Properties

Label 784.2.i.j.177.1
Level $784$
Weight $2$
Character 784.177
Analytic conductor $6.260$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 784.177
Dual form 784.2.i.j.753.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{3} +(2.00000 - 3.46410i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{3} +(2.00000 - 3.46410i) q^{5} +(-0.500000 + 0.866025i) q^{9} +8.00000 q^{15} +(1.00000 + 1.73205i) q^{17} +(-1.00000 + 1.73205i) q^{19} +(4.00000 - 6.92820i) q^{23} +(-5.50000 - 9.52628i) q^{25} +4.00000 q^{27} +2.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(3.00000 - 5.19615i) q^{37} -2.00000 q^{41} -8.00000 q^{43} +(2.00000 + 3.46410i) q^{45} +(-2.00000 + 3.46410i) q^{47} +(-2.00000 + 3.46410i) q^{51} +(5.00000 + 8.66025i) q^{53} -4.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(-6.00000 - 10.3923i) q^{67} +16.0000 q^{69} +(7.00000 + 12.1244i) q^{73} +(11.0000 - 19.0526i) q^{75} +(-4.00000 + 6.92820i) q^{79} +(5.50000 + 9.52628i) q^{81} -6.00000 q^{83} +8.00000 q^{85} +(2.00000 + 3.46410i) q^{87} +(-5.00000 + 8.66025i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(4.00000 + 6.92820i) q^{95} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} + 4q^{5} - q^{9} + O(q^{10}) \) \( 2q + 2q^{3} + 4q^{5} - q^{9} + 16q^{15} + 2q^{17} - 2q^{19} + 8q^{23} - 11q^{25} + 8q^{27} + 4q^{29} + 4q^{31} + 6q^{37} - 4q^{41} - 16q^{43} + 4q^{45} - 4q^{47} - 4q^{51} + 10q^{53} - 8q^{57} + 6q^{59} - 4q^{61} - 12q^{67} + 32q^{69} + 14q^{73} + 22q^{75} - 8q^{79} + 11q^{81} - 12q^{83} + 16q^{85} + 4q^{87} - 10q^{89} - 8q^{93} + 8q^{95} - 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.00000 + 1.73205i 0.577350 + 1.00000i 0.995782 + 0.0917517i \(0.0292466\pi\)
−0.418432 + 0.908248i \(0.637420\pi\)
\(4\) 0 0
\(5\) 2.00000 3.46410i 0.894427 1.54919i 0.0599153 0.998203i \(-0.480917\pi\)
0.834512 0.550990i \(-0.185750\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 8.00000 2.06559
\(16\) 0 0
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) 0 0
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0 0
\(45\) 2.00000 + 3.46410i 0.298142 + 0.516398i
\(46\) 0 0
\(47\) −2.00000 + 3.46410i −0.291730 + 0.505291i −0.974219 0.225605i \(-0.927564\pi\)
0.682489 + 0.730896i \(0.260898\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) 5.00000 + 8.66025i 0.686803 + 1.18958i 0.972867 + 0.231367i \(0.0743197\pi\)
−0.286064 + 0.958211i \(0.592347\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 0 0
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.00000 10.3923i −0.733017 1.26962i −0.955588 0.294706i \(-0.904778\pi\)
0.222571 0.974916i \(-0.428555\pi\)
\(68\) 0 0
\(69\) 16.0000 1.92617
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 7.00000 + 12.1244i 0.819288 + 1.41905i 0.906208 + 0.422833i \(0.138964\pi\)
−0.0869195 + 0.996215i \(0.527702\pi\)
\(74\) 0 0
\(75\) 11.0000 19.0526i 1.27017 2.20000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 0 0
\(87\) 2.00000 + 3.46410i 0.214423 + 0.371391i
\(88\) 0 0
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 + 6.92820i −0.414781 + 0.718421i
\(94\) 0 0
\(95\) 4.00000 + 6.92820i 0.410391 + 0.710819i
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.00000 10.3923i −0.597022 1.03407i −0.993258 0.115924i \(-0.963017\pi\)
0.396236 0.918149i \(-0.370316\pi\)
\(102\) 0 0
\(103\) −6.00000 + 10.3923i −0.591198 + 1.02398i 0.402874 + 0.915255i \(0.368011\pi\)
−0.994071 + 0.108729i \(0.965322\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) −5.00000 8.66025i −0.478913 0.829502i 0.520794 0.853682i \(-0.325636\pi\)
−0.999708 + 0.0241802i \(0.992302\pi\)
\(110\) 0 0
\(111\) 12.0000 1.13899
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −16.0000 27.7128i −1.49201 2.58423i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 0 0
\(123\) −2.00000 3.46410i −0.180334 0.312348i
\(124\) 0 0
\(125\) −24.0000 −2.14663
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) −8.00000 13.8564i −0.704361 1.21999i
\(130\) 0 0
\(131\) 7.00000 12.1244i 0.611593 1.05931i −0.379379 0.925241i \(-0.623862\pi\)
0.990972 0.134069i \(-0.0428042\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 8.00000 13.8564i 0.688530 1.19257i
\(136\) 0 0
\(137\) −1.00000 1.73205i −0.0854358 0.147979i 0.820141 0.572161i \(-0.193895\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(138\) 0 0
\(139\) −18.0000 −1.52674 −0.763370 0.645961i \(-0.776457\pi\)
−0.763370 + 0.645961i \(0.776457\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.00000 1.73205i 0.0819232 0.141895i −0.822153 0.569267i \(-0.807227\pi\)
0.904076 + 0.427372i \(0.140560\pi\)
\(150\) 0 0
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 16.0000 1.28515
\(156\) 0 0
\(157\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) −10.0000 + 17.3205i −0.793052 + 1.37361i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) 0 0
\(173\) −4.00000 + 6.92820i −0.304114 + 0.526742i −0.977064 0.212947i \(-0.931694\pi\)
0.672949 + 0.739689i \(0.265027\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 0 0
\(179\) −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) 0 0
\(181\) 8.00000 0.594635 0.297318 0.954779i \(-0.403908\pi\)
0.297318 + 0.954779i \(0.403908\pi\)
\(182\) 0 0
\(183\) −8.00000 −0.591377
\(184\) 0 0
\(185\) −12.0000 20.7846i −0.882258 1.52811i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.00000 + 6.92820i −0.289430 + 0.501307i −0.973674 0.227946i \(-0.926799\pi\)
0.684244 + 0.729253i \(0.260132\pi\)
\(192\) 0 0
\(193\) 9.00000 + 15.5885i 0.647834 + 1.12208i 0.983639 + 0.180150i \(0.0576584\pi\)
−0.335805 + 0.941932i \(0.609008\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −2.00000 3.46410i −0.141776 0.245564i 0.786389 0.617731i \(-0.211948\pi\)
−0.928166 + 0.372168i \(0.878615\pi\)
\(200\) 0 0
\(201\) 12.0000 20.7846i 0.846415 1.46603i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −4.00000 + 6.92820i −0.279372 + 0.483887i
\(206\) 0 0
\(207\) 4.00000 + 6.92820i 0.278019 + 0.481543i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −16.0000 + 27.7128i −1.09119 + 1.89000i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −14.0000 + 24.2487i −0.946032 + 1.63858i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 0 0
\(225\) 11.0000 0.733333
\(226\) 0 0
\(227\) 7.00000 + 12.1244i 0.464606 + 0.804722i 0.999184 0.0403978i \(-0.0128625\pi\)
−0.534577 + 0.845120i \(0.679529\pi\)
\(228\) 0 0
\(229\) 8.00000 13.8564i 0.528655 0.915657i −0.470787 0.882247i \(-0.656030\pi\)
0.999442 0.0334101i \(-0.0106368\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.0000 + 22.5167i −0.851658 + 1.47512i 0.0280525 + 0.999606i \(0.491069\pi\)
−0.879711 + 0.475509i \(0.842264\pi\)
\(234\) 0 0
\(235\) 8.00000 + 13.8564i 0.521862 + 0.903892i
\(236\) 0 0
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 1.00000 + 1.73205i 0.0644157 + 0.111571i 0.896435 0.443176i \(-0.146148\pi\)
−0.832019 + 0.554747i \(0.812815\pi\)
\(242\) 0 0
\(243\) −5.00000 + 8.66025i −0.320750 + 0.555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 14.0000 0.883672 0.441836 0.897096i \(-0.354327\pi\)
0.441836 + 0.897096i \(0.354327\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 8.00000 + 13.8564i 0.500979 + 0.867722i
\(256\) 0 0
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.00000 + 1.73205i −0.0618984 + 0.107211i
\(262\) 0 0
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) 40.0000 2.45718
\(266\) 0 0
\(267\) −20.0000 −1.22398
\(268\) 0 0
\(269\) 12.0000 + 20.7846i 0.731653 + 1.26726i 0.956176 + 0.292791i \(0.0945841\pi\)
−0.224523 + 0.974469i \(0.572083\pi\)
\(270\) 0 0
\(271\) 16.0000 27.7128i 0.971931 1.68343i 0.282218 0.959350i \(-0.408930\pi\)
0.689713 0.724083i \(-0.257737\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.0000 19.0526i −0.660926 1.14476i −0.980373 0.197153i \(-0.936830\pi\)
0.319447 0.947604i \(-0.396503\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −5.00000 8.66025i −0.297219 0.514799i 0.678280 0.734804i \(-0.262726\pi\)
−0.975499 + 0.220005i \(0.929393\pi\)
\(284\) 0 0
\(285\) −8.00000 + 13.8564i −0.473879 + 0.820783i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) −2.00000 3.46410i −0.117242 0.203069i
\(292\) 0 0
\(293\) −12.0000 −0.701047 −0.350524 0.936554i \(-0.613996\pi\)
−0.350524 + 0.936554i \(0.613996\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 12.0000 20.7846i 0.689382 1.19404i
\(304\) 0 0
\(305\) 8.00000 + 13.8564i 0.458079 + 0.793416i
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) −24.0000 −1.36531
\(310\) 0 0
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) −7.00000 + 12.1244i −0.395663 + 0.685309i −0.993186 0.116543i \(-0.962819\pi\)
0.597522 + 0.801852i \(0.296152\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 10.0000 17.3205i 0.553001 0.957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 6.92820i 0.219860 0.380808i −0.734905 0.678170i \(-0.762773\pi\)
0.954765 + 0.297361i \(0.0961066\pi\)
\(332\) 0 0
\(333\) 3.00000 + 5.19615i 0.164399 + 0.284747i
\(334\) 0 0
\(335\) −48.0000 −2.62252
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 6.00000 + 10.3923i 0.325875 + 0.564433i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 32.0000 55.4256i 1.72282 2.98402i
\(346\) 0 0
\(347\) −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) 0 0
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 15.0000 + 25.9808i 0.798369 + 1.38282i 0.920677 + 0.390324i \(0.127637\pi\)
−0.122308 + 0.992492i \(0.539030\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) 22.0000 1.15470
\(364\) 0 0
\(365\) 56.0000 2.93117
\(366\) 0 0
\(367\) 4.00000 + 6.92820i 0.208798 + 0.361649i 0.951336 0.308155i \(-0.0997115\pi\)
−0.742538 + 0.669804i \(0.766378\pi\)
\(368\) 0 0
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 17.0000 29.4449i 0.880227 1.52460i 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) 0 0
\(375\) −24.0000 41.5692i −1.23935 2.14663i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) −8.00000 13.8564i −0.409852 0.709885i
\(382\) 0 0
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000 6.92820i 0.203331 0.352180i
\(388\) 0 0
\(389\) −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i \(-0.248252\pi\)
−0.964490 + 0.264120i \(0.914918\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 28.0000 1.41241
\(394\) 0 0
\(395\) 16.0000 + 27.7128i 0.805047 + 1.39438i
\(396\) 0 0
\(397\) 4.00000 6.92820i 0.200754 0.347717i −0.748017 0.663679i \(-0.768994\pi\)
0.948772 + 0.315963i \(0.102327\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 44.0000 2.18638
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −3.00000 5.19615i −0.148340 0.256933i 0.782274 0.622935i \(-0.214060\pi\)
−0.930614 + 0.366002i \(0.880726\pi\)
\(410\) 0 0
\(411\) 2.00000 3.46410i 0.0986527 0.170872i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) 0 0
\(417\) −18.0000 31.1769i −0.881464 1.52674i
\(418\) 0 0
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 0 0
\(423\) −2.00000 3.46410i −0.0972433 0.168430i
\(424\) 0 0
\(425\) 11.0000 19.0526i 0.533578 0.924185i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 16.0000 0.767141
\(436\) 0 0
\(437\) 8.00000 + 13.8564i 0.382692 + 0.662842i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i \(-0.863626\pi\)
0.814595 + 0.580030i \(0.196959\pi\)
\(444\) 0 0
\(445\) 20.0000 + 34.6410i 0.948091 + 1.64214i
\(446\) 0 0
\(447\) 4.00000 0.189194
\(448\) 0 0
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −16.0000 + 27.7128i −0.751746 + 1.30206i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0000 + 19.0526i −0.514558 + 0.891241i 0.485299 + 0.874348i \(0.338711\pi\)
−0.999857 + 0.0168929i \(0.994623\pi\)
\(458\) 0 0
\(459\) 4.00000 + 6.92820i 0.186704 + 0.323381i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) 16.0000 + 27.7128i 0.741982 + 1.28515i
\(466\) 0 0
\(467\) 3.00000 5.19615i 0.138823 0.240449i −0.788228 0.615383i \(-0.789001\pi\)
0.927052 + 0.374934i \(0.122335\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 22.0000 1.00943
\(476\) 0 0
\(477\) −10.0000 −0.457869
\(478\) 0 0
\(479\) 2.00000 + 3.46410i 0.0913823 + 0.158279i 0.908093 0.418769i \(-0.137538\pi\)
−0.816711 + 0.577047i \(0.804205\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.00000 + 6.92820i −0.181631 + 0.314594i
\(486\) 0 0
\(487\) −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) 0 0
\(489\) 32.0000 1.44709
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 2.00000 + 3.46410i 0.0900755 + 0.156015i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) −12.0000 20.7846i −0.536120 0.928588i
\(502\) 0 0
\(503\) 32.0000 1.42681 0.713405 0.700752i \(-0.247152\pi\)
0.713405 + 0.700752i \(0.247152\pi\)
\(504\) 0 0
\(505\) −48.0000 −2.13597
\(506\) 0 0
\(507\) −13.0000 22.5167i −0.577350 1.00000i
\(508\) 0 0
\(509\) 12.0000 20.7846i 0.531891 0.921262i −0.467416 0.884037i \(-0.654815\pi\)
0.999307 0.0372243i \(-0.0118516\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −4.00000 + 6.92820i −0.176604 + 0.305888i
\(514\) 0 0
\(515\) 24.0000 + 41.5692i 1.05757 + 1.83176i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −16.0000 −0.702322
\(520\) 0 0
\(521\) 9.00000 + 15.5885i 0.394297 + 0.682943i 0.993011 0.118020i \(-0.0376547\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(522\) 0 0
\(523\) −17.0000 + 29.4449i −0.743358 + 1.28753i 0.207600 + 0.978214i \(0.433435\pi\)
−0.950958 + 0.309320i \(0.899899\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.00000 + 6.92820i −0.174243 + 0.301797i
\(528\) 0 0
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 24.0000 + 41.5692i 1.03761 + 1.79719i
\(536\) 0 0
\(537\) 4.00000 6.92820i 0.172613 0.298974i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −11.0000 + 19.0526i −0.472927 + 0.819133i −0.999520 0.0309841i \(-0.990136\pi\)
0.526593 + 0.850118i \(0.323469\pi\)
\(542\) 0 0
\(543\) 8.00000 + 13.8564i 0.343313 + 0.594635i
\(544\) 0 0
\(545\) −40.0000 −1.71341
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 0 0
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 0 0
\(551\) −2.00000 + 3.46410i −0.0852029 + 0.147576i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 24.0000 41.5692i 1.01874 1.76452i
\(556\) 0 0
\(557\) 13.0000 + 22.5167i 0.550828 + 0.954062i 0.998215 + 0.0597213i \(0.0190212\pi\)
−0.447387 + 0.894340i \(0.647645\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 17.0000 + 29.4449i 0.716465 + 1.24095i 0.962392 + 0.271665i \(0.0875742\pi\)
−0.245927 + 0.969288i \(0.579092\pi\)
\(564\) 0 0
\(565\) 12.0000 20.7846i 0.504844 0.874415i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21.0000 36.3731i 0.880366 1.52484i 0.0294311 0.999567i \(-0.490630\pi\)
0.850935 0.525271i \(-0.176036\pi\)
\(570\) 0 0
\(571\) −8.00000 13.8564i −0.334790 0.579873i 0.648655 0.761083i \(-0.275332\pi\)
−0.983444 + 0.181210i \(0.941999\pi\)
\(572\) 0 0
\(573\) −16.0000 −0.668410
\(574\) 0 0
\(575\) −88.0000 −3.66985
\(576\) 0 0
\(577\) −9.00000 15.5885i −0.374675 0.648956i 0.615603 0.788056i \(-0.288912\pi\)
−0.990278 + 0.139100i \(0.955579\pi\)
\(578\) 0 0
\(579\) −18.0000 + 31.1769i −0.748054 + 1.29567i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −10.0000 −0.412744 −0.206372 0.978474i \(-0.566166\pi\)
−0.206372 + 0.978474i \(0.566166\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −18.0000 31.1769i −0.740421 1.28245i
\(592\) 0 0
\(593\) −21.0000 + 36.3731i −0.862367 + 1.49366i 0.00727173 + 0.999974i \(0.497685\pi\)
−0.869638 + 0.493689i \(0.835648\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.00000 6.92820i 0.163709 0.283552i
\(598\) 0 0
\(599\) 20.0000 + 34.6410i 0.817178 + 1.41539i 0.907754 + 0.419504i \(0.137796\pi\)
−0.0905757 + 0.995890i \(0.528871\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 0 0
\(605\) −22.0000 38.1051i −0.894427 1.54919i
\(606\) 0 0
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −5.00000 8.66025i −0.201948 0.349784i 0.747208 0.664590i \(-0.231394\pi\)
−0.949156 + 0.314806i \(0.898061\pi\)
\(614\) 0 0
\(615\) −16.0000 −0.645182
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 3.00000 + 5.19615i 0.120580 + 0.208851i 0.919997 0.391926i \(-0.128191\pi\)
−0.799416 + 0.600777i \(0.794858\pi\)
\(620\) 0 0
\(621\) 16.0000 27.7128i 0.642058 1.11208i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −32.0000 −1.27390 −0.636950 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) 0 0
\(633\) −20.0000 34.6410i −0.794929 1.37686i
\(634\) 0 0
\(635\) −16.0000 + 27.7128i −0.634941 + 1.09975i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.00000 + 1.73205i 0.0394976 + 0.0684119i 0.885098 0.465404i \(-0.154091\pi\)
−0.845601 + 0.533816i \(0.820758\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 0 0
\(645\) −64.0000 −2.52000
\(646\) 0 0
\(647\) −18.0000 31.1769i −0.707653 1.22569i −0.965726 0.259565i \(-0.916421\pi\)
0.258073 0.966126i \(-0.416913\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.0000 19.0526i 0.430463 0.745584i −0.566450 0.824096i \(-0.691684\pi\)
0.996913 + 0.0785119i \(0.0250169\pi\)
\(654\) 0 0
\(655\) −28.0000 48.4974i −1.09405 1.89495i
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) 40.0000 1.55818 0.779089 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) −10.0000 17.3205i −0.388955 0.673690i 0.603354 0.797473i \(-0.293830\pi\)
−0.992309 + 0.123784i \(0.960497\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 0 0
\(669\) 24.0000 + 41.5692i 0.927894 + 1.60716i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) 0 0
\(675\) −22.0000 38.1051i −0.846780 1.46667i
\(676\) 0 0
\(677\) 12.0000 20.7846i 0.461197 0.798817i −0.537823 0.843057i \(-0.680753\pi\)
0.999021 + 0.0442400i \(0.0140866\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −14.0000 + 24.2487i −0.536481 + 0.929213i
\(682\) 0 0
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 0 0
\(685\) −8.00000 −0.305664
\(686\) 0 0
\(687\) 32.0000 1.22088
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 7.00000 12.1244i 0.266293 0.461232i −0.701609 0.712562i \(-0.747535\pi\)
0.967901 + 0.251330i \(0.0808679\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −36.0000 + 62.3538i −1.36556 + 2.36522i
\(696\) 0 0
\(697\) −2.00000 3.46410i −0.0757554 0.131212i
\(698\) 0 0
\(699\) −52.0000 −1.96682
\(700\) 0 0
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) 6.00000 + 10.3923i 0.226294 + 0.391953i
\(704\) 0 0
\(705\) −16.0000 + 27.7128i −0.602595 + 1.04372i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i \(-0.893462\pi\)
0.756730 + 0.653727i \(0.226796\pi\)
\(710\) 0 0
\(711\) −4.00000 6.92820i −0.150012 0.259828i
\(712\) 0 0
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 16.0000 + 27.7128i 0.597531 + 1.03495i
\(718\) 0 0
\(719\) 18.0000 31.1769i 0.671287 1.16270i −0.306253 0.951950i \(-0.599075\pi\)
0.977539 0.210752i \(-0.0675914\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −2.00000 + 3.46410i −0.0743808 + 0.128831i
\(724\) 0 0
\(725\) −11.0000 19.0526i −0.408530 0.707594i
\(726\) 0 0
\(727\) −20.0000 −0.741759 −0.370879 0.928681i \(-0.620944\pi\)
−0.370879 + 0.928681i \(0.620944\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −8.00000 13.8564i −0.295891 0.512498i
\(732\) 0 0
\(733\) −26.0000 + 45.0333i −0.960332 + 1.66334i −0.238667 + 0.971102i \(0.576710\pi\)
−0.721665 + 0.692242i \(0.756623\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) −4.00000 6.92820i −0.146549 0.253830i
\(746\) 0 0
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 0 0
\(753\) 14.0000 + 24.2487i 0.510188 + 0.883672i
\(754\) 0 0
\(755\) 64.0000 2.32920
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21.0000 36.3731i 0.761249 1.31852i −0.180957 0.983491i \(-0.557920\pi\)
0.942207 0.335032i \(-0.108747\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −4.00000 + 6.92820i −0.144620 + 0.250490i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −26.0000 −0.937584 −0.468792 0.883309i \(-0.655311\pi\)
−0.468792 + 0.883309i \(0.655311\pi\)
\(770\) 0 0
\(771\) −36.0000 −1.29651
\(772\) 0 0
\(773\) −2.00000 3.46410i −0.0719350 0.124595i 0.827814 0.561002i \(-0.189584\pi\)
−0.899749 + 0.436407i \(0.856251\pi\)
\(774\) 0 0
\(775\) 22.0000 38.1051i 0.790263 1.36878i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.00000 3.46410i 0.0716574 0.124114i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i \(-0.0384127\pi\)
−0.600620 + 0.799535i \(0.705079\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 40.0000 + 69.2820i 1.41865 + 2.45718i
\(796\) 0 0
\(797\) −24.0000 −0.850124 −0.425062 0.905164i \(-0.639748\pi\)
−0.425062 + 0.905164i \(0.639748\pi\)
\(798\) 0 0
\(799\) −8.00000 −0.283020
\(800\) 0 0
\(801\) −5.00000 8.66025i −0.176666 0.305995i
\(802\) 0 0