Properties

Label 324.6.e.d.109.1
Level $324$
Weight $6$
Character 324.109
Analytic conductor $51.964$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \( x^{2} - x + 1 \) Copy content Toggle raw display
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 109.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 324.109
Dual form 324.6.e.d.217.1

$q$-expansion

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

Character values

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

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

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
\(5\) 27.0000 46.7654i 0.482991 0.836564i −0.516819 0.856095i \(-0.672884\pi\)
0.999809 + 0.0195305i \(0.00621716\pi\)
\(6\) 0 0
\(7\) 44.0000 + 76.2102i 0.339397 + 0.587852i 0.984319 0.176396i \(-0.0564438\pi\)
−0.644923 + 0.764248i \(0.723110\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 270.000 + 467.654i 0.672794 + 1.16531i 0.977108 + 0.212742i \(0.0682393\pi\)
−0.304315 + 0.952572i \(0.598427\pi\)
\(12\) 0 0
\(13\) 209.000 361.999i 0.342995 0.594085i −0.641992 0.766711i \(-0.721892\pi\)
0.984987 + 0.172626i \(0.0552252\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −594.000 −0.498499 −0.249249 0.968439i \(-0.580184\pi\)
−0.249249 + 0.968439i \(0.580184\pi\)
\(18\) 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 0.104843 + 0.994489i \(0.466566\pi\)
−0.913674 + 0.406448i \(0.866767\pi\)
\(24\) 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 \(-0.187556\pi\)
−0.896950 + 0.442131i \(0.854223\pi\)
\(30\) 0 0
\(31\) −2128.00 + 3685.80i −0.397711 + 0.688855i −0.993443 0.114328i \(-0.963529\pi\)
0.595732 + 0.803183i \(0.296862\pi\)
\(32\) 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 −0.119296 0.992859i \(-0.538064\pi\)
0.919489 0.393116i \(-0.128603\pi\)
\(42\) 0 0
\(43\) 6050.00 + 10478.9i 0.498981 + 0.864261i 0.999999 0.00117594i \(-0.000374313\pi\)
−0.501018 + 0.865437i \(0.667041\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −648.000 1122.37i −0.0427888 0.0741124i 0.843838 0.536598i \(-0.180291\pi\)
−0.886627 + 0.462486i \(0.846958\pi\)
\(48\) 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 \(-0.658142\pi\)
−0.476630 + 0.879104i \(0.658142\pi\)
\(54\) 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 \(-0.879134\pi\)
0.785380 + 0.619013i \(0.212467\pi\)
\(60\) 0 0
\(61\) 17369.0 + 30084.0i 0.597655 + 1.03517i 0.993166 + 0.116707i \(0.0372339\pi\)
−0.395512 + 0.918461i \(0.629433\pi\)
\(62\) 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 −0.975404 0.220423i \(-0.929256\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 46872.0 1.10349 0.551744 0.834014i \(-0.313963\pi\)
0.551744 + 0.834014i \(0.313963\pi\)
\(72\) 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 0.970764 + 0.240037i \(0.0771597\pi\)
−0.277503 + 0.960725i \(0.589507\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 33858.0 + 58643.8i 0.539468 + 0.934387i 0.998933 + 0.0461905i \(0.0147081\pi\)
−0.459464 + 0.888196i \(0.651959\pi\)
\(84\) 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 \(-0.563797\pi\)
−0.199086 + 0.979982i \(0.563797\pi\)
\(90\) 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 0.980507 + 0.196482i \(0.0629517\pi\)
−0.320095 + 0.947385i \(0.603715\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5643.00 + 9773.96i 0.0550436 + 0.0953383i 0.892234 0.451573i \(-0.149137\pi\)
−0.837191 + 0.546911i \(0.815804\pi\)
\(102\) 0 0
\(103\) 13628.0 23604.4i 0.126572 0.219230i −0.795774 0.605594i \(-0.792936\pi\)
0.922346 + 0.386364i \(0.126269\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −122364. −1.03322 −0.516612 0.856220i \(-0.672807\pi\)
−0.516612 + 0.856220i \(0.672807\pi\)
\(108\) 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 \(-0.868164\pi\)
0.806244 + 0.591583i \(0.201497\pi\)
\(114\) 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 \(-0.750581\pi\)
0.965452 + 0.260582i \(0.0839143\pi\)
\(132\) 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 −0.960274 0.279059i \(-0.909978\pi\)
0.238465 0.971151i \(-0.423356\pi\)
\(138\) 0 0
\(139\) 74162.0 128452.i 0.325570 0.563904i −0.656058 0.754711i \(-0.727777\pi\)
0.981628 + 0.190807i \(0.0611105\pi\)
\(140\) 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 \(-0.715168\pi\)
0.988414 + 0.151782i \(0.0485013\pi\)
\(150\) 0 0
\(151\) −37180.0 64397.6i −0.132699 0.229841i 0.792017 0.610499i \(-0.209031\pi\)
−0.924716 + 0.380658i \(0.875698\pi\)
\(152\) 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 −0.947126 0.320861i \(-0.896028\pi\)
0.751437 + 0.659805i \(0.229361\pi\)
\(158\) 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 0.291936 + 0.956438i \(0.405701\pi\)
−0.974267 + 0.225395i \(0.927633\pi\)
\(168\) 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 0.829320 + 0.558773i \(0.188728\pi\)
0.0692518 + 0.997599i \(0.477939\pi\)
\(174\) 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 \(-0.695310\pi\)
−0.575801 + 0.817590i \(0.695310\pi\)
\(180\) 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 −0.961778 0.273830i \(-0.911709\pi\)
0.243745 0.969839i \(-0.421624\pi\)
\(192\) 0 0
\(193\) −3553.00 + 6153.98i −0.00686597 + 0.0118922i −0.869438 0.494042i \(-0.835519\pi\)
0.862572 + 0.505934i \(0.168852\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 530442. 0.973806 0.486903 0.873456i \(-0.338127\pi\)
0.486903 + 0.873456i \(0.338127\pi\)
\(198\) 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 −0.704590 0.709615i \(-0.748869\pi\)
0.966839 + 0.255385i \(0.0822023\pi\)
\(212\) 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 −0.999585 0.0288094i \(-0.990828\pi\)
0.474843 0.880071i \(-0.342505\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −372438. 645082.i −0.479722 0.830902i 0.520008 0.854162i \(-0.325929\pi\)
−0.999729 + 0.0232592i \(0.992596\pi\)
\(228\) 0 0
\(229\) 136373. 236205.i 0.171846 0.297646i −0.767219 0.641385i \(-0.778360\pi\)
0.939065 + 0.343739i \(0.111693\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 153846. 0.185651 0.0928253 0.995682i \(-0.470410\pi\)
0.0928253 + 0.995682i \(0.470410\pi\)
\(234\) 0 0
\(235\) −69984.0 −0.0826664
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 577368. 1.00003e6i 0.653820 1.13245i −0.328369 0.944550i \(-0.606499\pi\)
0.982188 0.187899i \(-0.0601678\pi\)
\(240\) 0 0
\(241\) −328537. 569043.i −0.364369 0.631106i 0.624306 0.781180i \(-0.285382\pi\)
−0.988675 + 0.150074i \(0.952049\pi\)
\(242\) 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 \(-0.734655\pi\)
−0.672211 + 0.740359i \(0.734655\pi\)
\(252\) 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 \(-0.813426\pi\)
0.895582 + 0.444897i \(0.146760\pi\)
\(258\) 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 \(-0.0285378\pi\)
−0.575531 + 0.817780i \(0.695204\pi\)
\(264\) 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 \(-0.633639\pi\)
−0.407613 + 0.913155i \(0.633639\pi\)
\(270\) 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 −0.861712 0.507397i \(-0.830608\pi\)
−0.00856270 0.999963i \(-0.502726\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −98307.0 170273.i −0.0742709 0.128641i 0.826498 0.562940i \(-0.190330\pi\)
−0.900769 + 0.434299i \(0.856996\pi\)
\(282\) 0 0
\(283\) 776138. 1.34431e6i 0.576067 0.997777i −0.419858 0.907590i \(-0.637920\pi\)
0.995925 0.0901872i \(-0.0287465\pi\)
\(284\) 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 \(-0.952199\pi\)
0.623937 + 0.781475i \(0.285532\pi\)
\(294\) 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 \(-0.902049\pi\)
0.738823 + 0.673900i \(0.235382\pi\)
\(312\) 0 0
\(313\) −292429. 506502.i −0.168717 0.292227i 0.769252 0.638946i \(-0.220629\pi\)
−0.937969 + 0.346719i \(0.887296\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.24143e6 2.15023e6i −0.693865 1.20181i −0.970562 0.240852i \(-0.922573\pi\)
0.276696 0.960957i \(-0.410760\pi\)
\(318\) 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 0.814722 0.579852i \(-0.196889\pi\)
−0.909527 + 0.415644i \(0.863556\pi\)
\(332\) 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 −0.932431 0.361349i \(-0.882316\pi\)
0.779153 + 0.626834i \(0.215650\pi\)
\(338\) 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 0.336215 + 0.941785i \(0.390853\pi\)
−0.983717 + 0.179722i \(0.942480\pi\)
\(348\) 0 0
\(349\) 1.99579e6 + 3.45680e6i 0.877102 + 1.51919i 0.854506 + 0.519441i \(0.173860\pi\)
0.0225958 + 0.999745i \(0.492807\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 714609. + 1.23774e6i 0.305233 + 0.528679i 0.977313 0.211799i \(-0.0679323\pi\)
−0.672080 + 0.740478i \(0.734599\pi\)
\(354\) 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 \(-0.576458\pi\)
−0.237897 + 0.971290i \(0.576458\pi\)
\(360\) 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 0.952049 0.305944i \(-0.0989721\pi\)
−0.740980 + 0.671527i \(0.765639\pi\)
\(368\) 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 0.330201 + 0.943911i \(0.392884\pi\)
−0.982551 + 0.185993i \(0.940450\pi\)
\(374\) 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 0.0805786 0.996748i \(-0.474323\pi\)
0.822920 0.568157i \(-0.192343\pi\)
\(384\) 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 \(-0.217562\pi\)
−0.934585 + 0.355740i \(0.884229\pi\)
\(390\) 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 \(-0.795464\pi\)
0.919249 + 0.393677i \(0.128797\pi\)
\(402\) 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 −0.992483 0.122382i \(-0.960947\pi\)
0.602228 + 0.798324i \(0.294280\pi\)
\(410\) 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 0.277959 + 0.960593i \(0.410342\pi\)
−0.970877 + 0.239577i \(0.922991\pi\)
\(420\) 0 0
\(421\) 118997. + 206109.i 0.0327213 + 0.0566750i 0.881922 0.471395i \(-0.156249\pi\)
−0.849201 + 0.528070i \(0.822916\pi\)
\(422\) 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 \(-0.332098\pi\)
0.503356 + 0.864079i \(0.332098\pi\)
\(432\) 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 0.916270 + 0.400560i \(0.131184\pi\)
−0.111240 + 0.993794i \(0.535482\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.30380e6 3.99030e6i −0.557745 0.966043i −0.997684 0.0680154i \(-0.978333\pi\)
0.439939 0.898028i \(-0.355000\pi\)
\(444\) 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 \(-0.645747\pi\)
−0.442046 + 0.896992i \(0.645747\pi\)
\(450\) 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 0.987324 0.158720i \(-0.0507368\pi\)
−0.631117 + 0.775687i \(0.717403\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.34274e6 + 5.78979e6i 0.732571 + 1.26885i 0.955781 + 0.294080i \(0.0950131\pi\)
−0.223210 + 0.974770i \(0.571654\pi\)
\(462\) 0 0
\(463\) 2.17561e6 3.76826e6i 0.471659 0.816937i −0.527815 0.849359i \(-0.676989\pi\)
0.999474 + 0.0324218i \(0.0103220\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.07994e6 −1.50223 −0.751117 0.660170i \(-0.770484\pi\)
−0.751117 + 0.660170i \(0.770484\pi\)
\(468\) 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 \(-0.0627142\pi\)
−0.659852 + 0.751396i \(0.729381\pi\)
\(480\) 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 \(-0.748263\pi\)
0.967324 + 0.253544i \(0.0815962\pi\)
\(492\) 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 −0.618028 0.786156i \(-0.712068\pi\)
0.989845 + 0.142150i \(0.0454016\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −8.33263e6 −1.46846 −0.734230 0.678901i \(-0.762457\pi\)
−0.734230 + 0.678901i \(0.762457\pi\)
\(504\) 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 \(-0.712233\pi\)
0.989771 + 0.142664i \(0.0455668\pi\)
\(510\) 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 \(-0.316883\pi\)
0.544070 + 0.839040i \(0.316883\pi\)
\(522\) 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 0.778587 0.627536i \(-0.215937\pi\)
−0.932756 + 0.360508i \(0.882603\pi\)
\(548\) 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 \(-0.441506\pi\)
0.182731 + 0.983163i \(0.441506\pi\)
\(558\) 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 \(-0.909245\pi\)
0.723401 + 0.690428i \(0.242578\pi\)
\(564\) 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 −0.892694 0.450663i \(-0.851188\pi\)
0.0560613 0.998427i \(-0.482146\pi\)
\(570\) 0 0
\(571\) 3.04179e6 5.26853e6i 0.390426 0.676237i −0.602080 0.798436i \(-0.705661\pi\)
0.992506 + 0.122199i \(0.0389945\pi\)
\(572\) 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 \(-0.0777772\pi\)
−0.694657 + 0.719341i \(0.744444\pi\)
\(588\) 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 \(-0.667698\pi\)
−0.502803 + 0.864401i \(0.667698\pi\)
\(594\) 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 \(-0.983514\pi\)
0.544163 + 0.838979i \(0.316847\pi\)
\(600\) 0 0
\(601\) −5.08700e6 8.81095e6i −0.574481 0.995031i −0.996098 0.0882567i \(-0.971870\pi\)
0.421616 0.906774i \(-0.361463\pi\)
\(602\) 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 −0.449861 0.893099i \(-0.648526\pi\)
0.998377 0.0569587i \(-0.0181403\pi\)
\(608\) 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 \(-0.673055\pi\)
0.999799 + 0.0200690i \(0.00638860\pi\)
\(618\) 0 0
\(619\) −3.22867e6 5.59222e6i −0.338686 0.586621i 0.645500 0.763760i \(-0.276649\pi\)
−0.984186 + 0.177139i \(0.943316\pi\)
\(620\) 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 \(-0.0331762\pi\)
−0.587386 + 0.809307i \(0.699843\pi\)
\(642\) 0 0
\(643\) −244282. + 423109.i −0.0233004 + 0.0403575i −0.877441 0.479685i \(-0.840751\pi\)
0.854140 + 0.520043i \(0.174084\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.48119e6 −0.233023 −0.116512 0.993189i \(-0.537171\pi\)
−0.116512 + 0.993189i \(0.537171\pi\)
\(648\) 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 \(-0.911399\pi\)
0.718711 + 0.695309i \(0.244733\pi\)
\(654\) 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 \(-0.0987019\pi\)
−0.740410 + 0.672156i \(0.765369\pi\)
\(660\) 0 0
\(661\) 3.08710e6 5.34702e6i 0.274819 0.476001i −0.695270 0.718748i \(-0.744715\pi\)
0.970090 + 0.242747i \(0.0780486\pi\)
\(662\) 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 0.993773 0.111421i \(-0.0355401\pi\)
−0.593380 + 0.804923i \(0.702207\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.50430e6 + 1.29978e7i 0.629272 + 1.08993i 0.987698 + 0.156373i \(0.0499802\pi\)
−0.358426 + 0.933558i \(0.616686\pi\)
\(678\) 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 \(-0.321455\pi\)
0.531963 + 0.846768i \(0.321455\pi\)
\(684\) 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 −0.824230 0.566255i \(-0.808392\pi\)
−0.0782761 0.996932i \(-0.524942\pi\)
\(692\) 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 \(-0.760866\pi\)
−0.730828 + 0.682562i \(0.760866\pi\)
\(702\) 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 −0.997028 0.0770376i \(-0.975454\pi\)
0.431798 0.901971i \(-0.357879\pi\)
\(710\) 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 \(-0.317585\pi\)
0.542217 + 0.840238i \(0.317585\pi\)
\(720\) 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 0.966260 0.257570i \(-0.0829217\pi\)
−0.706192 + 0.708021i \(0.749588\pi\)
\(728\) 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 −0.814299 0.580445i \(-0.802879\pi\)
0.909830 + 0.414981i \(0.136212\pi\)
\(734\) 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 \(-0.785888\pi\)
0.930674 + 0.365849i \(0.119221\pi\)
\(744\) 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 −0.155298 + 0.987868i \(0.549634\pi\)
−0.777869 + 0.628426i \(0.783700\pi\)
\(752\) 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 \(-0.787892\pi\)
0.928353 + 0.371700i \(0.121225\pi\)
\(762\) 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 −0.322699 0.946502i \(-0.604590\pi\)
0.981044 0.193785i \(-0.0620765\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.48400e7 0.893276 0.446638 0.894715i \(-0.352621\pi\)
0.446638 + 0.894715i \(0.352621\pi\)
\(774\) 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 −0.246699 0.969092i \(-0.579346\pi\)
0.962608 0.270898i \(-0.0873208\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −2.60885e6 −0.148254
\(792\) 0 0
\(793\) 1.45205e7 0.819970
\(794\) 0 0