Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 1493 x^{14} + 8791 x^{13} + 890490 x^{12} - 5107725 x^{11} - 269092298 x^{10} + \cdots - 23\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.97136\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97136 | −0.174245 | −0.0871227 | − | 0.996198i | \(-0.527767\pi\) | ||||
−0.0871227 | + | 0.996198i | \(0.527767\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | −124.114 | −0.969639 | ||||||||
\(5\) | −339.775 | −1.21562 | −0.607809 | − | 0.794083i | \(-0.707951\pi\) | ||||
−0.607809 | + | 0.794083i | \(0.707951\pi\) | |||||||
\(6\) | 53.2268 | 0.100601 | ||||||||
\(7\) | 364.700 | 0.401877 | 0.200938 | − | 0.979604i | \(-0.435601\pi\) | ||||
0.200938 | + | 0.979604i | \(0.435601\pi\) | |||||||
\(8\) | 497.007 | 0.343200 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 669.820 | 0.211816 | ||||||||
\(11\) | −3588.22 | −0.812840 | −0.406420 | − | 0.913686i | \(-0.633223\pi\) | ||||
−0.406420 | + | 0.913686i | \(0.633223\pi\) | |||||||
\(12\) | 3351.07 | 0.559821 | ||||||||
\(13\) | 857.316 | 0.108228 | 0.0541140 | − | 0.998535i | \(-0.482767\pi\) | ||||
0.0541140 | + | 0.998535i | \(0.482767\pi\) | |||||||
\(14\) | −718.956 | −0.0700252 | ||||||||
\(15\) | 9173.94 | 0.701837 | ||||||||
\(16\) | 14906.8 | 0.909837 | ||||||||
\(17\) | 3649.35 | 0.180154 | 0.0900771 | − | 0.995935i | \(-0.471289\pi\) | ||||
0.0900771 | + | 0.995935i | \(0.471289\pi\) | |||||||
\(18\) | −1437.12 | −0.0580818 | ||||||||
\(19\) | −9650.25 | −0.322776 | −0.161388 | − | 0.986891i | \(-0.551597\pi\) | ||||
−0.161388 | + | 0.986891i | \(0.551597\pi\) | |||||||
\(20\) | 42170.8 | 1.17871 | ||||||||
\(21\) | −9846.91 | −0.232024 | ||||||||
\(22\) | 7073.68 | 0.141634 | ||||||||
\(23\) | 116133. | 1.99024 | 0.995122 | − | 0.0986484i | \(-0.0314519\pi\) | ||||
0.995122 | + | 0.0986484i | \(0.0314519\pi\) | |||||||
\(24\) | −13419.2 | −0.198147 | ||||||||
\(25\) | 37322.4 | 0.477727 | ||||||||
\(26\) | −1690.08 | −0.0188582 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −45264.3 | −0.389675 | ||||||||
\(29\) | 247675. | 1.88577 | 0.942886 | − | 0.333116i | \(-0.108100\pi\) | ||||
0.942886 | + | 0.333116i | \(0.108100\pi\) | |||||||
\(30\) | −18085.1 | −0.122292 | ||||||||
\(31\) | 114054. | 0.687617 | 0.343808 | − | 0.939040i | \(-0.388283\pi\) | ||||
0.343808 | + | 0.939040i | \(0.388283\pi\) | |||||||
\(32\) | −93003.6 | −0.501735 | ||||||||
\(33\) | 96882.0 | 0.469293 | ||||||||
\(34\) | −7194.19 | −0.0313910 | ||||||||
\(35\) | −123916. | −0.488529 | ||||||||
\(36\) | −90478.9 | −0.323213 | ||||||||
\(37\) | −194589. | −0.631556 | −0.315778 | − | 0.948833i | \(-0.602266\pi\) | ||||
−0.315778 | + | 0.948833i | \(0.602266\pi\) | |||||||
\(38\) | 19024.1 | 0.0562422 | ||||||||
\(39\) | −23147.5 | −0.0624854 | ||||||||
\(40\) | −168871. | −0.417201 | ||||||||
\(41\) | −594925. | −1.34809 | −0.674045 | − | 0.738691i | \(-0.735444\pi\) | ||||
−0.674045 | + | 0.738691i | \(0.735444\pi\) | |||||||
\(42\) | 19411.8 | 0.0404290 | ||||||||
\(43\) | 247788. | 0.475270 | 0.237635 | − | 0.971354i | \(-0.423628\pi\) | ||||
0.237635 | + | 0.971354i | \(0.423628\pi\) | |||||||
\(44\) | 445348. | 0.788161 | ||||||||
\(45\) | −247696. | −0.405206 | ||||||||
\(46\) | −228939. | −0.346791 | ||||||||
\(47\) | −1.30718e6 | −1.83651 | −0.918254 | − | 0.395993i | \(-0.870400\pi\) | ||||
−0.918254 | + | 0.395993i | \(0.870400\pi\) | |||||||
\(48\) | −402483. | −0.525295 | ||||||||
\(49\) | −690537. | −0.838495 | ||||||||
\(50\) | −73575.9 | −0.0832416 | ||||||||
\(51\) | −98532.5 | −0.104012 | ||||||||
\(52\) | −106405. | −0.104942 | ||||||||
\(53\) | 1.20394e6 | 1.11081 | 0.555403 | − | 0.831581i | \(-0.312564\pi\) | ||||
0.555403 | + | 0.831581i | \(0.312564\pi\) | |||||||
\(54\) | 38802.3 | 0.0335335 | ||||||||
\(55\) | 1.21919e6 | 0.988102 | ||||||||
\(56\) | 181259. | 0.137924 | ||||||||
\(57\) | 260557. | 0.186355 | ||||||||
\(58\) | −488257. | −0.328587 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −1.13861e6 | −0.680528 | ||||||||
\(61\) | 428862. | 0.241915 | 0.120958 | − | 0.992658i | \(-0.461404\pi\) | ||||
0.120958 | + | 0.992658i | \(0.461404\pi\) | |||||||
\(62\) | −224843. | −0.119814 | ||||||||
\(63\) | 265866. | 0.133959 | ||||||||
\(64\) | −1.72472e6 | −0.822412 | ||||||||
\(65\) | −291295. | −0.131564 | ||||||||
\(66\) | −190989. | −0.0817722 | ||||||||
\(67\) | −2.01026e6 | −0.816565 | −0.408283 | − | 0.912856i | \(-0.633872\pi\) | ||||
−0.408283 | + | 0.912856i | \(0.633872\pi\) | |||||||
\(68\) | −452934. | −0.174684 | ||||||||
\(69\) | −3.13558e6 | −1.14907 | ||||||||
\(70\) | 244284. | 0.0851238 | ||||||||
\(71\) | 1.87858e6 | 0.622909 | 0.311454 | − | 0.950261i | \(-0.399184\pi\) | ||||
0.311454 | + | 0.950261i | \(0.399184\pi\) | |||||||
\(72\) | 362318. | 0.114400 | ||||||||
\(73\) | 2.35049e6 | 0.707178 | 0.353589 | − | 0.935401i | \(-0.384961\pi\) | ||||
0.353589 | + | 0.935401i | \(0.384961\pi\) | |||||||
\(74\) | 383605. | 0.110046 | ||||||||
\(75\) | −1.00770e6 | −0.275816 | ||||||||
\(76\) | 1.19773e6 | 0.312976 | ||||||||
\(77\) | −1.30863e6 | −0.326661 | ||||||||
\(78\) | 45632.2 | 0.0108878 | ||||||||
\(79\) | −3.74874e6 | −0.855442 | −0.427721 | − | 0.903911i | \(-0.640683\pi\) | ||||
−0.427721 | + | 0.903911i | \(0.640683\pi\) | |||||||
\(80\) | −5.06496e6 | −1.10601 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.17281e6 | 0.234898 | ||||||||
\(83\) | 3.21289e6 | 0.616768 | 0.308384 | − | 0.951262i | \(-0.400212\pi\) | ||||
0.308384 | + | 0.951262i | \(0.400212\pi\) | |||||||
\(84\) | 1.22214e6 | 0.224979 | ||||||||
\(85\) | −1.23996e6 | −0.218999 | ||||||||
\(86\) | −488480. | −0.0828137 | ||||||||
\(87\) | −6.68722e6 | −1.08875 | ||||||||
\(88\) | −1.78337e6 | −0.278967 | ||||||||
\(89\) | −544547. | −0.0818786 | −0.0409393 | − | 0.999162i | \(-0.513035\pi\) | ||||
−0.0409393 | + | 0.999162i | \(0.513035\pi\) | |||||||
\(90\) | 488299. | 0.0706053 | ||||||||
\(91\) | 312663. | 0.0434943 | ||||||||
\(92\) | −1.44136e7 | −1.92982 | ||||||||
\(93\) | −3.07947e6 | −0.396996 | ||||||||
\(94\) | 2.57692e6 | 0.320003 | ||||||||
\(95\) | 3.27892e6 | 0.392372 | ||||||||
\(96\) | 2.51110e6 | 0.289677 | ||||||||
\(97\) | −2.91764e6 | −0.324586 | −0.162293 | − | 0.986743i | \(-0.551889\pi\) | ||||
−0.162293 | + | 0.986743i | \(0.551889\pi\) | |||||||
\(98\) | 1.36130e6 | 0.146104 | ||||||||
\(99\) | −2.61581e6 | −0.270947 | ||||||||
\(100\) | −4.63222e6 | −0.463222 | ||||||||
\(101\) | −1.99790e7 | −1.92952 | −0.964761 | − | 0.263129i | \(-0.915246\pi\) | ||||
−0.964761 | + | 0.263129i | \(0.915246\pi\) | |||||||
\(102\) | 194243. | 0.0181236 | ||||||||
\(103\) | −1.14245e7 | −1.03016 | −0.515082 | − | 0.857141i | \(-0.672239\pi\) | ||||
−0.515082 | + | 0.857141i | \(0.672239\pi\) | |||||||
\(104\) | 426092. | 0.0371439 | ||||||||
\(105\) | 3.34574e6 | 0.282052 | ||||||||
\(106\) | −2.37340e6 | −0.193553 | ||||||||
\(107\) | 2.29986e7 | 1.81492 | 0.907460 | − | 0.420138i | \(-0.138018\pi\) | ||||
0.907460 | + | 0.420138i | \(0.138018\pi\) | |||||||
\(108\) | 2.44293e6 | 0.186607 | ||||||||
\(109\) | 2.02074e7 | 1.49457 | 0.747287 | − | 0.664502i | \(-0.231356\pi\) | ||||
0.747287 | + | 0.664502i | \(0.231356\pi\) | |||||||
\(110\) | −2.40346e6 | −0.172172 | ||||||||
\(111\) | 5.25390e6 | 0.364629 | ||||||||
\(112\) | 5.43650e6 | 0.365643 | ||||||||
\(113\) | −1.26444e7 | −0.824374 | −0.412187 | − | 0.911099i | \(-0.635235\pi\) | ||||
−0.412187 | + | 0.911099i | \(0.635235\pi\) | |||||||
\(114\) | −513651. | −0.0324714 | ||||||||
\(115\) | −3.94590e7 | −2.41938 | ||||||||
\(116\) | −3.07399e7 | −1.82852 | ||||||||
\(117\) | 624983. | 0.0360760 | ||||||||
\(118\) | −404876. | −0.0226848 | ||||||||
\(119\) | 1.33092e6 | 0.0723998 | ||||||||
\(120\) | 4.55951e6 | 0.240871 | ||||||||
\(121\) | −6.61184e6 | −0.339292 | ||||||||
\(122\) | −845441. | −0.0421526 | ||||||||
\(123\) | 1.60630e7 | 0.778320 | ||||||||
\(124\) | −1.41557e7 | −0.666740 | ||||||||
\(125\) | 1.38637e7 | 0.634885 | ||||||||
\(126\) | −524119. | −0.0233417 | ||||||||
\(127\) | 3.20643e7 | 1.38902 | 0.694509 | − | 0.719484i | \(-0.255621\pi\) | ||||
0.694509 | + | 0.719484i | \(0.255621\pi\) | |||||||
\(128\) | 1.53045e7 | 0.645037 | ||||||||
\(129\) | −6.69028e6 | −0.274398 | ||||||||
\(130\) | 574248. | 0.0229244 | ||||||||
\(131\) | −2.38103e7 | −0.925369 | −0.462684 | − | 0.886523i | \(-0.653114\pi\) | ||||
−0.462684 | + | 0.886523i | \(0.653114\pi\) | |||||||
\(132\) | −1.20244e7 | −0.455045 | ||||||||
\(133\) | −3.51945e6 | −0.129716 | ||||||||
\(134\) | 3.96295e6 | 0.142283 | ||||||||
\(135\) | 6.68780e6 | 0.233946 | ||||||||
\(136\) | 1.81375e6 | 0.0618290 | ||||||||
\(137\) | 2.13799e7 | 0.710370 | 0.355185 | − | 0.934796i | \(-0.384418\pi\) | ||||
0.355185 | + | 0.934796i | \(0.384418\pi\) | |||||||
\(138\) | 6.18136e6 | 0.200220 | ||||||||
\(139\) | −3.64257e7 | −1.15042 | −0.575209 | − | 0.818006i | \(-0.695079\pi\) | ||||
−0.575209 | + | 0.818006i | \(0.695079\pi\) | |||||||
\(140\) | 1.53797e7 | 0.473696 | ||||||||
\(141\) | 3.52938e7 | 1.06031 | ||||||||
\(142\) | −3.70335e6 | −0.108539 | ||||||||
\(143\) | −3.07624e6 | −0.0879719 | ||||||||
\(144\) | 1.08670e7 | 0.303279 | ||||||||
\(145\) | −8.41539e7 | −2.29238 | ||||||||
\(146\) | −4.63367e6 | −0.123222 | ||||||||
\(147\) | 1.86445e7 | 0.484105 | ||||||||
\(148\) | 2.41512e7 | 0.612381 | ||||||||
\(149\) | 95229.9 | 0.00235842 | 0.00117921 | − | 0.999999i | \(-0.499625\pi\) | ||||
0.00117921 | + | 0.999999i | \(0.499625\pi\) | |||||||
\(150\) | 1.98655e6 | 0.0480596 | ||||||||
\(151\) | 4.71653e7 | 1.11482 | 0.557408 | − | 0.830238i | \(-0.311796\pi\) | ||||
0.557408 | + | 0.830238i | \(0.311796\pi\) | |||||||
\(152\) | −4.79624e6 | −0.110777 | ||||||||
\(153\) | 2.66038e6 | 0.0600514 | ||||||||
\(154\) | 2.57977e6 | 0.0569192 | ||||||||
\(155\) | −3.87529e7 | −0.835879 | ||||||||
\(156\) | 2.87293e6 | 0.0605883 | ||||||||
\(157\) | 4.44571e7 | 0.916838 | 0.458419 | − | 0.888736i | \(-0.348416\pi\) | ||||
0.458419 | + | 0.888736i | \(0.348416\pi\) | |||||||
\(158\) | 7.39012e6 | 0.149057 | ||||||||
\(159\) | −3.25063e7 | −0.641324 | ||||||||
\(160\) | 3.16003e7 | 0.609918 | ||||||||
\(161\) | 4.23536e7 | 0.799833 | ||||||||
\(162\) | −1.04766e6 | −0.0193606 | ||||||||
\(163\) | −9.85994e7 | −1.78327 | −0.891636 | − | 0.452753i | \(-0.850442\pi\) | ||||
−0.891636 | + | 0.452753i | \(0.850442\pi\) | |||||||
\(164\) | 7.38384e7 | 1.30716 | ||||||||
\(165\) | −3.29181e7 | −0.570481 | ||||||||
\(166\) | −6.33376e6 | −0.107469 | ||||||||
\(167\) | 1.60639e7 | 0.266897 | 0.133449 | − | 0.991056i | \(-0.457395\pi\) | ||||
0.133449 | + | 0.991056i | \(0.457395\pi\) | |||||||
\(168\) | −4.89398e6 | −0.0796306 | ||||||||
\(169\) | −6.20135e7 | −0.988287 | ||||||||
\(170\) | 2.44441e6 | 0.0381595 | ||||||||
\(171\) | −7.03503e6 | −0.107592 | ||||||||
\(172\) | −3.07539e7 | −0.460841 | ||||||||
\(173\) | 9.63596e7 | 1.41493 | 0.707463 | − | 0.706751i | \(-0.249840\pi\) | ||||
0.707463 | + | 0.706751i | \(0.249840\pi\) | |||||||
\(174\) | 1.31829e7 | 0.189710 | ||||||||
\(175\) | 1.36115e7 | 0.191987 | ||||||||
\(176\) | −5.34888e7 | −0.739552 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 1.07350e6 | 0.0142670 | ||||||||
\(179\) | 6.96623e7 | 0.907846 | 0.453923 | − | 0.891041i | \(-0.350024\pi\) | ||||
0.453923 | + | 0.891041i | \(0.350024\pi\) | |||||||
\(180\) | 3.07425e7 | 0.392903 | ||||||||
\(181\) | −1.04761e8 | −1.31319 | −0.656593 | − | 0.754245i | \(-0.728003\pi\) | ||||
−0.656593 | + | 0.754245i | \(0.728003\pi\) | |||||||
\(182\) | −616372. | −0.00757868 | ||||||||
\(183\) | −1.15793e7 | −0.139670 | ||||||||
\(184\) | 5.77187e7 | 0.683053 | ||||||||
\(185\) | 6.61165e7 | 0.767731 | ||||||||
\(186\) | 6.07075e6 | 0.0691747 | ||||||||
\(187\) | −1.30947e7 | −0.146436 | ||||||||
\(188\) | 1.62239e8 | 1.78075 | ||||||||
\(189\) | −7.17839e6 | −0.0773412 | ||||||||
\(190\) | −6.46393e6 | −0.0683690 | ||||||||
\(191\) | 3.38716e7 | 0.351738 | 0.175869 | − | 0.984414i | \(-0.443727\pi\) | ||||
0.175869 | + | 0.984414i | \(0.443727\pi\) | |||||||
\(192\) | 4.65675e7 | 0.474820 | ||||||||
\(193\) | −5.74536e7 | −0.575264 | −0.287632 | − | 0.957741i | \(-0.592868\pi\) | ||||
−0.287632 | + | 0.957741i | \(0.592868\pi\) | |||||||
\(194\) | 5.75172e6 | 0.0565576 | ||||||||
\(195\) | 7.86496e6 | 0.0759584 | ||||||||
\(196\) | 8.57051e7 | 0.813037 | ||||||||
\(197\) | 7.82632e7 | 0.729333 | 0.364667 | − | 0.931138i | \(-0.381183\pi\) | ||||
0.364667 | + | 0.931138i | \(0.381183\pi\) | |||||||
\(198\) | 5.15671e6 | 0.0472112 | ||||||||
\(199\) | −1.18386e8 | −1.06491 | −0.532455 | − | 0.846458i | \(-0.678731\pi\) | ||||
−0.532455 | + | 0.846458i | \(0.678731\pi\) | |||||||
\(200\) | 1.85495e7 | 0.163956 | ||||||||
\(201\) | 5.42771e7 | 0.471444 | ||||||||
\(202\) | 3.93859e7 | 0.336210 | ||||||||
\(203\) | 9.03271e7 | 0.757848 | ||||||||
\(204\) | 1.22292e7 | 0.100854 | ||||||||
\(205\) | 2.02141e8 | 1.63876 | ||||||||
\(206\) | 2.25218e7 | 0.179501 | ||||||||
\(207\) | 8.46606e7 | 0.663415 | ||||||||
\(208\) | 1.27798e7 | 0.0984698 | ||||||||
\(209\) | 3.46272e7 | 0.262365 | ||||||||
\(210\) | −6.59566e6 | −0.0491463 | ||||||||
\(211\) | 4.78501e7 | 0.350666 | 0.175333 | − | 0.984509i | \(-0.443900\pi\) | ||||
0.175333 | + | 0.984509i | \(0.443900\pi\) | |||||||
\(212\) | −1.49425e8 | −1.07708 | ||||||||
\(213\) | −5.07215e7 | −0.359637 | ||||||||
\(214\) | −4.53385e7 | −0.316241 | ||||||||
\(215\) | −8.41923e7 | −0.577747 | ||||||||
\(216\) | −9.78259e6 | −0.0660489 | ||||||||
\(217\) | 4.15957e7 | 0.276337 | ||||||||
\(218\) | −3.98361e7 | −0.260423 | ||||||||
\(219\) | −6.34632e7 | −0.408289 | ||||||||
\(220\) | −1.51318e8 | −0.958102 | ||||||||
\(221\) | 3.12865e6 | 0.0194977 | ||||||||
\(222\) | −1.03573e7 | −0.0635349 | ||||||||
\(223\) | 1.24666e8 | 0.752800 | 0.376400 | − | 0.926457i | \(-0.377162\pi\) | ||||
0.376400 | + | 0.926457i | \(0.377162\pi\) | |||||||
\(224\) | −3.39184e7 | −0.201636 | ||||||||
\(225\) | 2.72080e7 | 0.159242 | ||||||||
\(226\) | 2.49267e7 | 0.143643 | ||||||||
\(227\) | 7.13606e7 | 0.404919 | 0.202460 | − | 0.979291i | \(-0.435107\pi\) | ||||
0.202460 | + | 0.979291i | \(0.435107\pi\) | |||||||
\(228\) | −3.23387e7 | −0.180697 | ||||||||
\(229\) | −3.39682e8 | −1.86917 | −0.934584 | − | 0.355743i | \(-0.884228\pi\) | ||||
−0.934584 | + | 0.355743i | \(0.884228\pi\) | |||||||
\(230\) | 7.77879e7 | 0.421565 | ||||||||
\(231\) | 3.53329e7 | 0.188598 | ||||||||
\(232\) | 1.23096e8 | 0.647198 | ||||||||
\(233\) | −3.19085e8 | −1.65257 | −0.826286 | − | 0.563250i | \(-0.809551\pi\) | ||||
−0.826286 | + | 0.563250i | \(0.809551\pi\) | |||||||
\(234\) | −1.23207e6 | −0.00628607 | ||||||||
\(235\) | 4.44147e8 | 2.23249 | ||||||||
\(236\) | −2.54904e7 | −0.126236 | ||||||||
\(237\) | 1.01216e8 | 0.493890 | ||||||||
\(238\) | −2.62372e6 | −0.0126153 | ||||||||
\(239\) | 2.48784e8 | 1.17877 | 0.589387 | − | 0.807851i | \(-0.299369\pi\) | ||||
0.589387 | + | 0.807851i | \(0.299369\pi\) | |||||||
\(240\) | 1.36754e8 | 0.638558 | ||||||||
\(241\) | −1.02085e8 | −0.469788 | −0.234894 | − | 0.972021i | \(-0.575474\pi\) | ||||
−0.234894 | + | 0.972021i | \(0.575474\pi\) | |||||||
\(242\) | 1.30343e7 | 0.0591200 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −5.32276e7 | −0.234570 | ||||||||
\(245\) | 2.34627e8 | 1.01929 | ||||||||
\(246\) | −3.16659e7 | −0.135619 | ||||||||
\(247\) | −8.27331e6 | −0.0349333 | ||||||||
\(248\) | 5.66859e7 | 0.235990 | ||||||||
\(249\) | −8.67479e7 | −0.356091 | ||||||||
\(250\) | −2.73304e7 | −0.110626 | ||||||||
\(251\) | 1.69390e8 | 0.676131 | 0.338066 | − | 0.941123i | \(-0.390227\pi\) | ||||
0.338066 | + | 0.941123i | \(0.390227\pi\) | |||||||
\(252\) | −3.29977e7 | −0.129892 | ||||||||
\(253\) | −4.16709e8 | −1.61775 | ||||||||
\(254\) | −6.32102e7 | −0.242030 | ||||||||
\(255\) | 3.34789e7 | 0.126439 | ||||||||
\(256\) | 1.90594e8 | 0.710018 | ||||||||
\(257\) | −4.15160e8 | −1.52563 | −0.762815 | − | 0.646617i | \(-0.776183\pi\) | ||||
−0.762815 | + | 0.646617i | \(0.776183\pi\) | |||||||
\(258\) | 1.31890e7 | 0.0478125 | ||||||||
\(259\) | −7.09666e7 | −0.253808 | ||||||||
\(260\) | 3.61537e7 | 0.127569 | ||||||||
\(261\) | 1.80555e8 | 0.628591 | ||||||||
\(262\) | 4.69387e7 | 0.161241 | ||||||||
\(263\) | −2.46530e8 | −0.835650 | −0.417825 | − | 0.908527i | \(-0.637208\pi\) | ||||
−0.417825 | + | 0.908527i | \(0.637208\pi\) | |||||||
\(264\) | 4.81511e7 | 0.161062 | ||||||||
\(265\) | −4.09068e8 | −1.35032 | ||||||||
\(266\) | 6.93810e6 | 0.0226024 | ||||||||
\(267\) | 1.47028e7 | 0.0472726 | ||||||||
\(268\) | 2.49501e8 | 0.791773 | ||||||||
\(269\) | 3.18928e8 | 0.998987 | 0.499494 | − | 0.866318i | \(-0.333519\pi\) | ||||
0.499494 | + | 0.866318i | \(0.333519\pi\) | |||||||
\(270\) | −1.31841e7 | −0.0407640 | ||||||||
\(271\) | −3.87904e8 | −1.18394 | −0.591972 | − | 0.805958i | \(-0.701651\pi\) | ||||
−0.591972 | + | 0.805958i | \(0.701651\pi\) | |||||||
\(272\) | 5.44000e7 | 0.163911 | ||||||||
\(273\) | −8.44191e6 | −0.0251114 | ||||||||
\(274\) | −4.21476e7 | −0.123779 | ||||||||
\(275\) | −1.33921e8 | −0.388315 | ||||||||
\(276\) | 3.89168e8 | 1.11418 | ||||||||
\(277\) | −7.42290e7 | −0.209843 | −0.104921 | − | 0.994481i | \(-0.533459\pi\) | ||||
−0.104921 | + | 0.994481i | \(0.533459\pi\) | |||||||
\(278\) | 7.18082e7 | 0.200455 | ||||||||
\(279\) | 8.31457e7 | 0.229206 | ||||||||
\(280\) | −6.15873e7 | −0.167663 | ||||||||
\(281\) | −6.16298e8 | −1.65698 | −0.828492 | − | 0.560001i | \(-0.810801\pi\) | ||||
−0.828492 | + | 0.560001i | \(0.810801\pi\) | |||||||
\(282\) | −6.95769e7 | −0.184754 | ||||||||
\(283\) | 7.96612e7 | 0.208927 | 0.104463 | − | 0.994529i | \(-0.466687\pi\) | ||||
0.104463 | + | 0.994529i | \(0.466687\pi\) | |||||||
\(284\) | −2.33157e8 | −0.603996 | ||||||||
\(285\) | −8.85308e7 | −0.226536 | ||||||||
\(286\) | 6.06438e6 | 0.0153287 | ||||||||
\(287\) | −2.16969e8 | −0.541766 | ||||||||
\(288\) | −6.77996e7 | −0.167245 | ||||||||
\(289\) | −3.97021e8 | −0.967544 | ||||||||
\(290\) | 1.65898e8 | 0.399436 | ||||||||
\(291\) | 7.87762e7 | 0.187400 | ||||||||
\(292\) | −2.91728e8 | −0.685707 | ||||||||
\(293\) | 2.50390e8 | 0.581542 | 0.290771 | − | 0.956793i | \(-0.406088\pi\) | ||||
0.290771 | + | 0.956793i | \(0.406088\pi\) | |||||||
\(294\) | −3.67550e7 | −0.0843531 | ||||||||
\(295\) | −6.97828e7 | −0.158260 | ||||||||
\(296\) | −9.67121e7 | −0.216750 | ||||||||
\(297\) | 7.06270e7 | 0.156431 | ||||||||
\(298\) | −187732. | −0.000410944 0 | ||||||||
\(299\) | 9.95623e7 | 0.215400 | ||||||||
\(300\) | 1.25070e8 | 0.267441 | ||||||||
\(301\) | 9.03684e7 | 0.191000 | ||||||||
\(302\) | −9.29799e7 | −0.194252 | ||||||||
\(303\) | 5.39434e8 | 1.11401 | ||||||||
\(304\) | −1.43854e8 | −0.293673 | ||||||||
\(305\) | −1.45717e8 | −0.294076 | ||||||||
\(306\) | −5.24456e6 | −0.0104637 | ||||||||
\(307\) | −3.31396e8 | −0.653677 | −0.326839 | − | 0.945080i | \(-0.605983\pi\) | ||||
−0.326839 | + | 0.945080i | \(0.605983\pi\) | |||||||
\(308\) | 1.62418e8 | 0.316743 | ||||||||
\(309\) | 3.08461e8 | 0.594766 | ||||||||
\(310\) | 7.63960e7 | 0.145648 | ||||||||
\(311\) | −9.41919e7 | −0.177563 | −0.0887815 | − | 0.996051i | \(-0.528297\pi\) | ||||
−0.0887815 | + | 0.996051i | \(0.528297\pi\) | |||||||
\(312\) | −1.15045e7 | −0.0214450 | ||||||||
\(313\) | −5.39491e8 | −0.994441 | −0.497220 | − | 0.867624i | \(-0.665646\pi\) | ||||
−0.497220 | + | 0.867624i | \(0.665646\pi\) | |||||||
\(314\) | −8.76411e7 | −0.159755 | ||||||||
\(315\) | −9.03349e7 | −0.162843 | ||||||||
\(316\) | 4.65270e8 | 0.829470 | ||||||||
\(317\) | 6.91838e8 | 1.21982 | 0.609912 | − | 0.792469i | \(-0.291205\pi\) | ||||
0.609912 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(318\) | 6.40817e7 | 0.111748 | ||||||||
\(319\) | −8.88713e8 | −1.53283 | ||||||||
\(320\) | 5.86019e8 | 0.999739 | ||||||||
\(321\) | −6.20961e8 | −1.04784 | ||||||||
\(322\) | −8.34942e7 | −0.139367 | ||||||||
\(323\) | −3.52171e7 | −0.0581494 | ||||||||
\(324\) | −6.59591e7 | −0.107738 | ||||||||
\(325\) | 3.19971e7 | 0.0517033 | ||||||||
\(326\) | 1.94375e8 | 0.310727 | ||||||||
\(327\) | −5.45599e8 | −0.862893 | ||||||||
\(328\) | −2.95682e8 | −0.462665 | ||||||||
\(329\) | −4.76729e8 | −0.738050 | ||||||||
\(330\) | 6.48935e7 | 0.0994037 | ||||||||
\(331\) | −8.54742e8 | −1.29550 | −0.647750 | − | 0.761853i | \(-0.724290\pi\) | ||||
−0.647750 | + | 0.761853i | \(0.724290\pi\) | |||||||
\(332\) | −3.98763e8 | −0.598042 | ||||||||
\(333\) | −1.41855e8 | −0.210519 | ||||||||
\(334\) | −3.16678e7 | −0.0465056 | ||||||||
\(335\) | 6.83038e8 | 0.992631 | ||||||||
\(336\) | −1.46786e8 | −0.211104 | ||||||||
\(337\) | 1.27131e8 | 0.180945 | 0.0904723 | − | 0.995899i | \(-0.471162\pi\) | ||||
0.0904723 | + | 0.995899i | \(0.471162\pi\) | |||||||
\(338\) | 1.22251e8 | 0.172204 | ||||||||
\(339\) | 3.41399e8 | 0.475952 | ||||||||
\(340\) | 1.53896e8 | 0.212349 | ||||||||
\(341\) | −4.09253e8 | −0.558922 | ||||||||
\(342\) | 1.38686e7 | 0.0187474 | ||||||||
\(343\) | −5.52185e8 | −0.738848 | ||||||||
\(344\) | 1.23152e8 | 0.163113 | ||||||||
\(345\) | 1.06539e9 | 1.39683 | ||||||||
\(346\) | −1.89960e8 | −0.246544 | ||||||||
\(347\) | −6.17139e7 | −0.0792920 | −0.0396460 | − | 0.999214i | \(-0.512623\pi\) | ||||
−0.0396460 | + | 0.999214i | \(0.512623\pi\) | |||||||
\(348\) | 8.29976e8 | 1.05569 | ||||||||
\(349\) | 3.92987e8 | 0.494868 | 0.247434 | − | 0.968905i | \(-0.420413\pi\) | ||||
0.247434 | + | 0.968905i | \(0.420413\pi\) | |||||||
\(350\) | −2.68332e7 | −0.0334529 | ||||||||
\(351\) | −1.68746e7 | −0.0208285 | ||||||||
\(352\) | 3.33717e8 | 0.407830 | ||||||||
\(353\) | −1.45872e9 | −1.76506 | −0.882531 | − | 0.470254i | \(-0.844162\pi\) | ||||
−0.882531 | + | 0.470254i | \(0.844162\pi\) | |||||||
\(354\) | 1.09317e7 | 0.0130971 | ||||||||
\(355\) | −6.38294e8 | −0.757219 | ||||||||
\(356\) | 6.75857e7 | 0.0793926 | ||||||||
\(357\) | −3.59348e7 | −0.0418000 | ||||||||
\(358\) | −1.37330e8 | −0.158188 | ||||||||
\(359\) | −1.00957e9 | −1.15162 | −0.575808 | − | 0.817585i | \(-0.695313\pi\) | ||||
−0.575808 | + | 0.817585i | \(0.695313\pi\) | |||||||
\(360\) | −1.23107e8 | −0.139067 | ||||||||
\(361\) | −8.00744e8 | −0.895816 | ||||||||
\(362\) | 2.06523e8 | 0.228817 | ||||||||
\(363\) | 1.78520e8 | 0.195890 | ||||||||
\(364\) | −3.88058e7 | −0.0421737 | ||||||||
\(365\) | −7.98639e8 | −0.859658 | ||||||||
\(366\) | 2.28269e7 | 0.0243368 | ||||||||
\(367\) | 6.89693e8 | 0.728324 | 0.364162 | − | 0.931336i | \(-0.381355\pi\) | ||||
0.364162 | + | 0.931336i | \(0.381355\pi\) | |||||||
\(368\) | 1.73116e9 | 1.81080 | ||||||||
\(369\) | −4.33700e8 | −0.449363 | ||||||||
\(370\) | −1.30340e8 | −0.133774 | ||||||||
\(371\) | 4.39076e8 | 0.446407 | ||||||||
\(372\) | 3.82205e8 | 0.384942 | ||||||||
\(373\) | 1.52953e7 | 0.0152608 | 0.00763041 | − | 0.999971i | \(-0.497571\pi\) | ||||
0.00763041 | + | 0.999971i | \(0.497571\pi\) | |||||||
\(374\) | 2.58143e7 | 0.0255159 | ||||||||
\(375\) | −3.74321e8 | −0.366551 | ||||||||
\(376\) | −6.49678e8 | −0.630290 | ||||||||
\(377\) | 2.12336e8 | 0.204093 | ||||||||
\(378\) | 1.41512e7 | 0.0134763 | ||||||||
\(379\) | −1.31066e9 | −1.23667 | −0.618335 | − | 0.785915i | \(-0.712192\pi\) | ||||
−0.618335 | + | 0.785915i | \(0.712192\pi\) | |||||||
\(380\) | −4.06959e8 | −0.380459 | ||||||||
\(381\) | −8.65735e8 | −0.801950 | ||||||||
\(382\) | −6.67731e7 | −0.0612886 | ||||||||
\(383\) | 6.67359e8 | 0.606966 | 0.303483 | − | 0.952837i | \(-0.401851\pi\) | ||||
0.303483 | + | 0.952837i | \(0.401851\pi\) | |||||||
\(384\) | −4.13222e8 | −0.372412 | ||||||||
\(385\) | 4.44639e8 | 0.397095 | ||||||||
\(386\) | 1.13262e8 | 0.100237 | ||||||||
\(387\) | 1.80638e8 | 0.158423 | ||||||||
\(388\) | 3.62119e8 | 0.314731 | ||||||||
\(389\) | 2.25715e9 | 1.94418 | 0.972089 | − | 0.234611i | \(-0.0753816\pi\) | ||||
0.972089 | + | 0.234611i | \(0.0753816\pi\) | |||||||
\(390\) | −1.55047e7 | −0.0132354 | ||||||||
\(391\) | 4.23808e8 | 0.358551 | ||||||||
\(392\) | −3.43202e8 | −0.287772 | ||||||||
\(393\) | 6.42877e8 | 0.534262 | ||||||||
\(394\) | −1.54285e8 | −0.127083 | ||||||||
\(395\) | 1.27373e9 | 1.03989 | ||||||||
\(396\) | 3.24658e8 | 0.262720 | ||||||||
\(397\) | −9.81086e8 | −0.786938 | −0.393469 | − | 0.919338i | \(-0.628725\pi\) | ||||
−0.393469 | + | 0.919338i | \(0.628725\pi\) | |||||||
\(398\) | 2.33381e8 | 0.185556 | ||||||||
\(399\) | 9.50251e7 | 0.0748916 | ||||||||
\(400\) | 5.56357e8 | 0.434654 | ||||||||
\(401\) | −5.90695e7 | −0.0457465 | −0.0228732 | − | 0.999738i | \(-0.507281\pi\) | ||||
−0.0228732 | + | 0.999738i | \(0.507281\pi\) | |||||||
\(402\) | −1.07000e8 | −0.0821470 | ||||||||
\(403\) | 9.77807e7 | 0.0744193 | ||||||||
\(404\) | 2.47967e9 | 1.87094 | ||||||||
\(405\) | −1.80571e8 | −0.135069 | ||||||||
\(406\) | −1.78067e8 | −0.132051 | ||||||||
\(407\) | 6.98228e8 | 0.513354 | ||||||||
\(408\) | −4.89713e7 | −0.0356970 | ||||||||
\(409\) | −7.74847e8 | −0.559995 | −0.279998 | − | 0.960001i | \(-0.590334\pi\) | ||||
−0.279998 | + | 0.960001i | \(0.590334\pi\) | |||||||
\(410\) | −3.98493e8 | −0.285547 | ||||||||
\(411\) | −5.77258e8 | −0.410132 | ||||||||
\(412\) | 1.41794e9 | 0.998887 | ||||||||
\(413\) | 7.49018e7 | 0.0523199 | ||||||||
\(414\) | −1.66897e8 | −0.115597 | ||||||||
\(415\) | −1.09166e9 | −0.749754 | ||||||||
\(416\) | −7.97335e7 | −0.0543018 | ||||||||
\(417\) | 9.83493e8 | 0.664194 | ||||||||
\(418\) | −6.82628e7 | −0.0457159 | ||||||||
\(419\) | 2.71966e8 | 0.180620 | 0.0903098 | − | 0.995914i | \(-0.471214\pi\) | ||||
0.0903098 | + | 0.995914i | \(0.471214\pi\) | |||||||
\(420\) | −4.15252e8 | −0.273489 | ||||||||
\(421\) | −8.59819e8 | −0.561591 | −0.280795 | − | 0.959768i | \(-0.590598\pi\) | ||||
−0.280795 | + | 0.959768i | \(0.590598\pi\) | |||||||
\(422\) | −9.43298e7 | −0.0611020 | ||||||||
\(423\) | −9.52934e8 | −0.612169 | ||||||||
\(424\) | 5.98366e8 | 0.381229 | ||||||||
\(425\) | 1.36202e8 | 0.0860644 | ||||||||
\(426\) | 9.99905e7 | 0.0626650 | ||||||||
\(427\) | 1.56406e8 | 0.0972200 | ||||||||
\(428\) | −2.85444e9 | −1.75982 | ||||||||
\(429\) | 8.30585e7 | 0.0507906 | ||||||||
\(430\) | 1.65973e8 | 0.100670 | ||||||||
\(431\) | −6.62428e8 | −0.398536 | −0.199268 | − | 0.979945i | \(-0.563856\pi\) | ||||
−0.199268 | + | 0.979945i | \(0.563856\pi\) | |||||||
\(432\) | −2.93410e8 | −0.175098 | ||||||||
\(433\) | 2.01470e9 | 1.19262 | 0.596312 | − | 0.802753i | \(-0.296632\pi\) | ||||
0.596312 | + | 0.802753i | \(0.296632\pi\) | |||||||
\(434\) | −8.20001e7 | −0.0481505 | ||||||||
\(435\) | 2.27215e9 | 1.32350 | ||||||||
\(436\) | −2.50801e9 | −1.44920 | ||||||||
\(437\) | −1.12071e9 | −0.642403 | ||||||||
\(438\) | 1.25109e8 | 0.0711425 | ||||||||
\(439\) | 2.41587e9 | 1.36285 | 0.681425 | − | 0.731888i | \(-0.261360\pi\) | ||||
0.681425 | + | 0.731888i | \(0.261360\pi\) | |||||||
\(440\) | 6.05946e8 | 0.339117 | ||||||||
\(441\) | −5.03401e8 | −0.279498 | ||||||||
\(442\) | −6.16769e6 | −0.00339739 | ||||||||
\(443\) | −2.74104e9 | −1.49796 | −0.748982 | − | 0.662590i | \(-0.769457\pi\) | ||||
−0.748982 | + | 0.662590i | \(0.769457\pi\) | |||||||
\(444\) | −6.52081e8 | −0.353558 | ||||||||
\(445\) | 1.85024e8 | 0.0995330 | ||||||||
\(446\) | −2.45761e8 | −0.131172 | ||||||||
\(447\) | −2.57121e6 | −0.00136163 | ||||||||
\(448\) | −6.29007e8 | −0.330508 | ||||||||
\(449\) | −1.37537e9 | −0.717063 | −0.358532 | − | 0.933518i | \(-0.616723\pi\) | ||||
−0.358532 | + | 0.933518i | \(0.616723\pi\) | |||||||
\(450\) | −5.36368e7 | −0.0277472 | ||||||||
\(451\) | 2.13472e9 | 1.09578 | ||||||||
\(452\) | 1.56935e9 | 0.799344 | ||||||||
\(453\) | −1.27346e9 | −0.643640 | ||||||||
\(454\) | −1.40678e8 | −0.0705553 | ||||||||
\(455\) | −1.06235e8 | −0.0528724 | ||||||||
\(456\) | 1.29499e8 | 0.0639570 | ||||||||
\(457\) | 1.14427e9 | 0.560816 | 0.280408 | − | 0.959881i | \(-0.409530\pi\) | ||||
0.280408 | + | 0.959881i | \(0.409530\pi\) | |||||||
\(458\) | 6.69636e8 | 0.325694 | ||||||||
\(459\) | −7.18302e7 | −0.0346707 | ||||||||
\(460\) | 4.89740e9 | 2.34592 | ||||||||
\(461\) | 7.69708e8 | 0.365909 | 0.182954 | − | 0.983121i | \(-0.441434\pi\) | ||||
0.182954 | + | 0.983121i | \(0.441434\pi\) | |||||||
\(462\) | −6.96539e7 | −0.0328623 | ||||||||
\(463\) | −2.23996e8 | −0.104884 | −0.0524418 | − | 0.998624i | \(-0.516700\pi\) | ||||
−0.0524418 | + | 0.998624i | \(0.516700\pi\) | |||||||
\(464\) | 3.69204e9 | 1.71575 | ||||||||
\(465\) | 1.04633e9 | 0.482595 | ||||||||
\(466\) | 6.29032e8 | 0.287953 | ||||||||
\(467\) | 3.61971e8 | 0.164462 | 0.0822308 | − | 0.996613i | \(-0.473796\pi\) | ||||
0.0822308 | + | 0.996613i | \(0.473796\pi\) | |||||||
\(468\) | −7.75690e7 | −0.0349806 | ||||||||
\(469\) | −7.33143e8 | −0.328159 | ||||||||
\(470\) | −8.75575e8 | −0.389001 | ||||||||
\(471\) | −1.20034e9 | −0.529337 | ||||||||
\(472\) | 1.02075e8 | 0.0446809 | ||||||||
\(473\) | −8.89119e8 | −0.386319 | ||||||||
\(474\) | −1.99533e8 | −0.0860580 | ||||||||
\(475\) | −3.60170e8 | −0.154199 | ||||||||
\(476\) | −1.65185e8 | −0.0702016 | ||||||||
\(477\) | 8.77670e8 | 0.370269 | ||||||||
\(478\) | −4.90444e8 | −0.205396 | ||||||||
\(479\) | −1.79221e9 | −0.745100 | −0.372550 | − | 0.928012i | \(-0.621516\pi\) | ||||
−0.372550 | + | 0.928012i | \(0.621516\pi\) | |||||||
\(480\) | −8.53209e8 | −0.352137 | ||||||||
\(481\) | −1.66824e8 | −0.0683520 | ||||||||
\(482\) | 2.01246e8 | 0.0818583 | ||||||||
\(483\) | −1.14355e9 | −0.461784 | ||||||||
\(484\) | 8.20620e8 | 0.328990 | ||||||||
\(485\) | 9.91341e8 | 0.394573 | ||||||||
\(486\) | 2.82869e7 | 0.0111778 | ||||||||
\(487\) | 1.52055e9 | 0.596554 | 0.298277 | − | 0.954479i | \(-0.403588\pi\) | ||||
0.298277 | + | 0.954479i | \(0.403588\pi\) | |||||||
\(488\) | 2.13147e8 | 0.0830253 | ||||||||
\(489\) | 2.66218e9 | 1.02957 | ||||||||
\(490\) | −4.62536e8 | −0.177606 | ||||||||
\(491\) | −3.45739e9 | −1.31815 | −0.659073 | − | 0.752079i | \(-0.729051\pi\) | ||||
−0.659073 | + | 0.752079i | \(0.729051\pi\) | |||||||
\(492\) | −1.99364e9 | −0.754689 | ||||||||
\(493\) | 9.03853e8 | 0.339730 | ||||||||
\(494\) | 1.63097e7 | 0.00608697 | ||||||||
\(495\) | 8.88789e8 | 0.329367 | ||||||||
\(496\) | 1.70018e9 | 0.625619 | ||||||||
\(497\) | 6.85117e8 | 0.250333 | ||||||||
\(498\) | 1.71011e8 | 0.0620472 | ||||||||
\(499\) | −5.24675e8 | −0.189033 | −0.0945167 | − | 0.995523i | \(-0.530131\pi\) | ||||
−0.0945167 | + | 0.995523i | \(0.530131\pi\) | |||||||
\(500\) | −1.72068e9 | −0.615609 | ||||||||
\(501\) | −4.33726e8 | −0.154093 | ||||||||
\(502\) | −3.33930e8 | −0.117813 | ||||||||
\(503\) | −2.08499e9 | −0.730492 | −0.365246 | − | 0.930911i | \(-0.619015\pi\) | ||||
−0.365246 | + | 0.930911i | \(0.619015\pi\) | |||||||
\(504\) | 1.32138e8 | 0.0459748 | ||||||||
\(505\) | 6.78839e9 | 2.34556 | ||||||||
\(506\) | 8.21485e8 | 0.281885 | ||||||||
\(507\) | 1.67437e9 | 0.570588 | ||||||||
\(508\) | −3.97961e9 | −1.34685 | ||||||||
\(509\) | 3.13440e9 | 1.05352 | 0.526760 | − | 0.850014i | \(-0.323407\pi\) | ||||
0.526760 | + | 0.850014i | \(0.323407\pi\) | |||||||
\(510\) | −6.59990e7 | −0.0220314 | ||||||||
\(511\) | 8.57224e8 | 0.284198 | ||||||||
\(512\) | −2.33471e9 | −0.768754 | ||||||||
\(513\) | 1.89946e8 | 0.0621182 | ||||||||
\(514\) | 8.18430e8 | 0.265834 | ||||||||
\(515\) | 3.88176e9 | 1.25229 | ||||||||
\(516\) | 8.30355e8 | 0.266066 | ||||||||
\(517\) | 4.69045e9 | 1.49279 | ||||||||
\(518\) | 1.39901e8 | 0.0442248 | ||||||||
\(519\) | −2.60171e9 | −0.816908 | ||||||||
\(520\) | −1.44776e8 | −0.0451527 | ||||||||
\(521\) | 9.76015e8 | 0.302360 | 0.151180 | − | 0.988506i | \(-0.451693\pi\) | ||||
0.151180 | + | 0.988506i | \(0.451693\pi\) | |||||||
\(522\) | −3.55939e8 | −0.109529 | ||||||||
\(523\) | −1.99309e9 | −0.609216 | −0.304608 | − | 0.952478i | \(-0.598526\pi\) | ||||
−0.304608 | + | 0.952478i | \(0.598526\pi\) | |||||||
\(524\) | 2.95518e9 | 0.897273 | ||||||||
\(525\) | −3.67510e8 | −0.110844 | ||||||||
\(526\) | 4.86000e8 | 0.145608 | ||||||||
\(527\) | 4.16225e8 | 0.123877 | ||||||||
\(528\) | 1.44420e9 | 0.426981 | ||||||||
\(529\) | 1.00819e10 | 2.96107 | ||||||||
\(530\) | 8.06422e8 | 0.235286 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 4.36812e8 | 0.125778 | ||||||||
\(533\) | −5.10039e8 | −0.145901 | ||||||||
\(534\) | −2.89845e7 | −0.00823703 | ||||||||
\(535\) | −7.81435e9 | −2.20625 | ||||||||
\(536\) | −9.99115e8 | −0.280246 | ||||||||
\(537\) | −1.88088e9 | −0.524145 | ||||||||
\(538\) | −6.28723e8 | −0.174069 | ||||||||
\(539\) | 2.47780e9 | 0.681562 | ||||||||
\(540\) | −8.30048e8 | −0.226843 | ||||||||
\(541\) | 3.17125e9 | 0.861072 | 0.430536 | − | 0.902573i | \(-0.358325\pi\) | ||||
0.430536 | + | 0.902573i | \(0.358325\pi\) | |||||||
\(542\) | 7.64698e8 | 0.206297 | ||||||||
\(543\) | 2.82856e9 | 0.758168 | ||||||||
\(544\) | −3.39403e8 | −0.0903897 | ||||||||
\(545\) | −6.86597e9 | −1.81683 | ||||||||
\(546\) | 1.66421e7 | 0.00437555 | ||||||||
\(547\) | 2.77827e9 | 0.725803 | 0.362901 | − | 0.931828i | \(-0.381786\pi\) | ||||
0.362901 | + | 0.931828i | \(0.381786\pi\) | |||||||
\(548\) | −2.65354e9 | −0.688802 | ||||||||
\(549\) | 3.12640e8 | 0.0806383 | ||||||||
\(550\) | 2.64007e8 | 0.0676621 | ||||||||
\(551\) | −2.39012e9 | −0.608681 | ||||||||
\(552\) | −1.55841e9 | −0.394361 | ||||||||
\(553\) | −1.36717e9 | −0.343782 | ||||||||
\(554\) | 1.46332e8 | 0.0365641 | ||||||||
\(555\) | −1.78515e9 | −0.443250 | ||||||||
\(556\) | 4.52093e9 | 1.11549 | ||||||||
\(557\) | −7.99807e8 | −0.196107 | −0.0980533 | − | 0.995181i | \(-0.531262\pi\) | ||||
−0.0980533 | + | 0.995181i | \(0.531262\pi\) | |||||||
\(558\) | −1.63910e8 | −0.0399380 | ||||||||
\(559\) | 2.12433e8 | 0.0514375 | ||||||||
\(560\) | −1.84719e9 | −0.444482 | ||||||||
\(561\) | 3.53556e8 | 0.0845451 | ||||||||
\(562\) | 1.21495e9 | 0.288722 | ||||||||
\(563\) | −1.37529e9 | −0.324800 | −0.162400 | − | 0.986725i | \(-0.551923\pi\) | ||||
−0.162400 | + | 0.986725i | \(0.551923\pi\) | |||||||
\(564\) | −4.38045e9 | −1.02812 | ||||||||
\(565\) | 4.29626e9 | 1.00212 | ||||||||
\(566\) | −1.57041e8 | −0.0364045 | ||||||||
\(567\) | 1.93817e8 | 0.0446530 | ||||||||
\(568\) | 9.33666e8 | 0.213783 | ||||||||
\(569\) | 4.45989e8 | 0.101492 | 0.0507459 | − | 0.998712i | \(-0.483840\pi\) | ||||
0.0507459 | + | 0.998712i | \(0.483840\pi\) | |||||||
\(570\) | 1.74526e8 | 0.0394728 | ||||||||
\(571\) | −7.16360e9 | −1.61029 | −0.805147 | − | 0.593076i | \(-0.797914\pi\) | ||||
−0.805147 | + | 0.593076i | \(0.797914\pi\) | |||||||
\(572\) | 3.81804e8 | 0.0853010 | ||||||||
\(573\) | −9.14533e8 | −0.203076 | ||||||||
\(574\) | 4.27725e8 | 0.0944002 | ||||||||
\(575\) | 4.33434e9 | 0.950793 | ||||||||
\(576\) | −1.25732e9 | −0.274137 | ||||||||
\(577\) | −5.75941e9 | −1.24814 | −0.624069 | − | 0.781369i | \(-0.714522\pi\) | ||||
−0.624069 | + | 0.781369i | \(0.714522\pi\) | |||||||
\(578\) | 7.82672e8 | 0.168590 | ||||||||
\(579\) | 1.55125e9 | 0.332129 | ||||||||
\(580\) | 1.04447e10 | 2.22278 | ||||||||
\(581\) | 1.17174e9 | 0.247865 | ||||||||
\(582\) | −1.55296e8 | −0.0326536 | ||||||||
\(583\) | −4.31999e9 | −0.902908 | ||||||||
\(584\) | 1.16821e9 | 0.242704 | ||||||||
\(585\) | −2.12354e8 | −0.0438546 | ||||||||
\(586\) | −4.93610e8 | −0.101331 | ||||||||
\(587\) | −2.89213e9 | −0.590180 | −0.295090 | − | 0.955469i | \(-0.595350\pi\) | ||||
−0.295090 | + | 0.955469i | \(0.595350\pi\) | |||||||
\(588\) | −2.31404e9 | −0.469407 | ||||||||
\(589\) | −1.10065e9 | −0.221946 | ||||||||
\(590\) | 1.37567e8 | 0.0275761 | ||||||||
\(591\) | −2.11311e9 | −0.421081 | ||||||||
\(592\) | −2.90069e9 | −0.574613 | ||||||||
\(593\) | −2.52669e9 | −0.497577 | −0.248789 | − | 0.968558i | \(-0.580032\pi\) | ||||
−0.248789 | + | 0.968558i | \(0.580032\pi\) | |||||||
\(594\) | −1.39231e8 | −0.0272574 | ||||||||
\(595\) | −4.52214e8 | −0.0880104 | ||||||||
\(596\) | −1.18193e7 | −0.00228682 | ||||||||
\(597\) | 3.19641e9 | 0.614826 | ||||||||
\(598\) | −1.96273e8 | −0.0375325 | ||||||||
\(599\) | −9.87541e9 | −1.87742 | −0.938709 | − | 0.344709i | \(-0.887977\pi\) | ||||
−0.938709 | + | 0.344709i | \(0.887977\pi\) | |||||||
\(600\) | −5.00836e8 | −0.0946600 | ||||||||
\(601\) | −1.69668e9 | −0.318815 | −0.159408 | − | 0.987213i | \(-0.550958\pi\) | ||||
−0.159408 | + | 0.987213i | \(0.550958\pi\) | |||||||
\(602\) | −1.78149e8 | −0.0332809 | ||||||||
\(603\) | −1.46548e9 | −0.272188 | ||||||||
\(604\) | −5.85386e9 | −1.08097 | ||||||||
\(605\) | 2.24654e9 | 0.412449 | ||||||||
\(606\) | −1.06342e9 | −0.194111 | ||||||||
\(607\) | −9.97951e9 | −1.81113 | −0.905564 | − | 0.424211i | \(-0.860552\pi\) | ||||
−0.905564 | + | 0.424211i | \(0.860552\pi\) | |||||||
\(608\) | 8.97507e8 | 0.161948 | ||||||||
\(609\) | −2.43883e9 | −0.437544 | ||||||||
\(610\) | 2.87260e8 | 0.0512414 | ||||||||
\(611\) | −1.12067e9 | −0.198761 | ||||||||
\(612\) | −3.30189e8 | −0.0582281 | ||||||||
\(613\) | −6.06527e9 | −1.06350 | −0.531751 | − | 0.846901i | \(-0.678466\pi\) | ||||
−0.531751 | + | 0.846901i | \(0.678466\pi\) | |||||||
\(614\) | 6.53302e8 | 0.113900 | ||||||||
\(615\) | −5.45780e9 | −0.946139 | ||||||||
\(616\) | −6.50396e8 | −0.112110 | ||||||||
\(617\) | −1.40806e9 | −0.241336 | −0.120668 | − | 0.992693i | \(-0.538504\pi\) | ||||
−0.120668 | + | 0.992693i | \(0.538504\pi\) | |||||||
\(618\) | −6.08089e8 | −0.103635 | ||||||||
\(619\) | −2.17547e9 | −0.368668 | −0.184334 | − | 0.982864i | \(-0.559013\pi\) | ||||
−0.184334 | + | 0.982864i | \(0.559013\pi\) | |||||||
\(620\) | 4.80977e9 | 0.810501 | ||||||||
\(621\) | −2.28584e9 | −0.383023 | ||||||||
\(622\) | 1.85686e8 | 0.0309395 | ||||||||
\(623\) | −1.98596e8 | −0.0329051 | ||||||||
\(624\) | −3.45055e8 | −0.0568516 | ||||||||
\(625\) | −7.62637e9 | −1.24950 | ||||||||
\(626\) | 1.06353e9 | 0.173277 | ||||||||
\(627\) | −9.34935e8 | −0.151476 | ||||||||
\(628\) | −5.51774e9 | −0.889001 | ||||||||
\(629\) | −7.10123e8 | −0.113777 | ||||||||
\(630\) | 1.78083e8 | 0.0283746 | ||||||||
\(631\) | −3.80261e9 | −0.602531 | −0.301266 | − | 0.953540i | \(-0.597409\pi\) | ||||
−0.301266 | + | 0.953540i | \(0.597409\pi\) | |||||||
\(632\) | −1.86315e9 | −0.293588 | ||||||||
\(633\) | −1.29195e9 | −0.202457 | ||||||||
\(634\) | −1.36386e9 | −0.212549 | ||||||||
\(635\) | −1.08946e10 | −1.68852 | ||||||||
\(636\) | 4.03448e9 | 0.621853 | ||||||||
\(637\) | −5.92008e8 | −0.0907486 | ||||||||
\(638\) | 1.75197e9 | 0.267089 | ||||||||
\(639\) | 1.36948e9 | 0.207636 | ||||||||
\(640\) | −5.20010e9 | −0.784118 | ||||||||
\(641\) | 3.59687e9 | 0.539413 | 0.269706 | − | 0.962943i | \(-0.413073\pi\) | ||||
0.269706 | + | 0.962943i | \(0.413073\pi\) | |||||||
\(642\) | 1.22414e9 | 0.182582 | ||||||||
\(643\) | 4.76649e9 | 0.707066 | 0.353533 | − | 0.935422i | \(-0.384980\pi\) | ||||
0.353533 | + | 0.935422i | \(0.384980\pi\) | |||||||
\(644\) | −5.25666e9 | −0.775549 | ||||||||
\(645\) | 2.27319e9 | 0.333562 | ||||||||
\(646\) | 6.94257e7 | 0.0101323 | ||||||||
\(647\) | 1.17944e9 | 0.171203 | 0.0856016 | − | 0.996329i | \(-0.472719\pi\) | ||||
0.0856016 | + | 0.996329i | \(0.472719\pi\) | |||||||
\(648\) | 2.64130e8 | 0.0381334 | ||||||||
\(649\) | −7.36945e8 | −0.105823 | ||||||||
\(650\) | −6.30778e7 | −0.00900907 | ||||||||
\(651\) | −1.12308e9 | −0.159543 | ||||||||
\(652\) | 1.22375e10 | 1.72913 | ||||||||
\(653\) | 8.76325e9 | 1.23160 | 0.615799 | − | 0.787903i | \(-0.288833\pi\) | ||||
0.615799 | + | 0.787903i | \(0.288833\pi\) | |||||||
\(654\) | 1.07557e9 | 0.150355 | ||||||||
\(655\) | 8.09015e9 | 1.12489 | ||||||||
\(656\) | −8.86841e9 | −1.22654 | ||||||||
\(657\) | 1.71351e9 | 0.235726 | ||||||||
\(658\) | 9.39804e8 | 0.128602 | ||||||||
\(659\) | −1.34224e10 | −1.82697 | −0.913487 | − | 0.406868i | \(-0.866621\pi\) | ||||
−0.913487 | + | 0.406868i | \(0.866621\pi\) | |||||||
\(660\) | 4.08559e9 | 0.553161 | ||||||||
\(661\) | −5.67841e9 | −0.764754 | −0.382377 | − | 0.924006i | \(-0.624894\pi\) | ||||
−0.382377 | + | 0.924006i | \(0.624894\pi\) | |||||||
\(662\) | 1.68501e9 | 0.225735 | ||||||||
\(663\) | −8.44735e7 | −0.0112570 | ||||||||
\(664\) | 1.59683e9 | 0.211675 | ||||||||
\(665\) | 1.19582e9 | 0.157685 | ||||||||
\(666\) | 2.79648e8 | 0.0366819 | ||||||||
\(667\) | 2.87631e10 | 3.75315 | ||||||||
\(668\) | −1.99375e9 | −0.258794 | ||||||||
\(669\) | −3.36597e9 | −0.434630 | ||||||||
\(670\) | −1.34651e9 | −0.172961 | ||||||||
\(671\) | −1.53885e9 | −0.196638 | ||||||||
\(672\) | 9.15797e8 | 0.116414 | ||||||||
\(673\) | 2.49548e9 | 0.315574 | 0.157787 | − | 0.987473i | \(-0.449564\pi\) | ||||
0.157787 | + | 0.987473i | \(0.449564\pi\) | |||||||
\(674\) | −2.50621e8 | −0.0315288 | ||||||||
\(675\) | −7.34617e8 | −0.0919385 | ||||||||
\(676\) | 7.69673e9 | 0.958281 | ||||||||
\(677\) | 5.54895e9 | 0.687307 | 0.343654 | − | 0.939097i | \(-0.388335\pi\) | ||||
0.343654 | + | 0.939097i | \(0.388335\pi\) | |||||||
\(678\) | −6.73021e8 | −0.0829325 | ||||||||
\(679\) | −1.06406e9 | −0.130444 | ||||||||
\(680\) | −6.16269e8 | −0.0751604 | ||||||||
\(681\) | −1.92674e9 | −0.233780 | ||||||||
\(682\) | 8.06785e8 | 0.0973896 | ||||||||
\(683\) | 4.93572e9 | 0.592759 | 0.296379 | − | 0.955070i | \(-0.404221\pi\) | ||||
0.296379 | + | 0.955070i | \(0.404221\pi\) | |||||||
\(684\) | 8.73144e8 | 0.104325 | ||||||||
\(685\) | −7.26438e9 | −0.863538 | ||||||||
\(686\) | 1.08856e9 | 0.128741 | ||||||||
\(687\) | 9.17141e9 | 1.07916 | ||||||||
\(688\) | 3.69372e9 | 0.432419 | ||||||||
\(689\) | 1.03215e9 | 0.120220 | ||||||||
\(690\) | −2.10027e9 | −0.243391 | ||||||||
\(691\) | −8.63015e9 | −0.995050 | −0.497525 | − | 0.867450i | \(-0.665758\pi\) | ||||
−0.497525 | + | 0.867450i | \(0.665758\pi\) | |||||||
\(692\) | −1.19595e10 | −1.37197 | ||||||||
\(693\) | −9.53988e8 | −0.108887 | ||||||||
\(694\) | 1.21660e8 | 0.0138163 | ||||||||
\(695\) | 1.23766e10 | 1.39847 | ||||||||
\(696\) | −3.32360e9 | −0.373660 | ||||||||
\(697\) | −2.17109e9 | −0.242864 | ||||||||
\(698\) | −7.74720e8 | −0.0862285 | ||||||||
\(699\) | 8.61529e9 | 0.954113 | ||||||||
\(700\) | −1.68937e9 | −0.186158 | ||||||||
\(701\) | 8.06267e9 | 0.884028 | 0.442014 | − | 0.897008i | \(-0.354264\pi\) | ||||
0.442014 | + | 0.897008i | \(0.354264\pi\) | |||||||
\(702\) | 3.32658e7 | 0.00362926 | ||||||||
\(703\) | 1.87783e9 | 0.203851 | ||||||||
\(704\) | 6.18869e9 | 0.668489 | ||||||||
\(705\) | −1.19920e10 | −1.28893 | ||||||||
\(706\) | 2.87566e9 | 0.307554 | ||||||||
\(707\) | −7.28636e9 | −0.775430 | ||||||||
\(708\) | 6.88240e8 | 0.0728825 | ||||||||
\(709\) | 1.13085e10 | 1.19163 | 0.595817 | − | 0.803120i | \(-0.296828\pi\) | ||||
0.595817 | + | 0.803120i | \(0.296828\pi\) | |||||||
\(710\) | 1.25831e9 | 0.131942 | ||||||||
\(711\) | −2.73283e9 | −0.285147 | ||||||||
\(712\) | −2.70644e8 | −0.0281008 | ||||||||
\(713\) | 1.32454e10 | 1.36853 | ||||||||
\(714\) | 7.08405e7 | 0.00728346 | ||||||||
\(715\) | 1.04523e9 | 0.106940 | ||||||||
\(716\) | −8.64605e9 | −0.880283 | ||||||||
\(717\) | −6.71718e9 | −0.680565 | ||||||||
\(718\) | 1.99024e9 | 0.200664 | ||||||||
\(719\) | −1.36390e10 | −1.36846 | −0.684231 | − | 0.729266i | \(-0.739862\pi\) | ||||
−0.684231 | + | 0.729266i | \(0.739862\pi\) | |||||||
\(720\) | −3.69235e9 | −0.368672 | ||||||||
\(721\) | −4.16652e9 | −0.413999 | ||||||||
\(722\) | 1.57856e9 | 0.156092 | ||||||||
\(723\) | 2.75629e9 | 0.271232 | ||||||||
\(724\) | 1.30023e10 | 1.27332 | ||||||||
\(725\) | 9.24382e9 | 0.900883 | ||||||||
\(726\) | −3.51927e8 | −0.0341330 | ||||||||
\(727\) | 3.69976e9 | 0.357111 | 0.178556 | − | 0.983930i | \(-0.442858\pi\) | ||||
0.178556 | + | 0.983930i | \(0.442858\pi\) | |||||||
\(728\) | 1.55396e8 | 0.0149273 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 1.57441e9 | 0.149791 | ||||||||
\(731\) | 9.04265e8 | 0.0856219 | ||||||||
\(732\) | 1.43715e9 | 0.135429 | ||||||||
\(733\) | 1.64513e10 | 1.54289 | 0.771447 | − | 0.636294i | \(-0.219533\pi\) | ||||
0.771447 | + | 0.636294i | \(0.219533\pi\) | |||||||
\(734\) | −1.35963e9 | −0.126907 | ||||||||
\(735\) | −6.33494e9 | −0.588487 | ||||||||
\(736\) | −1.08007e10 | −0.998576 | ||||||||
\(737\) | 7.21327e9 | 0.663737 | ||||||||
\(738\) | 8.54980e8 | 0.0782994 | ||||||||
\(739\) | −4.40695e9 | −0.401682 | −0.200841 | − | 0.979624i | \(-0.564367\pi\) | ||||
−0.200841 | + | 0.979624i | \(0.564367\pi\) | |||||||
\(740\) | −8.20597e9 | −0.744421 | ||||||||
\(741\) | 2.23379e8 | 0.0201688 | ||||||||
\(742\) | −8.65578e8 | −0.0777844 | ||||||||
\(743\) | 2.97820e9 | 0.266374 | 0.133187 | − | 0.991091i | \(-0.457479\pi\) | ||||
0.133187 | + | 0.991091i | \(0.457479\pi\) | |||||||
\(744\) | −1.53052e9 | −0.136249 | ||||||||
\(745\) | −3.23568e7 | −0.00286694 | ||||||||
\(746\) | −3.01526e7 | −0.00265913 | ||||||||
\(747\) | 2.34219e9 | 0.205589 | ||||||||
\(748\) | 1.62523e9 | 0.141990 | ||||||||
\(749\) | 8.38758e9 | 0.729374 | ||||||||
\(750\) | 7.37921e8 | 0.0638698 | ||||||||
\(751\) | 6.84373e9 | 0.589594 | 0.294797 | − | 0.955560i | \(-0.404748\pi\) | ||||
0.294797 | + | 0.955560i | \(0.404748\pi\) | |||||||
\(752\) | −1.94858e10 | −1.67092 | ||||||||
\(753\) | −4.57354e9 | −0.390364 | ||||||||
\(754\) | −4.18590e8 | −0.0355623 | ||||||||
\(755\) | −1.60256e10 | −1.35519 | ||||||||
\(756\) | 8.90937e8 | 0.0749930 | ||||||||
\(757\) | −1.28064e10 | −1.07298 | −0.536491 | − | 0.843906i | \(-0.680250\pi\) | ||||
−0.536491 | + | 0.843906i | \(0.680250\pi\) | |||||||
\(758\) | 2.58379e9 | 0.215484 | ||||||||
\(759\) | 1.12512e10 | 0.934008 | ||||||||
\(760\) | 1.62965e9 | 0.134662 | ||||||||
\(761\) | −1.33708e9 | −0.109979 | −0.0549897 | − | 0.998487i | \(-0.517513\pi\) | ||||
−0.0549897 | + | 0.998487i | \(0.517513\pi\) | |||||||
\(762\) | 1.70668e9 | 0.139736 | ||||||||
\(763\) | 7.36964e9 | 0.600634 | ||||||||
\(764\) | −4.20393e9 | −0.341058 | ||||||||
\(765\) | −9.03931e8 | −0.0729995 | ||||||||
\(766\) | −1.31561e9 | −0.105761 | ||||||||
\(767\) | 1.76075e8 | 0.0140901 | ||||||||
\(768\) | −5.14604e9 | −0.409929 | ||||||||
\(769\) | 1.10898e10 | 0.879390 | 0.439695 | − | 0.898147i | \(-0.355086\pi\) | ||||
0.439695 | + | 0.898147i | \(0.355086\pi\) | |||||||
\(770\) | −8.76544e8 | −0.0691920 | ||||||||
\(771\) | 1.12093e10 | 0.880823 | ||||||||
\(772\) | 7.13078e9 | 0.557798 | ||||||||
\(773\) | −1.78044e10 | −1.38644 | −0.693218 | − | 0.720728i | \(-0.743808\pi\) | ||||
−0.693218 | + | 0.720728i | \(0.743808\pi\) | |||||||
\(774\) | −3.56102e8 | −0.0276046 | ||||||||
\(775\) | 4.25679e9 | 0.328493 | ||||||||
\(776\) | −1.45009e9 | −0.111398 | ||||||||
\(777\) | 1.91610e9 | 0.146536 | ||||||||
\(778\) | −4.44965e9 | −0.338764 | ||||||||
\(779\) | 5.74117e9 | 0.435130 | ||||||||
\(780\) | −9.76150e8 | −0.0736522 | ||||||||
\(781\) | −6.74075e9 | −0.506325 | ||||||||
\(782\) | −8.35479e8 | −0.0624758 | ||||||||
\(783\) | −4.87499e9 | −0.362917 | ||||||||
\(784\) | −1.02937e10 | −0.762894 | ||||||||
\(785\) | −1.51054e10 | −1.11452 | ||||||||
\(786\) | −1.26734e9 | −0.0930927 | ||||||||
\(787\) | 1.97486e10 | 1.44419 | 0.722095 | − | 0.691794i | \(-0.243179\pi\) | ||||
0.722095 | + | 0.691794i | \(0.243179\pi\) | |||||||
\(788\) | −9.71354e9 | −0.707190 | ||||||||
\(789\) | 6.65631e9 | 0.482463 | ||||||||
\(790\) | −2.51098e9 | −0.181196 | ||||||||
\(791\) | −4.61142e9 | −0.331297 | ||||||||
\(792\) | −1.30008e9 | −0.0929890 | ||||||||
\(793\) | 3.67670e8 | 0.0261820 | ||||||||
\(794\) | 1.93408e9 | 0.137120 | ||||||||
\(795\) | 1.10448e10 | 0.779605 | ||||||||
\(796\) | 1.46933e10 | 1.03258 | ||||||||
\(797\) | 1.84228e10 | 1.28900 | 0.644499 | − | 0.764605i | \(-0.277066\pi\) | ||||
0.644499 | + | 0.764605i | \(0.277066\pi\) | |||||||
\(798\) | −1.87329e8 | −0.0130495 | ||||||||
\(799\) | −4.77035e9 | −0.330854 | ||||||||
\(800\) | −3.47112e9 | −0.239692 | ||||||||
\(801\) | −3.96975e8 | −0.0272929 | ||||||||
\(802\) | 1.16447e8 | 0.00797111 | ||||||||
\(803\) | −8.43408e9 | −0.574822 | ||||||||
\(804\) | −6.73653e9 | −0.457130 | ||||||||
\(805\) | −1.43907e10 | −0.972291 | ||||||||
\(806\) | −1.92761e8 | −0.0129672 | ||||||||
\(807\) | −8.61106e9 | −0.576766 | ||||||||
\(808\) | −9.92972e9 | −0.662213 | ||||||||
\(809\) | 1.12171e10 | 0.744838 | 0.372419 | − | 0.928065i | \(-0.378528\pi\) | ||||
0.372419 | + | 0.928065i | \(0.378528\pi\) | |||||||
\(810\) | 3.55970e8 | 0.0235351 | ||||||||
\(811\) | 1.91381e10 | 1.25987 | 0.629934 | − | 0.776649i | \(-0.283082\pi\) | ||||
0.629934 | + | 0.776649i | \(0.283082\pi\) | |||||||
\(812\) | −1.12108e10 | −0.734838 | ||||||||
\(813\) | 1.04734e10 | 0.683551 | ||||||||
\(814\) | −1.37646e9 | −0.0894495 | ||||||||
\(815\) | 3.35017e10 | 2.16778 | ||||||||
\(816\) | −1.46880e9 | −0.0946341 | ||||||||
\(817\) | −2.39122e9 | −0.153406 | ||||||||
\(818\) | 1.52750e9 | 0.0975766 | ||||||||
\(819\) | 2.27932e8 | 0.0144981 | ||||||||
\(820\) | −2.50885e10 | −1.58901 | ||||||||
\(821\) | 1.26324e10 | 0.796685 | 0.398342 | − | 0.917237i | \(-0.369586\pi\) | ||||
0.398342 | + | 0.917237i | \(0.369586\pi\) | |||||||
\(822\) | 1.13799e9 | 0.0714637 | ||||||||
\(823\) | −5.60518e9 | −0.350502 | −0.175251 | − | 0.984524i | \(-0.556074\pi\) | ||||
−0.175251 | + | 0.984524i | \(0.556074\pi\) | |||||||
\(824\) | −5.67806e9 | −0.353553 | ||||||||
\(825\) | 3.61587e9 | 0.224194 | ||||||||
\(826\) | −1.47658e8 | −0.00911650 | ||||||||
\(827\) | −9.05725e9 | −0.556836 | −0.278418 | − | 0.960460i | \(-0.589810\pi\) | ||||
−0.278418 | + | 0.960460i | \(0.589810\pi\) | |||||||
\(828\) | −1.05075e10 | −0.643273 | ||||||||
\(829\) | 1.80271e10 | 1.09897 | 0.549483 | − | 0.835505i | \(-0.314825\pi\) | ||||
0.549483 | + | 0.835505i | \(0.314825\pi\) | |||||||
\(830\) | 2.15206e9 | 0.130641 | ||||||||
\(831\) | 2.00418e9 | 0.121153 | ||||||||
\(832\) | −1.47863e9 | −0.0890080 | ||||||||
\(833\) | −2.52001e9 | −0.151058 | ||||||||
\(834\) | −1.93882e9 | −0.115733 | ||||||||
\(835\) | −5.45813e9 | −0.324445 | ||||||||
\(836\) | −4.29771e9 | −0.254399 | ||||||||
\(837\) | −2.24493e9 | −0.132332 | ||||||||
\(838\) | −5.36143e8 | −0.0314721 | ||||||||
\(839\) | 2.52101e10 | 1.47370 | 0.736848 | − | 0.676059i | \(-0.236313\pi\) | ||||
0.736848 | + | 0.676059i | \(0.236313\pi\) | |||||||
\(840\) | 1.66286e9 | 0.0968004 | ||||||||
\(841\) | 4.40930e10 | 2.55613 | ||||||||
\(842\) | 1.69501e9 | 0.0978546 | ||||||||
\(843\) | 1.66400e10 | 0.956660 | ||||||||
\(844\) | −5.93885e9 | −0.340020 | ||||||||
\(845\) | 2.10707e10 | 1.20138 | ||||||||
\(846\) | 1.87858e9 | 0.106668 | ||||||||
\(847\) | −2.41134e9 | −0.136353 | ||||||||
\(848\) | 1.79468e10 | 1.01065 | ||||||||
\(849\) | −2.15085e9 | −0.120624 | ||||||||
\(850\) | −2.68504e8 | −0.0149963 | ||||||||
\(851\) | −2.25981e10 | −1.25695 | ||||||||
\(852\) | 6.29524e9 | 0.348717 | ||||||||
\(853\) | −4.60485e9 | −0.254035 | −0.127017 | − | 0.991900i | \(-0.540540\pi\) | ||||
−0.127017 | + | 0.991900i | \(0.540540\pi\) | |||||||
\(854\) | −3.08333e8 | −0.0169401 | ||||||||
\(855\) | 2.39033e9 | 0.130791 | ||||||||
\(856\) | 1.14305e10 | 0.622881 | ||||||||
\(857\) | 2.64820e10 | 1.43720 | 0.718600 | − | 0.695423i | \(-0.244783\pi\) | ||||
0.718600 | + | 0.695423i | \(0.244783\pi\) | |||||||
\(858\) | −1.63738e8 | −0.00885003 | ||||||||
\(859\) | −3.30189e10 | −1.77740 | −0.888702 | − | 0.458485i | \(-0.848392\pi\) | ||||
−0.888702 | + | 0.458485i | \(0.848392\pi\) | |||||||
\(860\) | 1.04494e10 | 0.560206 | ||||||||
\(861\) | 5.85817e9 | 0.312789 | ||||||||
\(862\) | 1.30588e9 | 0.0694431 | ||||||||
\(863\) | −1.44548e10 | −0.765552 | −0.382776 | − | 0.923841i | \(-0.625032\pi\) | ||||
−0.382776 | + | 0.923841i | \(0.625032\pi\) | |||||||
\(864\) | 1.83059e9 | 0.0965590 | ||||||||
\(865\) | −3.27406e10 | −1.72001 | ||||||||
\(866\) | −3.97171e9 | −0.207809 | ||||||||
\(867\) | 1.07196e10 | 0.558612 | ||||||||
\(868\) | −5.16260e9 | −0.267947 | ||||||||
\(869\) | 1.34513e10 | 0.695337 | ||||||||
\(870\) | −4.47924e9 | −0.230615 | ||||||||
\(871\) | −1.72343e9 | −0.0883751 | ||||||||
\(872\) | 1.00432e10 | 0.512938 | ||||||||
\(873\) | −2.12696e9 | −0.108195 | ||||||||
\(874\) | 2.20932e9 | 0.111936 | ||||||||
\(875\) | 5.05610e9 | 0.255145 | ||||||||
\(876\) | 7.87666e9 | 0.395893 | ||||||||
\(877\) | 1.61500e9 | 0.0808491 | 0.0404245 | − | 0.999183i | \(-0.487129\pi\) | ||||
0.0404245 | + | 0.999183i | \(0.487129\pi\) | |||||||
\(878\) | −4.76256e9 | −0.237470 | ||||||||
\(879\) | −6.76054e9 | −0.335753 | ||||||||
\(880\) | 1.81742e10 | 0.899013 | ||||||||
\(881\) | 3.62460e10 | 1.78585 | 0.892925 | − | 0.450206i | \(-0.148649\pi\) | ||||
0.892925 | + | 0.450206i | \(0.148649\pi\) | |||||||
\(882\) | 9.92386e8 | 0.0487013 | ||||||||
\(883\) | 1.90627e10 | 0.931796 | 0.465898 | − | 0.884838i | \(-0.345731\pi\) | ||||
0.465898 | + | 0.884838i | \(0.345731\pi\) | |||||||
\(884\) | −3.88308e8 | −0.0189057 | ||||||||
\(885\) | 1.88413e9 | 0.0913714 | ||||||||
\(886\) | 5.40357e9 | 0.261013 | ||||||||
\(887\) | −1.75867e9 | −0.0846157 | −0.0423079 | − | 0.999105i | \(-0.513471\pi\) | ||||
−0.0423079 | + | 0.999105i | \(0.513471\pi\) | |||||||
\(888\) | 2.61123e9 | 0.125141 | ||||||||
\(889\) | 1.16938e10 | 0.558214 | ||||||||
\(890\) | −3.64748e8 | −0.0173432 | ||||||||
\(891\) | −1.90693e9 | −0.0903155 | ||||||||
\(892\) | −1.54727e10 | −0.729944 | ||||||||
\(893\) | 1.26146e10 | 0.592780 | ||||||||
\(894\) | 5.06878e6 | 0.000237259 0 | ||||||||
\(895\) | −2.36695e10 | −1.10359 | ||||||||
\(896\) | 5.58156e9 | 0.259225 | ||||||||
\(897\) | −2.68818e9 | −0.124361 | ||||||||
\(898\) | 2.71135e9 | 0.124945 | ||||||||
\(899\) | 2.82484e10 | 1.29669 | ||||||||
\(900\) | −3.37689e9 | −0.154407 | ||||||||
\(901\) | 4.39359e9 | 0.200116 | ||||||||
\(902\) | −4.20831e9 | −0.190935 | ||||||||
\(903\) | −2.43995e9 | −0.110274 | ||||||||
\(904\) | −6.28436e9 | −0.282925 | ||||||||
\(905\) | 3.55954e10 | 1.59633 | ||||||||
\(906\) | 2.51046e9 | 0.112151 | ||||||||
\(907\) | −3.74603e10 | −1.66704 | −0.833520 | − | 0.552489i | \(-0.813678\pi\) | ||||
−0.833520 | + | 0.552489i | \(0.813678\pi\) | |||||||
\(908\) | −8.85684e9 | −0.392625 | ||||||||
\(909\) | −1.45647e10 | −0.643174 | ||||||||
\(910\) | 2.09428e8 | 0.00921277 | ||||||||
\(911\) | 8.20611e9 | 0.359603 | 0.179801 | − | 0.983703i | \(-0.442455\pi\) | ||||
0.179801 | + | 0.983703i | \(0.442455\pi\) | |||||||
\(912\) | 3.88406e9 | 0.169552 | ||||||||
\(913\) | −1.15285e10 | −0.501334 | ||||||||
\(914\) | −2.25576e9 | −0.0977196 | ||||||||
\(915\) | 3.93435e9 | 0.169785 | ||||||||
\(916\) | 4.21592e10 | 1.81242 | ||||||||
\(917\) | −8.68361e9 | −0.371884 | ||||||||
\(918\) | 1.41603e8 | 0.00604121 | ||||||||
\(919\) | −1.35638e9 | −0.0576472 | −0.0288236 | − | 0.999585i | \(-0.509176\pi\) | ||||
−0.0288236 | + | 0.999585i | \(0.509176\pi\) | |||||||
\(920\) | −1.96114e10 | −0.830331 | ||||||||
\(921\) | 8.94770e9 | 0.377401 | ||||||||
\(922\) | −1.51737e9 | −0.0637579 | ||||||||
\(923\) | 1.61053e9 | 0.0674161 | ||||||||
\(924\) | −4.38530e9 | −0.182872 | ||||||||
\(925\) | −7.26252e9 | −0.301711 | ||||||||
\(926\) | 4.41578e8 | 0.0182755 | ||||||||
\(927\) | −8.32846e9 | −0.343388 | ||||||||
\(928\) | −2.30347e10 | −0.946158 | ||||||||
\(929\) | 6.23174e9 | 0.255008 | 0.127504 | − | 0.991838i | \(-0.459303\pi\) | ||||
0.127504 | + | 0.991838i | \(0.459303\pi\) | |||||||
\(930\) | −2.06269e9 | −0.0840899 | ||||||||
\(931\) | 6.66385e9 | 0.270646 | ||||||||
\(932\) | 3.96028e10 | 1.60240 | ||||||||
\(933\) | 2.54318e9 | 0.102516 | ||||||||
\(934\) | −7.13575e8 | −0.0286567 | ||||||||
\(935\) | 4.44925e9 | 0.178011 | ||||||||
\(936\) | 3.10621e8 | 0.0123813 | ||||||||
\(937\) | −3.18495e10 | −1.26478 | −0.632389 | − | 0.774651i | \(-0.717926\pi\) | ||||
−0.632389 | + | 0.774651i | \(0.717926\pi\) | |||||||
\(938\) | 1.44529e9 | 0.0571801 | ||||||||
\(939\) | 1.45663e10 | 0.574141 | ||||||||
\(940\) | −5.51248e10 | −2.16471 | ||||||||
\(941\) | −4.56004e10 | −1.78404 | −0.892021 | − | 0.451995i | \(-0.850713\pi\) | ||||
−0.892021 | + | 0.451995i | \(0.850713\pi\) | |||||||
\(942\) | 2.36631e9 | 0.0922345 | ||||||||
\(943\) | −6.90901e10 | −2.68303 | ||||||||
\(944\) | 3.06154e9 | 0.118451 | ||||||||
\(945\) | 2.43904e9 | 0.0940174 | ||||||||
\(946\) | 1.75277e9 | 0.0673142 | ||||||||
\(947\) | 1.39598e10 | 0.534138 | 0.267069 | − | 0.963677i | \(-0.413945\pi\) | ||||
0.267069 | + | 0.963677i | \(0.413945\pi\) | |||||||
\(948\) | −1.25623e10 | −0.478894 | ||||||||
\(949\) | 2.01511e9 | 0.0765363 | ||||||||
\(950\) | 7.10026e8 | 0.0268684 | ||||||||
\(951\) | −1.86796e10 | −0.704266 | ||||||||
\(952\) | 6.61476e8 | 0.0248476 | ||||||||
\(953\) | −1.88757e10 | −0.706444 | −0.353222 | − | 0.935540i | \(-0.614914\pi\) | ||||
−0.353222 | + | 0.935540i | \(0.614914\pi\) | |||||||
\(954\) | −1.73021e9 | −0.0645176 | ||||||||
\(955\) | −1.15087e10 | −0.427578 | ||||||||
\(956\) | −3.08776e10 | −1.14298 | ||||||||
\(957\) | 2.39952e10 | 0.884980 | ||||||||
\(958\) | 3.53309e9 | 0.129830 | ||||||||
\(959\) | 7.79727e9 | 0.285481 | ||||||||
\(960\) | −1.58225e10 | −0.577200 | ||||||||
\(961\) | −1.45042e10 | −0.527183 | ||||||||
\(962\) | 3.28871e8 | 0.0119100 | ||||||||
\(963\) | 1.67660e10 | 0.604973 | ||||||||
\(964\) | 1.26701e10 | 0.455524 | ||||||||
\(965\) | 1.95213e10 | 0.699301 | ||||||||
\(966\) | 2.25434e9 | 0.0804637 | ||||||||
\(967\) | −4.38222e10 | −1.55848 | −0.779241 | − | 0.626724i | \(-0.784395\pi\) | ||||
−0.779241 | + | 0.626724i | \(0.784395\pi\) | |||||||
\(968\) | −3.28613e9 | −0.116445 | ||||||||
\(969\) | 9.50862e8 | 0.0335726 | ||||||||
\(970\) | −1.95429e9 | −0.0687525 | ||||||||
\(971\) | 7.68907e8 | 0.0269529 | 0.0134765 | − | 0.999909i | \(-0.495710\pi\) | ||||
0.0134765 | + | 0.999909i | \(0.495710\pi\) | |||||||
\(972\) | 1.78090e9 | 0.0622023 | ||||||||
\(973\) | −1.32845e10 | −0.462326 | ||||||||
\(974\) | −2.99756e9 | −0.103947 | ||||||||
\(975\) | −8.63921e8 | −0.0298509 | ||||||||
\(976\) | 6.39295e9 | 0.220103 | ||||||||
\(977\) | −3.25858e10 | −1.11788 | −0.558942 | − | 0.829206i | \(-0.688793\pi\) | ||||
−0.558942 | + | 0.829206i | \(0.688793\pi\) | |||||||
\(978\) | −5.24813e9 | −0.179398 | ||||||||
\(979\) | 1.95395e9 | 0.0665541 | ||||||||
\(980\) | −2.91205e10 | −0.988342 | ||||||||
\(981\) | 1.47312e10 | 0.498191 | ||||||||
\(982\) | 6.81577e9 | 0.229681 | ||||||||
\(983\) | −3.29965e10 | −1.10798 | −0.553988 | − | 0.832525i | \(-0.686894\pi\) | ||||
−0.553988 | + | 0.832525i | \(0.686894\pi\) | |||||||
\(984\) | 7.98341e9 | 0.267120 | ||||||||
\(985\) | −2.65919e10 | −0.886590 | ||||||||
\(986\) | −1.78182e9 | −0.0591963 | ||||||||
\(987\) | 1.28717e10 | 0.426113 | ||||||||
\(988\) | 1.02683e9 | 0.0338727 | ||||||||
\(989\) | 2.87763e10 | 0.945904 | ||||||||
\(990\) | −1.75213e9 | −0.0573908 | ||||||||
\(991\) | 2.11125e10 | 0.689100 | 0.344550 | − | 0.938768i | \(-0.388031\pi\) | ||||
0.344550 | + | 0.938768i | \(0.388031\pi\) | |||||||
\(992\) | −1.06075e10 | −0.345002 | ||||||||
\(993\) | 2.30780e10 | 0.747957 | ||||||||
\(994\) | −1.35061e9 | −0.0436193 | ||||||||
\(995\) | 4.02245e10 | 1.29452 | ||||||||
\(996\) | 1.07666e10 | 0.345280 | ||||||||
\(997\) | −2.81284e10 | −0.898902 | −0.449451 | − | 0.893305i | \(-0.648380\pi\) | ||||
−0.449451 | + | 0.893305i | \(0.648380\pi\) | |||||||
\(998\) | 1.03432e9 | 0.0329382 | ||||||||
\(999\) | 3.83009e9 | 0.121543 |
(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 | 177.8.a.a.1.8 | ✓ | 16 | |
3.2 | odd | 2 | 531.8.a.b.1.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.a.1.8 | ✓ | 16 | 1.1 | even | 1 | trivial | |
531.8.a.b.1.9 | 16 | 3.2 | odd | 2 |