Properties

Label 1960.2.q.n.961.1
Level $1960$
Weight $2$
Character 1960.961
Analytic conductor $15.651$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1960.961
Dual form 1960.2.q.n.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-2.00000 - 3.46410i) q^{11} -2.00000 q^{13} +2.00000 q^{15} +(1.00000 - 1.73205i) q^{19} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{27} +10.0000 q^{29} +(2.00000 + 3.46410i) q^{31} +(4.00000 - 6.92820i) q^{33} +(1.00000 - 1.73205i) q^{37} +(-2.00000 - 3.46410i) q^{39} +12.0000 q^{41} -4.00000 q^{43} +(0.500000 + 0.866025i) q^{45} +(2.00000 - 3.46410i) q^{47} +(-1.00000 - 1.73205i) q^{53} -4.00000 q^{55} +4.00000 q^{57} +(5.00000 + 8.66025i) q^{59} +(3.00000 - 5.19615i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{67} +8.00000 q^{69} -12.0000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(1.00000 - 1.73205i) q^{75} +(2.00000 - 3.46410i) q^{79} +(5.50000 + 9.52628i) q^{81} -14.0000 q^{83} +(10.0000 + 17.3205i) q^{87} +(4.00000 - 6.92820i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(-1.00000 - 1.73205i) q^{95} +8.00000 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} + q^{5} - q^{9} + O(q^{10}) \) \( 2q + 2q^{3} + q^{5} - q^{9} - 4q^{11} - 4q^{13} + 4q^{15} + 2q^{19} + 4q^{23} - q^{25} + 8q^{27} + 20q^{29} + 4q^{31} + 8q^{33} + 2q^{37} - 4q^{39} + 24q^{41} - 8q^{43} + q^{45} + 4q^{47} - 2q^{53} - 8q^{55} + 8q^{57} + 10q^{59} + 6q^{61} - 2q^{65} - 4q^{67} + 16q^{69} - 24q^{71} - 4q^{73} + 2q^{75} + 4q^{79} + 11q^{81} - 28q^{83} + 20q^{87} + 8q^{89} - 8q^{93} - 2q^{95} + 16q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 + 1.73205i 0.577350 + 1.00000i 0.995782 + 0.0917517i \(0.0292466\pi\)
−0.418432 + 0.908248i \(0.637420\pi\)
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 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 −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 0 0
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) 10.0000 1.85695 0.928477 0.371391i \(-0.121119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 4.00000 6.92820i 0.696311 1.20605i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 0 0
\(39\) −2.00000 3.46410i −0.320256 0.554700i
\(40\) 0 0
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) 0 0
\(47\) 2.00000 3.46410i 0.291730 0.505291i −0.682489 0.730896i \(-0.739102\pi\)
0.974219 + 0.225605i \(0.0724358\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.00000 1.73205i −0.137361 0.237915i 0.789136 0.614218i \(-0.210529\pi\)
−0.926497 + 0.376303i \(0.877195\pi\)
\(54\) 0 0
\(55\) −4.00000 −0.539360
\(56\) 0 0
\(57\) 4.00000 0.529813
\(58\) 0 0
\(59\) 5.00000 + 8.66025i 0.650945 + 1.12747i 0.982894 + 0.184172i \(0.0589603\pi\)
−0.331949 + 0.943297i \(0.607706\pi\)
\(60\) 0 0
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.00000 + 1.73205i −0.124035 + 0.214834i
\(66\) 0 0
\(67\) −2.00000 3.46410i −0.244339 0.423207i 0.717607 0.696449i \(-0.245238\pi\)
−0.961946 + 0.273241i \(0.911904\pi\)
\(68\) 0 0
\(69\) 8.00000 0.963087
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) −2.00000 3.46410i −0.234082 0.405442i 0.724923 0.688830i \(-0.241875\pi\)
−0.959006 + 0.283387i \(0.908542\pi\)
\(74\) 0 0
\(75\) 1.00000 1.73205i 0.115470 0.200000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) −14.0000 −1.53670 −0.768350 0.640030i \(-0.778922\pi\)
−0.768350 + 0.640030i \(0.778922\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 10.0000 + 17.3205i 1.07211 + 1.85695i
\(88\) 0 0
\(89\) 4.00000 6.92820i 0.423999 0.734388i −0.572327 0.820025i \(-0.693959\pi\)
0.996326 + 0.0856373i \(0.0272926\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 + 6.92820i −0.414781 + 0.718421i
\(94\) 0 0
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 7.00000 + 12.1244i 0.696526 + 1.20642i 0.969664 + 0.244443i \(0.0786053\pi\)
−0.273138 + 0.961975i \(0.588061\pi\)
\(102\) 0 0
\(103\) 10.0000 17.3205i 0.985329 1.70664i 0.344865 0.938652i \(-0.387925\pi\)
0.640464 0.767988i \(-0.278742\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000 3.46410i 0.193347 0.334887i −0.753010 0.658009i \(-0.771399\pi\)
0.946357 + 0.323122i \(0.104732\pi\)
\(108\) 0 0
\(109\) −5.00000 8.66025i −0.478913 0.829502i 0.520794 0.853682i \(-0.325636\pi\)
−0.999708 + 0.0241802i \(0.992302\pi\)
\(110\) 0 0
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) −2.00000 3.46410i −0.186501 0.323029i
\(116\) 0 0
\(117\) 1.00000 1.73205i 0.0924500 0.160128i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) 12.0000 + 20.7846i 1.08200 + 1.87409i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 0 0
\(129\) −4.00000 6.92820i −0.352180 0.609994i
\(130\) 0 0
\(131\) −11.0000 + 19.0526i −0.961074 + 1.66463i −0.241264 + 0.970460i \(0.577562\pi\)
−0.719811 + 0.694170i \(0.755772\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.00000 3.46410i 0.172133 0.298142i
\(136\) 0 0
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 0 0
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 0 0
\(143\) 4.00000 + 6.92820i 0.334497 + 0.579365i
\(144\) 0 0
\(145\) 5.00000 8.66025i 0.415227 0.719195i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.00000 8.66025i 0.409616 0.709476i −0.585231 0.810867i \(-0.698996\pi\)
0.994847 + 0.101391i \(0.0323294\pi\)
\(150\) 0 0
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) 0 0
\(159\) 2.00000 3.46410i 0.158610 0.274721i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 0 0
\(165\) −4.00000 6.92820i −0.311400 0.539360i
\(166\) 0 0
\(167\) 4.00000 0.309529 0.154765 0.987951i \(-0.450538\pi\)
0.154765 + 0.987951i \(0.450538\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) 0 0
\(173\) 9.00000 15.5885i 0.684257 1.18517i −0.289412 0.957205i \(-0.593460\pi\)
0.973670 0.227964i \(-0.0732068\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −10.0000 + 17.3205i −0.751646 + 1.30189i
\(178\) 0 0
\(179\) −6.00000 10.3923i −0.448461 0.776757i 0.549825 0.835280i \(-0.314694\pi\)
−0.998286 + 0.0585225i \(0.981361\pi\)
\(180\) 0 0
\(181\) 22.0000 1.63525 0.817624 0.575753i \(-0.195291\pi\)
0.817624 + 0.575753i \(0.195291\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) 0 0
\(185\) −1.00000 1.73205i −0.0735215 0.127343i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i \(-0.879560\pi\)
0.784552 + 0.620063i \(0.212893\pi\)
\(192\) 0 0
\(193\) 9.00000 + 15.5885i 0.647834 + 1.12208i 0.983639 + 0.180150i \(0.0576584\pi\)
−0.335805 + 0.941932i \(0.609008\pi\)
\(194\) 0 0
\(195\) −4.00000 −0.286446
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 10.0000 + 17.3205i 0.708881 + 1.22782i 0.965272 + 0.261245i \(0.0841331\pi\)
−0.256391 + 0.966573i \(0.582534\pi\)
\(200\) 0 0
\(201\) 4.00000 6.92820i 0.282138 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 10.3923i 0.419058 0.725830i
\(206\) 0 0
\(207\) 2.00000 + 3.46410i 0.139010 + 0.240772i
\(208\) 0 0
\(209\) −8.00000 −0.553372
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −12.0000 20.7846i −0.822226 1.42414i
\(214\) 0 0
\(215\) −2.00000 + 3.46410i −0.136399 + 0.236250i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 4.00000 6.92820i 0.270295 0.468165i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 7.00000 + 12.1244i 0.464606 + 0.804722i 0.999184 0.0403978i \(-0.0128625\pi\)
−0.534577 + 0.845120i \(0.679529\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.00000 8.66025i 0.327561 0.567352i −0.654466 0.756091i \(-0.727107\pi\)
0.982027 + 0.188739i \(0.0604400\pi\)
\(234\) 0 0
\(235\) −2.00000 3.46410i −0.130466 0.225973i
\(236\) 0 0
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 2.00000 + 3.46410i 0.128831 + 0.223142i 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) 0 0
\(243\) −5.00000 + 8.66025i −0.320750 + 0.555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) 0 0
\(249\) −14.0000 24.2487i −0.887214 1.53670i
\(250\) 0 0
\(251\) −14.0000 −0.883672 −0.441836 0.897096i \(-0.645673\pi\)
−0.441836 + 0.897096i \(0.645673\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.0000 + 24.2487i −0.873296 + 1.51259i −0.0147291 + 0.999892i \(0.504689\pi\)
−0.858567 + 0.512702i \(0.828645\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −5.00000 + 8.66025i −0.309492 + 0.536056i
\(262\) 0 0
\(263\) 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 16.0000 0.979184
\(268\) 0 0
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 + 3.46410i −0.120605 + 0.208893i
\(276\) 0 0
\(277\) −13.0000 22.5167i −0.781094 1.35290i −0.931305 0.364241i \(-0.881328\pi\)
0.150210 0.988654i \(-0.452005\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) 0 0
\(283\) −5.00000 8.66025i −0.297219 0.514799i 0.678280 0.734804i \(-0.262726\pi\)
−0.975499 + 0.220005i \(0.929393\pi\)
\(284\) 0 0
\(285\) 2.00000 3.46410i 0.118470 0.205196i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) 8.00000 + 13.8564i 0.468968 + 0.812277i
\(292\) 0 0
\(293\) −22.0000 −1.28525 −0.642627 0.766179i \(-0.722155\pi\)
−0.642627 + 0.766179i \(0.722155\pi\)
\(294\) 0 0
\(295\) 10.0000 0.582223
\(296\) 0 0
\(297\) −8.00000 13.8564i −0.464207 0.804030i
\(298\) 0 0
\(299\) −4.00000 + 6.92820i −0.231326 + 0.400668i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −14.0000 + 24.2487i −0.804279 + 1.39305i
\(304\) 0 0
\(305\) −3.00000 5.19615i −0.171780 0.297531i
\(306\) 0 0
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) 0 0
\(309\) 40.0000 2.27552
\(310\) 0 0
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) −8.00000 + 13.8564i −0.452187 + 0.783210i −0.998522 0.0543564i \(-0.982689\pi\)
0.546335 + 0.837567i \(0.316023\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.0000 19.0526i 0.617822 1.07010i −0.372061 0.928208i \(-0.621349\pi\)
0.989882 0.141890i \(-0.0453179\pi\)
\(318\) 0 0
\(319\) −20.0000 34.6410i −1.11979 1.93952i
\(320\) 0 0
\(321\) 8.00000 0.446516
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 1.00000 + 1.73205i 0.0554700 + 0.0960769i
\(326\) 0 0
\(327\) 10.0000 17.3205i 0.553001 0.957826i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) 0 0
\(333\) 1.00000 + 1.73205i 0.0547997 + 0.0949158i
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) −18.0000 31.1769i −0.977626 1.69330i
\(340\) 0 0
\(341\) 8.00000 13.8564i 0.433224 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 4.00000 6.92820i 0.215353 0.373002i
\(346\) 0 0
\(347\) −2.00000 3.46410i −0.107366 0.185963i 0.807337 0.590091i \(-0.200908\pi\)
−0.914702 + 0.404128i \(0.867575\pi\)
\(348\) 0 0
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) −8.00000 −0.427008
\(352\) 0 0
\(353\) 6.00000 + 10.3923i 0.319348 + 0.553127i 0.980352 0.197256i \(-0.0632029\pi\)
−0.661004 + 0.750382i \(0.729870\pi\)
\(354\) 0 0
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.00000 13.8564i 0.422224 0.731313i −0.573933 0.818902i \(-0.694583\pi\)
0.996157 + 0.0875892i \(0.0279163\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 0 0
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 0 0
\(369\) −6.00000 + 10.3923i −0.312348 + 0.541002i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 15.0000 25.9808i 0.776671 1.34523i −0.157180 0.987570i \(-0.550240\pi\)
0.933851 0.357663i \(-0.116426\pi\)
\(374\) 0 0
\(375\) −1.00000 1.73205i −0.0516398 0.0894427i
\(376\) 0 0
\(377\) −20.0000 −1.03005
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 0 0
\(381\) −12.0000 20.7846i −0.614779 1.06483i
\(382\) 0 0
\(383\) −6.00000 + 10.3923i −0.306586 + 0.531022i −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) 0 0
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −44.0000 −2.21951
\(394\) 0 0
\(395\) −2.00000 3.46410i −0.100631 0.174298i
\(396\) 0 0
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) −4.00000 6.92820i −0.199254 0.345118i
\(404\) 0 0
\(405\) 11.0000 0.546594
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) −10.0000 17.3205i −0.494468 0.856444i 0.505511 0.862820i \(-0.331304\pi\)
−0.999980 + 0.00637586i \(0.997970\pi\)
\(410\) 0 0
\(411\) −18.0000 + 31.1769i −0.887875 + 1.53784i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −7.00000 + 12.1244i −0.343616 + 0.595161i
\(416\) 0 0
\(417\) 2.00000 + 3.46410i 0.0979404 + 0.169638i
\(418\) 0 0
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) 0 0
\(421\) 14.0000 0.682318 0.341159 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) 0 0
\(423\) 2.00000 + 3.46410i 0.0972433 + 0.168430i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −8.00000 + 13.8564i −0.386244 + 0.668994i
\(430\) 0 0
\(431\) −12.0000 20.7846i −0.578020 1.00116i −0.995706 0.0925683i \(-0.970492\pi\)
0.417687 0.908591i \(-0.362841\pi\)
\(432\) 0 0
\(433\) 32.0000 1.53782 0.768911 0.639356i \(-0.220799\pi\)
0.768911 + 0.639356i \(0.220799\pi\)
\(434\) 0 0
\(435\) 20.0000 0.958927
\(436\) 0 0
\(437\) −4.00000 6.92820i −0.191346 0.331421i
\(438\) 0 0
\(439\) 8.00000 13.8564i 0.381819 0.661330i −0.609503 0.792784i \(-0.708631\pi\)
0.991322 + 0.131453i \(0.0419644\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.0000 + 24.2487i −0.665160 + 1.15209i 0.314082 + 0.949396i \(0.398303\pi\)
−0.979242 + 0.202695i \(0.935030\pi\)
\(444\) 0 0
\(445\) −4.00000 6.92820i −0.189618 0.328428i
\(446\) 0 0
\(447\) 20.0000 0.945968
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 0 0
\(451\) −24.0000 41.5692i −1.13012 1.95742i
\(452\) 0 0
\(453\) −8.00000 + 13.8564i −0.375873 + 0.651031i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −3.00000 + 5.19615i −0.140334 + 0.243066i −0.927622 0.373519i \(-0.878151\pi\)
0.787288 + 0.616585i \(0.211484\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −42.0000 −1.95614 −0.978068 0.208288i \(-0.933211\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 4.00000 + 6.92820i 0.185496 + 0.321288i
\(466\) 0 0
\(467\) −13.0000 + 22.5167i −0.601568 + 1.04195i 0.391015 + 0.920384i \(0.372124\pi\)
−0.992584 + 0.121563i \(0.961209\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 14.0000 24.2487i 0.645086 1.11732i
\(472\) 0 0
\(473\) 8.00000 + 13.8564i 0.367840 + 0.637118i
\(474\) 0 0
\(475\) −2.00000 −0.0917663
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) 18.0000 + 31.1769i 0.822441 + 1.42451i 0.903859 + 0.427830i \(0.140722\pi\)
−0.0814184 + 0.996680i \(0.525945\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.00000 6.92820i 0.181631 0.314594i
\(486\) 0 0
\(487\) 14.0000 + 24.2487i 0.634401 + 1.09881i 0.986642 + 0.162905i \(0.0520863\pi\)
−0.352241 + 0.935909i \(0.614580\pi\)
\(488\) 0 0
\(489\) −40.0000 −1.80886
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 2.00000 3.46410i 0.0898933 0.155700i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −2.00000 + 3.46410i −0.0895323 + 0.155074i −0.907314 0.420455i \(-0.861871\pi\)
0.817781 + 0.575529i \(0.195204\pi\)
\(500\) 0 0
\(501\) 4.00000 + 6.92820i 0.178707 + 0.309529i
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 14.0000 0.622992
\(506\) 0 0
\(507\) −9.00000 15.5885i −0.399704 0.692308i
\(508\) 0 0
\(509\) −11.0000 + 19.0526i −0.487566 + 0.844490i −0.999898 0.0142980i \(-0.995449\pi\)
0.512331 + 0.858788i \(0.328782\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 4.00000 6.92820i 0.176604 0.305888i
\(514\) 0 0
\(515\) −10.0000 17.3205i −0.440653 0.763233i
\(516\) 0 0
\(517\) −16.0000 −0.703679
\(518\) 0 0
\(519\) 36.0000 1.58022
\(520\) 0 0
\(521\) 10.0000 + 17.3205i 0.438108 + 0.758825i 0.997544 0.0700486i \(-0.0223154\pi\)
−0.559436 + 0.828874i \(0.688982\pi\)
\(522\) 0 0
\(523\) −9.00000 + 15.5885i −0.393543 + 0.681636i −0.992914 0.118835i \(-0.962084\pi\)
0.599371 + 0.800471i \(0.295417\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) −24.0000 −1.03956
\(534\) 0 0
\(535\) −2.00000 3.46410i −0.0864675 0.149766i
\(536\) 0 0
\(537\) 12.0000 20.7846i 0.517838 0.896922i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −15.0000 + 25.9808i −0.644900 + 1.11700i 0.339424 + 0.940633i \(0.389768\pi\)
−0.984325 + 0.176367i \(0.943566\pi\)
\(542\) 0 0
\(543\) 22.0000 + 38.1051i 0.944110 + 1.63525i
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) −44.0000 −1.88130 −0.940652 0.339372i \(-0.889785\pi\)
−0.940652 + 0.339372i \(0.889785\pi\)
\(548\) 0 0
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) 0 0
\(551\) 10.0000 17.3205i 0.426014 0.737878i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 2.00000 3.46410i 0.0848953 0.147043i
\(556\) 0 0
\(557\) 15.0000 + 25.9808i 0.635570 + 1.10084i 0.986394 + 0.164399i \(0.0525683\pi\)
−0.350824 + 0.936442i \(0.614098\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.00000 + 1.73205i 0.0421450 + 0.0729972i 0.886328 0.463057i \(-0.153248\pi\)
−0.844183 + 0.536054i \(0.819914\pi\)
\(564\) 0 0
\(565\) −9.00000 + 15.5885i −0.378633 + 0.655811i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 6.00000 + 10.3923i 0.251092 + 0.434904i 0.963827 0.266529i \(-0.0858769\pi\)
−0.712735 + 0.701434i \(0.752544\pi\)
\(572\) 0 0
\(573\) −8.00000 −0.334205
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −6.00000 10.3923i −0.249783 0.432637i 0.713682 0.700470i \(-0.247026\pi\)
−0.963466 + 0.267832i \(0.913693\pi\)
\(578\) 0 0
\(579\) −18.0000 + 31.1769i −0.748054 + 1.29567i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −4.00000 + 6.92820i −0.165663 + 0.286937i
\(584\) 0 0
\(585\) −1.00000 1.73205i −0.0413449 0.0716115i
\(586\) 0 0
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 0 0
\(589\) 8.00000 0.329634
\(590\) 0 0
\(591\) −6.00000 10.3923i −0.246807 0.427482i
\(592\) 0 0
\(593\) −22.0000 + 38.1051i −0.903432 + 1.56479i −0.0804231 + 0.996761i \(0.525627\pi\)
−0.823009 + 0.568029i \(0.807706\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −20.0000 + 34.6410i −0.818546 + 1.41776i
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) 0 0
\(605\) 2.50000 + 4.33013i 0.101639 + 0.176045i
\(606\) 0 0
\(607\) 16.0000 27.7128i 0.649420 1.12483i −0.333842 0.942629i \(-0.608345\pi\)
0.983262 0.182199i \(-0.0583216\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.00000 + 6.92820i −0.161823 + 0.280285i
\(612\) 0 0
\(613\) 13.0000 + 22.5167i 0.525065 + 0.909439i 0.999574 + 0.0291886i \(0.00929235\pi\)
−0.474509 + 0.880251i \(0.657374\pi\)
\(614\) 0 0
\(615\) 24.0000 0.967773
\(616\) 0 0
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) −15.0000 25.9808i −0.602901 1.04425i −0.992379 0.123219i \(-0.960678\pi\)
0.389479 0.921036i \(-0.372655\pi\)
\(620\) 0 0
\(621\) 8.00000 13.8564i 0.321029 0.556038i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −8.00000 13.8564i −0.319489 0.553372i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) −4.00000 6.92820i −0.158986 0.275371i
\(634\) 0 0
\(635\) −6.00000 + 10.3923i −0.238103 + 0.412406i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 10.3923i 0.237356 0.411113i
\(640\) 0 0
\(641\) 7.00000 + 12.1244i 0.276483 + 0.478883i 0.970508 0.241068i \(-0.0774976\pi\)
−0.694025 + 0.719951i \(0.744164\pi\)
\(642\) 0 0
\(643\) 30.0000 1.18308 0.591542 0.806274i \(-0.298519\pi\)
0.591542 + 0.806274i \(0.298519\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) 6.00000 + 10.3923i 0.235884 + 0.408564i 0.959529 0.281609i \(-0.0908680\pi\)
−0.723645 + 0.690172i \(0.757535\pi\)
\(648\) 0 0
\(649\) 20.0000 34.6410i 0.785069 1.35978i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.00000 + 5.19615i −0.117399 + 0.203341i −0.918736 0.394872i \(-0.870789\pi\)
0.801337 + 0.598213i \(0.204122\pi\)
\(654\) 0 0
\(655\) 11.0000 + 19.0526i 0.429806 + 0.744445i
\(656\) 0 0
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) −28.0000 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 0 0
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 20.0000 34.6410i 0.774403 1.34131i
\(668\) 0 0
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) 0 0
\(677\) −7.00000 + 12.1244i −0.269032 + 0.465977i −0.968612 0.248577i \(-0.920037\pi\)
0.699580 + 0.714554i \(0.253370\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −14.0000 + 24.2487i −0.536481 + 0.929213i
\(682\) 0 0
\(683\) 18.0000 + 31.1769i 0.688751 + 1.19295i 0.972242 + 0.233977i \(0.0751739\pi\)
−0.283491 + 0.958975i \(0.591493\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 0 0
\(687\) −28.0000 −1.06827
\(688\) 0 0
\(689\) 2.00000 + 3.46410i 0.0761939 + 0.131972i
\(690\) 0 0
\(691\) 21.0000 36.3731i 0.798878 1.38370i −0.121470 0.992595i \(-0.538761\pi\)
0.920348 0.391102i \(-0.127906\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.00000 1.73205i 0.0379322 0.0657004i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 20.0000 0.756469
\(700\) 0 0
\(701\) 10.0000 0.377695 0.188847 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 0 0
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) 0 0
\(705\) 4.00000 6.92820i 0.150649 0.260931i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 3.00000 5.19615i 0.112667 0.195146i −0.804178 0.594389i \(-0.797394\pi\)
0.916845 + 0.399244i \(0.130727\pi\)
\(710\) 0 0
\(711\) 2.00000 + 3.46410i 0.0750059 + 0.129914i
\(712\) 0 0
\(713\) 16.0000 0.599205
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) 0 0
\(717\) 16.0000 + 27.7128i 0.597531 + 1.03495i
\(718\) 0 0
\(719\) 18.0000 31.1769i 0.671287 1.16270i −0.306253 0.951950i \(-0.599075\pi\)
0.977539 0.210752i \(-0.0675914\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4.00000 + 6.92820i −0.148762 + 0.257663i
\(724\) 0 0
\(725\) −5.00000 8.66025i −0.185695 0.321634i
\(726\) 0 0
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 7.00000 12.1244i 0.258551 0.447823i −0.707303 0.706910i \(-0.750088\pi\)
0.965854 + 0.259087i \(0.0834217\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −8.00000 + 13.8564i −0.294684 + 0.510407i
\(738\) 0 0
\(739\) −10.0000 17.3205i −0.367856 0.637145i 0.621374 0.783514i \(-0.286575\pi\)
−0.989230 + 0.146369i \(0.953241\pi\)
\(740\) 0 0
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) −5.00000 8.66025i −0.183186 0.317287i
\(746\) 0 0
\(747\) 7.00000 12.1244i 0.256117 0.443607i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −8.00000 + 13.8564i −0.291924 + 0.505627i −0.974265 0.225407i \(-0.927629\pi\)
0.682341 + 0.731034i \(0.260962\pi\)
\(752\) 0 0
\(753\) −14.0000 24.2487i −0.510188 0.883672i
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) −16.0000 27.7128i −0.580763 1.00591i
\(760\) 0 0
\(761\) −6.00000 + 10.3923i −0.217500 + 0.376721i −0.954043 0.299670i \(-0.903123\pi\)
0.736543 + 0.676391i \(0.236457\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.0000 17.3205i −0.361079 0.625407i
\(768\) 0 0
\(769\) 4.00000 0.144244 0.0721218 0.997396i \(-0.477023\pi\)
0.0721218 + 0.997396i \(0.477023\pi\)
\(770\) 0 0
\(771\) −56.0000 −2.01679
\(772\) 0 0
\(773\) 23.0000 + 39.8372i 0.827253 + 1.43284i 0.900186 + 0.435507i \(0.143431\pi\)
−0.0729331 + 0.997337i \(0.523236\pi\)
\(774\) 0 0
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.0000 20.7846i 0.429945 0.744686i
\(780\) 0 0
\(781\) 24.0000 + 41.5692i 0.858788 + 1.48746i
\(782\) 0 0
\(783\) 40.0000 1.42948
\(784\) 0 0
\(785\) −14.0000 −0.499681
\(786\) 0 0
\(787\) −21.0000 36.3731i −0.748569 1.29656i −0.948509 0.316752i \(-0.897408\pi\)
0.199939 0.979808i \(-0.435925\pi\)
\(788\) 0 0
\(789\) −16.0000 + 27.7128i −0.569615 + 0.986602i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −6.00000 + 10.3923i −0.213066 + 0.369042i
\(794\) 0 0
\(795\) −2.00000 3.46410i −0.0709327 0.122859i
\(796\) 0 0
\(797\) −50.0000 −1.77109 −0.885545 0.464553i \(-0.846215\pi\)
−0.885545 + 0.464553i \(0.846215\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 4.00000 + 6.92820i