\) 964.305 4289.47i 0.142959 0.635918i
\(358\) 0 0
\(359\) −3916.49 −0.575778 −0.287889 0.957664i \(-0.592953\pi\)
−0.287889 + 0.957664i \(0.592953\pi\)
\(360\) 0 0
\(361\) 5639.22 0.822164
\(362\) 0 0
\(363\) −1296.64 + 5767.79i −0.187482 + 0.833968i
\(364\) 0 0
\(365\) 5426.43i 0.778171i
\(366\) 0 0
\(367\) 9856.78i 1.40196i 0.713180 + 0.700980i \(0.247254\pi\)
−0.713180 + 0.700980i \(0.752746\pi\)
\(368\) 0 0
\(369\) 5315.52 11224.9i 0.749905 1.58359i
\(370\) 0 0
\(371\) 1977.13 0.276678
\(372\) 0 0
\(373\) −11058.4 −1.53508 −0.767538 0.641003i \(-0.778519\pi\)
−0.767538 + 0.641003i \(0.778519\pi\)
\(374\) 0 0
\(375\) 2636.97 + 592.809i 0.363126 + 0.0816335i
\(376\) 0 0
\(377\) 10213.6i 1.39529i
\(378\) 0 0
\(379\) 3764.44i 0.510202i −0.966914 0.255101i \(-0.917891\pi\)
0.966914 0.255101i \(-0.0821087\pi\)
\(380\) 0 0
\(381\) −1039.24 233.629i −0.139742 0.0314152i
\(382\) 0 0
\(383\) 10258.1 1.36858 0.684290 0.729210i \(-0.260112\pi\)
0.684290 + 0.729210i \(0.260112\pi\)
\(384\) 0 0
\(385\) 1425.26 0.188670
\(386\) 0 0
\(387\) 5751.48 12145.5i 0.755463 1.59533i
\(388\) 0 0
\(389\) 11610.0i 1.51324i 0.653857 + 0.756618i \(0.273150\pi\)
−0.653857 + 0.756618i \(0.726850\pi\)
\(390\) 0 0
\(391\) 18305.0i 2.36758i
\(392\) 0 0
\(393\) −51.1989 + 227.746i −0.00657162 + 0.0292322i
\(394\) 0 0
\(395\) 14453.1 1.84104
\(396\) 0 0
\(397\) 7004.43 0.885497 0.442749 0.896646i \(-0.354003\pi\)
0.442749 + 0.896646i \(0.354003\pi\)
\(398\) 0 0
\(399\) 278.628 1239.41i 0.0349595 0.155509i
\(400\) 0 0
\(401\) 2223.31i 0.276875i 0.990371 + 0.138438i \(0.0442080\pi\)
−0.990371 + 0.138438i \(0.955792\pi\)
\(402\) 0 0
\(403\) 2014.18i 0.248966i
\(404\) 0 0
\(405\) −8259.40 + 6765.17i −1.01337 + 0.830035i
\(406\) 0 0
\(407\) −3126.78 −0.380807
\(408\) 0 0
\(409\) −2310.73 −0.279359 −0.139680 0.990197i \(-0.544607\pi\)
−0.139680 + 0.990197i \(0.544607\pi\)
\(410\) 0 0
\(411\) −3696.43 830.985i −0.443629 0.0997311i
\(412\) 0 0
\(413\) 338.595i 0.0403418i
\(414\) 0 0
\(415\) 7101.33i 0.839977i
\(416\) 0 0
\(417\) −9583.20 2154.37i −1.12540 0.252998i
\(418\) 0 0
\(419\) −9808.83 −1.14366 −0.571829 0.820373i \(-0.693766\pi\)
−0.571829 + 0.820373i \(0.693766\pi\)
\(420\) 0 0
\(421\) −2381.84 −0.275733 −0.137867 0.990451i \(-0.544024\pi\)
−0.137867 + 0.990451i \(0.544024\pi\)
\(422\) 0 0
\(423\) −3279.45 1552.97i −0.376956 0.178506i
\(424\) 0 0
\(425\) 10816.1i 1.23449i
\(426\) 0 0
\(427\) 2405.16i 0.272585i
\(428\) 0 0
\(429\) −720.529 + 3205.09i −0.0810896 + 0.360707i
\(430\) 0 0
\(431\) −8717.18 −0.974227 −0.487114 0.873339i \(-0.661950\pi\)
−0.487114 + 0.873339i \(0.661950\pi\)
\(432\) 0 0
\(433\) 14091.6 1.56397 0.781983 0.623300i \(-0.214209\pi\)
0.781983 + 0.623300i \(0.214209\pi\)
\(434\) 0 0
\(435\) 3748.83 16675.7i 0.413201 1.83802i
\(436\) 0 0
\(437\) 5289.08i 0.578973i
\(438\) 0 0
\(439\) 6819.29i 0.741383i −0.928756 0.370691i \(-0.879121\pi\)
0.928756 0.370691i \(-0.120879\pi\)
\(440\) 0 0
\(441\) 1195.71 + 566.224i 0.129112 + 0.0611407i
\(442\) 0 0
\(443\) 9565.27 1.02587 0.512934 0.858428i \(-0.328558\pi\)
0.512934 + 0.858428i \(0.328558\pi\)
\(444\) 0 0
\(445\) 14360.5 1.52978
\(446\) 0 0
\(447\) 3725.76 + 837.578i 0.394233 + 0.0886266i
\(448\) 0 0
\(449\) 752.859i 0.0791306i −0.999217 0.0395653i \(-0.987403\pi\)
0.999217 0.0395653i \(-0.0125973\pi\)
\(450\) 0 0
\(451\) 6395.17i 0.667709i
\(452\) 0 0
\(453\) −5022.47 1129.09i −0.520919 0.117106i
\(454\) 0 0
\(455\) −4661.87 −0.480334
\(456\) 0 0
\(457\) −14222.2 −1.45577 −0.727884 0.685700i \(-0.759496\pi\)
−0.727884 + 0.685700i \(0.759496\pi\)
\(458\) 0 0
\(459\) −13361.3 10442.7i −1.35872 1.06192i
\(460\) 0 0
\(461\) 12808.3i 1.29401i 0.762484 + 0.647007i \(0.223980\pi\)
−0.762484 + 0.647007i \(0.776020\pi\)
\(462\) 0 0
\(463\) 1416.85i 0.142217i −0.997469 0.0711086i \(-0.977346\pi\)
0.997469 0.0711086i \(-0.0226537\pi\)
\(464\) 0 0
\(465\) −739.292 + 3288.56i −0.0737287 + 0.327964i
\(466\) 0 0
\(467\) −12720.2 −1.26043 −0.630215 0.776421i \(-0.717033\pi\)
−0.630215 + 0.776421i \(0.717033\pi\)
\(468\) 0 0
\(469\) 4751.55 0.467817
\(470\) 0 0
\(471\) 1733.25 7709.92i 0.169562 0.754256i
\(472\) 0 0
\(473\) 6919.68i 0.672658i
\(474\) 0 0
\(475\) 3125.24i 0.301886i
\(476\) 0 0
\(477\) 3263.84 6892.33i 0.313294 0.661589i
\(478\) 0 0
\(479\) −16314.1 −1.55618 −0.778092 0.628150i \(-0.783812\pi\)
−0.778092 + 0.628150i \(0.783812\pi\)
\(480\) 0 0
\(481\) 10227.4 0.969496
\(482\) 0 0
\(483\) 5374.20 + 1208.16i 0.506283 + 0.113816i
\(484\) 0 0
\(485\) 7155.65i 0.669941i
\(486\) 0 0
\(487\) 4903.33i 0.456244i 0.973632 + 0.228122i \(0.0732586\pi\)
−0.973632 + 0.228122i \(0.926741\pi\)
\(488\) 0 0
\(489\) −15897.4 3573.86i −1.47016 0.330502i
\(490\) 0 0
\(491\) −1213.14 −0.111503 −0.0557517 0.998445i \(-0.517756\pi\)
−0.0557517 + 0.998445i \(0.517756\pi\)
\(492\) 0 0
\(493\) 27148.3 2.48011
\(494\) 0 0
\(495\) 2352.82 4968.50i 0.213639 0.451146i
\(496\) 0 0
\(497\) 5743.93i 0.518411i
\(498\) 0 0
\(499\) 8093.93i 0.726121i −0.931766 0.363060i \(-0.881732\pi\)
0.931766 0.363060i \(-0.118268\pi\)
\(500\) 0 0
\(501\) 4644.64 20660.5i 0.414186 1.84240i
\(502\) 0 0
\(503\) 3991.77 0.353846 0.176923 0.984225i \(-0.443386\pi\)
0.176923 + 0.984225i \(0.443386\pi\)
\(504\) 0 0
\(505\) −2516.16 −0.221718
\(506\) 0 0
\(507\) −147.123 + 654.442i −0.0128875 + 0.0573270i
\(508\) 0 0
\(509\) 7309.19i 0.636491i 0.948008 + 0.318246i \(0.103094\pi\)
−0.948008 + 0.318246i \(0.896906\pi\)
\(510\) 0 0
\(511\) 2593.67i 0.224535i
\(512\) 0 0
\(513\) −3860.66 3017.32i −0.332265 0.259684i
\(514\) 0 0
\(515\) 17261.1 1.47692
\(516\) 0 0
\(517\) 1868.40 0.158941
\(518\) 0 0
\(519\) −3657.03 822.128i −0.309299 0.0695326i
\(520\) 0 0
\(521\) 1657.13i 0.139348i 0.997570 + 0.0696739i \(0.0221959\pi\)
−0.997570 + 0.0696739i \(0.977804\pi\)
\(522\) 0 0
\(523\) 5621.88i 0.470034i 0.971991 + 0.235017i \(0.0755145\pi\)
−0.971991 + 0.235017i \(0.924485\pi\)
\(524\) 0 0
\(525\) 3175.53 + 713.883i 0.263984 + 0.0593455i
\(526\) 0 0
\(527\) −5353.80 −0.442533
\(528\) 0 0
\(529\) 10767.0 0.884936
\(530\) 0 0
\(531\) −1180.35 558.953i −0.0964651 0.0456808i
\(532\) 0 0
\(533\) 20917.9i 1.69992i
\(534\) 0 0
\(535\) 5873.32i 0.474628i
\(536\) 0 0
\(537\) −4657.99 + 20719.9i −0.374315 + 1.66505i
\(538\) 0 0
\(539\) −681.232 −0.0544392
\(540\) 0 0
\(541\) 16776.8 1.33326 0.666629 0.745390i \(-0.267737\pi\)
0.666629 + 0.745390i \(0.267737\pi\)
\(542\) 0 0
\(543\) −4045.72 + 17996.4i −0.319739 + 1.42228i
\(544\) 0 0
\(545\) 12683.6i 0.996894i
\(546\) 0 0
\(547\) 19586.5i 1.53100i 0.643437 + 0.765499i \(0.277508\pi\)
−0.643437 + 0.765499i \(0.722492\pi\)
\(548\) 0 0
\(549\) 8384.46 + 3970.44i 0.651803 + 0.308660i
\(550\) 0 0
\(551\) 7844.27 0.606492
\(552\) 0 0
\(553\) −6908.13 −0.531218
\(554\) 0 0
\(555\) −16698.2 3753.89i −1.27712 0.287106i
\(556\) 0 0
\(557\) 13365.8i 1.01674i −0.861138 0.508372i \(-0.830248\pi\)
0.861138 0.508372i \(-0.169752\pi\)
\(558\) 0 0
\(559\) 22633.6i 1.71252i
\(560\) 0 0
\(561\) 8519.31 + 1915.20i 0.641151 + 0.144135i
\(562\) 0 0
\(563\) −10979.2 −0.821877 −0.410939 0.911663i \(-0.634799\pi\)
−0.410939 + 0.911663i \(0.634799\pi\)
\(564\) 0 0
\(565\) −6148.17 −0.457797
\(566\) 0 0
\(567\) 3947.75 3233.55i 0.292399 0.239500i
\(568\) 0 0
\(569\) 24903.3i 1.83480i 0.397969 + 0.917399i \(0.369715\pi\)
−0.397969 + 0.917399i \(0.630285\pi\)
\(570\) 0 0
\(571\) 3896.72i 0.285591i −0.989752 0.142796i \(-0.954391\pi\)
0.989752 0.142796i \(-0.0456091\pi\)
\(572\) 0 0
\(573\) −1446.88 + 6436.09i −0.105487 + 0.469234i
\(574\) 0 0
\(575\) 13551.3 0.982835
\(576\) 0 0
\(577\) 11824.8 0.853161 0.426581 0.904450i \(-0.359718\pi\)
0.426581 + 0.904450i \(0.359718\pi\)
\(578\) 0 0
\(579\) 2255.69 10033.9i 0.161906 0.720198i
\(580\) 0 0
\(581\) 3394.23i 0.242369i
\(582\) 0 0
\(583\) 3926.77i 0.278954i
\(584\) 0 0
\(585\) −7695.82 + 16251.4i −0.543903 + 1.14857i
\(586\) 0 0
\(587\) 5957.49 0.418896 0.209448 0.977820i \(-0.432833\pi\)
0.209448 + 0.977820i \(0.432833\pi\)
\(588\) 0 0
\(589\) −1546.94 −0.108218
\(590\) 0 0
\(591\) 23603.4 + 5306.22i 1.64283 + 0.369321i
\(592\) 0 0
\(593\) 11547.6i 0.799671i −0.916587 0.399836i \(-0.869067\pi\)
0.916587 0.399836i \(-0.130933\pi\)
\(594\) 0 0
\(595\) 12391.5i 0.853786i
\(596\) 0 0
\(597\) −843.476 189.620i −0.0578244 0.0129994i
\(598\) 0 0
\(599\) 27338.0 1.86477 0.932386 0.361464i \(-0.117723\pi\)
0.932386 + 0.361464i \(0.117723\pi\)
\(600\) 0 0
\(601\) −15844.1 −1.07536 −0.537682 0.843148i \(-0.680700\pi\)
−0.537682 + 0.843148i \(0.680700\pi\)
\(602\) 0 0
\(603\) 7843.86 16564.1i 0.529729 1.11864i
\(604\) 0 0
\(605\) 16662.1i 1.11969i
\(606\) 0 0
\(607\) 575.804i 0.0385027i −0.999815 0.0192514i \(-0.993872\pi\)
0.999815 0.0192514i \(-0.00612828\pi\)
\(608\) 0 0
\(609\) −1791.83 + 7970.51i −0.119226 + 0.530347i
\(610\) 0 0
\(611\) −6111.35 −0.404646
\(612\) 0 0
\(613\) 9646.06 0.635564 0.317782 0.948164i \(-0.397062\pi\)
0.317782 + 0.948164i \(0.397062\pi\)
\(614\) 0 0
\(615\) −7677.79 + 34152.8i −0.503412 + 2.23930i
\(616\) 0 0
\(617\) 18960.4i 1.23714i 0.785728 + 0.618572i \(0.212288\pi\)
−0.785728 + 0.618572i \(0.787712\pi\)
\(618\) 0 0
\(619\) 26238.0i 1.70370i −0.523783 0.851852i \(-0.675480\pi\)
0.523783 0.851852i \(-0.324520\pi\)
\(620\) 0 0
\(621\) 13083.4 16740.2i 0.845442 1.08174i
\(622\) 0 0
\(623\) −6863.90 −0.441406
\(624\) 0 0
\(625\) −18803.1 −1.20340
\(626\) 0 0
\(627\) 2461.59 + 553.383i 0.156788 + 0.0352472i
\(628\) 0 0
\(629\) 27184.9i 1.72326i
\(630\) 0 0
\(631\) 31385.8i 1.98011i 0.140680 + 0.990055i \(0.455071\pi\)
−0.140680 + 0.990055i \(0.544929\pi\)
\(632\) 0 0
\(633\) −9753.41 2192.64i −0.612422 0.137677i
\(634\) 0 0
\(635\) 3002.18 0.187619
\(636\) 0 0
\(637\) 2228.24 0.138597
\(638\) 0 0
\(639\) −20023.5 9482.08i −1.23962 0.587019i
\(640\) 0 0
\(641\) 6203.66i 0.382262i 0.981565 + 0.191131i \(0.0612155\pi\)
−0.981565 + 0.191131i \(0.938785\pi\)
\(642\) 0 0
\(643\) 1900.46i 0.116558i 0.998300 + 0.0582791i \(0.0185613\pi\)
−0.998300 + 0.0582791i \(0.981439\pi\)
\(644\) 0 0
\(645\) −8307.51 + 36953.9i −0.507144 + 2.25590i
\(646\) 0 0
\(647\) 5220.82 0.317236 0.158618 0.987340i \(-0.449296\pi\)
0.158618 + 0.987340i \(0.449296\pi\)
\(648\) 0 0
\(649\) 672.484 0.0406738
\(650\) 0 0
\(651\) 353.360 1571.83i 0.0212738 0.0946313i
\(652\) 0 0
\(653\) 5266.00i 0.315581i 0.987473 + 0.157790i \(0.0504370\pi\)
−0.987473 + 0.157790i \(0.949563\pi\)
\(654\) 0 0
\(655\) 657.917i 0.0392473i
\(656\) 0 0
\(657\) −9041.63 4281.64i −0.536906 0.254251i
\(658\) 0 0
\(659\) −19994.5 −1.18191 −0.590954 0.806706i \(-0.701248\pi\)
−0.590954 + 0.806706i \(0.701248\pi\)
\(660\) 0 0
\(661\) −16431.9 −0.966911 −0.483456 0.875369i \(-0.660619\pi\)
−0.483456 + 0.875369i \(0.660619\pi\)
\(662\) 0 0
\(663\) −27865.8 6264.44i −1.63230 0.366954i
\(664\) 0 0
\(665\) 3580.43i 0.208787i
\(666\) 0 0
\(667\) 34013.6i 1.97453i
\(668\) 0 0
\(669\) −16659.6 3745.20i −0.962775 0.216439i
\(670\) 0 0
\(671\) −4776.88 −0.274828
\(672\) 0 0
\(673\) −8167.51 −0.467807 −0.233904 0.972260i \(-0.575150\pi\)
−0.233904 + 0.972260i \(0.575150\pi\)
\(674\) 0 0
\(675\) 7730.78 9891.52i 0.440827 0.564037i
\(676\) 0 0
\(677\) 34191.6i 1.94105i 0.241000 + 0.970525i \(0.422524\pi\)
−0.241000 + 0.970525i \(0.577476\pi\)
\(678\) 0 0
\(679\) 3420.19i 0.193306i
\(680\) 0 0
\(681\) 5254.99 23375.5i 0.295700 1.31535i
\(682\) 0 0
\(683\) −22.6262 −0.00126760 −0.000633799 1.00000i \(-0.500202\pi\)
−0.000633799 1.00000i \(0.500202\pi\)
\(684\) 0 0
\(685\) 10678.3 0.595618
\(686\) 0 0
\(687\) −5813.47 + 25859.8i −0.322850 + 1.43612i
\(688\) 0 0
\(689\) 12844.1i 0.710188i
\(690\) 0 0
\(691\) 27943.6i 1.53839i 0.639016 + 0.769193i \(0.279342\pi\)
−0.639016 + 0.769193i \(0.720658\pi\)
\(692\) 0 0
\(693\) −1124.58 + 2374.80i −0.0616438 + 0.130175i
\(694\) 0 0
\(695\) 27684.2 1.51096
\(696\) 0 0
\(697\) −55601.0 −3.02158
\(698\) 0 0
\(699\) 35203.1 + 7913.91i 1.90487 + 0.428228i
\(700\) 0 0
\(701\) 4454.40i 0.240001i 0.992774 + 0.120000i \(0.0382896\pi\)
−0.992774 + 0.120000i \(0.961710\pi\)
\(702\) 0 0
\(703\) 7854.86i 0.421410i
\(704\) 0 0
\(705\) 9978.02 + 2243.13i 0.533041 + 0.119832i
\(706\) 0 0
\(707\) 1202.65 0.0639750
\(708\) 0 0
\(709\) 1733.18 0.0918067 0.0459034 0.998946i \(-0.485383\pi\)
0.0459034 + 0.998946i \(0.485383\pi\)
\(710\) 0 0
\(711\) −11403.9 + 24082.0i −0.601521 + 1.27025i
\(712\) 0 0
\(713\) 6707.68i 0.352321i
\(714\) 0 0
\(715\) 9258.94i 0.484287i
\(716\) 0 0
\(717\) 3893.36 17318.6i 0.202789 0.902059i
\(718\) 0 0
\(719\) 5157.90 0.267534 0.133767 0.991013i \(-0.457293\pi\)
0.133767 + 0.991013i \(0.457293\pi\)
\(720\) 0 0
\(721\) −8250.30 −0.426154
\(722\) 0 0
\(723\) 4245.12 18883.4i 0.218365 0.971341i
\(724\) 0 0
\(725\) 20098.1i 1.02955i
\(726\) 0 0
\(727\) 6924.59i 0.353259i 0.984277 + 0.176629i \(0.0565194\pi\)
−0.984277 + 0.176629i \(0.943481\pi\)
\(728\) 0 0
\(729\) −4755.32 19099.9i −0.241595 0.970377i
\(730\) 0 0
\(731\) −60161.2 −3.04397
\(732\) 0 0
\(733\) −17794.3 −0.896655 −0.448327 0.893869i \(-0.647980\pi\)
−0.448327 + 0.893869i \(0.647980\pi\)
\(734\) 0 0
\(735\) −3638.05 817.861i −0.182574 0.0410439i
\(736\) 0 0
\(737\) 9437.05i 0.471667i
\(738\) 0 0
\(739\) 619.992i 0.0308617i −0.999881 0.0154308i \(-0.995088\pi\)
0.999881 0.0154308i \(-0.00491198\pi\)
\(740\) 0 0
\(741\) −8051.60 1810.06i −0.399167 0.0897357i
\(742\) 0 0
\(743\) −9464.45 −0.467318 −0.233659 0.972319i \(-0.575070\pi\)
−0.233659 + 0.972319i \(0.575070\pi\)
\(744\) 0 0
\(745\) −10763.1 −0.529299
\(746\) 0 0
\(747\) 11832.4 + 5603.19i 0.579550 + 0.274444i
\(748\) 0 0
\(749\) 2807.27i 0.136950i
\(750\) 0 0
\(751\) 19159.6i 0.930953i −0.885060 0.465476i \(-0.845883\pi\)
0.885060 0.465476i \(-0.154117\pi\)
\(752\) 0 0
\(753\) 5077.64 22586.6i 0.245736 1.09310i
\(754\) 0 0
\(755\) 14509.0 0.699387
\(756\) 0 0
\(757\) −14913.4 −0.716031 −0.358016 0.933716i \(-0.616547\pi\)
−0.358016 + 0.933716i \(0.616547\pi\)
\(758\) 0 0
\(759\) −2399.53 + 10673.7i −0.114753 + 0.510449i
\(760\) 0 0
\(761\) 12228.8i 0.582515i −0.956645 0.291258i \(-0.905926\pi\)
0.956645 0.291258i \(-0.0940737\pi\)
\(762\) 0 0
\(763\) 6062.40i 0.287646i
\(764\) 0 0
\(765\) 43197.2 + 20455.9i 2.04157 + 0.966778i
\(766\) 0 0
\(767\) −2199.62 −0.103551
\(768\) 0 0
\(769\) 16296.5 0.764197 0.382099 0.924122i \(-0.375202\pi\)
0.382099 + 0.924122i \(0.375202\pi\)
\(770\) 0 0
\(771\) 5410.15 + 1216.24i 0.252713 + 0.0568118i
\(772\) 0 0
\(773\) 19766.2i 0.919714i 0.887993 + 0.459857i \(0.152099\pi\)
−0.887993 + 0.459857i \(0.847901\pi\)
\(774\) 0 0
\(775\) 3963.46i 0.183706i
\(776\) 0 0
\(777\) 7981.27 + 1794.25i 0.368502 + 0.0828421i
\(778\) 0 0
\(779\) −16065.5 −0.738903
\(780\) 0 0
\(781\) 11408.0 0.522677
\(782\) 0 0
\(783\) 24827.5 + 19404.1i 1.13316 + 0.885627i
\(784\) 0 0
\(785\) 22272.6i 1.01267i
\(786\) 0 0
\(787\) 16693.4i 0.756108i −0.925784 0.378054i \(-0.876593\pi\)
0.925784 0.378054i \(-0.123407\pi\)
\(788\) 0 0
\(789\) 3283.73 14606.8i 0.148167 0.659084i
\(790\) 0 0
\(791\) 2938.64 0.132094
\(792\) 0 0
\(793\) 15624.7 0.699684
\(794\) 0 0
\(795\) −4714.33 + 20970.5i −0.210315 + 0.935532i
\(796\) 0 0
\(797\) 6666.68i 0.296293i −0.988965 0.148147i \(-0.952669\pi\)
0.988965 0.148147i \(-0.0473308\pi\)
\(798\) 0 0
\(799\) 16244.3i 0.719252i