Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,20,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(22.8816696556\) |
Analytic rank: | \(0\) |
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 | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −512.000 | −0.707107 | ||||||||
\(3\) | −26622.0 | −0.780888 | −0.390444 | − | 0.920627i | \(-0.627678\pi\) | ||||
−0.390444 | + | 0.920627i | \(0.627678\pi\) | |||||||
\(4\) | 262144. | 0.500000 | ||||||||
\(5\) | −1.95312e6 | −0.447214 | ||||||||
\(6\) | 1.36305e7 | 0.552171 | ||||||||
\(7\) | −3.98840e7 | −0.373566 | −0.186783 | − | 0.982401i | \(-0.559806\pi\) | ||||
−0.186783 | + | 0.982401i | \(0.559806\pi\) | |||||||
\(8\) | −1.34218e8 | −0.353553 | ||||||||
\(9\) | −4.53531e8 | −0.390214 | ||||||||
\(10\) | 1.00000e9 | 0.316228 | ||||||||
\(11\) | −1.01616e10 | −1.29936 | −0.649682 | − | 0.760206i | \(-0.725098\pi\) | ||||
−0.649682 | + | 0.760206i | \(0.725098\pi\) | |||||||
\(12\) | −6.97880e9 | −0.390444 | ||||||||
\(13\) | −2.69706e10 | −0.705390 | −0.352695 | − | 0.935738i | \(-0.614735\pi\) | ||||
−0.352695 | + | 0.935738i | \(0.614735\pi\) | |||||||
\(14\) | 2.04206e10 | 0.264151 | ||||||||
\(15\) | 5.19961e10 | 0.349224 | ||||||||
\(16\) | 6.87195e10 | 0.250000 | ||||||||
\(17\) | −8.01548e10 | −0.163932 | −0.0819661 | − | 0.996635i | \(-0.526120\pi\) | ||||
−0.0819661 | + | 0.996635i | \(0.526120\pi\) | |||||||
\(18\) | 2.32208e11 | 0.275923 | ||||||||
\(19\) | −1.16977e12 | −0.831653 | −0.415826 | − | 0.909444i | \(-0.636508\pi\) | ||||
−0.415826 | + | 0.909444i | \(0.636508\pi\) | |||||||
\(20\) | −5.12000e11 | −0.223607 | ||||||||
\(21\) | 1.06179e12 | 0.291713 | ||||||||
\(22\) | 5.20273e12 | 0.918789 | ||||||||
\(23\) | 1.37959e13 | 1.59711 | 0.798555 | − | 0.601921i | \(-0.205598\pi\) | ||||
0.798555 | + | 0.601921i | \(0.205598\pi\) | |||||||
\(24\) | 3.57314e12 | 0.276086 | ||||||||
\(25\) | 3.81470e12 | 0.200000 | ||||||||
\(26\) | 1.38090e13 | 0.498786 | ||||||||
\(27\) | 4.30156e13 | 1.08560 | ||||||||
\(28\) | −1.04554e13 | −0.186783 | ||||||||
\(29\) | 6.53248e13 | 0.836174 | 0.418087 | − | 0.908407i | \(-0.362701\pi\) | ||||
0.418087 | + | 0.908407i | \(0.362701\pi\) | |||||||
\(30\) | −2.66220e13 | −0.246938 | ||||||||
\(31\) | −8.92654e12 | −0.0606383 | −0.0303192 | − | 0.999540i | \(-0.509652\pi\) | ||||
−0.0303192 | + | 0.999540i | \(0.509652\pi\) | |||||||
\(32\) | −3.51844e13 | −0.176777 | ||||||||
\(33\) | 2.70522e14 | 1.01466 | ||||||||
\(34\) | 4.10392e13 | 0.115918 | ||||||||
\(35\) | 7.78985e13 | 0.167064 | ||||||||
\(36\) | −1.18890e14 | −0.195107 | ||||||||
\(37\) | 5.25455e14 | 0.664690 | 0.332345 | − | 0.943158i | \(-0.392160\pi\) | ||||
0.332345 | + | 0.943158i | \(0.392160\pi\) | |||||||
\(38\) | 5.98923e14 | 0.588067 | ||||||||
\(39\) | 7.18013e14 | 0.550831 | ||||||||
\(40\) | 2.62144e14 | 0.158114 | ||||||||
\(41\) | −2.63523e15 | −1.25710 | −0.628552 | − | 0.777767i | \(-0.716352\pi\) | ||||
−0.628552 | + | 0.777767i | \(0.716352\pi\) | |||||||
\(42\) | −5.43638e14 | −0.206273 | ||||||||
\(43\) | −1.50171e15 | −0.455654 | −0.227827 | − | 0.973702i | \(-0.573162\pi\) | ||||
−0.227827 | + | 0.973702i | \(0.573162\pi\) | |||||||
\(44\) | −2.66380e15 | −0.649682 | ||||||||
\(45\) | 8.85802e14 | 0.174509 | ||||||||
\(46\) | −7.06349e15 | −1.12933 | ||||||||
\(47\) | −3.65161e15 | −0.475943 | −0.237971 | − | 0.971272i | \(-0.576482\pi\) | ||||
−0.237971 | + | 0.971272i | \(0.576482\pi\) | |||||||
\(48\) | −1.82945e15 | −0.195222 | ||||||||
\(49\) | −9.80816e15 | −0.860448 | ||||||||
\(50\) | −1.95312e15 | −0.141421 | ||||||||
\(51\) | 2.13388e15 | 0.128013 | ||||||||
\(52\) | −7.07019e15 | −0.352695 | ||||||||
\(53\) | 4.33068e16 | 1.80275 | 0.901375 | − | 0.433040i | \(-0.142559\pi\) | ||||
0.901375 | + | 0.433040i | \(0.142559\pi\) | |||||||
\(54\) | −2.20240e16 | −0.767636 | ||||||||
\(55\) | 1.98468e16 | 0.581093 | ||||||||
\(56\) | 5.35314e15 | 0.132076 | ||||||||
\(57\) | 3.11417e16 | 0.649428 | ||||||||
\(58\) | −3.34463e16 | −0.591265 | ||||||||
\(59\) | 5.16521e16 | 0.776236 | 0.388118 | − | 0.921610i | \(-0.373125\pi\) | ||||
0.388118 | + | 0.921610i | \(0.373125\pi\) | |||||||
\(60\) | 1.36305e16 | 0.174612 | ||||||||
\(61\) | 4.52000e16 | 0.494886 | 0.247443 | − | 0.968902i | \(-0.420410\pi\) | ||||
0.247443 | + | 0.968902i | \(0.420410\pi\) | |||||||
\(62\) | 4.57039e15 | 0.0428778 | ||||||||
\(63\) | 1.80886e16 | 0.145771 | ||||||||
\(64\) | 1.80144e16 | 0.125000 | ||||||||
\(65\) | 5.26771e16 | 0.315460 | ||||||||
\(66\) | −1.38507e17 | −0.717471 | ||||||||
\(67\) | 3.22077e17 | 1.44627 | 0.723135 | − | 0.690707i | \(-0.242700\pi\) | ||||
0.723135 | + | 0.690707i | \(0.242700\pi\) | |||||||
\(68\) | −2.10121e16 | −0.0819661 | ||||||||
\(69\) | −3.67274e17 | −1.24716 | ||||||||
\(70\) | −3.98840e16 | −0.118132 | ||||||||
\(71\) | 3.93293e17 | 1.01803 | 0.509017 | − | 0.860756i | \(-0.330009\pi\) | ||||
0.509017 | + | 0.860756i | \(0.330009\pi\) | |||||||
\(72\) | 6.08718e16 | 0.137961 | ||||||||
\(73\) | −6.72470e17 | −1.33692 | −0.668460 | − | 0.743748i | \(-0.733046\pi\) | ||||
−0.668460 | + | 0.743748i | \(0.733046\pi\) | |||||||
\(74\) | −2.69033e17 | −0.470006 | ||||||||
\(75\) | −1.01555e17 | −0.156178 | ||||||||
\(76\) | −3.06649e17 | −0.415826 | ||||||||
\(77\) | 4.05285e17 | 0.485398 | ||||||||
\(78\) | −3.67622e17 | −0.389496 | ||||||||
\(79\) | −4.82639e17 | −0.453070 | −0.226535 | − | 0.974003i | \(-0.572740\pi\) | ||||
−0.226535 | + | 0.974003i | \(0.572740\pi\) | |||||||
\(80\) | −1.34218e17 | −0.111803 | ||||||||
\(81\) | −6.18041e17 | −0.457519 | ||||||||
\(82\) | 1.34924e18 | 0.888907 | ||||||||
\(83\) | −3.13265e17 | −0.183938 | −0.0919688 | − | 0.995762i | \(-0.529316\pi\) | ||||
−0.0919688 | + | 0.995762i | \(0.529316\pi\) | |||||||
\(84\) | 2.78343e17 | 0.145857 | ||||||||
\(85\) | 1.56552e17 | 0.0733128 | ||||||||
\(86\) | 7.68875e17 | 0.322196 | ||||||||
\(87\) | −1.73908e18 | −0.652959 | ||||||||
\(88\) | 1.36386e18 | 0.459394 | ||||||||
\(89\) | −4.23010e18 | −1.27981 | −0.639905 | − | 0.768454i | \(-0.721026\pi\) | ||||
−0.639905 | + | 0.768454i | \(0.721026\pi\) | |||||||
\(90\) | −4.53531e17 | −0.123396 | ||||||||
\(91\) | 1.07570e18 | 0.263510 | ||||||||
\(92\) | 3.61651e18 | 0.798555 | ||||||||
\(93\) | 2.37642e17 | 0.0473517 | ||||||||
\(94\) | 1.86962e18 | 0.336542 | ||||||||
\(95\) | 2.28471e18 | 0.371926 | ||||||||
\(96\) | 9.36678e17 | 0.138043 | ||||||||
\(97\) | 3.54705e17 | 0.0473736 | 0.0236868 | − | 0.999719i | \(-0.492460\pi\) | ||||
0.0236868 | + | 0.999719i | \(0.492460\pi\) | |||||||
\(98\) | 5.02178e18 | 0.608429 | ||||||||
\(99\) | 4.60859e18 | 0.507030 | ||||||||
\(100\) | 1.00000e18 | 0.100000 | ||||||||
\(101\) | 1.29200e19 | 1.17546 | 0.587730 | − | 0.809057i | \(-0.300022\pi\) | ||||
0.587730 | + | 0.809057i | \(0.300022\pi\) | |||||||
\(102\) | −1.09255e18 | −0.0905187 | ||||||||
\(103\) | 1.35900e19 | 1.02628 | 0.513139 | − | 0.858305i | \(-0.328482\pi\) | ||||
0.513139 | + | 0.858305i | \(0.328482\pi\) | |||||||
\(104\) | 3.61994e18 | 0.249393 | ||||||||
\(105\) | −2.07381e18 | −0.130458 | ||||||||
\(106\) | −2.21731e19 | −1.27474 | ||||||||
\(107\) | −3.28307e19 | −1.72637 | −0.863185 | − | 0.504887i | \(-0.831534\pi\) | ||||
−0.863185 | + | 0.504887i | \(0.831534\pi\) | |||||||
\(108\) | 1.12763e19 | 0.542801 | ||||||||
\(109\) | −3.70765e19 | −1.63511 | −0.817554 | − | 0.575851i | \(-0.804671\pi\) | ||||
−0.817554 | + | 0.575851i | \(0.804671\pi\) | |||||||
\(110\) | −1.01616e19 | −0.410895 | ||||||||
\(111\) | −1.39887e19 | −0.519048 | ||||||||
\(112\) | −2.74081e18 | −0.0933916 | ||||||||
\(113\) | 2.45337e19 | 0.768277 | 0.384139 | − | 0.923275i | \(-0.374498\pi\) | ||||
0.384139 | + | 0.923275i | \(0.374498\pi\) | |||||||
\(114\) | −1.59445e19 | −0.459215 | ||||||||
\(115\) | −2.69451e19 | −0.714250 | ||||||||
\(116\) | 1.71245e19 | 0.418087 | ||||||||
\(117\) | 1.22320e19 | 0.275253 | ||||||||
\(118\) | −2.64459e19 | −0.548882 | ||||||||
\(119\) | 3.19689e18 | 0.0612396 | ||||||||
\(120\) | −6.97880e18 | −0.123469 | ||||||||
\(121\) | 4.20986e19 | 0.688346 | ||||||||
\(122\) | −2.31424e19 | −0.349937 | ||||||||
\(123\) | 7.01550e19 | 0.981658 | ||||||||
\(124\) | −2.34004e18 | −0.0303192 | ||||||||
\(125\) | −7.45058e18 | −0.0894427 | ||||||||
\(126\) | −9.26138e18 | −0.103075 | ||||||||
\(127\) | 3.49512e19 | 0.360850 | 0.180425 | − | 0.983589i | \(-0.442253\pi\) | ||||
0.180425 | + | 0.983589i | \(0.442253\pi\) | |||||||
\(128\) | −9.22337e18 | −0.0883883 | ||||||||
\(129\) | 3.99785e19 | 0.355815 | ||||||||
\(130\) | −2.69706e19 | −0.223064 | ||||||||
\(131\) | 2.02167e20 | 1.55465 | 0.777325 | − | 0.629099i | \(-0.216576\pi\) | ||||
0.777325 | + | 0.629099i | \(0.216576\pi\) | |||||||
\(132\) | 7.09156e19 | 0.507329 | ||||||||
\(133\) | 4.66552e19 | 0.310677 | ||||||||
\(134\) | −1.64904e20 | −1.02267 | ||||||||
\(135\) | −8.40149e19 | −0.485496 | ||||||||
\(136\) | 1.07582e19 | 0.0579588 | ||||||||
\(137\) | 1.09975e20 | 0.552647 | 0.276323 | − | 0.961065i | \(-0.410884\pi\) | ||||
0.276323 | + | 0.961065i | \(0.410884\pi\) | |||||||
\(138\) | 1.88044e20 | 0.881879 | ||||||||
\(139\) | −3.97605e20 | −1.74105 | −0.870526 | − | 0.492123i | \(-0.836221\pi\) | ||||
−0.870526 | + | 0.492123i | \(0.836221\pi\) | |||||||
\(140\) | 2.04206e19 | 0.0835319 | ||||||||
\(141\) | 9.72131e19 | 0.371658 | ||||||||
\(142\) | −2.01366e20 | −0.719859 | ||||||||
\(143\) | 2.74064e20 | 0.916559 | ||||||||
\(144\) | −3.11664e19 | −0.0975535 | ||||||||
\(145\) | −1.27587e20 | −0.373949 | ||||||||
\(146\) | 3.44304e20 | 0.945345 | ||||||||
\(147\) | 2.61113e20 | 0.671914 | ||||||||
\(148\) | 1.37745e20 | 0.332345 | ||||||||
\(149\) | −8.57609e20 | −1.94097 | −0.970487 | − | 0.241153i | \(-0.922475\pi\) | ||||
−0.970487 | + | 0.241153i | \(0.922475\pi\) | |||||||
\(150\) | 5.19961e19 | 0.110434 | ||||||||
\(151\) | −5.47594e20 | −1.09189 | −0.545944 | − | 0.837822i | \(-0.683829\pi\) | ||||
−0.545944 | + | 0.837822i | \(0.683829\pi\) | |||||||
\(152\) | 1.57004e20 | 0.294034 | ||||||||
\(153\) | 3.63526e19 | 0.0639687 | ||||||||
\(154\) | −2.07506e20 | −0.343228 | ||||||||
\(155\) | 1.74346e19 | 0.0271183 | ||||||||
\(156\) | 1.88223e20 | 0.275415 | ||||||||
\(157\) | −4.22122e20 | −0.581288 | −0.290644 | − | 0.956831i | \(-0.593869\pi\) | ||||
−0.290644 | + | 0.956831i | \(0.593869\pi\) | |||||||
\(158\) | 2.47111e20 | 0.320369 | ||||||||
\(159\) | −1.15291e21 | −1.40775 | ||||||||
\(160\) | 6.87195e19 | 0.0790569 | ||||||||
\(161\) | −5.50235e20 | −0.596627 | ||||||||
\(162\) | 3.16437e20 | 0.323515 | ||||||||
\(163\) | 1.28823e21 | 1.24226 | 0.621128 | − | 0.783710i | \(-0.286675\pi\) | ||||
0.621128 | + | 0.783710i | \(0.286675\pi\) | |||||||
\(164\) | −6.90809e20 | −0.628552 | ||||||||
\(165\) | −5.28362e20 | −0.453769 | ||||||||
\(166\) | 1.60392e20 | 0.130064 | ||||||||
\(167\) | 2.10976e21 | 1.61594 | 0.807972 | − | 0.589221i | \(-0.200565\pi\) | ||||
0.807972 | + | 0.589221i | \(0.200565\pi\) | |||||||
\(168\) | −1.42511e20 | −0.103136 | ||||||||
\(169\) | −7.34504e20 | −0.502424 | ||||||||
\(170\) | −8.01548e19 | −0.0518399 | ||||||||
\(171\) | 5.30527e20 | 0.324522 | ||||||||
\(172\) | −3.93664e20 | −0.227827 | ||||||||
\(173\) | 1.13537e21 | 0.621868 | 0.310934 | − | 0.950431i | \(-0.399358\pi\) | ||||
0.310934 | + | 0.950431i | \(0.399358\pi\) | |||||||
\(174\) | 8.90407e20 | 0.461711 | ||||||||
\(175\) | −1.52145e20 | −0.0747132 | ||||||||
\(176\) | −6.98298e20 | −0.324841 | ||||||||
\(177\) | −1.37508e21 | −0.606153 | ||||||||
\(178\) | 2.16581e21 | 0.904963 | ||||||||
\(179\) | 2.71859e21 | 1.07706 | 0.538530 | − | 0.842607i | \(-0.318980\pi\) | ||||
0.538530 | + | 0.842607i | \(0.318980\pi\) | |||||||
\(180\) | 2.32208e20 | 0.0872545 | ||||||||
\(181\) | 3.93952e21 | 1.40442 | 0.702209 | − | 0.711971i | \(-0.252197\pi\) | ||||
0.702209 | + | 0.711971i | \(0.252197\pi\) | |||||||
\(182\) | −5.50757e20 | −0.186330 | ||||||||
\(183\) | −1.20332e21 | −0.386451 | ||||||||
\(184\) | −1.85165e21 | −0.564664 | ||||||||
\(185\) | −1.02628e21 | −0.297258 | ||||||||
\(186\) | −1.21673e20 | −0.0334827 | ||||||||
\(187\) | 8.14499e20 | 0.213008 | ||||||||
\(188\) | −9.57247e20 | −0.237971 | ||||||||
\(189\) | −1.71564e21 | −0.405544 | ||||||||
\(190\) | −1.16977e21 | −0.262992 | ||||||||
\(191\) | 6.11189e21 | 1.30725 | 0.653625 | − | 0.756819i | \(-0.273248\pi\) | ||||
0.653625 | + | 0.756819i | \(0.273248\pi\) | |||||||
\(192\) | −4.79579e20 | −0.0976110 | ||||||||
\(193\) | −3.21787e21 | −0.623410 | −0.311705 | − | 0.950179i | \(-0.600900\pi\) | ||||
−0.311705 | + | 0.950179i | \(0.600900\pi\) | |||||||
\(194\) | −1.81609e20 | −0.0334982 | ||||||||
\(195\) | −1.40237e21 | −0.246339 | ||||||||
\(196\) | −2.57115e21 | −0.430224 | ||||||||
\(197\) | −4.85425e21 | −0.773915 | −0.386958 | − | 0.922098i | \(-0.626474\pi\) | ||||
−0.386958 | + | 0.922098i | \(0.626474\pi\) | |||||||
\(198\) | −2.35960e21 | −0.358524 | ||||||||
\(199\) | 2.76811e21 | 0.400939 | 0.200470 | − | 0.979700i | \(-0.435753\pi\) | ||||
0.200470 | + | 0.979700i | \(0.435753\pi\) | |||||||
\(200\) | −5.12000e20 | −0.0707107 | ||||||||
\(201\) | −8.57434e21 | −1.12937 | ||||||||
\(202\) | −6.61501e21 | −0.831176 | ||||||||
\(203\) | −2.60541e21 | −0.312366 | ||||||||
\(204\) | 5.59384e20 | 0.0640064 | ||||||||
\(205\) | 5.14693e21 | 0.562194 | ||||||||
\(206\) | −6.95807e21 | −0.725689 | ||||||||
\(207\) | −6.25686e21 | −0.623215 | ||||||||
\(208\) | −1.85341e21 | −0.176348 | ||||||||
\(209\) | 1.18867e22 | 1.08062 | ||||||||
\(210\) | 1.06179e21 | 0.0922479 | ||||||||
\(211\) | 3.92985e21 | 0.326356 | 0.163178 | − | 0.986597i | \(-0.447825\pi\) | ||||
0.163178 | + | 0.986597i | \(0.447825\pi\) | |||||||
\(212\) | 1.13526e22 | 0.901375 | ||||||||
\(213\) | −1.04703e22 | −0.794970 | ||||||||
\(214\) | 1.68093e22 | 1.22073 | ||||||||
\(215\) | 2.93302e21 | 0.203775 | ||||||||
\(216\) | −5.77346e21 | −0.383818 | ||||||||
\(217\) | 3.56026e20 | 0.0226524 | ||||||||
\(218\) | 1.89832e22 | 1.15620 | ||||||||
\(219\) | 1.79025e22 | 1.04399 | ||||||||
\(220\) | 5.20273e21 | 0.290547 | ||||||||
\(221\) | 2.16183e21 | 0.115636 | ||||||||
\(222\) | 7.16219e21 | 0.367022 | ||||||||
\(223\) | −3.09507e21 | −0.151976 | −0.0759880 | − | 0.997109i | \(-0.524211\pi\) | ||||
−0.0759880 | + | 0.997109i | \(0.524211\pi\) | |||||||
\(224\) | 1.40329e21 | 0.0660378 | ||||||||
\(225\) | −1.73008e21 | −0.0780428 | ||||||||
\(226\) | −1.25613e22 | −0.543254 | ||||||||
\(227\) | 1.39820e22 | 0.579859 | 0.289929 | − | 0.957048i | \(-0.406368\pi\) | ||||
0.289929 | + | 0.957048i | \(0.406368\pi\) | |||||||
\(228\) | 8.16360e21 | 0.324714 | ||||||||
\(229\) | −2.64165e22 | −1.00795 | −0.503975 | − | 0.863719i | \(-0.668129\pi\) | ||||
−0.503975 | + | 0.863719i | \(0.668129\pi\) | |||||||
\(230\) | 1.37959e22 | 0.505051 | ||||||||
\(231\) | −1.07895e22 | −0.379042 | ||||||||
\(232\) | −8.76774e21 | −0.295632 | ||||||||
\(233\) | −5.72660e22 | −1.85360 | −0.926800 | − | 0.375556i | \(-0.877452\pi\) | ||||
−0.926800 | + | 0.375556i | \(0.877452\pi\) | |||||||
\(234\) | −6.26279e21 | −0.194633 | ||||||||
\(235\) | 7.13205e21 | 0.212848 | ||||||||
\(236\) | 1.35403e22 | 0.388118 | ||||||||
\(237\) | 1.28488e22 | 0.353797 | ||||||||
\(238\) | −1.63681e21 | −0.0433029 | ||||||||
\(239\) | 5.61325e22 | 1.42703 | 0.713517 | − | 0.700638i | \(-0.247101\pi\) | ||||
0.713517 | + | 0.700638i | \(0.247101\pi\) | |||||||
\(240\) | 3.57314e21 | 0.0873059 | ||||||||
\(241\) | −4.77482e22 | −1.12149 | −0.560744 | − | 0.827989i | \(-0.689485\pi\) | ||||
−0.560744 | + | 0.827989i | \(0.689485\pi\) | |||||||
\(242\) | −2.15545e22 | −0.486734 | ||||||||
\(243\) | −3.35419e22 | −0.728330 | ||||||||
\(244\) | 1.18489e22 | 0.247443 | ||||||||
\(245\) | 1.91566e22 | 0.384804 | ||||||||
\(246\) | −3.59194e22 | −0.694137 | ||||||||
\(247\) | 3.15495e22 | 0.586640 | ||||||||
\(248\) | 1.19810e21 | 0.0214389 | ||||||||
\(249\) | 8.33975e21 | 0.143635 | ||||||||
\(250\) | 3.81470e21 | 0.0632456 | ||||||||
\(251\) | 1.05736e23 | 1.68781 | 0.843907 | − | 0.536490i | \(-0.180250\pi\) | ||||
0.843907 | + | 0.536490i | \(0.180250\pi\) | |||||||
\(252\) | 4.74182e21 | 0.0728854 | ||||||||
\(253\) | −1.40188e23 | −2.07523 | ||||||||
\(254\) | −1.78950e22 | −0.255160 | ||||||||
\(255\) | −4.16773e21 | −0.0572491 | ||||||||
\(256\) | 4.72237e21 | 0.0625000 | ||||||||
\(257\) | −3.19013e22 | −0.406859 | −0.203429 | − | 0.979090i | \(-0.565209\pi\) | ||||
−0.203429 | + | 0.979090i | \(0.565209\pi\) | |||||||
\(258\) | −2.04690e22 | −0.251599 | ||||||||
\(259\) | −2.09572e22 | −0.248306 | ||||||||
\(260\) | 1.38090e22 | 0.157730 | ||||||||
\(261\) | −2.96268e22 | −0.326287 | ||||||||
\(262\) | −1.03509e23 | −1.09930 | ||||||||
\(263\) | 5.93491e22 | 0.607903 | 0.303952 | − | 0.952687i | \(-0.401694\pi\) | ||||
0.303952 | + | 0.952687i | \(0.401694\pi\) | |||||||
\(264\) | −3.63088e22 | −0.358736 | ||||||||
\(265\) | −8.45836e22 | −0.806214 | ||||||||
\(266\) | −2.38875e22 | −0.219682 | ||||||||
\(267\) | 1.12614e23 | 0.999389 | ||||||||
\(268\) | 8.44306e22 | 0.723135 | ||||||||
\(269\) | 1.96711e23 | 1.62623 | 0.813115 | − | 0.582103i | \(-0.197770\pi\) | ||||
0.813115 | + | 0.582103i | \(0.197770\pi\) | |||||||
\(270\) | 4.30156e22 | 0.343297 | ||||||||
\(271\) | 1.06648e23 | 0.821760 | 0.410880 | − | 0.911689i | \(-0.365221\pi\) | ||||
0.410880 | + | 0.911689i | \(0.365221\pi\) | |||||||
\(272\) | −5.50819e21 | −0.0409831 | ||||||||
\(273\) | −2.86372e22 | −0.205772 | ||||||||
\(274\) | −5.63071e22 | −0.390780 | ||||||||
\(275\) | −3.87633e22 | −0.259873 | ||||||||
\(276\) | −9.62787e22 | −0.623582 | ||||||||
\(277\) | 6.44307e22 | 0.403213 | 0.201607 | − | 0.979467i | \(-0.435384\pi\) | ||||
0.201607 | + | 0.979467i | \(0.435384\pi\) | |||||||
\(278\) | 2.03574e23 | 1.23111 | ||||||||
\(279\) | 4.04846e21 | 0.0236619 | ||||||||
\(280\) | −1.04554e22 | −0.0590660 | ||||||||
\(281\) | 1.73023e23 | 0.944918 | 0.472459 | − | 0.881353i | \(-0.343367\pi\) | ||||
0.472459 | + | 0.881353i | \(0.343367\pi\) | |||||||
\(282\) | −4.97731e22 | −0.262802 | ||||||||
\(283\) | 7.83542e22 | 0.400029 | 0.200014 | − | 0.979793i | \(-0.435901\pi\) | ||||
0.200014 | + | 0.979793i | \(0.435901\pi\) | |||||||
\(284\) | 1.03099e23 | 0.509017 | ||||||||
\(285\) | −6.08236e22 | −0.290433 | ||||||||
\(286\) | −1.40321e23 | −0.648105 | ||||||||
\(287\) | 1.05103e23 | 0.469612 | ||||||||
\(288\) | 1.59572e22 | 0.0689807 | ||||||||
\(289\) | −2.32648e23 | −0.973126 | ||||||||
\(290\) | 6.53248e22 | 0.264422 | ||||||||
\(291\) | −9.44296e21 | −0.0369934 | ||||||||
\(292\) | −1.76284e23 | −0.668460 | ||||||||
\(293\) | 3.32561e23 | 1.22076 | 0.610379 | − | 0.792110i | \(-0.291017\pi\) | ||||
0.610379 | + | 0.792110i | \(0.291017\pi\) | |||||||
\(294\) | −1.33690e23 | −0.475115 | ||||||||
\(295\) | −1.00883e23 | −0.347143 | ||||||||
\(296\) | −7.05253e22 | −0.235003 | ||||||||
\(297\) | −4.37107e23 | −1.41059 | ||||||||
\(298\) | 4.39096e23 | 1.37248 | ||||||||
\(299\) | −3.72084e23 | −1.12659 | ||||||||
\(300\) | −2.66220e22 | −0.0780888 | ||||||||
\(301\) | 5.98942e22 | 0.170217 | ||||||||
\(302\) | 2.80368e23 | 0.772081 | ||||||||
\(303\) | −3.43955e23 | −0.917903 | ||||||||
\(304\) | −8.03861e22 | −0.207913 | ||||||||
\(305\) | −8.82813e22 | −0.221320 | ||||||||
\(306\) | −1.86125e22 | −0.0452327 | ||||||||
\(307\) | −4.74187e23 | −1.11721 | −0.558605 | − | 0.829434i | \(-0.688663\pi\) | ||||
−0.558605 | + | 0.829434i | \(0.688663\pi\) | |||||||
\(308\) | 1.06243e23 | 0.242699 | ||||||||
\(309\) | −3.61793e23 | −0.801409 | ||||||||
\(310\) | −8.92654e21 | −0.0191755 | ||||||||
\(311\) | 2.15965e23 | 0.449944 | 0.224972 | − | 0.974365i | \(-0.427771\pi\) | ||||
0.224972 | + | 0.974365i | \(0.427771\pi\) | |||||||
\(312\) | −9.63700e22 | −0.194748 | ||||||||
\(313\) | −5.79666e23 | −1.13634 | −0.568168 | − | 0.822913i | \(-0.692348\pi\) | ||||
−0.568168 | + | 0.822913i | \(0.692348\pi\) | |||||||
\(314\) | 2.16126e23 | 0.411032 | ||||||||
\(315\) | −3.53293e22 | −0.0651907 | ||||||||
\(316\) | −1.26521e23 | −0.226535 | ||||||||
\(317\) | 6.42977e23 | 1.11720 | 0.558602 | − | 0.829436i | \(-0.311338\pi\) | ||||
0.558602 | + | 0.829436i | \(0.311338\pi\) | |||||||
\(318\) | 5.90292e23 | 0.995426 | ||||||||
\(319\) | −6.63803e23 | −1.08649 | ||||||||
\(320\) | −3.51844e22 | −0.0559017 | ||||||||
\(321\) | 8.74018e23 | 1.34810 | ||||||||
\(322\) | 2.81721e23 | 0.421879 | ||||||||
\(323\) | 9.37628e22 | 0.136335 | ||||||||
\(324\) | −1.62016e23 | −0.228760 | ||||||||
\(325\) | −1.02885e23 | −0.141078 | ||||||||
\(326\) | −6.59573e23 | −0.878407 | ||||||||
\(327\) | 9.87050e23 | 1.27684 | ||||||||
\(328\) | 3.53694e23 | 0.444454 | ||||||||
\(329\) | 1.45641e23 | 0.177796 | ||||||||
\(330\) | 2.70522e23 | 0.320863 | ||||||||
\(331\) | 1.44955e24 | 1.67058 | 0.835288 | − | 0.549813i | \(-0.185301\pi\) | ||||
0.835288 | + | 0.549813i | \(0.185301\pi\) | |||||||
\(332\) | −8.21206e22 | −0.0919688 | ||||||||
\(333\) | −2.38310e23 | −0.259371 | ||||||||
\(334\) | −1.08020e24 | −1.14265 | ||||||||
\(335\) | −6.29057e23 | −0.646792 | ||||||||
\(336\) | 7.29658e22 | 0.0729283 | ||||||||
\(337\) | 1.33044e24 | 1.29274 | 0.646370 | − | 0.763024i | \(-0.276286\pi\) | ||||
0.646370 | + | 0.763024i | \(0.276286\pi\) | |||||||
\(338\) | 3.76066e23 | 0.355268 | ||||||||
\(339\) | −6.53137e23 | −0.599939 | ||||||||
\(340\) | 4.10392e22 | 0.0366564 | ||||||||
\(341\) | 9.07077e22 | 0.0787912 | ||||||||
\(342\) | −2.71630e23 | −0.229472 | ||||||||
\(343\) | 8.45823e23 | 0.695001 | ||||||||
\(344\) | 2.01556e23 | 0.161098 | ||||||||
\(345\) | 7.17332e23 | 0.557749 | ||||||||
\(346\) | −5.81308e23 | −0.439727 | ||||||||
\(347\) | −8.08452e23 | −0.595010 | −0.297505 | − | 0.954720i | \(-0.596154\pi\) | ||||
−0.297505 | + | 0.954720i | \(0.596154\pi\) | |||||||
\(348\) | −4.55888e23 | −0.326479 | ||||||||
\(349\) | 1.87880e24 | 1.30930 | 0.654648 | − | 0.755933i | \(-0.272817\pi\) | ||||
0.654648 | + | 0.755933i | \(0.272817\pi\) | |||||||
\(350\) | 7.78985e22 | 0.0528302 | ||||||||
\(351\) | −1.16016e24 | −0.765773 | ||||||||
\(352\) | 3.57529e23 | 0.229697 | ||||||||
\(353\) | −2.51702e24 | −1.57408 | −0.787039 | − | 0.616903i | \(-0.788387\pi\) | ||||
−0.787039 | + | 0.616903i | \(0.788387\pi\) | |||||||
\(354\) | 7.04042e23 | 0.428615 | ||||||||
\(355\) | −7.68151e23 | −0.455279 | ||||||||
\(356\) | −1.10890e24 | −0.639905 | ||||||||
\(357\) | −8.51077e22 | −0.0478212 | ||||||||
\(358\) | −1.39192e24 | −0.761596 | ||||||||
\(359\) | −2.04732e23 | −0.109091 | −0.0545453 | − | 0.998511i | \(-0.517371\pi\) | ||||
−0.0545453 | + | 0.998511i | \(0.517371\pi\) | |||||||
\(360\) | −1.18890e23 | −0.0616982 | ||||||||
\(361\) | −6.10053e23 | −0.308354 | ||||||||
\(362\) | −2.01703e24 | −0.993074 | ||||||||
\(363\) | −1.12075e24 | −0.537521 | ||||||||
\(364\) | 2.81988e23 | 0.131755 | ||||||||
\(365\) | 1.31342e24 | 0.597889 | ||||||||
\(366\) | 6.16098e23 | 0.273262 | ||||||||
\(367\) | −5.80738e23 | −0.250988 | −0.125494 | − | 0.992094i | \(-0.540052\pi\) | ||||
−0.125494 | + | 0.992094i | \(0.540052\pi\) | |||||||
\(368\) | 9.48046e23 | 0.399278 | ||||||||
\(369\) | 1.19516e24 | 0.490540 | ||||||||
\(370\) | 5.25455e23 | 0.210193 | ||||||||
\(371\) | −1.72725e24 | −0.673446 | ||||||||
\(372\) | 6.22965e22 | 0.0236759 | ||||||||
\(373\) | 4.35467e24 | 1.61332 | 0.806662 | − | 0.591012i | \(-0.201272\pi\) | ||||
0.806662 | + | 0.591012i | \(0.201272\pi\) | |||||||
\(374\) | −4.17023e23 | −0.150619 | ||||||||
\(375\) | 1.98349e23 | 0.0698447 | ||||||||
\(376\) | 4.90111e23 | 0.168271 | ||||||||
\(377\) | −1.76185e24 | −0.589829 | ||||||||
\(378\) | 8.78406e23 | 0.286763 | ||||||||
\(379\) | 2.38731e24 | 0.760041 | 0.380021 | − | 0.924978i | \(-0.375917\pi\) | ||||
0.380021 | + | 0.924978i | \(0.375917\pi\) | |||||||
\(380\) | 5.98923e23 | 0.185963 | ||||||||
\(381\) | −9.30471e23 | −0.281784 | ||||||||
\(382\) | −3.12929e24 | −0.924365 | ||||||||
\(383\) | −3.07728e24 | −0.886704 | −0.443352 | − | 0.896348i | \(-0.646211\pi\) | ||||
−0.443352 | + | 0.896348i | \(0.646211\pi\) | |||||||
\(384\) | 2.45545e23 | 0.0690214 | ||||||||
\(385\) | −7.91572e23 | −0.217077 | ||||||||
\(386\) | 1.64755e24 | 0.440818 | ||||||||
\(387\) | 6.81071e23 | 0.177803 | ||||||||
\(388\) | 9.29838e22 | 0.0236868 | ||||||||
\(389\) | 5.97646e24 | 1.48567 | 0.742836 | − | 0.669474i | \(-0.233480\pi\) | ||||
0.742836 | + | 0.669474i | \(0.233480\pi\) | |||||||
\(390\) | 7.18013e23 | 0.174188 | ||||||||
\(391\) | −1.10581e24 | −0.261818 | ||||||||
\(392\) | 1.31643e24 | 0.304214 | ||||||||
\(393\) | −5.38209e24 | −1.21401 | ||||||||
\(394\) | 2.48538e24 | 0.547241 | ||||||||
\(395\) | 9.42654e23 | 0.202619 | ||||||||
\(396\) | 1.20811e24 | 0.253515 | ||||||||
\(397\) | −2.25921e24 | −0.462856 | −0.231428 | − | 0.972852i | \(-0.574340\pi\) | ||||
−0.231428 | + | 0.972852i | \(0.574340\pi\) | |||||||
\(398\) | −1.41727e24 | −0.283507 | ||||||||
\(399\) | −1.24206e24 | −0.242604 | ||||||||
\(400\) | 2.62144e23 | 0.0500000 | ||||||||
\(401\) | 7.37768e22 | 0.0137419 | 0.00687097 | − | 0.999976i | \(-0.497813\pi\) | ||||
0.00687097 | + | 0.999976i | \(0.497813\pi\) | |||||||
\(402\) | 4.39006e24 | 0.798589 | ||||||||
\(403\) | 2.40755e23 | 0.0427737 | ||||||||
\(404\) | 3.38689e24 | 0.587730 | ||||||||
\(405\) | 1.20711e24 | 0.204609 | ||||||||
\(406\) | 1.33397e24 | 0.220876 | ||||||||
\(407\) | −5.33945e24 | −0.863673 | ||||||||
\(408\) | −2.86405e23 | −0.0452593 | ||||||||
\(409\) | 1.18987e25 | 1.83708 | 0.918539 | − | 0.395330i | \(-0.129370\pi\) | ||||
0.918539 | + | 0.395330i | \(0.129370\pi\) | |||||||
\(410\) | −2.63523e24 | −0.397531 | ||||||||
\(411\) | −2.92775e24 | −0.431555 | ||||||||
\(412\) | 3.56253e24 | 0.513139 | ||||||||
\(413\) | −2.06009e24 | −0.289976 | ||||||||
\(414\) | 3.20351e24 | 0.440679 | ||||||||
\(415\) | 6.11846e23 | 0.0822594 | ||||||||
\(416\) | 9.48945e23 | 0.124697 | ||||||||
\(417\) | 1.05850e25 | 1.35957 | ||||||||
\(418\) | −6.08601e24 | −0.764113 | ||||||||
\(419\) | −9.99966e24 | −1.22730 | −0.613652 | − | 0.789577i | \(-0.710300\pi\) | ||||
−0.613652 | + | 0.789577i | \(0.710300\pi\) | |||||||
\(420\) | −5.43638e23 | −0.0652291 | ||||||||
\(421\) | −3.46749e24 | −0.406757 | −0.203379 | − | 0.979100i | \(-0.565192\pi\) | ||||
−0.203379 | + | 0.979100i | \(0.565192\pi\) | |||||||
\(422\) | −2.01208e24 | −0.230769 | ||||||||
\(423\) | 1.65612e24 | 0.185719 | ||||||||
\(424\) | −5.81254e24 | −0.637368 | ||||||||
\(425\) | −3.05766e23 | −0.0327865 | ||||||||
\(426\) | 5.36077e24 | 0.562129 | ||||||||
\(427\) | −1.80276e24 | −0.184873 | ||||||||
\(428\) | −8.60637e24 | −0.863185 | ||||||||
\(429\) | −7.29614e24 | −0.715730 | ||||||||
\(430\) | −1.50171e24 | −0.144091 | ||||||||
\(431\) | −7.34068e24 | −0.688973 | −0.344487 | − | 0.938791i | \(-0.611947\pi\) | ||||
−0.344487 | + | 0.938791i | \(0.611947\pi\) | |||||||
\(432\) | 2.95601e24 | 0.271400 | ||||||||
\(433\) | −1.93970e24 | −0.174221 | −0.0871105 | − | 0.996199i | \(-0.527763\pi\) | ||||
−0.0871105 | + | 0.996199i | \(0.527763\pi\) | |||||||
\(434\) | −1.82285e23 | −0.0160177 | ||||||||
\(435\) | 3.39663e24 | 0.292012 | ||||||||
\(436\) | −9.71937e24 | −0.817554 | ||||||||
\(437\) | −1.61380e25 | −1.32824 | ||||||||
\(438\) | −9.16607e24 | −0.738209 | ||||||||
\(439\) | −1.07757e25 | −0.849241 | −0.424621 | − | 0.905371i | \(-0.639593\pi\) | ||||
−0.424621 | + | 0.905371i | \(0.639593\pi\) | |||||||
\(440\) | −2.66380e24 | −0.205447 | ||||||||
\(441\) | 4.44830e24 | 0.335759 | ||||||||
\(442\) | −1.10685e24 | −0.0817672 | ||||||||
\(443\) | 2.13229e25 | 1.54174 | 0.770871 | − | 0.636992i | \(-0.219822\pi\) | ||||
0.770871 | + | 0.636992i | \(0.219822\pi\) | |||||||
\(444\) | −3.66704e24 | −0.259524 | ||||||||
\(445\) | 8.26192e24 | 0.572349 | ||||||||
\(446\) | 1.58468e24 | 0.107463 | ||||||||
\(447\) | 2.28313e25 | 1.51568 | ||||||||
\(448\) | −7.18487e23 | −0.0466958 | ||||||||
\(449\) | −8.14780e24 | −0.518442 | −0.259221 | − | 0.965818i | \(-0.583466\pi\) | ||||
−0.259221 | + | 0.965818i | \(0.583466\pi\) | |||||||
\(450\) | 8.85802e23 | 0.0551846 | ||||||||
\(451\) | 2.67781e25 | 1.63344 | ||||||||
\(452\) | 6.43137e24 | 0.384139 | ||||||||
\(453\) | 1.45781e25 | 0.852642 | ||||||||
\(454\) | −7.15876e24 | −0.410022 | ||||||||
\(455\) | −2.10097e24 | −0.117845 | ||||||||
\(456\) | −4.17976e24 | −0.229607 | ||||||||
\(457\) | 7.48065e24 | 0.402472 | 0.201236 | − | 0.979543i | \(-0.435504\pi\) | ||||
0.201236 | + | 0.979543i | \(0.435504\pi\) | |||||||
\(458\) | 1.35253e25 | 0.712728 | ||||||||
\(459\) | −3.44791e24 | −0.177965 | ||||||||
\(460\) | −7.06349e24 | −0.357125 | ||||||||
\(461\) | −2.41292e25 | −1.19504 | −0.597522 | − | 0.801852i | \(-0.703848\pi\) | ||||
−0.597522 | + | 0.801852i | \(0.703848\pi\) | |||||||
\(462\) | 5.52422e24 | 0.268023 | ||||||||
\(463\) | 3.66162e25 | 1.74042 | 0.870209 | − | 0.492683i | \(-0.163984\pi\) | ||||
0.870209 | + | 0.492683i | \(0.163984\pi\) | |||||||
\(464\) | 4.48908e24 | 0.209044 | ||||||||
\(465\) | −4.64145e23 | −0.0211763 | ||||||||
\(466\) | 2.93202e25 | 1.31069 | ||||||||
\(467\) | −2.16793e25 | −0.949589 | −0.474794 | − | 0.880097i | \(-0.657478\pi\) | ||||
−0.474794 | + | 0.880097i | \(0.657478\pi\) | |||||||
\(468\) | 3.20655e24 | 0.137627 | ||||||||
\(469\) | −1.28457e25 | −0.540278 | ||||||||
\(470\) | −3.65161e24 | −0.150506 | ||||||||
\(471\) | 1.12377e25 | 0.453921 | ||||||||
\(472\) | −6.93263e24 | −0.274441 | ||||||||
\(473\) | 1.52597e25 | 0.592060 | ||||||||
\(474\) | −6.57859e24 | −0.250172 | ||||||||
\(475\) | −4.46233e24 | −0.166331 | ||||||||
\(476\) | 8.38047e23 | 0.0306198 | ||||||||
\(477\) | −1.96410e25 | −0.703458 | ||||||||
\(478\) | −2.87398e25 | −1.00906 | ||||||||
\(479\) | 3.20019e24 | 0.110151 | 0.0550754 | − | 0.998482i | \(-0.482460\pi\) | ||||
0.0550754 | + | 0.998482i | \(0.482460\pi\) | |||||||
\(480\) | −1.82945e24 | −0.0617346 | ||||||||
\(481\) | −1.41719e25 | −0.468866 | ||||||||
\(482\) | 2.44471e25 | 0.793012 | ||||||||
\(483\) | 1.46484e25 | 0.465899 | ||||||||
\(484\) | 1.10359e25 | 0.344173 | ||||||||
\(485\) | −6.92783e23 | −0.0211861 | ||||||||
\(486\) | 1.71735e25 | 0.515007 | ||||||||
\(487\) | −1.18018e25 | −0.347076 | −0.173538 | − | 0.984827i | \(-0.555520\pi\) | ||||
−0.173538 | + | 0.984827i | \(0.555520\pi\) | |||||||
\(488\) | −6.06665e24 | −0.174969 | ||||||||
\(489\) | −3.42952e25 | −0.970062 | ||||||||
\(490\) | −9.80816e24 | −0.272098 | ||||||||
\(491\) | −2.40797e25 | −0.655203 | −0.327602 | − | 0.944816i | \(-0.606240\pi\) | ||||
−0.327602 | + | 0.944816i | \(0.606240\pi\) | |||||||
\(492\) | 1.83907e25 | 0.490829 | ||||||||
\(493\) | −5.23609e24 | −0.137076 | ||||||||
\(494\) | −1.61534e25 | −0.414817 | ||||||||
\(495\) | −9.00115e24 | −0.226751 | ||||||||
\(496\) | −6.13427e23 | −0.0151596 | ||||||||
\(497\) | −1.56861e25 | −0.380303 | ||||||||
\(498\) | −4.26995e24 | −0.101565 | ||||||||
\(499\) | 2.32722e25 | 0.543102 | 0.271551 | − | 0.962424i | \(-0.412463\pi\) | ||||
0.271551 | + | 0.962424i | \(0.412463\pi\) | |||||||
\(500\) | −1.95313e24 | −0.0447214 | ||||||||
\(501\) | −5.61660e25 | −1.26187 | ||||||||
\(502\) | −5.41371e25 | −1.19346 | ||||||||
\(503\) | 3.42180e25 | 0.740216 | 0.370108 | − | 0.928989i | \(-0.379321\pi\) | ||||
0.370108 | + | 0.928989i | \(0.379321\pi\) | |||||||
\(504\) | −2.42781e24 | −0.0515377 | ||||||||
\(505\) | −2.52343e25 | −0.525682 | ||||||||
\(506\) | 7.17762e25 | 1.46741 | ||||||||
\(507\) | 1.95540e25 | 0.392337 | ||||||||
\(508\) | 9.16225e24 | 0.180425 | ||||||||
\(509\) | −4.64751e25 | −0.898259 | −0.449129 | − | 0.893467i | \(-0.648266\pi\) | ||||
−0.449129 | + | 0.893467i | \(0.648266\pi\) | |||||||
\(510\) | 2.13388e24 | 0.0404812 | ||||||||
\(511\) | 2.68208e25 | 0.499428 | ||||||||
\(512\) | −2.41785e24 | −0.0441942 | ||||||||
\(513\) | −5.03185e25 | −0.902843 | ||||||||
\(514\) | 1.63335e25 | 0.287693 | ||||||||
\(515\) | −2.65429e25 | −0.458966 | ||||||||
\(516\) | 1.04801e25 | 0.177907 | ||||||||
\(517\) | 3.71061e25 | 0.618422 | ||||||||
\(518\) | 1.07301e25 | 0.175579 | ||||||||
\(519\) | −3.02257e25 | −0.485609 | ||||||||
\(520\) | −7.07019e24 | −0.111532 | ||||||||
\(521\) | 6.75250e25 | 1.04594 | 0.522969 | − | 0.852351i | \(-0.324824\pi\) | ||||
0.522969 | + | 0.852351i | \(0.324824\pi\) | |||||||
\(522\) | 1.51689e25 | 0.230720 | ||||||||
\(523\) | −1.63639e25 | −0.244411 | −0.122206 | − | 0.992505i | \(-0.538997\pi\) | ||||
−0.122206 | + | 0.992505i | \(0.538997\pi\) | |||||||
\(524\) | 5.29969e25 | 0.777325 | ||||||||
\(525\) | 4.05042e24 | 0.0583427 | ||||||||
\(526\) | −3.03867e25 | −0.429853 | ||||||||
\(527\) | 7.15505e23 | 0.00994058 | ||||||||
\(528\) | 1.85901e25 | 0.253664 | ||||||||
\(529\) | 1.15711e26 | 1.55076 | ||||||||
\(530\) | 4.33068e25 | 0.570079 | ||||||||
\(531\) | −2.34258e25 | −0.302898 | ||||||||
\(532\) | 1.22304e25 | 0.155339 | ||||||||
\(533\) | 7.10738e25 | 0.886749 | ||||||||
\(534\) | −5.76582e25 | −0.706675 | ||||||||
\(535\) | 6.41224e25 | 0.772056 | ||||||||
\(536\) | −4.32285e25 | −0.511334 | ||||||||
\(537\) | −7.23742e25 | −0.841063 | ||||||||
\(538\) | −1.00716e26 | −1.14992 | ||||||||
\(539\) | 9.96664e25 | 1.11804 | ||||||||
\(540\) | −2.20240e25 | −0.242748 | ||||||||
\(541\) | 2.04269e25 | 0.221222 | 0.110611 | − | 0.993864i | \(-0.464719\pi\) | ||||
0.110611 | + | 0.993864i | \(0.464719\pi\) | |||||||
\(542\) | −5.46039e25 | −0.581072 | ||||||||
\(543\) | −1.04878e26 | −1.09669 | ||||||||
\(544\) | 2.82019e24 | 0.0289794 | ||||||||
\(545\) | 7.24150e25 | 0.731243 | ||||||||
\(546\) | 1.46623e25 | 0.145503 | ||||||||
\(547\) | 8.46896e25 | 0.825943 | 0.412972 | − | 0.910744i | \(-0.364491\pi\) | ||||
0.412972 | + | 0.910744i | \(0.364491\pi\) | |||||||
\(548\) | 2.88292e25 | 0.276323 | ||||||||
\(549\) | −2.04996e25 | −0.193112 | ||||||||
\(550\) | 1.98468e25 | 0.183758 | ||||||||
\(551\) | −7.64151e25 | −0.695407 | ||||||||
\(552\) | 4.92947e25 | 0.440939 | ||||||||
\(553\) | 1.92496e25 | 0.169252 | ||||||||
\(554\) | −3.29885e25 | −0.285115 | ||||||||
\(555\) | 2.73216e25 | 0.232125 | ||||||||
\(556\) | −1.04230e26 | −0.870526 | ||||||||
\(557\) | 8.29899e25 | 0.681398 | 0.340699 | − | 0.940172i | \(-0.389336\pi\) | ||||
0.340699 | + | 0.940172i | \(0.389336\pi\) | |||||||
\(558\) | −2.07281e24 | −0.0167315 | ||||||||
\(559\) | 4.05021e25 | 0.321414 | ||||||||
\(560\) | 5.35314e24 | 0.0417660 | ||||||||
\(561\) | −2.16836e25 | −0.166335 | ||||||||
\(562\) | −8.85878e25 | −0.668158 | ||||||||
\(563\) | 9.14845e24 | 0.0678450 | 0.0339225 | − | 0.999424i | \(-0.489200\pi\) | ||||
0.0339225 | + | 0.999424i | \(0.489200\pi\) | |||||||
\(564\) | 2.54838e25 | 0.185829 | ||||||||
\(565\) | −4.79174e25 | −0.343584 | ||||||||
\(566\) | −4.01174e25 | −0.282863 | ||||||||
\(567\) | 2.46499e25 | 0.170914 | ||||||||
\(568\) | −5.27869e25 | −0.359929 | ||||||||
\(569\) | −5.94829e24 | −0.0398865 | −0.0199432 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199432 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(570\) | 3.11417e25 | 0.205367 | ||||||||
\(571\) | −6.17752e25 | −0.400655 | −0.200328 | − | 0.979729i | \(-0.564201\pi\) | ||||
−0.200328 | + | 0.979729i | \(0.564201\pi\) | |||||||
\(572\) | 7.18443e25 | 0.458279 | ||||||||
\(573\) | −1.62711e26 | −1.02082 | ||||||||
\(574\) | −5.38130e25 | −0.332066 | ||||||||
\(575\) | 5.26271e25 | 0.319422 | ||||||||
\(576\) | −8.17008e24 | −0.0487767 | ||||||||
\(577\) | −5.21343e25 | −0.306163 | −0.153082 | − | 0.988214i | \(-0.548920\pi\) | ||||
−0.153082 | + | 0.988214i | \(0.548920\pi\) | |||||||
\(578\) | 1.19116e26 | 0.688104 | ||||||||
\(579\) | 8.56661e25 | 0.486814 | ||||||||
\(580\) | −3.34463e25 | −0.186974 | ||||||||
\(581\) | 1.24943e25 | 0.0687129 | ||||||||
\(582\) | 4.83480e24 | 0.0261583 | ||||||||
\(583\) | −4.40065e26 | −2.34243 | ||||||||
\(584\) | 9.02574e25 | 0.472673 | ||||||||
\(585\) | −2.38907e25 | −0.123097 | ||||||||
\(586\) | −1.70271e26 | −0.863206 | ||||||||
\(587\) | −7.85282e25 | −0.391709 | −0.195855 | − | 0.980633i | \(-0.562748\pi\) | ||||
−0.195855 | + | 0.980633i | \(0.562748\pi\) | |||||||
\(588\) | 6.84492e25 | 0.335957 | ||||||||
\(589\) | 1.04420e25 | 0.0504300 | ||||||||
\(590\) | 5.16521e25 | 0.245467 | ||||||||
\(591\) | 1.29230e26 | 0.604341 | ||||||||
\(592\) | 3.61090e25 | 0.166172 | ||||||||
\(593\) | −7.16513e25 | −0.324492 | −0.162246 | − | 0.986750i | \(-0.551874\pi\) | ||||
−0.162246 | + | 0.986750i | \(0.551874\pi\) | |||||||
\(594\) | 2.23799e26 | 0.997438 | ||||||||
\(595\) | −6.24393e24 | −0.0273872 | ||||||||
\(596\) | −2.24817e26 | −0.970487 | ||||||||
\(597\) | −7.36925e25 | −0.313089 | ||||||||
\(598\) | 1.90507e26 | 0.796617 | ||||||||
\(599\) | 6.18751e25 | 0.254660 | 0.127330 | − | 0.991860i | \(-0.459359\pi\) | ||||
0.127330 | + | 0.991860i | \(0.459359\pi\) | |||||||
\(600\) | 1.36305e25 | 0.0552171 | ||||||||
\(601\) | 2.47224e26 | 0.985789 | 0.492894 | − | 0.870089i | \(-0.335939\pi\) | ||||
0.492894 | + | 0.870089i | \(0.335939\pi\) | |||||||
\(602\) | −3.06658e25 | −0.120362 | ||||||||
\(603\) | −1.46072e26 | −0.564355 | ||||||||
\(604\) | −1.43549e26 | −0.545944 | ||||||||
\(605\) | −8.22238e25 | −0.307838 | ||||||||
\(606\) | 1.76105e26 | 0.649055 | ||||||||
\(607\) | −9.24185e25 | −0.335325 | −0.167663 | − | 0.985844i | \(-0.553622\pi\) | ||||
−0.167663 | + | 0.985844i | \(0.553622\pi\) | |||||||
\(608\) | 4.11577e25 | 0.147017 | ||||||||
\(609\) | 6.93613e25 | 0.243923 | ||||||||
\(610\) | 4.52000e25 | 0.156497 | ||||||||
\(611\) | 9.84863e25 | 0.335725 | ||||||||
\(612\) | 9.52962e24 | 0.0319843 | ||||||||
\(613\) | 7.50279e25 | 0.247941 | 0.123970 | − | 0.992286i | \(-0.460437\pi\) | ||||
0.123970 | + | 0.992286i | \(0.460437\pi\) | |||||||
\(614\) | 2.42784e26 | 0.789987 | ||||||||
\(615\) | −1.37022e26 | −0.439011 | ||||||||
\(616\) | −5.43964e25 | −0.171614 | ||||||||
\(617\) | 3.84695e26 | 1.19511 | 0.597554 | − | 0.801828i | \(-0.296139\pi\) | ||||
0.597554 | + | 0.801828i | \(0.296139\pi\) | |||||||
\(618\) | 1.85238e26 | 0.566682 | ||||||||
\(619\) | 1.19514e26 | 0.360044 | 0.180022 | − | 0.983663i | \(-0.442383\pi\) | ||||
0.180022 | + | 0.983663i | \(0.442383\pi\) | |||||||
\(620\) | 4.57039e24 | 0.0135591 | ||||||||
\(621\) | 5.93438e26 | 1.73383 | ||||||||
\(622\) | −1.10574e26 | −0.318159 | ||||||||
\(623\) | 1.68713e26 | 0.478094 | ||||||||
\(624\) | 4.93415e25 | 0.137708 | ||||||||
\(625\) | 1.45519e25 | 0.0400000 | ||||||||
\(626\) | 2.96789e26 | 0.803511 | ||||||||
\(627\) | −3.16449e26 | −0.843843 | ||||||||
\(628\) | −1.10657e26 | −0.290644 | ||||||||
\(629\) | −4.21177e25 | −0.108964 | ||||||||
\(630\) | 1.80886e25 | 0.0460968 | ||||||||
\(631\) | −8.74692e25 | −0.219572 | −0.109786 | − | 0.993955i | \(-0.535016\pi\) | ||||
−0.109786 | + | 0.993955i | \(0.535016\pi\) | |||||||
\(632\) | 6.47787e25 | 0.160184 | ||||||||
\(633\) | −1.04620e26 | −0.254848 | ||||||||
\(634\) | −3.29204e26 | −0.789982 | ||||||||
\(635\) | −6.82641e25 | −0.161377 | ||||||||
\(636\) | −3.02229e26 | −0.703873 | ||||||||
\(637\) | 2.64532e26 | 0.606952 | ||||||||
\(638\) | 3.39867e26 | 0.768268 | ||||||||
\(639\) | −1.78371e26 | −0.397251 | ||||||||
\(640\) | 1.80144e25 | 0.0395285 | ||||||||
\(641\) | −7.90635e26 | −1.70933 | −0.854663 | − | 0.519183i | \(-0.826236\pi\) | ||||
−0.854663 | + | 0.519183i | \(0.826236\pi\) | |||||||
\(642\) | −4.47497e26 | −0.953252 | ||||||||
\(643\) | 7.69562e25 | 0.161525 | 0.0807625 | − | 0.996733i | \(-0.474264\pi\) | ||||
0.0807625 | + | 0.996733i | \(0.474264\pi\) | |||||||
\(644\) | −1.44241e26 | −0.298313 | ||||||||
\(645\) | −7.80830e25 | −0.159125 | ||||||||
\(646\) | −4.80065e25 | −0.0964032 | ||||||||
\(647\) | −7.71883e26 | −1.52743 | −0.763714 | − | 0.645555i | \(-0.776626\pi\) | ||||
−0.763714 | + | 0.645555i | \(0.776626\pi\) | |||||||
\(648\) | 8.29520e25 | 0.161757 | ||||||||
\(649\) | −5.24867e26 | −1.00861 | ||||||||
\(650\) | 5.26771e25 | 0.0997573 | ||||||||
\(651\) | −9.47813e24 | −0.0176890 | ||||||||
\(652\) | 3.37701e26 | 0.621128 | ||||||||
\(653\) | 3.79913e26 | 0.688666 | 0.344333 | − | 0.938848i | \(-0.388105\pi\) | ||||
0.344333 | + | 0.938848i | \(0.388105\pi\) | |||||||
\(654\) | −5.05369e26 | −0.902860 | ||||||||
\(655\) | −3.94857e26 | −0.695261 | ||||||||
\(656\) | −1.81091e26 | −0.314276 | ||||||||
\(657\) | 3.04986e26 | 0.521685 | ||||||||
\(658\) | −7.45681e25 | −0.125721 | ||||||||
\(659\) | −4.70607e26 | −0.782072 | −0.391036 | − | 0.920375i | \(-0.627883\pi\) | ||||
−0.391036 | + | 0.920375i | \(0.627883\pi\) | |||||||
\(660\) | −1.38507e26 | −0.226884 | ||||||||
\(661\) | 1.07871e27 | 1.74177 | 0.870885 | − | 0.491486i | \(-0.163546\pi\) | ||||
0.870885 | + | 0.491486i | \(0.163546\pi\) | |||||||
\(662\) | −7.42168e26 | −1.18128 | ||||||||
\(663\) | −5.75521e25 | −0.0902990 | ||||||||
\(664\) | 4.20458e25 | 0.0650318 | ||||||||
\(665\) | −9.11235e25 | −0.138939 | ||||||||
\(666\) | 1.22015e26 | 0.183403 | ||||||||
\(667\) | 9.01213e26 | 1.33546 | ||||||||
\(668\) | 5.53061e26 | 0.807972 | ||||||||
\(669\) | 8.23970e25 | 0.118676 | ||||||||
\(670\) | 3.22077e26 | 0.457351 | ||||||||
\(671\) | −4.59304e26 | −0.643037 | ||||||||
\(672\) | −3.73585e25 | −0.0515681 | ||||||||
\(673\) | 1.37764e27 | 1.87497 | 0.937484 | − | 0.348029i | \(-0.113149\pi\) | ||||
0.937484 | + | 0.348029i | \(0.113149\pi\) | |||||||
\(674\) | −6.81185e26 | −0.914105 | ||||||||
\(675\) | 1.64092e26 | 0.217120 | ||||||||
\(676\) | −1.92546e26 | −0.251212 | ||||||||
\(677\) | 8.45165e26 | 1.08730 | 0.543650 | − | 0.839312i | \(-0.317042\pi\) | ||||
0.543650 | + | 0.839312i | \(0.317042\pi\) | |||||||
\(678\) | 3.34406e26 | 0.424221 | ||||||||
\(679\) | −1.41471e25 | −0.0176972 | ||||||||
\(680\) | −2.10121e25 | −0.0259200 | ||||||||
\(681\) | −3.72228e26 | −0.452805 | ||||||||
\(682\) | −4.64424e25 | −0.0557138 | ||||||||
\(683\) | −4.20176e26 | −0.497090 | −0.248545 | − | 0.968620i | \(-0.579952\pi\) | ||||
−0.248545 | + | 0.968620i | \(0.579952\pi\) | |||||||
\(684\) | 1.39075e26 | 0.162261 | ||||||||
\(685\) | −2.14795e26 | −0.247151 | ||||||||
\(686\) | −4.33061e26 | −0.491440 | ||||||||
\(687\) | 7.03261e26 | 0.787095 | ||||||||
\(688\) | −1.03197e26 | −0.113914 | ||||||||
\(689\) | −1.16801e27 | −1.27164 | ||||||||
\(690\) | −3.67274e26 | −0.394388 | ||||||||
\(691\) | 9.77912e26 | 1.03576 | 0.517879 | − | 0.855454i | \(-0.326722\pi\) | ||||
0.517879 | + | 0.855454i | \(0.326722\pi\) | |||||||
\(692\) | 2.97630e26 | 0.310934 | ||||||||
\(693\) | −1.83809e26 | −0.189409 | ||||||||
\(694\) | 4.13927e26 | 0.420735 | ||||||||
\(695\) | 7.76573e26 | 0.778622 | ||||||||
\(696\) | 2.33415e26 | 0.230856 | ||||||||
\(697\) | 2.11226e26 | 0.206080 | ||||||||
\(698\) | −9.61944e26 | −0.925813 | ||||||||
\(699\) | 1.52454e27 | 1.44745 | ||||||||
\(700\) | −3.98840e25 | −0.0373566 | ||||||||
\(701\) | −8.91378e25 | −0.0823646 | −0.0411823 | − | 0.999152i | \(-0.513112\pi\) | ||||
−0.0411823 | + | 0.999152i | \(0.513112\pi\) | |||||||
\(702\) | 5.94001e26 | 0.541483 | ||||||||
\(703\) | −6.14662e26 | −0.552791 | ||||||||
\(704\) | −1.83055e26 | −0.162420 | ||||||||
\(705\) | −1.89869e26 | −0.166210 | ||||||||
\(706\) | 1.28871e27 | 1.11304 | ||||||||
\(707\) | −5.15300e26 | −0.439112 | ||||||||
\(708\) | −3.60469e26 | −0.303077 | ||||||||
\(709\) | −1.16549e27 | −0.966869 | −0.483435 | − | 0.875380i | \(-0.660611\pi\) | ||||
−0.483435 | + | 0.875380i | \(0.660611\pi\) | |||||||
\(710\) | 3.93293e26 | 0.321931 | ||||||||
\(711\) | 2.18892e26 | 0.176794 | ||||||||
\(712\) | 5.67755e26 | 0.452481 | ||||||||
\(713\) | −1.23150e26 | −0.0968461 | ||||||||
\(714\) | 4.35752e25 | 0.0338147 | ||||||||
\(715\) | −5.35282e26 | −0.409897 | ||||||||
\(716\) | 7.12662e26 | 0.538530 | ||||||||
\(717\) | −1.49436e27 | −1.11435 | ||||||||
\(718\) | 1.04823e26 | 0.0771387 | ||||||||
\(719\) | −1.66537e27 | −1.20945 | −0.604723 | − | 0.796436i | \(-0.706716\pi\) | ||||
−0.604723 | + | 0.796436i | \(0.706716\pi\) | |||||||
\(720\) | 6.08718e25 | 0.0436272 | ||||||||
\(721\) | −5.42023e26 | −0.383383 | ||||||||
\(722\) | 3.12347e26 | 0.218039 | ||||||||
\(723\) | 1.27115e27 | 0.875757 | ||||||||
\(724\) | 1.03272e27 | 0.702209 | ||||||||
\(725\) | 2.49194e26 | 0.167235 | ||||||||
\(726\) | 5.73823e26 | 0.380085 | ||||||||
\(727\) | 1.92104e26 | 0.125591 | 0.0627955 | − | 0.998026i | \(-0.479998\pi\) | ||||
0.0627955 | + | 0.998026i | \(0.479998\pi\) | |||||||
\(728\) | −1.44378e26 | −0.0931649 | ||||||||
\(729\) | 1.61128e27 | 1.02626 | ||||||||
\(730\) | −6.72470e26 | −0.422771 | ||||||||
\(731\) | 1.20369e26 | 0.0746964 | ||||||||
\(732\) | −3.15442e26 | −0.193225 | ||||||||
\(733\) | −1.95377e27 | −1.18137 | −0.590684 | − | 0.806903i | \(-0.701142\pi\) | ||||
−0.590684 | + | 0.806903i | \(0.701142\pi\) | |||||||
\(734\) | 2.97338e26 | 0.177475 | ||||||||
\(735\) | −5.09986e26 | −0.300489 | ||||||||
\(736\) | −4.85400e26 | −0.282332 | ||||||||
\(737\) | −3.27281e27 | −1.87923 | ||||||||
\(738\) | −6.11920e26 | −0.346864 | ||||||||
\(739\) | −4.82280e26 | −0.269884 | −0.134942 | − | 0.990854i | \(-0.543085\pi\) | ||||
−0.134942 | + | 0.990854i | \(0.543085\pi\) | |||||||
\(740\) | −2.69033e26 | −0.148629 | ||||||||
\(741\) | −8.39911e26 | −0.458100 | ||||||||
\(742\) | 8.84352e26 | 0.476198 | ||||||||
\(743\) | 1.08282e27 | 0.575657 | 0.287828 | − | 0.957682i | \(-0.407067\pi\) | ||||
0.287828 | + | 0.957682i | \(0.407067\pi\) | |||||||
\(744\) | −3.18958e25 | −0.0167414 | ||||||||
\(745\) | 1.67502e27 | 0.868030 | ||||||||
\(746\) | −2.22959e27 | −1.14079 | ||||||||
\(747\) | 1.42075e26 | 0.0717750 | ||||||||
\(748\) | 2.13516e26 | 0.106504 | ||||||||
\(749\) | 1.30942e27 | 0.644914 | ||||||||
\(750\) | −1.01555e26 | −0.0493877 | ||||||||
\(751\) | −1.90953e27 | −0.916951 | −0.458475 | − | 0.888707i | \(-0.651604\pi\) | ||||
−0.458475 | + | 0.888707i | \(0.651604\pi\) | |||||||
\(752\) | −2.50937e26 | −0.118986 | ||||||||
\(753\) | −2.81492e27 | −1.31799 | ||||||||
\(754\) | 9.02068e26 | 0.417072 | ||||||||
\(755\) | 1.06952e27 | 0.488307 | ||||||||
\(756\) | −4.49744e26 | −0.202772 | ||||||||
\(757\) | −2.96368e26 | −0.131953 | −0.0659767 | − | 0.997821i | \(-0.521016\pi\) | ||||
−0.0659767 | + | 0.997821i | \(0.521016\pi\) | |||||||
\(758\) | −1.22231e27 | −0.537430 | ||||||||
\(759\) | 3.73208e27 | 1.62052 | ||||||||
\(760\) | −3.06649e26 | −0.131496 | ||||||||
\(761\) | −1.09087e27 | −0.461975 | −0.230988 | − | 0.972957i | \(-0.574196\pi\) | ||||
−0.230988 | + | 0.972957i | \(0.574196\pi\) | |||||||
\(762\) | 4.76401e26 | 0.199251 | ||||||||
\(763\) | 1.47876e27 | 0.610821 | ||||||||
\(764\) | 1.60219e27 | 0.653625 | ||||||||
\(765\) | −7.10012e25 | −0.0286077 | ||||||||
\(766\) | 1.57557e27 | 0.626995 | ||||||||
\(767\) | −1.39309e27 | −0.547549 | ||||||||
\(768\) | −1.25719e26 | −0.0488055 | ||||||||
\(769\) | 2.20592e27 | 0.845842 | 0.422921 | − | 0.906166i | \(-0.361005\pi\) | ||||
0.422921 | + | 0.906166i | \(0.361005\pi\) | |||||||
\(770\) | 4.05285e26 | 0.153496 | ||||||||
\(771\) | 8.49277e26 | 0.317711 | ||||||||
\(772\) | −8.43545e26 | −0.311705 | ||||||||
\(773\) | 1.83711e27 | 0.670550 | 0.335275 | − | 0.942120i | \(-0.391171\pi\) | ||||
0.335275 | + | 0.942120i | \(0.391171\pi\) | |||||||
\(774\) | −3.48708e26 | −0.125725 | ||||||||
\(775\) | −3.40520e25 | −0.0121277 | ||||||||
\(776\) | −4.76077e25 | −0.0167491 | ||||||||
\(777\) | 5.57924e26 | 0.193899 | ||||||||
\(778\) | −3.05995e27 | −1.05053 | ||||||||
\(779\) | 3.08261e27 | 1.04547 | ||||||||
\(780\) | −3.67622e26 | −0.123170 | ||||||||
\(781\) | −3.99648e27 | −1.32280 | ||||||||
\(782\) | 5.66173e26 | 0.185133 | ||||||||
\(783\) | 2.80998e27 | 0.907752 | ||||||||
\(784\) | −6.74012e26 | −0.215112 | ||||||||
\(785\) | 8.24457e26 | 0.259960 | ||||||||
\(786\) | 2.75563e27 | 0.858433 | ||||||||
\(787\) | −2.08651e26 | −0.0642187 | −0.0321093 | − | 0.999484i | \(-0.510222\pi\) | ||||
−0.0321093 | + | 0.999484i | \(0.510222\pi\) | |||||||
\(788\) | −1.27251e27 | −0.386958 | ||||||||
\(789\) | −1.57999e27 | −0.474704 | ||||||||
\(790\) | −4.82639e26 | −0.143273 | ||||||||
\(791\) | −9.78503e26 | −0.287003 | ||||||||
\(792\) | −6.18554e26 | −0.179262 | ||||||||
\(793\) | −1.21907e27 | −0.349088 | ||||||||
\(794\) | 1.15671e27 | 0.327289 | ||||||||
\(795\) | 2.25178e27 | 0.629563 | ||||||||
\(796\) | 7.25642e26 | 0.200470 | ||||||||
\(797\) | 4.57657e27 | 1.24936 | 0.624678 | − | 0.780883i | \(-0.285230\pi\) | ||||
0.624678 | + | 0.780883i | \(0.285230\pi\) | |||||||
\(798\) | 6.35932e26 | 0.171547 | ||||||||
\(799\) | 2.92694e26 | 0.0780224 | ||||||||
\(800\) | −1.34218e26 | −0.0353553 | ||||||||
\(801\) | 1.91848e27 | 0.499400 | ||||||||
\(802\) | −3.77737e25 | −0.00971702 | ||||||||
\(803\) | 6.83335e27 | 1.73715 | ||||||||
\(804\) | −2.24771e27 | −0.564687 | ||||||||
\(805\) | 1.07468e27 | 0.266820 | ||||||||
\(806\) | −1.23266e26 | −0.0302456 | ||||||||
\(807\) | −5.23684e27 | −1.26990 | ||||||||
\(808\) | −1.73409e27 | −0.415588 | ||||||||
\(809\) | 1.09533e27 | 0.259439 | 0.129720 | − | 0.991551i | \(-0.458592\pi\) | ||||
0.129720 | + | 0.991551i | \(0.458592\pi\) | |||||||
\(810\) | −6.18041e26 | −0.144680 | ||||||||
\(811\) | 1.55516e26 | 0.0359812 | 0.0179906 | − | 0.999838i | \(-0.494273\pi\) | ||||
0.0179906 | + | 0.999838i | \(0.494273\pi\) | |||||||
\(812\) | −6.82994e26 | −0.156183 | ||||||||
\(813\) | −2.83919e27 | −0.641703 | ||||||||
\(814\) | 2.73380e27 | 0.610709 | ||||||||
\(815\) | −2.51607e27 | −0.555553 | ||||||||
\(816\) | 1.46639e26 | 0.0320032 | ||||||||
\(817\) | 1.75666e27 | 0.378946 | ||||||||
\(818\) | −6.09213e27 | −1.29901 | ||||||||
\(819\) | −4.87862e26 | −0.102825 | ||||||||
\(820\) | 1.34924e27 | 0.281097 | ||||||||
\(821\) | −1.23074e27 | −0.253458 | −0.126729 | − | 0.991937i | \(-0.540448\pi\) | ||||
−0.126729 | + | 0.991937i | \(0.540448\pi\) | |||||||
\(822\) | 1.49901e27 | 0.305156 | ||||||||
\(823\) | −7.12638e27 | −1.43407 | −0.717035 | − | 0.697037i | \(-0.754501\pi\) | ||||
−0.717035 | + | 0.697037i | \(0.754501\pi\) | |||||||
\(824\) | −1.82402e27 | −0.362844 | ||||||||
\(825\) | 1.03196e27 | 0.202931 | ||||||||
\(826\) | 1.05477e27 | 0.205044 | ||||||||
\(827\) | 3.28596e27 | 0.631480 | 0.315740 | − | 0.948846i | \(-0.397747\pi\) | ||||
0.315740 | + | 0.948846i | \(0.397747\pi\) | |||||||
\(828\) | −1.64020e27 | −0.311607 | ||||||||
\(829\) | −7.47757e27 | −1.40441 | −0.702203 | − | 0.711977i | \(-0.747800\pi\) | ||||
−0.702203 | + | 0.711977i | \(0.747800\pi\) | |||||||
\(830\) | −3.13265e26 | −0.0581662 | ||||||||
\(831\) | −1.71527e27 | −0.314864 | ||||||||
\(832\) | −4.85860e26 | −0.0881738 | ||||||||
\(833\) | 7.86171e26 | 0.141055 | ||||||||
\(834\) | −5.41954e27 | −0.961358 | ||||||||
\(835\) | −4.12062e27 | −0.722672 | ||||||||
\(836\) | 3.11604e27 | 0.540310 | ||||||||
\(837\) | −3.83981e26 | −0.0658290 | ||||||||
\(838\) | 5.11983e27 | 0.867835 | ||||||||
\(839\) | −6.82604e27 | −1.14401 | −0.572006 | − | 0.820250i | \(-0.693834\pi\) | ||||
−0.572006 | + | 0.820250i | \(0.693834\pi\) | |||||||
\(840\) | 2.78343e26 | 0.0461239 | ||||||||
\(841\) | −1.83594e27 | −0.300812 | ||||||||
\(842\) | 1.77536e27 | 0.287621 | ||||||||
\(843\) | −4.60622e27 | −0.737875 | ||||||||
\(844\) | 1.03019e27 | 0.163178 | ||||||||
\(845\) | 1.43458e27 | 0.224691 | ||||||||
\(846\) | −8.47931e26 | −0.131323 | ||||||||
\(847\) | −1.67906e27 | −0.257143 | ||||||||
\(848\) | 2.97602e27 | 0.450687 | ||||||||
\(849\) | −2.08595e27 | −0.312378 | ||||||||
\(850\) | 1.56552e26 | 0.0231835 | ||||||||
\(851\) | 7.24911e27 | 1.06158 | ||||||||
\(852\) | −2.74471e27 | −0.397485 | ||||||||
\(853\) | 3.69477e27 | 0.529141 | 0.264571 | − | 0.964366i | \(-0.414770\pi\) | ||||
0.264571 | + | 0.964366i | \(0.414770\pi\) | |||||||
\(854\) | 9.23013e26 | 0.130725 | ||||||||
\(855\) | −1.03619e27 | −0.145131 | ||||||||
\(856\) | 4.40646e27 | 0.610364 | ||||||||
\(857\) | 8.05314e27 | 1.10318 | 0.551592 | − | 0.834114i | \(-0.314021\pi\) | ||||
0.551592 | + | 0.834114i | \(0.314021\pi\) | |||||||
\(858\) | 3.73562e27 | 0.506097 | ||||||||
\(859\) | −6.31890e26 | −0.0846655 | −0.0423328 | − | 0.999104i | \(-0.513479\pi\) | ||||
−0.0423328 | + | 0.999104i | \(0.513479\pi\) | |||||||
\(860\) | 7.68875e26 | 0.101887 | ||||||||
\(861\) | −2.79806e27 | −0.366714 | ||||||||
\(862\) | 3.75843e27 | 0.487178 | ||||||||
\(863\) | 7.45376e27 | 0.955592 | 0.477796 | − | 0.878471i | \(-0.341436\pi\) | ||||
0.477796 | + | 0.878471i | \(0.341436\pi\) | |||||||
\(864\) | −1.51348e27 | −0.191909 | ||||||||
\(865\) | −2.21751e27 | −0.278108 | ||||||||
\(866\) | 9.93128e26 | 0.123193 | ||||||||
\(867\) | 6.19355e27 | 0.759903 | ||||||||
\(868\) | 9.33302e25 | 0.0113262 | ||||||||
\(869\) | 4.90438e27 | 0.588702 | ||||||||
\(870\) | −1.73908e27 | −0.206484 | ||||||||
\(871\) | −8.68663e27 | −1.02019 | ||||||||
\(872\) | 4.97632e27 | 0.578098 | ||||||||
\(873\) | −1.60870e26 | −0.0184858 | ||||||||
\(874\) | 8.26268e27 | 0.939209 | ||||||||
\(875\) | 2.97159e26 | 0.0334128 | ||||||||
\(876\) | 4.69303e27 | 0.521993 | ||||||||
\(877\) | −2.72071e27 | −0.299355 | −0.149678 | − | 0.988735i | \(-0.547824\pi\) | ||||
−0.149678 | + | 0.988735i | \(0.547824\pi\) | |||||||
\(878\) | 5.51714e27 | 0.600504 | ||||||||
\(879\) | −8.85345e27 | −0.953275 | ||||||||
\(880\) | 1.36386e27 | 0.145273 | ||||||||
\(881\) | 8.26420e27 | 0.870822 | 0.435411 | − | 0.900232i | \(-0.356603\pi\) | ||||
0.435411 | + | 0.900232i | \(0.356603\pi\) | |||||||
\(882\) | −2.27753e27 | −0.237417 | ||||||||
\(883\) | 1.67843e28 | 1.73092 | 0.865459 | − | 0.500979i | \(-0.167027\pi\) | ||||
0.865459 | + | 0.500979i | \(0.167027\pi\) | |||||||
\(884\) | 5.66710e26 | 0.0578181 | ||||||||
\(885\) | 2.68571e27 | 0.271080 | ||||||||
\(886\) | −1.09173e28 | −1.09018 | ||||||||
\(887\) | −1.79212e28 | −1.77049 | −0.885245 | − | 0.465126i | \(-0.846009\pi\) | ||||
−0.885245 | + | 0.465126i | \(0.846009\pi\) | |||||||
\(888\) | 1.87753e27 | 0.183511 | ||||||||
\(889\) | −1.39400e27 | −0.134801 | ||||||||
\(890\) | −4.23010e27 | −0.404712 | ||||||||
\(891\) | 6.28027e27 | 0.594484 | ||||||||
\(892\) | −8.11355e26 | −0.0759880 | ||||||||
\(893\) | 4.27155e27 | 0.395819 | ||||||||
\(894\) | −1.16896e28 | −1.07175 | ||||||||
\(895\) | −5.30974e27 | −0.481676 | ||||||||
\(896\) | 3.67865e26 | 0.0330189 | ||||||||
\(897\) | 9.90562e27 | 0.879738 | ||||||||
\(898\) | 4.17167e27 | 0.366594 | ||||||||
\(899\) | −5.83124e26 | −0.0507042 | ||||||||
\(900\) | −4.53531e26 | −0.0390214 | ||||||||
\(901\) | −3.47125e27 | −0.295529 | ||||||||
\(902\) | −1.37104e28 | −1.15501 | ||||||||
\(903\) | −1.59450e27 | −0.132920 | ||||||||
\(904\) | −3.29286e27 | −0.271627 | ||||||||
\(905\) | −7.69437e27 | −0.628075 | ||||||||
\(906\) | −7.46396e27 | −0.602909 | ||||||||
\(907\) | −8.20682e27 | −0.656003 | −0.328001 | − | 0.944677i | \(-0.606375\pi\) | ||||
−0.328001 | + | 0.944677i | \(0.606375\pi\) | |||||||
\(908\) | 3.66529e27 | 0.289929 | ||||||||
\(909\) | −5.85959e27 | −0.458681 | ||||||||
\(910\) | 1.07570e27 | 0.0833292 | ||||||||
\(911\) | 1.30357e28 | 0.999331 | 0.499666 | − | 0.866218i | \(-0.333456\pi\) | ||||
0.499666 | + | 0.866218i | \(0.333456\pi\) | |||||||
\(912\) | 2.14004e27 | 0.162357 | ||||||||
\(913\) | 3.18327e27 | 0.239002 | ||||||||
\(914\) | −3.83009e27 | −0.284591 | ||||||||
\(915\) | 2.35023e27 | 0.172826 | ||||||||
\(916\) | −6.92493e27 | −0.503975 | ||||||||
\(917\) | −8.06323e27 | −0.580765 | ||||||||
\(918\) | 1.76533e27 | 0.125840 | ||||||||
\(919\) | 1.03919e27 | 0.0733155 | 0.0366578 | − | 0.999328i | \(-0.488329\pi\) | ||||
0.0366578 | + | 0.999328i | \(0.488329\pi\) | |||||||
\(920\) | 3.61651e27 | 0.252525 | ||||||||
\(921\) | 1.26238e28 | 0.872416 | ||||||||
\(922\) | 1.23542e28 | 0.845024 | ||||||||
\(923\) | −1.06074e28 | −0.718111 | ||||||||
\(924\) | −2.82840e27 | −0.189521 | ||||||||
\(925\) | 2.00445e27 | 0.132938 | ||||||||
\(926\) | −1.87475e28 | −1.23066 | ||||||||
\(927\) | −6.16347e27 | −0.400468 | ||||||||
\(928\) | −2.29841e27 | −0.147816 | ||||||||
\(929\) | −3.13678e27 | −0.199680 | −0.0998399 | − | 0.995004i | \(-0.531833\pi\) | ||||
−0.0998399 | + | 0.995004i | \(0.531833\pi\) | |||||||
\(930\) | 2.37642e26 | 0.0149739 | ||||||||
\(931\) | 1.14733e28 | 0.715594 | ||||||||
\(932\) | −1.50120e28 | −0.926800 | ||||||||
\(933\) | −5.74941e27 | −0.351356 | ||||||||
\(934\) | 1.10998e28 | 0.671460 | ||||||||
\(935\) | −1.59082e27 | −0.0952599 | ||||||||
\(936\) | −1.64175e27 | −0.0973167 | ||||||||
\(937\) | 9.68011e27 | 0.568008 | 0.284004 | − | 0.958823i | \(-0.408337\pi\) | ||||
0.284004 | + | 0.958823i | \(0.408337\pi\) | |||||||
\(938\) | 6.57702e27 | 0.382034 | ||||||||
\(939\) | 1.54319e28 | 0.887351 | ||||||||
\(940\) | 1.86962e27 | 0.106424 | ||||||||
\(941\) | 2.78537e28 | 1.56957 | 0.784785 | − | 0.619768i | \(-0.212773\pi\) | ||||
0.784785 | + | 0.619768i | \(0.212773\pi\) | |||||||
\(942\) | −5.75372e27 | −0.320970 | ||||||||
\(943\) | −3.63553e28 | −2.00774 | ||||||||
\(944\) | 3.54950e27 | 0.194059 | ||||||||
\(945\) | 3.35085e27 | 0.181365 | ||||||||
\(946\) | −7.81298e27 | −0.418650 | ||||||||
\(947\) | 6.85631e27 | 0.363719 | 0.181859 | − | 0.983325i | \(-0.441788\pi\) | ||||
0.181859 | + | 0.983325i | \(0.441788\pi\) | |||||||
\(948\) | 3.36824e27 | 0.176898 | ||||||||
\(949\) | 1.81369e28 | 0.943051 | ||||||||
\(950\) | 2.28471e27 | 0.117613 | ||||||||
\(951\) | −1.71173e28 | −0.872411 | ||||||||
\(952\) | −4.29080e26 | −0.0216515 | ||||||||
\(953\) | −2.64880e28 | −1.32332 | −0.661662 | − | 0.749802i | \(-0.730149\pi\) | ||||
−0.661662 | + | 0.749802i | \(0.730149\pi\) | |||||||
\(954\) | 1.00562e28 | 0.497420 | ||||||||
\(955\) | −1.19373e28 | −0.584620 | ||||||||
\(956\) | 1.47148e28 | 0.713517 | ||||||||
\(957\) | 1.76718e28 | 0.848431 | ||||||||
\(958\) | −1.63849e27 | −0.0778884 | ||||||||
\(959\) | −4.38624e27 | −0.206450 | ||||||||
\(960\) | 9.36678e26 | 0.0436530 | ||||||||
\(961\) | −2.15910e28 | −0.996323 | ||||||||
\(962\) | 7.25599e27 | 0.331538 | ||||||||
\(963\) | 1.48897e28 | 0.673654 | ||||||||
\(964\) | −1.25169e28 | −0.560744 | ||||||||
\(965\) | 6.28490e27 | 0.278798 | ||||||||
\(966\) | −7.49996e27 | −0.329440 | ||||||||
\(967\) | −8.38952e27 | −0.364910 | −0.182455 | − | 0.983214i | \(-0.558404\pi\) | ||||
−0.182455 | + | 0.983214i | \(0.558404\pi\) | |||||||
\(968\) | −5.65038e27 | −0.243367 | ||||||||
\(969\) | −2.49615e27 | −0.106462 | ||||||||
\(970\) | 3.54705e26 | 0.0149808 | ||||||||
\(971\) | −1.23262e28 | −0.515520 | −0.257760 | − | 0.966209i | \(-0.582984\pi\) | ||||
−0.257760 | + | 0.966209i | \(0.582984\pi\) | |||||||
\(972\) | −8.79281e27 | −0.364165 | ||||||||
\(973\) | 1.58581e28 | 0.650398 | ||||||||
\(974\) | 6.04254e27 | 0.245420 | ||||||||
\(975\) | 2.73900e27 | 0.110166 | ||||||||
\(976\) | 3.10612e27 | 0.123722 | ||||||||
\(977\) | 3.70018e28 | 1.45957 | 0.729784 | − | 0.683678i | \(-0.239621\pi\) | ||||
0.729784 | + | 0.683678i | \(0.239621\pi\) | |||||||
\(978\) | 1.75592e28 | 0.685937 | ||||||||
\(979\) | 4.29845e28 | 1.66294 | ||||||||
\(980\) | 5.02178e27 | 0.192402 | ||||||||
\(981\) | 1.68153e28 | 0.638042 | ||||||||
\(982\) | 1.23288e28 | 0.463299 | ||||||||
\(983\) | −2.36780e28 | −0.881223 | −0.440612 | − | 0.897698i | \(-0.645238\pi\) | ||||
−0.440612 | + | 0.897698i | \(0.645238\pi\) | |||||||
\(984\) | −9.41605e27 | −0.347068 | ||||||||
\(985\) | 9.48096e27 | 0.346105 | ||||||||
\(986\) | 2.68088e27 | 0.0969274 | ||||||||
\(987\) | −3.87725e27 | −0.138839 | ||||||||
\(988\) | 8.27052e27 | 0.293320 | ||||||||
\(989\) | −2.07174e28 | −0.727730 | ||||||||
\(990\) | 4.60859e27 | 0.160337 | ||||||||
\(991\) | 1.70262e28 | 0.586704 | 0.293352 | − | 0.956005i | \(-0.405229\pi\) | ||||
0.293352 | + | 0.956005i | \(0.405229\pi\) | |||||||
\(992\) | 3.14075e26 | 0.0107194 | ||||||||
\(993\) | −3.85898e28 | −1.30453 | ||||||||
\(994\) | 8.03129e27 | 0.268915 | ||||||||
\(995\) | −5.40646e27 | −0.179305 | ||||||||
\(996\) | 2.18622e27 | 0.0718173 | ||||||||
\(997\) | 3.10765e28 | 1.01118 | 0.505590 | − | 0.862774i | \(-0.331275\pi\) | ||||
0.505590 | + | 0.862774i | \(0.331275\pi\) | |||||||
\(998\) | −1.19153e28 | −0.384031 | ||||||||
\(999\) | 2.26028e28 | 0.721588 |
(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 | 10.20.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 90.20.a.e.1.1 | 1 | |||
4.3 | odd | 2 | 80.20.a.c.1.1 | 1 | |||
5.2 | odd | 4 | 50.20.b.e.49.1 | 2 | |||
5.3 | odd | 4 | 50.20.b.e.49.2 | 2 | |||
5.4 | even | 2 | 50.20.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.20.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
50.20.a.e.1.1 | 1 | 5.4 | even | 2 | |||
50.20.b.e.49.1 | 2 | 5.2 | odd | 4 | |||
50.20.b.e.49.2 | 2 | 5.3 | odd | 4 | |||
80.20.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
90.20.a.e.1.1 | 1 | 3.2 | odd | 2 |