Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,8,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(178.059464526\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4122x^{2} - 49773x + 620550 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.65975\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.00000 | 0.707107 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | 125.000 | 0.447214 | ||||||||
\(6\) | −216.000 | −0.408248 | ||||||||
\(7\) | −1165.98 | −1.28484 | −0.642420 | − | 0.766353i | \(-0.722069\pi\) | ||||
−0.642420 | + | 0.766353i | \(0.722069\pi\) | |||||||
\(8\) | 512.000 | 0.353553 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 1000.00 | 0.316228 | ||||||||
\(11\) | −144.005 | −0.0326214 | −0.0163107 | − | 0.999867i | \(-0.505192\pi\) | ||||
−0.0163107 | + | 0.999867i | \(0.505192\pi\) | |||||||
\(12\) | −1728.00 | −0.288675 | ||||||||
\(13\) | −3048.40 | −0.384832 | −0.192416 | − | 0.981313i | \(-0.561632\pi\) | ||||
−0.192416 | + | 0.981313i | \(0.561632\pi\) | |||||||
\(14\) | −9327.86 | −0.908519 | ||||||||
\(15\) | −3375.00 | −0.258199 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | 6703.52 | 0.330926 | 0.165463 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165463 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(18\) | 5832.00 | 0.235702 | ||||||||
\(19\) | 6859.00 | 0.229416 | ||||||||
\(20\) | 8000.00 | 0.223607 | ||||||||
\(21\) | 31481.5 | 0.741802 | ||||||||
\(22\) | −1152.04 | −0.0230668 | ||||||||
\(23\) | 15414.7 | 0.264172 | 0.132086 | − | 0.991238i | \(-0.457832\pi\) | ||||
0.132086 | + | 0.991238i | \(0.457832\pi\) | |||||||
\(24\) | −13824.0 | −0.204124 | ||||||||
\(25\) | 15625.0 | 0.200000 | ||||||||
\(26\) | −24387.2 | −0.272117 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −74622.9 | −0.642420 | ||||||||
\(29\) | 180651. | 1.37546 | 0.687730 | − | 0.725967i | \(-0.258607\pi\) | ||||
0.687730 | + | 0.725967i | \(0.258607\pi\) | |||||||
\(30\) | −27000.0 | −0.182574 | ||||||||
\(31\) | 173839. | 1.04805 | 0.524023 | − | 0.851704i | \(-0.324431\pi\) | ||||
0.524023 | + | 0.851704i | \(0.324431\pi\) | |||||||
\(32\) | 32768.0 | 0.176777 | ||||||||
\(33\) | 3888.13 | 0.0188340 | ||||||||
\(34\) | 53628.1 | 0.234000 | ||||||||
\(35\) | −145748. | −0.574598 | ||||||||
\(36\) | 46656.0 | 0.166667 | ||||||||
\(37\) | −452052. | −1.46718 | −0.733588 | − | 0.679595i | \(-0.762156\pi\) | ||||
−0.733588 | + | 0.679595i | \(0.762156\pi\) | |||||||
\(38\) | 54872.0 | 0.162221 | ||||||||
\(39\) | 82306.9 | 0.222183 | ||||||||
\(40\) | 64000.0 | 0.158114 | ||||||||
\(41\) | 338502. | 0.767040 | 0.383520 | − | 0.923533i | \(-0.374712\pi\) | ||||
0.383520 | + | 0.923533i | \(0.374712\pi\) | |||||||
\(42\) | 251852. | 0.524534 | ||||||||
\(43\) | −357281. | −0.685283 | −0.342642 | − | 0.939466i | \(-0.611322\pi\) | ||||
−0.342642 | + | 0.939466i | \(0.611322\pi\) | |||||||
\(44\) | −9216.30 | −0.0163107 | ||||||||
\(45\) | 91125.0 | 0.149071 | ||||||||
\(46\) | 123318. | 0.186798 | ||||||||
\(47\) | −486670. | −0.683741 | −0.341871 | − | 0.939747i | \(-0.611060\pi\) | ||||
−0.341871 | + | 0.939747i | \(0.611060\pi\) | |||||||
\(48\) | −110592. | −0.144338 | ||||||||
\(49\) | 535972. | 0.650813 | ||||||||
\(50\) | 125000. | 0.141421 | ||||||||
\(51\) | −180995. | −0.191060 | ||||||||
\(52\) | −195098. | −0.192416 | ||||||||
\(53\) | −1.80340e6 | −1.66389 | −0.831947 | − | 0.554856i | \(-0.812773\pi\) | ||||
−0.831947 | + | 0.554856i | \(0.812773\pi\) | |||||||
\(54\) | −157464. | −0.136083 | ||||||||
\(55\) | −18000.6 | −0.0145887 | ||||||||
\(56\) | −596983. | −0.454259 | ||||||||
\(57\) | −185193. | −0.132453 | ||||||||
\(58\) | 1.44521e6 | 0.972597 | ||||||||
\(59\) | 1.20379e6 | 0.763076 | 0.381538 | − | 0.924353i | \(-0.375395\pi\) | ||||
0.381538 | + | 0.924353i | \(0.375395\pi\) | |||||||
\(60\) | −216000. | −0.129099 | ||||||||
\(61\) | −614829. | −0.346817 | −0.173408 | − | 0.984850i | \(-0.555478\pi\) | ||||
−0.173408 | + | 0.984850i | \(0.555478\pi\) | |||||||
\(62\) | 1.39071e6 | 0.741080 | ||||||||
\(63\) | −850001. | −0.428280 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −381051. | −0.172102 | ||||||||
\(66\) | 31105.0 | 0.0133176 | ||||||||
\(67\) | 2.28349e6 | 0.927552 | 0.463776 | − | 0.885953i | \(-0.346494\pi\) | ||||
0.463776 | + | 0.885953i | \(0.346494\pi\) | |||||||
\(68\) | 429025. | 0.165463 | ||||||||
\(69\) | −416197. | −0.152520 | ||||||||
\(70\) | −1.16598e6 | −0.406302 | ||||||||
\(71\) | 2.30022e6 | 0.762721 | 0.381361 | − | 0.924426i | \(-0.375456\pi\) | ||||
0.381361 | + | 0.924426i | \(0.375456\pi\) | |||||||
\(72\) | 373248. | 0.117851 | ||||||||
\(73\) | −1.41070e6 | −0.424427 | −0.212214 | − | 0.977223i | \(-0.568067\pi\) | ||||
−0.212214 | + | 0.977223i | \(0.568067\pi\) | |||||||
\(74\) | −3.61641e6 | −1.03745 | ||||||||
\(75\) | −421875. | −0.115470 | ||||||||
\(76\) | 438976. | 0.114708 | ||||||||
\(77\) | 167907. | 0.0419133 | ||||||||
\(78\) | 658455. | 0.157107 | ||||||||
\(79\) | −5.82643e6 | −1.32956 | −0.664779 | − | 0.747040i | \(-0.731474\pi\) | ||||
−0.664779 | + | 0.747040i | \(0.731474\pi\) | |||||||
\(80\) | 512000. | 0.111803 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 2.70802e6 | 0.542379 | ||||||||
\(83\) | 5.65567e6 | 1.08570 | 0.542851 | − | 0.839829i | \(-0.317345\pi\) | ||||
0.542851 | + | 0.839829i | \(0.317345\pi\) | |||||||
\(84\) | 2.01482e6 | 0.370901 | ||||||||
\(85\) | 837939. | 0.147995 | ||||||||
\(86\) | −2.85825e6 | −0.484569 | ||||||||
\(87\) | −4.87758e6 | −0.794122 | ||||||||
\(88\) | −73730.4 | −0.0115334 | ||||||||
\(89\) | 5.01119e6 | 0.753487 | 0.376743 | − | 0.926318i | \(-0.377044\pi\) | ||||
0.376743 | + | 0.926318i | \(0.377044\pi\) | |||||||
\(90\) | 729000. | 0.105409 | ||||||||
\(91\) | 3.55439e6 | 0.494447 | ||||||||
\(92\) | 986540. | 0.132086 | ||||||||
\(93\) | −4.69364e6 | −0.605090 | ||||||||
\(94\) | −3.89336e6 | −0.483478 | ||||||||
\(95\) | 857375. | 0.102598 | ||||||||
\(96\) | −884736. | −0.102062 | ||||||||
\(97\) | −5.52163e6 | −0.614280 | −0.307140 | − | 0.951664i | \(-0.599372\pi\) | ||||
−0.307140 | + | 0.951664i | \(0.599372\pi\) | |||||||
\(98\) | 4.28778e6 | 0.460194 | ||||||||
\(99\) | −104979. | −0.0108738 | ||||||||
\(100\) | 1.00000e6 | 0.100000 | ||||||||
\(101\) | −1.91291e7 | −1.84743 | −0.923717 | − | 0.383076i | \(-0.874865\pi\) | ||||
−0.923717 | + | 0.383076i | \(0.874865\pi\) | |||||||
\(102\) | −1.44796e6 | −0.135100 | ||||||||
\(103\) | −1.88635e7 | −1.70095 | −0.850476 | − | 0.526013i | \(-0.823686\pi\) | ||||
−0.850476 | + | 0.526013i | \(0.823686\pi\) | |||||||
\(104\) | −1.56078e6 | −0.136059 | ||||||||
\(105\) | 3.93519e6 | 0.331744 | ||||||||
\(106\) | −1.44272e7 | −1.17655 | ||||||||
\(107\) | −7.28717e6 | −0.575063 | −0.287532 | − | 0.957771i | \(-0.592835\pi\) | ||||
−0.287532 | + | 0.957771i | \(0.592835\pi\) | |||||||
\(108\) | −1.25971e6 | −0.0962250 | ||||||||
\(109\) | −6.73832e6 | −0.498378 | −0.249189 | − | 0.968455i | \(-0.580164\pi\) | ||||
−0.249189 | + | 0.968455i | \(0.580164\pi\) | |||||||
\(110\) | −144005. | −0.0103158 | ||||||||
\(111\) | 1.22054e7 | 0.847074 | ||||||||
\(112\) | −4.77586e6 | −0.321210 | ||||||||
\(113\) | −1.27998e7 | −0.834507 | −0.417254 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417254 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(114\) | −1.48154e6 | −0.0936586 | ||||||||
\(115\) | 1.92684e6 | 0.118141 | ||||||||
\(116\) | 1.15617e7 | 0.687730 | ||||||||
\(117\) | −2.22229e6 | −0.128277 | ||||||||
\(118\) | 9.63030e6 | 0.539576 | ||||||||
\(119\) | −7.81618e6 | −0.425187 | ||||||||
\(120\) | −1.72800e6 | −0.0912871 | ||||||||
\(121\) | −1.94664e7 | −0.998936 | ||||||||
\(122\) | −4.91864e6 | −0.245237 | ||||||||
\(123\) | −9.13956e6 | −0.442851 | ||||||||
\(124\) | 1.11257e7 | 0.524023 | ||||||||
\(125\) | 1.95312e6 | 0.0894427 | ||||||||
\(126\) | −6.80001e6 | −0.302840 | ||||||||
\(127\) | 2.56926e7 | 1.11300 | 0.556501 | − | 0.830847i | \(-0.312144\pi\) | ||||
0.556501 | + | 0.830847i | \(0.312144\pi\) | |||||||
\(128\) | 2.09715e6 | 0.0883883 | ||||||||
\(129\) | 9.64659e6 | 0.395649 | ||||||||
\(130\) | −3.04840e6 | −0.121694 | ||||||||
\(131\) | 2.74701e7 | 1.06760 | 0.533802 | − | 0.845609i | \(-0.320763\pi\) | ||||
0.533802 | + | 0.845609i | \(0.320763\pi\) | |||||||
\(132\) | 248840. | 0.00941698 | ||||||||
\(133\) | −7.99747e6 | −0.294762 | ||||||||
\(134\) | 1.82680e7 | 0.655878 | ||||||||
\(135\) | −2.46038e6 | −0.0860663 | ||||||||
\(136\) | 3.43220e6 | 0.117000 | ||||||||
\(137\) | 5.09858e7 | 1.69405 | 0.847026 | − | 0.531551i | \(-0.178391\pi\) | ||||
0.847026 | + | 0.531551i | \(0.178391\pi\) | |||||||
\(138\) | −3.32957e6 | −0.107848 | ||||||||
\(139\) | −3.63943e7 | −1.14943 | −0.574714 | − | 0.818354i | \(-0.694887\pi\) | ||||
−0.574714 | + | 0.818354i | \(0.694887\pi\) | |||||||
\(140\) | −9.32786e6 | −0.287299 | ||||||||
\(141\) | 1.31401e7 | 0.394758 | ||||||||
\(142\) | 1.84018e7 | 0.539325 | ||||||||
\(143\) | 438985. | 0.0125537 | ||||||||
\(144\) | 2.98598e6 | 0.0833333 | ||||||||
\(145\) | 2.25814e7 | 0.615124 | ||||||||
\(146\) | −1.12856e7 | −0.300115 | ||||||||
\(147\) | −1.44713e7 | −0.375747 | ||||||||
\(148\) | −2.89313e7 | −0.733588 | ||||||||
\(149\) | 6.18264e7 | 1.53117 | 0.765583 | − | 0.643337i | \(-0.222451\pi\) | ||||
0.765583 | + | 0.643337i | \(0.222451\pi\) | |||||||
\(150\) | −3.37500e6 | −0.0816497 | ||||||||
\(151\) | −5.50315e7 | −1.30074 | −0.650372 | − | 0.759616i | \(-0.725387\pi\) | ||||
−0.650372 | + | 0.759616i | \(0.725387\pi\) | |||||||
\(152\) | 3.51181e6 | 0.0811107 | ||||||||
\(153\) | 4.88686e6 | 0.110309 | ||||||||
\(154\) | 1.34326e6 | 0.0296371 | ||||||||
\(155\) | 2.17298e7 | 0.468700 | ||||||||
\(156\) | 5.26764e6 | 0.111091 | ||||||||
\(157\) | −8.57283e7 | −1.76797 | −0.883986 | − | 0.467513i | \(-0.845150\pi\) | ||||
−0.883986 | + | 0.467513i | \(0.845150\pi\) | |||||||
\(158\) | −4.66114e7 | −0.940140 | ||||||||
\(159\) | 4.86917e7 | 0.960649 | ||||||||
\(160\) | 4.09600e6 | 0.0790569 | ||||||||
\(161\) | −1.79733e7 | −0.339419 | ||||||||
\(162\) | 4.25153e6 | 0.0785674 | ||||||||
\(163\) | 8.87150e7 | 1.60450 | 0.802251 | − | 0.596987i | \(-0.203636\pi\) | ||||
0.802251 | + | 0.596987i | \(0.203636\pi\) | |||||||
\(164\) | 2.16641e7 | 0.383520 | ||||||||
\(165\) | 486016. | 0.00842281 | ||||||||
\(166\) | 4.52453e7 | 0.767707 | ||||||||
\(167\) | −1.07059e8 | −1.77875 | −0.889377 | − | 0.457174i | \(-0.848862\pi\) | ||||
−0.889377 | + | 0.457174i | \(0.848862\pi\) | |||||||
\(168\) | 1.61185e7 | 0.262267 | ||||||||
\(169\) | −5.34557e7 | −0.851905 | ||||||||
\(170\) | 6.70352e6 | 0.104648 | ||||||||
\(171\) | 5.00021e6 | 0.0764719 | ||||||||
\(172\) | −2.28660e7 | −0.342642 | ||||||||
\(173\) | −1.80227e7 | −0.264642 | −0.132321 | − | 0.991207i | \(-0.542243\pi\) | ||||
−0.132321 | + | 0.991207i | \(0.542243\pi\) | |||||||
\(174\) | −3.90207e7 | −0.561529 | ||||||||
\(175\) | −1.82185e7 | −0.256968 | ||||||||
\(176\) | −589844. | −0.00815535 | ||||||||
\(177\) | −3.25022e7 | −0.440562 | ||||||||
\(178\) | 4.00895e7 | 0.532796 | ||||||||
\(179\) | 1.05848e8 | 1.37942 | 0.689711 | − | 0.724085i | \(-0.257738\pi\) | ||||
0.689711 | + | 0.724085i | \(0.257738\pi\) | |||||||
\(180\) | 5.83200e6 | 0.0745356 | ||||||||
\(181\) | −1.14320e8 | −1.43300 | −0.716502 | − | 0.697585i | \(-0.754258\pi\) | ||||
−0.716502 | + | 0.697585i | \(0.754258\pi\) | |||||||
\(182\) | 2.84351e7 | 0.349627 | ||||||||
\(183\) | 1.66004e7 | 0.200235 | ||||||||
\(184\) | 7.89232e6 | 0.0933991 | ||||||||
\(185\) | −5.65065e7 | −0.656141 | ||||||||
\(186\) | −3.75491e7 | −0.427863 | ||||||||
\(187\) | −965338. | −0.0107953 | ||||||||
\(188\) | −3.11469e7 | −0.341871 | ||||||||
\(189\) | 2.29500e7 | 0.247267 | ||||||||
\(190\) | 6.85900e6 | 0.0725476 | ||||||||
\(191\) | −2.93960e7 | −0.305261 | −0.152631 | − | 0.988283i | \(-0.548775\pi\) | ||||
−0.152631 | + | 0.988283i | \(0.548775\pi\) | |||||||
\(192\) | −7.07789e6 | −0.0721688 | ||||||||
\(193\) | −4.92637e7 | −0.493260 | −0.246630 | − | 0.969110i | \(-0.579323\pi\) | ||||
−0.246630 | + | 0.969110i | \(0.579323\pi\) | |||||||
\(194\) | −4.41730e7 | −0.434361 | ||||||||
\(195\) | 1.02884e7 | 0.0993631 | ||||||||
\(196\) | 3.43022e7 | 0.325406 | ||||||||
\(197\) | −6.14818e7 | −0.572948 | −0.286474 | − | 0.958088i | \(-0.592483\pi\) | ||||
−0.286474 | + | 0.958088i | \(0.592483\pi\) | |||||||
\(198\) | −839836. | −0.00768894 | ||||||||
\(199\) | 6.76104e7 | 0.608174 | 0.304087 | − | 0.952644i | \(-0.401649\pi\) | ||||
0.304087 | + | 0.952644i | \(0.401649\pi\) | |||||||
\(200\) | 8.00000e6 | 0.0707107 | ||||||||
\(201\) | −6.16544e7 | −0.535522 | ||||||||
\(202\) | −1.53033e8 | −1.30633 | ||||||||
\(203\) | −2.10636e8 | −1.76724 | ||||||||
\(204\) | −1.15837e7 | −0.0955302 | ||||||||
\(205\) | 4.23128e7 | 0.343031 | ||||||||
\(206\) | −1.50908e8 | −1.20276 | ||||||||
\(207\) | 1.12373e7 | 0.0880575 | ||||||||
\(208\) | −1.24863e7 | −0.0962079 | ||||||||
\(209\) | −987729. | −0.00748386 | ||||||||
\(210\) | 3.14815e7 | 0.234579 | ||||||||
\(211\) | −6.49827e7 | −0.476221 | −0.238111 | − | 0.971238i | \(-0.576528\pi\) | ||||
−0.238111 | + | 0.971238i | \(0.576528\pi\) | |||||||
\(212\) | −1.15417e8 | −0.831947 | ||||||||
\(213\) | −6.21060e7 | −0.440357 | ||||||||
\(214\) | −5.82973e7 | −0.406631 | ||||||||
\(215\) | −4.46601e7 | −0.306468 | ||||||||
\(216\) | −1.00777e7 | −0.0680414 | ||||||||
\(217\) | −2.02693e8 | −1.34657 | ||||||||
\(218\) | −5.39065e7 | −0.352406 | ||||||||
\(219\) | 3.80888e7 | 0.245043 | ||||||||
\(220\) | −1.15204e6 | −0.00729436 | ||||||||
\(221\) | −2.04350e7 | −0.127351 | ||||||||
\(222\) | 9.76432e7 | 0.598972 | ||||||||
\(223\) | −1.45234e8 | −0.877001 | −0.438501 | − | 0.898731i | \(-0.644490\pi\) | ||||
−0.438501 | + | 0.898731i | \(0.644490\pi\) | |||||||
\(224\) | −3.82069e7 | −0.227130 | ||||||||
\(225\) | 1.13906e7 | 0.0666667 | ||||||||
\(226\) | −1.02399e8 | −0.590086 | ||||||||
\(227\) | −1.49446e8 | −0.847997 | −0.423998 | − | 0.905663i | \(-0.639374\pi\) | ||||
−0.423998 | + | 0.905663i | \(0.639374\pi\) | |||||||
\(228\) | −1.18524e7 | −0.0662266 | ||||||||
\(229\) | −7.16910e7 | −0.394494 | −0.197247 | − | 0.980354i | \(-0.563200\pi\) | ||||
−0.197247 | + | 0.980354i | \(0.563200\pi\) | |||||||
\(230\) | 1.54147e7 | 0.0835387 | ||||||||
\(231\) | −4.53349e6 | −0.0241986 | ||||||||
\(232\) | 9.24934e7 | 0.486298 | ||||||||
\(233\) | 8.34184e7 | 0.432032 | 0.216016 | − | 0.976390i | \(-0.430694\pi\) | ||||
0.216016 | + | 0.976390i | \(0.430694\pi\) | |||||||
\(234\) | −1.77783e7 | −0.0907057 | ||||||||
\(235\) | −6.08337e7 | −0.305778 | ||||||||
\(236\) | 7.70424e7 | 0.381538 | ||||||||
\(237\) | 1.57314e8 | 0.767621 | ||||||||
\(238\) | −6.25295e7 | −0.300653 | ||||||||
\(239\) | −2.70927e8 | −1.28369 | −0.641845 | − | 0.766834i | \(-0.721831\pi\) | ||||
−0.641845 | + | 0.766834i | \(0.721831\pi\) | |||||||
\(240\) | −1.38240e7 | −0.0645497 | ||||||||
\(241\) | −1.55946e8 | −0.717652 | −0.358826 | − | 0.933405i | \(-0.616823\pi\) | ||||
−0.358826 | + | 0.933405i | \(0.616823\pi\) | |||||||
\(242\) | −1.55731e8 | −0.706354 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −3.93491e7 | −0.173408 | ||||||||
\(245\) | 6.69965e7 | 0.291052 | ||||||||
\(246\) | −7.31165e7 | −0.313143 | ||||||||
\(247\) | −2.09090e7 | −0.0882865 | ||||||||
\(248\) | 8.90054e7 | 0.370540 | ||||||||
\(249\) | −1.52703e8 | −0.626830 | ||||||||
\(250\) | 1.56250e7 | 0.0632456 | ||||||||
\(251\) | 4.06626e7 | 0.162307 | 0.0811535 | − | 0.996702i | \(-0.474140\pi\) | ||||
0.0811535 | + | 0.996702i | \(0.474140\pi\) | |||||||
\(252\) | −5.44001e7 | −0.214140 | ||||||||
\(253\) | −2.21979e6 | −0.00861767 | ||||||||
\(254\) | 2.05541e8 | 0.787011 | ||||||||
\(255\) | −2.26244e7 | −0.0854448 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −8.75166e7 | −0.321606 | −0.160803 | − | 0.986987i | \(-0.551408\pi\) | ||||
−0.160803 | + | 0.986987i | \(0.551408\pi\) | |||||||
\(258\) | 7.71727e7 | 0.279766 | ||||||||
\(259\) | 5.27084e8 | 1.88509 | ||||||||
\(260\) | −2.43872e7 | −0.0860510 | ||||||||
\(261\) | 1.31695e8 | 0.458487 | ||||||||
\(262\) | 2.19761e8 | 0.754910 | ||||||||
\(263\) | −2.53858e7 | −0.0860490 | −0.0430245 | − | 0.999074i | \(-0.513699\pi\) | ||||
−0.0430245 | + | 0.999074i | \(0.513699\pi\) | |||||||
\(264\) | 1.99072e6 | 0.00665881 | ||||||||
\(265\) | −2.25424e8 | −0.744116 | ||||||||
\(266\) | −6.39798e7 | −0.208429 | ||||||||
\(267\) | −1.35302e8 | −0.435026 | ||||||||
\(268\) | 1.46144e8 | 0.463776 | ||||||||
\(269\) | −1.27680e8 | −0.399934 | −0.199967 | − | 0.979803i | \(-0.564084\pi\) | ||||
−0.199967 | + | 0.979803i | \(0.564084\pi\) | |||||||
\(270\) | −1.96830e7 | −0.0608581 | ||||||||
\(271\) | −2.27746e8 | −0.695118 | −0.347559 | − | 0.937658i | \(-0.612989\pi\) | ||||
−0.347559 | + | 0.937658i | \(0.612989\pi\) | |||||||
\(272\) | 2.74576e7 | 0.0827316 | ||||||||
\(273\) | −9.59684e7 | −0.285469 | ||||||||
\(274\) | 4.07886e8 | 1.19788 | ||||||||
\(275\) | −2.25007e6 | −0.00652428 | ||||||||
\(276\) | −2.66366e7 | −0.0762600 | ||||||||
\(277\) | −2.02190e7 | −0.0571583 | −0.0285792 | − | 0.999592i | \(-0.509098\pi\) | ||||
−0.0285792 | + | 0.999592i | \(0.509098\pi\) | |||||||
\(278\) | −2.91155e8 | −0.812769 | ||||||||
\(279\) | 1.26728e8 | 0.349349 | ||||||||
\(280\) | −7.46229e7 | −0.203151 | ||||||||
\(281\) | −5.73631e8 | −1.54227 | −0.771135 | − | 0.636671i | \(-0.780311\pi\) | ||||
−0.771135 | + | 0.636671i | \(0.780311\pi\) | |||||||
\(282\) | 1.05121e8 | 0.279136 | ||||||||
\(283\) | −5.12585e8 | −1.34435 | −0.672176 | − | 0.740391i | \(-0.734640\pi\) | ||||
−0.672176 | + | 0.740391i | \(0.734640\pi\) | |||||||
\(284\) | 1.47214e8 | 0.381361 | ||||||||
\(285\) | −2.31491e7 | −0.0592349 | ||||||||
\(286\) | 3.51188e6 | 0.00887684 | ||||||||
\(287\) | −3.94688e8 | −0.985523 | ||||||||
\(288\) | 2.38879e7 | 0.0589256 | ||||||||
\(289\) | −3.65402e8 | −0.890488 | ||||||||
\(290\) | 1.80651e8 | 0.434958 | ||||||||
\(291\) | 1.49084e8 | 0.354654 | ||||||||
\(292\) | −9.02845e7 | −0.212214 | ||||||||
\(293\) | 1.24773e8 | 0.289791 | 0.144896 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144896 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(294\) | −1.15770e8 | −0.265693 | ||||||||
\(295\) | 1.50473e8 | 0.341258 | ||||||||
\(296\) | −2.31450e8 | −0.518725 | ||||||||
\(297\) | 2.83445e6 | 0.00627799 | ||||||||
\(298\) | 4.94611e8 | 1.08270 | ||||||||
\(299\) | −4.69902e7 | −0.101662 | ||||||||
\(300\) | −2.70000e7 | −0.0577350 | ||||||||
\(301\) | 4.16583e8 | 0.880479 | ||||||||
\(302\) | −4.40252e8 | −0.919765 | ||||||||
\(303\) | 5.16485e8 | 1.06662 | ||||||||
\(304\) | 2.80945e7 | 0.0573539 | ||||||||
\(305\) | −7.68537e7 | −0.155101 | ||||||||
\(306\) | 3.90949e7 | 0.0780001 | ||||||||
\(307\) | 7.43416e8 | 1.46638 | 0.733191 | − | 0.680022i | \(-0.238030\pi\) | ||||
0.733191 | + | 0.680022i | \(0.238030\pi\) | |||||||
\(308\) | 1.07461e7 | 0.0209566 | ||||||||
\(309\) | 5.09315e8 | 0.982046 | ||||||||
\(310\) | 1.73839e8 | 0.331421 | ||||||||
\(311\) | 7.14985e8 | 1.34783 | 0.673915 | − | 0.738809i | \(-0.264611\pi\) | ||||
0.673915 | + | 0.738809i | \(0.264611\pi\) | |||||||
\(312\) | 4.21411e7 | 0.0785535 | ||||||||
\(313\) | −4.67452e8 | −0.861652 | −0.430826 | − | 0.902435i | \(-0.641778\pi\) | ||||
−0.430826 | + | 0.902435i | \(0.641778\pi\) | |||||||
\(314\) | −6.85827e8 | −1.25015 | ||||||||
\(315\) | −1.06250e8 | −0.191533 | ||||||||
\(316\) | −3.72891e8 | −0.664779 | ||||||||
\(317\) | 4.40096e7 | 0.0775961 | 0.0387981 | − | 0.999247i | \(-0.487647\pi\) | ||||
0.0387981 | + | 0.999247i | \(0.487647\pi\) | |||||||
\(318\) | 3.89533e8 | 0.679282 | ||||||||
\(319\) | −2.60146e7 | −0.0448694 | ||||||||
\(320\) | 3.27680e7 | 0.0559017 | ||||||||
\(321\) | 1.96754e8 | 0.332013 | ||||||||
\(322\) | −1.43786e8 | −0.240006 | ||||||||
\(323\) | 4.59794e7 | 0.0759197 | ||||||||
\(324\) | 3.40122e7 | 0.0555556 | ||||||||
\(325\) | −4.76313e7 | −0.0769664 | ||||||||
\(326\) | 7.09720e8 | 1.13455 | ||||||||
\(327\) | 1.81935e8 | 0.287739 | ||||||||
\(328\) | 1.73313e8 | 0.271189 | ||||||||
\(329\) | 5.67448e8 | 0.878498 | ||||||||
\(330\) | 3.88813e6 | 0.00595582 | ||||||||
\(331\) | 1.96813e8 | 0.298302 | 0.149151 | − | 0.988814i | \(-0.452346\pi\) | ||||
0.149151 | + | 0.988814i | \(0.452346\pi\) | |||||||
\(332\) | 3.61963e8 | 0.542851 | ||||||||
\(333\) | −3.29546e8 | −0.489059 | ||||||||
\(334\) | −8.56473e8 | −1.25777 | ||||||||
\(335\) | 2.85437e8 | 0.414814 | ||||||||
\(336\) | 1.28948e8 | 0.185451 | ||||||||
\(337\) | −9.32816e8 | −1.32767 | −0.663837 | − | 0.747878i | \(-0.731073\pi\) | ||||
−0.663837 | + | 0.747878i | \(0.731073\pi\) | |||||||
\(338\) | −4.27646e8 | −0.602387 | ||||||||
\(339\) | 3.45596e8 | 0.481803 | ||||||||
\(340\) | 5.36281e7 | 0.0739974 | ||||||||
\(341\) | −2.50336e7 | −0.0341887 | ||||||||
\(342\) | 4.00017e7 | 0.0540738 | ||||||||
\(343\) | 3.35302e8 | 0.448650 | ||||||||
\(344\) | −1.82928e8 | −0.242284 | ||||||||
\(345\) | −5.20246e7 | −0.0682090 | ||||||||
\(346\) | −1.44182e8 | −0.187130 | ||||||||
\(347\) | −7.33690e8 | −0.942669 | −0.471335 | − | 0.881955i | \(-0.656228\pi\) | ||||
−0.471335 | + | 0.881955i | \(0.656228\pi\) | |||||||
\(348\) | −3.12165e8 | −0.397061 | ||||||||
\(349\) | −1.05594e9 | −1.32969 | −0.664843 | − | 0.746983i | \(-0.731502\pi\) | ||||
−0.664843 | + | 0.746983i | \(0.731502\pi\) | |||||||
\(350\) | −1.45748e8 | −0.181704 | ||||||||
\(351\) | 6.00018e7 | 0.0740609 | ||||||||
\(352\) | −4.71875e6 | −0.00576670 | ||||||||
\(353\) | −2.18673e8 | −0.264596 | −0.132298 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132298 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(354\) | −2.60018e8 | −0.311524 | ||||||||
\(355\) | 2.87528e8 | 0.341099 | ||||||||
\(356\) | 3.20716e8 | 0.376743 | ||||||||
\(357\) | 2.11037e8 | 0.245482 | ||||||||
\(358\) | 8.46784e8 | 0.975398 | ||||||||
\(359\) | 1.43158e8 | 0.163300 | 0.0816500 | − | 0.996661i | \(-0.473981\pi\) | ||||
0.0816500 | + | 0.996661i | \(0.473981\pi\) | |||||||
\(360\) | 4.66560e7 | 0.0527046 | ||||||||
\(361\) | 4.70459e7 | 0.0526316 | ||||||||
\(362\) | −9.14561e8 | −1.01329 | ||||||||
\(363\) | 5.25594e8 | 0.576736 | ||||||||
\(364\) | 2.27481e8 | 0.247224 | ||||||||
\(365\) | −1.76337e8 | −0.189810 | ||||||||
\(366\) | 1.32803e8 | 0.141587 | ||||||||
\(367\) | 3.29394e7 | 0.0347844 | 0.0173922 | − | 0.999849i | \(-0.494464\pi\) | ||||
0.0173922 | + | 0.999849i | \(0.494464\pi\) | |||||||
\(368\) | 6.31386e7 | 0.0660431 | ||||||||
\(369\) | 2.46768e8 | 0.255680 | ||||||||
\(370\) | −4.52052e8 | −0.463962 | ||||||||
\(371\) | 2.10273e9 | 2.13784 | ||||||||
\(372\) | −3.00393e8 | −0.302545 | ||||||||
\(373\) | −4.14192e8 | −0.413258 | −0.206629 | − | 0.978419i | \(-0.566249\pi\) | ||||
−0.206629 | + | 0.978419i | \(0.566249\pi\) | |||||||
\(374\) | −7.72271e6 | −0.00763341 | ||||||||
\(375\) | −5.27344e7 | −0.0516398 | ||||||||
\(376\) | −2.49175e8 | −0.241739 | ||||||||
\(377\) | −5.50698e8 | −0.529321 | ||||||||
\(378\) | 1.83600e8 | 0.174845 | ||||||||
\(379\) | −3.32558e8 | −0.313783 | −0.156892 | − | 0.987616i | \(-0.550147\pi\) | ||||
−0.156892 | + | 0.987616i | \(0.550147\pi\) | |||||||
\(380\) | 5.48720e7 | 0.0512989 | ||||||||
\(381\) | −6.93701e8 | −0.642591 | ||||||||
\(382\) | −2.35168e8 | −0.215852 | ||||||||
\(383\) | 1.62226e9 | 1.47545 | 0.737724 | − | 0.675102i | \(-0.235900\pi\) | ||||
0.737724 | + | 0.675102i | \(0.235900\pi\) | |||||||
\(384\) | −5.66231e7 | −0.0510310 | ||||||||
\(385\) | 2.09884e7 | 0.0187442 | ||||||||
\(386\) | −3.94109e8 | −0.348788 | ||||||||
\(387\) | −2.60458e8 | −0.228428 | ||||||||
\(388\) | −3.53384e8 | −0.307140 | ||||||||
\(389\) | −1.56167e9 | −1.34513 | −0.672566 | − | 0.740037i | \(-0.734808\pi\) | ||||
−0.672566 | + | 0.740037i | \(0.734808\pi\) | |||||||
\(390\) | 8.23069e7 | 0.0702603 | ||||||||
\(391\) | 1.03333e8 | 0.0874216 | ||||||||
\(392\) | 2.74418e8 | 0.230097 | ||||||||
\(393\) | −7.41692e8 | −0.616382 | ||||||||
\(394\) | −4.91854e8 | −0.405135 | ||||||||
\(395\) | −7.28303e8 | −0.594597 | ||||||||
\(396\) | −6.71869e6 | −0.00543690 | ||||||||
\(397\) | 1.02018e9 | 0.818297 | 0.409149 | − | 0.912468i | \(-0.365826\pi\) | ||||
0.409149 | + | 0.912468i | \(0.365826\pi\) | |||||||
\(398\) | 5.40883e8 | 0.430044 | ||||||||
\(399\) | 2.15932e8 | 0.170181 | ||||||||
\(400\) | 6.40000e7 | 0.0500000 | ||||||||
\(401\) | 1.24502e9 | 0.964207 | 0.482104 | − | 0.876114i | \(-0.339873\pi\) | ||||
0.482104 | + | 0.876114i | \(0.339873\pi\) | |||||||
\(402\) | −4.93235e8 | −0.378672 | ||||||||
\(403\) | −5.29930e8 | −0.403321 | ||||||||
\(404\) | −1.22426e9 | −0.923717 | ||||||||
\(405\) | 6.64301e7 | 0.0496904 | ||||||||
\(406\) | −1.68509e9 | −1.24963 | ||||||||
\(407\) | 6.50976e7 | 0.0478613 | ||||||||
\(408\) | −9.26694e7 | −0.0675501 | ||||||||
\(409\) | 3.36075e8 | 0.242887 | 0.121444 | − | 0.992598i | \(-0.461248\pi\) | ||||
0.121444 | + | 0.992598i | \(0.461248\pi\) | |||||||
\(410\) | 3.38502e8 | 0.242559 | ||||||||
\(411\) | −1.37662e9 | −0.978062 | ||||||||
\(412\) | −1.20726e9 | −0.850476 | ||||||||
\(413\) | −1.40359e9 | −0.980430 | ||||||||
\(414\) | 8.98985e7 | 0.0622660 | ||||||||
\(415\) | 7.06958e8 | 0.485540 | ||||||||
\(416\) | −9.98901e7 | −0.0680293 | ||||||||
\(417\) | 9.82647e8 | 0.663623 | ||||||||
\(418\) | −7.90183e6 | −0.00529189 | ||||||||
\(419\) | −1.63065e9 | −1.08296 | −0.541478 | − | 0.840715i | \(-0.682135\pi\) | ||||
−0.541478 | + | 0.840715i | \(0.682135\pi\) | |||||||
\(420\) | 2.51852e8 | 0.165872 | ||||||||
\(421\) | 4.71104e8 | 0.307702 | 0.153851 | − | 0.988094i | \(-0.450832\pi\) | ||||
0.153851 | + | 0.988094i | \(0.450832\pi\) | |||||||
\(422\) | −5.19861e8 | −0.336739 | ||||||||
\(423\) | −3.54782e8 | −0.227914 | ||||||||
\(424\) | −9.23339e8 | −0.588275 | ||||||||
\(425\) | 1.04742e8 | 0.0661853 | ||||||||
\(426\) | −4.96848e8 | −0.311380 | ||||||||
\(427\) | 7.16880e8 | 0.445604 | ||||||||
\(428\) | −4.66379e8 | −0.287532 | ||||||||
\(429\) | −1.18526e7 | −0.00724791 | ||||||||
\(430\) | −3.57281e8 | −0.216706 | ||||||||
\(431\) | 3.16809e9 | 1.90602 | 0.953008 | − | 0.302944i | \(-0.0979695\pi\) | ||||
0.953008 | + | 0.302944i | \(0.0979695\pi\) | |||||||
\(432\) | −8.06216e7 | −0.0481125 | ||||||||
\(433\) | 1.05873e9 | 0.626723 | 0.313362 | − | 0.949634i | \(-0.398545\pi\) | ||||
0.313362 | + | 0.949634i | \(0.398545\pi\) | |||||||
\(434\) | −1.62154e9 | −0.952169 | ||||||||
\(435\) | −6.09698e8 | −0.355142 | ||||||||
\(436\) | −4.31252e8 | −0.249189 | ||||||||
\(437\) | 1.05729e8 | 0.0606053 | ||||||||
\(438\) | 3.04710e8 | 0.173272 | ||||||||
\(439\) | −4.96163e8 | −0.279897 | −0.139949 | − | 0.990159i | \(-0.544694\pi\) | ||||
−0.139949 | + | 0.990159i | \(0.544694\pi\) | |||||||
\(440\) | −9.21630e6 | −0.00515789 | ||||||||
\(441\) | 3.90724e8 | 0.216938 | ||||||||
\(442\) | −1.63480e8 | −0.0900507 | ||||||||
\(443\) | 1.64604e9 | 0.899556 | 0.449778 | − | 0.893140i | \(-0.351503\pi\) | ||||
0.449778 | + | 0.893140i | \(0.351503\pi\) | |||||||
\(444\) | 7.81145e8 | 0.423537 | ||||||||
\(445\) | 6.26398e8 | 0.336969 | ||||||||
\(446\) | −1.16187e9 | −0.620134 | ||||||||
\(447\) | −1.66931e9 | −0.884019 | ||||||||
\(448\) | −3.05655e8 | −0.160605 | ||||||||
\(449\) | 2.58049e9 | 1.34536 | 0.672682 | − | 0.739932i | \(-0.265142\pi\) | ||||
0.672682 | + | 0.739932i | \(0.265142\pi\) | |||||||
\(450\) | 9.11250e7 | 0.0471405 | ||||||||
\(451\) | −4.87459e7 | −0.0250219 | ||||||||
\(452\) | −8.19190e8 | −0.417254 | ||||||||
\(453\) | 1.48585e9 | 0.750985 | ||||||||
\(454\) | −1.19557e9 | −0.599624 | ||||||||
\(455\) | 4.44298e8 | 0.221123 | ||||||||
\(456\) | −9.48188e7 | −0.0468293 | ||||||||
\(457\) | −3.45832e8 | −0.169496 | −0.0847479 | − | 0.996402i | \(-0.527008\pi\) | ||||
−0.0847479 | + | 0.996402i | \(0.527008\pi\) | |||||||
\(458\) | −5.73528e8 | −0.278949 | ||||||||
\(459\) | −1.31945e8 | −0.0636868 | ||||||||
\(460\) | 1.23318e8 | 0.0590707 | ||||||||
\(461\) | −4.77825e8 | −0.227152 | −0.113576 | − | 0.993529i | \(-0.536230\pi\) | ||||
−0.113576 | + | 0.993529i | \(0.536230\pi\) | |||||||
\(462\) | −3.62679e7 | −0.0171110 | ||||||||
\(463\) | −1.44249e9 | −0.675428 | −0.337714 | − | 0.941249i | \(-0.609654\pi\) | ||||
−0.337714 | + | 0.941249i | \(0.609654\pi\) | |||||||
\(464\) | 7.39947e8 | 0.343865 | ||||||||
\(465\) | −5.86705e8 | −0.270604 | ||||||||
\(466\) | 6.67347e8 | 0.305493 | ||||||||
\(467\) | 1.72538e9 | 0.783928 | 0.391964 | − | 0.919980i | \(-0.371796\pi\) | ||||
0.391964 | + | 0.919980i | \(0.371796\pi\) | |||||||
\(468\) | −1.42226e8 | −0.0641386 | ||||||||
\(469\) | −2.66252e9 | −1.19176 | ||||||||
\(470\) | −4.86670e8 | −0.216218 | ||||||||
\(471\) | 2.31466e9 | 1.02074 | ||||||||
\(472\) | 6.16339e8 | 0.269788 | ||||||||
\(473\) | 5.14502e7 | 0.0223549 | ||||||||
\(474\) | 1.25851e9 | 0.542790 | ||||||||
\(475\) | 1.07172e8 | 0.0458831 | ||||||||
\(476\) | −5.00236e8 | −0.212594 | ||||||||
\(477\) | −1.31468e9 | −0.554631 | ||||||||
\(478\) | −2.16742e9 | −0.907706 | ||||||||
\(479\) | 2.28041e9 | 0.948067 | 0.474034 | − | 0.880507i | \(-0.342798\pi\) | ||||
0.474034 | + | 0.880507i | \(0.342798\pi\) | |||||||
\(480\) | −1.10592e8 | −0.0456435 | ||||||||
\(481\) | 1.37804e9 | 0.564616 | ||||||||
\(482\) | −1.24757e9 | −0.507456 | ||||||||
\(483\) | 4.85278e8 | 0.195964 | ||||||||
\(484\) | −1.24585e9 | −0.499468 | ||||||||
\(485\) | −6.90204e8 | −0.274714 | ||||||||
\(486\) | −1.14791e8 | −0.0453609 | ||||||||
\(487\) | 1.27569e9 | 0.500490 | 0.250245 | − | 0.968183i | \(-0.419489\pi\) | ||||
0.250245 | + | 0.968183i | \(0.419489\pi\) | |||||||
\(488\) | −3.14793e8 | −0.122618 | ||||||||
\(489\) | −2.39530e9 | −0.926360 | ||||||||
\(490\) | 5.35972e8 | 0.205805 | ||||||||
\(491\) | 1.99246e9 | 0.759635 | 0.379818 | − | 0.925061i | \(-0.375987\pi\) | ||||
0.379818 | + | 0.925061i | \(0.375987\pi\) | |||||||
\(492\) | −5.84932e8 | −0.221425 | ||||||||
\(493\) | 1.21100e9 | 0.455176 | ||||||||
\(494\) | −1.67272e8 | −0.0624280 | ||||||||
\(495\) | −1.31224e7 | −0.00486291 | ||||||||
\(496\) | 7.12043e8 | 0.262011 | ||||||||
\(497\) | −2.68202e9 | −0.979974 | ||||||||
\(498\) | −1.22162e9 | −0.443236 | ||||||||
\(499\) | −2.86016e9 | −1.03048 | −0.515239 | − | 0.857046i | \(-0.672297\pi\) | ||||
−0.515239 | + | 0.857046i | \(0.672297\pi\) | |||||||
\(500\) | 1.25000e8 | 0.0447214 | ||||||||
\(501\) | 2.89060e9 | 1.02696 | ||||||||
\(502\) | 3.25301e8 | 0.114768 | ||||||||
\(503\) | −1.76061e9 | −0.616845 | −0.308423 | − | 0.951249i | \(-0.599801\pi\) | ||||
−0.308423 | + | 0.951249i | \(0.599801\pi\) | |||||||
\(504\) | −4.35201e8 | −0.151420 | ||||||||
\(505\) | −2.39113e9 | −0.826198 | ||||||||
\(506\) | −1.77583e7 | −0.00609361 | ||||||||
\(507\) | 1.44331e9 | 0.491847 | ||||||||
\(508\) | 1.64433e9 | 0.556501 | ||||||||
\(509\) | 4.26460e9 | 1.43340 | 0.716698 | − | 0.697384i | \(-0.245653\pi\) | ||||
0.716698 | + | 0.697384i | \(0.245653\pi\) | |||||||
\(510\) | −1.80995e8 | −0.0604186 | ||||||||
\(511\) | 1.64485e9 | 0.545321 | ||||||||
\(512\) | 1.34218e8 | 0.0441942 | ||||||||
\(513\) | −1.35006e8 | −0.0441511 | ||||||||
\(514\) | −7.00133e8 | −0.227410 | ||||||||
\(515\) | −2.35794e9 | −0.760689 | ||||||||
\(516\) | 6.17381e8 | 0.197824 | ||||||||
\(517\) | 7.00827e7 | 0.0223046 | ||||||||
\(518\) | 4.21668e9 | 1.33296 | ||||||||
\(519\) | 4.86613e8 | 0.152791 | ||||||||
\(520\) | −1.95098e8 | −0.0608472 | ||||||||
\(521\) | −1.50718e8 | −0.0466910 | −0.0233455 | − | 0.999727i | \(-0.507432\pi\) | ||||
−0.0233455 | + | 0.999727i | \(0.507432\pi\) | |||||||
\(522\) | 1.05356e9 | 0.324199 | ||||||||
\(523\) | −1.88541e9 | −0.576301 | −0.288150 | − | 0.957585i | \(-0.593040\pi\) | ||||
−0.288150 | + | 0.957585i | \(0.593040\pi\) | |||||||
\(524\) | 1.75809e9 | 0.533802 | ||||||||
\(525\) | 4.91899e8 | 0.148360 | ||||||||
\(526\) | −2.03086e8 | −0.0608458 | ||||||||
\(527\) | 1.16533e9 | 0.346826 | ||||||||
\(528\) | 1.59258e7 | 0.00470849 | ||||||||
\(529\) | −3.16721e9 | −0.930213 | ||||||||
\(530\) | −1.80340e9 | −0.526169 | ||||||||
\(531\) | 8.77561e8 | 0.254359 | ||||||||
\(532\) | −5.11838e8 | −0.147381 | ||||||||
\(533\) | −1.03189e9 | −0.295181 | ||||||||
\(534\) | −1.08242e9 | −0.307610 | ||||||||
\(535\) | −9.10896e8 | −0.257176 | ||||||||
\(536\) | 1.16915e9 | 0.327939 | ||||||||
\(537\) | −2.85789e9 | −0.796409 | ||||||||
\(538\) | −1.02144e9 | −0.282796 | ||||||||
\(539\) | −7.71826e7 | −0.0212304 | ||||||||
\(540\) | −1.57464e8 | −0.0430331 | ||||||||
\(541\) | −2.25346e8 | −0.0611870 | −0.0305935 | − | 0.999532i | \(-0.509740\pi\) | ||||
−0.0305935 | + | 0.999532i | \(0.509740\pi\) | |||||||
\(542\) | −1.82197e9 | −0.491522 | ||||||||
\(543\) | 3.08664e9 | 0.827345 | ||||||||
\(544\) | 2.19661e8 | 0.0585001 | ||||||||
\(545\) | −8.42290e8 | −0.222881 | ||||||||
\(546\) | −7.67748e8 | −0.201857 | ||||||||
\(547\) | −7.09512e9 | −1.85355 | −0.926775 | − | 0.375617i | \(-0.877431\pi\) | ||||
−0.926775 | + | 0.375617i | \(0.877431\pi\) | |||||||
\(548\) | 3.26309e9 | 0.847026 | ||||||||
\(549\) | −4.48211e8 | −0.115606 | ||||||||
\(550\) | −1.80006e7 | −0.00461336 | ||||||||
\(551\) | 1.23909e9 | 0.315552 | ||||||||
\(552\) | −2.13093e8 | −0.0539240 | ||||||||
\(553\) | 6.79351e9 | 1.70827 | ||||||||
\(554\) | −1.61752e8 | −0.0404170 | ||||||||
\(555\) | 1.52567e9 | 0.378823 | ||||||||
\(556\) | −2.32924e9 | −0.574714 | ||||||||
\(557\) | 2.69068e7 | 0.00659735 | 0.00329868 | − | 0.999995i | \(-0.498950\pi\) | ||||
0.00329868 | + | 0.999995i | \(0.498950\pi\) | |||||||
\(558\) | 1.01383e9 | 0.247027 | ||||||||
\(559\) | 1.08914e9 | 0.263719 | ||||||||
\(560\) | −5.96983e8 | −0.143649 | ||||||||
\(561\) | 2.60641e7 | 0.00623266 | ||||||||
\(562\) | −4.58905e9 | −1.09055 | ||||||||
\(563\) | −1.81117e9 | −0.427739 | −0.213870 | − | 0.976862i | \(-0.568607\pi\) | ||||
−0.213870 | + | 0.976862i | \(0.568607\pi\) | |||||||
\(564\) | 8.40965e8 | 0.197379 | ||||||||
\(565\) | −1.59998e9 | −0.373203 | ||||||||
\(566\) | −4.10068e9 | −0.950600 | ||||||||
\(567\) | −6.19651e8 | −0.142760 | ||||||||
\(568\) | 1.17771e9 | 0.269663 | ||||||||
\(569\) | −4.50289e9 | −1.02470 | −0.512352 | − | 0.858775i | \(-0.671226\pi\) | ||||
−0.512352 | + | 0.858775i | \(0.671226\pi\) | |||||||
\(570\) | −1.85193e8 | −0.0418854 | ||||||||
\(571\) | 8.04967e9 | 1.80947 | 0.904736 | − | 0.425973i | \(-0.140068\pi\) | ||||
0.904736 | + | 0.425973i | \(0.140068\pi\) | |||||||
\(572\) | 2.80950e7 | 0.00627687 | ||||||||
\(573\) | 7.93693e8 | 0.176243 | ||||||||
\(574\) | −3.15750e9 | −0.696870 | ||||||||
\(575\) | 2.40855e8 | 0.0528345 | ||||||||
\(576\) | 1.91103e8 | 0.0416667 | ||||||||
\(577\) | 8.84269e9 | 1.91633 | 0.958163 | − | 0.286225i | \(-0.0924003\pi\) | ||||
0.958163 | + | 0.286225i | \(0.0924003\pi\) | |||||||
\(578\) | −2.92321e9 | −0.629670 | ||||||||
\(579\) | 1.33012e9 | 0.284784 | ||||||||
\(580\) | 1.44521e9 | 0.307562 | ||||||||
\(581\) | −6.59441e9 | −1.39495 | ||||||||
\(582\) | 1.19267e9 | 0.250779 | ||||||||
\(583\) | 2.59698e8 | 0.0542785 | ||||||||
\(584\) | −7.22276e8 | −0.150058 | ||||||||
\(585\) | −2.77786e8 | −0.0573673 | ||||||||
\(586\) | 9.98186e8 | 0.204913 | ||||||||
\(587\) | 1.89609e9 | 0.386924 | 0.193462 | − | 0.981108i | \(-0.438028\pi\) | ||||
0.193462 | + | 0.981108i | \(0.438028\pi\) | |||||||
\(588\) | −9.26160e8 | −0.187873 | ||||||||
\(589\) | 1.19236e9 | 0.240438 | ||||||||
\(590\) | 1.20379e9 | 0.241306 | ||||||||
\(591\) | 1.66001e9 | 0.330791 | ||||||||
\(592\) | −1.85160e9 | −0.366794 | ||||||||
\(593\) | 1.38074e9 | 0.271906 | 0.135953 | − | 0.990715i | \(-0.456590\pi\) | ||||
0.135953 | + | 0.990715i | \(0.456590\pi\) | |||||||
\(594\) | 2.26756e7 | 0.00443921 | ||||||||
\(595\) | −9.77023e8 | −0.190150 | ||||||||
\(596\) | 3.95689e9 | 0.765583 | ||||||||
\(597\) | −1.82548e9 | −0.351129 | ||||||||
\(598\) | −3.75922e8 | −0.0718858 | ||||||||
\(599\) | −7.22264e9 | −1.37310 | −0.686550 | − | 0.727083i | \(-0.740876\pi\) | ||||
−0.686550 | + | 0.727083i | \(0.740876\pi\) | |||||||
\(600\) | −2.16000e8 | −0.0408248 | ||||||||
\(601\) | 9.06698e9 | 1.70373 | 0.851867 | − | 0.523758i | \(-0.175470\pi\) | ||||
0.851867 | + | 0.523758i | \(0.175470\pi\) | |||||||
\(602\) | 3.33267e9 | 0.622593 | ||||||||
\(603\) | 1.66467e9 | 0.309184 | ||||||||
\(604\) | −3.52202e9 | −0.650372 | ||||||||
\(605\) | −2.43330e9 | −0.446738 | ||||||||
\(606\) | 4.13188e9 | 0.754212 | ||||||||
\(607\) | 6.09436e9 | 1.10603 | 0.553016 | − | 0.833170i | \(-0.313477\pi\) | ||||
0.553016 | + | 0.833170i | \(0.313477\pi\) | |||||||
\(608\) | 2.24756e8 | 0.0405554 | ||||||||
\(609\) | 5.68718e9 | 1.02032 | ||||||||
\(610\) | −6.14829e8 | −0.109673 | ||||||||
\(611\) | 1.48357e9 | 0.263125 | ||||||||
\(612\) | 3.12759e8 | 0.0551544 | ||||||||
\(613\) | −9.22110e9 | −1.61686 | −0.808428 | − | 0.588596i | \(-0.799681\pi\) | ||||
−0.808428 | + | 0.588596i | \(0.799681\pi\) | |||||||
\(614\) | 5.94733e9 | 1.03689 | ||||||||
\(615\) | −1.14244e9 | −0.198049 | ||||||||
\(616\) | 8.59684e7 | 0.0148186 | ||||||||
\(617\) | −1.98507e9 | −0.340234 | −0.170117 | − | 0.985424i | \(-0.554415\pi\) | ||||
−0.170117 | + | 0.985424i | \(0.554415\pi\) | |||||||
\(618\) | 4.07452e9 | 0.694411 | ||||||||
\(619\) | 7.48090e9 | 1.26776 | 0.633880 | − | 0.773432i | \(-0.281461\pi\) | ||||
0.633880 | + | 0.773432i | \(0.281461\pi\) | |||||||
\(620\) | 1.39071e9 | 0.234350 | ||||||||
\(621\) | −3.03407e8 | −0.0508400 | ||||||||
\(622\) | 5.71988e9 | 0.953060 | ||||||||
\(623\) | −5.84296e9 | −0.968110 | ||||||||
\(624\) | 3.37129e8 | 0.0555457 | ||||||||
\(625\) | 2.44141e8 | 0.0400000 | ||||||||
\(626\) | −3.73961e9 | −0.609280 | ||||||||
\(627\) | 2.66687e7 | 0.00432081 | ||||||||
\(628\) | −5.48661e9 | −0.883986 | ||||||||
\(629\) | −3.03034e9 | −0.485527 | ||||||||
\(630\) | −8.50001e8 | −0.135434 | ||||||||
\(631\) | 1.88610e9 | 0.298856 | 0.149428 | − | 0.988773i | \(-0.452257\pi\) | ||||
0.149428 | + | 0.988773i | \(0.452257\pi\) | |||||||
\(632\) | −2.98313e9 | −0.470070 | ||||||||
\(633\) | 1.75453e9 | 0.274947 | ||||||||
\(634\) | 3.52077e8 | 0.0548688 | ||||||||
\(635\) | 3.21158e9 | 0.497749 | ||||||||
\(636\) | 3.11627e9 | 0.480325 | ||||||||
\(637\) | −1.63386e9 | −0.250453 | ||||||||
\(638\) | −2.08117e8 | −0.0317275 | ||||||||
\(639\) | 1.67686e9 | 0.254240 | ||||||||
\(640\) | 2.62144e8 | 0.0395285 | ||||||||
\(641\) | 4.81042e9 | 0.721406 | 0.360703 | − | 0.932681i | \(-0.382537\pi\) | ||||
0.360703 | + | 0.932681i | \(0.382537\pi\) | |||||||
\(642\) | 1.57403e9 | 0.234769 | ||||||||
\(643\) | 1.32954e10 | 1.97225 | 0.986125 | − | 0.166003i | \(-0.0530860\pi\) | ||||
0.986125 | + | 0.166003i | \(0.0530860\pi\) | |||||||
\(644\) | −1.15029e9 | −0.169710 | ||||||||
\(645\) | 1.20582e9 | 0.176939 | ||||||||
\(646\) | 3.67835e8 | 0.0536833 | ||||||||
\(647\) | −6.99878e9 | −1.01592 | −0.507958 | − | 0.861382i | \(-0.669599\pi\) | ||||
−0.507958 | + | 0.861382i | \(0.669599\pi\) | |||||||
\(648\) | 2.72098e8 | 0.0392837 | ||||||||
\(649\) | −1.73351e8 | −0.0248926 | ||||||||
\(650\) | −3.81051e8 | −0.0544234 | ||||||||
\(651\) | 5.47271e9 | 0.777443 | ||||||||
\(652\) | 5.67776e9 | 0.802251 | ||||||||
\(653\) | 9.55199e9 | 1.34245 | 0.671224 | − | 0.741254i | \(-0.265769\pi\) | ||||
0.671224 | + | 0.741254i | \(0.265769\pi\) | |||||||
\(654\) | 1.45548e9 | 0.203462 | ||||||||
\(655\) | 3.43376e9 | 0.477447 | ||||||||
\(656\) | 1.38650e9 | 0.191760 | ||||||||
\(657\) | −1.02840e9 | −0.141476 | ||||||||
\(658\) | 4.53959e9 | 0.621192 | ||||||||
\(659\) | −1.11552e9 | −0.151837 | −0.0759183 | − | 0.997114i | \(-0.524189\pi\) | ||||
−0.0759183 | + | 0.997114i | \(0.524189\pi\) | |||||||
\(660\) | 3.11050e7 | 0.00421140 | ||||||||
\(661\) | −7.86694e9 | −1.05950 | −0.529749 | − | 0.848154i | \(-0.677714\pi\) | ||||
−0.529749 | + | 0.848154i | \(0.677714\pi\) | |||||||
\(662\) | 1.57451e9 | 0.210931 | ||||||||
\(663\) | 5.51746e8 | 0.0735261 | ||||||||
\(664\) | 2.89570e9 | 0.383853 | ||||||||
\(665\) | −9.99684e8 | −0.131822 | ||||||||
\(666\) | −2.63637e9 | −0.345817 | ||||||||
\(667\) | 2.78468e9 | 0.363358 | ||||||||
\(668\) | −6.85178e9 | −0.889377 | ||||||||
\(669\) | 3.92131e9 | 0.506337 | ||||||||
\(670\) | 2.28349e9 | 0.293318 | ||||||||
\(671\) | 8.85384e7 | 0.0113136 | ||||||||
\(672\) | 1.03159e9 | 0.131133 | ||||||||
\(673\) | 6.46874e9 | 0.818026 | 0.409013 | − | 0.912529i | \(-0.365873\pi\) | ||||
0.409013 | + | 0.912529i | \(0.365873\pi\) | |||||||
\(674\) | −7.46253e9 | −0.938807 | ||||||||
\(675\) | −3.07547e8 | −0.0384900 | ||||||||
\(676\) | −3.42117e9 | −0.425952 | ||||||||
\(677\) | 3.31062e9 | 0.410061 | 0.205031 | − | 0.978756i | \(-0.434271\pi\) | ||||
0.205031 | + | 0.978756i | \(0.434271\pi\) | |||||||
\(678\) | 2.76477e9 | 0.340686 | ||||||||
\(679\) | 6.43812e9 | 0.789251 | ||||||||
\(680\) | 4.29025e8 | 0.0523241 | ||||||||
\(681\) | 4.03505e9 | 0.489591 | ||||||||
\(682\) | −2.00269e8 | −0.0241751 | ||||||||
\(683\) | 2.70297e9 | 0.324615 | 0.162308 | − | 0.986740i | \(-0.448106\pi\) | ||||
0.162308 | + | 0.986740i | \(0.448106\pi\) | |||||||
\(684\) | 3.20014e8 | 0.0382360 | ||||||||
\(685\) | 6.37322e9 | 0.757603 | ||||||||
\(686\) | 2.68242e9 | 0.317243 | ||||||||
\(687\) | 1.93566e9 | 0.227761 | ||||||||
\(688\) | −1.46342e9 | −0.171321 | ||||||||
\(689\) | 5.49748e9 | 0.640319 | ||||||||
\(690\) | −4.16197e8 | −0.0482311 | ||||||||
\(691\) | −1.40352e10 | −1.61825 | −0.809126 | − | 0.587636i | \(-0.800059\pi\) | ||||
−0.809126 | + | 0.587636i | \(0.800059\pi\) | |||||||
\(692\) | −1.15345e9 | −0.132321 | ||||||||
\(693\) | 1.22404e8 | 0.0139711 | ||||||||
\(694\) | −5.86952e9 | −0.666568 | ||||||||
\(695\) | −4.54929e9 | −0.514040 | ||||||||
\(696\) | −2.49732e9 | −0.280764 | ||||||||
\(697\) | 2.26915e9 | 0.253834 | ||||||||
\(698\) | −8.44750e9 | −0.940230 | ||||||||
\(699\) | −2.25230e9 | −0.249434 | ||||||||
\(700\) | −1.16598e9 | −0.128484 | ||||||||
\(701\) | 3.94768e9 | 0.432841 | 0.216421 | − | 0.976300i | \(-0.430562\pi\) | ||||
0.216421 | + | 0.976300i | \(0.430562\pi\) | |||||||
\(702\) | 4.80014e8 | 0.0523690 | ||||||||
\(703\) | −3.10062e9 | −0.336593 | ||||||||
\(704\) | −3.77500e7 | −0.00407767 | ||||||||
\(705\) | 1.64251e9 | 0.176541 | ||||||||
\(706\) | −1.74938e9 | −0.187098 | ||||||||
\(707\) | 2.23042e10 | 2.37366 | ||||||||
\(708\) | −2.08014e9 | −0.220281 | ||||||||
\(709\) | 6.98988e9 | 0.736559 | 0.368280 | − | 0.929715i | \(-0.379947\pi\) | ||||
0.368280 | + | 0.929715i | \(0.379947\pi\) | |||||||
\(710\) | 2.30022e9 | 0.241194 | ||||||||
\(711\) | −4.24747e9 | −0.443186 | ||||||||
\(712\) | 2.56573e9 | 0.266398 | ||||||||
\(713\) | 2.67967e9 | 0.276865 | ||||||||
\(714\) | 1.68830e9 | 0.173582 | ||||||||
\(715\) | 5.48731e7 | 0.00561421 | ||||||||
\(716\) | 6.77427e9 | 0.689711 | ||||||||
\(717\) | 7.31504e9 | 0.741139 | ||||||||
\(718\) | 1.14527e9 | 0.115471 | ||||||||
\(719\) | −8.57873e9 | −0.860740 | −0.430370 | − | 0.902653i | \(-0.641617\pi\) | ||||
−0.430370 | + | 0.902653i | \(0.641617\pi\) | |||||||
\(720\) | 3.73248e8 | 0.0372678 | ||||||||
\(721\) | 2.19945e10 | 2.18545 | ||||||||
\(722\) | 3.76367e8 | 0.0372161 | ||||||||
\(723\) | 4.21053e9 | 0.414336 | ||||||||
\(724\) | −7.31648e9 | −0.716502 | ||||||||
\(725\) | 2.82267e9 | 0.275092 | ||||||||
\(726\) | 4.20475e9 | 0.407814 | ||||||||
\(727\) | 1.74014e10 | 1.67963 | 0.839815 | − | 0.542873i | \(-0.182664\pi\) | ||||
0.839815 | + | 0.542873i | \(0.182664\pi\) | |||||||
\(728\) | 1.81985e9 | 0.174813 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.41070e9 | −0.134216 | ||||||||
\(731\) | −2.39504e9 | −0.226778 | ||||||||
\(732\) | 1.06243e9 | 0.100117 | ||||||||
\(733\) | −2.57715e9 | −0.241700 | −0.120850 | − | 0.992671i | \(-0.538562\pi\) | ||||
−0.120850 | + | 0.992671i | \(0.538562\pi\) | |||||||
\(734\) | 2.63515e8 | 0.0245963 | ||||||||
\(735\) | −1.80891e9 | −0.168039 | ||||||||
\(736\) | 5.05109e8 | 0.0466995 | ||||||||
\(737\) | −3.28834e8 | −0.0302580 | ||||||||
\(738\) | 1.97414e9 | 0.180793 | ||||||||
\(739\) | 6.14971e9 | 0.560531 | 0.280265 | − | 0.959923i | \(-0.409578\pi\) | ||||
0.280265 | + | 0.959923i | \(0.409578\pi\) | |||||||
\(740\) | −3.61641e9 | −0.328070 | ||||||||
\(741\) | 5.64543e8 | 0.0509722 | ||||||||
\(742\) | 1.68218e10 | 1.51168 | ||||||||
\(743\) | −1.88648e10 | −1.68729 | −0.843646 | − | 0.536899i | \(-0.819595\pi\) | ||||
−0.843646 | + | 0.536899i | \(0.819595\pi\) | |||||||
\(744\) | −2.40314e9 | −0.213931 | ||||||||
\(745\) | 7.72830e9 | 0.684758 | ||||||||
\(746\) | −3.31354e9 | −0.292217 | ||||||||
\(747\) | 4.12298e9 | 0.361900 | ||||||||
\(748\) | −6.17816e7 | −0.00539764 | ||||||||
\(749\) | 8.49671e9 | 0.738864 | ||||||||
\(750\) | −4.21875e8 | −0.0365148 | ||||||||
\(751\) | −4.86541e9 | −0.419160 | −0.209580 | − | 0.977792i | \(-0.567210\pi\) | ||||
−0.209580 | + | 0.977792i | \(0.567210\pi\) | |||||||
\(752\) | −1.99340e9 | −0.170935 | ||||||||
\(753\) | −1.09789e9 | −0.0937080 | ||||||||
\(754\) | −4.40558e9 | −0.374286 | ||||||||
\(755\) | −6.87894e9 | −0.581711 | ||||||||
\(756\) | 1.46880e9 | 0.123634 | ||||||||
\(757\) | 7.18694e9 | 0.602155 | 0.301077 | − | 0.953600i | \(-0.402654\pi\) | ||||
0.301077 | + | 0.953600i | \(0.402654\pi\) | |||||||
\(758\) | −2.66046e9 | −0.221878 | ||||||||
\(759\) | 5.99343e7 | 0.00497541 | ||||||||
\(760\) | 4.38976e8 | 0.0362738 | ||||||||
\(761\) | 1.80224e10 | 1.48240 | 0.741202 | − | 0.671282i | \(-0.234256\pi\) | ||||
0.741202 | + | 0.671282i | \(0.234256\pi\) | |||||||
\(762\) | −5.54961e9 | −0.454381 | ||||||||
\(763\) | 7.85676e9 | 0.640335 | ||||||||
\(764\) | −1.88135e9 | −0.152631 | ||||||||
\(765\) | 6.10858e8 | 0.0493316 | ||||||||
\(766\) | 1.29781e10 | 1.04330 | ||||||||
\(767\) | −3.66963e9 | −0.293656 | ||||||||
\(768\) | −4.52985e8 | −0.0360844 | ||||||||
\(769\) | −6.91004e8 | −0.0547947 | −0.0273973 | − | 0.999625i | \(-0.508722\pi\) | ||||
−0.0273973 | + | 0.999625i | \(0.508722\pi\) | |||||||
\(770\) | 1.67907e8 | 0.0132541 | ||||||||
\(771\) | 2.36295e9 | 0.185679 | ||||||||
\(772\) | −3.15288e9 | −0.246630 | ||||||||
\(773\) | 5.49161e9 | 0.427633 | 0.213816 | − | 0.976874i | \(-0.431411\pi\) | ||||
0.213816 | + | 0.976874i | \(0.431411\pi\) | |||||||
\(774\) | −2.08366e9 | −0.161523 | ||||||||
\(775\) | 2.71623e9 | 0.209609 | ||||||||
\(776\) | −2.82707e9 | −0.217181 | ||||||||
\(777\) | −1.42313e10 | −1.08835 | ||||||||
\(778\) | −1.24933e10 | −0.951152 | ||||||||
\(779\) | 2.32179e9 | 0.175971 | ||||||||
\(780\) | 6.58455e8 | 0.0496816 | ||||||||
\(781\) | −3.31243e8 | −0.0248810 | ||||||||
\(782\) | 8.26661e8 | 0.0618164 | ||||||||
\(783\) | −3.55576e9 | −0.264707 | ||||||||
\(784\) | 2.19534e9 | 0.162703 | ||||||||
\(785\) | −1.07160e10 | −0.790661 | ||||||||
\(786\) | −5.93354e9 | −0.435848 | ||||||||
\(787\) | 1.30151e10 | 0.951779 | 0.475889 | − | 0.879505i | \(-0.342126\pi\) | ||||
0.475889 | + | 0.879505i | \(0.342126\pi\) | |||||||
\(788\) | −3.93484e9 | −0.286474 | ||||||||
\(789\) | 6.85417e8 | 0.0496804 | ||||||||
\(790\) | −5.82643e9 | −0.420443 | ||||||||
\(791\) | 1.49244e10 | 1.07221 | ||||||||
\(792\) | −5.37495e7 | −0.00384447 | ||||||||
\(793\) | 1.87425e9 | 0.133466 | ||||||||
\(794\) | 8.16146e9 | 0.578623 | ||||||||
\(795\) | 6.08646e9 | 0.429615 | ||||||||
\(796\) | 4.32707e9 | 0.304087 | ||||||||
\(797\) | −1.41341e10 | −0.988930 | −0.494465 | − | 0.869198i | \(-0.664636\pi\) | ||||
−0.494465 | + | 0.869198i | \(0.664636\pi\) | |||||||
\(798\) | 1.72745e9 | 0.120336 | ||||||||
\(799\) | −3.26240e9 | −0.226268 | ||||||||
\(800\) | 5.12000e8 | 0.0353553 | ||||||||
\(801\) | 3.65316e9 | 0.251162 | ||||||||
\(802\) | 9.96014e9 | 0.681797 | ||||||||
\(803\) | 2.03147e8 | 0.0138454 | ||||||||
\(804\) | −3.94588e9 | −0.267761 | ||||||||
\(805\) | −2.24666e9 | −0.151793 | ||||||||
\(806\) | −4.23944e9 | −0.285191 | ||||||||
\(807\) | 3.44735e9 | 0.230902 | ||||||||
\(808\) | −9.79408e9 | −0.653166 | ||||||||
\(809\) | −2.02199e10 | −1.34264 | −0.671318 | − | 0.741169i | \(-0.734272\pi\) | ||||
−0.671318 | + | 0.741169i | \(0.734272\pi\) | |||||||
\(810\) | 5.31441e8 | 0.0351364 | ||||||||
\(811\) | 1.48939e10 | 0.980474 | 0.490237 | − | 0.871589i | \(-0.336910\pi\) | ||||
0.490237 | + | 0.871589i | \(0.336910\pi\) | |||||||
\(812\) | −1.34807e10 | −0.883622 | ||||||||
\(813\) | 6.14914e9 | 0.401326 | ||||||||
\(814\) | 5.20781e8 | 0.0338431 | ||||||||
\(815\) | 1.10894e10 | 0.717555 | ||||||||
\(816\) | −7.41355e8 | −0.0477651 | ||||||||
\(817\) | −2.45059e9 | −0.157215 | ||||||||
\(818\) | 2.68860e9 | 0.171747 | ||||||||
\(819\) | 2.59115e9 | 0.164816 | ||||||||
\(820\) | 2.70802e9 | 0.171515 | ||||||||
\(821\) | −2.34070e10 | −1.47620 | −0.738100 | − | 0.674691i | \(-0.764277\pi\) | ||||
−0.738100 | + | 0.674691i | \(0.764277\pi\) | |||||||
\(822\) | −1.10129e10 | −0.691594 | ||||||||
\(823\) | −1.69046e10 | −1.05707 | −0.528537 | − | 0.848911i | \(-0.677259\pi\) | ||||
−0.528537 | + | 0.848911i | \(0.677259\pi\) | |||||||
\(824\) | −9.65812e9 | −0.601378 | ||||||||
\(825\) | 6.07520e7 | 0.00376679 | ||||||||
\(826\) | −1.12288e10 | −0.693269 | ||||||||
\(827\) | −1.99843e10 | −1.22862 | −0.614312 | − | 0.789063i | \(-0.710566\pi\) | ||||
−0.614312 | + | 0.789063i | \(0.710566\pi\) | |||||||
\(828\) | 7.19188e8 | 0.0440287 | ||||||||
\(829\) | −7.50348e9 | −0.457427 | −0.228714 | − | 0.973494i | \(-0.573452\pi\) | ||||
−0.228714 | + | 0.973494i | \(0.573452\pi\) | |||||||
\(830\) | 5.65567e9 | 0.343329 | ||||||||
\(831\) | 5.45912e8 | 0.0330004 | ||||||||
\(832\) | −7.99121e8 | −0.0481040 | ||||||||
\(833\) | 3.59290e9 | 0.215371 | ||||||||
\(834\) | 7.86118e9 | 0.469252 | ||||||||
\(835\) | −1.33824e10 | −0.795483 | ||||||||
\(836\) | −6.32146e7 | −0.00374193 | ||||||||
\(837\) | −3.42167e9 | −0.201697 | ||||||||
\(838\) | −1.30452e10 | −0.765766 | ||||||||
\(839\) | −1.35129e10 | −0.789920 | −0.394960 | − | 0.918698i | \(-0.629242\pi\) | ||||
−0.394960 | + | 0.918698i | \(0.629242\pi\) | |||||||
\(840\) | 2.01482e9 | 0.117289 | ||||||||
\(841\) | 1.53850e10 | 0.891889 | ||||||||
\(842\) | 3.76883e9 | 0.217578 | ||||||||
\(843\) | 1.54880e10 | 0.890430 | ||||||||
\(844\) | −4.15889e9 | −0.238111 | ||||||||
\(845\) | −6.68197e9 | −0.380983 | ||||||||
\(846\) | −2.83826e9 | −0.161159 | ||||||||
\(847\) | 2.26975e10 | 1.28347 | ||||||||
\(848\) | −7.38671e9 | −0.415973 | ||||||||
\(849\) | 1.38398e10 | 0.776162 | ||||||||
\(850\) | 8.37939e8 | 0.0468001 | ||||||||
\(851\) | −6.96824e9 | −0.387587 | ||||||||
\(852\) | −3.97479e9 | −0.220179 | ||||||||
\(853\) | 2.07977e10 | 1.14734 | 0.573671 | − | 0.819086i | \(-0.305519\pi\) | ||||
0.573671 | + | 0.819086i | \(0.305519\pi\) | |||||||
\(854\) | 5.73504e9 | 0.315090 | ||||||||
\(855\) | 6.25026e8 | 0.0341993 | ||||||||
\(856\) | −3.73103e9 | −0.203316 | ||||||||
\(857\) | −1.07072e9 | −0.0581091 | −0.0290546 | − | 0.999578i | \(-0.509250\pi\) | ||||
−0.0290546 | + | 0.999578i | \(0.509250\pi\) | |||||||
\(858\) | −9.48207e7 | −0.00512505 | ||||||||
\(859\) | −5.19338e9 | −0.279559 | −0.139780 | − | 0.990183i | \(-0.544639\pi\) | ||||
−0.139780 | + | 0.990183i | \(0.544639\pi\) | |||||||
\(860\) | −2.85825e9 | −0.153234 | ||||||||
\(861\) | 1.06566e10 | 0.568992 | ||||||||
\(862\) | 2.53447e10 | 1.34776 | ||||||||
\(863\) | 1.63619e10 | 0.866555 | 0.433277 | − | 0.901261i | \(-0.357357\pi\) | ||||
0.433277 | + | 0.901261i | \(0.357357\pi\) | |||||||
\(864\) | −6.44973e8 | −0.0340207 | ||||||||
\(865\) | −2.25284e9 | −0.118352 | ||||||||
\(866\) | 8.46981e9 | 0.443160 | ||||||||
\(867\) | 9.86584e9 | 0.514123 | ||||||||
\(868\) | −1.29723e10 | −0.673285 | ||||||||
\(869\) | 8.39033e8 | 0.0433721 | ||||||||
\(870\) | −4.87758e9 | −0.251123 | ||||||||
\(871\) | −6.96102e9 | −0.356951 | ||||||||
\(872\) | −3.45002e9 | −0.176203 | ||||||||
\(873\) | −4.02527e9 | −0.204760 | ||||||||
\(874\) | 8.45835e8 | 0.0428544 | ||||||||
\(875\) | −2.27731e9 | −0.114920 | ||||||||
\(876\) | 2.43768e9 | 0.122522 | ||||||||
\(877\) | −1.72847e10 | −0.865294 | −0.432647 | − | 0.901563i | \(-0.642420\pi\) | ||||
−0.432647 | + | 0.901563i | \(0.642420\pi\) | |||||||
\(878\) | −3.96931e9 | −0.197917 | ||||||||
\(879\) | −3.36888e9 | −0.167311 | ||||||||
\(880\) | −7.37304e7 | −0.00364718 | ||||||||
\(881\) | −3.03943e10 | −1.49753 | −0.748766 | − | 0.662834i | \(-0.769353\pi\) | ||||
−0.748766 | + | 0.662834i | \(0.769353\pi\) | |||||||
\(882\) | 3.12579e9 | 0.153398 | ||||||||
\(883\) | −3.74396e10 | −1.83007 | −0.915036 | − | 0.403372i | \(-0.867838\pi\) | ||||
−0.915036 | + | 0.403372i | \(0.867838\pi\) | |||||||
\(884\) | −1.30784e9 | −0.0636755 | ||||||||
\(885\) | −4.06278e9 | −0.197025 | ||||||||
\(886\) | 1.31684e10 | 0.636082 | ||||||||
\(887\) | −2.70761e10 | −1.30273 | −0.651364 | − | 0.758766i | \(-0.725803\pi\) | ||||
−0.651364 | + | 0.758766i | \(0.725803\pi\) | |||||||
\(888\) | 6.24916e9 | 0.299486 | ||||||||
\(889\) | −2.99572e10 | −1.43003 | ||||||||
\(890\) | 5.01119e9 | 0.238273 | ||||||||
\(891\) | −7.65300e7 | −0.00362460 | ||||||||
\(892\) | −9.29495e9 | −0.438501 | ||||||||
\(893\) | −3.33807e9 | −0.156861 | ||||||||
\(894\) | −1.33545e10 | −0.625096 | ||||||||
\(895\) | 1.32310e10 | 0.616896 | ||||||||
\(896\) | −2.44524e9 | −0.113565 | ||||||||
\(897\) | 1.26874e9 | 0.0586945 | ||||||||
\(898\) | 2.06439e10 | 0.951316 | ||||||||
\(899\) | 3.14041e10 | 1.44154 | ||||||||
\(900\) | 7.29000e8 | 0.0333333 | ||||||||
\(901\) | −1.20891e10 | −0.550626 | ||||||||
\(902\) | −3.89967e8 | −0.0176932 | ||||||||
\(903\) | −1.12478e10 | −0.508345 | ||||||||
\(904\) | −6.55352e9 | −0.295043 | ||||||||
\(905\) | −1.42900e10 | −0.640859 | ||||||||
\(906\) | 1.18868e10 | 0.531027 | ||||||||
\(907\) | −1.02866e10 | −0.457770 | −0.228885 | − | 0.973454i | \(-0.573508\pi\) | ||||
−0.228885 | + | 0.973454i | \(0.573508\pi\) | |||||||
\(908\) | −9.56455e9 | −0.423998 | ||||||||
\(909\) | −1.39451e10 | −0.615811 | ||||||||
\(910\) | 3.55439e9 | 0.156358 | ||||||||
\(911\) | 1.93021e10 | 0.845844 | 0.422922 | − | 0.906166i | \(-0.361004\pi\) | ||||
0.422922 | + | 0.906166i | \(0.361004\pi\) | |||||||
\(912\) | −7.58551e8 | −0.0331133 | ||||||||
\(913\) | −8.14443e8 | −0.0354171 | ||||||||
\(914\) | −2.76666e9 | −0.119852 | ||||||||
\(915\) | 2.07505e9 | 0.0895477 | ||||||||
\(916\) | −4.58822e9 | −0.197247 | ||||||||
\(917\) | −3.20296e10 | −1.37170 | ||||||||
\(918\) | −1.05556e9 | −0.0450334 | ||||||||
\(919\) | 2.38844e10 | 1.01510 | 0.507551 | − | 0.861622i | \(-0.330551\pi\) | ||||
0.507551 | + | 0.861622i | \(0.330551\pi\) | |||||||
\(920\) | 9.86540e8 | 0.0417693 | ||||||||
\(921\) | −2.00722e10 | −0.846617 | ||||||||
\(922\) | −3.82260e9 | −0.160620 | ||||||||
\(923\) | −7.01201e9 | −0.293519 | ||||||||
\(924\) | −2.90143e8 | −0.0120993 | ||||||||
\(925\) | −7.06331e9 | −0.293435 | ||||||||
\(926\) | −1.15399e10 | −0.477600 | ||||||||
\(927\) | −1.37515e10 | −0.566984 | ||||||||
\(928\) | 5.91958e9 | 0.243149 | ||||||||
\(929\) | −3.05958e9 | −0.125201 | −0.0626004 | − | 0.998039i | \(-0.519939\pi\) | ||||
−0.0626004 | + | 0.998039i | \(0.519939\pi\) | |||||||
\(930\) | −4.69364e9 | −0.191346 | ||||||||
\(931\) | 3.67623e9 | 0.149307 | ||||||||
\(932\) | 5.33878e9 | 0.216016 | ||||||||
\(933\) | −1.93046e10 | −0.778170 | ||||||||
\(934\) | 1.38031e10 | 0.554321 | ||||||||
\(935\) | −1.20667e8 | −0.00482780 | ||||||||
\(936\) | −1.13781e9 | −0.0453529 | ||||||||
\(937\) | 3.74978e10 | 1.48908 | 0.744538 | − | 0.667580i | \(-0.232670\pi\) | ||||
0.744538 | + | 0.667580i | \(0.232670\pi\) | |||||||
\(938\) | −2.13001e10 | −0.842698 | ||||||||
\(939\) | 1.26212e10 | 0.497475 | ||||||||
\(940\) | −3.89336e9 | −0.152889 | ||||||||
\(941\) | −8.71231e9 | −0.340855 | −0.170427 | − | 0.985370i | \(-0.554515\pi\) | ||||
−0.170427 | + | 0.985370i | \(0.554515\pi\) | |||||||
\(942\) | 1.85173e10 | 0.721772 | ||||||||
\(943\) | 5.21791e9 | 0.202631 | ||||||||
\(944\) | 4.93071e9 | 0.190769 | ||||||||
\(945\) | 2.86875e9 | 0.110581 | ||||||||
\(946\) | 4.11601e8 | 0.0158073 | ||||||||
\(947\) | 1.30219e10 | 0.498254 | 0.249127 | − | 0.968471i | \(-0.419856\pi\) | ||||
0.249127 | + | 0.968471i | \(0.419856\pi\) | |||||||
\(948\) | 1.00681e10 | 0.383811 | ||||||||
\(949\) | 4.30037e9 | 0.163333 | ||||||||
\(950\) | 8.57375e8 | 0.0324443 | ||||||||
\(951\) | −1.18826e9 | −0.0448002 | ||||||||
\(952\) | −4.00189e9 | −0.150326 | ||||||||
\(953\) | 7.85485e9 | 0.293977 | 0.146988 | − | 0.989138i | \(-0.453042\pi\) | ||||
0.146988 | + | 0.989138i | \(0.453042\pi\) | |||||||
\(954\) | −1.05174e10 | −0.392183 | ||||||||
\(955\) | −3.67450e9 | −0.136517 | ||||||||
\(956\) | −1.73394e10 | −0.641845 | ||||||||
\(957\) | 7.02395e8 | 0.0259054 | ||||||||
\(958\) | 1.82433e10 | 0.670385 | ||||||||
\(959\) | −5.94485e10 | −2.17659 | ||||||||
\(960\) | −8.84736e8 | −0.0322749 | ||||||||
\(961\) | 2.70725e9 | 0.0984002 | ||||||||
\(962\) | 1.10243e10 | 0.399244 | ||||||||
\(963\) | −5.31235e9 | −0.191688 | ||||||||
\(964\) | −9.98052e9 | −0.358826 | ||||||||
\(965\) | −6.15796e9 | −0.220593 | ||||||||
\(966\) | 3.88222e9 | 0.138567 | ||||||||
\(967\) | 1.72618e10 | 0.613893 | 0.306946 | − | 0.951727i | \(-0.400693\pi\) | ||||
0.306946 | + | 0.951727i | \(0.400693\pi\) | |||||||
\(968\) | −9.96681e9 | −0.353177 | ||||||||
\(969\) | −1.24144e9 | −0.0438323 | ||||||||
\(970\) | −5.52163e9 | −0.194252 | ||||||||
\(971\) | −3.66194e10 | −1.28364 | −0.641821 | − | 0.766854i | \(-0.721821\pi\) | ||||
−0.641821 | + | 0.766854i | \(0.721821\pi\) | |||||||
\(972\) | −9.18330e8 | −0.0320750 | ||||||||
\(973\) | 4.24352e10 | 1.47683 | ||||||||
\(974\) | 1.02056e10 | 0.353900 | ||||||||
\(975\) | 1.28605e9 | 0.0444365 | ||||||||
\(976\) | −2.51834e9 | −0.0867042 | ||||||||
\(977\) | −3.24882e10 | −1.11454 | −0.557268 | − | 0.830333i | \(-0.688150\pi\) | ||||
−0.557268 | + | 0.830333i | \(0.688150\pi\) | |||||||
\(978\) | −1.91624e10 | −0.655035 | ||||||||
\(979\) | −7.21635e8 | −0.0245798 | ||||||||
\(980\) | 4.28778e9 | 0.145526 | ||||||||
\(981\) | −4.91223e9 | −0.166126 | ||||||||
\(982\) | 1.59397e10 | 0.537143 | ||||||||
\(983\) | 5.28599e10 | 1.77496 | 0.887480 | − | 0.460846i | \(-0.152454\pi\) | ||||
0.887480 | + | 0.460846i | \(0.152454\pi\) | |||||||
\(984\) | −4.67945e9 | −0.156571 | ||||||||
\(985\) | −7.68523e9 | −0.256230 | ||||||||
\(986\) | 9.68798e9 | 0.321858 | ||||||||
\(987\) | −1.53211e10 | −0.507201 | ||||||||
\(988\) | −1.33818e9 | −0.0441432 | ||||||||
\(989\) | −5.50738e9 | −0.181033 | ||||||||
\(990\) | −1.04979e8 | −0.00343860 | ||||||||
\(991\) | −2.55077e10 | −0.832555 | −0.416277 | − | 0.909238i | \(-0.636665\pi\) | ||||
−0.416277 | + | 0.909238i | \(0.636665\pi\) | |||||||
\(992\) | 5.69634e9 | 0.185270 | ||||||||
\(993\) | −5.31396e9 | −0.172225 | ||||||||
\(994\) | −2.14562e10 | −0.692947 | ||||||||
\(995\) | 8.45130e9 | 0.271984 | ||||||||
\(996\) | −9.77299e9 | −0.313415 | ||||||||
\(997\) | −8.42787e9 | −0.269330 | −0.134665 | − | 0.990891i | \(-0.542996\pi\) | ||||
−0.134665 | + | 0.990891i | \(0.542996\pi\) | |||||||
\(998\) | −2.28813e10 | −0.728659 | ||||||||
\(999\) | 8.89773e9 | 0.282358 |
(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 | 570.8.a.a.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.8.a.a.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |