Properties

Label 384.4.f.g.191.1
Level $384$
Weight $4$
Character 384.191
Analytic conductor $22.657$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 384.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.6567334422\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.12745506816.1
Defining polynomial: \(x^{8} + 23 x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 191.1
Root \(-0.323042 - 0.323042i\) of defining polynomial
Character \(\chi\) \(=\) 384.191
Dual form 384.4.f.g.191.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.44949 - 4.58258i) q^{3} +2.31464 q^{5} -29.6636i q^{7} +(-15.0000 + 22.4499i) q^{9} +O(q^{10})\) \(q+(-2.44949 - 4.58258i) q^{3} +2.31464 q^{5} -29.6636i q^{7} +(-15.0000 + 22.4499i) q^{9} -22.8348i q^{11} +8.66061i q^{13} +(-5.66970 - 10.6070i) q^{15} -93.3503i q^{17} +85.4402 q^{19} +(-135.936 + 72.6606i) q^{21} -116.661 q^{23} -119.642 q^{25} +(139.621 + 13.7477i) q^{27} +103.531 q^{29} +10.6070i q^{31} +(-104.642 + 55.9337i) q^{33} -68.6606i q^{35} +380.624i q^{37} +(39.6879 - 21.2141i) q^{39} -257.983i q^{41} -359.783 q^{43} +(-34.7197 + 51.9636i) q^{45} +293.285 q^{47} -536.927 q^{49} +(-427.785 + 228.661i) q^{51} -679.678 q^{53} -52.8545i q^{55} +(-209.285 - 391.536i) q^{57} -45.8258i q^{59} +595.230i q^{61} +(665.945 + 444.954i) q^{63} +20.0462i q^{65} +206.341 q^{67} +(285.759 + 534.606i) q^{69} -996.515 q^{71} -593.927 q^{73} +(293.063 + 548.270i) q^{75} -677.363 q^{77} +910.940i q^{79} +(-279.000 - 673.498i) q^{81} -332.889i q^{83} -216.073i q^{85} +(-253.597 - 474.436i) q^{87} +821.636i q^{89} +256.904 q^{91} +(48.6075 - 25.9818i) q^{93} +197.764 q^{95} +420.715 q^{97} +(512.641 + 342.523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 120 q^{9} + O(q^{10}) \) \( 8 q - 120 q^{9} - 192 q^{15} - 640 q^{23} + 216 q^{25} + 336 q^{33} + 1344 q^{39} - 776 q^{49} + 672 q^{57} + 2688 q^{63} - 640 q^{71} - 1232 q^{73} - 2232 q^{81} + 1344 q^{87} - 9856 q^{95} + 5712 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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
\(3\) −2.44949 4.58258i −0.471405 0.881917i
\(4\) 0 0
\(5\) 2.31464 0.207028 0.103514 0.994628i \(-0.466991\pi\)
0.103514 + 0.994628i \(0.466991\pi\)
\(6\) 0 0
\(7\) 29.6636i 1.60168i −0.598877 0.800841i \(-0.704386\pi\)
0.598877 0.800841i \(-0.295614\pi\)
\(8\) 0 0
\(9\) −15.0000 + 22.4499i −0.555556 + 0.831479i
\(10\) 0 0
\(11\) 22.8348i 0.625906i −0.949769 0.312953i \(-0.898682\pi\)
0.949769 0.312953i \(-0.101318\pi\)
\(12\) 0 0
\(13\) 8.66061i 0.184771i 0.995723 + 0.0923854i \(0.0294492\pi\)
−0.995723 + 0.0923854i \(0.970551\pi\)
\(14\) 0 0
\(15\) −5.66970 10.6070i −0.0975940 0.182582i
\(16\) 0 0
\(17\) 93.3503i 1.33181i −0.746036 0.665905i \(-0.768046\pi\)
0.746036 0.665905i \(-0.231954\pi\)
\(18\) 0 0
\(19\) 85.4402 1.03165 0.515824 0.856694i \(-0.327486\pi\)
0.515824 + 0.856694i \(0.327486\pi\)
\(20\) 0 0
\(21\) −135.936 + 72.6606i −1.41255 + 0.755040i
\(22\) 0 0
\(23\) −116.661 −1.05763 −0.528813 0.848738i \(-0.677363\pi\)
−0.528813 + 0.848738i \(0.677363\pi\)
\(24\) 0 0
\(25\) −119.642 −0.957139
\(26\) 0 0
\(27\) 139.621 + 13.7477i 0.995187 + 0.0979908i
\(28\) 0 0
\(29\) 103.531 0.662936 0.331468 0.943467i \(-0.392456\pi\)
0.331468 + 0.943467i \(0.392456\pi\)
\(30\) 0 0
\(31\) 10.6070i 0.0614542i 0.999528 + 0.0307271i \(0.00978227\pi\)
−0.999528 + 0.0307271i \(0.990218\pi\)
\(32\) 0 0
\(33\) −104.642 + 55.9337i −0.551997 + 0.295055i
\(34\) 0 0
\(35\) 68.6606i 0.331593i
\(36\) 0 0
\(37\) 380.624i 1.69120i 0.533820 + 0.845598i \(0.320756\pi\)
−0.533820 + 0.845598i \(0.679244\pi\)
\(38\) 0 0
\(39\) 39.6879 21.2141i 0.162952 0.0871018i
\(40\) 0 0
\(41\) 257.983i 0.982688i −0.870966 0.491344i \(-0.836506\pi\)
0.870966 0.491344i \(-0.163494\pi\)
\(42\) 0 0
\(43\) −359.783 −1.27596 −0.637981 0.770052i \(-0.720230\pi\)
−0.637981 + 0.770052i \(0.720230\pi\)
\(44\) 0 0
\(45\) −34.7197 + 51.9636i −0.115016 + 0.172140i
\(46\) 0 0
\(47\) 293.285 0.910213 0.455106 0.890437i \(-0.349601\pi\)
0.455106 + 0.890437i \(0.349601\pi\)
\(48\) 0 0
\(49\) −536.927 −1.56539
\(50\) 0 0
\(51\) −427.785 + 228.661i −1.17455 + 0.627821i
\(52\) 0 0
\(53\) −679.678 −1.76153 −0.880763 0.473557i \(-0.842970\pi\)
−0.880763 + 0.473557i \(0.842970\pi\)
\(54\) 0 0
\(55\) 52.8545i 0.129580i
\(56\) 0 0
\(57\) −209.285 391.536i −0.486324 0.909828i
\(58\) 0 0
\(59\) 45.8258i 0.101119i −0.998721 0.0505594i \(-0.983900\pi\)
0.998721 0.0505594i \(-0.0161004\pi\)
\(60\) 0 0
\(61\) 595.230i 1.24937i 0.780878 + 0.624684i \(0.214772\pi\)
−0.780878 + 0.624684i \(0.785228\pi\)
\(62\) 0 0
\(63\) 665.945 + 444.954i 1.33177 + 0.889823i
\(64\) 0 0
\(65\) 20.0462i 0.0382527i
\(66\) 0 0
\(67\) 206.341 0.376247 0.188124 0.982145i \(-0.439759\pi\)
0.188124 + 0.982145i \(0.439759\pi\)
\(68\) 0 0
\(69\) 285.759 + 534.606i 0.498570 + 0.932739i
\(70\) 0 0
\(71\) −996.515 −1.66570 −0.832849 0.553500i \(-0.813292\pi\)
−0.832849 + 0.553500i \(0.813292\pi\)
\(72\) 0 0
\(73\) −593.927 −0.952246 −0.476123 0.879379i \(-0.657958\pi\)
−0.476123 + 0.879379i \(0.657958\pi\)
\(74\) 0 0
\(75\) 293.063 + 548.270i 0.451200 + 0.844118i
\(76\) 0 0
\(77\) −677.363 −1.00250
\(78\) 0 0
\(79\) 910.940i 1.29733i 0.761075 + 0.648663i \(0.224672\pi\)
−0.761075 + 0.648663i \(0.775328\pi\)
\(80\) 0 0
\(81\) −279.000 673.498i −0.382716 0.923866i
\(82\) 0 0
\(83\) 332.889i 0.440233i −0.975474 0.220117i \(-0.929356\pi\)
0.975474 0.220117i \(-0.0706438\pi\)
\(84\) 0 0
\(85\) 216.073i 0.275722i
\(86\) 0 0
\(87\) −253.597 474.436i −0.312511 0.584654i
\(88\) 0 0
\(89\) 821.636i 0.978575i 0.872122 + 0.489288i \(0.162743\pi\)
−0.872122 + 0.489288i \(0.837257\pi\)
\(90\) 0 0
\(91\) 256.904 0.295944
\(92\) 0 0
\(93\) 48.6075 25.9818i 0.0541975 0.0289698i
\(94\) 0 0
\(95\) 197.764 0.213580
\(96\) 0 0
\(97\) 420.715 0.440383 0.220192 0.975457i \(-0.429332\pi\)
0.220192 + 0.975457i \(0.429332\pi\)
\(98\) 0 0
\(99\) 512.641 + 342.523i 0.520428 + 0.347726i
\(100\) 0 0
\(101\) 923.145 0.909469 0.454734 0.890627i \(-0.349734\pi\)
0.454734 + 0.890627i \(0.349734\pi\)
\(102\) 0 0
\(103\) 1426.19i 1.36434i −0.731195 0.682168i \(-0.761037\pi\)
0.731195 0.682168i \(-0.238963\pi\)
\(104\) 0 0
\(105\) −314.642 + 168.183i −0.292438 + 0.156315i
\(106\) 0 0
\(107\) 1581.83i 1.42917i −0.699550 0.714583i \(-0.746616\pi\)
0.699550 0.714583i \(-0.253384\pi\)
\(108\) 0 0
\(109\) 766.091i 0.673195i 0.941649 + 0.336597i \(0.109276\pi\)
−0.941649 + 0.336597i \(0.890724\pi\)
\(110\) 0 0
\(111\) 1744.24 932.335i 1.49149 0.797237i
\(112\) 0 0
\(113\) 1047.66i 0.872177i −0.899904 0.436088i \(-0.856364\pi\)
0.899904 0.436088i \(-0.143636\pi\)
\(114\) 0 0
\(115\) −270.028 −0.218958
\(116\) 0 0
\(117\) −194.430 129.909i −0.153633 0.102650i
\(118\) 0 0
\(119\) −2769.10 −2.13314
\(120\) 0 0
\(121\) 809.570 0.608242
\(122\) 0 0
\(123\) −1182.23 + 631.927i −0.866649 + 0.463244i
\(124\) 0 0
\(125\) −566.260 −0.405183
\(126\) 0 0
\(127\) 553.181i 0.386511i −0.981148 0.193256i \(-0.938095\pi\)
0.981148 0.193256i \(-0.0619046\pi\)
\(128\) 0 0
\(129\) 881.285 + 1648.73i 0.601495 + 1.12529i
\(130\) 0 0
\(131\) 2151.63i 1.43503i −0.696545 0.717513i \(-0.745280\pi\)
0.696545 0.717513i \(-0.254720\pi\)
\(132\) 0 0
\(133\) 2534.46i 1.65237i
\(134\) 0 0
\(135\) 323.173 + 31.8211i 0.206032 + 0.0202868i
\(136\) 0 0
\(137\) 1476.62i 0.920846i −0.887700 0.460423i \(-0.847698\pi\)
0.887700 0.460423i \(-0.152302\pi\)
\(138\) 0 0
\(139\) 1984.09 1.21071 0.605353 0.795957i \(-0.293032\pi\)
0.605353 + 0.795957i \(0.293032\pi\)
\(140\) 0 0
\(141\) −718.398 1344.00i −0.429078 0.802732i
\(142\) 0 0
\(143\) 197.764 0.115649
\(144\) 0 0
\(145\) 239.636 0.137246
\(146\) 0 0
\(147\) 1315.20 + 2460.51i 0.737930 + 1.38054i
\(148\) 0 0
\(149\) 3026.56 1.66406 0.832031 0.554729i \(-0.187178\pi\)
0.832031 + 0.554729i \(0.187178\pi\)
\(150\) 0 0
\(151\) 350.032i 0.188644i 0.995542 + 0.0943219i \(0.0300683\pi\)
−0.995542 + 0.0943219i \(0.969932\pi\)
\(152\) 0 0
\(153\) 2095.71 + 1400.25i 1.10737 + 0.739895i
\(154\) 0 0
\(155\) 24.5515i 0.0127227i
\(156\) 0 0
\(157\) 372.406i 0.189307i −0.995510 0.0946536i \(-0.969826\pi\)
0.995510 0.0946536i \(-0.0301744\pi\)
\(158\) 0 0
\(159\) 1664.86 + 3114.67i 0.830392 + 1.55352i
\(160\) 0 0
\(161\) 3460.57i 1.69398i
\(162\) 0 0
\(163\) −1353.69 −0.650487 −0.325243 0.945630i \(-0.605446\pi\)
−0.325243 + 0.945630i \(0.605446\pi\)
\(164\) 0 0
\(165\) −242.210 + 129.467i −0.114279 + 0.0610846i
\(166\) 0 0
\(167\) −2592.48 −1.20127 −0.600635 0.799523i \(-0.705085\pi\)
−0.600635 + 0.799523i \(0.705085\pi\)
\(168\) 0 0
\(169\) 2121.99 0.965860
\(170\) 0 0
\(171\) −1281.60 + 1918.13i −0.573138 + 0.857794i
\(172\) 0 0
\(173\) 3643.74 1.60132 0.800660 0.599118i \(-0.204482\pi\)
0.800660 + 0.599118i \(0.204482\pi\)
\(174\) 0 0
\(175\) 3549.02i 1.53303i
\(176\) 0 0
\(177\) −210.000 + 112.250i −0.0891783 + 0.0476678i
\(178\) 0 0
\(179\) 874.435i 0.365130i 0.983194 + 0.182565i \(0.0584400\pi\)
−0.983194 + 0.182565i \(0.941560\pi\)
\(180\) 0 0
\(181\) 2699.01i 1.10838i −0.832392 0.554188i \(-0.813029\pi\)
0.832392 0.554188i \(-0.186971\pi\)
\(182\) 0 0
\(183\) 2727.69 1458.01i 1.10184 0.588958i
\(184\) 0 0
\(185\) 881.010i 0.350125i
\(186\) 0 0
\(187\) −2131.64 −0.833588
\(188\) 0 0
\(189\) 407.807 4141.65i 0.156950 1.59397i
\(190\) 0 0
\(191\) 708.036 0.268229 0.134114 0.990966i \(-0.457181\pi\)
0.134114 + 0.990966i \(0.457181\pi\)
\(192\) 0 0
\(193\) 3531.07 1.31695 0.658476 0.752602i \(-0.271201\pi\)
0.658476 + 0.752602i \(0.271201\pi\)
\(194\) 0 0
\(195\) 91.8633 49.1030i 0.0337357 0.0180325i
\(196\) 0 0
\(197\) −4919.77 −1.77928 −0.889642 0.456658i \(-0.849046\pi\)
−0.889642 + 0.456658i \(0.849046\pi\)
\(198\) 0 0
\(199\) 264.092i 0.0940754i −0.998893 0.0470377i \(-0.985022\pi\)
0.998893 0.0470377i \(-0.0149781\pi\)
\(200\) 0 0
\(201\) −505.430 945.574i −0.177365 0.331819i
\(202\) 0 0
\(203\) 3071.08i 1.06181i
\(204\) 0 0
\(205\) 597.139i 0.203444i
\(206\) 0 0
\(207\) 1749.91 2619.02i 0.587570 0.879395i
\(208\) 0 0
\(209\) 1951.01i 0.645715i
\(210\) 0 0
\(211\) −3422.86 −1.11678 −0.558388 0.829580i \(-0.688580\pi\)
−0.558388 + 0.829580i \(0.688580\pi\)
\(212\) 0 0
\(213\) 2440.95 + 4566.61i 0.785218 + 1.46901i
\(214\) 0 0
\(215\) −832.770 −0.264160
\(216\) 0 0
\(217\) 314.642 0.0984300
\(218\) 0 0
\(219\) 1454.82 + 2721.72i 0.448893 + 0.839802i
\(220\) 0 0
\(221\) 808.470 0.246080
\(222\) 0 0
\(223\) 4432.09i 1.33092i −0.746434 0.665460i \(-0.768236\pi\)
0.746434 0.665460i \(-0.231764\pi\)
\(224\) 0 0
\(225\) 1794.64 2685.97i 0.531744 0.795842i
\(226\) 0 0
\(227\) 4674.99i 1.36692i −0.729990 0.683458i \(-0.760475\pi\)
0.729990 0.683458i \(-0.239525\pi\)
\(228\) 0 0
\(229\) 2317.95i 0.668883i −0.942417 0.334441i \(-0.891452\pi\)
0.942417 0.334441i \(-0.108548\pi\)
\(230\) 0 0
\(231\) 1659.19 + 3104.07i 0.472584 + 0.884124i
\(232\) 0 0
\(233\) 5342.54i 1.50215i 0.660215 + 0.751076i \(0.270465\pi\)
−0.660215 + 0.751076i \(0.729535\pi\)
\(234\) 0 0
\(235\) 678.850 0.188440
\(236\) 0 0
\(237\) 4174.45 2231.34i 1.14413 0.611566i
\(238\) 0 0
\(239\) −5306.42 −1.43617 −0.718084 0.695957i \(-0.754981\pi\)
−0.718084 + 0.695957i \(0.754981\pi\)
\(240\) 0 0
\(241\) −1220.35 −0.326182 −0.163091 0.986611i \(-0.552146\pi\)
−0.163091 + 0.986611i \(0.552146\pi\)
\(242\) 0 0
\(243\) −2402.95 + 2928.27i −0.634359 + 0.773038i
\(244\) 0 0
\(245\) −1242.80 −0.324079
\(246\) 0 0
\(247\) 739.964i 0.190618i
\(248\) 0 0
\(249\) −1525.49 + 815.409i −0.388249 + 0.207528i
\(250\) 0 0
\(251\) 385.695i 0.0969916i −0.998823 0.0484958i \(-0.984557\pi\)
0.998823 0.0484958i \(-0.0154427\pi\)
\(252\) 0 0
\(253\) 2663.93i 0.661975i
\(254\) 0 0
\(255\) −990.170 + 529.268i −0.243164 + 0.129977i
\(256\) 0 0
\(257\) 1158.77i 0.281253i 0.990063 + 0.140626i \(0.0449116\pi\)
−0.990063 + 0.140626i \(0.955088\pi\)
\(258\) 0 0
\(259\) 11290.7 2.70876
\(260\) 0 0
\(261\) −1552.96 + 2324.25i −0.368298 + 0.551217i
\(262\) 0 0
\(263\) 1677.25 0.393247 0.196623 0.980479i \(-0.437002\pi\)
0.196623 + 0.980479i \(0.437002\pi\)
\(264\) 0 0
\(265\) −1573.21 −0.364685
\(266\) 0 0
\(267\) 3765.21 2012.59i 0.863022 0.461305i
\(268\) 0 0
\(269\) −4080.38 −0.924852 −0.462426 0.886658i \(-0.653021\pi\)
−0.462426 + 0.886658i \(0.653021\pi\)
\(270\) 0 0
\(271\) 550.301i 0.123352i −0.998096 0.0616761i \(-0.980355\pi\)
0.998096 0.0616761i \(-0.0196446\pi\)
\(272\) 0 0
\(273\) −629.285 1177.28i −0.139509 0.260998i
\(274\) 0 0
\(275\) 2732.02i 0.599079i
\(276\) 0 0
\(277\) 468.115i 0.101539i 0.998710 + 0.0507695i \(0.0161674\pi\)
−0.998710 + 0.0507695i \(0.983833\pi\)
\(278\) 0 0
\(279\) −238.127 159.105i −0.0510979 0.0341412i
\(280\) 0 0
\(281\) 5322.22i 1.12988i −0.825131 0.564942i \(-0.808899\pi\)
0.825131 0.564942i \(-0.191101\pi\)
\(282\) 0 0
\(283\) 109.886 0.0230814 0.0115407 0.999933i \(-0.496326\pi\)
0.0115407 + 0.999933i \(0.496326\pi\)
\(284\) 0 0
\(285\) −484.420 906.267i −0.100683 0.188360i
\(286\) 0 0
\(287\) −7652.70 −1.57395
\(288\) 0 0
\(289\) −3801.28 −0.773718
\(290\) 0 0
\(291\) −1030.54 1927.96i −0.207599 0.388381i
\(292\) 0 0
\(293\) 2671.59 0.532683 0.266341 0.963879i \(-0.414185\pi\)
0.266341 + 0.963879i \(0.414185\pi\)
\(294\) 0 0
\(295\) 106.070i 0.0209344i
\(296\) 0 0
\(297\) 313.927 3188.22i 0.0613330 0.622894i
\(298\) 0 0
\(299\) 1010.35i 0.195419i
\(300\) 0 0
\(301\) 10672.4i 2.04369i
\(302\) 0 0
\(303\) −2261.23 4230.38i −0.428728 0.802076i
\(304\) 0 0
\(305\) 1377.75i 0.258654i
\(306\) 0 0
\(307\) −2441.80 −0.453944 −0.226972 0.973901i \(-0.572883\pi\)
−0.226972 + 0.973901i \(0.572883\pi\)
\(308\) 0 0
\(309\) −6535.62 + 3493.44i −1.20323 + 0.643154i
\(310\) 0 0
\(311\) 6897.58 1.25764 0.628820 0.777551i \(-0.283538\pi\)
0.628820 + 0.777551i \(0.283538\pi\)
\(312\) 0 0
\(313\) −5278.92 −0.953298 −0.476649 0.879094i \(-0.658149\pi\)
−0.476649 + 0.879094i \(0.658149\pi\)
\(314\) 0 0
\(315\) 1541.43 + 1029.91i 0.275713 + 0.184218i
\(316\) 0 0
\(317\) −1537.58 −0.272427 −0.136213 0.990680i \(-0.543493\pi\)
−0.136213 + 0.990680i \(0.543493\pi\)
\(318\) 0 0
\(319\) 2364.10i 0.414935i
\(320\) 0 0
\(321\) −7248.84 + 3874.67i −1.26041 + 0.673716i
\(322\) 0 0
\(323\) 7975.87i 1.37396i
\(324\) 0 0
\(325\) 1036.18i 0.176851i
\(326\) 0 0
\(327\) 3510.67 1876.53i 0.593702 0.317347i
\(328\) 0 0
\(329\) 8699.87i 1.45787i
\(330\) 0 0
\(331\) −8894.54 −1.47700 −0.738502 0.674252i \(-0.764466\pi\)
−0.738502 + 0.674252i \(0.764466\pi\)
\(332\) 0 0
\(333\) −8544.99 5709.36i −1.40619 0.939553i
\(334\) 0 0
\(335\) 477.606 0.0778938
\(336\) 0 0
\(337\) −6422.48 −1.03815 −0.519073 0.854730i \(-0.673723\pi\)
−0.519073 + 0.854730i \(0.673723\pi\)
\(338\) 0 0
\(339\) −4801.00 + 2566.24i −0.769187 + 0.411148i
\(340\) 0 0
\(341\) 242.210 0.0384645
\(342\) 0 0
\(343\) 5752.57i 0.905568i
\(344\) 0 0
\(345\) 661.430 + 1237.42i 0.103218 + 0.193103i
\(346\) 0 0
\(347\) 3357.43i 0.519413i 0.965688 + 0.259707i \(0.0836259\pi\)
−0.965688 + 0.259707i \(0.916374\pi\)
\(348\) 0 0
\(349\) 11693.7i 1.79354i 0.442493 + 0.896772i \(0.354094\pi\)
−0.442493 + 0.896772i \(0.645906\pi\)
\(350\) 0 0
\(351\) −119.064 + 1209.20i −0.0181058 + 0.183882i
\(352\) 0 0
\(353\) 9945.93i 1.49963i −0.661649 0.749813i \(-0.730143\pi\)
0.661649 0.749813i \(-0.269857\pi\)
\(354\) 0 0
\(355\) −2306.58 −0.344846
\(356\) 0 0
\(357\) 6782.89 + 12689.6i 1.00557 + 1.88125i
\(358\) 0 0
\(359\) 8527.75 1.25370 0.626849 0.779141i \(-0.284344\pi\)
0.626849 + 0.779141i \(0.284344\pi\)
\(360\) 0 0
\(361\) 441.024 0.0642986
\(362\) 0 0
\(363\) −1983.03 3709.91i −0.286728 0.536419i
\(364\) 0 0
\(365\) −1374.73 −0.197142
\(366\) 0 0
\(367\) 891.162i 0.126753i −0.997990 0.0633764i \(-0.979813\pi\)
0.997990 0.0633764i \(-0.0201869\pi\)
\(368\) 0 0
\(369\) 5791.71 + 3869.75i 0.817085 + 0.545938i
\(370\) 0 0
\(371\) 20161.7i 2.82141i
\(372\) 0 0
\(373\) 9107.23i 1.26422i −0.774878 0.632111i \(-0.782189\pi\)
0.774878 0.632111i \(-0.217811\pi\)
\(374\) 0 0
\(375\) 1387.05 + 2594.93i 0.191005 + 0.357338i
\(376\) 0 0
\(377\) 896.637i 0.122491i
\(378\) 0 0
\(379\) 1451.32 0.196699 0.0983497 0.995152i \(-0.468644\pi\)
0.0983497 + 0.995152i \(0.468644\pi\)
\(380\) 0 0
\(381\) −2535.00 + 1355.01i −0.340871 + 0.182203i
\(382\) 0 0
\(383\) −3320.30 −0.442975 −0.221488 0.975163i \(-0.571091\pi\)
−0.221488 + 0.975163i \(0.571091\pi\)
\(384\) 0 0
\(385\) −1567.85 −0.207546
\(386\) 0 0
\(387\) 5396.75 8077.11i 0.708868 1.06094i
\(388\) 0 0
\(389\) 5726.58 0.746399 0.373200 0.927751i \(-0.378261\pi\)
0.373200 + 0.927751i \(0.378261\pi\)
\(390\) 0 0
\(391\) 10890.3i 1.40856i
\(392\) 0 0
\(393\) −9859.99 + 5270.39i −1.26557 + 0.676478i
\(394\) 0 0
\(395\) 2108.50i 0.268583i
\(396\) 0 0
\(397\) 5389.36i 0.681321i 0.940186 + 0.340660i \(0.110651\pi\)
−0.940186 + 0.340660i \(0.889349\pi\)
\(398\) 0 0
\(399\) −11614.4 + 6208.14i −1.45726 + 0.778936i
\(400\) 0 0
\(401\) 573.267i 0.0713905i −0.999363 0.0356953i \(-0.988635\pi\)
0.999363 0.0356953i \(-0.0113646\pi\)
\(402\) 0 0
\(403\) −91.8633 −0.0113549
\(404\) 0 0
\(405\) −645.786 1558.91i −0.0792330 0.191266i
\(406\) 0 0
\(407\) 8691.50 1.05853
\(408\) 0 0
\(409\) −6576.42 −0.795069 −0.397535 0.917587i \(-0.630134\pi\)
−0.397535 + 0.917587i \(0.630134\pi\)
\(410\) 0 0
\(411\) −6766.71 + 3616.96i −0.812110 + 0.434091i
\(412\) 0 0
\(413\) −1359.36 −0.161960
\(414\) 0 0
\(415\) 770.521i 0.0911406i
\(416\) 0 0
\(417\) −4860.00 9092.23i −0.570732 1.06774i
\(418\) 0 0
\(419\) 8544.87i 0.996286i −0.867095 0.498143i \(-0.834015\pi\)
0.867095 0.498143i \(-0.165985\pi\)
\(420\) 0 0
\(421\) 1822.38i 0.210968i −0.994421 0.105484i \(-0.966361\pi\)
0.994421 0.105484i \(-0.0336392\pi\)
\(422\) 0 0
\(423\) −4399.27 + 6584.23i −0.505674 + 0.756823i
\(424\) 0 0
\(425\) 11168.7i 1.27473i
\(426\) 0 0
\(427\) 17656.7 2.00109
\(428\) 0 0
\(429\) −484.420 906.267i −0.0545175 0.101993i
\(430\) 0 0
\(431\) 2373.58 0.265269 0.132635 0.991165i \(-0.457656\pi\)
0.132635 + 0.991165i \(0.457656\pi\)
\(432\) 0 0
\(433\) 12307.8 1.36600 0.682999 0.730419i \(-0.260675\pi\)
0.682999 + 0.730419i \(0.260675\pi\)
\(434\) 0 0
\(435\) −586.987 1098.15i −0.0646985 0.121040i
\(436\) 0 0
\(437\) −9967.50 −1.09110
\(438\) 0 0
\(439\) 5371.26i 0.583955i −0.956425 0.291978i \(-0.905687\pi\)
0.956425 0.291978i \(-0.0943133\pi\)
\(440\) 0 0
\(441\) 8053.91 12054.0i 0.869659 1.30159i
\(442\) 0 0
\(443\) 9066.41i 0.972366i 0.873857 + 0.486183i \(0.161611\pi\)
−0.873857 + 0.486183i \(0.838389\pi\)
\(444\) 0 0
\(445\) 1901.79i 0.202593i
\(446\) 0 0
\(447\) −7413.52 13869.4i −0.784447 1.46757i
\(448\) 0 0
\(449\) 6049.97i 0.635892i −0.948109 0.317946i \(-0.897007\pi\)
0.948109 0.317946i \(-0.102993\pi\)
\(450\) 0 0
\(451\) −5891.01 −0.615070
\(452\) 0 0
\(453\) 1604.05 857.400i 0.166368 0.0889275i
\(454\) 0 0
\(455\) 594.642 0.0612687
\(456\) 0 0
\(457\) 6664.98 0.682220 0.341110 0.940023i \(-0.389197\pi\)
0.341110 + 0.940023i \(0.389197\pi\)
\(458\) 0 0
\(459\) 1283.35 13033.7i 0.130505 1.32540i
\(460\) 0 0
\(461\) −2588.66 −0.261531 −0.130766 0.991413i \(-0.541744\pi\)
−0.130766 + 0.991413i \(0.541744\pi\)
\(462\) 0 0
\(463\) 12241.7i 1.22877i −0.789006 0.614385i \(-0.789404\pi\)
0.789006 0.614385i \(-0.210596\pi\)
\(464\) 0 0
\(465\) 112.509 60.1387i 0.0112204 0.00599756i
\(466\) 0 0
\(467\) 6144.26i 0.608828i 0.952540 + 0.304414i \(0.0984606\pi\)
−0.952540 + 0.304414i \(0.901539\pi\)
\(468\) 0 0
\(469\) 6120.81i 0.602629i
\(470\) 0 0
\(471\) −1706.58 + 912.205i −0.166953 + 0.0892403i
\(472\) 0 0
\(473\) 8215.59i 0.798633i
\(474\) 0 0
\(475\) −10222.3 −0.987431
\(476\) 0 0
\(477\) 10195.2 15258.7i 0.978626 1.46467i
\(478\) 0 0
\(479\) 12210.4 1.16473 0.582365 0.812928i \(-0.302128\pi\)
0.582365 + 0.812928i \(0.302128\pi\)
\(480\) 0 0
\(481\) −3296.44 −0.312483
\(482\) 0 0
\(483\) 15858.3 8476.63i 1.49395 0.798551i
\(484\) 0 0
\(485\) 973.806 0.0911716
\(486\) 0 0
\(487\) 14354.5i 1.33565i −0.744317 0.667827i \(-0.767225\pi\)
0.744317 0.667827i \(-0.232775\pi\)
\(488\) 0 0
\(489\) 3315.85 + 6203.40i 0.306642 + 0.573675i
\(490\) 0 0
\(491\) 3894.57i 0.357962i −0.983853 0.178981i \(-0.942720\pi\)
0.983853 0.178981i \(-0.0572800\pi\)
\(492\) 0 0
\(493\) 9664.61i 0.882905i
\(494\) 0 0
\(495\) 1186.58 + 792.818i 0.107743 + 0.0719889i
\(496\) 0 0
\(497\) 29560.2i 2.66792i
\(498\) 0 0
\(499\) −13373.6 −1.19977 −0.599886 0.800086i \(-0.704787\pi\)
−0.599886 + 0.800086i \(0.704787\pi\)
\(500\) 0 0
\(501\) 6350.25 + 11880.2i 0.566284 + 1.05942i
\(502\) 0 0
\(503\) −3757.55 −0.333083 −0.166541 0.986034i \(-0.553260\pi\)
−0.166541 + 0.986034i \(0.553260\pi\)
\(504\) 0 0
\(505\) 2136.75 0.188286
\(506\) 0 0
\(507\) −5197.80 9724.20i −0.455311 0.851808i
\(508\) 0 0
\(509\) 5968.10 0.519708 0.259854 0.965648i \(-0.416326\pi\)
0.259854 + 0.965648i \(0.416326\pi\)
\(510\) 0 0
\(511\) 17618.0i 1.52519i
\(512\) 0 0
\(513\) 11929.2 + 1174.61i 1.02668 + 0.101092i
\(514\) 0 0
\(515\) 3301.12i 0.282456i
\(516\) 0 0
\(517\) 6697.12i 0.569708i
\(518\) 0 0
\(519\) −8925.31 16697.7i −0.754870 1.41223i
\(520\) 0 0
\(521\) 10169.5i 0.855151i −0.903980 0.427575i \(-0.859368\pi\)
0.903980 0.427575i \(-0.140632\pi\)
\(522\) 0 0
\(523\) 13759.2 1.15038 0.575188 0.818021i \(-0.304929\pi\)
0.575188 + 0.818021i \(0.304929\pi\)
\(524\) 0 0
\(525\) 16263.7 8693.29i 1.35201 0.722679i
\(526\) 0 0
\(527\) 990.170 0.0818453
\(528\) 0 0
\(529\) 1442.70 0.118575
\(530\) 0 0
\(531\) 1028.79 + 687.386i 0.0840781 + 0.0561771i
\(532\) 0 0
\(533\) 2234.29 0.181572
\(534\) 0 0
\(535\) 3661.36i 0.295878i
\(536\) 0 0
\(537\) 4007.16 2141.92i 0.322015 0.172124i
\(538\) 0 0
\(539\) 12260.7i 0.979784i
\(540\) 0 0
\(541\) 10310.6i 0.819386i −0.912223 0.409693i \(-0.865636\pi\)
0.912223 0.409693i \(-0.134364\pi\)
\(542\) 0 0
\(543\) −12368.4 + 6611.20i −0.977495 + 0.522493i
\(544\) 0 0
\(545\) 1773.23i 0.139370i
\(546\) 0 0
\(547\) 19226.5 1.50287 0.751433 0.659810i \(-0.229363\pi\)
0.751433 + 0.659810i \(0.229363\pi\)
\(548\) 0 0
\(549\) −13362.9 8928.45i −1.03882 0.694093i
\(550\) 0 0
\(551\) 8845.67 0.683917
\(552\) 0 0
\(553\) 27021.7 2.07791
\(554\) 0 0
\(555\) 4037.29 2158.02i 0.308781 0.165050i
\(556\) 0 0
\(557\) 14675.8 1.11640 0.558199 0.829707i \(-0.311492\pi\)
0.558199 + 0.829707i \(0.311492\pi\)
\(558\) 0 0
\(559\) 3115.94i 0.235761i
\(560\) 0 0
\(561\) 5221.43 + 9768.40i 0.392957 + 0.735156i
\(562\) 0 0
\(563\) 21002.2i 1.57218i 0.618110 + 0.786092i \(0.287899\pi\)
−0.618110 + 0.786092i \(0.712101\pi\)
\(564\) 0 0
\(565\) 2424.97i 0.180565i
\(566\) 0 0
\(567\) −19978.4 + 8276.14i −1.47974 + 0.612989i
\(568\) 0 0
\(569\) 4389.21i 0.323384i −0.986841 0.161692i \(-0.948305\pi\)
0.986841 0.161692i \(-0.0516951\pi\)
\(570\) 0 0
\(571\) 3964.70 0.290574 0.145287 0.989390i \(-0.453590\pi\)
0.145287 + 0.989390i \(0.453590\pi\)
\(572\) 0 0
\(573\) −1734.33 3244.63i −0.126444 0.236556i
\(574\) 0 0
\(575\) 13957.6 1.01230
\(576\) 0 0
\(577\) 5848.93 0.422000 0.211000 0.977486i \(-0.432328\pi\)
0.211000 + 0.977486i \(0.432328\pi\)
\(578\) 0 0
\(579\) −8649.31 16181.4i −0.620817 1.16144i
\(580\) 0 0
\(581\) −9874.69 −0.705114
\(582\) 0 0
\(583\) 15520.3i 1.10255i
\(584\) 0 0
\(585\) −450.037 300.693i −0.0318064 0.0212515i
\(586\) 0 0
\(587\) 7642.83i 0.537399i 0.963224 + 0.268700i \(0.0865939\pi\)
−0.963224 + 0.268700i \(0.913406\pi\)
\(588\) 0 0
\(589\) 906.267i 0.0633991i
\(590\) 0 0
\(591\) 12050.9 + 22545.2i 0.838763 + 1.56918i
\(592\) 0 0
\(593\) 16852.3i 1.16702i −0.812107 0.583509i \(-0.801679\pi\)
0.812107 0.583509i \(-0.198321\pi\)
\(594\) 0 0
\(595\) −6409.49 −0.441619
\(596\) 0 0
\(597\) −1210.22 + 646.891i −0.0829667 + 0.0443475i
\(598\) 0 0
\(599\) −7456.85 −0.508646 −0.254323 0.967119i \(-0.581853\pi\)
−0.254323 + 0.967119i \(0.581853\pi\)
\(600\) 0 0
\(601\) −8982.48 −0.609656 −0.304828 0.952407i \(-0.598599\pi\)
−0.304828 + 0.952407i \(0.598599\pi\)
\(602\) 0 0
\(603\) −3095.12 + 4632.35i −0.209026 + 0.312842i
\(604\) 0 0
\(605\) 1873.87 0.125923
\(606\) 0 0
\(607\) 6289.93i 0.420594i 0.977638 + 0.210297i \(0.0674431\pi\)
−0.977638 + 0.210297i \(0.932557\pi\)
\(608\) 0 0
\(609\) −14073.5 + 7522.59i −0.936430 + 0.500543i
\(610\) 0 0
\(611\) 2540.02i 0.168181i
\(612\) 0 0
\(613\) 11497.6i 0.757556i −0.925488 0.378778i \(-0.876344\pi\)
0.925488 0.378778i \(-0.123656\pi\)
\(614\) 0 0
\(615\) −2736.44 + 1462.69i −0.179421 + 0.0959044i
\(616\) 0 0
\(617\) 13336.4i 0.870181i 0.900387 + 0.435090i \(0.143284\pi\)
−0.900387 + 0.435090i \(0.856716\pi\)
\(618\) 0 0
\(619\) −27960.9 −1.81558 −0.907788 0.419429i \(-0.862230\pi\)
−0.907788 + 0.419429i \(0.862230\pi\)
\(620\) 0 0
\(621\) −16288.3 1603.82i −1.05254 0.103638i
\(622\) 0 0
\(623\) 24372.6 1.56737
\(624\) 0 0
\(625\) 13644.6 0.873255
\(626\) 0 0
\(627\) −8940.67 + 4778.99i −0.569467 + 0.304393i
\(628\) 0 0
\(629\) 35531.4 2.25235
\(630\) 0 0
\(631\) 2435.82i 0.153675i −0.997044 0.0768373i \(-0.975518\pi\)
0.997044 0.0768373i \(-0.0244822\pi\)
\(632\) 0 0
\(633\) 8384.27 + 15685.5i 0.526453 + 0.984903i
\(634\) 0 0
\(635\) 1280.42i 0.0800186i
\(636\) 0 0
\(637\) 4650.12i 0.289237i
\(638\) 0 0
\(639\) 14947.7 22371.7i 0.925388 1.38499i
\(640\) 0 0
\(641\) 882.215i 0.0543610i 0.999631 + 0.0271805i \(0.00865288\pi\)
−0.999631 + 0.0271805i \(0.991347\pi\)
\(642\) 0 0
\(643\) 3761.20 0.230680 0.115340 0.993326i \(-0.463204\pi\)
0.115340 + 0.993326i \(0.463204\pi\)
\(644\) 0 0
\(645\) 2039.86 + 3816.23i 0.124526 + 0.232967i
\(646\) 0 0
\(647\) −6601.59 −0.401137 −0.200568 0.979680i \(-0.564279\pi\)
−0.200568 + 0.979680i \(0.564279\pi\)
\(648\) 0 0
\(649\) −1046.42 −0.0632908
\(650\) 0 0
\(651\) −770.713 1441.87i −0.0464004 0.0868071i
\(652\) 0 0
\(653\) 13790.5 0.826436 0.413218 0.910632i \(-0.364405\pi\)
0.413218 + 0.910632i \(0.364405\pi\)
\(654\) 0 0
\(655\) 4980.25i 0.297091i
\(656\) 0 0
\(657\) 8908.91 13333.6i 0.529025 0.791773i
\(658\) 0 0
\(659\) 12482.7i 0.737868i 0.929456 + 0.368934i \(0.120277\pi\)
−0.929456 + 0.368934i \(0.879723\pi\)
\(660\) 0 0
\(661\) 6286.85i 0.369940i 0.982744 + 0.184970i \(0.0592188\pi\)
−0.982744 + 0.184970i \(0.940781\pi\)
\(662\) 0 0
\(663\) −1980.34 3704.88i −0.116003 0.217022i
\(664\) 0 0
\(665\) 5866.37i 0.342088i
\(666\) 0 0
\(667\) −12077.9 −0.701139
\(668\) 0 0
\(669\) −20310.4 + 10856.4i −1.17376 + 0.627401i
\(670\) 0 0
\(671\) 13592.0 0.781987
\(672\) 0 0
\(673\) 13687.8 0.783992 0.391996 0.919967i \(-0.371785\pi\)
0.391996 + 0.919967i \(0.371785\pi\)
\(674\) 0 0
\(675\) −16704.6 1644.81i −0.952533 0.0937908i
\(676\) 0 0
\(677\) −20519.0 −1.16486 −0.582428 0.812882i \(-0.697897\pi\)
−0.582428 + 0.812882i \(0.697897\pi\)
\(678\) 0 0
\(679\) 12479.9i 0.705354i
\(680\) 0 0
\(681\) −21423.5 + 11451.3i −1.20551 + 0.644370i
\(682\) 0 0
\(683\) 11851.0i 0.663933i −0.943291 0.331967i \(-0.892288\pi\)
0.943291 0.331967i \(-0.107712\pi\)
\(684\) 0 0
\(685\) 3417.84i 0.190641i
\(686\) 0 0
\(687\) −10622.2 + 5677.78i −0.589899 + 0.315314i
\(688\) 0 0
\(689\) 5886.42i 0.325479i
\(690\) 0 0
\(691\) 720.586 0.0396706 0.0198353 0.999803i \(-0.493686\pi\)
0.0198353 + 0.999803i \(0.493686\pi\)
\(692\) 0 0
\(693\) 10160.4 15206.8i 0.556946 0.833560i
\(694\) 0 0
\(695\) 4592.45 0.250650
\(696\) 0 0
\(697\) −24082.8 −1.30875
\(698\) 0 0
\(699\) 24482.6 13086.5i 1.32477 0.708122i
\(700\) 0 0
\(701\) −3475.26 −0.187245 −0.0936226 0.995608i \(-0.529845\pi\)
−0.0936226 + 0.995608i \(0.529845\pi\)
\(702\) 0 0
\(703\) 32520.6i 1.74472i
\(704\) 0 0
\(705\) −1662.84 3110.88i −0.0888313 0.166188i
\(706\) 0 0
\(707\) 27383.8i 1.45668i
\(708\) 0 0
\(709\) 3963.46i 0.209945i 0.994475 + 0.104972i \(0.0334754\pi\)
−0.994475 + 0.104972i \(0.966525\pi\)
\(710\) 0 0
\(711\) −20450.6 13664.1i −1.07870 0.720737i
\(712\) 0 0
\(713\) 1237.42i 0.0649956i
\(714\) 0 0
\(715\) 457.752 0.0239426
\(716\) 0 0
\(717\) 12998.0 + 24317.1i 0.677016 + 1.26658i
\(718\) 0 0
\(719\) 3328.38 0.172639 0.0863195 0.996268i \(-0.472489\pi\)
0.0863195 + 0.996268i \(0.472489\pi\)
\(720\) 0 0
\(721\) −42305.9 −2.18523
\(722\) 0 0
\(723\) 2989.24 + 5592.35i 0.153763 + 0.287665i
\(724\) 0 0
\(725\) −12386.6 −0.634522
\(726\) 0 0
\(727\) 19880.2i 1.01419i −0.861891 0.507094i \(-0.830720\pi\)
0.861891 0.507094i \(-0.169280\pi\)
\(728\) 0 0
\(729\) 19305.0 + 3838.94i 0.980796 + 0.195038i
\(730\) 0 0
\(731\) 33585.9i 1.69934i
\(732\) 0 0
\(733\) 11000.8i 0.554330i 0.960822 + 0.277165i \(0.0893949\pi\)
−0.960822 + 0.277165i \(0.910605\pi\)
\(734\) 0 0
\(735\) 3044.22 + 5695.20i 0.152772 + 0.285811i
\(736\) 0 0
\(737\) 4711.77i 0.235495i
\(738\) 0 0
\(739\) 24841.3 1.23654 0.618269 0.785966i \(-0.287834\pi\)
0.618269 + 0.785966i \(0.287834\pi\)
\(740\) 0 0
\(741\) 3390.94 1812.53i 0.168110 0.0898584i
\(742\) 0 0
\(743\) −40146.8 −1.98229 −0.991147 0.132769i \(-0.957613\pi\)
−0.991147 + 0.132769i \(0.957613\pi\)
\(744\) 0 0
\(745\) 7005.41 0.344508
\(746\) 0 0
\(747\) 7473.35 + 4993.34i 0.366045 + 0.244574i
\(748\) 0 0
\(749\) −46922.6 −2.28907
\(750\) 0 0
\(751\) 14430.3i 0.701159i 0.936533 + 0.350580i \(0.114015\pi\)
−0.936533 + 0.350580i \(0.885985\pi\)
\(752\) 0 0
\(753\) −1767.48 + 944.757i −0.0855385 + 0.0457223i
\(754\) 0 0
\(755\) 810.200i 0.0390546i
\(756\) 0 0
\(757\) 36743.8i 1.76417i 0.471091 + 0.882085i \(0.343860\pi\)
−0.471091 + 0.882085i \(0.656140\pi\)
\(758\) 0 0
\(759\) 12207.6 6525.26i 0.583807 0.312058i
\(760\) 0 0
\(761\) 12211.3i 0.581681i −0.956772 0.290841i \(-0.906065\pi\)
0.956772 0.290841i \(-0.0939350\pi\)
\(762\) 0 0
\(763\) 22725.0 1.07824
\(764\) 0 0
\(765\) 4850.82 + 3241.09i 0.229257 + 0.153179i
\(766\) 0 0
\(767\) 396.879 0.0186838
\(768\) 0 0
\(769\) 547.115 0.0256560 0.0128280 0.999918i \(-0.495917\pi\)
0.0128280 + 0.999918i \(0.495917\pi\)
\(770\) 0 0
\(771\) 5310.14 2838.39i 0.248041 0.132584i
\(772\) 0 0
\(773\) 25467.3 1.18499 0.592494 0.805575i \(-0.298143\pi\)
0.592494 + 0.805575i \(0.298143\pi\)
\(774\) 0 0
\(775\) 1269.05i 0.0588202i
\(776\) 0 0
\(777\) −27656.4 51740.4i −1.27692 2.38890i
\(778\) 0 0
\(779\) 22042.1i 1.01379i
\(780\) 0 0
\(781\) 22755.3i 1.04257i
\(782\) 0 0
\(783\) 14455.0 + 1423.31i 0.659745 + 0.0649616i
\(784\) 0 0
\(785\) 861.987i 0.0391919i
\(786\) 0 0
\(787\) 7196.98 0.325978 0.162989 0.986628i \(-0.447887\pi\)
0.162989 + 0.986628i \(0.447887\pi\)
\(788\) 0 0
\(789\) −4108.42 7686.15i −0.185378 0.346811i
\(790\) 0 0
\(791\) −31077.5 −1.39695
\(792\) 0 0
\(793\) −5155.05 −0.230847
\(794\) 0 0
\(795\) 3853.57 + 7209.36i 0.171914 + 0.321622i
\(796\) 0 0
\(797\) −30718.6 −1.36526 −0.682628 0.730766i \(-0.739163\pi\)