Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.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: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.56937\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56937 | 0.701844 | 0.350922 | − | 0.936405i | \(-0.385868\pi\) | ||||
0.350922 | + | 0.936405i | \(0.385868\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.21458 | 1.21500 | 0.607498 | − | 0.794321i | \(-0.292173\pi\) | ||||
0.607498 | + | 0.794321i | \(0.292173\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.96544 | −1.79865 | −0.899325 | − | 0.437282i | \(-0.855941\pi\) | ||||
−0.899325 | + | 0.437282i | \(0.855941\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.81457 | 0.780622 | 0.390311 | − | 0.920683i | \(-0.372368\pi\) | ||||
0.390311 | + | 0.920683i | \(0.372368\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.56937 | 0.405210 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.33096 | 1.05041 | 0.525207 | − | 0.850975i | \(-0.323988\pi\) | ||||
0.525207 | + | 0.850975i | \(0.323988\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.82798 | 1.10761 | 0.553807 | − | 0.832645i | \(-0.313175\pi\) | ||||
0.553807 | + | 0.832645i | \(0.313175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.21458 | 0.701478 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.36422 | 0.701489 | 0.350744 | − | 0.936471i | \(-0.385929\pi\) | ||||
0.350744 | + | 0.936471i | \(0.385929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.53708 | −0.507415 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.76511 | −1.62764 | −0.813820 | − | 0.581117i | \(-0.802616\pi\) | ||||
−0.813820 | + | 0.581117i | \(0.802616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.34104 | 0.420463 | 0.210231 | − | 0.977652i | \(-0.432578\pi\) | ||||
0.210231 | + | 0.977652i | \(0.432578\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.96544 | −1.03845 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.04486 | 0.852737 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.28651 | 1.19789 | 0.598947 | − | 0.800788i | \(-0.295586\pi\) | ||||
0.598947 | + | 0.800788i | \(0.295586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.81457 | 0.450692 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.39154 | −0.217322 | −0.108661 | − | 0.994079i | \(-0.534656\pi\) | ||||
−0.108661 | + | 0.994079i | \(0.534656\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.86513 | 0.436928 | 0.218464 | − | 0.975845i | \(-0.429895\pi\) | ||||
0.218464 | + | 0.975845i | \(0.429895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.56937 | 0.233948 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.87896 | 1.44099 | 0.720497 | − | 0.693458i | \(-0.243914\pi\) | ||||
0.720497 | + | 0.693458i | \(0.243914\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.33349 | 0.476213 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.33096 | 0.606456 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.2692 | −1.54794 | −0.773970 | − | 0.633223i | \(-0.781732\pi\) | ||||
−0.773970 | + | 0.633223i | \(0.781732\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.36199 | −1.26237 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.82798 | 0.639481 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.96751 | −0.256148 | −0.128074 | − | 0.991765i | \(-0.540879\pi\) | ||||
−0.128074 | + | 0.991765i | \(0.540879\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.76751 | −0.482381 | −0.241190 | − | 0.970478i | \(-0.577538\pi\) | ||||
−0.241190 | + | 0.970478i | \(0.577538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.21458 | 0.404998 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.41711 | 0.547875 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.6949 | 1.42875 | 0.714377 | − | 0.699761i | \(-0.246710\pi\) | ||||
0.714377 | + | 0.699761i | \(0.246710\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.36422 | 0.405005 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.01255 | −0.476202 | −0.238101 | − | 0.971240i | \(-0.576525\pi\) | ||||
−0.238101 | + | 0.971240i | \(0.576525\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.49415 | 0.994165 | 0.497082 | − | 0.867703i | \(-0.334405\pi\) | ||||
0.497082 | + | 0.867703i | \(0.334405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.53708 | −0.292956 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.1764 | −2.18535 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.69376 | 0.415580 | 0.207790 | − | 0.978173i | \(-0.433373\pi\) | ||||
0.207790 | + | 0.978173i | \(0.433373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.33948 | 0.915377 | 0.457688 | − | 0.889113i | \(-0.348677\pi\) | ||||
0.457688 | + | 0.889113i | \(0.348677\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.79689 | 0.737226 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.76511 | −0.939718 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.3598 | 1.31013 | 0.655067 | − | 0.755571i | \(-0.272640\pi\) | ||||
0.655067 | + | 0.755571i | \(0.272640\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.04765 | 0.948452 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.34104 | 0.242754 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.57689 | 0.777372 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.582982 | 0.0591929 | 0.0295964 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295964 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.96544 | −0.599550 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.44938 | 0.144218 | 0.0721091 | − | 0.997397i | \(-0.477027\pi\) | ||||
0.0721091 | + | 0.997397i | \(0.477027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.7825 | −1.45657 | −0.728284 | − | 0.685276i | \(-0.759682\pi\) | ||||
−0.728284 | + | 0.685276i | \(0.759682\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.04486 | 0.492328 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3485 | −1.00043 | −0.500214 | − | 0.865902i | \(-0.666745\pi\) | ||||
−0.500214 | + | 0.865902i | \(0.666745\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.71160 | −0.259724 | −0.129862 | − | 0.991532i | \(-0.541453\pi\) | ||||
−0.129862 | + | 0.991532i | \(0.541453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.28651 | 0.691605 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.419192 | −0.0394343 | −0.0197171 | − | 0.999806i | \(-0.506277\pi\) | ||||
−0.0197171 | + | 0.999806i | \(0.506277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.27971 | 0.492336 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.81457 | 0.260207 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.9222 | 1.27625 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 24.5865 | 2.23514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.39154 | −0.125471 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.8285 | −1.05797 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5074 | −1.28733 | −0.643663 | − | 0.765309i | \(-0.722586\pi\) | ||||
−0.643663 | + | 0.765309i | \(0.722586\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.86513 | 0.252260 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.6189 | 1.71411 | 0.857054 | − | 0.515226i | \(-0.172292\pi\) | ||||
0.857054 | + | 0.515226i | \(0.172292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.5199 | 1.34575 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.56937 | 0.135070 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.89669 | −0.674660 | −0.337330 | − | 0.941387i | \(-0.609524\pi\) | ||||
−0.337330 | + | 0.941387i | \(0.609524\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.36468 | −0.539845 | −0.269923 | − | 0.962882i | \(-0.586998\pi\) | ||||
−0.269923 | + | 0.962882i | \(0.586998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.87896 | 0.831958 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.7902 | −1.40406 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.7557 | −1.14235 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.33349 | 0.274942 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.16385 | 0.750732 | 0.375366 | − | 0.926877i | \(-0.377517\pi\) | ||||
0.375366 | + | 0.926877i | \(0.377517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2998 | 1.32646 | 0.663228 | − | 0.748418i | \(-0.269186\pi\) | ||||
0.663228 | + | 0.748418i | \(0.269186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.33096 | 0.350138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.67396 | 0.295099 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.2988 | 1.46040 | 0.730200 | − | 0.683233i | \(-0.239427\pi\) | ||||
0.730200 | + | 0.683233i | \(0.239427\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.2692 | −0.893703 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.8145 | 0.852306 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.82475 | −0.769534 | −0.384767 | − | 0.923014i | \(-0.625718\pi\) | ||||
−0.384767 | + | 0.923014i | \(0.625718\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.36199 | −0.728830 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.07819 | −0.390630 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.82798 | 0.369205 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.1154 | −1.45332 | −0.726658 | − | 0.687000i | \(-0.758927\pi\) | ||||
−0.726658 | + | 0.687000i | \(0.758927\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.15562 | −0.616507 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.96751 | −0.147887 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.40836 | −0.628471 | −0.314235 | − | 0.949345i | \(-0.601748\pi\) | ||||
−0.314235 | + | 0.949345i | \(0.601748\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.3287 | −1.51102 | −0.755510 | − | 0.655137i | \(-0.772611\pi\) | ||||
−0.755510 | + | 0.655137i | \(0.772611\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.76751 | −0.278503 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.4352 | 0.840735 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.8361 | −1.88932 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.21458 | 0.233826 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.2261 | 1.75294 | 0.876471 | − | 0.481454i | \(-0.159891\pi\) | ||||
0.876471 | + | 0.481454i | \(0.159891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.2851 | −0.884301 | −0.442151 | − | 0.896941i | \(-0.645784\pi\) | ||||
−0.442151 | + | 0.896941i | \(0.645784\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.41711 | 0.316316 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.3618 | −1.09448 | −0.547240 | − | 0.836976i | \(-0.684322\pi\) | ||||
−0.547240 | + | 0.836976i | \(0.684322\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.14641 | 0.577483 | 0.288742 | − | 0.957407i | \(-0.406763\pi\) | ||||
0.288742 | + | 0.957407i | \(0.406763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.6949 | 0.824892 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −28.1761 | −1.97757 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.18384 | −0.152526 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.36422 | 0.233830 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −28.8010 | −1.99221 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7610 | −0.878503 | −0.439251 | − | 0.898364i | \(-0.644756\pi\) | ||||
−0.439251 | + | 0.898364i | \(0.644756\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.01255 | −0.274936 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.49645 | 0.306655 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.52544 | 0.510860 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.49415 | 0.573981 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.1898 | 0.819975 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.88563 | 0.661991 | 0.330995 | − | 0.943632i | \(-0.392616\pi\) | ||||
0.330995 | + | 0.943632i | \(0.392616\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.53708 | −0.169138 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.485281 | −0.0322093 | −0.0161046 | − | 0.999870i | \(-0.505126\pi\) | ||||
−0.0161046 | + | 0.999870i | \(0.505126\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −28.3959 | −1.87646 | −0.938228 | − | 0.346019i | \(-0.887533\pi\) | ||||
−0.938228 | + | 0.346019i | \(0.887533\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −19.1764 | −1.26171 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.5196 | −1.73736 | −0.868679 | − | 0.495376i | \(-0.835030\pi\) | ||||
−0.868679 | + | 0.495376i | \(0.835030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.5037 | 1.01135 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.69376 | 0.239935 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.4261 | 0.868464 | 0.434232 | − | 0.900801i | \(-0.357020\pi\) | ||||
0.434232 | + | 0.900801i | \(0.357020\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4392 | 0.736865 | 0.368432 | − | 0.929655i | \(-0.379895\pi\) | ||||
0.368432 | + | 0.929655i | \(0.379895\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.23149 | 0.334228 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5887 | 0.864627 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.33948 | 0.528493 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.4258 | −1.03679 | −0.518395 | − | 0.855141i | \(-0.673470\pi\) | ||||
−0.518395 | + | 0.855141i | \(0.673470\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0691 | −1.26173 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.79689 | 0.425638 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6649 | 1.10190 | 0.550952 | − | 0.834537i | \(-0.314265\pi\) | ||||
0.550952 | + | 0.834537i | \(0.314265\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.4230 | 1.45544 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.76511 | −0.542547 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.60215 | 0.468768 | 0.234384 | − | 0.972144i | \(-0.424693\pi\) | ||||
0.234384 | + | 0.972144i | \(0.424693\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.6855 | −1.08641 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.3598 | 0.756406 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.33835 | −0.447427 | −0.223714 | − | 0.974655i | \(-0.571818\pi\) | ||||
−0.223714 | + | 0.974655i | \(0.571818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.7629 | 1.86871 | 0.934356 | − | 0.356340i | \(-0.115975\pi\) | ||||
0.934356 | + | 0.356340i | \(0.115975\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.04765 | 0.547589 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.1348 | 0.912662 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.0041 | 0.901508 | 0.450754 | − | 0.892648i | \(-0.351155\pi\) | ||||
0.450754 | + | 0.892648i | \(0.351155\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.34104 | 0.140154 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2001 | 0.608488 | 0.304244 | − | 0.952594i | \(-0.401596\pi\) | ||||
0.304244 | + | 0.952594i | \(0.401596\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.65541 | 0.157847 | 0.0789237 | − | 0.996881i | \(-0.474852\pi\) | ||||
0.0789237 | + | 0.996881i | \(0.474852\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.57689 | 0.448816 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.47321 | −0.264045 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.75725 | 0.103368 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.582982 | 0.0341750 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.0956 | 1.11558 | 0.557789 | − | 0.829983i | \(-0.311650\pi\) | ||||
0.557789 | + | 0.829983i | \(0.311650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.08775 | −0.179776 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.96544 | −0.346150 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.46885 | 0.547597 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.21017 | 0.530865 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.44938 | 0.0832644 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.91263 | −0.338556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.29511 | 0.130989 | 0.0654944 | − | 0.997853i | \(-0.479138\pi\) | ||||
0.0654944 | + | 0.997853i | \(0.479138\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7825 | −0.840950 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.877859 | −0.0497788 | −0.0248894 | − | 0.999690i | \(-0.507923\pi\) | ||||
−0.0248894 | + | 0.999690i | \(0.507923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9459 | −1.07089 | −0.535443 | − | 0.844571i | \(-0.679855\pi\) | ||||
−0.535443 | + | 0.844571i | \(0.679855\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.04486 | 0.284246 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.8653 | 1.84590 | 0.922950 | − | 0.384920i | \(-0.125771\pi\) | ||||
0.922950 | + | 0.384920i | \(0.125771\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 52.2878 | 2.92755 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3485 | −0.577598 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.9098 | 1.16345 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.14078 | −0.396099 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.71160 | −0.149952 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 31.7566 | 1.75080 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.81707 | 0.374700 | 0.187350 | − | 0.982293i | \(-0.440010\pi\) | ||||
0.187350 | + | 0.982293i | \(0.440010\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.28651 | 0.399298 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.3536 | 1.00276 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.6194 | −0.796372 | −0.398186 | − | 0.917305i | \(-0.630360\pi\) | ||||
−0.398186 | + | 0.917305i | \(0.630360\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.419192 | −0.0227674 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.9653 | −0.756265 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.7863 | −0.636398 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.27971 | 0.284250 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.2051 | 0.977301 | 0.488651 | − | 0.872480i | \(-0.337489\pi\) | ||||
0.488651 | + | 0.872480i | \(0.337489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8709 | 0.688964 | 0.344482 | − | 0.938793i | \(-0.388055\pi\) | ||||
0.344482 | + | 0.938793i | \(0.388055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.81457 | 0.150231 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9234 | 0.687841 | 0.343921 | − | 0.938999i | \(-0.388245\pi\) | ||||
0.343921 | + | 0.938999i | \(0.388245\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.29718 | −0.334220 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9222 | 0.736841 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.7806 | −1.14954 | −0.574769 | − | 0.818316i | \(-0.694908\pi\) | ||||
−0.574769 | + | 0.818316i | \(0.694908\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.30936 | 0.226808 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 24.5865 | 1.29046 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.3305 | 0.697749 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0839 | −0.943970 | −0.471985 | − | 0.881607i | \(-0.656462\pi\) | ||||
−0.471985 | + | 0.881607i | \(0.656462\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.39154 | −0.0724407 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −36.2256 | −1.88074 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.5524 | −1.47839 | −0.739193 | − | 0.673494i | \(-0.764793\pi\) | ||||
−0.739193 | + | 0.673494i | \(0.764793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.8285 | −0.610819 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −24.6700 | −1.27057 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.6698 | 1.52404 | 0.762019 | − | 0.647555i | \(-0.224208\pi\) | ||||
0.762019 | + | 0.647555i | \(0.224208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.5074 | −0.743237 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.8107 | 1.36996 | 0.684982 | − | 0.728560i | \(-0.259810\pi\) | ||||
0.684982 | + | 0.728560i | \(0.259810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −30.0948 | −1.53377 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.86513 | 0.145643 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.5430 | −1.39649 | −0.698243 | − | 0.715861i | \(-0.746035\pi\) | ||||
−0.698243 | + | 0.715861i | \(0.746035\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5703 | 0.736853 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.6189 | 0.989641 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.79687 | 0.291672 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.7322 | −0.789575 | −0.394787 | − | 0.918772i | \(-0.629182\pi\) | ||||
−0.394787 | + | 0.918772i | \(0.629182\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.5199 | 0.776966 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.71138 | −0.335150 | −0.167575 | − | 0.985859i | \(-0.553594\pi\) | ||||
−0.167575 | + | 0.985859i | \(0.553594\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.58902 | 0.328222 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.56937 | 0.0779827 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −43.4673 | −2.15459 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.3626 | −1.25410 | −0.627049 | − | 0.778980i | \(-0.715737\pi\) | ||||
−0.627049 | + | 0.778980i | \(0.715737\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.89669 | −0.389515 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.32470 | −0.311218 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0877 | 0.642452 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.36468 | −0.311680 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.52335 | −0.220980 | −0.110490 | − | 0.993877i | \(-0.535242\pi\) | ||||
−0.110490 | + | 0.993877i | \(0.535242\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.4294 | 1.23935 | 0.619677 | − | 0.784857i | \(-0.287264\pi\) | ||||
0.619677 | + | 0.784857i | \(0.287264\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.87896 | 0.480331 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.9880 | −0.532995 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.1110 | −0.586090 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.7902 | −0.810637 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.8778 | −1.43917 | −0.719583 | − | 0.694407i | \(-0.755667\pi\) | ||||
−0.719583 | + | 0.694407i | \(0.755667\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.1484 | 0.824100 | 0.412050 | − | 0.911161i | \(-0.364813\pi\) | ||||
0.412050 | + | 0.911161i | \(0.364813\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −13.7557 | −0.659536 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.2424 | 0.776979 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7954 | −0.753872 | −0.376936 | − | 0.926239i | \(-0.623022\pi\) | ||||
−0.376936 | + | 0.926239i | \(0.623022\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.33349 | 0.158738 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.8494 | 1.08561 | 0.542804 | − | 0.839860i | \(-0.317363\pi\) | ||||
0.542804 | + | 0.839860i | \(0.317363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.3971 | 0.919509 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.16385 | 0.433435 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.5104 | −0.731982 | −0.365991 | − | 0.930618i | \(-0.619270\pi\) | ||||
−0.365991 | + | 0.930618i | \(0.619270\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.30116 | 0.390886 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.2998 | 0.765830 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.1991 | 0.665665 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 36.1847 | 1.69265 | 0.846325 | − | 0.532666i | \(-0.178810\pi\) | ||||
0.846325 | + | 0.532666i | \(0.178810\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.33096 | 0.202152 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.1329 | −0.565085 | −0.282542 | − | 0.959255i | \(-0.591178\pi\) | ||||
−0.282542 | + | 0.959255i | \(0.591178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.5598 | 1.14139 | 0.570696 | − | 0.821161i | \(-0.306673\pi\) | ||||
0.570696 | + | 0.821161i | \(0.306673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.67396 | 0.170376 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.6629 | −1.04872 | −0.524358 | − | 0.851498i | \(-0.675695\pi\) | ||||
−0.524358 | + | 0.851498i | \(0.675695\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.5940 | 1.73593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 18.2988 | 0.843163 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.0918 | −0.785880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.2489 | −0.562020 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.2692 | −0.515980 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5978 | 0.529915 | 0.264958 | − | 0.964260i | \(-0.414642\pi\) | ||||
0.264958 | + | 0.964260i | \(0.414642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5084 | 0.935102 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.8145 | 0.492079 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.914916 | 0.0415442 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.9911 | −1.31371 | −0.656856 | − | 0.754016i | \(-0.728114\pi\) | ||||
−0.656856 | + | 0.754016i | \(0.728114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.82475 | −0.444291 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.7088 | −1.70177 | −0.850887 | − | 0.525349i | \(-0.823935\pi\) | ||||
−0.850887 | + | 0.525349i | \(0.823935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.9614 | −1.70969 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.36199 | −0.420790 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.8987 | −0.578584 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.0629 | 0.987669 | 0.493835 | − | 0.869556i | \(-0.335595\pi\) | ||||
0.493835 | + | 0.869556i | \(0.335595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.1216 | −1.43223 | −0.716117 | − | 0.697981i | \(-0.754082\pi\) | ||||
−0.716117 | + | 0.697981i | \(0.754082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.27461 | 0.101219 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.07819 | −0.225530 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.3655 | −0.947009 | −0.473504 | − | 0.880791i | \(-0.657011\pi\) | ||||
−0.473504 | + | 0.880791i | \(0.657011\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.3051 | 1.20791 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.82798 | 0.213160 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.1993 | −1.02228 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −58.9324 | −2.59184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.1154 | −0.839072 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.55492 | 0.199555 | 0.0997774 | − | 0.995010i | \(-0.468187\pi\) | ||||
0.0997774 | + | 0.995010i | \(0.468187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.01218 | 0.0879864 | 0.0439932 | − | 0.999032i | \(-0.485992\pi\) | ||||
0.0439932 | + | 0.999032i | \(0.485992\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.15562 | −0.355940 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.1389 | 0.441660 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.6820 | −0.507913 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.96751 | −0.0853826 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.91659 | −0.169646 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.2407 | −0.702145 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.40836 | −0.362848 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.8858 | −0.856541 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1502 | 0.737343 | 0.368672 | − | 0.929560i | \(-0.379813\pi\) | ||||
0.368672 | + | 0.929560i | \(0.379813\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.3287 | −0.872388 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.25550 | −0.182286 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.92215 | −0.253213 | −0.126606 | − | 0.991953i | \(-0.540408\pi\) | ||||
−0.126606 | + | 0.991953i | \(0.540408\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.76751 | −0.160794 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.3177 | −1.80280 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.8739 | 0.504928 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.4352 | 0.485399 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.1694 | 0.854603 | 0.427301 | − | 0.904109i | \(-0.359464\pi\) | ||||
0.427301 | + | 0.904109i | \(0.359464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.06410 | 0.341075 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.8361 | −1.09080 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.6864 | −1.50400 | −0.752002 | − | 0.659161i | \(-0.770911\pi\) | ||||
−0.752002 | + | 0.659161i | \(0.770911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.657868 | −0.0276767 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.21458 | 0.134999 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.0630 | −1.42800 | −0.713998 | − | 0.700148i | \(-0.753117\pi\) | ||||
−0.713998 | + | 0.700148i | \(0.753117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.9133 | 1.46108 | 0.730538 | − | 0.682872i | \(-0.239270\pi\) | ||||
0.730538 | + | 0.682872i | \(0.239270\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.2261 | 1.01206 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.53529 | −0.355946 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2801 | 0.636117 | 0.318059 | − | 0.948071i | \(-0.396969\pi\) | ||||
0.318059 | + | 0.948071i | \(0.396969\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.2851 | −0.510552 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.8079 | 1.11218 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 67.2256 | 2.78420 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.41711 | 0.182625 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.37405 | 0.180536 | 0.0902682 | − | 0.995917i | \(-0.471228\pi\) | ||||
0.0902682 | + | 0.995917i | \(0.471228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3025 | 0.465710 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.3618 | −0.631899 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.2932 | −1.36719 | −0.683595 | − | 0.729862i | \(-0.739584\pi\) | ||||
−0.683595 | + | 0.729862i | \(0.739584\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.8491 | 0.895726 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.14641 | 0.333410 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.35724 | 0.341468 | 0.170734 | − | 0.985317i | \(-0.445386\pi\) | ||||
0.170734 | + | 0.985317i | \(0.445386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2266 | −1.35534 | −0.677671 | − | 0.735365i | \(-0.737011\pi\) | ||||
−0.677671 | + | 0.735365i | \(0.737011\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.6949 | 0.476251 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 38.5854 | 1.56872 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.0042 | −0.690180 | −0.345090 | − | 0.938570i | \(-0.612152\pi\) | ||||
−0.345090 | + | 0.938570i | \(0.612152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.1761 | −1.14175 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 27.8050 | 1.12487 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.21522 | −0.170251 | −0.0851255 | − | 0.996370i | \(-0.527129\pi\) | ||||
−0.0851255 | + | 0.996370i | \(0.527129\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.18384 | −0.0880610 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.4867 | −1.83123 | −0.915613 | − | 0.402061i | \(-0.868294\pi\) | ||||
−0.915613 | + | 0.402061i | \(0.868294\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5216 | 0.704252 | 0.352126 | − | 0.935953i | \(-0.385459\pi\) | ||||
0.352126 | + | 0.935953i | \(0.385459\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.36422 | 0.135002 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 39.7314 | 1.59181 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.87787 | −0.235115 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −28.8010 | −1.15020 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.5576 | 1.25828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.8300 | −1.06809 | −0.534043 | − | 0.845458i | \(-0.679328\pi\) | ||||
−0.534043 | + | 0.845458i | \(0.679328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.7610 | −0.507204 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.7675 | −0.903501 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.38236 | 0.371743 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.01255 | −0.158734 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.25848 | 0.0892044 | 0.0446022 | − | 0.999005i | \(-0.485798\pi\) | ||||
0.0446022 | + | 0.999005i | \(0.485798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.0840 | −0.555418 | −0.277709 | − | 0.960665i | \(-0.589575\pi\) | ||||
−0.277709 | + | 0.960665i | \(0.589575\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.49645 | 0.177047 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.9010 | 0.743076 | 0.371538 | − | 0.928418i | \(-0.378831\pi\) | ||||
0.371538 | + | 0.928418i | \(0.378831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.7371 | 0.460720 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.52544 | 0.294945 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.4383 | −0.760680 | −0.380340 | − | 0.924847i | \(-0.624193\pi\) | ||||
−0.380340 | + | 0.924847i | \(0.624193\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.7893 | 1.20304 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.49415 | 0.331388 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.8476 | −0.851061 | −0.425531 | − | 0.904944i | \(-0.639912\pi\) | ||||
−0.425531 | + | 0.904944i | \(0.639912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.02092 | −0.311978 | −0.155989 | − | 0.987759i | \(-0.549856\pi\) | ||||
−0.155989 | + | 0.987759i | \(0.549856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.1898 | 0.473413 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.3565 | 0.944503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.4878 | −1.14177 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.88563 | 0.382201 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.4749 | 0.867634 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.07660 | 0.311330 | 0.155665 | − | 0.987810i | \(-0.450248\pi\) | ||||
0.155665 | + | 0.987810i | \(0.450248\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.53708 | −0.0976521 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −26.4185 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.87404 | 0.0719191 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.485281 | −0.0185960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −50.8346 | −1.94513 | −0.972565 | − | 0.232630i | \(-0.925267\pi\) | ||||
−0.972565 | + | 0.232630i | \(0.925267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.3928 | −0.473506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.3959 | −1.08337 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31.7179 | −1.20836 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.96602 | 0.0747910 | 0.0373955 | − | 0.999301i | \(-0.488094\pi\) | ||||
0.0373955 | + | 0.999301i | \(0.488094\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.1764 | −0.728450 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.98855 | −0.378887 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.02671 | −0.228278 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.5196 | −1.00306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9796 | 1.62332 | 0.811659 | − | 0.584132i | \(-0.198565\pi\) | ||||
0.811659 | + | 0.584132i | \(0.198565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.1791 | 1.32680 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.5037 | 0.583905 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.65913 | 0.175224 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.9765 | 0.675121 | 0.337561 | − | 0.941304i | \(-0.390398\pi\) | ||||
0.337561 | + | 0.941304i | \(0.390398\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.69376 | 0.138527 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.87577 | 0.294950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.3500 | −0.985434 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.4261 | 0.501408 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.1045 | −1.90588 | −0.952938 | − | 0.303165i | \(-0.901957\pi\) | ||||
−0.952938 | + | 0.303165i | \(0.901957\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.5196 | −1.76972 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.4392 | 0.425429 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.2377 | 0.825889 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.8541 | −0.810523 | −0.405262 | − | 0.914201i | \(-0.632820\pi\) | ||||
−0.405262 | + | 0.914201i | \(0.632820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.4088 | 0.458955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.5674 | −0.981290 | −0.490645 | − | 0.871360i | \(-0.663239\pi\) | ||||
−0.490645 | + | 0.871360i | \(0.663239\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.23149 | 0.192966 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −69.7650 | −2.56983 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.6605 | 1.79001 | 0.895003 | − | 0.446060i | \(-0.147173\pi\) | ||||
0.895003 | + | 0.446060i | \(0.147173\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.5887 | 0.499193 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.70496 | 0.282668 | 0.141334 | − | 0.989962i | \(-0.454861\pi\) | ||||
0.141334 | + | 0.989962i | \(0.454861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.3815 | 0.526896 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.33948 | 0.305126 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −33.2661 | −1.21552 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.01994 | −0.292652 | −0.146326 | − | 0.989236i | \(-0.546745\pi\) | ||||
−0.146326 | + | 0.989236i | \(0.546745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.4258 | −0.598591 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.5804 | 0.930965 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.5836 | 0.857161 | 0.428580 | − | 0.903504i | \(-0.359014\pi\) | ||||
0.428580 | + | 0.903504i | \(0.359014\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.0691 | −0.728462 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.8994 | −1.26510 | −0.632551 | − | 0.774518i | \(-0.717992\pi\) | ||||
−0.632551 | + | 0.774518i | \(0.717992\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.71663 | −0.315563 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.79689 | 0.245742 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.53769 | −0.199954 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.0487 | 0.470549 | 0.235275 | − | 0.971929i | \(-0.424401\pi\) | ||||
0.235275 | + | 0.971929i | \(0.424401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.6649 | 0.636185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.14375 | 0.256943 | 0.128471 | − | 0.991713i | \(-0.458993\pi\) | ||||
0.128471 | + | 0.991713i | \(0.458993\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.93939 | −0.213349 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 23.4230 | 0.840296 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.71832 | −0.240709 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.9367 | 0.856521 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.76511 | −0.313239 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.7176 | 1.02497 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.36950 | −0.262694 | −0.131347 | − | 0.991336i | \(-0.541930\pi\) | ||||
−0.131347 | + | 0.991336i | \(0.541930\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.60215 | 0.270644 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.34752 | −0.0479124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.6039 | −0.376557 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.6855 | −0.627240 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3558 | −0.402243 | −0.201122 | − | 0.979566i | \(-0.564459\pi\) | ||||
−0.201122 | + | 0.979566i | \(0.564459\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.7854 | 1.51364 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.3598 | 0.436711 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −50.6714 | −1.78815 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.9720 | 0.598186 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.33835 | −0.258322 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 40.4208 | 1.42112 | 0.710560 | − | 0.703637i | \(-0.248442\pi\) | ||||
0.710560 | + | 0.703637i | \(0.248442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.6275 | −1.35639 | −0.678197 | − | 0.734880i | \(-0.737238\pi\) | ||||
−0.678197 | + | 0.734880i | \(0.737238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.7629 | 1.07890 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.4187 | −0.540093 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8328 | 0.483947 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.04765 | 0.316151 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.1383 | 0.423631 | 0.211815 | − | 0.977310i | \(-0.432062\pi\) | ||||
0.211815 | + | 0.977310i | \(0.432062\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.6833 | 1.27870 | 0.639350 | − | 0.768915i | \(-0.279203\pi\) | ||||
0.639350 | + | 0.768915i | \(0.279203\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.1348 | 0.526925 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.4355 | −1.02357 | −0.511787 | − | 0.859113i | \(-0.671016\pi\) | ||||
−0.511787 | + | 0.859113i | \(0.671016\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.55858 | −0.297252 | −0.148626 | − | 0.988894i | \(-0.547485\pi\) | ||||
−0.148626 | + | 0.988894i | \(0.547485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.0041 | 0.520486 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.4372 | 0.500221 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.56937 | 0.0543103 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.34104 | 0.0809181 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 49.4086 | 1.70578 | 0.852888 | − | 0.522094i | \(-0.174849\pi\) | ||||
0.852888 | + | 0.522094i | \(0.174849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.8271 | 1.64921 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.2001 | 0.351311 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.96956 | −0.274161 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 79.0352 | 2.71568 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.65541 | 0.0911333 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.5134 | 0.840310 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.6271 | −0.980173 | −0.490087 | − | 0.871674i | \(-0.663035\pi\) | ||||
−0.490087 | + | 0.871674i | \(0.663035\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.57689 | 0.259124 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.9474 | −0.886346 | −0.443173 | − | 0.896436i | \(-0.646147\pi\) | ||||
−0.443173 | + | 0.896436i | \(0.646147\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.5220 | −1.07552 | −0.537758 | − | 0.843099i | \(-0.680729\pi\) | ||||
−0.537758 | + | 0.843099i | \(0.680729\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.47321 | −0.152447 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.3259 | 0.828065 | 0.414032 | − | 0.910262i | \(-0.364120\pi\) | ||||
0.414032 | + | 0.910262i | \(0.364120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.9991 | −1.02000 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.75725 | 0.0596793 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.0349 | −0.747483 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.9160 | 1.11532 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.582982 | 0.0197310 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.0235 | −1.28543 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.5288 | −1.13219 | −0.566094 | − | 0.824341i | \(-0.691546\pi\) | ||||
−0.566094 | + | 0.824341i | \(0.691546\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.0956 | 0.644079 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.6148 | 1.03144 | 0.515719 | − | 0.856758i | \(-0.327525\pi\) | ||||
0.515719 | + | 0.856758i | \(0.327525\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.0058 | −0.841511 | −0.420756 | − | 0.907174i | \(-0.638235\pi\) | ||||
−0.420756 | + | 0.907174i | \(0.638235\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.08775 | −0.103794 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.2595 | 0.445212 | 0.222606 | − | 0.974909i | \(-0.428544\pi\) | ||||
0.222606 | + | 0.974909i | \(0.428544\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46.6352 | −1.56409 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.96544 | −0.199850 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 47.6954 | 1.59606 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.1958 | −0.441088 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.46885 | 0.316156 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.5194 | −0.684362 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.8064 | −1.62598 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.21017 | 0.306495 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.9033 | −1.06050 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6968 | −0.753636 | −0.376818 | − | 0.926287i | \(-0.622982\pi\) | ||||
−0.376818 | + | 0.926287i | \(0.622982\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.44938 | 0.0480727 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.15372 | 0.0713559 | 0.0356780 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356780 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −49.7487 | −1.64644 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.91263 | −0.195465 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 63.0663 | 2.08263 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.83614 | 0.324464 | 0.162232 | − | 0.986753i | \(-0.448131\pi\) | ||||
0.162232 | + | 0.986753i | \(0.448131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.29511 | 0.0756264 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.2936 | −0.371734 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.4864 | −0.607830 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.7825 | −0.485523 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.1814 | 0.465277 | 0.232639 | − | 0.972563i | \(-0.425264\pi\) | ||||
0.232639 | + | 0.972563i | \(0.425264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.0940 | 0.527461 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.877859 | −0.0287398 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −40.5465 | −1.32601 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.82726 | −0.255705 | −0.127853 | − | 0.991793i | \(-0.540808\pi\) | ||||
−0.127853 | + | 0.991793i | \(0.540808\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.9459 | −0.618276 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.7609 | −1.36137 | −0.680683 | − | 0.732578i | \(-0.738317\pi\) | ||||
−0.680683 | + | 0.732578i | \(0.738317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.68145 | −0.152449 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.04486 | 0.164109 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.7498 | 0.901747 | 0.450874 | − | 0.892588i | \(-0.351113\pi\) | ||||
0.450874 | + | 0.892588i | \(0.351113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.9074 | 0.776067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.8653 | 1.06573 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.8241 | −0.804130 | −0.402065 | − | 0.915611i | \(-0.631707\pi\) | ||||
−0.402065 | + | 0.915611i | \(0.631707\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.0198 | 1.23029 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 52.2878 | 1.69022 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.3845 | −0.819708 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.5195 | −0.823211 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.3485 | −0.333476 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.2799 | −0.620641 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3164 | 0.685489 | 0.342744 | − | 0.939429i | \(-0.388644\pi\) | ||||
0.342744 | + | 0.939429i | \(0.388644\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 20.9098 | 0.671719 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.8650 | 1.18305 | 0.591527 | − | 0.806285i | \(-0.298525\pi\) | ||||
0.591527 | + | 0.806285i | \(0.298525\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.4597 | −0.655909 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.14078 | −0.228688 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.1237 | 0.547837 | 0.273918 | − | 0.961753i | \(-0.411680\pi\) | ||||
0.273918 | + | 0.961753i | \(0.411680\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −73.7316 | −2.35647 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.71160 | −0.0865746 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.0292 | −0.606936 | −0.303468 | − | 0.952842i | \(-0.598145\pi\) | ||||
−0.303468 | + | 0.952842i | \(0.598145\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.1083 | −0.768155 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 31.7566 | 1.01083 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.63893 | 0.306500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.2266 | 0.896648 | 0.448324 | − | 0.893871i | \(-0.352021\pi\) | ||||
0.448324 | + | 0.893871i | \(0.352021\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.81707 | 0.216333 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.7847 | 0.405303 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.3558 | −0.961379 | −0.480689 | − | 0.876891i | \(-0.659613\pi\) | ||||
−0.480689 | + | 0.876891i | \(0.659613\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.28651 | 0.230535 |
(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 | 4008.2.a.l.1.8 | ✓ | 12 | |
4.3 | odd | 2 | 8016.2.a.bf.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8016.2.a.bf.1.8 | 12 | 4.3 | odd | 2 |