Properties

Label 672.2.q.h.289.1
Level $672$
Weight $2$
Character 672.289
Analytic conductor $5.366$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 672.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.36594701583\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 672.289
Dual form 672.2.q.h.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} +1.00000 q^{13} +(1.00000 + 1.73205i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(2.50000 + 4.33013i) q^{25} -1.00000 q^{27} -8.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(4.50000 - 7.79423i) q^{37} +(0.500000 + 0.866025i) q^{39} +2.00000 q^{41} +1.00000 q^{43} +(-4.00000 + 6.92820i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-3.00000 - 5.19615i) q^{53} -5.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +(1.00000 - 1.73205i) q^{61} +(0.500000 - 2.59808i) q^{63} +(2.50000 + 4.33013i) q^{67} -6.00000 q^{69} +4.00000 q^{71} +(5.50000 + 9.52628i) q^{73} +(-2.50000 + 4.33013i) q^{75} +(-4.00000 - 3.46410i) q^{77} +(2.50000 - 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-4.00000 - 6.92820i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(-2.50000 + 0.866025i) q^{91} +(-1.50000 + 2.59808i) q^{93} +18.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 5q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - 5q^{7} - q^{9} + 2q^{11} + 2q^{13} + 2q^{17} - 5q^{19} - 4q^{21} - 6q^{23} + 5q^{25} - 2q^{27} - 16q^{29} + 3q^{31} - 2q^{33} + 9q^{37} + q^{39} + 4q^{41} + 2q^{43} - 8q^{47} + 11q^{49} - 2q^{51} - 6q^{53} - 10q^{57} - 6q^{59} + 2q^{61} + q^{63} + 5q^{67} - 12q^{69} + 8q^{71} + 11q^{73} - 5q^{75} - 8q^{77} + 5q^{79} - q^{81} - 8q^{87} - 12q^{89} - 5q^{91} - 3q^{93} + 36q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 0 0
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 0 0
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0 0
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) 0 0
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 4.50000 7.79423i 0.739795 1.28136i −0.212792 0.977098i \(-0.568256\pi\)
0.952587 0.304266i \(-0.0984111\pi\)
\(38\) 0 0
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i \(0.364968\pi\)
−0.995066 + 0.0992202i \(0.968365\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) −1.00000 + 1.73205i −0.140028 + 0.242536i
\(52\) 0 0
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −5.00000 −0.662266
\(58\) 0 0
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 0 0
\(63\) 0.500000 2.59808i 0.0629941 0.327327i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) 0 0
\(75\) −2.50000 + 4.33013i −0.288675 + 0.500000i
\(76\) 0 0
\(77\) −4.00000 3.46410i −0.455842 0.394771i
\(78\) 0 0
\(79\) 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i \(-0.742577\pi\)
0.971698 + 0.236225i \(0.0759104\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) 0 0
\(89\) −6.00000 + 10.3923i −0.635999 + 1.10158i 0.350304 + 0.936636i \(0.386078\pi\)
−0.986303 + 0.164946i \(0.947255\pi\)
\(90\) 0 0
\(91\) −2.50000 + 0.866025i −0.262071 + 0.0907841i
\(92\) 0 0
\(93\) −1.50000 + 2.59808i −0.155543 + 0.269408i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) 5.50000 9.52628i 0.541931 0.938652i −0.456862 0.889538i \(-0.651027\pi\)
0.998793 0.0491146i \(-0.0156400\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) 0 0
\(109\) 1.50000 + 2.59808i 0.143674 + 0.248851i 0.928877 0.370387i \(-0.120775\pi\)
−0.785203 + 0.619238i \(0.787442\pi\)
\(110\) 0 0
\(111\) 9.00000 0.854242
\(112\) 0 0
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) 0 0
\(119\) −4.00000 3.46410i −0.366679 0.317554i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 9.00000 0.798621 0.399310 0.916816i \(-0.369250\pi\)
0.399310 + 0.916816i \(0.369250\pi\)
\(128\) 0 0
\(129\) 0.500000 + 0.866025i 0.0440225 + 0.0762493i
\(130\) 0 0
\(131\) 5.00000 8.66025i 0.436852 0.756650i −0.560593 0.828092i \(-0.689427\pi\)
0.997445 + 0.0714417i \(0.0227600\pi\)
\(132\) 0 0
\(133\) 2.50000 12.9904i 0.216777 1.12641i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −15.0000 −1.27228 −0.636142 0.771572i \(-0.719471\pi\)
−0.636142 + 0.771572i \(0.719471\pi\)
\(140\) 0 0
\(141\) −8.00000 −0.673722
\(142\) 0 0
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 0 0
\(149\) 10.0000 17.3205i 0.819232 1.41895i −0.0870170 0.996207i \(-0.527733\pi\)
0.906249 0.422744i \(-0.138933\pi\)
\(150\) 0 0
\(151\) −8.00000 13.8564i −0.651031 1.12762i −0.982873 0.184284i \(-0.941004\pi\)
0.331842 0.943335i \(-0.392330\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.0000 + 19.0526i 0.877896 + 1.52056i 0.853646 + 0.520854i \(0.174386\pi\)
0.0242497 + 0.999706i \(0.492280\pi\)
\(158\) 0 0
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 3.00000 15.5885i 0.236433 1.22854i
\(162\) 0 0
\(163\) 10.0000 17.3205i 0.783260 1.35665i −0.146772 0.989170i \(-0.546888\pi\)
0.930033 0.367477i \(-0.119778\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −2.50000 4.33013i −0.191180 0.331133i
\(172\) 0 0
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 0 0
\(175\) −10.0000 8.66025i −0.755929 0.654654i
\(176\) 0 0
\(177\) 3.00000 5.19615i 0.225494 0.390567i
\(178\) 0 0
\(179\) −2.00000 3.46410i −0.149487 0.258919i 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) 0 0
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −2.00000 + 3.46410i −0.146254 + 0.253320i
\(188\) 0 0
\(189\) 2.50000 0.866025i 0.181848 0.0629941i
\(190\) 0 0
\(191\) −10.0000 + 17.3205i −0.723575 + 1.25327i 0.235983 + 0.971757i \(0.424169\pi\)
−0.959558 + 0.281511i \(0.909164\pi\)
\(192\) 0 0
\(193\) −3.50000 6.06218i −0.251936 0.436365i 0.712123 0.702055i \(-0.247734\pi\)
−0.964059 + 0.265689i \(0.914400\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.0000 −0.712470 −0.356235 0.934396i \(-0.615940\pi\)
−0.356235 + 0.934396i \(0.615940\pi\)
\(198\) 0 0
\(199\) 6.00000 + 10.3923i 0.425329 + 0.736691i 0.996451 0.0841740i \(-0.0268252\pi\)
−0.571122 + 0.820865i \(0.693492\pi\)
\(200\) 0 0
\(201\) −2.50000 + 4.33013i −0.176336 + 0.305424i
\(202\) 0 0
\(203\) 20.0000 6.92820i 1.40372 0.486265i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) 0 0
\(209\) −10.0000 −0.691714
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) 2.00000 + 3.46410i 0.137038 + 0.237356i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −6.00000 5.19615i −0.407307 0.352738i
\(218\) 0 0
\(219\) −5.50000 + 9.52628i −0.371656 + 0.643726i
\(220\) 0 0
\(221\) 1.00000 + 1.73205i 0.0672673 + 0.116510i
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) 0 0
\(227\) −11.0000 19.0526i −0.730096 1.26456i −0.956842 0.290609i \(-0.906142\pi\)
0.226746 0.973954i \(-0.427191\pi\)
\(228\) 0 0
\(229\) −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i \(-0.843853\pi\)
0.849032 + 0.528341i \(0.177186\pi\)
\(230\) 0 0
\(231\) 1.00000 5.19615i 0.0657952 0.341882i
\(232\) 0 0
\(233\) −2.00000 + 3.46410i −0.131024 + 0.226941i −0.924072 0.382219i \(-0.875160\pi\)
0.793047 + 0.609160i \(0.208493\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 5.00000 0.324785
\(238\) 0 0
\(239\) −22.0000 −1.42306 −0.711531 0.702655i \(-0.751998\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(240\) 0 0
\(241\) −5.00000 8.66025i −0.322078 0.557856i 0.658838 0.752285i \(-0.271048\pi\)
−0.980917 + 0.194429i \(0.937715\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.50000 + 4.33013i −0.159071 + 0.275519i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 16.0000 27.7128i 0.998053 1.72868i 0.445005 0.895528i \(-0.353202\pi\)
0.553047 0.833150i \(-0.313465\pi\)
\(258\) 0 0
\(259\) −4.50000 + 23.3827i −0.279616 + 1.45293i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 0 0
\(263\) 4.00000 + 6.92820i 0.246651 + 0.427211i 0.962594 0.270947i \(-0.0873367\pi\)
−0.715944 + 0.698158i \(0.754003\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) 0 0
\(269\) 13.0000 + 22.5167i 0.792624 + 1.37287i 0.924337 + 0.381577i \(0.124619\pi\)
−0.131713 + 0.991288i \(0.542048\pi\)
\(270\) 0 0
\(271\) 4.00000 6.92820i 0.242983 0.420858i −0.718580 0.695444i \(-0.755208\pi\)
0.961563 + 0.274586i \(0.0885408\pi\)
\(272\) 0 0
\(273\) −2.00000 1.73205i −0.121046 0.104828i
\(274\) 0 0
\(275\) −5.00000 + 8.66025i −0.301511 + 0.522233i
\(276\) 0 0
\(277\) 5.50000 + 9.52628i 0.330463 + 0.572379i 0.982603 0.185720i \(-0.0594618\pi\)
−0.652140 + 0.758099i \(0.726128\pi\)
\(278\) 0 0
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) 0 0
\(283\) 15.5000 + 26.8468i 0.921379 + 1.59588i 0.797283 + 0.603606i \(0.206270\pi\)
0.124096 + 0.992270i \(0.460397\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −5.00000 + 1.73205i −0.295141 + 0.102240i
\(288\) 0 0
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) 0 0
\(291\) 9.00000 + 15.5885i 0.527589 + 0.913812i
\(292\) 0 0
\(293\) 28.0000 1.63578 0.817889 0.575376i \(-0.195144\pi\)
0.817889 + 0.575376i \(0.195144\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) 0 0
\(299\) −3.00000 + 5.19615i −0.173494 + 0.300501i
\(300\) 0 0
\(301\) −2.50000 + 0.866025i −0.144098 + 0.0499169i
\(302\) 0 0
\(303\) −3.00000 + 5.19615i −0.172345 + 0.298511i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −25.0000 −1.42683 −0.713413 0.700744i \(-0.752851\pi\)
−0.713413 + 0.700744i \(0.752851\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) 5.00000 + 8.66025i 0.283524 + 0.491078i 0.972250 0.233944i \(-0.0751631\pi\)
−0.688726 + 0.725022i \(0.741830\pi\)
\(312\) 0 0
\(313\) −15.5000 + 26.8468i −0.876112 + 1.51747i −0.0205381 + 0.999789i \(0.506538\pi\)
−0.855574 + 0.517681i \(0.826795\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00000 + 3.46410i −0.112331 + 0.194563i −0.916710 0.399554i \(-0.869165\pi\)
0.804379 + 0.594117i \(0.202498\pi\)
\(318\) 0 0
\(319\) −8.00000 13.8564i −0.447914 0.775810i
\(320\) 0 0
\(321\) 18.0000 1.00466
\(322\) 0 0
\(323\) −10.0000 −0.556415
\(324\) 0 0
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) 0 0
\(327\) −1.50000 + 2.59808i −0.0829502 + 0.143674i
\(328\) 0 0
\(329\) 4.00000 20.7846i 0.220527 1.14589i
\(330\) 0 0
\(331\) 8.50000 14.7224i 0.467202 0.809218i −0.532096 0.846684i \(-0.678595\pi\)
0.999298 + 0.0374662i \(0.0119287\pi\)
\(332\) 0 0
\(333\) 4.50000 + 7.79423i 0.246598 + 0.427121i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −31.0000 −1.68868 −0.844339 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) 0 0
\(339\) −6.00000 10.3923i −0.325875 0.564433i
\(340\) 0 0
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.00000 + 15.5885i 0.483145 + 0.836832i 0.999813 0.0193540i \(-0.00616095\pi\)
−0.516667 + 0.856186i \(0.672828\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.00000 5.19615i 0.0529256 0.275010i
\(358\) 0 0
\(359\) −16.0000 + 27.7128i −0.844448 + 1.46263i 0.0416523 + 0.999132i \(0.486738\pi\)
−0.886100 + 0.463494i \(0.846596\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 18.5000 + 32.0429i 0.965692 + 1.67263i 0.707744 + 0.706469i \(0.249713\pi\)
0.257948 + 0.966159i \(0.416954\pi\)
\(368\) 0 0
\(369\) −1.00000 + 1.73205i −0.0520579 + 0.0901670i
\(370\) 0 0
\(371\) 12.0000 + 10.3923i 0.623009 + 0.539542i
\(372\) 0 0
\(373\) 0.500000 0.866025i 0.0258890 0.0448411i −0.852791 0.522253i \(-0.825092\pi\)
0.878680 + 0.477412i \(0.158425\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.00000 −0.412021
\(378\) 0 0
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) 4.50000 + 7.79423i 0.230542 + 0.399310i
\(382\) 0 0
\(383\) 1.00000 1.73205i 0.0510976 0.0885037i −0.839345 0.543599i \(-0.817061\pi\)
0.890443 + 0.455095i \(0.150395\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.500000 + 0.866025i −0.0254164 + 0.0440225i
\(388\) 0 0
\(389\) 4.00000 + 6.92820i 0.202808 + 0.351274i 0.949432 0.313972i \(-0.101660\pi\)
−0.746624 + 0.665246i \(0.768327\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 10.0000 0.504433
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i \(-0.956176\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(398\) 0 0
\(399\) 12.5000 4.33013i 0.625783 0.216777i
\(400\) 0 0
\(401\) 11.0000 19.0526i 0.549314 0.951439i −0.449008 0.893528i \(-0.648223\pi\)
0.998322 0.0579116i \(-0.0184442\pi\)
\(402\) 0 0
\(403\) 1.50000 + 2.59808i 0.0747203 + 0.129419i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 18.0000 0.892227
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 0 0
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) 0 0
\(413\) 12.0000 + 10.3923i 0.590481 + 0.511372i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −7.50000 12.9904i −0.367277 0.636142i
\(418\) 0 0
\(419\) −34.0000 −1.66101 −0.830504 0.557012i \(-0.811948\pi\)
−0.830504 + 0.557012i \(0.811948\pi\)
\(420\) 0 0
\(421\) −11.0000 −0.536107 −0.268054 0.963404i \(-0.586380\pi\)
−0.268054 + 0.963404i \(0.586380\pi\)
\(422\) 0 0
\(423\) −4.00000 6.92820i −0.194487 0.336861i
\(424\) 0 0
\(425\) −5.00000 + 8.66025i −0.242536 + 0.420084i
\(426\) 0 0
\(427\) −1.00000 + 5.19615i −0.0483934 + 0.251459i
\(428\) 0 0
\(429\) −1.00000 + 1.73205i −0.0482805 + 0.0836242i
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −15.0000 25.9808i −0.717547 1.24283i
\(438\) 0 0
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) 11.0000 19.0526i 0.522626 0.905214i −0.477028 0.878888i \(-0.658286\pi\)
0.999653 0.0263261i \(-0.00838082\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 20.0000 0.945968
\(448\) 0 0
\(449\) 24.0000 1.13263 0.566315 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) 0 0
\(451\) 2.00000 + 3.46410i 0.0941763 + 0.163118i
\(452\) 0 0
\(453\) 8.00000 13.8564i 0.375873 0.651031i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.500000 + 0.866025i −0.0233890 + 0.0405110i −0.877483 0.479608i \(-0.840779\pi\)
0.854094 + 0.520119i \(0.174112\pi\)
\(458\) 0 0
\(459\) −1.00000 1.73205i −0.0466760 0.0808452i
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 11.0000 0.511213 0.255607 0.966781i \(-0.417725\pi\)
0.255607 + 0.966781i \(0.417725\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −10.0000 + 17.3205i −0.462745 + 0.801498i −0.999097 0.0424970i \(-0.986469\pi\)
0.536352 + 0.843995i \(0.319802\pi\)
\(468\) 0 0
\(469\) −10.0000 8.66025i −0.461757 0.399893i
\(470\) 0 0
\(471\) −11.0000 + 19.0526i −0.506853 + 0.877896i
\(472\) 0 0
\(473\) 1.00000 + 1.73205i 0.0459800 + 0.0796398i
\(474\) 0 0
\(475\) −25.0000 −1.14708
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) 0 0
\(481\) 4.50000 7.79423i 0.205182 0.355386i
\(482\) 0 0
\(483\) 15.0000 5.19615i 0.682524 0.236433i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −3.50000 6.06218i −0.158600 0.274703i 0.775764 0.631023i \(-0.217365\pi\)
−0.934364 + 0.356320i \(0.884031\pi\)
\(488\) 0 0
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −8.00000 13.8564i −0.360302 0.624061i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.0000 + 3.46410i −0.448561 + 0.155386i
\(498\) 0 0
\(499\) 11.5000 19.9186i 0.514811 0.891678i −0.485042 0.874491i \(-0.661196\pi\)
0.999852 0.0171872i \(-0.00547113\pi\)
\(500\) 0 0
\(501\) 6.00000 + 10.3923i 0.268060 + 0.464294i
\(502\) 0 0
\(503\) 42.0000 1.87269 0.936344 0.351085i \(-0.114187\pi\)
0.936344 + 0.351085i \(0.114187\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 0 0
\(509\) 10.0000 17.3205i 0.443242 0.767718i −0.554686 0.832060i \(-0.687161\pi\)
0.997928 + 0.0643419i \(0.0204948\pi\)
\(510\) 0 0
\(511\) −22.0000 19.0526i −0.973223 0.842836i
\(512\) 0 0
\(513\) 2.50000 4.33013i 0.110378 0.191180i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −16.0000 −0.703679
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(522\) 0 0
\(523\) 6.50000 11.2583i 0.284225 0.492292i −0.688196 0.725525i \(-0.741597\pi\)
0.972421 + 0.233233i \(0.0749303\pi\)
\(524\) 0 0
\(525\) 2.50000 12.9904i 0.109109 0.566947i
\(526\) 0 0
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.00000 3.46410i 0.0863064 0.149487i
\(538\) 0 0
\(539\) 13.0000 + 5.19615i 0.559950 + 0.223814i
\(540\) 0 0
\(541\) −12.5000 + 21.6506i −0.537417 + 0.930834i 0.461625 + 0.887075i \(0.347267\pi\)
−0.999042 + 0.0437584i \(0.986067\pi\)
\(542\) 0 0
\(543\) 2.50000 + 4.33013i 0.107285 + 0.185824i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 28.0000 1.19719 0.598597 0.801050i \(-0.295725\pi\)
0.598597 + 0.801050i \(0.295725\pi\)
\(548\) 0 0
\(549\) 1.00000 + 1.73205i 0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 20.0000 34.6410i 0.852029 1.47576i
\(552\) 0 0
\(553\) −2.50000 + 12.9904i −0.106311 + 0.552407i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13.0000 22.5167i −0.550828 0.954062i −0.998215 0.0597213i \(-0.980979\pi\)
0.447387 0.894340i \(-0.352355\pi\)
\(558\) 0 0
\(559\) 1.00000 0.0422955
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) −10.0000 17.3205i −0.421450 0.729972i 0.574632 0.818412i \(-0.305145\pi\)
−0.996082 + 0.0884397i \(0.971812\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) −13.0000 + 22.5167i −0.544988 + 0.943948i 0.453619 + 0.891196i \(0.350133\pi\)
−0.998608 + 0.0527519i \(0.983201\pi\)
\(570\) 0 0
\(571\) 3.50000 + 6.06218i 0.146470 + 0.253694i 0.929921 0.367760i \(-0.119875\pi\)
−0.783450 + 0.621455i \(0.786542\pi\)
\(572\) 0 0
\(573\) −20.0000 −0.835512
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) 0 0
\(577\) 8.50000 + 14.7224i 0.353860 + 0.612903i 0.986922 0.161198i \(-0.0515357\pi\)
−0.633062 + 0.774101i \(0.718202\pi\)
\(578\) 0 0
\(579\) 3.50000 6.06218i 0.145455 0.251936i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 6.00000 10.3923i 0.248495 0.430405i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −15.0000 −0.618064
\(590\) 0 0
\(591\) −5.00000 8.66025i −0.205673 0.356235i
\(592\) 0 0
\(593\) −7.00000 + 12.1244i −0.287456 + 0.497888i −0.973202 0.229953i \(-0.926143\pi\)
0.685746 + 0.727841i \(0.259476\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.00000 + 10.3923i −0.245564 + 0.425329i
\(598\) 0 0
\(599\) −10.0000 17.3205i −0.408589 0.707697i 0.586143 0.810208i \(-0.300646\pi\)
−0.994732 + 0.102511i \(0.967312\pi\)
\(600\) 0 0
\(601\) 3.00000 0.122373 0.0611863 0.998126i \(-0.480512\pi\)
0.0611863 + 0.998126i \(0.480512\pi\)
\(602\) 0 0
\(603\) −5.00000 −0.203616
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.50000 11.2583i 0.263827 0.456962i −0.703429 0.710766i \(-0.748349\pi\)
0.967256 + 0.253804i \(0.0816819\pi\)
\(608\) 0 0
\(609\) 16.0000 + 13.8564i 0.648353 + 0.561490i
\(610\) 0 0
\(611\) −4.00000 + 6.92820i −0.161823 + 0.280285i
\(612\) 0 0
\(613\) −5.00000 8.66025i −0.201948 0.349784i 0.747208 0.664590i \(-0.231394\pi\)
−0.949156 + 0.314806i \(0.898061\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.0000 1.36879 0.684394 0.729112i \(-0.260067\pi\)
0.684394 + 0.729112i \(0.260067\pi\)
\(618\) 0 0
\(619\) 2.50000 + 4.33013i 0.100483 + 0.174042i 0.911884 0.410448i \(-0.134628\pi\)
−0.811400 + 0.584491i \(0.801294\pi\)
\(620\) 0 0
\(621\) 3.00000 5.19615i 0.120386 0.208514i
\(622\) 0 0
\(623\) 6.00000 31.1769i 0.240385 1.24908i
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) −5.00000 8.66025i −0.199681 0.345857i
\(628\) 0 0
\(629\) 18.0000 0.717707
\(630\) 0 0
\(631\) 44.0000 1.75161 0.875806 0.482663i \(-0.160330\pi\)
0.875806 + 0.482663i \(0.160330\pi\)
\(632\) 0 0
\(633\) 6.00000 + 10.3923i 0.238479 + 0.413057i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.50000 4.33013i 0.217918 0.171566i
\(638\) 0 0
\(639\) −2.00000 + 3.46410i −0.0791188 + 0.137038i
\(640\) 0 0
\(641\) 19.0000 + 32.9090i 0.750455 + 1.29983i 0.947602 + 0.319452i \(0.103499\pi\)
−0.197148 + 0.980374i \(0.563168\pi\)
\(642\) 0 0
\(643\) 13.0000 0.512670 0.256335 0.966588i \(-0.417485\pi\)
0.256335 + 0.966588i \(0.417485\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −21.0000 36.3731i −0.825595 1.42997i −0.901464 0.432855i \(-0.857506\pi\)
0.0758684 0.997118i \(-0.475827\pi\)
\(648\) 0 0
\(649\) 6.00000 10.3923i 0.235521 0.407934i
\(650\) 0 0
\(651\) 1.50000 7.79423i 0.0587896 0.305480i
\(652\) 0 0
\(653\) 19.0000 32.9090i 0.743527 1.28783i −0.207352 0.978266i \(-0.566485\pi\)
0.950880 0.309561i \(-0.100182\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −11.0000 −0.429151
\(658\) 0 0
\(659\) −6.00000 −0.233727 −0.116863 0.993148i \(-0.537284\pi\)
−0.116863 + 0.993148i \(0.537284\pi\)
\(660\) 0 0
\(661\) −7.50000 12.9904i −0.291716 0.505267i 0.682499 0.730886i \(-0.260893\pi\)
−0.974216 + 0.225619i \(0.927560\pi\)
\(662\) 0 0
\(663\) −1.00000 + 1.73205i −0.0388368 + 0.0672673i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 24.0000 41.5692i 0.929284 1.60957i
\(668\) 0 0
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 0 0
\(671\) 4.00000 0.154418
\(672\) 0 0
\(673\) 35.0000 1.34915 0.674575 0.738206i \(-0.264327\pi\)
0.674575 + 0.738206i \(0.264327\pi\)
\(674\) 0 0
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) 0 0
\(677\) −18.0000 + 31.1769i −0.691796 + 1.19823i 0.279453 + 0.960159i \(0.409847\pi\)
−0.971249 + 0.238067i \(0.923486\pi\)
\(678\) 0 0
\(679\) −45.0000 + 15.5885i −1.72694 + 0.598230i
\(680\) 0 0
\(681\) 11.0000 19.0526i 0.421521 0.730096i
\(682\) 0 0
\(683\) 9.00000 + 15.5885i 0.344375 + 0.596476i 0.985240 0.171178i \(-0.0547574\pi\)
−0.640865 + 0.767654i \(0.721424\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −1.00000 −0.0381524
\(688\) 0 0
\(689\) −3.00000 5.19615i −0.114291 0.197958i
\(690\) 0 0
\(691\) 14.5000 25.1147i 0.551606 0.955410i −0.446553 0.894757i \(-0.647349\pi\)
0.998159 0.0606524i \(-0.0193181\pi\)
\(692\) 0 0
\(693\) 5.00000 1.73205i 0.189934 0.0657952i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2.00000 + 3.46410i 0.0757554 + 0.131212i
\(698\) 0 0
\(699\) −4.00000 −0.151294
\(700\) 0 0
\(701\) −14.0000 −0.528773 −0.264386 0.964417i \(-0.585169\pi\)
−0.264386 + 0.964417i \(0.585169\pi\)
\(702\) 0 0
\(703\) 22.5000 + 38.9711i 0.848604 + 1.46982i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −12.0000 10.3923i −0.451306 0.390843i
\(708\) 0 0
\(709\) −5.00000 + 8.66025i −0.187779 + 0.325243i −0.944509 0.328484i \(-0.893462\pi\)
0.756730 + 0.653727i \(0.226796\pi\)
\(710\) 0 0
\(711\) 2.50000 + 4.33013i 0.0937573 + 0.162392i
\(712\) 0 0
\(713\) −18.0000 −0.674105
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −11.0000 19.0526i −0.410803 0.711531i
\(718\) 0 0
\(719\) −15.0000 + 25.9808i −0.559406 + 0.968919i 0.438141 + 0.898906i \(0.355637\pi\)
−0.997546 + 0.0700124i \(0.977696\pi\)
\(720\) 0 0
\(721\) −5.50000 + 28.5788i −0.204831 + 1.06433i
\(722\) 0 0
\(723\) 5.00000 8.66025i 0.185952 0.322078i
\(724\) 0 0
\(725\) −20.0000 34.6410i −0.742781 1.28654i
\(726\) 0 0
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 1.00000 + 1.73205i 0.0369863 + 0.0640622i
\(732\) 0 0
\(733\) 19.5000 33.7750i 0.720249 1.24751i −0.240651 0.970612i \(-0.577361\pi\)
0.960900 0.276896i \(-0.0893058\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.00000 + 8.66025i −0.184177 + 0.319005i
\(738\) 0 0
\(739\) −16.5000 28.5788i −0.606962 1.05129i −0.991738 0.128279i \(-0.959055\pi\)
0.384776 0.923010i \(-0.374279\pi\)
\(740\) 0 0
\(741\) −5.00000 −0.183680
\(742\) 0 0
\(743\) 54.0000 1.98107 0.990534 0.137268i \(-0.0438322\pi\)
0.990534 + 0.137268i \(0.0438322\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9.00000 + 46.7654i −0.328853 + 1.70877i
\(750\) 0 0
\(751\) 15.5000 26.8468i 0.565603 0.979653i −0.431390 0.902165i \(-0.641977\pi\)
0.996993 0.0774878i \(-0.0246899\pi\)
\(752\) 0 0
\(753\) 3.00000 + 5.19615i 0.109326 + 0.189358i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 0 0
\(759\) −6.00000 10.3923i −0.217786 0.377217i
\(760\) 0 0
\(761\) 25.0000 43.3013i 0.906249 1.56967i 0.0870179 0.996207i \(-0.472266\pi\)
0.819231 0.573463i \(-0.194400\pi\)
\(762\) 0 0
\(763\) −6.00000 5.19615i −0.217215 0.188113i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.00000 5.19615i −0.108324 0.187622i
\(768\) 0 0
\(769\) 23.0000 0.829401 0.414701 0.909958i \(-0.363886\pi\)
0.414701 + 0.909958i \(0.363886\pi\)
\(770\) 0 0
\(771\) 32.0000 1.15245
\(772\) 0 0
\(773\) −21.0000 36.3731i −0.755318 1.30825i −0.945216 0.326445i \(-0.894149\pi\)
0.189899 0.981804i \(-0.439184\pi\)
\(774\) 0 0
\(775\) −7.50000 + 12.9904i −0.269408 + 0.466628i
\(776\) 0 0
\(777\) −22.5000 + 7.79423i −0.807183 + 0.279616i
\(778\) 0 0
\(779\) −5.00000 + 8.66025i −0.179144 + 0.310286i
\(780\) 0 0
\(781\) 4.00000 + 6.92820i 0.143131 + 0.247911i
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 4.00000 + 6.92820i 0.142585 + 0.246964i 0.928469 0.371409i \(-0.121125\pi\)
−0.785885 + 0.618373i \(0.787792\pi\)
\(788\) 0 0
\(789\) −4.00000 + 6.92820i −0.142404 + 0.246651i
\(790\) 0 0
\(791\) 30.0000 10.3923i 1.06668 0.369508i
\(792\) 0 0
\(793\) 1.00000 1.73205i 0.0355110 0.0615069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.00000 0.212531 0.106265 0.994338i \(-0.466111\pi\)
0.106265 + 0.994338i \(0.466111\pi\)
\(798\) 0 0
\(799\) −16.0000 −0.566039
\(800\)