Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.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: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 845) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.76052\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.20556 | −1.55957 | −0.779783 | − | 0.626050i | \(-0.784671\pi\) | ||||
−0.779783 | + | 0.626050i | \(0.784671\pi\) | |||||||
\(3\) | 0.0130567 | 0.00753827 | 0.00376913 | − | 0.999993i | \(-0.498800\pi\) | ||||
0.00376913 | + | 0.999993i | \(0.498800\pi\) | |||||||
\(4\) | 2.86449 | 1.43225 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0287972 | −0.0117564 | ||||||||
\(7\) | −4.60897 | −1.74203 | −0.871013 | − | 0.491259i | \(-0.836537\pi\) | ||||
−0.871013 | + | 0.491259i | \(0.836537\pi\) | |||||||
\(8\) | −1.90669 | −0.674116 | ||||||||
\(9\) | −2.99983 | −0.999943 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93232 | 0.884128 | 0.442064 | − | 0.896984i | \(-0.354246\pi\) | ||||
0.442064 | + | 0.896984i | \(0.354246\pi\) | |||||||
\(12\) | 0.0374007 | 0.0107967 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 10.1654 | 2.71681 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.52367 | −0.380917 | ||||||||
\(17\) | 3.35206 | 0.812994 | 0.406497 | − | 0.913652i | \(-0.366750\pi\) | ||||
0.406497 | + | 0.913652i | \(0.366750\pi\) | |||||||
\(18\) | 6.61630 | 1.55948 | ||||||||
\(19\) | −2.46021 | −0.564410 | −0.282205 | − | 0.959354i | \(-0.591066\pi\) | ||||
−0.282205 | + | 0.959354i | \(0.591066\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.0601778 | −0.0131319 | ||||||||
\(22\) | −6.46741 | −1.37886 | ||||||||
\(23\) | 1.58329 | 0.330139 | 0.165069 | − | 0.986282i | \(-0.447215\pi\) | ||||
0.165069 | + | 0.986282i | \(0.447215\pi\) | |||||||
\(24\) | −0.0248950 | −0.00508167 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.0783378 | −0.0150761 | ||||||||
\(28\) | −13.2024 | −2.49501 | ||||||||
\(29\) | 8.26322 | 1.53444 | 0.767221 | − | 0.641383i | \(-0.221639\pi\) | ||||
0.767221 | + | 0.641383i | \(0.221639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.77959 | −1.75647 | −0.878233 | − | 0.478233i | \(-0.841277\pi\) | ||||
−0.878233 | + | 0.478233i | \(0.841277\pi\) | |||||||
\(32\) | 7.17392 | 1.26818 | ||||||||
\(33\) | 0.0382863 | 0.00666479 | ||||||||
\(34\) | −7.39317 | −1.26792 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.59299 | −1.43216 | ||||||||
\(37\) | −4.12917 | −0.678831 | −0.339416 | − | 0.940637i | \(-0.610229\pi\) | ||||
−0.339416 | + | 0.940637i | \(0.610229\pi\) | |||||||
\(38\) | 5.42613 | 0.880235 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.26508 | 1.13462 | 0.567308 | − | 0.823506i | \(-0.307985\pi\) | ||||
0.567308 | + | 0.823506i | \(0.307985\pi\) | |||||||
\(42\) | 0.132726 | 0.0204800 | ||||||||
\(43\) | 0.705329 | 0.107562 | 0.0537809 | − | 0.998553i | \(-0.482873\pi\) | ||||
0.0537809 | + | 0.998553i | \(0.482873\pi\) | |||||||
\(44\) | 8.39961 | 1.26629 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.49204 | −0.514873 | ||||||||
\(47\) | −8.57322 | −1.25053 | −0.625266 | − | 0.780411i | \(-0.715010\pi\) | ||||
−0.625266 | + | 0.780411i | \(0.715010\pi\) | |||||||
\(48\) | −0.0198940 | −0.00287146 | ||||||||
\(49\) | 14.2426 | 2.03466 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0437667 | 0.00612857 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.4639 | 1.71204 | 0.856022 | − | 0.516940i | \(-0.172929\pi\) | ||||
0.856022 | + | 0.516940i | \(0.172929\pi\) | |||||||
\(54\) | 0.172779 | 0.0235122 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.78787 | 1.17433 | ||||||||
\(57\) | −0.0321221 | −0.00425467 | ||||||||
\(58\) | −18.2250 | −2.39306 | ||||||||
\(59\) | −5.33445 | −0.694487 | −0.347243 | − | 0.937775i | \(-0.612882\pi\) | ||||
−0.347243 | + | 0.937775i | \(0.612882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.92092 | 0.245949 | 0.122974 | − | 0.992410i | \(-0.460757\pi\) | ||||
0.122974 | + | 0.992410i | \(0.460757\pi\) | |||||||
\(62\) | 21.5695 | 2.73932 | ||||||||
\(63\) | 13.8261 | 1.74193 | ||||||||
\(64\) | −12.7752 | −1.59690 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.0844427 | −0.0103942 | ||||||||
\(67\) | 7.29793 | 0.891584 | 0.445792 | − | 0.895137i | \(-0.352922\pi\) | ||||
0.445792 | + | 0.895137i | \(0.352922\pi\) | |||||||
\(68\) | 9.60195 | 1.16441 | ||||||||
\(69\) | 0.0206725 | 0.00248867 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.68083 | −0.792868 | −0.396434 | − | 0.918063i | \(-0.629752\pi\) | ||||
−0.396434 | + | 0.918063i | \(0.629752\pi\) | |||||||
\(72\) | 5.71974 | 0.674078 | ||||||||
\(73\) | 12.4541 | 1.45765 | 0.728824 | − | 0.684702i | \(-0.240067\pi\) | ||||
0.728824 | + | 0.684702i | \(0.240067\pi\) | |||||||
\(74\) | 9.10713 | 1.05868 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.04724 | −0.808374 | ||||||||
\(77\) | −13.5150 | −1.54017 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.984840 | 0.110803 | 0.0554016 | − | 0.998464i | \(-0.482356\pi\) | ||||
0.0554016 | + | 0.998464i | \(0.482356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99847 | 0.999830 | ||||||||
\(82\) | −16.0236 | −1.76951 | ||||||||
\(83\) | 7.84405 | 0.860997 | 0.430498 | − | 0.902591i | \(-0.358338\pi\) | ||||
0.430498 | + | 0.902591i | \(0.358338\pi\) | |||||||
\(84\) | −0.172379 | −0.0188081 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.55565 | −0.167750 | ||||||||
\(87\) | 0.107890 | 0.0115670 | ||||||||
\(88\) | −5.59102 | −0.596005 | ||||||||
\(89\) | −0.412834 | −0.0437604 | −0.0218802 | − | 0.999761i | \(-0.506965\pi\) | ||||
−0.0218802 | + | 0.999761i | \(0.506965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.53532 | 0.472840 | ||||||||
\(93\) | −0.127689 | −0.0132407 | ||||||||
\(94\) | 18.9087 | 1.95029 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0936675 | 0.00955989 | ||||||||
\(97\) | 3.38416 | 0.343609 | 0.171805 | − | 0.985131i | \(-0.445040\pi\) | ||||
0.171805 | + | 0.985131i | \(0.445040\pi\) | |||||||
\(98\) | −31.4129 | −3.17318 | ||||||||
\(99\) | −8.79646 | −0.884077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5432 | −1.04909 | −0.524545 | − | 0.851383i | \(-0.675765\pi\) | ||||
−0.524545 | + | 0.851383i | \(0.675765\pi\) | |||||||
\(102\) | −0.0965301 | −0.00955790 | ||||||||
\(103\) | −14.1152 | −1.39081 | −0.695404 | − | 0.718619i | \(-0.744774\pi\) | ||||
−0.695404 | + | 0.718619i | \(0.744774\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.4898 | −2.67004 | ||||||||
\(107\) | 3.97165 | 0.383954 | 0.191977 | − | 0.981399i | \(-0.438510\pi\) | ||||
0.191977 | + | 0.981399i | \(0.438510\pi\) | |||||||
\(108\) | −0.224398 | −0.0215927 | ||||||||
\(109\) | 10.1737 | 0.974460 | 0.487230 | − | 0.873274i | \(-0.338007\pi\) | ||||
0.487230 | + | 0.873274i | \(0.338007\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0539132 | −0.00511721 | ||||||||
\(112\) | 7.02254 | 0.663568 | ||||||||
\(113\) | 2.59984 | 0.244572 | 0.122286 | − | 0.992495i | \(-0.460977\pi\) | ||||
0.122286 | + | 0.992495i | \(0.460977\pi\) | |||||||
\(114\) | 0.0708472 | 0.00663545 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 23.6699 | 2.19770 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.7655 | 1.08310 | ||||||||
\(119\) | −15.4495 | −1.41626 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.40150 | −0.218318 | ||||||||
\(122\) | −4.23670 | −0.383573 | ||||||||
\(123\) | 0.0948578 | 0.00855304 | ||||||||
\(124\) | −28.0135 | −2.51569 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −30.4943 | −2.71665 | ||||||||
\(127\) | −19.9719 | −1.77222 | −0.886109 | − | 0.463476i | \(-0.846602\pi\) | ||||
−0.886109 | + | 0.463476i | \(0.846602\pi\) | |||||||
\(128\) | 13.8286 | 1.22228 | ||||||||
\(129\) | 0.00920925 | 0.000810829 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4400 | −0.999514 | −0.499757 | − | 0.866166i | \(-0.666577\pi\) | ||||
−0.499757 | + | 0.866166i | \(0.666577\pi\) | |||||||
\(132\) | 0.109671 | 0.00954562 | ||||||||
\(133\) | 11.3390 | 0.983217 | ||||||||
\(134\) | −16.0960 | −1.39048 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.39133 | −0.548052 | ||||||||
\(137\) | −3.12520 | −0.267004 | −0.133502 | − | 0.991049i | \(-0.542622\pi\) | ||||
−0.133502 | + | 0.991049i | \(0.542622\pi\) | |||||||
\(138\) | −0.0455944 | −0.00388125 | ||||||||
\(139\) | 6.09526 | 0.516993 | 0.258497 | − | 0.966012i | \(-0.416773\pi\) | ||||
0.258497 | + | 0.966012i | \(0.416773\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.111938 | −0.00942685 | ||||||||
\(142\) | 14.7350 | 1.23653 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.57075 | 0.380896 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −27.4684 | −2.27330 | ||||||||
\(147\) | 0.185961 | 0.0153378 | ||||||||
\(148\) | −11.8280 | −0.972253 | ||||||||
\(149\) | −14.6196 | −1.19769 | −0.598844 | − | 0.800866i | \(-0.704373\pi\) | ||||
−0.598844 | + | 0.800866i | \(0.704373\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.2510 | 0.996973 | 0.498487 | − | 0.866897i | \(-0.333889\pi\) | ||||
0.498487 | + | 0.866897i | \(0.333889\pi\) | |||||||
\(152\) | 4.69085 | 0.380478 | ||||||||
\(153\) | −10.0556 | −0.812948 | ||||||||
\(154\) | 29.8081 | 2.40200 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.13991 | −0.569827 | −0.284914 | − | 0.958553i | \(-0.591965\pi\) | ||||
−0.284914 | + | 0.958553i | \(0.591965\pi\) | |||||||
\(158\) | −2.17212 | −0.172805 | ||||||||
\(159\) | 0.162736 | 0.0129058 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.29733 | −0.575110 | ||||||||
\(162\) | −19.8467 | −1.55930 | ||||||||
\(163\) | −2.39002 | −0.187201 | −0.0936004 | − | 0.995610i | \(-0.529838\pi\) | ||||
−0.0936004 | + | 0.995610i | \(0.529838\pi\) | |||||||
\(164\) | 20.8108 | 1.62505 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.3005 | −1.34278 | ||||||||
\(167\) | 7.43841 | 0.575601 | 0.287801 | − | 0.957690i | \(-0.407076\pi\) | ||||
0.287801 | + | 0.957690i | \(0.407076\pi\) | |||||||
\(168\) | 0.114740 | 0.00885240 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.38020 | 0.564378 | ||||||||
\(172\) | 2.02041 | 0.154055 | ||||||||
\(173\) | −2.54119 | −0.193203 | −0.0966015 | − | 0.995323i | \(-0.530797\pi\) | ||||
−0.0966015 | + | 0.995323i | \(0.530797\pi\) | |||||||
\(174\) | −0.237958 | −0.0180396 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.46788 | −0.336779 | ||||||||
\(177\) | −0.0696502 | −0.00523523 | ||||||||
\(178\) | 0.910531 | 0.0682472 | ||||||||
\(179\) | −10.6913 | −0.799105 | −0.399553 | − | 0.916710i | \(-0.630835\pi\) | ||||
−0.399553 | + | 0.916710i | \(0.630835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7908 | −0.876402 | −0.438201 | − | 0.898877i | \(-0.644384\pi\) | ||||
−0.438201 | + | 0.898877i | \(0.644384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0250808 | 0.00185403 | ||||||||
\(184\) | −3.01884 | −0.222552 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.281625 | 0.0206498 | ||||||||
\(187\) | 9.82931 | 0.718790 | ||||||||
\(188\) | −24.5579 | −1.79107 | ||||||||
\(189\) | 0.361056 | 0.0262630 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.4746 | 0.974990 | 0.487495 | − | 0.873126i | \(-0.337911\pi\) | ||||
0.487495 | + | 0.873126i | \(0.337911\pi\) | |||||||
\(192\) | −0.166801 | −0.0120378 | ||||||||
\(193\) | −6.98737 | −0.502962 | −0.251481 | − | 0.967862i | \(-0.580918\pi\) | ||||
−0.251481 | + | 0.967862i | \(0.580918\pi\) | |||||||
\(194\) | −7.46397 | −0.535882 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 40.7978 | 2.91413 | ||||||||
\(197\) | −1.43795 | −0.102450 | −0.0512248 | − | 0.998687i | \(-0.516313\pi\) | ||||
−0.0512248 | + | 0.998687i | \(0.516313\pi\) | |||||||
\(198\) | 19.4011 | 1.37878 | ||||||||
\(199\) | −2.42852 | −0.172153 | −0.0860765 | − | 0.996289i | \(-0.527433\pi\) | ||||
−0.0860765 | + | 0.996289i | \(0.527433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.0952866 | 0.00672100 | ||||||||
\(202\) | 23.2537 | 1.63613 | ||||||||
\(203\) | −38.0849 | −2.67304 | ||||||||
\(204\) | 0.125369 | 0.00877761 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 31.1318 | 2.16906 | ||||||||
\(207\) | −4.74960 | −0.330120 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.21411 | −0.499011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2640 | 1.25735 | 0.628674 | − | 0.777669i | \(-0.283598\pi\) | ||||
0.628674 | + | 0.777669i | \(0.283598\pi\) | |||||||
\(212\) | 35.7026 | 2.45207 | ||||||||
\(213\) | −0.0872293 | −0.00597685 | ||||||||
\(214\) | −8.75970 | −0.598801 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.149366 | 0.0101631 | ||||||||
\(217\) | 45.0738 | 3.05981 | ||||||||
\(218\) | −22.4386 | −1.51973 | ||||||||
\(219\) | 0.162610 | 0.0109881 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.118909 | 0.00798063 | ||||||||
\(223\) | −15.5841 | −1.04359 | −0.521793 | − | 0.853072i | \(-0.674737\pi\) | ||||
−0.521793 | + | 0.853072i | \(0.674737\pi\) | |||||||
\(224\) | −33.0644 | −2.20921 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.73409 | −0.381426 | ||||||||
\(227\) | 4.03380 | 0.267733 | 0.133866 | − | 0.990999i | \(-0.457261\pi\) | ||||
0.133866 | + | 0.990999i | \(0.457261\pi\) | |||||||
\(228\) | −0.0920135 | −0.00609374 | ||||||||
\(229\) | 22.5147 | 1.48781 | 0.743906 | − | 0.668284i | \(-0.232971\pi\) | ||||
0.743906 | + | 0.668284i | \(0.232971\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.176460 | −0.0116102 | ||||||||
\(232\) | −15.7554 | −1.03439 | ||||||||
\(233\) | 7.69759 | 0.504286 | 0.252143 | − | 0.967690i | \(-0.418865\pi\) | ||||
0.252143 | + | 0.967690i | \(0.418865\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −15.2805 | −0.994676 | ||||||||
\(237\) | 0.0128587 | 0.000835264 0 | ||||||||
\(238\) | 34.0749 | 2.20875 | ||||||||
\(239\) | 18.7203 | 1.21092 | 0.605459 | − | 0.795877i | \(-0.292990\pi\) | ||||
0.605459 | + | 0.795877i | \(0.292990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.6183 | −1.45697 | −0.728486 | − | 0.685061i | \(-0.759775\pi\) | ||||
−0.728486 | + | 0.685061i | \(0.759775\pi\) | |||||||
\(242\) | 5.29665 | 0.340482 | ||||||||
\(243\) | 0.352503 | 0.0226131 | ||||||||
\(244\) | 5.50246 | 0.352259 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.209214 | −0.0133390 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 18.6466 | 1.18406 | ||||||||
\(249\) | 0.102417 | 0.00649042 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.78412 | 0.112612 | 0.0563062 | − | 0.998414i | \(-0.482068\pi\) | ||||
0.0563062 | + | 0.998414i | \(0.482068\pi\) | |||||||
\(252\) | 39.6048 | 2.49487 | ||||||||
\(253\) | 4.64271 | 0.291885 | ||||||||
\(254\) | 44.0492 | 2.76389 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.94936 | −0.309335 | ||||||||
\(257\) | 4.59847 | 0.286845 | 0.143422 | − | 0.989662i | \(-0.454189\pi\) | ||||
0.143422 | + | 0.989662i | \(0.454189\pi\) | |||||||
\(258\) | −0.0203115 | −0.00126454 | ||||||||
\(259\) | 19.0312 | 1.18254 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.7883 | −1.53435 | ||||||||
\(262\) | 25.2315 | 1.55881 | ||||||||
\(263\) | −18.8127 | −1.16004 | −0.580022 | − | 0.814601i | \(-0.696956\pi\) | ||||
−0.580022 | + | 0.814601i | \(0.696956\pi\) | |||||||
\(264\) | −0.0730001 | −0.00449284 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −25.0089 | −1.53339 | ||||||||
\(267\) | −0.00539024 | −0.000329877 0 | ||||||||
\(268\) | 20.9049 | 1.27697 | ||||||||
\(269\) | 1.85412 | 0.113048 | 0.0565238 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565238 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.149698 | 0.00909352 | 0.00454676 | − | 0.999990i | \(-0.498553\pi\) | ||||
0.00454676 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(272\) | −5.10743 | −0.309683 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.89281 | 0.416410 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.0592161 | 0.00356439 | ||||||||
\(277\) | −22.0184 | −1.32296 | −0.661478 | − | 0.749965i | \(-0.730071\pi\) | ||||
−0.661478 | + | 0.749965i | \(0.730071\pi\) | |||||||
\(278\) | −13.4435 | −0.806285 | ||||||||
\(279\) | 29.3371 | 1.75637 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.438029 | −0.0261306 | −0.0130653 | − | 0.999915i | \(-0.504159\pi\) | ||||
−0.0130653 | + | 0.999915i | \(0.504159\pi\) | |||||||
\(282\) | 0.246885 | 0.0147018 | ||||||||
\(283\) | −13.8290 | −0.822049 | −0.411025 | − | 0.911624i | \(-0.634829\pi\) | ||||
−0.411025 | + | 0.911624i | \(0.634829\pi\) | |||||||
\(284\) | −19.1372 | −1.13558 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33.4845 | −1.97653 | ||||||||
\(288\) | −21.5205 | −1.26811 | ||||||||
\(289\) | −5.76370 | −0.339041 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0441858 | 0.00259022 | ||||||||
\(292\) | 35.6748 | 2.08771 | ||||||||
\(293\) | −14.5656 | −0.850929 | −0.425464 | − | 0.904975i | \(-0.639889\pi\) | ||||
−0.425464 | + | 0.904975i | \(0.639889\pi\) | |||||||
\(294\) | −0.410148 | −0.0239203 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.87304 | 0.457611 | ||||||||
\(297\) | −0.229711 | −0.0133292 | ||||||||
\(298\) | 32.2445 | 1.86787 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.25084 | −0.187375 | ||||||||
\(302\) | −27.0203 | −1.55485 | ||||||||
\(303\) | −0.137659 | −0.00790833 | ||||||||
\(304\) | 3.74854 | 0.214994 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 22.1782 | 1.26785 | ||||||||
\(307\) | 9.05062 | 0.516546 | 0.258273 | − | 0.966072i | \(-0.416847\pi\) | ||||
0.258273 | + | 0.966072i | \(0.416847\pi\) | |||||||
\(308\) | −38.7135 | −2.20591 | ||||||||
\(309\) | −0.184297 | −0.0104843 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.28812 | 0.413272 | 0.206636 | − | 0.978418i | \(-0.433748\pi\) | ||||
0.206636 | + | 0.978418i | \(0.433748\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9725 | −0.733250 | −0.366625 | − | 0.930369i | \(-0.619487\pi\) | ||||
−0.366625 | + | 0.930369i | \(0.619487\pi\) | |||||||
\(314\) | 15.7475 | 0.888683 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.82107 | 0.158697 | ||||||||
\(317\) | −15.5048 | −0.870838 | −0.435419 | − | 0.900228i | \(-0.643400\pi\) | ||||
−0.435419 | + | 0.900228i | \(0.643400\pi\) | |||||||
\(318\) | −0.358925 | −0.0201275 | ||||||||
\(319\) | 24.2304 | 1.35664 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0518565 | 0.00289434 | ||||||||
\(322\) | 16.0947 | 0.896922 | ||||||||
\(323\) | −8.24676 | −0.458862 | ||||||||
\(324\) | 25.7760 | 1.43200 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.27133 | 0.291952 | ||||||||
\(327\) | 0.132834 | 0.00734574 | ||||||||
\(328\) | −13.8523 | −0.764863 | ||||||||
\(329\) | 39.5137 | 2.17846 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0853 | 1.43378 | 0.716890 | − | 0.697186i | \(-0.245565\pi\) | ||||
0.716890 | + | 0.697186i | \(0.245565\pi\) | |||||||
\(332\) | 22.4692 | 1.23316 | ||||||||
\(333\) | 12.3868 | 0.678793 | ||||||||
\(334\) | −16.4058 | −0.897688 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.0916910 | 0.00500215 | ||||||||
\(337\) | 14.4785 | 0.788697 | 0.394348 | − | 0.918961i | \(-0.370970\pi\) | ||||
0.394348 | + | 0.918961i | \(0.370970\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0339452 | 0.00184365 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.6769 | −1.55294 | ||||||||
\(342\) | −16.2775 | −0.880185 | ||||||||
\(343\) | −33.3809 | −1.80240 | ||||||||
\(344\) | −1.34484 | −0.0725091 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.60474 | 0.301313 | ||||||||
\(347\) | −6.81412 | −0.365801 | −0.182901 | − | 0.983131i | \(-0.558549\pi\) | ||||
−0.182901 | + | 0.983131i | \(0.558549\pi\) | |||||||
\(348\) | 0.309050 | 0.0165668 | ||||||||
\(349\) | −33.7357 | −1.80583 | −0.902915 | − | 0.429818i | \(-0.858578\pi\) | ||||
−0.902915 | + | 0.429818i | \(0.858578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 21.0362 | 1.12123 | ||||||||
\(353\) | 18.7215 | 0.996447 | 0.498223 | − | 0.867049i | \(-0.333986\pi\) | ||||
0.498223 | + | 0.867049i | \(0.333986\pi\) | |||||||
\(354\) | 0.153618 | 0.00816468 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.18256 | −0.0626756 | ||||||||
\(357\) | −0.201719 | −0.0106761 | ||||||||
\(358\) | 23.5803 | 1.24626 | ||||||||
\(359\) | −27.9262 | −1.47389 | −0.736945 | − | 0.675952i | \(-0.763732\pi\) | ||||
−0.736945 | + | 0.675952i | \(0.763732\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.9474 | −0.681441 | ||||||||
\(362\) | 26.0053 | 1.36681 | ||||||||
\(363\) | −0.0313556 | −0.00164574 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.0553172 | −0.00289148 | ||||||||
\(367\) | −2.50988 | −0.131015 | −0.0655074 | − | 0.997852i | \(-0.520867\pi\) | ||||
−0.0655074 | + | 0.997852i | \(0.520867\pi\) | |||||||
\(368\) | −2.41241 | −0.125755 | ||||||||
\(369\) | −21.7940 | −1.13455 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −57.4456 | −2.98243 | ||||||||
\(372\) | −0.365763 | −0.0189640 | ||||||||
\(373\) | −22.1779 | −1.14833 | −0.574165 | − | 0.818739i | \(-0.694673\pi\) | ||||
−0.574165 | + | 0.818739i | \(0.694673\pi\) | |||||||
\(374\) | −21.6791 | −1.12100 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.3465 | 0.843005 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.796331 | −0.0409589 | ||||||||
\(379\) | −1.42116 | −0.0730001 | −0.0365001 | − | 0.999334i | \(-0.511621\pi\) | ||||
−0.0365001 | + | 0.999334i | \(0.511621\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.260766 | −0.0133595 | ||||||||
\(382\) | −29.7191 | −1.52056 | ||||||||
\(383\) | −21.0733 | −1.07679 | −0.538397 | − | 0.842691i | \(-0.680970\pi\) | ||||
−0.538397 | + | 0.842691i | \(0.680970\pi\) | |||||||
\(384\) | 0.180555 | 0.00921390 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.4111 | 0.784402 | ||||||||
\(387\) | −2.11587 | −0.107556 | ||||||||
\(388\) | 9.69390 | 0.492133 | ||||||||
\(389\) | 13.4713 | 0.683021 | 0.341511 | − | 0.939878i | \(-0.389061\pi\) | ||||
0.341511 | + | 0.939878i | \(0.389061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.30728 | 0.268401 | ||||||||
\(392\) | −27.1562 | −1.37160 | ||||||||
\(393\) | −0.149368 | −0.00753461 | ||||||||
\(394\) | 3.17148 | 0.159777 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −25.1974 | −1.26622 | ||||||||
\(397\) | −27.1859 | −1.36442 | −0.682210 | − | 0.731156i | \(-0.738981\pi\) | ||||
−0.682210 | + | 0.731156i | \(0.738981\pi\) | |||||||
\(398\) | 5.35624 | 0.268484 | ||||||||
\(399\) | 0.148050 | 0.00741176 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.27520 | −0.163556 | −0.0817779 | − | 0.996651i | \(-0.526060\pi\) | ||||
−0.0817779 | + | 0.996651i | \(0.526060\pi\) | |||||||
\(402\) | −0.210160 | −0.0104818 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −30.2010 | −1.50256 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 83.9986 | 4.16878 | ||||||||
\(407\) | −12.1080 | −0.600173 | ||||||||
\(408\) | −0.0834495 | −0.00413137 | ||||||||
\(409\) | −19.1677 | −0.947782 | −0.473891 | − | 0.880583i | \(-0.657151\pi\) | ||||
−0.473891 | + | 0.880583i | \(0.657151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.0408047 | −0.00201275 | ||||||||
\(412\) | −40.4327 | −1.99198 | ||||||||
\(413\) | 24.5863 | 1.20981 | ||||||||
\(414\) | 10.4755 | 0.514844 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0795837 | 0.00389723 | ||||||||
\(418\) | 15.9112 | 0.778240 | ||||||||
\(419\) | 0.392463 | 0.0191731 | 0.00958653 | − | 0.999954i | \(-0.496948\pi\) | ||||
0.00958653 | + | 0.999954i | \(0.496948\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.1816 | 1.71465 | 0.857323 | − | 0.514779i | \(-0.172126\pi\) | ||||
0.857323 | + | 0.514779i | \(0.172126\pi\) | |||||||
\(422\) | −40.2824 | −1.96092 | ||||||||
\(423\) | 25.7182 | 1.25046 | ||||||||
\(424\) | −23.7647 | −1.15412 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.192389 | 0.00932130 | ||||||||
\(427\) | −8.85346 | −0.428449 | ||||||||
\(428\) | 11.3768 | 0.549916 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.27454 | 0.109561 | 0.0547803 | − | 0.998498i | \(-0.482554\pi\) | ||||
0.0547803 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(432\) | 0.119361 | 0.00574275 | ||||||||
\(433\) | −11.8827 | −0.571048 | −0.285524 | − | 0.958372i | \(-0.592168\pi\) | ||||
−0.285524 | + | 0.958372i | \(0.592168\pi\) | |||||||
\(434\) | −99.4130 | −4.77197 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29.1424 | 1.39567 | ||||||||
\(437\) | −3.89522 | −0.186334 | ||||||||
\(438\) | −0.358645 | −0.0171367 | ||||||||
\(439\) | −35.7273 | −1.70517 | −0.852585 | − | 0.522588i | \(-0.824967\pi\) | ||||
−0.852585 | + | 0.522588i | \(0.824967\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −42.7254 | −2.03454 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.98904 | −0.237036 | −0.118518 | − | 0.992952i | \(-0.537814\pi\) | ||||
−0.118518 | + | 0.992952i | \(0.537814\pi\) | |||||||
\(444\) | −0.154434 | −0.00732911 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 34.3716 | 1.62754 | ||||||||
\(447\) | −0.190884 | −0.00902849 | ||||||||
\(448\) | 58.8804 | 2.78184 | ||||||||
\(449\) | −23.4886 | −1.10850 | −0.554248 | − | 0.832352i | \(-0.686994\pi\) | ||||
−0.554248 | + | 0.832352i | \(0.686994\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.3035 | 1.00314 | ||||||||
\(452\) | 7.44721 | 0.350287 | ||||||||
\(453\) | 0.159957 | 0.00751545 | ||||||||
\(454\) | −8.89679 | −0.417547 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0612468 | 0.00286815 | ||||||||
\(457\) | −40.2510 | −1.88286 | −0.941430 | − | 0.337208i | \(-0.890518\pi\) | ||||
−0.941430 | + | 0.337208i | \(0.890518\pi\) | |||||||
\(458\) | −49.6575 | −2.32034 | ||||||||
\(459\) | −0.262593 | −0.0122568 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.2140 | −1.45378 | −0.726890 | − | 0.686754i | \(-0.759035\pi\) | ||||
−0.726890 | + | 0.686754i | \(0.759035\pi\) | |||||||
\(462\) | 0.389194 | 0.0181069 | ||||||||
\(463\) | 17.7491 | 0.824872 | 0.412436 | − | 0.910987i | \(-0.364678\pi\) | ||||
0.412436 | + | 0.910987i | \(0.364678\pi\) | |||||||
\(464\) | −12.5904 | −0.584495 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.9775 | −0.786467 | ||||||||
\(467\) | −26.6645 | −1.23389 | −0.616944 | − | 0.787007i | \(-0.711630\pi\) | ||||
−0.616944 | + | 0.787007i | \(0.711630\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.6359 | −1.55316 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0932234 | −0.00429551 | ||||||||
\(472\) | 10.1711 | 0.468165 | ||||||||
\(473\) | 2.06825 | 0.0950983 | ||||||||
\(474\) | −0.0283607 | −0.00130265 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −44.2551 | −2.02843 | ||||||||
\(477\) | −37.3895 | −1.71195 | ||||||||
\(478\) | −41.2888 | −1.88851 | ||||||||
\(479\) | −20.4630 | −0.934980 | −0.467490 | − | 0.883998i | \(-0.654842\pi\) | ||||
−0.467490 | + | 0.883998i | \(0.654842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 49.8860 | 2.27224 | ||||||||
\(483\) | −0.0952788 | −0.00433534 | ||||||||
\(484\) | −6.87908 | −0.312686 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.777467 | −0.0352666 | ||||||||
\(487\) | 8.11789 | 0.367857 | 0.183928 | − | 0.982940i | \(-0.441119\pi\) | ||||
0.183928 | + | 0.982940i | \(0.441119\pi\) | |||||||
\(488\) | −3.66260 | −0.165798 | ||||||||
\(489\) | −0.0312057 | −0.00141117 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.26996 | 0.147571 | 0.0737857 | − | 0.997274i | \(-0.476492\pi\) | ||||
0.0737857 | + | 0.997274i | \(0.476492\pi\) | |||||||
\(492\) | 0.271719 | 0.0122501 | ||||||||
\(493\) | 27.6988 | 1.24749 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.9008 | 0.669068 | ||||||||
\(497\) | 30.7917 | 1.38120 | ||||||||
\(498\) | −0.225887 | −0.0101222 | ||||||||
\(499\) | −8.89340 | −0.398123 | −0.199062 | − | 0.979987i | \(-0.563789\pi\) | ||||
−0.199062 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.0971208 | 0.00433904 | ||||||||
\(502\) | −3.93498 | −0.175627 | ||||||||
\(503\) | 23.7974 | 1.06107 | 0.530537 | − | 0.847662i | \(-0.321990\pi\) | ||||
0.530537 | + | 0.847662i | \(0.321990\pi\) | |||||||
\(504\) | −26.3621 | −1.17426 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10.2398 | −0.455213 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −57.2093 | −2.53825 | ||||||||
\(509\) | 1.26770 | 0.0561898 | 0.0280949 | − | 0.999605i | \(-0.491056\pi\) | ||||
0.0280949 | + | 0.999605i | \(0.491056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −57.4008 | −2.53926 | ||||||||
\(512\) | −16.7410 | −0.739855 | ||||||||
\(513\) | 0.192727 | 0.00850911 | ||||||||
\(514\) | −10.1422 | −0.447354 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.0263798 | 0.00116131 | ||||||||
\(517\) | −25.1394 | −1.10563 | ||||||||
\(518\) | −41.9745 | −1.84425 | ||||||||
\(519\) | −0.0331794 | −0.00145642 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.3916 | 0.630506 | 0.315253 | − | 0.949008i | \(-0.397911\pi\) | ||||
0.315253 | + | 0.949008i | \(0.397911\pi\) | |||||||
\(522\) | 54.6720 | 2.39293 | ||||||||
\(523\) | −19.0185 | −0.831622 | −0.415811 | − | 0.909451i | \(-0.636502\pi\) | ||||
−0.415811 | + | 0.909451i | \(0.636502\pi\) | |||||||
\(524\) | −32.7697 | −1.43155 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 41.4926 | 1.80916 | ||||||||
\(527\) | −32.7818 | −1.42800 | ||||||||
\(528\) | −0.0583357 | −0.00253873 | ||||||||
\(529\) | −20.4932 | −0.891008 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.0024 | 0.694447 | ||||||||
\(532\) | 32.4805 | 1.40821 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.0118885 | 0.000514465 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.9149 | −0.601031 | ||||||||
\(537\) | −0.139593 | −0.00602387 | ||||||||
\(538\) | −4.08937 | −0.176305 | ||||||||
\(539\) | 41.7638 | 1.79890 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8969 | 0.597475 | 0.298738 | − | 0.954335i | \(-0.403434\pi\) | ||||
0.298738 | + | 0.954335i | \(0.403434\pi\) | |||||||
\(542\) | −0.330168 | −0.0141819 | ||||||||
\(543\) | −0.153948 | −0.00660656 | ||||||||
\(544\) | 24.0474 | 1.03102 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.0840 | −1.58560 | −0.792798 | − | 0.609484i | \(-0.791377\pi\) | ||||
−0.792798 | + | 0.609484i | \(0.791377\pi\) | |||||||
\(548\) | −8.95211 | −0.382415 | ||||||||
\(549\) | −5.76243 | −0.245935 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.3292 | −0.866054 | ||||||||
\(552\) | −0.0394160 | −0.00167766 | ||||||||
\(553\) | −4.53910 | −0.193022 | ||||||||
\(554\) | 48.5628 | 2.06324 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.4598 | 0.740461 | ||||||||
\(557\) | −31.8065 | −1.34768 | −0.673842 | − | 0.738875i | \(-0.735357\pi\) | ||||
−0.673842 | + | 0.738875i | \(0.735357\pi\) | |||||||
\(558\) | −64.7047 | −2.73917 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.128338 | 0.00541843 | ||||||||
\(562\) | 0.966100 | 0.0407525 | ||||||||
\(563\) | −26.3595 | −1.11092 | −0.555461 | − | 0.831543i | \(-0.687458\pi\) | ||||
−0.555461 | + | 0.831543i | \(0.687458\pi\) | |||||||
\(564\) | −0.320645 | −0.0135016 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30.5007 | 1.28204 | ||||||||
\(567\) | −41.4736 | −1.74173 | ||||||||
\(568\) | 12.7383 | 0.534485 | ||||||||
\(569\) | 17.7846 | 0.745569 | 0.372785 | − | 0.927918i | \(-0.378403\pi\) | ||||
0.372785 | + | 0.927918i | \(0.378403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.6399 | 0.821903 | 0.410952 | − | 0.911657i | \(-0.365196\pi\) | ||||
0.410952 | + | 0.911657i | \(0.365196\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.175934 | 0.00734974 | ||||||||
\(574\) | 73.8522 | 3.08253 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 38.3233 | 1.59681 | ||||||||
\(577\) | −18.1454 | −0.755403 | −0.377701 | − | 0.925927i | \(-0.623285\pi\) | ||||
−0.377701 | + | 0.925927i | \(0.623285\pi\) | |||||||
\(578\) | 12.7122 | 0.528757 | ||||||||
\(579\) | −0.0912317 | −0.00379146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.1530 | −1.49988 | ||||||||
\(582\) | −0.0974545 | −0.00403962 | ||||||||
\(583\) | 36.5480 | 1.51366 | ||||||||
\(584\) | −23.7462 | −0.982624 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.1252 | 1.32708 | ||||||||
\(587\) | 0.423843 | 0.0174939 | 0.00874694 | − | 0.999962i | \(-0.497216\pi\) | ||||
0.00874694 | + | 0.999962i | \(0.497216\pi\) | |||||||
\(588\) | 0.532683 | 0.0219675 | ||||||||
\(589\) | 24.0598 | 0.991367 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0187748 | −0.000772293 0 | ||||||||
\(592\) | 6.29149 | 0.258578 | ||||||||
\(593\) | 47.5064 | 1.95085 | 0.975426 | − | 0.220327i | \(-0.0707125\pi\) | ||||
0.975426 | + | 0.220327i | \(0.0707125\pi\) | |||||||
\(594\) | 0.506642 | 0.0207878 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −41.8778 | −1.71538 | ||||||||
\(597\) | −0.0317083 | −0.00129774 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.7871 | 1.05363 | 0.526816 | − | 0.849979i | \(-0.323386\pi\) | ||||
0.526816 | + | 0.849979i | \(0.323386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6776 | −0.517130 | −0.258565 | − | 0.965994i | \(-0.583250\pi\) | ||||
−0.258565 | + | 0.965994i | \(0.583250\pi\) | |||||||
\(602\) | 7.16992 | 0.292224 | ||||||||
\(603\) | −21.8925 | −0.891533 | ||||||||
\(604\) | 35.0929 | 1.42791 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.303616 | 0.0123336 | ||||||||
\(607\) | 4.40448 | 0.178772 | 0.0893862 | − | 0.995997i | \(-0.471509\pi\) | ||||
0.0893862 | + | 0.995997i | \(0.471509\pi\) | |||||||
\(608\) | −17.6493 | −0.715775 | ||||||||
\(609\) | −0.497262 | −0.0201501 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −28.8042 | −1.16434 | ||||||||
\(613\) | 33.3599 | 1.34739 | 0.673696 | − | 0.739008i | \(-0.264706\pi\) | ||||
0.673696 | + | 0.739008i | \(0.264706\pi\) | |||||||
\(614\) | −19.9617 | −0.805588 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 25.7688 | 1.03826 | ||||||||
\(617\) | 32.5535 | 1.31055 | 0.655277 | − | 0.755389i | \(-0.272552\pi\) | ||||
0.655277 | + | 0.755389i | \(0.272552\pi\) | |||||||
\(618\) | 0.406477 | 0.0163509 | ||||||||
\(619\) | −35.5813 | −1.43013 | −0.715067 | − | 0.699056i | \(-0.753604\pi\) | ||||
−0.715067 | + | 0.699056i | \(0.753604\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.124031 | −0.00497721 | ||||||||
\(622\) | −16.0744 | −0.644524 | ||||||||
\(623\) | 1.90274 | 0.0762317 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.6116 | 1.14355 | ||||||||
\(627\) | −0.0941922 | −0.00376168 | ||||||||
\(628\) | −20.4522 | −0.816133 | ||||||||
\(629\) | −13.8412 | −0.551886 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4117 | 1.01162 | 0.505812 | − | 0.862644i | \(-0.331193\pi\) | ||||
0.505812 | + | 0.862644i | \(0.331193\pi\) | |||||||
\(632\) | −1.87778 | −0.0746942 | ||||||||
\(633\) | 0.238467 | 0.00947822 | ||||||||
\(634\) | 34.1968 | 1.35813 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.466157 | 0.0184843 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −53.4416 | −2.11577 | ||||||||
\(639\) | 20.0413 | 0.792823 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1479 | −0.400817 | −0.200408 | − | 0.979712i | \(-0.564227\pi\) | ||||
−0.200408 | + | 0.979712i | \(0.564227\pi\) | |||||||
\(642\) | −0.114372 | −0.00451392 | ||||||||
\(643\) | −1.85439 | −0.0731298 | −0.0365649 | − | 0.999331i | \(-0.511642\pi\) | ||||
−0.0365649 | + | 0.999331i | \(0.511642\pi\) | |||||||
\(644\) | −20.9032 | −0.823700 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.1887 | 0.715626 | ||||||||
\(647\) | 29.6034 | 1.16383 | 0.581914 | − | 0.813250i | \(-0.302304\pi\) | ||||
0.581914 | + | 0.813250i | \(0.302304\pi\) | |||||||
\(648\) | −17.1573 | −0.674001 | ||||||||
\(649\) | −15.6423 | −0.614015 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.588514 | 0.0230657 | ||||||||
\(652\) | −6.84619 | −0.268118 | ||||||||
\(653\) | −6.78882 | −0.265667 | −0.132834 | − | 0.991138i | \(-0.542408\pi\) | ||||
−0.132834 | + | 0.991138i | \(0.542408\pi\) | |||||||
\(654\) | −0.292973 | −0.0114562 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −11.0696 | −0.432195 | ||||||||
\(657\) | −37.3603 | −1.45756 | ||||||||
\(658\) | −87.1498 | −3.39745 | ||||||||
\(659\) | 7.94959 | 0.309672 | 0.154836 | − | 0.987940i | \(-0.450515\pi\) | ||||
0.154836 | + | 0.987940i | \(0.450515\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.3832 | 1.57072 | 0.785361 | − | 0.619038i | \(-0.212477\pi\) | ||||
0.785361 | + | 0.619038i | \(0.212477\pi\) | |||||||
\(662\) | −57.5328 | −2.23607 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.9562 | −0.580412 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −27.3198 | −1.05862 | ||||||||
\(667\) | 13.0831 | 0.506579 | ||||||||
\(668\) | 21.3073 | 0.824402 | ||||||||
\(669\) | −0.203476 | −0.00786684 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.63275 | 0.217450 | ||||||||
\(672\) | −0.431710 | −0.0166536 | ||||||||
\(673\) | −9.63920 | −0.371564 | −0.185782 | − | 0.982591i | \(-0.559482\pi\) | ||||
−0.185782 | + | 0.982591i | \(0.559482\pi\) | |||||||
\(674\) | −31.9333 | −1.23002 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −51.1565 | −1.96610 | −0.983051 | − | 0.183330i | \(-0.941312\pi\) | ||||
−0.983051 | + | 0.183330i | \(0.941312\pi\) | |||||||
\(678\) | −0.0748681 | −0.00287529 | ||||||||
\(679\) | −15.5975 | −0.598577 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0526680 | 0.00201824 | ||||||||
\(682\) | 63.2485 | 2.42191 | ||||||||
\(683\) | 8.34502 | 0.319313 | 0.159657 | − | 0.987173i | \(-0.448961\pi\) | ||||
0.159657 | + | 0.987173i | \(0.448961\pi\) | |||||||
\(684\) | 21.1405 | 0.808328 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 73.6236 | 2.81096 | ||||||||
\(687\) | 0.293967 | 0.0112155 | ||||||||
\(688\) | −1.07469 | −0.0409721 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.1243 | −1.37423 | −0.687117 | − | 0.726547i | \(-0.741124\pi\) | ||||
−0.687117 | + | 0.726547i | \(0.741124\pi\) | |||||||
\(692\) | −7.27921 | −0.276714 | ||||||||
\(693\) | 40.5426 | 1.54009 | ||||||||
\(694\) | 15.0289 | 0.570491 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.205713 | −0.00779753 | ||||||||
\(697\) | 24.3530 | 0.922435 | ||||||||
\(698\) | 74.4061 | 2.81631 | ||||||||
\(699\) | 0.100505 | 0.00380144 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.9823 | −1.73673 | −0.868364 | − | 0.495928i | \(-0.834828\pi\) | ||||
−0.868364 | + | 0.495928i | \(0.834828\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.1586 | 0.383139 | ||||||||
\(704\) | −37.4609 | −1.41186 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −41.2915 | −1.55402 | ||||||||
\(707\) | 48.5934 | 1.82754 | ||||||||
\(708\) | −0.199512 | −0.00749813 | ||||||||
\(709\) | 38.0949 | 1.43069 | 0.715343 | − | 0.698774i | \(-0.246271\pi\) | ||||
0.715343 | + | 0.698774i | \(0.246271\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.95435 | −0.110797 | ||||||||
\(712\) | 0.787147 | 0.0294996 | ||||||||
\(713\) | −15.4839 | −0.579877 | ||||||||
\(714\) | 0.444904 | 0.0166501 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −30.6251 | −1.14452 | ||||||||
\(717\) | 0.244425 | 0.00912822 | ||||||||
\(718\) | 61.5930 | 2.29863 | ||||||||
\(719\) | −27.8672 | −1.03927 | −0.519635 | − | 0.854388i | \(-0.673932\pi\) | ||||
−0.519635 | + | 0.854388i | \(0.673932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 65.0563 | 2.42282 | ||||||||
\(722\) | 28.5562 | 1.06275 | ||||||||
\(723\) | −0.295319 | −0.0109830 | ||||||||
\(724\) | −33.7746 | −1.25522 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.0691566 | 0.00256664 | ||||||||
\(727\) | 13.7750 | 0.510885 | 0.255443 | − | 0.966824i | \(-0.417779\pi\) | ||||
0.255443 | + | 0.966824i | \(0.417779\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9908 | −0.999659 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.36431 | 0.0874470 | ||||||||
\(732\) | 0.0718438 | 0.00265542 | ||||||||
\(733\) | 6.58392 | 0.243183 | 0.121591 | − | 0.992580i | \(-0.461200\pi\) | ||||
0.121591 | + | 0.992580i | \(0.461200\pi\) | |||||||
\(734\) | 5.53570 | 0.204326 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 11.3584 | 0.418676 | ||||||||
\(737\) | 21.3999 | 0.788274 | ||||||||
\(738\) | 48.0680 | 1.76941 | ||||||||
\(739\) | 5.47501 | 0.201401 | 0.100701 | − | 0.994917i | \(-0.467892\pi\) | ||||
0.100701 | + | 0.994917i | \(0.467892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 126.700 | 4.65129 | ||||||||
\(743\) | 26.6714 | 0.978479 | 0.489239 | − | 0.872150i | \(-0.337274\pi\) | ||||
0.489239 | + | 0.872150i | \(0.337274\pi\) | |||||||
\(744\) | 0.243463 | 0.00892578 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 48.9148 | 1.79090 | ||||||||
\(747\) | −23.5308 | −0.860948 | ||||||||
\(748\) | 28.1560 | 1.02948 | ||||||||
\(749\) | −18.3052 | −0.668857 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8067 | 0.795740 | 0.397870 | − | 0.917442i | \(-0.369750\pi\) | ||||
0.397870 | + | 0.917442i | \(0.369750\pi\) | |||||||
\(752\) | 13.0627 | 0.476349 | ||||||||
\(753\) | 0.0232946 | 0.000848903 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.03424 | 0.0376151 | ||||||||
\(757\) | 8.33422 | 0.302912 | 0.151456 | − | 0.988464i | \(-0.451604\pi\) | ||||
0.151456 | + | 0.988464i | \(0.451604\pi\) | |||||||
\(758\) | 3.13446 | 0.113849 | ||||||||
\(759\) | 0.0606183 | 0.00220031 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.33096 | −0.265747 | −0.132874 | − | 0.991133i | \(-0.542420\pi\) | ||||
−0.132874 | + | 0.991133i | \(0.542420\pi\) | |||||||
\(762\) | 0.575135 | 0.0208350 | ||||||||
\(763\) | −46.8901 | −1.69753 | ||||||||
\(764\) | 38.5980 | 1.39643 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 46.4783 | 1.67933 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.0646221 | −0.00233185 | ||||||||
\(769\) | −22.3346 | −0.805407 | −0.402703 | − | 0.915331i | \(-0.631929\pi\) | ||||
−0.402703 | + | 0.915331i | \(0.631929\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0600407 | 0.00216231 | ||||||||
\(772\) | −20.0153 | −0.720365 | ||||||||
\(773\) | 27.1591 | 0.976844 | 0.488422 | − | 0.872608i | \(-0.337573\pi\) | ||||
0.488422 | + | 0.872608i | \(0.337573\pi\) | |||||||
\(774\) | 4.66667 | 0.167740 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.45254 | −0.231633 | ||||||||
\(777\) | 0.248484 | 0.00891432 | ||||||||
\(778\) | −29.7117 | −1.06522 | ||||||||
\(779\) | −17.8736 | −0.640388 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.5903 | −0.700997 | ||||||||
\(782\) | −11.7055 | −0.418589 | ||||||||
\(783\) | −0.647322 | −0.0231334 | ||||||||
\(784\) | −21.7010 | −0.775036 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.329440 | 0.0117507 | ||||||||
\(787\) | −11.5806 | −0.412805 | −0.206403 | − | 0.978467i | \(-0.566176\pi\) | ||||
−0.206403 | + | 0.978467i | \(0.566176\pi\) | |||||||
\(788\) | −4.11899 | −0.146733 | ||||||||
\(789\) | −0.245632 | −0.00874472 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.9826 | −0.426051 | ||||||||
\(792\) | 16.7721 | 0.595971 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 59.9601 | 2.12790 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.95647 | −0.246566 | ||||||||
\(797\) | 47.7004 | 1.68963 | 0.844817 | − | 0.535055i | \(-0.179709\pi\) | ||||
0.844817 | + | 0.535055i | \(0.179709\pi\) | |||||||
\(798\) | −0.326532 | −0.0115591 | ||||||||
\(799\) | −28.7379 | −1.01668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.23843 | 0.0437579 | ||||||||
\(802\) | 7.22365 | 0.255076 | ||||||||
\(803\) | 36.5195 | 1.28875 | ||||||||
\(804\) | 0.272948 | 0.00962612 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.0242086 | 0.000852184 0 | ||||||||
\(808\) | 20.1027 | 0.707209 | ||||||||
\(809\) | 36.3910 | 1.27944 | 0.639720 | − | 0.768608i | \(-0.279050\pi\) | ||||
0.639720 | + | 0.768608i | \(0.279050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.8088 | −1.29253 | −0.646266 | − | 0.763112i | \(-0.723670\pi\) | ||||
−0.646266 | + | 0.763112i | \(0.723670\pi\) | |||||||
\(812\) | −109.094 | −3.82845 | ||||||||
\(813\) | 0.00195456 | 6.85494e−5 0 | ||||||||
\(814\) | 26.7050 | 0.936010 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.0666860 | −0.00233448 | ||||||||
\(817\) | −1.73526 | −0.0607089 | ||||||||
\(818\) | 42.2755 | 1.47813 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.6668 | 1.17498 | 0.587491 | − | 0.809231i | \(-0.300116\pi\) | ||||
0.587491 | + | 0.809231i | \(0.300116\pi\) | |||||||
\(822\) | 0.0899971 | 0.00313901 | ||||||||
\(823\) | −31.8809 | −1.11130 | −0.555649 | − | 0.831417i | \(-0.687530\pi\) | ||||
−0.555649 | + | 0.831417i | \(0.687530\pi\) | |||||||
\(824\) | 26.9132 | 0.937566 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −54.2266 | −1.88678 | ||||||||
\(827\) | 18.4625 | 0.642003 | 0.321002 | − | 0.947079i | \(-0.395981\pi\) | ||||
0.321002 | + | 0.947079i | \(0.395981\pi\) | |||||||
\(828\) | −13.6052 | −0.472813 | ||||||||
\(829\) | −34.9663 | −1.21443 | −0.607214 | − | 0.794538i | \(-0.707713\pi\) | ||||
−0.607214 | + | 0.794538i | \(0.707713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.287487 | −0.00997280 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 47.7420 | 1.65416 | ||||||||
\(834\) | −0.175527 | −0.00607799 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.6648 | −0.714706 | ||||||||
\(837\) | 0.766111 | 0.0264807 | ||||||||
\(838\) | −0.865600 | −0.0299017 | ||||||||
\(839\) | −28.7234 | −0.991641 | −0.495820 | − | 0.868425i | \(-0.665133\pi\) | ||||
−0.495820 | + | 0.868425i | \(0.665133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.2808 | 1.35451 | ||||||||
\(842\) | −77.5951 | −2.67410 | ||||||||
\(843\) | −0.00571920 | −0.000196980 0 | ||||||||
\(844\) | 52.3172 | 1.80083 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −56.7230 | −1.95018 | ||||||||
\(847\) | 11.0684 | 0.380316 | ||||||||
\(848\) | −18.9908 | −0.652147 | ||||||||
\(849\) | −0.180561 | −0.00619683 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.53767 | −0.224108 | ||||||||
\(852\) | −0.249868 | −0.00856032 | ||||||||
\(853\) | 13.7453 | 0.470629 | 0.235315 | − | 0.971919i | \(-0.424388\pi\) | ||||
0.235315 | + | 0.971919i | \(0.424388\pi\) | |||||||
\(854\) | 19.5268 | 0.668195 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.57269 | −0.258829 | ||||||||
\(857\) | 12.6495 | 0.432099 | 0.216049 | − | 0.976382i | \(-0.430683\pi\) | ||||
0.216049 | + | 0.976382i | \(0.430683\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0929 | −0.378485 | −0.189243 | − | 0.981930i | \(-0.560603\pi\) | ||||
−0.189243 | + | 0.981930i | \(0.560603\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.437196 | −0.0148996 | ||||||||
\(862\) | −5.01663 | −0.170867 | ||||||||
\(863\) | 33.0295 | 1.12434 | 0.562169 | − | 0.827022i | \(-0.309967\pi\) | ||||
0.562169 | + | 0.827022i | \(0.309967\pi\) | |||||||
\(864\) | −0.561989 | −0.0191192 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.2081 | 0.890587 | ||||||||
\(867\) | −0.0752546 | −0.00255578 | ||||||||
\(868\) | 129.114 | 4.38240 | ||||||||
\(869\) | 2.88787 | 0.0979641 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −19.3980 | −0.656899 | ||||||||
\(873\) | −10.1519 | −0.343590 | ||||||||
\(874\) | 8.59114 | 0.290600 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.465794 | 0.0157377 | ||||||||
\(877\) | −15.4397 | −0.521362 | −0.260681 | − | 0.965425i | \(-0.583947\pi\) | ||||
−0.260681 | + | 0.965425i | \(0.583947\pi\) | |||||||
\(878\) | 78.7987 | 2.65933 | ||||||||
\(879\) | −0.190178 | −0.00641453 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.6260 | −0.560143 | −0.280072 | − | 0.959979i | \(-0.590358\pi\) | ||||
−0.280072 | + | 0.959979i | \(0.590358\pi\) | |||||||
\(882\) | 94.2333 | 3.17300 | ||||||||
\(883\) | −57.2845 | −1.92778 | −0.963888 | − | 0.266309i | \(-0.914196\pi\) | ||||
−0.963888 | + | 0.266309i | \(0.914196\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.0036 | 0.369674 | ||||||||
\(887\) | −18.4657 | −0.620018 | −0.310009 | − | 0.950734i | \(-0.600332\pi\) | ||||
−0.310009 | + | 0.950734i | \(0.600332\pi\) | |||||||
\(888\) | 0.102796 | 0.00344960 | ||||||||
\(889\) | 92.0498 | 3.08725 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.3864 | 0.883977 | ||||||||
\(892\) | −44.6405 | −1.49467 | ||||||||
\(893\) | 21.0919 | 0.705813 | ||||||||
\(894\) | 0.421005 | 0.0140805 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −63.7354 | −2.12925 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 51.8055 | 1.72877 | ||||||||
\(899\) | −80.8109 | −2.69519 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 41.7796 | 1.39188 | ||||||||
\(902\) | −46.9862 | −1.56447 | ||||||||
\(903\) | −0.0424451 | −0.00141249 | ||||||||
\(904\) | −4.95708 | −0.164870 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.352795 | −0.0117208 | ||||||||
\(907\) | −44.9489 | −1.49250 | −0.746251 | − | 0.665664i | \(-0.768148\pi\) | ||||
−0.746251 | + | 0.665664i | \(0.768148\pi\) | |||||||
\(908\) | 11.5548 | 0.383459 | ||||||||
\(909\) | 31.6279 | 1.04903 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −44.3728 | −1.47014 | −0.735069 | − | 0.677992i | \(-0.762850\pi\) | ||||
−0.735069 | + | 0.677992i | \(0.762850\pi\) | |||||||
\(912\) | 0.0489434 | 0.00162068 | ||||||||
\(913\) | 23.0013 | 0.761231 | ||||||||
\(914\) | 88.7759 | 2.93645 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 64.4931 | 2.13091 | ||||||||
\(917\) | 52.7264 | 1.74118 | ||||||||
\(918\) | 0.579164 | 0.0191153 | ||||||||
\(919\) | 25.1680 | 0.830217 | 0.415108 | − | 0.909772i | \(-0.363744\pi\) | ||||
0.415108 | + | 0.909772i | \(0.363744\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.118171 | 0.00389386 | ||||||||
\(922\) | 68.8443 | 2.26726 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.505469 | −0.0166287 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −39.1468 | −1.28644 | ||||||||
\(927\) | 42.3430 | 1.39073 | ||||||||
\(928\) | 59.2797 | 1.94595 | ||||||||
\(929\) | −37.5601 | −1.23231 | −0.616153 | − | 0.787626i | \(-0.711310\pi\) | ||||
−0.616153 | + | 0.787626i | \(0.711310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.0397 | −1.14838 | ||||||||
\(932\) | 22.0497 | 0.722262 | ||||||||
\(933\) | 0.0951586 | 0.00311535 | ||||||||
\(934\) | 58.8102 | 1.92433 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.1212 | 0.559326 | 0.279663 | − | 0.960098i | \(-0.409777\pi\) | ||||
0.279663 | + | 0.960098i | \(0.409777\pi\) | |||||||
\(938\) | 74.1860 | 2.42226 | ||||||||
\(939\) | −0.169378 | −0.00552743 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.208568 | 0.00679913 | 0.00339956 | − | 0.999994i | \(-0.498918\pi\) | ||||
0.00339956 | + | 0.999994i | \(0.498918\pi\) | |||||||
\(942\) | 0.205610 | 0.00669913 | ||||||||
\(943\) | 11.5027 | 0.374580 | ||||||||
\(944\) | 8.12794 | 0.264542 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.56165 | −0.148312 | ||||||||
\(947\) | 0.414059 | 0.0134551 | 0.00672755 | − | 0.999977i | \(-0.497859\pi\) | ||||
0.00672755 | + | 0.999977i | \(0.497859\pi\) | |||||||
\(948\) | 0.0368337 | 0.00119630 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.202441 | −0.00656461 | ||||||||
\(952\) | 29.4575 | 0.954722 | ||||||||
\(953\) | 33.8593 | 1.09681 | 0.548404 | − | 0.836213i | \(-0.315235\pi\) | ||||
0.548404 | + | 0.836213i | \(0.315235\pi\) | |||||||
\(954\) | 82.4647 | 2.66989 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 53.6243 | 1.73433 | ||||||||
\(957\) | 0.316368 | 0.0102267 | ||||||||
\(958\) | 45.1324 | 1.45816 | ||||||||
\(959\) | 14.4039 | 0.465128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 64.6403 | 2.08517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.9143 | −0.383932 | ||||||||
\(964\) | −64.7899 | −2.08674 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.210143 | 0.00676124 | ||||||||
\(967\) | 13.2125 | 0.424885 | 0.212442 | − | 0.977174i | \(-0.431858\pi\) | ||||
0.212442 | + | 0.977174i | \(0.431858\pi\) | |||||||
\(968\) | 4.57892 | 0.147172 | ||||||||
\(969\) | −0.107675 | −0.00345902 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.6019 | −0.564872 | −0.282436 | − | 0.959286i | \(-0.591142\pi\) | ||||
−0.282436 | + | 0.959286i | \(0.591142\pi\) | |||||||
\(972\) | 1.00974 | 0.0323875 | ||||||||
\(973\) | −28.0929 | −0.900616 | ||||||||
\(974\) | −17.9045 | −0.573697 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.92685 | −0.0936861 | ||||||||
\(977\) | −11.7812 | −0.376913 | −0.188457 | − | 0.982082i | \(-0.560348\pi\) | ||||
−0.188457 | + | 0.982082i | \(0.560348\pi\) | |||||||
\(978\) | 0.0688260 | 0.00220081 | ||||||||
\(979\) | −1.21056 | −0.0386897 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.5192 | −0.974404 | ||||||||
\(982\) | −7.21210 | −0.230147 | ||||||||
\(983\) | −45.4985 | −1.45118 | −0.725589 | − | 0.688128i | \(-0.758433\pi\) | ||||
−0.725589 | + | 0.688128i | \(0.758433\pi\) | |||||||
\(984\) | −0.180864 | −0.00576574 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −61.0914 | −1.94555 | ||||||||
\(987\) | 0.515917 | 0.0164218 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.11674 | 0.0355103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.2685 | 1.05681 | 0.528405 | − | 0.848993i | \(-0.322790\pi\) | ||||
0.528405 | + | 0.848993i | \(0.322790\pi\) | |||||||
\(992\) | −70.1580 | −2.22752 | ||||||||
\(993\) | 0.340588 | 0.0108082 | ||||||||
\(994\) | −67.9130 | −2.15407 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.293373 | 0.00929589 | ||||||||
\(997\) | 39.7870 | 1.26007 | 0.630033 | − | 0.776568i | \(-0.283041\pi\) | ||||
0.630033 | + | 0.776568i | \(0.283041\pi\) | |||||||
\(998\) | 19.6149 | 0.620899 | ||||||||
\(999\) | 0.323470 | 0.0102341 |
(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 | 4225.2.a.bs.1.3 | 9 | ||
5.4 | even | 2 | 845.2.a.o.1.7 | yes | 9 | ||
13.12 | even | 2 | 4225.2.a.bt.1.7 | 9 | |||
15.14 | odd | 2 | 7605.2.a.cp.1.3 | 9 | |||
65.4 | even | 6 | 845.2.e.p.146.7 | 18 | |||
65.9 | even | 6 | 845.2.e.o.146.3 | 18 | |||
65.19 | odd | 12 | 845.2.m.j.361.5 | 36 | |||
65.24 | odd | 12 | 845.2.m.j.316.5 | 36 | |||
65.29 | even | 6 | 845.2.e.o.191.3 | 18 | |||
65.34 | odd | 4 | 845.2.c.h.506.14 | 18 | |||
65.44 | odd | 4 | 845.2.c.h.506.5 | 18 | |||
65.49 | even | 6 | 845.2.e.p.191.7 | 18 | |||
65.54 | odd | 12 | 845.2.m.j.316.14 | 36 | |||
65.59 | odd | 12 | 845.2.m.j.361.14 | 36 | |||
65.64 | even | 2 | 845.2.a.n.1.3 | ✓ | 9 | ||
195.194 | odd | 2 | 7605.2.a.cs.1.7 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.a.n.1.3 | ✓ | 9 | 65.64 | even | 2 | ||
845.2.a.o.1.7 | yes | 9 | 5.4 | even | 2 | ||
845.2.c.h.506.5 | 18 | 65.44 | odd | 4 | |||
845.2.c.h.506.14 | 18 | 65.34 | odd | 4 | |||
845.2.e.o.146.3 | 18 | 65.9 | even | 6 | |||
845.2.e.o.191.3 | 18 | 65.29 | even | 6 | |||
845.2.e.p.146.7 | 18 | 65.4 | even | 6 | |||
845.2.e.p.191.7 | 18 | 65.49 | even | 6 | |||
845.2.m.j.316.5 | 36 | 65.24 | odd | 12 | |||
845.2.m.j.316.14 | 36 | 65.54 | odd | 12 | |||
845.2.m.j.361.5 | 36 | 65.19 | odd | 12 | |||
845.2.m.j.361.14 | 36 | 65.59 | odd | 12 | |||
4225.2.a.bs.1.3 | 9 | 1.1 | even | 1 | trivial | ||
4225.2.a.bt.1.7 | 9 | 13.12 | even | 2 | |||
7605.2.a.cp.1.3 | 9 | 15.14 | odd | 2 | |||
7605.2.a.cs.1.7 | 9 | 195.194 | odd | 2 |