Properties

Label 3024.2.q.l.2305.1
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.1
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.11148 - 3.65719i) q^{5} +(-2.19338 + 1.47956i) q^{7} +O(q^{10})\) \(q+(-2.11148 - 3.65719i) q^{5} +(-2.19338 + 1.47956i) q^{7} +(-0.964575 + 1.67069i) q^{11} +(-0.291529 + 0.504943i) q^{13} +(-3.61082 - 6.25412i) q^{17} +(-2.10268 + 3.64194i) q^{19} +(-0.639939 - 1.10841i) q^{23} +(-6.41671 + 11.1141i) q^{25} +(4.20305 + 7.27990i) q^{29} +0.952121 q^{31} +(10.0423 + 4.89755i) q^{35} +(3.03329 - 5.25381i) q^{37} +(-1.31299 + 2.27416i) q^{41} +(-0.442349 - 0.766171i) q^{43} +5.76401 q^{47} +(2.62182 - 6.49046i) q^{49} +(0.962456 + 1.66702i) q^{53} +8.14673 q^{55} -4.55229 q^{59} -10.5802 q^{61} +2.46223 q^{65} +4.86383 q^{67} +11.5443 q^{71} +(0.446138 + 0.772734i) q^{73} +(-0.356209 - 5.09160i) q^{77} +11.8704 q^{79} +(-5.24250 - 9.08028i) q^{83} +(-15.2484 + 26.4109i) q^{85} +(-3.87906 + 6.71874i) q^{89} +(-0.107659 - 1.53887i) q^{91} +17.7591 q^{95} +(-1.98651 - 3.44073i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.11148 3.65719i −0.944283 1.63555i −0.757180 0.653206i \(-0.773423\pi\)
−0.187103 0.982340i \(-0.559910\pi\)
\(6\) 0 0
\(7\) −2.19338 + 1.47956i −0.829019 + 0.559220i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.964575 + 1.67069i −0.290830 + 0.503733i −0.974006 0.226521i \(-0.927265\pi\)
0.683176 + 0.730254i \(0.260598\pi\)
\(12\) 0 0
\(13\) −0.291529 + 0.504943i −0.0808557 + 0.140046i −0.903618 0.428340i \(-0.859099\pi\)
0.822762 + 0.568386i \(0.192432\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.61082 6.25412i −0.875753 1.51685i −0.855959 0.517044i \(-0.827032\pi\)
−0.0197936 0.999804i \(-0.506301\pi\)
\(18\) 0 0
\(19\) −2.10268 + 3.64194i −0.482387 + 0.835519i −0.999796 0.0202194i \(-0.993564\pi\)
0.517408 + 0.855739i \(0.326897\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.639939 1.10841i −0.133437 0.231119i 0.791563 0.611088i \(-0.209268\pi\)
−0.924999 + 0.379969i \(0.875935\pi\)
\(24\) 0 0
\(25\) −6.41671 + 11.1141i −1.28334 + 2.22281i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.20305 + 7.27990i 0.780487 + 1.35184i 0.931658 + 0.363335i \(0.118362\pi\)
−0.151171 + 0.988508i \(0.548305\pi\)
\(30\) 0 0
\(31\) 0.952121 0.171006 0.0855030 0.996338i \(-0.472750\pi\)
0.0855030 + 0.996338i \(0.472750\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 10.0423 + 4.89755i 1.69746 + 0.827837i
\(36\) 0 0
\(37\) 3.03329 5.25381i 0.498669 0.863721i −0.501330 0.865256i \(-0.667156\pi\)
0.999999 + 0.00153588i \(0.000488885\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.31299 + 2.27416i −0.205054 + 0.355164i −0.950150 0.311794i \(-0.899070\pi\)
0.745096 + 0.666957i \(0.232404\pi\)
\(42\) 0 0
\(43\) −0.442349 0.766171i −0.0674576 0.116840i 0.830324 0.557281i \(-0.188155\pi\)
−0.897782 + 0.440441i \(0.854822\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.76401 0.840767 0.420384 0.907346i \(-0.361895\pi\)
0.420384 + 0.907346i \(0.361895\pi\)
\(48\) 0 0
\(49\) 2.62182 6.49046i 0.374545 0.927209i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0.962456 + 1.66702i 0.132204 + 0.228983i 0.924526 0.381120i \(-0.124461\pi\)
−0.792322 + 0.610103i \(0.791128\pi\)
\(54\) 0 0
\(55\) 8.14673 1.09850
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.55229 −0.592657 −0.296329 0.955086i \(-0.595762\pi\)
−0.296329 + 0.955086i \(0.595762\pi\)
\(60\) 0 0
\(61\) −10.5802 −1.35465 −0.677325 0.735684i \(-0.736861\pi\)
−0.677325 + 0.735684i \(0.736861\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.46223 0.305403
\(66\) 0 0
\(67\) 4.86383 0.594211 0.297106 0.954845i \(-0.403979\pi\)
0.297106 + 0.954845i \(0.403979\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.5443 1.37005 0.685027 0.728518i \(-0.259791\pi\)
0.685027 + 0.728518i \(0.259791\pi\)
\(72\) 0 0
\(73\) 0.446138 + 0.772734i 0.0522165 + 0.0904417i 0.890952 0.454097i \(-0.150038\pi\)
−0.838736 + 0.544539i \(0.816705\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.356209 5.09160i −0.0405937 0.580242i
\(78\) 0 0
\(79\) 11.8704 1.33553 0.667763 0.744374i \(-0.267252\pi\)
0.667763 + 0.744374i \(0.267252\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.24250 9.08028i −0.575439 0.996690i −0.995994 0.0894227i \(-0.971498\pi\)
0.420555 0.907267i \(-0.361836\pi\)
\(84\) 0 0
\(85\) −15.2484 + 26.4109i −1.65392 + 2.86467i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.87906 + 6.71874i −0.411180 + 0.712185i −0.995019 0.0996849i \(-0.968217\pi\)
0.583839 + 0.811869i \(0.301550\pi\)
\(90\) 0 0
\(91\) −0.107659 1.53887i −0.0112857 0.161317i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 17.7591 1.82204
\(96\) 0 0
\(97\) −1.98651 3.44073i −0.201699 0.349353i 0.747377 0.664400i \(-0.231313\pi\)
−0.949076 + 0.315047i \(0.897980\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 8.38533 14.5238i 0.834372 1.44517i −0.0601687 0.998188i \(-0.519164\pi\)
0.894541 0.446986i \(-0.147503\pi\)
\(102\) 0 0
\(103\) 5.80569 + 10.0558i 0.572052 + 0.990823i 0.996355 + 0.0853025i \(0.0271857\pi\)
−0.424303 + 0.905520i \(0.639481\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.2454 + 17.7455i −0.990460 + 1.71553i −0.375890 + 0.926664i \(0.622663\pi\)
−0.614570 + 0.788862i \(0.710671\pi\)
\(108\) 0 0
\(109\) 2.46965 + 4.27756i 0.236550 + 0.409716i 0.959722 0.280951i \(-0.0906500\pi\)
−0.723172 + 0.690668i \(0.757317\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.42131 12.8541i 0.698138 1.20921i −0.270974 0.962587i \(-0.587346\pi\)
0.969111 0.246623i \(-0.0793210\pi\)
\(114\) 0 0
\(115\) −2.70244 + 4.68076i −0.252004 + 0.436484i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 17.1732 + 8.37524i 1.57427 + 0.767757i
\(120\) 0 0
\(121\) 3.63919 + 6.30326i 0.330836 + 0.573024i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 33.0802 2.95879
\(126\) 0 0
\(127\) 8.53648 0.757490 0.378745 0.925501i \(-0.376356\pi\)
0.378745 + 0.925501i \(0.376356\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.17342 + 2.03243i 0.102522 + 0.177574i 0.912723 0.408578i \(-0.133975\pi\)
−0.810201 + 0.586152i \(0.800642\pi\)
\(132\) 0 0
\(133\) −0.776499 11.0992i −0.0673310 0.962422i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.641815 1.11166i 0.0548340 0.0949752i −0.837305 0.546735i \(-0.815870\pi\)
0.892139 + 0.451760i \(0.149204\pi\)
\(138\) 0 0
\(139\) −0.610553 + 1.05751i −0.0517865 + 0.0896968i −0.890757 0.454481i \(-0.849825\pi\)
0.838970 + 0.544177i \(0.183158\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.562403 0.974111i −0.0470305 0.0814593i
\(144\) 0 0
\(145\) 17.7493 30.7427i 1.47400 2.55305i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.14729 + 5.45127i 0.257836 + 0.446585i 0.965662 0.259802i \(-0.0836572\pi\)
−0.707826 + 0.706387i \(0.750324\pi\)
\(150\) 0 0
\(151\) 1.17726 2.03908i 0.0958044 0.165938i −0.814140 0.580669i \(-0.802791\pi\)
0.909944 + 0.414731i \(0.136124\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.01039 3.48209i −0.161478 0.279688i
\(156\) 0 0
\(157\) −2.88873 −0.230546 −0.115273 0.993334i \(-0.536774\pi\)
−0.115273 + 0.993334i \(0.536774\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.04358 + 1.48433i 0.239868 + 0.116982i
\(162\) 0 0
\(163\) −2.60538 + 4.51265i −0.204069 + 0.353458i −0.949836 0.312749i \(-0.898750\pi\)
0.745767 + 0.666207i \(0.232083\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 10.5400 18.2558i 0.815610 1.41268i −0.0932784 0.995640i \(-0.529735\pi\)
0.908889 0.417039i \(-0.136932\pi\)
\(168\) 0 0
\(169\) 6.33002 + 10.9639i 0.486925 + 0.843378i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.07305 0.309669 0.154834 0.987940i \(-0.450516\pi\)
0.154834 + 0.987940i \(0.450516\pi\)
\(174\) 0 0
\(175\) −2.36963 33.8712i −0.179127 2.56042i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3.11088 5.38821i −0.232518 0.402733i 0.726030 0.687663i \(-0.241363\pi\)
−0.958549 + 0.284929i \(0.908030\pi\)
\(180\) 0 0
\(181\) 18.2396 1.35574 0.677868 0.735184i \(-0.262904\pi\)
0.677868 + 0.735184i \(0.262904\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −25.6189 −1.88354
\(186\) 0 0
\(187\) 13.9316 1.01878
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.38597 −0.534430 −0.267215 0.963637i \(-0.586103\pi\)
−0.267215 + 0.963637i \(0.586103\pi\)
\(192\) 0 0
\(193\) 19.5182 1.40495 0.702474 0.711709i \(-0.252079\pi\)
0.702474 + 0.711709i \(0.252079\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.77564 −0.553992 −0.276996 0.960871i \(-0.589339\pi\)
−0.276996 + 0.960871i \(0.589339\pi\)
\(198\) 0 0
\(199\) 3.85734 + 6.68110i 0.273439 + 0.473611i 0.969740 0.244139i \(-0.0785054\pi\)
−0.696301 + 0.717750i \(0.745172\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −19.9899 9.74891i −1.40302 0.684240i
\(204\) 0 0
\(205\) 11.0894 0.774515
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.05638 7.02585i −0.280586 0.485989i
\(210\) 0 0
\(211\) −11.7645 + 20.3767i −0.809899 + 1.40279i 0.103034 + 0.994678i \(0.467145\pi\)
−0.912933 + 0.408109i \(0.866188\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.86802 + 3.23551i −0.127398 + 0.220660i
\(216\) 0 0
\(217\) −2.08836 + 1.40872i −0.141767 + 0.0956301i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 4.21064 0.283238
\(222\) 0 0
\(223\) 4.83093 + 8.36742i 0.323503 + 0.560324i 0.981208 0.192952i \(-0.0618061\pi\)
−0.657705 + 0.753275i \(0.728473\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.98592 + 15.5641i −0.596417 + 1.03302i 0.396929 + 0.917850i \(0.370076\pi\)
−0.993345 + 0.115175i \(0.963257\pi\)
\(228\) 0 0
\(229\) 3.95834 + 6.85604i 0.261574 + 0.453060i 0.966660 0.256062i \(-0.0824250\pi\)
−0.705086 + 0.709122i \(0.749092\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.27796 + 5.67759i −0.214746 + 0.371951i −0.953194 0.302359i \(-0.902226\pi\)
0.738448 + 0.674311i \(0.235559\pi\)
\(234\) 0 0
\(235\) −12.1706 21.0801i −0.793922 1.37511i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.01922 + 13.8897i −0.518720 + 0.898450i 0.481043 + 0.876697i \(0.340258\pi\)
−0.999763 + 0.0217529i \(0.993075\pi\)
\(240\) 0 0
\(241\) −5.58957 + 9.68142i −0.360056 + 0.623635i −0.987970 0.154648i \(-0.950576\pi\)
0.627914 + 0.778283i \(0.283909\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −29.2728 + 4.11599i −1.87017 + 0.262961i
\(246\) 0 0
\(247\) −1.22598 2.12347i −0.0780075 0.135113i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 14.6169 0.922613 0.461307 0.887241i \(-0.347381\pi\)
0.461307 + 0.887241i \(0.347381\pi\)
\(252\) 0 0
\(253\) 2.46908 0.155230
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.45936 + 12.9200i 0.465302 + 0.805927i 0.999215 0.0396123i \(-0.0126123\pi\)
−0.533913 + 0.845540i \(0.679279\pi\)
\(258\) 0 0
\(259\) 1.12016 + 16.0115i 0.0696037 + 0.994907i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.1057 19.2357i 0.684808 1.18612i −0.288689 0.957423i \(-0.593219\pi\)
0.973497 0.228699i \(-0.0734472\pi\)
\(264\) 0 0
\(265\) 4.06442 7.03978i 0.249675 0.432450i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.73590 + 8.20281i 0.288753 + 0.500134i 0.973512 0.228635i \(-0.0734261\pi\)
−0.684760 + 0.728769i \(0.740093\pi\)
\(270\) 0 0
\(271\) −8.78188 + 15.2107i −0.533461 + 0.923982i 0.465775 + 0.884903i \(0.345776\pi\)
−0.999236 + 0.0390786i \(0.987558\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −12.3788 21.4407i −0.746469 1.29292i
\(276\) 0 0
\(277\) −6.77651 + 11.7373i −0.407161 + 0.705224i −0.994570 0.104066i \(-0.966815\pi\)
0.587409 + 0.809290i \(0.300148\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.14196 10.6382i −0.366398 0.634621i 0.622601 0.782539i \(-0.286076\pi\)
−0.989000 + 0.147919i \(0.952743\pi\)
\(282\) 0 0
\(283\) −14.0483 −0.835084 −0.417542 0.908658i \(-0.637108\pi\)
−0.417542 + 0.908658i \(0.637108\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.484873 6.93072i −0.0286212 0.409108i
\(288\) 0 0
\(289\) −17.5760 + 30.4426i −1.03388 + 1.79074i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.05863 + 7.02975i −0.237108 + 0.410682i −0.959883 0.280401i \(-0.909533\pi\)
0.722776 + 0.691083i \(0.242866\pi\)
\(294\) 0 0
\(295\) 9.61207 + 16.6486i 0.559636 + 0.969319i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.746244 0.0431564
\(300\) 0 0
\(301\) 2.10383 + 1.02602i 0.121263 + 0.0591390i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 22.3398 + 38.6937i 1.27917 + 2.21559i
\(306\) 0 0
\(307\) −6.61556 −0.377570 −0.188785 0.982018i \(-0.560455\pi\)
−0.188785 + 0.982018i \(0.560455\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −8.35961 −0.474030 −0.237015 0.971506i \(-0.576169\pi\)
−0.237015 + 0.971506i \(0.576169\pi\)
\(312\) 0 0
\(313\) 26.1083 1.47573 0.737864 0.674949i \(-0.235834\pi\)
0.737864 + 0.674949i \(0.235834\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −11.2148 −0.629887 −0.314943 0.949110i \(-0.601986\pi\)
−0.314943 + 0.949110i \(0.601986\pi\)
\(318\) 0 0
\(319\) −16.2166 −0.907957
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 30.3696 1.68981
\(324\) 0 0
\(325\) −3.74132 6.48015i −0.207531 0.359454i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −12.6427 + 8.52819i −0.697012 + 0.470174i
\(330\) 0 0
\(331\) 18.2329 1.00217 0.501086 0.865398i \(-0.332934\pi\)
0.501086 + 0.865398i \(0.332934\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.2699 17.7880i −0.561104 0.971860i
\(336\) 0 0
\(337\) 4.62148 8.00465i 0.251748 0.436041i −0.712259 0.701917i \(-0.752328\pi\)
0.964007 + 0.265876i \(0.0856612\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −0.918392 + 1.59070i −0.0497337 + 0.0861413i
\(342\) 0 0
\(343\) 3.85237 + 18.1152i 0.208009 + 0.978127i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −31.6649 −1.69986 −0.849931 0.526894i \(-0.823356\pi\)
−0.849931 + 0.526894i \(0.823356\pi\)
\(348\) 0 0
\(349\) −18.2112 31.5427i −0.974821 1.68844i −0.680525 0.732725i \(-0.738248\pi\)
−0.294296 0.955714i \(-0.595085\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.59888 6.23345i 0.191549 0.331773i −0.754215 0.656628i \(-0.771982\pi\)
0.945764 + 0.324855i \(0.105316\pi\)
\(354\) 0 0
\(355\) −24.3755 42.2196i −1.29372 2.24079i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.39891 + 12.8153i −0.390499 + 0.676365i −0.992515 0.122119i \(-0.961031\pi\)
0.602016 + 0.798484i \(0.294364\pi\)
\(360\) 0 0
\(361\) 0.657495 + 1.13881i 0.0346050 + 0.0599376i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.88402 3.26323i 0.0986144 0.170805i
\(366\) 0 0
\(367\) 2.09550 3.62951i 0.109384 0.189459i −0.806137 0.591729i \(-0.798445\pi\)
0.915521 + 0.402270i \(0.131779\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.57749 2.23240i −0.237651 0.115901i
\(372\) 0 0
\(373\) −8.70875 15.0840i −0.450922 0.781020i 0.547522 0.836792i \(-0.315571\pi\)
−0.998444 + 0.0557718i \(0.982238\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4.90125 −0.252427
\(378\) 0 0
\(379\) 11.1732 0.573927 0.286964 0.957941i \(-0.407354\pi\)
0.286964 + 0.957941i \(0.407354\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.5508 + 21.7386i 0.641316 + 1.11079i 0.985139 + 0.171758i \(0.0549448\pi\)
−0.343823 + 0.939035i \(0.611722\pi\)
\(384\) 0 0
\(385\) −17.8689 + 12.0536i −0.910681 + 0.614306i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.732011 1.26788i 0.0371144 0.0642841i −0.846872 0.531798i \(-0.821517\pi\)
0.883986 + 0.467513i \(0.154850\pi\)
\(390\) 0 0
\(391\) −4.62141 + 8.00452i −0.233715 + 0.404806i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −25.0641 43.4124i −1.26111 2.18431i
\(396\) 0 0
\(397\) −1.49591 + 2.59100i −0.0750778 + 0.130039i −0.901120 0.433570i \(-0.857254\pi\)
0.826042 + 0.563608i \(0.190587\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.1685 22.8086i −0.657605 1.13901i −0.981234 0.192821i \(-0.938236\pi\)
0.323629 0.946184i \(-0.395097\pi\)
\(402\) 0 0
\(403\) −0.277571 + 0.480767i −0.0138268 + 0.0239487i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.85166 + 10.1354i 0.290056 + 0.502392i
\(408\) 0 0
\(409\) 3.00784 0.148728 0.0743642 0.997231i \(-0.476307\pi\)
0.0743642 + 0.997231i \(0.476307\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 9.98489 6.73537i 0.491324 0.331426i
\(414\) 0 0
\(415\) −22.1389 + 38.3457i −1.08676 + 1.88232i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −17.2414 + 29.8630i −0.842297 + 1.45890i 0.0456508 + 0.998957i \(0.485464\pi\)
−0.887948 + 0.459944i \(0.847869\pi\)
\(420\) 0 0
\(421\) 9.86151 + 17.0806i 0.480620 + 0.832459i 0.999753 0.0222349i \(-0.00707818\pi\)
−0.519132 + 0.854694i \(0.673745\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 92.6783 4.49556
\(426\) 0 0
\(427\) 23.2063 15.6540i 1.12303 0.757548i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.4257 + 18.0578i 0.502188 + 0.869816i 0.999997 + 0.00252883i \(0.000804953\pi\)
−0.497808 + 0.867287i \(0.665862\pi\)
\(432\) 0 0
\(433\) 15.6324 0.751247 0.375624 0.926772i \(-0.377429\pi\)
0.375624 + 0.926772i \(0.377429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.38235 0.257473
\(438\) 0 0
\(439\) −35.6989 −1.70382 −0.851909 0.523690i \(-0.824555\pi\)
−0.851909 + 0.523690i \(0.824555\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 18.1157 0.860705 0.430352 0.902661i \(-0.358389\pi\)
0.430352 + 0.902661i \(0.358389\pi\)
\(444\) 0 0
\(445\) 32.7623 1.55308
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −17.4189 −0.822051 −0.411025 0.911624i \(-0.634829\pi\)
−0.411025 + 0.911624i \(0.634829\pi\)
\(450\) 0 0
\(451\) −2.53294 4.38719i −0.119272 0.206585i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −5.40061 + 3.64302i −0.253185 + 0.170787i
\(456\) 0 0
\(457\) 15.3584 0.718434 0.359217 0.933254i \(-0.383044\pi\)
0.359217 + 0.933254i \(0.383044\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.15140 + 10.6545i 0.286499 + 0.496231i 0.972972 0.230924i \(-0.0741750\pi\)
−0.686472 + 0.727156i \(0.740842\pi\)
\(462\) 0 0
\(463\) −9.18922 + 15.9162i −0.427059 + 0.739688i −0.996610 0.0822677i \(-0.973784\pi\)
0.569551 + 0.821956i \(0.307117\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −11.1020 + 19.2292i −0.513738 + 0.889820i 0.486135 + 0.873884i \(0.338406\pi\)
−0.999873 + 0.0159363i \(0.994927\pi\)
\(468\) 0 0
\(469\) −10.6682 + 7.19631i −0.492612 + 0.332295i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.70672 0.0784749
\(474\) 0 0
\(475\) −26.9845 46.7386i −1.23814 2.14451i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17.2969 29.9591i 0.790317 1.36887i −0.135454 0.990784i \(-0.543249\pi\)
0.925771 0.378085i \(-0.123417\pi\)
\(480\) 0 0
\(481\) 1.76858 + 3.06328i 0.0806405 + 0.139673i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.38895 + 14.5301i −0.380922 + 0.659777i
\(486\) 0 0
\(487\) −6.79789 11.7743i −0.308042 0.533544i 0.669892 0.742458i \(-0.266340\pi\)
−0.977934 + 0.208915i \(0.933007\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.01841 + 12.1563i −0.316737 + 0.548604i −0.979805 0.199955i \(-0.935920\pi\)
0.663069 + 0.748559i \(0.269254\pi\)
\(492\) 0 0
\(493\) 30.3529 52.5728i 1.36703 2.36776i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −25.3210 + 17.0804i −1.13580 + 0.766161i
\(498\) 0 0
\(499\) −15.1408 26.2246i −0.677794 1.17397i −0.975644 0.219362i \(-0.929603\pi\)
0.297849 0.954613i \(-0.403731\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −35.5942 −1.58707 −0.793533 0.608527i \(-0.791761\pi\)
−0.793533 + 0.608527i \(0.791761\pi\)
\(504\) 0 0
\(505\) −70.8219 −3.15153
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.23675 5.60621i −0.143466 0.248491i 0.785333 0.619073i \(-0.212492\pi\)
−0.928800 + 0.370582i \(0.879158\pi\)
\(510\) 0 0
\(511\) −2.12185 1.03481i −0.0938653 0.0457773i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 24.5172 42.4651i 1.08036 1.87123i
\(516\) 0 0
\(517\) −5.55982 + 9.62989i −0.244521 + 0.423522i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.18988 10.7212i −0.271184 0.469704i 0.697982 0.716116i \(-0.254082\pi\)
−0.969165 + 0.246412i \(0.920748\pi\)
\(522\) 0 0
\(523\) −11.0290 + 19.1028i −0.482265 + 0.835308i −0.999793 0.0203585i \(-0.993519\pi\)
0.517527 + 0.855667i \(0.326853\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.43794 5.95469i −0.149759 0.259390i
\(528\) 0 0
\(529\) 10.6810 18.5000i 0.464389 0.804346i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.765547 1.32597i −0.0331595 0.0574340i
\(534\) 0 0
\(535\) 86.5319 3.74110
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8.31462 + 10.6408i 0.358136 + 0.458331i
\(540\) 0 0
\(541\) 7.24989 12.5572i 0.311697 0.539875i −0.667033 0.745028i \(-0.732436\pi\)
0.978730 + 0.205153i \(0.0657693\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 10.4293 18.0640i 0.446740 0.773777i
\(546\) 0 0
\(547\) 12.4034 + 21.4834i 0.530332 + 0.918562i 0.999374 + 0.0353858i \(0.0112660\pi\)
−0.469042 + 0.883176i \(0.655401\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −35.3506 −1.50599
\(552\) 0 0
\(553\) −26.0363 + 17.5630i −1.10718 + 0.746853i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.02336 15.6289i −0.382332 0.662219i 0.609063 0.793122i \(-0.291546\pi\)
−0.991395 + 0.130903i \(0.958212\pi\)
\(558\) 0 0
\(559\) 0.515831 0.0218173
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19.0350 0.802228 0.401114 0.916028i \(-0.368623\pi\)
0.401114 + 0.916028i \(0.368623\pi\)
\(564\) 0 0
\(565\) −62.6798 −2.63696
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.36036 −0.392407 −0.196203 0.980563i \(-0.562861\pi\)
−0.196203 + 0.980563i \(0.562861\pi\)
\(570\) 0 0
\(571\) −35.3611 −1.47981 −0.739907 0.672709i \(-0.765131\pi\)
−0.739907 + 0.672709i \(0.765131\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 16.4252 0.684979
\(576\) 0 0
\(577\) 14.0160 + 24.2764i 0.583493 + 1.01064i 0.995061 + 0.0992610i \(0.0316479\pi\)
−0.411568 + 0.911379i \(0.635019\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 24.9336 + 12.1599i 1.03442 + 0.504478i
\(582\) 0 0
\(583\) −3.71344 −0.153795
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.7305 + 23.7819i 0.566718 + 0.981585i 0.996888 + 0.0788364i \(0.0251205\pi\)
−0.430169 + 0.902748i \(0.641546\pi\)
\(588\) 0 0
\(589\) −2.00200 + 3.46757i −0.0824912 + 0.142879i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11.1267 19.2719i 0.456917 0.791404i −0.541879 0.840457i \(-0.682287\pi\)
0.998796 + 0.0490525i \(0.0156202\pi\)
\(594\) 0 0
\(595\) −5.63108 80.4900i −0.230852 3.29977i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.74118 0.275437 0.137719 0.990471i \(-0.456023\pi\)
0.137719 + 0.990471i \(0.456023\pi\)
\(600\) 0 0
\(601\) 4.04153 + 7.00013i 0.164857 + 0.285541i 0.936605 0.350388i \(-0.113950\pi\)
−0.771747 + 0.635929i \(0.780617\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 15.3682 26.6185i 0.624805 1.08219i
\(606\) 0 0
\(607\) 15.8020 + 27.3698i 0.641382 + 1.11091i 0.985124 + 0.171843i \(0.0549720\pi\)
−0.343742 + 0.939064i \(0.611695\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.68038 + 2.91050i −0.0679808 + 0.117746i
\(612\) 0 0
\(613\) −3.10601 5.37977i −0.125451 0.217287i 0.796458 0.604693i \(-0.206704\pi\)
−0.921909 + 0.387407i \(0.873371\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.309009 0.535218i 0.0124402 0.0215471i −0.859738 0.510735i \(-0.829373\pi\)
0.872178 + 0.489188i \(0.162707\pi\)
\(618\) 0 0
\(619\) 20.0103 34.6589i 0.804283 1.39306i −0.112492 0.993653i \(-0.535883\pi\)
0.916774 0.399406i \(-0.130783\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.43250 20.4760i −0.0573920 0.820355i
\(624\) 0 0
\(625\) −37.7647 65.4105i −1.51059 2.61642i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −43.8106 −1.74684
\(630\) 0 0
\(631\) −5.20154 −0.207070 −0.103535 0.994626i \(-0.533015\pi\)
−0.103535 + 0.994626i \(0.533015\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −18.0246 31.2196i −0.715285 1.23891i
\(636\) 0 0
\(637\) 2.51298 + 3.21603i 0.0995678 + 0.127424i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −0.137294 + 0.237799i −0.00542277 + 0.00939251i −0.868724 0.495296i \(-0.835059\pi\)
0.863301 + 0.504689i \(0.168393\pi\)
\(642\) 0 0
\(643\) −11.2657 + 19.5128i −0.444277 + 0.769510i −0.998002 0.0631900i \(-0.979873\pi\)
0.553725 + 0.832700i \(0.313206\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.2737 + 21.2586i 0.482528 + 0.835763i 0.999799 0.0200588i \(-0.00638534\pi\)
−0.517271 + 0.855822i \(0.673052\pi\)
\(648\) 0 0
\(649\) 4.39102 7.60547i 0.172363 0.298541i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 16.5154 + 28.6055i 0.646298 + 1.11942i 0.984000 + 0.178167i \(0.0570169\pi\)
−0.337703 + 0.941253i \(0.609650\pi\)
\(654\) 0 0
\(655\) 4.95532 8.58286i 0.193620 0.335360i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 21.3813 + 37.0335i 0.832897 + 1.44262i 0.895731 + 0.444596i \(0.146653\pi\)
−0.0628336 + 0.998024i \(0.520014\pi\)
\(660\) 0 0
\(661\) −19.1083 −0.743227 −0.371614 0.928387i \(-0.621195\pi\)
−0.371614 + 0.928387i \(0.621195\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −38.9523 + 26.2756i −1.51051 + 1.01892i
\(666\) 0 0
\(667\) 5.37940 9.31739i 0.208291 0.360771i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.2054 17.6762i 0.393973 0.682382i
\(672\) 0 0
\(673\) −12.9345 22.4032i −0.498588 0.863579i 0.501411 0.865209i \(-0.332815\pi\)
−0.999999 + 0.00162995i \(0.999481\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.89337 −0.0727682 −0.0363841 0.999338i \(-0.511584\pi\)
−0.0363841 + 0.999338i \(0.511584\pi\)
\(678\) 0 0
\(679\) 9.44792 + 4.60767i 0.362578 + 0.176826i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −6.39573 11.0777i −0.244726 0.423878i 0.717329 0.696735i \(-0.245365\pi\)
−0.962055 + 0.272857i \(0.912031\pi\)
\(684\) 0 0
\(685\) −5.42072 −0.207115
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.12234 −0.0427576
\(690\) 0 0
\(691\) 36.0698 1.37216 0.686079 0.727527i \(-0.259330\pi\)
0.686079 + 0.727527i \(0.259330\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.15669 0.195604
\(696\) 0 0
\(697\) 18.9638 0.718306
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 20.2524 0.764922 0.382461 0.923972i \(-0.375077\pi\)
0.382461 + 0.923972i \(0.375077\pi\)
\(702\) 0 0
\(703\) 12.7560 + 22.0941i 0.481103 + 0.833296i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.09663 + 44.2628i 0.116461 + 1.66468i
\(708\) 0 0
\(709\) −6.76636 −0.254116 −0.127058 0.991895i \(-0.540553\pi\)
−0.127058 + 0.991895i \(0.540553\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.609300 1.05534i −0.0228185 0.0395227i
\(714\) 0 0
\(715\) −2.37501 + 4.11364i −0.0888203 + 0.153841i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.43767 11.1504i 0.240084 0.415839i −0.720654 0.693295i \(-0.756158\pi\)
0.960738 + 0.277457i \(0.0894915\pi\)
\(720\) 0 0
\(721\) −27.6121 13.4662i −1.02833 0.501508i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −107.879 −4.00653
\(726\) 0 0
\(727\) −14.3621 24.8758i −0.532659 0.922593i −0.999273 0.0381316i \(-0.987859\pi\)
0.466613 0.884461i \(-0.345474\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.19449 + 5.53301i −0.118152 + 0.204646i
\(732\) 0 0
\(733\) −2.33025 4.03611i −0.0860697 0.149077i 0.819777 0.572683i \(-0.194097\pi\)
−0.905847 + 0.423606i \(0.860764\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4.69153 + 8.12596i −0.172815 + 0.299324i
\(738\) 0 0
\(739\) −9.46395 16.3920i −0.348137 0.602991i 0.637782 0.770217i \(-0.279852\pi\)
−0.985919 + 0.167227i \(0.946519\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 6.64732 11.5135i 0.243867 0.422389i −0.717946 0.696099i \(-0.754917\pi\)
0.961812 + 0.273710i \(0.0882507\pi\)
\(744\) 0 0
\(745\) 13.2909 23.0205i 0.486941 0.843406i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.78353 54.0814i −0.138247 1.97609i
\(750\) 0 0
\(751\) −7.61766 13.1942i −0.277972 0.481462i 0.692908 0.721026i \(-0.256329\pi\)
−0.970881 + 0.239563i \(0.922996\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −9.94308 −0.361866
\(756\) 0 0
\(757\) 15.6279 0.568004 0.284002 0.958824i \(-0.408338\pi\)
0.284002 + 0.958824i \(0.408338\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 3.54797 + 6.14527i 0.128614 + 0.222766i 0.923140 0.384464i \(-0.125614\pi\)
−0.794526 + 0.607230i \(0.792281\pi\)
\(762\) 0 0
\(763\) −11.7458 5.72832i −0.425226 0.207379i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.32712 2.29865i 0.0479197 0.0829994i
\(768\) 0 0
\(769\) 5.71618 9.90071i 0.206131 0.357029i −0.744362 0.667777i \(-0.767246\pi\)
0.950492 + 0.310748i \(0.100579\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7.40125 12.8193i −0.266204 0.461080i 0.701674 0.712498i \(-0.252436\pi\)
−0.967878 + 0.251418i \(0.919103\pi\)
\(774\) 0 0
\(775\) −6.10949 + 10.5819i −0.219459 + 0.380114i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.52157 9.56364i −0.197831 0.342653i
\(780\) 0 0
\(781\) −11.1353 + 19.2869i −0.398453 + 0.690141i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.09951 + 10.5647i 0.217701 + 0.377069i
\(786\) 0 0
\(787\) 19.7177 0.702861 0.351431 0.936214i \(-0.385695\pi\)
0.351431 + 0.936214i \(0.385695\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.74062 + 39.1741i 0.0974452 + 1.39287i
\(792\) 0 0
\(793\) 3.08442 5.34238i 0.109531 0.189713i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.2215 + 38.4887i −0.787125 + 1.36334i 0.140597 + 0.990067i \(0.455098\pi\)
−0.927722 + 0.373273i \(0.878236\pi\)