Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(1,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1089.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.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: | \(8.69570878012\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 7x^{2} + 11 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.14896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.14896 | −1.51954 | −0.759772 | − | 0.650189i | \(-0.774690\pi\) | ||||
−0.759772 | + | 0.650189i | \(0.774690\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.61803 | 1.30902 | ||||||||
\(5\) | −2.14896 | −0.961045 | −0.480522 | − | 0.876982i | \(-0.659553\pi\) | ||||
−0.480522 | + | 0.876982i | \(0.659553\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.23607 | 1.60108 | 0.800542 | − | 0.599277i | \(-0.204545\pi\) | ||||
0.800542 | + | 0.599277i | \(0.204545\pi\) | |||||||
\(8\) | −1.32813 | −0.469565 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.61803 | 1.46035 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.236068 | −0.0654735 | −0.0327367 | − | 0.999464i | \(-0.510422\pi\) | ||||
−0.0327367 | + | 0.999464i | \(0.510422\pi\) | |||||||
\(14\) | −9.10315 | −2.43292 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.38197 | −0.595492 | ||||||||
\(17\) | 6.13335 | 1.48756 | 0.743778 | − | 0.668426i | \(-0.233032\pi\) | ||||
0.743778 | + | 0.668426i | \(0.233032\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.38197 | 0.546460 | 0.273230 | − | 0.961949i | \(-0.411908\pi\) | ||||
0.273230 | + | 0.961949i | \(0.411908\pi\) | |||||||
\(20\) | −5.62605 | −1.25802 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.98439 | 0.830803 | 0.415402 | − | 0.909638i | \(-0.363641\pi\) | ||||
0.415402 | + | 0.909638i | \(0.363641\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.381966 | −0.0763932 | ||||||||
\(26\) | 0.507301 | 0.0994899 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.0902 | 2.09585 | ||||||||
\(29\) | −6.95418 | −1.29136 | −0.645680 | − | 0.763608i | \(-0.723426\pi\) | ||||
−0.645680 | + | 0.763608i | \(0.723426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.61803 | −0.829423 | −0.414712 | − | 0.909953i | \(-0.636118\pi\) | ||||
−0.414712 | + | 0.909953i | \(0.636118\pi\) | |||||||
\(32\) | 7.77501 | 1.37444 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.1803 | −2.26041 | ||||||||
\(35\) | −9.10315 | −1.53871 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.76393 | 0.289989 | 0.144994 | − | 0.989432i | \(-0.453684\pi\) | ||||
0.144994 | + | 0.989432i | \(0.453684\pi\) | |||||||
\(38\) | −5.11875 | −0.830371 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.85410 | 0.451273 | ||||||||
\(41\) | 2.96979 | 0.463803 | 0.231902 | − | 0.972739i | \(-0.425505\pi\) | ||||
0.231902 | + | 0.972739i | \(0.425505\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.70820 | −0.412997 | −0.206499 | − | 0.978447i | \(-0.566207\pi\) | ||||
−0.206499 | + | 0.978447i | \(0.566207\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.56231 | −1.26244 | ||||||||
\(47\) | 3.47709 | 0.507186 | 0.253593 | − | 0.967311i | \(-0.418388\pi\) | ||||
0.253593 | + | 0.967311i | \(0.418388\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | 0.820830 | 0.116083 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.618034 | −0.0857059 | ||||||||
\(53\) | −1.83543 | −0.252116 | −0.126058 | − | 0.992023i | \(-0.540233\pi\) | ||||
−0.126058 | + | 0.992023i | \(0.540233\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.62605 | −0.751813 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.9443 | 1.96228 | ||||||||
\(59\) | −7.46149 | −0.971403 | −0.485701 | − | 0.874125i | \(-0.661436\pi\) | ||||
−0.485701 | + | 0.874125i | \(0.661436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3262 | 1.45018 | 0.725088 | − | 0.688656i | \(-0.241799\pi\) | ||||
0.725088 | + | 0.688656i | \(0.241799\pi\) | |||||||
\(62\) | 9.92398 | 1.26035 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −11.9443 | −1.49303 | ||||||||
\(65\) | 0.507301 | 0.0629229 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.85410 | −0.348684 | −0.174342 | − | 0.984685i | \(-0.555780\pi\) | ||||
−0.174342 | + | 0.984685i | \(0.555780\pi\) | |||||||
\(68\) | 16.0573 | 1.94724 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 19.5623 | 2.33814 | ||||||||
\(71\) | 10.7448 | 1.27517 | 0.637587 | − | 0.770378i | \(-0.279933\pi\) | ||||
0.637587 | + | 0.770378i | \(0.279933\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.47214 | −0.289342 | −0.144671 | − | 0.989480i | \(-0.546212\pi\) | ||||
−0.144671 | + | 0.989480i | \(0.546212\pi\) | |||||||
\(74\) | −3.79062 | −0.440651 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.23607 | 0.715326 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.47214 | 1.06570 | 0.532849 | − | 0.846210i | \(-0.321121\pi\) | ||||
0.532849 | + | 0.846210i | \(0.321121\pi\) | |||||||
\(80\) | 5.11875 | 0.572294 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.38197 | −0.704770 | ||||||||
\(83\) | −8.28232 | −0.909102 | −0.454551 | − | 0.890721i | \(-0.650200\pi\) | ||||
−0.454551 | + | 0.890721i | \(0.650200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.1803 | −1.42961 | ||||||||
\(86\) | 5.81983 | 0.627568 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.90937 | 0.944392 | 0.472196 | − | 0.881494i | \(-0.343462\pi\) | ||||
0.472196 | + | 0.881494i | \(0.343462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 10.4313 | 1.08754 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.47214 | −0.770692 | ||||||||
\(95\) | −5.11875 | −0.525173 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.7984 | 1.19794 | 0.598972 | − | 0.800770i | \(-0.295576\pi\) | ||||
0.598972 | + | 0.800770i | \(0.295576\pi\) | |||||||
\(98\) | −23.5188 | −2.37576 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 0.313529 | 0.0311973 | 0.0155987 | − | 0.999878i | \(-0.495035\pi\) | ||||
0.0155987 | + | 0.999878i | \(0.495035\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9443 | −1.07837 | −0.539186 | − | 0.842187i | \(-0.681268\pi\) | ||||
−0.539186 | + | 0.842187i | \(0.681268\pi\) | |||||||
\(104\) | 0.313529 | 0.0307441 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.94427 | 0.383102 | ||||||||
\(107\) | 10.9386 | 1.05747 | 0.528736 | − | 0.848786i | \(-0.322666\pi\) | ||||
0.528736 | + | 0.848786i | \(0.322666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.7082 | 1.31301 | 0.656504 | − | 0.754323i | \(-0.272035\pi\) | ||||
0.656504 | + | 0.754323i | \(0.272035\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.0902 | −0.953431 | ||||||||
\(113\) | 17.8928 | 1.68321 | 0.841605 | − | 0.540094i | \(-0.181611\pi\) | ||||
0.841605 | + | 0.540094i | \(0.181611\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.56231 | −0.798439 | ||||||||
\(116\) | −18.2063 | −1.69041 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.0344 | 1.47609 | ||||||||
\(119\) | 25.9813 | 2.38170 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −24.3396 | −2.20361 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.0902 | −1.08573 | ||||||||
\(125\) | 11.5656 | 1.03446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.76393 | 0.245259 | 0.122630 | − | 0.992453i | \(-0.460867\pi\) | ||||
0.122630 | + | 0.992453i | \(0.460867\pi\) | |||||||
\(128\) | 10.1177 | 0.894291 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.09017 | −0.0956142 | ||||||||
\(131\) | −2.46249 | −0.215149 | −0.107574 | − | 0.994197i | \(-0.534308\pi\) | ||||
−0.107574 | + | 0.994197i | \(0.534308\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.0902 | 0.874929 | ||||||||
\(134\) | 6.13335 | 0.529841 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.14590 | −0.698505 | ||||||||
\(137\) | 0.313529 | 0.0267866 | 0.0133933 | − | 0.999910i | \(-0.495737\pi\) | ||||
0.0133933 | + | 0.999910i | \(0.495737\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3820 | 0.965406 | 0.482703 | − | 0.875784i | \(-0.339655\pi\) | ||||
0.482703 | + | 0.875784i | \(0.339655\pi\) | |||||||
\(140\) | −23.8323 | −2.01420 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −23.0902 | −1.93768 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.9443 | 1.24105 | ||||||||
\(146\) | 5.31252 | 0.439668 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.61803 | 0.379600 | ||||||||
\(149\) | 4.61145 | 0.377785 | 0.188892 | − | 0.981998i | \(-0.439510\pi\) | ||||
0.188892 | + | 0.981998i | \(0.439510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2361 | 1.07714 | 0.538568 | − | 0.842582i | \(-0.318966\pi\) | ||||
0.538568 | + | 0.842582i | \(0.318966\pi\) | |||||||
\(152\) | −3.16356 | −0.256599 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.92398 | 0.797113 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.6525 | −1.64825 | −0.824124 | − | 0.566410i | \(-0.808332\pi\) | ||||
−0.824124 | + | 0.566410i | \(0.808332\pi\) | |||||||
\(158\) | −20.3553 | −1.61938 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.7082 | −1.32090 | ||||||||
\(161\) | 16.8782 | 1.33019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.38197 | 0.108244 | 0.0541220 | − | 0.998534i | \(-0.482764\pi\) | ||||
0.0541220 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(164\) | 7.77501 | 0.607127 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.7984 | 1.38142 | ||||||||
\(167\) | 10.7448 | 0.831458 | 0.415729 | − | 0.909489i | \(-0.363526\pi\) | ||||
0.415729 | + | 0.909489i | \(0.363526\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9443 | −0.995713 | ||||||||
\(170\) | 28.3240 | 2.17235 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.09017 | −0.540620 | ||||||||
\(173\) | 13.4011 | 1.01886 | 0.509432 | − | 0.860511i | \(-0.329855\pi\) | ||||
0.509432 | + | 0.860511i | \(0.329855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.61803 | −0.122312 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.1459 | −1.43505 | ||||||||
\(179\) | 1.95519 | 0.146138 | 0.0730689 | − | 0.997327i | \(-0.476721\pi\) | ||||
0.0730689 | + | 0.997327i | \(0.476721\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2361 | 0.909500 | 0.454750 | − | 0.890619i | \(-0.349729\pi\) | ||||
0.454750 | + | 0.890619i | \(0.349729\pi\) | |||||||
\(182\) | 2.14896 | 0.159292 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.29180 | −0.390116 | ||||||||
\(185\) | −3.79062 | −0.278692 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.10315 | 0.663915 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.0000 | 0.798024 | ||||||||
\(191\) | −9.92398 | −0.718074 | −0.359037 | − | 0.933323i | \(-0.616895\pi\) | ||||
−0.359037 | + | 0.933323i | \(0.616895\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.38197 | −0.531366 | −0.265683 | − | 0.964061i | \(-0.585597\pi\) | ||||
−0.265683 | + | 0.964061i | \(0.585597\pi\) | |||||||
\(194\) | −25.3542 | −1.82033 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 28.6525 | 2.04661 | ||||||||
\(197\) | 2.46249 | 0.175445 | 0.0877226 | − | 0.996145i | \(-0.472041\pi\) | ||||
0.0877226 | + | 0.996145i | \(0.472041\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.416408 | 0.0295184 | 0.0147592 | − | 0.999891i | \(-0.495302\pi\) | ||||
0.0147592 | + | 0.999891i | \(0.495302\pi\) | |||||||
\(200\) | 0.507301 | 0.0358716 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.673762 | −0.0474057 | ||||||||
\(203\) | −29.4584 | −2.06757 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.38197 | −0.445736 | ||||||||
\(206\) | 23.5188 | 1.63863 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.562306 | 0.0389889 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0344 | 1.24154 | 0.620771 | − | 0.783992i | \(-0.286820\pi\) | ||||
0.620771 | + | 0.783992i | \(0.286820\pi\) | |||||||
\(212\) | −4.80522 | −0.330024 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.5066 | −1.60688 | ||||||||
\(215\) | 5.81983 | 0.396909 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.5623 | −1.32798 | ||||||||
\(218\) | −29.4584 | −1.99517 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.44789 | −0.0973955 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.18034 | 0.212971 | 0.106486 | − | 0.994314i | \(-0.466040\pi\) | ||||
0.106486 | + | 0.994314i | \(0.466040\pi\) | |||||||
\(224\) | 32.9355 | 2.20059 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −38.4508 | −2.55771 | ||||||||
\(227\) | −10.9386 | −0.726019 | −0.363009 | − | 0.931785i | \(-0.618251\pi\) | ||||
−0.363009 | + | 0.931785i | \(0.618251\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4721 | −1.22067 | −0.610337 | − | 0.792142i | \(-0.708966\pi\) | ||||
−0.610337 | + | 0.792142i | \(0.708966\pi\) | |||||||
\(230\) | 18.4001 | 1.21326 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.23607 | 0.606378 | ||||||||
\(233\) | −23.0115 | −1.50753 | −0.753767 | − | 0.657142i | \(-0.771765\pi\) | ||||
−0.753767 | + | 0.657142i | \(0.771765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.47214 | −0.487428 | ||||||||
\(236\) | −19.5344 | −1.27158 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −55.8328 | −3.61910 | ||||||||
\(239\) | −11.4459 | −0.740372 | −0.370186 | − | 0.928958i | \(-0.620706\pi\) | ||||
−0.370186 | + | 0.928958i | \(0.620706\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0000 | −0.901819 | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 29.6525 | 1.89831 | ||||||||
\(245\) | −23.5188 | −1.50256 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.562306 | −0.0357787 | ||||||||
\(248\) | 6.13335 | 0.389468 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −24.8541 | −1.57191 | ||||||||
\(251\) | −22.6980 | −1.43268 | −0.716342 | − | 0.697749i | \(-0.754185\pi\) | ||||
−0.716342 | + | 0.697749i | \(0.754185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.93958 | −0.372683 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.14590 | 0.134119 | ||||||||
\(257\) | −12.3865 | −0.772647 | −0.386323 | − | 0.922363i | \(-0.626255\pi\) | ||||
−0.386323 | + | 0.922363i | \(0.626255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.47214 | 0.464296 | ||||||||
\(260\) | 1.32813 | 0.0823672 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.29180 | 0.326928 | ||||||||
\(263\) | 6.44688 | 0.397532 | 0.198766 | − | 0.980047i | \(-0.436307\pi\) | ||||
0.198766 | + | 0.980047i | \(0.436307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.94427 | 0.242295 | ||||||||
\(266\) | −21.6834 | −1.32949 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.47214 | −0.456433 | ||||||||
\(269\) | 20.2355 | 1.23378 | 0.616890 | − | 0.787049i | \(-0.288392\pi\) | ||||
0.616890 | + | 0.787049i | \(0.288392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.965558 | 0.0586535 | 0.0293267 | − | 0.999570i | \(-0.490664\pi\) | ||||
0.0293267 | + | 0.999570i | \(0.490664\pi\) | |||||||
\(272\) | −14.6094 | −0.885827 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.673762 | −0.0407035 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.3820 | −1.16455 | −0.582275 | − | 0.812992i | \(-0.697837\pi\) | ||||
−0.582275 | + | 0.812992i | \(0.697837\pi\) | |||||||
\(278\) | −24.4594 | −1.46698 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.0902 | 0.722526 | ||||||||
\(281\) | 16.5646 | 0.988163 | 0.494082 | − | 0.869416i | \(-0.335504\pi\) | ||||
0.494082 | + | 0.869416i | \(0.335504\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.9443 | 0.650569 | 0.325285 | − | 0.945616i | \(-0.394540\pi\) | ||||
0.325285 | + | 0.945616i | \(0.394540\pi\) | |||||||
\(284\) | 28.1303 | 1.66922 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.5802 | 0.742588 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 20.6180 | 1.21283 | ||||||||
\(290\) | −32.1147 | −1.88584 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.47214 | −0.378753 | ||||||||
\(293\) | 4.99899 | 0.292044 | 0.146022 | − | 0.989281i | \(-0.453353\pi\) | ||||
0.146022 | + | 0.989281i | \(0.453353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.0344 | 0.933561 | ||||||||
\(296\) | −2.34273 | −0.136169 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.90983 | −0.574061 | ||||||||
\(299\) | −0.940588 | −0.0543956 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.4721 | −0.661243 | ||||||||
\(302\) | −28.4438 | −1.63676 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.67376 | −0.325413 | ||||||||
\(305\) | −24.3396 | −1.39368 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2705 | −0.985680 | −0.492840 | − | 0.870120i | \(-0.664041\pi\) | ||||
−0.492840 | + | 0.870120i | \(0.664041\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.3262 | −1.21125 | ||||||||
\(311\) | −28.7573 | −1.63068 | −0.815339 | − | 0.578984i | \(-0.803449\pi\) | ||||
−0.815339 | + | 0.578984i | \(0.803449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.6525 | 1.78910 | 0.894552 | − | 0.446964i | \(-0.147495\pi\) | ||||
0.894552 | + | 0.446964i | \(0.147495\pi\) | |||||||
\(314\) | 44.3814 | 2.50459 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.7984 | 1.39502 | ||||||||
\(317\) | −0.313529 | −0.0176096 | −0.00880478 | − | 0.999961i | \(-0.502803\pi\) | ||||
−0.00880478 | + | 0.999961i | \(0.502803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 25.6678 | 1.43487 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −36.2705 | −2.02128 | ||||||||
\(323\) | 14.6094 | 0.812891 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0901699 | 0.00500173 | ||||||||
\(326\) | −2.96979 | −0.164482 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.94427 | −0.217786 | ||||||||
\(329\) | 14.7292 | 0.812047 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.29180 | 0.400793 | 0.200397 | − | 0.979715i | \(-0.435777\pi\) | ||||
0.200397 | + | 0.979715i | \(0.435777\pi\) | |||||||
\(332\) | −21.6834 | −1.19003 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.0902 | −1.26344 | ||||||||
\(335\) | 6.13335 | 0.335101 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.6525 | 1.45185 | 0.725926 | − | 0.687772i | \(-0.241411\pi\) | ||||
0.725926 | + | 0.687772i | \(0.241411\pi\) | |||||||
\(338\) | 27.8167 | 1.51303 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −34.5066 | −1.87138 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.7082 | 0.902158 | ||||||||
\(344\) | 3.59685 | 0.193929 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.7984 | −1.54821 | ||||||||
\(347\) | −25.1605 | −1.35069 | −0.675343 | − | 0.737504i | \(-0.736004\pi\) | ||||
−0.675343 | + | 0.737504i | \(0.736004\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.18034 | −0.491412 | −0.245706 | − | 0.969344i | \(-0.579020\pi\) | ||||
−0.245706 | + | 0.969344i | \(0.579020\pi\) | |||||||
\(350\) | 3.47709 | 0.185858 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.7563 | −1.79667 | −0.898334 | − | 0.439314i | \(-0.855222\pi\) | ||||
−0.898334 | + | 0.439314i | \(0.855222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.0902 | −1.22550 | ||||||||
\(356\) | 23.3250 | 1.23622 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.20163 | −0.222063 | ||||||||
\(359\) | −2.02920 | −0.107097 | −0.0535486 | − | 0.998565i | \(-0.517053\pi\) | ||||
−0.0535486 | + | 0.998565i | \(0.517053\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.3262 | −0.701381 | ||||||||
\(362\) | −26.2948 | −1.38203 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.61803 | −0.137222 | ||||||||
\(365\) | 5.31252 | 0.278070 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.0344 | 1.20239 | 0.601194 | − | 0.799103i | \(-0.294692\pi\) | ||||
0.601194 | + | 0.799103i | \(0.294692\pi\) | |||||||
\(368\) | −9.49069 | −0.494736 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.14590 | 0.423485 | ||||||||
\(371\) | −7.77501 | −0.403659 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4164 | 0.746453 | 0.373227 | − | 0.927740i | \(-0.378251\pi\) | ||||
0.373227 | + | 0.927740i | \(0.378251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.61803 | −0.238157 | ||||||||
\(377\) | 1.64166 | 0.0845498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.23607 | 0.320325 | 0.160163 | − | 0.987091i | \(-0.448798\pi\) | ||||
0.160163 | + | 0.987091i | \(0.448798\pi\) | |||||||
\(380\) | −13.4011 | −0.687460 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.3262 | 1.09115 | ||||||||
\(383\) | −34.0698 | −1.74089 | −0.870444 | − | 0.492267i | \(-0.836168\pi\) | ||||
−0.870444 | + | 0.492267i | \(0.836168\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.8636 | 0.807434 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30.8885 | 1.56813 | ||||||||
\(389\) | 22.3104 | 1.13118 | 0.565592 | − | 0.824685i | \(-0.308648\pi\) | ||||
0.565592 | + | 0.824685i | \(0.308648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.4377 | 1.23587 | ||||||||
\(392\) | −14.5354 | −0.734150 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.29180 | −0.266597 | ||||||||
\(395\) | −20.3553 | −1.02418 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.4164 | 1.22542 | 0.612712 | − | 0.790306i | \(-0.290078\pi\) | ||||
0.612712 | + | 0.790306i | \(0.290078\pi\) | |||||||
\(398\) | −0.894844 | −0.0448545 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.909830 | 0.0454915 | ||||||||
\(401\) | −19.0271 | −0.950169 | −0.475085 | − | 0.879940i | \(-0.657583\pi\) | ||||
−0.475085 | + | 0.879940i | \(0.657583\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.09017 | 0.0543052 | ||||||||
\(404\) | 0.820830 | 0.0408378 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 63.3050 | 3.14177 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.05573 | 0.249990 | 0.124995 | − | 0.992157i | \(-0.460109\pi\) | ||||
0.124995 | + | 0.992157i | \(0.460109\pi\) | |||||||
\(410\) | 13.7146 | 0.677316 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.6525 | −1.41161 | ||||||||
\(413\) | −31.6074 | −1.55530 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7984 | 0.873688 | ||||||||
\(416\) | −1.83543 | −0.0899895 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.2782 | −1.72345 | −0.861727 | − | 0.507372i | \(-0.830617\pi\) | ||||
−0.861727 | + | 0.507372i | \(0.830617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.2148 | −1.42384 | −0.711921 | − | 0.702260i | \(-0.752174\pi\) | ||||
−0.711921 | + | 0.702260i | \(0.752174\pi\) | |||||||
\(422\) | −38.7553 | −1.88658 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.43769 | 0.118385 | ||||||||
\(425\) | −2.34273 | −0.113639 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 47.9787 | 2.32185 | ||||||||
\(428\) | 28.6376 | 1.38425 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.5066 | −0.603121 | ||||||||
\(431\) | 35.5918 | 1.71439 | 0.857197 | − | 0.514988i | \(-0.172204\pi\) | ||||
0.857197 | + | 0.514988i | \(0.172204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.65248 | −0.127470 | −0.0637349 | − | 0.997967i | \(-0.520301\pi\) | ||||
−0.0637349 | + | 0.997967i | \(0.520301\pi\) | |||||||
\(434\) | 42.0386 | 2.01792 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 35.8885 | 1.71875 | ||||||||
\(437\) | 9.49069 | 0.454001 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0000 | 1.19318 | 0.596592 | − | 0.802544i | \(-0.296521\pi\) | ||||
0.596592 | + | 0.802544i | \(0.296521\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.11146 | 0.147997 | ||||||||
\(443\) | 21.8772 | 1.03941 | 0.519707 | − | 0.854344i | \(-0.326041\pi\) | ||||
0.519707 | + | 0.854344i | \(0.326041\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.1459 | −0.907603 | ||||||||
\(446\) | −6.83443 | −0.323619 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −50.5967 | −2.39047 | ||||||||
\(449\) | 29.4584 | 1.39023 | 0.695114 | − | 0.718900i | \(-0.255354\pi\) | ||||
0.695114 | + | 0.718900i | \(0.255354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 46.8439 | 2.20335 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 23.5066 | 1.10322 | ||||||||
\(455\) | 2.14896 | 0.100745 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.0902 | −1.64145 | −0.820724 | − | 0.571324i | \(-0.806430\pi\) | ||||
−0.820724 | + | 0.571324i | \(0.806430\pi\) | |||||||
\(458\) | 39.6959 | 1.85487 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −22.4164 | −1.04517 | ||||||||
\(461\) | −1.52190 | −0.0708821 | −0.0354410 | − | 0.999372i | \(-0.511284\pi\) | ||||
−0.0354410 | + | 0.999372i | \(0.511284\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5623 | −1.00209 | −0.501043 | − | 0.865423i | \(-0.667050\pi\) | ||||
−0.501043 | + | 0.865423i | \(0.667050\pi\) | |||||||
\(464\) | 16.5646 | 0.768994 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 49.4508 | 2.29077 | ||||||||
\(467\) | 21.1761 | 0.979912 | 0.489956 | − | 0.871747i | \(-0.337013\pi\) | ||||
0.489956 | + | 0.871747i | \(0.337013\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0902 | −0.558272 | ||||||||
\(470\) | 16.0573 | 0.740669 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.90983 | 0.456137 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.909830 | −0.0417459 | ||||||||
\(476\) | 68.0199 | 3.11769 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.5967 | 1.12503 | ||||||||
\(479\) | 36.8459 | 1.68353 | 0.841765 | − | 0.539844i | \(-0.181517\pi\) | ||||
0.841765 | + | 0.539844i | \(0.181517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.416408 | −0.0189866 | ||||||||
\(482\) | 30.0855 | 1.37035 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.3542 | −1.15128 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.8885 | 0.855922 | 0.427961 | − | 0.903797i | \(-0.359232\pi\) | ||||
0.427961 | + | 0.903797i | \(0.359232\pi\) | |||||||
\(488\) | −15.0427 | −0.680952 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 50.5410 | 2.28321 | ||||||||
\(491\) | 19.4147 | 0.876172 | 0.438086 | − | 0.898933i | \(-0.355657\pi\) | ||||
0.438086 | + | 0.898933i | \(0.355657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.6525 | −1.92097 | ||||||||
\(494\) | 1.20837 | 0.0543673 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.0000 | 0.493915 | ||||||||
\(497\) | 45.5157 | 2.04166 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.7426 | 1.46576 | 0.732881 | − | 0.680357i | \(-0.238175\pi\) | ||||
0.732881 | + | 0.680357i | \(0.238175\pi\) | |||||||
\(500\) | 30.2792 | 1.35413 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 48.7771 | 2.17703 | ||||||||
\(503\) | −5.93958 | −0.264833 | −0.132416 | − | 0.991194i | \(-0.542274\pi\) | ||||
−0.132416 | + | 0.991194i | \(0.542274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.673762 | −0.0299820 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.23607 | 0.321049 | ||||||||
\(509\) | 16.3709 | 0.725626 | 0.362813 | − | 0.931862i | \(-0.381816\pi\) | ||||
0.362813 | + | 0.931862i | \(0.381816\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.4721 | −0.463260 | ||||||||
\(512\) | −24.8469 | −1.09809 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 26.6180 | 1.17407 | ||||||||
\(515\) | 23.5188 | 1.03636 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −16.0573 | −0.705519 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.673762 | −0.0295464 | ||||||||
\(521\) | −26.8021 | −1.17422 | −0.587111 | − | 0.809506i | \(-0.699735\pi\) | ||||
−0.587111 | + | 0.809506i | \(0.699735\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.4508 | 1.63761 | 0.818806 | − | 0.574071i | \(-0.194637\pi\) | ||||
0.818806 | + | 0.574071i | \(0.194637\pi\) | |||||||
\(524\) | −6.44688 | −0.281633 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.8541 | −0.604068 | ||||||||
\(527\) | −28.3240 | −1.23381 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.12461 | −0.309766 | ||||||||
\(530\) | −8.47609 | −0.368178 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 26.4164 | 1.14530 | ||||||||
\(533\) | −0.701073 | −0.0303668 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.5066 | −1.01628 | ||||||||
\(536\) | 3.79062 | 0.163730 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −43.4853 | −1.87478 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.6312 | −1.66088 | −0.830442 | − | 0.557105i | \(-0.811912\pi\) | ||||
−0.830442 | + | 0.557105i | \(0.811912\pi\) | |||||||
\(542\) | −2.07495 | −0.0891266 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 47.6869 | 2.04456 | ||||||||
\(545\) | −29.4584 | −1.26186 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0344 | −0.856611 | −0.428305 | − | 0.903634i | \(-0.640889\pi\) | ||||
−0.428305 | + | 0.903634i | \(0.640889\pi\) | |||||||
\(548\) | 0.820830 | 0.0350641 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.5646 | −0.705677 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.1246 | 1.70627 | ||||||||
\(554\) | 41.6511 | 1.76959 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 29.7984 | 1.26373 | ||||||||
\(557\) | −5.43228 | −0.230173 | −0.115087 | − | 0.993355i | \(-0.536715\pi\) | ||||
−0.115087 | + | 0.993355i | \(0.536715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.639320 | 0.0270404 | ||||||||
\(560\) | 21.6834 | 0.916290 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.5967 | −1.50156 | ||||||||
\(563\) | −15.6240 | −0.658475 | −0.329237 | − | 0.944247i | \(-0.606792\pi\) | ||||
−0.329237 | + | 0.944247i | \(0.606792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −38.4508 | −1.61764 | ||||||||
\(566\) | −23.5188 | −0.988570 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.2705 | −0.598777 | ||||||||
\(569\) | −31.7271 | −1.33007 | −0.665035 | − | 0.746812i | \(-0.731583\pi\) | ||||
−0.665035 | + | 0.746812i | \(0.731583\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9787 | −0.501294 | −0.250647 | − | 0.968079i | \(-0.580643\pi\) | ||||
−0.250647 | + | 0.968079i | \(0.580643\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −27.0344 | −1.12840 | ||||||||
\(575\) | −1.52190 | −0.0634677 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.34752 | −0.0560982 | −0.0280491 | − | 0.999607i | \(-0.508929\pi\) | ||||
−0.0280491 | + | 0.999607i | \(0.508929\pi\) | |||||||
\(578\) | −44.3074 | −1.84294 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 39.1246 | 1.62456 | ||||||||
\(581\) | −35.0845 | −1.45555 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.28332 | 0.135865 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.7426 | −0.443775 | ||||||||
\(587\) | 36.7261 | 1.51585 | 0.757924 | − | 0.652342i | \(-0.226214\pi\) | ||||
0.757924 | + | 0.652342i | \(0.226214\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.0000 | −0.453247 | ||||||||
\(590\) | −34.4574 | −1.41859 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.20163 | −0.172686 | ||||||||
\(593\) | −27.3094 | −1.12146 | −0.560732 | − | 0.827997i | \(-0.689480\pi\) | ||||
−0.560732 | + | 0.827997i | \(0.689480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.8328 | −2.28892 | ||||||||
\(596\) | 12.0729 | 0.494527 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.02129 | 0.0826565 | ||||||||
\(599\) | 17.1917 | 0.702433 | 0.351217 | − | 0.936294i | \(-0.385768\pi\) | ||||
0.351217 | + | 0.936294i | \(0.385768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.36068 | 0.381830 | 0.190915 | − | 0.981607i | \(-0.438854\pi\) | ||||
0.190915 | + | 0.981607i | \(0.438854\pi\) | |||||||
\(602\) | 24.6532 | 1.00479 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 34.6525 | 1.40999 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.6180 | 1.16157 | 0.580785 | − | 0.814057i | \(-0.302746\pi\) | ||||
0.580785 | + | 0.814057i | \(0.302746\pi\) | |||||||
\(608\) | 18.5198 | 0.751078 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 52.3050 | 2.11777 | ||||||||
\(611\) | −0.820830 | −0.0332072 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.0557 | −1.01199 | −0.505996 | − | 0.862536i | \(-0.668875\pi\) | ||||
−0.505996 | + | 0.862536i | \(0.668875\pi\) | |||||||
\(614\) | 37.1137 | 1.49779 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.8782 | 0.679489 | 0.339745 | − | 0.940518i | \(-0.389659\pi\) | ||||
0.339745 | + | 0.940518i | \(0.389659\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.88854 | 0.276874 | 0.138437 | − | 0.990371i | \(-0.455792\pi\) | ||||
0.138437 | + | 0.990371i | \(0.455792\pi\) | |||||||
\(620\) | 25.9813 | 1.04343 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 61.7984 | 2.47789 | ||||||||
\(623\) | 37.7407 | 1.51205 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.9443 | −0.917771 | ||||||||
\(626\) | −68.0199 | −2.71862 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −54.0689 | −2.15758 | ||||||||
\(629\) | 10.8188 | 0.431375 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.3820 | −0.691965 | −0.345983 | − | 0.938241i | \(-0.612454\pi\) | ||||
−0.345983 | + | 0.938241i | \(0.612454\pi\) | |||||||
\(632\) | −12.5802 | −0.500415 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.673762 | 0.0267585 | ||||||||
\(635\) | −5.93958 | −0.235705 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.58359 | −0.102366 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −21.7426 | −0.859454 | ||||||||
\(641\) | −21.3699 | −0.844058 | −0.422029 | − | 0.906582i | \(-0.638682\pi\) | ||||
−0.422029 | + | 0.906582i | \(0.638682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.1591 | −1.62315 | −0.811577 | − | 0.584245i | \(-0.801391\pi\) | ||||
−0.811577 | + | 0.584245i | \(0.801391\pi\) | |||||||
\(644\) | 44.1876 | 1.74124 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.3951 | −1.23522 | ||||||||
\(647\) | −11.6854 | −0.459400 | −0.229700 | − | 0.973261i | \(-0.573775\pi\) | ||||
−0.229700 | + | 0.973261i | \(0.573775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.193772 | −0.00760035 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.61803 | 0.141693 | ||||||||
\(653\) | −34.1896 | −1.33794 | −0.668971 | − | 0.743288i | \(-0.733265\pi\) | ||||
−0.668971 | + | 0.743288i | \(0.733265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.29180 | 0.206768 | ||||||||
\(656\) | −7.07394 | −0.276191 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −31.6525 | −1.23394 | ||||||||
\(659\) | 33.7563 | 1.31496 | 0.657480 | − | 0.753472i | \(-0.271623\pi\) | ||||
0.657480 | + | 0.753472i | \(0.271623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.43769 | 0.0948153 | 0.0474077 | − | 0.998876i | \(-0.484904\pi\) | ||||
0.0474077 | + | 0.998876i | \(0.484904\pi\) | |||||||
\(662\) | −15.6698 | −0.609024 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11.0000 | 0.426883 | ||||||||
\(665\) | −21.6834 | −0.840846 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −27.7082 | −1.07287 | ||||||||
\(668\) | 28.1303 | 1.08839 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.1803 | −0.509201 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.2361 | −0.702949 | −0.351474 | − | 0.936198i | \(-0.614320\pi\) | ||||
−0.351474 | + | 0.936198i | \(0.614320\pi\) | |||||||
\(674\) | −57.2751 | −2.20616 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33.8885 | −1.30341 | ||||||||
\(677\) | 8.59584 | 0.330365 | 0.165183 | − | 0.986263i | \(-0.447179\pi\) | ||||
0.165183 | + | 0.986263i | \(0.447179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 49.9787 | 1.91801 | ||||||||
\(680\) | 17.5052 | 0.671294 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.940588 | −0.0359906 | −0.0179953 | − | 0.999838i | \(-0.505728\pi\) | ||||
−0.0179953 | + | 0.999838i | \(0.505728\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.673762 | −0.0257431 | ||||||||
\(686\) | −35.9053 | −1.37087 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.45085 | 0.245936 | ||||||||
\(689\) | 0.433287 | 0.0165069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.3607 | 1.23106 | 0.615529 | − | 0.788114i | \(-0.288942\pi\) | ||||
0.615529 | + | 0.788114i | \(0.288942\pi\) | |||||||
\(692\) | 35.0845 | 1.33371 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 54.0689 | 2.05243 | ||||||||
\(695\) | −24.4594 | −0.927798 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.2148 | 0.689934 | ||||||||
\(698\) | 19.7282 | 0.746723 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.23607 | −0.160108 | ||||||||
\(701\) | −23.3991 | −0.883770 | −0.441885 | − | 0.897072i | \(-0.645690\pi\) | ||||
−0.441885 | + | 0.897072i | \(0.645690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.20163 | 0.158467 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 72.5410 | 2.73012 | ||||||||
\(707\) | 1.32813 | 0.0499495 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.2016 | −0.570909 | −0.285455 | − | 0.958392i | \(-0.592145\pi\) | ||||
−0.285455 | + | 0.958392i | \(0.592145\pi\) | |||||||
\(710\) | 49.6199 | 1.86220 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.8328 | −0.443454 | ||||||||
\(713\) | −18.4001 | −0.689088 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.11875 | 0.191297 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.36068 | 0.162739 | ||||||||
\(719\) | −12.9678 | −0.483617 | −0.241808 | − | 0.970324i | \(-0.577741\pi\) | ||||
−0.241808 | + | 0.970324i | \(0.577741\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46.3607 | −1.72656 | ||||||||
\(722\) | 28.6376 | 1.06578 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 32.0344 | 1.19055 | ||||||||
\(725\) | 2.65626 | 0.0986511 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5623 | 0.725526 | 0.362763 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362763 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(728\) | 1.32813 | 0.0492238 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.4164 | −0.422540 | ||||||||
\(731\) | −16.6104 | −0.614357 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.6525 | 0.541202 | 0.270601 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270601 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(734\) | −49.5001 | −1.82708 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.9787 | 1.14189 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.2361 | −0.670825 | −0.335412 | − | 0.942071i | \(-0.608876\pi\) | ||||
−0.335412 | + | 0.942071i | \(0.608876\pi\) | |||||||
\(740\) | −9.92398 | −0.364813 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.7082 | 0.613377 | ||||||||
\(743\) | −18.1323 | −0.665209 | −0.332604 | − | 0.943066i | \(-0.607927\pi\) | ||||
−0.332604 | + | 0.943066i | \(0.607927\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.90983 | −0.363068 | ||||||||
\(746\) | −30.9803 | −1.13427 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.3366 | 1.69310 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.50658 | −0.0549758 | −0.0274879 | − | 0.999622i | \(-0.508751\pi\) | ||||
−0.0274879 | + | 0.999622i | \(0.508751\pi\) | |||||||
\(752\) | −8.28232 | −0.302025 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.52786 | −0.128477 | ||||||||
\(755\) | −28.4438 | −1.03518 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40.8885 | −1.48612 | −0.743060 | − | 0.669225i | \(-0.766626\pi\) | ||||
−0.743060 | + | 0.669225i | \(0.766626\pi\) | |||||||
\(758\) | −13.4011 | −0.486749 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.79837 | 0.246603 | ||||||||
\(761\) | −33.4428 | −1.21230 | −0.606150 | − | 0.795350i | \(-0.707287\pi\) | ||||
−0.606150 | + | 0.795350i | \(0.707287\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.0689 | 2.10223 | ||||||||
\(764\) | −25.9813 | −0.939971 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 73.2148 | 2.64536 | ||||||||
\(767\) | 1.76142 | 0.0636011 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2705 | 0.803095 | 0.401548 | − | 0.915838i | \(-0.368472\pi\) | ||||
0.401548 | + | 0.915838i | \(0.368472\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.3262 | −0.695567 | ||||||||
\(773\) | −33.6823 | −1.21147 | −0.605734 | − | 0.795667i | \(-0.707121\pi\) | ||||
−0.605734 | + | 0.795667i | \(0.707121\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.76393 | 0.0633623 | ||||||||
\(776\) | −15.6698 | −0.562513 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −47.9443 | −1.71889 | ||||||||
\(779\) | 7.07394 | 0.253450 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −52.5157 | −1.87796 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −26.0689 | −0.931032 | ||||||||
\(785\) | 44.3814 | 1.58404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.7771 | −0.990146 | −0.495073 | − | 0.868851i | \(-0.664859\pi\) | ||||
−0.495073 | + | 0.868851i | \(0.664859\pi\) | |||||||
\(788\) | 6.44688 | 0.229661 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 43.7426 | 1.55629 | ||||||||
\(791\) | 75.7950 | 2.69496 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.67376 | −0.0949481 | ||||||||
\(794\) | −52.4699 | −1.86209 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.09017 | 0.0386400 | ||||||||
\(797\) | 4.29792 | 0.152240 | 0.0761201 | − | 0.997099i | \(-0.475747\pi\) | ||||
0.0761201 | + | 0.997099i | \(0.475747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.3262 | 0.754468 | ||||||||
\(800\) | −2.96979 | −0.104998 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 40.8885 | 1.44382 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.2705 | −1.27837 | ||||||||
\(806\) | −2.34273 | −0.0825192 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.416408 | −0.0146492 | ||||||||
\(809\) | 7.07394 | 0.248707 | 0.124353 | − | 0.992238i | \(-0.460314\pi\) | ||||
0.124353 | + | 0.992238i | \(0.460314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.2148 | 1.55259 | 0.776295 | − | 0.630369i | \(-0.217096\pi\) | ||||
0.776295 | + | 0.630369i | \(0.217096\pi\) | |||||||
\(812\) | −77.1231 | −2.70649 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.96979 | −0.104027 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.45085 | −0.225687 | ||||||||
\(818\) | −10.8646 | −0.379871 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.7082 | −0.583476 | ||||||||
\(821\) | −39.7699 | −1.38798 | −0.693990 | − | 0.719985i | \(-0.744149\pi\) | ||||
−0.693990 | + | 0.719985i | \(0.744149\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.1115 | 0.666183 | 0.333092 | − | 0.942894i | \(-0.391908\pi\) | ||||
0.333092 | + | 0.942894i | \(0.391908\pi\) | |||||||
\(824\) | 14.5354 | 0.506366 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 67.9230 | 2.36334 | ||||||||
\(827\) | −11.6397 | −0.404750 | −0.202375 | − | 0.979308i | \(-0.564866\pi\) | ||||
−0.202375 | + | 0.979308i | \(0.564866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.0344 | 0.695825 | 0.347912 | − | 0.937527i | \(-0.386891\pi\) | ||||
0.347912 | + | 0.937527i | \(0.386891\pi\) | |||||||
\(830\) | −38.2480 | −1.32761 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.81966 | 0.0977541 | ||||||||
\(833\) | 67.1251 | 2.32575 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.0902 | −0.799068 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 75.8115 | 2.61887 | ||||||||
\(839\) | −13.9824 | −0.482725 | −0.241363 | − | 0.970435i | \(-0.577594\pi\) | ||||
−0.241363 | + | 0.970435i | \(0.577594\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.3607 | 0.667610 | ||||||||
\(842\) | 62.7814 | 2.16359 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 47.2148 | 1.62520 | ||||||||
\(845\) | 27.8167 | 0.956925 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.37194 | 0.150133 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.03444 | 0.172680 | ||||||||
\(851\) | 7.02820 | 0.240924 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.18034 | 0.0404141 | 0.0202070 | − | 0.999796i | \(-0.493567\pi\) | ||||
0.0202070 | + | 0.999796i | \(0.493567\pi\) | |||||||
\(854\) | −103.104 | −3.52816 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.5279 | −0.496552 | ||||||||
\(857\) | −13.8344 | −0.472573 | −0.236286 | − | 0.971683i | \(-0.575930\pi\) | ||||
−0.236286 | + | 0.971683i | \(0.575930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.4164 | 1.44723 | 0.723615 | − | 0.690204i | \(-0.242479\pi\) | ||||
0.723615 | + | 0.690204i | \(0.242479\pi\) | |||||||
\(860\) | 15.2365 | 0.519560 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −76.4853 | −2.60510 | ||||||||
\(863\) | −34.3834 | −1.17042 | −0.585212 | − | 0.810880i | \(-0.698989\pi\) | ||||
−0.585212 | + | 0.810880i | \(0.698989\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.7984 | −0.979174 | ||||||||
\(866\) | 5.70007 | 0.193696 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −51.2148 | −1.73834 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.673762 | 0.0228296 | ||||||||
\(872\) | −18.2063 | −0.616543 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.3951 | −0.689875 | ||||||||
\(875\) | 48.9928 | 1.65626 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.4721 | −0.387387 | −0.193693 | − | 0.981062i | \(-0.562047\pi\) | ||||
−0.193693 | + | 0.981062i | \(0.562047\pi\) | |||||||
\(878\) | −53.7240 | −1.81310 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.3376 | 1.15686 | 0.578432 | − | 0.815730i | \(-0.303665\pi\) | ||||
0.578432 | + | 0.815730i | \(0.303665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.1115 | −0.474888 | −0.237444 | − | 0.971401i | \(-0.576310\pi\) | ||||
−0.237444 | + | 0.971401i | \(0.576310\pi\) | |||||||
\(884\) | −3.79062 | −0.127492 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −47.0132 | −1.57944 | ||||||||
\(887\) | 56.5741 | 1.89957 | 0.949786 | − | 0.312902i | \(-0.101301\pi\) | ||||
0.949786 | + | 0.312902i | \(0.101301\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.7082 | 0.392681 | ||||||||
\(890\) | 41.1438 | 1.37914 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.32624 | 0.278783 | ||||||||
\(893\) | 8.28232 | 0.277157 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.20163 | −0.140445 | ||||||||
\(896\) | 42.8595 | 1.43183 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −63.3050 | −2.11251 | ||||||||
\(899\) | 32.1147 | 1.07108 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.2574 | −0.375037 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −23.7639 | −0.790377 | ||||||||
\(905\) | −26.2948 | −0.874070 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.8673 | −1.19095 | −0.595476 | − | 0.803373i | \(-0.703037\pi\) | ||||
−0.595476 | + | 0.803373i | \(0.703037\pi\) | |||||||
\(908\) | −28.6376 | −0.950371 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.61803 | −0.153086 | ||||||||
\(911\) | 9.53643 | 0.315956 | 0.157978 | − | 0.987443i | \(-0.449502\pi\) | ||||
0.157978 | + | 0.987443i | \(0.449502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 75.4074 | 2.49426 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −48.3607 | −1.59788 | ||||||||
\(917\) | −10.4313 | −0.344471 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.1803 | 0.830623 | 0.415311 | − | 0.909679i | \(-0.363673\pi\) | ||||
0.415311 | + | 0.909679i | \(0.363673\pi\) | |||||||
\(920\) | 11.3719 | 0.374919 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.27051 | 0.107709 | ||||||||
\(923\) | −2.53650 | −0.0834901 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.673762 | −0.0221532 | ||||||||
\(926\) | 46.3366 | 1.52271 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −54.0689 | −1.77490 | ||||||||
\(929\) | 42.0386 | 1.37924 | 0.689621 | − | 0.724170i | \(-0.257777\pi\) | ||||
0.689621 | + | 0.724170i | \(0.257777\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.0689 | 0.854373 | ||||||||
\(932\) | −60.2449 | −1.97339 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −45.5066 | −1.48902 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.8197 | −0.353463 | −0.176731 | − | 0.984259i | \(-0.556552\pi\) | ||||
−0.176731 | + | 0.984259i | \(0.556552\pi\) | |||||||
\(938\) | 25.9813 | 0.848320 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19.5623 | −0.638052 | ||||||||
\(941\) | 9.17716 | 0.299167 | 0.149583 | − | 0.988749i | \(-0.452207\pi\) | ||||
0.149583 | + | 0.988749i | \(0.452207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.8328 | 0.385329 | ||||||||
\(944\) | 17.7730 | 0.578462 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.3845 | −0.727397 | −0.363699 | − | 0.931517i | \(-0.618486\pi\) | ||||
−0.363699 | + | 0.931517i | \(0.618486\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.583592 | 0.0189442 | ||||||||
\(950\) | 1.95519 | 0.0634347 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −34.5066 | −1.11836 | ||||||||
\(953\) | −16.8041 | −0.544340 | −0.272170 | − | 0.962249i | \(-0.587741\pi\) | ||||
−0.272170 | + | 0.962249i | \(0.587741\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.3262 | 0.690101 | ||||||||
\(956\) | −29.9657 | −0.969160 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −79.1803 | −2.55820 | ||||||||
\(959\) | 1.32813 | 0.0428876 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.67376 | −0.312057 | ||||||||
\(962\) | 0.894844 | 0.0288509 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −36.6525 | −1.18050 | ||||||||
\(965\) | 15.8636 | 0.510666 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.6869 | 0.568773 | 0.284386 | − | 0.958710i | \(-0.408210\pi\) | ||||
0.284386 | + | 0.958710i | \(0.408210\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 54.4853 | 1.74942 | ||||||||
\(971\) | 1.01460 | 0.0325601 | 0.0162801 | − | 0.999867i | \(-0.494818\pi\) | ||||
0.0162801 | + | 0.999867i | \(0.494818\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.2148 | 1.54569 | ||||||||
\(974\) | −40.5907 | −1.30061 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.9787 | −0.863568 | ||||||||
\(977\) | −3.35733 | −0.107411 | −0.0537053 | − | 0.998557i | \(-0.517103\pi\) | ||||
−0.0537053 | + | 0.998557i | \(0.517103\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −61.5731 | −1.96688 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.7214 | −1.33138 | ||||||||
\(983\) | −50.7085 | −1.61735 | −0.808675 | − | 0.588256i | \(-0.799815\pi\) | ||||
−0.808675 | + | 0.588256i | \(0.799815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.29180 | −0.168611 | ||||||||
\(986\) | 91.6585 | 2.91900 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.47214 | −0.0468349 | ||||||||
\(989\) | −10.7905 | −0.343119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.2705 | −1.85102 | −0.925512 | − | 0.378719i | \(-0.876365\pi\) | ||||
−0.925512 | + | 0.378719i | \(0.876365\pi\) | |||||||
\(992\) | −35.9053 | −1.13999 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −97.8115 | −3.10239 | ||||||||
\(995\) | −0.894844 | −0.0283685 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.7426 | −1.22699 | −0.613496 | − | 0.789698i | \(-0.710237\pi\) | ||||
−0.613496 | + | 0.789698i | \(0.710237\pi\) | |||||||
\(998\) | −70.3627 | −2.22729 | ||||||||
\(999\) | 0 | 0 |
(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 | 1089.2.a.w.1.1 | 4 | ||
3.2 | odd | 2 | inner | 1089.2.a.w.1.4 | 4 | ||
11.2 | odd | 10 | 99.2.f.c.37.1 | ✓ | 8 | ||
11.6 | odd | 10 | 99.2.f.c.91.1 | yes | 8 | ||
11.10 | odd | 2 | 1089.2.a.v.1.4 | 4 | |||
33.2 | even | 10 | 99.2.f.c.37.2 | yes | 8 | ||
33.17 | even | 10 | 99.2.f.c.91.2 | yes | 8 | ||
33.32 | even | 2 | 1089.2.a.v.1.1 | 4 | |||
99.2 | even | 30 | 891.2.n.e.433.2 | 16 | |||
99.13 | odd | 30 | 891.2.n.e.136.2 | 16 | |||
99.50 | even | 30 | 891.2.n.e.784.2 | 16 | |||
99.61 | odd | 30 | 891.2.n.e.190.2 | 16 | |||
99.68 | even | 30 | 891.2.n.e.136.1 | 16 | |||
99.79 | odd | 30 | 891.2.n.e.433.1 | 16 | |||
99.83 | even | 30 | 891.2.n.e.190.1 | 16 | |||
99.94 | odd | 30 | 891.2.n.e.784.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.f.c.37.1 | ✓ | 8 | 11.2 | odd | 10 | ||
99.2.f.c.37.2 | yes | 8 | 33.2 | even | 10 | ||
99.2.f.c.91.1 | yes | 8 | 11.6 | odd | 10 | ||
99.2.f.c.91.2 | yes | 8 | 33.17 | even | 10 | ||
891.2.n.e.136.1 | 16 | 99.68 | even | 30 | |||
891.2.n.e.136.2 | 16 | 99.13 | odd | 30 | |||
891.2.n.e.190.1 | 16 | 99.83 | even | 30 | |||
891.2.n.e.190.2 | 16 | 99.61 | odd | 30 | |||
891.2.n.e.433.1 | 16 | 99.79 | odd | 30 | |||
891.2.n.e.433.2 | 16 | 99.2 | even | 30 | |||
891.2.n.e.784.1 | 16 | 99.94 | odd | 30 | |||
891.2.n.e.784.2 | 16 | 99.50 | even | 30 | |||
1089.2.a.v.1.1 | 4 | 33.32 | even | 2 | |||
1089.2.a.v.1.4 | 4 | 11.10 | odd | 2 | |||
1089.2.a.w.1.1 | 4 | 1.1 | even | 1 | trivial | ||
1089.2.a.w.1.4 | 4 | 3.2 | odd | 2 | inner |