Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,22,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(2.79477344287\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 | \(-0.716898\pi\) | ||||
−0.629885 | + | 0.776689i | \(0.716898\pi\) | |||||||
\(4\) | −2.01421e6 | −0.960449 | ||||||||
\(5\) | 2.16410e7 | 0.991040 | 0.495520 | − | 0.868596i | \(-0.334977\pi\) | ||||
0.495520 | + | 0.868596i | \(0.334977\pi\) | |||||||
\(6\) | 3.71071e7 | 0.250535 | ||||||||
\(7\) | −7.68079e8 | −1.02772 | −0.513862 | − | 0.857873i | \(-0.671786\pi\) | ||||
−0.513862 | + | 0.857873i | \(0.671786\pi\) | |||||||
\(8\) | 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 | \(-0.525843\pi\) | ||||
−0.0810993 | + | 0.996706i | \(0.525843\pi\) | |||||||
\(14\) | 2.21207e11 | 0.204387 | ||||||||
\(15\) | −2.78831e12 | −1.24848 | ||||||||
\(16\) | 3.88309e12 | 0.882912 | ||||||||
\(17\) | 3.05228e12 | 0.367207 | 0.183604 | − | 0.983000i | \(-0.441224\pi\) | ||||
0.183604 | + | 0.983000i | \(0.441224\pi\) | |||||||
\(18\) | −1.76844e12 | −0.116743 | ||||||||
\(19\) | −7.92079e12 | −0.296385 | −0.148192 | − | 0.988959i | \(-0.547345\pi\) | ||||
−0.148192 | + | 0.988959i | \(0.547345\pi\) | |||||||
\(20\) | −4.35894e13 | −0.951844 | ||||||||
\(21\) | 9.89623e13 | 1.29469 | ||||||||
\(22\) | 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 | ||||||||
\(28\) | 1.54707e15 | 0.987076 | ||||||||
\(29\) | −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 | \(-0.433229\pi\) | ||||
0.208233 | + | 0.978079i | \(0.433229\pi\) | |||||||
\(32\) | −3.60151e15 | −0.565470 | ||||||||
\(33\) | 1.22047e16 | 1.38718 | ||||||||
\(34\) | −8.79057e14 | −0.0730279 | ||||||||
\(35\) | −1.66220e16 | −1.01852 | ||||||||
\(36\) | −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 | \(-0.538281\pi\) | ||||
−0.119974 | + | 0.992777i | \(0.538281\pi\) | |||||||
\(42\) | −2.85012e16 | −0.257481 | ||||||||
\(43\) | −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 | \(-0.434680\pi\) | ||||
0.203771 | + | 0.979019i | \(0.434680\pi\) | |||||||
\(48\) | −5.00313e17 | −1.11227 | ||||||||
\(49\) | 3.13992e16 | 0.0562160 | ||||||||
\(50\) | 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 | ||||||||
\(56\) | −9.09460e17 | −0.400691 | ||||||||
\(57\) | 1.02055e18 | 0.373376 | ||||||||
\(58\) | 1.22487e18 | 0.373334 | ||||||||
\(59\) | −5.97588e18 | −1.52214 | −0.761072 | − | 0.648667i | \(-0.775327\pi\) | ||||
−0.761072 | + | 0.648667i | \(0.775327\pi\) | |||||||
\(60\) | 5.61623e18 | 1.19910 | ||||||||
\(61\) | 6.19062e18 | 1.11114 | 0.555572 | − | 0.831468i | \(-0.312499\pi\) | ||||
0.555572 | + | 0.831468i | \(0.312499\pi\) | |||||||
\(62\) | −5.47356e17 | −0.0828242 | ||||||||
\(63\) | −4.71633e18 | −0.603293 | ||||||||
\(64\) | −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 | ||||||||
\(70\) | 4.78712e18 | 0.202556 | ||||||||
\(71\) | −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 | \(-0.700638\pi\) | ||||
−0.589407 | + | 0.807837i | \(0.700638\pi\) | |||||||
\(74\) | −6.39113e18 | −0.150885 | ||||||||
\(75\) | 1.09600e18 | 0.0224734 | ||||||||
\(76\) | 1.59541e19 | 0.284662 | ||||||||
\(77\) | 7.27562e19 | 1.13166 | ||||||||
\(78\) | −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 | \(-0.444652\pi\) | ||||
0.173007 | + | 0.984921i | \(0.444652\pi\) | |||||||
\(84\) | −1.99331e20 | −1.24349 | ||||||||
\(85\) | 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 | \(-0.827779\pi\) | ||||
−0.857170 | + | 0.515034i | \(0.827779\pi\) | |||||||
\(90\) | −3.82708e19 | −0.115697 | ||||||||
\(91\) | 6.19239e19 | 0.166695 | ||||||||
\(92\) | 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 | \(-0.312163\pi\) | ||||
0.556450 | + | 0.830881i | \(0.312163\pi\) | |||||||
\(98\) | −9.04297e18 | −0.0111799 | ||||||||
\(99\) | −5.81651e20 | −0.646388 | ||||||||
\(100\) | 1.71337e19 | 0.0171337 | ||||||||
\(101\) | −1.00202e21 | −0.902612 | −0.451306 | − | 0.892369i | \(-0.649042\pi\) | ||||
−0.451306 | + | 0.892369i | \(0.649042\pi\) | |||||||
\(102\) | 1.13261e20 | 0.0919983 | ||||||||
\(103\) | −5.89747e20 | −0.432389 | −0.216195 | − | 0.976350i | \(-0.569365\pi\) | ||||
−0.216195 | + | 0.976350i | \(0.569365\pi\) | |||||||
\(104\) | −9.54620e19 | −0.0632383 | ||||||||
\(105\) | 2.14164e21 | 1.28309 | ||||||||
\(106\) | −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 | ||||||||
\(112\) | −2.98252e21 | −0.907389 | ||||||||
\(113\) | 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 | ||||||||
\(119\) | −2.34439e21 | −0.377387 | ||||||||
\(120\) | −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 | ||||||||
\(126\) | 1.35830e21 | 0.119979 | ||||||||
\(127\) | 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 | \(-0.633407\pi\) | ||||
−0.406949 | + | 0.913451i | \(0.633407\pi\) | |||||||
\(132\) | −2.45829e22 | −1.33231 | ||||||||
\(133\) | 6.08379e21 | 0.304601 | ||||||||
\(134\) | −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 | \(-0.250946\pi\) | ||||
0.705001 | + | 0.709206i | \(0.250946\pi\) | |||||||
\(140\) | 3.34801e22 | 0.978232 | ||||||||
\(141\) | −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 | ||||||||
\(147\) | −4.04560e21 | −0.0708191 | ||||||||
\(148\) | −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 | ||||||||
\(154\) | −2.09538e22 | −0.225058 | ||||||||
\(155\) | 4.11295e22 | 0.412735 | ||||||||
\(156\) | −2.09229e22 | −0.196251 | ||||||||
\(157\) | 6.35623e22 | 0.557511 | 0.278756 | − | 0.960362i | \(-0.410078\pi\) | ||||
0.278756 | + | 0.960362i | \(0.410078\pi\) | |||||||
\(158\) | 1.47643e22 | 0.121147 | ||||||||
\(159\) | −2.62618e23 | −2.01677 | ||||||||
\(160\) | −7.79400e22 | −0.560403 | ||||||||
\(161\) | 5.67191e22 | 0.381995 | ||||||||
\(162\) | 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 | \(-0.643026\pi\) | ||||
−0.434363 | + | 0.900738i | \(0.643026\pi\) | |||||||
\(168\) | 1.17179e23 | 0.504778 | ||||||||
\(169\) | −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 | \(-0.730507\pi\) | ||||
−0.662506 | + | 0.749057i | \(0.730507\pi\) | |||||||
\(174\) | −1.57818e23 | −0.470314 | ||||||||
\(175\) | 6.53362e21 | 0.0183339 | ||||||||
\(176\) | −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 | \(-0.509049\pi\) | ||||
−0.0284238 | + | 0.999596i | \(0.509049\pi\) | |||||||
\(182\) | −1.78341e22 | −0.0331513 | ||||||||
\(183\) | −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 | ||||||||
\(189\) | −4.27510e23 | −0.534685 | ||||||||
\(190\) | 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 | ||||||||
\(196\) | −6.32445e22 | −0.0539926 | ||||||||
\(197\) | −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 | \(-0.649732\pi\) | ||||
−0.453242 | + | 0.891388i | \(0.649732\pi\) | |||||||
\(200\) | −1.00722e22 | −0.00695522 | ||||||||
\(201\) | −2.18536e24 | −1.43207 | ||||||||
\(202\) | 2.88581e23 | 0.179506 | ||||||||
\(203\) | 3.26666e24 | 1.92928 | ||||||||
\(204\) | 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 | ||||||||
\(210\) | −6.16792e23 | −0.255174 | ||||||||
\(211\) | 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 | ||||||||
\(217\) | −1.45977e24 | −0.428012 | ||||||||
\(218\) | −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 | \(-0.674081\pi\) | ||||
−0.520035 | + | 0.854145i | \(0.674081\pi\) | |||||||
\(224\) | 2.76624e24 | 0.581147 | ||||||||
\(225\) | −5.22331e22 | −0.0104720 | ||||||||
\(226\) | −1.42793e23 | −0.0273256 | ||||||||
\(227\) | −5.44317e24 | −0.994444 | −0.497222 | − | 0.867623i | \(-0.665647\pi\) | ||||
−0.497222 | + | 0.867623i | \(0.665647\pi\) | |||||||
\(228\) | −2.05559e24 | −0.358609 | ||||||||
\(229\) | 6.90677e24 | 1.15081 | 0.575403 | − | 0.817870i | \(-0.304845\pi\) | ||||
0.575403 | + | 0.817870i | \(0.304845\pi\) | |||||||
\(230\) | 4.60249e23 | 0.0732572 | ||||||||
\(231\) | −9.37420e24 | −1.42564 | ||||||||
\(232\) | −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 | ||||||||
\(238\) | 6.75185e23 | 0.0750525 | ||||||||
\(239\) | −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 | \(-0.628970\pi\) | ||||
−0.394175 | + | 0.919035i | \(0.628970\pi\) | |||||||
\(242\) | −4.52898e23 | −0.0422609 | ||||||||
\(243\) | 1.16935e25 | 1.04491 | ||||||||
\(244\) | −1.24692e25 | −1.06720 | ||||||||
\(245\) | 6.79508e23 | 0.0557123 | ||||||||
\(246\) | −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 | \(-0.432291\pi\) | ||||
0.211113 | + | 0.977462i | \(0.432291\pi\) | |||||||
\(252\) | 9.49967e24 | 0.579432 | ||||||||
\(253\) | 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 | \(-0.487575\pi\) | ||||
0.0390249 | + | 0.999238i | \(0.487575\pi\) | |||||||
\(258\) | −7.18415e24 | −0.342270 | ||||||||
\(259\) | −1.70448e25 | −0.779729 | ||||||||
\(260\) | 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 | ||||||||
\(266\) | −1.75213e24 | −0.0605772 | ||||||||
\(267\) | 6.49765e25 | 2.15967 | ||||||||
\(268\) | −3.41636e25 | −1.09181 | ||||||||
\(269\) | −3.57975e25 | −1.10015 | −0.550077 | − | 0.835114i | \(-0.685402\pi\) | ||||
−0.550077 | + | 0.835114i | \(0.685402\pi\) | |||||||
\(270\) | −3.46904e24 | −0.102539 | ||||||||
\(271\) | 2.46104e25 | 0.699746 | 0.349873 | − | 0.936797i | \(-0.386225\pi\) | ||||
0.349873 | + | 0.936797i | \(0.386225\pi\) | |||||||
\(272\) | 1.18523e25 | 0.324212 | ||||||||
\(273\) | −7.97852e24 | −0.209998 | ||||||||
\(274\) | 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 | ||||||||
\(280\) | −1.96816e25 | −0.397101 | ||||||||
\(281\) | 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 | \(-0.260659\pi\) | ||||
0.683037 | + | 0.730383i | \(0.260659\pi\) | |||||||
\(284\) | 1.13455e25 | 0.197235 | ||||||||
\(285\) | 2.20856e25 | 0.370031 | ||||||||
\(286\) | −2.19943e24 | −0.0355194 | ||||||||
\(287\) | 1.58399e25 | 0.246600 | ||||||||
\(288\) | −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 | \(-0.400970\pi\) | ||||
0.306118 | + | 0.951994i | \(0.400970\pi\) | |||||||
\(294\) | 1.16513e24 | 0.0140841 | ||||||||
\(295\) | −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 | ||||||||
\(301\) | 1.48705e26 | 1.40403 | ||||||||
\(302\) | −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 | \(-0.815382\pi\) | ||||
−0.836466 | + | 0.548019i | \(0.815382\pi\) | |||||||
\(308\) | −1.46546e26 | −1.08691 | ||||||||
\(309\) | 7.59854e25 | 0.544711 | ||||||||
\(310\) | −1.18453e25 | −0.0820821 | ||||||||
\(311\) | −4.04644e25 | −0.271075 | −0.135538 | − | 0.990772i | \(-0.543276\pi\) | ||||
−0.135538 | + | 0.990772i | \(0.543276\pi\) | |||||||
\(312\) | 1.22997e25 | 0.0796657 | ||||||||
\(313\) | −8.74174e24 | −0.0547498 | −0.0273749 | − | 0.999625i | \(-0.508715\pi\) | ||||
−0.0273749 | + | 0.999625i | \(0.508715\pi\) | |||||||
\(314\) | −1.83060e25 | −0.110874 | ||||||||
\(315\) | −1.02066e26 | −0.597888 | ||||||||
\(316\) | 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 | ||||||||
\(322\) | −1.63351e25 | −0.0759688 | ||||||||
\(323\) | −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 | ||||||||
\(329\) | −1.12877e26 | −0.418841 | ||||||||
\(330\) | −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 | ||||||||
\(336\) | 3.84279e26 | 1.14310 | ||||||||
\(337\) | −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 | ||||||||
\(343\) | 4.04890e26 | 0.969949 | ||||||||
\(344\) | −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 | \(-0.736620\pi\) | ||||
−0.676767 | + | 0.736197i | \(0.736620\pi\) | |||||||
\(350\) | −1.88168e24 | −0.00364613 | ||||||||
\(351\) | −4.48739e25 | −0.0843857 | ||||||||
\(352\) | 3.41153e26 | 0.622660 | ||||||||
\(353\) | 6.84291e26 | 1.21229 | 0.606145 | − | 0.795354i | \(-0.292715\pi\) | ||||
0.606145 | + | 0.795354i | \(0.292715\pi\) | |||||||
\(354\) | −2.21748e26 | −0.381351 | ||||||||
\(355\) | −1.21898e26 | −0.203517 | ||||||||
\(356\) | 1.01577e27 | 1.64654 | ||||||||
\(357\) | 3.02061e26 | 0.475421 | ||||||||
\(358\) | −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 | ||||||||
\(364\) | −1.24728e26 | −0.160102 | ||||||||
\(365\) | −9.36723e26 | −1.16825 | ||||||||
\(366\) | 2.29716e26 | 0.278381 | ||||||||
\(367\) | 1.13575e27 | 1.33749 | 0.668745 | − | 0.743492i | \(-0.266832\pi\) | ||||
0.668745 | + | 0.743492i | \(0.266832\pi\) | |||||||
\(368\) | −2.86748e26 | −0.328170 | ||||||||
\(369\) | −1.26633e26 | −0.140854 | ||||||||
\(370\) | −1.38310e26 | −0.149533 | ||||||||
\(371\) | −1.56555e27 | −1.64528 | ||||||||
\(372\) | 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 | ||||||||
\(378\) | 1.23123e26 | 0.106335 | ||||||||
\(379\) | 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 | \(-0.674334\pi\) | ||||
−0.520712 | + | 0.853732i | \(0.674334\pi\) | |||||||
\(384\) | −1.23684e27 | −0.905388 | ||||||||
\(385\) | 1.57451e27 | 1.12152 | ||||||||
\(386\) | −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 | ||||||||
\(392\) | 3.71789e25 | 0.0219176 | ||||||||
\(393\) | 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 | \(-0.398904\pi\) | ||||
0.312291 | + | 0.949987i | \(0.398904\pi\) | |||||||
\(398\) | 3.58682e26 | 0.180276 | ||||||||
\(399\) | −7.83860e26 | −0.383728 | ||||||||
\(400\) | −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 | ||||||||
\(406\) | −9.40799e26 | −0.383684 | ||||||||
\(407\) | −2.10208e27 | −0.835427 | ||||||||
\(408\) | −4.65658e26 | −0.180358 | ||||||||
\(409\) | −4.45251e27 | −1.68078 | −0.840389 | − | 0.541984i | \(-0.817673\pi\) | ||||
−0.840389 | + | 0.541984i | \(0.817673\pi\) | |||||||
\(410\) | 1.28534e26 | 0.0472918 | ||||||||
\(411\) | 5.16393e27 | 1.85200 | ||||||||
\(412\) | 1.18787e27 | 0.415288 | ||||||||
\(413\) | 4.58995e27 | 1.56434 | ||||||||
\(414\) | 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 | \(-0.243258\pi\) | ||||
0.721925 | + | 0.691972i | \(0.243258\pi\) | |||||||
\(420\) | −4.31371e27 | −1.23235 | ||||||||
\(421\) | 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 | ||||||||
\(427\) | −4.75488e27 | −1.14195 | ||||||||
\(428\) | −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 | \(-0.355394\pi\) | ||||
0.438828 | + | 0.898571i | \(0.355394\pi\) | |||||||
\(434\) | 4.20412e26 | 0.0851203 | ||||||||
\(435\) | 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 | \(-0.366633\pi\) | ||||
0.406832 | + | 0.913503i | \(0.366633\pi\) | |||||||
\(440\) | −2.42727e27 | −0.425467 | ||||||||
\(441\) | 1.92804e26 | 0.0329998 | ||||||||
\(442\) | 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 | ||||||||
\(448\) | 5.45811e27 | 0.791815 | ||||||||
\(449\) | −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 | ||||||||
\(455\) | 1.34009e27 | 0.165202 | ||||||||
\(456\) | 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 | \(-0.314372\pi\) | ||||
0.550671 | + | 0.834723i | \(0.314372\pi\) | |||||||
\(462\) | 2.69977e27 | 0.283522 | ||||||||
\(463\) | −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 | \(-0.322819\pi\) | ||||
0.528329 | + | 0.849040i | \(0.322819\pi\) | |||||||
\(468\) | 9.97138e26 | 0.0914479 | ||||||||
\(469\) | −1.30276e28 | −1.16829 | ||||||||
\(470\) | −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 | ||||||||
\(476\) | 4.72210e27 | 0.362462 | ||||||||
\(477\) | 1.25158e28 | 0.939759 | ||||||||
\(478\) | 7.87660e26 | 0.0578557 | ||||||||
\(479\) | −1.17373e28 | −0.843422 | −0.421711 | − | 0.906730i | \(-0.638570\pi\) | ||||
−0.421711 | + | 0.906730i | \(0.638570\pi\) | |||||||
\(480\) | 1.00421e28 | 0.705979 | ||||||||
\(481\) | −1.78911e27 | −0.123059 | ||||||||
\(482\) | 2.32965e27 | 0.156782 | ||||||||
\(483\) | −7.30792e27 | −0.481226 | ||||||||
\(484\) | −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 | ||||||||
\(490\) | −1.95698e26 | −0.0110797 | ||||||||
\(491\) | −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 | ||||||||
\(497\) | 4.32640e27 | 0.211050 | ||||||||
\(498\) | 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 | \(-0.748657\pi\) | ||||
−0.704118 | + | 0.710083i | \(0.748657\pi\) | |||||||
\(504\) | −5.58447e27 | −0.235213 | ||||||||
\(505\) | −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 | \(-0.625596\pi\) | ||||
−0.384413 | + | 0.923161i | \(0.625596\pi\) | |||||||
\(510\) | 2.45108e27 | 0.0911740 | ||||||||
\(511\) | 3.32461e28 | 1.21149 | ||||||||
\(512\) | −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 | ||||||||
\(518\) | 4.90889e27 | 0.155068 | ||||||||
\(519\) | 5.39222e28 | 1.66921 | ||||||||
\(520\) | −2.06589e27 | −0.0626717 | ||||||||
\(521\) | 4.75207e27 | 0.141282 | 0.0706411 | − | 0.997502i | \(-0.477496\pi\) | ||||
0.0706411 | + | 0.997502i | \(0.477496\pi\) | |||||||
\(522\) | 7.52124e27 | 0.219154 | ||||||||
\(523\) | −1.28180e26 | −0.00366061 | −0.00183030 | − | 0.999998i | \(-0.500583\pi\) | ||||
−0.00183030 | + | 0.999998i | \(0.500583\pi\) | |||||||
\(524\) | 2.79269e28 | 0.781708 | ||||||||
\(525\) | −8.41817e26 | −0.0230964 | ||||||||
\(526\) | 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 | ||||||||
\(532\) | −1.22540e28 | −0.292554 | ||||||||
\(533\) | 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 | ||||||||
\(539\) | −2.97429e27 | −0.0619014 | ||||||||
\(540\) | −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 | ||||||||
\(546\) | 2.29781e27 | 0.0417630 | ||||||||
\(547\) | −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 | ||||||||
\(553\) | 3.93755e28 | 0.626055 | ||||||||
\(554\) | 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 | ||||||||
\(560\) | −6.45445e28 | −0.899259 | ||||||||
\(561\) | 3.72523e28 | 0.509382 | ||||||||
\(562\) | −5.00285e27 | −0.0671407 | ||||||||
\(563\) | −8.28332e28 | −1.09110 | −0.545552 | − | 0.838077i | \(-0.683680\pi\) | ||||
−0.545552 | + | 0.838077i | \(0.683680\pi\) | |||||||
\(564\) | 3.81390e28 | 0.493104 | ||||||||
\(565\) | 1.07298e28 | 0.136170 | ||||||||
\(566\) | −2.18084e28 | −0.271676 | ||||||||
\(567\) | 1.04417e29 | 1.27687 | ||||||||
\(568\) | −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 | ||||||||
\(574\) | −4.56190e27 | −0.0490423 | ||||||||
\(575\) | 6.28162e26 | 0.00663070 | ||||||||
\(576\) | −4.36350e28 | −0.452271 | ||||||||
\(577\) | 1.30727e28 | 0.133051 | 0.0665257 | − | 0.997785i | \(-0.478809\pi\) | ||||
0.0665257 | + | 0.997785i | \(0.478809\pi\) | |||||||
\(578\) | 1.72153e28 | 0.172057 | ||||||||
\(579\) | −1.11258e28 | −0.109196 | ||||||||
\(580\) | 1.85387e29 | 1.78684 | ||||||||
\(581\) | −3.75682e28 | −0.355607 | ||||||||
\(582\) | 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 | \(-0.759784\pi\) | ||||
−0.728503 | + | 0.685043i | \(0.759784\pi\) | |||||||
\(588\) | 8.14867e27 | 0.0680182 | ||||||||
\(589\) | −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 | \(-0.144721\pi\) | ||||
0.898412 | + | 0.439153i | \(0.144721\pi\) | |||||||
\(594\) | 1.51844e28 | 0.113931 | ||||||||
\(595\) | −5.07349e28 | −0.374006 | ||||||||
\(596\) | −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 | \(-0.538581\pi\) | ||||
−0.120908 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(602\) | −4.28269e28 | −0.279225 | ||||||||
\(603\) | 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 | \(-0.199125\pi\) | ||||
0.810630 | + | 0.585559i | \(0.199125\pi\) | |||||||
\(608\) | 2.85268e28 | 0.167597 | ||||||||
\(609\) | −4.20890e29 | −2.43045 | ||||||||
\(610\) | −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 | ||||||||
\(616\) | 8.61486e28 | 0.441215 | ||||||||
\(617\) | 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 | \(-0.404470\pi\) | ||||
0.295631 | + | 0.955302i | \(0.404470\pi\) | |||||||
\(620\) | −8.28434e28 | −0.396411 | ||||||||
\(621\) | −4.11022e28 | −0.193376 | ||||||||
\(622\) | 1.16538e28 | 0.0539097 | ||||||||
\(623\) | 3.87345e29 | 1.76187 | ||||||||
\(624\) | 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 | ||||||||
\(630\) | 2.93950e28 | 0.118904 | ||||||||
\(631\) | −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 | ||||||||
\(637\) | −2.53146e27 | −0.00911815 | ||||||||
\(638\) | −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 | \(-0.460541\pi\) | ||||
0.123647 | + | 0.992326i | \(0.460541\pi\) | |||||||
\(644\) | −1.14244e29 | −0.366887 | ||||||||
\(645\) | 5.39832e29 | 1.70562 | ||||||||
\(646\) | 6.96283e27 | 0.0216443 | ||||||||
\(647\) | −2.99088e29 | −0.914755 | −0.457377 | − | 0.889273i | \(-0.651211\pi\) | ||||
−0.457377 | + | 0.889273i | \(0.651211\pi\) | |||||||
\(648\) | −1.60969e29 | −0.484400 | ||||||||
\(649\) | 5.66065e29 | 1.67609 | ||||||||
\(650\) | −1.97512e26 | −0.000575443 0 | ||||||||
\(651\) | 1.88082e29 | 0.539196 | ||||||||
\(652\) | −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 | ||||||||
\(658\) | 3.25086e28 | 0.0832966 | ||||||||
\(659\) | 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 | \(-0.573542\pi\) | ||||
−0.228990 | + | 0.973429i | \(0.573542\pi\) | |||||||
\(662\) | 7.26379e28 | 0.174644 | ||||||||
\(663\) | 3.17060e28 | 0.0750325 | ||||||||
\(664\) | 5.79151e28 | 0.134905 | ||||||||
\(665\) | 1.31659e29 | 0.301872 | ||||||||
\(666\) | −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 | ||||||||
\(672\) | −3.56414e29 | −0.732111 | ||||||||
\(673\) | 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 | \(-0.780526\pi\) | ||||
−0.771565 | + | 0.636150i | \(0.780526\pi\) | |||||||
\(678\) | 1.83981e28 | 0.0344239 | ||||||||
\(679\) | −6.20819e29 | −1.14375 | ||||||||
\(680\) | 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 | ||||||||
\(686\) | −1.16608e29 | −0.192897 | ||||||||
\(687\) | −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 | \(-0.411327\pi\) | ||||
0.274985 | + | 0.961448i | \(0.411327\pi\) | |||||||
\(692\) | 8.42962e29 | 1.27261 | ||||||||
\(693\) | 4.46754e29 | 0.664308 | ||||||||
\(694\) | −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 | ||||||||
\(700\) | −1.31601e28 | −0.0176088 | ||||||||
\(701\) | −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 | ||||||||
\(707\) | 7.69629e29 | 0.927636 | ||||||||
\(708\) | −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 | ||||||||
\(714\) | −8.69936e28 | −0.0945488 | ||||||||
\(715\) | 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 | \(-0.585450\pi\) | ||||
−0.265236 | + | 0.964183i | \(0.585450\pi\) | |||||||
\(720\) | 5.16003e29 | 0.513642 | ||||||||
\(721\) | 4.52972e29 | 0.444377 | ||||||||
\(722\) | 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 | \(-0.394559\pi\) | ||||
0.325228 | + | 0.945636i | \(0.394559\pi\) | |||||||
\(728\) | 7.33223e28 | 0.0649915 | ||||||||
\(729\) | −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 | \(-0.837157\pi\) | ||||
−0.871969 | + | 0.489560i | \(0.837157\pi\) | |||||||
\(734\) | −3.27097e29 | −0.265992 | ||||||||
\(735\) | −8.75506e28 | −0.0701846 | ||||||||
\(736\) | 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 | ||||||||
\(742\) | 4.50878e29 | 0.327204 | ||||||||
\(743\) | 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 | ||||||||
\(749\) | −8.61862e29 | −0.566733 | ||||||||
\(750\) | −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 | ||||||||
\(756\) | 8.61095e29 | 0.513537 | ||||||||
\(757\) | 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 | \(-0.570202\pi\) | ||||
−0.218763 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(762\) | 6.07106e28 | 0.0333225 | ||||||||
\(763\) | −1.32412e30 | −0.716837 | ||||||||
\(764\) | −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 | \(-0.635020\pi\) | ||||
−0.411571 | + | 0.911378i | \(0.635020\pi\) | |||||||
\(770\) | −4.53460e29 | −0.223042 | ||||||||
\(771\) | −2.02644e29 | −0.0983247 | ||||||||
\(772\) | −1.73929e29 | −0.0832510 | ||||||||
\(773\) | 3.77930e30 | 1.78454 | 0.892271 | − | 0.451499i | \(-0.149111\pi\) | ||||
0.892271 | + | 0.451499i | \(0.149111\pi\) | |||||||
\(774\) | 3.42381e29 | 0.159488 | ||||||||
\(775\) | −1.61668e28 | −0.00742946 | ||||||||
\(776\) | 9.57056e29 | 0.433899 | ||||||||
\(777\) | 2.19612e30 | 0.982278 | ||||||||
\(778\) | −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 | ||||||||
\(784\) | 1.21926e29 | 0.0496337 | ||||||||
\(785\) | 1.37555e30 | 0.552516 | ||||||||
\(786\) | −5.14488e29 | −0.203910 | ||||||||
\(787\) | −3.58219e30 | −1.40092 | −0.700461 | − | 0.713691i | \(-0.747022\pi\) | ||||
−0.700461 | + | 0.713691i | \(0.747022\pi\) | |||||||
\(788\) | 1.40795e30 | 0.543327 | ||||||||
\(789\) | 4.38169e30 | 1.66853 | ||||||||
\(790\) | 3.19514e29 | 0.120062 | ||||||||
\(791\) | −3.80821e29 | −0.141211 | ||||||||
\(792\) | −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 | \(-0.776596\pi\) | ||||
−0.763654 | + | 0.645626i | \(0.776596\pi\) | |||||||
\(798\) | 2.25752e29 | 0.0763134 | ||||||||
\(799\) | 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 | ||||||||
\(805\) | 1.22746e30 | 0.378572 | ||||||||
\(806\) | 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 | \(-0.544905\pi\) | ||||
−0.140605 | + | 0.990066i | \(0.544905\pi\) | |||||||
\(812\) | −6.57974e30 | −1.85298 | ||||||||
\(813\) | −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 | ||||||||
\(819\) | 3.80239e29 | 0.0978533 | ||||||||
\(820\) | 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 | ||||||||
\(826\) | −1.32191e30 | −0.311107 | ||||||||
\(827\) | −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 | \(-0.466613\pi\) | ||||
0.104697 | + | 0.994504i | \(0.466613\pi\) | |||||||
\(830\) | −3.04848e29 | −0.0681966 | ||||||||
\(831\) | 7.88112e30 | 1.74091 | ||||||||
\(832\) | 5.72914e29 | 0.124967 | ||||||||
\(833\) | 9.58392e28 | 0.0206429 | ||||||||
\(834\) | 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 | \(-0.430115\pi\) | ||||
0.217791 | + | 0.975995i | \(0.430115\pi\) | |||||||
\(840\) | 2.53585e30 | 0.500255 | ||||||||
\(841\) | 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 | ||||||||
\(847\) | −1.20785e30 | −0.218393 | ||||||||
\(848\) | 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 | \(-0.616912\pi\) | ||||
−0.359087 | + | 0.933304i | \(0.616912\pi\) | |||||||
\(854\) | 1.36941e30 | 0.227104 | ||||||||
\(855\) | −1.05255e30 | −0.172424 | ||||||||
\(856\) | 1.32865e30 | 0.214998 | ||||||||
\(857\) | −1.76322e29 | −0.0281843 | −0.0140922 | − | 0.999901i | \(-0.504486\pi\) | ||||
−0.0140922 | + | 0.999901i | \(0.504486\pi\) | |||||||
\(858\) | 2.83383e29 | 0.0447463 | ||||||||
\(859\) | 4.74009e30 | 0.739365 | 0.369682 | − | 0.929158i | \(-0.379467\pi\) | ||||
0.369682 | + | 0.929158i | \(0.379467\pi\) | |||||||
\(860\) | 8.43916e30 | 1.30037 | ||||||||
\(861\) | −2.04088e30 | −0.310659 | ||||||||
\(862\) | 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 | ||||||||
\(868\) | 2.94027e30 | 0.411084 | ||||||||
\(869\) | 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 | ||||||||
\(875\) | 8.06736e30 | 1.03669 | ||||||||
\(876\) | −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 | \(-0.611883\pi\) | ||||
−0.344299 | + | 0.938860i | \(0.611883\pi\) | |||||||
\(882\) | −5.55276e28 | −0.00656280 | ||||||||
\(883\) | −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 | \(-0.575649\pi\) | ||||
−0.235428 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(888\) | −3.38554e30 | −0.372642 | ||||||||
\(889\) | −1.25665e30 | −0.136693 | ||||||||
\(890\) | 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 | ||||||||
\(896\) | −7.37317e30 | −0.738618 | ||||||||
\(897\) | −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 | ||||||||
\(903\) | −1.91597e31 | −1.76875 | ||||||||
\(904\) | 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 | ||||||||
\(910\) | −3.85946e29 | −0.0328543 | ||||||||
\(911\) | −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 | ||||||||
\(917\) | 1.06494e31 | 0.836463 | ||||||||
\(918\) | −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 | ||||||||
\(924\) | 1.88816e31 | 1.36925 | ||||||||
\(925\) | −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 | \(-0.660789\pi\) | ||||
−0.483925 | + | 0.875109i | \(0.660789\pi\) | |||||||
\(930\) | 1.52620e30 | 0.103404 | ||||||||
\(931\) | −2.48706e29 | −0.0166615 | ||||||||
\(932\) | −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 | \(-0.571652\pi\) | ||||
−0.223204 | + | 0.974772i | \(0.571652\pi\) | |||||||
\(938\) | 3.75196e30 | 0.232342 | ||||||||
\(939\) | 1.12632e30 | 0.0689721 | ||||||||
\(940\) | −6.40592e30 | −0.387917 | ||||||||
\(941\) | −1.07254e29 | −0.00642275 | −0.00321138 | − | 0.999995i | \(-0.501022\pi\) | ||||
−0.00321138 | + | 0.999995i | \(0.501022\pi\) | |||||||
\(942\) | 2.35861e30 | 0.139676 | ||||||||
\(943\) | 1.52290e30 | 0.0891864 | ||||||||
\(944\) | −2.32049e31 | −1.34392 | ||||||||
\(945\) | −9.25173e30 | −0.529894 | ||||||||
\(946\) | −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 | ||||||||
\(952\) | −2.77593e30 | −0.147137 | ||||||||
\(953\) | 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 | ||||||||
\(959\) | 3.07838e31 | 1.51087 | ||||||||
\(960\) | 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 | ||||||||
\(966\) | 2.10468e30 | 0.0957032 | ||||||||
\(967\) | −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 | \(-0.613684\pi\) | ||||
−0.349606 | + | 0.936897i | \(0.613684\pi\) | |||||||
\(972\) | −2.35532e31 | −1.00358 | ||||||||
\(973\) | −3.43780e31 | −1.44909 | ||||||||
\(974\) | −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 | ||||||||
\(980\) | −1.36867e30 | −0.0535088 | ||||||||
\(981\) | 1.05857e31 | 0.409445 | ||||||||
\(982\) | 7.48330e30 | 0.286367 | ||||||||
\(983\) | −2.41371e31 | −0.913846 | −0.456923 | − | 0.889506i | \(-0.651049\pi\) | ||||
−0.456923 | + | 0.889506i | \(0.651049\pi\) | |||||||
\(984\) | 3.14623e30 | 0.117853 | ||||||||
\(985\) | −1.51272e31 | −0.560632 | ||||||||
\(986\) | 3.73866e30 | 0.137091 | ||||||||
\(987\) | 1.45436e31 | 0.527643 | ||||||||
\(988\) | −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 | ||||||||
\(994\) | −1.24600e30 | −0.0419723 | ||||||||
\(995\) | −2.69521e31 | −0.898361 | ||||||||
\(996\) | 1.26935e31 | 0.418658 | ||||||||
\(997\) | 3.55036e31 | 1.15871 | 0.579354 | − | 0.815076i | \(-0.303305\pi\) | ||||
0.579354 | + | 0.815076i | \(0.303305\pi\) | |||||||
\(998\) | −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 | 1.22.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.22.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 16.22.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 25.22.b.a.24.1 | 2 | |||
5.3 | odd | 4 | 25.22.b.a.24.2 | 2 | |||
5.4 | even | 2 | 25.22.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 49.22.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 64.22.a.a.1.1 | 1 | |||
8.5 | even | 2 | 64.22.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.22.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.22.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
16.22.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
25.22.a.a.1.1 | 1 | 5.4 | even | 2 | |||
25.22.b.a.24.1 | 2 | 5.2 | odd | 4 | |||
25.22.b.a.24.2 | 2 | 5.3 | odd | 4 | |||
49.22.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
64.22.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
64.22.a.g.1.1 | 1 | 8.5 | even | 2 |