Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,8,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(13.4325560958\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 977 x^{9} + 2592 x^{8} + 344686 x^{7} - 1160956 x^{6} - 53409536 x^{5} + 209758592 x^{4} + 3410917248 x^{3} - 14180732672 x^{2} + \cdots + 238240894976 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(13.1261\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −15.1261 | −1.33697 | −0.668486 | − | 0.743725i | \(-0.733057\pi\) | ||||
−0.668486 | + | 0.743725i | \(0.733057\pi\) | |||||||
\(3\) | 62.8737 | 1.34445 | 0.672225 | − | 0.740347i | \(-0.265339\pi\) | ||||
0.672225 | + | 0.740347i | \(0.265339\pi\) | |||||||
\(4\) | 100.799 | 0.787495 | ||||||||
\(5\) | 12.0619 | 0.0431540 | 0.0215770 | − | 0.999767i | \(-0.493131\pi\) | ||||
0.0215770 | + | 0.999767i | \(0.493131\pi\) | |||||||
\(6\) | −951.035 | −1.79749 | ||||||||
\(7\) | −1248.65 | −1.37593 | −0.687966 | − | 0.725743i | \(-0.741496\pi\) | ||||
−0.687966 | + | 0.725743i | \(0.741496\pi\) | |||||||
\(8\) | 411.441 | 0.284114 | ||||||||
\(9\) | 1766.10 | 0.807545 | ||||||||
\(10\) | −182.450 | −0.0576956 | ||||||||
\(11\) | −2043.21 | −0.462849 | −0.231424 | − | 0.972853i | \(-0.574339\pi\) | ||||
−0.231424 | + | 0.972853i | \(0.574339\pi\) | |||||||
\(12\) | 6337.62 | 1.05875 | ||||||||
\(13\) | 9460.36 | 1.19428 | 0.597139 | − | 0.802137i | \(-0.296304\pi\) | ||||
0.597139 | + | 0.802137i | \(0.296304\pi\) | |||||||
\(14\) | 18887.2 | 1.83958 | ||||||||
\(15\) | 758.376 | 0.0580183 | ||||||||
\(16\) | −19125.8 | −1.16735 | ||||||||
\(17\) | −19027.5 | −0.939312 | −0.469656 | − | 0.882849i | \(-0.655622\pi\) | ||||
−0.469656 | + | 0.882849i | \(0.655622\pi\) | |||||||
\(18\) | −26714.2 | −1.07967 | ||||||||
\(19\) | −28326.9 | −0.947460 | −0.473730 | − | 0.880670i | \(-0.657093\pi\) | ||||
−0.473730 | + | 0.880670i | \(0.657093\pi\) | |||||||
\(20\) | 1215.83 | 0.0339835 | ||||||||
\(21\) | −78507.2 | −1.84987 | ||||||||
\(22\) | 30905.9 | 0.618816 | ||||||||
\(23\) | 2087.68 | 0.0357781 | 0.0178890 | − | 0.999840i | \(-0.494305\pi\) | ||||
0.0178890 | + | 0.999840i | \(0.494305\pi\) | |||||||
\(24\) | 25868.8 | 0.381977 | ||||||||
\(25\) | −77979.5 | −0.998138 | ||||||||
\(26\) | −143098. | −1.59672 | ||||||||
\(27\) | −26463.5 | −0.258746 | ||||||||
\(28\) | −125863. | −1.08354 | ||||||||
\(29\) | −111967. | −0.852508 | −0.426254 | − | 0.904603i | \(-0.640167\pi\) | ||||
−0.426254 | + | 0.904603i | \(0.640167\pi\) | |||||||
\(30\) | −11471.3 | −0.0775689 | ||||||||
\(31\) | 7978.79 | 0.0481029 | 0.0240514 | − | 0.999711i | \(-0.492343\pi\) | ||||
0.0240514 | + | 0.999711i | \(0.492343\pi\) | |||||||
\(32\) | 236635. | 1.27660 | ||||||||
\(33\) | −128464. | −0.622277 | ||||||||
\(34\) | 287812. | 1.25583 | ||||||||
\(35\) | −15061.1 | −0.0593769 | ||||||||
\(36\) | 178022. | 0.635937 | ||||||||
\(37\) | −185038. | −0.600559 | −0.300279 | − | 0.953851i | \(-0.597080\pi\) | ||||
−0.300279 | + | 0.953851i | \(0.597080\pi\) | |||||||
\(38\) | 428475. | 1.26673 | ||||||||
\(39\) | 594808. | 1.60565 | ||||||||
\(40\) | 4962.76 | 0.0122606 | ||||||||
\(41\) | −421826. | −0.955851 | −0.477925 | − | 0.878400i | \(-0.658611\pi\) | ||||
−0.477925 | + | 0.878400i | \(0.658611\pi\) | |||||||
\(42\) | 1.18751e6 | 2.47323 | ||||||||
\(43\) | 79507.0 | 0.152499 | ||||||||
\(44\) | −205954. | −0.364491 | ||||||||
\(45\) | 21302.5 | 0.0348488 | ||||||||
\(46\) | −31578.5 | −0.0478343 | ||||||||
\(47\) | 197368. | 0.277290 | 0.138645 | − | 0.990342i | \(-0.455725\pi\) | ||||
0.138645 | + | 0.990342i | \(0.455725\pi\) | |||||||
\(48\) | −1.20251e6 | −1.56944 | ||||||||
\(49\) | 735581. | 0.893191 | ||||||||
\(50\) | 1.17953e6 | 1.33448 | ||||||||
\(51\) | −1.19633e6 | −1.26286 | ||||||||
\(52\) | 953597. | 0.940488 | ||||||||
\(53\) | −2.01317e6 | −1.85744 | −0.928722 | − | 0.370778i | \(-0.879091\pi\) | ||||
−0.928722 | + | 0.370778i | \(0.879091\pi\) | |||||||
\(54\) | 400289. | 0.345936 | ||||||||
\(55\) | −24645.0 | −0.0199738 | ||||||||
\(56\) | −513745. | −0.390921 | ||||||||
\(57\) | −1.78101e6 | −1.27381 | ||||||||
\(58\) | 1.69363e6 | 1.13978 | ||||||||
\(59\) | −856041. | −0.542641 | −0.271321 | − | 0.962489i | \(-0.587460\pi\) | ||||
−0.271321 | + | 0.962489i | \(0.587460\pi\) | |||||||
\(60\) | 76443.8 | 0.0456891 | ||||||||
\(61\) | 2.61554e6 | 1.47539 | 0.737695 | − | 0.675135i | \(-0.235914\pi\) | ||||
0.737695 | + | 0.675135i | \(0.235914\pi\) | |||||||
\(62\) | −120688. | −0.0643122 | ||||||||
\(63\) | −2.20524e6 | −1.11113 | ||||||||
\(64\) | −1.13126e6 | −0.539427 | ||||||||
\(65\) | 114110. | 0.0515379 | ||||||||
\(66\) | 1.94317e6 | 0.831967 | ||||||||
\(67\) | 2.93249e6 | 1.19117 | 0.595587 | − | 0.803291i | \(-0.296920\pi\) | ||||
0.595587 | + | 0.803291i | \(0.296920\pi\) | |||||||
\(68\) | −1.91796e6 | −0.739703 | ||||||||
\(69\) | 131260. | 0.0481018 | ||||||||
\(70\) | 227816. | 0.0793853 | ||||||||
\(71\) | −3.20003e6 | −1.06109 | −0.530543 | − | 0.847658i | \(-0.678012\pi\) | ||||
−0.530543 | + | 0.847658i | \(0.678012\pi\) | |||||||
\(72\) | 726646. | 0.229435 | ||||||||
\(73\) | 4.19984e6 | 1.26358 | 0.631790 | − | 0.775140i | \(-0.282321\pi\) | ||||
0.631790 | + | 0.775140i | \(0.282321\pi\) | |||||||
\(74\) | 2.79891e6 | 0.802930 | ||||||||
\(75\) | −4.90286e6 | −1.34195 | ||||||||
\(76\) | −2.85533e6 | −0.746119 | ||||||||
\(77\) | 2.55125e6 | 0.636849 | ||||||||
\(78\) | −8.99713e6 | −2.14671 | ||||||||
\(79\) | 7.83389e6 | 1.78765 | 0.893825 | − | 0.448416i | \(-0.148012\pi\) | ||||
0.893825 | + | 0.448416i | \(0.148012\pi\) | |||||||
\(80\) | −230694. | −0.0503756 | ||||||||
\(81\) | −5.52632e6 | −1.15542 | ||||||||
\(82\) | 6.38059e6 | 1.27795 | ||||||||
\(83\) | 5.57533e6 | 1.07028 | 0.535140 | − | 0.844764i | \(-0.320259\pi\) | ||||
0.535140 | + | 0.844764i | \(0.320259\pi\) | |||||||
\(84\) | −7.91347e6 | −1.45676 | ||||||||
\(85\) | −229508. | −0.0405351 | ||||||||
\(86\) | −1.20263e6 | −0.203886 | ||||||||
\(87\) | −7.03981e6 | −1.14615 | ||||||||
\(88\) | −840660. | −0.131502 | ||||||||
\(89\) | −889160. | −0.133695 | −0.0668474 | − | 0.997763i | \(-0.521294\pi\) | ||||
−0.0668474 | + | 0.997763i | \(0.521294\pi\) | |||||||
\(90\) | −322225. | −0.0465918 | ||||||||
\(91\) | −1.18127e7 | −1.64325 | ||||||||
\(92\) | 210437. | 0.0281750 | ||||||||
\(93\) | 501656. | 0.0646719 | ||||||||
\(94\) | −2.98542e6 | −0.370730 | ||||||||
\(95\) | −341676. | −0.0408866 | ||||||||
\(96\) | 1.48781e7 | 1.71632 | ||||||||
\(97\) | 1.05709e7 | 1.17601 | 0.588003 | − | 0.808859i | \(-0.299914\pi\) | ||||
0.588003 | + | 0.808859i | \(0.299914\pi\) | |||||||
\(98\) | −1.11265e7 | −1.19417 | ||||||||
\(99\) | −3.60852e6 | −0.373771 | ||||||||
\(100\) | −7.86028e6 | −0.786028 | ||||||||
\(101\) | 613031. | 0.0592049 | 0.0296024 | − | 0.999562i | \(-0.490576\pi\) | ||||
0.0296024 | + | 0.999562i | \(0.490576\pi\) | |||||||
\(102\) | 1.80958e7 | 1.68841 | ||||||||
\(103\) | −1.58867e7 | −1.43253 | −0.716265 | − | 0.697828i | \(-0.754150\pi\) | ||||
−0.716265 | + | 0.697828i | \(0.754150\pi\) | |||||||
\(104\) | 3.89238e6 | 0.339311 | ||||||||
\(105\) | −946945. | −0.0798293 | ||||||||
\(106\) | 3.04515e7 | 2.48335 | ||||||||
\(107\) | −2.82221e6 | −0.222713 | −0.111357 | − | 0.993781i | \(-0.535520\pi\) | ||||
−0.111357 | + | 0.993781i | \(0.535520\pi\) | |||||||
\(108\) | −2.66750e6 | −0.203761 | ||||||||
\(109\) | −2.05758e6 | −0.152183 | −0.0760913 | − | 0.997101i | \(-0.524244\pi\) | ||||
−0.0760913 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(110\) | 372783. | 0.0267044 | ||||||||
\(111\) | −1.16340e7 | −0.807421 | ||||||||
\(112\) | 2.38814e7 | 1.60619 | ||||||||
\(113\) | 1.63742e6 | 0.106754 | 0.0533770 | − | 0.998574i | \(-0.483001\pi\) | ||||
0.0533770 | + | 0.998574i | \(0.483001\pi\) | |||||||
\(114\) | 2.69398e7 | 1.70305 | ||||||||
\(115\) | 25181.4 | 0.00154396 | ||||||||
\(116\) | −1.12862e7 | −0.671346 | ||||||||
\(117\) | 1.67079e7 | 0.964434 | ||||||||
\(118\) | 1.29486e7 | 0.725496 | ||||||||
\(119\) | 2.37586e7 | 1.29243 | ||||||||
\(120\) | 312027. | 0.0164838 | ||||||||
\(121\) | −1.53125e7 | −0.785771 | ||||||||
\(122\) | −3.95629e7 | −1.97255 | ||||||||
\(123\) | −2.65218e7 | −1.28509 | ||||||||
\(124\) | 804256. | 0.0378808 | ||||||||
\(125\) | −1.88292e6 | −0.0862276 | ||||||||
\(126\) | 3.33567e7 | 1.48555 | ||||||||
\(127\) | 6.60627e6 | 0.286183 | 0.143091 | − | 0.989709i | \(-0.454296\pi\) | ||||
0.143091 | + | 0.989709i | \(0.454296\pi\) | |||||||
\(128\) | −1.31777e7 | −0.555397 | ||||||||
\(129\) | 4.99890e6 | 0.205027 | ||||||||
\(130\) | −1.72604e6 | −0.0689047 | ||||||||
\(131\) | −5.79186e6 | −0.225096 | −0.112548 | − | 0.993646i | \(-0.535901\pi\) | ||||
−0.112548 | + | 0.993646i | \(0.535901\pi\) | |||||||
\(132\) | −1.29491e7 | −0.490040 | ||||||||
\(133\) | 3.53703e7 | 1.30364 | ||||||||
\(134\) | −4.43572e7 | −1.59257 | ||||||||
\(135\) | −319200. | −0.0111659 | ||||||||
\(136\) | −7.82868e6 | −0.266872 | ||||||||
\(137\) | 2.00914e7 | 0.667556 | 0.333778 | − | 0.942652i | \(-0.391676\pi\) | ||||
0.333778 | + | 0.942652i | \(0.391676\pi\) | |||||||
\(138\) | −1.98546e6 | −0.0643108 | ||||||||
\(139\) | 2.57362e7 | 0.812817 | 0.406408 | − | 0.913692i | \(-0.366781\pi\) | ||||
0.406408 | + | 0.913692i | \(0.366781\pi\) | |||||||
\(140\) | −1.51815e6 | −0.0467590 | ||||||||
\(141\) | 1.24093e7 | 0.372803 | ||||||||
\(142\) | 4.84041e7 | 1.41864 | ||||||||
\(143\) | −1.93295e7 | −0.552770 | ||||||||
\(144\) | −3.37781e7 | −0.942685 | ||||||||
\(145\) | −1.35054e6 | −0.0367891 | ||||||||
\(146\) | −6.35272e7 | −1.68937 | ||||||||
\(147\) | 4.62487e7 | 1.20085 | ||||||||
\(148\) | −1.86517e7 | −0.472937 | ||||||||
\(149\) | 2.86333e7 | 0.709121 | 0.354560 | − | 0.935033i | \(-0.384631\pi\) | ||||
0.354560 | + | 0.935033i | \(0.384631\pi\) | |||||||
\(150\) | 7.41612e7 | 1.79414 | ||||||||
\(151\) | −6.67796e7 | −1.57843 | −0.789213 | − | 0.614119i | \(-0.789511\pi\) | ||||
−0.789213 | + | 0.614119i | \(0.789511\pi\) | |||||||
\(152\) | −1.16548e7 | −0.269186 | ||||||||
\(153\) | −3.36045e7 | −0.758537 | ||||||||
\(154\) | −3.85906e7 | −0.851449 | ||||||||
\(155\) | 96239.3 | 0.00207583 | ||||||||
\(156\) | 5.99562e7 | 1.26444 | ||||||||
\(157\) | −8.44900e7 | −1.74243 | −0.871217 | − | 0.490898i | \(-0.836669\pi\) | ||||
−0.871217 | + | 0.490898i | \(0.836669\pi\) | |||||||
\(158\) | −1.18496e8 | −2.39004 | ||||||||
\(159\) | −1.26576e8 | −2.49724 | ||||||||
\(160\) | 2.85426e6 | 0.0550902 | ||||||||
\(161\) | −2.60678e6 | −0.0492282 | ||||||||
\(162\) | 8.35917e7 | 1.54476 | ||||||||
\(163\) | 6.39006e7 | 1.15571 | 0.577854 | − | 0.816140i | \(-0.303890\pi\) | ||||
0.577854 | + | 0.816140i | \(0.303890\pi\) | |||||||
\(164\) | −4.25198e7 | −0.752727 | ||||||||
\(165\) | −1.54952e6 | −0.0268537 | ||||||||
\(166\) | −8.43330e7 | −1.43093 | ||||||||
\(167\) | −1.62544e7 | −0.270061 | −0.135031 | − | 0.990841i | \(-0.543113\pi\) | ||||
−0.135031 | + | 0.990841i | \(0.543113\pi\) | |||||||
\(168\) | −3.23010e7 | −0.525574 | ||||||||
\(169\) | 2.67498e7 | 0.426302 | ||||||||
\(170\) | 3.47156e6 | 0.0541942 | ||||||||
\(171\) | −5.00281e7 | −0.765116 | ||||||||
\(172\) | 8.01425e6 | 0.120092 | ||||||||
\(173\) | −1.19428e8 | −1.75366 | −0.876830 | − | 0.480801i | \(-0.840346\pi\) | ||||
−0.876830 | + | 0.480801i | \(0.840346\pi\) | |||||||
\(174\) | 1.06485e8 | 1.53238 | ||||||||
\(175\) | 9.73690e7 | 1.37337 | ||||||||
\(176\) | 3.90781e7 | 0.540305 | ||||||||
\(177\) | −5.38225e7 | −0.729554 | ||||||||
\(178\) | 1.34495e7 | 0.178746 | ||||||||
\(179\) | 6.67618e7 | 0.870047 | 0.435023 | − | 0.900419i | \(-0.356740\pi\) | ||||
0.435023 | + | 0.900419i | \(0.356740\pi\) | |||||||
\(180\) | 2.14728e6 | 0.0274432 | ||||||||
\(181\) | 1.24721e8 | 1.56339 | 0.781693 | − | 0.623664i | \(-0.214357\pi\) | ||||
0.781693 | + | 0.623664i | \(0.214357\pi\) | |||||||
\(182\) | 1.78680e8 | 2.19698 | ||||||||
\(183\) | 1.64449e8 | 1.98359 | ||||||||
\(184\) | 858957. | 0.0101650 | ||||||||
\(185\) | −2.23191e6 | −0.0259165 | ||||||||
\(186\) | −7.58810e6 | −0.0864645 | ||||||||
\(187\) | 3.88772e7 | 0.434759 | ||||||||
\(188\) | 1.98946e7 | 0.218365 | ||||||||
\(189\) | 3.30436e7 | 0.356017 | ||||||||
\(190\) | 5.16822e6 | 0.0546643 | ||||||||
\(191\) | 7.43805e7 | 0.772400 | 0.386200 | − | 0.922415i | \(-0.373787\pi\) | ||||
0.386200 | + | 0.922415i | \(0.373787\pi\) | |||||||
\(192\) | −7.11265e7 | −0.725233 | ||||||||
\(193\) | 9.08749e7 | 0.909900 | 0.454950 | − | 0.890517i | \(-0.349657\pi\) | ||||
0.454950 | + | 0.890517i | \(0.349657\pi\) | |||||||
\(194\) | −1.59896e8 | −1.57229 | ||||||||
\(195\) | 7.17451e6 | 0.0692901 | ||||||||
\(196\) | 7.41460e7 | 0.703383 | ||||||||
\(197\) | −1.24750e8 | −1.16254 | −0.581270 | − | 0.813711i | \(-0.697444\pi\) | ||||
−0.581270 | + | 0.813711i | \(0.697444\pi\) | |||||||
\(198\) | 5.45829e7 | 0.499722 | ||||||||
\(199\) | −1.75151e8 | −1.57553 | −0.787767 | − | 0.615973i | \(-0.788763\pi\) | ||||
−0.787767 | + | 0.615973i | \(0.788763\pi\) | |||||||
\(200\) | −3.20839e7 | −0.283585 | ||||||||
\(201\) | 1.84377e8 | 1.60147 | ||||||||
\(202\) | −9.27277e6 | −0.0791553 | ||||||||
\(203\) | 1.39808e8 | 1.17299 | ||||||||
\(204\) | −1.20589e8 | −0.994494 | ||||||||
\(205\) | −5.08803e6 | −0.0412487 | ||||||||
\(206\) | 2.40304e8 | 1.91525 | ||||||||
\(207\) | 3.68706e6 | 0.0288924 | ||||||||
\(208\) | −1.80937e8 | −1.39414 | ||||||||
\(209\) | 5.78778e7 | 0.438530 | ||||||||
\(210\) | 1.43236e7 | 0.106730 | ||||||||
\(211\) | 8.95521e7 | 0.656277 | 0.328138 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328138 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(212\) | −2.02926e8 | −1.46273 | ||||||||
\(213\) | −2.01198e8 | −1.42658 | ||||||||
\(214\) | 4.26891e7 | 0.297761 | ||||||||
\(215\) | 959005. | 0.00658092 | ||||||||
\(216\) | −1.08881e7 | −0.0735133 | ||||||||
\(217\) | −9.96271e6 | −0.0661863 | ||||||||
\(218\) | 3.11233e7 | 0.203464 | ||||||||
\(219\) | 2.64059e8 | 1.69882 | ||||||||
\(220\) | −2.48420e6 | −0.0157292 | ||||||||
\(221\) | −1.80007e8 | −1.12180 | ||||||||
\(222\) | 1.75978e8 | 1.07950 | ||||||||
\(223\) | −1.68028e8 | −1.01464 | −0.507322 | − | 0.861757i | \(-0.669364\pi\) | ||||
−0.507322 | + | 0.861757i | \(0.669364\pi\) | |||||||
\(224\) | −2.95474e8 | −1.75651 | ||||||||
\(225\) | −1.37720e8 | −0.806041 | ||||||||
\(226\) | −2.47677e7 | −0.142727 | ||||||||
\(227\) | 1.05659e8 | 0.599538 | 0.299769 | − | 0.954012i | \(-0.403090\pi\) | ||||
0.299769 | + | 0.954012i | \(0.403090\pi\) | |||||||
\(228\) | −1.79525e8 | −1.00312 | ||||||||
\(229\) | −2.91314e8 | −1.60301 | −0.801506 | − | 0.597987i | \(-0.795967\pi\) | ||||
−0.801506 | + | 0.597987i | \(0.795967\pi\) | |||||||
\(230\) | −380897. | −0.00206424 | ||||||||
\(231\) | 1.60407e8 | 0.856211 | ||||||||
\(232\) | −4.60680e7 | −0.242209 | ||||||||
\(233\) | −2.72762e8 | −1.41266 | −0.706332 | − | 0.707881i | \(-0.749651\pi\) | ||||
−0.706332 | + | 0.707881i | \(0.749651\pi\) | |||||||
\(234\) | −2.52726e8 | −1.28942 | ||||||||
\(235\) | 2.38064e6 | 0.0119662 | ||||||||
\(236\) | −8.62884e7 | −0.427327 | ||||||||
\(237\) | 4.92545e8 | 2.40340 | ||||||||
\(238\) | −3.59376e8 | −1.72794 | ||||||||
\(239\) | 2.25857e8 | 1.07014 | 0.535069 | − | 0.844808i | \(-0.320285\pi\) | ||||
0.535069 | + | 0.844808i | \(0.320285\pi\) | |||||||
\(240\) | −1.45046e7 | −0.0677275 | ||||||||
\(241\) | 2.02550e8 | 0.932122 | 0.466061 | − | 0.884753i | \(-0.345673\pi\) | ||||
0.466061 | + | 0.884753i | \(0.345673\pi\) | |||||||
\(242\) | 2.31618e8 | 1.05055 | ||||||||
\(243\) | −2.89584e8 | −1.29465 | ||||||||
\(244\) | 2.63644e8 | 1.16186 | ||||||||
\(245\) | 8.87250e6 | 0.0385447 | ||||||||
\(246\) | 4.01171e8 | 1.71813 | ||||||||
\(247\) | −2.67982e8 | −1.13153 | ||||||||
\(248\) | 3.28280e6 | 0.0136667 | ||||||||
\(249\) | 3.50541e8 | 1.43894 | ||||||||
\(250\) | 2.84812e7 | 0.115284 | ||||||||
\(251\) | 4.56654e8 | 1.82276 | 0.911379 | − | 0.411567i | \(-0.135019\pi\) | ||||
0.911379 | + | 0.411567i | \(0.135019\pi\) | |||||||
\(252\) | −2.22287e8 | −0.875007 | ||||||||
\(253\) | −4.26557e6 | −0.0165598 | ||||||||
\(254\) | −9.99272e7 | −0.382618 | ||||||||
\(255\) | −1.44300e7 | −0.0544973 | ||||||||
\(256\) | 3.44128e8 | 1.28198 | ||||||||
\(257\) | 6.13602e7 | 0.225487 | 0.112743 | − | 0.993624i | \(-0.464036\pi\) | ||||
0.112743 | + | 0.993624i | \(0.464036\pi\) | |||||||
\(258\) | −7.56139e7 | −0.274115 | ||||||||
\(259\) | 2.31048e8 | 0.826328 | ||||||||
\(260\) | 1.15022e7 | 0.0405858 | ||||||||
\(261\) | −1.97746e8 | −0.688439 | ||||||||
\(262\) | 8.76083e7 | 0.300947 | ||||||||
\(263\) | −5.34920e8 | −1.81319 | −0.906596 | − | 0.422000i | \(-0.861328\pi\) | ||||
−0.906596 | + | 0.422000i | \(0.861328\pi\) | |||||||
\(264\) | −5.28554e7 | −0.176797 | ||||||||
\(265\) | −2.42827e7 | −0.0801560 | ||||||||
\(266\) | −5.35015e8 | −1.74293 | ||||||||
\(267\) | −5.59048e7 | −0.179746 | ||||||||
\(268\) | 2.95593e8 | 0.938043 | ||||||||
\(269\) | −1.68231e8 | −0.526956 | −0.263478 | − | 0.964665i | \(-0.584870\pi\) | ||||
−0.263478 | + | 0.964665i | \(0.584870\pi\) | |||||||
\(270\) | 4.82825e6 | 0.0149285 | ||||||||
\(271\) | 3.63723e8 | 1.11014 | 0.555071 | − | 0.831803i | \(-0.312691\pi\) | ||||
0.555071 | + | 0.831803i | \(0.312691\pi\) | |||||||
\(272\) | 3.63916e8 | 1.09650 | ||||||||
\(273\) | −7.42706e8 | −2.20926 | ||||||||
\(274\) | −3.03904e8 | −0.892504 | ||||||||
\(275\) | 1.59329e8 | 0.461987 | ||||||||
\(276\) | 1.32309e7 | 0.0378799 | ||||||||
\(277\) | −2.54748e8 | −0.720165 | −0.360083 | − | 0.932920i | \(-0.617252\pi\) | ||||
−0.360083 | + | 0.932920i | \(0.617252\pi\) | |||||||
\(278\) | −3.89289e8 | −1.08671 | ||||||||
\(279\) | 1.40913e7 | 0.0388452 | ||||||||
\(280\) | −6.19674e6 | −0.0168698 | ||||||||
\(281\) | −5.70700e8 | −1.53439 | −0.767195 | − | 0.641414i | \(-0.778348\pi\) | ||||
−0.767195 | + | 0.641414i | \(0.778348\pi\) | |||||||
\(282\) | −1.87704e8 | −0.498427 | ||||||||
\(283\) | −2.06689e8 | −0.542083 | −0.271041 | − | 0.962568i | \(-0.587368\pi\) | ||||
−0.271041 | + | 0.962568i | \(0.587368\pi\) | |||||||
\(284\) | −3.22561e8 | −0.835599 | ||||||||
\(285\) | −2.14824e7 | −0.0549700 | ||||||||
\(286\) | 2.92380e8 | 0.739039 | ||||||||
\(287\) | 5.26713e8 | 1.31519 | ||||||||
\(288\) | 4.17921e8 | 1.03091 | ||||||||
\(289\) | −4.82937e7 | −0.117692 | ||||||||
\(290\) | 2.04284e7 | 0.0491860 | ||||||||
\(291\) | 6.64629e8 | 1.58108 | ||||||||
\(292\) | 4.23341e8 | 0.995062 | ||||||||
\(293\) | 8.14731e8 | 1.89225 | 0.946123 | − | 0.323808i | \(-0.104963\pi\) | ||||
0.946123 | + | 0.323808i | \(0.104963\pi\) | |||||||
\(294\) | −6.99563e8 | −1.60550 | ||||||||
\(295\) | −1.03255e7 | −0.0234171 | ||||||||
\(296\) | −7.61323e7 | −0.170627 | ||||||||
\(297\) | 5.40705e7 | 0.119760 | ||||||||
\(298\) | −4.33111e8 | −0.948075 | ||||||||
\(299\) | 1.97502e7 | 0.0427290 | ||||||||
\(300\) | −4.94205e8 | −1.05678 | ||||||||
\(301\) | −9.92763e7 | −0.209828 | ||||||||
\(302\) | 1.01012e9 | 2.11031 | ||||||||
\(303\) | 3.85435e7 | 0.0795980 | ||||||||
\(304\) | 5.41774e8 | 1.10601 | ||||||||
\(305\) | 3.15484e7 | 0.0636689 | ||||||||
\(306\) | 5.08305e8 | 1.01414 | ||||||||
\(307\) | −1.50628e8 | −0.297112 | −0.148556 | − | 0.988904i | \(-0.547463\pi\) | ||||
−0.148556 | + | 0.988904i | \(0.547463\pi\) | |||||||
\(308\) | 2.57165e8 | 0.501515 | ||||||||
\(309\) | −9.98857e8 | −1.92597 | ||||||||
\(310\) | −1.45573e6 | −0.00277533 | ||||||||
\(311\) | −6.59750e8 | −1.24371 | −0.621853 | − | 0.783134i | \(-0.713620\pi\) | ||||
−0.621853 | + | 0.783134i | \(0.713620\pi\) | |||||||
\(312\) | 2.44728e8 | 0.456187 | ||||||||
\(313\) | −3.46916e8 | −0.639469 | −0.319735 | − | 0.947507i | \(-0.603594\pi\) | ||||
−0.319735 | + | 0.947507i | \(0.603594\pi\) | |||||||
\(314\) | 1.27801e9 | 2.32959 | ||||||||
\(315\) | −2.65994e7 | −0.0479496 | ||||||||
\(316\) | 7.89650e8 | 1.40776 | ||||||||
\(317\) | −9.98461e8 | −1.76045 | −0.880225 | − | 0.474557i | \(-0.842608\pi\) | ||||
−0.880225 | + | 0.474557i | \(0.842608\pi\) | |||||||
\(318\) | 1.91460e9 | 3.33874 | ||||||||
\(319\) | 2.28773e8 | 0.394582 | ||||||||
\(320\) | −1.36452e7 | −0.0232784 | ||||||||
\(321\) | −1.77443e8 | −0.299427 | ||||||||
\(322\) | 3.94305e7 | 0.0658167 | ||||||||
\(323\) | 5.38989e8 | 0.889961 | ||||||||
\(324\) | −5.57049e8 | −0.909884 | ||||||||
\(325\) | −7.37714e8 | −1.19205 | ||||||||
\(326\) | −9.66567e8 | −1.54515 | ||||||||
\(327\) | −1.29368e8 | −0.204602 | ||||||||
\(328\) | −1.73556e8 | −0.271570 | ||||||||
\(329\) | −2.46444e8 | −0.381533 | ||||||||
\(330\) | 2.34383e7 | 0.0359027 | ||||||||
\(331\) | 7.96597e8 | 1.20737 | 0.603686 | − | 0.797222i | \(-0.293698\pi\) | ||||
0.603686 | + | 0.797222i | \(0.293698\pi\) | |||||||
\(332\) | 5.61989e8 | 0.842839 | ||||||||
\(333\) | −3.26796e8 | −0.484978 | ||||||||
\(334\) | 2.45865e8 | 0.361065 | ||||||||
\(335\) | 3.53714e7 | 0.0514039 | ||||||||
\(336\) | 1.50151e9 | 2.15944 | ||||||||
\(337\) | −1.10141e9 | −1.56764 | −0.783818 | − | 0.620991i | \(-0.786730\pi\) | ||||
−0.783818 | + | 0.620991i | \(0.786730\pi\) | |||||||
\(338\) | −4.04621e8 | −0.569954 | ||||||||
\(339\) | 1.02950e8 | 0.143525 | ||||||||
\(340\) | −2.31342e7 | −0.0319211 | ||||||||
\(341\) | −1.63024e7 | −0.0222643 | ||||||||
\(342\) | 7.56731e8 | 1.02294 | ||||||||
\(343\) | 1.09834e8 | 0.146963 | ||||||||
\(344\) | 3.27124e7 | 0.0433269 | ||||||||
\(345\) | 1.58325e6 | 0.00207578 | ||||||||
\(346\) | 1.80648e9 | 2.34459 | ||||||||
\(347\) | −5.91060e8 | −0.759414 | −0.379707 | − | 0.925107i | \(-0.623975\pi\) | ||||
−0.379707 | + | 0.925107i | \(0.623975\pi\) | |||||||
\(348\) | −7.09607e8 | −0.902591 | ||||||||
\(349\) | 1.16064e9 | 1.46153 | 0.730764 | − | 0.682631i | \(-0.239164\pi\) | ||||
0.730764 | + | 0.682631i | \(0.239164\pi\) | |||||||
\(350\) | −1.47281e9 | −1.83616 | ||||||||
\(351\) | −2.50354e8 | −0.309015 | ||||||||
\(352\) | −4.83495e8 | −0.590871 | ||||||||
\(353\) | −2.28005e8 | −0.275888 | −0.137944 | − | 0.990440i | \(-0.544049\pi\) | ||||
−0.137944 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(354\) | 8.14125e8 | 0.975393 | ||||||||
\(355\) | −3.85985e7 | −0.0457900 | ||||||||
\(356\) | −8.96267e7 | −0.105284 | ||||||||
\(357\) | 1.49379e9 | 1.73761 | ||||||||
\(358\) | −1.00985e9 | −1.16323 | ||||||||
\(359\) | −1.34720e9 | −1.53674 | −0.768371 | − | 0.640005i | \(-0.778932\pi\) | ||||
−0.768371 | + | 0.640005i | \(0.778932\pi\) | |||||||
\(360\) | 8.76473e6 | 0.00990102 | ||||||||
\(361\) | −9.14611e7 | −0.102320 | ||||||||
\(362\) | −1.88655e9 | −2.09020 | ||||||||
\(363\) | −9.62751e8 | −1.05643 | ||||||||
\(364\) | −1.19071e9 | −1.29405 | ||||||||
\(365\) | 5.06580e7 | 0.0545285 | ||||||||
\(366\) | −2.48747e9 | −2.65200 | ||||||||
\(367\) | −9.77318e8 | −1.03206 | −0.516030 | − | 0.856571i | \(-0.672591\pi\) | ||||
−0.516030 | + | 0.856571i | \(0.672591\pi\) | |||||||
\(368\) | −3.99286e7 | −0.0417654 | ||||||||
\(369\) | −7.44988e8 | −0.771893 | ||||||||
\(370\) | 3.37602e7 | 0.0346496 | ||||||||
\(371\) | 2.51375e9 | 2.55572 | ||||||||
\(372\) | 5.05666e7 | 0.0509288 | ||||||||
\(373\) | 6.10073e8 | 0.608696 | 0.304348 | − | 0.952561i | \(-0.401561\pi\) | ||||
0.304348 | + | 0.952561i | \(0.401561\pi\) | |||||||
\(374\) | −5.88060e8 | −0.581261 | ||||||||
\(375\) | −1.18386e8 | −0.115929 | ||||||||
\(376\) | 8.12054e7 | 0.0787820 | ||||||||
\(377\) | −1.05925e9 | −1.01813 | ||||||||
\(378\) | −4.99821e8 | −0.475985 | ||||||||
\(379\) | 3.49421e8 | 0.329695 | 0.164847 | − | 0.986319i | \(-0.447287\pi\) | ||||
0.164847 | + | 0.986319i | \(0.447287\pi\) | |||||||
\(380\) | −3.44407e7 | −0.0321980 | ||||||||
\(381\) | 4.15361e8 | 0.384758 | ||||||||
\(382\) | −1.12509e9 | −1.03268 | ||||||||
\(383\) | 6.97644e8 | 0.634509 | 0.317255 | − | 0.948340i | \(-0.397239\pi\) | ||||
0.317255 | + | 0.948340i | \(0.397239\pi\) | |||||||
\(384\) | −8.28529e8 | −0.746704 | ||||||||
\(385\) | 3.07730e7 | 0.0274825 | ||||||||
\(386\) | −1.37458e9 | −1.21651 | ||||||||
\(387\) | 1.40417e8 | 0.123149 | ||||||||
\(388\) | 1.06554e9 | 0.926098 | ||||||||
\(389\) | 1.70449e9 | 1.46815 | 0.734077 | − | 0.679067i | \(-0.237615\pi\) | ||||
0.734077 | + | 0.679067i | \(0.237615\pi\) | |||||||
\(390\) | −1.08522e8 | −0.0926389 | ||||||||
\(391\) | −3.97233e7 | −0.0336068 | ||||||||
\(392\) | 3.02648e8 | 0.253768 | ||||||||
\(393\) | −3.64155e8 | −0.302631 | ||||||||
\(394\) | 1.88698e9 | 1.55428 | ||||||||
\(395\) | 9.44915e7 | 0.0771442 | ||||||||
\(396\) | −3.63736e8 | −0.294343 | ||||||||
\(397\) | −1.51386e7 | −0.0121428 | −0.00607138 | − | 0.999982i | \(-0.501933\pi\) | ||||
−0.00607138 | + | 0.999982i | \(0.501933\pi\) | |||||||
\(398\) | 2.64936e9 | 2.10645 | ||||||||
\(399\) | 2.22386e9 | 1.75268 | ||||||||
\(400\) | 1.49142e9 | 1.16517 | ||||||||
\(401\) | −1.18655e9 | −0.918928 | −0.459464 | − | 0.888196i | \(-0.651958\pi\) | ||||
−0.459464 | + | 0.888196i | \(0.651958\pi\) | |||||||
\(402\) | −2.78890e9 | −2.14112 | ||||||||
\(403\) | 7.54822e7 | 0.0574482 | ||||||||
\(404\) | 6.17931e7 | 0.0466235 | ||||||||
\(405\) | −6.66579e7 | −0.0498608 | ||||||||
\(406\) | −2.11475e9 | −1.56826 | ||||||||
\(407\) | 3.78072e8 | 0.277968 | ||||||||
\(408\) | −4.92218e8 | −0.358795 | ||||||||
\(409\) | 1.78027e9 | 1.28663 | 0.643315 | − | 0.765602i | \(-0.277559\pi\) | ||||
0.643315 | + | 0.765602i | \(0.277559\pi\) | |||||||
\(410\) | 7.69620e7 | 0.0551484 | ||||||||
\(411\) | 1.26322e9 | 0.897495 | ||||||||
\(412\) | −1.60137e9 | −1.12811 | ||||||||
\(413\) | 1.06890e9 | 0.746638 | ||||||||
\(414\) | −5.57708e7 | −0.0386283 | ||||||||
\(415\) | 6.72490e7 | 0.0461868 | ||||||||
\(416\) | 2.23865e9 | 1.52461 | ||||||||
\(417\) | 1.61813e9 | 1.09279 | ||||||||
\(418\) | −8.75466e8 | −0.586303 | ||||||||
\(419\) | 1.26485e9 | 0.840023 | 0.420012 | − | 0.907519i | \(-0.362026\pi\) | ||||
0.420012 | + | 0.907519i | \(0.362026\pi\) | |||||||
\(420\) | −9.54515e7 | −0.0628652 | ||||||||
\(421\) | 2.11626e8 | 0.138224 | 0.0691118 | − | 0.997609i | \(-0.477983\pi\) | ||||
0.0691118 | + | 0.997609i | \(0.477983\pi\) | |||||||
\(422\) | −1.35457e9 | −0.877424 | ||||||||
\(423\) | 3.48572e8 | 0.223925 | ||||||||
\(424\) | −8.28301e8 | −0.527725 | ||||||||
\(425\) | 1.48375e9 | 0.937563 | ||||||||
\(426\) | 3.04334e9 | 1.90729 | ||||||||
\(427\) | −3.26589e9 | −2.03004 | ||||||||
\(428\) | −2.84477e8 | −0.175385 | ||||||||
\(429\) | −1.21532e9 | −0.743172 | ||||||||
\(430\) | −1.45060e7 | −0.00879850 | ||||||||
\(431\) | 3.00302e8 | 0.180671 | 0.0903353 | − | 0.995911i | \(-0.471206\pi\) | ||||
0.0903353 | + | 0.995911i | \(0.471206\pi\) | |||||||
\(432\) | 5.06135e8 | 0.302046 | ||||||||
\(433\) | −1.41630e9 | −0.838392 | −0.419196 | − | 0.907896i | \(-0.637688\pi\) | ||||
−0.419196 | + | 0.907896i | \(0.637688\pi\) | |||||||
\(434\) | 1.50697e8 | 0.0884893 | ||||||||
\(435\) | −8.49134e7 | −0.0494611 | ||||||||
\(436\) | −2.07403e8 | −0.119843 | ||||||||
\(437\) | −5.91374e7 | −0.0338983 | ||||||||
\(438\) | −3.99419e9 | −2.27127 | ||||||||
\(439\) | 1.52173e9 | 0.858445 | 0.429223 | − | 0.903199i | \(-0.358788\pi\) | ||||
0.429223 | + | 0.903199i | \(0.358788\pi\) | |||||||
\(440\) | −1.01400e7 | −0.00567482 | ||||||||
\(441\) | 1.29911e9 | 0.721292 | ||||||||
\(442\) | 2.72280e9 | 1.49982 | ||||||||
\(443\) | 2.81273e8 | 0.153715 | 0.0768574 | − | 0.997042i | \(-0.475511\pi\) | ||||
0.0768574 | + | 0.997042i | \(0.475511\pi\) | |||||||
\(444\) | −1.17270e9 | −0.635840 | ||||||||
\(445\) | −1.07250e7 | −0.00576946 | ||||||||
\(446\) | 2.54160e9 | 1.35655 | ||||||||
\(447\) | 1.80028e9 | 0.953377 | ||||||||
\(448\) | 1.41255e9 | 0.742215 | ||||||||
\(449\) | 2.07207e9 | 1.08029 | 0.540146 | − | 0.841571i | \(-0.318369\pi\) | ||||
0.540146 | + | 0.841571i | \(0.318369\pi\) | |||||||
\(450\) | 2.08316e9 | 1.07765 | ||||||||
\(451\) | 8.61880e8 | 0.442414 | ||||||||
\(452\) | 1.65050e8 | 0.0840682 | ||||||||
\(453\) | −4.19868e9 | −2.12212 | ||||||||
\(454\) | −1.59821e9 | −0.801566 | ||||||||
\(455\) | −1.42483e8 | −0.0709126 | ||||||||
\(456\) | −7.32782e8 | −0.361908 | ||||||||
\(457\) | 6.18336e8 | 0.303053 | 0.151526 | − | 0.988453i | \(-0.451581\pi\) | ||||
0.151526 | + | 0.988453i | \(0.451581\pi\) | |||||||
\(458\) | 4.40644e9 | 2.14318 | ||||||||
\(459\) | 5.03533e8 | 0.243043 | ||||||||
\(460\) | 2.53827e6 | 0.00121586 | ||||||||
\(461\) | 1.04519e9 | 0.496867 | 0.248433 | − | 0.968649i | \(-0.420084\pi\) | ||||
0.248433 | + | 0.968649i | \(0.420084\pi\) | |||||||
\(462\) | −2.42633e9 | −1.14473 | ||||||||
\(463\) | −6.19870e8 | −0.290246 | −0.145123 | − | 0.989414i | \(-0.546358\pi\) | ||||
−0.145123 | + | 0.989414i | \(0.546358\pi\) | |||||||
\(464\) | 2.14147e9 | 0.995173 | ||||||||
\(465\) | 6.05092e6 | 0.00279085 | ||||||||
\(466\) | 4.12584e9 | 1.88869 | ||||||||
\(467\) | −4.18640e9 | −1.90209 | −0.951047 | − | 0.309047i | \(-0.899990\pi\) | ||||
−0.951047 | + | 0.309047i | \(0.899990\pi\) | |||||||
\(468\) | 1.68415e9 | 0.759487 | ||||||||
\(469\) | −3.66165e9 | −1.63897 | ||||||||
\(470\) | −3.60098e7 | −0.0159985 | ||||||||
\(471\) | −5.31220e9 | −2.34262 | ||||||||
\(472\) | −3.52210e8 | −0.154172 | ||||||||
\(473\) | −1.62450e8 | −0.0705838 | ||||||||
\(474\) | −7.45030e9 | −3.21329 | ||||||||
\(475\) | 2.20891e9 | 0.945695 | ||||||||
\(476\) | 2.39485e9 | 1.01778 | ||||||||
\(477\) | −3.55547e9 | −1.49997 | ||||||||
\(478\) | −3.41633e9 | −1.43075 | ||||||||
\(479\) | 2.16526e9 | 0.900193 | 0.450097 | − | 0.892980i | \(-0.351390\pi\) | ||||
0.450097 | + | 0.892980i | \(0.351390\pi\) | |||||||
\(480\) | 1.79458e8 | 0.0740660 | ||||||||
\(481\) | −1.75053e9 | −0.717235 | ||||||||
\(482\) | −3.06380e9 | −1.24622 | ||||||||
\(483\) | −1.63898e8 | −0.0661848 | ||||||||
\(484\) | −1.54349e9 | −0.618791 | ||||||||
\(485\) | 1.27505e8 | 0.0507493 | ||||||||
\(486\) | 4.38029e9 | 1.73091 | ||||||||
\(487\) | −4.04525e9 | −1.58706 | −0.793531 | − | 0.608530i | \(-0.791760\pi\) | ||||
−0.793531 | + | 0.608530i | \(0.791760\pi\) | |||||||
\(488\) | 1.07614e9 | 0.419178 | ||||||||
\(489\) | 4.01766e9 | 1.55379 | ||||||||
\(490\) | −1.34206e8 | −0.0515332 | ||||||||
\(491\) | 2.63031e9 | 1.00282 | 0.501408 | − | 0.865211i | \(-0.332816\pi\) | ||||
0.501408 | + | 0.865211i | \(0.332816\pi\) | |||||||
\(492\) | −2.67338e9 | −1.01200 | ||||||||
\(493\) | 2.13046e9 | 0.800772 | ||||||||
\(494\) | 4.05353e9 | 1.51283 | ||||||||
\(495\) | −4.35256e7 | −0.0161297 | ||||||||
\(496\) | −1.52601e8 | −0.0561527 | ||||||||
\(497\) | 3.99572e9 | 1.45998 | ||||||||
\(498\) | −5.30233e9 | −1.92382 | ||||||||
\(499\) | 3.10184e8 | 0.111755 | 0.0558775 | − | 0.998438i | \(-0.482204\pi\) | ||||
0.0558775 | + | 0.998438i | \(0.482204\pi\) | |||||||
\(500\) | −1.89797e8 | −0.0679037 | ||||||||
\(501\) | −1.02197e9 | −0.363084 | ||||||||
\(502\) | −6.90740e9 | −2.43698 | ||||||||
\(503\) | 4.58242e9 | 1.60549 | 0.802743 | − | 0.596325i | \(-0.203373\pi\) | ||||
0.802743 | + | 0.596325i | \(0.203373\pi\) | |||||||
\(504\) | −9.07326e8 | −0.315687 | ||||||||
\(505\) | 7.39432e6 | 0.00255493 | ||||||||
\(506\) | 6.45216e7 | 0.0221400 | ||||||||
\(507\) | 1.68186e9 | 0.573142 | ||||||||
\(508\) | 6.65908e8 | 0.225367 | ||||||||
\(509\) | −5.65113e8 | −0.189943 | −0.0949714 | − | 0.995480i | \(-0.530276\pi\) | ||||
−0.0949714 | + | 0.995480i | \(0.530276\pi\) | |||||||
\(510\) | 2.18270e8 | 0.0728614 | ||||||||
\(511\) | −5.24412e9 | −1.73860 | ||||||||
\(512\) | −3.51858e9 | −1.15857 | ||||||||
\(513\) | 7.49627e8 | 0.245151 | ||||||||
\(514\) | −9.28141e8 | −0.301469 | ||||||||
\(515\) | −1.91624e8 | −0.0618194 | ||||||||
\(516\) | 5.03886e8 | 0.161457 | ||||||||
\(517\) | −4.03265e8 | −0.128344 | ||||||||
\(518\) | −3.49486e9 | −1.10478 | ||||||||
\(519\) | −7.50889e9 | −2.35771 | ||||||||
\(520\) | 4.69494e7 | 0.0146426 | ||||||||
\(521\) | −5.02091e9 | −1.55543 | −0.777714 | − | 0.628618i | \(-0.783621\pi\) | ||||
−0.777714 | + | 0.628618i | \(0.783621\pi\) | |||||||
\(522\) | 2.99113e9 | 0.920424 | ||||||||
\(523\) | 4.46410e9 | 1.36452 | 0.682258 | − | 0.731112i | \(-0.260998\pi\) | ||||
0.682258 | + | 0.731112i | \(0.260998\pi\) | |||||||
\(524\) | −5.83815e8 | −0.177262 | ||||||||
\(525\) | 6.12195e9 | 1.84643 | ||||||||
\(526\) | 8.09126e9 | 2.42419 | ||||||||
\(527\) | −1.51816e8 | −0.0451836 | ||||||||
\(528\) | 2.45698e9 | 0.726413 | ||||||||
\(529\) | −3.40047e9 | −0.998720 | ||||||||
\(530\) | 3.67303e8 | 0.107166 | ||||||||
\(531\) | −1.51186e9 | −0.438207 | ||||||||
\(532\) | 3.56530e9 | 1.02661 | ||||||||
\(533\) | −3.99063e9 | −1.14155 | ||||||||
\(534\) | 8.45622e8 | 0.240315 | ||||||||
\(535\) | −3.40412e7 | −0.00961096 | ||||||||
\(536\) | 1.20655e9 | 0.338429 | ||||||||
\(537\) | 4.19756e9 | 1.16973 | ||||||||
\(538\) | 2.54469e9 | 0.704525 | ||||||||
\(539\) | −1.50295e9 | −0.413412 | ||||||||
\(540\) | −3.21751e7 | −0.00879310 | ||||||||
\(541\) | −4.10317e9 | −1.11411 | −0.557056 | − | 0.830475i | \(-0.688069\pi\) | ||||
−0.557056 | + | 0.830475i | \(0.688069\pi\) | |||||||
\(542\) | −5.50172e9 | −1.48423 | ||||||||
\(543\) | 7.84170e9 | 2.10189 | ||||||||
\(544\) | −4.50256e9 | −1.19912 | ||||||||
\(545\) | −2.48184e7 | −0.00656728 | ||||||||
\(546\) | 1.12343e10 | 2.95372 | ||||||||
\(547\) | −1.85474e9 | −0.484539 | −0.242269 | − | 0.970209i | \(-0.577892\pi\) | ||||
−0.242269 | + | 0.970209i | \(0.577892\pi\) | |||||||
\(548\) | 2.02520e9 | 0.525697 | ||||||||
\(549\) | 4.61930e9 | 1.19144 | ||||||||
\(550\) | −2.41002e9 | −0.617663 | ||||||||
\(551\) | 3.17168e9 | 0.807717 | ||||||||
\(552\) | 5.40058e7 | 0.0136664 | ||||||||
\(553\) | −9.78177e9 | −2.45969 | ||||||||
\(554\) | 3.85335e9 | 0.962841 | ||||||||
\(555\) | −1.40329e8 | −0.0348434 | ||||||||
\(556\) | 2.59419e9 | 0.640089 | ||||||||
\(557\) | −5.61884e9 | −1.37770 | −0.688848 | − | 0.724906i | \(-0.741883\pi\) | ||||
−0.688848 | + | 0.724906i | \(0.741883\pi\) | |||||||
\(558\) | −2.13147e8 | −0.0519350 | ||||||||
\(559\) | 7.52165e8 | 0.182126 | ||||||||
\(560\) | 2.88055e8 | 0.0693135 | ||||||||
\(561\) | 2.44435e9 | 0.584512 | ||||||||
\(562\) | 8.63247e9 | 2.05144 | ||||||||
\(563\) | −4.77175e9 | −1.12693 | −0.563467 | − | 0.826139i | \(-0.690533\pi\) | ||||
−0.563467 | + | 0.826139i | \(0.690533\pi\) | |||||||
\(564\) | 1.25085e9 | 0.293580 | ||||||||
\(565\) | 1.97503e7 | 0.00460686 | ||||||||
\(566\) | 3.12641e9 | 0.724749 | ||||||||
\(567\) | 6.90043e9 | 1.58977 | ||||||||
\(568\) | −1.31662e9 | −0.301469 | ||||||||
\(569\) | −3.47483e9 | −0.790753 | −0.395377 | − | 0.918519i | \(-0.629386\pi\) | ||||
−0.395377 | + | 0.918519i | \(0.629386\pi\) | |||||||
\(570\) | 3.24945e8 | 0.0734934 | ||||||||
\(571\) | 3.59894e9 | 0.809000 | 0.404500 | − | 0.914538i | \(-0.367446\pi\) | ||||
0.404500 | + | 0.914538i | \(0.367446\pi\) | |||||||
\(572\) | −1.94840e9 | −0.435304 | ||||||||
\(573\) | 4.67658e9 | 1.03845 | ||||||||
\(574\) | −7.96712e9 | −1.75837 | ||||||||
\(575\) | −1.62796e8 | −0.0357114 | ||||||||
\(576\) | −1.99792e9 | −0.435612 | ||||||||
\(577\) | 4.67766e9 | 1.01371 | 0.506855 | − | 0.862032i | \(-0.330808\pi\) | ||||
0.506855 | + | 0.862032i | \(0.330808\pi\) | |||||||
\(578\) | 7.30496e8 | 0.157351 | ||||||||
\(579\) | 5.71364e9 | 1.22331 | ||||||||
\(580\) | −1.36133e8 | −0.0289712 | ||||||||
\(581\) | −6.96163e9 | −1.47263 | ||||||||
\(582\) | −1.00533e10 | −2.11386 | ||||||||
\(583\) | 4.11334e9 | 0.859715 | ||||||||
\(584\) | 1.72798e9 | 0.359000 | ||||||||
\(585\) | 2.01530e8 | 0.0416192 | ||||||||
\(586\) | −1.23237e10 | −2.52988 | ||||||||
\(587\) | 5.27917e9 | 1.07729 | 0.538644 | − | 0.842533i | \(-0.318937\pi\) | ||||
0.538644 | + | 0.842533i | \(0.318937\pi\) | |||||||
\(588\) | 4.66184e9 | 0.945663 | ||||||||
\(589\) | −2.26014e8 | −0.0455755 | ||||||||
\(590\) | 1.56184e8 | 0.0313080 | ||||||||
\(591\) | −7.84348e9 | −1.56298 | ||||||||
\(592\) | 3.53901e9 | 0.701060 | ||||||||
\(593\) | −4.65728e9 | −0.917151 | −0.458575 | − | 0.888655i | \(-0.651640\pi\) | ||||
−0.458575 | + | 0.888655i | \(0.651640\pi\) | |||||||
\(594\) | −8.17876e8 | −0.160116 | ||||||||
\(595\) | 2.86574e8 | 0.0557735 | ||||||||
\(596\) | 2.88622e9 | 0.558429 | ||||||||
\(597\) | −1.10124e10 | −2.11823 | ||||||||
\(598\) | −2.98744e8 | −0.0571274 | ||||||||
\(599\) | −8.21418e9 | −1.56160 | −0.780801 | − | 0.624780i | \(-0.785189\pi\) | ||||
−0.780801 | + | 0.624780i | \(0.785189\pi\) | |||||||
\(600\) | −2.01724e9 | −0.381265 | ||||||||
\(601\) | 4.53542e9 | 0.852229 | 0.426115 | − | 0.904669i | \(-0.359882\pi\) | ||||
0.426115 | + | 0.904669i | \(0.359882\pi\) | |||||||
\(602\) | 1.50166e9 | 0.280534 | ||||||||
\(603\) | 5.17908e9 | 0.961926 | ||||||||
\(604\) | −6.73134e9 | −1.24300 | ||||||||
\(605\) | −1.84697e8 | −0.0339091 | ||||||||
\(606\) | −5.83014e8 | −0.106420 | ||||||||
\(607\) | 2.58768e9 | 0.469625 | 0.234812 | − | 0.972041i | \(-0.424552\pi\) | ||||
0.234812 | + | 0.972041i | \(0.424552\pi\) | |||||||
\(608\) | −6.70312e9 | −1.20952 | ||||||||
\(609\) | 8.79024e9 | 1.57703 | ||||||||
\(610\) | −4.77204e8 | −0.0851235 | ||||||||
\(611\) | 1.86717e9 | 0.331162 | ||||||||
\(612\) | −3.38731e9 | −0.597344 | ||||||||
\(613\) | 4.69723e9 | 0.823626 | 0.411813 | − | 0.911268i | \(-0.364896\pi\) | ||||
0.411813 | + | 0.911268i | \(0.364896\pi\) | |||||||
\(614\) | 2.27841e9 | 0.397231 | ||||||||
\(615\) | −3.19903e8 | −0.0554569 | ||||||||
\(616\) | 1.04969e9 | 0.180937 | ||||||||
\(617\) | −6.31709e9 | −1.08273 | −0.541363 | − | 0.840789i | \(-0.682092\pi\) | ||||
−0.541363 | + | 0.840789i | \(0.682092\pi\) | |||||||
\(618\) | 1.51088e10 | 2.57496 | ||||||||
\(619\) | 1.92907e9 | 0.326912 | 0.163456 | − | 0.986551i | \(-0.447736\pi\) | ||||
0.163456 | + | 0.986551i | \(0.447736\pi\) | |||||||
\(620\) | 9.70086e6 | 0.00163470 | ||||||||
\(621\) | −5.52473e7 | −0.00925742 | ||||||||
\(622\) | 9.97945e9 | 1.66280 | ||||||||
\(623\) | 1.11025e9 | 0.183955 | ||||||||
\(624\) | −1.13762e10 | −1.87435 | ||||||||
\(625\) | 6.06944e9 | 0.994417 | ||||||||
\(626\) | 5.24750e9 | 0.854953 | ||||||||
\(627\) | 3.63899e9 | 0.589582 | ||||||||
\(628\) | −8.51653e9 | −1.37216 | ||||||||
\(629\) | 3.52081e9 | 0.564112 | ||||||||
\(630\) | 4.02345e8 | 0.0641072 | ||||||||
\(631\) | −5.13248e9 | −0.813251 | −0.406626 | − | 0.913595i | \(-0.633295\pi\) | ||||
−0.406626 | + | 0.913595i | \(0.633295\pi\) | |||||||
\(632\) | 3.22318e9 | 0.507896 | ||||||||
\(633\) | 5.63047e9 | 0.882331 | ||||||||
\(634\) | 1.51028e10 | 2.35367 | ||||||||
\(635\) | 7.96842e7 | 0.0123499 | ||||||||
\(636\) | −1.27587e10 | −1.96656 | ||||||||
\(637\) | 6.95886e9 | 1.06672 | ||||||||
\(638\) | −3.46045e9 | −0.527546 | ||||||||
\(639\) | −5.65158e9 | −0.856874 | ||||||||
\(640\) | −1.58948e8 | −0.0239676 | ||||||||
\(641\) | −1.08820e10 | −1.63195 | −0.815976 | − | 0.578086i | \(-0.803800\pi\) | ||||
−0.815976 | + | 0.578086i | \(0.803800\pi\) | |||||||
\(642\) | 2.68402e9 | 0.400325 | ||||||||
\(643\) | 5.44950e9 | 0.808385 | 0.404192 | − | 0.914674i | \(-0.367553\pi\) | ||||
0.404192 | + | 0.914674i | \(0.367553\pi\) | |||||||
\(644\) | −2.62762e8 | −0.0387669 | ||||||||
\(645\) | 6.02962e7 | 0.00884771 | ||||||||
\(646\) | −8.15280e9 | −1.18985 | ||||||||
\(647\) | 2.41640e9 | 0.350754 | 0.175377 | − | 0.984501i | \(-0.443886\pi\) | ||||
0.175377 | + | 0.984501i | \(0.443886\pi\) | |||||||
\(648\) | −2.27375e9 | −0.328270 | ||||||||
\(649\) | 1.74907e9 | 0.251161 | ||||||||
\(650\) | 1.11587e10 | 1.59374 | ||||||||
\(651\) | −6.26392e8 | −0.0889842 | ||||||||
\(652\) | 6.44113e9 | 0.910114 | ||||||||
\(653\) | 7.41937e9 | 1.04273 | 0.521363 | − | 0.853335i | \(-0.325424\pi\) | ||||
0.521363 | + | 0.853335i | \(0.325424\pi\) | |||||||
\(654\) | 1.95683e9 | 0.273547 | ||||||||
\(655\) | −6.98608e7 | −0.00971380 | ||||||||
\(656\) | 8.06777e9 | 1.11581 | ||||||||
\(657\) | 7.41734e9 | 1.02040 | ||||||||
\(658\) | 3.72774e9 | 0.510099 | ||||||||
\(659\) | −4.19463e9 | −0.570945 | −0.285473 | − | 0.958387i | \(-0.592151\pi\) | ||||
−0.285473 | + | 0.958387i | \(0.592151\pi\) | |||||||
\(660\) | −1.56191e8 | −0.0211471 | ||||||||
\(661\) | −5.21211e9 | −0.701954 | −0.350977 | − | 0.936384i | \(-0.614151\pi\) | ||||
−0.350977 | + | 0.936384i | \(0.614151\pi\) | |||||||
\(662\) | −1.20494e10 | −1.61422 | ||||||||
\(663\) | −1.13177e10 | −1.50820 | ||||||||
\(664\) | 2.29392e9 | 0.304081 | ||||||||
\(665\) | 4.26633e8 | 0.0562573 | ||||||||
\(666\) | 4.94316e9 | 0.648402 | ||||||||
\(667\) | −2.33752e8 | −0.0305011 | ||||||||
\(668\) | −1.63843e9 | −0.212672 | ||||||||
\(669\) | −1.05645e10 | −1.36414 | ||||||||
\(670\) | −5.35032e8 | −0.0687255 | ||||||||
\(671\) | −5.34410e9 | −0.682882 | ||||||||
\(672\) | −1.85775e10 | −2.36154 | ||||||||
\(673\) | −1.45876e10 | −1.84473 | −0.922363 | − | 0.386325i | \(-0.873744\pi\) | ||||
−0.922363 | + | 0.386325i | \(0.873744\pi\) | |||||||
\(674\) | 1.66601e10 | 2.09589 | ||||||||
\(675\) | 2.06361e9 | 0.258264 | ||||||||
\(676\) | 2.69636e9 | 0.335711 | ||||||||
\(677\) | −5.06173e9 | −0.626958 | −0.313479 | − | 0.949595i | \(-0.601495\pi\) | ||||
−0.313479 | + | 0.949595i | \(0.601495\pi\) | |||||||
\(678\) | −1.55724e9 | −0.191890 | ||||||||
\(679\) | −1.31993e10 | −1.61810 | ||||||||
\(680\) | −9.44287e7 | −0.0115166 | ||||||||
\(681\) | 6.64318e9 | 0.806049 | ||||||||
\(682\) | 2.46591e8 | 0.0297668 | ||||||||
\(683\) | 3.88726e9 | 0.466844 | 0.233422 | − | 0.972376i | \(-0.425008\pi\) | ||||
0.233422 | + | 0.972376i | \(0.425008\pi\) | |||||||
\(684\) | −5.04280e9 | −0.602525 | ||||||||
\(685\) | 2.42340e8 | 0.0288077 | ||||||||
\(686\) | −1.66136e9 | −0.196485 | ||||||||
\(687\) | −1.83160e10 | −2.15517 | ||||||||
\(688\) | −1.52064e9 | −0.178019 | ||||||||
\(689\) | −1.90453e10 | −2.21831 | ||||||||
\(690\) | −2.39484e7 | −0.00277526 | ||||||||
\(691\) | −6.93681e9 | −0.799810 | −0.399905 | − | 0.916557i | \(-0.630957\pi\) | ||||
−0.399905 | + | 0.916557i | \(0.630957\pi\) | |||||||
\(692\) | −1.20383e10 | −1.38100 | ||||||||
\(693\) | 4.50577e9 | 0.514284 | ||||||||
\(694\) | 8.94045e9 | 1.01532 | ||||||||
\(695\) | 3.10428e8 | 0.0350763 | ||||||||
\(696\) | −2.89646e9 | −0.325638 | ||||||||
\(697\) | 8.02629e9 | 0.897842 | ||||||||
\(698\) | −1.75559e10 | −1.95402 | ||||||||
\(699\) | −1.71496e10 | −1.89926 | ||||||||
\(700\) | 9.81473e9 | 1.08152 | ||||||||
\(701\) | 3.87694e9 | 0.425085 | 0.212543 | − | 0.977152i | \(-0.431826\pi\) | ||||
0.212543 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(702\) | 3.78688e9 | 0.413144 | ||||||||
\(703\) | 5.24155e9 | 0.569005 | ||||||||
\(704\) | 2.31141e9 | 0.249673 | ||||||||
\(705\) | 1.49679e8 | 0.0160879 | ||||||||
\(706\) | 3.44883e9 | 0.368855 | ||||||||
\(707\) | −7.65460e8 | −0.0814619 | ||||||||
\(708\) | −5.42527e9 | −0.574520 | ||||||||
\(709\) | −1.10614e10 | −1.16559 | −0.582797 | − | 0.812618i | \(-0.698042\pi\) | ||||
−0.582797 | + | 0.812618i | \(0.698042\pi\) | |||||||
\(710\) | 5.83845e8 | 0.0612200 | ||||||||
\(711\) | 1.38354e10 | 1.44361 | ||||||||
\(712\) | −3.65836e8 | −0.0379846 | ||||||||
\(713\) | 1.66572e7 | 0.00172103 | ||||||||
\(714\) | −2.25953e10 | −2.32313 | ||||||||
\(715\) | −2.33151e8 | −0.0238542 | ||||||||
\(716\) | 6.72955e9 | 0.685157 | ||||||||
\(717\) | 1.42004e10 | 1.43875 | ||||||||
\(718\) | 2.03779e10 | 2.05458 | ||||||||
\(719\) | −1.72872e10 | −1.73450 | −0.867249 | − | 0.497875i | \(-0.834114\pi\) | ||||
−0.867249 | + | 0.497875i | \(0.834114\pi\) | |||||||
\(720\) | −4.07428e8 | −0.0406806 | ||||||||
\(721\) | 1.98369e10 | 1.97107 | ||||||||
\(722\) | 1.38345e9 | 0.136799 | ||||||||
\(723\) | 1.27351e10 | 1.25319 | ||||||||
\(724\) | 1.25718e10 | 1.23116 | ||||||||
\(725\) | 8.73116e9 | 0.850921 | ||||||||
\(726\) | 1.45627e10 | 1.41242 | ||||||||
\(727\) | 5.92252e9 | 0.571658 | 0.285829 | − | 0.958281i | \(-0.407731\pi\) | ||||
0.285829 | + | 0.958281i | \(0.407731\pi\) | |||||||
\(728\) | −4.86021e9 | −0.466869 | ||||||||
\(729\) | −6.12119e9 | −0.585180 | ||||||||
\(730\) | −7.66259e8 | −0.0729030 | ||||||||
\(731\) | −1.51282e9 | −0.143244 | ||||||||
\(732\) | 1.65763e10 | 1.56206 | ||||||||
\(733\) | 1.69133e10 | 1.58623 | 0.793114 | − | 0.609074i | \(-0.208459\pi\) | ||||
0.793114 | + | 0.609074i | \(0.208459\pi\) | |||||||
\(734\) | 1.47830e10 | 1.37983 | ||||||||
\(735\) | 5.57847e8 | 0.0518214 | ||||||||
\(736\) | 4.94018e8 | 0.0456741 | ||||||||
\(737\) | −5.99170e9 | −0.551333 | ||||||||
\(738\) | 1.12688e10 | 1.03200 | ||||||||
\(739\) | −2.73492e9 | −0.249281 | −0.124640 | − | 0.992202i | \(-0.539778\pi\) | ||||
−0.124640 | + | 0.992202i | \(0.539778\pi\) | |||||||
\(740\) | −2.24975e8 | −0.0204091 | ||||||||
\(741\) | −1.68490e10 | −1.52129 | ||||||||
\(742\) | −3.80232e10 | −3.41692 | ||||||||
\(743\) | −9.30626e9 | −0.832366 | −0.416183 | − | 0.909281i | \(-0.636632\pi\) | ||||
−0.416183 | + | 0.909281i | \(0.636632\pi\) | |||||||
\(744\) | 2.06402e8 | 0.0183742 | ||||||||
\(745\) | 3.45373e8 | 0.0306014 | ||||||||
\(746\) | −9.22803e9 | −0.813810 | ||||||||
\(747\) | 9.84659e9 | 0.864299 | ||||||||
\(748\) | 3.91879e9 | 0.342371 | ||||||||
\(749\) | 3.52395e9 | 0.306438 | ||||||||
\(750\) | 1.79072e9 | 0.154993 | ||||||||
\(751\) | 2.13212e9 | 0.183684 | 0.0918421 | − | 0.995774i | \(-0.470725\pi\) | ||||
0.0918421 | + | 0.995774i | \(0.470725\pi\) | |||||||
\(752\) | −3.77483e9 | −0.323694 | ||||||||
\(753\) | 2.87115e10 | 2.45061 | ||||||||
\(754\) | 1.60224e10 | 1.36122 | ||||||||
\(755\) | −8.05489e8 | −0.0681154 | ||||||||
\(756\) | 3.33077e9 | 0.280361 | ||||||||
\(757\) | 1.54717e10 | 1.29630 | 0.648148 | − | 0.761515i | \(-0.275544\pi\) | ||||
0.648148 | + | 0.761515i | \(0.275544\pi\) | |||||||
\(758\) | −5.28539e9 | −0.440793 | ||||||||
\(759\) | −2.68192e8 | −0.0222638 | ||||||||
\(760\) | −1.40579e8 | −0.0116165 | ||||||||
\(761\) | −1.05745e8 | −0.00869787 | −0.00434894 | − | 0.999991i | \(-0.501384\pi\) | ||||
−0.00434894 | + | 0.999991i | \(0.501384\pi\) | |||||||
\(762\) | −6.28279e9 | −0.514411 | ||||||||
\(763\) | 2.56920e9 | 0.209393 | ||||||||
\(764\) | 7.49750e9 | 0.608261 | ||||||||
\(765\) | −4.05334e8 | −0.0327339 | ||||||||
\(766\) | −1.05526e10 | −0.848321 | ||||||||
\(767\) | −8.09846e9 | −0.648065 | ||||||||
\(768\) | 2.16366e10 | 1.72356 | ||||||||
\(769\) | 1.45940e10 | 1.15726 | 0.578632 | − | 0.815589i | \(-0.303587\pi\) | ||||
0.578632 | + | 0.815589i | \(0.303587\pi\) | |||||||
\(770\) | −4.65475e8 | −0.0367434 | ||||||||
\(771\) | 3.85794e9 | 0.303155 | ||||||||
\(772\) | 9.16013e9 | 0.716541 | ||||||||
\(773\) | 7.67773e9 | 0.597867 | 0.298934 | − | 0.954274i | \(-0.403369\pi\) | ||||
0.298934 | + | 0.954274i | \(0.403369\pi\) | |||||||
\(774\) | −2.12397e9 | −0.164647 | ||||||||
\(775\) | −6.22182e8 | −0.0480133 | ||||||||
\(776\) | 4.34928e9 | 0.334119 | ||||||||
\(777\) | 1.45268e10 | 1.11096 | ||||||||
\(778\) | −2.57823e10 | −1.96288 | ||||||||
\(779\) | 1.19490e10 | 0.905630 | ||||||||
\(780\) | 7.23186e8 | 0.0545656 | ||||||||
\(781\) | 6.53835e9 | 0.491122 | ||||||||
\(782\) | 6.00859e8 | 0.0449313 | ||||||||
\(783\) | 2.96305e9 | 0.220583 | ||||||||
\(784\) | −1.40686e10 | −1.04266 | ||||||||
\(785\) | −1.01911e9 | −0.0751930 | ||||||||
\(786\) | 5.50826e9 | 0.404609 | ||||||||
\(787\) | −9.73198e9 | −0.711688 | −0.355844 | − | 0.934545i | \(-0.615807\pi\) | ||||
−0.355844 | + | 0.934545i | \(0.615807\pi\) | |||||||
\(788\) | −1.25747e10 | −0.915494 | ||||||||
\(789\) | −3.36324e10 | −2.43775 | ||||||||
\(790\) | −1.42929e9 | −0.103140 | ||||||||
\(791\) | −2.04456e9 | −0.146886 | ||||||||
\(792\) | −1.48469e9 | −0.106194 | ||||||||
\(793\) | 2.47439e10 | 1.76203 | ||||||||
\(794\) | 2.28988e8 | 0.0162345 | ||||||||
\(795\) | −1.52674e9 | −0.107766 | ||||||||
\(796\) | −1.76551e10 | −1.24073 | ||||||||
\(797\) | −4.83086e9 | −0.338003 | −0.169001 | − | 0.985616i | \(-0.554054\pi\) | ||||
−0.169001 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(798\) | −3.36384e10 | −2.34328 | ||||||||
\(799\) | −3.75542e9 | −0.260462 | ||||||||
\(800\) | −1.84527e10 | −1.27422 | ||||||||
\(801\) | −1.57035e9 | −0.107965 | ||||||||
\(802\) | 1.79479e10 | 1.22858 | ||||||||
\(803\) | −8.58116e9 | −0.584846 | ||||||||
\(804\) | 1.85850e10 | 1.26115 | ||||||||
\(805\) | −3.14427e7 | −0.00212439 | ||||||||
\(806\) | −1.14175e9 | −0.0768067 | ||||||||
\(807\) | −1.05773e10 | −0.708465 | ||||||||
\(808\) | 2.52226e8 | 0.0168209 | ||||||||
\(809\) | 1.46263e10 | 0.971216 | 0.485608 | − | 0.874177i | \(-0.338598\pi\) | ||||
0.485608 | + | 0.874177i | \(0.338598\pi\) | |||||||
\(810\) | 1.00828e9 | 0.0666625 | ||||||||
\(811\) | 2.93692e9 | 0.193339 | 0.0966694 | − | 0.995317i | \(-0.469181\pi\) | ||||
0.0966694 | + | 0.995317i | \(0.469181\pi\) | |||||||
\(812\) | 1.40925e10 | 0.923727 | ||||||||
\(813\) | 2.28686e10 | 1.49253 | ||||||||
\(814\) | −5.71876e9 | −0.371635 | ||||||||
\(815\) | 7.70762e8 | 0.0498734 | ||||||||
\(816\) | 2.28807e10 | 1.47419 | ||||||||
\(817\) | −2.25218e9 | −0.144486 | ||||||||
\(818\) | −2.69285e10 | −1.72019 | ||||||||
\(819\) | −2.08624e10 | −1.32700 | ||||||||
\(820\) | −5.12869e8 | −0.0324832 | ||||||||
\(821\) | 1.70106e10 | 1.07280 | 0.536401 | − | 0.843964i | \(-0.319784\pi\) | ||||
0.536401 | + | 0.843964i | \(0.319784\pi\) | |||||||
\(822\) | −1.91076e10 | −1.19993 | ||||||||
\(823\) | 7.47291e9 | 0.467294 | 0.233647 | − | 0.972321i | \(-0.424934\pi\) | ||||
0.233647 | + | 0.972321i | \(0.424934\pi\) | |||||||
\(824\) | −6.53644e9 | −0.407002 | ||||||||
\(825\) | 1.00176e10 | 0.621118 | ||||||||
\(826\) | −1.61682e10 | −0.998234 | ||||||||
\(827\) | −2.00025e10 | −1.22975 | −0.614873 | − | 0.788626i | \(-0.710793\pi\) | ||||
−0.614873 | + | 0.788626i | \(0.710793\pi\) | |||||||
\(828\) | 3.71653e8 | 0.0227526 | ||||||||
\(829\) | −8.27952e9 | −0.504736 | −0.252368 | − | 0.967631i | \(-0.581209\pi\) | ||||
−0.252368 | + | 0.967631i | \(0.581209\pi\) | |||||||
\(830\) | −1.01722e9 | −0.0617504 | ||||||||
\(831\) | −1.60170e10 | −0.968226 | ||||||||
\(832\) | −1.07021e10 | −0.644226 | ||||||||
\(833\) | −1.39963e10 | −0.838985 | ||||||||
\(834\) | −2.44760e10 | −1.46103 | ||||||||
\(835\) | −1.96059e8 | −0.0116542 | ||||||||
\(836\) | 5.83404e9 | 0.345340 | ||||||||
\(837\) | −2.11146e8 | −0.0124464 | ||||||||
\(838\) | −1.91323e10 | −1.12309 | ||||||||
\(839\) | 1.26666e10 | 0.740443 | 0.370222 | − | 0.928943i | \(-0.379282\pi\) | ||||
0.370222 | + | 0.928943i | \(0.379282\pi\) | |||||||
\(840\) | −3.89612e8 | −0.0226806 | ||||||||
\(841\) | −4.71317e9 | −0.273229 | ||||||||
\(842\) | −3.20108e9 | −0.184801 | ||||||||
\(843\) | −3.58820e10 | −2.06291 | ||||||||
\(844\) | 9.02679e9 | 0.516814 | ||||||||
\(845\) | 3.22654e8 | 0.0183966 | ||||||||
\(846\) | −5.27255e9 | −0.299381 | ||||||||
\(847\) | 1.91199e10 | 1.08117 | ||||||||
\(848\) | 3.85036e10 | 2.16828 | ||||||||
\(849\) | −1.29953e10 | −0.728803 | ||||||||
\(850\) | −2.24434e10 | −1.25350 | ||||||||
\(851\) | −3.86301e8 | −0.0214868 | ||||||||
\(852\) | −2.02806e10 | −1.12342 | ||||||||
\(853\) | −3.00382e10 | −1.65711 | −0.828556 | − | 0.559906i | \(-0.810837\pi\) | ||||
−0.828556 | + | 0.559906i | \(0.810837\pi\) | |||||||
\(854\) | 4.94002e10 | 2.71410 | ||||||||
\(855\) | −6.03434e8 | −0.0330178 | ||||||||
\(856\) | −1.16117e9 | −0.0632759 | ||||||||
\(857\) | 1.76722e10 | 0.959088 | 0.479544 | − | 0.877518i | \(-0.340802\pi\) | ||||
0.479544 | + | 0.877518i | \(0.340802\pi\) | |||||||
\(858\) | 1.83830e10 | 0.993600 | ||||||||
\(859\) | 1.84797e9 | 0.0994763 | 0.0497382 | − | 0.998762i | \(-0.484161\pi\) | ||||
0.0497382 | + | 0.998762i | \(0.484161\pi\) | |||||||
\(860\) | 9.66671e7 | 0.00518244 | ||||||||
\(861\) | 3.31164e10 | 1.76820 | ||||||||
\(862\) | −4.54240e9 | −0.241551 | ||||||||
\(863\) | −5.58485e9 | −0.295784 | −0.147892 | − | 0.989004i | \(-0.547249\pi\) | ||||
−0.147892 | + | 0.989004i | \(0.547249\pi\) | |||||||
\(864\) | −6.26218e9 | −0.330314 | ||||||||
\(865\) | −1.44053e9 | −0.0756774 | ||||||||
\(866\) | 2.14231e10 | 1.12091 | ||||||||
\(867\) | −3.03640e9 | −0.158231 | ||||||||
\(868\) | −1.00423e9 | −0.0521214 | ||||||||
\(869\) | −1.60063e10 | −0.827411 | ||||||||
\(870\) | 1.28441e9 | 0.0661281 | ||||||||
\(871\) | 2.77424e10 | 1.42259 | ||||||||
\(872\) | −8.46574e8 | −0.0432372 | ||||||||
\(873\) | 1.86692e10 | 0.949677 | ||||||||
\(874\) | 8.94519e8 | 0.0453210 | ||||||||
\(875\) | 2.35110e9 | 0.118643 | ||||||||
\(876\) | 2.66170e10 | 1.33781 | ||||||||
\(877\) | −2.49280e10 | −1.24793 | −0.623963 | − | 0.781454i | \(-0.714478\pi\) | ||||
−0.623963 | + | 0.781454i | \(0.714478\pi\) | |||||||
\(878\) | −2.30179e10 | −1.14772 | ||||||||
\(879\) | 5.12251e10 | 2.54403 | ||||||||
\(880\) | 4.71356e8 | 0.0233163 | ||||||||
\(881\) | −7.08433e9 | −0.349047 | −0.174523 | − | 0.984653i | \(-0.555838\pi\) | ||||
−0.174523 | + | 0.984653i | \(0.555838\pi\) | |||||||
\(882\) | −1.96505e10 | −0.964347 | ||||||||
\(883\) | −1.79072e9 | −0.0875316 | −0.0437658 | − | 0.999042i | \(-0.513936\pi\) | ||||
−0.0437658 | + | 0.999042i | \(0.513936\pi\) | |||||||
\(884\) | −1.81446e10 | −0.883412 | ||||||||
\(885\) | −6.49201e8 | −0.0314831 | ||||||||
\(886\) | −4.25457e9 | −0.205512 | ||||||||
\(887\) | 6.97503e9 | 0.335593 | 0.167797 | − | 0.985822i | \(-0.446335\pi\) | ||||
0.167797 | + | 0.985822i | \(0.446335\pi\) | |||||||
\(888\) | −4.78672e9 | −0.229399 | ||||||||
\(889\) | −8.24891e9 | −0.393768 | ||||||||
\(890\) | 1.62227e8 | 0.00771361 | ||||||||
\(891\) | 1.12914e10 | 0.534783 | ||||||||
\(892\) | −1.69371e10 | −0.799026 | ||||||||
\(893\) | −5.59082e9 | −0.262722 | ||||||||
\(894\) | −2.72313e10 | −1.27464 | ||||||||
\(895\) | 8.05275e8 | 0.0375460 | ||||||||
\(896\) | 1.64543e10 | 0.764189 | ||||||||
\(897\) | 1.24177e9 | 0.0574470 | ||||||||
\(898\) | −3.13423e10 | −1.44432 | ||||||||
\(899\) | −8.93364e8 | −0.0410081 | ||||||||
\(900\) | −1.38821e10 | −0.634753 | ||||||||
\(901\) | 3.83056e10 | 1.74472 | ||||||||
\(902\) | −1.30369e10 | −0.591495 | ||||||||
\(903\) | −6.24187e9 | −0.282103 | ||||||||
\(904\) | 6.73699e8 | 0.0303303 | ||||||||
\(905\) | 1.50438e9 | 0.0674663 | ||||||||
\(906\) | 6.35097e10 | 2.83721 | ||||||||
\(907\) | −6.43630e9 | −0.286425 | −0.143213 | − | 0.989692i | \(-0.545743\pi\) | ||||
−0.143213 | + | 0.989692i | \(0.545743\pi\) | |||||||
\(908\) | 1.06504e10 | 0.472133 | ||||||||
\(909\) | 1.08267e9 | 0.0478106 | ||||||||
\(910\) | 2.15522e9 | 0.0948082 | ||||||||
\(911\) | 1.55350e10 | 0.680766 | 0.340383 | − | 0.940287i | \(-0.389443\pi\) | ||||
0.340383 | + | 0.940287i | \(0.389443\pi\) | |||||||
\(912\) | 3.40633e10 | 1.48698 | ||||||||
\(913\) | −1.13916e10 | −0.495377 | ||||||||
\(914\) | −9.35302e9 | −0.405173 | ||||||||
\(915\) | 1.98356e9 | 0.0855996 | ||||||||
\(916\) | −2.93642e10 | −1.26236 | ||||||||
\(917\) | 7.23199e9 | 0.309717 | ||||||||
\(918\) | −7.61650e9 | −0.324942 | ||||||||
\(919\) | 3.73555e10 | 1.58763 | 0.793816 | − | 0.608158i | \(-0.208091\pi\) | ||||
0.793816 | + | 0.608158i | \(0.208091\pi\) | |||||||
\(920\) | 1.03607e7 | 0.000438662 0 | ||||||||
\(921\) | −9.47051e9 | −0.399452 | ||||||||
\(922\) | −1.58096e10 | −0.664297 | ||||||||
\(923\) | −3.02735e10 | −1.26723 | ||||||||
\(924\) | 1.61689e10 | 0.674261 | ||||||||
\(925\) | 1.44292e10 | 0.599440 | ||||||||
\(926\) | 9.37622e9 | 0.388051 | ||||||||
\(927\) | −2.80576e10 | −1.15683 | ||||||||
\(928\) | −2.64954e10 | −1.08831 | ||||||||
\(929\) | 2.51045e10 | 1.02730 | 0.513649 | − | 0.858001i | \(-0.328294\pi\) | ||||
0.513649 | + | 0.858001i | \(0.328294\pi\) | |||||||
\(930\) | −9.15270e7 | −0.00373129 | ||||||||
\(931\) | −2.08367e10 | −0.846262 | ||||||||
\(932\) | −2.74943e10 | −1.11247 | ||||||||
\(933\) | −4.14809e10 | −1.67210 | ||||||||
\(934\) | 6.33240e10 | 2.54305 | ||||||||
\(935\) | 4.68933e8 | 0.0187616 | ||||||||
\(936\) | 6.87433e9 | 0.274009 | ||||||||
\(937\) | −3.29027e10 | −1.30660 | −0.653300 | − | 0.757099i | \(-0.726616\pi\) | ||||
−0.653300 | + | 0.757099i | \(0.726616\pi\) | |||||||
\(938\) | 5.53866e10 | 2.19126 | ||||||||
\(939\) | −2.18119e10 | −0.859734 | ||||||||
\(940\) | 2.39967e8 | 0.00942330 | ||||||||
\(941\) | 1.27046e10 | 0.497048 | 0.248524 | − | 0.968626i | \(-0.420054\pi\) | ||||
0.248524 | + | 0.968626i | \(0.420054\pi\) | |||||||
\(942\) | 8.03529e10 | 3.13201 | ||||||||
\(943\) | −8.80638e8 | −0.0341985 | ||||||||
\(944\) | 1.63725e10 | 0.633450 | ||||||||
\(945\) | 3.98568e8 | 0.0153635 | ||||||||
\(946\) | 2.45723e9 | 0.0943685 | ||||||||
\(947\) | −2.04335e9 | −0.0781840 | −0.0390920 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390920 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(948\) | 4.96482e10 | 1.89267 | ||||||||
\(949\) | 3.97320e10 | 1.50907 | ||||||||
\(950\) | −3.34123e10 | −1.26437 | ||||||||
\(951\) | −6.27769e10 | −2.36684 | ||||||||
\(952\) | 9.77527e9 | 0.367197 | ||||||||
\(953\) | −1.23244e10 | −0.461253 | −0.230626 | − | 0.973042i | \(-0.574078\pi\) | ||||
−0.230626 | + | 0.973042i | \(0.574078\pi\) | |||||||
\(954\) | 5.37804e10 | 2.00542 | ||||||||
\(955\) | 8.97170e8 | 0.0333321 | ||||||||
\(956\) | 2.27662e10 | 0.842729 | ||||||||
\(957\) | 1.43838e10 | 0.530496 | ||||||||
\(958\) | −3.27520e10 | −1.20353 | ||||||||
\(959\) | −2.50871e10 | −0.918512 | ||||||||
\(960\) | −8.57921e8 | −0.0312967 | ||||||||
\(961\) | −2.74490e10 | −0.997686 | ||||||||
\(962\) | 2.64787e10 | 0.958923 | ||||||||
\(963\) | −4.98431e9 | −0.179851 | ||||||||
\(964\) | 2.04169e10 | 0.734041 | ||||||||
\(965\) | 1.09612e9 | 0.0392658 | ||||||||
\(966\) | 2.47914e9 | 0.0884873 | ||||||||
\(967\) | 1.28161e10 | 0.455788 | 0.227894 | − | 0.973686i | \(-0.426816\pi\) | ||||
0.227894 | + | 0.973686i | \(0.426816\pi\) | |||||||
\(968\) | −6.30017e9 | −0.223248 | ||||||||
\(969\) | 3.38882e10 | 1.19651 | ||||||||
\(970\) | −1.92865e9 | −0.0678504 | ||||||||
\(971\) | 2.66467e10 | 0.934063 | 0.467032 | − | 0.884241i | \(-0.345323\pi\) | ||||
0.467032 | + | 0.884241i | \(0.345323\pi\) | |||||||
\(972\) | −2.91899e10 | −1.01953 | ||||||||
\(973\) | −3.21355e10 | −1.11838 | ||||||||
\(974\) | 6.11889e10 | 2.12186 | ||||||||
\(975\) | −4.63828e10 | −1.60266 | ||||||||
\(976\) | −5.00243e10 | −1.72229 | ||||||||
\(977\) | 8.47518e9 | 0.290749 | 0.145374 | − | 0.989377i | \(-0.453561\pi\) | ||||
0.145374 | + | 0.989377i | \(0.453561\pi\) | |||||||
\(978\) | −6.07716e10 | −2.07738 | ||||||||
\(979\) | 1.81674e9 | 0.0618805 | ||||||||
\(980\) | 8.94342e8 | 0.0303538 | ||||||||
\(981\) | −3.63390e9 | −0.122894 | ||||||||
\(982\) | −3.97863e10 | −1.34074 | ||||||||
\(983\) | −2.76800e9 | −0.0929455 | −0.0464727 | − | 0.998920i | \(-0.514798\pi\) | ||||
−0.0464727 | + | 0.998920i | \(0.514798\pi\) | |||||||
\(984\) | −1.09121e10 | −0.365113 | ||||||||
\(985\) | −1.50472e9 | −0.0501682 | ||||||||
\(986\) | −3.22255e10 | −1.07061 | ||||||||
\(987\) | −1.54948e10 | −0.512952 | ||||||||
\(988\) | −2.70124e10 | −0.891075 | ||||||||
\(989\) | 1.65985e8 | 0.00545610 | ||||||||
\(990\) | 6.58373e8 | 0.0215650 | ||||||||
\(991\) | 2.88798e10 | 0.942621 | 0.471310 | − | 0.881967i | \(-0.343781\pi\) | ||||
0.471310 | + | 0.881967i | \(0.343781\pi\) | |||||||
\(992\) | 1.88806e9 | 0.0614080 | ||||||||
\(993\) | 5.00850e10 | 1.62325 | ||||||||
\(994\) | −6.04397e10 | −1.95196 | ||||||||
\(995\) | −2.11266e9 | −0.0679906 | ||||||||
\(996\) | 3.53343e10 | 1.13315 | ||||||||
\(997\) | 4.99664e9 | 0.159678 | 0.0798390 | − | 0.996808i | \(-0.474559\pi\) | ||||
0.0798390 | + | 0.996808i | \(0.474559\pi\) | |||||||
\(998\) | −4.69187e9 | −0.149413 | ||||||||
\(999\) | 4.89675e9 | 0.155392 |
(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 | 43.8.a.a.1.3 | ✓ | 11 | |
3.2 | odd | 2 | 387.8.a.b.1.9 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.a.a.1.3 | ✓ | 11 | 1.1 | even | 1 | trivial | |
387.8.a.b.1.9 | 11 | 3.2 | odd | 2 |