Properties

Label 1960.2.q.b.361.1
Level $1960$
Weight $2$
Character 1960.361
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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.b.961.1

$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) 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 0.389338 + 0.921095i \(0.372704\pi\)
−0.992361 + 0.123371i \(0.960630\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 0 0
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 0 0
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 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 \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 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 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 0 0
\(39\) −2.00000 + 3.46410i −0.320256 + 0.554700i
\(40\) 0 0
\(41\) −12.0000 −1.87409 −0.937043 0.349215i \(-0.886448\pi\)
−0.937043 + 0.349215i \(0.886448\pi\)
\(42\) 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 \(-0.260898\pi\)
−0.974219 + 0.225605i \(0.927564\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.00000 + 1.73205i −0.137361 + 0.237915i −0.926497 0.376303i \(-0.877195\pi\)
0.789136 + 0.614218i \(0.210529\pi\)
\(54\) 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 0.331949 + 0.943297i \(0.392294\pi\)
−0.982894 + 0.184172i \(0.941040\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 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 −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 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 \(-0.758125\pi\)
0.959006 + 0.283387i \(0.0914581\pi\)
\(74\) 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 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 0 0
\(83\) 14.0000 1.53670 0.768350 0.640030i \(-0.221078\pi\)
0.768350 + 0.640030i \(0.221078\pi\)
\(84\) 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 \(-0.306041\pi\)
−0.996326 + 0.0856373i \(0.972707\pi\)
\(90\) 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 \(-0.633125\pi\)
−0.406138 + 0.913812i \(0.633125\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −7.00000 + 12.1244i −0.696526 + 1.20642i 0.273138 + 0.961975i \(0.411939\pi\)
−0.969664 + 0.244443i \(0.921395\pi\)
\(102\) 0 0
\(103\) −10.0000 17.3205i −0.985329 1.70664i −0.640464 0.767988i \(-0.721258\pi\)
−0.344865 0.938652i \(-0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.00000 + 3.46410i 0.193347 + 0.334887i 0.946357 0.323122i \(-0.104732\pi\)
−0.753010 + 0.658009i \(0.771399\pi\)
\(108\) 0 0
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) 0 0
\(111\) −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 0.719811 + 0.694170i \(0.244228\pi\)
0.241264 + 0.970460i \(0.422438\pi\)
\(132\) 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 −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 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 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 0 0
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 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 −0.438948 0.898513i \(-0.644649\pi\)
0.997609 0.0691164i \(-0.0220180\pi\)
\(158\) 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 −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 0 0
\(165\) −4.00000 + 6.92820i −0.311400 + 0.539360i
\(166\) 0 0
\(167\) −4.00000 −0.309529 −0.154765 0.987951i \(-0.549462\pi\)
−0.154765 + 0.987951i \(0.549462\pi\)
\(168\) 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 −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 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 −0.998286 0.0585225i \(-0.981361\pi\)
0.549825 + 0.835280i \(0.314694\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 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 0.784552 0.620063i \(-0.212893\pi\)
−0.929267 + 0.369410i \(0.879560\pi\)
\(192\) 0 0
\(193\) 9.00000 15.5885i 0.647834 1.12208i −0.335805 0.941932i \(-0.609008\pi\)
0.983639 0.180150i \(-0.0576584\pi\)
\(194\) 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 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) 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 \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 5.00000 + 8.66025i 0.327561 + 0.567352i 0.982027 0.188739i \(-0.0604400\pi\)
−0.654466 + 0.756091i \(0.727107\pi\)
\(234\) 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 \(-0.874456\pi\)
0.794393 + 0.607404i \(0.207789\pi\)
\(242\) 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 \(-0.354327\pi\)
0.441836 + 0.897096i \(0.354327\pi\)
\(252\) 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 0.858567 + 0.512702i \(0.171355\pi\)
0.0147291 + 0.999892i \(0.495311\pi\)
\(258\) 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 −0.506669 0.862141i \(-0.669123\pi\)
0.999970 + 0.00771799i \(0.00245674\pi\)
\(264\) 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 \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 0 0
\(277\) −13.0000 + 22.5167i −0.781094 + 1.35290i 0.150210 + 0.988654i \(0.452005\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 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 \(-0.737274\pi\)
0.975499 + 0.220005i \(0.0706075\pi\)
\(284\) 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 \(-0.277845\pi\)
0.642627 + 0.766179i \(0.277845\pi\)
\(294\) 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 \(-0.369180\pi\)
0.399511 + 0.916728i \(0.369180\pi\)
\(308\) 0 0
\(309\) 40.0000 2.27552
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 8.00000 + 13.8564i 0.452187 + 0.783210i 0.998522 0.0543564i \(-0.0173107\pi\)
−0.546335 + 0.837567i \(0.683977\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.0000 + 19.0526i 0.617822 + 1.07010i 0.989882 + 0.141890i \(0.0453179\pi\)
−0.372061 + 0.928208i \(0.621349\pi\)
\(318\) 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 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 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 −0.914702 0.404128i \(-0.867575\pi\)
0.807337 + 0.590091i \(0.200908\pi\)
\(348\) 0 0
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) −8.00000 −0.427008
\(352\) 0 0
\(353\) −6.00000 + 10.3923i −0.319348 + 0.553127i −0.980352 0.197256i \(-0.936797\pi\)
0.661004 + 0.750382i \(0.270130\pi\)
\(354\) 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 0.996157 0.0875892i \(-0.0279163\pi\)
−0.573933 + 0.818902i \(0.694583\pi\)
\(360\) 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 \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 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 0.933851 + 0.357663i \(0.116426\pi\)
−0.157180 + 0.987570i \(0.550240\pi\)
\(374\) 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 \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 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 −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 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 0.998125 + 0.0612128i \(0.0194968\pi\)
−0.446051 + 0.895008i \(0.647170\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 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 \(-0.668696\pi\)
0.999980 + 0.00637586i \(0.00202951\pi\)
\(410\) 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 \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(420\) 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 0.417687 + 0.908591i \(0.362841\pi\)
−0.995706 + 0.0925683i \(0.970492\pi\)
\(432\) 0 0
\(433\) −32.0000 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(434\) 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 \(-0.291369\pi\)
−0.991322 + 0.131453i \(0.958036\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.0000 24.2487i −0.665160 1.15209i −0.979242 0.202695i \(-0.935030\pi\)
0.314082 0.949396i \(-0.398303\pi\)
\(444\) 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 0.787288 0.616585i \(-0.211484\pi\)
−0.927622 + 0.373519i \(0.878151\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 42.0000 1.95614 0.978068 0.208288i \(-0.0667892\pi\)
0.978068 + 0.208288i \(0.0667892\pi\)
\(462\) 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 0.992584 + 0.121563i \(0.0387905\pi\)
−0.391015 + 0.920384i \(0.627876\pi\)
\(468\) 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 0.0814184 + 0.996680i \(0.474055\pi\)
−0.903859 + 0.427830i \(0.859278\pi\)
\(480\) 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 −0.352241 0.935909i \(-0.614580\pi\)
0.986642 0.162905i \(-0.0520863\pi\)
\(488\) 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 0.817781 0.575529i \(-0.195204\pi\)
−0.907314 + 0.420455i \(0.861871\pi\)
\(500\) 0 0
\(501\) 4.00000 6.92820i 0.178707 0.309529i
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 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 \(-0.00455136\pi\)
−0.512331 + 0.858788i \(0.671218\pi\)
\(510\) 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 \(-0.977685\pi\)
0.559436 + 0.828874i \(0.311018\pi\)
\(522\) 0 0
\(523\) 9.00000 + 15.5885i 0.393543 + 0.681636i 0.992914 0.118835i \(-0.0379161\pi\)
−0.599371 + 0.800471i \(0.704583\pi\)
\(524\) 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 −0.984325 0.176367i \(-0.943566\pi\)
0.339424 0.940633i \(-0.389768\pi\)
\(542\) 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 −0.350824 0.936442i \(-0.614098\pi\)
0.986394 0.164399i \(-0.0525683\pi\)
\(558\) 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 \(-0.846752\pi\)
0.844183 + 0.536054i \(0.180086\pi\)
\(564\) 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 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) 6.00000 10.3923i 0.251092 0.434904i −0.712735 0.701434i \(-0.752544\pi\)
0.963827 + 0.266529i \(0.0858769\pi\)
\(572\) 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 \(-0.752974\pi\)
0.963466 + 0.267832i \(0.0863073\pi\)
\(578\) 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 \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 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 0.823009 + 0.568029i \(0.192294\pi\)
0.0804231 + 0.996761i \(0.474373\pi\)
\(594\) 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 −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 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 −0.983262 0.182199i \(-0.941678\pi\)
0.333842 0.942629i \(-0.391655\pi\)
\(608\) 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 −0.474509 0.880251i \(-0.657374\pi\)
0.999574 0.0291886i \(-0.00929235\pi\)
\(614\) 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 −0.389479 0.921036i \(-0.627345\pi\)
0.992379 0.123219i \(-0.0393219\pi\)
\(620\) 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 −0.694025 0.719951i \(-0.744164\pi\)
0.970508 + 0.241068i \(0.0774976\pi\)
\(642\) 0 0
\(643\) −30.0000 −1.18308 −0.591542 0.806274i \(-0.701481\pi\)
−0.591542 + 0.806274i \(0.701481\pi\)
\(644\) 0 0
\(645\) −8.00000 −0.315000
\(646\) 0 0
\(647\) −6.00000 + 10.3923i −0.235884 + 0.408564i −0.959529 0.281609i \(-0.909132\pi\)
0.723645 + 0.690172i \(0.242465\pi\)
\(648\) 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 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 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 \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 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 \(-0.0799630\pi\)
−0.699580 + 0.714554i \(0.746630\pi\)
\(678\) 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 −0.283491 0.958975i \(-0.591493\pi\)
0.972242 0.233977i \(-0.0751739\pi\)
\(684\) 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 −0.920348 0.391102i \(-0.872094\pi\)
0.121470 0.992595i \(-0.461239\pi\)
\(692\) 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 0.916845 0.399244i \(-0.130727\pi\)
−0.804178 + 0.594389i \(0.797394\pi\)
\(710\) 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 −0.977539 0.210752i \(-0.932409\pi\)
0.306253 0.951950i \(-0.400925\pi\)
\(720\) 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 \(-0.476367\pi\)
0.0741759 + 0.997245i \(0.476367\pi\)
\(728\) 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 \(-0.249912\pi\)
−0.965854 + 0.259087i \(0.916578\pi\)
\(734\) 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 −0.989230 0.146369i \(-0.953241\pi\)
0.621374 + 0.783514i \(0.286575\pi\)
\(740\) 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 0.682341 0.731034i \(-0.260962\pi\)
−0.974265 + 0.225407i \(0.927629\pi\)
\(752\) 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 \(-0.0968765\pi\)
−0.736543 + 0.676391i \(0.763543\pi\)
\(762\) 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 \(-0.522977\pi\)
−0.0721218 + 0.997396i \(0.522977\pi\)
\(770\) 0 0
\(771\) −56.0000 −2.01679
\(772\) 0 0
\(773\) −23.0000 + 39.8372i −0.827253 + 1.43284i 0.0729331 + 0.997337i \(0.476764\pi\)
−0.900186 + 0.435507i \(0.856569\pi\)
\(774\) 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 −0.199939 0.979808i \(-0.564075\pi\)
0.948509 0.316752i \(-0.102592\pi\)
\(788\) 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 \(-0.153785\pi\)
0.885545 + 0.464553i \(0.153785\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0