Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,8,Mod(1,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.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: | \(11.5582459429\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 1078 x^{9} + 4966 x^{8} + 379692 x^{7} - 1385588 x^{6} - 48765978 x^{5} + 87529978 x^{4} + 2159400643 x^{3} - 1763707223 x^{2} + \cdots + 6680404080 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-22.1395\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −21.1395 | −1.86849 | −0.934243 | − | 0.356636i | \(-0.883923\pi\) | ||||
−0.934243 | + | 0.356636i | \(0.883923\pi\) | |||||||
\(3\) | 34.2904 | 0.733242 | 0.366621 | − | 0.930370i | \(-0.380514\pi\) | ||||
0.366621 | + | 0.930370i | \(0.380514\pi\) | |||||||
\(4\) | 318.879 | 2.49124 | ||||||||
\(5\) | 463.709 | 1.65901 | 0.829507 | − | 0.558496i | \(-0.188621\pi\) | ||||
0.829507 | + | 0.558496i | \(0.188621\pi\) | |||||||
\(6\) | −724.881 | −1.37005 | ||||||||
\(7\) | 1277.57 | 1.40780 | 0.703901 | − | 0.710298i | \(-0.251440\pi\) | ||||
0.703901 | + | 0.710298i | \(0.251440\pi\) | |||||||
\(8\) | −4035.09 | −2.78637 | ||||||||
\(9\) | −1011.17 | −0.462355 | ||||||||
\(10\) | −9802.57 | −3.09985 | ||||||||
\(11\) | 5750.80 | 1.30273 | 0.651364 | − | 0.758765i | \(-0.274197\pi\) | ||||
0.651364 | + | 0.758765i | \(0.274197\pi\) | |||||||
\(12\) | 10934.5 | 1.82668 | ||||||||
\(13\) | −6791.38 | −0.857346 | −0.428673 | − | 0.903460i | \(-0.641019\pi\) | ||||
−0.428673 | + | 0.903460i | \(0.641019\pi\) | |||||||
\(14\) | −27007.2 | −2.63046 | ||||||||
\(15\) | 15900.7 | 1.21646 | ||||||||
\(16\) | 44483.3 | 2.71504 | ||||||||
\(17\) | 20526.6 | 1.01332 | 0.506660 | − | 0.862146i | \(-0.330880\pi\) | ||||
0.506660 | + | 0.862146i | \(0.330880\pi\) | |||||||
\(18\) | 21375.7 | 0.863905 | ||||||||
\(19\) | −14879.0 | −0.497662 | −0.248831 | − | 0.968547i | \(-0.580046\pi\) | ||||
−0.248831 | + | 0.968547i | \(0.580046\pi\) | |||||||
\(20\) | 147867. | 4.13301 | ||||||||
\(21\) | 43808.3 | 1.03226 | ||||||||
\(22\) | −121569. | −2.43413 | ||||||||
\(23\) | −45808.6 | −0.785054 | −0.392527 | − | 0.919741i | \(-0.628399\pi\) | ||||
−0.392527 | + | 0.919741i | \(0.628399\pi\) | |||||||
\(24\) | −138365. | −2.04308 | ||||||||
\(25\) | 136901. | 1.75233 | ||||||||
\(26\) | 143566. | 1.60194 | ||||||||
\(27\) | −109666. | −1.07226 | ||||||||
\(28\) | 407390. | 3.50718 | ||||||||
\(29\) | 90610.7 | 0.689900 | 0.344950 | − | 0.938621i | \(-0.387896\pi\) | ||||
0.344950 | + | 0.938621i | \(0.387896\pi\) | |||||||
\(30\) | −336134. | −2.27294 | ||||||||
\(31\) | −254777. | −1.53601 | −0.768006 | − | 0.640442i | \(-0.778751\pi\) | ||||
−0.768006 | + | 0.640442i | \(0.778751\pi\) | |||||||
\(32\) | −423864. | −2.28666 | ||||||||
\(33\) | 197197. | 0.955216 | ||||||||
\(34\) | −433923. | −1.89337 | ||||||||
\(35\) | 592420. | 2.33556 | ||||||||
\(36\) | −322441. | −1.15184 | ||||||||
\(37\) | −50653.0 | −0.164399 | ||||||||
\(38\) | 314534. | 0.929876 | ||||||||
\(39\) | −232879. | −0.628643 | ||||||||
\(40\) | −1.87110e6 | −4.62262 | ||||||||
\(41\) | 297846. | 0.674913 | 0.337457 | − | 0.941341i | \(-0.390433\pi\) | ||||
0.337457 | + | 0.941341i | \(0.390433\pi\) | |||||||
\(42\) | −926087. | −1.92876 | ||||||||
\(43\) | 588916. | 1.12957 | 0.564785 | − | 0.825238i | \(-0.308959\pi\) | ||||
0.564785 | + | 0.825238i | \(0.308959\pi\) | |||||||
\(44\) | 1.83381e6 | 3.24541 | ||||||||
\(45\) | −468889. | −0.767054 | ||||||||
\(46\) | 968371. | 1.46686 | ||||||||
\(47\) | 510631. | 0.717405 | 0.358702 | − | 0.933452i | \(-0.383219\pi\) | ||||
0.358702 | + | 0.933452i | \(0.383219\pi\) | |||||||
\(48\) | 1.52535e6 | 1.99079 | ||||||||
\(49\) | 808643. | 0.981907 | ||||||||
\(50\) | −2.89401e6 | −3.27420 | ||||||||
\(51\) | 703865. | 0.743009 | ||||||||
\(52\) | −2.16563e6 | −2.13586 | ||||||||
\(53\) | 271225. | 0.250245 | 0.125122 | − | 0.992141i | \(-0.460068\pi\) | ||||
0.125122 | + | 0.992141i | \(0.460068\pi\) | |||||||
\(54\) | 2.31829e6 | 2.00351 | ||||||||
\(55\) | 2.66670e6 | 2.16125 | ||||||||
\(56\) | −5.15511e6 | −3.92265 | ||||||||
\(57\) | −510205. | −0.364907 | ||||||||
\(58\) | −1.91547e6 | −1.28907 | ||||||||
\(59\) | −1.25856e6 | −0.797796 | −0.398898 | − | 0.916995i | \(-0.630607\pi\) | ||||
−0.398898 | + | 0.916995i | \(0.630607\pi\) | |||||||
\(60\) | 5.07041e6 | 3.03050 | ||||||||
\(61\) | 536625. | 0.302703 | 0.151351 | − | 0.988480i | \(-0.451637\pi\) | ||||
0.151351 | + | 0.988480i | \(0.451637\pi\) | |||||||
\(62\) | 5.38587e6 | 2.87002 | ||||||||
\(63\) | −1.29184e6 | −0.650905 | ||||||||
\(64\) | 3.26641e6 | 1.55755 | ||||||||
\(65\) | −3.14922e6 | −1.42235 | ||||||||
\(66\) | −4.16865e6 | −1.78481 | ||||||||
\(67\) | −2.35048e6 | −0.954762 | −0.477381 | − | 0.878696i | \(-0.658414\pi\) | ||||
−0.477381 | + | 0.878696i | \(0.658414\pi\) | |||||||
\(68\) | 6.54551e6 | 2.52442 | ||||||||
\(69\) | −1.57079e6 | −0.575635 | ||||||||
\(70\) | −1.25235e7 | −4.36397 | ||||||||
\(71\) | −217328. | −0.0720630 | −0.0360315 | − | 0.999351i | \(-0.511472\pi\) | ||||
−0.0360315 | + | 0.999351i | \(0.511472\pi\) | |||||||
\(72\) | 4.08017e6 | 1.28829 | ||||||||
\(73\) | −5.42444e6 | −1.63202 | −0.816009 | − | 0.578039i | \(-0.803818\pi\) | ||||
−0.816009 | + | 0.578039i | \(0.803818\pi\) | |||||||
\(74\) | 1.07078e6 | 0.307177 | ||||||||
\(75\) | 4.69437e6 | 1.28488 | ||||||||
\(76\) | −4.74459e6 | −1.23980 | ||||||||
\(77\) | 7.34705e6 | 1.83398 | ||||||||
\(78\) | 4.92294e6 | 1.17461 | ||||||||
\(79\) | −2.42081e6 | −0.552416 | −0.276208 | − | 0.961098i | \(-0.589078\pi\) | ||||
−0.276208 | + | 0.961098i | \(0.589078\pi\) | |||||||
\(80\) | 2.06273e7 | 4.50430 | ||||||||
\(81\) | −1.54907e6 | −0.323872 | ||||||||
\(82\) | −6.29632e6 | −1.26107 | ||||||||
\(83\) | 1.00120e7 | 1.92198 | 0.960991 | − | 0.276581i | \(-0.0892015\pi\) | ||||
0.960991 | + | 0.276581i | \(0.0892015\pi\) | |||||||
\(84\) | 1.39696e7 | 2.57161 | ||||||||
\(85\) | 9.51837e6 | 1.68111 | ||||||||
\(86\) | −1.24494e7 | −2.11059 | ||||||||
\(87\) | 3.10707e6 | 0.505864 | ||||||||
\(88\) | −2.32050e7 | −3.62988 | ||||||||
\(89\) | −2.99012e6 | −0.449598 | −0.224799 | − | 0.974405i | \(-0.572172\pi\) | ||||
−0.224799 | + | 0.974405i | \(0.572172\pi\) | |||||||
\(90\) | 9.91208e6 | 1.43323 | ||||||||
\(91\) | −8.67646e6 | −1.20697 | ||||||||
\(92\) | −1.46074e7 | −1.95576 | ||||||||
\(93\) | −8.73640e6 | −1.12627 | ||||||||
\(94\) | −1.07945e7 | −1.34046 | ||||||||
\(95\) | −6.89950e6 | −0.825629 | ||||||||
\(96\) | −1.45344e7 | −1.67667 | ||||||||
\(97\) | 8.35669e6 | 0.929680 | 0.464840 | − | 0.885395i | \(-0.346112\pi\) | ||||
0.464840 | + | 0.885395i | \(0.346112\pi\) | |||||||
\(98\) | −1.70943e7 | −1.83468 | ||||||||
\(99\) | −5.81505e6 | −0.602324 | ||||||||
\(100\) | 4.36547e7 | 4.36547 | ||||||||
\(101\) | −2.81077e6 | −0.271457 | −0.135729 | − | 0.990746i | \(-0.543338\pi\) | ||||
−0.135729 | + | 0.990746i | \(0.543338\pi\) | |||||||
\(102\) | −1.48794e7 | −1.38830 | ||||||||
\(103\) | 1.63311e6 | 0.147260 | 0.0736300 | − | 0.997286i | \(-0.476542\pi\) | ||||
0.0736300 | + | 0.997286i | \(0.476542\pi\) | |||||||
\(104\) | 2.74038e7 | 2.38888 | ||||||||
\(105\) | 2.03143e7 | 1.71253 | ||||||||
\(106\) | −5.73357e6 | −0.467579 | ||||||||
\(107\) | 1.44703e7 | 1.14192 | 0.570959 | − | 0.820979i | \(-0.306572\pi\) | ||||
0.570959 | + | 0.820979i | \(0.306572\pi\) | |||||||
\(108\) | −3.49703e7 | −2.67126 | ||||||||
\(109\) | −1.76263e7 | −1.30367 | −0.651835 | − | 0.758361i | \(-0.726000\pi\) | ||||
−0.651835 | + | 0.758361i | \(0.726000\pi\) | |||||||
\(110\) | −5.63727e7 | −4.03826 | ||||||||
\(111\) | −1.73691e6 | −0.120544 | ||||||||
\(112\) | 5.68305e7 | 3.82224 | ||||||||
\(113\) | −8.66686e6 | −0.565050 | −0.282525 | − | 0.959260i | \(-0.591172\pi\) | ||||
−0.282525 | + | 0.959260i | \(0.591172\pi\) | |||||||
\(114\) | 1.07855e7 | 0.681824 | ||||||||
\(115\) | −2.12418e7 | −1.30242 | ||||||||
\(116\) | 2.88938e7 | 1.71871 | ||||||||
\(117\) | 6.86725e6 | 0.396399 | ||||||||
\(118\) | 2.66053e7 | 1.49067 | ||||||||
\(119\) | 2.62242e7 | 1.42655 | ||||||||
\(120\) | −6.41609e7 | −3.38950 | ||||||||
\(121\) | 1.35845e7 | 0.697102 | ||||||||
\(122\) | −1.13440e7 | −0.565596 | ||||||||
\(123\) | 1.02132e7 | 0.494875 | ||||||||
\(124\) | −8.12431e7 | −3.82658 | ||||||||
\(125\) | 2.72548e7 | 1.24812 | ||||||||
\(126\) | 2.73089e7 | 1.21621 | ||||||||
\(127\) | 2.07630e7 | 0.899449 | 0.449724 | − | 0.893167i | \(-0.351522\pi\) | ||||
0.449724 | + | 0.893167i | \(0.351522\pi\) | |||||||
\(128\) | −1.47958e7 | −0.623595 | ||||||||
\(129\) | 2.01941e7 | 0.828249 | ||||||||
\(130\) | 6.65730e7 | 2.65764 | ||||||||
\(131\) | −3.89604e7 | −1.51417 | −0.757084 | − | 0.653318i | \(-0.773376\pi\) | ||||
−0.757084 | + | 0.653318i | \(0.773376\pi\) | |||||||
\(132\) | 6.28820e7 | 2.37967 | ||||||||
\(133\) | −1.90089e7 | −0.700610 | ||||||||
\(134\) | 4.96880e7 | 1.78396 | ||||||||
\(135\) | −5.08533e7 | −1.77890 | ||||||||
\(136\) | −8.28267e7 | −2.82348 | ||||||||
\(137\) | −1.86250e7 | −0.618833 | −0.309416 | − | 0.950927i | \(-0.600134\pi\) | ||||
−0.309416 | + | 0.950927i | \(0.600134\pi\) | |||||||
\(138\) | 3.32058e7 | 1.07557 | ||||||||
\(139\) | 5.31015e6 | 0.167708 | 0.0838542 | − | 0.996478i | \(-0.473277\pi\) | ||||
0.0838542 | + | 0.996478i | \(0.473277\pi\) | |||||||
\(140\) | 1.88910e8 | 5.81845 | ||||||||
\(141\) | 1.75097e7 | 0.526032 | ||||||||
\(142\) | 4.59421e6 | 0.134649 | ||||||||
\(143\) | −3.90559e7 | −1.11689 | ||||||||
\(144\) | −4.49802e7 | −1.25532 | ||||||||
\(145\) | 4.20169e7 | 1.14455 | ||||||||
\(146\) | 1.14670e8 | 3.04940 | ||||||||
\(147\) | 2.77286e7 | 0.719976 | ||||||||
\(148\) | −1.61522e7 | −0.409558 | ||||||||
\(149\) | −2.48865e7 | −0.616329 | −0.308164 | − | 0.951333i | \(-0.599715\pi\) | ||||
−0.308164 | + | 0.951333i | \(0.599715\pi\) | |||||||
\(150\) | −9.92367e7 | −2.40078 | ||||||||
\(151\) | 3.67328e7 | 0.868230 | 0.434115 | − | 0.900858i | \(-0.357061\pi\) | ||||
0.434115 | + | 0.900858i | \(0.357061\pi\) | |||||||
\(152\) | 6.00379e7 | 1.38667 | ||||||||
\(153\) | −2.07559e7 | −0.468514 | ||||||||
\(154\) | −1.55313e8 | −3.42677 | ||||||||
\(155\) | −1.18142e8 | −2.54827 | ||||||||
\(156\) | −7.42601e7 | −1.56610 | ||||||||
\(157\) | 4.28398e7 | 0.883483 | 0.441741 | − | 0.897142i | \(-0.354361\pi\) | ||||
0.441741 | + | 0.897142i | \(0.354361\pi\) | |||||||
\(158\) | 5.11748e7 | 1.03218 | ||||||||
\(159\) | 9.30041e6 | 0.183490 | ||||||||
\(160\) | −1.96549e8 | −3.79360 | ||||||||
\(161\) | −5.85237e7 | −1.10520 | ||||||||
\(162\) | 3.27466e7 | 0.605150 | ||||||||
\(163\) | −3.01638e7 | −0.545543 | −0.272772 | − | 0.962079i | \(-0.587940\pi\) | ||||
−0.272772 | + | 0.962079i | \(0.587940\pi\) | |||||||
\(164\) | 9.49768e7 | 1.68137 | ||||||||
\(165\) | 9.14420e7 | 1.58472 | ||||||||
\(166\) | −2.11650e8 | −3.59120 | ||||||||
\(167\) | 4.97323e7 | 0.826288 | 0.413144 | − | 0.910666i | \(-0.364431\pi\) | ||||
0.413144 | + | 0.910666i | \(0.364431\pi\) | |||||||
\(168\) | −1.76770e8 | −2.87625 | ||||||||
\(169\) | −1.66257e7 | −0.264958 | ||||||||
\(170\) | −2.01214e8 | −3.14113 | ||||||||
\(171\) | 1.50452e7 | 0.230097 | ||||||||
\(172\) | 1.87793e8 | 2.81403 | ||||||||
\(173\) | 3.40863e7 | 0.500516 | 0.250258 | − | 0.968179i | \(-0.419485\pi\) | ||||
0.250258 | + | 0.968179i | \(0.419485\pi\) | |||||||
\(174\) | −6.56820e7 | −0.945200 | ||||||||
\(175\) | 1.74900e8 | 2.46693 | ||||||||
\(176\) | 2.55815e8 | 3.53697 | ||||||||
\(177\) | −4.31564e7 | −0.584978 | ||||||||
\(178\) | 6.32097e7 | 0.840067 | ||||||||
\(179\) | −7.71597e7 | −1.00555 | −0.502776 | − | 0.864416i | \(-0.667688\pi\) | ||||
−0.502776 | + | 0.864416i | \(0.667688\pi\) | |||||||
\(180\) | −1.49519e8 | −1.91092 | ||||||||
\(181\) | −1.42751e8 | −1.78939 | −0.894695 | − | 0.446678i | \(-0.852607\pi\) | ||||
−0.894695 | + | 0.446678i | \(0.852607\pi\) | |||||||
\(182\) | 1.83416e8 | 2.25521 | ||||||||
\(183\) | 1.84011e7 | 0.221955 | ||||||||
\(184\) | 1.84842e8 | 2.18745 | ||||||||
\(185\) | −2.34882e7 | −0.272740 | ||||||||
\(186\) | 1.84683e8 | 2.10442 | ||||||||
\(187\) | 1.18045e8 | 1.32008 | ||||||||
\(188\) | 1.62829e8 | 1.78723 | ||||||||
\(189\) | −1.40107e8 | −1.50953 | ||||||||
\(190\) | 1.45852e8 | 1.54268 | ||||||||
\(191\) | −1.36996e8 | −1.42262 | −0.711312 | − | 0.702876i | \(-0.751899\pi\) | ||||
−0.711312 | + | 0.702876i | \(0.751899\pi\) | |||||||
\(192\) | 1.12006e8 | 1.14206 | ||||||||
\(193\) | −3.22984e7 | −0.323393 | −0.161696 | − | 0.986841i | \(-0.551697\pi\) | ||||
−0.161696 | + | 0.986841i | \(0.551697\pi\) | |||||||
\(194\) | −1.76656e8 | −1.73709 | ||||||||
\(195\) | −1.07988e8 | −1.04293 | ||||||||
\(196\) | 2.57859e8 | 2.44617 | ||||||||
\(197\) | −1.43900e8 | −1.34100 | −0.670498 | − | 0.741911i | \(-0.733920\pi\) | ||||
−0.670498 | + | 0.741911i | \(0.733920\pi\) | |||||||
\(198\) | 1.22927e8 | 1.12543 | ||||||||
\(199\) | 5.36192e6 | 0.0482319 | 0.0241160 | − | 0.999709i | \(-0.492323\pi\) | ||||
0.0241160 | + | 0.999709i | \(0.492323\pi\) | |||||||
\(200\) | −5.52406e8 | −4.88263 | ||||||||
\(201\) | −8.05989e7 | −0.700072 | ||||||||
\(202\) | 5.94184e7 | 0.507214 | ||||||||
\(203\) | 1.15761e8 | 0.971243 | ||||||||
\(204\) | 2.24448e8 | 1.85101 | ||||||||
\(205\) | 1.38114e8 | 1.11969 | ||||||||
\(206\) | −3.45231e7 | −0.275153 | ||||||||
\(207\) | 4.63203e7 | 0.362974 | ||||||||
\(208\) | −3.02103e8 | −2.32773 | ||||||||
\(209\) | −8.55659e7 | −0.648319 | ||||||||
\(210\) | −4.29434e8 | −3.19985 | ||||||||
\(211\) | 753318. | 0.00552064 | 0.00276032 | − | 0.999996i | \(-0.499121\pi\) | ||||
0.00276032 | + | 0.999996i | \(0.499121\pi\) | |||||||
\(212\) | 8.64881e7 | 0.623420 | ||||||||
\(213\) | −7.45226e6 | −0.0528396 | ||||||||
\(214\) | −3.05895e8 | −2.13366 | ||||||||
\(215\) | 2.73085e8 | 1.87397 | ||||||||
\(216\) | 4.42514e8 | 2.98771 | ||||||||
\(217\) | −3.25496e8 | −2.16240 | ||||||||
\(218\) | 3.72611e8 | 2.43589 | ||||||||
\(219\) | −1.86006e8 | −1.19666 | ||||||||
\(220\) | 8.50353e8 | 5.38419 | ||||||||
\(221\) | −1.39404e8 | −0.868765 | ||||||||
\(222\) | 3.67174e7 | 0.225235 | ||||||||
\(223\) | 2.36905e8 | 1.43057 | 0.715283 | − | 0.698835i | \(-0.246298\pi\) | ||||
0.715283 | + | 0.698835i | \(0.246298\pi\) | |||||||
\(224\) | −5.41515e8 | −3.21916 | ||||||||
\(225\) | −1.38430e8 | −0.810199 | ||||||||
\(226\) | 1.83213e8 | 1.05579 | ||||||||
\(227\) | −9.12788e7 | −0.517940 | −0.258970 | − | 0.965885i | \(-0.583383\pi\) | ||||
−0.258970 | + | 0.965885i | \(0.583383\pi\) | |||||||
\(228\) | −1.62694e8 | −0.909072 | ||||||||
\(229\) | −7.06190e7 | −0.388595 | −0.194297 | − | 0.980943i | \(-0.562243\pi\) | ||||
−0.194297 | + | 0.980943i | \(0.562243\pi\) | |||||||
\(230\) | 4.49042e8 | 2.43355 | ||||||||
\(231\) | 2.51933e8 | 1.34476 | ||||||||
\(232\) | −3.65622e8 | −1.92231 | ||||||||
\(233\) | −1.45360e8 | −0.752836 | −0.376418 | − | 0.926450i | \(-0.622844\pi\) | ||||
−0.376418 | + | 0.926450i | \(0.622844\pi\) | |||||||
\(234\) | −1.45170e8 | −0.740665 | ||||||||
\(235\) | 2.36784e8 | 1.19019 | ||||||||
\(236\) | −4.01328e8 | −1.98750 | ||||||||
\(237\) | −8.30106e7 | −0.405055 | ||||||||
\(238\) | −5.54367e8 | −2.66549 | ||||||||
\(239\) | 2.12567e8 | 1.00717 | 0.503585 | − | 0.863946i | \(-0.332014\pi\) | ||||
0.503585 | + | 0.863946i | \(0.332014\pi\) | |||||||
\(240\) | 7.07317e8 | 3.30274 | ||||||||
\(241\) | 1.12071e7 | 0.0515743 | 0.0257872 | − | 0.999667i | \(-0.491791\pi\) | ||||
0.0257872 | + | 0.999667i | \(0.491791\pi\) | |||||||
\(242\) | −2.87171e8 | −1.30253 | ||||||||
\(243\) | 1.86722e8 | 0.834784 | ||||||||
\(244\) | 1.71118e8 | 0.754106 | ||||||||
\(245\) | 3.74975e8 | 1.62900 | ||||||||
\(246\) | −2.15903e8 | −0.924668 | ||||||||
\(247\) | 1.01049e8 | 0.426669 | ||||||||
\(248\) | 1.02805e9 | 4.27989 | ||||||||
\(249\) | 3.43316e8 | 1.40928 | ||||||||
\(250\) | −5.76153e8 | −2.33210 | ||||||||
\(251\) | −8.14863e7 | −0.325257 | −0.162629 | − | 0.986687i | \(-0.551997\pi\) | ||||
−0.162629 | + | 0.986687i | \(0.551997\pi\) | |||||||
\(252\) | −4.11941e8 | −1.62156 | ||||||||
\(253\) | −2.63436e8 | −1.02271 | ||||||||
\(254\) | −4.38919e8 | −1.68061 | ||||||||
\(255\) | 3.26388e8 | 1.23266 | ||||||||
\(256\) | −1.05325e8 | −0.392367 | ||||||||
\(257\) | 1.82069e8 | 0.669066 | 0.334533 | − | 0.942384i | \(-0.391421\pi\) | ||||
0.334533 | + | 0.942384i | \(0.391421\pi\) | |||||||
\(258\) | −4.26894e8 | −1.54757 | ||||||||
\(259\) | −6.47128e7 | −0.231441 | ||||||||
\(260\) | −1.00422e9 | −3.54342 | ||||||||
\(261\) | −9.16229e7 | −0.318979 | ||||||||
\(262\) | 8.23604e8 | 2.82920 | ||||||||
\(263\) | −5.00302e8 | −1.69585 | −0.847924 | − | 0.530117i | \(-0.822148\pi\) | ||||
−0.847924 | + | 0.530117i | \(0.822148\pi\) | |||||||
\(264\) | −7.95707e8 | −2.66158 | ||||||||
\(265\) | 1.25770e8 | 0.415159 | ||||||||
\(266\) | 4.01839e8 | 1.30908 | ||||||||
\(267\) | −1.02532e8 | −0.329664 | ||||||||
\(268\) | −7.49519e8 | −2.37854 | ||||||||
\(269\) | 3.67711e8 | 1.15179 | 0.575895 | − | 0.817523i | \(-0.304654\pi\) | ||||
0.575895 | + | 0.817523i | \(0.304654\pi\) | |||||||
\(270\) | 1.07501e9 | 3.32384 | ||||||||
\(271\) | 4.33982e8 | 1.32458 | 0.662291 | − | 0.749247i | \(-0.269584\pi\) | ||||
0.662291 | + | 0.749247i | \(0.269584\pi\) | |||||||
\(272\) | 9.13091e8 | 2.75121 | ||||||||
\(273\) | −2.97519e8 | −0.885004 | ||||||||
\(274\) | 3.93722e8 | 1.15628 | ||||||||
\(275\) | 7.87289e8 | 2.28281 | ||||||||
\(276\) | −5.00893e8 | −1.43405 | ||||||||
\(277\) | 5.04242e8 | 1.42548 | 0.712738 | − | 0.701430i | \(-0.247455\pi\) | ||||
0.712738 | + | 0.701430i | \(0.247455\pi\) | |||||||
\(278\) | −1.12254e8 | −0.313361 | ||||||||
\(279\) | 2.57623e8 | 0.710184 | ||||||||
\(280\) | −2.39047e9 | −6.50773 | ||||||||
\(281\) | 3.34393e7 | 0.0899052 | 0.0449526 | − | 0.998989i | \(-0.485686\pi\) | ||||
0.0449526 | + | 0.998989i | \(0.485686\pi\) | |||||||
\(282\) | −3.70147e8 | −0.982883 | ||||||||
\(283\) | −4.04643e8 | −1.06125 | −0.530627 | − | 0.847605i | \(-0.678044\pi\) | ||||
−0.530627 | + | 0.847605i | \(0.678044\pi\) | |||||||
\(284\) | −6.93014e7 | −0.179526 | ||||||||
\(285\) | −2.36586e8 | −0.605386 | ||||||||
\(286\) | 8.25622e8 | 2.08689 | ||||||||
\(287\) | 3.80519e8 | 0.950145 | ||||||||
\(288\) | 4.28599e8 | 1.05725 | ||||||||
\(289\) | 1.10034e7 | 0.0268154 | ||||||||
\(290\) | −8.88218e8 | −2.13858 | ||||||||
\(291\) | 2.86554e8 | 0.681681 | ||||||||
\(292\) | −1.72974e9 | −4.06575 | ||||||||
\(293\) | −7.89372e8 | −1.83335 | −0.916674 | − | 0.399635i | \(-0.869137\pi\) | ||||
−0.916674 | + | 0.399635i | \(0.869137\pi\) | |||||||
\(294\) | −5.86170e8 | −1.34527 | ||||||||
\(295\) | −5.83605e8 | −1.32355 | ||||||||
\(296\) | 2.04389e8 | 0.458076 | ||||||||
\(297\) | −6.30670e8 | −1.39687 | ||||||||
\(298\) | 5.26089e8 | 1.15160 | ||||||||
\(299\) | 3.11103e8 | 0.673063 | ||||||||
\(300\) | 1.49694e9 | 3.20095 | ||||||||
\(301\) | 7.52381e8 | 1.59021 | ||||||||
\(302\) | −7.76513e8 | −1.62228 | ||||||||
\(303\) | −9.63825e7 | −0.199044 | ||||||||
\(304\) | −6.61865e8 | −1.35118 | ||||||||
\(305\) | 2.48838e8 | 0.502189 | ||||||||
\(306\) | 4.38770e8 | 0.875411 | ||||||||
\(307\) | −1.98514e7 | −0.0391567 | −0.0195784 | − | 0.999808i | \(-0.506232\pi\) | ||||
−0.0195784 | + | 0.999808i | \(0.506232\pi\) | |||||||
\(308\) | 2.34282e9 | 4.56890 | ||||||||
\(309\) | 5.59999e7 | 0.107977 | ||||||||
\(310\) | 2.49747e9 | 4.76140 | ||||||||
\(311\) | −6.48559e8 | −1.22261 | −0.611305 | − | 0.791395i | \(-0.709355\pi\) | ||||
−0.611305 | + | 0.791395i | \(0.709355\pi\) | |||||||
\(312\) | 9.39686e8 | 1.75163 | ||||||||
\(313\) | −3.98800e8 | −0.735106 | −0.367553 | − | 0.930003i | \(-0.619804\pi\) | ||||
−0.367553 | + | 0.930003i | \(0.619804\pi\) | |||||||
\(314\) | −9.05611e8 | −1.65078 | ||||||||
\(315\) | −5.99038e8 | −1.07986 | ||||||||
\(316\) | −7.71947e8 | −1.37620 | ||||||||
\(317\) | 1.08007e9 | 1.90434 | 0.952170 | − | 0.305569i | \(-0.0988466\pi\) | ||||
0.952170 | + | 0.305569i | \(0.0988466\pi\) | |||||||
\(318\) | −1.96606e8 | −0.342849 | ||||||||
\(319\) | 5.21084e8 | 0.898753 | ||||||||
\(320\) | 1.51466e9 | 2.58399 | ||||||||
\(321\) | 4.96192e8 | 0.837303 | ||||||||
\(322\) | 1.23716e9 | 2.06505 | ||||||||
\(323\) | −3.05415e8 | −0.504291 | ||||||||
\(324\) | −4.93966e8 | −0.806843 | ||||||||
\(325\) | −9.29744e8 | −1.50235 | ||||||||
\(326\) | 6.37648e8 | 1.01934 | ||||||||
\(327\) | −6.04411e8 | −0.955906 | ||||||||
\(328\) | −1.20183e9 | −1.88056 | ||||||||
\(329\) | 6.52366e8 | 1.00996 | ||||||||
\(330\) | −1.93304e9 | −2.96102 | ||||||||
\(331\) | −4.44536e8 | −0.673766 | −0.336883 | − | 0.941547i | \(-0.609373\pi\) | ||||
−0.336883 | + | 0.941547i | \(0.609373\pi\) | |||||||
\(332\) | 3.19263e9 | 4.78812 | ||||||||
\(333\) | 5.12189e7 | 0.0760108 | ||||||||
\(334\) | −1.05132e9 | −1.54391 | ||||||||
\(335\) | −1.08994e9 | −1.58396 | ||||||||
\(336\) | 1.94874e9 | 2.80263 | ||||||||
\(337\) | 1.13274e9 | 1.61223 | 0.806113 | − | 0.591762i | \(-0.201567\pi\) | ||||
0.806113 | + | 0.591762i | \(0.201567\pi\) | |||||||
\(338\) | 3.51459e8 | 0.495070 | ||||||||
\(339\) | −2.97190e8 | −0.414319 | ||||||||
\(340\) | 3.03521e9 | 4.18805 | ||||||||
\(341\) | −1.46517e9 | −2.00101 | ||||||||
\(342\) | −3.18048e8 | −0.429933 | ||||||||
\(343\) | −1.90364e7 | −0.0254715 | ||||||||
\(344\) | −2.37633e9 | −3.14740 | ||||||||
\(345\) | −7.28390e8 | −0.954986 | ||||||||
\(346\) | −7.20567e8 | −0.935208 | ||||||||
\(347\) | −9.61527e7 | −0.123540 | −0.0617701 | − | 0.998090i | \(-0.519675\pi\) | ||||
−0.0617701 | + | 0.998090i | \(0.519675\pi\) | |||||||
\(348\) | 9.90780e8 | 1.26023 | ||||||||
\(349\) | −1.44389e9 | −1.81821 | −0.909105 | − | 0.416568i | \(-0.863233\pi\) | ||||
−0.909105 | + | 0.416568i | \(0.863233\pi\) | |||||||
\(350\) | −3.69731e9 | −4.60943 | ||||||||
\(351\) | 7.44786e8 | 0.919299 | ||||||||
\(352\) | −2.43756e9 | −2.97889 | ||||||||
\(353\) | 9.51558e8 | 1.15139 | 0.575697 | − | 0.817663i | \(-0.304731\pi\) | ||||
0.575697 | + | 0.817663i | \(0.304731\pi\) | |||||||
\(354\) | 9.12306e8 | 1.09302 | ||||||||
\(355\) | −1.00777e8 | −0.119553 | ||||||||
\(356\) | −9.53487e8 | −1.12006 | ||||||||
\(357\) | 8.99237e8 | 1.04601 | ||||||||
\(358\) | 1.63112e9 | 1.87886 | ||||||||
\(359\) | 7.14118e8 | 0.814591 | 0.407296 | − | 0.913296i | \(-0.366472\pi\) | ||||
0.407296 | + | 0.913296i | \(0.366472\pi\) | |||||||
\(360\) | 1.89201e9 | 2.13729 | ||||||||
\(361\) | −6.72488e8 | −0.752332 | ||||||||
\(362\) | 3.01769e9 | 3.34345 | ||||||||
\(363\) | 4.65819e8 | 0.511145 | ||||||||
\(364\) | −2.76674e9 | −3.00686 | ||||||||
\(365\) | −2.51536e9 | −2.70754 | ||||||||
\(366\) | −3.88990e8 | −0.414719 | ||||||||
\(367\) | 4.02540e8 | 0.425087 | 0.212543 | − | 0.977152i | \(-0.431825\pi\) | ||||
0.212543 | + | 0.977152i | \(0.431825\pi\) | |||||||
\(368\) | −2.03772e9 | −2.13146 | ||||||||
\(369\) | −3.01173e8 | −0.312050 | ||||||||
\(370\) | 4.96530e8 | 0.509612 | ||||||||
\(371\) | 3.46509e8 | 0.352295 | ||||||||
\(372\) | −2.78586e9 | −2.80581 | ||||||||
\(373\) | −1.63963e9 | −1.63593 | −0.817966 | − | 0.575266i | \(-0.804898\pi\) | ||||
−0.817966 | + | 0.575266i | \(0.804898\pi\) | |||||||
\(374\) | −2.49540e9 | −2.46655 | ||||||||
\(375\) | 9.34576e8 | 0.915177 | ||||||||
\(376\) | −2.06044e9 | −1.99895 | ||||||||
\(377\) | −6.15371e8 | −0.591483 | ||||||||
\(378\) | 2.96178e9 | 2.82054 | ||||||||
\(379\) | 1.85624e9 | 1.75145 | 0.875724 | − | 0.482812i | \(-0.160384\pi\) | ||||
0.875724 | + | 0.482812i | \(0.160384\pi\) | |||||||
\(380\) | −2.20011e9 | −2.05684 | ||||||||
\(381\) | 7.11970e8 | 0.659514 | ||||||||
\(382\) | 2.89602e9 | 2.65815 | ||||||||
\(383\) | −3.89277e8 | −0.354049 | −0.177024 | − | 0.984206i | \(-0.556647\pi\) | ||||
−0.177024 | + | 0.984206i | \(0.556647\pi\) | |||||||
\(384\) | −5.07352e8 | −0.457246 | ||||||||
\(385\) | 3.40689e9 | 3.04261 | ||||||||
\(386\) | 6.82772e8 | 0.604255 | ||||||||
\(387\) | −5.95495e8 | −0.522263 | ||||||||
\(388\) | 2.66477e9 | 2.31606 | ||||||||
\(389\) | 1.57210e8 | 0.135412 | 0.0677059 | − | 0.997705i | \(-0.478432\pi\) | ||||
0.0677059 | + | 0.997705i | \(0.478432\pi\) | |||||||
\(390\) | 2.28281e9 | 1.94869 | ||||||||
\(391\) | −9.40295e8 | −0.795510 | ||||||||
\(392\) | −3.26294e9 | −2.73595 | ||||||||
\(393\) | −1.33597e9 | −1.11025 | ||||||||
\(394\) | 3.04197e9 | 2.50563 | ||||||||
\(395\) | −1.12255e9 | −0.916467 | ||||||||
\(396\) | −1.85430e9 | −1.50053 | ||||||||
\(397\) | −2.38343e9 | −1.91177 | −0.955883 | − | 0.293746i | \(-0.905098\pi\) | ||||
−0.955883 | + | 0.293746i | \(0.905098\pi\) | |||||||
\(398\) | −1.13348e8 | −0.0901207 | ||||||||
\(399\) | −6.51822e8 | −0.513717 | ||||||||
\(400\) | 6.08979e9 | 4.75765 | ||||||||
\(401\) | −5.12906e8 | −0.397222 | −0.198611 | − | 0.980078i | \(-0.563643\pi\) | ||||
−0.198611 | + | 0.980078i | \(0.563643\pi\) | |||||||
\(402\) | 1.70382e9 | 1.30808 | ||||||||
\(403\) | 1.73029e9 | 1.31689 | ||||||||
\(404\) | −8.96297e8 | −0.676265 | ||||||||
\(405\) | −7.18317e8 | −0.537308 | ||||||||
\(406\) | −2.44714e9 | −1.81475 | ||||||||
\(407\) | −2.91295e8 | −0.214167 | ||||||||
\(408\) | −2.84016e9 | −2.07029 | ||||||||
\(409\) | 5.86360e8 | 0.423772 | 0.211886 | − | 0.977294i | \(-0.432039\pi\) | ||||
0.211886 | + | 0.977294i | \(0.432039\pi\) | |||||||
\(410\) | −2.91966e9 | −2.09213 | ||||||||
\(411\) | −6.38656e8 | −0.453754 | ||||||||
\(412\) | 5.20764e8 | 0.366860 | ||||||||
\(413\) | −1.60790e9 | −1.12314 | ||||||||
\(414\) | −9.79189e8 | −0.678212 | ||||||||
\(415\) | 4.64267e9 | 3.18859 | ||||||||
\(416\) | 2.87862e9 | 1.96046 | ||||||||
\(417\) | 1.82087e8 | 0.122971 | ||||||||
\(418\) | 1.80882e9 | 1.21138 | ||||||||
\(419\) | −6.22382e8 | −0.413341 | −0.206670 | − | 0.978411i | \(-0.566263\pi\) | ||||
−0.206670 | + | 0.978411i | \(0.566263\pi\) | |||||||
\(420\) | 6.47780e9 | 4.26634 | ||||||||
\(421\) | −2.20235e9 | −1.43847 | −0.719233 | − | 0.694769i | \(-0.755507\pi\) | ||||
−0.719233 | + | 0.694769i | \(0.755507\pi\) | |||||||
\(422\) | −1.59248e7 | −0.0103152 | ||||||||
\(423\) | −5.16335e8 | −0.331696 | ||||||||
\(424\) | −1.09442e9 | −0.697273 | ||||||||
\(425\) | 2.81011e9 | 1.77567 | ||||||||
\(426\) | 1.57537e8 | 0.0987301 | ||||||||
\(427\) | 6.85576e8 | 0.426146 | ||||||||
\(428\) | 4.61428e9 | 2.84479 | ||||||||
\(429\) | −1.33924e9 | −0.818951 | ||||||||
\(430\) | −5.77289e9 | −3.50150 | ||||||||
\(431\) | 1.93493e9 | 1.16412 | 0.582058 | − | 0.813148i | \(-0.302248\pi\) | ||||
0.582058 | + | 0.813148i | \(0.302248\pi\) | |||||||
\(432\) | −4.87832e9 | −2.91124 | ||||||||
\(433\) | 2.83343e9 | 1.67728 | 0.838640 | − | 0.544687i | \(-0.183351\pi\) | ||||
0.838640 | + | 0.544687i | \(0.183351\pi\) | |||||||
\(434\) | 6.88082e9 | 4.04042 | ||||||||
\(435\) | 1.44078e9 | 0.839236 | ||||||||
\(436\) | −5.62064e9 | −3.24776 | ||||||||
\(437\) | 6.81584e8 | 0.390692 | ||||||||
\(438\) | 3.93208e9 | 2.23595 | ||||||||
\(439\) | 2.70042e8 | 0.152337 | 0.0761685 | − | 0.997095i | \(-0.475731\pi\) | ||||
0.0761685 | + | 0.997095i | \(0.475731\pi\) | |||||||
\(440\) | −1.07604e10 | −6.02202 | ||||||||
\(441\) | −8.17676e8 | −0.453990 | ||||||||
\(442\) | 2.94693e9 | 1.62328 | ||||||||
\(443\) | 1.71410e9 | 0.936750 | 0.468375 | − | 0.883530i | \(-0.344840\pi\) | ||||
0.468375 | + | 0.883530i | \(0.344840\pi\) | |||||||
\(444\) | −5.53864e8 | −0.300305 | ||||||||
\(445\) | −1.38655e9 | −0.745889 | ||||||||
\(446\) | −5.00807e9 | −2.67299 | ||||||||
\(447\) | −8.53368e8 | −0.451918 | ||||||||
\(448\) | 4.17307e9 | 2.19272 | ||||||||
\(449\) | 1.07309e9 | 0.559468 | 0.279734 | − | 0.960078i | \(-0.409754\pi\) | ||||
0.279734 | + | 0.960078i | \(0.409754\pi\) | |||||||
\(450\) | 2.92634e9 | 1.51385 | ||||||||
\(451\) | 1.71285e9 | 0.879229 | ||||||||
\(452\) | −2.76368e9 | −1.40768 | ||||||||
\(453\) | 1.25958e9 | 0.636623 | ||||||||
\(454\) | 1.92959e9 | 0.967764 | ||||||||
\(455\) | −4.02335e9 | −2.00239 | ||||||||
\(456\) | 2.05872e9 | 1.01676 | ||||||||
\(457\) | −1.32100e9 | −0.647434 | −0.323717 | − | 0.946154i | \(-0.604933\pi\) | ||||
−0.323717 | + | 0.946154i | \(0.604933\pi\) | |||||||
\(458\) | 1.49285e9 | 0.726084 | ||||||||
\(459\) | −2.25108e9 | −1.08654 | ||||||||
\(460\) | −6.77357e9 | −3.24463 | ||||||||
\(461\) | 2.81759e9 | 1.33944 | 0.669721 | − | 0.742613i | \(-0.266414\pi\) | ||||
0.669721 | + | 0.742613i | \(0.266414\pi\) | |||||||
\(462\) | −5.32574e9 | −2.51266 | ||||||||
\(463\) | 1.21643e9 | 0.569580 | 0.284790 | − | 0.958590i | \(-0.408076\pi\) | ||||
0.284790 | + | 0.958590i | \(0.408076\pi\) | |||||||
\(464\) | 4.03066e9 | 1.87311 | ||||||||
\(465\) | −4.05115e9 | −1.86850 | ||||||||
\(466\) | 3.07285e9 | 1.40666 | ||||||||
\(467\) | 1.33377e9 | 0.606000 | 0.303000 | − | 0.952991i | \(-0.402012\pi\) | ||||
0.303000 | + | 0.952991i | \(0.402012\pi\) | |||||||
\(468\) | 2.18982e9 | 0.987525 | ||||||||
\(469\) | −3.00291e9 | −1.34412 | ||||||||
\(470\) | −5.00549e9 | −2.22384 | ||||||||
\(471\) | 1.46899e9 | 0.647807 | ||||||||
\(472\) | 5.07840e9 | 2.22295 | ||||||||
\(473\) | 3.38674e9 | 1.47152 | ||||||||
\(474\) | 1.75480e9 | 0.756840 | ||||||||
\(475\) | −2.03694e9 | −0.872068 | ||||||||
\(476\) | 8.36234e9 | 3.55389 | ||||||||
\(477\) | −2.74255e8 | −0.115702 | ||||||||
\(478\) | −4.49356e9 | −1.88188 | ||||||||
\(479\) | 5.14618e8 | 0.213949 | 0.106975 | − | 0.994262i | \(-0.465884\pi\) | ||||
0.106975 | + | 0.994262i | \(0.465884\pi\) | |||||||
\(480\) | −6.73974e9 | −2.78163 | ||||||||
\(481\) | 3.44004e8 | 0.140947 | ||||||||
\(482\) | −2.36913e8 | −0.0963660 | ||||||||
\(483\) | −2.00680e9 | −0.810380 | ||||||||
\(484\) | 4.33183e9 | 1.73665 | ||||||||
\(485\) | 3.87507e9 | 1.54235 | ||||||||
\(486\) | −3.94722e9 | −1.55978 | ||||||||
\(487\) | −2.97786e8 | −0.116830 | −0.0584149 | − | 0.998292i | \(-0.518605\pi\) | ||||
−0.0584149 | + | 0.998292i | \(0.518605\pi\) | |||||||
\(488\) | −2.16533e9 | −0.843441 | ||||||||
\(489\) | −1.03433e9 | −0.400015 | ||||||||
\(490\) | −7.92678e9 | −3.04376 | ||||||||
\(491\) | −4.51780e8 | −0.172243 | −0.0861216 | − | 0.996285i | \(-0.527447\pi\) | ||||
−0.0861216 | + | 0.996285i | \(0.527447\pi\) | |||||||
\(492\) | 3.25679e9 | 1.23285 | ||||||||
\(493\) | 1.85993e9 | 0.699089 | ||||||||
\(494\) | −2.13612e9 | −0.797225 | ||||||||
\(495\) | −2.69649e9 | −0.999264 | ||||||||
\(496\) | −1.13333e10 | −4.17034 | ||||||||
\(497\) | −2.77652e8 | −0.101450 | ||||||||
\(498\) | −7.25754e9 | −2.63322 | ||||||||
\(499\) | 4.48528e9 | 1.61598 | 0.807992 | − | 0.589193i | \(-0.200554\pi\) | ||||
0.807992 | + | 0.589193i | \(0.200554\pi\) | |||||||
\(500\) | 8.69098e9 | 3.10938 | ||||||||
\(501\) | 1.70534e9 | 0.605869 | ||||||||
\(502\) | 1.72258e9 | 0.607738 | ||||||||
\(503\) | −1.27132e9 | −0.445419 | −0.222709 | − | 0.974885i | \(-0.571490\pi\) | ||||
−0.222709 | + | 0.974885i | \(0.571490\pi\) | |||||||
\(504\) | 5.21270e9 | 1.81366 | ||||||||
\(505\) | −1.30338e9 | −0.450351 | ||||||||
\(506\) | 5.56891e9 | 1.91092 | ||||||||
\(507\) | −5.70102e8 | −0.194278 | ||||||||
\(508\) | 6.62087e9 | 2.24074 | ||||||||
\(509\) | −2.73217e8 | −0.0918324 | −0.0459162 | − | 0.998945i | \(-0.514621\pi\) | ||||
−0.0459162 | + | 0.998945i | \(0.514621\pi\) | |||||||
\(510\) | −6.89969e9 | −2.30321 | ||||||||
\(511\) | −6.93010e9 | −2.29756 | ||||||||
\(512\) | 4.12038e9 | 1.35673 | ||||||||
\(513\) | 1.63172e9 | 0.533624 | ||||||||
\(514\) | −3.84884e9 | −1.25014 | ||||||||
\(515\) | 7.57287e8 | 0.244306 | ||||||||
\(516\) | 6.43948e9 | 2.06337 | ||||||||
\(517\) | 2.93654e9 | 0.934584 | ||||||||
\(518\) | 1.36800e9 | 0.432445 | ||||||||
\(519\) | 1.16883e9 | 0.367000 | ||||||||
\(520\) | 1.27074e10 | 3.96318 | ||||||||
\(521\) | −1.56251e9 | −0.484050 | −0.242025 | − | 0.970270i | \(-0.577812\pi\) | ||||
−0.242025 | + | 0.970270i | \(0.577812\pi\) | |||||||
\(522\) | 1.93686e9 | 0.596008 | ||||||||
\(523\) | −1.80565e9 | −0.551923 | −0.275961 | − | 0.961169i | \(-0.588996\pi\) | ||||
−0.275961 | + | 0.961169i | \(0.588996\pi\) | |||||||
\(524\) | −1.24237e10 | −3.77216 | ||||||||
\(525\) | 5.99739e9 | 1.80886 | ||||||||
\(526\) | 1.05761e10 | 3.16867 | ||||||||
\(527\) | −5.22972e9 | −1.55647 | ||||||||
\(528\) | 8.77197e9 | 2.59345 | ||||||||
\(529\) | −1.30640e9 | −0.383691 | ||||||||
\(530\) | −2.65871e9 | −0.775720 | ||||||||
\(531\) | 1.27262e9 | 0.368865 | ||||||||
\(532\) | −6.06154e9 | −1.74539 | ||||||||
\(533\) | −2.02278e9 | −0.578634 | ||||||||
\(534\) | 2.16748e9 | 0.615973 | ||||||||
\(535\) | 6.71001e9 | 1.89446 | ||||||||
\(536\) | 9.48440e9 | 2.66032 | ||||||||
\(537\) | −2.64583e9 | −0.737314 | ||||||||
\(538\) | −7.77323e9 | −2.15211 | ||||||||
\(539\) | 4.65034e9 | 1.27916 | ||||||||
\(540\) | −1.62160e10 | −4.43166 | ||||||||
\(541\) | 3.11802e8 | 0.0846619 | 0.0423310 | − | 0.999104i | \(-0.486522\pi\) | ||||
0.0423310 | + | 0.999104i | \(0.486522\pi\) | |||||||
\(542\) | −9.17416e9 | −2.47496 | ||||||||
\(543\) | −4.89499e9 | −1.31206 | ||||||||
\(544\) | −8.70049e9 | −2.31711 | ||||||||
\(545\) | −8.17345e9 | −2.16281 | ||||||||
\(546\) | 6.28941e9 | 1.65362 | ||||||||
\(547\) | 5.63775e9 | 1.47282 | 0.736411 | − | 0.676535i | \(-0.236519\pi\) | ||||
0.736411 | + | 0.676535i | \(0.236519\pi\) | |||||||
\(548\) | −5.93911e9 | −1.54166 | ||||||||
\(549\) | −5.42620e8 | −0.139956 | ||||||||
\(550\) | −1.66429e10 | −4.26540 | ||||||||
\(551\) | −1.34819e9 | −0.343337 | ||||||||
\(552\) | 6.33829e9 | 1.60393 | ||||||||
\(553\) | −3.09276e9 | −0.777693 | ||||||||
\(554\) | −1.06594e10 | −2.66348 | ||||||||
\(555\) | −8.05420e8 | −0.199985 | ||||||||
\(556\) | 1.69329e9 | 0.417802 | ||||||||
\(557\) | −1.42514e9 | −0.349434 | −0.174717 | − | 0.984619i | \(-0.555901\pi\) | ||||
−0.174717 | + | 0.984619i | \(0.555901\pi\) | |||||||
\(558\) | −5.44603e9 | −1.32697 | ||||||||
\(559\) | −3.99955e9 | −0.968433 | ||||||||
\(560\) | 2.63528e10 | 6.34116 | ||||||||
\(561\) | 4.04779e9 | 0.967939 | ||||||||
\(562\) | −7.06890e8 | −0.167987 | ||||||||
\(563\) | −1.42064e8 | −0.0335508 | −0.0167754 | − | 0.999859i | \(-0.505340\pi\) | ||||
−0.0167754 | + | 0.999859i | \(0.505340\pi\) | |||||||
\(564\) | 5.58348e9 | 1.31047 | ||||||||
\(565\) | −4.01890e9 | −0.937426 | ||||||||
\(566\) | 8.55395e9 | 1.98294 | ||||||||
\(567\) | −1.97905e9 | −0.455948 | ||||||||
\(568\) | 8.76939e8 | 0.200794 | ||||||||
\(569\) | 6.41286e9 | 1.45935 | 0.729674 | − | 0.683795i | \(-0.239672\pi\) | ||||
0.729674 | + | 0.683795i | \(0.239672\pi\) | |||||||
\(570\) | 5.00132e9 | 1.13116 | ||||||||
\(571\) | 2.13891e9 | 0.480801 | 0.240401 | − | 0.970674i | \(-0.422721\pi\) | ||||
0.240401 | + | 0.970674i | \(0.422721\pi\) | |||||||
\(572\) | −1.24541e10 | −2.78244 | ||||||||
\(573\) | −4.69763e9 | −1.04313 | ||||||||
\(574\) | −8.04399e9 | −1.77533 | ||||||||
\(575\) | −6.27123e9 | −1.37567 | ||||||||
\(576\) | −3.30290e9 | −0.720140 | ||||||||
\(577\) | 1.52123e9 | 0.329670 | 0.164835 | − | 0.986321i | \(-0.447291\pi\) | ||||
0.164835 | + | 0.986321i | \(0.447291\pi\) | |||||||
\(578\) | −2.32606e8 | −0.0501042 | ||||||||
\(579\) | −1.10752e9 | −0.237125 | ||||||||
\(580\) | 1.33983e10 | 2.85136 | ||||||||
\(581\) | 1.27911e10 | 2.70577 | ||||||||
\(582\) | −6.05761e9 | −1.27371 | ||||||||
\(583\) | 1.55976e9 | 0.326001 | ||||||||
\(584\) | 2.18881e10 | 4.54740 | ||||||||
\(585\) | 3.18440e9 | 0.657631 | ||||||||
\(586\) | 1.66869e10 | 3.42559 | ||||||||
\(587\) | −1.70891e9 | −0.348728 | −0.174364 | − | 0.984681i | \(-0.555787\pi\) | ||||
−0.174364 | + | 0.984681i | \(0.555787\pi\) | |||||||
\(588\) | 8.84208e9 | 1.79363 | ||||||||
\(589\) | 3.79082e9 | 0.764416 | ||||||||
\(590\) | 1.23371e10 | 2.47304 | ||||||||
\(591\) | −4.93437e9 | −0.983276 | ||||||||
\(592\) | −2.25321e9 | −0.446350 | ||||||||
\(593\) | 5.64855e9 | 1.11236 | 0.556180 | − | 0.831062i | \(-0.312267\pi\) | ||||
0.556180 | + | 0.831062i | \(0.312267\pi\) | |||||||
\(594\) | 1.33321e10 | 2.61002 | ||||||||
\(595\) | 1.21604e10 | 2.36667 | ||||||||
\(596\) | −7.93579e9 | −1.53542 | ||||||||
\(597\) | 1.83862e8 | 0.0353657 | ||||||||
\(598\) | −6.57657e9 | −1.25761 | ||||||||
\(599\) | 2.09091e9 | 0.397504 | 0.198752 | − | 0.980050i | \(-0.436311\pi\) | ||||
0.198752 | + | 0.980050i | \(0.436311\pi\) | |||||||
\(600\) | −1.89422e10 | −3.58015 | ||||||||
\(601\) | −2.90384e9 | −0.545647 | −0.272823 | − | 0.962064i | \(-0.587957\pi\) | ||||
−0.272823 | + | 0.962064i | \(0.587957\pi\) | |||||||
\(602\) | −1.59050e10 | −2.97129 | ||||||||
\(603\) | 2.37674e9 | 0.441439 | ||||||||
\(604\) | 1.17133e10 | 2.16297 | ||||||||
\(605\) | 6.29927e9 | 1.15650 | ||||||||
\(606\) | 2.03748e9 | 0.371911 | ||||||||
\(607\) | 2.35727e9 | 0.427809 | 0.213904 | − | 0.976855i | \(-0.431382\pi\) | ||||
0.213904 | + | 0.976855i | \(0.431382\pi\) | |||||||
\(608\) | 6.30665e9 | 1.13798 | ||||||||
\(609\) | 3.96950e9 | 0.712157 | ||||||||
\(610\) | −5.26031e9 | −0.938333 | ||||||||
\(611\) | −3.46789e9 | −0.615064 | ||||||||
\(612\) | −6.61863e9 | −1.16718 | ||||||||
\(613\) | −5.84011e9 | −1.02402 | −0.512011 | − | 0.858979i | \(-0.671099\pi\) | ||||
−0.512011 | + | 0.858979i | \(0.671099\pi\) | |||||||
\(614\) | 4.19648e8 | 0.0731638 | ||||||||
\(615\) | 4.73597e9 | 0.821005 | ||||||||
\(616\) | −2.96460e10 | −5.11015 | ||||||||
\(617\) | 1.14662e9 | 0.196527 | 0.0982637 | − | 0.995160i | \(-0.468671\pi\) | ||||
0.0982637 | + | 0.995160i | \(0.468671\pi\) | |||||||
\(618\) | −1.18381e9 | −0.201754 | ||||||||
\(619\) | −8.82033e9 | −1.49475 | −0.747373 | − | 0.664405i | \(-0.768685\pi\) | ||||
−0.747373 | + | 0.664405i | \(0.768685\pi\) | |||||||
\(620\) | −3.76731e10 | −6.34835 | ||||||||
\(621\) | 5.02366e9 | 0.841783 | ||||||||
\(622\) | 1.37102e10 | 2.28443 | ||||||||
\(623\) | −3.82009e9 | −0.632944 | ||||||||
\(624\) | −1.03592e10 | −1.70679 | ||||||||
\(625\) | 1.94291e9 | 0.318327 | ||||||||
\(626\) | 8.43043e9 | 1.37354 | ||||||||
\(627\) | −2.93409e9 | −0.475375 | ||||||||
\(628\) | 1.36607e10 | 2.20097 | ||||||||
\(629\) | −1.03973e9 | −0.166589 | ||||||||
\(630\) | 1.26634e10 | 2.01771 | ||||||||
\(631\) | 1.55001e9 | 0.245602 | 0.122801 | − | 0.992431i | \(-0.460812\pi\) | ||||
0.122801 | + | 0.992431i | \(0.460812\pi\) | |||||||
\(632\) | 9.76820e9 | 1.53923 | ||||||||
\(633\) | 2.58315e7 | 0.00404797 | ||||||||
\(634\) | −2.28322e10 | −3.55823 | ||||||||
\(635\) | 9.62797e9 | 1.49220 | ||||||||
\(636\) | 2.96571e9 | 0.457118 | ||||||||
\(637\) | −5.49180e9 | −0.841834 | ||||||||
\(638\) | −1.10155e10 | −1.67931 | ||||||||
\(639\) | 2.19756e8 | 0.0333187 | ||||||||
\(640\) | −6.86092e9 | −1.03455 | ||||||||
\(641\) | −4.65696e9 | −0.698392 | −0.349196 | − | 0.937050i | \(-0.613545\pi\) | ||||
−0.349196 | + | 0.937050i | \(0.613545\pi\) | |||||||
\(642\) | −1.04893e10 | −1.56449 | ||||||||
\(643\) | 3.05737e9 | 0.453533 | 0.226767 | − | 0.973949i | \(-0.427185\pi\) | ||||
0.226767 | + | 0.973949i | \(0.427185\pi\) | |||||||
\(644\) | −1.86620e10 | −2.75332 | ||||||||
\(645\) | 9.36419e9 | 1.37408 | ||||||||
\(646\) | 6.45632e9 | 0.942261 | ||||||||
\(647\) | −7.51191e8 | −0.109040 | −0.0545199 | − | 0.998513i | \(-0.517363\pi\) | ||||
−0.0545199 | + | 0.998513i | \(0.517363\pi\) | |||||||
\(648\) | 6.25063e9 | 0.902426 | ||||||||
\(649\) | −7.23772e9 | −1.03931 | ||||||||
\(650\) | 1.96543e10 | 2.80712 | ||||||||
\(651\) | −1.11614e10 | −1.58556 | ||||||||
\(652\) | −9.61859e9 | −1.35908 | ||||||||
\(653\) | 8.40509e9 | 1.18126 | 0.590631 | − | 0.806942i | \(-0.298879\pi\) | ||||
0.590631 | + | 0.806942i | \(0.298879\pi\) | |||||||
\(654\) | 1.27769e10 | 1.78610 | ||||||||
\(655\) | −1.80663e10 | −2.51203 | ||||||||
\(656\) | 1.32492e10 | 1.83242 | ||||||||
\(657\) | 5.48504e9 | 0.754572 | ||||||||
\(658\) | −1.37907e10 | −1.88710 | ||||||||
\(659\) | 9.63741e9 | 1.31178 | 0.655890 | − | 0.754856i | \(-0.272293\pi\) | ||||
0.655890 | + | 0.754856i | \(0.272293\pi\) | |||||||
\(660\) | 2.91589e10 | 3.94791 | ||||||||
\(661\) | −2.15965e9 | −0.290856 | −0.145428 | − | 0.989369i | \(-0.546456\pi\) | ||||
−0.145428 | + | 0.989369i | \(0.546456\pi\) | |||||||
\(662\) | 9.39727e9 | 1.25892 | ||||||||
\(663\) | −4.78021e9 | −0.637015 | ||||||||
\(664\) | −4.03994e10 | −5.35534 | ||||||||
\(665\) | −8.81460e9 | −1.16232 | ||||||||
\(666\) | −1.08274e9 | −0.142025 | ||||||||
\(667\) | −4.15075e9 | −0.541609 | ||||||||
\(668\) | 1.58586e10 | 2.05848 | ||||||||
\(669\) | 8.12357e9 | 1.04895 | ||||||||
\(670\) | 2.30408e10 | 2.95962 | ||||||||
\(671\) | 3.08603e9 | 0.394340 | ||||||||
\(672\) | −1.85688e10 | −2.36043 | ||||||||
\(673\) | −1.11530e10 | −1.41038 | −0.705192 | − | 0.709016i | \(-0.749139\pi\) | ||||
−0.705192 | + | 0.709016i | \(0.749139\pi\) | |||||||
\(674\) | −2.39456e10 | −3.01242 | ||||||||
\(675\) | −1.50134e10 | −1.87895 | ||||||||
\(676\) | −5.30159e9 | −0.660074 | ||||||||
\(677\) | −1.43527e10 | −1.77776 | −0.888882 | − | 0.458137i | \(-0.848517\pi\) | ||||
−0.888882 | + | 0.458137i | \(0.848517\pi\) | |||||||
\(678\) | 6.28244e9 | 0.774149 | ||||||||
\(679\) | 1.06763e10 | 1.30881 | ||||||||
\(680\) | −3.84075e10 | −4.68419 | ||||||||
\(681\) | −3.12998e9 | −0.379776 | ||||||||
\(682\) | 3.09731e10 | 3.73886 | ||||||||
\(683\) | 7.89840e9 | 0.948564 | 0.474282 | − | 0.880373i | \(-0.342708\pi\) | ||||
0.474282 | + | 0.880373i | \(0.342708\pi\) | |||||||
\(684\) | 4.79759e9 | 0.573227 | ||||||||
\(685\) | −8.63655e9 | −1.02665 | ||||||||
\(686\) | 4.02419e8 | 0.0475931 | ||||||||
\(687\) | −2.42155e9 | −0.284934 | ||||||||
\(688\) | 2.61969e10 | 3.06683 | ||||||||
\(689\) | −1.84199e9 | −0.214546 | ||||||||
\(690\) | 1.53978e10 | 1.78438 | ||||||||
\(691\) | −2.20339e9 | −0.254050 | −0.127025 | − | 0.991900i | \(-0.540543\pi\) | ||||
−0.127025 | + | 0.991900i | \(0.540543\pi\) | |||||||
\(692\) | 1.08694e10 | 1.24691 | ||||||||
\(693\) | −7.42913e9 | −0.847953 | ||||||||
\(694\) | 2.03262e9 | 0.230833 | ||||||||
\(695\) | 2.46236e9 | 0.278231 | ||||||||
\(696\) | −1.25373e10 | −1.40952 | ||||||||
\(697\) | 6.11377e9 | 0.683903 | ||||||||
\(698\) | 3.05230e10 | 3.39730 | ||||||||
\(699\) | −4.98446e9 | −0.552011 | ||||||||
\(700\) | 5.57720e10 | 6.14572 | ||||||||
\(701\) | 1.36665e10 | 1.49846 | 0.749228 | − | 0.662312i | \(-0.230425\pi\) | ||||
0.749228 | + | 0.662312i | \(0.230425\pi\) | |||||||
\(702\) | −1.57444e10 | −1.71770 | ||||||||
\(703\) | 7.53664e8 | 0.0818152 | ||||||||
\(704\) | 1.87845e10 | 2.02906 | ||||||||
\(705\) | 8.11940e9 | 0.872694 | ||||||||
\(706\) | −2.01155e10 | −2.15136 | ||||||||
\(707\) | −3.59096e9 | −0.382158 | ||||||||
\(708\) | −1.37617e10 | −1.45732 | ||||||||
\(709\) | −1.02722e10 | −1.08243 | −0.541216 | − | 0.840884i | \(-0.682036\pi\) | ||||
−0.541216 | + | 0.840884i | \(0.682036\pi\) | |||||||
\(710\) | 2.13038e9 | 0.223384 | ||||||||
\(711\) | 2.44786e9 | 0.255413 | ||||||||
\(712\) | 1.20654e10 | 1.25274 | ||||||||
\(713\) | 1.16710e10 | 1.20585 | ||||||||
\(714\) | −1.90094e10 | −1.95445 | ||||||||
\(715\) | −1.81105e10 | −1.85294 | ||||||||
\(716\) | −2.46046e10 | −2.50508 | ||||||||
\(717\) | 7.28899e9 | 0.738500 | ||||||||
\(718\) | −1.50961e10 | −1.52205 | ||||||||
\(719\) | −9.86949e9 | −0.990247 | −0.495123 | − | 0.868823i | \(-0.664877\pi\) | ||||
−0.495123 | + | 0.868823i | \(0.664877\pi\) | |||||||
\(720\) | −2.08577e10 | −2.08259 | ||||||||
\(721\) | 2.08641e9 | 0.207313 | ||||||||
\(722\) | 1.42161e10 | 1.40572 | ||||||||
\(723\) | 3.84296e8 | 0.0378165 | ||||||||
\(724\) | −4.55204e10 | −4.45780 | ||||||||
\(725\) | 1.24047e10 | 1.20893 | ||||||||
\(726\) | −9.84718e9 | −0.955067 | ||||||||
\(727\) | −1.04805e10 | −1.01160 | −0.505802 | − | 0.862650i | \(-0.668803\pi\) | ||||
−0.505802 | + | 0.862650i | \(0.668803\pi\) | |||||||
\(728\) | 3.50103e10 | 3.36307 | ||||||||
\(729\) | 9.79059e9 | 0.935971 | ||||||||
\(730\) | 5.31735e10 | 5.05900 | ||||||||
\(731\) | 1.20884e10 | 1.14462 | ||||||||
\(732\) | 5.86771e9 | 0.552943 | ||||||||
\(733\) | −1.01654e10 | −0.953369 | −0.476685 | − | 0.879074i | \(-0.658162\pi\) | ||||
−0.476685 | + | 0.879074i | \(0.658162\pi\) | |||||||
\(734\) | −8.50949e9 | −0.794269 | ||||||||
\(735\) | 1.28580e10 | 1.19445 | ||||||||
\(736\) | 1.94166e10 | 1.79515 | ||||||||
\(737\) | −1.35172e10 | −1.24380 | ||||||||
\(738\) | 6.36665e9 | 0.583061 | ||||||||
\(739\) | 1.10451e10 | 1.00673 | 0.503367 | − | 0.864073i | \(-0.332095\pi\) | ||||
0.503367 | + | 0.864073i | \(0.332095\pi\) | |||||||
\(740\) | −7.48990e9 | −0.679462 | ||||||||
\(741\) | 3.46499e9 | 0.312852 | ||||||||
\(742\) | −7.32504e9 | −0.658258 | ||||||||
\(743\) | −2.89185e9 | −0.258652 | −0.129326 | − | 0.991602i | \(-0.541281\pi\) | ||||
−0.129326 | + | 0.991602i | \(0.541281\pi\) | |||||||
\(744\) | 3.52522e10 | 3.13820 | ||||||||
\(745\) | −1.15401e10 | −1.02250 | ||||||||
\(746\) | 3.46610e10 | 3.05672 | ||||||||
\(747\) | −1.01239e10 | −0.888638 | ||||||||
\(748\) | 3.76419e10 | 3.28864 | ||||||||
\(749\) | 1.84868e10 | 1.60759 | ||||||||
\(750\) | −1.97565e10 | −1.71000 | ||||||||
\(751\) | −7.39191e9 | −0.636820 | −0.318410 | − | 0.947953i | \(-0.603149\pi\) | ||||
−0.318410 | + | 0.947953i | \(0.603149\pi\) | |||||||
\(752\) | 2.27145e10 | 1.94779 | ||||||||
\(753\) | −2.79420e9 | −0.238492 | ||||||||
\(754\) | 1.30086e10 | 1.10518 | ||||||||
\(755\) | 1.70333e10 | 1.44041 | ||||||||
\(756\) | −4.46770e10 | −3.76061 | ||||||||
\(757\) | 1.37247e10 | 1.14992 | 0.574959 | − | 0.818183i | \(-0.305018\pi\) | ||||
0.574959 | + | 0.818183i | \(0.305018\pi\) | |||||||
\(758\) | −3.92401e10 | −3.27256 | ||||||||
\(759\) | −9.03332e9 | −0.749896 | ||||||||
\(760\) | 2.78401e10 | 2.30050 | ||||||||
\(761\) | 3.46687e9 | 0.285161 | 0.142581 | − | 0.989783i | \(-0.454460\pi\) | ||||
0.142581 | + | 0.989783i | \(0.454460\pi\) | |||||||
\(762\) | −1.50507e10 | −1.23229 | ||||||||
\(763\) | −2.25188e10 | −1.83531 | ||||||||
\(764\) | −4.36851e10 | −3.54410 | ||||||||
\(765\) | −9.62470e9 | −0.777271 | ||||||||
\(766\) | 8.22912e9 | 0.661535 | ||||||||
\(767\) | 8.54735e9 | 0.683987 | ||||||||
\(768\) | −3.61164e9 | −0.287700 | ||||||||
\(769\) | 1.82468e10 | 1.44692 | 0.723461 | − | 0.690365i | \(-0.242550\pi\) | ||||
0.723461 | + | 0.690365i | \(0.242550\pi\) | |||||||
\(770\) | −7.20200e10 | −5.68507 | ||||||||
\(771\) | 6.24319e9 | 0.490588 | ||||||||
\(772\) | −1.02993e10 | −0.805649 | ||||||||
\(773\) | −1.29659e10 | −1.00966 | −0.504828 | − | 0.863220i | \(-0.668444\pi\) | ||||
−0.504828 | + | 0.863220i | \(0.668444\pi\) | |||||||
\(774\) | 1.25885e10 | 0.975842 | ||||||||
\(775\) | −3.48792e10 | −2.69160 | ||||||||
\(776\) | −3.37200e10 | −2.59043 | ||||||||
\(777\) | −2.21902e9 | −0.169703 | ||||||||
\(778\) | −3.32334e9 | −0.253015 | ||||||||
\(779\) | −4.43164e9 | −0.335879 | ||||||||
\(780\) | −3.44351e10 | −2.59818 | ||||||||
\(781\) | −1.24981e9 | −0.0938785 | ||||||||
\(782\) | 1.98774e10 | 1.48640 | ||||||||
\(783\) | −9.93695e9 | −0.739753 | ||||||||
\(784\) | 3.59711e10 | 2.66592 | ||||||||
\(785\) | 1.98652e10 | 1.46571 | ||||||||
\(786\) | 2.82417e10 | 2.07449 | ||||||||
\(787\) | 1.69567e9 | 0.124003 | 0.0620013 | − | 0.998076i | \(-0.480252\pi\) | ||||
0.0620013 | + | 0.998076i | \(0.480252\pi\) | |||||||
\(788\) | −4.58865e10 | −3.34075 | ||||||||
\(789\) | −1.71555e10 | −1.24347 | ||||||||
\(790\) | 2.37302e10 | 1.71241 | ||||||||
\(791\) | −1.10725e10 | −0.795479 | ||||||||
\(792\) | 2.34642e10 | 1.67829 | ||||||||
\(793\) | −3.64442e9 | −0.259521 | ||||||||
\(794\) | 5.03845e10 | 3.57211 | ||||||||
\(795\) | 4.31268e9 | 0.304413 | ||||||||
\(796\) | 1.70980e9 | 0.120157 | ||||||||
\(797\) | 1.49735e10 | 1.04766 | 0.523828 | − | 0.851824i | \(-0.324503\pi\) | ||||
0.523828 | + | 0.851824i | \(0.324503\pi\) | |||||||
\(798\) | 1.37792e10 | 0.959874 | ||||||||
\(799\) | 1.04815e10 | 0.726960 | ||||||||
\(800\) | −5.80272e10 | −4.00698 | ||||||||
\(801\) | 3.02353e9 | 0.207874 | ||||||||
\(802\) | 1.08426e10 | 0.742203 | ||||||||
\(803\) | −3.11949e10 | −2.12608 | ||||||||
\(804\) | −2.57013e10 | −1.74405 | ||||||||
\(805\) | −2.71379e10 | −1.83354 | ||||||||
\(806\) | −3.65775e10 | −2.46060 | ||||||||
\(807\) | 1.26089e10 | 0.844542 | ||||||||
\(808\) | 1.13417e10 | 0.756379 | ||||||||
\(809\) | −9.82683e9 | −0.652520 | −0.326260 | − | 0.945280i | \(-0.605788\pi\) | ||||
−0.326260 | + | 0.945280i | \(0.605788\pi\) | |||||||
\(810\) | 1.51849e10 | 1.00395 | ||||||||
\(811\) | 2.21461e10 | 1.45789 | 0.728945 | − | 0.684572i | \(-0.240011\pi\) | ||||
0.728945 | + | 0.684572i | \(0.240011\pi\) | |||||||
\(812\) | 3.69139e10 | 2.41960 | ||||||||
\(813\) | 1.48814e10 | 0.971240 | ||||||||
\(814\) | 6.15784e9 | 0.400169 | ||||||||
\(815\) | −1.39872e10 | −0.905064 | ||||||||
\(816\) | 3.13102e10 | 2.01730 | ||||||||
\(817\) | −8.76245e9 | −0.562145 | ||||||||
\(818\) | −1.23954e10 | −0.791813 | ||||||||
\(819\) | 8.77339e9 | 0.558051 | ||||||||
\(820\) | 4.40415e10 | 2.78942 | ||||||||
\(821\) | 5.54795e8 | 0.0349890 | 0.0174945 | − | 0.999847i | \(-0.494431\pi\) | ||||
0.0174945 | + | 0.999847i | \(0.494431\pi\) | |||||||
\(822\) | 1.35009e10 | 0.847834 | ||||||||
\(823\) | −2.49245e10 | −1.55857 | −0.779286 | − | 0.626668i | \(-0.784418\pi\) | ||||
−0.779286 | + | 0.626668i | \(0.784418\pi\) | |||||||
\(824\) | −6.58974e9 | −0.410320 | ||||||||
\(825\) | 2.69964e10 | 1.67385 | ||||||||
\(826\) | 3.39902e10 | 2.09857 | ||||||||
\(827\) | 4.78357e9 | 0.294092 | 0.147046 | − | 0.989130i | \(-0.453023\pi\) | ||||
0.147046 | + | 0.989130i | \(0.453023\pi\) | |||||||
\(828\) | 1.47706e10 | 0.904256 | ||||||||
\(829\) | 7.08659e9 | 0.432012 | 0.216006 | − | 0.976392i | \(-0.430697\pi\) | ||||
0.216006 | + | 0.976392i | \(0.430697\pi\) | |||||||
\(830\) | −9.81437e10 | −5.95784 | ||||||||
\(831\) | 1.72907e10 | 1.04522 | ||||||||
\(832\) | −2.21834e10 | −1.33536 | ||||||||
\(833\) | 1.65987e10 | 0.994985 | ||||||||
\(834\) | −3.84923e9 | −0.229769 | ||||||||
\(835\) | 2.30613e10 | 1.37082 | ||||||||
\(836\) | −2.72852e10 | −1.61512 | ||||||||
\(837\) | 2.79405e10 | 1.64701 | ||||||||
\(838\) | 1.31569e10 | 0.772322 | ||||||||
\(839\) | 1.68635e10 | 0.985782 | 0.492891 | − | 0.870091i | \(-0.335940\pi\) | ||||
0.492891 | + | 0.870091i | \(0.335940\pi\) | |||||||
\(840\) | −8.19700e10 | −4.77175 | ||||||||
\(841\) | −9.03959e9 | −0.524038 | ||||||||
\(842\) | 4.65567e10 | 2.68776 | ||||||||
\(843\) | 1.14664e9 | 0.0659223 | ||||||||
\(844\) | 2.40217e8 | 0.0137533 | ||||||||
\(845\) | −7.70949e9 | −0.439569 | ||||||||
\(846\) | 1.09151e10 | 0.619770 | ||||||||
\(847\) | 1.73552e10 | 0.981382 | ||||||||
\(848\) | 1.20650e10 | 0.679425 | ||||||||
\(849\) | −1.38754e10 | −0.778157 | ||||||||
\(850\) | −5.94043e10 | −3.31781 | ||||||||
\(851\) | 2.32034e9 | 0.129062 | ||||||||
\(852\) | −2.37637e9 | −0.131636 | ||||||||
\(853\) | 1.23581e10 | 0.681759 | 0.340880 | − | 0.940107i | \(-0.389275\pi\) | ||||
0.340880 | + | 0.940107i | \(0.389275\pi\) | |||||||
\(854\) | −1.44928e10 | −0.796248 | ||||||||
\(855\) | 6.97658e9 | 0.381734 | ||||||||
\(856\) | −5.83890e10 | −3.18180 | ||||||||
\(857\) | 3.83883e9 | 0.208337 | 0.104168 | − | 0.994560i | \(-0.466782\pi\) | ||||
0.104168 | + | 0.994560i | \(0.466782\pi\) | |||||||
\(858\) | 2.83109e10 | 1.53020 | ||||||||
\(859\) | 6.19149e9 | 0.333288 | 0.166644 | − | 0.986017i | \(-0.446707\pi\) | ||||
0.166644 | + | 0.986017i | \(0.446707\pi\) | |||||||
\(860\) | 8.70811e10 | 4.66852 | ||||||||
\(861\) | 1.30481e10 | 0.696686 | ||||||||
\(862\) | −4.09036e10 | −2.17513 | ||||||||
\(863\) | 1.63864e10 | 0.867851 | 0.433926 | − | 0.900949i | \(-0.357128\pi\) | ||||
0.433926 | + | 0.900949i | \(0.357128\pi\) | |||||||
\(864\) | 4.64836e10 | 2.45189 | ||||||||
\(865\) | 1.58061e10 | 0.830363 | ||||||||
\(866\) | −5.98974e10 | −3.13397 | ||||||||
\(867\) | 3.77310e8 | 0.0196622 | ||||||||
\(868\) | −1.03794e11 | −5.38707 | ||||||||
\(869\) | −1.39216e10 | −0.719649 | ||||||||
\(870\) | −3.04573e10 | −1.56810 | ||||||||
\(871\) | 1.59630e10 | 0.818561 | ||||||||
\(872\) | 7.11235e10 | 3.63250 | ||||||||
\(873\) | −8.45005e9 | −0.429842 | ||||||||
\(874\) | −1.44083e10 | −0.730002 | ||||||||
\(875\) | 3.48199e10 | 1.75711 | ||||||||
\(876\) | −5.93134e10 | −2.98118 | ||||||||
\(877\) | −1.42291e10 | −0.712326 | −0.356163 | − | 0.934424i | \(-0.615915\pi\) | ||||
−0.356163 | + | 0.934424i | \(0.615915\pi\) | |||||||
\(878\) | −5.70855e9 | −0.284639 | ||||||||
\(879\) | −2.70678e10 | −1.34429 | ||||||||
\(880\) | 1.18623e11 | 5.86788 | ||||||||
\(881\) | −2.08797e9 | −0.102875 | −0.0514375 | − | 0.998676i | \(-0.516380\pi\) | ||||
−0.0514375 | + | 0.998676i | \(0.516380\pi\) | |||||||
\(882\) | 1.72853e10 | 0.848274 | ||||||||
\(883\) | −8.08685e9 | −0.395291 | −0.197645 | − | 0.980274i | \(-0.563329\pi\) | ||||
−0.197645 | + | 0.980274i | \(0.563329\pi\) | |||||||
\(884\) | −4.44530e10 | −2.16430 | ||||||||
\(885\) | −2.00120e10 | −0.970486 | ||||||||
\(886\) | −3.62353e10 | −1.75031 | ||||||||
\(887\) | 3.27815e10 | 1.57723 | 0.788617 | − | 0.614884i | \(-0.210797\pi\) | ||||
0.788617 | + | 0.614884i | \(0.210797\pi\) | |||||||
\(888\) | 7.00858e9 | 0.335881 | ||||||||
\(889\) | 2.65261e10 | 1.26625 | ||||||||
\(890\) | 2.93109e10 | 1.39368 | ||||||||
\(891\) | −8.90839e9 | −0.421917 | ||||||||
\(892\) | 7.55442e10 | 3.56389 | ||||||||
\(893\) | −7.59765e9 | −0.357026 | ||||||||
\(894\) | 1.80398e10 | 0.844404 | ||||||||
\(895\) | −3.57796e10 | −1.66823 | ||||||||
\(896\) | −1.89026e10 | −0.877898 | ||||||||
\(897\) | 1.06678e10 | 0.493518 | ||||||||
\(898\) | −2.26847e10 | −1.04536 | ||||||||
\(899\) | −2.30855e10 | −1.05970 | ||||||||
\(900\) | −4.41424e10 | −2.01840 | ||||||||
\(901\) | 5.56734e9 | 0.253578 | ||||||||
\(902\) | −3.62089e10 | −1.64283 | ||||||||
\(903\) | 2.57994e10 | 1.16601 | ||||||||
\(904\) | 3.49715e10 | 1.57444 | ||||||||
\(905\) | −6.61950e10 | −2.96862 | ||||||||
\(906\) | −2.66269e10 | −1.18952 | ||||||||
\(907\) | 1.06210e10 | 0.472651 | 0.236325 | − | 0.971674i | \(-0.424057\pi\) | ||||
0.236325 | + | 0.971674i | \(0.424057\pi\) | |||||||
\(908\) | −2.91069e10 | −1.29031 | ||||||||
\(909\) | 2.84218e9 | 0.125510 | ||||||||
\(910\) | 8.50516e10 | 3.74143 | ||||||||
\(911\) | 2.54777e10 | 1.11647 | 0.558233 | − | 0.829684i | \(-0.311480\pi\) | ||||
0.558233 | + | 0.829684i | \(0.311480\pi\) | |||||||
\(912\) | −2.26956e10 | −0.990739 | ||||||||
\(913\) | 5.75772e10 | 2.50382 | ||||||||
\(914\) | 2.79253e10 | 1.20972 | ||||||||
\(915\) | 8.53274e9 | 0.368226 | ||||||||
\(916\) | −2.25189e10 | −0.968084 | ||||||||
\(917\) | −4.97746e10 | −2.13165 | ||||||||
\(918\) | 4.75868e10 | 2.03019 | ||||||||
\(919\) | −1.29356e10 | −0.549772 | −0.274886 | − | 0.961477i | \(-0.588640\pi\) | ||||
−0.274886 | + | 0.961477i | \(0.588640\pi\) | |||||||
\(920\) | 8.57127e10 | 3.62901 | ||||||||
\(921\) | −6.80711e8 | −0.0287114 | ||||||||
\(922\) | −5.95624e10 | −2.50273 | ||||||||
\(923\) | 1.47596e9 | 0.0617829 | ||||||||
\(924\) | 8.03361e10 | 3.35011 | ||||||||
\(925\) | −6.93443e9 | −0.288081 | ||||||||
\(926\) | −2.57148e10 | −1.06425 | ||||||||
\(927\) | −1.65135e9 | −0.0680865 | ||||||||
\(928\) | −3.84066e10 | −1.57757 | ||||||||
\(929\) | 1.63560e10 | 0.669303 | 0.334652 | − | 0.942342i | \(-0.391381\pi\) | ||||
0.334652 | + | 0.942342i | \(0.391381\pi\) | |||||||
\(930\) | 8.56392e10 | 3.49126 | ||||||||
\(931\) | −1.20318e10 | −0.488658 | ||||||||
\(932\) | −4.63524e10 | −1.87550 | ||||||||
\(933\) | −2.22393e10 | −0.896470 | ||||||||
\(934\) | −2.81953e10 | −1.13230 | ||||||||
\(935\) | 5.47383e10 | 2.19003 | ||||||||
\(936\) | −2.77099e10 | −1.10451 | ||||||||
\(937\) | 1.25975e10 | 0.500259 | 0.250129 | − | 0.968212i | \(-0.419527\pi\) | ||||
0.250129 | + | 0.968212i | \(0.419527\pi\) | |||||||
\(938\) | 6.34800e10 | 2.51146 | ||||||||
\(939\) | −1.36750e10 | −0.539011 | ||||||||
\(940\) | 7.55054e10 | 2.96504 | ||||||||
\(941\) | 4.27267e10 | 1.67161 | 0.835805 | − | 0.549026i | \(-0.185001\pi\) | ||||
0.835805 | + | 0.549026i | \(0.185001\pi\) | |||||||
\(942\) | −3.10537e10 | −1.21042 | ||||||||
\(943\) | −1.36439e10 | −0.529843 | ||||||||
\(944\) | −5.59848e10 | −2.16605 | ||||||||
\(945\) | −6.49686e10 | −2.50433 | ||||||||
\(946\) | −7.15940e10 | −2.74952 | ||||||||
\(947\) | −2.14494e9 | −0.0820713 | −0.0410356 | − | 0.999158i | \(-0.513066\pi\) | ||||
−0.0410356 | + | 0.999158i | \(0.513066\pi\) | |||||||
\(948\) | −2.64703e10 | −1.00909 | ||||||||
\(949\) | 3.68394e10 | 1.39920 | ||||||||
\(950\) | 4.30599e10 | 1.62945 | ||||||||
\(951\) | 3.70360e10 | 1.39634 | ||||||||
\(952\) | −1.05817e11 | −3.97490 | ||||||||
\(953\) | −4.21227e10 | −1.57649 | −0.788246 | − | 0.615361i | \(-0.789010\pi\) | ||||
−0.788246 | + | 0.615361i | \(0.789010\pi\) | |||||||
\(954\) | 5.79762e9 | 0.216188 | ||||||||
\(955\) | −6.35261e10 | −2.36015 | ||||||||
\(956\) | 6.77831e10 | 2.50910 | ||||||||
\(957\) | 1.78682e10 | 0.659004 | ||||||||
\(958\) | −1.08788e10 | −0.399761 | ||||||||
\(959\) | −2.37947e10 | −0.871194 | ||||||||
\(960\) | 5.19383e10 | 1.89469 | ||||||||
\(961\) | 3.73988e10 | 1.35933 | ||||||||
\(962\) | −7.27207e9 | −0.263357 | ||||||||
\(963\) | −1.46320e10 | −0.527972 | ||||||||
\(964\) | 3.57371e9 | 0.128484 | ||||||||
\(965\) | −1.49770e10 | −0.536513 | ||||||||
\(966\) | 4.24227e10 | 1.51418 | ||||||||
\(967\) | 4.69149e10 | 1.66847 | 0.834235 | − | 0.551409i | \(-0.185909\pi\) | ||||
0.834235 | + | 0.551409i | \(0.185909\pi\) | |||||||
\(968\) | −5.48148e10 | −1.94238 | ||||||||
\(969\) | −1.04728e10 | −0.369767 | ||||||||
\(970\) | −8.19171e10 | −2.88186 | ||||||||
\(971\) | 3.82889e10 | 1.34216 | 0.671082 | − | 0.741383i | \(-0.265830\pi\) | ||||
0.671082 | + | 0.741383i | \(0.265830\pi\) | |||||||
\(972\) | 5.95418e10 | 2.07965 | ||||||||
\(973\) | 6.78408e9 | 0.236100 | ||||||||
\(974\) | 6.29506e9 | 0.218295 | ||||||||
\(975\) | −3.18813e10 | −1.10159 | ||||||||
\(976\) | 2.38709e10 | 0.821852 | ||||||||
\(977\) | −4.93896e10 | −1.69436 | −0.847178 | − | 0.531309i | \(-0.821700\pi\) | ||||
−0.847178 | + | 0.531309i | \(0.821700\pi\) | |||||||
\(978\) | 2.18652e10 | 0.747423 | ||||||||
\(979\) | −1.71956e10 | −0.585704 | ||||||||
\(980\) | 1.19571e11 | 4.05823 | ||||||||
\(981\) | 1.78232e10 | 0.602759 | ||||||||
\(982\) | 9.55041e9 | 0.321834 | ||||||||
\(983\) | 2.20718e10 | 0.741141 | 0.370570 | − | 0.928804i | \(-0.379162\pi\) | ||||
0.370570 | + | 0.928804i | \(0.379162\pi\) | |||||||
\(984\) | −4.12113e10 | −1.37890 | ||||||||
\(985\) | −6.67275e10 | −2.22473 | ||||||||
\(986\) | −3.93180e10 | −1.30624 | ||||||||
\(987\) | 2.23699e10 | 0.740549 | ||||||||
\(988\) | 3.22223e10 | 1.06294 | ||||||||
\(989\) | −2.69774e10 | −0.886774 | ||||||||
\(990\) | 5.70024e10 | 1.86711 | ||||||||
\(991\) | −4.94638e10 | −1.61447 | −0.807235 | − | 0.590231i | \(-0.799037\pi\) | ||||
−0.807235 | + | 0.590231i | \(0.799037\pi\) | |||||||
\(992\) | 1.07991e11 | 3.51233 | ||||||||
\(993\) | −1.52433e10 | −0.494034 | ||||||||
\(994\) | 5.86943e9 | 0.189559 | ||||||||
\(995\) | 2.48637e9 | 0.0800174 | ||||||||
\(996\) | 1.09476e11 | 3.51085 | ||||||||
\(997\) | −3.10203e9 | −0.0991318 | −0.0495659 | − | 0.998771i | \(-0.515784\pi\) | ||||
−0.0495659 | + | 0.998771i | \(0.515784\pi\) | |||||||
\(998\) | −9.48165e10 | −3.01945 | ||||||||
\(999\) | 5.55493e9 | 0.176279 |
(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 | 37.8.a.b.1.1 | ✓ | 11 | |
3.2 | odd | 2 | 333.8.a.d.1.11 | 11 | |||
4.3 | odd | 2 | 592.8.a.g.1.5 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.8.a.b.1.1 | ✓ | 11 | 1.1 | even | 1 | trivial | |
333.8.a.d.1.11 | 11 | 3.2 | odd | 2 | |||
592.8.a.g.1.5 | 11 | 4.3 | odd | 2 |