Properties

Label 768.3.h.g.641.9
Level $768$
Weight $3$
Character 768.641
Analytic conductor $20.926$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 768.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.9264843029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} - 7060 x^{7} + 17714 x^{6} - 25496 x^{5} + 24840 x^{4} - 17932 x^{3} + 11724 x^{2} - 7056 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{34}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 641.9
Root \(-1.09921 + 2.65372i\) of defining polynomial
Character \(\chi\) \(=\) 768.641
Dual form 768.3.h.g.641.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.888828 - 2.86531i) q^{3} -8.59176 q^{5} -10.9340 q^{7} +(-7.41997 - 5.09353i) q^{9} +O(q^{10})\) \(q+(0.888828 - 2.86531i) q^{3} -8.59176 q^{5} -10.9340 q^{7} +(-7.41997 - 5.09353i) q^{9} +2.75255 q^{11} +4.43326i q^{13} +(-7.63660 + 24.6180i) q^{15} -25.4208i q^{17} +17.5426i q^{19} +(-9.71841 + 31.3291i) q^{21} -17.5482i q^{23} +48.8183 q^{25} +(-21.1896 + 16.7332i) q^{27} +19.6224 q^{29} +2.58322 q^{31} +(2.44655 - 7.88691i) q^{33} +93.9419 q^{35} +7.73178i q^{37} +(12.7026 + 3.94040i) q^{39} +58.0069i q^{41} +42.1932i q^{43} +(63.7506 + 43.7624i) q^{45} -17.4666i q^{47} +70.5514 q^{49} +(-72.8384 - 22.5947i) q^{51} +69.0052 q^{53} -23.6493 q^{55} +(50.2649 + 15.5923i) q^{57} -50.5878 q^{59} +32.5983i q^{61} +(81.1296 + 55.6924i) q^{63} -38.0895i q^{65} -48.0128i q^{67} +(-50.2811 - 15.5974i) q^{69} -22.1021i q^{71} +27.0316 q^{73} +(43.3911 - 139.880i) q^{75} -30.0963 q^{77} -97.4827 q^{79} +(29.1119 + 75.5877i) q^{81} -59.5252 q^{83} +218.409i q^{85} +(17.4409 - 56.2242i) q^{87} -110.469i q^{89} -48.4730i q^{91} +(2.29603 - 7.40171i) q^{93} -150.722i q^{95} +55.1169 q^{97} +(-20.4238 - 14.0202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{7} + O(q^{10}) \) \( 16q - 16q^{7} + 32q^{15} + 80q^{25} - 112q^{31} + 16q^{33} + 208q^{39} + 144q^{49} - 384q^{55} + 80q^{57} + 528q^{63} + 160q^{73} - 816q^{79} + 144q^{81} + 736q^{87} + 192q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(3\) 0.888828 2.86531i 0.296276 0.955102i
\(4\) 0 0
\(5\) −8.59176 −1.71835 −0.859176 0.511680i \(-0.829023\pi\)
−0.859176 + 0.511680i \(0.829023\pi\)
\(6\) 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
\(11\) 2.75255 0.250232 0.125116 0.992142i \(-0.460070\pi\)
0.125116 + 0.992142i \(0.460070\pi\)
\(12\) 0 0
\(13\) 4.43326i 0.341020i 0.985356 + 0.170510i \(0.0545415\pi\)
−0.985356 + 0.170510i \(0.945459\pi\)
\(14\) 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
\(19\) 17.5426i 0.923294i 0.887064 + 0.461647i \(0.152741\pi\)
−0.887064 + 0.461647i \(0.847259\pi\)
\(20\) 0 0
\(21\) −9.71841 + 31.3291i −0.462781 + 1.49186i
\(22\) 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
\(27\) −21.1896 + 16.7332i −0.784800 + 0.619749i
\(28\) 0 0
\(29\) 19.6224 0.676635 0.338317 0.941032i \(-0.390142\pi\)
0.338317 + 0.941032i \(0.390142\pi\)
\(30\) 0 0
\(31\) 2.58322 0.0833295 0.0416648 0.999132i \(-0.486734\pi\)
0.0416648 + 0.999132i \(0.486734\pi\)
\(32\) 0 0
\(33\) 2.44655 7.88691i 0.0741377 0.238997i
\(34\) 0 0
\(35\) 93.9419 2.68405
\(36\) 0 0
\(37\) 7.73178i 0.208967i 0.994527 + 0.104484i \(0.0333189\pi\)
−0.994527 + 0.104484i \(0.966681\pi\)
\(38\) 0 0
\(39\) 12.7026 + 3.94040i 0.325709 + 0.101036i
\(40\) 0 0
\(41\) 58.0069i 1.41480i 0.706812 + 0.707402i \(0.250133\pi\)
−0.706812 + 0.707402i \(0.749867\pi\)
\(42\) 0 0
\(43\) 42.1932i 0.981238i 0.871374 + 0.490619i \(0.163229\pi\)
−0.871374 + 0.490619i \(0.836771\pi\)
\(44\) 0 0
\(45\) 63.7506 + 43.7624i 1.41668 + 0.972498i
\(46\) 0 0
\(47\) 17.4666i 0.371629i −0.982585 0.185815i \(-0.940508\pi\)
0.982585 0.185815i \(-0.0594924\pi\)
\(48\) 0 0
\(49\) 70.5514 1.43982
\(50\) 0 0
\(51\) −72.8384 22.5947i −1.42820 0.443034i
\(52\) 0 0
\(53\) 69.0052 1.30198 0.650992 0.759085i \(-0.274353\pi\)
0.650992 + 0.759085i \(0.274353\pi\)
\(54\) 0 0
\(55\) −23.6493 −0.429987
\(56\) 0 0
\(57\) 50.2649 + 15.5923i 0.881840 + 0.273550i
\(58\) 0 0
\(59\) −50.5878 −0.857420 −0.428710 0.903442i \(-0.641032\pi\)
−0.428710 + 0.903442i \(0.641032\pi\)
\(60\) 0 0
\(61\) 32.5983i 0.534398i 0.963641 + 0.267199i \(0.0860981\pi\)
−0.963641 + 0.267199i \(0.913902\pi\)
\(62\) 0 0
\(63\) 81.1296 + 55.6924i 1.28777 + 0.884007i
\(64\) 0 0
\(65\) 38.0895i 0.585992i
\(66\) 0 0
\(67\) 48.0128i 0.716609i −0.933605 0.358305i \(-0.883355\pi\)
0.933605 0.358305i \(-0.116645\pi\)
\(68\) 0 0
\(69\) −50.2811 15.5974i −0.728711 0.226049i
\(70\) 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 \(-0.440724\pi\)
0.185148 + 0.982711i \(0.440724\pi\)
\(74\) 0 0
\(75\) 43.3911 139.880i 0.578548 1.86506i
\(76\) 0 0
\(77\) −30.0963 −0.390861
\(78\) 0 0
\(79\) −97.4827 −1.23396 −0.616979 0.786980i \(-0.711644\pi\)
−0.616979 + 0.786980i \(0.711644\pi\)
\(80\) 0 0
\(81\) 29.1119 + 75.5877i 0.359406 + 0.933181i
\(82\) 0 0
\(83\) −59.5252 −0.717170 −0.358585 0.933497i \(-0.616741\pi\)
−0.358585 + 0.933497i \(0.616741\pi\)
\(84\) 0 0
\(85\) 218.409i 2.56952i
\(86\) 0 0
\(87\) 17.4409 56.2242i 0.200471 0.646255i
\(88\) 0 0
\(89\) 110.469i 1.24122i −0.784119 0.620611i \(-0.786885\pi\)
0.784119 0.620611i \(-0.213115\pi\)
\(90\) 0 0
\(91\) 48.4730i 0.532671i
\(92\) 0 0
\(93\) 2.29603 7.40171i 0.0246885 0.0795882i
\(94\) 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
\(99\) −20.4238 14.0202i −0.206301 0.141618i
\(100\) 0 0
\(101\) 20.2294 0.200291 0.100146 0.994973i \(-0.468069\pi\)
0.100146 + 0.994973i \(0.468069\pi\)
\(102\) 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
\(107\) −10.3305 −0.0965468 −0.0482734 0.998834i \(-0.515372\pi\)
−0.0482734 + 0.998834i \(0.515372\pi\)
\(108\) 0 0
\(109\) 151.542i 1.39029i 0.718870 + 0.695145i \(0.244660\pi\)
−0.718870 + 0.695145i \(0.755340\pi\)
\(110\) 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
\(115\) 150.770i 1.31104i
\(116\) 0 0
\(117\) 22.5809 32.8946i 0.192999 0.281151i
\(118\) 0 0
\(119\) 277.950i 2.33571i
\(120\) 0 0
\(121\) −113.423 −0.937384
\(122\) 0 0
\(123\) 166.208 + 51.5582i 1.35128 + 0.419172i
\(124\) 0 0
\(125\) −204.641 −1.63713
\(126\) 0 0
\(127\) 112.285 0.884138 0.442069 0.896981i \(-0.354245\pi\)
0.442069 + 0.896981i \(0.354245\pi\)
\(128\) 0 0
\(129\) 120.897 + 37.5025i 0.937183 + 0.290717i
\(130\) 0 0
\(131\) −137.804 −1.05194 −0.525968 0.850504i \(-0.676297\pi\)
−0.525968 + 0.850504i \(0.676297\pi\)
\(132\) 0 0
\(133\) 191.810i 1.44218i
\(134\) 0 0
\(135\) 182.056 143.768i 1.34856 1.06495i
\(136\) 0 0
\(137\) 152.889i 1.11598i 0.829847 + 0.557990i \(0.188427\pi\)
−0.829847 + 0.557990i \(0.811573\pi\)
\(138\) 0 0
\(139\) 236.450i 1.70108i 0.525910 + 0.850540i \(0.323725\pi\)
−0.525910 + 0.850540i \(0.676275\pi\)
\(140\) 0 0
\(141\) −50.0471 15.5248i −0.354944 0.110105i
\(142\) 0 0
\(143\) 12.2028i 0.0853340i
\(144\) 0 0
\(145\) −168.591 −1.16270
\(146\) 0 0
\(147\) 62.7080 202.151i 0.426585 1.37518i
\(148\) 0 0
\(149\) 185.019 1.24174 0.620869 0.783914i \(-0.286780\pi\)
0.620869 + 0.783914i \(0.286780\pi\)
\(150\) 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
\(155\) −22.1944 −0.143189
\(156\) 0 0
\(157\) 32.9672i 0.209982i 0.994473 + 0.104991i \(0.0334814\pi\)
−0.994473 + 0.104991i \(0.966519\pi\)
\(158\) 0 0
\(159\) 61.3337 197.721i 0.385747 1.24353i
\(160\) 0 0
\(161\) 191.872i 1.19175i
\(162\) 0 0
\(163\) 248.216i 1.52280i 0.648283 + 0.761399i \(0.275487\pi\)
−0.648283 + 0.761399i \(0.724513\pi\)
\(164\) 0 0
\(165\) −21.0201 + 67.7624i −0.127395 + 0.410681i
\(166\) 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
\(171\) 89.3537 130.165i 0.522536 0.761201i
\(172\) 0 0
\(173\) 38.6880 0.223630 0.111815 0.993729i \(-0.464334\pi\)
0.111815 + 0.993729i \(0.464334\pi\)
\(174\) 0 0
\(175\) −533.777 −3.05016
\(176\) 0 0
\(177\) −44.9639 + 144.950i −0.254033 + 0.818924i
\(178\) 0 0
\(179\) 287.329 1.60519 0.802595 0.596524i \(-0.203452\pi\)
0.802595 + 0.596524i \(0.203452\pi\)
\(180\) 0 0
\(181\) 199.173i 1.10040i −0.835032 0.550201i \(-0.814551\pi\)
0.835032 0.550201i \(-0.185449\pi\)
\(182\) 0 0
\(183\) 93.4041 + 28.9743i 0.510405 + 0.158329i
\(184\) 0 0
\(185\) 66.4296i 0.359079i
\(186\) 0 0
\(187\) 69.9720i 0.374182i
\(188\) 0 0
\(189\) 231.686 182.960i 1.22585 0.968044i
\(190\) 0 0
\(191\) 227.555i 1.19139i 0.803211 + 0.595695i \(0.203123\pi\)
−0.803211 + 0.595695i \(0.796877\pi\)
\(192\) 0 0
\(193\) −23.8956 −0.123811 −0.0619056 0.998082i \(-0.519718\pi\)
−0.0619056 + 0.998082i \(0.519718\pi\)
\(194\) 0 0
\(195\) −109.138 33.8550i −0.559682 0.173615i
\(196\) 0 0
\(197\) 78.6009 0.398990 0.199495 0.979899i \(-0.436070\pi\)
0.199495 + 0.979899i \(0.436070\pi\)
\(198\) 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
\(203\) −214.550 −1.05690
\(204\) 0 0
\(205\) 498.382i 2.43113i
\(206\) 0 0
\(207\) −89.3824 + 130.207i −0.431799 + 0.629021i
\(208\) 0 0
\(209\) 48.2869i 0.231038i
\(210\) 0 0
\(211\) 2.18826i 0.0103709i 0.999987 + 0.00518544i \(0.00165058\pi\)
−0.999987 + 0.00518544i \(0.998349\pi\)
\(212\) 0 0
\(213\) −63.3292 19.6449i −0.297320 0.0922297i
\(214\) 0 0
\(215\) 362.514i 1.68611i
\(216\) 0 0
\(217\) −28.2448 −0.130160
\(218\) 0 0
\(219\) 24.0264 77.4537i 0.109710 0.353670i
\(220\) 0 0
\(221\) 112.697 0.509941
\(222\) 0 0
\(223\) 317.724 1.42477 0.712386 0.701788i \(-0.247615\pi\)
0.712386 + 0.701788i \(0.247615\pi\)
\(224\) 0 0
\(225\) −362.231 248.658i −1.60991 1.10515i
\(226\) 0 0
\(227\) −241.233 −1.06270 −0.531350 0.847152i \(-0.678315\pi\)
−0.531350 + 0.847152i \(0.678315\pi\)
\(228\) 0 0
\(229\) 58.1799i 0.254061i 0.991899 + 0.127030i \(0.0405446\pi\)
−0.991899 + 0.127030i \(0.959455\pi\)
\(230\) 0 0
\(231\) −26.7504 + 86.2351i −0.115803 + 0.373312i
\(232\) 0 0
\(233\) 242.432i 1.04048i 0.854020 + 0.520240i \(0.174158\pi\)
−0.854020 + 0.520240i \(0.825842\pi\)
\(234\) 0 0
\(235\) 150.069i 0.638590i
\(236\) 0 0
\(237\) −86.6453 + 279.318i −0.365592 + 1.17856i
\(238\) 0 0
\(239\) 215.651i 0.902304i 0.892447 + 0.451152i \(0.148987\pi\)
−0.892447 + 0.451152i \(0.851013\pi\)
\(240\) 0 0
\(241\) 123.252 0.511417 0.255709 0.966754i \(-0.417691\pi\)
0.255709 + 0.966754i \(0.417691\pi\)
\(242\) 0 0
\(243\) 242.457 16.2300i 0.997767 0.0667902i
\(244\) 0 0
\(245\) −606.160 −2.47412
\(246\) 0 0
\(247\) −77.7708 −0.314861
\(248\) 0 0
\(249\) −52.9076 + 170.558i −0.212480 + 0.684971i
\(250\) 0 0
\(251\) 194.768 0.775967 0.387984 0.921666i \(-0.373172\pi\)
0.387984 + 0.921666i \(0.373172\pi\)
\(252\) 0 0
\(253\) 48.3024i 0.190919i
\(254\) 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
\(259\) 84.5389i 0.326405i
\(260\) 0 0
\(261\) −145.598 99.9473i −0.557845 0.382940i
\(262\) 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
\(267\) −316.527 98.1877i −1.18549 0.367744i
\(268\) 0 0
\(269\) 64.1922 0.238633 0.119316 0.992856i \(-0.461930\pi\)
0.119316 + 0.992856i \(0.461930\pi\)
\(270\) 0 0
\(271\) −229.609 −0.847265 −0.423633 0.905834i \(-0.639245\pi\)
−0.423633 + 0.905834i \(0.639245\pi\)
\(272\) 0 0
\(273\) −138.890 43.0842i −0.508755 0.157818i
\(274\) 0 0
\(275\) 134.375 0.488636
\(276\) 0 0
\(277\) 329.621i 1.18997i −0.803738 0.594983i \(-0.797159\pi\)
0.803738 0.594983i \(-0.202841\pi\)
\(278\) 0 0
\(279\) −19.1674 13.1577i −0.0687003 0.0471602i
\(280\) 0 0
\(281\) 222.349i 0.791279i −0.918406 0.395640i \(-0.870523\pi\)
0.918406 0.395640i \(-0.129477\pi\)
\(282\) 0 0
\(283\) 550.386i 1.94483i 0.233261 + 0.972414i \(0.425060\pi\)
−0.233261 + 0.972414i \(0.574940\pi\)
\(284\) 0 0
\(285\) −431.864 133.966i −1.51531 0.470055i
\(286\) 0 0
\(287\) 634.245i 2.20991i
\(288\) 0 0
\(289\) −357.217 −1.23604
\(290\) 0 0
\(291\) 48.9894 157.927i 0.168349 0.542704i
\(292\) 0 0
\(293\) −322.712 −1.10141 −0.550703 0.834701i \(-0.685640\pi\)
−0.550703 + 0.834701i \(0.685640\pi\)
\(294\) 0 0
\(295\) 434.638 1.47335
\(296\) 0 0
\(297\) −58.3255 + 46.0590i −0.196382 + 0.155081i
\(298\) 0 0
\(299\) 77.7958 0.260187
\(300\) 0 0
\(301\) 461.339i 1.53269i
\(302\) 0 0
\(303\) 17.9805 57.9635i 0.0593415 0.191299i
\(304\) 0 0
\(305\) 280.077i 0.918284i
\(306\) 0 0
\(307\) 66.6568i 0.217123i −0.994090 0.108562i \(-0.965376\pi\)
0.994090 0.108562i \(-0.0346244\pi\)
\(308\) 0 0
\(309\) 58.0450 187.119i 0.187848 0.605563i
\(310\) 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 \(-0.390408\pi\)
0.337533 + 0.941314i \(0.390408\pi\)
\(314\) 0 0
\(315\) −697.046 478.496i −2.21284 1.51904i
\(316\) 0 0
\(317\) 238.040 0.750915 0.375457 0.926840i \(-0.377486\pi\)
0.375457 + 0.926840i \(0.377486\pi\)
\(318\) 0 0
\(319\) 54.0117 0.169316
\(320\) 0 0
\(321\) −9.18205 + 29.6001i −0.0286045 + 0.0922121i
\(322\) 0 0
\(323\) 445.946 1.38064
\(324\) 0 0
\(325\) 216.424i 0.665921i
\(326\) 0 0
\(327\) 434.213 + 134.694i 1.32787 + 0.411910i
\(328\) 0 0
\(329\) 190.979i 0.580483i
\(330\) 0 0
\(331\) 344.811i 1.04173i −0.853640 0.520863i \(-0.825610\pi\)
0.853640 0.520863i \(-0.174390\pi\)
\(332\) 0 0
\(333\) 39.3821 57.3696i 0.118264 0.172281i
\(334\) 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
\(339\) −304.803 94.5511i −0.899125 0.278912i
\(340\) 0 0
\(341\) 7.11043 0.0208517
\(342\) 0 0
\(343\) −235.642 −0.687002
\(344\) 0 0
\(345\) 432.003 + 134.009i 1.25218 + 0.388431i
\(346\) 0 0
\(347\) 73.9748 0.213184 0.106592 0.994303i \(-0.466006\pi\)
0.106592 + 0.994303i \(0.466006\pi\)
\(348\) 0 0
\(349\) 443.377i 1.27042i 0.772340 + 0.635210i \(0.219086\pi\)
−0.772340 + 0.635210i \(0.780914\pi\)
\(350\) 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
\(355\) 189.896i 0.534917i
\(356\) 0 0
\(357\) 796.411 + 247.050i 2.23084 + 0.692016i
\(358\) 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
\(363\) −100.814 + 324.993i −0.277724 + 0.895298i
\(364\) 0 0
\(365\) −232.249 −0.636298
\(366\) 0 0
\(367\) −305.686 −0.832932 −0.416466 0.909151i \(-0.636731\pi\)
−0.416466 + 0.909151i \(0.636731\pi\)
\(368\) 0 0
\(369\) 295.460 430.410i 0.800705 1.16642i
\(370\) 0 0
\(371\) −754.499 −2.03369
\(372\) 0 0
\(373\) 133.295i 0.357359i 0.983907 + 0.178679i \(0.0571825\pi\)
−0.983907 + 0.178679i \(0.942818\pi\)
\(374\) 0 0
\(375\) −181.891 + 586.361i −0.485043 + 1.56363i
\(376\) 0 0
\(377\) 86.9912i 0.230746i
\(378\) 0 0
\(379\) 239.300i 0.631399i −0.948859 0.315699i \(-0.897761\pi\)
0.948859 0.315699i \(-0.102239\pi\)
\(380\) 0 0
\(381\) 99.8025 321.732i 0.261949 0.844442i
\(382\) 0 0
\(383\) 249.576i 0.651634i 0.945433 + 0.325817i \(0.105639\pi\)
−0.945433 + 0.325817i \(0.894361\pi\)
\(384\) 0 0
\(385\) 258.580 0.671636
\(386\) 0 0
\(387\) 214.913 313.073i 0.555330 0.808973i
\(388\) 0 0
\(389\) 499.992 1.28533 0.642664 0.766148i \(-0.277829\pi\)
0.642664 + 0.766148i \(0.277829\pi\)
\(390\) 0 0
\(391\) −446.090 −1.14089
\(392\) 0 0
\(393\) −122.484 + 394.850i −0.311663 + 1.00471i
\(394\) 0 0
\(395\) 837.548 2.12037
\(396\) 0 0
\(397\) 302.418i 0.761759i 0.924625 + 0.380880i \(0.124379\pi\)
−0.924625 + 0.380880i \(0.875621\pi\)
\(398\) 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
\(403\) 11.4521i 0.0284170i
\(404\) 0 0
\(405\) −250.122 649.431i −0.617586 1.60353i
\(406\) 0 0
\(407\) 21.2821i 0.0522902i
\(408\) 0 0
\(409\) −108.812 −0.266044 −0.133022 0.991113i \(-0.542468\pi\)
−0.133022 + 0.991113i \(0.542468\pi\)
\(410\) 0 0
\(411\) 438.075 + 135.892i 1.06588 + 0.330638i
\(412\) 0 0
\(413\) 553.125 1.33929
\(414\) 0 0
\(415\) 511.426 1.23235
\(416\) 0 0
\(417\) 677.502 + 210.164i 1.62471 + 0.503989i
\(418\) 0 0
\(419\) 183.076 0.436936 0.218468 0.975844i \(-0.429894\pi\)
0.218468 + 0.975844i \(0.429894\pi\)
\(420\) 0 0
\(421\) 213.105i 0.506187i −0.967442 0.253093i \(-0.918552\pi\)
0.967442 0.253093i \(-0.0814480\pi\)
\(422\) 0 0
\(423\) −88.9666 + 129.602i −0.210323 + 0.306387i
\(424\) 0 0
\(425\) 1241.00i 2.92000i
\(426\) 0 0
\(427\) 356.428i 0.834727i
\(428\) 0 0
\(429\) 34.9647 + 10.8462i 0.0815027 + 0.0252824i
\(430\) 0 0
\(431\) 471.854i 1.09479i −0.836875 0.547394i \(-0.815620\pi\)
0.836875 0.547394i \(-0.184380\pi\)
\(432\) 0 0
\(433\) 396.992 0.916841 0.458421 0.888735i \(-0.348415\pi\)
0.458421 + 0.888735i \(0.348415\pi\)
\(434\) 0 0
\(435\) −149.848 + 483.065i −0.344479 + 1.11049i
\(436\) 0 0
\(437\) 307.841 0.704442
\(438\) 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
\(443\) −189.532 −0.427838 −0.213919 0.976851i \(-0.568623\pi\)
−0.213919 + 0.976851i \(0.568623\pi\)
\(444\) 0 0
\(445\) 949.121i 2.13286i
\(446\) 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
\(451\) 159.667i 0.354029i
\(452\) 0 0
\(453\) −251.841 + 811.858i −0.555940 + 1.79218i
\(454\) 0 0
\(455\) 416.469i 0.915316i
\(456\) 0 0
\(457\) 438.599 0.959734 0.479867 0.877341i \(-0.340685\pi\)
0.479867 + 0.877341i \(0.340685\pi\)
\(458\) 0 0
\(459\) 425.372 + 538.657i 0.926736 + 1.17354i
\(460\) 0 0
\(461\) 27.0211 0.0586142 0.0293071 0.999570i \(-0.490670\pi\)
0.0293071 + 0.999570i \(0.490670\pi\)
\(462\) 0 0
\(463\) −128.181 −0.276850 −0.138425 0.990373i \(-0.544204\pi\)
−0.138425 + 0.990373i \(0.544204\pi\)
\(464\) 0 0
\(465\) −19.7270 + 63.5937i −0.0424236 + 0.136761i
\(466\) 0 0
\(467\) −624.873 −1.33806 −0.669029 0.743236i \(-0.733290\pi\)
−0.669029 + 0.743236i \(0.733290\pi\)
\(468\) 0 0
\(469\) 524.970i 1.11934i
\(470\) 0 0
\(471\) 94.4612 + 29.3022i 0.200554 + 0.0622127i
\(472\) 0 0
\(473\) 116.139i 0.245537i
\(474\) 0 0
\(475\) 856.400i 1.80295i
\(476\) 0 0
\(477\) −512.016 351.480i −1.07341 0.736855i
\(478\) 0 0
\(479\) 782.010i 1.63259i 0.577636 + 0.816295i \(0.303975\pi\)
−0.577636 + 0.816295i \(0.696025\pi\)
\(480\) 0 0
\(481\) −34.2770 −0.0712619
\(482\) 0 0
\(483\) 549.771 + 170.541i 1.13824 + 0.353087i
\(484\) 0 0
\(485\) −473.551 −0.976393
\(486\) 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
\(491\) −65.5662 −0.133536 −0.0667680 0.997769i \(-0.521269\pi\)
−0.0667680 + 0.997769i \(0.521269\pi\)
\(492\) 0 0
\(493\) 498.817i 1.01180i
\(494\) 0 0
\(495\) 175.477 + 120.458i 0.354499 + 0.243350i
\(496\) 0 0
\(497\) 241.663i 0.486243i
\(498\) 0 0
\(499\) 846.549i 1.69649i 0.529604 + 0.848245i \(0.322341\pi\)
−0.529604 + 0.848245i \(0.677659\pi\)
\(500\) 0 0
\(501\) 673.933 + 209.056i 1.34518 + 0.417278i
\(502\) 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
\(507\) 132.743 427.923i 0.261821 0.844029i
\(508\) 0 0
\(509\) −996.730 −1.95821 −0.979106 0.203350i \(-0.934817\pi\)
−0.979106 + 0.203350i \(0.934817\pi\)
\(510\) 0 0
\(511\) −295.562 −0.578399
\(512\) 0 0
\(513\) −293.544 371.720i −0.572210 0.724601i
\(514\) 0 0
\(515\) −561.085 −1.08949
\(516\) 0 0
\(517\) 48.0777i 0.0929936i
\(518\) 0 0
\(519\) 34.3870 110.853i 0.0662563 0.213590i
\(520\) 0 0
\(521\) 471.553i 0.905092i −0.891741 0.452546i \(-0.850516\pi\)
0.891741 0.452546i \(-0.149484\pi\)
\(522\) 0 0
\(523\) 364.836i 0.697582i −0.937200 0.348791i \(-0.886592\pi\)
0.937200 0.348791i \(-0.113408\pi\)
\(524\) 0 0
\(525\) −474.436 + 1529.44i −0.903688 + 2.91321i
\(526\) 0 0
\(527\) 65.6674i 0.124606i
\(528\) 0 0
\(529\) 221.060 0.417882
\(530\) 0 0
\(531\) 375.360 + 257.671i 0.706893 + 0.485255i
\(532\) 0 0
\(533\) −257.160 −0.482476
\(534\) 0 0
\(535\) 88.7573 0.165901
\(536\) 0 0
\(537\) 255.386 823.286i 0.475579 1.53312i
\(538\) 0 0
\(539\) 194.196 0.360290
\(540\) 0 0
\(541\) 68.1097i 0.125896i 0.998017 + 0.0629480i \(0.0200502\pi\)
−0.998017 + 0.0629480i \(0.979950\pi\)
\(542\) 0 0
\(543\) −570.691 177.030i −1.05100 0.326023i
\(544\) 0 0
\(545\) 1302.01i 2.38901i
\(546\) 0 0
\(547\) 459.725i 0.840448i −0.907420 0.420224i \(-0.861951\pi\)
0.907420 0.420224i \(-0.138049\pi\)
\(548\) 0 0
\(549\) 166.040 241.878i 0.302442 0.440580i
\(550\) 0 0
\(551\) 344.228i 0.624733i
\(552\) 0 0
\(553\) 1065.87 1.92743
\(554\) 0 0
\(555\) −190.341 59.0445i −0.342957 0.106386i
\(556\) 0 0
\(557\) 95.1108 0.170756 0.0853778 0.996349i \(-0.472790\pi\)
0.0853778 + 0.996349i \(0.472790\pi\)
\(558\) 0 0
\(559\) −187.053 −0.334622
\(560\) 0 0
\(561\) −200.491 62.1931i −0.357382 0.110861i
\(562\) 0 0
\(563\) 422.228 0.749960 0.374980 0.927033i \(-0.377650\pi\)
0.374980 + 0.927033i \(0.377650\pi\)
\(564\) 0 0
\(565\) 913.967i 1.61764i
\(566\) 0 0
\(567\) −318.308 826.472i −0.561390 1.45762i
\(568\) 0 0
\(569\) 328.583i 0.577474i 0.957408 + 0.288737i \(0.0932354\pi\)
−0.957408 + 0.288737i \(0.906765\pi\)
\(570\) 0 0
\(571\) 503.834i 0.882371i −0.897416 0.441186i \(-0.854558\pi\)
0.897416 0.441186i \(-0.145442\pi\)
\(572\) 0 0
\(573\) 652.016 + 202.258i 1.13790 + 0.352980i
\(574\) 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
\(579\) −21.2391 + 68.4681i −0.0366823 + 0.118252i
\(580\) 0 0
\(581\) 650.845 1.12022
\(582\) 0 0
\(583\) 189.940 0.325798
\(584\) 0 0
\(585\) −194.010 + 282.623i −0.331641 + 0.483116i
\(586\) 0 0
\(587\) −501.148 −0.853745 −0.426872 0.904312i \(-0.640385\pi\)
−0.426872 + 0.904312i \(0.640385\pi\)
\(588\) 0 0
\(589\) 45.3163i 0.0769376i
\(590\) 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
\(595\) 2388.08i 4.01358i
\(596\) 0 0
\(597\) −161.599 + 520.945i −0.270685 + 0.872605i
\(598\) 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 \(-0.567385\pi\)
−0.210117 + 0.977676i \(0.567385\pi\)
\(602\) 0 0
\(603\) −244.555 + 356.254i −0.405564 + 0.590802i
\(604\) 0 0
\(605\) 974.507 1.61076
\(606\) 0 0
\(607\) 627.073 1.03307 0.516535 0.856266i \(-0.327222\pi\)
0.516535 + 0.856266i \(0.327222\pi\)
\(608\) 0 0
\(609\) −190.699 + 614.753i −0.313134 + 1.00945i
\(610\) 0 0
\(611\) 77.4339 0.126733
\(612\) 0 0
\(613\) 375.629i 0.612772i −0.951907 0.306386i \(-0.900880\pi\)
0.951907 0.306386i \(-0.0991198\pi\)
\(614\) 0 0
\(615\) −1428.02 442.976i −2.32198 0.720286i
\(616\) 0 0
\(617\) 161.548i 0.261829i 0.991394 + 0.130914i \(0.0417913\pi\)
−0.991394 + 0.130914i \(0.958209\pi\)
\(618\) 0 0
\(619\) 9.45164i 0.0152692i −0.999971 0.00763460i \(-0.997570\pi\)
0.999971 0.00763460i \(-0.00243019\pi\)
\(620\) 0 0
\(621\) 293.638 + 371.840i 0.472847 + 0.598776i
\(622\) 0 0
\(623\) 1207.86i 1.93878i
\(624\) 0 0
\(625\) 537.772 0.860435
\(626\) 0 0
\(627\) 138.357 + 42.9187i 0.220665 + 0.0684509i
\(628\) 0 0
\(629\) 196.548 0.312477
\(630\) 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
\(635\) −964.730 −1.51926
\(636\) 0 0
\(637\) 312.772i 0.491008i
\(638\) 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
\(643\) 339.764i 0.528405i −0.964467 0.264202i \(-0.914891\pi\)
0.964467 0.264202i \(-0.0851087\pi\)
\(644\) 0 0
\(645\) −1038.71 322.213i −1.61041 0.499555i
\(646\) 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
\(651\) −25.1047 + 80.9299i −0.0385633 + 0.124316i
\(652\) 0 0
\(653\) 970.043 1.48552 0.742759 0.669559i \(-0.233517\pi\)
0.742759 + 0.669559i \(0.233517\pi\)
\(654\) 0 0
\(655\) 1183.98 1.80760
\(656\) 0 0
\(657\) −200.573 137.686i −0.305287 0.209568i
\(658\) 0 0
\(659\) 302.641 0.459243 0.229622 0.973280i \(-0.426251\pi\)
0.229622 + 0.973280i \(0.426251\pi\)
\(660\) 0 0
\(661\) 406.011i 0.614237i −0.951671 0.307118i \(-0.900635\pi\)
0.951671 0.307118i \(-0.0993648\pi\)
\(662\) 0 0
\(663\) 100.168 322.911i 0.151083 0.487046i
\(664\) 0 0
\(665\) 1647.98i 2.47817i
\(666\) 0 0
\(667\) 344.338i 0.516250i
\(668\) 0 0
\(669\) 282.402 910.377i 0.422126 1.36080i
\(670\) 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
\(675\) −1034.44 + 816.888i −1.53251 + 1.21020i
\(676\) 0 0
\(677\) −791.131 −1.16858 −0.584292 0.811544i \(-0.698628\pi\)
−0.584292 + 0.811544i \(0.698628\pi\)
\(678\) 0 0
\(679\) −602.645 −0.887548
\(680\) 0 0
\(681\) −214.415 + 691.207i −0.314853 + 1.01499i
\(682\) 0 0
\(683\) −925.330 −1.35480 −0.677401 0.735614i \(-0.736894\pi\)
−0.677401 + 0.735614i \(0.736894\pi\)
\(684\) 0 0
\(685\) 1313.59i 1.91765i
\(686\) 0 0
\(687\) 166.703 + 51.7120i 0.242654 + 0.0752722i
\(688\) 0 0
\(689\) 305.918i 0.444002i
\(690\) 0 0
\(691\) 666.330i 0.964299i 0.876089 + 0.482149i \(0.160144\pi\)
−0.876089 + 0.482149i \(0.839856\pi\)
\(692\) 0 0
\(693\) 223.313 + 153.296i 0.322242 + 0.221207i
\(694\) 0 0
\(695\) 2031.52i 2.92305i
\(696\) 0 0
\(697\) 1474.58 2.11561
\(698\) 0 0
\(699\) 694.642 + 215.480i 0.993765 + 0.308269i
\(700\) 0 0
\(701\) −1238.38 −1.76659 −0.883294 0.468820i \(-0.844679\pi\)
−0.883294 + 0.468820i \(0.844679\pi\)
\(702\) 0 0
\(703\) −135.635 −0.192938
\(704\) 0 0
\(705\) 429.993 + 133.385i 0.609919 + 0.189199i
\(706\) 0 0
\(707\) −221.187 −0.312854
\(708\) 0 0
\(709\) 162.142i 0.228692i 0.993441 + 0.114346i \(0.0364772\pi\)
−0.993441 + 0.114346i \(0.963523\pi\)
\(710\) 0 0
\(711\) 723.318 + 496.531i 1.01733 + 0.698356i
\(712\) 0 0
\(713\) 45.3309i 0.0635776i
\(714\) 0 0
\(715\) 104.843i 0.146634i
\(716\) 0 0
\(717\) 617.906 + 191.676i 0.861793 + 0.267331i
\(718\) 0 0
\(719\) 534.958i 0.744031i −0.928226 0.372016i \(-0.878667\pi\)
0.928226 0.372016i \(-0.121333\pi\)
\(720\) 0 0
\(721\) −714.042 −0.990350
\(722\) 0 0
\(723\) 109.549 353.154i 0.151521 0.488456i
\(724\) 0 0
\(725\) 957.933 1.32129
\(726\) 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
\(731\) 1072.59 1.46729
\(732\) 0 0
\(733\) 473.296i 0.645697i 0.946451 + 0.322849i \(0.104640\pi\)
−0.946451 + 0.322849i \(0.895360\pi\)
\(734\) 0 0
\(735\) −538.772 + 1736.84i −0.733024 + 2.36304i
\(736\) 0 0
\(737\) 132.158i 0.179319i
\(738\) 0 0
\(739\) 724.955i 0.980994i 0.871443 + 0.490497i \(0.163185\pi\)
−0.871443 + 0.490497i \(0.836815\pi\)
\(740\) 0 0
\(741\) −69.1249 + 222.837i −0.0932859 + 0.300725i
\(742\) 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
\(747\) 441.675 + 303.193i 0.591265 + 0.405881i
\(748\) 0 0
\(749\) 112.953 0.150806
\(750\) 0 0
\(751\) 1039.66 1.38436 0.692181 0.721724i \(-0.256650\pi\)
0.692181 + 0.721724i \(0.256650\pi\)
\(752\) 0 0
\(753\) 173.115 558.070i 0.229901 0.741128i
\(754\) 0 0
\(755\) 2434.39 3.22436
\(756\) 0 0
\(757\) 826.135i 1.09133i 0.838004 + 0.545664i \(0.183722\pi\)
−0.838004 + 0.545664i \(0.816278\pi\)
\(758\) 0 0
\(759\) −138.401 42.9325i −0.182347 0.0565646i
\(760\) 0 0
\(761\) 159.752i 0.209924i 0.994476 + 0.104962i \(0.0334721\pi\)
−0.994476 + 0.104962i \(0.966528\pi\)
\(762\) 0 0
\(763\) 1656.95i 2.17162i
\(764\) 0 0
\(765\) 1112.47 1620.59i 1.45422 2.11842i
\(766\) 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
\(771\) −574.825 178.313i −0.745558 0.231275i
\(772\) 0 0
\(773\) 33.4297 0.0432466 0.0216233 0.999766i \(-0.493117\pi\)
0.0216233 + 0.999766i \(0.493117\pi\)
\(774\) 0 0
\(775\) 126.108 0.162720
\(776\) 0 0
\(777\) −242.230 75.1406i −0.311750 0.0967060i
\(778\) 0 0
\(779\) −1017.59 −1.30628
\(780\) 0 0
\(781\) 60.8370i 0.0778964i
\(782\) 0 0
\(783\) −415.791 + 328.346i −0.531023 + 0.419343i
\(784\) 0 0
\(785\) 283.246i 0.360823i
\(786\) 0 0
\(787\) 516.814i 0.656688i 0.944558 + 0.328344i \(0.106491\pi\)
−0.944558 + 0.328344i \(0.893509\pi\)
\(788\) 0 0
\(789\) −1260.86 391.123i −1.59805 0.495720i
\(790\) 0 0
\(791\) 1163.12i 1.47045i
\(792\) 0 0
\(793\) −144.517 −0.182240
\(794\) 0 0
\(795\) −526.965 + 1698.77i −0.662849 + 2.13682i
\(796\) 0 0
\(797\) −593.861 −0.745120 −0.372560 0.928008i \(-0.621520\pi\)
−0.372560 + 0.928008i \(0.621520\pi\)
\(798\) 0 0
\(799\) −444.014 −0.555713
\(800\) 0 0
\(801\) −562.676 + 819.675i