Properties

Label 648.2.i.e.433.1
Level $648$
Weight $2$
Character 648.433
Analytic conductor $5.174$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 433.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 648.433
Dual form 648.2.i.e.217.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +(-2.50000 - 4.33013i) q^{11} +(-2.00000 + 3.46410i) q^{13} -8.00000 q^{17} +2.00000 q^{19} +(-1.00000 + 1.73205i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-3.00000 - 5.19615i) q^{29} +(3.50000 - 6.06218i) q^{31} -3.00000 q^{35} -6.00000 q^{37} +(3.00000 - 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{43} +(-3.00000 - 5.19615i) q^{47} +(-1.00000 + 1.73205i) q^{49} +5.00000 q^{53} -5.00000 q^{55} +(2.00000 - 3.46410i) q^{59} +(4.00000 + 6.92820i) q^{61} +(2.00000 + 3.46410i) q^{65} +(5.00000 - 8.66025i) q^{67} -8.00000 q^{71} +1.00000 q^{73} +(-7.50000 + 12.9904i) q^{77} +(-8.00000 - 13.8564i) q^{79} +(5.50000 + 9.52628i) q^{83} +(-4.00000 + 6.92820i) q^{85} +6.00000 q^{89} +12.0000 q^{91} +(1.00000 - 1.73205i) q^{95} +(0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{5} - 3 q^{7} - 5 q^{11} - 4 q^{13} - 16 q^{17} + 4 q^{19} - 2 q^{23} + 4 q^{25} - 6 q^{29} + 7 q^{31} - 6 q^{35} - 12 q^{37} + 6 q^{41} + 2 q^{43} - 6 q^{47} - 2 q^{49} + 10 q^{53} - 10 q^{55} + 4 q^{59} + 8 q^{61} + 4 q^{65} + 10 q^{67} - 16 q^{71} + 2 q^{73} - 15 q^{77} - 16 q^{79} + 11 q^{83} - 8 q^{85} + 12 q^{89} + 24 q^{91} + 2 q^{95} + q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 0.500000 0.866025i 0.223607 0.387298i −0.732294 0.680989i \(-0.761550\pi\)
0.955901 + 0.293691i \(0.0948835\pi\)
\(6\) 0 0
\(7\) −1.50000 2.59808i −0.566947 0.981981i −0.996866 0.0791130i \(-0.974791\pi\)
0.429919 0.902867i \(-0.358542\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) 0 0
\(13\) −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i \(0.353834\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −8.00000 −1.94029 −0.970143 0.242536i \(-0.922021\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) 0 0
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) 3.50000 6.06218i 0.628619 1.08880i −0.359211 0.933257i \(-0.616954\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.00000 5.19615i 0.468521 0.811503i −0.530831 0.847477i \(-0.678120\pi\)
0.999353 + 0.0359748i \(0.0114536\pi\)
\(42\) 0 0
\(43\) 1.00000 + 1.73205i 0.152499 + 0.264135i 0.932145 0.362084i \(-0.117935\pi\)
−0.779647 + 0.626219i \(0.784601\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) 0 0
\(49\) −1.00000 + 1.73205i −0.142857 + 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 5.00000 0.686803 0.343401 0.939189i \(-0.388421\pi\)
0.343401 + 0.939189i \(0.388421\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.00000 + 3.46410i 0.248069 + 0.429669i
\(66\) 0 0
\(67\) 5.00000 8.66025i 0.610847 1.05802i −0.380251 0.924883i \(-0.624162\pi\)
0.991098 0.133135i \(-0.0425044\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) 1.00000 0.117041 0.0585206 0.998286i \(-0.481362\pi\)
0.0585206 + 0.998286i \(0.481362\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.50000 + 12.9904i −0.854704 + 1.48039i
\(78\) 0 0
\(79\) −8.00000 13.8564i −0.900070 1.55897i −0.827401 0.561611i \(-0.810182\pi\)
−0.0726692 0.997356i \(-0.523152\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.50000 + 9.52628i 0.603703 + 1.04565i 0.992255 + 0.124218i \(0.0396422\pi\)
−0.388552 + 0.921427i \(0.627024\pi\)
\(84\) 0 0
\(85\) −4.00000 + 6.92820i −0.433861 + 0.751469i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 12.0000 1.25794
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0 0
\(97\) 0.500000 + 0.866025i 0.0507673 + 0.0879316i 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) 0 0
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 0.870063 0.435031 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.00000 5.19615i 0.282216 0.488813i −0.689714 0.724082i \(-0.742264\pi\)
0.971930 + 0.235269i \(0.0755971\pi\)
\(114\) 0 0
\(115\) 1.00000 + 1.73205i 0.0932505 + 0.161515i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 12.0000 + 20.7846i 1.10004 + 1.90532i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −11.0000 −0.976092 −0.488046 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.500000 + 0.866025i −0.0436852 + 0.0756650i −0.887041 0.461690i \(-0.847243\pi\)
0.843356 + 0.537355i \(0.180577\pi\)
\(132\) 0 0
\(133\) −3.00000 5.19615i −0.260133 0.450564i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 0 0
\(139\) −6.00000 + 10.3923i −0.508913 + 0.881464i 0.491033 + 0.871141i \(0.336619\pi\)
−0.999947 + 0.0103230i \(0.996714\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 20.0000 1.67248
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.50000 + 6.06218i −0.286731 + 0.496633i −0.973028 0.230689i \(-0.925902\pi\)
0.686296 + 0.727322i \(0.259235\pi\)
\(150\) 0 0
\(151\) −2.50000 4.33013i −0.203447 0.352381i 0.746190 0.665733i \(-0.231881\pi\)
−0.949637 + 0.313353i \(0.898548\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.50000 6.06218i −0.281127 0.486926i
\(156\) 0 0
\(157\) 10.0000 17.3205i 0.798087 1.38233i −0.122774 0.992435i \(-0.539179\pi\)
0.920860 0.389892i \(-0.127488\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) 0 0
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3.00000 5.19615i 0.232147 0.402090i −0.726293 0.687386i \(-0.758758\pi\)
0.958440 + 0.285295i \(0.0920916\pi\)
\(168\) 0 0
\(169\) −1.50000 2.59808i −0.115385 0.199852i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 10.5000 + 18.1865i 0.798300 + 1.38270i 0.920722 + 0.390218i \(0.127601\pi\)
−0.122422 + 0.992478i \(0.539066\pi\)
\(174\) 0 0
\(175\) 6.00000 10.3923i 0.453557 0.785584i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) 20.0000 + 34.6410i 1.46254 + 2.53320i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0 0
\(193\) 9.50000 16.4545i 0.683825 1.18442i −0.289980 0.957033i \(-0.593649\pi\)
0.973805 0.227387i \(-0.0730182\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0 0
\(199\) −11.0000 −0.779769 −0.389885 0.920864i \(-0.627485\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −9.00000 + 15.5885i −0.631676 + 1.09410i
\(204\) 0 0
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.00000 8.66025i −0.345857 0.599042i
\(210\) 0 0
\(211\) −5.00000 + 8.66025i −0.344214 + 0.596196i −0.985211 0.171347i \(-0.945188\pi\)
0.640996 + 0.767544i \(0.278521\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.00000 0.136399
\(216\) 0 0
\(217\) −21.0000 −1.42557
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 16.0000 27.7128i 1.07628 1.86417i
\(222\) 0 0
\(223\) −8.00000 13.8564i −0.535720 0.927894i −0.999128 0.0417488i \(-0.986707\pi\)
0.463409 0.886145i \(-0.346626\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 0 0
\(229\) 1.00000 1.73205i 0.0660819 0.114457i −0.831092 0.556136i \(-0.812283\pi\)
0.897173 + 0.441679i \(0.145617\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −22.0000 −1.44127 −0.720634 0.693316i \(-0.756149\pi\)
−0.720634 + 0.693316i \(0.756149\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −11.0000 + 19.0526i −0.711531 + 1.23241i 0.252752 + 0.967531i \(0.418664\pi\)
−0.964282 + 0.264876i \(0.914669\pi\)
\(240\) 0 0
\(241\) −3.00000 5.19615i −0.193247 0.334714i 0.753077 0.657932i \(-0.228569\pi\)
−0.946324 + 0.323218i \(0.895235\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) 0 0
\(247\) −4.00000 + 6.92820i −0.254514 + 0.440831i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.0000 1.00991 0.504956 0.863145i \(-0.331509\pi\)
0.504956 + 0.863145i \(0.331509\pi\)
\(252\) 0 0
\(253\) 10.0000 0.628695
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.00000 + 3.46410i −0.124757 + 0.216085i −0.921638 0.388051i \(-0.873148\pi\)
0.796881 + 0.604136i \(0.206482\pi\)
\(258\) 0 0
\(259\) 9.00000 + 15.5885i 0.559233 + 0.968620i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.0000 22.5167i −0.801614 1.38844i −0.918553 0.395298i \(-0.870641\pi\)
0.116939 0.993139i \(-0.462692\pi\)
\(264\) 0 0
\(265\) 2.50000 4.33013i 0.153574 0.265998i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.00000 −0.121942 −0.0609711 0.998140i \(-0.519420\pi\)
−0.0609711 + 0.998140i \(0.519420\pi\)
\(270\) 0 0
\(271\) −13.0000 −0.789694 −0.394847 0.918747i \(-0.629202\pi\)
−0.394847 + 0.918747i \(0.629202\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.0000 17.3205i 0.603023 1.04447i
\(276\) 0 0
\(277\) 4.00000 + 6.92820i 0.240337 + 0.416275i 0.960810 0.277207i \(-0.0894088\pi\)
−0.720473 + 0.693482i \(0.756075\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.00000 13.8564i −0.477240 0.826604i 0.522420 0.852688i \(-0.325029\pi\)
−0.999660 + 0.0260845i \(0.991696\pi\)
\(282\) 0 0
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.0000 −1.06251
\(288\) 0 0
\(289\) 47.0000 2.76471
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3.00000 5.19615i 0.175262 0.303562i −0.764990 0.644042i \(-0.777256\pi\)
0.940252 + 0.340480i \(0.110589\pi\)
\(294\) 0 0
\(295\) −2.00000 3.46410i −0.116445 0.201688i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.00000 6.92820i −0.231326 0.400668i
\(300\) 0 0
\(301\) 3.00000 5.19615i 0.172917 0.299501i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.00000 0.458079
\(306\) 0 0
\(307\) 24.0000 1.36975 0.684876 0.728659i \(-0.259856\pi\)
0.684876 + 0.728659i \(0.259856\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 15.0000 25.9808i 0.850572 1.47323i −0.0301210 0.999546i \(-0.509589\pi\)
0.880693 0.473688i \(-0.157077\pi\)
\(312\) 0 0
\(313\) −10.5000 18.1865i −0.593495 1.02796i −0.993757 0.111563i \(-0.964414\pi\)
0.400262 0.916401i \(-0.368919\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.50000 7.79423i −0.252745 0.437767i 0.711535 0.702650i \(-0.248000\pi\)
−0.964281 + 0.264883i \(0.914667\pi\)
\(318\) 0 0
\(319\) −15.0000 + 25.9808i −0.839839 + 1.45464i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −16.0000 −0.890264
\(324\) 0 0
\(325\) −16.0000 −0.887520
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −9.00000 + 15.5885i −0.496186 + 0.859419i
\(330\) 0 0
\(331\) −7.00000 12.1244i −0.384755 0.666415i 0.606980 0.794717i \(-0.292381\pi\)
−0.991735 + 0.128302i \(0.959047\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −5.00000 8.66025i −0.273179 0.473160i
\(336\) 0 0
\(337\) 3.00000 5.19615i 0.163420 0.283052i −0.772673 0.634804i \(-0.781081\pi\)
0.936093 + 0.351752i \(0.114414\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −35.0000 −1.89536
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.5000 + 23.3827i −0.724718 + 1.25525i 0.234372 + 0.972147i \(0.424697\pi\)
−0.959090 + 0.283101i \(0.908637\pi\)
\(348\) 0 0
\(349\) −15.0000 25.9808i −0.802932 1.39072i −0.917679 0.397324i \(-0.869939\pi\)
0.114747 0.993395i \(-0.463394\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −11.0000 19.0526i −0.585471 1.01407i −0.994817 0.101686i \(-0.967576\pi\)
0.409346 0.912379i \(-0.365757\pi\)
\(354\) 0 0
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.500000 0.866025i 0.0261712 0.0453298i
\(366\) 0 0
\(367\) 5.50000 + 9.52628i 0.287098 + 0.497268i 0.973116 0.230317i \(-0.0739762\pi\)
−0.686018 + 0.727585i \(0.740643\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.50000 12.9904i −0.389381 0.674427i
\(372\) 0 0
\(373\) −4.00000 + 6.92820i −0.207112 + 0.358729i −0.950804 0.309794i \(-0.899740\pi\)
0.743691 + 0.668523i \(0.233073\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) 7.50000 + 12.9904i 0.382235 + 0.662051i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.500000 + 0.866025i 0.0253510 + 0.0439092i 0.878423 0.477885i \(-0.158596\pi\)
−0.853072 + 0.521794i \(0.825263\pi\)
\(390\) 0 0
\(391\) 8.00000 13.8564i 0.404577 0.700749i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −16.0000 −0.805047
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.00000 + 10.3923i −0.299626 + 0.518967i −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 0 0
\(403\) 14.0000 + 24.2487i 0.697390 + 1.20791i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 15.0000 + 25.9808i 0.743522 + 1.28782i
\(408\) 0 0
\(409\) 4.50000 7.79423i 0.222511 0.385400i −0.733059 0.680165i \(-0.761908\pi\)
0.955570 + 0.294765i \(0.0952414\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −12.0000 −0.590481
\(414\) 0 0
\(415\) 11.0000 0.539969
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.0000 31.1769i 0.879358 1.52309i 0.0273103 0.999627i \(-0.491306\pi\)
0.852047 0.523465i \(-0.175361\pi\)
\(420\) 0 0
\(421\) −4.00000 6.92820i −0.194948 0.337660i 0.751935 0.659237i \(-0.229121\pi\)
−0.946883 + 0.321577i \(0.895787\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −16.0000 27.7128i −0.776114 1.34427i
\(426\) 0 0
\(427\) 12.0000 20.7846i 0.580721 1.00584i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 34.0000 1.63772 0.818861 0.573992i \(-0.194606\pi\)
0.818861 + 0.573992i \(0.194606\pi\)
\(432\) 0 0
\(433\) 13.0000 0.624740 0.312370 0.949960i \(-0.398877\pi\)
0.312370 + 0.949960i \(0.398877\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.00000 + 3.46410i −0.0956730 + 0.165710i
\(438\) 0 0
\(439\) −4.50000 7.79423i −0.214773 0.371998i 0.738429 0.674331i \(-0.235568\pi\)
−0.953202 + 0.302333i \(0.902235\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) 0 0
\(445\) 3.00000 5.19615i 0.142214 0.246321i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) −30.0000 −1.41264
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.00000 10.3923i 0.281284 0.487199i
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.500000 + 0.866025i 0.0232873 + 0.0403348i 0.877434 0.479697i \(-0.159253\pi\)
−0.854147 + 0.520032i \(0.825920\pi\)
\(462\) 0 0
\(463\) 0.500000 0.866025i 0.0232370 0.0402476i −0.854173 0.519989i \(-0.825936\pi\)
0.877410 + 0.479741i \(0.159269\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.00000 −0.138823 −0.0694117 0.997588i \(-0.522112\pi\)
−0.0694117 + 0.997588i \(0.522112\pi\)
\(468\) 0 0
\(469\) −30.0000 −1.38527
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.00000 8.66025i 0.229900 0.398199i
\(474\) 0 0
\(475\) 4.00000 + 6.92820i 0.183533 + 0.317888i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 13.0000 + 22.5167i 0.593985 + 1.02881i 0.993689 + 0.112168i \(0.0357796\pi\)
−0.399704 + 0.916644i \(0.630887\pi\)
\(480\) 0 0
\(481\) 12.0000 20.7846i 0.547153 0.947697i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.00000 0.0454077
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.50000 7.79423i 0.203082 0.351749i −0.746438 0.665455i \(-0.768237\pi\)
0.949520 + 0.313707i \(0.101571\pi\)
\(492\) 0 0
\(493\) 24.0000 + 41.5692i 1.08091 + 1.87218i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 12.0000 + 20.7846i 0.538274 + 0.932317i
\(498\) 0 0
\(499\) −3.00000 + 5.19615i −0.134298 + 0.232612i −0.925329 0.379165i \(-0.876211\pi\)
0.791031 + 0.611776i \(0.209545\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) −9.00000 −0.400495
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −10.5000 + 18.1865i −0.465404 + 0.806104i −0.999220 0.0394971i \(-0.987424\pi\)
0.533815 + 0.845601i \(0.320758\pi\)
\(510\) 0 0
\(511\) −1.50000 2.59808i −0.0663561 0.114932i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.00000 + 3.46410i 0.0881305 + 0.152647i
\(516\) 0 0
\(517\) −15.0000 + 25.9808i −0.659699 + 1.14263i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 28.0000 1.22670 0.613351 0.789810i \(-0.289821\pi\)
0.613351 + 0.789810i \(0.289821\pi\)
\(522\) 0 0
\(523\) −8.00000 −0.349816 −0.174908 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −28.0000 + 48.4974i −1.21970 + 2.11258i
\(528\) 0 0
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 12.0000 + 20.7846i 0.519778 + 0.900281i
\(534\) 0 0
\(535\) 4.50000 7.79423i 0.194552 0.336974i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.0000 0.430730
\(540\) 0 0
\(541\) 36.0000 1.54776 0.773880 0.633332i \(-0.218313\pi\)
0.773880 + 0.633332i \(0.218313\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.00000 8.66025i 0.214176 0.370965i
\(546\) 0 0
\(547\) −16.0000 27.7128i −0.684111 1.18491i −0.973715 0.227768i \(-0.926857\pi\)
0.289605 0.957146i \(-0.406476\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −6.00000 10.3923i −0.255609 0.442727i
\(552\) 0 0
\(553\) −24.0000 + 41.5692i −1.02058 + 1.76770i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.00000 −0.0423714 −0.0211857 0.999776i \(-0.506744\pi\)
−0.0211857 + 0.999776i \(0.506744\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.50000 + 9.52628i −0.231797 + 0.401485i −0.958337 0.285640i \(-0.907794\pi\)
0.726540 + 0.687124i \(0.241127\pi\)
\(564\) 0 0
\(565\) −3.00000 5.19615i −0.126211 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 14.0000 + 24.2487i 0.586911 + 1.01656i 0.994634 + 0.103454i \(0.0329893\pi\)
−0.407724 + 0.913105i \(0.633677\pi\)
\(570\) 0 0
\(571\) 6.00000 10.3923i 0.251092 0.434904i −0.712735 0.701434i \(-0.752544\pi\)
0.963827 + 0.266529i \(0.0858769\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) 0 0
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16.5000 28.5788i 0.684535 1.18565i
\(582\) 0 0
\(583\) −12.5000 21.6506i −0.517697 0.896678i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.50000 + 16.4545i 0.392107 + 0.679149i 0.992727 0.120385i \(-0.0384130\pi\)
−0.600620 + 0.799534i \(0.705080\pi\)
\(588\) 0 0
\(589\) 7.00000 12.1244i 0.288430 0.499575i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −22.0000 −0.903432 −0.451716 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) 0 0
\(595\) 24.0000 0.983904
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.00000 + 5.19615i −0.122577 + 0.212309i −0.920783 0.390075i \(-0.872449\pi\)
0.798206 + 0.602384i \(0.205782\pi\)
\(600\) 0 0
\(601\) 2.50000 + 4.33013i 0.101977 + 0.176630i 0.912499 0.409079i \(-0.134150\pi\)
−0.810522 + 0.585708i \(0.800816\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 0 0
\(607\) 20.0000 34.6410i 0.811775 1.40604i −0.0998457 0.995003i \(-0.531835\pi\)
0.911621 0.411033i \(-0.134832\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24.0000 0.970936
\(612\) 0 0
\(613\) 14.0000 0.565455 0.282727 0.959200i \(-0.408761\pi\)
0.282727 + 0.959200i \(0.408761\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.00000 + 5.19615i −0.120775 + 0.209189i −0.920074 0.391745i \(-0.871871\pi\)
0.799298 + 0.600935i \(0.205205\pi\)
\(618\) 0 0
\(619\) −14.0000 24.2487i −0.562708 0.974638i −0.997259 0.0739910i \(-0.976426\pi\)
0.434551 0.900647i \(-0.356907\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −9.00000 15.5885i −0.360577 0.624538i
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 48.0000 1.91389
\(630\) 0 0
\(631\) 43.0000 1.71180 0.855901 0.517139i \(-0.173003\pi\)
0.855901 + 0.517139i \(0.173003\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.50000 + 9.52628i −0.218261 + 0.378039i
\(636\) 0 0
\(637\) −4.00000 6.92820i −0.158486 0.274505i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 11.0000 + 19.0526i 0.434474 + 0.752531i 0.997253 0.0740768i \(-0.0236010\pi\)
−0.562779 + 0.826608i \(0.690268\pi\)
\(642\) 0 0
\(643\) −6.00000 + 10.3923i −0.236617 + 0.409832i −0.959741 0.280885i \(-0.909372\pi\)
0.723124 + 0.690718i \(0.242705\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.0000 0.629025 0.314512 0.949253i \(-0.398159\pi\)
0.314512 + 0.949253i \(0.398159\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.50000 + 2.59808i −0.0586995 + 0.101671i −0.893882 0.448303i \(-0.852029\pi\)
0.835182 + 0.549973i \(0.185362\pi\)
\(654\) 0 0
\(655\) 0.500000 + 0.866025i 0.0195366 + 0.0338384i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10.5000 + 18.1865i 0.409022 + 0.708447i 0.994780 0.102039i \(-0.0325366\pi\)
−0.585758 + 0.810486i \(0.699203\pi\)
\(660\) 0 0
\(661\) −19.0000 + 32.9090i −0.739014 + 1.28001i 0.213925 + 0.976850i \(0.431375\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −6.00000 −0.232670
\(666\) 0 0
\(667\) 12.0000 0.464642
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 20.0000 34.6410i 0.772091 1.33730i
\(672\) 0 0
\(673\) −6.50000 11.2583i −0.250557 0.433977i 0.713123 0.701039i \(-0.247280\pi\)
−0.963679 + 0.267063i \(0.913947\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.0000 + 19.0526i 0.422764 + 0.732249i 0.996209 0.0869952i \(-0.0277265\pi\)
−0.573444 + 0.819244i \(0.694393\pi\)
\(678\) 0 0
\(679\) 1.50000 2.59808i 0.0575647 0.0997050i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 44.0000 1.68361 0.841807 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −10.0000 + 17.3205i −0.380970 + 0.659859i
\(690\) 0 0
\(691\) 2.00000 + 3.46410i 0.0760836 + 0.131781i 0.901557 0.432660i \(-0.142425\pi\)
−0.825473 + 0.564441i \(0.809092\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.00000 + 10.3923i 0.227593 + 0.394203i
\(696\) 0 0
\(697\) −24.0000 + 41.5692i −0.909065 + 1.57455i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.00000 −0.113308 −0.0566542 0.998394i \(-0.518043\pi\)
−0.0566542 + 0.998394i \(0.518043\pi\)
\(702\) 0 0
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −13.5000 + 23.3827i −0.507720 + 0.879396i
\(708\) 0 0
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.00000 + 12.1244i 0.262152 + 0.454061i
\(714\) 0 0
\(715\) 10.0000 17.3205i 0.373979 0.647750i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 20.0000 0.745874 0.372937 0.927857i \(-0.378351\pi\)
0.372937 + 0.927857i \(0.378351\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 12.0000 20.7846i 0.445669 0.771921i
\(726\) 0 0
\(727\) −1.50000 2.59808i −0.0556319 0.0963573i 0.836868 0.547404i \(-0.184384\pi\)
−0.892500 + 0.451047i \(0.851051\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) 0 0
\(733\) 23.0000 39.8372i 0.849524 1.47142i −0.0321090 0.999484i \(-0.510222\pi\)
0.881633 0.471935i \(-0.156444\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −50.0000 −1.84177
\(738\) 0 0
\(739\) −40.0000 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −10.0000 + 17.3205i −0.366864 + 0.635428i −0.989073 0.147423i \(-0.952902\pi\)
0.622209 + 0.782851i \(0.286235\pi\)
\(744\) 0 0
\(745\) 3.50000 + 6.06218i 0.128230 + 0.222101i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −13.5000 23.3827i −0.493279 0.854385i
\(750\) 0 0
\(751\) −22.5000 + 38.9711i −0.821037 + 1.42208i 0.0838743 + 0.996476i \(0.473271\pi\)
−0.904911 + 0.425601i \(0.860063\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.00000 −0.181969
\(756\) 0 0
\(757\) −46.0000 −1.67190 −0.835949 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 16.0000 27.7128i 0.580000 1.00459i −0.415479 0.909603i \(-0.636386\pi\)
0.995479 0.0949859i \(-0.0302806\pi\)
\(762\) 0 0
\(763\) −15.0000 25.9808i −0.543036 0.940567i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.00000 + 13.8564i 0.288863 + 0.500326i
\(768\) 0 0
\(769\) 3.50000 6.06218i 0.126213 0.218608i −0.795993 0.605305i \(-0.793051\pi\)
0.922207 + 0.386698i \(0.126384\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 30.0000 1.07903 0.539513 0.841978i \(-0.318609\pi\)
0.539513 + 0.841978i \(0.318609\pi\)
\(774\) 0 0
\(775\) 28.0000 1.00579
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.00000 10.3923i 0.214972 0.372343i
\(780\) 0 0
\(781\) 20.0000 + 34.6410i 0.715656 + 1.23955i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −10.0000 17.3205i −0.356915 0.618195i
\(786\) 0 0
\(787\) 16.0000 27.7128i 0.570338 0.987855i −0.426193 0.904632i \(-0.640145\pi\)
0.996531 0.0832226i \(-0.0265213\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) −32.0000 −1.13635
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −17.5000 + 30.3109i −0.619882 + 1.07367i 0.369625 + 0.929181i \(0.379486\pi\)
−0.989507 + 0.144486i \(0.953847\pi\)
\(798\) 0 0
\(799\) 24.0000 + 41.5692i 0.849059 + 1.47061i
\(800\) 0 0
\(801\) 0 0