Properties

Label 2592.2.s.f.1727.2
Level $2592$
Weight $2$
Character 2592.1727
Analytic conductor $20.697$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1727.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2592.1727
Dual form 2592.2.s.f.863.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.448288 + 0.258819i) q^{5} +(2.36603 + 1.36603i) q^{7} +O(q^{10})\) \(q+(-0.448288 + 0.258819i) q^{5} +(2.36603 + 1.36603i) q^{7} +(-0.189469 + 0.328169i) q^{11} +(1.23205 + 2.13397i) q^{13} -3.34607i q^{17} +4.73205i q^{19} +(-0.707107 - 1.22474i) q^{23} +(-2.36603 + 4.09808i) q^{25} +(5.91567 + 3.41542i) q^{29} +(-0.464102 + 0.267949i) q^{31} -1.41421 q^{35} -4.26795 q^{37} +(-4.57081 + 2.63896i) q^{41} +(4.56218 + 2.63397i) q^{43} +(4.76028 - 8.24504i) q^{47} +(0.232051 + 0.401924i) q^{49} -2.44949i q^{53} -0.196152i q^{55} +(6.83083 + 11.8313i) q^{59} +(-4.59808 + 7.96410i) q^{61} +(-1.10463 - 0.637756i) q^{65} +(9.63397 - 5.56218i) q^{67} -16.1112 q^{71} -10.2679 q^{73} +(-0.896575 + 0.517638i) q^{77} +(12.6340 + 7.29423i) q^{79} +(-0.378937 + 0.656339i) q^{83} +(0.866025 + 1.50000i) q^{85} -2.20925i q^{89} +6.73205i q^{91} +(-1.22474 - 2.12132i) q^{95} +(-7.19615 + 12.4641i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{7} - 4 q^{13} - 12 q^{25} + 24 q^{31} - 48 q^{37} - 12 q^{43} - 12 q^{49} - 16 q^{61} + 84 q^{67} - 96 q^{73} + 108 q^{79} - 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.448288 + 0.258819i −0.200480 + 0.115747i −0.596880 0.802331i \(-0.703593\pi\)
0.396399 + 0.918078i \(0.370260\pi\)
\(6\) 0 0
\(7\) 2.36603 + 1.36603i 0.894274 + 0.516309i 0.875338 0.483512i \(-0.160639\pi\)
0.0189356 + 0.999821i \(0.493972\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.189469 + 0.328169i −0.0571270 + 0.0989468i −0.893175 0.449710i \(-0.851527\pi\)
0.836048 + 0.548657i \(0.184861\pi\)
\(12\) 0 0
\(13\) 1.23205 + 2.13397i 0.341709 + 0.591858i 0.984750 0.173974i \(-0.0556608\pi\)
−0.643041 + 0.765832i \(0.722327\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.34607i 0.811540i −0.913975 0.405770i \(-0.867003\pi\)
0.913975 0.405770i \(-0.132997\pi\)
\(18\) 0 0
\(19\) 4.73205i 1.08561i 0.839860 + 0.542803i \(0.182637\pi\)
−0.839860 + 0.542803i \(0.817363\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.707107 1.22474i −0.147442 0.255377i 0.782839 0.622224i \(-0.213771\pi\)
−0.930281 + 0.366847i \(0.880437\pi\)
\(24\) 0 0
\(25\) −2.36603 + 4.09808i −0.473205 + 0.819615i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.91567 + 3.41542i 1.09851 + 0.634227i 0.935830 0.352452i \(-0.114652\pi\)
0.162683 + 0.986678i \(0.447985\pi\)
\(30\) 0 0
\(31\) −0.464102 + 0.267949i −0.0833551 + 0.0481251i −0.541098 0.840959i \(-0.681991\pi\)
0.457743 + 0.889085i \(0.348658\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1.41421 −0.239046
\(36\) 0 0
\(37\) −4.26795 −0.701647 −0.350823 0.936442i \(-0.614098\pi\)
−0.350823 + 0.936442i \(0.614098\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.57081 + 2.63896i −0.713841 + 0.412136i −0.812481 0.582987i \(-0.801884\pi\)
0.0986409 + 0.995123i \(0.468550\pi\)
\(42\) 0 0
\(43\) 4.56218 + 2.63397i 0.695726 + 0.401677i 0.805753 0.592251i \(-0.201761\pi\)
−0.110028 + 0.993929i \(0.535094\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.76028 8.24504i 0.694358 1.20266i −0.276039 0.961147i \(-0.589022\pi\)
0.970397 0.241517i \(-0.0776449\pi\)
\(48\) 0 0
\(49\) 0.232051 + 0.401924i 0.0331501 + 0.0574177i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.44949i 0.336463i −0.985747 0.168232i \(-0.946194\pi\)
0.985747 0.168232i \(-0.0538057\pi\)
\(54\) 0 0
\(55\) 0.196152i 0.0264492i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.83083 + 11.8313i 0.889298 + 1.54031i 0.840706 + 0.541491i \(0.182140\pi\)
0.0485922 + 0.998819i \(0.484527\pi\)
\(60\) 0 0
\(61\) −4.59808 + 7.96410i −0.588723 + 1.01970i 0.405677 + 0.914017i \(0.367036\pi\)
−0.994400 + 0.105682i \(0.966297\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.10463 0.637756i −0.137012 0.0791039i
\(66\) 0 0
\(67\) 9.63397 5.56218i 1.17698 0.679528i 0.221664 0.975123i \(-0.428851\pi\)
0.955313 + 0.295595i \(0.0955179\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −16.1112 −1.91204 −0.956021 0.293298i \(-0.905247\pi\)
−0.956021 + 0.293298i \(0.905247\pi\)
\(72\) 0 0
\(73\) −10.2679 −1.20177 −0.600886 0.799335i \(-0.705186\pi\)
−0.600886 + 0.799335i \(0.705186\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.896575 + 0.517638i −0.102174 + 0.0589903i
\(78\) 0 0
\(79\) 12.6340 + 7.29423i 1.42143 + 0.820665i 0.996422 0.0845230i \(-0.0269367\pi\)
0.425012 + 0.905188i \(0.360270\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.378937 + 0.656339i −0.0415938 + 0.0720425i −0.886073 0.463546i \(-0.846577\pi\)
0.844479 + 0.535589i \(0.179910\pi\)
\(84\) 0 0
\(85\) 0.866025 + 1.50000i 0.0939336 + 0.162698i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.20925i 0.234180i −0.993121 0.117090i \(-0.962643\pi\)
0.993121 0.117090i \(-0.0373567\pi\)
\(90\) 0 0
\(91\) 6.73205i 0.705711i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.22474 2.12132i −0.125656 0.217643i
\(96\) 0 0
\(97\) −7.19615 + 12.4641i −0.730659 + 1.26554i 0.225944 + 0.974140i \(0.427454\pi\)
−0.956602 + 0.291397i \(0.905880\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.01790 1.74238i −0.300292 0.173374i 0.342282 0.939597i \(-0.388800\pi\)
−0.642574 + 0.766224i \(0.722133\pi\)
\(102\) 0 0
\(103\) 3.46410 2.00000i 0.341328 0.197066i −0.319531 0.947576i \(-0.603525\pi\)
0.660859 + 0.750510i \(0.270192\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.69213 0.646953 0.323476 0.946236i \(-0.395148\pi\)
0.323476 + 0.946236i \(0.395148\pi\)
\(108\) 0 0
\(109\) −9.92820 −0.950949 −0.475475 0.879729i \(-0.657724\pi\)
−0.475475 + 0.879729i \(0.657724\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.58510 + 0.915158i −0.149114 + 0.0860908i −0.572700 0.819765i \(-0.694104\pi\)
0.423587 + 0.905856i \(0.360771\pi\)
\(114\) 0 0
\(115\) 0.633975 + 0.366025i 0.0591184 + 0.0341320i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.57081 7.91688i 0.419005 0.725739i
\(120\) 0 0
\(121\) 5.42820 + 9.40192i 0.493473 + 0.854720i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 5.03768i 0.450584i
\(126\) 0 0
\(127\) 3.12436i 0.277242i −0.990346 0.138621i \(-0.955733\pi\)
0.990346 0.138621i \(-0.0442669\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 9.84873 + 17.0585i 0.860487 + 1.49041i 0.871459 + 0.490468i \(0.163174\pi\)
−0.0109720 + 0.999940i \(0.503493\pi\)
\(132\) 0 0
\(133\) −6.46410 + 11.1962i −0.560509 + 0.970830i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 19.0597 + 11.0041i 1.62838 + 0.940146i 0.984577 + 0.174955i \(0.0559779\pi\)
0.643803 + 0.765191i \(0.277355\pi\)
\(138\) 0 0
\(139\) 7.26795 4.19615i 0.616459 0.355913i −0.159030 0.987274i \(-0.550837\pi\)
0.775489 + 0.631361i \(0.217503\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.933740 −0.0780833
\(144\) 0 0
\(145\) −3.53590 −0.293640
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −17.5068 + 10.1075i −1.43421 + 0.828042i −0.997438 0.0715293i \(-0.977212\pi\)
−0.436773 + 0.899572i \(0.643879\pi\)
\(150\) 0 0
\(151\) 12.9282 + 7.46410i 1.05208 + 0.607420i 0.923232 0.384244i \(-0.125538\pi\)
0.128851 + 0.991664i \(0.458871\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.138701 0.240237i 0.0111407 0.0192963i
\(156\) 0 0
\(157\) 3.33013 + 5.76795i 0.265773 + 0.460332i 0.967766 0.251852i \(-0.0810395\pi\)
−0.701993 + 0.712184i \(0.747706\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.86370i 0.304502i
\(162\) 0 0
\(163\) 22.3923i 1.75390i 0.480581 + 0.876950i \(0.340426\pi\)
−0.480581 + 0.876950i \(0.659574\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −10.2277 17.7148i −0.791440 1.37082i −0.925075 0.379784i \(-0.875998\pi\)
0.133635 0.991031i \(-0.457335\pi\)
\(168\) 0 0
\(169\) 3.46410 6.00000i 0.266469 0.461538i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.01669 + 0.586988i 0.0772978 + 0.0446279i 0.538151 0.842849i \(-0.319123\pi\)
−0.460853 + 0.887477i \(0.652456\pi\)
\(174\) 0 0
\(175\) −11.1962 + 6.46410i −0.846350 + 0.488640i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0716 −0.902272 −0.451136 0.892455i \(-0.648981\pi\)
−0.451136 + 0.892455i \(0.648981\pi\)
\(180\) 0 0
\(181\) 11.3205 0.841447 0.420723 0.907189i \(-0.361776\pi\)
0.420723 + 0.907189i \(0.361776\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.91327 1.10463i 0.140666 0.0812138i
\(186\) 0 0
\(187\) 1.09808 + 0.633975i 0.0802993 + 0.0463608i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.32868 9.22955i 0.385570 0.667827i −0.606278 0.795253i \(-0.707338\pi\)
0.991848 + 0.127426i \(0.0406715\pi\)
\(192\) 0 0
\(193\) 0.767949 + 1.33013i 0.0552782 + 0.0957446i 0.892340 0.451363i \(-0.149062\pi\)
−0.837062 + 0.547108i \(0.815729\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 17.1093i 1.21898i −0.792792 0.609492i \(-0.791373\pi\)
0.792792 0.609492i \(-0.208627\pi\)
\(198\) 0 0
\(199\) 8.00000i 0.567105i 0.958957 + 0.283552i \(0.0915130\pi\)
−0.958957 + 0.283552i \(0.908487\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.33109 + 16.1619i 0.654914 + 1.13434i
\(204\) 0 0
\(205\) 1.36603 2.36603i 0.0954074 0.165250i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.55291 0.896575i −0.107417 0.0620174i
\(210\) 0 0
\(211\) 4.43782 2.56218i 0.305512 0.176388i −0.339404 0.940641i \(-0.610225\pi\)
0.644917 + 0.764253i \(0.276892\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.72689 −0.185972
\(216\) 0 0
\(217\) −1.46410 −0.0993897
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 7.14042 4.12252i 0.480317 0.277311i
\(222\) 0 0
\(223\) 17.9545 + 10.3660i 1.20232 + 0.694160i 0.961071 0.276303i \(-0.0891092\pi\)
0.241250 + 0.970463i \(0.422443\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.1242 + 19.2677i −0.738342 + 1.27885i 0.214900 + 0.976636i \(0.431057\pi\)
−0.953242 + 0.302209i \(0.902276\pi\)
\(228\) 0 0
\(229\) −5.50000 9.52628i −0.363450 0.629514i 0.625076 0.780564i \(-0.285068\pi\)
−0.988526 + 0.151050i \(0.951735\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.24453i 0.212556i 0.994336 + 0.106278i \(0.0338934\pi\)
−0.994336 + 0.106278i \(0.966107\pi\)
\(234\) 0 0
\(235\) 4.92820i 0.321481i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4.62158 8.00481i −0.298945 0.517788i 0.676950 0.736029i \(-0.263301\pi\)
−0.975895 + 0.218241i \(0.929968\pi\)
\(240\) 0 0
\(241\) −4.06218 + 7.03590i −0.261668 + 0.453222i −0.966685 0.255968i \(-0.917606\pi\)
0.705017 + 0.709190i \(0.250939\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.208051 0.120118i −0.0132919 0.00767408i
\(246\) 0 0
\(247\) −10.0981 + 5.83013i −0.642525 + 0.370962i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.3533 0.969090 0.484545 0.874766i \(-0.338985\pi\)
0.484545 + 0.874766i \(0.338985\pi\)
\(252\) 0 0
\(253\) 0.535898 0.0336916
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.1607 + 8.17569i −0.883321 + 0.509986i −0.871752 0.489947i \(-0.837016\pi\)
−0.0115693 + 0.999933i \(0.503683\pi\)
\(258\) 0 0
\(259\) −10.0981 5.83013i −0.627464 0.362266i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 6.17449 10.6945i 0.380736 0.659453i −0.610432 0.792069i \(-0.709004\pi\)
0.991168 + 0.132615i \(0.0423375\pi\)
\(264\) 0 0
\(265\) 0.633975 + 1.09808i 0.0389447 + 0.0674543i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.4176i 0.940031i 0.882658 + 0.470015i \(0.155752\pi\)
−0.882658 + 0.470015i \(0.844248\pi\)
\(270\) 0 0
\(271\) 16.7321i 1.01640i −0.861239 0.508200i \(-0.830311\pi\)
0.861239 0.508200i \(-0.169689\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.896575 1.55291i −0.0540655 0.0936443i
\(276\) 0 0
\(277\) −7.46410 + 12.9282i −0.448474 + 0.776780i −0.998287 0.0585076i \(-0.981366\pi\)
0.549813 + 0.835288i \(0.314699\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.55412 2.05197i −0.212021 0.122410i 0.390229 0.920718i \(-0.372396\pi\)
−0.602250 + 0.798307i \(0.705729\pi\)
\(282\) 0 0
\(283\) 13.2679 7.66025i 0.788698 0.455355i −0.0508062 0.998709i \(-0.516179\pi\)
0.839504 + 0.543354i \(0.182846\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −14.4195 −0.851158
\(288\) 0 0
\(289\) 5.80385 0.341403
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.0060 5.77697i 0.584557 0.337494i −0.178385 0.983961i \(-0.557087\pi\)
0.762942 + 0.646466i \(0.223754\pi\)
\(294\) 0 0
\(295\) −6.12436 3.53590i −0.356574 0.205868i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.74238 3.01790i 0.100765 0.174529i
\(300\) 0 0
\(301\) 7.19615 + 12.4641i 0.414779 + 0.718419i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.76028i 0.272573i
\(306\) 0 0
\(307\) 18.0000i 1.02731i −0.857996 0.513657i \(-0.828290\pi\)
0.857996 0.513657i \(-0.171710\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.03768 8.72552i −0.285661 0.494779i 0.687109 0.726555i \(-0.258880\pi\)
−0.972769 + 0.231776i \(0.925546\pi\)
\(312\) 0 0
\(313\) 3.16025 5.47372i 0.178628 0.309393i −0.762783 0.646655i \(-0.776167\pi\)
0.941411 + 0.337262i \(0.109501\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.9384 + 9.77938i 0.951354 + 0.549265i 0.893501 0.449061i \(-0.148241\pi\)
0.0578527 + 0.998325i \(0.481575\pi\)
\(318\) 0 0
\(319\) −2.24167 + 1.29423i −0.125509 + 0.0724629i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.8338 0.881013
\(324\) 0 0
\(325\) −11.6603 −0.646795
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 22.5259 13.0053i 1.24189 0.717007i
\(330\) 0 0
\(331\) −15.7583 9.09808i −0.866156 0.500075i −8.71764e−5 1.00000i \(-0.500028\pi\)
−0.866069 + 0.499925i \(0.833361\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.87920 + 4.98691i −0.157307 + 0.272464i
\(336\) 0 0
\(337\) −4.46410 7.73205i −0.243175 0.421192i 0.718442 0.695587i \(-0.244856\pi\)
−0.961617 + 0.274395i \(0.911522\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.203072i 0.0109970i
\(342\) 0 0
\(343\) 17.8564i 0.964155i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.43211 + 7.67664i 0.237928 + 0.412104i 0.960120 0.279590i \(-0.0901984\pi\)
−0.722192 + 0.691693i \(0.756865\pi\)
\(348\) 0 0
\(349\) 14.9282 25.8564i 0.799088 1.38406i −0.121122 0.992638i \(-0.538649\pi\)
0.920210 0.391424i \(-0.128017\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −26.6806 15.4040i −1.42006 0.819875i −0.423761 0.905774i \(-0.639290\pi\)
−0.996304 + 0.0858996i \(0.972624\pi\)
\(354\) 0 0
\(355\) 7.22243 4.16987i 0.383327 0.221314i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.44949 −0.129279 −0.0646396 0.997909i \(-0.520590\pi\)
−0.0646396 + 0.997909i \(0.520590\pi\)
\(360\) 0 0
\(361\) −3.39230 −0.178542
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.60300 2.65754i 0.240932 0.139102i
\(366\) 0 0
\(367\) −16.8564 9.73205i −0.879897 0.508009i −0.00927272 0.999957i \(-0.502952\pi\)
−0.870625 + 0.491948i \(0.836285\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.34607 5.79555i 0.173719 0.300890i
\(372\) 0 0
\(373\) −8.12436 14.0718i −0.420663 0.728610i 0.575341 0.817913i \(-0.304869\pi\)
−0.996004 + 0.0893034i \(0.971536\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 16.8319i 0.866885i
\(378\) 0 0
\(379\) 6.39230i 0.328351i 0.986431 + 0.164175i \(0.0524963\pi\)
−0.986431 + 0.164175i \(0.947504\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.4369 21.5414i −0.635497 1.10071i −0.986410 0.164305i \(-0.947462\pi\)
0.350913 0.936408i \(-0.385871\pi\)
\(384\) 0 0
\(385\) 0.267949 0.464102i 0.0136560 0.0236528i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −28.8898 16.6796i −1.46477 0.845687i −0.465547 0.885023i \(-0.654142\pi\)
−0.999226 + 0.0393359i \(0.987476\pi\)
\(390\) 0 0
\(391\) −4.09808 + 2.36603i −0.207249 + 0.119655i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7.55154 −0.379959
\(396\) 0 0
\(397\) −9.58846 −0.481231 −0.240615 0.970621i \(-0.577349\pi\)
−0.240615 + 0.970621i \(0.577349\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.80984 + 1.62226i −0.140317 + 0.0810120i −0.568515 0.822673i \(-0.692482\pi\)
0.428198 + 0.903685i \(0.359149\pi\)
\(402\) 0 0
\(403\) −1.14359 0.660254i −0.0569665 0.0328896i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0.808643 1.40061i 0.0400829 0.0694257i
\(408\) 0 0
\(409\) −12.5981 21.8205i −0.622935 1.07895i −0.988936 0.148340i \(-0.952607\pi\)
0.366002 0.930614i \(-0.380726\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 37.3244i 1.83661i
\(414\) 0 0
\(415\) 0.392305i 0.0192575i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16.3514 + 28.3214i 0.798818 + 1.38359i 0.920387 + 0.391010i \(0.127874\pi\)
−0.121569 + 0.992583i \(0.538793\pi\)
\(420\) 0 0
\(421\) 9.42820 16.3301i 0.459503 0.795882i −0.539432 0.842029i \(-0.681361\pi\)
0.998935 + 0.0461474i \(0.0146944\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 13.7124 + 7.91688i 0.665151 + 0.384025i
\(426\) 0 0
\(427\) −21.7583 + 12.5622i −1.05296 + 0.607926i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.48528 0.408722 0.204361 0.978896i \(-0.434488\pi\)
0.204361 + 0.978896i \(0.434488\pi\)
\(432\) 0 0
\(433\) 28.1769 1.35410 0.677048 0.735939i \(-0.263259\pi\)
0.677048 + 0.735939i \(0.263259\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.79555 3.34607i 0.277239 0.160064i
\(438\) 0 0
\(439\) −0.464102 0.267949i −0.0221504 0.0127885i 0.488884 0.872349i \(-0.337404\pi\)
−0.511034 + 0.859560i \(0.670737\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −18.4219 + 31.9077i −0.875253 + 1.51598i −0.0187597 + 0.999824i \(0.505972\pi\)
−0.856493 + 0.516158i \(0.827362\pi\)
\(444\) 0 0
\(445\) 0.571797 + 0.990381i 0.0271058 + 0.0469486i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 27.9053i 1.31693i −0.752610 0.658467i \(-0.771205\pi\)
0.752610 0.658467i \(-0.228795\pi\)
\(450\) 0 0
\(451\) 2.00000i 0.0941763i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.74238 3.01790i −0.0816842 0.141481i
\(456\) 0 0
\(457\) 6.59808 11.4282i 0.308645 0.534589i −0.669421 0.742883i \(-0.733458\pi\)
0.978066 + 0.208294i \(0.0667912\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18.1309 + 10.4679i 0.844442 + 0.487539i 0.858772 0.512359i \(-0.171228\pi\)
−0.0143297 + 0.999897i \(0.504561\pi\)
\(462\) 0 0
\(463\) −2.07180 + 1.19615i −0.0962846 + 0.0555899i −0.547369 0.836891i \(-0.684371\pi\)
0.451085 + 0.892481i \(0.351037\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.8695 1.01200 0.506001 0.862533i \(-0.331123\pi\)
0.506001 + 0.862533i \(0.331123\pi\)
\(468\) 0 0
\(469\) 30.3923 1.40339
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.72878 + 0.998111i −0.0794894 + 0.0458932i
\(474\) 0 0
\(475\) −19.3923 11.1962i −0.889780 0.513715i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.50215 + 2.60179i −0.0686348 + 0.118879i −0.898301 0.439381i \(-0.855198\pi\)
0.829666 + 0.558260i \(0.188531\pi\)
\(480\) 0 0
\(481\) −5.25833 9.10770i −0.239759 0.415275i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 7.45001i 0.338287i
\(486\) 0 0
\(487\) 23.0718i 1.04548i −0.852491 0.522741i \(-0.824909\pi\)
0.852491 0.522741i \(-0.175091\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −16.9198 29.3059i −0.763580 1.32256i −0.940994 0.338423i \(-0.890107\pi\)
0.177415 0.984136i \(-0.443227\pi\)
\(492\) 0 0
\(493\) 11.4282 19.7942i 0.514700 0.891487i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −38.1194 22.0082i −1.70989 0.987205i
\(498\) 0 0
\(499\) −19.4378 + 11.2224i −0.870156 + 0.502385i −0.867400 0.497611i \(-0.834211\pi\)
−0.00275621 + 0.999996i \(0.500877\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 14.9743 0.667673 0.333836 0.942631i \(-0.391657\pi\)
0.333836 + 0.942631i \(0.391657\pi\)
\(504\) 0 0
\(505\) 1.80385 0.0802702
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.29719 + 1.32628i −0.101821 + 0.0587864i −0.550046 0.835135i \(-0.685390\pi\)
0.448225 + 0.893921i \(0.352056\pi\)
\(510\) 0 0
\(511\) −24.2942 14.0263i −1.07471 0.620486i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.03528 + 1.79315i −0.0456197 + 0.0790157i
\(516\) 0 0
\(517\) 1.80385 + 3.12436i 0.0793331 + 0.137409i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 29.9759i 1.31327i 0.754210 + 0.656634i \(0.228020\pi\)
−0.754210 + 0.656634i \(0.771980\pi\)
\(522\) 0 0
\(523\) 5.80385i 0.253785i −0.991917 0.126892i \(-0.959500\pi\)
0.991917 0.126892i \(-0.0405003\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.896575 + 1.55291i 0.0390554 + 0.0676460i
\(528\) 0 0
\(529\) 10.5000 18.1865i 0.456522 0.790719i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −11.2629 6.50266i −0.487852 0.281662i
\(534\) 0 0
\(535\) −3.00000 + 1.73205i −0.129701 + 0.0748831i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.175865 −0.00757506
\(540\) 0 0
\(541\) 7.00000 0.300954 0.150477 0.988614i \(-0.451919\pi\)
0.150477 + 0.988614i \(0.451919\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.45069 2.56961i 0.190647 0.110070i
\(546\) 0 0
\(547\) −28.8564 16.6603i −1.23381 0.712341i −0.265989 0.963976i \(-0.585698\pi\)
−0.967822 + 0.251635i \(0.919032\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −16.1619 + 27.9933i −0.688521 + 1.19255i
\(552\) 0 0
\(553\) 19.9282 + 34.5167i 0.847433 + 1.46780i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 19.1798i 0.812675i −0.913723 0.406337i \(-0.866806\pi\)
0.913723 0.406337i \(-0.133194\pi\)
\(558\) 0 0
\(559\) 12.9808i 0.549028i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −22.6646 39.2562i −0.955198 1.65445i −0.733914 0.679243i \(-0.762308\pi\)
−0.221284 0.975209i \(-0.571025\pi\)
\(564\) 0 0
\(565\) 0.473721 0.820508i 0.0199296 0.0345190i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 29.4261 + 16.9891i 1.23360 + 0.712222i 0.967779 0.251799i \(-0.0810223\pi\)
0.265825 + 0.964021i \(0.414356\pi\)
\(570\) 0 0
\(571\) 10.5167 6.07180i 0.440109 0.254097i −0.263535 0.964650i \(-0.584888\pi\)
0.703644 + 0.710553i \(0.251555\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.69213 0.279081
\(576\) 0 0
\(577\) 11.5359 0.480246 0.240123 0.970743i \(-0.422812\pi\)
0.240123 + 0.970743i \(0.422812\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.79315 + 1.03528i −0.0743924 + 0.0429505i
\(582\) 0 0
\(583\) 0.803848 + 0.464102i 0.0332920 + 0.0192211i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.50266 + 11.2629i −0.268394 + 0.464871i −0.968447 0.249219i \(-0.919826\pi\)
0.700054 + 0.714090i \(0.253159\pi\)
\(588\) 0 0
\(589\) −1.26795 2.19615i −0.0522449 0.0904909i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25.3915i 1.04270i 0.853342 + 0.521351i \(0.174572\pi\)
−0.853342 + 0.521351i \(0.825428\pi\)
\(594\) 0 0
\(595\) 4.73205i 0.193995i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0.138701 + 0.240237i 0.00566716 + 0.00981580i 0.868845 0.495084i \(-0.164863\pi\)
−0.863178 + 0.504900i \(0.831529\pi\)
\(600\) 0 0
\(601\) 18.8923 32.7224i 0.770633 1.33478i −0.166583 0.986027i \(-0.553273\pi\)
0.937216 0.348748i \(-0.113393\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.86679 2.80984i −0.197863 0.114236i
\(606\) 0 0
\(607\) −2.83013 + 1.63397i −0.114871 + 0.0663210i −0.556335 0.830958i \(-0.687793\pi\)
0.441464 + 0.897279i \(0.354459\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 23.4596 0.949075
\(612\) 0 0
\(613\) 34.3923 1.38909 0.694546 0.719448i \(-0.255605\pi\)
0.694546 + 0.719448i \(0.255605\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.81225 3.93305i 0.274251 0.158339i −0.356567 0.934270i \(-0.616053\pi\)
0.630818 + 0.775931i \(0.282720\pi\)
\(618\) 0 0
\(619\) 7.73205 + 4.46410i 0.310777 + 0.179427i 0.647274 0.762257i \(-0.275909\pi\)
−0.336497 + 0.941685i \(0.609242\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 3.01790 5.22715i 0.120909 0.209421i
\(624\) 0 0
\(625\) −10.5263 18.2321i −0.421051 0.729282i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 14.2808i 0.569414i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.808643 + 1.40061i 0.0320900 + 0.0555815i
\(636\) 0 0
\(637\) −0.571797 + 0.990381i −0.0226554 + 0.0392403i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3.94666 2.27860i −0.155884 0.0899994i 0.420029 0.907511i \(-0.362020\pi\)
−0.575913 + 0.817511i \(0.695353\pi\)
\(642\) 0 0
\(643\) −3.46410 + 2.00000i −0.136611 + 0.0788723i −0.566748 0.823891i \(-0.691799\pi\)
0.430137 + 0.902764i \(0.358465\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 42.1218 1.65598 0.827989 0.560744i \(-0.189485\pi\)
0.827989 + 0.560744i \(0.189485\pi\)
\(648\) 0 0
\(649\) −5.17691 −0.203212
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 39.3441 22.7153i 1.53966 0.888920i 0.540797 0.841153i \(-0.318123\pi\)
0.998859 0.0477670i \(-0.0152105\pi\)
\(654\) 0 0
\(655\) −8.83013 5.09808i −0.345022 0.199198i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3.81294 6.60420i 0.148531 0.257263i −0.782154 0.623085i \(-0.785879\pi\)
0.930685 + 0.365822i \(0.119212\pi\)
\(660\) 0 0
\(661\) −18.2583 31.6244i −0.710167 1.23004i −0.964794 0.263006i \(-0.915286\pi\)
0.254628 0.967039i \(-0.418047\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6.69213i 0.259510i
\(666\) 0 0
\(667\) 9.66025i 0.374047i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.74238 3.01790i −0.0672639 0.116505i
\(672\) 0 0
\(673\) 2.16025 3.74167i 0.0832717 0.144231i −0.821382 0.570379i \(-0.806796\pi\)
0.904653 + 0.426148i \(0.140130\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −38.5119 22.2349i −1.48013 0.854556i −0.480387 0.877057i \(-0.659504\pi\)
−0.999747 + 0.0225009i \(0.992837\pi\)
\(678\) 0 0
\(679\) −34.0526 + 19.6603i −1.30682 + 0.754491i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20.0764 −0.768202 −0.384101 0.923291i \(-0.625489\pi\)
−0.384101 + 0.923291i \(0.625489\pi\)
\(684\) 0 0
\(685\) −11.3923 −0.435278
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5.22715 3.01790i 0.199139 0.114973i
\(690\) 0 0
\(691\) 24.7583 + 14.2942i 0.941851 + 0.543778i 0.890540 0.454905i \(-0.150327\pi\)
0.0513111 + 0.998683i \(0.483660\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.17209 + 3.76217i −0.0823920 + 0.142707i
\(696\) 0 0
\(697\) 8.83013 + 15.2942i 0.334465 + 0.579310i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 30.1146i 1.13741i 0.822541 + 0.568706i \(0.192556\pi\)
−0.822541 + 0.568706i \(0.807444\pi\)
\(702\) 0 0
\(703\) 20.1962i 0.761712i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.76028 8.24504i −0.179029 0.310087i
\(708\) 0 0
\(709\) 6.50000 11.2583i 0.244113 0.422815i −0.717769 0.696281i \(-0.754837\pi\)
0.961882 + 0.273466i \(0.0881700\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0.656339 + 0.378937i 0.0245801 + 0.0141913i
\(714\) 0 0
\(715\) 0.418584 0.241670i 0.0156542 0.00903794i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −31.4916 −1.17444 −0.587220 0.809427i \(-0.699778\pi\)
−0.587220 + 0.809427i \(0.699778\pi\)
\(720\) 0 0
\(721\) 10.9282 0.406988
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −27.9933 + 16.1619i −1.03964 + 0.600239i
\(726\) 0 0
\(727\) −34.5622 19.9545i −1.28184 0.740071i −0.304656 0.952463i \(-0.598541\pi\)
−0.977185 + 0.212392i \(0.931875\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.81345 15.2653i 0.325977 0.564609i
\(732\) 0 0
\(733\) −2.33975 4.05256i −0.0864205 0.149685i 0.819575 0.572972i \(-0.194210\pi\)
−0.905996 + 0.423287i \(0.860876\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.21543i 0.155278i
\(738\) 0 0
\(739\) 32.0000i 1.17714i −0.808447 0.588570i \(-0.799691\pi\)
0.808447 0.588570i \(-0.200309\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.6980 + 42.7781i 0.906081 + 1.56938i 0.819460 + 0.573136i \(0.194273\pi\)
0.0866206 + 0.996241i \(0.472393\pi\)
\(744\) 0 0
\(745\) 5.23205 9.06218i 0.191688 0.332013i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 15.8338 + 9.14162i 0.578553 + 0.334028i
\(750\) 0 0
\(751\) 35.1506 20.2942i 1.28266 0.740547i 0.305330 0.952247i \(-0.401233\pi\)
0.977335 + 0.211700i \(0.0678999\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.72741 −0.281229
\(756\) 0 0
\(757\) 16.7846 0.610047 0.305024 0.952345i \(-0.401336\pi\)
0.305024 + 0.952345i \(0.401336\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 29.9945 17.3173i 1.08730 0.627752i 0.154443 0.988002i \(-0.450642\pi\)
0.932856 + 0.360250i \(0.117308\pi\)
\(762\) 0 0
\(763\) −23.4904 13.5622i −0.850409 0.490984i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −16.8319 + 29.1536i −0.607763 + 1.05268i
\(768\) 0 0
\(769\) −25.0167 43.3301i −0.902124 1.56252i −0.824732 0.565524i \(-0.808674\pi\)
−0.0773917 0.997001i \(-0.524659\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 53.1209i 1.91063i −0.295594 0.955314i \(-0.595517\pi\)
0.295594 0.955314i \(-0.404483\pi\)
\(774\) 0 0
\(775\) 2.53590i 0.0910922i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −12.4877 21.6293i −0.447418 0.774950i
\(780\) 0 0
\(781\) 3.05256 5.28719i 0.109229 0.189190i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.98571 1.72380i −0.106565 0.0615251i
\(786\) 0 0
\(787\) −18.4186 + 10.6340i −0.656552 + 0.379060i −0.790962 0.611866i \(-0.790419\pi\)
0.134410 + 0.990926i \(0.457086\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.00052 −0.177798
\(792\) 0 0
\(793\) −22.6603 −0.804689
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.30079 + 4.79246i −0.294029 + 0.169758i −0.639757 0.768577i \(-0.720965\pi\)
0.345728 + 0.938335i \(0.387632\pi\)
\(798\) 0 0
\(799\) −27.5885 15.9282i −0.976009 0.563499i
\(800\) 0 0
\(801\) 0 0