Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1084,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1084");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1084.18 | ||
Character | \(\chi\) | \(=\) | 1805.1084 |
Dual form | 1805.2.b.k.1084.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).
\(n\) | \(362\) | \(1446\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.47917i | 1.04593i | 0.852354 | + | 0.522965i | \(0.175174\pi\) | ||||
−0.852354 | + | 0.522965i | \(0.824826\pi\) | |||||||
\(3\) | 2.48321i | 1.43368i | 0.697238 | + | 0.716840i | \(0.254412\pi\) | ||||
−0.697238 | + | 0.716840i | \(0.745588\pi\) | |||||||
\(4\) | −0.187941 | −0.0939705 | ||||||||
\(5\) | 0.111989 | − | 2.23326i | 0.0500832 | − | 0.998745i | ||||
\(6\) | −3.67308 | −1.49953 | ||||||||
\(7\) | 3.24988i | 1.22834i | 0.789175 | + | 0.614169i | \(0.210509\pi\) | ||||
−0.789175 | + | 0.614169i | \(0.789491\pi\) | |||||||
\(8\) | 2.68034i | 0.947644i | ||||||||
\(9\) | −3.16631 | −1.05544 | ||||||||
\(10\) | 3.30337 | + | 0.165651i | 1.04462 | + | 0.0523836i | ||||
\(11\) | −4.18399 | −1.26152 | −0.630760 | − | 0.775978i | \(-0.717257\pi\) | ||||
−0.630760 | + | 0.775978i | \(0.717257\pi\) | |||||||
\(12\) | − | 0.466696i | − | 0.134724i | ||||||
\(13\) | 1.78413i | 0.494830i | 0.968910 | + | 0.247415i | \(0.0795811\pi\) | ||||
−0.968910 | + | 0.247415i | \(0.920419\pi\) | |||||||
\(14\) | −4.80712 | −1.28476 | ||||||||
\(15\) | 5.54565 | + | 0.278093i | 1.43188 | + | 0.0718033i | ||||
\(16\) | −4.34056 | −1.08514 | ||||||||
\(17\) | − | 6.33226i | − | 1.53580i | −0.640571 | − | 0.767899i | \(-0.721302\pi\) | ||
0.640571 | − | 0.767899i | \(-0.278698\pi\) | |||||||
\(18\) | − | 4.68351i | − | 1.10391i | ||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.0210474 | + | 0.419722i | −0.00470635 | + | 0.0938526i | ||||
\(21\) | −8.07011 | −1.76104 | ||||||||
\(22\) | − | 6.18883i | − | 1.31946i | ||||||
\(23\) | 1.43368i | 0.298942i | 0.988766 | + | 0.149471i | \(0.0477571\pi\) | ||||
−0.988766 | + | 0.149471i | \(0.952243\pi\) | |||||||
\(24\) | −6.65584 | −1.35862 | ||||||||
\(25\) | −4.97492 | − | 0.500204i | −0.994983 | − | 0.100041i | ||||
\(26\) | −2.63904 | −0.517558 | ||||||||
\(27\) | − | 0.412988i | − | 0.0794796i | ||||||
\(28\) | − | 0.610785i | − | 0.115428i | ||||||
\(29\) | 0.339390 | 0.0630231 | 0.0315116 | − | 0.999503i | \(-0.489968\pi\) | ||||
0.0315116 | + | 0.999503i | \(0.489968\pi\) | |||||||
\(30\) | −0.411347 | + | 8.20295i | −0.0751013 | + | 1.49765i | ||||
\(31\) | −2.77865 | −0.499060 | −0.249530 | − | 0.968367i | \(-0.580276\pi\) | ||||
−0.249530 | + | 0.968367i | \(0.580276\pi\) | |||||||
\(32\) | − | 1.05974i | − | 0.187337i | ||||||
\(33\) | − | 10.3897i | − | 1.80862i | ||||||
\(34\) | 9.36648 | 1.60634 | ||||||||
\(35\) | 7.25782 | + | 0.363952i | 1.22680 | + | 0.0615191i | ||||
\(36\) | 0.595080 | 0.0991800 | ||||||||
\(37\) | 2.70482i | 0.444670i | 0.974970 | + | 0.222335i | \(0.0713679\pi\) | ||||
−0.974970 | + | 0.222335i | \(0.928632\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.43037 | −0.709427 | ||||||||
\(40\) | 5.98590 | + | 0.300170i | 0.946455 | + | 0.0474611i | ||||
\(41\) | −7.13821 | −1.11480 | −0.557401 | − | 0.830244i | \(-0.688201\pi\) | ||||
−0.557401 | + | 0.830244i | \(0.688201\pi\) | |||||||
\(42\) | − | 11.9371i | − | 1.84193i | ||||||
\(43\) | 9.89425i | 1.50886i | 0.656381 | + | 0.754429i | \(0.272086\pi\) | ||||
−0.656381 | + | 0.754429i | \(0.727914\pi\) | |||||||
\(44\) | 0.786344 | 0.118546 | ||||||||
\(45\) | −0.354594 | + | 7.07120i | −0.0528597 | + | 1.05411i | ||||
\(46\) | −2.12065 | −0.312673 | ||||||||
\(47\) | 0.445441i | 0.0649743i | 0.999472 | + | 0.0324871i | \(0.0103428\pi\) | ||||
−0.999472 | + | 0.0324871i | \(0.989657\pi\) | |||||||
\(48\) | − | 10.7785i | − | 1.55574i | ||||||
\(49\) | −3.56169 | −0.508813 | ||||||||
\(50\) | 0.739886 | − | 7.35874i | 0.104636 | − | 1.04068i | ||||
\(51\) | 15.7243 | 2.20184 | ||||||||
\(52\) | − | 0.335312i | − | 0.0464994i | ||||||
\(53\) | − | 7.23734i | − | 0.994125i | −0.867715 | − | 0.497062i | \(-0.834412\pi\) | ||
0.867715 | − | 0.497062i | \(-0.165588\pi\) | |||||||
\(54\) | 0.610879 | 0.0831301 | ||||||||
\(55\) | −0.468563 | + | 9.34395i | −0.0631810 | + | 1.25994i | ||||
\(56\) | −8.71078 | −1.16403 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.502015i | 0.0659178i | ||||||||
\(59\) | −3.14263 | −0.409136 | −0.204568 | − | 0.978852i | \(-0.565579\pi\) | ||||
−0.204568 | + | 0.978852i | \(0.565579\pi\) | |||||||
\(60\) | −1.04226 | − | 0.0522651i | −0.134555 | − | 0.00674739i | ||||
\(61\) | −3.06562 | −0.392512 | −0.196256 | − | 0.980553i | \(-0.562878\pi\) | ||||
−0.196256 | + | 0.980553i | \(0.562878\pi\) | |||||||
\(62\) | − | 4.11009i | − | 0.521982i | ||||||
\(63\) | − | 10.2901i | − | 1.29643i | ||||||
\(64\) | −7.11359 | −0.889198 | ||||||||
\(65\) | 3.98444 | + | 0.199804i | 0.494209 | + | 0.0247827i | ||||
\(66\) | 15.3681 | 1.89169 | ||||||||
\(67\) | − | 8.55254i | − | 1.04486i | −0.852682 | − | 0.522430i | \(-0.825026\pi\) | ||
0.852682 | − | 0.522430i | \(-0.174974\pi\) | |||||||
\(68\) | 1.19009i | 0.144320i | ||||||||
\(69\) | −3.56011 | −0.428587 | ||||||||
\(70\) | −0.538346 | + | 10.7355i | −0.0643447 | + | 1.28314i | ||||
\(71\) | 12.8928 | 1.53009 | 0.765046 | − | 0.643975i | \(-0.222716\pi\) | ||||
0.765046 | + | 0.643975i | \(0.222716\pi\) | |||||||
\(72\) | − | 8.48680i | − | 1.00018i | ||||||
\(73\) | − | 1.82227i | − | 0.213281i | −0.994298 | − | 0.106640i | \(-0.965991\pi\) | ||
0.994298 | − | 0.106640i | \(-0.0340093\pi\) | |||||||
\(74\) | −4.00089 | −0.465094 | ||||||||
\(75\) | 1.24211 | − | 12.3537i | 0.143426 | − | 1.42649i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 13.5974i | − | 1.54957i | ||||||
\(78\) | − | 6.55327i | − | 0.742012i | ||||||
\(79\) | −0.698700 | −0.0786099 | −0.0393050 | − | 0.999227i | \(-0.512514\pi\) | ||||
−0.0393050 | + | 0.999227i | \(0.512514\pi\) | |||||||
\(80\) | −0.486097 | + | 9.69361i | −0.0543473 | + | 1.08378i | ||||
\(81\) | −8.47340 | −0.941489 | ||||||||
\(82\) | − | 10.5586i | − | 1.16600i | ||||||
\(83\) | − | 0.552985i | − | 0.0606980i | −0.999539 | − | 0.0303490i | \(-0.990338\pi\) | ||
0.999539 | − | 0.0303490i | \(-0.00966188\pi\) | |||||||
\(84\) | 1.51671 | 0.165486 | ||||||||
\(85\) | −14.1416 | − | 0.709146i | −1.53387 | − | 0.0769177i | ||||
\(86\) | −14.6353 | −1.57816 | ||||||||
\(87\) | 0.842775i | 0.0903550i | ||||||||
\(88\) | − | 11.2145i | − | 1.19547i | ||||||
\(89\) | −6.82870 | −0.723841 | −0.361920 | − | 0.932209i | \(-0.617879\pi\) | ||||
−0.361920 | + | 0.932209i | \(0.617879\pi\) | |||||||
\(90\) | −10.4595 | − | 0.524504i | −1.10253 | − | 0.0552876i | ||||
\(91\) | −5.79822 | −0.607818 | ||||||||
\(92\) | − | 0.269446i | − | 0.0280917i | ||||||
\(93\) | − | 6.89995i | − | 0.715492i | ||||||
\(94\) | −0.658883 | −0.0679586 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.63155 | 0.268582 | ||||||||
\(97\) | 13.2006i | 1.34032i | 0.742217 | + | 0.670160i | \(0.233774\pi\) | ||||
−0.742217 | + | 0.670160i | \(0.766226\pi\) | |||||||
\(98\) | − | 5.26835i | − | 0.532183i | ||||||
\(99\) | 13.2478 | 1.33146 | ||||||||
\(100\) | 0.934991 | + | 0.0940088i | 0.0934991 | + | 0.00940088i | ||||
\(101\) | 17.2757 | 1.71899 | 0.859496 | − | 0.511142i | \(-0.170777\pi\) | ||||
0.859496 | + | 0.511142i | \(0.170777\pi\) | |||||||
\(102\) | 23.2589i | 2.30297i | ||||||||
\(103\) | 13.8286i | 1.36257i | 0.732017 | + | 0.681286i | \(0.238579\pi\) | ||||
−0.732017 | + | 0.681286i | \(0.761421\pi\) | |||||||
\(104\) | −4.78209 | −0.468922 | ||||||||
\(105\) | −0.903768 | + | 18.0227i | −0.0881987 | + | 1.75883i | ||||
\(106\) | 10.7052 | 1.03979 | ||||||||
\(107\) | 3.26460i | 0.315600i | 0.987471 | + | 0.157800i | \(0.0504402\pi\) | ||||
−0.987471 | + | 0.157800i | \(0.949560\pi\) | |||||||
\(108\) | 0.0776174i | 0.00746874i | ||||||||
\(109\) | 3.22094 | 0.308510 | 0.154255 | − | 0.988031i | \(-0.450702\pi\) | ||||
0.154255 | + | 0.988031i | \(0.450702\pi\) | |||||||
\(110\) | −13.8213 | − | 0.693084i | −1.31781 | − | 0.0660829i | ||||
\(111\) | −6.71663 | −0.637514 | ||||||||
\(112\) | − | 14.1063i | − | 1.33292i | ||||||
\(113\) | 4.71007i | 0.443086i | 0.975151 | + | 0.221543i | \(0.0711093\pi\) | ||||
−0.975151 | + | 0.221543i | \(0.928891\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.20177 | + | 0.160557i | 0.298567 | + | 0.0149720i | ||||
\(116\) | −0.0637853 | −0.00592232 | ||||||||
\(117\) | − | 5.64913i | − | 0.522262i | ||||||
\(118\) | − | 4.64849i | − | 0.427928i | ||||||
\(119\) | 20.5791 | 1.88648 | ||||||||
\(120\) | −0.745384 | + | 14.8642i | −0.0680440 | + | 1.35691i | ||||
\(121\) | 6.50577 | 0.591434 | ||||||||
\(122\) | − | 4.53457i | − | 0.410541i | ||||||
\(123\) | − | 17.7257i | − | 1.59827i | ||||||
\(124\) | 0.522222 | 0.0468969 | ||||||||
\(125\) | −1.67422 | + | 11.0543i | −0.149747 | + | 0.988724i | ||||
\(126\) | 15.2208 | 1.35598 | ||||||||
\(127\) | − | 0.592012i | − | 0.0525325i | −0.999655 | − | 0.0262663i | \(-0.991638\pi\) | ||
0.999655 | − | 0.0262663i | \(-0.00836177\pi\) | |||||||
\(128\) | − | 12.6417i | − | 1.11738i | ||||||
\(129\) | −24.5695 | −2.16322 | ||||||||
\(130\) | −0.295544 | + | 5.89366i | −0.0259210 | + | 0.516908i | ||||
\(131\) | −20.5490 | −1.79538 | −0.897689 | − | 0.440629i | \(-0.854755\pi\) | ||||
−0.897689 | + | 0.440629i | \(0.854755\pi\) | |||||||
\(132\) | 1.95265i | 0.169957i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.6507 | 1.09285 | ||||||||
\(135\) | −0.922310 | − | 0.0462503i | −0.0793798 | − | 0.00398059i | ||||
\(136\) | 16.9726 | 1.45539 | ||||||||
\(137\) | − | 8.75406i | − | 0.747910i | −0.927447 | − | 0.373955i | \(-0.878001\pi\) | ||
0.927447 | − | 0.373955i | \(-0.121999\pi\) | |||||||
\(138\) | − | 5.26601i | − | 0.448272i | ||||||
\(139\) | −7.68939 | −0.652205 | −0.326103 | − | 0.945334i | \(-0.605736\pi\) | ||||
−0.326103 | + | 0.945334i | \(0.605736\pi\) | |||||||
\(140\) | −1.36404 | − | 0.0684015i | −0.115283 | − | 0.00578098i | ||||
\(141\) | −1.10612 | −0.0931523 | ||||||||
\(142\) | 19.0706i | 1.60037i | ||||||||
\(143\) | − | 7.46480i | − | 0.624238i | ||||||
\(144\) | 13.7436 | 1.14530 | ||||||||
\(145\) | 0.0380081 | − | 0.757947i | 0.00315640 | − | 0.0629440i | ||||
\(146\) | 2.69545 | 0.223077 | ||||||||
\(147\) | − | 8.84442i | − | 0.729475i | ||||||
\(148\) | − | 0.508347i | − | 0.0417859i | ||||||
\(149\) | 14.9414 | 1.22404 | 0.612022 | − | 0.790841i | \(-0.290356\pi\) | ||||
0.612022 | + | 0.790841i | \(0.290356\pi\) | |||||||
\(150\) | 18.2733 | + | 1.83729i | 1.49201 | + | 0.150014i | ||||
\(151\) | 13.1424 | 1.06951 | 0.534757 | − | 0.845006i | \(-0.320403\pi\) | ||||
0.534757 | + | 0.845006i | \(0.320403\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20.0499i | 1.62094i | ||||||||
\(154\) | 20.1129 | 1.62075 | ||||||||
\(155\) | −0.311179 | + | 6.20545i | −0.0249945 | + | 0.498434i | ||||
\(156\) | 0.832649 | 0.0666653 | ||||||||
\(157\) | − | 10.8372i | − | 0.864902i | −0.901657 | − | 0.432451i | \(-0.857649\pi\) | ||
0.901657 | − | 0.432451i | \(-0.142351\pi\) | |||||||
\(158\) | − | 1.03350i | − | 0.0822205i | ||||||
\(159\) | 17.9718 | 1.42526 | ||||||||
\(160\) | −2.36668 | − | 0.118680i | −0.187102 | − | 0.00938245i | ||||
\(161\) | −4.65927 | −0.367202 | ||||||||
\(162\) | − | 12.5336i | − | 0.984732i | ||||||
\(163\) | 8.44554i | 0.661506i | 0.943717 | + | 0.330753i | \(0.107303\pi\) | ||||
−0.943717 | + | 0.330753i | \(0.892697\pi\) | |||||||
\(164\) | 1.34156 | 0.104758 | ||||||||
\(165\) | −23.2029 | − | 1.16354i | −1.80635 | − | 0.0905813i | ||||
\(166\) | 0.817959 | 0.0634859 | ||||||||
\(167\) | 19.9012i | 1.54000i | 0.638041 | + | 0.770002i | \(0.279745\pi\) | ||||
−0.638041 | + | 0.770002i | \(0.720255\pi\) | |||||||
\(168\) | − | 21.6307i | − | 1.66884i | ||||||
\(169\) | 9.81686 | 0.755143 | ||||||||
\(170\) | 1.04895 | − | 20.9178i | 0.0804506 | − | 1.60432i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.85954i | − | 0.141788i | ||||||
\(173\) | 11.7211i | 0.891135i | 0.895248 | + | 0.445568i | \(0.146998\pi\) | ||||
−0.895248 | + | 0.445568i | \(0.853002\pi\) | |||||||
\(174\) | −1.24661 | −0.0945050 | ||||||||
\(175\) | 1.62560 | − | 16.1679i | 0.122884 | − | 1.22218i | ||||
\(176\) | 18.1609 | 1.36893 | ||||||||
\(177\) | − | 7.80380i | − | 0.586570i | ||||||
\(178\) | − | 10.1008i | − | 0.757087i | ||||||
\(179\) | −7.08378 | −0.529467 | −0.264733 | − | 0.964322i | \(-0.585284\pi\) | ||||
−0.264733 | + | 0.964322i | \(0.585284\pi\) | |||||||
\(180\) | 0.0666427 | − | 1.32897i | 0.00496726 | − | 0.0990556i | ||||
\(181\) | 9.28177 | 0.689908 | 0.344954 | − | 0.938620i | \(-0.387894\pi\) | ||||
0.344954 | + | 0.938620i | \(0.387894\pi\) | |||||||
\(182\) | − | 8.57654i | − | 0.635735i | ||||||
\(183\) | − | 7.61257i | − | 0.562737i | ||||||
\(184\) | −3.84274 | −0.283291 | ||||||||
\(185\) | 6.04057 | + | 0.302912i | 0.444112 | + | 0.0222705i | ||||
\(186\) | 10.2062 | 0.748355 | ||||||||
\(187\) | 26.4941i | 1.93744i | ||||||||
\(188\) | − | 0.0837167i | − | 0.00610567i | ||||||
\(189\) | 1.34216 | 0.0976277 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.12426 | 0.587850 | 0.293925 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293925 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(192\) | − | 17.6645i | − | 1.27483i | ||||||
\(193\) | 7.72342i | 0.555944i | 0.960589 | + | 0.277972i | \(0.0896623\pi\) | ||||
−0.960589 | + | 0.277972i | \(0.910338\pi\) | |||||||
\(194\) | −19.5259 | −1.40188 | ||||||||
\(195\) | −0.496155 | + | 9.89418i | −0.0355304 | + | 0.708537i | ||||
\(196\) | 0.669388 | 0.0478135 | ||||||||
\(197\) | − | 3.56762i | − | 0.254183i | −0.991891 | − | 0.127091i | \(-0.959436\pi\) | ||
0.991891 | − | 0.127091i | \(-0.0405641\pi\) | |||||||
\(198\) | 19.5958i | 1.39261i | ||||||||
\(199\) | 8.76938 | 0.621645 | 0.310822 | − | 0.950468i | \(-0.399396\pi\) | ||||
0.310822 | + | 0.950468i | \(0.399396\pi\) | |||||||
\(200\) | 1.34072 | − | 13.3345i | 0.0948030 | − | 0.942890i | ||||
\(201\) | 21.2377 | 1.49799 | ||||||||
\(202\) | 25.5536i | 1.79795i | ||||||||
\(203\) | 1.10298i | 0.0774137i | ||||||||
\(204\) | −2.95524 | −0.206908 | ||||||||
\(205\) | −0.799405 | + | 15.9415i | −0.0558328 | + | 1.11340i | ||||
\(206\) | −20.4548 | −1.42516 | ||||||||
\(207\) | − | 4.53946i | − | 0.315515i | ||||||
\(208\) | − | 7.74414i | − | 0.536960i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −26.6586 | − | 1.33683i | −1.83962 | − | 0.0922497i | ||||
\(211\) | 11.8171 | 0.813526 | 0.406763 | − | 0.913534i | \(-0.366657\pi\) | ||||
0.406763 | + | 0.913534i | \(0.366657\pi\) | |||||||
\(212\) | 1.36019i | 0.0934184i | ||||||||
\(213\) | 32.0155i | 2.19366i | ||||||||
\(214\) | −4.82889 | −0.330096 | ||||||||
\(215\) | 22.0964 | + | 1.10805i | 1.50696 | + | 0.0755685i | ||||
\(216\) | 1.10695 | 0.0753183 | ||||||||
\(217\) | − | 9.03026i | − | 0.613014i | ||||||
\(218\) | 4.76431i | 0.322680i | ||||||||
\(219\) | 4.52507 | 0.305776 | ||||||||
\(220\) | 0.0880622 | − | 1.75611i | 0.00593715 | − | 0.118397i | ||||
\(221\) | 11.2976 | 0.759959 | ||||||||
\(222\) | − | 9.93503i | − | 0.666796i | ||||||
\(223\) | 8.89760i | 0.595827i | 0.954593 | + | 0.297914i | \(0.0962908\pi\) | ||||
−0.954593 | + | 0.297914i | \(0.903709\pi\) | |||||||
\(224\) | 3.44402 | 0.230113 | ||||||||
\(225\) | 15.7521 | + | 1.58380i | 1.05014 | + | 0.105587i | ||||
\(226\) | −6.96698 | −0.463437 | ||||||||
\(227\) | 26.4080i | 1.75276i | 0.481620 | + | 0.876380i | \(0.340049\pi\) | ||||
−0.481620 | + | 0.876380i | \(0.659951\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.7852 | −1.43961 | −0.719804 | − | 0.694177i | \(-0.755768\pi\) | ||||
−0.719804 | + | 0.694177i | \(0.755768\pi\) | |||||||
\(230\) | −0.237490 | + | 4.73596i | −0.0156596 | + | 0.312280i | ||||
\(231\) | 33.7653 | 2.22159 | ||||||||
\(232\) | 0.909681i | 0.0597235i | ||||||||
\(233\) | 10.0009i | 0.655183i | 0.944820 | + | 0.327591i | \(0.106237\pi\) | ||||
−0.944820 | + | 0.327591i | \(0.893763\pi\) | |||||||
\(234\) | 8.35601 | 0.546250 | ||||||||
\(235\) | 0.994787 | + | 0.0498847i | 0.0648927 | + | 0.00325412i | ||||
\(236\) | 0.590630 | 0.0384467 | ||||||||
\(237\) | − | 1.73502i | − | 0.112701i | ||||||
\(238\) | 30.4399i | 1.97313i | ||||||||
\(239\) | −17.8365 | −1.15374 | −0.576872 | − | 0.816834i | \(-0.695727\pi\) | ||||
−0.576872 | + | 0.816834i | \(0.695727\pi\) | |||||||
\(240\) | −24.0712 | − | 1.20708i | −1.55379 | − | 0.0779166i | ||||
\(241\) | −17.1442 | −1.10435 | −0.552177 | − | 0.833727i | \(-0.686203\pi\) | ||||
−0.552177 | + | 0.833727i | \(0.686203\pi\) | |||||||
\(242\) | 9.62314i | 0.618599i | ||||||||
\(243\) | − | 22.2802i | − | 1.42927i | ||||||
\(244\) | 0.576156 | 0.0368846 | ||||||||
\(245\) | −0.398872 | + | 7.95419i | −0.0254830 | + | 0.508175i | ||||
\(246\) | 26.2192 | 1.67168 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 7.44772i | − | 0.472931i | ||||||
\(249\) | 1.37318 | 0.0870215 | ||||||||
\(250\) | −16.3511 | − | 2.47646i | −1.03414 | − | 0.156625i | ||||
\(251\) | 9.69585 | 0.611997 | 0.305998 | − | 0.952032i | \(-0.401010\pi\) | ||||
0.305998 | + | 0.952032i | \(0.401010\pi\) | |||||||
\(252\) | 1.93394i | 0.121827i | ||||||||
\(253\) | − | 5.99848i | − | 0.377121i | ||||||
\(254\) | 0.875685 | 0.0549454 | ||||||||
\(255\) | 1.76096 | − | 35.1165i | 0.110275 | − | 2.19908i | ||||
\(256\) | 4.47200 | 0.279500 | ||||||||
\(257\) | 10.0506i | 0.626942i | 0.949598 | + | 0.313471i | \(0.101492\pi\) | ||||
−0.949598 | + | 0.313471i | \(0.898508\pi\) | |||||||
\(258\) | − | 36.3424i | − | 2.26258i | ||||||
\(259\) | −8.79033 | −0.546205 | ||||||||
\(260\) | −0.748840 | − | 0.0375514i | −0.0464411 | − | 0.00232884i | ||||
\(261\) | −1.07461 | −0.0665170 | ||||||||
\(262\) | − | 30.3955i | − | 1.87784i | ||||||
\(263\) | − | 21.8306i | − | 1.34613i | −0.739583 | − | 0.673065i | \(-0.764977\pi\) | ||
0.739583 | − | 0.673065i | \(-0.235023\pi\) | |||||||
\(264\) | 27.8480 | 1.71392 | ||||||||
\(265\) | −16.1629 | − | 0.810506i | −0.992877 | − | 0.0497890i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 16.9571i | − | 1.03776i | ||||||
\(268\) | 1.60737i | 0.0981860i | ||||||||
\(269\) | −15.4551 | −0.942312 | −0.471156 | − | 0.882050i | \(-0.656163\pi\) | ||||
−0.471156 | + | 0.882050i | \(0.656163\pi\) | |||||||
\(270\) | 0.0684120 | − | 1.36425i | 0.00416342 | − | 0.0830258i | ||||
\(271\) | 5.16319 | 0.313642 | 0.156821 | − | 0.987627i | \(-0.449875\pi\) | ||||
0.156821 | + | 0.987627i | \(0.449875\pi\) | |||||||
\(272\) | 27.4855i | 1.66656i | ||||||||
\(273\) | − | 14.3982i | − | 0.871416i | ||||||
\(274\) | 12.9487 | 0.782262 | ||||||||
\(275\) | 20.8150 | + | 2.09285i | 1.25519 | + | 0.126203i | ||||
\(276\) | 0.669091 | 0.0402746 | ||||||||
\(277\) | 5.57030i | 0.334687i | 0.985899 | + | 0.167343i | \(0.0535189\pi\) | ||||
−0.985899 | + | 0.167343i | \(0.946481\pi\) | |||||||
\(278\) | − | 11.3739i | − | 0.682161i | ||||||
\(279\) | 8.79807 | 0.526726 | ||||||||
\(280\) | −0.975516 | + | 19.4534i | −0.0582982 | + | 1.16257i | ||||
\(281\) | 27.2729 | 1.62697 | 0.813483 | − | 0.581589i | \(-0.197569\pi\) | ||||
0.813483 | + | 0.581589i | \(0.197569\pi\) | |||||||
\(282\) | − | 1.63614i | − | 0.0974308i | ||||||
\(283\) | 15.0458i | 0.894379i | 0.894439 | + | 0.447190i | \(0.147575\pi\) | ||||
−0.894439 | + | 0.447190i | \(0.852425\pi\) | |||||||
\(284\) | −2.42308 | −0.143784 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.0417 | 0.652910 | ||||||||
\(287\) | − | 23.1983i | − | 1.36935i | ||||||
\(288\) | 3.35547i | 0.197723i | ||||||||
\(289\) | −23.0975 | −1.35868 | ||||||||
\(290\) | 1.12113 | + | 0.0562204i | 0.0658351 | + | 0.00330138i | ||||
\(291\) | −32.7799 | −1.92159 | ||||||||
\(292\) | 0.342479i | 0.0200421i | ||||||||
\(293\) | 7.82882i | 0.457364i | 0.973501 | + | 0.228682i | \(0.0734416\pi\) | ||||
−0.973501 | + | 0.228682i | \(0.926558\pi\) | |||||||
\(294\) | 13.0824 | 0.762981 | ||||||||
\(295\) | −0.351942 | + | 7.01832i | −0.0204908 | + | 0.408622i | ||||
\(296\) | −7.24985 | −0.421389 | ||||||||
\(297\) | 1.72794i | 0.100265i | ||||||||
\(298\) | 22.1008i | 1.28026i | ||||||||
\(299\) | −2.55787 | −0.147925 | ||||||||
\(300\) | −0.233443 | + | 2.32178i | −0.0134779 | + | 0.134048i | ||||
\(301\) | −32.1551 | −1.85339 | ||||||||
\(302\) | 19.4398i | 1.11864i | ||||||||
\(303\) | 42.8990i | 2.46449i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.343317 | + | 6.84633i | −0.0196583 | + | 0.392020i | ||||
\(306\) | −29.6572 | −1.69539 | ||||||||
\(307\) | − | 15.7146i | − | 0.896879i | −0.893813 | − | 0.448439i | \(-0.851980\pi\) | ||
0.893813 | − | 0.448439i | \(-0.148020\pi\) | |||||||
\(308\) | 2.55552i | 0.145614i | ||||||||
\(309\) | −34.3393 | −1.95349 | ||||||||
\(310\) | −9.17891 | − | 0.460287i | −0.521327 | − | 0.0261425i | ||||
\(311\) | 17.9812 | 1.01962 | 0.509810 | − | 0.860287i | \(-0.329716\pi\) | ||||
0.509810 | + | 0.860287i | \(0.329716\pi\) | |||||||
\(312\) | − | 11.8749i | − | 0.672285i | ||||||
\(313\) | − | 21.2005i | − | 1.19832i | −0.800628 | − | 0.599161i | \(-0.795501\pi\) | ||
0.800628 | − | 0.599161i | \(-0.204499\pi\) | |||||||
\(314\) | 16.0300 | 0.904627 | ||||||||
\(315\) | −22.9805 | − | 1.15239i | −1.29481 | − | 0.0649296i | ||||
\(316\) | 0.131314 | 0.00738702 | ||||||||
\(317\) | 3.06442i | 0.172115i | 0.996290 | + | 0.0860575i | \(0.0274269\pi\) | ||||
−0.996290 | + | 0.0860575i | \(0.972573\pi\) | |||||||
\(318\) | 26.5833i | 1.49072i | ||||||||
\(319\) | −1.42000 | −0.0795050 | ||||||||
\(320\) | −0.796647 | + | 15.8865i | −0.0445339 | + | 0.888082i | ||||
\(321\) | −8.10666 | −0.452470 | ||||||||
\(322\) | − | 6.89184i | − | 0.384067i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.59250 | 0.0884722 | ||||||||
\(325\) | 0.892431 | − | 8.87592i | 0.0495031 | − | 0.492347i | ||||
\(326\) | −12.4924 | −0.691889 | ||||||||
\(327\) | 7.99825i | 0.442304i | ||||||||
\(328\) | − | 19.1328i | − | 1.05643i | ||||||
\(329\) | −1.44763 | −0.0798103 | ||||||||
\(330\) | 1.72107 | − | 34.3211i | 0.0947418 | − | 1.88931i | ||||
\(331\) | −25.9509 | −1.42639 | −0.713195 | − | 0.700966i | \(-0.752753\pi\) | ||||
−0.713195 | + | 0.700966i | \(0.752753\pi\) | |||||||
\(332\) | 0.103929i | 0.00570383i | ||||||||
\(333\) | − | 8.56431i | − | 0.469321i | ||||||
\(334\) | −29.4373 | −1.61074 | ||||||||
\(335\) | −19.1001 | − | 0.957795i | −1.04355 | − | 0.0523299i | ||||
\(336\) | 35.0288 | 1.91098 | ||||||||
\(337\) | 10.0575i | 0.547865i | 0.961749 | + | 0.273933i | \(0.0883245\pi\) | ||||
−0.961749 | + | 0.273933i | \(0.911676\pi\) | |||||||
\(338\) | 14.5208i | 0.789828i | ||||||||
\(339\) | −11.6961 | −0.635243 | ||||||||
\(340\) | 2.65779 | + | 0.133278i | 0.144139 | + | 0.00722800i | ||||
\(341\) | 11.6258 | 0.629574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.1741i | 0.603343i | ||||||||
\(344\) | −26.5200 | −1.42986 | ||||||||
\(345\) | −0.398695 | + | 7.95066i | −0.0214650 | + | 0.428049i | ||||
\(346\) | −17.3374 | −0.932065 | ||||||||
\(347\) | 6.81801i | 0.366010i | 0.983112 | + | 0.183005i | \(0.0585824\pi\) | ||||
−0.983112 | + | 0.183005i | \(0.941418\pi\) | |||||||
\(348\) | − | 0.158392i | − | 0.00849071i | ||||||
\(349\) | −31.5966 | −1.69133 | −0.845663 | − | 0.533718i | \(-0.820795\pi\) | ||||
−0.845663 | + | 0.533718i | \(0.820795\pi\) | |||||||
\(350\) | 23.9150 | + | 2.40454i | 1.27831 | + | 0.128528i | ||||
\(351\) | 0.736826 | 0.0393289 | ||||||||
\(352\) | 4.43394i | 0.236330i | ||||||||
\(353\) | 6.30657i | 0.335665i | 0.985816 | + | 0.167832i | \(0.0536767\pi\) | ||||
−0.985816 | + | 0.167832i | \(0.946323\pi\) | |||||||
\(354\) | 11.5431 | 0.613511 | ||||||||
\(355\) | 1.44386 | − | 28.7930i | 0.0766320 | − | 1.52817i | ||||
\(356\) | 1.28339 | 0.0680197 | ||||||||
\(357\) | 51.1020i | 2.70461i | ||||||||
\(358\) | − | 10.4781i | − | 0.553785i | ||||||
\(359\) | −4.17666 | −0.220436 | −0.110218 | − | 0.993907i | \(-0.535155\pi\) | ||||
−0.110218 | + | 0.993907i | \(0.535155\pi\) | |||||||
\(360\) | −18.9532 | − | 0.950432i | −0.998924 | − | 0.0500922i | ||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 13.7293i | 0.721596i | ||||||||
\(363\) | 16.1552i | 0.847927i | ||||||||
\(364\) | 1.08972 | 0.0571170 | ||||||||
\(365\) | −4.06961 | − | 0.204075i | −0.213013 | − | 0.0106818i | ||||
\(366\) | 11.2603 | 0.588584 | ||||||||
\(367\) | − | 16.5710i | − | 0.864998i | −0.901634 | − | 0.432499i | \(-0.857632\pi\) | ||
0.901634 | − | 0.432499i | \(-0.142368\pi\) | |||||||
\(368\) | − | 6.22295i | − | 0.324394i | ||||||
\(369\) | 22.6018 | 1.17660 | ||||||||
\(370\) | −0.448057 | + | 8.93503i | −0.0232934 | + | 0.464510i | ||||
\(371\) | 23.5204 | 1.22112 | ||||||||
\(372\) | 1.29678i | 0.0672352i | ||||||||
\(373\) | 37.0004i | 1.91581i | 0.287085 | + | 0.957905i | \(0.407314\pi\) | ||||
−0.287085 | + | 0.957905i | \(0.592686\pi\) | |||||||
\(374\) | −39.1893 | −2.02643 | ||||||||
\(375\) | −27.4500 | − | 4.15744i | −1.41751 | − | 0.214689i | ||||
\(376\) | −1.19393 | −0.0615725 | ||||||||
\(377\) | 0.605517i | 0.0311857i | ||||||||
\(378\) | 1.98528i | 0.102112i | ||||||||
\(379\) | −31.5147 | −1.61880 | −0.809400 | − | 0.587257i | \(-0.800208\pi\) | ||||
−0.809400 | + | 0.587257i | \(0.800208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.47009 | 0.0753148 | ||||||||
\(382\) | 12.0171i | 0.614851i | ||||||||
\(383\) | 3.09813i | 0.158307i | 0.996862 | + | 0.0791536i | \(0.0252218\pi\) | ||||
−0.996862 | + | 0.0791536i | \(0.974778\pi\) | |||||||
\(384\) | 31.3919 | 1.60196 | ||||||||
\(385\) | −30.3667 | − | 1.52277i | −1.54763 | − | 0.0776076i | ||||
\(386\) | −11.4243 | −0.581479 | ||||||||
\(387\) | − | 31.3283i | − | 1.59251i | ||||||
\(388\) | − | 2.48094i | − | 0.125951i | ||||||
\(389\) | −26.0318 | −1.31986 | −0.659931 | − | 0.751326i | \(-0.729415\pi\) | ||||
−0.659931 | + | 0.751326i | \(0.729415\pi\) | |||||||
\(390\) | −14.6352 | − | 0.733897i | −0.741081 | − | 0.0371623i | ||||
\(391\) | 9.07840 | 0.459115 | ||||||||
\(392\) | − | 9.54655i | − | 0.482174i | ||||||
\(393\) | − | 51.0275i | − | 2.57400i | ||||||
\(394\) | 5.27712 | 0.265857 | ||||||||
\(395\) | −0.0782471 | + | 1.56038i | −0.00393704 | + | 0.0785113i | ||||
\(396\) | −2.48981 | −0.125118 | ||||||||
\(397\) | 12.6607i | 0.635423i | 0.948187 | + | 0.317712i | \(0.102914\pi\) | ||||
−0.948187 | + | 0.317712i | \(0.897086\pi\) | |||||||
\(398\) | 12.9714i | 0.650197i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 21.5939 | + | 2.17116i | 1.07970 | + | 0.108558i | ||||
\(401\) | −9.22180 | −0.460515 | −0.230257 | − | 0.973130i | \(-0.573957\pi\) | ||||
−0.230257 | + | 0.973130i | \(0.573957\pi\) | |||||||
\(402\) | 31.4142i | 1.56680i | ||||||||
\(403\) | − | 4.95748i | − | 0.246950i | ||||||
\(404\) | −3.24681 | −0.161535 | ||||||||
\(405\) | −0.948932 | + | 18.9233i | −0.0471528 | + | 0.940308i | ||||
\(406\) | −1.63149 | −0.0809693 | ||||||||
\(407\) | − | 11.3169i | − | 0.560960i | ||||||
\(408\) | 42.1465i | 2.08656i | ||||||||
\(409\) | −34.4572 | −1.70380 | −0.851899 | − | 0.523706i | \(-0.824549\pi\) | ||||
−0.851899 | + | 0.523706i | \(0.824549\pi\) | |||||||
\(410\) | −23.5802 | − | 1.18245i | −1.16454 | − | 0.0583973i | ||||
\(411\) | 21.7381 | 1.07226 | ||||||||
\(412\) | − | 2.59896i | − | 0.128042i | ||||||
\(413\) | − | 10.2132i | − | 0.502557i | ||||||
\(414\) | 6.71464 | 0.330006 | ||||||||
\(415\) | −1.23496 | − | 0.0619286i | −0.0606219 | − | 0.00303995i | ||||
\(416\) | 1.89072 | 0.0927001 | ||||||||
\(417\) | − | 19.0943i | − | 0.935053i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.86047 | 0.384009 | 0.192005 | − | 0.981394i | \(-0.438501\pi\) | ||||
0.192005 | + | 0.981394i | \(0.438501\pi\) | |||||||
\(420\) | 0.169855 | − | 3.38720i | 0.00828808 | − | 0.165278i | ||||
\(421\) | 10.4922 | 0.511360 | 0.255680 | − | 0.966761i | \(-0.417701\pi\) | ||||
0.255680 | + | 0.966761i | \(0.417701\pi\) | |||||||
\(422\) | 17.4796i | 0.850892i | ||||||||
\(423\) | − | 1.41041i | − | 0.0685763i | ||||||
\(424\) | 19.3985 | 0.942076 | ||||||||
\(425\) | −3.16742 | + | 31.5025i | −0.153642 | + | 1.52809i | ||||
\(426\) | −47.3563 | −2.29442 | ||||||||
\(427\) | − | 9.96288i | − | 0.482138i | ||||||
\(428\) | − | 0.613552i | − | 0.0296571i | ||||||
\(429\) | 18.5366 | 0.894957 | ||||||||
\(430\) | −1.63900 | + | 32.6844i | −0.0790394 | + | 1.57618i | ||||
\(431\) | 29.8923 | 1.43986 | 0.719931 | − | 0.694046i | \(-0.244173\pi\) | ||||
0.719931 | + | 0.694046i | \(0.244173\pi\) | |||||||
\(432\) | 1.79260i | 0.0862465i | ||||||||
\(433\) | − | 6.79977i | − | 0.326776i | −0.986562 | − | 0.163388i | \(-0.947758\pi\) | ||
0.986562 | − | 0.163388i | \(-0.0522422\pi\) | |||||||
\(434\) | 13.3573 | 0.641170 | ||||||||
\(435\) | 1.88214 | + | 0.0943820i | 0.0902416 | + | 0.00452527i | ||||
\(436\) | −0.605347 | −0.0289908 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 6.69335i | 0.319820i | ||||||||
\(439\) | −7.96606 | −0.380199 | −0.190100 | − | 0.981765i | \(-0.560881\pi\) | ||||
−0.190100 | + | 0.981765i | \(0.560881\pi\) | |||||||
\(440\) | −25.0450 | − | 1.25591i | −1.19397 | − | 0.0598731i | ||||
\(441\) | 11.2774 | 0.537021 | ||||||||
\(442\) | 16.7111i | 0.794864i | ||||||||
\(443\) | 21.7893i | 1.03524i | 0.855610 | + | 0.517621i | \(0.173182\pi\) | ||||
−0.855610 | + | 0.517621i | \(0.826818\pi\) | |||||||
\(444\) | 1.26233 | 0.0599076 | ||||||||
\(445\) | −0.764743 | + | 15.2503i | −0.0362523 | + | 0.722932i | ||||
\(446\) | −13.1611 | −0.623194 | ||||||||
\(447\) | 37.1025i | 1.75489i | ||||||||
\(448\) | − | 23.1183i | − | 1.09224i | ||||||
\(449\) | −18.7837 | −0.886458 | −0.443229 | − | 0.896409i | \(-0.646167\pi\) | ||||
−0.443229 | + | 0.896409i | \(0.646167\pi\) | |||||||
\(450\) | −2.34271 | + | 23.3001i | −0.110436 | + | 1.09838i | ||||
\(451\) | 29.8662 | 1.40634 | ||||||||
\(452\) | − | 0.885215i | − | 0.0416370i | ||||||
\(453\) | 32.6353i | 1.53334i | ||||||||
\(454\) | −39.0619 | −1.83327 | ||||||||
\(455\) | −0.649339 | + | 12.9489i | −0.0304415 | + | 0.607055i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.2368i | 1.32086i | 0.750887 | + | 0.660431i | \(0.229627\pi\) | ||||
−0.750887 | + | 0.660431i | \(0.770373\pi\) | |||||||
\(458\) | − | 32.2240i | − | 1.50573i | ||||||
\(459\) | −2.61515 | −0.122065 | ||||||||
\(460\) | −0.601745 | − | 0.0301752i | −0.0280565 | − | 0.00140692i | ||||
\(461\) | −0.196008 | −0.00912900 | −0.00456450 | − | 0.999990i | \(-0.501453\pi\) | ||||
−0.00456450 | + | 0.999990i | \(0.501453\pi\) | |||||||
\(462\) | 49.9445i | 2.32363i | ||||||||
\(463\) | − | 13.9641i | − | 0.648967i | −0.945891 | − | 0.324484i | \(-0.894809\pi\) | ||
0.945891 | − | 0.324484i | \(-0.105191\pi\) | |||||||
\(464\) | −1.47314 | −0.0683889 | ||||||||
\(465\) | −15.4094 | − | 0.772722i | −0.714594 | − | 0.0358341i | ||||
\(466\) | −14.7931 | −0.685275 | ||||||||
\(467\) | − | 32.1025i | − | 1.48553i | −0.669555 | − | 0.742763i | \(-0.733515\pi\) | ||
0.669555 | − | 0.742763i | \(-0.266485\pi\) | |||||||
\(468\) | 1.06170i | 0.0490772i | ||||||||
\(469\) | 27.7947 | 1.28344 | ||||||||
\(470\) | −0.0737880 | + | 1.47146i | −0.00340358 | + | 0.0678733i | ||||
\(471\) | 26.9110 | 1.23999 | ||||||||
\(472\) | − | 8.42333i | − | 0.387715i | ||||||
\(473\) | − | 41.3974i | − | 1.90346i | ||||||
\(474\) | 2.56638 | 0.117878 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.86765 | −0.177273 | ||||||||
\(477\) | 22.9157i | 1.04924i | ||||||||
\(478\) | − | 26.3831i | − | 1.20674i | ||||||
\(479\) | 1.98226 | 0.0905717 | 0.0452858 | − | 0.998974i | \(-0.485580\pi\) | ||||
0.0452858 | + | 0.998974i | \(0.485580\pi\) | |||||||
\(480\) | 0.294706 | − | 5.87694i | 0.0134514 | − | 0.268245i | ||||
\(481\) | −4.82576 | −0.220036 | ||||||||
\(482\) | − | 25.3591i | − | 1.15508i | ||||||
\(483\) | − | 11.5699i | − | 0.526450i | ||||||
\(484\) | −1.22270 | −0.0555774 | ||||||||
\(485\) | 29.4804 | + | 1.47833i | 1.33864 | + | 0.0671275i | ||||
\(486\) | 32.9561 | 1.49492 | ||||||||
\(487\) | 8.58916i | 0.389212i | 0.980881 | + | 0.194606i | \(0.0623428\pi\) | ||||
−0.980881 | + | 0.194606i | \(0.937657\pi\) | |||||||
\(488\) | − | 8.21691i | − | 0.371962i | ||||||
\(489\) | −20.9720 | −0.948387 | ||||||||
\(490\) | −11.7656 | − | 0.589999i | −0.531516 | − | 0.0266535i | ||||
\(491\) | 25.9002 | 1.16886 | 0.584430 | − | 0.811444i | \(-0.301318\pi\) | ||||
0.584430 | + | 0.811444i | \(0.301318\pi\) | |||||||
\(492\) | 3.33138i | 0.150190i | ||||||||
\(493\) | − | 2.14910i | − | 0.0967908i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.48362 | − | 29.5858i | 0.0666836 | − | 1.32979i | ||||
\(496\) | 12.0609 | 0.541550 | ||||||||
\(497\) | 41.9000i | 1.87947i | ||||||||
\(498\) | 2.03116i | 0.0910185i | ||||||||
\(499\) | 21.2038 | 0.949214 | 0.474607 | − | 0.880198i | \(-0.342590\pi\) | ||||
0.474607 | + | 0.880198i | \(0.342590\pi\) | |||||||
\(500\) | 0.314655 | − | 2.07755i | 0.0140718 | − | 0.0929109i | ||||
\(501\) | −49.4189 | −2.20787 | ||||||||
\(502\) | 14.3418i | 0.640106i | ||||||||
\(503\) | − | 25.5162i | − | 1.13771i | −0.822438 | − | 0.568855i | \(-0.807386\pi\) | ||
0.822438 | − | 0.568855i | \(-0.192614\pi\) | |||||||
\(504\) | 27.5810 | 1.22856 | ||||||||
\(505\) | 1.93469 | − | 38.5811i | 0.0860927 | − | 1.71684i | ||||
\(506\) | 8.87277 | 0.394443 | ||||||||
\(507\) | 24.3773i | 1.08263i | ||||||||
\(508\) | 0.111263i | 0.00493651i | ||||||||
\(509\) | 17.0407 | 0.755314 | 0.377657 | − | 0.925946i | \(-0.376730\pi\) | ||||
0.377657 | + | 0.925946i | \(0.376730\pi\) | |||||||
\(510\) | 51.9432 | + | 2.60475i | 2.30008 | + | 0.115340i | ||||
\(511\) | 5.92215 | 0.261981 | ||||||||
\(512\) | − | 18.6685i | − | 0.825039i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.8666 | −0.655738 | ||||||||
\(515\) | 30.8829 | + | 1.54866i | 1.36086 | + | 0.0682420i | ||||
\(516\) | 4.61761 | 0.203279 | ||||||||
\(517\) | − | 1.86372i | − | 0.0819664i | ||||||
\(518\) | − | 13.0024i | − | 0.571292i | ||||||
\(519\) | −29.1058 | −1.27760 | ||||||||
\(520\) | −0.535544 | + | 10.6797i | −0.0234851 | + | 0.468334i | ||||
\(521\) | 21.7817 | 0.954274 | 0.477137 | − | 0.878829i | \(-0.341675\pi\) | ||||
0.477137 | + | 0.878829i | \(0.341675\pi\) | |||||||
\(522\) | − | 1.58954i | − | 0.0695721i | ||||||
\(523\) | 17.4855i | 0.764589i | 0.924041 | + | 0.382294i | \(0.124866\pi\) | ||||
−0.924041 | + | 0.382294i | \(0.875134\pi\) | |||||||
\(524\) | 3.86201 | 0.168713 | ||||||||
\(525\) | 40.1481 | + | 4.03670i | 1.75221 | + | 0.176176i | ||||
\(526\) | 32.2911 | 1.40796 | ||||||||
\(527\) | 17.5951i | 0.766455i | ||||||||
\(528\) | 45.0972i | 1.96260i | ||||||||
\(529\) | 20.9446 | 0.910634 | ||||||||
\(530\) | 1.19887 | − | 23.9076i | 0.0520758 | − | 1.03848i | ||||
\(531\) | 9.95056 | 0.431817 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.7355i | − | 0.551637i | ||||||
\(534\) | 25.0824 | 1.08542 | ||||||||
\(535\) | 7.29070 | + | 0.365600i | 0.315204 | + | 0.0158063i | ||||
\(536\) | 22.9237 | 0.990154 | ||||||||
\(537\) | − | 17.5905i | − | 0.759086i | ||||||
\(538\) | − | 22.8607i | − | 0.985593i | ||||||
\(539\) | 14.9021 | 0.641878 | ||||||||
\(540\) | 0.173340 | + | 0.00869233i | 0.00745936 | + | 0.000374058i | ||||
\(541\) | 14.8091 | 0.636691 | 0.318346 | − | 0.947975i | \(-0.396873\pi\) | ||||
0.318346 | + | 0.947975i | \(0.396873\pi\) | |||||||
\(542\) | 7.63724i | 0.328047i | ||||||||
\(543\) | 23.0485i | 0.989108i | ||||||||
\(544\) | −6.71054 | −0.287712 | ||||||||
\(545\) | 0.360711 | − | 7.19320i | 0.0154512 | − | 0.308123i | ||||
\(546\) | 21.2973 | 0.911441 | ||||||||
\(547\) | − | 26.5735i | − | 1.13620i | −0.822959 | − | 0.568100i | \(-0.807679\pi\) | ||
0.822959 | − | 0.568100i | \(-0.192321\pi\) | |||||||
\(548\) | 1.64525i | 0.0702815i | ||||||||
\(549\) | 9.70671 | 0.414272 | ||||||||
\(550\) | −3.09568 | + | 30.7889i | −0.132000 | + | 1.31284i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | − | 9.54231i | − | 0.406148i | ||||||
\(553\) | − | 2.27069i | − | 0.0965595i | ||||||
\(554\) | −8.23942 | −0.350059 | ||||||||
\(555\) | −0.752192 | + | 15.0000i | −0.0319288 | + | 0.636714i | ||||
\(556\) | 1.44515 | 0.0612881 | ||||||||
\(557\) | − | 16.0752i | − | 0.681129i | −0.940221 | − | 0.340565i | \(-0.889382\pi\) | ||
0.940221 | − | 0.340565i | \(-0.110618\pi\) | |||||||
\(558\) | 13.0138i | 0.550919i | ||||||||
\(559\) | −17.6527 | −0.746628 | ||||||||
\(560\) | −31.5030 | − | 1.57976i | −1.33125 | − | 0.0667569i | ||||
\(561\) | −65.7903 | −2.77767 | ||||||||
\(562\) | 40.3413i | 1.70169i | ||||||||
\(563\) | 2.03145i | 0.0856155i | 0.999083 | + | 0.0428078i | \(0.0136303\pi\) | ||||
−0.999083 | + | 0.0428078i | \(0.986370\pi\) | |||||||
\(564\) | 0.207886 | 0.00875357 | ||||||||
\(565\) | 10.5188 | + | 0.527478i | 0.442530 | + | 0.0221912i | ||||
\(566\) | −22.2553 | −0.935459 | ||||||||
\(567\) | − | 27.5375i | − | 1.15647i | ||||||
\(568\) | 34.5571i | 1.44998i | ||||||||
\(569\) | 12.8224 | 0.537543 | 0.268772 | − | 0.963204i | \(-0.413382\pi\) | ||||
0.268772 | + | 0.963204i | \(0.413382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9168 | 0.540551 | 0.270276 | − | 0.962783i | \(-0.412885\pi\) | ||||
0.270276 | + | 0.962783i | \(0.412885\pi\) | |||||||
\(572\) | 1.40294i | 0.0586600i | ||||||||
\(573\) | 20.1742i | 0.842789i | ||||||||
\(574\) | 34.3142 | 1.43225 | ||||||||
\(575\) | 0.717130 | − | 7.13242i | 0.0299064 | − | 0.297442i | ||||
\(576\) | 22.5238 | 0.938493 | ||||||||
\(577\) | − | 8.11359i | − | 0.337773i | −0.985635 | − | 0.168887i | \(-0.945983\pi\) | ||
0.985635 | − | 0.168887i | \(-0.0540172\pi\) | |||||||
\(578\) | − | 34.1651i | − | 1.42108i | ||||||
\(579\) | −19.1789 | −0.797046 | ||||||||
\(580\) | −0.00714329 | + | 0.142449i | −0.000296609 | + | 0.00591489i | ||||
\(581\) | 1.79713 | 0.0745577 | ||||||||
\(582\) | − | 48.4869i | − | 2.00985i | ||||||
\(583\) | 30.2809i | 1.25411i | ||||||||
\(584\) | 4.88431 | 0.202114 | ||||||||
\(585\) | −12.6160 | − | 0.632643i | −0.521607 | − | 0.0261566i | ||||
\(586\) | −11.5801 | −0.478371 | ||||||||
\(587\) | 32.5617i | 1.34396i | 0.740568 | + | 0.671982i | \(0.234557\pi\) | ||||
−0.740568 | + | 0.671982i | \(0.765443\pi\) | |||||||
\(588\) | 1.66223i | 0.0685492i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −10.3813 | − | 0.520581i | −0.427391 | − | 0.0214320i | ||||
\(591\) | 8.85914 | 0.364416 | ||||||||
\(592\) | − | 11.7404i | − | 0.482529i | ||||||
\(593\) | − | 11.4752i | − | 0.471231i | −0.971846 | − | 0.235616i | \(-0.924289\pi\) | ||
0.971846 | − | 0.235616i | \(-0.0757106\pi\) | |||||||
\(594\) | −2.55591 | −0.104870 | ||||||||
\(595\) | 2.30464 | − | 45.9584i | 0.0944809 | − | 1.88411i | ||||
\(596\) | −2.80809 | −0.115024 | ||||||||
\(597\) | 21.7762i | 0.891239i | ||||||||
\(598\) | − | 3.78352i | − | 0.154720i | ||||||
\(599\) | −33.2099 | −1.35692 | −0.678460 | − | 0.734637i | \(-0.737352\pi\) | ||||
−0.678460 | + | 0.734637i | \(0.737352\pi\) | |||||||
\(600\) | 33.1123 | + | 3.32928i | 1.35180 | + | 0.135917i | ||||
\(601\) | 27.3180 | 1.11433 | 0.557163 | − | 0.830403i | \(-0.311890\pi\) | ||||
0.557163 | + | 0.830403i | \(0.311890\pi\) | |||||||
\(602\) | − | 47.5628i | − | 1.93851i | ||||||
\(603\) | 27.0800i | 1.10278i | ||||||||
\(604\) | −2.47000 | −0.100503 | ||||||||
\(605\) | 0.728578 | − | 14.5291i | 0.0296209 | − | 0.590692i | ||||
\(606\) | −63.4549 | −2.57768 | ||||||||
\(607\) | − | 25.7405i | − | 1.04478i | −0.852708 | − | 0.522388i | \(-0.825041\pi\) | ||
0.852708 | − | 0.522388i | \(-0.174959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.73892 | −0.110986 | ||||||||
\(610\) | −10.1269 | − | 0.507824i | −0.410025 | − | 0.0205612i | ||||
\(611\) | −0.794727 | −0.0321512 | ||||||||
\(612\) | − | 3.76820i | − | 0.152320i | ||||||
\(613\) | 40.6039i | 1.63997i | 0.572382 | + | 0.819987i | \(0.306020\pi\) | ||||
−0.572382 | + | 0.819987i | \(0.693980\pi\) | |||||||
\(614\) | 23.2445 | 0.938073 | ||||||||
\(615\) | −39.5860 | − | 1.98509i | −1.59626 | − | 0.0800464i | ||||
\(616\) | 36.4458 | 1.46844 | ||||||||
\(617\) | − | 14.2113i | − | 0.572125i | −0.958211 | − | 0.286063i | \(-0.907653\pi\) | ||
0.958211 | − | 0.286063i | \(-0.0923465\pi\) | |||||||
\(618\) | − | 50.7936i | − | 2.04322i | ||||||
\(619\) | 29.5635 | 1.18826 | 0.594129 | − | 0.804370i | \(-0.297497\pi\) | ||||
0.594129 | + | 0.804370i | \(0.297497\pi\) | |||||||
\(620\) | 0.0584834 | − | 1.16626i | 0.00234875 | − | 0.0468381i | ||||
\(621\) | 0.592091 | 0.0237598 | ||||||||
\(622\) | 26.5973i | 1.06645i | ||||||||
\(623\) | − | 22.1924i | − | 0.889121i | ||||||
\(624\) | 19.2303 | 0.769828 | ||||||||
\(625\) | 24.4996 | + | 4.97694i | 0.979984 | + | 0.199078i | ||||
\(626\) | 31.3591 | 1.25336 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.03675i | 0.0812753i | ||||||||
\(629\) | 17.1276 | 0.682923 | ||||||||
\(630\) | 1.70457 | − | 33.9921i | 0.0679118 | − | 1.35428i | ||||
\(631\) | −1.70763 | −0.0679798 | −0.0339899 | − | 0.999422i | \(-0.510821\pi\) | ||||
−0.0339899 | + | 0.999422i | \(0.510821\pi\) | |||||||
\(632\) | − | 1.87276i | − | 0.0744942i | ||||||
\(633\) | 29.3444i | 1.16634i | ||||||||
\(634\) | −4.53280 | −0.180020 | ||||||||
\(635\) | −1.32212 | − | 0.0662991i | −0.0524666 | − | 0.00263100i | ||||
\(636\) | −3.37764 | −0.133932 | ||||||||
\(637\) | − | 6.35454i | − | 0.251776i | ||||||
\(638\) | − | 2.10043i | − | 0.0831567i | ||||||
\(639\) | −40.8226 | −1.61492 | ||||||||
\(640\) | −28.2322 | − | 1.41573i | −1.11597 | − | 0.0559618i | ||||
\(641\) | 2.76200 | 0.109092 | 0.0545462 | − | 0.998511i | \(-0.482629\pi\) | ||||
0.0545462 | + | 0.998511i | \(0.482629\pi\) | |||||||
\(642\) | − | 11.9911i | − | 0.473252i | ||||||
\(643\) | 21.6971i | 0.855648i | 0.903862 | + | 0.427824i | \(0.140720\pi\) | ||||
−0.903862 | + | 0.427824i | \(0.859280\pi\) | |||||||
\(644\) | 0.875668 | 0.0345061 | ||||||||
\(645\) | −2.75152 | + | 54.8700i | −0.108341 | + | 2.16050i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.0268i | 1.10185i | 0.834556 | + | 0.550923i | \(0.185724\pi\) | ||||
−0.834556 | + | 0.550923i | \(0.814276\pi\) | |||||||
\(648\) | − | 22.7116i | − | 0.892196i | ||||||
\(649\) | 13.1487 | 0.516133 | ||||||||
\(650\) | 13.1290 | + | 1.32006i | 0.514961 | + | 0.0517768i | ||||
\(651\) | 22.4240 | 0.878866 | ||||||||
\(652\) | − | 1.58726i | − | 0.0621620i | ||||||
\(653\) | 7.59308i | 0.297140i | 0.988902 | + | 0.148570i | \(0.0474671\pi\) | ||||
−0.988902 | + | 0.148570i | \(0.952533\pi\) | |||||||
\(654\) | −11.8308 | −0.462620 | ||||||||
\(655\) | −2.30128 | + | 45.8914i | −0.0899183 | + | 1.79313i | ||||
\(656\) | 30.9838 | 1.20972 | ||||||||
\(657\) | 5.76988i | 0.225104i | ||||||||
\(658\) | − | 2.14129i | − | 0.0834761i | ||||||
\(659\) | −7.18394 | −0.279847 | −0.139923 | − | 0.990162i | \(-0.544686\pi\) | ||||
−0.139923 | + | 0.990162i | \(0.544686\pi\) | |||||||
\(660\) | 4.36079 | + | 0.218677i | 0.169743 | + | 0.00851198i | ||||
\(661\) | −28.8678 | −1.12283 | −0.561413 | − | 0.827536i | \(-0.689742\pi\) | ||||
−0.561413 | + | 0.827536i | \(0.689742\pi\) | |||||||
\(662\) | − | 38.3857i | − | 1.49190i | ||||||
\(663\) | 28.0543i | 1.08954i | ||||||||
\(664\) | 1.48219 | 0.0575201 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.6681 | 0.490877 | ||||||||
\(667\) | 0.486575i | 0.0188403i | ||||||||
\(668\) | − | 3.74026i | − | 0.144715i | ||||||
\(669\) | −22.0946 | −0.854226 | ||||||||
\(670\) | 1.41674 | − | 28.2522i | 0.0547334 | − | 1.09148i | ||||
\(671\) | 12.8265 | 0.495162 | ||||||||
\(672\) | 8.55222i | 0.329909i | ||||||||
\(673\) | − | 23.3191i | − | 0.898885i | −0.893309 | − | 0.449442i | \(-0.851623\pi\) | ||
0.893309 | − | 0.449442i | \(-0.148377\pi\) | |||||||
\(674\) | −14.8767 | −0.573029 | ||||||||
\(675\) | −0.206578 | + | 2.05458i | −0.00795119 | + | 0.0790808i | ||||
\(676\) | −1.84499 | −0.0709612 | ||||||||
\(677\) | − | 17.5099i | − | 0.672958i | −0.941691 | − | 0.336479i | \(-0.890764\pi\) | ||
0.941691 | − | 0.336479i | \(-0.109236\pi\) | |||||||
\(678\) | − | 17.3005i | − | 0.664420i | ||||||
\(679\) | −42.9004 | −1.64636 | ||||||||
\(680\) | 1.90075 | − | 37.9043i | 0.0728906 | − | 1.45356i | ||||
\(681\) | −65.5765 | −2.51290 | ||||||||
\(682\) | 17.1966i | 0.658491i | ||||||||
\(683\) | − | 22.0114i | − | 0.842243i | −0.907004 | − | 0.421122i | \(-0.861637\pi\) | ||
0.907004 | − | 0.421122i | \(-0.138363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5501 | − | 0.980363i | −0.746971 | − | 0.0374577i | ||||
\(686\) | −16.5283 | −0.631055 | ||||||||
\(687\) | − | 54.0972i | − | 2.06394i | ||||||
\(688\) | − | 42.9466i | − | 1.63732i | ||||||
\(689\) | 12.9124 | 0.491923 | ||||||||
\(690\) | −11.7604 | − | 0.589737i | −0.447710 | − | 0.0224509i | ||||
\(691\) | −2.65623 | −0.101048 | −0.0505238 | − | 0.998723i | \(-0.516089\pi\) | ||||
−0.0505238 | + | 0.998723i | \(0.516089\pi\) | |||||||
\(692\) | − | 2.20287i | − | 0.0837404i | ||||||
\(693\) | 43.0538i | 1.63548i | ||||||||
\(694\) | −10.0850 | −0.382821 | ||||||||
\(695\) | −0.861130 | + | 17.1724i | −0.0326645 | + | 0.651387i | ||||
\(696\) | −2.25893 | −0.0856244 | ||||||||
\(697\) | 45.2010i | 1.71211i | ||||||||
\(698\) | − | 46.7367i | − | 1.76901i | ||||||
\(699\) | −24.8344 | −0.939322 | ||||||||
\(700\) | −0.305517 | + | 3.03861i | −0.0115475 | + | 0.114848i | ||||
\(701\) | −7.36728 | −0.278258 | −0.139129 | − | 0.990274i | \(-0.544430\pi\) | ||||
−0.139129 | + | 0.990274i | \(0.544430\pi\) | |||||||
\(702\) | 1.08989i | 0.0411352i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 29.7632 | 1.12174 | ||||||||
\(705\) | −0.123874 | + | 2.47026i | −0.00466537 | + | 0.0930354i | ||||
\(706\) | −9.32848 | −0.351082 | ||||||||
\(707\) | 56.1438i | 2.11150i | ||||||||
\(708\) | 1.46666i | 0.0551203i | ||||||||
\(709\) | 5.99178 | 0.225026 | 0.112513 | − | 0.993650i | \(-0.464110\pi\) | ||||
0.112513 | + | 0.993650i | \(0.464110\pi\) | |||||||
\(710\) | 42.5897 | + | 2.13571i | 1.59836 | + | 0.0801517i | ||||
\(711\) | 2.21230 | 0.0829679 | ||||||||
\(712\) | − | 18.3032i | − | 0.685943i | ||||||
\(713\) | − | 3.98368i | − | 0.149190i | ||||||
\(714\) | −75.5885 | −2.82883 | ||||||||
\(715\) | −16.6709 | − | 0.835979i | −0.623455 | − | 0.0312639i | ||||
\(716\) | 1.33133 | 0.0497543 | ||||||||
\(717\) | − | 44.2916i | − | 1.65410i | ||||||
\(718\) | − | 6.17798i | − | 0.230560i | ||||||
\(719\) | −13.5815 | −0.506504 | −0.253252 | − | 0.967400i | \(-0.581500\pi\) | ||||
−0.253252 | + | 0.967400i | \(0.581500\pi\) | |||||||
\(720\) | 1.53914 | − | 30.6930i | 0.0573602 | − | 1.14386i | ||||
\(721\) | −44.9412 | −1.67370 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 42.5725i | − | 1.58329i | ||||||
\(724\) | −1.74443 | −0.0648311 | ||||||||
\(725\) | −1.68844 | − | 0.169764i | −0.0627070 | − | 0.00630488i | ||||
\(726\) | −23.8962 | −0.886872 | ||||||||
\(727\) | 41.2448i | 1.52968i | 0.644218 | + | 0.764842i | \(0.277183\pi\) | ||||
−0.644218 | + | 0.764842i | \(0.722817\pi\) | |||||||
\(728\) | − | 15.5412i | − | 0.575995i | ||||||
\(729\) | 29.9060 | 1.10763 | ||||||||
\(730\) | 0.301862 | − | 6.01963i | 0.0111724 | − | 0.222797i | ||||
\(731\) | 62.6529 | 2.31730 | ||||||||
\(732\) | 1.43071i | 0.0528807i | ||||||||
\(733\) | − | 0.123848i | − | 0.00457443i | −0.999997 | − | 0.00228722i | \(-0.999272\pi\) | ||
0.999997 | − | 0.00228722i | \(-0.000728044\pi\) | |||||||
\(734\) | 24.5113 | 0.904728 | ||||||||
\(735\) | −19.7519 | − | 0.990482i | −0.728560 | − | 0.0365345i | ||||
\(736\) | 1.51932 | 0.0560030 | ||||||||
\(737\) | 35.7837i | 1.31811i | ||||||||
\(738\) | 33.4319i | 1.23065i | ||||||||
\(739\) | 36.5134 | 1.34317 | 0.671584 | − | 0.740928i | \(-0.265614\pi\) | ||||
0.671584 | + | 0.740928i | \(0.265614\pi\) | |||||||
\(740\) | −1.13527 | − | 0.0569295i | −0.0417334 | − | 0.00209277i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 34.7907i | 1.27721i | ||||||||
\(743\) | 9.06197i | 0.332451i | 0.986088 | + | 0.166226i | \(0.0531580\pi\) | ||||
−0.986088 | + | 0.166226i | \(0.946842\pi\) | |||||||
\(744\) | 18.4942 | 0.678032 | ||||||||
\(745\) | 1.67328 | − | 33.3680i | 0.0613041 | − | 1.22251i | ||||
\(746\) | −54.7299 | −2.00380 | ||||||||
\(747\) | 1.75092i | 0.0640630i | ||||||||
\(748\) | − | 4.97933i | − | 0.182062i | ||||||
\(749\) | −10.6095 | −0.387664 | ||||||||
\(750\) | 6.14956 | − | 40.6032i | 0.224550 | − | 1.48262i | ||||
\(751\) | −4.08610 | −0.149104 | −0.0745519 | − | 0.997217i | \(-0.523753\pi\) | ||||
−0.0745519 | + | 0.997217i | \(0.523753\pi\) | |||||||
\(752\) | − | 1.93346i | − | 0.0705062i | ||||||
\(753\) | 24.0768i | 0.877407i | ||||||||
\(754\) | −0.895663 | −0.0326181 | ||||||||
\(755\) | 1.47181 | − | 29.3504i | 0.0535647 | − | 1.06817i | ||||
\(756\) | −0.252247 | −0.00917413 | ||||||||
\(757\) | 34.4597i | 1.25246i | 0.779638 | + | 0.626230i | \(0.215403\pi\) | ||||
−0.779638 | + | 0.626230i | \(0.784597\pi\) | |||||||
\(758\) | − | 46.6155i | − | 1.69315i | ||||||
\(759\) | 14.8955 | 0.540671 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.5813 | 0.746072 | 0.373036 | − | 0.927817i | \(-0.378317\pi\) | ||||
0.373036 | + | 0.927817i | \(0.378317\pi\) | |||||||
\(762\) | 2.17451i | 0.0787741i | ||||||||
\(763\) | 10.4676i | 0.378954i | ||||||||
\(764\) | −1.52688 | −0.0552406 | ||||||||
\(765\) | 44.7767 | + | 2.24538i | 1.61890 | + | 0.0811818i | ||||
\(766\) | −4.58266 | −0.165578 | ||||||||
\(767\) | − | 5.60688i | − | 0.202453i | ||||||
\(768\) | 11.1049i | 0.400714i | ||||||||
\(769\) | 30.3550 | 1.09463 | 0.547315 | − | 0.836927i | \(-0.315650\pi\) | ||||
0.547315 | + | 0.836927i | \(0.315650\pi\) | |||||||
\(770\) | 2.25244 | − | 44.9174i | 0.0811722 | − | 1.61871i | ||||
\(771\) | −24.9578 | −0.898834 | ||||||||
\(772\) | − | 1.45155i | − | 0.0522424i | ||||||
\(773\) | 19.5225i | 0.702176i | 0.936343 | + | 0.351088i | \(0.114188\pi\) | ||||
−0.936343 | + | 0.351088i | \(0.885812\pi\) | |||||||
\(774\) | 46.3398 | 1.66565 | ||||||||
\(775\) | 13.8235 | + | 1.38989i | 0.496556 | + | 0.0499263i | ||||
\(776\) | −35.3822 | −1.27015 | ||||||||
\(777\) | − | 21.8282i | − | 0.783083i | ||||||
\(778\) | − | 38.5054i | − | 1.38048i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.0932479 | − | 1.85952i | 0.00333881 | − | 0.0665816i | ||||
\(781\) | −53.9433 | −1.93024 | ||||||||
\(782\) | 13.4285i | 0.480202i | ||||||||
\(783\) | − | 0.140164i | − | 0.00500905i | ||||||
\(784\) | 15.4597 | 0.552134 | ||||||||
\(785\) | −24.2023 | − | 1.21365i | −0.863817 | − | 0.0433171i | ||||
\(786\) | 75.4783 | 2.69222 | ||||||||
\(787\) | 35.2236i | 1.25559i | 0.778380 | + | 0.627793i | \(0.216042\pi\) | ||||
−0.778380 | + | 0.627793i | \(0.783958\pi\) | |||||||
\(788\) | 0.670503i | 0.0238857i | ||||||||
\(789\) | 54.2098 | 1.92992 | ||||||||
\(790\) | −2.30807 | − | 0.115741i | −0.0821173 | − | 0.00411787i | ||||
\(791\) | −15.3071 | −0.544259 | ||||||||
\(792\) | 35.5087i | 1.26175i | ||||||||
\(793\) | − | 5.46948i | − | 0.194227i | ||||||
\(794\) | −18.7273 | −0.664608 | ||||||||
\(795\) | 2.01265 | − | 40.1357i | 0.0713814 | − | 1.42347i | ||||
\(796\) | −1.64813 | −0.0584163 | ||||||||
\(797\) | − | 28.7940i | − | 1.01994i | −0.860193 | − | 0.509969i | \(-0.829657\pi\) | ||
0.860193 | − | 0.509969i | \(-0.170343\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.82065 | 0.0997874 | ||||||||
\(800\) | −0.530086 | + | 5.27212i | −0.0187414 | + | 0.186397i | ||||
\(801\) | 21.6218 | 0.763969 | ||||||||
\(802\) | − | 13.6406i | − | 0.481666i | ||||||
\(803\) | 7.62436i | 0.269058i | ||||||||
\(804\) | −3.99144 | −0.140767 | ||||||||
\(805\) | −0.521789 | + | 10.4054i | −0.0183906 | + | 0.366741i | ||||
\(806\) | 7.33295 | 0.258292 | ||||||||
\(807\) | − | 38.3781i | − | 1.35097i | ||||||
\(808\) | 46.3047i | 1.62899i | ||||||||
\(809\) | 48.0068 | 1.68783 | 0.843915 | − | 0.536478i | \(-0.180245\pi\) | ||||
0.843915 | + | 0.536478i | \(0.180245\pi\) | |||||||
\(810\) | −27.9908 | − | 1.40363i | −0.983496 | − | 0.0493186i | ||||
\(811\) | −9.62886 | −0.338115 | −0.169057 | − | 0.985606i | \(-0.554072\pi\) | ||||
−0.169057 | + | 0.985606i | \(0.554072\pi\) | |||||||
\(812\) | − | 0.207294i | − | 0.00727461i | ||||||
\(813\) | 12.8213i | 0.449662i | ||||||||
\(814\) | 16.7397 | 0.586725 | ||||||||
\(815\) | 18.8611 | + | 0.945812i | 0.660675 | + | 0.0331303i | ||||
\(816\) | −68.2523 | −2.38931 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 50.9680i | − | 1.78205i | ||||||
\(819\) | 18.3590 | 0.641514 | ||||||||
\(820\) | 0.150241 | − | 2.99606i | 0.00524664 | − | 0.104627i | ||||
\(821\) | −25.7257 | −0.897834 | −0.448917 | − | 0.893573i | \(-0.648190\pi\) | ||||
−0.448917 | + | 0.893573i | \(0.648190\pi\) | |||||||
\(822\) | 32.1544i | 1.12151i | ||||||||
\(823\) | − | 13.4584i | − | 0.469132i | −0.972100 | − | 0.234566i | \(-0.924633\pi\) | ||
0.972100 | − | 0.234566i | \(-0.0753668\pi\) | |||||||
\(824\) | −37.0654 | −1.29123 | ||||||||
\(825\) | −5.19697 | + | 51.6879i | −0.180935 | + | 1.79954i | ||||
\(826\) | 15.1070 | 0.525640 | ||||||||
\(827\) | − | 0.172408i | − | 0.00599520i | −0.999996 | − | 0.00299760i | \(-0.999046\pi\) | ||
0.999996 | − | 0.00299760i | \(-0.000954168\pi\) | |||||||
\(828\) | 0.853152i | 0.0296491i | ||||||||
\(829\) | 42.3791 | 1.47189 | 0.735943 | − | 0.677044i | \(-0.236739\pi\) | ||||
0.735943 | + | 0.677044i | \(0.236739\pi\) | |||||||
\(830\) | 0.0916028 | − | 1.82672i | 0.00317958 | − | 0.0634063i | ||||
\(831\) | −13.8322 | −0.479834 | ||||||||
\(832\) | − | 12.6916i | − | 0.440002i | ||||||
\(833\) | 22.5536i | 0.781435i | ||||||||
\(834\) | 28.2437 | 0.978001 | ||||||||
\(835\) | 44.4447 | + | 2.22873i | 1.53807 | + | 0.0771284i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.14755i | 0.0396651i | ||||||||
\(838\) | 11.6270i | 0.401647i | ||||||||
\(839\) | −45.1399 | −1.55840 | −0.779200 | − | 0.626775i | \(-0.784375\pi\) | ||||
−0.779200 | + | 0.626775i | \(0.784375\pi\) | |||||||
\(840\) | −48.3069 | − | 2.42241i | −1.66675 | − | 0.0835810i | ||||
\(841\) | −28.8848 | −0.996028 | ||||||||
\(842\) | 15.5198i | 0.534847i | ||||||||
\(843\) | 67.7243i | 2.33255i | ||||||||
\(844\) | −2.22093 | −0.0764475 | ||||||||
\(845\) | 1.09939 | − | 21.9236i | 0.0378200 | − | 0.754196i | ||||
\(846\) | 2.08623 | 0.0717260 | ||||||||
\(847\) | 21.1430i | 0.726481i | ||||||||
\(848\) | 31.4141i | 1.07876i | ||||||||
\(849\) | −37.3618 | −1.28225 | ||||||||
\(850\) | −46.5975 | − | 4.68515i | −1.59828 | − | 0.160699i | ||||
\(851\) | −3.87784 | −0.132931 | ||||||||
\(852\) | − | 6.01702i | − | 0.206140i | ||||||
\(853\) | − | 46.3405i | − | 1.58667i | −0.608787 | − | 0.793333i | \(-0.708344\pi\) | ||
0.608787 | − | 0.793333i | \(-0.291656\pi\) | |||||||
\(854\) | 14.7368 | 0.504283 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.75023 | −0.299077 | ||||||||
\(857\) | − | 21.8934i | − | 0.747863i | −0.927456 | − | 0.373931i | \(-0.878010\pi\) | ||
0.927456 | − | 0.373931i | \(-0.121990\pi\) | |||||||
\(858\) | 27.4188i | 0.936063i | ||||||||
\(859\) | −33.4020 | −1.13966 | −0.569830 | − | 0.821762i | \(-0.692991\pi\) | ||||
−0.569830 | + | 0.821762i | \(0.692991\pi\) | |||||||
\(860\) | −4.15283 | − | 0.208248i | −0.141610 | − | 0.00710121i | ||||
\(861\) | 57.6062 | 1.96321 | ||||||||
\(862\) | 44.2158i | 1.50600i | ||||||||
\(863\) | − | 27.1254i | − | 0.923359i | −0.887047 | − | 0.461680i | \(-0.847247\pi\) | ||
0.887047 | − | 0.461680i | \(-0.152753\pi\) | |||||||
\(864\) | −0.437660 | −0.0148895 | ||||||||
\(865\) | 26.1762 | + | 1.31263i | 0.890017 | + | 0.0446309i | ||||
\(866\) | 10.0580 | 0.341785 | ||||||||
\(867\) | − | 57.3558i | − | 1.94791i | ||||||
\(868\) | 1.69716i | 0.0576052i | ||||||||
\(869\) | 2.92335 | 0.0991680 | ||||||||
\(870\) | −0.139607 | + | 2.78400i | −0.00473312 | + | 0.0943864i | ||||
\(871\) | 15.2589 | 0.517027 | ||||||||
\(872\) | 8.63321i | 0.292358i | ||||||||
\(873\) | − | 41.7973i | − | 1.41462i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.9250 | − | 5.44102i | −1.21449 | − | 0.183940i | ||||
\(876\) | −0.850447 | −0.0287339 | ||||||||
\(877\) | 49.0823i | 1.65739i | 0.559700 | + | 0.828695i | \(0.310916\pi\) | ||||
−0.559700 | + | 0.828695i | \(0.689084\pi\) | |||||||
\(878\) | − | 11.7832i | − | 0.397662i | ||||||
\(879\) | −19.4406 | −0.655714 | ||||||||
\(880\) | 2.03383 | − | 40.5580i | 0.0685602 | − | 1.36721i | ||||
\(881\) | 37.9778 | 1.27951 | 0.639753 | − | 0.768581i | \(-0.279037\pi\) | ||||
0.639753 | + | 0.768581i | \(0.279037\pi\) | |||||||
\(882\) | 16.6812i | 0.561686i | ||||||||
\(883\) | 33.2100i | 1.11761i | 0.829300 | + | 0.558803i | \(0.188739\pi\) | ||||
−0.829300 | + | 0.558803i | \(0.811261\pi\) | |||||||
\(884\) | −2.12328 | −0.0714137 | ||||||||
\(885\) | −17.4279 | − | 0.873944i | −0.585834 | − | 0.0293773i | ||||
\(886\) | −32.2301 | −1.08279 | ||||||||
\(887\) | − | 26.2525i | − | 0.881474i | −0.897636 | − | 0.440737i | \(-0.854717\pi\) | ||
0.897636 | − | 0.440737i | \(-0.145283\pi\) | |||||||
\(888\) | − | 18.0029i | − | 0.604136i | ||||||
\(889\) | 1.92396 | 0.0645277 | ||||||||
\(890\) | −22.5577 | − | 1.13118i | −0.756137 | − | 0.0379174i | ||||
\(891\) | 35.4526 | 1.18771 | ||||||||
\(892\) | − | 1.67222i | − | 0.0559902i | ||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −54.8808 | −1.83549 | ||||||||
\(895\) | −0.793309 | + | 15.8199i | −0.0265174 | + | 0.528802i | ||||
\(896\) | 41.0839 | 1.37252 | ||||||||
\(897\) | − | 6.35172i | − | 0.212078i | ||||||
\(898\) | − | 27.7843i | − | 0.927173i | ||||||
\(899\) | −0.943045 | −0.0314523 | ||||||||
\(900\) | −2.96047 | − | 0.297661i | −0.0986825 | − | 0.00992204i | ||||
\(901\) | −45.8287 | −1.52677 | ||||||||
\(902\) | 44.1772i | 1.47094i | ||||||||
\(903\) | − | 79.8477i | − | 2.65716i | ||||||
\(904\) | −12.6246 | −0.419888 | ||||||||
\(905\) | 1.03946 | − | 20.7286i | 0.0345528 | − | 0.689043i | ||||
\(906\) | −48.2731 | −1.60377 | ||||||||
\(907\) | − | 7.92760i | − | 0.263231i | −0.991301 | − | 0.131616i | \(-0.957983\pi\) | ||
0.991301 | − | 0.131616i | \(-0.0420165\pi\) | |||||||
\(908\) | − | 4.96315i | − | 0.164708i | ||||||
\(909\) | −54.7002 | −1.81429 | ||||||||
\(910\) | −19.1537 | − | 0.960482i | −0.634938 | − | 0.0318397i | ||||
\(911\) | −0.619746 | −0.0205331 | −0.0102665 | − | 0.999947i | \(-0.503268\pi\) | ||||
−0.0102665 | + | 0.999947i | \(0.503268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.31369i | 0.0765718i | ||||||||
\(914\) | −41.7670 | −1.38153 | ||||||||
\(915\) | −17.0009 | − | 0.852527i | −0.562031 | − | 0.0281837i | ||||
\(916\) | 4.09434 | 0.135281 | ||||||||
\(917\) | − | 66.7818i | − | 2.20533i | ||||||
\(918\) | − | 3.86824i | − | 0.127671i | ||||||
\(919\) | 35.0574 | 1.15644 | 0.578219 | − | 0.815882i | \(-0.303748\pi\) | ||||
0.578219 | + | 0.815882i | \(0.303748\pi\) | |||||||
\(920\) | −0.430346 | + | 8.58184i | −0.0141881 | + | 0.282935i | ||||
\(921\) | 39.0226 | 1.28584 | ||||||||
\(922\) | − | 0.289929i | − | 0.00954830i | ||||||
\(923\) | 23.0025i | 0.757135i | ||||||||
\(924\) | −6.34588 | −0.208764 | ||||||||
\(925\) | 1.35296 | − | 13.4563i | 0.0444851 | − | 0.442439i | ||||
\(926\) | 20.6553 | 0.678775 | ||||||||
\(927\) | − | 43.7857i | − | 1.43811i | ||||||
\(928\) | − | 0.359665i | − | 0.0118066i | ||||||
\(929\) | −12.0434 | −0.395132 | −0.197566 | − | 0.980290i | \(-0.563304\pi\) | ||||
−0.197566 | + | 0.980290i | \(0.563304\pi\) | |||||||
\(930\) | 1.14299 | − | 22.7931i | 0.0374800 | − | 0.747416i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 1.87959i | − | 0.0615679i | ||||||
\(933\) | 44.6511i | 1.46181i | ||||||||
\(934\) | 47.4850 | 1.55376 | ||||||||
\(935\) | 59.1683 | + | 2.96706i | 1.93501 | + | 0.0970333i | ||||
\(936\) | 15.1416 | 0.494918 | ||||||||
\(937\) | − | 14.9304i | − | 0.487757i | −0.969806 | − | 0.243878i | \(-0.921580\pi\) | ||
0.969806 | − | 0.243878i | \(-0.0784197\pi\) | |||||||
\(938\) | 41.1131i | 1.34239i | ||||||||
\(939\) | 52.6452 | 1.71801 | ||||||||
\(940\) | −0.186961 | − | 0.00937539i | −0.00609800 | − | 0.000305792i | ||||
\(941\) | 19.4198 | 0.633068 | 0.316534 | − | 0.948581i | \(-0.397481\pi\) | ||||
0.316534 | + | 0.948581i | \(0.397481\pi\) | |||||||
\(942\) | 39.8059i | 1.29695i | ||||||||
\(943\) | − | 10.2339i | − | 0.333261i | ||||||
\(944\) | 13.6408 | 0.443970 | ||||||||
\(945\) | 0.150308 | − | 2.99739i | 0.00488951 | − | 0.0975052i | ||||
\(946\) | 61.2338 | 1.99088 | ||||||||
\(947\) | − | 16.7369i | − | 0.543878i | −0.962315 | − | 0.271939i | \(-0.912335\pi\) | ||
0.962315 | − | 0.271939i | \(-0.0876648\pi\) | |||||||
\(948\) | 0.326081i | 0.0105906i | ||||||||
\(949\) | 3.25117 | 0.105538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.60959 | −0.246758 | ||||||||
\(952\) | 55.1589i | 1.78771i | ||||||||
\(953\) | − | 53.1772i | − | 1.72258i | −0.508114 | − | 0.861290i | \(-0.669657\pi\) | ||
0.508114 | − | 0.861290i | \(-0.330343\pi\) | |||||||
\(954\) | −33.8962 | −1.09743 | ||||||||
\(955\) | 0.909831 | − | 18.1436i | 0.0294414 | − | 0.587113i | ||||
\(956\) | 3.35220 | 0.108418 | ||||||||
\(957\) | − | 3.52616i | − | 0.113985i | ||||||
\(958\) | 2.93209i | 0.0947317i | ||||||||
\(959\) | 28.4496 | 0.918686 | ||||||||
\(960\) | −39.4495 | − | 1.97824i | −1.27323 | − | 0.0638474i | ||||
\(961\) | −23.2791 | −0.750939 | ||||||||
\(962\) | − | 7.13812i | − | 0.230142i | ||||||
\(963\) | − | 10.3367i | − | 0.333096i | ||||||
\(964\) | 3.22209 | 0.103777 | ||||||||
\(965\) | 17.2484 | + | 0.864942i | 0.555247 | + | 0.0278435i | ||||
\(966\) | 17.1139 | 0.550630 | ||||||||
\(967\) | − | 30.0281i | − | 0.965637i | −0.875720 | − | 0.482819i | \(-0.839613\pi\) | ||
0.875720 | − | 0.482819i | \(-0.160387\pi\) | |||||||
\(968\) | 17.4377i | 0.560469i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.18670 | + | 43.6065i | −0.0702107 | + | 1.40012i | ||||
\(971\) | 24.1413 | 0.774732 | 0.387366 | − | 0.921926i | \(-0.373385\pi\) | ||||
0.387366 | + | 0.921926i | \(0.373385\pi\) | |||||||
\(972\) | 4.18736i | 0.134310i | ||||||||
\(973\) | − | 24.9896i | − | 0.801128i | ||||||
\(974\) | −12.7048 | −0.407089 | ||||||||
\(975\) | 22.0407 | + | 2.21609i | 0.705869 | + | 0.0709717i | ||||
\(976\) | 13.3065 | 0.425931 | ||||||||
\(977\) | 9.57680i | 0.306389i | 0.988196 | + | 0.153195i | \(0.0489561\pi\) | ||||
−0.988196 | + | 0.153195i | \(0.951044\pi\) | |||||||
\(978\) | − | 31.0211i | − | 0.991947i | ||||||
\(979\) | 28.5712 | 0.913140 | ||||||||
\(980\) | 0.0749645 | − | 1.49492i | 0.00239465 | − | 0.0477535i | ||||
\(981\) | −10.1985 | −0.325613 | ||||||||
\(982\) | 38.3108i | 1.22255i | ||||||||
\(983\) | 31.1715i | 0.994216i | 0.867689 | + | 0.497108i | \(0.165605\pi\) | ||||
−0.867689 | + | 0.497108i | \(0.834395\pi\) | |||||||
\(984\) | 47.5108 | 1.51459 | ||||||||
\(985\) | −7.96743 | − | 0.399536i | −0.253864 | − | 0.0127303i | ||||
\(986\) | 3.17889 | 0.101236 | ||||||||
\(987\) | − | 3.59476i | − | 0.114422i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.1851 | −0.451061 | ||||||||
\(990\) | 43.7625 | + | 2.19452i | 1.39086 | + | 0.0697464i | ||||
\(991\) | −48.6643 | −1.54587 | −0.772937 | − | 0.634483i | \(-0.781213\pi\) | ||||
−0.772937 | + | 0.634483i | \(0.781213\pi\) | |||||||
\(992\) | 2.94464i | 0.0934925i | ||||||||
\(993\) | − | 64.4414i | − | 2.04499i | ||||||
\(994\) | −61.9771 | −1.96580 | ||||||||
\(995\) | 0.982078 | − | 19.5843i | 0.0311340 | − | 0.620865i | ||||
\(996\) | −0.258076 | −0.00817746 | ||||||||
\(997\) | − | 31.8954i | − | 1.01014i | −0.863080 | − | 0.505068i | \(-0.831467\pi\) | ||
0.863080 | − | 0.505068i | \(-0.168533\pi\) | |||||||
\(998\) | 31.3641i | 0.992812i | ||||||||
\(999\) | 1.11706 | 0.0353422 |
(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 | 1805.2.b.k.1084.18 | 24 | ||
5.2 | odd | 4 | 9025.2.a.cu.1.7 | 24 | |||
5.3 | odd | 4 | 9025.2.a.cu.1.18 | 24 | |||
5.4 | even | 2 | inner | 1805.2.b.k.1084.7 | 24 | ||
19.6 | even | 9 | 95.2.p.a.74.7 | yes | 48 | ||
19.16 | even | 9 | 95.2.p.a.9.2 | ✓ | 48 | ||
19.18 | odd | 2 | 1805.2.b.l.1084.7 | 24 | |||
57.35 | odd | 18 | 855.2.da.b.199.7 | 48 | |||
57.44 | odd | 18 | 855.2.da.b.739.2 | 48 | |||
95.18 | even | 4 | 9025.2.a.ct.1.7 | 24 | |||
95.37 | even | 4 | 9025.2.a.ct.1.18 | 24 | |||
95.44 | even | 18 | 95.2.p.a.74.2 | yes | 48 | ||
95.54 | even | 18 | 95.2.p.a.9.7 | yes | 48 | ||
95.63 | odd | 36 | 475.2.l.f.226.7 | 48 | |||
95.73 | odd | 36 | 475.2.l.f.351.7 | 48 | |||
95.82 | odd | 36 | 475.2.l.f.226.2 | 48 | |||
95.92 | odd | 36 | 475.2.l.f.351.2 | 48 | |||
95.94 | odd | 2 | 1805.2.b.l.1084.18 | 24 | |||
285.44 | odd | 18 | 855.2.da.b.739.7 | 48 | |||
285.149 | odd | 18 | 855.2.da.b.199.2 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.p.a.9.2 | ✓ | 48 | 19.16 | even | 9 | ||
95.2.p.a.9.7 | yes | 48 | 95.54 | even | 18 | ||
95.2.p.a.74.2 | yes | 48 | 95.44 | even | 18 | ||
95.2.p.a.74.7 | yes | 48 | 19.6 | even | 9 | ||
475.2.l.f.226.2 | 48 | 95.82 | odd | 36 | |||
475.2.l.f.226.7 | 48 | 95.63 | odd | 36 | |||
475.2.l.f.351.2 | 48 | 95.92 | odd | 36 | |||
475.2.l.f.351.7 | 48 | 95.73 | odd | 36 | |||
855.2.da.b.199.2 | 48 | 285.149 | odd | 18 | |||
855.2.da.b.199.7 | 48 | 57.35 | odd | 18 | |||
855.2.da.b.739.2 | 48 | 57.44 | odd | 18 | |||
855.2.da.b.739.7 | 48 | 285.44 | odd | 18 | |||
1805.2.b.k.1084.7 | 24 | 5.4 | even | 2 | inner | ||
1805.2.b.k.1084.18 | 24 | 1.1 | even | 1 | trivial | ||
1805.2.b.l.1084.7 | 24 | 19.18 | odd | 2 | |||
1805.2.b.l.1084.18 | 24 | 95.94 | odd | 2 | |||
9025.2.a.ct.1.7 | 24 | 95.18 | even | 4 | |||
9025.2.a.ct.1.18 | 24 | 95.37 | even | 4 | |||
9025.2.a.cu.1.7 | 24 | 5.2 | odd | 4 | |||
9025.2.a.cu.1.18 | 24 | 5.3 | odd | 4 |