Properties

Label 432.2.s.a.143.1
Level $432$
Weight $2$
Character 432.143
Analytic conductor $3.450$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 143.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 432.143
Dual form 432.2.s.a.287.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{7} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{7} +(-1.50000 + 2.59808i) q^{11} +(2.50000 + 4.33013i) q^{13} +6.92820i q^{17} +3.46410i q^{19} +(-4.50000 - 7.79423i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(-1.50000 - 0.866025i) q^{29} +(-4.50000 + 2.59808i) q^{31} +3.00000 q^{35} +2.00000 q^{37} +(4.50000 - 2.59808i) q^{41} +(4.50000 + 2.59808i) q^{43} +(-1.50000 + 2.59808i) q^{47} +(-2.00000 - 3.46410i) q^{49} -5.19615i q^{55} +(1.50000 + 2.59808i) q^{59} +(0.500000 - 0.866025i) q^{61} +(-7.50000 - 4.33013i) q^{65} +(7.50000 - 4.33013i) q^{67} +12.0000 q^{71} -2.00000 q^{73} +(4.50000 - 2.59808i) q^{77} +(-7.50000 - 4.33013i) q^{79} +(-7.50000 + 12.9904i) q^{83} +(-6.00000 - 10.3923i) q^{85} -6.92820i q^{89} -8.66025i q^{91} +(-3.00000 - 5.19615i) q^{95} +(2.50000 - 4.33013i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{5} - 3 q^{7} - 3 q^{11} + 5 q^{13} - 9 q^{23} - 2 q^{25} - 3 q^{29} - 9 q^{31} + 6 q^{35} + 4 q^{37} + 9 q^{41} + 9 q^{43} - 3 q^{47} - 4 q^{49} + 3 q^{59} + q^{61} - 15 q^{65} + 15 q^{67} + 24 q^{71} - 4 q^{73} + 9 q^{77} - 15 q^{79} - 15 q^{83} - 12 q^{85} - 6 q^{95} + 5 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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 0
\(4\) 0 0
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 0 0
\(7\) −1.50000 0.866025i −0.566947 0.327327i 0.188982 0.981981i \(-0.439481\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 2.50000 + 4.33013i 0.693375 + 1.20096i 0.970725 + 0.240192i \(0.0772105\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.92820i 1.68034i 0.542326 + 0.840168i \(0.317544\pi\)
−0.542326 + 0.840168i \(0.682456\pi\)
\(18\) 0 0
\(19\) 3.46410i 0.794719i 0.917663 + 0.397360i \(0.130073\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.50000 7.79423i −0.938315 1.62521i −0.768613 0.639713i \(-0.779053\pi\)
−0.169701 0.985496i \(-0.554280\pi\)
\(24\) 0 0
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.50000 0.866025i −0.278543 0.160817i 0.354221 0.935162i \(-0.384746\pi\)
−0.632764 + 0.774345i \(0.718080\pi\)
\(30\) 0 0
\(31\) −4.50000 + 2.59808i −0.808224 + 0.466628i −0.846339 0.532645i \(-0.821198\pi\)
0.0381148 + 0.999273i \(0.487865\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.00000 0.507093
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.50000 2.59808i 0.702782 0.405751i −0.105601 0.994409i \(-0.533677\pi\)
0.808383 + 0.588657i \(0.200343\pi\)
\(42\) 0 0
\(43\) 4.50000 + 2.59808i 0.686244 + 0.396203i 0.802203 0.597051i \(-0.203661\pi\)
−0.115960 + 0.993254i \(0.536994\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) 0 0
\(49\) −2.00000 3.46410i −0.285714 0.494872i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 5.19615i 0.700649i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.50000 + 2.59808i 0.195283 + 0.338241i 0.946993 0.321253i \(-0.104104\pi\)
−0.751710 + 0.659494i \(0.770771\pi\)
\(60\) 0 0
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −7.50000 4.33013i −0.930261 0.537086i
\(66\) 0 0
\(67\) 7.50000 4.33013i 0.916271 0.529009i 0.0338274 0.999428i \(-0.489230\pi\)
0.882443 + 0.470418i \(0.155897\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.50000 2.59808i 0.512823 0.296078i
\(78\) 0 0
\(79\) −7.50000 4.33013i −0.843816 0.487177i 0.0147436 0.999891i \(-0.495307\pi\)
−0.858559 + 0.512714i \(0.828640\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.50000 + 12.9904i −0.823232 + 1.42588i 0.0800311 + 0.996792i \(0.474498\pi\)
−0.903263 + 0.429087i \(0.858835\pi\)
\(84\) 0 0
\(85\) −6.00000 10.3923i −0.650791 1.12720i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.92820i 0.734388i −0.930144 0.367194i \(-0.880318\pi\)
0.930144 0.367194i \(-0.119682\pi\)
\(90\) 0 0
\(91\) 8.66025i 0.907841i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.00000 5.19615i −0.307794 0.533114i
\(96\) 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
\(101\) 4.50000 + 2.59808i 0.447767 + 0.258518i 0.706887 0.707327i \(-0.250099\pi\)
−0.259120 + 0.965845i \(0.583432\pi\)
\(102\) 0 0
\(103\) 1.50000 0.866025i 0.147799 0.0853320i −0.424277 0.905533i \(-0.639472\pi\)
0.572076 + 0.820201i \(0.306138\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −14.0000 −1.34096 −0.670478 0.741929i \(-0.733911\pi\)
−0.670478 + 0.741929i \(0.733911\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 10.5000 6.06218i 0.987757 0.570282i 0.0831539 0.996537i \(-0.473501\pi\)
0.904603 + 0.426255i \(0.140167\pi\)
\(114\) 0 0
\(115\) 13.5000 + 7.79423i 1.25888 + 0.726816i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 6.00000 10.3923i 0.550019 0.952661i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 10.3923i 0.922168i 0.887357 + 0.461084i \(0.152539\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) 0 0
\(133\) 3.00000 5.19615i 0.260133 0.450564i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.50000 4.33013i −0.640768 0.369948i 0.144142 0.989557i \(-0.453958\pi\)
−0.784910 + 0.619609i \(0.787291\pi\)
\(138\) 0 0
\(139\) 1.50000 0.866025i 0.127228 0.0734553i −0.435035 0.900414i \(-0.643264\pi\)
0.562263 + 0.826958i \(0.309931\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −15.0000 −1.25436
\(144\) 0 0
\(145\) 3.00000 0.249136
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.50000 + 4.33013i −0.614424 + 0.354738i −0.774695 0.632335i \(-0.782097\pi\)
0.160271 + 0.987073i \(0.448763\pi\)
\(150\) 0 0
\(151\) −7.50000 4.33013i −0.610341 0.352381i 0.162758 0.986666i \(-0.447961\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.50000 7.79423i 0.361449 0.626048i
\(156\) 0 0
\(157\) 0.500000 + 0.866025i 0.0399043 + 0.0691164i 0.885288 0.465044i \(-0.153961\pi\)
−0.845383 + 0.534160i \(0.820628\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.5885i 1.22854i
\(162\) 0 0
\(163\) 17.3205i 1.35665i 0.734763 + 0.678323i \(0.237293\pi\)
−0.734763 + 0.678323i \(0.762707\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.50000 + 2.59808i 0.116073 + 0.201045i 0.918208 0.396098i \(-0.129636\pi\)
−0.802135 + 0.597143i \(0.796303\pi\)
\(168\) 0 0
\(169\) −6.00000 + 10.3923i −0.461538 + 0.799408i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16.5000 + 9.52628i 1.25447 + 0.724270i 0.971994 0.235004i \(-0.0755104\pi\)
0.282477 + 0.959274i \(0.408844\pi\)
\(174\) 0 0
\(175\) 3.00000 1.73205i 0.226779 0.130931i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −3.00000 + 1.73205i −0.220564 + 0.127343i
\(186\) 0 0
\(187\) −18.0000 10.3923i −1.31629 0.759961i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) 0 0
\(193\) 6.50000 + 11.2583i 0.467880 + 0.810392i 0.999326 0.0366998i \(-0.0116845\pi\)
−0.531446 + 0.847092i \(0.678351\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.92820i 0.493614i 0.969065 + 0.246807i \(0.0793814\pi\)
−0.969065 + 0.246807i \(0.920619\pi\)
\(198\) 0 0
\(199\) 24.2487i 1.71895i −0.511182 0.859473i \(-0.670792\pi\)
0.511182 0.859473i \(-0.329208\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.50000 + 2.59808i 0.105279 + 0.182349i
\(204\) 0 0
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −9.00000 5.19615i −0.622543 0.359425i
\(210\) 0 0
\(211\) −16.5000 + 9.52628i −1.13591 + 0.655816i −0.945414 0.325872i \(-0.894342\pi\)
−0.190493 + 0.981689i \(0.561009\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −9.00000 −0.613795
\(216\) 0 0
\(217\) 9.00000 0.610960
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −30.0000 + 17.3205i −2.01802 + 1.16510i
\(222\) 0 0
\(223\) 22.5000 + 12.9904i 1.50671 + 0.869900i 0.999970 + 0.00780243i \(0.00248362\pi\)
0.506742 + 0.862098i \(0.330850\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 0 0
\(229\) 8.50000 + 14.7224i 0.561696 + 0.972886i 0.997349 + 0.0727709i \(0.0231842\pi\)
−0.435653 + 0.900115i \(0.643482\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.8564i 0.907763i 0.891062 + 0.453882i \(0.149961\pi\)
−0.891062 + 0.453882i \(0.850039\pi\)
\(234\) 0 0
\(235\) 5.19615i 0.338960i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.50000 + 12.9904i 0.485135 + 0.840278i 0.999854 0.0170808i \(-0.00543724\pi\)
−0.514719 + 0.857359i \(0.672104\pi\)
\(240\) 0 0
\(241\) 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i \(-0.648900\pi\)
0.998443 0.0557856i \(-0.0177663\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 6.00000 + 3.46410i 0.383326 + 0.221313i
\(246\) 0 0
\(247\) −15.0000 + 8.66025i −0.954427 + 0.551039i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.50000 + 0.866025i −0.0935674 + 0.0540212i −0.546054 0.837750i \(-0.683871\pi\)
0.452486 + 0.891771i \(0.350537\pi\)
\(258\) 0 0
\(259\) −3.00000 1.73205i −0.186411 0.107624i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.50000 7.79423i 0.277482 0.480613i −0.693276 0.720672i \(-0.743833\pi\)
0.970758 + 0.240059i \(0.0771668\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 27.7128i 1.68968i −0.535019 0.844840i \(-0.679696\pi\)
0.535019 0.844840i \(-0.320304\pi\)
\(270\) 0 0
\(271\) 24.2487i 1.47300i 0.676435 + 0.736502i \(0.263524\pi\)
−0.676435 + 0.736502i \(0.736476\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.00000 5.19615i −0.180907 0.313340i
\(276\) 0 0
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 16.5000 + 9.52628i 0.984307 + 0.568290i 0.903568 0.428445i \(-0.140938\pi\)
0.0807396 + 0.996735i \(0.474272\pi\)
\(282\) 0 0
\(283\) 13.5000 7.79423i 0.802492 0.463319i −0.0418500 0.999124i \(-0.513325\pi\)
0.844342 + 0.535805i \(0.179992\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.00000 −0.531253
\(288\) 0 0
\(289\) −31.0000 −1.82353
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.50000 + 0.866025i −0.0876309 + 0.0505937i −0.543175 0.839619i \(-0.682778\pi\)
0.455544 + 0.890213i \(0.349445\pi\)
\(294\) 0 0
\(295\) −4.50000 2.59808i −0.262000 0.151266i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 22.5000 38.9711i 1.30121 2.25376i
\(300\) 0 0
\(301\) −4.50000 7.79423i −0.259376 0.449252i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.73205i 0.0991769i
\(306\) 0 0
\(307\) 10.3923i 0.593120i −0.955014 0.296560i \(-0.904160\pi\)
0.955014 0.296560i \(-0.0958395\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7.50000 + 12.9904i 0.425286 + 0.736617i 0.996447 0.0842210i \(-0.0268402\pi\)
−0.571161 + 0.820838i \(0.693507\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.5000 + 6.06218i 0.589739 + 0.340486i 0.764994 0.644037i \(-0.222742\pi\)
−0.175255 + 0.984523i \(0.556075\pi\)
\(318\) 0 0
\(319\) 4.50000 2.59808i 0.251952 0.145464i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) −10.0000 −0.554700
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.50000 2.59808i 0.248093 0.143237i
\(330\) 0 0
\(331\) −1.50000 0.866025i −0.0824475 0.0476011i 0.458209 0.888844i \(-0.348491\pi\)
−0.540657 + 0.841243i \(0.681824\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −7.50000 + 12.9904i −0.409769 + 0.709740i
\(336\) 0 0
\(337\) −3.50000 6.06218i −0.190657 0.330228i 0.754811 0.655942i \(-0.227729\pi\)
−0.945468 + 0.325714i \(0.894395\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.5885i 0.844162i
\(342\) 0 0
\(343\) 19.0526i 1.02874i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.50000 7.79423i −0.241573 0.418416i 0.719590 0.694399i \(-0.244330\pi\)
−0.961162 + 0.275983i \(0.910997\pi\)
\(348\) 0 0
\(349\) 6.50000 11.2583i 0.347937 0.602645i −0.637946 0.770081i \(-0.720216\pi\)
0.985883 + 0.167437i \(0.0535490\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 4.50000 + 2.59808i 0.239511 + 0.138282i 0.614952 0.788565i \(-0.289175\pi\)
−0.375441 + 0.926846i \(0.622509\pi\)
\(354\) 0 0
\(355\) −18.0000 + 10.3923i −0.955341 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 7.00000 0.368421
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.00000 1.73205i 0.157027 0.0906597i
\(366\) 0 0
\(367\) 16.5000 + 9.52628i 0.861293 + 0.497268i 0.864445 0.502727i \(-0.167670\pi\)
−0.00315207 + 0.999995i \(0.501003\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.66025i 0.446026i
\(378\) 0 0
\(379\) 17.3205i 0.889695i −0.895606 0.444847i \(-0.853258\pi\)
0.895606 0.444847i \(-0.146742\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i \(0.0756427\pi\)
−0.282079 + 0.959391i \(0.591024\pi\)
\(384\) 0 0
\(385\) −4.50000 + 7.79423i −0.229341 + 0.397231i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −31.5000 18.1865i −1.59711 0.922094i −0.992040 0.125924i \(-0.959810\pi\)
−0.605074 0.796170i \(-0.706856\pi\)
\(390\) 0 0
\(391\) 54.0000 31.1769i 2.73090 1.57668i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 15.0000 0.754732
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 16.5000 9.52628i 0.823971 0.475720i −0.0278131 0.999613i \(-0.508854\pi\)
0.851784 + 0.523893i \(0.175521\pi\)
\(402\) 0 0
\(403\) −22.5000 12.9904i −1.12080 0.647097i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.00000 + 5.19615i −0.148704 + 0.257564i
\(408\) 0 0
\(409\) −15.5000 26.8468i −0.766426 1.32749i −0.939490 0.342578i \(-0.888700\pi\)
0.173064 0.984911i \(-0.444633\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 5.19615i 0.255686i
\(414\) 0 0
\(415\) 25.9808i 1.27535i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 7.50000 + 12.9904i 0.366399 + 0.634622i 0.989000 0.147918i \(-0.0472572\pi\)
−0.622601 + 0.782540i \(0.713924\pi\)
\(420\) 0 0
\(421\) 8.50000 14.7224i 0.414265 0.717527i −0.581086 0.813842i \(-0.697372\pi\)
0.995351 + 0.0963145i \(0.0307055\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −12.0000 6.92820i −0.582086 0.336067i
\(426\) 0 0
\(427\) −1.50000 + 0.866025i −0.0725901 + 0.0419099i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 27.0000 15.5885i 1.29159 0.745697i
\(438\) 0 0
\(439\) 4.50000 + 2.59808i 0.214773 + 0.123999i 0.603528 0.797342i \(-0.293761\pi\)
−0.388755 + 0.921341i \(0.627095\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.50000 7.79423i 0.213801 0.370315i −0.739100 0.673596i \(-0.764749\pi\)
0.952901 + 0.303281i \(0.0980821\pi\)
\(444\) 0 0
\(445\) 6.00000 + 10.3923i 0.284427 + 0.492642i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.7846i 0.980886i −0.871473 0.490443i \(-0.836835\pi\)
0.871473 0.490443i \(-0.163165\pi\)
\(450\) 0 0
\(451\) 15.5885i 0.734032i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 7.50000 + 12.9904i 0.351605 + 0.608998i
\(456\) 0 0
\(457\) 14.5000 25.1147i 0.678281 1.17482i −0.297217 0.954810i \(-0.596058\pi\)
0.975498 0.220008i \(-0.0706083\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 22.5000 + 12.9904i 1.04793 + 0.605022i 0.922069 0.387026i \(-0.126497\pi\)
0.125860 + 0.992048i \(0.459831\pi\)
\(462\) 0 0
\(463\) −16.5000 + 9.52628i −0.766820 + 0.442724i −0.831739 0.555167i \(-0.812654\pi\)
0.0649190 + 0.997891i \(0.479321\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 0 0
\(469\) −15.0000 −0.692636
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −13.5000 + 7.79423i −0.620731 + 0.358379i
\(474\) 0 0
\(475\) −6.00000 3.46410i −0.275299 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.50000 + 12.9904i −0.342684 + 0.593546i −0.984930 0.172953i \(-0.944669\pi\)
0.642246 + 0.766498i \(0.278003\pi\)
\(480\) 0 0
\(481\) 5.00000 + 8.66025i 0.227980 + 0.394874i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.66025i 0.393242i
\(486\) 0 0
\(487\) 3.46410i 0.156973i −0.996915 0.0784867i \(-0.974991\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i \(-0.323806\pi\)
−0.999552 + 0.0299272i \(0.990472\pi\)
\(492\) 0 0
\(493\) 6.00000 10.3923i 0.270226 0.468046i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −18.0000 10.3923i −0.807410 0.466159i
\(498\) 0 0
\(499\) 13.5000 7.79423i 0.604343 0.348918i −0.166405 0.986057i \(-0.553216\pi\)
0.770748 + 0.637140i \(0.219883\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) −9.00000 −0.400495
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −31.5000 + 18.1865i −1.39621 + 0.806104i −0.993993 0.109439i \(-0.965094\pi\)
−0.402219 + 0.915543i \(0.631761\pi\)
\(510\) 0 0
\(511\) 3.00000 + 1.73205i 0.132712 + 0.0766214i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.50000 + 2.59808i −0.0660979 + 0.114485i
\(516\) 0 0
\(517\) −4.50000 7.79423i −0.197910 0.342790i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 17.3205i 0.757373i −0.925525 0.378686i \(-0.876376\pi\)
0.925525 0.378686i \(-0.123624\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −18.0000 31.1769i −0.784092 1.35809i
\(528\) 0 0
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 22.5000 + 12.9904i 0.974583 + 0.562676i
\(534\) 0 0
\(535\) −18.0000 + 10.3923i −0.778208 + 0.449299i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 21.0000 12.1244i 0.899541 0.519350i
\(546\) 0 0
\(547\) 34.5000 + 19.9186i 1.47511 + 0.851657i 0.999606 0.0280547i \(-0.00893127\pi\)
0.475507 + 0.879712i \(0.342265\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 0 0
\(553\) 7.50000 + 12.9904i 0.318932 + 0.552407i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 27.7128i 1.17423i 0.809504 + 0.587115i \(0.199736\pi\)
−0.809504 + 0.587115i \(0.800264\pi\)
\(558\) 0 0
\(559\) 25.9808i 1.09887i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −4.50000 7.79423i −0.189652 0.328488i 0.755482 0.655169i \(-0.227403\pi\)
−0.945134 + 0.326682i \(0.894069\pi\)
\(564\) 0 0
\(565\) −10.5000 + 18.1865i −0.441738 + 0.765113i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.50000 0.866025i −0.0628833 0.0363057i 0.468229 0.883607i \(-0.344892\pi\)
−0.531112 + 0.847302i \(0.678226\pi\)
\(570\) 0 0
\(571\) −28.5000 + 16.4545i −1.19269 + 0.688599i −0.958915 0.283693i \(-0.908440\pi\)
−0.233773 + 0.972291i \(0.575107\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 18.0000 0.750652
\(576\) 0 0
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 22.5000 12.9904i 0.933457 0.538932i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.5000 + 33.7750i −0.804851 + 1.39404i 0.111540 + 0.993760i \(0.464422\pi\)
−0.916392 + 0.400283i \(0.868912\pi\)
\(588\) 0 0
\(589\) −9.00000 15.5885i −0.370839 0.642311i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 34.6410i 1.42254i 0.702921 + 0.711268i \(0.251879\pi\)
−0.702921 + 0.711268i \(0.748121\pi\)
\(594\) 0 0
\(595\) 20.7846i 0.852086i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −22.5000 38.9711i −0.919325 1.59232i −0.800443 0.599409i \(-0.795402\pi\)
−0.118882 0.992908i \(-0.537931\pi\)
\(600\) 0 0
\(601\) −5.50000 + 9.52628i −0.224350 + 0.388585i −0.956124 0.292962i \(-0.905359\pi\)
0.731774 + 0.681547i \(0.238692\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.00000 1.73205i −0.121967 0.0704179i
\(606\) 0 0
\(607\) 1.50000 0.866025i 0.0608831 0.0351509i −0.469249 0.883066i \(-0.655475\pi\)
0.530133 + 0.847915i \(0.322142\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15.0000 −0.606835
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −19.5000 + 11.2583i −0.785040 + 0.453243i −0.838214 0.545342i \(-0.816400\pi\)
0.0531732 + 0.998585i \(0.483066\pi\)
\(618\) 0 0
\(619\) −25.5000 14.7224i −1.02493 0.591744i −0.109403 0.993997i \(-0.534894\pi\)
−0.915529 + 0.402253i \(0.868227\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.00000 + 10.3923i −0.240385 + 0.416359i
\(624\) 0 0
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 13.8564i 0.552491i
\(630\) 0 0
\(631\) 17.3205i 0.689519i −0.938691 0.344759i \(-0.887961\pi\)
0.938691 0.344759i \(-0.112039\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.00000 15.5885i −0.357154 0.618609i
\(636\) 0 0
\(637\) 10.0000 17.3205i 0.396214 0.686264i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −25.5000 14.7224i −1.00719 0.581501i −0.0968219 0.995302i \(-0.530868\pi\)
−0.910368 + 0.413801i \(0.864201\pi\)
\(642\) 0 0
\(643\) −4.50000 + 2.59808i −0.177463 + 0.102458i −0.586100 0.810239i \(-0.699337\pi\)
0.408637 + 0.912697i \(0.366004\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 0 0
\(649\) −9.00000 −0.353281
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −13.5000 + 7.79423i −0.528296 + 0.305012i −0.740322 0.672252i \(-0.765327\pi\)
0.212026 + 0.977264i \(0.431994\pi\)
\(654\) 0 0
\(655\) −4.50000 2.59808i −0.175830 0.101515i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.50000 + 2.59808i −0.0584317 + 0.101207i −0.893762 0.448542i \(-0.851943\pi\)
0.835330 + 0.549749i \(0.185277\pi\)
\(660\) 0 0
\(661\) 24.5000 + 42.4352i 0.952940 + 1.65054i 0.739014 + 0.673690i \(0.235292\pi\)
0.213925 + 0.976850i \(0.431375\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10.3923i 0.402996i
\(666\) 0 0
\(667\) 15.5885i 0.603587i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.50000 + 2.59808i 0.0579069 + 0.100298i
\(672\) 0 0
\(673\) 18.5000 32.0429i 0.713123 1.23516i −0.250557 0.968102i \(-0.580614\pi\)
0.963679 0.267063i \(-0.0860531\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −31.5000 18.1865i −1.21064 0.698965i −0.247744 0.968826i \(-0.579689\pi\)
−0.962899 + 0.269860i \(0.913022\pi\)
\(678\) 0 0
\(679\) −7.50000 + 4.33013i −0.287824 + 0.166175i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) 15.0000 0.573121
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 4.50000 + 2.59808i 0.171188 + 0.0988355i 0.583146 0.812367i \(-0.301822\pi\)
−0.411958 + 0.911203i \(0.635155\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1.50000 + 2.59808i −0.0568982 + 0.0985506i
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 13.8564i 0.523349i 0.965156 + 0.261675i \(0.0842747\pi\)
−0.965156 + 0.261675i \(0.915725\pi\)
\(702\) 0 0
\(703\) 6.92820i 0.261302i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.50000 7.79423i −0.169240 0.293132i
\(708\) 0 0
\(709\) −9.50000 + 16.4545i −0.356780 + 0.617961i −0.987421 0.158114i \(-0.949459\pi\)
0.630641 + 0.776075i \(0.282792\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 40.5000 + 23.3827i 1.51674 + 0.875688i
\(714\) 0 0
\(715\) 22.5000 12.9904i 0.841452 0.485813i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) −3.00000 −0.111726
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.00000 1.73205i 0.111417 0.0643268i
\(726\) 0 0
\(727\) −31.5000 18.1865i −1.16827 0.674501i −0.214998 0.976614i \(-0.568975\pi\)
−0.953272 + 0.302113i \(0.902308\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −18.0000 + 31.1769i −0.665754 + 1.15312i
\(732\) 0 0
\(733\) 2.50000 + 4.33013i 0.0923396 + 0.159937i 0.908495 0.417895i \(-0.137232\pi\)
−0.816156 + 0.577832i \(0.803899\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 25.9808i 0.957014i
\(738\) 0 0
\(739\) 31.1769i 1.14686i −0.819254 0.573431i \(-0.805612\pi\)
0.819254 0.573431i \(-0.194388\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13.5000 + 23.3827i 0.495267 + 0.857828i 0.999985 0.00545664i \(-0.00173691\pi\)
−0.504718 + 0.863284i \(0.668404\pi\)
\(744\) 0 0
\(745\) 7.50000 12.9904i 0.274779 0.475931i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −18.0000 10.3923i −0.657706 0.379727i
\(750\) 0 0
\(751\) −10.5000 + 6.06218i −0.383150 + 0.221212i −0.679188 0.733964i \(-0.737668\pi\)
0.296038 + 0.955176i \(0.404335\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 15.0000 0.545906
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −19.5000 + 11.2583i −0.706874 + 0.408114i −0.809903 0.586564i \(-0.800480\pi\)
0.103028 + 0.994678i \(0.467147\pi\)
\(762\) 0 0
\(763\) 21.0000 + 12.1244i 0.760251 + 0.438931i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.50000 + 12.9904i −0.270809 + 0.469055i
\(768\) 0 0
\(769\) −11.5000 19.9186i −0.414701 0.718283i 0.580696 0.814120i \(-0.302780\pi\)
−0.995397 + 0.0958377i \(0.969447\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 27.7128i 0.996761i 0.866959 + 0.498380i \(0.166072\pi\)
−0.866959 + 0.498380i \(0.833928\pi\)
\(774\) 0 0
\(775\) 10.3923i 0.373303i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.00000 + 15.5885i 0.322458 + 0.558514i
\(780\) 0 0
\(781\) −18.0000 + 31.1769i −0.644091 + 1.11560i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1.50000 0.866025i −0.0535373 0.0309098i
\(786\) 0 0
\(787\) 25.5000 14.7224i 0.908977 0.524798i 0.0288750 0.999583i \(-0.490808\pi\)
0.880102 + 0.474785i \(0.157474\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −21.0000 −0.746674
\(792\) 0 0
\(793\) 5.00000 0.177555
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28.5000 16.4545i 1.00952 0.582848i 0.0984702 0.995140i \(-0.468605\pi\)
0.911052 + 0.412292i \(0.135272\pi\)
\(798\) 0 0
\(799\) −18.0000 10.3923i −0.636794 0.367653i
\(800\) 0 0
\(801\)