Properties

Label 648.4.i.e.433.1
Level $648$
Weight $4$
Character 648.433
Analytic conductor $38.233$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 648.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(38.2332376837\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 433.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 648.433
Dual form 648.4.i.e.217.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{5} +(-12.0000 - 20.7846i) q^{7} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{5} +(-12.0000 - 20.7846i) q^{7} +(-22.0000 - 38.1051i) q^{11} +(-11.0000 + 19.0526i) q^{13} -50.0000 q^{17} +44.0000 q^{19} +(-28.0000 + 48.4974i) q^{23} +(60.5000 + 104.789i) q^{25} +(99.0000 + 171.473i) q^{29} +(80.0000 - 138.564i) q^{31} +48.0000 q^{35} -162.000 q^{37} +(-99.0000 + 171.473i) q^{41} +(-26.0000 - 45.0333i) q^{43} +(264.000 + 457.261i) q^{47} +(-116.500 + 201.784i) q^{49} +242.000 q^{53} +88.0000 q^{55} +(-334.000 + 578.505i) q^{59} +(-275.000 - 476.314i) q^{61} +(-22.0000 - 38.1051i) q^{65} +(-94.0000 + 162.813i) q^{67} -728.000 q^{71} +154.000 q^{73} +(-528.000 + 914.523i) q^{77} +(328.000 + 568.113i) q^{79} +(118.000 + 204.382i) q^{83} +(50.0000 - 86.6025i) q^{85} -714.000 q^{89} +528.000 q^{91} +(-44.0000 + 76.2102i) q^{95} +(239.000 + 413.960i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{5} - 24q^{7} + O(q^{10}) \) \( 2q - 2q^{5} - 24q^{7} - 44q^{11} - 22q^{13} - 100q^{17} + 88q^{19} - 56q^{23} + 121q^{25} + 198q^{29} + 160q^{31} + 96q^{35} - 324q^{37} - 198q^{41} - 52q^{43} + 528q^{47} - 233q^{49} + 484q^{53} + 176q^{55} - 668q^{59} - 550q^{61} - 44q^{65} - 188q^{67} - 1456q^{71} + 308q^{73} - 1056q^{77} + 656q^{79} + 236q^{83} + 100q^{85} - 1428q^{89} + 1056q^{91} - 88q^{95} + 478q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −1.00000 + 1.73205i −0.0894427 + 0.154919i −0.907276 0.420536i \(-0.861842\pi\)
0.817833 + 0.575456i \(0.195175\pi\)
\(6\) 0 0
\(7\) −12.0000 20.7846i −0.647939 1.12226i −0.983614 0.180286i \(-0.942298\pi\)
0.335675 0.941978i \(-0.391036\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −22.0000 38.1051i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) −11.0000 + 19.0526i −0.234681 + 0.406479i −0.959180 0.282797i \(-0.908738\pi\)
0.724499 + 0.689276i \(0.242071\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −50.0000 −0.713340 −0.356670 0.934230i \(-0.616088\pi\)
−0.356670 + 0.934230i \(0.616088\pi\)
\(18\) 0 0
\(19\) 44.0000 0.531279 0.265639 0.964072i \(-0.414417\pi\)
0.265639 + 0.964072i \(0.414417\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −28.0000 + 48.4974i −0.253844 + 0.439670i −0.964581 0.263788i \(-0.915028\pi\)
0.710737 + 0.703458i \(0.248362\pi\)
\(24\) 0 0
\(25\) 60.5000 + 104.789i 0.484000 + 0.838313i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 99.0000 + 171.473i 0.633925 + 1.09799i 0.986742 + 0.162298i \(0.0518907\pi\)
−0.352816 + 0.935693i \(0.614776\pi\)
\(30\) 0 0
\(31\) 80.0000 138.564i 0.463498 0.802801i −0.535635 0.844450i \(-0.679928\pi\)
0.999132 + 0.0416484i \(0.0132609\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 48.0000 0.231814
\(36\) 0 0
\(37\) −162.000 −0.719801 −0.359900 0.932991i \(-0.617189\pi\)
−0.359900 + 0.932991i \(0.617189\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −99.0000 + 171.473i −0.377102 + 0.653161i −0.990639 0.136505i \(-0.956413\pi\)
0.613537 + 0.789666i \(0.289746\pi\)
\(42\) 0 0
\(43\) −26.0000 45.0333i −0.0922084 0.159710i 0.816232 0.577725i \(-0.196059\pi\)
−0.908440 + 0.418015i \(0.862726\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 264.000 + 457.261i 0.819327 + 1.41912i 0.906179 + 0.422894i \(0.138986\pi\)
−0.0868522 + 0.996221i \(0.527681\pi\)
\(48\) 0 0
\(49\) −116.500 + 201.784i −0.339650 + 0.588291i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 242.000 0.627194 0.313597 0.949556i \(-0.398466\pi\)
0.313597 + 0.949556i \(0.398466\pi\)
\(54\) 0 0
\(55\) 88.0000 0.215744
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −334.000 + 578.505i −0.737002 + 1.27652i 0.216838 + 0.976208i \(0.430426\pi\)
−0.953840 + 0.300317i \(0.902908\pi\)
\(60\) 0 0
\(61\) −275.000 476.314i −0.577215 0.999766i −0.995797 0.0915873i \(-0.970806\pi\)
0.418582 0.908179i \(-0.362527\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −22.0000 38.1051i −0.0419810 0.0727132i
\(66\) 0 0
\(67\) −94.0000 + 162.813i −0.171402 + 0.296877i −0.938910 0.344162i \(-0.888163\pi\)
0.767508 + 0.641039i \(0.221496\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −728.000 −1.21687 −0.608435 0.793604i \(-0.708202\pi\)
−0.608435 + 0.793604i \(0.708202\pi\)
\(72\) 0 0
\(73\) 154.000 0.246909 0.123454 0.992350i \(-0.460603\pi\)
0.123454 + 0.992350i \(0.460603\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −528.000 + 914.523i −0.781444 + 1.35350i
\(78\) 0 0
\(79\) 328.000 + 568.113i 0.467125 + 0.809084i 0.999295 0.0375534i \(-0.0119564\pi\)
−0.532170 + 0.846638i \(0.678623\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 118.000 + 204.382i 0.156050 + 0.270287i 0.933441 0.358731i \(-0.116790\pi\)
−0.777391 + 0.629018i \(0.783457\pi\)
\(84\) 0 0
\(85\) 50.0000 86.6025i 0.0638031 0.110510i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −714.000 −0.850380 −0.425190 0.905104i \(-0.639793\pi\)
−0.425190 + 0.905104i \(0.639793\pi\)
\(90\) 0 0
\(91\) 528.000 0.608236
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −44.0000 + 76.2102i −0.0475190 + 0.0823053i
\(96\) 0 0
\(97\) 239.000 + 413.960i 0.250173 + 0.433312i 0.963573 0.267444i \(-0.0861792\pi\)
−0.713400 + 0.700757i \(0.752846\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 783.000 + 1356.20i 0.771400 + 1.33610i 0.936796 + 0.349877i \(0.113777\pi\)
−0.165396 + 0.986227i \(0.552890\pi\)
\(102\) 0 0
\(103\) 484.000 838.313i 0.463009 0.801955i −0.536100 0.844154i \(-0.680103\pi\)
0.999109 + 0.0421991i \(0.0134364\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 780.000 0.704724 0.352362 0.935864i \(-0.385379\pi\)
0.352362 + 0.935864i \(0.385379\pi\)
\(108\) 0 0
\(109\) −1994.00 −1.75221 −0.876103 0.482123i \(-0.839866\pi\)
−0.876103 + 0.482123i \(0.839866\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −471.000 + 815.796i −0.392106 + 0.679147i −0.992727 0.120387i \(-0.961587\pi\)
0.600621 + 0.799534i \(0.294920\pi\)
\(114\) 0 0
\(115\) −56.0000 96.9948i −0.0454089 0.0786506i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 600.000 + 1039.23i 0.462201 + 0.800555i
\(120\) 0 0
\(121\) −302.500 + 523.945i −0.227273 + 0.393648i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −492.000 −0.352047
\(126\) 0 0
\(127\) 1408.00 0.983778 0.491889 0.870658i \(-0.336307\pi\)
0.491889 + 0.870658i \(0.336307\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1346.00 + 2331.34i −0.897714 + 1.55489i −0.0673052 + 0.997732i \(0.521440\pi\)
−0.830409 + 0.557154i \(0.811893\pi\)
\(132\) 0 0
\(133\) −528.000 914.523i −0.344236 0.596234i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 813.000 + 1408.16i 0.507002 + 0.878153i 0.999967 + 0.00810420i \(0.00257968\pi\)
−0.492965 + 0.870049i \(0.664087\pi\)
\(138\) 0 0
\(139\) 342.000 592.361i 0.208691 0.361464i −0.742611 0.669723i \(-0.766413\pi\)
0.951302 + 0.308259i \(0.0997463\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 968.000 0.566072
\(144\) 0 0
\(145\) −396.000 −0.226800
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 151.000 261.540i 0.0830228 0.143800i −0.821524 0.570174i \(-0.806876\pi\)
0.904547 + 0.426374i \(0.140209\pi\)
\(150\) 0 0
\(151\) −676.000 1170.87i −0.364319 0.631018i 0.624348 0.781146i \(-0.285365\pi\)
−0.988667 + 0.150128i \(0.952031\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 160.000 + 277.128i 0.0829130 + 0.143609i
\(156\) 0 0
\(157\) −1571.00 + 2721.05i −0.798595 + 1.38321i 0.121936 + 0.992538i \(0.461090\pi\)
−0.920531 + 0.390670i \(0.872244\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1344.00 0.657901
\(162\) 0 0
\(163\) 3036.00 1.45888 0.729441 0.684043i \(-0.239780\pi\)
0.729441 + 0.684043i \(0.239780\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −132.000 + 228.631i −0.0611645 + 0.105940i −0.894986 0.446094i \(-0.852815\pi\)
0.833822 + 0.552034i \(0.186148\pi\)
\(168\) 0 0
\(169\) 856.500 + 1483.50i 0.389850 + 0.675240i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1413.00 2447.39i −0.620973 1.07556i −0.989305 0.145863i \(-0.953404\pi\)
0.368331 0.929695i \(-0.379929\pi\)
\(174\) 0 0
\(175\) 1452.00 2514.94i 0.627205 1.08635i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −3084.00 −1.28776 −0.643880 0.765127i \(-0.722676\pi\)
−0.643880 + 0.765127i \(0.722676\pi\)
\(180\) 0 0
\(181\) −2418.00 −0.992975 −0.496488 0.868044i \(-0.665377\pi\)
−0.496488 + 0.868044i \(0.665377\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 162.000 280.592i 0.0643810 0.111511i
\(186\) 0 0
\(187\) 1100.00 + 1905.26i 0.430160 + 0.745059i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −480.000 831.384i −0.181841 0.314957i 0.760667 0.649143i \(-0.224872\pi\)
−0.942507 + 0.334185i \(0.891539\pi\)
\(192\) 0 0
\(193\) −1441.00 + 2495.89i −0.537438 + 0.930869i 0.461604 + 0.887086i \(0.347274\pi\)
−0.999041 + 0.0437828i \(0.986059\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1086.00 −0.392763 −0.196381 0.980528i \(-0.562919\pi\)
−0.196381 + 0.980528i \(0.562919\pi\)
\(198\) 0 0
\(199\) 88.0000 0.0313475 0.0156738 0.999877i \(-0.495011\pi\)
0.0156738 + 0.999877i \(0.495011\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2376.00 4115.35i 0.821490 1.42286i
\(204\) 0 0
\(205\) −198.000 342.946i −0.0674581 0.116841i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −968.000 1676.63i −0.320373 0.554902i
\(210\) 0 0
\(211\) 1738.00 3010.30i 0.567056 0.982170i −0.429799 0.902925i \(-0.641416\pi\)
0.996855 0.0792455i \(-0.0252511\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 104.000 0.0329895
\(216\) 0 0
\(217\) −3840.00 −1.20127
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 550.000 952.628i 0.167407 0.289958i
\(222\) 0 0
\(223\) −464.000 803.672i −0.139335 0.241336i 0.787910 0.615790i \(-0.211163\pi\)
−0.927245 + 0.374455i \(0.877830\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 78.0000 + 135.100i 0.0228064 + 0.0395018i 0.877203 0.480119i \(-0.159407\pi\)
−0.854397 + 0.519621i \(0.826073\pi\)
\(228\) 0 0
\(229\) 817.000 1415.09i 0.235759 0.408347i −0.723734 0.690079i \(-0.757576\pi\)
0.959493 + 0.281732i \(0.0909090\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 902.000 0.253614 0.126807 0.991927i \(-0.459527\pi\)
0.126807 + 0.991927i \(0.459527\pi\)
\(234\) 0 0
\(235\) −1056.00 −0.293131
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 808.000 1399.50i 0.218683 0.378770i −0.735723 0.677283i \(-0.763157\pi\)
0.954406 + 0.298513i \(0.0964907\pi\)
\(240\) 0 0
\(241\) −2409.00 4172.51i −0.643889 1.11525i −0.984557 0.175065i \(-0.943986\pi\)
0.340667 0.940184i \(-0.389347\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −233.000 403.568i −0.0607585 0.105237i
\(246\) 0 0
\(247\) −484.000 + 838.313i −0.124681 + 0.215954i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2140.00 0.538150 0.269075 0.963119i \(-0.413282\pi\)
0.269075 + 0.963119i \(0.413282\pi\)
\(252\) 0 0
\(253\) 2464.00 0.612294
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 385.000 666.840i 0.0934461 0.161853i −0.815513 0.578739i \(-0.803545\pi\)
0.908959 + 0.416886i \(0.136878\pi\)
\(258\) 0 0
\(259\) 1944.00 + 3367.11i 0.466387 + 0.807806i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3700.00 6408.59i −0.867497 1.50255i −0.864546 0.502554i \(-0.832394\pi\)
−0.00295121 0.999996i \(-0.500939\pi\)
\(264\) 0 0
\(265\) −242.000 + 419.156i −0.0560979 + 0.0971644i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2794.00 0.633283 0.316642 0.948545i \(-0.397445\pi\)
0.316642 + 0.948545i \(0.397445\pi\)
\(270\) 0 0
\(271\) 8624.00 1.93310 0.966551 0.256474i \(-0.0825608\pi\)
0.966551 + 0.256474i \(0.0825608\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2662.00 4610.72i 0.583726 1.01104i
\(276\) 0 0
\(277\) 937.000 + 1622.93i 0.203245 + 0.352031i 0.949572 0.313549i \(-0.101518\pi\)
−0.746327 + 0.665579i \(0.768185\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1669.00 + 2890.79i 0.354321 + 0.613702i 0.987002 0.160711i \(-0.0513787\pi\)
−0.632681 + 0.774413i \(0.718045\pi\)
\(282\) 0 0
\(283\) −3586.00 + 6211.13i −0.753235 + 1.30464i 0.193012 + 0.981196i \(0.438174\pi\)
−0.946247 + 0.323445i \(0.895159\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4752.00 0.977358
\(288\) 0 0
\(289\) −2413.00 −0.491146
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2607.00 4515.46i 0.519804 0.900327i −0.479931 0.877306i \(-0.659338\pi\)
0.999735 0.0230207i \(-0.00732835\pi\)
\(294\) 0 0
\(295\) −668.000 1157.01i −0.131839 0.228352i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −616.000 1066.94i −0.119144 0.206364i
\(300\) 0 0
\(301\) −624.000 + 1080.80i −0.119491 + 0.206964i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1100.00 0.206511
\(306\) 0 0
\(307\) 396.000 0.0736186 0.0368093 0.999322i \(-0.488281\pi\)
0.0368093 + 0.999322i \(0.488281\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2028.00 + 3512.60i −0.369766 + 0.640454i −0.989529 0.144335i \(-0.953896\pi\)
0.619762 + 0.784789i \(0.287229\pi\)
\(312\) 0 0
\(313\) −1077.00 1865.42i −0.194491 0.336868i 0.752243 0.658886i \(-0.228972\pi\)
−0.946733 + 0.322018i \(0.895639\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3693.00 6396.46i −0.654320 1.13332i −0.982064 0.188549i \(-0.939621\pi\)
0.327743 0.944767i \(-0.393712\pi\)
\(318\) 0 0
\(319\) 4356.00 7544.81i 0.764543 1.32423i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2200.00 −0.378982
\(324\) 0 0
\(325\) −2662.00 −0.454342
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6336.00 10974.3i 1.06175 1.83900i
\(330\) 0 0
\(331\) 566.000 + 980.341i 0.0939884 + 0.162793i 0.909186 0.416390i \(-0.136705\pi\)
−0.815198 + 0.579183i \(0.803372\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −188.000 325.626i −0.0306613 0.0531069i
\(336\) 0 0
\(337\) 1671.00 2894.26i 0.270104 0.467834i −0.698784 0.715333i \(-0.746275\pi\)
0.968888 + 0.247498i \(0.0796085\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −7040.00 −1.11800
\(342\) 0 0
\(343\) −2640.00 −0.415588
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1122.00 1943.36i 0.173580 0.300649i −0.766089 0.642734i \(-0.777800\pi\)
0.939669 + 0.342086i \(0.111133\pi\)
\(348\) 0 0
\(349\) 3261.00 + 5648.22i 0.500164 + 0.866310i 1.00000 0.000189686i \(6.03788e-5\pi\)
−0.499836 + 0.866120i \(0.666606\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5615.00 9725.47i −0.846618 1.46639i −0.884208 0.467093i \(-0.845301\pi\)
0.0375899 0.999293i \(-0.488032\pi\)
\(354\) 0 0
\(355\) 728.000 1260.93i 0.108840 0.188517i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1848.00 −0.271682 −0.135841 0.990731i \(-0.543374\pi\)
−0.135841 + 0.990731i \(0.543374\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −154.000 + 266.736i −0.0220842 + 0.0382509i
\(366\) 0 0
\(367\) −3560.00 6166.10i −0.506350 0.877024i −0.999973 0.00734805i \(-0.997661\pi\)
0.493623 0.869676i \(-0.335672\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2904.00 5029.88i −0.406383 0.703876i
\(372\) 0 0
\(373\) −3175.00 + 5499.26i −0.440738 + 0.763381i −0.997744 0.0671276i \(-0.978617\pi\)
0.557006 + 0.830508i \(0.311950\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −4356.00 −0.595081
\(378\) 0 0
\(379\) −7900.00 −1.07070 −0.535351 0.844630i \(-0.679821\pi\)
−0.535351 + 0.844630i \(0.679821\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 5184.00 8978.95i 0.691619 1.19792i −0.279688 0.960091i \(-0.590231\pi\)
0.971307 0.237828i \(-0.0764355\pi\)
\(384\) 0 0
\(385\) −1056.00 1829.05i −0.139789 0.242122i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4415.00 + 7647.00i 0.575448 + 0.996706i 0.995993 + 0.0894338i \(0.0285057\pi\)
−0.420544 + 0.907272i \(0.638161\pi\)
\(390\) 0 0
\(391\) 1400.00 2424.87i 0.181077 0.313634i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1312.00 −0.167124
\(396\) 0 0
\(397\) 9878.00 1.24877 0.624386 0.781116i \(-0.285349\pi\)
0.624386 + 0.781116i \(0.285349\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6567.00 + 11374.4i −0.817806 + 1.41648i 0.0894889 + 0.995988i \(0.471477\pi\)
−0.907295 + 0.420494i \(0.861857\pi\)
\(402\) 0 0
\(403\) 1760.00 + 3048.41i 0.217548 + 0.376804i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3564.00 + 6173.03i 0.434056 + 0.751808i
\(408\) 0 0
\(409\) −453.000 + 784.619i −0.0547663 + 0.0948580i −0.892109 0.451821i \(-0.850775\pi\)
0.837343 + 0.546679i \(0.184108\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16032.0 1.91013
\(414\) 0 0
\(415\) −472.000 −0.0558303
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2706.00 + 4686.93i −0.315505 + 0.546471i −0.979545 0.201226i \(-0.935507\pi\)
0.664039 + 0.747698i \(0.268841\pi\)
\(420\) 0 0
\(421\) 2321.00 + 4020.09i 0.268690 + 0.465385i 0.968524 0.248921i \(-0.0800758\pi\)
−0.699834 + 0.714306i \(0.746743\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3025.00 5239.45i −0.345257 0.598002i
\(426\) 0 0
\(427\) −6600.00 + 11431.5i −0.748001 + 1.29558i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −656.000 −0.0733142 −0.0366571 0.999328i \(-0.511671\pi\)
−0.0366571 + 0.999328i \(0.511671\pi\)
\(432\) 0 0
\(433\) 9490.00 1.05326 0.526629 0.850096i \(-0.323456\pi\)
0.526629 + 0.850096i \(0.323456\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1232.00 + 2133.89i −0.134862 + 0.233587i
\(438\) 0 0
\(439\) −2772.00 4801.24i −0.301368 0.521984i 0.675078 0.737746i \(-0.264110\pi\)
−0.976446 + 0.215762i \(0.930776\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 3826.00 + 6626.83i 0.410336 + 0.710722i 0.994926 0.100606i \(-0.0320782\pi\)
−0.584591 + 0.811328i \(0.698745\pi\)
\(444\) 0 0
\(445\) 714.000 1236.68i 0.0760603 0.131740i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 446.000 0.0468776 0.0234388 0.999725i \(-0.492539\pi\)
0.0234388 + 0.999725i \(0.492539\pi\)
\(450\) 0 0
\(451\) 8712.00 0.909605
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −528.000 + 914.523i −0.0544022 + 0.0942275i
\(456\) 0 0
\(457\) −781.000 1352.73i −0.0799423 0.138464i 0.823283 0.567632i \(-0.192140\pi\)
−0.903225 + 0.429168i \(0.858807\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 5291.00 + 9164.28i 0.534548 + 0.925864i 0.999185 + 0.0403626i \(0.0128513\pi\)
−0.464638 + 0.885501i \(0.653815\pi\)
\(462\) 0 0
\(463\) 5384.00 9325.36i 0.540423 0.936040i −0.458457 0.888717i \(-0.651598\pi\)
0.998880 0.0473229i \(-0.0150690\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9876.00 0.978601 0.489301 0.872115i \(-0.337252\pi\)
0.489301 + 0.872115i \(0.337252\pi\)
\(468\) 0 0
\(469\) 4512.00 0.444232
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1144.00 + 1981.47i −0.111208 + 0.192617i
\(474\) 0 0
\(475\) 2662.00 + 4610.72i 0.257139 + 0.445377i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −176.000 304.841i −0.0167884 0.0290784i 0.857509 0.514469i \(-0.172011\pi\)
−0.874298 + 0.485390i \(0.838677\pi\)
\(480\) 0 0
\(481\) 1782.00 3086.51i 0.168924 0.292584i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −956.000 −0.0895046
\(486\) 0 0
\(487\) −15176.0 −1.41209 −0.706047 0.708165i \(-0.749523\pi\)
−0.706047 + 0.708165i \(0.749523\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4422.00 + 7659.13i −0.406440 + 0.703975i −0.994488 0.104851i \(-0.966563\pi\)
0.588048 + 0.808826i \(0.299897\pi\)
\(492\) 0 0
\(493\) −4950.00 8573.65i −0.452204 0.783241i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8736.00 + 15131.2i 0.788457 + 1.36565i
\(498\) 0 0
\(499\) −9702.00 + 16804.4i −0.870383 + 1.50755i −0.00878220 + 0.999961i \(0.502795\pi\)
−0.861601 + 0.507586i \(0.830538\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16488.0 −1.46156 −0.730779 0.682614i \(-0.760843\pi\)
−0.730779 + 0.682614i \(0.760843\pi\)
\(504\) 0 0
\(505\) −3132.00 −0.275984
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −6477.00 + 11218.5i −0.564024 + 0.976917i 0.433116 + 0.901338i \(0.357414\pi\)
−0.997140 + 0.0755793i \(0.975919\pi\)
\(510\) 0 0
\(511\) −1848.00 3200.83i −0.159982 0.277097i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 968.000 + 1676.63i 0.0828256 + 0.143458i
\(516\) 0 0
\(517\) 11616.0 20119.5i 0.988145 1.71152i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −10970.0 −0.922465 −0.461233 0.887279i \(-0.652593\pi\)
−0.461233 + 0.887279i \(0.652593\pi\)
\(522\) 0 0
\(523\) −16940.0 −1.41632 −0.708159 0.706053i \(-0.750474\pi\)
−0.708159 + 0.706053i \(0.750474\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4000.00 + 6928.20i −0.330631 + 0.572670i
\(528\) 0 0
\(529\) 4515.50 + 7821.08i 0.371127 + 0.642811i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2178.00 3772.41i −0.176997 0.306569i
\(534\) 0 0
\(535\) −780.000 + 1351.00i −0.0630324 + 0.109175i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10252.0 0.819267
\(540\) 0 0
\(541\) 198.000 0.0157351 0.00786755 0.999969i \(-0.497496\pi\)
0.00786755 + 0.999969i \(0.497496\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1994.00 3453.71i 0.156722 0.271451i
\(546\) 0 0
\(547\) 7634.00 + 13222.5i 0.596721 + 1.03355i 0.993302 + 0.115551i \(0.0368633\pi\)
−0.396581 + 0.918000i \(0.629803\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4356.00 + 7544.81i 0.336791 + 0.583339i
\(552\) 0 0
\(553\) 7872.00 13634.7i 0.605337 1.04847i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −20854.0 −1.58638 −0.793189 0.608976i \(-0.791581\pi\)
−0.793189 + 0.608976i \(0.791581\pi\)
\(558\) 0 0
\(559\) 1144.00 0.0865582
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9658.00 + 16728.1i −0.722977 + 1.25223i 0.236824 + 0.971553i \(0.423894\pi\)
−0.959801 + 0.280681i \(0.909440\pi\)
\(564\) 0 0
\(565\) −942.000 1631.59i −0.0701420 0.121490i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3509.00 + 6077.77i 0.258532 + 0.447791i 0.965849 0.259106i \(-0.0834278\pi\)
−0.707317 + 0.706897i \(0.750094\pi\)
\(570\) 0 0
\(571\) −12210.0 + 21148.3i −0.894873 + 1.54997i −0.0609117 + 0.998143i \(0.519401\pi\)
−0.833961 + 0.551823i \(0.813933\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6776.00 −0.491441
\(576\) 0 0
\(577\) 23234.0 1.67633 0.838166 0.545415i \(-0.183628\pi\)
0.838166 + 0.545415i \(0.183628\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2832.00 4905.17i 0.202222 0.350259i
\(582\) 0 0
\(583\) −5324.00 9221.44i −0.378212 0.655082i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5302.00 9183.33i −0.372806 0.645718i 0.617190 0.786814i \(-0.288271\pi\)
−0.989996 + 0.141095i \(0.954938\pi\)
\(588\) 0 0
\(589\) 3520.00 6096.82i 0.246246 0.426511i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13838.0 0.958277 0.479139 0.877739i \(-0.340949\pi\)
0.479139 + 0.877739i \(0.340949\pi\)
\(594\) 0 0
\(595\) −2400.00 −0.165362
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1980.00 + 3429.46i −0.135059 + 0.233930i −0.925620 0.378454i \(-0.876456\pi\)
0.790561 + 0.612384i \(0.209789\pi\)
\(600\) 0 0
\(601\) 2971.00 + 5145.92i 0.201647 + 0.349262i 0.949059 0.315098i \(-0.102037\pi\)
−0.747412 + 0.664360i \(0.768704\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −605.000 1047.89i −0.0406558 0.0704179i
\(606\) 0 0
\(607\) 1520.00 2632.72i 0.101639 0.176044i −0.810721 0.585433i \(-0.800925\pi\)
0.912360 + 0.409389i \(0.134258\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −11616.0 −0.769121
\(612\) 0 0
\(613\) −2530.00 −0.166698 −0.0833489 0.996520i \(-0.526562\pi\)
−0.0833489 + 0.996520i \(0.526562\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9603.00 + 16632.9i −0.626584 + 1.08528i 0.361648 + 0.932315i \(0.382214\pi\)
−0.988232 + 0.152960i \(0.951119\pi\)
\(618\) 0 0
\(619\) −5498.00 9522.82i −0.357000 0.618343i 0.630458 0.776224i \(-0.282867\pi\)
−0.987458 + 0.157881i \(0.949534\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 8568.00 + 14840.2i 0.550995 + 0.954351i
\(624\) 0 0
\(625\) −7070.50 + 12246.5i −0.452512 + 0.783774i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 8100.00 0.513463
\(630\) 0 0
\(631\) −6680.00 −0.421437 −0.210718 0.977547i \(-0.567580\pi\)
−0.210718 + 0.977547i \(0.567580\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1408.00 + 2438.73i −0.0879918 + 0.152406i
\(636\) 0 0
\(637\) −2563.00 4439.25i −0.159419 0.276121i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3137.00 + 5433.44i 0.193298 + 0.334802i 0.946341 0.323169i \(-0.104748\pi\)
−0.753043 + 0.657971i \(0.771415\pi\)
\(642\) 0 0
\(643\) −4542.00 + 7866.97i −0.278568 + 0.482493i −0.971029 0.238962i \(-0.923193\pi\)
0.692461 + 0.721455i \(0.256526\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23656.0 1.43742 0.718712 0.695308i \(-0.244732\pi\)
0.718712 + 0.695308i \(0.244732\pi\)
\(648\) 0 0
\(649\) 29392.0 1.77771
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3381.00 + 5856.06i −0.202617 + 0.350943i −0.949371 0.314158i \(-0.898278\pi\)
0.746754 + 0.665100i \(0.231611\pi\)
\(654\) 0 0
\(655\) −2692.00 4662.68i −0.160588 0.278147i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 7638.00 + 13229.4i 0.451494 + 0.782010i 0.998479 0.0551323i \(-0.0175581\pi\)
−0.546986 + 0.837142i \(0.684225\pi\)
\(660\) 0 0
\(661\) −5527.00 + 9573.04i −0.325228 + 0.563311i −0.981558 0.191163i \(-0.938774\pi\)
0.656331 + 0.754473i \(0.272108\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2112.00 0.123158
\(666\) 0 0
\(667\) −11088.0 −0.643672
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12100.0 + 20957.8i −0.696148 + 1.20576i
\(672\) 0 0
\(673\) 10639.0 + 18427.3i 0.609366 + 1.05545i 0.991345 + 0.131282i \(0.0419093\pi\)
−0.381979 + 0.924171i \(0.624757\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4463.00 + 7730.14i 0.253363 + 0.438838i 0.964450 0.264266i \(-0.0851298\pi\)
−0.711086 + 0.703105i \(0.751796\pi\)
\(678\) 0 0
\(679\) 5736.00 9935.04i 0.324194 0.561520i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8116.00 −0.454685 −0.227343 0.973815i \(-0.573004\pi\)
−0.227343 + 0.973815i \(0.573004\pi\)
\(684\) 0 0
\(685\) −3252.00 −0.181391
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −2662.00 + 4610.72i −0.147190 + 0.254941i
\(690\) 0 0
\(691\) 5882.00 + 10187.9i 0.323823 + 0.560878i 0.981273 0.192620i \(-0.0616984\pi\)
−0.657450 + 0.753498i \(0.728365\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 684.000 + 1184.72i 0.0373318 + 0.0646606i
\(696\) 0 0
\(697\) 4950.00 8573.65i 0.269002 0.465926i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4698.00 0.253126 0.126563 0.991959i \(-0.459605\pi\)
0.126563 + 0.991959i \(0.459605\pi\)
\(702\) 0 0
\(703\) −7128.00 −0.382415
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 18792.0 32548.7i 0.999641 1.73143i
\(708\) 0 0
\(709\) −12319.0 21337.1i −0.652538 1.13023i −0.982505 0.186237i \(-0.940371\pi\)
0.329966 0.943993i \(-0.392963\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4480.00 + 7759.59i 0.235312 + 0.407572i
\(714\) 0 0
\(715\) −968.000 + 1676.63i −0.0506310 + 0.0876954i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −16624.0 −0.862268 −0.431134 0.902288i \(-0.641886\pi\)
−0.431134 + 0.902288i \(0.641886\pi\)
\(720\) 0 0
\(721\) −23232.0 −1.20001
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −11979.0 + 20748.2i −0.613640 + 1.06286i
\(726\) 0 0
\(727\) −15108.0 26167.8i −0.770735 1.33495i −0.937160 0.348899i \(-0.886556\pi\)
0.166425 0.986054i \(-0.446778\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1300.00 + 2251.67i 0.0657760 + 0.113927i
\(732\) 0 0
\(733\) 1661.00 2876.94i 0.0836977 0.144969i −0.821138 0.570730i \(-0.806660\pi\)
0.904836 + 0.425761i \(0.139994\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 8272.00 0.413437
\(738\) 0 0
\(739\) −14692.0 −0.731331 −0.365666 0.930746i \(-0.619159\pi\)
−0.365666 + 0.930746i \(0.619159\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14300.0 24768.3i 0.706078 1.22296i −0.260223 0.965549i \(-0.583796\pi\)
0.966301 0.257415i \(-0.0828707\pi\)
\(744\) 0 0
\(745\) 302.000 + 523.079i 0.0148516 + 0.0257237i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −9360.00 16212.0i −0.456618 0.790886i
\(750\) 0 0
\(751\) 14808.0 25648.2i 0.719509 1.24623i −0.241685 0.970355i \(-0.577700\pi\)
0.961194 0.275872i \(-0.0889666\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2704.00 0.130343
\(756\) 0 0
\(757\) 2894.00 0.138949 0.0694744 0.997584i \(-0.477868\pi\)
0.0694744 + 0.997584i \(0.477868\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7381.00 12784.3i 0.351591 0.608974i −0.634937 0.772564i \(-0.718974\pi\)
0.986528 + 0.163590i \(0.0523073\pi\)
\(762\) 0 0
\(763\) 23928.0 + 41444.5i 1.13532 + 1.96644i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7348.00 12727.1i −0.345920 0.599152i
\(768\) 0 0
\(769\) 3839.00 6649.34i 0.180023 0.311809i −0.761865 0.647736i \(-0.775716\pi\)
0.941888 + 0.335926i \(0.109049\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −27390.0 −1.27445 −0.637225 0.770678i \(-0.719918\pi\)
−0.637225 + 0.770678i \(0.719918\pi\)
\(774\) 0 0
\(775\) 19360.0 0.897331
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4356.00 + 7544.81i −0.200346 + 0.347010i
\(780\) 0 0
\(781\) 16016.0 + 27740.5i 0.733800 + 1.27098i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3142.00 5442.10i −0.142857 0.247436i
\(786\) 0 0
\(787\) −9878.00 + 17109.2i −0.447411 + 0.774939i −0.998217 0.0596946i \(-0.980987\pi\)
0.550805 + 0.834634i \(0.314321\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 22608.0 1.01624
\(792\) 0 0
\(793\) 12100.0 0.541846
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 19427.0 33648.6i 0.863412 1.49547i −0.00520266 0.999986i \(-0.501656\pi\)
0.868615 0.495488i \(-0.165011\pi\)
\(798\) 0 0
\(799\) −13200.0 22863.1i −0.584459 1.01231i
\(800\)