Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} - 20 x^{14} + 38 x^{13} + 155 x^{12} - 275 x^{11} - 593 x^{10} + 957 x^{9} + 1177 x^{8} - 1655 x^{7} - 1150 x^{6} + 1279 x^{5} + 474 x^{4} - 280 x^{3} - 83 x^{2} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(0.625678\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.625678 | 0.442421 | 0.221211 | − | 0.975226i | \(-0.428999\pi\) | ||||
0.221211 | + | 0.975226i | \(0.428999\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.60853 | −0.804264 | ||||||||
\(5\) | 0.920707 | 0.411753 | 0.205876 | − | 0.978578i | \(-0.433996\pi\) | ||||
0.205876 | + | 0.978578i | \(0.433996\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.25778 | −0.798244 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.576066 | 0.182168 | ||||||||
\(11\) | −0.186460 | −0.0562197 | −0.0281098 | − | 0.999605i | \(-0.508949\pi\) | ||||
−0.0281098 | + | 0.999605i | \(0.508949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.40951 | 0.945628 | 0.472814 | − | 0.881162i | \(-0.343238\pi\) | ||||
0.472814 | + | 0.881162i | \(0.343238\pi\) | |||||||
\(14\) | −0.625678 | −0.167219 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.80441 | 0.451104 | ||||||||
\(17\) | −6.65550 | −1.61420 | −0.807098 | − | 0.590418i | \(-0.798963\pi\) | ||||
−0.807098 | + | 0.590418i | \(0.798963\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.87673 | −1.57763 | −0.788815 | − | 0.614631i | \(-0.789305\pi\) | ||||
−0.788815 | + | 0.614631i | \(0.789305\pi\) | |||||||
\(20\) | −1.48098 | −0.331158 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.116664 | −0.0248728 | ||||||||
\(23\) | 4.83113 | 1.00736 | 0.503680 | − | 0.863890i | \(-0.331979\pi\) | ||||
0.503680 | + | 0.863890i | \(0.331979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.15230 | −0.830460 | ||||||||
\(26\) | 2.13326 | 0.418366 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.60853 | 0.303983 | ||||||||
\(29\) | 5.29105 | 0.982524 | 0.491262 | − | 0.871012i | \(-0.336536\pi\) | ||||
0.491262 | + | 0.871012i | \(0.336536\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.20074 | −0.574870 | −0.287435 | − | 0.957800i | \(-0.592803\pi\) | ||||
−0.287435 | + | 0.957800i | \(0.592803\pi\) | |||||||
\(32\) | 5.64453 | 0.997822 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.16420 | −0.714154 | ||||||||
\(35\) | −0.920707 | −0.155628 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.49716 | −0.903727 | −0.451864 | − | 0.892087i | \(-0.649241\pi\) | ||||
−0.451864 | + | 0.892087i | \(0.649241\pi\) | |||||||
\(38\) | −4.30261 | −0.697976 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.07875 | −0.328679 | ||||||||
\(41\) | 0.995032 | 0.155398 | 0.0776990 | − | 0.996977i | \(-0.475243\pi\) | ||||
0.0776990 | + | 0.996977i | \(0.475243\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.38517 | −0.821231 | −0.410616 | − | 0.911808i | \(-0.634686\pi\) | ||||
−0.410616 | + | 0.911808i | \(0.634686\pi\) | |||||||
\(44\) | 0.299925 | 0.0452154 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.02273 | 0.445677 | ||||||||
\(47\) | 12.1442 | 1.77142 | 0.885710 | − | 0.464239i | \(-0.153672\pi\) | ||||
0.885710 | + | 0.464239i | \(0.153672\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −2.59800 | −0.367413 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.48429 | −0.760534 | ||||||||
\(53\) | −2.21328 | −0.304017 | −0.152008 | − | 0.988379i | \(-0.548574\pi\) | ||||
−0.152008 | + | 0.988379i | \(0.548574\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.171675 | −0.0231486 | ||||||||
\(56\) | 2.25778 | 0.301708 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.31049 | 0.434689 | ||||||||
\(59\) | −0.266942 | −0.0347529 | −0.0173764 | − | 0.999849i | \(-0.505531\pi\) | ||||
−0.0173764 | + | 0.999849i | \(0.505531\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0006 | 1.53652 | 0.768261 | − | 0.640137i | \(-0.221123\pi\) | ||||
0.768261 | + | 0.640137i | \(0.221123\pi\) | |||||||
\(62\) | −2.00263 | −0.254335 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.0771703 | −0.00964629 | ||||||||
\(65\) | 3.13916 | 0.389365 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.28634 | −0.523660 | −0.261830 | − | 0.965114i | \(-0.584326\pi\) | ||||
−0.261830 | + | 0.965114i | \(0.584326\pi\) | |||||||
\(68\) | 10.7056 | 1.29824 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.576066 | −0.0688530 | ||||||||
\(71\) | 3.89809 | 0.462618 | 0.231309 | − | 0.972880i | \(-0.425699\pi\) | ||||
0.231309 | + | 0.972880i | \(0.425699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.02049 | 0.353521 | 0.176761 | − | 0.984254i | \(-0.443438\pi\) | ||||
0.176761 | + | 0.984254i | \(0.443438\pi\) | |||||||
\(74\) | −3.43945 | −0.399828 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.0614 | 1.26883 | ||||||||
\(77\) | 0.186460 | 0.0212490 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4416 | 1.39979 | 0.699894 | − | 0.714247i | \(-0.253231\pi\) | ||||
0.699894 | + | 0.714247i | \(0.253231\pi\) | |||||||
\(80\) | 1.66134 | 0.185743 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.622570 | 0.0687513 | ||||||||
\(83\) | 5.49252 | 0.602882 | 0.301441 | − | 0.953485i | \(-0.402532\pi\) | ||||
0.301441 | + | 0.953485i | \(0.402532\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.12776 | −0.664649 | ||||||||
\(86\) | −3.36938 | −0.363330 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.420984 | 0.0448770 | ||||||||
\(89\) | 0.466080 | 0.0494043 | 0.0247022 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247022 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.40951 | −0.357414 | ||||||||
\(92\) | −7.77100 | −0.810183 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.59838 | 0.783713 | ||||||||
\(95\) | −6.33145 | −0.649593 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2941 | 1.04521 | 0.522606 | − | 0.852574i | \(-0.324960\pi\) | ||||
0.522606 | + | 0.852574i | \(0.324960\pi\) | |||||||
\(98\) | 0.625678 | 0.0632030 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.67909 | 0.667909 | ||||||||
\(101\) | −10.6442 | −1.05914 | −0.529568 | − | 0.848268i | \(-0.677646\pi\) | ||||
−0.529568 | + | 0.848268i | \(0.677646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.97435 | −0.884269 | −0.442134 | − | 0.896949i | \(-0.645779\pi\) | ||||
−0.442134 | + | 0.896949i | \(0.645779\pi\) | |||||||
\(104\) | −7.69791 | −0.754842 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.38480 | −0.134503 | ||||||||
\(107\) | −8.95211 | −0.865433 | −0.432717 | − | 0.901530i | \(-0.642445\pi\) | ||||
−0.432717 | + | 0.901530i | \(0.642445\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.57339 | −0.725399 | −0.362700 | − | 0.931906i | \(-0.618145\pi\) | ||||
−0.362700 | + | 0.931906i | \(0.618145\pi\) | |||||||
\(110\) | −0.107413 | −0.0102414 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.80441 | −0.170501 | ||||||||
\(113\) | 6.77283 | 0.637134 | 0.318567 | − | 0.947900i | \(-0.396798\pi\) | ||||
0.318567 | + | 0.947900i | \(0.396798\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.44805 | 0.414783 | ||||||||
\(116\) | −8.51080 | −0.790208 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.167020 | −0.0153754 | ||||||||
\(119\) | 6.65550 | 0.610109 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9652 | −0.996839 | ||||||||
\(122\) | 7.50852 | 0.679789 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.14848 | 0.462347 | ||||||||
\(125\) | −8.42659 | −0.753697 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −11.3373 | −1.00209 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.96410 | 0.172263 | ||||||||
\(131\) | −4.90013 | −0.428126 | −0.214063 | − | 0.976820i | \(-0.568670\pi\) | ||||
−0.214063 | + | 0.976820i | \(0.568670\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.87673 | 0.596288 | ||||||||
\(134\) | −2.68187 | −0.231678 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.0266 | 1.28852 | ||||||||
\(137\) | 7.01111 | 0.599000 | 0.299500 | − | 0.954096i | \(-0.403180\pi\) | ||||
0.299500 | + | 0.954096i | \(0.403180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.1478 | 1.03036 | 0.515181 | − | 0.857081i | \(-0.327725\pi\) | ||||
0.515181 | + | 0.857081i | \(0.327725\pi\) | |||||||
\(140\) | 1.48098 | 0.125166 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.43895 | 0.204672 | ||||||||
\(143\) | −0.635736 | −0.0531629 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.87151 | 0.404557 | ||||||||
\(146\) | 1.88985 | 0.156405 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.84233 | 0.726835 | ||||||||
\(149\) | 13.8366 | 1.13354 | 0.566771 | − | 0.823876i | \(-0.308193\pi\) | ||||
0.566771 | + | 0.823876i | \(0.308193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.21945 | 0.261995 | 0.130998 | − | 0.991383i | \(-0.458182\pi\) | ||||
0.130998 | + | 0.991383i | \(0.458182\pi\) | |||||||
\(152\) | 15.5261 | 1.25933 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.116664 | 0.00940102 | ||||||||
\(155\) | −2.94694 | −0.236704 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.19781 | −0.654257 | −0.327128 | − | 0.944980i | \(-0.606081\pi\) | ||||
−0.327128 | + | 0.944980i | \(0.606081\pi\) | |||||||
\(158\) | 7.78442 | 0.619295 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.19696 | 0.410856 | ||||||||
\(161\) | −4.83113 | −0.380746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.27054 | 0.0995167 | 0.0497583 | − | 0.998761i | \(-0.484155\pi\) | ||||
0.0497583 | + | 0.998761i | \(0.484155\pi\) | |||||||
\(164\) | −1.60054 | −0.124981 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.43655 | 0.266728 | ||||||||
\(167\) | 15.9675 | 1.23560 | 0.617801 | − | 0.786334i | \(-0.288024\pi\) | ||||
0.617801 | + | 0.786334i | \(0.288024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.37523 | −0.105787 | ||||||||
\(170\) | −3.83401 | −0.294055 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.66220 | 0.660487 | ||||||||
\(173\) | 18.0461 | 1.37202 | 0.686011 | − | 0.727591i | \(-0.259360\pi\) | ||||
0.686011 | + | 0.727591i | \(0.259360\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.15230 | 0.313884 | ||||||||
\(176\) | −0.336450 | −0.0253609 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.291616 | 0.0218575 | ||||||||
\(179\) | 10.3836 | 0.776108 | 0.388054 | − | 0.921637i | \(-0.373147\pi\) | ||||
0.388054 | + | 0.921637i | \(0.373147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3899 | −0.772277 | −0.386138 | − | 0.922441i | \(-0.626191\pi\) | ||||
−0.386138 | + | 0.922441i | \(0.626191\pi\) | |||||||
\(182\) | −2.13326 | −0.158127 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.9076 | −0.804119 | ||||||||
\(185\) | −5.06127 | −0.372112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.24098 | 0.0907496 | ||||||||
\(188\) | −19.5343 | −1.42469 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.96145 | −0.287394 | ||||||||
\(191\) | 12.5717 | 0.909654 | 0.454827 | − | 0.890580i | \(-0.349701\pi\) | ||||
0.454827 | + | 0.890580i | \(0.349701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4024 | 1.46860 | 0.734298 | − | 0.678827i | \(-0.237511\pi\) | ||||
0.734298 | + | 0.678827i | \(0.237511\pi\) | |||||||
\(194\) | 6.44082 | 0.462424 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.60853 | −0.114895 | ||||||||
\(197\) | −18.2917 | −1.30323 | −0.651613 | − | 0.758551i | \(-0.725908\pi\) | ||||
−0.651613 | + | 0.758551i | \(0.725908\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.47355 | 0.458898 | 0.229449 | − | 0.973321i | \(-0.426308\pi\) | ||||
0.229449 | + | 0.973321i | \(0.426308\pi\) | |||||||
\(200\) | 9.37496 | 0.662910 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.65983 | −0.468584 | ||||||||
\(203\) | −5.29105 | −0.371359 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.916133 | 0.0639855 | ||||||||
\(206\) | −5.61505 | −0.391219 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.15217 | 0.426576 | ||||||||
\(209\) | 1.28223 | 0.0886938 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.9921 | 1.58284 | 0.791419 | − | 0.611274i | \(-0.209343\pi\) | ||||
0.791419 | + | 0.611274i | \(0.209343\pi\) | |||||||
\(212\) | 3.56011 | 0.244510 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.60114 | −0.382886 | ||||||||
\(215\) | −4.95817 | −0.338144 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.20074 | 0.217280 | ||||||||
\(218\) | −4.73850 | −0.320932 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.276143 | 0.0186176 | ||||||||
\(221\) | −22.6920 | −1.52643 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0825 | 1.27786 | 0.638929 | − | 0.769266i | \(-0.279378\pi\) | ||||
0.638929 | + | 0.769266i | \(0.279378\pi\) | |||||||
\(224\) | −5.64453 | −0.377141 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.23761 | 0.281881 | ||||||||
\(227\) | 2.61933 | 0.173851 | 0.0869255 | − | 0.996215i | \(-0.472296\pi\) | ||||
0.0869255 | + | 0.996215i | \(0.472296\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.9238 | −0.854028 | −0.427014 | − | 0.904245i | \(-0.640434\pi\) | ||||
−0.427014 | + | 0.904245i | \(0.640434\pi\) | |||||||
\(230\) | 2.78305 | 0.183509 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.9460 | −0.784294 | ||||||||
\(233\) | −13.8782 | −0.909188 | −0.454594 | − | 0.890699i | \(-0.650216\pi\) | ||||
−0.454594 | + | 0.890699i | \(0.650216\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.1813 | 0.729387 | ||||||||
\(236\) | 0.429384 | 0.0279505 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.16420 | 0.269925 | ||||||||
\(239\) | 14.3030 | 0.925187 | 0.462594 | − | 0.886570i | \(-0.346919\pi\) | ||||
0.462594 | + | 0.886570i | \(0.346919\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.9198 | 1.34757 | 0.673783 | − | 0.738929i | \(-0.264668\pi\) | ||||
0.673783 | + | 0.738929i | \(0.264668\pi\) | |||||||
\(242\) | −6.86070 | −0.441023 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −19.3033 | −1.23577 | ||||||||
\(245\) | 0.920707 | 0.0588218 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.4463 | −1.49185 | ||||||||
\(248\) | 7.22656 | 0.458887 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.27233 | −0.333451 | ||||||||
\(251\) | −10.5122 | −0.663523 | −0.331761 | − | 0.943363i | \(-0.607643\pi\) | ||||
−0.331761 | + | 0.943363i | \(0.607643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.900810 | −0.0566334 | ||||||||
\(254\) | −0.625678 | −0.0392585 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.93919 | −0.433699 | ||||||||
\(257\) | 16.2500 | 1.01365 | 0.506824 | − | 0.862049i | \(-0.330819\pi\) | ||||
0.506824 | + | 0.862049i | \(0.330819\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.49716 | 0.341577 | ||||||||
\(260\) | −5.04943 | −0.313152 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.06590 | −0.189412 | ||||||||
\(263\) | −10.7447 | −0.662546 | −0.331273 | − | 0.943535i | \(-0.607478\pi\) | ||||
−0.331273 | + | 0.943535i | \(0.607478\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.03778 | −0.125180 | ||||||||
\(266\) | 4.30261 | 0.263810 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.89470 | 0.421161 | ||||||||
\(269\) | 10.2239 | 0.623364 | 0.311682 | − | 0.950186i | \(-0.399108\pi\) | ||||
0.311682 | + | 0.950186i | \(0.399108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.3620 | 1.35840 | 0.679199 | − | 0.733954i | \(-0.262327\pi\) | ||||
0.679199 | + | 0.733954i | \(0.262327\pi\) | |||||||
\(272\) | −12.0093 | −0.728170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.38670 | 0.265010 | ||||||||
\(275\) | 0.774236 | 0.0466882 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.95567 | 0.357842 | 0.178921 | − | 0.983863i | \(-0.442739\pi\) | ||||
0.178921 | + | 0.983863i | \(0.442739\pi\) | |||||||
\(278\) | 7.60060 | 0.455854 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.07875 | 0.124229 | ||||||||
\(281\) | 26.0667 | 1.55501 | 0.777503 | − | 0.628879i | \(-0.216486\pi\) | ||||
0.777503 | + | 0.628879i | \(0.216486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.23332 | 0.548864 | 0.274432 | − | 0.961607i | \(-0.411510\pi\) | ||||
0.274432 | + | 0.961607i | \(0.411510\pi\) | |||||||
\(284\) | −6.27018 | −0.372067 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.397766 | −0.0235204 | ||||||||
\(287\) | −0.995032 | −0.0587349 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.2957 | 1.60563 | ||||||||
\(290\) | 3.04800 | 0.178984 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.85853 | −0.284324 | ||||||||
\(293\) | −5.84040 | −0.341200 | −0.170600 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170600 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.245775 | −0.0143096 | ||||||||
\(296\) | 12.4113 | 0.721395 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.65728 | 0.501503 | ||||||||
\(299\) | 16.4718 | 0.952588 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.38517 | 0.310396 | ||||||||
\(302\) | 2.01434 | 0.115912 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.4085 | −0.711674 | ||||||||
\(305\) | 11.0490 | 0.632667 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.3714 | −1.73339 | −0.866694 | − | 0.498841i | \(-0.833759\pi\) | ||||
−0.866694 | + | 0.498841i | \(0.833759\pi\) | |||||||
\(308\) | −0.299925 | −0.0170898 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.84384 | −0.104723 | ||||||||
\(311\) | −1.06093 | −0.0601600 | −0.0300800 | − | 0.999547i | \(-0.509576\pi\) | ||||
−0.0300800 | + | 0.999547i | \(0.509576\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.40971 | −0.136205 | −0.0681024 | − | 0.997678i | \(-0.521694\pi\) | ||||
−0.0681024 | + | 0.997678i | \(0.521694\pi\) | |||||||
\(314\) | −5.12919 | −0.289457 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.0126 | −1.12580 | ||||||||
\(317\) | −5.11130 | −0.287079 | −0.143540 | − | 0.989645i | \(-0.545848\pi\) | ||||
−0.143540 | + | 0.989645i | \(0.545848\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.986568 | −0.0552372 | ||||||||
\(320\) | −0.0710512 | −0.00397188 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.02273 | −0.168450 | ||||||||
\(323\) | 45.7680 | 2.54660 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.1573 | −0.785306 | ||||||||
\(326\) | 0.794951 | 0.0440283 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.24656 | −0.124045 | ||||||||
\(329\) | −12.1442 | −0.669534 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.99694 | 0.329621 | 0.164811 | − | 0.986325i | \(-0.447299\pi\) | ||||
0.164811 | + | 0.986325i | \(0.447299\pi\) | |||||||
\(332\) | −8.83487 | −0.484876 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.99051 | 0.546656 | ||||||||
\(335\) | −3.94646 | −0.215618 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.3255 | 1.54299 | 0.771494 | − | 0.636236i | \(-0.219510\pi\) | ||||
0.771494 | + | 0.636236i | \(0.219510\pi\) | |||||||
\(338\) | −0.860453 | −0.0468025 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.85668 | 0.534553 | ||||||||
\(341\) | 0.596809 | 0.0323190 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 12.1585 | 0.655543 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.2911 | 0.607012 | ||||||||
\(347\) | −12.5610 | −0.674311 | −0.337156 | − | 0.941449i | \(-0.609465\pi\) | ||||
−0.337156 | + | 0.941449i | \(0.609465\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.4710 | −0.614030 | −0.307015 | − | 0.951705i | \(-0.599330\pi\) | ||||
−0.307015 | + | 0.951705i | \(0.599330\pi\) | |||||||
\(350\) | 2.59800 | 0.138869 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.05248 | −0.0560972 | ||||||||
\(353\) | 9.93044 | 0.528544 | 0.264272 | − | 0.964448i | \(-0.414868\pi\) | ||||
0.264272 | + | 0.964448i | \(0.414868\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.58900 | 0.190484 | ||||||||
\(356\) | −0.749702 | −0.0397341 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.49680 | 0.343366 | ||||||||
\(359\) | −7.77712 | −0.410461 | −0.205230 | − | 0.978714i | \(-0.565794\pi\) | ||||
−0.205230 | + | 0.978714i | \(0.565794\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.2894 | 1.48891 | ||||||||
\(362\) | −6.50074 | −0.341671 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.48429 | 0.287455 | ||||||||
\(365\) | 2.78098 | 0.145563 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.9549 | −1.77243 | −0.886217 | − | 0.463270i | \(-0.846676\pi\) | ||||
−0.886217 | + | 0.463270i | \(0.846676\pi\) | |||||||
\(368\) | 8.71736 | 0.454424 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.16672 | −0.164630 | ||||||||
\(371\) | 2.21328 | 0.114908 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6464 | 1.01725 | 0.508625 | − | 0.860988i | \(-0.330154\pi\) | ||||
0.508625 | + | 0.860988i | \(0.330154\pi\) | |||||||
\(374\) | 0.776455 | 0.0401495 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.4190 | −1.41403 | ||||||||
\(377\) | 18.0399 | 0.929103 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.3610 | 0.583574 | 0.291787 | − | 0.956483i | \(-0.405750\pi\) | ||||
0.291787 | + | 0.956483i | \(0.405750\pi\) | |||||||
\(380\) | 10.1843 | 0.522444 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.86582 | 0.402450 | ||||||||
\(383\) | 35.3153 | 1.80453 | 0.902265 | − | 0.431182i | \(-0.141903\pi\) | ||||
0.902265 | + | 0.431182i | \(0.141903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.171675 | 0.00874935 | ||||||||
\(386\) | 12.7653 | 0.649738 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.5584 | −0.840626 | ||||||||
\(389\) | 11.9216 | 0.604450 | 0.302225 | − | 0.953237i | \(-0.402271\pi\) | ||||
0.302225 | + | 0.953237i | \(0.402271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.1536 | −1.62608 | ||||||||
\(392\) | −2.25778 | −0.114035 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.4447 | −0.576575 | ||||||||
\(395\) | 11.4550 | 0.576366 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00894 | −0.0506374 | −0.0253187 | − | 0.999679i | \(-0.508060\pi\) | ||||
−0.0253187 | + | 0.999679i | \(0.508060\pi\) | |||||||
\(398\) | 4.05036 | 0.203026 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.49247 | −0.374623 | ||||||||
\(401\) | 23.1876 | 1.15793 | 0.578967 | − | 0.815351i | \(-0.303456\pi\) | ||||
0.578967 | + | 0.815351i | \(0.303456\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.9130 | −0.543613 | ||||||||
\(404\) | 17.1214 | 0.851824 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.31049 | −0.164297 | ||||||||
\(407\) | 1.02500 | 0.0508072 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.46733 | 0.171448 | 0.0857242 | − | 0.996319i | \(-0.472680\pi\) | ||||
0.0857242 | + | 0.996319i | \(0.472680\pi\) | |||||||
\(410\) | 0.573204 | 0.0283085 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.4355 | 0.711185 | ||||||||
\(413\) | 0.266942 | 0.0131354 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.05700 | 0.248238 | ||||||||
\(416\) | 19.2451 | 0.943569 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.802264 | 0.0392400 | ||||||||
\(419\) | 30.6708 | 1.49836 | 0.749182 | − | 0.662364i | \(-0.230447\pi\) | ||||
0.749182 | + | 0.662364i | \(0.230447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9561 | 0.923866 | 0.461933 | − | 0.886915i | \(-0.347156\pi\) | ||||
0.461933 | + | 0.886915i | \(0.347156\pi\) | |||||||
\(422\) | 14.3856 | 0.700281 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.99708 | 0.242680 | ||||||||
\(425\) | 27.6356 | 1.34052 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.0006 | −0.580750 | ||||||||
\(428\) | 14.3997 | 0.696037 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.10222 | −0.149602 | ||||||||
\(431\) | −11.2659 | −0.542661 | −0.271330 | − | 0.962486i | \(-0.587464\pi\) | ||||
−0.271330 | + | 0.962486i | \(0.587464\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.4858 | 1.46505 | 0.732527 | − | 0.680738i | \(-0.238341\pi\) | ||||
0.732527 | + | 0.680738i | \(0.238341\pi\) | |||||||
\(434\) | 2.00263 | 0.0961295 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.1820 | 0.583412 | ||||||||
\(437\) | −33.2223 | −1.58924 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.6681 | −1.03416 | −0.517080 | − | 0.855937i | \(-0.672981\pi\) | ||||
−0.517080 | + | 0.855937i | \(0.672981\pi\) | |||||||
\(440\) | 0.387603 | 0.0184782 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.1979 | −0.675324 | ||||||||
\(443\) | 20.7860 | 0.987572 | 0.493786 | − | 0.869584i | \(-0.335613\pi\) | ||||
0.493786 | + | 0.869584i | \(0.335613\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.429123 | 0.0203424 | ||||||||
\(446\) | 11.9395 | 0.565351 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.0771703 | 0.00364595 | ||||||||
\(449\) | −37.3334 | −1.76187 | −0.880937 | − | 0.473234i | \(-0.843087\pi\) | ||||
−0.880937 | + | 0.473234i | \(0.843087\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.185533 | −0.00873642 | ||||||||
\(452\) | −10.8943 | −0.512424 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.63886 | 0.0769153 | ||||||||
\(455\) | −3.13916 | −0.147166 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.1132 | −1.17475 | −0.587374 | − | 0.809316i | \(-0.699838\pi\) | ||||
−0.587374 | + | 0.809316i | \(0.699838\pi\) | |||||||
\(458\) | −8.08613 | −0.377840 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.15481 | −0.333595 | ||||||||
\(461\) | −7.08390 | −0.329930 | −0.164965 | − | 0.986299i | \(-0.552751\pi\) | ||||
−0.164965 | + | 0.986299i | \(0.552751\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.197820 | −0.00919346 | −0.00459673 | − | 0.999989i | \(-0.501463\pi\) | ||||
−0.00459673 | + | 0.999989i | \(0.501463\pi\) | |||||||
\(464\) | 9.54726 | 0.443220 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.68326 | −0.402244 | ||||||||
\(467\) | 23.3627 | 1.08110 | 0.540549 | − | 0.841313i | \(-0.318217\pi\) | ||||
0.540549 | + | 0.841313i | \(0.318217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.28634 | 0.197925 | ||||||||
\(470\) | 6.99588 | 0.322696 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.602695 | 0.0277413 | ||||||||
\(473\) | 1.00412 | 0.0461694 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.5542 | 1.31016 | ||||||||
\(476\) | −10.7056 | −0.490688 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.94910 | 0.409322 | ||||||||
\(479\) | 11.5549 | 0.527957 | 0.263978 | − | 0.964529i | \(-0.414965\pi\) | ||||
0.263978 | + | 0.964529i | \(0.414965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.7426 | −0.854590 | ||||||||
\(482\) | 13.0891 | 0.596191 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.6379 | 0.801722 | ||||||||
\(485\) | 9.47789 | 0.430369 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.8422 | 0.581936 | 0.290968 | − | 0.956733i | \(-0.406023\pi\) | ||||
0.290968 | + | 0.956733i | \(0.406023\pi\) | |||||||
\(488\) | −27.0947 | −1.22652 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.576066 | 0.0260240 | ||||||||
\(491\) | 12.0736 | 0.544874 | 0.272437 | − | 0.962174i | \(-0.412170\pi\) | ||||
0.272437 | + | 0.962174i | \(0.412170\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.2146 | −1.58599 | ||||||||
\(494\) | −14.6698 | −0.660026 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.77546 | −0.259326 | ||||||||
\(497\) | −3.89809 | −0.174853 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.4440 | 1.45239 | 0.726197 | − | 0.687487i | \(-0.241286\pi\) | ||||
0.726197 | + | 0.687487i | \(0.241286\pi\) | |||||||
\(500\) | 13.5544 | 0.606171 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.57723 | −0.293556 | ||||||||
\(503\) | 34.3236 | 1.53041 | 0.765207 | − | 0.643785i | \(-0.222637\pi\) | ||||
0.765207 | + | 0.643785i | \(0.222637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.80017 | −0.436102 | ||||||||
\(506\) | −0.563617 | −0.0250558 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.60853 | 0.0713669 | ||||||||
\(509\) | 4.59653 | 0.203738 | 0.101869 | − | 0.994798i | \(-0.467518\pi\) | ||||
0.101869 | + | 0.994798i | \(0.467518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.02049 | −0.133618 | ||||||||
\(512\) | 18.3330 | 0.810212 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.1673 | 0.448460 | ||||||||
\(515\) | −8.26274 | −0.364100 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.26441 | −0.0995886 | ||||||||
\(518\) | 3.43945 | 0.151121 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.08752 | −0.310808 | ||||||||
\(521\) | −4.84146 | −0.212108 | −0.106054 | − | 0.994360i | \(-0.533822\pi\) | ||||
−0.106054 | + | 0.994360i | \(0.533822\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.2848 | 0.886992 | 0.443496 | − | 0.896276i | \(-0.353738\pi\) | ||||
0.443496 | + | 0.896276i | \(0.353738\pi\) | |||||||
\(524\) | 7.88199 | 0.344326 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.72271 | −0.293124 | ||||||||
\(527\) | 21.3025 | 0.927953 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.339797 | 0.0147738 | ||||||||
\(530\) | −1.27499 | −0.0553821 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.0614 | −0.479573 | ||||||||
\(533\) | 3.39257 | 0.146949 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.24227 | −0.356344 | ||||||||
\(536\) | 9.67759 | 0.418008 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.39688 | 0.275789 | ||||||||
\(539\) | −0.186460 | −0.00803138 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.52831 | 0.194687 | 0.0973435 | − | 0.995251i | \(-0.468965\pi\) | ||||
0.0973435 | + | 0.995251i | \(0.468965\pi\) | |||||||
\(542\) | 13.9914 | 0.600984 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −37.5672 | −1.61068 | ||||||||
\(545\) | −6.97287 | −0.298685 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.4649 | 0.703988 | 0.351994 | − | 0.936002i | \(-0.385504\pi\) | ||||
0.351994 | + | 0.936002i | \(0.385504\pi\) | |||||||
\(548\) | −11.2776 | −0.481754 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.484422 | 0.0206558 | ||||||||
\(551\) | −36.3851 | −1.55006 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.4416 | −0.529070 | ||||||||
\(554\) | 3.72633 | 0.158317 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.5401 | −0.828683 | ||||||||
\(557\) | −7.78271 | −0.329764 | −0.164882 | − | 0.986313i | \(-0.552724\pi\) | ||||
−0.164882 | + | 0.986313i | \(0.552724\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.3608 | −0.776580 | ||||||||
\(560\) | −1.66134 | −0.0702043 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.3093 | 0.687967 | ||||||||
\(563\) | 21.6814 | 0.913761 | 0.456881 | − | 0.889528i | \(-0.348967\pi\) | ||||
0.456881 | + | 0.889528i | \(0.348967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.23579 | 0.262342 | ||||||||
\(566\) | 5.77708 | 0.242829 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.80101 | −0.369282 | ||||||||
\(569\) | −27.8221 | −1.16636 | −0.583181 | − | 0.812342i | \(-0.698192\pi\) | ||||
−0.583181 | + | 0.812342i | \(0.698192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.0581 | −1.67638 | −0.838190 | − | 0.545378i | \(-0.816386\pi\) | ||||
−0.838190 | + | 0.545378i | \(0.816386\pi\) | |||||||
\(572\) | 1.02260 | 0.0427570 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.622570 | −0.0259856 | ||||||||
\(575\) | −20.0603 | −0.836572 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.86000 | 0.160694 | 0.0803469 | − | 0.996767i | \(-0.474397\pi\) | ||||
0.0803469 | + | 0.996767i | \(0.474397\pi\) | |||||||
\(578\) | 17.0783 | 0.710363 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.83596 | −0.325370 | ||||||||
\(581\) | −5.49252 | −0.227868 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.412686 | 0.0170917 | ||||||||
\(584\) | −6.81958 | −0.282196 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.65421 | −0.150954 | ||||||||
\(587\) | 19.8612 | 0.819758 | 0.409879 | − | 0.912140i | \(-0.365571\pi\) | ||||
0.409879 | + | 0.912140i | \(0.365571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.0106 | 0.906932 | ||||||||
\(590\) | −0.153776 | −0.00633087 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.91915 | −0.407675 | ||||||||
\(593\) | −42.1555 | −1.73112 | −0.865559 | − | 0.500808i | \(-0.833036\pi\) | ||||
−0.865559 | + | 0.500808i | \(0.833036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.12776 | 0.251214 | ||||||||
\(596\) | −22.2566 | −0.911666 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.3060 | 0.421445 | ||||||||
\(599\) | −28.6211 | −1.16942 | −0.584712 | − | 0.811241i | \(-0.698793\pi\) | ||||
−0.584712 | + | 0.811241i | \(0.698793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.7380 | −0.927501 | −0.463751 | − | 0.885966i | \(-0.653497\pi\) | ||||
−0.463751 | + | 0.885966i | \(0.653497\pi\) | |||||||
\(602\) | 3.36938 | 0.137326 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.17858 | −0.210713 | ||||||||
\(605\) | −10.0958 | −0.410451 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.36454 | 0.177151 | 0.0885756 | − | 0.996069i | \(-0.471769\pi\) | ||||
0.0885756 | + | 0.996069i | \(0.471769\pi\) | |||||||
\(608\) | −38.8159 | −1.57419 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.91314 | 0.279905 | ||||||||
\(611\) | 41.4059 | 1.67510 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4785 | −0.504001 | −0.252001 | − | 0.967727i | \(-0.581088\pi\) | ||||
−0.252001 | + | 0.967727i | \(0.581088\pi\) | |||||||
\(614\) | −19.0027 | −0.766887 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.420984 | −0.0169619 | ||||||||
\(617\) | −33.3765 | −1.34369 | −0.671845 | − | 0.740692i | \(-0.734498\pi\) | ||||
−0.671845 | + | 0.740692i | \(0.734498\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.2133 | 0.852637 | 0.426318 | − | 0.904573i | \(-0.359810\pi\) | ||||
0.426318 | + | 0.904573i | \(0.359810\pi\) | |||||||
\(620\) | 4.74024 | 0.190373 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.663802 | −0.0266160 | ||||||||
\(623\) | −0.466080 | −0.0186731 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.0031 | 0.520123 | ||||||||
\(626\) | −1.50770 | −0.0602599 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.1864 | 0.526195 | ||||||||
\(629\) | 36.5863 | 1.45879 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.7036 | 0.664960 | 0.332480 | − | 0.943110i | \(-0.392115\pi\) | ||||
0.332480 | + | 0.943110i | \(0.392115\pi\) | |||||||
\(632\) | −28.0903 | −1.11737 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.19803 | −0.127010 | ||||||||
\(635\) | −0.920707 | −0.0365371 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.40951 | 0.135090 | ||||||||
\(638\) | −0.617274 | −0.0244381 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.4384 | −0.412613 | ||||||||
\(641\) | 9.20283 | 0.363490 | 0.181745 | − | 0.983346i | \(-0.441825\pi\) | ||||
0.181745 | + | 0.983346i | \(0.441825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.1262 | −1.70073 | −0.850365 | − | 0.526193i | \(-0.823619\pi\) | ||||
−0.850365 | + | 0.526193i | \(0.823619\pi\) | |||||||
\(644\) | 7.77100 | 0.306220 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.6360 | 1.12667 | ||||||||
\(647\) | −13.7067 | −0.538866 | −0.269433 | − | 0.963019i | \(-0.586836\pi\) | ||||
−0.269433 | + | 0.963019i | \(0.586836\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.0497739 | 0.00195380 | ||||||||
\(650\) | −8.85791 | −0.347436 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.04370 | −0.0800376 | ||||||||
\(653\) | 6.63237 | 0.259545 | 0.129772 | − | 0.991544i | \(-0.458575\pi\) | ||||
0.129772 | + | 0.991544i | \(0.458575\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.51158 | −0.176282 | ||||||||
\(656\) | 1.79545 | 0.0701006 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.59838 | −0.296216 | ||||||||
\(659\) | −29.2407 | −1.13906 | −0.569528 | − | 0.821972i | \(-0.692874\pi\) | ||||
−0.569528 | + | 0.821972i | \(0.692874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.2116 | −1.79742 | −0.898711 | − | 0.438541i | \(-0.855495\pi\) | ||||
−0.898711 | + | 0.438541i | \(0.855495\pi\) | |||||||
\(662\) | 3.75215 | 0.145831 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.4009 | −0.481247 | ||||||||
\(665\) | 6.33145 | 0.245523 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.5618 | 0.989755 | ||||||||
\(668\) | −25.6842 | −0.993750 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.46921 | −0.0953941 | ||||||||
\(671\) | −2.23763 | −0.0863827 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6842 | 0.951506 | 0.475753 | − | 0.879579i | \(-0.342176\pi\) | ||||
0.475753 | + | 0.879579i | \(0.342176\pi\) | |||||||
\(674\) | 17.7226 | 0.682651 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.21210 | 0.0850808 | ||||||||
\(677\) | −26.3763 | −1.01372 | −0.506862 | − | 0.862027i | \(-0.669194\pi\) | ||||
−0.506862 | + | 0.862027i | \(0.669194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2941 | −0.395053 | ||||||||
\(680\) | 13.8351 | 0.530552 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.373410 | 0.0142986 | ||||||||
\(683\) | −37.5965 | −1.43859 | −0.719296 | − | 0.694704i | \(-0.755535\pi\) | ||||
−0.719296 | + | 0.694704i | \(0.755535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.45518 | 0.246640 | ||||||||
\(686\) | −0.625678 | −0.0238885 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.71709 | −0.370461 | ||||||||
\(689\) | −7.54619 | −0.287487 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.6125 | −1.46889 | −0.734444 | − | 0.678669i | \(-0.762557\pi\) | ||||
−0.734444 | + | 0.678669i | \(0.762557\pi\) | |||||||
\(692\) | −29.0277 | −1.10347 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.85915 | −0.298329 | ||||||||
\(695\) | 11.1846 | 0.424254 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.62244 | −0.250843 | ||||||||
\(698\) | −7.17717 | −0.271660 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.67909 | −0.252446 | ||||||||
\(701\) | −4.49148 | −0.169641 | −0.0848204 | − | 0.996396i | \(-0.527032\pi\) | ||||
−0.0848204 | + | 0.996396i | \(0.527032\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.8024 | 1.42575 | ||||||||
\(704\) | 0.0143891 | 0.000542311 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.21326 | 0.233839 | ||||||||
\(707\) | 10.6442 | 0.400315 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −53.1269 | −1.99522 | −0.997612 | − | 0.0690674i | \(-0.977998\pi\) | ||||
−0.997612 | + | 0.0690674i | \(0.977998\pi\) | |||||||
\(710\) | 2.24556 | 0.0842742 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.05230 | −0.0394367 | ||||||||
\(713\) | −15.4632 | −0.579101 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.585327 | −0.0218900 | ||||||||
\(716\) | −16.7023 | −0.624195 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.86597 | −0.181596 | ||||||||
\(719\) | −33.4034 | −1.24574 | −0.622869 | − | 0.782327i | \(-0.714033\pi\) | ||||
−0.622869 | + | 0.782327i | \(0.714033\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.97435 | 0.334222 | ||||||||
\(722\) | 17.7000 | 0.658727 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.7125 | 0.621114 | ||||||||
\(725\) | −21.9700 | −0.815947 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1975 | 0.786173 | 0.393086 | − | 0.919502i | \(-0.371407\pi\) | ||||
0.393086 | + | 0.919502i | \(0.371407\pi\) | |||||||
\(728\) | 7.69791 | 0.285304 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.74000 | 0.0644002 | ||||||||
\(731\) | 35.8410 | 1.32563 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.14227 | −0.226870 | −0.113435 | − | 0.993545i | \(-0.536185\pi\) | ||||
−0.113435 | + | 0.993545i | \(0.536185\pi\) | |||||||
\(734\) | −21.2449 | −0.784162 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.2695 | 1.00517 | ||||||||
\(737\) | 0.799229 | 0.0294400 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.53793 | 0.0933592 | 0.0466796 | − | 0.998910i | \(-0.485136\pi\) | ||||
0.0466796 | + | 0.998910i | \(0.485136\pi\) | |||||||
\(740\) | 8.14119 | 0.299276 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.38480 | 0.0508375 | ||||||||
\(743\) | 37.7650 | 1.38546 | 0.692731 | − | 0.721196i | \(-0.256407\pi\) | ||||
0.692731 | + | 0.721196i | \(0.256407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.7395 | 0.466739 | ||||||||
\(746\) | 12.2923 | 0.450053 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.99615 | −0.0729866 | ||||||||
\(749\) | 8.95211 | 0.327103 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.0073 | −0.547625 | −0.273812 | − | 0.961783i | \(-0.588285\pi\) | ||||
−0.273812 | + | 0.961783i | \(0.588285\pi\) | |||||||
\(752\) | 21.9132 | 0.799094 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.2872 | 0.411054 | ||||||||
\(755\) | 2.96417 | 0.107877 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.16228 | −0.223972 | −0.111986 | − | 0.993710i | \(-0.535721\pi\) | ||||
−0.111986 | + | 0.993710i | \(0.535721\pi\) | |||||||
\(758\) | 7.10831 | 0.258185 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14.2950 | 0.518534 | ||||||||
\(761\) | −27.0694 | −0.981265 | −0.490632 | − | 0.871367i | \(-0.663234\pi\) | ||||
−0.490632 | + | 0.871367i | \(0.663234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.57339 | 0.274175 | ||||||||
\(764\) | −20.2219 | −0.731602 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.0960 | 0.798362 | ||||||||
\(767\) | −0.910142 | −0.0328633 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.2404 | −0.585644 | −0.292822 | − | 0.956167i | \(-0.594594\pi\) | ||||
−0.292822 | + | 0.956167i | \(0.594594\pi\) | |||||||
\(770\) | 0.107413 | 0.00387090 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.8178 | −1.18114 | ||||||||
\(773\) | 41.9505 | 1.50886 | 0.754428 | − | 0.656383i | \(-0.227915\pi\) | ||||
0.754428 | + | 0.656383i | \(0.227915\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.2904 | 0.477406 | ||||||||
\(776\) | −23.2419 | −0.834335 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.45909 | 0.267421 | ||||||||
\(779\) | −6.84256 | −0.245160 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.726836 | −0.0260082 | ||||||||
\(782\) | −20.1178 | −0.719410 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.80441 | 0.0644434 | ||||||||
\(785\) | −7.54778 | −0.269392 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.0139 | 1.21247 | 0.606233 | − | 0.795287i | \(-0.292680\pi\) | ||||
0.606233 | + | 0.795287i | \(0.292680\pi\) | |||||||
\(788\) | 29.4226 | 1.04814 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.16717 | 0.254996 | ||||||||
\(791\) | −6.77283 | −0.240814 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.9162 | 1.45298 | ||||||||
\(794\) | −0.631273 | −0.0224030 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.4129 | −0.369075 | ||||||||
\(797\) | 19.6244 | 0.695130 | 0.347565 | − | 0.937656i | \(-0.387009\pi\) | ||||
0.347565 | + | 0.937656i | \(0.387009\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −80.8260 | −2.85942 | ||||||||
\(800\) | −23.4378 | −0.828651 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.5080 | 0.512294 | ||||||||
\(803\) | −0.563198 | −0.0198748 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.44805 | −0.156773 | ||||||||
\(806\) | −6.82800 | −0.240506 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 24.0322 | 0.845448 | ||||||||
\(809\) | 52.5671 | 1.84816 | 0.924080 | − | 0.382200i | \(-0.124833\pi\) | ||||
0.924080 | + | 0.382200i | \(0.124833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.33906 | 0.327939 | 0.163969 | − | 0.986465i | \(-0.447570\pi\) | ||||
0.163969 | + | 0.986465i | \(0.447570\pi\) | |||||||
\(812\) | 8.51080 | 0.298671 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.641318 | 0.0224782 | ||||||||
\(815\) | 1.16980 | 0.0409763 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.0324 | 1.29560 | ||||||||
\(818\) | 2.16943 | 0.0758524 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.47363 | −0.0514612 | ||||||||
\(821\) | −0.683311 | −0.0238477 | −0.0119239 | − | 0.999929i | \(-0.503796\pi\) | ||||
−0.0119239 | + | 0.999929i | \(0.503796\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.8593 | −1.42427 | −0.712133 | − | 0.702045i | \(-0.752271\pi\) | ||||
−0.712133 | + | 0.702045i | \(0.752271\pi\) | |||||||
\(824\) | 20.2621 | 0.705862 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.167020 | 0.00581136 | ||||||||
\(827\) | −42.8159 | −1.48885 | −0.744427 | − | 0.667704i | \(-0.767277\pi\) | ||||
−0.744427 | + | 0.667704i | \(0.767277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.7742 | 1.17303 | 0.586514 | − | 0.809939i | \(-0.300500\pi\) | ||||
0.586514 | + | 0.809939i | \(0.300500\pi\) | |||||||
\(830\) | 3.16405 | 0.109826 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.263113 | −0.00912180 | ||||||||
\(833\) | −6.65550 | −0.230599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.7014 | 0.508763 | ||||||||
\(836\) | −2.06250 | −0.0713332 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.1900 | 0.662908 | ||||||||
\(839\) | 11.7315 | 0.405017 | 0.202508 | − | 0.979281i | \(-0.435091\pi\) | ||||
0.202508 | + | 0.979281i | \(0.435091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.00475 | −0.0346465 | ||||||||
\(842\) | 11.8604 | 0.408738 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −36.9833 | −1.27302 | ||||||||
\(845\) | −1.26619 | −0.0435582 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9652 | 0.376770 | ||||||||
\(848\) | −3.99367 | −0.137143 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 17.2910 | 0.593076 | ||||||||
\(851\) | −26.5575 | −0.910378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.49984 | −0.222550 | −0.111275 | − | 0.993790i | \(-0.535493\pi\) | ||||
−0.111275 | + | 0.993790i | \(0.535493\pi\) | |||||||
\(854\) | −7.50852 | −0.256936 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.2119 | 0.690827 | ||||||||
\(857\) | 7.34627 | 0.250944 | 0.125472 | − | 0.992097i | \(-0.459956\pi\) | ||||
0.125472 | + | 0.992097i | \(0.459956\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.6811 | 0.398553 | 0.199276 | − | 0.979943i | \(-0.436141\pi\) | ||||
0.199276 | + | 0.979943i | \(0.436141\pi\) | |||||||
\(860\) | 7.97535 | 0.271957 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.04884 | −0.240085 | ||||||||
\(863\) | 54.3317 | 1.84947 | 0.924736 | − | 0.380610i | \(-0.124286\pi\) | ||||
0.924736 | + | 0.380610i | \(0.124286\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6152 | 0.564934 | ||||||||
\(866\) | 19.0743 | 0.648170 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.14848 | −0.174751 | ||||||||
\(869\) | −2.31985 | −0.0786956 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6143 | −0.495188 | ||||||||
\(872\) | 17.0990 | 0.579046 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −20.7865 | −0.703113 | ||||||||
\(875\) | 8.42659 | 0.284871 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.5254 | −1.53728 | −0.768642 | − | 0.639679i | \(-0.779067\pi\) | ||||
−0.768642 | + | 0.639679i | \(0.779067\pi\) | |||||||
\(878\) | −13.5572 | −0.457534 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.309772 | −0.0104424 | ||||||||
\(881\) | 26.9306 | 0.907316 | 0.453658 | − | 0.891176i | \(-0.350119\pi\) | ||||
0.453658 | + | 0.891176i | \(0.350119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.7174 | 1.63947 | 0.819735 | − | 0.572743i | \(-0.194121\pi\) | ||||
0.819735 | + | 0.572743i | \(0.194121\pi\) | |||||||
\(884\) | 36.5007 | 1.22765 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.0053 | 0.436922 | ||||||||
\(887\) | 43.8984 | 1.47396 | 0.736982 | − | 0.675913i | \(-0.236250\pi\) | ||||
0.736982 | + | 0.675913i | \(0.236250\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 0.268493 | 0.00899989 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.6947 | −1.02773 | ||||||||
\(893\) | −83.5126 | −2.79464 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.56027 | 0.319565 | ||||||||
\(896\) | 11.3373 | 0.378754 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.3587 | −0.779490 | ||||||||
\(899\) | −16.9353 | −0.564824 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.7305 | 0.490742 | ||||||||
\(902\) | −0.116084 | −0.00386518 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.2915 | −0.508588 | ||||||||
\(905\) | −9.56607 | −0.317987 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.3143 | −1.33861 | −0.669307 | − | 0.742986i | \(-0.733409\pi\) | ||||
−0.669307 | + | 0.742986i | \(0.733409\pi\) | |||||||
\(908\) | −4.21326 | −0.139822 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.96410 | −0.0651094 | ||||||||
\(911\) | 52.0297 | 1.72382 | 0.861910 | − | 0.507062i | \(-0.169268\pi\) | ||||
0.861910 | + | 0.507062i | \(0.169268\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.02413 | −0.0338939 | ||||||||
\(914\) | −15.7128 | −0.519733 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.7883 | 0.686863 | ||||||||
\(917\) | 4.90013 | 0.161817 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.4975 | 1.23693 | 0.618464 | − | 0.785813i | \(-0.287755\pi\) | ||||
0.618464 | + | 0.785813i | \(0.287755\pi\) | |||||||
\(920\) | −10.0427 | −0.331098 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.43224 | −0.145968 | ||||||||
\(923\) | 13.2906 | 0.437465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.8258 | 0.750509 | ||||||||
\(926\) | −0.123771 | −0.00406738 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29.8655 | 0.980384 | ||||||||
\(929\) | 44.8965 | 1.47300 | 0.736502 | − | 0.676435i | \(-0.236476\pi\) | ||||
0.736502 | + | 0.676435i | \(0.236476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.87673 | −0.225376 | ||||||||
\(932\) | 22.3234 | 0.731227 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 14.6175 | 0.478300 | ||||||||
\(935\) | 1.14258 | 0.0373664 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.2780 | 0.662453 | 0.331226 | − | 0.943551i | \(-0.392538\pi\) | ||||
0.331226 | + | 0.943551i | \(0.392538\pi\) | |||||||
\(938\) | 2.68187 | 0.0875661 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −17.9854 | −0.586619 | ||||||||
\(941\) | −11.3416 | −0.369725 | −0.184863 | − | 0.982764i | \(-0.559184\pi\) | ||||
−0.184863 | + | 0.982764i | \(0.559184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.80713 | 0.156542 | ||||||||
\(944\) | −0.481674 | −0.0156772 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.628254 | 0.0204263 | ||||||||
\(947\) | −46.8755 | −1.52325 | −0.761624 | − | 0.648019i | \(-0.775598\pi\) | ||||
−0.761624 | + | 0.648019i | \(0.775598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.2984 | 0.334300 | ||||||||
\(950\) | 17.8657 | 0.579641 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15.0266 | −0.487016 | ||||||||
\(953\) | −52.6734 | −1.70626 | −0.853129 | − | 0.521699i | \(-0.825298\pi\) | ||||
−0.853129 | + | 0.521699i | \(0.825298\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.5748 | 0.374553 | ||||||||
\(956\) | −23.0068 | −0.744095 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.22964 | 0.233579 | ||||||||
\(959\) | −7.01111 | −0.226401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7553 | −0.669524 | ||||||||
\(962\) | −11.7268 | −0.378089 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −33.6501 | −1.08380 | ||||||||
\(965\) | 18.7846 | 0.604699 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.2720 | −0.684062 | −0.342031 | − | 0.939689i | \(-0.611115\pi\) | ||||
−0.342031 | + | 0.939689i | \(0.611115\pi\) | |||||||
\(968\) | 24.7570 | 0.795721 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.93011 | 0.190404 | ||||||||
\(971\) | 10.1693 | 0.326347 | 0.163174 | − | 0.986597i | \(-0.447827\pi\) | ||||
0.163174 | + | 0.986597i | \(0.447827\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.1478 | −0.389440 | ||||||||
\(974\) | 8.03508 | 0.257461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 21.6541 | 0.693130 | ||||||||
\(977\) | 31.3392 | 1.00263 | 0.501314 | − | 0.865265i | \(-0.332850\pi\) | ||||
0.501314 | + | 0.865265i | \(0.332850\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0869050 | −0.00277750 | ||||||||
\(980\) | −1.48098 | −0.0473082 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.55419 | 0.241064 | ||||||||
\(983\) | −8.93368 | −0.284940 | −0.142470 | − | 0.989799i | \(-0.545504\pi\) | ||||
−0.142470 | + | 0.989799i | \(0.545504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.8413 | −0.536607 | ||||||||
\(986\) | −22.0330 | −0.701674 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 37.7140 | 1.19984 | ||||||||
\(989\) | −26.0165 | −0.827276 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.2418 | −1.88188 | −0.940939 | − | 0.338576i | \(-0.890055\pi\) | ||||
−0.940939 | + | 0.338576i | \(0.890055\pi\) | |||||||
\(992\) | −18.0667 | −0.573618 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.43895 | −0.0773587 | ||||||||
\(995\) | 5.96025 | 0.188953 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.7574 | 0.879086 | 0.439543 | − | 0.898222i | \(-0.355140\pi\) | ||||
0.439543 | + | 0.898222i | \(0.355140\pi\) | |||||||
\(998\) | 20.2995 | 0.642569 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.t.1.10 | 16 | ||
3.2 | odd | 2 | 889.2.a.c.1.7 | ✓ | 16 | ||
21.20 | even | 2 | 6223.2.a.k.1.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.c.1.7 | ✓ | 16 | 3.2 | odd | 2 | ||
6223.2.a.k.1.7 | 16 | 21.20 | even | 2 | |||
8001.2.a.t.1.10 | 16 | 1.1 | even | 1 | trivial |