Properties

Label 1568.2.i.j.1537.1
Level $1568$
Weight $2$
Character 1568.1537
Analytic conductor $12.521$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1568 = 2^{5} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1568.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.5205430369\)
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 224)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1537.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1568.1537
Dual form 1568.2.i.j.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{9} +(-2.00000 + 3.46410i) q^{11} +4.00000 q^{13} +(-1.00000 + 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{19} +(4.00000 + 6.92820i) q^{23} +(2.50000 - 4.33013i) q^{25} +4.00000 q^{27} +2.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(4.00000 + 6.92820i) q^{33} +(-5.00000 - 8.66025i) q^{37} +(4.00000 - 6.92820i) q^{39} +10.0000 q^{41} -4.00000 q^{43} +(-2.00000 - 3.46410i) q^{47} +(2.00000 + 3.46410i) q^{51} +(1.00000 - 1.73205i) q^{53} +12.0000 q^{57} +(-5.00000 + 8.66025i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-4.00000 + 6.92820i) q^{67} +16.0000 q^{69} +(-3.00000 + 5.19615i) q^{73} +(-5.00000 - 8.66025i) q^{75} +(-8.00000 - 13.8564i) q^{79} +(5.50000 - 9.52628i) q^{81} +2.00000 q^{83} +(2.00000 - 3.46410i) q^{87} +(9.00000 + 15.5885i) q^{89} +(-4.00000 - 6.92820i) q^{93} +2.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - q^{9} - 4q^{11} + 8q^{13} - 2q^{17} + 6q^{19} + 8q^{23} + 5q^{25} + 8q^{27} + 4q^{29} + 4q^{31} + 8q^{33} - 10q^{37} + 8q^{39} + 20q^{41} - 8q^{43} - 4q^{47} + 4q^{51} + 2q^{53} + 24q^{57} - 10q^{59} - 8q^{61} - 8q^{67} + 32q^{69} - 6q^{73} - 10q^{75} - 16q^{79} + 11q^{81} + 4q^{83} + 4q^{87} + 18q^{89} - 8q^{93} + 4q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(1471\) \(1473\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −2.00000 + 3.46410i −0.603023 + 1.04447i 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 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
\(19\) 3.00000 + 5.19615i 0.688247 + 1.19208i 0.972404 + 0.233301i \(0.0749529\pi\)
−0.284157 + 0.958778i \(0.591714\pi\)
\(20\) 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
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) 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
\(33\) 4.00000 + 6.92820i 0.696311 + 1.20605i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.00000 8.66025i −0.821995 1.42374i −0.904194 0.427121i \(-0.859528\pi\)
0.0821995 0.996616i \(-0.473806\pi\)
\(38\) 0 0
\(39\) 4.00000 6.92820i 0.640513 1.10940i
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 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
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 12.0000 1.58944
\(58\) 0 0
\(59\) −5.00000 + 8.66025i −0.650945 + 1.12747i 0.331949 + 0.943297i \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) 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
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 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
\(73\) −3.00000 + 5.19615i −0.351123 + 0.608164i −0.986447 0.164083i \(-0.947534\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) 0 0
\(75\) −5.00000 8.66025i −0.577350 1.00000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −8.00000 13.8564i −0.900070 1.55897i −0.827401 0.561611i \(-0.810182\pi\)
−0.0726692 0.997356i \(-0.523152\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 2.00000 3.46410i 0.214423 0.371391i
\(88\) 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
\(93\) −4.00000 6.92820i −0.414781 0.718421i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.00000 13.8564i −0.773389 1.33955i −0.935695 0.352809i \(-0.885227\pi\)
0.162306 0.986740i \(-0.448107\pi\)
\(108\) 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
\(111\) −20.0000 −1.89832
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −2.00000 3.46410i −0.184900 0.320256i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 0 0
\(123\) 10.0000 17.3205i 0.901670 1.56174i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 0 0
\(129\) −4.00000 + 6.92820i −0.352180 + 0.609994i
\(130\) 0 0
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.00000 12.1244i 0.598050 1.03585i −0.395058 0.918656i \(-0.629276\pi\)
0.993109 0.117198i \(-0.0373911\pi\)
\(138\) 0 0
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 0 0
\(143\) −8.00000 + 13.8564i −0.668994 + 1.15873i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.00000 5.19615i −0.245770 0.425685i 0.716578 0.697507i \(-0.245707\pi\)
−0.962348 + 0.271821i \(0.912374\pi\)
\(150\) 0 0
\(151\) −8.00000 + 13.8564i −0.651031 + 1.12762i 0.331842 + 0.943335i \(0.392330\pi\)
−0.982873 + 0.184284i \(0.941004\pi\)
\(152\) 0 0
\(153\) 2.00000 0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 6.00000 10.3923i 0.478852 0.829396i −0.520854 0.853646i \(-0.674386\pi\)
0.999706 + 0.0242497i \(0.00771967\pi\)
\(158\) 0 0
\(159\) −2.00000 3.46410i −0.158610 0.274721i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20.0000 1.54765 0.773823 0.633402i \(-0.218342\pi\)
0.773823 + 0.633402i \(0.218342\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 3.00000 5.19615i 0.229416 0.397360i
\(172\) 0 0
\(173\) −6.00000 10.3923i −0.456172 0.790112i 0.542583 0.840002i \(-0.317446\pi\)
−0.998755 + 0.0498898i \(0.984113\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 10.0000 + 17.3205i 0.751646 + 1.30189i
\(178\) 0 0
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 0 0
\(181\) 12.0000 0.891953 0.445976 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 0 0
\(183\) −16.0000 −1.18275
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −4.00000 6.92820i −0.292509 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 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
\(201\) 8.00000 + 13.8564i 0.564276 + 0.977356i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4.00000 6.92820i 0.278019 0.481543i
\(208\) 0 0
\(209\) −24.0000 −1.66011
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 6.00000 + 10.3923i 0.405442 + 0.702247i
\(220\) 0 0
\(221\) −4.00000 + 6.92820i −0.269069 + 0.466041i
\(222\) 0 0
\(223\) 24.0000 1.60716 0.803579 0.595198i \(-0.202926\pi\)
0.803579 + 0.595198i \(0.202926\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) 0 0
\(227\) 11.0000 19.0526i 0.730096 1.26456i −0.226746 0.973954i \(-0.572809\pi\)
0.956842 0.290609i \(-0.0938578\pi\)
\(228\) 0 0
\(229\) −10.0000 17.3205i −0.660819 1.14457i −0.980401 0.197013i \(-0.936876\pi\)
0.319582 0.947559i \(-0.396457\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −32.0000 −2.07862
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 7.00000 12.1244i 0.450910 0.780998i −0.547533 0.836784i \(-0.684433\pi\)
0.998443 + 0.0557856i \(0.0177663\pi\)
\(242\) 0 0
\(243\) −5.00000 8.66025i −0.320750 0.555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 12.0000 + 20.7846i 0.763542 + 1.32249i
\(248\) 0 0
\(249\) 2.00000 3.46410i 0.126745 0.219529i
\(250\) 0 0
\(251\) −10.0000 −0.631194 −0.315597 0.948893i \(-0.602205\pi\)
−0.315597 + 0.948893i \(0.602205\pi\)
\(252\) 0 0
\(253\) −32.0000 −2.01182
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.00000 + 1.73205i 0.0623783 + 0.108042i 0.895528 0.445005i \(-0.146798\pi\)
−0.833150 + 0.553047i \(0.813465\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.00000 1.73205i −0.0618984 0.107211i
\(262\) 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
\(265\) 0 0
\(266\) 0 0
\(267\) 36.0000 2.20316
\(268\) 0 0
\(269\) −6.00000 + 10.3923i −0.365826 + 0.633630i −0.988908 0.148527i \(-0.952547\pi\)
0.623082 + 0.782157i \(0.285880\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.0000 + 17.3205i 0.603023 + 1.04447i
\(276\) 0 0
\(277\) −7.00000 + 12.1244i −0.420589 + 0.728482i −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) 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
\(285\) 0 0
\(286\) 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
\(293\) −8.00000 −0.467365 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −8.00000 + 13.8564i −0.464207 + 0.804030i
\(298\) 0 0
\(299\) 16.0000 + 27.7128i 0.925304 + 1.60267i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 10.0000 0.570730 0.285365 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) −13.0000 22.5167i −0.734803 1.27272i −0.954810 0.297218i \(-0.903941\pi\)
0.220006 0.975499i \(-0.429392\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.0000 + 29.4449i 0.954815 + 1.65379i 0.734791 + 0.678294i \(0.237280\pi\)
0.220024 + 0.975494i \(0.429386\pi\)
\(318\) 0 0
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) 0 0
\(321\) −32.0000 −1.78607
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 10.0000 17.3205i 0.554700 0.960769i
\(326\) 0 0
\(327\) 10.0000 + 17.3205i 0.553001 + 0.957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 0 0
\(333\) −5.00000 + 8.66025i −0.273998 + 0.474579i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) 6.00000 10.3923i 0.325875 0.564433i
\(340\) 0 0
\(341\) 8.00000 + 13.8564i 0.433224 + 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) −20.0000 −1.07058 −0.535288 0.844670i \(-0.679797\pi\)
−0.535288 + 0.844670i \(0.679797\pi\)
\(350\) 0 0
\(351\) 16.0000 0.854017
\(352\) 0 0
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.00000 13.8564i −0.422224 0.731313i 0.573933 0.818902i \(-0.305417\pi\)
−0.996157 + 0.0875892i \(0.972084\pi\)
\(360\) 0 0
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 0 0
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.00000 + 6.92820i −0.208798 + 0.361649i −0.951336 0.308155i \(-0.900289\pi\)
0.742538 + 0.669804i \(0.233622\pi\)
\(368\) 0 0
\(369\) −5.00000 8.66025i −0.260290 0.450835i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) 16.0000 27.7128i 0.819705 1.41977i
\(382\) 0 0
\(383\) −10.0000 17.3205i −0.510976 0.885037i −0.999919 0.0127209i \(-0.995951\pi\)
0.488943 0.872316i \(-0.337383\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 0 0
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 0 0
\(391\) −16.0000 −0.809155
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −14.0000 24.2487i −0.702640 1.21701i −0.967537 0.252731i \(-0.918671\pi\)
0.264897 0.964277i \(-0.414662\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.00000 + 1.73205i 0.0499376 + 0.0864945i 0.889914 0.456129i \(-0.150764\pi\)
−0.839976 + 0.542623i \(0.817431\pi\)
\(402\) 0 0
\(403\) 8.00000 13.8564i 0.398508 0.690237i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 40.0000 1.98273
\(408\) 0 0
\(409\) −1.00000 + 1.73205i −0.0494468 + 0.0856444i −0.889689 0.456566i \(-0.849079\pi\)
0.840243 + 0.542211i \(0.182412\pi\)
\(410\) 0 0
\(411\) −14.0000 24.2487i −0.690569 1.19610i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −10.0000 + 17.3205i −0.489702 + 0.848189i
\(418\) 0 0
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 0 0
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) 0 0
\(423\) −2.00000 + 3.46410i −0.0972433 + 0.168430i
\(424\) 0 0
\(425\) 5.00000 + 8.66025i 0.242536 + 0.420084i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 16.0000 + 27.7128i 0.772487 + 1.33799i
\(430\) 0 0
\(431\) 4.00000 6.92820i 0.192673 0.333720i −0.753462 0.657491i \(-0.771618\pi\)
0.946135 + 0.323772i \(0.104951\pi\)
\(432\) 0 0
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −24.0000 + 41.5692i −1.14808 + 1.98853i
\(438\) 0 0
\(439\) −12.0000 20.7846i −0.572729 0.991995i −0.996284 0.0861252i \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) −20.0000 + 34.6410i −0.941763 + 1.63118i
\(452\) 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
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 0 0
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.00000 15.5885i −0.416470 0.721348i 0.579111 0.815249i \(-0.303400\pi\)
−0.995582 + 0.0939008i \(0.970066\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −12.0000 20.7846i −0.552931 0.957704i
\(472\) 0 0
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) 0 0
\(475\) 30.0000 1.37649
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 0 0
\(481\) −20.0000 34.6410i −0.911922 1.57949i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 12.0000 20.7846i 0.543772 0.941841i −0.454911 0.890537i \(-0.650329\pi\)
0.998683 0.0513038i \(-0.0163377\pi\)
\(488\) 0 0
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 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
\(499\) −4.00000 6.92820i −0.179065 0.310149i 0.762496 0.646993i \(-0.223974\pi\)
−0.941560 + 0.336844i \(0.890640\pi\)
\(500\) 0 0
\(501\) 20.0000 34.6410i 0.893534 1.54765i
\(502\) 0 0
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 5.19615i 0.133235 0.230769i
\(508\) 0 0
\(509\) 10.0000 + 17.3205i 0.443242 + 0.767718i 0.997928 0.0643419i \(-0.0204948\pi\)
−0.554686 + 0.832060i \(0.687161\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 12.0000 + 20.7846i 0.529813 + 0.917663i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) −24.0000 −1.05348
\(520\) 0 0
\(521\) 19.0000 32.9090i 0.832405 1.44177i −0.0637207 0.997968i \(-0.520297\pi\)
0.896126 0.443800i \(-0.146370\pi\)
\(522\) 0 0
\(523\) 7.00000 + 12.1244i 0.306089 + 0.530161i 0.977503 0.210921i \(-0.0676463\pi\)
−0.671414 + 0.741082i \(0.734313\pi\)
\(524\) 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
\(531\) 10.0000 0.433963
\(532\) 0 0
\(533\) 40.0000 1.73259
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −15.0000 25.9808i −0.644900 1.11700i −0.984325 0.176367i \(-0.943566\pi\)
0.339424 0.940633i \(-0.389768\pi\)
\(542\) 0 0
\(543\) 12.0000 20.7846i 0.514969 0.891953i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 0 0
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 0 0
\(551\) 6.00000 + 10.3923i 0.255609 + 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.0000 + 25.9808i −0.635570 + 1.10084i 0.350824 + 0.936442i \(0.385902\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(558\) 0 0
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) −16.0000 −0.675521
\(562\) 0 0
\(563\) −23.0000 + 39.8372i −0.969334 + 1.67894i −0.271846 + 0.962341i \(0.587634\pi\)
−0.697489 + 0.716596i \(0.745699\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −2.00000 + 3.46410i −0.0836974 + 0.144968i −0.904835 0.425762i \(-0.860006\pi\)
0.821138 + 0.570730i \(0.193340\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 40.0000 1.66812
\(576\) 0 0
\(577\) −7.00000 + 12.1244i −0.291414 + 0.504744i −0.974144 0.225927i \(-0.927459\pi\)
0.682730 + 0.730670i \(0.260792\pi\)
\(578\) 0 0
\(579\) 14.0000 + 24.2487i 0.581820 + 1.00774i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 4.00000 + 6.92820i 0.165663 + 0.286937i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) 0 0
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) 0 0
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.00000 + 6.92820i 0.163709 + 0.283552i
\(598\) 0 0
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) 46.0000 1.87638 0.938190 0.346122i \(-0.112502\pi\)
0.938190 + 0.346122i \(0.112502\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −24.0000 41.5692i −0.974130 1.68724i −0.682777 0.730627i \(-0.739228\pi\)
−0.291353 0.956616i \(-0.594105\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.00000 13.8564i −0.323645 0.560570i
\(612\) 0 0
\(613\) 11.0000 19.0526i 0.444286 0.769526i −0.553716 0.832705i \(-0.686791\pi\)
0.998002 + 0.0631797i \(0.0201241\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) 11.0000 19.0526i 0.442127 0.765787i −0.555720 0.831370i \(-0.687557\pi\)
0.997847 + 0.0655827i \(0.0208906\pi\)
\(620\) 0 0
\(621\) 16.0000 + 27.7128i 0.642058 + 1.11208i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 0 0
\(627\) −24.0000 + 41.5692i −0.958468 + 1.66011i
\(628\) 0 0
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) −8.00000 + 13.8564i −0.317971 + 0.550743i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 17.0000 29.4449i 0.671460 1.16300i −0.306031 0.952022i \(-0.599001\pi\)
0.977490 0.210981i \(-0.0676657\pi\)
\(642\) 0 0
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.00000 10.3923i 0.235884 0.408564i −0.723645 0.690172i \(-0.757535\pi\)
0.959529 + 0.281609i \(0.0908680\pi\)
\(648\) 0 0
\(649\) −20.0000 34.6410i −0.785069 1.35978i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 19.0000 + 32.9090i 0.743527 + 1.28783i 0.950880 + 0.309561i \(0.100182\pi\)
−0.207352 + 0.978266i \(0.566485\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 12.0000 20.7846i 0.466746 0.808428i −0.532533 0.846410i \(-0.678760\pi\)
0.999278 + 0.0379819i \(0.0120929\pi\)
\(662\) 0 0
\(663\) 8.00000 + 13.8564i 0.310694 + 0.538138i
\(664\) 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
\(671\) 32.0000 1.23535
\(672\) 0 0
\(673\) −6.00000 −0.231283 −0.115642 0.993291i \(-0.536892\pi\)
−0.115642 + 0.993291i \(0.536892\pi\)
\(674\) 0 0
\(675\) 10.0000 17.3205i 0.384900 0.666667i
\(676\) 0 0
\(677\) 18.0000 + 31.1769i 0.691796 + 1.19823i 0.971249 + 0.238067i \(0.0765137\pi\)
−0.279453 + 0.960159i \(0.590153\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −22.0000 38.1051i −0.843042 1.46019i
\(682\) 0 0
\(683\) −12.0000 + 20.7846i −0.459167 + 0.795301i −0.998917 0.0465244i \(-0.985185\pi\)
0.539750 + 0.841825i \(0.318519\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −40.0000 −1.52610
\(688\) 0 0
\(689\) 4.00000 6.92820i 0.152388 0.263944i
\(690\) 0 0
\(691\) 11.0000 + 19.0526i 0.418460 + 0.724793i 0.995785 0.0917209i \(-0.0292368\pi\)
−0.577325 + 0.816514i \(0.695903\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −10.0000 + 17.3205i −0.378777 + 0.656061i
\(698\) 0 0
\(699\) 12.0000 0.453882
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) 30.0000 51.9615i 1.13147 1.95977i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −13.0000 22.5167i −0.488225 0.845631i 0.511683 0.859174i \(-0.329022\pi\)
−0.999908 + 0.0135434i \(0.995689\pi\)
\(710\) 0 0
\(711\) −8.00000 + 13.8564i −0.300023 + 0.519656i
\(712\) 0 0
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −24.0000 + 41.5692i −0.896296 + 1.55243i
\(718\) 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
\(723\) −14.0000 24.2487i −0.520666 0.901819i
\(724\) 0 0
\(725\) 5.00000 8.66025i 0.185695 0.321634i
\(726\) 0 0
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 4.00000 6.92820i 0.147945 0.256249i
\(732\) 0 0
\(733\) 4.00000 + 6.92820i 0.147743 + 0.255899i 0.930393 0.366563i \(-0.119466\pi\)
−0.782650 + 0.622462i \(0.786132\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.0000 27.7128i −0.589368 1.02081i
\(738\) 0 0
\(739\) 2.00000 3.46410i 0.0735712 0.127429i −0.826893 0.562360i \(-0.809894\pi\)
0.900464 + 0.434930i \(0.143227\pi\)
\(740\) 0 0
\(741\) 48.0000 1.76332
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.00000 1.73205i −0.0365881 0.0633724i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 12.0000 + 20.7846i 0.437886 + 0.758441i 0.997526 0.0702946i \(-0.0223939\pi\)
−0.559640 + 0.828736i \(0.689061\pi\)
\(752\) 0 0
\(753\) −10.0000 + 17.3205i −0.364420 + 0.631194i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) −32.0000 + 55.4256i −1.16153 + 2.01182i
\(760\) 0 0
\(761\) 15.0000 + 25.9808i 0.543750 + 0.941802i 0.998684 + 0.0512772i \(0.0163292\pi\)
−0.454935 + 0.890525i \(0.650337\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −20.0000 + 34.6410i −0.722158 + 1.25081i
\(768\) 0 0
\(769\) −6.00000 −0.216366 −0.108183 0.994131i \(-0.534503\pi\)
−0.108183 + 0.994131i \(0.534503\pi\)
\(770\) 0 0
\(771\) 4.00000 0.144056
\(772\) 0 0
\(773\) −12.0000 + 20.7846i −0.431610 + 0.747570i −0.997012 0.0772449i \(-0.975388\pi\)
0.565402 + 0.824815i \(0.308721\pi\)
\(774\) 0 0
\(775\) −10.0000 17.3205i −0.359211 0.622171i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 30.0000 + 51.9615i 1.07486 + 1.86171i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 23.0000 39.8372i 0.819861 1.42004i −0.0859225 0.996302i \(-0.527384\pi\)
0.905784 0.423740i \(-0.139283\pi\)
\(788\) 0 0
\(789\) 16.0000 + 27.7128i 0.569615 + 0.986602i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −16.0000 27.7128i −0.568177 0.984111i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −20.0000 −0.708436 −0.354218 0.935163i \(-0.615253\pi\)
−0.354218 + 0.935163i \(0.615253\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0 0
\(801\) 9.00000 15.5885i 0.317999 0.550791i
\(802\) 0 0
\(803\) −12.0000 20.7846i −0.423471