Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.6152203125.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 20x^{5} + 26x^{4} - 35x^{3} - 27x^{2} + 16x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 625) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.47435\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47435 | 1.74963 | 0.874816 | − | 0.484455i | \(-0.160982\pi\) | ||||
0.874816 | + | 0.484455i | \(0.160982\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.12242 | 2.06121 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.973070 | 0.367786 | 0.183893 | − | 0.982946i | \(-0.441130\pi\) | ||||
0.183893 | + | 0.982946i | \(0.441130\pi\) | |||||||
\(8\) | 5.25163 | 1.85673 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.38225 | 1.62281 | 0.811405 | − | 0.584484i | \(-0.198703\pi\) | ||||
0.811405 | + | 0.584484i | \(0.198703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.99670 | 0.553785 | 0.276892 | − | 0.960901i | \(-0.410695\pi\) | ||||
0.276892 | + | 0.960901i | \(0.410695\pi\) | |||||||
\(14\) | 2.40772 | 0.643490 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.74954 | 1.18738 | ||||||||
\(17\) | −2.04301 | −0.495502 | −0.247751 | − | 0.968824i | \(-0.579692\pi\) | ||||
−0.247751 | + | 0.968824i | \(0.579692\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.20428 | 1.42336 | 0.711680 | − | 0.702504i | \(-0.247935\pi\) | ||||
0.711680 | + | 0.702504i | \(0.247935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 13.3176 | 2.83932 | ||||||||
\(23\) | 1.93813 | 0.404128 | 0.202064 | − | 0.979372i | \(-0.435235\pi\) | ||||
0.202064 | + | 0.979372i | \(0.435235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.94054 | 0.968920 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.01141 | 0.758085 | ||||||||
\(29\) | −4.81812 | −0.894702 | −0.447351 | − | 0.894359i | \(-0.647632\pi\) | ||||
−0.447351 | + | 0.894359i | \(0.647632\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.64014 | −1.19260 | −0.596302 | − | 0.802760i | \(-0.703364\pi\) | ||||
−0.596302 | + | 0.802760i | \(0.703364\pi\) | |||||||
\(32\) | 1.24877 | 0.220754 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.05512 | −0.866947 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.978913 | 0.160932 | 0.0804662 | − | 0.996757i | \(-0.474359\pi\) | ||||
0.0804662 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(38\) | 15.3516 | 2.49035 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.73319 | −0.426853 | −0.213427 | − | 0.976959i | \(-0.568462\pi\) | ||||
−0.213427 | + | 0.976959i | \(0.568462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.99413 | −0.609100 | −0.304550 | − | 0.952496i | \(-0.598506\pi\) | ||||
−0.304550 | + | 0.952496i | \(0.598506\pi\) | |||||||
\(44\) | 22.1879 | 3.34496 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.79562 | 0.707076 | ||||||||
\(47\) | 7.21339 | 1.05218 | 0.526091 | − | 0.850428i | \(-0.323657\pi\) | ||||
0.526091 | + | 0.850428i | \(0.323657\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05313 | −0.864734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.23125 | 1.14147 | ||||||||
\(53\) | 13.2746 | 1.82340 | 0.911700 | − | 0.410857i | \(-0.134770\pi\) | ||||
0.911700 | + | 0.410857i | \(0.134770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.11020 | 0.682880 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.9217 | −1.56540 | ||||||||
\(59\) | −6.54024 | −0.851467 | −0.425733 | − | 0.904849i | \(-0.639984\pi\) | ||||
−0.425733 | + | 0.904849i | \(0.639984\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.72672 | 0.349121 | 0.174560 | − | 0.984646i | \(-0.444150\pi\) | ||||
0.174560 | + | 0.984646i | \(0.444150\pi\) | |||||||
\(62\) | −16.4301 | −2.08662 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.40916 | −0.801146 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.56957 | −1.16911 | −0.584555 | − | 0.811354i | \(-0.698731\pi\) | ||||
−0.584555 | + | 0.811354i | \(0.698731\pi\) | |||||||
\(68\) | −8.42215 | −1.02134 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.68520 | 0.674710 | 0.337355 | − | 0.941378i | \(-0.390468\pi\) | ||||
0.337355 | + | 0.941378i | \(0.390468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.35281 | 1.09466 | 0.547332 | − | 0.836916i | \(-0.315644\pi\) | ||||
0.547332 | + | 0.836916i | \(0.315644\pi\) | |||||||
\(74\) | 2.42218 | 0.281572 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 25.5767 | 2.93385 | ||||||||
\(77\) | 5.23731 | 0.596847 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.18171 | −0.357970 | −0.178985 | − | 0.983852i | \(-0.557281\pi\) | ||||
−0.178985 | + | 0.983852i | \(0.557281\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.76289 | −0.746836 | ||||||||
\(83\) | 6.11387 | 0.671085 | 0.335542 | − | 0.942025i | \(-0.391080\pi\) | ||||
0.335542 | + | 0.942025i | \(0.391080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.88290 | −1.06570 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 28.2656 | 3.01312 | ||||||||
\(89\) | 3.00743 | 0.318787 | 0.159393 | − | 0.987215i | \(-0.449046\pi\) | ||||
0.159393 | + | 0.987215i | \(0.449046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.94293 | 0.203674 | ||||||||
\(92\) | 7.98980 | 0.832994 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 17.8485 | 1.84093 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.95526 | −0.604666 | −0.302333 | − | 0.953202i | \(-0.597765\pi\) | ||||
−0.302333 | + | 0.953202i | \(0.597765\pi\) | |||||||
\(98\) | −14.9776 | −1.51297 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.77373 | 0.773515 | 0.386758 | − | 0.922181i | \(-0.373595\pi\) | ||||
0.386758 | + | 0.922181i | \(0.373595\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.95056 | −0.487793 | −0.243897 | − | 0.969801i | \(-0.578426\pi\) | ||||
−0.243897 | + | 0.969801i | \(0.578426\pi\) | |||||||
\(104\) | 10.4859 | 1.02823 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 32.8459 | 3.19028 | ||||||||
\(107\) | 1.16798 | 0.112913 | 0.0564567 | − | 0.998405i | \(-0.482020\pi\) | ||||
0.0564567 | + | 0.998405i | \(0.482020\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.6879 | −1.69420 | −0.847099 | − | 0.531435i | \(-0.821653\pi\) | ||||
−0.847099 | + | 0.531435i | \(0.821653\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.62163 | 0.436703 | ||||||||
\(113\) | 5.03643 | 0.473787 | 0.236894 | − | 0.971536i | \(-0.423871\pi\) | ||||
0.236894 | + | 0.971536i | \(0.423871\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −19.8623 | −1.84417 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.1829 | −1.48975 | ||||||||
\(119\) | −1.98799 | −0.182239 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.9687 | 1.63351 | ||||||||
\(122\) | 6.74687 | 0.610833 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −27.3735 | −2.45821 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.79457 | −0.691656 | −0.345828 | − | 0.938298i | \(-0.612402\pi\) | ||||
−0.345828 | + | 0.938298i | \(0.612402\pi\) | |||||||
\(128\) | −18.3561 | −1.62246 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.79015 | 0.855369 | 0.427685 | − | 0.903928i | \(-0.359329\pi\) | ||||
0.427685 | + | 0.903928i | \(0.359329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.03720 | 0.523491 | ||||||||
\(134\) | −23.6785 | −2.04551 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.7291 | −0.920015 | ||||||||
\(137\) | −3.63326 | −0.310411 | −0.155205 | − | 0.987882i | \(-0.549604\pi\) | ||||
−0.155205 | + | 0.987882i | \(0.549604\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.86079 | −0.157830 | −0.0789149 | − | 0.996881i | \(-0.525146\pi\) | ||||
−0.0789149 | + | 0.996881i | \(0.525146\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.0672 | 1.18049 | ||||||||
\(143\) | 10.7467 | 0.898688 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 23.1421 | 1.91526 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.03550 | 0.331716 | ||||||||
\(149\) | −16.8530 | −1.38066 | −0.690328 | − | 0.723497i | \(-0.742534\pi\) | ||||
−0.690328 | + | 0.723497i | \(0.742534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.3201 | −1.16536 | −0.582678 | − | 0.812703i | \(-0.697995\pi\) | ||||
−0.582678 | + | 0.812703i | \(0.697995\pi\) | |||||||
\(152\) | 32.5826 | 2.64280 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.9590 | 1.04426 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6869 | 1.73080 | 0.865400 | − | 0.501081i | \(-0.167064\pi\) | ||||
0.865400 | + | 0.501081i | \(0.167064\pi\) | |||||||
\(158\) | −7.87266 | −0.626315 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.88594 | 0.148633 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.7210 | 1.54467 | 0.772334 | − | 0.635217i | \(-0.219089\pi\) | ||||
0.772334 | + | 0.635217i | \(0.219089\pi\) | |||||||
\(164\) | −11.2674 | −0.879835 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.1279 | 1.17415 | ||||||||
\(167\) | 6.07947 | 0.470444 | 0.235222 | − | 0.971942i | \(-0.424418\pi\) | ||||
0.235222 | + | 0.971942i | \(0.424418\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.01319 | −0.693322 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.4655 | −1.25548 | ||||||||
\(173\) | 15.0309 | 1.14278 | 0.571388 | − | 0.820680i | \(-0.306405\pi\) | ||||
0.571388 | + | 0.820680i | \(0.306405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.5632 | 1.92690 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.44144 | 0.557759 | ||||||||
\(179\) | 20.0167 | 1.49612 | 0.748060 | − | 0.663631i | \(-0.230986\pi\) | ||||
0.748060 | + | 0.663631i | \(0.230986\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2993 | 1.50883 | 0.754417 | − | 0.656395i | \(-0.227920\pi\) | ||||
0.754417 | + | 0.656395i | \(0.227920\pi\) | |||||||
\(182\) | 4.80749 | 0.356355 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.1783 | 0.750357 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.9960 | −0.804106 | ||||||||
\(188\) | 29.7367 | 2.16877 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.47681 | 0.685718 | 0.342859 | − | 0.939387i | \(-0.388605\pi\) | ||||
0.342859 | + | 0.939387i | \(0.388605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.72478 | −0.196134 | −0.0980671 | − | 0.995180i | \(-0.531266\pi\) | ||||
−0.0980671 | + | 0.995180i | \(0.531266\pi\) | |||||||
\(194\) | −14.7354 | −1.05794 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.9536 | −1.78240 | ||||||||
\(197\) | 0.780036 | 0.0555753 | 0.0277876 | − | 0.999614i | \(-0.491154\pi\) | ||||
0.0277876 | + | 0.999614i | \(0.491154\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.42526 | −0.526363 | −0.263181 | − | 0.964746i | \(-0.584772\pi\) | ||||
−0.263181 | + | 0.964746i | \(0.584772\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 19.2350 | 1.35337 | ||||||||
\(203\) | −4.68836 | −0.329059 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.2494 | −0.853459 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.48340 | 0.657555 | ||||||||
\(209\) | 33.3930 | 2.30984 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.98128 | −0.205240 | −0.102620 | − | 0.994721i | \(-0.532723\pi\) | ||||
−0.102620 | + | 0.994721i | \(0.532723\pi\) | |||||||
\(212\) | 54.7233 | 3.75841 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.89001 | 0.197557 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.46132 | −0.438623 | ||||||||
\(218\) | −43.7662 | −2.96422 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.07927 | −0.274402 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.8720 | −1.66556 | −0.832778 | − | 0.553607i | \(-0.813251\pi\) | ||||
−0.832778 | + | 0.553607i | \(0.813251\pi\) | |||||||
\(224\) | 1.21514 | 0.0811903 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.4619 | 0.828953 | ||||||||
\(227\) | −17.5594 | −1.16546 | −0.582729 | − | 0.812667i | \(-0.698015\pi\) | ||||
−0.582729 | + | 0.812667i | \(0.698015\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.01849 | 0.463795 | 0.231897 | − | 0.972740i | \(-0.425507\pi\) | ||||
0.231897 | + | 0.972740i | \(0.425507\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25.3030 | −1.66122 | ||||||||
\(233\) | −8.69126 | −0.569383 | −0.284692 | − | 0.958619i | \(-0.591891\pi\) | ||||
−0.284692 | + | 0.958619i | \(0.591891\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −26.9617 | −1.75505 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.91899 | −0.318851 | ||||||||
\(239\) | −21.3430 | −1.38057 | −0.690283 | − | 0.723540i | \(-0.742514\pi\) | ||||
−0.690283 | + | 0.723540i | \(0.742514\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.3897 | −1.37783 | −0.688916 | − | 0.724841i | \(-0.741913\pi\) | ||||
−0.688916 | + | 0.724841i | \(0.741913\pi\) | |||||||
\(242\) | 44.4608 | 2.85805 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.2407 | 0.719612 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.3881 | 0.788235 | ||||||||
\(248\) | −34.8716 | −2.21435 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9016 | −0.940580 | −0.470290 | − | 0.882512i | \(-0.655851\pi\) | ||||
−0.470290 | + | 0.882512i | \(0.655851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.4315 | 0.655823 | ||||||||
\(254\) | −19.2865 | −1.21014 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.6011 | −2.03757 | ||||||||
\(257\) | 19.0689 | 1.18948 | 0.594741 | − | 0.803917i | \(-0.297254\pi\) | ||||
0.594741 | + | 0.803917i | \(0.297254\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.952551 | 0.0591887 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 24.2243 | 1.49658 | ||||||||
\(263\) | −6.78341 | −0.418283 | −0.209142 | − | 0.977885i | \(-0.567067\pi\) | ||||
−0.209142 | + | 0.977885i | \(0.567067\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.9382 | 0.915917 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −39.4498 | −2.40978 | ||||||||
\(269\) | −0.494663 | −0.0301601 | −0.0150801 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150801 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.82610 | 0.596893 | 0.298446 | − | 0.954426i | \(-0.403532\pi\) | ||||
0.298446 | + | 0.954426i | \(0.403532\pi\) | |||||||
\(272\) | −9.70334 | −0.588352 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.98998 | −0.543104 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.1399 | −1.51051 | −0.755255 | − | 0.655431i | \(-0.772487\pi\) | ||||
−0.755255 | + | 0.655431i | \(0.772487\pi\) | |||||||
\(278\) | −4.60424 | −0.276144 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.77050 | 0.463549 | 0.231775 | − | 0.972770i | \(-0.425547\pi\) | ||||
0.231775 | + | 0.972770i | \(0.425547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.9617 | −1.72160 | −0.860798 | − | 0.508946i | \(-0.830035\pi\) | ||||
−0.860798 | + | 0.508946i | \(0.830035\pi\) | |||||||
\(284\) | 23.4368 | 1.39072 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.5912 | 1.57237 | ||||||||
\(287\) | −2.65959 | −0.156991 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8261 | −0.754477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 38.5562 | 2.25633 | ||||||||
\(293\) | −0.154329 | −0.00901602 | −0.00450801 | − | 0.999990i | \(-0.501435\pi\) | ||||
−0.00450801 | + | 0.999990i | \(0.501435\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.14089 | 0.298808 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −41.7004 | −2.41564 | ||||||||
\(299\) | 3.86987 | 0.223800 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.88657 | −0.224018 | ||||||||
\(302\) | −35.4330 | −2.03894 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 29.4675 | 1.69007 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.4875 | 0.826845 | 0.413423 | − | 0.910539i | \(-0.364333\pi\) | ||||
0.413423 | + | 0.910539i | \(0.364333\pi\) | |||||||
\(308\) | 21.5904 | 1.23023 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.5385 | −1.05122 | −0.525610 | − | 0.850726i | \(-0.676163\pi\) | ||||
−0.525610 | + | 0.850726i | \(0.676163\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.85703 | −0.387582 | −0.193791 | − | 0.981043i | \(-0.562078\pi\) | ||||
−0.193791 | + | 0.981043i | \(0.562078\pi\) | |||||||
\(314\) | 53.6610 | 3.02826 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.1163 | −0.737852 | ||||||||
\(317\) | −27.2810 | −1.53225 | −0.766127 | − | 0.642689i | \(-0.777819\pi\) | ||||
−0.766127 | + | 0.642689i | \(0.777819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.9323 | −1.45193 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.66647 | 0.260052 | ||||||||
\(323\) | −12.6754 | −0.705278 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 48.7967 | 2.70260 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −14.3537 | −0.792551 | ||||||||
\(329\) | 7.01914 | 0.386978 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0429 | −0.716901 | −0.358450 | − | 0.933549i | \(-0.616695\pi\) | ||||
−0.358450 | + | 0.933549i | \(0.616695\pi\) | |||||||
\(332\) | 25.2040 | 1.38325 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.0428 | 0.823103 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.6507 | 1.07044 | 0.535222 | − | 0.844712i | \(-0.320228\pi\) | ||||
0.535222 | + | 0.844712i | \(0.320228\pi\) | |||||||
\(338\) | −22.3018 | −1.21306 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.7389 | −1.93537 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.7016 | −0.685823 | ||||||||
\(344\) | −20.9757 | −1.13093 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 37.1917 | 1.99944 | ||||||||
\(347\) | 4.38943 | 0.235637 | 0.117818 | − | 0.993035i | \(-0.462410\pi\) | ||||
0.117818 | + | 0.993035i | \(0.462410\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.1955 | 1.45574 | 0.727872 | − | 0.685713i | \(-0.240510\pi\) | ||||
0.727872 | + | 0.685713i | \(0.240510\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.72122 | 0.358242 | ||||||||
\(353\) | −15.9317 | −0.847960 | −0.423980 | − | 0.905672i | \(-0.639367\pi\) | ||||
−0.423980 | + | 0.905672i | \(0.639367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.3979 | 0.657087 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 49.5284 | 2.61766 | ||||||||
\(359\) | 5.01508 | 0.264686 | 0.132343 | − | 0.991204i | \(-0.457750\pi\) | ||||
0.132343 | + | 0.991204i | \(0.457750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.4931 | 1.02595 | ||||||||
\(362\) | 50.2276 | 2.63991 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00958 | 0.419816 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.3669 | −1.48074 | −0.740370 | − | 0.672200i | \(-0.765349\pi\) | ||||
−0.740370 | + | 0.672200i | \(0.765349\pi\) | |||||||
\(368\) | 9.20522 | 0.479855 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.9171 | 0.670621 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 32.7218 | 1.69427 | 0.847135 | − | 0.531377i | \(-0.178325\pi\) | ||||
0.847135 | + | 0.531377i | \(0.178325\pi\) | |||||||
\(374\) | −27.2080 | −1.40689 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 37.8821 | 1.95362 | ||||||||
\(377\) | −9.62033 | −0.495472 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.48483 | 0.230370 | 0.115185 | − | 0.993344i | \(-0.463254\pi\) | ||||
0.115185 | + | 0.993344i | \(0.463254\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 23.4490 | 1.19975 | ||||||||
\(383\) | 16.2839 | 0.832069 | 0.416034 | − | 0.909349i | \(-0.363420\pi\) | ||||
0.416034 | + | 0.909349i | \(0.363420\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.74208 | −0.343163 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −24.5501 | −1.24634 | ||||||||
\(389\) | −21.4899 | −1.08958 | −0.544791 | − | 0.838572i | \(-0.683391\pi\) | ||||
−0.544791 | + | 0.838572i | \(0.683391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.95962 | −0.200246 | ||||||||
\(392\) | −31.7888 | −1.60558 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.93008 | 0.0972363 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8870 | 1.04829 | 0.524145 | − | 0.851629i | \(-0.324385\pi\) | ||||
0.524145 | + | 0.851629i | \(0.324385\pi\) | |||||||
\(398\) | −18.3727 | −0.920941 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.633423 | 0.0316316 | 0.0158158 | − | 0.999875i | \(-0.494965\pi\) | ||||
0.0158158 | + | 0.999875i | \(0.494965\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.2584 | −0.660447 | ||||||||
\(404\) | 32.0466 | 1.59438 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.6007 | −0.575732 | ||||||||
\(407\) | 5.26876 | 0.261163 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.29822 | −0.212534 | −0.106267 | − | 0.994338i | \(-0.533890\pi\) | ||||
−0.106267 | + | 0.994338i | \(0.533890\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.4083 | −1.00545 | ||||||||
\(413\) | −6.36411 | −0.313158 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.49343 | 0.122250 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 82.6261 | 4.04137 | ||||||||
\(419\) | −33.6215 | −1.64252 | −0.821258 | − | 0.570556i | \(-0.806728\pi\) | ||||
−0.821258 | + | 0.570556i | \(0.806728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.3768 | −1.04184 | −0.520920 | − | 0.853605i | \(-0.674411\pi\) | ||||
−0.520920 | + | 0.853605i | \(0.674411\pi\) | |||||||
\(422\) | −7.37674 | −0.359094 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 69.7130 | 3.38556 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.65329 | 0.128402 | ||||||||
\(428\) | 4.81493 | 0.232738 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.0905 | −1.25673 | −0.628367 | − | 0.777917i | \(-0.716277\pi\) | ||||
−0.628367 | + | 0.777917i | \(0.716277\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7676 | −0.565513 | −0.282757 | − | 0.959192i | \(-0.591249\pi\) | ||||
−0.282757 | + | 0.959192i | \(0.591249\pi\) | |||||||
\(434\) | −15.9876 | −0.767429 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −72.9172 | −3.49210 | ||||||||
\(437\) | 12.0247 | 0.575220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.92572 | 0.235092 | 0.117546 | − | 0.993067i | \(-0.462497\pi\) | ||||
0.117546 | + | 0.993067i | \(0.462497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.0936 | −0.480102 | ||||||||
\(443\) | 9.35961 | 0.444689 | 0.222344 | − | 0.974968i | \(-0.428629\pi\) | ||||
0.222344 | + | 0.974968i | \(0.428629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −61.5422 | −2.91411 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.23657 | −0.294650 | ||||||||
\(449\) | −7.41602 | −0.349983 | −0.174992 | − | 0.984570i | \(-0.555990\pi\) | ||||
−0.174992 | + | 0.984570i | \(0.555990\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.7107 | −0.692702 | ||||||||
\(452\) | 20.7623 | 0.976576 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −43.4481 | −2.03912 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.79714 | −0.411513 | −0.205756 | − | 0.978603i | \(-0.565965\pi\) | ||||
−0.205756 | + | 0.978603i | \(0.565965\pi\) | |||||||
\(458\) | 17.3662 | 0.811471 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.1526 | 1.96324 | 0.981621 | − | 0.190838i | \(-0.0611207\pi\) | ||||
0.981621 | + | 0.190838i | \(0.0611207\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.0565 | −1.07153 | −0.535763 | − | 0.844368i | \(-0.679976\pi\) | ||||
−0.535763 | + | 0.844368i | \(0.679976\pi\) | |||||||
\(464\) | −22.8838 | −1.06235 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −21.5053 | −0.996212 | ||||||||
\(467\) | 4.37964 | 0.202666 | 0.101333 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101333 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.31186 | −0.429982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −34.3469 | −1.58095 | ||||||||
\(473\) | −21.4974 | −0.988453 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.19534 | −0.375633 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −52.8102 | −2.41548 | ||||||||
\(479\) | −14.1913 | −0.648417 | −0.324209 | − | 0.945986i | \(-0.605098\pi\) | ||||
−0.324209 | + | 0.945986i | \(0.605098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.95460 | 0.0891219 | ||||||||
\(482\) | −52.9257 | −2.41070 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 74.0744 | 3.36702 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.0694 | −1.00006 | −0.500029 | − | 0.866009i | \(-0.666677\pi\) | ||||
−0.500029 | + | 0.866009i | \(0.666677\pi\) | |||||||
\(488\) | 14.3197 | 0.648223 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.95704 | 0.359096 | 0.179548 | − | 0.983749i | \(-0.442536\pi\) | ||||
0.179548 | + | 0.983749i | \(0.442536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.84345 | 0.443327 | ||||||||
\(494\) | 30.6525 | 1.37912 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −31.5376 | −1.41608 | ||||||||
\(497\) | 5.53210 | 0.248149 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.09384 | −0.183266 | −0.0916328 | − | 0.995793i | \(-0.529209\pi\) | ||||
−0.0916328 | + | 0.995793i | \(0.529209\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −36.8718 | −1.64567 | ||||||||
\(503\) | 26.9554 | 1.20188 | 0.600941 | − | 0.799293i | \(-0.294792\pi\) | ||||
0.600941 | + | 0.799293i | \(0.294792\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 25.8112 | 1.14745 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.1325 | −1.42565 | ||||||||
\(509\) | −33.8837 | −1.50187 | −0.750935 | − | 0.660376i | \(-0.770397\pi\) | ||||
−0.750935 | + | 0.660376i | \(0.770397\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.10093 | 0.402602 | ||||||||
\(512\) | −43.9545 | −1.94253 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 47.1831 | 2.08116 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 38.8243 | 1.70749 | ||||||||
\(518\) | 2.35695 | 0.103558 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.6469 | 1.16742 | 0.583711 | − | 0.811962i | \(-0.301600\pi\) | ||||
0.583711 | + | 0.811962i | \(0.301600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.80935 | 0.0791172 | 0.0395586 | − | 0.999217i | \(-0.487405\pi\) | ||||
0.0395586 | + | 0.999217i | \(0.487405\pi\) | |||||||
\(524\) | 40.3592 | 1.76310 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.7846 | −0.731842 | ||||||||
\(527\) | 13.5659 | 0.590938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2437 | −0.836680 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 24.8879 | 1.07903 | ||||||||
\(533\) | −5.45737 | −0.236385 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −50.2558 | −2.17072 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.22397 | −0.0527691 | ||||||||
\(539\) | −32.5795 | −1.40330 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.5233 | −1.44128 | −0.720640 | − | 0.693309i | \(-0.756152\pi\) | ||||
−0.720640 | + | 0.693309i | \(0.756152\pi\) | |||||||
\(542\) | 24.3132 | 1.04434 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.55126 | −0.109384 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.5146 | 1.17644 | 0.588219 | − | 0.808702i | \(-0.299829\pi\) | ||||
0.588219 | + | 0.808702i | \(0.299829\pi\) | |||||||
\(548\) | −14.9779 | −0.639822 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.8929 | −1.27348 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.09602 | −0.131656 | ||||||||
\(554\) | −62.2050 | −2.64284 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.67095 | −0.325321 | ||||||||
\(557\) | 2.16761 | 0.0918448 | 0.0459224 | − | 0.998945i | \(-0.485377\pi\) | ||||
0.0459224 | + | 0.998945i | \(0.485377\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.97509 | −0.337310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 19.2270 | 0.811040 | ||||||||
\(563\) | 33.4836 | 1.41116 | 0.705582 | − | 0.708628i | \(-0.250686\pi\) | ||||
0.705582 | + | 0.708628i | \(0.250686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −71.6616 | −3.01216 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 29.8566 | 1.25275 | ||||||||
\(569\) | −17.2323 | −0.722415 | −0.361208 | − | 0.932485i | \(-0.617635\pi\) | ||||
−0.361208 | + | 0.932485i | \(0.617635\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.7928 | 1.79082 | 0.895411 | − | 0.445240i | \(-0.146882\pi\) | ||||
0.895411 | + | 0.445240i | \(0.146882\pi\) | |||||||
\(572\) | 44.3027 | 1.85239 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.58076 | −0.274676 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.8385 | 1.32546 | 0.662728 | − | 0.748860i | \(-0.269399\pi\) | ||||
0.662728 | + | 0.748860i | \(0.269399\pi\) | |||||||
\(578\) | −31.7363 | −1.32006 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.94923 | 0.246816 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 71.4470 | 2.95903 | ||||||||
\(584\) | 49.1175 | 2.03250 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.381866 | −0.0157747 | ||||||||
\(587\) | −24.8027 | −1.02372 | −0.511858 | − | 0.859070i | \(-0.671043\pi\) | ||||
−0.511858 | + | 0.859070i | \(0.671043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.1973 | −1.69750 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.64938 | 0.191089 | ||||||||
\(593\) | 17.8431 | 0.732728 | 0.366364 | − | 0.930472i | \(-0.380603\pi\) | ||||
0.366364 | + | 0.930472i | \(0.380603\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −69.4754 | −2.84582 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.57541 | 0.391568 | ||||||||
\(599\) | 28.1028 | 1.14825 | 0.574126 | − | 0.818767i | \(-0.305342\pi\) | ||||
0.574126 | + | 0.818767i | \(0.305342\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.6296 | −1.08624 | −0.543121 | − | 0.839654i | \(-0.682758\pi\) | ||||
−0.543121 | + | 0.839654i | \(0.682758\pi\) | |||||||
\(602\) | −9.61675 | −0.391949 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −59.0336 | −2.40204 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.2757 | 0.782375 | 0.391187 | − | 0.920311i | \(-0.372064\pi\) | ||||
0.391187 | + | 0.920311i | \(0.372064\pi\) | |||||||
\(608\) | 7.74774 | 0.314213 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.4030 | 0.582682 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.465680 | 0.0188086 | 0.00940432 | − | 0.999956i | \(-0.497006\pi\) | ||||
0.00940432 | + | 0.999956i | \(0.497006\pi\) | |||||||
\(614\) | 35.8472 | 1.44668 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.5044 | 1.10818 | ||||||||
\(617\) | −44.2765 | −1.78251 | −0.891253 | − | 0.453507i | \(-0.850173\pi\) | ||||
−0.891253 | + | 0.453507i | \(0.850173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −36.1620 | −1.45347 | −0.726736 | − | 0.686917i | \(-0.758964\pi\) | ||||
−0.726736 | + | 0.686917i | \(0.758964\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −45.8707 | −1.83925 | ||||||||
\(623\) | 2.92644 | 0.117245 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.9667 | −0.678126 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 89.4025 | 3.56755 | ||||||||
\(629\) | −1.99993 | −0.0797424 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.199431 | −0.00793921 | −0.00396961 | − | 0.999992i | \(-0.501264\pi\) | ||||
−0.00396961 | + | 0.999992i | \(0.501264\pi\) | |||||||
\(632\) | −16.7091 | −0.664654 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −67.5028 | −2.68088 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0863 | −0.478876 | ||||||||
\(638\) | −64.1657 | −2.54035 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.9078 | 1.22079 | 0.610393 | − | 0.792099i | \(-0.291012\pi\) | ||||
0.610393 | + | 0.792099i | \(0.291012\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.2489 | 0.877412 | 0.438706 | − | 0.898631i | \(-0.355437\pi\) | ||||
0.438706 | + | 0.898631i | \(0.355437\pi\) | |||||||
\(644\) | 7.77463 | 0.306363 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.3634 | −1.23398 | ||||||||
\(647\) | −35.0696 | −1.37873 | −0.689364 | − | 0.724415i | \(-0.742110\pi\) | ||||
−0.689364 | + | 0.724415i | \(0.742110\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.2012 | −1.38177 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 81.2983 | 3.18389 | ||||||||
\(653\) | −4.00012 | −0.156537 | −0.0782683 | − | 0.996932i | \(-0.524939\pi\) | ||||
−0.0782683 | + | 0.996932i | \(0.524939\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −12.9814 | −0.506839 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 17.3678 | 0.677068 | ||||||||
\(659\) | −10.0349 | −0.390904 | −0.195452 | − | 0.980713i | \(-0.562617\pi\) | ||||
−0.195452 | + | 0.980713i | \(0.562617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −48.5672 | −1.88905 | −0.944523 | − | 0.328445i | \(-0.893475\pi\) | ||||
−0.944523 | + | 0.328445i | \(0.893475\pi\) | |||||||
\(662\) | −32.2727 | −1.25431 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.1078 | 1.24602 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.33814 | −0.361574 | ||||||||
\(668\) | 25.0622 | 0.969684 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.6759 | 0.566557 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.06306 | −0.195167 | −0.0975834 | − | 0.995227i | \(-0.531111\pi\) | ||||
−0.0975834 | + | 0.995227i | \(0.531111\pi\) | |||||||
\(674\) | 48.6229 | 1.87288 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −37.1562 | −1.42908 | ||||||||
\(677\) | 33.6669 | 1.29393 | 0.646963 | − | 0.762521i | \(-0.276039\pi\) | ||||
0.646963 | + | 0.762521i | \(0.276039\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.79489 | −0.222387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −88.4307 | −3.38619 | ||||||||
\(683\) | 32.4523 | 1.24175 | 0.620877 | − | 0.783908i | \(-0.286777\pi\) | ||||
0.620877 | + | 0.783908i | \(0.286777\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −31.4283 | −1.19994 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.9703 | −0.723235 | ||||||||
\(689\) | 26.5053 | 1.00977 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.7811 | −1.17097 | −0.585484 | − | 0.810684i | \(-0.699095\pi\) | ||||
−0.585484 | + | 0.810684i | \(0.699095\pi\) | |||||||
\(692\) | 61.9637 | 2.35550 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.8610 | 0.412278 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.58394 | 0.211507 | ||||||||
\(698\) | 67.2914 | 2.54702 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.1755 | 0.497633 | 0.248817 | − | 0.968551i | \(-0.419958\pi\) | ||||
0.248817 | + | 0.968551i | \(0.419958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.07345 | 0.229065 | ||||||||
\(704\) | −34.4958 | −1.30011 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −39.4207 | −1.48362 | ||||||||
\(707\) | 7.56439 | 0.284488 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.6307 | −0.399246 | −0.199623 | − | 0.979873i | \(-0.563972\pi\) | ||||
−0.199623 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.7939 | 0.591901 | ||||||||
\(713\) | −12.8695 | −0.481965 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 82.5174 | 3.08382 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.4091 | 0.463102 | ||||||||
\(719\) | 15.3464 | 0.572324 | 0.286162 | − | 0.958181i | \(-0.407620\pi\) | ||||
0.286162 | + | 0.958181i | \(0.407620\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.81724 | −0.179404 | ||||||||
\(722\) | 48.2328 | 1.79504 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 83.6823 | 3.11003 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.8156 | −0.883272 | −0.441636 | − | 0.897194i | \(-0.645602\pi\) | ||||
−0.441636 | + | 0.897194i | \(0.645602\pi\) | |||||||
\(728\) | 10.2035 | 0.378168 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.16005 | 0.301810 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.09180 | 0.151134 | 0.0755670 | − | 0.997141i | \(-0.475923\pi\) | ||||
0.0755670 | + | 0.997141i | \(0.475923\pi\) | |||||||
\(734\) | −70.1897 | −2.59075 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.42029 | 0.0892130 | ||||||||
\(737\) | −51.5059 | −1.89724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.45909 | 0.0904590 | 0.0452295 | − | 0.998977i | \(-0.485598\pi\) | ||||
0.0452295 | + | 0.998977i | \(0.485598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 31.9614 | 1.17334 | ||||||||
\(743\) | −11.1921 | −0.410598 | −0.205299 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205299 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 80.9653 | 2.96435 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −45.3301 | −1.65743 | ||||||||
\(749\) | 1.13653 | 0.0415279 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.3616 | −0.378101 | −0.189051 | − | 0.981967i | \(-0.560541\pi\) | ||||
−0.189051 | + | 0.981967i | \(0.560541\pi\) | |||||||
\(752\) | 34.2603 | 1.24934 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.8041 | −0.866894 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.84722 | 0.212521 | 0.106260 | − | 0.994338i | \(-0.466112\pi\) | ||||
0.106260 | + | 0.994338i | \(0.466112\pi\) | |||||||
\(758\) | 11.0971 | 0.403063 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.6931 | −1.51137 | −0.755687 | − | 0.654932i | \(-0.772697\pi\) | ||||
−0.755687 | + | 0.654932i | \(0.772697\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.2116 | −0.623102 | ||||||||
\(764\) | 39.0674 | 1.41341 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.2921 | 1.45581 | ||||||||
\(767\) | −13.0589 | −0.471530 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.3076 | −0.624129 | −0.312065 | − | 0.950061i | \(-0.601021\pi\) | ||||
−0.312065 | + | 0.950061i | \(0.601021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.2327 | −0.404274 | ||||||||
\(773\) | 17.8695 | 0.642723 | 0.321361 | − | 0.946957i | \(-0.395860\pi\) | ||||
0.321361 | + | 0.946957i | \(0.395860\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −31.2748 | −1.12270 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −53.1736 | −1.90637 | ||||||||
\(779\) | −16.9575 | −0.607565 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.5992 | 1.09493 | ||||||||
\(782\) | −9.79749 | −0.350358 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −28.7496 | −1.02677 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.91104 | −0.353290 | −0.176645 | − | 0.984275i | \(-0.556525\pi\) | ||||
−0.176645 | + | 0.984275i | \(0.556525\pi\) | |||||||
\(788\) | 3.21564 | 0.114552 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.90080 | 0.174252 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.44444 | 0.193338 | ||||||||
\(794\) | 51.6819 | 1.83412 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.6101 | −1.08495 | ||||||||
\(797\) | 39.7590 | 1.40834 | 0.704168 | − | 0.710034i | \(-0.251320\pi\) | ||||
0.704168 | + | 0.710034i | \(0.251320\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7370 | −0.521359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.56731 | 0.0553437 | ||||||||
\(803\) | 50.3392 | 1.77643 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −32.8059 | −1.15554 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 40.8248 | 1.43621 | ||||||||
\(809\) | 5.05110 | 0.177587 | 0.0887935 | − | 0.996050i | \(-0.471699\pi\) | ||||
0.0887935 | + | 0.996050i | \(0.471699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.7743 | 0.413452 | 0.206726 | − | 0.978399i | \(-0.433719\pi\) | ||||
0.206726 | + | 0.978399i | \(0.433719\pi\) | |||||||
\(812\) | −19.3274 | −0.678260 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.0368 | 0.456939 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.7807 | −0.866968 | ||||||||
\(818\) | −10.6353 | −0.371855 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.25401 | −0.183366 | −0.0916832 | − | 0.995788i | \(-0.529225\pi\) | ||||
−0.0916832 | + | 0.995788i | \(0.529225\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.0042 | 1.28989 | 0.644943 | − | 0.764230i | \(-0.276881\pi\) | ||||
0.644943 | + | 0.764230i | \(0.276881\pi\) | |||||||
\(824\) | −25.9985 | −0.905701 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.7471 | −0.547910 | ||||||||
\(827\) | 28.1147 | 0.977645 | 0.488822 | − | 0.872383i | \(-0.337427\pi\) | ||||
0.488822 | + | 0.872383i | \(0.337427\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4532 | −0.501979 | −0.250990 | − | 0.967990i | \(-0.580756\pi\) | ||||
−0.250990 | + | 0.967990i | \(0.580756\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.7972 | −0.443662 | ||||||||
\(833\) | 12.3666 | 0.428477 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 137.660 | 4.76108 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −83.1914 | −2.87380 | ||||||||
\(839\) | −16.3694 | −0.565134 | −0.282567 | − | 0.959248i | \(-0.591186\pi\) | ||||
−0.282567 | + | 0.959248i | \(0.591186\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.78575 | −0.199509 | ||||||||
\(842\) | −52.8937 | −1.82284 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.2901 | −0.423043 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.4848 | 0.600784 | ||||||||
\(848\) | 63.0480 | 2.16508 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.89726 | 0.0650373 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.8216 | 1.60314 | 0.801571 | − | 0.597900i | \(-0.203998\pi\) | ||||
0.801571 | + | 0.597900i | \(0.203998\pi\) | |||||||
\(854\) | 6.56517 | 0.224656 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.13382 | 0.209650 | ||||||||
\(857\) | 28.9569 | 0.989148 | 0.494574 | − | 0.869136i | \(-0.335324\pi\) | ||||
0.494574 | + | 0.869136i | \(0.335324\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.4996 | 0.835917 | 0.417959 | − | 0.908466i | \(-0.362746\pi\) | ||||
0.417959 | + | 0.908466i | \(0.362746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −64.5571 | −2.19882 | ||||||||
\(863\) | 10.4696 | 0.356391 | 0.178195 | − | 0.983995i | \(-0.442974\pi\) | ||||
0.178195 | + | 0.983995i | \(0.442974\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −29.1171 | −0.989440 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −26.6363 | −0.904096 | ||||||||
\(869\) | −17.1247 | −0.580917 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.1076 | −0.647435 | ||||||||
\(872\) | −92.8905 | −3.14567 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.7534 | 1.00642 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.9121 | −1.34774 | −0.673868 | − | 0.738852i | \(-0.735368\pi\) | ||||
−0.673868 | + | 0.738852i | \(0.735368\pi\) | |||||||
\(878\) | 12.1880 | 0.411324 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.88965 | 0.265809 | 0.132904 | − | 0.991129i | \(-0.457570\pi\) | ||||
0.132904 | + | 0.991129i | \(0.457570\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.1304 | 0.509178 | 0.254589 | − | 0.967049i | \(-0.418060\pi\) | ||||
0.254589 | + | 0.967049i | \(0.418060\pi\) | |||||||
\(884\) | −16.8165 | −0.565600 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.1590 | 0.778042 | ||||||||
\(887\) | 47.6886 | 1.60123 | 0.800614 | − | 0.599180i | \(-0.204507\pi\) | ||||
0.800614 | + | 0.599180i | \(0.204507\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.58466 | −0.254381 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −102.533 | −3.43306 | ||||||||
\(893\) | 44.7539 | 1.49763 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17.8618 | −0.596719 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.3498 | −0.612342 | ||||||||
\(899\) | 31.9930 | 1.06703 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.1200 | −0.903499 | ||||||||
\(902\) | −36.3996 | −1.21197 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 26.4494 | 0.879696 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.9321 | 1.29272 | 0.646359 | − | 0.763033i | \(-0.276291\pi\) | ||||
0.646359 | + | 0.763033i | \(0.276291\pi\) | |||||||
\(908\) | −72.3873 | −2.40226 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.6740 | −1.24819 | −0.624097 | − | 0.781347i | \(-0.714533\pi\) | ||||
−0.624097 | + | 0.781347i | \(0.714533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.9064 | 1.08904 | ||||||||
\(914\) | −21.7672 | −0.719996 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 28.9332 | 0.955980 | ||||||||
\(917\) | 9.52650 | 0.314593 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.4646 | 0.477145 | 0.238572 | − | 0.971125i | \(-0.423321\pi\) | ||||
0.238572 | + | 0.971125i | \(0.423321\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 104.300 | 3.43495 | ||||||||
\(923\) | 11.3516 | 0.373644 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −57.0499 | −1.87478 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.01674 | −0.197509 | ||||||||
\(929\) | 40.8990 | 1.34185 | 0.670927 | − | 0.741524i | \(-0.265897\pi\) | ||||
0.670927 | + | 0.741524i | \(0.265897\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.5553 | −1.23083 | ||||||||
\(932\) | −35.8291 | −1.17362 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.8368 | 0.354590 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.2563 | −1.08644 | −0.543218 | − | 0.839592i | \(-0.682794\pi\) | ||||
−0.543218 | + | 0.839592i | \(0.682794\pi\) | |||||||
\(938\) | −23.0408 | −0.752310 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.1577 | −1.27650 | −0.638252 | − | 0.769827i | \(-0.720342\pi\) | ||||
−0.638252 | + | 0.769827i | \(0.720342\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.29728 | −0.172503 | ||||||||
\(944\) | −31.0631 | −1.01102 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −53.1923 | −1.72943 | ||||||||
\(947\) | −28.5840 | −0.928854 | −0.464427 | − | 0.885611i | \(-0.653740\pi\) | ||||
−0.464427 | + | 0.885611i | \(0.653740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.6747 | 0.606208 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.4402 | −0.338368 | ||||||||
\(953\) | −43.3568 | −1.40446 | −0.702232 | − | 0.711948i | \(-0.747813\pi\) | ||||
−0.702232 | + | 0.711948i | \(0.747813\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −87.9850 | −2.84564 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −35.1143 | −1.13449 | ||||||||
\(959\) | −3.53542 | −0.114165 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.0915 | 0.422306 | ||||||||
\(962\) | 4.83636 | 0.155931 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −88.1775 | −2.84001 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.2551 | −1.03726 | −0.518628 | − | 0.855000i | \(-0.673557\pi\) | ||||
−0.518628 | + | 0.855000i | \(0.673557\pi\) | |||||||
\(968\) | 94.3647 | 3.03300 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.9579 | −0.351654 | −0.175827 | − | 0.984421i | \(-0.556260\pi\) | ||||
−0.175827 | + | 0.984421i | \(0.556260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.81068 | −0.0580476 | ||||||||
\(974\) | −54.6074 | −1.74973 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.9507 | 0.414540 | ||||||||
\(977\) | −20.1536 | −0.644770 | −0.322385 | − | 0.946609i | \(-0.604484\pi\) | ||||
−0.322385 | + | 0.946609i | \(0.604484\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.1867 | 0.517330 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.6885 | 0.628286 | ||||||||
\(983\) | −16.0511 | −0.511951 | −0.255975 | − | 0.966683i | \(-0.582397\pi\) | ||||
−0.255975 | + | 0.966683i | \(0.582397\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.3562 | 0.775659 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 51.0689 | 1.62472 | ||||||||
\(989\) | −7.74115 | −0.246154 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5569 | 0.653010 | 0.326505 | − | 0.945195i | \(-0.394129\pi\) | ||||
0.326505 | + | 0.945195i | \(0.394129\pi\) | |||||||
\(992\) | −8.29204 | −0.263272 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 13.6884 | 0.434169 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.7296 | −0.688183 | −0.344092 | − | 0.938936i | \(-0.611813\pi\) | ||||
−0.344092 | + | 0.938936i | \(0.611813\pi\) | |||||||
\(998\) | −10.1296 | −0.320647 | ||||||||
\(999\) | 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 | 5625.2.a.be.1.7 | 8 | ||
3.2 | odd | 2 | 625.2.a.e.1.2 | ✓ | 8 | ||
5.4 | even | 2 | 5625.2.a.s.1.2 | 8 | |||
12.11 | even | 2 | 10000.2.a.bn.1.6 | 8 | |||
15.2 | even | 4 | 625.2.b.d.624.2 | 16 | |||
15.8 | even | 4 | 625.2.b.d.624.15 | 16 | |||
15.14 | odd | 2 | 625.2.a.g.1.7 | yes | 8 | ||
60.59 | even | 2 | 10000.2.a.be.1.3 | 8 | |||
75.2 | even | 20 | 625.2.e.k.124.1 | 32 | |||
75.8 | even | 20 | 625.2.e.j.374.1 | 32 | |||
75.11 | odd | 10 | 625.2.d.p.501.1 | 16 | |||
75.14 | odd | 10 | 625.2.d.n.501.4 | 16 | |||
75.17 | even | 20 | 625.2.e.j.374.8 | 32 | |||
75.23 | even | 20 | 625.2.e.k.124.8 | 32 | |||
75.29 | odd | 10 | 625.2.d.m.376.1 | 16 | |||
75.38 | even | 20 | 625.2.e.k.499.1 | 32 | |||
75.41 | odd | 10 | 625.2.d.p.126.1 | 16 | |||
75.44 | odd | 10 | 625.2.d.m.251.1 | 16 | |||
75.47 | even | 20 | 625.2.e.j.249.1 | 32 | |||
75.53 | even | 20 | 625.2.e.j.249.8 | 32 | |||
75.56 | odd | 10 | 625.2.d.q.251.4 | 16 | |||
75.59 | odd | 10 | 625.2.d.n.126.4 | 16 | |||
75.62 | even | 20 | 625.2.e.k.499.8 | 32 | |||
75.71 | odd | 10 | 625.2.d.q.376.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
625.2.a.e.1.2 | ✓ | 8 | 3.2 | odd | 2 | ||
625.2.a.g.1.7 | yes | 8 | 15.14 | odd | 2 | ||
625.2.b.d.624.2 | 16 | 15.2 | even | 4 | |||
625.2.b.d.624.15 | 16 | 15.8 | even | 4 | |||
625.2.d.m.251.1 | 16 | 75.44 | odd | 10 | |||
625.2.d.m.376.1 | 16 | 75.29 | odd | 10 | |||
625.2.d.n.126.4 | 16 | 75.59 | odd | 10 | |||
625.2.d.n.501.4 | 16 | 75.14 | odd | 10 | |||
625.2.d.p.126.1 | 16 | 75.41 | odd | 10 | |||
625.2.d.p.501.1 | 16 | 75.11 | odd | 10 | |||
625.2.d.q.251.4 | 16 | 75.56 | odd | 10 | |||
625.2.d.q.376.4 | 16 | 75.71 | odd | 10 | |||
625.2.e.j.249.1 | 32 | 75.47 | even | 20 | |||
625.2.e.j.249.8 | 32 | 75.53 | even | 20 | |||
625.2.e.j.374.1 | 32 | 75.8 | even | 20 | |||
625.2.e.j.374.8 | 32 | 75.17 | even | 20 | |||
625.2.e.k.124.1 | 32 | 75.2 | even | 20 | |||
625.2.e.k.124.8 | 32 | 75.23 | even | 20 | |||
625.2.e.k.499.1 | 32 | 75.38 | even | 20 | |||
625.2.e.k.499.8 | 32 | 75.62 | even | 20 | |||
5625.2.a.s.1.2 | 8 | 5.4 | even | 2 | |||
5625.2.a.be.1.7 | 8 | 1.1 | even | 1 | trivial | ||
10000.2.a.be.1.3 | 8 | 60.59 | even | 2 | |||
10000.2.a.bn.1.6 | 8 | 12.11 | even | 2 |