Properties

Label 2592.2.i.w.1729.1
Level 2592
Weight 2
Character 2592.1729
Analytic conductor 20.697
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(20.6972242039\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1729.1
Root \(0.500000 - 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 2592.1729
Dual form 2592.2.i.w.865.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 3.46410i) q^{7} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{5} +(2.00000 + 3.46410i) q^{7} +(2.00000 + 3.46410i) q^{11} +(1.00000 - 1.73205i) q^{13} +6.00000 q^{17} -4.00000 q^{19} +(0.500000 + 0.866025i) q^{25} +(1.00000 + 1.73205i) q^{29} +(-2.00000 + 3.46410i) q^{31} +8.00000 q^{35} -2.00000 q^{37} +(1.00000 - 1.73205i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(4.00000 + 6.92820i) q^{47} +(-4.50000 + 7.79423i) q^{49} -10.0000 q^{53} +8.00000 q^{55} +(-2.00000 + 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} +(-2.00000 - 3.46410i) q^{65} +(-2.00000 + 3.46410i) q^{67} +16.0000 q^{71} -6.00000 q^{73} +(-8.00000 + 13.8564i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(6.00000 + 10.3923i) q^{83} +(6.00000 - 10.3923i) q^{85} -10.0000 q^{89} +8.00000 q^{91} +(-4.00000 + 6.92820i) q^{95} +(7.00000 + 12.1244i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 2q + 2q^{5} + 4q^{7} + 4q^{11} + 2q^{13} + 12q^{17} - 8q^{19} + q^{25} + 2q^{29} - 4q^{31} + 16q^{35} - 4q^{37} + 2q^{41} - 4q^{43} + 8q^{47} - 9q^{49} - 20q^{53} + 16q^{55} - 4q^{59} - 6q^{61} - 4q^{65} - 4q^{67} + 32q^{71} - 12q^{73} - 16q^{77} - 4q^{79} + 12q^{83} + 12q^{85} - 20q^{89} + 16q^{91} - 8q^{95} + 14q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(325\) \(1217\) \(2431\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 0 0
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.00000 + 1.73205i 0.185695 + 0.321634i 0.943811 0.330487i \(-0.107213\pi\)
−0.758115 + 0.652121i \(0.773880\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 8.00000 1.35225
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.00000 1.73205i 0.156174 0.270501i −0.777312 0.629115i \(-0.783417\pi\)
0.933486 + 0.358614i \(0.116751\pi\)
\(42\) 0 0
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 0 0
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 0 0
\(55\) 8.00000 1.07872
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.00000 + 3.46410i −0.260378 + 0.450988i −0.966342 0.257260i \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0 0
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.00000 3.46410i −0.248069 0.429669i
\(66\) 0 0
\(67\) −2.00000 + 3.46410i −0.244339 + 0.423207i −0.961946 0.273241i \(-0.911904\pi\)
0.717607 + 0.696449i \(0.245238\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −8.00000 + 13.8564i −0.911685 + 1.57908i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 0 0
\(85\) 6.00000 10.3923i 0.650791 1.12720i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 8.00000 0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) 0 0
\(97\) 7.00000 + 12.1244i 0.710742 + 1.23104i 0.964579 + 0.263795i \(0.0849741\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 6.00000 10.3923i 0.591198 1.02398i −0.402874 0.915255i \(-0.631989\pi\)
0.994071 0.108729i \(-0.0346780\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.00000 1.73205i 0.0940721 0.162938i −0.815149 0.579252i \(-0.803345\pi\)
0.909221 + 0.416314i \(0.136678\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 12.0000 + 20.7846i 1.10004 + 1.90532i
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.00000 3.46410i 0.174741 0.302660i −0.765331 0.643637i \(-0.777425\pi\)
0.940072 + 0.340977i \(0.110758\pi\)
\(132\) 0 0
\(133\) −8.00000 13.8564i −0.693688 1.20150i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.00000 + 15.5885i 0.768922 + 1.33181i 0.938148 + 0.346235i \(0.112540\pi\)
−0.169226 + 0.985577i \(0.554127\pi\)
\(138\) 0 0
\(139\) 10.0000 17.3205i 0.848189 1.46911i −0.0346338 0.999400i \(-0.511026\pi\)
0.882823 0.469706i \(-0.155640\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) 4.00000 0.332182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 0 0
\(151\) −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i \(-0.329040\pi\)
−0.999909 + 0.0134886i \(0.995706\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.00000 + 6.92820i 0.321288 + 0.556487i
\(156\) 0 0
\(157\) 5.00000 8.66025i 0.399043 0.691164i −0.594565 0.804048i \(-0.702676\pi\)
0.993608 + 0.112884i \(0.0360089\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4.00000 6.92820i 0.309529 0.536120i −0.668730 0.743505i \(-0.733162\pi\)
0.978259 + 0.207385i \(0.0664952\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2.00000 + 3.46410i −0.147043 + 0.254686i
\(186\) 0 0
\(187\) 12.0000 + 20.7846i 0.877527 + 1.51992i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) −9.00000 + 15.5885i −0.647834 + 1.12208i 0.335805 + 0.941932i \(0.390992\pi\)
−0.983639 + 0.180150i \(0.942342\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.00000 + 6.92820i −0.280745 + 0.486265i
\(204\) 0 0
\(205\) −2.00000 3.46410i −0.139686 0.241943i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.00000 13.8564i −0.553372 0.958468i
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.00000 −0.545595
\(216\) 0 0
\(217\) −16.0000 −1.08615
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i \(-0.123907\pi\)
−0.791258 + 0.611482i \(0.790574\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.00000 + 10.3923i 0.398234 + 0.689761i 0.993508 0.113761i \(-0.0362899\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000 0.393073 0.196537 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) 7.00000 + 12.1244i 0.450910 + 0.780998i 0.998443 0.0557856i \(-0.0177663\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 9.00000 + 15.5885i 0.574989 + 0.995910i
\(246\) 0 0
\(247\) −4.00000 + 6.92820i −0.254514 + 0.440831i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.00000 1.73205i 0.0623783 0.108042i −0.833150 0.553047i \(-0.813465\pi\)
0.895528 + 0.445005i \(0.146798\pi\)
\(258\) 0 0
\(259\) −4.00000 6.92820i −0.248548 0.430498i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.0000 20.7846i −0.739952 1.28163i −0.952517 0.304487i \(-0.901515\pi\)
0.212565 0.977147i \(-0.431818\pi\)
\(264\) 0 0
\(265\) −10.0000 + 17.3205i −0.614295 + 1.06399i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −18.0000 −1.09748 −0.548740 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) 0 0
\(271\) 12.0000 0.728948 0.364474 0.931214i \(-0.381249\pi\)
0.364474 + 0.931214i \(0.381249\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.00000 + 3.46410i −0.120605 + 0.208893i
\(276\) 0 0
\(277\) −11.0000 19.0526i −0.660926 1.14476i −0.980373 0.197153i \(-0.936830\pi\)
0.319447 0.947604i \(-0.396503\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.00000 5.19615i −0.178965 0.309976i 0.762561 0.646916i \(-0.223942\pi\)
−0.941526 + 0.336939i \(0.890608\pi\)
\(282\) 0 0
\(283\) −14.0000 + 24.2487i −0.832214 + 1.44144i 0.0640654 + 0.997946i \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.00000 0.472225
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −3.00000 + 5.19615i −0.175262 + 0.303562i −0.940252 0.340480i \(-0.889411\pi\)
0.764990 + 0.644042i \(0.222744\pi\)
\(294\) 0 0
\(295\) 4.00000 + 6.92820i 0.232889 + 0.403376i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 8.00000 13.8564i 0.461112 0.798670i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i \(-0.257869\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −16.0000 + 27.7128i −0.882109 + 1.52786i
\(330\) 0 0
\(331\) −14.0000 24.2487i −0.769510 1.33283i −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.00000 + 6.92820i 0.218543 + 0.378528i
\(336\) 0 0
\(337\) −1.00000 + 1.73205i −0.0544735 + 0.0943508i −0.891976 0.452082i \(-0.850681\pi\)
0.837503 + 0.546433i \(0.184015\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −16.0000 −0.866449
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 10.0000 17.3205i 0.536828 0.929814i −0.462244 0.886753i \(-0.652956\pi\)
0.999072 0.0430610i \(-0.0137110\pi\)
\(348\) 0 0
\(349\) 13.0000 + 22.5167i 0.695874 + 1.20529i 0.969885 + 0.243563i \(0.0783162\pi\)
−0.274011 + 0.961727i \(0.588351\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.00000 12.1244i −0.372572 0.645314i 0.617388 0.786659i \(-0.288191\pi\)
−0.989960 + 0.141344i \(0.954858\pi\)
\(354\) 0 0
\(355\) 16.0000 27.7128i 0.849192 1.47084i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −16.0000 −0.844448 −0.422224 0.906492i \(-0.638750\pi\)
−0.422224 + 0.906492i \(0.638750\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.00000 + 10.3923i −0.314054 + 0.543958i
\(366\) 0 0
\(367\) 6.00000 + 10.3923i 0.313197 + 0.542474i 0.979053 0.203607i \(-0.0652665\pi\)
−0.665855 + 0.746081i \(0.731933\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −20.0000 34.6410i −1.03835 1.79847i
\(372\) 0 0
\(373\) 17.0000 29.4449i 0.880227 1.52460i 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16.0000 27.7128i 0.817562 1.41606i −0.0899119 0.995950i \(-0.528659\pi\)
0.907474 0.420109i \(-0.138008\pi\)
\(384\) 0 0
\(385\) 16.0000 + 27.7128i 0.815436 + 1.41238i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −15.0000 25.9808i −0.760530 1.31728i −0.942578 0.333987i \(-0.891606\pi\)
0.182047 0.983290i \(-0.441728\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.00000 −0.402524
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.00000 8.66025i 0.249688 0.432472i −0.713751 0.700399i \(-0.753005\pi\)
0.963439 + 0.267927i \(0.0863386\pi\)
\(402\) 0 0
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.00000 6.92820i −0.198273 0.343418i
\(408\) 0 0
\(409\) −5.00000 + 8.66025i −0.247234 + 0.428222i −0.962757 0.270367i \(-0.912855\pi\)
0.715523 + 0.698589i \(0.246188\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −16.0000 −0.787309
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −10.0000 + 17.3205i −0.488532 + 0.846162i −0.999913 0.0131919i \(-0.995801\pi\)
0.511381 + 0.859354i \(0.329134\pi\)
\(420\) 0 0
\(421\) −19.0000 32.9090i −0.926003 1.60388i −0.789940 0.613185i \(-0.789888\pi\)
−0.136064 0.990700i \(-0.543445\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) 12.0000 20.7846i 0.580721 1.00584i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 0 0
\(445\) −10.0000 + 17.3205i −0.474045 + 0.821071i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) 8.00000 0.376705
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8.00000 13.8564i 0.375046 0.649598i
\(456\) 0 0
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i \(-0.211288\pi\)
−0.927392 + 0.374091i \(0.877955\pi\)
\(462\) 0 0
\(463\) 10.0000 17.3205i 0.464739 0.804952i −0.534450 0.845200i \(-0.679481\pi\)
0.999190 + 0.0402476i \(0.0128147\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) −16.0000 −0.738811
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) 0 0
\(475\) −2.00000 3.46410i −0.0917663 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 28.0000 1.27141
\(486\) 0 0
\(487\) −4.00000 −0.181257 −0.0906287 0.995885i \(-0.528888\pi\)
−0.0906287 + 0.995885i \(0.528888\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 14.0000 24.2487i 0.631811 1.09433i −0.355370 0.934726i \(-0.615645\pi\)
0.987181 0.159603i \(-0.0510215\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 32.0000 + 55.4256i 1.43540 + 2.48618i
\(498\) 0 0
\(499\) 6.00000 10.3923i 0.268597 0.465223i −0.699903 0.714238i \(-0.746773\pi\)
0.968500 + 0.249015i \(0.0801067\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) 0 0
\(511\) −12.0000 20.7846i −0.530849 0.919457i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.0000 20.7846i −0.528783 0.915879i
\(516\) 0 0
\(517\) −16.0000 + 27.7128i −0.703679 + 1.21881i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −12.0000 −0.524723 −0.262362 0.964970i \(-0.584501\pi\)
−0.262362 + 0.964970i \(0.584501\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.00000 3.46410i −0.0866296 0.150047i
\(534\) 0 0
\(535\) 4.00000 6.92820i 0.172935 0.299532i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −36.0000 −1.55063
\(540\) 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
\(545\) 14.0000 24.2487i 0.599694 1.03870i
\(546\) 0 0
\(547\) −6.00000 10.3923i −0.256541 0.444343i 0.708772 0.705438i \(-0.249250\pi\)
−0.965313 + 0.261095i \(0.915916\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4.00000 6.92820i −0.170406 0.295151i
\(552\) 0 0
\(553\) 8.00000 13.8564i 0.340195 0.589234i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.0000 0.932170 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6.00000 10.3923i 0.252870 0.437983i −0.711445 0.702742i \(-0.751959\pi\)
0.964315 + 0.264758i \(0.0852922\pi\)
\(564\) 0 0
\(565\) −2.00000 3.46410i −0.0841406 0.145736i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −23.0000 39.8372i −0.964210 1.67006i −0.711722 0.702461i \(-0.752085\pi\)
−0.252488 0.967600i \(-0.581249\pi\)
\(570\) 0 0
\(571\) −22.0000 + 38.1051i −0.920671 + 1.59465i −0.122292 + 0.992494i \(0.539025\pi\)
−0.798379 + 0.602155i \(0.794309\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −24.0000 + 41.5692i −0.995688 + 1.72458i
\(582\) 0 0
\(583\) −20.0000 34.6410i −0.828315 1.43468i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.0000 31.1769i −0.742940 1.28681i −0.951151 0.308725i \(-0.900098\pi\)
0.208212 0.978084i \(-0.433236\pi\)
\(588\) 0 0
\(589\) 8.00000 13.8564i 0.329634 0.570943i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 48.0000 1.96781
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.00000 + 13.8564i −0.326871 + 0.566157i −0.981889 0.189456i \(-0.939328\pi\)
0.655018 + 0.755613i \(0.272661\pi\)
\(600\) 0 0
\(601\) −5.00000 8.66025i −0.203954 0.353259i 0.745845 0.666120i \(-0.232046\pi\)
−0.949799 + 0.312861i \(0.898713\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) 10.0000 17.3205i 0.405887 0.703018i −0.588537 0.808470i \(-0.700296\pi\)
0.994424 + 0.105453i \(0.0336291\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.0000 0.647291
\(612\) 0 0
\(613\) −18.0000 −0.727013 −0.363507 0.931592i \(-0.618421\pi\)
−0.363507 + 0.931592i \(0.618421\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0000 36.3731i 0.845428 1.46432i −0.0398207 0.999207i \(-0.512679\pi\)
0.885249 0.465118i \(-0.153988\pi\)
\(618\) 0 0
\(619\) −6.00000 10.3923i −0.241160 0.417702i 0.719885 0.694094i \(-0.244195\pi\)
−0.961045 + 0.276392i \(0.910861\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −20.0000 34.6410i −0.801283 1.38786i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −20.0000 + 34.6410i −0.793676 + 1.37469i
\(636\) 0 0
\(637\) 9.00000 + 15.5885i 0.356593 + 0.617637i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.00000 + 8.66025i 0.197488 + 0.342059i 0.947713 0.319123i \(-0.103388\pi\)
−0.750225 + 0.661182i \(0.770055\pi\)
\(642\) 0 0
\(643\) −6.00000 + 10.3923i −0.236617 + 0.409832i −0.959741 0.280885i \(-0.909372\pi\)
0.723124 + 0.690718i \(0.242705\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −48.0000 −1.88707 −0.943537 0.331266i \(-0.892524\pi\)
−0.943537 + 0.331266i \(0.892524\pi\)
\(648\) 0 0
\(649\) −16.0000 −0.628055
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 5.00000 8.66025i 0.195665 0.338902i −0.751453 0.659786i \(-0.770647\pi\)
0.947118 + 0.320884i \(0.103980\pi\)
\(654\) 0 0
\(655\) −4.00000 6.92820i −0.156293 0.270707i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 18.0000 + 31.1769i 0.701180 + 1.21448i 0.968052 + 0.250748i \(0.0806766\pi\)
−0.266872 + 0.963732i \(0.585990\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −32.0000 −1.24091
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 12.0000 20.7846i 0.463255 0.802381i
\(672\) 0 0
\(673\) −1.00000 1.73205i −0.0385472 0.0667657i 0.846108 0.533011i \(-0.178940\pi\)
−0.884655 + 0.466246i \(0.845606\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.00000 12.1244i −0.269032 0.465977i 0.699580 0.714554i \(-0.253370\pi\)
−0.968612 + 0.248577i \(0.920037\pi\)
\(678\) 0 0
\(679\) −28.0000 + 48.4974i −1.07454 + 1.86116i
\(680\) 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
\(685\) 36.0000 1.37549
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −10.0000 + 17.3205i −0.380970 + 0.659859i
\(690\) 0 0
\(691\) 26.0000 + 45.0333i 0.989087 + 1.71315i 0.622139 + 0.782907i \(0.286264\pi\)
0.366947 + 0.930242i \(0.380403\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −20.0000 34.6410i −0.758643 1.31401i
\(696\) 0 0
\(697\) 6.00000 10.3923i 0.227266 0.393637i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.0000 20.7846i 0.451306 0.781686i
\(708\) 0 0
\(709\) −11.0000 19.0526i −0.413114 0.715534i 0.582115 0.813107i \(-0.302225\pi\)
−0.995228 + 0.0975728i \(0.968892\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 8.00000 13.8564i 0.299183 0.518200i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8.00000 −0.298350 −0.149175 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 0 0
\(721\) 48.0000 1.78761
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.00000 + 1.73205i −0.0371391 + 0.0643268i
\(726\) 0 0
\(727\) −6.00000 10.3923i −0.222528 0.385429i 0.733047 0.680178i \(-0.238097\pi\)
−0.955575 + 0.294749i \(0.904764\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) −7.00000 + 12.1244i −0.258551 + 0.447823i −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16.0000 −0.589368
\(738\) 0 0
\(739\) 20.0000 0.735712 0.367856 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 12.0000 20.7846i 0.440237 0.762513i −0.557470 0.830197i \(-0.688228\pi\)
0.997707 + 0.0676840i \(0.0215610\pi\)
\(744\) 0 0
\(745\) −18.0000 31.1769i −0.659469 1.14223i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.00000 + 13.8564i 0.292314 + 0.506302i
\(750\) 0 0
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −24.0000 −0.873449
\(756\) 0 0
\(757\) 6.00000 0.218074 0.109037 0.994038i \(-0.465223\pi\)
0.109037 + 0.994038i \(0.465223\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −15.0000 + 25.9808i −0.543750 + 0.941802i 0.454935 + 0.890525i \(0.349663\pi\)
−0.998684 + 0.0512772i \(0.983671\pi\)
\(762\) 0 0
\(763\) 28.0000 + 48.4974i 1.01367 + 1.75572i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.00000 + 6.92820i 0.144432 + 0.250163i
\(768\) 0 0
\(769\) 7.00000 12.1244i 0.252426 0.437215i −0.711767 0.702416i \(-0.752105\pi\)
0.964193 + 0.265200i \(0.0854381\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −42.0000 −1.51064 −0.755318 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4.00000 + 6.92820i −0.143315 + 0.248229i
\(780\) 0 0
\(781\) 32.0000 + 55.4256i 1.14505 + 1.98328i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −10.0000 17.3205i −0.356915 0.618195i
\(786\) 0 0
\(787\) −6.00000 + 10.3923i −0.213877 + 0.370446i −0.952925 0.303207i \(-0.901942\pi\)
0.739048 + 0.673653i \(0.235276\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 8.00000 0.284447
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.00000 + 5.19615i −0.106265 + 0.184057i −0.914255 0.405140i \(-0.867223\pi\)
0.807989 + 0.589197i \(0.200556\pi\)
\(798\) 0 0
\(799\) 24.0000 + 41.5692i 0.849059 + 1.47061i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12.0000 20.7846i −0.423471 0.733473i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 14.0000 0.492214 0.246107 0.969243i \(-0.420849\pi\)
0.246107 + 0.969243i \(0.420849\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −4.00000 + 6.92820i −0.140114 + 0.242684i
\(816\)