Properties

Label 1216.2.i.f.961.1
Level $1216$
Weight $2$
Character 1216.961
Analytic conductor $9.710$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.70980888579\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 152)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1216.961
Dual form 1216.2.i.f.577.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(-2.00000 + 3.46410i) q^{5} +(1.00000 + 1.73205i) q^{9} -3.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +(2.00000 + 3.46410i) q^{15} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 - 4.33013i) q^{19} +(-3.00000 - 5.19615i) q^{23} +(-5.50000 - 9.52628i) q^{25} +5.00000 q^{27} +(-2.00000 - 3.46410i) q^{29} -10.0000 q^{31} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{37} +2.00000 q^{39} +(-4.50000 + 7.79423i) q^{41} +(-2.00000 + 3.46410i) q^{43} -8.00000 q^{45} +(6.00000 + 10.3923i) q^{47} -7.00000 q^{49} +(1.00000 + 1.73205i) q^{51} +(-1.00000 - 1.73205i) q^{53} +(6.00000 - 10.3923i) q^{55} +(-4.00000 - 1.73205i) q^{57} +(-0.500000 + 0.866025i) q^{59} +(-4.00000 - 6.92820i) q^{61} -8.00000 q^{65} +(4.50000 + 7.79423i) q^{67} -6.00000 q^{69} +(3.00000 - 5.19615i) q^{71} +(4.50000 - 7.79423i) q^{73} -11.0000 q^{75} +(2.00000 - 3.46410i) q^{79} +(-0.500000 + 0.866025i) q^{81} +5.00000 q^{83} +(-4.00000 - 6.92820i) q^{85} -4.00000 q^{87} +(9.00000 + 15.5885i) q^{89} +(-5.00000 + 8.66025i) q^{93} +(16.0000 + 6.92820i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(-3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 4q^{5} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} - 4q^{5} + 2q^{9} - 6q^{11} + 2q^{13} + 4q^{15} - 2q^{17} - q^{19} - 6q^{23} - 11q^{25} + 10q^{27} - 4q^{29} - 20q^{31} - 3q^{33} - 4q^{37} + 4q^{39} - 9q^{41} - 4q^{43} - 16q^{45} + 12q^{47} - 14q^{49} + 2q^{51} - 2q^{53} + 12q^{55} - 8q^{57} - q^{59} - 8q^{61} - 16q^{65} + 9q^{67} - 12q^{69} + 6q^{71} + 9q^{73} - 22q^{75} + 4q^{79} - q^{81} + 10q^{83} - 8q^{85} - 8q^{87} + 18q^{89} - 10q^{93} + 32q^{95} - q^{97} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(705\) \(837\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) −2.00000 + 3.46410i −0.894427 + 1.54919i −0.0599153 + 0.998203i \(0.519083\pi\)
−0.834512 + 0.550990i \(0.814250\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) 1.00000 + 1.73205i 0.277350 + 0.480384i 0.970725 0.240192i \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 2.00000 + 3.46410i 0.516398 + 0.894427i
\(16\) 0 0
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 0 0
\(19\) −0.500000 4.33013i −0.114708 0.993399i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) −5.50000 9.52628i −1.10000 1.90526i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −2.00000 3.46410i −0.371391 0.643268i 0.618389 0.785872i \(-0.287786\pi\)
−0.989780 + 0.142605i \(0.954452\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0 0
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 0 0
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) 0 0
\(45\) −8.00000 −1.19257
\(46\) 0 0
\(47\) 6.00000 + 10.3923i 0.875190 + 1.51587i 0.856560 + 0.516047i \(0.172597\pi\)
0.0186297 + 0.999826i \(0.494070\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) 0 0
\(53\) −1.00000 1.73205i −0.137361 0.237915i 0.789136 0.614218i \(-0.210529\pi\)
−0.926497 + 0.376303i \(0.877195\pi\)
\(54\) 0 0
\(55\) 6.00000 10.3923i 0.809040 1.40130i
\(56\) 0 0
\(57\) −4.00000 1.73205i −0.529813 0.229416i
\(58\) 0 0
\(59\) −0.500000 + 0.866025i −0.0650945 + 0.112747i −0.896736 0.442566i \(-0.854068\pi\)
0.831641 + 0.555313i \(0.187402\pi\)
\(60\) 0 0
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.00000 −0.992278
\(66\) 0 0
\(67\) 4.50000 + 7.79423i 0.549762 + 0.952217i 0.998290 + 0.0584478i \(0.0186151\pi\)
−0.448528 + 0.893769i \(0.648052\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 0 0
\(73\) 4.50000 7.79423i 0.526685 0.912245i −0.472831 0.881153i \(-0.656768\pi\)
0.999517 0.0310925i \(-0.00989865\pi\)
\(74\) 0 0
\(75\) −11.0000 −1.27017
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 5.00000 0.548821 0.274411 0.961613i \(-0.411517\pi\)
0.274411 + 0.961613i \(0.411517\pi\)
\(84\) 0 0
\(85\) −4.00000 6.92820i −0.433861 0.751469i
\(86\) 0 0
\(87\) −4.00000 −0.428845
\(88\) 0 0
\(89\) 9.00000 + 15.5885i 0.953998 + 1.65237i 0.736644 + 0.676280i \(0.236409\pi\)
0.217354 + 0.976093i \(0.430258\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −5.00000 + 8.66025i −0.518476 + 0.898027i
\(94\) 0 0
\(95\) 16.0000 + 6.92820i 1.64157 + 0.710819i
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) −3.00000 5.19615i −0.301511 0.522233i
\(100\) 0 0
\(101\) 6.00000 + 10.3923i 0.597022 + 1.03407i 0.993258 + 0.115924i \(0.0369830\pi\)
−0.396236 + 0.918149i \(0.629684\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.0000 −1.54678 −0.773389 0.633932i \(-0.781440\pi\)
−0.773389 + 0.633932i \(0.781440\pi\)
\(108\) 0 0
\(109\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(110\) 0 0
\(111\) −1.00000 + 1.73205i −0.0949158 + 0.164399i
\(112\) 0 0
\(113\) −1.00000 −0.0940721 −0.0470360 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) 0 0
\(115\) 24.0000 2.23801
\(116\) 0 0
\(117\) −2.00000 + 3.46410i −0.184900 + 0.320256i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 4.50000 + 7.79423i 0.405751 + 0.702782i
\(124\) 0 0
\(125\) 24.0000 2.14663
\(126\) 0 0
\(127\) 3.00000 + 5.19615i 0.266207 + 0.461084i 0.967879 0.251416i \(-0.0808962\pi\)
−0.701672 + 0.712500i \(0.747563\pi\)
\(128\) 0 0
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −10.0000 + 17.3205i −0.860663 + 1.49071i
\(136\) 0 0
\(137\) −4.50000 7.79423i −0.384461 0.665906i 0.607233 0.794524i \(-0.292279\pi\)
−0.991694 + 0.128618i \(0.958946\pi\)
\(138\) 0 0
\(139\) −6.50000 11.2583i −0.551323 0.954919i −0.998179 0.0603135i \(-0.980790\pi\)
0.446857 0.894606i \(-0.352543\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 0 0
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 16.0000 1.32873
\(146\) 0 0
\(147\) −3.50000 + 6.06218i −0.288675 + 0.500000i
\(148\) 0 0
\(149\) −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i \(-0.967671\pi\)
0.585231 + 0.810867i \(0.301004\pi\)
\(150\) 0 0
\(151\) 2.00000 0.162758 0.0813788 0.996683i \(-0.474068\pi\)
0.0813788 + 0.996683i \(0.474068\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) 20.0000 34.6410i 1.60644 2.78243i
\(156\) 0 0
\(157\) 4.00000 6.92820i 0.319235 0.552931i −0.661094 0.750303i \(-0.729907\pi\)
0.980329 + 0.197372i \(0.0632408\pi\)
\(158\) 0 0
\(159\) −2.00000 −0.158610
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 0 0
\(165\) −6.00000 10.3923i −0.467099 0.809040i
\(166\) 0 0
\(167\) −8.00000 13.8564i −0.619059 1.07224i −0.989658 0.143448i \(-0.954181\pi\)
0.370599 0.928793i \(-0.379152\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 7.00000 5.19615i 0.535303 0.397360i
\(172\) 0 0
\(173\) −13.0000 + 22.5167i −0.988372 + 1.71191i −0.362500 + 0.931984i \(0.618077\pi\)
−0.625871 + 0.779926i \(0.715256\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0.500000 + 0.866025i 0.0375823 + 0.0650945i
\(178\) 0 0
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) 7.00000 + 12.1244i 0.520306 + 0.901196i 0.999721 + 0.0236082i \(0.00751541\pi\)
−0.479415 + 0.877588i \(0.659151\pi\)
\(182\) 0 0
\(183\) −8.00000 −0.591377
\(184\) 0 0
\(185\) 4.00000 6.92820i 0.294086 0.509372i
\(186\) 0 0
\(187\) 3.00000 5.19615i 0.219382 0.379980i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) 0 0
\(195\) −4.00000 + 6.92820i −0.286446 + 0.496139i
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 9.00000 + 15.5885i 0.637993 + 1.10504i 0.985873 + 0.167497i \(0.0535685\pi\)
−0.347879 + 0.937539i \(0.613098\pi\)
\(200\) 0 0
\(201\) 9.00000 0.634811
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −18.0000 31.1769i −1.25717 2.17749i
\(206\) 0 0
\(207\) 6.00000 10.3923i 0.417029 0.722315i
\(208\) 0 0
\(209\) 1.50000 + 12.9904i 0.103757 + 0.898563i
\(210\) 0 0
\(211\) −6.00000 + 10.3923i −0.413057 + 0.715436i −0.995222 0.0976347i \(-0.968872\pi\)
0.582165 + 0.813070i \(0.302206\pi\)
\(212\) 0 0
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) 0 0
\(215\) −8.00000 13.8564i −0.545595 0.944999i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −4.50000 7.79423i −0.304082 0.526685i
\(220\) 0 0
\(221\) −4.00000 −0.269069
\(222\) 0 0
\(223\) −5.00000 + 8.66025i −0.334825 + 0.579934i −0.983451 0.181173i \(-0.942010\pi\)
0.648626 + 0.761107i \(0.275344\pi\)
\(224\) 0 0
\(225\) 11.0000 19.0526i 0.733333 1.27017i
\(226\) 0 0
\(227\) −19.0000 −1.26107 −0.630537 0.776159i \(-0.717165\pi\)
−0.630537 + 0.776159i \(0.717165\pi\)
\(228\) 0 0
\(229\) 8.00000 0.528655 0.264327 0.964433i \(-0.414850\pi\)
0.264327 + 0.964433i \(0.414850\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.50000 + 9.52628i −0.360317 + 0.624087i −0.988013 0.154371i \(-0.950665\pi\)
0.627696 + 0.778459i \(0.283998\pi\)
\(234\) 0 0
\(235\) −48.0000 −3.13117
\(236\) 0 0
\(237\) −2.00000 3.46410i −0.129914 0.225018i
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −10.5000 18.1865i −0.676364 1.17150i −0.976068 0.217465i \(-0.930221\pi\)
0.299704 0.954032i \(-0.403112\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) 14.0000 24.2487i 0.894427 1.54919i
\(246\) 0 0
\(247\) 7.00000 5.19615i 0.445399 0.330623i
\(248\) 0 0
\(249\) 2.50000 4.33013i 0.158431 0.274411i
\(250\) 0 0
\(251\) 2.50000 + 4.33013i 0.157799 + 0.273315i 0.934075 0.357078i \(-0.116227\pi\)
−0.776276 + 0.630393i \(0.782894\pi\)
\(252\) 0 0
\(253\) 9.00000 + 15.5885i 0.565825 + 0.980038i
\(254\) 0 0
\(255\) −8.00000 −0.500979
\(256\) 0 0
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 0 0
\(263\) −8.00000 + 13.8564i −0.493301 + 0.854423i −0.999970 0.00771799i \(-0.997543\pi\)
0.506669 + 0.862141i \(0.330877\pi\)
\(264\) 0 0
\(265\) 8.00000 0.491436
\(266\) 0 0
\(267\) 18.0000 1.10158
\(268\) 0 0
\(269\) 2.00000 3.46410i 0.121942 0.211210i −0.798591 0.601874i \(-0.794421\pi\)
0.920534 + 0.390664i \(0.127754\pi\)
\(270\) 0 0
\(271\) 10.0000 17.3205i 0.607457 1.05215i −0.384201 0.923249i \(-0.625523\pi\)
0.991658 0.128897i \(-0.0411435\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 16.5000 + 28.5788i 0.994987 + 1.72337i
\(276\) 0 0
\(277\) −12.0000 −0.721010 −0.360505 0.932757i \(-0.617396\pi\)
−0.360505 + 0.932757i \(0.617396\pi\)
\(278\) 0 0
\(279\) −10.0000 17.3205i −0.598684 1.03695i
\(280\) 0 0
\(281\) 6.50000 + 11.2583i 0.387757 + 0.671616i 0.992148 0.125073i \(-0.0399165\pi\)
−0.604390 + 0.796689i \(0.706583\pi\)
\(282\) 0 0
\(283\) 6.50000 11.2583i 0.386385 0.669238i −0.605575 0.795788i \(-0.707057\pi\)
0.991960 + 0.126550i \(0.0403903\pi\)
\(284\) 0 0
\(285\) 14.0000 10.3923i 0.829288 0.615587i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) 0.500000 + 0.866025i 0.0293105 + 0.0507673i
\(292\) 0 0
\(293\) 4.00000 0.233682 0.116841 0.993151i \(-0.462723\pi\)
0.116841 + 0.993151i \(0.462723\pi\)
\(294\) 0 0
\(295\) −2.00000 3.46410i −0.116445 0.201688i
\(296\) 0 0
\(297\) −15.0000 −0.870388
\(298\) 0 0
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 12.0000 0.689382
\(304\) 0 0
\(305\) 32.0000 1.83231
\(306\) 0 0
\(307\) 12.5000 21.6506i 0.713413 1.23567i −0.250156 0.968206i \(-0.580482\pi\)
0.963569 0.267461i \(-0.0861848\pi\)
\(308\) 0 0
\(309\) −7.00000 + 12.1244i −0.398216 + 0.689730i
\(310\) 0 0
\(311\) −2.00000 −0.113410 −0.0567048 0.998391i \(-0.518059\pi\)
−0.0567048 + 0.998391i \(0.518059\pi\)
\(312\) 0 0
\(313\) 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i \(0.0137652\pi\)
−0.462093 + 0.886831i \(0.652902\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 0 0
\(319\) 6.00000 + 10.3923i 0.335936 + 0.581857i
\(320\) 0 0
\(321\) −8.00000 + 13.8564i −0.446516 + 0.773389i
\(322\) 0 0
\(323\) 8.00000 + 3.46410i 0.445132 + 0.192748i
\(324\) 0 0
\(325\) 11.0000 19.0526i 0.610170 1.05685i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −13.0000 −0.714545 −0.357272 0.934000i \(-0.616293\pi\)
−0.357272 + 0.934000i \(0.616293\pi\)
\(332\) 0 0
\(333\) −2.00000 3.46410i −0.109599 0.189832i
\(334\) 0 0
\(335\) −36.0000 −1.96689
\(336\) 0 0
\(337\) −1.50000 + 2.59808i −0.0817102 + 0.141526i −0.903985 0.427565i \(-0.859372\pi\)
0.822274 + 0.569091i \(0.192705\pi\)
\(338\) 0 0
\(339\) −0.500000 + 0.866025i −0.0271563 + 0.0470360i
\(340\) 0 0
\(341\) 30.0000 1.62459
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 12.0000 20.7846i 0.646058 1.11901i
\(346\) 0 0
\(347\) −4.50000 + 7.79423i −0.241573 + 0.418416i −0.961162 0.275983i \(-0.910997\pi\)
0.719590 + 0.694399i \(0.244330\pi\)
\(348\) 0 0
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) 0 0
\(351\) 5.00000 + 8.66025i 0.266880 + 0.462250i
\(352\) 0 0
\(353\) 11.0000 0.585471 0.292735 0.956193i \(-0.405434\pi\)
0.292735 + 0.956193i \(0.405434\pi\)
\(354\) 0 0
\(355\) 12.0000 + 20.7846i 0.636894 + 1.10313i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.00000 1.73205i 0.0527780 0.0914141i −0.838429 0.545010i \(-0.816526\pi\)
0.891207 + 0.453596i \(0.149859\pi\)
\(360\) 0 0
\(361\) −18.5000 + 4.33013i −0.973684 + 0.227901i
\(362\) 0 0
\(363\) −1.00000 + 1.73205i −0.0524864 + 0.0909091i
\(364\) 0 0
\(365\) 18.0000 + 31.1769i 0.942163 + 1.63187i
\(366\) 0 0
\(367\) 13.0000 + 22.5167i 0.678594 + 1.17536i 0.975404 + 0.220423i \(0.0707439\pi\)
−0.296810 + 0.954937i \(0.595923\pi\)
\(368\) 0 0
\(369\) −18.0000 −0.937043
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 12.0000 20.7846i 0.619677 1.07331i
\(376\) 0 0
\(377\) 4.00000 6.92820i 0.206010 0.356821i
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 6.00000 0.307389
\(382\) 0 0
\(383\) 4.00000 6.92820i 0.204390 0.354015i −0.745548 0.666452i \(-0.767812\pi\)
0.949938 + 0.312437i \(0.101145\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −8.00000 −0.406663
\(388\) 0 0
\(389\) 2.00000 + 3.46410i 0.101404 + 0.175637i 0.912263 0.409604i \(-0.134333\pi\)
−0.810859 + 0.585241i \(0.801000\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) 0 0
\(393\) 7.50000 + 12.9904i 0.378325 + 0.655278i
\(394\) 0 0
\(395\) 8.00000 + 13.8564i 0.402524 + 0.697191i
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.50000 2.59808i 0.0749064 0.129742i −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) 0 0
\(403\) −10.0000 17.3205i −0.498135 0.862796i
\(404\) 0 0
\(405\) −2.00000 3.46410i −0.0993808 0.172133i
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 17.5000 + 30.3109i 0.865319 + 1.49878i 0.866730 + 0.498778i \(0.166218\pi\)
−0.00141047 + 0.999999i \(0.500449\pi\)
\(410\) 0 0
\(411\) −9.00000 −0.443937
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −10.0000 + 17.3205i −0.490881 + 0.850230i
\(416\) 0 0
\(417\) −13.0000 −0.636613
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −11.0000 + 19.0526i −0.536107 + 0.928565i 0.463002 + 0.886357i \(0.346772\pi\)
−0.999109 + 0.0422075i \(0.986561\pi\)
\(422\) 0 0
\(423\) −12.0000 + 20.7846i −0.583460 + 1.01058i
\(424\) 0 0
\(425\) 22.0000 1.06716
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −6.00000 −0.289683
\(430\) 0 0
\(431\) 15.0000 + 25.9808i 0.722525 + 1.25145i 0.959985 + 0.280052i \(0.0903517\pi\)
−0.237460 + 0.971397i \(0.576315\pi\)
\(432\) 0 0
\(433\) −5.00000 8.66025i −0.240285 0.416185i 0.720511 0.693444i \(-0.243907\pi\)
−0.960795 + 0.277259i \(0.910574\pi\)
\(434\) 0 0
\(435\) 8.00000 13.8564i 0.383571 0.664364i
\(436\) 0 0
\(437\) −21.0000 + 15.5885i −1.00457 + 0.745697i
\(438\) 0 0
\(439\) 7.00000 12.1244i 0.334092 0.578664i −0.649218 0.760602i \(-0.724904\pi\)
0.983310 + 0.181938i \(0.0582371\pi\)
\(440\) 0 0
\(441\) −7.00000 12.1244i −0.333333 0.577350i
\(442\) 0 0
\(443\) 0.500000 + 0.866025i 0.0237557 + 0.0411461i 0.877659 0.479286i \(-0.159104\pi\)
−0.853903 + 0.520432i \(0.825771\pi\)
\(444\) 0 0
\(445\) −72.0000 −3.41313
\(446\) 0 0
\(447\) 5.00000 + 8.66025i 0.236492 + 0.409616i
\(448\) 0 0
\(449\) 33.0000 1.55737 0.778683 0.627417i \(-0.215888\pi\)
0.778683 + 0.627417i \(0.215888\pi\)
\(450\) 0 0
\(451\) 13.5000 23.3827i 0.635690 1.10105i
\(452\) 0 0
\(453\) 1.00000 1.73205i 0.0469841 0.0813788i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −11.0000 −0.514558 −0.257279 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) 0 0
\(459\) −5.00000 + 8.66025i −0.233380 + 0.404226i
\(460\) 0 0
\(461\) 3.00000 5.19615i 0.139724 0.242009i −0.787668 0.616100i \(-0.788712\pi\)
0.927392 + 0.374091i \(0.122045\pi\)
\(462\) 0 0
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 0 0
\(465\) −20.0000 34.6410i −0.927478 1.60644i
\(466\) 0 0
\(467\) −5.00000 −0.231372 −0.115686 0.993286i \(-0.536907\pi\)
−0.115686 + 0.993286i \(0.536907\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −4.00000 6.92820i −0.184310 0.319235i
\(472\) 0 0
\(473\) 6.00000 10.3923i 0.275880 0.477839i
\(474\) 0 0
\(475\) −38.5000 + 28.5788i −1.76650 + 1.31129i
\(476\) 0 0
\(477\) 2.00000 3.46410i 0.0915737 0.158610i
\(478\) 0 0
\(479\) −10.0000 17.3205i −0.456912 0.791394i 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) 0 0
\(481\) −2.00000 3.46410i −0.0911922 0.157949i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.00000 3.46410i −0.0908153 0.157297i
\(486\) 0 0
\(487\) −26.0000 −1.17817 −0.589086 0.808070i \(-0.700512\pi\)
−0.589086 + 0.808070i \(0.700512\pi\)
\(488\) 0 0
\(489\) 5.50000 9.52628i 0.248719 0.430793i
\(490\) 0 0
\(491\) 8.00000 13.8564i 0.361035 0.625331i −0.627096 0.778942i \(-0.715757\pi\)
0.988131 + 0.153611i \(0.0490902\pi\)
\(492\) 0 0
\(493\) 8.00000 0.360302
\(494\) 0 0
\(495\) 24.0000 1.07872
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.50000 6.06218i 0.156682 0.271380i −0.776989 0.629515i \(-0.783254\pi\)
0.933670 + 0.358134i \(0.116587\pi\)
\(500\) 0 0
\(501\) −16.0000 −0.714827
\(502\) 0 0
\(503\) 3.00000 + 5.19615i 0.133763 + 0.231685i 0.925124 0.379664i \(-0.123960\pi\)
−0.791361 + 0.611349i \(0.790627\pi\)
\(504\) 0 0
\(505\) −48.0000 −2.13597
\(506\) 0 0
\(507\) −4.50000 7.79423i −0.199852 0.346154i
\(508\) 0 0
\(509\) 8.00000 + 13.8564i 0.354594 + 0.614174i 0.987048 0.160423i \(-0.0512858\pi\)
−0.632455 + 0.774597i \(0.717953\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2.50000 21.6506i −0.110378 0.955899i
\(514\) 0 0
\(515\) 28.0000 48.4974i 1.23383 2.13705i
\(516\) 0 0
\(517\) −18.0000 31.1769i −0.791639 1.37116i
\(518\) 0 0
\(519\) 13.0000 + 22.5167i 0.570637 + 0.988372i
\(520\) 0 0
\(521\) 1.00000 0.0438108 0.0219054 0.999760i \(-0.493027\pi\)
0.0219054 + 0.999760i \(0.493027\pi\)
\(522\) 0 0
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.0000 17.3205i 0.435607 0.754493i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) −2.00000 −0.0867926
\(532\) 0 0
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) 32.0000 55.4256i 1.38348 2.39626i
\(536\) 0 0
\(537\) −4.50000 + 7.79423i −0.194189 + 0.336346i
\(538\) 0 0
\(539\) 21.0000 0.904534
\(540\) 0 0
\(541\) 2.00000 + 3.46410i 0.0859867 + 0.148933i 0.905811 0.423681i \(-0.139262\pi\)
−0.819825 + 0.572615i \(0.805929\pi\)
\(542\) 0 0
\(543\) 14.0000 0.600798
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 14.0000 + 24.2487i 0.598597 + 1.03680i 0.993028 + 0.117875i \(0.0376081\pi\)
−0.394432 + 0.918925i \(0.629059\pi\)
\(548\) 0 0
\(549\) 8.00000 13.8564i 0.341432 0.591377i
\(550\) 0 0
\(551\) −14.0000 + 10.3923i −0.596420 + 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −4.00000 6.92820i −0.169791 0.294086i
\(556\) 0 0
\(557\) −20.0000 34.6410i −0.847427 1.46779i −0.883497 0.468438i \(-0.844817\pi\)
0.0360693 0.999349i \(-0.488516\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) −3.00000 5.19615i −0.126660 0.219382i
\(562\) 0 0
\(563\) −11.0000 −0.463595 −0.231797 0.972764i \(-0.574461\pi\)
−0.231797 + 0.972764i \(0.574461\pi\)
\(564\) 0 0
\(565\) 2.00000 3.46410i 0.0841406 0.145736i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −46.0000 −1.92842 −0.964210 0.265139i \(-0.914582\pi\)
−0.964210 + 0.265139i \(0.914582\pi\)
\(570\) 0 0
\(571\) −17.0000 −0.711428 −0.355714 0.934595i \(-0.615762\pi\)
−0.355714 + 0.934595i \(0.615762\pi\)
\(572\) 0 0
\(573\) 6.00000 10.3923i 0.250654 0.434145i
\(574\) 0 0
\(575\) −33.0000 + 57.1577i −1.37620 + 2.38364i
\(576\) 0 0
\(577\) −37.0000 −1.54033 −0.770165 0.637845i \(-0.779826\pi\)
−0.770165 + 0.637845i \(0.779826\pi\)
\(578\) 0 0
\(579\) −3.00000 5.19615i −0.124676 0.215945i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 3.00000 + 5.19615i 0.124247 + 0.215203i
\(584\) 0 0
\(585\) −8.00000 13.8564i −0.330759 0.572892i
\(586\) 0 0
\(587\) 2.00000 3.46410i 0.0825488 0.142979i −0.821795 0.569783i \(-0.807027\pi\)
0.904344 + 0.426804i \(0.140361\pi\)
\(588\) 0 0
\(589\) 5.00000 + 43.3013i 0.206021 + 1.78420i
\(590\) 0 0
\(591\) 9.00000 15.5885i 0.370211 0.641223i
\(592\) 0 0
\(593\) 10.5000 + 18.1865i 0.431183 + 0.746831i 0.996976 0.0777165i \(-0.0247629\pi\)
−0.565792 + 0.824548i \(0.691430\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 18.0000 0.736691
\(598\) 0 0
\(599\) −19.0000 32.9090i −0.776319 1.34462i −0.934050 0.357142i \(-0.883751\pi\)
0.157731 0.987482i \(-0.449582\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) 0 0
\(603\) −9.00000 + 15.5885i −0.366508 + 0.634811i
\(604\) 0 0
\(605\) 4.00000 6.92820i 0.162623 0.281672i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12.0000 + 20.7846i −0.485468 + 0.840855i
\(612\) 0 0
\(613\) −11.0000 + 19.0526i −0.444286 + 0.769526i −0.998002 0.0631797i \(-0.979876\pi\)
0.553716 + 0.832705i \(0.313209\pi\)
\(614\) 0 0
\(615\) −36.0000 −1.45166
\(616\) 0 0
\(617\) −1.50000 2.59808i −0.0603877 0.104595i 0.834251 0.551385i \(-0.185900\pi\)
−0.894639 + 0.446790i \(0.852567\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) −15.0000 25.9808i −0.601929 1.04257i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −20.5000 + 35.5070i −0.820000 + 1.42028i
\(626\) 0 0
\(627\) 12.0000 + 5.19615i 0.479234 + 0.207514i
\(628\) 0 0
\(629\) 2.00000 3.46410i 0.0797452 0.138123i
\(630\) 0 0
\(631\) 4.00000 + 6.92820i 0.159237 + 0.275807i 0.934594 0.355716i \(-0.115763\pi\)
−0.775356 + 0.631524i \(0.782430\pi\)
\(632\) 0 0
\(633\) 6.00000 + 10.3923i 0.238479 + 0.413057i
\(634\) 0 0
\(635\) −24.0000 −0.952411
\(636\) 0 0
\(637\) −7.00000 12.1244i −0.277350 0.480384i
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 0 0
\(643\) 2.50000 4.33013i 0.0985904 0.170764i −0.812511 0.582946i \(-0.801900\pi\)
0.911101 + 0.412182i \(0.135233\pi\)
\(644\) 0 0
\(645\) −16.0000 −0.629999
\(646\) 0 0
\(647\) −14.0000 −0.550397 −0.275198 0.961387i \(-0.588744\pi\)
−0.275198 + 0.961387i \(0.588744\pi\)
\(648\) 0 0
\(649\) 1.50000 2.59808i 0.0588802 0.101983i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −36.0000 −1.40879 −0.704394 0.709809i \(-0.748781\pi\)
−0.704394 + 0.709809i \(0.748781\pi\)
\(654\) 0 0
\(655\) −30.0000 51.9615i −1.17220 2.03030i
\(656\) 0 0
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) 6.00000 + 10.3923i 0.233727 + 0.404827i 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 0 0
\(661\) 10.0000 + 17.3205i 0.388955 + 0.673690i 0.992309 0.123784i \(-0.0395028\pi\)
−0.603354 + 0.797473i \(0.706170\pi\)
\(662\) 0 0
\(663\) −2.00000 + 3.46410i −0.0776736 + 0.134535i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −12.0000 + 20.7846i −0.464642 + 0.804783i
\(668\) 0 0
\(669\) 5.00000 + 8.66025i 0.193311 + 0.334825i
\(670\) 0 0
\(671\) 12.0000 + 20.7846i 0.463255 + 0.802381i
\(672\) 0 0
\(673\) 30.0000 1.15642 0.578208 0.815890i \(-0.303752\pi\)
0.578208 + 0.815890i \(0.303752\pi\)
\(674\) 0 0
\(675\) −27.5000 47.6314i −1.05848 1.83333i
\(676\) 0 0
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −9.50000 + 16.4545i −0.364041 + 0.630537i
\(682\) 0 0
\(683\) 28.0000 1.07139 0.535695 0.844411i \(-0.320050\pi\)
0.535695 + 0.844411i \(0.320050\pi\)
\(684\) 0 0
\(685\) 36.0000 1.37549
\(686\) 0 0
\(687\) 4.00000 6.92820i 0.152610 0.264327i
\(688\) 0 0
\(689\) 2.00000 3.46410i 0.0761939 0.131972i
\(690\) 0 0
\(691\) −36.0000 −1.36950 −0.684752 0.728776i \(-0.740090\pi\)
−0.684752 + 0.728776i \(0.740090\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 52.0000 1.97247
\(696\) 0 0
\(697\) −9.00000 15.5885i −0.340899 0.590455i
\(698\) 0 0
\(699\) 5.50000 + 9.52628i 0.208029 + 0.360317i
\(700\) 0 0
\(701\) −6.00000 + 10.3923i −0.226617 + 0.392512i −0.956803 0.290736i \(-0.906100\pi\)
0.730186 + 0.683248i \(0.239433\pi\)
\(702\) 0 0
\(703\) 1.00000 + 8.66025i 0.0377157 + 0.326628i
\(704\) 0 0
\(705\) −24.0000 + 41.5692i −0.903892 + 1.56559i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 9.00000 + 15.5885i 0.338002 + 0.585437i 0.984057 0.177854i \(-0.0569156\pi\)
−0.646055 + 0.763291i \(0.723582\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) 30.0000 + 51.9615i 1.12351 + 1.94597i
\(714\) 0 0
\(715\) 24.0000 0.897549
\(716\) 0 0
\(717\) 6.00000 10.3923i 0.224074 0.388108i
\(718\) 0 0
\(719\) 17.0000 29.4449i 0.633993 1.09811i −0.352735 0.935723i \(-0.614748\pi\)
0.986728 0.162385i \(-0.0519185\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −21.0000 −0.780998
\(724\) 0 0
\(725\) −22.0000 + 38.1051i −0.817059 + 1.41519i
\(726\) 0 0
\(727\) 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i \(-0.785937\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) 0 0
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 0 0
\(735\) −14.0000 24.2487i −0.516398 0.894427i
\(736\) 0 0
\(737\) −13.5000 23.3827i −0.497279 0.861312i
\(738\) 0 0
\(739\) −2.50000 + 4.33013i −0.0919640 + 0.159286i −0.908337 0.418238i \(-0.862648\pi\)
0.816373 + 0.577524i \(0.195981\pi\)
\(740\) 0 0
\(741\) −1.00000 8.66025i −0.0367359 0.318142i
\(742\) 0 0
\(743\) 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i \(-0.798229\pi\)
0.915794 + 0.401648i \(0.131563\pi\)
\(744\) 0 0
\(745\) −20.0000 34.6410i −0.732743 1.26915i
\(746\) 0 0
\(747\) 5.00000 + 8.66025i 0.182940 + 0.316862i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −19.0000 32.9090i −0.693320 1.20087i −0.970744 0.240118i \(-0.922814\pi\)
0.277424 0.960748i \(-0.410519\pi\)
\(752\) 0 0
\(753\) 5.00000 0.182210
\(754\) 0 0
\(755\) −4.00000 + 6.92820i −0.145575 + 0.252143i
\(756\) 0 0
\(757\) 7.00000 12.1244i 0.254419 0.440667i −0.710318 0.703881i \(-0.751449\pi\)
0.964738 + 0.263213i \(0.0847823\pi\)
\(758\) 0 0
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) 17.0000 0.616250 0.308125 0.951346i \(-0.400299\pi\)
0.308125 + 0.951346i \(0.400299\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 8.00000 13.8564i 0.289241 0.500979i
\(766\) 0 0
\(767\) −2.00000 −0.0722158
\(768\) 0 0
\(769\) −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) 0 0
\(773\) 26.0000 + 45.0333i 0.935155 + 1.61974i 0.774357 + 0.632749i \(0.218073\pi\)
0.160798 + 0.986987i \(0.448593\pi\)
\(774\) 0 0
\(775\) 55.0000 + 95.2628i 1.97566 + 3.42194i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 36.0000 + 15.5885i 1.28983 + 0.558514i
\(780\) 0 0
\(781\) −9.00000 + 15.5885i −0.322045 + 0.557799i
\(782\) 0 0
\(783\) −10.0000 17.3205i −0.357371 0.618984i
\(784\) 0 0
\(785\) 16.0000 + 27.7128i 0.571064 + 0.989113i
\(786\) 0 0
\(787\) −41.0000 −1.46149 −0.730746 0.682649i \(-0.760828\pi\)
−0.730746 + 0.682649i \(0.760828\pi\)
\(788\) 0 0
\(789\) 8.00000 + 13.8564i 0.284808 + 0.493301i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 8.00000 13.8564i 0.284088 0.492055i
\(794\) 0 0
\(795\) 4.00000 6.92820i 0.141865 0.245718i
\(796\) 0 0
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0