Properties

Label 784.2.i.j.753.1
Level $784$
Weight $2$
Character 784.753
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 753.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 784.753
Dual form 784.2.i.j.177.1

$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.00000 1.73205i 0.577350 1.00000i −0.418432 0.908248i \(-0.637420\pi\)
0.995782 0.0917517i \(-0.0292466\pi\)
\(4\) 0 0
\(5\) 2.00000 + 3.46410i 0.894427 + 1.54919i 0.834512 + 0.550990i \(0.185750\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 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 −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i \(0.147321\pi\)
−0.0607377 + 0.998154i \(0.519345\pi\)
\(24\) 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 −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 + 5.19615i 0.493197 + 0.854242i 0.999969 0.00783774i \(-0.00249486\pi\)
−0.506772 + 0.862080i \(0.669162\pi\)
\(38\) 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 0.682489 0.730896i \(-0.260898\pi\)
−0.974219 + 0.225605i \(0.927564\pi\)
\(48\) 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 −0.286064 0.958211i \(-0.592347\pi\)
0.972867 0.231367i \(-0.0743197\pi\)
\(54\) 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 −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −6.00000 + 10.3923i −0.733017 + 1.26962i 0.222571 + 0.974916i \(0.428555\pi\)
−0.955588 + 0.294706i \(0.904778\pi\)
\(68\) 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 −0.0869195 0.996215i \(-0.527702\pi\)
0.906208 0.422833i \(-0.138964\pi\)
\(74\) 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 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 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 −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 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 0.396236 + 0.918149i \(0.370316\pi\)
−0.993258 + 0.115924i \(0.963017\pi\)
\(102\) 0 0
\(103\) −6.00000 10.3923i −0.591198 1.02398i −0.994071 0.108729i \(-0.965322\pi\)
0.402874 0.915255i \(-0.368011\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 10.3923i −0.580042 1.00466i −0.995474 0.0950377i \(-0.969703\pi\)
0.415432 0.909624i \(-0.363630\pi\)
\(108\) 0 0
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) 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 0.990972 + 0.134069i \(0.0428042\pi\)
−0.379379 + 0.925241i \(0.623862\pi\)
\(132\) 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 −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) 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 0.904076 0.427372i \(-0.140560\pi\)
−0.822153 + 0.569267i \(0.807227\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(158\) 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 0.988227 + 0.152992i \(0.0488907\pi\)
−0.361619 + 0.932326i \(0.617776\pi\)
\(164\) 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 0.672949 0.739689i \(-0.265027\pi\)
−0.977064 + 0.212947i \(0.931694\pi\)
\(174\) 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 −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) 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 0.684244 0.729253i \(-0.260132\pi\)
−0.973674 + 0.227946i \(0.926799\pi\)
\(192\) 0 0
\(193\) 9.00000 15.5885i 0.647834 1.12208i −0.335805 0.941932i \(-0.609008\pi\)
0.983639 0.180150i \(-0.0576584\pi\)
\(194\) 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 −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 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 −0.534577 0.845120i \(-0.679529\pi\)
0.999184 + 0.0403978i \(0.0128625\pi\)
\(228\) 0 0
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.0000 22.5167i −0.851658 1.47512i −0.879711 0.475509i \(-0.842264\pi\)
0.0280525 0.999606i \(-0.491069\pi\)
\(234\) 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 −0.832019 0.554747i \(-0.812815\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(242\) 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 −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 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 −0.224523 0.974469i \(-0.572083\pi\)
0.956176 0.292791i \(-0.0945841\pi\)
\(270\) 0 0
\(271\) 16.0000 + 27.7128i 0.971931 + 1.68343i 0.689713 + 0.724083i \(0.257737\pi\)
0.282218 + 0.959350i \(0.408930\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.0000 + 19.0526i −0.660926 + 1.14476i 0.319447 + 0.947604i \(0.396503\pi\)
−0.980373 + 0.197153i \(0.936830\pi\)
\(278\) 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 −0.975499 0.220005i \(-0.929393\pi\)
0.678280 + 0.734804i \(0.262726\pi\)
\(284\) 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 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 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 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 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 0.340293 + 0.940319i \(0.389474\pi\)
−0.984487 + 0.175457i \(0.943860\pi\)
\(348\) 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 −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 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 −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 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 0.851089 + 0.525022i \(0.175943\pi\)
0.0291379 + 0.999575i \(0.490724\pi\)
\(374\) 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 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 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 −0.964490 0.264120i \(-0.914918\pi\)
0.710980 + 0.703213i \(0.248252\pi\)
\(390\) 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 0.948772 0.315963i \(-0.102327\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 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 −0.930614 0.366002i \(-0.880726\pi\)
0.782274 + 0.622935i \(0.214060\pi\)
\(410\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 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 0.996284 + 0.0861252i \(0.0274485\pi\)
−0.423556 + 0.905870i \(0.639218\pi\)
\(440\) 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
\(445\) 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 −0.999857 0.0168929i \(-0.994623\pi\)
0.485299 0.874348i \(-0.338711\pi\)
\(458\) 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 0.927052 0.374934i \(-0.122335\pi\)
−0.788228 + 0.615383i \(0.789001\pi\)
\(468\) 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 −0.816711 0.577047i \(-0.804205\pi\)
0.908093 + 0.418769i \(0.137538\pi\)
\(480\) 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 −0.942309 0.334744i \(-0.891350\pi\)
0.761052 + 0.648691i \(0.224683\pi\)
\(488\) 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 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 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 0.999307 + 0.0372243i \(0.0118516\pi\)
−0.467416 + 0.884037i \(0.654815\pi\)
\(510\) 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 −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 0 0
\(523\) −17.0000 29.4449i −0.743358 1.28753i −0.950958 0.309320i \(-0.899899\pi\)
0.207600 0.978214i \(-0.433435\pi\)
\(524\) 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 0.526593 0.850118i \(-0.323469\pi\)
−0.999520 + 0.0309841i \(0.990136\pi\)
\(542\) 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 −0.447387 0.894340i \(-0.647645\pi\)
0.998215 0.0597213i \(-0.0190212\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 17.0000 29.4449i 0.716465 1.24095i −0.245927 0.969288i \(-0.579092\pi\)
0.962392 0.271665i \(-0.0875742\pi\)
\(564\) 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 0.850935 + 0.525271i \(0.176036\pi\)
0.0294311 + 0.999567i \(0.490630\pi\)
\(570\) 0 0
\(571\) −8.00000 + 13.8564i −0.334790 + 0.579873i −0.983444 0.181210i \(-0.941999\pi\)
0.648655 + 0.761083i \(0.275332\pi\)
\(572\) 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 −0.990278 0.139100i \(-0.955579\pi\)
0.615603 + 0.788056i \(0.288912\pi\)
\(578\) 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 −0.869638 0.493689i \(-0.835648\pi\)
0.00727173 0.999974i \(-0.497685\pi\)
\(594\) 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 −0.0905757 0.995890i \(-0.528871\pi\)
0.907754 0.419504i \(-0.137796\pi\)
\(600\) 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 −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −5.00000 + 8.66025i −0.201948 + 0.349784i −0.949156 0.314806i \(-0.898061\pi\)
0.747208 + 0.664590i \(0.231394\pi\)
\(614\) 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 −0.799416 0.600777i \(-0.794858\pi\)
0.919997 + 0.391926i \(0.128191\pi\)
\(620\) 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 −0.845601 0.533816i \(-0.820758\pi\)
0.885098 + 0.465404i \(0.154091\pi\)
\(642\) 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 0.258073 + 0.966126i \(0.416913\pi\)
−0.965726 + 0.259565i \(0.916421\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 11.0000 + 19.0526i 0.430463 + 0.745584i 0.996913 0.0785119i \(-0.0250169\pi\)
−0.566450 + 0.824096i \(0.691684\pi\)
\(654\) 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 −0.992309 0.123784i \(-0.960497\pi\)
0.603354 + 0.797473i \(0.293830\pi\)
\(662\) 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 0.999021 0.0442400i \(-0.0140866\pi\)
−0.537823 + 0.843057i \(0.680753\pi\)
\(678\) 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 −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 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 0.967901 0.251330i \(-0.0808679\pi\)
−0.701609 + 0.712562i \(0.747535\pi\)
\(692\) 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 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) 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 0.977539 + 0.210752i \(0.0675914\pi\)
−0.306253 + 0.951950i \(0.599075\pi\)
\(720\) 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 −0.721665 0.692242i \(-0.756623\pi\)
−0.238667 0.971102i \(-0.576710\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 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 0.995018 + 0.0996961i \(0.0317870\pi\)
−0.411170 + 0.911559i \(0.634880\pi\)
\(752\) 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 0.942207 + 0.335032i \(0.108747\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(762\) 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 −0.899749 0.436407i \(-0.856251\pi\)
0.827814 + 0.561002i \(0.189584\pi\)
\(774\) 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 −0.600620 0.799535i \(-0.705079\pi\)
0.992727 + 0.120384i \(0.0384127\pi\)
\(788\) 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