Properties

Label 672.2.q.d.193.1
Level $672$
Weight $2$
Character 672.193
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 193.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 672.193
Dual form 672.2.q.d.289.1

$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(421\) \(449\) \(577\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 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 \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 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 −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) 0 0
\(19\) 2.50000 + 4.33013i 0.573539 + 0.993399i 0.996199 + 0.0871106i \(0.0277634\pi\)
−0.422659 + 0.906289i \(0.638903\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 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 \(-0.920161\pi\)
0.699301 + 0.714827i \(0.253495\pi\)
\(32\) 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 0.952587 + 0.304266i \(0.0984111\pi\)
−0.212792 + 0.977098i \(0.568256\pi\)
\(38\) 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 \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 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 −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 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 \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 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 \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 0 0
\(73\) 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) 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 \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) 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 −0.986303 0.164946i \(-0.947255\pi\)
0.350304 0.936636i \(-0.386078\pi\)
\(90\) 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 −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) −5.50000 9.52628i −0.541931 0.938652i −0.998793 0.0491146i \(-0.984360\pi\)
0.456862 0.889538i \(-0.348973\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.00000 15.5885i −0.870063 1.50699i −0.861931 0.507026i \(-0.830745\pi\)
−0.00813215 0.999967i \(-0.502589\pi\)
\(108\) 0 0
\(109\) 1.50000 2.59808i 0.143674 0.248851i −0.785203 0.619238i \(-0.787442\pi\)
0.928877 + 0.370387i \(0.120775\pi\)
\(110\) 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 \(-0.630750\pi\)
−0.399310 + 0.916816i \(0.630750\pi\)
\(128\) 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 \(-0.310573\pi\)
−0.997445 + 0.0714417i \(0.977240\pi\)
\(132\) 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 −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 0 0
\(139\) 15.0000 1.27228 0.636142 0.771572i \(-0.280529\pi\)
0.636142 + 0.771572i \(0.280529\pi\)
\(140\) 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 0.906249 + 0.422744i \(0.138933\pi\)
−0.0870170 + 0.996207i \(0.527733\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 11.0000 19.0526i 0.877896 1.52056i 0.0242497 0.999706i \(-0.492280\pi\)
0.853646 0.520854i \(-0.174386\pi\)
\(158\) 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 −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −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 −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 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 \(-0.785571\pi\)
0.931038 + 0.364922i \(0.118904\pi\)
\(180\) 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 0.959558 + 0.281511i \(0.0908356\pi\)
−0.235983 + 0.971757i \(0.575831\pi\)
\(192\) 0 0
\(193\) −3.50000 + 6.06218i −0.251936 + 0.436365i −0.964059 0.265689i \(-0.914400\pi\)
0.712123 + 0.702055i \(0.247734\pi\)
\(194\) 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 \(-0.973175\pi\)
0.571122 + 0.820865i \(0.306508\pi\)
\(200\) 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 \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 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 \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 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
\(229\) −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i \(-0.177186\pi\)
−0.882073 + 0.471113i \(0.843853\pi\)
\(230\) 0 0
\(231\) −1.00000 5.19615i −0.0657952 0.341882i
\(232\) 0 0
\(233\) −2.00000 3.46410i −0.131024 0.226941i 0.793047 0.609160i \(-0.208493\pi\)
−0.924072 + 0.382219i \(0.875160\pi\)
\(234\) 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 \(-0.248002\pi\)
0.711531 + 0.702655i \(0.248002\pi\)
\(240\) 0 0
\(241\) −5.00000 + 8.66025i −0.322078 + 0.557856i −0.980917 0.194429i \(-0.937715\pi\)
0.658838 + 0.752285i \(0.271048\pi\)
\(242\) 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 \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 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 0.553047 + 0.833150i \(0.313465\pi\)
0.445005 + 0.895528i \(0.353202\pi\)
\(258\) 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 \(-0.912663\pi\)
0.715944 + 0.698158i \(0.245997\pi\)
\(264\) 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 −0.131713 0.991288i \(-0.542048\pi\)
0.924337 0.381577i \(-0.124619\pi\)
\(270\) 0 0
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 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 −0.652140 0.758099i \(-0.726128\pi\)
0.982603 + 0.185720i \(0.0594618\pi\)
\(278\) 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 −0.124096 + 0.992270i \(0.539603\pi\)
−0.797283 + 0.603606i \(0.793730\pi\)
\(284\) 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 \(-0.247149\pi\)
0.713413 + 0.700744i \(0.247149\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) 0 0
\(311\) −5.00000 + 8.66025i −0.283524 + 0.491078i −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 0 0
\(313\) −15.5000 26.8468i −0.876112 1.51747i −0.855574 0.517681i \(-0.826795\pi\)
−0.0205381 0.999789i \(-0.506538\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.00000 3.46410i −0.112331 0.194563i 0.804379 0.594117i \(-0.202498\pi\)
−0.916710 + 0.399554i \(0.869165\pi\)
\(318\) 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 \(-0.321405\pi\)
−0.999298 + 0.0374662i \(0.988071\pi\)
\(332\) 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 \(-0.993839\pi\)
0.516667 + 0.856186i \(0.327172\pi\)
\(348\) 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 −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 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 0.886100 + 0.463494i \(0.153404\pi\)
−0.0416523 + 0.999132i \(0.513262\pi\)
\(360\) 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 −0.257948 + 0.966159i \(0.583046\pi\)
−0.707744 + 0.706469i \(0.750287\pi\)
\(368\) 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 0.878680 0.477412i \(-0.158425\pi\)
−0.852791 + 0.522253i \(0.825092\pi\)
\(374\) 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 \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 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 \(-0.182939\pi\)
−0.890443 + 0.455095i \(0.849605\pi\)
\(384\) 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 −0.746624 0.665246i \(-0.768327\pi\)
0.949432 + 0.313972i \(0.101660\pi\)
\(390\) 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 0.614123 0.789210i \(-0.289510\pi\)
−0.990538 + 0.137241i \(0.956176\pi\)
\(398\) 0 0
\(399\) −12.5000 4.33013i −0.625783 0.216777i
\(400\) 0 0
\(401\) 11.0000 + 19.0526i 0.549314 + 0.951439i 0.998322 + 0.0579116i \(0.0184442\pi\)
−0.449008 + 0.893528i \(0.648223\pi\)
\(402\) 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 −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 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 \(-0.188052\pi\)
0.830504 + 0.557012i \(0.188052\pi\)
\(420\) 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 \(-0.740007\pi\)
0.973574 + 0.228373i \(0.0733406\pi\)
\(432\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 0 0
\(443\) −11.0000 19.0526i −0.522626 0.905214i −0.999653 0.0263261i \(-0.991619\pi\)
0.477028 0.878888i \(-0.341714\pi\)
\(444\) 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 0.854094 0.520119i \(-0.174112\pi\)
−0.877483 + 0.479608i \(0.840779\pi\)
\(458\) 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 \(-0.582275\pi\)
−0.255607 + 0.966781i \(0.582275\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 10.0000 + 17.3205i 0.462745 + 0.801498i 0.999097 0.0424970i \(-0.0135313\pi\)
−0.536352 + 0.843995i \(0.680198\pi\)
\(468\) 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 \(-0.789564\pi\)
0.926388 + 0.376571i \(0.122897\pi\)
\(480\) 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 \(-0.782635\pi\)
0.934364 + 0.356320i \(0.115969\pi\)
\(488\) 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 −0.999852 0.0171872i \(-0.994529\pi\)
0.485042 0.874491i \(-0.338804\pi\)
\(500\) 0 0
\(501\) 6.00000 10.3923i 0.268060 0.464294i
\(502\) 0 0
\(503\) −42.0000 −1.87269 −0.936344 0.351085i \(-0.885813\pi\)
−0.936344 + 0.351085i \(0.885813\pi\)
\(504\) 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 0.997928 0.0643419i \(-0.0204948\pi\)
−0.554686 + 0.832060i \(0.687161\pi\)
\(510\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(522\) 0 0
\(523\) −6.50000 11.2583i −0.284225 0.492292i 0.688196 0.725525i \(-0.258403\pi\)
−0.972421 + 0.233233i \(0.925070\pi\)
\(524\) 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 −0.999042 0.0437584i \(-0.986067\pi\)
0.461625 0.887075i \(-0.347267\pi\)
\(542\) 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 \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 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 0.447387 + 0.894340i \(0.352355\pi\)
−0.998215 + 0.0597213i \(0.980979\pi\)
\(558\) 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 \(-0.694855\pi\)
0.996082 + 0.0884397i \(0.0281881\pi\)
\(564\) 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 −0.998608 0.0527519i \(-0.983201\pi\)
0.453619 0.891196i \(-0.350133\pi\)
\(570\) 0 0
\(571\) −3.50000 + 6.06218i −0.146470 + 0.253694i −0.929921 0.367760i \(-0.880125\pi\)
0.783450 + 0.621455i \(0.213458\pi\)
\(572\) 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 −0.633062 0.774101i \(-0.718202\pi\)
0.986922 + 0.161198i \(0.0515357\pi\)
\(578\) 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 \(-0.664939\pi\)
−0.495293 + 0.868726i \(0.664939\pi\)
\(588\) 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 0.685746 0.727841i \(-0.259476\pi\)
−0.973202 + 0.229953i \(0.926143\pi\)
\(594\) 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 \(-0.699354\pi\)
0.994732 + 0.102511i \(0.0326876\pi\)
\(600\) 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 \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 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 −0.949156 0.314806i \(-0.898061\pi\)
0.747208 + 0.664590i \(0.231394\pi\)
\(614\) 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 \(-0.865372\pi\)
0.811400 + 0.584491i \(0.198706\pi\)
\(620\) 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 \(-0.839670\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) 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 −0.197148 0.980374i \(-0.563168\pi\)
0.947602 0.319452i \(-0.103499\pi\)
\(642\) 0 0
\(643\) −13.0000 −0.512670 −0.256335 0.966588i \(-0.582515\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21.0000 36.3731i 0.825595 1.42997i −0.0758684 0.997118i \(-0.524173\pi\)
0.901464 0.432855i \(-0.142494\pi\)
\(648\) 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 0.950880 + 0.309561i \(0.100182\pi\)
−0.207352 + 0.978266i \(0.566485\pi\)
\(654\) 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 \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) 0 0
\(661\) −7.50000 + 12.9904i −0.291716 + 0.505267i −0.974216 0.225619i \(-0.927560\pi\)
0.682499 + 0.730886i \(0.260893\pi\)
\(662\) 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 −0.971249 0.238067i \(-0.923486\pi\)
0.279453 0.960159i \(-0.409847\pi\)
\(678\) 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 \(-0.945243\pi\)
0.640865 + 0.767654i \(0.278576\pi\)
\(684\) 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 −0.998159 0.0606524i \(-0.980682\pi\)
0.446553 0.894757i \(-0.352651\pi\)
\(692\) 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 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) 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 0.997546 + 0.0700124i \(0.0223039\pi\)
−0.438141 + 0.898906i \(0.644363\pi\)
\(720\) 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 \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 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 0.960900 + 0.276896i \(0.0893058\pi\)
−0.240651 + 0.970612i \(0.577361\pi\)
\(734\) 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 −0.384776 0.923010i \(-0.625721\pi\)
0.991738 0.128279i \(-0.0409454\pi\)
\(740\) 0 0
\(741\) −5.00000 −0.183680
\(742\) 0 0
\(743\) −54.0000 −1.98107 −0.990534 0.137268i \(-0.956168\pi\)
−0.990534 + 0.137268i \(0.956168\pi\)
\(744\) 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 −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) 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 0.819231 + 0.573463i \(0.194400\pi\)
0.0870179 + 0.996207i \(0.472266\pi\)
\(762\) 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 0.189899 + 0.981804i \(0.439184\pi\)
−0.945216 + 0.326445i \(0.894149\pi\)
\(774\) 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 \(-0.878875\pi\)
0.785885 + 0.618373i \(0.212208\pi\)
\(788\) 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