Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.205225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1006) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.77799\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | 2.77799 | 1.60387 | 0.801937 | − | 0.597409i | \(-0.203803\pi\) | ||||
0.801937 | + | 0.597409i | \(0.203803\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.86114 | −1.27954 | −0.639771 | − | 0.768566i | \(-0.720971\pi\) | ||||
−0.639771 | + | 0.768566i | \(0.720971\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.41712 | −1.66952 | −0.834758 | − | 0.550618i | \(-0.814392\pi\) | ||||
−0.834758 | + | 0.550618i | \(0.814392\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.71723 | 1.57241 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.26928 | 1.58875 | 0.794374 | − | 0.607429i | \(-0.207799\pi\) | ||||
0.794374 | + | 0.607429i | \(0.207799\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.388086 | −0.107636 | −0.0538178 | − | 0.998551i | \(-0.517139\pi\) | ||||
−0.0538178 | + | 0.998551i | \(0.517139\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.94822 | −2.05222 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.44041 | 0.591886 | 0.295943 | − | 0.955206i | \(-0.404366\pi\) | ||||
0.295943 | + | 0.955206i | \(0.404366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.10049 | −1.17013 | −0.585066 | − | 0.810985i | \(-0.698932\pi\) | ||||
−0.585066 | + | 0.810985i | \(0.698932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.2707 | −2.67769 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.55115 | 1.15750 | 0.578748 | − | 0.815507i | \(-0.303542\pi\) | ||||
0.578748 | + | 0.815507i | \(0.303542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.18613 | 0.637226 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.77045 | 0.918073 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.70472 | −1.05934 | −0.529670 | − | 0.848204i | \(-0.677684\pi\) | ||||
−0.529670 | + | 0.848204i | \(0.677684\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.16125 | 1.28620 | 0.643099 | − | 0.765783i | \(-0.277648\pi\) | ||||
0.643099 | + | 0.765783i | \(0.277648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.6380 | 2.54815 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.6380 | 2.13621 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0188 | −1.64708 | −0.823539 | − | 0.567260i | \(-0.808003\pi\) | ||||
−0.823539 | + | 0.567260i | \(0.808003\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.07810 | −0.172634 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.949119 | 0.148227 | 0.0741137 | − | 0.997250i | \(-0.476387\pi\) | ||||
0.0741137 | + | 0.997250i | \(0.476387\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.06469 | 1.07736 | 0.538678 | − | 0.842512i | \(-0.318924\pi\) | ||||
0.538678 | + | 0.842512i | \(0.318924\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.4967 | −2.01196 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.52538 | 1.24355 | 0.621777 | − | 0.783194i | \(-0.286411\pi\) | ||||
0.621777 | + | 0.783194i | \(0.286411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.5110 | 1.78728 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.77943 | 0.949310 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.00665 | −0.550355 | −0.275178 | − | 0.961393i | \(-0.588737\pi\) | ||||
−0.275178 | + | 0.961393i | \(0.588737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.0762 | −2.03287 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −14.1691 | −1.87674 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.25587 | −1.20501 | −0.602506 | − | 0.798114i | \(-0.705831\pi\) | ||||
−0.602506 | + | 0.798114i | \(0.705831\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.57332 | −0.841627 | −0.420814 | − | 0.907147i | \(-0.638255\pi\) | ||||
−0.420814 | + | 0.907147i | \(0.638255\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −20.8366 | −2.62516 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.11037 | 0.137724 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6981 | −1.67349 | −0.836745 | − | 0.547593i | \(-0.815544\pi\) | ||||
−0.836745 | + | 0.547593i | \(0.815544\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.4211 | 1.85648 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.7319 | 1.74835 | 0.874175 | − | 0.485612i | \(-0.161403\pi\) | ||||
0.874175 | + | 0.485612i | \(0.161403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.383259 | 0.0448571 | 0.0224286 | − | 0.999748i | \(-0.492860\pi\) | ||||
0.0224286 | + | 0.999748i | \(0.492860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.85104 | 1.02203 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23.2751 | −2.65244 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00988 | 0.563655 | 0.281828 | − | 0.959465i | \(-0.409059\pi\) | ||||
0.281828 | + | 0.959465i | \(0.409059\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.899429 | −0.0999366 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.3761 | 1.13893 | 0.569464 | − | 0.822017i | \(-0.307151\pi\) | ||||
0.569464 | + | 0.822017i | \(0.307151\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.98235 | −0.757343 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.8477 | −1.69905 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8825 | 1.15354 | 0.576771 | − | 0.816906i | \(-0.304313\pi\) | ||||
0.576771 | + | 0.816906i | \(0.304313\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.71422 | 0.179699 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 19.8939 | 2.06290 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.5932 | 1.49723 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.81018 | −0.386865 | −0.193433 | − | 0.981114i | \(-0.561962\pi\) | ||||
−0.193433 | + | 0.981114i | \(0.561962\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.8564 | 2.49816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4917 | 1.24297 | 0.621485 | − | 0.783426i | \(-0.286530\pi\) | ||||
0.621485 | + | 0.783426i | \(0.286530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.6787 | 1.44634 | 0.723168 | − | 0.690672i | \(-0.242685\pi\) | ||||
0.723168 | + | 0.690672i | \(0.242685\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 35.1083 | 3.42622 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.98246 | 0.965041 | 0.482521 | − | 0.875885i | \(-0.339721\pi\) | ||||
0.482521 | + | 0.875885i | \(0.339721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.875847 | −0.0838909 | −0.0419454 | − | 0.999120i | \(-0.513356\pi\) | ||||
−0.0419454 | + | 0.999120i | \(0.513356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −27.8321 | −2.64170 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.23069 | 0.774278 | 0.387139 | − | 0.922021i | \(-0.373463\pi\) | ||||
0.387139 | + | 0.922021i | \(0.373463\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.8826 | −1.48106 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.83069 | −0.169247 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.7796 | −0.988163 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.7653 | 1.52412 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.63664 | 0.237738 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.18974 | 0.464184 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.99246 | 0.443009 | 0.221505 | − | 0.975159i | \(-0.428903\pi\) | ||||
0.221505 | + | 0.975159i | \(0.428903\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19.6256 | 1.72794 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.48542 | 0.654004 | 0.327002 | − | 0.945024i | \(-0.393962\pi\) | ||||
0.327002 | + | 0.945024i | \(0.393962\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22.5295 | 1.95355 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.6489 | −1.17471 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.3953 | 1.65705 | 0.828525 | − | 0.559952i | \(-0.189180\pi\) | ||||
0.828525 | + | 0.559952i | \(0.189180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.29884 | −0.110166 | −0.0550829 | − | 0.998482i | \(-0.517542\pi\) | ||||
−0.0550829 | + | 0.998482i | \(0.517542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.6834 | 1.99450 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.04493 | −0.171006 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3220 | 1.35547 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 34.7553 | 2.86657 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.7129 | −0.959560 | −0.479780 | − | 0.877389i | \(-0.659284\pi\) | ||||
−0.479780 | + | 0.877389i | \(0.659284\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8591 | −1.29060 | −0.645299 | − | 0.763930i | \(-0.723267\pi\) | ||||
−0.645299 | + | 0.763930i | \(0.723267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.5120 | 0.930688 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.4893 | −1.64574 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1874 | 1.05247 | 0.526236 | − | 0.850339i | \(-0.323603\pi\) | ||||
0.526236 | + | 0.850339i | \(0.323603\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.1304 | −0.882700 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.5201 | −1.93246 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.87472 | −0.773448 | −0.386724 | − | 0.922195i | \(-0.626393\pi\) | ||||
−0.386724 | + | 0.922195i | \(0.626393\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −41.8814 | −3.26046 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.78258 | 0.292705 | 0.146353 | − | 0.989232i | \(-0.453247\pi\) | ||||
0.146353 | + | 0.989232i | \(0.453247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8494 | −0.988415 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.0602 | −1.83993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.33969 | 0.177884 | 0.0889418 | − | 0.996037i | \(-0.471651\pi\) | ||||
0.0889418 | + | 0.996037i | \(0.471651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.0735 | −1.06386 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −25.7127 | −1.93269 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.8041 | 1.62971 | 0.814857 | − | 0.579662i | \(-0.196815\pi\) | ||||
0.814857 | + | 0.579662i | \(0.196815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1966 | 1.05522 | 0.527611 | − | 0.849486i | \(-0.323088\pi\) | ||||
0.527611 | + | 0.849486i | \(0.323088\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.2606 | −1.34986 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 28.6651 | 2.10750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.8592 | 0.940358 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.0717 | −1.53274 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.8117 | 1.43352 | 0.716762 | − | 0.697318i | \(-0.245623\pi\) | ||||
0.716762 | + | 0.697318i | \(0.245623\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9356 | 1.07509 | 0.537545 | − | 0.843235i | \(-0.319352\pi\) | ||||
0.537545 | + | 0.843235i | \(0.319352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.08459 | 0.220892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.14044 | 0.651230 | 0.325615 | − | 0.945502i | \(-0.394429\pi\) | ||||
0.325615 | + | 0.945502i | \(0.394429\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.183873 | 0.0130344 | 0.00651721 | − | 0.999979i | \(-0.497925\pi\) | ||||
0.00651721 | + | 0.999979i | \(0.497925\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −38.0532 | −2.68406 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 25.1984 | 1.76858 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.71556 | −0.189663 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 26.1861 | 1.82006 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.8759 | −1.85905 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.70810 | 0.324119 | 0.162059 | − | 0.986781i | \(-0.448186\pi\) | ||||
0.162059 | + | 0.986781i | \(0.448186\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40.9249 | 2.80413 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.2131 | −1.37852 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −31.6321 | −2.14733 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.06469 | 0.0719451 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.947088 | −0.0637080 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.74679 | 0.384833 | 0.192417 | − | 0.981313i | \(-0.438368\pi\) | ||||
0.192417 | + | 0.981313i | \(0.438368\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0297 | 1.00198 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.1278 | −1.40230 | −0.701151 | − | 0.713013i | \(-0.747330\pi\) | ||||
−0.701151 | + | 0.713013i | \(0.747330\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.39276 | −0.0920362 | −0.0460181 | − | 0.998941i | \(-0.514653\pi\) | ||||
−0.0460181 | + | 0.998941i | \(0.514653\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −64.6579 | −4.25418 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3430 | 0.808619 | 0.404310 | − | 0.914622i | \(-0.367512\pi\) | ||||
0.404310 | + | 0.914622i | \(0.367512\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.3923 | −1.59118 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.9174 | 0.904032 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.52471 | 0.486733 | 0.243367 | − | 0.969934i | \(-0.421748\pi\) | ||||
0.243367 | + | 0.969934i | \(0.421748\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.0844 | −1.93791 | −0.968953 | − | 0.247246i | \(-0.920474\pi\) | ||||
−0.968953 | + | 0.247246i | \(0.920474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.8100 | −1.07836 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −35.7956 | −2.28690 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.97943 | 0.125948 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 28.8248 | 1.82669 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7443 | 0.804413 | 0.402206 | − | 0.915549i | \(-0.368243\pi\) | ||||
0.402206 | + | 0.915549i | \(0.368243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.2506 | 1.83897 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.3969 | −1.21468 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.35968 | 0.396706 | 0.198353 | − | 0.980131i | \(-0.436441\pi\) | ||||
0.198353 | + | 0.980131i | \(0.436441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 44.2542 | 2.74982 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.9105 | −1.66572 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.38358 | −0.331966 | −0.165983 | − | 0.986129i | \(-0.553080\pi\) | ||||
−0.165983 | + | 0.986129i | \(0.553080\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.4636 | 0.704202 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.2315 | 1.85014 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.7333 | 1.08122 | 0.540609 | − | 0.841274i | \(-0.318194\pi\) | ||||
0.540609 | + | 0.841274i | \(0.318194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.7268 | 1.25906 | 0.629530 | − | 0.776976i | \(-0.283247\pi\) | ||||
0.629530 | + | 0.776976i | \(0.283247\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.76209 | 0.288215 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.7886 | 1.01239 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.7280 | −1.36559 | −0.682797 | − | 0.730608i | \(-0.739237\pi\) | ||||
−0.682797 | + | 0.730608i | \(0.739237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 33.7813 | 2.02243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.5814 | −0.989162 | −0.494581 | − | 0.869131i | \(-0.664679\pi\) | ||||
−0.494581 | + | 0.869131i | \(0.664679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.6737 | 1.05059 | 0.525296 | − | 0.850920i | \(-0.323955\pi\) | ||||
0.525296 | + | 0.850920i | \(0.323955\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40.5398 | 2.40137 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.19237 | −0.247468 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0444 | −0.649671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.5846 | −0.620483 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.55216 | 0.382781 | 0.191391 | − | 0.981514i | \(-0.438700\pi\) | ||||
0.191391 | + | 0.981514i | \(0.438700\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.4824 | 1.54186 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25.1368 | 1.45859 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.15432 | −0.124588 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.2056 | −1.79866 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.7018 | 1.99357 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.8072 | 1.07690 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.89018 | −0.336170 | −0.168085 | − | 0.985772i | \(-0.553758\pi\) | ||||
−0.168085 | + | 0.985772i | \(0.553758\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 40.7773 | 2.31974 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.5605 | −1.10917 | −0.554586 | − | 0.832126i | \(-0.687123\pi\) | ||||
−0.554586 | + | 0.832126i | \(0.687123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.25925 | 0.410317 | 0.205159 | − | 0.978729i | \(-0.434229\pi\) | ||||
0.205159 | + | 0.978729i | \(0.434229\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 59.6164 | 3.35900 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4711 | 1.26210 | 0.631051 | − | 0.775741i | \(-0.282624\pi\) | ||||
0.631051 | + | 0.775741i | \(0.282624\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.0598 | −1.68302 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.7312 | 1.54780 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.4473 | −0.692585 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.23649 | −0.0685882 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.43309 | −0.134550 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.6576 | −2.07613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.4449 | 1.50851 | 0.754254 | − | 0.656582i | \(-0.227999\pi\) | ||||
0.754254 | + | 0.656582i | \(0.227999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −47.2609 | −2.58988 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 39.1922 | 2.14130 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.1727 | 1.48019 | 0.740096 | − | 0.672501i | \(-0.234780\pi\) | ||||
0.740096 | + | 0.672501i | \(0.234780\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.8648 | 1.24184 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.7346 | 2.04344 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −24.3426 | −1.31438 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −44.1218 | −2.37544 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.69471 | −0.520440 | −0.260220 | − | 0.965549i | \(-0.583795\pi\) | ||||
−0.260220 | + | 0.965549i | \(0.583795\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.5404 | −1.79538 | −0.897689 | − | 0.440630i | \(-0.854755\pi\) | ||||
−0.897689 | + | 0.440630i | \(0.854755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.85134 | −0.0988174 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0918 | −0.643579 | −0.321790 | − | 0.946811i | \(-0.604284\pi\) | ||||
−0.321790 | + | 0.946811i | \(0.604284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42.1499 | −2.23709 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −29.9456 | −1.58489 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.38635 | 0.231503 | 0.115751 | − | 0.993278i | \(-0.463072\pi\) | ||||
0.115751 | + | 0.993278i | \(0.463072\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.01499 | 0.369210 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 46.5739 | 2.44450 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.09656 | −0.0573965 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5437 | −0.967974 | −0.483987 | − | 0.875075i | \(-0.660812\pi\) | ||||
−0.483987 | + | 0.875075i | \(0.660812\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.47721 | 0.233074 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 17.6978 | 0.918826 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.2488 | −1.51444 | −0.757222 | − | 0.653158i | \(-0.773444\pi\) | ||||
−0.757222 | + | 0.653158i | \(0.773444\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.4170 | 0.744493 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.21392 | 0.114023 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.10977 | −0.0570048 | −0.0285024 | − | 0.999594i | \(-0.509074\pi\) | ||||
−0.0285024 | + | 0.999594i | \(0.509074\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.8690 | 0.710531 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.22623 | −0.369243 | −0.184621 | − | 0.982810i | \(-0.559106\pi\) | ||||
−0.184621 | + | 0.982810i | \(0.559106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 66.5932 | 3.39390 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 33.3258 | 1.69404 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.4907 | −0.886814 | −0.443407 | − | 0.896320i | \(-0.646230\pi\) | ||||
−0.443407 | + | 0.896320i | \(0.646230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5471 | 0.685106 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.7944 | 1.04894 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.3340 | −0.721220 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8378 | −0.543933 | −0.271966 | − | 0.962307i | \(-0.587674\pi\) | ||||
−0.271966 | + | 0.962307i | \(0.587674\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 62.5867 | 3.13325 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.2985 | 1.36322 | 0.681611 | − | 0.731715i | \(-0.261280\pi\) | ||||
0.681611 | + | 0.731715i | \(0.261280\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.77918 | −0.138441 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.57339 | 0.127873 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −52.7918 | −2.61679 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.5561 | 1.01643 | 0.508217 | − | 0.861229i | \(-0.330305\pi\) | ||||
0.508217 | + | 0.861229i | \(0.330305\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 53.8799 | 2.65770 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.8843 | 2.01179 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.6875 | −1.45730 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.60815 | −0.176692 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.7529 | −1.01384 | −0.506922 | − | 0.861992i | \(-0.669217\pi\) | ||||
−0.506922 | + | 0.861992i | \(0.669217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.8137 | 1.35556 | 0.677780 | − | 0.735265i | \(-0.262942\pi\) | ||||
0.677780 | + | 0.735265i | \(0.262942\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 40.2162 | 1.95538 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.77546 | 0.377165 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 29.0352 | 1.40511 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.68080 | −0.274272 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.07019 | 0.340559 | 0.170280 | − | 0.985396i | \(-0.445533\pi\) | ||||
0.170280 | + | 0.985396i | \(0.445533\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.2977 | −1.35990 | −0.679949 | − | 0.733259i | \(-0.737998\pi\) | ||||
−0.679949 | + | 0.733259i | \(0.737998\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 45.3424 | 2.17400 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.3136 | −1.35442 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.2043 | 0.582479 | 0.291240 | − | 0.956650i | \(-0.405932\pi\) | ||||
0.291240 | + | 0.956650i | \(0.405932\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 59.0171 | 2.81034 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.6611 | 0.886614 | 0.443307 | − | 0.896370i | \(-0.353805\pi\) | ||||
0.443307 | + | 0.896370i | \(0.353805\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.1363 | −1.47600 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.5384 | −1.53901 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.3463 | 1.47932 | 0.739661 | − | 0.672979i | \(-0.234986\pi\) | ||||
0.739661 | + | 0.672979i | \(0.234986\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.00117 | 0.235496 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −44.0565 | −2.06995 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.90463 | −0.229933 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5025 | 0.959068 | 0.479534 | − | 0.877523i | \(-0.340806\pi\) | ||||
0.479534 | + | 0.877523i | \(0.340806\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.6418 | 0.543395 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.9423 | 1.34798 | 0.673990 | − | 0.738741i | \(-0.264579\pi\) | ||||
0.673990 | + | 0.738741i | \(0.264579\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.51527 | −0.0704208 | −0.0352104 | − | 0.999380i | \(-0.511210\pi\) | ||||
−0.0352104 | + | 0.999380i | \(0.511210\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −56.9192 | −2.63957 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.6493 | −1.41828 | −0.709139 | − | 0.705068i | \(-0.750916\pi\) | ||||
−0.709139 | + | 0.705068i | \(0.750916\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 60.5062 | 2.79392 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 36.6345 | 1.68803 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.2258 | 1.71165 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.2508 | −0.745639 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.9003 | −0.865384 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6034 | 1.03278 | 0.516388 | − | 0.856355i | \(-0.327276\pi\) | ||||
0.516388 | + | 0.856355i | \(0.327276\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.88815 | 0.177284 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −68.1167 | −3.09942 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.9015 | 0.495010 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.04914 | 0.274113 | 0.137056 | − | 0.990563i | \(-0.456236\pi\) | ||||
0.137056 | + | 0.990563i | \(0.456236\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −27.4319 | −1.24051 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.1868 | 1.00127 | 0.500637 | − | 0.865657i | \(-0.333099\pi\) | ||||
0.500637 | + | 0.865657i | \(0.333099\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.9218 | −0.627008 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −71.1177 | −3.19650 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −65.0724 | −2.91890 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.0030 | −1.38789 | −0.693943 | − | 0.720030i | \(-0.744128\pi\) | ||||
−0.693943 | + | 0.720030i | \(0.744128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.5080 | 0.469462 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.7405 | −1.59043 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.6955 | −1.58529 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.8647 | −0.969137 | −0.484569 | − | 0.874753i | \(-0.661023\pi\) | ||||
−0.484569 | + | 0.874753i | \(0.661023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.69290 | −0.0748896 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.3316 | −1.07427 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −41.9979 | −1.85065 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.9226 | 1.97569 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.49965 | 0.285303 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.92786 | −0.0844612 | −0.0422306 | − | 0.999108i | \(-0.513446\pi\) | ||||
−0.0422306 | + | 0.999108i | \(0.513446\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0191 | −0.831646 | −0.415823 | − | 0.909446i | \(-0.636506\pi\) | ||||
−0.415823 | + | 0.909446i | \(0.636506\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −39.0961 | −1.70629 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.4764 | 0.761283 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.81531 | 0.339796 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −43.6621 | −1.89477 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.368340 | −0.0159546 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.5612 | −1.23481 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 60.5715 | 2.61385 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 65.9238 | 2.83954 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.2620 | −1.08610 | −0.543049 | − | 0.839701i | \(-0.682730\pi\) | ||||
−0.543049 | + | 0.839701i | \(0.682730\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 39.4379 | 1.69244 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.50592 | 0.107342 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8303 | 0.676853 | 0.338427 | − | 0.940993i | \(-0.390105\pi\) | ||||
0.338427 | + | 0.940993i | \(0.390105\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.0079 | −1.32338 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.0969 | 1.23957 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.1292 | −0.941031 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 79.6315 | 3.38017 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.1472 | −0.938409 | −0.469204 | − | 0.883090i | \(-0.655459\pi\) | ||||
−0.469204 | + | 0.883090i | \(0.655459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.74171 | −0.115962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.7227 | 1.50821 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.30504 | −0.392161 | −0.196080 | − | 0.980588i | \(-0.562821\pi\) | ||||
−0.196080 | + | 0.980588i | \(0.562821\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.5492 | −0.990720 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.97289 | 0.166846 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.92502 | 0.206467 | 0.103234 | − | 0.994657i | \(-0.467081\pi\) | ||||
0.103234 | + | 0.994657i | \(0.467081\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.2749 | −0.722932 | −0.361466 | − | 0.932385i | \(-0.617724\pi\) | ||||
−0.361466 | + | 0.932385i | \(0.617724\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 55.0367 | 2.29919 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.6867 | 0.737586 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.9915 | 1.41509 | 0.707543 | − | 0.706671i | \(-0.249804\pi\) | ||||
0.707543 | + | 0.706671i | \(0.249804\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 41.4910 | 1.72431 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −45.8326 | −1.90146 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.1121 | −0.874375 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.23786 | 0.216559 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.4528 | −0.885451 | −0.442726 | − | 0.896657i | \(-0.645988\pi\) | ||||
−0.442726 | + | 0.896657i | \(0.645988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.5259 | −1.50502 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.3921 | 1.04449 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.9293 | −0.448815 | −0.224407 | − | 0.974495i | \(-0.572045\pi\) | ||||
−0.224407 | + | 0.974495i | \(0.572045\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.8419 | 1.26440 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.510798 | 0.0209056 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.0120 | −1.38969 | −0.694847 | − | 0.719158i | \(-0.744528\pi\) | ||||
−0.694847 | + | 0.719158i | \(0.744528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.6512 | 0.638425 | 0.319213 | − | 0.947683i | \(-0.396582\pi\) | ||||
0.319213 | + | 0.947683i | \(0.396582\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −64.6171 | −2.63141 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −47.9679 | −1.95017 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.42603 | 0.220236 | 0.110118 | − | 0.993919i | \(-0.464877\pi\) | ||||
0.110118 | + | 0.993919i | \(0.464877\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 70.0010 | 2.83658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.30858 | −0.133851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.8043 | 0.476771 | 0.238385 | − | 0.971171i | \(-0.423382\pi\) | ||||
0.238385 | + | 0.971171i | \(0.423382\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.54381 | −0.304196 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0439 | −0.887454 | −0.443727 | − | 0.896162i | \(-0.646344\pi\) | ||||
−0.443727 | + | 0.896162i | \(0.646344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.88761 | 0.156256 | 0.0781282 | − | 0.996943i | \(-0.475106\pi\) | ||||
0.0781282 | + | 0.996943i | \(0.475106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 26.4815 | 1.06267 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −48.0693 | −1.92586 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7792 | −1.23117 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −74.6610 | −2.98167 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.4499 | −0.974882 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.4500 | −1.68991 | −0.844953 | − | 0.534841i | \(-0.820372\pi\) | ||||
−0.844953 | + | 0.534841i | \(0.820372\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0790 | 0.519845 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.2841 | −0.566848 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.85533 | −0.192375 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 69.4935 | 2.74912 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.7521 | −0.780161 | −0.390080 | − | 0.920781i | \(-0.627553\pi\) | ||||
−0.390080 | + | 0.920781i | \(0.627553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.8338 | −1.25540 | −0.627701 | − | 0.778455i | \(-0.716004\pi\) | ||||
−0.627701 | + | 0.778455i | \(0.716004\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −56.1517 | −2.21097 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.56968 | 0.101024 | 0.0505122 | − | 0.998723i | \(-0.483915\pi\) | ||||
0.0505122 | + | 0.998723i | \(0.483915\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.7718 | −1.91446 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −87.8737 | −3.44404 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.4354 | 1.89543 | 0.947713 | − | 0.319125i | \(-0.103389\pi\) | ||||
0.947713 | + | 0.319125i | \(0.103389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.4169 | −0.836826 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.80792 | 0.0705338 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2938 | 0.751580 | 0.375790 | − | 0.926705i | \(-0.377371\pi\) | ||||
0.375790 | + | 0.926705i | \(0.377371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.6053 | 1.07372 | 0.536861 | − | 0.843671i | \(-0.319610\pi\) | ||||
0.536861 | + | 0.843671i | \(0.319610\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.63100 | −0.102180 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −64.4600 | −2.49965 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.6678 | −1.22618 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.9645 | 0.617224 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.6367 | −1.33713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.1806 | −0.469528 | −0.234764 | − | 0.972052i | \(-0.575432\pi\) | ||||
−0.234764 | + | 0.972052i | \(0.575432\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.1993 | 0.585020 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.3761 | 1.16745 | 0.583723 | − | 0.811953i | \(-0.301595\pi\) | ||||
0.583723 | + | 0.811953i | \(0.301595\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8300 | 0.645877 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −58.6928 | −2.24911 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.65487 | 0.331169 | 0.165585 | − | 0.986196i | \(-0.447049\pi\) | ||||
0.165585 | + | 0.986196i | \(0.447049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.4926 | −2.12026 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.86908 | −0.147614 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.55492 | 0.0592378 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.6457 | −0.747359 | −0.373679 | − | 0.927558i | \(-0.621904\pi\) | ||||
−0.373679 | + | 0.927558i | \(0.621904\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −109.794 | −4.17072 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.71615 | 0.140962 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.31624 | 0.0877338 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 34.2888 | 1.29692 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6055 | −0.476104 | −0.238052 | − | 0.971252i | \(-0.576509\pi\) | ||||
−0.238052 | + | 0.971252i | \(0.576509\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.1007 | 1.92730 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −67.7616 | −2.55205 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −55.1773 | −2.07516 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.8692 | 1.27199 | 0.635993 | − | 0.771695i | \(-0.280591\pi\) | ||||
0.635993 | + | 0.771695i | \(0.280591\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.6328 | 0.886297 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.7532 | 1.48877 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.85084 | 0.218809 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.9036 | 0.780659 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.9061 | −0.742372 | −0.371186 | − | 0.928559i | \(-0.621049\pi\) | ||||
−0.371186 | + | 0.928559i | \(0.621049\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −64.8377 | −2.41468 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −83.5741 | −3.10815 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −18.1760 | −0.675039 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.0664 | 1.78268 | 0.891342 | − | 0.453331i | \(-0.149764\pi\) | ||||
0.891342 | + | 0.453331i | \(0.149764\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.9996 | −1.62961 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.2407 | 0.637672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7845 | −0.804629 | −0.402314 | − | 0.915502i | \(-0.631794\pi\) | ||||
−0.402314 | + | 0.915502i | \(0.631794\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −99.4399 | −3.66790 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −72.1791 | −2.65875 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.4145 | −1.78096 | −0.890479 | − | 0.455024i | \(-0.849631\pi\) | ||||
−0.890479 | + | 0.455024i | \(0.849631\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.49883 | 0.202005 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.3436 | −1.29663 | −0.648316 | − | 0.761372i | \(-0.724526\pi\) | ||||
−0.648316 | + | 0.761372i | \(0.724526\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.5123 | 1.22780 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 48.9465 | 1.79086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −44.0938 | −1.61115 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.51093 | 0.164606 | 0.0823031 | − | 0.996607i | \(-0.473772\pi\) | ||||
0.0823031 | + | 0.996607i | \(0.473772\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 35.4035 | 1.29018 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45.3752 | 1.65137 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.09638 | 0.221577 | 0.110788 | − | 0.993844i | \(-0.464662\pi\) | ||||
0.110788 | + | 0.993844i | \(0.464662\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 81.2578 | 2.94947 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.2423 | −0.371284 | −0.185642 | − | 0.982617i | \(-0.559436\pi\) | ||||
−0.185642 | + | 0.982617i | \(0.559436\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.86872 | 0.140057 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.9374 | −1.19085 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.59207 | 0.129702 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.5975 | −0.959129 | −0.479565 | − | 0.877507i | \(-0.659205\pi\) | ||||
−0.479565 | + | 0.877507i | \(0.659205\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6671 | 0.636266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.6278 | −0.669995 | −0.334997 | − | 0.942219i | \(-0.608735\pi\) | ||||
−0.334997 | + | 0.942219i | \(0.608735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.8167 | 0.819599 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 122.938 | 4.41036 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.84097 | −0.173446 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 77.6263 | 2.77769 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27.2141 | −0.972551 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.7311 | −1.34668 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.7361 | 0.418347 | 0.209174 | − | 0.977879i | \(-0.432923\pi\) | ||||
0.209174 | + | 0.977879i | \(0.432923\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.9555 | −0.532431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.3559 | −1.29267 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.55101 | 0.0905891 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 31.8457 | 1.12945 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.1954 | −0.892468 | −0.446234 | − | 0.894916i | \(-0.647235\pi\) | ||||
−0.446234 | + | 0.894916i | \(0.647235\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.8054 | 0.736042 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 51.3352 | 1.81384 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.01950 | 0.0712666 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 70.1555 | 2.47266 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 49.2629 | 1.73414 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.8088 | −1.18866 | −0.594328 | − | 0.804223i | \(-0.702582\pi\) | ||||
−0.594328 | + | 0.804223i | \(0.702582\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.7547 | 1.71201 | 0.856005 | − | 0.516967i | \(-0.172939\pi\) | ||||
0.856005 | + | 0.516967i | \(0.172939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 57.5787 | 2.01937 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.2530 | 0.989659 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.0334 | −1.26065 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.08638 | 0.282561 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −56.3460 | −1.96649 | −0.983244 | − | 0.182295i | \(-0.941647\pi\) | ||||
−0.983244 | + | 0.182295i | \(0.941647\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.9547 | 1.18359 | 0.591793 | − | 0.806090i | \(-0.298420\pi\) | ||||
0.591793 | + | 0.806090i | \(0.298420\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 46.6386 | 1.62375 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.1900 | −1.01504 | −0.507518 | − | 0.861641i | \(-0.669437\pi\) | ||||
−0.507518 | + | 0.861641i | \(0.669437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.84344 | 0.168220 | 0.0841098 | − | 0.996456i | \(-0.473195\pi\) | ||||
0.0841098 | + | 0.996456i | \(0.473195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −63.1382 | −2.19024 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.5319 | 1.05787 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.8225 | −0.374528 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.1624 | 1.18082 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 51.8249 | 1.78919 | 0.894596 | − | 0.446875i | \(-0.147463\pi\) | ||||
0.894596 | + | 0.446875i | \(0.147463\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.54381 | 0.122200 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −46.0629 | −1.58649 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.7639 | 1.26472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −74.0544 | −2.54454 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 49.0973 | 1.68502 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.6158 | −1.90648 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.3479 | 1.00485 | 0.502427 | − | 0.864620i | \(-0.332441\pi\) | ||||
0.502427 | + | 0.864620i | \(0.332441\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 68.8396 | 2.35426 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.5484 | 0.736080 | 0.368040 | − | 0.929810i | \(-0.380029\pi\) | ||||
0.368040 | + | 0.929810i | \(0.380029\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.3226 | −0.693399 | −0.346700 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346700 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6464 | −0.396907 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.9037 | 1.56258 | 0.781291 | − | 0.624167i | \(-0.214562\pi\) | ||||
0.781291 | + | 0.624167i | \(0.214562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.69419 | −0.227609 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.6813 | −1.04199 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.3985 | 0.895506 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.31604 | 0.180127 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.9735 | −0.608311 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.9237 | −0.774963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.3822 | 1.59998 | 0.799992 | − | 0.600011i | \(-0.204837\pi\) | ||||
0.799992 | + | 0.600011i | \(0.204837\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.2018 | 0.613933 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.1715 | 1.18496 | 0.592479 | − | 0.805586i | \(-0.298149\pi\) | ||||
0.592479 | + | 0.805586i | \(0.298149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8095 | 0.632990 | 0.316495 | − | 0.948594i | \(-0.397494\pi\) | ||||
0.316495 | + | 0.948594i | \(0.397494\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 73.5677 | 2.47295 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.2215 | −1.41766 | −0.708830 | − | 0.705380i | \(-0.750776\pi\) | ||||
−0.708830 | + | 0.705380i | \(0.750776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.0523 | −0.739610 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.73934 | −0.158774 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.4836 | −1.45512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −62.3846 | −2.08529 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.98469 | −0.199823 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −40.8529 | −1.36252 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.77785 | −0.325747 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −86.6889 | −2.88482 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.6183 | −1.35020 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.13790 | 0.270214 | 0.135107 | − | 0.990831i | \(-0.456862\pi\) | ||||
0.135107 | + | 0.990831i | \(0.456862\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 58.9262 | 1.95446 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.335989 | −0.0111318 | −0.00556590 | − | 0.999985i | \(-0.501772\pi\) | ||||
−0.00556590 | + | 0.999985i | \(0.501772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.6747 | 1.80947 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 52.2462 | 1.72721 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.0640 | −1.09187 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.3906 | −1.33236 | −0.666182 | − | 0.745789i | \(-0.732073\pi\) | ||||
−0.666182 | + | 0.745789i | \(0.732073\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.3629 | −0.539174 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.71722 | −0.188185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.9211 | −1.04956 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 69.2429 | 2.27423 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.6253 | −0.873548 | −0.436774 | − | 0.899571i | \(-0.643879\pi\) | ||||
−0.436774 | + | 0.899571i | \(0.643879\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −63.8121 | −2.09136 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −54.3388 | −1.77897 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36.7920 | −1.20323 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.7576 | 0.351436 | 0.175718 | − | 0.984441i | \(-0.443775\pi\) | ||||
0.175718 | + | 0.984441i | \(0.443775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.1661 | 0.658097 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.3237 | −1.51011 | −0.755055 | − | 0.655662i | \(-0.772390\pi\) | ||||
−0.755055 | + | 0.655662i | \(0.772390\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.26870 | 0.171573 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 60.2890 | 1.96120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.0484 | −0.813962 | −0.406981 | − | 0.913437i | \(-0.633419\pi\) | ||||
−0.406981 | + | 0.913437i | \(0.633419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.148738 | −0.00482822 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 62.4245 | 2.02425 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.0611 | −0.649843 | −0.324921 | − | 0.945741i | \(-0.605338\pi\) | ||||
−0.324921 | + | 0.945741i | \(0.605338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −56.6841 | −1.83425 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −83.5057 | −2.69936 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −85.6713 | −2.76647 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.2835 | 0.654306 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 47.0896 | 1.51744 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.7329 | −1.37562 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.1889 | 0.713547 | 0.356773 | − | 0.934191i | \(-0.383877\pi\) | ||||
0.356773 | + | 0.934191i | \(0.383877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34.5784 | −1.11082 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 29.7101 | 0.953443 | 0.476721 | − | 0.879054i | \(-0.341825\pi\) | ||||
0.476721 | + | 0.879054i | \(0.341825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.73711 | 0.183923 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.43496 | −0.110007 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7076 | 0.502530 | 0.251265 | − | 0.967918i | \(-0.419153\pi\) | ||||
0.251265 | + | 0.967918i | \(0.419153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57.3429 | 1.83269 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.13157 | −0.131911 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −15.1215 | −0.482301 | −0.241150 | − | 0.970488i | \(-0.577525\pi\) | ||||
−0.241150 | + | 0.970488i | \(0.577525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.1521 | −0.833275 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −104.613 | −3.32985 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 39.2172 | 1.24703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.7879 | −1.86746 | −0.933730 | − | 0.357979i | \(-0.883466\pi\) | ||||
−0.933730 | + | 0.357979i | \(0.883466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 76.2417 | 2.41946 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.526087 | −0.0166781 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.4219 | 0.805120 | 0.402560 | − | 0.915394i | \(-0.368120\pi\) | ||||
0.402560 | + | 0.915394i | \(0.368120\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −47.7941 | −1.51214 |
(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 | 8048.2.a.o.1.5 | 5 | ||
4.3 | odd | 2 | 1006.2.a.h.1.1 | ✓ | 5 | ||
12.11 | even | 2 | 9054.2.a.ba.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1006.2.a.h.1.1 | ✓ | 5 | 4.3 | odd | 2 | ||
8048.2.a.o.1.5 | 5 | 1.1 | even | 1 | trivial | ||
9054.2.a.ba.1.5 | 5 | 12.11 | even | 2 |