Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4096,2,Mod(1,4096)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4096, 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("4096.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4096 = 2^{12} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4096.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: | \(32.7067246679\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{48})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 20x^{4} - 16x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1024) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.98289\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4096.1 |
$q$-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 | ||||||||
\(3\) | 2.93185 | 1.69271 | 0.846353 | − | 0.532623i | \(-0.178794\pi\) | ||||
0.846353 | + | 0.532623i | \(0.178794\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.396183 | −0.177178 | −0.0885892 | − | 0.996068i | \(-0.528236\pi\) | ||||
−0.0885892 | + | 0.996068i | \(0.528236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.33496 | 1.63846 | 0.819231 | − | 0.573464i | \(-0.194401\pi\) | ||||
0.819231 | + | 0.573464i | \(0.194401\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.59575 | 1.86525 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.96713 | 1.19613 | 0.598067 | − | 0.801446i | \(-0.295936\pi\) | ||||
0.598067 | + | 0.801446i | \(0.295936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.03886 | −0.565479 | −0.282739 | − | 0.959197i | \(-0.591243\pi\) | ||||
−0.282739 | + | 0.959197i | \(0.591243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.16155 | −0.299911 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.54587 | 1.10253 | 0.551267 | − | 0.834329i | \(-0.314144\pi\) | ||||
0.551267 | + | 0.834329i | \(0.314144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.578738 | 0.132772 | 0.0663858 | − | 0.997794i | \(-0.478853\pi\) | ||||
0.0663858 | + | 0.997794i | \(0.478853\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.7095 | 2.77343 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.24790 | −1.30278 | −0.651389 | − | 0.758744i | \(-0.725813\pi\) | ||||
−0.651389 | + | 0.758744i | \(0.725813\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.84304 | −0.968608 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.61037 | 1.46462 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.13851 | 0.954198 | 0.477099 | − | 0.878850i | \(-0.341688\pi\) | ||||
0.477099 | + | 0.878850i | \(0.341688\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0539984 | −0.00969841 | −0.00484920 | − | 0.999988i | \(-0.501544\pi\) | ||||
−0.00484920 | + | 0.999988i | \(0.501544\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.6310 | 2.02470 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.71744 | −0.290300 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.864289 | −0.142088 | −0.0710441 | − | 0.997473i | \(-0.522633\pi\) | ||||
−0.0710441 | + | 0.997473i | \(0.522633\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.97764 | −0.957189 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.878315 | −0.137170 | −0.0685849 | − | 0.997645i | \(-0.521848\pi\) | ||||
−0.0685849 | + | 0.997645i | \(0.521848\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.23972 | 0.341554 | 0.170777 | − | 0.985310i | \(-0.445372\pi\) | ||||
0.170777 | + | 0.985310i | \(0.445372\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.21694 | −0.330482 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.44387 | −1.37753 | −0.688765 | − | 0.724984i | \(-0.741847\pi\) | ||||
−0.688765 | + | 0.724984i | \(0.741847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.7919 | 1.68456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 13.3278 | 1.86627 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.8869 | 1.49543 | 0.747713 | − | 0.664022i | \(-0.231152\pi\) | ||||
0.747713 | + | 0.664022i | \(0.231152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.57171 | −0.211929 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.69677 | 0.224743 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.77025 | −1.01160 | −0.505800 | − | 0.862651i | \(-0.668803\pi\) | ||||
−0.505800 | + | 0.862651i | \(0.668803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5307 | −1.34832 | −0.674160 | − | 0.738586i | \(-0.735494\pi\) | ||||
−0.674160 | + | 0.738586i | \(0.735494\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.2574 | 3.05614 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.807763 | 0.100191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.15988 | 0.996888 | 0.498444 | − | 0.866922i | \(-0.333905\pi\) | ||||
0.498444 | + | 0.866922i | \(0.333905\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.3179 | −2.20522 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.23065 | −0.502085 | −0.251043 | − | 0.967976i | \(-0.580773\pi\) | ||||
−0.251043 | + | 0.967976i | \(0.580773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.12560 | −0.482865 | −0.241432 | − | 0.970418i | \(-0.577617\pi\) | ||||
−0.241432 | + | 0.970418i | \(0.577617\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.1991 | −1.63957 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.1974 | 1.95982 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.74836 | −0.646741 | −0.323370 | − | 0.946272i | \(-0.604816\pi\) | ||||
−0.323370 | + | 0.946272i | \(0.604816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.52520 | 0.613911 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.57749 | −0.392681 | −0.196340 | − | 0.980536i | \(-0.562906\pi\) | ||||
−0.196340 | + | 0.980536i | \(0.562906\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.80100 | −0.195345 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.0654 | 1.61518 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.36773 | −0.356978 | −0.178489 | − | 0.983942i | \(-0.557121\pi\) | ||||
−0.178489 | + | 0.983942i | \(0.557121\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.83839 | −0.926516 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.158315 | −0.0164165 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.229286 | −0.0235243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.2672 | 1.34708 | 0.673541 | − | 0.739150i | \(-0.264772\pi\) | ||||
0.673541 | + | 0.739150i | \(0.264772\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 22.1991 | 2.23109 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.7865 | −1.47131 | −0.735657 | − | 0.677355i | \(-0.763126\pi\) | ||||
−0.735657 | + | 0.677355i | \(0.763126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.60406 | 0.650718 | 0.325359 | − | 0.945591i | \(-0.394515\pi\) | ||||
0.325359 | + | 0.945591i | \(0.394515\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.03528 | −0.491393 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.25966 | −0.798491 | −0.399246 | − | 0.916844i | \(-0.630728\pi\) | ||||
−0.399246 | + | 0.916844i | \(0.630728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.66528 | −0.255288 | −0.127644 | − | 0.991820i | \(-0.540741\pi\) | ||||
−0.127644 | + | 0.991820i | \(0.540741\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.53397 | −0.240514 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.96472 | 0.467042 | 0.233521 | − | 0.972352i | \(-0.424975\pi\) | ||||
0.233521 | + | 0.972352i | \(0.424975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.47531 | 0.230824 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.4090 | −1.05476 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.7062 | 1.80646 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.73810 | 0.430737 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.57509 | −0.232188 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.89965 | 0.348795 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4530 | −1.37123 | −0.685614 | − | 0.727965i | \(-0.740466\pi\) | ||||
−0.685614 | + | 0.727965i | \(0.740466\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.56653 | 0.578151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4617 | 0.914043 | 0.457021 | − | 0.889456i | \(-0.348916\pi\) | ||||
0.457021 | + | 0.889456i | \(0.348916\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50881 | 0.217541 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.01510 | −0.259498 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2474 | −1.38811 | −0.694057 | − | 0.719920i | \(-0.744178\pi\) | ||||
−0.694057 | + | 0.719920i | \(0.744178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.49697 | 0.635885 | 0.317943 | − | 0.948110i | \(-0.397008\pi\) | ||||
0.317943 | + | 0.948110i | \(0.397008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.6880 | −2.33175 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.08843 | −0.676388 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.03579 | −0.169063 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 34.5721 | 2.85146 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.33025 | −0.518594 | −0.259297 | − | 0.965798i | \(-0.583491\pi\) | ||||
−0.259297 | + | 0.965798i | \(0.583491\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.7097 | −0.871546 | −0.435773 | − | 0.900057i | \(-0.643525\pi\) | ||||
−0.435773 | + | 0.900057i | \(0.643525\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 25.4375 | 2.05650 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0213933 | 0.00171835 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.15361 | −0.650729 | −0.325364 | − | 0.945589i | \(-0.605487\pi\) | ||||
−0.325364 | + | 0.945589i | \(0.605487\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 31.9187 | 2.53132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.0844 | −2.13455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.95983 | −0.466810 | −0.233405 | − | 0.972380i | \(-0.574987\pi\) | ||||
−0.233405 | + | 0.972380i | \(0.574987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.60802 | −0.358734 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.3851 | −1.57745 | −0.788725 | − | 0.614747i | \(-0.789258\pi\) | ||||
−0.788725 | + | 0.614747i | \(0.789258\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.84304 | −0.680234 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.23848 | 0.247653 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.3354 | 1.31799 | 0.658993 | − | 0.752149i | \(-0.270982\pi\) | ||||
0.658993 | + | 0.752149i | \(0.270982\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.9944 | −1.58703 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.7812 | −1.71234 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.40717 | 0.703125 | 0.351562 | − | 0.936164i | \(-0.385651\pi\) | ||||
0.351562 | + | 0.936164i | \(0.385651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.721790 | 0.0536502 | 0.0268251 | − | 0.999640i | \(-0.491460\pi\) | ||||
0.0268251 | + | 0.999640i | \(0.491460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −30.8745 | −2.28231 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.342417 | 0.0251750 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0340 | 1.31878 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 32.9907 | 2.39972 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1746 | 0.736209 | 0.368105 | − | 0.929784i | \(-0.380007\pi\) | ||||
0.368105 | + | 0.929784i | \(0.380007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7515 | 0.845889 | 0.422945 | − | 0.906156i | \(-0.360996\pi\) | ||||
0.422945 | + | 0.906156i | \(0.360996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.36824 | 0.169593 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.7016 | 1.11869 | 0.559347 | − | 0.828934i | \(-0.311052\pi\) | ||||
0.559347 | + | 0.828934i | \(0.311052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.29075 | 0.233275 | 0.116638 | − | 0.993175i | \(-0.462788\pi\) | ||||
0.116638 | + | 0.993175i | \(0.462788\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.9236 | 1.68744 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.2753 | 1.56342 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.347974 | 0.0243035 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −34.9617 | −2.43001 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.29593 | 0.158813 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2988 | 1.25974 | 0.629872 | − | 0.776699i | \(-0.283107\pi\) | ||||
0.629872 | + | 0.776699i | \(0.283107\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −12.4036 | −0.849883 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.887340 | −0.0605161 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.234081 | −0.0158905 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0956 | −0.817348 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.26840 | −0.623460 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.6471 | 1.44959 | 0.724797 | − | 0.688962i | \(-0.241934\pi\) | ||||
0.724797 | + | 0.688962i | \(0.241934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.1005 | −1.80670 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.59476 | 0.636826 | 0.318413 | − | 0.947952i | \(-0.396850\pi\) | ||||
0.318413 | + | 0.947952i | \(0.396850\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.7686 | 1.90108 | 0.950541 | − | 0.310599i | \(-0.100530\pi\) | ||||
0.950541 | + | 0.310599i | \(0.100530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 50.4201 | 3.31740 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.5580 | 1.67436 | 0.837180 | − | 0.546928i | \(-0.184203\pi\) | ||||
0.837180 | + | 0.546928i | \(0.184203\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.74150 | 0.244069 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.8533 | −1.09474 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0765 | 1.55738 | 0.778690 | − | 0.627409i | \(-0.215884\pi\) | ||||
0.778690 | + | 0.627409i | \(0.215884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3823 | −0.668785 | −0.334393 | − | 0.942434i | \(-0.608531\pi\) | ||||
−0.334393 | + | 0.942434i | \(0.608531\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.63203 | −0.425445 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.67175 | −0.298467 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.17997 | −0.0750796 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.4887 | −0.664693 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9345 | 1.57385 | 0.786927 | − | 0.617047i | \(-0.211671\pi\) | ||||
0.786927 | + | 0.617047i | \(0.211671\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.7862 | −1.55830 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.28025 | −0.330662 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7121 | −1.16723 | −0.583613 | − | 0.812032i | \(-0.698362\pi\) | ||||
−0.583613 | + | 0.812032i | \(0.698362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.74666 | −0.232806 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.7539 | 1.77982 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.25113 | 0.0771479 | 0.0385740 | − | 0.999256i | \(-0.487718\pi\) | ||||
0.0385740 | + | 0.999256i | \(0.487718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.31319 | −0.264957 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.87367 | −0.604259 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.2249 | 0.867306 | 0.433653 | − | 0.901080i | \(-0.357224\pi\) | ||||
0.433653 | + | 0.901080i | \(0.357224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.5598 | 1.06668 | 0.533341 | − | 0.845900i | \(-0.320936\pi\) | ||||
0.533341 | + | 0.845900i | \(0.320936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.9129 | −1.56832 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.2130 | −1.15858 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.3830 | −1.58520 | −0.792602 | − | 0.609740i | \(-0.791274\pi\) | ||||
−0.792602 | + | 0.609740i | \(0.791274\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.302162 | −0.0180900 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0082 | −1.43221 | −0.716105 | − | 0.697993i | \(-0.754077\pi\) | ||||
−0.716105 | + | 0.697993i | \(0.754077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.52104 | 0.209304 | 0.104652 | − | 0.994509i | \(-0.466627\pi\) | ||||
0.104652 | + | 0.994509i | \(0.466627\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.672233 | −0.0398197 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.80746 | −0.224747 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.66490 | 0.215582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 38.8975 | 2.28021 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.12386 | −0.182498 | −0.0912488 | − | 0.995828i | \(-0.529086\pi\) | ||||
−0.0912488 | + | 0.995828i | \(0.529086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.07844 | 0.179234 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 30.1913 | 1.75188 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.7386 | 0.736693 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.70911 | 0.559624 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.3519 | −2.49050 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.17209 | 0.238893 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.52709 | −0.486667 | −0.243333 | − | 0.969943i | \(-0.578241\pi\) | ||||
−0.243333 | + | 0.969943i | \(0.578241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.3621 | 1.10147 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.78833 | 0.271521 | 0.135761 | − | 0.990742i | \(-0.456652\pi\) | ||||
0.135761 | + | 0.990742i | \(0.456652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.7972 | −1.68424 | −0.842120 | − | 0.539291i | \(-0.818692\pi\) | ||||
−0.842120 | + | 0.539291i | \(0.818692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.61037 | −0.541483 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.1859 | 1.58308 | 0.791540 | − | 0.611117i | \(-0.209280\pi\) | ||||
0.791540 | + | 0.611117i | \(0.209280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.3851 | 1.14135 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.2161 | −1.35161 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.63087 | 0.146385 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.87429 | 0.547727 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.81422 | −0.432127 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −40.9389 | −2.25703 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.3733 | −1.72443 | −0.862217 | − | 0.506540i | \(-0.830924\pi\) | ||||
−0.862217 | + | 0.506540i | \(0.830924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.83635 | −0.265030 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.23281 | −0.176627 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.6957 | −1.94447 | −0.972234 | − | 0.234010i | \(-0.924815\pi\) | ||||
−0.972234 | + | 0.234010i | \(0.924815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.5558 | 0.790564 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.214219 | −0.0116006 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.7727 | 1.12162 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.25725 | 0.390717 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.2555 | 1.51684 | 0.758418 | − | 0.651768i | \(-0.225973\pi\) | ||||
0.758418 | + | 0.651768i | \(0.225973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.0593 | 0.699047 | 0.349524 | − | 0.936928i | \(-0.386343\pi\) | ||||
0.349524 | + | 0.936928i | \(0.386343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.5165 | −0.828209 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.4488 | −0.875479 | −0.437740 | − | 0.899102i | \(-0.644221\pi\) | ||||
−0.437740 | + | 0.899102i | \(0.644221\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.67611 | 0.0889587 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 57.7755 | 3.05781 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.54907 | −0.292869 | −0.146434 | − | 0.989220i | \(-0.546780\pi\) | ||||
−0.146434 | + | 0.989220i | \(0.546780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6651 | −0.982372 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.8914 | 0.729110 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.63449 | 0.0855533 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.9285 | 0.988061 | 0.494031 | − | 0.869444i | \(-0.335523\pi\) | ||||
0.494031 | + | 0.869444i | \(0.335523\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.91484 | −0.255856 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 47.1942 | 2.45020 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.4739 | −0.801206 | −0.400603 | − | 0.916252i | \(-0.631199\pi\) | ||||
−0.400603 | + | 0.916252i | \(0.631199\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.4332 | 0.590407 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.4767 | −0.539579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5269 | −1.10576 | −0.552881 | − | 0.833260i | \(-0.686471\pi\) | ||||
−0.552881 | + | 0.833260i | \(0.686471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.3058 | −2.32109 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.8953 | 0.761113 | 0.380556 | − | 0.924758i | \(-0.375732\pi\) | ||||
0.380556 | + | 0.924758i | \(0.375732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.81330 | −0.347238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.5329 | 0.637085 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.9048 | 1.00921 | 0.504606 | − | 0.863350i | \(-0.331638\pi\) | ||||
0.504606 | + | 0.863350i | \(0.331638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.4021 | −1.43636 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 30.6721 | 1.54721 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.27740 | 0.114589 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2817 | 0.817153 | 0.408577 | − | 0.912724i | \(-0.366025\pi\) | ||||
0.408577 | + | 0.912724i | \(0.366025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.35546 | 0.368233 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1297 | 1.30485 | 0.652427 | − | 0.757852i | \(-0.273751\pi\) | ||||
0.652427 | + | 0.757852i | \(0.273751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.110095 | 0.00548424 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.18899 | −0.108772 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.42875 | −0.169957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.8489 | −1.08036 | −0.540179 | − | 0.841550i | \(-0.681643\pi\) | ||||
−0.540179 | + | 0.841550i | \(0.681643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −47.6351 | −2.34967 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.6837 | −1.65747 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.41734 | 0.0695746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.9800 | 1.07637 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.1397 | −0.544212 | −0.272106 | − | 0.962267i | \(-0.587720\pi\) | ||||
−0.272106 | + | 0.962267i | \(0.587720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.2496 | −1.27932 | −0.639662 | − | 0.768656i | \(-0.720926\pi\) | ||||
−0.639662 | + | 0.768656i | \(0.720926\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −52.8456 | −2.56944 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.0158 | −1.06792 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −45.6502 | −2.20917 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.7141 | −1.14493 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4592 | 0.551972 | 0.275986 | − | 0.961162i | \(-0.410996\pi\) | ||||
0.275986 | + | 0.961162i | \(0.410996\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.0019 | −0.720946 | −0.360473 | − | 0.932770i | \(-0.617385\pi\) | ||||
−0.360473 | + | 0.932770i | \(0.617385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.96864 | −0.286174 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.61590 | −0.172972 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.7287 | −0.941600 | −0.470800 | − | 0.882240i | \(-0.656035\pi\) | ||||
−0.470800 | + | 0.882240i | \(0.656035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 65.9846 | 3.14212 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.7035 | −0.556049 | −0.278024 | − | 0.960574i | \(-0.589680\pi\) | ||||
−0.278024 | + | 0.960574i | \(0.589680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.33424 | 0.0632488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.5594 | −0.877827 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.74061 | 0.223723 | 0.111862 | − | 0.993724i | \(-0.464319\pi\) | ||||
0.111862 | + | 0.993724i | \(0.464319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.48439 | −0.164073 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −31.3994 | −1.47527 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.50162 | 0.164159 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4833 | 1.00495 | 0.502473 | − | 0.864593i | \(-0.332423\pi\) | ||||
0.502473 | + | 0.864593i | \(0.332423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34.5957 | 1.61479 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1181 | 0.750697 | 0.375348 | − | 0.926884i | \(-0.377523\pi\) | ||||
0.375348 | + | 0.926884i | \(0.377523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.4145 | −0.530477 | −0.265238 | − | 0.964183i | \(-0.585451\pi\) | ||||
−0.265238 | + | 0.964183i | \(0.585451\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0627219 | 0.00290866 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.91459 | −0.319969 | −0.159984 | − | 0.987120i | \(-0.551144\pi\) | ||||
−0.159984 | + | 0.987120i | \(0.551144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.3728 | 1.63336 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.9052 | −1.10149 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.88526 | 0.408545 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.80285 | −0.128604 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 60.9202 | 2.78935 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.2733 | −0.743545 | −0.371772 | − | 0.928324i | \(-0.621250\pi\) | ||||
−0.371772 | + | 0.928324i | \(0.621250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.76217 | 0.0803479 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −79.4075 | −3.61317 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.25625 | −0.238674 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.4658 | −0.836766 | −0.418383 | − | 0.908271i | \(-0.637403\pi\) | ||||
−0.418383 | + | 0.908271i | \(0.637403\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.4733 | −0.790172 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.3350 | −0.646930 | −0.323465 | − | 0.946240i | \(-0.604848\pi\) | ||||
−0.323465 | + | 0.946240i | \(0.604848\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.3590 | 1.05204 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.79490 | −0.395301 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.3397 | −0.822648 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.6551 | −1.10372 | −0.551858 | − | 0.833938i | \(-0.686081\pi\) | ||||
−0.551858 | + | 0.833938i | \(0.686081\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −59.7662 | −2.67016 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 41.0356 | 1.82969 | 0.914844 | − | 0.403808i | \(-0.132314\pi\) | ||||
0.914844 | + | 0.403808i | \(0.132314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.85817 | 0.260685 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.9265 | −1.15144 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.260792 | −0.0115594 | −0.00577971 | − | 0.999983i | \(-0.501840\pi\) | ||||
−0.00577971 | + | 0.999983i | \(0.501840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.8843 | −0.791156 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.40441 | 0.194459 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.61642 | −0.115293 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.4651 | −1.64771 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 50.8249 | 2.23096 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.32605 | 0.408581 | 0.204291 | − | 0.978910i | \(-0.434511\pi\) | ||||
0.204291 | + | 0.978910i | \(0.434511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.6379 | −1.42715 | −0.713577 | − | 0.700577i | \(-0.752926\pi\) | ||||
−0.713577 | + | 0.700577i | \(0.752926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −61.5525 | −2.68637 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.245470 | −0.0106928 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0363 | 0.697231 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −43.4804 | −1.88689 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.79076 | 0.0775666 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.27234 | 0.141475 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 27.5804 | 1.19018 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 46.7800 | 2.01496 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2713 | −0.613573 | −0.306786 | − | 0.951778i | \(-0.599254\pi\) | ||||
−0.306786 | + | 0.951778i | \(0.599254\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.11618 | 0.0908140 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.05594 | 0.0452315 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.7376 | 1.05771 | 0.528853 | − | 0.848714i | \(-0.322622\pi\) | ||||
0.528853 | + | 0.848714i | \(0.322622\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −58.9273 | −2.51495 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.97385 | 0.126690 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.9189 | −1.05966 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.00392 | 0.0426138 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.1124 | 0.809819 | 0.404909 | − | 0.914357i | \(-0.367303\pi\) | ||||
0.404909 | + | 0.914357i | \(0.367303\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.56648 | −0.193142 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.8731 | 2.23230 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.4787 | −1.32667 | −0.663336 | − | 0.748322i | \(-0.730860\pi\) | ||||
−0.663336 | + | 0.748322i | \(0.730860\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.96694 | −0.0827498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.9515 | 1.00587 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.6420 | −1.07497 | −0.537485 | − | 0.843273i | \(-0.680625\pi\) | ||||
−0.537485 | + | 0.843273i | \(0.680625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.41040 | −0.351964 | −0.175982 | − | 0.984393i | \(-0.556310\pi\) | ||||
−0.175982 | + | 0.984393i | \(0.556310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.8305 | 1.24619 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.2588 | 1.26188 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.2275 | −0.550669 | −0.275335 | − | 0.961348i | \(-0.588789\pi\) | ||||
−0.275335 | + | 0.961348i | \(0.588789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.4536 | 1.43184 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.5083 | −0.643393 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.1896 | 1.78873 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.52004 | 0.186881 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.6840 | 1.43156 | 0.715781 | − | 0.698325i | \(-0.246071\pi\) | ||||
0.715781 | + | 0.698325i | \(0.246071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0312510 | −0.00128767 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 46.0348 | 1.89362 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4869 | 1.53940 | 0.769700 | − | 0.638405i | \(-0.220406\pi\) | ||||
0.769700 | + | 0.638405i | \(0.220406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.80725 | −0.320066 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.64800 | 0.394866 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.73533 | 0.234339 | 0.117170 | − | 0.993112i | \(-0.462618\pi\) | ||||
0.117170 | + | 0.993112i | \(0.462618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.12581 | −0.0459229 | −0.0229614 | − | 0.999736i | \(-0.507309\pi\) | ||||
−0.0229614 | + | 0.999736i | \(0.507309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.6607 | 1.85945 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.87716 | −0.0763173 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.8854 | −0.563591 | −0.281795 | − | 0.959475i | \(-0.590930\pi\) | ||||
−0.281795 | + | 0.959475i | \(0.590930\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 65.3078 | 2.64640 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.2548 | 0.778964 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.2426 | 0.413694 | 0.206847 | − | 0.978373i | \(-0.433680\pi\) | ||||
0.206847 | + | 0.978373i | \(0.433680\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.02021 | 0.0411387 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.63302 | −0.307294 | −0.153647 | − | 0.988126i | \(-0.549102\pi\) | ||||
−0.153647 | + | 0.988126i | \(0.549102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.7880 | 1.35806 | 0.679028 | − | 0.734112i | \(-0.262401\pi\) | ||||
0.679028 | + | 0.734112i | \(0.262401\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −47.5488 | −1.90807 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.5990 | −0.584895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.6702 | 0.906809 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.73132 | 0.268823 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.92894 | −0.156657 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.9285 | −1.23124 | −0.615622 | − | 0.788042i | \(-0.711095\pi\) | ||||
−0.615622 | + | 0.788042i | \(0.711095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 53.6495 | 2.13238 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.12220 | 0.242952 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.0421 | −0.952582 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.6737 | −0.936515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.0037 | 1.34307 | 0.671533 | − | 0.740975i | \(-0.265636\pi\) | ||||
0.671533 | + | 0.740975i | \(0.265636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1833 | −0.401589 | −0.200794 | − | 0.979633i | \(-0.564352\pi\) | ||||
−0.200794 | + | 0.979633i | \(0.564352\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.60155 | −0.102436 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.9038 | −0.664558 | −0.332279 | − | 0.943181i | \(-0.607818\pi\) | ||||
−0.332279 | + | 0.943181i | \(0.607818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30.8256 | −1.21001 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.686292 | −0.0268979 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.2863 | 0.676467 | 0.338234 | − | 0.941062i | \(-0.390171\pi\) | ||||
0.338234 | + | 0.941062i | \(0.390171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.14475 | −0.161949 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −23.0858 | −0.900665 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.37890 | 0.131623 | 0.0658117 | − | 0.997832i | \(-0.479036\pi\) | ||||
0.0658117 | + | 0.997832i | \(0.479036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.4429 | 1.80642 | 0.903210 | − | 0.429198i | \(-0.141204\pi\) | ||||
0.903210 | + | 0.429198i | \(0.141204\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −27.1736 | −1.05533 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.993948 | −0.0385436 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.1049 | −1.24311 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 63.4660 | 2.45374 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.7767 | −1.61277 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.107425 | 0.00414091 | 0.00207046 | − | 0.999998i | \(-0.499341\pi\) | ||||
0.00207046 | + | 0.999998i | \(0.499341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −36.8573 | −1.41864 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.0929 | −0.426335 | −0.213167 | − | 0.977016i | \(-0.568378\pi\) | ||||
−0.213167 | + | 0.977016i | \(0.568378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 57.5129 | 2.20714 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.1304 | 1.07796 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.3645 | 1.04707 | 0.523537 | − | 0.852003i | \(-0.324612\pi\) | ||||
0.523537 | + | 0.852003i | \(0.324612\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.43696 | 0.245944 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 84.3452 | 3.21797 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.1968 | −0.845632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3845 | 1.15588 | 0.577941 | − | 0.816079i | \(-0.303856\pi\) | ||||
0.577941 | + | 0.816079i | \(0.303856\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 96.2322 | 3.65556 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.97017 | −0.112665 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.99270 | −0.151234 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 74.9322 | 2.83420 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.3877 | −1.03442 | −0.517210 | − | 0.855859i | \(-0.673029\pi\) | ||||
−0.517210 | + | 0.855859i | \(0.673029\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.500197 | −0.0188653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9695 | 0.413136 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −64.0990 | −2.41069 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.6900 | −1.79104 | −0.895518 | − | 0.445025i | \(-0.853195\pi\) | ||||
−0.895518 | + | 0.445025i | \(0.853195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −32.1664 | −1.20633 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.337377 | 0.0126349 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.20450 | 0.119841 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 70.5888 | 2.63619 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.5621 | 0.766835 | 0.383418 | − | 0.923575i | \(-0.374747\pi\) | ||||
0.383418 | + | 0.923575i | \(0.374747\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.6284 | 1.06618 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.4395 | −1.13206 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.8860 | −0.924244 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.21618 | −0.156369 | −0.0781847 | − | 0.996939i | \(-0.524912\pi\) | ||||
−0.0781847 | + | 0.996939i | \(0.524912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.0197 | −1.33406 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1815 | 0.376575 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.9118 | −1.76966 | −0.884831 | − | 0.465912i | \(-0.845726\pi\) | ||||
−0.884831 | + | 0.465912i | \(0.845726\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.6969 | −0.505217 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.3713 | 1.19241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8399 | −0.619466 | −0.309733 | − | 0.950824i | \(-0.600240\pi\) | ||||
−0.309733 | + | 0.950824i | \(0.600240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.45949 | −0.127088 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5221 | −0.789569 | −0.394784 | − | 0.918774i | \(-0.629181\pi\) | ||||
−0.394784 | + | 0.918774i | \(0.629181\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.50794 | 0.0918837 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.0188 | −0.732449 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.8053 | −1.30830 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.40389 | 0.160700 | 0.0803501 | − | 0.996767i | \(-0.474396\pi\) | ||||
0.0803501 | + | 0.996767i | \(0.474396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 73.1043 | 2.66407 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.24302 | 0.154419 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.2106 | 0.879950 | 0.439975 | − | 0.898010i | \(-0.354987\pi\) | ||||
0.439975 | + | 0.898010i | \(0.354987\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −72.6696 | −2.63774 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.63619 | −0.349312 | −0.174656 | − | 0.984630i | \(-0.555881\pi\) | ||||
−0.174656 | + | 0.984630i | \(0.555881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.5539 | −0.418280 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.0779 | −0.364368 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.8425 | 0.572038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.7366 | −0.603538 | −0.301769 | − | 0.953381i | \(-0.597577\pi\) | ||||
−0.301769 | + | 0.953381i | \(0.597577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −54.8610 | −1.97577 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.7678 | 0.531162 | 0.265581 | − | 0.964089i | \(-0.414436\pi\) | ||||
0.265581 | + | 0.964089i | \(0.414436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.261517 | 0.00939395 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.9847 | −0.394072 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.508315 | −0.0182123 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.7835 | −0.600561 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 39.1060 | 1.39753 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.23032 | 0.115295 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.81125 | −0.349733 | −0.174867 | − | 0.984592i | \(-0.555949\pi\) | ||||
−0.174867 | + | 0.984592i | \(0.555949\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.66812 | 0.130589 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.5219 | 0.765231 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.4707 | 0.762446 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.6456 | −0.448495 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −37.6674 | −1.33425 | −0.667125 | − | 0.744946i | \(-0.732475\pi\) | ||||
−0.667125 | + | 0.744946i | \(0.732475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −42.9306 | −1.51878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18.8450 | −0.665854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.3668 | −0.577571 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.7304 | 0.378197 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 41.7052 | 1.46809 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.32508 | 0.327853 | 0.163926 | − | 0.986473i | \(-0.447584\pi\) | ||||
0.163926 | + | 0.986473i | \(0.447584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.3933 | 1.10237 | 0.551183 | − | 0.834384i | \(-0.314177\pi\) | ||||
0.551183 | + | 0.834384i | \(0.314177\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.4827 | 1.80558 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.36118 | 0.0827087 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.29621 | 0.0453487 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −49.4575 | −1.72818 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.2233 | 1.01990 | 0.509950 | − | 0.860204i | \(-0.329664\pi\) | ||||
0.509950 | + | 0.860204i | \(0.329664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.704233 | 0.0245480 | 0.0122740 | − | 0.999925i | \(-0.496093\pi\) | ||||
0.0122740 | + | 0.999925i | \(0.496093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −56.3295 | −1.96114 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.4198 | −1.64895 | −0.824474 | − | 0.565900i | \(-0.808529\pi\) | ||||
−0.824474 | + | 0.565900i | \(0.808529\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.4060 | 1.09078 | 0.545388 | − | 0.838184i | \(-0.316382\pi\) | ||||
0.545388 | + | 0.838184i | \(0.316382\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −77.3512 | −2.68328 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 53.6044 | 1.85728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.07625 | 0.279490 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.410948 | −0.0142044 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.8294 | −1.37506 | −0.687532 | − | 0.726154i | \(-0.741306\pi\) | ||||
−0.687532 | + | 0.726154i | \(0.741306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.59569 | −0.0895064 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −70.3885 | −2.42431 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.50346 | 0.120523 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.5395 | 0.705746 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.3232 | 0.354290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.40000 | 0.185110 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.25003 | −0.282476 | −0.141238 | − | 0.989976i | \(-0.545108\pi\) | ||||
−0.141238 | + | 0.989976i | \(0.545108\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.28303 | −0.0438787 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.0746 | −0.412462 | −0.206231 | − | 0.978503i | \(-0.566120\pi\) | ||||
−0.206231 | + | 0.978503i | \(0.566120\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.85490 | −0.336245 | −0.168122 | − | 0.985766i | \(-0.553770\pi\) | ||||
−0.168122 | + | 0.985766i | \(0.553770\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.1629 | −0.380431 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.7816 | 0.605294 | 0.302647 | − | 0.953103i | \(-0.402130\pi\) | ||||
0.302647 | + | 0.953103i | \(0.402130\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.86800 | −0.233519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.7449 | 0.364917 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.8045 | −0.773589 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.6369 | −0.563719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 74.2401 | 2.51265 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.9048 | 0.571487 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1862 | 0.782942 | 0.391471 | − | 0.920191i | \(-0.371966\pi\) | ||||
0.391471 | + | 0.920191i | \(0.371966\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.15869 | −0.308915 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.5225 | −0.725113 | −0.362557 | − | 0.931962i | \(-0.618096\pi\) | ||||
−0.362557 | + | 0.931962i | \(0.618096\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.1426 | −1.01438 | −0.507190 | − | 0.861834i | \(-0.669316\pi\) | ||||
−0.507190 | + | 0.861834i | \(0.669316\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.02553 | 0.303390 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.7744 | 1.20119 | 0.600594 | − | 0.799554i | \(-0.294931\pi\) | ||||
0.600594 | + | 0.799554i | \(0.294931\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −66.9880 | −2.24671 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.9192 | 0.734320 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.46553 | −0.182897 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.72696 | −0.124579 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.3477 | 1.24700 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.277472 | −0.00925420 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 49.4903 | 1.64876 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.4657 | 0.947278 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.285961 | −0.00950566 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.1020 | 0.667475 | 0.333737 | − | 0.942666i | \(-0.391690\pi\) | ||||
0.333737 | + | 0.942666i | \(0.391690\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −82.7417 | −2.74437 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.0332 | −1.88960 | −0.944798 | − | 0.327655i | \(-0.893742\pi\) | ||||
−0.944798 | + | 0.327655i | \(0.893742\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.1924 | −0.469699 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.2319 | 0.404376 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.3511 | 1.49762 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.1609 | 0.335178 | 0.167589 | − | 0.985857i | \(-0.446402\pi\) | ||||
0.167589 | + | 0.985857i | \(0.446402\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.0002 | −0.823783 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.62571 | 0.283919 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.18579 | 0.137628 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.9547 | 1.21375 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.2751 | 0.763630 | 0.381815 | − | 0.924239i | \(-0.375299\pi\) | ||||
0.381815 | + | 0.924239i | \(0.375299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.82443 | 0.223662 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.0387 | 0.459606 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.14478 | −0.233659 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.7545 | −0.351333 | −0.175667 | − | 0.984450i | \(-0.556208\pi\) | ||||
−0.175667 | + | 0.984450i | \(0.556208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −87.3611 | −2.85092 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.97303 | 0.0969180 | 0.0484590 | − | 0.998825i | \(-0.484569\pi\) | ||||
0.0484590 | + | 0.998825i | \(0.484569\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.48763 | 0.178702 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.0703 | −0.425178 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.5098 | −0.763964 | −0.381982 | − | 0.924170i | \(-0.624758\pi\) | ||||
−0.381982 | + | 0.924170i | \(0.624758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.41153 | 0.273050 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 82.6370 | 2.67969 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.840764 | −0.0272350 | −0.0136175 | − | 0.999907i | \(-0.504335\pi\) | ||||
−0.0136175 | + | 0.999907i | \(0.504335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.03101 | −0.130440 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 59.7662 | 1.93197 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −70.4321 | −2.27437 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9971 | −0.999906 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −46.2190 | −1.48939 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.65573 | −0.149873 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.46721 | −0.240129 | −0.120065 | − | 0.992766i | \(-0.538310\pi\) | ||||
−0.120065 | + | 0.992766i | \(0.538310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.71331 | 0.247787 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49.5807 | 1.59112 | 0.795560 | − | 0.605875i | \(-0.207177\pi\) | ||||
0.795560 | + | 0.605875i | \(0.207177\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.4991 | 1.04187 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.9500 | 0.927141 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.5870 | −0.882586 | −0.441293 | − | 0.897363i | \(-0.645480\pi\) | ||||
−0.441293 | + | 0.897363i | \(0.645480\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.3602 | −0.426994 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9143 | −0.476176 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45.9415 | 1.46531 | 0.732654 | − | 0.680601i | \(-0.238281\pi\) | ||||
0.732654 | + | 0.680601i | \(0.238281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.22071 | −0.198208 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −120.027 | −3.82049 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.9936 | −0.444969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.6148 | 1.38547 | 0.692735 | − | 0.721192i | \(-0.256405\pi\) | ||||
0.692735 | + | 0.721192i | \(0.256405\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −91.9819 | −2.91896 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.30374 | −0.0413314 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.9880 | −1.04474 | −0.522370 | − | 0.852719i | \(-0.674952\pi\) | ||||
−0.522370 | + | 0.852719i | \(0.674952\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.57756 | −0.208105 |
(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 | 4096.2.a.s.1.7 | 8 | ||
4.3 | odd | 2 | 4096.2.a.i.1.1 | 8 | |||
8.3 | odd | 2 | inner | 4096.2.a.s.1.8 | 8 | ||
8.5 | even | 2 | 4096.2.a.i.1.2 | 8 | |||
64.3 | odd | 16 | 1024.2.g.d.641.4 | yes | 16 | ||
64.5 | even | 16 | 1024.2.g.f.897.4 | yes | 16 | ||
64.11 | odd | 16 | 1024.2.g.g.385.1 | yes | 16 | ||
64.13 | even | 16 | 1024.2.g.f.129.4 | yes | 16 | ||
64.19 | odd | 16 | 1024.2.g.a.129.4 | yes | 16 | ||
64.21 | even | 16 | 1024.2.g.d.385.1 | yes | 16 | ||
64.27 | odd | 16 | 1024.2.g.a.897.4 | yes | 16 | ||
64.29 | even | 16 | 1024.2.g.g.641.4 | yes | 16 | ||
64.35 | odd | 16 | 1024.2.g.g.641.1 | yes | 16 | ||
64.37 | even | 16 | 1024.2.g.a.897.1 | yes | 16 | ||
64.43 | odd | 16 | 1024.2.g.d.385.4 | yes | 16 | ||
64.45 | even | 16 | 1024.2.g.a.129.1 | ✓ | 16 | ||
64.51 | odd | 16 | 1024.2.g.f.129.1 | yes | 16 | ||
64.53 | even | 16 | 1024.2.g.g.385.4 | yes | 16 | ||
64.59 | odd | 16 | 1024.2.g.f.897.1 | yes | 16 | ||
64.61 | even | 16 | 1024.2.g.d.641.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.129.1 | ✓ | 16 | 64.45 | even | 16 | ||
1024.2.g.a.129.4 | yes | 16 | 64.19 | odd | 16 | ||
1024.2.g.a.897.1 | yes | 16 | 64.37 | even | 16 | ||
1024.2.g.a.897.4 | yes | 16 | 64.27 | odd | 16 | ||
1024.2.g.d.385.1 | yes | 16 | 64.21 | even | 16 | ||
1024.2.g.d.385.4 | yes | 16 | 64.43 | odd | 16 | ||
1024.2.g.d.641.1 | yes | 16 | 64.61 | even | 16 | ||
1024.2.g.d.641.4 | yes | 16 | 64.3 | odd | 16 | ||
1024.2.g.f.129.1 | yes | 16 | 64.51 | odd | 16 | ||
1024.2.g.f.129.4 | yes | 16 | 64.13 | even | 16 | ||
1024.2.g.f.897.1 | yes | 16 | 64.59 | odd | 16 | ||
1024.2.g.f.897.4 | yes | 16 | 64.5 | even | 16 | ||
1024.2.g.g.385.1 | yes | 16 | 64.11 | odd | 16 | ||
1024.2.g.g.385.4 | yes | 16 | 64.53 | even | 16 | ||
1024.2.g.g.641.1 | yes | 16 | 64.35 | odd | 16 | ||
1024.2.g.g.641.4 | yes | 16 | 64.29 | even | 16 | ||
4096.2.a.i.1.1 | 8 | 4.3 | odd | 2 | |||
4096.2.a.i.1.2 | 8 | 8.5 | even | 2 | |||
4096.2.a.s.1.7 | 8 | 1.1 | even | 1 | trivial | ||
4096.2.a.s.1.8 | 8 | 8.3 | odd | 2 | inner |