Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 14 x^{10} + 26 x^{9} + 71 x^{8} - 120 x^{7} - 162 x^{6} + 244 x^{5} + 170 x^{4} + \cdots + 17 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.23080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23080 | 0.870309 | 0.435154 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435154 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(3\) | −0.767488 | −0.443109 | −0.221555 | − | 0.975148i | \(-0.571113\pi\) | ||||
−0.221555 | + | 0.975148i | \(0.571113\pi\) | |||||||
\(4\) | −0.485126 | −0.242563 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.944626 | −0.385642 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.05870 | −1.08141 | ||||||||
\(9\) | −2.41096 | −0.803654 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.89133 | 0.871770 | 0.435885 | − | 0.900002i | \(-0.356435\pi\) | ||||
0.435885 | + | 0.900002i | \(0.356435\pi\) | |||||||
\(12\) | 0.372328 | 0.107482 | ||||||||
\(13\) | 5.98987 | 1.66129 | 0.830645 | − | 0.556802i | \(-0.187972\pi\) | ||||
0.830645 | + | 0.556802i | \(0.187972\pi\) | |||||||
\(14\) | −1.23080 | −0.328946 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.79440 | −0.698600 | ||||||||
\(17\) | −3.74500 | −0.908296 | −0.454148 | − | 0.890926i | \(-0.650056\pi\) | ||||
−0.454148 | + | 0.890926i | \(0.650056\pi\) | |||||||
\(18\) | −2.96742 | −0.699427 | ||||||||
\(19\) | 3.96859 | 0.910457 | 0.455229 | − | 0.890375i | \(-0.349558\pi\) | ||||
0.455229 | + | 0.890375i | \(0.349558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.767488 | 0.167480 | ||||||||
\(22\) | 3.55866 | 0.758709 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.34751 | 0.479184 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.37234 | 1.44584 | ||||||||
\(27\) | 4.15285 | 0.799216 | ||||||||
\(28\) | 0.485126 | 0.0916801 | ||||||||
\(29\) | −5.11682 | −0.950169 | −0.475084 | − | 0.879940i | \(-0.657582\pi\) | ||||
−0.475084 | + | 0.879940i | \(0.657582\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.68931 | −0.483013 | −0.241507 | − | 0.970399i | \(-0.577642\pi\) | ||||
−0.241507 | + | 0.970399i | \(0.577642\pi\) | |||||||
\(32\) | 2.67804 | 0.473415 | ||||||||
\(33\) | −2.21906 | −0.386289 | ||||||||
\(34\) | −4.60936 | −0.790498 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.16962 | 0.194937 | ||||||||
\(37\) | 0.781495 | 0.128477 | 0.0642385 | − | 0.997935i | \(-0.479538\pi\) | ||||
0.0642385 | + | 0.997935i | \(0.479538\pi\) | |||||||
\(38\) | 4.88455 | 0.792379 | ||||||||
\(39\) | −4.59715 | −0.736134 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.75841 | −0.586965 | −0.293483 | − | 0.955964i | \(-0.594814\pi\) | ||||
−0.293483 | + | 0.955964i | \(0.594814\pi\) | |||||||
\(42\) | 0.944626 | 0.145759 | ||||||||
\(43\) | −9.64575 | −1.47096 | −0.735481 | − | 0.677545i | \(-0.763044\pi\) | ||||
−0.735481 | + | 0.677545i | \(0.763044\pi\) | |||||||
\(44\) | −1.40266 | −0.211459 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.23080 | 0.181472 | ||||||||
\(47\) | 6.15313 | 0.897527 | 0.448763 | − | 0.893651i | \(-0.351865\pi\) | ||||
0.448763 | + | 0.893651i | \(0.351865\pi\) | |||||||
\(48\) | 2.14467 | 0.309556 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.87424 | 0.402475 | ||||||||
\(52\) | −2.90584 | −0.402967 | ||||||||
\(53\) | −2.86672 | −0.393774 | −0.196887 | − | 0.980426i | \(-0.563083\pi\) | ||||
−0.196887 | + | 0.980426i | \(0.563083\pi\) | |||||||
\(54\) | 5.11134 | 0.695565 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.05870 | 0.408736 | ||||||||
\(57\) | −3.04585 | −0.403432 | ||||||||
\(58\) | −6.29779 | −0.826940 | ||||||||
\(59\) | 5.12427 | 0.667124 | 0.333562 | − | 0.942728i | \(-0.391749\pi\) | ||||
0.333562 | + | 0.942728i | \(0.391749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.72146 | −0.220410 | −0.110205 | − | 0.993909i | \(-0.535151\pi\) | ||||
−0.110205 | + | 0.993909i | \(0.535151\pi\) | |||||||
\(62\) | −3.31000 | −0.420371 | ||||||||
\(63\) | 2.41096 | 0.303753 | ||||||||
\(64\) | 8.88494 | 1.11062 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.73123 | −0.336191 | ||||||||
\(67\) | 6.58076 | 0.803968 | 0.401984 | − | 0.915647i | \(-0.368321\pi\) | ||||
0.401984 | + | 0.915647i | \(0.368321\pi\) | |||||||
\(68\) | 1.81680 | 0.220319 | ||||||||
\(69\) | −0.767488 | −0.0923947 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5418 | −1.60712 | −0.803560 | − | 0.595224i | \(-0.797064\pi\) | ||||
−0.803560 | + | 0.595224i | \(0.797064\pi\) | |||||||
\(72\) | 7.37441 | 0.869082 | ||||||||
\(73\) | −15.6308 | −1.82944 | −0.914721 | − | 0.404086i | \(-0.867590\pi\) | ||||
−0.914721 | + | 0.404086i | \(0.867590\pi\) | |||||||
\(74\) | 0.961866 | 0.111815 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.92527 | −0.220843 | ||||||||
\(77\) | −2.89133 | −0.329498 | ||||||||
\(78\) | −5.65819 | −0.640663 | ||||||||
\(79\) | −3.72352 | −0.418929 | −0.209465 | − | 0.977816i | \(-0.567172\pi\) | ||||
−0.209465 | + | 0.977816i | \(0.567172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.04562 | 0.449514 | ||||||||
\(82\) | −4.62586 | −0.510841 | ||||||||
\(83\) | 0.558554 | 0.0613092 | 0.0306546 | − | 0.999530i | \(-0.490241\pi\) | ||||
0.0306546 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(84\) | −0.372328 | −0.0406243 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11.8720 | −1.28019 | ||||||||
\(87\) | 3.92709 | 0.421029 | ||||||||
\(88\) | −8.84372 | −0.942743 | ||||||||
\(89\) | −8.00892 | −0.848944 | −0.424472 | − | 0.905441i | \(-0.639540\pi\) | ||||
−0.424472 | + | 0.905441i | \(0.639540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.98987 | −0.627909 | ||||||||
\(92\) | −0.485126 | −0.0505779 | ||||||||
\(93\) | 2.06401 | 0.214028 | ||||||||
\(94\) | 7.57329 | 0.781125 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.05536 | −0.209775 | ||||||||
\(97\) | 12.4519 | 1.26430 | 0.632150 | − | 0.774846i | \(-0.282172\pi\) | ||||
0.632150 | + | 0.774846i | \(0.282172\pi\) | |||||||
\(98\) | 1.23080 | 0.124330 | ||||||||
\(99\) | −6.97089 | −0.700601 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −19.4640 | −1.93674 | −0.968371 | − | 0.249513i | \(-0.919729\pi\) | ||||
−0.968371 | + | 0.249513i | \(0.919729\pi\) | |||||||
\(102\) | 3.53763 | 0.350277 | ||||||||
\(103\) | −10.2504 | −1.01000 | −0.504999 | − | 0.863120i | \(-0.668507\pi\) | ||||
−0.504999 | + | 0.863120i | \(0.668507\pi\) | |||||||
\(104\) | −18.3212 | −1.79654 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.52837 | −0.342705 | ||||||||
\(107\) | −8.13181 | −0.786132 | −0.393066 | − | 0.919510i | \(-0.628586\pi\) | ||||
−0.393066 | + | 0.919510i | \(0.628586\pi\) | |||||||
\(108\) | −2.01465 | −0.193860 | ||||||||
\(109\) | −11.2492 | −1.07748 | −0.538741 | − | 0.842471i | \(-0.681100\pi\) | ||||
−0.538741 | + | 0.842471i | \(0.681100\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.599788 | −0.0569294 | ||||||||
\(112\) | 2.79440 | 0.264046 | ||||||||
\(113\) | 0.833318 | 0.0783920 | 0.0391960 | − | 0.999232i | \(-0.487520\pi\) | ||||
0.0391960 | + | 0.999232i | \(0.487520\pi\) | |||||||
\(114\) | −3.74884 | −0.351111 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.48230 | 0.230476 | ||||||||
\(117\) | −14.4413 | −1.33510 | ||||||||
\(118\) | 6.30697 | 0.580604 | ||||||||
\(119\) | 3.74500 | 0.343304 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.64019 | −0.240018 | ||||||||
\(122\) | −2.11877 | −0.191825 | ||||||||
\(123\) | 2.88454 | 0.260090 | ||||||||
\(124\) | 1.30465 | 0.117161 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.96742 | 0.264359 | ||||||||
\(127\) | −14.6167 | −1.29702 | −0.648510 | − | 0.761206i | \(-0.724608\pi\) | ||||
−0.648510 | + | 0.761206i | \(0.724608\pi\) | |||||||
\(128\) | 5.57953 | 0.493165 | ||||||||
\(129\) | 7.40300 | 0.651798 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3804 | 1.51853 | 0.759267 | − | 0.650780i | \(-0.225558\pi\) | ||||
0.759267 | + | 0.650780i | \(0.225558\pi\) | |||||||
\(132\) | 1.07652 | 0.0936994 | ||||||||
\(133\) | −3.96859 | −0.344121 | ||||||||
\(134\) | 8.09961 | 0.699700 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.4548 | 0.982243 | ||||||||
\(137\) | 6.15314 | 0.525698 | 0.262849 | − | 0.964837i | \(-0.415338\pi\) | ||||
0.262849 | + | 0.964837i | \(0.415338\pi\) | |||||||
\(138\) | −0.944626 | −0.0804119 | ||||||||
\(139\) | −7.94813 | −0.674152 | −0.337076 | − | 0.941477i | \(-0.609438\pi\) | ||||
−0.337076 | + | 0.941477i | \(0.609438\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.72246 | −0.397703 | ||||||||
\(142\) | −16.6673 | −1.39869 | ||||||||
\(143\) | 17.3187 | 1.44826 | ||||||||
\(144\) | 6.73720 | 0.561433 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.2384 | −1.59218 | ||||||||
\(147\) | −0.767488 | −0.0633013 | ||||||||
\(148\) | −0.379123 | −0.0311638 | ||||||||
\(149\) | −18.3219 | −1.50099 | −0.750496 | − | 0.660876i | \(-0.770185\pi\) | ||||
−0.750496 | + | 0.660876i | \(0.770185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2382 | −1.24007 | −0.620033 | − | 0.784576i | \(-0.712881\pi\) | ||||
−0.620033 | + | 0.784576i | \(0.712881\pi\) | |||||||
\(152\) | −12.1387 | −0.984581 | ||||||||
\(153\) | 9.02906 | 0.729956 | ||||||||
\(154\) | −3.55866 | −0.286765 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.23020 | 0.178559 | ||||||||
\(157\) | −7.09858 | −0.566528 | −0.283264 | − | 0.959042i | \(-0.591417\pi\) | ||||
−0.283264 | + | 0.959042i | \(0.591417\pi\) | |||||||
\(158\) | −4.58292 | −0.364598 | ||||||||
\(159\) | 2.20017 | 0.174485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 4.97936 | 0.391216 | ||||||||
\(163\) | −9.44101 | −0.739477 | −0.369739 | − | 0.929136i | \(-0.620553\pi\) | ||||
−0.369739 | + | 0.929136i | \(0.620553\pi\) | |||||||
\(164\) | 1.82330 | 0.142376 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.687469 | 0.0533579 | ||||||||
\(167\) | −15.1442 | −1.17189 | −0.585945 | − | 0.810351i | \(-0.699277\pi\) | ||||
−0.585945 | + | 0.810351i | \(0.699277\pi\) | |||||||
\(168\) | −2.34751 | −0.181115 | ||||||||
\(169\) | 22.8785 | 1.75989 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.56812 | −0.731693 | ||||||||
\(172\) | 4.67940 | 0.356801 | ||||||||
\(173\) | 19.2225 | 1.46146 | 0.730730 | − | 0.682667i | \(-0.239180\pi\) | ||||
0.730730 | + | 0.682667i | \(0.239180\pi\) | |||||||
\(174\) | 4.83348 | 0.366425 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.07955 | −0.609019 | ||||||||
\(177\) | −3.93282 | −0.295609 | ||||||||
\(178\) | −9.85740 | −0.738843 | ||||||||
\(179\) | 20.2975 | 1.51711 | 0.758554 | − | 0.651610i | \(-0.225906\pi\) | ||||
0.758554 | + | 0.651610i | \(0.225906\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0681 | −1.04568 | −0.522838 | − | 0.852432i | \(-0.675127\pi\) | ||||
−0.522838 | + | 0.852432i | \(0.675127\pi\) | |||||||
\(182\) | −7.37234 | −0.546474 | ||||||||
\(183\) | 1.32120 | 0.0976658 | ||||||||
\(184\) | −3.05870 | −0.225490 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.54039 | 0.186270 | ||||||||
\(187\) | −10.8280 | −0.791825 | ||||||||
\(188\) | −2.98504 | −0.217707 | ||||||||
\(189\) | −4.15285 | −0.302075 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.5272 | 1.84708 | 0.923540 | − | 0.383501i | \(-0.125282\pi\) | ||||
0.923540 | + | 0.383501i | \(0.125282\pi\) | |||||||
\(192\) | −6.81909 | −0.492125 | ||||||||
\(193\) | 20.2638 | 1.45862 | 0.729309 | − | 0.684184i | \(-0.239842\pi\) | ||||
0.729309 | + | 0.684184i | \(0.239842\pi\) | |||||||
\(194\) | 15.3259 | 1.10033 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.485126 | −0.0346518 | ||||||||
\(197\) | 18.5817 | 1.32389 | 0.661947 | − | 0.749551i | \(-0.269730\pi\) | ||||
0.661947 | + | 0.749551i | \(0.269730\pi\) | |||||||
\(198\) | −8.57979 | −0.609739 | ||||||||
\(199\) | −20.1872 | −1.43103 | −0.715517 | − | 0.698595i | \(-0.753809\pi\) | ||||
−0.715517 | + | 0.698595i | \(0.753809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.05065 | −0.356246 | ||||||||
\(202\) | −23.9564 | −1.68556 | ||||||||
\(203\) | 5.11682 | 0.359130 | ||||||||
\(204\) | −1.39437 | −0.0976254 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.6162 | −0.879010 | ||||||||
\(207\) | −2.41096 | −0.167573 | ||||||||
\(208\) | −16.7381 | −1.16058 | ||||||||
\(209\) | 11.4745 | 0.793709 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.7695 | −1.22330 | −0.611651 | − | 0.791128i | \(-0.709494\pi\) | ||||
−0.611651 | + | 0.791128i | \(0.709494\pi\) | |||||||
\(212\) | 1.39072 | 0.0955151 | ||||||||
\(213\) | 10.3932 | 0.712130 | ||||||||
\(214\) | −10.0087 | −0.684177 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −12.7023 | −0.864283 | ||||||||
\(217\) | 2.68931 | 0.182562 | ||||||||
\(218\) | −13.8456 | −0.937742 | ||||||||
\(219\) | 11.9964 | 0.810643 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.4321 | −1.50894 | ||||||||
\(222\) | −0.738221 | −0.0495461 | ||||||||
\(223\) | −8.45760 | −0.566363 | −0.283181 | − | 0.959066i | \(-0.591390\pi\) | ||||
−0.283181 | + | 0.959066i | \(0.591390\pi\) | |||||||
\(224\) | −2.67804 | −0.178934 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.02565 | 0.0682252 | ||||||||
\(227\) | 2.09203 | 0.138853 | 0.0694263 | − | 0.997587i | \(-0.477883\pi\) | ||||
0.0694263 | + | 0.997587i | \(0.477883\pi\) | |||||||
\(228\) | 1.47762 | 0.0978577 | ||||||||
\(229\) | −17.0381 | −1.12591 | −0.562956 | − | 0.826487i | \(-0.690336\pi\) | ||||
−0.562956 | + | 0.826487i | \(0.690336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.21906 | 0.146004 | ||||||||
\(232\) | 15.6508 | 1.02753 | ||||||||
\(233\) | 9.57962 | 0.627582 | 0.313791 | − | 0.949492i | \(-0.398401\pi\) | ||||
0.313791 | + | 0.949492i | \(0.398401\pi\) | |||||||
\(234\) | −17.7744 | −1.16195 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.48592 | −0.161819 | ||||||||
\(237\) | 2.85776 | 0.185631 | ||||||||
\(238\) | 4.60936 | 0.298780 | ||||||||
\(239\) | −12.6039 | −0.815277 | −0.407639 | − | 0.913143i | \(-0.633648\pi\) | ||||
−0.407639 | + | 0.913143i | \(0.633648\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.0405 | −1.29092 | −0.645460 | − | 0.763794i | \(-0.723334\pi\) | ||||
−0.645460 | + | 0.763794i | \(0.723334\pi\) | |||||||
\(242\) | −3.24956 | −0.208889 | ||||||||
\(243\) | −15.5635 | −0.998400 | ||||||||
\(244\) | 0.835123 | 0.0534633 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.55029 | 0.226358 | ||||||||
\(247\) | 23.7713 | 1.51253 | ||||||||
\(248\) | 8.22577 | 0.522337 | ||||||||
\(249\) | −0.428683 | −0.0271667 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.21018 | −0.0763860 | −0.0381930 | − | 0.999270i | \(-0.512160\pi\) | ||||
−0.0381930 | + | 0.999270i | \(0.512160\pi\) | |||||||
\(252\) | −1.16962 | −0.0736791 | ||||||||
\(253\) | 2.89133 | 0.181777 | ||||||||
\(254\) | −17.9902 | −1.12881 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9026 | −0.681412 | ||||||||
\(257\) | −22.7652 | −1.42005 | −0.710027 | − | 0.704174i | \(-0.751317\pi\) | ||||
−0.710027 | + | 0.704174i | \(0.751317\pi\) | |||||||
\(258\) | 9.11163 | 0.567265 | ||||||||
\(259\) | −0.781495 | −0.0485598 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.3364 | 0.763607 | ||||||||
\(262\) | 21.3918 | 1.32159 | ||||||||
\(263\) | 18.7574 | 1.15663 | 0.578317 | − | 0.815812i | \(-0.303710\pi\) | ||||
0.578317 | + | 0.815812i | \(0.303710\pi\) | |||||||
\(264\) | 6.78745 | 0.417738 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.88455 | −0.299491 | ||||||||
\(267\) | 6.14675 | 0.376175 | ||||||||
\(268\) | −3.19250 | −0.195013 | ||||||||
\(269\) | 5.50465 | 0.335624 | 0.167812 | − | 0.985819i | \(-0.446330\pi\) | ||||
0.167812 | + | 0.985819i | \(0.446330\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.5759 | 1.91810 | 0.959051 | − | 0.283234i | \(-0.0914072\pi\) | ||||
0.959051 | + | 0.283234i | \(0.0914072\pi\) | |||||||
\(272\) | 10.4650 | 0.634536 | ||||||||
\(273\) | 4.59715 | 0.278232 | ||||||||
\(274\) | 7.57330 | 0.457520 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.372328 | 0.0224115 | ||||||||
\(277\) | 10.4707 | 0.629124 | 0.314562 | − | 0.949237i | \(-0.398142\pi\) | ||||
0.314562 | + | 0.949237i | \(0.398142\pi\) | |||||||
\(278\) | −9.78258 | −0.586720 | ||||||||
\(279\) | 6.48381 | 0.388176 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.88701 | −0.231880 | −0.115940 | − | 0.993256i | \(-0.536988\pi\) | ||||
−0.115940 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(282\) | −5.81241 | −0.346124 | ||||||||
\(283\) | −3.50559 | −0.208386 | −0.104193 | − | 0.994557i | \(-0.533226\pi\) | ||||
−0.104193 | + | 0.994557i | \(0.533226\pi\) | |||||||
\(284\) | 6.56949 | 0.389828 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.3159 | 1.26044 | ||||||||
\(287\) | 3.75841 | 0.221852 | ||||||||
\(288\) | −6.45665 | −0.380462 | ||||||||
\(289\) | −2.97497 | −0.174998 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.55670 | −0.560224 | ||||||||
\(292\) | 7.58288 | 0.443755 | ||||||||
\(293\) | 7.54753 | 0.440931 | 0.220466 | − | 0.975395i | \(-0.429242\pi\) | ||||
0.220466 | + | 0.975395i | \(0.429242\pi\) | |||||||
\(294\) | −0.944626 | −0.0550917 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.39036 | −0.138937 | ||||||||
\(297\) | 12.0073 | 0.696732 | ||||||||
\(298\) | −22.5507 | −1.30633 | ||||||||
\(299\) | 5.98987 | 0.346403 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.64575 | 0.555972 | ||||||||
\(302\) | −18.7552 | −1.07924 | ||||||||
\(303\) | 14.9384 | 0.858189 | ||||||||
\(304\) | −11.0898 | −0.636046 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.1130 | 0.635287 | ||||||||
\(307\) | −3.40389 | −0.194270 | −0.0971351 | − | 0.995271i | \(-0.530968\pi\) | ||||
−0.0971351 | + | 0.995271i | \(0.530968\pi\) | |||||||
\(308\) | 1.40266 | 0.0799240 | ||||||||
\(309\) | 7.86703 | 0.447540 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.36739 | −0.531176 | −0.265588 | − | 0.964087i | \(-0.585566\pi\) | ||||
−0.265588 | + | 0.964087i | \(0.585566\pi\) | |||||||
\(312\) | 14.0613 | 0.796065 | ||||||||
\(313\) | 14.8907 | 0.841672 | 0.420836 | − | 0.907137i | \(-0.361737\pi\) | ||||
0.420836 | + | 0.907137i | \(0.361737\pi\) | |||||||
\(314\) | −8.73694 | −0.493054 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.80638 | 0.101617 | ||||||||
\(317\) | 18.1816 | 1.02118 | 0.510591 | − | 0.859824i | \(-0.329427\pi\) | ||||
0.510591 | + | 0.859824i | \(0.329427\pi\) | |||||||
\(318\) | 2.70798 | 0.151856 | ||||||||
\(319\) | −14.7944 | −0.828328 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.24107 | 0.348342 | ||||||||
\(322\) | −1.23080 | −0.0685899 | ||||||||
\(323\) | −14.8624 | −0.826965 | ||||||||
\(324\) | −1.96264 | −0.109035 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.6200 | −0.643573 | ||||||||
\(327\) | 8.63366 | 0.477442 | ||||||||
\(328\) | 11.4958 | 0.634752 | ||||||||
\(329\) | −6.15313 | −0.339233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.6377 | −1.57407 | −0.787036 | − | 0.616907i | \(-0.788385\pi\) | ||||
−0.787036 | + | 0.616907i | \(0.788385\pi\) | |||||||
\(332\) | −0.270969 | −0.0148713 | ||||||||
\(333\) | −1.88416 | −0.103251 | ||||||||
\(334\) | −18.6395 | −1.01991 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.14467 | −0.117001 | ||||||||
\(337\) | 27.8674 | 1.51803 | 0.759016 | − | 0.651072i | \(-0.225681\pi\) | ||||
0.759016 | + | 0.651072i | \(0.225681\pi\) | |||||||
\(338\) | 28.1589 | 1.53164 | ||||||||
\(339\) | −0.639562 | −0.0347362 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.77568 | −0.421076 | ||||||||
\(342\) | −11.7765 | −0.636798 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 29.5034 | 1.59072 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.6591 | 1.27192 | ||||||||
\(347\) | −19.0625 | −1.02333 | −0.511665 | − | 0.859185i | \(-0.670971\pi\) | ||||
−0.511665 | + | 0.859185i | \(0.670971\pi\) | |||||||
\(348\) | −1.90513 | −0.102126 | ||||||||
\(349\) | −0.155087 | −0.00830162 | −0.00415081 | − | 0.999991i | \(-0.501321\pi\) | ||||
−0.00415081 | + | 0.999991i | \(0.501321\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.8750 | 1.32773 | ||||||||
\(352\) | 7.74311 | 0.412709 | ||||||||
\(353\) | 12.9217 | 0.687754 | 0.343877 | − | 0.939015i | \(-0.388260\pi\) | ||||
0.343877 | + | 0.939015i | \(0.388260\pi\) | |||||||
\(354\) | −4.84052 | −0.257271 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.88533 | 0.205922 | ||||||||
\(357\) | −2.87424 | −0.152121 | ||||||||
\(358\) | 24.9822 | 1.32035 | ||||||||
\(359\) | 18.7962 | 0.992024 | 0.496012 | − | 0.868316i | \(-0.334797\pi\) | ||||
0.496012 | + | 0.868316i | \(0.334797\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.25028 | −0.171067 | ||||||||
\(362\) | −17.3151 | −0.910061 | ||||||||
\(363\) | 2.02632 | 0.106354 | ||||||||
\(364\) | 2.90584 | 0.152307 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.62613 | 0.0849994 | ||||||||
\(367\) | 33.1027 | 1.72795 | 0.863973 | − | 0.503539i | \(-0.167969\pi\) | ||||
0.863973 | + | 0.503539i | \(0.167969\pi\) | |||||||
\(368\) | −2.79440 | −0.145668 | ||||||||
\(369\) | 9.06139 | 0.471717 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.86672 | 0.148833 | ||||||||
\(372\) | −1.00130 | −0.0519152 | ||||||||
\(373\) | 28.0685 | 1.45333 | 0.726665 | − | 0.686992i | \(-0.241069\pi\) | ||||
0.726665 | + | 0.686992i | \(0.241069\pi\) | |||||||
\(374\) | −13.3272 | −0.689132 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.8206 | −0.970597 | ||||||||
\(377\) | −30.6491 | −1.57851 | ||||||||
\(378\) | −5.11134 | −0.262899 | ||||||||
\(379\) | 7.52475 | 0.386520 | 0.193260 | − | 0.981148i | \(-0.438094\pi\) | ||||
0.193260 | + | 0.981148i | \(0.438094\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.2181 | 0.574722 | ||||||||
\(382\) | 31.4189 | 1.60753 | ||||||||
\(383\) | 12.0417 | 0.615304 | 0.307652 | − | 0.951499i | \(-0.400457\pi\) | ||||
0.307652 | + | 0.951499i | \(0.400457\pi\) | |||||||
\(384\) | −4.28222 | −0.218526 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.9407 | 1.26945 | ||||||||
\(387\) | 23.2555 | 1.18215 | ||||||||
\(388\) | −6.04075 | −0.306672 | ||||||||
\(389\) | −7.41719 | −0.376066 | −0.188033 | − | 0.982163i | \(-0.560211\pi\) | ||||
−0.188033 | + | 0.982163i | \(0.560211\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.74500 | −0.189393 | ||||||||
\(392\) | −3.05870 | −0.154488 | ||||||||
\(393\) | −13.3393 | −0.672876 | ||||||||
\(394\) | 22.8704 | 1.15220 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.38176 | 0.169940 | ||||||||
\(397\) | −10.9981 | −0.551978 | −0.275989 | − | 0.961161i | \(-0.589005\pi\) | ||||
−0.275989 | + | 0.961161i | \(0.589005\pi\) | |||||||
\(398\) | −24.8465 | −1.24544 | ||||||||
\(399\) | 3.04585 | 0.152483 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.7534 | 1.43588 | 0.717938 | − | 0.696107i | \(-0.245086\pi\) | ||||
0.717938 | + | 0.696107i | \(0.245086\pi\) | |||||||
\(402\) | −6.21636 | −0.310044 | ||||||||
\(403\) | −16.1086 | −0.802426 | ||||||||
\(404\) | 9.44250 | 0.469782 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.29779 | 0.312554 | ||||||||
\(407\) | 2.25956 | 0.112002 | ||||||||
\(408\) | −8.79144 | −0.435241 | ||||||||
\(409\) | −19.0125 | −0.940108 | −0.470054 | − | 0.882638i | \(-0.655766\pi\) | ||||
−0.470054 | + | 0.882638i | \(0.655766\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.72246 | −0.232942 | ||||||||
\(412\) | 4.97271 | 0.244988 | ||||||||
\(413\) | −5.12427 | −0.252149 | ||||||||
\(414\) | −2.96742 | −0.145841 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.0411 | 0.786480 | ||||||||
\(417\) | 6.10010 | 0.298723 | ||||||||
\(418\) | 14.1229 | 0.690772 | ||||||||
\(419\) | −27.0953 | −1.32369 | −0.661846 | − | 0.749640i | \(-0.730227\pi\) | ||||
−0.661846 | + | 0.749640i | \(0.730227\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.9265 | −0.727472 | −0.363736 | − | 0.931502i | \(-0.618499\pi\) | ||||
−0.363736 | + | 0.931502i | \(0.618499\pi\) | |||||||
\(422\) | −21.8707 | −1.06465 | ||||||||
\(423\) | −14.8350 | −0.721301 | ||||||||
\(424\) | 8.76844 | 0.425833 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.7920 | 0.619773 | ||||||||
\(427\) | 1.72146 | 0.0833072 | ||||||||
\(428\) | 3.94495 | 0.190686 | ||||||||
\(429\) | −13.2919 | −0.641739 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.47468 | −0.456379 | −0.228190 | − | 0.973617i | \(-0.573281\pi\) | ||||
−0.228190 | + | 0.973617i | \(0.573281\pi\) | |||||||
\(432\) | −11.6047 | −0.558333 | ||||||||
\(433\) | −33.0972 | −1.59055 | −0.795275 | − | 0.606249i | \(-0.792673\pi\) | ||||
−0.795275 | + | 0.606249i | \(0.792673\pi\) | |||||||
\(434\) | 3.31000 | 0.158885 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.45730 | 0.261357 | ||||||||
\(437\) | 3.96859 | 0.189843 | ||||||||
\(438\) | 14.7652 | 0.705510 | ||||||||
\(439\) | 3.47236 | 0.165727 | 0.0828633 | − | 0.996561i | \(-0.473594\pi\) | ||||
0.0828633 | + | 0.996561i | \(0.473594\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.41096 | −0.114808 | ||||||||
\(442\) | −27.6094 | −1.31325 | ||||||||
\(443\) | −9.01324 | −0.428232 | −0.214116 | − | 0.976808i | \(-0.568687\pi\) | ||||
−0.214116 | + | 0.976808i | \(0.568687\pi\) | |||||||
\(444\) | 0.290973 | 0.0138090 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.4096 | −0.492910 | ||||||||
\(447\) | 14.0619 | 0.665103 | ||||||||
\(448\) | −8.88494 | −0.419774 | ||||||||
\(449\) | −2.25213 | −0.106284 | −0.0531422 | − | 0.998587i | \(-0.516924\pi\) | ||||
−0.0531422 | + | 0.998587i | \(0.516924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8668 | −0.511698 | ||||||||
\(452\) | −0.404264 | −0.0190150 | ||||||||
\(453\) | 11.6951 | 0.549485 | ||||||||
\(454\) | 2.57487 | 0.120845 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.31633 | 0.436277 | ||||||||
\(457\) | 20.5822 | 0.962795 | 0.481398 | − | 0.876502i | \(-0.340129\pi\) | ||||
0.481398 | + | 0.876502i | \(0.340129\pi\) | |||||||
\(458\) | −20.9706 | −0.979891 | ||||||||
\(459\) | −15.5524 | −0.725925 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.1061 | −1.26246 | −0.631229 | − | 0.775597i | \(-0.717449\pi\) | ||||
−0.631229 | + | 0.775597i | \(0.717449\pi\) | |||||||
\(462\) | 2.73123 | 0.127068 | ||||||||
\(463\) | −7.94045 | −0.369024 | −0.184512 | − | 0.982830i | \(-0.559070\pi\) | ||||
−0.184512 | + | 0.982830i | \(0.559070\pi\) | |||||||
\(464\) | 14.2984 | 0.663788 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7906 | 0.546190 | ||||||||
\(467\) | −23.9987 | −1.11053 | −0.555264 | − | 0.831674i | \(-0.687383\pi\) | ||||
−0.555264 | + | 0.831674i | \(0.687383\pi\) | |||||||
\(468\) | 7.00587 | 0.323846 | ||||||||
\(469\) | −6.58076 | −0.303871 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.44807 | 0.251034 | ||||||||
\(472\) | −15.6736 | −0.721436 | ||||||||
\(473\) | −27.8891 | −1.28234 | ||||||||
\(474\) | 3.51734 | 0.161557 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.81680 | −0.0832727 | ||||||||
\(477\) | 6.91156 | 0.316458 | ||||||||
\(478\) | −15.5129 | −0.709543 | ||||||||
\(479\) | 21.0540 | 0.961984 | 0.480992 | − | 0.876725i | \(-0.340277\pi\) | ||||
0.480992 | + | 0.876725i | \(0.340277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.68105 | 0.213438 | ||||||||
\(482\) | −24.6658 | −1.12350 | ||||||||
\(483\) | 0.767488 | 0.0349219 | ||||||||
\(484\) | 1.28083 | 0.0582194 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.1556 | −0.868916 | ||||||||
\(487\) | −10.7545 | −0.487333 | −0.243666 | − | 0.969859i | \(-0.578350\pi\) | ||||
−0.243666 | + | 0.969859i | \(0.578350\pi\) | |||||||
\(488\) | 5.26542 | 0.238354 | ||||||||
\(489\) | 7.24587 | 0.327669 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.1200 | −0.953132 | −0.476566 | − | 0.879139i | \(-0.658119\pi\) | ||||
−0.476566 | + | 0.879139i | \(0.658119\pi\) | |||||||
\(492\) | −1.39936 | −0.0630881 | ||||||||
\(493\) | 19.1625 | 0.863035 | ||||||||
\(494\) | 29.2578 | 1.31637 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.51500 | 0.337433 | ||||||||
\(497\) | 13.5418 | 0.607434 | ||||||||
\(498\) | −0.527624 | −0.0236434 | ||||||||
\(499\) | −12.4894 | −0.559104 | −0.279552 | − | 0.960131i | \(-0.590186\pi\) | ||||
−0.279552 | + | 0.960131i | \(0.590186\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.6230 | 0.519275 | ||||||||
\(502\) | −1.48950 | −0.0664794 | ||||||||
\(503\) | 8.79383 | 0.392097 | 0.196049 | − | 0.980594i | \(-0.437189\pi\) | ||||
0.196049 | + | 0.980594i | \(0.437189\pi\) | |||||||
\(504\) | −7.37441 | −0.328482 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.55866 | 0.158202 | ||||||||
\(507\) | −17.5590 | −0.779822 | ||||||||
\(508\) | 7.09092 | 0.314609 | ||||||||
\(509\) | −25.5340 | −1.13178 | −0.565888 | − | 0.824482i | \(-0.691467\pi\) | ||||
−0.565888 | + | 0.824482i | \(0.691467\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.6308 | 0.691464 | ||||||||
\(512\) | −24.5780 | −1.08620 | ||||||||
\(513\) | 16.4810 | 0.727652 | ||||||||
\(514\) | −28.0195 | −1.23589 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.59138 | −0.158102 | ||||||||
\(517\) | 17.7908 | 0.782436 | ||||||||
\(518\) | −0.961866 | −0.0422620 | ||||||||
\(519\) | −14.7530 | −0.647587 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.62227 | −0.333938 | −0.166969 | − | 0.985962i | \(-0.553398\pi\) | ||||
−0.166969 | + | 0.985962i | \(0.553398\pi\) | |||||||
\(522\) | 15.1837 | 0.664574 | ||||||||
\(523\) | −5.49203 | −0.240150 | −0.120075 | − | 0.992765i | \(-0.538313\pi\) | ||||
−0.120075 | + | 0.992765i | \(0.538313\pi\) | |||||||
\(524\) | −8.43168 | −0.368340 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.0867 | 1.00663 | ||||||||
\(527\) | 10.0715 | 0.438719 | ||||||||
\(528\) | 6.20095 | 0.269862 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.3544 | −0.536137 | ||||||||
\(532\) | 1.92527 | 0.0834709 | ||||||||
\(533\) | −22.5124 | −0.975120 | ||||||||
\(534\) | 7.56543 | 0.327388 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.1286 | −0.869421 | ||||||||
\(537\) | −15.5781 | −0.672245 | ||||||||
\(538\) | 6.77513 | 0.292097 | ||||||||
\(539\) | 2.89133 | 0.124539 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.8577 | 1.54164 | 0.770821 | − | 0.637052i | \(-0.219846\pi\) | ||||
0.770821 | + | 0.637052i | \(0.219846\pi\) | |||||||
\(542\) | 38.8637 | 1.66934 | ||||||||
\(543\) | 10.7971 | 0.463349 | ||||||||
\(544\) | −10.0293 | −0.430001 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.65819 | 0.242148 | ||||||||
\(547\) | 2.32908 | 0.0995842 | 0.0497921 | − | 0.998760i | \(-0.484144\pi\) | ||||
0.0497921 | + | 0.998760i | \(0.484144\pi\) | |||||||
\(548\) | −2.98505 | −0.127515 | ||||||||
\(549\) | 4.15037 | 0.177133 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.3065 | −0.865088 | ||||||||
\(552\) | 2.34751 | 0.0999169 | ||||||||
\(553\) | 3.72352 | 0.158340 | ||||||||
\(554\) | 12.8874 | 0.547532 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.85584 | 0.163524 | ||||||||
\(557\) | −34.7139 | −1.47087 | −0.735437 | − | 0.677593i | \(-0.763023\pi\) | ||||
−0.735437 | + | 0.677593i | \(0.763023\pi\) | |||||||
\(558\) | 7.98029 | 0.337833 | ||||||||
\(559\) | −57.7768 | −2.44370 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.31040 | 0.350865 | ||||||||
\(562\) | −4.78415 | −0.201807 | ||||||||
\(563\) | −27.0364 | −1.13945 | −0.569723 | − | 0.821837i | \(-0.692950\pi\) | ||||
−0.569723 | + | 0.821837i | \(0.692950\pi\) | |||||||
\(564\) | 2.29098 | 0.0964679 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.31469 | −0.181360 | ||||||||
\(567\) | −4.04562 | −0.169900 | ||||||||
\(568\) | 41.4204 | 1.73796 | ||||||||
\(569\) | 34.0755 | 1.42852 | 0.714260 | − | 0.699880i | \(-0.246763\pi\) | ||||
0.714260 | + | 0.699880i | \(0.246763\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.15405 | −0.131993 | −0.0659965 | − | 0.997820i | \(-0.521023\pi\) | ||||
−0.0659965 | + | 0.997820i | \(0.521023\pi\) | |||||||
\(572\) | −8.40175 | −0.351295 | ||||||||
\(573\) | −19.5918 | −0.818459 | ||||||||
\(574\) | 4.62586 | 0.193080 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −21.4213 | −0.892552 | ||||||||
\(577\) | 25.6456 | 1.06764 | 0.533821 | − | 0.845598i | \(-0.320756\pi\) | ||||
0.533821 | + | 0.845598i | \(0.320756\pi\) | |||||||
\(578\) | −3.66160 | −0.152302 | ||||||||
\(579\) | −15.5522 | −0.646328 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.558554 | −0.0231727 | ||||||||
\(582\) | −11.7624 | −0.487567 | ||||||||
\(583\) | −8.28865 | −0.343281 | ||||||||
\(584\) | 47.8098 | 1.97838 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.28951 | 0.383746 | ||||||||
\(587\) | 4.89265 | 0.201941 | 0.100971 | − | 0.994889i | \(-0.467805\pi\) | ||||
0.100971 | + | 0.994889i | \(0.467805\pi\) | |||||||
\(588\) | 0.372328 | 0.0153546 | ||||||||
\(589\) | −10.6728 | −0.439763 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.2613 | −0.586630 | ||||||||
\(592\) | −2.18381 | −0.0897541 | ||||||||
\(593\) | −7.29556 | −0.299593 | −0.149796 | − | 0.988717i | \(-0.547862\pi\) | ||||
−0.149796 | + | 0.988717i | \(0.547862\pi\) | |||||||
\(594\) | 14.7786 | 0.606372 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.88844 | 0.364085 | ||||||||
\(597\) | 15.4935 | 0.634105 | ||||||||
\(598\) | 7.37234 | 0.301478 | ||||||||
\(599\) | −13.8414 | −0.565546 | −0.282773 | − | 0.959187i | \(-0.591254\pi\) | ||||
−0.282773 | + | 0.959187i | \(0.591254\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.7356 | −0.764242 | −0.382121 | − | 0.924112i | \(-0.624806\pi\) | ||||
−0.382121 | + | 0.924112i | \(0.624806\pi\) | |||||||
\(602\) | 11.8720 | 0.483867 | ||||||||
\(603\) | −15.8660 | −0.646112 | ||||||||
\(604\) | 7.39243 | 0.300794 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.3862 | 0.746889 | ||||||||
\(607\) | 5.10356 | 0.207147 | 0.103574 | − | 0.994622i | \(-0.466972\pi\) | ||||
0.103574 | + | 0.994622i | \(0.466972\pi\) | |||||||
\(608\) | 10.6281 | 0.431024 | ||||||||
\(609\) | −3.92709 | −0.159134 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.8565 | 1.49105 | ||||||||
\(612\) | −4.38023 | −0.177060 | ||||||||
\(613\) | 42.2725 | 1.70737 | 0.853684 | − | 0.520791i | \(-0.174363\pi\) | ||||
0.853684 | + | 0.520791i | \(0.174363\pi\) | |||||||
\(614\) | −4.18951 | −0.169075 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.84372 | 0.356323 | ||||||||
\(617\) | −31.6837 | −1.27554 | −0.637769 | − | 0.770228i | \(-0.720142\pi\) | ||||
−0.637769 | + | 0.770228i | \(0.720142\pi\) | |||||||
\(618\) | 9.68276 | 0.389498 | ||||||||
\(619\) | −14.7816 | −0.594123 | −0.297062 | − | 0.954858i | \(-0.596007\pi\) | ||||
−0.297062 | + | 0.954858i | \(0.596007\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.15285 | 0.166648 | ||||||||
\(622\) | −11.5294 | −0.462287 | ||||||||
\(623\) | 8.00892 | 0.320871 | ||||||||
\(624\) | 12.8463 | 0.514263 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.3275 | 0.732515 | ||||||||
\(627\) | −8.80656 | −0.351700 | ||||||||
\(628\) | 3.44370 | 0.137419 | ||||||||
\(629\) | −2.92670 | −0.116695 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.1856 | 0.445294 | 0.222647 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222647 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(632\) | 11.3891 | 0.453035 | ||||||||
\(633\) | 13.6379 | 0.542056 | ||||||||
\(634\) | 22.3780 | 0.888744 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.06736 | −0.0423236 | ||||||||
\(637\) | 5.98987 | 0.237327 | ||||||||
\(638\) | −18.2090 | −0.720901 | ||||||||
\(639\) | 32.6489 | 1.29157 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.2835 | 1.35411 | 0.677057 | − | 0.735930i | \(-0.263255\pi\) | ||||
0.677057 | + | 0.735930i | \(0.263255\pi\) | |||||||
\(642\) | 7.68152 | 0.303165 | ||||||||
\(643\) | 9.14558 | 0.360666 | 0.180333 | − | 0.983606i | \(-0.442282\pi\) | ||||
0.180333 | + | 0.983606i | \(0.442282\pi\) | |||||||
\(644\) | 0.485126 | 0.0191166 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.2927 | −0.719715 | ||||||||
\(647\) | 47.8465 | 1.88104 | 0.940521 | − | 0.339737i | \(-0.110338\pi\) | ||||
0.940521 | + | 0.339737i | \(0.110338\pi\) | |||||||
\(648\) | −12.3743 | −0.486110 | ||||||||
\(649\) | 14.8160 | 0.581578 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.06401 | −0.0808949 | ||||||||
\(652\) | 4.58008 | 0.179370 | ||||||||
\(653\) | 3.38063 | 0.132294 | 0.0661472 | − | 0.997810i | \(-0.478929\pi\) | ||||
0.0661472 | + | 0.997810i | \(0.478929\pi\) | |||||||
\(654\) | 10.6263 | 0.415522 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.5025 | 0.410054 | ||||||||
\(657\) | 37.6852 | 1.47024 | ||||||||
\(658\) | −7.57329 | −0.295238 | ||||||||
\(659\) | −21.8518 | −0.851225 | −0.425613 | − | 0.904905i | \(-0.639941\pi\) | ||||
−0.425613 | + | 0.904905i | \(0.639941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.3381 | −1.49118 | −0.745589 | − | 0.666406i | \(-0.767832\pi\) | ||||
−0.745589 | + | 0.666406i | \(0.767832\pi\) | |||||||
\(662\) | −35.2474 | −1.36993 | ||||||||
\(663\) | 17.2163 | 0.668627 | ||||||||
\(664\) | −1.70845 | −0.0663006 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.31902 | −0.0898603 | ||||||||
\(667\) | −5.11682 | −0.198124 | ||||||||
\(668\) | 7.34682 | 0.284257 | ||||||||
\(669\) | 6.49111 | 0.250961 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97731 | −0.192147 | ||||||||
\(672\) | 2.05536 | 0.0792874 | ||||||||
\(673\) | 19.4719 | 0.750588 | 0.375294 | − | 0.926906i | \(-0.377542\pi\) | ||||
0.375294 | + | 0.926906i | \(0.377542\pi\) | |||||||
\(674\) | 34.2992 | 1.32116 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0990 | −0.426883 | ||||||||
\(677\) | 22.2957 | 0.856895 | 0.428447 | − | 0.903567i | \(-0.359061\pi\) | ||||
0.428447 | + | 0.903567i | \(0.359061\pi\) | |||||||
\(678\) | −0.787174 | −0.0302312 | ||||||||
\(679\) | −12.4519 | −0.477861 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.60560 | −0.0615269 | ||||||||
\(682\) | −9.57032 | −0.366467 | ||||||||
\(683\) | 25.5929 | 0.979284 | 0.489642 | − | 0.871924i | \(-0.337127\pi\) | ||||
0.489642 | + | 0.871924i | \(0.337127\pi\) | |||||||
\(684\) | 4.64174 | 0.177481 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.23080 | −0.0469923 | ||||||||
\(687\) | 13.0766 | 0.498902 | ||||||||
\(688\) | 26.9541 | 1.02762 | ||||||||
\(689\) | −17.1713 | −0.654174 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.12405 | −0.0427610 | −0.0213805 | − | 0.999771i | \(-0.506806\pi\) | ||||
−0.0213805 | + | 0.999771i | \(0.506806\pi\) | |||||||
\(692\) | −9.32533 | −0.354496 | ||||||||
\(693\) | 6.97089 | 0.264802 | ||||||||
\(694\) | −23.4622 | −0.890613 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0118 | −0.455306 | ||||||||
\(697\) | 14.0753 | 0.533138 | ||||||||
\(698\) | −0.190881 | −0.00722497 | ||||||||
\(699\) | −7.35224 | −0.278087 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7251 | 0.782776 | 0.391388 | − | 0.920226i | \(-0.371995\pi\) | ||||
0.391388 | + | 0.920226i | \(0.371995\pi\) | |||||||
\(702\) | 30.6162 | 1.15554 | ||||||||
\(703\) | 3.10144 | 0.116973 | ||||||||
\(704\) | 25.6893 | 0.968203 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.9041 | 0.598558 | ||||||||
\(707\) | 19.4640 | 0.732020 | ||||||||
\(708\) | 1.90791 | 0.0717037 | ||||||||
\(709\) | 41.3829 | 1.55417 | 0.777083 | − | 0.629398i | \(-0.216699\pi\) | ||||
0.777083 | + | 0.629398i | \(0.216699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.97727 | 0.336674 | ||||||||
\(712\) | 24.4969 | 0.918059 | ||||||||
\(713\) | −2.68931 | −0.100715 | ||||||||
\(714\) | −3.53763 | −0.132392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.84685 | −0.367994 | ||||||||
\(717\) | 9.67333 | 0.361257 | ||||||||
\(718\) | 23.1344 | 0.863367 | ||||||||
\(719\) | 2.54848 | 0.0950423 | 0.0475212 | − | 0.998870i | \(-0.484868\pi\) | ||||
0.0475212 | + | 0.998870i | \(0.484868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.2504 | 0.381743 | ||||||||
\(722\) | −4.00045 | −0.148881 | ||||||||
\(723\) | 15.3808 | 0.572019 | ||||||||
\(724\) | 6.82481 | 0.253642 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.49400 | 0.0925609 | ||||||||
\(727\) | −35.9776 | −1.33434 | −0.667168 | − | 0.744908i | \(-0.732493\pi\) | ||||
−0.667168 | + | 0.744908i | \(0.732493\pi\) | |||||||
\(728\) | 18.3212 | 0.679029 | ||||||||
\(729\) | −0.192061 | −0.00711339 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.1233 | 1.33607 | ||||||||
\(732\) | −0.640947 | −0.0236901 | ||||||||
\(733\) | 11.9046 | 0.439707 | 0.219853 | − | 0.975533i | \(-0.429442\pi\) | ||||
0.219853 | + | 0.975533i | \(0.429442\pi\) | |||||||
\(734\) | 40.7428 | 1.50385 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.67804 | 0.0987139 | ||||||||
\(737\) | 19.0272 | 0.700875 | ||||||||
\(738\) | 11.1528 | 0.410539 | ||||||||
\(739\) | 33.3063 | 1.22519 | 0.612597 | − | 0.790396i | \(-0.290125\pi\) | ||||
0.612597 | + | 0.790396i | \(0.290125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.2442 | −0.670218 | ||||||||
\(742\) | 3.52837 | 0.129530 | ||||||||
\(743\) | 7.37923 | 0.270718 | 0.135359 | − | 0.990797i | \(-0.456781\pi\) | ||||
0.135359 | + | 0.990797i | \(0.456781\pi\) | |||||||
\(744\) | −6.31318 | −0.231453 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 34.5467 | 1.26485 | ||||||||
\(747\) | −1.34665 | −0.0492714 | ||||||||
\(748\) | 5.25296 | 0.192067 | ||||||||
\(749\) | 8.13181 | 0.297130 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3270 | 0.778233 | 0.389116 | − | 0.921189i | \(-0.372780\pi\) | ||||
0.389116 | + | 0.921189i | \(0.372780\pi\) | |||||||
\(752\) | −17.1943 | −0.627012 | ||||||||
\(753\) | 0.928801 | 0.0338474 | ||||||||
\(754\) | −37.7229 | −1.37379 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.01465 | 0.0732722 | ||||||||
\(757\) | −50.3237 | −1.82904 | −0.914522 | − | 0.404535i | \(-0.867433\pi\) | ||||
−0.914522 | + | 0.404535i | \(0.867433\pi\) | |||||||
\(758\) | 9.26148 | 0.336392 | ||||||||
\(759\) | −2.21906 | −0.0805469 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.6697 | 1.11178 | 0.555889 | − | 0.831257i | \(-0.312378\pi\) | ||||
0.555889 | + | 0.831257i | \(0.312378\pi\) | |||||||
\(762\) | 13.8073 | 0.500185 | ||||||||
\(763\) | 11.2492 | 0.407250 | ||||||||
\(764\) | −12.3839 | −0.448033 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.8210 | 0.535504 | ||||||||
\(767\) | 30.6937 | 1.10829 | ||||||||
\(768\) | 8.36761 | 0.301940 | ||||||||
\(769\) | −7.06494 | −0.254768 | −0.127384 | − | 0.991853i | \(-0.540658\pi\) | ||||
−0.127384 | + | 0.991853i | \(0.540658\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.4720 | 0.629240 | ||||||||
\(772\) | −9.83048 | −0.353807 | ||||||||
\(773\) | −25.8433 | −0.929519 | −0.464759 | − | 0.885437i | \(-0.653859\pi\) | ||||
−0.464759 | + | 0.885437i | \(0.653859\pi\) | |||||||
\(774\) | 28.6230 | 1.02883 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −38.0867 | −1.36723 | ||||||||
\(777\) | 0.599788 | 0.0215173 | ||||||||
\(778\) | −9.12910 | −0.327294 | ||||||||
\(779\) | −14.9156 | −0.534407 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.1540 | −1.40104 | ||||||||
\(782\) | −4.60936 | −0.164830 | ||||||||
\(783\) | −21.2494 | −0.759390 | ||||||||
\(784\) | −2.79440 | −0.0998001 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.4180 | −0.585610 | ||||||||
\(787\) | −26.0828 | −0.929750 | −0.464875 | − | 0.885376i | \(-0.653901\pi\) | ||||
−0.464875 | + | 0.885376i | \(0.653901\pi\) | |||||||
\(788\) | −9.01448 | −0.321127 | ||||||||
\(789\) | −14.3961 | −0.512515 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.833318 | −0.0296294 | ||||||||
\(792\) | 21.3219 | 0.757639 | ||||||||
\(793\) | −10.3113 | −0.366165 | ||||||||
\(794\) | −13.5365 | −0.480392 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.79334 | 0.347116 | ||||||||
\(797\) | −29.8617 | −1.05776 | −0.528879 | − | 0.848698i | \(-0.677387\pi\) | ||||
−0.528879 | + | 0.848698i | \(0.677387\pi\) | |||||||
\(798\) | 3.74884 | 0.132707 | ||||||||
\(799\) | −23.0435 | −0.815220 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.3092 | 0.682257 | ||||||||
\(802\) | 35.3897 | 1.24965 | ||||||||
\(803\) | −45.1937 | −1.59485 | ||||||||
\(804\) | 2.45020 | 0.0864120 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −19.8265 | −0.698358 | ||||||||
\(807\) | −4.22475 | −0.148718 | ||||||||
\(808\) | 59.5346 | 2.09442 | ||||||||
\(809\) | 14.8724 | 0.522885 | 0.261442 | − | 0.965219i | \(-0.415802\pi\) | ||||
0.261442 | + | 0.965219i | \(0.415802\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.1398 | 0.953006 | 0.476503 | − | 0.879173i | \(-0.341904\pi\) | ||||
0.476503 | + | 0.879173i | \(0.341904\pi\) | |||||||
\(812\) | −2.48230 | −0.0871116 | ||||||||
\(813\) | −24.2342 | −0.849929 | ||||||||
\(814\) | 2.78108 | 0.0974766 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.03179 | −0.281169 | ||||||||
\(817\) | −38.2800 | −1.33925 | ||||||||
\(818\) | −23.4006 | −0.818184 | ||||||||
\(819\) | 14.4413 | 0.504621 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.7104 | 1.35100 | 0.675501 | − | 0.737359i | \(-0.263927\pi\) | ||||
0.675501 | + | 0.737359i | \(0.263927\pi\) | |||||||
\(822\) | −5.81242 | −0.202731 | ||||||||
\(823\) | −1.74724 | −0.0609050 | −0.0304525 | − | 0.999536i | \(-0.509695\pi\) | ||||
−0.0304525 | + | 0.999536i | \(0.509695\pi\) | |||||||
\(824\) | 31.3528 | 1.09222 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.30697 | −0.219448 | ||||||||
\(827\) | −8.83233 | −0.307130 | −0.153565 | − | 0.988139i | \(-0.549076\pi\) | ||||
−0.153565 | + | 0.988139i | \(0.549076\pi\) | |||||||
\(828\) | 1.16962 | 0.0406471 | ||||||||
\(829\) | 45.3881 | 1.57639 | 0.788197 | − | 0.615422i | \(-0.211015\pi\) | ||||
0.788197 | + | 0.615422i | \(0.211015\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.03614 | −0.278771 | ||||||||
\(832\) | 53.2196 | 1.84506 | ||||||||
\(833\) | −3.74500 | −0.129757 | ||||||||
\(834\) | 7.50802 | 0.259981 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.56658 | −0.192524 | ||||||||
\(837\) | −11.1683 | −0.386032 | ||||||||
\(838\) | −33.3490 | −1.15202 | ||||||||
\(839\) | −39.3294 | −1.35780 | −0.678901 | − | 0.734230i | \(-0.737543\pi\) | ||||
−0.678901 | + | 0.734230i | \(0.737543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.81820 | −0.0971793 | ||||||||
\(842\) | −18.3716 | −0.633126 | ||||||||
\(843\) | 2.98324 | 0.102748 | ||||||||
\(844\) | 8.62043 | 0.296728 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.2589 | −0.627754 | ||||||||
\(847\) | 2.64019 | 0.0907181 | ||||||||
\(848\) | 8.01077 | 0.275091 | ||||||||
\(849\) | 2.69050 | 0.0923378 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.781495 | 0.0267893 | ||||||||
\(852\) | −5.04201 | −0.172736 | ||||||||
\(853\) | −24.4401 | −0.836812 | −0.418406 | − | 0.908260i | \(-0.637411\pi\) | ||||
−0.418406 | + | 0.908260i | \(0.637411\pi\) | |||||||
\(854\) | 2.11877 | 0.0725029 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 24.8728 | 0.850133 | ||||||||
\(857\) | 4.64324 | 0.158610 | 0.0793050 | − | 0.996850i | \(-0.474730\pi\) | ||||
0.0793050 | + | 0.996850i | \(0.474730\pi\) | |||||||
\(858\) | −16.3597 | −0.558511 | ||||||||
\(859\) | 25.9289 | 0.884683 | 0.442341 | − | 0.896847i | \(-0.354148\pi\) | ||||
0.442341 | + | 0.896847i | \(0.354148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.88454 | −0.0983047 | ||||||||
\(862\) | −11.6615 | −0.397191 | ||||||||
\(863\) | −22.4148 | −0.763008 | −0.381504 | − | 0.924367i | \(-0.624594\pi\) | ||||
−0.381504 | + | 0.924367i | \(0.624594\pi\) | |||||||
\(864\) | 11.1215 | 0.378361 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −40.7361 | −1.38427 | ||||||||
\(867\) | 2.28325 | 0.0775433 | ||||||||
\(868\) | −1.30465 | −0.0442827 | ||||||||
\(869\) | −10.7659 | −0.365210 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.4179 | 1.33562 | ||||||||
\(872\) | 34.4080 | 1.16520 | ||||||||
\(873\) | −30.0211 | −1.01606 | ||||||||
\(874\) | 4.88455 | 0.165222 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.81977 | −0.196632 | ||||||||
\(877\) | 11.3179 | 0.382179 | 0.191090 | − | 0.981573i | \(-0.438798\pi\) | ||||
0.191090 | + | 0.981573i | \(0.438798\pi\) | |||||||
\(878\) | 4.27379 | 0.144233 | ||||||||
\(879\) | −5.79264 | −0.195381 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.8348 | −1.07254 | −0.536270 | − | 0.844046i | \(-0.680167\pi\) | ||||
−0.536270 | + | 0.844046i | \(0.680167\pi\) | |||||||
\(882\) | −2.96742 | −0.0999182 | ||||||||
\(883\) | −9.22964 | −0.310602 | −0.155301 | − | 0.987867i | \(-0.549635\pi\) | ||||
−0.155301 | + | 0.987867i | \(0.549635\pi\) | |||||||
\(884\) | 10.8824 | 0.366014 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.0935 | −0.372694 | ||||||||
\(887\) | −57.6424 | −1.93544 | −0.967722 | − | 0.252021i | \(-0.918905\pi\) | ||||
−0.967722 | + | 0.252021i | \(0.918905\pi\) | |||||||
\(888\) | 1.83457 | 0.0615642 | ||||||||
\(889\) | 14.6167 | 0.490227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.6972 | 0.391873 | ||||||||
\(892\) | 4.10300 | 0.137379 | ||||||||
\(893\) | 24.4193 | 0.817160 | ||||||||
\(894\) | 17.3074 | 0.578845 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.57953 | −0.186399 | ||||||||
\(897\) | −4.59715 | −0.153494 | ||||||||
\(898\) | −2.77192 | −0.0925002 | ||||||||
\(899\) | 13.7607 | 0.458944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7359 | 0.357664 | ||||||||
\(902\) | −13.3749 | −0.445336 | ||||||||
\(903\) | −7.40300 | −0.246356 | ||||||||
\(904\) | −2.54887 | −0.0847742 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 14.3944 | 0.478221 | ||||||||
\(907\) | −37.5533 | −1.24694 | −0.623468 | − | 0.781849i | \(-0.714277\pi\) | ||||
−0.623468 | + | 0.781849i | \(0.714277\pi\) | |||||||
\(908\) | −1.01490 | −0.0336805 | ||||||||
\(909\) | 46.9270 | 1.55647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.75690 | −0.290129 | −0.145065 | − | 0.989422i | \(-0.546339\pi\) | ||||
−0.145065 | + | 0.989422i | \(0.546339\pi\) | |||||||
\(912\) | 8.51132 | 0.281838 | ||||||||
\(913\) | 1.61496 | 0.0534475 | ||||||||
\(914\) | 25.3326 | 0.837929 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.26564 | 0.273104 | ||||||||
\(917\) | −17.3804 | −0.573952 | ||||||||
\(918\) | −19.1420 | −0.631779 | ||||||||
\(919\) | −35.0418 | −1.15592 | −0.577962 | − | 0.816064i | \(-0.696152\pi\) | ||||
−0.577962 | + | 0.816064i | \(0.696152\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.61244 | 0.0860829 | ||||||||
\(922\) | −33.3623 | −1.09873 | ||||||||
\(923\) | −81.1138 | −2.66989 | ||||||||
\(924\) | −1.07652 | −0.0354151 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.77312 | −0.321165 | ||||||||
\(927\) | 24.7132 | 0.811689 | ||||||||
\(928\) | −13.7030 | −0.449824 | ||||||||
\(929\) | 22.7412 | 0.746114 | 0.373057 | − | 0.927808i | \(-0.378310\pi\) | ||||
0.373057 | + | 0.927808i | \(0.378310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.96859 | 0.130065 | ||||||||
\(932\) | −4.64732 | −0.152228 | ||||||||
\(933\) | 7.18936 | 0.235369 | ||||||||
\(934\) | −29.5377 | −0.966503 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 44.1717 | 1.44380 | ||||||||
\(937\) | 16.7075 | 0.545811 | 0.272906 | − | 0.962041i | \(-0.412015\pi\) | ||||
0.272906 | + | 0.962041i | \(0.412015\pi\) | |||||||
\(938\) | −8.09961 | −0.264462 | ||||||||
\(939\) | −11.4284 | −0.372953 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.7145 | 0.903466 | 0.451733 | − | 0.892153i | \(-0.350806\pi\) | ||||
0.451733 | + | 0.892153i | \(0.350806\pi\) | |||||||
\(942\) | 6.70550 | 0.218477 | ||||||||
\(943\) | −3.75841 | −0.122391 | ||||||||
\(944\) | −14.3193 | −0.466053 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.3259 | −1.11603 | ||||||||
\(947\) | −11.8870 | −0.386275 | −0.193137 | − | 0.981172i | \(-0.561866\pi\) | ||||
−0.193137 | + | 0.981172i | \(0.561866\pi\) | |||||||
\(948\) | −1.38637 | −0.0450273 | ||||||||
\(949\) | −93.6262 | −3.03923 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.9542 | −0.452496 | ||||||||
\(952\) | −11.4548 | −0.371253 | ||||||||
\(953\) | 35.9688 | 1.16514 | 0.582572 | − | 0.812779i | \(-0.302047\pi\) | ||||
0.582572 | + | 0.812779i | \(0.302047\pi\) | |||||||
\(954\) | 8.50676 | 0.275417 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.11447 | 0.197756 | ||||||||
\(957\) | 11.3545 | 0.367040 | ||||||||
\(958\) | 25.9134 | 0.837223 | ||||||||
\(959\) | −6.15314 | −0.198695 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.7676 | −0.766698 | ||||||||
\(962\) | 5.76145 | 0.185757 | ||||||||
\(963\) | 19.6055 | 0.631778 | ||||||||
\(964\) | 9.72214 | 0.313129 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.944626 | 0.0303928 | ||||||||
\(967\) | −36.2305 | −1.16509 | −0.582547 | − | 0.812797i | \(-0.697944\pi\) | ||||
−0.582547 | + | 0.812797i | \(0.697944\pi\) | |||||||
\(968\) | 8.07556 | 0.259558 | ||||||||
\(969\) | 11.4067 | 0.366436 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.89397 | 0.0928719 | 0.0464359 | − | 0.998921i | \(-0.485214\pi\) | ||||
0.0464359 | + | 0.998921i | \(0.485214\pi\) | |||||||
\(972\) | 7.55026 | 0.242175 | ||||||||
\(973\) | 7.94813 | 0.254805 | ||||||||
\(974\) | −13.2367 | −0.424130 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.81044 | 0.153979 | ||||||||
\(977\) | 35.1806 | 1.12553 | 0.562764 | − | 0.826618i | \(-0.309738\pi\) | ||||
0.562764 | + | 0.826618i | \(0.309738\pi\) | |||||||
\(978\) | 8.91823 | 0.285173 | ||||||||
\(979\) | −23.1564 | −0.740083 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.1215 | 0.865923 | ||||||||
\(982\) | −25.9945 | −0.829519 | ||||||||
\(983\) | −14.6517 | −0.467317 | −0.233658 | − | 0.972319i | \(-0.575070\pi\) | ||||
−0.233658 | + | 0.972319i | \(0.575070\pi\) | |||||||
\(984\) | −8.82292 | −0.281265 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 23.5852 | 0.751107 | ||||||||
\(987\) | 4.72246 | 0.150317 | ||||||||
\(988\) | −11.5321 | −0.366885 | ||||||||
\(989\) | −9.64575 | −0.306717 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.5480 | −0.398601 | −0.199301 | − | 0.979938i | \(-0.563867\pi\) | ||||
−0.199301 | + | 0.979938i | \(0.563867\pi\) | |||||||
\(992\) | −7.20207 | −0.228666 | ||||||||
\(993\) | 21.9791 | 0.697486 | ||||||||
\(994\) | 16.6673 | 0.528655 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.207965 | 0.00658963 | ||||||||
\(997\) | −3.22687 | −0.102196 | −0.0510980 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510980 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(998\) | −15.3720 | −0.486593 | ||||||||
\(999\) | 3.24543 | 0.102681 |
(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 | 4025.2.a.y.1.8 | 12 | ||
5.2 | odd | 4 | 805.2.c.b.484.17 | yes | 24 | ||
5.3 | odd | 4 | 805.2.c.b.484.8 | ✓ | 24 | ||
5.4 | even | 2 | 4025.2.a.x.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.c.b.484.8 | ✓ | 24 | 5.3 | odd | 4 | ||
805.2.c.b.484.17 | yes | 24 | 5.2 | odd | 4 | ||
4025.2.a.x.1.5 | 12 | 5.4 | even | 2 | |||
4025.2.a.y.1.8 | 12 | 1.1 | even | 1 | trivial |