Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.07636\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −0.0763625 | −0.0440879 | −0.0220440 | − | 0.999757i | \(-0.507017\pi\) | ||||
−0.0220440 | + | 0.999757i | \(0.507017\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.17276 | 0.524472 | 0.262236 | − | 0.965004i | \(-0.415540\pi\) | ||||
0.262236 | + | 0.965004i | \(0.415540\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.469303 | −0.177380 | −0.0886899 | − | 0.996059i | \(-0.528268\pi\) | ||||
−0.0886899 | + | 0.996059i | \(0.528268\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99417 | −0.998056 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.74596 | 1.73247 | 0.866237 | − | 0.499634i | \(-0.166532\pi\) | ||||
0.866237 | + | 0.499634i | \(0.166532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.85873 | −0.515518 | −0.257759 | − | 0.966209i | \(-0.582984\pi\) | ||||
−0.257759 | + | 0.966209i | \(0.582984\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0895546 | −0.0231229 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.22916 | 1.26826 | 0.634129 | − | 0.773228i | \(-0.281359\pi\) | ||||
0.634129 | + | 0.773228i | \(0.281359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.12602 | −0.487743 | −0.243872 | − | 0.969808i | \(-0.578418\pi\) | ||||
−0.243872 | + | 0.969808i | \(0.578418\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0358371 | 0.00782030 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.171951 | −0.0358543 | −0.0179271 | − | 0.999839i | \(-0.505707\pi\) | ||||
−0.0179271 | + | 0.999839i | \(0.505707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.62464 | −0.724929 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.457730 | 0.0880902 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.19149 | −1.14973 | −0.574865 | − | 0.818248i | \(-0.694946\pi\) | ||||
−0.574865 | + | 0.818248i | \(0.694946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.396234 | 0.0711658 | 0.0355829 | − | 0.999367i | \(-0.488671\pi\) | ||||
0.0355829 | + | 0.999367i | \(0.488671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.438776 | −0.0763812 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.550377 | −0.0930307 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.17999 | −1.34478 | −0.672391 | − | 0.740196i | \(-0.734733\pi\) | ||||
−0.672391 | + | 0.740196i | \(0.734733\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.141937 | 0.0227281 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.4282 | −1.94095 | −0.970477 | − | 0.241193i | \(-0.922461\pi\) | ||||
−0.970477 | + | 0.241193i | \(0.922461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.97920 | 0.759321 | 0.379661 | − | 0.925126i | \(-0.376041\pi\) | ||||
0.379661 | + | 0.925126i | \(0.376041\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.51143 | −0.523453 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.521599 | 0.0760831 | 0.0380415 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380415 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77976 | −0.968536 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.399312 | −0.0559148 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.76106 | 1.20342 | 0.601712 | − | 0.798713i | \(-0.294486\pi\) | ||||
0.601712 | + | 0.798713i | \(0.294486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.73861 | 0.908634 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.162349 | 0.0215036 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.35297 | −0.436519 | −0.218260 | − | 0.975891i | \(-0.570038\pi\) | ||||
−0.218260 | + | 0.975891i | \(0.570038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.38243 | −0.689150 | −0.344575 | − | 0.938759i | \(-0.611977\pi\) | ||||
−0.344575 | + | 0.938759i | \(0.611977\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.40517 | 0.177035 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.17983 | −0.270375 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.42823 | −1.02967 | −0.514836 | − | 0.857289i | \(-0.672147\pi\) | ||||
−0.514836 | + | 0.857289i | \(0.672147\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0131306 | 0.00158074 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.47643 | −0.887289 | −0.443644 | − | 0.896203i | \(-0.646315\pi\) | ||||
−0.443644 | + | 0.896203i | \(0.646315\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.60009 | −0.538400 | −0.269200 | − | 0.963084i | \(-0.586759\pi\) | ||||
−0.269200 | + | 0.963084i | \(0.586759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.276787 | 0.0319606 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.69660 | −0.307306 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.1992 | 1.93506 | 0.967530 | − | 0.252758i | \(-0.0813376\pi\) | ||||
0.967530 | + | 0.252758i | \(0.0813376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.94755 | 0.994173 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.97721 | −0.656084 | −0.328042 | − | 0.944663i | \(-0.606389\pi\) | ||||
−0.328042 | + | 0.944663i | \(0.606389\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.13253 | 0.665166 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.472798 | 0.0506892 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.25595 | −0.451130 | −0.225565 | − | 0.974228i | \(-0.572423\pi\) | ||||
−0.225565 | + | 0.974228i | \(0.572423\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.872306 | 0.0914425 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0302574 | −0.00313755 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.49331 | −0.255808 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.64532 | −0.268592 | −0.134296 | − | 0.990941i | \(-0.542877\pi\) | ||||
−0.134296 | + | 0.990941i | \(0.542877\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.2044 | −1.72911 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.39045 | 0.635873 | 0.317937 | − | 0.948112i | \(-0.397010\pi\) | ||||
0.317937 | + | 0.948112i | \(0.397010\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6014 | 1.63578 | 0.817890 | − | 0.575375i | \(-0.195144\pi\) | ||||
0.817890 | + | 0.575375i | \(0.195144\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0420282 | 0.00410153 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.15760 | −0.885299 | −0.442649 | − | 0.896695i | \(-0.645961\pi\) | ||||
−0.442649 | + | 0.896695i | \(0.645961\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.51891 | 0.624398 | 0.312199 | − | 0.950017i | \(-0.398934\pi\) | ||||
0.312199 | + | 0.950017i | \(0.398934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.624645 | 0.0592887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.36694 | 0.128591 | 0.0642954 | − | 0.997931i | \(-0.479520\pi\) | ||||
0.0642954 | + | 0.997931i | \(0.479520\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.201656 | −0.0188046 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.56535 | 0.514516 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.45406 | −0.224963 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.0161 | 2.00146 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.949047 | 0.0855726 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.1146 | −0.904677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.77469 | −0.601157 | −0.300578 | − | 0.953757i | \(-0.597180\pi\) | ||||
−0.300578 | + | 0.953757i | \(0.597180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.380225 | −0.0334769 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.6839 | −1.45768 | −0.728838 | − | 0.684687i | \(-0.759939\pi\) | ||||
−0.728838 | + | 0.684687i | \(0.759939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.997748 | 0.0865158 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.536805 | 0.0462008 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0662 | 1.11632 | 0.558162 | − | 0.829732i | \(-0.311507\pi\) | ||||
0.558162 | + | 0.829732i | \(0.311507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8468 | 0.920017 | 0.460008 | − | 0.887915i | \(-0.347846\pi\) | ||||
0.460008 | + | 0.887915i | \(0.347846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.0398306 | −0.00335434 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.6802 | −0.893122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.26110 | −0.603002 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.517719 | 0.0427008 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.0210826 | 0.00172716 | 0.000863578 | − | 1.00000i | \(-0.499725\pi\) | ||||
0.000863578 | 1.00000i | \(0.499725\pi\) | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.1704 | −1.23455 | −0.617276 | − | 0.786746i | \(-0.711764\pi\) | ||||
−0.617276 | + | 0.786746i | \(0.711764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.6570 | −1.26579 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.464686 | 0.0373245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1437 | 0.889367 | 0.444684 | − | 0.895688i | \(-0.353316\pi\) | ||||
0.444684 | + | 0.895688i | \(0.353316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.669016 | −0.0530565 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0806970 | 0.00635982 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3388 | 0.809797 | 0.404899 | − | 0.914362i | \(-0.367307\pi\) | ||||
0.404899 | + | 0.914362i | \(0.367307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.514578 | −0.0400598 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.6444 | 1.21060 | 0.605300 | − | 0.795998i | \(-0.293053\pi\) | ||||
0.605300 | + | 0.795998i | \(0.293053\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.54513 | −0.734241 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.36567 | 0.486795 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.69316 | −0.432843 | −0.216422 | − | 0.976300i | \(-0.569439\pi\) | ||||
−0.216422 | + | 0.976300i | \(0.569439\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.70105 | 0.128588 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.256041 | 0.0192452 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8571 | −0.811495 | −0.405748 | − | 0.913985i | \(-0.632989\pi\) | ||||
−0.405748 | + | 0.913985i | \(0.632989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.26595 | 0.465744 | 0.232872 | − | 0.972507i | \(-0.425188\pi\) | ||||
0.232872 | + | 0.972507i | \(0.425188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.411016 | 0.0303832 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.59313 | −0.705301 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.0466 | 2.19722 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.214814 | −0.0156254 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.26296 | −0.597887 | −0.298943 | − | 0.954271i | \(-0.596634\pi\) | ||||
−0.298943 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8469 | −1.42861 | −0.714306 | − | 0.699833i | \(-0.753258\pi\) | ||||
−0.714306 | + | 0.699833i | \(0.753258\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.166458 | 0.0119203 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.24866 | −0.302704 | −0.151352 | − | 0.988480i | \(-0.548363\pi\) | ||||
−0.151352 | + | 0.988480i | \(0.548363\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.63286 | −0.328415 | −0.164207 | − | 0.986426i | \(-0.552507\pi\) | ||||
−0.164207 | + | 0.986426i | \(0.552507\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.643601 | 0.0453961 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.90568 | 0.203939 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.5752 | −1.01798 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.514850 | 0.0357846 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.2161 | −0.845002 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.2699 | −0.707007 | −0.353503 | − | 0.935433i | \(-0.615010\pi\) | ||||
−0.353503 | + | 0.935433i | \(0.615010\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.570919 | 0.0391187 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.83939 | 0.398243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.185954 | −0.0126234 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.351275 | 0.0237369 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.71958 | −0.653810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.7887 | −0.990326 | −0.495163 | − | 0.868800i | \(-0.664892\pi\) | ||||
−0.495163 | + | 0.868800i | \(0.664892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.8528 | 0.723520 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9154 | −0.989969 | −0.494984 | − | 0.868902i | \(-0.664826\pi\) | ||||
−0.494984 | + | 0.868902i | \(0.664826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.2488 | −1.20592 | −0.602959 | − | 0.797772i | \(-0.706012\pi\) | ||||
−0.602959 | + | 0.797772i | \(0.706012\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.205919 | 0.0135485 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.6741 | −1.09235 | −0.546177 | − | 0.837670i | \(-0.683918\pi\) | ||||
−0.546177 | + | 0.837670i | \(0.683918\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.611708 | 0.0399035 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.31337 | −0.0853127 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.3691 | −1.57631 | −0.788153 | − | 0.615479i | \(-0.788963\pi\) | ||||
−0.788153 | + | 0.615479i | \(0.788963\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1071 | 1.16638 | 0.583190 | − | 0.812336i | \(-0.301804\pi\) | ||||
0.583190 | + | 0.812336i | \(0.301804\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.05645 | −0.131921 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.95100 | −0.507971 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.95170 | 0.251441 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.456435 | 0.0289254 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.9687 | −1.70225 | −0.851124 | − | 0.524965i | \(-0.824078\pi\) | ||||
−0.851124 | + | 0.524965i | \(0.824078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.988024 | −0.0621165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.468295 | −0.0293258 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.3022 | 1.26642 | 0.633208 | − | 0.773982i | \(-0.281738\pi\) | ||||
0.633208 | + | 0.773982i | \(0.281738\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.83889 | 0.238537 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.5384 | 1.14750 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0595 | 0.743622 | 0.371811 | − | 0.928309i | \(-0.378737\pi\) | ||||
0.371811 | + | 0.928309i | \(0.378737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.2746 | 0.631162 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.324995 | 0.0198894 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.0120 | −1.52501 | −0.762506 | − | 0.646982i | \(-0.776031\pi\) | ||||
−0.762506 | + | 0.646982i | \(0.776031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0354 | 1.09557 | 0.547787 | − | 0.836618i | \(-0.315470\pi\) | ||||
0.547787 | + | 0.836618i | \(0.315470\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0666115 | −0.00403151 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.8271 | −1.25592 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.3688 | −1.76460 | −0.882301 | − | 0.470686i | \(-0.844006\pi\) | ||||
−0.882301 | + | 0.470686i | \(0.844006\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.18639 | −0.0710274 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0977 | 0.721686 | 0.360843 | − | 0.932626i | \(-0.382489\pi\) | ||||
0.360843 | + | 0.932626i | \(0.382489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.04149 | 0.478017 | 0.239009 | − | 0.971017i | \(-0.423178\pi\) | ||||
0.239009 | + | 0.971017i | \(0.423178\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.190395 | 0.0112780 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.83257 | 0.344286 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3441 | 0.608477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.202003 | 0.0118416 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.5236 | −0.790056 | −0.395028 | − | 0.918669i | \(-0.629265\pi\) | ||||
−0.395028 | + | 0.918669i | \(0.629265\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.93221 | −0.228942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.63010 | 0.152614 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.319610 | 0.0184835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.33675 | −0.134688 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.487991 | −0.0280343 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.31228 | −0.361440 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.60632 | −0.205824 | −0.102912 | − | 0.994690i | \(-0.532816\pi\) | ||||
−0.102912 | + | 0.994690i | \(0.532816\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.26772 | −0.0721181 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.5438 | 1.56187 | 0.780934 | − | 0.624613i | \(-0.214743\pi\) | ||||
0.780934 | + | 0.624613i | \(0.214743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.2190 | −1.70808 | −0.854039 | − | 0.520209i | \(-0.825854\pi\) | ||||
−0.854039 | + | 0.520209i | \(0.825854\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.64792 | 0.0928499 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.23152 | −0.293831 | −0.146916 | − | 0.989149i | \(-0.546935\pi\) | ||||
−0.146916 | + | 0.989149i | \(0.546935\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −35.5761 | −1.99188 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.699298 | 0.0390310 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.1173 | −0.618584 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.73723 | 0.373714 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.497800 | −0.0275284 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.244788 | −0.0134956 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.56111 | 0.305666 | 0.152833 | − | 0.988252i | \(-0.451160\pi\) | ||||
0.152833 | + | 0.988252i | \(0.451160\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 24.4923 | 1.34217 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.88426 | −0.540035 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.20314 | 0.0655392 | 0.0327696 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327696 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.104383 | −0.00566930 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.27675 | 0.123293 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.46688 | 0.349178 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0153990 | 0.000829054 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.8760 | −1.01332 | −0.506659 | − | 0.862147i | \(-0.669120\pi\) | ||||
−0.506659 | + | 0.862147i | \(0.669120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.3633 | 0.982966 | 0.491483 | − | 0.870887i | \(-0.336455\pi\) | ||||
0.491483 | + | 0.870887i | \(0.336455\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.850795 | −0.0454121 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.06519 | −0.109919 | −0.0549596 | − | 0.998489i | \(-0.517503\pi\) | ||||
−0.0549596 | + | 0.998489i | \(0.517503\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.76802 | −0.465358 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.187398 | 0.00991816 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.83605 | 0.413571 | 0.206786 | − | 0.978386i | \(-0.433700\pi\) | ||||
0.206786 | + | 0.978386i | \(0.433700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4800 | −0.762107 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.68121 | −0.0882404 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.39478 | −0.282376 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.3479 | −1.42755 | −0.713775 | − | 0.700375i | \(-0.753016\pi\) | ||||
−0.713775 | + | 0.700375i | \(0.753016\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 37.2120 | 1.93718 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.11159 | −0.213463 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.3381 | 1.62263 | 0.811313 | − | 0.584612i | \(-0.198753\pi\) | ||||
0.811313 | + | 0.584612i | \(0.198753\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.772376 | 0.0398853 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.5083 | 0.592707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.97192 | 0.101291 | 0.0506454 | − | 0.998717i | \(-0.483872\pi\) | ||||
0.0506454 | + | 0.998717i | \(0.483872\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.517333 | 0.0265038 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.9455 | 1.27466 | 0.637328 | − | 0.770593i | \(-0.280040\pi\) | ||||
0.637328 | + | 0.770593i | \(0.280040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.16245 | −0.161173 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.9086 | −0.757845 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.98152 | −0.455381 | −0.227691 | − | 0.973734i | \(-0.573117\pi\) | ||||
−0.227691 | + | 0.973734i | \(0.573117\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.899159 | −0.0454724 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.27402 | 0.0642659 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.1704 | 1.01488 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3125 | −0.517569 | −0.258784 | − | 0.965935i | \(-0.583322\pi\) | ||||
−0.258784 | + | 0.965935i | \(0.583322\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0761906 | −0.00381430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.2691 | −1.11207 | −0.556033 | − | 0.831160i | \(-0.687677\pi\) | ||||
−0.556033 | + | 0.831160i | \(0.687677\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.736492 | −0.0366873 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.4933 | 0.521416 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −47.0019 | −2.32980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.36108 | −0.462876 | −0.231438 | − | 0.972850i | \(-0.574343\pi\) | ||||
−0.231438 | + | 0.972850i | \(0.574343\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.997771 | −0.0492164 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.57356 | 0.0774297 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.00980 | −0.344098 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.828292 | −0.0405616 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.9797 | 1.70887 | 0.854436 | − | 0.519557i | \(-0.173903\pi\) | ||||
0.854436 | + | 0.519557i | \(0.173903\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9244 | 0.776107 | 0.388054 | − | 0.921637i | \(-0.373147\pi\) | ||||
0.388054 | + | 0.921637i | \(0.373147\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.56176 | −0.0759352 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.9538 | −0.919396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.52599 | 0.122241 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.815566 | 0.0393759 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.5257 | 1.80755 | 0.903775 | − | 0.428008i | \(-0.140785\pi\) | ||||
0.903775 | + | 0.428008i | \(0.140785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7776 | 1.33491 | 0.667454 | − | 0.744651i | \(-0.267384\pi\) | ||||
0.667454 | + | 0.744651i | \(0.267384\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.554476 | 0.0265851 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.365572 | 0.0174877 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.3507 | −1.78265 | −0.891327 | − | 0.453362i | \(-0.850225\pi\) | ||||
−0.891327 | + | 0.453362i | \(0.850225\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.2997 | 0.966654 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.8245 | −0.751844 | −0.375922 | − | 0.926651i | \(-0.622674\pi\) | ||||
−0.375922 | + | 0.926651i | \(0.622674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.99119 | −0.236605 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.00160992 | −7.61467e−5 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.0395 | −1.55923 | −0.779616 | − | 0.626258i | \(-0.784586\pi\) | ||||
−0.779616 | + | 0.626258i | \(0.784586\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −71.4118 | −3.36265 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.15845 | 0.0544289 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.02300 | 0.0479591 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.38585 | −0.298717 | −0.149359 | − | 0.988783i | \(-0.547721\pi\) | ||||
−0.149359 | + | 0.988783i | \(0.547721\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.39354 | 0.111721 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.10510 | 0.191193 | 0.0955967 | − | 0.995420i | \(-0.469524\pi\) | ||||
0.0955967 | + | 0.995420i | \(0.469524\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9482 | 1.02002 | 0.510011 | − | 0.860168i | \(-0.329641\pi\) | ||||
0.510011 | + | 0.860168i | \(0.329641\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.0354846 | −0.00164556 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.9539 | 0.969633 | 0.484816 | − | 0.874616i | \(-0.338886\pi\) | ||||
0.484816 | + | 0.874616i | \(0.338886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.95539 | 0.182643 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.850964 | −0.0392104 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.6103 | 1.31550 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.70608 | 0.353579 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.2321 | −1.20108 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.1617 | −1.83503 | −0.917517 | − | 0.397698i | \(-0.869809\pi\) | ||||
−0.917517 | + | 0.397698i | \(0.869809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2044 | 0.693260 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.00616223 | −0.000280391 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.10232 | −0.140869 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.56804 | 0.0710547 | 0.0355273 | − | 0.999369i | \(-0.488689\pi\) | ||||
0.0355273 | + | 0.999369i | \(0.488689\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.789497 | −0.0357023 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.66243 | −0.436059 | −0.218030 | − | 0.975942i | \(-0.569963\pi\) | ||||
−0.218030 | + | 0.975942i | \(0.569963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.3763 | −1.45815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.1765 | −0.906868 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.50871 | 0.157387 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.6363 | 0.923810 | 0.461905 | − | 0.886930i | \(-0.347166\pi\) | ||||
0.461905 | + | 0.886930i | \(0.347166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.19465 | −0.0533728 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.49444 | 0.333498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.728890 | 0.0323712 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.3284 | −1.03401 | −0.517006 | − | 0.855982i | \(-0.672953\pi\) | ||||
−0.517006 | + | 0.855982i | \(0.672953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.15883 | 0.0955012 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.973144 | −0.0429654 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 19.4693 | 0.857921 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.99709 | 0.131812 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.434744 | 0.0190832 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.2647 | −1.89546 | −0.947730 | − | 0.319073i | \(-0.896629\pi\) | ||||
−0.947730 | + | 0.319073i | \(0.896629\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.4082 | 1.89811 | 0.949054 | − | 0.315112i | \(-0.102042\pi\) | ||||
0.949054 | + | 0.315112i | \(0.102042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.129897 | −0.00566916 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.07197 | 0.0902565 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9704 | −0.998714 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.0394 | 0.435671 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.1006 | 1.00060 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.7396 | −0.464315 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.829073 | 0.0357771 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38.9562 | −1.67796 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.5657 | 1.40011 | 0.700054 | − | 0.714090i | \(-0.253159\pi\) | ||||
0.700054 | + | 0.714090i | \(0.253159\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.478484 | −0.0205337 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.64509 | 0.327480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8377 | −1.19025 | −0.595127 | − | 0.803631i | \(-0.702898\pi\) | ||||
−0.595127 | + | 0.803631i | \(0.702898\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.1159 | 0.687811 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.1633 | 0.560773 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.07162 | −0.343240 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.732556 | 0.0310953 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.7225 | 0.666182 | 0.333091 | − | 0.942895i | \(-0.391908\pi\) | ||||
0.333091 | + | 0.942895i | \(0.391908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.25498 | −0.391444 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.29443 | −0.0968710 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.7817 | 1.04442 | 0.522212 | − | 0.852816i | \(-0.325107\pi\) | ||||
0.522212 | + | 0.852816i | \(0.325107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.60309 | 0.0674423 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.19911 | −0.176346 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.95346 | 0.123816 | 0.0619078 | − | 0.998082i | \(-0.480282\pi\) | ||||
0.0619078 | + | 0.998082i | \(0.480282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7926 | 0.451656 | 0.225828 | − | 0.974167i | \(-0.427491\pi\) | ||||
0.225828 | + | 0.974167i | \(0.427491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.630981 | 0.0263596 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.623261 | 0.0259918 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.92593 | −0.246700 | −0.123350 | − | 0.992363i | \(-0.539364\pi\) | ||||
−0.123350 | + | 0.992363i | \(0.539364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.51556 | 0.0629845 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.80512 | 0.116376 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.3407 | 2.08490 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.52679 | 0.269850 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8090 | 0.611234 | 0.305617 | − | 0.952155i | \(-0.401137\pi\) | ||||
0.305617 | + | 0.952155i | \(0.401137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.842403 | −0.0347106 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.324438 | 0.0133456 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.4465 | 1.37348 | 0.686741 | − | 0.726902i | \(-0.259041\pi\) | ||||
0.686741 | + | 0.726902i | \(0.259041\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.87801 | −0.117987 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.353777 | 0.0144791 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.35823 | −0.382367 | −0.191183 | − | 0.981554i | \(-0.561233\pi\) | ||||
−0.191183 | + | 0.981554i | \(0.561233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.16182 | −0.251346 | −0.125673 | − | 0.992072i | \(-0.540109\pi\) | ||||
−0.125673 | + | 0.992072i | \(0.540109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.2355 | 1.02767 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.8195 | 1.04971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −35.7361 | −1.45048 | −0.725242 | − | 0.688494i | \(-0.758272\pi\) | ||||
−0.725242 | + | 0.688494i | \(0.758272\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.221885 | −0.00899124 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.969511 | −0.0392222 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.96528 | −0.0793771 | −0.0396885 | − | 0.999212i | \(-0.512637\pi\) | ||||
−0.0396885 | + | 0.999212i | \(0.512637\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.11300 | 0.0448805 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.4461 | −1.42701 | −0.713503 | − | 0.700652i | \(-0.752893\pi\) | ||||
−0.713503 | + | 0.700652i | \(0.752893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.4643 | 1.38524 | 0.692618 | − | 0.721304i | \(-0.256457\pi\) | ||||
0.692618 | + | 0.721304i | \(0.256457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0787071 | −0.00315841 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.99733 | 0.0800213 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.26126 | 0.250451 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.932849 | 0.0372544 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.7745 | −1.70553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.7560 | 1.18457 | 0.592284 | − | 0.805729i | \(-0.298226\pi\) | ||||
0.592284 | + | 0.805729i | \(0.298226\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.784233 | 0.0311705 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.94506 | −0.315290 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6017 | 0.499298 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.3857 | 0.885564 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.9327 | −1.30077 | −0.650383 | − | 0.759607i | \(-0.725391\pi\) | ||||
−0.650383 | + | 0.759607i | \(0.725391\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.492253 | 0.0194126 | 0.00970628 | − | 0.999953i | \(-0.496910\pi\) | ||||
0.00970628 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.445911 | −0.0175577 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.76376 | −0.147969 | −0.0739844 | − | 0.997259i | \(-0.523571\pi\) | ||||
−0.0739844 | + | 0.997259i | \(0.523571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.2660 | −0.756258 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0141999 | 0.000556538 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.5728 | 0.726809 | 0.363404 | − | 0.931631i | \(-0.381614\pi\) | ||||
0.363404 | + | 0.931631i | \(0.381614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19.5661 | −0.764510 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.7734 | 0.537353 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.1930 | 1.33197 | 0.665985 | − | 0.745965i | \(-0.268012\pi\) | ||||
0.665985 | + | 0.745965i | \(0.268012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5439 | 1.14912 | 0.574562 | − | 0.818461i | \(-0.305173\pi\) | ||||
0.574562 | + | 0.818461i | \(0.305173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.742212 | 0.0288251 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.17012 | 0.0453751 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.06463 | 0.0412227 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.12930 | 0.0436614 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.9273 | −1.19393 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.15185 | −0.352778 | −0.176389 | − | 0.984321i | \(-0.556442\pi\) | ||||
−0.176389 | + | 0.984321i | \(0.556442\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.65911 | −0.0638591 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.1256 | −1.27312 | −0.636561 | − | 0.771227i | \(-0.719644\pi\) | ||||
−0.636561 | + | 0.771227i | \(0.719644\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.24146 | 0.0476427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.13898 | 0.0436457 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −49.1452 | −1.88049 | −0.940245 | − | 0.340498i | \(-0.889404\pi\) | ||||
−0.940245 | + | 0.340498i | \(0.889404\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.3235 | 0.585481 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.39353 | 0.0531664 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.2844 | −0.620387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.1013 | −1.29727 | −0.648637 | − | 0.761098i | \(-0.724661\pi\) | ||||
−0.648637 | + | 0.761098i | \(0.724661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.07406 | 0.306708 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.7207 | 0.482523 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −64.9889 | −2.46163 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.27327 | 0.0481596 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.2590 | 0.991787 | 0.495894 | − | 0.868383i | \(-0.334841\pi\) | ||||
0.495894 | + | 0.868383i | \(0.334841\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.3909 | 0.655909 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.0467116 | −0.00175926 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.99905 | −0.112791 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.4811 | 1.06963 | 0.534815 | − | 0.844969i | \(-0.320381\pi\) | ||||
0.534815 | + | 0.844969i | \(0.320381\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −51.4973 | −1.93130 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.0681329 | −0.00255160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.5252 | −0.468418 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.86089 | 0.0694961 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.8368 | −0.516024 | −0.258012 | − | 0.966142i | \(-0.583067\pi\) | ||||
−0.258012 | + | 0.966142i | \(0.583067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.79106 | −0.290154 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.38270 | −0.0514233 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.4419 | 0.833473 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.61759 | −0.356697 | −0.178348 | − | 0.983967i | \(-0.557075\pi\) | ||||
−0.178348 | + | 0.983967i | \(0.557075\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.6856 | −0.988356 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.0370 | 0.963015 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.9530 | −0.626175 | −0.313087 | − | 0.949724i | \(-0.601363\pi\) | ||||
−0.313087 | + | 0.949724i | \(0.601363\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.607158 | 0.0223954 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48.4283 | −1.78388 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.82452 | −0.361401 | −0.180700 | − | 0.983538i | \(-0.557836\pi\) | ||||
−0.180700 | + | 0.983538i | \(0.557836\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.301762 | −0.0110855 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.8650 | −1.05896 | −0.529478 | − | 0.848324i | \(-0.677612\pi\) | ||||
−0.529478 | + | 0.848324i | \(0.677612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0247248 | 0.000905845 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.8968 | 0.654808 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.29769 | 0.157034 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.70834 | 0.354262 | 0.177131 | − | 0.984187i | \(-0.443318\pi\) | ||||
0.177131 | + | 0.984187i | \(0.443318\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.05940 | 0.0750486 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.7912 | −0.647489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.99476 | −0.217883 | −0.108942 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108942 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0754480 | 0.00273859 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4793 | 0.561123 | 0.280562 | − | 0.959836i | \(-0.409479\pi\) | ||||
0.280562 | + | 0.959836i | \(0.409479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.05934 | −0.110756 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.3618 | −0.663873 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.23226 | 0.225034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.9740 | −1.00877 | −0.504384 | − | 0.863480i | \(-0.668280\pi\) | ||||
−0.504384 | + | 0.863480i | \(0.668280\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.55033 | −0.0558336 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.7330 | 1.14136 | 0.570679 | − | 0.821173i | \(-0.306680\pi\) | ||||
0.570679 | + | 0.821173i | \(0.306680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.43621 | −0.0515901 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.293147 | −0.0105166 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.4226 | 0.946687 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.9593 | −1.53720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.83403 | −0.101280 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.0689 | 0.466448 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.1339 | −0.682051 | −0.341025 | − | 0.940054i | \(-0.610774\pi\) | ||||
−0.341025 | + | 0.940054i | \(0.610774\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.920895 | −0.0327847 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.641508 | −0.0228094 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0045 | 0.355270 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.784593 | −0.0278266 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.45993 | −0.0871352 | −0.0435676 | − | 0.999050i | \(-0.513872\pi\) | ||||
−0.0435676 | + | 0.999050i | \(0.513872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.72752 | 0.0964929 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.7430 | 0.450253 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.4320 | −0.932764 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0946379 | 0.00333555 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.90998 | 0.0672346 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.9350 | 0.595404 | 0.297702 | − | 0.954659i | \(-0.403780\pi\) | ||||
0.297702 | + | 0.954659i | \(0.403780\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.7584 | 0.834269 | 0.417135 | − | 0.908845i | \(-0.363034\pi\) | ||||
0.417135 | + | 0.908845i | \(0.363034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.37723 | −0.0483016 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.1249 | 0.424716 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5859 | −0.370354 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.61183 | −0.0912648 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.2765 | 0.672755 | 0.336378 | − | 0.941727i | \(-0.390798\pi\) | ||||
0.336378 | + | 0.941727i | \(0.390798\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −52.8192 | −1.84116 | −0.920580 | − | 0.390553i | \(-0.872284\pi\) | ||||
−0.920580 | + | 0.390553i | \(0.872284\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.59041 | 0.0553709 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7144 | 0.894176 | 0.447088 | − | 0.894490i | \(-0.352461\pi\) | ||||
0.447088 | + | 0.894490i | \(0.352461\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.3380 | 0.810562 | 0.405281 | − | 0.914192i | \(-0.367174\pi\) | ||||
0.405281 | + | 0.914192i | \(0.367174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.24268 | 0.0777976 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35.4524 | −1.22835 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.3471 | 0.634926 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.181368 | 0.00626900 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.8028 | −0.649144 | −0.324572 | − | 0.945861i | \(-0.605220\pi\) | ||||
−0.324572 | + | 0.945861i | \(0.605220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.33453 | 0.321880 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.923809 | −0.0318177 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1941 | −0.385089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.3322 | −0.355019 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.614069 | −0.0210748 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.40656 | 0.0482162 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.0553 | −1.54266 | −0.771332 | − | 0.636433i | \(-0.780409\pi\) | ||||
−0.771332 | + | 0.636433i | \(0.780409\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.46538 | 0.255311 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.4362 | −1.14216 | −0.571079 | − | 0.820895i | \(-0.693475\pi\) | ||||
−0.571079 | + | 0.820895i | \(0.693475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.4483 | −0.663567 | −0.331784 | − | 0.943355i | \(-0.607650\pi\) | ||||
−0.331784 | + | 0.943355i | \(0.607650\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.445390 | −0.0151789 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.1628 | 0.550186 | 0.275093 | − | 0.961418i | \(-0.411291\pi\) | ||||
0.275093 | + | 0.961418i | \(0.411291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.67669 | −0.227014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.789902 | −0.0268265 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 98.8259 | 3.35244 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.6658 | 0.530815 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.92054 | 0.268070 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.74681 | 0.160471 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3959 | −0.756255 | −0.378127 | − | 0.925754i | \(-0.623432\pi\) | ||||
−0.378127 | + | 0.925754i | \(0.623432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.03269 | 0.0348319 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4074 | 0.350633 | 0.175316 | − | 0.984512i | \(-0.443905\pi\) | ||||
0.175316 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.3582 | 0.617803 | 0.308902 | − | 0.951094i | \(-0.400039\pi\) | ||||
0.308902 | + | 0.951094i | \(0.400039\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.300274 | 0.0100936 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.9758 | 0.771453 | 0.385726 | − | 0.922613i | \(-0.373951\pi\) | ||||
0.385726 | + | 0.922613i | \(0.373951\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.17938 | 0.106633 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 51.4123 | 1.72238 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.10893 | −0.0371090 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.7327 | −0.425607 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0244062 | −0.000814900 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.45328 | −0.0818215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.8130 | 1.52625 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.178440 | 0.00593812 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.34843 | 0.244270 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.415835 | −0.0138076 | −0.00690378 | − | 0.999976i | \(-0.502198\pi\) | ||||
−0.00690378 | + | 0.999976i | \(0.502198\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.1341 | −0.634638 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.6089 | 0.450881 | 0.225441 | − | 0.974257i | \(-0.427618\pi\) | ||||
0.225441 | + | 0.974257i | \(0.427618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.3448 | −1.13665 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.482022 | 0.0159351 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.82978 | 0.258562 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.8913 | 0.491218 | 0.245609 | − | 0.969369i | \(-0.421012\pi\) | ||||
0.245609 | + | 0.969369i | \(0.421012\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.275388 | 0.00907433 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.8966 | 0.457414 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.6496 | 0.974871 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −49.7072 | −1.63260 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.4977 | −0.639699 | −0.319850 | − | 0.947468i | \(-0.603632\pi\) | ||||
−0.319850 | + | 0.947468i | \(0.603632\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.4139 | 0.472397 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.10332 | −0.0688595 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 35.2373 | 1.15238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.5125 | 0.408764 | 0.204382 | − | 0.978891i | \(-0.434481\pi\) | ||||
0.204382 | + | 0.978891i | \(0.434481\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.30760 | 0.0753056 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.08256 | 0.133088 | 0.0665439 | − | 0.997783i | \(-0.478803\pi\) | ||||
0.0665439 | + | 0.997783i | \(0.478803\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.13704 | 0.0695915 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.251924 | −0.00819509 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.698574 | 0.0227006 | 0.0113503 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113503 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.55032 | 0.277555 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.399492 | 0.0129544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.31223 | 0.236866 | 0.118433 | − | 0.992962i | \(-0.462213\pi\) | ||||
0.118433 | + | 0.992962i | \(0.462213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.69044 | −0.313575 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.71668 | 0.0878178 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.13202 | −0.198013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8430 | −0.994935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27.4194 | 0.883578 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.2756 | −0.749267 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.1107 | −1.22556 | −0.612778 | − | 0.790255i | \(-0.709948\pi\) | ||||
−0.612778 | + | 0.790255i | \(0.709948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.848946 | 0.0272721 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.0424 | 1.63803 | 0.819014 | − | 0.573773i | \(-0.194521\pi\) | ||||
0.819014 | + | 0.573773i | \(0.194521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.09045 | −0.163192 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.514472 | −0.0164763 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.4134 | 1.70885 | 0.854424 | − | 0.519577i | \(-0.173910\pi\) | ||||
0.854424 | + | 0.519577i | \(0.173910\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.4546 | −0.781571 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.5187 | −0.623185 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.20932 | −0.0385714 | −0.0192857 | − | 0.999814i | \(-0.506139\pi\) | ||||
−0.0192857 | + | 0.999814i | \(0.506139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.98264 | −0.158760 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.0186926 | 0.000594993 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.856179 | −0.0272249 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.3298 | 0.423433 | 0.211717 | − | 0.977331i | \(-0.432095\pi\) | ||||
0.211717 | + | 0.977331i | \(0.432095\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.424660 | −0.0134762 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.43321 | −0.172244 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2475 | −1.24298 | −0.621490 | − | 0.783422i | \(-0.713472\pi\) | ||||
−0.621490 | + | 0.783422i | \(0.713472\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.74423 | −0.118462 |
(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 | 8048.2.a.p.1.4 | 10 | ||
4.3 | odd | 2 | 503.2.a.e.1.4 | ✓ | 10 | ||
12.11 | even | 2 | 4527.2.a.k.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.4 | ✓ | 10 | 4.3 | odd | 2 | ||
4527.2.a.k.1.7 | 10 | 12.11 | even | 2 | |||
8048.2.a.p.1.4 | 10 | 1.1 | even | 1 | trivial |