Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(28.4270373191\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + \cdots - 7335224320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-19.0627\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 19.0627 | 1.68492 | 0.842461 | − | 0.538757i | \(-0.181106\pi\) | ||||
0.842461 | + | 0.538757i | \(0.181106\pi\) | |||||||
\(3\) | −86.0671 | −1.84040 | −0.920201 | − | 0.391446i | \(-0.871975\pi\) | ||||
−0.920201 | + | 0.391446i | \(0.871975\pi\) | |||||||
\(4\) | 235.388 | 1.83897 | ||||||||
\(5\) | −217.435 | −0.777920 | −0.388960 | − | 0.921255i | \(-0.627166\pi\) | ||||
−0.388960 | + | 0.921255i | \(0.627166\pi\) | |||||||
\(6\) | −1640.67 | −3.10094 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 2047.10 | 1.41359 | ||||||||
\(9\) | 5220.54 | 2.38708 | ||||||||
\(10\) | −4144.91 | −1.31073 | ||||||||
\(11\) | 1359.88 | 0.308054 | 0.154027 | − | 0.988067i | \(-0.450776\pi\) | ||||
0.154027 | + | 0.988067i | \(0.450776\pi\) | |||||||
\(12\) | −20259.1 | −3.38444 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | −6538.52 | −0.636841 | ||||||||
\(15\) | 18714.0 | 1.43168 | ||||||||
\(16\) | 8893.70 | 0.542828 | ||||||||
\(17\) | 18136.4 | 0.895321 | 0.447661 | − | 0.894204i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894204i | \(0.352257\pi\) | |||||||
\(18\) | 99517.8 | 4.02204 | ||||||||
\(19\) | 37526.7 | 1.25517 | 0.627586 | − | 0.778547i | \(-0.284043\pi\) | ||||
0.627586 | + | 0.778547i | \(0.284043\pi\) | |||||||
\(20\) | −51181.5 | −1.43057 | ||||||||
\(21\) | 29521.0 | 0.695606 | ||||||||
\(22\) | 25923.0 | 0.519047 | ||||||||
\(23\) | 106016. | 1.81687 | 0.908437 | − | 0.418021i | \(-0.137276\pi\) | ||||
0.908437 | + | 0.418021i | \(0.137276\pi\) | |||||||
\(24\) | −176188. | −2.60158 | ||||||||
\(25\) | −30846.9 | −0.394841 | ||||||||
\(26\) | −41880.8 | −0.467314 | ||||||||
\(27\) | −261088. | −2.55278 | ||||||||
\(28\) | −80737.9 | −0.695064 | ||||||||
\(29\) | 95658.1 | 0.728331 | 0.364165 | − | 0.931334i | \(-0.381354\pi\) | ||||
0.364165 | + | 0.931334i | \(0.381354\pi\) | |||||||
\(30\) | 356740. | 2.41228 | ||||||||
\(31\) | 134134. | 0.808672 | 0.404336 | − | 0.914611i | \(-0.367503\pi\) | ||||
0.404336 | + | 0.914611i | \(0.367503\pi\) | |||||||
\(32\) | −92490.6 | −0.498968 | ||||||||
\(33\) | −117041. | −0.566943 | ||||||||
\(34\) | 345728. | 1.50855 | ||||||||
\(35\) | 74580.3 | 0.294026 | ||||||||
\(36\) | 1.22885e6 | 4.38976 | ||||||||
\(37\) | 305719. | 0.992239 | 0.496120 | − | 0.868254i | \(-0.334758\pi\) | ||||
0.496120 | + | 0.868254i | \(0.334758\pi\) | |||||||
\(38\) | 715362. | 2.11487 | ||||||||
\(39\) | 189089. | 0.510436 | ||||||||
\(40\) | −445112. | −1.09966 | ||||||||
\(41\) | −428291. | −0.970500 | −0.485250 | − | 0.874375i | \(-0.661271\pi\) | ||||
−0.485250 | + | 0.874375i | \(0.661271\pi\) | |||||||
\(42\) | 562751. | 1.17204 | ||||||||
\(43\) | 314247. | 0.602743 | 0.301372 | − | 0.953507i | \(-0.402556\pi\) | ||||
0.301372 | + | 0.953507i | \(0.402556\pi\) | |||||||
\(44\) | 320099. | 0.566500 | ||||||||
\(45\) | −1.13513e6 | −1.85696 | ||||||||
\(46\) | 2.02096e6 | 3.06129 | ||||||||
\(47\) | −1.21612e6 | −1.70857 | −0.854284 | − | 0.519806i | \(-0.826004\pi\) | ||||
−0.854284 | + | 0.519806i | \(0.826004\pi\) | |||||||
\(48\) | −765455. | −0.999022 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −588027. | −0.665276 | ||||||||
\(51\) | −1.56094e6 | −1.64775 | ||||||||
\(52\) | −517146. | −0.510037 | ||||||||
\(53\) | 767929. | 0.708526 | 0.354263 | − | 0.935146i | \(-0.384732\pi\) | ||||
0.354263 | + | 0.935146i | \(0.384732\pi\) | |||||||
\(54\) | −4.97705e6 | −4.30124 | ||||||||
\(55\) | −295686. | −0.239641 | ||||||||
\(56\) | −702155. | −0.534288 | ||||||||
\(57\) | −3.22982e6 | −2.31002 | ||||||||
\(58\) | 1.82350e6 | 1.22718 | ||||||||
\(59\) | 186379. | 0.118145 | 0.0590724 | − | 0.998254i | \(-0.481186\pi\) | ||||
0.0590724 | + | 0.998254i | \(0.481186\pi\) | |||||||
\(60\) | 4.40505e6 | 2.63282 | ||||||||
\(61\) | 1.76366e6 | 0.994856 | 0.497428 | − | 0.867505i | \(-0.334278\pi\) | ||||
0.497428 | + | 0.867505i | \(0.334278\pi\) | |||||||
\(62\) | 2.55696e6 | 1.36255 | ||||||||
\(63\) | −1.79065e6 | −0.902231 | ||||||||
\(64\) | −2.90152e6 | −1.38355 | ||||||||
\(65\) | 477705. | 0.215756 | ||||||||
\(66\) | −2.23112e6 | −0.955255 | ||||||||
\(67\) | −410055. | −0.166564 | −0.0832819 | − | 0.996526i | \(-0.526540\pi\) | ||||
−0.0832819 | + | 0.996526i | \(0.526540\pi\) | |||||||
\(68\) | 4.26907e6 | 1.64646 | ||||||||
\(69\) | −9.12451e6 | −3.34378 | ||||||||
\(70\) | 1.42170e6 | 0.495411 | ||||||||
\(71\) | −641600. | −0.212745 | −0.106373 | − | 0.994326i | \(-0.533924\pi\) | ||||
−0.106373 | + | 0.994326i | \(0.533924\pi\) | |||||||
\(72\) | 1.06870e7 | 3.37436 | ||||||||
\(73\) | 4.66335e6 | 1.40303 | 0.701516 | − | 0.712654i | \(-0.252507\pi\) | ||||
0.701516 | + | 0.712654i | \(0.252507\pi\) | |||||||
\(74\) | 5.82784e6 | 1.67185 | ||||||||
\(75\) | 2.65491e6 | 0.726666 | ||||||||
\(76\) | 8.83333e6 | 2.30822 | ||||||||
\(77\) | −466439. | −0.116433 | ||||||||
\(78\) | 3.60456e6 | 0.860045 | ||||||||
\(79\) | −6.39172e6 | −1.45856 | −0.729278 | − | 0.684218i | \(-0.760144\pi\) | ||||
−0.729278 | + | 0.684218i | \(0.760144\pi\) | |||||||
\(80\) | −1.93380e6 | −0.422277 | ||||||||
\(81\) | 1.10538e7 | 2.31107 | ||||||||
\(82\) | −8.16440e6 | −1.63522 | ||||||||
\(83\) | −1.65238e6 | −0.317203 | −0.158601 | − | 0.987343i | \(-0.550699\pi\) | ||||
−0.158601 | + | 0.987343i | \(0.550699\pi\) | |||||||
\(84\) | 6.94888e6 | 1.27920 | ||||||||
\(85\) | −3.94348e6 | −0.696488 | ||||||||
\(86\) | 5.99041e6 | 1.01558 | ||||||||
\(87\) | −8.23301e6 | −1.34042 | ||||||||
\(88\) | 2.78381e6 | 0.435462 | ||||||||
\(89\) | 1.16301e7 | 1.74871 | 0.874353 | − | 0.485290i | \(-0.161286\pi\) | ||||
0.874353 | + | 0.485290i | \(0.161286\pi\) | |||||||
\(90\) | −2.16387e7 | −3.12883 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | 2.49549e7 | 3.34117 | ||||||||
\(93\) | −1.15445e7 | −1.48828 | ||||||||
\(94\) | −2.31825e7 | −2.87881 | ||||||||
\(95\) | −8.15963e6 | −0.976423 | ||||||||
\(96\) | 7.96040e6 | 0.918302 | ||||||||
\(97\) | 5.73307e6 | 0.637803 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(98\) | 2.24271e6 | 0.240703 | ||||||||
\(99\) | 7.09932e6 | 0.735349 | ||||||||
\(100\) | −7.26099e6 | −0.726099 | ||||||||
\(101\) | 1.29076e7 | 1.24658 | 0.623291 | − | 0.781990i | \(-0.285795\pi\) | ||||
0.623291 | + | 0.781990i | \(0.285795\pi\) | |||||||
\(102\) | −2.97558e7 | −2.77633 | ||||||||
\(103\) | −8.95372e6 | −0.807371 | −0.403686 | − | 0.914898i | \(-0.632271\pi\) | ||||
−0.403686 | + | 0.914898i | \(0.632271\pi\) | |||||||
\(104\) | −4.49748e6 | −0.392060 | ||||||||
\(105\) | −6.41891e6 | −0.541126 | ||||||||
\(106\) | 1.46388e7 | 1.19381 | ||||||||
\(107\) | −7.43785e6 | −0.586954 | −0.293477 | − | 0.955966i | \(-0.594812\pi\) | ||||
−0.293477 | + | 0.955966i | \(0.594812\pi\) | |||||||
\(108\) | −6.14569e7 | −4.69448 | ||||||||
\(109\) | 2.67013e7 | 1.97488 | 0.987438 | − | 0.158007i | \(-0.0505070\pi\) | ||||
0.987438 | + | 0.158007i | \(0.0505070\pi\) | |||||||
\(110\) | −5.63658e6 | −0.403777 | ||||||||
\(111\) | −2.63123e7 | −1.82612 | ||||||||
\(112\) | −3.05054e6 | −0.205170 | ||||||||
\(113\) | −6.91587e6 | −0.450892 | −0.225446 | − | 0.974256i | \(-0.572384\pi\) | ||||
−0.225446 | + | 0.974256i | \(0.572384\pi\) | |||||||
\(114\) | −6.15691e7 | −3.89221 | ||||||||
\(115\) | −2.30517e7 | −1.41338 | ||||||||
\(116\) | 2.25167e7 | 1.33937 | ||||||||
\(117\) | −1.14695e7 | −0.662057 | ||||||||
\(118\) | 3.55289e6 | 0.199065 | ||||||||
\(119\) | −6.22077e6 | −0.338400 | ||||||||
\(120\) | 3.83095e7 | 2.02382 | ||||||||
\(121\) | −1.76379e7 | −0.905103 | ||||||||
\(122\) | 3.36201e7 | 1.67626 | ||||||||
\(123\) | 3.68618e7 | 1.78611 | ||||||||
\(124\) | 3.15734e7 | 1.48712 | ||||||||
\(125\) | 2.36943e7 | 1.08507 | ||||||||
\(126\) | −3.41346e7 | −1.52019 | ||||||||
\(127\) | 2.32271e7 | 1.00619 | 0.503097 | − | 0.864230i | \(-0.332194\pi\) | ||||
0.503097 | + | 0.864230i | \(0.332194\pi\) | |||||||
\(128\) | −4.34720e7 | −1.83221 | ||||||||
\(129\) | −2.70464e7 | −1.10929 | ||||||||
\(130\) | 9.10636e6 | 0.363532 | ||||||||
\(131\) | 3.84927e7 | 1.49599 | 0.747996 | − | 0.663703i | \(-0.231016\pi\) | ||||
0.747996 | + | 0.663703i | \(0.231016\pi\) | |||||||
\(132\) | −2.75500e7 | −1.04259 | ||||||||
\(133\) | −1.28717e7 | −0.474410 | ||||||||
\(134\) | −7.81677e6 | −0.280647 | ||||||||
\(135\) | 5.67697e7 | 1.98586 | ||||||||
\(136\) | 3.71269e7 | 1.26562 | ||||||||
\(137\) | −735092. | −0.0244242 | −0.0122121 | − | 0.999925i | \(-0.503887\pi\) | ||||
−0.0122121 | + | 0.999925i | \(0.503887\pi\) | |||||||
\(138\) | −1.73938e8 | −5.63401 | ||||||||
\(139\) | 3.92490e7 | 1.23959 | 0.619794 | − | 0.784765i | \(-0.287216\pi\) | ||||
0.619794 | + | 0.784765i | \(0.287216\pi\) | |||||||
\(140\) | 1.75553e7 | 0.540704 | ||||||||
\(141\) | 1.04668e8 | 3.14445 | ||||||||
\(142\) | −1.22306e7 | −0.358460 | ||||||||
\(143\) | −2.98766e6 | −0.0854387 | ||||||||
\(144\) | 4.64299e7 | 1.29577 | ||||||||
\(145\) | −2.07994e7 | −0.566583 | ||||||||
\(146\) | 8.88961e7 | 2.36400 | ||||||||
\(147\) | −1.01257e7 | −0.262915 | ||||||||
\(148\) | 7.19624e7 | 1.82469 | ||||||||
\(149\) | −1.81663e6 | −0.0449899 | −0.0224949 | − | 0.999747i | \(-0.507161\pi\) | ||||
−0.0224949 | + | 0.999747i | \(0.507161\pi\) | |||||||
\(150\) | 5.06097e7 | 1.22438 | ||||||||
\(151\) | −7.20574e7 | −1.70317 | −0.851587 | − | 0.524213i | \(-0.824360\pi\) | ||||
−0.851587 | + | 0.524213i | \(0.824360\pi\) | |||||||
\(152\) | 7.68210e7 | 1.77430 | ||||||||
\(153\) | 9.46816e7 | 2.13720 | ||||||||
\(154\) | −8.89160e6 | −0.196181 | ||||||||
\(155\) | −2.91654e7 | −0.629082 | ||||||||
\(156\) | 4.45093e7 | 0.938673 | ||||||||
\(157\) | −3.93167e7 | −0.810828 | −0.405414 | − | 0.914133i | \(-0.632873\pi\) | ||||
−0.405414 | + | 0.914133i | \(0.632873\pi\) | |||||||
\(158\) | −1.21844e8 | −2.45755 | ||||||||
\(159\) | −6.60934e7 | −1.30397 | ||||||||
\(160\) | 2.01107e7 | 0.388157 | ||||||||
\(161\) | −3.63636e7 | −0.686714 | ||||||||
\(162\) | 2.10715e8 | 3.89397 | ||||||||
\(163\) | −1.54892e6 | −0.0280138 | −0.0140069 | − | 0.999902i | \(-0.504459\pi\) | ||||
−0.0140069 | + | 0.999902i | \(0.504459\pi\) | |||||||
\(164\) | −1.00814e8 | −1.78472 | ||||||||
\(165\) | 2.54488e7 | 0.441036 | ||||||||
\(166\) | −3.14989e7 | −0.534463 | ||||||||
\(167\) | 4.79827e7 | 0.797218 | 0.398609 | − | 0.917121i | \(-0.369493\pi\) | ||||
0.398609 | + | 0.917121i | \(0.369493\pi\) | |||||||
\(168\) | 6.04325e7 | 0.983304 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −7.51735e7 | −1.17353 | ||||||||
\(171\) | 1.95910e8 | 2.99619 | ||||||||
\(172\) | 7.39700e7 | 1.10842 | ||||||||
\(173\) | −9.90499e7 | −1.45443 | −0.727214 | − | 0.686410i | \(-0.759185\pi\) | ||||
−0.727214 | + | 0.686410i | \(0.759185\pi\) | |||||||
\(174\) | −1.56944e8 | −2.25851 | ||||||||
\(175\) | 1.05805e7 | 0.149236 | ||||||||
\(176\) | 1.20944e7 | 0.167220 | ||||||||
\(177\) | −1.60411e7 | −0.217434 | ||||||||
\(178\) | 2.21701e8 | 2.94644 | ||||||||
\(179\) | −6.36964e7 | −0.830098 | −0.415049 | − | 0.909799i | \(-0.636236\pi\) | ||||
−0.415049 | + | 0.909799i | \(0.636236\pi\) | |||||||
\(180\) | −2.67195e8 | −3.41488 | ||||||||
\(181\) | −2.18422e7 | −0.273793 | −0.136896 | − | 0.990585i | \(-0.543713\pi\) | ||||
−0.136896 | + | 0.990585i | \(0.543713\pi\) | |||||||
\(182\) | 1.43651e7 | 0.176628 | ||||||||
\(183\) | −1.51793e8 | −1.83093 | ||||||||
\(184\) | 2.17026e8 | 2.56832 | ||||||||
\(185\) | −6.64741e7 | −0.771882 | ||||||||
\(186\) | −2.20070e8 | −2.50764 | ||||||||
\(187\) | 2.46633e7 | 0.275807 | ||||||||
\(188\) | −2.86259e8 | −3.14200 | ||||||||
\(189\) | 8.95532e7 | 0.964861 | ||||||||
\(190\) | −1.55545e8 | −1.64520 | ||||||||
\(191\) | 1.15872e8 | 1.20326 | 0.601631 | − | 0.798774i | \(-0.294518\pi\) | ||||
0.601631 | + | 0.798774i | \(0.294518\pi\) | |||||||
\(192\) | 2.49725e8 | 2.54629 | ||||||||
\(193\) | 1.55286e8 | 1.55483 | 0.777414 | − | 0.628989i | \(-0.216531\pi\) | ||||
0.777414 | + | 0.628989i | \(0.216531\pi\) | |||||||
\(194\) | 1.09288e8 | 1.07465 | ||||||||
\(195\) | −4.11147e7 | −0.397078 | ||||||||
\(196\) | 2.76931e7 | 0.262709 | ||||||||
\(197\) | 1.08782e8 | 1.01374 | 0.506869 | − | 0.862023i | \(-0.330803\pi\) | ||||
0.506869 | + | 0.862023i | \(0.330803\pi\) | |||||||
\(198\) | 1.35332e8 | 1.23901 | ||||||||
\(199\) | 2.74085e7 | 0.246547 | 0.123273 | − | 0.992373i | \(-0.460661\pi\) | ||||
0.123273 | + | 0.992373i | \(0.460661\pi\) | |||||||
\(200\) | −6.31468e7 | −0.558144 | ||||||||
\(201\) | 3.52923e7 | 0.306544 | ||||||||
\(202\) | 2.46054e8 | 2.10039 | ||||||||
\(203\) | −3.28107e7 | −0.275283 | ||||||||
\(204\) | −3.67427e8 | −3.03016 | ||||||||
\(205\) | 9.31256e7 | 0.754971 | ||||||||
\(206\) | −1.70682e8 | −1.36036 | ||||||||
\(207\) | 5.53462e8 | 4.33702 | ||||||||
\(208\) | −1.95395e7 | −0.150554 | ||||||||
\(209\) | 5.10319e7 | 0.386660 | ||||||||
\(210\) | −1.22362e8 | −0.911756 | ||||||||
\(211\) | 9.93293e7 | 0.727929 | 0.363964 | − | 0.931413i | \(-0.381423\pi\) | ||||
0.363964 | + | 0.931413i | \(0.381423\pi\) | |||||||
\(212\) | 1.80761e8 | 1.30295 | ||||||||
\(213\) | 5.52206e7 | 0.391537 | ||||||||
\(214\) | −1.41786e8 | −0.988973 | ||||||||
\(215\) | −6.83285e7 | −0.468886 | ||||||||
\(216\) | −5.34473e8 | −3.60859 | ||||||||
\(217\) | −4.60079e7 | −0.305649 | ||||||||
\(218\) | 5.09000e8 | 3.32751 | ||||||||
\(219\) | −4.01361e8 | −2.58214 | ||||||||
\(220\) | −6.96008e7 | −0.440692 | ||||||||
\(221\) | −3.98456e7 | −0.248317 | ||||||||
\(222\) | −5.01585e8 | −3.07687 | ||||||||
\(223\) | −5.87540e7 | −0.354789 | −0.177395 | − | 0.984140i | \(-0.556767\pi\) | ||||
−0.177395 | + | 0.984140i | \(0.556767\pi\) | |||||||
\(224\) | 3.17243e7 | 0.188592 | ||||||||
\(225\) | −1.61038e8 | −0.942516 | ||||||||
\(226\) | −1.31835e8 | −0.759718 | ||||||||
\(227\) | 1.29241e8 | 0.733345 | 0.366673 | − | 0.930350i | \(-0.380497\pi\) | ||||
0.366673 | + | 0.930350i | \(0.380497\pi\) | |||||||
\(228\) | −7.60259e8 | −4.24805 | ||||||||
\(229\) | 1.86669e8 | 1.02718 | 0.513592 | − | 0.858034i | \(-0.328314\pi\) | ||||
0.513592 | + | 0.858034i | \(0.328314\pi\) | |||||||
\(230\) | −4.39427e8 | −2.38144 | ||||||||
\(231\) | 4.01451e7 | 0.214284 | ||||||||
\(232\) | 1.95822e8 | 1.02956 | ||||||||
\(233\) | −3.40765e8 | −1.76486 | −0.882428 | − | 0.470447i | \(-0.844093\pi\) | ||||
−0.882428 | + | 0.470447i | \(0.844093\pi\) | |||||||
\(234\) | −2.18641e8 | −1.11551 | ||||||||
\(235\) | 2.64426e8 | 1.32913 | ||||||||
\(236\) | 4.38713e7 | 0.217264 | ||||||||
\(237\) | 5.50117e8 | 2.68433 | ||||||||
\(238\) | −1.18585e8 | −0.570177 | ||||||||
\(239\) | −2.68486e8 | −1.27212 | −0.636061 | − | 0.771638i | \(-0.719438\pi\) | ||||
−0.636061 | + | 0.771638i | \(0.719438\pi\) | |||||||
\(240\) | 1.66437e8 | 0.777159 | ||||||||
\(241\) | −9.51070e7 | −0.437676 | −0.218838 | − | 0.975761i | \(-0.570227\pi\) | ||||
−0.218838 | + | 0.975761i | \(0.570227\pi\) | |||||||
\(242\) | −3.36226e8 | −1.52503 | ||||||||
\(243\) | −3.80365e8 | −1.70051 | ||||||||
\(244\) | 4.15143e8 | 1.82951 | ||||||||
\(245\) | −2.55810e7 | −0.111131 | ||||||||
\(246\) | 7.02686e8 | 3.00946 | ||||||||
\(247\) | −8.24462e7 | −0.348122 | ||||||||
\(248\) | 2.74585e8 | 1.14313 | ||||||||
\(249\) | 1.42216e8 | 0.583781 | ||||||||
\(250\) | 4.51679e8 | 1.82827 | ||||||||
\(251\) | 2.38071e8 | 0.950274 | 0.475137 | − | 0.879912i | \(-0.342399\pi\) | ||||
0.475137 | + | 0.879912i | \(0.342399\pi\) | |||||||
\(252\) | −4.21496e8 | −1.65917 | ||||||||
\(253\) | 1.44169e8 | 0.559695 | ||||||||
\(254\) | 4.42772e8 | 1.69536 | ||||||||
\(255\) | 3.39404e8 | 1.28182 | ||||||||
\(256\) | −4.57301e8 | −1.70358 | ||||||||
\(257\) | −2.70376e8 | −0.993580 | −0.496790 | − | 0.867871i | \(-0.665488\pi\) | ||||
−0.496790 | + | 0.867871i | \(0.665488\pi\) | |||||||
\(258\) | −5.15577e8 | −1.86907 | ||||||||
\(259\) | −1.04862e8 | −0.375031 | ||||||||
\(260\) | 1.12446e8 | 0.396768 | ||||||||
\(261\) | 4.99387e8 | 1.73858 | ||||||||
\(262\) | 7.33777e8 | 2.52063 | ||||||||
\(263\) | −4.80199e8 | −1.62771 | −0.813853 | − | 0.581070i | \(-0.802634\pi\) | ||||
−0.813853 | + | 0.581070i | \(0.802634\pi\) | |||||||
\(264\) | −2.39595e8 | −0.801426 | ||||||||
\(265\) | −1.66975e8 | −0.551176 | ||||||||
\(266\) | −2.45369e8 | −0.799345 | ||||||||
\(267\) | −1.00097e9 | −3.21832 | ||||||||
\(268\) | −9.65219e7 | −0.306305 | ||||||||
\(269\) | 5.58089e8 | 1.74812 | 0.874058 | − | 0.485822i | \(-0.161480\pi\) | ||||
0.874058 | + | 0.485822i | \(0.161480\pi\) | |||||||
\(270\) | 1.08219e9 | 3.34602 | ||||||||
\(271\) | −3.34296e8 | −1.02032 | −0.510162 | − | 0.860078i | \(-0.670415\pi\) | ||||
−0.510162 | + | 0.860078i | \(0.670415\pi\) | |||||||
\(272\) | 1.61299e8 | 0.486006 | ||||||||
\(273\) | −6.48577e7 | −0.192927 | ||||||||
\(274\) | −1.40129e7 | −0.0411529 | ||||||||
\(275\) | −4.19482e7 | −0.121632 | ||||||||
\(276\) | −2.14780e9 | −6.14909 | ||||||||
\(277\) | 1.72977e7 | 0.0489000 | 0.0244500 | − | 0.999701i | \(-0.492217\pi\) | ||||
0.0244500 | + | 0.999701i | \(0.492217\pi\) | |||||||
\(278\) | 7.48194e8 | 2.08861 | ||||||||
\(279\) | 7.00251e8 | 1.93036 | ||||||||
\(280\) | 1.52673e8 | 0.415633 | ||||||||
\(281\) | 6.56318e8 | 1.76458 | 0.882292 | − | 0.470703i | \(-0.156000\pi\) | ||||
0.882292 | + | 0.470703i | \(0.156000\pi\) | |||||||
\(282\) | 1.99525e9 | 5.29816 | ||||||||
\(283\) | −4.00939e8 | −1.05154 | −0.525770 | − | 0.850627i | \(-0.676223\pi\) | ||||
−0.525770 | + | 0.850627i | \(0.676223\pi\) | |||||||
\(284\) | −1.51025e8 | −0.391231 | ||||||||
\(285\) | 7.02276e8 | 1.79701 | ||||||||
\(286\) | −5.69529e7 | −0.143958 | ||||||||
\(287\) | 1.46904e8 | 0.366815 | ||||||||
\(288\) | −4.82851e8 | −1.19108 | ||||||||
\(289\) | −8.14111e7 | −0.198400 | ||||||||
\(290\) | −3.96494e8 | −0.954648 | ||||||||
\(291\) | −4.93429e8 | −1.17381 | ||||||||
\(292\) | 1.09769e9 | 2.58013 | ||||||||
\(293\) | −3.09442e8 | −0.718692 | −0.359346 | − | 0.933204i | \(-0.617000\pi\) | ||||
−0.359346 | + | 0.933204i | \(0.617000\pi\) | |||||||
\(294\) | −1.93024e8 | −0.442991 | ||||||||
\(295\) | −4.05253e7 | −0.0919072 | ||||||||
\(296\) | 6.25837e8 | 1.40262 | ||||||||
\(297\) | −3.55049e8 | −0.786394 | ||||||||
\(298\) | −3.46299e7 | −0.0758045 | ||||||||
\(299\) | −2.32918e8 | −0.503910 | ||||||||
\(300\) | 6.24932e8 | 1.33631 | ||||||||
\(301\) | −1.07787e8 | −0.227815 | ||||||||
\(302\) | −1.37361e9 | −2.86972 | ||||||||
\(303\) | −1.11092e9 | −2.29421 | ||||||||
\(304\) | 3.33751e8 | 0.681343 | ||||||||
\(305\) | −3.83481e8 | −0.773918 | ||||||||
\(306\) | 1.80489e9 | 3.60102 | ||||||||
\(307\) | −8.07175e8 | −1.59215 | −0.796074 | − | 0.605200i | \(-0.793093\pi\) | ||||
−0.796074 | + | 0.605200i | \(0.793093\pi\) | |||||||
\(308\) | −1.09794e8 | −0.214117 | ||||||||
\(309\) | 7.70621e8 | 1.48589 | ||||||||
\(310\) | −5.55972e8 | −1.05995 | ||||||||
\(311\) | −3.58067e8 | −0.674998 | −0.337499 | − | 0.941326i | \(-0.609581\pi\) | ||||
−0.337499 | + | 0.941326i | \(0.609581\pi\) | |||||||
\(312\) | 3.87085e8 | 0.721548 | ||||||||
\(313\) | 2.28625e8 | 0.421423 | 0.210712 | − | 0.977548i | \(-0.432422\pi\) | ||||
0.210712 | + | 0.977548i | \(0.432422\pi\) | |||||||
\(314\) | −7.49484e8 | −1.36618 | ||||||||
\(315\) | 3.89349e8 | 0.701863 | ||||||||
\(316\) | −1.50453e9 | −2.68223 | ||||||||
\(317\) | −3.66493e8 | −0.646187 | −0.323094 | − | 0.946367i | \(-0.604723\pi\) | ||||
−0.323094 | + | 0.946367i | \(0.604723\pi\) | |||||||
\(318\) | −1.25992e9 | −2.19709 | ||||||||
\(319\) | 1.30084e8 | 0.224365 | ||||||||
\(320\) | 6.30892e8 | 1.07629 | ||||||||
\(321\) | 6.40154e8 | 1.08023 | ||||||||
\(322\) | −6.93189e8 | −1.15706 | ||||||||
\(323\) | 6.80598e8 | 1.12378 | ||||||||
\(324\) | 2.60192e9 | 4.24997 | ||||||||
\(325\) | 6.77707e7 | 0.109509 | ||||||||
\(326\) | −2.95266e7 | −0.0472011 | ||||||||
\(327\) | −2.29810e9 | −3.63457 | ||||||||
\(328\) | −8.76755e8 | −1.37189 | ||||||||
\(329\) | 4.17128e8 | 0.645778 | ||||||||
\(330\) | 4.85124e8 | 0.743112 | ||||||||
\(331\) | −6.30923e7 | −0.0956265 | −0.0478132 | − | 0.998856i | \(-0.515225\pi\) | ||||
−0.0478132 | + | 0.998856i | \(0.515225\pi\) | |||||||
\(332\) | −3.88950e8 | −0.583325 | ||||||||
\(333\) | 1.59602e9 | 2.36855 | ||||||||
\(334\) | 9.14681e8 | 1.34325 | ||||||||
\(335\) | 8.91605e7 | 0.129573 | ||||||||
\(336\) | 2.62551e8 | 0.377595 | ||||||||
\(337\) | −6.80708e8 | −0.968850 | −0.484425 | − | 0.874833i | \(-0.660971\pi\) | ||||
−0.484425 | + | 0.874833i | \(0.660971\pi\) | |||||||
\(338\) | 9.20121e7 | 0.129609 | ||||||||
\(339\) | 5.95229e8 | 0.829822 | ||||||||
\(340\) | −9.28247e8 | −1.28082 | ||||||||
\(341\) | 1.82406e8 | 0.249114 | ||||||||
\(342\) | 3.73458e9 | 5.04836 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 6.43296e8 | 0.852033 | ||||||||
\(345\) | 1.98399e9 | 2.60119 | ||||||||
\(346\) | −1.88816e9 | −2.45060 | ||||||||
\(347\) | −1.01055e9 | −1.29838 | −0.649191 | − | 0.760625i | \(-0.724892\pi\) | ||||
−0.649191 | + | 0.760625i | \(0.724892\pi\) | |||||||
\(348\) | −1.93795e9 | −2.46499 | ||||||||
\(349\) | −4.66558e8 | −0.587512 | −0.293756 | − | 0.955880i | \(-0.594905\pi\) | ||||
−0.293756 | + | 0.955880i | \(0.594905\pi\) | |||||||
\(350\) | 2.01693e8 | 0.251451 | ||||||||
\(351\) | 5.73610e8 | 0.708014 | ||||||||
\(352\) | −1.25776e8 | −0.153709 | ||||||||
\(353\) | 1.10221e9 | 1.33369 | 0.666843 | − | 0.745198i | \(-0.267645\pi\) | ||||
0.666843 | + | 0.745198i | \(0.267645\pi\) | |||||||
\(354\) | −3.05787e8 | −0.366360 | ||||||||
\(355\) | 1.39506e8 | 0.165499 | ||||||||
\(356\) | 2.73757e9 | 3.21581 | ||||||||
\(357\) | 5.35404e8 | 0.622791 | ||||||||
\(358\) | −1.21423e9 | −1.39865 | ||||||||
\(359\) | 1.43530e9 | 1.63723 | 0.818617 | − | 0.574339i | \(-0.194741\pi\) | ||||
0.818617 | + | 0.574339i | \(0.194741\pi\) | |||||||
\(360\) | −2.32372e9 | −2.62498 | ||||||||
\(361\) | 5.14384e8 | 0.575456 | ||||||||
\(362\) | −4.16372e8 | −0.461319 | ||||||||
\(363\) | 1.51804e9 | 1.66575 | ||||||||
\(364\) | 1.77381e8 | 0.192776 | ||||||||
\(365\) | −1.01398e9 | −1.09145 | ||||||||
\(366\) | −2.89359e9 | −3.08498 | ||||||||
\(367\) | −2.60504e8 | −0.275095 | −0.137548 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137548 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(368\) | 9.42877e8 | 0.986251 | ||||||||
\(369\) | −2.23591e9 | −2.31666 | ||||||||
\(370\) | −1.26718e9 | −1.30056 | ||||||||
\(371\) | −2.63400e8 | −0.267798 | ||||||||
\(372\) | −2.71743e9 | −2.73690 | ||||||||
\(373\) | 5.70375e7 | 0.0569089 | 0.0284544 | − | 0.999595i | \(-0.490941\pi\) | ||||
0.0284544 | + | 0.999595i | \(0.490941\pi\) | |||||||
\(374\) | 4.70150e8 | 0.464714 | ||||||||
\(375\) | −2.03930e9 | −1.99697 | ||||||||
\(376\) | −2.48951e9 | −2.41522 | ||||||||
\(377\) | −2.10161e8 | −0.202003 | ||||||||
\(378\) | 1.70713e9 | 1.62572 | ||||||||
\(379\) | −1.33390e9 | −1.25860 | −0.629300 | − | 0.777163i | \(-0.716658\pi\) | ||||
−0.629300 | + | 0.777163i | \(0.716658\pi\) | |||||||
\(380\) | −1.92068e9 | −1.79561 | ||||||||
\(381\) | −1.99909e9 | −1.85180 | ||||||||
\(382\) | 2.20883e9 | 2.02740 | ||||||||
\(383\) | −1.22400e9 | −1.11323 | −0.556614 | − | 0.830771i | \(-0.687900\pi\) | ||||
−0.556614 | + | 0.830771i | \(0.687900\pi\) | |||||||
\(384\) | 3.74151e9 | 3.37200 | ||||||||
\(385\) | 1.01420e8 | 0.0905758 | ||||||||
\(386\) | 2.96018e9 | 2.61977 | ||||||||
\(387\) | 1.64054e9 | 1.43880 | ||||||||
\(388\) | 1.34949e9 | 1.17290 | ||||||||
\(389\) | 1.55921e9 | 1.34301 | 0.671507 | − | 0.740998i | \(-0.265647\pi\) | ||||
0.671507 | + | 0.740998i | \(0.265647\pi\) | |||||||
\(390\) | −7.83758e8 | −0.669046 | ||||||||
\(391\) | 1.92275e9 | 1.62669 | ||||||||
\(392\) | 2.40839e8 | 0.201942 | ||||||||
\(393\) | −3.31296e9 | −2.75323 | ||||||||
\(394\) | 2.07368e9 | 1.70807 | ||||||||
\(395\) | 1.38978e9 | 1.13464 | ||||||||
\(396\) | 1.67109e9 | 1.35228 | ||||||||
\(397\) | −4.39204e8 | −0.352289 | −0.176145 | − | 0.984364i | \(-0.556363\pi\) | ||||
−0.176145 | + | 0.984364i | \(0.556363\pi\) | |||||||
\(398\) | 5.22480e8 | 0.415412 | ||||||||
\(399\) | 1.10783e9 | 0.873106 | ||||||||
\(400\) | −2.74343e8 | −0.214331 | ||||||||
\(401\) | −1.09759e9 | −0.850034 | −0.425017 | − | 0.905185i | \(-0.639732\pi\) | ||||
−0.425017 | + | 0.905185i | \(0.639732\pi\) | |||||||
\(402\) | 6.72767e8 | 0.516504 | ||||||||
\(403\) | −2.94692e8 | −0.224285 | ||||||||
\(404\) | 3.03829e9 | 2.29242 | ||||||||
\(405\) | −2.40348e9 | −1.79782 | ||||||||
\(406\) | −6.25462e8 | −0.463831 | ||||||||
\(407\) | 4.15741e8 | 0.305663 | ||||||||
\(408\) | −3.19541e9 | −2.32925 | ||||||||
\(409\) | 1.61412e8 | 0.116656 | 0.0583278 | − | 0.998297i | \(-0.481423\pi\) | ||||
0.0583278 | + | 0.998297i | \(0.481423\pi\) | |||||||
\(410\) | 1.77523e9 | 1.27207 | ||||||||
\(411\) | 6.32672e7 | 0.0449503 | ||||||||
\(412\) | −2.10760e9 | −1.48473 | ||||||||
\(413\) | −6.39280e7 | −0.0446546 | ||||||||
\(414\) | 1.05505e10 | 7.30755 | ||||||||
\(415\) | 3.59286e8 | 0.246758 | ||||||||
\(416\) | 2.03202e8 | 0.138389 | ||||||||
\(417\) | −3.37805e9 | −2.28134 | ||||||||
\(418\) | 9.72807e8 | 0.651493 | ||||||||
\(419\) | −1.08282e9 | −0.719127 | −0.359563 | − | 0.933121i | \(-0.617074\pi\) | ||||
−0.359563 | + | 0.933121i | \(0.617074\pi\) | |||||||
\(420\) | −1.51093e9 | −0.995112 | ||||||||
\(421\) | 1.26221e9 | 0.824412 | 0.412206 | − | 0.911091i | \(-0.364758\pi\) | ||||
0.412206 | + | 0.911091i | \(0.364758\pi\) | |||||||
\(422\) | 1.89349e9 | 1.22650 | ||||||||
\(423\) | −6.34878e9 | −4.07849 | ||||||||
\(424\) | 1.57203e9 | 1.00157 | ||||||||
\(425\) | −5.59451e8 | −0.353509 | ||||||||
\(426\) | 1.05266e9 | 0.659710 | ||||||||
\(427\) | −6.04935e8 | −0.376020 | ||||||||
\(428\) | −1.75078e9 | −1.07939 | ||||||||
\(429\) | 2.57139e8 | 0.157242 | ||||||||
\(430\) | −1.30253e9 | −0.790036 | ||||||||
\(431\) | 1.81842e9 | 1.09402 | 0.547008 | − | 0.837127i | \(-0.315767\pi\) | ||||
0.547008 | + | 0.837127i | \(0.315767\pi\) | |||||||
\(432\) | −2.32204e9 | −1.38572 | ||||||||
\(433\) | −1.15848e9 | −0.685773 | −0.342887 | − | 0.939377i | \(-0.611405\pi\) | ||||
−0.342887 | + | 0.939377i | \(0.611405\pi\) | |||||||
\(434\) | −8.77036e8 | −0.514996 | ||||||||
\(435\) | 1.79015e9 | 1.04274 | ||||||||
\(436\) | 6.28516e9 | 3.63173 | ||||||||
\(437\) | 3.97844e9 | 2.28049 | ||||||||
\(438\) | −7.65103e9 | −4.35071 | ||||||||
\(439\) | −3.42765e9 | −1.93362 | −0.966809 | − | 0.255502i | \(-0.917759\pi\) | ||||
−0.966809 | + | 0.255502i | \(0.917759\pi\) | |||||||
\(440\) | −6.05299e8 | −0.338755 | ||||||||
\(441\) | 6.14191e8 | 0.341011 | ||||||||
\(442\) | −7.59565e8 | −0.418396 | ||||||||
\(443\) | −4.61882e8 | −0.252417 | −0.126208 | − | 0.992004i | \(-0.540281\pi\) | ||||
−0.126208 | + | 0.992004i | \(0.540281\pi\) | |||||||
\(444\) | −6.19360e9 | −3.35817 | ||||||||
\(445\) | −2.52878e9 | −1.36035 | ||||||||
\(446\) | −1.12001e9 | −0.597792 | ||||||||
\(447\) | 1.56352e8 | 0.0827994 | ||||||||
\(448\) | 9.95220e8 | 0.522933 | ||||||||
\(449\) | −1.29390e9 | −0.674588 | −0.337294 | − | 0.941399i | \(-0.609512\pi\) | ||||
−0.337294 | + | 0.941399i | \(0.609512\pi\) | |||||||
\(450\) | −3.06982e9 | −1.58807 | ||||||||
\(451\) | −5.82425e8 | −0.298966 | ||||||||
\(452\) | −1.62791e9 | −0.829174 | ||||||||
\(453\) | 6.20177e9 | 3.13453 | ||||||||
\(454\) | 2.46368e9 | 1.23563 | ||||||||
\(455\) | −1.63853e8 | −0.0815482 | ||||||||
\(456\) | −6.61176e9 | −3.26543 | ||||||||
\(457\) | −1.28790e8 | −0.0631210 | −0.0315605 | − | 0.999502i | \(-0.510048\pi\) | ||||
−0.0315605 | + | 0.999502i | \(0.510048\pi\) | |||||||
\(458\) | 3.55842e9 | 1.73073 | ||||||||
\(459\) | −4.73519e9 | −2.28556 | ||||||||
\(460\) | −5.42607e9 | −2.59916 | ||||||||
\(461\) | −2.81077e9 | −1.33620 | −0.668101 | − | 0.744070i | \(-0.732893\pi\) | ||||
−0.668101 | + | 0.744070i | \(0.732893\pi\) | |||||||
\(462\) | 7.65274e8 | 0.361052 | ||||||||
\(463\) | 2.40896e8 | 0.112796 | 0.0563982 | − | 0.998408i | \(-0.482038\pi\) | ||||
0.0563982 | + | 0.998408i | \(0.482038\pi\) | |||||||
\(464\) | 8.50754e8 | 0.395359 | ||||||||
\(465\) | 2.51018e9 | 1.15776 | ||||||||
\(466\) | −6.49591e9 | −2.97365 | ||||||||
\(467\) | −3.51134e8 | −0.159538 | −0.0797689 | − | 0.996813i | \(-0.525418\pi\) | ||||
−0.0797689 | + | 0.996813i | \(0.525418\pi\) | |||||||
\(468\) | −2.69978e9 | −1.21750 | ||||||||
\(469\) | 1.40649e8 | 0.0629552 | ||||||||
\(470\) | 5.04069e9 | 2.23948 | ||||||||
\(471\) | 3.38388e9 | 1.49225 | ||||||||
\(472\) | 3.81536e8 | 0.167009 | ||||||||
\(473\) | 4.27339e8 | 0.185677 | ||||||||
\(474\) | 1.04867e10 | 4.52289 | ||||||||
\(475\) | −1.15758e9 | −0.495593 | ||||||||
\(476\) | −1.46429e9 | −0.622305 | ||||||||
\(477\) | 4.00901e9 | 1.69131 | ||||||||
\(478\) | −5.11808e9 | −2.14343 | ||||||||
\(479\) | 1.52325e9 | 0.633281 | 0.316640 | − | 0.948546i | \(-0.397445\pi\) | ||||
0.316640 | + | 0.948546i | \(0.397445\pi\) | |||||||
\(480\) | −1.73087e9 | −0.714365 | ||||||||
\(481\) | −6.71665e8 | −0.275198 | ||||||||
\(482\) | −1.81300e9 | −0.737451 | ||||||||
\(483\) | 3.12971e9 | 1.26383 | ||||||||
\(484\) | −4.15174e9 | −1.66445 | ||||||||
\(485\) | −1.24657e9 | −0.496159 | ||||||||
\(486\) | −7.25080e9 | −2.86523 | ||||||||
\(487\) | 9.77957e8 | 0.383679 | 0.191840 | − | 0.981426i | \(-0.438555\pi\) | ||||
0.191840 | + | 0.981426i | \(0.438555\pi\) | |||||||
\(488\) | 3.61039e9 | 1.40632 | ||||||||
\(489\) | 1.33311e8 | 0.0515567 | ||||||||
\(490\) | −4.87644e8 | −0.187248 | ||||||||
\(491\) | 1.42118e9 | 0.541830 | 0.270915 | − | 0.962603i | \(-0.412674\pi\) | ||||
0.270915 | + | 0.962603i | \(0.412674\pi\) | |||||||
\(492\) | 8.67680e9 | 3.28460 | ||||||||
\(493\) | 1.73489e9 | 0.652090 | ||||||||
\(494\) | −1.57165e9 | −0.586559 | ||||||||
\(495\) | −1.54364e9 | −0.572042 | ||||||||
\(496\) | 1.19295e9 | 0.438970 | ||||||||
\(497\) | 2.20069e8 | 0.0804102 | ||||||||
\(498\) | 2.71102e9 | 0.983626 | ||||||||
\(499\) | 2.76996e9 | 0.997981 | 0.498990 | − | 0.866608i | \(-0.333704\pi\) | ||||
0.498990 | + | 0.866608i | \(0.333704\pi\) | |||||||
\(500\) | 5.57735e9 | 1.99541 | ||||||||
\(501\) | −4.12973e9 | −1.46720 | ||||||||
\(502\) | 4.53829e9 | 1.60114 | ||||||||
\(503\) | 4.40741e9 | 1.54417 | 0.772086 | − | 0.635517i | \(-0.219213\pi\) | ||||
0.772086 | + | 0.635517i | \(0.219213\pi\) | |||||||
\(504\) | −3.66563e9 | −1.27539 | ||||||||
\(505\) | −2.80657e9 | −0.969740 | ||||||||
\(506\) | 2.74826e9 | 0.943043 | ||||||||
\(507\) | −4.15429e8 | −0.141569 | ||||||||
\(508\) | 5.46737e9 | 1.85036 | ||||||||
\(509\) | −2.30464e8 | −0.0774624 | −0.0387312 | − | 0.999250i | \(-0.512332\pi\) | ||||
−0.0387312 | + | 0.999250i | \(0.512332\pi\) | |||||||
\(510\) | 6.46997e9 | 2.15976 | ||||||||
\(511\) | −1.59953e9 | −0.530296 | ||||||||
\(512\) | −3.15299e9 | −1.03819 | ||||||||
\(513\) | −9.79778e9 | −3.20418 | ||||||||
\(514\) | −5.15411e9 | −1.67411 | ||||||||
\(515\) | 1.94685e9 | 0.628070 | ||||||||
\(516\) | −6.36638e9 | −2.03994 | ||||||||
\(517\) | −1.65377e9 | −0.526331 | ||||||||
\(518\) | −1.99895e9 | −0.631899 | ||||||||
\(519\) | 8.52493e9 | 2.67673 | ||||||||
\(520\) | 9.77910e8 | 0.304991 | ||||||||
\(521\) | 2.00780e9 | 0.621997 | 0.310999 | − | 0.950410i | \(-0.399337\pi\) | ||||
0.310999 | + | 0.950410i | \(0.399337\pi\) | |||||||
\(522\) | 9.51968e9 | 2.92938 | ||||||||
\(523\) | 2.99708e9 | 0.916099 | 0.458050 | − | 0.888927i | \(-0.348548\pi\) | ||||
0.458050 | + | 0.888927i | \(0.348548\pi\) | |||||||
\(524\) | 9.06071e9 | 2.75108 | ||||||||
\(525\) | −9.10633e8 | −0.274654 | ||||||||
\(526\) | −9.15390e9 | −2.74256 | ||||||||
\(527\) | 2.43270e9 | 0.724021 | ||||||||
\(528\) | −1.04093e9 | −0.307753 | ||||||||
\(529\) | 7.83462e9 | 2.30103 | ||||||||
\(530\) | −3.18300e9 | −0.928690 | ||||||||
\(531\) | 9.72999e8 | 0.282021 | ||||||||
\(532\) | −3.02983e9 | −0.872424 | ||||||||
\(533\) | 9.40956e8 | 0.269168 | ||||||||
\(534\) | −1.90811e10 | −5.42263 | ||||||||
\(535\) | 1.61725e9 | 0.456603 | ||||||||
\(536\) | −8.39424e8 | −0.235453 | ||||||||
\(537\) | 5.48216e9 | 1.52771 | ||||||||
\(538\) | 1.06387e10 | 2.94544 | ||||||||
\(539\) | 1.59989e8 | 0.0440077 | ||||||||
\(540\) | 1.33629e10 | 3.65193 | ||||||||
\(541\) | −3.87356e8 | −0.105177 | −0.0525884 | − | 0.998616i | \(-0.516747\pi\) | ||||
−0.0525884 | + | 0.998616i | \(0.516747\pi\) | |||||||
\(542\) | −6.37259e9 | −1.71917 | ||||||||
\(543\) | 1.87990e9 | 0.503888 | ||||||||
\(544\) | −1.67744e9 | −0.446737 | ||||||||
\(545\) | −5.80580e9 | −1.53629 | ||||||||
\(546\) | −1.23636e9 | −0.325066 | ||||||||
\(547\) | −3.74739e9 | −0.978978 | −0.489489 | − | 0.872009i | \(-0.662817\pi\) | ||||
−0.489489 | + | 0.872009i | \(0.662817\pi\) | |||||||
\(548\) | −1.73032e8 | −0.0449152 | ||||||||
\(549\) | 9.20725e9 | 2.37480 | ||||||||
\(550\) | −7.99646e8 | −0.204941 | ||||||||
\(551\) | 3.58973e9 | 0.914180 | ||||||||
\(552\) | −1.86788e10 | −4.72674 | ||||||||
\(553\) | 2.19236e9 | 0.551282 | ||||||||
\(554\) | 3.29741e8 | 0.0823927 | ||||||||
\(555\) | 5.72123e9 | 1.42057 | ||||||||
\(556\) | 9.23874e9 | 2.27956 | ||||||||
\(557\) | 8.69904e8 | 0.213294 | 0.106647 | − | 0.994297i | \(-0.465989\pi\) | ||||
0.106647 | + | 0.994297i | \(0.465989\pi\) | |||||||
\(558\) | 1.33487e10 | 3.25251 | ||||||||
\(559\) | −6.90402e8 | −0.167171 | ||||||||
\(560\) | 6.63295e8 | 0.159606 | ||||||||
\(561\) | −2.12270e9 | −0.507596 | ||||||||
\(562\) | 1.25112e10 | 2.97319 | ||||||||
\(563\) | 3.77936e9 | 0.892563 | 0.446281 | − | 0.894893i | \(-0.352748\pi\) | ||||
0.446281 | + | 0.894893i | \(0.352748\pi\) | |||||||
\(564\) | 2.46374e10 | 5.78254 | ||||||||
\(565\) | 1.50375e9 | 0.350758 | ||||||||
\(566\) | −7.64299e9 | −1.77176 | ||||||||
\(567\) | −3.79144e9 | −0.873501 | ||||||||
\(568\) | −1.31342e9 | −0.300735 | ||||||||
\(569\) | 6.37372e9 | 1.45044 | 0.725220 | − | 0.688517i | \(-0.241738\pi\) | ||||
0.725220 | + | 0.688517i | \(0.241738\pi\) | |||||||
\(570\) | 1.33873e10 | 3.02782 | ||||||||
\(571\) | 1.03903e8 | 0.0233561 | 0.0116781 | − | 0.999932i | \(-0.496283\pi\) | ||||
0.0116781 | + | 0.999932i | \(0.496283\pi\) | |||||||
\(572\) | −7.03258e8 | −0.157119 | ||||||||
\(573\) | −9.97272e9 | −2.21448 | ||||||||
\(574\) | 2.80039e9 | 0.618054 | ||||||||
\(575\) | −3.27028e9 | −0.717376 | ||||||||
\(576\) | −1.51475e10 | −3.30265 | ||||||||
\(577\) | 7.63241e8 | 0.165404 | 0.0827021 | − | 0.996574i | \(-0.473645\pi\) | ||||
0.0827021 | + | 0.996574i | \(0.473645\pi\) | |||||||
\(578\) | −1.55192e9 | −0.334289 | ||||||||
\(579\) | −1.33650e10 | −2.86151 | ||||||||
\(580\) | −4.89593e9 | −1.04193 | ||||||||
\(581\) | 5.66767e8 | 0.119891 | ||||||||
\(582\) | −9.40610e9 | −1.97778 | ||||||||
\(583\) | 1.04429e9 | 0.218264 | ||||||||
\(584\) | 9.54634e9 | 1.98332 | ||||||||
\(585\) | 2.49388e9 | 0.515027 | ||||||||
\(586\) | −5.89881e9 | −1.21094 | ||||||||
\(587\) | −2.89106e9 | −0.589961 | −0.294981 | − | 0.955503i | \(-0.595313\pi\) | ||||
−0.294981 | + | 0.955503i | \(0.595313\pi\) | |||||||
\(588\) | −2.38347e9 | −0.483491 | ||||||||
\(589\) | 5.03360e9 | 1.01502 | ||||||||
\(590\) | −7.72524e8 | −0.154857 | ||||||||
\(591\) | −9.36255e9 | −1.86568 | ||||||||
\(592\) | 2.71897e9 | 0.538616 | ||||||||
\(593\) | −6.37282e8 | −0.125499 | −0.0627495 | − | 0.998029i | \(-0.519987\pi\) | ||||
−0.0627495 | + | 0.998029i | \(0.519987\pi\) | |||||||
\(594\) | −6.76820e9 | −1.32501 | ||||||||
\(595\) | 1.35261e9 | 0.263248 | ||||||||
\(596\) | −4.27612e8 | −0.0827348 | ||||||||
\(597\) | −2.35897e9 | −0.453745 | ||||||||
\(598\) | −4.44005e9 | −0.849050 | ||||||||
\(599\) | 2.02809e9 | 0.385561 | 0.192781 | − | 0.981242i | \(-0.438249\pi\) | ||||
0.192781 | + | 0.981242i | \(0.438249\pi\) | |||||||
\(600\) | 5.43486e9 | 1.02721 | ||||||||
\(601\) | −1.38106e9 | −0.259509 | −0.129755 | − | 0.991546i | \(-0.541419\pi\) | ||||
−0.129755 | + | 0.991546i | \(0.541419\pi\) | |||||||
\(602\) | −2.05471e9 | −0.383851 | ||||||||
\(603\) | −2.14071e9 | −0.397601 | ||||||||
\(604\) | −1.69614e10 | −3.13208 | ||||||||
\(605\) | 3.83510e9 | 0.704097 | ||||||||
\(606\) | −2.11772e10 | −3.86557 | ||||||||
\(607\) | −5.28213e9 | −0.958624 | −0.479312 | − | 0.877644i | \(-0.659114\pi\) | ||||
−0.479312 | + | 0.877644i | \(0.659114\pi\) | |||||||
\(608\) | −3.47087e9 | −0.626291 | ||||||||
\(609\) | 2.82392e9 | 0.506632 | ||||||||
\(610\) | −7.31020e9 | −1.30399 | ||||||||
\(611\) | 2.67181e9 | 0.473872 | ||||||||
\(612\) | 2.22869e10 | 3.93024 | ||||||||
\(613\) | −4.30516e9 | −0.754879 | −0.377440 | − | 0.926034i | \(-0.623195\pi\) | ||||
−0.377440 | + | 0.926034i | \(0.623195\pi\) | |||||||
\(614\) | −1.53869e10 | −2.68265 | ||||||||
\(615\) | −8.01505e9 | −1.38945 | ||||||||
\(616\) | −9.54848e8 | −0.164589 | ||||||||
\(617\) | 5.98875e9 | 1.02645 | 0.513226 | − | 0.858254i | \(-0.328450\pi\) | ||||
0.513226 | + | 0.858254i | \(0.328450\pi\) | |||||||
\(618\) | 1.46901e10 | 2.50361 | ||||||||
\(619\) | 5.70740e9 | 0.967211 | 0.483605 | − | 0.875286i | \(-0.339327\pi\) | ||||
0.483605 | + | 0.875286i | \(0.339327\pi\) | |||||||
\(620\) | −6.86518e9 | −1.15686 | ||||||||
\(621\) | −2.76796e10 | −4.63808 | ||||||||
\(622\) | −6.82572e9 | −1.13732 | ||||||||
\(623\) | −3.98911e9 | −0.660949 | ||||||||
\(624\) | 1.68170e9 | 0.277079 | ||||||||
\(625\) | −2.74206e9 | −0.449260 | ||||||||
\(626\) | 4.35821e9 | 0.710066 | ||||||||
\(627\) | −4.39217e9 | −0.711610 | ||||||||
\(628\) | −9.25467e9 | −1.49108 | ||||||||
\(629\) | 5.54463e9 | 0.888373 | ||||||||
\(630\) | 7.42206e9 | 1.18259 | ||||||||
\(631\) | 1.00384e10 | 1.59061 | 0.795305 | − | 0.606210i | \(-0.207311\pi\) | ||||
0.795305 | + | 0.606210i | \(0.207311\pi\) | |||||||
\(632\) | −1.30845e10 | −2.06180 | ||||||||
\(633\) | −8.54898e9 | −1.33968 | ||||||||
\(634\) | −6.98636e9 | −1.08878 | ||||||||
\(635\) | −5.05039e9 | −0.782738 | ||||||||
\(636\) | −1.55576e10 | −2.39796 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | 2.47975e9 | 0.378038 | ||||||||
\(639\) | −3.34950e9 | −0.507840 | ||||||||
\(640\) | 9.45235e9 | 1.42531 | ||||||||
\(641\) | 7.00300e9 | 1.05022 | 0.525111 | − | 0.851034i | \(-0.324024\pi\) | ||||
0.525111 | + | 0.851034i | \(0.324024\pi\) | |||||||
\(642\) | 1.22031e10 | 1.82011 | ||||||||
\(643\) | −8.34621e9 | −1.23809 | −0.619043 | − | 0.785357i | \(-0.712479\pi\) | ||||
−0.619043 | + | 0.785357i | \(0.712479\pi\) | |||||||
\(644\) | −8.55953e9 | −1.26284 | ||||||||
\(645\) | 5.88083e9 | 0.862938 | ||||||||
\(646\) | 1.29741e10 | 1.89349 | ||||||||
\(647\) | −3.70748e8 | −0.0538162 | −0.0269081 | − | 0.999638i | \(-0.508566\pi\) | ||||
−0.0269081 | + | 0.999638i | \(0.508566\pi\) | |||||||
\(648\) | 2.26281e10 | 3.26691 | ||||||||
\(649\) | 2.53453e8 | 0.0363950 | ||||||||
\(650\) | 1.29189e9 | 0.184514 | ||||||||
\(651\) | 3.95977e9 | 0.562517 | ||||||||
\(652\) | −3.64596e8 | −0.0515164 | ||||||||
\(653\) | −4.03555e8 | −0.0567161 | −0.0283581 | − | 0.999598i | \(-0.509028\pi\) | ||||
−0.0283581 | + | 0.999598i | \(0.509028\pi\) | |||||||
\(654\) | −4.38081e10 | −6.12396 | ||||||||
\(655\) | −8.36968e9 | −1.16376 | ||||||||
\(656\) | −3.80909e9 | −0.526815 | ||||||||
\(657\) | 2.43452e10 | 3.34915 | ||||||||
\(658\) | 7.95159e9 | 1.08809 | ||||||||
\(659\) | −3.72205e9 | −0.506621 | −0.253310 | − | 0.967385i | \(-0.581519\pi\) | ||||
−0.253310 | + | 0.967385i | \(0.581519\pi\) | |||||||
\(660\) | 5.99034e9 | 0.811050 | ||||||||
\(661\) | −2.05999e9 | −0.277435 | −0.138717 | − | 0.990332i | \(-0.544298\pi\) | ||||
−0.138717 | + | 0.990332i | \(0.544298\pi\) | |||||||
\(662\) | −1.20271e9 | −0.161123 | ||||||||
\(663\) | 3.42939e9 | 0.457004 | ||||||||
\(664\) | −3.38259e9 | −0.448396 | ||||||||
\(665\) | 2.79875e9 | 0.369053 | ||||||||
\(666\) | 3.04245e10 | 3.99083 | ||||||||
\(667\) | 1.01413e10 | 1.32329 | ||||||||
\(668\) | 1.12945e10 | 1.46606 | ||||||||
\(669\) | 5.05678e9 | 0.652955 | ||||||||
\(670\) | 1.69964e9 | 0.218321 | ||||||||
\(671\) | 2.39837e9 | 0.306469 | ||||||||
\(672\) | −2.73042e9 | −0.347085 | ||||||||
\(673\) | −1.09373e10 | −1.38311 | −0.691554 | − | 0.722325i | \(-0.743074\pi\) | ||||
−0.691554 | + | 0.722325i | \(0.743074\pi\) | |||||||
\(674\) | −1.29762e10 | −1.63244 | ||||||||
\(675\) | 8.05377e9 | 1.00794 | ||||||||
\(676\) | 1.13617e9 | 0.141459 | ||||||||
\(677\) | 1.43121e10 | 1.77273 | 0.886364 | − | 0.462989i | \(-0.153223\pi\) | ||||
0.886364 | + | 0.462989i | \(0.153223\pi\) | |||||||
\(678\) | 1.13467e10 | 1.39819 | ||||||||
\(679\) | −1.96644e9 | −0.241067 | ||||||||
\(680\) | −8.07270e9 | −0.984550 | ||||||||
\(681\) | −1.11234e10 | −1.34965 | ||||||||
\(682\) | 3.47716e9 | 0.419739 | ||||||||
\(683\) | 5.85021e9 | 0.702586 | 0.351293 | − | 0.936266i | \(-0.385742\pi\) | ||||
0.351293 | + | 0.936266i | \(0.385742\pi\) | |||||||
\(684\) | 4.61147e10 | 5.50990 | ||||||||
\(685\) | 1.59835e8 | 0.0190000 | ||||||||
\(686\) | −7.69250e8 | −0.0909773 | ||||||||
\(687\) | −1.60661e10 | −1.89043 | ||||||||
\(688\) | 2.79482e9 | 0.327186 | ||||||||
\(689\) | −1.68714e9 | −0.196510 | ||||||||
\(690\) | 3.78202e10 | 4.38281 | ||||||||
\(691\) | −7.27490e9 | −0.838791 | −0.419396 | − | 0.907804i | \(-0.637758\pi\) | ||||
−0.419396 | + | 0.907804i | \(0.637758\pi\) | |||||||
\(692\) | −2.33151e10 | −2.67464 | ||||||||
\(693\) | −2.43507e9 | −0.277936 | ||||||||
\(694\) | −1.92637e10 | −2.18767 | ||||||||
\(695\) | −8.53412e9 | −0.964300 | ||||||||
\(696\) | −1.68538e10 | −1.89481 | ||||||||
\(697\) | −7.76764e9 | −0.868909 | ||||||||
\(698\) | −8.89386e9 | −0.989912 | ||||||||
\(699\) | 2.93286e10 | 3.24804 | ||||||||
\(700\) | 2.49052e9 | 0.274439 | ||||||||
\(701\) | 1.07123e10 | 1.17455 | 0.587273 | − | 0.809389i | \(-0.300202\pi\) | ||||
0.587273 | + | 0.809389i | \(0.300202\pi\) | |||||||
\(702\) | 1.09346e10 | 1.19295 | ||||||||
\(703\) | 1.14726e10 | 1.24543 | ||||||||
\(704\) | −3.94572e9 | −0.426208 | ||||||||
\(705\) | −2.27584e10 | −2.44613 | ||||||||
\(706\) | 2.10112e10 | 2.24716 | ||||||||
\(707\) | −4.42731e9 | −0.471164 | ||||||||
\(708\) | −3.77587e9 | −0.399854 | ||||||||
\(709\) | −7.08677e9 | −0.746770 | −0.373385 | − | 0.927677i | \(-0.621803\pi\) | ||||
−0.373385 | + | 0.927677i | \(0.621803\pi\) | |||||||
\(710\) | 2.65937e9 | 0.278853 | ||||||||
\(711\) | −3.33682e10 | −3.48169 | ||||||||
\(712\) | 2.38079e10 | 2.47196 | ||||||||
\(713\) | 1.42204e10 | 1.46926 | ||||||||
\(714\) | 1.02063e10 | 1.04936 | ||||||||
\(715\) | 6.49622e8 | 0.0664645 | ||||||||
\(716\) | −1.49933e10 | −1.52652 | ||||||||
\(717\) | 2.31078e10 | 2.34122 | ||||||||
\(718\) | 2.73607e10 | 2.75861 | ||||||||
\(719\) | −4.85731e9 | −0.487354 | −0.243677 | − | 0.969856i | \(-0.578354\pi\) | ||||
−0.243677 | + | 0.969856i | \(0.578354\pi\) | |||||||
\(720\) | −1.00955e10 | −1.00801 | ||||||||
\(721\) | 3.07113e9 | 0.305158 | ||||||||
\(722\) | 9.80556e9 | 0.969599 | ||||||||
\(723\) | 8.18558e9 | 0.805500 | ||||||||
\(724\) | −5.14139e9 | −0.503495 | ||||||||
\(725\) | −2.95076e9 | −0.287575 | ||||||||
\(726\) | 2.89380e10 | 2.80667 | ||||||||
\(727\) | 9.82914e9 | 0.948735 | 0.474368 | − | 0.880327i | \(-0.342677\pi\) | ||||
0.474368 | + | 0.880327i | \(0.342677\pi\) | |||||||
\(728\) | 1.54264e9 | 0.148185 | ||||||||
\(729\) | 8.56235e9 | 0.818552 | ||||||||
\(730\) | −1.93291e10 | −1.83900 | ||||||||
\(731\) | 5.69931e9 | 0.539649 | ||||||||
\(732\) | −3.57302e10 | −3.36703 | ||||||||
\(733\) | 1.21200e10 | 1.13668 | 0.568340 | − | 0.822793i | \(-0.307586\pi\) | ||||
0.568340 | + | 0.822793i | \(0.307586\pi\) | |||||||
\(734\) | −4.96592e9 | −0.463515 | ||||||||
\(735\) | 2.20168e9 | 0.204526 | ||||||||
\(736\) | −9.80551e9 | −0.906562 | ||||||||
\(737\) | −5.57626e8 | −0.0513106 | ||||||||
\(738\) | −4.26226e10 | −3.90339 | ||||||||
\(739\) | −2.00332e10 | −1.82598 | −0.912988 | − | 0.407986i | \(-0.866231\pi\) | ||||
−0.912988 | + | 0.407986i | \(0.866231\pi\) | |||||||
\(740\) | −1.56472e10 | −1.41947 | ||||||||
\(741\) | 7.09591e9 | 0.640684 | ||||||||
\(742\) | −5.02112e9 | −0.451218 | ||||||||
\(743\) | 3.12428e9 | 0.279440 | 0.139720 | − | 0.990191i | \(-0.455380\pi\) | ||||
0.139720 | + | 0.990191i | \(0.455380\pi\) | |||||||
\(744\) | −2.36328e10 | −2.10382 | ||||||||
\(745\) | 3.94999e8 | 0.0349985 | ||||||||
\(746\) | 1.08729e9 | 0.0958870 | ||||||||
\(747\) | −8.62633e9 | −0.757188 | ||||||||
\(748\) | 5.80543e9 | 0.507200 | ||||||||
\(749\) | 2.55118e9 | 0.221848 | ||||||||
\(750\) | −3.88747e10 | −3.36475 | ||||||||
\(751\) | 1.48089e10 | 1.27580 | 0.637900 | − | 0.770120i | \(-0.279803\pi\) | ||||
0.637900 | + | 0.770120i | \(0.279803\pi\) | |||||||
\(752\) | −1.08158e10 | −0.927459 | ||||||||
\(753\) | −2.04901e10 | −1.74889 | ||||||||
\(754\) | −4.00624e9 | −0.340359 | ||||||||
\(755\) | 1.56678e10 | 1.32493 | ||||||||
\(756\) | 2.10797e10 | 1.77435 | ||||||||
\(757\) | −5.89815e8 | −0.0494174 | −0.0247087 | − | 0.999695i | \(-0.507866\pi\) | ||||
−0.0247087 | + | 0.999695i | \(0.507866\pi\) | |||||||
\(758\) | −2.54279e10 | −2.12064 | ||||||||
\(759\) | −1.24082e10 | −1.03006 | ||||||||
\(760\) | −1.67036e10 | −1.38026 | ||||||||
\(761\) | −1.80400e10 | −1.48385 | −0.741924 | − | 0.670484i | \(-0.766087\pi\) | ||||
−0.741924 | + | 0.670484i | \(0.766087\pi\) | |||||||
\(762\) | −3.81081e10 | −3.12014 | ||||||||
\(763\) | −9.15855e9 | −0.746433 | ||||||||
\(764\) | 2.72747e10 | 2.21276 | ||||||||
\(765\) | −2.05871e10 | −1.66257 | ||||||||
\(766\) | −2.33327e10 | −1.87570 | ||||||||
\(767\) | −4.09475e8 | −0.0327675 | ||||||||
\(768\) | 3.93586e10 | 3.13527 | ||||||||
\(769\) | 1.52750e10 | 1.21126 | 0.605631 | − | 0.795746i | \(-0.292921\pi\) | ||||
0.605631 | + | 0.795746i | \(0.292921\pi\) | |||||||
\(770\) | 1.93335e9 | 0.152613 | ||||||||
\(771\) | 2.32705e10 | 1.82859 | ||||||||
\(772\) | 3.65525e10 | 2.85928 | ||||||||
\(773\) | −1.06729e10 | −0.831099 | −0.415550 | − | 0.909570i | \(-0.636411\pi\) | ||||
−0.415550 | + | 0.909570i | \(0.636411\pi\) | |||||||
\(774\) | 3.12732e10 | 2.42426 | ||||||||
\(775\) | −4.13762e9 | −0.319297 | ||||||||
\(776\) | 1.17362e10 | 0.901593 | ||||||||
\(777\) | 9.02513e9 | 0.690208 | ||||||||
\(778\) | 2.97228e10 | 2.26288 | ||||||||
\(779\) | −1.60724e10 | −1.21814 | ||||||||
\(780\) | −9.67788e9 | −0.730213 | ||||||||
\(781\) | −8.72500e8 | −0.0655370 | ||||||||
\(782\) | 3.66528e10 | 2.74084 | ||||||||
\(783\) | −2.49752e10 | −1.85927 | ||||||||
\(784\) | 1.04633e9 | 0.0775469 | ||||||||
\(785\) | 8.54884e9 | 0.630759 | ||||||||
\(786\) | −6.31540e10 | −4.63897 | ||||||||
\(787\) | 2.31814e10 | 1.69522 | 0.847612 | − | 0.530616i | \(-0.178039\pi\) | ||||
0.847612 | + | 0.530616i | \(0.178039\pi\) | |||||||
\(788\) | 2.56059e10 | 1.86423 | ||||||||
\(789\) | 4.13293e10 | 2.99563 | ||||||||
\(790\) | 2.64931e10 | 1.91178 | ||||||||
\(791\) | 2.37214e9 | 0.170421 | ||||||||
\(792\) | 1.45330e10 | 1.03948 | ||||||||
\(793\) | −3.87476e9 | −0.275923 | ||||||||
\(794\) | −8.37242e9 | −0.593580 | ||||||||
\(795\) | 1.43710e10 | 1.01439 | ||||||||
\(796\) | 6.45161e9 | 0.453391 | ||||||||
\(797\) | 1.86371e10 | 1.30399 | 0.651996 | − | 0.758223i | \(-0.273932\pi\) | ||||
0.651996 | + | 0.758223i | \(0.273932\pi\) | |||||||
\(798\) | 2.11182e10 | 1.47112 | ||||||||
\(799\) | −2.20559e10 | −1.52972 | ||||||||
\(800\) | 2.85305e9 | 0.197013 | ||||||||
\(801\) | 6.07152e10 | 4.17430 | ||||||||
\(802\) | −2.09231e10 | −1.43224 | ||||||||
\(803\) | 6.34160e9 | 0.432209 | ||||||||
\(804\) | 8.30736e9 | 0.563724 | ||||||||
\(805\) | 7.90672e9 | 0.534208 | ||||||||
\(806\) | −5.61763e9 | −0.377903 | ||||||||
\(807\) | −4.80331e10 | −3.21724 | ||||||||
\(808\) | 2.64231e10 | 1.76216 | ||||||||
\(809\) | 1.53468e9 | 0.101905 | 0.0509527 | − | 0.998701i | \(-0.483774\pi\) | ||||
0.0509527 | + | 0.998701i | \(0.483774\pi\) | |||||||
\(810\) | −4.58168e10 | −3.02920 | ||||||||
\(811\) | 4.01760e9 | 0.264480 | 0.132240 | − | 0.991218i | \(-0.457783\pi\) | ||||
0.132240 | + | 0.991218i | \(0.457783\pi\) | |||||||
\(812\) | −7.72324e9 | −0.506236 | ||||||||
\(813\) | 2.87719e10 | 1.87781 | ||||||||
\(814\) | 7.92516e9 | 0.515019 | ||||||||
\(815\) | 3.36790e8 | 0.0217925 | ||||||||
\(816\) | −1.38826e10 | −0.894446 | ||||||||
\(817\) | 1.17927e10 | 0.756546 | ||||||||
\(818\) | 3.07696e9 | 0.196556 | ||||||||
\(819\) | 3.93405e9 | 0.250234 | ||||||||
\(820\) | 2.19206e10 | 1.38837 | ||||||||
\(821\) | −2.04115e10 | −1.28728 | −0.643640 | − | 0.765329i | \(-0.722577\pi\) | ||||
−0.643640 | + | 0.765329i | \(0.722577\pi\) | |||||||
\(822\) | 1.20605e9 | 0.0757378 | ||||||||
\(823\) | −5.94722e9 | −0.371890 | −0.185945 | − | 0.982560i | \(-0.559535\pi\) | ||||
−0.185945 | + | 0.982560i | \(0.559535\pi\) | |||||||
\(824\) | −1.83292e10 | −1.14129 | ||||||||
\(825\) | 3.61036e9 | 0.223852 | ||||||||
\(826\) | −1.21864e9 | −0.0752395 | ||||||||
\(827\) | −9.84300e9 | −0.605143 | −0.302572 | − | 0.953127i | \(-0.597845\pi\) | ||||
−0.302572 | + | 0.953127i | \(0.597845\pi\) | |||||||
\(828\) | 1.30278e11 | 7.97563 | ||||||||
\(829\) | −3.20244e10 | −1.95227 | −0.976135 | − | 0.217166i | \(-0.930319\pi\) | ||||
−0.976135 | + | 0.217166i | \(0.930319\pi\) | |||||||
\(830\) | 6.84897e9 | 0.415769 | ||||||||
\(831\) | −1.48876e9 | −0.0899956 | ||||||||
\(832\) | 6.37463e9 | 0.383728 | ||||||||
\(833\) | 2.13372e9 | 0.127903 | ||||||||
\(834\) | −6.43949e10 | −3.84388 | ||||||||
\(835\) | −1.04331e10 | −0.620171 | ||||||||
\(836\) | 1.20123e10 | 0.711055 | ||||||||
\(837\) | −3.50207e10 | −2.06436 | ||||||||
\(838\) | −2.06414e10 | −1.21167 | ||||||||
\(839\) | −2.48443e10 | −1.45231 | −0.726157 | − | 0.687529i | \(-0.758696\pi\) | ||||
−0.726157 | + | 0.687529i | \(0.758696\pi\) | |||||||
\(840\) | −1.31401e10 | −0.764932 | ||||||||
\(841\) | −8.09941e9 | −0.469534 | ||||||||
\(842\) | 2.40612e10 | 1.38907 | ||||||||
\(843\) | −5.64874e10 | −3.24754 | ||||||||
\(844\) | 2.33809e10 | 1.33864 | ||||||||
\(845\) | −1.04952e9 | −0.0598400 | ||||||||
\(846\) | −1.21025e11 | −6.87194 | ||||||||
\(847\) | 6.04980e9 | 0.342097 | ||||||||
\(848\) | 6.82973e9 | 0.384608 | ||||||||
\(849\) | 3.45077e10 | 1.93526 | ||||||||
\(850\) | −1.06647e10 | −0.595636 | ||||||||
\(851\) | 3.24112e10 | 1.80277 | ||||||||
\(852\) | 1.29983e10 | 0.720023 | ||||||||
\(853\) | −2.10601e9 | −0.116182 | −0.0580909 | − | 0.998311i | \(-0.518501\pi\) | ||||
−0.0580909 | + | 0.998311i | \(0.518501\pi\) | |||||||
\(854\) | −1.15317e10 | −0.633565 | ||||||||
\(855\) | −4.25977e10 | −2.33080 | ||||||||
\(856\) | −1.52260e10 | −0.829714 | ||||||||
\(857\) | 2.58468e10 | 1.40273 | 0.701366 | − | 0.712802i | \(-0.252574\pi\) | ||||
0.701366 | + | 0.712802i | \(0.252574\pi\) | |||||||
\(858\) | 4.90177e9 | 0.264940 | ||||||||
\(859\) | 5.54636e9 | 0.298560 | 0.149280 | − | 0.988795i | \(-0.452304\pi\) | ||||
0.149280 | + | 0.988795i | \(0.452304\pi\) | |||||||
\(860\) | −1.60837e10 | −0.862265 | ||||||||
\(861\) | −1.26436e10 | −0.675086 | ||||||||
\(862\) | 3.46640e10 | 1.84333 | ||||||||
\(863\) | −2.34967e10 | −1.24443 | −0.622213 | − | 0.782848i | \(-0.713766\pi\) | ||||
−0.622213 | + | 0.782848i | \(0.713766\pi\) | |||||||
\(864\) | 2.41482e10 | 1.27376 | ||||||||
\(865\) | 2.15369e10 | 1.13143 | ||||||||
\(866\) | −2.20838e10 | −1.15548 | ||||||||
\(867\) | 7.00682e9 | 0.365136 | ||||||||
\(868\) | −1.08297e10 | −0.562078 | ||||||||
\(869\) | −8.69198e9 | −0.449313 | ||||||||
\(870\) | 3.41251e10 | 1.75694 | ||||||||
\(871\) | 9.00892e8 | 0.0461965 | ||||||||
\(872\) | 5.46602e10 | 2.79167 | ||||||||
\(873\) | 2.99297e10 | 1.52249 | ||||||||
\(874\) | 7.58400e10 | 3.84245 | ||||||||
\(875\) | −8.12716e9 | −0.410120 | ||||||||
\(876\) | −9.44753e10 | −4.74847 | ||||||||
\(877\) | 1.75591e10 | 0.879031 | 0.439516 | − | 0.898235i | \(-0.355150\pi\) | ||||
0.439516 | + | 0.898235i | \(0.355150\pi\) | |||||||
\(878\) | −6.53403e10 | −3.25800 | ||||||||
\(879\) | 2.66328e10 | 1.32268 | ||||||||
\(880\) | −2.62974e9 | −0.130084 | ||||||||
\(881\) | −2.61430e10 | −1.28807 | −0.644036 | − | 0.764995i | \(-0.722741\pi\) | ||||
−0.644036 | + | 0.764995i | \(0.722741\pi\) | |||||||
\(882\) | 1.17082e10 | 0.574578 | ||||||||
\(883\) | 1.67966e10 | 0.821027 | 0.410514 | − | 0.911854i | \(-0.365349\pi\) | ||||
0.410514 | + | 0.911854i | \(0.365349\pi\) | |||||||
\(884\) | −9.37915e9 | −0.456647 | ||||||||
\(885\) | 3.48790e9 | 0.169146 | ||||||||
\(886\) | −8.80473e9 | −0.425303 | ||||||||
\(887\) | −6.94232e9 | −0.334019 | −0.167010 | − | 0.985955i | \(-0.553411\pi\) | ||||
−0.167010 | + | 0.985955i | \(0.553411\pi\) | |||||||
\(888\) | −5.38640e10 | −2.58139 | ||||||||
\(889\) | −7.96689e9 | −0.380306 | ||||||||
\(890\) | −4.82055e10 | −2.29209 | ||||||||
\(891\) | 1.50318e10 | 0.711933 | ||||||||
\(892\) | −1.38300e10 | −0.652445 | ||||||||
\(893\) | −4.56368e10 | −2.14455 | ||||||||
\(894\) | 2.98050e9 | 0.139511 | ||||||||
\(895\) | 1.38498e10 | 0.645750 | ||||||||
\(896\) | 1.49109e10 | 0.692510 | ||||||||
\(897\) | 2.00465e10 | 0.927397 | ||||||||
\(898\) | −2.46653e10 | −1.13663 | ||||||||
\(899\) | 1.28310e10 | 0.588981 | ||||||||
\(900\) | −3.79063e10 | −1.73325 | ||||||||
\(901\) | 1.39274e10 | 0.634358 | ||||||||
\(902\) | −1.11026e10 | −0.503735 | ||||||||
\(903\) | 9.27690e9 | 0.419272 | ||||||||
\(904\) | −1.41575e10 | −0.637377 | ||||||||
\(905\) | 4.74927e9 | 0.212989 | ||||||||
\(906\) | 1.18223e11 | 5.28143 | ||||||||
\(907\) | 2.16539e10 | 0.963630 | 0.481815 | − | 0.876273i | \(-0.339978\pi\) | ||||
0.481815 | + | 0.876273i | \(0.339978\pi\) | |||||||
\(908\) | 3.04216e10 | 1.34860 | ||||||||
\(909\) | 6.73847e10 | 2.97569 | ||||||||
\(910\) | −3.12348e9 | −0.137402 | ||||||||
\(911\) | 2.77454e10 | 1.21584 | 0.607920 | − | 0.793999i | \(-0.292004\pi\) | ||||
0.607920 | + | 0.793999i | \(0.292004\pi\) | |||||||
\(912\) | −2.87250e10 | −1.25394 | ||||||||
\(913\) | −2.24704e9 | −0.0977156 | ||||||||
\(914\) | −2.45508e9 | −0.106354 | ||||||||
\(915\) | 3.30051e10 | 1.42432 | ||||||||
\(916\) | 4.39396e10 | 1.88896 | ||||||||
\(917\) | −1.32030e10 | −0.565432 | ||||||||
\(918\) | −9.02656e10 | −3.85099 | ||||||||
\(919\) | −2.13902e10 | −0.909098 | −0.454549 | − | 0.890722i | \(-0.650200\pi\) | ||||
−0.454549 | + | 0.890722i | \(0.650200\pi\) | |||||||
\(920\) | −4.71891e10 | −1.99795 | ||||||||
\(921\) | 6.94712e10 | 2.93019 | ||||||||
\(922\) | −5.35810e10 | −2.25140 | ||||||||
\(923\) | 1.40960e9 | 0.0590050 | ||||||||
\(924\) | 9.44965e9 | 0.394061 | ||||||||
\(925\) | −9.43049e9 | −0.391776 | ||||||||
\(926\) | 4.59213e9 | 0.190053 | ||||||||
\(927\) | −4.67433e10 | −1.92726 | ||||||||
\(928\) | −8.84747e9 | −0.363414 | ||||||||
\(929\) | 2.10804e10 | 0.862628 | 0.431314 | − | 0.902202i | \(-0.358050\pi\) | ||||
0.431314 | + | 0.902202i | \(0.358050\pi\) | |||||||
\(930\) | 4.78509e10 | 1.95074 | ||||||||
\(931\) | 4.41498e9 | 0.179310 | ||||||||
\(932\) | −8.02119e10 | −3.24551 | ||||||||
\(933\) | 3.08177e10 | 1.24227 | ||||||||
\(934\) | −6.69356e9 | −0.268809 | ||||||||
\(935\) | −5.36267e9 | −0.214556 | ||||||||
\(936\) | −2.34793e10 | −0.935878 | ||||||||
\(937\) | −3.81672e10 | −1.51566 | −0.757830 | − | 0.652452i | \(-0.773740\pi\) | ||||
−0.757830 | + | 0.652452i | \(0.773740\pi\) | |||||||
\(938\) | 2.68115e9 | 0.106075 | ||||||||
\(939\) | −1.96771e10 | −0.775588 | ||||||||
\(940\) | 6.22427e10 | 2.44422 | ||||||||
\(941\) | 2.33560e10 | 0.913764 | 0.456882 | − | 0.889527i | \(-0.348966\pi\) | ||||
0.456882 | + | 0.889527i | \(0.348966\pi\) | |||||||
\(942\) | 6.45059e10 | 2.51432 | ||||||||
\(943\) | −4.54058e10 | −1.76328 | ||||||||
\(944\) | 1.65760e9 | 0.0641324 | ||||||||
\(945\) | −1.94720e10 | −0.750584 | ||||||||
\(946\) | 8.14625e9 | 0.312852 | ||||||||
\(947\) | −2.34273e10 | −0.896392 | −0.448196 | − | 0.893935i | \(-0.647933\pi\) | ||||
−0.448196 | + | 0.893935i | \(0.647933\pi\) | |||||||
\(948\) | 1.29491e11 | 4.93639 | ||||||||
\(949\) | −1.02454e10 | −0.389131 | ||||||||
\(950\) | −2.20667e10 | −0.835036 | ||||||||
\(951\) | 3.15430e10 | 1.18924 | ||||||||
\(952\) | −1.27345e10 | −0.478359 | ||||||||
\(953\) | 1.74489e10 | 0.653045 | 0.326523 | − | 0.945189i | \(-0.394123\pi\) | ||||
0.326523 | + | 0.945189i | \(0.394123\pi\) | |||||||
\(954\) | 7.64226e10 | 2.84972 | ||||||||
\(955\) | −2.51945e10 | −0.936041 | ||||||||
\(956\) | −6.31983e10 | −2.33939 | ||||||||
\(957\) | −1.11959e10 | −0.412922 | ||||||||
\(958\) | 2.90373e10 | 1.06703 | ||||||||
\(959\) | 2.52137e8 | 0.00923147 | ||||||||
\(960\) | −5.42990e10 | −1.98081 | ||||||||
\(961\) | −9.52073e9 | −0.346050 | ||||||||
\(962\) | −1.28038e10 | −0.463687 | ||||||||
\(963\) | −3.88296e10 | −1.40111 | ||||||||
\(964\) | −2.23870e10 | −0.804871 | ||||||||
\(965\) | −3.37647e10 | −1.20953 | ||||||||
\(966\) | 5.96607e10 | 2.12946 | ||||||||
\(967\) | −7.58541e9 | −0.269766 | −0.134883 | − | 0.990862i | \(-0.543066\pi\) | ||||
−0.134883 | + | 0.990862i | \(0.543066\pi\) | |||||||
\(968\) | −3.61065e10 | −1.27945 | ||||||||
\(969\) | −5.85771e10 | −2.06821 | ||||||||
\(970\) | −2.37631e10 | −0.835990 | ||||||||
\(971\) | −2.41799e10 | −0.847592 | −0.423796 | − | 0.905758i | \(-0.639303\pi\) | ||||
−0.423796 | + | 0.905758i | \(0.639303\pi\) | |||||||
\(972\) | −8.95332e10 | −3.12718 | ||||||||
\(973\) | −1.34624e10 | −0.468520 | ||||||||
\(974\) | 1.86425e10 | 0.646470 | ||||||||
\(975\) | −5.83283e9 | −0.201541 | ||||||||
\(976\) | 1.56855e10 | 0.540036 | ||||||||
\(977\) | −6.35056e9 | −0.217862 | −0.108931 | − | 0.994049i | \(-0.534743\pi\) | ||||
−0.108931 | + | 0.994049i | \(0.534743\pi\) | |||||||
\(978\) | 2.54127e9 | 0.0868690 | ||||||||
\(979\) | 1.58155e10 | 0.538696 | ||||||||
\(980\) | −6.02146e9 | −0.204367 | ||||||||
\(981\) | 1.39395e11 | 4.71418 | ||||||||
\(982\) | 2.70915e10 | 0.912941 | ||||||||
\(983\) | −9.54541e9 | −0.320522 | −0.160261 | − | 0.987075i | \(-0.551234\pi\) | ||||
−0.160261 | + | 0.987075i | \(0.551234\pi\) | |||||||
\(984\) | 7.54597e10 | 2.52483 | ||||||||
\(985\) | −2.36530e10 | −0.788606 | ||||||||
\(986\) | 3.30717e10 | 1.09872 | ||||||||
\(987\) | −3.59010e10 | −1.18849 | ||||||||
\(988\) | −1.94068e10 | −0.640184 | ||||||||
\(989\) | 3.33153e10 | 1.09511 | ||||||||
\(990\) | −2.94260e10 | −0.963847 | ||||||||
\(991\) | −4.58841e10 | −1.49763 | −0.748815 | − | 0.662779i | \(-0.769377\pi\) | ||||
−0.748815 | + | 0.662779i | \(0.769377\pi\) | |||||||
\(992\) | −1.24061e10 | −0.403502 | ||||||||
\(993\) | 5.43017e9 | 0.175991 | ||||||||
\(994\) | 4.19511e9 | 0.135485 | ||||||||
\(995\) | −5.95957e9 | −0.191794 | ||||||||
\(996\) | 3.34758e10 | 1.07355 | ||||||||
\(997\) | −6.08517e10 | −1.94464 | −0.972320 | − | 0.233652i | \(-0.924932\pi\) | ||||
−0.972320 | + | 0.233652i | \(0.924932\pi\) | |||||||
\(998\) | 5.28031e10 | 1.68152 | ||||||||
\(999\) | −7.98196e10 | −2.53297 |
(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 | 91.8.a.d.1.10 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.d.1.10 | ✓ | 10 | 1.1 | even | 1 | trivial |