Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4527,2,Mod(1,4527)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4527, 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("4527.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4527 = 3^{2} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4527.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: | \(36.1482769950\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.40552\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4527.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36113 | −0.962467 | −0.481234 | − | 0.876592i | \(-0.659811\pi\) | ||||
−0.481234 | + | 0.876592i | \(0.659811\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.147314 | −0.0736568 | ||||||||
\(5\) | −0.590303 | −0.263991 | −0.131996 | − | 0.991250i | \(-0.542139\pi\) | ||||
−0.131996 | + | 0.991250i | \(0.542139\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.95900 | 0.740431 | 0.370216 | − | 0.928946i | \(-0.379284\pi\) | ||||
0.370216 | + | 0.928946i | \(0.379284\pi\) | |||||||
\(8\) | 2.92278 | 1.03336 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.803481 | 0.254083 | ||||||||
\(11\) | 1.52746 | 0.460546 | 0.230273 | − | 0.973126i | \(-0.426038\pi\) | ||||
0.230273 | + | 0.973126i | \(0.426038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.67738 | −1.29727 | −0.648636 | − | 0.761099i | \(-0.724660\pi\) | ||||
−0.648636 | + | 0.761099i | \(0.724660\pi\) | |||||||
\(14\) | −2.66646 | −0.712641 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.68367 | −0.920918 | ||||||||
\(17\) | 3.04913 | 0.739523 | 0.369761 | − | 0.929127i | \(-0.379439\pi\) | ||||
0.369761 | + | 0.929127i | \(0.379439\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.338159 | 0.0775789 | 0.0387895 | − | 0.999247i | \(-0.487650\pi\) | ||||
0.0387895 | + | 0.999247i | \(0.487650\pi\) | |||||||
\(20\) | 0.0869597 | 0.0194448 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.07908 | −0.443261 | ||||||||
\(23\) | 7.98874 | 1.66577 | 0.832884 | − | 0.553448i | \(-0.186688\pi\) | ||||
0.832884 | + | 0.553448i | \(0.186688\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65154 | −0.930309 | ||||||||
\(26\) | 6.36654 | 1.24858 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.288587 | −0.0545378 | ||||||||
\(29\) | −6.01794 | −1.11750 | −0.558751 | − | 0.829335i | \(-0.688719\pi\) | ||||
−0.558751 | + | 0.829335i | \(0.688719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.17447 | −0.749758 | −0.374879 | − | 0.927074i | \(-0.622316\pi\) | ||||
−0.374879 | + | 0.927074i | \(0.622316\pi\) | |||||||
\(32\) | −0.831593 | −0.147006 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.15028 | −0.711767 | ||||||||
\(35\) | −1.15640 | −0.195468 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.0654 | −1.81914 | −0.909569 | − | 0.415553i | \(-0.863588\pi\) | ||||
−0.909569 | + | 0.415553i | \(0.863588\pi\) | |||||||
\(38\) | −0.460279 | −0.0746672 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.72533 | −0.272798 | ||||||||
\(41\) | 4.82359 | 0.753319 | 0.376659 | − | 0.926352i | \(-0.377073\pi\) | ||||
0.376659 | + | 0.926352i | \(0.377073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.4475 | 1.89822 | 0.949111 | − | 0.314941i | \(-0.101985\pi\) | ||||
0.949111 | + | 0.314941i | \(0.101985\pi\) | |||||||
\(44\) | −0.225016 | −0.0339224 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.8737 | −1.60325 | ||||||||
\(47\) | −11.0094 | −1.60589 | −0.802945 | − | 0.596052i | \(-0.796735\pi\) | ||||
−0.802945 | + | 0.596052i | \(0.796735\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.16233 | −0.451761 | ||||||||
\(50\) | 6.33137 | 0.895391 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.689042 | 0.0955529 | ||||||||
\(53\) | 3.43684 | 0.472087 | 0.236043 | − | 0.971743i | \(-0.424149\pi\) | ||||
0.236043 | + | 0.971743i | \(0.424149\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.901664 | −0.121580 | ||||||||
\(56\) | 5.72572 | 0.765132 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.19122 | 1.07556 | ||||||||
\(59\) | −2.63490 | −0.343034 | −0.171517 | − | 0.985181i | \(-0.554867\pi\) | ||||
−0.171517 | + | 0.985181i | \(0.554867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.4908 | 1.47125 | 0.735625 | − | 0.677389i | \(-0.236889\pi\) | ||||
0.735625 | + | 0.677389i | \(0.236889\pi\) | |||||||
\(62\) | 5.68202 | 0.721617 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.49925 | 1.06241 | ||||||||
\(65\) | 2.76107 | 0.342469 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2554 | −1.25289 | −0.626445 | − | 0.779465i | \(-0.715491\pi\) | ||||
−0.626445 | + | 0.779465i | \(0.715491\pi\) | |||||||
\(68\) | −0.449179 | −0.0544709 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.57402 | 0.188131 | ||||||||
\(71\) | −9.66931 | −1.14754 | −0.573768 | − | 0.819018i | \(-0.694519\pi\) | ||||
−0.573768 | + | 0.819018i | \(0.694519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.33688 | −0.741676 | −0.370838 | − | 0.928698i | \(-0.620929\pi\) | ||||
−0.370838 | + | 0.928698i | \(0.620929\pi\) | |||||||
\(74\) | 15.0615 | 1.75086 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0498154 | −0.00571422 | ||||||||
\(77\) | 2.99229 | 0.341003 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.667323 | −0.0750798 | −0.0375399 | − | 0.999295i | \(-0.511952\pi\) | ||||
−0.0375399 | + | 0.999295i | \(0.511952\pi\) | |||||||
\(80\) | 2.17448 | 0.243114 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.56556 | −0.725045 | ||||||||
\(83\) | 2.26231 | 0.248321 | 0.124161 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124161 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.79991 | −0.195228 | ||||||||
\(86\) | −16.9427 | −1.82698 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.46443 | 0.475910 | ||||||||
\(89\) | −2.21979 | −0.235297 | −0.117649 | − | 0.993055i | \(-0.537536\pi\) | ||||
−0.117649 | + | 0.993055i | \(0.537536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.16297 | −0.960541 | ||||||||
\(92\) | −1.17685 | −0.122695 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.9853 | 1.54562 | ||||||||
\(95\) | −0.199616 | −0.0204802 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.2878 | 1.45070 | 0.725352 | − | 0.688378i | \(-0.241677\pi\) | ||||
0.725352 | + | 0.688378i | \(0.241677\pi\) | |||||||
\(98\) | 4.30435 | 0.434806 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.685236 | 0.0685236 | ||||||||
\(101\) | 0.629834 | 0.0626708 | 0.0313354 | − | 0.999509i | \(-0.490024\pi\) | ||||
0.0313354 | + | 0.999509i | \(0.490024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.51410 | −0.444788 | −0.222394 | − | 0.974957i | \(-0.571387\pi\) | ||||
−0.222394 | + | 0.974957i | \(0.571387\pi\) | |||||||
\(104\) | −13.6710 | −1.34055 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.67801 | −0.454368 | ||||||||
\(107\) | −3.43562 | −0.332134 | −0.166067 | − | 0.986115i | \(-0.553107\pi\) | ||||
−0.166067 | + | 0.986115i | \(0.553107\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.90039 | 0.948285 | 0.474142 | − | 0.880448i | \(-0.342758\pi\) | ||||
0.474142 | + | 0.880448i | \(0.342758\pi\) | |||||||
\(110\) | 1.22729 | 0.117017 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.21630 | −0.681876 | ||||||||
\(113\) | 9.47684 | 0.891506 | 0.445753 | − | 0.895156i | \(-0.352936\pi\) | ||||
0.445753 | + | 0.895156i | \(0.352936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.71578 | −0.439748 | ||||||||
\(116\) | 0.886524 | 0.0823117 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.58645 | 0.330159 | ||||||||
\(119\) | 5.97324 | 0.547566 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.66687 | −0.787897 | ||||||||
\(122\) | −15.6406 | −1.41603 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.614957 | 0.0552248 | ||||||||
\(125\) | 5.69733 | 0.509585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3574 | −1.00781 | −0.503904 | − | 0.863760i | \(-0.668104\pi\) | ||||
−0.503904 | + | 0.863760i | \(0.668104\pi\) | |||||||
\(128\) | −9.90544 | −0.875525 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.75819 | −0.329615 | ||||||||
\(131\) | −15.9119 | −1.39023 | −0.695113 | − | 0.718900i | \(-0.744646\pi\) | ||||
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.662452 | 0.0574419 | ||||||||
\(134\) | 13.9589 | 1.20587 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.91195 | 0.764193 | ||||||||
\(137\) | 15.0390 | 1.28486 | 0.642432 | − | 0.766343i | \(-0.277925\pi\) | ||||
0.642432 | + | 0.766343i | \(0.277925\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.6486 | −1.41212 | −0.706059 | − | 0.708153i | \(-0.749529\pi\) | ||||
−0.706059 | + | 0.708153i | \(0.749529\pi\) | |||||||
\(140\) | 0.170354 | 0.0143975 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 13.1612 | 1.10447 | ||||||||
\(143\) | −7.14451 | −0.597454 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.55241 | 0.295011 | ||||||||
\(146\) | 8.62534 | 0.713838 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.63008 | 0.133992 | ||||||||
\(149\) | 12.0657 | 0.988463 | 0.494232 | − | 0.869330i | \(-0.335450\pi\) | ||||
0.494232 | + | 0.869330i | \(0.335450\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.4897 | −1.34192 | −0.670958 | − | 0.741495i | \(-0.734117\pi\) | ||||
−0.670958 | + | 0.741495i | \(0.734117\pi\) | |||||||
\(152\) | 0.988364 | 0.0801669 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.07291 | −0.328204 | ||||||||
\(155\) | 2.46420 | 0.197930 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.10607 | 0.327700 | 0.163850 | − | 0.986485i | \(-0.447609\pi\) | ||||
0.163850 | + | 0.986485i | \(0.447609\pi\) | |||||||
\(158\) | 0.908317 | 0.0722618 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.490892 | 0.0388084 | ||||||||
\(161\) | 15.6499 | 1.23339 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.2459 | 1.66411 | 0.832053 | − | 0.554696i | \(-0.187165\pi\) | ||||
0.832053 | + | 0.554696i | \(0.187165\pi\) | |||||||
\(164\) | −0.710581 | −0.0554871 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.07931 | −0.239001 | ||||||||
\(167\) | 5.96545 | 0.461620 | 0.230810 | − | 0.972999i | \(-0.425862\pi\) | ||||
0.230810 | + | 0.972999i | \(0.425862\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.87787 | 0.682913 | ||||||||
\(170\) | 2.44992 | 0.187900 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.83368 | −0.139817 | ||||||||
\(173\) | 16.2621 | 1.23638 | 0.618192 | − | 0.786027i | \(-0.287865\pi\) | ||||
0.618192 | + | 0.786027i | \(0.287865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.11236 | −0.688830 | ||||||||
\(176\) | −5.62666 | −0.424125 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.02143 | 0.226466 | ||||||||
\(179\) | −9.36724 | −0.700140 | −0.350070 | − | 0.936723i | \(-0.613842\pi\) | ||||
−0.350070 | + | 0.936723i | \(0.613842\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.62885 | 0.121072 | 0.0605358 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605358 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(182\) | 12.4720 | 0.924489 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.3493 | 1.72134 | ||||||||
\(185\) | 6.53193 | 0.480237 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.65742 | 0.340585 | ||||||||
\(188\) | 1.62184 | 0.118285 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.271704 | 0.0197115 | ||||||||
\(191\) | 8.41952 | 0.609215 | 0.304607 | − | 0.952478i | \(-0.401475\pi\) | ||||
0.304607 | + | 0.952478i | \(0.401475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.9514 | −1.79604 | −0.898022 | − | 0.439950i | \(-0.854996\pi\) | ||||
−0.898022 | + | 0.439950i | \(0.854996\pi\) | |||||||
\(194\) | −19.4476 | −1.39625 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.465854 | 0.0332753 | ||||||||
\(197\) | −2.36559 | −0.168541 | −0.0842705 | − | 0.996443i | \(-0.526856\pi\) | ||||
−0.0842705 | + | 0.996443i | \(0.526856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7817 | 0.835180 | 0.417590 | − | 0.908636i | \(-0.362875\pi\) | ||||
0.417590 | + | 0.908636i | \(0.362875\pi\) | |||||||
\(200\) | −13.5954 | −0.961343 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.857288 | −0.0603186 | ||||||||
\(203\) | −11.7891 | −0.827434 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.84738 | −0.198870 | ||||||||
\(206\) | 6.14430 | 0.428094 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.2299 | 1.19468 | ||||||||
\(209\) | 0.516524 | 0.0357287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.8124 | −1.15742 | −0.578708 | − | 0.815535i | \(-0.696443\pi\) | ||||
−0.578708 | + | 0.815535i | \(0.696443\pi\) | |||||||
\(212\) | −0.506294 | −0.0347724 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.67633 | 0.319668 | ||||||||
\(215\) | −7.34778 | −0.501115 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.17778 | −0.555144 | ||||||||
\(218\) | −13.4758 | −0.912693 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.132827 | 0.00895522 | ||||||||
\(221\) | −14.2619 | −0.959362 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.32490 | 0.557476 | 0.278738 | − | 0.960367i | \(-0.410084\pi\) | ||||
0.278738 | + | 0.960367i | \(0.410084\pi\) | |||||||
\(224\) | −1.62909 | −0.108848 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.8992 | −0.858045 | ||||||||
\(227\) | −6.35919 | −0.422074 | −0.211037 | − | 0.977478i | \(-0.567684\pi\) | ||||
−0.211037 | + | 0.977478i | \(0.567684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4619 | 0.757426 | 0.378713 | − | 0.925514i | \(-0.376367\pi\) | ||||
0.378713 | + | 0.925514i | \(0.376367\pi\) | |||||||
\(230\) | 6.41880 | 0.423243 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.5891 | −1.15478 | ||||||||
\(233\) | −21.5891 | −1.41435 | −0.707175 | − | 0.707039i | \(-0.750031\pi\) | ||||
−0.707175 | + | 0.707039i | \(0.750031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.49890 | 0.423941 | ||||||||
\(236\) | 0.388156 | 0.0252668 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.13038 | −0.527014 | ||||||||
\(239\) | 4.52568 | 0.292742 | 0.146371 | − | 0.989230i | \(-0.453241\pi\) | ||||
0.146371 | + | 0.989230i | \(0.453241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.84982 | −0.634483 | −0.317241 | − | 0.948345i | \(-0.602757\pi\) | ||||
−0.317241 | + | 0.948345i | \(0.602757\pi\) | |||||||
\(242\) | 11.7968 | 0.758325 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.69276 | −0.108368 | ||||||||
\(245\) | 1.86673 | 0.119261 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.58170 | −0.100641 | ||||||||
\(248\) | −12.2011 | −0.774769 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.75483 | −0.490459 | ||||||||
\(251\) | −22.0558 | −1.39215 | −0.696075 | − | 0.717969i | \(-0.745072\pi\) | ||||
−0.696075 | + | 0.717969i | \(0.745072\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2025 | 0.767163 | ||||||||
\(254\) | 15.4590 | 0.969982 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.51587 | −0.219742 | ||||||||
\(257\) | −25.3211 | −1.57948 | −0.789742 | − | 0.613439i | \(-0.789786\pi\) | ||||
−0.789742 | + | 0.613439i | \(0.789786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.6771 | −1.34695 | ||||||||
\(260\) | −0.406743 | −0.0252251 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 21.6582 | 1.33805 | ||||||||
\(263\) | −10.7243 | −0.661289 | −0.330644 | − | 0.943755i | \(-0.607266\pi\) | ||||
−0.330644 | + | 0.943755i | \(0.607266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.02878 | −0.124627 | ||||||||
\(266\) | −0.901686 | −0.0552859 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.51075 | 0.0922839 | ||||||||
\(269\) | 11.9609 | 0.729266 | 0.364633 | − | 0.931151i | \(-0.381194\pi\) | ||||
0.364633 | + | 0.931151i | \(0.381194\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.7258 | −0.712295 | −0.356147 | − | 0.934430i | \(-0.615910\pi\) | ||||
−0.356147 | + | 0.934430i | \(0.615910\pi\) | |||||||
\(272\) | −11.2320 | −0.681040 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.4700 | −1.23664 | ||||||||
\(275\) | −7.10504 | −0.428450 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.916745 | −0.0550819 | −0.0275409 | − | 0.999621i | \(-0.508768\pi\) | ||||
−0.0275409 | + | 0.999621i | \(0.508768\pi\) | |||||||
\(278\) | 22.6610 | 1.35912 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.37991 | −0.201988 | ||||||||
\(281\) | −21.7464 | −1.29728 | −0.648640 | − | 0.761096i | \(-0.724662\pi\) | ||||
−0.648640 | + | 0.761096i | \(0.724662\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.06684 | −0.479524 | −0.239762 | − | 0.970832i | \(-0.577069\pi\) | ||||
−0.239762 | + | 0.970832i | \(0.577069\pi\) | |||||||
\(284\) | 1.42442 | 0.0845238 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.72463 | 0.575030 | ||||||||
\(287\) | 9.44941 | 0.557781 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.70280 | −0.453106 | ||||||||
\(290\) | −4.83530 | −0.283939 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.933509 | 0.0546295 | ||||||||
\(293\) | 2.16609 | 0.126544 | 0.0632722 | − | 0.997996i | \(-0.479846\pi\) | ||||
0.0632722 | + | 0.997996i | \(0.479846\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.55539 | 0.0905581 | ||||||||
\(296\) | −32.3417 | −1.87982 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.4231 | −0.951363 | ||||||||
\(299\) | −37.3664 | −2.16095 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.3846 | 1.40550 | ||||||||
\(302\) | 22.4448 | 1.29155 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.24567 | −0.0714438 | ||||||||
\(305\) | −6.78307 | −0.388397 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.60523 | 0.376980 | 0.188490 | − | 0.982075i | \(-0.439641\pi\) | ||||
0.188490 | + | 0.982075i | \(0.439641\pi\) | |||||||
\(308\) | −0.440805 | −0.0251172 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.35411 | −0.190501 | ||||||||
\(311\) | −3.84184 | −0.217851 | −0.108925 | − | 0.994050i | \(-0.534741\pi\) | ||||
−0.108925 | + | 0.994050i | \(0.534741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4617 | −1.43918 | −0.719591 | − | 0.694398i | \(-0.755671\pi\) | ||||
−0.719591 | + | 0.694398i | \(0.755671\pi\) | |||||||
\(314\) | −5.58891 | −0.315401 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.0983058 | 0.00553014 | ||||||||
\(317\) | 8.23817 | 0.462702 | 0.231351 | − | 0.972870i | \(-0.425686\pi\) | ||||
0.231351 | + | 0.972870i | \(0.425686\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.19216 | −0.514662 | ||||||||
\(320\) | −5.01713 | −0.280466 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −21.3016 | −1.18709 | ||||||||
\(323\) | 1.03109 | 0.0573714 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.7570 | 1.20686 | ||||||||
\(326\) | −28.9185 | −1.60165 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.0983 | 0.778449 | ||||||||
\(329\) | −21.5675 | −1.18905 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.68597 | −0.367494 | −0.183747 | − | 0.982974i | \(-0.558823\pi\) | ||||
−0.183747 | + | 0.982974i | \(0.558823\pi\) | |||||||
\(332\) | −0.333270 | −0.0182906 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.11977 | −0.444294 | ||||||||
\(335\) | 6.05376 | 0.330752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.9491 | −1.90380 | −0.951899 | − | 0.306411i | \(-0.900872\pi\) | ||||
−0.951899 | + | 0.306411i | \(0.900872\pi\) | |||||||
\(338\) | −12.0840 | −0.657282 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.265151 | 0.0143799 | ||||||||
\(341\) | −6.37634 | −0.345298 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.9080 | −1.07493 | ||||||||
\(344\) | 36.3813 | 1.96155 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.1349 | −1.18998 | ||||||||
\(347\) | 16.1317 | 0.865998 | 0.432999 | − | 0.901394i | \(-0.357455\pi\) | ||||
0.432999 | + | 0.901394i | \(0.357455\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.2651 | −0.870653 | −0.435326 | − | 0.900273i | \(-0.643367\pi\) | ||||
−0.435326 | + | 0.900273i | \(0.643367\pi\) | |||||||
\(350\) | 12.4031 | 0.662976 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.27022 | −0.0677032 | ||||||||
\(353\) | −15.5427 | −0.827254 | −0.413627 | − | 0.910446i | \(-0.635738\pi\) | ||||
−0.413627 | + | 0.910446i | \(0.635738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.70782 | 0.302940 | ||||||||
\(356\) | 0.327005 | 0.0173312 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7501 | 0.673862 | ||||||||
\(359\) | 16.5339 | 0.872625 | 0.436312 | − | 0.899795i | \(-0.356284\pi\) | ||||
0.436312 | + | 0.899795i | \(0.356284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8856 | −0.993982 | ||||||||
\(362\) | −2.21708 | −0.116527 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.34983 | 0.0707504 | ||||||||
\(365\) | 3.74068 | 0.195796 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.62500 | 0.293623 | 0.146811 | − | 0.989165i | \(-0.453099\pi\) | ||||
0.146811 | + | 0.989165i | \(0.453099\pi\) | |||||||
\(368\) | −29.4279 | −1.53403 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.89083 | −0.462212 | ||||||||
\(371\) | 6.73277 | 0.349548 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0602 | −0.935122 | −0.467561 | − | 0.883961i | \(-0.654867\pi\) | ||||
−0.467561 | + | 0.883961i | \(0.654867\pi\) | |||||||
\(374\) | −6.33938 | −0.327802 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.1782 | −1.65946 | ||||||||
\(377\) | 28.1482 | 1.44970 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.42773 | −0.124704 | −0.0623521 | − | 0.998054i | \(-0.519860\pi\) | ||||
−0.0623521 | + | 0.998054i | \(0.519860\pi\) | |||||||
\(380\) | 0.0294062 | 0.00150850 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.4601 | −0.586349 | ||||||||
\(383\) | 16.2778 | 0.831757 | 0.415878 | − | 0.909420i | \(-0.363474\pi\) | ||||
0.415878 | + | 0.909420i | \(0.363474\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.76636 | −0.0900219 | ||||||||
\(386\) | 33.9623 | 1.72863 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.10478 | −0.106854 | ||||||||
\(389\) | 15.0862 | 0.764899 | 0.382450 | − | 0.923976i | \(-0.375081\pi\) | ||||
0.382450 | + | 0.923976i | \(0.375081\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.3587 | 1.23187 | ||||||||
\(392\) | −9.24280 | −0.466832 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.21988 | 0.162215 | ||||||||
\(395\) | 0.393923 | 0.0198204 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.7523 | −1.34266 | −0.671329 | − | 0.741160i | \(-0.734276\pi\) | ||||
−0.671329 | + | 0.741160i | \(0.734276\pi\) | |||||||
\(398\) | −16.0364 | −0.803834 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.1348 | 0.856738 | ||||||||
\(401\) | 21.1930 | 1.05833 | 0.529165 | − | 0.848519i | \(-0.322505\pi\) | ||||
0.529165 | + | 0.848519i | \(0.322505\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.5256 | 0.972639 | ||||||||
\(404\) | −0.0927831 | −0.00461613 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.0466 | 0.796378 | ||||||||
\(407\) | −16.9019 | −0.837797 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.2178 | 0.703023 | 0.351511 | − | 0.936184i | \(-0.385668\pi\) | ||||
0.351511 | + | 0.936184i | \(0.385668\pi\) | |||||||
\(410\) | 3.87567 | 0.191406 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.664989 | 0.0327617 | ||||||||
\(413\) | −5.16176 | −0.253993 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.33545 | −0.0655547 | ||||||||
\(416\) | 3.88968 | 0.190707 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.703058 | −0.0343877 | ||||||||
\(419\) | −40.7220 | −1.98940 | −0.994700 | − | 0.102818i | \(-0.967214\pi\) | ||||
−0.994700 | + | 0.102818i | \(0.967214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.2685 | 1.47519 | 0.737597 | − | 0.675241i | \(-0.235960\pi\) | ||||
0.737597 | + | 0.675241i | \(0.235960\pi\) | |||||||
\(422\) | 22.8840 | 1.11397 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.0451 | 0.487835 | ||||||||
\(425\) | −14.1832 | −0.687984 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.5105 | 1.08936 | ||||||||
\(428\) | 0.506113 | 0.0244639 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.0013 | 0.482306 | ||||||||
\(431\) | −14.3367 | −0.690572 | −0.345286 | − | 0.938497i | \(-0.612218\pi\) | ||||
−0.345286 | + | 0.938497i | \(0.612218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.4985 | −1.27344 | −0.636719 | − | 0.771096i | \(-0.719709\pi\) | ||||
−0.636719 | + | 0.771096i | \(0.719709\pi\) | |||||||
\(434\) | 11.1311 | 0.534308 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.45846 | −0.0698477 | ||||||||
\(437\) | 2.70146 | 0.129228 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.2176 | 0.917208 | 0.458604 | − | 0.888641i | \(-0.348350\pi\) | ||||
0.458604 | + | 0.888641i | \(0.348350\pi\) | |||||||
\(440\) | −2.63537 | −0.125636 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.4124 | 0.923355 | ||||||||
\(443\) | 5.97322 | 0.283796 | 0.141898 | − | 0.989881i | \(-0.454679\pi\) | ||||
0.141898 | + | 0.989881i | \(0.454679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.31035 | 0.0621164 | ||||||||
\(446\) | −11.3313 | −0.536553 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.6500 | 0.786639 | ||||||||
\(449\) | −1.84304 | −0.0869784 | −0.0434892 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434892 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.36785 | 0.346938 | ||||||||
\(452\) | −1.39607 | −0.0656655 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.65571 | 0.406233 | ||||||||
\(455\) | 5.40893 | 0.253575 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.3399 | 1.27891 | 0.639453 | − | 0.768830i | \(-0.279161\pi\) | ||||
0.639453 | + | 0.768830i | \(0.279161\pi\) | |||||||
\(458\) | −15.6012 | −0.728998 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.694698 | 0.0323905 | ||||||||
\(461\) | −35.1434 | −1.63679 | −0.818395 | − | 0.574656i | \(-0.805136\pi\) | ||||
−0.818395 | + | 0.574656i | \(0.805136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6765 | −0.867969 | −0.433984 | − | 0.900920i | \(-0.642893\pi\) | ||||
−0.433984 | + | 0.900920i | \(0.642893\pi\) | |||||||
\(464\) | 22.1681 | 1.02913 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.3857 | 1.36126 | ||||||||
\(467\) | 16.9925 | 0.786318 | 0.393159 | − | 0.919470i | \(-0.371382\pi\) | ||||
0.393159 | + | 0.919470i | \(0.371382\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0902 | −0.927680 | ||||||||
\(470\) | −8.84588 | −0.408030 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.70123 | −0.354478 | ||||||||
\(473\) | 19.0130 | 0.874220 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.57296 | −0.0721723 | ||||||||
\(476\) | −0.879940 | −0.0403320 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.16006 | −0.281755 | ||||||||
\(479\) | 11.4554 | 0.523409 | 0.261705 | − | 0.965148i | \(-0.415715\pi\) | ||||
0.261705 | + | 0.965148i | \(0.415715\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 51.7570 | 2.35992 | ||||||||
\(482\) | 13.4069 | 0.610669 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.27675 | 0.0580340 | ||||||||
\(485\) | −8.43411 | −0.382973 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.2183 | −0.644295 | −0.322147 | − | 0.946690i | \(-0.604405\pi\) | ||||
−0.322147 | + | 0.946690i | \(0.604405\pi\) | |||||||
\(488\) | 33.5852 | 1.52033 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.54087 | −0.114785 | ||||||||
\(491\) | 4.53402 | 0.204617 | 0.102309 | − | 0.994753i | \(-0.467377\pi\) | ||||
0.102309 | + | 0.994753i | \(0.467377\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.3495 | −0.826419 | ||||||||
\(494\) | 2.15290 | 0.0968636 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.3774 | 0.690465 | ||||||||
\(497\) | −18.9421 | −0.849671 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.1411 | −1.70743 | −0.853715 | − | 0.520741i | \(-0.825656\pi\) | ||||
−0.853715 | + | 0.520741i | \(0.825656\pi\) | |||||||
\(500\) | −0.839295 | −0.0375344 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 30.0209 | 1.33990 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.371793 | −0.0165446 | ||||||||
\(506\) | −16.6092 | −0.738369 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.67310 | 0.0742319 | ||||||||
\(509\) | −34.3114 | −1.52083 | −0.760413 | − | 0.649440i | \(-0.775003\pi\) | ||||
−0.760413 | + | 0.649440i | \(0.775003\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4139 | −0.549160 | ||||||||
\(512\) | 24.5965 | 1.08702 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 34.4654 | 1.52020 | ||||||||
\(515\) | 2.66469 | 0.117420 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.8165 | −0.739587 | ||||||||
\(518\) | 29.5054 | 1.29639 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.07001 | 0.353893 | ||||||||
\(521\) | −23.8175 | −1.04346 | −0.521732 | − | 0.853110i | \(-0.674714\pi\) | ||||
−0.521732 | + | 0.853110i | \(0.674714\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.16718 | −0.0947643 | −0.0473821 | − | 0.998877i | \(-0.515088\pi\) | ||||
−0.0473821 | + | 0.998877i | \(0.515088\pi\) | |||||||
\(524\) | 2.34404 | 0.102400 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.5972 | 0.636469 | ||||||||
\(527\) | −12.7285 | −0.554463 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.8200 | 1.77478 | ||||||||
\(530\) | 2.76144 | 0.119949 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.0975882 | −0.00423099 | ||||||||
\(533\) | −22.5618 | −0.977259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.02805 | 0.0876804 | ||||||||
\(536\) | −29.9742 | −1.29469 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.2803 | −0.701895 | ||||||||
\(539\) | −4.83033 | −0.208057 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.5019 | 0.580493 | 0.290246 | − | 0.956952i | \(-0.406263\pi\) | ||||
0.290246 | + | 0.956952i | \(0.406263\pi\) | |||||||
\(542\) | 15.9605 | 0.685560 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.53564 | −0.108714 | ||||||||
\(545\) | −5.84423 | −0.250339 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.05880 | −0.0452710 | −0.0226355 | − | 0.999744i | \(-0.507206\pi\) | ||||
−0.0226355 | + | 0.999744i | \(0.507206\pi\) | |||||||
\(548\) | −2.21544 | −0.0946390 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.67092 | 0.412369 | ||||||||
\(551\) | −2.03502 | −0.0866947 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.30728 | −0.0555914 | ||||||||
\(554\) | 1.24781 | 0.0530145 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.45257 | 0.104012 | ||||||||
\(557\) | 9.20176 | 0.389891 | 0.194946 | − | 0.980814i | \(-0.437547\pi\) | ||||
0.194946 | + | 0.980814i | \(0.437547\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −58.2216 | −2.46251 | ||||||||
\(560\) | 4.25980 | 0.180010 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29.5997 | 1.24859 | ||||||||
\(563\) | 29.6502 | 1.24961 | 0.624804 | − | 0.780782i | \(-0.285179\pi\) | ||||
0.624804 | + | 0.780782i | \(0.285179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.59420 | −0.235350 | ||||||||
\(566\) | 10.9800 | 0.461526 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.2613 | −1.18582 | ||||||||
\(569\) | −22.6715 | −0.950439 | −0.475220 | − | 0.879867i | \(-0.657631\pi\) | ||||
−0.475220 | + | 0.879867i | \(0.657631\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.2013 | −1.30573 | −0.652866 | − | 0.757473i | \(-0.726434\pi\) | ||||
−0.652866 | + | 0.757473i | \(0.726434\pi\) | |||||||
\(572\) | 1.05248 | 0.0440065 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.8619 | −0.536846 | ||||||||
\(575\) | −37.1600 | −1.54968 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.98191 | −0.165769 | −0.0828845 | − | 0.996559i | \(-0.526413\pi\) | ||||
−0.0828845 | + | 0.996559i | \(0.526413\pi\) | |||||||
\(578\) | 10.4845 | 0.436099 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.523318 | −0.0217296 | ||||||||
\(581\) | 4.43187 | 0.183865 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.24964 | 0.217418 | ||||||||
\(584\) | −18.5213 | −0.766418 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.94834 | −0.121795 | ||||||||
\(587\) | 12.7494 | 0.526225 | 0.263113 | − | 0.964765i | \(-0.415251\pi\) | ||||
0.263113 | + | 0.964765i | \(0.415251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.41163 | −0.0581654 | ||||||||
\(590\) | −2.11709 | −0.0871592 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 40.7612 | 1.67528 | ||||||||
\(593\) | 3.27771 | 0.134600 | 0.0672998 | − | 0.997733i | \(-0.478562\pi\) | ||||
0.0672998 | + | 0.997733i | \(0.478562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.52602 | −0.144553 | ||||||||
\(596\) | −1.77745 | −0.0728070 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 50.8606 | 2.07985 | ||||||||
\(599\) | −10.9237 | −0.446332 | −0.223166 | − | 0.974780i | \(-0.571639\pi\) | ||||
−0.223166 | + | 0.974780i | \(0.571639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.7446 | −1.21331 | −0.606653 | − | 0.794967i | \(-0.707488\pi\) | ||||
−0.606653 | + | 0.794967i | \(0.707488\pi\) | |||||||
\(602\) | −33.1907 | −1.35275 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.42916 | 0.0988413 | ||||||||
\(605\) | 5.11608 | 0.207998 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.8414 | −1.77947 | −0.889735 | − | 0.456478i | \(-0.849111\pi\) | ||||
−0.889735 | + | 0.456478i | \(0.849111\pi\) | |||||||
\(608\) | −0.281210 | −0.0114046 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.23267 | 0.373820 | ||||||||
\(611\) | 51.4953 | 2.08328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −32.3195 | −1.30537 | −0.652687 | − | 0.757628i | \(-0.726358\pi\) | ||||
−0.652687 | + | 0.757628i | \(0.726358\pi\) | |||||||
\(614\) | −8.99061 | −0.362831 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.74581 | 0.352379 | ||||||||
\(617\) | −40.9696 | −1.64937 | −0.824687 | − | 0.565589i | \(-0.808649\pi\) | ||||
−0.824687 | + | 0.565589i | \(0.808649\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.5775 | 0.907466 | 0.453733 | − | 0.891138i | \(-0.350092\pi\) | ||||
0.453733 | + | 0.891138i | \(0.350092\pi\) | |||||||
\(620\) | −0.363011 | −0.0145789 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.22926 | 0.209674 | ||||||||
\(623\) | −4.34856 | −0.174221 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.8946 | 0.795782 | ||||||||
\(626\) | 34.6568 | 1.38517 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.604880 | −0.0241373 | ||||||||
\(629\) | −33.7398 | −1.34529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.9719 | 1.35240 | 0.676199 | − | 0.736719i | \(-0.263626\pi\) | ||||
0.676199 | + | 0.736719i | \(0.263626\pi\) | |||||||
\(632\) | −1.95044 | −0.0775844 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.2132 | −0.445335 | ||||||||
\(635\) | 6.70432 | 0.266053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7914 | 0.586057 | ||||||||
\(638\) | 12.5118 | 0.495345 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.84721 | 0.231131 | ||||||||
\(641\) | 4.53431 | 0.179095 | 0.0895473 | − | 0.995983i | \(-0.471458\pi\) | ||||
0.0895473 | + | 0.995983i | \(0.471458\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.3929 | 1.51407 | 0.757033 | − | 0.653376i | \(-0.226648\pi\) | ||||
0.757033 | + | 0.653376i | \(0.226648\pi\) | |||||||
\(644\) | −2.30545 | −0.0908473 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.40345 | −0.0552181 | ||||||||
\(647\) | 0.255028 | 0.0100262 | 0.00501309 | − | 0.999987i | \(-0.498404\pi\) | ||||
0.00501309 | + | 0.999987i | \(0.498404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.02470 | −0.157983 | ||||||||
\(650\) | −29.6142 | −1.16157 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.12981 | −0.122573 | ||||||||
\(653\) | 2.04379 | 0.0799797 | 0.0399898 | − | 0.999200i | \(-0.487267\pi\) | ||||
0.0399898 | + | 0.999200i | \(0.487267\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.39282 | 0.367008 | ||||||||
\(656\) | −17.7685 | −0.693745 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29.3562 | 1.14442 | ||||||||
\(659\) | −10.0768 | −0.392534 | −0.196267 | − | 0.980550i | \(-0.562882\pi\) | ||||
−0.196267 | + | 0.980550i | \(0.562882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.53010 | −0.215096 | −0.107548 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107548 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(662\) | 9.10050 | 0.353701 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.61225 | 0.256605 | ||||||||
\(665\) | −0.391047 | −0.0151642 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.0757 | −1.86150 | ||||||||
\(668\) | −0.878791 | −0.0340015 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.23998 | −0.318338 | ||||||||
\(671\) | 17.5518 | 0.677579 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.16280 | −0.121917 | −0.0609585 | − | 0.998140i | \(-0.519416\pi\) | ||||
−0.0609585 | + | 0.998140i | \(0.519416\pi\) | |||||||
\(674\) | 47.5704 | 1.83234 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.30783 | −0.0503012 | ||||||||
\(677\) | 47.8219 | 1.83794 | 0.918972 | − | 0.394323i | \(-0.129021\pi\) | ||||
0.918972 | + | 0.394323i | \(0.129021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.9897 | 1.07415 | ||||||||
\(680\) | −5.26075 | −0.201740 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.67906 | 0.332338 | ||||||||
\(683\) | −13.2468 | −0.506873 | −0.253437 | − | 0.967352i | \(-0.581561\pi\) | ||||
−0.253437 | + | 0.967352i | \(0.581561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.87754 | −0.339193 | ||||||||
\(686\) | 27.0974 | 1.03458 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −45.8524 | −1.74811 | ||||||||
\(689\) | −16.0754 | −0.612425 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.80850 | −0.297049 | −0.148525 | − | 0.988909i | \(-0.547452\pi\) | ||||
−0.148525 | + | 0.988909i | \(0.547452\pi\) | |||||||
\(692\) | −2.39563 | −0.0910681 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.9575 | −0.833494 | ||||||||
\(695\) | 9.82774 | 0.372787 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7078 | 0.557097 | ||||||||
\(698\) | 22.1390 | 0.837975 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.34237 | 0.0507370 | ||||||||
\(701\) | −7.68972 | −0.290437 | −0.145218 | − | 0.989400i | \(-0.546388\pi\) | ||||
−0.145218 | + | 0.989400i | \(0.546388\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.74185 | −0.141127 | ||||||||
\(704\) | 12.9823 | 0.489288 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.1557 | 0.796205 | ||||||||
\(707\) | 1.23384 | 0.0464034 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.0522 | 1.16619 | 0.583096 | − | 0.812403i | \(-0.301841\pi\) | ||||
0.583096 | + | 0.812403i | \(0.301841\pi\) | |||||||
\(710\) | −7.76911 | −0.291569 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.48796 | −0.243146 | ||||||||
\(713\) | −33.3488 | −1.24892 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.21742 | 0.157723 | ||||||||
\(716\) | 1.37992 | 0.0515701 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.5048 | −0.839873 | ||||||||
\(719\) | 30.4494 | 1.13557 | 0.567786 | − | 0.823176i | \(-0.307800\pi\) | ||||
0.567786 | + | 0.823176i | \(0.307800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.84312 | −0.329335 | ||||||||
\(722\) | 25.7059 | 0.956675 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.239952 | −0.00891774 | ||||||||
\(725\) | 27.9927 | 1.03962 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.14587 | −0.227938 | −0.113969 | − | 0.993484i | \(-0.536356\pi\) | ||||
−0.113969 | + | 0.993484i | \(0.536356\pi\) | |||||||
\(728\) | −26.7814 | −0.992584 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.09156 | −0.188447 | ||||||||
\(731\) | 37.9540 | 1.40378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.4237 | −0.939046 | −0.469523 | − | 0.882920i | \(-0.655574\pi\) | ||||
−0.469523 | + | 0.882920i | \(0.655574\pi\) | |||||||
\(734\) | −7.65638 | −0.282602 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.64338 | −0.244878 | ||||||||
\(737\) | −15.6646 | −0.577014 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.8464 | −0.730063 | −0.365032 | − | 0.930995i | \(-0.618942\pi\) | ||||
−0.365032 | + | 0.930995i | \(0.618942\pi\) | |||||||
\(740\) | −0.962242 | −0.0353727 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.16420 | −0.336428 | ||||||||
\(743\) | 28.7154 | 1.05346 | 0.526732 | − | 0.850031i | \(-0.323417\pi\) | ||||
0.526732 | + | 0.850031i | \(0.323417\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.12243 | −0.260946 | ||||||||
\(746\) | 24.5824 | 0.900025 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.686102 | −0.0250864 | ||||||||
\(749\) | −6.73036 | −0.245922 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0374 | 0.877139 | 0.438569 | − | 0.898697i | \(-0.355485\pi\) | ||||
0.438569 | + | 0.898697i | \(0.355485\pi\) | |||||||
\(752\) | 40.5551 | 1.47889 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −38.3134 | −1.39529 | ||||||||
\(755\) | 9.73394 | 0.354254 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.2463 | −0.844902 | −0.422451 | − | 0.906386i | \(-0.638830\pi\) | ||||
−0.422451 | + | 0.906386i | \(0.638830\pi\) | |||||||
\(758\) | 3.30447 | 0.120024 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.583434 | −0.0211634 | ||||||||
\(761\) | −44.3555 | −1.60789 | −0.803943 | − | 0.594706i | \(-0.797268\pi\) | ||||
−0.803943 | + | 0.594706i | \(0.797268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3948 | 0.702140 | ||||||||
\(764\) | −1.24031 | −0.0448728 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.1563 | −0.800539 | ||||||||
\(767\) | 12.3244 | 0.445009 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.4534 | −0.629385 | −0.314693 | − | 0.949194i | \(-0.601901\pi\) | ||||
−0.314693 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(770\) | 2.40425 | 0.0866431 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.67569 | 0.132291 | ||||||||
\(773\) | 1.73607 | 0.0624422 | 0.0312211 | − | 0.999513i | \(-0.490060\pi\) | ||||
0.0312211 | + | 0.999513i | \(0.490060\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.4177 | 0.697506 | ||||||||
\(776\) | 41.7600 | 1.49910 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.5343 | −0.736190 | ||||||||
\(779\) | 1.63114 | 0.0584417 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.7695 | −0.528493 | ||||||||
\(782\) | −33.1555 | −1.18564 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.6490 | 0.416035 | ||||||||
\(785\) | −2.42383 | −0.0865100 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.1636 | −0.576169 | −0.288085 | − | 0.957605i | \(-0.593018\pi\) | ||||
−0.288085 | + | 0.957605i | \(0.593018\pi\) | |||||||
\(788\) | 0.348483 | 0.0124142 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.536182 | −0.0190765 | ||||||||
\(791\) | 18.5651 | 0.660099 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −53.7469 | −1.90861 | ||||||||
\(794\) | 36.4134 | 1.29226 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.73560 | −0.0615167 | ||||||||
\(797\) | 26.8208 | 0.950040 | 0.475020 | − | 0.879975i | \(-0.342441\pi\) | ||||
0.475020 | + | 0.879975i | \(0.342441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.5692 | −1.18759 | ||||||||
\(800\) | 3.86819 | 0.136761 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.8466 | −1.01861 | ||||||||
\(803\) | −9.67933 | −0.341576 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.23819 | −0.325603 | ||||||||
\(806\) | −26.5770 | −0.936133 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.84087 | 0.0647615 | ||||||||
\(809\) | −33.4065 | −1.17451 | −0.587255 | − | 0.809402i | \(-0.699791\pi\) | ||||
−0.587255 | + | 0.809402i | \(0.699791\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.8499 | 1.22375 | 0.611873 | − | 0.790956i | \(-0.290416\pi\) | ||||
0.611873 | + | 0.790956i | \(0.290416\pi\) | |||||||
\(812\) | 1.73670 | 0.0609462 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23.0058 | 0.806352 | ||||||||
\(815\) | −12.5415 | −0.439310 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.20922 | 0.147262 | ||||||||
\(818\) | −19.3523 | −0.676636 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.419458 | 0.0146481 | ||||||||
\(821\) | 24.4182 | 0.852201 | 0.426101 | − | 0.904676i | \(-0.359887\pi\) | ||||
0.426101 | + | 0.904676i | \(0.359887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.51039 | 0.157222 | 0.0786112 | − | 0.996905i | \(-0.474951\pi\) | ||||
0.0786112 | + | 0.996905i | \(0.474951\pi\) | |||||||
\(824\) | −13.1937 | −0.459626 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.02584 | 0.244460 | ||||||||
\(827\) | 2.91499 | 0.101364 | 0.0506821 | − | 0.998715i | \(-0.483860\pi\) | ||||
0.0506821 | + | 0.998715i | \(0.483860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.2382 | 1.22387 | 0.611937 | − | 0.790906i | \(-0.290390\pi\) | ||||
0.611937 | + | 0.790906i | \(0.290390\pi\) | |||||||
\(830\) | 1.81773 | 0.0630943 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −39.7542 | −1.37823 | ||||||||
\(833\) | −9.64236 | −0.334088 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.52142 | −0.121864 | ||||||||
\(836\) | −0.0760910 | −0.00263166 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 55.4281 | 1.91473 | ||||||||
\(839\) | 14.4876 | 0.500166 | 0.250083 | − | 0.968224i | \(-0.419542\pi\) | ||||
0.250083 | + | 0.968224i | \(0.419542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.21557 | 0.248813 | ||||||||
\(842\) | −41.1994 | −1.41983 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.47670 | 0.0852515 | ||||||||
\(845\) | −5.24063 | −0.180283 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.9784 | −0.583384 | ||||||||
\(848\) | −12.6602 | −0.434753 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.3052 | 0.662163 | ||||||||
\(851\) | −88.3985 | −3.03026 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.92917 | 0.168772 | 0.0843858 | − | 0.996433i | \(-0.473107\pi\) | ||||
0.0843858 | + | 0.996433i | \(0.473107\pi\) | |||||||
\(854\) | −30.6398 | −1.04847 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0416 | −0.343213 | ||||||||
\(857\) | −52.5344 | −1.79454 | −0.897270 | − | 0.441482i | \(-0.854453\pi\) | ||||
−0.897270 | + | 0.441482i | \(0.854453\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.5431 | 1.11036 | 0.555179 | − | 0.831731i | \(-0.312650\pi\) | ||||
0.555179 | + | 0.831731i | \(0.312650\pi\) | |||||||
\(860\) | 1.08243 | 0.0369105 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.5141 | 0.664653 | ||||||||
\(863\) | −51.5604 | −1.75514 | −0.877568 | − | 0.479451i | \(-0.840836\pi\) | ||||
−0.877568 | + | 0.479451i | \(0.840836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.59956 | −0.326395 | ||||||||
\(866\) | 36.0681 | 1.22564 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.20470 | 0.0408901 | ||||||||
\(869\) | −1.01931 | −0.0345777 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 47.9682 | 1.62534 | ||||||||
\(872\) | 28.9367 | 0.979919 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.67705 | −0.124378 | ||||||||
\(875\) | 11.1611 | 0.377313 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.8616 | 1.21096 | 0.605481 | − | 0.795860i | \(-0.292981\pi\) | ||||
0.605481 | + | 0.795860i | \(0.292981\pi\) | |||||||
\(878\) | −26.1578 | −0.882783 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.32143 | 0.111965 | ||||||||
\(881\) | 41.2432 | 1.38952 | 0.694759 | − | 0.719243i | \(-0.255511\pi\) | ||||
0.694759 | + | 0.719243i | \(0.255511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.3041 | 0.817898 | 0.408949 | − | 0.912557i | \(-0.365895\pi\) | ||||
0.408949 | + | 0.912557i | \(0.365895\pi\) | |||||||
\(884\) | 2.10098 | 0.0706636 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.13035 | −0.273144 | ||||||||
\(887\) | −51.7010 | −1.73595 | −0.867975 | − | 0.496608i | \(-0.834579\pi\) | ||||
−0.867975 | + | 0.496608i | \(0.834579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.2492 | −0.746213 | ||||||||
\(890\) | −1.78356 | −0.0597850 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.22637 | −0.0410619 | ||||||||
\(893\) | −3.72294 | −0.124583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.52951 | 0.184831 | ||||||||
\(896\) | −19.4047 | −0.648266 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.50862 | 0.0837138 | ||||||||
\(899\) | 25.1217 | 0.837856 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.4794 | 0.349119 | ||||||||
\(902\) | −10.0286 | −0.333917 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.6987 | 0.921246 | ||||||||
\(905\) | −0.961515 | −0.0319618 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.06194 | −0.168079 | −0.0840395 | − | 0.996462i | \(-0.526782\pi\) | ||||
−0.0840395 | + | 0.996462i | \(0.526782\pi\) | |||||||
\(908\) | 0.936796 | 0.0310887 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.36228 | −0.244057 | ||||||||
\(911\) | 40.4144 | 1.33899 | 0.669495 | − | 0.742817i | \(-0.266511\pi\) | ||||
0.669495 | + | 0.742817i | \(0.266511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.45559 | 0.114363 | ||||||||
\(914\) | −37.2133 | −1.23091 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.68850 | −0.0557896 | ||||||||
\(917\) | −31.1713 | −1.02937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.2276 | 1.03010 | 0.515052 | − | 0.857159i | \(-0.327773\pi\) | ||||
0.515052 | + | 0.857159i | \(0.327773\pi\) | |||||||
\(920\) | −13.7832 | −0.454418 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 47.8349 | 1.57536 | ||||||||
\(923\) | 45.2270 | 1.48867 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 51.4711 | 1.69236 | ||||||||
\(926\) | 25.4212 | 0.835391 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.00447 | 0.164280 | ||||||||
\(929\) | 51.3773 | 1.68563 | 0.842817 | − | 0.538201i | \(-0.180896\pi\) | ||||
0.842817 | + | 0.538201i | \(0.180896\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06937 | −0.0350472 | ||||||||
\(932\) | 3.18037 | 0.104176 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −23.1290 | −0.756805 | ||||||||
\(935\) | −2.74929 | −0.0899114 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.6093 | 0.738614 | 0.369307 | − | 0.929307i | \(-0.379595\pi\) | ||||
0.369307 | + | 0.929307i | \(0.379595\pi\) | |||||||
\(938\) | 27.3455 | 0.892861 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.957377 | −0.0312262 | ||||||||
\(941\) | 51.2485 | 1.67065 | 0.835326 | − | 0.549754i | \(-0.185279\pi\) | ||||
0.835326 | + | 0.549754i | \(0.185279\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.5344 | 1.25485 | ||||||||
\(944\) | 9.70610 | 0.315906 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.8793 | −0.841408 | ||||||||
\(947\) | 54.1474 | 1.75955 | 0.879777 | − | 0.475387i | \(-0.157692\pi\) | ||||
0.879777 | + | 0.475387i | \(0.157692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.6400 | 0.962155 | ||||||||
\(950\) | 2.14101 | 0.0694635 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 17.4585 | 0.565833 | ||||||||
\(953\) | 34.0986 | 1.10456 | 0.552281 | − | 0.833658i | \(-0.313758\pi\) | ||||
0.552281 | + | 0.833658i | \(0.313758\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.97006 | −0.160827 | ||||||||
\(956\) | −0.666695 | −0.0215624 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.5923 | −0.503764 | ||||||||
\(959\) | 29.4613 | 0.951354 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5738 | −0.437863 | ||||||||
\(962\) | −70.4482 | −2.27134 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.45101 | 0.0467340 | ||||||||
\(965\) | 14.7289 | 0.474140 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.9385 | 0.673336 | 0.336668 | − | 0.941623i | \(-0.390700\pi\) | ||||
0.336668 | + | 0.941623i | \(0.390700\pi\) | |||||||
\(968\) | −25.3314 | −0.814181 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.4800 | 0.368599 | ||||||||
\(971\) | 5.00722 | 0.160689 | 0.0803447 | − | 0.996767i | \(-0.474398\pi\) | ||||
0.0803447 | + | 0.996767i | \(0.474398\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.6146 | −1.04558 | ||||||||
\(974\) | 19.3531 | 0.620113 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.3284 | −1.35490 | ||||||||
\(977\) | −12.5547 | −0.401662 | −0.200831 | − | 0.979626i | \(-0.564364\pi\) | ||||
−0.200831 | + | 0.979626i | \(0.564364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.39064 | −0.108365 | ||||||||
\(980\) | −0.274995 | −0.00878440 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.17140 | −0.196937 | ||||||||
\(983\) | −1.43810 | −0.0458683 | −0.0229341 | − | 0.999737i | \(-0.507301\pi\) | ||||
−0.0229341 | + | 0.999737i | \(0.507301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.39641 | 0.0444934 | ||||||||
\(986\) | 24.9761 | 0.795401 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.233005 | 0.00741289 | ||||||||
\(989\) | 99.4397 | 3.16200 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.6595 | −1.32336 | −0.661678 | − | 0.749788i | \(-0.730155\pi\) | ||||
−0.661678 | + | 0.749788i | \(0.730155\pi\) | |||||||
\(992\) | 3.47146 | 0.110219 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.7828 | 0.817781 | ||||||||
\(995\) | −6.95475 | −0.220480 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.5145 | 1.47313 | 0.736564 | − | 0.676367i | \(-0.236447\pi\) | ||||
0.736564 | + | 0.676367i | \(0.236447\pi\) | |||||||
\(998\) | 51.9151 | 1.64334 | ||||||||
\(999\) | 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 | 4527.2.a.k.1.2 | 10 | ||
3.2 | odd | 2 | 503.2.a.e.1.9 | ✓ | 10 | ||
12.11 | even | 2 | 8048.2.a.p.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.9 | ✓ | 10 | 3.2 | odd | 2 | ||
4527.2.a.k.1.2 | 10 | 1.1 | even | 1 | trivial | ||
8048.2.a.p.1.9 | 10 | 12.11 | even | 2 |