Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(1.17662\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17662 | −0.831999 | −0.415999 | − | 0.909365i | \(-0.636568\pi\) | ||||
−0.415999 | + | 0.909365i | \(0.636568\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.615555 | −0.307778 | ||||||||
\(5\) | −2.85352 | −1.27613 | −0.638067 | − | 0.769981i | \(-0.720266\pi\) | ||||
−0.638067 | + | 0.769981i | \(0.720266\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.62966 | 1.37188 | 0.685941 | − | 0.727657i | \(-0.259391\pi\) | ||||
0.685941 | + | 0.727657i | \(0.259391\pi\) | |||||||
\(8\) | 3.07753 | 1.08807 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.35752 | 1.06174 | ||||||||
\(11\) | −1.39936 | −0.421923 | −0.210961 | − | 0.977494i | \(-0.567659\pi\) | ||||
−0.210961 | + | 0.977494i | \(0.567659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.03682 | 0.564913 | 0.282457 | − | 0.959280i | \(-0.408851\pi\) | ||||
0.282457 | + | 0.959280i | \(0.408851\pi\) | |||||||
\(14\) | −4.27074 | −1.14140 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.38998 | −0.597495 | ||||||||
\(17\) | 0.256641 | 0.0622445 | 0.0311223 | − | 0.999516i | \(-0.490092\pi\) | ||||
0.0311223 | + | 0.999516i | \(0.490092\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.59337 | 0.365543 | 0.182772 | − | 0.983155i | \(-0.441493\pi\) | ||||
0.182772 | + | 0.983155i | \(0.441493\pi\) | |||||||
\(20\) | 1.75650 | 0.392766 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.64652 | 0.351039 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.14260 | 0.628519 | ||||||||
\(26\) | −2.39658 | −0.470007 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.23426 | −0.422235 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.05203 | 0.548160 | 0.274080 | − | 0.961707i | \(-0.411627\pi\) | ||||
0.274080 | + | 0.961707i | \(0.411627\pi\) | |||||||
\(32\) | −3.34294 | −0.590954 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.301970 | −0.0517874 | ||||||||
\(35\) | −10.3573 | −1.75071 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.80359 | −0.954104 | −0.477052 | − | 0.878875i | \(-0.658295\pi\) | ||||
−0.477052 | + | 0.878875i | \(0.658295\pi\) | |||||||
\(38\) | −1.87479 | −0.304132 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.78179 | −1.38852 | ||||||||
\(41\) | −10.7828 | −1.68399 | −0.841993 | − | 0.539489i | \(-0.818617\pi\) | ||||
−0.841993 | + | 0.539489i | \(0.818617\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8584 | −1.65589 | −0.827944 | − | 0.560811i | \(-0.810489\pi\) | ||||
−0.827944 | + | 0.560811i | \(0.810489\pi\) | |||||||
\(44\) | 0.861383 | 0.129858 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.17662 | 0.173484 | ||||||||
\(47\) | −10.2706 | −1.49812 | −0.749060 | − | 0.662502i | \(-0.769494\pi\) | ||||
−0.749060 | + | 0.662502i | \(0.769494\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.17441 | 0.882059 | ||||||||
\(50\) | −3.69765 | −0.522927 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.25378 | −0.173868 | ||||||||
\(53\) | 9.74574 | 1.33868 | 0.669340 | − | 0.742956i | \(-0.266577\pi\) | ||||
0.669340 | + | 0.742956i | \(0.266577\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.99311 | 0.538430 | ||||||||
\(56\) | 11.1704 | 1.49270 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.17662 | −0.154498 | ||||||||
\(59\) | 4.00720 | 0.521693 | 0.260846 | − | 0.965380i | \(-0.415998\pi\) | ||||
0.260846 | + | 0.965380i | \(0.415998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.96095 | 1.01930 | 0.509648 | − | 0.860383i | \(-0.329776\pi\) | ||||
0.509648 | + | 0.860383i | \(0.329776\pi\) | |||||||
\(62\) | −3.59109 | −0.456068 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.71335 | 1.08917 | ||||||||
\(65\) | −5.81213 | −0.720905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.95063 | 0.238307 | 0.119154 | − | 0.992876i | \(-0.461982\pi\) | ||||
0.119154 | + | 0.992876i | \(0.461982\pi\) | |||||||
\(68\) | −0.157977 | −0.0191575 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 12.1867 | 1.45658 | ||||||||
\(71\) | 12.4876 | 1.48200 | 0.741000 | − | 0.671505i | \(-0.234352\pi\) | ||||
0.741000 | + | 0.671505i | \(0.234352\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.14520 | −0.953323 | −0.476662 | − | 0.879087i | \(-0.658153\pi\) | ||||
−0.476662 | + | 0.879087i | \(0.658153\pi\) | |||||||
\(74\) | 6.82864 | 0.793813 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.980806 | −0.112506 | ||||||||
\(77\) | −5.07920 | −0.578828 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.3016 | 1.83407 | 0.917037 | − | 0.398803i | \(-0.130574\pi\) | ||||
0.917037 | + | 0.398803i | \(0.130574\pi\) | |||||||
\(80\) | 6.81987 | 0.762484 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.6873 | 1.40107 | ||||||||
\(83\) | −6.27397 | −0.688658 | −0.344329 | − | 0.938849i | \(-0.611894\pi\) | ||||
−0.344329 | + | 0.938849i | \(0.611894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.732331 | −0.0794324 | ||||||||
\(86\) | 12.7762 | 1.37770 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.30657 | −0.459081 | ||||||||
\(89\) | −3.67645 | −0.389702 | −0.194851 | − | 0.980833i | \(-0.562422\pi\) | ||||
−0.194851 | + | 0.980833i | \(0.562422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.39297 | 0.774994 | ||||||||
\(92\) | 0.615555 | 0.0641761 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0846 | 1.24643 | ||||||||
\(95\) | −4.54671 | −0.466483 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.10595 | 0.823034 | 0.411517 | − | 0.911402i | \(-0.364999\pi\) | ||||
0.411517 | + | 0.911402i | \(0.364999\pi\) | |||||||
\(98\) | −7.26496 | −0.733872 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.93444 | −0.193444 | ||||||||
\(101\) | −10.7377 | −1.06844 | −0.534219 | − | 0.845346i | \(-0.679394\pi\) | ||||
−0.534219 | + | 0.845346i | \(0.679394\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.05373 | 0.793557 | 0.396779 | − | 0.917914i | \(-0.370128\pi\) | ||||
0.396779 | + | 0.917914i | \(0.370128\pi\) | |||||||
\(104\) | 6.26838 | 0.614665 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.4671 | −1.11378 | ||||||||
\(107\) | 5.29768 | 0.512146 | 0.256073 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256073 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0862 | 1.25343 | 0.626715 | − | 0.779248i | \(-0.284399\pi\) | ||||
0.626715 | + | 0.779248i | \(0.284399\pi\) | |||||||
\(110\) | −4.69838 | −0.447973 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.67481 | −0.819693 | ||||||||
\(113\) | −15.5519 | −1.46300 | −0.731498 | − | 0.681843i | \(-0.761179\pi\) | ||||
−0.731498 | + | 0.681843i | \(0.761179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.85352 | 0.266092 | ||||||||
\(116\) | −0.615555 | −0.0571529 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.71496 | −0.434048 | ||||||||
\(119\) | 0.931518 | 0.0853921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.04179 | −0.821981 | ||||||||
\(122\) | −9.36705 | −0.848053 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.87869 | −0.168711 | ||||||||
\(125\) | 5.30015 | 0.474059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.62028 | −0.321248 | −0.160624 | − | 0.987016i | \(-0.551351\pi\) | ||||
−0.160624 | + | 0.987016i | \(0.551351\pi\) | |||||||
\(128\) | −3.56645 | −0.315233 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.83869 | 0.599793 | ||||||||
\(131\) | −18.8807 | −1.64962 | −0.824809 | − | 0.565412i | \(-0.808717\pi\) | ||||
−0.824809 | + | 0.565412i | \(0.808717\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.78337 | 0.501482 | ||||||||
\(134\) | −2.29516 | −0.198271 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.789819 | 0.0677264 | ||||||||
\(137\) | 2.83524 | 0.242231 | 0.121116 | − | 0.992638i | \(-0.461353\pi\) | ||||
0.121116 | + | 0.992638i | \(0.461353\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.09684 | −0.771584 | −0.385792 | − | 0.922586i | \(-0.626072\pi\) | ||||
−0.385792 | + | 0.922586i | \(0.626072\pi\) | |||||||
\(140\) | 6.37550 | 0.538828 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.6932 | −1.23302 | ||||||||
\(143\) | −2.85025 | −0.238350 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.85352 | −0.236972 | ||||||||
\(146\) | 9.58383 | 0.793164 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.57243 | 0.293652 | ||||||||
\(149\) | 10.6033 | 0.868654 | 0.434327 | − | 0.900755i | \(-0.356986\pi\) | ||||
0.434327 | + | 0.900755i | \(0.356986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.73059 | 0.384970 | 0.192485 | − | 0.981300i | \(-0.438345\pi\) | ||||
0.192485 | + | 0.981300i | \(0.438345\pi\) | |||||||
\(152\) | 4.90363 | 0.397737 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.97630 | 0.481584 | ||||||||
\(155\) | −8.70903 | −0.699526 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.758791 | −0.0605581 | −0.0302791 | − | 0.999541i | \(-0.509640\pi\) | ||||
−0.0302791 | + | 0.999541i | \(0.509640\pi\) | |||||||
\(158\) | −19.1809 | −1.52595 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.53917 | 0.754137 | ||||||||
\(161\) | −3.62966 | −0.286057 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.4320 | −1.60035 | −0.800177 | − | 0.599763i | \(-0.795261\pi\) | ||||
−0.800177 | + | 0.599763i | \(0.795261\pi\) | |||||||
\(164\) | 6.63739 | 0.518293 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.38211 | 0.572963 | ||||||||
\(167\) | −9.96742 | −0.771302 | −0.385651 | − | 0.922645i | \(-0.626023\pi\) | ||||
−0.385651 | + | 0.922645i | \(0.626023\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.85135 | −0.680873 | ||||||||
\(170\) | 0.861678 | 0.0660877 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.68394 | 0.509645 | ||||||||
\(173\) | 25.3581 | 1.92794 | 0.963972 | − | 0.266004i | \(-0.0857033\pi\) | ||||
0.963972 | + | 0.266004i | \(0.0857033\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.4065 | 0.862254 | ||||||||
\(176\) | 3.34444 | 0.252097 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.32580 | 0.324232 | ||||||||
\(179\) | −4.55470 | −0.340434 | −0.170217 | − | 0.985407i | \(-0.554447\pi\) | ||||
−0.170217 | + | 0.985407i | \(0.554447\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.1724 | −1.72239 | −0.861195 | − | 0.508275i | \(-0.830283\pi\) | ||||
−0.861195 | + | 0.508275i | \(0.830283\pi\) | |||||||
\(182\) | −8.69875 | −0.644794 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.07753 | −0.226878 | ||||||||
\(185\) | 16.5607 | 1.21756 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.359133 | −0.0262624 | ||||||||
\(188\) | 6.32212 | 0.461088 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.34977 | 0.388113 | ||||||||
\(191\) | −4.19705 | −0.303688 | −0.151844 | − | 0.988404i | \(-0.548521\pi\) | ||||
−0.151844 | + | 0.988404i | \(0.548521\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.76911 | −0.127344 | −0.0636718 | − | 0.997971i | \(-0.520281\pi\) | ||||
−0.0636718 | + | 0.997971i | \(0.520281\pi\) | |||||||
\(194\) | −9.53766 | −0.684764 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.80069 | −0.271478 | ||||||||
\(197\) | 9.09621 | 0.648078 | 0.324039 | − | 0.946044i | \(-0.394959\pi\) | ||||
0.324039 | + | 0.946044i | \(0.394959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.30465 | −0.376037 | −0.188018 | − | 0.982166i | \(-0.560206\pi\) | ||||
−0.188018 | + | 0.982166i | \(0.560206\pi\) | |||||||
\(200\) | 9.67142 | 0.683873 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.6342 | 0.888939 | ||||||||
\(203\) | 3.62966 | 0.254752 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.7689 | 2.14899 | ||||||||
\(206\) | −9.47621 | −0.660239 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.86797 | −0.337533 | ||||||||
\(209\) | −2.22969 | −0.154231 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.16689 | 0.424546 | 0.212273 | − | 0.977210i | \(-0.431913\pi\) | ||||
0.212273 | + | 0.977210i | \(0.431913\pi\) | |||||||
\(212\) | −5.99904 | −0.412016 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.23337 | −0.426105 | ||||||||
\(215\) | 30.9846 | 2.11314 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.0778 | 0.752010 | ||||||||
\(218\) | −15.3975 | −1.04285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.45798 | −0.165717 | ||||||||
\(221\) | 0.522732 | 0.0351628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.50370 | −0.167660 | −0.0838300 | − | 0.996480i | \(-0.526715\pi\) | ||||
−0.0838300 | + | 0.996480i | \(0.526715\pi\) | |||||||
\(224\) | −12.1337 | −0.810719 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.2987 | 1.21721 | ||||||||
\(227\) | −6.26477 | −0.415808 | −0.207904 | − | 0.978149i | \(-0.566664\pi\) | ||||
−0.207904 | + | 0.978149i | \(0.566664\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.4865 | −1.41987 | −0.709935 | − | 0.704267i | \(-0.751276\pi\) | ||||
−0.709935 | + | 0.704267i | \(0.751276\pi\) | |||||||
\(230\) | −3.35752 | −0.221389 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.07753 | 0.202049 | ||||||||
\(233\) | 17.3695 | 1.13791 | 0.568955 | − | 0.822368i | \(-0.307348\pi\) | ||||
0.568955 | + | 0.822368i | \(0.307348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 29.3074 | 1.91180 | ||||||||
\(236\) | −2.46665 | −0.160565 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.09605 | −0.0710462 | ||||||||
\(239\) | 2.89711 | 0.187399 | 0.0936993 | − | 0.995601i | \(-0.470131\pi\) | ||||
0.0936993 | + | 0.995601i | \(0.470131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.98534 | −0.256718 | −0.128359 | − | 0.991728i | \(-0.540971\pi\) | ||||
−0.128359 | + | 0.991728i | \(0.540971\pi\) | |||||||
\(242\) | 10.6388 | 0.683887 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.90041 | −0.313717 | ||||||||
\(245\) | −17.6188 | −1.12563 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.24541 | 0.206500 | ||||||||
\(248\) | 9.39269 | 0.596436 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.23628 | −0.394417 | ||||||||
\(251\) | 16.9698 | 1.07113 | 0.535564 | − | 0.844495i | \(-0.320099\pi\) | ||||
0.535564 | + | 0.844495i | \(0.320099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.39936 | 0.0879770 | ||||||||
\(254\) | 4.25971 | 0.267278 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.2303 | −0.826895 | ||||||||
\(257\) | −7.22916 | −0.450943 | −0.225471 | − | 0.974250i | \(-0.572392\pi\) | ||||
−0.225471 | + | 0.974250i | \(0.572392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.0650 | −1.30892 | ||||||||
\(260\) | 3.57769 | 0.221879 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.2155 | 1.37248 | ||||||||
\(263\) | 11.9092 | 0.734355 | 0.367177 | − | 0.930151i | \(-0.380324\pi\) | ||||
0.367177 | + | 0.930151i | \(0.380324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −27.8097 | −1.70834 | ||||||||
\(266\) | −6.80486 | −0.417233 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.20072 | −0.0733456 | ||||||||
\(269\) | −17.5257 | −1.06856 | −0.534280 | − | 0.845307i | \(-0.679417\pi\) | ||||
−0.534280 | + | 0.845307i | \(0.679417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.8599 | 1.69237 | 0.846185 | − | 0.532889i | \(-0.178894\pi\) | ||||
0.846185 | + | 0.532889i | \(0.178894\pi\) | |||||||
\(272\) | −0.613367 | −0.0371908 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.33601 | −0.201536 | ||||||||
\(275\) | −4.39762 | −0.265187 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.82340 | 0.470062 | 0.235031 | − | 0.971988i | \(-0.424481\pi\) | ||||
0.235031 | + | 0.971988i | \(0.424481\pi\) | |||||||
\(278\) | 10.7036 | 0.641957 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −31.8749 | −1.90489 | ||||||||
\(281\) | 23.0361 | 1.37422 | 0.687111 | − | 0.726553i | \(-0.258879\pi\) | ||||
0.687111 | + | 0.726553i | \(0.258879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5239 | 0.625581 | 0.312791 | − | 0.949822i | \(-0.398736\pi\) | ||||
0.312791 | + | 0.949822i | \(0.398736\pi\) | |||||||
\(284\) | −7.68678 | −0.456127 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.35367 | 0.198307 | ||||||||
\(287\) | −39.1377 | −2.31023 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9341 | −0.996126 | ||||||||
\(290\) | 3.35752 | 0.197161 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.01382 | 0.293412 | ||||||||
\(293\) | −19.5780 | −1.14376 | −0.571878 | − | 0.820339i | \(-0.693785\pi\) | ||||
−0.571878 | + | 0.820339i | \(0.693785\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.4346 | −0.665750 | ||||||||
\(296\) | −17.8607 | −1.03813 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.4761 | −0.722720 | ||||||||
\(299\) | −2.03682 | −0.117793 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −39.4122 | −2.27168 | ||||||||
\(302\) | −5.56613 | −0.320295 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.80812 | −0.218410 | ||||||||
\(305\) | −22.7168 | −1.30076 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3395 | −0.932543 | −0.466272 | − | 0.884642i | \(-0.654403\pi\) | ||||
−0.466272 | + | 0.884642i | \(0.654403\pi\) | |||||||
\(308\) | 3.12653 | 0.178150 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.2472 | 0.582005 | ||||||||
\(311\) | 14.4849 | 0.821361 | 0.410681 | − | 0.911779i | \(-0.365291\pi\) | ||||
0.410681 | + | 0.911779i | \(0.365291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8990 | −0.898663 | −0.449331 | − | 0.893365i | \(-0.648338\pi\) | ||||
−0.449331 | + | 0.893365i | \(0.648338\pi\) | |||||||
\(314\) | 0.892812 | 0.0503843 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0345 | −0.564487 | ||||||||
\(317\) | 7.37522 | 0.414234 | 0.207117 | − | 0.978316i | \(-0.433592\pi\) | ||||
0.207117 | + | 0.978316i | \(0.433592\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.39936 | −0.0783491 | ||||||||
\(320\) | −24.8637 | −1.38993 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.27074 | 0.237999 | ||||||||
\(323\) | 0.408923 | 0.0227531 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.40092 | 0.355059 | ||||||||
\(326\) | 24.0407 | 1.33149 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −33.1842 | −1.83229 | ||||||||
\(329\) | −37.2787 | −2.05524 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.22314 | −0.122195 | −0.0610974 | − | 0.998132i | \(-0.519460\pi\) | ||||
−0.0610974 | + | 0.998132i | \(0.519460\pi\) | |||||||
\(332\) | 3.86198 | 0.211954 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.7279 | 0.641722 | ||||||||
\(335\) | −5.56616 | −0.304112 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.8928 | −1.19258 | −0.596288 | − | 0.802771i | \(-0.703358\pi\) | ||||
−0.596288 | + | 0.802771i | \(0.703358\pi\) | |||||||
\(338\) | 10.4147 | 0.566485 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.450790 | 0.0244475 | ||||||||
\(341\) | −4.27088 | −0.231281 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.99661 | −0.161802 | ||||||||
\(344\) | −33.4170 | −1.80172 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.8370 | −1.60405 | ||||||||
\(347\) | −32.5836 | −1.74918 | −0.874590 | − | 0.484863i | \(-0.838869\pi\) | ||||
−0.874590 | + | 0.484863i | \(0.838869\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.5157 | −1.25877 | −0.629384 | − | 0.777094i | \(-0.716693\pi\) | ||||
−0.629384 | + | 0.777094i | \(0.716693\pi\) | |||||||
\(350\) | −13.4212 | −0.717394 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.67798 | 0.249337 | ||||||||
\(353\) | 27.3657 | 1.45653 | 0.728263 | − | 0.685297i | \(-0.240328\pi\) | ||||
0.728263 | + | 0.685297i | \(0.240328\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −35.6335 | −1.89123 | ||||||||
\(356\) | 2.26306 | 0.119942 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.35917 | 0.283241 | ||||||||
\(359\) | −0.782857 | −0.0413176 | −0.0206588 | − | 0.999787i | \(-0.506576\pi\) | ||||
−0.0206588 | + | 0.999787i | \(0.506576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4612 | −0.866378 | ||||||||
\(362\) | 27.2652 | 1.43303 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.55079 | −0.238526 | ||||||||
\(365\) | 23.2425 | 1.21657 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.508753 | 0.0265567 | 0.0132784 | − | 0.999912i | \(-0.495773\pi\) | ||||
0.0132784 | + | 0.999912i | \(0.495773\pi\) | |||||||
\(368\) | 2.38998 | 0.124586 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.4857 | −1.01301 | ||||||||
\(371\) | 35.3737 | 1.83651 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.51685 | −0.285651 | −0.142826 | − | 0.989748i | \(-0.545619\pi\) | ||||
−0.142826 | + | 0.989748i | \(0.545619\pi\) | |||||||
\(374\) | 0.422564 | 0.0218503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31.6080 | −1.63006 | ||||||||
\(377\) | 2.03682 | 0.104902 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.9568 | −1.43605 | −0.718023 | − | 0.696019i | \(-0.754953\pi\) | ||||
−0.718023 | + | 0.696019i | \(0.754953\pi\) | |||||||
\(380\) | 2.79875 | 0.143573 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.93835 | 0.252668 | ||||||||
\(383\) | −5.58188 | −0.285221 | −0.142610 | − | 0.989779i | \(-0.545550\pi\) | ||||
−0.142610 | + | 0.989779i | \(0.545550\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4936 | 0.738662 | ||||||||
\(386\) | 2.08158 | 0.105950 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.98966 | −0.253312 | ||||||||
\(389\) | 3.74821 | 0.190042 | 0.0950210 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950210 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.256641 | −0.0129789 | ||||||||
\(392\) | 19.0019 | 0.959741 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.7028 | −0.539201 | ||||||||
\(395\) | −46.5170 | −2.34052 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3805 | 1.52475 | 0.762377 | − | 0.647133i | \(-0.224032\pi\) | ||||
0.762377 | + | 0.647133i | \(0.224032\pi\) | |||||||
\(398\) | 6.24158 | 0.312862 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.51074 | −0.375537 | ||||||||
\(401\) | −3.30262 | −0.164925 | −0.0824626 | − | 0.996594i | \(-0.526278\pi\) | ||||
−0.0824626 | + | 0.996594i | \(0.526278\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.21644 | 0.309663 | ||||||||
\(404\) | 6.60963 | 0.328841 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.27074 | −0.211953 | ||||||||
\(407\) | 8.12130 | 0.402558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.51701 | −0.322246 | −0.161123 | − | 0.986934i | \(-0.551512\pi\) | ||||
−0.161123 | + | 0.986934i | \(0.551512\pi\) | |||||||
\(410\) | −36.2034 | −1.78796 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.95751 | −0.244239 | ||||||||
\(413\) | 14.5447 | 0.715700 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.9029 | 0.878820 | ||||||||
\(416\) | −6.80899 | −0.333838 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.62351 | 0.128320 | ||||||||
\(419\) | −38.1773 | −1.86508 | −0.932541 | − | 0.361063i | \(-0.882414\pi\) | ||||
−0.932541 | + | 0.361063i | \(0.882414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.6872 | −1.73929 | −0.869644 | − | 0.493679i | \(-0.835652\pi\) | ||||
−0.869644 | + | 0.493679i | \(0.835652\pi\) | |||||||
\(422\) | −7.25612 | −0.353222 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29.9928 | 1.45658 | ||||||||
\(425\) | 0.806518 | 0.0391219 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.8955 | 1.39835 | ||||||||
\(428\) | −3.26101 | −0.157627 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −36.4573 | −1.75813 | ||||||||
\(431\) | −9.57775 | −0.461344 | −0.230672 | − | 0.973032i | \(-0.574092\pi\) | ||||
−0.230672 | + | 0.973032i | \(0.574092\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4518 | 0.550336 | 0.275168 | − | 0.961396i | \(-0.411266\pi\) | ||||
0.275168 | + | 0.961396i | \(0.411266\pi\) | |||||||
\(434\) | −13.0344 | −0.625672 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.05528 | −0.385778 | ||||||||
\(437\) | −1.59337 | −0.0762211 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.4092 | 0.878624 | 0.439312 | − | 0.898335i | \(-0.355222\pi\) | ||||
0.439312 | + | 0.898335i | \(0.355222\pi\) | |||||||
\(440\) | 12.2889 | 0.585850 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.615059 | −0.0292554 | ||||||||
\(443\) | −12.4019 | −0.589232 | −0.294616 | − | 0.955616i | \(-0.595192\pi\) | ||||
−0.294616 | + | 0.955616i | \(0.595192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.4908 | 0.497313 | ||||||||
\(446\) | 2.94591 | 0.139493 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 31.6265 | 1.49421 | ||||||||
\(449\) | 23.9157 | 1.12865 | 0.564327 | − | 0.825551i | \(-0.309136\pi\) | ||||
0.564327 | + | 0.825551i | \(0.309136\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0890 | 0.710512 | ||||||||
\(452\) | 9.57304 | 0.450278 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.37128 | 0.345952 | ||||||||
\(455\) | −21.0960 | −0.988997 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.61853 | 0.169268 | 0.0846339 | − | 0.996412i | \(-0.473028\pi\) | ||||
0.0846339 | + | 0.996412i | \(0.473028\pi\) | |||||||
\(458\) | 25.2816 | 1.18133 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.75650 | −0.0818973 | ||||||||
\(461\) | −7.97110 | −0.371251 | −0.185626 | − | 0.982621i | \(-0.559431\pi\) | ||||
−0.185626 | + | 0.982621i | \(0.559431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.8314 | −1.24696 | −0.623480 | − | 0.781840i | \(-0.714282\pi\) | ||||
−0.623480 | + | 0.781840i | \(0.714282\pi\) | |||||||
\(464\) | −2.38998 | −0.110952 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.4373 | −0.946740 | ||||||||
\(467\) | 12.0191 | 0.556175 | 0.278088 | − | 0.960556i | \(-0.410299\pi\) | ||||
0.278088 | + | 0.960556i | \(0.410299\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.08011 | 0.326929 | ||||||||
\(470\) | −34.4838 | −1.59062 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.3323 | 0.567638 | ||||||||
\(473\) | 15.1948 | 0.698657 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00731 | 0.229751 | ||||||||
\(476\) | −0.573401 | −0.0262818 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.40881 | −0.155915 | ||||||||
\(479\) | −26.7408 | −1.22182 | −0.610909 | − | 0.791701i | \(-0.709196\pi\) | ||||
−0.610909 | + | 0.791701i | \(0.709196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.8209 | −0.538986 | ||||||||
\(482\) | 4.68925 | 0.213589 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.56572 | 0.252987 | ||||||||
\(485\) | −23.1305 | −1.05030 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.3823 | −1.24081 | −0.620405 | − | 0.784281i | \(-0.713032\pi\) | ||||
−0.620405 | + | 0.784281i | \(0.713032\pi\) | |||||||
\(488\) | 24.5000 | 1.10906 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 20.7307 | 0.936519 | ||||||||
\(491\) | 30.2527 | 1.36529 | 0.682644 | − | 0.730751i | \(-0.260830\pi\) | ||||
0.682644 | + | 0.730751i | \(0.260830\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.256641 | 0.0115585 | ||||||||
\(494\) | −3.81863 | −0.171808 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.29428 | −0.327523 | ||||||||
\(497\) | 45.3255 | 2.03313 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.43684 | −0.377685 | −0.188842 | − | 0.982007i | \(-0.560474\pi\) | ||||
−0.188842 | + | 0.982007i | \(0.560474\pi\) | |||||||
\(500\) | −3.26253 | −0.145905 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.9671 | −0.891177 | ||||||||
\(503\) | −10.9875 | −0.489907 | −0.244953 | − | 0.969535i | \(-0.578773\pi\) | ||||
−0.244953 | + | 0.969535i | \(0.578773\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.6402 | 1.36347 | ||||||||
\(506\) | −1.64652 | −0.0731968 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.22849 | 0.0988730 | ||||||||
\(509\) | −13.4171 | −0.594704 | −0.297352 | − | 0.954768i | \(-0.596103\pi\) | ||||
−0.297352 | + | 0.954768i | \(0.596103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.5643 | −1.30785 | ||||||||
\(512\) | 22.7000 | 1.00321 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.50601 | 0.375184 | ||||||||
\(515\) | −22.9815 | −1.01269 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3723 | 0.632091 | ||||||||
\(518\) | 24.7856 | 1.08902 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.8870 | −0.784395 | ||||||||
\(521\) | −23.7404 | −1.04008 | −0.520042 | − | 0.854141i | \(-0.674084\pi\) | ||||
−0.520042 | + | 0.854141i | \(0.674084\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.9883 | −1.00521 | −0.502604 | − | 0.864517i | \(-0.667625\pi\) | ||||
−0.502604 | + | 0.864517i | \(0.667625\pi\) | |||||||
\(524\) | 11.6221 | 0.507716 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0127 | −0.610982 | ||||||||
\(527\) | 0.783274 | 0.0341200 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 32.7215 | 1.42133 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.55999 | −0.154345 | ||||||||
\(533\) | −21.9626 | −0.951306 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.1170 | −0.653567 | ||||||||
\(536\) | 6.00311 | 0.259295 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.6212 | 0.889042 | ||||||||
\(539\) | −8.64022 | −0.372161 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.3013 | −0.485881 | −0.242940 | − | 0.970041i | \(-0.578112\pi\) | ||||
−0.242940 | + | 0.970041i | \(0.578112\pi\) | |||||||
\(542\) | −32.7807 | −1.40805 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.857935 | −0.0367837 | ||||||||
\(545\) | −37.3418 | −1.59955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.2391 | −0.779847 | −0.389924 | − | 0.920847i | \(-0.627499\pi\) | ||||
−0.389924 | + | 0.920847i | \(0.627499\pi\) | |||||||
\(548\) | −1.74525 | −0.0745533 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.17435 | 0.220635 | ||||||||
\(551\) | 1.59337 | 0.0678797 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 59.1692 | 2.51613 | ||||||||
\(554\) | −9.20520 | −0.391091 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.59961 | 0.237476 | ||||||||
\(557\) | 30.9415 | 1.31103 | 0.655516 | − | 0.755181i | \(-0.272451\pi\) | ||||
0.655516 | + | 0.755181i | \(0.272451\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.1166 | −0.935433 | ||||||||
\(560\) | 24.7538 | 1.04604 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −27.1049 | −1.14335 | ||||||||
\(563\) | −41.8692 | −1.76458 | −0.882289 | − | 0.470709i | \(-0.843998\pi\) | ||||
−0.882289 | + | 0.470709i | \(0.843998\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 44.3776 | 1.86698 | ||||||||
\(566\) | −12.3827 | −0.520483 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 38.4308 | 1.61252 | ||||||||
\(569\) | −5.74370 | −0.240788 | −0.120394 | − | 0.992726i | \(-0.538416\pi\) | ||||
−0.120394 | + | 0.992726i | \(0.538416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.60570 | 0.276440 | 0.138220 | − | 0.990402i | \(-0.455862\pi\) | ||||
0.138220 | + | 0.990402i | \(0.455862\pi\) | |||||||
\(572\) | 1.75449 | 0.0733588 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 46.0504 | 1.92211 | ||||||||
\(575\) | −3.14260 | −0.131055 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.1911 | 1.75644 | 0.878220 | − | 0.478258i | \(-0.158731\pi\) | ||||
0.878220 | + | 0.478258i | \(0.158731\pi\) | |||||||
\(578\) | 19.9251 | 0.828775 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.75650 | 0.0729348 | ||||||||
\(581\) | −22.7724 | −0.944757 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.6378 | −0.564820 | ||||||||
\(584\) | −25.0671 | −1.03728 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.0359 | 0.951604 | ||||||||
\(587\) | −33.6266 | −1.38792 | −0.693959 | − | 0.720014i | \(-0.744135\pi\) | ||||
−0.693959 | + | 0.720014i | \(0.744135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.86300 | 0.200376 | ||||||||
\(590\) | 13.4543 | 0.553903 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 13.8705 | 0.570072 | ||||||||
\(593\) | −38.6906 | −1.58883 | −0.794417 | − | 0.607372i | \(-0.792224\pi\) | ||||
−0.794417 | + | 0.607372i | \(0.792224\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.65811 | −0.108972 | ||||||||
\(596\) | −6.52691 | −0.267352 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.39658 | 0.0980033 | ||||||||
\(599\) | −32.5145 | −1.32851 | −0.664254 | − | 0.747507i | \(-0.731251\pi\) | ||||
−0.664254 | + | 0.747507i | \(0.731251\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.4682 | −0.467800 | −0.233900 | − | 0.972261i | \(-0.575149\pi\) | ||||
−0.233900 | + | 0.972261i | \(0.575149\pi\) | |||||||
\(602\) | 46.3734 | 1.89004 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.91194 | −0.118485 | ||||||||
\(605\) | 25.8010 | 1.04896 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.4823 | −1.64313 | −0.821564 | − | 0.570117i | \(-0.806898\pi\) | ||||
−0.821564 | + | 0.570117i | \(0.806898\pi\) | |||||||
\(608\) | −5.32653 | −0.216019 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.7291 | 1.08223 | ||||||||
\(611\) | −20.9194 | −0.846308 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.2959 | −1.06208 | −0.531041 | − | 0.847346i | \(-0.678199\pi\) | ||||
−0.531041 | + | 0.847346i | \(0.678199\pi\) | |||||||
\(614\) | 19.2254 | 0.775875 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.6314 | −0.629805 | ||||||||
\(617\) | 2.31724 | 0.0932886 | 0.0466443 | − | 0.998912i | \(-0.485147\pi\) | ||||
0.0466443 | + | 0.998912i | \(0.485147\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.3929 | 0.699079 | 0.349540 | − | 0.936922i | \(-0.386338\pi\) | ||||
0.349540 | + | 0.936922i | \(0.386338\pi\) | |||||||
\(620\) | 5.36089 | 0.215298 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.0432 | −0.683372 | ||||||||
\(623\) | −13.3442 | −0.534626 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8371 | −1.23348 | ||||||||
\(626\) | 18.7071 | 0.747687 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.467078 | 0.0186384 | ||||||||
\(629\) | −1.48944 | −0.0593877 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.58190 | −0.102784 | −0.0513920 | − | 0.998679i | \(-0.516366\pi\) | ||||
−0.0513920 | + | 0.998679i | \(0.516366\pi\) | |||||||
\(632\) | 50.1686 | 1.99560 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.67787 | −0.344642 | ||||||||
\(635\) | 10.3306 | 0.409956 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.5762 | 0.498287 | ||||||||
\(638\) | 1.64652 | 0.0651864 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10.1770 | 0.402279 | ||||||||
\(641\) | 41.7793 | 1.65018 | 0.825092 | − | 0.564998i | \(-0.191123\pi\) | ||||
0.825092 | + | 0.564998i | \(0.191123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.2474 | −0.561864 | −0.280932 | − | 0.959728i | \(-0.590644\pi\) | ||||
−0.280932 | + | 0.959728i | \(0.590644\pi\) | |||||||
\(644\) | 2.23426 | 0.0880420 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.481149 | −0.0189305 | ||||||||
\(647\) | 39.6911 | 1.56042 | 0.780209 | − | 0.625519i | \(-0.215113\pi\) | ||||
0.780209 | + | 0.625519i | \(0.215113\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.60751 | −0.220114 | ||||||||
\(650\) | −7.53147 | −0.295409 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.5770 | 0.492554 | ||||||||
\(653\) | 11.1782 | 0.437438 | 0.218719 | − | 0.975788i | \(-0.429812\pi\) | ||||
0.218719 | + | 0.975788i | \(0.429812\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 53.8766 | 2.10513 | ||||||||
\(656\) | 25.7706 | 1.00617 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 43.8631 | 1.70996 | ||||||||
\(659\) | −40.4792 | −1.57684 | −0.788422 | − | 0.615134i | \(-0.789102\pi\) | ||||
−0.788422 | + | 0.615134i | \(0.789102\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.3921 | 0.443101 | 0.221551 | − | 0.975149i | \(-0.428888\pi\) | ||||
0.221551 | + | 0.975149i | \(0.428888\pi\) | |||||||
\(662\) | 2.61580 | 0.101666 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.3083 | −0.749308 | ||||||||
\(665\) | −16.5030 | −0.639959 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 6.13550 | 0.237390 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.54928 | 0.253021 | ||||||||
\(671\) | −11.1402 | −0.430064 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8502 | 1.42047 | 0.710235 | − | 0.703964i | \(-0.248589\pi\) | ||||
0.710235 | + | 0.703964i | \(0.248589\pi\) | |||||||
\(674\) | 25.7596 | 0.992222 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.44849 | 0.209557 | ||||||||
\(677\) | 18.5311 | 0.712209 | 0.356104 | − | 0.934446i | \(-0.384105\pi\) | ||||
0.356104 | + | 0.934446i | \(0.384105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.4218 | 1.12911 | ||||||||
\(680\) | −2.25377 | −0.0864280 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.02522 | 0.192426 | ||||||||
\(683\) | −20.8679 | −0.798489 | −0.399244 | − | 0.916845i | \(-0.630727\pi\) | ||||
−0.399244 | + | 0.916845i | \(0.630727\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.09043 | −0.309119 | ||||||||
\(686\) | 3.52588 | 0.134619 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25.9513 | 0.989385 | ||||||||
\(689\) | 19.8504 | 0.756238 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.5961 | 0.479178 | 0.239589 | − | 0.970874i | \(-0.422987\pi\) | ||||
0.239589 | + | 0.970874i | \(0.422987\pi\) | |||||||
\(692\) | −15.6093 | −0.593378 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 38.3387 | 1.45532 | ||||||||
\(695\) | 25.9580 | 0.984645 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.76730 | −0.104819 | ||||||||
\(698\) | 27.6692 | 1.04729 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.02136 | −0.265383 | ||||||||
\(701\) | −37.2561 | −1.40714 | −0.703572 | − | 0.710624i | \(-0.748413\pi\) | ||||
−0.703572 | + | 0.710624i | \(0.748413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.24724 | −0.348766 | ||||||||
\(704\) | −12.1931 | −0.459545 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.1991 | −1.21183 | ||||||||
\(707\) | −38.9740 | −1.46577 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.74456 | −0.178186 | −0.0890928 | − | 0.996023i | \(-0.528397\pi\) | ||||
−0.0890928 | + | 0.996023i | \(0.528397\pi\) | |||||||
\(710\) | 41.9273 | 1.57350 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.3144 | −0.424023 | ||||||||
\(713\) | −3.05203 | −0.114299 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.13325 | 0.304166 | ||||||||
\(716\) | 2.80367 | 0.104778 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.921128 | 0.0343762 | ||||||||
\(719\) | 22.5184 | 0.839793 | 0.419897 | − | 0.907572i | \(-0.362066\pi\) | ||||
0.419897 | + | 0.907572i | \(0.362066\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.2323 | 1.08867 | ||||||||
\(722\) | 19.3686 | 0.720826 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.2639 | 0.530113 | ||||||||
\(725\) | 3.14260 | 0.116713 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0168 | −0.594031 | −0.297016 | − | 0.954873i | \(-0.595991\pi\) | ||||
−0.297016 | + | 0.954873i | \(0.595991\pi\) | |||||||
\(728\) | 22.7521 | 0.843248 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −27.3477 | −1.01218 | ||||||||
\(731\) | −2.78670 | −0.103070 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.9162 | −1.80676 | −0.903380 | − | 0.428840i | \(-0.858922\pi\) | ||||
−0.903380 | + | 0.428840i | \(0.858922\pi\) | |||||||
\(734\) | −0.598612 | −0.0220952 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.34294 | 0.123223 | ||||||||
\(737\) | −2.72963 | −0.100547 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3156 | 0.747322 | 0.373661 | − | 0.927565i | \(-0.378102\pi\) | ||||
0.373661 | + | 0.927565i | \(0.378102\pi\) | |||||||
\(740\) | −10.1940 | −0.374739 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −41.6215 | −1.52797 | ||||||||
\(743\) | 10.8760 | 0.399003 | 0.199502 | − | 0.979898i | \(-0.436068\pi\) | ||||
0.199502 | + | 0.979898i | \(0.436068\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.2567 | −1.10852 | ||||||||
\(746\) | 6.49125 | 0.237662 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.221066 | 0.00808298 | ||||||||
\(749\) | 19.2287 | 0.702603 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.1517 | 0.552895 | 0.276447 | − | 0.961029i | \(-0.410843\pi\) | ||||
0.276447 | + | 0.961029i | \(0.410843\pi\) | |||||||
\(752\) | 24.5465 | 0.895119 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.39658 | −0.0872782 | ||||||||
\(755\) | −13.4989 | −0.491274 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.21203 | 0.153089 | 0.0765444 | − | 0.997066i | \(-0.475611\pi\) | ||||
0.0765444 | + | 0.997066i | \(0.475611\pi\) | |||||||
\(758\) | 32.8947 | 1.19479 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.9926 | −0.507566 | ||||||||
\(761\) | 54.5237 | 1.97648 | 0.988242 | − | 0.152901i | \(-0.0488614\pi\) | ||||
0.988242 | + | 0.152901i | \(0.0488614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 47.4984 | 1.71956 | ||||||||
\(764\) | 2.58352 | 0.0934684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.56778 | 0.237304 | ||||||||
\(767\) | 8.16195 | 0.294711 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.5349 | 1.13718 | 0.568590 | − | 0.822621i | \(-0.307489\pi\) | ||||
0.568590 | + | 0.822621i | \(0.307489\pi\) | |||||||
\(770\) | −17.0535 | −0.614566 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.08899 | 0.0391935 | ||||||||
\(773\) | 10.3929 | 0.373806 | 0.186903 | − | 0.982378i | \(-0.440155\pi\) | ||||
0.186903 | + | 0.982378i | \(0.440155\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.59128 | 0.344529 | ||||||||
\(776\) | 24.9463 | 0.895519 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.41024 | −0.158115 | ||||||||
\(779\) | −17.1809 | −0.615570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.4746 | −0.625290 | ||||||||
\(782\) | 0.301970 | 0.0107984 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.7567 | −0.527026 | ||||||||
\(785\) | 2.16523 | 0.0772803 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.22731 | −0.0437487 | −0.0218744 | − | 0.999761i | \(-0.506963\pi\) | ||||
−0.0218744 | + | 0.999761i | \(0.506963\pi\) | |||||||
\(788\) | −5.59922 | −0.199464 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 54.7330 | 1.94731 | ||||||||
\(791\) | −56.4479 | −2.00706 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.2151 | 0.575814 | ||||||||
\(794\) | −35.7464 | −1.26859 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.26530 | 0.115736 | ||||||||
\(797\) | −48.7301 | −1.72611 | −0.863054 | − | 0.505112i | \(-0.831451\pi\) | ||||
−0.863054 | + | 0.505112i | \(0.831451\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.63585 | −0.0932498 | ||||||||
\(800\) | −10.5055 | −0.371426 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.88595 | 0.137218 | ||||||||
\(803\) | 11.3981 | 0.402229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3573 | 0.365047 | ||||||||
\(806\) | −7.31441 | −0.257639 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33.0454 | −1.16253 | ||||||||
\(809\) | −40.2800 | −1.41617 | −0.708084 | − | 0.706128i | \(-0.750440\pi\) | ||||
−0.708084 | + | 0.706128i | \(0.750440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.8631 | −1.04863 | −0.524317 | − | 0.851523i | \(-0.675679\pi\) | ||||
−0.524317 | + | 0.851523i | \(0.675679\pi\) | |||||||
\(812\) | −2.23426 | −0.0784070 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.55572 | −0.334928 | ||||||||
\(815\) | 58.3031 | 2.04227 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.3014 | −0.605299 | ||||||||
\(818\) | 7.66808 | 0.268108 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −18.9399 | −0.661412 | ||||||||
\(821\) | 16.0595 | 0.560480 | 0.280240 | − | 0.959930i | \(-0.409586\pi\) | ||||
0.280240 | + | 0.959930i | \(0.409586\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.8721 | 0.483552 | 0.241776 | − | 0.970332i | \(-0.422270\pi\) | ||||
0.241776 | + | 0.970332i | \(0.422270\pi\) | |||||||
\(824\) | 24.7855 | 0.863445 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.1137 | −0.595462 | ||||||||
\(827\) | −41.4361 | −1.44087 | −0.720436 | − | 0.693521i | \(-0.756058\pi\) | ||||
−0.720436 | + | 0.693521i | \(0.756058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.5188 | −0.608455 | −0.304227 | − | 0.952599i | \(-0.598398\pi\) | ||||
−0.304227 | + | 0.952599i | \(0.598398\pi\) | |||||||
\(830\) | −21.0650 | −0.731178 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 17.7476 | 0.615286 | ||||||||
\(833\) | 1.58461 | 0.0549033 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.4423 | 0.984285 | ||||||||
\(836\) | 1.37250 | 0.0474689 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 44.9203 | 1.55175 | ||||||||
\(839\) | −2.33207 | −0.0805121 | −0.0402561 | − | 0.999189i | \(-0.512817\pi\) | ||||
−0.0402561 | + | 0.999189i | \(0.512817\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 41.9904 | 1.44709 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.79606 | −0.130666 | ||||||||
\(845\) | 25.2575 | 0.868885 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.8186 | −1.12766 | ||||||||
\(848\) | −23.2921 | −0.799855 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.948969 | −0.0325494 | ||||||||
\(851\) | 5.80359 | 0.198944 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.2974 | −1.17432 | −0.587160 | − | 0.809471i | \(-0.699754\pi\) | ||||
−0.587160 | + | 0.809471i | \(0.699754\pi\) | |||||||
\(854\) | −33.9992 | −1.16343 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.3037 | 0.557250 | ||||||||
\(857\) | −4.44845 | −0.151956 | −0.0759780 | − | 0.997109i | \(-0.524208\pi\) | ||||
−0.0759780 | + | 0.997109i | \(0.524208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.6653 | 0.773329 | 0.386664 | − | 0.922220i | \(-0.373627\pi\) | ||||
0.386664 | + | 0.922220i | \(0.373627\pi\) | |||||||
\(860\) | −19.0728 | −0.650376 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.2694 | 0.383838 | ||||||||
\(863\) | 16.6196 | 0.565739 | 0.282870 | − | 0.959158i | \(-0.408714\pi\) | ||||
0.282870 | + | 0.959158i | \(0.408714\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.3601 | −2.46032 | ||||||||
\(866\) | −13.4744 | −0.457879 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.81900 | −0.231452 | ||||||||
\(869\) | −22.8118 | −0.773838 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.97309 | 0.134623 | ||||||||
\(872\) | 40.2731 | 1.36382 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.87479 | 0.0634158 | ||||||||
\(875\) | 19.2377 | 0.650353 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.0821 | 1.25217 | 0.626087 | − | 0.779753i | \(-0.284656\pi\) | ||||
0.626087 | + | 0.779753i | \(0.284656\pi\) | |||||||
\(878\) | −21.6607 | −0.731014 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.54345 | −0.321709 | ||||||||
\(881\) | 25.6008 | 0.862511 | 0.431256 | − | 0.902230i | \(-0.358071\pi\) | ||||
0.431256 | + | 0.902230i | \(0.358071\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.6206 | 0.492022 | 0.246011 | − | 0.969267i | \(-0.420880\pi\) | ||||
0.246011 | + | 0.969267i | \(0.420880\pi\) | |||||||
\(884\) | −0.321771 | −0.0108223 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.5924 | 0.490240 | ||||||||
\(887\) | 40.2276 | 1.35071 | 0.675356 | − | 0.737492i | \(-0.263990\pi\) | ||||
0.675356 | + | 0.737492i | \(0.263990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.1404 | −0.440714 | ||||||||
\(890\) | −12.3438 | −0.413764 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.54116 | 0.0516020 | ||||||||
\(893\) | −16.3648 | −0.547628 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.9969 | 0.434440 | ||||||||
\(896\) | −12.9450 | −0.432462 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.1398 | −0.939039 | ||||||||
\(899\) | 3.05203 | 0.101791 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.50115 | 0.0833255 | ||||||||
\(902\) | −17.7540 | −0.591145 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −47.8613 | −1.59184 | ||||||||
\(905\) | 66.1229 | 2.19800 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.0277 | −1.59474 | −0.797368 | − | 0.603494i | \(-0.793775\pi\) | ||||
−0.797368 | + | 0.603494i | \(0.793775\pi\) | |||||||
\(908\) | 3.85632 | 0.127976 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 24.8221 | 0.822844 | ||||||||
\(911\) | −33.9316 | −1.12420 | −0.562102 | − | 0.827068i | \(-0.690007\pi\) | ||||
−0.562102 | + | 0.827068i | \(0.690007\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.77955 | 0.290561 | ||||||||
\(914\) | −4.25765 | −0.140831 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.2262 | 0.437005 | ||||||||
\(917\) | −68.5306 | −2.26308 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.863726 | −0.0284917 | −0.0142458 | − | 0.999899i | \(-0.504535\pi\) | ||||
−0.0142458 | + | 0.999899i | \(0.504535\pi\) | |||||||
\(920\) | 8.78179 | 0.289527 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.37899 | 0.308881 | ||||||||
\(923\) | 25.4350 | 0.837202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.2383 | −0.599672 | ||||||||
\(926\) | 31.5704 | 1.03747 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.34294 | −0.109737 | ||||||||
\(929\) | −4.15824 | −0.136427 | −0.0682137 | − | 0.997671i | \(-0.521730\pi\) | ||||
−0.0682137 | + | 0.997671i | \(0.521730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.83810 | 0.322431 | ||||||||
\(932\) | −10.6919 | −0.350224 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.1419 | −0.462737 | ||||||||
\(935\) | 1.02479 | 0.0335143 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.0339 | 1.07917 | 0.539584 | − | 0.841931i | \(-0.318581\pi\) | ||||
0.539584 | + | 0.841931i | \(0.318581\pi\) | |||||||
\(938\) | −8.33063 | −0.272005 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0403 | −0.588410 | ||||||||
\(941\) | 40.0659 | 1.30611 | 0.653056 | − | 0.757309i | \(-0.273487\pi\) | ||||
0.653056 | + | 0.757309i | \(0.273487\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.7828 | 0.351135 | ||||||||
\(944\) | −9.57712 | −0.311709 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.8785 | −0.581282 | ||||||||
\(947\) | −5.68021 | −0.184582 | −0.0922911 | − | 0.995732i | \(-0.529419\pi\) | ||||
−0.0922911 | + | 0.995732i | \(0.529419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.5903 | −0.538545 | ||||||||
\(950\) | −5.89172 | −0.191153 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.86677 | 0.0929126 | ||||||||
\(953\) | −31.6297 | −1.02459 | −0.512293 | − | 0.858811i | \(-0.671204\pi\) | ||||
−0.512293 | + | 0.858811i | \(0.671204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.9764 | 0.387547 | ||||||||
\(956\) | −1.78333 | −0.0576771 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.4639 | 1.01655 | ||||||||
\(959\) | 10.2910 | 0.332312 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6851 | −0.699521 | ||||||||
\(962\) | 13.9087 | 0.448436 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.45320 | 0.0790122 | ||||||||
\(965\) | 5.04821 | 0.162508 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3461 | 0.589972 | 0.294986 | − | 0.955502i | \(-0.404685\pi\) | ||||
0.294986 | + | 0.955502i | \(0.404685\pi\) | |||||||
\(968\) | −27.8264 | −0.894373 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 27.2159 | 0.873851 | ||||||||
\(971\) | 16.7230 | 0.536668 | 0.268334 | − | 0.963326i | \(-0.413527\pi\) | ||||
0.268334 | + | 0.963326i | \(0.413527\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.0184 | −1.05852 | ||||||||
\(974\) | 32.2187 | 1.03235 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.0265 | −0.609024 | ||||||||
\(977\) | −23.7818 | −0.760849 | −0.380424 | − | 0.924812i | \(-0.624222\pi\) | ||||
−0.380424 | + | 0.924812i | \(0.624222\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.14467 | 0.164424 | ||||||||
\(980\) | 10.8454 | 0.346442 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.5961 | −1.13592 | ||||||||
\(983\) | −12.9711 | −0.413714 | −0.206857 | − | 0.978371i | \(-0.566324\pi\) | ||||
−0.206857 | + | 0.978371i | \(0.566324\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.9563 | −0.827035 | ||||||||
\(986\) | −0.301970 | −0.00961668 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.99773 | −0.0635562 | ||||||||
\(989\) | 10.8584 | 0.345276 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.1423 | −1.33870 | −0.669348 | − | 0.742949i | \(-0.733426\pi\) | ||||
−0.669348 | + | 0.742949i | \(0.733426\pi\) | |||||||
\(992\) | −10.2027 | −0.323937 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −53.3311 | −1.69156 | ||||||||
\(995\) | 15.1369 | 0.479873 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.5460 | −1.69582 | −0.847909 | − | 0.530142i | \(-0.822139\pi\) | ||||
−0.847909 | + | 0.530142i | \(0.822139\pi\) | |||||||
\(998\) | 9.92699 | 0.314233 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.m.1.5 | 11 | ||
3.2 | odd | 2 | 2001.2.a.l.1.7 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.l.1.7 | ✓ | 11 | 3.2 | odd | 2 | ||
6003.2.a.m.1.5 | 11 | 1.1 | even | 1 | trivial |