Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0687697 | 0.0486275 | 0.0243138 | − | 0.999704i | \(-0.492260\pi\) | ||||
0.0243138 | + | 0.999704i | \(0.492260\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.99527 | −0.997635 | ||||||||
\(5\) | 0.966871 | 0.432398 | 0.216199 | − | 0.976349i | \(-0.430634\pi\) | ||||
0.216199 | + | 0.976349i | \(0.430634\pi\) | |||||||
\(6\) | −0.0687697 | −0.0280751 | ||||||||
\(7\) | 0.824977 | 0.311812 | 0.155906 | − | 0.987772i | \(-0.450170\pi\) | ||||
0.155906 | + | 0.987772i | \(0.450170\pi\) | |||||||
\(8\) | −0.274754 | −0.0971400 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.0664914 | 0.0210264 | ||||||||
\(11\) | 2.54836 | 0.768359 | 0.384179 | − | 0.923259i | \(-0.374484\pi\) | ||||
0.384179 | + | 0.923259i | \(0.374484\pi\) | |||||||
\(12\) | 1.99527 | 0.575985 | ||||||||
\(13\) | −0.576726 | −0.159955 | −0.0799775 | − | 0.996797i | \(-0.525485\pi\) | ||||
−0.0799775 | + | 0.996797i | \(0.525485\pi\) | |||||||
\(14\) | 0.0567334 | 0.0151626 | ||||||||
\(15\) | −0.966871 | −0.249645 | ||||||||
\(16\) | 3.97165 | 0.992912 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0.0687697 | 0.0162092 | ||||||||
\(19\) | 3.08913 | 0.708695 | 0.354347 | − | 0.935114i | \(-0.384703\pi\) | ||||
0.354347 | + | 0.935114i | \(0.384703\pi\) | |||||||
\(20\) | −1.92917 | −0.431375 | ||||||||
\(21\) | −0.824977 | −0.180025 | ||||||||
\(22\) | 0.175250 | 0.0373634 | ||||||||
\(23\) | −2.04623 | −0.426668 | −0.213334 | − | 0.976979i | \(-0.568432\pi\) | ||||
−0.213334 | + | 0.976979i | \(0.568432\pi\) | |||||||
\(24\) | 0.274754 | 0.0560838 | ||||||||
\(25\) | −4.06516 | −0.813032 | ||||||||
\(26\) | −0.0396613 | −0.00777822 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.64605 | −0.311075 | ||||||||
\(29\) | 2.52229 | 0.468377 | 0.234189 | − | 0.972191i | \(-0.424757\pi\) | ||||
0.234189 | + | 0.972191i | \(0.424757\pi\) | |||||||
\(30\) | −0.0664914 | −0.0121396 | ||||||||
\(31\) | −6.07647 | −1.09137 | −0.545683 | − | 0.837992i | \(-0.683730\pi\) | ||||
−0.545683 | + | 0.837992i | \(0.683730\pi\) | |||||||
\(32\) | 0.822636 | 0.145423 | ||||||||
\(33\) | −2.54836 | −0.443612 | ||||||||
\(34\) | −0.0687697 | −0.0117939 | ||||||||
\(35\) | 0.797646 | 0.134827 | ||||||||
\(36\) | −1.99527 | −0.332545 | ||||||||
\(37\) | −5.31637 | −0.874005 | −0.437003 | − | 0.899460i | \(-0.643960\pi\) | ||||
−0.437003 | + | 0.899460i | \(0.643960\pi\) | |||||||
\(38\) | 0.212438 | 0.0344621 | ||||||||
\(39\) | 0.576726 | 0.0923501 | ||||||||
\(40\) | −0.265651 | −0.0420031 | ||||||||
\(41\) | 3.31387 | 0.517540 | 0.258770 | − | 0.965939i | \(-0.416683\pi\) | ||||
0.258770 | + | 0.965939i | \(0.416683\pi\) | |||||||
\(42\) | −0.0567334 | −0.00875416 | ||||||||
\(43\) | 4.06976 | 0.620632 | 0.310316 | − | 0.950633i | \(-0.399565\pi\) | ||||
0.310316 | + | 0.950633i | \(0.399565\pi\) | |||||||
\(44\) | −5.08466 | −0.766542 | ||||||||
\(45\) | 0.966871 | 0.144133 | ||||||||
\(46\) | −0.140718 | −0.0207478 | ||||||||
\(47\) | −6.63993 | −0.968533 | −0.484266 | − | 0.874921i | \(-0.660913\pi\) | ||||
−0.484266 | + | 0.874921i | \(0.660913\pi\) | |||||||
\(48\) | −3.97165 | −0.573258 | ||||||||
\(49\) | −6.31941 | −0.902773 | ||||||||
\(50\) | −0.279560 | −0.0395357 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 1.15073 | 0.159577 | ||||||||
\(53\) | −10.1015 | −1.38755 | −0.693777 | − | 0.720190i | \(-0.744055\pi\) | ||||
−0.693777 | + | 0.720190i | \(0.744055\pi\) | |||||||
\(54\) | −0.0687697 | −0.00935837 | ||||||||
\(55\) | 2.46393 | 0.332236 | ||||||||
\(56\) | −0.226665 | −0.0302894 | ||||||||
\(57\) | −3.08913 | −0.409165 | ||||||||
\(58\) | 0.173457 | 0.0227760 | ||||||||
\(59\) | −10.1129 | −1.31659 | −0.658295 | − | 0.752760i | \(-0.728722\pi\) | ||||
−0.658295 | + | 0.752760i | \(0.728722\pi\) | |||||||
\(60\) | 1.92917 | 0.249055 | ||||||||
\(61\) | 3.84193 | 0.491909 | 0.245955 | − | 0.969281i | \(-0.420899\pi\) | ||||
0.245955 | + | 0.969281i | \(0.420899\pi\) | |||||||
\(62\) | −0.417877 | −0.0530704 | ||||||||
\(63\) | 0.824977 | 0.103937 | ||||||||
\(64\) | −7.88672 | −0.985840 | ||||||||
\(65\) | −0.557620 | −0.0691642 | ||||||||
\(66\) | −0.175250 | −0.0215717 | ||||||||
\(67\) | 12.8564 | 1.57066 | 0.785328 | − | 0.619080i | \(-0.212494\pi\) | ||||
0.785328 | + | 0.619080i | \(0.212494\pi\) | |||||||
\(68\) | 1.99527 | 0.241962 | ||||||||
\(69\) | 2.04623 | 0.246337 | ||||||||
\(70\) | 0.0548539 | 0.00655629 | ||||||||
\(71\) | 6.40860 | 0.760560 | 0.380280 | − | 0.924871i | \(-0.375828\pi\) | ||||
0.380280 | + | 0.924871i | \(0.375828\pi\) | |||||||
\(72\) | −0.274754 | −0.0323800 | ||||||||
\(73\) | 10.2174 | 1.19586 | 0.597929 | − | 0.801549i | \(-0.295991\pi\) | ||||
0.597929 | + | 0.801549i | \(0.295991\pi\) | |||||||
\(74\) | −0.365605 | −0.0425007 | ||||||||
\(75\) | 4.06516 | 0.469404 | ||||||||
\(76\) | −6.16365 | −0.707019 | ||||||||
\(77\) | 2.10234 | 0.239583 | ||||||||
\(78\) | 0.0396613 | 0.00449076 | ||||||||
\(79\) | −2.90388 | −0.326712 | −0.163356 | − | 0.986567i | \(-0.552232\pi\) | ||||
−0.163356 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(80\) | 3.84007 | 0.429333 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.227894 | 0.0251667 | ||||||||
\(83\) | −3.83473 | −0.420916 | −0.210458 | − | 0.977603i | \(-0.567495\pi\) | ||||
−0.210458 | + | 0.977603i | \(0.567495\pi\) | |||||||
\(84\) | 1.64605 | 0.179599 | ||||||||
\(85\) | −0.966871 | −0.104872 | ||||||||
\(86\) | 0.279876 | 0.0301798 | ||||||||
\(87\) | −2.52229 | −0.270418 | ||||||||
\(88\) | −0.700170 | −0.0746384 | ||||||||
\(89\) | 16.7151 | 1.77180 | 0.885901 | − | 0.463874i | \(-0.153541\pi\) | ||||
0.885901 | + | 0.463874i | \(0.153541\pi\) | |||||||
\(90\) | 0.0664914 | 0.00700881 | ||||||||
\(91\) | −0.475786 | −0.0498759 | ||||||||
\(92\) | 4.08278 | 0.425659 | ||||||||
\(93\) | 6.07647 | 0.630100 | ||||||||
\(94\) | −0.456626 | −0.0470973 | ||||||||
\(95\) | 2.98679 | 0.306438 | ||||||||
\(96\) | −0.822636 | −0.0839599 | ||||||||
\(97\) | −4.28099 | −0.434669 | −0.217334 | − | 0.976097i | \(-0.569736\pi\) | ||||
−0.217334 | + | 0.976097i | \(0.569736\pi\) | |||||||
\(98\) | −0.434584 | −0.0438996 | ||||||||
\(99\) | 2.54836 | 0.256120 | ||||||||
\(100\) | 8.11110 | 0.811110 | ||||||||
\(101\) | 9.43930 | 0.939245 | 0.469623 | − | 0.882867i | \(-0.344390\pi\) | ||||
0.469623 | + | 0.882867i | \(0.344390\pi\) | |||||||
\(102\) | 0.0687697 | 0.00680921 | ||||||||
\(103\) | −12.0973 | −1.19198 | −0.595990 | − | 0.802992i | \(-0.703240\pi\) | ||||
−0.595990 | + | 0.802992i | \(0.703240\pi\) | |||||||
\(104\) | 0.158458 | 0.0155380 | ||||||||
\(105\) | −0.797646 | −0.0778423 | ||||||||
\(106\) | −0.694680 | −0.0674733 | ||||||||
\(107\) | 4.73549 | 0.457797 | 0.228899 | − | 0.973450i | \(-0.426488\pi\) | ||||
0.228899 | + | 0.973450i | \(0.426488\pi\) | |||||||
\(108\) | 1.99527 | 0.191995 | ||||||||
\(109\) | −0.611447 | −0.0585660 | −0.0292830 | − | 0.999571i | \(-0.509322\pi\) | ||||
−0.0292830 | + | 0.999571i | \(0.509322\pi\) | |||||||
\(110\) | 0.169444 | 0.0161558 | ||||||||
\(111\) | 5.31637 | 0.504607 | ||||||||
\(112\) | 3.27652 | 0.309602 | ||||||||
\(113\) | −3.91752 | −0.368530 | −0.184265 | − | 0.982877i | \(-0.558990\pi\) | ||||
−0.184265 | + | 0.982877i | \(0.558990\pi\) | |||||||
\(114\) | −0.212438 | −0.0198967 | ||||||||
\(115\) | −1.97844 | −0.184490 | ||||||||
\(116\) | −5.03265 | −0.467270 | ||||||||
\(117\) | −0.576726 | −0.0533184 | ||||||||
\(118\) | −0.695463 | −0.0640225 | ||||||||
\(119\) | −0.824977 | −0.0756255 | ||||||||
\(120\) | 0.265651 | 0.0242505 | ||||||||
\(121\) | −4.50588 | −0.409625 | ||||||||
\(122\) | 0.264209 | 0.0239203 | ||||||||
\(123\) | −3.31387 | −0.298802 | ||||||||
\(124\) | 12.1242 | 1.08878 | ||||||||
\(125\) | −8.76484 | −0.783951 | ||||||||
\(126\) | 0.0567334 | 0.00505421 | ||||||||
\(127\) | 7.91384 | 0.702240 | 0.351120 | − | 0.936330i | \(-0.385801\pi\) | ||||
0.351120 | + | 0.936330i | \(0.385801\pi\) | |||||||
\(128\) | −2.18764 | −0.193362 | ||||||||
\(129\) | −4.06976 | −0.358322 | ||||||||
\(130\) | −0.0383473 | −0.00336328 | ||||||||
\(131\) | −21.4229 | −1.87173 | −0.935865 | − | 0.352358i | \(-0.885380\pi\) | ||||
−0.935865 | + | 0.352358i | \(0.885380\pi\) | |||||||
\(132\) | 5.08466 | 0.442563 | ||||||||
\(133\) | 2.54846 | 0.220980 | ||||||||
\(134\) | 0.884129 | 0.0763771 | ||||||||
\(135\) | −0.966871 | −0.0832150 | ||||||||
\(136\) | 0.274754 | 0.0235599 | ||||||||
\(137\) | 11.9255 | 1.01887 | 0.509434 | − | 0.860510i | \(-0.329855\pi\) | ||||
0.509434 | + | 0.860510i | \(0.329855\pi\) | |||||||
\(138\) | 0.140718 | 0.0119787 | ||||||||
\(139\) | 21.8098 | 1.84989 | 0.924944 | − | 0.380104i | \(-0.124112\pi\) | ||||
0.924944 | + | 0.380104i | \(0.124112\pi\) | |||||||
\(140\) | −1.59152 | −0.134508 | ||||||||
\(141\) | 6.63993 | 0.559183 | ||||||||
\(142\) | 0.440717 | 0.0369842 | ||||||||
\(143\) | −1.46970 | −0.122903 | ||||||||
\(144\) | 3.97165 | 0.330971 | ||||||||
\(145\) | 2.43873 | 0.202525 | ||||||||
\(146\) | 0.702648 | 0.0581516 | ||||||||
\(147\) | 6.31941 | 0.521216 | ||||||||
\(148\) | 10.6076 | 0.871939 | ||||||||
\(149\) | −8.52523 | −0.698414 | −0.349207 | − | 0.937046i | \(-0.613549\pi\) | ||||
−0.349207 | + | 0.937046i | \(0.613549\pi\) | |||||||
\(150\) | 0.279560 | 0.0228260 | ||||||||
\(151\) | −13.9347 | −1.13399 | −0.566994 | − | 0.823722i | \(-0.691894\pi\) | ||||
−0.566994 | + | 0.823722i | \(0.691894\pi\) | |||||||
\(152\) | −0.848749 | −0.0688426 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.144577 | 0.0116503 | ||||||||
\(155\) | −5.87516 | −0.471904 | ||||||||
\(156\) | −1.15073 | −0.0921317 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −0.199699 | −0.0158872 | ||||||||
\(159\) | 10.1015 | 0.801105 | ||||||||
\(160\) | 0.795382 | 0.0628805 | ||||||||
\(161\) | −1.68809 | −0.133040 | ||||||||
\(162\) | 0.0687697 | 0.00540306 | ||||||||
\(163\) | −9.69336 | −0.759243 | −0.379621 | − | 0.925142i | \(-0.623946\pi\) | ||||
−0.379621 | + | 0.925142i | \(0.623946\pi\) | |||||||
\(164\) | −6.61207 | −0.516316 | ||||||||
\(165\) | −2.46393 | −0.191817 | ||||||||
\(166\) | −0.263713 | −0.0204681 | ||||||||
\(167\) | −9.75695 | −0.755015 | −0.377508 | − | 0.926006i | \(-0.623219\pi\) | ||||
−0.377508 | + | 0.926006i | \(0.623219\pi\) | |||||||
\(168\) | 0.226665 | 0.0174876 | ||||||||
\(169\) | −12.6674 | −0.974414 | ||||||||
\(170\) | −0.0664914 | −0.00509966 | ||||||||
\(171\) | 3.08913 | 0.236232 | ||||||||
\(172\) | −8.12026 | −0.619164 | ||||||||
\(173\) | 0.531310 | 0.0403948 | 0.0201974 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201974 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(174\) | −0.173457 | −0.0131497 | ||||||||
\(175\) | −3.35367 | −0.253513 | ||||||||
\(176\) | 10.1212 | 0.762912 | ||||||||
\(177\) | 10.1129 | 0.760134 | ||||||||
\(178\) | 1.14950 | 0.0861583 | ||||||||
\(179\) | −9.59285 | −0.717003 | −0.358502 | − | 0.933529i | \(-0.616712\pi\) | ||||
−0.358502 | + | 0.933529i | \(0.616712\pi\) | |||||||
\(180\) | −1.92917 | −0.143792 | ||||||||
\(181\) | −9.73938 | −0.723922 | −0.361961 | − | 0.932193i | \(-0.617893\pi\) | ||||
−0.361961 | + | 0.932193i | \(0.617893\pi\) | |||||||
\(182\) | −0.0327197 | −0.00242534 | ||||||||
\(183\) | −3.84193 | −0.284004 | ||||||||
\(184\) | 0.562208 | 0.0414465 | ||||||||
\(185\) | −5.14024 | −0.377918 | ||||||||
\(186\) | 0.417877 | 0.0306402 | ||||||||
\(187\) | −2.54836 | −0.186354 | ||||||||
\(188\) | 13.2484 | 0.966242 | ||||||||
\(189\) | −0.824977 | −0.0600083 | ||||||||
\(190\) | 0.205400 | 0.0149013 | ||||||||
\(191\) | 6.94877 | 0.502795 | 0.251398 | − | 0.967884i | \(-0.419110\pi\) | ||||
0.251398 | + | 0.967884i | \(0.419110\pi\) | |||||||
\(192\) | 7.88672 | 0.569175 | ||||||||
\(193\) | 3.53567 | 0.254503 | 0.127251 | − | 0.991870i | \(-0.459384\pi\) | ||||
0.127251 | + | 0.991870i | \(0.459384\pi\) | |||||||
\(194\) | −0.294402 | −0.0211369 | ||||||||
\(195\) | 0.557620 | 0.0399320 | ||||||||
\(196\) | 12.6089 | 0.900639 | ||||||||
\(197\) | 5.99851 | 0.427376 | 0.213688 | − | 0.976902i | \(-0.431452\pi\) | ||||
0.213688 | + | 0.976902i | \(0.431452\pi\) | |||||||
\(198\) | 0.175250 | 0.0124545 | ||||||||
\(199\) | 13.5931 | 0.963591 | 0.481796 | − | 0.876284i | \(-0.339985\pi\) | ||||
0.481796 | + | 0.876284i | \(0.339985\pi\) | |||||||
\(200\) | 1.11692 | 0.0789780 | ||||||||
\(201\) | −12.8564 | −0.906819 | ||||||||
\(202\) | 0.649138 | 0.0456732 | ||||||||
\(203\) | 2.08083 | 0.146046 | ||||||||
\(204\) | −1.99527 | −0.139697 | ||||||||
\(205\) | 3.20408 | 0.223783 | ||||||||
\(206\) | −0.831926 | −0.0579630 | ||||||||
\(207\) | −2.04623 | −0.142223 | ||||||||
\(208\) | −2.29055 | −0.158821 | ||||||||
\(209\) | 7.87220 | 0.544532 | ||||||||
\(210\) | −0.0548539 | −0.00378528 | ||||||||
\(211\) | −14.8816 | −1.02449 | −0.512247 | − | 0.858838i | \(-0.671187\pi\) | ||||
−0.512247 | + | 0.858838i | \(0.671187\pi\) | |||||||
\(212\) | 20.1553 | 1.38427 | ||||||||
\(213\) | −6.40860 | −0.439110 | ||||||||
\(214\) | 0.325658 | 0.0222615 | ||||||||
\(215\) | 3.93493 | 0.268360 | ||||||||
\(216\) | 0.274754 | 0.0186946 | ||||||||
\(217\) | −5.01295 | −0.340301 | ||||||||
\(218\) | −0.0420490 | −0.00284792 | ||||||||
\(219\) | −10.2174 | −0.690429 | ||||||||
\(220\) | −4.91621 | −0.331451 | ||||||||
\(221\) | 0.576726 | 0.0387948 | ||||||||
\(222\) | 0.365605 | 0.0245378 | ||||||||
\(223\) | −4.95072 | −0.331525 | −0.165762 | − | 0.986166i | \(-0.553008\pi\) | ||||
−0.165762 | + | 0.986166i | \(0.553008\pi\) | |||||||
\(224\) | 0.678656 | 0.0453446 | ||||||||
\(225\) | −4.06516 | −0.271011 | ||||||||
\(226\) | −0.269407 | −0.0179207 | ||||||||
\(227\) | −11.0409 | −0.732809 | −0.366405 | − | 0.930456i | \(-0.619411\pi\) | ||||
−0.366405 | + | 0.930456i | \(0.619411\pi\) | |||||||
\(228\) | 6.16365 | 0.408198 | ||||||||
\(229\) | 9.24283 | 0.610783 | 0.305392 | − | 0.952227i | \(-0.401213\pi\) | ||||
0.305392 | + | 0.952227i | \(0.401213\pi\) | |||||||
\(230\) | −0.136056 | −0.00897130 | ||||||||
\(231\) | −2.10234 | −0.138324 | ||||||||
\(232\) | −0.693007 | −0.0454982 | ||||||||
\(233\) | 2.08683 | 0.136713 | 0.0683565 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683565 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(234\) | −0.0396613 | −0.00259274 | ||||||||
\(235\) | −6.41995 | −0.418791 | ||||||||
\(236\) | 20.1780 | 1.31348 | ||||||||
\(237\) | 2.90388 | 0.188627 | ||||||||
\(238\) | −0.0567334 | −0.00367748 | ||||||||
\(239\) | 0.540533 | 0.0349642 | 0.0174821 | − | 0.999847i | \(-0.494435\pi\) | ||||
0.0174821 | + | 0.999847i | \(0.494435\pi\) | |||||||
\(240\) | −3.84007 | −0.247875 | ||||||||
\(241\) | 9.24566 | 0.595565 | 0.297783 | − | 0.954634i | \(-0.403753\pi\) | ||||
0.297783 | + | 0.954634i | \(0.403753\pi\) | |||||||
\(242\) | −0.309868 | −0.0199191 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.66570 | −0.490746 | ||||||||
\(245\) | −6.11005 | −0.390357 | ||||||||
\(246\) | −0.227894 | −0.0145300 | ||||||||
\(247\) | −1.78158 | −0.113359 | ||||||||
\(248\) | 1.66953 | 0.106015 | ||||||||
\(249\) | 3.83473 | 0.243016 | ||||||||
\(250\) | −0.602755 | −0.0381216 | ||||||||
\(251\) | −17.7905 | −1.12293 | −0.561463 | − | 0.827502i | \(-0.689761\pi\) | ||||
−0.561463 | + | 0.827502i | \(0.689761\pi\) | |||||||
\(252\) | −1.64605 | −0.103692 | ||||||||
\(253\) | −5.21452 | −0.327834 | ||||||||
\(254\) | 0.544232 | 0.0341482 | ||||||||
\(255\) | 0.966871 | 0.0605478 | ||||||||
\(256\) | 15.6230 | 0.976437 | ||||||||
\(257\) | −2.87289 | −0.179206 | −0.0896029 | − | 0.995978i | \(-0.528560\pi\) | ||||
−0.0896029 | + | 0.995978i | \(0.528560\pi\) | |||||||
\(258\) | −0.279876 | −0.0174243 | ||||||||
\(259\) | −4.38588 | −0.272525 | ||||||||
\(260\) | 1.11260 | 0.0690007 | ||||||||
\(261\) | 2.52229 | 0.156126 | ||||||||
\(262\) | −1.47325 | −0.0910176 | ||||||||
\(263\) | 18.6756 | 1.15159 | 0.575794 | − | 0.817595i | \(-0.304693\pi\) | ||||
0.575794 | + | 0.817595i | \(0.304693\pi\) | |||||||
\(264\) | 0.700170 | 0.0430925 | ||||||||
\(265\) | −9.76689 | −0.599975 | ||||||||
\(266\) | 0.175257 | 0.0107457 | ||||||||
\(267\) | −16.7151 | −1.02295 | ||||||||
\(268\) | −25.6519 | −1.56694 | ||||||||
\(269\) | 14.3871 | 0.877195 | 0.438597 | − | 0.898684i | \(-0.355475\pi\) | ||||
0.438597 | + | 0.898684i | \(0.355475\pi\) | |||||||
\(270\) | −0.0664914 | −0.00404654 | ||||||||
\(271\) | 21.8858 | 1.32947 | 0.664734 | − | 0.747080i | \(-0.268545\pi\) | ||||
0.664734 | + | 0.747080i | \(0.268545\pi\) | |||||||
\(272\) | −3.97165 | −0.240816 | ||||||||
\(273\) | 0.475786 | 0.0287959 | ||||||||
\(274\) | 0.820116 | 0.0495450 | ||||||||
\(275\) | −10.3595 | −0.624700 | ||||||||
\(276\) | −4.08278 | −0.245754 | ||||||||
\(277\) | −26.1129 | −1.56897 | −0.784485 | − | 0.620147i | \(-0.787073\pi\) | ||||
−0.784485 | + | 0.620147i | \(0.787073\pi\) | |||||||
\(278\) | 1.49986 | 0.0899554 | ||||||||
\(279\) | −6.07647 | −0.363789 | ||||||||
\(280\) | −0.219156 | −0.0130971 | ||||||||
\(281\) | −11.3572 | −0.677516 | −0.338758 | − | 0.940874i | \(-0.610007\pi\) | ||||
−0.338758 | + | 0.940874i | \(0.610007\pi\) | |||||||
\(282\) | 0.456626 | 0.0271917 | ||||||||
\(283\) | −11.2005 | −0.665803 | −0.332901 | − | 0.942962i | \(-0.608028\pi\) | ||||
−0.332901 | + | 0.942962i | \(0.608028\pi\) | |||||||
\(284\) | −12.7869 | −0.758762 | ||||||||
\(285\) | −2.98679 | −0.176922 | ||||||||
\(286\) | −0.101071 | −0.00597646 | ||||||||
\(287\) | 2.73387 | 0.161375 | ||||||||
\(288\) | 0.822636 | 0.0484743 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.167710 | 0.00984829 | ||||||||
\(291\) | 4.28099 | 0.250956 | ||||||||
\(292\) | −20.3865 | −1.19303 | ||||||||
\(293\) | −30.9160 | −1.80613 | −0.903066 | − | 0.429503i | \(-0.858689\pi\) | ||||
−0.903066 | + | 0.429503i | \(0.858689\pi\) | |||||||
\(294\) | 0.434584 | 0.0253455 | ||||||||
\(295\) | −9.77789 | −0.569291 | ||||||||
\(296\) | 1.46069 | 0.0849009 | ||||||||
\(297\) | −2.54836 | −0.147871 | ||||||||
\(298\) | −0.586278 | −0.0339621 | ||||||||
\(299\) | 1.18011 | 0.0682477 | ||||||||
\(300\) | −8.11110 | −0.468294 | ||||||||
\(301\) | 3.35746 | 0.193521 | ||||||||
\(302\) | −0.958283 | −0.0551430 | ||||||||
\(303\) | −9.43930 | −0.542274 | ||||||||
\(304\) | 12.2689 | 0.703671 | ||||||||
\(305\) | 3.71465 | 0.212700 | ||||||||
\(306\) | −0.0687697 | −0.00393130 | ||||||||
\(307\) | 1.62405 | 0.0926896 | 0.0463448 | − | 0.998926i | \(-0.485243\pi\) | ||||
0.0463448 | + | 0.998926i | \(0.485243\pi\) | |||||||
\(308\) | −4.19473 | −0.239017 | ||||||||
\(309\) | 12.0973 | 0.688190 | ||||||||
\(310\) | −0.404033 | −0.0229475 | ||||||||
\(311\) | −11.2601 | −0.638504 | −0.319252 | − | 0.947670i | \(-0.603432\pi\) | ||||
−0.319252 | + | 0.947670i | \(0.603432\pi\) | |||||||
\(312\) | −0.158458 | −0.00897089 | ||||||||
\(313\) | −22.5098 | −1.27233 | −0.636164 | − | 0.771554i | \(-0.719480\pi\) | ||||
−0.636164 | + | 0.771554i | \(0.719480\pi\) | |||||||
\(314\) | −0.0687697 | −0.00388090 | ||||||||
\(315\) | 0.797646 | 0.0449423 | ||||||||
\(316\) | 5.79403 | 0.325940 | ||||||||
\(317\) | −2.96039 | −0.166272 | −0.0831360 | − | 0.996538i | \(-0.526494\pi\) | ||||
−0.0831360 | + | 0.996538i | \(0.526494\pi\) | |||||||
\(318\) | 0.694680 | 0.0389557 | ||||||||
\(319\) | 6.42769 | 0.359882 | ||||||||
\(320\) | −7.62544 | −0.426275 | ||||||||
\(321\) | −4.73549 | −0.264309 | ||||||||
\(322\) | −0.116089 | −0.00646941 | ||||||||
\(323\) | −3.08913 | −0.171884 | ||||||||
\(324\) | −1.99527 | −0.110848 | ||||||||
\(325\) | 2.34449 | 0.130049 | ||||||||
\(326\) | −0.666609 | −0.0369201 | ||||||||
\(327\) | 0.611447 | 0.0338131 | ||||||||
\(328\) | −0.910498 | −0.0502738 | ||||||||
\(329\) | −5.47779 | −0.302000 | ||||||||
\(330\) | −0.169444 | −0.00932757 | ||||||||
\(331\) | 4.04784 | 0.222490 | 0.111245 | − | 0.993793i | \(-0.464516\pi\) | ||||
0.111245 | + | 0.993793i | \(0.464516\pi\) | |||||||
\(332\) | 7.65132 | 0.419921 | ||||||||
\(333\) | −5.31637 | −0.291335 | ||||||||
\(334\) | −0.670982 | −0.0367145 | ||||||||
\(335\) | 12.4304 | 0.679148 | ||||||||
\(336\) | −3.27652 | −0.178749 | ||||||||
\(337\) | 0.477945 | 0.0260353 | 0.0130177 | − | 0.999915i | \(-0.495856\pi\) | ||||
0.0130177 | + | 0.999915i | \(0.495856\pi\) | |||||||
\(338\) | −0.871132 | −0.0473833 | ||||||||
\(339\) | 3.91752 | 0.212771 | ||||||||
\(340\) | 1.92917 | 0.104624 | ||||||||
\(341\) | −15.4850 | −0.838560 | ||||||||
\(342\) | 0.212438 | 0.0114874 | ||||||||
\(343\) | −10.9882 | −0.593308 | ||||||||
\(344\) | −1.11818 | −0.0602882 | ||||||||
\(345\) | 1.97844 | 0.106515 | ||||||||
\(346\) | 0.0365380 | 0.00196430 | ||||||||
\(347\) | −25.3343 | −1.36002 | −0.680009 | − | 0.733204i | \(-0.738024\pi\) | ||||
−0.680009 | + | 0.733204i | \(0.738024\pi\) | |||||||
\(348\) | 5.03265 | 0.269778 | ||||||||
\(349\) | 15.8302 | 0.847372 | 0.423686 | − | 0.905809i | \(-0.360736\pi\) | ||||
0.423686 | + | 0.905809i | \(0.360736\pi\) | |||||||
\(350\) | −0.230631 | −0.0123277 | ||||||||
\(351\) | 0.576726 | 0.0307834 | ||||||||
\(352\) | 2.09637 | 0.111737 | ||||||||
\(353\) | −24.6173 | −1.31024 | −0.655122 | − | 0.755523i | \(-0.727383\pi\) | ||||
−0.655122 | + | 0.755523i | \(0.727383\pi\) | |||||||
\(354\) | 0.695463 | 0.0369634 | ||||||||
\(355\) | 6.19628 | 0.328865 | ||||||||
\(356\) | −33.3512 | −1.76761 | ||||||||
\(357\) | 0.824977 | 0.0436624 | ||||||||
\(358\) | −0.659697 | −0.0348661 | ||||||||
\(359\) | −7.01481 | −0.370228 | −0.185114 | − | 0.982717i | \(-0.559265\pi\) | ||||
−0.185114 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(360\) | −0.265651 | −0.0140010 | ||||||||
\(361\) | −9.45729 | −0.497752 | ||||||||
\(362\) | −0.669774 | −0.0352025 | ||||||||
\(363\) | 4.50588 | 0.236497 | ||||||||
\(364\) | 0.949322 | 0.0497580 | ||||||||
\(365\) | 9.87892 | 0.517086 | ||||||||
\(366\) | −0.264209 | −0.0138104 | ||||||||
\(367\) | 3.84028 | 0.200461 | 0.100231 | − | 0.994964i | \(-0.468042\pi\) | ||||
0.100231 | + | 0.994964i | \(0.468042\pi\) | |||||||
\(368\) | −8.12689 | −0.423643 | ||||||||
\(369\) | 3.31387 | 0.172513 | ||||||||
\(370\) | −0.353493 | −0.0183772 | ||||||||
\(371\) | −8.33355 | −0.432656 | ||||||||
\(372\) | −12.1242 | −0.628610 | ||||||||
\(373\) | 24.4529 | 1.26612 | 0.633062 | − | 0.774101i | \(-0.281798\pi\) | ||||
0.633062 | + | 0.774101i | \(0.281798\pi\) | |||||||
\(374\) | −0.175250 | −0.00906195 | ||||||||
\(375\) | 8.76484 | 0.452614 | ||||||||
\(376\) | 1.82434 | 0.0940833 | ||||||||
\(377\) | −1.45467 | −0.0749193 | ||||||||
\(378\) | −0.0567334 | −0.00291805 | ||||||||
\(379\) | 13.3686 | 0.686697 | 0.343349 | − | 0.939208i | \(-0.388439\pi\) | ||||
0.343349 | + | 0.939208i | \(0.388439\pi\) | |||||||
\(380\) | −5.95945 | −0.305713 | ||||||||
\(381\) | −7.91384 | −0.405438 | ||||||||
\(382\) | 0.477864 | 0.0244497 | ||||||||
\(383\) | −32.9298 | −1.68264 | −0.841318 | − | 0.540541i | \(-0.818220\pi\) | ||||
−0.841318 | + | 0.540541i | \(0.818220\pi\) | |||||||
\(384\) | 2.18764 | 0.111637 | ||||||||
\(385\) | 2.03269 | 0.103595 | ||||||||
\(386\) | 0.243147 | 0.0123758 | ||||||||
\(387\) | 4.06976 | 0.206877 | ||||||||
\(388\) | 8.54173 | 0.433641 | ||||||||
\(389\) | −0.409278 | −0.0207512 | −0.0103756 | − | 0.999946i | \(-0.503303\pi\) | ||||
−0.0103756 | + | 0.999946i | \(0.503303\pi\) | |||||||
\(390\) | 0.0383473 | 0.00194179 | ||||||||
\(391\) | 2.04623 | 0.103482 | ||||||||
\(392\) | 1.73628 | 0.0876954 | ||||||||
\(393\) | 21.4229 | 1.08064 | ||||||||
\(394\) | 0.412516 | 0.0207822 | ||||||||
\(395\) | −2.80768 | −0.141270 | ||||||||
\(396\) | −5.08466 | −0.255514 | ||||||||
\(397\) | 7.91068 | 0.397026 | 0.198513 | − | 0.980098i | \(-0.436389\pi\) | ||||
0.198513 | + | 0.980098i | \(0.436389\pi\) | |||||||
\(398\) | 0.934795 | 0.0468570 | ||||||||
\(399\) | −2.54846 | −0.127583 | ||||||||
\(400\) | −16.1454 | −0.807269 | ||||||||
\(401\) | 32.2072 | 1.60835 | 0.804175 | − | 0.594393i | \(-0.202608\pi\) | ||||
0.804175 | + | 0.594393i | \(0.202608\pi\) | |||||||
\(402\) | −0.884129 | −0.0440963 | ||||||||
\(403\) | 3.50446 | 0.174569 | ||||||||
\(404\) | −18.8340 | −0.937024 | ||||||||
\(405\) | 0.966871 | 0.0480442 | ||||||||
\(406\) | 0.143098 | 0.00710184 | ||||||||
\(407\) | −13.5480 | −0.671549 | ||||||||
\(408\) | −0.274754 | −0.0136023 | ||||||||
\(409\) | −5.31972 | −0.263043 | −0.131522 | − | 0.991313i | \(-0.541986\pi\) | ||||
−0.131522 | + | 0.991313i | \(0.541986\pi\) | |||||||
\(410\) | 0.220344 | 0.0108820 | ||||||||
\(411\) | −11.9255 | −0.588244 | ||||||||
\(412\) | 24.1373 | 1.18916 | ||||||||
\(413\) | −8.34293 | −0.410529 | ||||||||
\(414\) | −0.140718 | −0.00691593 | ||||||||
\(415\) | −3.70768 | −0.182003 | ||||||||
\(416\) | −0.474436 | −0.0232611 | ||||||||
\(417\) | −21.8098 | −1.06803 | ||||||||
\(418\) | 0.541369 | 0.0264792 | ||||||||
\(419\) | −30.2684 | −1.47871 | −0.739353 | − | 0.673318i | \(-0.764869\pi\) | ||||
−0.739353 | + | 0.673318i | \(0.764869\pi\) | |||||||
\(420\) | 1.59152 | 0.0776582 | ||||||||
\(421\) | −4.19061 | −0.204238 | −0.102119 | − | 0.994772i | \(-0.532562\pi\) | ||||
−0.102119 | + | 0.994772i | \(0.532562\pi\) | |||||||
\(422\) | −1.02341 | −0.0498186 | ||||||||
\(423\) | −6.63993 | −0.322844 | ||||||||
\(424\) | 2.77544 | 0.134787 | ||||||||
\(425\) | 4.06516 | 0.197189 | ||||||||
\(426\) | −0.440717 | −0.0213528 | ||||||||
\(427\) | 3.16951 | 0.153383 | ||||||||
\(428\) | −9.44859 | −0.456715 | ||||||||
\(429\) | 1.46970 | 0.0709580 | ||||||||
\(430\) | 0.270604 | 0.0130497 | ||||||||
\(431\) | 0.408370 | 0.0196705 | 0.00983525 | − | 0.999952i | \(-0.496869\pi\) | ||||
0.00983525 | + | 0.999952i | \(0.496869\pi\) | |||||||
\(432\) | −3.97165 | −0.191086 | ||||||||
\(433\) | −33.2431 | −1.59756 | −0.798781 | − | 0.601622i | \(-0.794521\pi\) | ||||
−0.798781 | + | 0.601622i | \(0.794521\pi\) | |||||||
\(434\) | −0.344739 | −0.0165480 | ||||||||
\(435\) | −2.43873 | −0.116928 | ||||||||
\(436\) | 1.22000 | 0.0584275 | ||||||||
\(437\) | −6.32106 | −0.302377 | ||||||||
\(438\) | −0.702648 | −0.0335738 | ||||||||
\(439\) | 19.7194 | 0.941155 | 0.470577 | − | 0.882359i | \(-0.344046\pi\) | ||||
0.470577 | + | 0.882359i | \(0.344046\pi\) | |||||||
\(440\) | −0.676974 | −0.0322735 | ||||||||
\(441\) | −6.31941 | −0.300924 | ||||||||
\(442\) | 0.0396613 | 0.00188649 | ||||||||
\(443\) | −7.83890 | −0.372438 | −0.186219 | − | 0.982508i | \(-0.559623\pi\) | ||||
−0.186219 | + | 0.982508i | \(0.559623\pi\) | |||||||
\(444\) | −10.6076 | −0.503414 | ||||||||
\(445\) | 16.1614 | 0.766123 | ||||||||
\(446\) | −0.340460 | −0.0161212 | ||||||||
\(447\) | 8.52523 | 0.403230 | ||||||||
\(448\) | −6.50637 | −0.307397 | ||||||||
\(449\) | −1.68732 | −0.0796294 | −0.0398147 | − | 0.999207i | \(-0.512677\pi\) | ||||
−0.0398147 | + | 0.999207i | \(0.512677\pi\) | |||||||
\(450\) | −0.279560 | −0.0131786 | ||||||||
\(451\) | 8.44493 | 0.397656 | ||||||||
\(452\) | 7.81652 | 0.367658 | ||||||||
\(453\) | 13.9347 | 0.654708 | ||||||||
\(454\) | −0.759278 | −0.0356347 | ||||||||
\(455\) | −0.460024 | −0.0215662 | ||||||||
\(456\) | 0.848749 | 0.0397463 | ||||||||
\(457\) | −35.9817 | −1.68315 | −0.841577 | − | 0.540137i | \(-0.818373\pi\) | ||||
−0.841577 | + | 0.540137i | \(0.818373\pi\) | |||||||
\(458\) | 0.635626 | 0.0297009 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 3.94752 | 0.184054 | ||||||||
\(461\) | −30.0935 | −1.40159 | −0.700796 | − | 0.713361i | \(-0.747172\pi\) | ||||
−0.700796 | + | 0.713361i | \(0.747172\pi\) | |||||||
\(462\) | −0.144577 | −0.00672633 | ||||||||
\(463\) | −10.7252 | −0.498443 | −0.249221 | − | 0.968447i | \(-0.580175\pi\) | ||||
−0.249221 | + | 0.968447i | \(0.580175\pi\) | |||||||
\(464\) | 10.0176 | 0.465057 | ||||||||
\(465\) | 5.87516 | 0.272454 | ||||||||
\(466\) | 0.143511 | 0.00664801 | ||||||||
\(467\) | 17.6134 | 0.815050 | 0.407525 | − | 0.913194i | \(-0.366392\pi\) | ||||
0.407525 | + | 0.913194i | \(0.366392\pi\) | |||||||
\(468\) | 1.15073 | 0.0531923 | ||||||||
\(469\) | 10.6062 | 0.489749 | ||||||||
\(470\) | −0.441498 | −0.0203648 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 2.77856 | 0.127894 | ||||||||
\(473\) | 10.3712 | 0.476868 | ||||||||
\(474\) | 0.199699 | 0.00917248 | ||||||||
\(475\) | −12.5578 | −0.576192 | ||||||||
\(476\) | 1.64605 | 0.0754467 | ||||||||
\(477\) | −10.1015 | −0.462518 | ||||||||
\(478\) | 0.0371723 | 0.00170022 | ||||||||
\(479\) | 29.8068 | 1.36191 | 0.680955 | − | 0.732325i | \(-0.261565\pi\) | ||||
0.680955 | + | 0.732325i | \(0.261565\pi\) | |||||||
\(480\) | −0.795382 | −0.0363041 | ||||||||
\(481\) | 3.06609 | 0.139802 | ||||||||
\(482\) | 0.635821 | 0.0289609 | ||||||||
\(483\) | 1.68809 | 0.0768108 | ||||||||
\(484\) | 8.99044 | 0.408657 | ||||||||
\(485\) | −4.13916 | −0.187950 | ||||||||
\(486\) | −0.0687697 | −0.00311946 | ||||||||
\(487\) | 14.5380 | 0.658782 | 0.329391 | − | 0.944194i | \(-0.393157\pi\) | ||||
0.329391 | + | 0.944194i | \(0.393157\pi\) | |||||||
\(488\) | −1.05558 | −0.0477841 | ||||||||
\(489\) | 9.69336 | 0.438349 | ||||||||
\(490\) | −0.420186 | −0.0189821 | ||||||||
\(491\) | 18.0350 | 0.813907 | 0.406954 | − | 0.913449i | \(-0.366591\pi\) | ||||
0.406954 | + | 0.913449i | \(0.366591\pi\) | |||||||
\(492\) | 6.61207 | 0.298095 | ||||||||
\(493\) | −2.52229 | −0.113598 | ||||||||
\(494\) | −0.122519 | −0.00551238 | ||||||||
\(495\) | 2.46393 | 0.110745 | ||||||||
\(496\) | −24.1336 | −1.08363 | ||||||||
\(497\) | 5.28695 | 0.237152 | ||||||||
\(498\) | 0.263713 | 0.0118173 | ||||||||
\(499\) | −17.6642 | −0.790759 | −0.395380 | − | 0.918518i | \(-0.629387\pi\) | ||||
−0.395380 | + | 0.918518i | \(0.629387\pi\) | |||||||
\(500\) | 17.4882 | 0.782097 | ||||||||
\(501\) | 9.75695 | 0.435908 | ||||||||
\(502\) | −1.22345 | −0.0546051 | ||||||||
\(503\) | 10.6248 | 0.473738 | 0.236869 | − | 0.971542i | \(-0.423879\pi\) | ||||
0.236869 | + | 0.971542i | \(0.423879\pi\) | |||||||
\(504\) | −0.226665 | −0.0100965 | ||||||||
\(505\) | 9.12658 | 0.406127 | ||||||||
\(506\) | −0.358601 | −0.0159417 | ||||||||
\(507\) | 12.6674 | 0.562578 | ||||||||
\(508\) | −15.7903 | −0.700579 | ||||||||
\(509\) | 3.24495 | 0.143830 | 0.0719148 | − | 0.997411i | \(-0.477089\pi\) | ||||
0.0719148 | + | 0.997411i | \(0.477089\pi\) | |||||||
\(510\) | 0.0664914 | 0.00294429 | ||||||||
\(511\) | 8.42913 | 0.372883 | ||||||||
\(512\) | 5.44967 | 0.240844 | ||||||||
\(513\) | −3.08913 | −0.136388 | ||||||||
\(514\) | −0.197568 | −0.00871433 | ||||||||
\(515\) | −11.6965 | −0.515409 | ||||||||
\(516\) | 8.12026 | 0.357475 | ||||||||
\(517\) | −16.9209 | −0.744180 | ||||||||
\(518\) | −0.301616 | −0.0132522 | ||||||||
\(519\) | −0.531310 | −0.0233219 | ||||||||
\(520\) | 0.153208 | 0.00671861 | ||||||||
\(521\) | −10.2212 | −0.447799 | −0.223900 | − | 0.974612i | \(-0.571879\pi\) | ||||
−0.223900 | + | 0.974612i | \(0.571879\pi\) | |||||||
\(522\) | 0.173457 | 0.00759200 | ||||||||
\(523\) | 10.4413 | 0.456565 | 0.228283 | − | 0.973595i | \(-0.426689\pi\) | ||||
0.228283 | + | 0.973595i | \(0.426689\pi\) | |||||||
\(524\) | 42.7446 | 1.86730 | ||||||||
\(525\) | 3.35367 | 0.146366 | ||||||||
\(526\) | 1.28432 | 0.0559989 | ||||||||
\(527\) | 6.07647 | 0.264695 | ||||||||
\(528\) | −10.1212 | −0.440468 | ||||||||
\(529\) | −18.8130 | −0.817955 | ||||||||
\(530\) | −0.671666 | −0.0291753 | ||||||||
\(531\) | −10.1129 | −0.438864 | ||||||||
\(532\) | −5.08487 | −0.220457 | ||||||||
\(533\) | −1.91120 | −0.0827831 | ||||||||
\(534\) | −1.14950 | −0.0497435 | ||||||||
\(535\) | 4.57861 | 0.197951 | ||||||||
\(536\) | −3.53233 | −0.152574 | ||||||||
\(537\) | 9.59285 | 0.413962 | ||||||||
\(538\) | 0.989394 | 0.0426558 | ||||||||
\(539\) | −16.1041 | −0.693654 | ||||||||
\(540\) | 1.92917 | 0.0830182 | ||||||||
\(541\) | −32.5297 | −1.39856 | −0.699280 | − | 0.714848i | \(-0.746496\pi\) | ||||
−0.699280 | + | 0.714848i | \(0.746496\pi\) | |||||||
\(542\) | 1.50508 | 0.0646487 | ||||||||
\(543\) | 9.73938 | 0.417957 | ||||||||
\(544\) | −0.822636 | −0.0352702 | ||||||||
\(545\) | −0.591190 | −0.0253238 | ||||||||
\(546\) | 0.0327197 | 0.00140027 | ||||||||
\(547\) | −39.2313 | −1.67741 | −0.838705 | − | 0.544586i | \(-0.816687\pi\) | ||||
−0.838705 | + | 0.544586i | \(0.816687\pi\) | |||||||
\(548\) | −23.7947 | −1.01646 | ||||||||
\(549\) | 3.84193 | 0.163970 | ||||||||
\(550\) | −0.712418 | −0.0303776 | ||||||||
\(551\) | 7.79167 | 0.331936 | ||||||||
\(552\) | −0.562208 | −0.0239292 | ||||||||
\(553\) | −2.39564 | −0.101873 | ||||||||
\(554\) | −1.79577 | −0.0762951 | ||||||||
\(555\) | 5.14024 | 0.218191 | ||||||||
\(556\) | −43.5166 | −1.84551 | ||||||||
\(557\) | −10.5474 | −0.446908 | −0.223454 | − | 0.974714i | \(-0.571733\pi\) | ||||
−0.223454 | + | 0.974714i | \(0.571733\pi\) | |||||||
\(558\) | −0.417877 | −0.0176901 | ||||||||
\(559\) | −2.34714 | −0.0992732 | ||||||||
\(560\) | 3.16797 | 0.133871 | ||||||||
\(561\) | 2.54836 | 0.107592 | ||||||||
\(562\) | −0.781033 | −0.0329459 | ||||||||
\(563\) | 6.89047 | 0.290399 | 0.145199 | − | 0.989402i | \(-0.453618\pi\) | ||||
0.145199 | + | 0.989402i | \(0.453618\pi\) | |||||||
\(564\) | −13.2484 | −0.557860 | ||||||||
\(565\) | −3.78774 | −0.159351 | ||||||||
\(566\) | −0.770257 | −0.0323763 | ||||||||
\(567\) | 0.824977 | 0.0346458 | ||||||||
\(568\) | −1.76078 | −0.0738809 | ||||||||
\(569\) | −27.2018 | −1.14036 | −0.570179 | − | 0.821521i | \(-0.693126\pi\) | ||||
−0.570179 | + | 0.821521i | \(0.693126\pi\) | |||||||
\(570\) | −0.205400 | −0.00860328 | ||||||||
\(571\) | −25.2597 | −1.05709 | −0.528543 | − | 0.848906i | \(-0.677262\pi\) | ||||
−0.528543 | + | 0.848906i | \(0.677262\pi\) | |||||||
\(572\) | 2.93246 | 0.122612 | ||||||||
\(573\) | −6.94877 | −0.290289 | ||||||||
\(574\) | 0.188007 | 0.00784727 | ||||||||
\(575\) | 8.31824 | 0.346895 | ||||||||
\(576\) | −7.88672 | −0.328613 | ||||||||
\(577\) | −37.0556 | −1.54265 | −0.771323 | − | 0.636444i | \(-0.780405\pi\) | ||||
−0.771323 | + | 0.636444i | \(0.780405\pi\) | |||||||
\(578\) | 0.0687697 | 0.00286044 | ||||||||
\(579\) | −3.53567 | −0.146937 | ||||||||
\(580\) | −4.86592 | −0.202046 | ||||||||
\(581\) | −3.16356 | −0.131247 | ||||||||
\(582\) | 0.294402 | 0.0122034 | ||||||||
\(583\) | −25.7424 | −1.06614 | ||||||||
\(584\) | −2.80727 | −0.116166 | ||||||||
\(585\) | −0.557620 | −0.0230547 | ||||||||
\(586\) | −2.12608 | −0.0878277 | ||||||||
\(587\) | 17.3541 | 0.716282 | 0.358141 | − | 0.933668i | \(-0.383411\pi\) | ||||
0.358141 | + | 0.933668i | \(0.383411\pi\) | |||||||
\(588\) | −12.6089 | −0.519984 | ||||||||
\(589\) | −18.7710 | −0.773445 | ||||||||
\(590\) | −0.672423 | −0.0276832 | ||||||||
\(591\) | −5.99851 | −0.246746 | ||||||||
\(592\) | −21.1147 | −0.867810 | ||||||||
\(593\) | 29.6823 | 1.21890 | 0.609452 | − | 0.792823i | \(-0.291389\pi\) | ||||
0.609452 | + | 0.792823i | \(0.291389\pi\) | |||||||
\(594\) | −0.175250 | −0.00719058 | ||||||||
\(595\) | −0.797646 | −0.0327003 | ||||||||
\(596\) | 17.0101 | 0.696763 | ||||||||
\(597\) | −13.5931 | −0.556330 | ||||||||
\(598\) | 0.0811560 | 0.00331871 | ||||||||
\(599\) | −41.6829 | −1.70312 | −0.851558 | − | 0.524260i | \(-0.824342\pi\) | ||||
−0.851558 | + | 0.524260i | \(0.824342\pi\) | |||||||
\(600\) | −1.11692 | −0.0455980 | ||||||||
\(601\) | 19.5374 | 0.796947 | 0.398474 | − | 0.917180i | \(-0.369540\pi\) | ||||
0.398474 | + | 0.917180i | \(0.369540\pi\) | |||||||
\(602\) | 0.230891 | 0.00941042 | ||||||||
\(603\) | 12.8564 | 0.523552 | ||||||||
\(604\) | 27.8035 | 1.13131 | ||||||||
\(605\) | −4.35660 | −0.177121 | ||||||||
\(606\) | −0.649138 | −0.0263694 | ||||||||
\(607\) | −17.4722 | −0.709175 | −0.354587 | − | 0.935023i | \(-0.615379\pi\) | ||||
−0.354587 | + | 0.935023i | \(0.615379\pi\) | |||||||
\(608\) | 2.54123 | 0.103060 | ||||||||
\(609\) | −2.08083 | −0.0843195 | ||||||||
\(610\) | 0.255455 | 0.0103431 | ||||||||
\(611\) | 3.82942 | 0.154922 | ||||||||
\(612\) | 1.99527 | 0.0806540 | ||||||||
\(613\) | −28.1104 | −1.13537 | −0.567684 | − | 0.823246i | \(-0.692161\pi\) | ||||
−0.567684 | + | 0.823246i | \(0.692161\pi\) | |||||||
\(614\) | 0.111686 | 0.00450726 | ||||||||
\(615\) | −3.20408 | −0.129201 | ||||||||
\(616\) | −0.577624 | −0.0232731 | ||||||||
\(617\) | −0.102618 | −0.00413123 | −0.00206562 | − | 0.999998i | \(-0.500658\pi\) | ||||
−0.00206562 | + | 0.999998i | \(0.500658\pi\) | |||||||
\(618\) | 0.831926 | 0.0334650 | ||||||||
\(619\) | −22.8024 | −0.916504 | −0.458252 | − | 0.888822i | \(-0.651524\pi\) | ||||
−0.458252 | + | 0.888822i | \(0.651524\pi\) | |||||||
\(620\) | 11.7225 | 0.470788 | ||||||||
\(621\) | 2.04623 | 0.0821122 | ||||||||
\(622\) | −0.774356 | −0.0310489 | ||||||||
\(623\) | 13.7896 | 0.552469 | ||||||||
\(624\) | 2.29055 | 0.0916955 | ||||||||
\(625\) | 11.8513 | 0.474054 | ||||||||
\(626\) | −1.54799 | −0.0618702 | ||||||||
\(627\) | −7.87220 | −0.314385 | ||||||||
\(628\) | 1.99527 | 0.0796200 | ||||||||
\(629\) | 5.31637 | 0.211977 | ||||||||
\(630\) | 0.0548539 | 0.00218543 | ||||||||
\(631\) | 41.4338 | 1.64945 | 0.824727 | − | 0.565531i | \(-0.191329\pi\) | ||||
0.824727 | + | 0.565531i | \(0.191329\pi\) | |||||||
\(632\) | 0.797851 | 0.0317368 | ||||||||
\(633\) | 14.8816 | 0.591492 | ||||||||
\(634\) | −0.203585 | −0.00808539 | ||||||||
\(635\) | 7.65166 | 0.303647 | ||||||||
\(636\) | −20.1553 | −0.799211 | ||||||||
\(637\) | 3.64457 | 0.144403 | ||||||||
\(638\) | 0.442030 | 0.0175001 | ||||||||
\(639\) | 6.40860 | 0.253520 | ||||||||
\(640\) | −2.11516 | −0.0836092 | ||||||||
\(641\) | 4.64518 | 0.183474 | 0.0917368 | − | 0.995783i | \(-0.470758\pi\) | ||||
0.0917368 | + | 0.995783i | \(0.470758\pi\) | |||||||
\(642\) | −0.325658 | −0.0128527 | ||||||||
\(643\) | −15.1821 | −0.598726 | −0.299363 | − | 0.954139i | \(-0.596774\pi\) | ||||
−0.299363 | + | 0.954139i | \(0.596774\pi\) | |||||||
\(644\) | 3.36820 | 0.132726 | ||||||||
\(645\) | −3.93493 | −0.154938 | ||||||||
\(646\) | −0.212438 | −0.00835828 | ||||||||
\(647\) | 17.5083 | 0.688324 | 0.344162 | − | 0.938910i | \(-0.388163\pi\) | ||||
0.344162 | + | 0.938910i | \(0.388163\pi\) | |||||||
\(648\) | −0.274754 | −0.0107933 | ||||||||
\(649\) | −25.7713 | −1.01161 | ||||||||
\(650\) | 0.161230 | 0.00632394 | ||||||||
\(651\) | 5.01295 | 0.196473 | ||||||||
\(652\) | 19.3409 | 0.757447 | ||||||||
\(653\) | −3.82453 | −0.149665 | −0.0748327 | − | 0.997196i | \(-0.523842\pi\) | ||||
−0.0748327 | + | 0.997196i | \(0.523842\pi\) | |||||||
\(654\) | 0.0420490 | 0.00164425 | ||||||||
\(655\) | −20.7132 | −0.809332 | ||||||||
\(656\) | 13.1615 | 0.513871 | ||||||||
\(657\) | 10.2174 | 0.398619 | ||||||||
\(658\) | −0.376706 | −0.0146855 | ||||||||
\(659\) | −38.8396 | −1.51297 | −0.756487 | − | 0.654008i | \(-0.773086\pi\) | ||||
−0.756487 | + | 0.654008i | \(0.773086\pi\) | |||||||
\(660\) | 4.91621 | 0.191363 | ||||||||
\(661\) | 9.57670 | 0.372490 | 0.186245 | − | 0.982503i | \(-0.440368\pi\) | ||||
0.186245 | + | 0.982503i | \(0.440368\pi\) | |||||||
\(662\) | 0.278369 | 0.0108191 | ||||||||
\(663\) | −0.576726 | −0.0223982 | ||||||||
\(664\) | 1.05360 | 0.0408878 | ||||||||
\(665\) | 2.46403 | 0.0955510 | ||||||||
\(666\) | −0.365605 | −0.0141669 | ||||||||
\(667\) | −5.16117 | −0.199841 | ||||||||
\(668\) | 19.4678 | 0.753230 | ||||||||
\(669\) | 4.95072 | 0.191406 | ||||||||
\(670\) | 0.854838 | 0.0330253 | ||||||||
\(671\) | 9.79062 | 0.377963 | ||||||||
\(672\) | −0.678656 | −0.0261797 | ||||||||
\(673\) | −39.4313 | −1.51996 | −0.759982 | − | 0.649944i | \(-0.774792\pi\) | ||||
−0.759982 | + | 0.649944i | \(0.774792\pi\) | |||||||
\(674\) | 0.0328681 | 0.00126603 | ||||||||
\(675\) | 4.06516 | 0.156468 | ||||||||
\(676\) | 25.2749 | 0.972110 | ||||||||
\(677\) | −0.00774676 | −0.000297732 0 | −0.000148866 | − | 1.00000i | \(-0.500047\pi\) | ||||
−0.000148866 | 1.00000i | \(0.500047\pi\) | ||||||||
\(678\) | 0.269407 | 0.0103465 | ||||||||
\(679\) | −3.53172 | −0.135535 | ||||||||
\(680\) | 0.265651 | 0.0101873 | ||||||||
\(681\) | 11.0409 | 0.423087 | ||||||||
\(682\) | −1.06490 | −0.0407771 | ||||||||
\(683\) | 27.0165 | 1.03376 | 0.516879 | − | 0.856058i | \(-0.327094\pi\) | ||||
0.516879 | + | 0.856058i | \(0.327094\pi\) | |||||||
\(684\) | −6.16365 | −0.235673 | ||||||||
\(685\) | 11.5305 | 0.440556 | ||||||||
\(686\) | −0.755656 | −0.0288511 | ||||||||
\(687\) | −9.24283 | −0.352636 | ||||||||
\(688\) | 16.1636 | 0.616233 | ||||||||
\(689\) | 5.82583 | 0.221946 | ||||||||
\(690\) | 0.136056 | 0.00517958 | ||||||||
\(691\) | −9.29832 | −0.353725 | −0.176862 | − | 0.984236i | \(-0.556595\pi\) | ||||
−0.176862 | + | 0.984236i | \(0.556595\pi\) | |||||||
\(692\) | −1.06011 | −0.0402993 | ||||||||
\(693\) | 2.10234 | 0.0798612 | ||||||||
\(694\) | −1.74223 | −0.0661343 | ||||||||
\(695\) | 21.0873 | 0.799887 | ||||||||
\(696\) | 0.693007 | 0.0262684 | ||||||||
\(697\) | −3.31387 | −0.125522 | ||||||||
\(698\) | 1.08864 | 0.0412056 | ||||||||
\(699\) | −2.08683 | −0.0789313 | ||||||||
\(700\) | 6.69147 | 0.252914 | ||||||||
\(701\) | 5.52829 | 0.208800 | 0.104400 | − | 0.994535i | \(-0.466708\pi\) | ||||
0.104400 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(702\) | 0.0396613 | 0.00149692 | ||||||||
\(703\) | −16.4229 | −0.619403 | ||||||||
\(704\) | −20.0982 | −0.757479 | ||||||||
\(705\) | 6.41995 | 0.241789 | ||||||||
\(706\) | −1.69292 | −0.0637139 | ||||||||
\(707\) | 7.78721 | 0.292868 | ||||||||
\(708\) | −20.1780 | −0.758337 | ||||||||
\(709\) | −28.3740 | −1.06561 | −0.532805 | − | 0.846238i | \(-0.678862\pi\) | ||||
−0.532805 | + | 0.846238i | \(0.678862\pi\) | |||||||
\(710\) | 0.426116 | 0.0159919 | ||||||||
\(711\) | −2.90388 | −0.108904 | ||||||||
\(712\) | −4.59255 | −0.172113 | ||||||||
\(713\) | 12.4338 | 0.465651 | ||||||||
\(714\) | 0.0567334 | 0.00212319 | ||||||||
\(715\) | −1.42101 | −0.0531429 | ||||||||
\(716\) | 19.1403 | 0.715308 | ||||||||
\(717\) | −0.540533 | −0.0201866 | ||||||||
\(718\) | −0.482406 | −0.0180032 | ||||||||
\(719\) | 23.2060 | 0.865436 | 0.432718 | − | 0.901529i | \(-0.357555\pi\) | ||||
0.432718 | + | 0.901529i | \(0.357555\pi\) | |||||||
\(720\) | 3.84007 | 0.143111 | ||||||||
\(721\) | −9.97998 | −0.371674 | ||||||||
\(722\) | −0.650375 | −0.0242044 | ||||||||
\(723\) | −9.24566 | −0.343850 | ||||||||
\(724\) | 19.4327 | 0.722211 | ||||||||
\(725\) | −10.2535 | −0.380806 | ||||||||
\(726\) | 0.309868 | 0.0115003 | ||||||||
\(727\) | 26.9755 | 1.00047 | 0.500233 | − | 0.865891i | \(-0.333248\pi\) | ||||
0.500233 | + | 0.865891i | \(0.333248\pi\) | |||||||
\(728\) | 0.130724 | 0.00484495 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.679370 | 0.0251446 | ||||||||
\(731\) | −4.06976 | −0.150525 | ||||||||
\(732\) | 7.66570 | 0.283332 | ||||||||
\(733\) | −29.4234 | −1.08678 | −0.543389 | − | 0.839481i | \(-0.682859\pi\) | ||||
−0.543389 | + | 0.839481i | \(0.682859\pi\) | |||||||
\(734\) | 0.264095 | 0.00974792 | ||||||||
\(735\) | 6.11005 | 0.225373 | ||||||||
\(736\) | −1.68330 | −0.0620472 | ||||||||
\(737\) | 32.7626 | 1.20683 | ||||||||
\(738\) | 0.227894 | 0.00838889 | ||||||||
\(739\) | −21.4206 | −0.787971 | −0.393986 | − | 0.919117i | \(-0.628904\pi\) | ||||
−0.393986 | + | 0.919117i | \(0.628904\pi\) | |||||||
\(740\) | 10.2562 | 0.377024 | ||||||||
\(741\) | 1.78158 | 0.0654480 | ||||||||
\(742\) | −0.573095 | −0.0210390 | ||||||||
\(743\) | 11.6596 | 0.427748 | 0.213874 | − | 0.976861i | \(-0.431392\pi\) | ||||
0.213874 | + | 0.976861i | \(0.431392\pi\) | |||||||
\(744\) | −1.66953 | −0.0612080 | ||||||||
\(745\) | −8.24280 | −0.301993 | ||||||||
\(746\) | 1.68162 | 0.0615684 | ||||||||
\(747\) | −3.83473 | −0.140305 | ||||||||
\(748\) | 5.08466 | 0.185914 | ||||||||
\(749\) | 3.90667 | 0.142747 | ||||||||
\(750\) | 0.602755 | 0.0220095 | ||||||||
\(751\) | 51.9532 | 1.89580 | 0.947899 | − | 0.318570i | \(-0.103203\pi\) | ||||
0.947899 | + | 0.318570i | \(0.103203\pi\) | |||||||
\(752\) | −26.3714 | −0.961667 | ||||||||
\(753\) | 17.7905 | 0.648322 | ||||||||
\(754\) | −0.100037 | −0.00364314 | ||||||||
\(755\) | −13.4730 | −0.490334 | ||||||||
\(756\) | 1.64605 | 0.0598664 | ||||||||
\(757\) | 36.6772 | 1.33306 | 0.666528 | − | 0.745480i | \(-0.267780\pi\) | ||||
0.666528 | + | 0.745480i | \(0.267780\pi\) | |||||||
\(758\) | 0.919352 | 0.0333924 | ||||||||
\(759\) | 5.21452 | 0.189275 | ||||||||
\(760\) | −0.820630 | −0.0297674 | ||||||||
\(761\) | −20.0013 | −0.725048 | −0.362524 | − | 0.931974i | \(-0.618085\pi\) | ||||
−0.362524 | + | 0.931974i | \(0.618085\pi\) | |||||||
\(762\) | −0.544232 | −0.0197155 | ||||||||
\(763\) | −0.504430 | −0.0182616 | ||||||||
\(764\) | −13.8647 | −0.501606 | ||||||||
\(765\) | −0.966871 | −0.0349573 | ||||||||
\(766\) | −2.26457 | −0.0818224 | ||||||||
\(767\) | 5.83239 | 0.210595 | ||||||||
\(768\) | −15.6230 | −0.563746 | ||||||||
\(769\) | −32.7710 | −1.18175 | −0.590876 | − | 0.806762i | \(-0.701218\pi\) | ||||
−0.590876 | + | 0.806762i | \(0.701218\pi\) | |||||||
\(770\) | 0.139787 | 0.00503758 | ||||||||
\(771\) | 2.87289 | 0.103465 | ||||||||
\(772\) | −7.05461 | −0.253901 | ||||||||
\(773\) | −2.69412 | −0.0969008 | −0.0484504 | − | 0.998826i | \(-0.515428\pi\) | ||||
−0.0484504 | + | 0.998826i | \(0.515428\pi\) | |||||||
\(774\) | 0.279876 | 0.0100599 | ||||||||
\(775\) | 24.7018 | 0.887315 | ||||||||
\(776\) | 1.17622 | 0.0422237 | ||||||||
\(777\) | 4.38588 | 0.157343 | ||||||||
\(778\) | −0.0281459 | −0.00100908 | ||||||||
\(779\) | 10.2370 | 0.366778 | ||||||||
\(780\) | −1.11260 | −0.0398375 | ||||||||
\(781\) | 16.3314 | 0.584383 | ||||||||
\(782\) | 0.140718 | 0.00503208 | ||||||||
\(783\) | −2.52229 | −0.0901392 | ||||||||
\(784\) | −25.0985 | −0.896374 | ||||||||
\(785\) | −0.966871 | −0.0345091 | ||||||||
\(786\) | 1.47325 | 0.0525490 | ||||||||
\(787\) | −12.8933 | −0.459597 | −0.229799 | − | 0.973238i | \(-0.573807\pi\) | ||||
−0.229799 | + | 0.973238i | \(0.573807\pi\) | |||||||
\(788\) | −11.9687 | −0.426366 | ||||||||
\(789\) | −18.6756 | −0.664870 | ||||||||
\(790\) | −0.193083 | −0.00686959 | ||||||||
\(791\) | −3.23187 | −0.114912 | ||||||||
\(792\) | −0.700170 | −0.0248795 | ||||||||
\(793\) | −2.21574 | −0.0786834 | ||||||||
\(794\) | 0.544015 | 0.0193064 | ||||||||
\(795\) | 9.76689 | 0.346396 | ||||||||
\(796\) | −27.1220 | −0.961313 | ||||||||
\(797\) | 7.58947 | 0.268833 | 0.134416 | − | 0.990925i | \(-0.457084\pi\) | ||||
0.134416 | + | 0.990925i | \(0.457084\pi\) | |||||||
\(798\) | −0.175257 | −0.00620402 | ||||||||
\(799\) | 6.63993 | 0.234904 | ||||||||
\(800\) | −3.34415 | −0.118233 | ||||||||
\(801\) | 16.7151 | 0.590601 | ||||||||
\(802\) | 2.21488 | 0.0782100 | ||||||||
\(803\) | 26.0376 | 0.918847 | ||||||||
\(804\) | 25.6519 | 0.904674 | ||||||||
\(805\) | −1.63216 | −0.0575263 | ||||||||
\(806\) | 0.241000 | 0.00848888 | ||||||||
\(807\) | −14.3871 | −0.506449 | ||||||||
\(808\) | −2.59348 | −0.0912383 | ||||||||
\(809\) | −19.7295 | −0.693652 | −0.346826 | − | 0.937930i | \(-0.612741\pi\) | ||||
−0.346826 | + | 0.937930i | \(0.612741\pi\) | |||||||
\(810\) | 0.0664914 | 0.00233627 | ||||||||
\(811\) | −14.5012 | −0.509206 | −0.254603 | − | 0.967046i | \(-0.581945\pi\) | ||||
−0.254603 | + | 0.967046i | \(0.581945\pi\) | |||||||
\(812\) | −4.15182 | −0.145700 | ||||||||
\(813\) | −21.8858 | −0.767569 | ||||||||
\(814\) | −0.931692 | −0.0326558 | ||||||||
\(815\) | −9.37222 | −0.328295 | ||||||||
\(816\) | 3.97165 | 0.139035 | ||||||||
\(817\) | 12.5720 | 0.439839 | ||||||||
\(818\) | −0.365835 | −0.0127911 | ||||||||
\(819\) | −0.475786 | −0.0166253 | ||||||||
\(820\) | −6.39302 | −0.223254 | ||||||||
\(821\) | 21.5499 | 0.752096 | 0.376048 | − | 0.926600i | \(-0.377283\pi\) | ||||
0.376048 | + | 0.926600i | \(0.377283\pi\) | |||||||
\(822\) | −0.820116 | −0.0286048 | ||||||||
\(823\) | −40.1187 | −1.39845 | −0.699226 | − | 0.714901i | \(-0.746472\pi\) | ||||
−0.699226 | + | 0.714901i | \(0.746472\pi\) | |||||||
\(824\) | 3.32377 | 0.115789 | ||||||||
\(825\) | 10.3595 | 0.360671 | ||||||||
\(826\) | −0.573741 | −0.0199630 | ||||||||
\(827\) | 29.5649 | 1.02807 | 0.514037 | − | 0.857768i | \(-0.328150\pi\) | ||||
0.514037 | + | 0.857768i | \(0.328150\pi\) | |||||||
\(828\) | 4.08278 | 0.141886 | ||||||||
\(829\) | 13.1440 | 0.456510 | 0.228255 | − | 0.973601i | \(-0.426698\pi\) | ||||
0.228255 | + | 0.973601i | \(0.426698\pi\) | |||||||
\(830\) | −0.254976 | −0.00885035 | ||||||||
\(831\) | 26.1129 | 0.905846 | ||||||||
\(832\) | 4.54848 | 0.157690 | ||||||||
\(833\) | 6.31941 | 0.218955 | ||||||||
\(834\) | −1.49986 | −0.0519358 | ||||||||
\(835\) | −9.43371 | −0.326467 | ||||||||
\(836\) | −15.7072 | −0.543244 | ||||||||
\(837\) | 6.07647 | 0.210033 | ||||||||
\(838\) | −2.08155 | −0.0719058 | ||||||||
\(839\) | 11.9853 | 0.413780 | 0.206890 | − | 0.978364i | \(-0.433666\pi\) | ||||
0.206890 | + | 0.978364i | \(0.433666\pi\) | |||||||
\(840\) | 0.219156 | 0.00756160 | ||||||||
\(841\) | −22.6381 | −0.780623 | ||||||||
\(842\) | −0.288187 | −0.00993157 | ||||||||
\(843\) | 11.3572 | 0.391164 | ||||||||
\(844\) | 29.6929 | 1.02207 | ||||||||
\(845\) | −12.2477 | −0.421335 | ||||||||
\(846\) | −0.456626 | −0.0156991 | ||||||||
\(847\) | −3.71725 | −0.127726 | ||||||||
\(848\) | −40.1198 | −1.37772 | ||||||||
\(849\) | 11.2005 | 0.384401 | ||||||||
\(850\) | 0.279560 | 0.00958882 | ||||||||
\(851\) | 10.8785 | 0.372910 | ||||||||
\(852\) | 12.7869 | 0.438071 | ||||||||
\(853\) | −40.7194 | −1.39421 | −0.697103 | − | 0.716971i | \(-0.745528\pi\) | ||||
−0.697103 | + | 0.716971i | \(0.745528\pi\) | |||||||
\(854\) | 0.217966 | 0.00745864 | ||||||||
\(855\) | 2.98679 | 0.102146 | ||||||||
\(856\) | −1.30109 | −0.0444705 | ||||||||
\(857\) | 44.0574 | 1.50497 | 0.752486 | − | 0.658608i | \(-0.228854\pi\) | ||||
0.752486 | + | 0.658608i | \(0.228854\pi\) | |||||||
\(858\) | 0.101071 | 0.00345051 | ||||||||
\(859\) | −11.1755 | −0.381305 | −0.190652 | − | 0.981658i | \(-0.561060\pi\) | ||||
−0.190652 | + | 0.981658i | \(0.561060\pi\) | |||||||
\(860\) | −7.85124 | −0.267725 | ||||||||
\(861\) | −2.73387 | −0.0931700 | ||||||||
\(862\) | 0.0280835 | 0.000956527 0 | ||||||||
\(863\) | 19.0744 | 0.649299 | 0.324650 | − | 0.945834i | \(-0.394754\pi\) | ||||
0.324650 | + | 0.945834i | \(0.394754\pi\) | |||||||
\(864\) | −0.822636 | −0.0279866 | ||||||||
\(865\) | 0.513708 | 0.0174666 | ||||||||
\(866\) | −2.28612 | −0.0776855 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 10.0022 | 0.339496 | ||||||||
\(869\) | −7.40012 | −0.251032 | ||||||||
\(870\) | −0.167710 | −0.00568592 | ||||||||
\(871\) | −7.41461 | −0.251234 | ||||||||
\(872\) | 0.167997 | 0.00568910 | ||||||||
\(873\) | −4.28099 | −0.144890 | ||||||||
\(874\) | −0.434697 | −0.0147038 | ||||||||
\(875\) | −7.23079 | −0.244445 | ||||||||
\(876\) | 20.3865 | 0.688796 | ||||||||
\(877\) | −28.8006 | −0.972526 | −0.486263 | − | 0.873812i | \(-0.661640\pi\) | ||||
−0.486263 | + | 0.873812i | \(0.661640\pi\) | |||||||
\(878\) | 1.35610 | 0.0457660 | ||||||||
\(879\) | 30.9160 | 1.04277 | ||||||||
\(880\) | 9.78586 | 0.329881 | ||||||||
\(881\) | 8.52856 | 0.287335 | 0.143667 | − | 0.989626i | \(-0.454110\pi\) | ||||
0.143667 | + | 0.989626i | \(0.454110\pi\) | |||||||
\(882\) | −0.434584 | −0.0146332 | ||||||||
\(883\) | −18.6902 | −0.628975 | −0.314488 | − | 0.949262i | \(-0.601833\pi\) | ||||
−0.314488 | + | 0.949262i | \(0.601833\pi\) | |||||||
\(884\) | −1.15073 | −0.0387031 | ||||||||
\(885\) | 9.77789 | 0.328680 | ||||||||
\(886\) | −0.539079 | −0.0181107 | ||||||||
\(887\) | 21.3802 | 0.717876 | 0.358938 | − | 0.933361i | \(-0.383139\pi\) | ||||
0.358938 | + | 0.933361i | \(0.383139\pi\) | |||||||
\(888\) | −1.46069 | −0.0490176 | ||||||||
\(889\) | 6.52874 | 0.218967 | ||||||||
\(890\) | 1.11141 | 0.0372547 | ||||||||
\(891\) | 2.54836 | 0.0853732 | ||||||||
\(892\) | 9.87803 | 0.330741 | ||||||||
\(893\) | −20.5116 | −0.686394 | ||||||||
\(894\) | 0.586278 | 0.0196081 | ||||||||
\(895\) | −9.27504 | −0.310030 | ||||||||
\(896\) | −1.80475 | −0.0602925 | ||||||||
\(897\) | −1.18011 | −0.0394028 | ||||||||
\(898\) | −0.116036 | −0.00387218 | ||||||||
\(899\) | −15.3266 | −0.511171 | ||||||||
\(900\) | 8.11110 | 0.270370 | ||||||||
\(901\) | 10.1015 | 0.336531 | ||||||||
\(902\) | 0.580755 | 0.0193370 | ||||||||
\(903\) | −3.35746 | −0.111729 | ||||||||
\(904\) | 1.07635 | 0.0357990 | ||||||||
\(905\) | −9.41672 | −0.313022 | ||||||||
\(906\) | 0.958283 | 0.0318368 | ||||||||
\(907\) | 34.0469 | 1.13051 | 0.565254 | − | 0.824917i | \(-0.308778\pi\) | ||||
0.565254 | + | 0.824917i | \(0.308778\pi\) | |||||||
\(908\) | 22.0295 | 0.731076 | ||||||||
\(909\) | 9.43930 | 0.313082 | ||||||||
\(910\) | −0.0316357 | −0.00104871 | ||||||||
\(911\) | 4.73100 | 0.156745 | 0.0783725 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783725 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(912\) | −12.2689 | −0.406265 | ||||||||
\(913\) | −9.77225 | −0.323414 | ||||||||
\(914\) | −2.47445 | −0.0818476 | ||||||||
\(915\) | −3.71465 | −0.122803 | ||||||||
\(916\) | −18.4419 | −0.609339 | ||||||||
\(917\) | −17.6734 | −0.583628 | ||||||||
\(918\) | 0.0687697 | 0.00226974 | ||||||||
\(919\) | −8.05465 | −0.265698 | −0.132849 | − | 0.991136i | \(-0.542413\pi\) | ||||
−0.132849 | + | 0.991136i | \(0.542413\pi\) | |||||||
\(920\) | 0.543582 | 0.0179214 | ||||||||
\(921\) | −1.62405 | −0.0535143 | ||||||||
\(922\) | −2.06952 | −0.0681560 | ||||||||
\(923\) | −3.69601 | −0.121656 | ||||||||
\(924\) | 4.19473 | 0.137996 | ||||||||
\(925\) | 21.6119 | 0.710595 | ||||||||
\(926\) | −0.737569 | −0.0242380 | ||||||||
\(927\) | −12.0973 | −0.397327 | ||||||||
\(928\) | 2.07492 | 0.0681127 | ||||||||
\(929\) | 17.9894 | 0.590215 | 0.295107 | − | 0.955464i | \(-0.404645\pi\) | ||||
0.295107 | + | 0.955464i | \(0.404645\pi\) | |||||||
\(930\) | 0.404033 | 0.0132488 | ||||||||
\(931\) | −19.5215 | −0.639791 | ||||||||
\(932\) | −4.16380 | −0.136390 | ||||||||
\(933\) | 11.2601 | 0.368640 | ||||||||
\(934\) | 1.21127 | 0.0396339 | ||||||||
\(935\) | −2.46393 | −0.0805792 | ||||||||
\(936\) | 0.158458 | 0.00517935 | ||||||||
\(937\) | −37.1453 | −1.21348 | −0.606742 | − | 0.794899i | \(-0.707524\pi\) | ||||
−0.606742 | + | 0.794899i | \(0.707524\pi\) | |||||||
\(938\) | 0.729386 | 0.0238153 | ||||||||
\(939\) | 22.5098 | 0.734579 | ||||||||
\(940\) | 12.8095 | 0.417801 | ||||||||
\(941\) | −9.88039 | −0.322092 | −0.161046 | − | 0.986947i | \(-0.551487\pi\) | ||||
−0.161046 | + | 0.986947i | \(0.551487\pi\) | |||||||
\(942\) | 0.0687697 | 0.00224064 | ||||||||
\(943\) | −6.78093 | −0.220818 | ||||||||
\(944\) | −40.1650 | −1.30726 | ||||||||
\(945\) | −0.797646 | −0.0259474 | ||||||||
\(946\) | 0.713223 | 0.0231889 | ||||||||
\(947\) | 48.1681 | 1.56525 | 0.782626 | − | 0.622492i | \(-0.213880\pi\) | ||||
0.782626 | + | 0.622492i | \(0.213880\pi\) | |||||||
\(948\) | −5.79403 | −0.188181 | ||||||||
\(949\) | −5.89265 | −0.191284 | ||||||||
\(950\) | −0.863596 | −0.0280188 | ||||||||
\(951\) | 2.96039 | 0.0959972 | ||||||||
\(952\) | 0.226665 | 0.00734627 | ||||||||
\(953\) | 0.832859 | 0.0269789 | 0.0134895 | − | 0.999909i | \(-0.495706\pi\) | ||||
0.0134895 | + | 0.999909i | \(0.495706\pi\) | |||||||
\(954\) | −0.694680 | −0.0224911 | ||||||||
\(955\) | 6.71856 | 0.217407 | ||||||||
\(956\) | −1.07851 | −0.0348815 | ||||||||
\(957\) | −6.42769 | −0.207778 | ||||||||
\(958\) | 2.04981 | 0.0662263 | ||||||||
\(959\) | 9.83830 | 0.317695 | ||||||||
\(960\) | 7.62544 | 0.246110 | ||||||||
\(961\) | 5.92345 | 0.191079 | ||||||||
\(962\) | 0.210854 | 0.00679820 | ||||||||
\(963\) | 4.73549 | 0.152599 | ||||||||
\(964\) | −18.4476 | −0.594157 | ||||||||
\(965\) | 3.41853 | 0.110046 | ||||||||
\(966\) | 0.116089 | 0.00373512 | ||||||||
\(967\) | −45.0988 | −1.45028 | −0.725139 | − | 0.688602i | \(-0.758225\pi\) | ||||
−0.725139 | + | 0.688602i | \(0.758225\pi\) | |||||||
\(968\) | 1.23801 | 0.0397910 | ||||||||
\(969\) | 3.08913 | 0.0992371 | ||||||||
\(970\) | −0.284649 | −0.00913953 | ||||||||
\(971\) | 13.6771 | 0.438919 | 0.219460 | − | 0.975622i | \(-0.429571\pi\) | ||||
0.219460 | + | 0.975622i | \(0.429571\pi\) | |||||||
\(972\) | 1.99527 | 0.0639983 | ||||||||
\(973\) | 17.9926 | 0.576817 | ||||||||
\(974\) | 0.999777 | 0.0320349 | ||||||||
\(975\) | −2.34449 | −0.0750836 | ||||||||
\(976\) | 15.2588 | 0.488422 | ||||||||
\(977\) | −12.5137 | −0.400350 | −0.200175 | − | 0.979760i | \(-0.564151\pi\) | ||||
−0.200175 | + | 0.979760i | \(0.564151\pi\) | |||||||
\(978\) | 0.666609 | 0.0213158 | ||||||||
\(979\) | 42.5962 | 1.36138 | ||||||||
\(980\) | 12.1912 | 0.389434 | ||||||||
\(981\) | −0.611447 | −0.0195220 | ||||||||
\(982\) | 1.24026 | 0.0395783 | ||||||||
\(983\) | 8.65602 | 0.276084 | 0.138042 | − | 0.990426i | \(-0.455919\pi\) | ||||
0.138042 | + | 0.990426i | \(0.455919\pi\) | |||||||
\(984\) | 0.910498 | 0.0290256 | ||||||||
\(985\) | 5.79978 | 0.184796 | ||||||||
\(986\) | −0.173457 | −0.00552399 | ||||||||
\(987\) | 5.47779 | 0.174360 | ||||||||
\(988\) | 3.55474 | 0.113091 | ||||||||
\(989\) | −8.32764 | −0.264804 | ||||||||
\(990\) | 0.169444 | 0.00538528 | ||||||||
\(991\) | 22.1611 | 0.703971 | 0.351986 | − | 0.936005i | \(-0.385507\pi\) | ||||
0.351986 | + | 0.936005i | \(0.385507\pi\) | |||||||
\(992\) | −4.99872 | −0.158710 | ||||||||
\(993\) | −4.04784 | −0.128454 | ||||||||
\(994\) | 0.363582 | 0.0115321 | ||||||||
\(995\) | 13.1428 | 0.416655 | ||||||||
\(996\) | −7.65132 | −0.242441 | ||||||||
\(997\) | −4.89419 | −0.155001 | −0.0775003 | − | 0.996992i | \(-0.524694\pi\) | ||||
−0.0775003 | + | 0.996992i | \(0.524694\pi\) | |||||||
\(998\) | −1.21476 | −0.0384527 | ||||||||
\(999\) | 5.31637 | 0.168202 |
(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 | 8007.2.a.f.1.25 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.25 | ✓ | 48 | 1.1 | even | 1 | trivial |