Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(28.4270373191\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + 186018392 x^{5} + 10752389517 x^{4} + 491049966 x^{3} + \cdots + 59402280000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-12.7078\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 13.7078 | 1.21161 | 0.605806 | − | 0.795613i | \(-0.292851\pi\) | ||||
0.605806 | + | 0.795613i | \(0.292851\pi\) | |||||||
\(3\) | 50.2321 | 1.07413 | 0.537065 | − | 0.843541i | \(-0.319533\pi\) | ||||
0.537065 | + | 0.843541i | \(0.319533\pi\) | |||||||
\(4\) | 59.9043 | 0.468002 | ||||||||
\(5\) | 544.453 | 1.94789 | 0.973947 | − | 0.226778i | \(-0.0728191\pi\) | ||||
0.973947 | + | 0.226778i | \(0.0728191\pi\) | |||||||
\(6\) | 688.573 | 1.30143 | ||||||||
\(7\) | 343.000 | 0.377964 | ||||||||
\(8\) | −933.443 | −0.644574 | ||||||||
\(9\) | 336.267 | 0.153757 | ||||||||
\(10\) | 7463.26 | 2.36009 | ||||||||
\(11\) | 3185.05 | 0.721509 | 0.360755 | − | 0.932661i | \(-0.382519\pi\) | ||||
0.360755 | + | 0.932661i | \(0.382519\pi\) | |||||||
\(12\) | 3009.12 | 0.502696 | ||||||||
\(13\) | 2197.00 | 0.277350 | ||||||||
\(14\) | 4701.78 | 0.457946 | ||||||||
\(15\) | 27349.0 | 2.09229 | ||||||||
\(16\) | −20463.2 | −1.24898 | ||||||||
\(17\) | 18610.0 | 0.918702 | 0.459351 | − | 0.888255i | \(-0.348082\pi\) | ||||
0.459351 | + | 0.888255i | \(0.348082\pi\) | |||||||
\(18\) | 4609.48 | 0.186294 | ||||||||
\(19\) | −48240.1 | −1.61351 | −0.806753 | − | 0.590889i | \(-0.798777\pi\) | ||||
−0.806753 | + | 0.590889i | \(0.798777\pi\) | |||||||
\(20\) | 32615.1 | 0.911619 | ||||||||
\(21\) | 17229.6 | 0.405983 | ||||||||
\(22\) | 43660.1 | 0.874189 | ||||||||
\(23\) | −101451. | −1.73864 | −0.869321 | − | 0.494249i | \(-0.835443\pi\) | ||||
−0.869321 | + | 0.494249i | \(0.835443\pi\) | |||||||
\(24\) | −46888.8 | −0.692357 | ||||||||
\(25\) | 218304. | 2.79429 | ||||||||
\(26\) | 30116.1 | 0.336041 | ||||||||
\(27\) | −92966.3 | −0.908976 | ||||||||
\(28\) | 20547.2 | 0.176888 | ||||||||
\(29\) | 163486. | 1.24476 | 0.622381 | − | 0.782714i | \(-0.286165\pi\) | ||||
0.622381 | + | 0.782714i | \(0.286165\pi\) | |||||||
\(30\) | 374895. | 2.53504 | ||||||||
\(31\) | −76991.3 | −0.464169 | −0.232084 | − | 0.972696i | \(-0.574555\pi\) | ||||
−0.232084 | + | 0.972696i | \(0.574555\pi\) | |||||||
\(32\) | −161025. | −0.868699 | ||||||||
\(33\) | 159992. | 0.774995 | ||||||||
\(34\) | 255102. | 1.11311 | ||||||||
\(35\) | 186747. | 0.736234 | ||||||||
\(36\) | 20143.8 | 0.0719586 | ||||||||
\(37\) | 224246. | 0.727811 | 0.363906 | − | 0.931436i | \(-0.381443\pi\) | ||||
0.363906 | + | 0.931436i | \(0.381443\pi\) | |||||||
\(38\) | −661266. | −1.95494 | ||||||||
\(39\) | 110360. | 0.297910 | ||||||||
\(40\) | −508216. | −1.25556 | ||||||||
\(41\) | −71118.9 | −0.161154 | −0.0805771 | − | 0.996748i | \(-0.525676\pi\) | ||||
−0.0805771 | + | 0.996748i | \(0.525676\pi\) | |||||||
\(42\) | 236181. | 0.491894 | ||||||||
\(43\) | −366021. | −0.702048 | −0.351024 | − | 0.936366i | \(-0.614166\pi\) | ||||
−0.351024 | + | 0.936366i | \(0.614166\pi\) | |||||||
\(44\) | 190798. | 0.337668 | ||||||||
\(45\) | 183081. | 0.299502 | ||||||||
\(46\) | −1.39068e6 | −2.10656 | ||||||||
\(47\) | 545639. | 0.766590 | 0.383295 | − | 0.923626i | \(-0.374789\pi\) | ||||
0.383295 | + | 0.923626i | \(0.374789\pi\) | |||||||
\(48\) | −1.02791e6 | −1.34156 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 2.99247e6 | 3.38559 | ||||||||
\(51\) | 934819. | 0.986806 | ||||||||
\(52\) | 131610. | 0.129801 | ||||||||
\(53\) | 1.16583e6 | 1.07565 | 0.537825 | − | 0.843057i | \(-0.319246\pi\) | ||||
0.537825 | + | 0.843057i | \(0.319246\pi\) | |||||||
\(54\) | −1.27436e6 | −1.10133 | ||||||||
\(55\) | 1.73411e6 | 1.40542 | ||||||||
\(56\) | −320171. | −0.243626 | ||||||||
\(57\) | −2.42320e6 | −1.73312 | ||||||||
\(58\) | 2.24103e6 | 1.50817 | ||||||||
\(59\) | 67871.3 | 0.0430233 | 0.0215117 | − | 0.999769i | \(-0.493152\pi\) | ||||
0.0215117 | + | 0.999769i | \(0.493152\pi\) | |||||||
\(60\) | 1.63832e6 | 0.979198 | ||||||||
\(61\) | −2.67077e6 | −1.50655 | −0.753273 | − | 0.657708i | \(-0.771526\pi\) | ||||
−0.753273 | + | 0.657708i | \(0.771526\pi\) | |||||||
\(62\) | −1.05538e6 | −0.562392 | ||||||||
\(63\) | 115339. | 0.0581147 | ||||||||
\(64\) | 411985. | 0.196450 | ||||||||
\(65\) | 1.19616e6 | 0.540248 | ||||||||
\(66\) | 2.19314e6 | 0.938993 | ||||||||
\(67\) | −803728. | −0.326473 | −0.163237 | − | 0.986587i | \(-0.552193\pi\) | ||||
−0.163237 | + | 0.986587i | \(0.552193\pi\) | |||||||
\(68\) | 1.11482e6 | 0.429955 | ||||||||
\(69\) | −5.09611e6 | −1.86753 | ||||||||
\(70\) | 2.55990e6 | 0.892030 | ||||||||
\(71\) | −3.09022e6 | −1.02467 | −0.512337 | − | 0.858785i | \(-0.671220\pi\) | ||||
−0.512337 | + | 0.858785i | \(0.671220\pi\) | |||||||
\(72\) | −313886. | −0.0991078 | ||||||||
\(73\) | 1.19301e6 | 0.358935 | 0.179468 | − | 0.983764i | \(-0.442563\pi\) | ||||
0.179468 | + | 0.983764i | \(0.442563\pi\) | |||||||
\(74\) | 3.07393e6 | 0.881825 | ||||||||
\(75\) | 1.09659e7 | 3.00143 | ||||||||
\(76\) | −2.88979e6 | −0.755125 | ||||||||
\(77\) | 1.09247e6 | 0.272705 | ||||||||
\(78\) | 1.51279e6 | 0.360952 | ||||||||
\(79\) | −466693. | −0.106497 | −0.0532484 | − | 0.998581i | \(-0.516958\pi\) | ||||
−0.0532484 | + | 0.998581i | \(0.516958\pi\) | |||||||
\(80\) | −1.11413e7 | −2.43287 | ||||||||
\(81\) | −5.40531e6 | −1.13012 | ||||||||
\(82\) | −974885. | −0.195256 | ||||||||
\(83\) | −3.98882e6 | −0.765721 | −0.382861 | − | 0.923806i | \(-0.625061\pi\) | ||||
−0.382861 | + | 0.923806i | \(0.625061\pi\) | |||||||
\(84\) | 1.03213e6 | 0.190001 | ||||||||
\(85\) | 1.01323e7 | 1.78953 | ||||||||
\(86\) | −5.01736e6 | −0.850610 | ||||||||
\(87\) | 8.21223e6 | 1.33704 | ||||||||
\(88\) | −2.97306e6 | −0.465066 | ||||||||
\(89\) | −387371. | −0.0582454 | −0.0291227 | − | 0.999576i | \(-0.509271\pi\) | ||||
−0.0291227 | + | 0.999576i | \(0.509271\pi\) | |||||||
\(90\) | 2.50964e6 | 0.362880 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −6.07737e6 | −0.813688 | ||||||||
\(93\) | −3.86744e6 | −0.498578 | ||||||||
\(94\) | 7.47952e6 | 0.928809 | ||||||||
\(95\) | −2.62644e7 | −3.14294 | ||||||||
\(96\) | −8.08865e6 | −0.933097 | ||||||||
\(97\) | 8.39907e6 | 0.934394 | 0.467197 | − | 0.884153i | \(-0.345264\pi\) | ||||
0.467197 | + | 0.884153i | \(0.345264\pi\) | |||||||
\(98\) | 1.61271e6 | 0.173087 | ||||||||
\(99\) | 1.07103e6 | 0.110937 | ||||||||
\(100\) | 1.30773e7 | 1.30773 | ||||||||
\(101\) | −1.65322e7 | −1.59663 | −0.798315 | − | 0.602239i | \(-0.794275\pi\) | ||||
−0.798315 | + | 0.602239i | \(0.794275\pi\) | |||||||
\(102\) | 1.28143e7 | 1.19563 | ||||||||
\(103\) | −1.04478e7 | −0.942095 | −0.471048 | − | 0.882108i | \(-0.656124\pi\) | ||||
−0.471048 | + | 0.882108i | \(0.656124\pi\) | |||||||
\(104\) | −2.05078e6 | −0.178773 | ||||||||
\(105\) | 9.38071e6 | 0.790812 | ||||||||
\(106\) | 1.59810e7 | 1.30327 | ||||||||
\(107\) | −9.15329e6 | −0.722327 | −0.361164 | − | 0.932502i | \(-0.617620\pi\) | ||||
−0.361164 | + | 0.932502i | \(0.617620\pi\) | |||||||
\(108\) | −5.56908e6 | −0.425403 | ||||||||
\(109\) | 1.76810e7 | 1.30772 | 0.653859 | − | 0.756617i | \(-0.273149\pi\) | ||||
0.653859 | + | 0.756617i | \(0.273149\pi\) | |||||||
\(110\) | 2.37708e7 | 1.70283 | ||||||||
\(111\) | 1.12644e7 | 0.781765 | ||||||||
\(112\) | −7.01889e6 | −0.472069 | ||||||||
\(113\) | −1.51600e7 | −0.988380 | −0.494190 | − | 0.869354i | \(-0.664535\pi\) | ||||
−0.494190 | + | 0.869354i | \(0.664535\pi\) | |||||||
\(114\) | −3.32168e7 | −2.09986 | ||||||||
\(115\) | −5.52354e7 | −3.38669 | ||||||||
\(116\) | 9.79349e6 | 0.582552 | ||||||||
\(117\) | 738778. | 0.0426445 | ||||||||
\(118\) | 930367. | 0.0521276 | ||||||||
\(119\) | 6.38322e6 | 0.347237 | ||||||||
\(120\) | −2.55288e7 | −1.34864 | ||||||||
\(121\) | −9.34263e6 | −0.479425 | ||||||||
\(122\) | −3.66104e7 | −1.82535 | ||||||||
\(123\) | −3.57245e6 | −0.173101 | ||||||||
\(124\) | −4.61211e6 | −0.217232 | ||||||||
\(125\) | 7.63207e7 | 3.49508 | ||||||||
\(126\) | 1.58105e6 | 0.0704124 | ||||||||
\(127\) | −2.11379e7 | −0.915690 | −0.457845 | − | 0.889032i | \(-0.651378\pi\) | ||||
−0.457845 | + | 0.889032i | \(0.651378\pi\) | |||||||
\(128\) | 2.62587e7 | 1.10672 | ||||||||
\(129\) | −1.83860e7 | −0.754092 | ||||||||
\(130\) | 1.63968e7 | 0.654571 | ||||||||
\(131\) | 1.89064e7 | 0.734783 | 0.367392 | − | 0.930066i | \(-0.380251\pi\) | ||||
0.367392 | + | 0.930066i | \(0.380251\pi\) | |||||||
\(132\) | 9.58420e6 | 0.362700 | ||||||||
\(133\) | −1.65464e7 | −0.609848 | ||||||||
\(134\) | −1.10174e7 | −0.395559 | ||||||||
\(135\) | −5.06157e7 | −1.77059 | ||||||||
\(136\) | −1.73714e7 | −0.592172 | ||||||||
\(137\) | −4.59503e7 | −1.52675 | −0.763373 | − | 0.645958i | \(-0.776458\pi\) | ||||
−0.763373 | + | 0.645958i | \(0.776458\pi\) | |||||||
\(138\) | −6.98566e7 | −2.26272 | ||||||||
\(139\) | 3.80955e7 | 1.20315 | 0.601577 | − | 0.798815i | \(-0.294539\pi\) | ||||
0.601577 | + | 0.798815i | \(0.294539\pi\) | |||||||
\(140\) | 1.11870e7 | 0.344559 | ||||||||
\(141\) | 2.74086e7 | 0.823418 | ||||||||
\(142\) | −4.23602e7 | −1.24151 | ||||||||
\(143\) | 6.99755e6 | 0.200111 | ||||||||
\(144\) | −6.88110e6 | −0.192039 | ||||||||
\(145\) | 8.90102e7 | 2.42466 | ||||||||
\(146\) | 1.63536e7 | 0.434890 | ||||||||
\(147\) | 5.90976e6 | 0.153447 | ||||||||
\(148\) | 1.34333e7 | 0.340618 | ||||||||
\(149\) | −3.25299e7 | −0.805621 | −0.402811 | − | 0.915283i | \(-0.631967\pi\) | ||||
−0.402811 | + | 0.915283i | \(0.631967\pi\) | |||||||
\(150\) | 1.50318e8 | 3.63657 | ||||||||
\(151\) | 7.90428e7 | 1.86829 | 0.934143 | − | 0.356900i | \(-0.116166\pi\) | ||||
0.934143 | + | 0.356900i | \(0.116166\pi\) | |||||||
\(152\) | 4.50294e7 | 1.04002 | ||||||||
\(153\) | 6.25791e6 | 0.141257 | ||||||||
\(154\) | 1.49754e7 | 0.330412 | ||||||||
\(155\) | −4.19181e7 | −0.904151 | ||||||||
\(156\) | 6.61104e6 | 0.139423 | ||||||||
\(157\) | 1.42411e6 | 0.0293693 | 0.0146847 | − | 0.999892i | \(-0.495326\pi\) | ||||
0.0146847 | + | 0.999892i | \(0.495326\pi\) | |||||||
\(158\) | −6.39734e6 | −0.129033 | ||||||||
\(159\) | 5.85623e7 | 1.15539 | ||||||||
\(160\) | −8.76707e7 | −1.69213 | ||||||||
\(161\) | −3.47978e7 | −0.657145 | ||||||||
\(162\) | −7.40950e7 | −1.36926 | ||||||||
\(163\) | 9.91388e7 | 1.79303 | 0.896514 | − | 0.443015i | \(-0.146091\pi\) | ||||
0.896514 | + | 0.443015i | \(0.146091\pi\) | |||||||
\(164\) | −4.26033e6 | −0.0754206 | ||||||||
\(165\) | 8.71080e7 | 1.50961 | ||||||||
\(166\) | −5.46780e7 | −0.927756 | ||||||||
\(167\) | −3.00881e7 | −0.499905 | −0.249952 | − | 0.968258i | \(-0.580415\pi\) | ||||
−0.249952 | + | 0.968258i | \(0.580415\pi\) | |||||||
\(168\) | −1.60829e7 | −0.261686 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | 1.38891e8 | 2.16822 | ||||||||
\(171\) | −1.62215e7 | −0.248088 | ||||||||
\(172\) | −2.19263e7 | −0.328560 | ||||||||
\(173\) | 4.37139e7 | 0.641886 | 0.320943 | − | 0.947099i | \(-0.396000\pi\) | ||||
0.320943 | + | 0.947099i | \(0.396000\pi\) | |||||||
\(174\) | 1.12572e8 | 1.61997 | ||||||||
\(175\) | 7.48782e7 | 1.05614 | ||||||||
\(176\) | −6.51764e7 | −0.901148 | ||||||||
\(177\) | 3.40932e6 | 0.0462127 | ||||||||
\(178\) | −5.31001e6 | −0.0705708 | ||||||||
\(179\) | 1.33672e8 | 1.74203 | 0.871013 | − | 0.491260i | \(-0.163463\pi\) | ||||
0.871013 | + | 0.491260i | \(0.163463\pi\) | |||||||
\(180\) | 1.09674e7 | 0.140168 | ||||||||
\(181\) | 4.30566e7 | 0.539716 | 0.269858 | − | 0.962900i | \(-0.413023\pi\) | ||||
0.269858 | + | 0.962900i | \(0.413023\pi\) | |||||||
\(182\) | 1.03298e7 | 0.127011 | ||||||||
\(183\) | −1.34158e8 | −1.61823 | ||||||||
\(184\) | 9.46990e7 | 1.12068 | ||||||||
\(185\) | 1.22091e8 | 1.41770 | ||||||||
\(186\) | −5.30142e7 | −0.604083 | ||||||||
\(187\) | 5.92737e7 | 0.662852 | ||||||||
\(188\) | 3.26861e7 | 0.358766 | ||||||||
\(189\) | −3.18874e7 | −0.343561 | ||||||||
\(190\) | −3.60028e8 | −3.80802 | ||||||||
\(191\) | −1.71611e8 | −1.78208 | −0.891042 | − | 0.453921i | \(-0.850025\pi\) | ||||
−0.891042 | + | 0.453921i | \(0.850025\pi\) | |||||||
\(192\) | 2.06949e7 | 0.211013 | ||||||||
\(193\) | 1.81584e7 | 0.181814 | 0.0909069 | − | 0.995859i | \(-0.471023\pi\) | ||||
0.0909069 | + | 0.995859i | \(0.471023\pi\) | |||||||
\(194\) | 1.15133e8 | 1.13212 | ||||||||
\(195\) | 6.00858e7 | 0.580297 | ||||||||
\(196\) | 7.04768e6 | 0.0668575 | ||||||||
\(197\) | 7.06759e7 | 0.658627 | 0.329313 | − | 0.944221i | \(-0.393183\pi\) | ||||
0.329313 | + | 0.944221i | \(0.393183\pi\) | |||||||
\(198\) | 1.46814e7 | 0.134413 | ||||||||
\(199\) | −9.03017e6 | −0.0812289 | −0.0406144 | − | 0.999175i | \(-0.512932\pi\) | ||||
−0.0406144 | + | 0.999175i | \(0.512932\pi\) | |||||||
\(200\) | −2.03774e8 | −1.80113 | ||||||||
\(201\) | −4.03730e7 | −0.350675 | ||||||||
\(202\) | −2.26620e8 | −1.93450 | ||||||||
\(203\) | 5.60756e7 | 0.470476 | ||||||||
\(204\) | 5.59997e7 | 0.461828 | ||||||||
\(205\) | −3.87209e7 | −0.313911 | ||||||||
\(206\) | −1.43217e8 | −1.14145 | ||||||||
\(207\) | −3.41147e7 | −0.267328 | ||||||||
\(208\) | −4.49577e7 | −0.346404 | ||||||||
\(209\) | −1.53647e8 | −1.16416 | ||||||||
\(210\) | 1.28589e8 | 0.958157 | ||||||||
\(211\) | 7.31185e7 | 0.535845 | 0.267922 | − | 0.963441i | \(-0.413663\pi\) | ||||
0.267922 | + | 0.963441i | \(0.413663\pi\) | |||||||
\(212\) | 6.98384e7 | 0.503406 | ||||||||
\(213\) | −1.55228e8 | −1.10063 | ||||||||
\(214\) | −1.25472e8 | −0.875180 | ||||||||
\(215\) | −1.99281e8 | −1.36751 | ||||||||
\(216\) | 8.67788e7 | 0.585902 | ||||||||
\(217\) | −2.64080e7 | −0.175439 | ||||||||
\(218\) | 2.42368e8 | 1.58445 | ||||||||
\(219\) | 5.99277e7 | 0.385543 | ||||||||
\(220\) | 1.03881e8 | 0.657741 | ||||||||
\(221\) | 4.08861e7 | 0.254802 | ||||||||
\(222\) | 1.54410e8 | 0.947195 | ||||||||
\(223\) | 1.37129e8 | 0.828060 | 0.414030 | − | 0.910263i | \(-0.364121\pi\) | ||||
0.414030 | + | 0.910263i | \(0.364121\pi\) | |||||||
\(224\) | −5.52317e7 | −0.328338 | ||||||||
\(225\) | 7.34082e7 | 0.429641 | ||||||||
\(226\) | −2.07810e8 | −1.19753 | ||||||||
\(227\) | −9.17915e7 | −0.520849 | −0.260425 | − | 0.965494i | \(-0.583863\pi\) | ||||
−0.260425 | + | 0.965494i | \(0.583863\pi\) | |||||||
\(228\) | −1.45160e8 | −0.811103 | ||||||||
\(229\) | −9.94686e7 | −0.547346 | −0.273673 | − | 0.961823i | \(-0.588239\pi\) | ||||
−0.273673 | + | 0.961823i | \(0.588239\pi\) | |||||||
\(230\) | −7.57157e8 | −4.10335 | ||||||||
\(231\) | 5.48772e7 | 0.292921 | ||||||||
\(232\) | −1.52605e8 | −0.802342 | ||||||||
\(233\) | 1.68551e8 | 0.872944 | 0.436472 | − | 0.899718i | \(-0.356228\pi\) | ||||
0.436472 | + | 0.899718i | \(0.356228\pi\) | |||||||
\(234\) | 1.01270e7 | 0.0516686 | ||||||||
\(235\) | 2.97075e8 | 1.49323 | ||||||||
\(236\) | 4.06578e6 | 0.0201350 | ||||||||
\(237\) | −2.34430e7 | −0.114391 | ||||||||
\(238\) | 8.75001e7 | 0.420716 | ||||||||
\(239\) | −4.75224e7 | −0.225167 | −0.112584 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112584 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(240\) | −5.59649e8 | −2.61322 | ||||||||
\(241\) | 1.39642e8 | 0.642622 | 0.321311 | − | 0.946974i | \(-0.395877\pi\) | ||||
0.321311 | + | 0.946974i | \(0.395877\pi\) | |||||||
\(242\) | −1.28067e8 | −0.580876 | ||||||||
\(243\) | −6.82029e7 | −0.304916 | ||||||||
\(244\) | −1.59991e8 | −0.705067 | ||||||||
\(245\) | 6.40543e7 | 0.278270 | ||||||||
\(246\) | −4.89706e7 | −0.209731 | ||||||||
\(247\) | −1.05983e8 | −0.447506 | ||||||||
\(248\) | 7.18671e7 | 0.299191 | ||||||||
\(249\) | −2.00367e8 | −0.822485 | ||||||||
\(250\) | 1.04619e9 | 4.23468 | ||||||||
\(251\) | −1.74028e8 | −0.694643 | −0.347322 | − | 0.937746i | \(-0.612909\pi\) | ||||
−0.347322 | + | 0.937746i | \(0.612909\pi\) | |||||||
\(252\) | 6.90933e6 | 0.0271978 | ||||||||
\(253\) | −3.23127e8 | −1.25445 | ||||||||
\(254\) | −2.89754e8 | −1.10946 | ||||||||
\(255\) | 5.08965e8 | 1.92219 | ||||||||
\(256\) | 3.07215e8 | 1.14447 | ||||||||
\(257\) | 3.63317e8 | 1.33512 | 0.667559 | − | 0.744557i | \(-0.267339\pi\) | ||||
0.667559 | + | 0.744557i | \(0.267339\pi\) | |||||||
\(258\) | −2.52032e8 | −0.913666 | ||||||||
\(259\) | 7.69164e7 | 0.275087 | ||||||||
\(260\) | 7.16553e7 | 0.252838 | ||||||||
\(261\) | 5.49747e7 | 0.191391 | ||||||||
\(262\) | 2.59165e8 | 0.890272 | ||||||||
\(263\) | 1.43176e8 | 0.485318 | 0.242659 | − | 0.970112i | \(-0.421980\pi\) | ||||
0.242659 | + | 0.970112i | \(0.421980\pi\) | |||||||
\(264\) | −1.49343e8 | −0.499542 | ||||||||
\(265\) | 6.34741e8 | 2.09525 | ||||||||
\(266\) | −2.26814e8 | −0.738899 | ||||||||
\(267\) | −1.94585e7 | −0.0625632 | ||||||||
\(268\) | −4.81468e7 | −0.152790 | ||||||||
\(269\) | −6.42270e7 | −0.201180 | −0.100590 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100590 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(270\) | −6.93831e8 | −2.14526 | ||||||||
\(271\) | 4.55860e8 | 1.39136 | 0.695679 | − | 0.718352i | \(-0.255103\pi\) | ||||
0.695679 | + | 0.718352i | \(0.255103\pi\) | |||||||
\(272\) | −3.80820e8 | −1.14744 | ||||||||
\(273\) | 3.78535e7 | 0.112600 | ||||||||
\(274\) | −6.29879e8 | −1.84982 | ||||||||
\(275\) | 6.95308e8 | 2.01610 | ||||||||
\(276\) | −3.05279e8 | −0.874008 | ||||||||
\(277\) | 4.81356e8 | 1.36078 | 0.680389 | − | 0.732851i | \(-0.261811\pi\) | ||||
0.680389 | + | 0.732851i | \(0.261811\pi\) | |||||||
\(278\) | 5.22206e8 | 1.45776 | ||||||||
\(279\) | −2.58896e7 | −0.0713692 | ||||||||
\(280\) | −1.74318e8 | −0.474558 | ||||||||
\(281\) | 5.23317e8 | 1.40700 | 0.703498 | − | 0.710697i | \(-0.251620\pi\) | ||||
0.703498 | + | 0.710697i | \(0.251620\pi\) | |||||||
\(282\) | 3.75712e8 | 0.997662 | ||||||||
\(283\) | −2.76148e6 | −0.00724252 | −0.00362126 | − | 0.999993i | \(-0.501153\pi\) | ||||
−0.00362126 | + | 0.999993i | \(0.501153\pi\) | |||||||
\(284\) | −1.85118e8 | −0.479550 | ||||||||
\(285\) | −1.31932e9 | −3.37592 | ||||||||
\(286\) | 9.59212e7 | 0.242456 | ||||||||
\(287\) | −2.43938e7 | −0.0609106 | ||||||||
\(288\) | −5.41475e7 | −0.133569 | ||||||||
\(289\) | −6.40074e7 | −0.155987 | ||||||||
\(290\) | 1.22014e9 | 2.93775 | ||||||||
\(291\) | 4.21903e8 | 1.00366 | ||||||||
\(292\) | 7.14667e7 | 0.167982 | ||||||||
\(293\) | 5.25307e8 | 1.22005 | 0.610023 | − | 0.792384i | \(-0.291160\pi\) | ||||
0.610023 | + | 0.792384i | \(0.291160\pi\) | |||||||
\(294\) | 8.10099e7 | 0.185918 | ||||||||
\(295\) | 3.69527e7 | 0.0838049 | ||||||||
\(296\) | −2.09321e8 | −0.469129 | ||||||||
\(297\) | −2.96102e8 | −0.655834 | ||||||||
\(298\) | −4.45914e8 | −0.976100 | ||||||||
\(299\) | −2.22888e8 | −0.482212 | ||||||||
\(300\) | 6.56902e8 | 1.40468 | ||||||||
\(301\) | −1.25545e8 | −0.265349 | ||||||||
\(302\) | 1.08350e9 | 2.26364 | ||||||||
\(303\) | −8.30445e8 | −1.71499 | ||||||||
\(304\) | 9.87148e8 | 2.01523 | ||||||||
\(305\) | −1.45411e9 | −2.93459 | ||||||||
\(306\) | 8.57823e7 | 0.171148 | ||||||||
\(307\) | −5.59927e8 | −1.10445 | −0.552227 | − | 0.833694i | \(-0.686222\pi\) | ||||
−0.552227 | + | 0.833694i | \(0.686222\pi\) | |||||||
\(308\) | 6.54438e7 | 0.127626 | ||||||||
\(309\) | −5.24816e8 | −1.01193 | ||||||||
\(310\) | −5.74606e8 | −1.09548 | ||||||||
\(311\) | −6.45480e8 | −1.21681 | −0.608403 | − | 0.793628i | \(-0.708189\pi\) | ||||
−0.608403 | + | 0.793628i | \(0.708189\pi\) | |||||||
\(312\) | −1.03015e8 | −0.192025 | ||||||||
\(313\) | −5.61337e8 | −1.03471 | −0.517355 | − | 0.855771i | \(-0.673083\pi\) | ||||
−0.517355 | + | 0.855771i | \(0.673083\pi\) | |||||||
\(314\) | 1.95214e7 | 0.0355842 | ||||||||
\(315\) | 6.27968e7 | 0.113201 | ||||||||
\(316\) | −2.79569e7 | −0.0498407 | ||||||||
\(317\) | −9.48152e8 | −1.67175 | −0.835874 | − | 0.548922i | \(-0.815038\pi\) | ||||
−0.835874 | + | 0.548922i | \(0.815038\pi\) | |||||||
\(318\) | 8.02761e8 | 1.39988 | ||||||||
\(319\) | 5.20710e8 | 0.898107 | ||||||||
\(320\) | 2.24306e8 | 0.382663 | ||||||||
\(321\) | −4.59789e8 | −0.775874 | ||||||||
\(322\) | −4.77002e8 | −0.796204 | ||||||||
\(323\) | −8.97747e8 | −1.48233 | ||||||||
\(324\) | −3.23801e8 | −0.528897 | ||||||||
\(325\) | 4.79613e8 | 0.774996 | ||||||||
\(326\) | 1.35898e9 | 2.17245 | ||||||||
\(327\) | 8.88154e8 | 1.40466 | ||||||||
\(328\) | 6.63855e7 | 0.103876 | ||||||||
\(329\) | 1.87154e8 | 0.289744 | ||||||||
\(330\) | 1.19406e9 | 1.82906 | ||||||||
\(331\) | 1.27938e8 | 0.193911 | 0.0969556 | − | 0.995289i | \(-0.469090\pi\) | ||||
0.0969556 | + | 0.995289i | \(0.469090\pi\) | |||||||
\(332\) | −2.38947e8 | −0.358359 | ||||||||
\(333\) | 7.54065e7 | 0.111906 | ||||||||
\(334\) | −4.12442e8 | −0.605690 | ||||||||
\(335\) | −4.37592e8 | −0.635935 | ||||||||
\(336\) | −3.52574e8 | −0.507063 | ||||||||
\(337\) | 1.12221e8 | 0.159724 | 0.0798620 | − | 0.996806i | \(-0.474552\pi\) | ||||
0.0798620 | + | 0.996806i | \(0.474552\pi\) | |||||||
\(338\) | 6.61650e7 | 0.0932009 | ||||||||
\(339\) | −7.61518e8 | −1.06165 | ||||||||
\(340\) | 6.06966e8 | 0.837506 | ||||||||
\(341\) | −2.45221e8 | −0.334902 | ||||||||
\(342\) | −2.22362e8 | −0.300586 | ||||||||
\(343\) | 4.03536e7 | 0.0539949 | ||||||||
\(344\) | 3.41660e8 | 0.452522 | ||||||||
\(345\) | −2.77459e9 | −3.63774 | ||||||||
\(346\) | 5.99222e8 | 0.777716 | ||||||||
\(347\) | 1.44603e9 | 1.85791 | 0.928954 | − | 0.370196i | \(-0.120710\pi\) | ||||
0.928954 | + | 0.370196i | \(0.120710\pi\) | |||||||
\(348\) | 4.91948e8 | 0.625737 | ||||||||
\(349\) | −3.90752e7 | −0.0492054 | −0.0246027 | − | 0.999697i | \(-0.507832\pi\) | ||||
−0.0246027 | + | 0.999697i | \(0.507832\pi\) | |||||||
\(350\) | 1.02642e9 | 1.27963 | ||||||||
\(351\) | −2.04247e8 | −0.252104 | ||||||||
\(352\) | −5.12874e8 | −0.626775 | ||||||||
\(353\) | 7.97761e8 | 0.965298 | 0.482649 | − | 0.875814i | \(-0.339675\pi\) | ||||
0.482649 | + | 0.875814i | \(0.339675\pi\) | |||||||
\(354\) | 4.67343e7 | 0.0559918 | ||||||||
\(355\) | −1.68248e9 | −1.99595 | ||||||||
\(356\) | −2.32052e7 | −0.0272590 | ||||||||
\(357\) | 3.20643e8 | 0.372978 | ||||||||
\(358\) | 1.83235e9 | 2.11066 | ||||||||
\(359\) | 1.01654e9 | 1.15956 | 0.579779 | − | 0.814774i | \(-0.303139\pi\) | ||||
0.579779 | + | 0.814774i | \(0.303139\pi\) | |||||||
\(360\) | −1.70896e8 | −0.193051 | ||||||||
\(361\) | 1.43323e9 | 1.60340 | ||||||||
\(362\) | 5.90213e8 | 0.653926 | ||||||||
\(363\) | −4.69300e8 | −0.514965 | ||||||||
\(364\) | 4.51421e7 | 0.0490600 | ||||||||
\(365\) | 6.49540e8 | 0.699167 | ||||||||
\(366\) | −1.83902e9 | −1.96066 | ||||||||
\(367\) | 8.06715e8 | 0.851901 | 0.425950 | − | 0.904747i | \(-0.359940\pi\) | ||||
0.425950 | + | 0.904747i | \(0.359940\pi\) | |||||||
\(368\) | 2.07602e9 | 2.17152 | ||||||||
\(369\) | −2.39149e7 | −0.0247786 | ||||||||
\(370\) | 1.67361e9 | 1.71770 | ||||||||
\(371\) | 3.99881e8 | 0.406557 | ||||||||
\(372\) | −2.31676e8 | −0.233336 | ||||||||
\(373\) | −1.13638e9 | −1.13381 | −0.566907 | − | 0.823782i | \(-0.691860\pi\) | ||||
−0.566907 | + | 0.823782i | \(0.691860\pi\) | |||||||
\(374\) | 8.12513e8 | 0.803119 | ||||||||
\(375\) | 3.83375e9 | 3.75417 | ||||||||
\(376\) | −5.09323e8 | −0.494124 | ||||||||
\(377\) | 3.59178e8 | 0.345235 | ||||||||
\(378\) | −4.37107e8 | −0.416262 | ||||||||
\(379\) | 1.89687e8 | 0.178979 | 0.0894893 | − | 0.995988i | \(-0.471477\pi\) | ||||
0.0894893 | + | 0.995988i | \(0.471477\pi\) | |||||||
\(380\) | −1.57335e9 | −1.47090 | ||||||||
\(381\) | −1.06180e9 | −0.983570 | ||||||||
\(382\) | −2.35241e9 | −2.15919 | ||||||||
\(383\) | 3.11890e7 | 0.0283665 | 0.0141833 | − | 0.999899i | \(-0.495485\pi\) | ||||
0.0141833 | + | 0.999899i | \(0.495485\pi\) | |||||||
\(384\) | 1.31903e9 | 1.18876 | ||||||||
\(385\) | 5.94799e8 | 0.531200 | ||||||||
\(386\) | 2.48912e8 | 0.220288 | ||||||||
\(387\) | −1.23081e8 | −0.107945 | ||||||||
\(388\) | 5.03140e8 | 0.437299 | ||||||||
\(389\) | −1.97500e9 | −1.70115 | −0.850575 | − | 0.525854i | \(-0.823746\pi\) | ||||
−0.850575 | + | 0.525854i | \(0.823746\pi\) | |||||||
\(390\) | 8.23645e8 | 0.703095 | ||||||||
\(391\) | −1.88801e9 | −1.59729 | ||||||||
\(392\) | −1.09819e8 | −0.0920821 | ||||||||
\(393\) | 9.49708e8 | 0.789253 | ||||||||
\(394\) | 9.68812e8 | 0.798000 | ||||||||
\(395\) | −2.54092e8 | −0.207444 | ||||||||
\(396\) | 6.41590e7 | 0.0519188 | ||||||||
\(397\) | −1.01548e9 | −0.814524 | −0.407262 | − | 0.913311i | \(-0.633516\pi\) | ||||
−0.407262 | + | 0.913311i | \(0.633516\pi\) | |||||||
\(398\) | −1.23784e8 | −0.0984178 | ||||||||
\(399\) | −8.31158e8 | −0.655056 | ||||||||
\(400\) | −4.46720e9 | −3.49000 | ||||||||
\(401\) | 1.88819e9 | 1.46231 | 0.731157 | − | 0.682210i | \(-0.238981\pi\) | ||||
0.731157 | + | 0.682210i | \(0.238981\pi\) | |||||||
\(402\) | −5.53426e8 | −0.424882 | ||||||||
\(403\) | −1.69150e8 | −0.128737 | ||||||||
\(404\) | −9.90347e8 | −0.747227 | ||||||||
\(405\) | −2.94293e9 | −2.20134 | ||||||||
\(406\) | 7.68674e8 | 0.570034 | ||||||||
\(407\) | 7.14235e8 | 0.525123 | ||||||||
\(408\) | −8.72600e8 | −0.636070 | ||||||||
\(409\) | −2.45154e9 | −1.77177 | −0.885886 | − | 0.463904i | \(-0.846448\pi\) | ||||
−0.885886 | + | 0.463904i | \(0.846448\pi\) | |||||||
\(410\) | −5.30779e8 | −0.380338 | ||||||||
\(411\) | −2.30818e9 | −1.63992 | ||||||||
\(412\) | −6.25869e8 | −0.440903 | ||||||||
\(413\) | 2.32799e7 | 0.0162613 | ||||||||
\(414\) | −4.67637e8 | −0.323898 | ||||||||
\(415\) | −2.17172e9 | −1.49154 | ||||||||
\(416\) | −3.53773e8 | −0.240934 | ||||||||
\(417\) | 1.91362e9 | 1.29235 | ||||||||
\(418\) | −2.10617e9 | −1.41051 | ||||||||
\(419\) | 1.83732e8 | 0.122021 | 0.0610105 | − | 0.998137i | \(-0.480568\pi\) | ||||
0.0610105 | + | 0.998137i | \(0.480568\pi\) | |||||||
\(420\) | 5.61945e8 | 0.370102 | ||||||||
\(421\) | −3.42562e8 | −0.223744 | −0.111872 | − | 0.993723i | \(-0.535685\pi\) | ||||
−0.111872 | + | 0.993723i | \(0.535685\pi\) | |||||||
\(422\) | 1.00230e9 | 0.649235 | ||||||||
\(423\) | 1.83480e8 | 0.117869 | ||||||||
\(424\) | −1.08824e9 | −0.693336 | ||||||||
\(425\) | 4.06263e9 | 2.56712 | ||||||||
\(426\) | −2.12784e9 | −1.33354 | ||||||||
\(427\) | −9.16074e8 | −0.569421 | ||||||||
\(428\) | −5.48322e8 | −0.338051 | ||||||||
\(429\) | 3.51502e8 | 0.214945 | ||||||||
\(430\) | −2.73171e9 | −1.65690 | ||||||||
\(431\) | −8.39710e8 | −0.505195 | −0.252597 | − | 0.967571i | \(-0.581285\pi\) | ||||
−0.252597 | + | 0.967571i | \(0.581285\pi\) | |||||||
\(432\) | 1.90239e9 | 1.13529 | ||||||||
\(433\) | 1.04393e9 | 0.617963 | 0.308981 | − | 0.951068i | \(-0.400012\pi\) | ||||
0.308981 | + | 0.951068i | \(0.400012\pi\) | |||||||
\(434\) | −3.61997e8 | −0.212564 | ||||||||
\(435\) | 4.47117e9 | 2.60441 | ||||||||
\(436\) | 1.05917e9 | 0.612015 | ||||||||
\(437\) | 4.89402e9 | 2.80531 | ||||||||
\(438\) | 8.21478e8 | 0.467129 | ||||||||
\(439\) | −6.15666e8 | −0.347312 | −0.173656 | − | 0.984806i | \(-0.555558\pi\) | ||||
−0.173656 | + | 0.984806i | \(0.555558\pi\) | |||||||
\(440\) | −1.61869e9 | −0.905899 | ||||||||
\(441\) | 3.95614e7 | 0.0219653 | ||||||||
\(442\) | 5.60460e8 | 0.308721 | ||||||||
\(443\) | 2.86221e7 | 0.0156419 | 0.00782093 | − | 0.999969i | \(-0.497510\pi\) | ||||
0.00782093 | + | 0.999969i | \(0.497510\pi\) | |||||||
\(444\) | 6.74784e8 | 0.365868 | ||||||||
\(445\) | −2.10905e8 | −0.113456 | ||||||||
\(446\) | 1.87974e9 | 1.00329 | ||||||||
\(447\) | −1.63405e9 | −0.865343 | ||||||||
\(448\) | 1.41311e8 | 0.0742511 | ||||||||
\(449\) | −1.95784e9 | −1.02074 | −0.510370 | − | 0.859955i | \(-0.670491\pi\) | ||||
−0.510370 | + | 0.859955i | \(0.670491\pi\) | |||||||
\(450\) | 1.00627e9 | 0.520558 | ||||||||
\(451\) | −2.26517e8 | −0.116274 | ||||||||
\(452\) | −9.08148e8 | −0.462564 | ||||||||
\(453\) | 3.97049e9 | 2.00678 | ||||||||
\(454\) | −1.25826e9 | −0.631067 | ||||||||
\(455\) | 4.10284e8 | 0.204195 | ||||||||
\(456\) | 2.26192e9 | 1.11712 | ||||||||
\(457\) | 1.67574e9 | 0.821299 | 0.410649 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410649 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(458\) | −1.36350e9 | −0.663171 | ||||||||
\(459\) | −1.73010e9 | −0.835078 | ||||||||
\(460\) | −3.30884e9 | −1.58498 | ||||||||
\(461\) | −1.66083e9 | −0.789537 | −0.394768 | − | 0.918781i | \(-0.629175\pi\) | ||||
−0.394768 | + | 0.918781i | \(0.629175\pi\) | |||||||
\(462\) | 7.52247e8 | 0.354906 | ||||||||
\(463\) | 6.87351e8 | 0.321844 | 0.160922 | − | 0.986967i | \(-0.448553\pi\) | ||||
0.160922 | + | 0.986967i | \(0.448553\pi\) | |||||||
\(464\) | −3.34544e9 | −1.55468 | ||||||||
\(465\) | −2.10564e9 | −0.971177 | ||||||||
\(466\) | 2.31047e9 | 1.05767 | ||||||||
\(467\) | 1.76187e9 | 0.800506 | 0.400253 | − | 0.916405i | \(-0.368922\pi\) | ||||
0.400253 | + | 0.916405i | \(0.368922\pi\) | |||||||
\(468\) | 4.42560e7 | 0.0199577 | ||||||||
\(469\) | −2.75679e8 | −0.123395 | ||||||||
\(470\) | 4.07225e9 | 1.80922 | ||||||||
\(471\) | 7.15360e7 | 0.0315465 | ||||||||
\(472\) | −6.33540e7 | −0.0277317 | ||||||||
\(473\) | −1.16580e9 | −0.506534 | ||||||||
\(474\) | −3.21352e8 | −0.138598 | ||||||||
\(475\) | −1.05310e10 | −4.50860 | ||||||||
\(476\) | 3.82383e8 | 0.162508 | ||||||||
\(477\) | 3.92031e8 | 0.165389 | ||||||||
\(478\) | −6.51428e8 | −0.272815 | ||||||||
\(479\) | 3.42957e8 | 0.142582 | 0.0712911 | − | 0.997456i | \(-0.477288\pi\) | ||||
0.0712911 | + | 0.997456i | \(0.477288\pi\) | |||||||
\(480\) | −4.40389e9 | −1.81757 | ||||||||
\(481\) | 4.92669e8 | 0.201859 | ||||||||
\(482\) | 1.91418e9 | 0.778608 | ||||||||
\(483\) | −1.74797e9 | −0.705859 | ||||||||
\(484\) | −5.59664e8 | −0.224372 | ||||||||
\(485\) | 4.57290e9 | 1.82010 | ||||||||
\(486\) | −9.34913e8 | −0.369440 | ||||||||
\(487\) | −6.48627e6 | −0.00254474 | −0.00127237 | − | 0.999999i | \(-0.500405\pi\) | ||||
−0.00127237 | + | 0.999999i | \(0.500405\pi\) | |||||||
\(488\) | 2.49301e9 | 0.971080 | ||||||||
\(489\) | 4.97995e9 | 1.92595 | ||||||||
\(490\) | 8.78045e8 | 0.337156 | ||||||||
\(491\) | −2.70060e9 | −1.02962 | −0.514808 | − | 0.857306i | \(-0.672137\pi\) | ||||
−0.514808 | + | 0.857306i | \(0.672137\pi\) | |||||||
\(492\) | −2.14005e8 | −0.0810115 | ||||||||
\(493\) | 3.04246e9 | 1.14357 | ||||||||
\(494\) | −1.45280e9 | −0.542203 | ||||||||
\(495\) | 5.83123e8 | 0.216094 | ||||||||
\(496\) | 1.57549e9 | 0.579736 | ||||||||
\(497\) | −1.05995e9 | −0.387290 | ||||||||
\(498\) | −2.74659e9 | −0.996532 | ||||||||
\(499\) | −4.53628e8 | −0.163436 | −0.0817180 | − | 0.996655i | \(-0.526041\pi\) | ||||
−0.0817180 | + | 0.996655i | \(0.526041\pi\) | |||||||
\(500\) | 4.57194e9 | 1.63571 | ||||||||
\(501\) | −1.51139e9 | −0.536963 | ||||||||
\(502\) | −2.38555e9 | −0.841638 | ||||||||
\(503\) | 2.63093e9 | 0.921767 | 0.460884 | − | 0.887461i | \(-0.347533\pi\) | ||||
0.460884 | + | 0.887461i | \(0.347533\pi\) | |||||||
\(504\) | −1.07663e8 | −0.0374592 | ||||||||
\(505\) | −9.00097e9 | −3.11007 | ||||||||
\(506\) | −4.42937e9 | −1.51990 | ||||||||
\(507\) | 2.42461e8 | 0.0826254 | ||||||||
\(508\) | −1.26625e9 | −0.428545 | ||||||||
\(509\) | 2.69397e9 | 0.905485 | 0.452742 | − | 0.891641i | \(-0.350446\pi\) | ||||
0.452742 | + | 0.891641i | \(0.350446\pi\) | |||||||
\(510\) | 6.97679e9 | 2.32895 | ||||||||
\(511\) | 4.09204e8 | 0.135665 | ||||||||
\(512\) | 8.50138e8 | 0.279927 | ||||||||
\(513\) | 4.48470e9 | 1.46664 | ||||||||
\(514\) | 4.98028e9 | 1.61764 | ||||||||
\(515\) | −5.68834e9 | −1.83510 | ||||||||
\(516\) | −1.10140e9 | −0.352917 | ||||||||
\(517\) | 1.73789e9 | 0.553101 | ||||||||
\(518\) | 1.05436e9 | 0.333298 | ||||||||
\(519\) | 2.19584e9 | 0.689469 | ||||||||
\(520\) | −1.11655e9 | −0.348230 | ||||||||
\(521\) | −2.33917e9 | −0.724651 | −0.362326 | − | 0.932052i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932052i | \(0.618017\pi\) | |||||||
\(522\) | 7.53584e8 | 0.231891 | ||||||||
\(523\) | 1.44074e9 | 0.440381 | 0.220191 | − | 0.975457i | \(-0.429332\pi\) | ||||
0.220191 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(524\) | 1.13257e9 | 0.343880 | ||||||||
\(525\) | 3.76129e9 | 1.13443 | ||||||||
\(526\) | 1.96263e9 | 0.588016 | ||||||||
\(527\) | −1.43281e9 | −0.426433 | ||||||||
\(528\) | −3.27395e9 | −0.967950 | ||||||||
\(529\) | 6.88753e9 | 2.02287 | ||||||||
\(530\) | 8.70091e9 | 2.53863 | ||||||||
\(531\) | 2.28228e7 | 0.00661514 | ||||||||
\(532\) | −9.91198e8 | −0.285410 | ||||||||
\(533\) | −1.56248e8 | −0.0446961 | ||||||||
\(534\) | −2.66733e8 | −0.0758023 | ||||||||
\(535\) | −4.98353e9 | −1.40702 | ||||||||
\(536\) | 7.50235e8 | 0.210436 | ||||||||
\(537\) | 6.71463e9 | 1.87116 | ||||||||
\(538\) | −8.80412e8 | −0.243752 | ||||||||
\(539\) | 3.74718e8 | 0.103073 | ||||||||
\(540\) | −3.03210e9 | −0.828639 | ||||||||
\(541\) | −2.49039e9 | −0.676202 | −0.338101 | − | 0.941110i | \(-0.609785\pi\) | ||||
−0.338101 | + | 0.941110i | \(0.609785\pi\) | |||||||
\(542\) | 6.24885e9 | 1.68579 | ||||||||
\(543\) | 2.16283e9 | 0.579725 | ||||||||
\(544\) | −2.99668e9 | −0.798076 | ||||||||
\(545\) | 9.62646e9 | 2.54729 | ||||||||
\(546\) | 5.18889e8 | 0.136427 | ||||||||
\(547\) | −3.38305e9 | −0.883798 | −0.441899 | − | 0.897065i | \(-0.645695\pi\) | ||||
−0.441899 | + | 0.897065i | \(0.645695\pi\) | |||||||
\(548\) | −2.75262e9 | −0.714520 | ||||||||
\(549\) | −8.98091e8 | −0.231642 | ||||||||
\(550\) | 9.53116e9 | 2.44273 | ||||||||
\(551\) | −7.88656e9 | −2.00843 | ||||||||
\(552\) | 4.75693e9 | 1.20376 | ||||||||
\(553\) | −1.60076e8 | −0.0402520 | ||||||||
\(554\) | 6.59834e9 | 1.64873 | ||||||||
\(555\) | 6.13291e9 | 1.52279 | ||||||||
\(556\) | 2.28208e9 | 0.563079 | ||||||||
\(557\) | −3.56492e9 | −0.874092 | −0.437046 | − | 0.899439i | \(-0.643975\pi\) | ||||
−0.437046 | + | 0.899439i | \(0.643975\pi\) | |||||||
\(558\) | −3.54890e8 | −0.0864717 | ||||||||
\(559\) | −8.04149e8 | −0.194713 | ||||||||
\(560\) | −3.82145e9 | −0.919539 | ||||||||
\(561\) | 2.97744e9 | 0.711989 | ||||||||
\(562\) | 7.17354e9 | 1.70473 | ||||||||
\(563\) | 1.98385e9 | 0.468522 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(564\) | 1.64189e9 | 0.385361 | ||||||||
\(565\) | −8.25389e9 | −1.92526 | ||||||||
\(566\) | −3.78539e7 | −0.00877512 | ||||||||
\(567\) | −1.85402e9 | −0.427144 | ||||||||
\(568\) | 2.88455e9 | 0.660478 | ||||||||
\(569\) | −2.67463e9 | −0.608653 | −0.304327 | − | 0.952568i | \(-0.598431\pi\) | ||||
−0.304327 | + | 0.952568i | \(0.598431\pi\) | |||||||
\(570\) | −1.80850e10 | −4.09031 | ||||||||
\(571\) | −3.17840e8 | −0.0714468 | −0.0357234 | − | 0.999362i | \(-0.511374\pi\) | ||||
−0.0357234 | + | 0.999362i | \(0.511374\pi\) | |||||||
\(572\) | 4.19184e8 | 0.0936522 | ||||||||
\(573\) | −8.62038e9 | −1.91419 | ||||||||
\(574\) | −3.34386e8 | −0.0737999 | ||||||||
\(575\) | −2.21472e10 | −4.85826 | ||||||||
\(576\) | 1.38537e8 | 0.0302055 | ||||||||
\(577\) | 7.42047e9 | 1.60811 | 0.804056 | − | 0.594554i | \(-0.202671\pi\) | ||||
0.804056 | + | 0.594554i | \(0.202671\pi\) | |||||||
\(578\) | −8.77402e8 | −0.188995 | ||||||||
\(579\) | 9.12135e8 | 0.195292 | ||||||||
\(580\) | 5.33209e9 | 1.13475 | ||||||||
\(581\) | −1.36816e9 | −0.289415 | ||||||||
\(582\) | 5.78337e9 | 1.21605 | ||||||||
\(583\) | 3.71324e9 | 0.776091 | ||||||||
\(584\) | −1.11361e9 | −0.231360 | ||||||||
\(585\) | 4.02229e8 | 0.0830669 | ||||||||
\(586\) | 7.20081e9 | 1.47822 | ||||||||
\(587\) | 6.74146e9 | 1.37569 | 0.687845 | − | 0.725858i | \(-0.258557\pi\) | ||||
0.687845 | + | 0.725858i | \(0.258557\pi\) | |||||||
\(588\) | 3.54020e8 | 0.0718137 | ||||||||
\(589\) | 3.71407e9 | 0.748939 | ||||||||
\(590\) | 5.06541e8 | 0.101539 | ||||||||
\(591\) | 3.55020e9 | 0.707451 | ||||||||
\(592\) | −4.58880e9 | −0.909019 | ||||||||
\(593\) | 2.47701e9 | 0.487794 | 0.243897 | − | 0.969801i | \(-0.421574\pi\) | ||||
0.243897 | + | 0.969801i | \(0.421574\pi\) | |||||||
\(594\) | −4.05892e9 | −0.794616 | ||||||||
\(595\) | 3.47536e9 | 0.676380 | ||||||||
\(596\) | −1.94868e9 | −0.377033 | ||||||||
\(597\) | −4.53605e8 | −0.0872504 | ||||||||
\(598\) | −3.05531e9 | −0.584254 | ||||||||
\(599\) | 4.69524e9 | 0.892614 | 0.446307 | − | 0.894880i | \(-0.352739\pi\) | ||||
0.446307 | + | 0.894880i | \(0.352739\pi\) | |||||||
\(600\) | −1.02360e10 | −1.93465 | ||||||||
\(601\) | −1.29838e9 | −0.243973 | −0.121986 | − | 0.992532i | \(-0.538926\pi\) | ||||
−0.121986 | + | 0.992532i | \(0.538926\pi\) | |||||||
\(602\) | −1.72095e9 | −0.321500 | ||||||||
\(603\) | −2.70267e8 | −0.0501975 | ||||||||
\(604\) | 4.73501e9 | 0.874362 | ||||||||
\(605\) | −5.08662e9 | −0.933868 | ||||||||
\(606\) | −1.13836e10 | −2.07790 | ||||||||
\(607\) | −2.74419e9 | −0.498028 | −0.249014 | − | 0.968500i | \(-0.580107\pi\) | ||||
−0.249014 | + | 0.968500i | \(0.580107\pi\) | |||||||
\(608\) | 7.76788e9 | 1.40165 | ||||||||
\(609\) | 2.81679e9 | 0.505353 | ||||||||
\(610\) | −1.99327e10 | −3.55558 | ||||||||
\(611\) | 1.19877e9 | 0.212614 | ||||||||
\(612\) | 3.74876e8 | 0.0661085 | ||||||||
\(613\) | −2.10437e9 | −0.368986 | −0.184493 | − | 0.982834i | \(-0.559064\pi\) | ||||
−0.184493 | + | 0.982834i | \(0.559064\pi\) | |||||||
\(614\) | −7.67538e9 | −1.33817 | ||||||||
\(615\) | −1.94503e9 | −0.337182 | ||||||||
\(616\) | −1.01976e9 | −0.175779 | ||||||||
\(617\) | −4.96827e9 | −0.851545 | −0.425772 | − | 0.904830i | \(-0.639998\pi\) | ||||
−0.425772 | + | 0.904830i | \(0.639998\pi\) | |||||||
\(618\) | −7.19408e9 | −1.22607 | ||||||||
\(619\) | 8.25149e9 | 1.39835 | 0.699174 | − | 0.714952i | \(-0.253551\pi\) | ||||
0.699174 | + | 0.714952i | \(0.253551\pi\) | |||||||
\(620\) | −2.51108e9 | −0.423145 | ||||||||
\(621\) | 9.43154e9 | 1.58038 | ||||||||
\(622\) | −8.84812e9 | −1.47430 | ||||||||
\(623\) | −1.32868e8 | −0.0220147 | ||||||||
\(624\) | −2.25832e9 | −0.372083 | ||||||||
\(625\) | 2.44980e10 | 4.01375 | ||||||||
\(626\) | −7.69471e9 | −1.25367 | ||||||||
\(627\) | −7.71802e9 | −1.25046 | ||||||||
\(628\) | 8.53102e7 | 0.0137449 | ||||||||
\(629\) | 4.17322e9 | 0.668642 | ||||||||
\(630\) | 8.60808e8 | 0.137156 | ||||||||
\(631\) | −1.03604e10 | −1.64162 | −0.820811 | − | 0.571200i | \(-0.806478\pi\) | ||||
−0.820811 | + | 0.571200i | \(0.806478\pi\) | |||||||
\(632\) | 4.35631e8 | 0.0686451 | ||||||||
\(633\) | 3.67290e9 | 0.575567 | ||||||||
\(634\) | −1.29971e10 | −2.02551 | ||||||||
\(635\) | −1.15086e10 | −1.78367 | ||||||||
\(636\) | 3.50813e9 | 0.540724 | ||||||||
\(637\) | 2.58475e8 | 0.0396214 | ||||||||
\(638\) | 7.13779e9 | 1.08816 | ||||||||
\(639\) | −1.03914e9 | −0.157551 | ||||||||
\(640\) | 1.42966e10 | 2.15577 | ||||||||
\(641\) | 4.44804e9 | 0.667061 | 0.333531 | − | 0.942739i | \(-0.391760\pi\) | ||||
0.333531 | + | 0.942739i | \(0.391760\pi\) | |||||||
\(642\) | −6.30271e9 | −0.940058 | ||||||||
\(643\) | 6.76162e9 | 1.00303 | 0.501513 | − | 0.865150i | \(-0.332777\pi\) | ||||
0.501513 | + | 0.865150i | \(0.332777\pi\) | |||||||
\(644\) | −2.08454e9 | −0.307545 | ||||||||
\(645\) | −1.00103e10 | −1.46889 | ||||||||
\(646\) | −1.23062e10 | −1.79601 | ||||||||
\(647\) | −1.96787e9 | −0.285648 | −0.142824 | − | 0.989748i | \(-0.545618\pi\) | ||||
−0.142824 | + | 0.989748i | \(0.545618\pi\) | |||||||
\(648\) | 5.04555e9 | 0.728444 | ||||||||
\(649\) | 2.16173e8 | 0.0310417 | ||||||||
\(650\) | 6.57445e9 | 0.938994 | ||||||||
\(651\) | −1.32653e9 | −0.188445 | ||||||||
\(652\) | 5.93884e9 | 0.839141 | ||||||||
\(653\) | 9.11572e9 | 1.28114 | 0.640568 | − | 0.767902i | \(-0.278699\pi\) | ||||
0.640568 | + | 0.767902i | \(0.278699\pi\) | |||||||
\(654\) | 1.21747e10 | 1.70190 | ||||||||
\(655\) | 1.02936e10 | 1.43128 | ||||||||
\(656\) | 1.45532e9 | 0.201278 | ||||||||
\(657\) | 4.01171e8 | 0.0551888 | ||||||||
\(658\) | 2.56548e9 | 0.351057 | ||||||||
\(659\) | 2.16900e9 | 0.295230 | 0.147615 | − | 0.989045i | \(-0.452840\pi\) | ||||
0.147615 | + | 0.989045i | \(0.452840\pi\) | |||||||
\(660\) | 5.21814e9 | 0.706500 | ||||||||
\(661\) | −1.00456e9 | −0.135292 | −0.0676459 | − | 0.997709i | \(-0.521549\pi\) | ||||
−0.0676459 | + | 0.997709i | \(0.521549\pi\) | |||||||
\(662\) | 1.75376e9 | 0.234945 | ||||||||
\(663\) | 2.05380e9 | 0.273691 | ||||||||
\(664\) | 3.72333e9 | 0.493564 | ||||||||
\(665\) | −9.00870e9 | −1.18792 | ||||||||
\(666\) | 1.03366e9 | 0.135587 | ||||||||
\(667\) | −1.65858e10 | −2.16420 | ||||||||
\(668\) | −1.80241e9 | −0.233957 | ||||||||
\(669\) | 6.88827e9 | 0.889444 | ||||||||
\(670\) | −5.99843e9 | −0.770506 | ||||||||
\(671\) | −8.50654e9 | −1.08699 | ||||||||
\(672\) | −2.77441e9 | −0.352677 | ||||||||
\(673\) | 1.05631e10 | 1.33579 | 0.667894 | − | 0.744257i | \(-0.267196\pi\) | ||||
0.667894 | + | 0.744257i | \(0.267196\pi\) | |||||||
\(674\) | 1.53831e9 | 0.193523 | ||||||||
\(675\) | −2.02949e10 | −2.53994 | ||||||||
\(676\) | 2.89147e8 | 0.0360002 | ||||||||
\(677\) | 4.37092e9 | 0.541393 | 0.270697 | − | 0.962665i | \(-0.412746\pi\) | ||||
0.270697 | + | 0.962665i | \(0.412746\pi\) | |||||||
\(678\) | −1.04387e10 | −1.28631 | ||||||||
\(679\) | 2.88088e9 | 0.353168 | ||||||||
\(680\) | −9.45788e9 | −1.15349 | ||||||||
\(681\) | −4.61088e9 | −0.559460 | ||||||||
\(682\) | −3.36145e9 | −0.405771 | ||||||||
\(683\) | 2.59419e9 | 0.311551 | 0.155776 | − | 0.987792i | \(-0.450212\pi\) | ||||
0.155776 | + | 0.987792i | \(0.450212\pi\) | |||||||
\(684\) | −9.71739e8 | −0.116106 | ||||||||
\(685\) | −2.50178e10 | −2.97394 | ||||||||
\(686\) | 5.53160e8 | 0.0654209 | ||||||||
\(687\) | −4.99652e9 | −0.587921 | ||||||||
\(688\) | 7.48998e9 | 0.876842 | ||||||||
\(689\) | 2.56133e9 | 0.298331 | ||||||||
\(690\) | −3.80336e10 | −4.40753 | ||||||||
\(691\) | −5.26255e9 | −0.606769 | −0.303384 | − | 0.952868i | \(-0.598117\pi\) | ||||
−0.303384 | + | 0.952868i | \(0.598117\pi\) | |||||||
\(692\) | 2.61865e9 | 0.300404 | ||||||||
\(693\) | 3.67362e8 | 0.0419303 | ||||||||
\(694\) | 1.98219e10 | 2.25106 | ||||||||
\(695\) | 2.07412e10 | 2.34362 | ||||||||
\(696\) | −7.66565e9 | −0.861820 | ||||||||
\(697\) | −1.32352e9 | −0.148053 | ||||||||
\(698\) | −5.35636e8 | −0.0596178 | ||||||||
\(699\) | 8.46669e9 | 0.937656 | ||||||||
\(700\) | 4.48552e9 | 0.494277 | ||||||||
\(701\) | −8.38476e8 | −0.0919343 | −0.0459671 | − | 0.998943i | \(-0.514637\pi\) | ||||
−0.0459671 | + | 0.998943i | \(0.514637\pi\) | |||||||
\(702\) | −2.79978e9 | −0.305453 | ||||||||
\(703\) | −1.08177e10 | −1.17433 | ||||||||
\(704\) | 1.31219e9 | 0.141740 | ||||||||
\(705\) | 1.49227e10 | 1.60393 | ||||||||
\(706\) | 1.09356e10 | 1.16957 | ||||||||
\(707\) | −5.67053e9 | −0.603470 | ||||||||
\(708\) | 2.04233e8 | 0.0216276 | ||||||||
\(709\) | 9.93910e8 | 0.104733 | 0.0523667 | − | 0.998628i | \(-0.483324\pi\) | ||||
0.0523667 | + | 0.998628i | \(0.483324\pi\) | |||||||
\(710\) | −2.30631e10 | −2.41832 | ||||||||
\(711\) | −1.56933e8 | −0.0163746 | ||||||||
\(712\) | 3.61589e8 | 0.0375435 | ||||||||
\(713\) | 7.81087e9 | 0.807023 | ||||||||
\(714\) | 4.39531e9 | 0.451904 | ||||||||
\(715\) | 3.80984e9 | 0.389794 | ||||||||
\(716\) | 8.00753e9 | 0.815273 | ||||||||
\(717\) | −2.38715e9 | −0.241859 | ||||||||
\(718\) | 1.39345e10 | 1.40493 | ||||||||
\(719\) | 1.44874e10 | 1.45358 | 0.726791 | − | 0.686859i | \(-0.241011\pi\) | ||||
0.726791 | + | 0.686859i | \(0.241011\pi\) | |||||||
\(720\) | −3.74643e9 | −0.374071 | ||||||||
\(721\) | −3.58360e9 | −0.356079 | ||||||||
\(722\) | 1.96465e10 | 1.94270 | ||||||||
\(723\) | 7.01450e9 | 0.690260 | ||||||||
\(724\) | 2.57928e9 | 0.252588 | ||||||||
\(725\) | 3.56895e10 | 3.47822 | ||||||||
\(726\) | −6.43308e9 | −0.623937 | ||||||||
\(727\) | −2.04576e9 | −0.197462 | −0.0987311 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987311 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(728\) | −7.03416e8 | −0.0675698 | ||||||||
\(729\) | 8.39543e9 | 0.802596 | ||||||||
\(730\) | 8.90378e9 | 0.847119 | ||||||||
\(731\) | −6.81165e9 | −0.644973 | ||||||||
\(732\) | −8.03667e9 | −0.757334 | ||||||||
\(733\) | −3.60556e9 | −0.338150 | −0.169075 | − | 0.985603i | \(-0.554078\pi\) | ||||
−0.169075 | + | 0.985603i | \(0.554078\pi\) | |||||||
\(734\) | 1.10583e10 | 1.03217 | ||||||||
\(735\) | 3.21758e9 | 0.298899 | ||||||||
\(736\) | 1.63362e10 | 1.51036 | ||||||||
\(737\) | −2.55991e9 | −0.235553 | ||||||||
\(738\) | −3.27821e8 | −0.0300220 | ||||||||
\(739\) | −1.83001e10 | −1.66800 | −0.834002 | − | 0.551761i | \(-0.813956\pi\) | ||||
−0.834002 | + | 0.551761i | \(0.813956\pi\) | |||||||
\(740\) | 7.31380e9 | 0.663487 | ||||||||
\(741\) | −5.32378e9 | −0.480680 | ||||||||
\(742\) | 5.48149e9 | 0.492589 | ||||||||
\(743\) | 8.66858e8 | 0.0775331 | 0.0387665 | − | 0.999248i | \(-0.487657\pi\) | ||||
0.0387665 | + | 0.999248i | \(0.487657\pi\) | |||||||
\(744\) | 3.61004e9 | 0.321371 | ||||||||
\(745\) | −1.77110e10 | −1.56926 | ||||||||
\(746\) | −1.55772e10 | −1.37374 | ||||||||
\(747\) | −1.34130e9 | −0.117735 | ||||||||
\(748\) | 3.55075e9 | 0.310216 | ||||||||
\(749\) | −3.13958e9 | −0.273014 | ||||||||
\(750\) | 5.25523e10 | 4.54860 | ||||||||
\(751\) | 4.42366e9 | 0.381103 | 0.190552 | − | 0.981677i | \(-0.438972\pi\) | ||||
0.190552 | + | 0.981677i | \(0.438972\pi\) | |||||||
\(752\) | −1.11655e10 | −0.957452 | ||||||||
\(753\) | −8.74181e9 | −0.746138 | ||||||||
\(754\) | 4.92354e9 | 0.418291 | ||||||||
\(755\) | 4.30351e10 | 3.63922 | ||||||||
\(756\) | −1.91019e9 | −0.160787 | ||||||||
\(757\) | 3.88102e9 | 0.325170 | 0.162585 | − | 0.986695i | \(-0.448017\pi\) | ||||
0.162585 | + | 0.986695i | \(0.448017\pi\) | |||||||
\(758\) | 2.60020e9 | 0.216853 | ||||||||
\(759\) | −1.62314e10 | −1.34744 | ||||||||
\(760\) | 2.45164e10 | 2.02586 | ||||||||
\(761\) | −2.25509e10 | −1.85488 | −0.927442 | − | 0.373967i | \(-0.877997\pi\) | ||||
−0.927442 | + | 0.373967i | \(0.877997\pi\) | |||||||
\(762\) | −1.45550e10 | −1.19171 | ||||||||
\(763\) | 6.06458e9 | 0.494271 | ||||||||
\(764\) | −1.02802e10 | −0.834019 | ||||||||
\(765\) | 3.40714e9 | 0.275153 | ||||||||
\(766\) | 4.27534e8 | 0.0343692 | ||||||||
\(767\) | 1.49113e8 | 0.0119325 | ||||||||
\(768\) | 1.54321e10 | 1.22931 | ||||||||
\(769\) | −4.41602e9 | −0.350178 | −0.175089 | − | 0.984553i | \(-0.556021\pi\) | ||||
−0.175089 | + | 0.984553i | \(0.556021\pi\) | |||||||
\(770\) | 8.15340e9 | 0.643608 | ||||||||
\(771\) | 1.82502e10 | 1.43409 | ||||||||
\(772\) | 1.08777e9 | 0.0850893 | ||||||||
\(773\) | −1.44577e10 | −1.12583 | −0.562913 | − | 0.826516i | \(-0.690320\pi\) | ||||
−0.562913 | + | 0.826516i | \(0.690320\pi\) | |||||||
\(774\) | −1.68717e9 | −0.130787 | ||||||||
\(775\) | −1.68075e10 | −1.29702 | ||||||||
\(776\) | −7.84006e9 | −0.602287 | ||||||||
\(777\) | 3.86368e9 | 0.295479 | ||||||||
\(778\) | −2.70729e10 | −2.06113 | ||||||||
\(779\) | 3.43078e9 | 0.260023 | ||||||||
\(780\) | 3.59940e9 | 0.271581 | ||||||||
\(781\) | −9.84251e9 | −0.739311 | ||||||||
\(782\) | −2.58804e10 | −1.93530 | ||||||||
\(783\) | −1.51986e10 | −1.13146 | ||||||||
\(784\) | −2.40748e9 | −0.178425 | ||||||||
\(785\) | 7.75360e8 | 0.0572083 | ||||||||
\(786\) | 1.30184e10 | 0.956268 | ||||||||
\(787\) | 2.10751e10 | 1.54120 | 0.770598 | − | 0.637321i | \(-0.219958\pi\) | ||||
0.770598 | + | 0.637321i | \(0.219958\pi\) | |||||||
\(788\) | 4.23379e9 | 0.308239 | ||||||||
\(789\) | 7.19205e9 | 0.521295 | ||||||||
\(790\) | −3.48305e9 | −0.251342 | ||||||||
\(791\) | −5.19987e9 | −0.373572 | ||||||||
\(792\) | −9.99742e8 | −0.0715072 | ||||||||
\(793\) | −5.86768e9 | −0.417840 | ||||||||
\(794\) | −1.39200e10 | −0.986886 | ||||||||
\(795\) | 3.18844e10 | 2.25057 | ||||||||
\(796\) | −5.40946e8 | −0.0380153 | ||||||||
\(797\) | −1.76476e10 | −1.23476 | −0.617380 | − | 0.786665i | \(-0.711806\pi\) | ||||
−0.617380 | + | 0.786665i | \(0.711806\pi\) | |||||||
\(798\) | −1.13934e10 | −0.793674 | ||||||||
\(799\) | 1.01543e10 | 0.704267 | ||||||||
\(800\) | −3.51524e10 | −2.42740 | ||||||||
\(801\) | −1.30260e8 | −0.00895564 | ||||||||
\(802\) | 2.58830e10 | 1.77176 | ||||||||
\(803\) | 3.79981e9 | 0.258975 | ||||||||
\(804\) | −2.41852e9 | −0.164117 | ||||||||
\(805\) | −1.89457e10 | −1.28005 | ||||||||
\(806\) | −2.31868e9 | −0.155980 | ||||||||
\(807\) | −3.22626e9 | −0.216094 | ||||||||
\(808\) | 1.54318e10 | 1.02915 | ||||||||
\(809\) | −5.90754e9 | −0.392272 | −0.196136 | − | 0.980577i | \(-0.562839\pi\) | ||||
−0.196136 | + | 0.980577i | \(0.562839\pi\) | |||||||
\(810\) | −4.03412e10 | −2.66717 | ||||||||
\(811\) | −2.45675e10 | −1.61729 | −0.808646 | − | 0.588295i | \(-0.799799\pi\) | ||||
−0.808646 | + | 0.588295i | \(0.799799\pi\) | |||||||
\(812\) | 3.35917e9 | 0.220184 | ||||||||
\(813\) | 2.28988e10 | 1.49450 | ||||||||
\(814\) | 9.79060e9 | 0.636245 | ||||||||
\(815\) | 5.39764e10 | 3.49263 | ||||||||
\(816\) | −1.91294e10 | −1.23250 | ||||||||
\(817\) | 1.76569e10 | 1.13276 | ||||||||
\(818\) | −3.36053e10 | −2.14670 | ||||||||
\(819\) | 2.53401e8 | 0.0161181 | ||||||||
\(820\) | −2.31955e9 | −0.146911 | ||||||||
\(821\) | −1.65259e10 | −1.04223 | −0.521115 | − | 0.853487i | \(-0.674484\pi\) | ||||
−0.521115 | + | 0.853487i | \(0.674484\pi\) | |||||||
\(822\) | −3.16401e10 | −1.98695 | ||||||||
\(823\) | 9.90852e9 | 0.619597 | 0.309799 | − | 0.950802i | \(-0.399738\pi\) | ||||
0.309799 | + | 0.950802i | \(0.399738\pi\) | |||||||
\(824\) | 9.75244e9 | 0.607251 | ||||||||
\(825\) | 3.49268e10 | 2.16556 | ||||||||
\(826\) | 3.19116e8 | 0.0197024 | ||||||||
\(827\) | −1.09902e10 | −0.675671 | −0.337835 | − | 0.941205i | \(-0.609695\pi\) | ||||
−0.337835 | + | 0.941205i | \(0.609695\pi\) | |||||||
\(828\) | −2.04361e9 | −0.125110 | ||||||||
\(829\) | −1.40135e10 | −0.854294 | −0.427147 | − | 0.904182i | \(-0.640481\pi\) | ||||
−0.427147 | + | 0.904182i | \(0.640481\pi\) | |||||||
\(830\) | −2.97696e10 | −1.80717 | ||||||||
\(831\) | 2.41795e10 | 1.46165 | ||||||||
\(832\) | 9.05132e8 | 0.0544854 | ||||||||
\(833\) | 2.18945e9 | 0.131243 | ||||||||
\(834\) | 2.62315e10 | 1.56582 | ||||||||
\(835\) | −1.63816e10 | −0.973761 | ||||||||
\(836\) | −9.20412e9 | −0.544829 | ||||||||
\(837\) | 7.15760e9 | 0.421918 | ||||||||
\(838\) | 2.51856e9 | 0.147842 | ||||||||
\(839\) | 4.20630e9 | 0.245886 | 0.122943 | − | 0.992414i | \(-0.460767\pi\) | ||||
0.122943 | + | 0.992414i | \(0.460767\pi\) | |||||||
\(840\) | −8.75636e9 | −0.509737 | ||||||||
\(841\) | 9.47766e9 | 0.549433 | ||||||||
\(842\) | −4.69578e9 | −0.271091 | ||||||||
\(843\) | 2.62874e10 | 1.51130 | ||||||||
\(844\) | 4.38011e9 | 0.250777 | ||||||||
\(845\) | 2.62797e9 | 0.149838 | ||||||||
\(846\) | 2.51511e9 | 0.142811 | ||||||||
\(847\) | −3.20452e9 | −0.181206 | ||||||||
\(848\) | −2.38567e10 | −1.34346 | ||||||||
\(849\) | −1.38715e8 | −0.00777941 | ||||||||
\(850\) | 5.56898e10 | 3.11035 | ||||||||
\(851\) | −2.27500e10 | −1.26540 | ||||||||
\(852\) | −9.29885e9 | −0.515099 | ||||||||
\(853\) | −5.04693e9 | −0.278423 | −0.139212 | − | 0.990263i | \(-0.544457\pi\) | ||||
−0.139212 | + | 0.990263i | \(0.544457\pi\) | |||||||
\(854\) | −1.25574e10 | −0.689916 | ||||||||
\(855\) | −8.83185e9 | −0.483248 | ||||||||
\(856\) | 8.54408e9 | 0.465594 | ||||||||
\(857\) | −2.34862e10 | −1.27462 | −0.637310 | − | 0.770607i | \(-0.719953\pi\) | ||||
−0.637310 | + | 0.770607i | \(0.719953\pi\) | |||||||
\(858\) | 4.81833e9 | 0.260430 | ||||||||
\(859\) | −3.57907e10 | −1.92661 | −0.963305 | − | 0.268408i | \(-0.913503\pi\) | ||||
−0.963305 | + | 0.268408i | \(0.913503\pi\) | |||||||
\(860\) | −1.19378e10 | −0.640000 | ||||||||
\(861\) | −1.22535e9 | −0.0654259 | ||||||||
\(862\) | −1.15106e10 | −0.612100 | ||||||||
\(863\) | −1.96959e10 | −1.04313 | −0.521565 | − | 0.853212i | \(-0.674651\pi\) | ||||
−0.521565 | + | 0.853212i | \(0.674651\pi\) | |||||||
\(864\) | 1.49699e10 | 0.789627 | ||||||||
\(865\) | 2.38001e10 | 1.25032 | ||||||||
\(866\) | 1.43100e10 | 0.748731 | ||||||||
\(867\) | −3.21523e9 | −0.167550 | ||||||||
\(868\) | −1.58195e9 | −0.0821060 | ||||||||
\(869\) | −1.48644e9 | −0.0768384 | ||||||||
\(870\) | 6.12900e10 | 3.15553 | ||||||||
\(871\) | −1.76579e9 | −0.0905474 | ||||||||
\(872\) | −1.65042e10 | −0.842921 | ||||||||
\(873\) | 2.82433e9 | 0.143670 | ||||||||
\(874\) | 6.70863e10 | 3.39894 | ||||||||
\(875\) | 2.61780e10 | 1.32102 | ||||||||
\(876\) | 3.58993e9 | 0.180435 | ||||||||
\(877\) | −1.17028e10 | −0.585857 | −0.292929 | − | 0.956134i | \(-0.594630\pi\) | ||||
−0.292929 | + | 0.956134i | \(0.594630\pi\) | |||||||
\(878\) | −8.43944e9 | −0.420807 | ||||||||
\(879\) | 2.63873e10 | 1.31049 | ||||||||
\(880\) | −3.54855e10 | −1.75534 | ||||||||
\(881\) | −4.39739e9 | −0.216660 | −0.108330 | − | 0.994115i | \(-0.534550\pi\) | ||||
−0.108330 | + | 0.994115i | \(0.534550\pi\) | |||||||
\(882\) | 5.42301e8 | 0.0266134 | ||||||||
\(883\) | −3.98937e10 | −1.95003 | −0.975017 | − | 0.222131i | \(-0.928699\pi\) | ||||
−0.975017 | + | 0.222131i | \(0.928699\pi\) | |||||||
\(884\) | 2.44925e9 | 0.119248 | ||||||||
\(885\) | 1.85621e9 | 0.0900174 | ||||||||
\(886\) | 3.92346e8 | 0.0189518 | ||||||||
\(887\) | 3.19786e10 | 1.53860 | 0.769302 | − | 0.638885i | \(-0.220604\pi\) | ||||
0.769302 | + | 0.638885i | \(0.220604\pi\) | |||||||
\(888\) | −1.05146e10 | −0.503906 | ||||||||
\(889\) | −7.25029e9 | −0.346098 | ||||||||
\(890\) | −2.89105e9 | −0.137464 | ||||||||
\(891\) | −1.72162e10 | −0.815389 | ||||||||
\(892\) | 8.21461e9 | 0.387534 | ||||||||
\(893\) | −2.63217e10 | −1.23690 | ||||||||
\(894\) | −2.23992e10 | −1.04846 | ||||||||
\(895\) | 7.27781e10 | 3.39328 | ||||||||
\(896\) | 9.00673e9 | 0.418301 | ||||||||
\(897\) | −1.11962e10 | −0.517959 | ||||||||
\(898\) | −2.68377e10 | −1.23674 | ||||||||
\(899\) | −1.25870e10 | −0.577780 | ||||||||
\(900\) | 4.39747e9 | 0.201073 | ||||||||
\(901\) | 2.16961e10 | 0.988201 | ||||||||
\(902\) | −3.10506e9 | −0.140879 | ||||||||
\(903\) | −6.30641e9 | −0.285020 | ||||||||
\(904\) | 1.41510e10 | 0.637084 | ||||||||
\(905\) | 2.34423e10 | 1.05131 | ||||||||
\(906\) | 5.44267e10 | 2.43144 | ||||||||
\(907\) | −3.40207e10 | −1.51397 | −0.756985 | − | 0.653432i | \(-0.773329\pi\) | ||||
−0.756985 | + | 0.653432i | \(0.773329\pi\) | |||||||
\(908\) | −5.49871e9 | −0.243759 | ||||||||
\(909\) | −5.55921e9 | −0.245493 | ||||||||
\(910\) | 5.62410e9 | 0.247405 | ||||||||
\(911\) | −9.45648e9 | −0.414396 | −0.207198 | − | 0.978299i | \(-0.566434\pi\) | ||||
−0.207198 | + | 0.978299i | \(0.566434\pi\) | |||||||
\(912\) | 4.95865e10 | 2.16462 | ||||||||
\(913\) | −1.27046e10 | −0.552475 | ||||||||
\(914\) | 2.29708e10 | 0.995095 | ||||||||
\(915\) | −7.30429e10 | −3.15213 | ||||||||
\(916\) | −5.95860e9 | −0.256159 | ||||||||
\(917\) | 6.48489e9 | 0.277722 | ||||||||
\(918\) | −2.37159e10 | −1.01179 | ||||||||
\(919\) | −4.30221e9 | −0.182847 | −0.0914234 | − | 0.995812i | \(-0.529142\pi\) | ||||
−0.0914234 | + | 0.995812i | \(0.529142\pi\) | |||||||
\(920\) | 5.15591e10 | 2.18297 | ||||||||
\(921\) | −2.81263e10 | −1.18633 | ||||||||
\(922\) | −2.27664e10 | −0.956612 | ||||||||
\(923\) | −6.78922e9 | −0.284193 | ||||||||
\(924\) | 3.28738e9 | 0.137088 | ||||||||
\(925\) | 4.89538e10 | 2.03371 | ||||||||
\(926\) | 9.42208e9 | 0.389950 | ||||||||
\(927\) | −3.51325e9 | −0.144854 | ||||||||
\(928\) | −2.63253e10 | −1.08132 | ||||||||
\(929\) | 1.94090e10 | 0.794235 | 0.397118 | − | 0.917768i | \(-0.370010\pi\) | ||||
0.397118 | + | 0.917768i | \(0.370010\pi\) | |||||||
\(930\) | −2.88637e10 | −1.17669 | ||||||||
\(931\) | −5.67540e9 | −0.230501 | ||||||||
\(932\) | 1.00969e10 | 0.408540 | ||||||||
\(933\) | −3.24238e10 | −1.30701 | ||||||||
\(934\) | 2.41514e10 | 0.969902 | ||||||||
\(935\) | 3.22717e10 | 1.29116 | ||||||||
\(936\) | −6.89607e8 | −0.0274876 | ||||||||
\(937\) | 3.16846e10 | 1.25823 | 0.629114 | − | 0.777313i | \(-0.283418\pi\) | ||||
0.629114 | + | 0.777313i | \(0.283418\pi\) | |||||||
\(938\) | −3.77896e9 | −0.149507 | ||||||||
\(939\) | −2.81972e10 | −1.11141 | ||||||||
\(940\) | 1.77961e10 | 0.698837 | ||||||||
\(941\) | 1.04030e10 | 0.407001 | 0.203501 | − | 0.979075i | \(-0.434768\pi\) | ||||
0.203501 | + | 0.979075i | \(0.434768\pi\) | |||||||
\(942\) | 9.80602e8 | 0.0382221 | ||||||||
\(943\) | 7.21510e9 | 0.280189 | ||||||||
\(944\) | −1.38887e9 | −0.0537351 | ||||||||
\(945\) | −1.73612e10 | −0.669219 | ||||||||
\(946\) | −1.59805e10 | −0.613723 | ||||||||
\(947\) | −2.96702e10 | −1.13526 | −0.567631 | − | 0.823283i | \(-0.692140\pi\) | ||||
−0.567631 | + | 0.823283i | \(0.692140\pi\) | |||||||
\(948\) | −1.40433e9 | −0.0535355 | ||||||||
\(949\) | 2.62105e9 | 0.0995507 | ||||||||
\(950\) | −1.44357e11 | −5.46267 | ||||||||
\(951\) | −4.76277e10 | −1.79568 | ||||||||
\(952\) | −5.95838e9 | −0.223820 | ||||||||
\(953\) | 3.63188e10 | 1.35927 | 0.679637 | − | 0.733549i | \(-0.262137\pi\) | ||||
0.679637 | + | 0.733549i | \(0.262137\pi\) | |||||||
\(954\) | 5.37388e9 | 0.200387 | ||||||||
\(955\) | −9.34340e10 | −3.47131 | ||||||||
\(956\) | −2.84679e9 | −0.105379 | ||||||||
\(957\) | 2.61564e10 | 0.964685 | ||||||||
\(958\) | 4.70119e9 | 0.172754 | ||||||||
\(959\) | −1.57610e10 | −0.577055 | ||||||||
\(960\) | 1.12674e10 | 0.411031 | ||||||||
\(961\) | −2.15849e10 | −0.784547 | ||||||||
\(962\) | 6.75341e9 | 0.244574 | ||||||||
\(963\) | −3.07795e9 | −0.111063 | ||||||||
\(964\) | 8.36514e9 | 0.300748 | ||||||||
\(965\) | 9.88639e9 | 0.354154 | ||||||||
\(966\) | −2.39608e10 | −0.855227 | ||||||||
\(967\) | −1.26084e10 | −0.448403 | −0.224202 | − | 0.974543i | \(-0.571977\pi\) | ||||
−0.224202 | + | 0.974543i | \(0.571977\pi\) | |||||||
\(968\) | 8.72082e9 | 0.309025 | ||||||||
\(969\) | −4.50957e10 | −1.59222 | ||||||||
\(970\) | 6.26844e10 | 2.20525 | ||||||||
\(971\) | −4.35074e10 | −1.52509 | −0.762546 | − | 0.646935i | \(-0.776051\pi\) | ||||
−0.762546 | + | 0.646935i | \(0.776051\pi\) | |||||||
\(972\) | −4.08565e9 | −0.142702 | ||||||||
\(973\) | 1.30667e10 | 0.454750 | ||||||||
\(974\) | −8.89126e7 | −0.00308324 | ||||||||
\(975\) | 2.40920e10 | 0.832447 | ||||||||
\(976\) | 5.46526e10 | 1.88164 | ||||||||
\(977\) | −1.29363e10 | −0.443793 | −0.221897 | − | 0.975070i | \(-0.571225\pi\) | ||||
−0.221897 | + | 0.975070i | \(0.571225\pi\) | |||||||
\(978\) | 6.82643e10 | 2.33350 | ||||||||
\(979\) | −1.23380e9 | −0.0420246 | ||||||||
\(980\) | 3.83713e9 | 0.130231 | ||||||||
\(981\) | 5.94553e9 | 0.201071 | ||||||||
\(982\) | −3.70193e10 | −1.24749 | ||||||||
\(983\) | −3.80363e10 | −1.27721 | −0.638604 | − | 0.769536i | \(-0.720488\pi\) | ||||
−0.638604 | + | 0.769536i | \(0.720488\pi\) | |||||||
\(984\) | 3.33468e9 | 0.111576 | ||||||||
\(985\) | 3.84797e10 | 1.28293 | ||||||||
\(986\) | 4.17055e10 | 1.38556 | ||||||||
\(987\) | 9.40115e9 | 0.311223 | ||||||||
\(988\) | −6.34887e9 | −0.209434 | ||||||||
\(989\) | 3.71333e10 | 1.22061 | ||||||||
\(990\) | 7.99334e9 | 0.261821 | ||||||||
\(991\) | 4.33456e10 | 1.41477 | 0.707387 | − | 0.706827i | \(-0.249874\pi\) | ||||
0.707387 | + | 0.706827i | \(0.249874\pi\) | |||||||
\(992\) | 1.23976e10 | 0.403223 | ||||||||
\(993\) | 6.42662e9 | 0.208286 | ||||||||
\(994\) | −1.45295e10 | −0.469245 | ||||||||
\(995\) | −4.91650e9 | −0.158225 | ||||||||
\(996\) | −1.20028e10 | −0.384925 | ||||||||
\(997\) | −4.73692e9 | −0.151378 | −0.0756890 | − | 0.997131i | \(-0.524116\pi\) | ||||
−0.0756890 | + | 0.997131i | \(0.524116\pi\) | |||||||
\(998\) | −6.21825e9 | −0.198021 | ||||||||
\(999\) | −2.08473e10 | −0.661563 |
(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 | 91.8.a.e.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.e.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial |