Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,2,Mod(1,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1932.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.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: | \(15.4270976705\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1932.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.85410 | 1.72361 | 0.861803 | − | 0.507242i | \(-0.169335\pi\) | ||||
0.861803 | + | 0.507242i | \(0.169335\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.381966 | −0.105938 | −0.0529692 | − | 0.998596i | \(-0.516869\pi\) | ||||
−0.0529692 | + | 0.998596i | \(0.516869\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.85410 | 0.995125 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.47214 | −0.357045 | −0.178523 | − | 0.983936i | \(-0.557132\pi\) | ||||
−0.178523 | + | 0.983936i | \(0.557132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.236068 | 0.0541577 | 0.0270789 | − | 0.999633i | \(-0.491379\pi\) | ||||
0.0270789 | + | 0.999633i | \(0.491379\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.85410 | 1.97082 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.76393 | 1.03523 | 0.517616 | − | 0.855613i | \(-0.326819\pi\) | ||||
0.517616 | + | 0.855613i | \(0.326819\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.85410 | 0.651462 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.23607 | −0.696405 | −0.348203 | − | 0.937419i | \(-0.613208\pi\) | ||||
−0.348203 | + | 0.937419i | \(0.613208\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.381966 | −0.0611635 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | 0.468521 | 0.234261 | − | 0.972174i | \(-0.424733\pi\) | ||||
0.234261 | + | 0.972174i | \(0.424733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.61803 | −0.246748 | −0.123374 | − | 0.992360i | \(-0.539371\pi\) | ||||
−0.123374 | + | 0.992360i | \(0.539371\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.85410 | 0.574536 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.23607 | −0.472029 | −0.236015 | − | 0.971750i | \(-0.575841\pi\) | ||||
−0.236015 | + | 0.971750i | \(0.575841\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.47214 | −0.206140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.32624 | −0.319533 | −0.159767 | − | 0.987155i | \(-0.551074\pi\) | ||||
−0.159767 | + | 0.987155i | \(0.551074\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.5623 | 1.55906 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.236068 | 0.0312680 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.5623 | −1.76566 | −0.882831 | − | 0.469691i | \(-0.844365\pi\) | ||||
−0.882831 | + | 0.469691i | \(0.844365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.85410 | −0.621504 | −0.310752 | − | 0.950491i | \(-0.600581\pi\) | ||||
−0.310752 | + | 0.950491i | \(0.600581\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.47214 | −0.182596 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.32624 | 0.284195 | 0.142098 | − | 0.989853i | \(-0.454615\pi\) | ||||
0.142098 | + | 0.989853i | \(0.454615\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.61803 | 0.904094 | 0.452047 | − | 0.891994i | \(-0.350694\pi\) | ||||
0.452047 | + | 0.891994i | \(0.350694\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.94427 | −0.695724 | −0.347862 | − | 0.937546i | \(-0.613092\pi\) | ||||
−0.347862 | + | 0.937546i | \(0.613092\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.85410 | 1.13785 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.00000 | 0.341882 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.47214 | −1.06570 | −0.532849 | − | 0.846210i | \(-0.678879\pi\) | ||||
−0.532849 | + | 0.846210i | \(0.678879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2361 | 1.34308 | 0.671541 | − | 0.740967i | \(-0.265633\pi\) | ||||
0.671541 | + | 0.740967i | \(0.265633\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.67376 | −0.615406 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.00000 | −0.536056 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.56231 | −0.695603 | −0.347802 | − | 0.937568i | \(-0.613072\pi\) | ||||
−0.347802 | + | 0.937568i | \(0.613072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.381966 | −0.0400409 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.76393 | 0.597692 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.909830 | 0.0933466 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.94427 | −0.197411 | −0.0987055 | − | 0.995117i | \(-0.531470\pi\) | ||||
−0.0987055 | + | 0.995117i | \(0.531470\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.56231 | −0.752478 | −0.376239 | − | 0.926523i | \(-0.622783\pi\) | ||||
−0.376239 | + | 0.926523i | \(0.622783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.9443 | 1.27544 | 0.637719 | − | 0.770270i | \(-0.279878\pi\) | ||||
0.637719 | + | 0.770270i | \(0.279878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.85410 | 0.376122 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.5623 | 1.21444 | 0.607222 | − | 0.794532i | \(-0.292284\pi\) | ||||
0.607222 | + | 0.794532i | \(0.292284\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.90983 | −0.470276 | −0.235138 | − | 0.971962i | \(-0.575554\pi\) | ||||
−0.235138 | + | 0.971962i | \(0.575554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.23607 | −0.402070 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.03444 | −0.755817 | −0.377908 | − | 0.925843i | \(-0.623357\pi\) | ||||
−0.377908 | + | 0.925843i | \(0.623357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.85410 | −0.359397 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.381966 | −0.0353128 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.47214 | −0.134950 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.00000 | 0.270501 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.7082 | 1.67331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.32624 | 0.295156 | 0.147578 | − | 0.989050i | \(-0.452852\pi\) | ||||
0.147578 | + | 0.989050i | \(0.452852\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.61803 | −0.142460 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | 0.262111 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.236068 | 0.0204697 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.85410 | 0.331708 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.41641 | 0.719062 | 0.359531 | − | 0.933133i | \(-0.382937\pi\) | ||||
0.359531 | + | 0.933133i | \(0.382937\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.7984 | −0.915906 | −0.457953 | − | 0.888976i | \(-0.651417\pi\) | ||||
−0.457953 | + | 0.888976i | \(0.651417\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.23607 | −0.272526 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.14590 | −0.0958248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.2705 | −1.60033 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.1803 | 1.32555 | 0.662773 | − | 0.748821i | \(-0.269380\pi\) | ||||
0.662773 | + | 0.748821i | \(0.269380\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.6525 | −1.84343 | −0.921716 | − | 0.387865i | \(-0.873213\pi\) | ||||
−0.921716 | + | 0.387865i | \(0.873213\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.47214 | −0.119015 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.2148 | 1.78433 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.76393 | −0.539821 | −0.269910 | − | 0.962885i | \(-0.586994\pi\) | ||||
−0.269910 | + | 0.962885i | \(0.586994\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.32624 | −0.184483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.67376 | 0.444403 | 0.222202 | − | 0.975001i | \(-0.428676\pi\) | ||||
0.222202 | + | 0.975001i | \(0.428676\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.5623 | 0.900124 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.41641 | 0.651281 | 0.325641 | − | 0.945494i | \(-0.394420\pi\) | ||||
0.325641 | + | 0.945494i | \(0.394420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8541 | −0.988777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.236068 | 0.0180526 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.4721 | −1.32838 | −0.664191 | − | 0.747563i | \(-0.731224\pi\) | ||||
−0.664191 | + | 0.747563i | \(0.731224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.85410 | 0.744900 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.5623 | −1.01941 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.5623 | 1.61164 | 0.805821 | − | 0.592159i | \(-0.201724\pi\) | ||||
0.805821 | + | 0.592159i | \(0.201724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.41641 | 0.476928 | 0.238464 | − | 0.971151i | \(-0.423356\pi\) | ||||
0.238464 | + | 0.971151i | \(0.423356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.85410 | −0.358826 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.3262 | −1.20033 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.41641 | −0.322960 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.7639 | 0.923566 | 0.461783 | − | 0.886993i | \(-0.347210\pi\) | ||||
0.461783 | + | 0.886993i | \(0.347210\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.6525 | 1.77452 | 0.887262 | − | 0.461266i | \(-0.152605\pi\) | ||||
0.887262 | + | 0.461266i | \(0.152605\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.47214 | −0.105422 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.09017 | 0.291413 | 0.145706 | − | 0.989328i | \(-0.453455\pi\) | ||||
0.145706 | + | 0.989328i | \(0.453455\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.7984 | 0.765476 | 0.382738 | − | 0.923857i | \(-0.374981\pi\) | ||||
0.382738 | + | 0.923857i | \(0.374981\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.32624 | 0.164080 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00000 | −0.350931 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.5623 | 0.807546 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.708204 | 0.0489875 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.23607 | 0.291623 | 0.145811 | − | 0.989312i | \(-0.453421\pi\) | ||||
0.145811 | + | 0.989312i | \(0.453421\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.61803 | 0.521979 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.23607 | −0.425296 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.76393 | 0.391281 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.94427 | −0.401677 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.562306 | 0.0378248 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.32624 | −0.289706 | −0.144853 | − | 0.989453i | \(-0.546271\pi\) | ||||
−0.144853 | + | 0.989453i | \(0.546271\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.85410 | 0.656940 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.618034 | 0.0410204 | 0.0205102 | − | 0.999790i | \(-0.493471\pi\) | ||||
0.0205102 | + | 0.999790i | \(0.493471\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.43769 | −0.161087 | −0.0805437 | − | 0.996751i | \(-0.525666\pi\) | ||||
−0.0805437 | + | 0.996751i | \(0.525666\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00000 | 0.197386 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.1459 | −1.05775 | −0.528876 | − | 0.848699i | \(-0.677387\pi\) | ||||
−0.528876 | + | 0.848699i | \(0.677387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.4721 | −0.813592 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.47214 | −0.615281 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.67376 | −0.367005 | −0.183503 | − | 0.983019i | \(-0.558744\pi\) | ||||
−0.183503 | + | 0.983019i | \(0.558744\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.05573 | −0.132421 | −0.0662105 | − | 0.997806i | \(-0.521091\pi\) | ||||
−0.0662105 | + | 0.997806i | \(0.521091\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.85410 | 0.246230 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0901699 | −0.00573738 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.2361 | 0.775429 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.2361 | 0.835453 | 0.417727 | − | 0.908573i | \(-0.362827\pi\) | ||||
0.417727 | + | 0.908573i | \(0.362827\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.67376 | −0.355305 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.763932 | −0.0476528 | −0.0238264 | − | 0.999716i | \(-0.507585\pi\) | ||||
−0.0238264 | + | 0.999716i | \(0.507585\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.23607 | −0.263216 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.00000 | −0.309492 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.2918 | 1.06626 | 0.533129 | − | 0.846034i | \(-0.321016\pi\) | ||||
0.533129 | + | 0.846034i | \(0.321016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.96556 | −0.550750 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.56231 | −0.401607 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.67376 | 0.528849 | 0.264424 | − | 0.964406i | \(-0.414818\pi\) | ||||
0.264424 | + | 0.964406i | \(0.414818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4164 | 1.48319 | 0.741596 | − | 0.670847i | \(-0.234069\pi\) | ||||
0.741596 | + | 0.670847i | \(0.234069\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.381966 | −0.0231176 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 29.5623 | 1.78267 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.32624 | 0.199854 | 0.0999271 | − | 0.994995i | \(-0.468139\pi\) | ||||
0.0999271 | + | 0.994995i | \(0.468139\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.76393 | 0.345078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.1246 | −1.14088 | −0.570439 | − | 0.821340i | \(-0.693227\pi\) | ||||
−0.570439 | + | 0.821340i | \(0.693227\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.0344 | −1.54759 | −0.773793 | − | 0.633438i | \(-0.781643\pi\) | ||||
−0.773793 | + | 0.633438i | \(0.781643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.909830 | 0.0538937 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.00000 | 0.177084 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8328 | −0.872519 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.94427 | −0.113975 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.9443 | 0.756212 | 0.378106 | − | 0.925762i | \(-0.376575\pi\) | ||||
0.378106 | + | 0.925762i | \(0.376575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −52.2705 | −3.04331 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.00000 | 0.174078 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.381966 | 0.0220897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.61803 | −0.0932619 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.56231 | −0.434443 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.7082 | −1.07123 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.6525 | −1.34992 | −0.674959 | − | 0.737855i | \(-0.735839\pi\) | ||||
−0.674959 | + | 0.737855i | \(0.735839\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.9443 | 0.736374 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3820 | −0.928936 | −0.464468 | − | 0.885590i | \(-0.653754\pi\) | ||||
−0.464468 | + | 0.885590i | \(0.653754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | −0.678280 | −0.339140 | − | 0.940736i | \(-0.610136\pi\) | ||||
−0.339140 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.85410 | 0.217154 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.0344 | 1.68690 | 0.843451 | − | 0.537206i | \(-0.180520\pi\) | ||||
0.843451 | + | 0.537206i | \(0.180520\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0000 | −0.839839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5623 | 0.701160 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.347524 | −0.0193368 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.76393 | −0.208785 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.90983 | −0.271514 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.23607 | −0.178410 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.3607 | −1.00919 | −0.504597 | − | 0.863355i | \(-0.668359\pi\) | ||||
−0.504597 | + | 0.863355i | \(0.668359\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.23607 | −0.232135 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.96556 | 0.489841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.20163 | −0.228877 | −0.114439 | − | 0.993430i | \(-0.536507\pi\) | ||||
−0.114439 | + | 0.993430i | \(0.536507\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.03444 | −0.436371 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.2918 | 0.936403 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.85410 | −0.207498 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.5967 | −1.53515 | −0.767577 | − | 0.640957i | \(-0.778538\pi\) | ||||
−0.767577 | + | 0.640957i | \(0.778538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.4508 | −1.46941 | −0.734705 | − | 0.678387i | \(-0.762679\pi\) | ||||
−0.734705 | + | 0.678387i | \(0.762679\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.381966 | −0.0203878 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.4164 | 1.61890 | 0.809451 | − | 0.587187i | \(-0.199765\pi\) | ||||
0.809451 | + | 0.587187i | \(0.199765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 29.3607 | 1.55830 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.47214 | −0.0779137 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.8541 | −1.25897 | −0.629486 | − | 0.777012i | \(-0.716734\pi\) | ||||
−0.629486 | + | 0.777012i | \(0.716734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9443 | −0.997067 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.9098 | −1.19916 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.43769 | 0.0750470 | 0.0375235 | − | 0.999296i | \(-0.488053\pi\) | ||||
0.0375235 | + | 0.999296i | \(0.488053\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.00000 | 0.156174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.32624 | −0.120772 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.2361 | −0.840672 | −0.420336 | − | 0.907369i | \(-0.638088\pi\) | ||||
−0.420336 | + | 0.907369i | \(0.638088\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.7082 | 0.966087 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.90983 | 0.0983613 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.32624 | 0.170408 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.70820 | −0.138383 | −0.0691914 | − | 0.997603i | \(-0.522042\pi\) | ||||
−0.0691914 | + | 0.997603i | \(0.522042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.5623 | 0.589270 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.61803 | −0.0822493 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.1803 | −0.769674 | −0.384837 | − | 0.922985i | \(-0.625742\pi\) | ||||
−0.384837 | + | 0.922985i | \(0.625742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.47214 | 0.0744491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −36.5066 | −1.83685 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.76393 | 0.239095 | 0.119547 | − | 0.992828i | \(-0.461856\pi\) | ||||
0.119547 | + | 0.992828i | \(0.461856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.236068 | 0.0118182 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 35.5410 | 1.77483 | 0.887417 | − | 0.460968i | \(-0.152498\pi\) | ||||
0.887417 | + | 0.460968i | \(0.152498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.20163 | −0.109671 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.85410 | 0.191512 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7082 | −0.629922 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.18034 | 0.0583641 | 0.0291820 | − | 0.999574i | \(-0.490710\pi\) | ||||
0.0291820 | + | 0.999574i | \(0.490710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.41641 | 0.415151 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.5623 | −0.667357 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.1591 | 2.31495 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.7984 | −0.528799 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.6869 | 1.40145 | 0.700724 | − | 0.713433i | \(-0.252861\pi\) | ||||
0.700724 | + | 0.713433i | \(0.252861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.2705 | −1.76772 | −0.883858 | − | 0.467755i | \(-0.845063\pi\) | ||||
−0.883858 | + | 0.467755i | \(0.845063\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.23607 | −0.157343 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.5066 | −0.703672 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.85410 | −0.234906 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.14590 | −0.0553245 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.0344 | −1.49488 | −0.747438 | − | 0.664331i | \(-0.768716\pi\) | ||||
−0.747438 | + | 0.664331i | \(0.768716\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.7082 | −0.754888 | −0.377444 | − | 0.926032i | \(-0.623197\pi\) | ||||
−0.377444 | + | 0.926032i | \(0.623197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.2705 | −0.923950 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.236068 | −0.0112927 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.1803 | 0.819973 | 0.409986 | − | 0.912092i | \(-0.365533\pi\) | ||||
0.409986 | + | 0.912092i | \(0.365533\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4164 | 1.30259 | 0.651296 | − | 0.758823i | \(-0.274225\pi\) | ||||
0.651296 | + | 0.758823i | \(0.274225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.2918 | −1.19895 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.1803 | 0.765304 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.2705 | −1.28697 | −0.643487 | − | 0.765457i | \(-0.722513\pi\) | ||||
−0.643487 | + | 0.765457i | \(0.722513\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | 0.423793 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.6525 | −1.06431 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.47214 | −0.0690148 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.97871 | −0.232894 | −0.116447 | − | 0.993197i | \(-0.537151\pi\) | ||||
−0.116447 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.47214 | −0.0687134 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.56231 | −0.165913 | −0.0829566 | − | 0.996553i | \(-0.526436\pi\) | ||||
−0.0829566 | + | 0.996553i | \(0.526436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.3607 | −0.899767 | −0.449884 | − | 0.893087i | \(-0.648535\pi\) | ||||
−0.449884 | + | 0.893087i | \(0.648535\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.2148 | 1.03019 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.6525 | 0.816859 | 0.408430 | − | 0.912790i | \(-0.366077\pi\) | ||||
0.408430 | + | 0.912790i | \(0.366077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.32624 | 0.107416 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.76393 | −0.311666 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.85410 | −0.223192 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.32624 | 0.106735 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.32624 | −0.106511 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0557 | −0.916370 | −0.458185 | − | 0.888857i | \(-0.651500\pi\) | ||||
−0.458185 | + | 0.888857i | \(0.651500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.61803 | 0.0737760 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.49342 | −0.340259 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.8328 | −1.07997 | −0.539984 | − | 0.841675i | \(-0.681570\pi\) | ||||
−0.539984 | + | 0.841675i | \(0.681570\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.67376 | 0.256576 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.03444 | 0.407719 | 0.203859 | − | 0.979000i | \(-0.434651\pi\) | ||||
0.203859 | + | 0.979000i | \(0.434651\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.36068 | 0.331508 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.5623 | 0.519687 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.61803 | 0.341716 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.4508 | 1.58700 | 0.793499 | − | 0.608572i | \(-0.208257\pi\) | ||||
0.793499 | + | 0.608572i | \(0.208257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.41641 | 0.376017 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.0344419 | 0.00153569 | 0.000767843 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000767843 | 1.00000i | \(0.499756\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.1459 | −1.29698 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8541 | −0.570871 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.7082 | −1.13950 | −0.569748 | − | 0.821819i | \(-0.692959\pi\) | ||||
−0.569748 | + | 0.821819i | \(0.692959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.94427 | −0.262959 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.236068 | 0.0104227 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 49.8885 | 2.19835 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.70820 | −0.426966 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.4721 | −0.766942 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.4164 | −1.81449 | −0.907243 | − | 0.420607i | \(-0.861817\pi\) | ||||
−0.907243 | + | 0.420607i | \(0.861817\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.4721 | 1.24500 | 0.622500 | − | 0.782620i | \(-0.286117\pi\) | ||||
0.622500 | + | 0.782620i | \(0.286117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.85410 | 0.430068 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.48529 | −0.369625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.5623 | −0.588554 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.14590 | −0.0496344 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.4164 | 2.09322 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 21.5623 | 0.930482 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.29180 | −0.270505 | −0.135253 | − | 0.990811i | \(-0.543185\pi\) | ||||
−0.135253 | + | 0.990811i | \(0.543185\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.41641 | 0.275354 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.9230 | −0.810572 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.8541 | −0.763386 | −0.381693 | − | 0.924289i | \(-0.624659\pi\) | ||||
−0.381693 | + | 0.924289i | \(0.624659\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.85410 | −0.207168 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.18034 | −0.0502842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.47214 | −0.402796 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.3262 | −0.693010 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −25.2361 | −1.06929 | −0.534643 | − | 0.845078i | \(-0.679554\pi\) | ||||
−0.534643 | + | 0.845078i | \(0.679554\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.618034 | 0.0261401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.41641 | −0.186461 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.50658 | 0.147785 | 0.0738923 | − | 0.997266i | \(-0.476458\pi\) | ||||
0.0738923 | + | 0.997266i | \(0.476458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.9656 | −1.30273 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.8885 | 0.917615 | 0.458808 | − | 0.888536i | \(-0.348277\pi\) | ||||
0.458808 | + | 0.888536i | \(0.348277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.5279 | 1.02646 | 0.513230 | − | 0.858251i | \(-0.328449\pi\) | ||||
0.513230 | + | 0.858251i | \(0.328449\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.7639 | 0.533221 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.85410 | −0.410944 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3607 | 0.431321 | 0.215660 | − | 0.976468i | \(-0.430810\pi\) | ||||
0.215660 | + | 0.976468i | \(0.430810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.6525 | 1.02452 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.2361 | 0.507638 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.97871 | −0.289029 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.47214 | −0.0608653 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.6738 | 0.688200 | 0.344100 | − | 0.938933i | \(-0.388184\pi\) | ||||
0.344100 | + | 0.938933i | \(0.388184\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.36068 | 0.0560658 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.09017 | 0.168247 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.1246 | 1.60666 | 0.803328 | − | 0.595537i | \(-0.203061\pi\) | ||||
0.803328 | + | 0.595537i | \(0.203061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.67376 | −0.232602 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.7984 | 0.441948 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.7426 | −0.765804 | −0.382902 | − | 0.923789i | \(-0.625075\pi\) | ||||
−0.382902 | + | 0.923789i | \(0.625075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.5623 | 1.28745 | 0.643727 | − | 0.765256i | \(-0.277387\pi\) | ||||
0.643727 | + | 0.765256i | \(0.277387\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.32624 | 0.0947317 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.70820 | −0.313383 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.5066 | 1.44117 | 0.720584 | − | 0.693368i | \(-0.243874\pi\) | ||||
0.720584 | + | 0.693368i | \(0.243874\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.00000 | −0.202610 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.23607 | 0.0500060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.4164 | −1.55162 | −0.775812 | − | 0.630964i | \(-0.782660\pi\) | ||||
−0.775812 | + | 0.630964i | \(0.782660\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.5623 | 0.466237 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.56231 | 0.183672 | 0.0918358 | − | 0.995774i | \(-0.470727\pi\) | ||||
0.0918358 | + | 0.995774i | \(0.470727\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.32624 | 0.133693 | 0.0668464 | − | 0.997763i | \(-0.478706\pi\) | ||||
0.0668464 | + | 0.997763i | \(0.478706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.56231 | −0.262913 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.8328 | 0.913313 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.708204 | 0.0282829 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.23607 | 0.248648 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6525 | −0.463878 | −0.231939 | − | 0.972730i | \(-0.574507\pi\) | ||||
−0.231939 | + | 0.972730i | \(0.574507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.23607 | 0.168369 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.8197 | 0.508733 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.381966 | −0.0151340 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.61803 | 0.301365 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.9787 | 0.552126 | 0.276063 | − | 0.961140i | \(-0.410970\pi\) | ||||
0.276063 | + | 0.961140i | \(0.410970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7426 | 0.423649 | 0.211824 | − | 0.977308i | \(-0.432060\pi\) | ||||
0.211824 | + | 0.977308i | \(0.432060\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.23607 | −0.245545 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.32624 | 0.0914538 | 0.0457269 | − | 0.998954i | \(-0.485440\pi\) | ||||
0.0457269 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.6869 | −1.59710 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.76393 | 0.225906 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.5623 | −0.452468 | −0.226234 | − | 0.974073i | \(-0.572641\pi\) | ||||
−0.226234 | + | 0.974073i | \(0.572641\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.5623 | 0.451777 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.94427 | −0.231908 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.0000 | −0.506408 | −0.253204 | − | 0.967413i | \(-0.581484\pi\) | ||||
−0.253204 | + | 0.967413i | \(0.581484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.4164 | 1.33864 | 0.669322 | − | 0.742973i | \(-0.266585\pi\) | ||||
0.669322 | + | 0.742973i | \(0.266585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.562306 | 0.0218382 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.909830 | 0.0352817 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.00000 | 0.193601 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.32624 | −0.167262 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.5623 | −0.562172 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.4164 | −0.864089 | −0.432045 | − | 0.901852i | \(-0.642208\pi\) | ||||
−0.432045 | + | 0.901852i | \(0.642208\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.85410 | 0.379285 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.9098 | −1.14953 | −0.574764 | − | 0.818319i | \(-0.694906\pi\) | ||||
−0.574764 | + | 0.818319i | \(0.694906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.94427 | −0.0746143 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.618034 | 0.0236831 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.0689 | −1.26535 | −0.632673 | − | 0.774419i | \(-0.718042\pi\) | ||||
−0.632673 | + | 0.774419i | \(0.718042\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.4377 | 1.23938 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.43769 | −0.0930038 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.888544 | 0.0338508 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.3262 | 0.583038 | 0.291519 | − | 0.956565i | \(-0.405839\pi\) | ||||
0.291519 | + | 0.956565i | \(0.405839\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.00000 | 0.113961 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.6180 | −1.57866 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.41641 | −0.167283 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.1459 | −0.610694 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.437694 | 0.0165315 | 0.00826574 | − | 0.999966i | \(-0.497369\pi\) | ||||
0.00826574 | + | 0.999966i | \(0.497369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.00000 | −0.0377157 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.4721 | −0.469728 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7.56231 | −0.284410 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.6738 | −1.30220 | −0.651100 | − | 0.758992i | \(-0.725692\pi\) | ||||
−0.651100 | + | 0.758992i | \(0.725692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.47214 | −0.355233 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.76393 | −0.215861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.41641 | −0.165164 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.67376 | −0.211891 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.2361 | 1.05303 | 0.526514 | − | 0.850167i | \(-0.323499\pi\) | ||||
0.526514 | + | 0.850167i | \(0.323499\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.9443 | 0.482070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.05573 | −0.0764534 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −49.2705 | −1.82986 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.0689 | 0.633050 | 0.316525 | − | 0.948584i | \(-0.397484\pi\) | ||||
0.316525 | + | 0.948584i | \(0.397484\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.38197 | 0.0881002 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.59675 | −0.354464 | −0.177232 | − | 0.984169i | \(-0.556714\pi\) | ||||
−0.177232 | + | 0.984169i | \(0.556714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.85410 | 0.142161 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.97871 | 0.257064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.1803 | −1.29413 | −0.647065 | − | 0.762435i | \(-0.724004\pi\) | ||||
−0.647065 | + | 0.762435i | \(0.724004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0901699 | −0.00331248 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.14590 | 0.298844 | 0.149422 | − | 0.988774i | \(-0.452259\pi\) | ||||
0.149422 | + | 0.988774i | \(0.452259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 62.3607 | 2.28472 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2361 | 0.447694 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.5623 | 0.459017 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.50658 | 0.0914663 | 0.0457332 | − | 0.998954i | \(-0.485438\pi\) | ||||
0.0457332 | + | 0.998954i | \(0.485438\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.2361 | 0.482349 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −87.3050 | −3.17735 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.18034 | −0.115591 | −0.0577957 | − | 0.998328i | \(-0.518407\pi\) | ||||
−0.0577957 | + | 0.998328i | \(0.518407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.00000 | −0.108893 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.5279 | 1.36038 | 0.680192 | − | 0.733034i | \(-0.261896\pi\) | ||||
0.680192 | + | 0.733034i | \(0.261896\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.90983 | −0.177748 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.67376 | −0.205135 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.18034 | 0.187051 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.0689 | −1.30068 | −0.650339 | − | 0.759644i | \(-0.725373\pi\) | ||||
−0.650339 | + | 0.759644i | \(0.725373\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.763932 | −0.0275123 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.23607 | 0.152361 | 0.0761804 | − | 0.997094i | \(-0.475728\pi\) | ||||
0.0761804 | + | 0.997094i | \(0.475728\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 56.7984 | 2.04026 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.23607 | −0.151968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.708204 | 0.0253740 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.8541 | 0.817784 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.00000 | −0.178685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.0689 | −0.930438 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.4377 | 0.799817 | 0.399909 | − | 0.916555i | \(-0.369042\pi\) | ||||
0.399909 | + | 0.916555i | \(0.369042\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.2918 | 0.615604 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.03444 | −0.285672 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.85410 | 0.0658411 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.96556 | −0.317976 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.2918 | 0.647929 | 0.323964 | − | 0.946069i | \(-0.394984\pi\) | ||||
0.323964 | + | 0.946069i | \(0.394984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.76393 | 0.168536 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.56231 | −0.231868 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.8328 | −0.629306 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.85410 | −0.135839 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.67376 | 0.305331 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 43.7984 | 1.53987 | 0.769934 | − | 0.638123i | \(-0.220289\pi\) | ||||
0.769934 | + | 0.638123i | \(0.220289\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.7771 | −1.01050 | −0.505250 | − | 0.862973i | \(-0.668600\pi\) | ||||
−0.505250 | + | 0.862973i | \(0.668600\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.4164 | 0.856321 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 21.8673 | 0.765977 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.381966 | −0.0133633 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.381966 | −0.0133470 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.29180 | 0.219585 | 0.109793 | − | 0.993955i | \(-0.464981\pi\) | ||||
0.109793 | + | 0.993955i | \(0.464981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.7426 | 1.94307 | 0.971533 | − | 0.236903i | \(-0.0761324\pi\) | ||||
0.971533 | + | 0.236903i | \(0.0761324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 29.5623 | 1.02923 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.0902 | 1.22020 | 0.610102 | − | 0.792323i | \(-0.291128\pi\) | ||||
0.610102 | + | 0.792323i | \(0.291128\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.2918 | 0.600569 | 0.300284 | − | 0.953850i | \(-0.402918\pi\) | ||||
0.300284 | + | 0.953850i | \(0.402918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.32624 | 0.115386 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.47214 | −0.0510065 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.4377 | 1.12255 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.76393 | 0.199231 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.6869 | −1.30110 | −0.650548 | − | 0.759465i | \(-0.725461\pi\) | ||||
−0.650548 | + | 0.759465i | \(0.725461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.1246 | −0.658687 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −49.5410 | −1.70426 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.0344 | −0.893500 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.23607 | 0.145211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5967 | −0.602501 | −0.301251 | − | 0.953545i | \(-0.597404\pi\) | ||||
−0.301251 | + | 0.953545i | \(0.597404\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.909830 | 0.0311155 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.0689 | −0.685540 | −0.342770 | − | 0.939419i | \(-0.611365\pi\) | ||||
−0.342770 | + | 0.939419i | \(0.611365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 52.4721 | 1.79033 | 0.895163 | − | 0.445739i | \(-0.147059\pi\) | ||||
0.895163 | + | 0.445739i | \(0.147059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | 0.102240 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.76393 | 0.230247 | 0.115123 | − | 0.993351i | \(-0.463274\pi\) | ||||
0.115123 | + | 0.993351i | \(0.463274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −67.3394 | −2.28961 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.8328 | −0.503749 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.4164 | −0.963961 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.888544 | −0.0301072 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.94427 | −0.0658036 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.7082 | 0.632453 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.94427 | −0.166956 | −0.0834781 | − | 0.996510i | \(-0.526603\pi\) | ||||
−0.0834781 | + | 0.996510i | \(0.526603\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.9443 | 0.436599 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.5967 | 1.13190 | 0.565952 | − | 0.824438i | \(-0.308509\pi\) | ||||
0.565952 | + | 0.824438i | \(0.308509\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.97871 | 0.133894 | 0.0669472 | − | 0.997757i | \(-0.478674\pi\) | ||||
0.0669472 | + | 0.997757i | \(0.478674\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −52.2705 | −1.75705 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.7426 | −0.696470 | −0.348235 | − | 0.937407i | \(-0.613219\pi\) | ||||
−0.348235 | + | 0.937407i | \(0.613219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.32624 | 0.111558 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | 0.100504 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.763932 | −0.0255640 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 83.1033 | 2.77784 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.381966 | 0.0127535 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28.8197 | −0.961189 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.42454 | 0.114088 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.61803 | −0.0538448 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24.7295 | 0.822036 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.38197 | −0.112296 | −0.0561482 | − | 0.998422i | \(-0.517882\pi\) | ||||
−0.0561482 | + | 0.998422i | \(0.517882\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.56231 | −0.250826 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.5967 | 1.17937 | 0.589686 | − | 0.807632i | \(-0.299251\pi\) | ||||
0.589686 | + | 0.807632i | \(0.299251\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.7082 | 1.21486 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.7082 | −0.618474 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.00000 | 0.0990687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.5967 | −1.73501 | −0.867503 | − | 0.497431i | \(-0.834277\pi\) | ||||
−0.867503 | + | 0.497431i | \(0.834277\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.6525 | −0.779376 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.90983 | −0.0957782 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.7426 | −1.37249 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.9443 | 0.425146 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41.5623 | 1.36362 | 0.681808 | − | 0.731532i | \(-0.261194\pi\) | ||||
0.681808 | + | 0.731532i | \(0.261194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.236068 | 0.00773682 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.3820 | −0.536321 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.0213 | −0.556656 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.5410 | 1.48776 | 0.743880 | − | 0.668313i | \(-0.232983\pi\) | ||||
0.743880 | + | 0.668313i | \(0.232983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.0000 | −0.391605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.5836 | −0.540610 | −0.270305 | − | 0.962775i | \(-0.587124\pi\) | ||||
−0.270305 | + | 0.962775i | \(0.587124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.00000 | −0.0976934 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.85410 | 0.125374 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.4721 | 1.44515 | 0.722575 | − | 0.691292i | \(-0.242958\pi\) | ||||
0.722575 | + | 0.691292i | \(0.242958\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.27051 | 0.0737039 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.0344 | 0.973934 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.96556 | −0.160850 | −0.0804251 | − | 0.996761i | \(-0.525628\pi\) | ||||
−0.0804251 | + | 0.996761i | \(0.525628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 49.1935 | 1.59186 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.0000 | −0.484881 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.41641 | 0.271780 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.22291 | 0.0717069 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.5623 | 0.404815 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 95.0132 | 3.05858 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.0000 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.347524 | −0.0111641 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.2705 | 1.03561 | 0.517805 | − | 0.855499i | \(-0.326749\pi\) | ||||
0.517805 | + | 0.855499i | \(0.326749\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.7984 | −0.346180 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.76393 | −0.120542 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.43769 | −0.301939 | −0.150969 | − | 0.988538i | \(-0.548239\pi\) | ||||
−0.150969 | + | 0.988538i | \(0.548239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.6869 | −0.629197 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.90983 | −0.156759 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −40.5967 | −1.29484 | −0.647418 | − | 0.762135i | \(-0.724151\pi\) | ||||
−0.647418 | + | 0.762135i | \(0.724151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.7639 | 0.502281 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.23607 | −0.103005 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.61803 | 0.0514505 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.8673 | 1.77468 | 0.887341 | − | 0.461114i | \(-0.152550\pi\) | ||||
0.887341 | + | 0.461114i | \(0.152550\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.3607 | −0.582659 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.6180 | 1.31938 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.5967 | −0.778987 | −0.389493 | − | 0.921029i | \(-0.627350\pi\) | ||||
−0.389493 | + | 0.921029i | \(0.627350\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.23607 | −0.134023 |
(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 | 1932.2.a.h.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 5796.2.a.j.1.1 | 2 | |||
4.3 | odd | 2 | 7728.2.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.a.h.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
5796.2.a.j.1.1 | 2 | 3.2 | odd | 2 | |||
7728.2.a.bb.1.2 | 2 | 4.3 | odd | 2 |