Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −102.341 | −1.13072 | −0.565358 | − | 0.824846i | \(-0.691262\pi\) | ||||
−0.565358 | + | 0.824846i | \(0.691262\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 2281.63 | 0.278519 | ||||||||
\(5\) | 1529.46 | 0.0437757 | 0.0218878 | − | 0.999760i | \(-0.493032\pi\) | ||||
0.0218878 | + | 0.999760i | \(0.493032\pi\) | |||||||
\(6\) | −74606.4 | −0.652819 | ||||||||
\(7\) | −106408. | −0.341850 | −0.170925 | − | 0.985284i | \(-0.554676\pi\) | ||||
−0.170925 | + | 0.985284i | \(0.554676\pi\) | |||||||
\(8\) | 604872. | 0.815790 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −156526. | −0.0494979 | ||||||||
\(11\) | 6.31074e6 | 1.07406 | 0.537029 | − | 0.843564i | \(-0.319547\pi\) | ||||
0.537029 | + | 0.843564i | \(0.319547\pi\) | |||||||
\(12\) | 1.66331e6 | 0.160803 | ||||||||
\(13\) | 2.25991e7 | 1.29855 | 0.649275 | − | 0.760553i | \(-0.275072\pi\) | ||||
0.649275 | + | 0.760553i | \(0.275072\pi\) | |||||||
\(14\) | 1.08898e7 | 0.386536 | ||||||||
\(15\) | 1.11498e6 | 0.0252739 | ||||||||
\(16\) | −8.05941e7 | −1.20095 | ||||||||
\(17\) | −5.20100e7 | −0.522599 | −0.261299 | − | 0.965258i | \(-0.584151\pi\) | ||||
−0.261299 | + | 0.965258i | \(0.584151\pi\) | |||||||
\(18\) | −5.43881e7 | −0.376905 | ||||||||
\(19\) | −1.84618e8 | −0.900278 | −0.450139 | − | 0.892959i | \(-0.648625\pi\) | ||||
−0.450139 | + | 0.892959i | \(0.648625\pi\) | |||||||
\(20\) | 3.48966e6 | 0.0121924 | ||||||||
\(21\) | −7.75713e7 | −0.197367 | ||||||||
\(22\) | −6.45845e8 | −1.21445 | ||||||||
\(23\) | 9.02060e8 | 1.27059 | 0.635294 | − | 0.772271i | \(-0.280879\pi\) | ||||
0.635294 | + | 0.772271i | \(0.280879\pi\) | |||||||
\(24\) | 4.40952e8 | 0.470997 | ||||||||
\(25\) | −1.21836e9 | −0.998084 | ||||||||
\(26\) | −2.31281e9 | −1.46829 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −2.42783e8 | −0.0952118 | ||||||||
\(29\) | −6.01315e9 | −1.87722 | −0.938609 | − | 0.344982i | \(-0.887885\pi\) | ||||
−0.938609 | + | 0.344982i | \(0.887885\pi\) | |||||||
\(30\) | −1.14107e8 | −0.0285776 | ||||||||
\(31\) | 4.64702e8 | 0.0940424 | 0.0470212 | − | 0.998894i | \(-0.485027\pi\) | ||||
0.0470212 | + | 0.998894i | \(0.485027\pi\) | |||||||
\(32\) | 3.29295e9 | 0.542139 | ||||||||
\(33\) | 4.60053e9 | 0.620107 | ||||||||
\(34\) | 5.32274e9 | 0.590911 | ||||||||
\(35\) | −1.62746e8 | −0.0149647 | ||||||||
\(36\) | 1.21255e9 | 0.0928397 | ||||||||
\(37\) | −3.80685e9 | −0.243924 | −0.121962 | − | 0.992535i | \(-0.538919\pi\) | ||||
−0.121962 | + | 0.992535i | \(0.538919\pi\) | |||||||
\(38\) | 1.88940e10 | 1.01796 | ||||||||
\(39\) | 1.64747e10 | 0.749719 | ||||||||
\(40\) | 9.25127e8 | 0.0357118 | ||||||||
\(41\) | 4.44026e10 | 1.45987 | 0.729933 | − | 0.683519i | \(-0.239551\pi\) | ||||
0.729933 | + | 0.683519i | \(0.239551\pi\) | |||||||
\(42\) | 7.93870e9 | 0.223167 | ||||||||
\(43\) | −2.92077e10 | −0.704616 | −0.352308 | − | 0.935884i | \(-0.614603\pi\) | ||||
−0.352308 | + | 0.935884i | \(0.614603\pi\) | |||||||
\(44\) | 1.43987e10 | 0.299145 | ||||||||
\(45\) | 8.12817e8 | 0.0145919 | ||||||||
\(46\) | −9.23175e10 | −1.43667 | ||||||||
\(47\) | 6.84933e10 | 0.926856 | 0.463428 | − | 0.886135i | \(-0.346619\pi\) | ||||
0.463428 | + | 0.886135i | \(0.346619\pi\) | |||||||
\(48\) | −5.87531e10 | −0.693367 | ||||||||
\(49\) | −8.55664e10 | −0.883138 | ||||||||
\(50\) | 1.24688e11 | 1.12855 | ||||||||
\(51\) | −3.79153e10 | −0.301723 | ||||||||
\(52\) | 5.15627e10 | 0.361671 | ||||||||
\(53\) | −2.50028e11 | −1.54951 | −0.774756 | − | 0.632261i | \(-0.782127\pi\) | ||||
−0.774756 | + | 0.632261i | \(0.782127\pi\) | |||||||
\(54\) | −3.96489e10 | −0.217606 | ||||||||
\(55\) | 9.65202e9 | 0.0470176 | ||||||||
\(56\) | −6.43631e10 | −0.278878 | ||||||||
\(57\) | −1.34587e11 | −0.519775 | ||||||||
\(58\) | 6.15390e11 | 2.12260 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | 2.54396e9 | 0.00703926 | ||||||||
\(61\) | 1.92463e9 | 0.00478302 | 0.00239151 | − | 0.999997i | \(-0.499239\pi\) | ||||
0.00239151 | + | 0.999997i | \(0.499239\pi\) | |||||||
\(62\) | −4.75580e10 | −0.106335 | ||||||||
\(63\) | −5.65495e10 | −0.113950 | ||||||||
\(64\) | 3.23224e11 | 0.587941 | ||||||||
\(65\) | 3.45644e10 | 0.0568450 | ||||||||
\(66\) | −4.70821e11 | −0.701166 | ||||||||
\(67\) | −4.84490e11 | −0.654332 | −0.327166 | − | 0.944967i | \(-0.606094\pi\) | ||||
−0.327166 | + | 0.944967i | \(0.606094\pi\) | |||||||
\(68\) | −1.18667e11 | −0.145554 | ||||||||
\(69\) | 6.57602e11 | 0.733574 | ||||||||
\(70\) | 1.66556e10 | 0.0169209 | ||||||||
\(71\) | −7.15002e11 | −0.662411 | −0.331206 | − | 0.943559i | \(-0.607455\pi\) | ||||
−0.331206 | + | 0.943559i | \(0.607455\pi\) | |||||||
\(72\) | 3.21454e11 | 0.271930 | ||||||||
\(73\) | −1.30970e12 | −1.01291 | −0.506457 | − | 0.862265i | \(-0.669045\pi\) | ||||
−0.506457 | + | 0.862265i | \(0.669045\pi\) | |||||||
\(74\) | 3.89595e11 | 0.275809 | ||||||||
\(75\) | −8.88187e11 | −0.576244 | ||||||||
\(76\) | −4.21230e11 | −0.250744 | ||||||||
\(77\) | −6.71511e11 | −0.367167 | ||||||||
\(78\) | −1.68604e12 | −0.847719 | ||||||||
\(79\) | 1.45826e12 | 0.674932 | 0.337466 | − | 0.941338i | \(-0.390430\pi\) | ||||
0.337466 | + | 0.941338i | \(0.390430\pi\) | |||||||
\(80\) | −1.23265e11 | −0.0525722 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −4.54419e12 | −1.65069 | ||||||||
\(83\) | 5.72285e12 | 1.92134 | 0.960671 | − | 0.277689i | \(-0.0895683\pi\) | ||||
0.960671 | + | 0.277689i | \(0.0895683\pi\) | |||||||
\(84\) | −1.76989e11 | −0.0549706 | ||||||||
\(85\) | −7.95471e10 | −0.0228771 | ||||||||
\(86\) | 2.98914e12 | 0.796721 | ||||||||
\(87\) | −4.38358e12 | −1.08381 | ||||||||
\(88\) | 3.81719e12 | 0.876206 | ||||||||
\(89\) | −6.89076e12 | −1.46971 | −0.734855 | − | 0.678224i | \(-0.762750\pi\) | ||||
−0.734855 | + | 0.678224i | \(0.762750\pi\) | |||||||
\(90\) | −8.31843e10 | −0.0164993 | ||||||||
\(91\) | −2.40472e12 | −0.443910 | ||||||||
\(92\) | 2.05817e12 | 0.353883 | ||||||||
\(93\) | 3.38768e11 | 0.0542954 | ||||||||
\(94\) | −7.00966e12 | −1.04801 | ||||||||
\(95\) | −2.82366e11 | −0.0394103 | ||||||||
\(96\) | 2.40056e12 | 0.313004 | ||||||||
\(97\) | −2.72516e12 | −0.332182 | −0.166091 | − | 0.986110i | \(-0.553115\pi\) | ||||
−0.166091 | + | 0.986110i | \(0.553115\pi\) | |||||||
\(98\) | 8.75693e12 | 0.998579 | ||||||||
\(99\) | 3.35378e12 | 0.358019 | ||||||||
\(100\) | −2.77985e12 | −0.277985 | ||||||||
\(101\) | 1.25517e13 | 1.17656 | 0.588279 | − | 0.808658i | \(-0.299806\pi\) | ||||
0.588279 | + | 0.808658i | \(0.299806\pi\) | |||||||
\(102\) | 3.88028e12 | 0.341163 | ||||||||
\(103\) | 5.14295e12 | 0.424395 | 0.212198 | − | 0.977227i | \(-0.431938\pi\) | ||||
0.212198 | + | 0.977227i | \(0.431938\pi\) | |||||||
\(104\) | 1.36695e13 | 1.05935 | ||||||||
\(105\) | −1.18642e11 | −0.00863989 | ||||||||
\(106\) | 2.55880e13 | 1.75206 | ||||||||
\(107\) | 7.13818e12 | 0.459826 | 0.229913 | − | 0.973211i | \(-0.426156\pi\) | ||||
0.229913 | + | 0.973211i | \(0.426156\pi\) | |||||||
\(108\) | 8.83949e11 | 0.0536010 | ||||||||
\(109\) | −1.53597e13 | −0.877225 | −0.438612 | − | 0.898676i | \(-0.644530\pi\) | ||||
−0.438612 | + | 0.898676i | \(0.644530\pi\) | |||||||
\(110\) | −9.87794e11 | −0.0531636 | ||||||||
\(111\) | −2.77519e12 | −0.140829 | ||||||||
\(112\) | 8.57584e12 | 0.410544 | ||||||||
\(113\) | −1.02932e13 | −0.465094 | −0.232547 | − | 0.972585i | \(-0.574706\pi\) | ||||
−0.232547 | + | 0.972585i | \(0.574706\pi\) | |||||||
\(114\) | 1.37737e13 | 0.587719 | ||||||||
\(115\) | 1.37966e12 | 0.0556208 | ||||||||
\(116\) | −1.37198e13 | −0.522841 | ||||||||
\(117\) | 1.20101e13 | 0.432850 | ||||||||
\(118\) | −4.31679e12 | −0.147207 | ||||||||
\(119\) | 5.53426e12 | 0.178651 | ||||||||
\(120\) | 6.74418e11 | 0.0206182 | ||||||||
\(121\) | 5.30268e12 | 0.153600 | ||||||||
\(122\) | −1.96968e11 | −0.00540824 | ||||||||
\(123\) | 3.23695e13 | 0.842854 | ||||||||
\(124\) | 1.06028e12 | 0.0261926 | ||||||||
\(125\) | −3.73045e12 | −0.0874675 | ||||||||
\(126\) | 5.78731e12 | 0.128845 | ||||||||
\(127\) | 6.31473e13 | 1.33546 | 0.667729 | − | 0.744404i | \(-0.267266\pi\) | ||||
0.667729 | + | 0.744404i | \(0.267266\pi\) | |||||||
\(128\) | −6.00548e13 | −1.20693 | ||||||||
\(129\) | −2.12924e13 | −0.406810 | ||||||||
\(130\) | −3.53734e12 | −0.0642755 | ||||||||
\(131\) | 4.73681e12 | 0.0818885 | 0.0409442 | − | 0.999161i | \(-0.486963\pi\) | ||||
0.0409442 | + | 0.999161i | \(0.486963\pi\) | |||||||
\(132\) | 1.04967e13 | 0.172712 | ||||||||
\(133\) | 1.96448e13 | 0.307760 | ||||||||
\(134\) | 4.95830e13 | 0.739864 | ||||||||
\(135\) | 5.92544e11 | 0.00842463 | ||||||||
\(136\) | −3.14594e13 | −0.426331 | ||||||||
\(137\) | 6.91099e13 | 0.893010 | 0.446505 | − | 0.894781i | \(-0.352668\pi\) | ||||
0.446505 | + | 0.894781i | \(0.352668\pi\) | |||||||
\(138\) | −6.72995e13 | −0.829464 | ||||||||
\(139\) | −1.08617e14 | −1.27733 | −0.638663 | − | 0.769487i | \(-0.720512\pi\) | ||||
−0.638663 | + | 0.769487i | \(0.720512\pi\) | |||||||
\(140\) | −3.71327e11 | −0.00416796 | ||||||||
\(141\) | 4.99316e13 | 0.535121 | ||||||||
\(142\) | 7.31738e13 | 0.748999 | ||||||||
\(143\) | 1.42617e14 | 1.39472 | ||||||||
\(144\) | −4.28310e13 | −0.400315 | ||||||||
\(145\) | −9.19687e12 | −0.0821765 | ||||||||
\(146\) | 1.34035e14 | 1.14532 | ||||||||
\(147\) | −6.23779e13 | −0.509880 | ||||||||
\(148\) | −8.68580e12 | −0.0679374 | ||||||||
\(149\) | −9.85943e13 | −0.738144 | −0.369072 | − | 0.929401i | \(-0.620324\pi\) | ||||
−0.369072 | + | 0.929401i | \(0.620324\pi\) | |||||||
\(150\) | 9.08977e13 | 0.651568 | ||||||||
\(151\) | 2.16339e14 | 1.48520 | 0.742598 | − | 0.669738i | \(-0.233593\pi\) | ||||
0.742598 | + | 0.669738i | \(0.233593\pi\) | |||||||
\(152\) | −1.11670e14 | −0.734438 | ||||||||
\(153\) | −2.76402e13 | −0.174200 | ||||||||
\(154\) | 6.87230e13 | 0.415162 | ||||||||
\(155\) | 7.10743e11 | 0.00411677 | ||||||||
\(156\) | 3.75892e13 | 0.208811 | ||||||||
\(157\) | 1.12977e14 | 0.602063 | 0.301032 | − | 0.953614i | \(-0.402669\pi\) | ||||
0.301032 | + | 0.953614i | \(0.402669\pi\) | |||||||
\(158\) | −1.49240e14 | −0.763156 | ||||||||
\(159\) | −1.82270e14 | −0.894611 | ||||||||
\(160\) | 5.03644e12 | 0.0237325 | ||||||||
\(161\) | −9.59862e13 | −0.434351 | ||||||||
\(162\) | −2.89040e13 | −0.125635 | ||||||||
\(163\) | 3.88172e14 | 1.62108 | 0.810541 | − | 0.585681i | \(-0.199173\pi\) | ||||
0.810541 | + | 0.585681i | \(0.199173\pi\) | |||||||
\(164\) | 1.01310e14 | 0.406600 | ||||||||
\(165\) | 7.03632e12 | 0.0271456 | ||||||||
\(166\) | −5.85681e14 | −2.17249 | ||||||||
\(167\) | 3.68501e14 | 1.31456 | 0.657282 | − | 0.753645i | \(-0.271706\pi\) | ||||
0.657282 | + | 0.753645i | \(0.271706\pi\) | |||||||
\(168\) | −4.69207e13 | −0.161010 | ||||||||
\(169\) | 2.07843e14 | 0.686235 | ||||||||
\(170\) | 8.14091e12 | 0.0258675 | ||||||||
\(171\) | −9.81138e13 | −0.300093 | ||||||||
\(172\) | −6.66411e13 | −0.196249 | ||||||||
\(173\) | −3.12651e14 | −0.886666 | −0.443333 | − | 0.896357i | \(-0.646204\pi\) | ||||
−0.443333 | + | 0.896357i | \(0.646204\pi\) | |||||||
\(174\) | 4.48619e14 | 1.22548 | ||||||||
\(175\) | 1.29643e14 | 0.341195 | ||||||||
\(176\) | −5.08608e14 | −1.28989 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 7.05205e14 | 1.66183 | ||||||||
\(179\) | −2.02854e14 | −0.460935 | −0.230467 | − | 0.973080i | \(-0.574026\pi\) | ||||
−0.230467 | + | 0.973080i | \(0.574026\pi\) | |||||||
\(180\) | 1.85455e12 | 0.00406412 | ||||||||
\(181\) | −4.19098e14 | −0.885940 | −0.442970 | − | 0.896536i | \(-0.646075\pi\) | ||||
−0.442970 | + | 0.896536i | \(0.646075\pi\) | |||||||
\(182\) | 2.46101e14 | 0.501936 | ||||||||
\(183\) | 1.40305e12 | 0.00276148 | ||||||||
\(184\) | 5.45631e14 | 1.03653 | ||||||||
\(185\) | −5.82242e12 | −0.0106779 | ||||||||
\(186\) | −3.46698e13 | −0.0613927 | ||||||||
\(187\) | −3.28221e14 | −0.561301 | ||||||||
\(188\) | 1.56276e14 | 0.258147 | ||||||||
\(189\) | −4.12245e13 | −0.0657891 | ||||||||
\(190\) | 2.88976e13 | 0.0445618 | ||||||||
\(191\) | −1.97529e14 | −0.294384 | −0.147192 | − | 0.989108i | \(-0.547024\pi\) | ||||
−0.147192 | + | 0.989108i | \(0.547024\pi\) | |||||||
\(192\) | 2.35630e14 | 0.339448 | ||||||||
\(193\) | −6.05085e14 | −0.842740 | −0.421370 | − | 0.906889i | \(-0.638451\pi\) | ||||
−0.421370 | + | 0.906889i | \(0.638451\pi\) | |||||||
\(194\) | 2.78895e14 | 0.375604 | ||||||||
\(195\) | 2.51974e13 | 0.0328195 | ||||||||
\(196\) | −1.95231e14 | −0.245971 | ||||||||
\(197\) | −1.50473e15 | −1.83412 | −0.917061 | − | 0.398746i | \(-0.869446\pi\) | ||||
−0.917061 | + | 0.398746i | \(0.869446\pi\) | |||||||
\(198\) | −3.43229e14 | −0.404818 | ||||||||
\(199\) | −6.00792e14 | −0.685771 | −0.342885 | − | 0.939377i | \(-0.611404\pi\) | ||||
−0.342885 | + | 0.939377i | \(0.611404\pi\) | |||||||
\(200\) | −7.36954e14 | −0.814227 | ||||||||
\(201\) | −3.53193e14 | −0.377779 | ||||||||
\(202\) | −1.28455e15 | −1.33035 | ||||||||
\(203\) | 6.39846e14 | 0.641728 | ||||||||
\(204\) | −8.65085e13 | −0.0840355 | ||||||||
\(205\) | 6.79119e13 | 0.0639066 | ||||||||
\(206\) | −5.26333e14 | −0.479870 | ||||||||
\(207\) | 4.79392e14 | 0.423529 | ||||||||
\(208\) | −1.82135e15 | −1.55949 | ||||||||
\(209\) | −1.16508e15 | −0.966950 | ||||||||
\(210\) | 1.21419e13 | 0.00976927 | ||||||||
\(211\) | −5.03758e14 | −0.392994 | −0.196497 | − | 0.980504i | \(-0.562957\pi\) | ||||
−0.196497 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(212\) | −5.70470e14 | −0.431568 | ||||||||
\(213\) | −5.21236e14 | −0.382443 | ||||||||
\(214\) | −7.30527e14 | −0.519932 | ||||||||
\(215\) | −4.46720e13 | −0.0308451 | ||||||||
\(216\) | 2.34340e14 | 0.156999 | ||||||||
\(217\) | −4.94479e13 | −0.0321484 | ||||||||
\(218\) | 1.57192e15 | 0.991892 | ||||||||
\(219\) | −9.54770e14 | −0.584806 | ||||||||
\(220\) | 2.20223e13 | 0.0130953 | ||||||||
\(221\) | −1.17538e15 | −0.678621 | ||||||||
\(222\) | 2.84015e14 | 0.159238 | ||||||||
\(223\) | 1.84546e15 | 1.00490 | 0.502452 | − | 0.864605i | \(-0.332432\pi\) | ||||
0.502452 | + | 0.864605i | \(0.332432\pi\) | |||||||
\(224\) | −3.50396e14 | −0.185330 | ||||||||
\(225\) | −6.47489e14 | −0.332695 | ||||||||
\(226\) | 1.05341e15 | 0.525889 | ||||||||
\(227\) | −2.00281e15 | −0.971563 | −0.485782 | − | 0.874080i | \(-0.661465\pi\) | ||||
−0.485782 | + | 0.874080i | \(0.661465\pi\) | |||||||
\(228\) | −3.07077e14 | −0.144767 | ||||||||
\(229\) | −3.33246e15 | −1.52698 | −0.763492 | − | 0.645817i | \(-0.776517\pi\) | ||||
−0.763492 | + | 0.645817i | \(0.776517\pi\) | |||||||
\(230\) | −1.41196e14 | −0.0628914 | ||||||||
\(231\) | −4.89532e14 | −0.211984 | ||||||||
\(232\) | −3.63718e15 | −1.53142 | ||||||||
\(233\) | −6.34104e14 | −0.259625 | −0.129813 | − | 0.991539i | \(-0.541438\pi\) | ||||
−0.129813 | + | 0.991539i | \(0.541438\pi\) | |||||||
\(234\) | −1.22912e15 | −0.489431 | ||||||||
\(235\) | 1.04758e14 | 0.0405738 | ||||||||
\(236\) | 9.62403e13 | 0.0362601 | ||||||||
\(237\) | 1.06307e15 | 0.389672 | ||||||||
\(238\) | −5.66381e14 | −0.202003 | ||||||||
\(239\) | −4.18435e15 | −1.45225 | −0.726125 | − | 0.687563i | \(-0.758681\pi\) | ||||
−0.726125 | + | 0.687563i | \(0.758681\pi\) | |||||||
\(240\) | −8.98605e13 | −0.0303526 | ||||||||
\(241\) | 2.57972e15 | 0.848127 | 0.424064 | − | 0.905632i | \(-0.360603\pi\) | ||||
0.424064 | + | 0.905632i | \(0.360603\pi\) | |||||||
\(242\) | −5.42681e14 | −0.173678 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 4.39128e12 | 0.00133216 | ||||||||
\(245\) | −1.30870e14 | −0.0386600 | ||||||||
\(246\) | −3.31272e15 | −0.953029 | ||||||||
\(247\) | −4.17220e15 | −1.16906 | ||||||||
\(248\) | 2.81085e14 | 0.0767189 | ||||||||
\(249\) | 4.17196e15 | 1.10929 | ||||||||
\(250\) | 3.81777e14 | 0.0989009 | ||||||||
\(251\) | −5.22753e15 | −1.31952 | −0.659762 | − | 0.751475i | \(-0.729343\pi\) | ||||
−0.659762 | + | 0.751475i | \(0.729343\pi\) | |||||||
\(252\) | −1.29025e14 | −0.0317373 | ||||||||
\(253\) | 5.69266e15 | 1.36468 | ||||||||
\(254\) | −6.46254e15 | −1.51002 | ||||||||
\(255\) | −5.79899e13 | −0.0132081 | ||||||||
\(256\) | 3.49821e15 | 0.776758 | ||||||||
\(257\) | −2.00233e15 | −0.433482 | −0.216741 | − | 0.976229i | \(-0.569543\pi\) | ||||
−0.216741 | + | 0.976229i | \(0.569543\pi\) | |||||||
\(258\) | 2.17908e15 | 0.459987 | ||||||||
\(259\) | 4.05078e14 | 0.0833854 | ||||||||
\(260\) | 7.88630e13 | 0.0158324 | ||||||||
\(261\) | −3.19563e15 | −0.625740 | ||||||||
\(262\) | −4.84769e14 | −0.0925926 | ||||||||
\(263\) | −5.60907e15 | −1.04515 | −0.522575 | − | 0.852593i | \(-0.675028\pi\) | ||||
−0.522575 | + | 0.852593i | \(0.675028\pi\) | |||||||
\(264\) | 2.78273e15 | 0.505878 | ||||||||
\(265\) | −3.82407e14 | −0.0678309 | ||||||||
\(266\) | −2.01047e15 | −0.347989 | ||||||||
\(267\) | −5.02336e15 | −0.848538 | ||||||||
\(268\) | −1.10542e15 | −0.182244 | ||||||||
\(269\) | 3.75970e15 | 0.605012 | 0.302506 | − | 0.953148i | \(-0.402177\pi\) | ||||
0.302506 | + | 0.953148i | \(0.402177\pi\) | |||||||
\(270\) | −6.06414e13 | −0.00952587 | ||||||||
\(271\) | −5.50924e15 | −0.844872 | −0.422436 | − | 0.906393i | \(-0.638825\pi\) | ||||
−0.422436 | + | 0.906393i | \(0.638825\pi\) | |||||||
\(272\) | 4.19170e15 | 0.627613 | ||||||||
\(273\) | −1.75304e15 | −0.256292 | ||||||||
\(274\) | −7.07276e15 | −1.00974 | ||||||||
\(275\) | −7.68877e15 | −1.07200 | ||||||||
\(276\) | 1.50040e15 | 0.204314 | ||||||||
\(277\) | 1.01600e16 | 1.35137 | 0.675683 | − | 0.737192i | \(-0.263849\pi\) | ||||
0.675683 | + | 0.737192i | \(0.263849\pi\) | |||||||
\(278\) | 1.11159e16 | 1.44429 | ||||||||
\(279\) | 2.46962e14 | 0.0313475 | ||||||||
\(280\) | −9.84407e13 | −0.0122081 | ||||||||
\(281\) | −1.32081e16 | −1.60048 | −0.800241 | − | 0.599679i | \(-0.795295\pi\) | ||||
−0.800241 | + | 0.599679i | \(0.795295\pi\) | |||||||
\(282\) | −5.11004e15 | −0.605069 | ||||||||
\(283\) | −1.14497e16 | −1.32490 | −0.662449 | − | 0.749107i | \(-0.730483\pi\) | ||||
−0.662449 | + | 0.749107i | \(0.730483\pi\) | |||||||
\(284\) | −1.63137e15 | −0.184494 | ||||||||
\(285\) | −2.05845e14 | −0.0227535 | ||||||||
\(286\) | −1.45955e16 | −1.57703 | ||||||||
\(287\) | −4.72478e15 | −0.499056 | ||||||||
\(288\) | 1.75001e15 | 0.180713 | ||||||||
\(289\) | −7.19954e15 | −0.726890 | ||||||||
\(290\) | 9.41214e14 | 0.0929183 | ||||||||
\(291\) | −1.98664e15 | −0.191785 | ||||||||
\(292\) | −2.98824e15 | −0.282116 | ||||||||
\(293\) | 1.75776e16 | 1.62301 | 0.811505 | − | 0.584345i | \(-0.198649\pi\) | ||||
0.811505 | + | 0.584345i | \(0.198649\pi\) | |||||||
\(294\) | 6.38380e15 | 0.576530 | ||||||||
\(295\) | 6.45134e13 | 0.00569911 | ||||||||
\(296\) | −2.30265e15 | −0.198991 | ||||||||
\(297\) | 2.44491e15 | 0.206702 | ||||||||
\(298\) | 1.00902e16 | 0.834632 | ||||||||
\(299\) | 2.03857e16 | 1.64992 | ||||||||
\(300\) | −2.02651e15 | −0.160495 | ||||||||
\(301\) | 3.10793e15 | 0.240873 | ||||||||
\(302\) | −2.21402e16 | −1.67933 | ||||||||
\(303\) | 9.15019e15 | 0.679286 | ||||||||
\(304\) | 1.48792e16 | 1.08118 | ||||||||
\(305\) | 2.94364e12 | 0.000209380 0 | ||||||||
\(306\) | 2.82872e15 | 0.196970 | ||||||||
\(307\) | 1.90489e16 | 1.29858 | 0.649292 | − | 0.760539i | \(-0.275065\pi\) | ||||
0.649292 | + | 0.760539i | \(0.275065\pi\) | |||||||
\(308\) | −1.53214e15 | −0.102263 | ||||||||
\(309\) | 3.74921e15 | 0.245025 | ||||||||
\(310\) | −7.27380e13 | −0.00465490 | ||||||||
\(311\) | 3.05342e14 | 0.0191357 | 0.00956784 | − | 0.999954i | \(-0.496954\pi\) | ||||
0.00956784 | + | 0.999954i | \(0.496954\pi\) | |||||||
\(312\) | 9.96510e15 | 0.611613 | ||||||||
\(313\) | −8.27645e14 | −0.0497515 | −0.0248757 | − | 0.999691i | \(-0.507919\pi\) | ||||
−0.0248757 | + | 0.999691i | \(0.507919\pi\) | |||||||
\(314\) | −1.15621e16 | −0.680762 | ||||||||
\(315\) | −8.64901e13 | −0.00498824 | ||||||||
\(316\) | 3.32721e15 | 0.187981 | ||||||||
\(317\) | 4.47773e15 | 0.247840 | 0.123920 | − | 0.992292i | \(-0.460453\pi\) | ||||
0.123920 | + | 0.992292i | \(0.460453\pi\) | |||||||
\(318\) | 1.86537e16 | 1.01155 | ||||||||
\(319\) | −3.79474e16 | −2.01624 | ||||||||
\(320\) | 4.94358e14 | 0.0257375 | ||||||||
\(321\) | 5.20374e15 | 0.265480 | ||||||||
\(322\) | 9.82330e15 | 0.491128 | ||||||||
\(323\) | 9.60199e15 | 0.470484 | ||||||||
\(324\) | 6.44399e14 | 0.0309466 | ||||||||
\(325\) | −2.75339e16 | −1.29606 | ||||||||
\(326\) | −3.97258e16 | −1.83298 | ||||||||
\(327\) | −1.11972e16 | −0.506466 | ||||||||
\(328\) | 2.68579e16 | 1.19094 | ||||||||
\(329\) | −7.28822e15 | −0.316846 | ||||||||
\(330\) | −7.20102e14 | −0.0306940 | ||||||||
\(331\) | 3.61947e16 | 1.51273 | 0.756367 | − | 0.654147i | \(-0.226972\pi\) | ||||
0.756367 | + | 0.654147i | \(0.226972\pi\) | |||||||
\(332\) | 1.30574e16 | 0.535130 | ||||||||
\(333\) | −2.02311e15 | −0.0813079 | ||||||||
\(334\) | −3.77127e16 | −1.48640 | ||||||||
\(335\) | −7.41007e14 | −0.0286438 | ||||||||
\(336\) | 6.25179e15 | 0.237028 | ||||||||
\(337\) | −2.27536e16 | −0.846166 | −0.423083 | − | 0.906091i | \(-0.639052\pi\) | ||||
−0.423083 | + | 0.906091i | \(0.639052\pi\) | |||||||
\(338\) | −2.12708e16 | −0.775937 | ||||||||
\(339\) | −7.50374e15 | −0.268522 | ||||||||
\(340\) | −1.81497e14 | −0.00637171 | ||||||||
\(341\) | 2.93261e15 | 0.101007 | ||||||||
\(342\) | 1.00410e16 | 0.339319 | ||||||||
\(343\) | 1.94147e16 | 0.643752 | ||||||||
\(344\) | −1.76669e16 | −0.574819 | ||||||||
\(345\) | 1.00578e15 | 0.0321127 | ||||||||
\(346\) | 3.19969e16 | 1.00257 | ||||||||
\(347\) | −1.47556e16 | −0.453748 | −0.226874 | − | 0.973924i | \(-0.572851\pi\) | ||||
−0.226874 | + | 0.973924i | \(0.572851\pi\) | |||||||
\(348\) | −1.00017e16 | −0.301862 | ||||||||
\(349\) | 5.27288e16 | 1.56200 | 0.781002 | − | 0.624528i | \(-0.214709\pi\) | ||||
0.781002 | + | 0.624528i | \(0.214709\pi\) | |||||||
\(350\) | −1.32678e16 | −0.385795 | ||||||||
\(351\) | 8.75535e15 | 0.249906 | ||||||||
\(352\) | 2.07810e16 | 0.582288 | ||||||||
\(353\) | −1.22538e16 | −0.337081 | −0.168541 | − | 0.985695i | \(-0.553905\pi\) | ||||
−0.168541 | + | 0.985695i | \(0.553905\pi\) | |||||||
\(354\) | −3.14694e15 | −0.0849898 | ||||||||
\(355\) | −1.09357e15 | −0.0289975 | ||||||||
\(356\) | −1.57221e16 | −0.409342 | ||||||||
\(357\) | 4.03448e15 | 0.103144 | ||||||||
\(358\) | 2.07603e16 | 0.521186 | ||||||||
\(359\) | 4.36531e16 | 1.07622 | 0.538110 | − | 0.842875i | \(-0.319139\pi\) | ||||
0.538110 | + | 0.842875i | \(0.319139\pi\) | |||||||
\(360\) | 4.91650e14 | 0.0119039 | ||||||||
\(361\) | −7.96906e15 | −0.189500 | ||||||||
\(362\) | 4.28908e16 | 1.00175 | ||||||||
\(363\) | 3.86566e15 | 0.0886809 | ||||||||
\(364\) | −5.48667e15 | −0.123637 | ||||||||
\(365\) | −2.00313e15 | −0.0443410 | ||||||||
\(366\) | −1.43589e14 | −0.00312245 | ||||||||
\(367\) | −3.93339e16 | −0.840306 | −0.420153 | − | 0.907453i | \(-0.638024\pi\) | ||||
−0.420153 | + | 0.907453i | \(0.638024\pi\) | |||||||
\(368\) | −7.27008e16 | −1.52591 | ||||||||
\(369\) | 2.35973e16 | 0.486622 | ||||||||
\(370\) | 5.95870e14 | 0.0120737 | ||||||||
\(371\) | 2.66049e16 | 0.529701 | ||||||||
\(372\) | 7.72942e14 | 0.0151223 | ||||||||
\(373\) | 1.21380e16 | 0.233368 | 0.116684 | − | 0.993169i | \(-0.462774\pi\) | ||||
0.116684 | + | 0.993169i | \(0.462774\pi\) | |||||||
\(374\) | 3.35904e16 | 0.634673 | ||||||||
\(375\) | −2.71950e15 | −0.0504994 | ||||||||
\(376\) | 4.14297e16 | 0.756120 | ||||||||
\(377\) | −1.35892e17 | −2.43766 | ||||||||
\(378\) | 4.21895e15 | 0.0743888 | ||||||||
\(379\) | −7.55338e15 | −0.130914 | −0.0654570 | − | 0.997855i | \(-0.520851\pi\) | ||||
−0.0654570 | + | 0.997855i | \(0.520851\pi\) | |||||||
\(380\) | −6.44255e14 | −0.0109765 | ||||||||
\(381\) | 4.60344e16 | 0.771027 | ||||||||
\(382\) | 2.02153e16 | 0.332865 | ||||||||
\(383\) | −9.47897e16 | −1.53451 | −0.767254 | − | 0.641343i | \(-0.778378\pi\) | ||||
−0.767254 | + | 0.641343i | \(0.778378\pi\) | |||||||
\(384\) | −4.37800e16 | −0.696823 | ||||||||
\(385\) | −1.02705e15 | −0.0160730 | ||||||||
\(386\) | 6.19248e16 | 0.952900 | ||||||||
\(387\) | −1.55222e16 | −0.234872 | ||||||||
\(388\) | −6.21781e15 | −0.0925190 | ||||||||
\(389\) | −1.09943e17 | −1.60877 | −0.804384 | − | 0.594109i | \(-0.797505\pi\) | ||||
−0.804384 | + | 0.594109i | \(0.797505\pi\) | |||||||
\(390\) | −2.57872e15 | −0.0371095 | ||||||||
\(391\) | −4.69161e16 | −0.664008 | ||||||||
\(392\) | −5.17567e16 | −0.720456 | ||||||||
\(393\) | 3.45314e15 | 0.0472783 | ||||||||
\(394\) | 1.53995e17 | 2.07387 | ||||||||
\(395\) | 2.23035e15 | 0.0295456 | ||||||||
\(396\) | 7.65209e15 | 0.0997151 | ||||||||
\(397\) | 1.55360e16 | 0.199159 | 0.0995795 | − | 0.995030i | \(-0.468250\pi\) | ||||
0.0995795 | + | 0.995030i | \(0.468250\pi\) | |||||||
\(398\) | 6.14855e16 | 0.775412 | ||||||||
\(399\) | 1.43211e16 | 0.177685 | ||||||||
\(400\) | 9.81930e16 | 1.19864 | ||||||||
\(401\) | 1.37551e16 | 0.165206 | 0.0826031 | − | 0.996583i | \(-0.473677\pi\) | ||||
0.0826031 | + | 0.996583i | \(0.473677\pi\) | |||||||
\(402\) | 3.61460e16 | 0.427161 | ||||||||
\(403\) | 1.05018e16 | 0.122119 | ||||||||
\(404\) | 2.86383e16 | 0.327694 | ||||||||
\(405\) | 4.31965e14 | 0.00486396 | ||||||||
\(406\) | −6.54823e16 | −0.725612 | ||||||||
\(407\) | −2.40240e16 | −0.261988 | ||||||||
\(408\) | −2.29339e16 | −0.246142 | ||||||||
\(409\) | 4.84606e16 | 0.511903 | 0.255951 | − | 0.966690i | \(-0.417611\pi\) | ||||
0.255951 | + | 0.966690i | \(0.417611\pi\) | |||||||
\(410\) | −6.95016e15 | −0.0722603 | ||||||||
\(411\) | 5.03811e16 | 0.515580 | ||||||||
\(412\) | 1.17343e16 | 0.118202 | ||||||||
\(413\) | −4.48834e15 | −0.0445051 | ||||||||
\(414\) | −4.90613e16 | −0.478891 | ||||||||
\(415\) | 8.75287e15 | 0.0841081 | ||||||||
\(416\) | 7.44177e16 | 0.703995 | ||||||||
\(417\) | −7.91818e16 | −0.737464 | ||||||||
\(418\) | 1.19235e17 | 1.09335 | ||||||||
\(419\) | −7.28361e15 | −0.0657591 | −0.0328795 | − | 0.999459i | \(-0.510468\pi\) | ||||
−0.0328795 | + | 0.999459i | \(0.510468\pi\) | |||||||
\(420\) | −2.70697e14 | −0.00240637 | ||||||||
\(421\) | −1.01720e17 | −0.890377 | −0.445189 | − | 0.895437i | \(-0.646863\pi\) | ||||
−0.445189 | + | 0.895437i | \(0.646863\pi\) | |||||||
\(422\) | 5.15549e16 | 0.444364 | ||||||||
\(423\) | 3.64002e16 | 0.308952 | ||||||||
\(424\) | −1.51235e17 | −1.26408 | ||||||||
\(425\) | 6.33671e16 | 0.521598 | ||||||||
\(426\) | 5.33437e16 | 0.432435 | ||||||||
\(427\) | −2.04795e14 | −0.00163508 | ||||||||
\(428\) | 1.62867e16 | 0.128070 | ||||||||
\(429\) | 1.03968e17 | 0.805241 | ||||||||
\(430\) | 4.57177e15 | 0.0348770 | ||||||||
\(431\) | −1.41942e17 | −1.06662 | −0.533308 | − | 0.845921i | \(-0.679051\pi\) | ||||
−0.533308 | + | 0.845921i | \(0.679051\pi\) | |||||||
\(432\) | −3.12238e16 | −0.231122 | ||||||||
\(433\) | −9.22989e16 | −0.673016 | −0.336508 | − | 0.941681i | \(-0.609246\pi\) | ||||
−0.336508 | + | 0.941681i | \(0.609246\pi\) | |||||||
\(434\) | 5.06054e15 | 0.0363508 | ||||||||
\(435\) | −6.70452e15 | −0.0474446 | ||||||||
\(436\) | −3.50451e16 | −0.244324 | ||||||||
\(437\) | −1.66537e17 | −1.14388 | ||||||||
\(438\) | 9.77118e16 | 0.661250 | ||||||||
\(439\) | −2.62205e17 | −1.74832 | −0.874161 | − | 0.485637i | \(-0.838588\pi\) | ||||
−0.874161 | + | 0.485637i | \(0.838588\pi\) | |||||||
\(440\) | 5.83823e15 | 0.0383565 | ||||||||
\(441\) | −4.54735e16 | −0.294379 | ||||||||
\(442\) | 1.20289e17 | 0.767328 | ||||||||
\(443\) | −5.28987e16 | −0.332522 | −0.166261 | − | 0.986082i | \(-0.553169\pi\) | ||||
−0.166261 | + | 0.986082i | \(0.553169\pi\) | |||||||
\(444\) | −6.33195e15 | −0.0392237 | ||||||||
\(445\) | −1.05391e16 | −0.0643376 | ||||||||
\(446\) | −1.88866e17 | −1.13626 | ||||||||
\(447\) | −7.18753e16 | −0.426168 | ||||||||
\(448\) | −3.43935e16 | −0.200988 | ||||||||
\(449\) | −6.99570e16 | −0.402930 | −0.201465 | − | 0.979496i | \(-0.564570\pi\) | ||||
−0.201465 | + | 0.979496i | \(0.564570\pi\) | |||||||
\(450\) | 6.62645e16 | 0.376183 | ||||||||
\(451\) | 2.80213e17 | 1.56798 | ||||||||
\(452\) | −2.34852e16 | −0.129537 | ||||||||
\(453\) | 1.57711e17 | 0.857478 | ||||||||
\(454\) | 2.04969e17 | 1.09856 | ||||||||
\(455\) | −3.67792e15 | −0.0194325 | ||||||||
\(456\) | −8.14078e16 | −0.424028 | ||||||||
\(457\) | −9.30047e16 | −0.477584 | −0.238792 | − | 0.971071i | \(-0.576751\pi\) | ||||
−0.238792 | + | 0.971071i | \(0.576751\pi\) | |||||||
\(458\) | 3.41047e17 | 1.72659 | ||||||||
\(459\) | −2.01497e16 | −0.100574 | ||||||||
\(460\) | 3.14788e15 | 0.0154915 | ||||||||
\(461\) | −1.68488e16 | −0.0817548 | −0.0408774 | − | 0.999164i | \(-0.513015\pi\) | ||||
−0.0408774 | + | 0.999164i | \(0.513015\pi\) | |||||||
\(462\) | 5.00990e16 | 0.239694 | ||||||||
\(463\) | 1.80072e17 | 0.849513 | 0.424757 | − | 0.905308i | \(-0.360360\pi\) | ||||
0.424757 | + | 0.905308i | \(0.360360\pi\) | |||||||
\(464\) | 4.84624e17 | 2.25444 | ||||||||
\(465\) | 5.18132e14 | 0.00237682 | ||||||||
\(466\) | 6.48946e16 | 0.293562 | ||||||||
\(467\) | 8.00154e16 | 0.356955 | 0.178478 | − | 0.983944i | \(-0.442883\pi\) | ||||
0.178478 | + | 0.983944i | \(0.442883\pi\) | |||||||
\(468\) | 2.74025e16 | 0.120557 | ||||||||
\(469\) | 5.15535e16 | 0.223684 | ||||||||
\(470\) | −1.07210e16 | −0.0458774 | ||||||||
\(471\) | 8.23602e16 | 0.347601 | ||||||||
\(472\) | 2.55138e16 | 0.106207 | ||||||||
\(473\) | −1.84322e17 | −0.756798 | ||||||||
\(474\) | −1.08796e17 | −0.440608 | ||||||||
\(475\) | 2.24932e17 | 0.898552 | ||||||||
\(476\) | 1.26271e16 | 0.0497576 | ||||||||
\(477\) | −1.32875e17 | −0.516504 | ||||||||
\(478\) | 4.28229e17 | 1.64208 | ||||||||
\(479\) | 2.38875e17 | 0.903627 | 0.451813 | − | 0.892113i | \(-0.350777\pi\) | ||||
0.451813 | + | 0.892113i | \(0.350777\pi\) | |||||||
\(480\) | 3.67156e15 | 0.0137020 | ||||||||
\(481\) | −8.60312e16 | −0.316747 | ||||||||
\(482\) | −2.64010e17 | −0.958991 | ||||||||
\(483\) | −6.99740e16 | −0.250773 | ||||||||
\(484\) | 1.20987e16 | 0.0427805 | ||||||||
\(485\) | −4.16803e15 | −0.0145415 | ||||||||
\(486\) | −2.10711e16 | −0.0725355 | ||||||||
\(487\) | −4.75150e17 | −1.61396 | −0.806980 | − | 0.590579i | \(-0.798900\pi\) | ||||
−0.806980 | + | 0.590579i | \(0.798900\pi\) | |||||||
\(488\) | 1.16415e15 | 0.00390194 | ||||||||
\(489\) | 2.82978e17 | 0.935933 | ||||||||
\(490\) | 1.33934e16 | 0.0437135 | ||||||||
\(491\) | −4.14099e17 | −1.33375 | −0.666875 | − | 0.745169i | \(-0.732369\pi\) | ||||
−0.666875 | + | 0.745169i | \(0.732369\pi\) | |||||||
\(492\) | 7.38551e16 | 0.234751 | ||||||||
\(493\) | 3.12744e17 | 0.981033 | ||||||||
\(494\) | 4.26987e17 | 1.32187 | ||||||||
\(495\) | 5.12948e15 | 0.0156725 | ||||||||
\(496\) | −3.74523e16 | −0.112940 | ||||||||
\(497\) | 7.60817e16 | 0.226446 | ||||||||
\(498\) | −4.26961e17 | −1.25429 | ||||||||
\(499\) | 2.83779e17 | 0.822861 | 0.411430 | − | 0.911441i | \(-0.365029\pi\) | ||||
0.411430 | + | 0.911441i | \(0.365029\pi\) | |||||||
\(500\) | −8.51151e15 | −0.0243614 | ||||||||
\(501\) | 2.68637e17 | 0.758964 | ||||||||
\(502\) | 5.34989e17 | 1.49201 | ||||||||
\(503\) | 1.06001e17 | 0.291821 | 0.145910 | − | 0.989298i | \(-0.453389\pi\) | ||||
0.145910 | + | 0.989298i | \(0.453389\pi\) | |||||||
\(504\) | −3.42052e16 | −0.0929594 | ||||||||
\(505\) | 1.91973e16 | 0.0515047 | ||||||||
\(506\) | −5.82592e17 | −1.54307 | ||||||||
\(507\) | 1.51518e17 | 0.396198 | ||||||||
\(508\) | 1.44079e17 | 0.371951 | ||||||||
\(509\) | −7.25268e17 | −1.84856 | −0.924278 | − | 0.381719i | \(-0.875332\pi\) | ||||
−0.924278 | + | 0.381719i | \(0.875332\pi\) | |||||||
\(510\) | 5.93473e15 | 0.0149346 | ||||||||
\(511\) | 1.39362e17 | 0.346265 | ||||||||
\(512\) | 1.33960e17 | 0.328641 | ||||||||
\(513\) | −7.15249e16 | −0.173258 | ||||||||
\(514\) | 2.04920e17 | 0.490145 | ||||||||
\(515\) | 7.86593e15 | 0.0185782 | ||||||||
\(516\) | −4.85814e16 | −0.113304 | ||||||||
\(517\) | 4.32243e17 | 0.995497 | ||||||||
\(518\) | −4.14560e16 | −0.0942852 | ||||||||
\(519\) | −2.27923e17 | −0.511917 | ||||||||
\(520\) | 2.09070e16 | 0.0463736 | ||||||||
\(521\) | −5.54722e17 | −1.21515 | −0.607576 | − | 0.794262i | \(-0.707858\pi\) | ||||
−0.607576 | + | 0.794262i | \(0.707858\pi\) | |||||||
\(522\) | 3.27043e17 | 0.707534 | ||||||||
\(523\) | −2.91816e17 | −0.623518 | −0.311759 | − | 0.950161i | \(-0.600918\pi\) | ||||
−0.311759 | + | 0.950161i | \(0.600918\pi\) | |||||||
\(524\) | 1.08076e16 | 0.0228075 | ||||||||
\(525\) | 9.45100e16 | 0.196989 | ||||||||
\(526\) | 5.74036e17 | 1.18177 | ||||||||
\(527\) | −2.41691e16 | −0.0491465 | ||||||||
\(528\) | −3.70775e17 | −0.744716 | ||||||||
\(529\) | 3.09676e17 | 0.614393 | ||||||||
\(530\) | 3.91358e16 | 0.0766975 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | 4.48222e16 | 0.0857171 | ||||||||
\(533\) | 1.00346e18 | 1.89571 | ||||||||
\(534\) | 5.14095e17 | 0.959456 | ||||||||
\(535\) | 1.09176e16 | 0.0201292 | ||||||||
\(536\) | −2.93054e17 | −0.533798 | ||||||||
\(537\) | −1.47881e17 | −0.266121 | ||||||||
\(538\) | −3.84771e17 | −0.684096 | ||||||||
\(539\) | −5.39987e17 | −0.948541 | ||||||||
\(540\) | 1.35196e15 | 0.00234642 | ||||||||
\(541\) | 6.17352e17 | 1.05865 | 0.529323 | − | 0.848420i | \(-0.322446\pi\) | ||||
0.529323 | + | 0.848420i | \(0.322446\pi\) | |||||||
\(542\) | 5.63819e17 | 0.955311 | ||||||||
\(543\) | −3.05522e17 | −0.511498 | ||||||||
\(544\) | −1.71266e17 | −0.283321 | ||||||||
\(545\) | −2.34921e16 | −0.0384011 | ||||||||
\(546\) | 1.79407e17 | 0.289793 | ||||||||
\(547\) | −1.41119e17 | −0.225252 | −0.112626 | − | 0.993637i | \(-0.535926\pi\) | ||||
−0.112626 | + | 0.993637i | \(0.535926\pi\) | |||||||
\(548\) | 1.57683e17 | 0.248720 | ||||||||
\(549\) | 1.02283e15 | 0.00159434 | ||||||||
\(550\) | 7.86875e17 | 1.21213 | ||||||||
\(551\) | 1.11014e18 | 1.69002 | ||||||||
\(552\) | 3.97765e17 | 0.598443 | ||||||||
\(553\) | −1.55171e17 | −0.230726 | ||||||||
\(554\) | −1.03978e18 | −1.52801 | ||||||||
\(555\) | −4.24454e15 | −0.00616490 | ||||||||
\(556\) | −2.47824e17 | −0.355759 | ||||||||
\(557\) | −1.27646e18 | −1.81113 | −0.905564 | − | 0.424211i | \(-0.860552\pi\) | ||||
−0.905564 | + | 0.424211i | \(0.860552\pi\) | |||||||
\(558\) | −2.52743e16 | −0.0354451 | ||||||||
\(559\) | −6.60067e17 | −0.914980 | ||||||||
\(560\) | 1.31164e16 | 0.0179718 | ||||||||
\(561\) | −2.39273e17 | −0.324068 | ||||||||
\(562\) | 1.35173e18 | 1.80969 | ||||||||
\(563\) | 1.52130e17 | 0.201331 | 0.100666 | − | 0.994920i | \(-0.467903\pi\) | ||||
0.100666 | + | 0.994920i | \(0.467903\pi\) | |||||||
\(564\) | 1.13925e17 | 0.149041 | ||||||||
\(565\) | −1.57430e16 | −0.0203598 | ||||||||
\(566\) | 1.17177e18 | 1.49808 | ||||||||
\(567\) | −3.00527e16 | −0.0379834 | ||||||||
\(568\) | −4.32484e17 | −0.540389 | ||||||||
\(569\) | −1.00692e18 | −1.24385 | −0.621923 | − | 0.783079i | \(-0.713648\pi\) | ||||
−0.621923 | + | 0.783079i | \(0.713648\pi\) | |||||||
\(570\) | 2.10663e16 | 0.0257278 | ||||||||
\(571\) | 6.00964e17 | 0.725628 | 0.362814 | − | 0.931862i | \(-0.381816\pi\) | ||||
0.362814 | + | 0.931862i | \(0.381816\pi\) | |||||||
\(572\) | 3.25398e17 | 0.388456 | ||||||||
\(573\) | −1.43999e17 | −0.169963 | ||||||||
\(574\) | 4.83537e17 | 0.564290 | ||||||||
\(575\) | −1.09904e18 | −1.26815 | ||||||||
\(576\) | 1.71774e17 | 0.195980 | ||||||||
\(577\) | 1.02307e18 | 1.15416 | 0.577078 | − | 0.816689i | \(-0.304193\pi\) | ||||
0.577078 | + | 0.816689i | \(0.304193\pi\) | |||||||
\(578\) | 7.36806e17 | 0.821907 | ||||||||
\(579\) | −4.41107e17 | −0.486556 | ||||||||
\(580\) | −2.09838e16 | −0.0228877 | ||||||||
\(581\) | −6.08956e17 | −0.656812 | ||||||||
\(582\) | 2.03315e17 | 0.216855 | ||||||||
\(583\) | −1.57786e18 | −1.66426 | ||||||||
\(584\) | −7.92199e17 | −0.826325 | ||||||||
\(585\) | 1.83689e16 | 0.0189483 | ||||||||
\(586\) | −1.79891e18 | −1.83516 | ||||||||
\(587\) | 9.39897e17 | 0.948271 | 0.474135 | − | 0.880452i | \(-0.342761\pi\) | ||||
0.474135 | + | 0.880452i | \(0.342761\pi\) | |||||||
\(588\) | −1.42323e17 | −0.142011 | ||||||||
\(589\) | −8.57926e16 | −0.0846643 | ||||||||
\(590\) | −6.60235e15 | −0.00644407 | ||||||||
\(591\) | −1.09695e18 | −1.05893 | ||||||||
\(592\) | 3.06809e17 | 0.292939 | ||||||||
\(593\) | 1.79832e18 | 1.69829 | 0.849144 | − | 0.528162i | \(-0.177119\pi\) | ||||
0.849144 | + | 0.528162i | \(0.177119\pi\) | |||||||
\(594\) | −2.50214e17 | −0.233722 | ||||||||
\(595\) | 8.46443e15 | 0.00782056 | ||||||||
\(596\) | −2.24956e17 | −0.205587 | ||||||||
\(597\) | −4.37977e17 | −0.395930 | ||||||||
\(598\) | −2.08629e18 | −1.86559 | ||||||||
\(599\) | 1.52088e18 | 1.34531 | 0.672654 | − | 0.739958i | \(-0.265154\pi\) | ||||
0.672654 | + | 0.739958i | \(0.265154\pi\) | |||||||
\(600\) | −5.37240e17 | −0.470094 | ||||||||
\(601\) | −5.27603e17 | −0.456692 | −0.228346 | − | 0.973580i | \(-0.573332\pi\) | ||||
−0.228346 | + | 0.973580i | \(0.573332\pi\) | |||||||
\(602\) | −3.18068e17 | −0.272359 | ||||||||
\(603\) | −2.57478e17 | −0.218111 | ||||||||
\(604\) | 4.93604e17 | 0.413655 | ||||||||
\(605\) | 8.11024e15 | 0.00672394 | ||||||||
\(606\) | −9.36437e17 | −0.768080 | ||||||||
\(607\) | −1.67289e18 | −1.35750 | −0.678750 | − | 0.734370i | \(-0.737478\pi\) | ||||
−0.678750 | + | 0.734370i | \(0.737478\pi\) | |||||||
\(608\) | −6.07939e17 | −0.488075 | ||||||||
\(609\) | 4.66447e17 | 0.370502 | ||||||||
\(610\) | −3.01254e14 | −0.000236749 0 | ||||||||
\(611\) | 1.54789e18 | 1.20357 | ||||||||
\(612\) | −6.30647e16 | −0.0485179 | ||||||||
\(613\) | 7.87641e17 | 0.599564 | 0.299782 | − | 0.954008i | \(-0.403086\pi\) | ||||
0.299782 | + | 0.954008i | \(0.403086\pi\) | |||||||
\(614\) | −1.94948e18 | −1.46833 | ||||||||
\(615\) | 4.95078e16 | 0.0368965 | ||||||||
\(616\) | −4.06178e17 | −0.299531 | ||||||||
\(617\) | 3.24559e17 | 0.236831 | 0.118416 | − | 0.992964i | \(-0.462218\pi\) | ||||
0.118416 | + | 0.992964i | \(0.462218\pi\) | |||||||
\(618\) | −3.83697e17 | −0.277053 | ||||||||
\(619\) | 1.69953e18 | 1.21434 | 0.607171 | − | 0.794571i | \(-0.292304\pi\) | ||||
0.607171 | + | 0.794571i | \(0.292304\pi\) | |||||||
\(620\) | 1.62165e15 | 0.00114660 | ||||||||
\(621\) | 3.49477e17 | 0.244525 | ||||||||
\(622\) | −3.12489e16 | −0.0216370 | ||||||||
\(623\) | 7.33230e17 | 0.502421 | ||||||||
\(624\) | −1.32777e18 | −0.900372 | ||||||||
\(625\) | 1.48156e18 | 0.994255 | ||||||||
\(626\) | 8.47018e16 | 0.0562548 | ||||||||
\(627\) | −8.49342e17 | −0.558269 | ||||||||
\(628\) | 2.57771e17 | 0.167686 | ||||||||
\(629\) | 1.97994e17 | 0.127474 | ||||||||
\(630\) | 8.85146e15 | 0.00564029 | ||||||||
\(631\) | 1.32431e18 | 0.835218 | 0.417609 | − | 0.908627i | \(-0.362868\pi\) | ||||
0.417609 | + | 0.908627i | \(0.362868\pi\) | |||||||
\(632\) | 8.82062e17 | 0.550603 | ||||||||
\(633\) | −3.67239e17 | −0.226895 | ||||||||
\(634\) | −4.58254e17 | −0.280237 | ||||||||
\(635\) | 9.65812e16 | 0.0584606 | ||||||||
\(636\) | −4.15872e17 | −0.249166 | ||||||||
\(637\) | −1.93372e18 | −1.14680 | ||||||||
\(638\) | 3.88356e18 | 2.27980 | ||||||||
\(639\) | −3.79981e17 | −0.220804 | ||||||||
\(640\) | −9.18514e16 | −0.0528343 | ||||||||
\(641\) | −3.07525e18 | −1.75107 | −0.875536 | − | 0.483154i | \(-0.839491\pi\) | ||||
−0.875536 | + | 0.483154i | \(0.839491\pi\) | |||||||
\(642\) | −5.32554e17 | −0.300183 | ||||||||
\(643\) | −1.63493e18 | −0.912278 | −0.456139 | − | 0.889908i | \(-0.650768\pi\) | ||||
−0.456139 | + | 0.889908i | \(0.650768\pi\) | |||||||
\(644\) | −2.19005e17 | −0.120975 | ||||||||
\(645\) | −3.25659e16 | −0.0178084 | ||||||||
\(646\) | −9.82675e17 | −0.531984 | ||||||||
\(647\) | 1.20541e18 | 0.646039 | 0.323019 | − | 0.946392i | \(-0.395302\pi\) | ||||
0.323019 | + | 0.946392i | \(0.395302\pi\) | |||||||
\(648\) | 1.70834e17 | 0.0906434 | ||||||||
\(649\) | 2.66190e17 | 0.139830 | ||||||||
\(650\) | 2.81784e18 | 1.46548 | ||||||||
\(651\) | −3.60475e16 | −0.0185609 | ||||||||
\(652\) | 8.85665e17 | 0.451502 | ||||||||
\(653\) | 1.53790e18 | 0.776233 | 0.388116 | − | 0.921610i | \(-0.373126\pi\) | ||||
0.388116 | + | 0.921610i | \(0.373126\pi\) | |||||||
\(654\) | 1.14593e18 | 0.572669 | ||||||||
\(655\) | 7.24476e15 | 0.00358472 | ||||||||
\(656\) | −3.57859e18 | −1.75322 | ||||||||
\(657\) | −6.96027e17 | −0.337638 | ||||||||
\(658\) | 7.45882e17 | 0.358263 | ||||||||
\(659\) | −3.71920e18 | −1.76886 | −0.884431 | − | 0.466671i | \(-0.845453\pi\) | ||||
−0.884431 | + | 0.466671i | \(0.845453\pi\) | |||||||
\(660\) | 1.60543e16 | 0.00756057 | ||||||||
\(661\) | 2.21280e18 | 1.03189 | 0.515944 | − | 0.856622i | \(-0.327441\pi\) | ||||
0.515944 | + | 0.856622i | \(0.327441\pi\) | |||||||
\(662\) | −3.70419e18 | −1.71047 | ||||||||
\(663\) | −8.56850e17 | −0.391802 | ||||||||
\(664\) | 3.46159e18 | 1.56741 | ||||||||
\(665\) | 3.00460e16 | 0.0134724 | ||||||||
\(666\) | 2.07047e17 | 0.0919362 | ||||||||
\(667\) | −5.42422e18 | −2.38517 | ||||||||
\(668\) | 8.40782e17 | 0.366131 | ||||||||
\(669\) | 1.34534e18 | 0.580181 | ||||||||
\(670\) | 7.58352e16 | 0.0323880 | ||||||||
\(671\) | 1.21458e16 | 0.00513724 | ||||||||
\(672\) | −2.55438e17 | −0.107001 | ||||||||
\(673\) | −4.99922e17 | −0.207398 | −0.103699 | − | 0.994609i | \(-0.533068\pi\) | ||||
−0.103699 | + | 0.994609i | \(0.533068\pi\) | |||||||
\(674\) | 2.32862e18 | 0.956773 | ||||||||
\(675\) | −4.72019e17 | −0.192081 | ||||||||
\(676\) | 4.74221e17 | 0.191129 | ||||||||
\(677\) | −1.30863e18 | −0.522384 | −0.261192 | − | 0.965287i | \(-0.584116\pi\) | ||||
−0.261192 | + | 0.965287i | \(0.584116\pi\) | |||||||
\(678\) | 7.67938e17 | 0.303622 | ||||||||
\(679\) | 2.89979e17 | 0.113557 | ||||||||
\(680\) | −4.81158e16 | −0.0186629 | ||||||||
\(681\) | −1.46005e18 | −0.560932 | ||||||||
\(682\) | −3.00126e17 | −0.114210 | ||||||||
\(683\) | −8.18357e17 | −0.308467 | −0.154233 | − | 0.988034i | \(-0.549291\pi\) | ||||
−0.154233 | + | 0.988034i | \(0.549291\pi\) | |||||||
\(684\) | −2.23859e17 | −0.0835815 | ||||||||
\(685\) | 1.05701e17 | 0.0390921 | ||||||||
\(686\) | −1.98691e18 | −0.727900 | ||||||||
\(687\) | −2.42937e18 | −0.881605 | ||||||||
\(688\) | 2.35397e18 | 0.846206 | ||||||||
\(689\) | −5.65039e18 | −2.01212 | ||||||||
\(690\) | −1.02932e17 | −0.0363104 | ||||||||
\(691\) | 7.83108e17 | 0.273662 | 0.136831 | − | 0.990594i | \(-0.456308\pi\) | ||||
0.136831 | + | 0.990594i | \(0.456308\pi\) | |||||||
\(692\) | −7.13353e17 | −0.246953 | ||||||||
\(693\) | −3.56869e17 | −0.122389 | ||||||||
\(694\) | 1.51010e18 | 0.513060 | ||||||||
\(695\) | −1.66125e17 | −0.0559158 | ||||||||
\(696\) | −2.65151e18 | −0.884164 | ||||||||
\(697\) | −2.30938e18 | −0.762925 | ||||||||
\(698\) | −5.39630e18 | −1.76618 | ||||||||
\(699\) | −4.62262e17 | −0.149895 | ||||||||
\(700\) | 2.95798e17 | 0.0950294 | ||||||||
\(701\) | −4.90218e18 | −1.56035 | −0.780175 | − | 0.625561i | \(-0.784870\pi\) | ||||
−0.780175 | + | 0.625561i | \(0.784870\pi\) | |||||||
\(702\) | −8.96029e17 | −0.282573 | ||||||||
\(703\) | 7.02814e17 | 0.219599 | ||||||||
\(704\) | 2.03978e18 | 0.631482 | ||||||||
\(705\) | 7.63684e16 | 0.0234253 | ||||||||
\(706\) | 1.25406e18 | 0.381143 | ||||||||
\(707\) | −1.33560e18 | −0.402207 | ||||||||
\(708\) | 7.01591e16 | 0.0209348 | ||||||||
\(709\) | −4.31843e18 | −1.27681 | −0.638404 | − | 0.769701i | \(-0.720405\pi\) | ||||
−0.638404 | + | 0.769701i | \(0.720405\pi\) | |||||||
\(710\) | 1.11916e17 | 0.0327879 | ||||||||
\(711\) | 7.74981e17 | 0.224977 | ||||||||
\(712\) | −4.16803e18 | −1.19898 | ||||||||
\(713\) | 4.19189e17 | 0.119489 | ||||||||
\(714\) | −4.12892e17 | −0.116627 | ||||||||
\(715\) | 2.18127e17 | 0.0610548 | ||||||||
\(716\) | −4.62838e17 | −0.128379 | ||||||||
\(717\) | −3.05039e18 | −0.838457 | ||||||||
\(718\) | −4.46749e18 | −1.21690 | ||||||||
\(719\) | 2.27574e18 | 0.614307 | 0.307154 | − | 0.951660i | \(-0.400623\pi\) | ||||
0.307154 | + | 0.951660i | \(0.400623\pi\) | |||||||
\(720\) | −6.55083e16 | −0.0175241 | ||||||||
\(721\) | −5.47250e17 | −0.145080 | ||||||||
\(722\) | 8.15559e17 | 0.214271 | ||||||||
\(723\) | 1.88061e18 | 0.489667 | ||||||||
\(724\) | −9.56225e17 | −0.246751 | ||||||||
\(725\) | 7.32620e18 | 1.87362 | ||||||||
\(726\) | −3.95614e17 | −0.100273 | ||||||||
\(727\) | −2.45034e18 | −0.615535 | −0.307768 | − | 0.951462i | \(-0.599582\pi\) | ||||
−0.307768 | + | 0.951462i | \(0.599582\pi\) | |||||||
\(728\) | −1.45455e18 | −0.362138 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 2.05002e17 | 0.0501371 | ||||||||
\(731\) | 1.51909e18 | 0.368232 | ||||||||
\(732\) | 3.20124e15 | 0.000769124 0 | ||||||||
\(733\) | −1.01405e17 | −0.0241481 | −0.0120741 | − | 0.999927i | \(-0.503843\pi\) | ||||
−0.0120741 | + | 0.999927i | \(0.503843\pi\) | |||||||
\(734\) | 4.02546e18 | 0.950148 | ||||||||
\(735\) | −9.54045e16 | −0.0223204 | ||||||||
\(736\) | 2.97044e18 | 0.688835 | ||||||||
\(737\) | −3.05749e18 | −0.702790 | ||||||||
\(738\) | −2.41497e18 | −0.550231 | ||||||||
\(739\) | −4.58611e18 | −1.03575 | −0.517875 | − | 0.855456i | \(-0.673277\pi\) | ||||
−0.517875 | + | 0.855456i | \(0.673277\pi\) | |||||||
\(740\) | −1.32846e16 | −0.00297401 | ||||||||
\(741\) | −3.04154e18 | −0.674955 | ||||||||
\(742\) | −2.72276e18 | −0.598942 | ||||||||
\(743\) | −9.55597e17 | −0.208376 | −0.104188 | − | 0.994558i | \(-0.533224\pi\) | ||||
−0.104188 | + | 0.994558i | \(0.533224\pi\) | |||||||
\(744\) | 2.04911e17 | 0.0442937 | ||||||||
\(745\) | −1.50796e17 | −0.0323128 | ||||||||
\(746\) | −1.24221e18 | −0.263873 | ||||||||
\(747\) | 3.04136e18 | 0.640447 | ||||||||
\(748\) | −7.48878e17 | −0.156333 | ||||||||
\(749\) | −7.59558e17 | −0.157192 | ||||||||
\(750\) | 2.78316e17 | 0.0571005 | ||||||||
\(751\) | −2.08850e18 | −0.424792 | −0.212396 | − | 0.977184i | \(-0.568127\pi\) | ||||
−0.212396 | + | 0.977184i | \(0.568127\pi\) | |||||||
\(752\) | −5.52016e18 | −1.11310 | ||||||||
\(753\) | −3.81087e18 | −0.761827 | ||||||||
\(754\) | 1.39072e19 | 2.75631 | ||||||||
\(755\) | 3.30881e17 | 0.0650155 | ||||||||
\(756\) | −9.40591e16 | −0.0183235 | ||||||||
\(757\) | 1.91674e18 | 0.370203 | 0.185101 | − | 0.982719i | \(-0.440739\pi\) | ||||
0.185101 | + | 0.982719i | \(0.440739\pi\) | |||||||
\(758\) | 7.73018e17 | 0.148027 | ||||||||
\(759\) | 4.14995e18 | 0.787901 | ||||||||
\(760\) | −1.70795e17 | −0.0321505 | ||||||||
\(761\) | 8.83939e18 | 1.64976 | 0.824882 | − | 0.565304i | \(-0.191241\pi\) | ||||
0.824882 | + | 0.565304i | \(0.191241\pi\) | |||||||
\(762\) | −4.71119e18 | −0.871813 | ||||||||
\(763\) | 1.63439e18 | 0.299880 | ||||||||
\(764\) | −4.50689e17 | −0.0819917 | ||||||||
\(765\) | −4.22746e16 | −0.00762571 | ||||||||
\(766\) | 9.70085e18 | 1.73509 | ||||||||
\(767\) | 9.53241e17 | 0.169057 | ||||||||
\(768\) | 2.55019e18 | 0.448461 | ||||||||
\(769\) | 7.22170e18 | 1.25927 | 0.629634 | − | 0.776892i | \(-0.283205\pi\) | ||||
0.629634 | + | 0.776892i | \(0.283205\pi\) | |||||||
\(770\) | 1.05109e17 | 0.0181740 | ||||||||
\(771\) | −1.45970e18 | −0.250271 | ||||||||
\(772\) | −1.38058e18 | −0.234719 | ||||||||
\(773\) | 1.06736e19 | 1.79946 | 0.899732 | − | 0.436444i | \(-0.143762\pi\) | ||||
0.899732 | + | 0.436444i | \(0.143762\pi\) | |||||||
\(774\) | 1.58855e18 | 0.265574 | ||||||||
\(775\) | −5.66176e17 | −0.0938622 | ||||||||
\(776\) | −1.64838e18 | −0.270991 | ||||||||
\(777\) | 2.95302e17 | 0.0481426 | ||||||||
\(778\) | 1.12516e19 | 1.81906 | ||||||||
\(779\) | −8.19753e18 | −1.31428 | ||||||||
\(780\) | 5.74911e16 | 0.00914084 | ||||||||
\(781\) | −4.51219e18 | −0.711468 | ||||||||
\(782\) | 4.80143e18 | 0.750804 | ||||||||
\(783\) | −2.32962e18 | −0.361271 | ||||||||
\(784\) | 6.89615e18 | 1.06060 | ||||||||
\(785\) | 1.72794e17 | 0.0263557 | ||||||||
\(786\) | −3.53397e17 | −0.0534584 | ||||||||
\(787\) | 2.08479e18 | 0.312771 | 0.156385 | − | 0.987696i | \(-0.450016\pi\) | ||||
0.156385 | + | 0.987696i | \(0.450016\pi\) | |||||||
\(788\) | −3.43324e18 | −0.510838 | ||||||||
\(789\) | −4.08901e18 | −0.603417 | ||||||||
\(790\) | −2.28256e17 | −0.0334077 | ||||||||
\(791\) | 1.09528e18 | 0.158992 | ||||||||
\(792\) | 2.02861e18 | 0.292069 | ||||||||
\(793\) | 4.34948e16 | 0.00621100 | ||||||||
\(794\) | −1.58996e18 | −0.225192 | ||||||||
\(795\) | −2.78775e17 | −0.0391622 | ||||||||
\(796\) | −1.37078e18 | −0.191000 | ||||||||
\(797\) | 1.23684e19 | 1.70936 | 0.854681 | − | 0.519153i | \(-0.173753\pi\) | ||||
0.854681 | + | 0.519153i | \(0.173753\pi\) | |||||||
\(798\) | −1.46563e18 | −0.200912 | ||||||||
\(799\) | −3.56234e18 | −0.484374 | ||||||||
\(800\) | −4.01201e18 | −0.541100 | ||||||||
\(801\) | −3.66203e18 | −0.489904 | ||||||||
\(802\) | −1.40771e18 | −0.186801 | ||||||||
\(803\) | −8.26516e18 | −1.08793 | ||||||||
\(804\) | −8.05855e17 | −0.105219 | ||||||||
\(805\) | −1.46807e17 | −0.0190140 | ||||||||
\(806\) | −1.07477e18 | −0.138082 | ||||||||
\(807\) | 2.74082e18 | 0.349304 | ||||||||
\(808\) | 7.59217e18 | 0.959825 | ||||||||
\(809\) | −6.22916e18 | −0.781204 | −0.390602 | − | 0.920560i | \(-0.627733\pi\) | ||||
−0.390602 | + | 0.920560i | \(0.627733\pi\) | |||||||
\(810\) | −4.42076e16 | −0.00549976 | ||||||||
\(811\) | 8.72181e17 | 0.107639 | 0.0538197 | − | 0.998551i | \(-0.482860\pi\) | ||||
0.0538197 | + | 0.998551i | \(0.482860\pi\) | |||||||
\(812\) | 1.45989e18 | 0.178733 | ||||||||
\(813\) | −4.01623e18 | −0.487787 | ||||||||
\(814\) | 2.45863e18 | 0.296234 | ||||||||
\(815\) | 5.93694e17 | 0.0709640 | ||||||||
\(816\) | 3.05575e18 | 0.362353 | ||||||||
\(817\) | 5.39228e18 | 0.634350 | ||||||||
\(818\) | −4.95949e18 | −0.578817 | ||||||||
\(819\) | −1.27797e18 | −0.147970 | ||||||||
\(820\) | 1.54950e17 | 0.0177992 | ||||||||
\(821\) | 3.23751e18 | 0.368961 | 0.184481 | − | 0.982836i | \(-0.440940\pi\) | ||||
0.184481 | + | 0.982836i | \(0.440940\pi\) | |||||||
\(822\) | −5.15604e18 | −0.582974 | ||||||||
\(823\) | 1.42567e19 | 1.59926 | 0.799631 | − | 0.600491i | \(-0.205028\pi\) | ||||
0.799631 | + | 0.600491i | \(0.205028\pi\) | |||||||
\(824\) | 3.11083e18 | 0.346217 | ||||||||
\(825\) | −5.60512e18 | −0.618919 | ||||||||
\(826\) | 4.59340e17 | 0.0503227 | ||||||||
\(827\) | 1.74865e19 | 1.90072 | 0.950359 | − | 0.311157i | \(-0.100717\pi\) | ||||
0.950359 | + | 0.311157i | \(0.100717\pi\) | |||||||
\(828\) | 1.09379e18 | 0.117961 | ||||||||
\(829\) | 4.55030e18 | 0.486895 | 0.243447 | − | 0.969914i | \(-0.421722\pi\) | ||||
0.243447 | + | 0.969914i | \(0.421722\pi\) | |||||||
\(830\) | −8.95775e17 | −0.0951024 | ||||||||
\(831\) | 7.40661e18 | 0.780212 | ||||||||
\(832\) | 7.30456e18 | 0.763471 | ||||||||
\(833\) | 4.45031e18 | 0.461527 | ||||||||
\(834\) | 8.10352e18 | 0.833863 | ||||||||
\(835\) | 5.63607e17 | 0.0575459 | ||||||||
\(836\) | −2.65827e18 | −0.269314 | ||||||||
\(837\) | 1.80035e17 | 0.0180985 | ||||||||
\(838\) | 7.45410e17 | 0.0743548 | ||||||||
\(839\) | 5.01380e18 | 0.496266 | 0.248133 | − | 0.968726i | \(-0.420183\pi\) | ||||
0.248133 | + | 0.968726i | \(0.420183\pi\) | |||||||
\(840\) | −7.17633e16 | −0.00704834 | ||||||||
\(841\) | 2.58973e19 | 2.52395 | ||||||||
\(842\) | 1.04101e19 | 1.00676 | ||||||||
\(843\) | −9.62874e18 | −0.924038 | ||||||||
\(844\) | −1.14939e18 | −0.109456 | ||||||||
\(845\) | 3.17888e17 | 0.0300404 | ||||||||
\(846\) | −3.72522e18 | −0.349337 | ||||||||
\(847\) | −5.64247e17 | −0.0525082 | ||||||||
\(848\) | 2.01508e19 | 1.86088 | ||||||||
\(849\) | −8.34684e18 | −0.764931 | ||||||||
\(850\) | −6.48503e18 | −0.589779 | ||||||||
\(851\) | −3.43400e18 | −0.309926 | ||||||||
\(852\) | −1.18927e18 | −0.106518 | ||||||||
\(853\) | 1.22198e19 | 1.08617 | 0.543083 | − | 0.839679i | \(-0.317257\pi\) | ||||
0.543083 | + | 0.839679i | \(0.317257\pi\) | |||||||
\(854\) | 2.09589e16 | 0.00184881 | ||||||||
\(855\) | −1.50061e17 | −0.0131368 | ||||||||
\(856\) | 4.31769e18 | 0.375121 | ||||||||
\(857\) | −2.08802e19 | −1.80036 | −0.900180 | − | 0.435517i | \(-0.856565\pi\) | ||||
−0.900180 | + | 0.435517i | \(0.856565\pi\) | |||||||
\(858\) | −1.06401e19 | −0.910499 | ||||||||
\(859\) | −9.24720e18 | −0.785334 | −0.392667 | − | 0.919681i | \(-0.628448\pi\) | ||||
−0.392667 | + | 0.919681i | \(0.628448\pi\) | |||||||
\(860\) | −1.01925e17 | −0.00859093 | ||||||||
\(861\) | −3.44436e18 | −0.288130 | ||||||||
\(862\) | 1.45264e19 | 1.20604 | ||||||||
\(863\) | −1.93714e19 | −1.59621 | −0.798107 | − | 0.602515i | \(-0.794165\pi\) | ||||
−0.798107 | + | 0.602515i | \(0.794165\pi\) | |||||||
\(864\) | 1.27576e18 | 0.104335 | ||||||||
\(865\) | −4.78187e17 | −0.0388144 | ||||||||
\(866\) | 9.44594e18 | 0.760990 | ||||||||
\(867\) | −5.24847e18 | −0.419670 | ||||||||
\(868\) | −1.12822e17 | −0.00895395 | ||||||||
\(869\) | 9.20271e18 | 0.724915 | ||||||||
\(870\) | 6.86145e17 | 0.0536464 | ||||||||
\(871\) | −1.09490e19 | −0.849684 | ||||||||
\(872\) | −9.29066e18 | −0.715631 | ||||||||
\(873\) | −1.44826e18 | −0.110727 | ||||||||
\(874\) | 1.70435e19 | 1.29341 | ||||||||
\(875\) | 3.96949e17 | 0.0299008 | ||||||||
\(876\) | −2.17843e18 | −0.162880 | ||||||||
\(877\) | 6.89977e18 | 0.512079 | 0.256040 | − | 0.966666i | \(-0.417582\pi\) | ||||
0.256040 | + | 0.966666i | \(0.417582\pi\) | |||||||
\(878\) | 2.68342e19 | 1.97685 | ||||||||
\(879\) | 1.28141e19 | 0.937045 | ||||||||
\(880\) | −7.77896e17 | −0.0564656 | ||||||||
\(881\) | −1.47931e19 | −1.06590 | −0.532950 | − | 0.846147i | \(-0.678917\pi\) | ||||
−0.532950 | + | 0.846147i | \(0.678917\pi\) | |||||||
\(882\) | 4.65379e18 | 0.332860 | ||||||||
\(883\) | 4.88085e18 | 0.346538 | 0.173269 | − | 0.984875i | \(-0.444567\pi\) | ||||
0.173269 | + | 0.984875i | \(0.444567\pi\) | |||||||
\(884\) | −2.68177e18 | −0.189009 | ||||||||
\(885\) | 4.70303e16 | 0.00329038 | ||||||||
\(886\) | 5.41369e18 | 0.375988 | ||||||||
\(887\) | 2.31901e19 | 1.59882 | 0.799409 | − | 0.600787i | \(-0.205146\pi\) | ||||
0.799409 | + | 0.600787i | \(0.205146\pi\) | |||||||
\(888\) | −1.67863e18 | −0.114887 | ||||||||
\(889\) | −6.71936e18 | −0.456527 | ||||||||
\(890\) | 1.07858e18 | 0.0727476 | ||||||||
\(891\) | 1.78234e18 | 0.119340 | ||||||||
\(892\) | 4.21066e18 | 0.279885 | ||||||||
\(893\) | −1.26451e19 | −0.834428 | ||||||||
\(894\) | 7.35577e18 | 0.481875 | ||||||||
\(895\) | −3.10257e17 | −0.0201777 | ||||||||
\(896\) | 6.39030e18 | 0.412591 | ||||||||
\(897\) | 1.48612e19 | 0.952583 | ||||||||
\(898\) | 7.15945e18 | 0.455600 | ||||||||
\(899\) | −2.79432e18 | −0.176538 | ||||||||
\(900\) | −1.47733e18 | −0.0926617 | ||||||||
\(901\) | 1.30039e19 | 0.809773 | ||||||||
\(902\) | −2.86772e19 | −1.77294 | ||||||||
\(903\) | 2.26568e18 | 0.139068 | ||||||||
\(904\) | −6.22606e18 | −0.379419 | ||||||||
\(905\) | −6.40993e17 | −0.0387826 | ||||||||
\(906\) | −1.61402e19 | −0.969564 | ||||||||
\(907\) | −1.09262e19 | −0.651659 | −0.325829 | − | 0.945429i | \(-0.605643\pi\) | ||||
−0.325829 | + | 0.945429i | \(0.605643\pi\) | |||||||
\(908\) | −4.56966e18 | −0.270599 | ||||||||
\(909\) | 6.67049e18 | 0.392186 | ||||||||
\(910\) | 3.76401e17 | 0.0219726 | ||||||||
\(911\) | −2.77598e18 | −0.160897 | −0.0804484 | − | 0.996759i | \(-0.525635\pi\) | ||||
−0.0804484 | + | 0.996759i | \(0.525635\pi\) | |||||||
\(912\) | 1.08469e19 | 0.624222 | ||||||||
\(913\) | 3.61154e19 | 2.06363 | ||||||||
\(914\) | 9.51817e18 | 0.540012 | ||||||||
\(915\) | 2.14591e15 | 0.000120886 0 | ||||||||
\(916\) | −7.60344e18 | −0.425294 | ||||||||
\(917\) | −5.04034e17 | −0.0279936 | ||||||||
\(918\) | 2.06214e18 | 0.113721 | ||||||||
\(919\) | 8.95952e18 | 0.490607 | 0.245304 | − | 0.969446i | \(-0.421112\pi\) | ||||
0.245304 | + | 0.969446i | \(0.421112\pi\) | |||||||
\(920\) | 8.34520e17 | 0.0453749 | ||||||||
\(921\) | 1.38866e19 | 0.749737 | ||||||||
\(922\) | 1.72432e18 | 0.0924415 | ||||||||
\(923\) | −1.61584e19 | −0.860175 | ||||||||
\(924\) | −1.11693e18 | −0.0590416 | ||||||||
\(925\) | 4.63812e18 | 0.243456 | ||||||||
\(926\) | −1.84287e19 | −0.960558 | ||||||||
\(927\) | 2.73317e18 | 0.141465 | ||||||||
\(928\) | −1.98010e19 | −1.01771 | ||||||||
\(929\) | −3.24021e19 | −1.65375 | −0.826877 | − | 0.562383i | \(-0.809885\pi\) | ||||
−0.826877 | + | 0.562383i | \(0.809885\pi\) | |||||||
\(930\) | −5.30260e16 | −0.00268751 | ||||||||
\(931\) | 1.57971e19 | 0.795070 | ||||||||
\(932\) | −1.44679e18 | −0.0723105 | ||||||||
\(933\) | 2.22594e17 | 0.0110480 | ||||||||
\(934\) | −8.18883e18 | −0.403615 | ||||||||
\(935\) | −5.02001e17 | −0.0245714 | ||||||||
\(936\) | 7.26456e18 | 0.353115 | ||||||||
\(937\) | 2.09195e19 | 1.00982 | 0.504909 | − | 0.863172i | \(-0.331526\pi\) | ||||
0.504909 | + | 0.863172i | \(0.331526\pi\) | |||||||
\(938\) | −5.27602e18 | −0.252923 | ||||||||
\(939\) | −6.03353e17 | −0.0287240 | ||||||||
\(940\) | 2.39018e17 | 0.0113006 | ||||||||
\(941\) | −8.55635e18 | −0.401750 | −0.200875 | − | 0.979617i | \(-0.564379\pi\) | ||||
−0.200875 | + | 0.979617i | \(0.564379\pi\) | |||||||
\(942\) | −8.42880e18 | −0.393038 | ||||||||
\(943\) | 4.00538e19 | 1.85489 | ||||||||
\(944\) | −3.39950e18 | −0.156350 | ||||||||
\(945\) | −6.30513e16 | −0.00287996 | ||||||||
\(946\) | 1.88637e19 | 0.855724 | ||||||||
\(947\) | 6.95835e18 | 0.313495 | 0.156748 | − | 0.987639i | \(-0.449899\pi\) | ||||
0.156748 | + | 0.987639i | \(0.449899\pi\) | |||||||
\(948\) | 2.42554e18 | 0.108531 | ||||||||
\(949\) | −2.95980e19 | −1.31532 | ||||||||
\(950\) | −2.30197e19 | −1.01601 | ||||||||
\(951\) | 3.26426e18 | 0.143091 | ||||||||
\(952\) | 3.34752e18 | 0.145741 | ||||||||
\(953\) | −4.30005e19 | −1.85939 | −0.929693 | − | 0.368336i | \(-0.879928\pi\) | ||||
−0.929693 | + | 0.368336i | \(0.879928\pi\) | |||||||
\(954\) | 1.35985e19 | 0.584019 | ||||||||
\(955\) | −3.02113e17 | −0.0128869 | ||||||||
\(956\) | −9.54712e18 | −0.404479 | ||||||||
\(957\) | −2.76636e19 | −1.16408 | ||||||||
\(958\) | −2.44466e19 | −1.02175 | ||||||||
\(959\) | −7.35383e18 | −0.305276 | ||||||||
\(960\) | 3.60387e17 | 0.0148596 | ||||||||
\(961\) | −2.42016e19 | −0.991156 | ||||||||
\(962\) | 8.80450e18 | 0.358151 | ||||||||
\(963\) | 3.79352e18 | 0.153275 | ||||||||
\(964\) | 5.88595e18 | 0.236220 | ||||||||
\(965\) | −9.25452e17 | −0.0368915 | ||||||||
\(966\) | 7.16119e18 | 0.283553 | ||||||||
\(967\) | 7.62426e18 | 0.299865 | 0.149932 | − | 0.988696i | \(-0.452094\pi\) | ||||
0.149932 | + | 0.988696i | \(0.452094\pi\) | |||||||
\(968\) | 3.20744e18 | 0.125305 | ||||||||
\(969\) | 6.99985e18 | 0.271634 | ||||||||
\(970\) | 4.26559e17 | 0.0164423 | ||||||||
\(971\) | 2.09545e19 | 0.802327 | 0.401164 | − | 0.916006i | \(-0.368606\pi\) | ||||
0.401164 | + | 0.916006i | \(0.368606\pi\) | |||||||
\(972\) | 4.69767e17 | 0.0178670 | ||||||||
\(973\) | 1.15577e19 | 0.436654 | ||||||||
\(974\) | 4.86272e19 | 1.82493 | ||||||||
\(975\) | −2.00722e19 | −0.748282 | ||||||||
\(976\) | −1.55114e17 | −0.00574415 | ||||||||
\(977\) | −5.08060e19 | −1.86896 | −0.934480 | − | 0.356015i | \(-0.884135\pi\) | ||||
−0.934480 | + | 0.356015i | \(0.884135\pi\) | |||||||
\(978\) | −2.89601e19 | −1.05827 | ||||||||
\(979\) | −4.34858e19 | −1.57855 | ||||||||
\(980\) | −2.98597e17 | −0.0107675 | ||||||||
\(981\) | −8.16278e18 | −0.292408 | ||||||||
\(982\) | 4.23792e19 | 1.50809 | ||||||||
\(983\) | 1.01969e19 | 0.360469 | 0.180235 | − | 0.983624i | \(-0.442314\pi\) | ||||
0.180235 | + | 0.983624i | \(0.442314\pi\) | |||||||
\(984\) | 1.95794e19 | 0.687592 | ||||||||
\(985\) | −2.30143e18 | −0.0802900 | ||||||||
\(986\) | −3.20064e19 | −1.10927 | ||||||||
\(987\) | −5.31311e18 | −0.182931 | ||||||||
\(988\) | −9.51942e18 | −0.325604 | ||||||||
\(989\) | −2.63471e19 | −0.895277 | ||||||||
\(990\) | −5.24954e17 | −0.0177212 | ||||||||
\(991\) | −5.55649e18 | −0.186347 | −0.0931734 | − | 0.995650i | \(-0.529701\pi\) | ||||
−0.0931734 | + | 0.995650i | \(0.529701\pi\) | |||||||
\(992\) | 1.53024e18 | 0.0509841 | ||||||||
\(993\) | 2.63859e19 | 0.873378 | ||||||||
\(994\) | −7.78626e18 | −0.256046 | ||||||||
\(995\) | −9.18887e17 | −0.0300201 | ||||||||
\(996\) | 9.51885e18 | 0.308958 | ||||||||
\(997\) | −5.87125e19 | −1.89327 | −0.946634 | − | 0.322310i | \(-0.895541\pi\) | ||||
−0.946634 | + | 0.322310i | \(0.895541\pi\) | |||||||
\(998\) | −2.90421e19 | −0.930422 | ||||||||
\(999\) | −1.47485e18 | −0.0469431 |
(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 | 177.14.a.a.1.9 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.9 | ✓ | 30 | 1.1 | even | 1 | trivial |