Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1215,2,Mod(1,1215)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1215, 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("1215.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1215 = 3^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1215.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: | \(9.70182384559\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1215.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30278 | −1.62831 | −0.814154 | − | 0.580649i | \(-0.802799\pi\) | ||||
−0.814154 | + | 0.580649i | \(0.802799\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.30278 | 1.65139 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.30278 | 0.492403 | 0.246201 | − | 0.969219i | \(-0.420818\pi\) | ||||
0.246201 | + | 0.969219i | \(0.420818\pi\) | |||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.30278 | −0.728202 | ||||||||
\(11\) | −2.30278 | −0.694313 | −0.347156 | − | 0.937807i | \(-0.612853\pi\) | ||||
−0.347156 | + | 0.937807i | \(0.612853\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.60555 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | −5.30278 | −1.28611 | −0.643056 | − | 0.765819i | \(-0.722334\pi\) | ||||
−0.643056 | + | 0.765819i | \(0.722334\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.30278 | −1.44596 | −0.722978 | − | 0.690871i | \(-0.757227\pi\) | ||||
−0.722978 | + | 0.690871i | \(0.757227\pi\) | |||||||
\(20\) | 3.30278 | 0.738523 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.30278 | 1.13056 | ||||||||
\(23\) | −3.00000 | −0.625543 | −0.312772 | − | 0.949828i | \(-0.601257\pi\) | ||||
−0.312772 | + | 0.949828i | \(0.601257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −8.30278 | −1.62831 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.30278 | 0.813148 | ||||||||
\(29\) | −7.60555 | −1.41232 | −0.706158 | − | 0.708055i | \(-0.749573\pi\) | ||||
−0.706158 | + | 0.708055i | \(0.749573\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.21110 | 0.935942 | 0.467971 | − | 0.883744i | \(-0.344985\pi\) | ||||
0.467971 | + | 0.883744i | \(0.344985\pi\) | |||||||
\(32\) | 5.30278 | 0.937407 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.2111 | 2.09419 | ||||||||
\(35\) | 1.30278 | 0.220209 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.90833 | −1.30012 | −0.650060 | − | 0.759882i | \(-0.725256\pi\) | ||||
−0.650060 | + | 0.759882i | \(0.725256\pi\) | |||||||
\(38\) | 14.5139 | 2.35446 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | −0.474342 | ||||||||
\(41\) | −6.69722 | −1.04593 | −0.522965 | − | 0.852354i | \(-0.675174\pi\) | ||||
−0.522965 | + | 0.852354i | \(0.675174\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.21110 | −1.09968 | −0.549841 | − | 0.835269i | \(-0.685312\pi\) | ||||
−0.549841 | + | 0.835269i | \(0.685312\pi\) | |||||||
\(44\) | −7.60555 | −1.14658 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.90833 | 1.01858 | ||||||||
\(47\) | 6.69722 | 0.976891 | 0.488445 | − | 0.872595i | \(-0.337564\pi\) | ||||
0.488445 | + | 0.872595i | \(0.337564\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.30278 | −0.757539 | ||||||||
\(50\) | −2.30278 | −0.325662 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.9083 | 1.65139 | ||||||||
\(53\) | 8.51388 | 1.16947 | 0.584736 | − | 0.811224i | \(-0.301198\pi\) | ||||
0.584736 | + | 0.811224i | \(0.301198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.30278 | −0.310506 | ||||||||
\(56\) | −3.90833 | −0.522272 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 17.5139 | 2.29968 | ||||||||
\(59\) | −1.39445 | −0.181542 | −0.0907709 | − | 0.995872i | \(-0.528933\pi\) | ||||
−0.0907709 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.605551 | 0.0775329 | 0.0387664 | − | 0.999248i | \(-0.487657\pi\) | ||||
0.0387664 | + | 0.999248i | \(0.487657\pi\) | |||||||
\(62\) | −12.0000 | −1.52400 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8167 | −1.60208 | ||||||||
\(65\) | 3.60555 | 0.447214 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3028 | 1.25868 | 0.629342 | − | 0.777128i | \(-0.283324\pi\) | ||||
0.629342 | + | 0.777128i | \(0.283324\pi\) | |||||||
\(68\) | −17.5139 | −2.12387 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | −1.60555 | −0.190544 | −0.0952719 | − | 0.995451i | \(-0.530372\pi\) | ||||
−0.0952719 | + | 0.995451i | \(0.530372\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.6056 | 1.47537 | 0.737684 | − | 0.675146i | \(-0.235919\pi\) | ||||
0.737684 | + | 0.675146i | \(0.235919\pi\) | |||||||
\(74\) | 18.2111 | 2.11700 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.8167 | −2.38783 | ||||||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5139 | −1.40792 | −0.703961 | − | 0.710239i | \(-0.748587\pi\) | ||||
−0.703961 | + | 0.710239i | \(0.748587\pi\) | |||||||
\(80\) | 0.302776 | 0.0338513 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.4222 | 1.70310 | ||||||||
\(83\) | 14.7250 | 1.61628 | 0.808138 | − | 0.588993i | \(-0.200475\pi\) | ||||
0.808138 | + | 0.588993i | \(0.200475\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.30278 | −0.575167 | ||||||||
\(86\) | 16.6056 | 1.79062 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.90833 | 0.736430 | ||||||||
\(89\) | 4.81665 | 0.510564 | 0.255282 | − | 0.966867i | \(-0.417832\pi\) | ||||
0.255282 | + | 0.966867i | \(0.417832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.69722 | 0.492403 | ||||||||
\(92\) | −9.90833 | −1.03301 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.4222 | −1.59068 | ||||||||
\(95\) | −6.30278 | −0.646651 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7250 | −1.59663 | −0.798315 | − | 0.602240i | \(-0.794275\pi\) | ||||
−0.798315 | + | 0.602240i | \(0.794275\pi\) | |||||||
\(98\) | 12.2111 | 1.23351 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.30278 | 0.330278 | ||||||||
\(101\) | −17.7250 | −1.76370 | −0.881851 | − | 0.471529i | \(-0.843702\pi\) | ||||
−0.881851 | + | 0.471529i | \(0.843702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.81665 | −0.868731 | −0.434365 | − | 0.900737i | \(-0.643027\pi\) | ||||
−0.434365 | + | 0.900737i | \(0.643027\pi\) | |||||||
\(104\) | −10.8167 | −1.06066 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −19.6056 | −1.90426 | ||||||||
\(107\) | 2.09167 | 0.202210 | 0.101105 | − | 0.994876i | \(-0.467762\pi\) | ||||
0.101105 | + | 0.994876i | \(0.467762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.9083 | −1.61952 | −0.809762 | − | 0.586758i | \(-0.800404\pi\) | ||||
−0.809762 | + | 0.586758i | \(0.800404\pi\) | |||||||
\(110\) | 5.30278 | 0.505600 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.394449 | 0.0372719 | ||||||||
\(113\) | −6.21110 | −0.584291 | −0.292146 | − | 0.956374i | \(-0.594369\pi\) | ||||
−0.292146 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | −0.279751 | ||||||||
\(116\) | −25.1194 | −2.33228 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.21110 | 0.295606 | ||||||||
\(119\) | −6.90833 | −0.633285 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.69722 | −0.517929 | ||||||||
\(122\) | −1.39445 | −0.126247 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 17.2111 | 1.54560 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.605551 | 0.0537340 | 0.0268670 | − | 0.999639i | \(-0.491447\pi\) | ||||
0.0268670 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(128\) | 18.9083 | 1.67128 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.30278 | −0.728202 | ||||||||
\(131\) | 10.8167 | 0.945055 | 0.472528 | − | 0.881316i | \(-0.343342\pi\) | ||||
0.472528 | + | 0.881316i | \(0.343342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.21110 | −0.711993 | ||||||||
\(134\) | −23.7250 | −2.04953 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.9083 | 1.36413 | ||||||||
\(137\) | −15.0000 | −1.28154 | −0.640768 | − | 0.767734i | \(-0.721384\pi\) | ||||
−0.640768 | + | 0.767734i | \(0.721384\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0000 | 0.933008 | 0.466504 | − | 0.884519i | \(-0.345513\pi\) | ||||
0.466504 | + | 0.884519i | \(0.345513\pi\) | |||||||
\(140\) | 4.30278 | 0.363651 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.69722 | 0.310264 | ||||||||
\(143\) | −8.30278 | −0.694313 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.60555 | −0.631607 | ||||||||
\(146\) | −29.0278 | −2.40235 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −26.1194 | −2.14700 | ||||||||
\(149\) | 16.1194 | 1.32056 | 0.660278 | − | 0.751022i | \(-0.270439\pi\) | ||||
0.660278 | + | 0.751022i | \(0.270439\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1194 | −0.904886 | −0.452443 | − | 0.891793i | \(-0.649447\pi\) | ||||
−0.452443 | + | 0.891793i | \(0.649447\pi\) | |||||||
\(152\) | 18.9083 | 1.53367 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.90833 | 0.556689 | ||||||||
\(155\) | 5.21110 | 0.418566 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.81665 | −0.224793 | −0.112397 | − | 0.993663i | \(-0.535853\pi\) | ||||
−0.112397 | + | 0.993663i | \(0.535853\pi\) | |||||||
\(158\) | 28.8167 | 2.29253 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.30278 | 0.419221 | ||||||||
\(161\) | −3.90833 | −0.308019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | −22.1194 | −1.72724 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.9083 | −2.63180 | ||||||||
\(167\) | −18.9083 | −1.46317 | −0.731585 | − | 0.681750i | \(-0.761219\pi\) | ||||
−0.731585 | + | 0.681750i | \(0.761219\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 12.2111 | 0.936549 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −23.8167 | −1.81600 | ||||||||
\(173\) | −1.18335 | −0.0899681 | −0.0449841 | − | 0.998988i | \(-0.514324\pi\) | ||||
−0.0449841 | + | 0.998988i | \(0.514324\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.30278 | 0.0984806 | ||||||||
\(176\) | −0.697224 | −0.0525553 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.0917 | −0.831356 | ||||||||
\(179\) | 19.6056 | 1.46539 | 0.732694 | − | 0.680558i | \(-0.238263\pi\) | ||||
0.732694 | + | 0.680558i | \(0.238263\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.90833 | −0.587821 | −0.293911 | − | 0.955833i | \(-0.594957\pi\) | ||||
−0.293911 | + | 0.955833i | \(0.594957\pi\) | |||||||
\(182\) | −10.8167 | −0.801784 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.00000 | 0.663489 | ||||||||
\(185\) | −7.90833 | −0.581432 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.2111 | 0.892964 | ||||||||
\(188\) | 22.1194 | 1.61323 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.5139 | 1.05295 | ||||||||
\(191\) | −7.60555 | −0.550318 | −0.275159 | − | 0.961399i | \(-0.588731\pi\) | ||||
−0.275159 | + | 0.961399i | \(0.588731\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | 0.359908 | 0.179954 | − | 0.983675i | \(-0.442405\pi\) | ||||
0.179954 | + | 0.983675i | \(0.442405\pi\) | |||||||
\(194\) | 36.2111 | 2.59981 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17.5139 | −1.25099 | ||||||||
\(197\) | −20.7250 | −1.47659 | −0.738297 | − | 0.674476i | \(-0.764370\pi\) | ||||
−0.738297 | + | 0.674476i | \(0.764370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.4222 | 1.66036 | 0.830178 | − | 0.557498i | \(-0.188239\pi\) | ||||
0.830178 | + | 0.557498i | \(0.188239\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 40.8167 | 2.87185 | ||||||||
\(203\) | −9.90833 | −0.695428 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.69722 | −0.467754 | ||||||||
\(206\) | 20.3028 | 1.41456 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.09167 | 0.0756939 | ||||||||
\(209\) | 14.5139 | 1.00395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.18335 | −0.150308 | −0.0751539 | − | 0.997172i | \(-0.523945\pi\) | ||||
−0.0751539 | + | 0.997172i | \(0.523945\pi\) | |||||||
\(212\) | 28.1194 | 1.93125 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.81665 | −0.329260 | ||||||||
\(215\) | −7.21110 | −0.491793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.78890 | 0.460860 | ||||||||
\(218\) | 38.9361 | 2.63708 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.60555 | −0.512766 | ||||||||
\(221\) | −19.1194 | −1.28611 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.9083 | 1.40013 | 0.700063 | − | 0.714082i | \(-0.253155\pi\) | ||||
0.700063 | + | 0.714082i | \(0.253155\pi\) | |||||||
\(224\) | 6.90833 | 0.461582 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.3028 | 0.951406 | ||||||||
\(227\) | −7.60555 | −0.504798 | −0.252399 | − | 0.967623i | \(-0.581220\pi\) | ||||
−0.252399 | + | 0.967623i | \(0.581220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.2111 | 0.939096 | 0.469548 | − | 0.882907i | \(-0.344417\pi\) | ||||
0.469548 | + | 0.882907i | \(0.344417\pi\) | |||||||
\(230\) | 6.90833 | 0.455522 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.8167 | 1.49799 | ||||||||
\(233\) | 22.8167 | 1.49477 | 0.747384 | − | 0.664392i | \(-0.231309\pi\) | ||||
0.747384 | + | 0.664392i | \(0.231309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.69722 | 0.436879 | ||||||||
\(236\) | −4.60555 | −0.299796 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.9083 | 1.03118 | ||||||||
\(239\) | −20.0278 | −1.29549 | −0.647744 | − | 0.761858i | \(-0.724287\pi\) | ||||
−0.647744 | + | 0.761858i | \(0.724287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.39445 | −0.154240 | −0.0771200 | − | 0.997022i | \(-0.524572\pi\) | ||||
−0.0771200 | + | 0.997022i | \(0.524572\pi\) | |||||||
\(242\) | 13.1194 | 0.843349 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −5.30278 | −0.338782 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.7250 | −1.44596 | ||||||||
\(248\) | −15.6333 | −0.992716 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.30278 | −0.145640 | ||||||||
\(251\) | 2.09167 | 0.132025 | 0.0660126 | − | 0.997819i | \(-0.478972\pi\) | ||||
0.0660126 | + | 0.997819i | \(0.478972\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.90833 | 0.434323 | ||||||||
\(254\) | −1.39445 | −0.0874955 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | −9.90833 | −0.618064 | −0.309032 | − | 0.951052i | \(-0.600005\pi\) | ||||
−0.309032 | + | 0.951052i | \(0.600005\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3028 | −0.640183 | ||||||||
\(260\) | 11.9083 | 0.738523 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −24.9083 | −1.53884 | ||||||||
\(263\) | −5.51388 | −0.340000 | −0.170000 | − | 0.985444i | \(-0.554377\pi\) | ||||
−0.170000 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.51388 | 0.523003 | ||||||||
\(266\) | 18.9083 | 1.15934 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 34.0278 | 2.07858 | ||||||||
\(269\) | 21.6972 | 1.32290 | 0.661452 | − | 0.749988i | \(-0.269941\pi\) | ||||
0.661452 | + | 0.749988i | \(0.269941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0278 | −0.912871 | −0.456436 | − | 0.889756i | \(-0.650874\pi\) | ||||
−0.456436 | + | 0.889756i | \(0.650874\pi\) | |||||||
\(272\) | −1.60555 | −0.0973508 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 34.5416 | 2.08674 | ||||||||
\(275\) | −2.30278 | −0.138863 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.51388 | −0.211128 | −0.105564 | − | 0.994412i | \(-0.533665\pi\) | ||||
−0.105564 | + | 0.994412i | \(0.533665\pi\) | |||||||
\(278\) | −25.3305 | −1.51922 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.90833 | −0.233567 | ||||||||
\(281\) | 7.81665 | 0.466302 | 0.233151 | − | 0.972440i | \(-0.425096\pi\) | ||||
0.233151 | + | 0.972440i | \(0.425096\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.11943 | 0.185431 | 0.0927154 | − | 0.995693i | \(-0.470445\pi\) | ||||
0.0927154 | + | 0.995693i | \(0.470445\pi\) | |||||||
\(284\) | −5.30278 | −0.314662 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.1194 | 1.13056 | ||||||||
\(287\) | −8.72498 | −0.515019 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1194 | 0.654084 | ||||||||
\(290\) | 17.5139 | 1.02845 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 41.6333 | 2.43641 | ||||||||
\(293\) | 8.72498 | 0.509719 | 0.254859 | − | 0.966978i | \(-0.417971\pi\) | ||||
0.254859 | + | 0.966978i | \(0.417971\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.39445 | −0.0811879 | ||||||||
\(296\) | 23.7250 | 1.37899 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −37.1194 | −2.15027 | ||||||||
\(299\) | −10.8167 | −0.625543 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.39445 | −0.541487 | ||||||||
\(302\) | 25.6056 | 1.47343 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.90833 | −0.109450 | ||||||||
\(305\) | 0.605551 | 0.0346738 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3028 | −0.702156 | −0.351078 | − | 0.936346i | \(-0.614185\pi\) | ||||
−0.351078 | + | 0.936346i | \(0.614185\pi\) | |||||||
\(308\) | −9.90833 | −0.564579 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.0000 | −0.681554 | ||||||||
\(311\) | 6.00000 | 0.340229 | 0.170114 | − | 0.985424i | \(-0.445586\pi\) | ||||
0.170114 | + | 0.985424i | \(0.445586\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7250 | 0.945352 | 0.472676 | − | 0.881236i | \(-0.343288\pi\) | ||||
0.472676 | + | 0.881236i | \(0.343288\pi\) | |||||||
\(314\) | 6.48612 | 0.366033 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −41.3305 | −2.32502 | ||||||||
\(317\) | 6.21110 | 0.348850 | 0.174425 | − | 0.984670i | \(-0.444193\pi\) | ||||
0.174425 | + | 0.984670i | \(0.444193\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.5139 | 0.980589 | ||||||||
\(320\) | −12.8167 | −0.716473 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.00000 | 0.501550 | ||||||||
\(323\) | 33.4222 | 1.85966 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.60555 | 0.200000 | ||||||||
\(326\) | 23.0278 | 1.27539 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.0917 | 1.10938 | ||||||||
\(329\) | 8.72498 | 0.481024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9361 | 0.601102 | 0.300551 | − | 0.953766i | \(-0.402830\pi\) | ||||
0.300551 | + | 0.953766i | \(0.402830\pi\) | |||||||
\(332\) | 48.6333 | 2.66910 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 43.5416 | 2.38249 | ||||||||
\(335\) | 10.3028 | 0.562901 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.5139 | 1.06299 | 0.531494 | − | 0.847062i | \(-0.321631\pi\) | ||||
0.531494 | + | 0.847062i | \(0.321631\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −17.5139 | −0.949823 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0278 | −0.865417 | ||||||||
\(344\) | 21.6333 | 1.16639 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.72498 | 0.146496 | ||||||||
\(347\) | −13.1194 | −0.704288 | −0.352144 | − | 0.935946i | \(-0.614547\pi\) | ||||
−0.352144 | + | 0.935946i | \(0.614547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.48612 | −0.240137 | −0.120068 | − | 0.992766i | \(-0.538311\pi\) | ||||
−0.120068 | + | 0.992766i | \(0.538311\pi\) | |||||||
\(350\) | −3.00000 | −0.160357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.2111 | −0.650854 | ||||||||
\(353\) | −24.0000 | −1.27739 | −0.638696 | − | 0.769460i | \(-0.720526\pi\) | ||||
−0.638696 | + | 0.769460i | \(0.720526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.60555 | −0.0852138 | ||||||||
\(356\) | 15.9083 | 0.843140 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −45.1472 | −2.38610 | ||||||||
\(359\) | 25.5416 | 1.34804 | 0.674018 | − | 0.738715i | \(-0.264567\pi\) | ||||
0.674018 | + | 0.738715i | \(0.264567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 20.7250 | 1.09079 | ||||||||
\(362\) | 18.2111 | 0.957154 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.5139 | 0.813148 | ||||||||
\(365\) | 12.6056 | 0.659805 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.0278 | 1.77623 | 0.888117 | − | 0.459617i | \(-0.152013\pi\) | ||||
0.888117 | + | 0.459617i | \(0.152013\pi\) | |||||||
\(368\) | −0.908327 | −0.0473498 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.2111 | 0.946750 | ||||||||
\(371\) | 11.0917 | 0.575851 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.577795 | −0.0299171 | −0.0149585 | − | 0.999888i | \(-0.504762\pi\) | ||||
−0.0149585 | + | 0.999888i | \(0.504762\pi\) | |||||||
\(374\) | −28.1194 | −1.45402 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.0917 | −1.03615 | ||||||||
\(377\) | −27.4222 | −1.41232 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1194 | −0.571167 | −0.285583 | − | 0.958354i | \(-0.592187\pi\) | ||||
−0.285583 | + | 0.958354i | \(0.592187\pi\) | |||||||
\(380\) | −20.8167 | −1.06787 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 17.5139 | 0.896088 | ||||||||
\(383\) | −12.0000 | −0.613171 | −0.306586 | − | 0.951843i | \(-0.599187\pi\) | ||||
−0.306586 | + | 0.951843i | \(0.599187\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | −11.5139 | −0.586041 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −51.9361 | −2.63666 | ||||||||
\(389\) | −28.8167 | −1.46106 | −0.730531 | − | 0.682879i | \(-0.760727\pi\) | ||||
−0.730531 | + | 0.682879i | \(0.760727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9083 | 0.804519 | ||||||||
\(392\) | 15.9083 | 0.803492 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 47.7250 | 2.40435 | ||||||||
\(395\) | −12.5139 | −0.629642 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.51388 | 0.377111 | 0.188555 | − | 0.982063i | \(-0.439620\pi\) | ||||
0.188555 | + | 0.982063i | \(0.439620\pi\) | |||||||
\(398\) | −53.9361 | −2.70357 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.302776 | 0.0151388 | ||||||||
\(401\) | 19.8167 | 0.989596 | 0.494798 | − | 0.869008i | \(-0.335242\pi\) | ||||
0.494798 | + | 0.869008i | \(0.335242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.7889 | 0.935942 | ||||||||
\(404\) | −58.5416 | −2.91256 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.8167 | 1.13237 | ||||||||
\(407\) | 18.2111 | 0.902691 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.63331 | −0.377443 | −0.188721 | − | 0.982031i | \(-0.560434\pi\) | ||||
−0.188721 | + | 0.982031i | \(0.560434\pi\) | |||||||
\(410\) | 15.4222 | 0.761648 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −29.1194 | −1.43461 | ||||||||
\(413\) | −1.81665 | −0.0893917 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.7250 | 0.722821 | ||||||||
\(416\) | 19.1194 | 0.937407 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −33.4222 | −1.63473 | ||||||||
\(419\) | 5.02776 | 0.245622 | 0.122811 | − | 0.992430i | \(-0.460809\pi\) | ||||
0.122811 | + | 0.992430i | \(0.460809\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.69722 | 0.423877 | 0.211938 | − | 0.977283i | \(-0.432022\pi\) | ||||
0.211938 | + | 0.977283i | \(0.432022\pi\) | |||||||
\(422\) | 5.02776 | 0.244747 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.5416 | −1.24041 | ||||||||
\(425\) | −5.30278 | −0.257222 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.788897 | 0.0381774 | ||||||||
\(428\) | 6.90833 | 0.333927 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 16.6056 | 0.800791 | ||||||||
\(431\) | 40.8167 | 1.96607 | 0.983035 | − | 0.183421i | \(-0.0587170\pi\) | ||||
0.983035 | + | 0.183421i | \(0.0587170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.0278 | −0.866359 | −0.433179 | − | 0.901308i | \(-0.642608\pi\) | ||||
−0.433179 | + | 0.901308i | \(0.642608\pi\) | |||||||
\(434\) | −15.6333 | −0.750423 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −55.8444 | −2.67446 | ||||||||
\(437\) | 18.9083 | 0.904508 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.1194 | −0.960248 | −0.480124 | − | 0.877201i | \(-0.659408\pi\) | ||||
−0.480124 | + | 0.877201i | \(0.659408\pi\) | |||||||
\(440\) | 6.90833 | 0.329342 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 44.0278 | 2.09419 | ||||||||
\(443\) | 9.27502 | 0.440669 | 0.220335 | − | 0.975424i | \(-0.429285\pi\) | ||||
0.220335 | + | 0.975424i | \(0.429285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.81665 | 0.228331 | ||||||||
\(446\) | −48.1472 | −2.27984 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.6972 | −0.788870 | ||||||||
\(449\) | −39.2111 | −1.85049 | −0.925243 | − | 0.379375i | \(-0.876139\pi\) | ||||
−0.925243 | + | 0.379375i | \(0.876139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.4222 | 0.726203 | ||||||||
\(452\) | −20.5139 | −0.964892 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.5139 | 0.821967 | ||||||||
\(455\) | 4.69722 | 0.220209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.5139 | 0.632153 | 0.316076 | − | 0.948734i | \(-0.397634\pi\) | ||||
0.316076 | + | 0.948734i | \(0.397634\pi\) | |||||||
\(458\) | −32.7250 | −1.52914 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.90833 | −0.461978 | ||||||||
\(461\) | −33.0000 | −1.53696 | −0.768482 | − | 0.639872i | \(-0.778987\pi\) | ||||
−0.768482 | + | 0.639872i | \(0.778987\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.3305 | −0.944840 | −0.472420 | − | 0.881374i | \(-0.656619\pi\) | ||||
−0.472420 | + | 0.881374i | \(0.656619\pi\) | |||||||
\(464\) | −2.30278 | −0.106904 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −52.5416 | −2.43394 | ||||||||
\(467\) | −31.3305 | −1.44980 | −0.724902 | − | 0.688852i | \(-0.758115\pi\) | ||||
−0.724902 | + | 0.688852i | \(0.758115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4222 | 0.619780 | ||||||||
\(470\) | −15.4222 | −0.711373 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.18335 | 0.192554 | ||||||||
\(473\) | 16.6056 | 0.763524 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.30278 | −0.289191 | ||||||||
\(476\) | −22.8167 | −1.04580 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 46.1194 | 2.10945 | ||||||||
\(479\) | 14.7250 | 0.672802 | 0.336401 | − | 0.941719i | \(-0.390790\pi\) | ||||
0.336401 | + | 0.941719i | \(0.390790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.5139 | −1.30012 | ||||||||
\(482\) | 5.51388 | 0.251150 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.8167 | −0.855302 | ||||||||
\(485\) | −15.7250 | −0.714035 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.18335 | −0.234880 | −0.117440 | − | 0.993080i | \(-0.537469\pi\) | ||||
−0.117440 | + | 0.993080i | \(0.537469\pi\) | |||||||
\(488\) | −1.81665 | −0.0822361 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 12.2111 | 0.551641 | ||||||||
\(491\) | −24.6972 | −1.11457 | −0.557285 | − | 0.830321i | \(-0.688157\pi\) | ||||
−0.557285 | + | 0.830321i | \(0.688157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.3305 | 1.81640 | ||||||||
\(494\) | 52.3305 | 2.35446 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.57779 | 0.0708451 | ||||||||
\(497\) | −2.09167 | −0.0938244 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.78890 | 0.0800820 | 0.0400410 | − | 0.999198i | \(-0.487251\pi\) | ||||
0.0400410 | + | 0.999198i | \(0.487251\pi\) | |||||||
\(500\) | 3.30278 | 0.147705 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.81665 | −0.214978 | ||||||||
\(503\) | −12.6972 | −0.566141 | −0.283071 | − | 0.959099i | \(-0.591353\pi\) | ||||
−0.283071 | + | 0.959099i | \(0.591353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.7250 | −0.788751 | ||||||||
\(506\) | −15.9083 | −0.707211 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | −33.8444 | −1.50013 | −0.750064 | − | 0.661366i | \(-0.769977\pi\) | ||||
−0.750064 | + | 0.661366i | \(0.769977\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.4222 | 0.726476 | ||||||||
\(512\) | 3.42221 | 0.151242 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.8167 | 1.00640 | ||||||||
\(515\) | −8.81665 | −0.388508 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.4222 | −0.678268 | ||||||||
\(518\) | 23.7250 | 1.04242 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.8167 | −0.474342 | ||||||||
\(521\) | 5.93608 | 0.260065 | 0.130032 | − | 0.991510i | \(-0.458492\pi\) | ||||
0.130032 | + | 0.991510i | \(0.458492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3305 | 1.06390 | 0.531950 | − | 0.846776i | \(-0.321459\pi\) | ||||
0.531950 | + | 0.846776i | \(0.321459\pi\) | |||||||
\(524\) | 35.7250 | 1.56065 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.6972 | 0.553625 | ||||||||
\(527\) | −27.6333 | −1.20373 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.0000 | −0.608696 | ||||||||
\(530\) | −19.6056 | −0.851611 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −27.1194 | −1.17578 | ||||||||
\(533\) | −24.1472 | −1.04593 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.09167 | 0.0904309 | ||||||||
\(536\) | −30.9083 | −1.33504 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −49.9638 | −2.15409 | ||||||||
\(539\) | 12.2111 | 0.525969 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.30278 | 0.184991 | 0.0924954 | − | 0.995713i | \(-0.470516\pi\) | ||||
0.0924954 | + | 0.995713i | \(0.470516\pi\) | |||||||
\(542\) | 34.6056 | 1.48644 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −28.1194 | −1.20561 | ||||||||
\(545\) | −16.9083 | −0.724273 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.21110 | −0.180054 | −0.0900269 | − | 0.995939i | \(-0.528695\pi\) | ||||
−0.0900269 | + | 0.995939i | \(0.528695\pi\) | |||||||
\(548\) | −49.5416 | −2.11631 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.30278 | 0.226111 | ||||||||
\(551\) | 47.9361 | 2.04215 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.3028 | −0.693265 | ||||||||
\(554\) | 8.09167 | 0.343782 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.3305 | 1.54076 | ||||||||
\(557\) | −9.00000 | −0.381342 | −0.190671 | − | 0.981654i | \(-0.561066\pi\) | ||||
−0.190671 | + | 0.981654i | \(0.561066\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.0000 | −1.09968 | ||||||||
\(560\) | 0.394449 | 0.0166685 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | 24.6333 | 1.03817 | 0.519085 | − | 0.854723i | \(-0.326273\pi\) | ||||
0.519085 | + | 0.854723i | \(0.326273\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.21110 | −0.261303 | ||||||||
\(566\) | −7.18335 | −0.301939 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.81665 | 0.202102 | ||||||||
\(569\) | −28.8167 | −1.20806 | −0.604028 | − | 0.796963i | \(-0.706439\pi\) | ||||
−0.604028 | + | 0.796963i | \(0.706439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.8167 | −1.62443 | −0.812213 | − | 0.583361i | \(-0.801737\pi\) | ||||
−0.812213 | + | 0.583361i | \(0.801737\pi\) | |||||||
\(572\) | −27.4222 | −1.14658 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.0917 | 0.838610 | ||||||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.6333 | 0.858976 | 0.429488 | − | 0.903073i | \(-0.358694\pi\) | ||||
0.429488 | + | 0.903073i | \(0.358694\pi\) | |||||||
\(578\) | −25.6056 | −1.06505 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25.1194 | −1.04303 | ||||||||
\(581\) | 19.1833 | 0.795859 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.6056 | −0.811979 | ||||||||
\(584\) | −37.8167 | −1.56486 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.0917 | −0.829979 | ||||||||
\(587\) | 28.5416 | 1.17804 | 0.589020 | − | 0.808119i | \(-0.299514\pi\) | ||||
0.589020 | + | 0.808119i | \(0.299514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.8444 | −1.35333 | ||||||||
\(590\) | 3.21110 | 0.132199 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.39445 | −0.0984112 | ||||||||
\(593\) | −21.6972 | −0.890998 | −0.445499 | − | 0.895282i | \(-0.646974\pi\) | ||||
−0.445499 | + | 0.895282i | \(0.646974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.90833 | −0.283214 | ||||||||
\(596\) | 53.2389 | 2.18075 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.9083 | 1.01858 | ||||||||
\(599\) | 34.7527 | 1.41996 | 0.709979 | − | 0.704223i | \(-0.248704\pi\) | ||||
0.709979 | + | 0.704223i | \(0.248704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1833 | 0.741714 | 0.370857 | − | 0.928690i | \(-0.379064\pi\) | ||||
0.370857 | + | 0.928690i | \(0.379064\pi\) | |||||||
\(602\) | 21.6333 | 0.881708 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −36.7250 | −1.49432 | ||||||||
\(605\) | −5.69722 | −0.231625 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.2111 | −0.779755 | −0.389877 | − | 0.920867i | \(-0.627483\pi\) | ||||
−0.389877 | + | 0.920867i | \(0.627483\pi\) | |||||||
\(608\) | −33.4222 | −1.35545 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.39445 | −0.0564596 | ||||||||
\(611\) | 24.1472 | 0.976891 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.5139 | 1.15166 | 0.575832 | − | 0.817568i | \(-0.304678\pi\) | ||||
0.575832 | + | 0.817568i | \(0.304678\pi\) | |||||||
\(614\) | 28.3305 | 1.14333 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.00000 | 0.362620 | ||||||||
\(617\) | −34.8167 | −1.40167 | −0.700833 | − | 0.713326i | \(-0.747188\pi\) | ||||
−0.700833 | + | 0.713326i | \(0.747188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.5416 | 0.986412 | 0.493206 | − | 0.869913i | \(-0.335825\pi\) | ||||
0.493206 | + | 0.869913i | \(0.335825\pi\) | |||||||
\(620\) | 17.2111 | 0.691215 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.8167 | −0.553997 | ||||||||
\(623\) | 6.27502 | 0.251403 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −38.5139 | −1.53932 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.30278 | −0.371221 | ||||||||
\(629\) | 41.9361 | 1.67210 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.7889 | 0.548927 | 0.274464 | − | 0.961597i | \(-0.411500\pi\) | ||||
0.274464 | + | 0.961597i | \(0.411500\pi\) | |||||||
\(632\) | 37.5416 | 1.49333 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.3028 | −0.568036 | ||||||||
\(635\) | 0.605551 | 0.0240306 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.1194 | −0.757539 | ||||||||
\(638\) | −40.3305 | −1.59670 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.9083 | 0.747417 | ||||||||
\(641\) | 21.6333 | 0.854464 | 0.427232 | − | 0.904142i | \(-0.359489\pi\) | ||||
0.427232 | + | 0.904142i | \(0.359489\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.42221 | −0.0560863 | −0.0280431 | − | 0.999607i | \(-0.508928\pi\) | ||||
−0.0280431 | + | 0.999607i | \(0.508928\pi\) | |||||||
\(644\) | −12.9083 | −0.508659 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −76.9638 | −3.02810 | ||||||||
\(647\) | 38.2389 | 1.50332 | 0.751662 | − | 0.659548i | \(-0.229252\pi\) | ||||
0.751662 | + | 0.659548i | \(0.229252\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.21110 | 0.126047 | ||||||||
\(650\) | −8.30278 | −0.325662 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.0278 | −1.29347 | ||||||||
\(653\) | 9.21110 | 0.360458 | 0.180229 | − | 0.983625i | \(-0.442316\pi\) | ||||
0.180229 | + | 0.983625i | \(0.442316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.8167 | 0.422642 | ||||||||
\(656\) | −2.02776 | −0.0791706 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.0917 | −0.783255 | ||||||||
\(659\) | 26.7889 | 1.04355 | 0.521774 | − | 0.853084i | \(-0.325271\pi\) | ||||
0.521774 | + | 0.853084i | \(0.325271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.84441 | −0.305112 | −0.152556 | − | 0.988295i | \(-0.548750\pi\) | ||||
−0.152556 | + | 0.988295i | \(0.548750\pi\) | |||||||
\(662\) | −25.1833 | −0.978779 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −44.1749 | −1.71432 | ||||||||
\(665\) | −8.21110 | −0.318413 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.8167 | 0.883464 | ||||||||
\(668\) | −62.4500 | −2.41626 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.7250 | −0.916576 | ||||||||
\(671\) | −1.39445 | −0.0538321 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 51.1194 | 1.97051 | 0.985255 | − | 0.171095i | \(-0.0547304\pi\) | ||||
0.985255 | + | 0.171095i | \(0.0547304\pi\) | |||||||
\(674\) | −44.9361 | −1.73087 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5416 | 1.09694 | 0.548472 | − | 0.836169i | \(-0.315210\pi\) | ||||
0.548472 | + | 0.836169i | \(0.315210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.4861 | −0.786185 | ||||||||
\(680\) | 15.9083 | 0.610056 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.6333 | 1.05813 | ||||||||
\(683\) | −4.81665 | −0.184304 | −0.0921521 | − | 0.995745i | \(-0.529375\pi\) | ||||
−0.0921521 | + | 0.995745i | \(0.529375\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.0000 | −0.573121 | ||||||||
\(686\) | 36.9083 | 1.40917 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.18335 | −0.0832393 | ||||||||
\(689\) | 30.6972 | 1.16947 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.6056 | 0.593663 | 0.296832 | − | 0.954930i | \(-0.404070\pi\) | ||||
0.296832 | + | 0.954930i | \(0.404070\pi\) | |||||||
\(692\) | −3.90833 | −0.148572 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30.2111 | 1.14680 | ||||||||
\(695\) | 11.0000 | 0.417254 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.5139 | 1.34518 | ||||||||
\(698\) | 10.3305 | 0.391016 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.30278 | 0.162630 | ||||||||
\(701\) | −19.6056 | −0.740491 | −0.370246 | − | 0.928934i | \(-0.620727\pi\) | ||||
−0.370246 | + | 0.928934i | \(0.620727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.8444 | 1.87992 | ||||||||
\(704\) | 29.5139 | 1.11235 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 55.2666 | 2.07999 | ||||||||
\(707\) | −23.0917 | −0.868452 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.76114 | −0.0661410 | −0.0330705 | − | 0.999453i | \(-0.510529\pi\) | ||||
−0.0330705 | + | 0.999453i | \(0.510529\pi\) | |||||||
\(710\) | 3.69722 | 0.138754 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14.4500 | −0.541535 | ||||||||
\(713\) | −15.6333 | −0.585472 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.30278 | −0.310506 | ||||||||
\(716\) | 64.7527 | 2.41992 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −58.8167 | −2.19502 | ||||||||
\(719\) | 20.7250 | 0.772911 | 0.386456 | − | 0.922308i | \(-0.373699\pi\) | ||||
0.386456 | + | 0.922308i | \(0.373699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.4861 | −0.427766 | ||||||||
\(722\) | −47.7250 | −1.77614 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −26.1194 | −0.970721 | ||||||||
\(725\) | −7.60555 | −0.282463 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −48.7250 | −1.80711 | −0.903555 | − | 0.428473i | \(-0.859052\pi\) | ||||
−0.903555 | + | 0.428473i | \(0.859052\pi\) | |||||||
\(728\) | −14.0917 | −0.522272 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.0278 | −1.07437 | ||||||||
\(731\) | 38.2389 | 1.41432 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0000 | 1.07114 | 0.535570 | − | 0.844491i | \(-0.320097\pi\) | ||||
0.535570 | + | 0.844491i | \(0.320097\pi\) | |||||||
\(734\) | −78.3583 | −2.89226 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.9083 | −0.586389 | ||||||||
\(737\) | −23.7250 | −0.873921 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −49.8444 | −1.83356 | −0.916778 | − | 0.399397i | \(-0.869220\pi\) | ||||
−0.916778 | + | 0.399397i | \(0.869220\pi\) | |||||||
\(740\) | −26.1194 | −0.960169 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.5416 | −0.937663 | ||||||||
\(743\) | 16.6056 | 0.609199 | 0.304599 | − | 0.952481i | \(-0.401477\pi\) | ||||
0.304599 | + | 0.952481i | \(0.401477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.1194 | 0.590570 | ||||||||
\(746\) | 1.33053 | 0.0487142 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 40.3305 | 1.47463 | ||||||||
\(749\) | 2.72498 | 0.0995686 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6056 | 0.788398 | 0.394199 | − | 0.919025i | \(-0.371022\pi\) | ||||
0.394199 | + | 0.919025i | \(0.371022\pi\) | |||||||
\(752\) | 2.02776 | 0.0739447 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 63.1472 | 2.29968 | ||||||||
\(755\) | −11.1194 | −0.404677 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.880571 | 0.0320049 | 0.0160024 | − | 0.999872i | \(-0.494906\pi\) | ||||
0.0160024 | + | 0.999872i | \(0.494906\pi\) | |||||||
\(758\) | 25.6056 | 0.930036 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.9083 | 0.685877 | ||||||||
\(761\) | −42.3583 | −1.53549 | −0.767743 | − | 0.640757i | \(-0.778620\pi\) | ||||
−0.767743 | + | 0.640757i | \(0.778620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.0278 | −0.797458 | ||||||||
\(764\) | −25.1194 | −0.908789 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.6333 | 0.998432 | ||||||||
\(767\) | −5.02776 | −0.181542 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.7250 | 1.14403 | 0.572016 | − | 0.820242i | \(-0.306162\pi\) | ||||
0.572016 | + | 0.820242i | \(0.306162\pi\) | |||||||
\(770\) | 6.90833 | 0.248959 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.5139 | 0.594347 | ||||||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.21110 | 0.187188 | ||||||||
\(776\) | 47.1749 | 1.69348 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 66.3583 | 2.37906 | ||||||||
\(779\) | 42.2111 | 1.51237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.69722 | 0.132297 | ||||||||
\(782\) | −36.6333 | −1.31000 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.60555 | −0.0573411 | ||||||||
\(785\) | −2.81665 | −0.100531 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.8722 | 1.56387 | 0.781937 | − | 0.623358i | \(-0.214232\pi\) | ||||
0.781937 | + | 0.623358i | \(0.214232\pi\) | |||||||
\(788\) | −68.4500 | −2.43843 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 28.8167 | 1.02525 | ||||||||
\(791\) | −8.09167 | −0.287707 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.18335 | 0.0775329 | ||||||||
\(794\) | −17.3028 | −0.614053 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 77.3583 | 2.74189 | ||||||||
\(797\) | 17.5778 | 0.622637 | 0.311319 | − | 0.950306i | \(-0.399229\pi\) | ||||
0.311319 | + | 0.950306i | \(0.399229\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.5139 | −1.25639 | ||||||||
\(800\) | 5.30278 | 0.187481 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −45.6333 | −1.61137 | ||||||||
\(803\) | −29.0278 | −1.02437 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.90833 | −0.137750 | ||||||||
\(806\) | −43.2666 | −1.52400 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 53.1749 | 1.87069 | ||||||||
\(809\) | −3.06392 | −0.107722 | −0.0538608 | − | 0.998548i | \(-0.517153\pi\) | ||||
−0.0538608 | + | 0.998548i | \(0.517153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.2111 | 1.65781 | 0.828903 | − | 0.559392i | \(-0.188965\pi\) | ||||
0.828903 | + | 0.559392i | \(0.188965\pi\) | |||||||
\(812\) | −32.7250 | −1.14842 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −41.9361 | −1.46986 | ||||||||
\(815\) | −10.0000 | −0.350285 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.4500 | 1.59009 | ||||||||
\(818\) | 17.5778 | 0.614593 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.1194 | −0.772444 | ||||||||
\(821\) | −17.0917 | −0.596504 | −0.298252 | − | 0.954487i | \(-0.596403\pi\) | ||||
−0.298252 | + | 0.954487i | \(0.596403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.1833 | −0.389827 | −0.194913 | − | 0.980820i | \(-0.562443\pi\) | ||||
−0.194913 | + | 0.980820i | \(0.562443\pi\) | |||||||
\(824\) | 26.4500 | 0.921428 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.18335 | 0.145557 | ||||||||
\(827\) | −16.3944 | −0.570091 | −0.285045 | − | 0.958514i | \(-0.592009\pi\) | ||||
−0.285045 | + | 0.958514i | \(0.592009\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.2389 | −1.05024 | −0.525119 | − | 0.851029i | \(-0.675979\pi\) | ||||
−0.525119 | + | 0.851029i | \(0.675979\pi\) | |||||||
\(830\) | −33.9083 | −1.17698 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −46.2111 | −1.60208 | ||||||||
\(833\) | 28.1194 | 0.974280 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.9083 | −0.654350 | ||||||||
\(836\) | 47.9361 | 1.65790 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −11.5778 | −0.399948 | ||||||||
\(839\) | 14.5778 | 0.503281 | 0.251641 | − | 0.967821i | \(-0.419030\pi\) | ||||
0.251641 | + | 0.967821i | \(0.419030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8444 | 0.994635 | ||||||||
\(842\) | −20.0278 | −0.690202 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.21110 | −0.248216 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.42221 | −0.255030 | ||||||||
\(848\) | 2.57779 | 0.0885218 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.2111 | 0.418837 | ||||||||
\(851\) | 23.7250 | 0.813282 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.6972 | −0.468984 | −0.234492 | − | 0.972118i | \(-0.575343\pi\) | ||||
−0.234492 | + | 0.972118i | \(0.575343\pi\) | |||||||
\(854\) | −1.81665 | −0.0621646 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.27502 | −0.214476 | ||||||||
\(857\) | 13.6056 | 0.464757 | 0.232378 | − | 0.972625i | \(-0.425349\pi\) | ||||
0.232378 | + | 0.972625i | \(0.425349\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.39445 | −0.184056 | −0.0920281 | − | 0.995756i | \(-0.529335\pi\) | ||||
−0.0920281 | + | 0.995756i | \(0.529335\pi\) | |||||||
\(860\) | −23.8167 | −0.812141 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −93.9916 | −3.20137 | ||||||||
\(863\) | 39.2111 | 1.33476 | 0.667381 | − | 0.744717i | \(-0.267415\pi\) | ||||
0.667381 | + | 0.744717i | \(0.267415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.18335 | −0.0402350 | ||||||||
\(866\) | 41.5139 | 1.41070 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 22.4222 | 0.761059 | ||||||||
\(869\) | 28.8167 | 0.977538 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.1472 | 1.25868 | ||||||||
\(872\) | 50.7250 | 1.71776 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −43.5416 | −1.47282 | ||||||||
\(875\) | 1.30278 | 0.0440419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.7889 | −0.431850 | −0.215925 | − | 0.976410i | \(-0.569277\pi\) | ||||
−0.215925 | + | 0.976410i | \(0.569277\pi\) | |||||||
\(878\) | 46.3305 | 1.56358 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.697224 | −0.0235034 | ||||||||
\(881\) | 10.6056 | 0.357310 | 0.178655 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178655 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0000 | 0.572096 | 0.286048 | − | 0.958215i | \(-0.407658\pi\) | ||||
0.286048 | + | 0.958215i | \(0.407658\pi\) | |||||||
\(884\) | −63.1472 | −2.12387 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.3583 | −0.717546 | ||||||||
\(887\) | 19.1833 | 0.644114 | 0.322057 | − | 0.946720i | \(-0.395626\pi\) | ||||
0.322057 | + | 0.946720i | \(0.395626\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.788897 | 0.0264588 | ||||||||
\(890\) | −11.0917 | −0.371794 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 69.0555 | 2.31215 | ||||||||
\(893\) | −42.2111 | −1.41254 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.6056 | 0.655341 | ||||||||
\(896\) | 24.6333 | 0.822941 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 90.2944 | 3.01316 | ||||||||
\(899\) | −39.6333 | −1.32184 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.1472 | −1.50407 | ||||||||
\(902\) | −35.5139 | −1.18248 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.6333 | 0.619735 | ||||||||
\(905\) | −7.90833 | −0.262882 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.3944 | 1.60691 | 0.803456 | − | 0.595365i | \(-0.202992\pi\) | ||||
0.803456 | + | 0.595365i | \(0.202992\pi\) | |||||||
\(908\) | −25.1194 | −0.833618 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.8167 | −0.358569 | ||||||||
\(911\) | −38.9361 | −1.29001 | −0.645005 | − | 0.764178i | \(-0.723145\pi\) | ||||
−0.645005 | + | 0.764178i | \(0.723145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33.9083 | −1.12220 | ||||||||
\(914\) | −31.1194 | −1.02934 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46.9361 | 1.55081 | ||||||||
\(917\) | 14.0917 | 0.465348 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.2111 | −1.22748 | −0.613741 | − | 0.789508i | \(-0.710336\pi\) | ||||
−0.613741 | + | 0.789508i | \(0.710336\pi\) | |||||||
\(920\) | 9.00000 | 0.296721 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 75.9916 | 2.50265 | ||||||||
\(923\) | −5.78890 | −0.190544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.90833 | −0.260024 | ||||||||
\(926\) | 46.8167 | 1.53849 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40.3305 | −1.32391 | ||||||||
\(929\) | −28.3305 | −0.929495 | −0.464747 | − | 0.885443i | \(-0.653855\pi\) | ||||
−0.464747 | + | 0.885443i | \(0.653855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.4222 | 1.09537 | ||||||||
\(932\) | 75.3583 | 2.46844 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 72.1472 | 2.36073 | ||||||||
\(935\) | 12.2111 | 0.399346 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.2111 | 0.366251 | 0.183125 | − | 0.983090i | \(-0.441379\pi\) | ||||
0.183125 | + | 0.983090i | \(0.441379\pi\) | |||||||
\(938\) | −30.9083 | −1.00919 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 22.1194 | 0.721456 | ||||||||
\(941\) | 25.7527 | 0.839515 | 0.419758 | − | 0.907636i | \(-0.362115\pi\) | ||||
0.419758 | + | 0.907636i | \(0.362115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.0917 | 0.654275 | ||||||||
\(944\) | −0.422205 | −0.0137416 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.2389 | −1.24325 | ||||||||
\(947\) | 34.8167 | 1.13139 | 0.565695 | − | 0.824615i | \(-0.308608\pi\) | ||||
0.565695 | + | 0.824615i | \(0.308608\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.4500 | 1.47537 | ||||||||
\(950\) | 14.5139 | 0.470892 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 20.7250 | 0.671700 | ||||||||
\(953\) | −35.0278 | −1.13466 | −0.567330 | − | 0.823490i | \(-0.692024\pi\) | ||||
−0.567330 | + | 0.823490i | \(0.692024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.60555 | −0.246110 | ||||||||
\(956\) | −66.1472 | −2.13935 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33.9083 | −1.09553 | ||||||||
\(959\) | −19.5416 | −0.631032 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.84441 | −0.124013 | ||||||||
\(962\) | 65.6611 | 2.11700 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.90833 | −0.254710 | ||||||||
\(965\) | 5.00000 | 0.160956 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.1833 | −0.842000 | −0.421000 | − | 0.907061i | \(-0.638321\pi\) | ||||
−0.421000 | + | 0.907061i | \(0.638321\pi\) | |||||||
\(968\) | 17.0917 | 0.549347 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.2111 | 1.16267 | ||||||||
\(971\) | −57.3583 | −1.84072 | −0.920358 | − | 0.391078i | \(-0.872102\pi\) | ||||
−0.920358 | + | 0.391078i | \(0.872102\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.3305 | 0.459416 | ||||||||
\(974\) | 11.9361 | 0.382457 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.183346 | 0.00586877 | ||||||||
\(977\) | 7.60555 | 0.243323 | 0.121662 | − | 0.992572i | \(-0.461178\pi\) | ||||
0.121662 | + | 0.992572i | \(0.461178\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.0917 | −0.354491 | ||||||||
\(980\) | −17.5139 | −0.559460 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56.8722 | 1.81486 | ||||||||
\(983\) | −28.8167 | −0.919109 | −0.459554 | − | 0.888150i | \(-0.651991\pi\) | ||||
−0.459554 | + | 0.888150i | \(0.651991\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.7250 | −0.660353 | ||||||||
\(986\) | −92.8722 | −2.95765 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −75.0555 | −2.38783 | ||||||||
\(989\) | 21.6333 | 0.687899 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 27.6333 | 0.877358 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.81665 | 0.152775 | ||||||||
\(995\) | 23.4222 | 0.742534 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.7889 | −1.35514 | −0.677569 | − | 0.735459i | \(-0.736966\pi\) | ||||
−0.677569 | + | 0.735459i | \(0.736966\pi\) | |||||||
\(998\) | −4.11943 | −0.130398 | ||||||||
\(999\) | 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 | 1215.2.a.k.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1215.2.a.m.1.2 | yes | 2 | ||
5.4 | even | 2 | 6075.2.a.bo.1.2 | 2 | |||
9.2 | odd | 6 | 1215.2.e.l.811.1 | 4 | |||
9.4 | even | 3 | 1215.2.e.n.406.2 | 4 | |||
9.5 | odd | 6 | 1215.2.e.l.406.1 | 4 | |||
9.7 | even | 3 | 1215.2.e.n.811.2 | 4 | |||
15.14 | odd | 2 | 6075.2.a.bk.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1215.2.a.k.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1215.2.a.m.1.2 | yes | 2 | 3.2 | odd | 2 | ||
1215.2.e.l.406.1 | 4 | 9.5 | odd | 6 | |||
1215.2.e.l.811.1 | 4 | 9.2 | odd | 6 | |||
1215.2.e.n.406.2 | 4 | 9.4 | even | 3 | |||
1215.2.e.n.811.2 | 4 | 9.7 | even | 3 | |||
6075.2.a.bk.1.1 | 2 | 15.14 | odd | 2 | |||
6075.2.a.bo.1.2 | 2 | 5.4 | even | 2 |