Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, 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("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(5\) | 1.66086 | 0.742759 | 0.371380 | − | 0.928481i | \(-0.378885\pi\) | ||||
0.371380 | + | 0.928481i | \(0.378885\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.19144 | −0.828287 | −0.414144 | − | 0.910212i | \(-0.635919\pi\) | ||||
−0.414144 | + | 0.910212i | \(0.635919\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.33796 | −1.60946 | −0.804728 | − | 0.593643i | \(-0.797689\pi\) | ||||
−0.804728 | + | 0.593643i | \(0.797689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.06619 | 0.573058 | 0.286529 | − | 0.958072i | \(-0.407498\pi\) | ||||
0.286529 | + | 0.958072i | \(0.407498\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.66086 | −0.428832 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.14459 | 0.762675 | 0.381337 | − | 0.924436i | \(-0.375464\pi\) | ||||
0.381337 | + | 0.924436i | \(0.375464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.10656 | −1.40094 | −0.700470 | − | 0.713681i | \(-0.747026\pi\) | ||||
−0.700470 | + | 0.713681i | \(0.747026\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.19144 | 0.478212 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.59981 | 1.37616 | 0.688078 | − | 0.725637i | \(-0.258455\pi\) | ||||
0.688078 | + | 0.725637i | \(0.258455\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.24154 | −0.448309 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.96547 | 1.66485 | 0.832423 | − | 0.554141i | \(-0.186953\pi\) | ||||
0.832423 | + | 0.554141i | \(0.186953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.89365 | −1.23814 | −0.619068 | − | 0.785337i | \(-0.712490\pi\) | ||||
−0.619068 | + | 0.785337i | \(0.712490\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.33796 | 0.929220 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.63968 | −0.615218 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.91614 | −0.808208 | −0.404104 | − | 0.914713i | \(-0.632417\pi\) | ||||
−0.404104 | + | 0.914713i | \(0.632417\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.06619 | −0.330855 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.27622 | 0.824007 | 0.412004 | − | 0.911182i | \(-0.364829\pi\) | ||||
0.412004 | + | 0.911182i | \(0.364829\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.91190 | 0.749058 | 0.374529 | − | 0.927215i | \(-0.377804\pi\) | ||||
0.374529 | + | 0.927215i | \(0.377804\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.66086 | 0.247586 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.585390 | 0.0853879 | 0.0426939 | − | 0.999088i | \(-0.486406\pi\) | ||||
0.0426939 | + | 0.999088i | \(0.486406\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.19758 | −0.313940 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.14459 | −0.440330 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.07199 | −1.24613 | −0.623067 | − | 0.782169i | \(-0.714114\pi\) | ||||
−0.623067 | + | 0.782169i | \(0.714114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.86561 | −1.19544 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.10656 | 0.808834 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.2559 | −1.85596 | −0.927980 | − | 0.372630i | \(-0.878456\pi\) | ||||
−0.927980 | + | 0.372630i | \(0.878456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.61736 | 0.847266 | 0.423633 | − | 0.905834i | \(-0.360755\pi\) | ||||
0.423633 | + | 0.905834i | \(0.360755\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.19144 | −0.276096 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.43166 | 0.425644 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.16554 | −0.631072 | −0.315536 | − | 0.948914i | \(-0.602184\pi\) | ||||
−0.315536 | + | 0.948914i | \(0.602184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.59981 | −0.794524 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.933881 | 0.110831 | 0.0554156 | − | 0.998463i | \(-0.482352\pi\) | ||||
0.0554156 | + | 0.998463i | \(0.482352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.11727 | 0.715973 | 0.357986 | − | 0.933727i | \(-0.383463\pi\) | ||||
0.357986 | + | 0.933727i | \(0.383463\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.24154 | 0.258831 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.6978 | 1.33309 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6499 | 1.64824 | 0.824121 | − | 0.566414i | \(-0.191669\pi\) | ||||
0.824121 | + | 0.566414i | \(0.191669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.4496 | 1.58604 | 0.793022 | − | 0.609193i | \(-0.208506\pi\) | ||||
0.793022 | + | 0.609193i | \(0.208506\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.22272 | 0.566484 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.96547 | −0.961199 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.02821 | −0.532989 | −0.266494 | − | 0.963836i | \(-0.585865\pi\) | ||||
−0.266494 | + | 0.963836i | \(0.585865\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.52794 | −0.474657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.89365 | 0.714839 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.1421 | −1.04056 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.45055 | 0.654954 | 0.327477 | − | 0.944859i | \(-0.393802\pi\) | ||||
0.327477 | + | 0.944859i | \(0.393802\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.33796 | −0.536485 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.19379 | 0.118787 | 0.0593933 | − | 0.998235i | \(-0.481083\pi\) | ||||
0.0593933 | + | 0.998235i | \(0.481083\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0291429 | −0.00287153 | −0.00143577 | − | 0.999999i | \(-0.500457\pi\) | ||||
−0.00143577 | + | 0.999999i | \(0.500457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.63968 | 0.355196 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.85598 | 0.952814 | 0.476407 | − | 0.879225i | \(-0.341939\pi\) | ||||
0.476407 | + | 0.879225i | \(0.341939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.98381 | 0.285797 | 0.142899 | − | 0.989737i | \(-0.454358\pi\) | ||||
0.142899 | + | 0.989737i | \(0.454358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.91614 | 0.466619 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.4015 | 1.63699 | 0.818496 | − | 0.574512i | \(-0.194808\pi\) | ||||
0.818496 | + | 0.574512i | \(0.194808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.9614 | 1.02215 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.06619 | 0.191019 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.89118 | −0.631714 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.4938 | 1.59035 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.27622 | −0.475741 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0272 | −1.07574 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.66062 | 0.147357 | 0.0736783 | − | 0.997282i | \(-0.476526\pi\) | ||||
0.0736783 | + | 0.997282i | \(0.476526\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.91190 | −0.432469 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.1407 | 1.75970 | 0.879848 | − | 0.475254i | \(-0.157644\pi\) | ||||
0.879848 | + | 0.475254i | \(0.157644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.3822 | 1.16038 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.66086 | −0.142944 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.06701 | −0.347468 | −0.173734 | − | 0.984793i | \(-0.555583\pi\) | ||||
−0.173734 | + | 0.984793i | \(0.555583\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.8088 | −1.17125 | −0.585625 | − | 0.810582i | \(-0.699151\pi\) | ||||
−0.585625 | + | 0.810582i | \(0.699151\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.585390 | −0.0492987 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.0293 | −0.922313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.8904 | 1.23658 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.19758 | 0.181253 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0931 | −1.31840 | −0.659201 | − | 0.751967i | \(-0.729105\pi\) | ||||
−0.659201 | + | 0.751967i | \(0.729105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.44235 | −0.361514 | −0.180757 | − | 0.983528i | \(-0.557855\pi\) | ||||
−0.180757 | + | 0.983528i | \(0.557855\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.14459 | 0.254225 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4494 | −0.919638 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.9994 | 1.11727 | 0.558637 | − | 0.829412i | \(-0.311324\pi\) | ||||
0.558637 | + | 0.829412i | \(0.311324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.07199 | 0.719456 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.4631 | −1.13985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.7013 | 1.54313 | 0.771564 | − | 0.636152i | \(-0.219475\pi\) | ||||
0.771564 | + | 0.636152i | \(0.219475\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.86561 | 0.690187 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.46294 | 0.267970 | 0.133985 | − | 0.990983i | \(-0.457223\pi\) | ||||
0.133985 | + | 0.990983i | \(0.457223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.73085 | −0.671604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.10656 | −0.466980 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.4526 | 1.55498 | 0.777492 | − | 0.628893i | \(-0.216492\pi\) | ||||
0.777492 | + | 0.628893i | \(0.216492\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.91221 | 0.371328 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.2559 | 1.07154 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.85284 | −0.213231 | −0.106616 | − | 0.994300i | \(-0.534001\pi\) | ||||
−0.106616 | + | 0.994300i | \(0.534001\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.3472 | −1.80972 | −0.904858 | − | 0.425714i | \(-0.860023\pi\) | ||||
−0.904858 | + | 0.425714i | \(0.860023\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.61736 | −0.489169 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.16501 | −0.600304 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.7857 | −1.22749 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.19144 | 0.159404 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5918 | −0.983466 | −0.491733 | − | 0.870746i | \(-0.663636\pi\) | ||||
−0.491733 | + | 0.870746i | \(0.663636\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.53334 | 0.542262 | 0.271131 | − | 0.962542i | \(-0.412602\pi\) | ||||
0.271131 | + | 0.962542i | \(0.412602\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.43166 | −0.245746 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.1311 | −1.00680 | −0.503400 | − | 0.864053i | \(-0.667918\pi\) | ||||
−0.503400 | + | 0.864053i | \(0.667918\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7899 | 1.61553 | 0.807765 | − | 0.589505i | \(-0.200677\pi\) | ||||
0.807765 | + | 0.589505i | \(0.200677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.16554 | 0.364349 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.6473 | −1.37897 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.76307 | 0.612039 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.59981 | 0.458719 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 32.5966 | 2.25475 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.65829 | −0.527218 | −0.263609 | − | 0.964630i | \(-0.584913\pi\) | ||||
−0.263609 | + | 0.964630i | \(0.584913\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.933881 | −0.0639884 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.15798 | 0.556370 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.1070 | 1.02553 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.11727 | −0.413367 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.49732 | 0.437057 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.07674 | 0.540858 | 0.270429 | − | 0.962740i | \(-0.412834\pi\) | ||||
0.270429 | + | 0.962740i | \(0.412834\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.24154 | −0.149436 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.147080 | −0.00976204 | −0.00488102 | − | 0.999988i | \(-0.501554\pi\) | ||||
−0.00488102 | + | 0.999988i | \(0.501554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.49007 | 0.494958 | 0.247479 | − | 0.968893i | \(-0.420398\pi\) | ||||
0.247479 | + | 0.968893i | \(0.420398\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6978 | −0.769661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.92844 | 0.322873 | 0.161436 | − | 0.986883i | \(-0.448387\pi\) | ||||
0.161436 | + | 0.986883i | \(0.448387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.972250 | 0.0634226 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.6499 | −0.951613 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.3298 | 1.44440 | 0.722198 | − | 0.691687i | \(-0.243132\pi\) | ||||
0.722198 | + | 0.691687i | \(0.243132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4515 | 1.57506 | 0.787531 | − | 0.616275i | \(-0.211359\pi\) | ||||
0.787531 | + | 0.616275i | \(0.211359\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.64988 | −0.233182 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.6173 | −0.802821 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.4496 | −0.915703 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.0449 | 1.32834 | 0.664171 | − | 0.747581i | \(-0.268785\pi\) | ||||
0.664171 | + | 0.747581i | \(0.268785\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.2295 | −2.21486 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.22272 | −0.327060 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.75251 | 0.171697 | 0.0858483 | − | 0.996308i | \(-0.472640\pi\) | ||||
0.0858483 | + | 0.996308i | \(0.472640\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.7734 | 0.669428 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.96547 | 0.554949 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.6221 | −0.839974 | −0.419987 | − | 0.907530i | \(-0.637965\pi\) | ||||
−0.419987 | + | 0.907530i | \(0.637965\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0673 | −0.925577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.02821 | 0.307721 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7203 | 0.897512 | 0.448756 | − | 0.893654i | \(-0.351867\pi\) | ||||
0.448756 | + | 0.893654i | \(0.351867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.6221 | 1.49569 | 0.747843 | − | 0.663875i | \(-0.231089\pi\) | ||||
0.747843 | + | 0.663875i | \(0.231089\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.52794 | 0.274043 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.9653 | 0.721533 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.30852 | −0.559295 | −0.279647 | − | 0.960103i | \(-0.590218\pi\) | ||||
−0.279647 | + | 0.960103i | \(0.590218\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.89365 | −0.412712 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.6196 | 0.991439 | 0.495720 | − | 0.868483i | \(-0.334904\pi\) | ||||
0.495720 | + | 0.868483i | \(0.334904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.3083 | 1.20720 | 0.603601 | − | 0.797287i | \(-0.293732\pi\) | ||||
0.603601 | + | 0.797287i | \(0.293732\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.1421 | 0.600769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5625 | −0.682515 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.11156 | −0.418327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.45055 | −0.378138 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.6240 | −1.43855 | −0.719274 | − | 0.694726i | \(-0.755526\pi\) | ||||
−0.719274 | + | 0.694726i | \(0.755526\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.6771 | −1.37853 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.33796 | 0.309740 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.6365 | 0.788618 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7641 | −0.620435 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.19379 | −0.0685815 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.9905 | 0.629315 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.4179 | −0.594583 | −0.297291 | − | 0.954787i | \(-0.596083\pi\) | ||||
−0.297291 | + | 0.954787i | \(0.596083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.0291429 | 0.00165788 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.91872 | −0.108801 | −0.0544004 | − | 0.998519i | \(-0.517325\pi\) | ||||
−0.0544004 | + | 0.998519i | \(0.517325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.82382 | 0.103089 | 0.0515443 | − | 0.998671i | \(-0.483586\pi\) | ||||
0.0515443 | + | 0.998671i | \(0.483586\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.63968 | −0.205073 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.41306 | 0.191696 | 0.0958482 | − | 0.995396i | \(-0.469444\pi\) | ||||
0.0958482 | + | 0.995396i | \(0.469444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −47.8574 | −2.67950 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.85598 | −0.550107 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.2026 | −1.06846 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.63146 | −0.256907 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.98381 | −0.165005 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.28285 | −0.0707257 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.04725 | 0.497282 | 0.248641 | − | 0.968596i | \(-0.420016\pi\) | ||||
0.248641 | + | 0.968596i | \(0.420016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.91614 | −0.269403 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.57925 | −0.468734 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.3261 | 0.616973 | 0.308486 | − | 0.951229i | \(-0.400178\pi\) | ||||
0.308486 | + | 0.951229i | \(0.400178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.4015 | −0.945118 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.7981 | 1.99273 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1560 | 1.08832 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.9614 | −0.590140 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.7826 | 1.11567 | 0.557835 | − | 0.829952i | \(-0.311632\pi\) | ||||
0.557835 | + | 0.829952i | \(0.311632\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.2172 | −1.67102 | −0.835510 | − | 0.549475i | \(-0.814828\pi\) | ||||
−0.835510 | + | 0.549475i | \(0.814828\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.06619 | −0.110285 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.358336 | −0.0190723 | −0.00953615 | − | 0.999955i | \(-0.503035\pi\) | ||||
−0.00953615 | + | 0.999955i | \(0.503035\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.55105 | 0.0823209 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.89118 | 0.364720 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.61015 | 0.243315 | 0.121657 | − | 0.992572i | \(-0.461179\pi\) | ||||
0.121657 | + | 0.992572i | \(0.461179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.2901 | 0.962635 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.4938 | −0.918189 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.1599 | 0.531795 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.2475 | 1.16131 | 0.580654 | − | 0.814151i | \(-0.302797\pi\) | ||||
0.580654 | + | 0.814151i | \(0.302797\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.27622 | 0.274669 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.8807 | 1.03216 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.6478 | 0.603101 | 0.301551 | − | 0.953450i | \(-0.402496\pi\) | ||||
0.301551 | + | 0.953450i | \(0.402496\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0272 | 0.621081 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.5244 | 0.954054 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.2261 | 1.50125 | 0.750623 | − | 0.660731i | \(-0.229753\pi\) | ||||
0.750623 | + | 0.660731i | \(0.229753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.66062 | −0.0850764 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.6186 | −0.593684 | −0.296842 | − | 0.954927i | \(-0.595934\pi\) | ||||
−0.296842 | + | 0.954927i | \(0.595934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.4285 | 0.990167 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.91190 | 0.249686 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.4729 | −0.581700 | −0.290850 | − | 0.956769i | \(-0.593938\pi\) | ||||
−0.290850 | + | 0.956769i | \(0.593938\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.7537 | 1.04956 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.1407 | −1.01596 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.3314 | 1.22425 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.3119 | 1.62169 | 0.810844 | − | 0.585263i | \(-0.199009\pi\) | ||||
0.810844 | + | 0.585263i | \(0.199009\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.3822 | −0.669947 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.0821 | 1.35241 | 0.676207 | − | 0.736712i | \(-0.263622\pi\) | ||||
0.676207 | + | 0.736712i | \(0.263622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.2436 | −0.709525 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.66086 | 0.0825288 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.2421 | 1.30078 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.54024 | −0.224501 | −0.112250 | − | 0.993680i | \(-0.535806\pi\) | ||||
−0.112250 | + | 0.993680i | \(0.535806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.06701 | 0.200611 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 31.2410 | 1.53727 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.9987 | 1.17805 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.8088 | 0.676222 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.64005 | 0.128975 | 0.0644874 | − | 0.997919i | \(-0.479459\pi\) | ||||
0.0644874 | + | 0.997919i | \(0.479459\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.17913 | 0.301153 | 0.150576 | − | 0.988598i | \(-0.451887\pi\) | ||||
0.150576 | + | 0.988598i | \(0.451887\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.585390 | 0.0284626 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.04873 | −0.341914 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5016 | −0.701779 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.0293 | 0.532497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.9296 | −1.20081 | −0.600407 | − | 0.799694i | \(-0.704995\pi\) | ||||
−0.600407 | + | 0.799694i | \(0.704995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.2764 | −1.59916 | −0.799582 | − | 0.600557i | \(-0.794945\pi\) | ||||
−0.799582 | + | 0.600557i | \(0.794945\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.8904 | −0.713940 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −40.3021 | −1.92791 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.63803 | −0.459998 | −0.229999 | − | 0.973191i | \(-0.573872\pi\) | ||||
−0.229999 | + | 0.973191i | \(0.573872\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.19758 | −0.104647 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0899656 | 0.00427439 | 0.00213720 | − | 0.999998i | \(-0.499320\pi\) | ||||
0.00213720 | + | 0.999998i | \(0.499320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.35115 | −0.395882 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.0931 | 0.761179 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.5182 | −1.67621 | −0.838105 | − | 0.545509i | \(-0.816336\pi\) | ||||
−0.838105 | + | 0.545509i | \(0.816336\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.1643 | −1.32620 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.44235 | 0.208720 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.52027 | −0.352556 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.84536 | −0.0863224 | −0.0431612 | − | 0.999068i | \(-0.513743\pi\) | ||||
−0.0431612 | + | 0.999068i | \(0.513743\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.14459 | −0.146777 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.49076 | 0.395454 | 0.197727 | − | 0.980257i | \(-0.436644\pi\) | ||||
0.197727 | + | 0.980257i | \(0.436644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7515 | 0.824980 | 0.412490 | − | 0.910962i | \(-0.364659\pi\) | ||||
0.412490 | + | 0.910962i | \(0.364659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.4494 | 0.530953 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.8382 | 1.01055 | 0.505277 | − | 0.862957i | \(-0.331390\pi\) | ||||
0.505277 | + | 0.862957i | \(0.331390\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3200 | 0.522709 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.9994 | −0.645059 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.2196 | −1.20558 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.6881 | 0.628054 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.07199 | −0.415378 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.5567 | −0.482346 | −0.241173 | − | 0.970482i | \(-0.577532\pi\) | ||||
−0.241173 | + | 0.970482i | \(0.577532\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.1577 | −0.463150 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.4631 | 0.658094 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.7135 | 0.486473 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.4461 | 1.74216 | 0.871079 | − | 0.491143i | \(-0.163421\pi\) | ||||
0.871079 | + | 0.491143i | \(0.163421\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.7013 | −0.890925 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.5555 | 1.06305 | 0.531523 | − | 0.847044i | \(-0.321620\pi\) | ||||
0.531523 | + | 0.847044i | \(0.321620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.1927 | 1.26974 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.86561 | −0.398480 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.04655 | −0.0918001 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.38552 | −0.420153 | −0.210077 | − | 0.977685i | \(-0.567371\pi\) | ||||
−0.210077 | + | 0.977685i | \(0.567371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.46294 | −0.154713 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.98272 | 0.0882299 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.73085 | 0.387751 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.7744 | −1.14243 | −0.571216 | − | 0.820800i | \(-0.693528\pi\) | ||||
−0.571216 | + | 0.820800i | \(0.693528\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.4056 | −0.593031 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.10656 | 0.269611 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.0484022 | −0.00213286 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.12479 | −0.137428 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.4526 | −0.897770 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.0801 | 1.05497 | 0.527485 | − | 0.849565i | \(-0.323135\pi\) | ||||
0.527485 | + | 0.849565i | \(0.323135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.63721 | −0.290225 | −0.145112 | − | 0.989415i | \(-0.546354\pi\) | ||||
−0.145112 | + | 0.989415i | \(0.546354\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.91221 | −0.214387 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.6777 | −0.944295 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.5575 | 0.893804 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.2559 | −0.618653 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.9017 | 0.472204 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.3694 | 0.707711 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.85284 | 0.123109 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.7306 | 0.505273 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.9536 | 0.556920 | 0.278460 | − | 0.960448i | \(-0.410176\pi\) | ||||
0.278460 | + | 0.960448i | \(0.410176\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.3472 | 1.04484 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.95569 | 0.212279 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.34331 | −0.100193 | −0.0500963 | − | 0.998744i | \(-0.515953\pi\) | ||||
−0.0500963 | + | 0.998744i | \(0.515953\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.61736 | 0.282422 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.7482 | −2.33235 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32.1044 | −1.36522 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.16501 | 0.346586 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.61332 | −0.237844 | −0.118922 | − | 0.992904i | \(-0.537944\pi\) | ||||
−0.118922 | + | 0.992904i | \(0.537944\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.1489 | 0.429254 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.7857 | 0.708693 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.7429 | −0.537051 | −0.268526 | − | 0.963273i | \(-0.586536\pi\) | ||||
−0.268526 | + | 0.963273i | \(0.586536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.9014 | 1.21589 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.19144 | −0.0920319 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.8081 | 0.746556 | 0.373278 | − | 0.927719i | \(-0.378234\pi\) | ||||
0.373278 | + | 0.927719i | \(0.378234\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.87762 | −0.371517 | −0.185758 | − | 0.982595i | \(-0.559474\pi\) | ||||
−0.185758 | + | 0.982595i | \(0.559474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.5918 | 0.567804 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.7938 | −0.616942 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.2463 | −0.676343 | −0.338171 | − | 0.941085i | \(-0.609808\pi\) | ||||
−0.338171 | + | 0.941085i | \(0.609808\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.53334 | −0.313075 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.6654 | −1.31370 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.4259 | 2.00560 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.43166 | 0.141881 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.3685 | 0.469230 | 0.234615 | − | 0.972088i | \(-0.424617\pi\) | ||||
0.234615 | + | 0.972088i | \(0.424617\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.0965 | 1.73456 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.1311 | 0.581277 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.05429 | 0.371815 | 0.185908 | − | 0.982567i | \(-0.440477\pi\) | ||||
0.185908 | + | 0.982567i | \(0.440477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4453 | −0.469211 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.7899 | −0.932727 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.1251 | −0.413699 | −0.206850 | − | 0.978373i | \(-0.566321\pi\) | ||||
−0.206850 | + | 0.978373i | \(0.566321\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.0267 | 0.816905 | 0.408453 | − | 0.912780i | \(-0.366069\pi\) | ||||
0.408453 | + | 0.912780i | \(0.366069\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.16554 | −0.210357 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.0548 | 1.18125 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.57996 | −0.348250 | −0.174125 | − | 0.984724i | \(-0.555710\pi\) | ||||
−0.174125 | + | 0.984724i | \(0.555710\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.6473 | 0.796149 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.20953 | 0.0489322 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.4875 | 1.71605 | 0.858027 | − | 0.513605i | \(-0.171690\pi\) | ||||
0.858027 | + | 0.513605i | \(0.171690\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.76307 | −0.353361 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.4029 | −0.620098 | −0.310049 | − | 0.950721i | \(-0.600345\pi\) | ||||
−0.310049 | + | 0.950721i | \(0.600345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.4638 | −0.500962 | −0.250481 | − | 0.968122i | \(-0.580589\pi\) | ||||
−0.250481 | + | 0.968122i | \(0.580589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.59981 | −0.264841 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.0190 | 0.441468 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.76777 | −0.350711 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −32.5966 | −1.30178 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.4592 | −0.616400 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.5054 | 0.657068 | 0.328534 | − | 0.944492i | \(-0.393445\pi\) | ||||
0.328534 | + | 0.944492i | \(0.393445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.65829 | 0.304390 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.75806 | 0.109450 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.54062 | −0.179906 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.933881 | 0.0369437 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.5686 | −1.56287 | −0.781434 | − | 0.623988i | \(-0.785511\pi\) | ||||
−0.781434 | + | 0.623988i | \(0.785511\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.00236 | 0.157838 | 0.0789188 | − | 0.996881i | \(-0.474853\pi\) | ||||
0.0789188 | + | 0.996881i | \(0.474853\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.15798 | −0.321220 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.8934 | 1.56837 | 0.784185 | − | 0.620527i | \(-0.213081\pi\) | ||||
0.784185 | + | 0.620527i | \(0.213081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 76.0975 | 2.98709 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.1070 | −0.592092 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.3492 | −1.22679 | −0.613395 | − | 0.789776i | \(-0.710197\pi\) | ||||
−0.613395 | + | 0.789776i | \(0.710197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 33.4508 | 1.30703 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.11727 | 0.238658 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.50681 | −0.331378 | −0.165689 | − | 0.986178i | \(-0.552985\pi\) | ||||
−0.165689 | + | 0.986178i | \(0.552985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.1308 | −1.36643 | −0.683214 | − | 0.730218i | \(-0.739419\pi\) | ||||
−0.683214 | + | 0.730218i | \(0.739419\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.49732 | −0.252335 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.2259 | 0.861884 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59.1704 | 2.29109 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.07674 | −0.312265 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.3232 | −1.36364 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.9890 | 1.07889 | 0.539447 | − | 0.842019i | \(-0.318633\pi\) | ||||
0.539447 | + | 0.842019i | \(0.318633\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.24154 | 0.0862770 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.9681 | −0.844303 | −0.422152 | − | 0.906525i | \(-0.638725\pi\) | ||||
−0.422152 | + | 0.906525i | \(0.638725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.1360 | −0.542490 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.147080 | 0.00563612 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.2488 | 1.61661 | 0.808303 | − | 0.588767i | \(-0.200386\pi\) | ||||
0.808303 | + | 0.588767i | \(0.200386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.75474 | −0.258085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.49007 | −0.285764 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.7445 | −0.714107 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7773 | −0.448030 | −0.224015 | − | 0.974586i | \(-0.571916\pi\) | ||||
−0.224015 | + | 0.974586i | \(0.571916\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.6978 | 0.444364 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.9345 | −0.869957 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.5915 | 0.628450 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.92844 | −0.186411 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.0699 | 1.32457 | 0.662286 | − | 0.749251i | \(-0.269586\pi\) | ||||
0.662286 | + | 0.749251i | \(0.269586\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0207 | 1.13225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.972250 | −0.0366171 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.61612 | −0.0983895 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.8879 | −0.446460 | −0.223230 | − | 0.974766i | \(-0.571660\pi\) | ||||
−0.223230 | + | 0.974766i | \(0.571660\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6499 | 0.549414 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −45.4968 | −1.70387 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.3180 | −0.685056 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.3298 | −0.833922 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.5011 | −1.54773 | −0.773864 | − | 0.633351i | \(-0.781679\pi\) | ||||
−0.773864 | + | 0.633351i | \(0.781679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0638649 | 0.00237845 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.4515 | −0.909363 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.0965 | −0.746365 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.63564 | −0.171926 | −0.0859631 | − | 0.996298i | \(-0.527397\pi\) | ||||
−0.0859631 | + | 0.996298i | \(0.527397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.4459 | 0.571288 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.9082 | −1.25243 | −0.626214 | − | 0.779651i | \(-0.715396\pi\) | ||||
−0.626214 | + | 0.779651i | \(0.715396\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.64988 | 0.134628 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.5735 | 1.01568 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.4784 | 1.63617 | 0.818083 | − | 0.575100i | \(-0.195037\pi\) | ||||
0.818083 | + | 0.575100i | \(0.195037\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.6173 | 0.463509 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 52.3349 | 1.91998 | 0.959991 | − | 0.280029i | \(-0.0903442\pi\) | ||||
0.959991 | + | 0.280029i | \(0.0903442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.7285 | −0.979255 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.4496 | 0.528681 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.5988 | −0.789204 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4116 | −0.452907 | −0.226453 | − | 0.974022i | \(-0.572713\pi\) | ||||
−0.226453 | + | 0.974022i | \(0.572713\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.0449 | −0.766919 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.37813 | −0.268518 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.2759 | 1.24578 | 0.622889 | − | 0.782310i | \(-0.285959\pi\) | ||||
0.622889 | + | 0.782310i | \(0.285959\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 35.2295 | 1.27875 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.8836 | 1.98953 | 0.994764 | − | 0.102195i | \(-0.0325867\pi\) | ||||
0.994764 | + | 0.102195i | \(0.0325867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.53885 | −0.236722 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.22272 | 0.188828 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.4554 | −1.06357 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.9900 | 1.51420 | 0.757100 | − | 0.653299i | \(-0.226616\pi\) | ||||
0.757100 | + | 0.653299i | \(0.226616\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.75251 | −0.0991291 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.70881 | 0.169364 | 0.0846821 | − | 0.996408i | \(-0.473013\pi\) | ||||
0.0846821 | + | 0.996408i | \(0.473013\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.4524 | 0.555067 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.7734 | −0.386494 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −32.2196 | −1.15439 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.98502 | −0.178378 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.96547 | −0.320400 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.2511 | 0.829866 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.0114 | −0.356869 | −0.178434 | − | 0.983952i | \(-0.557103\pi\) | ||||
−0.178434 | + | 0.983952i | \(0.557103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.6221 | 0.484959 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −38.1343 | −1.35590 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6727 | 0.485533 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.0673 | 0.534382 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.9405 | −0.670906 | −0.335453 | − | 0.942057i | \(-0.608889\pi\) | ||||
−0.335453 | + | 0.942057i | \(0.608889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.84081 | 0.0651232 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.02821 | −0.177663 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.6538 | −1.15233 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24.0212 | −0.846636 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.7203 | −0.518179 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.9960 | 1.37103 | 0.685513 | − | 0.728060i | \(-0.259578\pi\) | ||||
0.685513 | + | 0.728060i | \(0.259578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6649 | 0.514954 | 0.257477 | − | 0.966284i | \(-0.417109\pi\) | ||||
0.257477 | + | 0.966284i | \(0.417109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.6221 | −0.863535 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.7212 | 1.14617 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.9948 | −1.04939 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.52794 | −0.158219 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.7644 | 1.21329 | 0.606644 | − | 0.794974i | \(-0.292515\pi\) | ||||
0.606644 | + | 0.794974i | \(0.292515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.09906 | 0.177742 | 0.0888710 | − | 0.996043i | \(-0.471674\pi\) | ||||
0.0888710 | + | 0.996043i | \(0.471674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.9653 | −0.416577 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.4953 | −1.79067 | −0.895333 | − | 0.445397i | \(-0.853063\pi\) | ||||
−0.895333 | + | 0.445397i | \(0.853063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.1193 | −0.872431 | −0.436216 | − | 0.899842i | \(-0.643681\pi\) | ||||
−0.436216 | + | 0.899842i | \(0.643681\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.30852 | 0.322909 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.91049 | −0.239434 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.75146 | 0.199037 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.89365 | 0.238280 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.6231 | −0.573894 | −0.286947 | − | 0.957947i | \(-0.592640\pi\) | ||||
−0.286947 | + | 0.957947i | \(0.592640\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.3797 | 1.77171 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.6196 | −0.572408 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.5007 | −0.498840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.3368 | −1.31727 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.3083 | −0.696978 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.4456 | −1.11222 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.6366 | 1.01474 | 0.507369 | − | 0.861729i | \(-0.330618\pi\) | ||||
0.507369 | + | 0.861729i | \(0.330618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.1421 | −0.346854 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.9547 | −1.67226 | −0.836131 | − | 0.548530i | \(-0.815188\pi\) | ||||
−0.836131 | + | 0.548530i | \(0.815188\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45.1888 | 1.54182 | 0.770911 | − | 0.636943i | \(-0.219801\pi\) | ||||
0.770911 | + | 0.636943i | \(0.219801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.5625 | 0.394050 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.0059 | −1.36182 | −0.680908 | − | 0.732369i | \(-0.738415\pi\) | ||||
−0.680908 | + | 0.732369i | \(0.738415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.9689 | 1.15498 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.11156 | 0.241521 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −78.2006 | −2.65277 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.6730 | −0.361641 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.45055 | 0.218318 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.3569 | 0.891026 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.2538 | −0.582618 | −0.291309 | − | 0.956629i | \(-0.594091\pi\) | ||||
−0.291309 | + | 0.956629i | \(0.594091\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.6240 | 0.830547 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.0815 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7054 | −1.06697 | −0.533487 | − | 0.845809i | \(-0.679118\pi\) | ||||
−0.533487 | + | 0.845809i | \(0.679118\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.6771 | 0.795896 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.0799 | −0.808524 | −0.404262 | − | 0.914643i | \(-0.632472\pi\) | ||||
−0.404262 | + | 0.914643i | \(0.632472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.63916 | −0.122054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.33796 | −0.178828 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.57472 | −0.119623 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.73816 | −0.158379 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13.6365 | −0.455309 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −61.8049 | −2.06131 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.5277 | −0.950395 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.7641 | 0.358208 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.4374 | −1.34418 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.3179 | −0.475417 | −0.237708 | − | 0.971337i | \(-0.576396\pi\) | ||||
−0.237708 | + | 0.971337i | \(0.576396\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.19379 | 0.0395956 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.9490 | 0.495283 | 0.247641 | − | 0.968852i | \(-0.420345\pi\) | ||||
0.247641 | + | 0.968852i | \(0.420345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −77.1312 | −2.55267 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.9905 | −0.363335 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.1371 | −1.45753 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.8620 | 0.589213 | 0.294606 | − | 0.955619i | \(-0.404811\pi\) | ||||
0.294606 | + | 0.955619i | \(0.404811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.4179 | 0.343283 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.92958 | 0.0635128 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0197 | 0.362326 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.0291429 | −0.000957177 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.6229 | −0.840660 | −0.420330 | − | 0.907371i | \(-0.638086\pi\) | ||||
−0.420330 | + | 0.907371i | \(0.638086\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.4197 | 0.439812 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.91872 | 0.0628162 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.8787 | −0.911731 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.0701 | −1.04769 | −0.523843 | − | 0.851815i | \(-0.675502\pi\) | ||||
−0.523843 | + | 0.851815i | \(0.675502\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.82382 | −0.0595182 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 49.7470 | 1.62171 | 0.810853 | − | 0.585250i | \(-0.199004\pi\) | ||||
0.810853 | + | 0.585250i | \(0.199004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.8221 | 1.13396 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.63968 | 0.118399 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.22332 | −0.0397525 | −0.0198762 | − | 0.999802i | \(-0.506327\pi\) | ||||
−0.0198762 | + | 0.999802i | \(0.506327\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.6395 | 0.410294 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.41306 | −0.110676 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.0873 | −1.26616 | −0.633082 | − | 0.774085i | \(-0.718210\pi\) | ||||
−0.633082 | + | 0.774085i | \(0.718210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.5740 | −0.730478 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 47.8574 | 1.54701 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.91262 | 0.287804 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.5225 | 0.532982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.85598 | 0.317605 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.5118 | 0.402770 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.7425 | −0.441931 | −0.220965 | − | 0.975282i | \(-0.570921\pi\) | ||||
−0.220965 | + | 0.975282i | \(0.570921\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.2026 | 0.616877 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.1756 | −1.12884 | −0.564419 | − | 0.825488i | \(-0.690900\pi\) | ||||
−0.564419 | + | 0.825488i | \(0.690900\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.2613 | 0.970132 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.63146 | 0.148325 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.3306 | −0.330504 | −0.165252 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165252 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 26.8404 | 0.857822 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.98381 | 0.0952657 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.60170 | 0.210561 | 0.105281 | − | 0.994443i | \(-0.466426\pi\) | ||||
0.105281 | + | 0.994443i | \(0.466426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.4698 | −0.747810 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.28285 | 0.0408335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.4176 | 1.03082 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.878981 | −0.0279217 | −0.0139609 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139609 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.04725 | −0.287106 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.8508 | 1.19995 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8322 | 0.533081 | 0.266541 | − | 0.963824i | \(-0.414119\pi\) | ||||
0.266541 | + | 0.963824i | \(0.414119\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.91614 | 0.155540 |
(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 | 6036.2.a.i.1.17 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.17 | ✓ | 26 | 1.1 | even | 1 | trivial |