Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8649,2,Mod(1,8649)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8649, 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("8649.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8649 = 3^{2} \cdot 31^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8649.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: | \(69.0626127082\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 19x^{10} + 129x^{8} - 379x^{6} + 473x^{4} - 210x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 279) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.937929\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8649.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.937929 | 0.663216 | 0.331608 | − | 0.943417i | \(-0.392409\pi\) | ||||
0.331608 | + | 0.943417i | \(0.392409\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.12029 | −0.560144 | ||||||||
\(5\) | 3.32313 | 1.48615 | 0.743074 | − | 0.669209i | \(-0.233367\pi\) | ||||
0.743074 | + | 0.669209i | \(0.233367\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23052 | −1.22102 | −0.610511 | − | 0.792008i | \(-0.709036\pi\) | ||||
−0.610511 | + | 0.792008i | \(0.709036\pi\) | |||||||
\(8\) | −2.92661 | −1.03471 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.11686 | 0.985637 | ||||||||
\(11\) | −0.334610 | −0.100889 | −0.0504444 | − | 0.998727i | \(-0.516064\pi\) | ||||
−0.0504444 | + | 0.998727i | \(0.516064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81267 | 0.780093 | 0.390047 | − | 0.920795i | \(-0.372459\pi\) | ||||
0.390047 | + | 0.920795i | \(0.372459\pi\) | |||||||
\(14\) | −3.03000 | −0.809801 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.504375 | −0.126094 | ||||||||
\(17\) | 0.999838 | 0.242496 | 0.121248 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121248 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.23052 | 0.511716 | 0.255858 | − | 0.966714i | \(-0.417642\pi\) | ||||
0.255858 | + | 0.966714i | \(0.417642\pi\) | |||||||
\(20\) | −3.72286 | −0.832458 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.313840 | −0.0669110 | ||||||||
\(23\) | −5.04233 | −1.05140 | −0.525699 | − | 0.850671i | \(-0.676196\pi\) | ||||
−0.525699 | + | 0.850671i | \(0.676196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.04318 | 1.20864 | ||||||||
\(26\) | 2.63808 | 0.517370 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.61911 | 0.683948 | ||||||||
\(29\) | −5.55488 | −1.03152 | −0.515758 | − | 0.856734i | \(-0.672490\pi\) | ||||
−0.515758 | + | 0.856734i | \(0.672490\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | ||||||||
\(32\) | 5.38015 | 0.951085 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.937777 | 0.160827 | ||||||||
\(35\) | −10.7354 | −1.81462 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.688947 | −0.113262 | −0.0566311 | − | 0.998395i | \(-0.518036\pi\) | ||||
−0.0566311 | + | 0.998395i | \(0.518036\pi\) | |||||||
\(38\) | 2.09207 | 0.339378 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.72550 | −1.53774 | ||||||||
\(41\) | −9.91069 | −1.54779 | −0.773895 | − | 0.633314i | \(-0.781694\pi\) | ||||
−0.773895 | + | 0.633314i | \(0.781694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.5341 | 1.91143 | 0.955714 | − | 0.294298i | \(-0.0950857\pi\) | ||||
0.955714 | + | 0.294298i | \(0.0950857\pi\) | |||||||
\(44\) | 0.374860 | 0.0565123 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.72934 | −0.697304 | ||||||||
\(47\) | 9.95339 | 1.45185 | 0.725925 | − | 0.687774i | \(-0.241412\pi\) | ||||
0.725925 | + | 0.687774i | \(0.241412\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.43625 | 0.490893 | ||||||||
\(50\) | 5.66808 | 0.801587 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.15100 | −0.436965 | ||||||||
\(53\) | 13.6157 | 1.87026 | 0.935132 | − | 0.354300i | \(-0.115281\pi\) | ||||
0.935132 | + | 0.354300i | \(0.115281\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.11195 | −0.149936 | ||||||||
\(56\) | 9.45447 | 1.26341 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.21009 | −0.684118 | ||||||||
\(59\) | 3.14518 | 0.409468 | 0.204734 | − | 0.978818i | \(-0.434367\pi\) | ||||
0.204734 | + | 0.978818i | \(0.434367\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8984 | −1.39539 | −0.697696 | − | 0.716394i | \(-0.745792\pi\) | ||||
−0.697696 | + | 0.716394i | \(0.745792\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.05495 | 0.756869 | ||||||||
\(65\) | 9.34685 | 1.15933 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.24648 | −0.518790 | −0.259395 | − | 0.965771i | \(-0.583523\pi\) | ||||
−0.259395 | + | 0.965771i | \(0.583523\pi\) | |||||||
\(68\) | −1.12011 | −0.135833 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −10.0691 | −1.20348 | ||||||||
\(71\) | 4.80108 | 0.569784 | 0.284892 | − | 0.958560i | \(-0.408042\pi\) | ||||
0.284892 | + | 0.958560i | \(0.408042\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.96780 | −0.932561 | −0.466280 | − | 0.884637i | \(-0.654406\pi\) | ||||
−0.466280 | + | 0.884637i | \(0.654406\pi\) | |||||||
\(74\) | −0.646183 | −0.0751173 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.49883 | −0.286635 | ||||||||
\(77\) | 1.08096 | 0.123187 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.26511 | 0.254844 | 0.127422 | − | 0.991849i | \(-0.459330\pi\) | ||||
0.127422 | + | 0.991849i | \(0.459330\pi\) | |||||||
\(80\) | −1.67610 | −0.187394 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.29553 | −1.02652 | ||||||||
\(83\) | 16.3640 | 1.79618 | 0.898091 | − | 0.439810i | \(-0.144954\pi\) | ||||
0.898091 | + | 0.439810i | \(0.144954\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.32259 | 0.360385 | ||||||||
\(86\) | 11.7561 | 1.26769 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.979273 | 0.104391 | ||||||||
\(89\) | 12.8544 | 1.36256 | 0.681280 | − | 0.732023i | \(-0.261424\pi\) | ||||
0.681280 | + | 0.732023i | \(0.261424\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.08637 | −0.952510 | ||||||||
\(92\) | 5.64886 | 0.588934 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.33557 | 0.962891 | ||||||||
\(95\) | 7.41230 | 0.760486 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6661 | 1.38758 | 0.693792 | − | 0.720175i | \(-0.255939\pi\) | ||||
0.693792 | + | 0.720175i | \(0.255939\pi\) | |||||||
\(98\) | 3.22296 | 0.325568 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.77011 | −0.677011 | ||||||||
\(101\) | −17.5233 | −1.74364 | −0.871818 | − | 0.489829i | \(-0.837059\pi\) | ||||
−0.871818 | + | 0.489829i | \(0.837059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.66916 | 0.657132 | 0.328566 | − | 0.944481i | \(-0.393435\pi\) | ||||
0.328566 | + | 0.944481i | \(0.393435\pi\) | |||||||
\(104\) | −8.23158 | −0.807172 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.7706 | 1.24039 | ||||||||
\(107\) | −4.80853 | −0.464858 | −0.232429 | − | 0.972613i | \(-0.574667\pi\) | ||||
−0.232429 | + | 0.972613i | \(0.574667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.323585 | 0.0309939 | 0.0154969 | − | 0.999880i | \(-0.495067\pi\) | ||||
0.0154969 | + | 0.999880i | \(0.495067\pi\) | |||||||
\(110\) | −1.04293 | −0.0994397 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.62939 | 0.153963 | ||||||||
\(113\) | −10.2403 | −0.963329 | −0.481664 | − | 0.876356i | \(-0.659968\pi\) | ||||
−0.481664 | + | 0.876356i | \(0.659968\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.7563 | −1.56253 | ||||||||
\(116\) | 6.22307 | 0.577798 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.94996 | 0.271565 | ||||||||
\(119\) | −3.22999 | −0.296093 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8880 | −0.989821 | ||||||||
\(122\) | −10.2219 | −0.925447 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.46663 | 0.310065 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.84316 | 0.163554 | 0.0817769 | − | 0.996651i | \(-0.473941\pi\) | ||||
0.0817769 | + | 0.996651i | \(0.473941\pi\) | |||||||
\(128\) | −5.08119 | −0.449118 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.76668 | 0.768889 | ||||||||
\(131\) | 9.89286 | 0.864343 | 0.432172 | − | 0.901791i | \(-0.357747\pi\) | ||||
0.432172 | + | 0.901791i | \(0.357747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.20573 | −0.624816 | ||||||||
\(134\) | −3.98290 | −0.344070 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.92614 | −0.250914 | ||||||||
\(137\) | 16.7143 | 1.42800 | 0.713999 | − | 0.700146i | \(-0.246882\pi\) | ||||
0.713999 | + | 0.700146i | \(0.246882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.9838 | 1.35573 | 0.677864 | − | 0.735187i | \(-0.262906\pi\) | ||||
0.677864 | + | 0.735187i | \(0.262906\pi\) | |||||||
\(140\) | 12.0268 | 1.01645 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.50308 | 0.377890 | ||||||||
\(143\) | −0.941146 | −0.0787026 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.4596 | −1.53299 | ||||||||
\(146\) | −7.47323 | −0.618489 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.771820 | 0.0634432 | ||||||||
\(149\) | −9.35389 | −0.766301 | −0.383150 | − | 0.923686i | \(-0.625161\pi\) | ||||
−0.383150 | + | 0.923686i | \(0.625161\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.5609 | 1.83598 | 0.917990 | − | 0.396604i | \(-0.129811\pi\) | ||||
0.917990 | + | 0.396604i | \(0.129811\pi\) | |||||||
\(152\) | −6.52786 | −0.529479 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.01387 | 0.0816998 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4691 | 1.31438 | 0.657190 | − | 0.753725i | \(-0.271745\pi\) | ||||
0.657190 | + | 0.753725i | \(0.271745\pi\) | |||||||
\(158\) | 2.12451 | 0.169017 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.8789 | 1.41345 | ||||||||
\(161\) | 16.2893 | 1.28378 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2308 | −1.34962 | −0.674811 | − | 0.737991i | \(-0.735775\pi\) | ||||
−0.674811 | + | 0.737991i | \(0.735775\pi\) | |||||||
\(164\) | 11.1028 | 0.866986 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.3483 | 1.19126 | ||||||||
\(167\) | 12.7718 | 0.988310 | 0.494155 | − | 0.869374i | \(-0.335478\pi\) | ||||
0.494155 | + | 0.869374i | \(0.335478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.08891 | −0.391455 | ||||||||
\(170\) | 3.11635 | 0.239013 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −14.0418 | −1.07068 | ||||||||
\(173\) | 2.43050 | 0.184787 | 0.0923937 | − | 0.995723i | \(-0.470548\pi\) | ||||
0.0923937 | + | 0.995723i | \(0.470548\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.5226 | −1.47577 | ||||||||
\(176\) | 0.168769 | 0.0127214 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.0565 | 0.903671 | ||||||||
\(179\) | 2.14995 | 0.160694 | 0.0803472 | − | 0.996767i | \(-0.474397\pi\) | ||||
0.0803472 | + | 0.996767i | \(0.474397\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.62790 | 0.269660 | 0.134830 | − | 0.990869i | \(-0.456951\pi\) | ||||
0.134830 | + | 0.990869i | \(0.456951\pi\) | |||||||
\(182\) | −8.52237 | −0.631720 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.7569 | 1.08789 | ||||||||
\(185\) | −2.28946 | −0.168324 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.334556 | −0.0244651 | ||||||||
\(188\) | −11.1507 | −0.813246 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.95221 | 0.504366 | ||||||||
\(191\) | −8.66318 | −0.626846 | −0.313423 | − | 0.949614i | \(-0.601476\pi\) | ||||
−0.313423 | + | 0.949614i | \(0.601476\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3715 | 1.17845 | 0.589224 | − | 0.807970i | \(-0.299434\pi\) | ||||
0.589224 | + | 0.807970i | \(0.299434\pi\) | |||||||
\(194\) | 12.8179 | 0.920268 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.84959 | −0.274971 | ||||||||
\(197\) | 3.61105 | 0.257277 | 0.128639 | − | 0.991692i | \(-0.458939\pi\) | ||||
0.128639 | + | 0.991692i | \(0.458939\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.70200 | 0.191540 | 0.0957698 | − | 0.995404i | \(-0.469469\pi\) | ||||
0.0957698 | + | 0.995404i | \(0.469469\pi\) | |||||||
\(200\) | −17.6860 | −1.25059 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −16.4356 | −1.15641 | ||||||||
\(203\) | 17.9452 | 1.25950 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.9345 | −2.30025 | ||||||||
\(206\) | 6.25520 | 0.435820 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.41864 | −0.0983648 | ||||||||
\(209\) | −0.746354 | −0.0516264 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.21680 | −0.496825 | −0.248412 | − | 0.968654i | \(-0.579909\pi\) | ||||
−0.248412 | + | 0.968654i | \(0.579909\pi\) | |||||||
\(212\) | −15.2535 | −1.04762 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.51006 | −0.308301 | ||||||||
\(215\) | 41.6523 | 2.84066 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.303500 | 0.0205556 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.24571 | 0.0839856 | ||||||||
\(221\) | 2.81221 | 0.189170 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8817 | 0.795661 | 0.397830 | − | 0.917459i | \(-0.369763\pi\) | ||||
0.397830 | + | 0.917459i | \(0.369763\pi\) | |||||||
\(224\) | −17.3807 | −1.16130 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.60470 | −0.638895 | ||||||||
\(227\) | 4.85328 | 0.322124 | 0.161062 | − | 0.986944i | \(-0.448508\pi\) | ||||
0.161062 | + | 0.986944i | \(0.448508\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0135 | 0.859956 | 0.429978 | − | 0.902839i | \(-0.358521\pi\) | ||||
0.429978 | + | 0.902839i | \(0.358521\pi\) | |||||||
\(230\) | −15.7162 | −1.03630 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.2570 | 1.06732 | ||||||||
\(233\) | 4.53957 | 0.297397 | 0.148698 | − | 0.988883i | \(-0.452492\pi\) | ||||
0.148698 | + | 0.988883i | \(0.452492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.0764 | 2.15767 | ||||||||
\(236\) | −3.52351 | −0.229361 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.02951 | −0.196374 | ||||||||
\(239\) | 3.58117 | 0.231647 | 0.115823 | − | 0.993270i | \(-0.463049\pi\) | ||||
0.115823 | + | 0.993270i | \(0.463049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.09725 | 0.457174 | 0.228587 | − | 0.973523i | \(-0.426589\pi\) | ||||
0.228587 | + | 0.973523i | \(0.426589\pi\) | |||||||
\(242\) | −10.2122 | −0.656465 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.2093 | 0.781622 | ||||||||
\(245\) | 11.4191 | 0.729539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.27370 | 0.399186 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.25146 | 0.205640 | ||||||||
\(251\) | 14.4295 | 0.910780 | 0.455390 | − | 0.890292i | \(-0.349500\pi\) | ||||
0.455390 | + | 0.890292i | \(0.349500\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.68721 | 0.106074 | ||||||||
\(254\) | 1.72875 | 0.108471 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.8757 | −1.05473 | ||||||||
\(257\) | 11.1555 | 0.695859 | 0.347929 | − | 0.937521i | \(-0.386885\pi\) | ||||
0.347929 | + | 0.937521i | \(0.386885\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.22566 | 0.138295 | ||||||||
\(260\) | −10.4712 | −0.649395 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9.27880 | 0.573246 | ||||||||
\(263\) | −4.02975 | −0.248485 | −0.124243 | − | 0.992252i | \(-0.539650\pi\) | ||||
−0.124243 | + | 0.992252i | \(0.539650\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 45.2468 | 2.77949 | ||||||||
\(266\) | −6.75846 | −0.414388 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.75729 | 0.290597 | ||||||||
\(269\) | −20.4854 | −1.24902 | −0.624510 | − | 0.781017i | \(-0.714701\pi\) | ||||
−0.624510 | + | 0.781017i | \(0.714701\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.68981 | 0.467123 | 0.233561 | − | 0.972342i | \(-0.424962\pi\) | ||||
0.233561 | + | 0.972342i | \(0.424962\pi\) | |||||||
\(272\) | −0.504293 | −0.0305773 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.6768 | 0.947072 | ||||||||
\(275\) | −2.02211 | −0.121938 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.29137 | −0.197759 | −0.0988797 | − | 0.995099i | \(-0.531526\pi\) | ||||
−0.0988797 | + | 0.995099i | \(0.531526\pi\) | |||||||
\(278\) | 14.9917 | 0.899141 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 31.4184 | 1.87761 | ||||||||
\(281\) | 26.2518 | 1.56605 | 0.783024 | − | 0.621991i | \(-0.213676\pi\) | ||||
0.783024 | + | 0.621991i | \(0.213676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.6328 | 1.10761 | 0.553803 | − | 0.832648i | \(-0.313176\pi\) | ||||
0.553803 | + | 0.832648i | \(0.313176\pi\) | |||||||
\(284\) | −5.37860 | −0.319161 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.882728 | −0.0521968 | ||||||||
\(287\) | 32.0167 | 1.88988 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0003 | −0.941196 | ||||||||
\(290\) | −17.3138 | −1.01670 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.92624 | 0.522369 | ||||||||
\(293\) | 22.8158 | 1.33291 | 0.666457 | − | 0.745544i | \(-0.267810\pi\) | ||||
0.666457 | + | 0.745544i | \(0.267810\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.4518 | 0.608530 | ||||||||
\(296\) | 2.01628 | 0.117194 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.77329 | −0.508223 | ||||||||
\(299\) | −14.1824 | −0.820188 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −40.4915 | −2.33389 | ||||||||
\(302\) | 21.1605 | 1.21765 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.12502 | −0.0645242 | ||||||||
\(305\) | −36.2167 | −2.07376 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.73615 | −0.441525 | −0.220763 | − | 0.975328i | \(-0.570855\pi\) | ||||
−0.220763 | + | 0.975328i | \(0.570855\pi\) | |||||||
\(308\) | −1.21099 | −0.0690027 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.3500 | −0.643601 | −0.321800 | − | 0.946808i | \(-0.604288\pi\) | ||||
−0.321800 | + | 0.946808i | \(0.604288\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.6477 | −1.22360 | −0.611801 | − | 0.791011i | \(-0.709555\pi\) | ||||
−0.611801 | + | 0.791011i | \(0.709555\pi\) | |||||||
\(314\) | 15.4469 | 0.871718 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.53757 | −0.142750 | ||||||||
\(317\) | 15.6499 | 0.878987 | 0.439493 | − | 0.898246i | \(-0.355158\pi\) | ||||
0.439493 | + | 0.898246i | \(0.355158\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.85872 | 0.104068 | ||||||||
\(320\) | 20.1214 | 1.12482 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.2782 | 0.851423 | ||||||||
\(323\) | 2.23016 | 0.124089 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.9975 | 0.942849 | ||||||||
\(326\) | −16.1613 | −0.895091 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29.0047 | 1.60152 | ||||||||
\(329\) | −32.1546 | −1.77274 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.9903 | −1.09877 | −0.549384 | − | 0.835570i | \(-0.685138\pi\) | ||||
−0.549384 | + | 0.835570i | \(0.685138\pi\) | |||||||
\(332\) | −18.3324 | −1.00612 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.9790 | 0.655463 | ||||||||
\(335\) | −14.1116 | −0.770999 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.54853 | −0.138827 | −0.0694136 | − | 0.997588i | \(-0.522113\pi\) | ||||
−0.0694136 | + | 0.997588i | \(0.522113\pi\) | |||||||
\(338\) | −4.77304 | −0.259619 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.72226 | −0.201868 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5128 | 0.621631 | ||||||||
\(344\) | −36.6823 | −1.97778 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.27963 | 0.122554 | ||||||||
\(347\) | 26.3242 | 1.41316 | 0.706578 | − | 0.707635i | \(-0.250238\pi\) | ||||
0.706578 | + | 0.707635i | \(0.250238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.9172 | 0.744971 | 0.372486 | − | 0.928038i | \(-0.378506\pi\) | ||||
0.372486 | + | 0.928038i | \(0.378506\pi\) | |||||||
\(350\) | −18.3108 | −0.978755 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.80025 | −0.0959538 | ||||||||
\(353\) | −2.74298 | −0.145994 | −0.0729970 | − | 0.997332i | \(-0.523256\pi\) | ||||
−0.0729970 | + | 0.997332i | \(0.523256\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.9546 | 0.846783 | ||||||||
\(356\) | −14.4006 | −0.763230 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.01650 | 0.106575 | ||||||||
\(359\) | 8.93111 | 0.471366 | 0.235683 | − | 0.971830i | \(-0.424267\pi\) | ||||
0.235683 | + | 0.971830i | \(0.424267\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0248 | −0.738147 | ||||||||
\(362\) | 3.40271 | 0.178843 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.1794 | 0.533543 | ||||||||
\(365\) | −26.4780 | −1.38592 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5480 | 0.863800 | 0.431900 | − | 0.901922i | \(-0.357843\pi\) | ||||
0.431900 | + | 0.901922i | \(0.357843\pi\) | |||||||
\(368\) | 2.54322 | 0.132575 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.14735 | −0.111635 | ||||||||
\(371\) | −43.9859 | −2.28363 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8477 | 0.924121 | 0.462060 | − | 0.886849i | \(-0.347110\pi\) | ||||
0.462060 | + | 0.886849i | \(0.347110\pi\) | |||||||
\(374\) | −0.313790 | −0.0162257 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −29.1297 | −1.50225 | ||||||||
\(377\) | −15.6240 | −0.804678 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3086 | −0.786350 | −0.393175 | − | 0.919464i | \(-0.628623\pi\) | ||||
−0.393175 | + | 0.919464i | \(0.628623\pi\) | |||||||
\(380\) | −8.30392 | −0.425982 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.12545 | −0.415734 | ||||||||
\(383\) | 4.68977 | 0.239636 | 0.119818 | − | 0.992796i | \(-0.461769\pi\) | ||||
0.119818 | + | 0.992796i | \(0.461769\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.59218 | 0.183075 | ||||||||
\(386\) | 15.3553 | 0.781566 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.3100 | −0.777248 | ||||||||
\(389\) | −30.3909 | −1.54088 | −0.770441 | − | 0.637511i | \(-0.779964\pi\) | ||||
−0.770441 | + | 0.637511i | \(0.779964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.04151 | −0.254960 | ||||||||
\(392\) | −10.0566 | −0.507933 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.38691 | 0.170630 | ||||||||
\(395\) | 7.52724 | 0.378737 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.6017 | 1.23472 | 0.617361 | − | 0.786680i | \(-0.288202\pi\) | ||||
0.617361 | + | 0.786680i | \(0.288202\pi\) | |||||||
\(398\) | 2.53428 | 0.127032 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.04803 | −0.152401 | ||||||||
\(401\) | 17.1414 | 0.856002 | 0.428001 | − | 0.903778i | \(-0.359218\pi\) | ||||
0.428001 | + | 0.903778i | \(0.359218\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 19.6312 | 0.976689 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.8313 | 0.835322 | ||||||||
\(407\) | 0.230529 | 0.0114269 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.8218 | 1.42515 | 0.712573 | − | 0.701598i | \(-0.247530\pi\) | ||||
0.712573 | + | 0.701598i | \(0.247530\pi\) | |||||||
\(410\) | −30.8902 | −1.52556 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.47138 | −0.368089 | ||||||||
\(413\) | −10.1606 | −0.499969 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 54.3796 | 2.66939 | ||||||||
\(416\) | 15.1326 | 0.741935 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.700027 | −0.0342394 | ||||||||
\(419\) | −13.1340 | −0.641638 | −0.320819 | − | 0.947141i | \(-0.603958\pi\) | ||||
−0.320819 | + | 0.947141i | \(0.603958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.884246 | −0.0430955 | −0.0215478 | − | 0.999768i | \(-0.506859\pi\) | ||||
−0.0215478 | + | 0.999768i | \(0.506859\pi\) | |||||||
\(422\) | −6.76885 | −0.329502 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −39.8479 | −1.93519 | ||||||||
\(425\) | 6.04220 | 0.293090 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.2074 | 1.70380 | ||||||||
\(428\) | 5.38694 | 0.260388 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 39.0669 | 1.88397 | ||||||||
\(431\) | 24.6917 | 1.18936 | 0.594679 | − | 0.803963i | \(-0.297279\pi\) | ||||
0.594679 | + | 0.803963i | \(0.297279\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.5897 | −1.08559 | −0.542796 | − | 0.839864i | \(-0.682635\pi\) | ||||
−0.542796 | + | 0.839864i | \(0.682635\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.362509 | −0.0173610 | ||||||||
\(437\) | −11.2470 | −0.538017 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.6637 | −1.03395 | −0.516977 | − | 0.855999i | \(-0.672943\pi\) | ||||
−0.516977 | + | 0.855999i | \(0.672943\pi\) | |||||||
\(440\) | 3.25425 | 0.155140 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.63765 | 0.125460 | ||||||||
\(443\) | 3.45850 | 0.164318 | 0.0821592 | − | 0.996619i | \(-0.473818\pi\) | ||||
0.0821592 | + | 0.996619i | \(0.473818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 42.7167 | 2.02497 | ||||||||
\(446\) | 11.1442 | 0.527695 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.5606 | −0.924153 | ||||||||
\(449\) | −22.7874 | −1.07541 | −0.537703 | − | 0.843134i | \(-0.680708\pi\) | ||||
−0.537703 | + | 0.843134i | \(0.680708\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.31622 | 0.156155 | ||||||||
\(452\) | 11.4721 | 0.539603 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.55204 | 0.213638 | ||||||||
\(455\) | −30.1952 | −1.41557 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.754779 | 0.0353070 | 0.0176535 | − | 0.999844i | \(-0.494380\pi\) | ||||
0.0176535 | + | 0.999844i | \(0.494380\pi\) | |||||||
\(458\) | 12.2057 | 0.570336 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 18.7719 | 0.875244 | ||||||||
\(461\) | 2.35672 | 0.109763 | 0.0548817 | − | 0.998493i | \(-0.482522\pi\) | ||||
0.0548817 | + | 0.998493i | \(0.482522\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.1479 | 1.40109 | 0.700547 | − | 0.713606i | \(-0.252939\pi\) | ||||
0.700547 | + | 0.713606i | \(0.252939\pi\) | |||||||
\(464\) | 2.80174 | 0.130068 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.25779 | 0.197238 | ||||||||
\(467\) | −27.5707 | −1.27582 | −0.637910 | − | 0.770111i | \(-0.720201\pi\) | ||||
−0.637910 | + | 0.770111i | \(0.720201\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7183 | 0.633454 | ||||||||
\(470\) | 31.0233 | 1.43100 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.20472 | −0.423681 | ||||||||
\(473\) | −4.19403 | −0.192841 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.4794 | 0.618479 | ||||||||
\(476\) | 3.61853 | 0.165855 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.35889 | 0.153632 | ||||||||
\(479\) | 15.2674 | 0.697587 | 0.348793 | − | 0.937200i | \(-0.386592\pi\) | ||||
0.348793 | + | 0.937200i | \(0.386592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.93778 | −0.0883550 | ||||||||
\(482\) | 6.65672 | 0.303205 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.1977 | 0.554443 | ||||||||
\(485\) | 45.4143 | 2.06216 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.84600 | −0.310222 | −0.155111 | − | 0.987897i | \(-0.549574\pi\) | ||||
−0.155111 | + | 0.987897i | \(0.549574\pi\) | |||||||
\(488\) | 31.8953 | 1.44383 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.7103 | 0.483842 | ||||||||
\(491\) | 30.1317 | 1.35982 | 0.679912 | − | 0.733294i | \(-0.262018\pi\) | ||||
0.679912 | + | 0.733294i | \(0.262018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.55398 | −0.250139 | ||||||||
\(494\) | 5.88429 | 0.264747 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.5100 | −0.695718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.1887 | 1.66480 | 0.832398 | − | 0.554178i | \(-0.186967\pi\) | ||||
0.832398 | + | 0.554178i | \(0.186967\pi\) | |||||||
\(500\) | −3.88363 | −0.173681 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.5338 | 0.604044 | ||||||||
\(503\) | −15.4086 | −0.687035 | −0.343517 | − | 0.939146i | \(-0.611618\pi\) | ||||
−0.343517 | + | 0.939146i | \(0.611618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −58.2323 | −2.59130 | ||||||||
\(506\) | 1.58249 | 0.0703501 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.06487 | −0.0916137 | ||||||||
\(509\) | −16.3722 | −0.725685 | −0.362843 | − | 0.931850i | \(-0.618194\pi\) | ||||
−0.362843 | + | 0.931850i | \(0.618194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.7401 | 1.13868 | ||||||||
\(512\) | −5.66583 | −0.250397 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.4630 | 0.461505 | ||||||||
\(515\) | 22.1625 | 0.976595 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.33050 | −0.146475 | ||||||||
\(518\) | 2.08751 | 0.0917198 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −27.3546 | −1.19958 | ||||||||
\(521\) | −27.8806 | −1.22147 | −0.610735 | − | 0.791835i | \(-0.709126\pi\) | ||||
−0.610735 | + | 0.791835i | \(0.709126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.3134 | −0.625880 | −0.312940 | − | 0.949773i | \(-0.601314\pi\) | ||||
−0.312940 | + | 0.949773i | \(0.601314\pi\) | |||||||
\(524\) | −11.0829 | −0.484157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.77962 | −0.164799 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.42504 | 0.105437 | ||||||||
\(530\) | 42.4383 | 1.84340 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.07250 | 0.349987 | ||||||||
\(533\) | −27.8755 | −1.20742 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.9794 | −0.690848 | ||||||||
\(536\) | 12.4278 | 0.536799 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.2139 | −0.828370 | ||||||||
\(539\) | −1.14980 | −0.0495255 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.6556 | −0.458121 | −0.229061 | − | 0.973412i | \(-0.573565\pi\) | ||||
−0.229061 | + | 0.973412i | \(0.573565\pi\) | |||||||
\(542\) | 7.21249 | 0.309803 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.37928 | 0.230635 | ||||||||
\(545\) | 1.07532 | 0.0460615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.3669 | 0.443257 | 0.221629 | − | 0.975131i | \(-0.428863\pi\) | ||||
0.221629 | + | 0.975131i | \(0.428863\pi\) | |||||||
\(548\) | −18.7248 | −0.799886 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.89660 | −0.0808711 | ||||||||
\(551\) | −12.3903 | −0.527843 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.31747 | −0.311170 | ||||||||
\(554\) | −3.08707 | −0.131157 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.9065 | −0.759404 | ||||||||
\(557\) | 21.0838 | 0.893347 | 0.446674 | − | 0.894697i | \(-0.352608\pi\) | ||||
0.446674 | + | 0.894697i | \(0.352608\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.2541 | 1.49109 | ||||||||
\(560\) | 5.41468 | 0.228812 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24.6223 | 1.03863 | ||||||||
\(563\) | −12.4385 | −0.524221 | −0.262110 | − | 0.965038i | \(-0.584418\pi\) | ||||
−0.262110 | + | 0.965038i | \(0.584418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.0299 | −1.43165 | ||||||||
\(566\) | 17.4763 | 0.734582 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.0509 | −0.589562 | ||||||||
\(569\) | −16.0051 | −0.670967 | −0.335483 | − | 0.942046i | \(-0.608900\pi\) | ||||
−0.335483 | + | 0.942046i | \(0.608900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.7111 | 1.45261 | 0.726307 | − | 0.687371i | \(-0.241235\pi\) | ||||
0.726307 | + | 0.687371i | \(0.241235\pi\) | |||||||
\(572\) | 1.05436 | 0.0440848 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 30.0294 | 1.25340 | ||||||||
\(575\) | −30.4717 | −1.27076 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.2404 | 0.509574 | 0.254787 | − | 0.966997i | \(-0.417995\pi\) | ||||
0.254787 | + | 0.966997i | \(0.417995\pi\) | |||||||
\(578\) | −15.0072 | −0.624216 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.6801 | 0.858693 | ||||||||
\(581\) | −52.8642 | −2.19318 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.55596 | −0.188689 | ||||||||
\(584\) | 23.3186 | 0.964932 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3996 | 0.884010 | ||||||||
\(587\) | −24.6103 | −1.01577 | −0.507887 | − | 0.861424i | \(-0.669573\pi\) | ||||
−0.507887 | + | 0.861424i | \(0.669573\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 9.80308 | 0.403587 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.347487 | 0.0142816 | ||||||||
\(593\) | −6.92065 | −0.284197 | −0.142099 | − | 0.989853i | \(-0.545385\pi\) | ||||
−0.142099 | + | 0.989853i | \(0.545385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.7337 | −0.440038 | ||||||||
\(596\) | 10.4791 | 0.429239 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.3021 | −0.543962 | ||||||||
\(599\) | −28.8675 | −1.17950 | −0.589748 | − | 0.807588i | \(-0.700773\pi\) | ||||
−0.589748 | + | 0.807588i | \(0.700773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.5571 | 0.716169 | 0.358085 | − | 0.933689i | \(-0.383430\pi\) | ||||
0.358085 | + | 0.933689i | \(0.383430\pi\) | |||||||
\(602\) | −37.9782 | −1.54788 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.2747 | −1.02841 | ||||||||
\(605\) | −36.1823 | −1.47102 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.52381 | −0.183616 | −0.0918078 | − | 0.995777i | \(-0.529265\pi\) | ||||
−0.0918078 | + | 0.995777i | \(0.529265\pi\) | |||||||
\(608\) | 12.0005 | 0.486686 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −33.9687 | −1.37535 | ||||||||
\(611\) | 27.9955 | 1.13258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.5091 | −0.828353 | −0.414177 | − | 0.910197i | \(-0.635930\pi\) | ||||
−0.414177 | + | 0.910197i | \(0.635930\pi\) | |||||||
\(614\) | −7.25596 | −0.292827 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.16356 | −0.127463 | ||||||||
\(617\) | −33.1358 | −1.33400 | −0.666999 | − | 0.745059i | \(-0.732421\pi\) | ||||
−0.666999 | + | 0.745059i | \(0.732421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0674 | 0.404644 | 0.202322 | − | 0.979319i | \(-0.435151\pi\) | ||||
0.202322 | + | 0.979319i | \(0.435151\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.6455 | −0.426846 | ||||||||
\(623\) | −41.5262 | −1.66371 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.6958 | −0.747834 | ||||||||
\(626\) | −20.3040 | −0.811513 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.4502 | −0.736243 | ||||||||
\(629\) | −0.688835 | −0.0274657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.5723 | −0.818972 | −0.409486 | − | 0.912316i | \(-0.634292\pi\) | ||||
−0.409486 | + | 0.912316i | \(0.634292\pi\) | |||||||
\(632\) | −6.62908 | −0.263691 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.6785 | 0.582958 | ||||||||
\(635\) | 6.12505 | 0.243065 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.66502 | 0.382942 | ||||||||
\(638\) | 1.74335 | 0.0690198 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.8854 | −0.667456 | ||||||||
\(641\) | 25.3655 | 1.00188 | 0.500938 | − | 0.865483i | \(-0.332989\pi\) | ||||
0.500938 | + | 0.865483i | \(0.332989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.5622 | 1.24469 | 0.622345 | − | 0.782743i | \(-0.286180\pi\) | ||||
0.622345 | + | 0.782743i | \(0.286180\pi\) | |||||||
\(644\) | −18.2487 | −0.719101 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.09173 | 0.0822980 | ||||||||
\(647\) | −8.43852 | −0.331753 | −0.165876 | − | 0.986147i | \(-0.553045\pi\) | ||||
−0.165876 | + | 0.986147i | \(0.553045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.05241 | −0.0413107 | ||||||||
\(650\) | 15.9424 | 0.625313 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.3035 | 0.755983 | ||||||||
\(653\) | 2.26014 | 0.0884461 | 0.0442231 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442231 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.8753 | 1.28454 | ||||||||
\(656\) | 4.99870 | 0.195167 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −30.1587 | −1.17571 | ||||||||
\(659\) | −39.1765 | −1.52610 | −0.763050 | − | 0.646340i | \(-0.776299\pi\) | ||||
−0.763050 | + | 0.646340i | \(0.776299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.2343 | 1.05929 | 0.529645 | − | 0.848219i | \(-0.322325\pi\) | ||||
0.529645 | + | 0.848219i | \(0.322325\pi\) | |||||||
\(662\) | −18.7495 | −0.728720 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −47.8910 | −1.85853 | ||||||||
\(665\) | −23.9456 | −0.928569 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0095 | 1.08453 | ||||||||
\(668\) | −14.3081 | −0.553596 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.2357 | −0.511339 | ||||||||
\(671\) | 3.64670 | 0.140779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.3279 | −1.13051 | −0.565253 | − | 0.824918i | \(-0.691221\pi\) | ||||
−0.565253 | + | 0.824918i | \(0.691221\pi\) | |||||||
\(674\) | −2.39034 | −0.0920724 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.70105 | 0.219271 | ||||||||
\(677\) | 1.27454 | 0.0489844 | 0.0244922 | − | 0.999700i | \(-0.492203\pi\) | ||||
0.0244922 | + | 0.999700i | \(0.492203\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −44.1487 | −1.69427 | ||||||||
\(680\) | −9.72392 | −0.372895 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.6193 | 0.750713 | 0.375357 | − | 0.926881i | \(-0.377520\pi\) | ||||
0.375357 | + | 0.926881i | \(0.377520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.5438 | 2.12222 | ||||||||
\(686\) | 10.7982 | 0.412275 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.32187 | −0.241019 | ||||||||
\(689\) | 38.2965 | 1.45898 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.366769 | −0.0139526 | −0.00697628 | − | 0.999976i | \(-0.502221\pi\) | ||||
−0.00697628 | + | 0.999976i | \(0.502221\pi\) | |||||||
\(692\) | −2.72286 | −0.103508 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.6902 | 0.937227 | ||||||||
\(695\) | 53.1163 | 2.01481 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.90909 | −0.375333 | ||||||||
\(698\) | 13.0534 | 0.494077 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.8710 | 0.826645 | ||||||||
\(701\) | 15.1616 | 0.572647 | 0.286324 | − | 0.958133i | \(-0.407567\pi\) | ||||
0.286324 | + | 0.958133i | \(0.407567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.53671 | −0.0579581 | ||||||||
\(704\) | −2.02605 | −0.0763595 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.57272 | −0.0968255 | ||||||||
\(707\) | 56.6095 | 2.12902 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.7219 | 0.590448 | 0.295224 | − | 0.955428i | \(-0.404606\pi\) | ||||
0.295224 | + | 0.955428i | \(0.404606\pi\) | |||||||
\(710\) | 14.9643 | 0.561600 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −37.6197 | −1.40986 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.12755 | −0.116964 | ||||||||
\(716\) | −2.40856 | −0.0900121 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.37675 | 0.312618 | ||||||||
\(719\) | −25.5678 | −0.953518 | −0.476759 | − | 0.879034i | \(-0.658189\pi\) | ||||
−0.476759 | + | 0.879034i | \(0.658189\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21.5448 | −0.802372 | ||||||||
\(722\) | −13.1543 | −0.489551 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.06430 | −0.151048 | ||||||||
\(725\) | −33.5692 | −1.24673 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.9397 | −0.591170 | −0.295585 | − | 0.955317i | \(-0.595514\pi\) | ||||
−0.295585 | + | 0.955317i | \(0.595514\pi\) | |||||||
\(728\) | 26.5923 | 0.985575 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.8345 | −0.919167 | ||||||||
\(731\) | 12.5320 | 0.463514 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.7453 | −1.24641 | −0.623205 | − | 0.782059i | \(-0.714170\pi\) | ||||
−0.623205 | + | 0.782059i | \(0.714170\pi\) | |||||||
\(734\) | 15.5209 | 0.572886 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27.1285 | −0.999969 | ||||||||
\(737\) | 1.42091 | 0.0523401 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.4900 | −1.59981 | −0.799903 | − | 0.600129i | \(-0.795116\pi\) | ||||
−0.799903 | + | 0.600129i | \(0.795116\pi\) | |||||||
\(740\) | 2.56486 | 0.0942860 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −41.2556 | −1.51454 | ||||||||
\(743\) | −40.8299 | −1.49790 | −0.748952 | − | 0.662624i | \(-0.769443\pi\) | ||||
−0.748952 | + | 0.662624i | \(0.769443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.0842 | −1.13884 | ||||||||
\(746\) | 16.7399 | 0.612892 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.374799 | 0.0137040 | ||||||||
\(749\) | 15.5340 | 0.567602 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.5276 | 1.73431 | 0.867153 | − | 0.498041i | \(-0.165947\pi\) | ||||
0.867153 | + | 0.498041i | \(0.165947\pi\) | |||||||
\(752\) | −5.02024 | −0.183069 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.6542 | −0.533676 | ||||||||
\(755\) | 74.9728 | 2.72854 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.123210 | −0.00447814 | −0.00223907 | − | 0.999997i | \(-0.500713\pi\) | ||||
−0.00223907 | + | 0.999997i | \(0.500713\pi\) | |||||||
\(758\) | −14.3584 | −0.521520 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.6929 | −0.786885 | ||||||||
\(761\) | 32.1088 | 1.16394 | 0.581972 | − | 0.813209i | \(-0.302281\pi\) | ||||
0.581972 | + | 0.813209i | \(0.302281\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.04535 | −0.0378442 | ||||||||
\(764\) | 9.70526 | 0.351124 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.39867 | 0.158930 | ||||||||
\(767\) | 8.84634 | 0.319423 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.79859 | −0.245164 | −0.122582 | − | 0.992458i | \(-0.539117\pi\) | ||||
−0.122582 | + | 0.992458i | \(0.539117\pi\) | |||||||
\(770\) | 3.36921 | 0.121418 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −18.3408 | −0.660101 | ||||||||
\(773\) | −39.1251 | −1.40723 | −0.703615 | − | 0.710581i | \(-0.748432\pi\) | ||||
−0.703615 | + | 0.710581i | \(0.748432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −39.9954 | −1.43575 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28.5046 | −1.02194 | ||||||||
\(779\) | −22.1060 | −0.792029 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.60649 | −0.0574847 | ||||||||
\(782\) | −4.72858 | −0.169094 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.73316 | −0.0618985 | ||||||||
\(785\) | 54.7291 | 1.95336 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.45432 | −0.265718 | −0.132859 | − | 0.991135i | \(-0.542416\pi\) | ||||
−0.132859 | + | 0.991135i | \(0.542416\pi\) | |||||||
\(788\) | −4.04542 | −0.144112 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.06002 | 0.251184 | ||||||||
\(791\) | 33.0816 | 1.17624 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.6535 | −1.08854 | ||||||||
\(794\) | 23.0746 | 0.818887 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.02702 | −0.107290 | ||||||||
\(797\) | −50.1923 | −1.77790 | −0.888951 | − | 0.458002i | \(-0.848565\pi\) | ||||
−0.888951 | + | 0.458002i | \(0.848565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.95177 | 0.352068 | ||||||||
\(800\) | 32.5132 | 1.14952 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.0774 | 0.567714 | ||||||||
\(803\) | 2.66611 | 0.0940848 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.1315 | 1.90789 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 51.2840 | 1.80416 | ||||||||
\(809\) | 26.9576 | 0.947780 | 0.473890 | − | 0.880584i | \(-0.342849\pi\) | ||||
0.473890 | + | 0.880584i | \(0.342849\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.2946 | −0.642412 | −0.321206 | − | 0.947009i | \(-0.604088\pi\) | ||||
−0.321206 | + | 0.947009i | \(0.604088\pi\) | |||||||
\(812\) | −20.1038 | −0.705504 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.216219 | 0.00757849 | ||||||||
\(815\) | −57.2602 | −2.00574 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.9575 | 0.978108 | ||||||||
\(818\) | 27.0328 | 0.945179 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 36.8962 | 1.28847 | ||||||||
\(821\) | 19.1193 | 0.667267 | 0.333634 | − | 0.942703i | \(-0.391725\pi\) | ||||
0.333634 | + | 0.942703i | \(0.391725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.06118 | −0.315853 | −0.157926 | − | 0.987451i | \(-0.550481\pi\) | ||||
−0.157926 | + | 0.987451i | \(0.550481\pi\) | |||||||
\(824\) | −19.5180 | −0.679943 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.52989 | −0.331587 | ||||||||
\(827\) | 21.9892 | 0.764640 | 0.382320 | − | 0.924030i | \(-0.375125\pi\) | ||||
0.382320 | + | 0.924030i | \(0.375125\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.7043 | −1.55265 | −0.776323 | − | 0.630336i | \(-0.782917\pi\) | ||||
−0.776323 | + | 0.630336i | \(0.782917\pi\) | |||||||
\(830\) | 51.0043 | 1.77038 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17.0306 | 0.590428 | ||||||||
\(833\) | 3.43569 | 0.119040 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.4423 | 1.46878 | ||||||||
\(836\) | 0.836132 | 0.0289182 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.3188 | −0.425544 | ||||||||
\(839\) | −26.9212 | −0.929423 | −0.464712 | − | 0.885462i | \(-0.653842\pi\) | ||||
−0.464712 | + | 0.885462i | \(0.653842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.85673 | 0.0640251 | ||||||||
\(842\) | −0.829360 | −0.0285816 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.08490 | 0.278294 | ||||||||
\(845\) | −16.9111 | −0.581760 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.1740 | 1.20859 | ||||||||
\(848\) | −6.86743 | −0.235828 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.66716 | 0.194382 | ||||||||
\(851\) | 3.47389 | 0.119084 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.1937 | −0.999572 | −0.499786 | − | 0.866149i | \(-0.666588\pi\) | ||||
−0.499786 | + | 0.866149i | \(0.666588\pi\) | |||||||
\(854\) | 33.0220 | 1.12999 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.0727 | 0.480995 | ||||||||
\(857\) | −12.5597 | −0.429032 | −0.214516 | − | 0.976720i | \(-0.568817\pi\) | ||||
−0.214516 | + | 0.976720i | \(0.568817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0549 | −0.411307 | −0.205654 | − | 0.978625i | \(-0.565932\pi\) | ||||
−0.205654 | + | 0.978625i | \(0.565932\pi\) | |||||||
\(860\) | −46.6626 | −1.59118 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.1591 | 0.788801 | ||||||||
\(863\) | 50.0546 | 1.70388 | 0.851940 | − | 0.523639i | \(-0.175426\pi\) | ||||
0.851940 | + | 0.523639i | \(0.175426\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.07686 | 0.274621 | ||||||||
\(866\) | −21.1876 | −0.719983 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.757927 | −0.0257109 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.9439 | −0.404705 | ||||||||
\(872\) | −0.947008 | −0.0320698 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.5489 | −0.356821 | ||||||||
\(875\) | −11.1990 | −0.378596 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.84583 | 0.264935 | 0.132467 | − | 0.991187i | \(-0.457710\pi\) | ||||
0.132467 | + | 0.991187i | \(0.457710\pi\) | |||||||
\(878\) | −20.3190 | −0.685735 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.560841 | 0.0189059 | ||||||||
\(881\) | −31.9914 | −1.07782 | −0.538909 | − | 0.842364i | \(-0.681163\pi\) | ||||
−0.538909 | + | 0.842364i | \(0.681163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.0077 | −0.740619 | −0.370309 | − | 0.928908i | \(-0.620748\pi\) | ||||
−0.370309 | + | 0.928908i | \(0.620748\pi\) | |||||||
\(884\) | −3.15049 | −0.105962 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.24383 | 0.108979 | ||||||||
\(887\) | −8.28596 | −0.278215 | −0.139108 | − | 0.990277i | \(-0.544423\pi\) | ||||
−0.139108 | + | 0.990277i | \(0.544423\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.95435 | −0.199703 | ||||||||
\(890\) | 40.0652 | 1.34299 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.3110 | −0.445685 | ||||||||
\(893\) | 22.2012 | 0.742935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.14454 | 0.238816 | ||||||||
\(896\) | 16.4149 | 0.548383 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.3730 | −0.713227 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6135 | 0.453532 | ||||||||
\(902\) | 3.11038 | 0.103564 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 29.9694 | 0.996769 | ||||||||
\(905\) | 12.0560 | 0.400754 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.67318 | −0.287988 | −0.143994 | − | 0.989579i | \(-0.545995\pi\) | ||||
−0.143994 | + | 0.989579i | \(0.545995\pi\) | |||||||
\(908\) | −5.43708 | −0.180436 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −28.3209 | −0.938830 | ||||||||
\(911\) | 23.0473 | 0.763593 | 0.381796 | − | 0.924247i | \(-0.375306\pi\) | ||||
0.381796 | + | 0.924247i | \(0.375306\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.47555 | −0.181214 | ||||||||
\(914\) | 0.707929 | 0.0234162 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.5789 | −0.481699 | ||||||||
\(917\) | −31.9591 | −1.05538 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.5467 | 1.79933 | 0.899664 | − | 0.436582i | \(-0.143811\pi\) | ||||
0.899664 | + | 0.436582i | \(0.143811\pi\) | |||||||
\(920\) | 49.0391 | 1.61677 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.21044 | 0.0727968 | ||||||||
\(923\) | 13.5038 | 0.444484 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.16343 | −0.136893 | ||||||||
\(926\) | 28.2766 | 0.929228 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.8861 | −0.981060 | ||||||||
\(929\) | 42.1963 | 1.38442 | 0.692208 | − | 0.721698i | \(-0.256638\pi\) | ||||
0.692208 | + | 0.721698i | \(0.256638\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.66462 | 0.251198 | ||||||||
\(932\) | −5.08563 | −0.166585 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.8594 | −0.846145 | ||||||||
\(935\) | −1.11177 | −0.0363588 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.68306 | −0.250995 | −0.125497 | − | 0.992094i | \(-0.540053\pi\) | ||||
−0.125497 | + | 0.992094i | \(0.540053\pi\) | |||||||
\(938\) | 12.8668 | 0.420117 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −37.0551 | −1.20860 | ||||||||
\(941\) | 49.0904 | 1.60030 | 0.800151 | − | 0.599799i | \(-0.204753\pi\) | ||||
0.800151 | + | 0.599799i | \(0.204753\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49.9729 | 1.62734 | ||||||||
\(944\) | −1.58635 | −0.0516313 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.93370 | −0.127896 | ||||||||
\(947\) | 31.2317 | 1.01489 | 0.507447 | − | 0.861683i | \(-0.330589\pi\) | ||||
0.507447 | + | 0.861683i | \(0.330589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4108 | −0.727484 | ||||||||
\(950\) | 12.6428 | 0.410185 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.45293 | 0.306371 | ||||||||
\(953\) | −46.5281 | −1.50719 | −0.753596 | − | 0.657338i | \(-0.771682\pi\) | ||||
−0.753596 | + | 0.657338i | \(0.771682\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −28.7889 | −0.931586 | ||||||||
\(956\) | −4.01195 | −0.129756 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.3198 | 0.462651 | ||||||||
\(959\) | −53.9958 | −1.74362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0 | 0 | ||||||||
\(962\) | −1.81750 | −0.0585985 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.95097 | −0.256083 | ||||||||
\(965\) | 54.4047 | 1.75135 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.4544 | 1.59035 | 0.795174 | − | 0.606382i | \(-0.207380\pi\) | ||||
0.795174 | + | 0.606382i | \(0.207380\pi\) | |||||||
\(968\) | 31.8650 | 1.02418 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 42.5954 | 1.36766 | ||||||||
\(971\) | −8.88234 | −0.285048 | −0.142524 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142524 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −51.6360 | −1.65537 | ||||||||
\(974\) | −6.42106 | −0.205744 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.49686 | 0.175950 | ||||||||
\(977\) | 54.4355 | 1.74155 | 0.870773 | − | 0.491685i | \(-0.163619\pi\) | ||||
0.870773 | + | 0.491685i | \(0.163619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.30120 | −0.137467 | ||||||||
\(980\) | −12.7927 | −0.408647 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 28.2614 | 0.901857 | ||||||||
\(983\) | −41.7509 | −1.33165 | −0.665823 | − | 0.746110i | \(-0.731919\pi\) | ||||
−0.665823 | + | 0.746110i | \(0.731919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | 0.382352 | ||||||||
\(986\) | −5.20924 | −0.165896 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.02836 | −0.223602 | ||||||||
\(989\) | −63.2009 | −2.00967 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.9011 | 0.727478 | 0.363739 | − | 0.931501i | \(-0.381500\pi\) | ||||
0.363739 | + | 0.931501i | \(0.381500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −14.5473 | −0.461411 | ||||||||
\(995\) | 8.97909 | 0.284656 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.4025 | 0.899517 | 0.449759 | − | 0.893150i | \(-0.351510\pi\) | ||||
0.449759 | + | 0.893150i | \(0.351510\pi\) | |||||||
\(998\) | 34.8804 | 1.10412 | ||||||||
\(999\) | 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 | 8649.2.a.bo.1.8 | 12 | ||
3.2 | odd | 2 | inner | 8649.2.a.bo.1.5 | 12 | ||
31.23 | odd | 10 | 279.2.i.d.64.3 | ✓ | 24 | ||
31.27 | odd | 10 | 279.2.i.d.109.3 | yes | 24 | ||
31.30 | odd | 2 | 8649.2.a.bn.1.8 | 12 | |||
93.23 | even | 10 | 279.2.i.d.64.4 | yes | 24 | ||
93.89 | even | 10 | 279.2.i.d.109.4 | yes | 24 | ||
93.92 | even | 2 | 8649.2.a.bn.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
279.2.i.d.64.3 | ✓ | 24 | 31.23 | odd | 10 | ||
279.2.i.d.64.4 | yes | 24 | 93.23 | even | 10 | ||
279.2.i.d.109.3 | yes | 24 | 31.27 | odd | 10 | ||
279.2.i.d.109.4 | yes | 24 | 93.89 | even | 10 | ||
8649.2.a.bn.1.5 | 12 | 93.92 | even | 2 | |||
8649.2.a.bn.1.8 | 12 | 31.30 | odd | 2 | |||
8649.2.a.bo.1.5 | 12 | 3.2 | odd | 2 | inner | ||
8649.2.a.bo.1.8 | 12 | 1.1 | even | 1 | trivial |