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: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 26x^{16} + 281x^{14} - 1632x^{12} + 5482x^{10} - 10620x^{8} + 11052x^{6} - 5165x^{4} + 760x^{2} - 29 \) |
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 | 1.8 | ||
Root | \(-0.395078\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.395078 | −0.279362 | −0.139681 | − | 0.990197i | \(-0.544608\pi\) | ||||
−0.139681 | + | 0.990197i | \(0.544608\pi\) | |||||||
\(3\) | −2.73651 | −1.57992 | −0.789961 | − | 0.613157i | \(-0.789899\pi\) | ||||
−0.789961 | + | 0.613157i | \(0.789899\pi\) | |||||||
\(4\) | −1.84391 | −0.921957 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.08113 | 0.441371 | ||||||||
\(7\) | −0.629405 | −0.237893 | −0.118946 | − | 0.992901i | \(-0.537952\pi\) | ||||
−0.118946 | + | 0.992901i | \(0.537952\pi\) | |||||||
\(8\) | 1.51865 | 0.536922 | ||||||||
\(9\) | 4.48846 | 1.49615 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.49747 | −1.65755 | −0.828775 | − | 0.559582i | \(-0.810962\pi\) | ||||
−0.828775 | + | 0.559582i | \(0.810962\pi\) | |||||||
\(12\) | 5.04588 | 1.45662 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.248664 | 0.0664583 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.08784 | 0.771961 | ||||||||
\(17\) | 4.25364 | 1.03166 | 0.515830 | − | 0.856691i | \(-0.327484\pi\) | ||||
0.515830 | + | 0.856691i | \(0.327484\pi\) | |||||||
\(18\) | −1.77329 | −0.417969 | ||||||||
\(19\) | −3.61686 | −0.829765 | −0.414883 | − | 0.909875i | \(-0.636177\pi\) | ||||
−0.414883 | + | 0.909875i | \(0.636177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.72237 | 0.375852 | ||||||||
\(22\) | 2.17193 | 0.463057 | ||||||||
\(23\) | −7.05869 | −1.47184 | −0.735919 | − | 0.677069i | \(-0.763250\pi\) | ||||
−0.735919 | + | 0.677069i | \(0.763250\pi\) | |||||||
\(24\) | −4.15578 | −0.848296 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.07319 | −0.783885 | ||||||||
\(28\) | 1.16057 | 0.219327 | ||||||||
\(29\) | 2.09557 | 0.389137 | 0.194568 | − | 0.980889i | \(-0.437669\pi\) | ||||
0.194568 | + | 0.980889i | \(0.437669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.97582 | −0.534474 | −0.267237 | − | 0.963631i | \(-0.586111\pi\) | ||||
−0.267237 | + | 0.963631i | \(0.586111\pi\) | |||||||
\(32\) | −4.25723 | −0.752579 | ||||||||
\(33\) | 15.0439 | 2.61880 | ||||||||
\(34\) | −1.68052 | −0.288207 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.27634 | −1.37939 | ||||||||
\(37\) | −0.817814 | −0.134448 | −0.0672239 | − | 0.997738i | \(-0.521414\pi\) | ||||
−0.0672239 | + | 0.997738i | \(0.521414\pi\) | |||||||
\(38\) | 1.42894 | 0.231805 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.89390 | 0.764298 | 0.382149 | − | 0.924101i | \(-0.375184\pi\) | ||||
0.382149 | + | 0.924101i | \(0.375184\pi\) | |||||||
\(42\) | −0.680471 | −0.104999 | ||||||||
\(43\) | 9.91411 | 1.51189 | 0.755944 | − | 0.654636i | \(-0.227178\pi\) | ||||
0.755944 | + | 0.654636i | \(0.227178\pi\) | |||||||
\(44\) | 10.1369 | 1.52819 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.78873 | 0.411176 | ||||||||
\(47\) | 2.29494 | 0.334751 | 0.167375 | − | 0.985893i | \(-0.446471\pi\) | ||||
0.167375 | + | 0.985893i | \(0.446471\pi\) | |||||||
\(48\) | −8.44990 | −1.21964 | ||||||||
\(49\) | −6.60385 | −0.943407 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.6401 | −1.62994 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.84288 | 0.802581 | 0.401291 | − | 0.915951i | \(-0.368562\pi\) | ||||
0.401291 | + | 0.915951i | \(0.368562\pi\) | |||||||
\(54\) | 1.60923 | 0.218988 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.955844 | −0.127730 | ||||||||
\(57\) | 9.89756 | 1.31096 | ||||||||
\(58\) | −0.827912 | −0.108710 | ||||||||
\(59\) | −5.19393 | −0.676192 | −0.338096 | − | 0.941112i | \(-0.609783\pi\) | ||||
−0.338096 | + | 0.941112i | \(0.609783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.92410 | 0.758503 | 0.379252 | − | 0.925294i | \(-0.376181\pi\) | ||||
0.379252 | + | 0.925294i | \(0.376181\pi\) | |||||||
\(62\) | 1.17568 | 0.149312 | ||||||||
\(63\) | −2.82506 | −0.355924 | ||||||||
\(64\) | −4.49375 | −0.561718 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.94350 | −0.731595 | ||||||||
\(67\) | 13.7031 | 1.67410 | 0.837052 | − | 0.547124i | \(-0.184277\pi\) | ||||
0.837052 | + | 0.547124i | \(0.184277\pi\) | |||||||
\(68\) | −7.84335 | −0.951146 | ||||||||
\(69\) | 19.3161 | 2.32539 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.210677 | −0.0250028 | −0.0125014 | − | 0.999922i | \(-0.503979\pi\) | ||||
−0.0125014 | + | 0.999922i | \(0.503979\pi\) | |||||||
\(72\) | 6.81639 | 0.803319 | ||||||||
\(73\) | 12.4282 | 1.45461 | 0.727306 | − | 0.686314i | \(-0.240772\pi\) | ||||
0.727306 | + | 0.686314i | \(0.240772\pi\) | |||||||
\(74\) | 0.323100 | 0.0375596 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.66918 | 0.765007 | ||||||||
\(77\) | 3.46014 | 0.394319 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.19084 | −0.809032 | −0.404516 | − | 0.914531i | \(-0.632560\pi\) | ||||
−0.404516 | + | 0.914531i | \(0.632560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.31909 | −0.257677 | ||||||||
\(82\) | −1.93347 | −0.213516 | ||||||||
\(83\) | 6.61897 | 0.726526 | 0.363263 | − | 0.931687i | \(-0.381663\pi\) | ||||
0.363263 | + | 0.931687i | \(0.381663\pi\) | |||||||
\(84\) | −3.17590 | −0.346519 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.91685 | −0.422365 | ||||||||
\(87\) | −5.73453 | −0.614806 | ||||||||
\(88\) | −8.34872 | −0.889976 | ||||||||
\(89\) | −3.66109 | −0.388074 | −0.194037 | − | 0.980994i | \(-0.562158\pi\) | ||||
−0.194037 | + | 0.980994i | \(0.562158\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 13.0156 | 1.35697 | ||||||||
\(93\) | 8.14336 | 0.844427 | ||||||||
\(94\) | −0.906679 | −0.0935168 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 11.6499 | 1.18902 | ||||||||
\(97\) | 4.54596 | 0.461573 | 0.230786 | − | 0.973004i | \(-0.425870\pi\) | ||||
0.230786 | + | 0.973004i | \(0.425870\pi\) | |||||||
\(98\) | 2.60904 | 0.263552 | ||||||||
\(99\) | −24.6752 | −2.47995 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.5652 | 1.05128 | 0.525639 | − | 0.850708i | \(-0.323826\pi\) | ||||
0.525639 | + | 0.850708i | \(0.323826\pi\) | |||||||
\(102\) | 4.59876 | 0.455345 | ||||||||
\(103\) | 8.11584 | 0.799677 | 0.399839 | − | 0.916586i | \(-0.369066\pi\) | ||||
0.399839 | + | 0.916586i | \(0.369066\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.30839 | −0.224211 | ||||||||
\(107\) | 4.75614 | 0.459793 | 0.229897 | − | 0.973215i | \(-0.426161\pi\) | ||||
0.229897 | + | 0.973215i | \(0.426161\pi\) | |||||||
\(108\) | 7.51060 | 0.722708 | ||||||||
\(109\) | −2.23043 | −0.213636 | −0.106818 | − | 0.994279i | \(-0.534066\pi\) | ||||
−0.106818 | + | 0.994279i | \(0.534066\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.23795 | 0.212417 | ||||||||
\(112\) | −1.94350 | −0.183644 | ||||||||
\(113\) | 6.66337 | 0.626837 | 0.313419 | − | 0.949615i | \(-0.398526\pi\) | ||||
0.313419 | + | 0.949615i | \(0.398526\pi\) | |||||||
\(114\) | −3.91031 | −0.366234 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.86404 | −0.358767 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.05201 | 0.188903 | ||||||||
\(119\) | −2.67726 | −0.245424 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 19.2222 | 1.74747 | ||||||||
\(122\) | −2.34048 | −0.211897 | ||||||||
\(123\) | −13.3922 | −1.20753 | ||||||||
\(124\) | 5.48716 | 0.492761 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.11612 | 0.0994319 | ||||||||
\(127\) | −10.6090 | −0.941398 | −0.470699 | − | 0.882294i | \(-0.655998\pi\) | ||||
−0.470699 | + | 0.882294i | \(0.655998\pi\) | |||||||
\(128\) | 10.2898 | 0.909502 | ||||||||
\(129\) | −27.1300 | −2.38867 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.888454 | 0.0776246 | 0.0388123 | − | 0.999247i | \(-0.487643\pi\) | ||||
0.0388123 | + | 0.999247i | \(0.487643\pi\) | |||||||
\(132\) | −27.7396 | −2.41442 | ||||||||
\(133\) | 2.27647 | 0.197395 | ||||||||
\(134\) | −5.41380 | −0.467682 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.45978 | 0.553921 | ||||||||
\(137\) | −2.66255 | −0.227477 | −0.113738 | − | 0.993511i | \(-0.536283\pi\) | ||||
−0.113738 | + | 0.993511i | \(0.536283\pi\) | |||||||
\(138\) | −7.63138 | −0.649627 | ||||||||
\(139\) | 13.9094 | 1.17978 | 0.589892 | − | 0.807482i | \(-0.299170\pi\) | ||||
0.589892 | + | 0.807482i | \(0.299170\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.28011 | −0.528880 | ||||||||
\(142\) | 0.0832340 | 0.00698484 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.8597 | 1.15497 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.91011 | −0.406364 | ||||||||
\(147\) | 18.0715 | 1.49051 | ||||||||
\(148\) | 1.50798 | 0.123955 | ||||||||
\(149\) | −11.4154 | −0.935186 | −0.467593 | − | 0.883944i | \(-0.654879\pi\) | ||||
−0.467593 | + | 0.883944i | \(0.654879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1691 | −1.07169 | −0.535843 | − | 0.844317i | \(-0.680006\pi\) | ||||
−0.535843 | + | 0.844317i | \(0.680006\pi\) | |||||||
\(152\) | −5.49273 | −0.445519 | ||||||||
\(153\) | 19.0923 | 1.54352 | ||||||||
\(154\) | −1.36702 | −0.110158 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.24976 | −0.578593 | −0.289297 | − | 0.957239i | \(-0.593421\pi\) | ||||
−0.289297 | + | 0.957239i | \(0.593421\pi\) | |||||||
\(158\) | 2.84094 | 0.226013 | ||||||||
\(159\) | −15.9891 | −1.26802 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.44277 | 0.350140 | ||||||||
\(162\) | 0.916221 | 0.0719851 | ||||||||
\(163\) | −14.3271 | −1.12218 | −0.561091 | − | 0.827754i | \(-0.689618\pi\) | ||||
−0.561091 | + | 0.827754i | \(0.689618\pi\) | |||||||
\(164\) | −9.02392 | −0.704650 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.61501 | −0.202964 | ||||||||
\(167\) | −18.1705 | −1.40608 | −0.703038 | − | 0.711152i | \(-0.748174\pi\) | ||||
−0.703038 | + | 0.711152i | \(0.748174\pi\) | |||||||
\(168\) | 2.61567 | 0.201803 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.2342 | −1.24146 | ||||||||
\(172\) | −18.2808 | −1.39390 | ||||||||
\(173\) | −13.3976 | −1.01860 | −0.509300 | − | 0.860589i | \(-0.670095\pi\) | ||||
−0.509300 | + | 0.860589i | \(0.670095\pi\) | |||||||
\(174\) | 2.26559 | 0.171754 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.9753 | −1.27956 | ||||||||
\(177\) | 14.2132 | 1.06833 | ||||||||
\(178\) | 1.44642 | 0.108413 | ||||||||
\(179\) | −4.87440 | −0.364330 | −0.182165 | − | 0.983268i | \(-0.558310\pi\) | ||||
−0.182165 | + | 0.983268i | \(0.558310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.6211 | 1.60708 | 0.803541 | − | 0.595249i | \(-0.202947\pi\) | ||||
0.803541 | + | 0.595249i | \(0.202947\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.2113 | −1.19838 | ||||||||
\(184\) | −10.7196 | −0.790263 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.21726 | −0.235901 | ||||||||
\(187\) | −23.3843 | −1.71003 | ||||||||
\(188\) | −4.23166 | −0.308626 | ||||||||
\(189\) | 2.56369 | 0.186481 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.40566 | 0.246425 | 0.123212 | − | 0.992380i | \(-0.460680\pi\) | ||||
0.123212 | + | 0.992380i | \(0.460680\pi\) | |||||||
\(192\) | 12.2972 | 0.887471 | ||||||||
\(193\) | −12.8482 | −0.924832 | −0.462416 | − | 0.886663i | \(-0.653017\pi\) | ||||
−0.462416 | + | 0.886663i | \(0.653017\pi\) | |||||||
\(194\) | −1.79601 | −0.128946 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.1769 | 0.869780 | ||||||||
\(197\) | 6.29884 | 0.448774 | 0.224387 | − | 0.974500i | \(-0.427962\pi\) | ||||
0.224387 | + | 0.974500i | \(0.427962\pi\) | |||||||
\(198\) | 9.74863 | 0.692805 | ||||||||
\(199\) | 5.91708 | 0.419451 | 0.209725 | − | 0.977760i | \(-0.432743\pi\) | ||||
0.209725 | + | 0.977760i | \(0.432743\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −37.4987 | −2.64495 | ||||||||
\(202\) | −4.17408 | −0.293687 | ||||||||
\(203\) | −1.31896 | −0.0925728 | ||||||||
\(204\) | 21.4634 | 1.50274 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.20639 | −0.223400 | ||||||||
\(207\) | −31.6827 | −2.20210 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.8836 | 1.37538 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4670 | 0.720578 | 0.360289 | − | 0.932841i | \(-0.382678\pi\) | ||||
0.360289 | + | 0.932841i | \(0.382678\pi\) | |||||||
\(212\) | −10.7738 | −0.739945 | ||||||||
\(213\) | 0.576520 | 0.0395025 | ||||||||
\(214\) | −1.87905 | −0.128449 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.18573 | −0.420886 | ||||||||
\(217\) | 1.87300 | 0.127147 | ||||||||
\(218\) | 0.881193 | 0.0596819 | ||||||||
\(219\) | −34.0099 | −2.29817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −0.884166 | −0.0593413 | ||||||||
\(223\) | −11.0759 | −0.741696 | −0.370848 | − | 0.928693i | \(-0.620933\pi\) | ||||
−0.370848 | + | 0.928693i | \(0.620933\pi\) | |||||||
\(224\) | 2.67952 | 0.179033 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.63255 | −0.175115 | ||||||||
\(227\) | 23.2890 | 1.54574 | 0.772872 | − | 0.634562i | \(-0.218819\pi\) | ||||
0.772872 | + | 0.634562i | \(0.218819\pi\) | |||||||
\(228\) | −18.2502 | −1.20865 | ||||||||
\(229\) | −7.19056 | −0.475166 | −0.237583 | − | 0.971367i | \(-0.576355\pi\) | ||||
−0.237583 | + | 0.971367i | \(0.576355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.46869 | −0.622994 | ||||||||
\(232\) | 3.18242 | 0.208936 | ||||||||
\(233\) | −3.46735 | −0.227154 | −0.113577 | − | 0.993529i | \(-0.536231\pi\) | ||||
−0.113577 | + | 0.993529i | \(0.536231\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.57716 | 0.623420 | ||||||||
\(237\) | 19.6778 | 1.27821 | ||||||||
\(238\) | 1.05773 | 0.0685624 | ||||||||
\(239\) | 18.4358 | 1.19251 | 0.596255 | − | 0.802795i | \(-0.296655\pi\) | ||||
0.596255 | + | 0.802795i | \(0.296655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.22700 | 0.529948 | 0.264974 | − | 0.964256i | \(-0.414637\pi\) | ||||
0.264974 | + | 0.964256i | \(0.414637\pi\) | |||||||
\(242\) | −7.59427 | −0.488178 | ||||||||
\(243\) | 18.5658 | 1.19099 | ||||||||
\(244\) | −10.9235 | −0.699307 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.29096 | 0.337339 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.51922 | −0.286971 | ||||||||
\(249\) | −18.1129 | −1.14786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.0068 | −1.83089 | −0.915446 | − | 0.402442i | \(-0.868162\pi\) | ||||
−0.915446 | + | 0.402442i | \(0.868162\pi\) | |||||||
\(252\) | 5.20917 | 0.328147 | ||||||||
\(253\) | 38.8049 | 2.43965 | ||||||||
\(254\) | 4.19139 | 0.262991 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.92220 | 0.307638 | ||||||||
\(257\) | −11.3098 | −0.705488 | −0.352744 | − | 0.935720i | \(-0.614751\pi\) | ||||
−0.352744 | + | 0.935720i | \(0.614751\pi\) | |||||||
\(258\) | 10.7185 | 0.667303 | ||||||||
\(259\) | 0.514736 | 0.0319841 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.40587 | 0.582209 | ||||||||
\(262\) | −0.351009 | −0.0216854 | ||||||||
\(263\) | 14.9504 | 0.921882 | 0.460941 | − | 0.887431i | \(-0.347512\pi\) | ||||
0.460941 | + | 0.887431i | \(0.347512\pi\) | |||||||
\(264\) | 22.8463 | 1.40609 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.899384 | −0.0551448 | ||||||||
\(267\) | 10.0186 | 0.613127 | ||||||||
\(268\) | −25.2674 | −1.54345 | ||||||||
\(269\) | −19.1369 | −1.16680 | −0.583398 | − | 0.812187i | \(-0.698277\pi\) | ||||
−0.583398 | + | 0.812187i | \(0.698277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.95487 | −0.483224 | −0.241612 | − | 0.970373i | \(-0.577676\pi\) | ||||
−0.241612 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(272\) | 13.1346 | 0.796401 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.05191 | 0.0635484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −35.6173 | −2.14391 | ||||||||
\(277\) | −32.0550 | −1.92600 | −0.963000 | − | 0.269502i | \(-0.913141\pi\) | ||||
−0.963000 | + | 0.269502i | \(0.913141\pi\) | |||||||
\(278\) | −5.49532 | −0.329587 | ||||||||
\(279\) | −13.3569 | −0.799655 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1240 | −0.902221 | −0.451110 | − | 0.892468i | \(-0.648972\pi\) | ||||
−0.451110 | + | 0.892468i | \(0.648972\pi\) | |||||||
\(282\) | 2.48113 | 0.147749 | ||||||||
\(283\) | 12.0333 | 0.715306 | 0.357653 | − | 0.933855i | \(-0.383577\pi\) | ||||
0.357653 | + | 0.933855i | \(0.383577\pi\) | |||||||
\(284\) | 0.388471 | 0.0230515 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.08024 | −0.181821 | ||||||||
\(288\) | −19.1084 | −1.12597 | ||||||||
\(289\) | 1.09348 | 0.0643224 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.4401 | −0.729249 | ||||||||
\(292\) | −22.9165 | −1.34109 | ||||||||
\(293\) | −23.1522 | −1.35257 | −0.676283 | − | 0.736642i | \(-0.736410\pi\) | ||||
−0.676283 | + | 0.736642i | \(0.736410\pi\) | |||||||
\(294\) | −7.13964 | −0.416392 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.24197 | −0.0721880 | ||||||||
\(297\) | 22.3922 | 1.29933 | ||||||||
\(298\) | 4.50997 | 0.261256 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.23999 | −0.359667 | ||||||||
\(302\) | 5.20283 | 0.299389 | ||||||||
\(303\) | −28.9117 | −1.66094 | ||||||||
\(304\) | −11.1683 | −0.640546 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −7.54296 | −0.431202 | ||||||||
\(307\) | −24.6921 | −1.40925 | −0.704627 | − | 0.709578i | \(-0.748886\pi\) | ||||
−0.704627 | + | 0.709578i | \(0.748886\pi\) | |||||||
\(308\) | −6.38019 | −0.363545 | ||||||||
\(309\) | −22.2090 | −1.26343 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.8313 | −1.06782 | −0.533912 | − | 0.845540i | \(-0.679279\pi\) | ||||
−0.533912 | + | 0.845540i | \(0.679279\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.10639 | 0.345154 | 0.172577 | − | 0.984996i | \(-0.444791\pi\) | ||||
0.172577 | + | 0.984996i | \(0.444791\pi\) | |||||||
\(314\) | 2.86422 | 0.161637 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.2593 | 0.745893 | ||||||||
\(317\) | 8.97504 | 0.504088 | 0.252044 | − | 0.967716i | \(-0.418897\pi\) | ||||
0.252044 | + | 0.967716i | \(0.418897\pi\) | |||||||
\(318\) | 6.31693 | 0.354236 | ||||||||
\(319\) | −11.5203 | −0.645014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.0152 | −0.726437 | ||||||||
\(322\) | −1.75524 | −0.0978159 | ||||||||
\(323\) | −15.3848 | −0.856035 | ||||||||
\(324\) | 4.27620 | 0.237567 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.66031 | 0.313495 | ||||||||
\(327\) | 6.10358 | 0.337529 | ||||||||
\(328\) | 7.43210 | 0.410369 | ||||||||
\(329\) | −1.44445 | −0.0796348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.89045 | −0.433698 | −0.216849 | − | 0.976205i | \(-0.569578\pi\) | ||||
−0.216849 | + | 0.976205i | \(0.569578\pi\) | |||||||
\(332\) | −12.2048 | −0.669826 | ||||||||
\(333\) | −3.67073 | −0.201155 | ||||||||
\(334\) | 7.17877 | 0.392805 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.31841 | 0.290143 | ||||||||
\(337\) | −0.643374 | −0.0350468 | −0.0175234 | − | 0.999846i | \(-0.505578\pi\) | ||||
−0.0175234 | + | 0.999846i | \(0.505578\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.2344 | −0.990354 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.3595 | 0.885917 | ||||||||
\(342\) | 6.41376 | 0.346816 | ||||||||
\(343\) | 8.56233 | 0.462323 | ||||||||
\(344\) | 15.0560 | 0.811767 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.29309 | 0.284558 | ||||||||
\(347\) | 14.2788 | 0.766527 | 0.383264 | − | 0.923639i | \(-0.374800\pi\) | ||||
0.383264 | + | 0.923639i | \(0.374800\pi\) | |||||||
\(348\) | 10.5740 | 0.566824 | ||||||||
\(349\) | 22.5207 | 1.20551 | 0.602753 | − | 0.797927i | \(-0.294070\pi\) | ||||
0.602753 | + | 0.797927i | \(0.294070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.4040 | 1.24744 | ||||||||
\(353\) | 1.49751 | 0.0797047 | 0.0398523 | − | 0.999206i | \(-0.487311\pi\) | ||||
0.0398523 | + | 0.999206i | \(0.487311\pi\) | |||||||
\(354\) | −5.61533 | −0.298452 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.75073 | 0.357788 | ||||||||
\(357\) | 7.32635 | 0.387752 | ||||||||
\(358\) | 1.92577 | 0.101780 | ||||||||
\(359\) | −31.3295 | −1.65351 | −0.826753 | − | 0.562566i | \(-0.809814\pi\) | ||||
−0.826753 | + | 0.562566i | \(0.809814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.91831 | −0.311490 | ||||||||
\(362\) | −8.54202 | −0.448959 | ||||||||
\(363\) | −52.6017 | −2.76087 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.40474 | 0.334781 | ||||||||
\(367\) | 8.02558 | 0.418932 | 0.209466 | − | 0.977816i | \(-0.432827\pi\) | ||||
0.209466 | + | 0.977816i | \(0.432827\pi\) | |||||||
\(368\) | −21.7961 | −1.13620 | ||||||||
\(369\) | 21.9661 | 1.14351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.67754 | −0.190928 | ||||||||
\(372\) | −15.0156 | −0.778525 | ||||||||
\(373\) | −26.3733 | −1.36556 | −0.682778 | − | 0.730626i | \(-0.739228\pi\) | ||||
−0.682778 | + | 0.730626i | \(0.739228\pi\) | |||||||
\(374\) | 9.23862 | 0.477718 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.48520 | 0.179735 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.01286 | −0.0520957 | ||||||||
\(379\) | 28.5043 | 1.46417 | 0.732085 | − | 0.681214i | \(-0.238547\pi\) | ||||
0.732085 | + | 0.681214i | \(0.238547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.0316 | 1.48734 | ||||||||
\(382\) | −1.34550 | −0.0688418 | ||||||||
\(383\) | −14.8547 | −0.759038 | −0.379519 | − | 0.925184i | \(-0.623911\pi\) | ||||
−0.379519 | + | 0.925184i | \(0.623911\pi\) | |||||||
\(384\) | −28.1582 | −1.43694 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.07603 | 0.258363 | ||||||||
\(387\) | 44.4991 | 2.26202 | ||||||||
\(388\) | −8.38236 | −0.425550 | ||||||||
\(389\) | −21.1231 | −1.07098 | −0.535491 | − | 0.844541i | \(-0.679873\pi\) | ||||
−0.535491 | + | 0.844541i | \(0.679873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.0251 | −1.51844 | ||||||||
\(392\) | −10.0289 | −0.506536 | ||||||||
\(393\) | −2.43126 | −0.122641 | ||||||||
\(394\) | −2.48854 | −0.125371 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 45.4989 | 2.28641 | ||||||||
\(397\) | −23.0726 | −1.15798 | −0.578991 | − | 0.815334i | \(-0.696553\pi\) | ||||
−0.578991 | + | 0.815334i | \(0.696553\pi\) | |||||||
\(398\) | −2.33771 | −0.117179 | ||||||||
\(399\) | −6.22958 | −0.311869 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.4998 | 0.774021 | 0.387011 | − | 0.922075i | \(-0.373508\pi\) | ||||
0.387011 | + | 0.922075i | \(0.373508\pi\) | |||||||
\(402\) | 14.8149 | 0.738900 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −19.4813 | −0.969232 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.521092 | 0.0258614 | ||||||||
\(407\) | 4.49591 | 0.222854 | ||||||||
\(408\) | −17.6772 | −0.875153 | ||||||||
\(409\) | −35.7519 | −1.76782 | −0.883908 | − | 0.467661i | \(-0.845097\pi\) | ||||
−0.883908 | + | 0.467661i | \(0.845097\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.28607 | 0.359395 | ||||||||
\(412\) | −14.9649 | −0.737268 | ||||||||
\(413\) | 3.26909 | 0.160861 | ||||||||
\(414\) | 12.5171 | 0.615183 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.0633 | −1.86397 | ||||||||
\(418\) | −7.85558 | −0.384229 | ||||||||
\(419\) | 28.9110 | 1.41239 | 0.706196 | − | 0.708016i | \(-0.250410\pi\) | ||||
0.706196 | + | 0.708016i | \(0.250410\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.1416 | 0.981640 | 0.490820 | − | 0.871261i | \(-0.336697\pi\) | ||||
0.490820 | + | 0.871261i | \(0.336697\pi\) | |||||||
\(422\) | −4.13528 | −0.201302 | ||||||||
\(423\) | 10.3007 | 0.500839 | ||||||||
\(424\) | 8.87327 | 0.430924 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.227770 | −0.0110355 | ||||||||
\(427\) | −3.72866 | −0.180442 | ||||||||
\(428\) | −8.76990 | −0.423909 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.3861 | −1.36731 | −0.683656 | − | 0.729805i | \(-0.739611\pi\) | ||||
−0.683656 | + | 0.729805i | \(0.739611\pi\) | |||||||
\(432\) | −12.5774 | −0.605129 | ||||||||
\(433\) | 4.76509 | 0.228996 | 0.114498 | − | 0.993423i | \(-0.463474\pi\) | ||||
0.114498 | + | 0.993423i | \(0.463474\pi\) | |||||||
\(434\) | −0.739981 | −0.0355202 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.11271 | 0.196963 | ||||||||
\(437\) | 25.5303 | 1.22128 | ||||||||
\(438\) | 13.4365 | 0.642023 | ||||||||
\(439\) | 16.0627 | 0.766630 | 0.383315 | − | 0.923618i | \(-0.374782\pi\) | ||||
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.6411 | −1.41148 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.76501 | 0.273904 | 0.136952 | − | 0.990578i | \(-0.456269\pi\) | ||||
0.136952 | + | 0.990578i | \(0.456269\pi\) | |||||||
\(444\) | −4.12659 | −0.195839 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.37584 | 0.207202 | ||||||||
\(447\) | 31.2383 | 1.47752 | ||||||||
\(448\) | 2.82839 | 0.133629 | ||||||||
\(449\) | 16.4687 | 0.777208 | 0.388604 | − | 0.921405i | \(-0.372957\pi\) | ||||
0.388604 | + | 0.921405i | \(0.372957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.9041 | −1.26686 | ||||||||
\(452\) | −12.2867 | −0.577917 | ||||||||
\(453\) | 36.0373 | 1.69318 | ||||||||
\(454\) | −9.20097 | −0.431823 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.0309 | 0.703886 | ||||||||
\(457\) | 22.3227 | 1.04421 | 0.522106 | − | 0.852880i | \(-0.325146\pi\) | ||||
0.522106 | + | 0.852880i | \(0.325146\pi\) | |||||||
\(458\) | 2.84083 | 0.132743 | ||||||||
\(459\) | −17.3259 | −0.808703 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6864 | 0.544289 | 0.272145 | − | 0.962256i | \(-0.412267\pi\) | ||||
0.272145 | + | 0.962256i | \(0.412267\pi\) | |||||||
\(462\) | 3.74087 | 0.174041 | ||||||||
\(463\) | −13.7716 | −0.640020 | −0.320010 | − | 0.947414i | \(-0.603686\pi\) | ||||
−0.320010 | + | 0.947414i | \(0.603686\pi\) | |||||||
\(464\) | 6.47078 | 0.300398 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.36987 | 0.0634582 | ||||||||
\(467\) | 9.80830 | 0.453874 | 0.226937 | − | 0.973909i | \(-0.427129\pi\) | ||||
0.226937 | + | 0.973909i | \(0.427129\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.62482 | −0.398257 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.8390 | 0.914133 | ||||||||
\(472\) | −7.88774 | −0.363063 | ||||||||
\(473\) | −54.5026 | −2.50603 | ||||||||
\(474\) | −7.77425 | −0.357083 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.93664 | 0.226271 | ||||||||
\(477\) | 26.2255 | 1.20079 | ||||||||
\(478\) | −7.28357 | −0.333143 | ||||||||
\(479\) | −4.30152 | −0.196541 | −0.0982707 | − | 0.995160i | \(-0.531331\pi\) | ||||
−0.0982707 | + | 0.995160i | \(0.531331\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −3.25031 | −0.148048 | ||||||||
\(483\) | −12.1577 | −0.553193 | ||||||||
\(484\) | −35.4441 | −1.61109 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.33493 | −0.332719 | ||||||||
\(487\) | −32.0389 | −1.45182 | −0.725910 | − | 0.687790i | \(-0.758581\pi\) | ||||
−0.725910 | + | 0.687790i | \(0.758581\pi\) | |||||||
\(488\) | 8.99661 | 0.407257 | ||||||||
\(489\) | 39.2061 | 1.77296 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.3710 | 0.738812 | 0.369406 | − | 0.929268i | \(-0.379561\pi\) | ||||
0.369406 | + | 0.929268i | \(0.379561\pi\) | |||||||
\(492\) | 24.6940 | 1.11329 | ||||||||
\(493\) | 8.91379 | 0.401457 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.18887 | −0.412593 | ||||||||
\(497\) | 0.132601 | 0.00594799 | ||||||||
\(498\) | 7.15599 | 0.320668 | ||||||||
\(499\) | −13.4370 | −0.601523 | −0.300761 | − | 0.953699i | \(-0.597241\pi\) | ||||
−0.300761 | + | 0.953699i | \(0.597241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 49.7237 | 2.22149 | ||||||||
\(502\) | 11.4599 | 0.511482 | ||||||||
\(503\) | 12.8188 | 0.571561 | 0.285781 | − | 0.958295i | \(-0.407747\pi\) | ||||
0.285781 | + | 0.958295i | \(0.407747\pi\) | |||||||
\(504\) | −4.29027 | −0.191104 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.3310 | −0.681545 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.5621 | 0.867928 | ||||||||
\(509\) | −4.55682 | −0.201978 | −0.100989 | − | 0.994888i | \(-0.532201\pi\) | ||||
−0.100989 | + | 0.994888i | \(0.532201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.82238 | −0.346042 | ||||||||
\(512\) | −22.5243 | −0.995445 | ||||||||
\(513\) | 14.7322 | 0.650441 | ||||||||
\(514\) | 4.46827 | 0.197087 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 50.0254 | 2.20225 | ||||||||
\(517\) | −12.6164 | −0.554867 | ||||||||
\(518\) | −0.203361 | −0.00893517 | ||||||||
\(519\) | 36.6626 | 1.60931 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.5910 | −1.07735 | −0.538675 | − | 0.842513i | \(-0.681075\pi\) | ||||
−0.538675 | + | 0.842513i | \(0.681075\pi\) | |||||||
\(522\) | −3.71605 | −0.162647 | ||||||||
\(523\) | 0.369116 | 0.0161403 | 0.00807015 | − | 0.999967i | \(-0.497431\pi\) | ||||
0.00807015 | + | 0.999967i | \(0.497431\pi\) | |||||||
\(524\) | −1.63823 | −0.0715665 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.90658 | −0.257539 | ||||||||
\(527\) | −12.6581 | −0.551395 | ||||||||
\(528\) | 46.4531 | 2.02161 | ||||||||
\(529\) | 26.8251 | 1.16631 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −23.3128 | −1.01169 | ||||||||
\(532\) | −4.19762 | −0.181990 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −3.95812 | −0.171285 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.8102 | 0.898864 | ||||||||
\(537\) | 13.3388 | 0.575612 | ||||||||
\(538\) | 7.56056 | 0.325959 | ||||||||
\(539\) | 36.3045 | 1.56374 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.1173 | 1.46682 | 0.733408 | − | 0.679789i | \(-0.237929\pi\) | ||||
0.733408 | + | 0.679789i | \(0.237929\pi\) | |||||||
\(542\) | 3.14280 | 0.134995 | ||||||||
\(543\) | −59.1662 | −2.53907 | ||||||||
\(544\) | −18.1087 | −0.776406 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8903 | 0.593908 | 0.296954 | − | 0.954892i | \(-0.404029\pi\) | ||||
0.296954 | + | 0.954892i | \(0.404029\pi\) | |||||||
\(548\) | 4.90950 | 0.209724 | ||||||||
\(549\) | 26.5901 | 1.13484 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.57937 | −0.322892 | ||||||||
\(552\) | 29.3344 | 1.24855 | ||||||||
\(553\) | 4.52595 | 0.192463 | ||||||||
\(554\) | 12.6642 | 0.538052 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −25.6478 | −1.08771 | ||||||||
\(557\) | −30.5369 | −1.29389 | −0.646945 | − | 0.762537i | \(-0.723954\pi\) | ||||
−0.646945 | + | 0.762537i | \(0.723954\pi\) | |||||||
\(558\) | 5.27701 | 0.223394 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 63.9912 | 2.70171 | ||||||||
\(562\) | 5.97515 | 0.252047 | ||||||||
\(563\) | 35.3205 | 1.48858 | 0.744292 | − | 0.667855i | \(-0.232787\pi\) | ||||
0.744292 | + | 0.667855i | \(0.232787\pi\) | |||||||
\(564\) | 11.5800 | 0.487605 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.75410 | −0.199830 | ||||||||
\(567\) | 1.45965 | 0.0612994 | ||||||||
\(568\) | −0.319944 | −0.0134246 | ||||||||
\(569\) | 34.7921 | 1.45856 | 0.729280 | − | 0.684215i | \(-0.239855\pi\) | ||||
0.729280 | + | 0.684215i | \(0.239855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.332839 | 0.0139289 | 0.00696445 | − | 0.999976i | \(-0.497783\pi\) | ||||
0.00696445 | + | 0.999976i | \(0.497783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.31960 | −0.389332 | ||||||||
\(574\) | 1.21694 | 0.0507940 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −20.1700 | −0.840417 | ||||||||
\(577\) | −24.1460 | −1.00521 | −0.502605 | − | 0.864516i | \(-0.667625\pi\) | ||||
−0.502605 | + | 0.864516i | \(0.667625\pi\) | |||||||
\(578\) | −0.432010 | −0.0179693 | ||||||||
\(579\) | 35.1591 | 1.46116 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.16601 | −0.172835 | ||||||||
\(582\) | 4.91479 | 0.203725 | ||||||||
\(583\) | −32.1211 | −1.33032 | ||||||||
\(584\) | 18.8740 | 0.781013 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.14693 | 0.377856 | ||||||||
\(587\) | 12.9251 | 0.533476 | 0.266738 | − | 0.963769i | \(-0.414054\pi\) | ||||
0.266738 | + | 0.963769i | \(0.414054\pi\) | |||||||
\(588\) | −33.3222 | −1.37419 | ||||||||
\(589\) | 10.7631 | 0.443488 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.2368 | −0.709028 | ||||||||
\(592\) | −2.52528 | −0.103788 | ||||||||
\(593\) | 23.5928 | 0.968840 | 0.484420 | − | 0.874836i | \(-0.339031\pi\) | ||||
0.484420 | + | 0.874836i | \(0.339031\pi\) | |||||||
\(594\) | −8.84668 | −0.362984 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.0490 | 0.862201 | ||||||||
\(597\) | −16.1921 | −0.662699 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.4577 | 1.89821 | 0.949105 | − | 0.314961i | \(-0.101991\pi\) | ||||
0.949105 | + | 0.314961i | \(0.101991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.0915 | −1.51300 | −0.756498 | − | 0.653996i | \(-0.773091\pi\) | ||||
−0.756498 | + | 0.653996i | \(0.773091\pi\) | |||||||
\(602\) | 2.46528 | 0.100478 | ||||||||
\(603\) | 61.5060 | 2.50472 | ||||||||
\(604\) | 24.2827 | 0.988049 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.4224 | 0.464003 | ||||||||
\(607\) | 20.2943 | 0.823722 | 0.411861 | − | 0.911247i | \(-0.364879\pi\) | ||||
0.411861 | + | 0.911247i | \(0.364879\pi\) | |||||||
\(608\) | 15.3978 | 0.624464 | ||||||||
\(609\) | 3.60934 | 0.146258 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −35.2046 | −1.42306 | ||||||||
\(613\) | 41.3558 | 1.67035 | 0.835173 | − | 0.549987i | \(-0.185367\pi\) | ||||
0.835173 | + | 0.549987i | \(0.185367\pi\) | |||||||
\(614\) | 9.75532 | 0.393693 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.25472 | 0.211719 | ||||||||
\(617\) | −38.5909 | −1.55361 | −0.776806 | − | 0.629739i | \(-0.783162\pi\) | ||||
−0.776806 | + | 0.629739i | \(0.783162\pi\) | |||||||
\(618\) | 8.77430 | 0.352954 | ||||||||
\(619\) | 13.0016 | 0.522579 | 0.261289 | − | 0.965261i | \(-0.415852\pi\) | ||||
0.261289 | + | 0.965261i | \(0.415852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.7514 | 1.15375 | ||||||||
\(622\) | 7.43983 | 0.298310 | ||||||||
\(623\) | 2.30431 | 0.0923201 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.41250 | −0.0964229 | ||||||||
\(627\) | −54.4116 | −2.17299 | ||||||||
\(628\) | 13.3679 | 0.533438 | ||||||||
\(629\) | −3.47869 | −0.138704 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.2897 | −0.847531 | −0.423765 | − | 0.905772i | \(-0.639292\pi\) | ||||
−0.423765 | + | 0.905772i | \(0.639292\pi\) | |||||||
\(632\) | −10.9203 | −0.434388 | ||||||||
\(633\) | −28.6430 | −1.13846 | ||||||||
\(634\) | −3.54584 | −0.140823 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 29.4825 | 1.16906 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.55142 | 0.180193 | ||||||||
\(639\) | −0.945617 | −0.0374080 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.9061 | −0.983732 | −0.491866 | − | 0.870671i | \(-0.663685\pi\) | ||||
−0.491866 | + | 0.870671i | \(0.663685\pi\) | |||||||
\(642\) | 5.14202 | 0.202939 | ||||||||
\(643\) | −32.6396 | −1.28718 | −0.643590 | − | 0.765370i | \(-0.722556\pi\) | ||||
−0.643590 | + | 0.765370i | \(0.722556\pi\) | |||||||
\(644\) | −8.19209 | −0.322814 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.07821 | 0.239144 | ||||||||
\(647\) | −20.8586 | −0.820037 | −0.410019 | − | 0.912077i | \(-0.634478\pi\) | ||||
−0.410019 | + | 0.912077i | \(0.634478\pi\) | |||||||
\(648\) | −3.52188 | −0.138352 | ||||||||
\(649\) | 28.5535 | 1.12082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.12547 | −0.200883 | ||||||||
\(652\) | 26.4179 | 1.03460 | ||||||||
\(653\) | −30.6745 | −1.20038 | −0.600192 | − | 0.799856i | \(-0.704909\pi\) | ||||
−0.600192 | + | 0.799856i | \(0.704909\pi\) | |||||||
\(654\) | −2.41139 | −0.0942928 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.1116 | 0.590008 | ||||||||
\(657\) | 55.7835 | 2.17632 | ||||||||
\(658\) | 0.570669 | 0.0222470 | ||||||||
\(659\) | −13.5866 | −0.529259 | −0.264630 | − | 0.964350i | \(-0.585250\pi\) | ||||
−0.264630 | + | 0.964350i | \(0.585250\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.3974 | −1.92134 | −0.960668 | − | 0.277701i | \(-0.910428\pi\) | ||||
−0.960668 | + | 0.277701i | \(0.910428\pi\) | |||||||
\(662\) | 3.11734 | 0.121159 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.0519 | 0.390088 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.45022 | 0.0561950 | ||||||||
\(667\) | −14.7919 | −0.572746 | ||||||||
\(668\) | 33.5048 | 1.29634 | ||||||||
\(669\) | 30.3092 | 1.17182 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.5676 | −1.25726 | ||||||||
\(672\) | −7.33253 | −0.282859 | ||||||||
\(673\) | 34.5275 | 1.33094 | 0.665469 | − | 0.746426i | \(-0.268232\pi\) | ||||
0.665469 | + | 0.746426i | \(0.268232\pi\) | |||||||
\(674\) | 0.254183 | 0.00979077 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.0871 | 1.42537 | 0.712686 | − | 0.701483i | \(-0.247478\pi\) | ||||
0.712686 | + | 0.701483i | \(0.247478\pi\) | |||||||
\(678\) | 7.20400 | 0.276668 | ||||||||
\(679\) | −2.86125 | −0.109805 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −63.7304 | −2.44216 | ||||||||
\(682\) | −6.46328 | −0.247492 | ||||||||
\(683\) | 23.2145 | 0.888278 | 0.444139 | − | 0.895958i | \(-0.353510\pi\) | ||||
0.444139 | + | 0.895958i | \(0.353510\pi\) | |||||||
\(684\) | 29.9344 | 1.14457 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.38279 | −0.129156 | ||||||||
\(687\) | 19.6770 | 0.750725 | ||||||||
\(688\) | 30.6132 | 1.16712 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.0405 | 1.71342 | 0.856710 | − | 0.515798i | \(-0.172504\pi\) | ||||
0.856710 | + | 0.515798i | \(0.172504\pi\) | |||||||
\(692\) | 24.7040 | 0.939104 | ||||||||
\(693\) | 15.5307 | 0.589962 | ||||||||
\(694\) | −5.64125 | −0.214139 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.70872 | −0.330103 | ||||||||
\(697\) | 20.8169 | 0.788496 | ||||||||
\(698\) | −8.89745 | −0.336773 | ||||||||
\(699\) | 9.48842 | 0.358885 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.01190 | 0.227066 | 0.113533 | − | 0.993534i | \(-0.463783\pi\) | ||||
0.113533 | + | 0.993534i | \(0.463783\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.95792 | 0.111560 | ||||||||
\(704\) | 24.7042 | 0.931076 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.591635 | −0.0222665 | ||||||||
\(707\) | −6.64979 | −0.250091 | ||||||||
\(708\) | −26.2080 | −0.984955 | ||||||||
\(709\) | −1.93887 | −0.0728159 | −0.0364080 | − | 0.999337i | \(-0.511592\pi\) | ||||
−0.0364080 | + | 0.999337i | \(0.511592\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.2758 | −1.21044 | ||||||||
\(712\) | −5.55989 | −0.208366 | ||||||||
\(713\) | 21.0054 | 0.786659 | ||||||||
\(714\) | −2.89448 | −0.108323 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.98797 | 0.335896 | ||||||||
\(717\) | −50.4496 | −1.88407 | ||||||||
\(718\) | 12.3776 | 0.461927 | ||||||||
\(719\) | −32.3056 | −1.20479 | −0.602397 | − | 0.798197i | \(-0.705788\pi\) | ||||
−0.602397 | + | 0.798197i | \(0.705788\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.10815 | −0.190237 | ||||||||
\(722\) | 2.33819 | 0.0870186 | ||||||||
\(723\) | −22.5132 | −0.837276 | ||||||||
\(724\) | −39.8674 | −1.48166 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.7818 | 0.771284 | ||||||||
\(727\) | 13.3705 | 0.495883 | 0.247941 | − | 0.968775i | \(-0.420246\pi\) | ||||
0.247941 | + | 0.968775i | \(0.420246\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8480 | −1.62400 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.1711 | 1.55975 | ||||||||
\(732\) | 29.8923 | 1.10485 | ||||||||
\(733\) | −29.5619 | −1.09189 | −0.545946 | − | 0.837820i | \(-0.683830\pi\) | ||||
−0.545946 | + | 0.837820i | \(0.683830\pi\) | |||||||
\(734\) | −3.17073 | −0.117034 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 30.0505 | 1.10767 | ||||||||
\(737\) | −75.3326 | −2.77491 | ||||||||
\(738\) | −8.67832 | −0.319453 | ||||||||
\(739\) | −8.79626 | −0.323576 | −0.161788 | − | 0.986826i | \(-0.551726\pi\) | ||||
−0.161788 | + | 0.986826i | \(0.551726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.45291 | 0.0533382 | ||||||||
\(743\) | 19.0280 | 0.698069 | 0.349035 | − | 0.937110i | \(-0.386510\pi\) | ||||
0.349035 | + | 0.937110i | \(0.386510\pi\) | |||||||
\(744\) | 12.3669 | 0.453392 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.4195 | 0.381485 | ||||||||
\(747\) | 29.7090 | 1.08700 | ||||||||
\(748\) | 43.1186 | 1.57657 | ||||||||
\(749\) | −2.99354 | −0.109381 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7174 | 0.464066 | 0.232033 | − | 0.972708i | \(-0.425462\pi\) | ||||
0.232033 | + | 0.972708i | \(0.425462\pi\) | |||||||
\(752\) | 7.08640 | 0.258415 | ||||||||
\(753\) | 79.3772 | 2.89267 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.72721 | −0.171927 | ||||||||
\(757\) | 2.74724 | 0.0998501 | 0.0499251 | − | 0.998753i | \(-0.484102\pi\) | ||||
0.0499251 | + | 0.998753i | \(0.484102\pi\) | |||||||
\(758\) | −11.2614 | −0.409034 | ||||||||
\(759\) | −106.190 | −3.85445 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8209 | −1.08101 | −0.540503 | − | 0.841342i | \(-0.681766\pi\) | ||||
−0.540503 | + | 0.841342i | \(0.681766\pi\) | |||||||
\(762\) | −11.4698 | −0.415506 | ||||||||
\(763\) | 1.40384 | 0.0508225 | ||||||||
\(764\) | −6.27973 | −0.227193 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.86876 | 0.212047 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −13.4696 | −0.486043 | ||||||||
\(769\) | 6.64765 | 0.239720 | 0.119860 | − | 0.992791i | \(-0.461755\pi\) | ||||
0.119860 | + | 0.992791i | \(0.461755\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.9494 | 1.11462 | ||||||||
\(772\) | 23.6909 | 0.852655 | ||||||||
\(773\) | −29.8954 | −1.07526 | −0.537631 | − | 0.843180i | \(-0.680681\pi\) | ||||
−0.537631 | + | 0.843180i | \(0.680681\pi\) | |||||||
\(774\) | −17.5806 | −0.631923 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.90371 | 0.247829 | ||||||||
\(777\) | −1.40858 | −0.0505325 | ||||||||
\(778\) | 8.34526 | 0.299192 | ||||||||
\(779\) | −17.7006 | −0.634188 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.15819 | 0.0414434 | ||||||||
\(782\) | 11.8623 | 0.424194 | ||||||||
\(783\) | −8.53563 | −0.305039 | ||||||||
\(784\) | −20.3916 | −0.728273 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.960538 | 0.0342613 | ||||||||
\(787\) | 42.7877 | 1.52522 | 0.762608 | − | 0.646861i | \(-0.223919\pi\) | ||||
0.762608 | + | 0.646861i | \(0.223919\pi\) | |||||||
\(788\) | −11.6145 | −0.413750 | ||||||||
\(789\) | −40.9119 | −1.45650 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.19396 | −0.149120 | ||||||||
\(792\) | −37.4729 | −1.33154 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.11549 | 0.323497 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.9106 | −0.386715 | ||||||||
\(797\) | −30.7061 | −1.08766 | −0.543832 | − | 0.839194i | \(-0.683027\pi\) | ||||
−0.543832 | + | 0.839194i | \(0.683027\pi\) | |||||||
\(798\) | 2.46117 | 0.0871245 | ||||||||
\(799\) | 9.76184 | 0.345349 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.4327 | −0.580619 | ||||||||
\(802\) | −6.12362 | −0.216233 | ||||||||
\(803\) | −68.3237 | −2.41109 | ||||||||
\(804\) | 69.1443 | 2.43853 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 52.3681 | 1.84345 | ||||||||
\(808\) | 16.0448 | 0.564454 | ||||||||
\(809\) | −26.6310 | −0.936296 | −0.468148 | − | 0.883650i | \(-0.655079\pi\) | ||||
−0.468148 | + | 0.883650i | \(0.655079\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.8696 | 0.873290 | 0.436645 | − | 0.899634i | \(-0.356167\pi\) | ||||
0.436645 | + | 0.899634i | \(0.356167\pi\) | |||||||
\(812\) | 2.43205 | 0.0853481 | ||||||||
\(813\) | 21.7686 | 0.763457 | ||||||||
\(814\) | −1.77624 | −0.0622570 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −35.9429 | −1.25825 | ||||||||
\(817\) | −35.8580 | −1.25451 | ||||||||
\(818\) | 14.1248 | 0.493861 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.0239 | −1.53644 | −0.768222 | − | 0.640184i | \(-0.778858\pi\) | ||||
−0.768222 | + | 0.640184i | \(0.778858\pi\) | |||||||
\(822\) | −2.87857 | −0.100402 | ||||||||
\(823\) | 27.4490 | 0.956812 | 0.478406 | − | 0.878139i | \(-0.341215\pi\) | ||||
0.478406 | + | 0.878139i | \(0.341215\pi\) | |||||||
\(824\) | 12.3251 | 0.429365 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.29154 | −0.0449386 | ||||||||
\(827\) | −15.8828 | −0.552299 | −0.276150 | − | 0.961115i | \(-0.589059\pi\) | ||||
−0.276150 | + | 0.961115i | \(0.589059\pi\) | |||||||
\(828\) | 58.4201 | 2.03024 | ||||||||
\(829\) | 23.2845 | 0.808704 | 0.404352 | − | 0.914603i | \(-0.367497\pi\) | ||||
0.404352 | + | 0.914603i | \(0.367497\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 87.7188 | 3.04293 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.0904 | −0.973275 | ||||||||
\(834\) | 15.0380 | 0.520722 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −36.6636 | −1.26804 | ||||||||
\(837\) | 12.1211 | 0.418966 | ||||||||
\(838\) | −11.4221 | −0.394569 | ||||||||
\(839\) | −20.4521 | −0.706084 | −0.353042 | − | 0.935607i | \(-0.614853\pi\) | ||||
−0.353042 | + | 0.935607i | \(0.614853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.6086 | −0.848573 | ||||||||
\(842\) | −7.95749 | −0.274233 | ||||||||
\(843\) | 41.3868 | 1.42544 | ||||||||
\(844\) | −19.3002 | −0.664342 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.06960 | −0.139916 | ||||||||
\(847\) | −12.0986 | −0.415711 | ||||||||
\(848\) | 18.0419 | 0.619561 | ||||||||
\(849\) | −32.9292 | −1.13013 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.77269 | 0.197885 | ||||||||
\(852\) | −1.06305 | −0.0364196 | ||||||||
\(853\) | 38.9677 | 1.33423 | 0.667114 | − | 0.744956i | \(-0.267530\pi\) | ||||
0.667114 | + | 0.744956i | \(0.267530\pi\) | |||||||
\(854\) | 1.47311 | 0.0504088 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.22289 | 0.246873 | ||||||||
\(857\) | 20.6596 | 0.705719 | 0.352860 | − | 0.935676i | \(-0.385209\pi\) | ||||
0.352860 | + | 0.935676i | \(0.385209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.07452 | −0.241380 | −0.120690 | − | 0.992690i | \(-0.538511\pi\) | ||||
−0.120690 | + | 0.992690i | \(0.538511\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.42911 | 0.287263 | ||||||||
\(862\) | 11.2147 | 0.381975 | ||||||||
\(863\) | 28.3108 | 0.963710 | 0.481855 | − | 0.876251i | \(-0.339963\pi\) | ||||
0.481855 | + | 0.876251i | \(0.339963\pi\) | |||||||
\(864\) | 17.3405 | 0.589936 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.88258 | −0.0639728 | ||||||||
\(867\) | −2.99232 | −0.101624 | ||||||||
\(868\) | −3.45365 | −0.117224 | ||||||||
\(869\) | 39.5314 | 1.34101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.38723 | −0.114706 | ||||||||
\(873\) | 20.4044 | 0.690584 | ||||||||
\(874\) | −10.0865 | −0.341180 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 62.7112 | 2.11882 | ||||||||
\(877\) | 47.3468 | 1.59879 | 0.799395 | − | 0.600806i | \(-0.205154\pi\) | ||||
0.799395 | + | 0.600806i | \(0.205154\pi\) | |||||||
\(878\) | −6.34601 | −0.214168 | ||||||||
\(879\) | 63.3562 | 2.13695 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.9584 | 1.17778 | 0.588890 | − | 0.808213i | \(-0.299565\pi\) | ||||
0.588890 | + | 0.808213i | \(0.299565\pi\) | |||||||
\(882\) | 11.7106 | 0.394315 | ||||||||
\(883\) | −18.1140 | −0.609583 | −0.304792 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304792 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.27763 | −0.0765184 | ||||||||
\(887\) | −6.12777 | −0.205751 | −0.102875 | − | 0.994694i | \(-0.532804\pi\) | ||||
−0.102875 | + | 0.994694i | \(0.532804\pi\) | |||||||
\(888\) | 3.39866 | 0.114051 | ||||||||
\(889\) | 6.67737 | 0.223952 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.7491 | 0.427112 | ||||||||
\(892\) | 20.4230 | 0.683812 | ||||||||
\(893\) | −8.30047 | −0.277765 | ||||||||
\(894\) | −12.3416 | −0.412764 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.47648 | −0.216364 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.50644 | −0.217123 | ||||||||
\(899\) | −6.23603 | −0.207983 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.8535 | 0.827991 | ||||||||
\(902\) | 10.6292 | 0.353914 | ||||||||
\(903\) | 17.0758 | 0.568246 | ||||||||
\(904\) | 10.1193 | 0.336563 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −14.2376 | −0.473011 | ||||||||
\(907\) | −11.3755 | −0.377717 | −0.188858 | − | 0.982004i | \(-0.560479\pi\) | ||||
−0.188858 | + | 0.982004i | \(0.560479\pi\) | |||||||
\(908\) | −42.9429 | −1.42511 | ||||||||
\(909\) | 47.4215 | 1.57287 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.21214 | −0.0401600 | −0.0200800 | − | 0.999798i | \(-0.506392\pi\) | ||||
−0.0200800 | + | 0.999798i | \(0.506392\pi\) | |||||||
\(912\) | 30.5621 | 1.01201 | ||||||||
\(913\) | −36.3876 | −1.20425 | ||||||||
\(914\) | −8.81922 | −0.291714 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.2588 | 0.438082 | ||||||||
\(917\) | −0.559198 | −0.0184663 | ||||||||
\(918\) | 6.84508 | 0.225921 | ||||||||
\(919\) | −44.7911 | −1.47752 | −0.738761 | − | 0.673968i | \(-0.764589\pi\) | ||||
−0.738761 | + | 0.673968i | \(0.764589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 67.5701 | 2.22651 | ||||||||
\(922\) | −4.61704 | −0.152054 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 17.4594 | 0.574373 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.44085 | 0.178798 | ||||||||
\(927\) | 36.4276 | 1.19644 | ||||||||
\(928\) | −8.92131 | −0.292856 | ||||||||
\(929\) | −1.59021 | −0.0521731 | −0.0260865 | − | 0.999660i | \(-0.508305\pi\) | ||||
−0.0260865 | + | 0.999660i | \(0.508305\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.8852 | 0.782806 | ||||||||
\(932\) | 6.39349 | 0.209426 | ||||||||
\(933\) | 51.5320 | 1.68708 | ||||||||
\(934\) | −3.87505 | −0.126795 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.6224 | −0.445025 | −0.222513 | − | 0.974930i | \(-0.571426\pi\) | ||||
−0.222513 | + | 0.974930i | \(0.571426\pi\) | |||||||
\(938\) | 3.40748 | 0.111258 | ||||||||
\(939\) | −16.7102 | −0.545316 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.6484 | −1.52069 | −0.760346 | − | 0.649518i | \(-0.774971\pi\) | ||||
−0.760346 | + | 0.649518i | \(0.774971\pi\) | |||||||
\(942\) | −7.83795 | −0.255374 | ||||||||
\(943\) | −34.5445 | −1.12492 | ||||||||
\(944\) | −16.0380 | −0.521994 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.5328 | 0.700091 | ||||||||
\(947\) | −0.787397 | −0.0255870 | −0.0127935 | − | 0.999918i | \(-0.504072\pi\) | ||||
−0.0127935 | + | 0.999918i | \(0.504072\pi\) | |||||||
\(948\) | −36.2841 | −1.17845 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.5602 | −0.796420 | ||||||||
\(952\) | −4.06582 | −0.131774 | ||||||||
\(953\) | −13.7138 | −0.444232 | −0.222116 | − | 0.975020i | \(-0.571296\pi\) | ||||
−0.222116 | + | 0.975020i | \(0.571296\pi\) | |||||||
\(954\) | −10.3611 | −0.335454 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33.9939 | −1.09944 | ||||||||
\(957\) | 31.5254 | 1.01907 | ||||||||
\(958\) | 1.69944 | 0.0549063 | ||||||||
\(959\) | 1.67582 | 0.0541150 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1445 | −0.714338 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.3477 | 0.687922 | ||||||||
\(964\) | −15.1699 | −0.488589 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.80323 | 0.154541 | ||||||||
\(967\) | −29.1127 | −0.936202 | −0.468101 | − | 0.883675i | \(-0.655062\pi\) | ||||
−0.468101 | + | 0.883675i | \(0.655062\pi\) | |||||||
\(968\) | 29.1917 | 0.938258 | ||||||||
\(969\) | 42.1007 | 1.35247 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.89669 | 0.125051 | 0.0625253 | − | 0.998043i | \(-0.480085\pi\) | ||||
0.0625253 | + | 0.998043i | \(0.480085\pi\) | |||||||
\(972\) | −34.2337 | −1.09804 | ||||||||
\(973\) | −8.75468 | −0.280662 | ||||||||
\(974\) | 12.6579 | 0.405584 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.2927 | 0.585535 | ||||||||
\(977\) | −42.5418 | −1.36103 | −0.680516 | − | 0.732733i | \(-0.738244\pi\) | ||||
−0.680516 | + | 0.732733i | \(0.738244\pi\) | |||||||
\(978\) | −15.4895 | −0.495299 | ||||||||
\(979\) | 20.1267 | 0.643253 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0112 | −0.319633 | ||||||||
\(982\) | −6.46782 | −0.206396 | ||||||||
\(983\) | −21.7356 | −0.693257 | −0.346629 | − | 0.938002i | \(-0.612674\pi\) | ||||
−0.346629 | + | 0.938002i | \(0.612674\pi\) | |||||||
\(984\) | −20.3380 | −0.648351 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.52164 | −0.112152 | ||||||||
\(987\) | 3.95273 | 0.125817 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69.9806 | −2.22525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.0574 | −1.46306 | −0.731530 | − | 0.681809i | \(-0.761194\pi\) | ||||
−0.731530 | + | 0.681809i | \(0.761194\pi\) | |||||||
\(992\) | 12.6688 | 0.402234 | ||||||||
\(993\) | 21.5923 | 0.685210 | ||||||||
\(994\) | −0.0523879 | −0.00166164 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 33.3985 | 1.05827 | ||||||||
\(997\) | 40.8120 | 1.29253 | 0.646265 | − | 0.763113i | \(-0.276330\pi\) | ||||
0.646265 | + | 0.763113i | \(0.276330\pi\) | |||||||
\(998\) | 5.30867 | 0.168043 | ||||||||
\(999\) | 3.33111 | 0.105392 |
(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.ca.1.8 | 18 | ||
5.2 | odd | 4 | 845.2.b.g.339.8 | ✓ | 18 | ||
5.3 | odd | 4 | 845.2.b.g.339.11 | yes | 18 | ||
5.4 | even | 2 | inner | 4225.2.a.ca.1.11 | 18 | ||
13.12 | even | 2 | 4225.2.a.cb.1.11 | 18 | |||
65.2 | even | 12 | 845.2.l.g.654.21 | 72 | |||
65.3 | odd | 12 | 845.2.n.i.529.8 | 36 | |||
65.7 | even | 12 | 845.2.l.g.699.16 | 72 | |||
65.8 | even | 4 | 845.2.d.e.844.15 | 36 | |||
65.12 | odd | 4 | 845.2.b.h.339.11 | yes | 18 | ||
65.17 | odd | 12 | 845.2.n.h.484.11 | 36 | |||
65.18 | even | 4 | 845.2.d.e.844.21 | 36 | |||
65.22 | odd | 12 | 845.2.n.i.484.8 | 36 | |||
65.23 | odd | 12 | 845.2.n.h.529.11 | 36 | |||
65.28 | even | 12 | 845.2.l.g.654.16 | 72 | |||
65.32 | even | 12 | 845.2.l.g.699.22 | 72 | |||
65.33 | even | 12 | 845.2.l.g.699.21 | 72 | |||
65.37 | even | 12 | 845.2.l.g.654.15 | 72 | |||
65.38 | odd | 4 | 845.2.b.h.339.8 | yes | 18 | ||
65.42 | odd | 12 | 845.2.n.i.529.11 | 36 | |||
65.43 | odd | 12 | 845.2.n.h.484.8 | 36 | |||
65.47 | even | 4 | 845.2.d.e.844.22 | 36 | |||
65.48 | odd | 12 | 845.2.n.i.484.11 | 36 | |||
65.57 | even | 4 | 845.2.d.e.844.16 | 36 | |||
65.58 | even | 12 | 845.2.l.g.699.15 | 72 | |||
65.62 | odd | 12 | 845.2.n.h.529.8 | 36 | |||
65.63 | even | 12 | 845.2.l.g.654.22 | 72 | |||
65.64 | even | 2 | 4225.2.a.cb.1.8 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
845.2.b.g.339.8 | ✓ | 18 | 5.2 | odd | 4 | ||
845.2.b.g.339.11 | yes | 18 | 5.3 | odd | 4 | ||
845.2.b.h.339.8 | yes | 18 | 65.38 | odd | 4 | ||
845.2.b.h.339.11 | yes | 18 | 65.12 | odd | 4 | ||
845.2.d.e.844.15 | 36 | 65.8 | even | 4 | |||
845.2.d.e.844.16 | 36 | 65.57 | even | 4 | |||
845.2.d.e.844.21 | 36 | 65.18 | even | 4 | |||
845.2.d.e.844.22 | 36 | 65.47 | even | 4 | |||
845.2.l.g.654.15 | 72 | 65.37 | even | 12 | |||
845.2.l.g.654.16 | 72 | 65.28 | even | 12 | |||
845.2.l.g.654.21 | 72 | 65.2 | even | 12 | |||
845.2.l.g.654.22 | 72 | 65.63 | even | 12 | |||
845.2.l.g.699.15 | 72 | 65.58 | even | 12 | |||
845.2.l.g.699.16 | 72 | 65.7 | even | 12 | |||
845.2.l.g.699.21 | 72 | 65.33 | even | 12 | |||
845.2.l.g.699.22 | 72 | 65.32 | even | 12 | |||
845.2.n.h.484.8 | 36 | 65.43 | odd | 12 | |||
845.2.n.h.484.11 | 36 | 65.17 | odd | 12 | |||
845.2.n.h.529.8 | 36 | 65.62 | odd | 12 | |||
845.2.n.h.529.11 | 36 | 65.23 | odd | 12 | |||
845.2.n.i.484.8 | 36 | 65.22 | odd | 12 | |||
845.2.n.i.484.11 | 36 | 65.48 | odd | 12 | |||
845.2.n.i.529.8 | 36 | 65.3 | odd | 12 | |||
845.2.n.i.529.11 | 36 | 65.42 | odd | 12 | |||
4225.2.a.ca.1.8 | 18 | 1.1 | even | 1 | trivial | ||
4225.2.a.ca.1.11 | 18 | 5.4 | even | 2 | inner | ||
4225.2.a.cb.1.8 | 18 | 65.64 | even | 2 | |||
4225.2.a.cb.1.11 | 18 | 13.12 | even | 2 |