Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(1,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.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: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.27700337.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 19x^{4} + 17x^{3} + 103x^{2} - 71x - 127 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.72245\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.920510 | −0.411665 | −0.205832 | − | 0.978587i | \(-0.565990\pi\) | ||||
−0.205832 | + | 0.978587i | \(0.565990\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.87031 | −1.84080 | −0.920401 | − | 0.390975i | \(-0.872138\pi\) | ||||
−0.920401 | + | 0.390975i | \(0.872138\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.964624 | −0.290845 | −0.145422 | − | 0.989370i | \(-0.546454\pi\) | ||||
−0.145422 | + | 0.989370i | \(0.546454\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.920510 | −0.237675 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.47547 | 0.600389 | 0.300195 | − | 0.953878i | \(-0.402948\pi\) | ||||
0.300195 | + | 0.953878i | \(0.402948\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12841 | 0.717706 | 0.358853 | − | 0.933394i | \(-0.383168\pi\) | ||||
0.358853 | + | 0.933394i | \(0.383168\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.87031 | −1.06279 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.92788 | −1.02753 | −0.513767 | − | 0.857930i | \(-0.671750\pi\) | ||||
−0.513767 | + | 0.857930i | \(0.671750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.15266 | −0.830532 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.90825 | 1.28283 | 0.641415 | − | 0.767194i | \(-0.278348\pi\) | ||||
0.641415 | + | 0.767194i | \(0.278348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.61253 | −0.828435 | −0.414218 | − | 0.910178i | \(-0.635945\pi\) | ||||
−0.414218 | + | 0.910178i | \(0.635945\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.964624 | −0.167919 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.48317 | 0.757793 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.81522 | 0.791617 | 0.395808 | − | 0.918333i | \(-0.370464\pi\) | ||||
0.395808 | + | 0.918333i | \(0.370464\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.43483 | −0.536431 | −0.268216 | − | 0.963359i | \(-0.586434\pi\) | ||||
−0.268216 | + | 0.963359i | \(0.586434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.0752 | 1.53646 | 0.768229 | − | 0.640175i | \(-0.221138\pi\) | ||||
0.768229 | + | 0.640175i | \(0.221138\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.920510 | −0.137222 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.64406 | −1.26087 | −0.630433 | − | 0.776244i | \(-0.717122\pi\) | ||||
−0.630433 | + | 0.776244i | \(0.717122\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16.7199 | 2.38855 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.47547 | 0.346635 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.841166 | 0.115543 | 0.0577715 | − | 0.998330i | \(-0.481601\pi\) | ||||
0.0577715 | + | 0.998330i | \(0.481601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.887946 | 0.119731 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.12841 | 0.414368 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.35767 | −1.21826 | −0.609132 | − | 0.793069i | \(-0.708482\pi\) | ||||
−0.609132 | + | 0.793069i | \(0.708482\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.793428 | 0.101588 | 0.0507940 | − | 0.998709i | \(-0.483825\pi\) | ||||
0.0507940 | + | 0.998709i | \(0.483825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.87031 | −0.613601 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.99350 | 0.854392 | 0.427196 | − | 0.904159i | \(-0.359501\pi\) | ||||
0.427196 | + | 0.904159i | \(0.359501\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.92788 | −0.593247 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.5279 | 1.84282 | 0.921411 | − | 0.388588i | \(-0.127037\pi\) | ||||
0.921411 | + | 0.388588i | \(0.127037\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.72664 | 0.670253 | 0.335126 | − | 0.942173i | \(-0.391221\pi\) | ||||
0.335126 | + | 0.942173i | \(0.391221\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.15266 | −0.479508 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.69801 | 0.535388 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.8726 | −1.56079 | −0.780395 | − | 0.625287i | \(-0.784982\pi\) | ||||
−0.780395 | + | 0.625287i | \(0.784982\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.8552 | 1.63057 | 0.815284 | − | 0.579061i | \(-0.196581\pi\) | ||||
0.815284 | + | 0.579061i | \(0.196581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.27869 | −0.247159 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.90825 | 0.740642 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6563 | −1.12957 | −0.564783 | − | 0.825239i | \(-0.691040\pi\) | ||||
−0.564783 | + | 0.825239i | \(0.691040\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.61253 | −0.478297 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.87973 | −0.295454 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.53602 | 0.968236 | 0.484118 | − | 0.875003i | \(-0.339141\pi\) | ||||
0.484118 | + | 0.875003i | \(0.339141\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.964624 | −0.0969483 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.3566 | 1.92605 | 0.963025 | − | 0.269413i | \(-0.0868295\pi\) | ||||
0.963025 | + | 0.269413i | \(0.0868295\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.7878 | −1.06295 | −0.531477 | − | 0.847073i | \(-0.678363\pi\) | ||||
−0.531477 | + | 0.847073i | \(0.678363\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.48317 | 0.437512 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.55352 | −0.246859 | −0.123429 | − | 0.992353i | \(-0.539389\pi\) | ||||
−0.123429 | + | 0.992353i | \(0.539389\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.1717 | 1.07005 | 0.535027 | − | 0.844835i | \(-0.320301\pi\) | ||||
0.535027 | + | 0.844835i | \(0.320301\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.81522 | 0.457040 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1234 | 1.14047 | 0.570236 | − | 0.821481i | \(-0.306852\pi\) | ||||
0.570236 | + | 0.821481i | \(0.306852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.53616 | 0.422999 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.0563 | −1.10520 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0695 | −0.915409 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.43483 | −0.309709 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.42512 | 0.753565 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.8748 | 1.76360 | 0.881802 | − | 0.471619i | \(-0.156330\pi\) | ||||
0.881802 | + | 0.471619i | \(0.156330\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.0752 | 0.887074 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.5906 | 1.53690 | 0.768450 | − | 0.639910i | \(-0.221028\pi\) | ||||
0.768450 | + | 0.639910i | \(0.221028\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.2363 | −1.32115 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.920510 | −0.0792249 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.3054 | 1.47850 | 0.739251 | − | 0.673430i | \(-0.235180\pi\) | ||||
0.739251 | + | 0.673430i | \(0.235180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.2816 | 1.04171 | 0.520856 | − | 0.853644i | \(-0.325613\pi\) | ||||
0.520856 | + | 0.853644i | \(0.325613\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.64406 | −0.727961 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.35911 | −0.528095 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.7199 | 1.37903 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.37832 | 0.194840 | 0.0974199 | − | 0.995243i | \(-0.468941\pi\) | ||||
0.0974199 | + | 0.995243i | \(0.468941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.80104 | 0.553460 | 0.276730 | − | 0.960948i | \(-0.410749\pi\) | ||||
0.276730 | + | 0.960948i | \(0.410749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.47547 | 0.200130 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.24588 | 0.341037 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8025 | −1.26118 | −0.630588 | − | 0.776118i | \(-0.717186\pi\) | ||||
−0.630588 | + | 0.776118i | \(0.717186\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.841166 | 0.0667088 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0003 | 1.89149 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.66375 | 0.130315 | 0.0651575 | − | 0.997875i | \(-0.479245\pi\) | ||||
0.0651575 | + | 0.997875i | \(0.479245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.887946 | 0.0691265 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.04374 | 0.467679 | 0.233839 | − | 0.972275i | \(-0.424871\pi\) | ||||
0.233839 | + | 0.972275i | \(0.424871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.12841 | 0.239235 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9425 | 0.831946 | 0.415973 | − | 0.909377i | \(-0.363441\pi\) | ||||
0.415973 | + | 0.909377i | \(0.363441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.2247 | 1.52885 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.35767 | −0.703365 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.06741 | −0.154525 | −0.0772627 | − | 0.997011i | \(-0.524618\pi\) | ||||
−0.0772627 | + | 0.997011i | \(0.524618\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.10368 | −0.379353 | −0.189677 | − | 0.981847i | \(-0.560744\pi\) | ||||
−0.189677 | + | 0.981847i | \(0.560744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.793428 | 0.0586519 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.43245 | −0.325881 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.38790 | −0.174620 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.87031 | −0.354263 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.862551 | 0.0624120 | 0.0312060 | − | 0.999513i | \(-0.490065\pi\) | ||||
0.0312060 | + | 0.999513i | \(0.490065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.55727 | −0.400021 | −0.200010 | − | 0.979794i | \(-0.564098\pi\) | ||||
−0.200010 | + | 0.979794i | \(0.564098\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.78884 | 0.483685 | 0.241842 | − | 0.970316i | \(-0.422248\pi\) | ||||
0.241842 | + | 0.970316i | \(0.422248\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.51699 | 0.532865 | 0.266433 | − | 0.963854i | \(-0.414155\pi\) | ||||
0.266433 | + | 0.963854i | \(0.414155\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.99350 | 0.493283 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −33.6453 | −2.36143 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.16180 | 0.220830 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.92788 | −0.342511 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.01774 | −0.208741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9780 | 1.09997 | 0.549984 | − | 0.835175i | \(-0.314634\pi\) | ||||
0.549984 | + | 0.835175i | \(0.314634\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.5279 | 1.06395 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.27435 | −0.632505 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.4644 | 1.52499 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.72664 | 0.386971 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.5641 | −1.77887 | −0.889433 | − | 0.457066i | \(-0.848900\pi\) | ||||
−0.889433 | + | 0.457066i | \(0.848900\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.15266 | −0.276844 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.03932 | −0.599961 | −0.299980 | − | 0.953945i | \(-0.596980\pi\) | ||||
−0.299980 | + | 0.953945i | \(0.596980\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.5057 | −0.694235 | −0.347118 | − | 0.937822i | \(-0.612840\pi\) | ||||
−0.347118 | + | 0.937822i | \(0.612840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.69801 | 0.309106 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.7349 | −1.03083 | −0.515415 | − | 0.856941i | \(-0.672362\pi\) | ||||
−0.515415 | + | 0.856941i | \(0.672362\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.95694 | 0.519054 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8726 | −0.901122 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.3360 | −1.18606 | −0.593028 | − | 0.805182i | \(-0.702068\pi\) | ||||
−0.593028 | + | 0.805182i | \(0.702068\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.01936 | 0.194494 | 0.0972471 | − | 0.995260i | \(-0.468996\pi\) | ||||
0.0972471 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.3908 | −0.983283 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.8552 | 0.941409 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.3054 | 1.09231 | 0.546154 | − | 0.837685i | \(-0.316091\pi\) | ||||
0.546154 | + | 0.837685i | \(0.316091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.75355 | 0.298853 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.27869 | −0.142697 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.83635 | −0.426440 | −0.213220 | − | 0.977004i | \(-0.568395\pi\) | ||||
−0.213220 | + | 0.977004i | \(0.568395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.4516 | −1.45721 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.90825 | 0.427610 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.720029 | 0.0443989 | 0.0221995 | − | 0.999754i | \(-0.492933\pi\) | ||||
0.0221995 | + | 0.999754i | \(0.492933\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.774302 | −0.0475650 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.6563 | −0.652156 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1138 | 0.677622 | 0.338811 | − | 0.940854i | \(-0.389975\pi\) | ||||
0.338811 | + | 0.940854i | \(0.389975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3436 | 1.29653 | 0.648266 | − | 0.761414i | \(-0.275494\pi\) | ||||
0.648266 | + | 0.761414i | \(0.275494\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00576 | 0.241556 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9693 | −1.01959 | −0.509794 | − | 0.860296i | \(-0.670279\pi\) | ||||
−0.509794 | + | 0.860296i | \(0.670279\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.61253 | −0.276145 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.9782 | 1.90766 | 0.953829 | − | 0.300349i | \(-0.0971031\pi\) | ||||
0.953829 | + | 0.300349i | \(0.0971031\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.7438 | −0.757541 | −0.378770 | − | 0.925491i | \(-0.623653\pi\) | ||||
−0.378770 | + | 0.925491i | \(0.623653\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.87973 | −0.170581 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.7287 | 0.987464 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8721 | −0.639533 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.53602 | 0.559011 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.9771 | −1.69286 | −0.846431 | − | 0.532498i | \(-0.821253\pi\) | ||||
−0.846431 | + | 0.532498i | \(0.821253\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.61383 | 0.501516 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.964624 | −0.0559731 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.0694 | −2.82832 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.3566 | 1.11201 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.730358 | −0.0418202 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.8992 | −1.30693 | −0.653464 | − | 0.756957i | \(-0.726685\pi\) | ||||
−0.653464 | + | 0.756957i | \(0.726685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.7878 | −0.613696 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.8141 | −1.91742 | −0.958710 | − | 0.284385i | \(-0.908211\pi\) | ||||
−0.958710 | + | 0.284385i | \(0.908211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.1846 | −0.632190 | −0.316095 | − | 0.948728i | \(-0.602372\pi\) | ||||
−0.316095 | + | 0.948728i | \(0.602372\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.48317 | 0.252598 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4998 | 1.26372 | 0.631858 | − | 0.775084i | \(-0.282292\pi\) | ||||
0.631858 | + | 0.775084i | \(0.282292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.66386 | −0.373104 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.55352 | −0.142524 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.74427 | 0.430903 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.1717 | 0.617796 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 42.0992 | 2.32100 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.39583 | 0.461477 | 0.230738 | − | 0.973016i | \(-0.425886\pi\) | ||||
0.230738 | + | 0.973016i | \(0.425886\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.81522 | 0.263872 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.43759 | −0.351723 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.76684 | 0.205193 | 0.102596 | − | 0.994723i | \(-0.467285\pi\) | ||||
0.102596 | + | 0.994723i | \(0.467285\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.1234 | 0.658451 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.44936 | 0.240946 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −47.3387 | −2.55605 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.53616 | 0.244219 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3473 | 0.555470 | 0.277735 | − | 0.960658i | \(-0.410416\pi\) | ||||
0.277735 | + | 0.960658i | \(0.410416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.75407 | −0.361537 | −0.180769 | − | 0.983526i | \(-0.557859\pi\) | ||||
−0.180769 | + | 0.983526i | \(0.557859\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.6346 | 1.25794 | 0.628972 | − | 0.777428i | \(-0.283476\pi\) | ||||
0.628972 | + | 0.777428i | \(0.283476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.2936 | −0.758625 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0563 | −0.638086 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.87652 | −0.468485 | −0.234242 | − | 0.972178i | \(-0.575261\pi\) | ||||
−0.234242 | + | 0.972178i | \(0.575261\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.21307 | −0.484898 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.0695 | −0.528512 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.27143 | −0.275919 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.13397 | −0.0591929 | −0.0295965 | − | 0.999562i | \(-0.509422\pi\) | ||||
−0.0295965 | + | 0.999562i | \(0.509422\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.43483 | −0.178810 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.09674 | −0.212692 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0604 | −0.728020 | −0.364010 | − | 0.931395i | \(-0.618593\pi\) | ||||
−0.364010 | + | 0.931395i | \(0.618593\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.42512 | 0.435071 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.1182 | −1.23887 | −0.619435 | − | 0.785048i | \(-0.712638\pi\) | ||||
−0.619435 | + | 0.785048i | \(0.712638\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.8748 | 1.01822 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.39256 | −0.377742 | −0.188871 | − | 0.982002i | \(-0.560483\pi\) | ||||
−0.188871 | + | 0.982002i | \(0.560483\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.32457 | −0.220400 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0752 | 0.512153 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.4230 | 1.79602 | 0.898010 | − | 0.439975i | \(-0.145013\pi\) | ||||
0.898010 | + | 0.439975i | \(0.145013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.1988 | −0.616920 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.5906 | 0.887330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.7699 | 0.642522 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4553 | 0.926244 | 0.463122 | − | 0.886294i | \(-0.346729\pi\) | ||||
0.463122 | + | 0.886294i | \(0.346729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.2363 | −0.762769 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.9812 | 1.09769 | 0.548845 | − | 0.835924i | \(-0.315068\pi\) | ||||
0.548845 | + | 0.835924i | \(0.315068\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.920510 | −0.0457405 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.64487 | −0.230238 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.1327 | 0.550479 | 0.275239 | − | 0.961376i | \(-0.411243\pi\) | ||||
0.275239 | + | 0.961376i | \(0.411243\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.3054 | 0.853613 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 45.5747 | 2.24258 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.6743 | −0.671247 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.2816 | 0.601433 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.42461 | 0.362716 | 0.181358 | − | 0.983417i | \(-0.441951\pi\) | ||||
0.181358 | + | 0.983417i | \(0.441951\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3283 | 0.698318 | 0.349159 | − | 0.937064i | \(-0.386467\pi\) | ||||
0.349159 | + | 0.937064i | \(0.386467\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.64406 | −0.420288 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.2798 | −0.498643 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.86424 | −0.187003 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3212 | −1.07517 | −0.537586 | − | 0.843209i | \(-0.680664\pi\) | ||||
−0.537586 | + | 0.843209i | \(0.680664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −37.0848 | −1.78218 | −0.891092 | − | 0.453823i | \(-0.850060\pi\) | ||||
−0.891092 | + | 0.453823i | \(0.850060\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.35911 | −0.304896 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15.4164 | −0.737467 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.458627 | −0.0218891 | −0.0109445 | − | 0.999940i | \(-0.503484\pi\) | ||||
−0.0109445 | + | 0.999940i | \(0.503484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.7199 | 0.796184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.0996 | −0.669893 | −0.334947 | − | 0.942237i | \(-0.608718\pi\) | ||||
−0.334947 | + | 0.942237i | \(0.608718\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.80924 | 0.465003 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.37832 | 0.112491 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6386 | 0.879608 | 0.439804 | − | 0.898094i | \(-0.355048\pi\) | ||||
0.439804 | + | 0.898094i | \(0.355048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.31332 | 0.156018 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.80104 | 0.319541 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6100 | −0.589869 | −0.294934 | − | 0.955518i | \(-0.595298\pi\) | ||||
−0.294934 | + | 0.955518i | \(0.595298\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.47547 | 0.115545 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.05767 | 0.235559 | 0.117780 | − | 0.993040i | \(-0.462422\pi\) | ||||
0.117780 | + | 0.993040i | \(0.462422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.32946 | 0.154733 | 0.0773665 | − | 0.997003i | \(-0.475349\pi\) | ||||
0.0773665 | + | 0.997003i | \(0.475349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.24588 | 0.196898 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.4337 | 0.853009 | 0.426504 | − | 0.904486i | \(-0.359745\pi\) | ||||
0.426504 | + | 0.904486i | \(0.359745\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.0605 | −1.57277 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.8025 | −0.728140 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.71880 | −0.446871 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.9912 | −0.596078 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.841166 | 0.0385144 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.8641 | −1.41022 | −0.705108 | − | 0.709100i | \(-0.749102\pi\) | ||||
−0.705108 | + | 0.709100i | \(0.749102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.0003 | 1.09205 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.77800 | −0.398588 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.52808 | −0.0692438 | −0.0346219 | − | 0.999400i | \(-0.511023\pi\) | ||||
−0.0346219 | + | 0.999400i | \(0.511023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.66375 | 0.0752374 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −42.2011 | −1.90451 | −0.952254 | − | 0.305308i | \(-0.901241\pi\) | ||||
−0.952254 | + | 0.305308i | \(0.901241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.1011 | 0.770197 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.887946 | 0.0399102 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −75.6256 | −3.39227 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.73294 | −0.211875 | −0.105938 | − | 0.994373i | \(-0.533784\pi\) | ||||
−0.105938 | + | 0.994373i | \(0.533784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.04374 | 0.270014 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.83801 | 0.0819529 | 0.0409765 | − | 0.999160i | \(-0.486953\pi\) | ||||
0.0409765 | + | 0.999160i | \(0.486953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.8179 | −0.792887 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 39.7800 | 1.76322 | 0.881608 | − | 0.471982i | \(-0.156461\pi\) | ||||
0.881608 | + | 0.471982i | \(0.156461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.8905 | −1.23380 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.12841 | 0.138123 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.93028 | 0.437580 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.33826 | 0.366716 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.9425 | 0.480324 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.3812 | 0.805295 | 0.402648 | − | 0.915355i | \(-0.368090\pi\) | ||||
0.402648 | + | 0.915355i | \(0.368090\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9577 | 0.522874 | 0.261437 | − | 0.965221i | \(-0.415804\pi\) | ||||
0.261437 | + | 0.965221i | \(0.415804\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.2247 | 0.882679 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.4182 | −0.497384 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.28399 | 0.0558256 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.35767 | −0.406088 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.35055 | 0.101623 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.06741 | −0.0892153 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.1284 | −0.694699 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.9455 | 1.71739 | 0.858696 | − | 0.512485i | \(-0.171275\pi\) | ||||
0.858696 | + | 0.512485i | \(0.171275\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.10368 | −0.219020 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.2837 | −0.440504 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.0434 | −1.54110 | −0.770551 | − | 0.637378i | \(-0.780019\pi\) | ||||
−0.770551 | + | 0.637378i | \(0.780019\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.793428 | 0.0338627 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.6118 | 0.920694 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 67.5638 | 2.87310 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.43245 | −0.188147 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.2929 | 0.605611 | 0.302806 | − | 0.953052i | \(-0.402077\pi\) | ||||
0.302806 | + | 0.953052i | \(0.402077\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.38790 | −0.100817 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.32405 | −0.0558021 | −0.0279010 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0279010 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.1597 | −0.469492 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.87031 | −0.204534 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.3321 | 0.726598 | 0.363299 | − | 0.931673i | \(-0.381650\pi\) | ||||
0.363299 | + | 0.931673i | \(0.381650\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.6753 | −0.530446 | −0.265223 | − | 0.964187i | \(-0.585446\pi\) | ||||
−0.265223 | + | 0.964187i | \(0.585446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.862551 | 0.0360336 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.4638 | 0.853400 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.62372 | −0.234119 | −0.117059 | − | 0.993125i | \(-0.537347\pi\) | ||||
−0.117059 | + | 0.993125i | \(0.537347\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.55727 | −0.230952 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −72.3493 | −3.00155 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.811409 | −0.0336051 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.3576 | 0.798973 | 0.399487 | − | 0.916739i | \(-0.369188\pi\) | ||||
0.399487 | + | 0.916739i | \(0.369188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.4299 | −0.594573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.78884 | 0.279255 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.31980 | −0.136328 | −0.0681638 | − | 0.997674i | \(-0.521714\pi\) | ||||
−0.0681638 | + | 0.997674i | \(0.521714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.0979 | 0.454971 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.51699 | 0.307650 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.9233 | 0.528032 | 0.264016 | − | 0.964518i | \(-0.414953\pi\) | ||||
0.264016 | + | 0.964518i | \(0.414953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.5474 | 1.89871 | 0.949354 | − | 0.314208i | \(-0.101739\pi\) | ||||
0.949354 | + | 0.314208i | \(0.101739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.99350 | 0.284797 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.26908 | 0.376842 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.28623 | −0.214562 | −0.107281 | − | 0.994229i | \(-0.534214\pi\) | ||||
−0.107281 | + | 0.994229i | \(0.534214\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.6453 | −1.36338 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.9724 | −0.806678 | −0.403339 | − | 0.915051i | \(-0.632150\pi\) | ||||
−0.403339 | + | 0.915051i | \(0.632150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.16180 | 0.127496 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.8208 | −1.44209 | −0.721045 | − | 0.692888i | \(-0.756338\pi\) | ||||
−0.721045 | + | 0.692888i | \(0.756338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.1115 | 1.53183 | 0.765915 | − | 0.642942i | \(-0.222287\pi\) | ||||
0.765915 | + | 0.642942i | \(0.222287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.92788 | −0.197749 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.8995 | 2.07931 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.0079 | 0.520316 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.01774 | −0.120517 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.9199 | 0.475278 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.5675 | −0.460494 | −0.230247 | − | 0.973132i | \(-0.573953\pi\) | ||||
−0.230247 | + | 0.973132i | \(0.573953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.9780 | 0.635067 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.2950 | −0.726014 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.5279 | 0.614274 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.9802 | −1.22364 | −0.611822 | − | 0.790995i | \(-0.709563\pi\) | ||||
−0.611822 | + | 0.790995i | \(0.709563\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.04913 | 0.277991 | 0.138995 | − | 0.990293i | \(-0.455613\pi\) | ||||
0.138995 | + | 0.990293i | \(0.455613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.27435 | −0.365177 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.7204 | −0.618033 | −0.309016 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309016 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.02663 | 0.354326 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.4644 | 0.880451 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.6261 | 1.74635 | 0.873177 | − | 0.487403i | \(-0.162056\pi\) | ||||
0.873177 | + | 0.487403i | \(0.162056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.1924 | −0.632688 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.72664 | 0.223418 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.3994 | 1.26210 | 0.631050 | − | 0.775742i | \(-0.282624\pi\) | ||||
0.631050 | + | 0.775742i | \(0.282624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3068 | 1.64555 | 0.822773 | − | 0.568371i | \(-0.192426\pi\) | ||||
0.822773 | + | 0.568371i | \(0.192426\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.0252 | 0.543873 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.0430 | −1.31815 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.5641 | −1.02703 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.765359 | −0.0295464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3519 | 0.900150 | 0.450075 | − | 0.892991i | \(-0.351397\pi\) | ||||
0.450075 | + | 0.892991i | \(0.351397\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.15266 | −0.159836 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.86331 | −0.225345 | −0.112673 | − | 0.993632i | \(-0.535941\pi\) | ||||
−0.112673 | + | 0.993632i | \(0.535941\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −46.4433 | −1.78233 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.03932 | −0.346387 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7385 | 0.984857 | 0.492428 | − | 0.870353i | \(-0.336109\pi\) | ||||
0.492428 | + | 0.870353i | \(0.336109\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.9298 | −0.608647 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.5057 | −0.400817 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.7218 | 1.24479 | 0.622397 | − | 0.782701i | \(-0.286159\pi\) | ||||
0.622397 | + | 0.782701i | \(0.286159\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.69801 | 0.178463 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.3053 | −0.428836 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.50282 | −0.322067 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.7349 | −0.595150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.3888 | 1.41216 | 0.706078 | − | 0.708134i | \(-0.250463\pi\) | ||||
0.706078 | + | 0.708134i | \(0.250463\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.0640 | 0.568148 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.95694 | 0.299676 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −94.2724 | −3.54548 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.5069 | −0.770153 | −0.385076 | − | 0.922885i | \(-0.625825\pi\) | ||||
−0.385076 | + | 0.922885i | \(0.625825\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8726 | −0.520263 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.7300 | 0.851245 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.3360 | −0.684770 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.8237 | 0.888476 | 0.444238 | − | 0.895909i | \(-0.353475\pi\) | ||||
0.444238 | + | 0.895909i | \(0.353475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.5399 | 1.95669 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.01936 | 0.112291 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.6876 | −1.06543 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.65273 | 0.0612962 | 0.0306481 | − | 0.999530i | \(-0.490243\pi\) | ||||
0.0306481 | + | 0.999530i | \(0.490243\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.9409 | 0.922473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.0736 | −1.55402 | −0.777011 | − | 0.629486i | \(-0.783265\pi\) | ||||
−0.777011 | + | 0.629486i | \(0.783265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.3908 | −0.567699 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.74609 | −0.248496 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.0726 | 1.54766 | 0.773832 | − | 0.633391i | \(-0.218337\pi\) | ||||
0.773832 | + | 0.633391i | \(0.218337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.78602 | 0.359014 | 0.179507 | − | 0.983757i | \(-0.442550\pi\) | ||||
0.179507 | + | 0.983757i | \(0.442550\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.18927 | −0.0802086 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.8552 | 0.543523 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.4364 | 0.454418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.7737 | −0.940495 | −0.470247 | − | 0.882535i | \(-0.655835\pi\) | ||||
−0.470247 | + | 0.882535i | \(0.655835\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.3054 | 0.630644 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.26042 | −0.227840 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.6200 | −0.749446 | −0.374723 | − | 0.927137i | \(-0.622262\pi\) | ||||
−0.374723 | + | 0.927137i | \(0.622262\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.75355 | 0.172543 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.18524 | 0.187965 | 0.0939824 | − | 0.995574i | \(-0.470040\pi\) | ||||
0.0939824 | + | 0.995574i | \(0.470040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −54.4096 | −1.96976 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.27869 | −0.0823863 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.1989 | 1.62992 | 0.814958 | − | 0.579521i | \(-0.196760\pi\) | ||||
0.814958 | + | 0.579521i | \(0.196760\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.83635 | −0.246205 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.0422 | 0.433130 | 0.216565 | − | 0.976268i | \(-0.430515\pi\) | ||||
0.216565 | + | 0.976268i | \(0.430515\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.1543 | 0.688042 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.4516 | −0.841320 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.7456 | −0.385000 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9786 | −0.535976 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.90825 | 0.246881 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.5463 | 0.519181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.1313 | −1.43053 | −0.715264 | − | 0.698855i | \(-0.753693\pi\) | ||||
−0.715264 | + | 0.698855i | \(0.753693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.720029 | 0.0256337 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −59.0445 | −2.09938 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.774302 | −0.0274617 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.86591 | 0.314047 | 0.157023 | − | 0.987595i | \(-0.449810\pi\) | ||||
0.157023 | + | 0.987595i | \(0.449810\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.3981 | −0.757010 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.6563 | −0.376522 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.52405 | −0.194940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.0925 | −0.778658 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.1138 | 0.391225 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.3977 | −0.998411 | −0.499206 | − | 0.866484i | \(-0.666375\pi\) | ||||
−0.499206 | + | 0.866484i | \(0.666375\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.6373 | −0.865132 | −0.432566 | − | 0.901602i | \(-0.642392\pi\) | ||||
−0.432566 | + | 0.901602i | \(0.642392\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.3436 | 0.748554 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.53150 | −0.0536461 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.5194 | 1.10272 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.2417 | 0.462139 | 0.231070 | − | 0.972937i | \(-0.425777\pi\) | ||||
0.231070 | + | 0.972937i | \(0.425777\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4249 | 0.886257 | 0.443129 | − | 0.896458i | \(-0.353868\pi\) | ||||
0.443129 | + | 0.896458i | \(0.353868\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.00576 | 0.139462 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.5293 | −1.54844 | −0.774218 | − | 0.632920i | \(-0.781856\pi\) | ||||
−0.774218 | + | 0.632920i | \(0.781856\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.7843 | −1.10392 | −0.551958 | − | 0.833872i | \(-0.686119\pi\) | ||||
−0.551958 | + | 0.833872i | \(0.686119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.9693 | −0.588660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 41.3895 | 1.43406 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.56332 | −0.192527 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.61253 | −0.159432 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.0143 | 1.76121 | 0.880604 | − | 0.473853i | \(-0.157137\pi\) | ||||
0.880604 | + | 0.473853i | \(0.157137\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.7239 | 0.645651 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.9782 | 1.10139 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 49.0415 | 1.68509 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.7438 | −0.437366 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.7288 | −0.813413 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.34869 | −0.0461784 | −0.0230892 | − | 0.999733i | \(-0.507350\pi\) | ||||
−0.0230892 | + | 0.999733i | \(0.507350\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.87973 | −0.0984847 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.7695 | −0.846112 | −0.423056 | − | 0.906104i | \(-0.639043\pi\) | ||||
−0.423056 | + | 0.906104i | \(0.639043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.2069 | −1.33772 | −0.668861 | − | 0.743387i | \(-0.733218\pi\) | ||||
−0.668861 | + | 0.743387i | \(0.733218\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.7287 | 0.570112 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.70416 | 0.330333 | 0.165167 | − | 0.986266i | \(-0.447184\pi\) | ||||
0.165167 | + | 0.986266i | \(0.447184\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0727 | −0.342483 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.8721 | −0.369234 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.3818 | 0.453948 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.53602 | 0.322745 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.0329 | −1.38716 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.7250 | −1.67910 | −0.839548 | − | 0.543286i | \(-0.817180\pi\) | ||||
−0.839548 | + | 0.543286i | \(0.817180\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.9771 | −0.977375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.1672 | −0.746831 | −0.373416 | − | 0.927664i | \(-0.621813\pi\) | ||||
−0.373416 | + | 0.927664i | \(0.621813\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.2133 | −1.52155 | −0.760774 | − | 0.649016i | \(-0.775181\pi\) | ||||
−0.760774 | + | 0.649016i | \(0.775181\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.61383 | 0.289551 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.5752 | 1.53027 | 0.765133 | − | 0.643872i | \(-0.222673\pi\) | ||||
0.765133 | + | 0.643872i | \(0.222673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −96.7964 | −3.24645 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.964624 | −0.0323161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.0421 | −0.904930 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.90307 | 0.0636126 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.8645 | −1.06274 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.08228 | 0.0693708 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −49.0694 | −1.63293 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.69799 | 0.156166 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.0483 | 1.03094 | 0.515471 | − | 0.856907i | \(-0.327617\pi\) | ||||
0.515471 | + | 0.856907i | \(0.327617\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.3566 | 0.642017 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.2719 | 1.59932 | 0.799660 | − | 0.600454i | \(-0.205013\pi\) | ||||
0.799660 | + | 0.600454i | \(0.205013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.3297 | −0.474243 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.730358 | −0.0241449 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −85.6717 | −2.82913 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.4700 | −1.00511 | −0.502557 | − | 0.864544i | \(-0.667607\pi\) | ||||
−0.502557 | + | 0.864544i | \(0.667607\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.8992 | −0.754555 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.9960 | −0.657463 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.7878 | −0.354318 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.335144 | −0.0109957 | −0.00549787 | − | 0.999985i | \(-0.501750\pi\) | ||||
−0.00549787 | + | 0.999985i | \(0.501750\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 52.3066 | 1.71428 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.8141 | −1.10702 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.19808 | 0.0718850 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.6902 | −1.32929 | −0.664646 | − | 0.747158i | \(-0.731418\pi\) | ||||
−0.664646 | + | 0.747158i | \(0.731418\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.1846 | −0.364995 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.6192 | −1.48714 | −0.743572 | − | 0.668655i | \(-0.766870\pi\) | ||||
−0.743572 | + | 0.668655i | \(0.766870\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9264 | 0.551201 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.48317 | 0.145837 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.60704 | 0.312187 | 0.156093 | − | 0.987742i | \(-0.450110\pi\) | ||||
0.156093 | + | 0.987742i | \(0.450110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.4998 | 0.729607 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.36871 | −0.0767299 | −0.0383650 | − | 0.999264i | \(-0.512215\pi\) | ||||
−0.0383650 | + | 0.999264i | \(0.512215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.793986 | −0.0256928 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.66386 | −0.215412 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −84.2827 | −2.72163 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.72455 | −0.313695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.55352 | −0.0822862 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.11552 | 0.164674 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.08026 | −0.0347388 | −0.0173694 | − | 0.999849i | \(-0.505529\pi\) | ||||
−0.0173694 | + | 0.999849i | \(0.505529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.74427 | 0.248782 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.3056 | 0.876278 | 0.438139 | − | 0.898907i | \(-0.355638\pi\) | ||||
0.438139 | + | 0.898907i | \(0.355638\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.8152 | −1.91759 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.9136 | 0.765064 | 0.382532 | − | 0.923942i | \(-0.375052\pi\) | ||||
0.382532 | + | 0.923942i | \(0.375052\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.2793 | 0.328529 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.1717 | 0.356685 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.89131 | 0.283589 | 0.141794 | − | 0.989896i | \(-0.454713\pi\) | ||||
0.141794 | + | 0.989896i | \(0.454713\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.24919 | −0.199116 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 42.0992 | 1.34003 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −49.6495 | −1.57876 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.8568 | 0.694303 | 0.347152 | − | 0.937809i | \(-0.387149\pi\) | ||||
0.347152 | + | 0.937809i | \(0.387149\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.39583 | 0.266434 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.91947 | −0.219362 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.9135 | −1.23240 | −0.616202 | − | 0.787589i | \(-0.711329\pi\) | ||||
−0.616202 | + | 0.787589i | \(0.711329\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.81522 | 0.152347 |
(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 | 4056.2.a.bi.1.3 | yes | 6 | |
4.3 | odd | 2 | 8112.2.a.cu.1.3 | 6 | |||
13.5 | odd | 4 | 4056.2.c.r.337.7 | 12 | |||
13.8 | odd | 4 | 4056.2.c.r.337.6 | 12 | |||
13.12 | even | 2 | 4056.2.a.bh.1.4 | ✓ | 6 | ||
52.51 | odd | 2 | 8112.2.a.ct.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4056.2.a.bh.1.4 | ✓ | 6 | 13.12 | even | 2 | ||
4056.2.a.bi.1.3 | yes | 6 | 1.1 | even | 1 | trivial | |
4056.2.c.r.337.6 | 12 | 13.8 | odd | 4 | |||
4056.2.c.r.337.7 | 12 | 13.5 | odd | 4 | |||
8112.2.a.ct.1.4 | 6 | 52.51 | odd | 2 | |||
8112.2.a.cu.1.3 | 6 | 4.3 | odd | 2 |