Properties

Label 1296.2.i.l.865.1
Level $1296$
Weight $2$
Character 1296.865
Analytic conductor $10.349$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1296.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.3486121020\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
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 865.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1296.865
Dual form 1296.2.i.l.433.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) 1.50000 2.59808i 0.566947 0.981981i −0.429919 0.902867i \(-0.641458\pi\)
0.996866 0.0791130i \(-0.0252088\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0 0
\(13\) −2.00000 3.46410i −0.554700 0.960769i −0.997927 0.0643593i \(-0.979500\pi\)
0.443227 0.896410i \(-0.353834\pi\)
\(14\) 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 \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) 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 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) −3.50000 6.06218i −0.628619 1.08880i −0.987829 0.155543i \(-0.950287\pi\)
0.359211 0.933257i \(-0.383046\pi\)
\(32\) 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 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 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 \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 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 −0.991098 0.133135i \(-0.957496\pi\)
0.380251 0.924883i \(-0.375838\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 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 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.50000 + 9.52628i −0.603703 + 1.04565i 0.388552 + 0.921427i \(0.372976\pi\)
−0.992255 + 0.124218i \(0.960358\pi\)
\(84\) 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 −0.839525 0.543321i \(-0.817167\pi\)
0.890292 + 0.455389i \(0.150500\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.50000 + 7.79423i −0.447767 + 0.775555i −0.998240 0.0592978i \(-0.981114\pi\)
0.550474 + 0.834853i \(0.314447\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 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 0.971930 0.235269i \(-0.0755971\pi\)
−0.689714 + 0.724082i \(0.742264\pi\)
\(114\) 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 \(-0.337710\pi\)
0.488046 + 0.872818i \(0.337710\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.500000 + 0.866025i 0.0436852 + 0.0756650i 0.887041 0.461690i \(-0.152757\pi\)
−0.843356 + 0.537355i \(0.819423\pi\)
\(132\) 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 −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) 0 0
\(139\) 6.00000 + 10.3923i 0.508913 + 0.881464i 0.999947 + 0.0103230i \(0.00328598\pi\)
−0.491033 + 0.871141i \(0.663381\pi\)
\(140\) 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 0.686296 0.727322i \(-0.259235\pi\)
−0.973028 + 0.230689i \(0.925902\pi\)
\(150\) 0 0
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 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 0.920860 + 0.389892i \(0.127488\pi\)
−0.122774 + 0.992435i \(0.539179\pi\)
\(158\) 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 \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.00000 5.19615i −0.232147 0.402090i 0.726293 0.687386i \(-0.241242\pi\)
−0.958440 + 0.285295i \(0.907908\pi\)
\(168\) 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 −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) 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 \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 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 \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0 0
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) 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 \(-0.372515\pi\)
0.389885 + 0.920864i \(0.372515\pi\)
\(200\) 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 \(-0.0548120\pi\)
−0.640996 + 0.767544i \(0.721479\pi\)
\(212\) 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 −0.463409 0.886145i \(-0.653374\pi\)
0.999128 0.0417488i \(-0.0132929\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 0 0
\(229\) 1.00000 + 1.73205i 0.0660819 + 0.114457i 0.897173 0.441679i \(-0.145617\pi\)
−0.831092 + 0.556136i \(0.812283\pi\)
\(230\) 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 0.964282 + 0.264876i \(0.0853311\pi\)
−0.252752 + 0.967531i \(0.581336\pi\)
\(240\) 0 0
\(241\) −3.00000 + 5.19615i −0.193247 + 0.334714i −0.946324 0.323218i \(-0.895235\pi\)
0.753077 + 0.657932i \(0.228569\pi\)
\(242\) 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 \(-0.668491\pi\)
−0.504956 + 0.863145i \(0.668491\pi\)
\(252\) 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 0.796881 0.604136i \(-0.206482\pi\)
−0.921638 + 0.388051i \(0.873148\pi\)
\(258\) 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 −0.116939 0.993139i \(-0.537308\pi\)
0.918553 0.395298i \(-0.129359\pi\)
\(264\) 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 \(-0.370798\pi\)
0.394847 + 0.918747i \(0.370798\pi\)
\(272\) 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 −0.720473 0.693482i \(-0.756075\pi\)
0.960810 + 0.277207i \(0.0894088\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.00000 + 13.8564i −0.477240 + 0.826604i −0.999660 0.0260845i \(-0.991696\pi\)
0.522420 + 0.852688i \(0.325029\pi\)
\(282\) 0 0
\(283\) 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 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 0.940252 0.340480i \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) 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 \(-0.740144\pi\)
−0.684876 + 0.728659i \(0.740144\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.0000 25.9808i −0.850572 1.47323i −0.880693 0.473688i \(-0.842923\pi\)
0.0301210 0.999546i \(-0.490411\pi\)
\(312\) 0 0
\(313\) −10.5000 + 18.1865i −0.593495 + 1.02796i 0.400262 + 0.916401i \(0.368919\pi\)
−0.993757 + 0.111563i \(0.964414\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.50000 + 7.79423i −0.252745 + 0.437767i −0.964281 0.264883i \(-0.914667\pi\)
0.711535 + 0.702650i \(0.248000\pi\)
\(318\) 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 \(-0.707619\pi\)
0.991735 + 0.128302i \(0.0409527\pi\)
\(332\) 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 0.936093 0.351752i \(-0.114414\pi\)
−0.772673 + 0.634804i \(0.781081\pi\)
\(338\) 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 0.959090 + 0.283101i \(0.0913633\pi\)
−0.234372 + 0.972147i \(0.575303\pi\)
\(348\) 0 0
\(349\) −15.0000 + 25.9808i −0.802932 + 1.39072i 0.114747 + 0.993395i \(0.463394\pi\)
−0.917679 + 0.397324i \(0.869939\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −11.0000 + 19.0526i −0.585471 + 1.01407i 0.409346 + 0.912379i \(0.365757\pi\)
−0.994817 + 0.101686i \(0.967576\pi\)
\(354\) 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 \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 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 \(-0.926024\pi\)
0.686018 + 0.727585i \(0.259357\pi\)
\(368\) 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 0.743691 0.668523i \(-0.233073\pi\)
−0.950804 + 0.309794i \(0.899740\pi\)
\(374\) 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 \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 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 −0.853072 0.521794i \(-0.825263\pi\)
0.878423 + 0.477885i \(0.158596\pi\)
\(390\) 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 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) 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 0.955570 0.294765i \(-0.0952414\pi\)
−0.733059 + 0.680165i \(0.761908\pi\)
\(410\) 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 −0.852047 0.523465i \(-0.824639\pi\)
−0.0273103 0.999627i \(-0.508694\pi\)
\(420\) 0 0
\(421\) −4.00000 + 6.92820i −0.194948 + 0.337660i −0.946883 0.321577i \(-0.895787\pi\)
0.751935 + 0.659237i \(0.229121\pi\)
\(422\) 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 \(-0.805394\pi\)
−0.818861 + 0.573992i \(0.805394\pi\)
\(432\) 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 \(-0.764432\pi\)
0.953202 + 0.302333i \(0.0977654\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.00000 3.46410i 0.0950229 0.164584i −0.814595 0.580030i \(-0.803041\pi\)
0.909618 + 0.415445i \(0.136374\pi\)
\(444\) 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 −0.854094 0.520119i \(-0.825888\pi\)
0.877483 + 0.479608i \(0.159221\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.500000 0.866025i 0.0232873 0.0403348i −0.854147 0.520032i \(-0.825920\pi\)
0.877434 + 0.479697i \(0.159253\pi\)
\(462\) 0 0
\(463\) −0.500000 0.866025i −0.0232370 0.0402476i 0.854173 0.519989i \(-0.174064\pi\)
−0.877410 + 0.479741i \(0.840731\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) 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 0.399704 + 0.916644i \(0.369113\pi\)
−0.993689 + 0.112168i \(0.964220\pi\)
\(480\) 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 \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.50000 7.79423i −0.203082 0.351749i 0.746438 0.665455i \(-0.231763\pi\)
−0.949520 + 0.313707i \(0.898429\pi\)
\(492\) 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 \(-0.123789\pi\)
−0.791031 + 0.611776i \(0.790455\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6.00000 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(504\) 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 0.533815 0.845601i \(-0.320758\pi\)
−0.999220 + 0.0394971i \(0.987424\pi\)
\(510\) 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 \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) 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 −0.289605 0.957146i \(-0.593524\pi\)
0.973715 0.227768i \(-0.0731428\pi\)
\(548\) 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 \(-0.0922060\pi\)
−0.726540 + 0.687124i \(0.758873\pi\)
\(564\) 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 −0.407724 0.913105i \(-0.633677\pi\)
0.994634 0.103454i \(-0.0329893\pi\)
\(570\) 0 0
\(571\) −6.00000 10.3923i −0.251092 0.434904i 0.712735 0.701434i \(-0.247456\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(572\) 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 \(-0.961587\pi\)
0.600620 + 0.799534i \(0.294920\pi\)
\(588\) 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 \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 0 0
\(601\) 2.50000 4.33013i 0.101977 0.176630i −0.810522 0.585708i \(-0.800816\pi\)
0.912499 + 0.409079i \(0.134150\pi\)
\(602\) 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 −0.911621 0.411033i \(-0.865168\pi\)
0.0998457 0.995003i \(-0.468165\pi\)
\(608\) 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 0.799298 0.600935i \(-0.205205\pi\)
−0.920074 + 0.391745i \(0.871871\pi\)
\(618\) 0 0
\(619\) 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i \(-0.643093\pi\)
0.997259 0.0739910i \(-0.0235736\pi\)
\(620\) 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 \(-0.826997\pi\)
−0.855901 + 0.517139i \(0.826997\pi\)
\(632\) 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 −0.562779 0.826608i \(-0.690268\pi\)
0.997253 + 0.0740768i \(0.0236010\pi\)
\(642\) 0 0
\(643\) 6.00000 + 10.3923i 0.236617 + 0.409832i 0.959741 0.280885i \(-0.0906280\pi\)
−0.723124 + 0.690718i \(0.757295\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.0000 −0.629025 −0.314512 0.949253i \(-0.601841\pi\)
−0.314512 + 0.949253i \(0.601841\pi\)
\(648\) 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 0.835182 0.549973i \(-0.185362\pi\)
−0.893882 + 0.448303i \(0.852029\pi\)
\(654\) 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 \(-0.967463\pi\)
0.585758 + 0.810486i \(0.300797\pi\)
\(660\) 0 0
\(661\) −19.0000 32.9090i −0.739014 1.28001i −0.952940 0.303160i \(-0.901958\pi\)
0.213925 0.976850i \(-0.431375\pi\)
\(662\) 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 −0.963679 0.267063i \(-0.913947\pi\)
0.713123 + 0.701039i \(0.247280\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.0000 19.0526i 0.422764 0.732249i −0.573444 0.819244i \(-0.694393\pi\)
0.996209 + 0.0869952i \(0.0277265\pi\)
\(678\) 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 \(-0.818508\pi\)
−0.841807 + 0.539779i \(0.818508\pi\)
\(684\) 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 \(-0.857575\pi\)
0.825473 + 0.564441i \(0.190908\pi\)
\(692\) 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 −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 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 \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) 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 \(-0.815616\pi\)
0.892500 + 0.451047i \(0.148949\pi\)
\(728\) 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 0.881633 + 0.471935i \(0.156444\pi\)
−0.0321090 + 0.999484i \(0.510222\pi\)
\(734\) 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 \(-0.236848\pi\)
0.735712 + 0.677295i \(0.236848\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 10.0000 + 17.3205i 0.366864 + 0.635428i 0.989073 0.147423i \(-0.0470980\pi\)
−0.622209 + 0.782851i \(0.713765\pi\)
\(744\) 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 0.904911 + 0.425601i \(0.139937\pi\)
−0.0838743 + 0.996476i \(0.526729\pi\)
\(752\) 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 0.995479 + 0.0949859i \(0.0302806\pi\)
−0.415479 + 0.909603i \(0.636386\pi\)
\(762\) 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 0.922207 0.386698i \(-0.126384\pi\)
−0.795993 + 0.605305i \(0.793051\pi\)
\(770\) 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 −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 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 −0.989507 0.144486i \(-0.953847\pi\)
0.369625 0.929181i \(-0.379486\pi\)
\(798\) 0 0
\(799\) −24.0000 + 41.5692i −0.849059 + 1.47061i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.50000 4.33013i 0.0882231 0.152807i