Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(47,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.47");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(134.149125258\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + \cdots + 19\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{68}\cdot 3^{56}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.12 | ||
Root | \(0.500000 + 5.87639e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.47 |
Dual form | 48.22.c.b.47.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 94418.3 | + | 39313.4i | 0.923172 | + | 0.384386i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.52523e7i | − | 1.15642i | −0.815887 | − | 0.578211i | \(-0.803751\pi\) | ||
0.815887 | − | 0.578211i | \(-0.196249\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.86298e8i | 0.249275i | 0.992202 | + | 0.124637i | \(0.0397768\pi\) | ||||
−0.992202 | + | 0.124637i | \(0.960223\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.36926e9 | + | 7.42381e9i | 0.704494 | + | 0.709710i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.28845e10 | 0.847251 | 0.423625 | − | 0.905837i | \(-0.360757\pi\) | ||||
0.423625 | + | 0.905837i | \(0.360757\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.38397e11 | 0.881987 | 0.440994 | − | 0.897510i | \(-0.354626\pi\) | ||||
0.440994 | + | 0.897510i | \(0.354626\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.92756e11 | − | 2.38428e12i | 0.444513 | − | 1.06758i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.98100e12i | − | 0.719549i | −0.933039 | − | 0.359774i | \(-0.882854\pi\) | ||
0.933039 | − | 0.359774i | \(-0.117146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.42697e12i | − | 0.165651i | −0.996564 | − | 0.0828255i | \(-0.973606\pi\) | ||
0.996564 | − | 0.0828255i | \(-0.0263944\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.32401e12 | + | 1.75899e13i | −0.0958178 | + | 0.230124i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.50087e13 | 0.226545 | 0.113272 | − | 0.993564i | \(-0.463867\pi\) | ||||
0.113272 | + | 0.993564i | \(0.463867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.60843e14 | −0.337312 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.03937e14 | + | 9.90654e14i | 0.377567 | + | 0.925982i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.46454e15i | − | 0.646433i | −0.946325 | − | 0.323217i | \(-0.895236\pi\) | ||
0.946325 | − | 0.323217i | \(-0.104764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.97978e15i | 1.74861i | 0.485377 | + | 0.874305i | \(0.338682\pi\) | ||||
−0.485377 | + | 0.874305i | \(0.661318\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.88163e15 | + | 2.86534e15i | 0.782159 | + | 0.325672i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.70445e15 | 0.288267 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.35027e15 | −0.285484 | −0.142742 | − | 0.989760i | \(-0.545592\pi\) | ||||
−0.142742 | + | 0.989760i | \(0.545592\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.13927e16 | + | 1.72349e16i | 0.814226 | + | 0.339024i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.72853e16i | − | 0.317467i | −0.987321 | − | 0.158734i | \(-0.949259\pi\) | ||
0.987321 | − | 0.158734i | \(-0.0507411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.09024e16i | 0.0769313i | 0.999260 | + | 0.0384656i | \(0.0122470\pi\) | ||||
−0.999260 | + | 0.0384656i | \(0.987753\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.87469e17 | − | 1.86091e17i | 0.820724 | − | 0.814693i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.14126e17 | −1.14843 | −0.574215 | − | 0.818704i | \(-0.694693\pi\) | ||||
−0.574215 | + | 0.818704i | \(0.694693\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.23839e17 | 0.937862 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.35134e17 | − | 5.64716e17i | 0.276585 | − | 0.664268i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.78175e18i | − | 1.39943i | −0.714424 | − | 0.699713i | \(-0.753311\pi\) | ||
0.714424 | − | 0.699713i | \(-0.246689\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.84050e18i | − | 0.979780i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.74040e17 | − | 4.17987e17i | 0.0636740 | − | 0.152924i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.28502e17 | 0.109146 | 0.0545729 | − | 0.998510i | \(-0.482620\pi\) | ||||
0.0545729 | + | 0.998510i | \(0.482620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.27850e18 | 1.66538 | 0.832692 | − | 0.553736i | \(-0.186798\pi\) | ||||
0.832692 | + | 0.553736i | \(0.186798\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.38304e18 | + | 1.37288e18i | −0.176913 | + | 0.175613i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 1.10705e19i | − | 1.01995i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.56309e19i | 1.71782i | 0.512124 | + | 0.858912i | \(0.328859\pi\) | ||||
−0.512124 | + | 0.858912i | \(0.671141\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.24964e18 | + | 1.76945e18i | 0.209140 | + | 0.0870808i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.34639e19 | 0.855435 | 0.427718 | − | 0.903912i | \(-0.359318\pi\) | ||||
0.427718 | + | 0.903912i | \(0.359318\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.85702e19 | −0.778077 | −0.389039 | − | 0.921221i | \(-0.627193\pi\) | ||||
−0.389039 | + | 0.921221i | \(0.627193\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.51865e19 | − | 6.32328e18i | −0.311397 | − | 0.129658i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.35782e19i | 0.211198i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 8.48441e19i | − | 1.00818i | −0.863652 | − | 0.504089i | \(-0.831828\pi\) | ||
0.863652 | − | 0.504089i | \(-0.168172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.06992e17 | + | 1.09416e20i | −0.00737525 | + | 0.999973i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.81890e19 | −0.482385 | −0.241193 | − | 0.970477i | \(-0.577539\pi\) | ||||
−0.241193 | + | 0.970477i | \(0.577539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.51034e20 | −0.832102 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.75763e19 | − | 1.38280e20i | 0.248480 | − | 0.596769i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.17387e19i | − | 0.277864i | −0.990302 | − | 0.138932i | \(-0.955633\pi\) | ||
0.990302 | − | 0.138932i | \(-0.0443670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.16724e19i | 0.219857i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.13712e20 | + | 7.53437e20i | −0.672142 | + | 1.61427i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.11791e20 | −0.191562 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.73058e19 | 0.120210 | 0.0601049 | − | 0.998192i | \(-0.480856\pi\) | ||||
0.0601049 | + | 0.998192i | \(0.480856\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.37105e20 | + | 5.41081e20i | 0.596884 | + | 0.601302i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.50948e21i | − | 1.35973i | −0.733338 | − | 0.679864i | \(-0.762039\pi\) | ||
0.733338 | − | 0.679864i | \(-0.237961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.56986e19i | 0.0555005i | 0.999615 | + | 0.0277503i | \(0.00883432\pi\) | ||||
−0.999615 | + | 0.0277503i | \(0.991166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.44186e20 | + | 1.84948e20i | 0.266120 | + | 0.110806i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.43960e21 | 1.19892 | 0.599459 | − | 0.800405i | \(-0.295382\pi\) | ||||
0.599459 | + | 0.800405i | \(0.295382\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.19375e21 | 0.887584 | 0.443792 | − | 0.896130i | \(-0.353633\pi\) | ||||
0.443792 | + | 0.896130i | \(0.353633\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.88418e20 | − | 3.28278e20i | −0.263551 | − | 0.109736i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.05656e21i | − | 1.12418i | −0.827077 | − | 0.562088i | \(-0.809998\pi\) | ||
0.827077 | − | 0.562088i | \(-0.190002\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.13657e21i | − | 0.261982i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.23066e21 | + | 3.25458e21i | 0.621355 | + | 0.625955i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.11425e21 | 0.179365 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.08810e21 | −0.282166 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.07268e21 | − | 2.57623e21i | 0.122030 | − | 0.293077i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 7.97959e21i | − | 0.766347i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.04934e22i | − | 1.66600i | −0.553273 | − | 0.833000i | \(-0.686622\pi\) | ||
0.553273 | − | 0.833000i | \(-0.313378\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.28610e20 | + | 1.02938e21i | −0.0295713 | + | 0.0710208i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.31046e22 | 1.35628 | 0.678140 | − | 0.734933i | \(-0.262786\pi\) | ||||
0.678140 | + | 0.734933i | \(0.262786\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.24736e20 | 0.0412926 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.50163e22 | − | 1.02004e22i | 1.07083 | − | 0.436627i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.33031e22i | 1.58838i | 0.607673 | + | 0.794188i | \(0.292103\pi\) | ||||
−0.607673 | + | 0.794188i | \(0.707897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.70660e22i | 1.48269i | 0.671121 | + | 0.741347i | \(0.265813\pi\) | ||||
−0.671121 | + | 0.741347i | \(0.734187\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.91010e22 | − | 1.62807e22i | −1.06020 | − | 0.441441i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.19523e22 | 0.747264 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.69832e22 | −0.747550 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.94600e22 | + | 2.05939e22i | 0.865808 | + | 0.360501i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.85592e22i | 1.04138i | 0.853745 | + | 0.520691i | \(0.174326\pi\) | ||||
−0.853745 | + | 0.520691i | \(0.825674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.04699e23i | − | 1.38257i | −0.722583 | − | 0.691284i | \(-0.757045\pi\) | ||
0.722583 | − | 0.691284i | \(-0.242955\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.44018e22 | − | 4.40756e22i | 0.510671 | − | 0.506918i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.01508e23 | 2.02213 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.06383e22 | 0.444153 | 0.222077 | − | 0.975029i | \(-0.428716\pi\) | ||||
0.222077 | + | 0.975029i | \(0.428716\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.00467e22 | − | 1.68230e23i | 0.537920 | − | 1.29191i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.38503e21i | 0.0564720i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.05777e23i | − | 1.21738i | −0.793408 | − | 0.608690i | \(-0.791695\pi\) | ||
0.793408 | − | 0.608690i | \(-0.208305\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.23565e22 | − | 1.73777e23i | 0.376614 | − | 0.904506i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.91171e23 | 1.33544 | 0.667721 | − | 0.744412i | \(-0.267270\pi\) | ||||
0.667721 | + | 0.744412i | \(0.267270\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.48727e22 | −0.222099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.28650e22 | − | 3.26235e22i | 0.117564 | − | 0.116700i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 2.35485e23i | − | 0.745553i | −0.927921 | − | 0.372776i | \(-0.878406\pi\) | ||
0.927921 | − | 0.372776i | \(-0.121594\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.99647e22i | − | 0.0840834i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.04584e22 | + | 1.68459e22i | 0.100760 | + | 0.0419541i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.51869e23 | 1.88545 | 0.942727 | − | 0.333565i | \(-0.108252\pi\) | ||||
0.942727 | + | 0.333565i | \(0.108252\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.73258e23 | 1.32604 | 0.663020 | − | 0.748601i | \(-0.269274\pi\) | ||||
0.663020 | + | 0.748601i | \(0.269274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.76060e23 | + | 3.64770e23i | 1.53744 | + | 0.640151i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.10864e23i | 0.330140i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.35922e23i | − | 0.609638i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.84557e23 | + | 7.52526e22i | −0.230824 | + | 0.0941180i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.73954e23 | 0.754710 | 0.377355 | − | 0.926069i | \(-0.376834\pi\) | ||||
0.377355 | + | 0.926069i | \(0.376834\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.02993e24 | −1.03385 | −0.516925 | − | 0.856031i | \(-0.672923\pi\) | ||||
−0.516925 | + | 0.856031i | \(0.672923\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.35221e23 | − | 1.04526e24i | 0.392055 | − | 0.941589i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.84549e23i | − | 0.473070i | −0.971623 | − | 0.236535i | \(-0.923988\pi\) | ||
0.971623 | − | 0.236535i | \(-0.0760118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.82477e22i | − | 0.0278386i | −0.999903 | − | 0.0139193i | \(-0.995569\pi\) | ||
0.999903 | − | 0.0139193i | \(-0.00443080\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00764e24 | + | 2.42002e24i | −0.660308 | + | 1.58585i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.72842e23 | 0.161140 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.89018e23 | −0.367126 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.31681e23 | + | 3.34136e23i | 0.159600 | + | 0.160781i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.22658e23i | − | 0.140348i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.45976e24i | − | 0.968116i | −0.875036 | − | 0.484058i | \(-0.839162\pi\) | ||
0.875036 | − | 0.484058i | \(-0.160838\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.21542e24 | + | 9.22446e23i | 0.789714 | + | 0.328818i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.75311e23 | 0.0889650 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.48662e24 | −0.435885 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.69755e24 | − | 1.12319e24i | −0.718299 | − | 0.299082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.62205e24i | − | 0.634633i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.13530e24i | 0.690365i | 0.938536 | + | 0.345182i | \(0.112183\pi\) | ||||
−0.938536 | + | 0.345182i | \(0.887817\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.18529e24 | − | 1.19407e24i | −0.237634 | − | 0.239393i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.05206e23 | −0.0922991 | −0.0461495 | − | 0.998935i | \(-0.514695\pi\) | ||||
−0.0461495 | + | 0.998935i | \(0.514695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.80507e24 | 0.800622 | 0.400311 | − | 0.916379i | \(-0.368902\pi\) | ||||
0.400311 | + | 0.916379i | \(0.368902\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.33807e23 | + | 1.28203e24i | −0.0811818 | + | 0.194972i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.01142e24i | 0.696184i | 0.937460 | + | 0.348092i | \(0.113170\pi\) | ||||
−0.937460 | + | 0.348092i | \(0.886830\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.04576e25i | 1.32807i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.33551e24 | − | 8.01083e24i | 0.387530 | − | 0.930722i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.24013e24 | −0.982879 | −0.491440 | − | 0.870912i | \(-0.663529\pi\) | ||||
−0.491440 | + | 0.870912i | \(0.663529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.94660e24 | 0.579548 | 0.289774 | − | 0.957095i | \(-0.406420\pi\) | ||||
0.289774 | + | 0.957095i | \(0.406420\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.37771e24 | + | 1.02991e25i | −0.391184 | + | 0.920312i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.32282e25i | − | 1.08456i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.94077e24i | − | 0.146102i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.43828e24 | − | 2.68074e24i | −0.445325 | − | 0.185422i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.06445e25 | −1.94885 | −0.974424 | − | 0.224716i | \(-0.927855\pi\) | ||||
−0.974424 | + | 0.224716i | \(0.927855\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.28044e24 | 0.191940 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.42604e25 | − | 5.93767e24i | −0.768174 | − | 0.319849i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.02169e25i | 1.49952i | 0.661709 | + | 0.749761i | \(0.269831\pi\) | ||||
−0.661709 | + | 0.749761i | \(0.730169\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.55564e24i | − | 0.0711641i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.08725e25 | − | 1.07926e25i | 0.458780 | − | 0.455409i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.19177e25 | −1.24307 | −0.621535 | − | 0.783386i | \(-0.713491\pi\) | ||||
−0.621535 | + | 0.783386i | \(0.713491\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.49933e25 | −1.61833 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.21343e24 | − | 7.71763e24i | 0.106807 | − | 0.256517i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.07028e25i | 1.25091i | 0.780261 | + | 0.625454i | \(0.215086\pi\) | ||||
−0.780261 | + | 0.625454i | \(0.784914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.29299e24i | − | 0.150496i | −0.997165 | − | 0.0752478i | \(-0.976025\pi\) | ||
0.997165 | − | 0.0752478i | \(-0.0239748\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.21082e24 | + | 7.71137e24i | −0.0845101 | + | 0.202966i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.17230e25 | −0.285788 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.90441e24 | −0.201172 | −0.100586 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100586 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.92404e25 | + | 5.88051e25i | −1.24101 | + | 1.23189i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.92998e25i | − | 0.569440i | −0.958611 | − | 0.284720i | \(-0.908099\pi\) | ||
0.958611 | − | 0.284720i | \(-0.0919007\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.56490e25i | 1.72553i | 0.505603 | + | 0.862766i | \(0.331270\pi\) | ||||
−0.505603 | + | 0.862766i | \(0.668730\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.05551e25 | − | 4.39490e24i | −0.176845 | − | 0.0736340i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.08320e24 | 0.0791366 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.33196e25 | 0.482250 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.24326e24 | + | 3.43229e24i | 0.110974 | + | 0.0462070i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.41328e24i | − | 0.117932i | −0.998260 | − | 0.0589659i | \(-0.981220\pi\) | ||
0.998260 | − | 0.0589659i | \(-0.0187803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.08207e25i | − | 0.126219i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.94408e25 | + | 7.22034e25i | 0.319894 | + | 0.784539i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.97317e25 | 0.199810 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.03109e24 | −0.0191770 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.93427e25 | − | 1.42522e26i | 0.522661 | − | 1.25526i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.34304e26i | − | 1.92589i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.23603e26i | − | 0.948582i | −0.880368 | − | 0.474291i | \(-0.842704\pi\) | ||
0.880368 | − | 0.474291i | \(-0.157296\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.97597e24 | + | 7.14733e24i | −0.0213336 | + | 0.0512365i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.19989e25 | 0.415336 | 0.207668 | − | 0.978199i | \(-0.433413\pi\) | ||||
0.207668 | + | 0.978199i | \(0.433413\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.01777e26 | 0.637433 | 0.318716 | − | 0.947850i | \(-0.396748\pi\) | ||||
0.318716 | + | 0.947850i | \(0.396748\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.46684e25 | + | 3.49250e25i | 0.203082 | + | 0.204586i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.08782e24i | − | 0.0443312i | −0.999754 | − | 0.0221656i | \(-0.992944\pi\) | ||
0.999754 | − | 0.0221656i | \(-0.00705611\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.06743e26i | − | 0.547691i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.30343e26 | + | 9.59092e25i | 1.10681 | + | 0.460848i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.64777e25 | −0.119194 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.05130e25 | −0.297505 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.07130e26 | + | 8.62439e25i | 0.819393 | + | 0.341175i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.71508e25i | − | 0.286275i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.32094e25i | − | 0.254902i | −0.991845 | − | 0.127451i | \(-0.959320\pi\) | ||
0.991845 | − | 0.127451i | \(-0.0406795\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.15353e25 | − | 6.19908e25i | −0.201122 | − | 0.202611i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.47240e26 | 1.98653 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.15782e26 | −1.48714 | −0.743570 | − | 0.668658i | \(-0.766869\pi\) | ||||
−0.743570 | + | 0.668658i | \(0.766869\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.59477e26 | − | 3.83013e26i | 0.432118 | − | 1.03781i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.81602e26i | 1.48151i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.01646e26i | 0.483060i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.46827e25 | − | 1.07313e26i | 0.100702 | − | 0.241854i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.07840e26 | 1.71343 | 0.856714 | − | 0.515791i | \(-0.172502\pi\) | ||||
0.856714 | + | 0.515791i | \(0.172502\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.13783e26 | −0.826238 | −0.413119 | − | 0.910677i | \(-0.635561\pi\) | ||||
−0.413119 | + | 0.910677i | \(0.635561\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.77085e26 | + | 4.34300e26i | 0.333009 | + | 0.816704i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.06496e25i | 0.0897309i | 0.998993 | + | 0.0448654i | \(0.0142859\pi\) | ||||
−0.998993 | + | 0.0448654i | \(0.985714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 5.92518e26i | − | 0.989244i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.05205e26 | + | 4.38049e25i | 0.165585 | + | 0.0689456i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.19382e26 | −0.177193 | −0.0885966 | − | 0.996068i | \(-0.528238\pi\) | ||||
−0.0885966 | + | 0.996068i | \(0.528238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.94611e26 | 0.972560 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.97154e26 | − | 8.20903e25i | −0.260488 | − | 0.108461i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.21463e26i | 0.899786i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.97480e26i | − | 0.350319i | −0.984540 | − | 0.175159i | \(-0.943956\pi\) | ||
0.984540 | − | 0.175159i | \(-0.0560441\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.02561e26 | − | 2.01073e26i | 0.225309 | − | 0.223654i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.31936e26 | 0.348842 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.26477e27 | −1.25623 | −0.628113 | − | 0.778122i | \(-0.716172\pi\) | ||||
−0.628113 | + | 0.778122i | \(0.716172\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.13705e26 | − | 7.53419e26i | 0.294573 | − | 0.707471i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.42052e26i | − | 0.570146i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.14429e25i | − | 0.0180124i | −0.999959 | − | 0.00900619i | \(-0.997133\pi\) | ||
0.999959 | − | 0.00900619i | \(-0.00286680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.05666e26 | − | 1.93495e27i | 0.640387 | − | 1.53800i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.44306e26 | −0.484736 | −0.242368 | − | 0.970184i | \(-0.577924\pi\) | ||||
−0.242368 | + | 0.970184i | \(0.577924\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.42882e26 | 0.244234 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.09373e25 | + | 8.03426e25i | −0.0545989 | + | 0.0541977i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.83774e26i | 0.500864i | 0.968134 | + | 0.250432i | \(0.0805727\pi\) | ||||
−0.968134 | + | 0.250432i | \(0.919427\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.69197e26i | − | 0.163010i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.18149e27 | + | 9.08320e26i | 1.25208 | + | 0.521336i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.14251e27 | −1.16588 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.46679e26 | −0.230513 | −0.115256 | − | 0.993336i | \(-0.536769\pi\) | ||||
−0.115256 | + | 0.993336i | \(0.536769\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.78701e25 | + | 3.24232e25i | 0.0381202 | + | 0.0158723i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.13140e27i | − | 1.45453i | −0.686357 | − | 0.727265i | \(-0.740791\pi\) | ||
0.686357 | − | 0.727265i | \(-0.259209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.49831e27i | 1.54225i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.76301e27 | + | 2.03784e25i | 1.15639 | + | 0.00852890i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.08605e26 | −0.241877 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.40894e27 | −1.28684 | −0.643420 | − | 0.765514i | \(-0.722485\pi\) | ||||
−0.643420 | + | 0.765514i | \(0.722485\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.70239e27 | + | 4.08860e27i | −0.610550 | + | 1.46634i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.98290e25i | 0.0272073i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.72193e27i | 0.557841i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.85033e27 | + | 4.44389e27i | −0.569928 | + | 1.36878i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.37162e27 | −0.694700 | −0.347350 | − | 0.937736i | \(-0.612918\pi\) | ||||
−0.347350 | + | 0.937736i | \(0.612918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.84452e27 | −0.513949 | −0.256975 | − | 0.966418i | \(-0.582726\pi\) | ||||
−0.256975 | + | 0.966418i | \(0.582726\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.05180e27 | − | 3.07439e27i | −0.809063 | − | 0.815052i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.62001e26i | 0.242712i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.72856e27i | 0.415138i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.01688e27 | + | 1.25616e27i | 0.689854 | + | 0.287238i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.64442e27 | −1.22916 | −0.614579 | − | 0.788855i | \(-0.710674\pi\) | ||||
−0.614579 | + | 0.788855i | \(0.710674\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.36146e27 | −1.31957 | −0.659787 | − | 0.751452i | \(-0.729354\pi\) | ||||
−0.659787 | + | 0.751452i | \(0.729354\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.49189e27 | − | 1.45394e27i | −0.690117 | − | 0.287348i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.99252e26i | − | 0.0375274i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.32681e27i | − | 1.31534i | −0.753307 | − | 0.657669i | \(-0.771543\pi\) | ||
0.753307 | − | 0.657669i | \(-0.228457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.86031e27 | + | 3.88888e27i | 0.660719 | + | 0.665610i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.94318e27 | −0.480372 | −0.240186 | − | 0.970727i | \(-0.577208\pi\) | ||||
−0.240186 | + | 0.970727i | \(0.577208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.06409e27 | −0.321328 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.69530e27 | + | 6.47324e27i | −0.400293 | + | 0.961375i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.05123e27i | − | 0.148974i | −0.997222 | − | 0.0744868i | \(-0.976268\pi\) | ||
0.997222 | − | 0.0744868i | \(-0.0237319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.98868e27i | − | 0.268974i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.11609e27 | − | 9.88554e27i | 0.531440 | − | 1.27635i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.06242e27 | 0.254248 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.20730e28 | −1.42132 | −0.710662 | − | 0.703533i | \(-0.751605\pi\) | ||||
−0.710662 | + | 0.703533i | \(0.751605\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.92511e27 | − | 2.41595e27i | 0.666289 | − | 0.271678i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.61355e26i | 0.0817951i | 0.999163 | + | 0.0408976i | \(0.0130217\pi\) | ||||
−0.999163 | + | 0.0408976i | \(0.986978\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.71097e28i | 1.75647i | 0.478227 | + | 0.878236i | \(0.341280\pi\) | ||||
−0.478227 | + | 0.878236i | \(0.658720\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.90260e28 | + | 7.92197e27i | 1.86678 | + | 0.777279i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.44975e28 | −1.35977 | −0.679885 | − | 0.733319i | \(-0.737970\pi\) | ||||
−0.679885 | + | 0.733319i | \(0.737970\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.77498e27 | −0.428210 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.78118e27 | + | 1.99077e27i | 0.410030 | + | 0.170726i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.94615e26i | 0.0651801i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.12047e26i | 0.0558760i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.32274e28 | − | 1.31302e28i | 0.993186 | − | 0.985888i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.47684e28 | 1.77982 | 0.889910 | − | 0.456137i | \(-0.150767\pi\) | ||||
0.889910 | + | 0.456137i | \(0.150767\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.66073e27 | −0.251794 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.29644e26 | + | 7.91700e26i | −0.0217070 | + | 0.0521333i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.20468e27i | − | 0.139013i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.13030e27i | − | 0.490967i | −0.969401 | − | 0.245484i | \(-0.921053\pi\) | ||
0.969401 | − | 0.245484i | \(-0.0789468\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.08979e27 | − | 1.94291e28i | 0.467944 | − | 1.12385i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.17252e28 | 0.649778 | 0.324889 | − | 0.945752i | \(-0.394673\pi\) | ||||
0.324889 | + | 0.945752i | \(0.394673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.75944e27 | −0.465140 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.36636e28 | − | 1.35632e28i | 0.695359 | − | 0.690249i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.37127e27i | 0.213239i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.49942e28i | − | 1.63659i | −0.574798 | − | 0.818296i | \(-0.694919\pi\) | ||
0.574798 | − | 0.818296i | \(-0.305081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.74918e28 | + | 1.14469e28i | 1.23284 | + | 0.513325i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.52525e28 | 1.08603 | 0.543013 | − | 0.839724i | \(-0.317283\pi\) | ||||
0.543013 | + | 0.839724i | \(0.317283\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.81178e28 | −1.57242 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.18098e27 | − | 2.15723e27i | −0.205035 | − | 0.0853717i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.18459e28i | 0.829531i | 0.909928 | + | 0.414765i | \(0.136136\pi\) | ||||
−0.909928 | + | 0.414765i | \(0.863864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.32256e27i | − | 0.193955i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.38560e27 | − | 1.78822e27i | 0.153390 | − | 0.0625444i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.91157e27 | 0.0641820 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.01834e28 | −0.973009 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.25771e27 | − | 2.22340e28i | 0.286580 | − | 0.688274i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.54801e28i | 0.757538i | 0.925491 | + | 0.378769i | \(0.123653\pi\) | ||||
−0.925491 | + | 0.378769i | \(0.876347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.85601e28i | 1.10121i | 0.834766 | + | 0.550605i | \(0.185603\pi\) | ||||
−0.834766 | + | 0.550605i | \(0.814397\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.17801e27 | − | 2.82921e27i | 0.0323205 | − | 0.0776234i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.77271e28 | 1.25821 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.74458e28 | −0.948677 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.15774e27 | + | 3.18112e27i | 0.0768926 | + | 0.0774618i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.19618e28i | − | 0.280002i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6.16057e28i | − | 1.38646i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.04320e28 | + | 3.34899e28i | 1.74060 | + | 0.724743i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.81798e28 | 0.794605 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.99029e28 | −1.59953 | −0.799763 | − | 0.600316i | \(-0.795042\pi\) | ||||
−0.799763 | + | 0.600316i | \(0.795042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.35679e28 | + | 2.64681e28i | 1.22416 | + | 0.509712i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 5.53973e28i | − | 1.02642i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.74325e28i | 0.310809i | 0.987851 | + | 0.155404i | \(0.0496680\pi\) | ||||
−0.987851 | + | 0.155404i | \(0.950332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.83757e28 | + | 6.88818e28i | 1.17325 | + | 1.18194i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.48350e27 | −0.107082 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.58063e28 | 0.251313 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.28978e27 | + | 1.99094e28i | −0.126901 | + | 0.304777i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 2.75381e28i | − | 0.405933i | −0.979186 | − | 0.202966i | \(-0.934942\pi\) | ||
0.979186 | − | 0.202966i | \(-0.0650582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.77957e27i | 0.0678524i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.71376e28 | − | 4.11590e28i | 0.234337 | − | 0.562801i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.77185e28 | −1.28718 | −0.643589 | − | 0.765371i | \(-0.722556\pi\) | ||||
−0.643589 | + | 0.765371i | \(0.722556\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.02438e29 | −1.30002 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.03840e28 | − | 1.50341e26i | −0.249268 | − | 0.00183846i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.03279e29i | − | 1.21712i | −0.793509 | − | 0.608558i | \(-0.791748\pi\) | ||
0.793509 | − | 0.608558i | \(-0.208252\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.75848e28i | 1.10842i | 0.832378 | + | 0.554208i | \(0.186979\pi\) | ||||
−0.832378 | + | 0.554208i | \(0.813021\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.36336e28 | + | 2.64955e28i | 0.696727 | + | 0.290100i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.23933e27 | −0.0764163 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.63410e28 | 0.675206 | 0.337603 | − | 0.941289i | \(-0.390384\pi\) | ||||
0.337603 | + | 0.941289i | \(0.390384\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.72446e28 | − | 4.04902e28i | −0.954422 | − | 0.397398i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1.27035e28i | − | 0.120247i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.29862e29i | − | 1.18567i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.21856e28 | − | 8.15817e28i | 0.723868 | − | 0.718549i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.32148e29 | −1.12295 | −0.561474 | − | 0.827494i | \(-0.689766\pi\) | ||||
−0.561474 | + | 0.827494i | \(0.689766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.53263e28 | 0.289659 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.29806e28 | − | 5.51921e28i | 0.181842 | − | 0.436725i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.26760e29i | 0.968073i | 0.875048 | + | 0.484037i | \(0.160830\pi\) | ||||
−0.875048 | + | 0.484037i | \(0.839170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.81374e28i | − | 0.207422i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.50365e27 | − | 3.61128e27i | 0.0107008 | − | 0.0256998i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.20473e27 | −0.0151486 | −0.00757432 | − | 0.999971i | \(-0.502411\pi\) | ||||
−0.00757432 | + | 0.999971i | \(0.502411\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.82280e28 | −0.651708 | −0.325854 | − | 0.945420i | \(-0.605652\pi\) | ||||
−0.325854 | + | 0.945420i | \(0.605652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.90279e29 | + | 1.88881e29i | −1.21916 | + | 1.21020i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.27293e28i | 0.326303i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.46388e29i | 0.875034i | 0.899210 | + | 0.437517i | \(0.144142\pi\) | ||||
−0.899210 | + | 0.437517i | \(0.855858\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.57612e28 | + | 1.07263e28i | 0.148760 | + | 0.0619398i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.81551e29 | −1.01290 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.64193e29 | −1.42425 | −0.712125 | − | 0.702052i | \(-0.752267\pi\) | ||||
−0.712125 | + | 0.702052i | \(0.752267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.50559e28 | − | 2.70877e28i | −0.338920 | − | 0.141118i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.70244e28i | 0.488525i | 0.969709 | + | 0.244263i | \(0.0785459\pi\) | ||||
−0.969709 | + | 0.244263i | \(0.921454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.48597e29i | 1.69657i | 0.529539 | + | 0.848285i | \(0.322365\pi\) | ||||
−0.529539 | + | 0.848285i | \(0.677635\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.81807e28 | + | 4.45881e28i | 0.0855359 | + | 0.209777i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.52277e28 | 0.0692646 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.78199e29 | −1.22353 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.26848e28 | − | 3.04648e28i | 0.0539478 | − | 0.129565i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.99430e28i | 0.205420i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.73495e29i | 0.690206i | 0.938565 | + | 0.345103i | \(0.112156\pi\) | ||||
−0.938565 | + | 0.345103i | \(0.887844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.67017e28 | − | 2.32246e29i | 0.372130 | − | 0.893738i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.17506e29 | −1.92660 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.29649e29 | 0.827182 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.72911e29 | + | 1.74191e29i | 0.602649 | + | 0.607111i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.71022e29i | 1.92594i | 0.269604 | + | 0.962971i | \(0.413107\pi\) | ||||
−0.269604 | + | 0.962971i | \(0.586893\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.96431e29i | − | 0.641203i | −0.947214 | − | 0.320601i | \(-0.896115\pi\) | ||
0.947214 | − | 0.320601i | \(-0.103885\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.59944e28 | + | 1.08234e28i | 0.0821300 | + | 0.0341969i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.00829e29 | 1.53177 | 0.765887 | − | 0.642975i | \(-0.222300\pi\) | ||||
0.765887 | + | 0.642975i | \(0.222300\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.12312e28 | 0.0924739 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.40364e29 | − | 5.84440e28i | −0.402397 | − | 0.167548i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 5.42218e29i | − | 1.50517i | −0.658495 | − | 0.752585i | \(-0.728807\pi\) | ||
0.658495 | − | 0.752585i | \(-0.271193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 5.83444e29i | − | 1.56843i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.10541e29 | − | 2.12100e29i | −0.548151 | − | 0.552209i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.80613e29 | −1.71634 | −0.858170 | − | 0.513366i | \(-0.828398\pi\) | ||||
−0.858170 | + | 0.513366i | \(0.828398\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.35616e29 | 0.331280 | 0.165640 | − | 0.986186i | \(-0.447031\pi\) | ||||
0.165640 | + | 0.986186i | \(0.447031\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.03082e29 | − | 2.47570e29i | 0.243944 | − | 0.585875i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.08265e28i | − | 0.0477517i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.59173e28i | − | 0.146446i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.23260e29 | + | 2.96030e29i | −0.265367 | + | 0.637325i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.76259e29 | 1.41100 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.91865e29 | 0.590233 | 0.295116 | − | 0.955461i | \(-0.404642\pi\) | ||||
0.295116 | + | 0.955461i | \(0.404642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.49704e28 | − | 1.59340e29i | −0.127358 | − | 0.312345i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.15331e29i | − | 0.409190i | −0.978847 | − | 0.204595i | \(-0.934412\pi\) | ||
0.978847 | − | 0.204595i | \(-0.0655878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.62649e28i | 0.0299653i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.77007e28 | − | 1.98614e28i | −0.0852080 | − | 0.0354785i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.41610e29 | 0.764929 | 0.382465 | − | 0.923970i | \(-0.375075\pi\) | ||||
0.382465 | + | 0.923970i | \(0.375075\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.09350e30 | 1.83683 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.53687e29 | + | 1.88904e29i | 0.739112 | + | 0.307748i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 7.81113e29i | − | 1.23428i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.29378e29i | 0.504865i | 0.967615 | + | 0.252432i | \(0.0812305\pi\) | ||||
−0.967615 | + | 0.252432i | \(0.918769\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.00802e29 | + | 1.00062e29i | −0.149889 | + | 0.148788i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.18853e30 | 1.71462 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.63194e29 | −0.228433 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.97016e29 | + | 4.73170e29i | −0.267604 | + | 0.642698i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.96564e29i | − | 0.654539i | −0.944931 | − | 0.327270i | \(-0.893871\pi\) | ||
0.944931 | − | 0.327270i | \(-0.106129\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.69664e28i | 0.0472908i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.11126e29 | + | 9.87392e29i | −0.510492 | + | 1.22604i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.81212e29 | 0.338946 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.87065e28 | −0.0920926 | −0.0460463 | − | 0.998939i | \(-0.514662\pi\) | ||||
−0.0460463 | + | 0.998939i | \(0.514662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.29866e29 | − | 6.25238e29i | 0.715513 | − | 0.710255i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.59159e29i | 0.396139i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 8.06871e29i | − | 0.864153i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.72437e29 | − | 3.63261e29i | −0.907367 | − | 0.377805i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.27107e29 | 0.835427 | 0.417713 | − | 0.908579i | \(-0.362832\pi\) | ||||
0.417713 | + | 0.908579i | \(0.362832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.41025e28 | −0.0138349 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.61467e29 | + | 2.33781e29i | 0.535023 | + | 0.222770i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.35561e29i | 0.218050i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.01486e30i | − | 0.912631i | −0.889818 | − | 0.456315i | \(-0.849169\pi\) | ||
0.889818 | − | 0.456315i | \(-0.150831\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.18231e29 | + | 8.00324e29i | −0.714886 | + | 0.699241i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.52072e28 | 0.0553558 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.22596e28 | −0.0183623 | −0.00918114 | − | 0.999958i | \(-0.502922\pi\) | ||||
−0.00918114 | + | 0.999958i | \(0.502922\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.20044e29 | − | 1.24898e30i | 0.416892 | − | 1.00124i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.86810e30i | 1.45543i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.57388e30i | 1.19180i | 0.803057 | + | 0.595902i | \(0.203205\pi\) | ||||
−0.803057 | + | 0.595902i | \(0.796795\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.62984e28 | − | 1.83244e29i | 0.0561596 | − | 0.134877i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.70225e29 | 0.479554 | 0.239777 | − | 0.970828i | \(-0.422926\pi\) | ||||
0.239777 | + | 0.970828i | \(0.422926\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.73128e30 | 1.20428 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.02502e29 | − | 5.06222e29i | −0.339838 | − | 0.342353i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.54493e29i | 0.298860i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.47240e30i | − | 0.941469i | −0.882275 | − | 0.470734i | \(-0.843989\pi\) | ||
0.882275 | − | 0.470734i | \(-0.156011\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.89340e30 | − | 1.20474e30i | −1.79912 | − | 0.749111i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.64390e30 | −1.59883 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.20620e30 | 0.709432 | 0.354716 | − | 0.934974i | \(-0.384578\pi\) | ||||
0.354716 | + | 0.934974i | \(0.384578\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.09733e29 | + | 1.28965e29i | 0.177194 | + | 0.0737793i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.79298e30i | − | 1.55428i | −0.629330 | − | 0.777139i | \(-0.716670\pi\) | ||
0.629330 | − | 0.777139i | \(-0.283330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.08691e29i | 0.221252i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.11301e30 | − | 1.12125e30i | −0.586211 | − | 0.590551i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.87854e29 | 0.0962652 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.21748e30 | 1.10569 | 0.552844 | − | 0.833285i | \(-0.313542\pi\) | ||||
0.552844 | + | 0.833285i | \(0.313542\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.18793e30 | + | 2.85303e30i | −0.576395 | + | 1.38432i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.67008e30i | 1.73297i | 0.499205 | + | 0.866484i | \(0.333625\pi\) | ||||
−0.499205 | + | 0.866484i | \(0.666375\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.28349e30i | − | 0.589827i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.11575e28 | − | 1.46881e29i | 0.0273545 | − | 0.0656967i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.20791e29 | −0.0525887 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.71015e30 | 0.724769 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.45086e30 | − | 5.91584e29i | 0.598586 | − | 0.244072i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.27874e30i | − | 0.513629i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.02180e30i | 1.57284i | 0.617690 | + | 0.786422i | \(0.288069\pi\) | ||||
−0.617690 | + | 0.786422i | \(0.711931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.01361e30 | − | 1.25479e30i | −1.14757 | − | 0.477819i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.55729e29 | 0.280229 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.06767e30 | 1.46885 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.24819e30 | − | 1.76884e30i | −1.49400 | − | 0.622063i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.15532e30i | − | 0.738242i | −0.929381 | − | 0.369121i | \(-0.879659\pi\) | ||
0.929381 | − | 0.369121i | \(-0.120341\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.47689e30i | 0.826352i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.06813e29 | − | 6.02354e29i | 0.197203 | − | 0.195754i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.08232e30 | −0.659227 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.11741e29 | 0.0653054 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.60017e30 | + | 3.84309e30i | −0.480832 | + | 1.15480i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.35179e29i | − | 0.0688556i | −0.999407 | − | 0.0344278i | \(-0.989039\pi\) | ||
0.999407 | − | 0.0344278i | \(-0.0109609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.43433e30i | − | 0.409195i | −0.978846 | − | 0.204598i | \(-0.934411\pi\) | ||
0.978846 | − | 0.204598i | \(-0.0655886\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.08086e29 | − | 4.99755e29i | 0.0578484 | − | 0.138933i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.19634e30 | −1.40780 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.82646e28 | 0.0127437 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.06321e29 | + | 6.01865e29i | −0.156035 | + | 0.154888i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.72474e30i | 1.43600i | 0.696046 | + | 0.717998i | \(0.254941\pi\) | ||||
−0.696046 | + | 0.717998i | \(0.745059\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.72061e30i | 0.909738i | 0.890558 | + | 0.454869i | \(0.150314\pi\) | ||||
−0.890558 | + | 0.454869i | \(0.849686\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.10686e30 | − | 4.60869e29i | −0.263831 | − | 0.109853i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.34712e30 | −1.70730 | −0.853649 | − | 0.520849i | \(-0.825616\pi\) | ||||
−0.853649 | + | 0.520849i | \(0.825616\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.50473e28 | −0.0170025 | −0.00850125 | − | 0.999964i | \(-0.502706\pi\) | ||||
−0.00850125 | + | 0.999964i | \(0.502706\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.40739e29 | − | 3.50063e29i | −0.185716 | − | 0.0773277i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.13308e30i | − | 0.674838i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 7.35274e30i | − | 1.54433i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.90520e30 | + | 3.22333e30i | −1.61918 | + | 0.660218i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.85066e30 | 0.369681 | 0.184840 | − | 0.982769i | \(-0.440823\pi\) | ||||
0.184840 | + | 0.982769i | \(0.440823\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.98795e30 | 0.582124 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.15188e30 | − | 2.76644e30i | 0.218885 | − | 0.525692i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.38566e30i | 0.256840i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.89008e29i | − | 0.0703368i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.76029e30 | + | 9.03102e30i | −0.663271 | + | 1.59296i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.75835e29 | −0.0646750 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.34530e29 | −0.140113 | −0.0700563 | − | 0.997543i | \(-0.522318\pi\) | ||||
−0.0700563 | + | 0.997543i | \(0.522318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.23820e29 | − | 8.29918e29i | −0.134955 | − | 0.135954i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 6.07917e30i | − | 0.971730i | −0.874034 | − | 0.485865i | \(-0.838505\pi\) | ||
0.874034 | − | 0.485865i | \(-0.161495\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.75485e29i | 0.0273724i | 0.999906 | + | 0.0136862i | \(0.00435658\pi\) | ||||
−0.999906 | + | 0.0136862i | \(0.995643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.79947e29 | + | 1.99838e29i | 0.0730567 | + | 0.0304190i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.73201e30 | −0.405853 | −0.202926 | − | 0.979194i | \(-0.565045\pi\) | ||||
−0.202926 | + | 0.979194i | \(0.565045\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.94653e30 | −0.862174 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.14597e30 | + | 1.30991e30i | 0.445199 | + | 0.185370i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.18382e30i | − | 0.854179i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.12365e31i | 1.51510i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.43379e29 | + | 6.48142e29i | 0.0846872 | + | 0.0853141i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.48658e30 | 0.191031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.32126e31 | 1.65765 | 0.828824 | − | 0.559509i | \(-0.189010\pi\) | ||||
0.828824 | + | 0.559509i | \(0.189010\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.70068e29 | − | 8.88785e29i | 0.0453313 | − | 0.108871i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.38546e30i | 1.00295i | 0.865172 | + | 0.501476i | \(0.167209\pi\) | ||||
−0.865172 | + | 0.501476i | \(0.832791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.14860e31i | 1.34147i | 0.741698 | + | 0.670734i | \(0.234021\pi\) | ||||
−0.741698 | + | 0.670734i | \(0.765979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.25398e29 | − | 1.02167e30i | 0.0485167 | − | 0.116521i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.19825e31 | 1.33460 | 0.667298 | − | 0.744791i | \(-0.267451\pi\) | ||||
0.667298 | + | 0.744791i | \(0.267451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.81788e30 | 0.415292 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.88173e28 | + | 7.97473e30i | −0.00624869 | + | 0.847228i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.83332e30i | 0.190239i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.15117e31i | − | 2.18038i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.86303e30 | + | 7.75720e29i | 0.184459 | + | 0.0768041i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.16867e31 | 1.13036 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.06566e31 | −1.00696 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.91772e29 | − | 7.98492e28i | −0.0177037 | − | 0.00737139i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.70013e31i | − | 1.53346i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.08168e30i | − | 0.183458i | −0.995784 | − | 0.0917291i | \(-0.970761\pi\) | ||
0.995784 | − | 0.0917291i | \(-0.0292394\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.12061e31 | − | 1.11237e31i | 0.965012 | − | 0.957921i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.52106e30 | 0.717052 | 0.358526 | − | 0.933520i | \(-0.383279\pi\) | ||||
0.358526 | + | 0.933520i | \(0.383279\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.96992e30 | −0.408701 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.21128e30 | − | 2.21225e31i | 0.740284 | − | 1.77793i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.30433e30i | 0.338087i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.50335e31i | − | 1.15411i | −0.816705 | − | 0.577056i | \(-0.804202\pi\) | ||
0.816705 | − | 0.577056i | \(-0.195798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.85925e30 | − | 1.16703e31i | 0.364622 | − | 0.875705i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.02865e31 | 0.754483 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.34308e30 | 0.0962973 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.61972e29 | + | 5.57843e29i | −0.0393892 | + | 0.0390998i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.18121e31i | 1.49463i | 0.664472 | + | 0.747314i | \(0.268657\pi\) | ||||
−0.664472 | + | 0.747314i | \(0.731343\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.31902e30i | − | 0.155358i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.85383e30 | + | 2.43739e30i | 0.383427 | + | 0.159650i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.10081e31 | −0.704999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.27481e30 | 0.580817 | 0.290409 | − | 0.956903i | \(-0.406209\pi\) | ||||
0.290409 | + | 0.956903i | \(0.406209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.60961e30 | + | 4.00121e30i | 0.588460 | + | 0.245020i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.62274e31i | − | 1.57059i | −0.619120 | − | 0.785296i | \(-0.712511\pi\) | ||
0.619120 | − | 0.785296i | \(-0.287489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.22808e30i | − | 0.0719205i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.90030e30 | + | 4.66049e30i | 0.108840 | + | 0.266930i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.86298e31 | 1.04360 | 0.521800 | − | 0.853068i | \(-0.325261\pi\) | ||||
0.521800 | + | 0.853068i | \(0.325261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.25251e31 | −0.686254 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.17960e29 | − | 7.63638e29i | 0.0170403 | − | 0.0409253i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.44161e31i | 1.80420i | 0.431523 | + | 0.902102i | \(0.357976\pi\) | ||||
−0.431523 | + | 0.902102i | \(0.642024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.70189e31i | − | 0.872763i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.19642e30 | − | 1.00785e31i | 0.210525 | − | 0.505613i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.06728e30 | −0.395942 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.28513e31 | −2.05764 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.79781e31 | + | 1.81112e31i | 0.844632 | + | 0.850884i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.60082e31i | 1.19557i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.06414e31i | 1.37826i | 0.724639 | + | 0.689129i | \(0.242007\pi\) | ||||
−0.724639 | + | 0.689129i | \(0.757993\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.49998e30 | − | 1.04093e30i | −0.110037 | − | 0.0458165i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.62652e31 | 1.56203 | 0.781014 | − | 0.624514i | \(-0.214703\pi\) | ||||
0.781014 | + | 0.624514i | \(0.214703\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.76829e30 | −0.369599 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.65771e30 | − | 2.77211e30i | −0.274648 | − | 0.114357i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.32636e31i | − | 0.535512i | −0.963487 | − | 0.267756i | \(-0.913718\pi\) | ||
0.963487 | − | 0.267756i | \(-0.0862820\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.95749e30i | − | 0.235421i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.61663e31 | + | 1.62860e31i | 0.625298 | + | 0.629927i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.95223e31 | −1.49634 | −0.748171 | − | 0.663506i | \(-0.769068\pi\) | ||||
−0.748171 | + | 0.663506i | \(0.769068\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.47612e31 | −0.547069 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.03306e30 | − | 7.28444e30i | 0.110040 | − | 0.264281i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.90703e29i | 0.0174284i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.70998e31i | 0.942306i | 0.882051 | + | 0.471153i | \(0.156162\pi\) | ||||
−0.882051 | + | 0.471153i | \(0.843838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.87811e30 | − | 6.91230e30i | 0.0979807 | − | 0.235318i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.65842e29 | −0.0321932 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.09599e30 | 0.0357690 | 0.0178845 | − | 0.999840i | \(-0.494307\pi\) | ||||
0.0178845 | + | 0.999840i | \(0.494307\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.37298e30 | − | 8.27223e30i | −0.107790 | − | 0.264353i |
(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 | 48.22.c.b.47.12 | yes | 12 | |
3.2 | odd | 2 | inner | 48.22.c.b.47.2 | yes | 12 | |
4.3 | odd | 2 | inner | 48.22.c.b.47.1 | ✓ | 12 | |
12.11 | even | 2 | inner | 48.22.c.b.47.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.22.c.b.47.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
48.22.c.b.47.2 | yes | 12 | 3.2 | odd | 2 | inner | |
48.22.c.b.47.11 | yes | 12 | 12.11 | even | 2 | inner | |
48.22.c.b.47.12 | yes | 12 | 1.1 | even | 1 | trivial |