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: | \(0\) |
Dimension: | \(22\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.33644 | 0.0590628 | 0.0295314 | − | 0.999564i | \(-0.490599\pi\) | ||||
0.0295314 | + | 0.999564i | \(0.490599\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | −510.214 | −0.996512 | ||||||||
\(5\) | 2090.38 | 1.49575 | 0.747877 | − | 0.663838i | \(-0.231073\pi\) | ||||
0.747877 | + | 0.663838i | \(0.231073\pi\) | |||||||
\(6\) | −108.251 | −0.0340999 | ||||||||
\(7\) | 107.167 | 0.0168701 | 0.00843506 | − | 0.999964i | \(-0.497315\pi\) | ||||
0.00843506 | + | 0.999964i | \(0.497315\pi\) | |||||||
\(8\) | −1366.13 | −0.117919 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | 2793.66 | 0.0883433 | ||||||||
\(11\) | −839.126 | −0.0172807 | −0.00864033 | − | 0.999963i | \(-0.502750\pi\) | ||||
−0.00864033 | + | 0.999963i | \(0.502750\pi\) | |||||||
\(12\) | 41327.3 | 0.575336 | ||||||||
\(13\) | 34005.3 | 0.330218 | 0.165109 | − | 0.986275i | \(-0.447202\pi\) | ||||
0.165109 | + | 0.986275i | \(0.447202\pi\) | |||||||
\(14\) | 143.222 | 0.000996396 0 | ||||||||
\(15\) | −169321. | −0.863574 | ||||||||
\(16\) | 259404. | 0.989547 | ||||||||
\(17\) | −84723.3 | −0.246027 | −0.123013 | − | 0.992405i | \(-0.539256\pi\) | ||||
−0.123013 | + | 0.992405i | \(0.539256\pi\) | |||||||
\(18\) | 8768.37 | 0.0196876 | ||||||||
\(19\) | 928571. | 1.63465 | 0.817323 | − | 0.576179i | \(-0.195457\pi\) | ||||
0.817323 | + | 0.576179i | \(0.195457\pi\) | |||||||
\(20\) | −1.06654e6 | −1.49054 | ||||||||
\(21\) | −8680.50 | −0.00973997 | ||||||||
\(22\) | −1121.44 | −0.00102064 | ||||||||
\(23\) | −971930. | −0.724202 | −0.362101 | − | 0.932139i | \(-0.617940\pi\) | ||||
−0.362101 | + | 0.932139i | \(0.617940\pi\) | |||||||
\(24\) | 110656. | 0.0680808 | ||||||||
\(25\) | 2.41656e6 | 1.23728 | ||||||||
\(26\) | 45445.9 | 0.0195036 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | −54677.9 | −0.0168113 | ||||||||
\(29\) | 534314. | 0.140283 | 0.0701415 | − | 0.997537i | \(-0.477655\pi\) | ||||
0.0701415 | + | 0.997537i | \(0.477655\pi\) | |||||||
\(30\) | −226287. | −0.0510050 | ||||||||
\(31\) | −1.99772e6 | −0.388514 | −0.194257 | − | 0.980951i | \(-0.562230\pi\) | ||||
−0.194257 | + | 0.980951i | \(0.562230\pi\) | |||||||
\(32\) | 1.04613e6 | 0.176365 | ||||||||
\(33\) | 67969.2 | 0.00997699 | ||||||||
\(34\) | −113227. | −0.0145310 | ||||||||
\(35\) | 224019. | 0.0252335 | ||||||||
\(36\) | −3.34751e6 | −0.332171 | ||||||||
\(37\) | −9.60421e6 | −0.842469 | −0.421235 | − | 0.906952i | \(-0.638403\pi\) | ||||
−0.421235 | + | 0.906952i | \(0.638403\pi\) | |||||||
\(38\) | 1.24098e6 | 0.0965468 | ||||||||
\(39\) | −2.75443e6 | −0.190652 | ||||||||
\(40\) | −2.85572e6 | −0.176378 | ||||||||
\(41\) | 1.18062e7 | 0.652506 | 0.326253 | − | 0.945283i | \(-0.394214\pi\) | ||||
0.326253 | + | 0.945283i | \(0.394214\pi\) | |||||||
\(42\) | −11600.9 | −0.000575270 0 | ||||||||
\(43\) | −1.85229e7 | −0.826230 | −0.413115 | − | 0.910679i | \(-0.635559\pi\) | ||||
−0.413115 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(44\) | 428134. | 0.0172204 | ||||||||
\(45\) | 1.37150e7 | 0.498584 | ||||||||
\(46\) | −1.29892e6 | −0.0427734 | ||||||||
\(47\) | −1.01847e7 | −0.304445 | −0.152223 | − | 0.988346i | \(-0.548643\pi\) | ||||
−0.152223 | + | 0.988346i | \(0.548643\pi\) | |||||||
\(48\) | −2.10117e7 | −0.571315 | ||||||||
\(49\) | −4.03421e7 | −0.999715 | ||||||||
\(50\) | 3.22958e6 | 0.0730771 | ||||||||
\(51\) | 6.86258e6 | 0.142044 | ||||||||
\(52\) | −1.73500e7 | −0.329066 | ||||||||
\(53\) | −3.57403e7 | −0.622181 | −0.311090 | − | 0.950380i | \(-0.600694\pi\) | ||||
−0.311090 | + | 0.950380i | \(0.600694\pi\) | |||||||
\(54\) | −710238. | −0.0113666 | ||||||||
\(55\) | −1.75409e6 | −0.0258476 | ||||||||
\(56\) | −146403. | −0.00198932 | ||||||||
\(57\) | −7.52143e7 | −0.943764 | ||||||||
\(58\) | 714077. | 0.00828551 | ||||||||
\(59\) | 1.21174e7 | 0.130189 | ||||||||
\(60\) | 8.63898e7 | 0.860561 | ||||||||
\(61\) | −6.03548e7 | −0.558120 | −0.279060 | − | 0.960274i | \(-0.590023\pi\) | ||||
−0.279060 | + | 0.960274i | \(0.590023\pi\) | |||||||
\(62\) | −2.66983e6 | −0.0229467 | ||||||||
\(63\) | 703120. | 0.00562338 | ||||||||
\(64\) | −1.31417e8 | −0.979130 | ||||||||
\(65\) | 7.10839e7 | 0.493925 | ||||||||
\(66\) | 90836.6 | 0.000589268 0 | ||||||||
\(67\) | 2.83501e8 | 1.71877 | 0.859386 | − | 0.511327i | \(-0.170846\pi\) | ||||
0.859386 | + | 0.511327i | \(0.170846\pi\) | |||||||
\(68\) | 4.32270e7 | 0.245169 | ||||||||
\(69\) | 7.87263e7 | 0.418118 | ||||||||
\(70\) | 299387. | 0.00149036 | ||||||||
\(71\) | 3.57688e8 | 1.67048 | 0.835241 | − | 0.549884i | \(-0.185328\pi\) | ||||
0.835241 | + | 0.549884i | \(0.185328\pi\) | |||||||
\(72\) | −8.96315e6 | −0.0393065 | ||||||||
\(73\) | 3.74577e8 | 1.54379 | 0.771895 | − | 0.635750i | \(-0.219309\pi\) | ||||
0.771895 | + | 0.635750i | \(0.219309\pi\) | |||||||
\(74\) | −1.28354e7 | −0.0497585 | ||||||||
\(75\) | −1.95741e8 | −0.714343 | ||||||||
\(76\) | −4.73770e8 | −1.62894 | ||||||||
\(77\) | −89926.3 | −0.000291527 0 | ||||||||
\(78\) | −3.68112e6 | −0.0112604 | ||||||||
\(79\) | 6.00766e7 | 0.173534 | 0.0867668 | − | 0.996229i | \(-0.472346\pi\) | ||||
0.0867668 | + | 0.996229i | \(0.472346\pi\) | |||||||
\(80\) | 5.42252e8 | 1.48012 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 1.57783e7 | 0.0385388 | ||||||||
\(83\) | 6.16047e8 | 1.42483 | 0.712414 | − | 0.701759i | \(-0.247602\pi\) | ||||
0.712414 | + | 0.701759i | \(0.247602\pi\) | |||||||
\(84\) | 4.42891e6 | 0.00970599 | ||||||||
\(85\) | −1.77104e8 | −0.367995 | ||||||||
\(86\) | −2.47547e7 | −0.0487994 | ||||||||
\(87\) | −4.32794e7 | −0.0809925 | ||||||||
\(88\) | 1.14635e6 | 0.00203773 | ||||||||
\(89\) | 1.58856e8 | 0.268379 | 0.134189 | − | 0.990956i | \(-0.457157\pi\) | ||||
0.134189 | + | 0.990956i | \(0.457157\pi\) | |||||||
\(90\) | 1.83292e7 | 0.0294478 | ||||||||
\(91\) | 3.64423e6 | 0.00557083 | ||||||||
\(92\) | 4.95892e8 | 0.721676 | ||||||||
\(93\) | 1.61815e8 | 0.224309 | ||||||||
\(94\) | −1.36113e7 | −0.0179814 | ||||||||
\(95\) | 1.94107e9 | 2.44503 | ||||||||
\(96\) | −8.47368e7 | −0.101824 | ||||||||
\(97\) | 1.10346e9 | 1.26557 | 0.632784 | − | 0.774328i | \(-0.281912\pi\) | ||||
0.632784 | + | 0.774328i | \(0.281912\pi\) | |||||||
\(98\) | −5.39147e7 | −0.0590460 | ||||||||
\(99\) | −5.50551e6 | −0.00576022 | ||||||||
\(100\) | −1.23296e9 | −1.23296 | ||||||||
\(101\) | −2.92749e7 | −0.0279930 | −0.0139965 | − | 0.999902i | \(-0.504455\pi\) | ||||
−0.0139965 | + | 0.999902i | \(0.504455\pi\) | |||||||
\(102\) | 9.17142e6 | 0.00838949 | ||||||||
\(103\) | −5.30706e8 | −0.464608 | −0.232304 | − | 0.972643i | \(-0.574626\pi\) | ||||
−0.232304 | + | 0.972643i | \(0.574626\pi\) | |||||||
\(104\) | −4.64555e7 | −0.0389392 | ||||||||
\(105\) | −1.81455e7 | −0.0145686 | ||||||||
\(106\) | −4.77646e7 | −0.0367477 | ||||||||
\(107\) | −1.46128e9 | −1.07772 | −0.538860 | − | 0.842395i | \(-0.681145\pi\) | ||||
−0.538860 | + | 0.842395i | \(0.681145\pi\) | |||||||
\(108\) | 2.71149e8 | 0.191779 | ||||||||
\(109\) | −6.89292e8 | −0.467718 | −0.233859 | − | 0.972271i | \(-0.575135\pi\) | ||||
−0.233859 | + | 0.972271i | \(0.575135\pi\) | |||||||
\(110\) | −2.34423e6 | −0.00152663 | ||||||||
\(111\) | 7.77941e8 | 0.486400 | ||||||||
\(112\) | 2.77994e7 | 0.0166938 | ||||||||
\(113\) | 1.55105e9 | 0.894899 | 0.447450 | − | 0.894309i | \(-0.352332\pi\) | ||||
0.447450 | + | 0.894309i | \(0.352332\pi\) | |||||||
\(114\) | −1.00519e8 | −0.0557413 | ||||||||
\(115\) | −2.03170e9 | −1.08323 | ||||||||
\(116\) | −2.72614e8 | −0.139794 | ||||||||
\(117\) | 2.23109e8 | 0.110073 | ||||||||
\(118\) | 1.61941e7 | 0.00768932 | ||||||||
\(119\) | −9.07950e6 | −0.00415050 | ||||||||
\(120\) | 2.31313e8 | 0.101832 | ||||||||
\(121\) | −2.35724e9 | −0.999701 | ||||||||
\(122\) | −8.06605e7 | −0.0329641 | ||||||||
\(123\) | −9.56305e8 | −0.376724 | ||||||||
\(124\) | 1.01926e9 | 0.387159 | ||||||||
\(125\) | 9.68752e8 | 0.354909 | ||||||||
\(126\) | 939676. | 0.000332132 0 | ||||||||
\(127\) | 5.03627e9 | 1.71788 | 0.858939 | − | 0.512078i | \(-0.171124\pi\) | ||||
0.858939 | + | 0.512078i | \(0.171124\pi\) | |||||||
\(128\) | −7.11250e8 | −0.234195 | ||||||||
\(129\) | 1.50035e9 | 0.477024 | ||||||||
\(130\) | 9.49992e7 | 0.0291726 | ||||||||
\(131\) | 1.31283e9 | 0.389482 | 0.194741 | − | 0.980855i | \(-0.437613\pi\) | ||||
0.194741 | + | 0.980855i | \(0.437613\pi\) | |||||||
\(132\) | −3.46788e7 | −0.00994218 | ||||||||
\(133\) | 9.95118e7 | 0.0275767 | ||||||||
\(134\) | 3.78882e8 | 0.101515 | ||||||||
\(135\) | −1.11091e9 | −0.287858 | ||||||||
\(136\) | 1.15743e8 | 0.0290114 | ||||||||
\(137\) | 1.89177e9 | 0.458803 | 0.229401 | − | 0.973332i | \(-0.426323\pi\) | ||||
0.229401 | + | 0.973332i | \(0.426323\pi\) | |||||||
\(138\) | 1.05213e8 | 0.0246952 | ||||||||
\(139\) | 4.40133e9 | 1.00004 | 0.500020 | − | 0.866014i | \(-0.333326\pi\) | ||||
0.500020 | + | 0.866014i | \(0.333326\pi\) | |||||||
\(140\) | −1.14298e8 | −0.0251455 | ||||||||
\(141\) | 8.24963e8 | 0.175772 | ||||||||
\(142\) | 4.78028e8 | 0.0986632 | ||||||||
\(143\) | −2.85347e7 | −0.00570639 | ||||||||
\(144\) | 1.70195e9 | 0.329849 | ||||||||
\(145\) | 1.11692e9 | 0.209829 | ||||||||
\(146\) | 5.00599e8 | 0.0911805 | ||||||||
\(147\) | 3.26771e9 | 0.577186 | ||||||||
\(148\) | 4.90020e9 | 0.839530 | ||||||||
\(149\) | 1.12491e10 | 1.86973 | 0.934865 | − | 0.355002i | \(-0.115520\pi\) | ||||
0.934865 | + | 0.355002i | \(0.115520\pi\) | |||||||
\(150\) | −2.61596e8 | −0.0421911 | ||||||||
\(151\) | −1.01153e9 | −0.158337 | −0.0791685 | − | 0.996861i | \(-0.525227\pi\) | ||||
−0.0791685 | + | 0.996861i | \(0.525227\pi\) | |||||||
\(152\) | −1.26854e9 | −0.192757 | ||||||||
\(153\) | −5.55869e8 | −0.0820089 | ||||||||
\(154\) | −120181. | −1.72184e−5 0 | ||||||||
\(155\) | −4.17599e9 | −0.581121 | ||||||||
\(156\) | 1.40535e9 | 0.189987 | ||||||||
\(157\) | 5.95184e9 | 0.781813 | 0.390906 | − | 0.920430i | \(-0.372162\pi\) | ||||
0.390906 | + | 0.920430i | \(0.372162\pi\) | |||||||
\(158\) | 8.02887e7 | 0.0102494 | ||||||||
\(159\) | 2.89496e9 | 0.359216 | ||||||||
\(160\) | 2.18681e9 | 0.263798 | ||||||||
\(161\) | −1.04158e8 | −0.0122174 | ||||||||
\(162\) | 5.75293e7 | 0.00656253 | ||||||||
\(163\) | 1.40093e10 | 1.55443 | 0.777216 | − | 0.629233i | \(-0.216631\pi\) | ||||
0.777216 | + | 0.629233i | \(0.216631\pi\) | |||||||
\(164\) | −6.02371e9 | −0.650229 | ||||||||
\(165\) | 1.42081e8 | 0.0149231 | ||||||||
\(166\) | 8.23309e8 | 0.0841543 | ||||||||
\(167\) | 1.03853e9 | 0.103322 | 0.0516612 | − | 0.998665i | \(-0.483548\pi\) | ||||
0.0516612 | + | 0.998665i | \(0.483548\pi\) | |||||||
\(168\) | 1.18586e7 | 0.00114853 | ||||||||
\(169\) | −9.44814e9 | −0.890956 | ||||||||
\(170\) | −2.36688e8 | −0.0217348 | ||||||||
\(171\) | 6.09235e9 | 0.544882 | ||||||||
\(172\) | 9.45064e9 | 0.823347 | ||||||||
\(173\) | 1.27196e9 | 0.107961 | 0.0539804 | − | 0.998542i | \(-0.482809\pi\) | ||||
0.0539804 | + | 0.998542i | \(0.482809\pi\) | |||||||
\(174\) | −5.78402e7 | −0.00478364 | ||||||||
\(175\) | 2.58974e8 | 0.0208730 | ||||||||
\(176\) | −2.17672e8 | −0.0171000 | ||||||||
\(177\) | −9.81506e8 | −0.0751646 | ||||||||
\(178\) | 2.12301e8 | 0.0158512 | ||||||||
\(179\) | 4.05826e9 | 0.295462 | 0.147731 | − | 0.989028i | \(-0.452803\pi\) | ||||
0.147731 | + | 0.989028i | \(0.452803\pi\) | |||||||
\(180\) | −6.99757e9 | −0.496845 | ||||||||
\(181\) | 1.52164e8 | 0.0105380 | 0.00526900 | − | 0.999986i | \(-0.498323\pi\) | ||||
0.00526900 | + | 0.999986i | \(0.498323\pi\) | |||||||
\(182\) | 4.87029e6 | 0.000329028 0 | ||||||||
\(183\) | 4.88874e9 | 0.322231 | ||||||||
\(184\) | 1.32778e9 | 0.0853975 | ||||||||
\(185\) | −2.00764e10 | −1.26013 | ||||||||
\(186\) | 2.16256e8 | 0.0132483 | ||||||||
\(187\) | 7.10935e7 | 0.00425150 | ||||||||
\(188\) | 5.19639e9 | 0.303383 | ||||||||
\(189\) | −5.69527e7 | −0.00324666 | ||||||||
\(190\) | 2.59411e9 | 0.144410 | ||||||||
\(191\) | −1.40242e10 | −0.762481 | −0.381241 | − | 0.924476i | \(-0.624503\pi\) | ||||
−0.381241 | + | 0.924476i | \(0.624503\pi\) | |||||||
\(192\) | 1.06447e10 | 0.565301 | ||||||||
\(193\) | 8.79613e9 | 0.456335 | 0.228167 | − | 0.973622i | \(-0.426727\pi\) | ||||
0.228167 | + | 0.973622i | \(0.426727\pi\) | |||||||
\(194\) | 1.47471e9 | 0.0747480 | ||||||||
\(195\) | −5.75780e9 | −0.285168 | ||||||||
\(196\) | 2.05831e10 | 0.996228 | ||||||||
\(197\) | −1.58607e10 | −0.750281 | −0.375140 | − | 0.926968i | \(-0.622405\pi\) | ||||
−0.375140 | + | 0.926968i | \(0.622405\pi\) | |||||||
\(198\) | −7.35777e6 | −0.000340214 0 | ||||||||
\(199\) | 1.69260e8 | 0.00765094 | 0.00382547 | − | 0.999993i | \(-0.498782\pi\) | ||||
0.00382547 | + | 0.999993i | \(0.498782\pi\) | |||||||
\(200\) | −3.30132e9 | −0.145899 | ||||||||
\(201\) | −2.29636e10 | −0.992334 | ||||||||
\(202\) | −3.91241e7 | −0.00165334 | ||||||||
\(203\) | 5.72606e7 | 0.00236659 | ||||||||
\(204\) | −3.50139e9 | −0.141548 | ||||||||
\(205\) | 2.46795e10 | 0.975987 | ||||||||
\(206\) | −7.09255e8 | −0.0274410 | ||||||||
\(207\) | −6.37683e9 | −0.241401 | ||||||||
\(208\) | 8.82110e9 | 0.326767 | ||||||||
\(209\) | −7.79188e8 | −0.0282478 | ||||||||
\(210\) | −2.42504e7 | −0.000860461 0 | ||||||||
\(211\) | −3.98459e10 | −1.38393 | −0.691963 | − | 0.721933i | \(-0.743254\pi\) | ||||
−0.691963 | + | 0.721933i | \(0.743254\pi\) | |||||||
\(212\) | 1.82352e10 | 0.620010 | ||||||||
\(213\) | −2.89727e10 | −0.964453 | ||||||||
\(214\) | −1.95291e9 | −0.0636531 | ||||||||
\(215\) | −3.87199e10 | −1.23584 | ||||||||
\(216\) | 7.26015e8 | 0.0226936 | ||||||||
\(217\) | −2.14089e8 | −0.00655428 | ||||||||
\(218\) | −9.21196e8 | −0.0276247 | ||||||||
\(219\) | −3.03407e10 | −0.891307 | ||||||||
\(220\) | 8.94962e8 | 0.0257574 | ||||||||
\(221\) | −2.88104e9 | −0.0812426 | ||||||||
\(222\) | 1.03967e9 | 0.0287281 | ||||||||
\(223\) | 3.61870e10 | 0.979897 | 0.489949 | − | 0.871751i | \(-0.337016\pi\) | ||||
0.489949 | + | 0.871751i | \(0.337016\pi\) | |||||||
\(224\) | 1.12111e8 | 0.00297530 | ||||||||
\(225\) | 1.58550e10 | 0.412426 | ||||||||
\(226\) | 2.07289e9 | 0.0528552 | ||||||||
\(227\) | 3.37796e10 | 0.844381 | 0.422191 | − | 0.906507i | \(-0.361261\pi\) | ||||
0.422191 | + | 0.906507i | \(0.361261\pi\) | |||||||
\(228\) | 3.83754e10 | 0.940472 | ||||||||
\(229\) | −2.50877e10 | −0.602838 | −0.301419 | − | 0.953492i | \(-0.597460\pi\) | ||||
−0.301419 | + | 0.953492i | \(0.597460\pi\) | |||||||
\(230\) | −2.71524e9 | −0.0639784 | ||||||||
\(231\) | 7.28403e6 | 0.000168313 0 | ||||||||
\(232\) | −7.29939e8 | −0.0165421 | ||||||||
\(233\) | 3.91412e10 | 0.870027 | 0.435014 | − | 0.900424i | \(-0.356744\pi\) | ||||
0.435014 | + | 0.900424i | \(0.356744\pi\) | |||||||
\(234\) | 2.98171e8 | 0.00650120 | ||||||||
\(235\) | −2.12899e10 | −0.455375 | ||||||||
\(236\) | −6.18245e9 | −0.129735 | ||||||||
\(237\) | −4.86621e9 | −0.100190 | ||||||||
\(238\) | −1.21342e7 | −0.000245140 0 | ||||||||
\(239\) | 7.66958e10 | 1.52048 | 0.760241 | − | 0.649642i | \(-0.225081\pi\) | ||||
0.760241 | + | 0.649642i | \(0.225081\pi\) | |||||||
\(240\) | −4.39224e10 | −0.854547 | ||||||||
\(241\) | −2.55250e10 | −0.487405 | −0.243702 | − | 0.969850i | \(-0.578362\pi\) | ||||
−0.243702 | + | 0.969850i | \(0.578362\pi\) | |||||||
\(242\) | −3.15031e9 | −0.0590451 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 3.07939e10 | 0.556173 | ||||||||
\(245\) | −8.43303e10 | −1.49533 | ||||||||
\(246\) | −1.27804e9 | −0.0222504 | ||||||||
\(247\) | 3.15763e10 | 0.539790 | ||||||||
\(248\) | 2.72914e9 | 0.0458134 | ||||||||
\(249\) | −4.98998e10 | −0.822625 | ||||||||
\(250\) | 1.29468e9 | 0.0209619 | ||||||||
\(251\) | 1.01377e11 | 1.61215 | 0.806076 | − | 0.591811i | \(-0.201587\pi\) | ||||
0.806076 | + | 0.591811i | \(0.201587\pi\) | |||||||
\(252\) | −3.58742e8 | −0.00560376 | ||||||||
\(253\) | 8.15572e8 | 0.0125147 | ||||||||
\(254\) | 6.73066e9 | 0.101463 | ||||||||
\(255\) | 1.43454e10 | 0.212462 | ||||||||
\(256\) | 6.63348e10 | 0.965298 | ||||||||
\(257\) | −1.07253e10 | −0.153360 | −0.0766799 | − | 0.997056i | \(-0.524432\pi\) | ||||
−0.0766799 | + | 0.997056i | \(0.524432\pi\) | |||||||
\(258\) | 2.00513e9 | 0.0281744 | ||||||||
\(259\) | −1.02925e9 | −0.0142126 | ||||||||
\(260\) | −3.62680e10 | −0.492202 | ||||||||
\(261\) | 3.50563e9 | 0.0467610 | ||||||||
\(262\) | 1.75452e9 | 0.0230039 | ||||||||
\(263\) | −8.11509e10 | −1.04591 | −0.522953 | − | 0.852362i | \(-0.675170\pi\) | ||||
−0.522953 | + | 0.852362i | \(0.675170\pi\) | |||||||
\(264\) | −9.28545e7 | −0.00117648 | ||||||||
\(265\) | −7.47107e10 | −0.930629 | ||||||||
\(266\) | 1.32991e8 | 0.00162876 | ||||||||
\(267\) | −1.28673e10 | −0.154948 | ||||||||
\(268\) | −1.44646e11 | −1.71278 | ||||||||
\(269\) | −1.41843e10 | −0.165166 | −0.0825831 | − | 0.996584i | \(-0.526317\pi\) | ||||
−0.0825831 | + | 0.996584i | \(0.526317\pi\) | |||||||
\(270\) | −1.48467e9 | −0.0170017 | ||||||||
\(271\) | 7.53268e10 | 0.848375 | 0.424188 | − | 0.905574i | \(-0.360560\pi\) | ||||
0.424188 | + | 0.905574i | \(0.360560\pi\) | |||||||
\(272\) | −2.19775e10 | −0.243455 | ||||||||
\(273\) | −2.95183e8 | −0.00321632 | ||||||||
\(274\) | 2.52824e9 | 0.0270982 | ||||||||
\(275\) | −2.02780e9 | −0.0213810 | ||||||||
\(276\) | −4.01673e10 | −0.416660 | ||||||||
\(277\) | −2.76122e10 | −0.281801 | −0.140900 | − | 0.990024i | \(-0.545000\pi\) | ||||
−0.140900 | + | 0.990024i | \(0.545000\pi\) | |||||||
\(278\) | 5.88210e9 | 0.0590651 | ||||||||
\(279\) | −1.31070e10 | −0.129505 | ||||||||
\(280\) | −3.06038e8 | −0.00297553 | ||||||||
\(281\) | −8.87886e10 | −0.849531 | −0.424765 | − | 0.905304i | \(-0.639643\pi\) | ||||
−0.424765 | + | 0.905304i | \(0.639643\pi\) | |||||||
\(282\) | 1.10251e9 | 0.0103816 | ||||||||
\(283\) | −1.21939e10 | −0.113006 | −0.0565032 | − | 0.998402i | \(-0.517995\pi\) | ||||
−0.0565032 | + | 0.998402i | \(0.517995\pi\) | |||||||
\(284\) | −1.82497e11 | −1.66465 | ||||||||
\(285\) | −1.57226e11 | −1.41164 | ||||||||
\(286\) | −3.81349e7 | −0.000337035 0 | ||||||||
\(287\) | 1.26523e9 | 0.0110079 | ||||||||
\(288\) | 6.86368e9 | 0.0587883 | ||||||||
\(289\) | −1.11410e11 | −0.939471 | ||||||||
\(290\) | 1.49269e9 | 0.0123931 | ||||||||
\(291\) | −8.93806e10 | −0.730676 | ||||||||
\(292\) | −1.91114e11 | −1.53840 | ||||||||
\(293\) | 6.57189e10 | 0.520938 | 0.260469 | − | 0.965482i | \(-0.416123\pi\) | ||||
0.260469 | + | 0.965482i | \(0.416123\pi\) | |||||||
\(294\) | 4.36709e9 | 0.0340902 | ||||||||
\(295\) | 2.53299e10 | 0.194730 | ||||||||
\(296\) | 1.31206e10 | 0.0993435 | ||||||||
\(297\) | 4.45946e8 | 0.00332566 | ||||||||
\(298\) | 1.50337e10 | 0.110431 | ||||||||
\(299\) | −3.30508e10 | −0.239145 | ||||||||
\(300\) | 9.98699e10 | 0.711851 | ||||||||
\(301\) | −1.98504e9 | −0.0139386 | ||||||||
\(302\) | −1.35185e9 | −0.00935182 | ||||||||
\(303\) | 2.37127e9 | 0.0161618 | ||||||||
\(304\) | 2.40875e11 | 1.61756 | ||||||||
\(305\) | −1.26164e11 | −0.834810 | ||||||||
\(306\) | −7.42885e8 | −0.00484367 | ||||||||
\(307\) | −1.26973e11 | −0.815808 | −0.407904 | − | 0.913025i | \(-0.633740\pi\) | ||||
−0.407904 | + | 0.913025i | \(0.633740\pi\) | |||||||
\(308\) | 4.58816e7 | 0.000290510 0 | ||||||||
\(309\) | 4.29872e10 | 0.268241 | ||||||||
\(310\) | −5.58095e9 | −0.0343226 | ||||||||
\(311\) | −1.42906e11 | −0.866220 | −0.433110 | − | 0.901341i | \(-0.642584\pi\) | ||||
−0.433110 | + | 0.901341i | \(0.642584\pi\) | |||||||
\(312\) | 3.76289e9 | 0.0224815 | ||||||||
\(313\) | −1.33349e11 | −0.785308 | −0.392654 | − | 0.919686i | \(-0.628443\pi\) | ||||
−0.392654 | + | 0.919686i | \(0.628443\pi\) | |||||||
\(314\) | 7.95426e9 | 0.0461760 | ||||||||
\(315\) | 1.46979e9 | 0.00841118 | ||||||||
\(316\) | −3.06519e10 | −0.172928 | ||||||||
\(317\) | 2.43695e11 | 1.35544 | 0.677718 | − | 0.735322i | \(-0.262969\pi\) | ||||
0.677718 | + | 0.735322i | \(0.262969\pi\) | |||||||
\(318\) | 3.86894e9 | 0.0212163 | ||||||||
\(319\) | −4.48357e8 | −0.00242418 | ||||||||
\(320\) | −2.74711e11 | −1.46454 | ||||||||
\(321\) | 1.18364e11 | 0.622222 | ||||||||
\(322\) | −1.39201e8 | −0.000721592 0 | ||||||||
\(323\) | −7.86716e10 | −0.402167 | ||||||||
\(324\) | −2.19630e10 | −0.110724 | ||||||||
\(325\) | 8.21757e10 | 0.408572 | ||||||||
\(326\) | 1.87225e10 | 0.0918091 | ||||||||
\(327\) | 5.58326e10 | 0.270037 | ||||||||
\(328\) | −1.61288e10 | −0.0769431 | ||||||||
\(329\) | −1.09146e9 | −0.00513603 | ||||||||
\(330\) | 1.89883e8 | 0.000881400 0 | ||||||||
\(331\) | 1.55235e11 | 0.710825 | 0.355413 | − | 0.934710i | \(-0.384340\pi\) | ||||
0.355413 | + | 0.934710i | \(0.384340\pi\) | |||||||
\(332\) | −3.14316e11 | −1.41986 | ||||||||
\(333\) | −6.30132e10 | −0.280823 | ||||||||
\(334\) | 1.38793e9 | 0.00610251 | ||||||||
\(335\) | 5.92625e11 | 2.57086 | ||||||||
\(336\) | −2.25175e9 | −0.00963816 | ||||||||
\(337\) | −1.06540e11 | −0.449963 | −0.224981 | − | 0.974363i | \(-0.572232\pi\) | ||||
−0.224981 | + | 0.974363i | \(0.572232\pi\) | |||||||
\(338\) | −1.26269e10 | −0.0526223 | ||||||||
\(339\) | −1.25635e11 | −0.516670 | ||||||||
\(340\) | 9.03608e10 | 0.366712 | ||||||||
\(341\) | 1.67634e9 | 0.00671378 | ||||||||
\(342\) | 8.14205e9 | 0.0321823 | ||||||||
\(343\) | −8.64789e9 | −0.0337355 | ||||||||
\(344\) | 2.53046e10 | 0.0974286 | ||||||||
\(345\) | 1.64568e11 | 0.625402 | ||||||||
\(346\) | 1.69989e9 | 0.00637646 | ||||||||
\(347\) | −3.12994e11 | −1.15892 | −0.579460 | − | 0.815001i | \(-0.696736\pi\) | ||||
−0.579460 | + | 0.815001i | \(0.696736\pi\) | |||||||
\(348\) | 2.20818e10 | 0.0807099 | ||||||||
\(349\) | 4.73312e11 | 1.70779 | 0.853893 | − | 0.520448i | \(-0.174235\pi\) | ||||
0.853893 | + | 0.520448i | \(0.174235\pi\) | |||||||
\(350\) | 3.46103e8 | 0.00123282 | ||||||||
\(351\) | −1.80718e10 | −0.0635506 | ||||||||
\(352\) | −8.77838e8 | −0.00304770 | ||||||||
\(353\) | −6.70290e10 | −0.229761 | −0.114881 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114881 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(354\) | −1.31172e9 | −0.00443943 | ||||||||
\(355\) | 7.47703e11 | 2.49863 | ||||||||
\(356\) | −8.10504e10 | −0.267442 | ||||||||
\(357\) | 7.35440e8 | 0.00239629 | ||||||||
\(358\) | 5.42361e9 | 0.0174508 | ||||||||
\(359\) | 4.49086e10 | 0.142694 | 0.0713468 | − | 0.997452i | \(-0.477270\pi\) | ||||
0.0713468 | + | 0.997452i | \(0.477270\pi\) | |||||||
\(360\) | −1.87364e10 | −0.0587928 | ||||||||
\(361\) | 5.39557e11 | 1.67207 | ||||||||
\(362\) | 2.03358e8 | 0.000622403 0 | ||||||||
\(363\) | 1.90937e11 | 0.577178 | ||||||||
\(364\) | −1.85934e9 | −0.00555139 | ||||||||
\(365\) | 7.83008e11 | 2.30913 | ||||||||
\(366\) | 6.53350e9 | 0.0190318 | ||||||||
\(367\) | 4.86775e11 | 1.40065 | 0.700327 | − | 0.713822i | \(-0.253037\pi\) | ||||
0.700327 | + | 0.713822i | \(0.253037\pi\) | |||||||
\(368\) | −2.52122e11 | −0.716632 | ||||||||
\(369\) | 7.74607e10 | 0.217502 | ||||||||
\(370\) | −2.68309e10 | −0.0744265 | ||||||||
\(371\) | −3.83016e9 | −0.0104963 | ||||||||
\(372\) | −8.25604e10 | −0.223526 | ||||||||
\(373\) | 4.49243e11 | 1.20169 | 0.600844 | − | 0.799367i | \(-0.294831\pi\) | ||||
0.600844 | + | 0.799367i | \(0.294831\pi\) | |||||||
\(374\) | 9.50120e7 | 0.000251106 0 | ||||||||
\(375\) | −7.84689e10 | −0.204907 | ||||||||
\(376\) | 1.39136e10 | 0.0359000 | ||||||||
\(377\) | 1.81695e10 | 0.0463241 | ||||||||
\(378\) | −7.61138e7 | −0.000191757 0 | ||||||||
\(379\) | −2.57491e11 | −0.641041 | −0.320520 | − | 0.947242i | \(-0.603858\pi\) | ||||
−0.320520 | + | 0.947242i | \(0.603858\pi\) | |||||||
\(380\) | −9.90359e11 | −2.43650 | ||||||||
\(381\) | −4.07938e11 | −0.991817 | ||||||||
\(382\) | −1.87425e10 | −0.0450342 | ||||||||
\(383\) | −2.56704e11 | −0.609591 | −0.304796 | − | 0.952418i | \(-0.598588\pi\) | ||||
−0.304796 | + | 0.952418i | \(0.598588\pi\) | |||||||
\(384\) | 5.76113e10 | 0.135213 | ||||||||
\(385\) | −1.87980e8 | −0.000436052 0 | ||||||||
\(386\) | 1.17555e10 | 0.0269524 | ||||||||
\(387\) | −1.21529e11 | −0.275410 | ||||||||
\(388\) | −5.63003e11 | −1.26115 | ||||||||
\(389\) | −2.78839e10 | −0.0617418 | −0.0308709 | − | 0.999523i | \(-0.509828\pi\) | ||||
−0.0308709 | + | 0.999523i | \(0.509828\pi\) | |||||||
\(390\) | −7.69494e9 | −0.0168428 | ||||||||
\(391\) | 8.23451e10 | 0.178173 | ||||||||
\(392\) | 5.51124e10 | 0.117886 | ||||||||
\(393\) | −1.06339e11 | −0.224868 | ||||||||
\(394\) | −2.11968e10 | −0.0443136 | ||||||||
\(395\) | 1.25583e11 | 0.259563 | ||||||||
\(396\) | 2.80899e9 | 0.00574012 | ||||||||
\(397\) | 5.56039e10 | 0.112344 | 0.0561718 | − | 0.998421i | \(-0.482111\pi\) | ||||
0.0561718 | + | 0.998421i | \(0.482111\pi\) | |||||||
\(398\) | 2.26205e8 | 0.000451886 0 | ||||||||
\(399\) | −8.06046e9 | −0.0159214 | ||||||||
\(400\) | 6.26864e11 | 1.22434 | ||||||||
\(401\) | −3.14865e11 | −0.608100 | −0.304050 | − | 0.952656i | \(-0.598339\pi\) | ||||
−0.304050 | + | 0.952656i | \(0.598339\pi\) | |||||||
\(402\) | −3.06894e10 | −0.0586100 | ||||||||
\(403\) | −6.79330e10 | −0.128295 | ||||||||
\(404\) | 1.49365e10 | 0.0278954 | ||||||||
\(405\) | 8.99840e10 | 0.166195 | ||||||||
\(406\) | 7.65252e7 | 0.000139778 0 | ||||||||
\(407\) | 8.05914e9 | 0.0145584 | ||||||||
\(408\) | −9.37515e9 | −0.0167497 | ||||||||
\(409\) | −7.50752e11 | −1.32660 | −0.663302 | − | 0.748352i | \(-0.730846\pi\) | ||||
−0.663302 | + | 0.748352i | \(0.730846\pi\) | |||||||
\(410\) | 3.29826e10 | 0.0576445 | ||||||||
\(411\) | −1.53234e11 | −0.264890 | ||||||||
\(412\) | 2.70773e11 | 0.462987 | ||||||||
\(413\) | 1.29858e9 | 0.00219630 | ||||||||
\(414\) | −8.52224e9 | −0.0142578 | ||||||||
\(415\) | 1.28777e12 | 2.13119 | ||||||||
\(416\) | 3.55741e10 | 0.0582389 | ||||||||
\(417\) | −3.56508e11 | −0.577373 | ||||||||
\(418\) | −1.04134e9 | −0.00166839 | ||||||||
\(419\) | 7.08699e11 | 1.12331 | 0.561653 | − | 0.827373i | \(-0.310165\pi\) | ||||
0.561653 | + | 0.827373i | \(0.310165\pi\) | |||||||
\(420\) | 9.25810e9 | 0.0145178 | ||||||||
\(421\) | 5.65648e11 | 0.877560 | 0.438780 | − | 0.898594i | \(-0.355411\pi\) | ||||
0.438780 | + | 0.898594i | \(0.355411\pi\) | |||||||
\(422\) | −5.32516e10 | −0.0817385 | ||||||||
\(423\) | −6.68220e10 | −0.101482 | ||||||||
\(424\) | 4.88257e10 | 0.0733672 | ||||||||
\(425\) | −2.04739e11 | −0.304404 | ||||||||
\(426\) | −3.87202e10 | −0.0569633 | ||||||||
\(427\) | −6.46802e9 | −0.00941556 | ||||||||
\(428\) | 7.45565e11 | 1.07396 | ||||||||
\(429\) | 2.31131e9 | 0.00329459 | ||||||||
\(430\) | −5.17467e10 | −0.0729919 | ||||||||
\(431\) | −3.52572e11 | −0.492153 | −0.246076 | − | 0.969250i | \(-0.579141\pi\) | ||||
−0.246076 | + | 0.969250i | \(0.579141\pi\) | |||||||
\(432\) | −1.37858e11 | −0.190438 | ||||||||
\(433\) | 8.77496e10 | 0.119964 | 0.0599818 | − | 0.998199i | \(-0.480896\pi\) | ||||
0.0599818 | + | 0.998199i | \(0.480896\pi\) | |||||||
\(434\) | −2.86116e8 | −0.000387114 0 | ||||||||
\(435\) | −9.04704e10 | −0.121145 | ||||||||
\(436\) | 3.51686e11 | 0.466086 | ||||||||
\(437\) | −9.02506e11 | −1.18381 | ||||||||
\(438\) | −4.05485e10 | −0.0526431 | ||||||||
\(439\) | 3.23555e11 | 0.415775 | 0.207887 | − | 0.978153i | \(-0.433341\pi\) | ||||
0.207887 | + | 0.978153i | \(0.433341\pi\) | |||||||
\(440\) | 2.39631e9 | 0.00304793 | ||||||||
\(441\) | −2.64685e11 | −0.333238 | ||||||||
\(442\) | −3.85033e9 | −0.00479841 | ||||||||
\(443\) | 1.05919e12 | 1.30664 | 0.653319 | − | 0.757083i | \(-0.273376\pi\) | ||||
0.653319 | + | 0.757083i | \(0.273376\pi\) | |||||||
\(444\) | −3.96916e11 | −0.484703 | ||||||||
\(445\) | 3.32069e11 | 0.401428 | ||||||||
\(446\) | 4.83616e10 | 0.0578754 | ||||||||
\(447\) | −9.11176e11 | −1.07949 | ||||||||
\(448\) | −1.40835e10 | −0.0165181 | ||||||||
\(449\) | −4.93194e11 | −0.572676 | −0.286338 | − | 0.958129i | \(-0.592438\pi\) | ||||
−0.286338 | + | 0.958129i | \(0.592438\pi\) | |||||||
\(450\) | 2.11893e10 | 0.0243590 | ||||||||
\(451\) | −9.90692e9 | −0.0112757 | ||||||||
\(452\) | −7.91370e11 | −0.891777 | ||||||||
\(453\) | 8.19339e10 | 0.0914159 | ||||||||
\(454\) | 4.51444e10 | 0.0498715 | ||||||||
\(455\) | 7.61782e9 | 0.00833258 | ||||||||
\(456\) | 1.02752e11 | 0.111288 | ||||||||
\(457\) | −7.63784e11 | −0.819121 | −0.409560 | − | 0.912283i | \(-0.634318\pi\) | ||||
−0.409560 | + | 0.912283i | \(0.634318\pi\) | |||||||
\(458\) | −3.35281e10 | −0.0356053 | ||||||||
\(459\) | 4.50254e10 | 0.0473479 | ||||||||
\(460\) | 1.03660e12 | 1.07945 | ||||||||
\(461\) | −8.27441e11 | −0.853263 | −0.426631 | − | 0.904426i | \(-0.640300\pi\) | ||||
−0.426631 | + | 0.904426i | \(0.640300\pi\) | |||||||
\(462\) | 9.73465e6 | 9.94103e−6 0 | ||||||||
\(463\) | 1.49878e12 | 1.51574 | 0.757869 | − | 0.652407i | \(-0.226241\pi\) | ||||
0.757869 | + | 0.652407i | \(0.226241\pi\) | |||||||
\(464\) | 1.38603e11 | 0.138817 | ||||||||
\(465\) | 3.38255e11 | 0.335511 | ||||||||
\(466\) | 5.23098e10 | 0.0513862 | ||||||||
\(467\) | 4.33053e11 | 0.421323 | 0.210661 | − | 0.977559i | \(-0.432438\pi\) | ||||
0.210661 | + | 0.977559i | \(0.432438\pi\) | |||||||
\(468\) | −1.13833e11 | −0.109689 | ||||||||
\(469\) | 3.03819e10 | 0.0289959 | ||||||||
\(470\) | −2.84527e10 | −0.0268957 | ||||||||
\(471\) | −4.82099e11 | −0.451380 | ||||||||
\(472\) | −1.65538e10 | −0.0153518 | ||||||||
\(473\) | 1.55430e10 | 0.0142778 | ||||||||
\(474\) | −6.50338e9 | −0.00591748 | ||||||||
\(475\) | 2.24395e12 | 2.02251 | ||||||||
\(476\) | 4.63249e9 | 0.00413603 | ||||||||
\(477\) | −2.34492e11 | −0.207394 | ||||||||
\(478\) | 1.02499e11 | 0.0898038 | ||||||||
\(479\) | 1.89550e12 | 1.64518 | 0.822592 | − | 0.568631i | \(-0.192527\pi\) | ||||
0.822592 | + | 0.568631i | \(0.192527\pi\) | |||||||
\(480\) | −1.77132e11 | −0.152304 | ||||||||
\(481\) | −3.26594e11 | −0.278199 | ||||||||
\(482\) | −3.41126e10 | −0.0287875 | ||||||||
\(483\) | 8.43684e9 | 0.00705371 | ||||||||
\(484\) | 1.20270e12 | 0.996214 | ||||||||
\(485\) | 2.30666e12 | 1.89298 | ||||||||
\(486\) | −4.65987e9 | −0.00378888 | ||||||||
\(487\) | 2.33531e12 | 1.88133 | 0.940663 | − | 0.339343i | \(-0.110205\pi\) | ||||
0.940663 | + | 0.339343i | \(0.110205\pi\) | |||||||
\(488\) | 8.24522e10 | 0.0658132 | ||||||||
\(489\) | −1.13475e12 | −0.897452 | ||||||||
\(490\) | −1.12702e11 | −0.0883182 | ||||||||
\(491\) | 1.57618e12 | 1.22388 | 0.611942 | − | 0.790903i | \(-0.290389\pi\) | ||||
0.611942 | + | 0.790903i | \(0.290389\pi\) | |||||||
\(492\) | 4.87920e11 | 0.375410 | ||||||||
\(493\) | −4.52688e10 | −0.0345134 | ||||||||
\(494\) | 4.21998e10 | 0.0318815 | ||||||||
\(495\) | −1.15086e10 | −0.00861586 | ||||||||
\(496\) | −5.18216e11 | −0.384453 | ||||||||
\(497\) | 3.83322e10 | 0.0281812 | ||||||||
\(498\) | −6.66880e10 | −0.0485865 | ||||||||
\(499\) | 1.54552e11 | 0.111589 | 0.0557947 | − | 0.998442i | \(-0.482231\pi\) | ||||
0.0557947 | + | 0.998442i | \(0.482231\pi\) | |||||||
\(500\) | −4.94271e11 | −0.353671 | ||||||||
\(501\) | −8.41208e10 | −0.0596532 | ||||||||
\(502\) | 1.35484e11 | 0.0952182 | ||||||||
\(503\) | −1.11366e12 | −0.775708 | −0.387854 | − | 0.921721i | \(-0.626784\pi\) | ||||
−0.387854 | + | 0.921721i | \(0.626784\pi\) | |||||||
\(504\) | −9.60550e8 | −0.000663106 0 | ||||||||
\(505\) | −6.11957e10 | −0.0418706 | ||||||||
\(506\) | 1.08996e9 | 0.000739152 0 | ||||||||
\(507\) | 7.65299e11 | 0.514394 | ||||||||
\(508\) | −2.56958e12 | −1.71189 | ||||||||
\(509\) | −1.16983e12 | −0.772490 | −0.386245 | − | 0.922396i | \(-0.626228\pi\) | ||||
−0.386245 | + | 0.922396i | \(0.626228\pi\) | |||||||
\(510\) | 1.91717e10 | 0.0125486 | ||||||||
\(511\) | 4.01421e10 | 0.0260439 | ||||||||
\(512\) | 4.52812e11 | 0.291208 | ||||||||
\(513\) | −4.93481e11 | −0.314588 | ||||||||
\(514\) | −1.43337e10 | −0.00905785 | ||||||||
\(515\) | −1.10938e12 | −0.694938 | ||||||||
\(516\) | −7.65502e11 | −0.475360 | ||||||||
\(517\) | 8.54627e9 | 0.00526101 | ||||||||
\(518\) | −1.37553e9 | −0.000839433 0 | ||||||||
\(519\) | −1.03029e11 | −0.0623312 | ||||||||
\(520\) | −9.71095e10 | −0.0582434 | ||||||||
\(521\) | −1.13256e12 | −0.673428 | −0.336714 | − | 0.941607i | \(-0.609315\pi\) | ||||
−0.336714 | + | 0.941607i | \(0.609315\pi\) | |||||||
\(522\) | 4.68506e9 | 0.00276184 | ||||||||
\(523\) | 1.29127e12 | 0.754674 | 0.377337 | − | 0.926076i | \(-0.376840\pi\) | ||||
0.377337 | + | 0.926076i | \(0.376840\pi\) | |||||||
\(524\) | −6.69825e11 | −0.388124 | ||||||||
\(525\) | −2.09769e10 | −0.0120511 | ||||||||
\(526\) | −1.08453e11 | −0.0617741 | ||||||||
\(527\) | 1.69253e11 | 0.0955849 | ||||||||
\(528\) | 1.76315e10 | 0.00987270 | ||||||||
\(529\) | −8.56504e11 | −0.475531 | ||||||||
\(530\) | −9.98462e10 | −0.0549655 | ||||||||
\(531\) | 7.95020e10 | 0.0433963 | ||||||||
\(532\) | −5.07723e10 | −0.0274805 | ||||||||
\(533\) | 4.01475e11 | 0.215469 | ||||||||
\(534\) | −1.71964e10 | −0.00915168 | ||||||||
\(535\) | −3.05463e12 | −1.61200 | ||||||||
\(536\) | −3.87298e11 | −0.202677 | ||||||||
\(537\) | −3.28719e11 | −0.170585 | ||||||||
\(538\) | −1.89564e10 | −0.00975518 | ||||||||
\(539\) | 3.38521e10 | 0.0172757 | ||||||||
\(540\) | 5.66803e11 | 0.286854 | ||||||||
\(541\) | −1.73934e12 | −0.872964 | −0.436482 | − | 0.899713i | \(-0.643776\pi\) | ||||
−0.436482 | + | 0.899713i | \(0.643776\pi\) | |||||||
\(542\) | 1.00670e11 | 0.0501074 | ||||||||
\(543\) | −1.23253e10 | −0.00608412 | ||||||||
\(544\) | −8.86318e10 | −0.0433905 | ||||||||
\(545\) | −1.44088e12 | −0.699590 | ||||||||
\(546\) | −3.94493e8 | −0.000189965 0 | ||||||||
\(547\) | 1.01841e12 | 0.486385 | 0.243193 | − | 0.969978i | \(-0.421805\pi\) | ||||
0.243193 | + | 0.969978i | \(0.421805\pi\) | |||||||
\(548\) | −9.65208e11 | −0.457202 | ||||||||
\(549\) | −3.95988e11 | −0.186040 | ||||||||
\(550\) | −2.71002e9 | −0.00126282 | ||||||||
\(551\) | 4.96148e11 | 0.229313 | ||||||||
\(552\) | −1.07550e11 | −0.0493043 | ||||||||
\(553\) | 6.43821e9 | 0.00292753 | ||||||||
\(554\) | −3.69020e10 | −0.0166439 | ||||||||
\(555\) | 1.62619e12 | 0.727534 | ||||||||
\(556\) | −2.24562e12 | −0.996551 | ||||||||
\(557\) | 2.18895e12 | 0.963578 | 0.481789 | − | 0.876287i | \(-0.339987\pi\) | ||||
0.481789 | + | 0.876287i | \(0.339987\pi\) | |||||||
\(558\) | −1.75167e10 | −0.00764891 | ||||||||
\(559\) | −6.29876e11 | −0.272836 | ||||||||
\(560\) | 5.81113e10 | 0.0249698 | ||||||||
\(561\) | −5.75857e9 | −0.00245461 | ||||||||
\(562\) | −1.18660e11 | −0.0501756 | ||||||||
\(563\) | −3.42758e12 | −1.43780 | −0.718901 | − | 0.695112i | \(-0.755355\pi\) | ||||
−0.718901 | + | 0.695112i | \(0.755355\pi\) | |||||||
\(564\) | −4.20908e11 | −0.175158 | ||||||||
\(565\) | 3.24229e12 | 1.33855 | ||||||||
\(566\) | −1.62964e10 | −0.00667447 | ||||||||
\(567\) | 4.61317e9 | 0.00187446 | ||||||||
\(568\) | −4.88646e11 | −0.196982 | ||||||||
\(569\) | −4.02290e12 | −1.60892 | −0.804460 | − | 0.594007i | \(-0.797545\pi\) | ||||
−0.804460 | + | 0.594007i | \(0.797545\pi\) | |||||||
\(570\) | −2.10123e11 | −0.0833752 | ||||||||
\(571\) | 9.47651e11 | 0.373066 | 0.186533 | − | 0.982449i | \(-0.440275\pi\) | ||||
0.186533 | + | 0.982449i | \(0.440275\pi\) | |||||||
\(572\) | 1.45588e10 | 0.00568648 | ||||||||
\(573\) | 1.13596e12 | 0.440219 | ||||||||
\(574\) | 1.69091e9 | 0.000650154 0 | ||||||||
\(575\) | −2.34873e12 | −0.896039 | ||||||||
\(576\) | −8.62225e11 | −0.326377 | ||||||||
\(577\) | −1.11164e12 | −0.417517 | −0.208759 | − | 0.977967i | \(-0.566942\pi\) | ||||
−0.208759 | + | 0.977967i | \(0.566942\pi\) | |||||||
\(578\) | −1.48892e11 | −0.0554877 | ||||||||
\(579\) | −7.12486e11 | −0.263465 | ||||||||
\(580\) | −5.69867e11 | −0.209097 | ||||||||
\(581\) | 6.60197e10 | 0.0240370 | ||||||||
\(582\) | −1.19452e11 | −0.0431558 | ||||||||
\(583\) | 2.99906e10 | 0.0107517 | ||||||||
\(584\) | −5.11719e11 | −0.182043 | ||||||||
\(585\) | 4.66382e11 | 0.164642 | ||||||||
\(586\) | 8.78292e10 | 0.0307680 | ||||||||
\(587\) | −1.50367e12 | −0.522735 | −0.261368 | − | 0.965239i | \(-0.584174\pi\) | ||||
−0.261368 | + | 0.965239i | \(0.584174\pi\) | |||||||
\(588\) | −1.66723e12 | −0.575172 | ||||||||
\(589\) | −1.85502e12 | −0.635084 | ||||||||
\(590\) | 3.38518e10 | 0.0115013 | ||||||||
\(591\) | 1.28471e12 | 0.433175 | ||||||||
\(592\) | −2.49137e12 | −0.833663 | ||||||||
\(593\) | −2.18166e12 | −0.724504 | −0.362252 | − | 0.932080i | \(-0.617992\pi\) | ||||
−0.362252 | + | 0.932080i | \(0.617992\pi\) | |||||||
\(594\) | 5.95979e8 | 0.000196423 0 | ||||||||
\(595\) | −1.89796e10 | −0.00620813 | ||||||||
\(596\) | −5.73944e12 | −1.86321 | ||||||||
\(597\) | −1.37100e10 | −0.00441727 | ||||||||
\(598\) | −4.41703e10 | −0.0141246 | ||||||||
\(599\) | 1.70673e12 | 0.541681 | 0.270841 | − | 0.962624i | \(-0.412698\pi\) | ||||
0.270841 | + | 0.962624i | \(0.412698\pi\) | |||||||
\(600\) | 2.67407e11 | 0.0842349 | ||||||||
\(601\) | 4.09698e12 | 1.28094 | 0.640470 | − | 0.767983i | \(-0.278740\pi\) | ||||
0.640470 | + | 0.767983i | \(0.278740\pi\) | |||||||
\(602\) | −2.65288e9 | −0.000823252 0 | ||||||||
\(603\) | 1.86005e12 | 0.572924 | ||||||||
\(604\) | 5.16096e11 | 0.157785 | ||||||||
\(605\) | −4.92753e12 | −1.49531 | ||||||||
\(606\) | 3.16905e9 | 0.000954559 0 | ||||||||
\(607\) | −4.05392e12 | −1.21206 | −0.606032 | − | 0.795440i | \(-0.707240\pi\) | ||||
−0.606032 | + | 0.795440i | \(0.707240\pi\) | |||||||
\(608\) | 9.71409e11 | 0.288294 | ||||||||
\(609\) | −4.63811e9 | −0.00136635 | ||||||||
\(610\) | −1.68611e11 | −0.0493062 | ||||||||
\(611\) | −3.46335e11 | −0.100533 | ||||||||
\(612\) | 2.83612e11 | 0.0817229 | ||||||||
\(613\) | 2.62140e12 | 0.749828 | 0.374914 | − | 0.927060i | \(-0.377672\pi\) | ||||
0.374914 | + | 0.927060i | \(0.377672\pi\) | |||||||
\(614\) | −1.69691e11 | −0.0481839 | ||||||||
\(615\) | −1.99904e12 | −0.563487 | ||||||||
\(616\) | 1.22851e8 | 3.43767e−5 0 | ||||||||
\(617\) | −1.92608e11 | −0.0535046 | −0.0267523 | − | 0.999642i | \(-0.508517\pi\) | ||||
−0.0267523 | + | 0.999642i | \(0.508517\pi\) | |||||||
\(618\) | 5.74497e10 | 0.0158431 | ||||||||
\(619\) | 2.14110e12 | 0.586178 | 0.293089 | − | 0.956085i | \(-0.405317\pi\) | ||||
0.293089 | + | 0.956085i | \(0.405317\pi\) | |||||||
\(620\) | 2.13065e12 | 0.579094 | ||||||||
\(621\) | 5.16524e11 | 0.139373 | ||||||||
\(622\) | −1.90985e11 | −0.0511614 | ||||||||
\(623\) | 1.70240e10 | 0.00452758 | ||||||||
\(624\) | −7.14509e11 | −0.188659 | ||||||||
\(625\) | −2.69478e12 | −0.706421 | ||||||||
\(626\) | −1.78213e11 | −0.0463825 | ||||||||
\(627\) | 6.31142e10 | 0.0163089 | ||||||||
\(628\) | −3.03671e12 | −0.779085 | ||||||||
\(629\) | 8.13700e11 | 0.207270 | ||||||||
\(630\) | 1.96428e9 | 0.000496788 0 | ||||||||
\(631\) | 1.85087e12 | 0.464776 | 0.232388 | − | 0.972623i | \(-0.425346\pi\) | ||||
0.232388 | + | 0.972623i | \(0.425346\pi\) | |||||||
\(632\) | −8.20722e10 | −0.0204630 | ||||||||
\(633\) | 3.22752e12 | 0.799010 | ||||||||
\(634\) | 3.25683e11 | 0.0800558 | ||||||||
\(635\) | 1.05277e13 | 2.56952 | ||||||||
\(636\) | −1.47705e12 | −0.357963 | ||||||||
\(637\) | −1.37185e12 | −0.330124 | ||||||||
\(638\) | −5.99201e8 | −0.000143179 0 | ||||||||
\(639\) | 2.34679e12 | 0.556827 | ||||||||
\(640\) | −1.48678e12 | −0.350298 | ||||||||
\(641\) | 2.62055e12 | 0.613099 | 0.306550 | − | 0.951855i | \(-0.400825\pi\) | ||||
0.306550 | + | 0.951855i | \(0.400825\pi\) | |||||||
\(642\) | 1.58186e11 | 0.0367501 | ||||||||
\(643\) | −2.10252e12 | −0.485054 | −0.242527 | − | 0.970145i | \(-0.577976\pi\) | ||||
−0.242527 | + | 0.970145i | \(0.577976\pi\) | |||||||
\(644\) | 5.31431e10 | 0.0121748 | ||||||||
\(645\) | 3.13631e12 | 0.713510 | ||||||||
\(646\) | −1.05140e11 | −0.0237531 | ||||||||
\(647\) | 8.42611e11 | 0.189042 | 0.0945209 | − | 0.995523i | \(-0.469868\pi\) | ||||
0.0945209 | + | 0.995523i | \(0.469868\pi\) | |||||||
\(648\) | −5.88072e10 | −0.0131022 | ||||||||
\(649\) | −1.01680e10 | −0.00224975 | ||||||||
\(650\) | 1.09823e11 | 0.0241314 | ||||||||
\(651\) | 1.73412e10 | 0.00378412 | ||||||||
\(652\) | −7.14774e12 | −1.54901 | ||||||||
\(653\) | 6.38379e12 | 1.37395 | 0.686973 | − | 0.726683i | \(-0.258939\pi\) | ||||
0.686973 | + | 0.726683i | \(0.258939\pi\) | |||||||
\(654\) | 7.46168e10 | 0.0159491 | ||||||||
\(655\) | 2.74431e12 | 0.582570 | ||||||||
\(656\) | 3.06258e12 | 0.645685 | ||||||||
\(657\) | 2.45760e12 | 0.514597 | ||||||||
\(658\) | −1.45867e9 | −0.000303348 0 | ||||||||
\(659\) | −7.01173e12 | −1.44824 | −0.724120 | − | 0.689674i | \(-0.757754\pi\) | ||||
−0.724120 | + | 0.689674i | \(0.757754\pi\) | |||||||
\(660\) | −7.24919e10 | −0.0148711 | ||||||||
\(661\) | −4.26630e12 | −0.869250 | −0.434625 | − | 0.900611i | \(-0.643119\pi\) | ||||
−0.434625 | + | 0.900611i | \(0.643119\pi\) | |||||||
\(662\) | 2.07461e11 | 0.0419833 | ||||||||
\(663\) | 2.33364e11 | 0.0469054 | ||||||||
\(664\) | −8.41598e11 | −0.168015 | ||||||||
\(665\) | 2.08017e11 | 0.0412479 | ||||||||
\(666\) | −8.42133e10 | −0.0165862 | ||||||||
\(667\) | −5.19316e11 | −0.101593 | ||||||||
\(668\) | −5.29872e11 | −0.102962 | ||||||||
\(669\) | −2.93115e12 | −0.565744 | ||||||||
\(670\) | 7.92007e11 | 0.151842 | ||||||||
\(671\) | 5.06453e10 | 0.00964468 | ||||||||
\(672\) | −9.08095e9 | −0.00171779 | ||||||||
\(673\) | 4.19265e12 | 0.787809 | 0.393905 | − | 0.919151i | \(-0.371124\pi\) | ||||
0.393905 | + | 0.919151i | \(0.371124\pi\) | |||||||
\(674\) | −1.42384e11 | −0.0265760 | ||||||||
\(675\) | −1.28426e12 | −0.238114 | ||||||||
\(676\) | 4.82057e12 | 0.887848 | ||||||||
\(677\) | −4.51587e12 | −0.826214 | −0.413107 | − | 0.910682i | \(-0.635557\pi\) | ||||
−0.413107 | + | 0.910682i | \(0.635557\pi\) | |||||||
\(678\) | −1.67904e11 | −0.0305160 | ||||||||
\(679\) | 1.18255e11 | 0.0213503 | ||||||||
\(680\) | 2.41946e11 | 0.0433938 | ||||||||
\(681\) | −2.73615e12 | −0.487504 | ||||||||
\(682\) | 2.24032e9 | 0.000396534 0 | ||||||||
\(683\) | −1.90757e12 | −0.335419 | −0.167709 | − | 0.985836i | \(-0.553637\pi\) | ||||
−0.167709 | + | 0.985836i | \(0.553637\pi\) | |||||||
\(684\) | −3.10840e12 | −0.542982 | ||||||||
\(685\) | 3.95452e12 | 0.686256 | ||||||||
\(686\) | −1.15574e10 | −0.00199251 | ||||||||
\(687\) | 2.03210e12 | 0.348048 | ||||||||
\(688\) | −4.80491e12 | −0.817593 | ||||||||
\(689\) | −1.21536e12 | −0.205455 | ||||||||
\(690\) | 2.19935e11 | 0.0369380 | ||||||||
\(691\) | 9.17365e12 | 1.53070 | 0.765352 | − | 0.643612i | \(-0.222565\pi\) | ||||
0.765352 | + | 0.643612i | \(0.222565\pi\) | |||||||
\(692\) | −6.48971e11 | −0.107584 | ||||||||
\(693\) | −5.90006e8 | −9.71756e−5 0 | ||||||||
\(694\) | −4.18297e11 | −0.0684490 | ||||||||
\(695\) | 9.20044e12 | 1.49581 | ||||||||
\(696\) | 5.91251e10 | 0.00955059 | ||||||||
\(697\) | −1.00026e12 | −0.160534 | ||||||||
\(698\) | 6.32553e11 | 0.100867 | ||||||||
\(699\) | −3.17044e12 | −0.502310 | ||||||||
\(700\) | −1.32132e11 | −0.0208002 | ||||||||
\(701\) | 7.00511e12 | 1.09568 | 0.547840 | − | 0.836583i | \(-0.315450\pi\) | ||||
0.547840 | + | 0.836583i | \(0.315450\pi\) | |||||||
\(702\) | −2.41518e10 | −0.00375347 | ||||||||
\(703\) | −8.91819e12 | −1.37714 | ||||||||
\(704\) | 1.10275e11 | 0.0169200 | ||||||||
\(705\) | 1.72449e12 | 0.262911 | ||||||||
\(706\) | −8.95801e10 | −0.0135703 | ||||||||
\(707\) | −3.13729e9 | −0.000472246 0 | ||||||||
\(708\) | 5.00778e11 | 0.0749024 | ||||||||
\(709\) | 2.04764e12 | 0.304331 | 0.152166 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152166 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(710\) | 9.99259e11 | 0.147576 | ||||||||
\(711\) | 3.94163e11 | 0.0578445 | ||||||||
\(712\) | −2.17017e11 | −0.0316471 | ||||||||
\(713\) | 1.94164e12 | 0.281363 | ||||||||
\(714\) | 9.82870e8 | 0.000141532 0 | ||||||||
\(715\) | −5.96484e10 | −0.00853535 | ||||||||
\(716\) | −2.07058e12 | −0.294431 | ||||||||
\(717\) | −6.21236e12 | −0.877850 | ||||||||
\(718\) | 6.00175e10 | 0.00842788 | ||||||||
\(719\) | −8.05377e12 | −1.12388 | −0.561939 | − | 0.827178i | \(-0.689945\pi\) | ||||
−0.561939 | + | 0.827178i | \(0.689945\pi\) | |||||||
\(720\) | 3.55772e12 | 0.493373 | ||||||||
\(721\) | −5.68739e10 | −0.00783799 | ||||||||
\(722\) | 7.21084e11 | 0.0987571 | ||||||||
\(723\) | 2.06753e12 | 0.281403 | ||||||||
\(724\) | −7.76362e10 | −0.0105012 | ||||||||
\(725\) | 1.29120e12 | 0.173569 | ||||||||
\(726\) | 2.55175e11 | 0.0340897 | ||||||||
\(727\) | −4.54514e12 | −0.603451 | −0.301726 | − | 0.953395i | \(-0.597563\pi\) | ||||
−0.301726 | + | 0.953395i | \(0.597563\pi\) | |||||||
\(728\) | −4.97848e9 | −0.000656909 0 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | 1.04644e12 | 0.136384 | ||||||||
\(731\) | 1.56932e12 | 0.203275 | ||||||||
\(732\) | −2.49430e12 | −0.321107 | ||||||||
\(733\) | 2.35412e12 | 0.301204 | 0.150602 | − | 0.988594i | \(-0.451879\pi\) | ||||
0.150602 | + | 0.988594i | \(0.451879\pi\) | |||||||
\(734\) | 6.50545e11 | 0.0827266 | ||||||||
\(735\) | 6.83076e12 | 0.863328 | ||||||||
\(736\) | −1.01677e12 | −0.127724 | ||||||||
\(737\) | −2.37893e11 | −0.0297015 | ||||||||
\(738\) | 1.03521e11 | 0.0128463 | ||||||||
\(739\) | −6.71592e12 | −0.828335 | −0.414167 | − | 0.910201i | \(-0.635927\pi\) | ||||
−0.414167 | + | 0.910201i | \(0.635927\pi\) | |||||||
\(740\) | 1.02433e13 | 1.25573 | ||||||||
\(741\) | −2.55768e12 | −0.311648 | ||||||||
\(742\) | −5.11878e9 | −0.000619938 0 | ||||||||
\(743\) | 4.74711e12 | 0.571452 | 0.285726 | − | 0.958311i | \(-0.407765\pi\) | ||||
0.285726 | + | 0.958311i | \(0.407765\pi\) | |||||||
\(744\) | −2.21060e11 | −0.0264504 | ||||||||
\(745\) | 2.35149e13 | 2.79666 | ||||||||
\(746\) | 6.00385e11 | 0.0709750 | ||||||||
\(747\) | 4.04189e12 | 0.474943 | ||||||||
\(748\) | −3.62729e10 | −0.00423667 | ||||||||
\(749\) | −1.56600e11 | −0.0181813 | ||||||||
\(750\) | −1.04869e11 | −0.0121024 | ||||||||
\(751\) | 3.17332e12 | 0.364028 | 0.182014 | − | 0.983296i | \(-0.441738\pi\) | ||||
0.182014 | + | 0.983296i | \(0.441738\pi\) | |||||||
\(752\) | −2.64196e12 | −0.301263 | ||||||||
\(753\) | −8.21151e12 | −0.930777 | ||||||||
\(754\) | 2.42824e10 | 0.00273603 | ||||||||
\(755\) | −2.11448e12 | −0.236833 | ||||||||
\(756\) | 2.90581e10 | 0.00323533 | ||||||||
\(757\) | 4.08571e12 | 0.452206 | 0.226103 | − | 0.974103i | \(-0.427401\pi\) | ||||
0.226103 | + | 0.974103i | \(0.427401\pi\) | |||||||
\(758\) | −3.44121e11 | −0.0378616 | ||||||||
\(759\) | −6.60613e10 | −0.00722536 | ||||||||
\(760\) | −2.65174e12 | −0.288317 | ||||||||
\(761\) | 7.13469e12 | 0.771159 | 0.385580 | − | 0.922675i | \(-0.374002\pi\) | ||||
0.385580 | + | 0.922675i | \(0.374002\pi\) | |||||||
\(762\) | −5.45184e11 | −0.0585795 | ||||||||
\(763\) | −7.38691e10 | −0.00789046 | ||||||||
\(764\) | 7.15536e12 | 0.759821 | ||||||||
\(765\) | −1.16198e12 | −0.122665 | ||||||||
\(766\) | −3.43069e11 | −0.0360041 | ||||||||
\(767\) | 4.12054e11 | 0.0429908 | ||||||||
\(768\) | −5.37312e12 | −0.557315 | ||||||||
\(769\) | −1.06805e13 | −1.10134 | −0.550672 | − | 0.834722i | \(-0.685628\pi\) | ||||
−0.550672 | + | 0.834722i | \(0.685628\pi\) | |||||||
\(770\) | −2.51224e8 | −2.57544e−5 0 | ||||||||
\(771\) | 8.68752e11 | 0.0885423 | ||||||||
\(772\) | −4.48791e12 | −0.454743 | ||||||||
\(773\) | 6.56372e12 | 0.661214 | 0.330607 | − | 0.943768i | \(-0.392747\pi\) | ||||
0.330607 | + | 0.943768i | \(0.392747\pi\) | |||||||
\(774\) | −1.62416e11 | −0.0162665 | ||||||||
\(775\) | −4.82761e12 | −0.480700 | ||||||||
\(776\) | −1.50747e12 | −0.149235 | ||||||||
\(777\) | 8.33693e10 | 0.00820563 | ||||||||
\(778\) | −3.72650e10 | −0.00364664 | ||||||||
\(779\) | 1.09629e13 | 1.06662 | ||||||||
\(780\) | 2.93771e12 | 0.284173 | ||||||||
\(781\) | −3.00145e11 | −0.0288670 | ||||||||
\(782\) | 1.10049e11 | 0.0105234 | ||||||||
\(783\) | −2.83956e11 | −0.0269975 | ||||||||
\(784\) | −1.04649e13 | −0.989265 | ||||||||
\(785\) | 1.24416e13 | 1.16940 | ||||||||
\(786\) | −1.42116e11 | −0.0132813 | ||||||||
\(787\) | 1.61828e12 | 0.150372 | 0.0751860 | − | 0.997170i | \(-0.476045\pi\) | ||||
0.0751860 | + | 0.997170i | \(0.476045\pi\) | |||||||
\(788\) | 8.09234e12 | 0.747663 | ||||||||
\(789\) | 6.57322e12 | 0.603854 | ||||||||
\(790\) | 1.67834e11 | 0.0153305 | ||||||||
\(791\) | 1.66221e11 | 0.0150971 | ||||||||
\(792\) | 7.52121e9 | 0.000679242 0 | ||||||||
\(793\) | −2.05238e12 | −0.184302 | ||||||||
\(794\) | 7.43112e10 | 0.00663532 | ||||||||
\(795\) | 6.05157e12 | 0.537299 | ||||||||
\(796\) | −8.63587e10 | −0.00762425 | ||||||||
\(797\) | −1.19360e13 | −1.04784 | −0.523922 | − | 0.851766i | \(-0.675532\pi\) | ||||
−0.523922 | + | 0.851766i | \(0.675532\pi\) | |||||||
\(798\) | −1.07723e10 | −0.000940363 0 | ||||||||
\(799\) | 8.62884e11 | 0.0749017 | ||||||||
\(800\) | 2.52804e12 | 0.218212 | ||||||||
\(801\) | 1.04225e12 | 0.0894595 | ||||||||
\(802\) | −4.20798e11 | −0.0359161 | ||||||||
\(803\) | −3.14317e11 | −0.0266777 | ||||||||
\(804\) | 1.17164e13 | 0.988872 | ||||||||
\(805\) | −2.17731e11 | −0.0182742 | ||||||||
\(806\) | −9.07882e10 | −0.00757743 | ||||||||
\(807\) | 1.14893e12 | 0.0953588 | ||||||||
\(808\) | 3.99932e10 | 0.00330092 | ||||||||
\(809\) | −1.73505e13 | −1.42411 | −0.712054 | − | 0.702124i | \(-0.752235\pi\) | ||||
−0.712054 | + | 0.702124i | \(0.752235\pi\) | |||||||
\(810\) | 1.20258e11 | 0.00981592 | ||||||||
\(811\) | 8.18568e12 | 0.664448 | 0.332224 | − | 0.943201i | \(-0.392201\pi\) | ||||
0.332224 | + | 0.943201i | \(0.392201\pi\) | |||||||
\(812\) | −2.92151e10 | −0.00235834 | ||||||||
\(813\) | −6.10147e12 | −0.489810 | ||||||||
\(814\) | 1.07705e10 | 0.000859860 0 | ||||||||
\(815\) | 2.92847e13 | 2.32505 | ||||||||
\(816\) | 1.78018e12 | 0.140559 | ||||||||
\(817\) | −1.71998e13 | −1.35059 | ||||||||
\(818\) | −1.00333e12 | −0.0783529 | ||||||||
\(819\) | 2.39098e10 | 0.00185694 | ||||||||
\(820\) | −1.25918e13 | −0.972583 | ||||||||
\(821\) | 6.64204e12 | 0.510220 | 0.255110 | − | 0.966912i | \(-0.417888\pi\) | ||||
0.255110 | + | 0.966912i | \(0.417888\pi\) | |||||||
\(822\) | −2.04787e11 | −0.0156451 | ||||||||
\(823\) | 5.51708e11 | 0.0419189 | 0.0209594 | − | 0.999780i | \(-0.493328\pi\) | ||||
0.0209594 | + | 0.999780i | \(0.493328\pi\) | |||||||
\(824\) | 7.25010e11 | 0.0547863 | ||||||||
\(825\) | 1.64252e11 | 0.0123443 | ||||||||
\(826\) | 1.73547e9 | 0.000129720 0 | ||||||||
\(827\) | −1.63550e13 | −1.21584 | −0.607919 | − | 0.793999i | \(-0.707996\pi\) | ||||
−0.607919 | + | 0.793999i | \(0.707996\pi\) | |||||||
\(828\) | 3.25355e12 | 0.240559 | ||||||||
\(829\) | 2.05391e12 | 0.151038 | 0.0755188 | − | 0.997144i | \(-0.475939\pi\) | ||||
0.0755188 | + | 0.997144i | \(0.475939\pi\) | |||||||
\(830\) | 1.72103e12 | 0.125874 | ||||||||
\(831\) | 2.23659e12 | 0.162698 | ||||||||
\(832\) | −4.46886e12 | −0.323327 | ||||||||
\(833\) | 3.41792e12 | 0.245957 | ||||||||
\(834\) | −4.76450e11 | −0.0341013 | ||||||||
\(835\) | 2.17092e12 | 0.154545 | ||||||||
\(836\) | 3.97553e11 | 0.0281492 | ||||||||
\(837\) | 1.06167e12 | 0.0747696 | ||||||||
\(838\) | 9.47131e11 | 0.0663456 | ||||||||
\(839\) | −9.49604e12 | −0.661628 | −0.330814 | − | 0.943696i | \(-0.607323\pi\) | ||||
−0.330814 | + | 0.943696i | \(0.607323\pi\) | |||||||
\(840\) | 2.47891e10 | 0.00171792 | ||||||||
\(841\) | −1.42217e13 | −0.980321 | ||||||||
\(842\) | 7.55953e11 | 0.0518311 | ||||||||
\(843\) | 7.19188e12 | 0.490477 | ||||||||
\(844\) | 2.03300e13 | 1.37910 | ||||||||
\(845\) | −1.97502e13 | −1.33265 | ||||||||
\(846\) | −8.93035e10 | −0.00599379 | ||||||||
\(847\) | −2.52618e11 | −0.0168651 | ||||||||
\(848\) | −9.27116e12 | −0.615677 | ||||||||
\(849\) | 9.87705e11 | 0.0652443 | ||||||||
\(850\) | −2.73621e11 | −0.0179789 | ||||||||
\(851\) | 9.33462e12 | 0.610118 | ||||||||
\(852\) | 1.47823e13 | 0.961089 | ||||||||
\(853\) | −3.90438e12 | −0.252512 | −0.126256 | − | 0.991998i | \(-0.540296\pi\) | ||||
−0.126256 | + | 0.991998i | \(0.540296\pi\) | |||||||
\(854\) | −8.64411e9 | −0.000556109 0 | ||||||||
\(855\) | 1.27353e13 | 0.815010 | ||||||||
\(856\) | 1.99629e12 | 0.127084 | ||||||||
\(857\) | −3.20675e12 | −0.203073 | −0.101536 | − | 0.994832i | \(-0.532376\pi\) | ||||
−0.101536 | + | 0.994832i | \(0.532376\pi\) | |||||||
\(858\) | 3.08892e9 | 0.000194587 0 | ||||||||
\(859\) | −2.54347e13 | −1.59389 | −0.796944 | − | 0.604053i | \(-0.793552\pi\) | ||||
−0.796944 | + | 0.604053i | \(0.793552\pi\) | |||||||
\(860\) | 1.97554e13 | 1.23152 | ||||||||
\(861\) | −1.02484e11 | −0.00635539 | ||||||||
\(862\) | −4.71190e11 | −0.0290679 | ||||||||
\(863\) | −6.71265e12 | −0.411951 | −0.205975 | − | 0.978557i | \(-0.566037\pi\) | ||||
−0.205975 | + | 0.978557i | \(0.566037\pi\) | |||||||
\(864\) | −5.55958e11 | −0.0339414 | ||||||||
\(865\) | 2.65888e12 | 0.161483 | ||||||||
\(866\) | 1.17272e11 | 0.00708538 | ||||||||
\(867\) | 9.02420e12 | 0.542404 | ||||||||
\(868\) | 1.09231e11 | 0.00653142 | ||||||||
\(869\) | −5.04119e10 | −0.00299877 | ||||||||
\(870\) | −1.20908e11 | −0.00715514 | ||||||||
\(871\) | 9.64054e12 | 0.567570 | ||||||||
\(872\) | 9.41659e11 | 0.0551530 | ||||||||
\(873\) | 7.23983e12 | 0.421856 | ||||||||
\(874\) | −1.20614e12 | −0.0699194 | ||||||||
\(875\) | 1.03818e11 | 0.00598736 | ||||||||
\(876\) | 1.54803e13 | 0.888198 | ||||||||
\(877\) | −4.93714e12 | −0.281823 | −0.140912 | − | 0.990022i | \(-0.545003\pi\) | ||||
−0.140912 | + | 0.990022i | \(0.545003\pi\) | |||||||
\(878\) | 4.32412e11 | 0.0245568 | ||||||||
\(879\) | −5.32323e12 | −0.300764 | ||||||||
\(880\) | −4.55018e11 | −0.0255774 | ||||||||
\(881\) | 2.75278e13 | 1.53950 | 0.769750 | − | 0.638345i | \(-0.220381\pi\) | ||||
0.769750 | + | 0.638345i | \(0.220381\pi\) | |||||||
\(882\) | −3.53735e11 | −0.0196820 | ||||||||
\(883\) | 2.27999e13 | 1.26215 | 0.631073 | − | 0.775724i | \(-0.282615\pi\) | ||||
0.631073 | + | 0.775724i | \(0.282615\pi\) | |||||||
\(884\) | 1.46995e12 | 0.0809592 | ||||||||
\(885\) | −2.05172e12 | −0.112428 | ||||||||
\(886\) | 1.41554e12 | 0.0771737 | ||||||||
\(887\) | −3.41001e13 | −1.84969 | −0.924847 | − | 0.380339i | \(-0.875807\pi\) | ||||
−0.924847 | + | 0.380339i | \(0.875807\pi\) | |||||||
\(888\) | −1.06277e12 | −0.0573560 | ||||||||
\(889\) | 5.39720e11 | 0.0289808 | ||||||||
\(890\) | 4.43789e11 | 0.0237095 | ||||||||
\(891\) | −3.61216e10 | −0.00192007 | ||||||||
\(892\) | −1.84631e13 | −0.976479 | ||||||||
\(893\) | −9.45725e12 | −0.497661 | ||||||||
\(894\) | −1.21773e12 | −0.0637576 | ||||||||
\(895\) | 8.48330e12 | 0.441938 | ||||||||
\(896\) | −7.62223e10 | −0.00395090 | ||||||||
\(897\) | 2.67711e12 | 0.138070 | ||||||||
\(898\) | −6.59123e11 | −0.0338239 | ||||||||
\(899\) | −1.06741e12 | −0.0545020 | ||||||||
\(900\) | −8.08946e12 | −0.410987 | ||||||||
\(901\) | 3.02803e12 | 0.153073 | ||||||||
\(902\) | −1.32400e10 | −0.000665975 0 | ||||||||
\(903\) | 1.60788e11 | 0.00804745 | ||||||||
\(904\) | −2.11893e12 | −0.105526 | ||||||||
\(905\) | 3.18080e11 | 0.0157623 | ||||||||
\(906\) | 1.09500e11 | 0.00539927 | ||||||||
\(907\) | 2.77919e12 | 0.136359 | 0.0681797 | − | 0.997673i | \(-0.478281\pi\) | ||||
0.0681797 | + | 0.997673i | \(0.478281\pi\) | |||||||
\(908\) | −1.72348e13 | −0.841436 | ||||||||
\(909\) | −1.92073e11 | −0.00933100 | ||||||||
\(910\) | 1.01807e10 | 0.000492145 0 | ||||||||
\(911\) | −1.37455e13 | −0.661193 | −0.330596 | − | 0.943772i | \(-0.607250\pi\) | ||||
−0.330596 | + | 0.943772i | \(0.607250\pi\) | |||||||
\(912\) | −1.95109e13 | −0.933899 | ||||||||
\(913\) | −5.16941e11 | −0.0246220 | ||||||||
\(914\) | −1.02075e12 | −0.0483795 | ||||||||
\(915\) | 1.02193e13 | 0.481978 | ||||||||
\(916\) | 1.28001e13 | 0.600735 | ||||||||
\(917\) | 1.40692e11 | 0.00657062 | ||||||||
\(918\) | 6.01737e10 | 0.00279650 | ||||||||
\(919\) | 1.00087e13 | 0.462869 | 0.231435 | − | 0.972850i | \(-0.425658\pi\) | ||||
0.231435 | + | 0.972850i | \(0.425658\pi\) | |||||||
\(920\) | 2.77556e12 | 0.127734 | ||||||||
\(921\) | 1.02848e13 | 0.471007 | ||||||||
\(922\) | −1.10582e12 | −0.0503960 | ||||||||
\(923\) | 1.21633e13 | 0.551624 | ||||||||
\(924\) | −3.71641e9 | −0.000167726 0 | ||||||||
\(925\) | −2.32091e13 | −1.04237 | ||||||||
\(926\) | 2.00303e12 | 0.0895237 | ||||||||
\(927\) | −3.48196e12 | −0.154869 | ||||||||
\(928\) | 5.58963e11 | 0.0247410 | ||||||||
\(929\) | 2.63958e13 | 1.16269 | 0.581345 | − | 0.813657i | \(-0.302527\pi\) | ||||
0.581345 | + | 0.813657i | \(0.302527\pi\) | |||||||
\(930\) | 4.52057e11 | 0.0198162 | ||||||||
\(931\) | −3.74605e13 | −1.63418 | ||||||||
\(932\) | −1.99704e13 | −0.866992 | ||||||||
\(933\) | 1.15754e13 | 0.500113 | ||||||||
\(934\) | 5.78748e11 | 0.0248845 | ||||||||
\(935\) | 1.48612e11 | 0.00635920 | ||||||||
\(936\) | −3.04794e11 | −0.0129797 | ||||||||
\(937\) | −3.45669e13 | −1.46498 | −0.732492 | − | 0.680776i | \(-0.761643\pi\) | ||||
−0.732492 | + | 0.680776i | \(0.761643\pi\) | |||||||
\(938\) | 4.06035e10 | 0.00171258 | ||||||||
\(939\) | 1.08013e13 | 0.453398 | ||||||||
\(940\) | 1.08624e13 | 0.453787 | ||||||||
\(941\) | 7.72112e12 | 0.321016 | 0.160508 | − | 0.987035i | \(-0.448687\pi\) | ||||
0.160508 | + | 0.987035i | \(0.448687\pi\) | |||||||
\(942\) | −6.44295e11 | −0.0266597 | ||||||||
\(943\) | −1.14748e13 | −0.472546 | ||||||||
\(944\) | 3.14329e12 | 0.128828 | ||||||||
\(945\) | −1.19053e11 | −0.00485620 | ||||||||
\(946\) | 2.07723e10 | 0.000843286 0 | ||||||||
\(947\) | 3.74173e13 | 1.51181 | 0.755906 | − | 0.654680i | \(-0.227197\pi\) | ||||
0.755906 | + | 0.654680i | \(0.227197\pi\) | |||||||
\(948\) | 2.48281e12 | 0.0998402 | ||||||||
\(949\) | 1.27376e13 | 0.509788 | ||||||||
\(950\) | 2.99889e12 | 0.119455 | ||||||||
\(951\) | −1.97393e13 | −0.782562 | ||||||||
\(952\) | 1.24037e10 | 0.000489425 0 | ||||||||
\(953\) | 1.56325e13 | 0.613918 | 0.306959 | − | 0.951723i | \(-0.400689\pi\) | ||||
0.306959 | + | 0.951723i | \(0.400689\pi\) | |||||||
\(954\) | −3.13384e11 | −0.0122492 | ||||||||
\(955\) | −2.93160e13 | −1.14048 | ||||||||
\(956\) | −3.91313e13 | −1.51518 | ||||||||
\(957\) | 3.63169e10 | 0.00139960 | ||||||||
\(958\) | 2.53322e12 | 0.0971692 | ||||||||
\(959\) | 2.02735e11 | 0.00774006 | ||||||||
\(960\) | 2.22516e13 | 0.845551 | ||||||||
\(961\) | −2.24487e13 | −0.849057 | ||||||||
\(962\) | −4.36472e11 | −0.0164312 | ||||||||
\(963\) | −9.58745e12 | −0.359240 | ||||||||
\(964\) | 1.30232e13 | 0.485705 | ||||||||
\(965\) | 1.83872e13 | 0.682564 | ||||||||
\(966\) | 1.12753e10 | 0.000416612 0 | ||||||||
\(967\) | −1.73605e13 | −0.638475 | −0.319237 | − | 0.947675i | \(-0.603427\pi\) | ||||
−0.319237 | + | 0.947675i | \(0.603427\pi\) | |||||||
\(968\) | 3.22029e12 | 0.117884 | ||||||||
\(969\) | 6.37240e12 | 0.232191 | ||||||||
\(970\) | 3.08271e12 | 0.111805 | ||||||||
\(971\) | −3.63320e13 | −1.31161 | −0.655803 | − | 0.754932i | \(-0.727670\pi\) | ||||
−0.655803 | + | 0.754932i | \(0.727670\pi\) | |||||||
\(972\) | 1.77901e12 | 0.0639262 | ||||||||
\(973\) | 4.71676e11 | 0.0168708 | ||||||||
\(974\) | 3.12099e12 | 0.111116 | ||||||||
\(975\) | −6.65624e12 | −0.235889 | ||||||||
\(976\) | −1.56563e13 | −0.552286 | ||||||||
\(977\) | 1.69592e13 | 0.595498 | 0.297749 | − | 0.954644i | \(-0.403764\pi\) | ||||
0.297749 | + | 0.954644i | \(0.403764\pi\) | |||||||
\(978\) | −1.51653e12 | −0.0530060 | ||||||||
\(979\) | −1.33300e11 | −0.00463776 | ||||||||
\(980\) | 4.30265e13 | 1.49011 | ||||||||
\(981\) | −4.52244e12 | −0.155906 | ||||||||
\(982\) | 2.10647e12 | 0.0722859 | ||||||||
\(983\) | −4.74799e13 | −1.62188 | −0.810941 | − | 0.585128i | \(-0.801044\pi\) | ||||
−0.810941 | + | 0.585128i | \(0.801044\pi\) | |||||||
\(984\) | 1.30643e12 | 0.0444231 | ||||||||
\(985\) | −3.31548e13 | −1.12223 | ||||||||
\(986\) | −6.04989e10 | −0.00203846 | ||||||||
\(987\) | 8.84085e10 | 0.00296529 | ||||||||
\(988\) | −1.61107e13 | −0.537907 | ||||||||
\(989\) | 1.80030e13 | 0.598357 | ||||||||
\(990\) | −1.53805e10 | −0.000508877 0 | ||||||||
\(991\) | −1.07567e13 | −0.354281 | −0.177141 | − | 0.984186i | \(-0.556685\pi\) | ||||
−0.177141 | + | 0.984186i | \(0.556685\pi\) | |||||||
\(992\) | −2.08988e12 | −0.0685203 | ||||||||
\(993\) | −1.25740e13 | −0.410395 | ||||||||
\(994\) | 5.12286e10 | 0.00166446 | ||||||||
\(995\) | 3.53817e11 | 0.0114439 | ||||||||
\(996\) | 2.54596e13 | 0.819755 | ||||||||
\(997\) | −4.06172e13 | −1.30191 | −0.650956 | − | 0.759115i | \(-0.725632\pi\) | ||||
−0.650956 | + | 0.759115i | \(0.725632\pi\) | |||||||
\(998\) | 2.06550e11 | 0.00659078 | ||||||||
\(999\) | 5.10407e12 | 0.162133 |
(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.c.1.12 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.c.1.12 | ✓ | 22 | 1.1 | even | 1 | trivial |