Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | −0.288675 | − | 0.957427i | \(-0.593215\pi\) | ||||
−0.288675 | + | 0.957427i | \(0.593215\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.732051 | −0.327383 | −0.163692 | − | 0.986512i | \(-0.552340\pi\) | ||||
−0.163692 | + | 0.986512i | \(0.552340\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.267949 | 0.101275 | 0.0506376 | − | 0.998717i | \(-0.483875\pi\) | ||||
0.0506376 | + | 0.998717i | \(0.483875\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0.732051 | 0.231495 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | −0.267949 | −0.0716124 | ||||||||
\(15\) | 0.732051 | 0.189015 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.46410 | −1.81031 | −0.905155 | − | 0.425081i | \(-0.860246\pi\) | ||||
−0.905155 | + | 0.425081i | \(0.860246\pi\) | |||||||
\(18\) | 2.00000 | 0.471405 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −0.732051 | −0.163692 | ||||||||
\(21\) | −0.267949 | −0.0584713 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | 3.46410 | 0.679366 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0.267949 | 0.0506376 | ||||||||
\(29\) | 1.73205 | 0.321634 | 0.160817 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160817 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(30\) | −0.732051 | −0.133654 | ||||||||
\(31\) | −1.46410 | −0.262960 | −0.131480 | − | 0.991319i | \(-0.541973\pi\) | ||||
−0.131480 | + | 0.991319i | \(0.541973\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.46410 | 1.28008 | ||||||||
\(35\) | −0.196152 | −0.0331558 | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | −6.46410 | −1.06269 | −0.531346 | − | 0.847155i | \(-0.678314\pi\) | ||||
−0.531346 | + | 0.847155i | \(0.678314\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 3.46410 | 0.554700 | ||||||||
\(40\) | 0.732051 | 0.115747 | ||||||||
\(41\) | −10.7321 | −1.67606 | −0.838032 | − | 0.545621i | \(-0.816294\pi\) | ||||
−0.838032 | + | 0.545621i | \(0.816294\pi\) | |||||||
\(42\) | 0.267949 | 0.0413455 | ||||||||
\(43\) | 4.92820 | 0.751544 | 0.375772 | − | 0.926712i | \(-0.377378\pi\) | ||||
0.375772 | + | 0.926712i | \(0.377378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.46410 | 0.218255 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 12.4641 | 1.81808 | 0.909038 | − | 0.416713i | \(-0.136818\pi\) | ||||
0.909038 | + | 0.416713i | \(0.136818\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.92820 | −0.989743 | ||||||||
\(50\) | 4.46410 | 0.631319 | ||||||||
\(51\) | 7.46410 | 1.04518 | ||||||||
\(52\) | −3.46410 | −0.480384 | ||||||||
\(53\) | −9.92820 | −1.36374 | −0.681872 | − | 0.731472i | \(-0.738834\pi\) | ||||
−0.681872 | + | 0.731472i | \(0.738834\pi\) | |||||||
\(54\) | −5.00000 | −0.680414 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.267949 | −0.0358062 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −1.73205 | −0.227429 | ||||||||
\(59\) | −9.39230 | −1.22277 | −0.611387 | − | 0.791332i | \(-0.709388\pi\) | ||||
−0.611387 | + | 0.791332i | \(0.709388\pi\) | |||||||
\(60\) | 0.732051 | 0.0945074 | ||||||||
\(61\) | 1.26795 | 0.162344 | 0.0811721 | − | 0.996700i | \(-0.474134\pi\) | ||||
0.0811721 | + | 0.996700i | \(0.474134\pi\) | |||||||
\(62\) | 1.46410 | 0.185941 | ||||||||
\(63\) | −0.535898 | −0.0675169 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.53590 | 0.314539 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0000 | 1.71037 | 0.855186 | − | 0.518321i | \(-0.173443\pi\) | ||||
0.855186 | + | 0.518321i | \(0.173443\pi\) | |||||||
\(68\) | −7.46410 | −0.905155 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0.196152 | 0.0234447 | ||||||||
\(71\) | 14.1962 | 1.68477 | 0.842387 | − | 0.538874i | \(-0.181150\pi\) | ||||
0.842387 | + | 0.538874i | \(0.181150\pi\) | |||||||
\(72\) | 2.00000 | 0.235702 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 6.46410 | 0.751437 | ||||||||
\(75\) | 4.46410 | 0.515470 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.46410 | −0.392232 | ||||||||
\(79\) | −2.19615 | −0.247086 | −0.123543 | − | 0.992339i | \(-0.539426\pi\) | ||||
−0.123543 | + | 0.992339i | \(0.539426\pi\) | |||||||
\(80\) | −0.732051 | −0.0818458 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.7321 | 1.18516 | ||||||||
\(83\) | −3.80385 | −0.417527 | −0.208763 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208763 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(84\) | −0.267949 | −0.0292357 | ||||||||
\(85\) | 5.46410 | 0.592665 | ||||||||
\(86\) | −4.92820 | −0.531422 | ||||||||
\(87\) | −1.73205 | −0.185695 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.1962 | 1.29279 | 0.646395 | − | 0.763003i | \(-0.276276\pi\) | ||||
0.646395 | + | 0.763003i | \(0.276276\pi\) | |||||||
\(90\) | −1.46410 | −0.154330 | ||||||||
\(91\) | −0.928203 | −0.0973021 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 1.46410 | 0.151820 | ||||||||
\(94\) | −12.4641 | −1.28557 | ||||||||
\(95\) | −0.732051 | −0.0751068 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 13.4641 | 1.36707 | 0.683536 | − | 0.729917i | \(-0.260441\pi\) | ||||
0.683536 | + | 0.729917i | \(0.260441\pi\) | |||||||
\(98\) | 6.92820 | 0.699854 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.46410 | −0.446410 | ||||||||
\(101\) | −16.5885 | −1.65061 | −0.825307 | − | 0.564685i | \(-0.808998\pi\) | ||||
−0.825307 | + | 0.564685i | \(0.808998\pi\) | |||||||
\(102\) | −7.46410 | −0.739056 | ||||||||
\(103\) | −2.73205 | −0.269197 | −0.134598 | − | 0.990900i | \(-0.542974\pi\) | ||||
−0.134598 | + | 0.990900i | \(0.542974\pi\) | |||||||
\(104\) | 3.46410 | 0.339683 | ||||||||
\(105\) | 0.196152 | 0.0191425 | ||||||||
\(106\) | 9.92820 | 0.964312 | ||||||||
\(107\) | −2.80385 | −0.271058 | −0.135529 | − | 0.990773i | \(-0.543273\pi\) | ||||
−0.135529 | + | 0.990773i | \(0.543273\pi\) | |||||||
\(108\) | 5.00000 | 0.481125 | ||||||||
\(109\) | −6.12436 | −0.586607 | −0.293303 | − | 0.956019i | \(-0.594755\pi\) | ||||
−0.293303 | + | 0.956019i | \(0.594755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.46410 | 0.613545 | ||||||||
\(112\) | 0.267949 | 0.0253188 | ||||||||
\(113\) | −4.73205 | −0.445154 | −0.222577 | − | 0.974915i | \(-0.571447\pi\) | ||||
−0.222577 | + | 0.974915i | \(0.571447\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 0.732051 | 0.0682641 | ||||||||
\(116\) | 1.73205 | 0.160817 | ||||||||
\(117\) | 6.92820 | 0.640513 | ||||||||
\(118\) | 9.39230 | 0.864632 | ||||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | −0.732051 | −0.0668268 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −1.26795 | −0.114795 | ||||||||
\(123\) | 10.7321 | 0.967676 | ||||||||
\(124\) | −1.46410 | −0.131480 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0.535898 | 0.0477416 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.92820 | −0.433904 | ||||||||
\(130\) | −2.53590 | −0.222413 | ||||||||
\(131\) | −20.9282 | −1.82851 | −0.914253 | − | 0.405144i | \(-0.867221\pi\) | ||||
−0.914253 | + | 0.405144i | \(0.867221\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.267949 | 0.0232341 | ||||||||
\(134\) | −14.0000 | −1.20942 | ||||||||
\(135\) | −3.66025 | −0.315025 | ||||||||
\(136\) | 7.46410 | 0.640041 | ||||||||
\(137\) | 9.46410 | 0.808573 | 0.404286 | − | 0.914632i | \(-0.367520\pi\) | ||||
0.404286 | + | 0.914632i | \(0.367520\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −6.53590 | −0.554368 | −0.277184 | − | 0.960817i | \(-0.589401\pi\) | ||||
−0.277184 | + | 0.960817i | \(0.589401\pi\) | |||||||
\(140\) | −0.196152 | −0.0165779 | ||||||||
\(141\) | −12.4641 | −1.04967 | ||||||||
\(142\) | −14.1962 | −1.19131 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | −1.26795 | −0.105297 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 6.92820 | 0.571429 | ||||||||
\(148\) | −6.46410 | −0.531346 | ||||||||
\(149\) | 11.3205 | 0.927412 | 0.463706 | − | 0.885989i | \(-0.346519\pi\) | ||||
0.463706 | + | 0.885989i | \(0.346519\pi\) | |||||||
\(150\) | −4.46410 | −0.364492 | ||||||||
\(151\) | −20.7321 | −1.68715 | −0.843575 | − | 0.537011i | \(-0.819553\pi\) | ||||
−0.843575 | + | 0.537011i | \(0.819553\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 14.9282 | 1.20687 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.07180 | 0.0860888 | ||||||||
\(156\) | 3.46410 | 0.277350 | ||||||||
\(157\) | −5.26795 | −0.420428 | −0.210214 | − | 0.977655i | \(-0.567416\pi\) | ||||
−0.210214 | + | 0.977655i | \(0.567416\pi\) | |||||||
\(158\) | 2.19615 | 0.174717 | ||||||||
\(159\) | 9.92820 | 0.787358 | ||||||||
\(160\) | 0.732051 | 0.0578737 | ||||||||
\(161\) | −0.267949 | −0.0211174 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 17.3205 | 1.35665 | 0.678323 | − | 0.734763i | \(-0.262707\pi\) | ||||
0.678323 | + | 0.734763i | \(0.262707\pi\) | |||||||
\(164\) | −10.7321 | −0.838032 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.80385 | 0.295236 | ||||||||
\(167\) | −3.46410 | −0.268060 | −0.134030 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134030 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(168\) | 0.267949 | 0.0206727 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | −5.46410 | −0.419077 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 4.92820 | 0.375772 | ||||||||
\(173\) | −4.12436 | −0.313569 | −0.156784 | − | 0.987633i | \(-0.550113\pi\) | ||||
−0.156784 | + | 0.987633i | \(0.550113\pi\) | |||||||
\(174\) | 1.73205 | 0.131306 | ||||||||
\(175\) | −1.19615 | −0.0904206 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.39230 | 0.705969 | ||||||||
\(178\) | −12.1962 | −0.914140 | ||||||||
\(179\) | −2.07180 | −0.154853 | −0.0774267 | − | 0.996998i | \(-0.524670\pi\) | ||||
−0.0774267 | + | 0.996998i | \(0.524670\pi\) | |||||||
\(180\) | 1.46410 | 0.109128 | ||||||||
\(181\) | 24.3923 | 1.81307 | 0.906533 | − | 0.422135i | \(-0.138719\pi\) | ||||
0.906533 | + | 0.422135i | \(0.138719\pi\) | |||||||
\(182\) | 0.928203 | 0.0688030 | ||||||||
\(183\) | −1.26795 | −0.0937295 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 4.73205 | 0.347907 | ||||||||
\(186\) | −1.46410 | −0.107353 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.4641 | 0.909038 | ||||||||
\(189\) | 1.33975 | 0.0974522 | ||||||||
\(190\) | 0.732051 | 0.0531085 | ||||||||
\(191\) | −17.3923 | −1.25846 | −0.629232 | − | 0.777218i | \(-0.716630\pi\) | ||||
−0.629232 | + | 0.777218i | \(0.716630\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.5359 | 0.902354 | 0.451177 | − | 0.892435i | \(-0.351004\pi\) | ||||
0.451177 | + | 0.892435i | \(0.351004\pi\) | |||||||
\(194\) | −13.4641 | −0.966666 | ||||||||
\(195\) | −2.53590 | −0.181599 | ||||||||
\(196\) | −6.92820 | −0.494872 | ||||||||
\(197\) | 5.07180 | 0.361351 | 0.180675 | − | 0.983543i | \(-0.442172\pi\) | ||||
0.180675 | + | 0.983543i | \(0.442172\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9282 | 1.20001 | 0.600004 | − | 0.799997i | \(-0.295166\pi\) | ||||
0.600004 | + | 0.799997i | \(0.295166\pi\) | |||||||
\(200\) | 4.46410 | 0.315660 | ||||||||
\(201\) | −14.0000 | −0.987484 | ||||||||
\(202\) | 16.5885 | 1.16716 | ||||||||
\(203\) | 0.464102 | 0.0325735 | ||||||||
\(204\) | 7.46410 | 0.522592 | ||||||||
\(205\) | 7.85641 | 0.548715 | ||||||||
\(206\) | 2.73205 | 0.190351 | ||||||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | −3.46410 | −0.240192 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.196152 | −0.0135358 | ||||||||
\(211\) | −4.12436 | −0.283932 | −0.141966 | − | 0.989872i | \(-0.545342\pi\) | ||||
−0.141966 | + | 0.989872i | \(0.545342\pi\) | |||||||
\(212\) | −9.92820 | −0.681872 | ||||||||
\(213\) | −14.1962 | −0.972704 | ||||||||
\(214\) | 2.80385 | 0.191667 | ||||||||
\(215\) | −3.60770 | −0.246043 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | −0.392305 | −0.0266314 | ||||||||
\(218\) | 6.12436 | 0.414794 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.8564 | 1.73929 | ||||||||
\(222\) | −6.46410 | −0.433842 | ||||||||
\(223\) | 13.1244 | 0.878872 | 0.439436 | − | 0.898274i | \(-0.355178\pi\) | ||||
0.439436 | + | 0.898274i | \(0.355178\pi\) | |||||||
\(224\) | −0.267949 | −0.0179031 | ||||||||
\(225\) | 8.92820 | 0.595214 | ||||||||
\(226\) | 4.73205 | 0.314771 | ||||||||
\(227\) | 8.39230 | 0.557017 | 0.278508 | − | 0.960434i | \(-0.410160\pi\) | ||||
0.278508 | + | 0.960434i | \(0.410160\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | −12.3923 | −0.818907 | −0.409453 | − | 0.912331i | \(-0.634281\pi\) | ||||
−0.409453 | + | 0.912331i | \(0.634281\pi\) | |||||||
\(230\) | −0.732051 | −0.0482700 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.73205 | −0.113715 | ||||||||
\(233\) | −8.26795 | −0.541651 | −0.270826 | − | 0.962628i | \(-0.587297\pi\) | ||||
−0.270826 | + | 0.962628i | \(0.587297\pi\) | |||||||
\(234\) | −6.92820 | −0.452911 | ||||||||
\(235\) | −9.12436 | −0.595207 | ||||||||
\(236\) | −9.39230 | −0.611387 | ||||||||
\(237\) | 2.19615 | 0.142655 | ||||||||
\(238\) | 2.00000 | 0.129641 | ||||||||
\(239\) | −14.1244 | −0.913629 | −0.456814 | − | 0.889562i | \(-0.651010\pi\) | ||||
−0.456814 | + | 0.889562i | \(0.651010\pi\) | |||||||
\(240\) | 0.732051 | 0.0472537 | ||||||||
\(241\) | 11.2679 | 0.725832 | 0.362916 | − | 0.931822i | \(-0.381781\pi\) | ||||
0.362916 | + | 0.931822i | \(0.381781\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | 1.26795 | 0.0811721 | ||||||||
\(245\) | 5.07180 | 0.324025 | ||||||||
\(246\) | −10.7321 | −0.684251 | ||||||||
\(247\) | −3.46410 | −0.220416 | ||||||||
\(248\) | 1.46410 | 0.0929705 | ||||||||
\(249\) | 3.80385 | 0.241059 | ||||||||
\(250\) | −6.92820 | −0.438178 | ||||||||
\(251\) | 8.53590 | 0.538781 | 0.269391 | − | 0.963031i | \(-0.413178\pi\) | ||||
0.269391 | + | 0.963031i | \(0.413178\pi\) | |||||||
\(252\) | −0.535898 | −0.0337584 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.00000 | −0.250982 | ||||||||
\(255\) | −5.46410 | −0.342175 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.32051 | −0.207128 | −0.103564 | − | 0.994623i | \(-0.533025\pi\) | ||||
−0.103564 | + | 0.994623i | \(0.533025\pi\) | |||||||
\(258\) | 4.92820 | 0.306817 | ||||||||
\(259\) | −1.73205 | −0.107624 | ||||||||
\(260\) | 2.53590 | 0.157270 | ||||||||
\(261\) | −3.46410 | −0.214423 | ||||||||
\(262\) | 20.9282 | 1.29295 | ||||||||
\(263\) | 24.7846 | 1.52828 | 0.764142 | − | 0.645048i | \(-0.223163\pi\) | ||||
0.764142 | + | 0.645048i | \(0.223163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.26795 | 0.446467 | ||||||||
\(266\) | −0.267949 | −0.0164290 | ||||||||
\(267\) | −12.1962 | −0.746392 | ||||||||
\(268\) | 14.0000 | 0.855186 | ||||||||
\(269\) | −29.7846 | −1.81600 | −0.908000 | − | 0.418970i | \(-0.862391\pi\) | ||||
−0.908000 | + | 0.418970i | \(0.862391\pi\) | |||||||
\(270\) | 3.66025 | 0.222756 | ||||||||
\(271\) | −7.32051 | −0.444689 | −0.222345 | − | 0.974968i | \(-0.571371\pi\) | ||||
−0.222345 | + | 0.974968i | \(0.571371\pi\) | |||||||
\(272\) | −7.46410 | −0.452578 | ||||||||
\(273\) | 0.928203 | 0.0561774 | ||||||||
\(274\) | −9.46410 | −0.571747 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 15.1244 | 0.908734 | 0.454367 | − | 0.890814i | \(-0.349865\pi\) | ||||
0.454367 | + | 0.890814i | \(0.349865\pi\) | |||||||
\(278\) | 6.53590 | 0.391997 | ||||||||
\(279\) | 2.92820 | 0.175307 | ||||||||
\(280\) | 0.196152 | 0.0117223 | ||||||||
\(281\) | 16.0526 | 0.957615 | 0.478808 | − | 0.877920i | \(-0.341069\pi\) | ||||
0.478808 | + | 0.877920i | \(0.341069\pi\) | |||||||
\(282\) | 12.4641 | 0.742226 | ||||||||
\(283\) | 21.4641 | 1.27591 | 0.637954 | − | 0.770074i | \(-0.279781\pi\) | ||||
0.637954 | + | 0.770074i | \(0.279781\pi\) | |||||||
\(284\) | 14.1962 | 0.842387 | ||||||||
\(285\) | 0.732051 | 0.0433629 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.87564 | −0.169744 | ||||||||
\(288\) | 2.00000 | 0.117851 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 1.26795 | 0.0744565 | ||||||||
\(291\) | −13.4641 | −0.789280 | ||||||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | 12.1244 | 0.708312 | 0.354156 | − | 0.935186i | \(-0.384768\pi\) | ||||
0.354156 | + | 0.935186i | \(0.384768\pi\) | |||||||
\(294\) | −6.92820 | −0.404061 | ||||||||
\(295\) | 6.87564 | 0.400315 | ||||||||
\(296\) | 6.46410 | 0.375718 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.3205 | −0.655779 | ||||||||
\(299\) | 3.46410 | 0.200334 | ||||||||
\(300\) | 4.46410 | 0.257735 | ||||||||
\(301\) | 1.32051 | 0.0761128 | ||||||||
\(302\) | 20.7321 | 1.19300 | ||||||||
\(303\) | 16.5885 | 0.952982 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −0.928203 | −0.0531488 | ||||||||
\(306\) | −14.9282 | −0.853389 | ||||||||
\(307\) | 15.5885 | 0.889680 | 0.444840 | − | 0.895610i | \(-0.353260\pi\) | ||||
0.444840 | + | 0.895610i | \(0.353260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.73205 | 0.155421 | ||||||||
\(310\) | −1.07180 | −0.0608740 | ||||||||
\(311\) | −1.60770 | −0.0911640 | −0.0455820 | − | 0.998961i | \(-0.514514\pi\) | ||||
−0.0455820 | + | 0.998961i | \(0.514514\pi\) | |||||||
\(312\) | −3.46410 | −0.196116 | ||||||||
\(313\) | 13.5359 | 0.765094 | 0.382547 | − | 0.923936i | \(-0.375047\pi\) | ||||
0.382547 | + | 0.923936i | \(0.375047\pi\) | |||||||
\(314\) | 5.26795 | 0.297288 | ||||||||
\(315\) | 0.392305 | 0.0221039 | ||||||||
\(316\) | −2.19615 | −0.123543 | ||||||||
\(317\) | −20.7846 | −1.16738 | −0.583690 | − | 0.811977i | \(-0.698392\pi\) | ||||
−0.583690 | + | 0.811977i | \(0.698392\pi\) | |||||||
\(318\) | −9.92820 | −0.556746 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.732051 | −0.0409229 | ||||||||
\(321\) | 2.80385 | 0.156496 | ||||||||
\(322\) | 0.267949 | 0.0149322 | ||||||||
\(323\) | −7.46410 | −0.415314 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 15.4641 | 0.857794 | ||||||||
\(326\) | −17.3205 | −0.959294 | ||||||||
\(327\) | 6.12436 | 0.338678 | ||||||||
\(328\) | 10.7321 | 0.592578 | ||||||||
\(329\) | 3.33975 | 0.184126 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.7846 | 1.19739 | 0.598695 | − | 0.800977i | \(-0.295686\pi\) | ||||
0.598695 | + | 0.800977i | \(0.295686\pi\) | |||||||
\(332\) | −3.80385 | −0.208763 | ||||||||
\(333\) | 12.9282 | 0.708461 | ||||||||
\(334\) | 3.46410 | 0.189547 | ||||||||
\(335\) | −10.2487 | −0.559947 | ||||||||
\(336\) | −0.267949 | −0.0146178 | ||||||||
\(337\) | −24.1962 | −1.31805 | −0.659024 | − | 0.752122i | \(-0.729031\pi\) | ||||
−0.659024 | + | 0.752122i | \(0.729031\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 4.73205 | 0.257010 | ||||||||
\(340\) | 5.46410 | 0.296333 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 2.00000 | 0.108148 | ||||||||
\(343\) | −3.73205 | −0.201512 | ||||||||
\(344\) | −4.92820 | −0.265711 | ||||||||
\(345\) | −0.732051 | −0.0394123 | ||||||||
\(346\) | 4.12436 | 0.221727 | ||||||||
\(347\) | 10.0526 | 0.539650 | 0.269825 | − | 0.962909i | \(-0.413034\pi\) | ||||
0.269825 | + | 0.962909i | \(0.413034\pi\) | |||||||
\(348\) | −1.73205 | −0.0928477 | ||||||||
\(349\) | −14.7846 | −0.791402 | −0.395701 | − | 0.918379i | \(-0.629498\pi\) | ||||
−0.395701 | + | 0.918379i | \(0.629498\pi\) | |||||||
\(350\) | 1.19615 | 0.0639370 | ||||||||
\(351\) | −17.3205 | −0.924500 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.46410 | −0.344049 | −0.172025 | − | 0.985093i | \(-0.555031\pi\) | ||||
−0.172025 | + | 0.985093i | \(0.555031\pi\) | |||||||
\(354\) | −9.39230 | −0.499195 | ||||||||
\(355\) | −10.3923 | −0.551566 | ||||||||
\(356\) | 12.1962 | 0.646395 | ||||||||
\(357\) | 2.00000 | 0.105851 | ||||||||
\(358\) | 2.07180 | 0.109498 | ||||||||
\(359\) | 28.3923 | 1.49849 | 0.749244 | − | 0.662294i | \(-0.230417\pi\) | ||||
0.749244 | + | 0.662294i | \(0.230417\pi\) | |||||||
\(360\) | −1.46410 | −0.0771649 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −24.3923 | −1.28203 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.928203 | −0.0486511 | ||||||||
\(365\) | −1.46410 | −0.0766346 | ||||||||
\(366\) | 1.26795 | 0.0662768 | ||||||||
\(367\) | −22.8564 | −1.19309 | −0.596547 | − | 0.802578i | \(-0.703461\pi\) | ||||
−0.596547 | + | 0.802578i | \(0.703461\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 21.4641 | 1.11738 | ||||||||
\(370\) | −4.73205 | −0.246008 | ||||||||
\(371\) | −2.66025 | −0.138114 | ||||||||
\(372\) | 1.46410 | 0.0759101 | ||||||||
\(373\) | −16.8038 | −0.870070 | −0.435035 | − | 0.900413i | \(-0.643264\pi\) | ||||
−0.435035 | + | 0.900413i | \(0.643264\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.92820 | −0.357771 | ||||||||
\(376\) | −12.4641 | −0.642787 | ||||||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | −1.33975 | −0.0689091 | ||||||||
\(379\) | 23.9282 | 1.22911 | 0.614555 | − | 0.788874i | \(-0.289336\pi\) | ||||
0.614555 | + | 0.788874i | \(0.289336\pi\) | |||||||
\(380\) | −0.732051 | −0.0375534 | ||||||||
\(381\) | −4.00000 | −0.204926 | ||||||||
\(382\) | 17.3923 | 0.889868 | ||||||||
\(383\) | 33.4641 | 1.70994 | 0.854968 | − | 0.518681i | \(-0.173577\pi\) | ||||
0.854968 | + | 0.518681i | \(0.173577\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.5359 | −0.638060 | ||||||||
\(387\) | −9.85641 | −0.501029 | ||||||||
\(388\) | 13.4641 | 0.683536 | ||||||||
\(389\) | −0.588457 | −0.0298360 | −0.0149180 | − | 0.999889i | \(-0.504749\pi\) | ||||
−0.0149180 | + | 0.999889i | \(0.504749\pi\) | |||||||
\(390\) | 2.53590 | 0.128410 | ||||||||
\(391\) | 7.46410 | 0.377476 | ||||||||
\(392\) | 6.92820 | 0.349927 | ||||||||
\(393\) | 20.9282 | 1.05569 | ||||||||
\(394\) | −5.07180 | −0.255513 | ||||||||
\(395\) | 1.60770 | 0.0808919 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.60770 | 0.281442 | 0.140721 | − | 0.990049i | \(-0.455058\pi\) | ||||
0.140721 | + | 0.990049i | \(0.455058\pi\) | |||||||
\(398\) | −16.9282 | −0.848534 | ||||||||
\(399\) | −0.267949 | −0.0134142 | ||||||||
\(400\) | −4.46410 | −0.223205 | ||||||||
\(401\) | −16.0526 | −0.801627 | −0.400813 | − | 0.916160i | \(-0.631272\pi\) | ||||
−0.400813 | + | 0.916160i | \(0.631272\pi\) | |||||||
\(402\) | 14.0000 | 0.698257 | ||||||||
\(403\) | 5.07180 | 0.252644 | ||||||||
\(404\) | −16.5885 | −0.825307 | ||||||||
\(405\) | −0.732051 | −0.0363759 | ||||||||
\(406\) | −0.464102 | −0.0230330 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.46410 | −0.369528 | ||||||||
\(409\) | 13.4641 | 0.665757 | 0.332878 | − | 0.942970i | \(-0.391980\pi\) | ||||
0.332878 | + | 0.942970i | \(0.391980\pi\) | |||||||
\(410\) | −7.85641 | −0.388000 | ||||||||
\(411\) | −9.46410 | −0.466830 | ||||||||
\(412\) | −2.73205 | −0.134598 | ||||||||
\(413\) | −2.51666 | −0.123837 | ||||||||
\(414\) | −2.00000 | −0.0982946 | ||||||||
\(415\) | 2.78461 | 0.136691 | ||||||||
\(416\) | 3.46410 | 0.169842 | ||||||||
\(417\) | 6.53590 | 0.320064 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.4449 | −1.58504 | −0.792518 | − | 0.609849i | \(-0.791230\pi\) | ||||
−0.792518 | + | 0.609849i | \(0.791230\pi\) | |||||||
\(420\) | 0.196152 | 0.00957126 | ||||||||
\(421\) | −1.67949 | −0.0818534 | −0.0409267 | − | 0.999162i | \(-0.513031\pi\) | ||||
−0.0409267 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(422\) | 4.12436 | 0.200770 | ||||||||
\(423\) | −24.9282 | −1.21205 | ||||||||
\(424\) | 9.92820 | 0.482156 | ||||||||
\(425\) | 33.3205 | 1.61628 | ||||||||
\(426\) | 14.1962 | 0.687806 | ||||||||
\(427\) | 0.339746 | 0.0164415 | ||||||||
\(428\) | −2.80385 | −0.135529 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.60770 | 0.173979 | ||||||||
\(431\) | 23.6603 | 1.13967 | 0.569837 | − | 0.821758i | \(-0.307006\pi\) | ||||
0.569837 | + | 0.821758i | \(0.307006\pi\) | |||||||
\(432\) | 5.00000 | 0.240563 | ||||||||
\(433\) | 18.7846 | 0.902731 | 0.451365 | − | 0.892339i | \(-0.350937\pi\) | ||||
0.451365 | + | 0.892339i | \(0.350937\pi\) | |||||||
\(434\) | 0.392305 | 0.0188312 | ||||||||
\(435\) | 1.26795 | 0.0607935 | ||||||||
\(436\) | −6.12436 | −0.293303 | ||||||||
\(437\) | −1.00000 | −0.0478365 | ||||||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | 17.4641 | 0.833516 | 0.416758 | − | 0.909017i | \(-0.363166\pi\) | ||||
0.416758 | + | 0.909017i | \(0.363166\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.8564 | 0.659829 | ||||||||
\(442\) | −25.8564 | −1.22986 | ||||||||
\(443\) | 18.0000 | 0.855206 | 0.427603 | − | 0.903967i | \(-0.359358\pi\) | ||||
0.427603 | + | 0.903967i | \(0.359358\pi\) | |||||||
\(444\) | 6.46410 | 0.306773 | ||||||||
\(445\) | −8.92820 | −0.423237 | ||||||||
\(446\) | −13.1244 | −0.621456 | ||||||||
\(447\) | −11.3205 | −0.535442 | ||||||||
\(448\) | 0.267949 | 0.0126594 | ||||||||
\(449\) | 27.8564 | 1.31463 | 0.657313 | − | 0.753618i | \(-0.271693\pi\) | ||||
0.657313 | + | 0.753618i | \(0.271693\pi\) | |||||||
\(450\) | −8.92820 | −0.420880 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.73205 | −0.222577 | ||||||||
\(453\) | 20.7321 | 0.974077 | ||||||||
\(454\) | −8.39230 | −0.393870 | ||||||||
\(455\) | 0.679492 | 0.0318551 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −25.4449 | −1.19026 | −0.595130 | − | 0.803629i | \(-0.702900\pi\) | ||||
−0.595130 | + | 0.803629i | \(0.702900\pi\) | |||||||
\(458\) | 12.3923 | 0.579054 | ||||||||
\(459\) | −37.3205 | −1.74197 | ||||||||
\(460\) | 0.732051 | 0.0341320 | ||||||||
\(461\) | −28.1962 | −1.31323 | −0.656613 | − | 0.754228i | \(-0.728011\pi\) | ||||
−0.656613 | + | 0.754228i | \(0.728011\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | 1.73205 | 0.0804084 | ||||||||
\(465\) | −1.07180 | −0.0497034 | ||||||||
\(466\) | 8.26795 | 0.383005 | ||||||||
\(467\) | 33.7128 | 1.56004 | 0.780021 | − | 0.625753i | \(-0.215208\pi\) | ||||
0.780021 | + | 0.625753i | \(0.215208\pi\) | |||||||
\(468\) | 6.92820 | 0.320256 | ||||||||
\(469\) | 3.75129 | 0.173218 | ||||||||
\(470\) | 9.12436 | 0.420875 | ||||||||
\(471\) | 5.26795 | 0.242734 | ||||||||
\(472\) | 9.39230 | 0.432316 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.19615 | −0.100873 | ||||||||
\(475\) | −4.46410 | −0.204827 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 19.8564 | 0.909162 | ||||||||
\(478\) | 14.1244 | 0.646033 | ||||||||
\(479\) | −31.7321 | −1.44987 | −0.724937 | − | 0.688815i | \(-0.758131\pi\) | ||||
−0.724937 | + | 0.688815i | \(0.758131\pi\) | |||||||
\(480\) | −0.732051 | −0.0334134 | ||||||||
\(481\) | 22.3923 | 1.02100 | ||||||||
\(482\) | −11.2679 | −0.513241 | ||||||||
\(483\) | 0.267949 | 0.0121921 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.85641 | −0.447556 | ||||||||
\(486\) | 16.0000 | 0.725775 | ||||||||
\(487\) | 27.1769 | 1.23150 | 0.615752 | − | 0.787940i | \(-0.288852\pi\) | ||||
0.615752 | + | 0.787940i | \(0.288852\pi\) | |||||||
\(488\) | −1.26795 | −0.0573974 | ||||||||
\(489\) | −17.3205 | −0.783260 | ||||||||
\(490\) | −5.07180 | −0.229120 | ||||||||
\(491\) | 3.60770 | 0.162813 | 0.0814065 | − | 0.996681i | \(-0.474059\pi\) | ||||
0.0814065 | + | 0.996681i | \(0.474059\pi\) | |||||||
\(492\) | 10.7321 | 0.483838 | ||||||||
\(493\) | −12.9282 | −0.582257 | ||||||||
\(494\) | 3.46410 | 0.155857 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.46410 | −0.0657401 | ||||||||
\(497\) | 3.80385 | 0.170626 | ||||||||
\(498\) | −3.80385 | −0.170454 | ||||||||
\(499\) | 21.2679 | 0.952084 | 0.476042 | − | 0.879423i | \(-0.342071\pi\) | ||||
0.476042 | + | 0.879423i | \(0.342071\pi\) | |||||||
\(500\) | 6.92820 | 0.309839 | ||||||||
\(501\) | 3.46410 | 0.154765 | ||||||||
\(502\) | −8.53590 | −0.380976 | ||||||||
\(503\) | −0.660254 | −0.0294393 | −0.0147196 | − | 0.999892i | \(-0.504686\pi\) | ||||
−0.0147196 | + | 0.999892i | \(0.504686\pi\) | |||||||
\(504\) | 0.535898 | 0.0238708 | ||||||||
\(505\) | 12.1436 | 0.540383 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 4.00000 | 0.177471 | ||||||||
\(509\) | 33.9282 | 1.50384 | 0.751921 | − | 0.659254i | \(-0.229128\pi\) | ||||
0.751921 | + | 0.659254i | \(0.229128\pi\) | |||||||
\(510\) | 5.46410 | 0.241954 | ||||||||
\(511\) | 0.535898 | 0.0237067 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.00000 | 0.220755 | ||||||||
\(514\) | 3.32051 | 0.146461 | ||||||||
\(515\) | 2.00000 | 0.0881305 | ||||||||
\(516\) | −4.92820 | −0.216952 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.73205 | 0.0761019 | ||||||||
\(519\) | 4.12436 | 0.181039 | ||||||||
\(520\) | −2.53590 | −0.111207 | ||||||||
\(521\) | −17.3205 | −0.758825 | −0.379413 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379413 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(522\) | 3.46410 | 0.151620 | ||||||||
\(523\) | 9.33975 | 0.408399 | 0.204199 | − | 0.978929i | \(-0.434541\pi\) | ||||
0.204199 | + | 0.978929i | \(0.434541\pi\) | |||||||
\(524\) | −20.9282 | −0.914253 | ||||||||
\(525\) | 1.19615 | 0.0522044 | ||||||||
\(526\) | −24.7846 | −1.08066 | ||||||||
\(527\) | 10.9282 | 0.476040 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | −7.26795 | −0.315700 | ||||||||
\(531\) | 18.7846 | 0.815183 | ||||||||
\(532\) | 0.267949 | 0.0116171 | ||||||||
\(533\) | 37.1769 | 1.61031 | ||||||||
\(534\) | 12.1962 | 0.527779 | ||||||||
\(535\) | 2.05256 | 0.0887399 | ||||||||
\(536\) | −14.0000 | −0.604708 | ||||||||
\(537\) | 2.07180 | 0.0894046 | ||||||||
\(538\) | 29.7846 | 1.28411 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.66025 | −0.157512 | ||||||||
\(541\) | 27.1769 | 1.16843 | 0.584213 | − | 0.811600i | \(-0.301403\pi\) | ||||
0.584213 | + | 0.811600i | \(0.301403\pi\) | |||||||
\(542\) | 7.32051 | 0.314443 | ||||||||
\(543\) | −24.3923 | −1.04677 | ||||||||
\(544\) | 7.46410 | 0.320021 | ||||||||
\(545\) | 4.48334 | 0.192045 | ||||||||
\(546\) | −0.928203 | −0.0397234 | ||||||||
\(547\) | −4.80385 | −0.205398 | −0.102699 | − | 0.994712i | \(-0.532748\pi\) | ||||
−0.102699 | + | 0.994712i | \(0.532748\pi\) | |||||||
\(548\) | 9.46410 | 0.404286 | ||||||||
\(549\) | −2.53590 | −0.108230 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.73205 | 0.0737878 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −0.588457 | −0.0250237 | ||||||||
\(554\) | −15.1244 | −0.642572 | ||||||||
\(555\) | −4.73205 | −0.200864 | ||||||||
\(556\) | −6.53590 | −0.277184 | ||||||||
\(557\) | 23.1769 | 0.982037 | 0.491019 | − | 0.871149i | \(-0.336625\pi\) | ||||
0.491019 | + | 0.871149i | \(0.336625\pi\) | |||||||
\(558\) | −2.92820 | −0.123961 | ||||||||
\(559\) | −17.0718 | −0.722060 | ||||||||
\(560\) | −0.196152 | −0.00828895 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.0526 | −0.677136 | ||||||||
\(563\) | −24.6603 | −1.03931 | −0.519653 | − | 0.854377i | \(-0.673939\pi\) | ||||
−0.519653 | + | 0.854377i | \(0.673939\pi\) | |||||||
\(564\) | −12.4641 | −0.524833 | ||||||||
\(565\) | 3.46410 | 0.145736 | ||||||||
\(566\) | −21.4641 | −0.902203 | ||||||||
\(567\) | 0.267949 | 0.0112528 | ||||||||
\(568\) | −14.1962 | −0.595657 | ||||||||
\(569\) | 39.7128 | 1.66485 | 0.832424 | − | 0.554139i | \(-0.186953\pi\) | ||||
0.832424 | + | 0.554139i | \(0.186953\pi\) | |||||||
\(570\) | −0.732051 | −0.0306622 | ||||||||
\(571\) | 22.9808 | 0.961715 | 0.480857 | − | 0.876799i | \(-0.340325\pi\) | ||||
0.480857 | + | 0.876799i | \(0.340325\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.3923 | 0.726574 | ||||||||
\(574\) | 2.87564 | 0.120027 | ||||||||
\(575\) | 4.46410 | 0.186166 | ||||||||
\(576\) | −2.00000 | −0.0833333 | ||||||||
\(577\) | −33.1769 | −1.38117 | −0.690587 | − | 0.723250i | \(-0.742648\pi\) | ||||
−0.690587 | + | 0.723250i | \(0.742648\pi\) | |||||||
\(578\) | −38.7128 | −1.61024 | ||||||||
\(579\) | −12.5359 | −0.520974 | ||||||||
\(580\) | −1.26795 | −0.0526487 | ||||||||
\(581\) | −1.01924 | −0.0422851 | ||||||||
\(582\) | 13.4641 | 0.558105 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | −5.07180 | −0.209693 | ||||||||
\(586\) | −12.1244 | −0.500853 | ||||||||
\(587\) | −31.3731 | −1.29491 | −0.647453 | − | 0.762106i | \(-0.724166\pi\) | ||||
−0.647453 | + | 0.762106i | \(0.724166\pi\) | |||||||
\(588\) | 6.92820 | 0.285714 | ||||||||
\(589\) | −1.46410 | −0.0603273 | ||||||||
\(590\) | −6.87564 | −0.283066 | ||||||||
\(591\) | −5.07180 | −0.208626 | ||||||||
\(592\) | −6.46410 | −0.265673 | ||||||||
\(593\) | −1.87564 | −0.0770235 | −0.0385117 | − | 0.999258i | \(-0.512262\pi\) | ||||
−0.0385117 | + | 0.999258i | \(0.512262\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.46410 | 0.0600223 | ||||||||
\(596\) | 11.3205 | 0.463706 | ||||||||
\(597\) | −16.9282 | −0.692825 | ||||||||
\(598\) | −3.46410 | −0.141658 | ||||||||
\(599\) | −19.6077 | −0.801149 | −0.400574 | − | 0.916264i | \(-0.631189\pi\) | ||||
−0.400574 | + | 0.916264i | \(0.631189\pi\) | |||||||
\(600\) | −4.46410 | −0.182246 | ||||||||
\(601\) | −18.7846 | −0.766240 | −0.383120 | − | 0.923699i | \(-0.625150\pi\) | ||||
−0.383120 | + | 0.923699i | \(0.625150\pi\) | |||||||
\(602\) | −1.32051 | −0.0538199 | ||||||||
\(603\) | −28.0000 | −1.14025 | ||||||||
\(604\) | −20.7321 | −0.843575 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.5885 | −0.673860 | ||||||||
\(607\) | 3.26795 | 0.132642 | 0.0663210 | − | 0.997798i | \(-0.478874\pi\) | ||||
0.0663210 | + | 0.997798i | \(0.478874\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −0.464102 | −0.0188063 | ||||||||
\(610\) | 0.928203 | 0.0375819 | ||||||||
\(611\) | −43.1769 | −1.74675 | ||||||||
\(612\) | 14.9282 | 0.603437 | ||||||||
\(613\) | 22.1962 | 0.896494 | 0.448247 | − | 0.893910i | \(-0.352048\pi\) | ||||
0.448247 | + | 0.893910i | \(0.352048\pi\) | |||||||
\(614\) | −15.5885 | −0.629099 | ||||||||
\(615\) | −7.85641 | −0.316801 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.92820 | −0.0776265 | −0.0388133 | − | 0.999246i | \(-0.512358\pi\) | ||||
−0.0388133 | + | 0.999246i | \(0.512358\pi\) | |||||||
\(618\) | −2.73205 | −0.109899 | ||||||||
\(619\) | 34.3923 | 1.38234 | 0.691172 | − | 0.722691i | \(-0.257095\pi\) | ||||
0.691172 | + | 0.722691i | \(0.257095\pi\) | |||||||
\(620\) | 1.07180 | 0.0430444 | ||||||||
\(621\) | −5.00000 | −0.200643 | ||||||||
\(622\) | 1.60770 | 0.0644627 | ||||||||
\(623\) | 3.26795 | 0.130928 | ||||||||
\(624\) | 3.46410 | 0.138675 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | −13.5359 | −0.541003 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.26795 | −0.210214 | ||||||||
\(629\) | 48.2487 | 1.92380 | ||||||||
\(630\) | −0.392305 | −0.0156298 | ||||||||
\(631\) | −21.2487 | −0.845898 | −0.422949 | − | 0.906154i | \(-0.639005\pi\) | ||||
−0.422949 | + | 0.906154i | \(0.639005\pi\) | |||||||
\(632\) | 2.19615 | 0.0873583 | ||||||||
\(633\) | 4.12436 | 0.163928 | ||||||||
\(634\) | 20.7846 | 0.825462 | ||||||||
\(635\) | −2.92820 | −0.116202 | ||||||||
\(636\) | 9.92820 | 0.393679 | ||||||||
\(637\) | 24.0000 | 0.950915 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −28.3923 | −1.12318 | ||||||||
\(640\) | 0.732051 | 0.0289368 | ||||||||
\(641\) | −33.8038 | −1.33517 | −0.667586 | − | 0.744533i | \(-0.732672\pi\) | ||||
−0.667586 | + | 0.744533i | \(0.732672\pi\) | |||||||
\(642\) | −2.80385 | −0.110659 | ||||||||
\(643\) | −17.7128 | −0.698525 | −0.349263 | − | 0.937025i | \(-0.613568\pi\) | ||||
−0.349263 | + | 0.937025i | \(0.613568\pi\) | |||||||
\(644\) | −0.267949 | −0.0105587 | ||||||||
\(645\) | 3.60770 | 0.142053 | ||||||||
\(646\) | 7.46410 | 0.293671 | ||||||||
\(647\) | −3.14359 | −0.123587 | −0.0617937 | − | 0.998089i | \(-0.519682\pi\) | ||||
−0.0617937 | + | 0.998089i | \(0.519682\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −15.4641 | −0.606552 | ||||||||
\(651\) | 0.392305 | 0.0153756 | ||||||||
\(652\) | 17.3205 | 0.678323 | ||||||||
\(653\) | −2.67949 | −0.104857 | −0.0524283 | − | 0.998625i | \(-0.516696\pi\) | ||||
−0.0524283 | + | 0.998625i | \(0.516696\pi\) | |||||||
\(654\) | −6.12436 | −0.239481 | ||||||||
\(655\) | 15.3205 | 0.598622 | ||||||||
\(656\) | −10.7321 | −0.419016 | ||||||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | −3.33975 | −0.130197 | ||||||||
\(659\) | 17.3205 | 0.674711 | 0.337356 | − | 0.941377i | \(-0.390468\pi\) | ||||
0.337356 | + | 0.941377i | \(0.390468\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2487 | 0.748688 | 0.374344 | − | 0.927290i | \(-0.377868\pi\) | ||||
0.374344 | + | 0.927290i | \(0.377868\pi\) | |||||||
\(662\) | −21.7846 | −0.846683 | ||||||||
\(663\) | −25.8564 | −1.00418 | ||||||||
\(664\) | 3.80385 | 0.147618 | ||||||||
\(665\) | −0.196152 | −0.00760646 | ||||||||
\(666\) | −12.9282 | −0.500958 | ||||||||
\(667\) | −1.73205 | −0.0670653 | ||||||||
\(668\) | −3.46410 | −0.134030 | ||||||||
\(669\) | −13.1244 | −0.507417 | ||||||||
\(670\) | 10.2487 | 0.395942 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.267949 | 0.0103364 | ||||||||
\(673\) | −14.5885 | −0.562344 | −0.281172 | − | 0.959657i | \(-0.590723\pi\) | ||||
−0.281172 | + | 0.959657i | \(0.590723\pi\) | |||||||
\(674\) | 24.1962 | 0.932001 | ||||||||
\(675\) | −22.3205 | −0.859117 | ||||||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | 36.6603 | 1.40897 | 0.704484 | − | 0.709720i | \(-0.251178\pi\) | ||||
0.704484 | + | 0.709720i | \(0.251178\pi\) | |||||||
\(678\) | −4.73205 | −0.181733 | ||||||||
\(679\) | 3.60770 | 0.138451 | ||||||||
\(680\) | −5.46410 | −0.209539 | ||||||||
\(681\) | −8.39230 | −0.321594 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.7846 | −0.871829 | −0.435914 | − | 0.899988i | \(-0.643575\pi\) | ||||
−0.435914 | + | 0.899988i | \(0.643575\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | −6.92820 | −0.264713 | ||||||||
\(686\) | 3.73205 | 0.142490 | ||||||||
\(687\) | 12.3923 | 0.472796 | ||||||||
\(688\) | 4.92820 | 0.187886 | ||||||||
\(689\) | 34.3923 | 1.31024 | ||||||||
\(690\) | 0.732051 | 0.0278687 | ||||||||
\(691\) | 28.0526 | 1.06717 | 0.533585 | − | 0.845747i | \(-0.320845\pi\) | ||||
0.533585 | + | 0.845747i | \(0.320845\pi\) | |||||||
\(692\) | −4.12436 | −0.156784 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.0526 | −0.381590 | ||||||||
\(695\) | 4.78461 | 0.181491 | ||||||||
\(696\) | 1.73205 | 0.0656532 | ||||||||
\(697\) | 80.1051 | 3.03420 | ||||||||
\(698\) | 14.7846 | 0.559606 | ||||||||
\(699\) | 8.26795 | 0.312723 | ||||||||
\(700\) | −1.19615 | −0.0452103 | ||||||||
\(701\) | −9.46410 | −0.357454 | −0.178727 | − | 0.983899i | \(-0.557198\pi\) | ||||
−0.178727 | + | 0.983899i | \(0.557198\pi\) | |||||||
\(702\) | 17.3205 | 0.653720 | ||||||||
\(703\) | −6.46410 | −0.243798 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.12436 | 0.343643 | ||||||||
\(706\) | 6.46410 | 0.243280 | ||||||||
\(707\) | −4.44486 | −0.167166 | ||||||||
\(708\) | 9.39230 | 0.352984 | ||||||||
\(709\) | 9.85641 | 0.370165 | 0.185083 | − | 0.982723i | \(-0.440745\pi\) | ||||
0.185083 | + | 0.982723i | \(0.440745\pi\) | |||||||
\(710\) | 10.3923 | 0.390016 | ||||||||
\(711\) | 4.39230 | 0.164724 | ||||||||
\(712\) | −12.1962 | −0.457070 | ||||||||
\(713\) | 1.46410 | 0.0548310 | ||||||||
\(714\) | −2.00000 | −0.0748481 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.07180 | −0.0774267 | ||||||||
\(717\) | 14.1244 | 0.527484 | ||||||||
\(718\) | −28.3923 | −1.05959 | ||||||||
\(719\) | −16.0000 | −0.596699 | −0.298350 | − | 0.954457i | \(-0.596436\pi\) | ||||
−0.298350 | + | 0.954457i | \(0.596436\pi\) | |||||||
\(720\) | 1.46410 | 0.0545638 | ||||||||
\(721\) | −0.732051 | −0.0272630 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | −11.2679 | −0.419060 | ||||||||
\(724\) | 24.3923 | 0.906533 | ||||||||
\(725\) | −7.73205 | −0.287161 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.3205 | −1.05035 | −0.525175 | − | 0.850994i | \(-0.676000\pi\) | ||||
−0.525175 | + | 0.850994i | \(0.676000\pi\) | |||||||
\(728\) | 0.928203 | 0.0344015 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 1.46410 | 0.0541888 | ||||||||
\(731\) | −36.7846 | −1.36053 | ||||||||
\(732\) | −1.26795 | −0.0468648 | ||||||||
\(733\) | 5.07180 | 0.187331 | 0.0936655 | − | 0.995604i | \(-0.470142\pi\) | ||||
0.0936655 | + | 0.995604i | \(0.470142\pi\) | |||||||
\(734\) | 22.8564 | 0.843645 | ||||||||
\(735\) | −5.07180 | −0.187076 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −21.4641 | −0.790104 | ||||||||
\(739\) | −31.6603 | −1.16464 | −0.582321 | − | 0.812959i | \(-0.697855\pi\) | ||||
−0.582321 | + | 0.812959i | \(0.697855\pi\) | |||||||
\(740\) | 4.73205 | 0.173954 | ||||||||
\(741\) | 3.46410 | 0.127257 | ||||||||
\(742\) | 2.66025 | 0.0976610 | ||||||||
\(743\) | −12.5359 | −0.459898 | −0.229949 | − | 0.973203i | \(-0.573856\pi\) | ||||
−0.229949 | + | 0.973203i | \(0.573856\pi\) | |||||||
\(744\) | −1.46410 | −0.0536766 | ||||||||
\(745\) | −8.28719 | −0.303619 | ||||||||
\(746\) | 16.8038 | 0.615233 | ||||||||
\(747\) | 7.60770 | 0.278351 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.751289 | −0.0274515 | ||||||||
\(750\) | 6.92820 | 0.252982 | ||||||||
\(751\) | −12.0000 | −0.437886 | −0.218943 | − | 0.975738i | \(-0.570261\pi\) | ||||
−0.218943 | + | 0.975738i | \(0.570261\pi\) | |||||||
\(752\) | 12.4641 | 0.454519 | ||||||||
\(753\) | −8.53590 | −0.311065 | ||||||||
\(754\) | 6.00000 | 0.218507 | ||||||||
\(755\) | 15.1769 | 0.552344 | ||||||||
\(756\) | 1.33975 | 0.0487261 | ||||||||
\(757\) | −21.3731 | −0.776817 | −0.388409 | − | 0.921487i | \(-0.626975\pi\) | ||||
−0.388409 | + | 0.921487i | \(0.626975\pi\) | |||||||
\(758\) | −23.9282 | −0.869111 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.732051 | 0.0265543 | ||||||||
\(761\) | −48.7654 | −1.76774 | −0.883872 | − | 0.467729i | \(-0.845072\pi\) | ||||
−0.883872 | + | 0.467729i | \(0.845072\pi\) | |||||||
\(762\) | 4.00000 | 0.144905 | ||||||||
\(763\) | −1.64102 | −0.0594088 | ||||||||
\(764\) | −17.3923 | −0.629232 | ||||||||
\(765\) | −10.9282 | −0.395110 | ||||||||
\(766\) | −33.4641 | −1.20911 | ||||||||
\(767\) | 32.5359 | 1.17480 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 27.5885 | 0.994865 | 0.497433 | − | 0.867503i | \(-0.334276\pi\) | ||||
0.497433 | + | 0.867503i | \(0.334276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.32051 | 0.119585 | ||||||||
\(772\) | 12.5359 | 0.451177 | ||||||||
\(773\) | 6.60770 | 0.237662 | 0.118831 | − | 0.992914i | \(-0.462085\pi\) | ||||
0.118831 | + | 0.992914i | \(0.462085\pi\) | |||||||
\(774\) | 9.85641 | 0.354281 | ||||||||
\(775\) | 6.53590 | 0.234776 | ||||||||
\(776\) | −13.4641 | −0.483333 | ||||||||
\(777\) | 1.73205 | 0.0621370 | ||||||||
\(778\) | 0.588457 | 0.0210972 | ||||||||
\(779\) | −10.7321 | −0.384516 | ||||||||
\(780\) | −2.53590 | −0.0907997 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −7.46410 | −0.266916 | ||||||||
\(783\) | 8.66025 | 0.309492 | ||||||||
\(784\) | −6.92820 | −0.247436 | ||||||||
\(785\) | 3.85641 | 0.137641 | ||||||||
\(786\) | −20.9282 | −0.746484 | ||||||||
\(787\) | −13.0526 | −0.465273 | −0.232637 | − | 0.972564i | \(-0.574735\pi\) | ||||
−0.232637 | + | 0.972564i | \(0.574735\pi\) | |||||||
\(788\) | 5.07180 | 0.180675 | ||||||||
\(789\) | −24.7846 | −0.882355 | ||||||||
\(790\) | −1.60770 | −0.0571992 | ||||||||
\(791\) | −1.26795 | −0.0450831 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.39230 | −0.155975 | ||||||||
\(794\) | −5.60770 | −0.199010 | ||||||||
\(795\) | −7.26795 | −0.257768 | ||||||||
\(796\) | 16.9282 | 0.600004 | ||||||||
\(797\) | 11.6077 | 0.411166 | 0.205583 | − | 0.978640i | \(-0.434091\pi\) | ||||
0.205583 | + | 0.978640i | \(0.434091\pi\) | |||||||
\(798\) | 0.267949 | 0.00948530 | ||||||||
\(799\) | −93.0333 | −3.29128 | ||||||||
\(800\) | 4.46410 | 0.157830 | ||||||||
\(801\) | −24.3923 | −0.861860 | ||||||||
\(802\) | 16.0526 | 0.566836 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −14.0000 | −0.493742 | ||||||||
\(805\) | 0.196152 | 0.00691346 | ||||||||
\(806\) | −5.07180 | −0.178646 | ||||||||
\(807\) | 29.7846 | 1.04847 | ||||||||
\(808\) | 16.5885 | 0.583580 | ||||||||
\(809\) | −19.1962 | −0.674901 | −0.337450 | − | 0.941343i | \(-0.609565\pi\) | ||||
−0.337450 | + | 0.941343i | \(0.609565\pi\) | |||||||
\(810\) | 0.732051 | 0.0257216 | ||||||||
\(811\) | 46.7654 | 1.64215 | 0.821077 | − | 0.570817i | \(-0.193374\pi\) | ||||
0.821077 | + | 0.570817i | \(0.193374\pi\) | |||||||
\(812\) | 0.464102 | 0.0162868 | ||||||||
\(813\) | 7.32051 | 0.256741 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.6795 | −0.444143 | ||||||||
\(816\) | 7.46410 | 0.261296 | ||||||||
\(817\) | 4.92820 | 0.172416 | ||||||||
\(818\) | −13.4641 | −0.470761 | ||||||||
\(819\) | 1.85641 | 0.0648681 | ||||||||
\(820\) | 7.85641 | 0.274358 | ||||||||
\(821\) | −42.0526 | −1.46764 | −0.733822 | − | 0.679342i | \(-0.762265\pi\) | ||||
−0.733822 | + | 0.679342i | \(0.762265\pi\) | |||||||
\(822\) | 9.46410 | 0.330098 | ||||||||
\(823\) | −21.5359 | −0.750694 | −0.375347 | − | 0.926884i | \(-0.622476\pi\) | ||||
−0.375347 | + | 0.926884i | \(0.622476\pi\) | |||||||
\(824\) | 2.73205 | 0.0951755 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.51666 | 0.0875658 | ||||||||
\(827\) | 21.3205 | 0.741387 | 0.370693 | − | 0.928755i | \(-0.379120\pi\) | ||||
0.370693 | + | 0.928755i | \(0.379120\pi\) | |||||||
\(828\) | 2.00000 | 0.0695048 | ||||||||
\(829\) | 18.6410 | 0.647429 | 0.323715 | − | 0.946155i | \(-0.395068\pi\) | ||||
0.323715 | + | 0.946155i | \(0.395068\pi\) | |||||||
\(830\) | −2.78461 | −0.0966552 | ||||||||
\(831\) | −15.1244 | −0.524658 | ||||||||
\(832\) | −3.46410 | −0.120096 | ||||||||
\(833\) | 51.7128 | 1.79174 | ||||||||
\(834\) | −6.53590 | −0.226320 | ||||||||
\(835\) | 2.53590 | 0.0877584 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.32051 | −0.253034 | ||||||||
\(838\) | 32.4449 | 1.12079 | ||||||||
\(839\) | 14.9808 | 0.517193 | 0.258597 | − | 0.965985i | \(-0.416740\pi\) | ||||
0.258597 | + | 0.965985i | \(0.416740\pi\) | |||||||
\(840\) | −0.196152 | −0.00676790 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | 1.67949 | 0.0578791 | ||||||||
\(843\) | −16.0526 | −0.552879 | ||||||||
\(844\) | −4.12436 | −0.141966 | ||||||||
\(845\) | 0.732051 | 0.0251833 | ||||||||
\(846\) | 24.9282 | 0.857049 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.92820 | −0.340936 | ||||||||
\(849\) | −21.4641 | −0.736646 | ||||||||
\(850\) | −33.3205 | −1.14288 | ||||||||
\(851\) | 6.46410 | 0.221587 | ||||||||
\(852\) | −14.1962 | −0.486352 | ||||||||
\(853\) | −54.1051 | −1.85252 | −0.926262 | − | 0.376880i | \(-0.876997\pi\) | ||||
−0.926262 | + | 0.376880i | \(0.876997\pi\) | |||||||
\(854\) | −0.339746 | −0.0116259 | ||||||||
\(855\) | 1.46410 | 0.0500712 | ||||||||
\(856\) | 2.80385 | 0.0958335 | ||||||||
\(857\) | −16.5359 | −0.564856 | −0.282428 | − | 0.959289i | \(-0.591140\pi\) | ||||
−0.282428 | + | 0.959289i | \(0.591140\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.9474 | −0.680598 | −0.340299 | − | 0.940317i | \(-0.610528\pi\) | ||||
−0.340299 | + | 0.940317i | \(0.610528\pi\) | |||||||
\(860\) | −3.60770 | −0.123021 | ||||||||
\(861\) | 2.87564 | 0.0980017 | ||||||||
\(862\) | −23.6603 | −0.805871 | ||||||||
\(863\) | −42.9282 | −1.46129 | −0.730647 | − | 0.682756i | \(-0.760781\pi\) | ||||
−0.730647 | + | 0.682756i | \(0.760781\pi\) | |||||||
\(864\) | −5.00000 | −0.170103 | ||||||||
\(865\) | 3.01924 | 0.102657 | ||||||||
\(866\) | −18.7846 | −0.638327 | ||||||||
\(867\) | −38.7128 | −1.31476 | ||||||||
\(868\) | −0.392305 | −0.0133157 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.26795 | −0.0429875 | ||||||||
\(871\) | −48.4974 | −1.64327 | ||||||||
\(872\) | 6.12436 | 0.207397 | ||||||||
\(873\) | −26.9282 | −0.911382 | ||||||||
\(874\) | 1.00000 | 0.0338255 | ||||||||
\(875\) | 1.85641 | 0.0627580 | ||||||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 37.8564 | 1.27832 | 0.639160 | − | 0.769074i | \(-0.279282\pi\) | ||||
0.639160 | + | 0.769074i | \(0.279282\pi\) | |||||||
\(878\) | −17.4641 | −0.589385 | ||||||||
\(879\) | −12.1244 | −0.408944 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.5359 | −0.456036 | −0.228018 | − | 0.973657i | \(-0.573225\pi\) | ||||
−0.228018 | + | 0.973657i | \(0.573225\pi\) | |||||||
\(882\) | −13.8564 | −0.466569 | ||||||||
\(883\) | −24.5885 | −0.827467 | −0.413734 | − | 0.910398i | \(-0.635776\pi\) | ||||
−0.413734 | + | 0.910398i | \(0.635776\pi\) | |||||||
\(884\) | 25.8564 | 0.869645 | ||||||||
\(885\) | −6.87564 | −0.231122 | ||||||||
\(886\) | −18.0000 | −0.604722 | ||||||||
\(887\) | 29.6603 | 0.995894 | 0.497947 | − | 0.867208i | \(-0.334087\pi\) | ||||
0.497947 | + | 0.867208i | \(0.334087\pi\) | |||||||
\(888\) | −6.46410 | −0.216921 | ||||||||
\(889\) | 1.07180 | 0.0359469 | ||||||||
\(890\) | 8.92820 | 0.299274 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.1244 | 0.439436 | ||||||||
\(893\) | 12.4641 | 0.417095 | ||||||||
\(894\) | 11.3205 | 0.378614 | ||||||||
\(895\) | 1.51666 | 0.0506964 | ||||||||
\(896\) | −0.267949 | −0.00895155 | ||||||||
\(897\) | −3.46410 | −0.115663 | ||||||||
\(898\) | −27.8564 | −0.929580 | ||||||||
\(899\) | −2.53590 | −0.0845769 | ||||||||
\(900\) | 8.92820 | 0.297607 | ||||||||
\(901\) | 74.1051 | 2.46880 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.32051 | −0.0439438 | ||||||||
\(904\) | 4.73205 | 0.157386 | ||||||||
\(905\) | −17.8564 | −0.593567 | ||||||||
\(906\) | −20.7321 | −0.688776 | ||||||||
\(907\) | 29.2487 | 0.971188 | 0.485594 | − | 0.874185i | \(-0.338603\pi\) | ||||
0.485594 | + | 0.874185i | \(0.338603\pi\) | |||||||
\(908\) | 8.39230 | 0.278508 | ||||||||
\(909\) | 33.1769 | 1.10041 | ||||||||
\(910\) | −0.679492 | −0.0225249 | ||||||||
\(911\) | 4.58846 | 0.152022 | 0.0760112 | − | 0.997107i | \(-0.475782\pi\) | ||||
0.0760112 | + | 0.997107i | \(0.475782\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 25.4449 | 0.841641 | ||||||||
\(915\) | 0.928203 | 0.0306855 | ||||||||
\(916\) | −12.3923 | −0.409453 | ||||||||
\(917\) | −5.60770 | −0.185182 | ||||||||
\(918\) | 37.3205 | 1.23176 | ||||||||
\(919\) | −54.1051 | −1.78476 | −0.892382 | − | 0.451282i | \(-0.850967\pi\) | ||||
−0.892382 | + | 0.451282i | \(0.850967\pi\) | |||||||
\(920\) | −0.732051 | −0.0241350 | ||||||||
\(921\) | −15.5885 | −0.513657 | ||||||||
\(922\) | 28.1962 | 0.928591 | ||||||||
\(923\) | −49.1769 | −1.61868 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8564 | 0.948793 | ||||||||
\(926\) | −26.0000 | −0.854413 | ||||||||
\(927\) | 5.46410 | 0.179465 | ||||||||
\(928\) | −1.73205 | −0.0568574 | ||||||||
\(929\) | −58.0333 | −1.90401 | −0.952006 | − | 0.306080i | \(-0.900982\pi\) | ||||
−0.952006 | + | 0.306080i | \(0.900982\pi\) | |||||||
\(930\) | 1.07180 | 0.0351456 | ||||||||
\(931\) | −6.92820 | −0.227063 | ||||||||
\(932\) | −8.26795 | −0.270826 | ||||||||
\(933\) | 1.60770 | 0.0526336 | ||||||||
\(934\) | −33.7128 | −1.10312 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.92820 | −0.226455 | ||||||||
\(937\) | 29.8756 | 0.975995 | 0.487997 | − | 0.872845i | \(-0.337728\pi\) | ||||
0.487997 | + | 0.872845i | \(0.337728\pi\) | |||||||
\(938\) | −3.75129 | −0.122484 | ||||||||
\(939\) | −13.5359 | −0.441727 | ||||||||
\(940\) | −9.12436 | −0.297604 | ||||||||
\(941\) | 24.2487 | 0.790485 | 0.395243 | − | 0.918577i | \(-0.370660\pi\) | ||||
0.395243 | + | 0.918577i | \(0.370660\pi\) | |||||||
\(942\) | −5.26795 | −0.171639 | ||||||||
\(943\) | 10.7321 | 0.349484 | ||||||||
\(944\) | −9.39230 | −0.305693 | ||||||||
\(945\) | −0.980762 | −0.0319042 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7128 | 0.770563 | 0.385281 | − | 0.922799i | \(-0.374104\pi\) | ||||
0.385281 | + | 0.922799i | \(0.374104\pi\) | |||||||
\(948\) | 2.19615 | 0.0713277 | ||||||||
\(949\) | −6.92820 | −0.224899 | ||||||||
\(950\) | 4.46410 | 0.144835 | ||||||||
\(951\) | 20.7846 | 0.673987 | ||||||||
\(952\) | 2.00000 | 0.0648204 | ||||||||
\(953\) | −14.9808 | −0.485274 | −0.242637 | − | 0.970117i | \(-0.578012\pi\) | ||||
−0.242637 | + | 0.970117i | \(0.578012\pi\) | |||||||
\(954\) | −19.8564 | −0.642875 | ||||||||
\(955\) | 12.7321 | 0.411999 | ||||||||
\(956\) | −14.1244 | −0.456814 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.7321 | 1.02522 | ||||||||
\(959\) | 2.53590 | 0.0818884 | ||||||||
\(960\) | 0.732051 | 0.0236268 | ||||||||
\(961\) | −28.8564 | −0.930852 | ||||||||
\(962\) | −22.3923 | −0.721957 | ||||||||
\(963\) | 5.60770 | 0.180705 | ||||||||
\(964\) | 11.2679 | 0.362916 | ||||||||
\(965\) | −9.17691 | −0.295415 | ||||||||
\(966\) | −0.267949 | −0.00862112 | ||||||||
\(967\) | 8.51666 | 0.273877 | 0.136939 | − | 0.990580i | \(-0.456274\pi\) | ||||
0.136939 | + | 0.990580i | \(0.456274\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.46410 | 0.239781 | ||||||||
\(970\) | 9.85641 | 0.316470 | ||||||||
\(971\) | 20.4641 | 0.656724 | 0.328362 | − | 0.944552i | \(-0.393503\pi\) | ||||
0.328362 | + | 0.944552i | \(0.393503\pi\) | |||||||
\(972\) | −16.0000 | −0.513200 | ||||||||
\(973\) | −1.75129 | −0.0561437 | ||||||||
\(974\) | −27.1769 | −0.870805 | ||||||||
\(975\) | −15.4641 | −0.495248 | ||||||||
\(976\) | 1.26795 | 0.0405861 | ||||||||
\(977\) | −20.5359 | −0.657002 | −0.328501 | − | 0.944504i | \(-0.606543\pi\) | ||||
−0.328501 | + | 0.944504i | \(0.606543\pi\) | |||||||
\(978\) | 17.3205 | 0.553849 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.07180 | 0.162013 | ||||||||
\(981\) | 12.2487 | 0.391071 | ||||||||
\(982\) | −3.60770 | −0.115126 | ||||||||
\(983\) | 10.9808 | 0.350232 | 0.175116 | − | 0.984548i | \(-0.443970\pi\) | ||||
0.175116 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(984\) | −10.7321 | −0.342125 | ||||||||
\(985\) | −3.71281 | −0.118300 | ||||||||
\(986\) | 12.9282 | 0.411718 | ||||||||
\(987\) | −3.33975 | −0.106305 | ||||||||
\(988\) | −3.46410 | −0.110208 | ||||||||
\(989\) | −4.92820 | −0.156708 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0526 | −0.509926 | −0.254963 | − | 0.966951i | \(-0.582063\pi\) | ||||
−0.254963 | + | 0.966951i | \(0.582063\pi\) | |||||||
\(992\) | 1.46410 | 0.0464853 | ||||||||
\(993\) | −21.7846 | −0.691314 | ||||||||
\(994\) | −3.80385 | −0.120651 | ||||||||
\(995\) | −12.3923 | −0.392862 | ||||||||
\(996\) | 3.80385 | 0.120530 | ||||||||
\(997\) | 10.3397 | 0.327463 | 0.163732 | − | 0.986505i | \(-0.447647\pi\) | ||||
0.163732 | + | 0.986505i | \(0.447647\pi\) | |||||||
\(998\) | −21.2679 | −0.673225 | ||||||||
\(999\) | −32.3205 | −1.02258 |
(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 | 4598.2.a.w.1.1 | ✓ | 2 | |
11.10 | odd | 2 | 4598.2.a.bf.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.w.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
4598.2.a.bf.1.1 | yes | 2 | 11.10 | odd | 2 |