Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,8,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, 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("21.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(6.56008553517\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{67}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 67 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(8.18535\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.3707 | 1.97731 | 0.988655 | − | 0.150205i | \(-0.0479934\pi\) | ||||
0.988655 | + | 0.150205i | \(0.0479934\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 372.448 | 2.90975 | ||||||||
\(5\) | 118.966 | 0.425624 | 0.212812 | − | 0.977093i | \(-0.431738\pi\) | ||||
0.212812 | + | 0.977093i | \(0.431738\pi\) | |||||||
\(6\) | −604.009 | −1.14160 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 5468.48 | 3.77617 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2661.35 | 0.841591 | ||||||||
\(11\) | −3521.80 | −0.797793 | −0.398896 | − | 0.916996i | \(-0.630607\pi\) | ||||
−0.398896 | + | 0.916996i | \(0.630607\pi\) | |||||||
\(12\) | −10056.1 | −1.67995 | ||||||||
\(13\) | −5256.76 | −0.663616 | −0.331808 | − | 0.943347i | \(-0.607659\pi\) | ||||
−0.331808 | + | 0.943347i | \(0.607659\pi\) | |||||||
\(14\) | −7673.15 | −0.747353 | ||||||||
\(15\) | −3212.07 | −0.245734 | ||||||||
\(16\) | 74660.5 | 4.55691 | ||||||||
\(17\) | −37023.1 | −1.82769 | −0.913844 | − | 0.406066i | \(-0.866900\pi\) | ||||
−0.913844 | + | 0.406066i | \(0.866900\pi\) | |||||||
\(18\) | 16308.2 | 0.659103 | ||||||||
\(19\) | 5165.26 | 0.172764 | 0.0863822 | − | 0.996262i | \(-0.472469\pi\) | ||||
0.0863822 | + | 0.996262i | \(0.472469\pi\) | |||||||
\(20\) | 44308.6 | 1.23846 | ||||||||
\(21\) | 9261.00 | 0.218218 | ||||||||
\(22\) | −78785.1 | −1.57748 | ||||||||
\(23\) | 34550.9 | 0.592123 | 0.296061 | − | 0.955169i | \(-0.404327\pi\) | ||||
0.296061 | + | 0.955169i | \(0.404327\pi\) | |||||||
\(24\) | −147649. | −2.18018 | ||||||||
\(25\) | −63972.2 | −0.818844 | ||||||||
\(26\) | −117598. | −1.31217 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −127750. | −1.09978 | ||||||||
\(29\) | 6382.04 | 0.0485922 | 0.0242961 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242961 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(30\) | −71856.3 | −0.485893 | ||||||||
\(31\) | 155842. | 0.939549 | 0.469774 | − | 0.882786i | \(-0.344335\pi\) | ||||
0.469774 | + | 0.882786i | \(0.344335\pi\) | |||||||
\(32\) | 970241. | 5.23425 | ||||||||
\(33\) | 95088.5 | 0.460606 | ||||||||
\(34\) | −828233. | −3.61390 | ||||||||
\(35\) | −40805.2 | −0.160871 | ||||||||
\(36\) | 271515. | 0.969918 | ||||||||
\(37\) | 18789.3 | 0.0609825 | 0.0304913 | − | 0.999535i | \(-0.490293\pi\) | ||||
0.0304913 | + | 0.999535i | \(0.490293\pi\) | |||||||
\(38\) | 115550. | 0.341609 | ||||||||
\(39\) | 141933. | 0.383139 | ||||||||
\(40\) | 650562. | 1.60723 | ||||||||
\(41\) | 261595. | 0.592769 | 0.296384 | − | 0.955069i | \(-0.404219\pi\) | ||||
0.296384 | + | 0.955069i | \(0.404219\pi\) | |||||||
\(42\) | 207175. | 0.431484 | ||||||||
\(43\) | −134629. | −0.258225 | −0.129112 | − | 0.991630i | \(-0.541213\pi\) | ||||
−0.129112 | + | 0.991630i | \(0.541213\pi\) | |||||||
\(44\) | −1.31169e6 | −2.32138 | ||||||||
\(45\) | 86726.0 | 0.141875 | ||||||||
\(46\) | 772928. | 1.17081 | ||||||||
\(47\) | 1.08722e6 | 1.52748 | 0.763741 | − | 0.645523i | \(-0.223360\pi\) | ||||
0.763741 | + | 0.645523i | \(0.223360\pi\) | |||||||
\(48\) | −2.01583e6 | −2.63093 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | −1.43110e6 | −1.61911 | ||||||||
\(51\) | 999624. | 1.05522 | ||||||||
\(52\) | −1.95787e6 | −1.93096 | ||||||||
\(53\) | 404711. | 0.373405 | 0.186702 | − | 0.982417i | \(-0.440220\pi\) | ||||
0.186702 | + | 0.982417i | \(0.440220\pi\) | |||||||
\(54\) | −440323. | −0.380533 | ||||||||
\(55\) | −418973. | −0.339560 | ||||||||
\(56\) | −1.87569e6 | −1.42726 | ||||||||
\(57\) | −139462. | −0.0997456 | ||||||||
\(58\) | 142771. | 0.0960818 | ||||||||
\(59\) | 2.34681e6 | 1.48763 | 0.743816 | − | 0.668385i | \(-0.233014\pi\) | ||||
0.743816 | + | 0.668385i | \(0.233014\pi\) | |||||||
\(60\) | −1.19633e6 | −0.715027 | ||||||||
\(61\) | −306843. | −0.173086 | −0.0865431 | − | 0.996248i | \(-0.527582\pi\) | ||||
−0.0865431 | + | 0.996248i | \(0.527582\pi\) | |||||||
\(62\) | 3.48630e6 | 1.85778 | ||||||||
\(63\) | −250047. | −0.125988 | ||||||||
\(64\) | 1.21484e7 | 5.79283 | ||||||||
\(65\) | −625374. | −0.282451 | ||||||||
\(66\) | 2.12720e6 | 0.910760 | ||||||||
\(67\) | −2.72369e6 | −1.10636 | −0.553179 | − | 0.833063i | \(-0.686585\pi\) | ||||
−0.553179 | + | 0.833063i | \(0.686585\pi\) | |||||||
\(68\) | −1.37892e7 | −5.31812 | ||||||||
\(69\) | −932874. | −0.341862 | ||||||||
\(70\) | −912841. | −0.318092 | ||||||||
\(71\) | −1.21376e6 | −0.402465 | −0.201233 | − | 0.979543i | \(-0.564495\pi\) | ||||
−0.201233 | + | 0.979543i | \(0.564495\pi\) | |||||||
\(72\) | 3.98653e6 | 1.25872 | ||||||||
\(73\) | −4.24836e6 | −1.27818 | −0.639089 | − | 0.769133i | \(-0.720688\pi\) | ||||
−0.639089 | + | 0.769133i | \(0.720688\pi\) | |||||||
\(74\) | 420331. | 0.120581 | ||||||||
\(75\) | 1.72725e6 | 0.472760 | ||||||||
\(76\) | 1.92379e6 | 0.502702 | ||||||||
\(77\) | 1.20798e6 | 0.301537 | ||||||||
\(78\) | 3.17513e6 | 0.757584 | ||||||||
\(79\) | −4.67709e6 | −1.06729 | −0.533643 | − | 0.845710i | \(-0.679177\pi\) | ||||
−0.533643 | + | 0.845710i | \(0.679177\pi\) | |||||||
\(80\) | 8.88203e6 | 1.93953 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 5.85206e6 | 1.17209 | ||||||||
\(83\) | 1.16593e6 | 0.223821 | 0.111910 | − | 0.993718i | \(-0.464303\pi\) | ||||
0.111910 | + | 0.993718i | \(0.464303\pi\) | |||||||
\(84\) | 3.44925e6 | 0.634960 | ||||||||
\(85\) | −4.40448e6 | −0.777908 | ||||||||
\(86\) | −3.01174e6 | −0.510590 | ||||||||
\(87\) | −172315. | −0.0280547 | ||||||||
\(88\) | −1.92589e7 | −3.01260 | ||||||||
\(89\) | 2.59661e6 | 0.390428 | 0.195214 | − | 0.980761i | \(-0.437460\pi\) | ||||
0.195214 | + | 0.980761i | \(0.437460\pi\) | |||||||
\(90\) | 1.94012e6 | 0.280530 | ||||||||
\(91\) | 1.80307e6 | 0.250823 | ||||||||
\(92\) | 1.28684e7 | 1.72293 | ||||||||
\(93\) | −4.20774e6 | −0.542449 | ||||||||
\(94\) | 2.43219e7 | 3.02031 | ||||||||
\(95\) | 614488. | 0.0735328 | ||||||||
\(96\) | −2.61965e7 | −3.02200 | ||||||||
\(97\) | −1.06794e7 | −1.18808 | −0.594040 | − | 0.804435i | \(-0.702468\pi\) | ||||
−0.594040 | + | 0.804435i | \(0.702468\pi\) | |||||||
\(98\) | 2.63189e6 | 0.282473 | ||||||||
\(99\) | −2.56739e6 | −0.265931 | ||||||||
\(100\) | −2.38263e7 | −2.38263 | ||||||||
\(101\) | −246324. | −0.0237893 | −0.0118946 | − | 0.999929i | \(-0.503786\pi\) | ||||
−0.0118946 | + | 0.999929i | \(0.503786\pi\) | |||||||
\(102\) | 2.23623e7 | 2.08649 | ||||||||
\(103\) | 1.10660e7 | 0.997841 | 0.498920 | − | 0.866648i | \(-0.333730\pi\) | ||||
0.498920 | + | 0.866648i | \(0.333730\pi\) | |||||||
\(104\) | −2.87465e7 | −2.50593 | ||||||||
\(105\) | 1.10174e6 | 0.0928789 | ||||||||
\(106\) | 9.05368e6 | 0.738337 | ||||||||
\(107\) | −2.58805e6 | −0.204234 | −0.102117 | − | 0.994772i | \(-0.532562\pi\) | ||||
−0.102117 | + | 0.994772i | \(0.532562\pi\) | |||||||
\(108\) | −7.33090e6 | −0.559982 | ||||||||
\(109\) | 1.35463e7 | 1.00191 | 0.500955 | − | 0.865473i | \(-0.332982\pi\) | ||||
0.500955 | + | 0.865473i | \(0.332982\pi\) | |||||||
\(110\) | −9.37272e6 | −0.671415 | ||||||||
\(111\) | −507312. | −0.0352083 | ||||||||
\(112\) | −2.56085e7 | −1.72235 | ||||||||
\(113\) | 5.00074e6 | 0.326032 | 0.163016 | − | 0.986623i | \(-0.447878\pi\) | ||||
0.163016 | + | 0.986623i | \(0.447878\pi\) | |||||||
\(114\) | −3.11986e6 | −0.197228 | ||||||||
\(115\) | 4.11037e6 | 0.252022 | ||||||||
\(116\) | 2.37698e6 | 0.141391 | ||||||||
\(117\) | −3.83218e6 | −0.221205 | ||||||||
\(118\) | 5.24997e7 | 2.94151 | ||||||||
\(119\) | 1.26989e7 | 0.690801 | ||||||||
\(120\) | −1.75652e7 | −0.927936 | ||||||||
\(121\) | −7.08411e6 | −0.363527 | ||||||||
\(122\) | −6.86430e6 | −0.342245 | ||||||||
\(123\) | −7.06306e6 | −0.342235 | ||||||||
\(124\) | 5.80432e7 | 2.73386 | ||||||||
\(125\) | −1.69047e7 | −0.774144 | ||||||||
\(126\) | −5.59373e6 | −0.249118 | ||||||||
\(127\) | 1.40147e7 | 0.607116 | 0.303558 | − | 0.952813i | \(-0.401825\pi\) | ||||
0.303558 | + | 0.952813i | \(0.401825\pi\) | |||||||
\(128\) | 1.47578e8 | 6.21996 | ||||||||
\(129\) | 3.63497e6 | 0.149086 | ||||||||
\(130\) | −1.39901e7 | −0.558493 | ||||||||
\(131\) | 1.85461e7 | 0.720780 | 0.360390 | − | 0.932802i | \(-0.382644\pi\) | ||||
0.360390 | + | 0.932802i | \(0.382644\pi\) | |||||||
\(132\) | 3.54156e7 | 1.34025 | ||||||||
\(133\) | −1.77168e6 | −0.0652988 | ||||||||
\(134\) | −6.09308e7 | −2.18761 | ||||||||
\(135\) | −2.34160e6 | −0.0819115 | ||||||||
\(136\) | −2.02460e8 | −6.90167 | ||||||||
\(137\) | 1.88670e7 | 0.626877 | 0.313438 | − | 0.949609i | \(-0.398519\pi\) | ||||
0.313438 | + | 0.949609i | \(0.398519\pi\) | |||||||
\(138\) | −2.08691e7 | −0.675968 | ||||||||
\(139\) | −2.19684e7 | −0.693819 | −0.346910 | − | 0.937899i | \(-0.612769\pi\) | ||||
−0.346910 | + | 0.937899i | \(0.612769\pi\) | |||||||
\(140\) | −1.51978e7 | −0.468095 | ||||||||
\(141\) | −2.93550e7 | −0.881892 | ||||||||
\(142\) | −2.71526e7 | −0.795798 | ||||||||
\(143\) | 1.85133e7 | 0.529428 | ||||||||
\(144\) | 5.44275e7 | 1.51897 | ||||||||
\(145\) | 759244. | 0.0206820 | ||||||||
\(146\) | −9.50388e7 | −2.52735 | ||||||||
\(147\) | −3.17652e6 | −0.0824786 | ||||||||
\(148\) | 6.99806e6 | 0.177444 | ||||||||
\(149\) | −5.67614e7 | −1.40573 | −0.702864 | − | 0.711325i | \(-0.748096\pi\) | ||||
−0.702864 | + | 0.711325i | \(0.748096\pi\) | |||||||
\(150\) | 3.86398e7 | 0.934792 | ||||||||
\(151\) | 5.28273e7 | 1.24864 | 0.624322 | − | 0.781167i | \(-0.285375\pi\) | ||||
0.624322 | + | 0.781167i | \(0.285375\pi\) | |||||||
\(152\) | 2.82461e7 | 0.652389 | ||||||||
\(153\) | −2.69899e7 | −0.609229 | ||||||||
\(154\) | 2.70233e7 | 0.596233 | ||||||||
\(155\) | 1.85399e7 | 0.399895 | ||||||||
\(156\) | 5.28626e7 | 1.11484 | ||||||||
\(157\) | 7.51444e7 | 1.54970 | 0.774850 | − | 0.632145i | \(-0.217825\pi\) | ||||
0.774850 | + | 0.632145i | \(0.217825\pi\) | |||||||
\(158\) | −1.04630e8 | −2.11035 | ||||||||
\(159\) | −1.09272e7 | −0.215585 | ||||||||
\(160\) | 1.15425e8 | 2.22783 | ||||||||
\(161\) | −1.18510e7 | −0.223801 | ||||||||
\(162\) | 1.18887e7 | 0.219701 | ||||||||
\(163\) | −6.33322e7 | −1.14543 | −0.572714 | − | 0.819755i | \(-0.694110\pi\) | ||||
−0.572714 | + | 0.819755i | \(0.694110\pi\) | |||||||
\(164\) | 9.74306e7 | 1.72481 | ||||||||
\(165\) | 1.13123e7 | 0.196045 | ||||||||
\(166\) | 2.60827e7 | 0.442563 | ||||||||
\(167\) | 8.08576e6 | 0.134342 | 0.0671712 | − | 0.997741i | \(-0.478603\pi\) | ||||
0.0671712 | + | 0.997741i | \(0.478603\pi\) | |||||||
\(168\) | 5.06436e7 | 0.824029 | ||||||||
\(169\) | −3.51150e7 | −0.559614 | ||||||||
\(170\) | −9.85313e7 | −1.53817 | ||||||||
\(171\) | 3.76547e6 | 0.0575882 | ||||||||
\(172\) | −5.01422e7 | −0.751370 | ||||||||
\(173\) | 4.62544e7 | 0.679190 | 0.339595 | − | 0.940572i | \(-0.389710\pi\) | ||||
0.339595 | + | 0.940572i | \(0.389710\pi\) | |||||||
\(174\) | −3.85481e6 | −0.0554729 | ||||||||
\(175\) | 2.19425e7 | 0.309494 | ||||||||
\(176\) | −2.62939e8 | −3.63547 | ||||||||
\(177\) | −6.33638e7 | −0.858884 | ||||||||
\(178\) | 5.80879e7 | 0.771998 | ||||||||
\(179\) | 1.24705e8 | 1.62517 | 0.812586 | − | 0.582841i | \(-0.198059\pi\) | ||||
0.812586 | + | 0.582841i | \(0.198059\pi\) | |||||||
\(180\) | 3.23009e7 | 0.412821 | ||||||||
\(181\) | −7.77417e7 | −0.974494 | −0.487247 | − | 0.873264i | \(-0.661999\pi\) | ||||
−0.487247 | + | 0.873264i | \(0.661999\pi\) | |||||||
\(182\) | 4.03359e7 | 0.495955 | ||||||||
\(183\) | 8.28477e6 | 0.0999314 | ||||||||
\(184\) | 1.88941e8 | 2.23596 | ||||||||
\(185\) | 2.23529e6 | 0.0259557 | ||||||||
\(186\) | −9.41302e7 | −1.07259 | ||||||||
\(187\) | 1.30388e8 | 1.45812 | ||||||||
\(188\) | 4.04935e8 | 4.44460 | ||||||||
\(189\) | 6.75127e6 | 0.0727393 | ||||||||
\(190\) | 1.37465e7 | 0.145397 | ||||||||
\(191\) | 1.88867e7 | 0.196128 | 0.0980639 | − | 0.995180i | \(-0.468735\pi\) | ||||
0.0980639 | + | 0.995180i | \(0.468735\pi\) | |||||||
\(192\) | −3.28008e8 | −3.34449 | ||||||||
\(193\) | −1.49723e8 | −1.49913 | −0.749564 | − | 0.661932i | \(-0.769737\pi\) | ||||
−0.749564 | + | 0.661932i | \(0.769737\pi\) | |||||||
\(194\) | −2.38906e8 | −2.34920 | ||||||||
\(195\) | 1.68851e7 | 0.163073 | ||||||||
\(196\) | 4.38182e7 | 0.415679 | ||||||||
\(197\) | −6.84902e7 | −0.638259 | −0.319129 | − | 0.947711i | \(-0.603390\pi\) | ||||
−0.319129 | + | 0.947711i | \(0.603390\pi\) | |||||||
\(198\) | −5.74343e7 | −0.525828 | ||||||||
\(199\) | 1.04209e8 | 0.937390 | 0.468695 | − | 0.883360i | \(-0.344724\pi\) | ||||
0.468695 | + | 0.883360i | \(0.344724\pi\) | |||||||
\(200\) | −3.49831e8 | −3.09210 | ||||||||
\(201\) | 7.35395e7 | 0.638756 | ||||||||
\(202\) | −5.51043e6 | −0.0470387 | ||||||||
\(203\) | −2.18904e6 | −0.0183661 | ||||||||
\(204\) | 3.72309e8 | 3.07042 | ||||||||
\(205\) | 3.11208e7 | 0.252297 | ||||||||
\(206\) | 2.47555e8 | 1.97304 | ||||||||
\(207\) | 2.51876e7 | 0.197374 | ||||||||
\(208\) | −3.92472e8 | −3.02404 | ||||||||
\(209\) | −1.81910e7 | −0.137830 | ||||||||
\(210\) | 2.46467e7 | 0.183650 | ||||||||
\(211\) | 2.55635e7 | 0.187341 | 0.0936703 | − | 0.995603i | \(-0.470140\pi\) | ||||
0.0936703 | + | 0.995603i | \(0.470140\pi\) | |||||||
\(212\) | 1.50734e8 | 1.08652 | ||||||||
\(213\) | 3.27715e7 | 0.232363 | ||||||||
\(214\) | −5.78964e7 | −0.403835 | ||||||||
\(215\) | −1.60162e7 | −0.109907 | ||||||||
\(216\) | −1.07636e8 | −0.726725 | ||||||||
\(217\) | −5.34539e7 | −0.355116 | ||||||||
\(218\) | 3.03041e8 | 1.98109 | ||||||||
\(219\) | 1.14706e8 | 0.737956 | ||||||||
\(220\) | −1.56046e8 | −0.988036 | ||||||||
\(221\) | 1.94622e8 | 1.21288 | ||||||||
\(222\) | −1.13489e7 | −0.0696177 | ||||||||
\(223\) | −2.25176e8 | −1.35974 | −0.679869 | − | 0.733333i | \(-0.737964\pi\) | ||||
−0.679869 | + | 0.733333i | \(0.737964\pi\) | |||||||
\(224\) | −3.32793e8 | −1.97836 | ||||||||
\(225\) | −4.66357e7 | −0.272948 | ||||||||
\(226\) | 1.11870e8 | 0.644666 | ||||||||
\(227\) | −2.20854e8 | −1.25318 | −0.626591 | − | 0.779348i | \(-0.715550\pi\) | ||||
−0.626591 | + | 0.779348i | \(0.715550\pi\) | |||||||
\(228\) | −5.19424e7 | −0.290235 | ||||||||
\(229\) | −2.35878e8 | −1.29796 | −0.648982 | − | 0.760804i | \(-0.724805\pi\) | ||||
−0.648982 | + | 0.760804i | \(0.724805\pi\) | |||||||
\(230\) | 9.19519e7 | 0.498326 | ||||||||
\(231\) | −3.26154e7 | −0.174093 | ||||||||
\(232\) | 3.49001e7 | 0.183493 | ||||||||
\(233\) | −3.34403e8 | −1.73191 | −0.865953 | − | 0.500125i | \(-0.833287\pi\) | ||||
−0.865953 | + | 0.500125i | \(0.833287\pi\) | |||||||
\(234\) | −8.57286e7 | −0.437391 | ||||||||
\(235\) | 1.29342e8 | 0.650134 | ||||||||
\(236\) | 8.74065e8 | 4.32864 | ||||||||
\(237\) | 1.26281e8 | 0.616197 | ||||||||
\(238\) | 2.84084e8 | 1.36593 | ||||||||
\(239\) | −1.48232e8 | −0.702345 | −0.351172 | − | 0.936311i | \(-0.614217\pi\) | ||||
−0.351172 | + | 0.936311i | \(0.614217\pi\) | |||||||
\(240\) | −2.39815e8 | −1.11979 | ||||||||
\(241\) | −4.10445e8 | −1.88884 | −0.944421 | − | 0.328738i | \(-0.893377\pi\) | ||||
−0.944421 | + | 0.328738i | \(0.893377\pi\) | |||||||
\(242\) | −1.58477e8 | −0.718805 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −1.14283e8 | −0.503638 | ||||||||
\(245\) | 1.39962e7 | 0.0608035 | ||||||||
\(246\) | −1.58006e8 | −0.676705 | ||||||||
\(247\) | −2.71525e7 | −0.114649 | ||||||||
\(248\) | 8.52221e8 | 3.54790 | ||||||||
\(249\) | −3.14802e7 | −0.129223 | ||||||||
\(250\) | −3.78170e8 | −1.53072 | ||||||||
\(251\) | 8.73950e7 | 0.348842 | 0.174421 | − | 0.984671i | \(-0.444195\pi\) | ||||
0.174421 | + | 0.984671i | \(0.444195\pi\) | |||||||
\(252\) | −9.31296e7 | −0.366595 | ||||||||
\(253\) | −1.21681e8 | −0.472391 | ||||||||
\(254\) | 3.13519e8 | 1.20046 | ||||||||
\(255\) | 1.18921e8 | 0.449126 | ||||||||
\(256\) | 1.74643e9 | 6.50596 | ||||||||
\(257\) | 9.99571e7 | 0.367323 | 0.183661 | − | 0.982990i | \(-0.441205\pi\) | ||||
0.183661 | + | 0.982990i | \(0.441205\pi\) | |||||||
\(258\) | 8.13169e7 | 0.294789 | ||||||||
\(259\) | −6.44474e6 | −0.0230492 | ||||||||
\(260\) | −2.32920e8 | −0.821863 | ||||||||
\(261\) | 4.65251e6 | 0.0161974 | ||||||||
\(262\) | 4.14889e8 | 1.42521 | ||||||||
\(263\) | −3.69452e7 | −0.125231 | −0.0626156 | − | 0.998038i | \(-0.519944\pi\) | ||||
−0.0626156 | + | 0.998038i | \(0.519944\pi\) | |||||||
\(264\) | 5.19990e8 | 1.73933 | ||||||||
\(265\) | 4.81468e7 | 0.158930 | ||||||||
\(266\) | −3.96338e7 | −0.129116 | ||||||||
\(267\) | −7.01084e7 | −0.225414 | ||||||||
\(268\) | −1.01443e9 | −3.21923 | ||||||||
\(269\) | −1.07622e8 | −0.337106 | −0.168553 | − | 0.985693i | \(-0.553909\pi\) | ||||
−0.168553 | + | 0.985693i | \(0.553909\pi\) | |||||||
\(270\) | −5.23833e7 | −0.161964 | ||||||||
\(271\) | 3.47931e8 | 1.06194 | 0.530971 | − | 0.847390i | \(-0.321827\pi\) | ||||
0.530971 | + | 0.847390i | \(0.321827\pi\) | |||||||
\(272\) | −2.76416e9 | −8.32861 | ||||||||
\(273\) | −4.86829e7 | −0.144813 | ||||||||
\(274\) | 4.22069e8 | 1.23953 | ||||||||
\(275\) | 2.25297e8 | 0.653268 | ||||||||
\(276\) | −3.47448e8 | −0.994735 | ||||||||
\(277\) | 4.33727e8 | 1.22613 | 0.613066 | − | 0.790031i | \(-0.289936\pi\) | ||||
0.613066 | + | 0.790031i | \(0.289936\pi\) | |||||||
\(278\) | −4.91448e8 | −1.37190 | ||||||||
\(279\) | 1.13609e8 | 0.313183 | ||||||||
\(280\) | −2.23143e8 | −0.607477 | ||||||||
\(281\) | 1.95616e8 | 0.525935 | 0.262967 | − | 0.964805i | \(-0.415299\pi\) | ||||
0.262967 | + | 0.964805i | \(0.415299\pi\) | |||||||
\(282\) | −6.56693e8 | −1.74377 | ||||||||
\(283\) | −2.02622e8 | −0.531416 | −0.265708 | − | 0.964054i | \(-0.585606\pi\) | ||||
−0.265708 | + | 0.964054i | \(0.585606\pi\) | |||||||
\(284\) | −4.52063e8 | −1.17107 | ||||||||
\(285\) | −1.65912e7 | −0.0424542 | ||||||||
\(286\) | 4.14155e8 | 1.04684 | ||||||||
\(287\) | −8.97270e7 | −0.224046 | ||||||||
\(288\) | 7.07306e8 | 1.74475 | ||||||||
\(289\) | 9.60373e8 | 2.34044 | ||||||||
\(290\) | 1.69848e7 | 0.0408948 | ||||||||
\(291\) | 2.88344e8 | 0.685939 | ||||||||
\(292\) | −1.58229e9 | −3.71918 | ||||||||
\(293\) | 2.99557e8 | 0.695734 | 0.347867 | − | 0.937544i | \(-0.386906\pi\) | ||||
0.347867 | + | 0.937544i | \(0.386906\pi\) | |||||||
\(294\) | −7.10611e7 | −0.163086 | ||||||||
\(295\) | 2.79189e8 | 0.633172 | ||||||||
\(296\) | 1.02749e8 | 0.230281 | ||||||||
\(297\) | 6.93195e7 | 0.153535 | ||||||||
\(298\) | −1.26979e9 | −2.77956 | ||||||||
\(299\) | −1.81626e8 | −0.392942 | ||||||||
\(300\) | 6.43311e8 | 1.37561 | ||||||||
\(301\) | 4.61776e7 | 0.0975998 | ||||||||
\(302\) | 1.18178e9 | 2.46896 | ||||||||
\(303\) | 6.65073e6 | 0.0137347 | ||||||||
\(304\) | 3.85641e8 | 0.787273 | ||||||||
\(305\) | −3.65038e7 | −0.0736697 | ||||||||
\(306\) | −6.03782e8 | −1.20463 | ||||||||
\(307\) | −3.74127e8 | −0.737964 | −0.368982 | − | 0.929437i | \(-0.620294\pi\) | ||||
−0.368982 | + | 0.929437i | \(0.620294\pi\) | |||||||
\(308\) | 4.49909e8 | 0.877399 | ||||||||
\(309\) | −2.98783e8 | −0.576104 | ||||||||
\(310\) | 4.14750e8 | 0.790716 | ||||||||
\(311\) | −9.65713e8 | −1.82048 | −0.910241 | − | 0.414078i | \(-0.864104\pi\) | ||||
−0.910241 | + | 0.414078i | \(0.864104\pi\) | |||||||
\(312\) | 7.76156e8 | 1.44680 | ||||||||
\(313\) | 4.56220e8 | 0.840948 | 0.420474 | − | 0.907305i | \(-0.361864\pi\) | ||||
0.420474 | + | 0.907305i | \(0.361864\pi\) | |||||||
\(314\) | 1.68103e9 | 3.06424 | ||||||||
\(315\) | −2.97470e7 | −0.0536236 | ||||||||
\(316\) | −1.74197e9 | −3.10554 | ||||||||
\(317\) | 9.27114e8 | 1.63465 | 0.817327 | − | 0.576174i | \(-0.195455\pi\) | ||||
0.817327 | + | 0.576174i | \(0.195455\pi\) | |||||||
\(318\) | −2.44449e8 | −0.426279 | ||||||||
\(319\) | −2.24763e7 | −0.0387665 | ||||||||
\(320\) | 1.44525e9 | 2.46557 | ||||||||
\(321\) | 6.98773e7 | 0.117915 | ||||||||
\(322\) | −2.65114e8 | −0.442525 | ||||||||
\(323\) | −1.91234e8 | −0.315759 | ||||||||
\(324\) | 1.97934e8 | 0.323306 | ||||||||
\(325\) | 3.36287e8 | 0.543398 | ||||||||
\(326\) | −1.41679e9 | −2.26487 | ||||||||
\(327\) | −3.65751e8 | −0.578453 | ||||||||
\(328\) | 1.43053e9 | 2.23840 | ||||||||
\(329\) | −3.72917e8 | −0.577334 | ||||||||
\(330\) | 2.53063e8 | 0.387642 | ||||||||
\(331\) | 9.78966e8 | 1.48378 | 0.741890 | − | 0.670522i | \(-0.233930\pi\) | ||||
0.741890 | + | 0.670522i | \(0.233930\pi\) | |||||||
\(332\) | 4.34250e8 | 0.651263 | ||||||||
\(333\) | 1.36974e7 | 0.0203275 | ||||||||
\(334\) | 1.80884e8 | 0.265637 | ||||||||
\(335\) | −3.24025e8 | −0.470893 | ||||||||
\(336\) | 6.91430e8 | 0.994400 | ||||||||
\(337\) | 4.88207e7 | 0.0694863 | 0.0347431 | − | 0.999396i | \(-0.488939\pi\) | ||||
0.0347431 | + | 0.999396i | \(0.488939\pi\) | |||||||
\(338\) | −7.85546e8 | −1.10653 | ||||||||
\(339\) | −1.35020e8 | −0.188235 | ||||||||
\(340\) | −1.64044e9 | −2.26352 | ||||||||
\(341\) | −5.48845e8 | −0.749565 | ||||||||
\(342\) | 8.42363e7 | 0.113870 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | −7.36214e8 | −0.975101 | ||||||||
\(345\) | −1.10980e8 | −0.145505 | ||||||||
\(346\) | 1.03474e9 | 1.34297 | ||||||||
\(347\) | −1.24915e8 | −0.160495 | −0.0802474 | − | 0.996775i | \(-0.525571\pi\) | ||||
−0.0802474 | + | 0.996775i | \(0.525571\pi\) | |||||||
\(348\) | −6.41785e7 | −0.0816323 | ||||||||
\(349\) | −7.80485e8 | −0.982823 | −0.491411 | − | 0.870928i | \(-0.663519\pi\) | ||||
−0.491411 | + | 0.870928i | \(0.663519\pi\) | |||||||
\(350\) | 4.90868e8 | 0.611965 | ||||||||
\(351\) | 1.03469e8 | 0.127713 | ||||||||
\(352\) | −3.41699e9 | −4.17585 | ||||||||
\(353\) | 6.57963e8 | 0.796141 | 0.398070 | − | 0.917355i | \(-0.369680\pi\) | ||||
0.398070 | + | 0.917355i | \(0.369680\pi\) | |||||||
\(354\) | −1.41749e9 | −1.69828 | ||||||||
\(355\) | −1.44396e8 | −0.171299 | ||||||||
\(356\) | 9.67103e8 | 1.13605 | ||||||||
\(357\) | −3.42871e8 | −0.398834 | ||||||||
\(358\) | 2.78975e9 | 3.21347 | ||||||||
\(359\) | −1.17200e9 | −1.33689 | −0.668446 | − | 0.743761i | \(-0.733040\pi\) | ||||
−0.668446 | + | 0.743761i | \(0.733040\pi\) | |||||||
\(360\) | 4.74260e8 | 0.535744 | ||||||||
\(361\) | −8.67192e8 | −0.970152 | ||||||||
\(362\) | −1.73914e9 | −1.92688 | ||||||||
\(363\) | 1.91271e8 | 0.209882 | ||||||||
\(364\) | 6.71551e8 | 0.729834 | ||||||||
\(365\) | −5.05409e8 | −0.544023 | ||||||||
\(366\) | 1.85336e8 | 0.197595 | ||||||||
\(367\) | −1.53053e9 | −1.61625 | −0.808127 | − | 0.589008i | \(-0.799519\pi\) | ||||
−0.808127 | + | 0.589008i | \(0.799519\pi\) | |||||||
\(368\) | 2.57959e9 | 2.69825 | ||||||||
\(369\) | 1.90703e8 | 0.197590 | ||||||||
\(370\) | 5.00049e7 | 0.0513224 | ||||||||
\(371\) | −1.38816e8 | −0.141134 | ||||||||
\(372\) | −1.56717e9 | −1.57839 | ||||||||
\(373\) | 1.08425e9 | 1.08181 | 0.540903 | − | 0.841085i | \(-0.318083\pi\) | ||||
0.540903 | + | 0.841085i | \(0.318083\pi\) | |||||||
\(374\) | 2.91687e9 | 2.88315 | ||||||||
\(375\) | 4.56426e8 | 0.446952 | ||||||||
\(376\) | 5.94546e9 | 5.76804 | ||||||||
\(377\) | −3.35489e7 | −0.0322466 | ||||||||
\(378\) | 1.51031e8 | 0.143828 | ||||||||
\(379\) | 1.59392e9 | 1.50394 | 0.751968 | − | 0.659199i | \(-0.229105\pi\) | ||||
0.751968 | + | 0.659199i | \(0.229105\pi\) | |||||||
\(380\) | 2.28865e8 | 0.213962 | ||||||||
\(381\) | −3.78398e8 | −0.350518 | ||||||||
\(382\) | 4.22509e8 | 0.387805 | ||||||||
\(383\) | −7.14242e8 | −0.649605 | −0.324803 | − | 0.945782i | \(-0.605298\pi\) | ||||
−0.324803 | + | 0.945782i | \(0.605298\pi\) | |||||||
\(384\) | −3.98461e9 | −3.59110 | ||||||||
\(385\) | 1.43708e8 | 0.128342 | ||||||||
\(386\) | −3.34941e9 | −2.96424 | ||||||||
\(387\) | −9.81442e7 | −0.0860749 | ||||||||
\(388\) | −3.97753e9 | −3.45702 | ||||||||
\(389\) | 1.27967e9 | 1.10223 | 0.551116 | − | 0.834429i | \(-0.314202\pi\) | ||||
0.551116 | + | 0.834429i | \(0.314202\pi\) | |||||||
\(390\) | 3.77732e8 | 0.322446 | ||||||||
\(391\) | −1.27918e9 | −1.08222 | ||||||||
\(392\) | 6.43362e8 | 0.539453 | ||||||||
\(393\) | −5.00744e8 | −0.416143 | ||||||||
\(394\) | −1.53217e9 | −1.26203 | ||||||||
\(395\) | −5.56413e8 | −0.454263 | ||||||||
\(396\) | −9.56221e8 | −0.773793 | ||||||||
\(397\) | 3.71121e7 | 0.0297679 | 0.0148840 | − | 0.999889i | \(-0.495262\pi\) | ||||
0.0148840 | + | 0.999889i | \(0.495262\pi\) | |||||||
\(398\) | 2.33123e9 | 1.85351 | ||||||||
\(399\) | 4.78355e7 | 0.0377003 | ||||||||
\(400\) | −4.77619e9 | −3.73140 | ||||||||
\(401\) | 1.16802e9 | 0.904574 | 0.452287 | − | 0.891872i | \(-0.350608\pi\) | ||||
0.452287 | + | 0.891872i | \(0.350608\pi\) | |||||||
\(402\) | 1.64513e9 | 1.26302 | ||||||||
\(403\) | −8.19226e8 | −0.623499 | ||||||||
\(404\) | −9.17428e7 | −0.0692209 | ||||||||
\(405\) | 6.32232e7 | 0.0472916 | ||||||||
\(406\) | −4.89704e7 | −0.0363155 | ||||||||
\(407\) | −6.61723e7 | −0.0486514 | ||||||||
\(408\) | 5.46643e9 | 3.98468 | ||||||||
\(409\) | −1.71549e8 | −0.123982 | −0.0619909 | − | 0.998077i | \(-0.519745\pi\) | ||||
−0.0619909 | + | 0.998077i | \(0.519745\pi\) | |||||||
\(410\) | 6.96194e8 | 0.498869 | ||||||||
\(411\) | −5.09410e8 | −0.361927 | ||||||||
\(412\) | 4.12152e9 | 2.90347 | ||||||||
\(413\) | −8.04955e8 | −0.562272 | ||||||||
\(414\) | 5.63464e8 | 0.390270 | ||||||||
\(415\) | 1.38706e8 | 0.0952635 | ||||||||
\(416\) | −5.10033e9 | −3.47353 | ||||||||
\(417\) | 5.93146e8 | 0.400577 | ||||||||
\(418\) | −4.06945e8 | −0.272533 | ||||||||
\(419\) | 1.61069e9 | 1.06970 | 0.534852 | − | 0.844946i | \(-0.320367\pi\) | ||||
0.534852 | + | 0.844946i | \(0.320367\pi\) | |||||||
\(420\) | 4.10342e8 | 0.270255 | ||||||||
\(421\) | 2.37944e8 | 0.155413 | 0.0777064 | − | 0.996976i | \(-0.475240\pi\) | ||||
0.0777064 | + | 0.996976i | \(0.475240\pi\) | |||||||
\(422\) | 5.71874e8 | 0.370430 | ||||||||
\(423\) | 7.92586e8 | 0.509161 | ||||||||
\(424\) | 2.21316e9 | 1.41004 | ||||||||
\(425\) | 2.36845e9 | 1.49659 | ||||||||
\(426\) | 7.33121e8 | 0.459454 | ||||||||
\(427\) | 1.05247e8 | 0.0654204 | ||||||||
\(428\) | −9.63914e8 | −0.594272 | ||||||||
\(429\) | −4.99858e8 | −0.305665 | ||||||||
\(430\) | −3.58293e8 | −0.217320 | ||||||||
\(431\) | 7.32984e8 | 0.440985 | 0.220493 | − | 0.975389i | \(-0.429233\pi\) | ||||
0.220493 | + | 0.975389i | \(0.429233\pi\) | |||||||
\(432\) | −1.46954e9 | −0.876978 | ||||||||
\(433\) | −3.01359e9 | −1.78392 | −0.891962 | − | 0.452111i | \(-0.850671\pi\) | ||||
−0.891962 | + | 0.452111i | \(0.850671\pi\) | |||||||
\(434\) | −1.19580e9 | −0.702175 | ||||||||
\(435\) | −2.04996e7 | −0.0119408 | ||||||||
\(436\) | 5.04531e9 | 2.91531 | ||||||||
\(437\) | 1.78464e8 | 0.102298 | ||||||||
\(438\) | 2.56605e9 | 1.45917 | ||||||||
\(439\) | 9.23499e8 | 0.520967 | 0.260484 | − | 0.965478i | \(-0.416118\pi\) | ||||
0.260484 | + | 0.965478i | \(0.416118\pi\) | |||||||
\(440\) | −2.29115e9 | −1.28224 | ||||||||
\(441\) | 8.57661e7 | 0.0476190 | ||||||||
\(442\) | 4.35383e9 | 2.39824 | ||||||||
\(443\) | −1.24106e9 | −0.678236 | −0.339118 | − | 0.940744i | \(-0.610129\pi\) | ||||
−0.339118 | + | 0.940744i | \(0.610129\pi\) | |||||||
\(444\) | −1.88948e8 | −0.102447 | ||||||||
\(445\) | 3.08907e8 | 0.166176 | ||||||||
\(446\) | −5.03735e9 | −2.68862 | ||||||||
\(447\) | 1.53256e9 | 0.811597 | ||||||||
\(448\) | −4.16691e9 | −2.18948 | ||||||||
\(449\) | 2.34362e9 | 1.22187 | 0.610936 | − | 0.791680i | \(-0.290793\pi\) | ||||
0.610936 | + | 0.791680i | \(0.290793\pi\) | |||||||
\(450\) | −1.04327e9 | −0.539703 | ||||||||
\(451\) | −9.21284e8 | −0.472907 | ||||||||
\(452\) | 1.86252e9 | 0.948672 | ||||||||
\(453\) | −1.42634e9 | −0.720905 | ||||||||
\(454\) | −4.94065e9 | −2.47793 | ||||||||
\(455\) | 2.14503e8 | 0.106756 | ||||||||
\(456\) | −7.62646e8 | −0.376657 | ||||||||
\(457\) | −1.41919e9 | −0.695560 | −0.347780 | − | 0.937576i | \(-0.613064\pi\) | ||||
−0.347780 | + | 0.937576i | \(0.613064\pi\) | |||||||
\(458\) | −5.27675e9 | −2.56648 | ||||||||
\(459\) | 7.28726e8 | 0.351739 | ||||||||
\(460\) | 1.53090e9 | 0.733322 | ||||||||
\(461\) | 3.22509e9 | 1.53317 | 0.766583 | − | 0.642145i | \(-0.221955\pi\) | ||||
0.766583 | + | 0.642145i | \(0.221955\pi\) | |||||||
\(462\) | −7.29629e8 | −0.344235 | ||||||||
\(463\) | −2.60402e9 | −1.21930 | −0.609651 | − | 0.792670i | \(-0.708690\pi\) | ||||
−0.609651 | + | 0.792670i | \(0.708690\pi\) | |||||||
\(464\) | 4.76486e8 | 0.221430 | ||||||||
\(465\) | −5.00577e8 | −0.230879 | ||||||||
\(466\) | −7.48083e9 | −3.42452 | ||||||||
\(467\) | 6.16965e8 | 0.280318 | 0.140159 | − | 0.990129i | \(-0.455239\pi\) | ||||
0.140159 | + | 0.990129i | \(0.455239\pi\) | |||||||
\(468\) | −1.42729e9 | −0.643653 | ||||||||
\(469\) | 9.34224e8 | 0.418164 | ||||||||
\(470\) | 2.89348e9 | 1.28552 | ||||||||
\(471\) | −2.02890e9 | −0.894720 | ||||||||
\(472\) | 1.28335e10 | 5.61756 | ||||||||
\(473\) | 4.74135e8 | 0.206010 | ||||||||
\(474\) | 2.82500e9 | 1.21841 | ||||||||
\(475\) | −3.30433e8 | −0.141467 | ||||||||
\(476\) | 4.72970e9 | 2.01006 | ||||||||
\(477\) | 2.95035e8 | 0.124468 | ||||||||
\(478\) | −3.31606e9 | −1.38875 | ||||||||
\(479\) | 2.90828e9 | 1.20910 | 0.604550 | − | 0.796567i | \(-0.293353\pi\) | ||||
0.604550 | + | 0.796567i | \(0.293353\pi\) | |||||||
\(480\) | −3.11648e9 | −1.28624 | ||||||||
\(481\) | −9.87711e7 | −0.0404690 | ||||||||
\(482\) | −9.18195e9 | −3.73483 | ||||||||
\(483\) | 3.19976e8 | 0.129212 | ||||||||
\(484\) | −2.63847e9 | −1.05777 | ||||||||
\(485\) | −1.27048e9 | −0.505676 | ||||||||
\(486\) | −3.20995e8 | −0.126844 | ||||||||
\(487\) | 1.46877e8 | 0.0576240 | 0.0288120 | − | 0.999585i | \(-0.490828\pi\) | ||||
0.0288120 | + | 0.999585i | \(0.490828\pi\) | |||||||
\(488\) | −1.67797e9 | −0.653604 | ||||||||
\(489\) | 1.70997e9 | 0.661313 | ||||||||
\(490\) | 3.13105e8 | 0.120227 | ||||||||
\(491\) | −3.73895e9 | −1.42549 | −0.712745 | − | 0.701423i | \(-0.752548\pi\) | ||||
−0.712745 | + | 0.701423i | \(0.752548\pi\) | |||||||
\(492\) | −2.63062e9 | −0.995821 | ||||||||
\(493\) | −2.36283e8 | −0.0888114 | ||||||||
\(494\) | −6.07422e8 | −0.226697 | ||||||||
\(495\) | −3.05431e8 | −0.113187 | ||||||||
\(496\) | 1.16353e10 | 4.28144 | ||||||||
\(497\) | 4.16319e8 | 0.152118 | ||||||||
\(498\) | −7.04234e8 | −0.255514 | ||||||||
\(499\) | 2.15882e9 | 0.777793 | 0.388896 | − | 0.921282i | \(-0.372856\pi\) | ||||
0.388896 | + | 0.921282i | \(0.372856\pi\) | |||||||
\(500\) | −6.29612e9 | −2.25257 | ||||||||
\(501\) | −2.18316e8 | −0.0775626 | ||||||||
\(502\) | 1.95509e9 | 0.689768 | ||||||||
\(503\) | −4.39095e9 | −1.53840 | −0.769202 | − | 0.639006i | \(-0.779346\pi\) | ||||
−0.769202 | + | 0.639006i | \(0.779346\pi\) | |||||||
\(504\) | −1.36738e9 | −0.475753 | ||||||||
\(505\) | −2.93040e7 | −0.0101253 | ||||||||
\(506\) | −2.72210e9 | −0.934064 | ||||||||
\(507\) | 9.48104e8 | 0.323093 | ||||||||
\(508\) | 5.21976e9 | 1.76656 | ||||||||
\(509\) | 3.89569e9 | 1.30940 | 0.654699 | − | 0.755889i | \(-0.272795\pi\) | ||||
0.654699 | + | 0.755889i | \(0.272795\pi\) | |||||||
\(510\) | 2.66035e9 | 0.888060 | ||||||||
\(511\) | 1.45719e9 | 0.483106 | ||||||||
\(512\) | 2.01789e10 | 6.64434 | ||||||||
\(513\) | −1.01668e8 | −0.0332485 | ||||||||
\(514\) | 2.23611e9 | 0.726311 | ||||||||
\(515\) | 1.31648e9 | 0.424705 | ||||||||
\(516\) | 1.35384e9 | 0.433804 | ||||||||
\(517\) | −3.82898e9 | −1.21861 | ||||||||
\(518\) | −1.44173e8 | −0.0455755 | ||||||||
\(519\) | −1.24887e9 | −0.392131 | ||||||||
\(520\) | −3.41985e9 | −1.06658 | ||||||||
\(521\) | 3.49790e9 | 1.08362 | 0.541808 | − | 0.840503i | \(-0.317740\pi\) | ||||
0.541808 | + | 0.840503i | \(0.317740\pi\) | |||||||
\(522\) | 1.04080e8 | 0.0320273 | ||||||||
\(523\) | 1.69050e9 | 0.516725 | 0.258362 | − | 0.966048i | \(-0.416817\pi\) | ||||
0.258362 | + | 0.966048i | \(0.416817\pi\) | |||||||
\(524\) | 6.90746e9 | 2.09729 | ||||||||
\(525\) | −5.92446e8 | −0.178686 | ||||||||
\(526\) | −8.26490e8 | −0.247621 | ||||||||
\(527\) | −5.76977e9 | −1.71720 | ||||||||
\(528\) | 7.09935e9 | 2.09894 | ||||||||
\(529\) | −2.21106e9 | −0.649390 | ||||||||
\(530\) | 1.07708e9 | 0.314254 | ||||||||
\(531\) | 1.71082e9 | 0.495877 | ||||||||
\(532\) | −6.59861e8 | −0.190004 | ||||||||
\(533\) | −1.37514e9 | −0.393371 | ||||||||
\(534\) | −1.56837e9 | −0.445713 | ||||||||
\(535\) | −3.07889e8 | −0.0869272 | ||||||||
\(536\) | −1.48944e10 | −4.17780 | ||||||||
\(537\) | −3.36704e9 | −0.938294 | ||||||||
\(538\) | −2.40757e9 | −0.666563 | ||||||||
\(539\) | −4.14336e8 | −0.113970 | ||||||||
\(540\) | −8.72126e8 | −0.238342 | ||||||||
\(541\) | −1.34175e9 | −0.364318 | −0.182159 | − | 0.983269i | \(-0.558309\pi\) | ||||
−0.182159 | + | 0.983269i | \(0.558309\pi\) | |||||||
\(542\) | 7.78347e9 | 2.09979 | ||||||||
\(543\) | 2.09903e9 | 0.562624 | ||||||||
\(544\) | −3.59214e10 | −9.56658 | ||||||||
\(545\) | 1.61155e9 | 0.426438 | ||||||||
\(546\) | −1.08907e9 | −0.286340 | ||||||||
\(547\) | 6.96823e9 | 1.82040 | 0.910200 | − | 0.414169i | \(-0.135928\pi\) | ||||
0.910200 | + | 0.414169i | \(0.135928\pi\) | |||||||
\(548\) | 7.02700e9 | 1.82406 | ||||||||
\(549\) | −2.23689e8 | −0.0576954 | ||||||||
\(550\) | 5.04005e9 | 1.29171 | ||||||||
\(551\) | 3.29649e7 | 0.00839501 | ||||||||
\(552\) | −5.10141e9 | −1.29093 | ||||||||
\(553\) | 1.60424e9 | 0.403396 | ||||||||
\(554\) | 9.70278e9 | 2.42444 | ||||||||
\(555\) | −6.03527e7 | −0.0149855 | ||||||||
\(556\) | −8.18209e9 | −2.01884 | ||||||||
\(557\) | −5.01746e9 | −1.23024 | −0.615121 | − | 0.788433i | \(-0.710893\pi\) | ||||
−0.615121 | + | 0.788433i | \(0.710893\pi\) | |||||||
\(558\) | 2.54151e9 | 0.619260 | ||||||||
\(559\) | 7.07711e8 | 0.171362 | ||||||||
\(560\) | −3.04654e9 | −0.733075 | ||||||||
\(561\) | −3.52047e9 | −0.841843 | ||||||||
\(562\) | 4.37606e9 | 1.03994 | ||||||||
\(563\) | 2.11565e9 | 0.499648 | 0.249824 | − | 0.968291i | \(-0.419627\pi\) | ||||
0.249824 | + | 0.968291i | \(0.419627\pi\) | |||||||
\(564\) | −1.09332e10 | −2.56609 | ||||||||
\(565\) | 5.94917e8 | 0.138767 | ||||||||
\(566\) | −4.53280e9 | −1.05077 | ||||||||
\(567\) | −1.82284e8 | −0.0419961 | ||||||||
\(568\) | −6.63742e9 | −1.51978 | ||||||||
\(569\) | 1.64764e9 | 0.374947 | 0.187474 | − | 0.982270i | \(-0.439970\pi\) | ||||
0.187474 | + | 0.982270i | \(0.439970\pi\) | |||||||
\(570\) | −3.71157e8 | −0.0839451 | ||||||||
\(571\) | 5.07137e9 | 1.13999 | 0.569993 | − | 0.821650i | \(-0.306946\pi\) | ||||
0.569993 | + | 0.821650i | \(0.306946\pi\) | |||||||
\(572\) | 6.89523e9 | 1.54050 | ||||||||
\(573\) | −5.09941e8 | −0.113234 | ||||||||
\(574\) | −2.00726e9 | −0.443008 | ||||||||
\(575\) | −2.21030e9 | −0.484856 | ||||||||
\(576\) | 8.85621e9 | 1.93094 | ||||||||
\(577\) | 4.71321e9 | 1.02141 | 0.510707 | − | 0.859755i | \(-0.329384\pi\) | ||||
0.510707 | + | 0.859755i | \(0.329384\pi\) | |||||||
\(578\) | 2.14842e10 | 4.62778 | ||||||||
\(579\) | 4.04253e9 | 0.865522 | ||||||||
\(580\) | 2.82779e8 | 0.0601796 | ||||||||
\(581\) | −3.99915e8 | −0.0845962 | ||||||||
\(582\) | 6.45046e9 | 1.35631 | ||||||||
\(583\) | −1.42531e9 | −0.297900 | ||||||||
\(584\) | −2.32321e10 | −4.82662 | ||||||||
\(585\) | −4.55898e8 | −0.0941504 | ||||||||
\(586\) | 6.70131e9 | 1.37568 | ||||||||
\(587\) | 6.75924e9 | 1.37932 | 0.689659 | − | 0.724134i | \(-0.257760\pi\) | ||||
0.689659 | + | 0.724134i | \(0.257760\pi\) | |||||||
\(588\) | −1.18309e9 | −0.239992 | ||||||||
\(589\) | 8.04966e8 | 0.162321 | ||||||||
\(590\) | 6.24566e9 | 1.25198 | ||||||||
\(591\) | 1.84924e9 | 0.368499 | ||||||||
\(592\) | 1.40282e9 | 0.277892 | ||||||||
\(593\) | −5.51671e9 | −1.08640 | −0.543199 | − | 0.839604i | \(-0.682787\pi\) | ||||
−0.543199 | + | 0.839604i | \(0.682787\pi\) | |||||||
\(594\) | 1.55073e9 | 0.303587 | ||||||||
\(595\) | 1.51074e9 | 0.294022 | ||||||||
\(596\) | −2.11407e10 | −4.09032 | ||||||||
\(597\) | −2.81365e9 | −0.541202 | ||||||||
\(598\) | −4.06310e9 | −0.776968 | ||||||||
\(599\) | −4.81408e9 | −0.915208 | −0.457604 | − | 0.889156i | \(-0.651292\pi\) | ||||
−0.457604 | + | 0.889156i | \(0.651292\pi\) | |||||||
\(600\) | 9.44543e9 | 1.78522 | ||||||||
\(601\) | −3.48220e8 | −0.0654324 | −0.0327162 | − | 0.999465i | \(-0.510416\pi\) | ||||
−0.0327162 | + | 0.999465i | \(0.510416\pi\) | |||||||
\(602\) | 1.03303e9 | 0.192985 | ||||||||
\(603\) | −1.98557e9 | −0.368786 | ||||||||
\(604\) | 1.96754e10 | 3.63325 | ||||||||
\(605\) | −8.42766e8 | −0.154726 | ||||||||
\(606\) | 1.48782e8 | 0.0271578 | ||||||||
\(607\) | 8.43348e8 | 0.153055 | 0.0765273 | − | 0.997067i | \(-0.475617\pi\) | ||||
0.0765273 | + | 0.997067i | \(0.475617\pi\) | |||||||
\(608\) | 5.01155e9 | 0.904293 | ||||||||
\(609\) | 5.91041e7 | 0.0106037 | ||||||||
\(610\) | −8.16616e8 | −0.145668 | ||||||||
\(611\) | −5.71527e9 | −1.01366 | ||||||||
\(612\) | −1.00523e10 | −1.77271 | ||||||||
\(613\) | −9.13491e9 | −1.60174 | −0.800871 | − | 0.598837i | \(-0.795630\pi\) | ||||
−0.800871 | + | 0.598837i | \(0.795630\pi\) | |||||||
\(614\) | −8.36949e9 | −1.45918 | ||||||||
\(615\) | −8.40261e8 | −0.145664 | ||||||||
\(616\) | 6.60580e9 | 1.13866 | ||||||||
\(617\) | −4.80233e9 | −0.823103 | −0.411552 | − | 0.911386i | \(-0.635013\pi\) | ||||
−0.411552 | + | 0.911386i | \(0.635013\pi\) | |||||||
\(618\) | −6.68398e9 | −1.13914 | ||||||||
\(619\) | 7.91703e9 | 1.34167 | 0.670834 | − | 0.741608i | \(-0.265936\pi\) | ||||
0.670834 | + | 0.741608i | \(0.265936\pi\) | |||||||
\(620\) | 6.90515e9 | 1.16360 | ||||||||
\(621\) | −6.80065e8 | −0.113954 | ||||||||
\(622\) | −2.16037e10 | −3.59966 | ||||||||
\(623\) | −8.90636e8 | −0.147568 | ||||||||
\(624\) | 1.05968e10 | 1.74593 | ||||||||
\(625\) | 2.98675e9 | 0.489349 | ||||||||
\(626\) | 1.02060e10 | 1.66281 | ||||||||
\(627\) | 4.91157e8 | 0.0795763 | ||||||||
\(628\) | 2.79874e10 | 4.50925 | ||||||||
\(629\) | −6.95640e8 | −0.111457 | ||||||||
\(630\) | −6.65461e8 | −0.106031 | ||||||||
\(631\) | −2.99670e8 | −0.0474832 | −0.0237416 | − | 0.999718i | \(-0.507558\pi\) | ||||
−0.0237416 | + | 0.999718i | \(0.507558\pi\) | |||||||
\(632\) | −2.55766e10 | −4.03026 | ||||||||
\(633\) | −6.90215e8 | −0.108161 | ||||||||
\(634\) | 2.07402e10 | 3.23222 | ||||||||
\(635\) | 1.66727e9 | 0.258403 | ||||||||
\(636\) | −4.06982e9 | −0.627300 | ||||||||
\(637\) | −6.18453e8 | −0.0948022 | ||||||||
\(638\) | −5.02810e8 | −0.0766534 | ||||||||
\(639\) | −8.84830e8 | −0.134155 | ||||||||
\(640\) | 1.75567e10 | 2.64737 | ||||||||
\(641\) | −5.58996e8 | −0.0838312 | −0.0419156 | − | 0.999121i | \(-0.513346\pi\) | ||||
−0.0419156 | + | 0.999121i | \(0.513346\pi\) | |||||||
\(642\) | 1.56320e9 | 0.233154 | ||||||||
\(643\) | −6.60776e9 | −0.980203 | −0.490102 | − | 0.871665i | \(-0.663040\pi\) | ||||
−0.490102 | + | 0.871665i | \(0.663040\pi\) | |||||||
\(644\) | −4.41387e9 | −0.651207 | ||||||||
\(645\) | 4.32437e8 | 0.0634547 | ||||||||
\(646\) | −4.27804e9 | −0.624354 | ||||||||
\(647\) | −6.38752e9 | −0.927187 | −0.463593 | − | 0.886048i | \(-0.653440\pi\) | ||||
−0.463593 | + | 0.886048i | \(0.653440\pi\) | |||||||
\(648\) | 2.90618e9 | 0.419575 | ||||||||
\(649\) | −8.26498e9 | −1.18682 | ||||||||
\(650\) | 7.52297e9 | 1.07447 | ||||||||
\(651\) | 1.44326e9 | 0.205026 | ||||||||
\(652\) | −2.35880e10 | −3.33291 | ||||||||
\(653\) | −5.31297e9 | −0.746691 | −0.373346 | − | 0.927692i | \(-0.621789\pi\) | ||||
−0.373346 | + | 0.927692i | \(0.621789\pi\) | |||||||
\(654\) | −8.18211e9 | −1.14378 | ||||||||
\(655\) | 2.20635e9 | 0.306782 | ||||||||
\(656\) | 1.95308e10 | 2.70120 | ||||||||
\(657\) | −3.09705e9 | −0.426059 | ||||||||
\(658\) | −8.34243e9 | −1.14157 | ||||||||
\(659\) | 1.31533e10 | 1.79035 | 0.895173 | − | 0.445719i | \(-0.147052\pi\) | ||||
0.895173 | + | 0.445719i | \(0.147052\pi\) | |||||||
\(660\) | 4.21324e9 | 0.570443 | ||||||||
\(661\) | −7.31153e9 | −0.984698 | −0.492349 | − | 0.870398i | \(-0.663862\pi\) | ||||
−0.492349 | + | 0.870398i | \(0.663862\pi\) | |||||||
\(662\) | 2.19002e10 | 2.93389 | ||||||||
\(663\) | −5.25479e9 | −0.700258 | ||||||||
\(664\) | 6.37588e9 | 0.845185 | ||||||||
\(665\) | −2.10770e8 | −0.0277928 | ||||||||
\(666\) | 3.06421e8 | 0.0401938 | ||||||||
\(667\) | 2.20505e8 | 0.0287726 | ||||||||
\(668\) | 3.01153e9 | 0.390903 | ||||||||
\(669\) | 6.07976e9 | 0.785046 | ||||||||
\(670\) | −7.24867e9 | −0.931101 | ||||||||
\(671\) | 1.08064e9 | 0.138087 | ||||||||
\(672\) | 8.98540e9 | 1.14221 | ||||||||
\(673\) | 3.62533e9 | 0.458453 | 0.229227 | − | 0.973373i | \(-0.426380\pi\) | ||||
0.229227 | + | 0.973373i | \(0.426380\pi\) | |||||||
\(674\) | 1.09215e9 | 0.137396 | ||||||||
\(675\) | 1.25916e9 | 0.157587 | ||||||||
\(676\) | −1.30785e10 | −1.62834 | ||||||||
\(677\) | 7.55267e9 | 0.935492 | 0.467746 | − | 0.883863i | \(-0.345066\pi\) | ||||
0.467746 | + | 0.883863i | \(0.345066\pi\) | |||||||
\(678\) | −3.02049e9 | −0.372198 | ||||||||
\(679\) | 3.66304e9 | 0.449052 | ||||||||
\(680\) | −2.40858e10 | −2.93752 | ||||||||
\(681\) | 5.96305e9 | 0.723525 | ||||||||
\(682\) | −1.22780e10 | −1.48212 | ||||||||
\(683\) | −1.10499e10 | −1.32704 | −0.663522 | − | 0.748157i | \(-0.730939\pi\) | ||||
−0.663522 | + | 0.748157i | \(0.730939\pi\) | |||||||
\(684\) | 1.40244e9 | 0.167567 | ||||||||
\(685\) | 2.24453e9 | 0.266814 | ||||||||
\(686\) | −9.02739e8 | −0.106765 | ||||||||
\(687\) | 6.36870e9 | 0.749380 | ||||||||
\(688\) | −1.00514e10 | −1.17671 | ||||||||
\(689\) | −2.12747e9 | −0.247797 | ||||||||
\(690\) | −2.48270e9 | −0.287708 | ||||||||
\(691\) | 1.91692e9 | 0.221020 | 0.110510 | − | 0.993875i | \(-0.464752\pi\) | ||||
0.110510 | + | 0.993875i | \(0.464752\pi\) | |||||||
\(692\) | 1.72274e10 | 1.97628 | ||||||||
\(693\) | 8.80615e8 | 0.100512 | ||||||||
\(694\) | −2.79443e9 | −0.317348 | ||||||||
\(695\) | −2.61348e9 | −0.295306 | ||||||||
\(696\) | −9.42303e8 | −0.105940 | ||||||||
\(697\) | −9.68505e9 | −1.08340 | ||||||||
\(698\) | −1.74600e10 | −1.94335 | ||||||||
\(699\) | 9.02888e9 | 0.999917 | ||||||||
\(700\) | 8.17243e9 | 0.900551 | ||||||||
\(701\) | 8.88383e9 | 0.974064 | 0.487032 | − | 0.873384i | \(-0.338080\pi\) | ||||
0.487032 | + | 0.873384i | \(0.338080\pi\) | |||||||
\(702\) | 2.31467e9 | 0.252528 | ||||||||
\(703\) | 9.70518e7 | 0.0105356 | ||||||||
\(704\) | −4.27843e10 | −4.62147 | ||||||||
\(705\) | −3.49224e9 | −0.375355 | ||||||||
\(706\) | 1.47191e10 | 1.57422 | ||||||||
\(707\) | 8.44890e7 | 0.00899150 | ||||||||
\(708\) | −2.35997e10 | −2.49914 | ||||||||
\(709\) | 1.32525e10 | 1.39649 | 0.698244 | − | 0.715859i | \(-0.253965\pi\) | ||||
0.698244 | + | 0.715859i | \(0.253965\pi\) | |||||||
\(710\) | −3.23023e9 | −0.338711 | ||||||||
\(711\) | −3.40960e9 | −0.355762 | ||||||||
\(712\) | 1.41995e10 | 1.47433 | ||||||||
\(713\) | 5.38449e9 | 0.556328 | ||||||||
\(714\) | −7.67027e9 | −0.788618 | ||||||||
\(715\) | 2.20244e9 | 0.225337 | ||||||||
\(716\) | 4.64463e10 | 4.72885 | ||||||||
\(717\) | 4.00227e9 | 0.405499 | ||||||||
\(718\) | −2.62184e10 | −2.64345 | ||||||||
\(719\) | −3.38868e9 | −0.340000 | −0.170000 | − | 0.985444i | \(-0.554377\pi\) | ||||
−0.170000 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(720\) | 6.47500e9 | 0.646511 | ||||||||
\(721\) | −3.79565e9 | −0.377148 | ||||||||
\(722\) | −1.93997e10 | −1.91829 | ||||||||
\(723\) | 1.10820e10 | 1.09052 | ||||||||
\(724\) | −2.89548e10 | −2.83554 | ||||||||
\(725\) | −4.08273e8 | −0.0397894 | ||||||||
\(726\) | 4.27887e9 | 0.415003 | ||||||||
\(727\) | −1.18748e9 | −0.114619 | −0.0573096 | − | 0.998356i | \(-0.518252\pi\) | ||||
−0.0573096 | + | 0.998356i | \(0.518252\pi\) | |||||||
\(728\) | 9.86006e9 | 0.947152 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −1.13063e10 | −1.07570 | ||||||||
\(731\) | 4.98437e9 | 0.471954 | ||||||||
\(732\) | 3.08565e9 | 0.290776 | ||||||||
\(733\) | −1.18089e10 | −1.10750 | −0.553752 | − | 0.832681i | \(-0.686805\pi\) | ||||
−0.553752 | + | 0.832681i | \(0.686805\pi\) | |||||||
\(734\) | −3.42390e10 | −3.19584 | ||||||||
\(735\) | −3.77897e8 | −0.0351049 | ||||||||
\(736\) | 3.35227e10 | 3.09932 | ||||||||
\(737\) | 9.59227e9 | 0.882643 | ||||||||
\(738\) | 4.26615e9 | 0.390696 | ||||||||
\(739\) | 7.76067e9 | 0.707365 | 0.353683 | − | 0.935366i | \(-0.384929\pi\) | ||||
0.353683 | + | 0.935366i | \(0.384929\pi\) | |||||||
\(740\) | 8.32529e8 | 0.0755246 | ||||||||
\(741\) | 7.33119e8 | 0.0661928 | ||||||||
\(742\) | −3.10541e9 | −0.279065 | ||||||||
\(743\) | 8.01232e9 | 0.716634 | 0.358317 | − | 0.933600i | \(-0.383351\pi\) | ||||
0.358317 | + | 0.933600i | \(0.383351\pi\) | |||||||
\(744\) | −2.30100e10 | −2.04838 | ||||||||
\(745\) | −6.75266e9 | −0.598312 | ||||||||
\(746\) | 2.42555e10 | 2.13907 | ||||||||
\(747\) | 8.49965e8 | 0.0746069 | ||||||||
\(748\) | 4.85628e10 | 4.24276 | ||||||||
\(749\) | 8.87700e8 | 0.0771934 | ||||||||
\(750\) | 1.02106e10 | 0.883763 | ||||||||
\(751\) | −7.92531e8 | −0.0682774 | −0.0341387 | − | 0.999417i | \(-0.510869\pi\) | ||||
−0.0341387 | + | 0.999417i | \(0.510869\pi\) | |||||||
\(752\) | 8.11726e10 | 6.96060 | ||||||||
\(753\) | −2.35966e9 | −0.201404 | ||||||||
\(754\) | −7.50512e8 | −0.0637614 | ||||||||
\(755\) | 6.28463e9 | 0.531453 | ||||||||
\(756\) | 2.51450e9 | 0.211653 | ||||||||
\(757\) | 1.47532e10 | 1.23609 | 0.618047 | − | 0.786141i | \(-0.287924\pi\) | ||||
0.618047 | + | 0.786141i | \(0.287924\pi\) | |||||||
\(758\) | 3.56571e10 | 2.97375 | ||||||||
\(759\) | 3.28539e9 | 0.272735 | ||||||||
\(760\) | 3.36032e9 | 0.277673 | ||||||||
\(761\) | −3.42569e9 | −0.281775 | −0.140887 | − | 0.990026i | \(-0.544996\pi\) | ||||
−0.140887 | + | 0.990026i | \(0.544996\pi\) | |||||||
\(762\) | −8.46502e9 | −0.693084 | ||||||||
\(763\) | −4.64639e9 | −0.378687 | ||||||||
\(764\) | 7.03432e9 | 0.570684 | ||||||||
\(765\) | −3.21087e9 | −0.259303 | ||||||||
\(766\) | −1.59781e10 | −1.28447 | ||||||||
\(767\) | −1.23366e10 | −0.987216 | ||||||||
\(768\) | −4.71536e10 | −3.75622 | ||||||||
\(769\) | 1.89295e10 | 1.50106 | 0.750530 | − | 0.660837i | \(-0.229798\pi\) | ||||
0.750530 | + | 0.660837i | \(0.229798\pi\) | |||||||
\(770\) | 3.21484e9 | 0.253771 | ||||||||
\(771\) | −2.69884e9 | −0.212074 | ||||||||
\(772\) | −5.57642e10 | −4.36209 | ||||||||
\(773\) | −2.17372e10 | −1.69268 | −0.846340 | − | 0.532642i | \(-0.821199\pi\) | ||||
−0.846340 | + | 0.532642i | \(0.821199\pi\) | |||||||
\(774\) | −2.19556e9 | −0.170197 | ||||||||
\(775\) | −9.96957e9 | −0.769344 | ||||||||
\(776\) | −5.84002e10 | −4.48640 | ||||||||
\(777\) | 1.74008e8 | 0.0133075 | ||||||||
\(778\) | 2.86270e10 | 2.17945 | ||||||||
\(779\) | 1.35120e9 | 0.102409 | ||||||||
\(780\) | 6.28883e9 | 0.474503 | ||||||||
\(781\) | 4.27461e9 | 0.321084 | ||||||||
\(782\) | −2.86162e10 | −2.13988 | ||||||||
\(783\) | −1.25618e8 | −0.00935157 | ||||||||
\(784\) | 8.78373e9 | 0.650988 | ||||||||
\(785\) | 8.93960e9 | 0.659590 | ||||||||
\(786\) | −1.12020e10 | −0.822843 | ||||||||
\(787\) | 1.69867e10 | 1.24221 | 0.621107 | − | 0.783726i | \(-0.286683\pi\) | ||||
0.621107 | + | 0.783726i | \(0.286683\pi\) | |||||||
\(788\) | −2.55091e10 | −1.85718 | ||||||||
\(789\) | 9.97520e8 | 0.0723023 | ||||||||
\(790\) | −1.24473e10 | −0.898218 | ||||||||
\(791\) | −1.71525e9 | −0.123228 | ||||||||
\(792\) | −1.40397e10 | −1.00420 | ||||||||
\(793\) | 1.61300e9 | 0.114863 | ||||||||
\(794\) | 8.30224e8 | 0.0588604 | ||||||||
\(795\) | −1.29996e9 | −0.0917584 | ||||||||
\(796\) | 3.88126e10 | 2.72757 | ||||||||
\(797\) | 1.21624e10 | 0.850972 | 0.425486 | − | 0.904965i | \(-0.360103\pi\) | ||||
0.425486 | + | 0.904965i | \(0.360103\pi\) | |||||||
\(798\) | 1.07011e9 | 0.0745452 | ||||||||
\(799\) | −4.02524e10 | −2.79176 | ||||||||
\(800\) | −6.20684e10 | −4.28604 | ||||||||
\(801\) | 1.89293e9 | 0.130143 | ||||||||
\(802\) | 2.61294e10 | 1.78862 | ||||||||
\(803\) | 1.49619e10 | 1.01972 | ||||||||
\(804\) | 2.73897e10 | 1.85862 | ||||||||
\(805\) | −1.40986e9 | −0.0952554 | ||||||||
\(806\) | −1.83267e10 | −1.23285 | ||||||||
\(807\) | 2.90578e9 | 0.194628 | ||||||||
\(808\) | −1.34702e9 | −0.0898324 | ||||||||
\(809\) | −4.64855e8 | −0.0308672 | −0.0154336 | − | 0.999881i | \(-0.504913\pi\) | ||||
−0.0154336 | + | 0.999881i | \(0.504913\pi\) | |||||||
\(810\) | 1.41435e9 | 0.0935101 | ||||||||
\(811\) | −8.27001e9 | −0.544419 | −0.272209 | − | 0.962238i | \(-0.587754\pi\) | ||||
−0.272209 | + | 0.962238i | \(0.587754\pi\) | |||||||
\(812\) | −8.15305e8 | −0.0534409 | ||||||||
\(813\) | −9.39415e9 | −0.613113 | ||||||||
\(814\) | −1.48032e9 | −0.0961989 | ||||||||
\(815\) | −7.53436e9 | −0.487522 | ||||||||
\(816\) | 7.46324e10 | 4.80853 | ||||||||
\(817\) | −6.95392e8 | −0.0446121 | ||||||||
\(818\) | −3.83768e9 | −0.245150 | ||||||||
\(819\) | 1.31444e9 | 0.0836077 | ||||||||
\(820\) | 1.15909e10 | 0.734122 | ||||||||
\(821\) | 1.90387e10 | 1.20070 | 0.600352 | − | 0.799736i | \(-0.295027\pi\) | ||||
0.600352 | + | 0.799736i | \(0.295027\pi\) | |||||||
\(822\) | −1.13959e10 | −0.715642 | ||||||||
\(823\) | −2.71902e10 | −1.70025 | −0.850126 | − | 0.526579i | \(-0.823474\pi\) | ||||
−0.850126 | + | 0.526579i | \(0.823474\pi\) | |||||||
\(824\) | 6.05144e10 | 3.76802 | ||||||||
\(825\) | −6.08302e9 | −0.377164 | ||||||||
\(826\) | −1.80074e10 | −1.11179 | ||||||||
\(827\) | −1.62749e10 | −1.00057 | −0.500286 | − | 0.865860i | \(-0.666772\pi\) | ||||
−0.500286 | + | 0.865860i | \(0.666772\pi\) | |||||||
\(828\) | 9.38108e9 | 0.574311 | ||||||||
\(829\) | −6.34273e9 | −0.386665 | −0.193333 | − | 0.981133i | \(-0.561930\pi\) | ||||
−0.193333 | + | 0.981133i | \(0.561930\pi\) | |||||||
\(830\) | 3.10295e9 | 0.188365 | ||||||||
\(831\) | −1.17106e10 | −0.707908 | ||||||||
\(832\) | −6.38615e10 | −3.84421 | ||||||||
\(833\) | −4.35573e9 | −0.261098 | ||||||||
\(834\) | 1.32691e10 | 0.792064 | ||||||||
\(835\) | 9.61928e8 | 0.0571794 | ||||||||
\(836\) | −6.77521e9 | −0.401052 | ||||||||
\(837\) | −3.06744e9 | −0.180816 | ||||||||
\(838\) | 3.60323e10 | 2.11513 | ||||||||
\(839\) | −2.76715e10 | −1.61758 | −0.808791 | − | 0.588096i | \(-0.799878\pi\) | ||||
−0.808791 | + | 0.588096i | \(0.799878\pi\) | |||||||
\(840\) | 6.02485e9 | 0.350727 | ||||||||
\(841\) | −1.72091e10 | −0.997639 | ||||||||
\(842\) | 5.32297e9 | 0.307299 | ||||||||
\(843\) | −5.28163e9 | −0.303648 | ||||||||
\(844\) | 9.52109e9 | 0.545115 | ||||||||
\(845\) | −4.17747e9 | −0.238185 | ||||||||
\(846\) | 1.77307e10 | 1.00677 | ||||||||
\(847\) | 2.42985e9 | 0.137400 | ||||||||
\(848\) | 3.02159e10 | 1.70157 | ||||||||
\(849\) | 5.47080e9 | 0.306813 | ||||||||
\(850\) | 5.29839e10 | 2.95922 | ||||||||
\(851\) | 6.49189e8 | 0.0361092 | ||||||||
\(852\) | 1.22057e10 | 0.676120 | ||||||||
\(853\) | 2.62262e10 | 1.44682 | 0.723409 | − | 0.690420i | \(-0.242574\pi\) | ||||
0.723409 | + | 0.690420i | \(0.242574\pi\) | |||||||
\(854\) | 2.35446e9 | 0.129356 | ||||||||
\(855\) | 4.47962e8 | 0.0245109 | ||||||||
\(856\) | −1.41527e10 | −0.771225 | ||||||||
\(857\) | −1.11062e10 | −0.602743 | −0.301372 | − | 0.953507i | \(-0.597444\pi\) | ||||
−0.301372 | + | 0.953507i | \(0.597444\pi\) | |||||||
\(858\) | −1.11822e10 | −0.604395 | ||||||||
\(859\) | −1.02974e10 | −0.554307 | −0.277153 | − | 0.960826i | \(-0.589391\pi\) | ||||
−0.277153 | + | 0.960826i | \(0.589391\pi\) | |||||||
\(860\) | −5.96520e9 | −0.319802 | ||||||||
\(861\) | 2.42263e9 | 0.129353 | ||||||||
\(862\) | 1.63974e10 | 0.871965 | ||||||||
\(863\) | −1.09948e10 | −0.582302 | −0.291151 | − | 0.956677i | \(-0.594038\pi\) | ||||
−0.291151 | + | 0.956677i | \(0.594038\pi\) | |||||||
\(864\) | −1.90973e10 | −1.00733 | ||||||||
\(865\) | 5.50268e9 | 0.289080 | ||||||||
\(866\) | −6.74161e10 | −3.52737 | ||||||||
\(867\) | −2.59301e10 | −1.35125 | ||||||||
\(868\) | −1.99088e10 | −1.03330 | ||||||||
\(869\) | 1.64717e10 | 0.851472 | ||||||||
\(870\) | −4.58590e8 | −0.0236106 | ||||||||
\(871\) | 1.43178e10 | 0.734196 | ||||||||
\(872\) | 7.40779e10 | 3.78339 | ||||||||
\(873\) | −7.78528e9 | −0.396027 | ||||||||
\(874\) | 3.99237e9 | 0.202274 | ||||||||
\(875\) | 5.79831e9 | 0.292599 | ||||||||
\(876\) | 4.27219e10 | 2.14727 | ||||||||
\(877\) | 6.82900e9 | 0.341868 | 0.170934 | − | 0.985282i | \(-0.445322\pi\) | ||||
0.170934 | + | 0.985282i | \(0.445322\pi\) | |||||||
\(878\) | 2.06593e10 | 1.03011 | ||||||||
\(879\) | −8.08804e9 | −0.401682 | ||||||||
\(880\) | −3.12807e10 | −1.54735 | ||||||||
\(881\) | 7.79828e9 | 0.384223 | 0.192111 | − | 0.981373i | \(-0.438466\pi\) | ||||
0.192111 | + | 0.981373i | \(0.438466\pi\) | |||||||
\(882\) | 1.91865e9 | 0.0941576 | ||||||||
\(883\) | 1.04123e10 | 0.508960 | 0.254480 | − | 0.967078i | \(-0.418096\pi\) | ||||
0.254480 | + | 0.967078i | \(0.418096\pi\) | |||||||
\(884\) | 7.24866e10 | 3.52919 | ||||||||
\(885\) | −7.53811e9 | −0.365562 | ||||||||
\(886\) | −2.77635e10 | −1.34108 | ||||||||
\(887\) | 1.72418e10 | 0.829563 | 0.414781 | − | 0.909921i | \(-0.363858\pi\) | ||||
0.414781 | + | 0.909921i | \(0.363858\pi\) | |||||||
\(888\) | −2.77423e9 | −0.132953 | ||||||||
\(889\) | −4.80705e9 | −0.229468 | ||||||||
\(890\) | 6.91047e9 | 0.328581 | ||||||||
\(891\) | −1.87163e9 | −0.0886436 | ||||||||
\(892\) | −8.38665e10 | −3.95651 | ||||||||
\(893\) | 5.61579e9 | 0.263895 | ||||||||
\(894\) | 3.42844e10 | 1.60478 | ||||||||
\(895\) | 1.48356e10 | 0.691713 | ||||||||
\(896\) | −5.06194e10 | −2.35092 | ||||||||
\(897\) | 4.90390e9 | 0.226865 | ||||||||
\(898\) | 5.24285e10 | 2.41602 | ||||||||
\(899\) | 9.94592e8 | 0.0456548 | ||||||||
\(900\) | −1.73694e10 | −0.794211 | ||||||||
\(901\) | −1.49837e10 | −0.682467 | ||||||||
\(902\) | −2.06098e10 | −0.935083 | ||||||||
\(903\) | −1.24680e9 | −0.0563492 | ||||||||
\(904\) | 2.73465e10 | 1.23115 | ||||||||
\(905\) | −9.24860e9 | −0.414769 | ||||||||
\(906\) | −3.19081e10 | −1.42545 | ||||||||
\(907\) | 3.74992e10 | 1.66877 | 0.834385 | − | 0.551183i | \(-0.185823\pi\) | ||||
0.834385 | + | 0.551183i | \(0.185823\pi\) | |||||||
\(908\) | −8.22566e10 | −3.64645 | ||||||||
\(909\) | −1.79570e8 | −0.00792976 | ||||||||
\(910\) | 4.79859e9 | 0.211091 | ||||||||
\(911\) | 3.32750e9 | 0.145816 | 0.0729078 | − | 0.997339i | \(-0.476772\pi\) | ||||
0.0729078 | + | 0.997339i | \(0.476772\pi\) | |||||||
\(912\) | −1.04123e10 | −0.454532 | ||||||||
\(913\) | −4.10618e9 | −0.178562 | ||||||||
\(914\) | −3.17483e10 | −1.37534 | ||||||||
\(915\) | 9.85603e8 | 0.0425332 | ||||||||
\(916\) | −8.78523e10 | −3.77675 | ||||||||
\(917\) | −6.36131e9 | −0.272429 | ||||||||
\(918\) | 1.63021e10 | 0.695496 | ||||||||
\(919\) | −9.77356e9 | −0.415383 | −0.207691 | − | 0.978194i | \(-0.566595\pi\) | ||||
−0.207691 | + | 0.978194i | \(0.566595\pi\) | |||||||
\(920\) | 2.24775e10 | 0.951679 | ||||||||
\(921\) | 1.01014e10 | 0.426064 | ||||||||
\(922\) | 7.21476e10 | 3.03154 | ||||||||
\(923\) | 6.38044e9 | 0.267082 | ||||||||
\(924\) | −1.21475e10 | −0.506567 | ||||||||
\(925\) | −1.20200e9 | −0.0499352 | ||||||||
\(926\) | −5.82538e10 | −2.41094 | ||||||||
\(927\) | 8.06713e9 | 0.332614 | ||||||||
\(928\) | 6.19212e9 | 0.254344 | ||||||||
\(929\) | 3.48231e10 | 1.42499 | 0.712496 | − | 0.701676i | \(-0.247565\pi\) | ||||
0.712496 | + | 0.701676i | \(0.247565\pi\) | |||||||
\(930\) | −1.11983e10 | −0.456520 | ||||||||
\(931\) | 6.07688e8 | 0.0246806 | ||||||||
\(932\) | −1.24548e11 | −5.03942 | ||||||||
\(933\) | 2.60742e10 | 1.05106 | ||||||||
\(934\) | 1.38019e10 | 0.554276 | ||||||||
\(935\) | 1.55117e10 | 0.620609 | ||||||||
\(936\) | −2.09562e10 | −0.835310 | ||||||||
\(937\) | 3.40725e10 | 1.35306 | 0.676528 | − | 0.736417i | \(-0.263484\pi\) | ||||
0.676528 | + | 0.736417i | \(0.263484\pi\) | |||||||
\(938\) | 2.08993e10 | 0.826839 | ||||||||
\(939\) | −1.23179e10 | −0.485521 | ||||||||
\(940\) | 4.81733e10 | 1.89173 | ||||||||
\(941\) | 3.17499e9 | 0.124216 | 0.0621082 | − | 0.998069i | \(-0.480218\pi\) | ||||
0.0621082 | + | 0.998069i | \(0.480218\pi\) | |||||||
\(942\) | −4.53879e10 | −1.76914 | ||||||||
\(943\) | 9.03833e9 | 0.350992 | ||||||||
\(944\) | 1.75214e11 | 6.77901 | ||||||||
\(945\) | 8.03169e8 | 0.0309596 | ||||||||
\(946\) | 1.06067e10 | 0.407345 | ||||||||
\(947\) | −2.26834e10 | −0.867927 | −0.433964 | − | 0.900930i | \(-0.642885\pi\) | ||||
−0.433964 | + | 0.900930i | \(0.642885\pi\) | |||||||
\(948\) | 4.70333e10 | 1.79298 | ||||||||
\(949\) | 2.23326e10 | 0.848219 | ||||||||
\(950\) | −7.39202e9 | −0.279724 | ||||||||
\(951\) | −2.50321e10 | −0.943768 | ||||||||
\(952\) | 6.94439e10 | 2.60858 | ||||||||
\(953\) | 1.87055e10 | 0.700075 | 0.350037 | − | 0.936736i | \(-0.386169\pi\) | ||||
0.350037 | + | 0.936736i | \(0.386169\pi\) | |||||||
\(954\) | 6.60013e9 | 0.246112 | ||||||||
\(955\) | 2.24687e9 | 0.0834768 | ||||||||
\(956\) | −5.52089e10 | −2.04365 | ||||||||
\(957\) | 6.06859e8 | 0.0223819 | ||||||||
\(958\) | 6.50603e10 | 2.39076 | ||||||||
\(959\) | −6.47140e9 | −0.236937 | ||||||||
\(960\) | −3.90217e10 | −1.42350 | ||||||||
\(961\) | −3.22580e9 | −0.117248 | ||||||||
\(962\) | −2.20958e9 | −0.0800197 | ||||||||
\(963\) | −1.88669e9 | −0.0680781 | ||||||||
\(964\) | −1.52870e11 | −5.49607 | ||||||||
\(965\) | −1.78119e10 | −0.638065 | ||||||||
\(966\) | 7.15809e9 | 0.255492 | ||||||||
\(967\) | −3.29948e10 | −1.17342 | −0.586709 | − | 0.809798i | \(-0.699577\pi\) | ||||
−0.586709 | + | 0.809798i | \(0.699577\pi\) | |||||||
\(968\) | −3.87394e10 | −1.37274 | ||||||||
\(969\) | 5.16332e9 | 0.182304 | ||||||||
\(970\) | −2.84216e10 | −0.999878 | ||||||||
\(971\) | 5.53455e10 | 1.94006 | 0.970029 | − | 0.242989i | \(-0.0781279\pi\) | ||||
0.970029 | + | 0.242989i | \(0.0781279\pi\) | |||||||
\(972\) | −5.34423e9 | −0.186661 | ||||||||
\(973\) | 7.53516e9 | 0.262239 | ||||||||
\(974\) | 3.28575e9 | 0.113940 | ||||||||
\(975\) | −9.07974e9 | −0.313731 | ||||||||
\(976\) | −2.29091e10 | −0.788739 | ||||||||
\(977\) | −3.47635e10 | −1.19259 | −0.596297 | − | 0.802764i | \(-0.703362\pi\) | ||||
−0.596297 | + | 0.802764i | \(0.703362\pi\) | |||||||
\(978\) | 3.82532e10 | 1.30762 | ||||||||
\(979\) | −9.14473e9 | −0.311481 | ||||||||
\(980\) | 5.21286e9 | 0.176923 | ||||||||
\(981\) | 9.87528e9 | 0.333970 | ||||||||
\(982\) | −8.36429e10 | −2.81864 | ||||||||
\(983\) | 8.82839e9 | 0.296445 | 0.148222 | − | 0.988954i | \(-0.452645\pi\) | ||||
0.148222 | + | 0.988954i | \(0.452645\pi\) | |||||||
\(984\) | −3.86242e10 | −1.29234 | ||||||||
\(985\) | −8.14798e9 | −0.271658 | ||||||||
\(986\) | −5.28582e9 | −0.175608 | ||||||||
\(987\) | 1.00688e10 | 0.333324 | ||||||||
\(988\) | −1.01129e10 | −0.333601 | ||||||||
\(989\) | −4.65154e9 | −0.152901 | ||||||||
\(990\) | −6.83271e9 | −0.223805 | ||||||||
\(991\) | 5.32608e10 | 1.73840 | 0.869200 | − | 0.494461i | \(-0.164634\pi\) | ||||
0.869200 | + | 0.494461i | \(0.164634\pi\) | |||||||
\(992\) | 1.51205e11 | 4.91784 | ||||||||
\(993\) | −2.64321e10 | −0.856661 | ||||||||
\(994\) | 9.31336e9 | 0.300783 | ||||||||
\(995\) | 1.23973e10 | 0.398976 | ||||||||
\(996\) | −1.17247e10 | −0.376007 | ||||||||
\(997\) | 1.69055e10 | 0.540249 | 0.270125 | − | 0.962825i | \(-0.412935\pi\) | ||||
0.270125 | + | 0.962825i | \(0.412935\pi\) | |||||||
\(998\) | 4.82943e10 | 1.53794 | ||||||||
\(999\) | −3.69831e8 | −0.0117361 |
(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 | 21.8.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 63.8.a.c.1.1 | 2 | |||
4.3 | odd | 2 | 336.8.a.p.1.2 | 2 | |||
5.4 | even | 2 | 525.8.a.d.1.1 | 2 | |||
7.2 | even | 3 | 147.8.e.f.67.1 | 4 | |||
7.3 | odd | 6 | 147.8.e.e.79.1 | 4 | |||
7.4 | even | 3 | 147.8.e.f.79.1 | 4 | |||
7.5 | odd | 6 | 147.8.e.e.67.1 | 4 | |||
7.6 | odd | 2 | 147.8.a.d.1.2 | 2 | |||
21.20 | even | 2 | 441.8.a.h.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.8.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
63.8.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
147.8.a.d.1.2 | 2 | 7.6 | odd | 2 | |||
147.8.e.e.67.1 | 4 | 7.5 | odd | 6 | |||
147.8.e.e.79.1 | 4 | 7.3 | odd | 6 | |||
147.8.e.f.67.1 | 4 | 7.2 | even | 3 | |||
147.8.e.f.79.1 | 4 | 7.4 | even | 3 | |||
336.8.a.p.1.2 | 2 | 4.3 | odd | 2 | |||
441.8.a.h.1.1 | 2 | 21.20 | even | 2 | |||
525.8.a.d.1.1 | 2 | 5.4 | even | 2 |