Properties

Label 2592.2.s.a.863.3
Level $2592$
Weight $2$
Character 2592.863
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 863.3
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2592.863
Dual form 2592.2.s.a.1727.3

$q$-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 \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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 0.437187 0.899371i \(-0.355975\pi\)
−0.560285 + 0.828300i \(0.689308\pi\)
\(6\) 0 0
\(7\) −1.25529 + 0.724745i −0.474457 + 0.273928i −0.718104 0.695936i \(-0.754990\pi\)
0.243647 + 0.969864i \(0.421656\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.548188 + 0.949490i 0.165285 + 0.286282i 0.936756 0.349982i \(-0.113812\pi\)
−0.771471 + 0.636264i \(0.780479\pi\)
\(12\) 0 0
\(13\) −1.44949 + 2.51059i −0.402016 + 0.696312i −0.993969 0.109660i \(-0.965024\pi\)
0.591953 + 0.805972i \(0.298357\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.46410i 0.840168i −0.907485 0.420084i \(-0.862001\pi\)
0.907485 0.420084i \(-0.137999\pi\)
\(18\) 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 \(-0.928614\pi\)
0.680074 + 0.733144i \(0.261948\pi\)
\(24\) 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 0.467493 0.883997i \(-0.345157\pi\)
0.999310 + 0.0371370i \(0.0118238\pi\)
\(30\) 0 0
\(31\) 6.45145 + 3.72474i 1.15871 + 0.668984i 0.950996 0.309205i \(-0.100063\pi\)
0.207719 + 0.978189i \(0.433396\pi\)
\(32\) 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 0.983662 0.180023i \(-0.0576174\pi\)
0.335926 + 0.941888i \(0.390951\pi\)
\(42\) 0 0
\(43\) −5.97469 + 3.44949i −0.911132 + 0.526042i −0.880795 0.473497i \(-0.842991\pi\)
−0.0303367 + 0.999540i \(0.509658\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.56048 + 7.89898i 0.665214 + 1.15218i 0.979227 + 0.202766i \(0.0649931\pi\)
−0.314013 + 0.949419i \(0.601674\pi\)
\(48\) 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 \(0.0981228\pi\)
−0.952862 + 0.303403i \(0.901877\pi\)
\(54\) 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 0.400002 + 0.916514i \(0.369009\pi\)
−0.993726 + 0.111845i \(0.964324\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 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 \(-0.434196\pi\)
−0.744956 + 0.667113i \(0.767530\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.56388 0.897667 0.448834 0.893615i \(-0.351840\pi\)
0.448834 + 0.893615i \(0.351840\pi\)
\(72\) 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 \(-0.630778\pi\)
0.594261 + 0.804272i \(0.297445\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.93709 + 13.7474i 0.871209 + 1.50898i 0.860747 + 0.509033i \(0.169997\pi\)
0.0104623 + 0.999945i \(0.496670\pi\)
\(84\) 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 \(-0.781693\pi\)
0.773893 0.633316i \(-0.218307\pi\)
\(90\) 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 0.964579 0.263795i \(-0.0849741\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 13.6237 7.86566i 1.35561 0.782663i 0.366582 0.930386i \(-0.380528\pi\)
0.989029 + 0.147723i \(0.0471944\pi\)
\(102\) 0 0
\(103\) 8.66025 + 5.00000i 0.853320 + 0.492665i 0.861770 0.507300i \(-0.169356\pi\)
−0.00844953 + 0.999964i \(0.502690\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 8.66025 0.837218 0.418609 0.908166i \(-0.362518\pi\)
0.418609 + 0.908166i \(0.362518\pi\)
\(108\) 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 0.949409 0.314044i \(-0.101684\pi\)
0.202735 + 0.979234i \(0.435017\pi\)
\(114\) 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 \(-0.791449\pi\)
0.924141 + 0.382052i \(0.124782\pi\)
\(132\) 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 −0.0499218 0.998753i \(-0.515897\pi\)
0.839985 + 0.542610i \(0.182564\pi\)
\(138\) 0 0
\(139\) −17.3205 10.0000i −1.46911 0.848189i −0.469706 0.882823i \(-0.655640\pi\)
−0.999400 + 0.0346338i \(0.988974\pi\)
\(140\) 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 0.628124 0.778114i \(-0.283823\pi\)
−0.359804 + 0.933028i \(0.617157\pi\)
\(150\) 0 0
\(151\) 14.9367 8.62372i 1.21553 0.701789i 0.251574 0.967838i \(-0.419052\pi\)
0.963959 + 0.266049i \(0.0857184\pi\)
\(152\) 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 −0.447633 0.894217i \(-0.647733\pi\)
0.998231 0.0594472i \(-0.0189338\pi\)
\(158\) 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 −0.0479862 + 0.998848i \(0.515280\pi\)
−0.841035 + 0.540981i \(0.818053\pi\)
\(168\) 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 −0.313826 0.949481i \(-0.601611\pi\)
0.665361 + 0.746522i \(0.268278\pi\)
\(174\) 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 \(-0.604910\pi\)
−0.323649 + 0.946177i \(0.604910\pi\)
\(180\) 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 0.986094 + 0.166190i \(0.0531464\pi\)
−0.349123 + 0.937077i \(0.613520\pi\)
\(192\) 0 0
\(193\) −1.05051 + 1.81954i −0.0756174 + 0.130973i −0.901355 0.433082i \(-0.857426\pi\)
0.825737 + 0.564055i \(0.190759\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.2672i 0.874003i −0.899461 0.437002i \(-0.856040\pi\)
0.899461 0.437002i \(-0.143960\pi\)
\(198\) 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 −0.946848 0.321680i \(-0.895752\pi\)
−0.752007 0.659155i \(-0.770914\pi\)
\(212\) 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 \(-0.664513\pi\)
0.505847 + 0.862623i \(0.331180\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.83183 + 10.1010i 0.387072 + 0.670428i 0.992054 0.125811i \(-0.0401532\pi\)
−0.604982 + 0.796239i \(0.706820\pi\)
\(228\) 0 0
\(229\) −1.00000 + 1.73205i −0.0660819 + 0.114457i −0.897173 0.441679i \(-0.854383\pi\)
0.831092 + 0.556136i \(0.187717\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.2207i 0.866119i 0.901365 + 0.433059i \(0.142566\pi\)
−0.901365 + 0.433059i \(0.857434\pi\)
\(234\) 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 −0.293071 0.956091i \(-0.594677\pi\)
0.974534 0.224239i \(-0.0719895\pi\)
\(240\) 0 0
\(241\) 9.89898 + 17.1455i 0.637649 + 1.10444i 0.985947 + 0.167057i \(0.0534264\pi\)
−0.348298 + 0.937384i \(0.613240\pi\)
\(242\) 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 \(-0.315910\pi\)
0.546630 + 0.837374i \(0.315910\pi\)
\(252\) 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 0.150700 0.988579i \(-0.451847\pi\)
−0.780785 + 0.624800i \(0.785180\pi\)
\(258\) 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 −0.939066 0.343738i \(-0.888307\pi\)
0.171847 0.985124i \(-0.445026\pi\)
\(264\) 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 \(-0.897387\pi\)
0.948487 0.316815i \(-0.102613\pi\)
\(270\) 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 0.995378 0.0960358i \(-0.0306163\pi\)
−0.580858 + 0.814005i \(0.697283\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.797959 + 0.460702i −0.0476022 + 0.0274832i −0.523612 0.851957i \(-0.675416\pi\)
0.476010 + 0.879440i \(0.342083\pi\)
\(282\) 0 0
\(283\) −2.68556 1.55051i −0.159640 0.0921683i 0.418052 0.908423i \(-0.362713\pi\)
−0.577692 + 0.816255i \(0.696046\pi\)
\(284\) 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 0.644196 0.764860i \(-0.277192\pi\)
−0.340290 + 0.940321i \(0.610525\pi\)
\(294\) 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 \(-0.796250\pi\)
0.918274 + 0.395945i \(0.129583\pi\)
\(312\) 0 0
\(313\) −14.7474 25.5433i −0.833575 1.44379i −0.895185 0.445694i \(-0.852957\pi\)
0.0616102 0.998100i \(-0.480376\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −25.6237 + 14.7939i −1.43917 + 0.830906i −0.997792 0.0664143i \(-0.978844\pi\)
−0.441380 + 0.897320i \(0.645511\pi\)
\(318\) 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 \(-0.672764\pi\)
0.483321 + 0.875443i \(0.339430\pi\)
\(332\) 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 −0.917560 0.397598i \(-0.869844\pi\)
0.803110 + 0.595831i \(0.203177\pi\)
\(338\) 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 \(-0.786326\pi\)
0.930170 + 0.367130i \(0.119659\pi\)
\(348\) 0 0
\(349\) −12.4495 21.5631i −0.666406 1.15425i −0.978902 0.204330i \(-0.934498\pi\)
0.312496 0.949919i \(-0.398835\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.2474 7.07107i 0.651866 0.376355i −0.137305 0.990529i \(-0.543844\pi\)
0.789171 + 0.614174i \(0.210511\pi\)
\(354\) 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 \(-0.139940\pi\)
0.904907 + 0.425610i \(0.139940\pi\)
\(360\) 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 \(-0.595027\pi\)
0.680658 + 0.732601i \(0.261694\pi\)
\(368\) 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 −0.0568261 + 0.998384i \(0.518098\pi\)
−0.836213 + 0.548405i \(0.815235\pi\)
\(374\) 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 \(-0.863875\pi\)
0.814140 + 0.580669i \(0.197209\pi\)
\(384\) 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 −0.995195 0.0979078i \(-0.968785\pi\)
−0.412807 + 0.910818i \(0.635452\pi\)
\(390\) 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 −0.0767343 0.997052i \(-0.524449\pi\)
−0.901839 + 0.432072i \(0.857783\pi\)
\(402\) 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 −0.766426 0.642333i \(-0.777967\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 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 −0.348690 0.937238i \(-0.613373\pi\)
0.986017 0.166645i \(-0.0532933\pi\)
\(420\) 0 0
\(421\) 14.8990 + 25.8058i 0.726132 + 1.25770i 0.958506 + 0.285071i \(0.0920171\pi\)
−0.232375 + 0.972626i \(0.574650\pi\)
\(422\) 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 \(-0.729025\pi\)
−0.659011 + 0.752133i \(0.729025\pi\)
\(432\) 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 \(-0.818572\pi\)
0.0463579 + 0.998925i \(0.485239\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.3171 24.7980i −0.680226 1.17819i −0.974912 0.222592i \(-0.928548\pi\)
0.294685 0.955594i \(-0.404785\pi\)
\(444\) 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 \(0.176752\pi\)
−0.849751 + 0.527185i \(0.823248\pi\)
\(450\) 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 −0.994910 0.100771i \(-0.967869\pi\)
0.410184 0.912003i \(-0.365464\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.62372 + 0.937458i −0.0756244 + 0.0436618i −0.537335 0.843369i \(-0.680569\pi\)
0.461711 + 0.887030i \(0.347236\pi\)
\(462\) 0 0
\(463\) 23.4220 + 13.5227i 1.08851 + 0.628453i 0.933180 0.359409i \(-0.117022\pi\)
0.155333 + 0.987862i \(0.450355\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.174973 −0.00809677 −0.00404838 0.999992i \(-0.501289\pi\)
−0.00404838 + 0.999992i \(0.501289\pi\)
\(468\) 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 −0.993394 0.114753i \(-0.963392\pi\)
0.397318 0.917681i \(-0.369941\pi\)
\(480\) 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 \(-0.938045\pi\)
0.658057 + 0.752968i \(0.271379\pi\)
\(492\) 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 \(-0.225109\pi\)
−0.182571 + 0.983193i \(0.558442\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −31.1127 −1.38725 −0.693623 0.720338i \(-0.743987\pi\)
−0.693623 + 0.720338i \(0.743987\pi\)
\(504\) 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 −0.109249 0.994014i \(-0.534845\pi\)
−0.915466 + 0.402395i \(0.868178\pi\)
\(510\) 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 \(-0.842275\pi\)
0.879727 0.475479i \(-0.157725\pi\)
\(522\) 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 \(-0.496769\pi\)
0.871055 + 0.491185i \(0.163436\pi\)
\(548\) 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 \(0.0856832\pi\)
−0.963989 + 0.265943i \(0.914317\pi\)
\(558\) 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 \(-0.673787\pi\)
0.999750 + 0.0223687i \(0.00712076\pi\)
\(564\) 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 −0.343715 0.939074i \(-0.611685\pi\)
0.641405 + 0.767203i \(0.278352\pi\)
\(570\) 0 0
\(571\) −17.1455 9.89898i −0.717518 0.414259i 0.0963203 0.995350i \(-0.469293\pi\)
−0.813839 + 0.581091i \(0.802626\pi\)
\(572\) 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 \(-0.324752\pi\)
−0.999637 + 0.0269553i \(0.991419\pi\)
\(588\) 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 \(0.0534206\pi\)
−0.985950 + 0.167039i \(0.946579\pi\)
\(594\) 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 −0.478331 0.878180i \(-0.658758\pi\)
0.999691 0.0248434i \(-0.00790872\pi\)
\(600\) 0 0
\(601\) −5.15153 8.92271i −0.210135 0.363965i 0.741621 0.670819i \(-0.234057\pi\)
−0.951757 + 0.306854i \(0.900724\pi\)
\(602\) 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 \(-0.493773\pi\)
−0.856080 + 0.516844i \(0.827107\pi\)
\(608\) 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 −0.0750552 0.997179i \(-0.523913\pi\)
−0.901110 + 0.433590i \(0.857247\pi\)
\(618\) 0 0
\(619\) 18.7026 10.7980i 0.751722 0.434007i −0.0745941 0.997214i \(-0.523766\pi\)
0.826316 + 0.563207i \(0.190433\pi\)
\(620\) 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 −0.700320 + 0.713829i \(0.746959\pi\)
−0.968354 + 0.249580i \(0.919707\pi\)
\(642\) 0 0
\(643\) 32.3840 + 18.6969i 1.27710 + 0.737335i 0.976315 0.216356i \(-0.0694171\pi\)
0.300788 + 0.953691i \(0.402750\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.7846 0.817127 0.408564 0.912730i \(-0.366030\pi\)
0.408564 + 0.912730i \(0.366030\pi\)
\(648\) 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 0.780362 0.625328i \(-0.215035\pi\)
−0.151369 + 0.988477i \(0.548368\pi\)
\(654\) 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 −0.998793 0.0491088i \(-0.984362\pi\)
0.456867 0.889535i \(-0.348971\pi\)
\(660\) 0 0
\(661\) 2.24745 3.89270i 0.0874156 0.151408i −0.819002 0.573790i \(-0.805473\pi\)
0.906418 + 0.422382i \(0.138806\pi\)
\(662\) 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 0.966571 + 0.256400i \(0.0825365\pi\)
−0.261236 + 0.965275i \(0.584130\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9.49490 5.48188i 0.364919 0.210686i −0.306318 0.951929i \(-0.599097\pi\)
0.671236 + 0.741244i \(0.265764\pi\)
\(678\) 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 \(-0.436287\pi\)
0.198825 + 0.980035i \(0.436287\pi\)
\(684\) 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 \(-0.642425\pi\)
0.564441 + 0.825473i \(0.309092\pi\)
\(692\) 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 \(0.260948\pi\)
−0.682374 + 0.731003i \(0.739052\pi\)
\(702\) 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 0.947282 + 0.320400i \(0.103817\pi\)
−0.196167 + 0.980571i \(0.562849\pi\)
\(710\) 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 \(-0.541237\pi\)
−0.129189 + 0.991620i \(0.541237\pi\)
\(720\) 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 \(-0.709576\pi\)
0.379073 + 0.925367i \(0.376243\pi\)
\(728\) 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 −0.904542 0.426384i \(-0.859787\pi\)
0.821531 + 0.570164i \(0.193120\pi\)
\(734\) 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 0.418681 + 0.908133i \(0.362493\pi\)
−0.995807 + 0.0914785i \(0.970841\pi\)
\(744\) 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 −0.999948 0.0101819i \(-0.996759\pi\)
−0.508792 0.860890i \(-0.669908\pi\)
\(752\) 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 0.972630 + 0.232361i \(0.0746449\pi\)
0.687545 + 0.726142i \(0.258688\pi\)
\(762\) 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 −0.950850 0.309652i \(-0.899787\pi\)
0.743592 + 0.668634i \(0.233121\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 34.2911i 1.23336i 0.787212 + 0.616682i \(0.211524\pi\)
−0.787212 + 0.616682i \(0.788476\pi\)
\(774\) 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 \(-0.549143\pi\)
−0.932613 + 0.360879i \(0.882477\pi\)
\(788\) 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 0.607006 0.794697i \(-0.292370\pi\)
−0.384725 + 0.923031i \(0.625704\pi\)
\(798\) 0 0
\(799\) 27.3629 15.7980i 0.968029 0.558892i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0