Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,10,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(101.462059724\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −38.2269 | −1.68941 | −0.844703 | − | 0.535235i | \(-0.820223\pi\) | ||||
−0.844703 | + | 0.535235i | \(0.820223\pi\) | |||||||
\(3\) | −153.641 | −1.09512 | −0.547560 | − | 0.836766i | \(-0.684443\pi\) | ||||
−0.547560 | + | 0.836766i | \(0.684443\pi\) | |||||||
\(4\) | 949.295 | 1.85409 | ||||||||
\(5\) | 2107.84 | 1.50825 | 0.754124 | − | 0.656732i | \(-0.228062\pi\) | ||||
0.754124 | + | 0.656732i | \(0.228062\pi\) | |||||||
\(6\) | 5873.22 | 1.85010 | ||||||||
\(7\) | 5202.74 | 0.819013 | 0.409507 | − | 0.912307i | \(-0.365701\pi\) | ||||
0.409507 | + | 0.912307i | \(0.365701\pi\) | |||||||
\(8\) | −16716.4 | −1.44291 | ||||||||
\(9\) | 3922.60 | 0.199289 | ||||||||
\(10\) | −80576.2 | −2.54804 | ||||||||
\(11\) | 14459.1 | 0.297766 | 0.148883 | − | 0.988855i | \(-0.452432\pi\) | ||||
0.148883 | + | 0.988855i | \(0.452432\pi\) | |||||||
\(12\) | −145851. | −2.03045 | ||||||||
\(13\) | −27160.2 | −0.263748 | −0.131874 | − | 0.991267i | \(-0.542099\pi\) | ||||
−0.131874 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(14\) | −198885. | −1.38365 | ||||||||
\(15\) | −323851. | −1.65171 | ||||||||
\(16\) | 152978. | 0.583565 | ||||||||
\(17\) | 305985. | 0.888547 | 0.444274 | − | 0.895891i | \(-0.353462\pi\) | ||||
0.444274 | + | 0.895891i | \(0.353462\pi\) | |||||||
\(18\) | −149949. | −0.336680 | ||||||||
\(19\) | 750970. | 1.32200 | 0.661000 | − | 0.750386i | \(-0.270132\pi\) | ||||
0.661000 | + | 0.750386i | \(0.270132\pi\) | |||||||
\(20\) | 2.00096e6 | 2.79643 | ||||||||
\(21\) | −799355. | −0.896918 | ||||||||
\(22\) | −552727. | −0.503047 | ||||||||
\(23\) | 30312.0 | 0.0225860 | 0.0112930 | − | 0.999936i | \(-0.496405\pi\) | ||||
0.0112930 | + | 0.999936i | \(0.496405\pi\) | |||||||
\(24\) | 2.56833e6 | 1.58016 | ||||||||
\(25\) | 2.48987e6 | 1.27481 | ||||||||
\(26\) | 1.03825e6 | 0.445577 | ||||||||
\(27\) | 2.42145e6 | 0.876875 | ||||||||
\(28\) | 4.93893e6 | 1.51853 | ||||||||
\(29\) | 3.93647e6 | 1.03351 | 0.516757 | − | 0.856132i | \(-0.327139\pi\) | ||||
0.516757 | + | 0.856132i | \(0.327139\pi\) | |||||||
\(30\) | 1.23798e7 | 2.79041 | ||||||||
\(31\) | 952075. | 0.185158 | 0.0925792 | − | 0.995705i | \(-0.470489\pi\) | ||||
0.0925792 | + | 0.995705i | \(0.470489\pi\) | |||||||
\(32\) | 2.71094e6 | 0.457029 | ||||||||
\(33\) | −2.22152e6 | −0.326089 | ||||||||
\(34\) | −1.16969e7 | −1.50112 | ||||||||
\(35\) | 1.09665e7 | 1.23527 | ||||||||
\(36\) | 3.72371e6 | 0.369500 | ||||||||
\(37\) | −267723. | −0.0234843 | −0.0117422 | − | 0.999931i | \(-0.503738\pi\) | ||||
−0.0117422 | + | 0.999931i | \(0.503738\pi\) | |||||||
\(38\) | −2.87072e7 | −2.23339 | ||||||||
\(39\) | 4.17293e6 | 0.288835 | ||||||||
\(40\) | −3.52356e7 | −2.17626 | ||||||||
\(41\) | 1.05316e7 | 0.582056 | 0.291028 | − | 0.956714i | \(-0.406003\pi\) | ||||
0.291028 | + | 0.956714i | \(0.406003\pi\) | |||||||
\(42\) | 3.05568e7 | 1.51526 | ||||||||
\(43\) | 8.50472e6 | 0.379360 | 0.189680 | − | 0.981846i | \(-0.439255\pi\) | ||||
0.189680 | + | 0.981846i | \(0.439255\pi\) | |||||||
\(44\) | 1.37260e7 | 0.552085 | ||||||||
\(45\) | 8.26822e6 | 0.300577 | ||||||||
\(46\) | −1.15873e6 | −0.0381569 | ||||||||
\(47\) | 7.59559e6 | 0.227050 | 0.113525 | − | 0.993535i | \(-0.463786\pi\) | ||||
0.113525 | + | 0.993535i | \(0.463786\pi\) | |||||||
\(48\) | −2.35037e7 | −0.639074 | ||||||||
\(49\) | −1.32851e7 | −0.329218 | ||||||||
\(50\) | −9.51799e7 | −2.15367 | ||||||||
\(51\) | −4.70120e7 | −0.973066 | ||||||||
\(52\) | −2.57831e7 | −0.489012 | ||||||||
\(53\) | 4.98917e7 | 0.868534 | 0.434267 | − | 0.900784i | \(-0.357007\pi\) | ||||
0.434267 | + | 0.900784i | \(0.357007\pi\) | |||||||
\(54\) | −9.25643e7 | −1.48140 | ||||||||
\(55\) | 3.04775e7 | 0.449105 | ||||||||
\(56\) | −8.69712e7 | −1.18176 | ||||||||
\(57\) | −1.15380e8 | −1.44775 | ||||||||
\(58\) | −1.50479e8 | −1.74602 | ||||||||
\(59\) | 6.81953e6 | 0.0732690 | 0.0366345 | − | 0.999329i | \(-0.488336\pi\) | ||||
0.0366345 | + | 0.999329i | \(0.488336\pi\) | |||||||
\(60\) | −3.07430e8 | −3.06243 | ||||||||
\(61\) | 1.19460e8 | 1.10469 | 0.552343 | − | 0.833617i | \(-0.313734\pi\) | ||||
0.552343 | + | 0.833617i | \(0.313734\pi\) | |||||||
\(62\) | −3.63949e7 | −0.312808 | ||||||||
\(63\) | 2.04083e7 | 0.163220 | ||||||||
\(64\) | −1.81955e8 | −1.35567 | ||||||||
\(65\) | −5.72495e7 | −0.397797 | ||||||||
\(66\) | 8.49217e7 | 0.550897 | ||||||||
\(67\) | −5.06638e7 | −0.307157 | −0.153579 | − | 0.988136i | \(-0.549080\pi\) | ||||
−0.153579 | + | 0.988136i | \(0.549080\pi\) | |||||||
\(68\) | 2.90470e8 | 1.64745 | ||||||||
\(69\) | −4.65716e6 | −0.0247344 | ||||||||
\(70\) | −4.19217e8 | −2.08688 | ||||||||
\(71\) | −2.45300e8 | −1.14560 | −0.572802 | − | 0.819694i | \(-0.694144\pi\) | ||||
−0.572802 | + | 0.819694i | \(0.694144\pi\) | |||||||
\(72\) | −6.55719e7 | −0.287555 | ||||||||
\(73\) | 1.17975e8 | 0.486225 | 0.243112 | − | 0.969998i | \(-0.421832\pi\) | ||||
0.243112 | + | 0.969998i | \(0.421832\pi\) | |||||||
\(74\) | 1.02342e7 | 0.0396745 | ||||||||
\(75\) | −3.82546e8 | −1.39607 | ||||||||
\(76\) | 7.12892e8 | 2.45111 | ||||||||
\(77\) | 7.52270e7 | 0.243874 | ||||||||
\(78\) | −1.59518e8 | −0.487960 | ||||||||
\(79\) | 5.16564e8 | 1.49212 | 0.746058 | − | 0.665882i | \(-0.231944\pi\) | ||||
0.746058 | + | 0.665882i | \(0.231944\pi\) | |||||||
\(80\) | 3.22454e8 | 0.880161 | ||||||||
\(81\) | −4.49242e8 | −1.15957 | ||||||||
\(82\) | −4.02589e8 | −0.983330 | ||||||||
\(83\) | 3.97742e7 | 0.0919919 | 0.0459960 | − | 0.998942i | \(-0.485354\pi\) | ||||
0.0459960 | + | 0.998942i | \(0.485354\pi\) | |||||||
\(84\) | −7.58824e8 | −1.66297 | ||||||||
\(85\) | 6.44969e8 | 1.34015 | ||||||||
\(86\) | −3.25109e8 | −0.640893 | ||||||||
\(87\) | −6.04804e8 | −1.13182 | ||||||||
\(88\) | −2.41705e8 | −0.429649 | ||||||||
\(89\) | 1.21044e8 | 0.204498 | 0.102249 | − | 0.994759i | \(-0.467396\pi\) | ||||
0.102249 | + | 0.994759i | \(0.467396\pi\) | |||||||
\(90\) | −3.16068e8 | −0.507796 | ||||||||
\(91\) | −1.41308e8 | −0.216013 | ||||||||
\(92\) | 2.87750e7 | 0.0418765 | ||||||||
\(93\) | −1.46278e8 | −0.202771 | ||||||||
\(94\) | −2.90356e8 | −0.383579 | ||||||||
\(95\) | 1.58293e9 | 1.99390 | ||||||||
\(96\) | −4.16511e8 | −0.500502 | ||||||||
\(97\) | −5.64314e7 | −0.0647214 | −0.0323607 | − | 0.999476i | \(-0.510303\pi\) | ||||
−0.0323607 | + | 0.999476i | \(0.510303\pi\) | |||||||
\(98\) | 5.07849e8 | 0.556182 | ||||||||
\(99\) | 5.67174e7 | 0.0593414 | ||||||||
\(100\) | 2.36362e9 | 2.36362 | ||||||||
\(101\) | −4.08268e8 | −0.390391 | −0.195195 | − | 0.980764i | \(-0.562534\pi\) | ||||
−0.195195 | + | 0.980764i | \(0.562534\pi\) | |||||||
\(102\) | 1.79712e9 | 1.64390 | ||||||||
\(103\) | −6.99257e8 | −0.612166 | −0.306083 | − | 0.952005i | \(-0.599018\pi\) | ||||
−0.306083 | + | 0.952005i | \(0.599018\pi\) | |||||||
\(104\) | 4.54022e8 | 0.380564 | ||||||||
\(105\) | −1.68491e9 | −1.35277 | ||||||||
\(106\) | −1.90720e9 | −1.46731 | ||||||||
\(107\) | −9.08297e8 | −0.669886 | −0.334943 | − | 0.942238i | \(-0.608717\pi\) | ||||
−0.334943 | + | 0.942238i | \(0.608717\pi\) | |||||||
\(108\) | 2.29867e9 | 1.62581 | ||||||||
\(109\) | 1.34403e7 | 0.00911989 | 0.00455994 | − | 0.999990i | \(-0.498549\pi\) | ||||
0.00455994 | + | 0.999990i | \(0.498549\pi\) | |||||||
\(110\) | −1.16506e9 | −0.758720 | ||||||||
\(111\) | 4.11333e7 | 0.0257181 | ||||||||
\(112\) | 7.95905e8 | 0.477948 | ||||||||
\(113\) | −2.36910e7 | −0.0136688 | −0.00683440 | − | 0.999977i | \(-0.502175\pi\) | ||||
−0.00683440 | + | 0.999977i | \(0.502175\pi\) | |||||||
\(114\) | 4.41061e9 | 2.44584 | ||||||||
\(115\) | 6.38928e7 | 0.0340652 | ||||||||
\(116\) | 3.73687e9 | 1.91623 | ||||||||
\(117\) | −1.06539e8 | −0.0525619 | ||||||||
\(118\) | −2.60689e8 | −0.123781 | ||||||||
\(119\) | 1.59196e9 | 0.727732 | ||||||||
\(120\) | 5.41363e9 | 2.38327 | ||||||||
\(121\) | −2.14888e9 | −0.911335 | ||||||||
\(122\) | −4.56659e9 | −1.86626 | ||||||||
\(123\) | −1.61808e9 | −0.637422 | ||||||||
\(124\) | 9.03800e8 | 0.343301 | ||||||||
\(125\) | 1.13137e9 | 0.414484 | ||||||||
\(126\) | −7.80144e8 | −0.275745 | ||||||||
\(127\) | 1.36484e8 | 0.0465547 | 0.0232774 | − | 0.999729i | \(-0.492590\pi\) | ||||
0.0232774 | + | 0.999729i | \(0.492590\pi\) | |||||||
\(128\) | 5.56759e9 | 1.83325 | ||||||||
\(129\) | −1.30667e9 | −0.415445 | ||||||||
\(130\) | 2.18847e9 | 0.672040 | ||||||||
\(131\) | −1.63921e9 | −0.486310 | −0.243155 | − | 0.969987i | \(-0.578182\pi\) | ||||
−0.243155 | + | 0.969987i | \(0.578182\pi\) | |||||||
\(132\) | −2.10887e9 | −0.604600 | ||||||||
\(133\) | 3.90710e9 | 1.08274 | ||||||||
\(134\) | 1.93672e9 | 0.518913 | ||||||||
\(135\) | 5.10402e9 | 1.32255 | ||||||||
\(136\) | −5.11499e9 | −1.28209 | ||||||||
\(137\) | 2.43866e9 | 0.591438 | 0.295719 | − | 0.955275i | \(-0.404441\pi\) | ||||
0.295719 | + | 0.955275i | \(0.404441\pi\) | |||||||
\(138\) | 1.78029e8 | 0.0417864 | ||||||||
\(139\) | −4.13325e9 | −0.939128 | −0.469564 | − | 0.882899i | \(-0.655589\pi\) | ||||
−0.469564 | + | 0.882899i | \(0.655589\pi\) | |||||||
\(140\) | 1.04105e10 | 2.29031 | ||||||||
\(141\) | −1.16700e9 | −0.248647 | ||||||||
\(142\) | 9.37704e9 | 1.93539 | ||||||||
\(143\) | −3.92713e8 | −0.0785351 | ||||||||
\(144\) | 6.00072e8 | 0.116298 | ||||||||
\(145\) | 8.29745e9 | 1.55879 | ||||||||
\(146\) | −4.50982e9 | −0.821431 | ||||||||
\(147\) | 2.04114e9 | 0.360533 | ||||||||
\(148\) | −2.54148e8 | −0.0435421 | ||||||||
\(149\) | −6.01056e9 | −0.999025 | −0.499513 | − | 0.866307i | \(-0.666488\pi\) | ||||
−0.499513 | + | 0.866307i | \(0.666488\pi\) | |||||||
\(150\) | 1.46235e10 | 2.35853 | ||||||||
\(151\) | 1.06469e10 | 1.66658 | 0.833291 | − | 0.552834i | \(-0.186454\pi\) | ||||
0.833291 | + | 0.552834i | \(0.186454\pi\) | |||||||
\(152\) | −1.25535e10 | −1.90752 | ||||||||
\(153\) | 1.20026e9 | 0.177077 | ||||||||
\(154\) | −2.87570e9 | −0.412002 | ||||||||
\(155\) | 2.00682e9 | 0.279265 | ||||||||
\(156\) | 3.96134e9 | 0.535528 | ||||||||
\(157\) | −6.94726e9 | −0.912567 | −0.456284 | − | 0.889834i | \(-0.650820\pi\) | ||||
−0.456284 | + | 0.889834i | \(0.650820\pi\) | |||||||
\(158\) | −1.97466e10 | −2.52079 | ||||||||
\(159\) | −7.66542e9 | −0.951149 | ||||||||
\(160\) | 5.71422e9 | 0.689314 | ||||||||
\(161\) | 1.57705e8 | 0.0184982 | ||||||||
\(162\) | 1.71731e10 | 1.95899 | ||||||||
\(163\) | −9.81379e9 | −1.08891 | −0.544455 | − | 0.838790i | \(-0.683264\pi\) | ||||
−0.544455 | + | 0.838790i | \(0.683264\pi\) | |||||||
\(164\) | 9.99755e9 | 1.07919 | ||||||||
\(165\) | −4.68260e9 | −0.491824 | ||||||||
\(166\) | −1.52044e9 | −0.155412 | ||||||||
\(167\) | 1.52995e10 | 1.52213 | 0.761067 | − | 0.648673i | \(-0.224676\pi\) | ||||
0.761067 | + | 0.648673i | \(0.224676\pi\) | |||||||
\(168\) | 1.33624e10 | 1.29417 | ||||||||
\(169\) | −9.86682e9 | −0.930437 | ||||||||
\(170\) | −2.46551e10 | −2.26406 | ||||||||
\(171\) | 2.94576e9 | 0.263460 | ||||||||
\(172\) | 8.07349e9 | 0.703369 | ||||||||
\(173\) | 1.50390e10 | 1.27647 | 0.638235 | − | 0.769842i | \(-0.279665\pi\) | ||||
0.638235 | + | 0.769842i | \(0.279665\pi\) | |||||||
\(174\) | 2.31198e10 | 1.91211 | ||||||||
\(175\) | 1.29541e10 | 1.04409 | ||||||||
\(176\) | 2.21193e9 | 0.173766 | ||||||||
\(177\) | −1.04776e9 | −0.0802384 | ||||||||
\(178\) | −4.62715e9 | −0.345480 | ||||||||
\(179\) | 2.77580e8 | 0.0202092 | 0.0101046 | − | 0.999949i | \(-0.496784\pi\) | ||||
0.0101046 | + | 0.999949i | \(0.496784\pi\) | |||||||
\(180\) | 7.84898e9 | 0.557297 | ||||||||
\(181\) | −1.00484e10 | −0.695897 | −0.347948 | − | 0.937514i | \(-0.613122\pi\) | ||||
−0.347948 | + | 0.937514i | \(0.613122\pi\) | |||||||
\(182\) | 5.40175e9 | 0.364933 | ||||||||
\(183\) | −1.83540e10 | −1.20976 | ||||||||
\(184\) | −5.06708e8 | −0.0325895 | ||||||||
\(185\) | −5.64317e8 | −0.0354202 | ||||||||
\(186\) | 5.59175e9 | 0.342562 | ||||||||
\(187\) | 4.42428e9 | 0.264579 | ||||||||
\(188\) | 7.21046e9 | 0.420971 | ||||||||
\(189\) | 1.25981e10 | 0.718172 | ||||||||
\(190\) | −6.05103e10 | −3.36851 | ||||||||
\(191\) | −1.52351e10 | −0.828315 | −0.414158 | − | 0.910205i | \(-0.635924\pi\) | ||||
−0.414158 | + | 0.910205i | \(0.635924\pi\) | |||||||
\(192\) | 2.79558e10 | 1.48463 | ||||||||
\(193\) | −3.17609e9 | −0.164772 | −0.0823862 | − | 0.996600i | \(-0.526254\pi\) | ||||
−0.0823862 | + | 0.996600i | \(0.526254\pi\) | |||||||
\(194\) | 2.15720e9 | 0.109341 | ||||||||
\(195\) | 8.79587e9 | 0.435636 | ||||||||
\(196\) | −1.26115e10 | −0.610400 | ||||||||
\(197\) | 1.50614e9 | 0.0712470 | ||||||||
\(198\) | −2.16813e9 | −0.100252 | ||||||||
\(199\) | 1.28543e10 | 0.581044 | 0.290522 | − | 0.956868i | \(-0.406171\pi\) | ||||
0.290522 | + | 0.956868i | \(0.406171\pi\) | |||||||
\(200\) | −4.16217e10 | −1.83944 | ||||||||
\(201\) | 7.78404e9 | 0.336374 | ||||||||
\(202\) | 1.56068e10 | 0.659529 | ||||||||
\(203\) | 2.04804e10 | 0.846461 | ||||||||
\(204\) | −4.46282e10 | −1.80415 | ||||||||
\(205\) | 2.21988e10 | 0.877885 | ||||||||
\(206\) | 2.67304e10 | 1.03420 | ||||||||
\(207\) | 1.18902e8 | 0.00450113 | ||||||||
\(208\) | −4.15492e9 | −0.153914 | ||||||||
\(209\) | 1.08584e10 | 0.393646 | ||||||||
\(210\) | 6.44090e10 | 2.28539 | ||||||||
\(211\) | 3.19945e10 | 1.11123 | 0.555616 | − | 0.831439i | \(-0.312482\pi\) | ||||
0.555616 | + | 0.831439i | \(0.312482\pi\) | |||||||
\(212\) | 4.73619e10 | 1.61034 | ||||||||
\(213\) | 3.76881e10 | 1.25457 | ||||||||
\(214\) | 3.47214e10 | 1.13171 | ||||||||
\(215\) | 1.79266e10 | 0.572169 | ||||||||
\(216\) | −4.04779e10 | −1.26525 | ||||||||
\(217\) | 4.95340e9 | 0.151647 | ||||||||
\(218\) | −5.13781e8 | −0.0154072 | ||||||||
\(219\) | −1.81258e10 | −0.532475 | ||||||||
\(220\) | 2.89322e10 | 0.832682 | ||||||||
\(221\) | −8.31064e9 | −0.234352 | ||||||||
\(222\) | −1.57240e9 | −0.0434484 | ||||||||
\(223\) | 6.58160e10 | 1.78221 | 0.891107 | − | 0.453793i | \(-0.149929\pi\) | ||||
0.891107 | + | 0.453793i | \(0.149929\pi\) | |||||||
\(224\) | 1.41043e10 | 0.374313 | ||||||||
\(225\) | 9.76675e9 | 0.254056 | ||||||||
\(226\) | 9.05634e8 | 0.0230922 | ||||||||
\(227\) | −5.91660e10 | −1.47896 | −0.739479 | − | 0.673179i | \(-0.764928\pi\) | ||||
−0.739479 | + | 0.673179i | \(0.764928\pi\) | |||||||
\(228\) | −1.09530e11 | −2.68426 | ||||||||
\(229\) | −3.32122e10 | −0.798065 | −0.399033 | − | 0.916937i | \(-0.630654\pi\) | ||||
−0.399033 | + | 0.916937i | \(0.630654\pi\) | |||||||
\(230\) | −2.44242e9 | −0.0575500 | ||||||||
\(231\) | −1.15580e10 | −0.267072 | ||||||||
\(232\) | −6.58038e10 | −1.49126 | ||||||||
\(233\) | −1.36784e9 | −0.0304041 | −0.0152021 | − | 0.999884i | \(-0.504839\pi\) | ||||
−0.0152021 | + | 0.999884i | \(0.504839\pi\) | |||||||
\(234\) | 4.07265e9 | 0.0887985 | ||||||||
\(235\) | 1.60103e10 | 0.342447 | ||||||||
\(236\) | 6.47375e9 | 0.135847 | ||||||||
\(237\) | −7.93655e10 | −1.63405 | ||||||||
\(238\) | −6.08558e10 | −1.22943 | ||||||||
\(239\) | −8.40292e10 | −1.66586 | −0.832932 | − | 0.553375i | \(-0.813339\pi\) | ||||
−0.832932 | + | 0.553375i | \(0.813339\pi\) | |||||||
\(240\) | −4.95421e10 | −0.963882 | ||||||||
\(241\) | 5.38143e9 | 0.102759 | 0.0513796 | − | 0.998679i | \(-0.483638\pi\) | ||||
0.0513796 | + | 0.998679i | \(0.483638\pi\) | |||||||
\(242\) | 8.21451e10 | 1.53962 | ||||||||
\(243\) | 2.13608e10 | 0.392997 | ||||||||
\(244\) | 1.13403e11 | 2.04819 | ||||||||
\(245\) | −2.80029e10 | −0.496542 | ||||||||
\(246\) | 6.18542e10 | 1.07686 | ||||||||
\(247\) | −2.03965e10 | −0.348674 | ||||||||
\(248\) | −1.59153e10 | −0.267167 | ||||||||
\(249\) | −6.11095e9 | −0.100742 | ||||||||
\(250\) | −4.32486e10 | −0.700232 | ||||||||
\(251\) | −5.96891e10 | −0.949212 | −0.474606 | − | 0.880198i | \(-0.657409\pi\) | ||||
−0.474606 | + | 0.880198i | \(0.657409\pi\) | |||||||
\(252\) | 1.93735e10 | 0.302625 | ||||||||
\(253\) | 4.38284e8 | 0.00672533 | ||||||||
\(254\) | −5.21734e9 | −0.0786498 | ||||||||
\(255\) | −9.90937e10 | −1.46763 | ||||||||
\(256\) | −1.19671e11 | −1.74144 | ||||||||
\(257\) | −1.06712e11 | −1.52585 | −0.762926 | − | 0.646486i | \(-0.776238\pi\) | ||||
−0.762926 | + | 0.646486i | \(0.776238\pi\) | |||||||
\(258\) | 4.99501e10 | 0.701855 | ||||||||
\(259\) | −1.39289e9 | −0.0192340 | ||||||||
\(260\) | −5.43466e10 | −0.737552 | ||||||||
\(261\) | 1.54412e10 | 0.205968 | ||||||||
\(262\) | 6.26619e10 | 0.821576 | ||||||||
\(263\) | 1.62217e10 | 0.209072 | 0.104536 | − | 0.994521i | \(-0.466664\pi\) | ||||
0.104536 | + | 0.994521i | \(0.466664\pi\) | |||||||
\(264\) | 3.71358e10 | 0.470517 | ||||||||
\(265\) | 1.05164e11 | 1.30996 | ||||||||
\(266\) | −1.49356e11 | −1.82918 | ||||||||
\(267\) | −1.85974e10 | −0.223950 | ||||||||
\(268\) | −4.80949e10 | −0.569498 | ||||||||
\(269\) | −1.05738e11 | −1.23125 | −0.615624 | − | 0.788040i | \(-0.711096\pi\) | ||||
−0.615624 | + | 0.788040i | \(0.711096\pi\) | |||||||
\(270\) | −1.95111e11 | −2.23432 | ||||||||
\(271\) | 1.03622e11 | 1.16705 | 0.583527 | − | 0.812094i | \(-0.301672\pi\) | ||||
0.583527 | + | 0.812094i | \(0.301672\pi\) | |||||||
\(272\) | 4.68091e10 | 0.518525 | ||||||||
\(273\) | 2.17107e10 | 0.236560 | ||||||||
\(274\) | −9.32225e10 | −0.999179 | ||||||||
\(275\) | 3.60013e10 | 0.379595 | ||||||||
\(276\) | −4.42102e9 | −0.0458598 | ||||||||
\(277\) | 1.03616e11 | 1.05747 | 0.528734 | − | 0.848788i | \(-0.322667\pi\) | ||||
0.528734 | + | 0.848788i | \(0.322667\pi\) | |||||||
\(278\) | 1.58001e11 | 1.58657 | ||||||||
\(279\) | 3.73461e9 | 0.0369000 | ||||||||
\(280\) | −1.83321e11 | −1.78239 | ||||||||
\(281\) | −4.10264e10 | −0.392541 | −0.196271 | − | 0.980550i | \(-0.562883\pi\) | ||||
−0.196271 | + | 0.980550i | \(0.562883\pi\) | |||||||
\(282\) | 4.46106e10 | 0.420066 | ||||||||
\(283\) | 8.45522e9 | 0.0783584 | 0.0391792 | − | 0.999232i | \(-0.487526\pi\) | ||||
0.0391792 | + | 0.999232i | \(0.487526\pi\) | |||||||
\(284\) | −2.32862e11 | −2.12405 | ||||||||
\(285\) | −2.43202e11 | −2.18356 | ||||||||
\(286\) | 1.50122e10 | 0.132678 | ||||||||
\(287\) | 5.47929e10 | 0.476712 | ||||||||
\(288\) | 1.06339e10 | 0.0910808 | ||||||||
\(289\) | −2.49608e10 | −0.210483 | ||||||||
\(290\) | −3.17186e11 | −2.63344 | ||||||||
\(291\) | 8.67018e9 | 0.0708777 | ||||||||
\(292\) | 1.11993e11 | 0.901505 | ||||||||
\(293\) | 7.16759e10 | 0.568158 | 0.284079 | − | 0.958801i | \(-0.408312\pi\) | ||||
0.284079 | + | 0.958801i | \(0.408312\pi\) | |||||||
\(294\) | −7.80265e10 | −0.609086 | ||||||||
\(295\) | 1.43745e10 | 0.110508 | ||||||||
\(296\) | 4.47537e9 | 0.0338857 | ||||||||
\(297\) | 3.50120e10 | 0.261104 | ||||||||
\(298\) | 2.29765e11 | 1.68776 | ||||||||
\(299\) | −8.23280e8 | −0.00595700 | ||||||||
\(300\) | −3.63149e11 | −2.58845 | ||||||||
\(301\) | 4.42478e10 | 0.310701 | ||||||||
\(302\) | −4.06998e11 | −2.81553 | ||||||||
\(303\) | 6.27268e10 | 0.427525 | ||||||||
\(304\) | 1.14882e11 | 0.771473 | ||||||||
\(305\) | 2.51803e11 | 1.66614 | ||||||||
\(306\) | −4.58822e10 | −0.299156 | ||||||||
\(307\) | 1.84404e11 | 1.18481 | 0.592404 | − | 0.805641i | \(-0.298179\pi\) | ||||
0.592404 | + | 0.805641i | \(0.298179\pi\) | |||||||
\(308\) | 7.14127e10 | 0.452165 | ||||||||
\(309\) | 1.07435e11 | 0.670395 | ||||||||
\(310\) | −7.67146e10 | −0.471792 | ||||||||
\(311\) | −6.53057e9 | −0.0395849 | −0.0197924 | − | 0.999804i | \(-0.506301\pi\) | ||||
−0.0197924 | + | 0.999804i | \(0.506301\pi\) | |||||||
\(312\) | −6.97565e10 | −0.416763 | ||||||||
\(313\) | 2.62007e11 | 1.54299 | 0.771495 | − | 0.636235i | \(-0.219509\pi\) | ||||
0.771495 | + | 0.636235i | \(0.219509\pi\) | |||||||
\(314\) | 2.65572e11 | 1.54170 | ||||||||
\(315\) | 4.30174e10 | 0.246176 | ||||||||
\(316\) | 4.90372e11 | 2.76652 | ||||||||
\(317\) | −1.33176e11 | −0.740727 | −0.370363 | − | 0.928887i | \(-0.620767\pi\) | ||||
−0.370363 | + | 0.928887i | \(0.620767\pi\) | |||||||
\(318\) | 2.93025e11 | 1.60688 | ||||||||
\(319\) | 5.69179e10 | 0.307745 | ||||||||
\(320\) | −3.83533e11 | −2.04469 | ||||||||
\(321\) | 1.39552e11 | 0.733606 | ||||||||
\(322\) | −6.02858e9 | −0.0312510 | ||||||||
\(323\) | 2.29786e11 | 1.17466 | ||||||||
\(324\) | −4.26463e11 | −2.14995 | ||||||||
\(325\) | −6.76254e10 | −0.336229 | ||||||||
\(326\) | 3.75151e11 | 1.83961 | ||||||||
\(327\) | −2.06498e9 | −0.00998738 | ||||||||
\(328\) | −1.76050e11 | −0.839854 | ||||||||
\(329\) | 3.95179e10 | 0.185957 | ||||||||
\(330\) | 1.79001e11 | 0.830890 | ||||||||
\(331\) | 2.27005e11 | 1.03946 | 0.519732 | − | 0.854329i | \(-0.326032\pi\) | ||||
0.519732 | + | 0.854329i | \(0.326032\pi\) | |||||||
\(332\) | 3.77574e10 | 0.170561 | ||||||||
\(333\) | −1.05017e9 | −0.00468016 | ||||||||
\(334\) | −5.84852e11 | −2.57150 | ||||||||
\(335\) | −1.06791e11 | −0.463269 | ||||||||
\(336\) | −1.22284e11 | −0.523410 | ||||||||
\(337\) | −7.17572e9 | −0.0303062 | −0.0151531 | − | 0.999885i | \(-0.504824\pi\) | ||||
−0.0151531 | + | 0.999885i | \(0.504824\pi\) | |||||||
\(338\) | 3.77178e11 | 1.57189 | ||||||||
\(339\) | 3.63991e9 | 0.0149690 | ||||||||
\(340\) | 6.12265e11 | 2.48476 | ||||||||
\(341\) | 1.37662e10 | 0.0551339 | ||||||||
\(342\) | −1.12607e11 | −0.445090 | ||||||||
\(343\) | −2.79068e11 | −1.08865 | ||||||||
\(344\) | −1.42169e11 | −0.547382 | ||||||||
\(345\) | −9.81656e9 | −0.0373055 | ||||||||
\(346\) | −5.74893e11 | −2.15648 | ||||||||
\(347\) | 8.58364e10 | 0.317826 | 0.158913 | − | 0.987293i | \(-0.449201\pi\) | ||||
0.158913 | + | 0.987293i | \(0.449201\pi\) | |||||||
\(348\) | −5.74137e11 | −2.09850 | ||||||||
\(349\) | 1.96745e11 | 0.709888 | 0.354944 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354944 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(350\) | −4.95196e11 | −1.76389 | ||||||||
\(351\) | −6.57671e10 | −0.231274 | ||||||||
\(352\) | 3.91977e10 | 0.136088 | ||||||||
\(353\) | 5.13579e11 | 1.76044 | 0.880219 | − | 0.474567i | \(-0.157395\pi\) | ||||
0.880219 | + | 0.474567i | \(0.157395\pi\) | |||||||
\(354\) | 4.00526e10 | 0.135555 | ||||||||
\(355\) | −5.17053e11 | −1.72785 | ||||||||
\(356\) | 1.14907e11 | 0.379159 | ||||||||
\(357\) | −2.44591e11 | −0.796954 | ||||||||
\(358\) | −1.06110e10 | −0.0341416 | ||||||||
\(359\) | 1.92052e11 | 0.610229 | 0.305115 | − | 0.952316i | \(-0.401305\pi\) | ||||
0.305115 | + | 0.952316i | \(0.401305\pi\) | |||||||
\(360\) | −1.38215e11 | −0.433705 | ||||||||
\(361\) | 2.41268e11 | 0.747684 | ||||||||
\(362\) | 3.84120e11 | 1.17565 | ||||||||
\(363\) | 3.30157e11 | 0.998022 | ||||||||
\(364\) | −1.34143e11 | −0.400508 | ||||||||
\(365\) | 2.48672e11 | 0.733347 | ||||||||
\(366\) | 7.01616e11 | 2.04378 | ||||||||
\(367\) | −7.10357e10 | −0.204399 | −0.102200 | − | 0.994764i | \(-0.532588\pi\) | ||||
−0.102200 | + | 0.994764i | \(0.532588\pi\) | |||||||
\(368\) | 4.63707e9 | 0.0131804 | ||||||||
\(369\) | 4.13111e10 | 0.115997 | ||||||||
\(370\) | 2.15721e10 | 0.0598390 | ||||||||
\(371\) | 2.59573e11 | 0.711341 | ||||||||
\(372\) | −1.38861e11 | −0.375956 | ||||||||
\(373\) | 5.97727e11 | 1.59887 | 0.799435 | − | 0.600753i | \(-0.205132\pi\) | ||||
0.799435 | + | 0.600753i | \(0.205132\pi\) | |||||||
\(374\) | −1.69127e11 | −0.446981 | ||||||||
\(375\) | −1.73824e11 | −0.453910 | ||||||||
\(376\) | −1.26971e11 | −0.327612 | ||||||||
\(377\) | −1.06916e11 | −0.272587 | ||||||||
\(378\) | −4.81588e11 | −1.21328 | ||||||||
\(379\) | 6.94367e11 | 1.72867 | 0.864336 | − | 0.502914i | \(-0.167739\pi\) | ||||
0.864336 | + | 0.502914i | \(0.167739\pi\) | |||||||
\(380\) | 1.50266e12 | 3.69688 | ||||||||
\(381\) | −2.09695e10 | −0.0509830 | ||||||||
\(382\) | 5.82391e11 | 1.39936 | ||||||||
\(383\) | −2.01772e11 | −0.479145 | −0.239572 | − | 0.970879i | \(-0.577007\pi\) | ||||
−0.239572 | + | 0.970879i | \(0.577007\pi\) | |||||||
\(384\) | −8.55411e11 | −2.00763 | ||||||||
\(385\) | 1.58567e11 | 0.367823 | ||||||||
\(386\) | 1.21412e11 | 0.278367 | ||||||||
\(387\) | 3.33606e10 | 0.0756022 | ||||||||
\(388\) | −5.35701e10 | −0.119999 | ||||||||
\(389\) | 3.61861e9 | 0.00801250 | 0.00400625 | − | 0.999992i | \(-0.498725\pi\) | ||||
0.00400625 | + | 0.999992i | \(0.498725\pi\) | |||||||
\(390\) | −3.36239e11 | −0.735965 | ||||||||
\(391\) | 9.27502e9 | 0.0200687 | ||||||||
\(392\) | 2.22080e11 | 0.475031 | ||||||||
\(393\) | 2.51850e11 | 0.532569 | ||||||||
\(394\) | −5.75750e10 | −0.120365 | ||||||||
\(395\) | 1.08883e12 | 2.25048 | ||||||||
\(396\) | 5.38415e10 | 0.110024 | ||||||||
\(397\) | 5.85838e11 | 1.18364 | 0.591821 | − | 0.806069i | \(-0.298409\pi\) | ||||
0.591821 | + | 0.806069i | \(0.298409\pi\) | |||||||
\(398\) | −4.91379e11 | −0.981619 | ||||||||
\(399\) | −6.00291e11 | −1.18573 | ||||||||
\(400\) | 3.80895e11 | 0.743936 | ||||||||
\(401\) | 5.63448e11 | 1.08819 | 0.544094 | − | 0.839024i | \(-0.316873\pi\) | ||||
0.544094 | + | 0.839024i | \(0.316873\pi\) | |||||||
\(402\) | −2.97560e11 | −0.568272 | ||||||||
\(403\) | −2.58586e10 | −0.0488351 | ||||||||
\(404\) | −3.87567e11 | −0.723821 | ||||||||
\(405\) | −9.46931e11 | −1.74892 | ||||||||
\(406\) | −7.82903e11 | −1.43002 | ||||||||
\(407\) | −3.87104e9 | −0.00699283 | ||||||||
\(408\) | 7.85872e11 | 1.40405 | ||||||||
\(409\) | −1.05392e12 | −1.86232 | −0.931161 | − | 0.364608i | \(-0.881203\pi\) | ||||
−0.931161 | + | 0.364608i | \(0.881203\pi\) | |||||||
\(410\) | −8.48592e11 | −1.48310 | ||||||||
\(411\) | −3.74679e11 | −0.647696 | ||||||||
\(412\) | −6.63801e11 | −1.13501 | ||||||||
\(413\) | 3.54802e10 | 0.0600083 | ||||||||
\(414\) | −4.54524e9 | −0.00760423 | ||||||||
\(415\) | 8.38376e10 | 0.138747 | ||||||||
\(416\) | −7.36297e10 | −0.120540 | ||||||||
\(417\) | 6.35037e11 | 1.02846 | ||||||||
\(418\) | −4.15082e11 | −0.665029 | ||||||||
\(419\) | 3.21361e11 | 0.509367 | 0.254683 | − | 0.967025i | \(-0.418029\pi\) | ||||
0.254683 | + | 0.967025i | \(0.418029\pi\) | |||||||
\(420\) | −1.59948e12 | −2.50817 | ||||||||
\(421\) | −9.38143e11 | −1.45546 | −0.727729 | − | 0.685865i | \(-0.759424\pi\) | ||||
−0.727729 | + | 0.685865i | \(0.759424\pi\) | |||||||
\(422\) | −1.22305e12 | −1.87732 | ||||||||
\(423\) | 2.97945e10 | 0.0452485 | ||||||||
\(424\) | −8.34011e11 | −1.25321 | ||||||||
\(425\) | 7.61863e11 | 1.13273 | ||||||||
\(426\) | −1.44070e12 | −2.11948 | ||||||||
\(427\) | 6.21520e11 | 0.904752 | ||||||||
\(428\) | −8.62242e11 | −1.24203 | ||||||||
\(429\) | 6.03369e10 | 0.0860054 | ||||||||
\(430\) | −6.85278e11 | −0.966626 | ||||||||
\(431\) | 9.37611e11 | 1.30881 | 0.654403 | − | 0.756146i | \(-0.272920\pi\) | ||||
0.654403 | + | 0.756146i | \(0.272920\pi\) | |||||||
\(432\) | 3.70428e11 | 0.511714 | ||||||||
\(433\) | 7.64066e11 | 1.04456 | 0.522282 | − | 0.852773i | \(-0.325081\pi\) | ||||
0.522282 | + | 0.852773i | \(0.325081\pi\) | |||||||
\(434\) | −1.89353e11 | −0.256194 | ||||||||
\(435\) | −1.27483e12 | −1.70707 | ||||||||
\(436\) | 1.27588e10 | 0.0169091 | ||||||||
\(437\) | 2.27634e10 | 0.0298586 | ||||||||
\(438\) | 6.92893e11 | 0.899566 | ||||||||
\(439\) | −2.67401e10 | −0.0343616 | −0.0171808 | − | 0.999852i | \(-0.505469\pi\) | ||||
−0.0171808 | + | 0.999852i | \(0.505469\pi\) | |||||||
\(440\) | −5.09476e11 | −0.648017 | ||||||||
\(441\) | −5.21122e10 | −0.0656094 | ||||||||
\(442\) | 3.17690e11 | 0.395916 | ||||||||
\(443\) | −2.85059e10 | −0.0351656 | −0.0175828 | − | 0.999845i | \(-0.505597\pi\) | ||||
−0.0175828 | + | 0.999845i | \(0.505597\pi\) | |||||||
\(444\) | 3.90476e10 | 0.0476838 | ||||||||
\(445\) | 2.55142e11 | 0.308434 | ||||||||
\(446\) | −2.51594e12 | −3.01088 | ||||||||
\(447\) | 9.23469e11 | 1.09405 | ||||||||
\(448\) | −9.46666e11 | −1.11031 | ||||||||
\(449\) | −1.51978e12 | −1.76471 | −0.882353 | − | 0.470589i | \(-0.844042\pi\) | ||||
−0.882353 | + | 0.470589i | \(0.844042\pi\) | |||||||
\(450\) | −3.73353e11 | −0.429203 | ||||||||
\(451\) | 1.52277e11 | 0.173317 | ||||||||
\(452\) | −2.24898e10 | −0.0253432 | ||||||||
\(453\) | −1.63580e12 | −1.82511 | ||||||||
\(454\) | 2.26173e12 | 2.49856 | ||||||||
\(455\) | −2.97854e11 | −0.325801 | ||||||||
\(456\) | 1.92874e12 | 2.08897 | ||||||||
\(457\) | 5.95490e11 | 0.638633 | 0.319317 | − | 0.947648i | \(-0.396547\pi\) | ||||
0.319317 | + | 0.947648i | \(0.396547\pi\) | |||||||
\(458\) | 1.26960e12 | 1.34826 | ||||||||
\(459\) | 7.40927e11 | 0.779145 | ||||||||
\(460\) | 6.06531e10 | 0.0631601 | ||||||||
\(461\) | −1.24624e12 | −1.28513 | −0.642565 | − | 0.766231i | \(-0.722130\pi\) | ||||
−0.642565 | + | 0.766231i | \(0.722130\pi\) | |||||||
\(462\) | 4.41825e11 | 0.451192 | ||||||||
\(463\) | 1.26834e12 | 1.28269 | 0.641346 | − | 0.767252i | \(-0.278376\pi\) | ||||
0.641346 | + | 0.767252i | \(0.278376\pi\) | |||||||
\(464\) | 6.02194e11 | 0.603122 | ||||||||
\(465\) | −3.08330e11 | −0.305829 | ||||||||
\(466\) | 5.22881e10 | 0.0513649 | ||||||||
\(467\) | −7.05768e11 | −0.686651 | −0.343325 | − | 0.939217i | \(-0.611553\pi\) | ||||
−0.343325 | + | 0.939217i | \(0.611553\pi\) | |||||||
\(468\) | −1.01137e11 | −0.0974547 | ||||||||
\(469\) | −2.63590e11 | −0.251566 | ||||||||
\(470\) | −6.12024e11 | −0.578533 | ||||||||
\(471\) | 1.06738e12 | 0.999371 | ||||||||
\(472\) | −1.13998e11 | −0.105720 | ||||||||
\(473\) | 1.22971e11 | 0.112961 | ||||||||
\(474\) | 3.03390e12 | 2.76057 | ||||||||
\(475\) | 1.86982e12 | 1.68530 | ||||||||
\(476\) | 1.51124e12 | 1.34928 | ||||||||
\(477\) | 1.95705e11 | 0.173089 | ||||||||
\(478\) | 3.21217e12 | 2.81432 | ||||||||
\(479\) | 1.12193e12 | 0.973768 | 0.486884 | − | 0.873467i | \(-0.338133\pi\) | ||||
0.486884 | + | 0.873467i | \(0.338133\pi\) | |||||||
\(480\) | −8.77939e11 | −0.754882 | ||||||||
\(481\) | 7.27142e9 | 0.00619393 | ||||||||
\(482\) | −2.05715e11 | −0.173602 | ||||||||
\(483\) | −2.42300e10 | −0.0202578 | ||||||||
\(484\) | −2.03992e12 | −1.68970 | ||||||||
\(485\) | −1.18948e11 | −0.0976159 | ||||||||
\(486\) | −8.16556e11 | −0.663931 | ||||||||
\(487\) | 8.32354e11 | 0.670545 | 0.335272 | − | 0.942121i | \(-0.391172\pi\) | ||||
0.335272 | + | 0.942121i | \(0.391172\pi\) | |||||||
\(488\) | −1.99695e12 | −1.59396 | ||||||||
\(489\) | 1.50780e12 | 1.19249 | ||||||||
\(490\) | 1.07046e12 | 0.838861 | ||||||||
\(491\) | 1.54507e12 | 1.19973 | 0.599863 | − | 0.800103i | \(-0.295222\pi\) | ||||
0.599863 | + | 0.800103i | \(0.295222\pi\) | |||||||
\(492\) | −1.53604e12 | −1.18184 | ||||||||
\(493\) | 1.20450e12 | 0.918326 | ||||||||
\(494\) | 7.79696e11 | 0.589053 | ||||||||
\(495\) | 1.19551e11 | 0.0895015 | ||||||||
\(496\) | 1.45647e11 | 0.108052 | ||||||||
\(497\) | −1.27623e12 | −0.938264 | ||||||||
\(498\) | 2.33603e11 | 0.170194 | ||||||||
\(499\) | 1.13614e12 | 0.820310 | 0.410155 | − | 0.912016i | \(-0.365475\pi\) | ||||
0.410155 | + | 0.912016i | \(0.365475\pi\) | |||||||
\(500\) | 1.07400e12 | 0.768492 | ||||||||
\(501\) | −2.35063e12 | −1.66692 | ||||||||
\(502\) | 2.28173e12 | 1.60360 | ||||||||
\(503\) | −1.29522e12 | −0.902170 | −0.451085 | − | 0.892481i | \(-0.648963\pi\) | ||||
−0.451085 | + | 0.892481i | \(0.648963\pi\) | |||||||
\(504\) | −3.41153e11 | −0.235512 | ||||||||
\(505\) | −8.60565e11 | −0.588806 | ||||||||
\(506\) | −1.67542e10 | −0.0113618 | ||||||||
\(507\) | 1.51595e12 | 1.01894 | ||||||||
\(508\) | 1.29563e11 | 0.0863167 | ||||||||
\(509\) | −9.48803e11 | −0.626536 | −0.313268 | − | 0.949665i | \(-0.601424\pi\) | ||||
−0.313268 | + | 0.949665i | \(0.601424\pi\) | |||||||
\(510\) | 3.78804e12 | 2.47942 | ||||||||
\(511\) | 6.13793e11 | 0.398224 | ||||||||
\(512\) | 1.72403e12 | 1.10874 | ||||||||
\(513\) | 1.81843e12 | 1.15923 | ||||||||
\(514\) | 4.07925e12 | 2.57778 | ||||||||
\(515\) | −1.47392e12 | −0.923298 | ||||||||
\(516\) | −1.24042e12 | −0.770274 | ||||||||
\(517\) | 1.09826e11 | 0.0676077 | ||||||||
\(518\) | 5.32459e10 | 0.0324940 | ||||||||
\(519\) | −2.31060e12 | −1.39789 | ||||||||
\(520\) | 9.57007e11 | 0.573984 | ||||||||
\(521\) | −2.46207e12 | −1.46396 | −0.731981 | − | 0.681325i | \(-0.761404\pi\) | ||||
−0.731981 | + | 0.681325i | \(0.761404\pi\) | |||||||
\(522\) | −5.90269e11 | −0.347963 | ||||||||
\(523\) | 2.42753e12 | 1.41875 | 0.709377 | − | 0.704829i | \(-0.248976\pi\) | ||||
0.709377 | + | 0.704829i | \(0.248976\pi\) | |||||||
\(524\) | −1.55609e12 | −0.901664 | ||||||||
\(525\) | −1.99029e12 | −1.14340 | ||||||||
\(526\) | −6.20106e11 | −0.353208 | ||||||||
\(527\) | 2.91321e11 | 0.164522 | ||||||||
\(528\) | −3.39843e11 | −0.190295 | ||||||||
\(529\) | −1.80023e12 | −0.999490 | ||||||||
\(530\) | −4.02008e12 | −2.21306 | ||||||||
\(531\) | 2.67503e10 | 0.0146017 | ||||||||
\(532\) | 3.70899e12 | 2.00749 | ||||||||
\(533\) | −2.86040e11 | −0.153516 | ||||||||
\(534\) | 7.10921e11 | 0.378343 | ||||||||
\(535\) | −1.91455e12 | −1.01035 | ||||||||
\(536\) | 8.46917e11 | 0.443200 | ||||||||
\(537\) | −4.26477e10 | −0.0221315 | ||||||||
\(538\) | 4.04203e12 | 2.08008 | ||||||||
\(539\) | −1.92091e11 | −0.0980298 | ||||||||
\(540\) | 4.84522e12 | 2.45212 | ||||||||
\(541\) | −3.08748e12 | −1.54959 | −0.774795 | − | 0.632213i | \(-0.782147\pi\) | ||||
−0.774795 | + | 0.632213i | \(0.782147\pi\) | |||||||
\(542\) | −3.96115e12 | −1.97163 | ||||||||
\(543\) | 1.54385e12 | 0.762091 | ||||||||
\(544\) | 8.29507e11 | 0.406092 | ||||||||
\(545\) | 2.83300e10 | 0.0137551 | ||||||||
\(546\) | −8.29931e11 | −0.399646 | ||||||||
\(547\) | 7.65281e11 | 0.365492 | 0.182746 | − | 0.983160i | \(-0.441501\pi\) | ||||
0.182746 | + | 0.983160i | \(0.441501\pi\) | |||||||
\(548\) | 2.31501e12 | 1.09658 | ||||||||
\(549\) | 4.68594e11 | 0.220151 | ||||||||
\(550\) | −1.37622e12 | −0.641291 | ||||||||
\(551\) | 2.95617e12 | 1.36630 | ||||||||
\(552\) | 7.78512e10 | 0.0356894 | ||||||||
\(553\) | 2.68755e12 | 1.22206 | ||||||||
\(554\) | −3.96091e12 | −1.78649 | ||||||||
\(555\) | 8.67023e10 | 0.0387893 | ||||||||
\(556\) | −3.92367e12 | −1.74123 | ||||||||
\(557\) | −1.37829e12 | −0.606727 | −0.303364 | − | 0.952875i | \(-0.598110\pi\) | ||||
−0.303364 | + | 0.952875i | \(0.598110\pi\) | |||||||
\(558\) | −1.42762e11 | −0.0623390 | ||||||||
\(559\) | −2.30990e11 | −0.100055 | ||||||||
\(560\) | 1.67764e12 | 0.720863 | ||||||||
\(561\) | −6.79752e11 | −0.289746 | ||||||||
\(562\) | 1.56831e12 | 0.663161 | ||||||||
\(563\) | 2.62254e12 | 1.10011 | 0.550054 | − | 0.835129i | \(-0.314607\pi\) | ||||
0.550054 | + | 0.835129i | \(0.314607\pi\) | |||||||
\(564\) | −1.10782e12 | −0.461014 | ||||||||
\(565\) | −4.99369e10 | −0.0206160 | ||||||||
\(566\) | −3.23217e11 | −0.132379 | ||||||||
\(567\) | −2.33729e12 | −0.949705 | ||||||||
\(568\) | 4.10054e12 | 1.65300 | ||||||||
\(569\) | 9.63896e11 | 0.385501 | 0.192750 | − | 0.981248i | \(-0.438259\pi\) | ||||
0.192750 | + | 0.981248i | \(0.438259\pi\) | |||||||
\(570\) | 9.29687e12 | 3.68893 | ||||||||
\(571\) | −2.36629e12 | −0.931550 | −0.465775 | − | 0.884903i | \(-0.654224\pi\) | ||||
−0.465775 | + | 0.884903i | \(0.654224\pi\) | |||||||
\(572\) | −3.72801e11 | −0.145611 | ||||||||
\(573\) | 2.34074e12 | 0.907105 | ||||||||
\(574\) | −2.09456e12 | −0.805360 | ||||||||
\(575\) | 7.54727e10 | 0.0287929 | ||||||||
\(576\) | −7.13738e11 | −0.270170 | ||||||||
\(577\) | −3.34486e11 | −0.125628 | −0.0628140 | − | 0.998025i | \(-0.520008\pi\) | ||||
−0.0628140 | + | 0.998025i | \(0.520008\pi\) | |||||||
\(578\) | 9.54173e11 | 0.355592 | ||||||||
\(579\) | 4.87977e11 | 0.180446 | ||||||||
\(580\) | 7.87673e12 | 2.89015 | ||||||||
\(581\) | 2.06935e11 | 0.0753426 | ||||||||
\(582\) | −3.31434e11 | −0.119741 | ||||||||
\(583\) | 7.21390e11 | 0.258620 | ||||||||
\(584\) | −1.97212e12 | −0.701578 | ||||||||
\(585\) | −2.24567e11 | −0.0792764 | ||||||||
\(586\) | −2.73995e12 | −0.959849 | ||||||||
\(587\) | 2.97724e12 | 1.03501 | 0.517503 | − | 0.855682i | \(-0.326862\pi\) | ||||
0.517503 | + | 0.855682i | \(0.326862\pi\) | |||||||
\(588\) | 1.93765e12 | 0.668461 | ||||||||
\(589\) | 7.14980e11 | 0.244779 | ||||||||
\(590\) | −5.49492e11 | −0.186693 | ||||||||
\(591\) | −2.31405e11 | −0.0780241 | ||||||||
\(592\) | −4.09558e10 | −0.0137046 | ||||||||
\(593\) | −2.95484e12 | −0.981269 | −0.490634 | − | 0.871366i | \(-0.663235\pi\) | ||||
−0.490634 | + | 0.871366i | \(0.663235\pi\) | |||||||
\(594\) | −1.33840e12 | −0.441110 | ||||||||
\(595\) | 3.35560e12 | 1.09760 | ||||||||
\(596\) | −5.70579e12 | −1.85228 | ||||||||
\(597\) | −1.97495e12 | −0.636313 | ||||||||
\(598\) | 3.14714e10 | 0.0100638 | ||||||||
\(599\) | −2.19881e12 | −0.697857 | −0.348929 | − | 0.937149i | \(-0.613454\pi\) | ||||
−0.348929 | + | 0.937149i | \(0.613454\pi\) | |||||||
\(600\) | 6.39480e12 | 2.01440 | ||||||||
\(601\) | 1.04958e12 | 0.328156 | 0.164078 | − | 0.986447i | \(-0.447535\pi\) | ||||
0.164078 | + | 0.986447i | \(0.447535\pi\) | |||||||
\(602\) | −1.69146e12 | −0.524900 | ||||||||
\(603\) | −1.98734e11 | −0.0612130 | ||||||||
\(604\) | 1.01070e13 | 3.09000 | ||||||||
\(605\) | −4.52950e12 | −1.37452 | ||||||||
\(606\) | −2.39785e12 | −0.722263 | ||||||||
\(607\) | 4.96644e11 | 0.148490 | 0.0742449 | − | 0.997240i | \(-0.476345\pi\) | ||||
0.0742449 | + | 0.997240i | \(0.476345\pi\) | |||||||
\(608\) | 2.03583e12 | 0.604193 | ||||||||
\(609\) | −3.14664e12 | −0.926977 | ||||||||
\(610\) | −9.62564e12 | −2.81479 | ||||||||
\(611\) | −2.06298e11 | −0.0598839 | ||||||||
\(612\) | 1.13940e12 | 0.328318 | ||||||||
\(613\) | −2.11053e11 | −0.0603699 | −0.0301849 | − | 0.999544i | \(-0.509610\pi\) | ||||
−0.0301849 | + | 0.999544i | \(0.509610\pi\) | |||||||
\(614\) | −7.04919e12 | −2.00162 | ||||||||
\(615\) | −3.41065e12 | −0.961390 | ||||||||
\(616\) | −1.25753e12 | −0.351888 | ||||||||
\(617\) | −3.15337e12 | −0.875974 | −0.437987 | − | 0.898981i | \(-0.644308\pi\) | ||||
−0.437987 | + | 0.898981i | \(0.644308\pi\) | |||||||
\(618\) | −4.10689e12 | −1.13257 | ||||||||
\(619\) | 1.40671e12 | 0.385121 | 0.192561 | − | 0.981285i | \(-0.438321\pi\) | ||||
0.192561 | + | 0.981285i | \(0.438321\pi\) | |||||||
\(620\) | 1.90507e12 | 0.517783 | ||||||||
\(621\) | 7.33988e10 | 0.0198051 | ||||||||
\(622\) | 2.49643e11 | 0.0668749 | ||||||||
\(623\) | 6.29762e11 | 0.167487 | ||||||||
\(624\) | 6.38367e11 | 0.168554 | ||||||||
\(625\) | −2.47828e12 | −0.649667 | ||||||||
\(626\) | −1.00157e13 | −2.60674 | ||||||||
\(627\) | −1.66829e12 | −0.431090 | ||||||||
\(628\) | −6.59500e12 | −1.69198 | ||||||||
\(629\) | −8.19193e10 | −0.0208669 | ||||||||
\(630\) | −1.64442e12 | −0.415892 | ||||||||
\(631\) | 4.63510e12 | 1.16393 | 0.581966 | − | 0.813213i | \(-0.302284\pi\) | ||||
0.581966 | + | 0.813213i | \(0.302284\pi\) | |||||||
\(632\) | −8.63511e12 | −2.15298 | ||||||||
\(633\) | −4.91568e12 | −1.21693 | ||||||||
\(634\) | 5.09089e12 | 1.25139 | ||||||||
\(635\) | 2.87686e11 | 0.0702160 | ||||||||
\(636\) | −7.27674e12 | −1.76352 | ||||||||
\(637\) | 3.60827e11 | 0.0868304 | ||||||||
\(638\) | −2.17580e12 | −0.519906 | ||||||||
\(639\) | −9.62213e11 | −0.228306 | ||||||||
\(640\) | 1.17356e13 | 2.76500 | ||||||||
\(641\) | 2.74470e12 | 0.642145 | 0.321073 | − | 0.947055i | \(-0.395957\pi\) | ||||
0.321073 | + | 0.947055i | \(0.395957\pi\) | |||||||
\(642\) | −5.33463e12 | −1.23936 | ||||||||
\(643\) | −4.81477e12 | −1.11078 | −0.555388 | − | 0.831591i | \(-0.687430\pi\) | ||||
−0.555388 | + | 0.831591i | \(0.687430\pi\) | |||||||
\(644\) | 1.49709e11 | 0.0342974 | ||||||||
\(645\) | −2.75426e12 | −0.626594 | ||||||||
\(646\) | −8.78400e12 | −1.98448 | ||||||||
\(647\) | −7.31467e12 | −1.64106 | −0.820531 | − | 0.571602i | \(-0.806322\pi\) | ||||
−0.820531 | + | 0.571602i | \(0.806322\pi\) | |||||||
\(648\) | 7.50973e12 | 1.67316 | ||||||||
\(649\) | 9.86044e10 | 0.0218170 | ||||||||
\(650\) | 2.58511e12 | 0.568027 | ||||||||
\(651\) | −7.61045e11 | −0.166072 | ||||||||
\(652\) | −9.31618e12 | −2.01894 | ||||||||
\(653\) | −4.80438e12 | −1.03402 | −0.517009 | − | 0.855980i | \(-0.672955\pi\) | ||||
−0.517009 | + | 0.855980i | \(0.672955\pi\) | |||||||
\(654\) | 7.89379e10 | 0.0168727 | ||||||||
\(655\) | −3.45519e12 | −0.733477 | ||||||||
\(656\) | 1.61110e12 | 0.339668 | ||||||||
\(657\) | 4.62769e11 | 0.0968991 | ||||||||
\(658\) | −1.51065e12 | −0.314156 | ||||||||
\(659\) | −3.89676e12 | −0.804858 | −0.402429 | − | 0.915451i | \(-0.631834\pi\) | ||||
−0.402429 | + | 0.915451i | \(0.631834\pi\) | |||||||
\(660\) | −4.44517e12 | −0.911887 | ||||||||
\(661\) | 3.64506e12 | 0.742673 | 0.371336 | − | 0.928498i | \(-0.378900\pi\) | ||||
0.371336 | + | 0.928498i | \(0.378900\pi\) | |||||||
\(662\) | −8.67769e12 | −1.75608 | ||||||||
\(663\) | 1.27686e12 | 0.256644 | ||||||||
\(664\) | −6.64882e11 | −0.132736 | ||||||||
\(665\) | 8.23555e12 | 1.63303 | ||||||||
\(666\) | 4.01447e10 | 0.00790669 | ||||||||
\(667\) | 1.19322e11 | 0.0233429 | ||||||||
\(668\) | 1.45237e13 | 2.82218 | ||||||||
\(669\) | −1.01121e13 | −1.95174 | ||||||||
\(670\) | 4.08229e12 | 0.782650 | ||||||||
\(671\) | 1.72729e12 | 0.328938 | ||||||||
\(672\) | −2.16700e12 | −0.409918 | ||||||||
\(673\) | 5.49056e12 | 1.03169 | 0.515844 | − | 0.856682i | \(-0.327478\pi\) | ||||
0.515844 | + | 0.856682i | \(0.327478\pi\) | |||||||
\(674\) | 2.74306e11 | 0.0511994 | ||||||||
\(675\) | 6.02908e12 | 1.11785 | ||||||||
\(676\) | −9.36652e12 | −1.72512 | ||||||||
\(677\) | −1.69761e12 | −0.310591 | −0.155296 | − | 0.987868i | \(-0.549633\pi\) | ||||
−0.155296 | + | 0.987868i | \(0.549633\pi\) | |||||||
\(678\) | −1.39143e11 | −0.0252887 | ||||||||
\(679\) | −2.93598e11 | −0.0530077 | ||||||||
\(680\) | −1.07816e13 | −1.93371 | ||||||||
\(681\) | 9.09033e12 | 1.61964 | ||||||||
\(682\) | −5.26238e11 | −0.0931435 | ||||||||
\(683\) | −7.52172e9 | −0.00132259 | −0.000661293 | − | 1.00000i | \(-0.500210\pi\) | ||||
−0.000661293 | 1.00000i | \(0.500210\pi\) | ||||||||
\(684\) | 2.79639e12 | 0.488478 | ||||||||
\(685\) | 5.14031e12 | 0.892036 | ||||||||
\(686\) | 1.06679e13 | 1.83917 | ||||||||
\(687\) | 5.10277e12 | 0.873978 | ||||||||
\(688\) | 1.30104e12 | 0.221381 | ||||||||
\(689\) | −1.35507e12 | −0.229074 | ||||||||
\(690\) | 3.75256e11 | 0.0630242 | ||||||||
\(691\) | −3.24633e12 | −0.541679 | −0.270840 | − | 0.962625i | \(-0.587301\pi\) | ||||
−0.270840 | + | 0.962625i | \(0.587301\pi\) | |||||||
\(692\) | 1.42764e13 | 2.36669 | ||||||||
\(693\) | 2.95086e11 | 0.0486014 | ||||||||
\(694\) | −3.28126e12 | −0.536937 | ||||||||
\(695\) | −8.71222e12 | −1.41644 | ||||||||
\(696\) | 1.01102e13 | 1.63311 | ||||||||
\(697\) | 3.22250e12 | 0.517185 | ||||||||
\(698\) | −7.52096e12 | −1.19929 | ||||||||
\(699\) | 2.10156e11 | 0.0332962 | ||||||||
\(700\) | 1.22973e13 | 1.93583 | ||||||||
\(701\) | 1.14756e12 | 0.179492 | 0.0897462 | − | 0.995965i | \(-0.471394\pi\) | ||||
0.0897462 | + | 0.995965i | \(0.471394\pi\) | |||||||
\(702\) | 2.51407e12 | 0.390715 | ||||||||
\(703\) | −2.01052e11 | −0.0310463 | ||||||||
\(704\) | −2.63092e12 | −0.403673 | ||||||||
\(705\) | −2.45984e12 | −0.375021 | ||||||||
\(706\) | −1.96325e13 | −2.97410 | ||||||||
\(707\) | −2.12411e12 | −0.319735 | ||||||||
\(708\) | −9.94634e11 | −0.148769 | ||||||||
\(709\) | −1.08250e13 | −1.60886 | −0.804432 | − | 0.594044i | \(-0.797530\pi\) | ||||
−0.804432 | + | 0.594044i | \(0.797530\pi\) | |||||||
\(710\) | 1.97653e13 | 2.91905 | ||||||||
\(711\) | 2.02627e12 | 0.297362 | ||||||||
\(712\) | −2.02343e12 | −0.295072 | ||||||||
\(713\) | 2.88592e10 | 0.00418198 | ||||||||
\(714\) | 9.34995e12 | 1.34638 | ||||||||
\(715\) | −8.27777e11 | −0.118450 | ||||||||
\(716\) | 2.63505e11 | 0.0374698 | ||||||||
\(717\) | 1.29103e13 | 1.82432 | ||||||||
\(718\) | −7.34154e12 | −1.03093 | ||||||||
\(719\) | −7.26303e12 | −1.01353 | −0.506766 | − | 0.862083i | \(-0.669159\pi\) | ||||
−0.506766 | + | 0.862083i | \(0.669159\pi\) | |||||||
\(720\) | 1.26486e12 | 0.175406 | ||||||||
\(721\) | −3.63805e12 | −0.501372 | ||||||||
\(722\) | −9.22294e12 | −1.26314 | ||||||||
\(723\) | −8.26809e11 | −0.112534 | ||||||||
\(724\) | −9.53893e12 | −1.29026 | ||||||||
\(725\) | 9.80129e12 | 1.31753 | ||||||||
\(726\) | −1.26209e13 | −1.68606 | ||||||||
\(727\) | −7.97647e11 | −0.105902 | −0.0529512 | − | 0.998597i | \(-0.516863\pi\) | ||||
−0.0529512 | + | 0.998597i | \(0.516863\pi\) | |||||||
\(728\) | 2.36216e12 | 0.311687 | ||||||||
\(729\) | 5.56054e12 | 0.729194 | ||||||||
\(730\) | −9.50597e12 | −1.23892 | ||||||||
\(731\) | 2.60232e12 | 0.337080 | ||||||||
\(732\) | −1.74234e13 | −2.24301 | ||||||||
\(733\) | −3.30785e12 | −0.423232 | −0.211616 | − | 0.977353i | \(-0.567873\pi\) | ||||
−0.211616 | + | 0.977353i | \(0.567873\pi\) | |||||||
\(734\) | 2.71547e12 | 0.345313 | ||||||||
\(735\) | 4.30240e12 | 0.543773 | ||||||||
\(736\) | 8.21737e10 | 0.0103225 | ||||||||
\(737\) | −7.32554e11 | −0.0914609 | ||||||||
\(738\) | −1.57919e12 | −0.195966 | ||||||||
\(739\) | 9.17440e12 | 1.13156 | 0.565780 | − | 0.824556i | \(-0.308575\pi\) | ||||
0.565780 | + | 0.824556i | \(0.308575\pi\) | |||||||
\(740\) | −5.35704e11 | −0.0656722 | ||||||||
\(741\) | 3.13375e12 | 0.381840 | ||||||||
\(742\) | −9.92269e12 | −1.20174 | ||||||||
\(743\) | 1.29134e13 | 1.55451 | 0.777253 | − | 0.629189i | \(-0.216613\pi\) | ||||
0.777253 | + | 0.629189i | \(0.216613\pi\) | |||||||
\(744\) | 2.44524e12 | 0.292580 | ||||||||
\(745\) | −1.26693e13 | −1.50678 | ||||||||
\(746\) | −2.28492e13 | −2.70114 | ||||||||
\(747\) | 1.56018e11 | 0.0183329 | ||||||||
\(748\) | 4.19995e12 | 0.490554 | ||||||||
\(749\) | −4.72563e12 | −0.548645 | ||||||||
\(750\) | 6.64477e12 | 0.766839 | ||||||||
\(751\) | 1.13700e13 | 1.30431 | 0.652153 | − | 0.758087i | \(-0.273866\pi\) | ||||
0.652153 | + | 0.758087i | \(0.273866\pi\) | |||||||
\(752\) | 1.16196e12 | 0.132498 | ||||||||
\(753\) | 9.17070e12 | 1.03950 | ||||||||
\(754\) | 4.08705e12 | 0.460510 | ||||||||
\(755\) | 2.24420e13 | 2.51362 | ||||||||
\(756\) | 1.19594e13 | 1.33156 | ||||||||
\(757\) | 6.02655e12 | 0.667017 | 0.333509 | − | 0.942747i | \(-0.391767\pi\) | ||||
0.333509 | + | 0.942747i | \(0.391767\pi\) | |||||||
\(758\) | −2.65435e13 | −2.92043 | ||||||||
\(759\) | −6.73385e10 | −0.00736505 | ||||||||
\(760\) | −2.64609e13 | −2.87702 | ||||||||
\(761\) | −9.14307e11 | −0.0988237 | −0.0494119 | − | 0.998778i | \(-0.515735\pi\) | ||||
−0.0494119 | + | 0.998778i | \(0.515735\pi\) | |||||||
\(762\) | 8.01598e11 | 0.0861310 | ||||||||
\(763\) | 6.99263e10 | 0.00746931 | ||||||||
\(764\) | −1.44626e13 | −1.53577 | ||||||||
\(765\) | 2.52995e12 | 0.267077 | ||||||||
\(766\) | 7.71312e12 | 0.809470 | ||||||||
\(767\) | −1.85220e11 | −0.0193245 | ||||||||
\(768\) | 1.83863e13 | 1.90708 | ||||||||
\(769\) | 3.48454e12 | 0.359316 | 0.179658 | − | 0.983729i | \(-0.442501\pi\) | ||||
0.179658 | + | 0.983729i | \(0.442501\pi\) | |||||||
\(770\) | −6.06151e12 | −0.621402 | ||||||||
\(771\) | 1.63953e13 | 1.67099 | ||||||||
\(772\) | −3.01504e12 | −0.305503 | ||||||||
\(773\) | −9.06972e12 | −0.913663 | −0.456832 | − | 0.889553i | \(-0.651016\pi\) | ||||
−0.456832 | + | 0.889553i | \(0.651016\pi\) | |||||||
\(774\) | −1.27527e12 | −0.127723 | ||||||||
\(775\) | 2.37054e12 | 0.236042 | ||||||||
\(776\) | 9.43332e11 | 0.0933871 | ||||||||
\(777\) | 2.14006e11 | 0.0210635 | ||||||||
\(778\) | −1.38328e11 | −0.0135364 | ||||||||
\(779\) | 7.90888e12 | 0.769479 | ||||||||
\(780\) | 8.34988e12 | 0.807708 | ||||||||
\(781\) | −3.54682e12 | −0.341122 | ||||||||
\(782\) | −3.54555e11 | −0.0339042 | ||||||||
\(783\) | 9.53195e12 | 0.906262 | ||||||||
\(784\) | −2.03233e12 | −0.192120 | ||||||||
\(785\) | −1.46437e13 | −1.37638 | ||||||||
\(786\) | −9.62744e12 | −0.899724 | ||||||||
\(787\) | −2.91276e12 | −0.270657 | −0.135328 | − | 0.990801i | \(-0.543209\pi\) | ||||
−0.135328 | + | 0.990801i | \(0.543209\pi\) | |||||||
\(788\) | 1.42977e12 | 0.132099 | ||||||||
\(789\) | −2.49232e12 | −0.228959 | ||||||||
\(790\) | −4.16228e13 | −3.80197 | ||||||||
\(791\) | −1.23258e11 | −0.0111949 | ||||||||
\(792\) | −9.48112e11 | −0.0856242 | ||||||||
\(793\) | −3.24457e12 | −0.291358 | ||||||||
\(794\) | −2.23948e13 | −1.99965 | ||||||||
\(795\) | −1.61575e13 | −1.43457 | ||||||||
\(796\) | 1.22025e13 | 1.07731 | ||||||||
\(797\) | 1.37467e13 | 1.20680 | 0.603400 | − | 0.797439i | \(-0.293812\pi\) | ||||
0.603400 | + | 0.797439i | \(0.293812\pi\) | |||||||
\(798\) | 2.29473e13 | 2.00317 | ||||||||
\(799\) | 2.32414e12 | 0.201745 | ||||||||
\(800\) | 6.74987e12 | 0.582627 | ||||||||
\(801\) | 4.74809e11 | 0.0407542 | ||||||||
\(802\) | −2.15389e13 | −1.83839 | ||||||||
\(803\) | 1.70582e12 | 0.144781 | ||||||||
\(804\) | 7.38935e12 | 0.623669 | ||||||||
\(805\) | 3.32417e11 | 0.0278999 | ||||||||
\(806\) | 9.88493e11 | 0.0825023 | ||||||||
\(807\) | 1.62457e13 | 1.34837 | ||||||||
\(808\) | 6.82479e12 | 0.563298 | ||||||||
\(809\) | 2.09640e13 | 1.72070 | 0.860352 | − | 0.509700i | \(-0.170244\pi\) | ||||
0.860352 | + | 0.509700i | \(0.170244\pi\) | |||||||
\(810\) | 3.61982e13 | 2.95464 | ||||||||
\(811\) | 1.80143e13 | 1.46226 | 0.731130 | − | 0.682238i | \(-0.238993\pi\) | ||||
0.731130 | + | 0.682238i | \(0.238993\pi\) | |||||||
\(812\) | 1.94420e13 | 1.56942 | ||||||||
\(813\) | −1.59206e13 | −1.27806 | ||||||||
\(814\) | 1.47978e11 | 0.0118137 | ||||||||
\(815\) | −2.06859e13 | −1.64235 | ||||||||
\(816\) | −7.19180e12 | −0.567848 | ||||||||
\(817\) | 6.38679e12 | 0.501514 | ||||||||
\(818\) | 4.02883e13 | 3.14622 | ||||||||
\(819\) | −5.54294e11 | −0.0430489 | ||||||||
\(820\) | 2.10732e13 | 1.62768 | ||||||||
\(821\) | −1.41619e13 | −1.08787 | −0.543934 | − | 0.839128i | \(-0.683066\pi\) | ||||
−0.543934 | + | 0.839128i | \(0.683066\pi\) | |||||||
\(822\) | 1.43228e13 | 1.09422 | ||||||||
\(823\) | 1.99084e13 | 1.51264 | 0.756321 | − | 0.654201i | \(-0.226995\pi\) | ||||
0.756321 | + | 0.654201i | \(0.226995\pi\) | |||||||
\(824\) | 1.16891e13 | 0.883299 | ||||||||
\(825\) | −5.53128e12 | −0.415703 | ||||||||
\(826\) | −1.35630e12 | −0.101378 | ||||||||
\(827\) | −1.21535e12 | −0.0903497 | −0.0451749 | − | 0.998979i | \(-0.514385\pi\) | ||||
−0.0451749 | + | 0.998979i | \(0.514385\pi\) | |||||||
\(828\) | 1.12873e11 | 0.00834551 | ||||||||
\(829\) | 1.43806e13 | 1.05750 | 0.528752 | − | 0.848777i | \(-0.322660\pi\) | ||||
0.528752 | + | 0.848777i | \(0.322660\pi\) | |||||||
\(830\) | −3.20485e12 | −0.234399 | ||||||||
\(831\) | −1.59196e13 | −1.15805 | ||||||||
\(832\) | 4.94195e12 | 0.357556 | ||||||||
\(833\) | −4.06505e12 | −0.292525 | ||||||||
\(834\) | −2.42755e13 | −1.73748 | ||||||||
\(835\) | 3.22489e13 | 2.29576 | ||||||||
\(836\) | 1.03078e13 | 0.729857 | ||||||||
\(837\) | 2.30540e12 | 0.162361 | ||||||||
\(838\) | −1.22846e13 | −0.860527 | ||||||||
\(839\) | 1.95134e11 | 0.0135958 | 0.00679790 | − | 0.999977i | \(-0.497836\pi\) | ||||
0.00679790 | + | 0.999977i | \(0.497836\pi\) | |||||||
\(840\) | 2.81657e13 | 1.95193 | ||||||||
\(841\) | 9.88657e11 | 0.0681497 | ||||||||
\(842\) | 3.58623e13 | 2.45886 | ||||||||
\(843\) | 6.30335e12 | 0.429880 | ||||||||
\(844\) | 3.03723e13 | 2.06033 | ||||||||
\(845\) | −2.07977e13 | −1.40333 | ||||||||
\(846\) | −1.13895e12 | −0.0764430 | ||||||||
\(847\) | −1.11801e13 | −0.746396 | ||||||||
\(848\) | 7.63234e12 | 0.506846 | ||||||||
\(849\) | −1.29907e12 | −0.0858119 | ||||||||
\(850\) | −2.91237e13 | −1.91364 | ||||||||
\(851\) | −8.11520e9 | −0.000530416 0 | ||||||||
\(852\) | 3.57772e13 | 2.32610 | ||||||||
\(853\) | −1.61260e13 | −1.04293 | −0.521467 | − | 0.853271i | \(-0.674615\pi\) | ||||
−0.521467 | + | 0.853271i | \(0.674615\pi\) | |||||||
\(854\) | −2.37588e13 | −1.52849 | ||||||||
\(855\) | 6.20918e12 | 0.397363 | ||||||||
\(856\) | 1.51835e13 | 0.966584 | ||||||||
\(857\) | 2.32841e13 | 1.47450 | 0.737252 | − | 0.675618i | \(-0.236123\pi\) | ||||
0.737252 | + | 0.675618i | \(0.236123\pi\) | |||||||
\(858\) | −2.30649e12 | −0.145298 | ||||||||
\(859\) | −2.80294e13 | −1.75649 | −0.878244 | − | 0.478212i | \(-0.841285\pi\) | ||||
−0.878244 | + | 0.478212i | \(0.841285\pi\) | |||||||
\(860\) | 1.70176e13 | 1.06085 | ||||||||
\(861\) | −8.41845e12 | −0.522057 | ||||||||
\(862\) | −3.58420e13 | −2.21110 | ||||||||
\(863\) | 1.95516e13 | 1.19987 | 0.599933 | − | 0.800050i | \(-0.295194\pi\) | ||||
0.599933 | + | 0.800050i | \(0.295194\pi\) | |||||||
\(864\) | 6.56438e12 | 0.400758 | ||||||||
\(865\) | 3.16997e13 | 1.92523 | ||||||||
\(866\) | −2.92079e13 | −1.76469 | ||||||||
\(867\) | 3.83500e12 | 0.230505 | ||||||||
\(868\) | 4.70223e12 | 0.281168 | ||||||||
\(869\) | 7.46906e12 | 0.444301 | ||||||||
\(870\) | 4.87328e13 | 2.88393 | ||||||||
\(871\) | 1.37604e12 | 0.0810120 | ||||||||
\(872\) | −2.24674e11 | −0.0131592 | ||||||||
\(873\) | −2.21358e11 | −0.0128982 | ||||||||
\(874\) | −8.70173e11 | −0.0504434 | ||||||||
\(875\) | 5.88620e12 | 0.339468 | ||||||||
\(876\) | −1.72067e13 | −0.987257 | ||||||||
\(877\) | −2.28721e13 | −1.30560 | −0.652798 | − | 0.757532i | \(-0.726405\pi\) | ||||
−0.652798 | + | 0.757532i | \(0.726405\pi\) | |||||||
\(878\) | 1.02219e12 | 0.0580506 | ||||||||
\(879\) | −1.10124e13 | −0.622201 | ||||||||
\(880\) | 4.66240e12 | 0.262082 | ||||||||
\(881\) | −1.32499e13 | −0.741007 | −0.370504 | − | 0.928831i | \(-0.620815\pi\) | ||||
−0.370504 | + | 0.928831i | \(0.620815\pi\) | |||||||
\(882\) | 1.99209e12 | 0.110841 | ||||||||
\(883\) | 4.12981e12 | 0.228616 | 0.114308 | − | 0.993445i | \(-0.463535\pi\) | ||||
0.114308 | + | 0.993445i | \(0.463535\pi\) | |||||||
\(884\) | −7.88925e12 | −0.434511 | ||||||||
\(885\) | −2.20851e12 | −0.121019 | ||||||||
\(886\) | 1.08969e12 | 0.0594089 | ||||||||
\(887\) | 2.42722e13 | 1.31660 | 0.658298 | − | 0.752757i | \(-0.271277\pi\) | ||||
0.658298 | + | 0.752757i | \(0.271277\pi\) | |||||||
\(888\) | −6.87601e11 | −0.0371089 | ||||||||
\(889\) | 7.10088e11 | 0.0381289 | ||||||||
\(890\) | −9.75329e12 | −0.521070 | ||||||||
\(891\) | −6.49565e12 | −0.345281 | ||||||||
\(892\) | 6.24788e13 | 3.30439 | ||||||||
\(893\) | 5.70406e12 | 0.300160 | ||||||||
\(894\) | −3.53013e13 | −1.84830 | ||||||||
\(895\) | 5.85094e11 | 0.0304805 | ||||||||
\(896\) | 2.89667e13 | 1.50146 | ||||||||
\(897\) | 1.26490e11 | 0.00652363 | ||||||||
\(898\) | 5.80965e13 | 2.98130 | ||||||||
\(899\) | 3.74781e12 | 0.191364 | ||||||||
\(900\) | 9.27153e12 | 0.471043 | ||||||||
\(901\) | 1.52661e13 | 0.771734 | ||||||||
\(902\) | −5.82108e12 | −0.292802 | ||||||||
\(903\) | −6.79829e12 | −0.340255 | ||||||||
\(904\) | 3.96029e11 | 0.0197228 | ||||||||
\(905\) | −2.11805e13 | −1.04958 | ||||||||
\(906\) | 6.25316e13 | 3.08335 | ||||||||
\(907\) | 3.60325e12 | 0.176792 | 0.0883958 | − | 0.996085i | \(-0.471826\pi\) | ||||
0.0883958 | + | 0.996085i | \(0.471826\pi\) | |||||||
\(908\) | −5.61660e13 | −2.74212 | ||||||||
\(909\) | −1.60147e12 | −0.0778005 | ||||||||
\(910\) | 1.13860e13 | 0.550410 | ||||||||
\(911\) | 1.38844e12 | 0.0667872 | 0.0333936 | − | 0.999442i | \(-0.489369\pi\) | ||||
0.0333936 | + | 0.999442i | \(0.489369\pi\) | |||||||
\(912\) | −1.76506e13 | −0.844856 | ||||||||
\(913\) | 5.75100e11 | 0.0273920 | ||||||||
\(914\) | −2.27637e13 | −1.07891 | ||||||||
\(915\) | −3.86873e13 | −1.82462 | ||||||||
\(916\) | −3.15282e13 | −1.47969 | ||||||||
\(917\) | −8.52838e12 | −0.398295 | ||||||||
\(918\) | −2.83233e13 | −1.31629 | ||||||||
\(919\) | 1.30682e13 | 0.604361 | 0.302180 | − | 0.953251i | \(-0.402285\pi\) | ||||
0.302180 | + | 0.953251i | \(0.402285\pi\) | |||||||
\(920\) | −1.06806e12 | −0.0491530 | ||||||||
\(921\) | −2.83320e13 | −1.29751 | ||||||||
\(922\) | 4.76398e13 | 2.17111 | ||||||||
\(923\) | 6.66240e12 | 0.302150 | ||||||||
\(924\) | −1.09719e13 | −0.495175 | ||||||||
\(925\) | −6.66594e11 | −0.0299381 | ||||||||
\(926\) | −4.84848e13 | −2.16699 | ||||||||
\(927\) | −2.74290e12 | −0.121998 | ||||||||
\(928\) | 1.06715e13 | 0.472346 | ||||||||
\(929\) | −2.19012e13 | −0.964709 | −0.482354 | − | 0.875976i | \(-0.660218\pi\) | ||||
−0.482354 | + | 0.875976i | \(0.660218\pi\) | |||||||
\(930\) | 1.17865e13 | 0.516669 | ||||||||
\(931\) | −9.97673e12 | −0.435226 | ||||||||
\(932\) | −1.29848e12 | −0.0563720 | ||||||||
\(933\) | 1.00336e12 | 0.0433502 | ||||||||
\(934\) | 2.69793e13 | 1.16003 | ||||||||
\(935\) | 9.32568e12 | 0.399051 | ||||||||
\(936\) | 1.78095e12 | 0.0758421 | ||||||||
\(937\) | 1.20196e13 | 0.509403 | 0.254701 | − | 0.967020i | \(-0.418023\pi\) | ||||
0.254701 | + | 0.967020i | \(0.418023\pi\) | |||||||
\(938\) | 1.00762e13 | 0.424997 | ||||||||
\(939\) | −4.02550e13 | −1.68976 | ||||||||
\(940\) | 1.51985e13 | 0.634929 | ||||||||
\(941\) | 2.50039e13 | 1.03957 | 0.519786 | − | 0.854297i | \(-0.326012\pi\) | ||||
0.519786 | + | 0.854297i | \(0.326012\pi\) | |||||||
\(942\) | −4.08028e13 | −1.68834 | ||||||||
\(943\) | 3.19232e11 | 0.0131463 | ||||||||
\(944\) | 1.04324e12 | 0.0427573 | ||||||||
\(945\) | 2.65549e13 | 1.08318 | ||||||||
\(946\) | −4.70079e12 | −0.190836 | ||||||||
\(947\) | 3.96314e13 | 1.60127 | 0.800636 | − | 0.599151i | \(-0.204495\pi\) | ||||
0.800636 | + | 0.599151i | \(0.204495\pi\) | |||||||
\(948\) | −7.53413e13 | −3.02967 | ||||||||
\(949\) | −3.20423e12 | −0.128241 | ||||||||
\(950\) | −7.14772e13 | −2.84716 | ||||||||
\(951\) | 2.04613e13 | 0.811185 | ||||||||
\(952\) | −2.66119e13 | −1.05005 | ||||||||
\(953\) | −6.42157e12 | −0.252187 | −0.126094 | − | 0.992018i | \(-0.540244\pi\) | ||||
−0.126094 | + | 0.992018i | \(0.540244\pi\) | |||||||
\(954\) | −7.48120e12 | −0.292418 | ||||||||
\(955\) | −3.21132e13 | −1.24930 | ||||||||
\(956\) | −7.97685e13 | −3.08866 | ||||||||
\(957\) | −8.74494e12 | −0.337018 | ||||||||
\(958\) | −4.28878e13 | −1.64509 | ||||||||
\(959\) | 1.26877e13 | 0.484396 | ||||||||
\(960\) | 5.89265e13 | 2.23918 | ||||||||
\(961\) | −2.55332e13 | −0.965716 | ||||||||
\(962\) | −2.77964e11 | −0.0104641 | ||||||||
\(963\) | −3.56289e12 | −0.133501 | ||||||||
\(964\) | 5.10857e12 | 0.190525 | ||||||||
\(965\) | −6.69468e12 | −0.248518 | ||||||||
\(966\) | 9.26238e11 | 0.0342236 | ||||||||
\(967\) | 3.50542e13 | 1.28920 | 0.644600 | − | 0.764520i | \(-0.277024\pi\) | ||||
0.644600 | + | 0.764520i | \(0.277024\pi\) | |||||||
\(968\) | 3.59216e13 | 1.31497 | ||||||||
\(969\) | −3.53046e13 | −1.28639 | ||||||||
\(970\) | 4.54703e12 | 0.164913 | ||||||||
\(971\) | −5.00924e13 | −1.80836 | −0.904181 | − | 0.427150i | \(-0.859517\pi\) | ||||
−0.904181 | + | 0.427150i | \(0.859517\pi\) | |||||||
\(972\) | 2.02777e13 | 0.728652 | ||||||||
\(973\) | −2.15042e13 | −0.769158 | ||||||||
\(974\) | −3.18183e13 | −1.13282 | ||||||||
\(975\) | 1.03900e13 | 0.368211 | ||||||||
\(976\) | 1.82748e13 | 0.644656 | ||||||||
\(977\) | −3.04571e13 | −1.06946 | −0.534728 | − | 0.845024i | \(-0.679586\pi\) | ||||
−0.534728 | + | 0.845024i | \(0.679586\pi\) | |||||||
\(978\) | −5.76386e13 | −2.01460 | ||||||||
\(979\) | 1.75020e12 | 0.0608926 | ||||||||
\(980\) | −2.65830e13 | −0.920634 | ||||||||
\(981\) | 5.27209e10 | 0.00181749 | ||||||||
\(982\) | −5.90633e13 | −2.02682 | ||||||||
\(983\) | −4.68733e13 | −1.60116 | −0.800579 | − | 0.599227i | \(-0.795475\pi\) | ||||
−0.800579 | + | 0.599227i | \(0.795475\pi\) | |||||||
\(984\) | 2.70485e13 | 0.919741 | ||||||||
\(985\) | 3.17470e12 | 0.107458 | ||||||||
\(986\) | −4.60444e13 | −1.55142 | ||||||||
\(987\) | −6.07157e12 | −0.203645 | ||||||||
\(988\) | −1.93623e13 | −0.646474 | ||||||||
\(989\) | 2.57795e11 | 0.00856822 | ||||||||
\(990\) | −4.57007e12 | −0.151204 | ||||||||
\(991\) | −1.75561e13 | −0.578224 | −0.289112 | − | 0.957295i | \(-0.593360\pi\) | ||||
−0.289112 | + | 0.957295i | \(0.593360\pi\) | |||||||
\(992\) | 2.58101e12 | 0.0846228 | ||||||||
\(993\) | −3.48773e13 | −1.13834 | ||||||||
\(994\) | 4.87863e13 | 1.58511 | ||||||||
\(995\) | 2.70948e13 | 0.876358 | ||||||||
\(996\) | −5.80109e12 | −0.186785 | ||||||||
\(997\) | 2.86332e13 | 0.917787 | 0.458893 | − | 0.888491i | \(-0.348246\pi\) | ||||
0.458893 | + | 0.888491i | \(0.348246\pi\) | |||||||
\(998\) | −4.34310e13 | −1.38584 | ||||||||
\(999\) | −6.48277e11 | −0.0205928 |
(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 | 197.10.a.b.1.8 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.b.1.8 | ✓ | 76 | 1.1 | even | 1 | trivial |