Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, 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("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.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: | \(43.4785439006\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 3x^{6} + 22x^{5} - 3x^{4} - 32x^{3} + 9x^{2} + 8x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.04904\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.04904 | −1.44889 | −0.724447 | − | 0.689331i | \(-0.757905\pi\) | ||||
−0.724447 | + | 0.689331i | \(0.757905\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.19858 | 1.09929 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.589936 | 0.222975 | 0.111487 | − | 0.993766i | \(-0.464439\pi\) | ||||
0.111487 | + | 0.993766i | \(0.464439\pi\) | |||||||
\(8\) | −0.406903 | −0.143862 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.04904 | 0.647965 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50491 | −0.417388 | −0.208694 | − | 0.977981i | \(-0.566921\pi\) | ||||
−0.208694 | + | 0.977981i | \(0.566921\pi\) | |||||||
\(14\) | −1.20880 | −0.323067 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.56340 | −0.890850 | ||||||||
\(17\) | 4.92000 | 1.19327 | 0.596637 | − | 0.802511i | \(-0.296503\pi\) | ||||
0.596637 | + | 0.802511i | \(0.296503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.82060 | −1.56475 | −0.782376 | − | 0.622806i | \(-0.785993\pi\) | ||||
−0.782376 | + | 0.622806i | \(0.785993\pi\) | |||||||
\(20\) | −2.19858 | −0.491618 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0822934 | 0.0171594 | 0.00857968 | − | 0.999963i | \(-0.497269\pi\) | ||||
0.00857968 | + | 0.999963i | \(0.497269\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.08363 | 0.604751 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.29702 | 0.245114 | ||||||||
\(29\) | 8.42443 | 1.56438 | 0.782188 | − | 0.623042i | \(-0.214103\pi\) | ||||
0.782188 | + | 0.623042i | \(0.214103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.97913 | −0.355463 | −0.177731 | − | 0.984079i | \(-0.556876\pi\) | ||||
−0.177731 | + | 0.984079i | \(0.556876\pi\) | |||||||
\(32\) | 8.11537 | 1.43461 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.0813 | −1.72893 | ||||||||
\(35\) | −0.589936 | −0.0997173 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.57997 | −0.588543 | −0.294272 | − | 0.955722i | \(-0.595077\pi\) | ||||
−0.294272 | + | 0.955722i | \(0.595077\pi\) | |||||||
\(38\) | 13.9757 | 2.26716 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.406903 | 0.0643371 | ||||||||
\(41\) | 4.07321 | 0.636129 | 0.318064 | − | 0.948069i | \(-0.396967\pi\) | ||||
0.318064 | + | 0.948069i | \(0.396967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.86148 | −0.741369 | −0.370685 | − | 0.928759i | \(-0.620877\pi\) | ||||
−0.370685 | + | 0.928759i | \(0.620877\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.168623 | −0.0248621 | ||||||||
\(47\) | −5.77852 | −0.842884 | −0.421442 | − | 0.906855i | \(-0.638476\pi\) | ||||
−0.421442 | + | 0.906855i | \(0.638476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65198 | −0.950282 | ||||||||
\(50\) | −2.04904 | −0.289779 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.30868 | −0.458831 | ||||||||
\(53\) | −6.77365 | −0.930433 | −0.465217 | − | 0.885197i | \(-0.654024\pi\) | ||||
−0.465217 | + | 0.885197i | \(0.654024\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.240047 | −0.0320776 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −17.2620 | −2.26661 | ||||||||
\(59\) | 5.58403 | 0.726979 | 0.363490 | − | 0.931598i | \(-0.381585\pi\) | ||||
0.363490 | + | 0.931598i | \(0.381585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.960246 | 0.122947 | 0.0614735 | − | 0.998109i | \(-0.480420\pi\) | ||||
0.0614735 | + | 0.998109i | \(0.480420\pi\) | |||||||
\(62\) | 4.05533 | 0.515027 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.50196 | −1.18774 | ||||||||
\(65\) | 1.50491 | 0.186662 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.6559 | 1.66834 | 0.834168 | − | 0.551511i | \(-0.185948\pi\) | ||||
0.834168 | + | 0.551511i | \(0.185948\pi\) | |||||||
\(68\) | 10.8170 | 1.31176 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.20880 | 0.144480 | ||||||||
\(71\) | 1.28379 | 0.152358 | 0.0761791 | − | 0.997094i | \(-0.475728\pi\) | ||||
0.0761791 | + | 0.997094i | \(0.475728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6271 | 1.82901 | 0.914507 | − | 0.404569i | \(-0.132579\pi\) | ||||
0.914507 | + | 0.404569i | \(0.132579\pi\) | |||||||
\(74\) | 7.33551 | 0.852736 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.9956 | −1.72012 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1522 | 1.25472 | 0.627360 | − | 0.778729i | \(-0.284135\pi\) | ||||
0.627360 | + | 0.778729i | \(0.284135\pi\) | |||||||
\(80\) | 3.56340 | 0.398400 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.34619 | −0.921683 | ||||||||
\(83\) | −4.01215 | −0.440391 | −0.220196 | − | 0.975456i | \(-0.570670\pi\) | ||||
−0.220196 | + | 0.975456i | \(0.570670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.92000 | −0.533648 | ||||||||
\(86\) | 9.96139 | 1.07416 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.08177 | −0.644667 | −0.322333 | − | 0.946626i | \(-0.604467\pi\) | ||||
−0.322333 | + | 0.946626i | \(0.604467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.887802 | −0.0930670 | ||||||||
\(92\) | 0.180929 | 0.0188631 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.8404 | 1.22125 | ||||||||
\(95\) | 6.82060 | 0.699779 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.70578 | −0.680868 | −0.340434 | − | 0.940268i | \(-0.610574\pi\) | ||||
−0.340434 | + | 0.940268i | \(0.610574\pi\) | |||||||
\(98\) | 13.6302 | 1.37686 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.19858 | 0.219858 | ||||||||
\(101\) | −5.94562 | −0.591611 | −0.295806 | − | 0.955248i | \(-0.595588\pi\) | ||||
−0.295806 | + | 0.955248i | \(0.595588\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.93558 | 0.190718 | 0.0953592 | − | 0.995443i | \(-0.469600\pi\) | ||||
0.0953592 | + | 0.995443i | \(0.469600\pi\) | |||||||
\(104\) | 0.612355 | 0.0600463 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.8795 | 1.34810 | ||||||||
\(107\) | 8.28721 | 0.801154 | 0.400577 | − | 0.916263i | \(-0.368810\pi\) | ||||
0.400577 | + | 0.916263i | \(0.368810\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.18782 | −0.305338 | −0.152669 | − | 0.988277i | \(-0.548787\pi\) | ||||
−0.152669 | + | 0.988277i | \(0.548787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.10218 | −0.198637 | ||||||||
\(113\) | −11.4906 | −1.08094 | −0.540470 | − | 0.841363i | \(-0.681754\pi\) | ||||
−0.540470 | + | 0.841363i | \(0.681754\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0822934 | −0.00767390 | ||||||||
\(116\) | 18.5218 | 1.71971 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.4419 | −1.05331 | ||||||||
\(119\) | 2.90248 | 0.266070 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.96759 | −0.178137 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.35128 | −0.390757 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1914 | −1.61423 | −0.807115 | − | 0.590395i | \(-0.798972\pi\) | ||||
−0.807115 | + | 0.590395i | \(0.798972\pi\) | |||||||
\(128\) | 3.23918 | 0.286306 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.08363 | −0.270453 | ||||||||
\(131\) | 18.7758 | 1.64045 | 0.820225 | − | 0.572041i | \(-0.193848\pi\) | ||||
0.820225 | + | 0.572041i | \(0.193848\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.02371 | −0.348900 | ||||||||
\(134\) | −27.9816 | −2.41724 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00196 | −0.171667 | ||||||||
\(137\) | 4.72703 | 0.403857 | 0.201929 | − | 0.979400i | \(-0.435279\pi\) | ||||
0.201929 | + | 0.979400i | \(0.435279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.4737 | 1.56692 | 0.783460 | − | 0.621442i | \(-0.213453\pi\) | ||||
0.783460 | + | 0.621442i | \(0.213453\pi\) | |||||||
\(140\) | −1.29702 | −0.109618 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.63055 | −0.220751 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.42443 | −0.699611 | ||||||||
\(146\) | −32.0206 | −2.65005 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.87085 | −0.646980 | ||||||||
\(149\) | 15.5011 | 1.26990 | 0.634949 | − | 0.772554i | \(-0.281021\pi\) | ||||
0.634949 | + | 0.772554i | \(0.281021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.55440 | −0.452011 | −0.226005 | − | 0.974126i | \(-0.572567\pi\) | ||||
−0.226005 | + | 0.974126i | \(0.572567\pi\) | |||||||
\(152\) | 2.77532 | 0.225109 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.97913 | 0.158968 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.5115 | −1.47738 | −0.738689 | − | 0.674046i | \(-0.764555\pi\) | ||||
−0.738689 | + | 0.674046i | \(0.764555\pi\) | |||||||
\(158\) | −22.8513 | −1.81796 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.11537 | −0.641577 | ||||||||
\(161\) | 0.0485478 | 0.00382610 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.81457 | 0.612085 | 0.306042 | − | 0.952018i | \(-0.400995\pi\) | ||||
0.306042 | + | 0.952018i | \(0.400995\pi\) | |||||||
\(164\) | 8.95529 | 0.699291 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.22108 | 0.638080 | ||||||||
\(167\) | 5.96190 | 0.461345 | 0.230673 | − | 0.973031i | \(-0.425907\pi\) | ||||
0.230673 | + | 0.973031i | \(0.425907\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7352 | −0.825787 | ||||||||
\(170\) | 10.0813 | 0.773200 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.6884 | −0.814981 | ||||||||
\(173\) | −16.5738 | −1.26009 | −0.630043 | − | 0.776560i | \(-0.716963\pi\) | ||||
−0.630043 | + | 0.776560i | \(0.716963\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.589936 | 0.0445949 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.4618 | 0.934053 | ||||||||
\(179\) | 21.5447 | 1.61033 | 0.805163 | − | 0.593054i | \(-0.202078\pi\) | ||||
0.805163 | + | 0.593054i | \(0.202078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.1704 | −1.49925 | −0.749627 | − | 0.661861i | \(-0.769767\pi\) | ||||
−0.749627 | + | 0.661861i | \(0.769767\pi\) | |||||||
\(182\) | 1.81915 | 0.134844 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.0334855 | −0.00246858 | ||||||||
\(185\) | 3.57997 | 0.263204 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −12.7046 | −0.926575 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.9757 | −1.01390 | ||||||||
\(191\) | −16.2891 | −1.17864 | −0.589321 | − | 0.807899i | \(-0.700605\pi\) | ||||
−0.589321 | + | 0.807899i | \(0.700605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.34948 | −0.241101 | −0.120551 | − | 0.992707i | \(-0.538466\pi\) | ||||
−0.120551 | + | 0.992707i | \(0.538466\pi\) | |||||||
\(194\) | 13.7404 | 0.986506 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.6249 | −1.04464 | ||||||||
\(197\) | −9.78158 | −0.696909 | −0.348454 | − | 0.937326i | \(-0.613293\pi\) | ||||
−0.348454 | + | 0.937326i | \(0.613293\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.89054 | 0.701121 | 0.350561 | − | 0.936540i | \(-0.385991\pi\) | ||||
0.350561 | + | 0.936540i | \(0.385991\pi\) | |||||||
\(200\) | −0.406903 | −0.0287724 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.1828 | 0.857181 | ||||||||
\(203\) | 4.96987 | 0.348817 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.07321 | −0.284485 | ||||||||
\(206\) | −3.96609 | −0.276331 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.36261 | 0.371830 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.1686 | 1.52615 | 0.763076 | − | 0.646309i | \(-0.223688\pi\) | ||||
0.763076 | + | 0.646309i | \(0.223688\pi\) | |||||||
\(212\) | −14.8924 | −1.02282 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.9809 | −1.16079 | ||||||||
\(215\) | 4.86148 | 0.331550 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.16756 | −0.0792592 | ||||||||
\(218\) | 6.53199 | 0.442402 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.40417 | −0.498058 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.3398 | 0.826336 | 0.413168 | − | 0.910655i | \(-0.364422\pi\) | ||||
0.413168 | + | 0.910655i | \(0.364422\pi\) | |||||||
\(224\) | 4.78755 | 0.319882 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.5447 | 1.56617 | ||||||||
\(227\) | −8.22158 | −0.545685 | −0.272843 | − | 0.962059i | \(-0.587964\pi\) | ||||
−0.272843 | + | 0.962059i | \(0.587964\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.0445 | 1.78715 | 0.893576 | − | 0.448911i | \(-0.148188\pi\) | ||||
0.893576 | + | 0.448911i | \(0.148188\pi\) | |||||||
\(230\) | 0.168623 | 0.0111187 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.42793 | −0.225055 | ||||||||
\(233\) | 25.0042 | 1.63808 | 0.819040 | − | 0.573737i | \(-0.194507\pi\) | ||||
0.819040 | + | 0.573737i | \(0.194507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.77852 | 0.376949 | ||||||||
\(236\) | 12.2770 | 0.799162 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.94731 | −0.385507 | ||||||||
\(239\) | −20.7212 | −1.34035 | −0.670173 | − | 0.742205i | \(-0.733780\pi\) | ||||
−0.670173 | + | 0.742205i | \(0.733780\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.4295 | 1.50923 | 0.754615 | − | 0.656168i | \(-0.227824\pi\) | ||||
0.754615 | + | 0.656168i | \(0.227824\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.11118 | 0.135154 | ||||||||
\(245\) | 6.65198 | 0.424979 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.2644 | 0.653109 | ||||||||
\(248\) | 0.805316 | 0.0511376 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.04904 | 0.129593 | ||||||||
\(251\) | 10.2697 | 0.648220 | 0.324110 | − | 0.946019i | \(-0.394935\pi\) | ||||
0.324110 | + | 0.946019i | \(0.394935\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 37.2751 | 2.33885 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.3667 | 0.772918 | ||||||||
\(257\) | 1.94941 | 0.121601 | 0.0608006 | − | 0.998150i | \(-0.480635\pi\) | ||||
0.0608006 | + | 0.998150i | \(0.480635\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.11195 | −0.131230 | ||||||||
\(260\) | 3.30868 | 0.205195 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −38.4725 | −2.37684 | ||||||||
\(263\) | 8.80234 | 0.542775 | 0.271388 | − | 0.962470i | \(-0.412517\pi\) | ||||
0.271388 | + | 0.962470i | \(0.412517\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.77365 | 0.416102 | ||||||||
\(266\) | 8.24477 | 0.505519 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 30.0237 | 1.83399 | ||||||||
\(269\) | 12.1842 | 0.742883 | 0.371441 | − | 0.928456i | \(-0.378864\pi\) | ||||
0.371441 | + | 0.928456i | \(0.378864\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.3655 | −0.751152 | −0.375576 | − | 0.926792i | \(-0.622555\pi\) | ||||
−0.375576 | + | 0.926792i | \(0.622555\pi\) | |||||||
\(272\) | −17.5319 | −1.06303 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.68590 | −0.585146 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.5289 | −1.23346 | −0.616731 | − | 0.787174i | \(-0.711543\pi\) | ||||
−0.616731 | + | 0.787174i | \(0.711543\pi\) | |||||||
\(278\) | −37.8535 | −2.27030 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.240047 | 0.0143455 | ||||||||
\(281\) | −11.4270 | −0.681677 | −0.340838 | − | 0.940122i | \(-0.610711\pi\) | ||||
−0.340838 | + | 0.940122i | \(0.610711\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.5320 | −1.75550 | −0.877749 | − | 0.479121i | \(-0.840956\pi\) | ||||
−0.877749 | + | 0.479121i | \(0.840956\pi\) | |||||||
\(284\) | 2.82252 | 0.167486 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.40293 | 0.141841 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.20636 | 0.423904 | ||||||||
\(290\) | 17.2620 | 1.01366 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 34.3575 | 2.01062 | ||||||||
\(293\) | −11.5964 | −0.677471 | −0.338735 | − | 0.940882i | \(-0.609999\pi\) | ||||
−0.338735 | + | 0.940882i | \(0.609999\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.58403 | −0.325115 | ||||||||
\(296\) | 1.45670 | 0.0846690 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −31.7624 | −1.83995 | ||||||||
\(299\) | −0.123844 | −0.00716211 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.86796 | −0.165307 | ||||||||
\(302\) | 11.3812 | 0.654915 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 24.3045 | 1.39396 | ||||||||
\(305\) | −0.960246 | −0.0549835 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.27309 | −0.0726593 | −0.0363296 | − | 0.999340i | \(-0.511567\pi\) | ||||
−0.0363296 | + | 0.999340i | \(0.511567\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.05533 | −0.230327 | ||||||||
\(311\) | 4.90545 | 0.278163 | 0.139081 | − | 0.990281i | \(-0.455585\pi\) | ||||
0.139081 | + | 0.990281i | \(0.455585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.4197 | −0.871572 | −0.435786 | − | 0.900050i | \(-0.643530\pi\) | ||||
−0.435786 | + | 0.900050i | \(0.643530\pi\) | |||||||
\(314\) | 37.9309 | 2.14056 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.5190 | 1.37930 | ||||||||
\(317\) | 33.5845 | 1.88630 | 0.943148 | − | 0.332374i | \(-0.107849\pi\) | ||||
0.943148 | + | 0.332374i | \(0.107849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 9.50196 | 0.531175 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0994766 | −0.00554361 | ||||||||
\(323\) | −33.5573 | −1.86718 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.50491 | −0.0834776 | ||||||||
\(326\) | −16.0124 | −0.886845 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.65740 | −0.0915148 | ||||||||
\(329\) | −3.40896 | −0.187942 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.50564 | −0.522477 | −0.261239 | − | 0.965274i | \(-0.584131\pi\) | ||||
−0.261239 | + | 0.965274i | \(0.584131\pi\) | |||||||
\(332\) | −8.82105 | −0.484118 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.2162 | −0.668440 | ||||||||
\(335\) | −13.6559 | −0.746102 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.6144 | −1.39530 | −0.697651 | − | 0.716437i | \(-0.745772\pi\) | ||||
−0.697651 | + | 0.716437i | \(0.745772\pi\) | |||||||
\(338\) | 21.9970 | 1.19648 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −10.8170 | −0.586635 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.05379 | −0.434864 | ||||||||
\(344\) | 1.97815 | 0.106655 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 33.9605 | 1.82573 | ||||||||
\(347\) | 27.9083 | 1.49820 | 0.749099 | − | 0.662458i | \(-0.230487\pi\) | ||||
0.749099 | + | 0.662458i | \(0.230487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6089 | 0.567884 | 0.283942 | − | 0.958841i | \(-0.408358\pi\) | ||||
0.283942 | + | 0.958841i | \(0.408358\pi\) | |||||||
\(350\) | −1.20880 | −0.0646133 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.0702 | −1.54725 | −0.773627 | − | 0.633642i | \(-0.781559\pi\) | ||||
−0.773627 | + | 0.633642i | \(0.781559\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.28379 | −0.0681366 | ||||||||
\(356\) | −13.3713 | −0.708676 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −44.1460 | −2.33319 | ||||||||
\(359\) | 30.2307 | 1.59552 | 0.797758 | − | 0.602978i | \(-0.206019\pi\) | ||||
0.797758 | + | 0.602978i | \(0.206019\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 27.5206 | 1.44845 | ||||||||
\(362\) | 41.3300 | 2.17226 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.95191 | −0.102308 | ||||||||
\(365\) | −15.6271 | −0.817960 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.6556 | −1.23481 | −0.617406 | − | 0.786644i | \(-0.711817\pi\) | ||||
−0.617406 | + | 0.786644i | \(0.711817\pi\) | |||||||
\(368\) | −0.293244 | −0.0152864 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.33551 | −0.381355 | ||||||||
\(371\) | −3.99602 | −0.207463 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.5998 | 0.755949 | 0.377974 | − | 0.925816i | \(-0.376621\pi\) | ||||
0.377974 | + | 0.925816i | \(0.376621\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.35130 | 0.121259 | ||||||||
\(377\) | −12.6780 | −0.652952 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.70370 | 0.344346 | 0.172173 | − | 0.985067i | \(-0.444921\pi\) | ||||
0.172173 | + | 0.985067i | \(0.444921\pi\) | |||||||
\(380\) | 14.9956 | 0.769260 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 33.3772 | 1.70773 | ||||||||
\(383\) | 31.5283 | 1.61102 | 0.805510 | − | 0.592582i | \(-0.201892\pi\) | ||||
0.805510 | + | 0.592582i | \(0.201892\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.86324 | 0.349330 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.7432 | −0.748473 | ||||||||
\(389\) | 38.9837 | 1.97655 | 0.988277 | − | 0.152672i | \(-0.0487879\pi\) | ||||
0.988277 | + | 0.152672i | \(0.0487879\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.404883 | 0.0204758 | ||||||||
\(392\) | 2.70671 | 0.136710 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.0429 | 1.00975 | ||||||||
\(395\) | −11.1522 | −0.561128 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.1682 | 1.36353 | 0.681766 | − | 0.731570i | \(-0.261212\pi\) | ||||
0.681766 | + | 0.731570i | \(0.261212\pi\) | |||||||
\(398\) | −20.2661 | −1.01585 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.56340 | −0.178170 | ||||||||
\(401\) | −13.1942 | −0.658889 | −0.329445 | − | 0.944175i | \(-0.606861\pi\) | ||||
−0.329445 | + | 0.944175i | \(0.606861\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.97842 | 0.148366 | ||||||||
\(404\) | −13.0719 | −0.650353 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.1835 | −0.505398 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.92734 | 0.490875 | 0.245438 | − | 0.969412i | \(-0.421068\pi\) | ||||
0.245438 | + | 0.969412i | \(0.421068\pi\) | |||||||
\(410\) | 8.34619 | 0.412189 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.25553 | 0.209655 | ||||||||
\(413\) | 3.29422 | 0.162098 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.01215 | 0.196949 | ||||||||
\(416\) | −12.2129 | −0.598788 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.4274 | 1.29107 | 0.645533 | − | 0.763733i | \(-0.276635\pi\) | ||||
0.645533 | + | 0.763733i | \(0.276635\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7490 | 0.670086 | 0.335043 | − | 0.942203i | \(-0.391249\pi\) | ||||
0.335043 | + | 0.942203i | \(0.391249\pi\) | |||||||
\(422\) | −45.4245 | −2.21123 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.75622 | 0.133854 | ||||||||
\(425\) | 4.92000 | 0.238655 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.566483 | 0.0274141 | ||||||||
\(428\) | 18.2201 | 0.880702 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.96139 | −0.480381 | ||||||||
\(431\) | 19.9719 | 0.962011 | 0.481005 | − | 0.876718i | \(-0.340272\pi\) | ||||
0.481005 | + | 0.876718i | \(0.340272\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.6024 | 0.797858 | 0.398929 | − | 0.916982i | \(-0.369382\pi\) | ||||
0.398929 | + | 0.916982i | \(0.369382\pi\) | |||||||
\(434\) | 2.39238 | 0.114838 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.00869 | −0.335655 | ||||||||
\(437\) | −0.561290 | −0.0268501 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.3645 | 1.35376 | 0.676882 | − | 0.736091i | \(-0.263331\pi\) | ||||
0.676882 | + | 0.736091i | \(0.263331\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.1715 | 0.721633 | ||||||||
\(443\) | −22.6826 | −1.07768 | −0.538842 | − | 0.842407i | \(-0.681138\pi\) | ||||
−0.538842 | + | 0.842407i | \(0.681138\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.08177 | 0.288304 | ||||||||
\(446\) | −25.2848 | −1.19727 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.60554 | −0.264837 | ||||||||
\(449\) | −4.58187 | −0.216232 | −0.108116 | − | 0.994138i | \(-0.534482\pi\) | ||||
−0.108116 | + | 0.994138i | \(0.534482\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −25.2629 | −1.18827 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.8464 | 0.790639 | ||||||||
\(455\) | 0.887802 | 0.0416208 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.72587 | −0.314623 | −0.157311 | − | 0.987549i | \(-0.550283\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550283\pi\) | |||||||
\(458\) | −55.4154 | −2.58939 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.180929 | −0.00843585 | ||||||||
\(461\) | −2.83529 | −0.132053 | −0.0660263 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660263 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5498 | 0.955029 | 0.477515 | − | 0.878624i | \(-0.341538\pi\) | ||||
0.477515 | + | 0.878624i | \(0.341538\pi\) | |||||||
\(464\) | −30.0196 | −1.39363 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −51.2347 | −2.37340 | ||||||||
\(467\) | 11.7594 | 0.544158 | 0.272079 | − | 0.962275i | \(-0.412289\pi\) | ||||
0.272079 | + | 0.962275i | \(0.412289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.05611 | 0.371997 | ||||||||
\(470\) | −11.8404 | −0.546159 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.27216 | −0.104585 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.82060 | −0.312951 | ||||||||
\(476\) | 6.38134 | 0.292488 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 42.4587 | 1.94202 | ||||||||
\(479\) | 1.52231 | 0.0695563 | 0.0347781 | − | 0.999395i | \(-0.488928\pi\) | ||||
0.0347781 | + | 0.999395i | \(0.488928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.38754 | 0.245651 | ||||||||
\(482\) | −48.0082 | −2.18671 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.70578 | 0.304494 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.4979 | 1.60857 | 0.804283 | − | 0.594247i | \(-0.202550\pi\) | ||||
0.804283 | + | 0.594247i | \(0.202550\pi\) | |||||||
\(488\) | −0.390727 | −0.0176874 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.6302 | −0.615749 | ||||||||
\(491\) | 12.6774 | 0.572123 | 0.286062 | − | 0.958211i | \(-0.407654\pi\) | ||||
0.286062 | + | 0.958211i | \(0.407654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.4482 | 1.86673 | ||||||||
\(494\) | −21.0322 | −0.946285 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.05244 | 0.316664 | ||||||||
\(497\) | 0.757355 | 0.0339720 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21.0578 | 0.942675 | 0.471337 | − | 0.881953i | \(-0.343771\pi\) | ||||
0.471337 | + | 0.881953i | \(0.343771\pi\) | |||||||
\(500\) | −2.19858 | −0.0983236 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.0431 | −0.939201 | ||||||||
\(503\) | 25.0768 | 1.11812 | 0.559059 | − | 0.829128i | \(-0.311163\pi\) | ||||
0.559059 | + | 0.829128i | \(0.311163\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.94562 | 0.264577 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −39.9954 | −1.77451 | ||||||||
\(509\) | 36.6853 | 1.62605 | 0.813024 | − | 0.582230i | \(-0.197820\pi\) | ||||
0.813024 | + | 0.582230i | \(0.197820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.21899 | 0.407824 | ||||||||
\(512\) | −31.8182 | −1.40618 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.99444 | −0.176187 | ||||||||
\(515\) | −1.93558 | −0.0852919 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.32748 | 0.190139 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.612355 | −0.0268535 | ||||||||
\(521\) | −28.3519 | −1.24212 | −0.621059 | − | 0.783764i | \(-0.713297\pi\) | ||||
−0.621059 | + | 0.783764i | \(0.713297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.7845 | −1.17120 | −0.585601 | − | 0.810599i | \(-0.699142\pi\) | ||||
−0.585601 | + | 0.810599i | \(0.699142\pi\) | |||||||
\(524\) | 41.2802 | 1.80333 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −18.0364 | −0.786423 | ||||||||
\(527\) | −9.73732 | −0.424164 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9932 | −0.999706 | ||||||||
\(530\) | −13.8795 | −0.602888 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −8.84647 | −0.383543 | ||||||||
\(533\) | −6.12983 | −0.265513 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.28721 | −0.358287 | ||||||||
\(536\) | −5.55664 | −0.240010 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −24.9659 | −1.07636 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.7331 | −0.719412 | −0.359706 | − | 0.933066i | \(-0.617123\pi\) | ||||
−0.359706 | + | 0.933066i | \(0.617123\pi\) | |||||||
\(542\) | 25.3375 | 1.08834 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 39.9276 | 1.71188 | ||||||||
\(545\) | 3.18782 | 0.136551 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4016 | 0.915067 | 0.457534 | − | 0.889192i | \(-0.348733\pi\) | ||||
0.457534 | + | 0.889192i | \(0.348733\pi\) | |||||||
\(548\) | 10.3928 | 0.443957 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −57.4596 | −2.44786 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.57908 | 0.279771 | ||||||||
\(554\) | 42.0646 | 1.78715 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 40.6160 | 1.72250 | ||||||||
\(557\) | 42.8947 | 1.81751 | 0.908754 | − | 0.417331i | \(-0.137035\pi\) | ||||
0.908754 | + | 0.417331i | \(0.137035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.31611 | 0.309439 | ||||||||
\(560\) | 2.10218 | 0.0888332 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.4144 | 0.987677 | ||||||||
\(563\) | 32.9570 | 1.38897 | 0.694487 | − | 0.719506i | \(-0.255632\pi\) | ||||
0.694487 | + | 0.719506i | \(0.255632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.4906 | 0.483411 | ||||||||
\(566\) | 60.5125 | 2.54353 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.522380 | −0.0219186 | ||||||||
\(569\) | 3.36920 | 0.141244 | 0.0706220 | − | 0.997503i | \(-0.477502\pi\) | ||||
0.0706220 | + | 0.997503i | \(0.477502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.267599 | 0.0111987 | 0.00559934 | − | 0.999984i | \(-0.498218\pi\) | ||||
0.00559934 | + | 0.999984i | \(0.498218\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.92372 | −0.205512 | ||||||||
\(575\) | 0.0822934 | 0.00343187 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.8943 | 1.57756 | 0.788781 | − | 0.614675i | \(-0.210713\pi\) | ||||
0.788781 | + | 0.614675i | \(0.210713\pi\) | |||||||
\(578\) | −14.7662 | −0.614191 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −18.5218 | −0.769076 | ||||||||
\(581\) | −2.36691 | −0.0981961 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −6.35872 | −0.263126 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.7616 | 0.981583 | ||||||||
\(587\) | 16.8569 | 0.695760 | 0.347880 | − | 0.937539i | \(-0.386902\pi\) | ||||
0.347880 | + | 0.937539i | \(0.386902\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4989 | 0.556211 | ||||||||
\(590\) | 11.4419 | 0.471057 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 12.7569 | 0.524304 | ||||||||
\(593\) | 11.0211 | 0.452580 | 0.226290 | − | 0.974060i | \(-0.427340\pi\) | ||||
0.226290 | + | 0.974060i | \(0.427340\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.90248 | −0.118990 | ||||||||
\(596\) | 34.0804 | 1.39599 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.253763 | 0.0103771 | ||||||||
\(599\) | −16.6951 | −0.682142 | −0.341071 | − | 0.940038i | \(-0.610790\pi\) | ||||
−0.341071 | + | 0.940038i | \(0.610790\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.75665 | 0.316400 | 0.158200 | − | 0.987407i | \(-0.449431\pi\) | ||||
0.158200 | + | 0.987407i | \(0.449431\pi\) | |||||||
\(602\) | 5.87658 | 0.239512 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.2118 | −0.496891 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8958 | −1.29461 | −0.647305 | − | 0.762231i | \(-0.724104\pi\) | ||||
−0.647305 | + | 0.762231i | \(0.724104\pi\) | |||||||
\(608\) | −55.3517 | −2.24481 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.96759 | 0.0796652 | ||||||||
\(611\) | 8.69618 | 0.351810 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8029 | 1.72879 | 0.864396 | − | 0.502811i | \(-0.167701\pi\) | ||||
0.864396 | + | 0.502811i | \(0.167701\pi\) | |||||||
\(614\) | 2.60862 | 0.105276 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.7979 | 0.877550 | 0.438775 | − | 0.898597i | \(-0.355412\pi\) | ||||
0.438775 | + | 0.898597i | \(0.355412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.6332 | 1.35183 | 0.675916 | − | 0.736979i | \(-0.263748\pi\) | ||||
0.675916 | + | 0.736979i | \(0.263748\pi\) | |||||||
\(620\) | 4.35128 | 0.174752 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −10.0515 | −0.403028 | ||||||||
\(623\) | −3.58786 | −0.143744 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.5956 | 1.26281 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −40.6990 | −1.62407 | ||||||||
\(629\) | −17.6134 | −0.702293 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.4552 | −0.854120 | −0.427060 | − | 0.904223i | \(-0.640451\pi\) | ||||
−0.427060 | + | 0.904223i | \(0.640451\pi\) | |||||||
\(632\) | −4.53787 | −0.180507 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −68.8162 | −2.73304 | ||||||||
\(635\) | 18.1914 | 0.721905 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0107 | 0.396636 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.23918 | −0.128040 | ||||||||
\(641\) | −44.6847 | −1.76494 | −0.882469 | − | 0.470370i | \(-0.844120\pi\) | ||||
−0.882469 | + | 0.470370i | \(0.844120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.59101 | 0.338796 | 0.169398 | − | 0.985548i | \(-0.445818\pi\) | ||||
0.169398 | + | 0.985548i | \(0.445818\pi\) | |||||||
\(644\) | 0.106736 | 0.00420600 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 68.7604 | 2.70534 | ||||||||
\(647\) | −8.94435 | −0.351639 | −0.175819 | − | 0.984422i | \(-0.556257\pi\) | ||||
−0.175819 | + | 0.984422i | \(0.556257\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.08363 | 0.120950 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.1810 | 0.672859 | ||||||||
\(653\) | 13.9470 | 0.545788 | 0.272894 | − | 0.962044i | \(-0.412019\pi\) | ||||
0.272894 | + | 0.962044i | \(0.412019\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.7758 | −0.733632 | ||||||||
\(656\) | −14.5145 | −0.566696 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.98510 | 0.272308 | ||||||||
\(659\) | −6.61492 | −0.257681 | −0.128840 | − | 0.991665i | \(-0.541125\pi\) | ||||
−0.128840 | + | 0.991665i | \(0.541125\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.5635 | 0.916515 | 0.458257 | − | 0.888820i | \(-0.348474\pi\) | ||||
0.458257 | + | 0.888820i | \(0.348474\pi\) | |||||||
\(662\) | 19.4775 | 0.757013 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.63256 | 0.0633556 | ||||||||
\(665\) | 4.02371 | 0.156033 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.693275 | 0.0268437 | ||||||||
\(668\) | 13.1077 | 0.507153 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 27.9816 | 1.08102 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.21365 | −0.162424 | −0.0812122 | − | 0.996697i | \(-0.525879\pi\) | ||||
−0.0812122 | + | 0.996697i | \(0.525879\pi\) | |||||||
\(674\) | 52.4849 | 2.02164 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.6023 | −0.907781 | ||||||||
\(677\) | −17.0035 | −0.653497 | −0.326748 | − | 0.945111i | \(-0.605953\pi\) | ||||
−0.326748 | + | 0.945111i | \(0.605953\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.95598 | −0.151816 | ||||||||
\(680\) | 2.00196 | 0.0767718 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.6114 | −0.750409 | −0.375204 | − | 0.926942i | \(-0.622427\pi\) | ||||
−0.375204 | + | 0.926942i | \(0.622427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.72703 | −0.180611 | ||||||||
\(686\) | 16.5026 | 0.630071 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.3234 | 0.660449 | ||||||||
\(689\) | 10.1938 | 0.388352 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.66999 | 0.291780 | 0.145890 | − | 0.989301i | \(-0.453395\pi\) | ||||
0.145890 | + | 0.989301i | \(0.453395\pi\) | |||||||
\(692\) | −36.4390 | −1.38520 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −57.1854 | −2.17073 | ||||||||
\(695\) | −18.4737 | −0.700748 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0402 | 0.759076 | ||||||||
\(698\) | −21.7382 | −0.822803 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.29702 | 0.0490228 | ||||||||
\(701\) | 21.9331 | 0.828403 | 0.414202 | − | 0.910185i | \(-0.364061\pi\) | ||||
0.414202 | + | 0.910185i | \(0.364061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.4175 | 0.920924 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 59.5662 | 2.24180 | ||||||||
\(707\) | −3.50753 | −0.131914 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.22476 | −0.271332 | −0.135666 | − | 0.990755i | \(-0.543317\pi\) | ||||
−0.135666 | + | 0.990755i | \(0.543317\pi\) | |||||||
\(710\) | 2.63055 | 0.0987227 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.47469 | 0.0927431 | ||||||||
\(713\) | −0.162869 | −0.00609951 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 47.3678 | 1.77022 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −61.9440 | −2.31173 | ||||||||
\(719\) | 19.2225 | 0.716879 | 0.358439 | − | 0.933553i | \(-0.383309\pi\) | ||||
0.358439 | + | 0.933553i | \(0.383309\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.14187 | 0.0425254 | ||||||||
\(722\) | −56.3909 | −2.09865 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −44.3463 | −1.64812 | ||||||||
\(725\) | 8.42443 | 0.312875 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.9775 | −1.26015 | −0.630077 | − | 0.776532i | \(-0.716977\pi\) | ||||
−0.630077 | + | 0.776532i | \(0.716977\pi\) | |||||||
\(728\) | 0.361250 | 0.0133888 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 32.0206 | 1.18514 | ||||||||
\(731\) | −23.9185 | −0.884657 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.49826 | −0.240019 | −0.120009 | − | 0.992773i | \(-0.538292\pi\) | ||||
−0.120009 | + | 0.992773i | \(0.538292\pi\) | |||||||
\(734\) | 48.4714 | 1.78911 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.667841 | 0.0246170 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.7140 | 0.688405 | 0.344203 | − | 0.938895i | \(-0.388149\pi\) | ||||
0.344203 | + | 0.938895i | \(0.388149\pi\) | |||||||
\(740\) | 7.87085 | 0.289338 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.18802 | 0.300592 | ||||||||
\(743\) | 8.79889 | 0.322800 | 0.161400 | − | 0.986889i | \(-0.448399\pi\) | ||||
0.161400 | + | 0.986889i | \(0.448399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.5011 | −0.567915 | ||||||||
\(746\) | −29.9156 | −1.09529 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.88892 | 0.178637 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.7867 | 0.940971 | 0.470485 | − | 0.882408i | \(-0.344079\pi\) | ||||
0.470485 | + | 0.882408i | \(0.344079\pi\) | |||||||
\(752\) | 20.5912 | 0.750884 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.9779 | 0.946058 | ||||||||
\(755\) | 5.55440 | 0.202145 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.0699 | 1.45636 | 0.728182 | − | 0.685384i | \(-0.240366\pi\) | ||||
0.728182 | + | 0.685384i | \(0.240366\pi\) | |||||||
\(758\) | −13.7362 | −0.498920 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.77532 | −0.100672 | ||||||||
\(761\) | 17.9355 | 0.650162 | 0.325081 | − | 0.945686i | \(-0.394608\pi\) | ||||
0.325081 | + | 0.945686i | \(0.394608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.88061 | −0.0680827 | ||||||||
\(764\) | −35.8130 | −1.29567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −64.6028 | −2.33420 | ||||||||
\(767\) | −8.40349 | −0.303432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8431 | 0.391011 | 0.195506 | − | 0.980703i | \(-0.437365\pi\) | ||||
0.195506 | + | 0.980703i | \(0.437365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.36412 | −0.265040 | ||||||||
\(773\) | 6.86871 | 0.247050 | 0.123525 | − | 0.992341i | \(-0.460580\pi\) | ||||
0.123525 | + | 0.992341i | \(0.460580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.97913 | −0.0710925 | ||||||||
\(776\) | 2.72860 | 0.0979512 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −79.8794 | −2.86381 | ||||||||
\(779\) | −27.7817 | −0.995384 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.829623 | −0.0296673 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.7037 | 0.846559 | ||||||||
\(785\) | 18.5115 | 0.660704 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.26967 | −0.0809050 | −0.0404525 | − | 0.999181i | \(-0.512880\pi\) | ||||
−0.0404525 | + | 0.999181i | \(0.512880\pi\) | |||||||
\(788\) | −21.5056 | −0.766106 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.8513 | 0.813014 | ||||||||
\(791\) | −6.77869 | −0.241022 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.44509 | −0.0513166 | ||||||||
\(794\) | −55.6688 | −1.97561 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.7452 | 0.770737 | ||||||||
\(797\) | −11.0564 | −0.391636 | −0.195818 | − | 0.980640i | \(-0.562736\pi\) | ||||
−0.195818 | + | 0.980640i | \(0.562736\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.4303 | −1.00579 | ||||||||
\(800\) | 8.11537 | 0.286922 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 27.0356 | 0.954660 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0485478 | −0.00171109 | ||||||||
\(806\) | −6.10292 | −0.214966 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.41929 | 0.0851104 | ||||||||
\(809\) | 4.30271 | 0.151275 | 0.0756377 | − | 0.997135i | \(-0.475901\pi\) | ||||
0.0756377 | + | 0.997135i | \(0.475901\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.7204 | 0.657361 | 0.328681 | − | 0.944441i | \(-0.393396\pi\) | ||||
0.328681 | + | 0.944441i | \(0.393396\pi\) | |||||||
\(812\) | 10.9267 | 0.383451 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.81457 | −0.273733 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.1582 | 1.16006 | ||||||||
\(818\) | −20.3416 | −0.711226 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.95529 | −0.312732 | ||||||||
\(821\) | 36.4237 | 1.27119 | 0.635597 | − | 0.772021i | \(-0.280754\pi\) | ||||
0.635597 | + | 0.772021i | \(0.280754\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.52202 | −0.0530542 | −0.0265271 | − | 0.999648i | \(-0.508445\pi\) | ||||
−0.0265271 | + | 0.999648i | \(0.508445\pi\) | |||||||
\(824\) | −0.787594 | −0.0274371 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.75000 | −0.234863 | ||||||||
\(827\) | 25.4190 | 0.883904 | 0.441952 | − | 0.897039i | \(-0.354286\pi\) | ||||
0.441952 | + | 0.897039i | \(0.354286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.50118 | −0.295258 | −0.147629 | − | 0.989043i | \(-0.547164\pi\) | ||||
−0.147629 | + | 0.989043i | \(0.547164\pi\) | |||||||
\(830\) | −8.22108 | −0.285358 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.2996 | 0.495750 | ||||||||
\(833\) | −32.7277 | −1.13395 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.96190 | −0.206320 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −54.1510 | −1.87062 | ||||||||
\(839\) | 44.4716 | 1.53533 | 0.767666 | − | 0.640850i | \(-0.221418\pi\) | ||||
0.767666 | + | 0.640850i | \(0.221418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41.9710 | 1.44728 | ||||||||
\(842\) | −28.1723 | −0.970883 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 48.7396 | 1.67769 | ||||||||
\(845\) | 10.7352 | 0.369303 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.1372 | 0.828877 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.0813 | −0.345785 | ||||||||
\(851\) | −0.294608 | −0.0100990 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.8719 | −0.954315 | −0.477158 | − | 0.878818i | \(-0.658333\pi\) | ||||
−0.477158 | + | 0.878818i | \(0.658333\pi\) | |||||||
\(854\) | −1.16075 | −0.0397200 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.37209 | −0.115256 | ||||||||
\(857\) | 23.1342 | 0.790249 | 0.395125 | − | 0.918628i | \(-0.370701\pi\) | ||||
0.395125 | + | 0.918628i | \(0.370701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 51.9912 | 1.77392 | 0.886959 | − | 0.461849i | \(-0.152814\pi\) | ||||
0.886959 | + | 0.461849i | \(0.152814\pi\) | |||||||
\(860\) | 10.6884 | 0.364470 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40.9232 | −1.39385 | ||||||||
\(863\) | 29.2084 | 0.994266 | 0.497133 | − | 0.867674i | \(-0.334386\pi\) | ||||
0.497133 | + | 0.867674i | \(0.334386\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.5738 | 0.563528 | ||||||||
\(866\) | −34.0190 | −1.15601 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.56698 | −0.0871289 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.5510 | −0.696343 | ||||||||
\(872\) | 1.29714 | 0.0439266 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.15011 | 0.0389030 | ||||||||
\(875\) | −0.589936 | −0.0199435 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.5757 | −1.16754 | −0.583769 | − | 0.811920i | \(-0.698423\pi\) | ||||
−0.583769 | + | 0.811920i | \(0.698423\pi\) | |||||||
\(878\) | −58.1202 | −1.96146 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.3728 | −1.49496 | −0.747479 | − | 0.664285i | \(-0.768736\pi\) | ||||
−0.747479 | + | 0.664285i | \(0.768736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.7786 | −0.968477 | −0.484238 | − | 0.874936i | \(-0.660903\pi\) | ||||
−0.484238 | + | 0.874936i | \(0.660903\pi\) | |||||||
\(884\) | −16.2787 | −0.547511 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 46.4777 | 1.56145 | ||||||||
\(887\) | −9.30878 | −0.312558 | −0.156279 | − | 0.987713i | \(-0.549950\pi\) | ||||
−0.156279 | + | 0.987713i | \(0.549950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.7318 | −0.359932 | ||||||||
\(890\) | −12.4618 | −0.417721 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.1301 | 0.908383 | ||||||||
\(893\) | 39.4130 | 1.31891 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.5447 | −0.720160 | ||||||||
\(896\) | 1.91091 | 0.0638390 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.38845 | 0.313296 | ||||||||
\(899\) | −16.6731 | −0.556078 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.3264 | −1.11026 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.67555 | 0.155506 | ||||||||
\(905\) | 20.1704 | 0.670487 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.4044 | −1.47442 | −0.737212 | − | 0.675662i | \(-0.763858\pi\) | ||||
−0.737212 | + | 0.675662i | \(0.763858\pi\) | |||||||
\(908\) | −18.0758 | −0.599867 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.81915 | −0.0603041 | ||||||||
\(911\) | −23.6358 | −0.783088 | −0.391544 | − | 0.920159i | \(-0.628059\pi\) | ||||
−0.391544 | + | 0.920159i | \(0.628059\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13.7816 | 0.455855 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 59.4596 | 1.96460 | ||||||||
\(917\) | 11.0765 | 0.365779 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.85429 | −0.226102 | −0.113051 | − | 0.993589i | \(-0.536062\pi\) | ||||
−0.113051 | + | 0.993589i | \(0.536062\pi\) | |||||||
\(920\) | 0.0334855 | 0.00110398 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.80963 | 0.191330 | ||||||||
\(923\) | −1.93200 | −0.0635925 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.57997 | −0.117709 | ||||||||
\(926\) | −42.1074 | −1.38374 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 68.3674 | 2.24427 | ||||||||
\(929\) | 28.4759 | 0.934265 | 0.467132 | − | 0.884187i | \(-0.345287\pi\) | ||||
0.467132 | + | 0.884187i | \(0.345287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.3705 | 1.48696 | ||||||||
\(932\) | 54.9738 | 1.80073 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.0954 | −0.788427 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.1324 | 1.27840 | 0.639199 | − | 0.769041i | \(-0.279266\pi\) | ||||
0.639199 | + | 0.769041i | \(0.279266\pi\) | |||||||
\(938\) | −16.5073 | −0.538983 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.7046 | 0.414377 | ||||||||
\(941\) | −38.0674 | −1.24096 | −0.620480 | − | 0.784222i | \(-0.713062\pi\) | ||||
−0.620480 | + | 0.784222i | \(0.713062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.335198 | 0.0109156 | ||||||||
\(944\) | −19.8981 | −0.647629 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.37140 | −0.207043 | −0.103521 | − | 0.994627i | \(-0.533011\pi\) | ||||
−0.103521 | + | 0.994627i | \(0.533011\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.5175 | −0.763409 | ||||||||
\(950\) | 13.9757 | 0.453432 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.18103 | −0.0382774 | ||||||||
\(953\) | −2.90339 | −0.0940500 | −0.0470250 | − | 0.998894i | \(-0.514974\pi\) | ||||
−0.0470250 | + | 0.998894i | \(0.514974\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.2891 | 0.527104 | ||||||||
\(956\) | −45.5573 | −1.47343 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.11929 | −0.100780 | ||||||||
\(959\) | 2.78864 | 0.0900500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0830 | −0.873646 | ||||||||
\(962\) | −11.0393 | −0.355922 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 51.5118 | 1.65908 | ||||||||
\(965\) | 3.34948 | 0.107824 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.58404 | 0.308202 | 0.154101 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154101 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −13.7404 | −0.441179 | ||||||||
\(971\) | 53.8394 | 1.72779 | 0.863895 | − | 0.503672i | \(-0.168018\pi\) | ||||
0.863895 | + | 0.503672i | \(0.168018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.8983 | 0.349384 | ||||||||
\(974\) | −72.7369 | −2.33064 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.42174 | −0.109527 | ||||||||
\(977\) | 29.4618 | 0.942568 | 0.471284 | − | 0.881982i | \(-0.343791\pi\) | ||||
0.471284 | + | 0.881982i | \(0.343791\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.6249 | 0.467176 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.9766 | −0.828946 | ||||||||
\(983\) | −44.9732 | −1.43442 | −0.717211 | − | 0.696856i | \(-0.754581\pi\) | ||||
−0.717211 | + | 0.696856i | \(0.754581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.78158 | 0.311667 | ||||||||
\(986\) | −84.9291 | −2.70469 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 22.5672 | 0.717957 | ||||||||
\(989\) | −0.400068 | −0.0127214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.3468 | 0.963997 | 0.481998 | − | 0.876172i | \(-0.339911\pi\) | ||||
0.481998 | + | 0.876172i | \(0.339911\pi\) | |||||||
\(992\) | −16.0614 | −0.509950 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.55185 | −0.0492218 | ||||||||
\(995\) | −9.89054 | −0.313551 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.2808 | 0.768981 | 0.384490 | − | 0.923129i | \(-0.374377\pi\) | ||||
0.384490 | + | 0.923129i | \(0.374377\pi\) | |||||||
\(998\) | −43.1483 | −1.36583 | ||||||||
\(999\) | 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 | 5445.2.a.cc.1.1 | 8 | ||
3.2 | odd | 2 | 5445.2.a.cb.1.8 | 8 | |||
11.7 | odd | 10 | 495.2.n.h.181.4 | yes | 16 | ||
11.8 | odd | 10 | 495.2.n.h.361.4 | yes | 16 | ||
11.10 | odd | 2 | 5445.2.a.ca.1.8 | 8 | |||
33.8 | even | 10 | 495.2.n.g.361.1 | yes | 16 | ||
33.29 | even | 10 | 495.2.n.g.181.1 | ✓ | 16 | ||
33.32 | even | 2 | 5445.2.a.cd.1.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.n.g.181.1 | ✓ | 16 | 33.29 | even | 10 | ||
495.2.n.g.361.1 | yes | 16 | 33.8 | even | 10 | ||
495.2.n.h.181.4 | yes | 16 | 11.7 | odd | 10 | ||
495.2.n.h.361.4 | yes | 16 | 11.8 | odd | 10 | ||
5445.2.a.ca.1.8 | 8 | 11.10 | odd | 2 | |||
5445.2.a.cb.1.8 | 8 | 3.2 | odd | 2 | |||
5445.2.a.cc.1.1 | 8 | 1.1 | even | 1 | trivial | ||
5445.2.a.cd.1.1 | 8 | 33.32 | even | 2 |