Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, 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("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | 10.10.52900342088704.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 18x^{8} + 123x^{6} - 390x^{4} + 548x^{2} - 241 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 414) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.09112\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.77954 | 0.795834 | 0.397917 | − | 0.917421i | \(-0.369733\pi\) | ||||
0.397917 | + | 0.917421i | \(0.369733\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.833869 | 0.315173 | 0.157586 | − | 0.987505i | \(-0.449629\pi\) | ||||
0.157586 | + | 0.987505i | \(0.449629\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.77954 | 0.562740 | ||||||||
\(11\) | 3.92552 | 1.18359 | 0.591794 | − | 0.806089i | \(-0.298420\pi\) | ||||
0.591794 | + | 0.806089i | \(0.298420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.58435 | 1.27147 | 0.635736 | − | 0.771907i | \(-0.280697\pi\) | ||||
0.635736 | + | 0.771907i | \(0.280697\pi\) | |||||||
\(14\) | 0.833869 | 0.222861 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.16645 | 0.282905 | 0.141452 | − | 0.989945i | \(-0.454823\pi\) | ||||
0.141452 | + | 0.989945i | \(0.454823\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.74764 | −0.859767 | −0.429883 | − | 0.902884i | \(-0.641445\pi\) | ||||
−0.429883 | + | 0.902884i | \(0.641445\pi\) | |||||||
\(20\) | 1.77954 | 0.397917 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.92552 | 0.836923 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.83324 | −0.366648 | ||||||||
\(26\) | 4.58435 | 0.899066 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.833869 | 0.157586 | ||||||||
\(29\) | 1.08844 | 0.202118 | 0.101059 | − | 0.994880i | \(-0.467777\pi\) | ||||
0.101059 | + | 0.994880i | \(0.467777\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.05081 | 1.26636 | 0.633182 | − | 0.774003i | \(-0.281749\pi\) | ||||
0.633182 | + | 0.774003i | \(0.281749\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.16645 | 0.200044 | ||||||||
\(35\) | 1.48390 | 0.250825 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.44758 | 0.895577 | 0.447788 | − | 0.894140i | \(-0.352212\pi\) | ||||
0.447788 | + | 0.894140i | \(0.352212\pi\) | |||||||
\(38\) | −3.74764 | −0.607947 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.77954 | 0.281370 | ||||||||
\(41\) | −1.45280 | −0.226889 | −0.113445 | − | 0.993544i | \(-0.536188\pi\) | ||||
−0.113445 | + | 0.993544i | \(0.536188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.91817 | 0.597515 | 0.298757 | − | 0.954329i | \(-0.403428\pi\) | ||||
0.298757 | + | 0.954329i | \(0.403428\pi\) | |||||||
\(44\) | 3.92552 | 0.591794 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.02025 | −0.732279 | −0.366139 | − | 0.930560i | \(-0.619321\pi\) | ||||
−0.366139 | + | 0.930560i | \(0.619321\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.30466 | −0.900666 | ||||||||
\(50\) | −1.83324 | −0.259259 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.58435 | 0.635736 | ||||||||
\(53\) | 11.2107 | 1.53990 | 0.769952 | − | 0.638102i | \(-0.220280\pi\) | ||||
0.769952 | + | 0.638102i | \(0.220280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.98562 | 0.941940 | ||||||||
\(56\) | 0.833869 | 0.111430 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.08844 | 0.142919 | ||||||||
\(59\) | −3.91737 | −0.509999 | −0.254999 | − | 0.966941i | \(-0.582075\pi\) | ||||
−0.254999 | + | 0.966941i | \(0.582075\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.19099 | −0.536601 | −0.268301 | − | 0.963335i | \(-0.586462\pi\) | ||||
−0.268301 | + | 0.963335i | \(0.586462\pi\) | |||||||
\(62\) | 7.05081 | 0.895454 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.15804 | 1.01188 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.05678 | 0.251276 | 0.125638 | − | 0.992076i | \(-0.459902\pi\) | ||||
0.125638 | + | 0.992076i | \(0.459902\pi\) | |||||||
\(68\) | 1.16645 | 0.141452 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.48390 | 0.177360 | ||||||||
\(71\) | −7.83463 | −0.929800 | −0.464900 | − | 0.885363i | \(-0.653910\pi\) | ||||
−0.464900 | + | 0.885363i | \(0.653910\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8102 | 1.61636 | 0.808178 | − | 0.588938i | \(-0.200454\pi\) | ||||
0.808178 | + | 0.588938i | \(0.200454\pi\) | |||||||
\(74\) | 5.44758 | 0.633268 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.74764 | −0.429883 | ||||||||
\(77\) | 3.27337 | 0.373035 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.56891 | −1.07659 | −0.538293 | − | 0.842758i | \(-0.680931\pi\) | ||||
−0.538293 | + | 0.842758i | \(0.680931\pi\) | |||||||
\(80\) | 1.77954 | 0.198959 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.45280 | −0.160435 | ||||||||
\(83\) | −12.8937 | −1.41527 | −0.707634 | − | 0.706579i | \(-0.750238\pi\) | ||||
−0.707634 | + | 0.706579i | \(0.750238\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.07574 | 0.225145 | ||||||||
\(86\) | 3.91817 | 0.422507 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.92552 | 0.418462 | ||||||||
\(89\) | 2.07244 | 0.219678 | 0.109839 | − | 0.993949i | \(-0.464967\pi\) | ||||
0.109839 | + | 0.993949i | \(0.464967\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.82275 | 0.400733 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.02025 | −0.517799 | ||||||||
\(95\) | −6.66907 | −0.684232 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.5515 | −1.27441 | −0.637203 | − | 0.770696i | \(-0.719909\pi\) | ||||
−0.637203 | + | 0.770696i | \(0.719909\pi\) | |||||||
\(98\) | −6.30466 | −0.636867 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.83324 | −0.183324 | ||||||||
\(101\) | 12.0480 | 1.19882 | 0.599409 | − | 0.800443i | \(-0.295402\pi\) | ||||
0.599409 | + | 0.800443i | \(0.295402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0230 | 1.28320 | 0.641598 | − | 0.767041i | \(-0.278272\pi\) | ||||
0.641598 | + | 0.767041i | \(0.278272\pi\) | |||||||
\(104\) | 4.58435 | 0.449533 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2107 | 1.08888 | ||||||||
\(107\) | 4.83960 | 0.467862 | 0.233931 | − | 0.972253i | \(-0.424841\pi\) | ||||
0.233931 | + | 0.972253i | \(0.424841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.00790 | 0.0965392 | 0.0482696 | − | 0.998834i | \(-0.484629\pi\) | ||||
0.0482696 | + | 0.998834i | \(0.484629\pi\) | |||||||
\(110\) | 6.98562 | 0.666052 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.833869 | 0.0787932 | ||||||||
\(113\) | 10.5034 | 0.988072 | 0.494036 | − | 0.869441i | \(-0.335521\pi\) | ||||
0.494036 | + | 0.869441i | \(0.335521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.08844 | 0.101059 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.91737 | −0.360624 | ||||||||
\(119\) | 0.972663 | 0.0891639 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.40970 | 0.400882 | ||||||||
\(122\) | −4.19099 | −0.379434 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.05081 | 0.633182 | ||||||||
\(125\) | −12.1600 | −1.08763 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.34381 | −0.474187 | −0.237093 | − | 0.971487i | \(-0.576195\pi\) | ||||
−0.237093 | + | 0.971487i | \(0.576195\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.15804 | 0.715507 | ||||||||
\(131\) | 10.6159 | 0.927517 | 0.463759 | − | 0.885962i | \(-0.346501\pi\) | ||||
0.463759 | + | 0.885962i | \(0.346501\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.12504 | −0.270975 | ||||||||
\(134\) | 2.05678 | 0.177679 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.16645 | 0.100022 | ||||||||
\(137\) | 11.2545 | 0.961534 | 0.480767 | − | 0.876848i | \(-0.340358\pi\) | ||||
0.480767 | + | 0.876848i | \(0.340358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.20054 | −0.441104 | −0.220552 | − | 0.975375i | \(-0.570786\pi\) | ||||
−0.220552 | + | 0.975375i | \(0.570786\pi\) | |||||||
\(140\) | 1.48390 | 0.125413 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.83463 | −0.657468 | ||||||||
\(143\) | 17.9960 | 1.50490 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.93692 | 0.160852 | ||||||||
\(146\) | 13.8102 | 1.14294 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.44758 | 0.447788 | ||||||||
\(149\) | −19.1329 | −1.56743 | −0.783715 | − | 0.621121i | \(-0.786678\pi\) | ||||
−0.783715 | + | 0.621121i | \(0.786678\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.6172 | −0.945393 | −0.472697 | − | 0.881225i | \(-0.656719\pi\) | ||||
−0.472697 | + | 0.881225i | \(0.656719\pi\) | |||||||
\(152\) | −3.74764 | −0.303973 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.27337 | 0.263776 | ||||||||
\(155\) | 12.5472 | 1.00782 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.80726 | −0.224044 | −0.112022 | − | 0.993706i | \(-0.535733\pi\) | ||||
−0.112022 | + | 0.993706i | \(0.535733\pi\) | |||||||
\(158\) | −9.56891 | −0.761262 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.77954 | 0.140685 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.2284 | −1.74107 | −0.870533 | − | 0.492110i | \(-0.836226\pi\) | ||||
−0.870533 | + | 0.492110i | \(0.836226\pi\) | |||||||
\(164\) | −1.45280 | −0.113445 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.8937 | −1.00075 | ||||||||
\(167\) | −19.2351 | −1.48846 | −0.744228 | − | 0.667925i | \(-0.767183\pi\) | ||||
−0.744228 | + | 0.667925i | \(0.767183\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.01630 | 0.616639 | ||||||||
\(170\) | 2.07574 | 0.159202 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.91817 | 0.298757 | ||||||||
\(173\) | −22.1624 | −1.68498 | −0.842488 | − | 0.538715i | \(-0.818910\pi\) | ||||
−0.842488 | + | 0.538715i | \(0.818910\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.52868 | −0.115557 | ||||||||
\(176\) | 3.92552 | 0.295897 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.07244 | 0.155336 | ||||||||
\(179\) | 8.71096 | 0.651088 | 0.325544 | − | 0.945527i | \(-0.394453\pi\) | ||||
0.325544 | + | 0.945527i | \(0.394453\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2676 | 1.50648 | 0.753240 | − | 0.657746i | \(-0.228490\pi\) | ||||
0.753240 | + | 0.657746i | \(0.228490\pi\) | |||||||
\(182\) | 3.82275 | 0.283361 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.69419 | 0.712731 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.57890 | 0.334843 | ||||||||
\(188\) | −5.02025 | −0.366139 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.66907 | −0.483825 | ||||||||
\(191\) | 22.2062 | 1.60678 | 0.803391 | − | 0.595452i | \(-0.203027\pi\) | ||||
0.803391 | + | 0.595452i | \(0.203027\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.1010 | −1.37492 | −0.687460 | − | 0.726222i | \(-0.741274\pi\) | ||||
−0.687460 | + | 0.726222i | \(0.741274\pi\) | |||||||
\(194\) | −12.5515 | −0.901142 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.30466 | −0.450333 | ||||||||
\(197\) | −23.1223 | −1.64740 | −0.823699 | − | 0.567028i | \(-0.808093\pi\) | ||||
−0.823699 | + | 0.567028i | \(0.808093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2797 | 1.08315 | 0.541576 | − | 0.840652i | \(-0.317828\pi\) | ||||
0.541576 | + | 0.840652i | \(0.317828\pi\) | |||||||
\(200\) | −1.83324 | −0.129630 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0480 | 0.847692 | ||||||||
\(203\) | 0.907615 | 0.0637021 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.58532 | −0.180566 | ||||||||
\(206\) | 13.0230 | 0.907357 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.58435 | 0.317868 | ||||||||
\(209\) | −14.7114 | −1.01761 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.20798 | −0.427375 | −0.213688 | − | 0.976902i | \(-0.568547\pi\) | ||||
−0.213688 | + | 0.976902i | \(0.568547\pi\) | |||||||
\(212\) | 11.2107 | 0.769952 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.83960 | 0.330828 | ||||||||
\(215\) | 6.97253 | 0.475523 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.87946 | 0.399123 | ||||||||
\(218\) | 1.00790 | 0.0682635 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.98562 | 0.470970 | ||||||||
\(221\) | 5.34740 | 0.359705 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4778 | 1.03647 | 0.518234 | − | 0.855239i | \(-0.326590\pi\) | ||||
0.518234 | + | 0.855239i | \(0.326590\pi\) | |||||||
\(224\) | 0.833869 | 0.0557152 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.5034 | 0.698673 | ||||||||
\(227\) | 13.0742 | 0.867762 | 0.433881 | − | 0.900970i | \(-0.357144\pi\) | ||||
0.433881 | + | 0.900970i | \(0.357144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.8420 | 1.64160 | 0.820801 | − | 0.571214i | \(-0.193527\pi\) | ||||
0.820801 | + | 0.571214i | \(0.193527\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.08844 | 0.0714594 | ||||||||
\(233\) | −5.11474 | −0.335078 | −0.167539 | − | 0.985865i | \(-0.553582\pi\) | ||||
−0.167539 | + | 0.985865i | \(0.553582\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.93374 | −0.582773 | ||||||||
\(236\) | −3.91737 | −0.254999 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.972663 | 0.0630484 | ||||||||
\(239\) | 24.3989 | 1.57824 | 0.789118 | − | 0.614241i | \(-0.210538\pi\) | ||||
0.789118 | + | 0.614241i | \(0.210538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.08856 | −0.585445 | −0.292723 | − | 0.956197i | \(-0.594561\pi\) | ||||
−0.292723 | + | 0.956197i | \(0.594561\pi\) | |||||||
\(242\) | 4.40970 | 0.283466 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.19099 | −0.268301 | ||||||||
\(245\) | −11.2194 | −0.716781 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.1805 | −1.09317 | ||||||||
\(248\) | 7.05081 | 0.447727 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.1600 | −0.769067 | ||||||||
\(251\) | 2.53733 | 0.160155 | 0.0800776 | − | 0.996789i | \(-0.474483\pi\) | ||||
0.0800776 | + | 0.996789i | \(0.474483\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −5.34381 | −0.335300 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −29.1594 | −1.81891 | −0.909457 | − | 0.415797i | \(-0.863503\pi\) | ||||
−0.909457 | + | 0.415797i | \(0.863503\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.54257 | 0.282262 | ||||||||
\(260\) | 8.15804 | 0.505940 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.6159 | 0.655854 | ||||||||
\(263\) | −3.88223 | −0.239389 | −0.119694 | − | 0.992811i | \(-0.538191\pi\) | ||||
−0.119694 | + | 0.992811i | \(0.538191\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.9498 | 1.22551 | ||||||||
\(266\) | −3.12504 | −0.191608 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.05678 | 0.125638 | ||||||||
\(269\) | 3.55327 | 0.216647 | 0.108323 | − | 0.994116i | \(-0.465452\pi\) | ||||
0.108323 | + | 0.994116i | \(0.465452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.1590 | −1.34606 | −0.673031 | − | 0.739615i | \(-0.735008\pi\) | ||||
−0.673031 | + | 0.739615i | \(0.735008\pi\) | |||||||
\(272\) | 1.16645 | 0.0707261 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.2545 | 0.679907 | ||||||||
\(275\) | −7.19641 | −0.433960 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4979 | −0.811008 | −0.405504 | − | 0.914093i | \(-0.632904\pi\) | ||||
−0.405504 | + | 0.914093i | \(0.632904\pi\) | |||||||
\(278\) | −5.20054 | −0.311908 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.48390 | 0.0886802 | ||||||||
\(281\) | 30.7477 | 1.83425 | 0.917126 | − | 0.398597i | \(-0.130503\pi\) | ||||
0.917126 | + | 0.398597i | \(0.130503\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.5356 | −1.22072 | −0.610358 | − | 0.792125i | \(-0.708975\pi\) | ||||
−0.610358 | + | 0.792125i | \(0.708975\pi\) | |||||||
\(284\) | −7.83463 | −0.464900 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.9960 | 1.06412 | ||||||||
\(287\) | −1.21145 | −0.0715094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6394 | −0.919965 | ||||||||
\(290\) | 1.93692 | 0.113740 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.8102 | 0.808178 | ||||||||
\(293\) | −7.66535 | −0.447815 | −0.223907 | − | 0.974610i | \(-0.571881\pi\) | ||||
−0.223907 | + | 0.974610i | \(0.571881\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.97112 | −0.405875 | ||||||||
\(296\) | 5.44758 | 0.316634 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.1329 | −1.10834 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.26724 | 0.188320 | ||||||||
\(302\) | −11.6172 | −0.668494 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.74764 | −0.214942 | ||||||||
\(305\) | −7.45803 | −0.427046 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.803500 | 0.0458582 | 0.0229291 | − | 0.999737i | \(-0.492701\pi\) | ||||
0.0229291 | + | 0.999737i | \(0.492701\pi\) | |||||||
\(308\) | 3.27337 | 0.186518 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 12.5472 | 0.712633 | ||||||||
\(311\) | 26.2869 | 1.49059 | 0.745297 | − | 0.666732i | \(-0.232307\pi\) | ||||
0.745297 | + | 0.666732i | \(0.232307\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.3715 | 0.925371 | 0.462685 | − | 0.886523i | \(-0.346886\pi\) | ||||
0.462685 | + | 0.886523i | \(0.346886\pi\) | |||||||
\(314\) | −2.80726 | −0.158423 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.56891 | −0.538293 | ||||||||
\(317\) | 12.8264 | 0.720400 | 0.360200 | − | 0.932875i | \(-0.382708\pi\) | ||||
0.360200 | + | 0.932875i | \(0.382708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.27268 | 0.239224 | ||||||||
\(320\) | 1.77954 | 0.0994793 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.37141 | −0.243232 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.40421 | −0.466182 | ||||||||
\(326\) | −22.2284 | −1.23112 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.45280 | −0.0802175 | ||||||||
\(329\) | −4.18623 | −0.230794 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.6654 | 0.751118 | 0.375559 | − | 0.926798i | \(-0.377451\pi\) | ||||
0.375559 | + | 0.926798i | \(0.377451\pi\) | |||||||
\(332\) | −12.8937 | −0.707634 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.2351 | −1.05250 | ||||||||
\(335\) | 3.66012 | 0.199974 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.3043 | −0.561312 | −0.280656 | − | 0.959808i | \(-0.590552\pi\) | ||||
−0.280656 | + | 0.959808i | \(0.590552\pi\) | |||||||
\(338\) | 8.01630 | 0.436029 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.07574 | 0.112573 | ||||||||
\(341\) | 27.6781 | 1.49885 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.0943 | −0.599038 | ||||||||
\(344\) | 3.91817 | 0.211253 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.1624 | −1.19146 | ||||||||
\(347\) | −28.8990 | −1.55138 | −0.775689 | − | 0.631116i | \(-0.782597\pi\) | ||||
−0.775689 | + | 0.631116i | \(0.782597\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.4738 | 0.667710 | 0.333855 | − | 0.942624i | \(-0.391650\pi\) | ||||
0.333855 | + | 0.942624i | \(0.391650\pi\) | |||||||
\(350\) | −1.52868 | −0.0817114 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.92552 | 0.209231 | ||||||||
\(353\) | 36.8722 | 1.96251 | 0.981255 | − | 0.192712i | \(-0.0617284\pi\) | ||||
0.981255 | + | 0.192712i | \(0.0617284\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.9420 | −0.739966 | ||||||||
\(356\) | 2.07244 | 0.109839 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.71096 | 0.460389 | ||||||||
\(359\) | 6.19788 | 0.327112 | 0.163556 | − | 0.986534i | \(-0.447704\pi\) | ||||
0.163556 | + | 0.986534i | \(0.447704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.95522 | −0.260801 | ||||||||
\(362\) | 20.2676 | 1.06524 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.82275 | 0.200367 | ||||||||
\(365\) | 24.5757 | 1.28635 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.47250 | −0.494460 | −0.247230 | − | 0.968957i | \(-0.579520\pi\) | ||||
−0.247230 | + | 0.968957i | \(0.579520\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.69419 | 0.503977 | ||||||||
\(371\) | 9.34823 | 0.485336 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.7862 | 1.59405 | 0.797025 | − | 0.603946i | \(-0.206406\pi\) | ||||
0.797025 | + | 0.603946i | \(0.206406\pi\) | |||||||
\(374\) | 4.57890 | 0.236769 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.02025 | −0.258900 | ||||||||
\(377\) | 4.98978 | 0.256987 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.9229 | −1.43430 | −0.717152 | − | 0.696917i | \(-0.754555\pi\) | ||||
−0.717152 | + | 0.696917i | \(0.754555\pi\) | |||||||
\(380\) | −6.66907 | −0.342116 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.2062 | 1.13617 | ||||||||
\(383\) | −3.92038 | −0.200322 | −0.100161 | − | 0.994971i | \(-0.531936\pi\) | ||||
−0.100161 | + | 0.994971i | \(0.531936\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.82509 | 0.296874 | ||||||||
\(386\) | −19.1010 | −0.972215 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.5515 | −0.637203 | ||||||||
\(389\) | 34.8692 | 1.76794 | 0.883969 | − | 0.467545i | \(-0.154861\pi\) | ||||
0.883969 | + | 0.467545i | \(0.154861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −6.30466 | −0.318434 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.1223 | −1.16489 | ||||||||
\(395\) | −17.0283 | −0.856784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.01697 | −0.101229 | −0.0506145 | − | 0.998718i | \(-0.516118\pi\) | ||||
−0.0506145 | + | 0.998718i | \(0.516118\pi\) | |||||||
\(398\) | 15.2797 | 0.765905 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.83324 | −0.0916619 | ||||||||
\(401\) | −21.4584 | −1.07158 | −0.535791 | − | 0.844351i | \(-0.679986\pi\) | ||||
−0.535791 | + | 0.844351i | \(0.679986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.3234 | 1.61014 | ||||||||
\(404\) | 12.0480 | 0.599409 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.907615 | 0.0450442 | ||||||||
\(407\) | 21.3846 | 1.05999 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.8889 | −0.785656 | −0.392828 | − | 0.919612i | \(-0.628503\pi\) | ||||
−0.392828 | + | 0.919612i | \(0.628503\pi\) | |||||||
\(410\) | −2.58532 | −0.127680 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.0230 | 0.641598 | ||||||||
\(413\) | −3.26658 | −0.160738 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.9449 | −1.12632 | ||||||||
\(416\) | 4.58435 | 0.224766 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.7114 | −0.719559 | ||||||||
\(419\) | 27.8283 | 1.35950 | 0.679751 | − | 0.733443i | \(-0.262088\pi\) | ||||
0.679751 | + | 0.733443i | \(0.262088\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7105 | 0.619471 | 0.309735 | − | 0.950823i | \(-0.399760\pi\) | ||||
0.309735 | + | 0.950823i | \(0.399760\pi\) | |||||||
\(422\) | −6.20798 | −0.302200 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.2107 | 0.544438 | ||||||||
\(425\) | −2.13837 | −0.103726 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.49474 | −0.169122 | ||||||||
\(428\) | 4.83960 | 0.233931 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.97253 | 0.336245 | ||||||||
\(431\) | 36.6618 | 1.76593 | 0.882967 | − | 0.469435i | \(-0.155542\pi\) | ||||
0.882967 | + | 0.469435i | \(0.155542\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.94566 | −0.333787 | −0.166893 | − | 0.985975i | \(-0.553374\pi\) | ||||
−0.166893 | + | 0.985975i | \(0.553374\pi\) | |||||||
\(434\) | 5.87946 | 0.282223 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00790 | 0.0482696 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.3866 | 1.06845 | 0.534227 | − | 0.845341i | \(-0.320603\pi\) | ||||
0.534227 | + | 0.845341i | \(0.320603\pi\) | |||||||
\(440\) | 6.98562 | 0.333026 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.34740 | 0.254350 | ||||||||
\(443\) | −29.0072 | −1.37817 | −0.689087 | − | 0.724679i | \(-0.741988\pi\) | ||||
−0.689087 | + | 0.724679i | \(0.741988\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.68798 | 0.174827 | ||||||||
\(446\) | 15.4778 | 0.732893 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.833869 | 0.0393966 | ||||||||
\(449\) | 37.0126 | 1.74673 | 0.873367 | − | 0.487063i | \(-0.161932\pi\) | ||||
0.873367 | + | 0.487063i | \(0.161932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.70300 | −0.268544 | ||||||||
\(452\) | 10.5034 | 0.494036 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.0742 | 0.613600 | ||||||||
\(455\) | 6.80274 | 0.318917 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.38589 | −0.298719 | −0.149360 | − | 0.988783i | \(-0.547721\pi\) | ||||
−0.149360 | + | 0.988783i | \(0.547721\pi\) | |||||||
\(458\) | 24.8420 | 1.16079 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.03086 | 0.280885 | 0.140443 | − | 0.990089i | \(-0.455147\pi\) | ||||
0.140443 | + | 0.990089i | \(0.455147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.06935 | 0.0496970 | 0.0248485 | − | 0.999691i | \(-0.492090\pi\) | ||||
0.0248485 | + | 0.999691i | \(0.492090\pi\) | |||||||
\(464\) | 1.08844 | 0.0505295 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.11474 | −0.236936 | ||||||||
\(467\) | −0.947753 | −0.0438568 | −0.0219284 | − | 0.999760i | \(-0.506981\pi\) | ||||
−0.0219284 | + | 0.999760i | \(0.506981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.71509 | 0.0791953 | ||||||||
\(470\) | −8.93374 | −0.412083 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.91737 | −0.180312 | ||||||||
\(473\) | 15.3808 | 0.707212 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.87031 | 0.315232 | ||||||||
\(476\) | 0.972663 | 0.0445819 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.3989 | 1.11598 | ||||||||
\(479\) | −17.5466 | −0.801726 | −0.400863 | − | 0.916138i | \(-0.631290\pi\) | ||||
−0.400863 | + | 0.916138i | \(0.631290\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.9736 | 1.13870 | ||||||||
\(482\) | −9.08856 | −0.413972 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.40970 | 0.200441 | ||||||||
\(485\) | −22.3358 | −1.01422 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.5801 | 1.47635 | 0.738174 | − | 0.674611i | \(-0.235688\pi\) | ||||
0.738174 | + | 0.674611i | \(0.235688\pi\) | |||||||
\(488\) | −4.19099 | −0.189717 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.2194 | −0.506841 | ||||||||
\(491\) | −20.2982 | −0.916047 | −0.458023 | − | 0.888940i | \(-0.651442\pi\) | ||||
−0.458023 | + | 0.888940i | \(0.651442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.26960 | 0.0571801 | ||||||||
\(494\) | −17.1805 | −0.772987 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.05081 | 0.316591 | ||||||||
\(497\) | −6.53306 | −0.293048 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.83390 | −0.350694 | −0.175347 | − | 0.984507i | \(-0.556105\pi\) | ||||
−0.175347 | + | 0.984507i | \(0.556105\pi\) | |||||||
\(500\) | −12.1600 | −0.543813 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.53733 | 0.113247 | ||||||||
\(503\) | 12.8212 | 0.571667 | 0.285833 | − | 0.958279i | \(-0.407730\pi\) | ||||
0.285833 | + | 0.958279i | \(0.407730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.4398 | 0.954060 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.34381 | −0.237093 | ||||||||
\(509\) | −7.07163 | −0.313444 | −0.156722 | − | 0.987643i | \(-0.550093\pi\) | ||||
−0.156722 | + | 0.987643i | \(0.550093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.5159 | 0.509432 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.1594 | −1.28617 | ||||||||
\(515\) | 23.1750 | 1.02121 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.7071 | −0.866717 | ||||||||
\(518\) | 4.54257 | 0.199589 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.15804 | 0.357754 | ||||||||
\(521\) | 26.4413 | 1.15841 | 0.579207 | − | 0.815180i | \(-0.303362\pi\) | ||||
0.579207 | + | 0.815180i | \(0.303362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.7344 | −1.30019 | −0.650097 | − | 0.759851i | \(-0.725272\pi\) | ||||
−0.650097 | + | 0.759851i | \(0.725272\pi\) | |||||||
\(524\) | 10.6159 | 0.463759 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.88223 | −0.169273 | ||||||||
\(527\) | 8.22439 | 0.358260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 19.9498 | 0.866565 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.12504 | −0.135488 | ||||||||
\(533\) | −6.66016 | −0.288483 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.61226 | 0.372340 | ||||||||
\(536\) | 2.05678 | 0.0888394 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.55327 | 0.153192 | ||||||||
\(539\) | −24.7491 | −1.06602 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.72627 | −0.289185 | −0.144593 | − | 0.989491i | \(-0.546187\pi\) | ||||
−0.144593 | + | 0.989491i | \(0.546187\pi\) | |||||||
\(542\) | −22.1590 | −0.951809 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.16645 | 0.0500109 | ||||||||
\(545\) | 1.79360 | 0.0768292 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.1456 | −1.84477 | −0.922386 | − | 0.386269i | \(-0.873764\pi\) | ||||
−0.922386 | + | 0.386269i | \(0.873764\pi\) | |||||||
\(548\) | 11.2545 | 0.480767 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.19641 | −0.306856 | ||||||||
\(551\) | −4.07907 | −0.173774 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.97922 | −0.339311 | ||||||||
\(554\) | −13.4979 | −0.573469 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.20054 | −0.220552 | ||||||||
\(557\) | 20.2095 | 0.856302 | 0.428151 | − | 0.903707i | \(-0.359165\pi\) | ||||
0.428151 | + | 0.903707i | \(0.359165\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.9623 | 0.759723 | ||||||||
\(560\) | 1.48390 | 0.0627064 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 30.7477 | 1.29701 | ||||||||
\(563\) | −3.33199 | −0.140427 | −0.0702133 | − | 0.997532i | \(-0.522368\pi\) | ||||
−0.0702133 | + | 0.997532i | \(0.522368\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.6911 | 0.786342 | ||||||||
\(566\) | −20.5356 | −0.863177 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.83463 | −0.328734 | ||||||||
\(569\) | −10.9839 | −0.460469 | −0.230234 | − | 0.973135i | \(-0.573949\pi\) | ||||
−0.230234 | + | 0.973135i | \(0.573949\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7979 | −0.744818 | −0.372409 | − | 0.928069i | \(-0.621468\pi\) | ||||
−0.372409 | + | 0.928069i | \(0.621468\pi\) | |||||||
\(572\) | 17.9960 | 0.752449 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.21145 | −0.0505648 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.39513 | −0.266233 | −0.133116 | − | 0.991100i | \(-0.542498\pi\) | ||||
−0.133116 | + | 0.991100i | \(0.542498\pi\) | |||||||
\(578\) | −15.6394 | −0.650513 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.93692 | 0.0804261 | ||||||||
\(581\) | −10.7517 | −0.446054 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 44.0077 | 1.82261 | ||||||||
\(584\) | 13.8102 | 0.571468 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.66535 | −0.316653 | ||||||||
\(587\) | −9.11251 | −0.376114 | −0.188057 | − | 0.982158i | \(-0.560219\pi\) | ||||
−0.188057 | + | 0.982158i | \(0.560219\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.4239 | −1.08878 | ||||||||
\(590\) | −6.97112 | −0.286997 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.44758 | 0.223894 | ||||||||
\(593\) | 37.1777 | 1.52670 | 0.763352 | − | 0.645983i | \(-0.223552\pi\) | ||||
0.763352 | + | 0.645983i | \(0.223552\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.73089 | 0.0709597 | ||||||||
\(596\) | −19.1329 | −0.783715 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.27761 | 0.297355 | 0.148677 | − | 0.988886i | \(-0.452498\pi\) | ||||
0.148677 | + | 0.988886i | \(0.452498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.8840 | 1.42295 | 0.711475 | − | 0.702712i | \(-0.248028\pi\) | ||||
0.711475 | + | 0.702712i | \(0.248028\pi\) | |||||||
\(602\) | 3.26724 | 0.133163 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.6172 | −0.472697 | ||||||||
\(605\) | 7.84724 | 0.319036 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.8471 | −1.25205 | −0.626024 | − | 0.779804i | \(-0.715319\pi\) | ||||
−0.626024 | + | 0.779804i | \(0.715319\pi\) | |||||||
\(608\) | −3.74764 | −0.151987 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.45803 | −0.301967 | ||||||||
\(611\) | −23.0146 | −0.931071 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.1703 | 0.491553 | 0.245777 | − | 0.969327i | \(-0.420957\pi\) | ||||
0.245777 | + | 0.969327i | \(0.420957\pi\) | |||||||
\(614\) | 0.803500 | 0.0324266 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.27337 | 0.131888 | ||||||||
\(617\) | 4.11400 | 0.165623 | 0.0828116 | − | 0.996565i | \(-0.473610\pi\) | ||||
0.0828116 | + | 0.996565i | \(0.473610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.2972 | −1.13736 | −0.568680 | − | 0.822559i | \(-0.692546\pi\) | ||||
−0.568680 | + | 0.822559i | \(0.692546\pi\) | |||||||
\(620\) | 12.5472 | 0.503908 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.2869 | 1.05401 | ||||||||
\(623\) | 1.72814 | 0.0692365 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4730 | −0.498922 | ||||||||
\(626\) | 16.3715 | 0.654336 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.80726 | −0.112022 | ||||||||
\(629\) | 6.35431 | 0.253363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8555 | −0.710816 | −0.355408 | − | 0.934711i | \(-0.615658\pi\) | ||||
−0.355408 | + | 0.934711i | \(0.615658\pi\) | |||||||
\(632\) | −9.56891 | −0.380631 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.8264 | 0.509400 | ||||||||
\(635\) | −9.50952 | −0.377374 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.9028 | −1.14517 | ||||||||
\(638\) | 4.27268 | 0.169157 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.77954 | 0.0703425 | ||||||||
\(641\) | −40.9767 | −1.61848 | −0.809241 | − | 0.587476i | \(-0.800122\pi\) | ||||
−0.809241 | + | 0.587476i | \(0.800122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.3907 | −0.883003 | −0.441501 | − | 0.897261i | \(-0.645554\pi\) | ||||
−0.441501 | + | 0.897261i | \(0.645554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.37141 | −0.171991 | ||||||||
\(647\) | 6.61041 | 0.259882 | 0.129941 | − | 0.991522i | \(-0.458521\pi\) | ||||
0.129941 | + | 0.991522i | \(0.458521\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.3777 | −0.603629 | ||||||||
\(650\) | −8.40421 | −0.329640 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.2284 | −0.870533 | ||||||||
\(653\) | 40.7556 | 1.59489 | 0.797444 | − | 0.603393i | \(-0.206185\pi\) | ||||
0.797444 | + | 0.603393i | \(0.206185\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.8914 | 0.738150 | ||||||||
\(656\) | −1.45280 | −0.0567224 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.18623 | −0.163196 | ||||||||
\(659\) | −27.3344 | −1.06480 | −0.532399 | − | 0.846494i | \(-0.678709\pi\) | ||||
−0.532399 | + | 0.846494i | \(0.678709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0559 | 0.391129 | 0.195564 | − | 0.980691i | \(-0.437346\pi\) | ||||
0.195564 | + | 0.980691i | \(0.437346\pi\) | |||||||
\(662\) | 13.6654 | 0.531121 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.8937 | −0.500373 | ||||||||
\(665\) | −5.56113 | −0.215651 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −19.2351 | −0.744228 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.66012 | 0.141403 | ||||||||
\(671\) | −16.4518 | −0.635115 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5255 | −0.675557 | −0.337779 | − | 0.941226i | \(-0.609676\pi\) | ||||
−0.337779 | + | 0.941226i | \(0.609676\pi\) | |||||||
\(674\) | −10.3043 | −0.396908 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.01630 | 0.308319 | ||||||||
\(677\) | −9.23238 | −0.354829 | −0.177415 | − | 0.984136i | \(-0.556773\pi\) | ||||
−0.177415 | + | 0.984136i | \(0.556773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.4663 | −0.401659 | ||||||||
\(680\) | 2.07574 | 0.0796008 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.6781 | 1.05985 | ||||||||
\(683\) | 30.7576 | 1.17691 | 0.588453 | − | 0.808531i | \(-0.299737\pi\) | ||||
0.588453 | + | 0.808531i | \(0.299737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.0278 | 0.765222 | ||||||||
\(686\) | −11.0943 | −0.423584 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.91817 | 0.149379 | ||||||||
\(689\) | 51.3937 | 1.95794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.1989 | 1.49119 | 0.745597 | − | 0.666397i | \(-0.232164\pi\) | ||||
0.745597 | + | 0.666397i | \(0.232164\pi\) | |||||||
\(692\) | −22.1624 | −0.842488 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.8990 | −1.09699 | ||||||||
\(695\) | −9.25457 | −0.351046 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.69461 | −0.0641881 | ||||||||
\(698\) | 12.4738 | 0.472142 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.52868 | −0.0577787 | ||||||||
\(701\) | −33.3259 | −1.25870 | −0.629351 | − | 0.777121i | \(-0.716679\pi\) | ||||
−0.629351 | + | 0.777121i | \(0.716679\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.4156 | −0.769987 | ||||||||
\(704\) | 3.92552 | 0.147949 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 36.8722 | 1.38770 | ||||||||
\(707\) | 10.0464 | 0.377835 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.15309 | −0.0808608 | −0.0404304 | − | 0.999182i | \(-0.512873\pi\) | ||||
−0.0404304 | + | 0.999182i | \(0.512873\pi\) | |||||||
\(710\) | −13.9420 | −0.523235 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.07244 | 0.0776678 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0245 | 1.19765 | ||||||||
\(716\) | 8.71096 | 0.325544 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.19788 | 0.231303 | ||||||||
\(719\) | −4.28248 | −0.159710 | −0.0798548 | − | 0.996807i | \(-0.525446\pi\) | ||||
−0.0798548 | + | 0.996807i | \(0.525446\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8595 | 0.404429 | ||||||||
\(722\) | −4.95522 | −0.184414 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.2676 | 0.753240 | ||||||||
\(725\) | −1.99537 | −0.0741060 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.7807 | −1.40121 | −0.700603 | − | 0.713551i | \(-0.747086\pi\) | ||||
−0.700603 | + | 0.713551i | \(0.747086\pi\) | |||||||
\(728\) | 3.82275 | 0.141681 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24.5757 | 0.909588 | ||||||||
\(731\) | 4.57033 | 0.169040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.6316 | 1.64851 | 0.824254 | − | 0.566221i | \(-0.191595\pi\) | ||||
0.824254 | + | 0.566221i | \(0.191595\pi\) | |||||||
\(734\) | −9.47250 | −0.349636 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.07393 | 0.297407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.7631 | −0.837356 | −0.418678 | − | 0.908135i | \(-0.637506\pi\) | ||||
−0.418678 | + | 0.908135i | \(0.637506\pi\) | |||||||
\(740\) | 9.69419 | 0.356365 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.34823 | 0.343184 | ||||||||
\(743\) | 3.30466 | 0.121236 | 0.0606181 | − | 0.998161i | \(-0.480693\pi\) | ||||
0.0606181 | + | 0.998161i | \(0.480693\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.0478 | −1.24741 | ||||||||
\(746\) | 30.7862 | 1.12716 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.57890 | 0.167421 | ||||||||
\(749\) | 4.03559 | 0.147457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.8035 | −1.92683 | −0.963413 | − | 0.268020i | \(-0.913631\pi\) | ||||
−0.963413 | + | 0.268020i | \(0.913631\pi\) | |||||||
\(752\) | −5.02025 | −0.183070 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.98978 | 0.181717 | ||||||||
\(755\) | −20.6732 | −0.752376 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6559 | −0.532677 | −0.266338 | − | 0.963880i | \(-0.585814\pi\) | ||||
−0.266338 | + | 0.963880i | \(0.585814\pi\) | |||||||
\(758\) | −27.9229 | −1.01421 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.66907 | −0.241913 | ||||||||
\(761\) | 25.9170 | 0.939492 | 0.469746 | − | 0.882802i | \(-0.344346\pi\) | ||||
0.469746 | + | 0.882802i | \(0.344346\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.840456 | 0.0304266 | ||||||||
\(764\) | 22.2062 | 0.803391 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.92038 | −0.141649 | ||||||||
\(767\) | −17.9586 | −0.648449 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −52.5864 | −1.89631 | −0.948157 | − | 0.317801i | \(-0.897055\pi\) | ||||
−0.948157 | + | 0.317801i | \(0.897055\pi\) | |||||||
\(770\) | 5.82509 | 0.209922 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.1010 | −0.687460 | ||||||||
\(773\) | 4.07182 | 0.146453 | 0.0732266 | − | 0.997315i | \(-0.476670\pi\) | ||||
0.0732266 | + | 0.997315i | \(0.476670\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.9258 | −0.464309 | ||||||||
\(776\) | −12.5515 | −0.450571 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 34.8692 | 1.25012 | ||||||||
\(779\) | 5.44457 | 0.195072 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.7550 | −1.10050 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.30466 | −0.225167 | ||||||||
\(785\) | −4.99563 | −0.178302 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.0689694 | −0.00245849 | −0.00122925 | − | 0.999999i | \(-0.500391\pi\) | ||||
−0.00122925 | + | 0.999999i | \(0.500391\pi\) | |||||||
\(788\) | −23.1223 | −0.823699 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.0283 | −0.605838 | ||||||||
\(791\) | 8.75842 | 0.311414 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.2130 | −0.682273 | ||||||||
\(794\) | −2.01697 | −0.0715797 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.2797 | 0.541576 | ||||||||
\(797\) | 2.14410 | 0.0759481 | 0.0379740 | − | 0.999279i | \(-0.487910\pi\) | ||||
0.0379740 | + | 0.999279i | \(0.487910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.85585 | −0.207165 | ||||||||
\(800\) | −1.83324 | −0.0648148 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.4584 | −0.757723 | ||||||||
\(803\) | 54.2120 | 1.91310 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.3234 | 1.13854 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.0480 | 0.423846 | ||||||||
\(809\) | −25.7785 | −0.906325 | −0.453162 | − | 0.891428i | \(-0.649704\pi\) | ||||
−0.453162 | + | 0.891428i | \(0.649704\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1268 | −0.741861 | −0.370930 | − | 0.928661i | \(-0.620961\pi\) | ||||
−0.370930 | + | 0.928661i | \(0.620961\pi\) | |||||||
\(812\) | 0.907615 | 0.0318510 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 21.3846 | 0.749529 | ||||||||
\(815\) | −39.5564 | −1.38560 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.6839 | −0.513723 | ||||||||
\(818\) | −15.8889 | −0.555543 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.58532 | −0.0902832 | ||||||||
\(821\) | −30.0621 | −1.04917 | −0.524587 | − | 0.851357i | \(-0.675780\pi\) | ||||
−0.524587 | + | 0.851357i | \(0.675780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.7965 | 0.655204 | 0.327602 | − | 0.944816i | \(-0.393760\pi\) | ||||
0.327602 | + | 0.944816i | \(0.393760\pi\) | |||||||
\(824\) | 13.0230 | 0.453678 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.26658 | −0.113659 | ||||||||
\(827\) | 49.2602 | 1.71295 | 0.856473 | − | 0.516192i | \(-0.172651\pi\) | ||||
0.856473 | + | 0.516192i | \(0.172651\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0455 | 0.348896 | 0.174448 | − | 0.984666i | \(-0.444186\pi\) | ||||
0.174448 | + | 0.984666i | \(0.444186\pi\) | |||||||
\(830\) | −22.9449 | −0.796428 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.58435 | 0.158934 | ||||||||
\(833\) | −7.35404 | −0.254803 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.2296 | −1.18457 | ||||||||
\(836\) | −14.7114 | −0.508805 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 27.8283 | 0.961312 | ||||||||
\(839\) | 1.36255 | 0.0470406 | 0.0235203 | − | 0.999723i | \(-0.492513\pi\) | ||||
0.0235203 | + | 0.999723i | \(0.492513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.8153 | −0.959148 | ||||||||
\(842\) | 12.7105 | 0.438032 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.20798 | −0.213688 | ||||||||
\(845\) | 14.2653 | 0.490742 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.67711 | 0.126347 | ||||||||
\(848\) | 11.2107 | 0.384976 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.13837 | −0.0733456 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.5275 | −1.04524 | −0.522620 | − | 0.852565i | \(-0.675045\pi\) | ||||
−0.522620 | + | 0.852565i | \(0.675045\pi\) | |||||||
\(854\) | −3.49474 | −0.119587 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.83960 | 0.165414 | ||||||||
\(857\) | −5.62391 | −0.192109 | −0.0960545 | − | 0.995376i | \(-0.530622\pi\) | ||||
−0.0960545 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.4852 | −1.04014 | −0.520070 | − | 0.854123i | \(-0.674094\pi\) | ||||
−0.520070 | + | 0.854123i | \(0.674094\pi\) | |||||||
\(860\) | 6.97253 | 0.237761 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.6618 | 1.24870 | ||||||||
\(863\) | −30.7008 | −1.04507 | −0.522535 | − | 0.852618i | \(-0.675013\pi\) | ||||
−0.522535 | + | 0.852618i | \(0.675013\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −39.4389 | −1.34096 | ||||||||
\(866\) | −6.94566 | −0.236023 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.87946 | 0.199562 | ||||||||
\(869\) | −37.5629 | −1.27424 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.42901 | 0.319490 | ||||||||
\(872\) | 1.00790 | 0.0341318 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1399 | −0.342790 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.4974 | 1.77271 | 0.886356 | − | 0.463005i | \(-0.153229\pi\) | ||||
0.886356 | + | 0.463005i | \(0.153229\pi\) | |||||||
\(878\) | 22.3866 | 0.755510 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.98562 | 0.235485 | ||||||||
\(881\) | −5.56489 | −0.187486 | −0.0937429 | − | 0.995596i | \(-0.529883\pi\) | ||||
−0.0937429 | + | 0.995596i | \(0.529883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.8536 | 0.937350 | 0.468675 | − | 0.883371i | \(-0.344732\pi\) | ||||
0.468675 | + | 0.883371i | \(0.344732\pi\) | |||||||
\(884\) | 5.34740 | 0.179852 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −29.0072 | −0.974516 | ||||||||
\(887\) | 8.02769 | 0.269544 | 0.134772 | − | 0.990877i | \(-0.456970\pi\) | ||||
0.134772 | + | 0.990877i | \(0.456970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.45604 | −0.149451 | ||||||||
\(890\) | 3.68798 | 0.123621 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.4778 | 0.518234 | ||||||||
\(893\) | 18.8141 | 0.629589 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.5015 | 0.518158 | ||||||||
\(896\) | 0.833869 | 0.0278576 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.0126 | 1.23513 | ||||||||
\(899\) | 7.67437 | 0.255955 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.0766 | 0.435646 | ||||||||
\(902\) | −5.70300 | −0.189889 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.5034 | 0.349336 | ||||||||
\(905\) | 36.0670 | 1.19891 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52.8322 | −1.75427 | −0.877133 | − | 0.480248i | \(-0.840547\pi\) | ||||
−0.877133 | + | 0.480248i | \(0.840547\pi\) | |||||||
\(908\) | 13.0742 | 0.433881 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.80274 | 0.225509 | ||||||||
\(911\) | 9.32564 | 0.308972 | 0.154486 | − | 0.987995i | \(-0.450628\pi\) | ||||
0.154486 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −50.6145 | −1.67510 | ||||||||
\(914\) | −6.38589 | −0.211227 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.8420 | 0.820801 | ||||||||
\(917\) | 8.85229 | 0.292328 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.1566 | 0.433997 | 0.216998 | − | 0.976172i | \(-0.430373\pi\) | ||||
0.216998 | + | 0.976172i | \(0.430373\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.03086 | 0.198616 | ||||||||
\(923\) | −35.9167 | −1.18221 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.98672 | −0.328361 | ||||||||
\(926\) | 1.06935 | 0.0351411 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.08844 | 0.0357297 | ||||||||
\(929\) | −29.9879 | −0.983872 | −0.491936 | − | 0.870631i | \(-0.663711\pi\) | ||||
−0.491936 | + | 0.870631i | \(0.663711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.6276 | 0.774363 | ||||||||
\(932\) | −5.11474 | −0.167539 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.947753 | −0.0310114 | ||||||||
\(935\) | 8.14834 | 0.266479 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.3742 | 0.698265 | 0.349132 | − | 0.937073i | \(-0.386476\pi\) | ||||
0.349132 | + | 0.937073i | \(0.386476\pi\) | |||||||
\(938\) | 1.71509 | 0.0559995 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.93374 | −0.291386 | ||||||||
\(941\) | −5.27352 | −0.171912 | −0.0859559 | − | 0.996299i | \(-0.527394\pi\) | ||||
−0.0859559 | + | 0.996299i | \(0.527394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −3.91737 | −0.127500 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.3808 | 0.500074 | ||||||||
\(947\) | 6.75876 | 0.219630 | 0.109815 | − | 0.993952i | \(-0.464974\pi\) | ||||
0.109815 | + | 0.993952i | \(0.464974\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 63.3106 | 2.05515 | ||||||||
\(950\) | 6.87031 | 0.222902 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.972663 | 0.0315242 | ||||||||
\(953\) | 8.65623 | 0.280403 | 0.140201 | − | 0.990123i | \(-0.455225\pi\) | ||||
0.140201 | + | 0.990123i | \(0.455225\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.5168 | 1.27873 | ||||||||
\(956\) | 24.3989 | 0.789118 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.5466 | −0.566906 | ||||||||
\(959\) | 9.38475 | 0.303049 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.7140 | 0.603676 | ||||||||
\(962\) | 24.9736 | 0.805182 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.08856 | −0.292723 | ||||||||
\(965\) | −33.9910 | −1.09421 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.42139 | 0.302971 | 0.151486 | − | 0.988459i | \(-0.451594\pi\) | ||||
0.151486 | + | 0.988459i | \(0.451594\pi\) | |||||||
\(968\) | 4.40970 | 0.141733 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −22.3358 | −0.717160 | ||||||||
\(971\) | 36.0574 | 1.15714 | 0.578569 | − | 0.815633i | \(-0.303611\pi\) | ||||
0.578569 | + | 0.815633i | \(0.303611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.33657 | −0.139024 | ||||||||
\(974\) | 32.5801 | 1.04394 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.19099 | −0.134150 | ||||||||
\(977\) | 43.1184 | 1.37948 | 0.689740 | − | 0.724057i | \(-0.257725\pi\) | ||||
0.689740 | + | 0.724057i | \(0.257725\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.13539 | 0.260008 | ||||||||
\(980\) | −11.2194 | −0.358390 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.2982 | −0.647743 | ||||||||
\(983\) | −7.15082 | −0.228076 | −0.114038 | − | 0.993476i | \(-0.536379\pi\) | ||||
−0.114038 | + | 0.993476i | \(0.536379\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.1471 | −1.31106 | ||||||||
\(986\) | 1.26960 | 0.0404324 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.1805 | −0.546584 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.9221 | 0.886974 | 0.443487 | − | 0.896281i | \(-0.353741\pi\) | ||||
0.443487 | + | 0.896281i | \(0.353741\pi\) | |||||||
\(992\) | 7.05081 | 0.223864 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.53306 | −0.207216 | ||||||||
\(995\) | 27.1909 | 0.862010 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.05093 | 0.223305 | 0.111653 | − | 0.993747i | \(-0.464386\pi\) | ||||
0.111653 | + | 0.993747i | \(0.464386\pi\) | |||||||
\(998\) | −7.83390 | −0.247978 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9522.2.a.cj.1.6 | 10 | ||
3.2 | odd | 2 | 9522.2.a.cg.1.5 | 10 | |||
23.13 | even | 11 | 414.2.i.g.307.1 | ✓ | 20 | ||
23.16 | even | 11 | 414.2.i.g.325.1 | yes | 20 | ||
23.22 | odd | 2 | 9522.2.a.ci.1.5 | 10 | |||
69.59 | odd | 22 | 414.2.i.h.307.2 | yes | 20 | ||
69.62 | odd | 22 | 414.2.i.h.325.2 | yes | 20 | ||
69.68 | even | 2 | 9522.2.a.ch.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.2.i.g.307.1 | ✓ | 20 | 23.13 | even | 11 | ||
414.2.i.g.325.1 | yes | 20 | 23.16 | even | 11 | ||
414.2.i.h.307.2 | yes | 20 | 69.59 | odd | 22 | ||
414.2.i.h.325.2 | yes | 20 | 69.62 | odd | 22 | ||
9522.2.a.cg.1.5 | 10 | 3.2 | odd | 2 | |||
9522.2.a.ch.1.6 | 10 | 69.68 | even | 2 | |||
9522.2.a.ci.1.5 | 10 | 23.22 | odd | 2 | |||
9522.2.a.cj.1.6 | 10 | 1.1 | even | 1 | trivial |