Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,22,Mod(1,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.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: | \(136.943898701\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 49.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −288.000 | −0.198874 | −0.0994369 | − | 0.995044i | \(-0.531704\pi\) | ||||
−0.0994369 | + | 0.995044i | \(0.531704\pi\) | |||||||
\(3\) | 128844. | 1.25977 | 0.629885 | − | 0.776689i | \(-0.283102\pi\) | ||||
0.629885 | + | 0.776689i | \(0.283102\pi\) | |||||||
\(4\) | −2.01421e6 | −0.960449 | ||||||||
\(5\) | −2.16410e7 | −0.991040 | −0.495520 | − | 0.868596i | \(-0.665023\pi\) | ||||
−0.495520 | + | 0.868596i | \(0.665023\pi\) | |||||||
\(6\) | −3.71071e7 | −0.250535 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.18407e9 | 0.389882 | ||||||||
\(9\) | 6.14042e9 | 0.587019 | ||||||||
\(10\) | 6.23259e9 | 0.197092 | ||||||||
\(11\) | −9.47249e10 | −1.10114 | −0.550568 | − | 0.834790i | \(-0.685589\pi\) | ||||
−0.550568 | + | 0.834790i | \(0.685589\pi\) | |||||||
\(12\) | −2.59519e11 | −1.20994 | ||||||||
\(13\) | 8.06218e10 | 0.162199 | 0.0810993 | − | 0.996706i | \(-0.474157\pi\) | ||||
0.0810993 | + | 0.996706i | \(0.474157\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.78831e12 | −1.24848 | ||||||||
\(16\) | 3.88309e12 | 0.882912 | ||||||||
\(17\) | −3.05228e12 | −0.367207 | −0.183604 | − | 0.983000i | \(-0.558776\pi\) | ||||
−0.183604 | + | 0.983000i | \(0.558776\pi\) | |||||||
\(18\) | −1.76844e12 | −0.116743 | ||||||||
\(19\) | 7.92079e12 | 0.296385 | 0.148192 | − | 0.988959i | \(-0.452655\pi\) | ||||
0.148192 | + | 0.988959i | \(0.452655\pi\) | |||||||
\(20\) | 4.35894e13 | 0.951844 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.72808e13 | 0.218987 | ||||||||
\(23\) | −7.38454e13 | −0.371690 | −0.185845 | − | 0.982579i | \(-0.559502\pi\) | ||||
−0.185845 | + | 0.982579i | \(0.559502\pi\) | |||||||
\(24\) | 1.52561e14 | 0.491161 | ||||||||
\(25\) | −8.50644e12 | −0.0178393 | ||||||||
\(26\) | −2.32191e13 | −0.0322571 | ||||||||
\(27\) | −5.56597e14 | −0.520261 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.25303e15 | −1.87724 | −0.938620 | − | 0.344954i | \(-0.887895\pi\) | ||||
−0.938620 | + | 0.344954i | \(0.887895\pi\) | |||||||
\(30\) | 8.03032e14 | 0.248290 | ||||||||
\(31\) | −1.90054e15 | −0.416466 | −0.208233 | − | 0.978079i | \(-0.566771\pi\) | ||||
−0.208233 | + | 0.978079i | \(0.566771\pi\) | |||||||
\(32\) | −3.60151e15 | −0.565470 | ||||||||
\(33\) | −1.22047e16 | −1.38718 | ||||||||
\(34\) | 8.79057e14 | 0.0730279 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.23681e16 | −0.563802 | ||||||||
\(37\) | 2.21914e16 | 0.758695 | 0.379347 | − | 0.925254i | \(-0.376149\pi\) | ||||
0.379347 | + | 0.925254i | \(0.376149\pi\) | |||||||
\(38\) | −2.28119e15 | −0.0589431 | ||||||||
\(39\) | 1.03876e16 | 0.204333 | ||||||||
\(40\) | −2.56244e16 | −0.386389 | ||||||||
\(41\) | 2.06228e16 | 0.239948 | 0.119974 | − | 0.992777i | \(-0.461719\pi\) | ||||
0.119974 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.93606e17 | −1.36615 | −0.683077 | − | 0.730346i | \(-0.739359\pi\) | ||||
−0.683077 | + | 0.730346i | \(0.739359\pi\) | |||||||
\(44\) | 1.90796e17 | 1.05759 | ||||||||
\(45\) | −1.32885e17 | −0.581759 | ||||||||
\(46\) | 2.12675e16 | 0.0739195 | ||||||||
\(47\) | −1.46961e17 | −0.407543 | −0.203771 | − | 0.979019i | \(-0.565320\pi\) | ||||
−0.203771 | + | 0.979019i | \(0.565320\pi\) | |||||||
\(48\) | 5.00313e17 | 1.11227 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.44986e15 | 0.00354777 | ||||||||
\(51\) | −3.93268e17 | −0.462596 | ||||||||
\(52\) | −1.62389e17 | −0.155784 | ||||||||
\(53\) | 2.03827e18 | 1.60090 | 0.800450 | − | 0.599399i | \(-0.204594\pi\) | ||||
0.800450 | + | 0.599399i | \(0.204594\pi\) | |||||||
\(54\) | 1.60300e17 | 0.103466 | ||||||||
\(55\) | 2.04994e18 | 1.09127 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.02055e18 | 0.373376 | ||||||||
\(58\) | 1.22487e18 | 0.373334 | ||||||||
\(59\) | 5.97588e18 | 1.52214 | 0.761072 | − | 0.648667i | \(-0.224673\pi\) | ||||
0.761072 | + | 0.648667i | \(0.224673\pi\) | |||||||
\(60\) | 5.61623e18 | 1.19910 | ||||||||
\(61\) | −6.19062e18 | −1.11114 | −0.555572 | − | 0.831468i | \(-0.687501\pi\) | ||||
−0.555572 | + | 0.831468i | \(0.687501\pi\) | |||||||
\(62\) | 5.47356e17 | 0.0828242 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.10619e18 | −0.770455 | ||||||||
\(65\) | −1.74473e18 | −0.160745 | ||||||||
\(66\) | 3.51496e18 | 0.275873 | ||||||||
\(67\) | 1.69613e19 | 1.13677 | 0.568387 | − | 0.822761i | \(-0.307568\pi\) | ||||
0.568387 | + | 0.822761i | \(0.307568\pi\) | |||||||
\(68\) | 6.14793e18 | 0.352684 | ||||||||
\(69\) | −9.51454e18 | −0.468244 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.63276e18 | −0.205357 | −0.102678 | − | 0.994715i | \(-0.532741\pi\) | ||||
−0.102678 | + | 0.994715i | \(0.532741\pi\) | |||||||
\(72\) | 7.27070e18 | 0.228868 | ||||||||
\(73\) | 4.32848e19 | 1.17881 | 0.589407 | − | 0.807837i | \(-0.299362\pi\) | ||||
0.589407 | + | 0.807837i | \(0.299362\pi\) | |||||||
\(74\) | −6.39113e18 | −0.150885 | ||||||||
\(75\) | −1.09600e18 | −0.0224734 | ||||||||
\(76\) | −1.59541e19 | −0.284662 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.99164e18 | −0.0406365 | ||||||||
\(79\) | −5.12649e19 | −0.609166 | −0.304583 | − | 0.952486i | \(-0.598517\pi\) | ||||
−0.304583 | + | 0.952486i | \(0.598517\pi\) | |||||||
\(80\) | −8.40337e19 | −0.875001 | ||||||||
\(81\) | −1.35945e20 | −1.24243 | ||||||||
\(82\) | −5.93937e18 | −0.0477194 | ||||||||
\(83\) | −4.89119e19 | −0.346014 | −0.173007 | − | 0.984921i | \(-0.555348\pi\) | ||||
−0.173007 | + | 0.984921i | \(0.555348\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.60543e19 | 0.363917 | ||||||||
\(86\) | 5.57585e19 | 0.271692 | ||||||||
\(87\) | −5.47978e20 | −2.36489 | ||||||||
\(88\) | −1.12161e20 | −0.429313 | ||||||||
\(89\) | 5.04303e20 | 1.71434 | 0.857170 | − | 0.515034i | \(-0.172221\pi\) | ||||
0.857170 | + | 0.515034i | \(0.172221\pi\) | |||||||
\(90\) | 3.82708e19 | 0.115697 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.48740e20 | 0.356990 | ||||||||
\(93\) | −2.44873e20 | −0.524651 | ||||||||
\(94\) | 4.23246e19 | 0.0810496 | ||||||||
\(95\) | −1.71413e20 | −0.293729 | ||||||||
\(96\) | −4.64033e20 | −0.712362 | ||||||||
\(97\) | −8.08275e20 | −1.11290 | −0.556450 | − | 0.830881i | \(-0.687837\pi\) | ||||
−0.556450 | + | 0.830881i | \(0.687837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.81651e20 | −0.646388 | ||||||||
\(100\) | 1.71337e19 | 0.0171337 | ||||||||
\(101\) | 1.00202e21 | 0.902612 | 0.451306 | − | 0.892369i | \(-0.350958\pi\) | ||||
0.451306 | + | 0.892369i | \(0.350958\pi\) | |||||||
\(102\) | 1.13261e20 | 0.0919983 | ||||||||
\(103\) | 5.89747e20 | 0.432389 | 0.216195 | − | 0.976350i | \(-0.430635\pi\) | ||||
0.216195 | + | 0.976350i | \(0.430635\pi\) | |||||||
\(104\) | 9.54620e19 | 0.0632383 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.87021e20 | −0.318377 | ||||||||
\(107\) | 1.12210e21 | 0.551445 | 0.275723 | − | 0.961237i | \(-0.411083\pi\) | ||||
0.275723 | + | 0.961237i | \(0.411083\pi\) | |||||||
\(108\) | 1.12110e21 | 0.499684 | ||||||||
\(109\) | 1.72394e21 | 0.697499 | 0.348750 | − | 0.937216i | \(-0.386606\pi\) | ||||
0.348750 | + | 0.937216i | \(0.386606\pi\) | |||||||
\(110\) | −5.90382e20 | −0.217025 | ||||||||
\(111\) | 2.85923e21 | 0.955781 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.95810e20 | 0.137402 | 0.0687008 | − | 0.997637i | \(-0.478115\pi\) | ||||
0.0687008 | + | 0.997637i | \(0.478115\pi\) | |||||||
\(114\) | −2.93917e20 | −0.0742547 | ||||||||
\(115\) | 1.59809e21 | 0.368360 | ||||||||
\(116\) | 8.56649e21 | 1.80299 | ||||||||
\(117\) | 4.95052e20 | 0.0952136 | ||||||||
\(118\) | −1.72105e21 | −0.302715 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.30155e21 | −0.486761 | ||||||||
\(121\) | 1.57256e21 | 0.212501 | ||||||||
\(122\) | 1.78290e21 | 0.220978 | ||||||||
\(123\) | 2.65712e21 | 0.302279 | ||||||||
\(124\) | 3.82809e21 | 0.399994 | ||||||||
\(125\) | 1.05033e22 | 1.00872 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.63609e21 | 0.133005 | 0.0665027 | − | 0.997786i | \(-0.478816\pi\) | ||||
0.0665027 | + | 0.997786i | \(0.478816\pi\) | |||||||
\(128\) | 9.59949e21 | 0.718693 | ||||||||
\(129\) | −2.49450e22 | −1.72104 | ||||||||
\(130\) | 5.02483e20 | 0.0319680 | ||||||||
\(131\) | 1.38650e22 | 0.813898 | 0.406949 | − | 0.913451i | \(-0.366593\pi\) | ||||
0.406949 | + | 0.913451i | \(0.366593\pi\) | |||||||
\(132\) | 2.45829e22 | 1.33231 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.88486e21 | −0.226075 | ||||||||
\(135\) | 1.20453e22 | 0.515600 | ||||||||
\(136\) | −3.61412e21 | −0.143167 | ||||||||
\(137\) | −4.00789e22 | −1.47011 | −0.735055 | − | 0.678007i | \(-0.762844\pi\) | ||||
−0.735055 | + | 0.678007i | \(0.762844\pi\) | |||||||
\(138\) | 2.74019e21 | 0.0931215 | ||||||||
\(139\) | −4.47585e22 | −1.41000 | −0.705001 | − | 0.709206i | \(-0.749054\pi\) | ||||
−0.705001 | + | 0.709206i | \(0.749054\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.89350e22 | −0.513410 | ||||||||
\(142\) | 1.62223e21 | 0.0408400 | ||||||||
\(143\) | −7.63689e21 | −0.178603 | ||||||||
\(144\) | 2.38438e22 | 0.518286 | ||||||||
\(145\) | 9.20396e22 | 1.86042 | ||||||||
\(146\) | −1.24660e22 | −0.234435 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.46982e22 | −0.728688 | ||||||||
\(149\) | 4.93289e22 | 0.749283 | 0.374641 | − | 0.927170i | \(-0.377766\pi\) | ||||
0.374641 | + | 0.927170i | \(0.377766\pi\) | |||||||
\(150\) | 3.15649e20 | 0.00446937 | ||||||||
\(151\) | 5.70415e22 | 0.753239 | 0.376620 | − | 0.926368i | \(-0.377086\pi\) | ||||
0.376620 | + | 0.926368i | \(0.377086\pi\) | |||||||
\(152\) | 9.37878e21 | 0.115555 | ||||||||
\(153\) | −1.87423e22 | −0.215557 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.11295e22 | 0.412735 | ||||||||
\(156\) | −2.09229e22 | −0.196251 | ||||||||
\(157\) | −6.35623e22 | −0.557511 | −0.278756 | − | 0.960362i | \(-0.589922\pi\) | ||||
−0.278756 | + | 0.960362i | \(0.589922\pi\) | |||||||
\(158\) | 1.47643e22 | 0.121147 | ||||||||
\(159\) | 2.62618e23 | 2.01677 | ||||||||
\(160\) | 7.79400e22 | 0.560403 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3.91522e22 | 0.247086 | ||||||||
\(163\) | 8.68484e22 | 0.513797 | 0.256899 | − | 0.966438i | \(-0.417299\pi\) | ||||
0.256899 | + | 0.966438i | \(0.417299\pi\) | |||||||
\(164\) | −4.15386e22 | −0.230458 | ||||||||
\(165\) | 2.64122e23 | 1.37475 | ||||||||
\(166\) | 1.40866e22 | 0.0688132 | ||||||||
\(167\) | 1.89411e23 | 0.868726 | 0.434363 | − | 0.900738i | \(-0.356974\pi\) | ||||
0.434363 | + | 0.900738i | \(0.356974\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.40565e23 | −0.973692 | ||||||||
\(170\) | −1.90236e22 | −0.0723736 | ||||||||
\(171\) | 4.86370e22 | 0.173983 | ||||||||
\(172\) | 3.89962e23 | 1.31212 | ||||||||
\(173\) | 4.18508e23 | 1.32501 | 0.662506 | − | 0.749057i | \(-0.269493\pi\) | ||||
0.662506 | + | 0.749057i | \(0.269493\pi\) | |||||||
\(174\) | 1.57818e23 | 0.470314 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.67825e23 | −0.972206 | ||||||||
\(177\) | 7.69957e23 | 1.91755 | ||||||||
\(178\) | −1.45239e23 | −0.340937 | ||||||||
\(179\) | 4.76752e23 | 1.05520 | 0.527601 | − | 0.849493i | \(-0.323092\pi\) | ||||
0.527601 | + | 0.849493i | \(0.323092\pi\) | |||||||
\(180\) | 2.67657e23 | 0.558750 | ||||||||
\(181\) | 2.88627e22 | 0.0568476 | 0.0284238 | − | 0.999596i | \(-0.490951\pi\) | ||||
0.0284238 | + | 0.999596i | \(0.490951\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.97624e23 | −1.39979 | ||||||||
\(184\) | −8.74383e22 | −0.144915 | ||||||||
\(185\) | −4.80244e23 | −0.751897 | ||||||||
\(186\) | 7.05235e22 | 0.104339 | ||||||||
\(187\) | 2.89127e23 | 0.404345 | ||||||||
\(188\) | 2.96009e23 | 0.391424 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.93671e22 | 0.0584150 | ||||||||
\(191\) | 8.86378e23 | 0.992587 | 0.496293 | − | 0.868155i | \(-0.334694\pi\) | ||||
0.496293 | + | 0.868155i | \(0.334694\pi\) | |||||||
\(192\) | −9.15590e23 | −0.970595 | ||||||||
\(193\) | 8.63509e22 | 0.0866792 | 0.0433396 | − | 0.999060i | \(-0.486200\pi\) | ||||
0.0433396 | + | 0.999060i | \(0.486200\pi\) | |||||||
\(194\) | 2.32783e23 | 0.221327 | ||||||||
\(195\) | −2.24798e23 | −0.202502 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.99008e23 | −0.565701 | −0.282850 | − | 0.959164i | \(-0.591280\pi\) | ||||
−0.282850 | + | 0.959164i | \(0.591280\pi\) | |||||||
\(198\) | 1.67516e23 | 0.128550 | ||||||||
\(199\) | 1.24542e24 | 0.906483 | 0.453242 | − | 0.891388i | \(-0.350268\pi\) | ||||
0.453242 | + | 0.891388i | \(0.350268\pi\) | |||||||
\(200\) | −1.00722e22 | −0.00695522 | ||||||||
\(201\) | 2.18536e24 | 1.43207 | ||||||||
\(202\) | −2.88581e23 | −0.179506 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.92124e23 | 0.444300 | ||||||||
\(205\) | −4.46297e23 | −0.237798 | ||||||||
\(206\) | −1.69847e23 | −0.0859909 | ||||||||
\(207\) | −4.53442e23 | −0.218189 | ||||||||
\(208\) | 3.13061e23 | 0.143207 | ||||||||
\(209\) | −7.50296e23 | −0.326360 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.50841e24 | 1.38085 | 0.690423 | − | 0.723406i | \(-0.257425\pi\) | ||||
0.690423 | + | 0.723406i | \(0.257425\pi\) | |||||||
\(212\) | −4.10549e24 | −1.53758 | ||||||||
\(213\) | −7.25747e23 | −0.258702 | ||||||||
\(214\) | −3.23165e23 | −0.109668 | ||||||||
\(215\) | 4.18981e24 | 1.35391 | ||||||||
\(216\) | −6.59051e23 | −0.202840 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.96495e23 | −0.138714 | ||||||||
\(219\) | 5.57698e24 | 1.48503 | ||||||||
\(220\) | −4.12900e24 | −1.04811 | ||||||||
\(221\) | −2.46081e23 | −0.0595605 | ||||||||
\(222\) | −8.23459e23 | −0.190080 | ||||||||
\(223\) | 4.72350e24 | 1.04007 | 0.520035 | − | 0.854145i | \(-0.325919\pi\) | ||||
0.520035 | + | 0.854145i | \(0.325919\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.22331e22 | −0.0104720 | ||||||||
\(226\) | −1.42793e23 | −0.0273256 | ||||||||
\(227\) | 5.44317e24 | 0.994444 | 0.497222 | − | 0.867623i | \(-0.334353\pi\) | ||||
0.497222 | + | 0.867623i | \(0.334353\pi\) | |||||||
\(228\) | −2.05559e24 | −0.358609 | ||||||||
\(229\) | −6.90677e24 | −1.15081 | −0.575403 | − | 0.817870i | \(-0.695155\pi\) | ||||
−0.575403 | + | 0.817870i | \(0.695155\pi\) | |||||||
\(230\) | −4.60249e23 | −0.0732572 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.03589e24 | −0.731902 | ||||||||
\(233\) | 4.53650e24 | 0.630208 | 0.315104 | − | 0.949057i | \(-0.397961\pi\) | ||||
0.315104 | + | 0.949057i | \(0.397961\pi\) | |||||||
\(234\) | −1.42575e23 | −0.0189355 | ||||||||
\(235\) | 3.18036e24 | 0.403891 | ||||||||
\(236\) | −1.20367e25 | −1.46194 | ||||||||
\(237\) | −6.60518e24 | −0.767409 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.73493e24 | −0.290916 | −0.145458 | − | 0.989364i | \(-0.546466\pi\) | ||||
−0.145458 | + | 0.989364i | \(0.546466\pi\) | |||||||
\(240\) | −1.08272e25 | −1.10230 | ||||||||
\(241\) | 8.08907e24 | 0.788351 | 0.394175 | − | 0.919035i | \(-0.371030\pi\) | ||||
0.394175 | + | 0.919035i | \(0.371030\pi\) | |||||||
\(242\) | −4.52898e23 | −0.0422609 | ||||||||
\(243\) | −1.16935e25 | −1.04491 | ||||||||
\(244\) | 1.24692e25 | 1.06720 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.65252e23 | −0.0601154 | ||||||||
\(247\) | 6.38588e23 | 0.0480732 | ||||||||
\(248\) | −2.25038e24 | −0.162373 | ||||||||
\(249\) | −6.30200e24 | −0.435898 | ||||||||
\(250\) | −3.02495e24 | −0.200608 | ||||||||
\(251\) | −6.63927e24 | −0.422227 | −0.211113 | − | 0.977462i | \(-0.567709\pi\) | ||||
−0.211113 | + | 0.977462i | \(0.567709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.99500e24 | 0.409282 | ||||||||
\(254\) | −4.71195e23 | −0.0264513 | ||||||||
\(255\) | 8.51070e24 | 0.458452 | ||||||||
\(256\) | 1.21381e25 | 0.627526 | ||||||||
\(257\) | −1.57278e24 | −0.0780497 | −0.0390249 | − | 0.999238i | \(-0.512425\pi\) | ||||
−0.0390249 | + | 0.999238i | \(0.512425\pi\) | |||||||
\(258\) | 7.18415e24 | 0.342270 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.51425e24 | 0.154388 | ||||||||
\(261\) | −2.61154e25 | −1.10197 | ||||||||
\(262\) | −3.99311e24 | −0.161863 | ||||||||
\(263\) | −3.40077e25 | −1.32447 | −0.662235 | − | 0.749296i | \(-0.730392\pi\) | ||||
−0.662235 | + | 0.749296i | \(0.730392\pi\) | |||||||
\(264\) | −1.44513e25 | −0.540836 | ||||||||
\(265\) | −4.41100e25 | −1.58656 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.49765e25 | 2.15967 | ||||||||
\(268\) | −3.41636e25 | −1.09181 | ||||||||
\(269\) | 3.57975e25 | 1.10015 | 0.550077 | − | 0.835114i | \(-0.314598\pi\) | ||||
0.550077 | + | 0.835114i | \(0.314598\pi\) | |||||||
\(270\) | −3.46904e24 | −0.102539 | ||||||||
\(271\) | −2.46104e25 | −0.699746 | −0.349873 | − | 0.936797i | \(-0.613775\pi\) | ||||
−0.349873 | + | 0.936797i | \(0.613775\pi\) | |||||||
\(272\) | −1.18523e25 | −0.324212 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.15427e25 | 0.292366 | ||||||||
\(275\) | 8.05772e23 | 0.0196435 | ||||||||
\(276\) | 1.91643e25 | 0.449725 | ||||||||
\(277\) | −6.11679e25 | −1.38193 | −0.690965 | − | 0.722888i | \(-0.742814\pi\) | ||||
−0.690965 | + | 0.722888i | \(0.742814\pi\) | |||||||
\(278\) | 1.28904e25 | 0.280413 | ||||||||
\(279\) | −1.16701e25 | −0.244473 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.73710e25 | 0.337605 | 0.168802 | − | 0.985650i | \(-0.446010\pi\) | ||||
0.168802 | + | 0.985650i | \(0.446010\pi\) | |||||||
\(282\) | 5.45327e24 | 0.102104 | ||||||||
\(283\) | −7.57237e25 | −1.36607 | −0.683037 | − | 0.730383i | \(-0.739341\pi\) | ||||
−0.683037 | + | 0.730383i | \(0.739341\pi\) | |||||||
\(284\) | 1.13455e25 | 0.197235 | ||||||||
\(285\) | −2.20856e25 | −0.370031 | ||||||||
\(286\) | 2.19943e24 | 0.0355194 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.21148e25 | −0.331941 | ||||||||
\(289\) | −5.97755e25 | −0.865159 | ||||||||
\(290\) | −2.65074e25 | −0.369989 | ||||||||
\(291\) | −1.04141e26 | −1.40200 | ||||||||
\(292\) | −8.71845e25 | −1.13219 | ||||||||
\(293\) | −4.88684e25 | −0.612235 | −0.306118 | − | 0.951994i | \(-0.599030\pi\) | ||||
−0.306118 | + | 0.951994i | \(0.599030\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.29324e26 | −1.50851 | ||||||||
\(296\) | 2.62762e25 | 0.295801 | ||||||||
\(297\) | 5.27236e25 | 0.572878 | ||||||||
\(298\) | −1.42067e25 | −0.149013 | ||||||||
\(299\) | −5.95355e24 | −0.0602877 | ||||||||
\(300\) | 2.20758e24 | 0.0215846 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.64279e25 | −0.149800 | ||||||||
\(303\) | 1.29104e26 | 1.13708 | ||||||||
\(304\) | 3.07571e25 | 0.261681 | ||||||||
\(305\) | 1.33971e26 | 1.10119 | ||||||||
\(306\) | 5.39778e24 | 0.0428687 | ||||||||
\(307\) | 2.17987e26 | 1.67293 | 0.836466 | − | 0.548019i | \(-0.184618\pi\) | ||||
0.836466 | + | 0.548019i | \(0.184618\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.59854e25 | 0.544711 | ||||||||
\(310\) | −1.18453e25 | −0.0820821 | ||||||||
\(311\) | 4.04644e25 | 0.271075 | 0.135538 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135538 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(312\) | 1.22997e25 | 0.0796657 | ||||||||
\(313\) | 8.74174e24 | 0.0547498 | 0.0273749 | − | 0.999625i | \(-0.491285\pi\) | ||||
0.0273749 | + | 0.999625i | \(0.491285\pi\) | |||||||
\(314\) | 1.83060e25 | 0.110874 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.03258e26 | 0.585073 | ||||||||
\(317\) | −3.19758e25 | −0.175267 | −0.0876334 | − | 0.996153i | \(-0.527930\pi\) | ||||
−0.0876334 | + | 0.996153i | \(0.527930\pi\) | |||||||
\(318\) | −7.56341e25 | −0.401082 | ||||||||
\(319\) | 4.02868e26 | 2.06710 | ||||||||
\(320\) | 1.53785e26 | 0.763552 | ||||||||
\(321\) | 1.44576e26 | 0.694694 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.41765e25 | −0.108835 | ||||||||
\(324\) | 2.73822e26 | 1.19329 | ||||||||
\(325\) | −6.85805e23 | −0.00289351 | ||||||||
\(326\) | −2.50123e25 | −0.102181 | ||||||||
\(327\) | 2.22119e26 | 0.878688 | ||||||||
\(328\) | 2.44189e25 | 0.0935514 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.60672e25 | −0.273402 | ||||||||
\(331\) | −2.52215e26 | −0.878166 | −0.439083 | − | 0.898446i | \(-0.644697\pi\) | ||||
−0.439083 | + | 0.898446i | \(0.644697\pi\) | |||||||
\(332\) | 9.85186e25 | 0.332329 | ||||||||
\(333\) | 1.36265e26 | 0.445368 | ||||||||
\(334\) | −5.45504e25 | −0.172767 | ||||||||
\(335\) | −3.67059e26 | −1.12659 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.53127e26 | −0.441507 | −0.220753 | − | 0.975330i | \(-0.570852\pi\) | ||||
−0.220753 | + | 0.975330i | \(0.570852\pi\) | |||||||
\(338\) | 6.92826e25 | 0.193642 | ||||||||
\(339\) | 6.38821e25 | 0.173094 | ||||||||
\(340\) | −1.33047e26 | −0.349524 | ||||||||
\(341\) | 1.80029e26 | 0.458586 | ||||||||
\(342\) | −1.40075e25 | −0.0346007 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.29243e26 | −0.532639 | ||||||||
\(345\) | 2.05904e26 | 0.464049 | ||||||||
\(346\) | −1.20530e26 | −0.263510 | ||||||||
\(347\) | 3.23436e26 | 0.686008 | 0.343004 | − | 0.939334i | \(-0.388556\pi\) | ||||
0.343004 | + | 0.939334i | \(0.388556\pi\) | |||||||
\(348\) | 1.10374e27 | 2.27136 | ||||||||
\(349\) | 6.77854e26 | 1.35353 | 0.676767 | − | 0.736197i | \(-0.263380\pi\) | ||||
0.676767 | + | 0.736197i | \(0.263380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.48739e25 | −0.0843857 | ||||||||
\(352\) | 3.41153e26 | 0.622660 | ||||||||
\(353\) | −6.84291e26 | −1.21229 | −0.606145 | − | 0.795354i | \(-0.707285\pi\) | ||||
−0.606145 | + | 0.795354i | \(0.707285\pi\) | |||||||
\(354\) | −2.21748e26 | −0.381351 | ||||||||
\(355\) | 1.21898e26 | 0.203517 | ||||||||
\(356\) | −1.01577e27 | −1.64654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.37304e26 | −0.209852 | ||||||||
\(359\) | −6.85500e25 | −0.101746 | −0.0508728 | − | 0.998705i | \(-0.516200\pi\) | ||||
−0.0508728 | + | 0.998705i | \(0.516200\pi\) | |||||||
\(360\) | −1.57345e26 | −0.226817 | ||||||||
\(361\) | −6.51471e26 | −0.912156 | ||||||||
\(362\) | −8.31247e24 | −0.0113055 | ||||||||
\(363\) | 2.02615e26 | 0.267703 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.36723e26 | −1.16825 | ||||||||
\(366\) | 2.29716e26 | 0.278381 | ||||||||
\(367\) | −1.13575e27 | −1.33749 | −0.668745 | − | 0.743492i | \(-0.733168\pi\) | ||||
−0.668745 | + | 0.743492i | \(0.733168\pi\) | |||||||
\(368\) | −2.86748e26 | −0.328170 | ||||||||
\(369\) | 1.26633e26 | 0.140854 | ||||||||
\(370\) | 1.38310e26 | 0.149533 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.93226e26 | 0.503901 | ||||||||
\(373\) | 3.82975e26 | 0.380389 | 0.190195 | − | 0.981746i | \(-0.439088\pi\) | ||||
0.190195 | + | 0.981746i | \(0.439088\pi\) | |||||||
\(374\) | −8.32687e25 | −0.0804136 | ||||||||
\(375\) | 1.35329e27 | 1.27075 | ||||||||
\(376\) | −1.74012e26 | −0.158894 | ||||||||
\(377\) | −3.42887e26 | −0.304486 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.14767e25 | 0.0600417 | 0.0300208 | − | 0.999549i | \(-0.490443\pi\) | ||||
0.0300208 | + | 0.999549i | \(0.490443\pi\) | |||||||
\(380\) | 3.45262e26 | 0.282112 | ||||||||
\(381\) | 2.10801e26 | 0.167556 | ||||||||
\(382\) | −2.55277e26 | −0.197400 | ||||||||
\(383\) | 1.38425e27 | 1.04142 | 0.520712 | − | 0.853732i | \(-0.325666\pi\) | ||||
0.520712 | + | 0.853732i | \(0.325666\pi\) | |||||||
\(384\) | 1.23684e27 | 0.905388 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.48690e25 | −0.0172382 | ||||||||
\(387\) | −1.18882e27 | −0.801958 | ||||||||
\(388\) | 1.62803e27 | 1.06888 | ||||||||
\(389\) | 1.63213e27 | 1.04300 | 0.521500 | − | 0.853251i | \(-0.325373\pi\) | ||||
0.521500 | + | 0.853251i | \(0.325373\pi\) | |||||||
\(390\) | 6.47419e25 | 0.0402724 | ||||||||
\(391\) | 2.25397e26 | 0.136487 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.78642e27 | 1.02532 | ||||||||
\(394\) | 2.01314e26 | 0.112503 | ||||||||
\(395\) | 1.10942e27 | 0.603708 | ||||||||
\(396\) | 1.17157e27 | 0.620823 | ||||||||
\(397\) | −1.21029e27 | −0.624581 | −0.312291 | − | 0.949987i | \(-0.601096\pi\) | ||||
−0.312291 | + | 0.949987i | \(0.601096\pi\) | |||||||
\(398\) | −3.58682e26 | −0.180276 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.30313e25 | −0.0157505 | ||||||||
\(401\) | −6.51358e26 | −0.302555 | −0.151277 | − | 0.988491i | \(-0.548339\pi\) | ||||
−0.151277 | + | 0.988491i | \(0.548339\pi\) | |||||||
\(402\) | −6.29385e26 | −0.284802 | ||||||||
\(403\) | −1.53225e26 | −0.0675502 | ||||||||
\(404\) | −2.01827e27 | −0.866913 | ||||||||
\(405\) | 2.94198e27 | 1.23130 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.10208e27 | −0.835427 | ||||||||
\(408\) | −4.65658e26 | −0.180358 | ||||||||
\(409\) | 4.45251e27 | 1.68078 | 0.840389 | − | 0.541984i | \(-0.182327\pi\) | ||||
0.840389 | + | 0.541984i | \(0.182327\pi\) | |||||||
\(410\) | 1.28534e26 | 0.0472918 | ||||||||
\(411\) | −5.16393e27 | −1.85200 | ||||||||
\(412\) | −1.18787e27 | −0.415288 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.30591e26 | 0.0433921 | ||||||||
\(415\) | 1.05850e27 | 0.342914 | ||||||||
\(416\) | −2.90360e26 | −0.0917185 | ||||||||
\(417\) | −5.76686e27 | −1.77628 | ||||||||
\(418\) | 2.16085e26 | 0.0649044 | ||||||||
\(419\) | −4.92912e27 | −1.44385 | −0.721925 | − | 0.691972i | \(-0.756742\pi\) | ||||
−0.721925 | + | 0.691972i | \(0.756742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.50145e27 | 0.418359 | 0.209180 | − | 0.977877i | \(-0.432921\pi\) | ||||
0.209180 | + | 0.977877i | \(0.432921\pi\) | |||||||
\(422\) | −1.01042e27 | −0.274614 | ||||||||
\(423\) | −9.02400e26 | −0.239235 | ||||||||
\(424\) | 2.41345e27 | 0.624162 | ||||||||
\(425\) | 2.59641e25 | 0.00655072 | ||||||||
\(426\) | 2.09015e26 | 0.0514490 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.26014e27 | −0.529635 | ||||||||
\(429\) | −9.83968e26 | −0.224998 | ||||||||
\(430\) | −1.20667e27 | −0.269258 | ||||||||
\(431\) | −7.19221e27 | −1.56621 | −0.783107 | − | 0.621887i | \(-0.786366\pi\) | ||||
−0.783107 | + | 0.621887i | \(0.786366\pi\) | |||||||
\(432\) | −2.16132e27 | −0.459345 | ||||||||
\(433\) | −4.23104e27 | −0.877656 | −0.438828 | − | 0.898571i | \(-0.644606\pi\) | ||||
−0.438828 | + | 0.898571i | \(0.644606\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.18588e28 | 2.34370 | ||||||||
\(436\) | −3.47237e27 | −0.669913 | ||||||||
\(437\) | −5.84914e26 | −0.110163 | ||||||||
\(438\) | −1.60617e27 | −0.295334 | ||||||||
\(439\) | −4.53235e27 | −0.813665 | −0.406832 | − | 0.913503i | \(-0.633367\pi\) | ||||
−0.406832 | + | 0.913503i | \(0.633367\pi\) | |||||||
\(440\) | 2.42727e27 | 0.425467 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.08712e25 | 0.0118450 | ||||||||
\(443\) | −4.61186e27 | −0.752726 | −0.376363 | − | 0.926472i | \(-0.622826\pi\) | ||||
−0.376363 | + | 0.926472i | \(0.622826\pi\) | |||||||
\(444\) | −5.75909e27 | −0.917979 | ||||||||
\(445\) | −1.09136e28 | −1.69898 | ||||||||
\(446\) | −1.36037e27 | −0.206843 | ||||||||
\(447\) | 6.35573e27 | 0.943923 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.25692e26 | −0.0178123 | −0.00890615 | − | 0.999960i | \(-0.502835\pi\) | ||||
−0.00890615 | + | 0.999960i | \(0.502835\pi\) | |||||||
\(450\) | 1.50431e25 | 0.00208261 | ||||||||
\(451\) | −1.95349e27 | −0.264216 | ||||||||
\(452\) | −9.98664e26 | −0.131967 | ||||||||
\(453\) | 7.34945e27 | 0.948907 | ||||||||
\(454\) | −1.56763e27 | −0.197769 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.20840e27 | 0.145573 | ||||||||
\(457\) | 1.15924e28 | 1.36475 | 0.682374 | − | 0.731003i | \(-0.260948\pi\) | ||||
0.682374 | + | 0.731003i | \(0.260948\pi\) | |||||||
\(458\) | 1.98915e27 | 0.228865 | ||||||||
\(459\) | 1.69889e27 | 0.191044 | ||||||||
\(460\) | −3.21888e27 | −0.353791 | ||||||||
\(461\) | −1.02514e28 | −1.10134 | −0.550671 | − | 0.834723i | \(-0.685628\pi\) | ||||
−0.550671 | + | 0.834723i | \(0.685628\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.72801e27 | −0.588035 | −0.294017 | − | 0.955800i | \(-0.594992\pi\) | ||||
−0.294017 | + | 0.955800i | \(0.594992\pi\) | |||||||
\(464\) | −1.65149e28 | −1.65744 | ||||||||
\(465\) | 5.29929e27 | 0.519950 | ||||||||
\(466\) | −1.30651e27 | −0.125332 | ||||||||
\(467\) | −1.12658e28 | −1.05666 | −0.528329 | − | 0.849040i | \(-0.677181\pi\) | ||||
−0.528329 | + | 0.849040i | \(0.677181\pi\) | |||||||
\(468\) | −9.97138e26 | −0.0914479 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.15945e26 | −0.0803234 | ||||||||
\(471\) | −8.18963e27 | −0.702335 | ||||||||
\(472\) | 7.07587e27 | 0.593457 | ||||||||
\(473\) | 1.83393e28 | 1.50432 | ||||||||
\(474\) | 1.90229e27 | 0.152618 | ||||||||
\(475\) | −6.73777e25 | −0.00528729 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.25158e28 | 0.939759 | ||||||||
\(478\) | 7.87660e26 | 0.0578557 | ||||||||
\(479\) | 1.17373e28 | 0.843422 | 0.421711 | − | 0.906730i | \(-0.361430\pi\) | ||||
0.421711 | + | 0.906730i | \(0.361430\pi\) | |||||||
\(480\) | 1.00421e28 | 0.705979 | ||||||||
\(481\) | 1.78911e27 | 0.123059 | ||||||||
\(482\) | −2.32965e27 | −0.156782 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.16747e27 | −0.204097 | ||||||||
\(485\) | 1.74918e28 | 1.10293 | ||||||||
\(486\) | 3.36773e27 | 0.207805 | ||||||||
\(487\) | 4.75272e27 | 0.287004 | 0.143502 | − | 0.989650i | \(-0.454164\pi\) | ||||
0.143502 | + | 0.989650i | \(0.454164\pi\) | |||||||
\(488\) | −7.33013e27 | −0.433215 | ||||||||
\(489\) | 1.11899e28 | 0.647266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.59837e28 | −1.43994 | −0.719971 | − | 0.694004i | \(-0.755845\pi\) | ||||
−0.719971 | + | 0.694004i | \(0.755845\pi\) | |||||||
\(492\) | −5.35200e27 | −0.290324 | ||||||||
\(493\) | 1.29815e28 | 0.689336 | ||||||||
\(494\) | −1.83913e26 | −0.00956049 | ||||||||
\(495\) | 1.25875e28 | 0.640596 | ||||||||
\(496\) | −7.37997e27 | −0.367703 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.81498e27 | 0.0866887 | ||||||||
\(499\) | 3.84508e28 | 1.79825 | 0.899124 | − | 0.437695i | \(-0.144205\pi\) | ||||
0.899124 | + | 0.437695i | \(0.144205\pi\) | |||||||
\(500\) | −2.11558e28 | −0.968824 | ||||||||
\(501\) | 2.44045e28 | 1.09439 | ||||||||
\(502\) | 1.91211e27 | 0.0839699 | ||||||||
\(503\) | 3.27446e28 | 1.40824 | 0.704118 | − | 0.710083i | \(-0.251343\pi\) | ||||
0.704118 | + | 0.710083i | \(0.251343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.16846e28 | −0.894525 | ||||||||
\(506\) | −2.01456e27 | −0.0813954 | ||||||||
\(507\) | −3.09953e28 | −1.22663 | ||||||||
\(508\) | −3.29543e27 | −0.127745 | ||||||||
\(509\) | 2.02472e28 | 0.768826 | 0.384413 | − | 0.923161i | \(-0.374404\pi\) | ||||
0.384413 | + | 0.923161i | \(0.374404\pi\) | |||||||
\(510\) | −2.45108e27 | −0.0911740 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.36274e28 | −0.843492 | ||||||||
\(513\) | −4.40869e27 | −0.154197 | ||||||||
\(514\) | 4.52962e26 | 0.0155220 | ||||||||
\(515\) | −1.27627e28 | −0.428515 | ||||||||
\(516\) | 5.02443e28 | 1.65297 | ||||||||
\(517\) | 1.39208e28 | 0.448760 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.39222e28 | 1.66921 | ||||||||
\(520\) | −2.06589e27 | −0.0626717 | ||||||||
\(521\) | −4.75207e27 | −0.141282 | −0.0706411 | − | 0.997502i | \(-0.522504\pi\) | ||||
−0.0706411 | + | 0.997502i | \(0.522504\pi\) | |||||||
\(522\) | 7.52124e27 | 0.219154 | ||||||||
\(523\) | 1.28180e26 | 0.00366061 | 0.00183030 | − | 0.999998i | \(-0.499417\pi\) | ||||
0.00183030 | + | 0.999998i | \(0.499417\pi\) | |||||||
\(524\) | −2.79269e28 | −0.781708 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.79422e27 | 0.263402 | ||||||||
\(527\) | 5.80099e27 | 0.152929 | ||||||||
\(528\) | −4.73921e28 | −1.22476 | ||||||||
\(529\) | −3.40184e28 | −0.861846 | ||||||||
\(530\) | 1.27037e28 | 0.315525 | ||||||||
\(531\) | 3.66944e28 | 0.893527 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.66265e27 | 0.0389192 | ||||||||
\(534\) | −1.87132e28 | −0.429502 | ||||||||
\(535\) | −2.42833e28 | −0.546504 | ||||||||
\(536\) | 2.00834e28 | 0.443208 | ||||||||
\(537\) | 6.14266e28 | 1.32931 | ||||||||
\(538\) | −1.03097e28 | −0.218792 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.42617e28 | −0.495207 | ||||||||
\(541\) | 3.42747e28 | 0.686123 | 0.343061 | − | 0.939313i | \(-0.388536\pi\) | ||||
0.343061 | + | 0.939313i | \(0.388536\pi\) | |||||||
\(542\) | 7.08778e27 | 0.139161 | ||||||||
\(543\) | 3.71879e27 | 0.0716149 | ||||||||
\(544\) | 1.09928e28 | 0.207645 | ||||||||
\(545\) | −3.73077e28 | −0.691250 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.30329e28 | −1.30212 | −0.651061 | − | 0.759026i | \(-0.725676\pi\) | ||||
−0.651061 | + | 0.759026i | \(0.725676\pi\) | |||||||
\(548\) | 8.07273e28 | 1.41197 | ||||||||
\(549\) | −3.80130e28 | −0.652263 | ||||||||
\(550\) | −2.32062e26 | −0.00390658 | ||||||||
\(551\) | −3.36874e28 | −0.556385 | ||||||||
\(552\) | −1.12659e28 | −0.182560 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.76164e28 | 0.274830 | ||||||||
\(555\) | −6.18765e28 | −0.947217 | ||||||||
\(556\) | 9.01529e28 | 1.35424 | ||||||||
\(557\) | −3.32597e28 | −0.490274 | −0.245137 | − | 0.969488i | \(-0.578833\pi\) | ||||
−0.245137 | + | 0.969488i | \(0.578833\pi\) | |||||||
\(558\) | 3.36100e27 | 0.0486193 | ||||||||
\(559\) | −1.56089e28 | −0.221588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.72523e28 | 0.509382 | ||||||||
\(562\) | −5.00285e27 | −0.0671407 | ||||||||
\(563\) | 8.28332e28 | 1.09110 | 0.545552 | − | 0.838077i | \(-0.316320\pi\) | ||||
0.545552 | + | 0.838077i | \(0.316320\pi\) | |||||||
\(564\) | 3.81390e28 | 0.493104 | ||||||||
\(565\) | −1.07298e28 | −0.136170 | ||||||||
\(566\) | 2.18084e28 | 0.271676 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.66959e27 | −0.0800648 | ||||||||
\(569\) | 7.35414e28 | 0.866669 | 0.433335 | − | 0.901233i | \(-0.357337\pi\) | ||||
0.433335 | + | 0.901233i | \(0.357337\pi\) | |||||||
\(570\) | 6.36065e27 | 0.0735894 | ||||||||
\(571\) | 1.09131e29 | 1.23956 | 0.619780 | − | 0.784776i | \(-0.287222\pi\) | ||||
0.619780 | + | 0.784776i | \(0.287222\pi\) | |||||||
\(572\) | 1.53823e28 | 0.171539 | ||||||||
\(573\) | 1.14204e29 | 1.25043 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.28162e26 | 0.00663070 | ||||||||
\(576\) | −4.36350e28 | −0.452271 | ||||||||
\(577\) | −1.30727e28 | −0.133051 | −0.0665257 | − | 0.997785i | \(-0.521191\pi\) | ||||
−0.0665257 | + | 0.997785i | \(0.521191\pi\) | |||||||
\(578\) | 1.72153e28 | 0.172057 | ||||||||
\(579\) | 1.11258e28 | 0.109196 | ||||||||
\(580\) | −1.85387e29 | −1.78684 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.99927e28 | 0.278820 | ||||||||
\(583\) | −1.93075e29 | −1.76281 | ||||||||
\(584\) | 5.12523e28 | 0.459598 | ||||||||
\(585\) | −1.07134e28 | −0.0943605 | ||||||||
\(586\) | 1.40741e28 | 0.121758 | ||||||||
\(587\) | 1.71459e29 | 1.45701 | 0.728503 | − | 0.685043i | \(-0.240216\pi\) | ||||
0.728503 | + | 0.685043i | \(0.240216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.50538e28 | −0.123434 | ||||||||
\(590\) | 3.72452e28 | 0.300002 | ||||||||
\(591\) | −9.00630e28 | −0.712652 | ||||||||
\(592\) | 8.61713e28 | 0.669861 | ||||||||
\(593\) | −2.35277e29 | −1.79682 | −0.898412 | − | 0.439153i | \(-0.855279\pi\) | ||||
−0.898412 | + | 0.439153i | \(0.855279\pi\) | |||||||
\(594\) | −1.51844e28 | −0.113931 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.93587e28 | −0.719648 | ||||||||
\(597\) | 1.60465e29 | 1.14196 | ||||||||
\(598\) | 1.71462e27 | 0.0119896 | ||||||||
\(599\) | −1.33384e29 | −0.916481 | −0.458240 | − | 0.888828i | \(-0.651520\pi\) | ||||
−0.458240 | + | 0.888828i | \(0.651520\pi\) | |||||||
\(600\) | −1.29775e27 | −0.00876197 | ||||||||
\(601\) | 3.64474e28 | 0.241816 | 0.120908 | − | 0.992664i | \(-0.461419\pi\) | ||||
0.120908 | + | 0.992664i | \(0.461419\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.04150e29 | 0.667308 | ||||||||
\(604\) | −1.14893e29 | −0.723448 | ||||||||
\(605\) | −3.40317e28 | −0.210597 | ||||||||
\(606\) | −3.71820e28 | −0.226136 | ||||||||
\(607\) | −2.71228e29 | −1.62126 | −0.810630 | − | 0.585559i | \(-0.800875\pi\) | ||||
−0.810630 | + | 0.585559i | \(0.800875\pi\) | |||||||
\(608\) | −2.85268e28 | −0.167597 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.85836e28 | −0.218998 | ||||||||
\(611\) | −1.18482e28 | −0.0661029 | ||||||||
\(612\) | 3.77509e28 | 0.207032 | ||||||||
\(613\) | −2.02699e29 | −1.09274 | −0.546370 | − | 0.837544i | \(-0.683991\pi\) | ||||
−0.546370 | + | 0.837544i | \(0.683991\pi\) | |||||||
\(614\) | −6.27803e28 | −0.332702 | ||||||||
\(615\) | −5.75027e28 | −0.299571 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.04169e29 | 1.53151 | 0.765757 | − | 0.643130i | \(-0.222364\pi\) | ||||
0.765757 | + | 0.643130i | \(0.222364\pi\) | |||||||
\(618\) | −2.18838e28 | −0.108329 | ||||||||
\(619\) | −1.21487e29 | −0.591262 | −0.295631 | − | 0.955302i | \(-0.595530\pi\) | ||||
−0.295631 | + | 0.955302i | \(0.595530\pi\) | |||||||
\(620\) | −8.28434e28 | −0.396411 | ||||||||
\(621\) | 4.11022e28 | 0.193376 | ||||||||
\(622\) | −1.16538e28 | −0.0539097 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.03361e28 | 0.180408 | ||||||||
\(625\) | −2.23245e29 | −0.981842 | ||||||||
\(626\) | −2.51762e27 | −0.0108883 | ||||||||
\(627\) | −9.66712e28 | −0.411138 | ||||||||
\(628\) | 1.28028e29 | 0.535461 | ||||||||
\(629\) | −6.77345e28 | −0.278598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.79118e29 | −0.712577 | −0.356288 | − | 0.934376i | \(-0.615958\pi\) | ||||
−0.356288 | + | 0.934376i | \(0.615958\pi\) | |||||||
\(632\) | −6.07014e28 | −0.237503 | ||||||||
\(633\) | 4.52038e29 | 1.73955 | ||||||||
\(634\) | 9.20904e27 | 0.0348560 | ||||||||
\(635\) | −3.54066e28 | −0.131814 | ||||||||
\(636\) | −5.28968e29 | −1.93700 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.16026e29 | −0.411091 | ||||||||
\(639\) | −3.45875e28 | −0.120548 | ||||||||
\(640\) | −2.07742e29 | −0.712254 | ||||||||
\(641\) | −3.41742e29 | −1.15263 | −0.576315 | − | 0.817228i | \(-0.695510\pi\) | ||||
−0.576315 | + | 0.817228i | \(0.695510\pi\) | |||||||
\(642\) | −4.16379e28 | −0.138156 | ||||||||
\(643\) | −7.57582e28 | −0.247294 | −0.123647 | − | 0.992326i | \(-0.539459\pi\) | ||||
−0.123647 | + | 0.992326i | \(0.539459\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.39832e29 | 1.70562 | ||||||||
\(646\) | 6.96283e27 | 0.0216443 | ||||||||
\(647\) | 2.99088e29 | 0.914755 | 0.457377 | − | 0.889273i | \(-0.348789\pi\) | ||||
0.457377 | + | 0.889273i | \(0.348789\pi\) | |||||||
\(648\) | −1.60969e29 | −0.484400 | ||||||||
\(649\) | −5.66065e29 | −1.67609 | ||||||||
\(650\) | 1.97512e26 | 0.000575443 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.74931e29 | −0.493476 | ||||||||
\(653\) | 5.40507e28 | 0.150042 | 0.0750210 | − | 0.997182i | \(-0.476098\pi\) | ||||
0.0750210 | + | 0.997182i | \(0.476098\pi\) | |||||||
\(654\) | −6.39703e28 | −0.174748 | ||||||||
\(655\) | −3.00051e29 | −0.806606 | ||||||||
\(656\) | 8.00802e28 | 0.211853 | ||||||||
\(657\) | 2.65787e29 | 0.691985 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.26606e28 | 0.0571446 | 0.0285723 | − | 0.999592i | \(-0.490904\pi\) | ||||
0.0285723 | + | 0.999592i | \(0.490904\pi\) | |||||||
\(660\) | −5.31997e29 | −1.32038 | ||||||||
\(661\) | 1.87483e29 | 0.457980 | 0.228990 | − | 0.973429i | \(-0.426458\pi\) | ||||
0.228990 | + | 0.973429i | \(0.426458\pi\) | |||||||
\(662\) | 7.26379e28 | 0.174644 | ||||||||
\(663\) | −3.17060e28 | −0.0750325 | ||||||||
\(664\) | −5.79151e28 | −0.134905 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.92443e28 | −0.0885720 | ||||||||
\(667\) | 3.14067e29 | 0.697752 | ||||||||
\(668\) | −3.81513e29 | −0.834367 | ||||||||
\(669\) | 6.08595e29 | 1.31025 | ||||||||
\(670\) | 1.05713e29 | 0.224049 | ||||||||
\(671\) | 5.86406e29 | 1.22352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.53001e29 | 1.52278 | 0.761390 | − | 0.648294i | \(-0.224517\pi\) | ||||
0.761390 | + | 0.648294i | \(0.224517\pi\) | |||||||
\(674\) | 4.41005e28 | 0.0878041 | ||||||||
\(675\) | 4.73466e27 | 0.00928109 | ||||||||
\(676\) | 4.84547e29 | 0.935181 | ||||||||
\(677\) | 8.12052e29 | 1.54313 | 0.771565 | − | 0.636150i | \(-0.219474\pi\) | ||||
0.771565 | + | 0.636150i | \(0.219474\pi\) | |||||||
\(678\) | −1.83981e28 | −0.0344239 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.82130e28 | 0.141885 | ||||||||
\(681\) | 7.01320e29 | 1.25277 | ||||||||
\(682\) | −5.18482e28 | −0.0912007 | ||||||||
\(683\) | 4.69973e29 | 0.814058 | 0.407029 | − | 0.913415i | \(-0.366565\pi\) | ||||
0.407029 | + | 0.913415i | \(0.366565\pi\) | |||||||
\(684\) | −9.79650e28 | −0.167102 | ||||||||
\(685\) | 8.67346e29 | 1.45694 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.89896e29 | −1.44975 | ||||||||
\(688\) | −7.51789e29 | −1.20619 | ||||||||
\(689\) | 1.64329e29 | 0.259664 | ||||||||
\(690\) | −5.93003e28 | −0.0922871 | ||||||||
\(691\) | −3.58806e29 | −0.549971 | −0.274985 | − | 0.961448i | \(-0.588673\pi\) | ||||
−0.274985 | + | 0.961448i | \(0.588673\pi\) | |||||||
\(692\) | −8.42962e29 | −1.27261 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.31496e28 | −0.136429 | ||||||||
\(695\) | 9.68616e29 | 1.39737 | ||||||||
\(696\) | −6.48845e29 | −0.922027 | ||||||||
\(697\) | −6.29466e28 | −0.0881106 | ||||||||
\(698\) | −1.95222e29 | −0.269183 | ||||||||
\(699\) | 5.84501e29 | 0.793917 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.33110e29 | −0.966339 | −0.483170 | − | 0.875527i | \(-0.660515\pi\) | ||||
−0.483170 | + | 0.875527i | \(0.660515\pi\) | |||||||
\(702\) | 1.29237e28 | 0.0167821 | ||||||||
\(703\) | 1.75774e29 | 0.224865 | ||||||||
\(704\) | 6.73133e29 | 0.848376 | ||||||||
\(705\) | 4.09771e29 | 0.508810 | ||||||||
\(706\) | 1.97076e29 | 0.241093 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.55085e30 | −1.84171 | ||||||||
\(709\) | 1.20909e30 | 1.41473 | 0.707365 | − | 0.706848i | \(-0.249884\pi\) | ||||
0.707365 | + | 0.706848i | \(0.249884\pi\) | |||||||
\(710\) | −3.51067e28 | −0.0404741 | ||||||||
\(711\) | −3.14788e29 | −0.357592 | ||||||||
\(712\) | 5.97131e29 | 0.668390 | ||||||||
\(713\) | 1.40346e29 | 0.154796 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.65270e29 | 0.177003 | ||||||||
\(716\) | −9.60277e29 | −1.01347 | ||||||||
\(717\) | −3.52379e29 | −0.366488 | ||||||||
\(718\) | 1.97424e28 | 0.0202345 | ||||||||
\(719\) | 5.25189e29 | 0.530472 | 0.265236 | − | 0.964183i | \(-0.414550\pi\) | ||||
0.265236 | + | 0.964183i | \(0.414550\pi\) | |||||||
\(720\) | −5.16003e29 | −0.513642 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.87624e29 | 0.181404 | ||||||||
\(723\) | 1.04223e30 | 0.993140 | ||||||||
\(724\) | −5.81356e28 | −0.0545993 | ||||||||
\(725\) | 3.61782e28 | 0.0334886 | ||||||||
\(726\) | −5.83532e28 | −0.0532390 | ||||||||
\(727\) | −7.23318e29 | −0.650456 | −0.325228 | − | 0.945636i | \(-0.605441\pi\) | ||||
−0.325228 | + | 0.945636i | \(0.605441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.46052e28 | −0.0739193 | ||||||||
\(730\) | 2.69776e29 | 0.232335 | ||||||||
\(731\) | 5.90940e29 | 0.501662 | ||||||||
\(732\) | 1.60658e30 | 1.34442 | ||||||||
\(733\) | 2.11409e30 | 1.74394 | 0.871969 | − | 0.489560i | \(-0.162843\pi\) | ||||
0.871969 | + | 0.489560i | \(0.162843\pi\) | |||||||
\(734\) | 3.27097e29 | 0.265992 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.65955e29 | 0.210180 | ||||||||
\(737\) | −1.60666e30 | −1.25174 | ||||||||
\(738\) | −3.64702e28 | −0.0280122 | ||||||||
\(739\) | −7.42069e29 | −0.561924 | −0.280962 | − | 0.959719i | \(-0.590653\pi\) | ||||
−0.280962 | + | 0.959719i | \(0.590653\pi\) | |||||||
\(740\) | 9.67311e29 | 0.722159 | ||||||||
\(741\) | 8.22782e28 | 0.0605611 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.69968e30 | 1.21614 | 0.608071 | − | 0.793882i | \(-0.291943\pi\) | ||||
0.608071 | + | 0.793882i | \(0.291943\pi\) | |||||||
\(744\) | −2.89948e29 | −0.204552 | ||||||||
\(745\) | −1.06752e30 | −0.742569 | ||||||||
\(746\) | −1.10297e29 | −0.0756494 | ||||||||
\(747\) | −3.00339e29 | −0.203117 | ||||||||
\(748\) | −5.82362e29 | −0.388353 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.89747e29 | −0.252720 | ||||||||
\(751\) | 5.90225e29 | 0.377397 | 0.188698 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188698 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(752\) | −5.70661e29 | −0.359824 | ||||||||
\(753\) | −8.55430e29 | −0.531909 | ||||||||
\(754\) | 9.87515e28 | 0.0605542 | ||||||||
\(755\) | −1.23443e30 | −0.746490 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.33308e30 | 0.784058 | 0.392029 | − | 0.919953i | \(-0.371773\pi\) | ||||
0.392029 | + | 0.919953i | \(0.371773\pi\) | |||||||
\(758\) | −2.05853e28 | −0.0119407 | ||||||||
\(759\) | 9.01264e29 | 0.515601 | ||||||||
\(760\) | −2.02966e29 | −0.114520 | ||||||||
\(761\) | 7.86217e29 | 0.437526 | 0.218763 | − | 0.975778i | \(-0.429798\pi\) | ||||
0.218763 | + | 0.975778i | \(0.429798\pi\) | |||||||
\(762\) | −6.07106e28 | −0.0333225 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.78535e30 | −0.953329 | ||||||||
\(765\) | 4.05601e29 | 0.213626 | ||||||||
\(766\) | −3.98665e29 | −0.207112 | ||||||||
\(767\) | 4.81786e29 | 0.246890 | ||||||||
\(768\) | 1.56392e30 | 0.790537 | ||||||||
\(769\) | 1.65083e30 | 0.823142 | 0.411571 | − | 0.911378i | \(-0.364980\pi\) | ||||
0.411571 | + | 0.911378i | \(0.364980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.02644e29 | −0.0983247 | ||||||||
\(772\) | −1.73929e29 | −0.0832510 | ||||||||
\(773\) | −3.77930e30 | −1.78454 | −0.892271 | − | 0.451499i | \(-0.850889\pi\) | ||||
−0.892271 | + | 0.451499i | \(0.850889\pi\) | |||||||
\(774\) | 3.42381e29 | 0.159488 | ||||||||
\(775\) | 1.61668e28 | 0.00742946 | ||||||||
\(776\) | −9.57056e29 | −0.433899 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.70054e29 | −0.207425 | ||||||||
\(779\) | 1.63349e29 | 0.0711169 | ||||||||
\(780\) | 4.52790e29 | 0.194493 | ||||||||
\(781\) | 5.33563e29 | 0.226126 | ||||||||
\(782\) | −6.49144e28 | −0.0271438 | ||||||||
\(783\) | 2.36723e30 | 0.976655 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.37555e30 | 0.552516 | ||||||||
\(786\) | −5.14488e29 | −0.203910 | ||||||||
\(787\) | 3.58219e30 | 1.40092 | 0.700461 | − | 0.713691i | \(-0.252978\pi\) | ||||
0.700461 | + | 0.713691i | \(0.252978\pi\) | |||||||
\(788\) | 1.40795e30 | 0.543327 | ||||||||
\(789\) | −4.38169e30 | −1.66853 | ||||||||
\(790\) | −3.19514e29 | −0.120062 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.88717e29 | −0.252015 | ||||||||
\(793\) | −4.99099e29 | −0.180226 | ||||||||
\(794\) | 3.48564e29 | 0.124213 | ||||||||
\(795\) | −5.68331e30 | −1.99870 | ||||||||
\(796\) | −2.50854e30 | −0.870631 | ||||||||
\(797\) | 4.45901e30 | 1.52731 | 0.763654 | − | 0.645626i | \(-0.223404\pi\) | ||||
0.763654 | + | 0.645626i | \(0.223404\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.48565e29 | 0.149653 | ||||||||
\(800\) | 3.06360e28 | 0.0100876 | ||||||||
\(801\) | 3.09664e30 | 1.00635 | ||||||||
\(802\) | 1.87591e29 | 0.0601702 | ||||||||
\(803\) | −4.10015e30 | −1.29803 | ||||||||
\(804\) | −4.40178e30 | −1.37543 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.41288e28 | 0.0134340 | ||||||||
\(807\) | 4.61229e30 | 1.38594 | ||||||||
\(808\) | 1.18646e30 | 0.351912 | ||||||||
\(809\) | 3.09156e30 | 0.905144 | 0.452572 | − | 0.891728i | \(-0.350507\pi\) | ||||
0.452572 | + | 0.891728i | \(0.350507\pi\) | |||||||
\(810\) | −8.47291e29 | −0.244872 | ||||||||
\(811\) | 9.85711e29 | 0.281210 | 0.140605 | − | 0.990066i | \(-0.455095\pi\) | ||||
0.140605 | + | 0.990066i | \(0.455095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.17090e30 | −0.881518 | ||||||||
\(814\) | 6.05400e29 | 0.166144 | ||||||||
\(815\) | −1.87948e30 | −0.509194 | ||||||||
\(816\) | −1.52710e30 | −0.408432 | ||||||||
\(817\) | −1.53351e30 | −0.404907 | ||||||||
\(818\) | −1.28232e30 | −0.334262 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.98935e29 | 0.228393 | ||||||||
\(821\) | −5.81930e30 | −1.45971 | −0.729856 | − | 0.683601i | \(-0.760413\pi\) | ||||
−0.729856 | + | 0.683601i | \(0.760413\pi\) | |||||||
\(822\) | 1.48721e30 | 0.368314 | ||||||||
\(823\) | 1.82848e30 | 0.447086 | 0.223543 | − | 0.974694i | \(-0.428238\pi\) | ||||
0.223543 | + | 0.974694i | \(0.428238\pi\) | |||||||
\(824\) | 6.98303e29 | 0.168581 | ||||||||
\(825\) | 1.03819e29 | 0.0247463 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.80997e30 | −0.885347 | −0.442673 | − | 0.896683i | \(-0.645970\pi\) | ||||
−0.442673 | + | 0.896683i | \(0.645970\pi\) | |||||||
\(828\) | 9.13327e29 | 0.209560 | ||||||||
\(829\) | −9.24247e29 | −0.209395 | −0.104697 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104697 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(830\) | −3.04848e29 | −0.0681966 | ||||||||
\(831\) | −7.88112e30 | −1.74091 | ||||||||
\(832\) | −5.72914e29 | −0.124967 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.66086e30 | 0.353255 | ||||||||
\(835\) | −4.09904e30 | −0.860942 | ||||||||
\(836\) | 1.51125e30 | 0.313452 | ||||||||
\(837\) | 1.05784e30 | 0.216671 | ||||||||
\(838\) | 1.41959e30 | 0.287144 | ||||||||
\(839\) | −2.18057e30 | −0.435582 | −0.217791 | − | 0.975995i | \(-0.569885\pi\) | ||||
−0.217791 | + | 0.975995i | \(0.569885\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.29554e31 | 2.52403 | ||||||||
\(842\) | −4.32418e29 | −0.0832007 | ||||||||
\(843\) | 2.23815e30 | 0.425304 | ||||||||
\(844\) | −7.06668e30 | −1.32623 | ||||||||
\(845\) | 5.20605e30 | 0.964968 | ||||||||
\(846\) | 2.59891e29 | 0.0475776 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.91477e30 | 1.41345 | ||||||||
\(849\) | −9.75655e30 | −1.72094 | ||||||||
\(850\) | −7.47765e27 | −0.00130277 | ||||||||
\(851\) | −1.63874e30 | −0.282000 | ||||||||
\(852\) | 1.46181e30 | 0.248470 | ||||||||
\(853\) | 4.27754e30 | 0.718173 | 0.359087 | − | 0.933304i | \(-0.383088\pi\) | ||||
0.359087 | + | 0.933304i | \(0.383088\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.05255e30 | −0.172424 | ||||||||
\(856\) | 1.32865e30 | 0.214998 | ||||||||
\(857\) | 1.76322e29 | 0.0281843 | 0.0140922 | − | 0.999901i | \(-0.495514\pi\) | ||||
0.0140922 | + | 0.999901i | \(0.495514\pi\) | |||||||
\(858\) | 2.83383e29 | 0.0447463 | ||||||||
\(859\) | −4.74009e30 | −0.739365 | −0.369682 | − | 0.929158i | \(-0.620533\pi\) | ||||
−0.369682 | + | 0.929158i | \(0.620533\pi\) | |||||||
\(860\) | −8.43916e30 | −1.30037 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.07136e30 | 0.311479 | ||||||||
\(863\) | 8.10824e29 | 0.120452 | 0.0602259 | − | 0.998185i | \(-0.480818\pi\) | ||||
0.0602259 | + | 0.998185i | \(0.480818\pi\) | |||||||
\(864\) | 2.00459e30 | 0.294192 | ||||||||
\(865\) | −9.05691e30 | −1.31314 | ||||||||
\(866\) | 1.21854e30 | 0.174543 | ||||||||
\(867\) | −7.70171e30 | −1.08990 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.85607e30 | 0.670775 | ||||||||
\(870\) | −3.41532e30 | −0.466100 | ||||||||
\(871\) | 1.36745e30 | 0.184383 | ||||||||
\(872\) | 2.04127e30 | 0.271942 | ||||||||
\(873\) | −4.96315e30 | −0.653293 | ||||||||
\(874\) | 1.68455e29 | 0.0219086 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.12332e31 | −1.42630 | ||||||||
\(877\) | 1.55255e30 | 0.194782 | 0.0973912 | − | 0.995246i | \(-0.468950\pi\) | ||||
0.0973912 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(878\) | 1.30532e30 | 0.161817 | ||||||||
\(879\) | −6.29641e30 | −0.771275 | ||||||||
\(880\) | 7.96009e30 | 0.963496 | ||||||||
\(881\) | 5.75722e30 | 0.688598 | 0.344299 | − | 0.938860i | \(-0.388117\pi\) | ||||
0.344299 | + | 0.938860i | \(0.388117\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.29134e31 | −1.50818 | −0.754088 | − | 0.656774i | \(-0.771921\pi\) | ||||
−0.754088 | + | 0.656774i | \(0.771921\pi\) | |||||||
\(884\) | 4.95657e29 | 0.0572048 | ||||||||
\(885\) | −1.66626e31 | −1.90037 | ||||||||
\(886\) | 1.32822e30 | 0.149698 | ||||||||
\(887\) | 4.22752e30 | 0.470856 | 0.235428 | − | 0.971892i | \(-0.424351\pi\) | ||||
0.235428 | + | 0.971892i | \(0.424351\pi\) | |||||||
\(888\) | 3.38554e30 | 0.372642 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.14312e30 | 0.337883 | ||||||||
\(891\) | 1.28774e31 | 1.36808 | ||||||||
\(892\) | −9.51411e30 | −0.998935 | ||||||||
\(893\) | −1.16404e30 | −0.120789 | ||||||||
\(894\) | −1.83045e30 | −0.187722 | ||||||||
\(895\) | −1.03174e31 | −1.04575 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.67079e29 | −0.0759486 | ||||||||
\(898\) | 3.61992e28 | 0.00354240 | ||||||||
\(899\) | 8.08306e30 | 0.781806 | ||||||||
\(900\) | 1.05208e29 | 0.0100578 | ||||||||
\(901\) | −6.22137e30 | −0.587862 | ||||||||
\(902\) | 5.62606e29 | 0.0525455 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.87074e29 | 0.0535704 | ||||||||
\(905\) | −6.24617e29 | −0.0563383 | ||||||||
\(906\) | −2.11664e30 | −0.188713 | ||||||||
\(907\) | 1.34786e31 | 1.18787 | 0.593935 | − | 0.804513i | \(-0.297574\pi\) | ||||
0.593935 | + | 0.804513i | \(0.297574\pi\) | |||||||
\(908\) | −1.09637e31 | −0.955113 | ||||||||
\(909\) | 6.15281e30 | 0.529850 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.28886e31 | −1.08458 | −0.542292 | − | 0.840190i | \(-0.682443\pi\) | ||||
−0.542292 | + | 0.840190i | \(0.682443\pi\) | |||||||
\(912\) | 3.96287e30 | 0.329658 | ||||||||
\(913\) | 4.63317e30 | 0.381009 | ||||||||
\(914\) | −3.33860e30 | −0.271413 | ||||||||
\(915\) | 1.72613e31 | 1.38724 | ||||||||
\(916\) | 1.39117e31 | 1.10529 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.89281e29 | −0.0379936 | ||||||||
\(919\) | 1.25018e30 | 0.0959753 | 0.0479876 | − | 0.998848i | \(-0.484719\pi\) | ||||
0.0479876 | + | 0.998848i | \(0.484719\pi\) | |||||||
\(920\) | 1.89225e30 | 0.143617 | ||||||||
\(921\) | 2.80864e31 | 2.10751 | ||||||||
\(922\) | 2.95239e30 | 0.219028 | ||||||||
\(923\) | −4.54123e29 | −0.0333086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.88770e29 | −0.0135346 | ||||||||
\(926\) | 1.64967e30 | 0.116945 | ||||||||
\(927\) | 3.62130e30 | 0.253821 | ||||||||
\(928\) | 1.53173e31 | 1.06152 | ||||||||
\(929\) | 1.41245e31 | 0.967850 | 0.483925 | − | 0.875109i | \(-0.339211\pi\) | ||||
0.483925 | + | 0.875109i | \(0.339211\pi\) | |||||||
\(930\) | −1.52620e30 | −0.103404 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.13746e30 | −0.605283 | ||||||||
\(933\) | 5.21360e30 | 0.341492 | ||||||||
\(934\) | 3.24455e30 | 0.210142 | ||||||||
\(935\) | −6.25699e30 | −0.400722 | ||||||||
\(936\) | 5.86177e29 | 0.0371221 | ||||||||
\(937\) | 7.12851e30 | 0.446409 | 0.223204 | − | 0.974772i | \(-0.428348\pi\) | ||||
0.223204 | + | 0.974772i | \(0.428348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.12632e30 | 0.0689721 | ||||||||
\(940\) | −6.40592e30 | −0.387917 | ||||||||
\(941\) | 1.07254e29 | 0.00642275 | 0.00321138 | − | 0.999995i | \(-0.498978\pi\) | ||||
0.00321138 | + | 0.999995i | \(0.498978\pi\) | |||||||
\(942\) | 2.35861e30 | 0.139676 | ||||||||
\(943\) | −1.52290e30 | −0.0891864 | ||||||||
\(944\) | 2.32049e31 | 1.34392 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.28172e30 | −0.299170 | ||||||||
\(947\) | 2.92935e31 | 1.64095 | 0.820477 | − | 0.571680i | \(-0.193708\pi\) | ||||
0.820477 | + | 0.571680i | \(0.193708\pi\) | |||||||
\(948\) | 1.33042e31 | 0.737058 | ||||||||
\(949\) | 3.48969e30 | 0.191202 | ||||||||
\(950\) | 1.94048e28 | 0.00105150 | ||||||||
\(951\) | −4.11989e30 | −0.220796 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.04320e31 | 1.59535 | 0.797675 | − | 0.603088i | \(-0.206063\pi\) | ||||
0.797675 | + | 0.603088i | \(0.206063\pi\) | |||||||
\(954\) | −3.60456e30 | −0.186893 | ||||||||
\(955\) | −1.91821e31 | −0.983694 | ||||||||
\(956\) | 5.50872e30 | 0.279410 | ||||||||
\(957\) | 5.19071e31 | 2.60406 | ||||||||
\(958\) | −3.38034e30 | −0.167735 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.98142e31 | 0.961899 | ||||||||
\(961\) | −1.72134e31 | −0.826556 | ||||||||
\(962\) | −5.15264e29 | −0.0244733 | ||||||||
\(963\) | 6.89017e30 | 0.323709 | ||||||||
\(964\) | −1.62931e31 | −0.757171 | ||||||||
\(965\) | −1.86871e30 | −0.0859026 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.78485e31 | −1.70244 | −0.851218 | − | 0.524813i | \(-0.824135\pi\) | ||||
−0.851218 | + | 0.524813i | \(0.824135\pi\) | |||||||
\(968\) | 1.86203e30 | 0.0828504 | ||||||||
\(969\) | −3.11500e30 | −0.137106 | ||||||||
\(970\) | −5.03765e30 | −0.219344 | ||||||||
\(971\) | 1.62334e31 | 0.699212 | 0.349606 | − | 0.936897i | \(-0.386316\pi\) | ||||
0.349606 | + | 0.936897i | \(0.386316\pi\) | |||||||
\(972\) | 2.35532e31 | 1.00358 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.36878e30 | −0.0570776 | ||||||||
\(975\) | −8.83618e28 | −0.00364516 | ||||||||
\(976\) | −2.40387e31 | −0.981043 | ||||||||
\(977\) | 2.98858e30 | 0.120662 | 0.0603312 | − | 0.998178i | \(-0.480784\pi\) | ||||
0.0603312 | + | 0.998178i | \(0.480784\pi\) | |||||||
\(978\) | −3.22269e30 | −0.128724 | ||||||||
\(979\) | −4.77701e31 | −1.88772 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.05857e31 | 0.409445 | ||||||||
\(982\) | 7.48330e30 | 0.286367 | ||||||||
\(983\) | 2.41371e31 | 0.913846 | 0.456923 | − | 0.889506i | \(-0.348951\pi\) | ||||
0.456923 | + | 0.889506i | \(0.348951\pi\) | |||||||
\(984\) | 3.14623e30 | 0.117853 | ||||||||
\(985\) | 1.51272e31 | 0.560632 | ||||||||
\(986\) | −3.73866e30 | −0.137091 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.28625e30 | −0.0461718 | ||||||||
\(989\) | 1.42969e31 | 0.507786 | ||||||||
\(990\) | −3.62520e30 | −0.127398 | ||||||||
\(991\) | −2.29436e31 | −0.797790 | −0.398895 | − | 0.916997i | \(-0.630606\pi\) | ||||
−0.398895 | + | 0.916997i | \(0.630606\pi\) | |||||||
\(992\) | 6.84481e30 | 0.235499 | ||||||||
\(993\) | −3.24964e31 | −1.10629 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.69521e31 | −0.898361 | ||||||||
\(996\) | 1.26935e31 | 0.418658 | ||||||||
\(997\) | −3.55036e31 | −1.15871 | −0.579354 | − | 0.815076i | \(-0.696695\pi\) | ||||
−0.579354 | + | 0.815076i | \(0.696695\pi\) | |||||||
\(998\) | −1.10738e31 | −0.357624 | ||||||||
\(999\) | −1.23517e31 | −0.394719 |
(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 | 49.22.a.a.1.1 | 1 | ||
7.6 | odd | 2 | 1.22.a.a.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 9.22.a.c.1.1 | 1 | |||
28.27 | even | 2 | 16.22.a.c.1.1 | 1 | |||
35.13 | even | 4 | 25.22.b.a.24.2 | 2 | |||
35.27 | even | 4 | 25.22.b.a.24.1 | 2 | |||
35.34 | odd | 2 | 25.22.a.a.1.1 | 1 | |||
56.13 | odd | 2 | 64.22.a.g.1.1 | 1 | |||
56.27 | even | 2 | 64.22.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.22.a.a.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
9.22.a.c.1.1 | 1 | 21.20 | even | 2 | |||
16.22.a.c.1.1 | 1 | 28.27 | even | 2 | |||
25.22.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
25.22.b.a.24.1 | 2 | 35.27 | even | 4 | |||
25.22.b.a.24.2 | 2 | 35.13 | even | 4 | |||
49.22.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
64.22.a.a.1.1 | 1 | 56.27 | even | 2 | |||
64.22.a.g.1.1 | 1 | 56.13 | odd | 2 |