Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.87274 | 0.347929 | 0.173965 | − | 0.984752i | \(-0.444342\pi\) | ||||
0.173965 | + | 0.984752i | \(0.444342\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −450.020 | −0.878945 | ||||||||
\(5\) | −1394.70 | −0.997968 | −0.498984 | − | 0.866611i | \(-0.666293\pi\) | ||||
−0.498984 | + | 0.866611i | \(0.666293\pi\) | |||||||
\(6\) | −637.692 | −0.200877 | ||||||||
\(7\) | −8519.00 | −1.34106 | −0.670529 | − | 0.741883i | \(-0.733933\pi\) | ||||
−0.670529 | + | 0.741883i | \(0.733933\pi\) | |||||||
\(8\) | −7573.74 | −0.653740 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −10980.1 | −0.347222 | ||||||||
\(11\) | −32784.5 | −0.675151 | −0.337576 | − | 0.941298i | \(-0.609607\pi\) | ||||
−0.337576 | + | 0.941298i | \(0.609607\pi\) | |||||||
\(12\) | 36451.6 | 0.507459 | ||||||||
\(13\) | 173232. | 1.68222 | 0.841109 | − | 0.540866i | \(-0.181903\pi\) | ||||
0.841109 | + | 0.540866i | \(0.181903\pi\) | |||||||
\(14\) | −67067.9 | −0.466593 | ||||||||
\(15\) | 112971. | 0.576177 | ||||||||
\(16\) | 170784. | 0.651490 | ||||||||
\(17\) | 557614. | 1.61925 | 0.809625 | − | 0.586948i | \(-0.199671\pi\) | ||||
0.809625 | + | 0.586948i | \(0.199671\pi\) | |||||||
\(18\) | 51653.1 | 0.115976 | ||||||||
\(19\) | 329203. | 0.579525 | 0.289763 | − | 0.957099i | \(-0.406424\pi\) | ||||
0.289763 | + | 0.957099i | \(0.406424\pi\) | |||||||
\(20\) | 627644. | 0.877159 | ||||||||
\(21\) | 690039. | 0.774260 | ||||||||
\(22\) | −258104. | −0.234905 | ||||||||
\(23\) | 121336. | 0.0904098 | 0.0452049 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452049 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(24\) | 613473. | 0.377437 | ||||||||
\(25\) | −7930.40 | −0.00406037 | ||||||||
\(26\) | 1.36381e6 | 0.585293 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 3.83372e6 | 1.17872 | ||||||||
\(29\) | −5991.02 | −0.00157293 | −0.000786466 | − | 1.00000i | \(-0.500250\pi\) | ||||
−0.000786466 | 1.00000i | \(0.500250\pi\) | ||||||||
\(30\) | 889391. | 0.200469 | ||||||||
\(31\) | −7.64818e6 | −1.48741 | −0.743705 | − | 0.668508i | \(-0.766933\pi\) | ||||
−0.743705 | + | 0.668508i | \(0.766933\pi\) | |||||||
\(32\) | 5.22229e6 | 0.880413 | ||||||||
\(33\) | 2.65554e6 | 0.389799 | ||||||||
\(34\) | 4.38995e6 | 0.563384 | ||||||||
\(35\) | 1.18815e7 | 1.33833 | ||||||||
\(36\) | −2.95258e6 | −0.292982 | ||||||||
\(37\) | −7.81561e6 | −0.685575 | −0.342788 | − | 0.939413i | \(-0.611371\pi\) | ||||
−0.342788 | + | 0.939413i | \(0.611371\pi\) | |||||||
\(38\) | 2.59173e6 | 0.201634 | ||||||||
\(39\) | −1.40318e7 | −0.971229 | ||||||||
\(40\) | 1.05631e7 | 0.652412 | ||||||||
\(41\) | −1.42595e7 | −0.788092 | −0.394046 | − | 0.919091i | \(-0.628925\pi\) | ||||
−0.394046 | + | 0.919091i | \(0.628925\pi\) | |||||||
\(42\) | 5.43250e6 | 0.269388 | ||||||||
\(43\) | 1.08394e7 | 0.483502 | 0.241751 | − | 0.970338i | \(-0.422278\pi\) | ||||
0.241751 | + | 0.970338i | \(0.422278\pi\) | |||||||
\(44\) | 1.47537e7 | 0.593421 | ||||||||
\(45\) | −9.15064e6 | −0.332656 | ||||||||
\(46\) | 955249. | 0.0314562 | ||||||||
\(47\) | 1.53262e7 | 0.458137 | 0.229069 | − | 0.973410i | \(-0.426432\pi\) | ||||
0.229069 | + | 0.973410i | \(0.426432\pi\) | |||||||
\(48\) | −1.38335e7 | −0.376138 | ||||||||
\(49\) | 3.22198e7 | 0.798437 | ||||||||
\(50\) | −62434.0 | −0.00141272 | ||||||||
\(51\) | −4.51668e7 | −0.934874 | ||||||||
\(52\) | −7.79577e7 | −1.47858 | ||||||||
\(53\) | −2.75622e6 | −0.0479813 | −0.0239907 | − | 0.999712i | \(-0.507637\pi\) | ||||
−0.0239907 | + | 0.999712i | \(0.507637\pi\) | |||||||
\(54\) | −4.18390e6 | −0.0669590 | ||||||||
\(55\) | 4.57246e7 | 0.673779 | ||||||||
\(56\) | 6.45207e7 | 0.876704 | ||||||||
\(57\) | −2.66654e7 | −0.334589 | ||||||||
\(58\) | −47165.8 | −0.000547269 0 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −5.08391e7 | −0.506428 | ||||||||
\(61\) | 1.86412e8 | 1.72381 | 0.861906 | − | 0.507067i | \(-0.169270\pi\) | ||||
0.861906 | + | 0.507067i | \(0.169270\pi\) | |||||||
\(62\) | −6.02122e7 | −0.517514 | ||||||||
\(63\) | −5.58932e7 | −0.447019 | ||||||||
\(64\) | −4.63277e7 | −0.345168 | ||||||||
\(65\) | −2.41607e8 | −1.67880 | ||||||||
\(66\) | 2.09064e7 | 0.135622 | ||||||||
\(67\) | −3.01770e7 | −0.182953 | −0.0914765 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914765 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(68\) | −2.50938e8 | −1.42323 | ||||||||
\(69\) | −9.82824e6 | −0.0521981 | ||||||||
\(70\) | 9.35398e7 | 0.465645 | ||||||||
\(71\) | −9.51388e6 | −0.0444319 | −0.0222160 | − | 0.999753i | \(-0.507072\pi\) | ||||
−0.0222160 | + | 0.999753i | \(0.507072\pi\) | |||||||
\(72\) | −4.96913e7 | −0.217913 | ||||||||
\(73\) | 2.10691e8 | 0.868348 | 0.434174 | − | 0.900829i | \(-0.357040\pi\) | ||||
0.434174 | + | 0.900829i | \(0.357040\pi\) | |||||||
\(74\) | −6.15303e7 | −0.238532 | ||||||||
\(75\) | 642363. | 0.00234425 | ||||||||
\(76\) | −1.48148e8 | −0.509371 | ||||||||
\(77\) | 2.79291e8 | 0.905417 | ||||||||
\(78\) | −1.10468e8 | −0.337919 | ||||||||
\(79\) | 3.67936e7 | 0.106280 | 0.0531398 | − | 0.998587i | \(-0.483077\pi\) | ||||
0.0531398 | + | 0.998587i | \(0.483077\pi\) | |||||||
\(80\) | −2.38193e8 | −0.650166 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | −1.12261e8 | −0.274200 | ||||||||
\(83\) | 8.97616e7 | 0.207606 | 0.103803 | − | 0.994598i | \(-0.466899\pi\) | ||||
0.103803 | + | 0.994598i | \(0.466899\pi\) | |||||||
\(84\) | −3.10531e8 | −0.680532 | ||||||||
\(85\) | −7.77706e8 | −1.61596 | ||||||||
\(86\) | 8.53361e7 | 0.168225 | ||||||||
\(87\) | 485273. | 0.000908133 0 | ||||||||
\(88\) | 2.48301e8 | 0.441374 | ||||||||
\(89\) | −8.83063e7 | −0.149189 | −0.0745944 | − | 0.997214i | \(-0.523766\pi\) | ||||
−0.0745944 | + | 0.997214i | \(0.523766\pi\) | |||||||
\(90\) | −7.20407e7 | −0.115741 | ||||||||
\(91\) | −1.47576e9 | −2.25595 | ||||||||
\(92\) | −5.46037e7 | −0.0794652 | ||||||||
\(93\) | 6.19503e8 | 0.858756 | ||||||||
\(94\) | 1.20660e8 | 0.159399 | ||||||||
\(95\) | −4.59140e8 | −0.578347 | ||||||||
\(96\) | −4.23006e8 | −0.508306 | ||||||||
\(97\) | −1.72684e8 | −0.198053 | −0.0990263 | − | 0.995085i | \(-0.531573\pi\) | ||||
−0.0990263 | + | 0.995085i | \(0.531573\pi\) | |||||||
\(98\) | 2.53658e8 | 0.277800 | ||||||||
\(99\) | −2.15099e8 | −0.225050 | ||||||||
\(100\) | 3.56884e6 | 0.00356884 | ||||||||
\(101\) | 1.82690e9 | 1.74690 | 0.873452 | − | 0.486911i | \(-0.161876\pi\) | ||||
0.873452 | + | 0.486911i | \(0.161876\pi\) | |||||||
\(102\) | −3.55586e8 | −0.325270 | ||||||||
\(103\) | 1.49179e9 | 1.30599 | 0.652994 | − | 0.757363i | \(-0.273513\pi\) | ||||
0.652994 | + | 0.757363i | \(0.273513\pi\) | |||||||
\(104\) | −1.31201e9 | −1.09973 | ||||||||
\(105\) | −9.62399e8 | −0.772687 | ||||||||
\(106\) | −2.16990e7 | −0.0166941 | ||||||||
\(107\) | −1.25467e9 | −0.925344 | −0.462672 | − | 0.886529i | \(-0.653109\pi\) | ||||
−0.462672 | + | 0.886529i | \(0.653109\pi\) | |||||||
\(108\) | 2.39159e8 | 0.169153 | ||||||||
\(109\) | −6.65149e7 | −0.0451335 | −0.0225668 | − | 0.999745i | \(-0.507184\pi\) | ||||
−0.0225668 | + | 0.999745i | \(0.507184\pi\) | |||||||
\(110\) | 3.59978e8 | 0.234428 | ||||||||
\(111\) | 6.33064e8 | 0.395817 | ||||||||
\(112\) | −1.45491e9 | −0.873685 | ||||||||
\(113\) | 2.19833e9 | 1.26835 | 0.634177 | − | 0.773188i | \(-0.281339\pi\) | ||||
0.634177 | + | 0.773188i | \(0.281339\pi\) | |||||||
\(114\) | −2.09930e8 | −0.116413 | ||||||||
\(115\) | −1.69228e8 | −0.0902260 | ||||||||
\(116\) | 2.69608e6 | 0.00138252 | ||||||||
\(117\) | 1.13657e9 | 0.560739 | ||||||||
\(118\) | −9.53969e7 | −0.0452965 | ||||||||
\(119\) | −4.75032e9 | −2.17151 | ||||||||
\(120\) | −8.55612e8 | −0.376670 | ||||||||
\(121\) | −1.28313e9 | −0.544171 | ||||||||
\(122\) | 1.46758e9 | 0.599765 | ||||||||
\(123\) | 1.15502e9 | 0.455005 | ||||||||
\(124\) | 3.44183e9 | 1.30735 | ||||||||
\(125\) | 2.73509e9 | 1.00202 | ||||||||
\(126\) | −4.40033e8 | −0.155531 | ||||||||
\(127\) | 2.05903e9 | 0.702337 | 0.351169 | − | 0.936312i | \(-0.385784\pi\) | ||||
0.351169 | + | 0.936312i | \(0.385784\pi\) | |||||||
\(128\) | −3.03854e9 | −1.00051 | ||||||||
\(129\) | −8.77994e8 | −0.279150 | ||||||||
\(130\) | −1.90211e9 | −0.584104 | ||||||||
\(131\) | −5.98798e9 | −1.77648 | −0.888239 | − | 0.459381i | \(-0.848071\pi\) | ||||
−0.888239 | + | 0.459381i | \(0.848071\pi\) | |||||||
\(132\) | −1.19505e9 | −0.342612 | ||||||||
\(133\) | −2.80448e9 | −0.777177 | ||||||||
\(134\) | −2.37576e8 | −0.0636547 | ||||||||
\(135\) | 7.41202e8 | 0.192059 | ||||||||
\(136\) | −4.22322e9 | −1.05857 | ||||||||
\(137\) | 2.48377e9 | 0.602377 | 0.301189 | − | 0.953565i | \(-0.402617\pi\) | ||||
0.301189 | + | 0.953565i | \(0.402617\pi\) | |||||||
\(138\) | −7.73752e7 | −0.0181613 | ||||||||
\(139\) | −3.99988e9 | −0.908825 | −0.454413 | − | 0.890791i | \(-0.650151\pi\) | ||||
−0.454413 | + | 0.890791i | \(0.650151\pi\) | |||||||
\(140\) | −5.34690e9 | −1.17632 | ||||||||
\(141\) | −1.24143e9 | −0.264506 | ||||||||
\(142\) | −7.49003e7 | −0.0154592 | ||||||||
\(143\) | −5.67931e9 | −1.13575 | ||||||||
\(144\) | 1.12051e9 | 0.217163 | ||||||||
\(145\) | 8.35569e6 | 0.00156974 | ||||||||
\(146\) | 1.65872e9 | 0.302124 | ||||||||
\(147\) | −2.60980e9 | −0.460978 | ||||||||
\(148\) | 3.51718e9 | 0.602583 | ||||||||
\(149\) | −1.05074e10 | −1.74645 | −0.873226 | − | 0.487316i | \(-0.837976\pi\) | ||||
−0.873226 | + | 0.487316i | \(0.837976\pi\) | |||||||
\(150\) | 5.05716e6 | 0.000815635 0 | ||||||||
\(151\) | 4.68248e9 | 0.732960 | 0.366480 | − | 0.930426i | \(-0.380563\pi\) | ||||
0.366480 | + | 0.930426i | \(0.380563\pi\) | |||||||
\(152\) | −2.49329e9 | −0.378859 | ||||||||
\(153\) | 3.65851e9 | 0.539750 | ||||||||
\(154\) | 2.19879e9 | 0.315021 | ||||||||
\(155\) | 1.06669e10 | 1.48439 | ||||||||
\(156\) | 6.31457e9 | 0.853657 | ||||||||
\(157\) | 1.03498e10 | 1.35951 | 0.679756 | − | 0.733439i | \(-0.262086\pi\) | ||||
0.679756 | + | 0.733439i | \(0.262086\pi\) | |||||||
\(158\) | 2.89666e8 | 0.0369778 | ||||||||
\(159\) | 2.23254e8 | 0.0277020 | ||||||||
\(160\) | −7.28354e9 | −0.878623 | ||||||||
\(161\) | −1.03366e9 | −0.121245 | ||||||||
\(162\) | 3.38896e8 | 0.0386588 | ||||||||
\(163\) | −1.12940e10 | −1.25315 | −0.626577 | − | 0.779359i | \(-0.715545\pi\) | ||||
−0.626577 | + | 0.779359i | \(0.715545\pi\) | |||||||
\(164\) | 6.41706e9 | 0.692690 | ||||||||
\(165\) | −3.70369e9 | −0.389007 | ||||||||
\(166\) | 7.06670e8 | 0.0722321 | ||||||||
\(167\) | −4.72352e9 | −0.469940 | −0.234970 | − | 0.972003i | \(-0.575499\pi\) | ||||
−0.234970 | + | 0.972003i | \(0.575499\pi\) | |||||||
\(168\) | −5.22617e9 | −0.506165 | ||||||||
\(169\) | 1.94047e10 | 1.82986 | ||||||||
\(170\) | −6.12268e9 | −0.562240 | ||||||||
\(171\) | 2.15990e9 | 0.193175 | ||||||||
\(172\) | −4.87796e9 | −0.424972 | ||||||||
\(173\) | 7.29035e9 | 0.618787 | 0.309393 | − | 0.950934i | \(-0.399874\pi\) | ||||
0.309393 | + | 0.950934i | \(0.399874\pi\) | |||||||
\(174\) | 3.82043e6 | 0.000315966 0 | ||||||||
\(175\) | 6.75591e7 | 0.00544519 | ||||||||
\(176\) | −5.59907e9 | −0.439854 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −6.95213e8 | −0.0519072 | ||||||||
\(179\) | 1.12010e10 | 0.815491 | 0.407745 | − | 0.913096i | \(-0.366315\pi\) | ||||
0.407745 | + | 0.913096i | \(0.366315\pi\) | |||||||
\(180\) | 4.11797e9 | 0.292386 | ||||||||
\(181\) | −2.04979e10 | −1.41957 | −0.709783 | − | 0.704421i | \(-0.751207\pi\) | ||||
−0.709783 | + | 0.704421i | \(0.751207\pi\) | |||||||
\(182\) | −1.16183e10 | −0.784912 | ||||||||
\(183\) | −1.50994e10 | −0.995244 | ||||||||
\(184\) | −9.18969e8 | −0.0591045 | ||||||||
\(185\) | 1.09004e10 | 0.684182 | ||||||||
\(186\) | 4.87719e9 | 0.298787 | ||||||||
\(187\) | −1.82811e10 | −1.09324 | ||||||||
\(188\) | −6.89712e9 | −0.402677 | ||||||||
\(189\) | 4.52735e9 | 0.258087 | ||||||||
\(190\) | −3.61469e9 | −0.201224 | ||||||||
\(191\) | −3.24595e10 | −1.76479 | −0.882393 | − | 0.470514i | \(-0.844069\pi\) | ||||
−0.882393 | + | 0.470514i | \(0.844069\pi\) | |||||||
\(192\) | 3.75254e9 | 0.199283 | ||||||||
\(193\) | −2.97274e10 | −1.54223 | −0.771114 | − | 0.636697i | \(-0.780300\pi\) | ||||
−0.771114 | + | 0.636697i | \(0.780300\pi\) | |||||||
\(194\) | −1.35950e9 | −0.0689083 | ||||||||
\(195\) | 1.95701e10 | 0.969255 | ||||||||
\(196\) | −1.44995e10 | −0.701782 | ||||||||
\(197\) | −3.17107e10 | −1.50006 | −0.750029 | − | 0.661405i | \(-0.769960\pi\) | ||||
−0.750029 | + | 0.661405i | \(0.769960\pi\) | |||||||
\(198\) | −1.69342e9 | −0.0783016 | ||||||||
\(199\) | −2.20685e9 | −0.0997548 | −0.0498774 | − | 0.998755i | \(-0.515883\pi\) | ||||
−0.0498774 | + | 0.998755i | \(0.515883\pi\) | |||||||
\(200\) | 6.00628e7 | 0.00265442 | ||||||||
\(201\) | 2.44434e9 | 0.105628 | ||||||||
\(202\) | 1.43827e10 | 0.607799 | ||||||||
\(203\) | 5.10375e7 | 0.00210939 | ||||||||
\(204\) | 2.03259e10 | 0.821703 | ||||||||
\(205\) | 1.98878e10 | 0.786491 | ||||||||
\(206\) | 1.17445e10 | 0.454392 | ||||||||
\(207\) | 7.96087e8 | 0.0301366 | ||||||||
\(208\) | 2.95852e10 | 1.09595 | ||||||||
\(209\) | −1.07927e10 | −0.391267 | ||||||||
\(210\) | −7.57672e9 | −0.268840 | ||||||||
\(211\) | −4.43141e10 | −1.53911 | −0.769556 | − | 0.638579i | \(-0.779523\pi\) | ||||
−0.769556 | + | 0.638579i | \(0.779523\pi\) | |||||||
\(212\) | 1.24035e9 | 0.0421730 | ||||||||
\(213\) | 7.70624e8 | 0.0256528 | ||||||||
\(214\) | −9.87771e9 | −0.321954 | ||||||||
\(215\) | −1.51178e10 | −0.482520 | ||||||||
\(216\) | 4.02499e9 | 0.125812 | ||||||||
\(217\) | 6.51549e10 | 1.99470 | ||||||||
\(218\) | −5.23654e8 | −0.0157033 | ||||||||
\(219\) | −1.70660e10 | −0.501341 | ||||||||
\(220\) | −2.05770e10 | −0.592215 | ||||||||
\(221\) | 9.65965e10 | 2.72393 | ||||||||
\(222\) | 4.98395e9 | 0.137716 | ||||||||
\(223\) | 3.13863e10 | 0.849900 | 0.424950 | − | 0.905217i | \(-0.360292\pi\) | ||||
0.424950 | + | 0.905217i | \(0.360292\pi\) | |||||||
\(224\) | −4.44887e10 | −1.18068 | ||||||||
\(225\) | −5.20314e7 | −0.00135346 | ||||||||
\(226\) | 1.73069e10 | 0.441298 | ||||||||
\(227\) | −1.35755e10 | −0.339342 | −0.169671 | − | 0.985501i | \(-0.554271\pi\) | ||||
−0.169671 | + | 0.985501i | \(0.554271\pi\) | |||||||
\(228\) | 1.20000e10 | 0.294085 | ||||||||
\(229\) | −3.87818e10 | −0.931898 | −0.465949 | − | 0.884812i | \(-0.654287\pi\) | ||||
−0.465949 | + | 0.884812i | \(0.654287\pi\) | |||||||
\(230\) | −1.33229e9 | −0.0313923 | ||||||||
\(231\) | −2.26226e10 | −0.522743 | ||||||||
\(232\) | 4.53744e7 | 0.00102829 | ||||||||
\(233\) | 4.13830e10 | 0.919856 | 0.459928 | − | 0.887956i | \(-0.347875\pi\) | ||||
0.459928 | + | 0.887956i | \(0.347875\pi\) | |||||||
\(234\) | 8.94795e9 | 0.195098 | ||||||||
\(235\) | −2.13755e10 | −0.457206 | ||||||||
\(236\) | 5.45305e9 | 0.114429 | ||||||||
\(237\) | −2.98028e9 | −0.0613606 | ||||||||
\(238\) | −3.73980e10 | −0.755531 | ||||||||
\(239\) | 1.41322e10 | 0.280168 | 0.140084 | − | 0.990140i | \(-0.455263\pi\) | ||||
0.140084 | + | 0.990140i | \(0.455263\pi\) | |||||||
\(240\) | 1.92936e10 | 0.375373 | ||||||||
\(241\) | 6.77959e9 | 0.129457 | 0.0647287 | − | 0.997903i | \(-0.479382\pi\) | ||||
0.0647287 | + | 0.997903i | \(0.479382\pi\) | |||||||
\(242\) | −1.01017e10 | −0.189333 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | −8.38892e10 | −1.51514 | ||||||||
\(245\) | −4.49370e10 | −0.796814 | ||||||||
\(246\) | 9.09318e9 | 0.158310 | ||||||||
\(247\) | 5.70283e10 | 0.974887 | ||||||||
\(248\) | 5.79253e10 | 0.972380 | ||||||||
\(249\) | −7.27069e9 | −0.119861 | ||||||||
\(250\) | 2.15327e10 | 0.348632 | ||||||||
\(251\) | 5.23978e10 | 0.833262 | 0.416631 | − | 0.909076i | \(-0.363211\pi\) | ||||
0.416631 | + | 0.909076i | \(0.363211\pi\) | |||||||
\(252\) | 2.51530e10 | 0.392905 | ||||||||
\(253\) | −3.97795e9 | −0.0610403 | ||||||||
\(254\) | 1.62102e10 | 0.244364 | ||||||||
\(255\) | 6.29942e10 | 0.932974 | ||||||||
\(256\) | −2.01862e8 | −0.00293748 | ||||||||
\(257\) | 1.29728e11 | 1.85497 | 0.927483 | − | 0.373866i | \(-0.121968\pi\) | ||||
0.927483 | + | 0.373866i | \(0.121968\pi\) | |||||||
\(258\) | −6.91223e9 | −0.0971246 | ||||||||
\(259\) | 6.65812e10 | 0.919396 | ||||||||
\(260\) | 1.08728e11 | 1.47557 | ||||||||
\(261\) | −3.93071e7 | −0.000524311 0 | ||||||||
\(262\) | −4.71419e10 | −0.618089 | ||||||||
\(263\) | −3.39579e10 | −0.437663 | −0.218831 | − | 0.975763i | \(-0.570224\pi\) | ||||
−0.218831 | + | 0.975763i | \(0.570224\pi\) | |||||||
\(264\) | −2.01124e10 | −0.254827 | ||||||||
\(265\) | 3.84410e9 | 0.0478838 | ||||||||
\(266\) | −2.20789e10 | −0.270403 | ||||||||
\(267\) | 7.15281e9 | 0.0861342 | ||||||||
\(268\) | 1.35803e10 | 0.160806 | ||||||||
\(269\) | 2.99218e10 | 0.348419 | 0.174210 | − | 0.984709i | \(-0.444263\pi\) | ||||
0.174210 | + | 0.984709i | \(0.444263\pi\) | |||||||
\(270\) | 5.83529e9 | 0.0668230 | ||||||||
\(271\) | −1.27158e11 | −1.43212 | −0.716061 | − | 0.698037i | \(-0.754057\pi\) | ||||
−0.716061 | + | 0.698037i | \(0.754057\pi\) | |||||||
\(272\) | 9.52317e10 | 1.05492 | ||||||||
\(273\) | 1.19537e11 | 1.30247 | ||||||||
\(274\) | 1.95541e10 | 0.209585 | ||||||||
\(275\) | 2.59994e8 | 0.00274136 | ||||||||
\(276\) | 4.42290e9 | 0.0458793 | ||||||||
\(277\) | −6.25830e10 | −0.638700 | −0.319350 | − | 0.947637i | \(-0.603465\pi\) | ||||
−0.319350 | + | 0.947637i | \(0.603465\pi\) | |||||||
\(278\) | −3.14900e10 | −0.316207 | ||||||||
\(279\) | −5.01797e10 | −0.495803 | ||||||||
\(280\) | −8.99871e10 | −0.874922 | ||||||||
\(281\) | −5.33771e10 | −0.510712 | −0.255356 | − | 0.966847i | \(-0.582193\pi\) | ||||
−0.255356 | + | 0.966847i | \(0.582193\pi\) | |||||||
\(282\) | −9.77343e9 | −0.0920293 | ||||||||
\(283\) | 1.22464e11 | 1.13493 | 0.567465 | − | 0.823397i | \(-0.307924\pi\) | ||||
0.567465 | + | 0.823397i | \(0.307924\pi\) | |||||||
\(284\) | 4.28144e9 | 0.0390532 | ||||||||
\(285\) | 3.71903e10 | 0.333909 | ||||||||
\(286\) | −4.47117e10 | −0.395161 | ||||||||
\(287\) | 1.21477e11 | 1.05688 | ||||||||
\(288\) | 3.42635e10 | 0.293471 | ||||||||
\(289\) | 1.92346e11 | 1.62197 | ||||||||
\(290\) | 6.57822e7 | 0.000546157 0 | ||||||||
\(291\) | 1.39874e10 | 0.114346 | ||||||||
\(292\) | −9.48153e10 | −0.763231 | ||||||||
\(293\) | 1.36171e11 | 1.07939 | 0.539697 | − | 0.841859i | \(-0.318539\pi\) | ||||
0.539697 | + | 0.841859i | \(0.318539\pi\) | |||||||
\(294\) | −2.05463e10 | −0.160388 | ||||||||
\(295\) | 1.69001e10 | 0.129924 | ||||||||
\(296\) | 5.91934e10 | 0.448188 | ||||||||
\(297\) | 1.74230e10 | 0.129933 | ||||||||
\(298\) | −8.27220e10 | −0.607642 | ||||||||
\(299\) | 2.10193e10 | 0.152089 | ||||||||
\(300\) | −2.89076e8 | −0.00206047 | ||||||||
\(301\) | −9.23412e10 | −0.648405 | ||||||||
\(302\) | 3.68640e10 | 0.255018 | ||||||||
\(303\) | −1.47979e11 | −1.00858 | ||||||||
\(304\) | 5.62226e10 | 0.377555 | ||||||||
\(305\) | −2.59990e11 | −1.72031 | ||||||||
\(306\) | 2.88025e10 | 0.187795 | ||||||||
\(307\) | 1.35328e11 | 0.869494 | 0.434747 | − | 0.900553i | \(-0.356838\pi\) | ||||
0.434747 | + | 0.900553i | \(0.356838\pi\) | |||||||
\(308\) | −1.25686e11 | −0.795812 | ||||||||
\(309\) | −1.20835e11 | −0.754012 | ||||||||
\(310\) | 8.39781e10 | 0.516462 | ||||||||
\(311\) | 1.26392e11 | 0.766122 | 0.383061 | − | 0.923723i | \(-0.374870\pi\) | ||||
0.383061 | + | 0.923723i | \(0.374870\pi\) | |||||||
\(312\) | 1.06273e11 | 0.634931 | ||||||||
\(313\) | 3.20969e11 | 1.89022 | 0.945111 | − | 0.326748i | \(-0.105953\pi\) | ||||
0.945111 | + | 0.326748i | \(0.105953\pi\) | |||||||
\(314\) | 8.14812e10 | 0.473014 | ||||||||
\(315\) | 7.79543e10 | 0.446111 | ||||||||
\(316\) | −1.65578e10 | −0.0934139 | ||||||||
\(317\) | −2.55439e11 | −1.42076 | −0.710381 | − | 0.703818i | \(-0.751477\pi\) | ||||
−0.710381 | + | 0.703818i | \(0.751477\pi\) | |||||||
\(318\) | 1.75762e9 | 0.00963835 | ||||||||
\(319\) | 1.96412e8 | 0.00106197 | ||||||||
\(320\) | 6.46133e10 | 0.344467 | ||||||||
\(321\) | 1.01628e11 | 0.534248 | ||||||||
\(322\) | −8.13777e9 | −0.0421846 | ||||||||
\(323\) | 1.83568e11 | 0.938396 | ||||||||
\(324\) | −1.93719e10 | −0.0976606 | ||||||||
\(325\) | −1.37380e9 | −0.00683042 | ||||||||
\(326\) | −8.89150e10 | −0.436009 | ||||||||
\(327\) | 5.38770e9 | 0.0260579 | ||||||||
\(328\) | 1.07998e11 | 0.515208 | ||||||||
\(329\) | −1.30564e11 | −0.614388 | ||||||||
\(330\) | −2.91582e10 | −0.135347 | ||||||||
\(331\) | −1.73240e11 | −0.793272 | −0.396636 | − | 0.917976i | \(-0.629822\pi\) | ||||
−0.396636 | + | 0.917976i | \(0.629822\pi\) | |||||||
\(332\) | −4.03945e10 | −0.182474 | ||||||||
\(333\) | −5.12782e10 | −0.228525 | ||||||||
\(334\) | −3.71871e10 | −0.163506 | ||||||||
\(335\) | 4.20879e10 | 0.182581 | ||||||||
\(336\) | 1.17848e11 | 0.504423 | ||||||||
\(337\) | −2.70295e11 | −1.14157 | −0.570785 | − | 0.821099i | \(-0.693361\pi\) | ||||
−0.570785 | + | 0.821099i | \(0.693361\pi\) | |||||||
\(338\) | 1.52768e11 | 0.636661 | ||||||||
\(339\) | −1.78065e11 | −0.732284 | ||||||||
\(340\) | 3.49983e11 | 1.42034 | ||||||||
\(341\) | 2.50742e11 | 1.00423 | ||||||||
\(342\) | 1.70043e10 | 0.0672113 | ||||||||
\(343\) | 6.92920e10 | 0.270308 | ||||||||
\(344\) | −8.20950e10 | −0.316085 | ||||||||
\(345\) | 1.37075e10 | 0.0520920 | ||||||||
\(346\) | 5.73951e10 | 0.215294 | ||||||||
\(347\) | 1.51065e9 | 0.00559345 | 0.00279673 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279673 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(348\) | −2.18382e8 | −0.000798199 0 | ||||||||
\(349\) | −2.59300e11 | −0.935595 | −0.467798 | − | 0.883836i | \(-0.654952\pi\) | ||||
−0.467798 | + | 0.883836i | \(0.654952\pi\) | |||||||
\(350\) | 5.31876e8 | 0.00189454 | ||||||||
\(351\) | −9.20624e10 | −0.323743 | ||||||||
\(352\) | −1.71210e11 | −0.594412 | ||||||||
\(353\) | −7.36010e10 | −0.252289 | −0.126144 | − | 0.992012i | \(-0.540260\pi\) | ||||
−0.126144 | + | 0.992012i | \(0.540260\pi\) | |||||||
\(354\) | 7.72715e9 | 0.0261520 | ||||||||
\(355\) | 1.32690e10 | 0.0443416 | ||||||||
\(356\) | 3.97396e10 | 0.131129 | ||||||||
\(357\) | 3.84776e11 | 1.25372 | ||||||||
\(358\) | 8.81828e10 | 0.283733 | ||||||||
\(359\) | −3.72647e11 | −1.18406 | −0.592028 | − | 0.805917i | \(-0.701673\pi\) | ||||
−0.592028 | + | 0.805917i | \(0.701673\pi\) | |||||||
\(360\) | 6.93045e10 | 0.217471 | ||||||||
\(361\) | −2.14313e11 | −0.664151 | ||||||||
\(362\) | −1.61375e11 | −0.493909 | ||||||||
\(363\) | 1.03933e11 | 0.314177 | ||||||||
\(364\) | 6.64122e11 | 1.98286 | ||||||||
\(365\) | −2.93852e11 | −0.866584 | ||||||||
\(366\) | −1.18874e11 | −0.346275 | ||||||||
\(367\) | −3.22104e11 | −0.926827 | −0.463414 | − | 0.886142i | \(-0.653376\pi\) | ||||
−0.463414 | + | 0.886142i | \(0.653376\pi\) | |||||||
\(368\) | 2.07223e10 | 0.0589010 | ||||||||
\(369\) | −9.35566e10 | −0.262697 | ||||||||
\(370\) | 8.58164e10 | 0.238047 | ||||||||
\(371\) | 2.34802e10 | 0.0643457 | ||||||||
\(372\) | −2.78789e11 | −0.754800 | ||||||||
\(373\) | −3.92320e11 | −1.04942 | −0.524711 | − | 0.851280i | \(-0.675827\pi\) | ||||
−0.524711 | + | 0.851280i | \(0.675827\pi\) | |||||||
\(374\) | −1.43922e11 | −0.380370 | ||||||||
\(375\) | −2.21542e11 | −0.578516 | ||||||||
\(376\) | −1.16077e11 | −0.299503 | ||||||||
\(377\) | −1.03783e9 | −0.00264601 | ||||||||
\(378\) | 3.56426e10 | 0.0897960 | ||||||||
\(379\) | −4.57826e11 | −1.13979 | −0.569894 | − | 0.821718i | \(-0.693016\pi\) | ||||
−0.569894 | + | 0.821718i | \(0.693016\pi\) | |||||||
\(380\) | 2.06622e11 | 0.508336 | ||||||||
\(381\) | −1.66781e11 | −0.405495 | ||||||||
\(382\) | −2.55545e11 | −0.614021 | ||||||||
\(383\) | 1.14027e11 | 0.270777 | 0.135389 | − | 0.990793i | \(-0.456772\pi\) | ||||
0.135389 | + | 0.990793i | \(0.456772\pi\) | |||||||
\(384\) | 2.46122e11 | 0.577643 | ||||||||
\(385\) | −3.89528e11 | −0.903577 | ||||||||
\(386\) | −2.34036e11 | −0.536586 | ||||||||
\(387\) | 7.11176e10 | 0.161167 | ||||||||
\(388\) | 7.77115e10 | 0.174077 | ||||||||
\(389\) | 2.66221e11 | 0.589480 | 0.294740 | − | 0.955577i | \(-0.404767\pi\) | ||||
0.294740 | + | 0.955577i | \(0.404767\pi\) | |||||||
\(390\) | 1.54071e11 | 0.337232 | ||||||||
\(391\) | 6.76588e10 | 0.146396 | ||||||||
\(392\) | −2.44024e11 | −0.521970 | ||||||||
\(393\) | 4.85027e11 | 1.02565 | ||||||||
\(394\) | −2.49650e11 | −0.521914 | ||||||||
\(395\) | −5.13161e10 | −0.106064 | ||||||||
\(396\) | 9.67988e10 | 0.197807 | ||||||||
\(397\) | −7.04699e11 | −1.42379 | −0.711896 | − | 0.702285i | \(-0.752163\pi\) | ||||
−0.711896 | + | 0.702285i | \(0.752163\pi\) | |||||||
\(398\) | −1.73740e10 | −0.0347076 | ||||||||
\(399\) | 2.27163e11 | 0.448703 | ||||||||
\(400\) | −1.35439e9 | −0.00264529 | ||||||||
\(401\) | 3.31737e11 | 0.640685 | 0.320343 | − | 0.947302i | \(-0.396202\pi\) | ||||
0.320343 | + | 0.947302i | \(0.396202\pi\) | |||||||
\(402\) | 1.92436e10 | 0.0367511 | ||||||||
\(403\) | −1.32491e12 | −2.50215 | ||||||||
\(404\) | −8.22142e11 | −1.53543 | ||||||||
\(405\) | −6.00374e10 | −0.110885 | ||||||||
\(406\) | 4.01805e8 | 0.000733920 0 | ||||||||
\(407\) | 2.56231e11 | 0.462867 | ||||||||
\(408\) | 3.42081e11 | 0.611165 | ||||||||
\(409\) | 4.79405e11 | 0.847125 | 0.423563 | − | 0.905867i | \(-0.360779\pi\) | ||||
0.423563 | + | 0.905867i | \(0.360779\pi\) | |||||||
\(410\) | 1.56571e11 | 0.273643 | ||||||||
\(411\) | −2.01185e11 | −0.347783 | ||||||||
\(412\) | −6.71334e11 | −1.14789 | ||||||||
\(413\) | 1.03228e11 | 0.174591 | ||||||||
\(414\) | 6.26739e9 | 0.0104854 | ||||||||
\(415\) | −1.25191e11 | −0.207184 | ||||||||
\(416\) | 9.04666e11 | 1.48105 | ||||||||
\(417\) | 3.23990e11 | 0.524710 | ||||||||
\(418\) | −8.49685e10 | −0.136133 | ||||||||
\(419\) | 8.85242e11 | 1.40313 | 0.701566 | − | 0.712604i | \(-0.252484\pi\) | ||||
0.701566 | + | 0.712604i | \(0.252484\pi\) | |||||||
\(420\) | 4.33099e11 | 0.679149 | ||||||||
\(421\) | −1.09924e12 | −1.70539 | −0.852697 | − | 0.522405i | \(-0.825035\pi\) | ||||
−0.852697 | + | 0.522405i | \(0.825035\pi\) | |||||||
\(422\) | −3.48873e11 | −0.535503 | ||||||||
\(423\) | 1.00555e11 | 0.152712 | ||||||||
\(424\) | 2.08749e10 | 0.0313673 | ||||||||
\(425\) | −4.42211e9 | −0.00657475 | ||||||||
\(426\) | 6.06693e9 | 0.00892536 | ||||||||
\(427\) | −1.58805e12 | −2.31173 | ||||||||
\(428\) | 5.64628e11 | 0.813327 | ||||||||
\(429\) | 4.60024e11 | 0.655726 | ||||||||
\(430\) | −1.19018e11 | −0.167883 | ||||||||
\(431\) | 5.15254e10 | 0.0719240 | 0.0359620 | − | 0.999353i | \(-0.488550\pi\) | ||||
0.0359620 | + | 0.999353i | \(0.488550\pi\) | |||||||
\(432\) | −9.07617e10 | −0.125379 | ||||||||
\(433\) | −7.35694e11 | −1.00578 | −0.502888 | − | 0.864351i | \(-0.667729\pi\) | ||||
−0.502888 | + | 0.864351i | \(0.667729\pi\) | |||||||
\(434\) | 5.12948e11 | 0.694016 | ||||||||
\(435\) | −6.76811e8 | −0.000906287 0 | ||||||||
\(436\) | 2.99330e10 | 0.0396699 | ||||||||
\(437\) | 3.99442e10 | 0.0523947 | ||||||||
\(438\) | −1.34356e11 | −0.174431 | ||||||||
\(439\) | −4.53463e11 | −0.582708 | −0.291354 | − | 0.956615i | \(-0.594106\pi\) | ||||
−0.291354 | + | 0.956615i | \(0.594106\pi\) | |||||||
\(440\) | −3.46306e11 | −0.440477 | ||||||||
\(441\) | 2.11394e11 | 0.266146 | ||||||||
\(442\) | 7.60479e11 | 0.947735 | ||||||||
\(443\) | 3.20088e11 | 0.394869 | 0.197434 | − | 0.980316i | \(-0.436739\pi\) | ||||
0.197434 | + | 0.980316i | \(0.436739\pi\) | |||||||
\(444\) | −2.84892e11 | −0.347901 | ||||||||
\(445\) | 1.23161e11 | 0.148886 | ||||||||
\(446\) | 2.47096e11 | 0.295705 | ||||||||
\(447\) | 8.51098e11 | 1.00831 | ||||||||
\(448\) | 3.94666e11 | 0.462891 | ||||||||
\(449\) | −1.45474e12 | −1.68918 | −0.844590 | − | 0.535413i | \(-0.820156\pi\) | ||||
−0.844590 | + | 0.535413i | \(0.820156\pi\) | |||||||
\(450\) | −4.09630e8 | −0.000470907 0 | ||||||||
\(451\) | 4.67490e11 | 0.532081 | ||||||||
\(452\) | −9.89293e11 | −1.11481 | ||||||||
\(453\) | −3.79281e11 | −0.423174 | ||||||||
\(454\) | −1.06876e11 | −0.118067 | ||||||||
\(455\) | 2.05825e12 | 2.25137 | ||||||||
\(456\) | 2.01957e11 | 0.218734 | ||||||||
\(457\) | −6.52938e11 | −0.700243 | −0.350122 | − | 0.936704i | \(-0.613860\pi\) | ||||
−0.350122 | + | 0.936704i | \(0.613860\pi\) | |||||||
\(458\) | −3.05319e11 | −0.324235 | ||||||||
\(459\) | −2.96339e11 | −0.311625 | ||||||||
\(460\) | 7.61560e10 | 0.0793037 | ||||||||
\(461\) | 1.56956e12 | 1.61854 | 0.809272 | − | 0.587435i | \(-0.199862\pi\) | ||||
0.809272 | + | 0.587435i | \(0.199862\pi\) | |||||||
\(462\) | −1.78102e11 | −0.181878 | ||||||||
\(463\) | −1.86374e12 | −1.88482 | −0.942412 | − | 0.334454i | \(-0.891448\pi\) | ||||
−0.942412 | + | 0.334454i | \(0.891448\pi\) | |||||||
\(464\) | −1.02317e9 | −0.00102475 | ||||||||
\(465\) | −8.64022e11 | −0.857011 | ||||||||
\(466\) | 3.25798e11 | 0.320045 | ||||||||
\(467\) | −3.21350e11 | −0.312646 | −0.156323 | − | 0.987706i | \(-0.549964\pi\) | ||||
−0.156323 | + | 0.987706i | \(0.549964\pi\) | |||||||
\(468\) | −5.11480e11 | −0.492859 | ||||||||
\(469\) | 2.57078e11 | 0.245351 | ||||||||
\(470\) | −1.68284e11 | −0.159075 | ||||||||
\(471\) | −8.38333e11 | −0.784914 | ||||||||
\(472\) | 9.17737e10 | 0.0851097 | ||||||||
\(473\) | −3.55365e11 | −0.326437 | ||||||||
\(474\) | −2.34630e10 | −0.0213491 | ||||||||
\(475\) | −2.61071e9 | −0.00235308 | ||||||||
\(476\) | 2.13774e12 | 1.90864 | ||||||||
\(477\) | −1.80836e10 | −0.0159938 | ||||||||
\(478\) | 1.11259e11 | 0.0974788 | ||||||||
\(479\) | 1.47615e12 | 1.28121 | 0.640604 | − | 0.767871i | \(-0.278684\pi\) | ||||
0.640604 | + | 0.767871i | \(0.278684\pi\) | |||||||
\(480\) | 5.89967e11 | 0.507273 | ||||||||
\(481\) | −1.35391e12 | −1.15329 | ||||||||
\(482\) | 5.33740e10 | 0.0450420 | ||||||||
\(483\) | 8.37268e10 | 0.0700007 | ||||||||
\(484\) | 5.77432e11 | 0.478296 | ||||||||
\(485\) | 2.40843e11 | 0.197650 | ||||||||
\(486\) | −2.74506e10 | −0.0223197 | ||||||||
\(487\) | 4.49035e11 | 0.361742 | 0.180871 | − | 0.983507i | \(-0.442108\pi\) | ||||
0.180871 | + | 0.983507i | \(0.442108\pi\) | |||||||
\(488\) | −1.41184e12 | −1.12693 | ||||||||
\(489\) | 9.14816e11 | 0.723509 | ||||||||
\(490\) | −3.53778e11 | −0.277235 | ||||||||
\(491\) | 1.06546e12 | 0.827314 | 0.413657 | − | 0.910433i | \(-0.364251\pi\) | ||||
0.413657 | + | 0.910433i | \(0.364251\pi\) | |||||||
\(492\) | −5.19782e11 | −0.399925 | ||||||||
\(493\) | −3.34068e9 | −0.00254697 | ||||||||
\(494\) | 4.48970e11 | 0.339192 | ||||||||
\(495\) | 2.99999e11 | 0.224593 | ||||||||
\(496\) | −1.30619e12 | −0.969032 | ||||||||
\(497\) | 8.10488e10 | 0.0595858 | ||||||||
\(498\) | −5.72403e10 | −0.0417032 | ||||||||
\(499\) | 2.45188e11 | 0.177030 | 0.0885152 | − | 0.996075i | \(-0.471788\pi\) | ||||
0.0885152 | + | 0.996075i | \(0.471788\pi\) | |||||||
\(500\) | −1.23084e12 | −0.880720 | ||||||||
\(501\) | 3.82605e11 | 0.271320 | ||||||||
\(502\) | 4.12514e11 | 0.289916 | ||||||||
\(503\) | 9.03179e11 | 0.629097 | 0.314549 | − | 0.949241i | \(-0.398147\pi\) | ||||
0.314549 | + | 0.949241i | \(0.398147\pi\) | |||||||
\(504\) | 4.23320e11 | 0.292235 | ||||||||
\(505\) | −2.54798e12 | −1.74335 | ||||||||
\(506\) | −3.13173e10 | −0.0212377 | ||||||||
\(507\) | −1.57178e12 | −1.05647 | ||||||||
\(508\) | −9.26604e11 | −0.617316 | ||||||||
\(509\) | 1.50017e12 | 0.990625 | 0.495312 | − | 0.868715i | \(-0.335054\pi\) | ||||
0.495312 | + | 0.868715i | \(0.335054\pi\) | |||||||
\(510\) | 4.95937e11 | 0.324609 | ||||||||
\(511\) | −1.79488e12 | −1.16451 | ||||||||
\(512\) | 1.55414e12 | 0.999485 | ||||||||
\(513\) | −1.74952e11 | −0.111530 | ||||||||
\(514\) | 1.02132e12 | 0.645397 | ||||||||
\(515\) | −2.08060e12 | −1.30333 | ||||||||
\(516\) | 3.95115e11 | 0.245358 | ||||||||
\(517\) | −5.02463e11 | −0.309312 | ||||||||
\(518\) | 5.24177e11 | 0.319885 | ||||||||
\(519\) | −5.90518e11 | −0.357257 | ||||||||
\(520\) | 1.82986e12 | 1.09750 | ||||||||
\(521\) | −2.75051e12 | −1.63547 | −0.817737 | − | 0.575592i | \(-0.804772\pi\) | ||||
−0.817737 | + | 0.575592i | \(0.804772\pi\) | |||||||
\(522\) | −3.09455e8 | −0.000182423 0 | ||||||||
\(523\) | −5.31073e11 | −0.310382 | −0.155191 | − | 0.987884i | \(-0.549599\pi\) | ||||
−0.155191 | + | 0.987884i | \(0.549599\pi\) | |||||||
\(524\) | 2.69471e12 | 1.56143 | ||||||||
\(525\) | −5.47229e9 | −0.00314378 | ||||||||
\(526\) | −2.67341e11 | −0.152276 | ||||||||
\(527\) | −4.26474e12 | −2.40849 | ||||||||
\(528\) | 4.53524e11 | 0.253950 | ||||||||
\(529\) | −1.78643e12 | −0.991826 | ||||||||
\(530\) | 3.02636e10 | 0.0166602 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | 1.26207e12 | 0.683096 | ||||||||
\(533\) | −2.47020e12 | −1.32574 | ||||||||
\(534\) | 5.63122e10 | 0.0299686 | ||||||||
\(535\) | 1.74989e12 | 0.923464 | ||||||||
\(536\) | 2.28553e11 | 0.119604 | ||||||||
\(537\) | −9.07283e11 | −0.470824 | ||||||||
\(538\) | 2.35567e11 | 0.121225 | ||||||||
\(539\) | −1.05631e12 | −0.539065 | ||||||||
\(540\) | −3.33556e11 | −0.168809 | ||||||||
\(541\) | 2.81202e12 | 1.41134 | 0.705668 | − | 0.708543i | \(-0.250647\pi\) | ||||
0.705668 | + | 0.708543i | \(0.250647\pi\) | |||||||
\(542\) | −1.00108e12 | −0.498278 | ||||||||
\(543\) | 1.66033e12 | 0.819587 | ||||||||
\(544\) | 2.91202e12 | 1.42561 | ||||||||
\(545\) | 9.27684e10 | 0.0450418 | ||||||||
\(546\) | 9.41081e11 | 0.453169 | ||||||||
\(547\) | 2.80003e12 | 1.33727 | 0.668637 | − | 0.743589i | \(-0.266878\pi\) | ||||
0.668637 | + | 0.743589i | \(0.266878\pi\) | |||||||
\(548\) | −1.11775e12 | −0.529456 | ||||||||
\(549\) | 1.22305e12 | 0.574604 | ||||||||
\(550\) | 2.04687e9 | 0.000953800 0 | ||||||||
\(551\) | −1.97226e9 | −0.000911554 0 | ||||||||
\(552\) | 7.44365e10 | 0.0341240 | ||||||||
\(553\) | −3.13444e11 | −0.142527 | ||||||||
\(554\) | −4.92700e11 | −0.222223 | ||||||||
\(555\) | −8.82936e11 | −0.395013 | ||||||||
\(556\) | 1.80003e12 | 0.798807 | ||||||||
\(557\) | 1.98817e12 | 0.875195 | 0.437597 | − | 0.899171i | \(-0.355830\pi\) | ||||
0.437597 | + | 0.899171i | \(0.355830\pi\) | |||||||
\(558\) | −3.95052e11 | −0.172505 | ||||||||
\(559\) | 1.87773e12 | 0.813356 | ||||||||
\(560\) | 2.02917e12 | 0.871910 | ||||||||
\(561\) | 1.48077e12 | 0.631181 | ||||||||
\(562\) | −4.20224e11 | −0.177692 | ||||||||
\(563\) | −2.61155e12 | −1.09549 | −0.547747 | − | 0.836644i | \(-0.684514\pi\) | ||||
−0.547747 | + | 0.836644i | \(0.684514\pi\) | |||||||
\(564\) | 5.58666e11 | 0.232486 | ||||||||
\(565\) | −3.06602e12 | −1.26578 | ||||||||
\(566\) | 9.64127e11 | 0.394876 | ||||||||
\(567\) | −3.66715e11 | −0.149006 | ||||||||
\(568\) | 7.20556e10 | 0.0290469 | ||||||||
\(569\) | 6.12579e11 | 0.244995 | 0.122497 | − | 0.992469i | \(-0.460910\pi\) | ||||
0.122497 | + | 0.992469i | \(0.460910\pi\) | |||||||
\(570\) | 2.92790e11 | 0.116177 | ||||||||
\(571\) | 1.92887e12 | 0.759347 | 0.379673 | − | 0.925121i | \(-0.376036\pi\) | ||||
0.379673 | + | 0.925121i | \(0.376036\pi\) | |||||||
\(572\) | 2.55580e12 | 0.998263 | ||||||||
\(573\) | 2.62922e12 | 1.01890 | ||||||||
\(574\) | 9.56355e11 | 0.367719 | ||||||||
\(575\) | −9.62246e8 | −0.000367097 0 | ||||||||
\(576\) | −3.03956e11 | −0.115056 | ||||||||
\(577\) | 1.13524e12 | 0.426381 | 0.213190 | − | 0.977011i | \(-0.431615\pi\) | ||||
0.213190 | + | 0.977011i | \(0.431615\pi\) | |||||||
\(578\) | 1.51429e12 | 0.564331 | ||||||||
\(579\) | 2.40792e12 | 0.890405 | ||||||||
\(580\) | −3.76023e9 | −0.00137971 | ||||||||
\(581\) | −7.64679e11 | −0.278411 | ||||||||
\(582\) | 1.10120e11 | 0.0397842 | ||||||||
\(583\) | 9.03612e10 | 0.0323947 | ||||||||
\(584\) | −1.59572e12 | −0.567674 | ||||||||
\(585\) | −1.58518e12 | −0.559600 | ||||||||
\(586\) | 1.07204e12 | 0.375553 | ||||||||
\(587\) | 1.79042e12 | 0.622420 | 0.311210 | − | 0.950341i | \(-0.399266\pi\) | ||||
0.311210 | + | 0.950341i | \(0.399266\pi\) | |||||||
\(588\) | 1.17446e12 | 0.405174 | ||||||||
\(589\) | −2.51780e12 | −0.861991 | ||||||||
\(590\) | 1.33050e11 | 0.0452045 | ||||||||
\(591\) | 2.56857e12 | 0.866058 | ||||||||
\(592\) | −1.33478e12 | −0.446645 | ||||||||
\(593\) | −8.61080e11 | −0.285955 | −0.142977 | − | 0.989726i | \(-0.545668\pi\) | ||||
−0.142977 | + | 0.989726i | \(0.545668\pi\) | |||||||
\(594\) | 1.37167e11 | 0.0452075 | ||||||||
\(595\) | 6.62528e12 | 2.16709 | ||||||||
\(596\) | 4.72853e12 | 1.53504 | ||||||||
\(597\) | 1.78755e11 | 0.0575935 | ||||||||
\(598\) | 1.65479e11 | 0.0529162 | ||||||||
\(599\) | −3.61522e12 | −1.14740 | −0.573699 | − | 0.819066i | \(-0.694492\pi\) | ||||
−0.573699 | + | 0.819066i | \(0.694492\pi\) | |||||||
\(600\) | −4.86509e9 | −0.00153253 | ||||||||
\(601\) | 6.50374e11 | 0.203343 | 0.101671 | − | 0.994818i | \(-0.467581\pi\) | ||||
0.101671 | + | 0.994818i | \(0.467581\pi\) | |||||||
\(602\) | −7.26979e11 | −0.225599 | ||||||||
\(603\) | −1.97991e11 | −0.0609843 | ||||||||
\(604\) | −2.10721e12 | −0.644231 | ||||||||
\(605\) | 1.78958e12 | 0.543065 | ||||||||
\(606\) | −1.16500e12 | −0.350913 | ||||||||
\(607\) | −1.14782e12 | −0.343181 | −0.171590 | − | 0.985168i | \(-0.554891\pi\) | ||||
−0.171590 | + | 0.985168i | \(0.554891\pi\) | |||||||
\(608\) | 1.71919e12 | 0.510221 | ||||||||
\(609\) | −4.13404e9 | −0.00121786 | ||||||||
\(610\) | −2.04683e12 | −0.598546 | ||||||||
\(611\) | 2.65499e12 | 0.770686 | ||||||||
\(612\) | −1.64640e12 | −0.474410 | ||||||||
\(613\) | 3.57940e12 | 1.02385 | 0.511927 | − | 0.859029i | \(-0.328932\pi\) | ||||
0.511927 | + | 0.859029i | \(0.328932\pi\) | |||||||
\(614\) | 1.06541e12 | 0.302522 | ||||||||
\(615\) | −1.61091e12 | −0.454081 | ||||||||
\(616\) | −2.11528e12 | −0.591907 | ||||||||
\(617\) | 2.70222e12 | 0.750650 | 0.375325 | − | 0.926893i | \(-0.377531\pi\) | ||||
0.375325 | + | 0.926893i | \(0.377531\pi\) | |||||||
\(618\) | −9.51301e11 | −0.262343 | ||||||||
\(619\) | 5.10159e12 | 1.39668 | 0.698341 | − | 0.715765i | \(-0.253922\pi\) | ||||
0.698341 | + | 0.715765i | \(0.253922\pi\) | |||||||
\(620\) | −4.80033e12 | −1.30469 | ||||||||
\(621\) | −6.44831e10 | −0.0173994 | ||||||||
\(622\) | 9.95052e11 | 0.266556 | ||||||||
\(623\) | 7.52281e11 | 0.200071 | ||||||||
\(624\) | −2.39640e12 | −0.632746 | ||||||||
\(625\) | −3.79915e12 | −0.995923 | ||||||||
\(626\) | 2.52690e12 | 0.657664 | ||||||||
\(627\) | 8.74212e11 | 0.225898 | ||||||||
\(628\) | −4.65761e12 | −1.19494 | ||||||||
\(629\) | −4.35809e12 | −1.11012 | ||||||||
\(630\) | 6.13715e11 | 0.155215 | ||||||||
\(631\) | −5.04642e12 | −1.26722 | −0.633609 | − | 0.773654i | \(-0.718427\pi\) | ||||
−0.633609 | + | 0.773654i | \(0.718427\pi\) | |||||||
\(632\) | −2.78665e11 | −0.0694792 | ||||||||
\(633\) | 3.58944e12 | 0.888607 | ||||||||
\(634\) | −2.01101e12 | −0.494325 | ||||||||
\(635\) | −2.87173e12 | −0.700910 | ||||||||
\(636\) | −1.00469e11 | −0.0243486 | ||||||||
\(637\) | 5.58149e12 | 1.34314 | ||||||||
\(638\) | 1.54631e9 | 0.000369490 0 | ||||||||
\(639\) | −6.24206e10 | −0.0148106 | ||||||||
\(640\) | 4.23786e12 | 0.998474 | ||||||||
\(641\) | 3.76398e12 | 0.880614 | 0.440307 | − | 0.897847i | \(-0.354870\pi\) | ||||
0.440307 | + | 0.897847i | \(0.354870\pi\) | |||||||
\(642\) | 8.00095e11 | 0.185881 | ||||||||
\(643\) | −3.84154e12 | −0.886250 | −0.443125 | − | 0.896460i | \(-0.646130\pi\) | ||||
−0.443125 | + | 0.896460i | \(0.646130\pi\) | |||||||
\(644\) | 4.65169e11 | 0.106567 | ||||||||
\(645\) | 1.22454e12 | 0.278583 | ||||||||
\(646\) | 1.44519e12 | 0.326495 | ||||||||
\(647\) | −2.67586e12 | −0.600336 | −0.300168 | − | 0.953886i | \(-0.597043\pi\) | ||||
−0.300168 | + | 0.953886i | \(0.597043\pi\) | |||||||
\(648\) | −3.26024e11 | −0.0726378 | ||||||||
\(649\) | 3.97261e11 | 0.0878972 | ||||||||
\(650\) | −1.08156e10 | −0.00237650 | ||||||||
\(651\) | −5.27755e12 | −1.15164 | ||||||||
\(652\) | 5.08254e12 | 1.10145 | ||||||||
\(653\) | 1.56783e12 | 0.337434 | 0.168717 | − | 0.985665i | \(-0.446038\pi\) | ||||
0.168717 | + | 0.985665i | \(0.446038\pi\) | |||||||
\(654\) | 4.24160e10 | 0.00906630 | ||||||||
\(655\) | 8.35146e12 | 1.77287 | ||||||||
\(656\) | −2.43530e12 | −0.513434 | ||||||||
\(657\) | 1.38235e12 | 0.289449 | ||||||||
\(658\) | −1.02790e12 | −0.213764 | ||||||||
\(659\) | 1.34203e12 | 0.277191 | 0.138596 | − | 0.990349i | \(-0.455741\pi\) | ||||
0.138596 | + | 0.990349i | \(0.455741\pi\) | |||||||
\(660\) | 1.66673e12 | 0.341915 | ||||||||
\(661\) | −2.80128e12 | −0.570755 | −0.285378 | − | 0.958415i | \(-0.592119\pi\) | ||||
−0.285378 | + | 0.958415i | \(0.592119\pi\) | |||||||
\(662\) | −1.36387e12 | −0.276003 | ||||||||
\(663\) | −7.82431e12 | −1.57266 | ||||||||
\(664\) | −6.79831e11 | −0.135720 | ||||||||
\(665\) | 3.91141e12 | 0.775597 | ||||||||
\(666\) | −4.03700e11 | −0.0795106 | ||||||||
\(667\) | −7.26928e8 | −0.000142208 0 | ||||||||
\(668\) | 2.12568e12 | 0.413051 | ||||||||
\(669\) | −2.54229e12 | −0.490690 | ||||||||
\(670\) | 3.31348e11 | 0.0635254 | ||||||||
\(671\) | −6.11143e12 | −1.16383 | ||||||||
\(672\) | 3.60359e12 | 0.681668 | ||||||||
\(673\) | 3.95540e12 | 0.743229 | 0.371614 | − | 0.928387i | \(-0.378804\pi\) | ||||
0.371614 | + | 0.928387i | \(0.378804\pi\) | |||||||
\(674\) | −2.12796e12 | −0.397186 | ||||||||
\(675\) | 4.21454e9 | 0.000781418 0 | ||||||||
\(676\) | −8.73251e12 | −1.60834 | ||||||||
\(677\) | −4.10835e12 | −0.751655 | −0.375828 | − | 0.926690i | \(-0.622641\pi\) | ||||
−0.375828 | + | 0.926690i | \(0.622641\pi\) | |||||||
\(678\) | −1.40186e12 | −0.254783 | ||||||||
\(679\) | 1.47110e12 | 0.265600 | ||||||||
\(680\) | 5.89014e12 | 1.05642 | ||||||||
\(681\) | 1.09961e12 | 0.195919 | ||||||||
\(682\) | 1.97402e12 | 0.349400 | ||||||||
\(683\) | −2.63864e12 | −0.463966 | −0.231983 | − | 0.972720i | \(-0.574521\pi\) | ||||
−0.231983 | + | 0.972720i | \(0.574521\pi\) | |||||||
\(684\) | −9.71998e11 | −0.169790 | ||||||||
\(685\) | −3.46412e12 | −0.601153 | ||||||||
\(686\) | 5.45518e11 | 0.0940482 | ||||||||
\(687\) | 3.14133e12 | 0.538032 | ||||||||
\(688\) | 1.85120e12 | 0.314997 | ||||||||
\(689\) | −4.77464e11 | −0.0807150 | ||||||||
\(690\) | 1.07915e11 | 0.0181243 | ||||||||
\(691\) | −4.12989e12 | −0.689109 | −0.344554 | − | 0.938766i | \(-0.611970\pi\) | ||||
−0.344554 | + | 0.938766i | \(0.611970\pi\) | |||||||
\(692\) | −3.28080e12 | −0.543879 | ||||||||
\(693\) | 1.83243e12 | 0.301806 | ||||||||
\(694\) | 1.18929e10 | 0.00194613 | ||||||||
\(695\) | 5.57864e12 | 0.906978 | ||||||||
\(696\) | −3.67533e9 | −0.000593683 0 | ||||||||
\(697\) | −7.95130e12 | −1.27612 | ||||||||
\(698\) | −2.04140e12 | −0.325521 | ||||||||
\(699\) | −3.35202e12 | −0.531079 | ||||||||
\(700\) | −3.04029e10 | −0.00478602 | ||||||||
\(701\) | −3.39242e12 | −0.530613 | −0.265307 | − | 0.964164i | \(-0.585473\pi\) | ||||
−0.265307 | + | 0.964164i | \(0.585473\pi\) | |||||||
\(702\) | −7.24784e11 | −0.112640 | ||||||||
\(703\) | −2.57292e12 | −0.397308 | ||||||||
\(704\) | 1.51883e12 | 0.233041 | ||||||||
\(705\) | 1.73142e12 | 0.263968 | ||||||||
\(706\) | −5.79442e11 | −0.0877786 | ||||||||
\(707\) | −1.55634e13 | −2.34270 | ||||||||
\(708\) | −4.41697e11 | −0.0660656 | ||||||||
\(709\) | −9.50357e12 | −1.41247 | −0.706234 | − | 0.707979i | \(-0.749607\pi\) | ||||
−0.706234 | + | 0.707979i | \(0.749607\pi\) | |||||||
\(710\) | 1.04464e11 | 0.0154278 | ||||||||
\(711\) | 2.41403e11 | 0.0354265 | ||||||||
\(712\) | 6.68808e11 | 0.0975308 | ||||||||
\(713\) | −9.28002e11 | −0.134476 | ||||||||
\(714\) | 3.02924e12 | 0.436206 | ||||||||
\(715\) | 7.92094e12 | 1.13344 | ||||||||
\(716\) | −5.04068e12 | −0.716772 | ||||||||
\(717\) | −1.14471e12 | −0.161755 | ||||||||
\(718\) | −2.93375e12 | −0.411968 | ||||||||
\(719\) | 6.87302e12 | 0.959108 | 0.479554 | − | 0.877512i | \(-0.340799\pi\) | ||||
0.479554 | + | 0.877512i | \(0.340799\pi\) | |||||||
\(720\) | −1.56278e12 | −0.216722 | ||||||||
\(721\) | −1.27085e13 | −1.75141 | ||||||||
\(722\) | −1.68723e12 | −0.231078 | ||||||||
\(723\) | −5.49147e11 | −0.0747423 | ||||||||
\(724\) | 9.22446e12 | 1.24772 | ||||||||
\(725\) | 4.75112e7 | 6.38668e−6 0 | ||||||||
\(726\) | 8.18240e11 | 0.109311 | ||||||||
\(727\) | 1.23689e13 | 1.64220 | 0.821099 | − | 0.570786i | \(-0.193362\pi\) | ||||
0.821099 | + | 0.570786i | \(0.193362\pi\) | |||||||
\(728\) | 1.11770e13 | 1.47481 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −2.31342e12 | −0.301510 | ||||||||
\(731\) | 6.04423e12 | 0.782911 | ||||||||
\(732\) | 6.79503e12 | 0.874765 | ||||||||
\(733\) | −1.42337e13 | −1.82116 | −0.910581 | − | 0.413330i | \(-0.864366\pi\) | ||||
−0.910581 | + | 0.413330i | \(0.864366\pi\) | |||||||
\(734\) | −2.53584e12 | −0.322470 | ||||||||
\(735\) | 3.63990e12 | 0.460041 | ||||||||
\(736\) | 6.33653e11 | 0.0795979 | ||||||||
\(737\) | 9.89337e11 | 0.123521 | ||||||||
\(738\) | −7.36547e11 | −0.0914002 | ||||||||
\(739\) | 4.57007e12 | 0.563668 | 0.281834 | − | 0.959463i | \(-0.409057\pi\) | ||||
0.281834 | + | 0.959463i | \(0.409057\pi\) | |||||||
\(740\) | −4.90542e12 | −0.601358 | ||||||||
\(741\) | −4.61930e12 | −0.562852 | ||||||||
\(742\) | 1.84854e11 | 0.0223878 | ||||||||
\(743\) | −4.31982e12 | −0.520015 | −0.260008 | − | 0.965607i | \(-0.583725\pi\) | ||||
−0.260008 | + | 0.965607i | \(0.583725\pi\) | |||||||
\(744\) | −4.69195e12 | −0.561404 | ||||||||
\(745\) | 1.46547e13 | 1.74290 | ||||||||
\(746\) | −3.08863e12 | −0.365125 | ||||||||
\(747\) | 5.88926e11 | 0.0692019 | ||||||||
\(748\) | 8.22685e12 | 0.960896 | ||||||||
\(749\) | 1.06886e13 | 1.24094 | ||||||||
\(750\) | −1.74414e12 | −0.201283 | ||||||||
\(751\) | −1.64985e13 | −1.89262 | −0.946311 | − | 0.323258i | \(-0.895222\pi\) | ||||
−0.946311 | + | 0.323258i | \(0.895222\pi\) | |||||||
\(752\) | 2.61748e12 | 0.298472 | ||||||||
\(753\) | −4.24422e12 | −0.481084 | ||||||||
\(754\) | −8.17061e9 | −0.000920626 0 | ||||||||
\(755\) | −6.53067e12 | −0.731470 | ||||||||
\(756\) | −2.03740e12 | −0.226844 | ||||||||
\(757\) | 9.88795e12 | 1.09440 | 0.547199 | − | 0.837003i | \(-0.315694\pi\) | ||||
0.547199 | + | 0.837003i | \(0.315694\pi\) | |||||||
\(758\) | −3.60435e12 | −0.396566 | ||||||||
\(759\) | 3.22214e11 | 0.0352416 | ||||||||
\(760\) | 3.47740e12 | 0.378089 | ||||||||
\(761\) | −6.61292e11 | −0.0714763 | −0.0357382 | − | 0.999361i | \(-0.511378\pi\) | ||||
−0.0357382 | + | 0.999361i | \(0.511378\pi\) | |||||||
\(762\) | −1.31303e12 | −0.141083 | ||||||||
\(763\) | 5.66640e11 | 0.0605267 | ||||||||
\(764\) | 1.46074e13 | 1.55115 | ||||||||
\(765\) | −5.10253e12 | −0.538653 | ||||||||
\(766\) | 8.97703e11 | 0.0942114 | ||||||||
\(767\) | −2.09911e12 | −0.219006 | ||||||||
\(768\) | 1.63508e10 | 0.00169595 | ||||||||
\(769\) | −1.35353e12 | −0.139572 | −0.0697861 | − | 0.997562i | \(-0.522232\pi\) | ||||
−0.0697861 | + | 0.997562i | \(0.522232\pi\) | |||||||
\(770\) | −3.06665e12 | −0.314381 | ||||||||
\(771\) | −1.05080e13 | −1.07096 | ||||||||
\(772\) | 1.33779e13 | 1.35553 | ||||||||
\(773\) | −4.96259e12 | −0.499920 | −0.249960 | − | 0.968256i | \(-0.580417\pi\) | ||||
−0.249960 | + | 0.968256i | \(0.580417\pi\) | |||||||
\(774\) | 5.59890e11 | 0.0560749 | ||||||||
\(775\) | 6.06532e10 | 0.00603943 | ||||||||
\(776\) | 1.30787e12 | 0.129475 | ||||||||
\(777\) | −5.39308e12 | −0.530813 | ||||||||
\(778\) | 2.09589e12 | 0.205098 | ||||||||
\(779\) | −4.69427e12 | −0.456719 | ||||||||
\(780\) | −8.80695e12 | −0.851922 | ||||||||
\(781\) | 3.11908e11 | 0.0299983 | ||||||||
\(782\) | 5.32661e11 | 0.0509355 | ||||||||
\(783\) | 3.18388e9 | 0.000302711 0 | ||||||||
\(784\) | 5.50263e12 | 0.520173 | ||||||||
\(785\) | −1.44349e13 | −1.35675 | ||||||||
\(786\) | 3.81849e12 | 0.356854 | ||||||||
\(787\) | −5.22654e12 | −0.485655 | −0.242827 | − | 0.970069i | \(-0.578075\pi\) | ||||
−0.242827 | + | 0.970069i | \(0.578075\pi\) | |||||||
\(788\) | 1.42704e13 | 1.31847 | ||||||||
\(789\) | 2.75059e12 | 0.252685 | ||||||||
\(790\) | −4.03998e11 | −0.0369026 | ||||||||
\(791\) | −1.87276e13 | −1.70094 | ||||||||
\(792\) | 1.62910e12 | 0.147125 | ||||||||
\(793\) | 3.22925e13 | 2.89983 | ||||||||
\(794\) | −5.54791e12 | −0.495379 | ||||||||
\(795\) | −3.11372e11 | −0.0276457 | ||||||||
\(796\) | 9.93126e11 | 0.0876790 | ||||||||
\(797\) | −5.16094e12 | −0.453071 | −0.226536 | − | 0.974003i | \(-0.572740\pi\) | ||||
−0.226536 | + | 0.974003i | \(0.572740\pi\) | |||||||
\(798\) | 1.78839e12 | 0.156117 | ||||||||
\(799\) | 8.54613e12 | 0.741838 | ||||||||
\(800\) | −4.14149e10 | −0.00357480 | ||||||||
\(801\) | −5.79377e11 | −0.0497296 | ||||||||
\(802\) | 2.61168e12 | 0.222913 | ||||||||
\(803\) | −6.90741e12 | −0.586266 | ||||||||
\(804\) | −1.10000e12 | −0.0928412 | ||||||||
\(805\) | 1.44165e12 | 0.120998 | ||||||||
\(806\) | −1.04307e13 | −0.870571 | ||||||||
\(807\) | −2.42367e12 | −0.201160 | ||||||||
\(808\) | −1.38365e13 | −1.14202 | ||||||||
\(809\) | 3.07165e12 | 0.252118 | 0.126059 | − | 0.992023i | \(-0.459767\pi\) | ||||
0.126059 | + | 0.992023i | \(0.459767\pi\) | |||||||
\(810\) | −4.72659e11 | −0.0385803 | ||||||||
\(811\) | −1.64233e13 | −1.33311 | −0.666556 | − | 0.745455i | \(-0.732232\pi\) | ||||
−0.666556 | + | 0.745455i | \(0.732232\pi\) | |||||||
\(812\) | −2.29679e10 | −0.00185404 | ||||||||
\(813\) | 1.02998e13 | 0.826837 | ||||||||
\(814\) | 2.01724e12 | 0.161045 | ||||||||
\(815\) | 1.57518e13 | 1.25061 | ||||||||
\(816\) | −7.71376e12 | −0.609061 | ||||||||
\(817\) | 3.56837e12 | 0.280202 | ||||||||
\(818\) | 3.77423e12 | 0.294740 | ||||||||
\(819\) | −9.68247e12 | −0.751984 | ||||||||
\(820\) | −8.94989e12 | −0.691282 | ||||||||
\(821\) | 2.30152e13 | 1.76795 | 0.883976 | − | 0.467532i | \(-0.154857\pi\) | ||||
0.883976 | + | 0.467532i | \(0.154857\pi\) | |||||||
\(822\) | −1.58388e12 | −0.121004 | ||||||||
\(823\) | −8.71598e11 | −0.0662242 | −0.0331121 | − | 0.999452i | \(-0.510542\pi\) | ||||
−0.0331121 | + | 0.999452i | \(0.510542\pi\) | |||||||
\(824\) | −1.12984e13 | −0.853777 | ||||||||
\(825\) | −2.10595e10 | −0.00158273 | ||||||||
\(826\) | 8.12686e11 | 0.0607453 | ||||||||
\(827\) | 3.51025e12 | 0.260954 | 0.130477 | − | 0.991451i | \(-0.458349\pi\) | ||||
0.130477 | + | 0.991451i | \(0.458349\pi\) | |||||||
\(828\) | −3.58255e11 | −0.0264884 | ||||||||
\(829\) | −1.62965e13 | −1.19839 | −0.599195 | − | 0.800603i | \(-0.704513\pi\) | ||||
−0.599195 | + | 0.800603i | \(0.704513\pi\) | |||||||
\(830\) | −9.85595e11 | −0.0720853 | ||||||||
\(831\) | 5.06922e12 | 0.368754 | ||||||||
\(832\) | −8.02542e12 | −0.580648 | ||||||||
\(833\) | 1.79662e13 | 1.29287 | ||||||||
\(834\) | 2.55069e12 | 0.182562 | ||||||||
\(835\) | 6.58791e12 | 0.468984 | ||||||||
\(836\) | 4.85695e12 | 0.343902 | ||||||||
\(837\) | 4.06456e12 | 0.286252 | ||||||||
\(838\) | 6.96928e12 | 0.488191 | ||||||||
\(839\) | 2.35510e12 | 0.164089 | 0.0820446 | − | 0.996629i | \(-0.473855\pi\) | ||||
0.0820446 | + | 0.996629i | \(0.473855\pi\) | |||||||
\(840\) | 7.28896e12 | 0.505136 | ||||||||
\(841\) | −1.45071e13 | −0.999998 | ||||||||
\(842\) | −8.65407e12 | −0.593357 | ||||||||
\(843\) | 4.32354e12 | 0.294860 | ||||||||
\(844\) | 1.99422e13 | 1.35280 | ||||||||
\(845\) | −2.70638e13 | −1.82614 | ||||||||
\(846\) | 7.91648e11 | 0.0531331 | ||||||||
\(847\) | 1.09310e13 | 0.729765 | ||||||||
\(848\) | −4.70718e11 | −0.0312593 | ||||||||
\(849\) | −9.91958e12 | −0.655252 | ||||||||
\(850\) | −3.48141e10 | −0.00228755 | ||||||||
\(851\) | −9.48317e11 | −0.0619827 | ||||||||
\(852\) | −3.46796e11 | −0.0225474 | ||||||||
\(853\) | 8.18557e12 | 0.529393 | 0.264696 | − | 0.964332i | \(-0.414728\pi\) | ||||
0.264696 | + | 0.964332i | \(0.414728\pi\) | |||||||
\(854\) | −1.25023e13 | −0.804320 | ||||||||
\(855\) | −3.01242e12 | −0.192782 | ||||||||
\(856\) | 9.50256e12 | 0.604935 | ||||||||
\(857\) | −4.09656e12 | −0.259421 | −0.129711 | − | 0.991552i | \(-0.541405\pi\) | ||||
−0.129711 | + | 0.991552i | \(0.541405\pi\) | |||||||
\(858\) | 3.62165e12 | 0.228146 | ||||||||
\(859\) | 1.63156e13 | 1.02243 | 0.511214 | − | 0.859453i | \(-0.329196\pi\) | ||||
0.511214 | + | 0.859453i | \(0.329196\pi\) | |||||||
\(860\) | 6.80331e12 | 0.424109 | ||||||||
\(861\) | −9.83962e12 | −0.610188 | ||||||||
\(862\) | 4.05646e11 | 0.0250245 | ||||||||
\(863\) | −1.09372e13 | −0.671211 | −0.335606 | − | 0.942003i | \(-0.608941\pi\) | ||||
−0.335606 | + | 0.942003i | \(0.608941\pi\) | |||||||
\(864\) | −2.77534e12 | −0.169435 | ||||||||
\(865\) | −1.01679e13 | −0.617529 | ||||||||
\(866\) | −5.79193e12 | −0.349939 | ||||||||
\(867\) | −1.55800e13 | −0.936444 | ||||||||
\(868\) | −2.93210e13 | −1.75323 | ||||||||
\(869\) | −1.20626e12 | −0.0717548 | ||||||||
\(870\) | −5.32836e9 | −0.000315324 0 | ||||||||
\(871\) | −5.22761e12 | −0.307767 | ||||||||
\(872\) | 5.03766e11 | 0.0295056 | ||||||||
\(873\) | −1.13298e12 | −0.0660175 | ||||||||
\(874\) | 3.14471e11 | 0.0182297 | ||||||||
\(875\) | −2.33002e13 | −1.34377 | ||||||||
\(876\) | 7.68004e12 | 0.440651 | ||||||||
\(877\) | 6.57105e12 | 0.375091 | 0.187546 | − | 0.982256i | \(-0.439947\pi\) | ||||
0.187546 | + | 0.982256i | \(0.439947\pi\) | |||||||
\(878\) | −3.57000e12 | −0.202741 | ||||||||
\(879\) | −1.10298e13 | −0.623189 | ||||||||
\(880\) | 7.80903e12 | 0.438960 | ||||||||
\(881\) | 2.58625e11 | 0.0144637 | 0.00723184 | − | 0.999974i | \(-0.497698\pi\) | ||||
0.00723184 | + | 0.999974i | \(0.497698\pi\) | |||||||
\(882\) | 1.66425e12 | 0.0925998 | ||||||||
\(883\) | −3.12545e13 | −1.73017 | −0.865086 | − | 0.501623i | \(-0.832736\pi\) | ||||
−0.865086 | + | 0.501623i | \(0.832736\pi\) | |||||||
\(884\) | −4.34703e13 | −2.39419 | ||||||||
\(885\) | −1.36891e12 | −0.0750118 | ||||||||
\(886\) | 2.51997e12 | 0.137386 | ||||||||
\(887\) | −2.78715e13 | −1.51183 | −0.755916 | − | 0.654668i | \(-0.772808\pi\) | ||||
−0.755916 | + | 0.654668i | \(0.772808\pi\) | |||||||
\(888\) | −4.79466e12 | −0.258761 | ||||||||
\(889\) | −1.75409e13 | −0.941875 | ||||||||
\(890\) | 9.69615e11 | 0.0518017 | ||||||||
\(891\) | −1.41126e12 | −0.0750168 | ||||||||
\(892\) | −1.41244e13 | −0.747015 | ||||||||
\(893\) | 5.04544e12 | 0.265502 | ||||||||
\(894\) | 6.70048e12 | 0.350822 | ||||||||
\(895\) | −1.56221e13 | −0.813833 | ||||||||
\(896\) | 2.58853e13 | 1.34174 | ||||||||
\(897\) | −1.70256e12 | −0.0878086 | ||||||||
\(898\) | −1.14528e13 | −0.587716 | ||||||||
\(899\) | 4.58204e10 | 0.00233959 | ||||||||
\(900\) | 2.34152e10 | 0.00118961 | ||||||||
\(901\) | −1.53691e12 | −0.0776937 | ||||||||
\(902\) | 3.68043e12 | 0.185127 | ||||||||
\(903\) | 7.47964e12 | 0.374357 | ||||||||
\(904\) | −1.66496e13 | −0.829174 | ||||||||
\(905\) | 2.85885e13 | 1.41668 | ||||||||
\(906\) | −2.98598e12 | −0.147235 | ||||||||
\(907\) | 9.71090e12 | 0.476460 | 0.238230 | − | 0.971209i | \(-0.423433\pi\) | ||||
0.238230 | + | 0.971209i | \(0.423433\pi\) | |||||||
\(908\) | 6.10922e12 | 0.298263 | ||||||||
\(909\) | 1.19863e13 | 0.582301 | ||||||||
\(910\) | 1.62041e13 | 0.783317 | ||||||||
\(911\) | −2.34403e13 | −1.12754 | −0.563768 | − | 0.825933i | \(-0.690649\pi\) | ||||
−0.563768 | + | 0.825933i | \(0.690649\pi\) | |||||||
\(912\) | −4.55403e12 | −0.217981 | ||||||||
\(913\) | −2.94279e12 | −0.140165 | ||||||||
\(914\) | −5.14041e12 | −0.243635 | ||||||||
\(915\) | 2.10592e13 | 0.993221 | ||||||||
\(916\) | 1.74526e13 | 0.819087 | ||||||||
\(917\) | 5.10117e13 | 2.38236 | ||||||||
\(918\) | −2.33300e12 | −0.108423 | ||||||||
\(919\) | 1.71926e13 | 0.795099 | 0.397550 | − | 0.917581i | \(-0.369861\pi\) | ||||
0.397550 | + | 0.917581i | \(0.369861\pi\) | |||||||
\(920\) | 1.28169e12 | 0.0589844 | ||||||||
\(921\) | −1.09616e13 | −0.502002 | ||||||||
\(922\) | 1.23568e13 | 0.563139 | ||||||||
\(923\) | −1.64811e12 | −0.0747442 | ||||||||
\(924\) | 1.01806e13 | 0.459462 | ||||||||
\(925\) | 6.19809e10 | 0.00278369 | ||||||||
\(926\) | −1.46727e13 | −0.655786 | ||||||||
\(927\) | 9.78761e12 | 0.435329 | ||||||||
\(928\) | −3.12869e10 | −0.00138483 | ||||||||
\(929\) | 2.39639e13 | 1.05557 | 0.527785 | − | 0.849378i | \(-0.323023\pi\) | ||||
0.527785 | + | 0.849378i | \(0.323023\pi\) | |||||||
\(930\) | −6.80222e12 | −0.298179 | ||||||||
\(931\) | 1.06068e13 | 0.462714 | ||||||||
\(932\) | −1.86232e13 | −0.808503 | ||||||||
\(933\) | −1.02377e13 | −0.442321 | ||||||||
\(934\) | −2.52991e12 | −0.108779 | ||||||||
\(935\) | 2.54967e13 | 1.09102 | ||||||||
\(936\) | −8.60810e12 | −0.366578 | ||||||||
\(937\) | 3.32009e13 | 1.40709 | 0.703544 | − | 0.710652i | \(-0.251600\pi\) | ||||
0.703544 | + | 0.710652i | \(0.251600\pi\) | |||||||
\(938\) | 2.02391e12 | 0.0853647 | ||||||||
\(939\) | −2.59985e13 | −1.09132 | ||||||||
\(940\) | 9.61942e12 | 0.401859 | ||||||||
\(941\) | −1.23066e13 | −0.511665 | −0.255832 | − | 0.966721i | \(-0.582350\pi\) | ||||
−0.255832 | + | 0.966721i | \(0.582350\pi\) | |||||||
\(942\) | −6.59998e12 | −0.273095 | ||||||||
\(943\) | −1.73020e12 | −0.0712512 | ||||||||
\(944\) | −2.06945e12 | −0.0848167 | ||||||||
\(945\) | −6.31430e12 | −0.257562 | ||||||||
\(946\) | −2.79770e12 | −0.113577 | ||||||||
\(947\) | 2.39621e13 | 0.968167 | 0.484084 | − | 0.875022i | \(-0.339153\pi\) | ||||
0.484084 | + | 0.875022i | \(0.339153\pi\) | |||||||
\(948\) | 1.34118e12 | 0.0539326 | ||||||||
\(949\) | 3.64984e13 | 1.46075 | ||||||||
\(950\) | −2.05535e10 | −0.000818707 0 | ||||||||
\(951\) | 2.06906e13 | 0.820277 | ||||||||
\(952\) | 3.59777e13 | 1.41960 | ||||||||
\(953\) | 1.41217e13 | 0.554584 | 0.277292 | − | 0.960786i | \(-0.410563\pi\) | ||||
0.277292 | + | 0.960786i | \(0.410563\pi\) | |||||||
\(954\) | −1.42367e11 | −0.00556470 | ||||||||
\(955\) | 4.52714e13 | 1.76120 | ||||||||
\(956\) | −6.35977e12 | −0.246253 | ||||||||
\(957\) | −1.59094e10 | −0.000613127 0 | ||||||||
\(958\) | 1.16213e13 | 0.445770 | ||||||||
\(959\) | −2.11592e13 | −0.807823 | ||||||||
\(960\) | −5.23368e12 | −0.198878 | ||||||||
\(961\) | 3.20551e13 | 1.21239 | ||||||||
\(962\) | −1.06590e13 | −0.401262 | ||||||||
\(963\) | −8.23191e12 | −0.308448 | ||||||||
\(964\) | −3.05095e12 | −0.113786 | ||||||||
\(965\) | 4.14608e13 | 1.53909 | ||||||||
\(966\) | 6.59159e11 | 0.0243553 | ||||||||
\(967\) | 2.92844e12 | 0.107700 | 0.0538502 | − | 0.998549i | \(-0.482851\pi\) | ||||
0.0538502 | + | 0.998549i | \(0.482851\pi\) | |||||||
\(968\) | 9.71806e12 | 0.355746 | ||||||||
\(969\) | −1.48690e13 | −0.541783 | ||||||||
\(970\) | 1.89610e12 | 0.0687683 | ||||||||
\(971\) | 5.04989e12 | 0.182304 | 0.0911518 | − | 0.995837i | \(-0.470945\pi\) | ||||
0.0911518 | + | 0.995837i | \(0.470945\pi\) | |||||||
\(972\) | 1.56912e12 | 0.0563844 | ||||||||
\(973\) | 3.40750e13 | 1.21879 | ||||||||
\(974\) | 3.53513e12 | 0.125861 | ||||||||
\(975\) | 1.11278e11 | 0.00394354 | ||||||||
\(976\) | 3.18362e13 | 1.12305 | ||||||||
\(977\) | 4.83238e13 | 1.69682 | 0.848410 | − | 0.529339i | \(-0.177560\pi\) | ||||
0.848410 | + | 0.529339i | \(0.177560\pi\) | |||||||
\(978\) | 7.20211e12 | 0.251730 | ||||||||
\(979\) | 2.89507e12 | 0.100725 | ||||||||
\(980\) | 2.02226e13 | 0.700356 | ||||||||
\(981\) | −4.36404e11 | −0.0150445 | ||||||||
\(982\) | 8.38810e12 | 0.287847 | ||||||||
\(983\) | 2.76295e11 | 0.00943804 | 0.00471902 | − | 0.999989i | \(-0.498498\pi\) | ||||
0.00471902 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(984\) | −8.74782e12 | −0.297455 | ||||||||
\(985\) | 4.42270e13 | 1.49701 | ||||||||
\(986\) | −2.63003e10 | −0.000886166 0 | ||||||||
\(987\) | 1.05757e13 | 0.354717 | ||||||||
\(988\) | −2.56639e13 | −0.856873 | ||||||||
\(989\) | 1.31522e12 | 0.0437134 | ||||||||
\(990\) | 2.36181e12 | 0.0781425 | ||||||||
\(991\) | −4.44286e13 | −1.46329 | −0.731646 | − | 0.681685i | \(-0.761248\pi\) | ||||
−0.731646 | + | 0.681685i | \(0.761248\pi\) | |||||||
\(992\) | −3.99410e13 | −1.30953 | ||||||||
\(993\) | 1.40324e13 | 0.457996 | ||||||||
\(994\) | 6.38076e11 | 0.0207316 | ||||||||
\(995\) | 3.07790e12 | 0.0995521 | ||||||||
\(996\) | 3.27196e12 | 0.105351 | ||||||||
\(997\) | 4.47458e13 | 1.43425 | 0.717124 | − | 0.696946i | \(-0.245458\pi\) | ||||
0.717124 | + | 0.696946i | \(0.245458\pi\) | |||||||
\(998\) | 1.93031e12 | 0.0615940 | ||||||||
\(999\) | 4.15353e12 | 0.131939 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.10.a.b.1.12 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.12 | ✓ | 21 | 1.1 | even | 1 | trivial |