Properties

Label 2592.2.s.a.1727.4
Level $2592$
Weight $2$
Character 2592.1727
Analytic conductor $20.697$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2592.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 864)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1727.4
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2592.1727
Dual form 2592.2.s.a.863.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.275255 + 0.158919i) q^{5} +(1.25529 + 0.724745i) q^{7} +O(q^{10})\) \(q+(-0.275255 + 0.158919i) q^{5} +(1.25529 + 0.724745i) q^{7} +(-0.548188 + 0.949490i) q^{11} +(-1.44949 - 2.51059i) q^{13} +3.46410i q^{17} -4.89898i q^{19} +(1.41421 + 2.44949i) q^{23} +(-2.44949 + 4.24264i) q^{25} +(7.89898 + 4.56048i) q^{29} +(-6.45145 + 3.72474i) q^{31} -0.460702 q^{35} +4.89898 q^{37} +(8.44949 - 4.87832i) q^{41} +(5.97469 + 3.44949i) q^{43} +(-4.56048 + 7.89898i) q^{47} +(-2.44949 - 4.24264i) q^{49} -4.41761i q^{53} -0.348469i q^{55} +(4.56048 + 7.89898i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(0.797959 + 0.460702i) q^{65} +(4.41761 - 2.55051i) q^{67} -7.56388 q^{71} +1.89898 q^{73} +(-1.37628 + 0.794593i) q^{77} +(-1.73205 - 1.00000i) q^{79} +(-7.93709 + 13.7474i) q^{83} +(-0.550510 - 0.953512i) q^{85} +11.9494i q^{89} -4.20204i q^{91} +(0.778539 + 1.34847i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 12q^{5} + O(q^{10}) \) \( 8q - 12q^{5} + 8q^{13} + 24q^{29} + 48q^{41} - 16q^{61} - 72q^{65} - 24q^{73} - 60q^{77} - 24q^{85} + 20q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −0.275255 + 0.158919i −0.123098 + 0.0710706i −0.560285 0.828300i \(-0.689308\pi\)
0.437187 + 0.899371i \(0.355975\pi\)
\(6\) 0 0
\(7\) 1.25529 + 0.724745i 0.474457 + 0.273928i 0.718104 0.695936i \(-0.245010\pi\)
−0.243647 + 0.969864i \(0.578344\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.548188 + 0.949490i −0.165285 + 0.286282i −0.936756 0.349982i \(-0.886188\pi\)
0.771471 + 0.636264i \(0.219521\pi\)
\(12\) 0 0
\(13\) −1.44949 2.51059i −0.402016 0.696312i 0.591953 0.805972i \(-0.298357\pi\)
−0.993969 + 0.109660i \(0.965024\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.46410i 0.840168i 0.907485 + 0.420084i \(0.137999\pi\)
−0.907485 + 0.420084i \(0.862001\pi\)
\(18\) 0 0
\(19\) 4.89898i 1.12390i −0.827170 0.561951i \(-0.810051\pi\)
0.827170 0.561951i \(-0.189949\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.41421 + 2.44949i 0.294884 + 0.510754i 0.974958 0.222390i \(-0.0713857\pi\)
−0.680074 + 0.733144i \(0.738052\pi\)
\(24\) 0 0
\(25\) −2.44949 + 4.24264i −0.489898 + 0.848528i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.89898 + 4.56048i 1.46680 + 0.846859i 0.999310 0.0371370i \(-0.0118238\pi\)
0.467493 + 0.883997i \(0.345157\pi\)
\(30\) 0 0
\(31\) −6.45145 + 3.72474i −1.15871 + 0.668984i −0.950996 0.309205i \(-0.899937\pi\)
−0.207719 + 0.978189i \(0.566604\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.460702 −0.0778728
\(36\) 0 0
\(37\) 4.89898 0.805387 0.402694 0.915335i \(-0.368074\pi\)
0.402694 + 0.915335i \(0.368074\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8.44949 4.87832i 1.31959 0.761865i 0.335926 0.941888i \(-0.390951\pi\)
0.983662 + 0.180023i \(0.0576174\pi\)
\(42\) 0 0
\(43\) 5.97469 + 3.44949i 0.911132 + 0.526042i 0.880795 0.473497i \(-0.157009\pi\)
0.0303367 + 0.999540i \(0.490342\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.56048 + 7.89898i −0.665214 + 1.15218i 0.314013 + 0.949419i \(0.398326\pi\)
−0.979227 + 0.202766i \(0.935007\pi\)
\(48\) 0 0
\(49\) −2.44949 4.24264i −0.349927 0.606092i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.41761i 0.606806i −0.952862 0.303403i \(-0.901877\pi\)
0.952862 0.303403i \(-0.0981228\pi\)
\(54\) 0 0
\(55\) 0.348469i 0.0469876i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.56048 + 7.89898i 0.593724 + 1.02836i 0.993726 + 0.111845i \(0.0356761\pi\)
−0.400002 + 0.916514i \(0.630991\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.797959 + 0.460702i 0.0989746 + 0.0571430i
\(66\) 0 0
\(67\) 4.41761 2.55051i 0.539697 0.311594i −0.205259 0.978708i \(-0.565804\pi\)
0.744956 + 0.667113i \(0.232470\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.56388 −0.897667 −0.448834 0.893615i \(-0.648160\pi\)
−0.448834 + 0.893615i \(0.648160\pi\)
\(72\) 0 0
\(73\) 1.89898 0.222259 0.111129 0.993806i \(-0.464553\pi\)
0.111129 + 0.993806i \(0.464553\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.37628 + 0.794593i −0.156841 + 0.0905523i
\(78\) 0 0
\(79\) −1.73205 1.00000i −0.194871 0.112509i 0.399390 0.916781i \(-0.369222\pi\)
−0.594261 + 0.804272i \(0.702555\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.93709 + 13.7474i −0.871209 + 1.50898i −0.0104623 + 0.999945i \(0.503330\pi\)
−0.860747 + 0.509033i \(0.830003\pi\)
\(84\) 0 0
\(85\) −0.550510 0.953512i −0.0597112 0.103423i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 11.9494i 1.26663i 0.773893 + 0.633316i \(0.218307\pi\)
−0.773893 + 0.633316i \(0.781693\pi\)
\(90\) 0 0
\(91\) 4.20204i 0.440494i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.778539 + 1.34847i 0.0798764 + 0.138350i
\(96\) 0 0
\(97\) 2.50000 4.33013i 0.253837 0.439658i −0.710742 0.703452i \(-0.751641\pi\)
0.964579 + 0.263795i \(0.0849741\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.6237 + 7.86566i 1.35561 + 0.782663i 0.989029 0.147723i \(-0.0471944\pi\)
0.366582 + 0.930386i \(0.380528\pi\)
\(102\) 0 0
\(103\) −8.66025 + 5.00000i −0.853320 + 0.492665i −0.861770 0.507300i \(-0.830644\pi\)
0.00844953 + 0.999964i \(0.497310\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.66025 −0.837218 −0.418609 0.908166i \(-0.637482\pi\)
−0.418609 + 0.908166i \(0.637482\pi\)
\(108\) 0 0
\(109\) −4.89898 −0.469237 −0.234619 0.972088i \(-0.575384\pi\)
−0.234619 + 0.972088i \(0.575384\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 12.2474 7.07107i 1.15214 0.665190i 0.202735 0.979234i \(-0.435017\pi\)
0.949409 + 0.314044i \(0.101684\pi\)
\(114\) 0 0
\(115\) −0.778539 0.449490i −0.0725991 0.0419151i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.51059 + 4.34847i −0.230145 + 0.398624i
\(120\) 0 0
\(121\) 4.89898 + 8.48528i 0.445362 + 0.771389i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.14626i 0.281410i
\(126\) 0 0
\(127\) 15.2474i 1.35299i 0.736446 + 0.676496i \(0.236502\pi\)
−0.736446 + 0.676496i \(0.763498\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.50170 2.60102i −0.131204 0.227252i 0.792937 0.609304i \(-0.208551\pi\)
−0.924141 + 0.382052i \(0.875218\pi\)
\(132\) 0 0
\(133\) 3.55051 6.14966i 0.307868 0.533244i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.24745 + 5.33902i 0.790063 + 0.456143i 0.839985 0.542610i \(-0.182564\pi\)
−0.0499218 + 0.998753i \(0.515897\pi\)
\(138\) 0 0
\(139\) 17.3205 10.0000i 1.46911 0.848189i 0.469706 0.882823i \(-0.344360\pi\)
0.999400 + 0.0346338i \(0.0110265\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.17837 0.265789
\(144\) 0 0
\(145\) −2.89898 −0.240747
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.27526 1.89097i 0.268319 0.154914i −0.359804 0.933028i \(-0.617157\pi\)
0.628124 + 0.778114i \(0.283823\pi\)
\(150\) 0 0
\(151\) −14.9367 8.62372i −1.21553 0.701789i −0.251574 0.967838i \(-0.580948\pi\)
−0.963959 + 0.266049i \(0.914282\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.18386 2.05051i 0.0950901 0.164701i
\(156\) 0 0
\(157\) 6.89898 + 11.9494i 0.550599 + 0.953665i 0.998231 + 0.0594472i \(0.0189338\pi\)
−0.447633 + 0.894217i \(0.647733\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.09978i 0.323108i
\(162\) 0 0
\(163\) 6.00000i 0.469956i −0.972001 0.234978i \(-0.924498\pi\)
0.972001 0.234978i \(-0.0755019\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 11.4887 + 19.8990i 0.889021 + 1.53983i 0.841035 + 0.540981i \(0.181947\pi\)
0.0479862 + 0.998848i \(0.484720\pi\)
\(168\) 0 0
\(169\) 2.29796 3.98018i 0.176766 0.306168i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.62372 + 2.66951i 0.351535 + 0.202959i 0.665361 0.746522i \(-0.268278\pi\)
−0.313826 + 0.949481i \(0.601611\pi\)
\(174\) 0 0
\(175\) −6.14966 + 3.55051i −0.464871 + 0.268393i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.66025 0.647298 0.323649 0.946177i \(-0.395090\pi\)
0.323649 + 0.946177i \(0.395090\pi\)
\(180\) 0 0
\(181\) −9.79796 −0.728277 −0.364138 0.931345i \(-0.618636\pi\)
−0.364138 + 0.931345i \(0.618636\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.34847 + 0.778539i −0.0991414 + 0.0572393i
\(186\) 0 0
\(187\) −3.28913 1.89898i −0.240525 0.138867i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.80312 + 15.2474i −0.636971 + 1.10327i 0.349123 + 0.937077i \(0.386480\pi\)
−0.986094 + 0.166190i \(0.946854\pi\)
\(192\) 0 0
\(193\) −1.05051 1.81954i −0.0756174 0.130973i 0.825737 0.564055i \(-0.190759\pi\)
−0.901355 + 0.433082i \(0.857426\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.2672i 0.874003i 0.899461 + 0.437002i \(0.143960\pi\)
−0.899461 + 0.437002i \(0.856040\pi\)
\(198\) 0 0
\(199\) 20.3485i 1.44246i 0.692693 + 0.721232i \(0.256424\pi\)
−0.692693 + 0.721232i \(0.743576\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.61037 + 11.4495i 0.463957 + 0.803597i
\(204\) 0 0
\(205\) −1.55051 + 2.68556i −0.108292 + 0.187568i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.65153 + 2.68556i 0.321753 + 0.185764i
\(210\) 0 0
\(211\) 24.6773 14.2474i 1.69886 0.980835i 0.752007 0.659155i \(-0.229086\pi\)
0.946848 0.321680i \(-0.104248\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.19275 −0.149544
\(216\) 0 0
\(217\) −10.7980 −0.733013
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 8.69694 5.02118i 0.585019 0.337761i
\(222\) 0 0
\(223\) −0.174973 0.101021i −0.0117170 0.00676483i 0.494130 0.869388i \(-0.335487\pi\)
−0.505847 + 0.862623i \(0.668820\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.83183 + 10.1010i −0.387072 + 0.670428i −0.992054 0.125811i \(-0.959847\pi\)
0.604982 + 0.796239i \(0.293180\pi\)
\(228\) 0 0
\(229\) −1.00000 1.73205i −0.0660819 0.114457i 0.831092 0.556136i \(-0.187717\pi\)
−0.897173 + 0.441679i \(0.854383\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.2207i 0.866119i −0.901365 0.433059i \(-0.857434\pi\)
0.901365 0.433059i \(-0.142566\pi\)
\(234\) 0 0
\(235\) 2.89898i 0.189109i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −10.5352 18.2474i −0.681463 1.18033i −0.974534 0.224239i \(-0.928011\pi\)
0.293071 0.956091i \(-0.405323\pi\)
\(240\) 0 0
\(241\) 9.89898 17.1455i 0.637649 1.10444i −0.348298 0.937384i \(-0.613240\pi\)
0.985947 0.167057i \(-0.0534264\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.34847 + 0.778539i 0.0861505 + 0.0497390i
\(246\) 0 0
\(247\) −12.2993 + 7.10102i −0.782588 + 0.451827i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −17.3205 −1.09326 −0.546630 0.837374i \(-0.684090\pi\)
−0.546630 + 0.837374i \(0.684090\pi\)
\(252\) 0 0
\(253\) −3.10102 −0.194959
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −10.1010 + 5.83183i −0.630084 + 0.363779i −0.780785 0.624800i \(-0.785180\pi\)
0.150700 + 0.988579i \(0.451847\pi\)
\(258\) 0 0
\(259\) 6.14966 + 3.55051i 0.382122 + 0.220618i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.4422 21.5505i 0.767218 1.32886i −0.171847 0.985124i \(-0.554974\pi\)
0.939066 0.343738i \(-0.111693\pi\)
\(264\) 0 0
\(265\) 0.702041 + 1.21597i 0.0431260 + 0.0746965i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 10.3923i 0.633630i 0.948487 + 0.316815i \(0.102613\pi\)
−0.948487 + 0.316815i \(0.897387\pi\)
\(270\) 0 0
\(271\) 12.5505i 0.762389i 0.924495 + 0.381195i \(0.124487\pi\)
−0.924495 + 0.381195i \(0.875513\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.68556 4.65153i −0.161946 0.280498i
\(276\) 0 0
\(277\) 6.89898 11.9494i 0.414520 0.717969i −0.580858 0.814005i \(-0.697283\pi\)
0.995378 + 0.0960358i \(0.0306163\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.797959 0.460702i −0.0476022 0.0274832i 0.476010 0.879440i \(-0.342083\pi\)
−0.523612 + 0.851957i \(0.675416\pi\)
\(282\) 0 0
\(283\) 2.68556 1.55051i 0.159640 0.0921683i −0.418052 0.908423i \(-0.637287\pi\)
0.577692 + 0.816255i \(0.303954\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 14.1421 0.834784
\(288\) 0 0
\(289\) 5.00000 0.294118
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5.20204 3.00340i 0.303906 0.175460i −0.340290 0.940321i \(-0.610525\pi\)
0.644196 + 0.764860i \(0.277192\pi\)
\(294\) 0 0
\(295\) −2.51059 1.44949i −0.146172 0.0843926i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.09978 7.10102i 0.237096 0.410663i
\(300\) 0 0
\(301\) 5.00000 + 8.66025i 0.288195 + 0.499169i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.27135i 0.0727972i
\(306\) 0 0
\(307\) 18.0000i 1.02731i −0.857996 0.513657i \(-0.828290\pi\)
0.857996 0.513657i \(-0.171710\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.04989 3.55051i −0.116238 0.201331i 0.802036 0.597276i \(-0.203750\pi\)
−0.918274 + 0.395945i \(0.870417\pi\)
\(312\) 0 0
\(313\) −14.7474 + 25.5433i −0.833575 + 1.44379i 0.0616102 + 0.998100i \(0.480376\pi\)
−0.895185 + 0.445694i \(0.852957\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −25.6237 14.7939i −1.43917 0.830906i −0.441380 0.897320i \(-0.645511\pi\)
−0.997792 + 0.0664143i \(0.978844\pi\)
\(318\) 0 0
\(319\) −8.66025 + 5.00000i −0.484881 + 0.279946i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 16.9706 0.944267
\(324\) 0 0
\(325\) 14.2020 0.787787
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −11.4495 + 6.61037i −0.631231 + 0.364441i
\(330\) 0 0
\(331\) 0.603566 + 0.348469i 0.0331750 + 0.0191536i 0.516496 0.856290i \(-0.327236\pi\)
−0.483321 + 0.875443i \(0.660570\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.810647 + 1.40408i −0.0442904 + 0.0767132i
\(336\) 0 0
\(337\) −2.10102 3.63907i −0.114450 0.198233i 0.803110 0.595831i \(-0.203177\pi\)
−0.917560 + 0.397598i \(0.869844\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 8.16744i 0.442292i
\(342\) 0 0
\(343\) 17.2474i 0.931275i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.74094 4.74745i −0.147141 0.254856i 0.783028 0.621986i \(-0.213674\pi\)
−0.930170 + 0.367130i \(0.880341\pi\)
\(348\) 0 0
\(349\) −12.4495 + 21.5631i −0.666406 + 1.15425i 0.312496 + 0.949919i \(0.398835\pi\)
−0.978902 + 0.204330i \(0.934498\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.2474 + 7.07107i 0.651866 + 0.376355i 0.789171 0.614174i \(-0.210511\pi\)
−0.137305 + 0.990529i \(0.543844\pi\)
\(354\) 0 0
\(355\) 2.08200 1.20204i 0.110501 0.0637977i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −34.2911 −1.80981 −0.904907 0.425610i \(-0.860060\pi\)
−0.904907 + 0.425610i \(0.860060\pi\)
\(360\) 0 0
\(361\) −5.00000 −0.263158
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.522704 + 0.301783i −0.0273596 + 0.0157961i
\(366\) 0 0
\(367\) −7.40496 4.27526i −0.386536 0.223167i 0.294122 0.955768i \(-0.404973\pi\)
−0.680658 + 0.732601i \(0.738306\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.20164 5.54541i 0.166221 0.287903i
\(372\) 0 0
\(373\) −17.2474 29.8735i −0.893039 1.54679i −0.836213 0.548405i \(-0.815235\pi\)
−0.0568261 0.998384i \(-0.518098\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 26.4415i 1.36180i
\(378\) 0 0
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.87492 + 3.24745i 0.0958037 + 0.165937i 0.909944 0.414732i \(-0.136125\pi\)
−0.814140 + 0.580669i \(0.802791\pi\)
\(384\) 0 0
\(385\) 0.252551 0.437432i 0.0128712 0.0222936i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −27.7702 16.0331i −1.40800 0.812911i −0.412807 0.910818i \(-0.635452\pi\)
−0.995195 + 0.0979078i \(0.968785\pi\)
\(390\) 0 0
\(391\) −8.48528 + 4.89898i −0.429119 + 0.247752i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.635674 0.0319843
\(396\) 0 0
\(397\) 8.69694 0.436487 0.218243 0.975894i \(-0.429967\pi\)
0.218243 + 0.975894i \(0.429967\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −19.5959 + 11.3137i −0.978573 + 0.564980i −0.901839 0.432072i \(-0.857783\pi\)
−0.0767343 + 0.997052i \(0.524449\pi\)
\(402\) 0 0
\(403\) 18.7026 + 10.7980i 0.931644 + 0.537885i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.68556 + 4.65153i −0.133118 + 0.230568i
\(408\) 0 0
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 13.2207i 0.650550i
\(414\) 0 0
\(415\) 5.04541i 0.247669i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13.0458 22.5959i −0.637327 1.10388i −0.986017 0.166645i \(-0.946707\pi\)
0.348690 0.937238i \(-0.386627\pi\)
\(420\) 0 0
\(421\) 14.8990 25.8058i 0.726132 1.25770i −0.232375 0.972626i \(-0.574650\pi\)
0.958506 0.285071i \(-0.0920171\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −14.6969 8.48528i −0.712906 0.411597i
\(426\) 0 0
\(427\) −5.02118 + 2.89898i −0.242992 + 0.140291i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.3629 1.31802 0.659011 0.752133i \(-0.270975\pi\)
0.659011 + 0.752133i \(0.270975\pi\)
\(432\) 0 0
\(433\) 32.3939 1.55675 0.778375 0.627799i \(-0.216044\pi\)
0.778375 + 0.627799i \(0.216044\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 12.0000 6.92820i 0.574038 0.331421i
\(438\) 0 0
\(439\) 16.6688 + 9.62372i 0.795557 + 0.459315i 0.841915 0.539610i \(-0.181428\pi\)
−0.0463579 + 0.998925i \(0.514761\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 14.3171 24.7980i 0.680226 1.17819i −0.294685 0.955594i \(-0.595215\pi\)
0.974912 0.222592i \(-0.0714518\pi\)
\(444\) 0 0
\(445\) −1.89898 3.28913i −0.0900203 0.155920i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.3417i 1.05437i −0.849751 0.527185i \(-0.823248\pi\)
0.849751 0.527185i \(-0.176752\pi\)
\(450\) 0 0
\(451\) 10.6969i 0.503699i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.667783 + 1.15663i 0.0313061 + 0.0542238i
\(456\) 0 0
\(457\) −12.5000 + 21.6506i −0.584725 + 1.01277i 0.410184 + 0.912003i \(0.365464\pi\)
−0.994910 + 0.100771i \(0.967869\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.62372 0.937458i −0.0756244 0.0436618i 0.461711 0.887030i \(-0.347236\pi\)
−0.537335 + 0.843369i \(0.680569\pi\)
\(462\) 0 0
\(463\) −23.4220 + 13.5227i −1.08851 + 0.628453i −0.933180 0.359409i \(-0.882978\pi\)
−0.155333 + 0.987862i \(0.549645\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.174973 0.00809677 0.00404838 0.999992i \(-0.498711\pi\)
0.00404838 + 0.999992i \(0.498711\pi\)
\(468\) 0 0
\(469\) 7.39388 0.341418
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.55051 + 3.78194i −0.301193 + 0.173894i
\(474\) 0 0
\(475\) 20.7846 + 12.0000i 0.953663 + 0.550598i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 13.0458 22.5959i 0.596076 1.03243i −0.397318 0.917681i \(-0.630059\pi\)
0.993394 0.114753i \(-0.0366076\pi\)
\(480\) 0 0
\(481\) −7.10102 12.2993i −0.323779 0.560801i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.58919i 0.0721612i
\(486\) 0 0
\(487\) 3.79796i 0.172102i 0.996291 + 0.0860510i \(0.0274248\pi\)
−0.996291 + 0.0860510i \(0.972575\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.15855 + 12.3990i 0.323061 + 0.559558i 0.981118 0.193410i \(-0.0619548\pi\)
−0.658057 + 0.752968i \(0.728621\pi\)
\(492\) 0 0
\(493\) −15.7980 + 27.3629i −0.711504 + 1.23236i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −9.49490 5.48188i −0.425904 0.245896i
\(498\) 0 0
\(499\) −12.9029 + 7.44949i −0.577613 + 0.333485i −0.760184 0.649708i \(-0.774891\pi\)
0.182571 + 0.983193i \(0.441558\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 31.1127 1.38725 0.693623 0.720338i \(-0.256013\pi\)
0.693623 + 0.720338i \(0.256013\pi\)
\(504\) 0 0
\(505\) −5.00000 −0.222497
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −23.1186 + 13.3475i −1.02471 + 0.591619i −0.915466 0.402395i \(-0.868178\pi\)
−0.109249 + 0.994014i \(0.534845\pi\)
\(510\) 0 0
\(511\) 2.38378 + 1.37628i 0.105452 + 0.0608828i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.58919 2.75255i 0.0700279 0.121292i
\(516\) 0 0
\(517\) −5.00000 8.66025i −0.219900 0.380878i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 21.7060i 0.950958i 0.879727 + 0.475479i \(0.157725\pi\)
−0.879727 + 0.475479i \(0.842275\pi\)
\(522\) 0 0
\(523\) 27.3939i 1.19785i −0.800805 0.598925i \(-0.795595\pi\)
0.800805 0.598925i \(-0.204405\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.9029 22.3485i −0.562059 0.973515i
\(528\) 0 0
\(529\) 7.50000 12.9904i 0.326087 0.564799i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −24.4949 14.1421i −1.06099 0.612564i
\(534\) 0 0
\(535\) 2.38378 1.37628i 0.103060 0.0595016i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.37113 0.231351
\(540\) 0 0
\(541\) −20.0000 −0.859867 −0.429934 0.902861i \(-0.641463\pi\)
−0.429934 + 0.902861i \(0.641463\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.34847 0.778539i 0.0577621 0.0333489i
\(546\) 0 0
\(547\) −20.6096 11.8990i −0.881204 0.508764i −0.0101491 0.999948i \(-0.503231\pi\)
−0.871055 + 0.491185i \(0.836564\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 22.3417 38.6969i 0.951788 1.64855i
\(552\) 0 0
\(553\) −1.44949 2.51059i −0.0616386 0.106761i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 12.5529i 0.531886i −0.963989 0.265943i \(-0.914317\pi\)
0.963989 0.265943i \(-0.0856832\pi\)
\(558\) 0 0
\(559\) 20.0000i 0.845910i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11.4012 19.7474i −0.480503 0.832256i 0.519247 0.854624i \(-0.326213\pi\)
−0.999750 + 0.0223687i \(0.992879\pi\)
\(564\) 0 0
\(565\) −2.24745 + 3.89270i −0.0945509 + 0.163767i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.10102 + 4.09978i 0.297690 + 0.171872i 0.641405 0.767203i \(-0.278352\pi\)
−0.343715 + 0.939074i \(0.611685\pi\)
\(570\) 0 0
\(571\) 17.1455 9.89898i 0.717518 0.414259i −0.0963203 0.995350i \(-0.530707\pi\)
0.813839 + 0.581091i \(0.197374\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −13.8564 −0.577852
\(576\) 0 0
\(577\) −3.79796 −0.158111 −0.0790556 0.996870i \(-0.525190\pi\)
−0.0790556 + 0.996870i \(0.525190\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −19.9268 + 11.5047i −0.826702 + 0.477297i
\(582\) 0 0
\(583\) 4.19448 + 2.42168i 0.173718 + 0.100296i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.5441 19.9949i 0.476474 0.825278i −0.523162 0.852233i \(-0.675248\pi\)
0.999637 + 0.0269553i \(0.00858119\pi\)
\(588\) 0 0
\(589\) 18.2474 + 31.6055i 0.751873 + 1.30228i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.13534i 0.334078i −0.985950 0.167039i \(-0.946579\pi\)
0.985950 0.167039i \(-0.0534206\pi\)
\(594\) 0 0
\(595\) 1.59592i 0.0654263i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −12.7600 22.1010i −0.521361 0.903023i −0.999691 0.0248434i \(-0.992091\pi\)
0.478331 0.878180i \(-0.341242\pi\)
\(600\) 0 0
\(601\) −5.15153 + 8.92271i −0.210135 + 0.363965i −0.951757 0.306854i \(-0.900724\pi\)
0.741621 + 0.670819i \(0.234057\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.69694 1.55708i −0.109646 0.0633042i
\(606\) 0 0
\(607\) 20.6096 11.8990i 0.836519 0.482965i −0.0195602 0.999809i \(-0.506227\pi\)
0.856080 + 0.516844i \(0.172893\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 26.4415 1.06971
\(612\) 0 0
\(613\) 30.0000 1.21169 0.605844 0.795583i \(-0.292835\pi\)
0.605844 + 0.795583i \(0.292835\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −24.2474 + 13.9993i −0.976166 + 0.563589i −0.901110 0.433590i \(-0.857247\pi\)
−0.0750552 + 0.997179i \(0.523913\pi\)
\(618\) 0 0
\(619\) −18.7026 10.7980i −0.751722 0.434007i 0.0745941 0.997214i \(-0.476234\pi\)
−0.826316 + 0.563207i \(0.809567\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8.66025 + 15.0000i −0.346966 + 0.600962i
\(624\) 0 0
\(625\) −11.7474 20.3472i −0.469898 0.813887i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 16.9706i 0.676661i
\(630\) 0 0
\(631\) 45.7423i 1.82097i 0.413538 + 0.910487i \(0.364293\pi\)
−0.413538 + 0.910487i \(0.635707\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −2.42310 4.19694i −0.0961579 0.166550i
\(636\) 0 0
\(637\) −7.10102 + 12.2993i −0.281353 + 0.487317i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −42.2474 24.3916i −1.66867 0.963409i −0.968354 0.249580i \(-0.919707\pi\)
−0.700320 0.713829i \(-0.746959\pi\)
\(642\) 0 0
\(643\) −32.3840 + 18.6969i −1.27710 + 0.737335i −0.976315 0.216356i \(-0.930583\pi\)
−0.300788 + 0.953691i \(0.597250\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.7846 −0.817127 −0.408564 0.912730i \(-0.633970\pi\)
−0.408564 + 0.912730i \(0.633970\pi\)
\(648\) 0 0
\(649\) −10.0000 −0.392534
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16.0732 9.27987i 0.628993 0.363150i −0.151369 0.988477i \(-0.548368\pi\)
0.780362 + 0.625328i \(0.215035\pi\)
\(654\) 0 0
\(655\) 0.826701 + 0.477296i 0.0323019 + 0.0186495i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 13.9118 24.0959i 0.541926 0.938644i −0.456867 0.889535i \(-0.651029\pi\)
0.998793 0.0491088i \(-0.0156381\pi\)
\(660\) 0 0
\(661\) 2.24745 + 3.89270i 0.0874156 + 0.151408i 0.906418 0.422382i \(-0.138806\pi\)
−0.819002 + 0.573790i \(0.805473\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.25697i 0.0875215i
\(666\) 0 0
\(667\) 25.7980i 0.998901i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.19275 3.79796i −0.0846503 0.146619i
\(672\) 0 0
\(673\) 18.2980 31.6930i 0.705334 1.22168i −0.261236 0.965275i \(-0.584130\pi\)
0.966571 0.256400i \(-0.0825365\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9.49490 + 5.48188i 0.364919 + 0.210686i 0.671236 0.741244i \(-0.265764\pi\)
−0.306318 + 0.951929i \(0.599097\pi\)
\(678\) 0 0
\(679\) 6.27647 3.62372i 0.240869 0.139066i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −10.3923 −0.397650 −0.198825 0.980035i \(-0.563713\pi\)
−0.198825 + 0.980035i \(0.563713\pi\)
\(684\) 0 0
\(685\) −3.39388 −0.129673
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −11.0908 + 6.40329i −0.422526 + 0.243946i
\(690\) 0 0
\(691\) −3.46410 2.00000i −0.131781 0.0760836i 0.432660 0.901557i \(-0.357575\pi\)
−0.564441 + 0.825473i \(0.690908\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.17837 + 5.50510i −0.120563 + 0.208820i
\(696\) 0 0
\(697\) 16.8990 + 29.2699i 0.640094 + 1.10868i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 38.7087i 1.46201i −0.682374 0.731003i \(-0.739052\pi\)
0.682374 0.731003i \(-0.260948\pi\)
\(702\) 0 0
\(703\) 24.0000i 0.905177i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11.4012 + 19.7474i 0.428786 + 0.742679i
\(708\) 0 0
\(709\) 20.0000 34.6410i 0.751116 1.30097i −0.196167 0.980571i \(-0.562849\pi\)
0.947282 0.320400i \(-0.103817\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −18.2474 10.5352i −0.683372 0.394545i
\(714\) 0 0
\(715\) −0.874863 + 0.505103i −0.0327180 + 0.0188898i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.92820 0.258378 0.129189 0.991620i \(-0.458763\pi\)
0.129189 + 0.991620i \(0.458763\pi\)
\(720\) 0 0
\(721\) −14.4949 −0.539818
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −38.6969 + 22.3417i −1.43717 + 0.829749i
\(726\) 0 0
\(727\) 6.27647 + 3.62372i 0.232782 + 0.134396i 0.611855 0.790970i \(-0.290424\pi\)
−0.379073 + 0.925367i \(0.623757\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −11.9494 + 20.6969i −0.441964 + 0.765504i
\(732\) 0 0
\(733\) −2.24745 3.89270i −0.0830114 0.143780i 0.821531 0.570164i \(-0.193120\pi\)
−0.904542 + 0.426384i \(0.859787\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.59264i 0.206007i
\(738\) 0 0
\(739\) 19.3939i 0.713415i 0.934216 + 0.356708i \(0.116101\pi\)
−0.934216 + 0.356708i \(0.883899\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 15.7313 + 27.2474i 0.577126 + 0.999612i 0.995807 + 0.0914785i \(0.0291593\pi\)
−0.418681 + 0.908133i \(0.637507\pi\)
\(744\) 0 0
\(745\) −0.601021 + 1.04100i −0.0220197 + 0.0381392i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −10.8712 6.27647i −0.397224 0.229337i
\(750\) 0 0
\(751\) 41.3461 23.8712i 1.50874 0.871071i 0.508792 0.860890i \(-0.330092\pi\)
0.999948 0.0101819i \(-0.00324107\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.48188 0.199506
\(756\) 0 0
\(757\) −39.3939 −1.43179 −0.715897 0.698205i \(-0.753982\pi\)
−0.715897 + 0.698205i \(0.753982\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 45.7980 26.4415i 1.66017 0.958502i 0.687545 0.726142i \(-0.258688\pi\)
0.972630 0.232361i \(-0.0746449\pi\)
\(762\) 0 0
\(763\) −6.14966 3.55051i −0.222633 0.128537i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 13.2207 22.8990i 0.477373 0.826834i
\(768\) 0 0
\(769\) −5.74745 9.95487i −0.207258 0.358982i 0.743592 0.668634i \(-0.233121\pi\)
−0.950850 + 0.309652i \(0.899787\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34.2911i 1.23336i −0.787212 0.616682i \(-0.788476\pi\)
0.787212 0.616682i \(-0.211524\pi\)
\(774\) 0 0
\(775\) 36.4949i 1.31094i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −23.8988 41.3939i −0.856262 1.48309i
\(780\) 0 0
\(781\) 4.14643 7.18182i 0.148371 0.256986i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.79796 2.19275i −0.135555 0.0782627i
\(786\) 0 0
\(787\) 30.4770 17.5959i 1.08639 0.627227i 0.153776 0.988106i \(-0.450857\pi\)
0.932613 + 0.360879i \(0.117523\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 20.4989 0.728856
\(792\) 0 0
\(793\) 11.5959 0.411783
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.27526 3.62302i 0.222281 0.128334i −0.384725 0.923031i \(-0.625704\pi\)
0.607006 + 0.794697i \(0.292370\pi\)
\(798\) 0 0
\(799\) −27.3629 15.7980i −0.968029 0.558892i
\(800\) 0 0
\(801\) 0 0
\(802\) 0