Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + 26911 x^{5} - 72240 x^{4} - 14532 x^{3} + 112850 x^{2} - 72184 x + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-4.02595\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(5\) | −4.02595 | −1.80046 | −0.900229 | − | 0.435416i | \(-0.856601\pi\) | ||||
−0.900229 | + | 0.435416i | \(0.856601\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.910115 | −0.343991 | −0.171996 | − | 0.985098i | \(-0.555021\pi\) | ||||
−0.171996 | + | 0.985098i | \(0.555021\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.64943 | 1.70337 | 0.851683 | − | 0.524058i | \(-0.175582\pi\) | ||||
0.851683 | + | 0.524058i | \(0.175582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.43968 | 1.78605 | 0.893023 | − | 0.450011i | \(-0.148580\pi\) | ||||
0.893023 | + | 0.450011i | \(0.148580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.02595 | 1.03950 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.30990 | 0.802770 | 0.401385 | − | 0.915909i | \(-0.368529\pi\) | ||||
0.401385 | + | 0.915909i | \(0.368529\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.28987 | −0.295915 | −0.147958 | − | 0.988994i | \(-0.547270\pi\) | ||||
−0.147958 | + | 0.988994i | \(0.547270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.910115 | 0.198603 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.24783 | 1.92830 | 0.964152 | − | 0.265349i | \(-0.0854871\pi\) | ||||
0.964152 | + | 0.265349i | \(0.0854871\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.2083 | 2.24165 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.90838 | 0.540072 | 0.270036 | − | 0.962850i | \(-0.412964\pi\) | ||||
0.270036 | + | 0.962850i | \(0.412964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6281 | 1.90886 | 0.954431 | − | 0.298432i | \(-0.0964635\pi\) | ||||
0.954431 | + | 0.298432i | \(0.0964635\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.64943 | −0.983439 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.66408 | 0.619342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.18976 | 0.524393 | 0.262196 | − | 0.965015i | \(-0.415553\pi\) | ||||
0.262196 | + | 0.965015i | \(0.415553\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.43968 | −1.03117 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.79168 | 0.279813 | 0.139907 | − | 0.990165i | \(-0.455320\pi\) | ||||
0.139907 | + | 0.990165i | \(0.455320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.55965 | −0.390344 | −0.195172 | − | 0.980769i | \(-0.562526\pi\) | ||||
−0.195172 | + | 0.980769i | \(0.562526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.02595 | −0.600153 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.91679 | −0.279593 | −0.139797 | − | 0.990180i | \(-0.544645\pi\) | ||||
−0.139797 | + | 0.990180i | \(0.544645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.17169 | −0.881670 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.30990 | −0.463479 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.55631 | −0.900579 | −0.450289 | − | 0.892883i | \(-0.648679\pi\) | ||||
−0.450289 | + | 0.892883i | \(0.648679\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22.7443 | −3.06684 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.28987 | 0.170847 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.97385 | 0.387162 | 0.193581 | − | 0.981084i | \(-0.437990\pi\) | ||||
0.193581 | + | 0.981084i | \(0.437990\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.34803 | 1.06886 | 0.534428 | − | 0.845214i | \(-0.320527\pi\) | ||||
0.534428 | + | 0.845214i | \(0.320527\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.910115 | −0.114664 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −25.9258 | −3.21570 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.23967 | −0.517959 | −0.258979 | − | 0.965883i | \(-0.583386\pi\) | ||||
−0.258979 | + | 0.965883i | \(0.583386\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.24783 | −1.11331 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.1160 | −1.20055 | −0.600276 | − | 0.799793i | \(-0.704943\pi\) | ||||
−0.600276 | + | 0.799793i | \(0.704943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.27643 | 0.149395 | 0.0746974 | − | 0.997206i | \(-0.476201\pi\) | ||||
0.0746974 | + | 0.997206i | \(0.476201\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −11.2083 | −1.29422 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.14163 | −0.585943 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.79214 | 0.201631 | 0.100816 | − | 0.994905i | \(-0.467855\pi\) | ||||
0.100816 | + | 0.994905i | \(0.467855\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8633 | −1.52169 | −0.760846 | − | 0.648932i | \(-0.775216\pi\) | ||||
−0.760846 | + | 0.648932i | \(0.775216\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.3255 | −1.44535 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.90838 | −0.311811 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.45522 | 0.578252 | 0.289126 | − | 0.957291i | \(-0.406635\pi\) | ||||
0.289126 | + | 0.957291i | \(0.406635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.86085 | −0.614384 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.6281 | −1.10208 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.19293 | 0.532783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0108 | 1.32105 | 0.660525 | − | 0.750804i | \(-0.270334\pi\) | ||||
0.660525 | + | 0.750804i | \(0.270334\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.64943 | 0.567789 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.5075 | 1.34405 | 0.672023 | − | 0.740530i | \(-0.265425\pi\) | ||||
0.672023 | + | 0.740530i | \(0.265425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.77840 | 0.273763 | 0.136882 | − | 0.990587i | \(-0.456292\pi\) | ||||
0.136882 | + | 0.990587i | \(0.456292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.66408 | −0.357577 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.24267 | −0.313480 | −0.156740 | − | 0.987640i | \(-0.550099\pi\) | ||||
−0.156740 | + | 0.987640i | \(0.550099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.99492 | 0.957339 | 0.478670 | − | 0.877995i | \(-0.341119\pi\) | ||||
0.478670 | + | 0.877995i | \(0.341119\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.18976 | −0.302758 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.1305 | 1.14114 | 0.570571 | − | 0.821249i | \(-0.306722\pi\) | ||||
0.570571 | + | 0.821249i | \(0.306722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −37.2313 | −3.47183 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.43968 | 0.595349 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.01239 | −0.276146 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.9160 | 1.90145 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.79168 | −0.161550 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −24.9941 | −2.23554 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.6803 | −1.12520 | −0.562599 | − | 0.826730i | \(-0.690198\pi\) | ||||
−0.562599 | + | 0.826730i | \(0.690198\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.55965 | 0.225365 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.08979 | −0.619438 | −0.309719 | − | 0.950828i | \(-0.600235\pi\) | ||||
−0.309719 | + | 0.950828i | \(0.600235\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.17393 | 0.101792 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.02595 | 0.346498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.44562 | 0.123508 | 0.0617538 | − | 0.998091i | \(-0.480331\pi\) | ||||
0.0617538 | + | 0.998091i | \(0.480331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4215 | 1.64731 | 0.823656 | − | 0.567089i | \(-0.191931\pi\) | ||||
0.823656 | + | 0.567089i | \(0.191931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.91679 | 0.161423 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 36.3805 | 3.04229 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.7090 | −0.972378 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.17169 | 0.509032 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6988 | 0.876482 | 0.438241 | − | 0.898858i | \(-0.355602\pi\) | ||||
0.438241 | + | 0.898858i | \(0.355602\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.13414 | −0.0922949 | −0.0461474 | − | 0.998935i | \(-0.514694\pi\) | ||||
−0.0461474 | + | 0.998935i | \(0.514694\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.30990 | 0.267590 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −42.7882 | −3.43683 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.13747 | −0.170589 | −0.0852944 | − | 0.996356i | \(-0.527183\pi\) | ||||
−0.0852944 | + | 0.996356i | \(0.527183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.55631 | 0.519949 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.41658 | −0.663320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.75643 | 0.685857 | 0.342928 | − | 0.939362i | \(-0.388581\pi\) | ||||
0.342928 | + | 0.939362i | \(0.388581\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 22.7443 | 1.77064 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.4695 | 2.18996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.28987 | −0.0986384 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.7771 | 1.57966 | 0.789829 | − | 0.613328i | \(-0.210169\pi\) | ||||
0.789829 | + | 0.613328i | \(0.210169\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.2008 | −0.771108 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.97385 | −0.223528 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.6874 | −1.54625 | −0.773123 | − | 0.634256i | \(-0.781307\pi\) | ||||
−0.773123 | + | 0.634256i | \(0.781307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6867 | −0.794335 | −0.397167 | − | 0.917746i | \(-0.630007\pi\) | ||||
−0.397167 | + | 0.917746i | \(0.630007\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.34803 | −0.617104 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.8418 | −0.944148 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.6991 | 1.36741 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.910115 | 0.0662011 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.7568 | −1.71898 | −0.859489 | − | 0.511154i | \(-0.829218\pi\) | ||||
−0.859489 | + | 0.511154i | \(0.829218\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.301545 | 0.0217057 | 0.0108528 | − | 0.999941i | \(-0.496545\pi\) | ||||
0.0108528 | + | 0.999941i | \(0.496545\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 25.9258 | 1.85659 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.9860 | −1.56644 | −0.783218 | − | 0.621747i | \(-0.786423\pi\) | ||||
−0.783218 | + | 0.621747i | \(0.786423\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.3274 | 1.29920 | 0.649598 | − | 0.760278i | \(-0.274937\pi\) | ||||
0.649598 | + | 0.760278i | \(0.274937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.23967 | 0.299044 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.64696 | −0.185780 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.21321 | −0.503792 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.24783 | 0.642768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.28700 | −0.504052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.9537 | −1.78673 | −0.893363 | − | 0.449336i | \(-0.851661\pi\) | ||||
−0.893363 | + | 0.449336i | \(0.851661\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.1160 | 0.693139 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.3050 | 0.702798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.67279 | −0.656631 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.27643 | −0.0862531 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.3147 | 1.43378 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.8575 | 1.59761 | 0.798807 | − | 0.601588i | \(-0.205465\pi\) | ||||
0.798807 | + | 0.601588i | \(0.205465\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.2083 | 0.747217 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.8006 | −0.783233 | −0.391616 | − | 0.920129i | \(-0.628084\pi\) | ||||
−0.391616 | + | 0.920129i | \(0.628084\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.93628 | 0.326199 | 0.163099 | − | 0.986610i | \(-0.447851\pi\) | ||||
0.163099 | + | 0.986610i | \(0.447851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.14163 | 0.338294 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.2292 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.71692 | 0.503396 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.79214 | −0.116412 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.31462 | 0.602513 | 0.301256 | − | 0.953543i | \(-0.402594\pi\) | ||||
0.301256 | + | 0.953543i | \(0.402594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.96831 | −0.577700 | −0.288850 | − | 0.957374i | \(-0.593273\pi\) | ||||
−0.288850 | + | 0.957374i | \(0.593273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.8469 | 1.58741 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.30632 | −0.528518 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.8633 | 0.878550 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5794 | −1.29896 | −0.649480 | − | 0.760379i | \(-0.725013\pi\) | ||||
−0.649480 | + | 0.760379i | \(0.725013\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 52.2449 | 3.28461 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.3255 | 0.834476 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.3369 | −1.76761 | −0.883803 | − | 0.467859i | \(-0.845025\pi\) | ||||
−0.883803 | + | 0.467859i | \(0.845025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.90304 | −0.180386 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.90838 | 0.180024 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.9168 | −1.35145 | −0.675723 | − | 0.737156i | \(-0.736168\pi\) | ||||
−0.675723 | + | 0.737156i | \(0.736168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.3954 | 1.62146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.45522 | −0.333854 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.34233 | 0.508641 | 0.254320 | − | 0.967120i | \(-0.418148\pi\) | ||||
0.254320 | + | 0.967120i | \(0.418148\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.97049 | 0.362681 | 0.181341 | − | 0.983420i | \(-0.441956\pi\) | ||||
0.181341 | + | 0.983420i | \(0.441956\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.86085 | 0.354715 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 63.3202 | 3.81835 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.35540 | −0.141522 | −0.0707610 | − | 0.997493i | \(-0.522543\pi\) | ||||
−0.0707610 | + | 0.997493i | \(0.522543\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.6281 | 0.636287 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.45133 | −0.563819 | −0.281909 | − | 0.959441i | \(-0.590968\pi\) | ||||
−0.281909 | + | 0.959441i | \(0.590968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.76734 | −0.580608 | −0.290304 | − | 0.956934i | \(-0.593756\pi\) | ||||
−0.290304 | + | 0.956934i | \(0.593756\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.19293 | −0.307603 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.63063 | −0.0962532 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.04453 | −0.355561 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.0108 | −0.762709 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.86304 | 0.108840 | 0.0544200 | − | 0.998518i | \(-0.482669\pi\) | ||||
0.0544200 | + | 0.998518i | \(0.482669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9726 | −0.697069 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.64943 | −0.327813 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 59.5530 | 3.44404 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.32958 | 0.134275 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.5075 | −0.775986 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.6087 | −1.92443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9878 | −0.684178 | −0.342089 | − | 0.939668i | \(-0.611134\pi\) | ||||
−0.342089 | + | 0.939668i | \(0.611134\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.77840 | −0.158057 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.72229 | 0.437891 | 0.218946 | − | 0.975737i | \(-0.429738\pi\) | ||||
0.218946 | + | 0.975737i | \(0.429738\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.5266 | −1.55590 | −0.777949 | − | 0.628328i | \(-0.783740\pi\) | ||||
−0.777949 | + | 0.628328i | \(0.783740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.66408 | 0.206447 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.6703 | −1.66645 | −0.833225 | − | 0.552934i | \(-0.813508\pi\) | ||||
−0.833225 | + | 0.552934i | \(0.813508\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4307 | 0.919940 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.24267 | 0.180988 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.26933 | −0.237552 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 72.1776 | 4.00369 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.99492 | −0.552720 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.74450 | 0.0961776 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.06789 | 0.498416 | 0.249208 | − | 0.968450i | \(-0.419830\pi\) | ||||
0.249208 | + | 0.968450i | \(0.419830\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.18976 | 0.174798 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17.0687 | 0.932563 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.1926 | 1.31785 | 0.658927 | − | 0.752207i | \(-0.271011\pi\) | ||||
0.658927 | + | 0.752207i | \(0.271011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.1305 | −0.658838 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 60.0426 | 3.25149 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.9878 | 0.647278 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.2313 | 2.00446 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.3260 | −0.608011 | −0.304006 | − | 0.952670i | \(-0.598324\pi\) | ||||
−0.304006 | + | 0.952670i | \(0.598324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.8336 | −1.65048 | −0.825241 | − | 0.564781i | \(-0.808961\pi\) | ||||
−0.825241 | + | 0.564781i | \(0.808961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.43968 | −0.343725 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −29.5939 | −1.57512 | −0.787562 | − | 0.616236i | \(-0.788657\pi\) | ||||
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 40.7266 | 2.16155 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.01239 | 0.159433 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.0055 | 0.580847 | 0.290423 | − | 0.956898i | \(-0.406204\pi\) | ||||
0.290423 | + | 0.956898i | \(0.406204\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3362 | −0.912434 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −20.9160 | −1.09781 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.13884 | −0.268979 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.8033 | 1.19032 | 0.595161 | − | 0.803606i | \(-0.297088\pi\) | ||||
0.595161 | + | 0.803606i | \(0.297088\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.79168 | 0.0932711 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.96700 | 0.309791 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.84106 | −0.354217 | −0.177108 | − | 0.984191i | \(-0.556674\pi\) | ||||
−0.177108 | + | 0.984191i | \(0.556674\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 24.9941 | 1.29069 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.7290 | 0.964593 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.7773 | −0.861789 | −0.430895 | − | 0.902402i | \(-0.641802\pi\) | ||||
−0.430895 | + | 0.902402i | \(0.641802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6803 | 0.649633 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.9407 | 0.916726 | 0.458363 | − | 0.888765i | \(-0.348436\pi\) | ||||
0.458363 | + | 0.888765i | \(0.348436\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.6999 | 1.05497 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.55965 | −0.130115 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.8167 | 0.801939 | 0.400970 | − | 0.916091i | \(-0.368673\pi\) | ||||
0.400970 | + | 0.916091i | \(0.368673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.6094 | 1.54798 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.08979 | 0.357633 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.21506 | −0.363029 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.10390 | 0.155781 | 0.0778903 | − | 0.996962i | \(-0.475182\pi\) | ||||
0.0778903 | + | 0.996962i | \(0.475182\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.17393 | −0.0587698 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.30176 | 0.314695 | 0.157348 | − | 0.987543i | \(-0.449706\pi\) | ||||
0.157348 | + | 0.987543i | \(0.449706\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 68.4415 | 3.40931 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.02595 | −0.200051 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.0203 | 0.893233 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0912 | 0.795658 | 0.397829 | − | 0.917460i | \(-0.369764\pi\) | ||||
0.397829 | + | 0.917460i | \(0.369764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.44562 | −0.0713071 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.70654 | −0.133180 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 55.8129 | 2.73975 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.4215 | −0.951076 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0306 | −1.36938 | −0.684691 | − | 0.728833i | \(-0.740063\pi\) | ||||
−0.684691 | + | 0.728833i | \(0.740063\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.41757 | 0.166562 | 0.0832811 | − | 0.996526i | \(-0.473460\pi\) | ||||
0.0832811 | + | 0.996526i | \(0.473460\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.91679 | −0.0931977 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37.0983 | 1.79953 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.59767 | −0.367677 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −36.3805 | −1.75647 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.43379 | −0.261737 | −0.130868 | − | 0.991400i | \(-0.541777\pi\) | ||||
−0.130868 | + | 0.991400i | \(0.541777\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.9533 | 1.96809 | 0.984044 | − | 0.177923i | \(-0.0569378\pi\) | ||||
0.984044 | + | 0.177923i | \(0.0569378\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.7090 | 0.561402 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.9284 | −0.570615 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.0418 | 0.526994 | 0.263497 | − | 0.964660i | \(-0.415124\pi\) | ||||
0.263497 | + | 0.964660i | \(0.415124\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.17169 | −0.293890 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.25699 | 0.107233 | 0.0536164 | − | 0.998562i | \(-0.482925\pi\) | ||||
0.0536164 | + | 0.998562i | \(0.482925\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.9624 | −1.04112 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6988 | −0.506037 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.4263 | −1.62468 | −0.812339 | − | 0.583185i | \(-0.801806\pi\) | ||||
−0.812339 | + | 0.583185i | \(0.801806\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.1220 | 0.476624 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.13414 | 0.0532865 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.5955 | 1.10617 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.47846 | 0.256271 | 0.128136 | − | 0.991757i | \(-0.459101\pi\) | ||||
0.128136 | + | 0.991757i | \(0.459101\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.30990 | −0.154493 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.7152 | 1.01138 | 0.505689 | − | 0.862716i | \(-0.331238\pi\) | ||||
0.505689 | + | 0.862716i | \(0.331238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.49087 | −0.208709 | −0.104354 | − | 0.994540i | \(-0.533278\pi\) | ||||
−0.104354 | + | 0.994540i | \(0.533278\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 42.7882 | 1.98425 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.0664030 | −0.00307277 | −0.00153638 | − | 0.999999i | \(-0.500489\pi\) | ||||
−0.00153638 | + | 0.999999i | \(0.500489\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.85859 | 0.178173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.13747 | 0.0984895 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14.4606 | −0.664898 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.4571 | −0.663339 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.55631 | −0.300193 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.4840 | −1.30147 | −0.650733 | − | 0.759307i | \(-0.725538\pi\) | ||||
−0.650733 | + | 0.759307i | \(0.725538\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5410 | 0.936589 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.41658 | 0.382968 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −52.3810 | −2.37850 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.2150 | 1.77700 | 0.888502 | − | 0.458873i | \(-0.151747\pi\) | ||||
0.888502 | + | 0.458873i | \(0.151747\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.75643 | −0.395980 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.5329 | −1.15228 | −0.576141 | − | 0.817350i | \(-0.695442\pi\) | ||||
−0.576141 | + | 0.817350i | \(0.695442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.62645 | 0.433554 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −22.7443 | −1.02228 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.20675 | 0.412979 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.9599 | −1.16212 | −0.581061 | − | 0.813860i | \(-0.697362\pi\) | ||||
−0.581061 | + | 0.813860i | \(0.697362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.3605 | 1.53206 | 0.766030 | − | 0.642805i | \(-0.222230\pi\) | ||||
0.766030 | + | 0.642805i | \(0.222230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −54.3805 | −2.41990 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.4695 | −1.26437 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.1390 | 0.803998 | 0.401999 | − | 0.915640i | \(-0.368315\pi\) | ||||
0.401999 | + | 0.915640i | \(0.368315\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.16170 | −0.0513905 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.28987 | 0.0569489 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.1857 | −0.492900 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.8288 | −0.476250 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.7771 | −0.912016 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7860 | −0.823031 | −0.411515 | − | 0.911403i | \(-0.635000\pi\) | ||||
−0.411515 | + | 0.911403i | \(0.635000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.94829 | 0.128920 | 0.0644600 | − | 0.997920i | \(-0.479468\pi\) | ||||
0.0644600 | + | 0.997920i | \(0.479468\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.2008 | 0.445200 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 35.1780 | 1.53238 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.5223 | 2.71836 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.97385 | 0.129054 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.5378 | 0.499759 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.0548 | 0.564409 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.6874 | 0.892726 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.8665 | −1.50181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.9263 | 0.512751 | 0.256375 | − | 0.966577i | \(-0.417472\pi\) | ||||
0.256375 | + | 0.966577i | \(0.417472\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.6867 | 0.458609 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40.2390 | −1.72365 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.94329 | 0.382387 | 0.191194 | − | 0.981552i | \(-0.438764\pi\) | ||||
0.191194 | + | 0.981552i | \(0.438764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.34803 | 0.356285 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.75141 | −0.159816 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.63105 | −0.0693594 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.8418 | 0.545104 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.5579 | −1.63375 | −0.816876 | − | 0.576814i | \(-0.804296\pi\) | ||||
−0.816876 | + | 0.576814i | \(0.804296\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.4834 | −0.697172 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.6991 | −0.789475 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.8490 | −0.457232 | −0.228616 | − | 0.973517i | \(-0.573420\pi\) | ||||
−0.228616 | + | 0.973517i | \(0.573420\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −48.8368 | −2.05458 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.910115 | −0.0382212 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.09232 | −0.0877148 | −0.0438574 | − | 0.999038i | \(-0.513965\pi\) | ||||
−0.0438574 | + | 0.999038i | \(0.513965\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.2241 | 0.846352 | 0.423176 | − | 0.906047i | \(-0.360915\pi\) | ||||
0.423176 | + | 0.906047i | \(0.360915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.7568 | 0.992453 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 103.652 | 4.32259 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.9254 | 1.32907 | 0.664536 | − | 0.747256i | \(-0.268629\pi\) | ||||
0.664536 | + | 0.747256i | \(0.268629\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.301545 | −0.0125318 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6172 | 0.523449 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.0394 | −1.53402 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.9258 | −1.07190 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.2855 | −0.837274 | −0.418637 | − | 0.908154i | \(-0.637492\pi\) | ||||
−0.418637 | + | 0.908154i | \(0.637492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7088 | −0.564862 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.9860 | 0.904382 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.1257 | 0.621139 | 0.310570 | − | 0.950551i | \(-0.399480\pi\) | ||||
0.310570 | + | 0.950551i | \(0.399480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.1277 | 0.497189 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.3274 | −0.750091 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.7919 | −1.21727 | −0.608633 | − | 0.793452i | \(-0.708282\pi\) | ||||
−0.608633 | + | 0.793452i | \(0.708282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0228 | −1.06149 | −0.530746 | − | 0.847531i | \(-0.678088\pi\) | ||||
−0.530746 | + | 0.847531i | \(0.678088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.23967 | −0.172653 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −84.2068 | −3.42349 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.81543 | −0.114275 | −0.0571373 | − | 0.998366i | \(-0.518197\pi\) | ||||
−0.0571373 | + | 0.998366i | \(0.518197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.64696 | 0.107260 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.3435 | −0.499366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.9337 | −0.845504 | −0.422752 | − | 0.906245i | \(-0.638936\pi\) | ||||
−0.422752 | + | 0.906245i | \(0.638936\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.21321 | 0.290865 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.3534 | 0.698623 | 0.349312 | − | 0.937007i | \(-0.386415\pi\) | ||||
0.349312 | + | 0.937007i | \(0.386415\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.9527 | −0.842159 | −0.421079 | − | 0.907024i | \(-0.638349\pi\) | ||||
−0.421079 | + | 0.907024i | \(0.638349\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.24783 | −0.371102 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.96488 | −0.198914 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 44.5838 | 1.78335 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.28700 | 0.291015 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.5578 | 0.420967 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.6037 | −0.660983 | −0.330492 | − | 0.943809i | \(-0.607215\pi\) | ||||
−0.330492 | + | 0.943809i | \(0.607215\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.9537 | 1.03157 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 51.0504 | 2.02587 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39.7437 | −1.57470 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.1160 | −0.400184 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.1161 | 0.913033 | 0.456516 | − | 0.889715i | \(-0.349097\pi\) | ||||
0.456516 | + | 0.889715i | \(0.349097\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.04889 | 0.277981 | 0.138991 | − | 0.990294i | \(-0.455614\pi\) | ||||
0.138991 | + | 0.990294i | \(0.455614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.3050 | −0.405761 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.6485 | 0.615206 | 0.307603 | − | 0.951515i | \(-0.400473\pi\) | ||||
0.307603 | + | 0.951515i | \(0.400473\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.8005 | 0.659478 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.67279 | 0.379106 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.5382 | −1.27332 | −0.636658 | − | 0.771146i | \(-0.719684\pi\) | ||||
−0.636658 | + | 0.771146i | \(0.719684\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.5431 | 1.11527 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.27643 | 0.0497983 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.89404 | 0.307508 | 0.153754 | − | 0.988109i | \(-0.450864\pi\) | ||||
0.153754 | + | 0.988109i | \(0.450864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.82653 | −0.382208 | −0.191104 | − | 0.981570i | \(-0.561207\pi\) | ||||
−0.191104 | + | 0.981570i | \(0.561207\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.3147 | −0.827795 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.72616 | −0.183273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.8962 | 1.04142 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.8575 | −0.922382 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47.1616 | 1.82065 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2177 | −0.470959 | −0.235480 | − | 0.971879i | \(-0.575666\pi\) | ||||
−0.235480 | + | 0.971879i | \(0.575666\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.2083 | −0.431406 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.9900 | −0.691413 | −0.345706 | − | 0.938343i | \(-0.612361\pi\) | ||||
−0.345706 | + | 0.938343i | \(0.612361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.8414 | −0.454430 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8006 | 0.452200 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.4906 | −1.47280 | −0.736401 | − | 0.676545i | \(-0.763476\pi\) | ||||
−0.736401 | + | 0.676545i | \(0.763476\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.81999 | −0.222370 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.93628 | −0.188331 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −42.2206 | −1.60848 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.2590 | −0.656565 | −0.328283 | − | 0.944580i | \(-0.606470\pi\) | ||||
−0.328283 | + | 0.944580i | \(0.606470\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.14163 | −0.195314 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −78.1901 | −2.96592 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.93028 | 0.224626 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20.2292 | −0.765139 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.5288 | −1.03975 | −0.519874 | − | 0.854243i | \(-0.674021\pi\) | ||||
−0.519874 | + | 0.854243i | \(0.674021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.11436 | −0.155176 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.71692 | −0.290636 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.2934 | −0.462340 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.1421 | 1.65779 | 0.828895 | − | 0.559404i | \(-0.188970\pi\) | ||||
0.828895 | + | 0.559404i | \(0.188970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.79214 | 0.0672104 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 98.2868 | 3.68087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −146.466 | −5.47752 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.31462 | −0.347861 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.3261 | −0.758037 | −0.379018 | − | 0.925389i | \(-0.623738\pi\) | ||||
−0.379018 | + | 0.925389i | \(0.623738\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.52866 | −0.0941722 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.96831 | 0.333535 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.5979 | 1.21065 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.3208 | −1.56959 | −0.784796 | − | 0.619754i | \(-0.787233\pi\) | ||||
−0.784796 | + | 0.619754i | \(0.787233\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.47221 | −0.313356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.9178 | −0.624874 | −0.312437 | − | 0.949938i | \(-0.601145\pi\) | ||||
−0.312437 | + | 0.949938i | \(0.601145\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −24.8469 | −0.916492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.9517 | −0.882273 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.57315 | −0.278583 | −0.139291 | − | 0.990251i | \(-0.544482\pi\) | ||||
−0.139291 | + | 0.990251i | \(0.544482\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.30632 | 0.305140 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.7667 | 1.60565 | 0.802823 | − | 0.596218i | \(-0.203330\pi\) | ||||
0.802823 | + | 0.596218i | \(0.203330\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.0729 | −1.57807 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.8633 | −0.507231 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.95120 | 0.107834 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.8474 | −1.27160 | −0.635800 | − | 0.771854i | \(-0.719330\pi\) | ||||
−0.635800 | + | 0.771854i | \(0.719330\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.5794 | 0.749954 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.56598 | 0.166173 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.95171 | 0.325356 | 0.162678 | − | 0.986679i | \(-0.447987\pi\) | ||||
0.162678 | + | 0.986679i | \(0.447987\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −52.2449 | −1.89637 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.90648 | 0.0691098 | 0.0345549 | − | 0.999403i | \(-0.488999\pi\) | ||||
0.0345549 | + | 0.999403i | \(0.488999\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.09652 | −0.329316 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.3255 | −0.481785 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.1506 | 0.691489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.7489 | 1.57763 | 0.788813 | − | 0.614633i | \(-0.210696\pi\) | ||||
0.788813 | + | 0.614633i | \(0.210696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.3369 | 1.02053 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.8809 | 1.75812 | 0.879062 | − | 0.476708i | \(-0.158170\pi\) | ||||
0.879062 | + | 0.476708i | \(0.158170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 119.122 | 4.27900 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.90304 | 0.104146 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.31102 | −0.0828010 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.1498 | −2.04498 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.90838 | −0.103937 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.60535 | 0.307138 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.8888 | −1.70705 | −0.853525 | − | 0.521052i | \(-0.825540\pi\) | ||||
−0.853525 | + | 0.521052i | \(0.825540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.9168 | 0.780258 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0401 | −0.392542 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.7586 | 1.90903 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.3954 | −0.936148 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.4221 | 1.64436 | 0.822178 | − | 0.569231i | \(-0.192759\pi\) | ||||
0.822178 | + | 0.569231i | \(0.192759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.34441 | −0.224449 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.45522 | 0.192751 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.21109 | 0.254474 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.8847 | 1.19428 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.34233 | −0.293664 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.3954 | −0.717065 | −0.358533 | − | 0.933517i | \(-0.616723\pi\) | ||||
−0.358533 | + | 0.933517i | \(0.616723\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1993 | 0.955097 | 0.477549 | − | 0.878605i | \(-0.341525\pi\) | ||||
0.477549 | + | 0.878605i | \(0.341525\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.97049 | −0.209394 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −35.2529 | −1.23486 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.30161 | 0.115509 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.86085 | −0.204795 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.9559 | 1.88308 | 0.941538 | − | 0.336908i | \(-0.109381\pi\) | ||||
0.941538 | + | 0.336908i | \(0.109381\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.3519 | 0.709421 | 0.354711 | − | 0.934976i | \(-0.384579\pi\) | ||||
0.354711 | + | 0.934976i | \(0.384579\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −63.3202 | −2.20453 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.5345 | 1.33998 | 0.669988 | − | 0.742372i | \(-0.266299\pi\) | ||||
0.669988 | + | 0.742372i | \(0.266299\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.7280 | 0.928302 | 0.464151 | − | 0.885756i | \(-0.346360\pi\) | ||||
0.464151 | + | 0.885756i | \(0.346360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.35540 | 0.0817077 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −20.4277 | −0.707778 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.02595 | −0.139324 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.6281 | −0.367361 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.9538 | 0.516261 | 0.258131 | − | 0.966110i | \(-0.416893\pi\) | ||||
0.258131 | + | 0.966110i | \(0.416893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5413 | −0.708322 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.45133 | 0.325521 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −114.617 | −3.94293 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.0360 | −0.654084 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.76734 | 0.335214 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.4983 | 1.01119 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.85973 | 0.132155 | 0.0660773 | − | 0.997815i | \(-0.478952\pi\) | ||||
0.0660773 | + | 0.997815i | \(0.478952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.19293 | 0.177594 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.1803 | 0.689347 | 0.344674 | − | 0.938723i | \(-0.387990\pi\) | ||||
0.344674 | + | 0.938723i | \(0.387990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.19182 | 0.177143 | 0.0885713 | − | 0.996070i | \(-0.471770\pi\) | ||||
0.0885713 | + | 0.996070i | \(0.471770\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.63063 | 0.0555718 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.6739 | 0.839908 | 0.419954 | − | 0.907545i | \(-0.362046\pi\) | ||||
0.419954 | + | 0.907545i | \(0.362046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −83.6477 | −2.84411 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.04453 | 0.205283 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.1246 | 0.343452 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.3021 | −0.925098 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.0108 | 0.440350 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.7475 | 0.769007 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.5120 | −0.726409 | −0.363205 | − | 0.931709i | \(-0.618317\pi\) | ||||
−0.363205 | + | 0.931709i | \(0.618317\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.86304 | −0.0628388 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.28798 | 0.245538 | 0.122769 | − | 0.992435i | \(-0.460823\pi\) | ||||
0.122769 | + | 0.992435i | \(0.460823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −46.9312 | −1.57936 | −0.789681 | − | 0.613517i | \(-0.789754\pi\) | ||||
−0.789681 | + | 0.613517i | \(0.789754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.9726 | 0.402453 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.7405 | 0.494939 | 0.247469 | − | 0.968896i | \(-0.420401\pi\) | ||||
0.247469 | + | 0.968896i | \(0.420401\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.5406 | 0.387058 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.64943 | 0.189263 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.47241 | 0.0827359 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 83.2863 | 2.78395 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −59.5530 | −1.98842 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.9105 | 1.03092 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.7008 | −0.722958 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.32958 | −0.0775236 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43.0240 | 1.43017 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −49.1909 | −1.63336 | −0.816678 | − | 0.577093i | \(-0.804187\pi\) | ||||
−0.816678 | + | 0.577093i | \(0.804187\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.5075 | 0.448016 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.1824 | 0.801198 | 0.400599 | − | 0.916254i | \(-0.368802\pi\) | ||||
0.400599 | + | 0.916254i | \(0.368802\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −78.3196 | −2.59200 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.6087 | 1.11107 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.45253 | 0.213081 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.1032 | 1.55379 | 0.776895 | − | 0.629630i | \(-0.216793\pi\) | ||||
0.776895 | + | 0.629630i | \(0.216793\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.9878 | 0.395010 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −65.1440 | −2.14424 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.7516 | 1.17551 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.77840 | 0.0912545 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.7341 | −0.778690 | −0.389345 | − | 0.921092i | \(-0.627299\pi\) | ||||
−0.389345 | + | 0.921092i | \(0.627299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.96065 | 0.260900 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.72229 | −0.252817 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −75.2814 | −2.46197 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.3550 | 1.61236 | 0.806179 | − | 0.591672i | \(-0.201532\pi\) | ||||
0.806179 | + | 0.591672i | \(0.201532\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.5266 | 0.898298 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.4267 | −0.372499 | −0.186249 | − | 0.982502i | \(-0.559633\pi\) | ||||
−0.186249 | + | 0.982502i | \(0.559633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.5691 | 0.539565 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.66408 | −0.119192 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.8099 | 1.13117 | 0.565585 | − | 0.824690i | \(-0.308650\pi\) | ||||
0.565585 | + | 0.824690i | \(0.308650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.21980 | 0.266826 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.6703 | 0.962126 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.3657 | −1.79347 | −0.896736 | − | 0.442566i | \(-0.854068\pi\) | ||||
−0.896736 | + | 0.442566i | \(0.854068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 95.6435 | 3.09495 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.4307 | −0.531128 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.31568 | −0.0424855 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81.9564 | 2.64375 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.24267 | −0.104493 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.21400 | −0.0390801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.9967 | −1.35052 | −0.675261 | − | 0.737579i | \(-0.735969\pi\) | ||||
−0.675261 | + | 0.737579i | \(0.735969\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.26933 | 0.137151 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.16677 | 0.0374435 | 0.0187218 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187218 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.6758 | −0.566661 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −72.1776 | −2.31153 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.0060 | −1.66382 | −0.831909 | − | 0.554912i | \(-0.812752\pi\) | ||||
−0.831909 | + | 0.554912i | \(0.812752\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.8189 | 0.984975 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.99492 | 0.319113 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.8873 | −0.538622 | −0.269311 | − | 0.963053i | \(-0.586796\pi\) | ||||
−0.269311 | + | 0.963053i | \(0.586796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 88.5144 | 2.82030 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.74450 | −0.0555281 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.6712 | −0.752702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.8021 | 0.597269 | 0.298634 | − | 0.954368i | \(-0.403469\pi\) | ||||
0.298634 | + | 0.954368i | \(0.403469\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.06789 | −0.287761 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73.7853 | −2.33915 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.11330 | 0.0352587 | 0.0176294 | − | 0.999845i | \(-0.494388\pi\) | ||||
0.0176294 | + | 0.999845i | \(0.494388\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.18976 | −0.100919 |
(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 | 8016.2.a.bg.1.1 | 13 | ||
4.3 | odd | 2 | 4008.2.a.m.1.1 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.1 | ✓ | 13 | 4.3 | odd | 2 | ||
8016.2.a.bg.1.1 | 13 | 1.1 | even | 1 | trivial |