Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4056,2,Mod(1,4056)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4056, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4056.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4056 = 2^{3} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4056.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: | \(32.3873230598\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.27700337.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 19x^{4} + 17x^{3} + 103x^{2} - 71x - 127 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.88227\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4056.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.12925 | −1.39944 | −0.699721 | − | 0.714416i | \(-0.746692\pi\) | ||||
−0.699721 | + | 0.714416i | \(0.746692\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.48962 | −0.563024 | −0.281512 | − | 0.959558i | \(-0.590836\pi\) | ||||
−0.281512 | + | 0.959558i | \(0.590836\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.83677 | −1.45834 | −0.729171 | − | 0.684332i | \(-0.760094\pi\) | ||||
−0.729171 | + | 0.684332i | \(0.760094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.12925 | −0.807968 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.32731 | 0.806991 | 0.403496 | − | 0.914982i | \(-0.367795\pi\) | ||||
0.403496 | + | 0.914982i | \(0.367795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.82127 | −0.876659 | −0.438330 | − | 0.898814i | \(-0.644430\pi\) | ||||
−0.438330 | + | 0.898814i | \(0.644430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.48962 | −0.325062 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.77770 | −0.996220 | −0.498110 | − | 0.867114i | \(-0.665972\pi\) | ||||
−0.498110 | + | 0.867114i | \(0.665972\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.79219 | 0.958438 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.70085 | 0.687231 | 0.343615 | − | 0.939110i | \(-0.388348\pi\) | ||||
0.343615 | + | 0.939110i | \(0.388348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.48614 | −1.16495 | −0.582473 | − | 0.812850i | \(-0.697915\pi\) | ||||
−0.582473 | + | 0.812850i | \(0.697915\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.83677 | −0.841974 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.66140 | 0.787920 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.68535 | 0.770267 | 0.385133 | − | 0.922861i | \(-0.374155\pi\) | ||||
0.385133 | + | 0.922861i | \(0.374155\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.72224 | 1.51836 | 0.759179 | − | 0.650882i | \(-0.225601\pi\) | ||||
0.759179 | + | 0.650882i | \(0.225601\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.75872 | −0.878197 | −0.439098 | − | 0.898439i | \(-0.644702\pi\) | ||||
−0.439098 | + | 0.898439i | \(0.644702\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.12925 | −0.466481 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.73028 | 1.12758 | 0.563788 | − | 0.825919i | \(-0.309343\pi\) | ||||
0.563788 | + | 0.825919i | \(0.309343\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.78103 | −0.683004 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.32731 | 0.465917 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.29590 | 1.13953 | 0.569765 | − | 0.821808i | \(-0.307034\pi\) | ||||
0.569765 | + | 0.821808i | \(0.307034\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.1355 | 2.04086 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.82127 | −0.506139 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.4763 | 1.88466 | 0.942330 | − | 0.334687i | \(-0.108630\pi\) | ||||
0.942330 | + | 0.334687i | \(0.108630\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.18968 | −0.920544 | −0.460272 | − | 0.887778i | \(-0.652248\pi\) | ||||
−0.460272 | + | 0.887778i | \(0.652248\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.48962 | −0.187675 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.81807 | 0.466452 | 0.233226 | − | 0.972423i | \(-0.425072\pi\) | ||||
0.233226 | + | 0.972423i | \(0.425072\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.77770 | −0.575168 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.09590 | −0.604773 | −0.302386 | − | 0.953185i | \(-0.597783\pi\) | ||||
−0.302386 | + | 0.953185i | \(0.597783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.7451 | −1.84282 | −0.921412 | − | 0.388588i | \(-0.872963\pi\) | ||||
−0.921412 | + | 0.388588i | \(0.872963\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.79219 | 0.553355 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.20496 | 0.821082 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1000 | 1.24885 | 0.624424 | − | 0.781085i | \(-0.285334\pi\) | ||||
0.624424 | + | 0.781085i | \(0.285334\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.06158 | −0.445816 | −0.222908 | − | 0.974839i | \(-0.571555\pi\) | ||||
−0.222908 | + | 0.974839i | \(0.571555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.4120 | −1.12934 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.70085 | 0.396773 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.9172 | 1.79322 | 0.896608 | − | 0.442824i | \(-0.146023\pi\) | ||||
0.896608 | + | 0.442824i | \(0.146023\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.48614 | −0.672582 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.9577 | 1.22683 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.9132 | 1.71728 | 0.858638 | − | 0.512582i | \(-0.171311\pi\) | ||||
0.858638 | + | 0.512582i | \(0.171311\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.83677 | −0.486114 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.1598 | −1.60796 | −0.803978 | − | 0.594659i | \(-0.797287\pi\) | ||||
−0.803978 | + | 0.594659i | \(0.797287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0686 | −0.992091 | −0.496046 | − | 0.868296i | \(-0.665215\pi\) | ||||
−0.496046 | + | 0.868296i | \(0.665215\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.66140 | 0.454906 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.1710 | 1.17661 | 0.588307 | − | 0.808638i | \(-0.299795\pi\) | ||||
0.588307 | + | 0.808638i | \(0.299795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.74502 | 0.646056 | 0.323028 | − | 0.946389i | \(-0.395299\pi\) | ||||
0.323028 | + | 0.946389i | \(0.395299\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.68535 | 0.444714 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9767 | 1.03260 | 0.516300 | − | 0.856408i | \(-0.327309\pi\) | ||||
0.516300 | + | 0.856408i | \(0.327309\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.9506 | 1.39415 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.95643 | −0.454356 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.3944 | 1.12676 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.72224 | 0.876624 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.650283 | 0.0581631 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.01527 | 0.356298 | 0.178149 | − | 0.984004i | \(-0.442989\pi\) | ||||
0.178149 | + | 0.984004i | \(0.442989\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.75872 | −0.507027 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.7892 | −1.03002 | −0.515012 | − | 0.857183i | \(-0.672213\pi\) | ||||
−0.515012 | + | 0.857183i | \(0.672213\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.69225 | 0.493580 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.12925 | −0.269323 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3096 | 1.13711 | 0.568557 | − | 0.822644i | \(-0.307502\pi\) | ||||
0.568557 | + | 0.822644i | \(0.307502\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.14114 | 0.436066 | 0.218033 | − | 0.975941i | \(-0.430036\pi\) | ||||
0.218033 | + | 0.975941i | \(0.430036\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.73028 | 0.651007 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.5809 | −0.961740 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.78103 | −0.394332 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.28026 | −0.350653 | −0.175326 | − | 0.984510i | \(-0.556098\pi\) | ||||
−0.175326 | + | 0.984510i | \(0.556098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5496 | −1.34679 | −0.673393 | − | 0.739284i | \(-0.735164\pi\) | ||||
−0.673393 | + | 0.739284i | \(0.735164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.32731 | 0.268997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.2968 | 1.63027 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.5076 | −1.71650 | −0.858248 | − | 0.513236i | \(-0.828447\pi\) | ||||
−0.858248 | + | 0.513236i | \(0.828447\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.29590 | 0.657907 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.11697 | 0.560896 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.62970 | 0.519278 | 0.259639 | − | 0.965706i | \(-0.416396\pi\) | ||||
0.259639 | + | 0.965706i | \(0.416396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.1355 | 1.17829 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.06853 | 0.314832 | 0.157416 | − | 0.987532i | \(-0.449684\pi\) | ||||
0.157416 | + | 0.987532i | \(0.449684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.82127 | −0.292220 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.886940 | 0.0674328 | 0.0337164 | − | 0.999431i | \(-0.489266\pi\) | ||||
0.0337164 | + | 0.999431i | \(0.489266\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.13855 | −0.539624 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.4763 | 1.08811 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.90942 | 0.516434 | 0.258217 | − | 0.966087i | \(-0.416865\pi\) | ||||
0.258217 | + | 0.966087i | \(0.416865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.57338 | 0.339937 | 0.169968 | − | 0.985450i | \(-0.445633\pi\) | ||||
0.169968 | + | 0.985450i | \(0.445633\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.18968 | −0.531477 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.6616 | −1.07794 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.0934 | −1.17687 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.48962 | −0.108354 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.81213 | 0.709981 | 0.354991 | − | 0.934870i | \(-0.384484\pi\) | ||||
0.354991 | + | 0.934870i | \(0.384484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.3006 | 1.82118 | 0.910588 | − | 0.413315i | \(-0.135629\pi\) | ||||
0.910588 | + | 0.413315i | \(0.135629\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.5048 | −1.17592 | −0.587959 | − | 0.808891i | \(-0.700068\pi\) | ||||
−0.587959 | + | 0.808891i | \(0.700068\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0642 | 1.84764 | 0.923820 | − | 0.382826i | \(-0.125049\pi\) | ||||
0.923820 | + | 0.382826i | \(0.125049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.81807 | 0.269306 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.51287 | −0.386928 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.4233 | −2.12485 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.77770 | −0.332073 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.4826 | 1.27847 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6270 | 0.800437 | 0.400218 | − | 0.916420i | \(-0.368934\pi\) | ||||
0.400218 | + | 0.916420i | \(0.368934\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.09590 | −0.349166 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.0205 | 1.22899 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.66190 | 0.655893 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.7451 | −1.06395 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.7959 | 1.32563 | 0.662816 | − | 0.748782i | \(-0.269361\pi\) | ||||
0.662816 | + | 0.748782i | \(0.269361\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.79219 | 0.319479 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.01162 | −0.266261 | −0.133130 | − | 0.991099i | \(-0.542503\pi\) | ||||
−0.133130 | + | 0.991099i | \(0.542503\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.49817 | −0.231166 | −0.115583 | − | 0.993298i | \(-0.536874\pi\) | ||||
−0.115583 | + | 0.993298i | \(0.536874\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.20496 | 0.474052 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.79848 | 0.576408 | 0.288204 | − | 0.957569i | \(-0.406942\pi\) | ||||
0.288204 | + | 0.957569i | \(0.406942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.1900 | −1.57798 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.1000 | 0.721023 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.8723 | −1.09138 | −0.545691 | − | 0.837987i | \(-0.683733\pi\) | ||||
−0.545691 | + | 0.837987i | \(0.683733\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.22284 | 0.594095 | 0.297048 | − | 0.954863i | \(-0.403998\pi\) | ||||
0.297048 | + | 0.954863i | \(0.403998\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.9610 | 0.955824 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.06158 | −0.257392 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.02019 | −0.190633 | −0.0953164 | − | 0.995447i | \(-0.530386\pi\) | ||||
−0.0953164 | + | 0.995447i | \(0.530386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.1087 | 1.45283 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.4120 | −0.652023 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.7035 | 1.54096 | 0.770480 | − | 0.637464i | \(-0.220017\pi\) | ||||
0.770480 | + | 0.637464i | \(0.220017\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.97940 | −0.433679 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.70085 | 0.229077 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.12833 | −0.0695759 | −0.0347880 | − | 0.999395i | \(-0.511076\pi\) | ||||
−0.0347880 | + | 0.999395i | \(0.511076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.9599 | −1.59471 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9172 | 1.03531 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6337 | 0.709318 | 0.354659 | − | 0.934996i | \(-0.384597\pi\) | ||||
0.354659 | + | 0.934996i | \(0.384597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7332 | 0.834234 | 0.417117 | − | 0.908853i | \(-0.363041\pi\) | ||||
0.417117 | + | 0.908853i | \(0.363041\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.1787 | −1.39773 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.0414 | −1.74493 | −0.872463 | − | 0.488680i | \(-0.837479\pi\) | ||||
−0.872463 | + | 0.488680i | \(0.837479\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.48614 | −0.388315 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.8066 | −0.883286 | −0.441643 | − | 0.897191i | \(-0.645604\pi\) | ||||
−0.441643 | + | 0.897191i | \(0.645604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.17771 | −0.248339 | −0.124170 | − | 0.992261i | \(-0.539627\pi\) | ||||
−0.124170 | + | 0.992261i | \(0.539627\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.9577 | 0.708313 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.4825 | −0.854872 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.92901 | −0.348765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.9132 | 0.991470 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2069 | 0.654712 | 0.327356 | − | 0.944901i | \(-0.393842\pi\) | ||||
0.327356 | + | 0.944901i | \(0.393842\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −45.3001 | −2.63747 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.83677 | −0.280658 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.57832 | 0.494446 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.1598 | −0.928354 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.4983 | 1.28825 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.32884 | −0.0758408 | −0.0379204 | − | 0.999281i | \(-0.512073\pi\) | ||||
−0.0379204 | + | 0.999281i | \(0.512073\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.0686 | −0.572784 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.83416 | 0.217415 | 0.108708 | − | 0.994074i | \(-0.465329\pi\) | ||||
0.108708 | + | 0.994074i | \(0.465329\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.96014 | −0.223841 | −0.111920 | − | 0.993717i | \(-0.535700\pi\) | ||||
−0.111920 | + | 0.993717i | \(0.535700\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.66140 | 0.262640 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.0459 | 0.845063 | 0.422532 | − | 0.906348i | \(-0.361142\pi\) | ||||
0.422532 | + | 0.906348i | \(0.361142\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.9002 | −1.00222 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1710 | 0.679318 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.7145 | −0.707456 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.74502 | 0.373000 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.5152 | −0.634853 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.6635 | −0.805980 | −0.402990 | − | 0.915204i | \(-0.632029\pi\) | ||||
−0.402990 | + | 0.915204i | \(0.632029\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.68535 | 0.256756 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.9477 | −0.652773 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.1320 | 0.933238 | 0.466619 | − | 0.884458i | \(-0.345472\pi\) | ||||
0.466619 | + | 0.884458i | \(0.345472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.9767 | 0.596172 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.3720 | 1.69889 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.5493 | 0.947572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.9506 | 0.804914 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.3813 | −1.04044 | −0.520222 | − | 0.854031i | \(-0.674151\pi\) | ||||
−0.520222 | + | 0.854031i | \(0.674151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.3434 | −1.62425 | −0.812123 | − | 0.583486i | \(-0.801688\pi\) | ||||
−0.812123 | + | 0.583486i | \(0.801688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.10175 | 0.111865 | 0.0559324 | − | 0.998435i | \(-0.482187\pi\) | ||||
0.0559324 | + | 0.998435i | \(0.482187\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.9463 | 0.846344 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.95643 | −0.262322 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.0220 | −1.69005 | −0.845027 | − | 0.534723i | \(-0.820416\pi\) | ||||
−0.845027 | + | 0.534723i | \(0.820416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.39790 | −0.231468 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.3944 | 0.650535 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.2703 | 2.57892 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.3627 | 1.63712 | 0.818560 | − | 0.574421i | \(-0.194773\pi\) | ||||
0.818560 | + | 0.574421i | \(0.194773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.72224 | 0.506119 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.3577 | −0.641582 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.2351 | 0.581732 | 0.290866 | − | 0.956764i | \(-0.406057\pi\) | ||||
0.290866 | + | 0.956764i | \(0.406057\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.650283 | 0.0335805 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3499 | 0.942571 | 0.471286 | − | 0.881981i | \(-0.343790\pi\) | ||||
0.471286 | + | 0.881981i | \(0.343790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.01527 | 0.205709 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.2718 | −1.44462 | −0.722310 | − | 0.691569i | \(-0.756920\pi\) | ||||
−0.722310 | + | 0.691569i | \(0.756920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.5461 | −1.14906 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.75872 | −0.292732 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.65286 | −0.438717 | −0.219359 | − | 0.975644i | \(-0.570396\pi\) | ||||
−0.219359 | + | 0.975644i | \(0.570396\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.8969 | −0.803941 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.7892 | −0.594685 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −34.7347 | −1.74769 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.3710 | −1.17296 | −0.586478 | − | 0.809965i | \(-0.699486\pi\) | ||||
−0.586478 | + | 0.809965i | \(0.699486\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.69225 | 0.284969 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.7237 | −1.58421 | −0.792103 | − | 0.610387i | \(-0.791014\pi\) | ||||
−0.792103 | + | 0.610387i | \(0.791014\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.12925 | −0.155494 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.6620 | −1.12331 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1860 | 0.503663 | 0.251832 | − | 0.967771i | \(-0.418967\pi\) | ||||
0.251832 | + | 0.967771i | \(0.418967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.3096 | 0.656513 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −21.5643 | −1.06111 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.7097 | 0.623894 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.14114 | 0.251763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2901 | 0.746972 | 0.373486 | − | 0.927636i | \(-0.378162\pi\) | ||||
0.373486 | + | 0.927636i | \(0.378162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.07704 | −0.149966 | −0.0749828 | − | 0.997185i | \(-0.523890\pi\) | ||||
−0.0749828 | + | 0.997185i | \(0.523890\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.73028 | 0.375859 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.9451 | 0.773451 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7099 | 0.518289 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.41397 | 0.0681086 | 0.0340543 | − | 0.999420i | \(-0.489158\pi\) | ||||
0.0340543 | + | 0.999420i | \(0.489158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.8920 | 1.38846 | 0.694231 | − | 0.719752i | \(-0.255744\pi\) | ||||
0.694231 | + | 0.719752i | \(0.255744\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.5809 | −0.555261 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.2569 | 0.873346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.9827 | −1.24009 | −0.620044 | − | 0.784567i | \(-0.712885\pi\) | ||||
−0.620044 | + | 0.784567i | \(0.712885\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.78103 | −0.227668 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.1177 | −0.575728 | −0.287864 | − | 0.957671i | \(-0.592945\pi\) | ||||
−0.287864 | + | 0.957671i | \(0.592945\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −52.9380 | −2.50950 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.28026 | −0.202450 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.12274 | −0.147371 | −0.0736856 | − | 0.997282i | \(-0.523476\pi\) | ||||
−0.0736856 | + | 0.997282i | \(0.523476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −47.0242 | −2.21428 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.5496 | −0.777568 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.9608 | 1.63540 | 0.817698 | − | 0.575647i | \(-0.195250\pi\) | ||||
0.817698 | + | 0.575647i | \(0.195250\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.32731 | 0.155306 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.1820 | 1.03312 | 0.516560 | − | 0.856251i | \(-0.327212\pi\) | ||||
0.516560 | + | 0.856251i | \(0.327212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8864 | −0.505935 | −0.252968 | − | 0.967475i | \(-0.581407\pi\) | ||||
−0.252968 | + | 0.967475i | \(0.581407\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.2968 | 0.941239 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.2373 | −0.519999 | −0.259999 | − | 0.965609i | \(-0.583722\pi\) | ||||
−0.259999 | + | 0.965609i | \(0.583722\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.68749 | −0.262624 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −21.5076 | −0.991019 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 27.8536 | 1.28071 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.3123 | −0.840224 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.29590 | 0.379843 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0400 | −1.09841 | −0.549207 | − | 0.835686i | \(-0.685070\pi\) | ||||
−0.549207 | + | 0.835686i | \(0.685070\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.11697 | 0.323833 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −52.9256 | −2.40323 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.19612 | 0.280773 | 0.140387 | − | 0.990097i | \(-0.455165\pi\) | ||||
0.140387 | + | 0.990097i | \(0.455165\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.62970 | 0.299805 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.4948 | 0.699272 | 0.349636 | − | 0.936886i | \(-0.386305\pi\) | ||||
0.349636 | + | 0.936886i | \(0.386305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.3139 | 0.554589 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.1355 | 0.680288 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.59097 | 0.340502 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.6496 | −1.64066 | −0.820330 | − | 0.571890i | \(-0.806210\pi\) | ||||
−0.820330 | + | 0.571890i | \(0.806210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.06853 | 0.181768 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 36.1335 | 1.61111 | 0.805556 | − | 0.592520i | \(-0.201867\pi\) | ||||
0.805556 | + | 0.592520i | \(0.201867\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 50.5679 | 2.25024 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.8488 | 0.746809 | 0.373404 | − | 0.927669i | \(-0.378190\pi\) | ||||
0.373404 | + | 0.927669i | \(0.378190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.4542 | 1.03755 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.82127 | −0.168713 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 31.5072 | 1.38837 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.3896 | −1.64439 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.886940 | 0.0389323 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.9718 | −0.524496 | −0.262248 | − | 0.965001i | \(-0.584464\pi\) | ||||
−0.262248 | + | 0.965001i | \(0.584464\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.1292 | −1.01137 | −0.505684 | − | 0.862719i | \(-0.668760\pi\) | ||||
−0.505684 | + | 0.862719i | \(0.668760\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.13855 | −0.311552 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.5814 | −0.940101 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.173551 | −0.00754568 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.4763 | 0.628220 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −38.0860 | −1.64660 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.90942 | 0.298163 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 23.1247 | 0.996053 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.1983 | 1.16935 | 0.584673 | − | 0.811269i | \(-0.301223\pi\) | ||||
0.584673 | + | 0.811269i | \(0.301223\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.57338 | 0.196262 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.1068 | −0.904118 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0521 | 1.62699 | 0.813494 | − | 0.581573i | \(-0.197563\pi\) | ||||
0.813494 | + | 0.581573i | \(0.197563\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.18968 | −0.306848 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.1419 | −0.602467 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.5348 | −0.703132 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14.6616 | −0.622351 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.34390 | −0.141686 | −0.0708429 | − | 0.997487i | \(-0.522569\pi\) | ||||
−0.0708429 | + | 0.997487i | \(0.522569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.0934 | −0.679466 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.58489 | 0.151085 | 0.0755425 | − | 0.997143i | \(-0.475931\pi\) | ||||
0.0755425 | + | 0.997143i | \(0.475931\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.3488 | −1.44506 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.48962 | −0.0625582 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.3537 | 1.39826 | 0.699130 | − | 0.714994i | \(-0.253571\pi\) | ||||
0.699130 | + | 0.714994i | \(0.253571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.35708 | −0.140489 | −0.0702446 | − | 0.997530i | \(-0.522378\pi\) | ||||
−0.0702446 | + | 0.997530i | \(0.522378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.81213 | 0.409908 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.8957 | −0.954816 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.4308 | 0.559132 | 0.279566 | − | 0.960127i | \(-0.409809\pi\) | ||||
0.279566 | + | 0.960127i | \(0.409809\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.3006 | 1.05146 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.05022 | 0.251005 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.1254 | −1.66182 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.5648 | −1.09645 | −0.548224 | − | 0.836331i | \(-0.684696\pi\) | ||||
−0.548224 | + | 0.836331i | \(0.684696\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.7853 | 1.02126 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.5048 | −0.678916 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.4999 | 0.636504 | 0.318252 | − | 0.948006i | \(-0.396904\pi\) | ||||
0.318252 | + | 0.948006i | \(0.396904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.5099 | 0.635844 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.0642 | 1.06674 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.2092 | −1.19346 | −0.596728 | − | 0.802444i | \(-0.703533\pi\) | ||||
−0.596728 | + | 0.802444i | \(0.703533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0346 | −0.450112 | −0.225056 | − | 0.974346i | \(-0.572256\pi\) | ||||
−0.225056 | + | 0.974346i | \(0.572256\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.81807 | 0.155484 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −38.7850 | −1.57684 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.3186 | −0.946474 | −0.473237 | − | 0.880935i | \(-0.656915\pi\) | ||||
−0.473237 | + | 0.880935i | \(0.656915\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.51287 | −0.223393 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.5992 | 0.670434 | 0.335217 | − | 0.942141i | \(-0.391190\pi\) | ||||
0.335217 | + | 0.942141i | \(0.391190\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −30.4233 | −1.22679 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.8524 | 0.799226 | 0.399613 | − | 0.916684i | \(-0.369144\pi\) | ||||
0.399613 | + | 0.916684i | \(0.369144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.8532 | −0.436228 | −0.218114 | − | 0.975923i | \(-0.569990\pi\) | ||||
−0.218114 | + | 0.975923i | \(0.569990\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.77770 | −0.191723 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.2002 | −1.00962 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.9959 | −1.03983 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.4826 | 0.738124 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.5896 | 0.621598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4302 | 0.654077 | 0.327039 | − | 0.945011i | \(-0.393949\pi\) | ||||
0.327039 | + | 0.945011i | \(0.393949\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.6270 | 0.462132 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.5648 | −0.498618 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.09590 | −0.201591 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.56950 | −0.101489 | −0.0507446 | − | 0.998712i | \(-0.516159\pi\) | ||||
−0.0507446 | + | 0.998712i | \(0.516159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.4067 | −0.765324 | −0.382662 | − | 0.923888i | \(-0.624993\pi\) | ||||
−0.382662 | + | 0.923888i | \(0.624993\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.0205 | 0.709555 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.9837 | 1.61124 | 0.805618 | − | 0.592436i | \(-0.201834\pi\) | ||||
0.805618 | + | 0.592436i | \(0.201834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −70.0188 | −2.74848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.66190 | 0.378680 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.0938 | 1.21679 | 0.608397 | − | 0.793633i | \(-0.291813\pi\) | ||||
0.608397 | + | 0.793633i | \(0.291813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.8912 | 1.44146 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.7451 | −0.614274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.1087 | 0.939142 | 0.469571 | − | 0.882895i | \(-0.344409\pi\) | ||||
0.469571 | + | 0.882895i | \(0.344409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.19648 | 0.163224 | 0.0816121 | − | 0.996664i | \(-0.473993\pi\) | ||||
0.0816121 | + | 0.996664i | \(0.473993\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.8125 | −0.690737 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.6816 | −0.684633 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.7959 | 0.765354 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.7748 | 1.34247 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.36676 | −0.0912318 | −0.0456159 | − | 0.998959i | \(-0.514525\pi\) | ||||
−0.0456159 | + | 0.998959i | \(0.514525\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.79219 | 0.184452 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.03853 | −0.270513 | −0.135256 | − | 0.990811i | \(-0.543186\pi\) | ||||
−0.135256 | + | 0.990811i | \(0.543186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.1943 | −0.966868 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.01162 | −0.153726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.1863 | −1.04025 | −0.520127 | − | 0.854089i | \(-0.674115\pi\) | ||||
−0.520127 | + | 0.854089i | \(0.674115\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.6489 | −1.59132 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.49817 | −0.133464 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.5884 | 1.84839 | 0.924194 | − | 0.381923i | \(-0.124738\pi\) | ||||
0.924194 | + | 0.381923i | \(0.124738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.20496 | 0.273694 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.0879 | −0.610249 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.3489 | 1.22530 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.79848 | 0.332789 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.7456 | 0.443625 | 0.221812 | − | 0.975089i | \(-0.428803\pi\) | ||||
0.221812 | + | 0.975089i | \(0.428803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.9040 | −0.675261 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.1900 | −0.911046 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.0719 | 0.905318 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.9538 | −1.57561 | −0.787804 | − | 0.615926i | \(-0.788782\pi\) | ||||
−0.787804 | + | 0.615926i | \(0.788782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.1000 | 0.416283 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.9889 | 1.16054 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.8723 | −0.630109 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.9578 | 1.67664 | 0.838322 | − | 0.545176i | \(-0.183537\pi\) | ||||
0.838322 | + | 0.545176i | \(0.183537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9985 | 0.558571 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.22284 | 0.343001 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.7352 | 0.658668 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.84927 | −0.0685857 | −0.0342928 | − | 0.999412i | \(-0.510918\pi\) | ||||
−0.0342928 | + | 0.999412i | \(0.510918\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.1610 | −0.708697 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0976 | 0.409898 | 0.204949 | − | 0.978773i | \(-0.434297\pi\) | ||||
0.204949 | + | 0.978773i | \(0.434297\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.9610 | 0.551845 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.4672 | −0.680246 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.2648 | 1.59152 | 0.795761 | − | 0.605611i | \(-0.207071\pi\) | ||||
0.795761 | + | 0.605611i | \(0.207071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.92296 | 0.0705467 | 0.0352734 | − | 0.999378i | \(-0.488770\pi\) | ||||
0.0352734 | + | 0.999378i | \(0.488770\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3940 | 0.490718 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.06158 | −0.148605 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.1302 | −0.662462 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.2821 | 0.922557 | 0.461279 | − | 0.887255i | \(-0.347391\pi\) | ||||
0.461279 | + | 0.887255i | \(0.347391\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.02019 | −0.110062 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.7878 | 1.88475 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.72509 | −0.0626993 | −0.0313497 | − | 0.999508i | \(-0.509981\pi\) | ||||
−0.0313497 | + | 0.999508i | \(0.509981\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.1087 | 0.838791 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.6005 | 1.07302 | 0.536509 | − | 0.843895i | \(-0.319743\pi\) | ||||
0.536509 | + | 0.843895i | \(0.319743\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0475 | −0.363745 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.4120 | −0.376446 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.321666 | −0.0115996 | −0.00579978 | − | 0.999983i | \(-0.501846\pi\) | ||||
−0.00579978 | + | 0.999983i | \(0.501846\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.7035 | 0.889674 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.2148 | −1.12272 | −0.561359 | − | 0.827572i | \(-0.689721\pi\) | ||||
−0.561359 | + | 0.827572i | \(0.689721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31.0828 | −1.11653 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.97940 | −0.250384 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −37.1513 | −1.33108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.6477 | 0.881965 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.70085 | 0.132258 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 67.3027 | 2.40214 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.9712 | 0.854480 | 0.427240 | − | 0.904138i | \(-0.359486\pi\) | ||||
0.427240 | + | 0.904138i | \(0.359486\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.12833 | −0.0401697 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.3511 | −0.581378 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.9599 | −0.920703 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.0863 | −0.676070 | −0.338035 | − | 0.941133i | \(-0.609762\pi\) | ||||
−0.338035 | + | 0.941133i | \(0.609762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.7210 | 0.909945 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.9172 | 0.597739 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 76.1554 | 2.68747 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.2708 | −0.784941 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.6337 | 0.409525 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.329314 | 0.0115781 | 0.00578904 | − | 0.999983i | \(-0.498157\pi\) | ||||
0.00578904 | + | 0.999983i | \(0.498157\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.2741 | 1.55467 | 0.777337 | − | 0.629085i | \(-0.216570\pi\) | ||||
0.777337 | + | 0.629085i | \(0.216570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.7332 | 0.481645 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.7460 | −0.726700 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0056 | 0.769879 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.0495 | 1.60714 | 0.803568 | − | 0.595212i | \(-0.202932\pi\) | ||||
0.803568 | + | 0.595212i | \(0.202932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.7087 | −0.373281 | −0.186641 | − | 0.982428i | \(-0.559760\pi\) | ||||
−0.186641 | + | 0.982428i | \(0.559760\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −23.1787 | −0.806980 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.6297 | 0.647820 | 0.323910 | − | 0.946088i | \(-0.395003\pi\) | ||||
0.323910 | + | 0.946088i | \(0.395003\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.8185 | 1.00091 | 0.500454 | − | 0.865763i | \(-0.333166\pi\) | ||||
0.500454 | + | 0.865763i | \(0.333166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.0414 | −1.00743 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.9080 | −0.551178 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.7314 | −0.440589 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.48614 | −0.224194 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.0413 | 1.65857 | 0.829284 | − | 0.558827i | \(-0.188748\pi\) | ||||
0.829284 | + | 0.558827i | \(0.188748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3037 | −0.527714 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.8066 | −0.509965 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.4629 | −0.634393 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.17771 | −0.143379 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.3852 | −0.767355 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.2568 | −0.453906 | −0.226953 | − | 0.973906i | \(-0.572876\pi\) | ||||
−0.226953 | + | 0.973906i | \(0.572876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.9577 | 0.408945 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.5164 | −1.34986 | −0.674928 | − | 0.737884i | \(-0.735825\pi\) | ||||
−0.674928 | + | 0.737884i | \(0.735825\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.3382 | −1.17161 | −0.585803 | − | 0.810454i | \(-0.699221\pi\) | ||||
−0.585803 | + | 0.810454i | \(0.699221\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.4825 | −0.493561 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.7547 | −1.28518 | −0.642592 | − | 0.766209i | \(-0.722141\pi\) | ||||
−0.642592 | + | 0.766209i | \(0.722141\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.77545 | −0.0943683 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.92901 | −0.201360 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −53.6882 | −1.82125 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.9132 | 0.572426 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.968676 | −0.0327472 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.14218 | −0.106104 | −0.0530519 | − | 0.998592i | \(-0.516895\pi\) | ||||
−0.0530519 | + | 0.998592i | \(0.516895\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.2069 | 0.377998 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.8867 | −1.20905 | −0.604527 | − | 0.796585i | \(-0.706638\pi\) | ||||
−0.604527 | + | 0.796585i | \(0.706638\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.2723 | −1.32162 | −0.660810 | − | 0.750554i | \(-0.729787\pi\) | ||||
−0.660810 | + | 0.750554i | \(0.729787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.3001 | −1.52274 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −49.5023 | −1.66212 | −0.831062 | − | 0.556179i | \(-0.812267\pi\) | ||||
−0.831062 | + | 0.556179i | \(0.812267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.98124 | −0.200604 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.83677 | −0.162038 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.5395 | −0.988501 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.6213 | −0.722719 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0043 | −0.800587 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.6030 | 0.919590 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.57832 | 0.285468 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.3112 | −0.475722 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.2459 | −1.13712 | −0.568558 | − | 0.822643i | \(-0.692498\pi\) | ||||
−0.568558 | + | 0.822643i | \(0.692498\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.1598 | −0.535985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.6128 | 0.981117 | 0.490558 | − | 0.871408i | \(-0.336793\pi\) | ||||
0.490558 | + | 0.871408i | \(0.336793\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.6449 | 0.650152 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.4983 | 0.743771 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5614 | 0.579928 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.6710 | −0.582913 | −0.291457 | − | 0.956584i | \(-0.594140\pi\) | ||||
−0.291457 | + | 0.956584i | \(0.594140\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.32884 | −0.0437867 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.4531 | 0.738253 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.0686 | −0.330697 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.3131 | 0.535216 | 0.267608 | − | 0.963528i | \(-0.413767\pi\) | ||||
0.267608 | + | 0.963528i | \(0.413767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.2696 | 0.598762 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.83416 | 0.125525 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 50.3604 | 1.64696 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.3202 | −1.31720 | −0.658602 | − | 0.752492i | \(-0.728852\pi\) | ||||
−0.658602 | + | 0.752492i | \(0.728852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.96014 | −0.129234 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.8965 | −0.355216 | −0.177608 | − | 0.984101i | \(-0.556836\pi\) | ||||
−0.177608 | + | 0.984101i | \(0.556836\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −46.4500 | −1.51262 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.66140 | 0.151635 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.64336 | −0.248376 | −0.124188 | − | 0.992259i | \(-0.539633\pi\) | ||||
−0.124188 | + | 0.992259i | \(0.539633\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.0459 | 0.487897 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.61098 | 0.278937 | 0.139468 | − | 0.990227i | \(-0.455461\pi\) | ||||
0.139468 | + | 0.990227i | \(0.455461\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.7046 | −0.993578 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.9002 | −0.578630 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.8262 | −0.640222 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0701 | 0.357099 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.1710 | 0.392205 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −79.1718 | −2.54863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.5227 | 1.11017 | 0.555087 | − | 0.831792i | \(-0.312685\pi\) | ||||
0.555087 | + | 0.831792i | \(0.312685\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.7145 | −0.408450 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.5678 | 1.14142 | 0.570712 | − | 0.821150i | \(-0.306667\pi\) | ||||
0.570712 | + | 0.821150i | \(0.306667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.65836 | −0.245516 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.2619 | −1.35208 | −0.676039 | − | 0.736866i | \(-0.736305\pi\) | ||||
−0.676039 | + | 0.736866i | \(0.736305\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −81.8245 | −2.61512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.74502 | 0.215352 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.7605 | 1.45953 | 0.729766 | − | 0.683697i | \(-0.239629\pi\) | ||||
0.729766 | + | 0.683697i | \(0.239629\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 51.6476 | 1.64563 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −11.5152 | −0.366533 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.5135 | 0.874877 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.73491 | 0.182175 | 0.0910877 | − | 0.995843i | \(-0.470966\pi\) | ||||
0.0910877 | + | 0.995843i | \(0.470966\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.6635 | −0.465333 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −81.5613 | −2.58567 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.5872 | −1.69712 | −0.848561 | − | 0.529097i | \(-0.822531\pi\) | ||||
−0.848561 | + | 0.529097i | \(0.822531\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.68535 | 0.148238 |
(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 | 4056.2.a.bi.1.1 | yes | 6 | |
4.3 | odd | 2 | 8112.2.a.cu.1.1 | 6 | |||
13.5 | odd | 4 | 4056.2.c.r.337.11 | 12 | |||
13.8 | odd | 4 | 4056.2.c.r.337.2 | 12 | |||
13.12 | even | 2 | 4056.2.a.bh.1.6 | ✓ | 6 | ||
52.51 | odd | 2 | 8112.2.a.ct.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4056.2.a.bh.1.6 | ✓ | 6 | 13.12 | even | 2 | ||
4056.2.a.bi.1.1 | yes | 6 | 1.1 | even | 1 | trivial | |
4056.2.c.r.337.2 | 12 | 13.8 | odd | 4 | |||
4056.2.c.r.337.11 | 12 | 13.5 | odd | 4 | |||
8112.2.a.ct.1.6 | 6 | 52.51 | odd | 2 | |||
8112.2.a.cu.1.1 | 6 | 4.3 | odd | 2 |