Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,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, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
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: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −31.8892 | −1.40932 | −0.704658 | − | 0.709547i | \(-0.748900\pi\) | ||||
−0.704658 | + | 0.709547i | \(0.748900\pi\) | |||||||
\(3\) | 81.0000 | 0.577350 | ||||||||
\(4\) | 504.921 | 0.986174 | ||||||||
\(5\) | −1889.12 | −1.35174 | −0.675870 | − | 0.737021i | \(-0.736232\pi\) | ||||
−0.675870 | + | 0.737021i | \(0.736232\pi\) | |||||||
\(6\) | −2583.03 | −0.813670 | ||||||||
\(7\) | 12272.3 | 1.93190 | 0.965951 | − | 0.258726i | \(-0.0833027\pi\) | ||||
0.965951 | + | 0.258726i | \(0.0833027\pi\) | |||||||
\(8\) | 225.735 | 0.0194847 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 60242.4 | 1.90503 | ||||||||
\(11\) | −17051.0 | −0.351142 | −0.175571 | − | 0.984467i | \(-0.556177\pi\) | ||||
−0.175571 | + | 0.984467i | \(0.556177\pi\) | |||||||
\(12\) | 40898.6 | 0.569368 | ||||||||
\(13\) | 2771.93 | 0.0269176 | 0.0134588 | − | 0.999909i | \(-0.495716\pi\) | ||||
0.0134588 | + | 0.999909i | \(0.495716\pi\) | |||||||
\(14\) | −391354. | −2.72266 | ||||||||
\(15\) | −153018. | −0.780428 | ||||||||
\(16\) | −265718. | −1.01363 | ||||||||
\(17\) | −307419. | −0.892711 | −0.446356 | − | 0.894856i | \(-0.647278\pi\) | ||||
−0.446356 | + | 0.894856i | \(0.647278\pi\) | |||||||
\(18\) | −209225. | −0.469772 | ||||||||
\(19\) | 334845. | 0.589458 | 0.294729 | − | 0.955581i | \(-0.404771\pi\) | ||||
0.294729 | + | 0.955581i | \(0.404771\pi\) | |||||||
\(20\) | −953854. | −1.33305 | ||||||||
\(21\) | 994057. | 1.11538 | ||||||||
\(22\) | 543743. | 0.494871 | ||||||||
\(23\) | −829855. | −0.618340 | −0.309170 | − | 0.951007i | \(-0.600051\pi\) | ||||
−0.309170 | + | 0.951007i | \(0.600051\pi\) | |||||||
\(24\) | 18284.6 | 0.0112495 | ||||||||
\(25\) | 1.61563e6 | 0.827203 | ||||||||
\(26\) | −88394.6 | −0.0379355 | ||||||||
\(27\) | 531441. | 0.192450 | ||||||||
\(28\) | 6.19655e6 | 1.90519 | ||||||||
\(29\) | −1.06708e6 | −0.280161 | −0.140081 | − | 0.990140i | \(-0.544736\pi\) | ||||
−0.140081 | + | 0.990140i | \(0.544736\pi\) | |||||||
\(30\) | 4.87963e6 | 1.09987 | ||||||||
\(31\) | −806611. | −0.156869 | −0.0784344 | − | 0.996919i | \(-0.524992\pi\) | ||||
−0.0784344 | + | 0.996919i | \(0.524992\pi\) | |||||||
\(32\) | 8.35797e6 | 1.40905 | ||||||||
\(33\) | −1.38113e6 | −0.202732 | ||||||||
\(34\) | 9.80336e6 | 1.25811 | ||||||||
\(35\) | −2.31838e7 | −2.61143 | ||||||||
\(36\) | 3.31279e6 | 0.328725 | ||||||||
\(37\) | −298636. | −0.0261960 | −0.0130980 | − | 0.999914i | \(-0.504169\pi\) | ||||
−0.0130980 | + | 0.999914i | \(0.504169\pi\) | |||||||
\(38\) | −1.06780e7 | −0.830733 | ||||||||
\(39\) | 224526. | 0.0155409 | ||||||||
\(40\) | −426440. | −0.0263383 | ||||||||
\(41\) | 957358. | 0.0529111 | 0.0264556 | − | 0.999650i | \(-0.491578\pi\) | ||||
0.0264556 | + | 0.999650i | \(0.491578\pi\) | |||||||
\(42\) | −3.16997e7 | −1.57193 | ||||||||
\(43\) | −1.34324e7 | −0.599164 | −0.299582 | − | 0.954071i | \(-0.596847\pi\) | ||||
−0.299582 | + | 0.954071i | \(0.596847\pi\) | |||||||
\(44\) | −8.60942e6 | −0.346288 | ||||||||
\(45\) | −1.23945e7 | −0.450580 | ||||||||
\(46\) | 2.64634e7 | 0.871437 | ||||||||
\(47\) | 2.47451e6 | 0.0739690 | 0.0369845 | − | 0.999316i | \(-0.488225\pi\) | ||||
0.0369845 | + | 0.999316i | \(0.488225\pi\) | |||||||
\(48\) | −2.15232e7 | −0.585222 | ||||||||
\(49\) | 1.10256e8 | 2.73224 | ||||||||
\(50\) | −5.15212e7 | −1.16579 | ||||||||
\(51\) | −2.49010e7 | −0.515407 | ||||||||
\(52\) | 1.39961e6 | 0.0265455 | ||||||||
\(53\) | −1.59804e7 | −0.278193 | −0.139097 | − | 0.990279i | \(-0.544420\pi\) | ||||
−0.139097 | + | 0.990279i | \(0.544420\pi\) | |||||||
\(54\) | −1.69472e7 | −0.271223 | ||||||||
\(55\) | 3.22113e7 | 0.474653 | ||||||||
\(56\) | 2.77029e6 | 0.0376426 | ||||||||
\(57\) | 2.71225e7 | 0.340324 | ||||||||
\(58\) | 3.40285e7 | 0.394836 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | −7.72622e7 | −0.769638 | ||||||||
\(61\) | 4.27262e7 | 0.395102 | 0.197551 | − | 0.980293i | \(-0.436701\pi\) | ||||
0.197551 | + | 0.980293i | \(0.436701\pi\) | |||||||
\(62\) | 2.57222e7 | 0.221078 | ||||||||
\(63\) | 8.05186e7 | 0.643967 | ||||||||
\(64\) | −1.30481e8 | −0.972160 | ||||||||
\(65\) | −5.23649e6 | −0.0363857 | ||||||||
\(66\) | 4.40432e7 | 0.285714 | ||||||||
\(67\) | −1.05151e8 | −0.637498 | −0.318749 | − | 0.947839i | \(-0.603263\pi\) | ||||
−0.318749 | + | 0.947839i | \(0.603263\pi\) | |||||||
\(68\) | −1.55223e8 | −0.880369 | ||||||||
\(69\) | −6.72183e7 | −0.356999 | ||||||||
\(70\) | 7.39313e8 | 3.68033 | ||||||||
\(71\) | −2.00930e6 | −0.00938386 | −0.00469193 | − | 0.999989i | \(-0.501493\pi\) | ||||
−0.00469193 | + | 0.999989i | \(0.501493\pi\) | |||||||
\(72\) | 1.48105e6 | 0.00649491 | ||||||||
\(73\) | 4.31697e8 | 1.77921 | 0.889603 | − | 0.456734i | \(-0.150981\pi\) | ||||
0.889603 | + | 0.456734i | \(0.150981\pi\) | |||||||
\(74\) | 9.52327e6 | 0.0369185 | ||||||||
\(75\) | 1.30866e8 | 0.477586 | ||||||||
\(76\) | 1.69071e8 | 0.581309 | ||||||||
\(77\) | −2.09255e8 | −0.678372 | ||||||||
\(78\) | −7.15996e6 | −0.0219021 | ||||||||
\(79\) | −3.46731e8 | −1.00154 | −0.500772 | − | 0.865579i | \(-0.666951\pi\) | ||||
−0.500772 | + | 0.865579i | \(0.666951\pi\) | |||||||
\(80\) | 5.01972e8 | 1.37017 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −3.05294e7 | −0.0745686 | ||||||||
\(83\) | 2.37127e8 | 0.548440 | 0.274220 | − | 0.961667i | \(-0.411580\pi\) | ||||
0.274220 | + | 0.961667i | \(0.411580\pi\) | |||||||
\(84\) | 5.01920e8 | 1.09996 | ||||||||
\(85\) | 5.80750e8 | 1.20671 | ||||||||
\(86\) | 4.28349e8 | 0.844412 | ||||||||
\(87\) | −8.64338e7 | −0.161751 | ||||||||
\(88\) | −3.84902e6 | −0.00684192 | ||||||||
\(89\) | 5.27887e8 | 0.891837 | 0.445919 | − | 0.895073i | \(-0.352877\pi\) | ||||
0.445919 | + | 0.895073i | \(0.352877\pi\) | |||||||
\(90\) | 3.95250e8 | 0.635010 | ||||||||
\(91\) | 3.40180e7 | 0.0520022 | ||||||||
\(92\) | −4.19012e8 | −0.609791 | ||||||||
\(93\) | −6.53355e7 | −0.0905683 | ||||||||
\(94\) | −7.89103e7 | −0.104246 | ||||||||
\(95\) | −6.32561e8 | −0.796795 | ||||||||
\(96\) | 6.76995e8 | 0.813514 | ||||||||
\(97\) | 9.13439e8 | 1.04763 | 0.523814 | − | 0.851833i | \(-0.324509\pi\) | ||||
0.523814 | + | 0.851833i | \(0.324509\pi\) | |||||||
\(98\) | −3.51597e9 | −3.85060 | ||||||||
\(99\) | −1.11872e8 | −0.117047 | ||||||||
\(100\) | 8.15766e8 | 0.815766 | ||||||||
\(101\) | −1.51441e9 | −1.44810 | −0.724050 | − | 0.689748i | \(-0.757721\pi\) | ||||
−0.724050 | + | 0.689748i | \(0.757721\pi\) | |||||||
\(102\) | 7.94072e8 | 0.726372 | ||||||||
\(103\) | −1.02106e9 | −0.893892 | −0.446946 | − | 0.894561i | \(-0.647488\pi\) | ||||
−0.446946 | + | 0.894561i | \(0.647488\pi\) | |||||||
\(104\) | 625722. | 0.000524483 0 | ||||||||
\(105\) | −1.87789e9 | −1.50771 | ||||||||
\(106\) | 5.09602e8 | 0.392062 | ||||||||
\(107\) | 8.43566e8 | 0.622146 | 0.311073 | − | 0.950386i | \(-0.399312\pi\) | ||||
0.311073 | + | 0.950386i | \(0.399312\pi\) | |||||||
\(108\) | 2.68336e8 | 0.189789 | ||||||||
\(109\) | −2.50291e9 | −1.69834 | −0.849172 | − | 0.528117i | \(-0.822898\pi\) | ||||
−0.849172 | + | 0.528117i | \(0.822898\pi\) | |||||||
\(110\) | −1.02719e9 | −0.668937 | ||||||||
\(111\) | −2.41895e7 | −0.0151243 | ||||||||
\(112\) | −3.26097e9 | −1.95824 | ||||||||
\(113\) | −1.87981e9 | −1.08458 | −0.542288 | − | 0.840192i | \(-0.682442\pi\) | ||||
−0.542288 | + | 0.840192i | \(0.682442\pi\) | |||||||
\(114\) | −8.64914e8 | −0.479624 | ||||||||
\(115\) | 1.56769e9 | 0.835835 | ||||||||
\(116\) | −5.38794e8 | −0.276288 | ||||||||
\(117\) | 1.81866e7 | 0.00897255 | ||||||||
\(118\) | −3.86413e8 | −0.183477 | ||||||||
\(119\) | −3.77274e9 | −1.72463 | ||||||||
\(120\) | −3.45416e7 | −0.0152064 | ||||||||
\(121\) | −2.06721e9 | −0.876699 | ||||||||
\(122\) | −1.36250e9 | −0.556824 | ||||||||
\(123\) | 7.75460e7 | 0.0305483 | ||||||||
\(124\) | −4.07275e8 | −0.154700 | ||||||||
\(125\) | 6.37566e8 | 0.233577 | ||||||||
\(126\) | −2.56767e9 | −0.907554 | ||||||||
\(127\) | −3.26424e9 | −1.11343 | −0.556717 | − | 0.830702i | \(-0.687939\pi\) | ||||
−0.556717 | + | 0.830702i | \(0.687939\pi\) | |||||||
\(128\) | −1.18339e8 | −0.0389658 | ||||||||
\(129\) | −1.08803e9 | −0.345928 | ||||||||
\(130\) | 1.66988e8 | 0.0512789 | ||||||||
\(131\) | 1.77758e9 | 0.527363 | 0.263681 | − | 0.964610i | \(-0.415063\pi\) | ||||
0.263681 | + | 0.964610i | \(0.415063\pi\) | |||||||
\(132\) | −6.97363e8 | −0.199929 | ||||||||
\(133\) | 4.10932e9 | 1.13878 | ||||||||
\(134\) | 3.35319e9 | 0.898436 | ||||||||
\(135\) | −1.00395e9 | −0.260143 | ||||||||
\(136\) | −6.93954e7 | −0.0173942 | ||||||||
\(137\) | −9.42311e8 | −0.228535 | −0.114267 | − | 0.993450i | \(-0.536452\pi\) | ||||
−0.114267 | + | 0.993450i | \(0.536452\pi\) | |||||||
\(138\) | 2.14354e9 | 0.503124 | ||||||||
\(139\) | −3.94122e9 | −0.895496 | −0.447748 | − | 0.894160i | \(-0.647774\pi\) | ||||
−0.447748 | + | 0.894160i | \(0.647774\pi\) | |||||||
\(140\) | −1.17060e10 | −2.57533 | ||||||||
\(141\) | 2.00436e8 | 0.0427060 | ||||||||
\(142\) | 6.40749e7 | 0.0132248 | ||||||||
\(143\) | −4.72642e7 | −0.00945192 | ||||||||
\(144\) | −1.74338e9 | −0.337878 | ||||||||
\(145\) | 2.01585e9 | 0.378705 | ||||||||
\(146\) | −1.37665e10 | −2.50747 | ||||||||
\(147\) | 8.93073e9 | 1.57746 | ||||||||
\(148\) | −1.50788e8 | −0.0258338 | ||||||||
\(149\) | 8.74194e9 | 1.45301 | 0.726507 | − | 0.687159i | \(-0.241143\pi\) | ||||
0.726507 | + | 0.687159i | \(0.241143\pi\) | |||||||
\(150\) | −4.17321e9 | −0.673070 | ||||||||
\(151\) | −6.56954e9 | −1.02835 | −0.514173 | − | 0.857687i | \(-0.671901\pi\) | ||||
−0.514173 | + | 0.857687i | \(0.671901\pi\) | |||||||
\(152\) | 7.55864e7 | 0.0114854 | ||||||||
\(153\) | −2.01698e9 | −0.297570 | ||||||||
\(154\) | 6.67298e9 | 0.956042 | ||||||||
\(155\) | 1.52378e9 | 0.212046 | ||||||||
\(156\) | 1.13368e8 | 0.0153260 | ||||||||
\(157\) | 1.03687e10 | 1.36200 | 0.681001 | − | 0.732282i | \(-0.261545\pi\) | ||||
0.681001 | + | 0.732282i | \(0.261545\pi\) | |||||||
\(158\) | 1.10570e10 | 1.41149 | ||||||||
\(159\) | −1.29441e9 | −0.160615 | ||||||||
\(160\) | −1.57892e10 | −1.90467 | ||||||||
\(161\) | −1.01842e10 | −1.19457 | ||||||||
\(162\) | −1.37273e9 | −0.156591 | ||||||||
\(163\) | 6.31177e9 | 0.700337 | 0.350168 | − | 0.936687i | \(-0.386124\pi\) | ||||
0.350168 | + | 0.936687i | \(0.386124\pi\) | |||||||
\(164\) | 4.83390e8 | 0.0521796 | ||||||||
\(165\) | 2.60912e9 | 0.274041 | ||||||||
\(166\) | −7.56179e9 | −0.772926 | ||||||||
\(167\) | 7.50187e8 | 0.0746355 | 0.0373177 | − | 0.999303i | \(-0.488119\pi\) | ||||
0.0373177 | + | 0.999303i | \(0.488119\pi\) | |||||||
\(168\) | 2.24394e8 | 0.0217330 | ||||||||
\(169\) | −1.05968e10 | −0.999275 | ||||||||
\(170\) | −1.85197e10 | −1.70064 | ||||||||
\(171\) | 2.19692e9 | 0.196486 | ||||||||
\(172\) | −6.78231e9 | −0.590880 | ||||||||
\(173\) | −1.26990e10 | −1.07786 | −0.538929 | − | 0.842351i | \(-0.681171\pi\) | ||||
−0.538929 | + | 0.842351i | \(0.681171\pi\) | |||||||
\(174\) | 2.75631e9 | 0.227959 | ||||||||
\(175\) | 1.98275e10 | 1.59807 | ||||||||
\(176\) | 4.53077e9 | 0.355930 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −1.68339e10 | −1.25688 | ||||||||
\(179\) | −1.79316e10 | −1.30551 | −0.652754 | − | 0.757570i | \(-0.726387\pi\) | ||||
−0.652754 | + | 0.757570i | \(0.726387\pi\) | |||||||
\(180\) | −6.25824e9 | −0.444351 | ||||||||
\(181\) | −1.71696e10 | −1.18907 | −0.594534 | − | 0.804070i | \(-0.702664\pi\) | ||||
−0.594534 | + | 0.804070i | \(0.702664\pi\) | |||||||
\(182\) | −1.08481e9 | −0.0732876 | ||||||||
\(183\) | 3.46082e9 | 0.228112 | ||||||||
\(184\) | −1.87328e8 | −0.0120482 | ||||||||
\(185\) | 5.64158e8 | 0.0354102 | ||||||||
\(186\) | 2.08350e9 | 0.127639 | ||||||||
\(187\) | 5.24181e9 | 0.313469 | ||||||||
\(188\) | 1.24943e9 | 0.0729463 | ||||||||
\(189\) | 6.52201e9 | 0.371795 | ||||||||
\(190\) | 2.01719e10 | 1.12294 | ||||||||
\(191\) | −2.64175e10 | −1.43629 | −0.718143 | − | 0.695895i | \(-0.755008\pi\) | ||||
−0.718143 | + | 0.695895i | \(0.755008\pi\) | |||||||
\(192\) | −1.05690e10 | −0.561277 | ||||||||
\(193\) | −2.24534e10 | −1.16486 | −0.582431 | − | 0.812880i | \(-0.697898\pi\) | ||||
−0.582431 | + | 0.812880i | \(0.697898\pi\) | |||||||
\(194\) | −2.91288e10 | −1.47644 | ||||||||
\(195\) | −4.24156e8 | −0.0210073 | ||||||||
\(196\) | 5.56705e10 | 2.69447 | ||||||||
\(197\) | 2.52454e10 | 1.19422 | 0.597110 | − | 0.802160i | \(-0.296316\pi\) | ||||
0.597110 | + | 0.802160i | \(0.296316\pi\) | |||||||
\(198\) | 3.56750e9 | 0.164957 | ||||||||
\(199\) | 1.59249e10 | 0.719843 | 0.359922 | − | 0.932983i | \(-0.382803\pi\) | ||||
0.359922 | + | 0.932983i | \(0.382803\pi\) | |||||||
\(200\) | 3.64705e8 | 0.0161178 | ||||||||
\(201\) | −8.51727e9 | −0.368059 | ||||||||
\(202\) | 4.82934e10 | 2.04083 | ||||||||
\(203\) | −1.30956e10 | −0.541244 | ||||||||
\(204\) | −1.25730e10 | −0.508281 | ||||||||
\(205\) | −1.80856e9 | −0.0715221 | ||||||||
\(206\) | 3.25609e10 | 1.25978 | ||||||||
\(207\) | −5.44468e9 | −0.206113 | ||||||||
\(208\) | −7.36552e8 | −0.0272847 | ||||||||
\(209\) | −5.70945e9 | −0.206984 | ||||||||
\(210\) | 5.98843e10 | 2.12484 | ||||||||
\(211\) | 1.80597e10 | 0.627250 | 0.313625 | − | 0.949547i | \(-0.398457\pi\) | ||||
0.313625 | + | 0.949547i | \(0.398457\pi\) | |||||||
\(212\) | −8.06885e9 | −0.274347 | ||||||||
\(213\) | −1.62753e8 | −0.00541777 | ||||||||
\(214\) | −2.69006e10 | −0.876800 | ||||||||
\(215\) | 2.53754e10 | 0.809915 | ||||||||
\(216\) | 1.19965e8 | 0.00374984 | ||||||||
\(217\) | −9.89898e9 | −0.303055 | ||||||||
\(218\) | 7.98157e10 | 2.39350 | ||||||||
\(219\) | 3.49675e10 | 1.02723 | ||||||||
\(220\) | 1.62642e10 | 0.468091 | ||||||||
\(221\) | −8.52144e8 | −0.0240297 | ||||||||
\(222\) | 7.71385e8 | 0.0213149 | ||||||||
\(223\) | −5.79827e10 | −1.57010 | −0.785048 | − | 0.619434i | \(-0.787362\pi\) | ||||
−0.785048 | + | 0.619434i | \(0.787362\pi\) | |||||||
\(224\) | 1.02572e11 | 2.72214 | ||||||||
\(225\) | 1.06002e10 | 0.275734 | ||||||||
\(226\) | 5.99456e10 | 1.52851 | ||||||||
\(227\) | −1.84397e10 | −0.460931 | −0.230466 | − | 0.973080i | \(-0.574025\pi\) | ||||
−0.230466 | + | 0.973080i | \(0.574025\pi\) | |||||||
\(228\) | 1.36947e10 | 0.335619 | ||||||||
\(229\) | 3.07282e10 | 0.738376 | 0.369188 | − | 0.929355i | \(-0.379636\pi\) | ||||
0.369188 | + | 0.929355i | \(0.379636\pi\) | |||||||
\(230\) | −4.99925e10 | −1.17796 | ||||||||
\(231\) | −1.69497e10 | −0.391658 | ||||||||
\(232\) | −2.40879e8 | −0.00545887 | ||||||||
\(233\) | −6.81886e10 | −1.51569 | −0.757845 | − | 0.652435i | \(-0.773747\pi\) | ||||
−0.757845 | + | 0.652435i | \(0.773747\pi\) | |||||||
\(234\) | −5.79957e8 | −0.0126452 | ||||||||
\(235\) | −4.67464e9 | −0.0999868 | ||||||||
\(236\) | 6.11831e9 | 0.128389 | ||||||||
\(237\) | −2.80852e10 | −0.578242 | ||||||||
\(238\) | 1.20310e11 | 2.43055 | ||||||||
\(239\) | −7.97104e10 | −1.58024 | −0.790122 | − | 0.612949i | \(-0.789983\pi\) | ||||
−0.790122 | + | 0.612949i | \(0.789983\pi\) | |||||||
\(240\) | 4.06598e10 | 0.791069 | ||||||||
\(241\) | −3.16837e10 | −0.605005 | −0.302503 | − | 0.953149i | \(-0.597822\pi\) | ||||
−0.302503 | + | 0.953149i | \(0.597822\pi\) | |||||||
\(242\) | 6.59217e10 | 1.23555 | ||||||||
\(243\) | 3.48678e9 | 0.0641500 | ||||||||
\(244\) | 2.15733e10 | 0.389640 | ||||||||
\(245\) | −2.08286e11 | −3.69328 | ||||||||
\(246\) | −2.47288e9 | −0.0430522 | ||||||||
\(247\) | 9.28167e8 | 0.0158668 | ||||||||
\(248\) | −1.82081e8 | −0.00305655 | ||||||||
\(249\) | 1.92073e10 | 0.316642 | ||||||||
\(250\) | −2.03315e10 | −0.329184 | ||||||||
\(251\) | −1.06582e11 | −1.69494 | −0.847468 | − | 0.530846i | \(-0.821874\pi\) | ||||
−0.847468 | + | 0.530846i | \(0.821874\pi\) | |||||||
\(252\) | 4.06556e10 | 0.635064 | ||||||||
\(253\) | 1.41499e10 | 0.217125 | ||||||||
\(254\) | 1.04094e11 | 1.56918 | ||||||||
\(255\) | 4.70408e10 | 0.696697 | ||||||||
\(256\) | 7.05801e10 | 1.02708 | ||||||||
\(257\) | −5.57546e10 | −0.797227 | −0.398613 | − | 0.917119i | \(-0.630508\pi\) | ||||
−0.398613 | + | 0.917119i | \(0.630508\pi\) | |||||||
\(258\) | 3.46963e10 | 0.487522 | ||||||||
\(259\) | −3.66496e9 | −0.0506081 | ||||||||
\(260\) | −2.64402e9 | −0.0358826 | ||||||||
\(261\) | −7.00114e9 | −0.0933870 | ||||||||
\(262\) | −5.66857e10 | −0.743221 | ||||||||
\(263\) | −2.12500e10 | −0.273879 | −0.136939 | − | 0.990579i | \(-0.543727\pi\) | ||||
−0.136939 | + | 0.990579i | \(0.543727\pi\) | |||||||
\(264\) | −3.11770e8 | −0.00395018 | ||||||||
\(265\) | 3.01888e10 | 0.376045 | ||||||||
\(266\) | −1.31043e11 | −1.60490 | ||||||||
\(267\) | 4.27588e10 | 0.514903 | ||||||||
\(268\) | −5.30932e10 | −0.628684 | ||||||||
\(269\) | 2.74501e9 | 0.0319638 | 0.0159819 | − | 0.999872i | \(-0.494913\pi\) | ||||
0.0159819 | + | 0.999872i | \(0.494913\pi\) | |||||||
\(270\) | 3.20153e10 | 0.366623 | ||||||||
\(271\) | 1.67543e11 | 1.88697 | 0.943485 | − | 0.331414i | \(-0.107526\pi\) | ||||
0.943485 | + | 0.331414i | \(0.107526\pi\) | |||||||
\(272\) | 8.16869e10 | 0.904883 | ||||||||
\(273\) | 2.75545e9 | 0.0300235 | ||||||||
\(274\) | 3.00496e10 | 0.322078 | ||||||||
\(275\) | −2.75481e10 | −0.290466 | ||||||||
\(276\) | −3.39399e10 | −0.352063 | ||||||||
\(277\) | 1.37791e11 | 1.40625 | 0.703123 | − | 0.711068i | \(-0.251788\pi\) | ||||
0.703123 | + | 0.711068i | \(0.251788\pi\) | |||||||
\(278\) | 1.25682e11 | 1.26204 | ||||||||
\(279\) | −5.29218e9 | −0.0522896 | ||||||||
\(280\) | −5.23340e9 | −0.0508830 | ||||||||
\(281\) | −1.47914e11 | −1.41524 | −0.707622 | − | 0.706591i | \(-0.750232\pi\) | ||||
−0.707622 | + | 0.706591i | \(0.750232\pi\) | |||||||
\(282\) | −6.39173e9 | −0.0601863 | ||||||||
\(283\) | 4.45401e10 | 0.412774 | 0.206387 | − | 0.978470i | \(-0.433829\pi\) | ||||
0.206387 | + | 0.978470i | \(0.433829\pi\) | |||||||
\(284\) | −1.01454e9 | −0.00925412 | ||||||||
\(285\) | −5.12375e10 | −0.460030 | ||||||||
\(286\) | 1.50722e9 | 0.0133208 | ||||||||
\(287\) | 1.17490e10 | 0.102219 | ||||||||
\(288\) | 5.48366e10 | 0.469683 | ||||||||
\(289\) | −2.40813e10 | −0.203067 | ||||||||
\(290\) | −6.42837e10 | −0.533716 | ||||||||
\(291\) | 7.39886e10 | 0.604848 | ||||||||
\(292\) | 2.17973e11 | 1.75461 | ||||||||
\(293\) | 1.85472e11 | 1.47019 | 0.735097 | − | 0.677962i | \(-0.237137\pi\) | ||||
0.735097 | + | 0.677962i | \(0.237137\pi\) | |||||||
\(294\) | −2.84794e11 | −2.22314 | ||||||||
\(295\) | −2.28911e10 | −0.175982 | ||||||||
\(296\) | −6.74128e7 | −0.000510422 0 | ||||||||
\(297\) | −9.06161e9 | −0.0675774 | ||||||||
\(298\) | −2.78774e11 | −2.04776 | ||||||||
\(299\) | −2.30030e9 | −0.0166442 | ||||||||
\(300\) | 6.60771e10 | 0.470983 | ||||||||
\(301\) | −1.64847e11 | −1.15753 | ||||||||
\(302\) | 2.09497e11 | 1.44926 | ||||||||
\(303\) | −1.22668e11 | −0.836060 | ||||||||
\(304\) | −8.89745e10 | −0.597495 | ||||||||
\(305\) | −8.07146e10 | −0.534076 | ||||||||
\(306\) | 6.43198e10 | 0.419371 | ||||||||
\(307\) | 1.62747e11 | 1.04566 | 0.522830 | − | 0.852437i | \(-0.324876\pi\) | ||||
0.522830 | + | 0.852437i | \(0.324876\pi\) | |||||||
\(308\) | −1.05657e11 | −0.668993 | ||||||||
\(309\) | −8.27061e10 | −0.516089 | ||||||||
\(310\) | −4.85922e10 | −0.298840 | ||||||||
\(311\) | −1.22720e10 | −0.0743862 | −0.0371931 | − | 0.999308i | \(-0.511842\pi\) | ||||
−0.0371931 | + | 0.999308i | \(0.511842\pi\) | |||||||
\(312\) | 5.06835e7 | 0.000302811 0 | ||||||||
\(313\) | −1.67219e11 | −0.984776 | −0.492388 | − | 0.870376i | \(-0.663876\pi\) | ||||
−0.492388 | + | 0.870376i | \(0.663876\pi\) | |||||||
\(314\) | −3.30651e11 | −1.91949 | ||||||||
\(315\) | −1.52109e11 | −0.870477 | ||||||||
\(316\) | −1.75072e11 | −0.987698 | ||||||||
\(317\) | −2.57818e11 | −1.43399 | −0.716996 | − | 0.697078i | \(-0.754483\pi\) | ||||
−0.716996 | + | 0.697078i | \(0.754483\pi\) | |||||||
\(318\) | 4.12778e10 | 0.226357 | ||||||||
\(319\) | 1.81949e10 | 0.0983764 | ||||||||
\(320\) | 2.46494e11 | 1.31411 | ||||||||
\(321\) | 6.83288e10 | 0.359196 | ||||||||
\(322\) | 3.24767e11 | 1.68353 | ||||||||
\(323\) | −1.02938e11 | −0.526216 | ||||||||
\(324\) | 2.17352e10 | 0.109575 | ||||||||
\(325\) | 4.47841e9 | 0.0222663 | ||||||||
\(326\) | −2.01277e11 | −0.986996 | ||||||||
\(327\) | −2.02736e11 | −0.980539 | ||||||||
\(328\) | 2.16110e8 | 0.00103096 | ||||||||
\(329\) | 3.03680e10 | 0.142901 | ||||||||
\(330\) | −8.32027e10 | −0.386211 | ||||||||
\(331\) | 2.79741e11 | 1.28095 | 0.640473 | − | 0.767981i | \(-0.278738\pi\) | ||||
0.640473 | + | 0.767981i | \(0.278738\pi\) | |||||||
\(332\) | 1.19730e11 | 0.540858 | ||||||||
\(333\) | −1.95935e9 | −0.00873200 | ||||||||
\(334\) | −2.39229e10 | −0.105185 | ||||||||
\(335\) | 1.98643e11 | 0.861731 | ||||||||
\(336\) | −2.64139e11 | −1.13059 | ||||||||
\(337\) | 1.93079e11 | 0.815454 | 0.407727 | − | 0.913104i | \(-0.366321\pi\) | ||||
0.407727 | + | 0.913104i | \(0.366321\pi\) | |||||||
\(338\) | 3.37924e11 | 1.40830 | ||||||||
\(339\) | −1.52264e11 | −0.626181 | ||||||||
\(340\) | 2.93233e11 | 1.19003 | ||||||||
\(341\) | 1.37535e10 | 0.0550833 | ||||||||
\(342\) | −7.00580e10 | −0.276911 | ||||||||
\(343\) | 8.57862e11 | 3.34652 | ||||||||
\(344\) | −3.03217e9 | −0.0116746 | ||||||||
\(345\) | 1.26983e11 | 0.482570 | ||||||||
\(346\) | 4.04961e11 | 1.51904 | ||||||||
\(347\) | 4.07789e11 | 1.50992 | 0.754959 | − | 0.655773i | \(-0.227657\pi\) | ||||
0.754959 | + | 0.655773i | \(0.227657\pi\) | |||||||
\(348\) | −4.36423e10 | −0.159515 | ||||||||
\(349\) | −1.82090e11 | −0.657009 | −0.328505 | − | 0.944502i | \(-0.606545\pi\) | ||||
−0.328505 | + | 0.944502i | \(0.606545\pi\) | |||||||
\(350\) | −6.32284e11 | −2.25219 | ||||||||
\(351\) | 1.47312e9 | 0.00518030 | ||||||||
\(352\) | −1.42512e11 | −0.494776 | ||||||||
\(353\) | −5.32848e10 | −0.182649 | −0.0913245 | − | 0.995821i | \(-0.529110\pi\) | ||||
−0.0913245 | + | 0.995821i | \(0.529110\pi\) | |||||||
\(354\) | −3.12995e10 | −0.105931 | ||||||||
\(355\) | 3.79579e9 | 0.0126845 | ||||||||
\(356\) | 2.66541e11 | 0.879507 | ||||||||
\(357\) | −3.05592e11 | −0.995716 | ||||||||
\(358\) | 5.71824e11 | 1.83988 | ||||||||
\(359\) | 5.41580e11 | 1.72083 | 0.860414 | − | 0.509595i | \(-0.170205\pi\) | ||||
0.860414 | + | 0.509595i | \(0.170205\pi\) | |||||||
\(360\) | −2.79787e9 | −0.00877944 | ||||||||
\(361\) | −2.10566e11 | −0.652539 | ||||||||
\(362\) | 5.47525e11 | 1.67577 | ||||||||
\(363\) | −1.67444e11 | −0.506162 | ||||||||
\(364\) | 1.71764e10 | 0.0512833 | ||||||||
\(365\) | −8.15526e11 | −2.40503 | ||||||||
\(366\) | −1.10363e11 | −0.321483 | ||||||||
\(367\) | −1.14857e11 | −0.330492 | −0.165246 | − | 0.986252i | \(-0.552842\pi\) | ||||
−0.165246 | + | 0.986252i | \(0.552842\pi\) | |||||||
\(368\) | 2.20508e11 | 0.626771 | ||||||||
\(369\) | 6.28123e9 | 0.0176370 | ||||||||
\(370\) | −1.79906e10 | −0.0499042 | ||||||||
\(371\) | −1.96116e11 | −0.537442 | ||||||||
\(372\) | −3.29893e10 | −0.0893161 | ||||||||
\(373\) | −1.42587e11 | −0.381409 | −0.190705 | − | 0.981647i | \(-0.561077\pi\) | ||||
−0.190705 | + | 0.981647i | \(0.561077\pi\) | |||||||
\(374\) | −1.67157e11 | −0.441777 | ||||||||
\(375\) | 5.16428e10 | 0.134856 | ||||||||
\(376\) | 5.58585e8 | 0.00144127 | ||||||||
\(377\) | −2.95788e9 | −0.00754128 | ||||||||
\(378\) | −2.07982e11 | −0.523976 | ||||||||
\(379\) | −7.82015e11 | −1.94688 | −0.973438 | − | 0.228949i | \(-0.926471\pi\) | ||||
−0.973438 | + | 0.228949i | \(0.926471\pi\) | |||||||
\(380\) | −3.19394e11 | −0.785778 | ||||||||
\(381\) | −2.64403e11 | −0.642842 | ||||||||
\(382\) | 8.42432e11 | 2.02418 | ||||||||
\(383\) | 3.21255e11 | 0.762878 | 0.381439 | − | 0.924394i | \(-0.375429\pi\) | ||||
0.381439 | + | 0.924394i | \(0.375429\pi\) | |||||||
\(384\) | −9.58546e9 | −0.0224969 | ||||||||
\(385\) | 3.95307e11 | 0.916984 | ||||||||
\(386\) | 7.16021e11 | 1.64166 | ||||||||
\(387\) | −8.81300e10 | −0.199721 | ||||||||
\(388\) | 4.61215e11 | 1.03314 | ||||||||
\(389\) | 1.78363e11 | 0.394939 | 0.197470 | − | 0.980309i | \(-0.436728\pi\) | ||||
0.197470 | + | 0.980309i | \(0.436728\pi\) | |||||||
\(390\) | 1.35260e10 | 0.0296059 | ||||||||
\(391\) | 2.55114e11 | 0.551999 | ||||||||
\(392\) | 2.48886e10 | 0.0532370 | ||||||||
\(393\) | 1.43984e11 | 0.304473 | ||||||||
\(394\) | −8.05055e11 | −1.68303 | ||||||||
\(395\) | 6.55014e11 | 1.35383 | ||||||||
\(396\) | −5.64864e10 | −0.115429 | ||||||||
\(397\) | 6.49654e11 | 1.31258 | 0.656289 | − | 0.754510i | \(-0.272125\pi\) | ||||
0.656289 | + | 0.754510i | \(0.272125\pi\) | |||||||
\(398\) | −5.07833e11 | −1.01449 | ||||||||
\(399\) | 3.32855e11 | 0.657472 | ||||||||
\(400\) | −4.29302e11 | −0.838481 | ||||||||
\(401\) | −1.09019e11 | −0.210550 | −0.105275 | − | 0.994443i | \(-0.533572\pi\) | ||||
−0.105275 | + | 0.994443i | \(0.533572\pi\) | |||||||
\(402\) | 2.71609e11 | 0.518712 | ||||||||
\(403\) | −2.23587e9 | −0.00422254 | ||||||||
\(404\) | −7.64660e11 | −1.42808 | ||||||||
\(405\) | −8.13202e10 | −0.150193 | ||||||||
\(406\) | 4.17608e11 | 0.762784 | ||||||||
\(407\) | 5.09205e9 | 0.00919852 | ||||||||
\(408\) | −5.62103e9 | −0.0100426 | ||||||||
\(409\) | −4.91552e11 | −0.868590 | −0.434295 | − | 0.900771i | \(-0.643002\pi\) | ||||
−0.434295 | + | 0.900771i | \(0.643002\pi\) | |||||||
\(410\) | 5.76735e10 | 0.100797 | ||||||||
\(411\) | −7.63272e10 | −0.131944 | ||||||||
\(412\) | −5.15556e11 | −0.881533 | ||||||||
\(413\) | 1.48708e11 | 0.251512 | ||||||||
\(414\) | 1.73627e11 | 0.290479 | ||||||||
\(415\) | −4.47960e11 | −0.741349 | ||||||||
\(416\) | 2.31677e10 | 0.0379282 | ||||||||
\(417\) | −3.19239e11 | −0.517015 | ||||||||
\(418\) | 1.82070e11 | 0.291706 | ||||||||
\(419\) | 1.82329e11 | 0.288997 | 0.144499 | − | 0.989505i | \(-0.453843\pi\) | ||||
0.144499 | + | 0.989505i | \(0.453843\pi\) | |||||||
\(420\) | −9.48185e11 | −1.48686 | ||||||||
\(421\) | −1.14800e12 | −1.78104 | −0.890519 | − | 0.454947i | \(-0.849658\pi\) | ||||
−0.890519 | + | 0.454947i | \(0.849658\pi\) | |||||||
\(422\) | −5.75911e11 | −0.883994 | ||||||||
\(423\) | 1.62353e10 | 0.0246563 | ||||||||
\(424\) | −3.60734e9 | −0.00542052 | ||||||||
\(425\) | −4.96676e11 | −0.738453 | ||||||||
\(426\) | 5.19006e9 | 0.00763536 | ||||||||
\(427\) | 5.24348e11 | 0.763299 | ||||||||
\(428\) | 4.25934e11 | 0.613544 | ||||||||
\(429\) | −3.82840e9 | −0.00545707 | ||||||||
\(430\) | −8.09200e11 | −1.14143 | ||||||||
\(431\) | 9.10456e11 | 1.27090 | 0.635450 | − | 0.772142i | \(-0.280815\pi\) | ||||
0.635450 | + | 0.772142i | \(0.280815\pi\) | |||||||
\(432\) | −1.41214e11 | −0.195074 | ||||||||
\(433\) | −1.35384e12 | −1.85085 | −0.925426 | − | 0.378929i | \(-0.876292\pi\) | ||||
−0.925426 | + | 0.378929i | \(0.876292\pi\) | |||||||
\(434\) | 3.15671e11 | 0.427101 | ||||||||
\(435\) | 1.63283e11 | 0.218646 | ||||||||
\(436\) | −1.26377e12 | −1.67486 | ||||||||
\(437\) | −2.77873e11 | −0.364485 | ||||||||
\(438\) | −1.11508e12 | −1.44769 | ||||||||
\(439\) | −5.31193e11 | −0.682593 | −0.341297 | − | 0.939956i | \(-0.610866\pi\) | ||||
−0.341297 | + | 0.939956i | \(0.610866\pi\) | |||||||
\(440\) | 7.27124e9 | 0.00924850 | ||||||||
\(441\) | 7.23389e11 | 0.910748 | ||||||||
\(442\) | 2.71742e10 | 0.0338654 | ||||||||
\(443\) | 2.93695e11 | 0.362309 | 0.181155 | − | 0.983455i | \(-0.442017\pi\) | ||||
0.181155 | + | 0.983455i | \(0.442017\pi\) | |||||||
\(444\) | −1.22138e10 | −0.0149152 | ||||||||
\(445\) | −9.97239e11 | −1.20553 | ||||||||
\(446\) | 1.84902e12 | 2.21276 | ||||||||
\(447\) | 7.08097e11 | 0.838898 | ||||||||
\(448\) | −1.60130e12 | −1.87812 | ||||||||
\(449\) | −2.96345e11 | −0.344104 | −0.172052 | − | 0.985088i | \(-0.555040\pi\) | ||||
−0.172052 | + | 0.985088i | \(0.555040\pi\) | |||||||
\(450\) | −3.38030e11 | −0.388597 | ||||||||
\(451\) | −1.63239e10 | −0.0185793 | ||||||||
\(452\) | −9.49155e11 | −1.06958 | ||||||||
\(453\) | −5.32133e11 | −0.593715 | ||||||||
\(454\) | 5.88026e11 | 0.649599 | ||||||||
\(455\) | −6.42638e10 | −0.0702935 | ||||||||
\(456\) | 6.12250e9 | 0.00663112 | ||||||||
\(457\) | −1.56401e12 | −1.67733 | −0.838664 | − | 0.544650i | \(-0.816663\pi\) | ||||
−0.838664 | + | 0.544650i | \(0.816663\pi\) | |||||||
\(458\) | −9.79898e11 | −1.04061 | ||||||||
\(459\) | −1.63375e11 | −0.171802 | ||||||||
\(460\) | 7.91561e11 | 0.824279 | ||||||||
\(461\) | −1.01947e12 | −1.05128 | −0.525642 | − | 0.850706i | \(-0.676175\pi\) | ||||
−0.525642 | + | 0.850706i | \(0.676175\pi\) | |||||||
\(462\) | 5.40512e11 | 0.551971 | ||||||||
\(463\) | −3.45994e11 | −0.349908 | −0.174954 | − | 0.984577i | \(-0.555978\pi\) | ||||
−0.174954 | + | 0.984577i | \(0.555978\pi\) | |||||||
\(464\) | 2.83544e11 | 0.283981 | ||||||||
\(465\) | 1.23426e11 | 0.122425 | ||||||||
\(466\) | 2.17448e12 | 2.13609 | ||||||||
\(467\) | 5.45802e11 | 0.531018 | 0.265509 | − | 0.964108i | \(-0.414460\pi\) | ||||
0.265509 | + | 0.964108i | \(0.414460\pi\) | |||||||
\(468\) | 9.18281e9 | 0.00884850 | ||||||||
\(469\) | −1.29045e12 | −1.23158 | ||||||||
\(470\) | 1.49071e11 | 0.140913 | ||||||||
\(471\) | 8.39869e11 | 0.786353 | ||||||||
\(472\) | 2.73532e9 | 0.00253670 | ||||||||
\(473\) | 2.29036e11 | 0.210392 | ||||||||
\(474\) | 8.95614e11 | 0.814927 | ||||||||
\(475\) | 5.40986e11 | 0.487601 | ||||||||
\(476\) | −1.90494e12 | −1.70079 | ||||||||
\(477\) | −1.04847e11 | −0.0927311 | ||||||||
\(478\) | 2.54190e12 | 2.22706 | ||||||||
\(479\) | −3.74861e11 | −0.325357 | −0.162679 | − | 0.986679i | \(-0.552013\pi\) | ||||
−0.162679 | + | 0.986679i | \(0.552013\pi\) | |||||||
\(480\) | −1.27892e12 | −1.09966 | ||||||||
\(481\) | −8.27799e8 | −0.000705134 0 | ||||||||
\(482\) | 1.01037e12 | 0.852644 | ||||||||
\(483\) | −8.24923e11 | −0.689686 | ||||||||
\(484\) | −1.04378e12 | −0.864578 | ||||||||
\(485\) | −1.72559e12 | −1.41612 | ||||||||
\(486\) | −1.11191e11 | −0.0904077 | ||||||||
\(487\) | −1.96357e12 | −1.58185 | −0.790924 | − | 0.611914i | \(-0.790400\pi\) | ||||
−0.790924 | + | 0.611914i | \(0.790400\pi\) | |||||||
\(488\) | 9.64480e9 | 0.00769847 | ||||||||
\(489\) | 5.11253e11 | 0.404339 | ||||||||
\(490\) | 6.64208e12 | 5.20501 | ||||||||
\(491\) | −1.40585e12 | −1.09162 | −0.545809 | − | 0.837910i | \(-0.683778\pi\) | ||||
−0.545809 | + | 0.837910i | \(0.683778\pi\) | |||||||
\(492\) | 3.91546e10 | 0.0301259 | ||||||||
\(493\) | 3.28042e11 | 0.250103 | ||||||||
\(494\) | −2.95985e10 | −0.0223614 | ||||||||
\(495\) | 2.11339e11 | 0.158218 | ||||||||
\(496\) | 2.14331e11 | 0.159008 | ||||||||
\(497\) | −2.46587e10 | −0.0181287 | ||||||||
\(498\) | −6.12505e11 | −0.446249 | ||||||||
\(499\) | −1.21146e12 | −0.874696 | −0.437348 | − | 0.899292i | \(-0.644082\pi\) | ||||
−0.437348 | + | 0.899292i | \(0.644082\pi\) | |||||||
\(500\) | 3.21921e11 | 0.230348 | ||||||||
\(501\) | 6.07651e10 | 0.0430908 | ||||||||
\(502\) | 3.39882e12 | 2.38870 | ||||||||
\(503\) | −1.83565e12 | −1.27860 | −0.639298 | − | 0.768959i | \(-0.720775\pi\) | ||||
−0.639298 | + | 0.768959i | \(0.720775\pi\) | |||||||
\(504\) | 1.81759e10 | 0.0125475 | ||||||||
\(505\) | 2.86090e12 | 1.95745 | ||||||||
\(506\) | −4.51228e11 | −0.305998 | ||||||||
\(507\) | −8.58342e11 | −0.576932 | ||||||||
\(508\) | −1.64818e12 | −1.09804 | ||||||||
\(509\) | −7.98947e11 | −0.527579 | −0.263790 | − | 0.964580i | \(-0.584972\pi\) | ||||
−0.263790 | + | 0.964580i | \(0.584972\pi\) | |||||||
\(510\) | −1.50009e12 | −0.981866 | ||||||||
\(511\) | 5.29792e12 | 3.43725 | ||||||||
\(512\) | −2.19015e12 | −1.40851 | ||||||||
\(513\) | 1.77951e11 | 0.113441 | ||||||||
\(514\) | 1.77797e12 | 1.12354 | ||||||||
\(515\) | 1.92890e12 | 1.20831 | ||||||||
\(516\) | −5.49367e11 | −0.341145 | ||||||||
\(517\) | −4.21930e10 | −0.0259736 | ||||||||
\(518\) | 1.16873e11 | 0.0713228 | ||||||||
\(519\) | −1.02862e12 | −0.622302 | ||||||||
\(520\) | −1.18206e9 | −0.000708965 0 | ||||||||
\(521\) | 1.73968e12 | 1.03443 | 0.517214 | − | 0.855856i | \(-0.326969\pi\) | ||||
0.517214 | + | 0.855856i | \(0.326969\pi\) | |||||||
\(522\) | 2.23261e11 | 0.131612 | ||||||||
\(523\) | 1.07649e12 | 0.629150 | 0.314575 | − | 0.949233i | \(-0.398138\pi\) | ||||
0.314575 | + | 0.949233i | \(0.398138\pi\) | |||||||
\(524\) | 8.97540e11 | 0.520072 | ||||||||
\(525\) | 1.60603e12 | 0.922649 | ||||||||
\(526\) | 6.77647e11 | 0.385982 | ||||||||
\(527\) | 2.47968e11 | 0.140039 | ||||||||
\(528\) | 3.66992e11 | 0.205496 | ||||||||
\(529\) | −1.11249e12 | −0.617656 | ||||||||
\(530\) | −9.62698e11 | −0.529967 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | 2.07489e12 | 1.12303 | ||||||||
\(533\) | 2.65373e9 | 0.00142424 | ||||||||
\(534\) | −1.36354e12 | −0.725661 | ||||||||
\(535\) | −1.59359e12 | −0.840980 | ||||||||
\(536\) | −2.37364e10 | −0.0124215 | ||||||||
\(537\) | −1.45246e12 | −0.753736 | ||||||||
\(538\) | −8.75362e10 | −0.0450472 | ||||||||
\(539\) | −1.87997e12 | −0.959406 | ||||||||
\(540\) | −5.06917e11 | −0.256546 | ||||||||
\(541\) | 6.48663e11 | 0.325560 | 0.162780 | − | 0.986662i | \(-0.447954\pi\) | ||||
0.162780 | + | 0.986662i | \(0.447954\pi\) | |||||||
\(542\) | −5.34282e12 | −2.65934 | ||||||||
\(543\) | −1.39074e12 | −0.686509 | ||||||||
\(544\) | −2.56940e12 | −1.25787 | ||||||||
\(545\) | 4.72828e12 | 2.29572 | ||||||||
\(546\) | −8.78693e10 | −0.0423126 | ||||||||
\(547\) | −3.36177e12 | −1.60555 | −0.802777 | − | 0.596279i | \(-0.796645\pi\) | ||||
−0.802777 | + | 0.596279i | \(0.796645\pi\) | |||||||
\(548\) | −4.75793e11 | −0.225375 | ||||||||
\(549\) | 2.80326e11 | 0.131701 | ||||||||
\(550\) | 8.78488e11 | 0.409359 | ||||||||
\(551\) | −3.57308e11 | −0.165143 | ||||||||
\(552\) | −1.51735e10 | −0.00695603 | ||||||||
\(553\) | −4.25519e12 | −1.93489 | ||||||||
\(554\) | −4.39404e12 | −1.98185 | ||||||||
\(555\) | 4.56968e10 | 0.0204441 | ||||||||
\(556\) | −1.99000e12 | −0.883116 | ||||||||
\(557\) | −1.25211e12 | −0.551180 | −0.275590 | − | 0.961275i | \(-0.588873\pi\) | ||||
−0.275590 | + | 0.961275i | \(0.588873\pi\) | |||||||
\(558\) | 1.68763e11 | 0.0736927 | ||||||||
\(559\) | −3.72337e10 | −0.0161281 | ||||||||
\(560\) | 6.16036e12 | 2.64704 | ||||||||
\(561\) | 4.24587e11 | 0.180981 | ||||||||
\(562\) | 4.71687e12 | 1.99453 | ||||||||
\(563\) | −8.31880e11 | −0.348958 | −0.174479 | − | 0.984661i | \(-0.555824\pi\) | ||||
−0.174479 | + | 0.984661i | \(0.555824\pi\) | |||||||
\(564\) | 1.01204e11 | 0.0421156 | ||||||||
\(565\) | 3.55117e12 | 1.46607 | ||||||||
\(566\) | −1.42035e12 | −0.581730 | ||||||||
\(567\) | 5.28283e11 | 0.214656 | ||||||||
\(568\) | −4.53569e8 | −0.000182842 0 | ||||||||
\(569\) | 1.53041e12 | 0.612071 | 0.306035 | − | 0.952020i | \(-0.400997\pi\) | ||||
0.306035 | + | 0.952020i | \(0.400997\pi\) | |||||||
\(570\) | 1.63392e12 | 0.648328 | ||||||||
\(571\) | 1.08360e12 | 0.426586 | 0.213293 | − | 0.976988i | \(-0.431581\pi\) | ||||
0.213293 | + | 0.976988i | \(0.431581\pi\) | |||||||
\(572\) | −2.38647e10 | −0.00932124 | ||||||||
\(573\) | −2.13982e12 | −0.829241 | ||||||||
\(574\) | −3.74666e11 | −0.144059 | ||||||||
\(575\) | −1.34074e12 | −0.511492 | ||||||||
\(576\) | −8.56087e11 | −0.324053 | ||||||||
\(577\) | 1.84892e12 | 0.694429 | 0.347215 | − | 0.937786i | \(-0.387128\pi\) | ||||
0.347215 | + | 0.937786i | \(0.387128\pi\) | |||||||
\(578\) | 7.67932e11 | 0.286185 | ||||||||
\(579\) | −1.81873e12 | −0.672533 | ||||||||
\(580\) | 1.01784e12 | 0.373469 | ||||||||
\(581\) | 2.91009e12 | 1.05953 | ||||||||
\(582\) | −2.35944e12 | −0.852423 | ||||||||
\(583\) | 2.72482e11 | 0.0976854 | ||||||||
\(584\) | 9.74493e10 | 0.0346674 | ||||||||
\(585\) | −3.43566e10 | −0.0121286 | ||||||||
\(586\) | −5.91456e12 | −2.07197 | ||||||||
\(587\) | −1.65737e11 | −0.0576168 | −0.0288084 | − | 0.999585i | \(-0.509171\pi\) | ||||
−0.0288084 | + | 0.999585i | \(0.509171\pi\) | |||||||
\(588\) | 4.50931e12 | 1.55565 | ||||||||
\(589\) | −2.70090e11 | −0.0924676 | ||||||||
\(590\) | 7.29979e11 | 0.248014 | ||||||||
\(591\) | 2.04488e12 | 0.689483 | ||||||||
\(592\) | 7.93531e10 | 0.0265532 | ||||||||
\(593\) | −1.00017e12 | −0.332146 | −0.166073 | − | 0.986113i | \(-0.553109\pi\) | ||||
−0.166073 | + | 0.986113i | \(0.553109\pi\) | |||||||
\(594\) | 2.88967e11 | 0.0952379 | ||||||||
\(595\) | 7.12715e12 | 2.33125 | ||||||||
\(596\) | 4.41399e12 | 1.43292 | ||||||||
\(597\) | 1.28992e12 | 0.415602 | ||||||||
\(598\) | 7.33547e10 | 0.0234570 | ||||||||
\(599\) | −3.62898e12 | −1.15176 | −0.575882 | − | 0.817533i | \(-0.695341\pi\) | ||||
−0.575882 | + | 0.817533i | \(0.695341\pi\) | |||||||
\(600\) | 2.95411e10 | 0.00930563 | ||||||||
\(601\) | 4.56853e12 | 1.42837 | 0.714186 | − | 0.699956i | \(-0.246797\pi\) | ||||
0.714186 | + | 0.699956i | \(0.246797\pi\) | |||||||
\(602\) | 5.25683e12 | 1.63132 | ||||||||
\(603\) | −6.89898e11 | −0.212499 | ||||||||
\(604\) | −3.31710e12 | −1.01413 | ||||||||
\(605\) | 3.90520e12 | 1.18507 | ||||||||
\(606\) | 3.91177e12 | 1.17827 | ||||||||
\(607\) | 3.24449e11 | 0.0970058 | 0.0485029 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485029 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(608\) | 2.79863e12 | 0.830575 | ||||||||
\(609\) | −1.06074e12 | −0.312487 | ||||||||
\(610\) | 2.57393e12 | 0.752682 | ||||||||
\(611\) | 6.85918e9 | 0.00199107 | ||||||||
\(612\) | −1.01842e12 | −0.293456 | ||||||||
\(613\) | −4.26225e12 | −1.21918 | −0.609588 | − | 0.792718i | \(-0.708665\pi\) | ||||
−0.609588 | + | 0.792718i | \(0.708665\pi\) | |||||||
\(614\) | −5.18988e12 | −1.47367 | ||||||||
\(615\) | −1.46493e11 | −0.0412933 | ||||||||
\(616\) | −4.72363e10 | −0.0132179 | ||||||||
\(617\) | −4.33447e11 | −0.120407 | −0.0602037 | − | 0.998186i | \(-0.519175\pi\) | ||||
−0.0602037 | + | 0.998186i | \(0.519175\pi\) | |||||||
\(618\) | 2.63743e12 | 0.727332 | ||||||||
\(619\) | 1.15536e12 | 0.316306 | 0.158153 | − | 0.987415i | \(-0.449446\pi\) | ||||
0.158153 | + | 0.987415i | \(0.449446\pi\) | |||||||
\(620\) | 7.69390e11 | 0.209114 | ||||||||
\(621\) | −4.41019e11 | −0.119000 | ||||||||
\(622\) | 3.91343e11 | 0.104834 | ||||||||
\(623\) | 6.47839e12 | 1.72294 | ||||||||
\(624\) | −5.96607e10 | −0.0157528 | ||||||||
\(625\) | −4.35996e12 | −1.14294 | ||||||||
\(626\) | 5.33250e12 | 1.38786 | ||||||||
\(627\) | −4.62466e11 | −0.119502 | ||||||||
\(628\) | 5.23540e12 | 1.34317 | ||||||||
\(629\) | 9.18066e10 | 0.0233855 | ||||||||
\(630\) | 4.85063e12 | 1.22678 | ||||||||
\(631\) | 2.05136e12 | 0.515121 | 0.257560 | − | 0.966262i | \(-0.417081\pi\) | ||||
0.257560 | + | 0.966262i | \(0.417081\pi\) | |||||||
\(632\) | −7.82694e10 | −0.0195148 | ||||||||
\(633\) | 1.46284e12 | 0.362143 | ||||||||
\(634\) | 8.22161e12 | 2.02095 | ||||||||
\(635\) | 6.16652e12 | 1.50508 | ||||||||
\(636\) | −6.53577e11 | −0.158394 | ||||||||
\(637\) | 3.05621e11 | 0.0735455 | ||||||||
\(638\) | −5.80220e11 | −0.138644 | ||||||||
\(639\) | −1.31830e10 | −0.00312795 | ||||||||
\(640\) | 2.23556e11 | 0.0526716 | ||||||||
\(641\) | 7.24358e12 | 1.69470 | 0.847349 | − | 0.531036i | \(-0.178197\pi\) | ||||
0.847349 | + | 0.531036i | \(0.178197\pi\) | |||||||
\(642\) | −2.17895e12 | −0.506221 | ||||||||
\(643\) | −9.75907e11 | −0.225143 | −0.112572 | − | 0.993644i | \(-0.535909\pi\) | ||||
−0.112572 | + | 0.993644i | \(0.535909\pi\) | |||||||
\(644\) | −5.14224e12 | −1.17806 | ||||||||
\(645\) | 2.05540e12 | 0.467604 | ||||||||
\(646\) | 3.28261e12 | 0.741605 | ||||||||
\(647\) | −5.08148e12 | −1.14004 | −0.570021 | − | 0.821630i | \(-0.693065\pi\) | ||||
−0.570021 | + | 0.821630i | \(0.693065\pi\) | |||||||
\(648\) | 9.71717e9 | 0.00216497 | ||||||||
\(649\) | −2.06613e11 | −0.0457148 | ||||||||
\(650\) | −1.42813e11 | −0.0313803 | ||||||||
\(651\) | −8.01818e11 | −0.174969 | ||||||||
\(652\) | 3.18695e12 | 0.690654 | ||||||||
\(653\) | 2.74396e12 | 0.590565 | 0.295283 | − | 0.955410i | \(-0.404586\pi\) | ||||
0.295283 | + | 0.955410i | \(0.404586\pi\) | |||||||
\(654\) | 6.46507e12 | 1.38189 | ||||||||
\(655\) | −3.35806e12 | −0.712858 | ||||||||
\(656\) | −2.54387e11 | −0.0536326 | ||||||||
\(657\) | 2.83237e12 | 0.593069 | ||||||||
\(658\) | −9.68411e11 | −0.201392 | ||||||||
\(659\) | −2.37620e12 | −0.490793 | −0.245396 | − | 0.969423i | \(-0.578918\pi\) | ||||
−0.245396 | + | 0.969423i | \(0.578918\pi\) | |||||||
\(660\) | 1.31740e12 | 0.270252 | ||||||||
\(661\) | −3.46172e12 | −0.705319 | −0.352659 | − | 0.935752i | \(-0.614723\pi\) | ||||
−0.352659 | + | 0.935752i | \(0.614723\pi\) | |||||||
\(662\) | −8.92073e12 | −1.80526 | ||||||||
\(663\) | −6.90237e10 | −0.0138735 | ||||||||
\(664\) | 5.35279e10 | 0.0106862 | ||||||||
\(665\) | −7.76299e12 | −1.53933 | ||||||||
\(666\) | 6.24822e10 | 0.0123062 | ||||||||
\(667\) | 8.85526e11 | 0.173235 | ||||||||
\(668\) | 3.78785e11 | 0.0736036 | ||||||||
\(669\) | −4.69660e12 | −0.906496 | ||||||||
\(670\) | −6.33457e12 | −1.21445 | ||||||||
\(671\) | −7.28524e11 | −0.138737 | ||||||||
\(672\) | 8.30829e12 | 1.57163 | ||||||||
\(673\) | −6.67858e12 | −1.25492 | −0.627461 | − | 0.778648i | \(-0.715906\pi\) | ||||
−0.627461 | + | 0.778648i | \(0.715906\pi\) | |||||||
\(674\) | −6.15712e12 | −1.14923 | ||||||||
\(675\) | 8.58612e11 | 0.159195 | ||||||||
\(676\) | −5.35056e12 | −0.985460 | ||||||||
\(677\) | 4.44582e11 | 0.0813398 | 0.0406699 | − | 0.999173i | \(-0.487051\pi\) | ||||
0.0406699 | + | 0.999173i | \(0.487051\pi\) | |||||||
\(678\) | 4.85559e12 | 0.882487 | ||||||||
\(679\) | 1.12100e13 | 2.02391 | ||||||||
\(680\) | 1.31096e11 | 0.0235125 | ||||||||
\(681\) | −1.49361e12 | −0.266119 | ||||||||
\(682\) | −4.38590e11 | −0.0776298 | ||||||||
\(683\) | 9.48001e12 | 1.66692 | 0.833462 | − | 0.552577i | \(-0.186355\pi\) | ||||
0.833462 | + | 0.552577i | \(0.186355\pi\) | |||||||
\(684\) | 1.10927e12 | 0.193770 | ||||||||
\(685\) | 1.78013e12 | 0.308919 | ||||||||
\(686\) | −2.73565e13 | −4.71631 | ||||||||
\(687\) | 2.48899e12 | 0.426302 | ||||||||
\(688\) | 3.56924e12 | 0.607334 | ||||||||
\(689\) | −4.42966e10 | −0.00748830 | ||||||||
\(690\) | −4.04939e12 | −0.680093 | ||||||||
\(691\) | −5.25166e12 | −0.876284 | −0.438142 | − | 0.898906i | \(-0.644363\pi\) | ||||
−0.438142 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(692\) | −6.41199e12 | −1.06296 | ||||||||
\(693\) | −1.37292e12 | −0.226124 | ||||||||
\(694\) | −1.30041e13 | −2.12795 | ||||||||
\(695\) | 7.44541e12 | 1.21048 | ||||||||
\(696\) | −1.95112e10 | −0.00315168 | ||||||||
\(697\) | −2.94310e11 | −0.0472344 | ||||||||
\(698\) | 5.80670e12 | 0.925934 | ||||||||
\(699\) | −5.52328e12 | −0.875084 | ||||||||
\(700\) | 1.00113e13 | 1.57598 | ||||||||
\(701\) | −9.50022e12 | −1.48594 | −0.742972 | − | 0.669323i | \(-0.766584\pi\) | ||||
−0.742972 | + | 0.669323i | \(0.766584\pi\) | |||||||
\(702\) | −4.69765e10 | −0.00730069 | ||||||||
\(703\) | −9.99970e10 | −0.0154414 | ||||||||
\(704\) | 2.22484e12 | 0.341367 | ||||||||
\(705\) | −3.78646e11 | −0.0577274 | ||||||||
\(706\) | 1.69921e12 | 0.257410 | ||||||||
\(707\) | −1.85853e13 | −2.79759 | ||||||||
\(708\) | 4.95583e11 | 0.0741254 | ||||||||
\(709\) | 3.80257e12 | 0.565158 | 0.282579 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282579 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(710\) | −1.21045e11 | −0.0178765 | ||||||||
\(711\) | −2.27490e12 | −0.333848 | ||||||||
\(712\) | 1.19163e11 | 0.0173772 | ||||||||
\(713\) | 6.69371e11 | 0.0969983 | ||||||||
\(714\) | 9.74509e12 | 1.40328 | ||||||||
\(715\) | 8.92875e10 | 0.0127765 | ||||||||
\(716\) | −9.05403e12 | −1.28746 | ||||||||
\(717\) | −6.45654e12 | −0.912354 | ||||||||
\(718\) | −1.72706e13 | −2.42519 | ||||||||
\(719\) | −4.75843e12 | −0.664024 | −0.332012 | − | 0.943275i | \(-0.607727\pi\) | ||||
−0.332012 | + | 0.943275i | \(0.607727\pi\) | |||||||
\(720\) | 3.29344e12 | 0.456724 | ||||||||
\(721\) | −1.25308e13 | −1.72691 | ||||||||
\(722\) | 6.71479e12 | 0.919634 | ||||||||
\(723\) | −2.56638e12 | −0.349300 | ||||||||
\(724\) | −8.66930e12 | −1.17263 | ||||||||
\(725\) | −1.72401e12 | −0.231750 | ||||||||
\(726\) | 5.33966e12 | 0.713343 | ||||||||
\(727\) | −8.46722e11 | −0.112418 | −0.0562090 | − | 0.998419i | \(-0.517901\pi\) | ||||
−0.0562090 | + | 0.998419i | \(0.517901\pi\) | |||||||
\(728\) | 7.67906e9 | 0.00101325 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 2.60065e13 | 3.38944 | ||||||||
\(731\) | 4.12938e12 | 0.534881 | ||||||||
\(732\) | 1.74744e12 | 0.224959 | ||||||||
\(733\) | 1.49200e13 | 1.90898 | 0.954490 | − | 0.298244i | \(-0.0964009\pi\) | ||||
0.954490 | + | 0.298244i | \(0.0964009\pi\) | |||||||
\(734\) | 3.66270e12 | 0.465767 | ||||||||
\(735\) | −1.68712e13 | −2.13232 | ||||||||
\(736\) | −6.93590e12 | −0.871270 | ||||||||
\(737\) | 1.79294e12 | 0.223852 | ||||||||
\(738\) | −2.00303e11 | −0.0248562 | ||||||||
\(739\) | −1.33358e12 | −0.164482 | −0.0822409 | − | 0.996612i | \(-0.526208\pi\) | ||||
−0.0822409 | + | 0.996612i | \(0.526208\pi\) | |||||||
\(740\) | 2.84856e11 | 0.0349206 | ||||||||
\(741\) | 7.51816e10 | 0.00916072 | ||||||||
\(742\) | 6.25400e12 | 0.757426 | ||||||||
\(743\) | 1.73699e12 | 0.209097 | 0.104548 | − | 0.994520i | \(-0.466660\pi\) | ||||
0.104548 | + | 0.994520i | \(0.466660\pi\) | |||||||
\(744\) | −1.47485e10 | −0.00176470 | ||||||||
\(745\) | −1.65145e13 | −1.96410 | ||||||||
\(746\) | 4.54700e12 | 0.537527 | ||||||||
\(747\) | 1.55579e12 | 0.182813 | ||||||||
\(748\) | 2.64670e12 | 0.309135 | ||||||||
\(749\) | 1.03525e13 | 1.20192 | ||||||||
\(750\) | −1.64685e12 | −0.190054 | ||||||||
\(751\) | −1.71628e12 | −0.196883 | −0.0984415 | − | 0.995143i | \(-0.531386\pi\) | ||||
−0.0984415 | + | 0.995143i | \(0.531386\pi\) | |||||||
\(752\) | −6.57523e11 | −0.0749775 | ||||||||
\(753\) | −8.63317e12 | −0.978572 | ||||||||
\(754\) | 9.43245e10 | 0.0106280 | ||||||||
\(755\) | 1.24106e13 | 1.39006 | ||||||||
\(756\) | 3.29310e12 | 0.366654 | ||||||||
\(757\) | −1.73787e12 | −0.192348 | −0.0961739 | − | 0.995365i | \(-0.530660\pi\) | ||||
−0.0961739 | + | 0.995365i | \(0.530660\pi\) | |||||||
\(758\) | 2.49378e13 | 2.74377 | ||||||||
\(759\) | 1.14614e12 | 0.125357 | ||||||||
\(760\) | −1.42791e11 | −0.0155253 | ||||||||
\(761\) | 2.45314e12 | 0.265150 | 0.132575 | − | 0.991173i | \(-0.457675\pi\) | ||||
0.132575 | + | 0.991173i | \(0.457675\pi\) | |||||||
\(762\) | 8.43161e12 | 0.905968 | ||||||||
\(763\) | −3.07164e13 | −3.28103 | ||||||||
\(764\) | −1.33387e13 | −1.41643 | ||||||||
\(765\) | 3.81030e12 | 0.402238 | ||||||||
\(766\) | −1.02446e13 | −1.07514 | ||||||||
\(767\) | 3.35885e10 | 0.00350438 | ||||||||
\(768\) | 5.71699e12 | 0.592982 | ||||||||
\(769\) | 6.92178e12 | 0.713755 | 0.356878 | − | 0.934151i | \(-0.383841\pi\) | ||||
0.356878 | + | 0.934151i | \(0.383841\pi\) | |||||||
\(770\) | −1.26060e13 | −1.29232 | ||||||||
\(771\) | −4.51612e12 | −0.460279 | ||||||||
\(772\) | −1.13372e13 | −1.14876 | ||||||||
\(773\) | 7.14953e12 | 0.720228 | 0.360114 | − | 0.932908i | \(-0.382738\pi\) | ||||
0.360114 | + | 0.932908i | \(0.382738\pi\) | |||||||
\(774\) | 2.81040e12 | 0.281471 | ||||||||
\(775\) | −1.30319e12 | −0.129762 | ||||||||
\(776\) | 2.06196e11 | 0.0204127 | ||||||||
\(777\) | −2.96861e11 | −0.0292186 | ||||||||
\(778\) | −5.68784e12 | −0.556595 | ||||||||
\(779\) | 3.20567e11 | 0.0311889 | ||||||||
\(780\) | −2.14165e11 | −0.0207168 | ||||||||
\(781\) | 3.42605e10 | 0.00329507 | ||||||||
\(782\) | −8.13537e12 | −0.777941 | ||||||||
\(783\) | −5.67092e11 | −0.0539170 | ||||||||
\(784\) | −2.92970e13 | −2.76950 | ||||||||
\(785\) | −1.95878e13 | −1.84107 | ||||||||
\(786\) | −4.59155e12 | −0.429099 | ||||||||
\(787\) | 5.46600e12 | 0.507906 | 0.253953 | − | 0.967217i | \(-0.418269\pi\) | ||||
0.253953 | + | 0.967217i | \(0.418269\pi\) | |||||||
\(788\) | 1.27469e13 | 1.17771 | ||||||||
\(789\) | −1.72125e12 | −0.158124 | ||||||||
\(790\) | −2.08879e13 | −1.90797 | ||||||||
\(791\) | −2.30696e13 | −2.09530 | ||||||||
\(792\) | −2.52534e10 | −0.00228064 | ||||||||
\(793\) | 1.18434e11 | 0.0106352 | ||||||||
\(794\) | −2.07170e13 | −1.84984 | ||||||||
\(795\) | 2.44530e12 | 0.217110 | ||||||||
\(796\) | 8.04082e12 | 0.709891 | ||||||||
\(797\) | −1.83343e13 | −1.60954 | −0.804770 | − | 0.593587i | \(-0.797711\pi\) | ||||
−0.804770 | + | 0.593587i | \(0.797711\pi\) | |||||||
\(798\) | −1.06145e13 | −0.926587 | ||||||||
\(799\) | −7.60713e11 | −0.0660329 | ||||||||
\(800\) | 1.35034e13 | 1.16557 | ||||||||
\(801\) | 3.46346e12 | 0.297279 | ||||||||
\(802\) | 3.47654e12 | 0.296731 | ||||||||
\(803\) | −7.36088e12 | −0.624755 | ||||||||
\(804\) | −4.30055e12 | −0.362971 | ||||||||
\(805\) | 1.92392e13 | 1.61475 | ||||||||
\(806\) | 7.13001e10 | 0.00595090 | ||||||||
\(807\) | 2.22346e11 | 0.0184543 | ||||||||
\(808\) | −3.41857e11 | −0.0282158 | ||||||||
\(809\) | 1.45650e13 | 1.19548 | 0.597741 | − | 0.801689i | \(-0.296065\pi\) | ||||
0.597741 | + | 0.801689i | \(0.296065\pi\) | |||||||
\(810\) | 2.59324e12 | 0.211670 | ||||||||
\(811\) | −7.14300e12 | −0.579811 | −0.289906 | − | 0.957055i | \(-0.593624\pi\) | ||||
−0.289906 | + | 0.957055i | \(0.593624\pi\) | |||||||
\(812\) | −6.61224e12 | −0.533761 | ||||||||
\(813\) | 1.35710e13 | 1.08944 | ||||||||
\(814\) | −1.62381e11 | −0.0129636 | ||||||||
\(815\) | −1.19237e13 | −0.946673 | ||||||||
\(816\) | 6.61664e12 | 0.522434 | ||||||||
\(817\) | −4.49778e12 | −0.353182 | ||||||||
\(818\) | 1.56752e13 | 1.22412 | ||||||||
\(819\) | 2.23192e11 | 0.0173341 | ||||||||
\(820\) | −9.13180e11 | −0.0705333 | ||||||||
\(821\) | 1.86782e13 | 1.43480 | 0.717399 | − | 0.696663i | \(-0.245333\pi\) | ||||
0.717399 | + | 0.696663i | \(0.245333\pi\) | |||||||
\(822\) | 2.43401e12 | 0.185952 | ||||||||
\(823\) | −1.64592e13 | −1.25057 | −0.625286 | − | 0.780395i | \(-0.715018\pi\) | ||||
−0.625286 | + | 0.780395i | \(0.715018\pi\) | |||||||
\(824\) | −2.30490e11 | −0.0174172 | ||||||||
\(825\) | −2.23140e12 | −0.167701 | ||||||||
\(826\) | −4.74218e12 | −0.354460 | ||||||||
\(827\) | 1.92951e13 | 1.43440 | 0.717202 | − | 0.696865i | \(-0.245422\pi\) | ||||
0.717202 | + | 0.696865i | \(0.245422\pi\) | |||||||
\(828\) | −2.74914e12 | −0.203264 | ||||||||
\(829\) | −2.67671e12 | −0.196836 | −0.0984182 | − | 0.995145i | \(-0.531378\pi\) | ||||
−0.0984182 | + | 0.995145i | \(0.531378\pi\) | |||||||
\(830\) | 1.42851e13 | 1.04480 | ||||||||
\(831\) | 1.11611e13 | 0.811896 | ||||||||
\(832\) | −3.61684e11 | −0.0261683 | ||||||||
\(833\) | −3.38948e13 | −2.43910 | ||||||||
\(834\) | 1.01803e13 | 0.728638 | ||||||||
\(835\) | −1.41719e12 | −0.100888 | ||||||||
\(836\) | −2.88282e12 | −0.204122 | ||||||||
\(837\) | −4.28666e11 | −0.0301894 | ||||||||
\(838\) | −5.81434e12 | −0.407288 | ||||||||
\(839\) | 2.29406e13 | 1.59836 | 0.799182 | − | 0.601089i | \(-0.205266\pi\) | ||||
0.799182 | + | 0.601089i | \(0.205266\pi\) | |||||||
\(840\) | −4.23906e11 | −0.0293773 | ||||||||
\(841\) | −1.33685e13 | −0.921510 | ||||||||
\(842\) | 3.66088e13 | 2.51005 | ||||||||
\(843\) | −1.19811e13 | −0.817092 | ||||||||
\(844\) | 9.11875e12 | 0.618578 | ||||||||
\(845\) | 2.00186e13 | 1.35076 | ||||||||
\(846\) | −5.17730e11 | −0.0347486 | ||||||||
\(847\) | −2.53694e13 | −1.69370 | ||||||||
\(848\) | 4.24629e12 | 0.281986 | ||||||||
\(849\) | 3.60775e12 | 0.238315 | ||||||||
\(850\) | 1.58386e13 | 1.04071 | ||||||||
\(851\) | 2.47825e11 | 0.0161980 | ||||||||
\(852\) | −8.21774e10 | −0.00534287 | ||||||||
\(853\) | 2.67496e12 | 0.173000 | 0.0865001 | − | 0.996252i | \(-0.472432\pi\) | ||||
0.0865001 | + | 0.996252i | \(0.472432\pi\) | |||||||
\(854\) | −1.67211e13 | −1.07573 | ||||||||
\(855\) | −4.15023e12 | −0.265598 | ||||||||
\(856\) | 1.90423e11 | 0.0121223 | ||||||||
\(857\) | 9.53553e12 | 0.603853 | 0.301926 | − | 0.953331i | \(-0.402370\pi\) | ||||
0.301926 | + | 0.953331i | \(0.402370\pi\) | |||||||
\(858\) | 1.22085e11 | 0.00769074 | ||||||||
\(859\) | 2.42971e13 | 1.52260 | 0.761298 | − | 0.648402i | \(-0.224562\pi\) | ||||
0.761298 | + | 0.648402i | \(0.224562\pi\) | |||||||
\(860\) | 1.28126e13 | 0.798717 | ||||||||
\(861\) | 9.51668e11 | 0.0590162 | ||||||||
\(862\) | −2.90337e13 | −1.79110 | ||||||||
\(863\) | 5.09925e12 | 0.312938 | 0.156469 | − | 0.987683i | \(-0.449989\pi\) | ||||
0.156469 | + | 0.987683i | \(0.449989\pi\) | |||||||
\(864\) | 4.44177e12 | 0.271171 | ||||||||
\(865\) | 2.39899e13 | 1.45699 | ||||||||
\(866\) | 4.31729e13 | 2.60844 | ||||||||
\(867\) | −1.95058e12 | −0.117241 | ||||||||
\(868\) | −4.99821e12 | −0.298865 | ||||||||
\(869\) | 5.91211e12 | 0.351685 | ||||||||
\(870\) | −5.20698e12 | −0.308141 | ||||||||
\(871\) | −2.91472e11 | −0.0171599 | ||||||||
\(872\) | −5.64995e11 | −0.0330918 | ||||||||
\(873\) | 5.99307e12 | 0.349209 | ||||||||
\(874\) | 8.86116e12 | 0.513676 | ||||||||
\(875\) | 7.82440e12 | 0.451248 | ||||||||
\(876\) | 1.76558e13 | 1.01302 | ||||||||
\(877\) | −1.18486e13 | −0.676348 | −0.338174 | − | 0.941084i | \(-0.609809\pi\) | ||||
−0.338174 | + | 0.941084i | \(0.609809\pi\) | |||||||
\(878\) | 1.69393e13 | 0.961990 | ||||||||
\(879\) | 1.50233e13 | 0.848817 | ||||||||
\(880\) | −8.55914e12 | −0.481125 | ||||||||
\(881\) | −2.69059e13 | −1.50472 | −0.752360 | − | 0.658752i | \(-0.771085\pi\) | ||||
−0.752360 | + | 0.658752i | \(0.771085\pi\) | |||||||
\(882\) | −2.30683e13 | −1.28353 | ||||||||
\(883\) | −2.48397e12 | −0.137507 | −0.0687534 | − | 0.997634i | \(-0.521902\pi\) | ||||
−0.0687534 | + | 0.997634i | \(0.521902\pi\) | |||||||
\(884\) | −4.30266e11 | −0.0236975 | ||||||||
\(885\) | −1.85418e12 | −0.101603 | ||||||||
\(886\) | −9.36569e12 | −0.510608 | ||||||||
\(887\) | −1.74257e13 | −0.945223 | −0.472611 | − | 0.881271i | \(-0.656689\pi\) | ||||
−0.472611 | + | 0.881271i | \(0.656689\pi\) | |||||||
\(888\) | −5.46043e9 | −0.000294692 0 | ||||||||
\(889\) | −4.00597e13 | −2.15105 | ||||||||
\(890\) | 3.18011e13 | 1.69898 | ||||||||
\(891\) | −7.33990e11 | −0.0390158 | ||||||||
\(892\) | −2.92767e13 | −1.54839 | ||||||||
\(893\) | 8.28579e11 | 0.0436016 | ||||||||
\(894\) | −2.25807e13 | −1.18227 | ||||||||
\(895\) | 3.38748e13 | 1.76471 | ||||||||
\(896\) | −1.45229e12 | −0.0752780 | ||||||||
\(897\) | −1.86324e11 | −0.00960956 | ||||||||
\(898\) | 9.45022e12 | 0.484951 | ||||||||
\(899\) | 8.60723e11 | 0.0439486 | ||||||||
\(900\) | 5.35224e12 | 0.271922 | ||||||||
\(901\) | 4.91269e12 | 0.248346 | ||||||||
\(902\) | 5.20557e11 | 0.0261842 | ||||||||
\(903\) | −1.33526e13 | −0.668298 | ||||||||
\(904\) | −4.24339e11 | −0.0211327 | ||||||||
\(905\) | 3.24354e13 | 1.60731 | ||||||||
\(906\) | 1.69693e13 | 0.836733 | ||||||||
\(907\) | −1.84102e13 | −0.903286 | −0.451643 | − | 0.892199i | \(-0.649162\pi\) | ||||
−0.451643 | + | 0.892199i | \(0.649162\pi\) | |||||||
\(908\) | −9.31057e12 | −0.454559 | ||||||||
\(909\) | −9.93607e12 | −0.482700 | ||||||||
\(910\) | 2.04932e12 | 0.0990659 | ||||||||
\(911\) | 2.95844e13 | 1.42308 | 0.711542 | − | 0.702644i | \(-0.247997\pi\) | ||||
0.711542 | + | 0.702644i | \(0.247997\pi\) | |||||||
\(912\) | −7.20693e12 | −0.344964 | ||||||||
\(913\) | −4.04325e12 | −0.192581 | ||||||||
\(914\) | 4.98752e13 | 2.36389 | ||||||||
\(915\) | −6.53789e12 | −0.308349 | ||||||||
\(916\) | 1.55153e13 | 0.728168 | ||||||||
\(917\) | 2.18151e13 | 1.01881 | ||||||||
\(918\) | 5.20991e12 | 0.242124 | ||||||||
\(919\) | 2.24233e13 | 1.03700 | 0.518501 | − | 0.855077i | \(-0.326490\pi\) | ||||
0.518501 | + | 0.855077i | \(0.326490\pi\) | |||||||
\(920\) | 3.53884e11 | 0.0162860 | ||||||||
\(921\) | 1.31825e13 | 0.603712 | ||||||||
\(922\) | 3.25101e13 | 1.48159 | ||||||||
\(923\) | −5.56963e9 | −0.000252591 0 | ||||||||
\(924\) | −8.55825e12 | −0.386244 | ||||||||
\(925\) | −4.82486e11 | −0.0216694 | ||||||||
\(926\) | 1.10335e13 | 0.493131 | ||||||||
\(927\) | −6.69919e12 | −0.297964 | ||||||||
\(928\) | −8.91866e12 | −0.394760 | ||||||||
\(929\) | 2.64278e13 | 1.16410 | 0.582050 | − | 0.813153i | \(-0.302251\pi\) | ||||
0.582050 | + | 0.813153i | \(0.302251\pi\) | |||||||
\(930\) | −3.93597e12 | −0.172535 | ||||||||
\(931\) | 3.69187e13 | 1.61054 | ||||||||
\(932\) | −3.44299e13 | −1.49473 | ||||||||
\(933\) | −9.94029e11 | −0.0429469 | ||||||||
\(934\) | −1.74052e13 | −0.748372 | ||||||||
\(935\) | −9.90238e12 | −0.423728 | ||||||||
\(936\) | 4.10536e9 | 0.000174828 0 | ||||||||
\(937\) | 4.85245e12 | 0.205652 | 0.102826 | − | 0.994699i | \(-0.467212\pi\) | ||||
0.102826 | + | 0.994699i | \(0.467212\pi\) | |||||||
\(938\) | 4.11514e13 | 1.73569 | ||||||||
\(939\) | −1.35448e13 | −0.568560 | ||||||||
\(940\) | −2.36033e12 | −0.0986045 | ||||||||
\(941\) | 2.17271e13 | 0.903336 | 0.451668 | − | 0.892186i | \(-0.350829\pi\) | ||||
0.451668 | + | 0.892186i | \(0.350829\pi\) | |||||||
\(942\) | −2.67827e13 | −1.10822 | ||||||||
\(943\) | −7.94469e11 | −0.0327171 | ||||||||
\(944\) | −3.21980e12 | −0.131964 | ||||||||
\(945\) | −1.23208e13 | −0.502570 | ||||||||
\(946\) | −7.30378e12 | −0.296509 | ||||||||
\(947\) | 2.12970e13 | 0.860486 | 0.430243 | − | 0.902713i | \(-0.358428\pi\) | ||||
0.430243 | + | 0.902713i | \(0.358428\pi\) | |||||||
\(948\) | −1.41808e13 | −0.570248 | ||||||||
\(949\) | 1.19663e12 | 0.0478920 | ||||||||
\(950\) | −1.72516e13 | −0.687185 | ||||||||
\(951\) | −2.08833e13 | −0.827915 | ||||||||
\(952\) | −8.51642e11 | −0.0336040 | ||||||||
\(953\) | −8.67033e11 | −0.0340500 | −0.0170250 | − | 0.999855i | \(-0.505419\pi\) | ||||
−0.0170250 | + | 0.999855i | \(0.505419\pi\) | |||||||
\(954\) | 3.34350e12 | 0.130687 | ||||||||
\(955\) | 4.99057e13 | 1.94149 | ||||||||
\(956\) | −4.02475e13 | −1.55840 | ||||||||
\(957\) | 1.47378e12 | 0.0567977 | ||||||||
\(958\) | 1.19540e13 | 0.458532 | ||||||||
\(959\) | −1.15643e13 | −0.441506 | ||||||||
\(960\) | 1.99660e13 | 0.758701 | ||||||||
\(961\) | −2.57890e13 | −0.975392 | ||||||||
\(962\) | 2.63978e10 | 0.000993758 0 | ||||||||
\(963\) | 5.53464e12 | 0.207382 | ||||||||
\(964\) | −1.59978e13 | −0.596641 | ||||||||
\(965\) | 4.24171e13 | 1.57459 | ||||||||
\(966\) | 2.63061e13 | 0.971986 | ||||||||
\(967\) | −4.69969e12 | −0.172842 | −0.0864212 | − | 0.996259i | \(-0.527543\pi\) | ||||
−0.0864212 | + | 0.996259i | \(0.527543\pi\) | |||||||
\(968\) | −4.66642e11 | −0.0170823 | ||||||||
\(969\) | −8.33797e12 | −0.303811 | ||||||||
\(970\) | 5.50277e13 | 1.99576 | ||||||||
\(971\) | 4.65362e13 | 1.67998 | 0.839990 | − | 0.542602i | \(-0.182561\pi\) | ||||
0.839990 | + | 0.542602i | \(0.182561\pi\) | |||||||
\(972\) | 1.76055e12 | 0.0632631 | ||||||||
\(973\) | −4.83678e13 | −1.73001 | ||||||||
\(974\) | 6.26165e13 | 2.22933 | ||||||||
\(975\) | 3.62751e11 | 0.0128555 | ||||||||
\(976\) | −1.13531e13 | −0.400489 | ||||||||
\(977\) | −6.68165e12 | −0.234616 | −0.117308 | − | 0.993096i | \(-0.537427\pi\) | ||||
−0.117308 | + | 0.993096i | \(0.537427\pi\) | |||||||
\(978\) | −1.63035e13 | −0.569842 | ||||||||
\(979\) | −9.00100e12 | −0.313162 | ||||||||
\(980\) | −1.05168e14 | −3.64222 | ||||||||
\(981\) | −1.64216e13 | −0.566115 | ||||||||
\(982\) | 4.48313e13 | 1.53844 | ||||||||
\(983\) | −4.01992e13 | −1.37318 | −0.686589 | − | 0.727046i | \(-0.740893\pi\) | ||||
−0.686589 | + | 0.727046i | \(0.740893\pi\) | |||||||
\(984\) | 1.75049e10 | 0.000595225 0 | ||||||||
\(985\) | −4.76914e13 | −1.61427 | ||||||||
\(986\) | −1.04610e13 | −0.352474 | ||||||||
\(987\) | 2.45981e12 | 0.0825038 | ||||||||
\(988\) | 4.68651e11 | 0.0156475 | ||||||||
\(989\) | 1.11470e13 | 0.370487 | ||||||||
\(990\) | −6.73942e12 | −0.222979 | ||||||||
\(991\) | 1.10880e13 | 0.365191 | 0.182596 | − | 0.983188i | \(-0.441550\pi\) | ||||
0.182596 | + | 0.983188i | \(0.441550\pi\) | |||||||
\(992\) | −6.74163e12 | −0.221036 | ||||||||
\(993\) | 2.26591e13 | 0.739555 | ||||||||
\(994\) | 7.86346e11 | 0.0255491 | ||||||||
\(995\) | −3.00840e13 | −0.973042 | ||||||||
\(996\) | 9.69816e12 | 0.312264 | ||||||||
\(997\) | −4.99784e13 | −1.60197 | −0.800985 | − | 0.598685i | \(-0.795690\pi\) | ||||
−0.800985 | + | 0.598685i | \(0.795690\pi\) | |||||||
\(998\) | 3.86325e13 | 1.23272 | ||||||||
\(999\) | −1.58708e11 | −0.00504142 |
(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 | 177.10.a.a.1.4 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.a.1.4 | ✓ | 21 | 1.1 | even | 1 | trivial |