Properties

Label 324.6.e.a.217.1
Level $324$
Weight $6$
Character 324.217
Analytic conductor $51.964$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 324.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(51.9643576194\)
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 4)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 217.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 324.217
Dual form 324.6.e.a.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-27.0000 - 46.7654i) q^{5} +(44.0000 - 76.2102i) q^{7} +O(q^{10})\) \(q+(-27.0000 - 46.7654i) q^{5} +(44.0000 - 76.2102i) q^{7} +(-270.000 + 467.654i) q^{11} +(209.000 + 361.999i) q^{13} +594.000 q^{17} +836.000 q^{19} +(2052.00 + 3554.17i) q^{23} +(104.500 - 180.999i) q^{25} +(297.000 - 514.419i) q^{29} +(-2128.00 - 3685.80i) q^{31} -4752.00 q^{35} -298.000 q^{37} +(-8613.00 - 14918.2i) q^{41} +(6050.00 - 10478.9i) q^{43} +(648.000 - 1122.37i) q^{47} +(4531.50 + 7848.79i) q^{49} +19494.0 q^{53} +29160.0 q^{55} +(3834.00 + 6640.68i) q^{59} +(17369.0 - 30084.0i) q^{61} +(11286.0 - 19547.9i) q^{65} +(-10906.0 - 18889.7i) q^{67} -46872.0 q^{71} +67562.0 q^{73} +(23760.0 + 41153.5i) q^{77} +(38456.0 - 66607.7i) q^{79} +(-33858.0 + 58643.8i) q^{83} +(-16038.0 - 27778.6i) q^{85} +29754.0 q^{89} +36784.0 q^{91} +(-22572.0 - 39095.9i) q^{95} +(61199.0 - 106000. i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 54 q^{5} + 88 q^{7} + O(q^{10}) \) \( 2 q - 54 q^{5} + 88 q^{7} - 540 q^{11} + 418 q^{13} + 1188 q^{17} + 1672 q^{19} + 4104 q^{23} + 209 q^{25} + 594 q^{29} - 4256 q^{31} - 9504 q^{35} - 596 q^{37} - 17226 q^{41} + 12100 q^{43} + 1296 q^{47} + 9063 q^{49} + 38988 q^{53} + 58320 q^{55} + 7668 q^{59} + 34738 q^{61} + 22572 q^{65} - 21812 q^{67} - 93744 q^{71} + 135124 q^{73} + 47520 q^{77} + 76912 q^{79} - 67716 q^{83} - 32076 q^{85} + 59508 q^{89} + 73568 q^{91} - 45144 q^{95} + 122398 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) −27.0000 46.7654i −0.482991 0.836564i 0.516819 0.856095i \(-0.327116\pi\)
−0.999809 + 0.0195305i \(0.993783\pi\)
\(6\) 0 0
\(7\) 44.0000 76.2102i 0.339397 0.587852i −0.644923 0.764248i \(-0.723110\pi\)
0.984319 + 0.176396i \(0.0564438\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −270.000 + 467.654i −0.672794 + 1.16531i 0.304315 + 0.952572i \(0.401573\pi\)
−0.977108 + 0.212742i \(0.931761\pi\)
\(12\) 0 0
\(13\) 209.000 + 361.999i 0.342995 + 0.594085i 0.984987 0.172626i \(-0.0552252\pi\)
−0.641992 + 0.766711i \(0.721892\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 594.000 0.498499 0.249249 0.968439i \(-0.419816\pi\)
0.249249 + 0.968439i \(0.419816\pi\)
\(18\) 0 0
\(19\) 836.000 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
\(23\) 2052.00 + 3554.17i 0.808831 + 1.40094i 0.913674 + 0.406448i \(0.133233\pi\)
−0.104843 + 0.994489i \(0.533434\pi\)
\(24\) 0 0
\(25\) 104.500 180.999i 0.0334400 0.0579198i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 297.000 514.419i 0.0655785 0.113585i −0.831372 0.555716i \(-0.812444\pi\)
0.896950 + 0.442131i \(0.145777\pi\)
\(30\) 0 0
\(31\) −2128.00 3685.80i −0.397711 0.688855i 0.595732 0.803183i \(-0.296862\pi\)
−0.993443 + 0.114328i \(0.963529\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4752.00 −0.655702
\(36\) 0 0
\(37\) −298.000 −0.0357859 −0.0178930 0.999840i \(-0.505696\pi\)
−0.0178930 + 0.999840i \(0.505696\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8613.00 14918.2i −0.800193 1.38598i −0.919489 0.393116i \(-0.871397\pi\)
0.119296 0.992859i \(-0.461936\pi\)
\(42\) 0 0
\(43\) 6050.00 10478.9i 0.498981 0.864261i −0.501018 0.865437i \(-0.667041\pi\)
0.999999 + 0.00117594i \(0.000374313\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 648.000 1122.37i 0.0427888 0.0741124i −0.843838 0.536598i \(-0.819709\pi\)
0.886627 + 0.462486i \(0.153042\pi\)
\(48\) 0 0
\(49\) 4531.50 + 7848.79i 0.269620 + 0.466995i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 19494.0 0.953260 0.476630 0.879104i \(-0.341858\pi\)
0.476630 + 0.879104i \(0.341858\pi\)
\(54\) 0 0
\(55\) 29160.0 1.29981
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3834.00 + 6640.68i 0.143391 + 0.248361i 0.928772 0.370653i \(-0.120866\pi\)
−0.785380 + 0.619013i \(0.787533\pi\)
\(60\) 0 0
\(61\) 17369.0 30084.0i 0.597655 1.03517i −0.395512 0.918461i \(-0.629433\pi\)
0.993166 0.116707i \(-0.0372339\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11286.0 19547.9i 0.331327 0.573875i
\(66\) 0 0
\(67\) −10906.0 18889.7i −0.296810 0.514090i 0.678594 0.734513i \(-0.262589\pi\)
−0.975404 + 0.220423i \(0.929256\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −46872.0 −1.10349 −0.551744 0.834014i \(-0.686037\pi\)
−0.551744 + 0.834014i \(0.686037\pi\)
\(72\) 0 0
\(73\) 67562.0 1.48387 0.741934 0.670473i \(-0.233909\pi\)
0.741934 + 0.670473i \(0.233909\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 23760.0 + 41153.5i 0.456688 + 0.791007i
\(78\) 0 0
\(79\) 38456.0 66607.7i 0.693260 1.20076i −0.277503 0.960725i \(-0.589507\pi\)
0.970764 0.240037i \(-0.0771597\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −33858.0 + 58643.8i −0.539468 + 0.934387i 0.459464 + 0.888196i \(0.348041\pi\)
−0.998933 + 0.0461905i \(0.985292\pi\)
\(84\) 0 0
\(85\) −16038.0 27778.6i −0.240770 0.417026i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 29754.0 0.398172 0.199086 0.979982i \(-0.436203\pi\)
0.199086 + 0.979982i \(0.436203\pi\)
\(90\) 0 0
\(91\) 36784.0 0.465646
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −22572.0 39095.9i −0.256603 0.444449i
\(96\) 0 0
\(97\) 61199.0 106000.i 0.660412 1.14387i −0.320095 0.947385i \(-0.603715\pi\)
0.980507 0.196482i \(-0.0629517\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5643.00 + 9773.96i −0.0550436 + 0.0953383i −0.892234 0.451573i \(-0.850863\pi\)
0.837191 + 0.546911i \(0.184196\pi\)
\(102\) 0 0
\(103\) 13628.0 + 23604.4i 0.126572 + 0.219230i 0.922346 0.386364i \(-0.126269\pi\)
−0.795774 + 0.605594i \(0.792936\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 122364. 1.03322 0.516612 0.856220i \(-0.327193\pi\)
0.516612 + 0.856220i \(0.327193\pi\)
\(108\) 0 0
\(109\) 99902.0 0.805393 0.402697 0.915334i \(-0.368073\pi\)
0.402697 + 0.915334i \(0.368073\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14823.0 + 25674.2i 0.109204 + 0.189148i 0.915448 0.402436i \(-0.131836\pi\)
−0.806244 + 0.591583i \(0.798503\pi\)
\(114\) 0 0
\(115\) 110808. 191925.i 0.781316 1.35328i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 26136.0 45268.9i 0.169189 0.293044i
\(120\) 0 0
\(121\) −65274.5 113059.i −0.405303 0.702006i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −180036. −1.03059
\(126\) 0 0
\(127\) 336512. 1.85136 0.925681 0.378305i \(-0.123493\pi\)
0.925681 + 0.378305i \(0.123493\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −50490.0 87451.2i −0.257056 0.445233i 0.708396 0.705815i \(-0.249419\pi\)
−0.965452 + 0.260582i \(0.916086\pi\)
\(132\) 0 0
\(133\) 36784.0 63711.8i 0.180314 0.312313i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 158571. 274653.i 0.721809 1.25021i −0.238465 0.971151i \(-0.576644\pi\)
0.960274 0.279059i \(-0.0900225\pi\)
\(138\) 0 0
\(139\) 74162.0 + 128452.i 0.325570 + 0.563904i 0.981628 0.190807i \(-0.0611105\pi\)
−0.656058 + 0.754711i \(0.727777\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −225720. −0.923060
\(144\) 0 0
\(145\) −32076.0 −0.126695
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −98307.0 170273.i −0.362759 0.628318i 0.625654 0.780100i \(-0.284832\pi\)
−0.988414 + 0.151782i \(0.951499\pi\)
\(150\) 0 0
\(151\) −37180.0 + 64397.6i −0.132699 + 0.229841i −0.924716 0.380658i \(-0.875698\pi\)
0.792017 + 0.610499i \(0.209031\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −114912. + 199033.i −0.384181 + 0.665421i
\(156\) 0 0
\(157\) −60439.0 104683.i −0.195690 0.338945i 0.751437 0.659805i \(-0.229361\pi\)
−0.947126 + 0.320861i \(0.896028\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 361152. 1.09806
\(162\) 0 0
\(163\) −111340. −0.328233 −0.164116 0.986441i \(-0.552477\pi\)
−0.164116 + 0.986441i \(0.552477\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 245916. + 425939.i 0.682332 + 1.18183i 0.974267 + 0.225395i \(0.0723674\pi\)
−0.291936 + 0.956438i \(0.594299\pi\)
\(168\) 0 0
\(169\) 98284.5 170234.i 0.264709 0.458489i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −353727. + 612673.i −0.898572 + 1.55637i −0.0692518 + 0.997599i \(0.522061\pi\)
−0.829320 + 0.558773i \(0.811272\pi\)
\(174\) 0 0
\(175\) −9196.00 15927.9i −0.0226988 0.0393156i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 493668. 1.15160 0.575801 0.817590i \(-0.304690\pi\)
0.575801 + 0.817590i \(0.304690\pi\)
\(180\) 0 0
\(181\) −559450. −1.26930 −0.634651 0.772799i \(-0.718856\pi\)
−0.634651 + 0.772799i \(0.718856\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8046.00 + 13936.1i 0.0172843 + 0.0299372i
\(186\) 0 0
\(187\) −160380. + 277786.i −0.335387 + 0.580907i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 362016. 627030.i 0.718033 1.24367i −0.243745 0.969839i \(-0.578376\pi\)
0.961778 0.273830i \(-0.0882906\pi\)
\(192\) 0 0
\(193\) −3553.00 6153.98i −0.00686597 0.0118922i 0.862572 0.505934i \(-0.168852\pi\)
−0.869438 + 0.494042i \(0.835519\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −530442. −0.973806 −0.486903 0.873456i \(-0.661873\pi\)
−0.486903 + 0.873456i \(0.661873\pi\)
\(198\) 0 0
\(199\) 56168.0 0.100544 0.0502720 0.998736i \(-0.483991\pi\)
0.0502720 + 0.998736i \(0.483991\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −26136.0 45268.9i −0.0445142 0.0771009i
\(204\) 0 0
\(205\) −465102. + 805580.i −0.772972 + 1.33883i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −225720. + 390959.i −0.357441 + 0.619106i
\(210\) 0 0
\(211\) 169598. + 293752.i 0.262249 + 0.454229i 0.966839 0.255385i \(-0.0822023\pi\)
−0.704590 + 0.709615i \(0.748869\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −653400. −0.964013
\(216\) 0 0
\(217\) −374528. −0.539927
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 124146. + 215027.i 0.170983 + 0.296151i
\(222\) 0 0
\(223\) −389680. + 674946.i −0.524742 + 0.908880i 0.474843 + 0.880071i \(0.342505\pi\)
−0.999585 + 0.0288094i \(0.990828\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 372438. 645082.i 0.479722 0.830902i −0.520008 0.854162i \(-0.674071\pi\)
0.999729 + 0.0232592i \(0.00740430\pi\)
\(228\) 0 0
\(229\) 136373. + 236205.i 0.171846 + 0.297646i 0.939065 0.343739i \(-0.111693\pi\)
−0.767219 + 0.641385i \(0.778360\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −153846. −0.185651 −0.0928253 0.995682i \(-0.529590\pi\)
−0.0928253 + 0.995682i \(0.529590\pi\)
\(234\) 0 0
\(235\) −69984.0 −0.0826664
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −577368. 1.00003e6i −0.653820 1.13245i −0.982188 0.187899i \(-0.939832\pi\)
0.328369 0.944550i \(-0.393501\pi\)
\(240\) 0 0
\(241\) −328537. + 569043.i −0.364369 + 0.631106i −0.988675 0.150074i \(-0.952049\pi\)
0.624306 + 0.781180i \(0.285382\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 244701. 423835.i 0.260448 0.451109i
\(246\) 0 0
\(247\) 174724. + 302631.i 0.182226 + 0.315625i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.34190e6 1.34442 0.672211 0.740359i \(-0.265345\pi\)
0.672211 + 0.740359i \(0.265345\pi\)
\(252\) 0 0
\(253\) −2.21616e6 −2.17671
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −66177.0 114622.i −0.0624992 0.108252i 0.833083 0.553148i \(-0.186574\pi\)
−0.895582 + 0.444897i \(0.853240\pi\)
\(258\) 0 0
\(259\) −13112.0 + 22710.7i −0.0121456 + 0.0210368i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −471636. + 816898.i −0.420453 + 0.728246i −0.995984 0.0895341i \(-0.971462\pi\)
0.575531 + 0.817780i \(0.304796\pi\)
\(264\) 0 0
\(265\) −526338. 911644.i −0.460416 0.797463i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 967518. 0.815227 0.407613 0.913155i \(-0.366361\pi\)
0.407613 + 0.913155i \(0.366361\pi\)
\(270\) 0 0
\(271\) −518320. −0.428721 −0.214360 0.976755i \(-0.568767\pi\)
−0.214360 + 0.976755i \(0.568767\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 56430.0 + 97739.6i 0.0449965 + 0.0779361i
\(276\) 0 0
\(277\) −1.11136e6 + 1.92494e6i −0.870275 + 1.50736i −0.00856270 + 0.999963i \(0.502726\pi\)
−0.861712 + 0.507397i \(0.830608\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 98307.0 170273.i 0.0742709 0.128641i −0.826498 0.562940i \(-0.809670\pi\)
0.900769 + 0.434299i \(0.143004\pi\)
\(282\) 0 0
\(283\) 776138. + 1.34431e6i 0.576067 + 0.997777i 0.995925 + 0.0901872i \(0.0287465\pi\)
−0.419858 + 0.907590i \(0.637920\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.51589e6 −1.08633
\(288\) 0 0
\(289\) −1.06702e6 −0.751499
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 536085. + 928526.i 0.364808 + 0.631866i 0.988745 0.149608i \(-0.0478012\pi\)
−0.623937 + 0.781475i \(0.714468\pi\)
\(294\) 0 0
\(295\) 207036. 358597.i 0.138513 0.239912i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −857736. + 1.48564e6i −0.554850 + 0.961029i
\(300\) 0 0
\(301\) −532400. 922144.i −0.338705 0.586655i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.87585e6 −1.15465
\(306\) 0 0
\(307\) 1.58589e6 0.960346 0.480173 0.877174i \(-0.340574\pi\)
0.480173 + 0.877174i \(0.340574\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 365364. + 632829.i 0.214203 + 0.371010i 0.953026 0.302890i \(-0.0979514\pi\)
−0.738823 + 0.673900i \(0.764618\pi\)
\(312\) 0 0
\(313\) −292429. + 506502.i −0.168717 + 0.292227i −0.937969 0.346719i \(-0.887296\pi\)
0.769252 + 0.638946i \(0.220629\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.24143e6 2.15023e6i 0.693865 1.20181i −0.276696 0.960957i \(-0.589240\pi\)
0.970562 0.240852i \(-0.0774270\pi\)
\(318\) 0 0
\(319\) 160380. + 277786.i 0.0882416 + 0.152839i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 496584. 0.264842
\(324\) 0 0
\(325\) 87362.0 0.0458790
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −57024.0 98768.5i −0.0290448 0.0503070i
\(330\) 0 0
\(331\) −188974. + 327313.i −0.0948052 + 0.164207i −0.909527 0.415644i \(-0.863556\pi\)
0.814722 + 0.579852i \(0.196889\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −588924. + 1.02005e6i −0.286713 + 0.496601i
\(336\) 0 0
\(337\) −319561. 553496.i −0.153278 0.265485i 0.779153 0.626834i \(-0.215650\pi\)
−0.932431 + 0.361349i \(0.882316\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.29824e6 1.07031
\(342\) 0 0
\(343\) 2.27656e6 1.04483
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.45233e6 + 2.51551e6i 0.647503 + 1.12151i 0.983717 + 0.179722i \(0.0575199\pi\)
−0.336215 + 0.941785i \(0.609147\pi\)
\(348\) 0 0
\(349\) 1.99579e6 3.45680e6i 0.877102 1.51919i 0.0225958 0.999745i \(-0.492807\pi\)
0.854506 0.519441i \(-0.173860\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −714609. + 1.23774e6i −0.305233 + 0.528679i −0.977313 0.211799i \(-0.932068\pi\)
0.672080 + 0.740478i \(0.265401\pi\)
\(354\) 0 0
\(355\) 1.26554e6 + 2.19199e6i 0.532974 + 0.923139i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.16186e6 0.475794 0.237897 0.971290i \(-0.423542\pi\)
0.237897 + 0.971290i \(0.423542\pi\)
\(360\) 0 0
\(361\) −1.77720e6 −0.717743
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.82417e6 3.15956e6i −0.716695 1.24135i
\(366\) 0 0
\(367\) 544616. 943303.i 0.211069 0.365583i −0.740980 0.671527i \(-0.765639\pi\)
0.952049 + 0.305944i \(0.0989721\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 857736. 1.48564e6i 0.323533 0.560376i
\(372\) 0 0
\(373\) −1.75288e6 3.03608e6i −0.652350 1.12990i −0.982551 0.185993i \(-0.940450\pi\)
0.330201 0.943911i \(-0.392884\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 248292. 0.0899724
\(378\) 0 0
\(379\) 4.04385e6 1.44610 0.723048 0.690798i \(-0.242740\pi\)
0.723048 + 0.690798i \(0.242740\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.59373e6 4.49247e6i −0.903499 1.56491i −0.822920 0.568157i \(-0.807657\pi\)
−0.0805786 0.996748i \(-0.525677\pi\)
\(384\) 0 0
\(385\) 1.28304e6 2.22229e6i 0.441152 0.764098i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 475173. 823024.i 0.159213 0.275765i −0.775372 0.631504i \(-0.782438\pi\)
0.934585 + 0.355740i \(0.115771\pi\)
\(390\) 0 0
\(391\) 1.21889e6 + 2.11118e6i 0.403201 + 0.698365i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.15325e6 −1.33935
\(396\) 0 0
\(397\) −520738. −0.165822 −0.0829112 0.996557i \(-0.526422\pi\)
−0.0829112 + 0.996557i \(0.526422\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −382185. 661964.i −0.118690 0.205576i 0.800559 0.599254i \(-0.204536\pi\)
−0.919249 + 0.393677i \(0.871203\pi\)
\(402\) 0 0
\(403\) 889504. 1.54067e6i 0.272826 0.472548i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 80460.0 139361.i 0.0240765 0.0417018i
\(408\) 0 0
\(409\) −1.32025e6 2.28675e6i −0.390255 0.675942i 0.602228 0.798324i \(-0.294280\pi\)
−0.992483 + 0.122382i \(0.960947\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 674784. 0.194666
\(414\) 0 0
\(415\) 3.65666e6 1.04223
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.49010e6 + 4.31298e6i 0.692918 + 1.20017i 0.970877 + 0.239577i \(0.0770087\pi\)
−0.277959 + 0.960593i \(0.589658\pi\)
\(420\) 0 0
\(421\) 118997. 206109.i 0.0327213 0.0566750i −0.849201 0.528070i \(-0.822916\pi\)
0.881922 + 0.471395i \(0.156249\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 62073.0 107514.i 0.0166698 0.0288729i
\(426\) 0 0
\(427\) −1.52847e6 2.64739e6i −0.405684 0.702665i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3.88238e6 −1.00671 −0.503356 0.864079i \(-0.667902\pi\)
−0.503356 + 0.864079i \(0.667902\pi\)
\(432\) 0 0
\(433\) −66958.0 −0.0171626 −0.00858129 0.999963i \(-0.502732\pi\)
−0.00858129 + 0.999963i \(0.502732\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.71547e6 + 2.97128e6i 0.429715 + 0.744287i
\(438\) 0 0
\(439\) 3.25068e6 5.63034e6i 0.805031 1.39435i −0.111240 0.993794i \(-0.535482\pi\)
0.916270 0.400560i \(-0.131184\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.30380e6 3.99030e6i 0.557745 0.966043i −0.439939 0.898028i \(-0.645000\pi\)
0.997684 0.0680154i \(-0.0216667\pi\)
\(444\) 0 0
\(445\) −803358. 1.39146e6i −0.192313 0.333096i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.77671e6 0.884092 0.442046 0.896992i \(-0.354253\pi\)
0.442046 + 0.896992i \(0.354253\pi\)
\(450\) 0 0
\(451\) 9.30204e6 2.15346
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −993168. 1.72022e6i −0.224902 0.389543i
\(456\) 0 0
\(457\) 1.59035e6 2.75456e6i 0.356206 0.616967i −0.631117 0.775687i \(-0.717403\pi\)
0.987324 + 0.158720i \(0.0507368\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.34274e6 + 5.78979e6i −0.732571 + 1.26885i 0.223210 + 0.974770i \(0.428346\pi\)
−0.955781 + 0.294080i \(0.904987\pi\)
\(462\) 0 0
\(463\) 2.17561e6 + 3.76826e6i 0.471659 + 0.816937i 0.999474 0.0324218i \(-0.0103220\pi\)
−0.527815 + 0.849359i \(0.676989\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.07994e6 1.50223 0.751117 0.660170i \(-0.229516\pi\)
0.751117 + 0.660170i \(0.229516\pi\)
\(468\) 0 0
\(469\) −1.91946e6 −0.402945
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.26700e6 + 5.65861e6i 0.671423 + 1.16294i
\(474\) 0 0
\(475\) 87362.0 151315.i 0.0177660 0.0307715i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.61093e6 + 2.79021e6i −0.320802 + 0.555646i −0.980654 0.195750i \(-0.937286\pi\)
0.659852 + 0.751396i \(0.270619\pi\)
\(480\) 0 0
\(481\) −62282.0 107876.i −0.0122744 0.0212599i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.60949e6 −1.27589
\(486\) 0 0
\(487\) 2.29710e6 0.438891 0.219446 0.975625i \(-0.429575\pi\)
0.219446 + 0.975625i \(0.429575\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.41075e6 2.44349e6i −0.264087 0.457411i 0.703237 0.710955i \(-0.251737\pi\)
−0.967324 + 0.253544i \(0.918404\pi\)
\(492\) 0 0
\(493\) 176418. 305565.i 0.0326908 0.0566221i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.06237e6 + 3.57213e6i −0.374520 + 0.648688i
\(498\) 0 0
\(499\) 2.06814e6 + 3.58213e6i 0.371817 + 0.644006i 0.989845 0.142150i \(-0.0454016\pi\)
−0.618028 + 0.786156i \(0.712068\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.33263e6 1.46846 0.734230 0.678901i \(-0.237543\pi\)
0.734230 + 0.678901i \(0.237543\pi\)
\(504\) 0 0
\(505\) 609444. 0.106342
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −2.17050e6 3.75942e6i −0.371335 0.643171i 0.618436 0.785835i \(-0.287767\pi\)
−0.989771 + 0.142664i \(0.954433\pi\)
\(510\) 0 0
\(511\) 2.97273e6 5.14892e6i 0.503620 0.872295i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 735912. 1.27464e6i 0.122267 0.211772i
\(516\) 0 0
\(517\) 349920. + 606079.i 0.0575761 + 0.0997248i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.74185e6 −1.08814 −0.544070 0.839040i \(-0.683117\pi\)
−0.544070 + 0.839040i \(0.683117\pi\)
\(522\) 0 0
\(523\) −7.72196e6 −1.23445 −0.617224 0.786787i \(-0.711743\pi\)
−0.617224 + 0.786787i \(0.711743\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.26403e6 2.18937e6i −0.198258 0.343394i
\(528\) 0 0
\(529\) −5.20324e6 + 9.01227e6i −0.808415 + 1.40022i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.60023e6 6.23579e6i 0.548925 0.950765i
\(534\) 0 0
\(535\) −3.30383e6 5.72240e6i −0.499037 0.864358i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.89402e6 −0.725594
\(540\) 0 0
\(541\) −682066. −0.100192 −0.0500960 0.998744i \(-0.515953\pi\)
−0.0500960 + 0.998744i \(0.515953\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.69735e6 4.67195e6i −0.388997 0.673763i
\(546\) 0 0
\(547\) −1.07886e6 + 1.86864e6i −0.154169 + 0.267028i −0.932756 0.360508i \(-0.882603\pi\)
0.778587 + 0.627536i \(0.215937\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 248292. 430054.i 0.0348404 0.0603454i
\(552\) 0 0
\(553\) −3.38413e6 5.86148e6i −0.470581 0.815069i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.67597e6 −0.365463 −0.182731 0.983163i \(-0.558494\pi\)
−0.182731 + 0.983163i \(0.558494\pi\)
\(558\) 0 0
\(559\) 5.05780e6 0.684592
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.77665e6 + 3.07725e6i 0.236228 + 0.409159i 0.959629 0.281269i \(-0.0907554\pi\)
−0.723401 + 0.690428i \(0.757422\pi\)
\(564\) 0 0
\(565\) 800442. 1.38641e6i 0.105489 0.182713i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.46123e6 1.11912e7i 0.836633 1.44909i −0.0560613 0.998427i \(-0.517854\pi\)
0.892694 0.450663i \(-0.148812\pi\)
\(570\) 0 0
\(571\) 3.04179e6 + 5.26853e6i 0.390426 + 0.676237i 0.992506 0.122199i \(-0.0389945\pi\)
−0.602080 + 0.798436i \(0.705661\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 857736. 0.108189
\(576\) 0 0
\(577\) −1.58241e7 −1.97869 −0.989347 0.145579i \(-0.953495\pi\)
−0.989347 + 0.145579i \(0.953495\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.97950e6 + 5.16065e6i 0.366188 + 0.634256i
\(582\) 0 0
\(583\) −5.26338e6 + 9.11644e6i −0.641347 + 1.11085i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.30110e6 + 3.98563e6i −0.275639 + 0.477421i −0.970296 0.241920i \(-0.922223\pi\)
0.694657 + 0.719341i \(0.255556\pi\)
\(588\) 0 0
\(589\) −1.77901e6 3.08133e6i −0.211295 0.365974i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.61122e6 1.00561 0.502803 0.864401i \(-0.332302\pi\)
0.502803 + 0.864401i \(0.332302\pi\)
\(594\) 0 0
\(595\) −2.82269e6 −0.326867
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 3.99114e6 + 6.91286e6i 0.454496 + 0.787210i 0.998659 0.0517695i \(-0.0164861\pi\)
−0.544163 + 0.838979i \(0.683153\pi\)
\(600\) 0 0
\(601\) −5.08700e6 + 8.81095e6i −0.574481 + 0.995031i 0.421616 + 0.906774i \(0.361463\pi\)
−0.996098 + 0.0882567i \(0.971870\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.52482e6 + 6.10517e6i −0.391515 + 0.678125i
\(606\) 0 0
\(607\) 4.97922e6 + 8.62426e6i 0.548516 + 0.950057i 0.998377 + 0.0569587i \(0.0181403\pi\)
−0.449861 + 0.893099i \(0.648526\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 541728. 0.0587054
\(612\) 0 0
\(613\) 4.19586e6 0.450993 0.225497 0.974244i \(-0.427600\pi\)
0.225497 + 0.974244i \(0.427600\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.56276e6 7.90293e6i −0.482519 0.835747i 0.517280 0.855816i \(-0.326945\pi\)
−0.999799 + 0.0200690i \(0.993611\pi\)
\(618\) 0 0
\(619\) −3.22867e6 + 5.59222e6i −0.338686 + 0.586621i −0.984186 0.177139i \(-0.943316\pi\)
0.645500 + 0.763760i \(0.276649\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.30918e6 2.26756e6i 0.135138 0.234066i
\(624\) 0 0
\(625\) 4.53441e6 + 7.85383e6i 0.464324 + 0.804232i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −177012. −0.0178392
\(630\) 0 0
\(631\) −1.40514e7 −1.40490 −0.702450 0.711733i \(-0.747910\pi\)
−0.702450 + 0.711733i \(0.747910\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −9.08582e6 1.57371e7i −0.894190 1.54878i
\(636\) 0 0
\(637\) −1.89417e6 + 3.28079e6i −0.184957 + 0.320354i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.23584e6 + 7.33669e6i −0.407188 + 0.705270i −0.994573 0.104037i \(-0.966824\pi\)
0.587386 + 0.809307i \(0.300157\pi\)
\(642\) 0 0
\(643\) −244282. 423109.i −0.0233004 0.0403575i 0.854140 0.520043i \(-0.174084\pi\)
−0.877441 + 0.479685i \(0.840751\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 2.48119e6 0.233023 0.116512 0.993189i \(-0.462829\pi\)
0.116512 + 0.993189i \(0.462829\pi\)
\(648\) 0 0
\(649\) −4.14072e6 −0.385891
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.64565e6 + 4.58240e6i 0.242800 + 0.420543i 0.961511 0.274767i \(-0.0886007\pi\)
−0.718711 + 0.695309i \(0.755267\pi\)
\(654\) 0 0
\(655\) −2.72646e6 + 4.72237e6i −0.248311 + 0.430087i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.36234e6 + 4.09169e6i −0.211899 + 0.367019i −0.952309 0.305136i \(-0.901298\pi\)
0.740410 + 0.672156i \(0.234631\pi\)
\(660\) 0 0
\(661\) 3.08710e6 + 5.34702e6i 0.274819 + 0.476001i 0.970090 0.242747i \(-0.0780486\pi\)
−0.695270 + 0.718748i \(0.744715\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.97267e6 −0.348360
\(666\) 0 0
\(667\) 2.43778e6 0.212168
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9.37926e6 + 1.62454e7i 0.804197 + 1.39291i
\(672\) 0 0
\(673\) 4.70462e6 8.14865e6i 0.400394 0.693502i −0.593380 0.804923i \(-0.702207\pi\)
0.993773 + 0.111421i \(0.0355401\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.50430e6 + 1.29978e7i −0.629272 + 1.08993i 0.358426 + 0.933558i \(0.383314\pi\)
−0.987698 + 0.156373i \(0.950020\pi\)
\(678\) 0 0
\(679\) −5.38551e6 9.32798e6i −0.448283 0.776449i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.29707e7 −1.06393 −0.531963 0.846768i \(-0.678545\pi\)
−0.531963 + 0.846768i \(0.678545\pi\)
\(684\) 0 0
\(685\) −1.71257e7 −1.39451
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.07425e6 + 7.05680e6i 0.326963 + 0.566317i
\(690\) 0 0
\(691\) −1.13278e7 + 1.96203e7i −0.902506 + 1.56319i −0.0782761 + 0.996932i \(0.524942\pi\)
−0.824230 + 0.566255i \(0.808392\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.00475e6 6.93643e6i 0.314495 0.544721i
\(696\) 0 0
\(697\) −5.11612e6 8.86138e6i −0.398895 0.690907i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.90169e7 1.46166 0.730828 0.682562i \(-0.239134\pi\)
0.730828 + 0.682562i \(0.239134\pi\)
\(702\) 0 0
\(703\) −249128. −0.0190123
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 496584. + 860109.i 0.0373632 + 0.0647150i
\(708\) 0 0
\(709\) −7.56556e6 + 1.31039e7i −0.565231 + 0.979008i 0.431798 + 0.901971i \(0.357879\pi\)
−0.997028 + 0.0770376i \(0.975454\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 8.73331e6 1.51265e7i 0.643362 1.11434i
\(714\) 0 0
\(715\) 6.09444e6 + 1.05559e7i 0.445829 + 0.772199i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.50323e7 −1.08443 −0.542217 0.840238i \(-0.682415\pi\)
−0.542217 + 0.840238i \(0.682415\pi\)
\(720\) 0 0
\(721\) 2.39853e6 0.171833
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −62073.0 107514.i −0.00438589 0.00759658i
\(726\) 0 0
\(727\) 3.70615e6 6.41924e6i 0.260068 0.450451i −0.706192 0.708021i \(-0.749588\pi\)
0.966260 + 0.257570i \(0.0829217\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.59370e6 6.22447e6i 0.248742 0.430833i
\(732\) 0 0
\(733\) 1.38964e6 + 2.40693e6i 0.0955306 + 0.165464i 0.909830 0.414981i \(-0.136212\pi\)
−0.814299 + 0.580445i \(0.802879\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.17785e7 0.798768
\(738\) 0 0
\(739\) −1.21046e7 −0.815342 −0.407671 0.913129i \(-0.633659\pi\)
−0.407671 + 0.913129i \(0.633659\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.23463e6 3.87049e6i −0.148502 0.257214i 0.782172 0.623063i \(-0.214112\pi\)
−0.930674 + 0.365849i \(0.880779\pi\)
\(744\) 0 0
\(745\) −5.30858e6 + 9.19473e6i −0.350419 + 0.606943i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.38402e6 9.32539e6i 0.350673 0.607383i
\(750\) 0 0
\(751\) −1.44231e7 2.49816e7i −0.933168 1.61629i −0.777869 0.628426i \(-0.783700\pi\)
−0.155298 0.987868i \(-0.549634\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 4.01544e6 0.256369
\(756\) 0 0
\(757\) 9.60868e6 0.609430 0.304715 0.952444i \(-0.401439\pi\)
0.304715 + 0.952444i \(0.401439\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.27294e6 3.93685e6i −0.142274 0.246426i 0.786078 0.618127i \(-0.212108\pi\)
−0.928353 + 0.371700i \(0.878775\pi\)
\(762\) 0 0
\(763\) 4.39569e6 7.61355e6i 0.273348 0.473452i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.60261e6 + 2.77581e6i −0.0983649 + 0.170373i
\(768\) 0 0
\(769\) 1.07962e7 + 1.86995e7i 0.658345 + 1.14029i 0.981044 + 0.193785i \(0.0620765\pi\)
−0.322699 + 0.946502i \(0.604590\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.48400e7 −0.893276 −0.446638 0.894715i \(-0.647379\pi\)
−0.446638 + 0.894715i \(0.647379\pi\)
\(774\) 0 0
\(775\) −889504. −0.0531978
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.20047e6 1.24716e7i −0.425125 0.736339i
\(780\) 0 0
\(781\) 1.26554e7 2.19199e7i 0.742420 1.28591i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.26371e6 + 5.65290e6i −0.189033 + 0.327414i
\(786\) 0 0
\(787\) 1.24393e7 + 2.15454e7i 0.715909 + 1.23999i 0.962608 + 0.270898i \(0.0873208\pi\)
−0.246699 + 0.969092i \(0.579346\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.60885e6 0.148254
\(792\) 0 0
\(793\) 1.45205e7 0.819970
\(794\) 0 0
\(795\) 0 0
\(796\) 0