Properties

Label 384.3.e.a.257.1
Level $384$
Weight $3$
Character 384.257
Analytic conductor $10.463$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 18 x^{6} + 99 x^{4} + 170 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 257.1
Root \(0.888828i\) of defining polynomial
Character \(\chi\) \(=\) 384.257
Dual form 384.3.e.a.257.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.86531 - 0.888828i) q^{3} +8.59176i q^{5} -10.9340 q^{7} +(7.41997 + 5.09353i) q^{9} +O(q^{10})\) \(q+(-2.86531 - 0.888828i) q^{3} +8.59176i q^{5} -10.9340 q^{7} +(7.41997 + 5.09353i) q^{9} +2.75255i q^{11} -4.43326 q^{13} +(7.63660 - 24.6180i) q^{15} -25.4208i q^{17} +17.5426 q^{19} +(31.3291 + 9.71841i) q^{21} -17.5482i q^{23} -48.8183 q^{25} +(-16.7332 - 21.1896i) q^{27} +19.6224i q^{29} -2.58322 q^{31} +(2.44655 - 7.88691i) q^{33} -93.9419i q^{35} +7.73178 q^{37} +(12.7026 + 3.94040i) q^{39} -58.0069i q^{41} -42.1932 q^{43} +(-43.7624 + 63.7506i) q^{45} +17.4666i q^{47} +70.5514 q^{49} +(-22.5947 + 72.8384i) q^{51} -69.0052i q^{53} -23.6493 q^{55} +(-50.2649 - 15.5923i) q^{57} -50.5878i q^{59} -32.5983 q^{61} +(-81.1296 - 55.6924i) q^{63} -38.0895i q^{65} -48.0128 q^{67} +(-15.5974 + 50.2811i) q^{69} -22.1021i q^{71} -27.0316 q^{73} +(139.880 + 43.3911i) q^{75} -30.0963i q^{77} +97.4827 q^{79} +(29.1119 + 75.5877i) q^{81} +59.5252i q^{83} +218.409 q^{85} +(17.4409 - 56.2242i) q^{87} +110.469i q^{89} +48.4730 q^{91} +(7.40171 + 2.29603i) q^{93} +150.722i q^{95} +55.1169 q^{97} +(-14.0202 + 20.4238i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} - 8q^{7} + O(q^{10}) \) \( 8q - 4q^{3} - 8q^{7} - 16q^{15} + 24q^{19} + 16q^{21} - 40q^{25} + 44q^{27} + 56q^{31} + 8q^{33} + 32q^{37} + 104q^{39} - 136q^{43} - 80q^{45} + 72q^{49} - 176q^{51} - 192q^{55} - 40q^{57} - 160q^{61} - 264q^{63} + 280q^{67} + 80q^{69} - 80q^{73} + 348q^{75} + 408q^{79} + 72q^{81} + 192q^{85} + 368q^{87} - 336q^{91} + 160q^{93} + 96q^{97} - 432q^{99} + O(q^{100}) \)

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
\(3\) −2.86531 0.888828i −0.955102 0.296276i
\(4\) 0 0
\(5\) 8.59176i 1.71835i 0.511680 + 0.859176i \(0.329023\pi\)
−0.511680 + 0.859176i \(0.670977\pi\)
\(6\) 0 0
\(7\) −10.9340 −1.56199 −0.780997 0.624535i \(-0.785288\pi\)
−0.780997 + 0.624535i \(0.785288\pi\)
\(8\) 0 0
\(9\) 7.41997 + 5.09353i 0.824441 + 0.565948i
\(10\) 0 0
\(11\) 2.75255i 0.250232i 0.992142 + 0.125116i \(0.0399303\pi\)
−0.992142 + 0.125116i \(0.960070\pi\)
\(12\) 0 0
\(13\) −4.43326 −0.341020 −0.170510 0.985356i \(-0.554541\pi\)
−0.170510 + 0.985356i \(0.554541\pi\)
\(14\) 0 0
\(15\) 7.63660 24.6180i 0.509107 1.64120i
\(16\) 0 0
\(17\) 25.4208i 1.49534i −0.664070 0.747670i \(-0.731172\pi\)
0.664070 0.747670i \(-0.268828\pi\)
\(18\) 0 0
\(19\) 17.5426 0.923294 0.461647 0.887064i \(-0.347259\pi\)
0.461647 + 0.887064i \(0.347259\pi\)
\(20\) 0 0
\(21\) 31.3291 + 9.71841i 1.49186 + 0.462781i
\(22\) 0 0
\(23\) 17.5482i 0.762966i −0.924376 0.381483i \(-0.875413\pi\)
0.924376 0.381483i \(-0.124587\pi\)
\(24\) 0 0
\(25\) −48.8183 −1.95273
\(26\) 0 0
\(27\) −16.7332 21.1896i −0.619749 0.784800i
\(28\) 0 0
\(29\) 19.6224i 0.676635i 0.941032 + 0.338317i \(0.109858\pi\)
−0.941032 + 0.338317i \(0.890142\pi\)
\(30\) 0 0
\(31\) −2.58322 −0.0833295 −0.0416648 0.999132i \(-0.513266\pi\)
−0.0416648 + 0.999132i \(0.513266\pi\)
\(32\) 0 0
\(33\) 2.44655 7.88691i 0.0741377 0.238997i
\(34\) 0 0
\(35\) 93.9419i 2.68405i
\(36\) 0 0
\(37\) 7.73178 0.208967 0.104484 0.994527i \(-0.466681\pi\)
0.104484 + 0.994527i \(0.466681\pi\)
\(38\) 0 0
\(39\) 12.7026 + 3.94040i 0.325709 + 0.101036i
\(40\) 0 0
\(41\) 58.0069i 1.41480i −0.706812 0.707402i \(-0.749867\pi\)
0.706812 0.707402i \(-0.250133\pi\)
\(42\) 0 0
\(43\) −42.1932 −0.981238 −0.490619 0.871374i \(-0.663229\pi\)
−0.490619 + 0.871374i \(0.663229\pi\)
\(44\) 0 0
\(45\) −43.7624 + 63.7506i −0.972498 + 1.41668i
\(46\) 0 0
\(47\) 17.4666i 0.371629i 0.982585 + 0.185815i \(0.0594924\pi\)
−0.982585 + 0.185815i \(0.940508\pi\)
\(48\) 0 0
\(49\) 70.5514 1.43982
\(50\) 0 0
\(51\) −22.5947 + 72.8384i −0.443034 + 1.42820i
\(52\) 0 0
\(53\) 69.0052i 1.30198i −0.759085 0.650992i \(-0.774353\pi\)
0.759085 0.650992i \(-0.225647\pi\)
\(54\) 0 0
\(55\) −23.6493 −0.429987
\(56\) 0 0
\(57\) −50.2649 15.5923i −0.881840 0.273550i
\(58\) 0 0
\(59\) 50.5878i 0.857420i −0.903442 0.428710i \(-0.858968\pi\)
0.903442 0.428710i \(-0.141032\pi\)
\(60\) 0 0
\(61\) −32.5983 −0.534398 −0.267199 0.963641i \(-0.586098\pi\)
−0.267199 + 0.963641i \(0.586098\pi\)
\(62\) 0 0
\(63\) −81.1296 55.6924i −1.28777 0.884007i
\(64\) 0 0
\(65\) 38.0895i 0.585992i
\(66\) 0 0
\(67\) −48.0128 −0.716609 −0.358305 0.933605i \(-0.616645\pi\)
−0.358305 + 0.933605i \(0.616645\pi\)
\(68\) 0 0
\(69\) −15.5974 + 50.2811i −0.226049 + 0.728711i
\(70\) 0 0
\(71\) 22.1021i 0.311297i −0.987813 0.155648i \(-0.950253\pi\)
0.987813 0.155648i \(-0.0497466\pi\)
\(72\) 0 0
\(73\) −27.0316 −0.370295 −0.185148 0.982711i \(-0.559276\pi\)
−0.185148 + 0.982711i \(0.559276\pi\)
\(74\) 0 0
\(75\) 139.880 + 43.3911i 1.86506 + 0.578548i
\(76\) 0 0
\(77\) 30.0963i 0.390861i
\(78\) 0 0
\(79\) 97.4827 1.23396 0.616979 0.786980i \(-0.288356\pi\)
0.616979 + 0.786980i \(0.288356\pi\)
\(80\) 0 0
\(81\) 29.1119 + 75.5877i 0.359406 + 0.933181i
\(82\) 0 0
\(83\) 59.5252i 0.717170i 0.933497 + 0.358585i \(0.116741\pi\)
−0.933497 + 0.358585i \(0.883259\pi\)
\(84\) 0 0
\(85\) 218.409 2.56952
\(86\) 0 0
\(87\) 17.4409 56.2242i 0.200471 0.646255i
\(88\) 0 0
\(89\) 110.469i 1.24122i 0.784119 + 0.620611i \(0.213115\pi\)
−0.784119 + 0.620611i \(0.786885\pi\)
\(90\) 0 0
\(91\) 48.4730 0.532671
\(92\) 0 0
\(93\) 7.40171 + 2.29603i 0.0795882 + 0.0246885i
\(94\) 0 0
\(95\) 150.722i 1.58654i
\(96\) 0 0
\(97\) 55.1169 0.568215 0.284108 0.958792i \(-0.408303\pi\)
0.284108 + 0.958792i \(0.408303\pi\)
\(98\) 0 0
\(99\) −14.0202 + 20.4238i −0.141618 + 0.206301i
\(100\) 0 0
\(101\) 20.2294i 0.200291i −0.994973 0.100146i \(-0.968069\pi\)
0.994973 0.100146i \(-0.0319309\pi\)
\(102\) 0 0
\(103\) 65.3051 0.634030 0.317015 0.948421i \(-0.397320\pi\)
0.317015 + 0.948421i \(0.397320\pi\)
\(104\) 0 0
\(105\) −83.4982 + 269.172i −0.795221 + 2.56355i
\(106\) 0 0
\(107\) 10.3305i 0.0965468i −0.998834 0.0482734i \(-0.984628\pi\)
0.998834 0.0482734i \(-0.0153719\pi\)
\(108\) 0 0
\(109\) −151.542 −1.39029 −0.695145 0.718870i \(-0.744660\pi\)
−0.695145 + 0.718870i \(0.744660\pi\)
\(110\) 0 0
\(111\) −22.1539 6.87222i −0.199585 0.0619119i
\(112\) 0 0
\(113\) 106.377i 0.941391i −0.882296 0.470696i \(-0.844003\pi\)
0.882296 0.470696i \(-0.155997\pi\)
\(114\) 0 0
\(115\) 150.770 1.31104
\(116\) 0 0
\(117\) −32.8946 22.5809i −0.281151 0.192999i
\(118\) 0 0
\(119\) 277.950i 2.33571i
\(120\) 0 0
\(121\) 113.423 0.937384
\(122\) 0 0
\(123\) −51.5582 + 166.208i −0.419172 + 1.35128i
\(124\) 0 0
\(125\) 204.641i 1.63713i
\(126\) 0 0
\(127\) −112.285 −0.884138 −0.442069 0.896981i \(-0.645755\pi\)
−0.442069 + 0.896981i \(0.645755\pi\)
\(128\) 0 0
\(129\) 120.897 + 37.5025i 0.937183 + 0.290717i
\(130\) 0 0
\(131\) 137.804i 1.05194i 0.850504 + 0.525968i \(0.176297\pi\)
−0.850504 + 0.525968i \(0.823703\pi\)
\(132\) 0 0
\(133\) −191.810 −1.44218
\(134\) 0 0
\(135\) 182.056 143.768i 1.34856 1.06495i
\(136\) 0 0
\(137\) 152.889i 1.11598i −0.829847 0.557990i \(-0.811573\pi\)
0.829847 0.557990i \(-0.188427\pi\)
\(138\) 0 0
\(139\) −236.450 −1.70108 −0.850540 0.525910i \(-0.823725\pi\)
−0.850540 + 0.525910i \(0.823725\pi\)
\(140\) 0 0
\(141\) 15.5248 50.0471i 0.110105 0.354944i
\(142\) 0 0
\(143\) 12.2028i 0.0853340i
\(144\) 0 0
\(145\) −168.591 −1.16270
\(146\) 0 0
\(147\) −202.151 62.7080i −1.37518 0.426585i
\(148\) 0 0
\(149\) 185.019i 1.24174i −0.783914 0.620869i \(-0.786780\pi\)
0.783914 0.620869i \(-0.213220\pi\)
\(150\) 0 0
\(151\) −283.340 −1.87643 −0.938214 0.346057i \(-0.887520\pi\)
−0.938214 + 0.346057i \(0.887520\pi\)
\(152\) 0 0
\(153\) 129.482 188.621i 0.846285 1.23282i
\(154\) 0 0
\(155\) 22.1944i 0.143189i
\(156\) 0 0
\(157\) −32.9672 −0.209982 −0.104991 0.994473i \(-0.533481\pi\)
−0.104991 + 0.994473i \(0.533481\pi\)
\(158\) 0 0
\(159\) −61.3337 + 197.721i −0.385747 + 1.24353i
\(160\) 0 0
\(161\) 191.872i 1.19175i
\(162\) 0 0
\(163\) 248.216 1.52280 0.761399 0.648283i \(-0.224513\pi\)
0.761399 + 0.648283i \(0.224513\pi\)
\(164\) 0 0
\(165\) 67.7624 + 21.0201i 0.410681 + 0.127395i
\(166\) 0 0
\(167\) 235.204i 1.40841i 0.709997 + 0.704205i \(0.248696\pi\)
−0.709997 + 0.704205i \(0.751304\pi\)
\(168\) 0 0
\(169\) −149.346 −0.883706
\(170\) 0 0
\(171\) 130.165 + 89.3537i 0.761201 + 0.522536i
\(172\) 0 0
\(173\) 38.6880i 0.223630i 0.993729 + 0.111815i \(0.0356664\pi\)
−0.993729 + 0.111815i \(0.964334\pi\)
\(174\) 0 0
\(175\) 533.777 3.05016
\(176\) 0 0
\(177\) −44.9639 + 144.950i −0.254033 + 0.818924i
\(178\) 0 0
\(179\) 287.329i 1.60519i −0.596524 0.802595i \(-0.703452\pi\)
0.596524 0.802595i \(-0.296548\pi\)
\(180\) 0 0
\(181\) −199.173 −1.10040 −0.550201 0.835032i \(-0.685449\pi\)
−0.550201 + 0.835032i \(0.685449\pi\)
\(182\) 0 0
\(183\) 93.4041 + 28.9743i 0.510405 + 0.158329i
\(184\) 0 0
\(185\) 66.4296i 0.359079i
\(186\) 0 0
\(187\) 69.9720 0.374182
\(188\) 0 0
\(189\) 182.960 + 231.686i 0.968044 + 1.22585i
\(190\) 0 0
\(191\) 227.555i 1.19139i −0.803211 0.595695i \(-0.796877\pi\)
0.803211 0.595695i \(-0.203123\pi\)
\(192\) 0 0
\(193\) −23.8956 −0.123811 −0.0619056 0.998082i \(-0.519718\pi\)
−0.0619056 + 0.998082i \(0.519718\pi\)
\(194\) 0 0
\(195\) −33.8550 + 109.138i −0.173615 + 0.559682i
\(196\) 0 0
\(197\) 78.6009i 0.398990i −0.979899 0.199495i \(-0.936070\pi\)
0.979899 0.199495i \(-0.0639301\pi\)
\(198\) 0 0
\(199\) −181.811 −0.913625 −0.456812 0.889563i \(-0.651009\pi\)
−0.456812 + 0.889563i \(0.651009\pi\)
\(200\) 0 0
\(201\) 137.571 + 42.6751i 0.684435 + 0.212314i
\(202\) 0 0
\(203\) 214.550i 1.05690i
\(204\) 0 0
\(205\) 498.382 2.43113
\(206\) 0 0
\(207\) 89.3824 130.207i 0.431799 0.629021i
\(208\) 0 0
\(209\) 48.2869i 0.231038i
\(210\) 0 0
\(211\) 2.18826 0.0103709 0.00518544 0.999987i \(-0.498349\pi\)
0.00518544 + 0.999987i \(0.498349\pi\)
\(212\) 0 0
\(213\) −19.6449 + 63.3292i −0.0922297 + 0.297320i
\(214\) 0 0
\(215\) 362.514i 1.68611i
\(216\) 0 0
\(217\) 28.2448 0.130160
\(218\) 0 0
\(219\) 77.4537 + 24.0264i 0.353670 + 0.109710i
\(220\) 0 0
\(221\) 112.697i 0.509941i
\(222\) 0 0
\(223\) −317.724 −1.42477 −0.712386 0.701788i \(-0.752385\pi\)
−0.712386 + 0.701788i \(0.752385\pi\)
\(224\) 0 0
\(225\) −362.231 248.658i −1.60991 1.10515i
\(226\) 0 0
\(227\) 241.233i 1.06270i 0.847152 + 0.531350i \(0.178315\pi\)
−0.847152 + 0.531350i \(0.821685\pi\)
\(228\) 0 0
\(229\) 58.1799 0.254061 0.127030 0.991899i \(-0.459455\pi\)
0.127030 + 0.991899i \(0.459455\pi\)
\(230\) 0 0
\(231\) −26.7504 + 86.2351i −0.115803 + 0.373312i
\(232\) 0 0
\(233\) 242.432i 1.04048i −0.854020 0.520240i \(-0.825842\pi\)
0.854020 0.520240i \(-0.174158\pi\)
\(234\) 0 0
\(235\) −150.069 −0.638590
\(236\) 0 0
\(237\) −279.318 86.6453i −1.17856 0.365592i
\(238\) 0 0
\(239\) 215.651i 0.902304i −0.892447 0.451152i \(-0.851013\pi\)
0.892447 0.451152i \(-0.148987\pi\)
\(240\) 0 0
\(241\) 123.252 0.511417 0.255709 0.966754i \(-0.417691\pi\)
0.255709 + 0.966754i \(0.417691\pi\)
\(242\) 0 0
\(243\) −16.2300 242.457i −0.0667902 0.997767i
\(244\) 0 0
\(245\) 606.160i 2.47412i
\(246\) 0 0
\(247\) −77.7708 −0.314861
\(248\) 0 0
\(249\) 52.9076 170.558i 0.212480 0.684971i
\(250\) 0 0
\(251\) 194.768i 0.775967i 0.921666 + 0.387984i \(0.126828\pi\)
−0.921666 + 0.387984i \(0.873172\pi\)
\(252\) 0 0
\(253\) 48.3024 0.190919
\(254\) 0 0
\(255\) −625.810 194.128i −2.45416 0.761288i
\(256\) 0 0
\(257\) 200.615i 0.780605i −0.920687 0.390303i \(-0.872370\pi\)
0.920687 0.390303i \(-0.127630\pi\)
\(258\) 0 0
\(259\) −84.5389 −0.326405
\(260\) 0 0
\(261\) −99.9473 + 145.598i −0.382940 + 0.557845i
\(262\) 0 0
\(263\) 440.044i 1.67317i −0.547837 0.836585i \(-0.684549\pi\)
0.547837 0.836585i \(-0.315451\pi\)
\(264\) 0 0
\(265\) 592.876 2.23727
\(266\) 0 0
\(267\) 98.1877 316.527i 0.367744 1.18549i
\(268\) 0 0
\(269\) 64.1922i 0.238633i 0.992856 + 0.119316i \(0.0380703\pi\)
−0.992856 + 0.119316i \(0.961930\pi\)
\(270\) 0 0
\(271\) 229.609 0.847265 0.423633 0.905834i \(-0.360755\pi\)
0.423633 + 0.905834i \(0.360755\pi\)
\(272\) 0 0
\(273\) −138.890 43.0842i −0.508755 0.157818i
\(274\) 0 0
\(275\) 134.375i 0.488636i
\(276\) 0 0
\(277\) −329.621 −1.18997 −0.594983 0.803738i \(-0.702841\pi\)
−0.594983 + 0.803738i \(0.702841\pi\)
\(278\) 0 0
\(279\) −19.1674 13.1577i −0.0687003 0.0471602i
\(280\) 0 0
\(281\) 222.349i 0.791279i 0.918406 + 0.395640i \(0.129477\pi\)
−0.918406 + 0.395640i \(0.870523\pi\)
\(282\) 0 0
\(283\) −550.386 −1.94483 −0.972414 0.233261i \(-0.925060\pi\)
−0.972414 + 0.233261i \(0.925060\pi\)
\(284\) 0 0
\(285\) 133.966 431.864i 0.470055 1.51531i
\(286\) 0 0
\(287\) 634.245i 2.20991i
\(288\) 0 0
\(289\) −357.217 −1.23604
\(290\) 0 0
\(291\) −157.927 48.9894i −0.542704 0.168349i
\(292\) 0 0
\(293\) 322.712i 1.10141i 0.834701 + 0.550703i \(0.185640\pi\)
−0.834701 + 0.550703i \(0.814360\pi\)
\(294\) 0 0
\(295\) 434.638 1.47335
\(296\) 0 0
\(297\) 58.3255 46.0590i 0.196382 0.155081i
\(298\) 0 0
\(299\) 77.7958i 0.260187i
\(300\) 0 0
\(301\) 461.339 1.53269
\(302\) 0 0
\(303\) −17.9805 + 57.9635i −0.0593415 + 0.191299i
\(304\) 0 0
\(305\) 280.077i 0.918284i
\(306\) 0 0
\(307\) −66.6568 −0.217123 −0.108562 0.994090i \(-0.534624\pi\)
−0.108562 + 0.994090i \(0.534624\pi\)
\(308\) 0 0
\(309\) −187.119 58.0450i −0.605563 0.187848i
\(310\) 0 0
\(311\) 20.7250i 0.0666398i 0.999445 + 0.0333199i \(0.0106080\pi\)
−0.999445 + 0.0333199i \(0.989392\pi\)
\(312\) 0 0
\(313\) −211.296 −0.675066 −0.337533 0.941314i \(-0.609592\pi\)
−0.337533 + 0.941314i \(0.609592\pi\)
\(314\) 0 0
\(315\) 478.496 697.046i 1.51904 2.21284i
\(316\) 0 0
\(317\) 238.040i 0.750915i 0.926840 + 0.375457i \(0.122514\pi\)
−0.926840 + 0.375457i \(0.877486\pi\)
\(318\) 0 0
\(319\) −54.0117 −0.169316
\(320\) 0 0
\(321\) −9.18205 + 29.6001i −0.0286045 + 0.0922121i
\(322\) 0 0
\(323\) 445.946i 1.38064i
\(324\) 0 0
\(325\) 216.424 0.665921
\(326\) 0 0
\(327\) 434.213 + 134.694i 1.32787 + 0.411910i
\(328\) 0 0
\(329\) 190.979i 0.580483i
\(330\) 0 0
\(331\) 344.811 1.04173 0.520863 0.853640i \(-0.325610\pi\)
0.520863 + 0.853640i \(0.325610\pi\)
\(332\) 0 0
\(333\) 57.3696 + 39.3821i 0.172281 + 0.118264i
\(334\) 0 0
\(335\) 412.515i 1.23139i
\(336\) 0 0
\(337\) −355.471 −1.05481 −0.527405 0.849614i \(-0.676835\pi\)
−0.527405 + 0.849614i \(0.676835\pi\)
\(338\) 0 0
\(339\) −94.5511 + 304.803i −0.278912 + 0.899125i
\(340\) 0 0
\(341\) 7.11043i 0.0208517i
\(342\) 0 0
\(343\) −235.642 −0.687002
\(344\) 0 0
\(345\) −432.003 134.009i −1.25218 0.388431i
\(346\) 0 0
\(347\) 73.9748i 0.213184i 0.994303 + 0.106592i \(0.0339939\pi\)
−0.994303 + 0.106592i \(0.966006\pi\)
\(348\) 0 0
\(349\) −443.377 −1.27042 −0.635210 0.772340i \(-0.719086\pi\)
−0.635210 + 0.772340i \(0.719086\pi\)
\(350\) 0 0
\(351\) 74.1827 + 93.9390i 0.211347 + 0.267632i
\(352\) 0 0
\(353\) 553.017i 1.56662i 0.621630 + 0.783311i \(0.286471\pi\)
−0.621630 + 0.783311i \(0.713529\pi\)
\(354\) 0 0
\(355\) 189.896 0.534917
\(356\) 0 0
\(357\) 247.050 796.411i 0.692016 2.23084i
\(358\) 0 0
\(359\) 352.615i 0.982214i −0.871099 0.491107i \(-0.836592\pi\)
0.871099 0.491107i \(-0.163408\pi\)
\(360\) 0 0
\(361\) −53.2578 −0.147529
\(362\) 0 0
\(363\) −324.993 100.814i −0.895298 0.277724i
\(364\) 0 0
\(365\) 232.249i 0.636298i
\(366\) 0 0
\(367\) 305.686 0.832932 0.416466 0.909151i \(-0.363269\pi\)
0.416466 + 0.909151i \(0.363269\pi\)
\(368\) 0 0
\(369\) 295.460 430.410i 0.800705 1.16642i
\(370\) 0 0
\(371\) 754.499i 2.03369i
\(372\) 0 0
\(373\) 133.295 0.357359 0.178679 0.983907i \(-0.442818\pi\)
0.178679 + 0.983907i \(0.442818\pi\)
\(374\) 0 0
\(375\) −181.891 + 586.361i −0.485043 + 1.56363i
\(376\) 0 0
\(377\) 86.9912i 0.230746i
\(378\) 0 0
\(379\) 239.300 0.631399 0.315699 0.948859i \(-0.397761\pi\)
0.315699 + 0.948859i \(0.397761\pi\)
\(380\) 0 0
\(381\) 321.732 + 99.8025i 0.844442 + 0.261949i
\(382\) 0 0
\(383\) 249.576i 0.651634i −0.945433 0.325817i \(-0.894361\pi\)
0.945433 0.325817i \(-0.105639\pi\)
\(384\) 0 0
\(385\) 258.580 0.671636
\(386\) 0 0
\(387\) −313.073 214.913i −0.808973 0.555330i
\(388\) 0 0
\(389\) 499.992i 1.28533i −0.766148 0.642664i \(-0.777829\pi\)
0.766148 0.642664i \(-0.222171\pi\)
\(390\) 0 0
\(391\) −446.090 −1.14089
\(392\) 0 0
\(393\) 122.484 394.850i 0.311663 1.00471i
\(394\) 0 0
\(395\) 837.548i 2.12037i
\(396\) 0 0
\(397\) −302.418 −0.761759 −0.380880 0.924625i \(-0.624379\pi\)
−0.380880 + 0.924625i \(0.624379\pi\)
\(398\) 0 0
\(399\) 549.594 + 170.486i 1.37743 + 0.427283i
\(400\) 0 0
\(401\) 799.221i 1.99307i 0.0831706 + 0.996535i \(0.473495\pi\)
−0.0831706 + 0.996535i \(0.526505\pi\)
\(402\) 0 0
\(403\) 11.4521 0.0284170
\(404\) 0 0
\(405\) −649.431 + 250.122i −1.60353 + 0.617586i
\(406\) 0 0
\(407\) 21.2821i 0.0522902i
\(408\) 0 0
\(409\) 108.812 0.266044 0.133022 0.991113i \(-0.457532\pi\)
0.133022 + 0.991113i \(0.457532\pi\)
\(410\) 0 0
\(411\) −135.892 + 438.075i −0.330638 + 1.06588i
\(412\) 0 0
\(413\) 553.125i 1.33929i
\(414\) 0 0
\(415\) −511.426 −1.23235
\(416\) 0 0
\(417\) 677.502 + 210.164i 1.62471 + 0.503989i
\(418\) 0 0
\(419\) 183.076i 0.436936i −0.975844 0.218468i \(-0.929894\pi\)
0.975844 0.218468i \(-0.0701059\pi\)
\(420\) 0 0
\(421\) −213.105 −0.506187 −0.253093 0.967442i \(-0.581448\pi\)
−0.253093 + 0.967442i \(0.581448\pi\)
\(422\) 0 0
\(423\) −88.9666 + 129.602i −0.210323 + 0.306387i
\(424\) 0 0
\(425\) 1241.00i 2.92000i
\(426\) 0 0
\(427\) 356.428 0.834727
\(428\) 0 0
\(429\) −10.8462 + 34.9647i −0.0252824 + 0.0815027i
\(430\) 0 0
\(431\) 471.854i 1.09479i 0.836875 + 0.547394i \(0.184380\pi\)
−0.836875 + 0.547394i \(0.815620\pi\)
\(432\) 0 0
\(433\) 396.992 0.916841 0.458421 0.888735i \(-0.348415\pi\)
0.458421 + 0.888735i \(0.348415\pi\)
\(434\) 0 0
\(435\) 483.065 + 149.848i 1.11049 + 0.344479i
\(436\) 0 0
\(437\) 307.841i 0.704442i
\(438\) 0 0
\(439\) −201.084 −0.458050 −0.229025 0.973420i \(-0.573554\pi\)
−0.229025 + 0.973420i \(0.573554\pi\)
\(440\) 0 0
\(441\) 523.489 + 359.356i 1.18705 + 0.814865i
\(442\) 0 0
\(443\) 189.532i 0.427838i −0.976851 0.213919i \(-0.931377\pi\)
0.976851 0.213919i \(-0.0686229\pi\)
\(444\) 0 0
\(445\) −949.121 −2.13286
\(446\) 0 0
\(447\) −164.450 + 530.136i −0.367897 + 1.18599i
\(448\) 0 0
\(449\) 49.3773i 0.109972i −0.998487 0.0549859i \(-0.982489\pi\)
0.998487 0.0549859i \(-0.0175114\pi\)
\(450\) 0 0
\(451\) 159.667 0.354029
\(452\) 0 0
\(453\) 811.858 + 251.841i 1.79218 + 0.555940i
\(454\) 0 0
\(455\) 416.469i 0.915316i
\(456\) 0 0
\(457\) −438.599 −0.959734 −0.479867 0.877341i \(-0.659315\pi\)
−0.479867 + 0.877341i \(0.659315\pi\)
\(458\) 0 0
\(459\) −538.657 + 425.372i −1.17354 + 0.926736i
\(460\) 0 0
\(461\) 27.0211i 0.0586142i 0.999570 + 0.0293071i \(0.00933007\pi\)
−0.999570 + 0.0293071i \(0.990670\pi\)
\(462\) 0 0
\(463\) 128.181 0.276850 0.138425 0.990373i \(-0.455796\pi\)
0.138425 + 0.990373i \(0.455796\pi\)
\(464\) 0 0
\(465\) −19.7270 + 63.5937i −0.0424236 + 0.136761i
\(466\) 0 0
\(467\) 624.873i 1.33806i 0.743236 + 0.669029i \(0.233290\pi\)
−0.743236 + 0.669029i \(0.766710\pi\)
\(468\) 0 0
\(469\) 524.970 1.11934
\(470\) 0 0
\(471\) 94.4612 + 29.3022i 0.200554 + 0.0622127i
\(472\) 0 0
\(473\) 116.139i 0.245537i
\(474\) 0 0
\(475\) −856.400 −1.80295
\(476\) 0 0
\(477\) 351.480 512.016i 0.736855 1.07341i
\(478\) 0 0
\(479\) 782.010i 1.63259i −0.577636 0.816295i \(-0.696025\pi\)
0.577636 0.816295i \(-0.303975\pi\)
\(480\) 0 0
\(481\) −34.2770 −0.0712619
\(482\) 0 0
\(483\) 170.541 549.771i 0.353087 1.13824i
\(484\) 0 0
\(485\) 473.551i 0.976393i
\(486\) 0 0
\(487\) 732.325 1.50375 0.751874 0.659307i \(-0.229150\pi\)
0.751874 + 0.659307i \(0.229150\pi\)
\(488\) 0 0
\(489\) −711.215 220.621i −1.45443 0.451169i
\(490\) 0 0
\(491\) 65.5662i 0.133536i −0.997769 0.0667680i \(-0.978731\pi\)
0.997769 0.0667680i \(-0.0212687\pi\)
\(492\) 0 0
\(493\) 498.817 1.01180
\(494\) 0 0
\(495\) −175.477 120.458i −0.354499 0.243350i
\(496\) 0 0
\(497\) 241.663i 0.486243i
\(498\) 0 0
\(499\) 846.549 1.69649 0.848245 0.529604i \(-0.177659\pi\)
0.848245 + 0.529604i \(0.177659\pi\)
\(500\) 0 0
\(501\) 209.056 673.933i 0.417278 1.34518i
\(502\) 0 0
\(503\) 186.077i 0.369934i 0.982745 + 0.184967i \(0.0592179\pi\)
−0.982745 + 0.184967i \(0.940782\pi\)
\(504\) 0 0
\(505\) 173.806 0.344171
\(506\) 0 0
\(507\) 427.923 + 132.743i 0.844029 + 0.261821i
\(508\) 0 0
\(509\) 996.730i 1.95821i −0.203350 0.979106i \(-0.565183\pi\)
0.203350 0.979106i \(-0.434817\pi\)
\(510\) 0 0
\(511\) 295.562 0.578399
\(512\) 0 0
\(513\) −293.544 371.720i −0.572210 0.724601i
\(514\) 0 0
\(515\) 561.085i 1.08949i
\(516\) 0 0
\(517\) −48.0777 −0.0929936
\(518\) 0 0
\(519\) 34.3870 110.853i 0.0662563 0.213590i
\(520\) 0 0
\(521\) 471.553i 0.905092i 0.891741 + 0.452546i \(0.149484\pi\)
−0.891741 + 0.452546i \(0.850516\pi\)
\(522\) 0 0
\(523\) 364.836 0.697582 0.348791 0.937200i \(-0.386592\pi\)
0.348791 + 0.937200i \(0.386592\pi\)
\(524\) 0 0
\(525\) −1529.44 474.436i −2.91321 0.903688i
\(526\) 0 0
\(527\) 65.6674i 0.124606i
\(528\) 0 0
\(529\) 221.060 0.417882
\(530\) 0 0
\(531\) 257.671 375.360i 0.485255 0.706893i
\(532\) 0 0
\(533\) 257.160i 0.482476i
\(534\) 0 0
\(535\) 88.7573 0.165901
\(536\) 0 0
\(537\) −255.386 + 823.286i −0.475579 + 1.53312i
\(538\) 0 0
\(539\) 194.196i 0.360290i
\(540\) 0 0
\(541\) −68.1097 −0.125896 −0.0629480 0.998017i \(-0.520050\pi\)
−0.0629480 + 0.998017i \(0.520050\pi\)
\(542\) 0 0
\(543\) 570.691 + 177.030i 1.05100 + 0.326023i
\(544\) 0 0
\(545\) 1302.01i 2.38901i
\(546\) 0 0
\(547\) −459.725 −0.840448 −0.420224 0.907420i \(-0.638049\pi\)
−0.420224 + 0.907420i \(0.638049\pi\)
\(548\) 0 0
\(549\) −241.878 166.040i −0.440580 0.302442i
\(550\) 0 0
\(551\) 344.228i 0.624733i
\(552\) 0 0
\(553\) −1065.87 −1.92743
\(554\) 0 0
\(555\) 59.0445 190.341i 0.106386 0.342957i
\(556\) 0 0
\(557\) 95.1108i 0.170756i 0.996349 + 0.0853778i \(0.0272097\pi\)
−0.996349 + 0.0853778i \(0.972790\pi\)
\(558\) 0 0
\(559\) 187.053 0.334622
\(560\) 0 0
\(561\) −200.491 62.1931i −0.357382 0.110861i
\(562\) 0 0
\(563\) 422.228i 0.749960i −0.927033 0.374980i \(-0.877650\pi\)
0.927033 0.374980i \(-0.122350\pi\)
\(564\) 0 0
\(565\) 913.967 1.61764
\(566\) 0 0
\(567\) −318.308 826.472i −0.561390 1.45762i
\(568\) 0 0
\(569\) 328.583i 0.577474i −0.957408 0.288737i \(-0.906765\pi\)
0.957408 0.288737i \(-0.0932354\pi\)
\(570\) 0 0
\(571\) 503.834 0.882371 0.441186 0.897416i \(-0.354558\pi\)
0.441186 + 0.897416i \(0.354558\pi\)
\(572\) 0 0
\(573\) −202.258 + 652.016i −0.352980 + 1.13790i
\(574\) 0 0
\(575\) 856.675i 1.48987i
\(576\) 0 0
\(577\) 1035.33 1.79433 0.897163 0.441700i \(-0.145624\pi\)
0.897163 + 0.441700i \(0.145624\pi\)
\(578\) 0 0
\(579\) 68.4681 + 21.2391i 0.118252 + 0.0366823i
\(580\) 0 0
\(581\) 650.845i 1.12022i
\(582\) 0 0
\(583\) 189.940 0.325798
\(584\) 0 0
\(585\) 194.010 282.623i 0.331641 0.483116i
\(586\) 0 0
\(587\) 501.148i 0.853745i −0.904312 0.426872i \(-0.859615\pi\)
0.904312 0.426872i \(-0.140385\pi\)
\(588\) 0 0
\(589\) −45.3163 −0.0769376
\(590\) 0 0
\(591\) −69.8627 + 225.216i −0.118211 + 0.381076i
\(592\) 0 0
\(593\) 737.286i 1.24332i −0.783289 0.621658i \(-0.786459\pi\)
0.783289 0.621658i \(-0.213541\pi\)
\(594\) 0 0
\(595\) −2388.08 −4.01358
\(596\) 0 0
\(597\) 520.945 + 161.599i 0.872605 + 0.270685i
\(598\) 0 0
\(599\) 801.823i 1.33860i 0.742991 + 0.669301i \(0.233407\pi\)
−0.742991 + 0.669301i \(0.766593\pi\)
\(600\) 0 0
\(601\) 252.561 0.420234 0.210117 0.977676i \(-0.432615\pi\)
0.210117 + 0.977676i \(0.432615\pi\)
\(602\) 0 0
\(603\) −356.254 244.555i −0.590802 0.405564i
\(604\) 0 0
\(605\) 974.507i 1.61076i
\(606\) 0 0
\(607\) −627.073 −1.03307 −0.516535 0.856266i \(-0.672778\pi\)
−0.516535 + 0.856266i \(0.672778\pi\)
\(608\) 0 0
\(609\) −190.699 + 614.753i −0.313134 + 1.00945i
\(610\) 0 0
\(611\) 77.4339i 0.126733i
\(612\) 0 0
\(613\) −375.629 −0.612772 −0.306386 0.951907i \(-0.599120\pi\)
−0.306386 + 0.951907i \(0.599120\pi\)
\(614\) 0 0
\(615\) −1428.02 442.976i −2.32198 0.720286i
\(616\) 0 0
\(617\) 161.548i 0.261829i −0.991394 0.130914i \(-0.958209\pi\)
0.991394 0.130914i \(-0.0417913\pi\)
\(618\) 0 0
\(619\) 9.45164 0.0152692 0.00763460 0.999971i \(-0.497570\pi\)
0.00763460 + 0.999971i \(0.497570\pi\)
\(620\) 0 0
\(621\) −371.840 + 293.638i −0.598776 + 0.472847i
\(622\) 0 0
\(623\) 1207.86i 1.93878i
\(624\) 0 0
\(625\) 537.772 0.860435
\(626\) 0 0
\(627\) 42.9187 138.357i 0.0684509 0.220665i
\(628\) 0 0
\(629\) 196.548i 0.312477i
\(630\) 0 0
\(631\) 1073.00 1.70048 0.850239 0.526398i \(-0.176458\pi\)
0.850239 + 0.526398i \(0.176458\pi\)
\(632\) 0 0
\(633\) −6.27002 1.94498i −0.00990525 0.00307264i
\(634\) 0 0
\(635\) 964.730i 1.51926i
\(636\) 0 0
\(637\) −312.772 −0.491008
\(638\) 0 0
\(639\) 112.578 163.997i 0.176178 0.256646i
\(640\) 0 0
\(641\) 713.963i 1.11383i 0.830570 + 0.556914i \(0.188015\pi\)
−0.830570 + 0.556914i \(0.811985\pi\)
\(642\) 0 0
\(643\) −339.764 −0.528405 −0.264202 0.964467i \(-0.585109\pi\)
−0.264202 + 0.964467i \(0.585109\pi\)
\(644\) 0 0
\(645\) −322.213 + 1038.71i −0.499555 + 1.61041i
\(646\) 0 0
\(647\) 108.874i 0.168275i −0.996454 0.0841375i \(-0.973187\pi\)
0.996454 0.0841375i \(-0.0268135\pi\)
\(648\) 0 0
\(649\) 139.246 0.214554
\(650\) 0 0
\(651\) −80.9299 25.1047i −0.124316 0.0385633i
\(652\) 0 0
\(653\) 970.043i 1.48552i 0.669559 + 0.742759i \(0.266483\pi\)
−0.669559 + 0.742759i \(0.733517\pi\)
\(654\) 0 0
\(655\) −1183.98 −1.80760
\(656\) 0 0
\(657\) −200.573 137.686i −0.305287 0.209568i
\(658\) 0 0
\(659\) 302.641i 0.459243i −0.973280 0.229622i \(-0.926251\pi\)
0.973280 0.229622i \(-0.0737489\pi\)
\(660\) 0 0
\(661\) −406.011 −0.614237 −0.307118 0.951671i \(-0.599365\pi\)
−0.307118 + 0.951671i \(0.599365\pi\)
\(662\) 0 0
\(663\) 100.168 322.911i 0.151083 0.487046i
\(664\) 0 0
\(665\) 1647.98i 2.47817i
\(666\) 0 0
\(667\) 344.338 0.516250
\(668\) 0 0
\(669\) 910.377 + 282.402i 1.36080 + 0.422126i
\(670\) 0 0
\(671\) 89.7285i 0.133724i
\(672\) 0 0
\(673\) −143.090 −0.212615 −0.106307 0.994333i \(-0.533903\pi\)
−0.106307 + 0.994333i \(0.533903\pi\)
\(674\) 0 0
\(675\) 816.888 + 1034.44i 1.21020 + 1.53251i
\(676\) 0 0
\(677\) 791.131i 1.16858i 0.811544 + 0.584292i \(0.198628\pi\)
−0.811544 + 0.584292i \(0.801372\pi\)
\(678\) 0 0
\(679\) −602.645 −0.887548
\(680\) 0 0
\(681\) 214.415 691.207i 0.314853 1.01499i
\(682\) 0 0
\(683\) 925.330i 1.35480i −0.735614 0.677401i \(-0.763106\pi\)
0.735614 0.677401i \(-0.236894\pi\)
\(684\) 0 0
\(685\) 1313.59 1.91765
\(686\) 0 0
\(687\) −166.703 51.7120i −0.242654 0.0752722i
\(688\) 0 0
\(689\) 305.918i 0.444002i
\(690\) 0 0
\(691\) 666.330 0.964299 0.482149 0.876089i \(-0.339856\pi\)
0.482149 + 0.876089i \(0.339856\pi\)
\(692\) 0 0
\(693\) 153.296 223.313i 0.221207 0.322242i
\(694\) 0 0
\(695\) 2031.52i 2.92305i
\(696\) 0 0
\(697\) −1474.58 −2.11561
\(698\) 0 0
\(699\) −215.480 + 694.642i −0.308269 + 0.993765i
\(700\) 0 0
\(701\) 1238.38i 1.76659i −0.468820 0.883294i \(-0.655321\pi\)
0.468820 0.883294i \(-0.344679\pi\)
\(702\) 0 0
\(703\) 135.635 0.192938
\(704\) 0 0
\(705\) 429.993 + 133.385i 0.609919 + 0.189199i
\(706\) 0 0
\(707\) 221.187i 0.312854i
\(708\) 0 0
\(709\) 162.142 0.228692 0.114346 0.993441i \(-0.463523\pi\)
0.114346 + 0.993441i \(0.463523\pi\)
\(710\) 0 0
\(711\) 723.318 + 496.531i 1.01733 + 0.698356i
\(712\) 0 0
\(713\) 45.3309i 0.0635776i
\(714\) 0 0
\(715\) 104.843 0.146634
\(716\) 0 0
\(717\) −191.676 + 617.906i −0.267331 + 0.861793i
\(718\) 0 0
\(719\) 534.958i 0.744031i 0.928226 + 0.372016i \(0.121333\pi\)
−0.928226 + 0.372016i \(0.878667\pi\)
\(720\) 0 0
\(721\) −714.042 −0.990350
\(722\) 0 0
\(723\) −353.154 109.549i −0.488456 0.151521i
\(724\) 0 0
\(725\) 957.933i 1.32129i
\(726\) 0 0
\(727\) 723.175 0.994738 0.497369 0.867539i \(-0.334299\pi\)
0.497369 + 0.867539i \(0.334299\pi\)
\(728\) 0 0
\(729\) −168.999 + 709.141i −0.231823 + 0.972758i
\(730\) 0 0
\(731\) 1072.59i 1.46729i
\(732\) 0 0
\(733\) −473.296 −0.645697 −0.322849 0.946451i \(-0.604640\pi\)
−0.322849 + 0.946451i \(0.604640\pi\)
\(734\) 0 0
\(735\) 538.772 1736.84i 0.733024 2.36304i
\(736\) 0 0
\(737\) 132.158i 0.179319i
\(738\) 0 0
\(739\) 724.955 0.980994 0.490497 0.871443i \(-0.336815\pi\)
0.490497 + 0.871443i \(0.336815\pi\)
\(740\) 0 0
\(741\) 222.837 + 69.1249i 0.300725 + 0.0932859i
\(742\) 0 0
\(743\) 905.636i 1.21889i −0.792828 0.609445i \(-0.791392\pi\)
0.792828 0.609445i \(-0.208608\pi\)
\(744\) 0 0
\(745\) 1589.64 2.13374
\(746\) 0 0
\(747\) −303.193 + 441.675i −0.405881 + 0.591265i
\(748\) 0 0
\(749\) 112.953i 0.150806i
\(750\) 0 0
\(751\) −1039.66 −1.38436 −0.692181 0.721724i \(-0.743350\pi\)
−0.692181 + 0.721724i \(0.743350\pi\)
\(752\) 0 0
\(753\) 173.115 558.070i 0.229901 0.741128i
\(754\) 0 0
\(755\) 2434.39i 3.22436i
\(756\) 0 0
\(757\) 826.135 1.09133 0.545664 0.838004i \(-0.316278\pi\)
0.545664 + 0.838004i \(0.316278\pi\)
\(758\) 0 0
\(759\) −138.401 42.9325i −0.182347 0.0565646i
\(760\) 0 0
\(761\) 159.752i 0.209924i −0.994476 0.104962i \(-0.966528\pi\)
0.994476 0.104962i \(-0.0334721\pi\)
\(762\) 0 0
\(763\) 1656.95 2.17162
\(764\) 0 0
\(765\) 1620.59 + 1112.47i 2.11842 + 1.45422i
\(766\) 0 0
\(767\) 224.269i 0.292397i
\(768\) 0 0
\(769\) −1382.69 −1.79804 −0.899020 0.437908i \(-0.855720\pi\)
−0.899020 + 0.437908i \(0.855720\pi\)
\(770\) 0 0
\(771\) −178.313 + 574.825i −0.231275 + 0.745558i
\(772\) 0 0
\(773\) 33.4297i 0.0432466i −0.999766 0.0216233i \(-0.993117\pi\)
0.999766 0.0216233i \(-0.00688345\pi\)
\(774\) 0 0
\(775\) 126.108 0.162720
\(776\) 0 0
\(777\) 242.230 + 75.1406i 0.311750 + 0.0967060i
\(778\) 0 0
\(779\) 1017.59i 1.30628i
\(780\) 0 0
\(781\) 60.8370 0.0778964
\(782\) 0 0
\(783\) 415.791 328.346i 0.531023 0.419343i
\(784\) 0 0
\(785\) 283.246i 0.360823i
\(786\) 0 0
\(787\) 516.814 0.656688 0.328344 0.944558i \(-0.393509\pi\)
0.328344 + 0.944558i \(0.393509\pi\)
\(788\) 0 0
\(789\) −391.123 + 1260.86i −0.495720 + 1.59805i
\(790\) 0 0
\(791\) 1163.12i 1.47045i
\(792\) 0 0
\(793\) 144.517 0.182240
\(794\) 0 0
\(795\) −1698.77 526.965i −2.13682 0.662849i
\(796\) 0 0
\(797\) 593.861i 0.745120i −0.928008 0.372560i \(-0.878480\pi\)
0.928008 0.372560i \(-0.121520\pi\)
\(798\) 0 0
\(799\) 444.014 0.555713
\(800\) 0 0