Properties

Label 2352.2.q.p.961.1
Level $2352$
Weight $2$
Character 2352.961
Analytic conductor $18.781$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.7808145554\)
Analytic rank: \(1\)
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: no (minimal twist has level 588)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2352.961
Dual form 2352.2.q.p.1537.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -4.00000 q^{13} -2.00000 q^{15} +(-3.00000 - 5.19615i) q^{17} +(4.00000 - 6.92820i) q^{19} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -10.0000 q^{29} +(2.00000 + 3.46410i) q^{31} +(-1.00000 + 1.73205i) q^{33} +(-3.00000 + 5.19615i) q^{37} +(-2.00000 - 3.46410i) q^{39} -6.00000 q^{41} -4.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(4.00000 - 6.92820i) q^{47} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{53} -4.00000 q^{55} +8.00000 q^{57} +(-2.00000 - 3.46410i) q^{59} +(4.00000 - 6.92820i) q^{61} +(4.00000 - 6.92820i) q^{65} +(-4.00000 - 6.92820i) q^{67} -6.00000 q^{69} +10.0000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} +12.0000 q^{85} +(-5.00000 - 8.66025i) q^{87} +(7.00000 - 12.1244i) q^{89} +(-2.00000 + 3.46410i) q^{93} +(8.00000 + 13.8564i) q^{95} +4.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - 2q^{5} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - 2q^{5} - q^{9} + 2q^{11} - 8q^{13} - 4q^{15} - 6q^{17} + 8q^{19} - 6q^{23} + q^{25} - 2q^{27} - 20q^{29} + 4q^{31} - 2q^{33} - 6q^{37} - 4q^{39} - 12q^{41} - 8q^{43} - 2q^{45} + 8q^{47} + 6q^{51} - 2q^{53} - 8q^{55} + 16q^{57} - 4q^{59} + 8q^{61} + 8q^{65} - 8q^{67} - 12q^{69} + 20q^{71} - 4q^{73} - q^{75} + 4q^{79} - q^{81} - 24q^{83} + 24q^{85} - 10q^{87} + 14q^{89} - 4q^{93} + 16q^{95} + 8q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1471\) \(1765\) \(2257\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 0 0
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0 0
\(19\) 4.00000 6.92820i 0.917663 1.58944i 0.114708 0.993399i \(-0.463407\pi\)
0.802955 0.596040i \(-0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −10.0000 −1.85695 −0.928477 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 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
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i \(-0.997505\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(38\) 0 0
\(39\) −2.00000 3.46410i −0.320256 0.554700i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 0 0
\(47\) 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i \(-0.635032\pi\)
0.995066 0.0992202i \(-0.0316348\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) 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
\(57\) 8.00000 1.05963
\(58\) 0 0
\(59\) −2.00000 3.46410i −0.260378 0.450988i 0.705965 0.708247i \(-0.250514\pi\)
−0.966342 + 0.257260i \(0.917180\pi\)
\(60\) 0 0
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.00000 6.92820i 0.496139 0.859338i
\(66\) 0 0
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 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
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 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
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 12.0000 1.30158
\(86\) 0 0
\(87\) −5.00000 8.66025i −0.536056 0.928477i
\(88\) 0 0
\(89\) 7.00000 12.1244i 0.741999 1.28518i −0.209585 0.977790i \(-0.567211\pi\)
0.951584 0.307389i \(-0.0994552\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 + 3.46410i −0.207390 + 0.359211i
\(94\) 0 0
\(95\) 8.00000 + 13.8564i 0.820783 + 1.42164i
\(96\) 0 0
\(97\) 4.00000 0.406138 0.203069 0.979164i \(-0.434908\pi\)
0.203069 + 0.979164i \(0.434908\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) 5.00000 + 8.66025i 0.497519 + 0.861727i 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) 0 0
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.00000 + 12.1244i −0.676716 + 1.17211i 0.299249 + 0.954175i \(0.403264\pi\)
−0.975964 + 0.217931i \(0.930069\pi\)
\(108\) 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
\(111\) −6.00000 −0.569495
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) −6.00000 10.3923i −0.559503 0.969087i
\(116\) 0 0
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −3.00000 5.19615i −0.270501 0.468521i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 4.00000 0.354943 0.177471 0.984126i \(-0.443208\pi\)
0.177471 + 0.984126i \(0.443208\pi\)
\(128\) 0 0
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 0 0
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 1.00000 1.73205i 0.0860663 0.149071i
\(136\) 0 0
\(137\) 5.00000 + 8.66025i 0.427179 + 0.739895i 0.996621 0.0821359i \(-0.0261741\pi\)
−0.569442 + 0.822031i \(0.692841\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 0 0
\(143\) −4.00000 6.92820i −0.334497 0.579365i
\(144\) 0 0
\(145\) 10.0000 17.3205i 0.830455 1.43839i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.00000 + 1.73205i −0.0819232 + 0.141895i −0.904076 0.427372i \(-0.859440\pi\)
0.822153 + 0.569267i \(0.192773\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 8.00000 + 13.8564i 0.638470 + 1.10586i 0.985769 + 0.168107i \(0.0537655\pi\)
−0.347299 + 0.937754i \(0.612901\pi\)
\(158\) 0 0
\(159\) 1.00000 1.73205i 0.0793052 0.137361i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 12.0000 20.7846i 0.939913 1.62798i 0.174282 0.984696i \(-0.444240\pi\)
0.765631 0.643280i \(-0.222427\pi\)
\(164\) 0 0
\(165\) −2.00000 3.46410i −0.155700 0.269680i
\(166\) 0 0
\(167\) −16.0000 −1.23812 −0.619059 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 4.00000 + 6.92820i 0.305888 + 0.529813i
\(172\) 0 0
\(173\) 1.00000 1.73205i 0.0760286 0.131685i −0.825505 0.564396i \(-0.809109\pi\)
0.901533 + 0.432710i \(0.142443\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 2.00000 3.46410i 0.150329 0.260378i
\(178\) 0 0
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) 0 0
\(185\) −6.00000 10.3923i −0.441129 0.764057i
\(186\) 0 0
\(187\) 6.00000 10.3923i 0.438763 0.759961i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) 0 0
\(195\) 8.00000 0.572892
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 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
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) 0 0
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 5.00000 + 8.66025i 0.342594 + 0.593391i
\(214\) 0 0
\(215\) 4.00000 6.92820i 0.272798 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 2.00000 3.46410i 0.135147 0.234082i
\(220\) 0 0
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) 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
\(227\) 2.00000 + 3.46410i 0.132745 + 0.229920i 0.924734 0.380615i \(-0.124288\pi\)
−0.791989 + 0.610535i \(0.790954\pi\)
\(228\) 0 0
\(229\) −10.0000 + 17.3205i −0.660819 + 1.14457i 0.319582 + 0.947559i \(0.396457\pi\)
−0.980401 + 0.197013i \(0.936876\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.00000 + 12.1244i −0.458585 + 0.794293i −0.998886 0.0471787i \(-0.984977\pi\)
0.540301 + 0.841472i \(0.318310\pi\)
\(234\) 0 0
\(235\) 8.00000 + 13.8564i 0.521862 + 0.903892i
\(236\) 0 0
\(237\) 4.00000 0.259828
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) −14.0000 24.2487i −0.901819 1.56200i −0.825131 0.564942i \(-0.808899\pi\)
−0.0766885 0.997055i \(-0.524435\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −16.0000 + 27.7128i −1.01806 + 1.76332i
\(248\) 0 0
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 28.0000 1.76734 0.883672 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 0 0
\(255\) 6.00000 + 10.3923i 0.375735 + 0.650791i
\(256\) 0 0
\(257\) −5.00000 + 8.66025i −0.311891 + 0.540212i −0.978772 0.204953i \(-0.934296\pi\)
0.666880 + 0.745165i \(0.267629\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 5.00000 8.66025i 0.309492 0.536056i
\(262\) 0 0
\(263\) 13.0000 + 22.5167i 0.801614 + 1.38844i 0.918553 + 0.395298i \(0.129359\pi\)
−0.116939 + 0.993139i \(0.537308\pi\)
\(264\) 0 0
\(265\) 4.00000 0.245718
\(266\) 0 0
\(267\) 14.0000 0.856786
\(268\) 0 0
\(269\) −1.00000 1.73205i −0.0609711 0.105605i 0.833929 0.551872i \(-0.186086\pi\)
−0.894900 + 0.446267i \(0.852753\pi\)
\(270\) 0 0
\(271\) −2.00000 + 3.46410i −0.121491 + 0.210429i −0.920356 0.391082i \(-0.872101\pi\)
0.798865 + 0.601511i \(0.205434\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 0 0
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 8.00000 + 13.8564i 0.475551 + 0.823678i 0.999608 0.0280052i \(-0.00891551\pi\)
−0.524057 + 0.851683i \(0.675582\pi\)
\(284\) 0 0
\(285\) −8.00000 + 13.8564i −0.473879 + 0.820783i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 2.00000 + 3.46410i 0.117242 + 0.203069i
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) 0 0
\(299\) 12.0000 20.7846i 0.693978 1.20201i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −5.00000 + 8.66025i −0.287242 + 0.497519i
\(304\) 0 0
\(305\) 8.00000 + 13.8564i 0.458079 + 0.793416i
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 8.00000 + 13.8564i 0.453638 + 0.785725i 0.998609 0.0527306i \(-0.0167924\pi\)
−0.544970 + 0.838455i \(0.683459\pi\)
\(312\) 0 0
\(313\) −12.0000 + 20.7846i −0.678280 + 1.17482i 0.297218 + 0.954810i \(0.403941\pi\)
−0.975499 + 0.220006i \(0.929392\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) −10.0000 17.3205i −0.559893 0.969762i
\(320\) 0 0
\(321\) −14.0000 −0.781404
\(322\) 0 0
\(323\) −48.0000 −2.67079
\(324\) 0 0
\(325\) −2.00000 3.46410i −0.110940 0.192154i
\(326\) 0 0
\(327\) 5.00000 8.66025i 0.276501 0.478913i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 0 0
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) 0 0
\(335\) 16.0000 0.874173
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) −7.00000 12.1244i −0.380188 0.658505i
\(340\) 0 0
\(341\) −4.00000 + 6.92820i −0.216612 + 0.375183i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 6.00000 10.3923i 0.323029 0.559503i
\(346\) 0 0
\(347\) −9.00000 15.5885i −0.483145 0.836832i 0.516667 0.856186i \(-0.327172\pi\)
−0.999813 + 0.0193540i \(0.993839\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 0 0
\(355\) −10.0000 + 17.3205i −0.530745 + 0.919277i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.0000 19.0526i 0.580558 1.00556i −0.414855 0.909887i \(-0.636168\pi\)
0.995413 0.0956683i \(-0.0304988\pi\)
\(360\) 0 0
\(361\) −22.5000 38.9711i −1.18421 2.05111i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 8.00000 0.418739
\(366\) 0 0
\(367\) 8.00000 + 13.8564i 0.417597 + 0.723299i 0.995697 0.0926670i \(-0.0295392\pi\)
−0.578101 + 0.815966i \(0.696206\pi\)
\(368\) 0 0
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 13.0000 22.5167i 0.673114 1.16587i −0.303902 0.952703i \(-0.598289\pi\)
0.977016 0.213165i \(-0.0683772\pi\)
\(374\) 0 0
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 0 0
\(377\) 40.0000 2.06010
\(378\) 0 0
\(379\) 36.0000 1.84920 0.924598 0.380945i \(-0.124401\pi\)
0.924598 + 0.380945i \(0.124401\pi\)
\(380\) 0 0
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) 0 0
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 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 \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 0 0
\(393\) −12.0000 −0.605320
\(394\) 0 0
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) 0 0
\(397\) −16.0000 + 27.7128i −0.803017 + 1.39087i 0.114605 + 0.993411i \(0.463440\pi\)
−0.917622 + 0.397455i \(0.869893\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 0 0
\(403\) −8.00000 13.8564i −0.398508 0.690237i
\(404\) 0 0
\(405\) 2.00000 0.0993808
\(406\) 0 0
\(407\) −12.0000 −0.594818
\(408\) 0 0
\(409\) −6.00000 10.3923i −0.296681 0.513866i 0.678694 0.734422i \(-0.262546\pi\)
−0.975375 + 0.220555i \(0.929213\pi\)
\(410\) 0 0
\(411\) −5.00000 + 8.66025i −0.246632 + 0.427179i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 12.0000 20.7846i 0.589057 1.02028i
\(416\) 0 0
\(417\) −6.00000 10.3923i −0.293821 0.508913i
\(418\) 0 0
\(419\) 4.00000 0.195413 0.0977064 0.995215i \(-0.468849\pi\)
0.0977064 + 0.995215i \(0.468849\pi\)
\(420\) 0 0
\(421\) −6.00000 −0.292422 −0.146211 0.989253i \(-0.546708\pi\)
−0.146211 + 0.989253i \(0.546708\pi\)
\(422\) 0 0
\(423\) 4.00000 + 6.92820i 0.194487 + 0.336861i
\(424\) 0 0
\(425\) 3.00000 5.19615i 0.145521 0.252050i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.00000 6.92820i 0.193122 0.334497i
\(430\) 0 0
\(431\) −1.00000 1.73205i −0.0481683 0.0834300i 0.840936 0.541135i \(-0.182005\pi\)
−0.889104 + 0.457705i \(0.848672\pi\)
\(432\) 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
\(437\) 24.0000 + 41.5692i 1.14808 + 1.98853i
\(438\) 0 0
\(439\) −12.0000 + 20.7846i −0.572729 + 0.991995i 0.423556 + 0.905870i \(0.360782\pi\)
−0.996284 + 0.0861252i \(0.972552\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.00000 + 15.5885i −0.427603 + 0.740630i −0.996660 0.0816684i \(-0.973975\pi\)
0.569057 + 0.822298i \(0.307309\pi\)
\(444\) 0 0
\(445\) 14.0000 + 24.2487i 0.663664 + 1.14950i
\(446\) 0 0
\(447\) −2.00000 −0.0945968
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −6.00000 10.3923i −0.282529 0.489355i
\(452\) 0 0
\(453\) 4.00000 6.92820i 0.187936 0.325515i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) 0 0
\(459\) 3.00000 + 5.19615i 0.140028 + 0.242536i
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 0 0
\(465\) −4.00000 6.92820i −0.185496 0.321288i
\(466\) 0 0
\(467\) −10.0000 + 17.3205i −0.462745 + 0.801498i −0.999097 0.0424970i \(-0.986469\pi\)
0.536352 + 0.843995i \(0.319802\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −8.00000 + 13.8564i −0.368621 + 0.638470i
\(472\) 0 0
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) 8.00000 0.367065
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) 0 0
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) 12.0000 20.7846i 0.547153 0.947697i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.00000 + 6.92820i −0.181631 + 0.314594i
\(486\) 0 0
\(487\) 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) 0 0
\(489\) 24.0000 1.08532
\(490\) 0 0
\(491\) −6.00000 −0.270776 −0.135388 0.990793i \(-0.543228\pi\)
−0.135388 + 0.990793i \(0.543228\pi\)
\(492\) 0 0
\(493\) 30.0000 + 51.9615i 1.35113 + 2.34023i
\(494\) 0 0
\(495\) 2.00000 3.46410i 0.0898933 0.155700i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −18.0000 + 31.1769i −0.805791 + 1.39567i 0.109965 + 0.993935i \(0.464926\pi\)
−0.915756 + 0.401735i \(0.868407\pi\)
\(500\) 0 0
\(501\) −8.00000 13.8564i −0.357414 0.619059i
\(502\) 0 0
\(503\) −16.0000 −0.713405 −0.356702 0.934218i \(-0.616099\pi\)
−0.356702 + 0.934218i \(0.616099\pi\)
\(504\) 0 0
\(505\) −20.0000 −0.889988
\(506\) 0 0
\(507\) 1.50000 + 2.59808i 0.0666173 + 0.115385i
\(508\) 0 0
\(509\) −5.00000 + 8.66025i −0.221621 + 0.383859i −0.955300 0.295637i \(-0.904468\pi\)
0.733679 + 0.679496i \(0.237801\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −4.00000 + 6.92820i −0.176604 + 0.305888i
\(514\) 0 0
\(515\) −4.00000 6.92820i −0.176261 0.305293i
\(516\) 0 0
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) −11.0000 19.0526i −0.481919 0.834708i 0.517866 0.855462i \(-0.326727\pi\)
−0.999785 + 0.0207541i \(0.993393\pi\)
\(522\) 0 0
\(523\) −2.00000 + 3.46410i −0.0874539 + 0.151475i −0.906434 0.422347i \(-0.861206\pi\)
0.818980 + 0.573822i \(0.194540\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) −14.0000 24.2487i −0.605273 1.04836i
\(536\) 0 0
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −17.0000 + 29.4449i −0.730887 + 1.26593i 0.225617 + 0.974216i \(0.427560\pi\)
−0.956504 + 0.291718i \(0.905773\pi\)
\(542\) 0 0
\(543\) −10.0000 17.3205i −0.429141 0.743294i
\(544\) 0 0
\(545\) 20.0000 0.856706
\(546\) 0 0
\(547\) −16.0000 −0.684111 −0.342055 0.939680i \(-0.611123\pi\)
−0.342055 + 0.939680i \(0.611123\pi\)
\(548\) 0 0
\(549\) 4.00000 + 6.92820i 0.170716 + 0.295689i
\(550\) 0 0
\(551\) −40.0000 + 69.2820i −1.70406 + 2.95151i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 6.00000 10.3923i 0.254686 0.441129i
\(556\) 0 0
\(557\) 3.00000 + 5.19615i 0.127114 + 0.220168i 0.922557 0.385860i \(-0.126095\pi\)
−0.795443 + 0.606028i \(0.792762\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 12.0000 0.506640
\(562\) 0 0
\(563\) 2.00000 + 3.46410i 0.0842900 + 0.145994i 0.905088 0.425223i \(-0.139804\pi\)
−0.820798 + 0.571218i \(0.806471\pi\)
\(564\) 0 0
\(565\) 14.0000 24.2487i 0.588984 1.02015i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) 4.00000 + 6.92820i 0.166522 + 0.288425i 0.937195 0.348806i \(-0.113413\pi\)
−0.770673 + 0.637231i \(0.780080\pi\)
\(578\) 0 0
\(579\) −5.00000 + 8.66025i −0.207793 + 0.359908i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2.00000 3.46410i 0.0828315 0.143468i
\(584\) 0 0
\(585\) 4.00000 + 6.92820i 0.165380 + 0.286446i
\(586\) 0 0
\(587\) 4.00000 0.165098 0.0825488 0.996587i \(-0.473694\pi\)
0.0825488 + 0.996587i \(0.473694\pi\)
\(588\) 0 0
\(589\) 32.0000 1.31854
\(590\) 0 0
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) 0 0
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 4.00000 6.92820i 0.163709 0.283552i
\(598\) 0 0
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) 0 0
\(605\) 7.00000 + 12.1244i 0.284590 + 0.492925i
\(606\) 0 0
\(607\) 12.0000 20.7846i 0.487065 0.843621i −0.512824 0.858494i \(-0.671401\pi\)
0.999889 + 0.0148722i \(0.00473415\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16.0000 + 27.7128i −0.647291 + 1.12114i
\(612\) 0 0
\(613\) −13.0000 22.5167i −0.525065 0.909439i −0.999574 0.0291886i \(-0.990708\pi\)
0.474509 0.880251i \(-0.342626\pi\)
\(614\) 0 0
\(615\) 12.0000 0.483887
\(616\) 0 0
\(617\) −2.00000 −0.0805170 −0.0402585 0.999189i \(-0.512818\pi\)
−0.0402585 + 0.999189i \(0.512818\pi\)
\(618\) 0 0
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) 0 0
\(621\) 3.00000 5.19615i 0.120386 0.208514i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 8.00000 + 13.8564i 0.319489 + 0.553372i
\(628\) 0 0
\(629\) 36.0000 1.43541
\(630\) 0 0
\(631\) −12.0000 −0.477712 −0.238856 0.971055i \(-0.576772\pi\)
−0.238856 + 0.971055i \(0.576772\pi\)
\(632\) 0 0
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) 0 0
\(635\) −4.00000 + 6.92820i −0.158735 + 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −5.00000 + 8.66025i −0.197797 + 0.342594i
\(640\) 0 0
\(641\) 13.0000 + 22.5167i 0.513469 + 0.889355i 0.999878 + 0.0156233i \(0.00497325\pi\)
−0.486409 + 0.873731i \(0.661693\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 0 0
\(647\) −24.0000 41.5692i −0.943537 1.63425i −0.758654 0.651494i \(-0.774142\pi\)
−0.184884 0.982760i \(-0.559191\pi\)
\(648\) 0 0
\(649\) 4.00000 6.92820i 0.157014 0.271956i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 17.0000 29.4449i 0.665261 1.15227i −0.313953 0.949439i \(-0.601653\pi\)
0.979214 0.202828i \(-0.0650132\pi\)
\(654\) 0 0
\(655\) −12.0000 20.7846i −0.468879 0.812122i
\(656\) 0 0
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) 14.0000 0.545363 0.272681 0.962104i \(-0.412090\pi\)
0.272681 + 0.962104i \(0.412090\pi\)
\(660\) 0 0
\(661\) −4.00000 6.92820i −0.155582 0.269476i 0.777689 0.628649i \(-0.216392\pi\)
−0.933271 + 0.359174i \(0.883059\pi\)
\(662\) 0 0
\(663\) −12.0000 + 20.7846i −0.466041 + 0.807207i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 30.0000 51.9615i 1.16160 2.01196i
\(668\) 0 0
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 0 0
\(671\) 16.0000 0.617673
\(672\) 0 0
\(673\) −22.0000 −0.848038 −0.424019 0.905653i \(-0.639381\pi\)
−0.424019 + 0.905653i \(0.639381\pi\)
\(674\) 0 0
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 0 0
\(677\) −15.0000 + 25.9808i −0.576497 + 0.998522i 0.419380 + 0.907811i \(0.362247\pi\)
−0.995877 + 0.0907112i \(0.971086\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −2.00000 + 3.46410i −0.0766402 + 0.132745i
\(682\) 0 0
\(683\) 11.0000 + 19.0526i 0.420903 + 0.729026i 0.996028 0.0890398i \(-0.0283798\pi\)
−0.575125 + 0.818066i \(0.695047\pi\)
\(684\) 0 0
\(685\) −20.0000 −0.764161
\(686\) 0 0
\(687\) −20.0000 −0.763048
\(688\) 0 0
\(689\) 4.00000 + 6.92820i 0.152388 + 0.263944i
\(690\) 0 0
\(691\) −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i \(-0.957553\pi\)
0.610704 + 0.791859i \(0.290887\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 12.0000 20.7846i 0.455186 0.788405i
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 0 0
\(699\) −14.0000 −0.529529
\(700\) 0 0
\(701\) −50.0000 −1.88847 −0.944237 0.329267i \(-0.893198\pi\)
−0.944237 + 0.329267i \(0.893198\pi\)
\(702\) 0 0
\(703\) 24.0000 + 41.5692i 0.905177 + 1.56781i
\(704\) 0 0
\(705\) −8.00000 + 13.8564i −0.301297 + 0.521862i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 7.00000 12.1244i 0.262891 0.455340i −0.704118 0.710083i \(-0.748658\pi\)
0.967009 + 0.254743i \(0.0819909\pi\)
\(710\) 0 0
\(711\) 2.00000 + 3.46410i 0.0750059 + 0.129914i
\(712\) 0 0
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) 16.0000 0.598366
\(716\) 0 0
\(717\) −9.00000 15.5885i −0.336111 0.582162i
\(718\) 0 0
\(719\) 24.0000 41.5692i 0.895049 1.55027i 0.0613050 0.998119i \(-0.480474\pi\)
0.833744 0.552151i \(-0.186193\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 14.0000 24.2487i 0.520666 0.901819i
\(724\) 0 0
\(725\) −5.00000 8.66025i −0.185695 0.321634i
\(726\) 0 0
\(727\) −44.0000 −1.63187 −0.815935 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) 0 0
\(733\) −2.00000 + 3.46410i −0.0738717 + 0.127950i −0.900595 0.434659i \(-0.856869\pi\)
0.826723 + 0.562609i \(0.190202\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8.00000 13.8564i 0.294684 0.510407i
\(738\) 0 0
\(739\) 20.0000 + 34.6410i 0.735712 + 1.27429i 0.954410 + 0.298498i \(0.0964856\pi\)
−0.218698 + 0.975793i \(0.570181\pi\)
\(740\) 0 0
\(741\) −32.0000 −1.17555
\(742\) 0 0
\(743\) 18.0000 0.660356 0.330178 0.943919i \(-0.392891\pi\)
0.330178 + 0.943919i \(0.392891\pi\)
\(744\) 0 0
\(745\) −2.00000 3.46410i −0.0732743 0.126915i
\(746\) 0 0
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −24.0000 + 41.5692i −0.875772 + 1.51688i −0.0198348 + 0.999803i \(0.506314\pi\)
−0.855938 + 0.517079i \(0.827019\pi\)
\(752\) 0 0
\(753\) 14.0000 + 24.2487i 0.510188 + 0.883672i
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) −14.0000 −0.508839 −0.254419 0.967094i \(-0.581884\pi\)
−0.254419 + 0.967094i \(0.581884\pi\)
\(758\) 0 0
\(759\) −6.00000 10.3923i −0.217786 0.377217i
\(760\) 0 0
\(761\) 11.0000 19.0526i 0.398750 0.690655i −0.594822 0.803857i \(-0.702778\pi\)
0.993572 + 0.113203i \(0.0361109\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −6.00000 + 10.3923i −0.216930 + 0.375735i
\(766\) 0 0
\(767\) 8.00000 + 13.8564i 0.288863 + 0.500326i
\(768\) 0 0
\(769\) 32.0000 1.15395 0.576975 0.816762i \(-0.304233\pi\)
0.576975 + 0.816762i \(0.304233\pi\)
\(770\) 0 0
\(771\) −10.0000 −0.360141
\(772\) 0 0
\(773\) −3.00000 5.19615i −0.107903 0.186893i 0.807018 0.590527i \(-0.201080\pi\)
−0.914920 + 0.403634i \(0.867747\pi\)
\(774\) 0 0
\(775\) −2.00000 + 3.46410i −0.0718421 + 0.124434i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24.0000 + 41.5692i −0.859889 + 1.48937i
\(780\) 0 0
\(781\) 10.0000 + 17.3205i 0.357828 + 0.619777i
\(782\) 0 0
\(783\) 10.0000 0.357371
\(784\) 0 0
\(785\) −32.0000 −1.14213
\(786\) 0 0
\(787\) 2.00000 + 3.46410i 0.0712923 + 0.123482i 0.899468 0.436987i \(-0.143954\pi\)
−0.828176 + 0.560469i \(0.810621\pi\)
\(788\) 0 0
\(789\) −13.0000 + 22.5167i −0.462812 + 0.801614i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −16.0000 + 27.7128i −0.568177 + 0.984111i
\(794\) 0 0
\(795\) 2.00000 + 3.46410i 0.0709327 + 0.122859i
\(796\) 0 0
\(797\) 6.00000 0.212531 0.106265 0.994338i \(-0.466111\pi\)
0.106265 + 0.994338i \(0.466111\pi\)
\(798\) 0 0
\(799\) −48.0000 −1.69812
\(800\)