Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 8 x^{17} - 4 x^{16} + 178 x^{15} - 265 x^{14} - 1405 x^{13} + 3503 x^{12} + 4295 x^{11} - 17374 x^{10} - 893 x^{9} + 38112 x^{8} - 18700 x^{7} - 32137 x^{6} + 26381 x^{5} + \cdots - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.0880346\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0880346 | 0.0508268 | 0.0254134 | − | 0.999677i | \(-0.491910\pi\) | ||||
0.0254134 | + | 0.999677i | \(0.491910\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20461 | −0.985933 | −0.492967 | − | 0.870048i | \(-0.664088\pi\) | ||||
−0.492967 | + | 0.870048i | \(0.664088\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.606938 | 0.229401 | 0.114701 | − | 0.993400i | \(-0.463409\pi\) | ||||
0.114701 | + | 0.993400i | \(0.463409\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99225 | −0.997417 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.81846 | −1.75433 | −0.877165 | − | 0.480189i | \(-0.840568\pi\) | ||||
−0.877165 | + | 0.480189i | \(0.840568\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.556004 | −0.154208 | −0.0771039 | − | 0.997023i | \(-0.524567\pi\) | ||||
−0.0771039 | + | 0.997023i | \(0.524567\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.194082 | −0.0501118 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.49281 | −1.71897 | −0.859484 | − | 0.511163i | \(-0.829215\pi\) | ||||
−0.859484 | + | 0.511163i | \(0.829215\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0534316 | 0.0116597 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.33989 | 1.11344 | 0.556722 | − | 0.830699i | \(-0.312059\pi\) | ||||
0.556722 | + | 0.830699i | \(0.312059\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.139679 | −0.0279358 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.527525 | −0.101522 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.38138 | −0.999298 | −0.499649 | − | 0.866228i | \(-0.666538\pi\) | ||||
−0.499649 | + | 0.866228i | \(0.666538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.26105 | 0.585701 | 0.292851 | − | 0.956158i | \(-0.405396\pi\) | ||||
0.292851 | + | 0.956158i | \(0.405396\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.512225 | −0.0891670 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.33806 | −0.226174 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.04730 | 0.172174 | 0.0860872 | − | 0.996288i | \(-0.472564\pi\) | ||||
0.0860872 | + | 0.996288i | \(0.472564\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0489476 | −0.00783789 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.39425 | 1.46713 | 0.733567 | − | 0.679617i | \(-0.237854\pi\) | ||||
0.733567 | + | 0.679617i | \(0.237854\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.399244 | 0.0608841 | 0.0304420 | − | 0.999537i | \(-0.490309\pi\) | ||||
0.0304420 | + | 0.999537i | \(0.490309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.59675 | 0.983386 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.48970 | 0.800755 | 0.400378 | − | 0.916350i | \(-0.368879\pi\) | ||||
0.400378 | + | 0.916350i | \(0.368879\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.63163 | −0.947375 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0880346 | −0.0123273 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.91311 | 0.812228 | 0.406114 | − | 0.913822i | \(-0.366883\pi\) | ||||
0.406114 | + | 0.913822i | \(0.366883\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.8274 | 1.72965 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.659626 | −0.0873696 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.48911 | 1.21496 | 0.607478 | − | 0.794337i | \(-0.292181\pi\) | ||||
0.607478 | + | 0.794337i | \(0.292181\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.81611 | −0.228808 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.22577 | 0.152039 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.59463 | −0.439154 | −0.219577 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219577 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.470095 | 0.0565928 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.94804 | 1.18062 | 0.590308 | − | 0.807178i | \(-0.299006\pi\) | ||||
0.590308 | + | 0.807178i | \(0.299006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.60630 | −0.656168 | −0.328084 | − | 0.944649i | \(-0.606403\pi\) | ||||
−0.328084 | + | 0.944649i | \(0.606403\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.0122966 | −0.00141989 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.53144 | −0.402445 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.91694 | −0.328182 | −0.164091 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164091 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.93031 | 0.992257 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.42285 | −1.03429 | −0.517146 | − | 0.855897i | \(-0.673006\pi\) | ||||
−0.517146 | + | 0.855897i | \(0.673006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.20461 | 0.239124 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.473748 | −0.0507911 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.776620 | −0.0823216 | −0.0411608 | − | 0.999153i | \(-0.513106\pi\) | ||||
−0.0411608 | + | 0.999153i | \(0.513106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.337460 | −0.0353754 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.287085 | 0.0297693 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.5187 | 1.69479 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.1488 | −1.13199 | −0.565996 | − | 0.824408i | \(-0.691508\pi\) | ||||
−0.565996 | + | 0.824408i | \(0.691508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.4103 | 1.74980 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.20456 | 0.716880 | 0.358440 | − | 0.933553i | \(-0.383309\pi\) | ||||
0.358440 | + | 0.933553i | \(0.383309\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.8332 | 1.16595 | 0.582977 | − | 0.812488i | \(-0.301888\pi\) | ||||
0.582977 | + | 0.812488i | \(0.301888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.117796 | −0.0114957 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.12416 | −0.205350 | −0.102675 | − | 0.994715i | \(-0.532740\pi\) | ||||
−0.102675 | + | 0.994715i | \(0.532740\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.03598 | 0.195011 | 0.0975057 | − | 0.995235i | \(-0.468914\pi\) | ||||
0.0975057 | + | 0.995235i | \(0.468914\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0921982 | 0.00875107 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.35175 | 0.879739 | 0.439869 | − | 0.898062i | \(-0.355025\pi\) | ||||
0.439869 | + | 0.898062i | \(0.355025\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.7724 | −1.09778 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.66370 | 0.153809 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.606938 | −0.0556379 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.8544 | 2.07767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.827019 | 0.0745698 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3310 | 1.01348 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.582629 | 0.0517000 | 0.0258500 | − | 0.999666i | \(-0.491771\pi\) | ||||
0.0258500 | + | 0.999666i | \(0.491771\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.0351472 | 0.00309454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.26541 | 0.285300 | 0.142650 | − | 0.989773i | \(-0.454438\pi\) | ||||
0.142650 | + | 0.989773i | \(0.454438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.54767 | −0.394333 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.16299 | 0.100094 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.67211 | −0.740908 | −0.370454 | − | 0.928851i | \(-0.620798\pi\) | ||||
−0.370454 | + | 0.928851i | \(0.620798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.8261 | −1.51199 | −0.755997 | − | 0.654575i | \(-0.772848\pi\) | ||||
−0.755997 | + | 0.654575i | \(0.772848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.483284 | 0.0406998 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.23509 | 0.270531 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.8639 | 0.985241 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.583812 | −0.0481520 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.54834 | 0.208768 | 0.104384 | − | 0.994537i | \(-0.466713\pi\) | ||||
0.104384 | + | 0.994537i | \(0.466713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.81464 | −0.798704 | −0.399352 | − | 0.916798i | \(-0.630765\pi\) | ||||
−0.399352 | + | 0.916798i | \(0.630765\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.99225 | 0.241909 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.18935 | −0.577462 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.46261 | −0.515772 | −0.257886 | − | 0.966175i | \(-0.583026\pi\) | ||||
−0.257886 | + | 0.966175i | \(0.583026\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.520558 | 0.0412830 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.24099 | 0.255425 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.26184 | 0.177161 | 0.0885803 | − | 0.996069i | \(-0.471767\pi\) | ||||
0.0885803 | + | 0.996069i | \(0.471767\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.12926 | 0.0879127 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.1845 | 1.25240 | 0.626198 | − | 0.779664i | \(-0.284610\pi\) | ||||
0.626198 | + | 0.779664i | \(0.284610\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6909 | −0.976220 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.4203 | 1.71453 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9302 | −1.43923 | −0.719617 | − | 0.694371i | \(-0.755683\pi\) | ||||
−0.719617 | + | 0.694371i | \(0.755683\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0847767 | −0.00640851 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0880346 | −0.00661708 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.6054 | 1.09166 | 0.545829 | − | 0.837897i | \(-0.316215\pi\) | ||||
0.545829 | + | 0.837897i | \(0.316215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.8847 | −0.809056 | −0.404528 | − | 0.914526i | \(-0.632564\pi\) | ||||
−0.404528 | + | 0.914526i | \(0.632564\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.835370 | 0.0617523 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.30888 | −0.169752 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.81846 | 0.425488 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.320175 | −0.0232893 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.36071 | 0.460245 | 0.230123 | − | 0.973162i | \(-0.426087\pi\) | ||||
0.230123 | + | 0.973162i | \(0.426087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.7850 | 1.28019 | 0.640097 | − | 0.768294i | \(-0.278894\pi\) | ||||
0.640097 | + | 0.768294i | \(0.278894\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.107911 | 0.00772763 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.27138 | −0.589312 | −0.294656 | − | 0.955603i | \(-0.595205\pi\) | ||||
−0.294656 | + | 0.955603i | \(0.595205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.16843 | −0.295493 | −0.147746 | − | 0.989025i | \(-0.547202\pi\) | ||||
−0.147746 | + | 0.989025i | \(0.547202\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.316451 | −0.0223208 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.26617 | −0.229240 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.7107 | −1.44650 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.9783 | −1.11057 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 43.5966 | 3.01564 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.60899 | −0.454982 | −0.227491 | − | 0.973780i | \(-0.573052\pi\) | ||||
−0.227491 | + | 0.973780i | \(0.573052\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.875772 | 0.0600069 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.880178 | −0.0600276 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.97925 | 0.134361 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.493549 | −0.0333509 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.556004 | 0.0374009 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.9658 | 1.00219 | 0.501093 | − | 0.865394i | \(-0.332932\pi\) | ||||
0.501093 | + | 0.865394i | \(0.332932\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.417955 | 0.0278637 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.0729 | −1.00042 | −0.500212 | − | 0.865903i | \(-0.666744\pi\) | ||||
−0.500212 | + | 0.865903i | \(0.666744\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3127 | 0.813645 | 0.406823 | − | 0.913507i | \(-0.366637\pi\) | ||||
0.406823 | + | 0.913507i | \(0.366637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.310889 | −0.0204550 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.63811 | −0.631413 | −0.315707 | − | 0.948857i | \(-0.602242\pi\) | ||||
−0.315707 | + | 0.948857i | \(0.602242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.1027 | −0.789491 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.256792 | −0.0166804 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4945 | 1.32568 | 0.662839 | − | 0.748762i | \(-0.269351\pi\) | ||||
0.662839 | + | 0.748762i | \(0.269351\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.7543 | 0.757160 | 0.378580 | − | 0.925569i | \(-0.376412\pi\) | ||||
0.378580 | + | 0.925569i | \(0.376412\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.36875 | 0.151955 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.6202 | 0.934049 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.16603 | 0.265078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.829537 | −0.0525698 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.08421 | 0.384032 | 0.192016 | − | 0.981392i | \(-0.438497\pi\) | ||||
0.192016 | + | 0.981392i | \(0.438497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31.0699 | −1.95335 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.194082 | 0.0121539 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.27216 | 0.516003 | 0.258001 | − | 0.966145i | \(-0.416936\pi\) | ||||
0.258001 | + | 0.966145i | \(0.416936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.635644 | 0.0394970 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.1024 | 0.996716 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.3149 | −1.31433 | −0.657167 | − | 0.753745i | \(-0.728245\pi\) | ||||
−0.657167 | + | 0.753745i | \(0.728245\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.0361 | −0.800803 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.0683695 | −0.00418414 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.9867 | 1.09667 | 0.548333 | − | 0.836260i | \(-0.315263\pi\) | ||||
0.548333 | + | 0.836260i | \(0.315263\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.56872 | 0.520513 | 0.260256 | − | 0.965540i | \(-0.416193\pi\) | ||||
0.260256 | + | 0.965540i | \(0.416193\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0297082 | −0.00179802 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.812717 | 0.0490087 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.39045 | 0.203713 | 0.101856 | − | 0.994799i | \(-0.467522\pi\) | ||||
0.101856 | + | 0.994799i | \(0.467522\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.75787 | −0.584188 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6604 | 0.814913 | 0.407456 | − | 0.913225i | \(-0.366416\pi\) | ||||
0.407456 | + | 0.913225i | \(0.366416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6437 | −0.751589 | −0.375794 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.45422 | 0.0861406 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.70173 | 0.336562 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.981483 | −0.0575356 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.1243 | 1.81830 | 0.909152 | − | 0.416465i | \(-0.136731\pi\) | ||||
0.909152 | + | 0.416465i | \(0.136731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.20461 | 0.128358 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.06938 | 0.178104 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.96900 | −0.171702 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.242316 | 0.0139669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.634250 | 0.0364367 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.9198 | −1.19787 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.40991 | −0.422906 | −0.211453 | − | 0.977388i | \(-0.567820\pi\) | ||||
−0.211453 | + | 0.977388i | \(0.567820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.04173 | 0.0592617 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.9674 | −0.848722 | −0.424361 | − | 0.905493i | \(-0.639501\pi\) | ||||
−0.424361 | + | 0.905493i | \(0.639501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.82878 | 0.216415 | 0.108208 | − | 0.994128i | \(-0.465489\pi\) | ||||
0.108208 | + | 0.994128i | \(0.465489\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.00382 | 0.225590 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7445 | 0.828132 | 0.414066 | − | 0.910247i | \(-0.364108\pi\) | ||||
0.414066 | + | 0.910247i | \(0.364108\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.3113 | 1.75310 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.187000 | −0.0104373 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.49281 | 0.416911 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.0776622 | 0.00430793 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.179237 | 0.00991181 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.33191 | 0.183694 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1023 | 0.940026 | 0.470013 | − | 0.882659i | \(-0.344249\pi\) | ||||
0.470013 | + | 0.882659i | \(0.344249\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.13377 | −0.171730 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.92476 | 0.432976 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0556 | −1.41934 | −0.709669 | − | 0.704535i | \(-0.751156\pi\) | ||||
−0.709669 | + | 0.704535i | \(0.751156\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.823277 | 0.0447143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9743 | −1.02751 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.27356 | −0.446730 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.03638 | −0.0557967 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.7388 | 1.22068 | 0.610340 | − | 0.792140i | \(-0.291033\pi\) | ||||
0.610340 | + | 0.792140i | \(0.291033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5643 | −0.619025 | −0.309512 | − | 0.950895i | \(-0.600166\pi\) | ||||
−0.309512 | + | 0.950895i | \(0.600166\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.293306 | 0.0156555 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.5310 | −1.83790 | −0.918951 | − | 0.394373i | \(-0.870962\pi\) | ||||
−0.918951 | + | 0.394373i | \(0.870962\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −21.9316 | −1.16401 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0534316 | −0.00282790 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.1188 | 1.58961 | 0.794805 | − | 0.606865i | \(-0.207573\pi\) | ||||
0.794805 | + | 0.606865i | \(0.207573\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.1421 | 1.95485 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.01198 | 0.105602 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.3597 | 0.646938 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.7791 | −0.875863 | −0.437932 | − | 0.899008i | \(-0.644289\pi\) | ||||
−0.437932 | + | 0.899008i | \(0.644289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −28.1099 | −1.46334 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.58889 | 0.186326 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.5242 | −1.52871 | −0.764353 | − | 0.644798i | \(-0.776942\pi\) | ||||
−0.764353 | + | 0.644798i | \(0.776942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.997520 | 0.0515117 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.99207 | 0.154100 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.08720 | −0.466778 | −0.233389 | − | 0.972383i | \(-0.574982\pi\) | ||||
−0.233389 | + | 0.972383i | \(0.574982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0512915 | 0.00262774 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.9004 | 1.17015 | 0.585077 | − | 0.810978i | \(-0.301064\pi\) | ||||
0.585077 | + | 0.810978i | \(0.301064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.78547 | 0.396784 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.19464 | −0.0607268 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.57905 | −0.181465 | −0.0907325 | − | 0.995875i | \(-0.528921\pi\) | ||||
−0.0907325 | + | 0.995875i | \(0.528921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.33989 | −0.270050 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.287469 | 0.0145009 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.43073 | 0.323565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3379 | −0.669411 | −0.334705 | − | 0.942323i | \(-0.608637\pi\) | ||||
−0.334705 | + | 0.942323i | \(0.608637\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.400352 | −0.0200427 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.35489 | 0.117598 | 0.0587988 | − | 0.998270i | \(-0.481273\pi\) | ||||
0.0587988 | + | 0.998270i | \(0.481273\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.81316 | −0.0903197 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −19.6879 | −0.978299 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.09364 | −0.302051 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.9520 | −1.28324 | −0.641622 | − | 0.767021i | \(-0.721738\pi\) | ||||
−0.641622 | + | 0.767021i | \(0.721738\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.763446 | −0.0376580 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.606938 | −0.0298655 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.7738 | 1.01974 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.56932 | −0.0768498 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.7079 | 0.816236 | 0.408118 | − | 0.912929i | \(-0.366185\pi\) | ||||
0.408118 | + | 0.912929i | \(0.366185\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.7099 | 1.49671 | 0.748354 | − | 0.663300i | \(-0.230845\pi\) | ||||
0.748354 | + | 0.663300i | \(0.230845\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.4266 | −0.798687 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.139679 | 0.00677544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.75930 | 0.278712 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.284799 | 0.0137502 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0193 | 0.675288 | 0.337644 | − | 0.941274i | \(-0.390370\pi\) | ||||
0.337644 | + | 0.941274i | \(0.390370\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6414 | 0.943905 | 0.471953 | − | 0.881624i | \(-0.343549\pi\) | ||||
0.471953 | + | 0.881624i | \(0.343549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.04443 | 0.0500766 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −40.0108 | −1.91398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.2666 | 0.776361 | 0.388181 | − | 0.921583i | \(-0.373104\pi\) | ||||
0.388181 | + | 0.921583i | \(0.373104\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.8435 | 0.944928 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.5740 | 0.549898 | 0.274949 | − | 0.961459i | \(-0.411339\pi\) | ||||
0.274949 | + | 0.961459i | \(0.411339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.71215 | 0.0811636 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.224342 | 0.0106110 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.6693 | −0.645096 | −0.322548 | − | 0.946553i | \(-0.604539\pi\) | ||||
−0.322548 | + | 0.946553i | \(0.604539\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −54.6600 | −2.57384 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.864028 | −0.0405956 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.743969 | 0.0348778 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.1850 | 0.990993 | 0.495496 | − | 0.868610i | \(-0.334986\pi\) | ||||
0.495496 | + | 0.868610i | \(0.334986\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.527525 | 0.0246228 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.9707 | 0.743832 | 0.371916 | − | 0.928266i | \(-0.378701\pi\) | ||||
0.371916 | + | 0.928266i | \(0.378701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.2268 | −0.986493 | −0.493247 | − | 0.869889i | \(-0.664190\pi\) | ||||
−0.493247 | + | 0.869889i | \(0.664190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.632911 | −0.0293505 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.2175 | 1.30575 | 0.652875 | − | 0.757466i | \(-0.273563\pi\) | ||||
0.652875 | + | 0.757466i | \(0.273563\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.18172 | −0.100742 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.568933 | −0.0262151 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.32298 | −0.106811 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.04659 | 0.0480208 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.6935 | −0.810130 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.77349 | −0.172415 | −0.0862076 | − | 0.996277i | \(-0.527475\pi\) | ||||
−0.0862076 | + | 0.996277i | \(0.527475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.582301 | −0.0265506 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.285319 | 0.0129825 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.5789 | 1.11607 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5598 | 1.29417 | 0.647085 | − | 0.762418i | \(-0.275988\pi\) | ||||
0.647085 | + | 0.762418i | \(0.275988\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.199120 | 0.00900451 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.7356 | −0.710139 | −0.355069 | − | 0.934840i | \(-0.615543\pi\) | ||||
−0.355069 | + | 0.934840i | \(0.615543\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.38138 | 0.242365 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −38.3829 | −1.72518 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.03785 | 0.270835 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.8155 | 1.28996 | 0.644979 | − | 0.764200i | \(-0.276866\pi\) | ||||
0.644979 | + | 0.764200i | \(0.276866\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.42480 | 0.0636553 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.7016 | −0.477162 | −0.238581 | − | 0.971123i | \(-0.576682\pi\) | ||||
−0.238581 | + | 0.971123i | \(0.576682\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.8833 | −0.706796 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.11723 | −0.0496181 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.197801 | 0.00876736 | 0.00438368 | − | 0.999990i | \(-0.498605\pi\) | ||||
0.00438368 | + | 0.999990i | \(0.498605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.40268 | −0.150526 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.95264 | 0.174513 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −26.0875 | −1.14955 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31.9416 | −1.40479 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.66651 | −0.0731516 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.7114 | −1.52073 | −0.760366 | − | 0.649495i | \(-0.774981\pi\) | ||||
−0.760366 | + | 0.649495i | \(0.774981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.587145 | 0.0256741 | 0.0128370 | − | 0.999918i | \(-0.495914\pi\) | ||||
0.0128370 | + | 0.999918i | \(0.495914\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.00746328 | −0.000325724 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.26105 | −0.142053 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.51446 | 0.239759 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.99225 | 0.129853 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.22324 | −0.226244 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.68296 | 0.202462 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.28578 | 0.0554855 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 38.5858 | 1.66201 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.2713 | −1.64541 | −0.822705 | − | 0.568468i | \(-0.807536\pi\) | ||||
−0.822705 | + | 0.568468i | \(0.807536\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.958233 | −0.0411217 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.48855 | −0.192268 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.6049 | 1.18030 | 0.590151 | − | 0.807293i | \(-0.299068\pi\) | ||||
0.590151 | + | 0.807293i | \(0.299068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.3938 | −1.21182 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.3217 | 1.71776 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.77040 | −0.0752852 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.203261 | −0.00862797 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.16580 | −0.303625 | −0.151812 | − | 0.988409i | \(-0.548511\pi\) | ||||
−0.151812 | + | 0.988409i | \(0.548511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.221981 | −0.00938880 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.512225 | 0.0216262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.9228 | 1.85113 | 0.925563 | − | 0.378594i | \(-0.123592\pi\) | ||||
0.925563 | + | 0.378594i | \(0.123592\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.6170 | −0.867363 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.42015 | 0.227625 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.8409 | −1.12523 | −0.562615 | − | 0.826719i | \(-0.690205\pi\) | ||||
−0.562615 | + | 0.826719i | \(0.690205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.7315 | −0.909433 | −0.454717 | − | 0.890636i | \(-0.650259\pi\) | ||||
−0.454717 | + | 0.890636i | \(0.650259\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.559963 | 0.0233928 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.745872 | −0.0311050 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.3570 | 0.764211 | 0.382106 | − | 0.924119i | \(-0.375199\pi\) | ||||
0.382106 | + | 0.924119i | \(0.375199\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.56570 | 0.0650681 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.71909 | −0.237268 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.4052 | −1.42492 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.66782 | −0.151646 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.5526 | 0.765747 | 0.382873 | − | 0.923801i | \(-0.374935\pi\) | ||||
0.382873 | + | 0.923801i | \(0.374935\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.4344 | −1.00680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.728168 | −0.0299528 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.4689 | −1.78505 | −0.892527 | − | 0.450993i | \(-0.851070\pi\) | ||||
−0.892527 | + | 0.450993i | \(0.851070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.33806 | 0.0548553 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.366966 | −0.0150189 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2451 | 1.27664 | 0.638320 | − | 0.769771i | \(-0.279630\pi\) | ||||
0.638320 | + | 0.769771i | \(0.279630\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.5430 | −1.53141 | −0.765706 | − | 0.643191i | \(-0.777610\pi\) | ||||
−0.765706 | + | 0.643191i | \(0.777610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.7560 | 0.438019 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −50.3852 | −2.04845 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.78102 | −0.194055 | −0.0970277 | − | 0.995282i | \(-0.530934\pi\) | ||||
−0.0970277 | + | 0.995282i | \(0.530934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.287536 | −0.0116515 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.05230 | −0.123483 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3232 | 0.861234 | 0.430617 | − | 0.902535i | \(-0.358296\pi\) | ||||
0.430617 | + | 0.902535i | \(0.358296\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.82326 | −0.0735208 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −38.0873 | −1.53334 | −0.766668 | − | 0.642043i | \(-0.778087\pi\) | ||||
−0.766668 | + | 0.642043i | \(0.778087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.53037 | −0.101704 | −0.0508522 | − | 0.998706i | \(-0.516194\pi\) | ||||
−0.0508522 | + | 0.998706i | \(0.516194\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.81693 | −0.113039 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.471361 | −0.0188847 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2821 | −0.971284 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.83800 | 0.153275 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.04730 | −0.0417584 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.80239 | −0.191180 | −0.0955900 | − | 0.995421i | \(-0.530474\pi\) | ||||
−0.0955900 | + | 0.995421i | \(0.530474\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.581820 | −0.0231253 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.28447 | −0.0509727 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.68721 | 0.146093 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.7670 | −1.17757 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.6244 | −1.32808 | −0.664042 | − | 0.747695i | \(-0.731160\pi\) | ||||
−0.664042 | + | 0.747695i | \(0.731160\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5015 | 0.847937 | 0.423969 | − | 0.905677i | \(-0.360637\pi\) | ||||
0.423969 | + | 0.905677i | \(0.360637\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0774861 | −0.00305101 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8583 | 0.702082 | 0.351041 | − | 0.936360i | \(-0.385828\pi\) | ||||
0.351041 | + | 0.936360i | \(0.385828\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.81846 | 0.228394 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.174243 | 0.00682911 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.48258 | 0.0971510 | 0.0485755 | − | 0.998820i | \(-0.484532\pi\) | ||||
0.0485755 | + | 0.998820i | \(0.484532\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.19896 | −0.281287 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.7755 | 0.654473 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.5036 | −0.564979 | −0.282489 | − | 0.959270i | \(-0.591160\pi\) | ||||
−0.282489 | + | 0.959270i | \(0.591160\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8368 | −0.849352 | −0.424676 | − | 0.905345i | \(-0.639612\pi\) | ||||
−0.424676 | + | 0.905345i | \(0.639612\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0489476 | 0.00190097 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0259 | 0.388786 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.7360 | −1.11266 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.31751 | 0.0509378 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −55.2120 | −2.13143 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.01503 | −0.116221 | −0.0581104 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581104 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.0736843 | 0.00283611 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.9748 | −1.45949 | −0.729744 | − | 0.683720i | \(-0.760361\pi\) | ||||
−0.729744 | + | 0.683720i | \(0.760361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.76665 | −0.259680 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.32694 | −0.0508483 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.15378 | −0.235468 | −0.117734 | − | 0.993045i | \(-0.537563\pi\) | ||||
−0.117734 | + | 0.993045i | \(0.537563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.1187 | 0.730486 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.08394 | 0.0413550 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.28772 | −0.125252 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.1340 | 0.727893 | 0.363946 | − | 0.931420i | \(-0.381429\pi\) | ||||
0.363946 | + | 0.931420i | \(0.381429\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.5670 | 0.401406 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39.2998 | 1.49072 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.39425 | −0.355832 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.848487 | −0.0320927 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.1965 | 0.725042 | 0.362521 | − | 0.931976i | \(-0.381916\pi\) | ||||
0.362521 | + | 0.931976i | \(0.381916\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.84718 | −0.295962 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.06545 | −0.0401273 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.37272 | 0.164453 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.5762 | 1.67409 | 0.837046 | − | 0.547132i | \(-0.184280\pi\) | ||||
0.837046 | + | 0.547132i | \(0.184280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.72822 | 0.327334 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.4136 | 0.652146 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.13211 | −0.266726 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.80422 | 0.0673800 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.8206 | −0.925652 | −0.462826 | − | 0.886449i | \(-0.653164\pi\) | ||||
−0.462826 | + | 0.886449i | \(0.653164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.18199 | 0.267471 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.03478 | 0.0384840 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.751668 | 0.0279162 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.5971 | 1.35731 | 0.678655 | − | 0.734457i | \(-0.262563\pi\) | ||||
0.678655 | + | 0.734457i | \(0.262563\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5824 | −0.984533 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.399244 | −0.0147666 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.47046 | −0.312863 | −0.156432 | − | 0.987689i | \(-0.549999\pi\) | ||||
−0.156432 | + | 0.987689i | \(0.549999\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.28708 | 0.0474747 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.9152 | 0.770420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.3741 | 0.896617 | 0.448309 | − | 0.893879i | \(-0.352027\pi\) | ||||
0.448309 | + | 0.893879i | \(0.352027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.366755 | 0.0134731 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.5396 | 1.12039 | 0.560194 | − | 0.828361i | \(-0.310727\pi\) | ||||
0.560194 | + | 0.828361i | \(0.310727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.61811 | −0.205832 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.1955 | 1.03162 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.28924 | −0.0471076 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2444 | 0.556276 | 0.278138 | − | 0.960541i | \(-0.410283\pi\) | ||||
0.278138 | + | 0.960541i | \(0.410283\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.535621 | 0.0195191 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.6375 | 0.787469 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.4647 | −1.17995 | −0.589974 | − | 0.807422i | \(-0.700862\pi\) | ||||
−0.589974 | + | 0.807422i | \(0.700862\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.73523 | −0.0992825 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 47.5122 | 1.72231 | 0.861157 | − | 0.508339i | \(-0.169740\pi\) | ||||
0.861157 | + | 0.508339i | \(0.169740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.23571 | 0.0447359 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.59675 | −0.238506 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.556004 | 0.0200761 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.98091 | 0.143555 | 0.0717776 | − | 0.997421i | \(-0.477133\pi\) | ||||
0.0717776 | + | 0.997421i | \(0.477133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.728236 | 0.0262268 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.1856 | −0.438286 | −0.219143 | − | 0.975693i | \(-0.570326\pi\) | ||||
−0.219143 | + | 0.975693i | \(0.570326\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.455500 | −0.0163621 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0559586 | 0.00200750 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −70.3893 | −2.52196 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.8823 | −2.07119 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.83882 | 0.101451 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.2476 | 0.508517 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.3667 | 0.512118 | 0.256059 | − | 0.966661i | \(-0.417576\pi\) | ||||
0.256059 | + | 0.966661i | \(0.417576\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.87645 | −0.0668033 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.67594 | 0.201813 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.27598 | −0.187356 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.14763 | −0.0407022 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.2362 | 1.46066 | 0.730331 | − | 0.683093i | \(-0.239366\pi\) | ||||
0.730331 | + | 0.683093i | \(0.239366\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.48970 | −0.194212 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.32384 | 0.0821089 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.6200 | 1.15114 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.14512 | −0.251832 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.58345 | 0.0557400 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.35950 | 0.118114 | 0.0590569 | − | 0.998255i | \(-0.481191\pi\) | ||||
0.0590569 | + | 0.998255i | \(0.481191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.1318 | 1.23364 | 0.616822 | − | 0.787103i | \(-0.288420\pi\) | ||||
0.616822 | + | 0.787103i | \(0.288420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.754344 | 0.0264560 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.98647 | −0.174669 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.99145 | −0.104658 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.00977 | 0.0352841 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.9929 | −1.36086 | −0.680432 | − | 0.732812i | \(-0.738208\pi\) | ||||
−0.680432 | + | 0.732812i | \(0.738208\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.0567 | −1.15229 | −0.576143 | − | 0.817349i | \(-0.695443\pi\) | ||||
−0.576143 | + | 0.817349i | \(0.695443\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0715472 | 0.00249095 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.7228 | −0.859697 | −0.429849 | − | 0.902901i | \(-0.641433\pi\) | ||||
−0.429849 | + | 0.902901i | \(0.641433\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0698 | 1.56534 | 0.782669 | − | 0.622439i | \(-0.213858\pi\) | ||||
0.782669 | + | 0.622439i | \(0.213858\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.298477 | 0.0103541 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.63163 | 0.229772 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.6806 | −1.23478 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.72028 | −0.0594617 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.25823 | 0.0779628 | 0.0389814 | − | 0.999240i | \(-0.487589\pi\) | ||||
0.0389814 | + | 0.999240i | \(0.487589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.0407033 | −0.00140356 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.20259 | 0.0414194 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.9784 | 0.962488 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.8712 | 0.476621 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.11308 | −0.0382008 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.59245 | 0.191707 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.1564 | 0.347748 | 0.173874 | − | 0.984768i | \(-0.444371\pi\) | ||||
0.173874 | + | 0.984768i | \(0.444371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −49.4282 | −1.69041 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.6624 | 0.500860 | 0.250430 | − | 0.968135i | \(-0.419428\pi\) | ||||
0.250430 | + | 0.968135i | \(0.419428\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.8702 | 1.76979 | 0.884895 | − | 0.465791i | \(-0.154230\pi\) | ||||
0.884895 | + | 0.465791i | \(0.154230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.501949 | 0.0171064 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.25436 | 0.246941 | 0.123471 | − | 0.992348i | \(-0.460597\pi\) | ||||
0.123471 | + | 0.992348i | \(0.460597\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.7337 | 1.41899 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.0880346 | 0.00298981 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.9721 | 0.575739 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.99863 | 0.0677209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.3601 | 1.12907 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.87722 | 0.232493 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8317 | −1.54763 | −0.773813 | − | 0.633414i | \(-0.781653\pi\) | ||||
−0.773813 | + | 0.633414i | \(0.781653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.74002 | 0.0924185 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8391 | 0.466250 | 0.233125 | − | 0.972447i | \(-0.425105\pi\) | ||||
0.233125 | + | 0.972447i | \(0.425105\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.4604 | 1.02507 | 0.512536 | − | 0.858666i | \(-0.328706\pi\) | ||||
0.512536 | + | 0.858666i | \(0.328706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.194082 | 0.00652400 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.0747 | 0.472581 | 0.236291 | − | 0.971682i | \(-0.424068\pi\) | ||||
0.236291 | + | 0.971682i | \(0.424068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.353620 | 0.0118600 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −51.9606 | −1.74075 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −41.1333 | −1.37647 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.1992 | −1.07630 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.261375 | −0.00872705 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.5489 | −0.585290 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.91311 | −0.196994 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0213322 | 0.000709891 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.9966 | 0.797675 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30.9486 | −1.02763 | −0.513816 | − | 0.857901i | \(-0.671769\pi\) | ||||
−0.513816 | + | 0.857901i | \(0.671769\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.5578 | −0.715028 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.9041 | 0.758845 | 0.379423 | − | 0.925223i | \(-0.376123\pi\) | ||||
0.379423 | + | 0.925223i | \(0.376123\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.8265 | 1.81449 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.84167 | −0.0608836 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.98190 | 0.0654481 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.0673641 | −0.00222214 | −0.00111107 | − | 0.999999i | \(-0.500354\pi\) | ||||
−0.00111107 | + | 0.999999i | \(0.500354\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.652329 | −0.0214950 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.53115 | −0.182060 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.146285 | −0.00480984 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −35.4077 | −1.16294 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.0077 | 1.67351 | 0.836754 | − | 0.547579i | \(-0.184451\pi\) | ||||
0.836754 | + | 0.547579i | \(0.184451\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.6895 | 1.62851 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.31765 | −0.0431378 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.8274 | −0.419502 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.2385 | −0.367146 | −0.183573 | − | 0.983006i | \(-0.558766\pi\) | ||||
−0.183573 | + | 0.983006i | \(0.558766\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.337065 | 0.0109997 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.51945 | −0.147330 | −0.0736649 | − | 0.997283i | \(-0.523470\pi\) | ||||
−0.0736649 | + | 0.997283i | \(0.523470\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50.1643 | 1.63357 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.705863 | 0.0229617 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.1090 | 0.783438 | 0.391719 | − | 0.920085i | \(-0.371881\pi\) | ||||
0.391719 | + | 0.920085i | \(0.371881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.11713 | 0.101186 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.29802 | 0.0420913 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.9162 | −0.871902 | −0.435951 | − | 0.899970i | \(-0.643588\pi\) | ||||
−0.435951 | + | 0.899970i | \(0.643588\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0229 | −0.453771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.75648 | 0.0891044 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.26344 | −0.169965 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.3656 | −0.656954 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.35602 | 0.204820 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.2091 | −1.26218 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −56.9043 | −1.82992 | −0.914959 | − | 0.403547i | \(-0.867777\pi\) | ||||
−0.914959 | + | 0.403547i | \(0.867777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.659626 | 0.0211902 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.957032 | 0.0307126 | 0.0153563 | − | 0.999882i | \(-0.495112\pi\) | ||||
0.0153563 | + | 0.999882i | \(0.495112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.8194 | −0.346853 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.00683696 | 0.000218958 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.0859 | −0.546628 | −0.273314 | − | 0.961925i | \(-0.588120\pi\) | ||||
−0.273314 | + | 0.961925i | \(0.588120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.51873 | 0.144419 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.09216 | −0.194508 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −49.6978 | −1.58511 | −0.792557 | − | 0.609798i | \(-0.791251\pi\) | ||||
−0.792557 | + | 0.609798i | \(0.791251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.2352 | 0.581022 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.293323 | 0.00933658 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.13192 | 0.0677911 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.7871 | 1.83567 | 0.917834 | − | 0.396964i | \(-0.129936\pi\) | ||||
0.917834 | + | 0.396964i | \(0.129936\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.50559 | 0.0477785 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.18979 | 0.291336 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.8749 | −1.07283 | −0.536415 | − | 0.843954i | \(-0.680222\pi\) | ||||
−0.536415 | + | 0.843954i | \(0.680222\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.552475 | −0.0174795 |
(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 | 4012.2.a.i.1.8 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.i.1.8 | ✓ | 18 | 1.1 | even | 1 | trivial |