Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(38.6276877123\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{4729}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1182 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-33.8839\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 24.8839 | 1.09972 | 0.549861 | − | 0.835256i | \(-0.314681\pi\) | ||||
0.549861 | + | 0.835256i | \(0.314681\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 107.207 | 0.209388 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2015.59 | −0.634925 | ||||||||
\(7\) | 4010.50 | 0.631332 | 0.315666 | − | 0.948870i | \(-0.397772\pi\) | ||||
0.315666 | + | 0.948870i | \(0.397772\pi\) | |||||||
\(8\) | −10072.8 | −0.869453 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 84861.3 | 1.74760 | 0.873801 | − | 0.486283i | \(-0.161648\pi\) | ||||
0.873801 | + | 0.486283i | \(0.161648\pi\) | |||||||
\(12\) | −8683.74 | −0.120890 | ||||||||
\(13\) | −119425. | −1.15971 | −0.579857 | − | 0.814718i | \(-0.696892\pi\) | ||||
−0.579857 | + | 0.814718i | \(0.696892\pi\) | |||||||
\(14\) | 99796.8 | 0.694289 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −305541. | −1.16554 | ||||||||
\(17\) | −116934. | −0.339562 | −0.169781 | − | 0.985482i | \(-0.554306\pi\) | ||||
−0.169781 | + | 0.985482i | \(0.554306\pi\) | |||||||
\(18\) | 163263. | 0.366574 | ||||||||
\(19\) | −234932. | −0.413571 | −0.206786 | − | 0.978386i | \(-0.566300\pi\) | ||||
−0.206786 | + | 0.978386i | \(0.566300\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −324851. | −0.364500 | ||||||||
\(22\) | 2.11168e6 | 1.92188 | ||||||||
\(23\) | −2.34570e6 | −1.74782 | −0.873912 | − | 0.486084i | \(-0.838425\pi\) | ||||
−0.873912 | + | 0.486084i | \(0.838425\pi\) | |||||||
\(24\) | 815899. | 0.501979 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.97176e6 | −1.27536 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 429953. | 0.132193 | ||||||||
\(29\) | −464196. | −0.121874 | −0.0609369 | − | 0.998142i | \(-0.519409\pi\) | ||||
−0.0609369 | + | 0.998142i | \(0.519409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.11766e6 | −0.995277 | −0.497638 | − | 0.867385i | \(-0.665799\pi\) | ||||
−0.497638 | + | 0.867385i | \(0.665799\pi\) | |||||||
\(32\) | −2.44574e6 | −0.412321 | ||||||||
\(33\) | −6.87377e6 | −1.00898 | ||||||||
\(34\) | −2.90976e6 | −0.373423 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 703383. | 0.0697960 | ||||||||
\(37\) | −8.69354e6 | −0.762586 | −0.381293 | − | 0.924454i | \(-0.624521\pi\) | ||||
−0.381293 | + | 0.924454i | \(0.624521\pi\) | |||||||
\(38\) | −5.84601e6 | −0.454813 | ||||||||
\(39\) | 9.67345e6 | 0.669562 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.05805e6 | −0.500619 | −0.250310 | − | 0.968166i | \(-0.580532\pi\) | ||||
−0.250310 | + | 0.968166i | \(0.580532\pi\) | |||||||
\(42\) | −8.08354e6 | −0.400848 | ||||||||
\(43\) | −8.63491e6 | −0.385168 | −0.192584 | − | 0.981281i | \(-0.561687\pi\) | ||||
−0.192584 | + | 0.981281i | \(0.561687\pi\) | |||||||
\(44\) | 9.09769e6 | 0.365927 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.83701e7 | −1.92212 | ||||||||
\(47\) | −3.31511e7 | −0.990964 | −0.495482 | − | 0.868618i | \(-0.665009\pi\) | ||||
−0.495482 | + | 0.868618i | \(0.665009\pi\) | |||||||
\(48\) | 2.47488e7 | 0.672927 | ||||||||
\(49\) | −2.42695e7 | −0.601420 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.47161e6 | 0.196046 | ||||||||
\(52\) | −1.28032e7 | −0.242830 | ||||||||
\(53\) | 6.41254e7 | 1.11632 | 0.558160 | − | 0.829733i | \(-0.311508\pi\) | ||||
0.558160 | + | 0.829733i | \(0.311508\pi\) | |||||||
\(54\) | −1.32243e7 | −0.211642 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.03971e7 | −0.548914 | ||||||||
\(57\) | 1.90295e7 | 0.238775 | ||||||||
\(58\) | −1.15510e7 | −0.134027 | ||||||||
\(59\) | 1.49407e8 | 1.60523 | 0.802613 | − | 0.596500i | \(-0.203442\pi\) | ||||
0.802613 | + | 0.596500i | \(0.203442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.54634e8 | 1.42995 | 0.714973 | − | 0.699152i | \(-0.246439\pi\) | ||||
0.714973 | + | 0.699152i | \(0.246439\pi\) | |||||||
\(62\) | −1.27347e8 | −1.09453 | ||||||||
\(63\) | 2.63129e7 | 0.210444 | ||||||||
\(64\) | 9.55772e7 | 0.712106 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.71046e8 | −1.10960 | ||||||||
\(67\) | −2.72755e8 | −1.65362 | −0.826811 | − | 0.562479i | \(-0.809848\pi\) | ||||
−0.826811 | + | 0.562479i | \(0.809848\pi\) | |||||||
\(68\) | −1.25360e7 | −0.0711001 | ||||||||
\(69\) | 1.90002e8 | 1.00911 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.56924e8 | −1.66691 | −0.833457 | − | 0.552584i | \(-0.813642\pi\) | ||||
−0.833457 | + | 0.552584i | \(0.813642\pi\) | |||||||
\(72\) | −6.60878e7 | −0.289818 | ||||||||
\(73\) | −2.06253e8 | −0.850057 | −0.425029 | − | 0.905180i | \(-0.639736\pi\) | ||||
−0.425029 | + | 0.905180i | \(0.639736\pi\) | |||||||
\(74\) | −2.16329e8 | −0.838632 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.51862e7 | −0.0865968 | ||||||||
\(77\) | 3.40337e8 | 1.10332 | ||||||||
\(78\) | 2.40713e8 | 0.736331 | ||||||||
\(79\) | −4.04380e8 | −1.16807 | −0.584033 | − | 0.811730i | \(-0.698526\pi\) | ||||
−0.584033 | + | 0.811730i | \(0.698526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −2.25399e8 | −0.550542 | ||||||||
\(83\) | 5.17034e6 | 0.0119582 | 0.00597912 | − | 0.999982i | \(-0.498097\pi\) | ||||
0.00597912 | + | 0.999982i | \(0.498097\pi\) | |||||||
\(84\) | −3.48262e7 | −0.0763218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.14870e8 | −0.423577 | ||||||||
\(87\) | 3.75999e7 | 0.0703639 | ||||||||
\(88\) | −8.54793e8 | −1.51946 | ||||||||
\(89\) | 4.32242e8 | 0.730250 | 0.365125 | − | 0.930958i | \(-0.381026\pi\) | ||||
0.365125 | + | 0.930958i | \(0.381026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.78955e8 | −0.732165 | ||||||||
\(92\) | −2.51475e8 | −0.365973 | ||||||||
\(93\) | 4.14530e8 | 0.574623 | ||||||||
\(94\) | −8.24928e8 | −1.08978 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.98105e8 | 0.238054 | ||||||||
\(97\) | 1.32066e9 | 1.51468 | 0.757338 | − | 0.653023i | \(-0.226499\pi\) | ||||
0.757338 | + | 0.653023i | \(0.226499\pi\) | |||||||
\(98\) | −6.03918e8 | −0.661395 | ||||||||
\(99\) | 5.56775e8 | 0.582534 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.30458e8 | 0.507230 | 0.253615 | − | 0.967305i | \(-0.418380\pi\) | ||||
0.253615 | + | 0.967305i | \(0.418380\pi\) | |||||||
\(102\) | 2.35690e8 | 0.215596 | ||||||||
\(103\) | 6.07207e7 | 0.0531580 | 0.0265790 | − | 0.999647i | \(-0.491539\pi\) | ||||
0.0265790 | + | 0.999647i | \(0.491539\pi\) | |||||||
\(104\) | 1.20295e9 | 1.00832 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.59569e9 | 1.22764 | ||||||||
\(107\) | 1.00828e9 | 0.743625 | 0.371812 | − | 0.928308i | \(-0.378736\pi\) | ||||
0.371812 | + | 0.928308i | \(0.378736\pi\) | |||||||
\(108\) | −5.69740e7 | −0.0402967 | ||||||||
\(109\) | −1.77424e9 | −1.20391 | −0.601954 | − | 0.798531i | \(-0.705611\pi\) | ||||
−0.601954 | + | 0.798531i | \(0.705611\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.04177e8 | 0.440279 | ||||||||
\(112\) | −1.22537e9 | −0.735846 | ||||||||
\(113\) | −9.45495e8 | −0.545514 | −0.272757 | − | 0.962083i | \(-0.587936\pi\) | ||||
−0.272757 | + | 0.962083i | \(0.587936\pi\) | |||||||
\(114\) | 4.73526e8 | 0.262586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.97649e7 | −0.0255189 | ||||||||
\(117\) | −7.83549e8 | −0.386572 | ||||||||
\(118\) | 3.71782e9 | 1.76530 | ||||||||
\(119\) | −4.68962e8 | −0.214376 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.84349e9 | 2.05411 | ||||||||
\(122\) | 3.84788e9 | 1.57254 | ||||||||
\(123\) | 7.33702e8 | 0.289033 | ||||||||
\(124\) | −5.48647e8 | −0.208399 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.54767e8 | 0.231430 | ||||||||
\(127\) | 5.19758e9 | 1.77290 | 0.886450 | − | 0.462825i | \(-0.153164\pi\) | ||||
0.886450 | + | 0.462825i | \(0.153164\pi\) | |||||||
\(128\) | 3.63055e9 | 1.19544 | ||||||||
\(129\) | 6.99428e8 | 0.222377 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.28408e8 | 0.156765 | 0.0783824 | − | 0.996923i | \(-0.475024\pi\) | ||||
0.0783824 | + | 0.996923i | \(0.475024\pi\) | |||||||
\(132\) | −7.36913e8 | −0.211268 | ||||||||
\(133\) | −9.42194e8 | −0.261101 | ||||||||
\(134\) | −6.78720e9 | −1.81852 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.17785e9 | 0.295233 | ||||||||
\(137\) | −5.01761e9 | −1.21690 | −0.608449 | − | 0.793593i | \(-0.708208\pi\) | ||||
−0.608449 | + | 0.793593i | \(0.708208\pi\) | |||||||
\(138\) | 4.72798e9 | 1.10974 | ||||||||
\(139\) | 3.51872e9 | 0.799499 | 0.399750 | − | 0.916624i | \(-0.369097\pi\) | ||||
0.399750 | + | 0.916624i | \(0.369097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.68524e9 | 0.572133 | ||||||||
\(142\) | −8.88165e9 | −1.83314 | ||||||||
\(143\) | −1.01346e10 | −2.02672 | ||||||||
\(144\) | −2.00465e9 | −0.388515 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.13238e9 | −0.934827 | ||||||||
\(147\) | 1.96583e9 | 0.347230 | ||||||||
\(148\) | −9.32005e8 | −0.159676 | ||||||||
\(149\) | 4.32815e9 | 0.719390 | 0.359695 | − | 0.933070i | \(-0.382881\pi\) | ||||
0.359695 | + | 0.933070i | \(0.382881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.61832e9 | −0.879448 | −0.439724 | − | 0.898133i | \(-0.644924\pi\) | ||||
−0.439724 | + | 0.898133i | \(0.644924\pi\) | |||||||
\(152\) | 2.36642e9 | 0.359581 | ||||||||
\(153\) | −7.67201e8 | −0.113187 | ||||||||
\(154\) | 8.46889e9 | 1.21334 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.03706e9 | 0.140198 | ||||||||
\(157\) | −1.55603e9 | −0.204394 | −0.102197 | − | 0.994764i | \(-0.532587\pi\) | ||||
−0.102197 | + | 0.994764i | \(0.532587\pi\) | |||||||
\(158\) | −1.00625e10 | −1.28455 | ||||||||
\(159\) | −5.19416e9 | −0.644507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.40745e9 | −1.10346 | ||||||||
\(162\) | 1.07117e9 | 0.122191 | ||||||||
\(163\) | 1.15580e10 | 1.28245 | 0.641224 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641224 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(164\) | −9.71083e8 | −0.104824 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.28658e8 | 0.0131507 | ||||||||
\(167\) | 1.50486e10 | 1.49717 | 0.748585 | − | 0.663039i | \(-0.230734\pi\) | ||||
0.748585 | + | 0.663039i | \(0.230734\pi\) | |||||||
\(168\) | 3.27216e9 | 0.316915 | ||||||||
\(169\) | 3.65789e9 | 0.344938 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.54139e9 | −0.137857 | ||||||||
\(172\) | −9.25719e8 | −0.0806494 | ||||||||
\(173\) | −2.23157e10 | −1.89410 | −0.947052 | − | 0.321081i | \(-0.895954\pi\) | ||||
−0.947052 | + | 0.321081i | \(0.895954\pi\) | |||||||
\(174\) | 9.35630e8 | 0.0773807 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.59286e10 | −2.03691 | ||||||||
\(177\) | −1.21019e10 | −0.926778 | ||||||||
\(178\) | 1.07558e10 | 0.803072 | ||||||||
\(179\) | −1.73543e10 | −1.26348 | −0.631742 | − | 0.775179i | \(-0.717660\pi\) | ||||
−0.631742 | + | 0.775179i | \(0.717660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.34040e10 | −0.928282 | −0.464141 | − | 0.885761i | \(-0.653637\pi\) | ||||
−0.464141 | + | 0.885761i | \(0.653637\pi\) | |||||||
\(182\) | −1.19183e10 | −0.805178 | ||||||||
\(183\) | −1.25253e10 | −0.825580 | ||||||||
\(184\) | 2.36278e10 | 1.51965 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.03151e10 | 0.631926 | ||||||||
\(187\) | −9.92313e9 | −0.593419 | ||||||||
\(188\) | −3.55402e9 | −0.207496 | ||||||||
\(189\) | −2.13135e9 | −0.121500 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.01312e9 | −0.326926 | −0.163463 | − | 0.986549i | \(-0.552266\pi\) | ||||
−0.163463 | + | 0.986549i | \(0.552266\pi\) | |||||||
\(192\) | −7.74175e9 | −0.411134 | ||||||||
\(193\) | 6.91844e9 | 0.358922 | 0.179461 | − | 0.983765i | \(-0.442565\pi\) | ||||
0.179461 | + | 0.983765i | \(0.442565\pi\) | |||||||
\(194\) | 3.28632e10 | 1.66572 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.60185e9 | −0.125930 | ||||||||
\(197\) | −1.66139e10 | −0.785909 | −0.392955 | − | 0.919558i | \(-0.628547\pi\) | ||||
−0.392955 | + | 0.919558i | \(0.628547\pi\) | |||||||
\(198\) | 1.38547e10 | 0.640625 | ||||||||
\(199\) | −3.06711e10 | −1.38641 | −0.693204 | − | 0.720742i | \(-0.743801\pi\) | ||||
−0.693204 | + | 0.720742i | \(0.743801\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.20932e10 | 0.954719 | ||||||||
\(202\) | 1.31998e10 | 0.557812 | ||||||||
\(203\) | −1.86166e9 | −0.0769428 | ||||||||
\(204\) | 1.01542e9 | 0.0410497 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.51096e9 | 0.0584591 | ||||||||
\(207\) | −1.53902e10 | −0.582608 | ||||||||
\(208\) | 3.64893e10 | 1.35170 | ||||||||
\(209\) | −1.99366e10 | −0.722758 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.85598e10 | 1.33926 | 0.669628 | − | 0.742697i | \(-0.266454\pi\) | ||||
0.669628 | + | 0.742697i | \(0.266454\pi\) | |||||||
\(212\) | 6.87467e9 | 0.233744 | ||||||||
\(213\) | 2.89108e10 | 0.962393 | ||||||||
\(214\) | 2.50899e10 | 0.817780 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.35311e9 | 0.167326 | ||||||||
\(217\) | −2.05244e10 | −0.628350 | ||||||||
\(218\) | −4.41500e10 | −1.32396 | ||||||||
\(219\) | 1.67065e10 | 0.490781 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.39648e10 | 0.393795 | ||||||||
\(222\) | 1.75226e10 | 0.484185 | ||||||||
\(223\) | 3.11357e10 | 0.843115 | 0.421558 | − | 0.906802i | \(-0.361484\pi\) | ||||
0.421558 | + | 0.906802i | \(0.361484\pi\) | |||||||
\(224\) | −9.80866e9 | −0.260312 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.35276e10 | −0.599914 | ||||||||
\(227\) | 1.14589e10 | 0.286436 | 0.143218 | − | 0.989691i | \(-0.454255\pi\) | ||||
0.143218 | + | 0.989691i | \(0.454255\pi\) | |||||||
\(228\) | 2.04008e9 | 0.0499967 | ||||||||
\(229\) | −3.04556e10 | −0.731825 | −0.365913 | − | 0.930649i | \(-0.619243\pi\) | ||||
−0.365913 | + | 0.930649i | \(0.619243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.75673e10 | −0.637000 | ||||||||
\(232\) | 4.67576e9 | 0.105964 | ||||||||
\(233\) | −2.83630e9 | −0.0630451 | −0.0315225 | − | 0.999503i | \(-0.510036\pi\) | ||||
−0.0315225 | + | 0.999503i | \(0.510036\pi\) | |||||||
\(234\) | −1.94977e10 | −0.425121 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.60174e10 | 0.336115 | ||||||||
\(237\) | 3.27548e10 | 0.674384 | ||||||||
\(238\) | −1.16696e10 | −0.235754 | ||||||||
\(239\) | −6.25862e10 | −1.24076 | −0.620381 | − | 0.784301i | \(-0.713022\pi\) | ||||
−0.620381 | + | 0.784301i | \(0.713022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.24015e10 | 1.38252 | 0.691259 | − | 0.722607i | \(-0.257056\pi\) | ||||
0.691259 | + | 0.722607i | \(0.257056\pi\) | |||||||
\(242\) | 1.20525e11 | 2.25895 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 1.65778e10 | 0.299414 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.82573e10 | 0.317855 | ||||||||
\(247\) | 2.80568e10 | 0.479624 | ||||||||
\(248\) | 5.15493e10 | 0.865347 | ||||||||
\(249\) | −4.18797e8 | −0.00690410 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.65927e10 | −0.899971 | −0.449986 | − | 0.893036i | \(-0.648571\pi\) | ||||
−0.449986 | + | 0.893036i | \(0.648571\pi\) | |||||||
\(252\) | 2.82092e9 | 0.0440644 | ||||||||
\(253\) | −1.99059e11 | −3.05450 | ||||||||
\(254\) | 1.29336e11 | 1.94970 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.14066e10 | 0.602545 | ||||||||
\(257\) | −4.95688e10 | −0.708777 | −0.354388 | − | 0.935098i | \(-0.615311\pi\) | ||||
−0.354388 | + | 0.935098i | \(0.615311\pi\) | |||||||
\(258\) | 1.74045e10 | 0.244552 | ||||||||
\(259\) | −3.48655e10 | −0.481445 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.04559e9 | −0.0406246 | ||||||||
\(262\) | 1.31488e10 | 0.172398 | ||||||||
\(263\) | −3.59498e10 | −0.463336 | −0.231668 | − | 0.972795i | \(-0.574418\pi\) | ||||
−0.231668 | + | 0.972795i | \(0.574418\pi\) | |||||||
\(264\) | 6.92382e10 | 0.877260 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.34454e10 | −0.287138 | ||||||||
\(267\) | −3.50116e10 | −0.421610 | ||||||||
\(268\) | −2.92412e10 | −0.346249 | ||||||||
\(269\) | −7.09650e10 | −0.826340 | −0.413170 | − | 0.910654i | \(-0.635579\pi\) | ||||
−0.413170 | + | 0.910654i | \(0.635579\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.47201e11 | 1.65786 | 0.828930 | − | 0.559352i | \(-0.188950\pi\) | ||||
0.828930 | + | 0.559352i | \(0.188950\pi\) | |||||||
\(272\) | 3.57279e10 | 0.395774 | ||||||||
\(273\) | 3.87954e10 | 0.422716 | ||||||||
\(274\) | −1.24857e11 | −1.33825 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.03695e10 | 0.211295 | ||||||||
\(277\) | 2.87336e10 | 0.293245 | 0.146622 | − | 0.989193i | \(-0.453160\pi\) | ||||
0.146622 | + | 0.989193i | \(0.453160\pi\) | |||||||
\(278\) | 8.75593e10 | 0.879227 | ||||||||
\(279\) | −3.35770e10 | −0.331759 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.17071e10 | 0.494734 | 0.247367 | − | 0.968922i | \(-0.420435\pi\) | ||||
0.247367 | + | 0.968922i | \(0.420435\pi\) | |||||||
\(282\) | 6.68192e10 | 0.629187 | ||||||||
\(283\) | 3.22434e9 | 0.0298814 | 0.0149407 | − | 0.999888i | \(-0.495244\pi\) | ||||
0.0149407 | + | 0.999888i | \(0.495244\pi\) | |||||||
\(284\) | −3.82646e10 | −0.349032 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.52188e11 | −2.22883 | ||||||||
\(287\) | −3.63273e10 | −0.316057 | ||||||||
\(288\) | −1.60465e10 | −0.137440 | ||||||||
\(289\) | −1.04914e11 | −0.884698 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.06974e11 | −0.874499 | ||||||||
\(292\) | −2.21117e10 | −0.177992 | ||||||||
\(293\) | 1.13591e11 | 0.900409 | 0.450204 | − | 0.892926i | \(-0.351351\pi\) | ||||
0.450204 | + | 0.892926i | \(0.351351\pi\) | |||||||
\(294\) | 4.89174e10 | 0.381856 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.75685e10 | 0.663033 | ||||||||
\(297\) | −4.50988e10 | −0.336326 | ||||||||
\(298\) | 1.07701e11 | 0.791129 | ||||||||
\(299\) | 2.80136e11 | 2.02698 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.46303e10 | −0.243169 | ||||||||
\(302\) | −1.39805e11 | −0.967148 | ||||||||
\(303\) | −4.29671e10 | −0.292849 | ||||||||
\(304\) | 7.17811e10 | 0.482036 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.90909e10 | −0.124474 | ||||||||
\(307\) | 2.30543e10 | 0.148125 | 0.0740627 | − | 0.997254i | \(-0.476403\pi\) | ||||
0.0740627 | + | 0.997254i | \(0.476403\pi\) | |||||||
\(308\) | 3.64863e10 | 0.231021 | ||||||||
\(309\) | −4.91837e9 | −0.0306908 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.71709e10 | 0.467769 | 0.233885 | − | 0.972264i | \(-0.424856\pi\) | ||||
0.233885 | + | 0.972264i | \(0.424856\pi\) | |||||||
\(312\) | −9.74389e10 | −0.582152 | ||||||||
\(313\) | 4.68832e10 | 0.276101 | 0.138050 | − | 0.990425i | \(-0.455916\pi\) | ||||
0.138050 | + | 0.990425i | \(0.455916\pi\) | |||||||
\(314\) | −3.87200e10 | −0.224777 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.33522e10 | −0.244579 | ||||||||
\(317\) | −2.19420e11 | −1.22042 | −0.610210 | − | 0.792240i | \(-0.708915\pi\) | ||||
−0.610210 | + | 0.792240i | \(0.708915\pi\) | |||||||
\(318\) | −1.29251e11 | −0.708779 | ||||||||
\(319\) | −3.93923e10 | −0.212987 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.16706e10 | −0.429332 | ||||||||
\(322\) | −2.34094e11 | −1.21350 | ||||||||
\(323\) | 2.74714e10 | 0.140433 | ||||||||
\(324\) | 4.61489e9 | 0.0232653 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.87609e11 | 1.41034 | ||||||||
\(327\) | 1.43714e11 | 0.695077 | ||||||||
\(328\) | 9.12401e10 | 0.435265 | ||||||||
\(329\) | −1.32953e11 | −0.625627 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.89075e9 | 0.0178159 | 0.00890794 | − | 0.999960i | \(-0.497164\pi\) | ||||
0.00890794 | + | 0.999960i | \(0.497164\pi\) | |||||||
\(332\) | 5.54295e8 | 0.00250391 | ||||||||
\(333\) | −5.70383e10 | −0.254195 | ||||||||
\(334\) | 3.74466e11 | 1.64647 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.92551e10 | 0.424841 | ||||||||
\(337\) | 1.48259e11 | 0.626163 | 0.313082 | − | 0.949726i | \(-0.398639\pi\) | ||||
0.313082 | + | 0.949726i | \(0.398639\pi\) | |||||||
\(338\) | 9.10225e10 | 0.379336 | ||||||||
\(339\) | 7.65851e10 | 0.314953 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.34291e11 | −1.73935 | ||||||||
\(342\) | −3.83556e10 | −0.151604 | ||||||||
\(343\) | −2.59171e11 | −1.01103 | ||||||||
\(344\) | 8.69779e10 | 0.334885 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.55302e11 | −2.08299 | ||||||||
\(347\) | 1.63695e11 | 0.606114 | 0.303057 | − | 0.952972i | \(-0.401993\pi\) | ||||
0.303057 | + | 0.952972i | \(0.401993\pi\) | |||||||
\(348\) | 4.03096e9 | 0.0147333 | ||||||||
\(349\) | 7.02057e10 | 0.253313 | 0.126657 | − | 0.991947i | \(-0.459575\pi\) | ||||
0.126657 | + | 0.991947i | \(0.459575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.34675e10 | 0.223187 | ||||||||
\(352\) | −2.07549e11 | −0.720574 | ||||||||
\(353\) | 1.55727e10 | 0.0533798 | 0.0266899 | − | 0.999644i | \(-0.491503\pi\) | ||||
0.0266899 | + | 0.999644i | \(0.491503\pi\) | |||||||
\(354\) | −3.01143e11 | −1.01920 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.63392e10 | 0.152906 | ||||||||
\(357\) | 3.79859e10 | 0.123770 | ||||||||
\(358\) | −4.31843e11 | −1.38948 | ||||||||
\(359\) | 3.28525e10 | 0.104386 | 0.0521931 | − | 0.998637i | \(-0.483379\pi\) | ||||
0.0521931 | + | 0.998637i | \(0.483379\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.67495e11 | −0.828959 | ||||||||
\(362\) | −3.33543e11 | −1.02085 | ||||||||
\(363\) | −3.92323e11 | −1.18594 | ||||||||
\(364\) | −5.13472e10 | −0.153306 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.11679e11 | −0.907908 | ||||||||
\(367\) | 4.76030e11 | 1.36974 | 0.684868 | − | 0.728667i | \(-0.259860\pi\) | ||||
0.684868 | + | 0.728667i | \(0.259860\pi\) | |||||||
\(368\) | 7.16707e11 | 2.03717 | ||||||||
\(369\) | −5.94299e10 | −0.166873 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.57175e11 | 0.704768 | ||||||||
\(372\) | 4.44404e10 | 0.120319 | ||||||||
\(373\) | 9.72745e10 | 0.260201 | 0.130101 | − | 0.991501i | \(-0.458470\pi\) | ||||
0.130101 | + | 0.991501i | \(0.458470\pi\) | |||||||
\(374\) | −2.46926e11 | −0.652596 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.33925e11 | 0.861597 | ||||||||
\(377\) | 5.54367e10 | 0.141339 | ||||||||
\(378\) | −5.30361e10 | −0.133616 | ||||||||
\(379\) | 4.45171e11 | 1.10828 | 0.554141 | − | 0.832423i | \(-0.313047\pi\) | ||||
0.554141 | + | 0.832423i | \(0.313047\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.21004e11 | −1.02358 | ||||||||
\(382\) | −1.49630e11 | −0.359528 | ||||||||
\(383\) | −2.19414e11 | −0.521039 | −0.260519 | − | 0.965469i | \(-0.583894\pi\) | ||||
−0.260519 | + | 0.965469i | \(0.583894\pi\) | |||||||
\(384\) | −2.94075e11 | −0.690187 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.72157e11 | 0.394714 | ||||||||
\(387\) | −5.66536e10 | −0.128389 | ||||||||
\(388\) | 1.41584e11 | 0.317155 | ||||||||
\(389\) | −3.71956e11 | −0.823603 | −0.411801 | − | 0.911274i | \(-0.635100\pi\) | ||||
−0.411801 | + | 0.911274i | \(0.635100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.74291e11 | 0.593494 | ||||||||
\(392\) | 2.44462e11 | 0.522907 | ||||||||
\(393\) | −4.28011e10 | −0.0905082 | ||||||||
\(394\) | −4.13417e11 | −0.864281 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.96900e10 | 0.121976 | ||||||||
\(397\) | 1.38786e11 | 0.280406 | 0.140203 | − | 0.990123i | \(-0.455224\pi\) | ||||
0.140203 | + | 0.990123i | \(0.455224\pi\) | |||||||
\(398\) | −7.63216e11 | −1.52466 | ||||||||
\(399\) | 7.63177e10 | 0.150747 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.95127e11 | 1.34250 | 0.671251 | − | 0.741231i | \(-0.265757\pi\) | ||||
0.671251 | + | 0.741231i | \(0.265757\pi\) | |||||||
\(402\) | 5.49763e11 | 1.04993 | ||||||||
\(403\) | 6.11178e11 | 1.15424 | ||||||||
\(404\) | 5.68686e10 | 0.106208 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.63253e10 | −0.0846157 | ||||||||
\(407\) | −7.37745e11 | −1.33270 | ||||||||
\(408\) | −9.54059e10 | −0.170453 | ||||||||
\(409\) | 9.10800e11 | 1.60942 | 0.804708 | − | 0.593671i | \(-0.202322\pi\) | ||||
0.804708 | + | 0.593671i | \(0.202322\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.06426e11 | 0.702577 | ||||||||
\(412\) | 6.50966e9 | 0.0111307 | ||||||||
\(413\) | 5.99196e11 | 1.01343 | ||||||||
\(414\) | −3.82967e11 | −0.640707 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.92084e11 | 0.478175 | ||||||||
\(417\) | −2.85016e11 | −0.461591 | ||||||||
\(418\) | −4.96100e11 | −0.794832 | ||||||||
\(419\) | 3.11152e11 | 0.493184 | 0.246592 | − | 0.969119i | \(-0.420689\pi\) | ||||
0.246592 | + | 0.969119i | \(0.420689\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.63941e11 | 1.18520 | 0.592598 | − | 0.805498i | \(-0.298102\pi\) | ||||
0.592598 | + | 0.805498i | \(0.298102\pi\) | |||||||
\(422\) | 9.59516e11 | 1.47281 | ||||||||
\(423\) | −2.17505e11 | −0.330321 | ||||||||
\(424\) | −6.45924e11 | −0.970588 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.19414e11 | 1.05836 | ||||||||
\(427\) | 6.20159e11 | 0.902771 | ||||||||
\(428\) | 1.08094e11 | 0.155706 | ||||||||
\(429\) | 8.20901e11 | 1.17013 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.54629e10 | 0.0913792 | 0.0456896 | − | 0.998956i | \(-0.485451\pi\) | ||||
0.0456896 | + | 0.998956i | \(0.485451\pi\) | |||||||
\(432\) | 1.62377e11 | 0.224309 | ||||||||
\(433\) | 7.87434e11 | 1.07651 | 0.538256 | − | 0.842781i | \(-0.319083\pi\) | ||||
0.538256 | + | 0.842781i | \(0.319083\pi\) | |||||||
\(434\) | −5.10726e11 | −0.691010 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.90210e11 | −0.252084 | ||||||||
\(437\) | 5.51080e11 | 0.722850 | ||||||||
\(438\) | 4.15723e11 | 0.539722 | ||||||||
\(439\) | −8.39211e11 | −1.07840 | −0.539201 | − | 0.842177i | \(-0.681274\pi\) | ||||
−0.539201 | + | 0.842177i | \(0.681274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.59232e11 | −0.200473 | ||||||||
\(442\) | 3.47499e11 | 0.433065 | ||||||||
\(443\) | 1.28252e12 | 1.58215 | 0.791074 | − | 0.611720i | \(-0.209522\pi\) | ||||
0.791074 | + | 0.611720i | \(0.209522\pi\) | |||||||
\(444\) | 7.54924e10 | 0.0921891 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.74777e11 | 0.927192 | ||||||||
\(447\) | −3.50581e11 | −0.415340 | ||||||||
\(448\) | 3.83313e11 | 0.449575 | ||||||||
\(449\) | 8.02030e10 | 0.0931284 | 0.0465642 | − | 0.998915i | \(-0.485173\pi\) | ||||
0.0465642 | + | 0.998915i | \(0.485173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.68678e11 | −0.874883 | ||||||||
\(452\) | −1.01363e11 | −0.114224 | ||||||||
\(453\) | 4.55084e11 | 0.507749 | ||||||||
\(454\) | 2.85143e11 | 0.315000 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.91680e11 | −0.207604 | ||||||||
\(457\) | −1.27085e11 | −0.136292 | −0.0681461 | − | 0.997675i | \(-0.521708\pi\) | ||||
−0.0681461 | + | 0.997675i | \(0.521708\pi\) | |||||||
\(458\) | −7.57853e11 | −0.804804 | ||||||||
\(459\) | 6.21433e10 | 0.0653487 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.39880e11 | −0.762970 | −0.381485 | − | 0.924375i | \(-0.624587\pi\) | ||||
−0.381485 | + | 0.924375i | \(0.624587\pi\) | |||||||
\(462\) | −6.85980e11 | −0.700523 | ||||||||
\(463\) | −5.71025e11 | −0.577485 | −0.288742 | − | 0.957407i | \(-0.593237\pi\) | ||||
−0.288742 | + | 0.957407i | \(0.593237\pi\) | |||||||
\(464\) | 1.41831e11 | 0.142049 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.05782e10 | −0.0693320 | ||||||||
\(467\) | −1.19075e12 | −1.15850 | −0.579249 | − | 0.815150i | \(-0.696654\pi\) | ||||
−0.579249 | + | 0.815150i | \(0.696654\pi\) | |||||||
\(468\) | −8.40017e10 | −0.0809434 | ||||||||
\(469\) | −1.09389e12 | −1.04398 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.26038e11 | 0.118007 | ||||||||
\(472\) | −1.50495e12 | −1.39567 | ||||||||
\(473\) | −7.32770e11 | −0.673120 | ||||||||
\(474\) | 8.15065e11 | 0.741634 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.02759e10 | −0.0448878 | ||||||||
\(477\) | 4.20727e11 | 0.372107 | ||||||||
\(478\) | −1.55739e12 | −1.36449 | ||||||||
\(479\) | 1.46074e12 | 1.26784 | 0.633919 | − | 0.773400i | \(-0.281445\pi\) | ||||
0.633919 | + | 0.773400i | \(0.281445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.03823e12 | 0.884382 | ||||||||
\(482\) | 1.80163e12 | 1.52038 | ||||||||
\(483\) | 7.62003e11 | 0.637081 | ||||||||
\(484\) | 5.19254e11 | 0.430107 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.67647e10 | −0.0705472 | ||||||||
\(487\) | 1.46931e12 | 1.18368 | 0.591839 | − | 0.806056i | \(-0.298402\pi\) | ||||
0.591839 | + | 0.806056i | \(0.298402\pi\) | |||||||
\(488\) | −1.55760e12 | −1.24327 | ||||||||
\(489\) | −9.36201e11 | −0.740422 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.76138e12 | −1.36769 | −0.683843 | − | 0.729629i | \(-0.739693\pi\) | ||||
−0.683843 | + | 0.729629i | \(0.739693\pi\) | |||||||
\(492\) | 7.86577e10 | 0.0605199 | ||||||||
\(493\) | 5.42801e10 | 0.0413837 | ||||||||
\(494\) | 6.98161e11 | 0.527453 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.56365e12 | 1.16004 | ||||||||
\(497\) | −1.43145e12 | −1.05238 | ||||||||
\(498\) | −1.04213e10 | −0.00759259 | ||||||||
\(499\) | −1.63016e12 | −1.17700 | −0.588502 | − | 0.808496i | \(-0.700282\pi\) | ||||
−0.588502 | + | 0.808496i | \(0.700282\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.21893e12 | −0.864391 | ||||||||
\(502\) | −1.40825e12 | −0.989718 | ||||||||
\(503\) | −9.47625e11 | −0.660056 | −0.330028 | − | 0.943971i | \(-0.607058\pi\) | ||||
−0.330028 | + | 0.943971i | \(0.607058\pi\) | |||||||
\(504\) | −2.65045e11 | −0.182971 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.95337e12 | −3.35910 | ||||||||
\(507\) | −2.96289e11 | −0.199150 | ||||||||
\(508\) | 5.57214e11 | 0.371224 | ||||||||
\(509\) | −2.90709e11 | −0.191968 | −0.0959838 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959838 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.27180e11 | −0.536668 | ||||||||
\(512\) | −8.28486e11 | −0.532808 | ||||||||
\(513\) | 1.24852e11 | 0.0795918 | ||||||||
\(514\) | −1.23346e12 | −0.779457 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.49833e10 | 0.0465630 | ||||||||
\(517\) | −2.81325e12 | −1.73181 | ||||||||
\(518\) | −8.67587e11 | −0.529455 | ||||||||
\(519\) | 1.80757e12 | 1.09356 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.04811e12 | −1.21782 | −0.608910 | − | 0.793240i | \(-0.708393\pi\) | ||||
−0.608910 | + | 0.793240i | \(0.708393\pi\) | |||||||
\(522\) | −7.57860e10 | −0.0446758 | ||||||||
\(523\) | −8.49299e10 | −0.0496367 | −0.0248184 | − | 0.999692i | \(-0.507901\pi\) | ||||
−0.0248184 | + | 0.999692i | \(0.507901\pi\) | |||||||
\(524\) | 5.66488e10 | 0.0328247 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.94570e11 | −0.509540 | ||||||||
\(527\) | 5.98426e11 | 0.337958 | ||||||||
\(528\) | 2.10021e12 | 1.17601 | ||||||||
\(529\) | 3.70117e12 | 2.05489 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.80258e11 | 0.535075 | ||||||||
\(532\) | −1.01009e11 | −0.0546713 | ||||||||
\(533\) | 1.08176e12 | 0.580575 | ||||||||
\(534\) | −8.71224e11 | −0.463654 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.74741e12 | 1.43775 | ||||||||
\(537\) | 1.40570e12 | 0.729472 | ||||||||
\(538\) | −1.76588e12 | −0.908745 | ||||||||
\(539\) | −2.05954e12 | −1.05104 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.29101e12 | −0.647949 | −0.323974 | − | 0.946066i | \(-0.605019\pi\) | ||||
−0.323974 | + | 0.946066i | \(0.605019\pi\) | |||||||
\(542\) | 3.66292e12 | 1.82318 | ||||||||
\(543\) | 1.08572e12 | 0.535944 | ||||||||
\(544\) | 2.85989e11 | 0.140009 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.65379e11 | 0.464870 | ||||||||
\(547\) | 5.30222e11 | 0.253230 | 0.126615 | − | 0.991952i | \(-0.459589\pi\) | ||||
0.126615 | + | 0.991952i | \(0.459589\pi\) | |||||||
\(548\) | −5.37921e11 | −0.254804 | ||||||||
\(549\) | 1.01455e12 | 0.476649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.09054e11 | 0.0504035 | ||||||||
\(552\) | −1.91386e12 | −0.877371 | ||||||||
\(553\) | −1.62177e12 | −0.737438 | ||||||||
\(554\) | 7.15002e11 | 0.322488 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.77230e11 | 0.167405 | ||||||||
\(557\) | −8.17386e11 | −0.359815 | −0.179907 | − | 0.983684i | \(-0.557580\pi\) | ||||
−0.179907 | + | 0.983684i | \(0.557580\pi\) | |||||||
\(558\) | −8.35525e11 | −0.364842 | ||||||||
\(559\) | 1.03123e12 | 0.446684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.03773e11 | 0.342611 | ||||||||
\(562\) | 1.28667e12 | 0.544069 | ||||||||
\(563\) | 1.42197e12 | 0.596488 | 0.298244 | − | 0.954490i | \(-0.403599\pi\) | ||||
0.298244 | + | 0.954490i | \(0.403599\pi\) | |||||||
\(564\) | 2.87876e11 | 0.119798 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.02339e10 | 0.0328613 | ||||||||
\(567\) | 1.72639e11 | 0.0701480 | ||||||||
\(568\) | 3.59523e12 | 1.44930 | ||||||||
\(569\) | −1.04614e12 | −0.418394 | −0.209197 | − | 0.977874i | \(-0.567085\pi\) | ||||
−0.209197 | + | 0.977874i | \(0.567085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.09508e12 | 0.824780 | 0.412390 | − | 0.911007i | \(-0.364694\pi\) | ||||
0.412390 | + | 0.911007i | \(0.364694\pi\) | |||||||
\(572\) | −1.08649e12 | −0.424371 | ||||||||
\(573\) | 4.87063e11 | 0.188751 | ||||||||
\(574\) | −9.03965e11 | −0.347575 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.27082e11 | 0.237369 | ||||||||
\(577\) | −2.68760e12 | −1.00942 | −0.504711 | − | 0.863288i | \(-0.668401\pi\) | ||||
−0.504711 | + | 0.863288i | \(0.668401\pi\) | |||||||
\(578\) | −2.61068e12 | −0.972921 | ||||||||
\(579\) | −5.60394e11 | −0.207224 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.07357e10 | 0.00754962 | ||||||||
\(582\) | −2.66192e12 | −0.961705 | ||||||||
\(583\) | 5.44176e12 | 1.95088 | ||||||||
\(584\) | 2.07755e12 | 0.739085 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.82658e12 | 0.990199 | ||||||||
\(587\) | −1.61925e12 | −0.562913 | −0.281457 | − | 0.959574i | \(-0.590818\pi\) | ||||
−0.281457 | + | 0.959574i | \(0.590818\pi\) | |||||||
\(588\) | 2.10750e11 | 0.0727058 | ||||||||
\(589\) | 1.20230e12 | 0.411618 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.34572e12 | 0.453745 | ||||||||
\(592\) | 2.65623e12 | 0.888828 | ||||||||
\(593\) | −5.82677e12 | −1.93500 | −0.967502 | − | 0.252863i | \(-0.918628\pi\) | ||||
−0.967502 | + | 0.252863i | \(0.918628\pi\) | |||||||
\(594\) | −1.12223e12 | −0.369865 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.64007e11 | 0.150632 | ||||||||
\(597\) | 2.48436e12 | 0.800442 | ||||||||
\(598\) | 6.97087e12 | 2.22911 | ||||||||
\(599\) | −3.89086e12 | −1.23488 | −0.617441 | − | 0.786617i | \(-0.711831\pi\) | ||||
−0.617441 | + | 0.786617i | \(0.711831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.13051e12 | 0.666115 | 0.333058 | − | 0.942907i | \(-0.391920\pi\) | ||||
0.333058 | + | 0.942907i | \(0.391920\pi\) | |||||||
\(602\) | −8.61737e11 | −0.267418 | ||||||||
\(603\) | −1.78955e12 | −0.551207 | ||||||||
\(604\) | −6.02321e11 | −0.184146 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.06919e12 | −0.322053 | ||||||||
\(607\) | 2.52733e12 | 0.755637 | 0.377818 | − | 0.925880i | \(-0.376674\pi\) | ||||
0.377818 | + | 0.925880i | \(0.376674\pi\) | |||||||
\(608\) | 5.74582e11 | 0.170524 | ||||||||
\(609\) | 1.50794e11 | 0.0444230 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.95908e12 | 1.14924 | ||||||||
\(612\) | −8.22490e10 | −0.0237000 | ||||||||
\(613\) | −1.89788e12 | −0.542870 | −0.271435 | − | 0.962457i | \(-0.587498\pi\) | ||||
−0.271435 | + | 0.962457i | \(0.587498\pi\) | |||||||
\(614\) | 5.73681e11 | 0.162897 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.42815e12 | −0.959283 | ||||||||
\(617\) | 1.40480e12 | 0.390240 | 0.195120 | − | 0.980779i | \(-0.437490\pi\) | ||||
0.195120 | + | 0.980779i | \(0.437490\pi\) | |||||||
\(618\) | −1.22388e11 | −0.0337514 | ||||||||
\(619\) | −2.81250e12 | −0.769989 | −0.384995 | − | 0.922919i | \(-0.625797\pi\) | ||||
−0.384995 | + | 0.922919i | \(0.625797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.24660e12 | 0.336369 | ||||||||
\(622\) | 1.92031e12 | 0.514416 | ||||||||
\(623\) | 1.73351e12 | 0.461030 | ||||||||
\(624\) | −2.95563e12 | −0.780404 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.16664e12 | 0.303634 | ||||||||
\(627\) | 1.61486e12 | 0.417284 | ||||||||
\(628\) | −1.66817e11 | −0.0427977 | ||||||||
\(629\) | 1.01657e12 | 0.258945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.92653e12 | −0.483775 | −0.241888 | − | 0.970304i | \(-0.577767\pi\) | ||||
−0.241888 | + | 0.970304i | \(0.577767\pi\) | |||||||
\(632\) | 4.07325e12 | 1.01558 | ||||||||
\(633\) | −3.12334e12 | −0.773219 | ||||||||
\(634\) | −5.46001e12 | −1.34212 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.56848e11 | −0.134952 | ||||||||
\(637\) | 2.89839e12 | 0.697476 | ||||||||
\(638\) | −9.80232e11 | −0.234226 | ||||||||
\(639\) | −2.34178e12 | −0.555638 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.10318e12 | −1.66185 | −0.830924 | − | 0.556385i | \(-0.812188\pi\) | ||||
−0.830924 | + | 0.556385i | \(0.812188\pi\) | |||||||
\(642\) | −2.03228e12 | −0.472146 | ||||||||
\(643\) | −3.40733e12 | −0.786077 | −0.393038 | − | 0.919522i | \(-0.628576\pi\) | ||||
−0.393038 | + | 0.919522i | \(0.628576\pi\) | |||||||
\(644\) | −1.00854e12 | −0.231051 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.83594e11 | 0.154437 | ||||||||
\(647\) | 4.31347e12 | 0.967737 | 0.483868 | − | 0.875141i | \(-0.339231\pi\) | ||||
0.483868 | + | 0.875141i | \(0.339231\pi\) | |||||||
\(648\) | −4.33602e11 | −0.0966059 | ||||||||
\(649\) | 1.26789e13 | 2.80530 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.66248e12 | 0.362778 | ||||||||
\(652\) | 1.23910e12 | 0.268529 | ||||||||
\(653\) | 2.53169e12 | 0.544880 | 0.272440 | − | 0.962173i | \(-0.412169\pi\) | ||||
0.272440 | + | 0.962173i | \(0.412169\pi\) | |||||||
\(654\) | 3.57615e12 | 0.764391 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.76760e12 | 0.583494 | ||||||||
\(657\) | −1.35323e12 | −0.283352 | ||||||||
\(658\) | −3.30838e12 | −0.688016 | ||||||||
\(659\) | −4.43263e12 | −0.915540 | −0.457770 | − | 0.889071i | \(-0.651352\pi\) | ||||
−0.457770 | + | 0.889071i | \(0.651352\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.79827e11 | 0.199638 | 0.0998189 | − | 0.995006i | \(-0.468174\pi\) | ||||
0.0998189 | + | 0.995006i | \(0.468174\pi\) | |||||||
\(662\) | 9.68168e10 | 0.0195925 | ||||||||
\(663\) | −1.13115e12 | −0.227358 | ||||||||
\(664\) | −5.20799e10 | −0.0103971 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.41933e12 | −0.279544 | ||||||||
\(667\) | 1.08887e12 | 0.213014 | ||||||||
\(668\) | 1.61331e12 | 0.313489 | ||||||||
\(669\) | −2.52199e12 | −0.486773 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.31224e13 | 2.49898 | ||||||||
\(672\) | 7.94502e11 | 0.150291 | ||||||||
\(673\) | −7.69434e12 | −1.44578 | −0.722892 | − | 0.690961i | \(-0.757188\pi\) | ||||
−0.722892 | + | 0.690961i | \(0.757188\pi\) | |||||||
\(674\) | 3.68927e12 | 0.688605 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.92151e11 | 0.0722258 | ||||||||
\(677\) | −2.45111e12 | −0.448451 | −0.224225 | − | 0.974537i | \(-0.571985\pi\) | ||||
−0.224225 | + | 0.974537i | \(0.571985\pi\) | |||||||
\(678\) | 1.90573e12 | 0.346360 | ||||||||
\(679\) | 5.29653e12 | 0.956264 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.28174e11 | −0.165374 | ||||||||
\(682\) | −1.08068e13 | −1.91280 | ||||||||
\(683\) | −3.13070e12 | −0.550488 | −0.275244 | − | 0.961374i | \(-0.588759\pi\) | ||||
−0.275244 | + | 0.961374i | \(0.588759\pi\) | |||||||
\(684\) | −1.65247e11 | −0.0288656 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.44918e12 | −1.11185 | ||||||||
\(687\) | 2.46690e12 | 0.422519 | ||||||||
\(688\) | 2.63831e12 | 0.448930 | ||||||||
\(689\) | −7.65819e12 | −1.29461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.92815e12 | −1.48974 | −0.744870 | − | 0.667210i | \(-0.767488\pi\) | ||||
−0.744870 | + | 0.667210i | \(0.767488\pi\) | |||||||
\(692\) | −2.39239e12 | −0.396602 | ||||||||
\(693\) | 2.23295e12 | 0.367772 | ||||||||
\(694\) | 4.07338e12 | 0.666556 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.78737e11 | −0.0611781 | ||||||||
\(697\) | 1.05919e12 | 0.169991 | ||||||||
\(698\) | 1.74699e12 | 0.278574 | ||||||||
\(699\) | 2.29741e11 | 0.0363991 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.44295e12 | −0.225695 | −0.112847 | − | 0.993612i | \(-0.535997\pi\) | ||||
−0.112847 | + | 0.993612i | \(0.535997\pi\) | |||||||
\(702\) | 1.57932e12 | 0.245444 | ||||||||
\(703\) | 2.04239e12 | 0.315383 | ||||||||
\(704\) | 8.11081e12 | 1.24448 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.87509e11 | 0.0587030 | ||||||||
\(707\) | 2.12740e12 | 0.320230 | ||||||||
\(708\) | −1.29741e12 | −0.194056 | ||||||||
\(709\) | −7.40550e12 | −1.10064 | −0.550321 | − | 0.834953i | \(-0.685495\pi\) | ||||
−0.550321 | + | 0.834953i | \(0.685495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.65314e12 | −0.389355 | ||||||||
\(712\) | −4.35390e12 | −0.634919 | ||||||||
\(713\) | 1.20045e13 | 1.73957 | ||||||||
\(714\) | 9.45237e11 | 0.136113 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.86050e12 | −0.264558 | ||||||||
\(717\) | 5.06949e12 | 0.716354 | ||||||||
\(718\) | 8.17496e11 | 0.114796 | ||||||||
\(719\) | −3.90289e12 | −0.544636 | −0.272318 | − | 0.962207i | \(-0.587790\pi\) | ||||
−0.272318 | + | 0.962207i | \(0.587790\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.43520e11 | 0.0335604 | ||||||||
\(722\) | −6.65631e12 | −0.911624 | ||||||||
\(723\) | −5.86452e12 | −0.798197 | ||||||||
\(724\) | −1.43699e12 | −0.194371 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.76251e12 | −1.30421 | ||||||||
\(727\) | −1.33674e12 | −0.177477 | −0.0887384 | − | 0.996055i | \(-0.528284\pi\) | ||||
−0.0887384 | + | 0.996055i | \(0.528284\pi\) | |||||||
\(728\) | 4.82443e12 | 0.636583 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.00971e12 | 0.130788 | ||||||||
\(732\) | −1.34280e12 | −0.172866 | ||||||||
\(733\) | 5.98863e11 | 0.0766231 | 0.0383116 | − | 0.999266i | \(-0.487802\pi\) | ||||
0.0383116 | + | 0.999266i | \(0.487802\pi\) | |||||||
\(734\) | 1.18455e13 | 1.50633 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.73699e12 | 0.720665 | ||||||||
\(737\) | −2.31464e13 | −2.88987 | ||||||||
\(738\) | −1.47884e12 | −0.183514 | ||||||||
\(739\) | −1.40697e13 | −1.73534 | −0.867671 | − | 0.497138i | \(-0.834384\pi\) | ||||
−0.867671 | + | 0.497138i | \(0.834384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.27260e12 | −0.276911 | ||||||||
\(742\) | 6.39951e12 | 0.775049 | ||||||||
\(743\) | 2.52604e12 | 0.304082 | 0.152041 | − | 0.988374i | \(-0.451415\pi\) | ||||
0.152041 | + | 0.988374i | \(0.451415\pi\) | |||||||
\(744\) | −4.17549e12 | −0.499608 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.42056e12 | 0.286149 | ||||||||
\(747\) | 3.39226e10 | 0.00398608 | ||||||||
\(748\) | −1.06383e12 | −0.124255 | ||||||||
\(749\) | 4.04371e12 | 0.469474 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.78704e12 | 0.434430 | 0.217215 | − | 0.976124i | \(-0.430303\pi\) | ||||
0.217215 | + | 0.976124i | \(0.430303\pi\) | |||||||
\(752\) | 1.01290e13 | 1.15501 | ||||||||
\(753\) | 4.58401e12 | 0.519599 | ||||||||
\(754\) | 1.37948e12 | 0.155433 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.28494e11 | −0.0254406 | ||||||||
\(757\) | −3.55646e12 | −0.393629 | −0.196814 | − | 0.980441i | \(-0.563060\pi\) | ||||
−0.196814 | + | 0.980441i | \(0.563060\pi\) | |||||||
\(758\) | 1.10776e13 | 1.21880 | ||||||||
\(759\) | 1.61238e13 | 1.76352 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.67100e13 | 1.80612 | 0.903058 | − | 0.429519i | \(-0.141317\pi\) | ||||
0.903058 | + | 0.429519i | \(0.141317\pi\) | |||||||
\(762\) | −1.04762e13 | −1.12566 | ||||||||
\(763\) | −7.11560e12 | −0.760066 | ||||||||
\(764\) | −6.44647e11 | −0.0684544 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.45987e12 | −0.572997 | ||||||||
\(767\) | −1.78429e13 | −1.86160 | ||||||||
\(768\) | −3.35393e12 | −0.347880 | ||||||||
\(769\) | −7.51512e12 | −0.774939 | −0.387469 | − | 0.921883i | \(-0.626651\pi\) | ||||
−0.387469 | + | 0.921883i | \(0.626651\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.01507e12 | 0.409213 | ||||||||
\(772\) | 7.41702e11 | 0.0751540 | ||||||||
\(773\) | 8.52580e12 | 0.858870 | 0.429435 | − | 0.903098i | \(-0.358713\pi\) | ||||
0.429435 | + | 0.903098i | \(0.358713\pi\) | |||||||
\(774\) | −1.40976e12 | −0.141192 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.33028e13 | −1.31694 | ||||||||
\(777\) | 2.82410e12 | 0.277962 | ||||||||
\(778\) | −9.25569e12 | −0.905734 | ||||||||
\(779\) | 2.12802e12 | 0.207042 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.02890e13 | −2.91310 | ||||||||
\(782\) | 6.82543e12 | 0.652679 | ||||||||
\(783\) | 2.46693e11 | 0.0234546 | ||||||||
\(784\) | 7.41531e12 | 0.700982 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.06506e12 | −0.0995338 | ||||||||
\(787\) | −3.20742e12 | −0.298037 | −0.149018 | − | 0.988834i | \(-0.547611\pi\) | ||||
−0.149018 | + | 0.988834i | \(0.547611\pi\) | |||||||
\(788\) | −1.78112e12 | −0.164560 | ||||||||
\(789\) | 2.91194e12 | 0.267507 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.79191e12 | −0.344401 | ||||||||
\(792\) | −5.60830e12 | −0.506486 | ||||||||
\(793\) | −1.84672e13 | −1.65833 | ||||||||
\(794\) | 3.45353e12 | 0.308369 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.28815e12 | −0.290297 | ||||||||
\(797\) | 1.83036e13 | 1.60684 | 0.803421 | − | 0.595412i | \(-0.203011\pi\) | ||||
0.803421 | + | 0.595412i | \(0.203011\pi\) | |||||||
\(798\) | 1.89908e12 | 0.165779 | ||||||||
\(799\) | 3.87648e12 | 0.336494 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.83594e12 | 0.243417 | ||||||||
\(802\) | 1.72975e13 | 1.47638 | ||||||||
\(803\) | −1.75029e13 | −1.48556 | ||||||||
\(804\) | 2.36853e12 | 0.199907 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.52085e13 | 1.26934 | ||||||||
\(807\) | 5.74817e12 | 0.477088 | ||||||||
\(808\) | −5.34321e12 | −0.441013 | ||||||||
\(809\) | 9.38919e12 | 0.770655 | 0.385327 | − | 0.922780i | \(-0.374089\pi\) | ||||
0.385327 | + | 0.922780i | \(0.374089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.03949e13 | 1.65549 | 0.827746 | − | 0.561103i | \(-0.189623\pi\) | ||||
0.827746 | + | 0.561103i | \(0.189623\pi\) | |||||||
\(812\) | −1.99582e11 | −0.0161109 | ||||||||
\(813\) | −1.19232e13 | −0.957166 | ||||||||
\(814\) | −1.83579e13 | −1.46560 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.89396e12 | −0.228500 | ||||||||
\(817\) | 2.02861e12 | 0.159294 | ||||||||
\(818\) | 2.26642e13 | 1.76991 | ||||||||
\(819\) | −3.14243e12 | −0.244055 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.52259e13 | −1.16961 | −0.584803 | − | 0.811176i | \(-0.698828\pi\) | ||||
−0.584803 | + | 0.811176i | \(0.698828\pi\) | |||||||
\(822\) | 1.01135e13 | 0.772639 | ||||||||
\(823\) | 2.70705e12 | 0.205682 | 0.102841 | − | 0.994698i | \(-0.467207\pi\) | ||||
0.102841 | + | 0.994698i | \(0.467207\pi\) | |||||||
\(824\) | −6.11629e11 | −0.0462184 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.49103e13 | 1.11449 | ||||||||
\(827\) | −5.67203e10 | −0.00421661 | −0.00210831 | − | 0.999998i | \(-0.500671\pi\) | ||||
−0.00210831 | + | 0.999998i | \(0.500671\pi\) | |||||||
\(828\) | −1.64993e12 | −0.121991 | ||||||||
\(829\) | −1.43206e13 | −1.05309 | −0.526547 | − | 0.850146i | \(-0.676513\pi\) | ||||
−0.526547 | + | 0.850146i | \(0.676513\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.32742e12 | −0.169305 | ||||||||
\(832\) | −1.14143e13 | −0.825839 | ||||||||
\(833\) | 2.83791e12 | 0.204219 | ||||||||
\(834\) | −7.09231e12 | −0.507622 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.13734e12 | −0.151337 | ||||||||
\(837\) | 2.71973e12 | 0.191541 | ||||||||
\(838\) | 7.74265e12 | 0.542365 | ||||||||
\(839\) | −2.13693e13 | −1.48889 | −0.744443 | − | 0.667686i | \(-0.767285\pi\) | ||||
−0.744443 | + | 0.667686i | \(0.767285\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.42917e13 | −0.985147 | ||||||||
\(842\) | 1.90098e13 | 1.30339 | ||||||||
\(843\) | −4.18827e12 | −0.285635 | ||||||||
\(844\) | 4.13386e12 | 0.280424 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.41235e12 | −0.363262 | ||||||||
\(847\) | 1.94248e13 | 1.29683 | ||||||||
\(848\) | −1.95929e13 | −1.30112 | ||||||||
\(849\) | −2.61171e11 | −0.0172521 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.03925e13 | 1.33287 | ||||||||
\(852\) | 3.09943e12 | 0.201514 | ||||||||
\(853\) | 1.18123e13 | 0.763948 | 0.381974 | − | 0.924173i | \(-0.375244\pi\) | ||||
0.381974 | + | 0.924173i | \(0.375244\pi\) | |||||||
\(854\) | 1.54319e13 | 0.992797 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.01562e13 | −0.646547 | ||||||||
\(857\) | −2.69459e13 | −1.70640 | −0.853198 | − | 0.521587i | \(-0.825340\pi\) | ||||
−0.853198 | + | 0.521587i | \(0.825340\pi\) | |||||||
\(858\) | 2.04272e13 | 1.28681 | ||||||||
\(859\) | 9.66669e12 | 0.605771 | 0.302885 | − | 0.953027i | \(-0.402050\pi\) | ||||
0.302885 | + | 0.953027i | \(0.402050\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.94251e12 | 0.182475 | ||||||||
\(862\) | 1.62897e12 | 0.100492 | ||||||||
\(863\) | −2.80982e12 | −0.172437 | −0.0862185 | − | 0.996276i | \(-0.527478\pi\) | ||||
−0.0862185 | + | 0.996276i | \(0.527478\pi\) | |||||||
\(864\) | 1.29977e12 | 0.0793513 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.95944e13 | 1.18386 | ||||||||
\(867\) | 8.49807e12 | 0.510781 | ||||||||
\(868\) | −2.20035e12 | −0.131569 | ||||||||
\(869\) | −3.43162e13 | −2.04132 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.25739e13 | 1.91773 | ||||||||
\(872\) | 1.78716e13 | 1.04674 | ||||||||
\(873\) | 8.66488e12 | 0.504892 | ||||||||
\(874\) | 1.37130e13 | 0.794933 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.79105e12 | 0.102764 | ||||||||
\(877\) | −3.37045e13 | −1.92393 | −0.961966 | − | 0.273169i | \(-0.911928\pi\) | ||||
−0.961966 | + | 0.273169i | \(0.911928\pi\) | |||||||
\(878\) | −2.08828e13 | −1.18594 | ||||||||
\(879\) | −9.20087e12 | −0.519851 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.20571e13 | −0.674297 | −0.337148 | − | 0.941452i | \(-0.609462\pi\) | ||||
−0.337148 | + | 0.941452i | \(0.609462\pi\) | |||||||
\(882\) | −3.96231e12 | −0.220465 | ||||||||
\(883\) | 1.91595e13 | 1.06062 | 0.530311 | − | 0.847803i | \(-0.322075\pi\) | ||||
0.530311 | + | 0.847803i | \(0.322075\pi\) | |||||||
\(884\) | 1.49712e12 | 0.0824559 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.19140e13 | 1.73992 | ||||||||
\(887\) | 2.24991e13 | 1.22042 | 0.610209 | − | 0.792241i | \(-0.291086\pi\) | ||||
0.610209 | + | 0.792241i | \(0.291086\pi\) | |||||||
\(888\) | −7.09305e12 | −0.382802 | ||||||||
\(889\) | 2.08449e13 | 1.11929 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.65300e12 | 0.194178 | ||||||||
\(892\) | 3.33795e12 | 0.176538 | ||||||||
\(893\) | 7.78825e12 | 0.409834 | ||||||||
\(894\) | −8.72380e12 | −0.456759 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.45603e13 | 0.754719 | ||||||||
\(897\) | −2.26910e13 | −1.17028 | ||||||||
\(898\) | 1.99576e12 | 0.102415 | ||||||||
\(899\) | 2.37560e12 | 0.121298 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.49841e12 | −0.379060 | ||||||||
\(902\) | −1.91277e13 | −0.962128 | ||||||||
\(903\) | 2.80506e12 | 0.140393 | ||||||||
\(904\) | 9.52380e12 | 0.474299 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.13242e13 | 0.558383 | ||||||||
\(907\) | 2.39724e13 | 1.17619 | 0.588096 | − | 0.808791i | \(-0.299878\pi\) | ||||
0.588096 | + | 0.808791i | \(0.299878\pi\) | |||||||
\(908\) | 1.22847e12 | 0.0599763 | ||||||||
\(909\) | 3.48033e12 | 0.169077 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.54470e12 | −0.314816 | −0.157408 | − | 0.987534i | \(-0.550314\pi\) | ||||
−0.157408 | + | 0.987534i | \(0.550314\pi\) | |||||||
\(912\) | −5.81427e12 | −0.278303 | ||||||||
\(913\) | 4.38762e11 | 0.0208983 | ||||||||
\(914\) | −3.16236e12 | −0.149884 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.26504e12 | −0.153235 | ||||||||
\(917\) | 2.11918e12 | 0.0989706 | ||||||||
\(918\) | 1.54636e12 | 0.0718654 | ||||||||
\(919\) | 2.63348e12 | 0.121789 | 0.0608947 | − | 0.998144i | \(-0.480605\pi\) | ||||
0.0608947 | + | 0.998144i | \(0.480605\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.86740e12 | −0.0855203 | ||||||||
\(922\) | −1.84111e13 | −0.839055 | ||||||||
\(923\) | 4.26258e13 | 1.93314 | ||||||||
\(924\) | −2.95539e12 | −0.133380 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.42093e13 | −0.635073 | ||||||||
\(927\) | 3.98388e11 | 0.0177193 | ||||||||
\(928\) | 1.13530e12 | 0.0502512 | ||||||||
\(929\) | 2.94271e13 | 1.29621 | 0.648106 | − | 0.761550i | \(-0.275561\pi\) | ||||
0.648106 | + | 0.761550i | \(0.275561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.70166e12 | 0.248730 | ||||||||
\(932\) | −3.04070e11 | −0.0132009 | ||||||||
\(933\) | −6.25084e12 | −0.270067 | ||||||||
\(934\) | −2.96305e13 | −1.27403 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.89255e12 | 0.336106 | ||||||||
\(937\) | 1.71769e13 | 0.727974 | 0.363987 | − | 0.931404i | \(-0.381415\pi\) | ||||
0.363987 | + | 0.931404i | \(0.381415\pi\) | |||||||
\(938\) | −2.72201e13 | −1.14809 | ||||||||
\(939\) | −3.79754e12 | −0.159407 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.46944e13 | −1.02670 | −0.513352 | − | 0.858178i | \(-0.671596\pi\) | ||||
−0.513352 | + | 0.858178i | \(0.671596\pi\) | |||||||
\(942\) | 3.13632e12 | 0.129775 | ||||||||
\(943\) | 2.12475e13 | 0.874994 | ||||||||
\(944\) | −4.56498e13 | −1.87096 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.82341e13 | −0.740244 | ||||||||
\(947\) | 1.19428e12 | 0.0482537 | 0.0241268 | − | 0.999709i | \(-0.492319\pi\) | ||||
0.0241268 | + | 0.999709i | \(0.492319\pi\) | |||||||
\(948\) | 3.51153e12 | 0.141208 | ||||||||
\(949\) | 2.46319e13 | 0.985824 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.77730e13 | 0.704610 | ||||||||
\(952\) | 4.72377e12 | 0.186390 | ||||||||
\(953\) | −1.47694e13 | −0.580023 | −0.290011 | − | 0.957023i | \(-0.593659\pi\) | ||||
−0.290011 | + | 0.957023i | \(0.593659\pi\) | |||||||
\(954\) | 1.04693e13 | 0.409214 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.70966e12 | −0.259800 | ||||||||
\(957\) | 3.19077e12 | 0.122968 | ||||||||
\(958\) | 3.63489e13 | 1.39427 | ||||||||
\(959\) | −2.01231e13 | −0.768267 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.49176e11 | −0.00942435 | ||||||||
\(962\) | 2.58351e13 | 0.972574 | ||||||||
\(963\) | 6.61532e12 | 0.247875 | ||||||||
\(964\) | 7.76192e12 | 0.289483 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.89616e13 | 0.700612 | ||||||||
\(967\) | 8.95584e12 | 0.329372 | 0.164686 | − | 0.986346i | \(-0.447339\pi\) | ||||
0.164686 | + | 0.986346i | \(0.447339\pi\) | |||||||
\(968\) | −4.87876e13 | −1.78596 | ||||||||
\(969\) | −2.22518e12 | −0.0810790 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.20587e13 | −0.796330 | −0.398165 | − | 0.917314i | \(-0.630353\pi\) | ||||
−0.398165 | + | 0.917314i | \(0.630353\pi\) | |||||||
\(972\) | −3.73806e11 | −0.0134322 | ||||||||
\(973\) | 1.41118e13 | 0.504749 | ||||||||
\(974\) | 3.65621e13 | 1.30172 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.72469e13 | −1.66667 | ||||||||
\(977\) | −3.56972e13 | −1.25345 | −0.626727 | − | 0.779239i | \(-0.715606\pi\) | ||||
−0.626727 | + | 0.779239i | \(0.715606\pi\) | |||||||
\(978\) | −2.32963e13 | −0.814258 | ||||||||
\(979\) | 3.66806e13 | 1.27619 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.16408e13 | −0.401303 | ||||||||
\(982\) | −4.38300e13 | −1.50408 | ||||||||
\(983\) | −3.19525e13 | −1.09147 | −0.545737 | − | 0.837956i | \(-0.683750\pi\) | ||||
−0.545737 | + | 0.837956i | \(0.683750\pi\) | |||||||
\(984\) | −7.39045e12 | −0.251300 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.35070e12 | 0.0455105 | ||||||||
\(987\) | 1.07692e13 | 0.361206 | ||||||||
\(988\) | 3.00787e12 | 0.100428 | ||||||||
\(989\) | 2.02549e13 | 0.673205 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.56883e13 | 0.516706 | 0.258353 | − | 0.966051i | \(-0.416820\pi\) | ||||
0.258353 | + | 0.966051i | \(0.416820\pi\) | |||||||
\(992\) | 1.25165e13 | 0.410374 | ||||||||
\(993\) | −3.15151e11 | −0.0102860 | ||||||||
\(994\) | −3.56199e13 | −1.15732 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.48979e10 | −0.00144563 | ||||||||
\(997\) | −6.52145e12 | −0.209033 | −0.104517 | − | 0.994523i | \(-0.533330\pi\) | ||||
−0.104517 | + | 0.994523i | \(0.533330\pi\) | |||||||
\(998\) | −4.05647e13 | −1.29438 | ||||||||
\(999\) | 4.62010e12 | 0.146760 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.10.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 225.10.a.j.1.1 | 2 | |||
5.2 | odd | 4 | 75.10.b.e.49.3 | 4 | |||
5.3 | odd | 4 | 75.10.b.e.49.2 | 4 | |||
5.4 | even | 2 | 15.10.a.c.1.1 | ✓ | 2 | ||
15.2 | even | 4 | 225.10.b.g.199.2 | 4 | |||
15.8 | even | 4 | 225.10.b.g.199.3 | 4 | |||
15.14 | odd | 2 | 45.10.a.e.1.2 | 2 | |||
20.19 | odd | 2 | 240.10.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.c.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
45.10.a.e.1.2 | 2 | 15.14 | odd | 2 | |||
75.10.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
75.10.b.e.49.2 | 4 | 5.3 | odd | 4 | |||
75.10.b.e.49.3 | 4 | 5.2 | odd | 4 | |||
225.10.a.j.1.1 | 2 | 3.2 | odd | 2 | |||
225.10.b.g.199.2 | 4 | 15.2 | even | 4 | |||
225.10.b.g.199.3 | 4 | 15.8 | even | 4 | |||
240.10.a.m.1.1 | 2 | 20.19 | odd | 2 |