Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(4049,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4400.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.1 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.4049 |
Dual form | 4400.2.b.t.4049.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4400\mathbb{Z}\right)^\times\).
\(n\) | \(177\) | \(1201\) | \(2751\) | \(3301\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 2.56155i | − 1.47891i | −0.673204 | − | 0.739457i | \(-0.735083\pi\) | ||||
0.673204 | − | 0.739457i | \(-0.264917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56155i | 0.968176i | 0.875019 | + | 0.484088i | \(0.160849\pi\) | ||||
−0.875019 | + | 0.484088i | \(0.839151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.56155 | −1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.00000i | − 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 0.561553i | − 0.136197i | −0.997679 | − | 0.0680983i | \(-0.978307\pi\) | ||||
0.997679 | − | 0.0680983i | \(-0.0216931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.56155 | 0.587661 | 0.293830 | − | 0.955858i | \(-0.405070\pi\) | ||||
0.293830 | + | 0.955858i | \(0.405070\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.56155 | 1.43185 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.12311i | 1.06824i | 0.845408 | + | 0.534121i | \(0.179357\pi\) | ||||
−0.845408 | + | 0.534121i | \(0.820643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845i | 0.276829i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.68466 | −1.79840 | −0.899198 | − | 0.437542i | \(-0.855849\pi\) | ||||
−0.899198 | + | 0.437542i | \(0.855849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.56155 | −1.17849 | −0.589245 | − | 0.807955i | \(-0.700575\pi\) | ||||
−0.589245 | + | 0.807955i | \(0.700575\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.56155i | 0.445909i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.68466i | − 0.934552i | −0.884111 | − | 0.467276i | \(-0.845235\pi\) | ||||
0.884111 | − | 0.467276i | \(-0.154765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.12311 | −0.820353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2462i | 1.56253i | 0.624198 | + | 0.781266i | \(0.285426\pi\) | ||||
−0.624198 | + | 0.781266i | \(0.714574\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.1231i | 1.91420i | 0.289755 | + | 0.957101i | \(0.406426\pi\) | ||||
−0.289755 | + | 0.957101i | \(0.593574\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.438447 | 0.0626353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.43845 | −0.201423 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 4.56155i | − 0.626577i | −0.949658 | − | 0.313289i | \(-0.898569\pi\) | ||||
0.949658 | − | 0.313289i | \(-0.101431\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 6.56155i | − 0.869099i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.12311 | 0.146216 | 0.0731079 | − | 0.997324i | \(-0.476708\pi\) | ||||
0.0731079 | + | 0.997324i | \(0.476708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.31534 | 0.296449 | 0.148225 | − | 0.988954i | \(-0.452644\pi\) | ||||
0.148225 | + | 0.988954i | \(0.452644\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 9.12311i | − 1.14940i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.24621i | − 0.763096i | −0.924349 | − | 0.381548i | \(-0.875391\pi\) | ||||
0.924349 | − | 0.381548i | \(-0.124609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.1231 | 1.57984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.68466 | −0.437289 | −0.218644 | − | 0.975805i | \(-0.570163\pi\) | ||||
−0.218644 | + | 0.975805i | \(0.570163\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.56155i | − 0.291916i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.3693 | −1.72918 | −0.864592 | − | 0.502475i | \(-0.832423\pi\) | ||||
−0.864592 | + | 0.502475i | \(0.832423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.12311i | 0.562334i | 0.959659 | + | 0.281167i | \(0.0907215\pi\) | ||||
−0.959659 | + | 0.281167i | \(0.909279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.8078i | 2.65967i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.5616 | 1.33152 | 0.665761 | − | 0.746165i | \(-0.268107\pi\) | ||||
0.665761 | + | 0.746165i | \(0.268107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.12311 | 0.537047 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.8078i | 1.74288i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.12311i | 0.723242i | 0.932325 | + | 0.361621i | \(0.117777\pi\) | ||||
−0.932325 | + | 0.361621i | \(0.882223\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.56155 | 0.357950 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24621 | −0.422514 | −0.211257 | − | 0.977431i | \(-0.567756\pi\) | ||||
−0.211257 | + | 0.977431i | \(0.567756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.2462i | 1.00959i | 0.863239 | + | 0.504795i | \(0.168432\pi\) | ||||
−0.863239 | + | 0.504795i | \(0.831568\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0000i | 1.54678i | 0.633932 | + | 0.773389i | \(0.281440\pi\) | ||||
−0.633932 | + | 0.773389i | \(0.718560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.4924 | −1.77125 | −0.885626 | − | 0.464398i | \(-0.846271\pi\) | ||||
−0.885626 | + | 0.464398i | \(0.846271\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.5616 | −1.38212 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.1231i | 1.79895i | 0.436972 | + | 0.899475i | \(0.356051\pi\) | ||||
−0.436972 | + | 0.899475i | \(0.643949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.12311i | 0.658531i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.43845 | 0.131862 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.12311i | − 0.461935i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 14.2462i | − 1.26415i | −0.774909 | − | 0.632073i | \(-0.782204\pi\) | ||||
0.774909 | − | 0.632073i | \(-0.217796\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 26.2462 | 2.31085 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.68466 | 0.671412 | 0.335706 | − | 0.941967i | \(-0.391025\pi\) | ||||
0.335706 | + | 0.941967i | \(0.391025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.56155i | 0.568959i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.6155i | 1.67587i | 0.545772 | + | 0.837934i | \(0.316237\pi\) | ||||
−0.545772 | + | 0.837934i | \(0.683763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.6155 | 2.83094 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.00000i | 0.167248i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 1.12311i | − 0.0926322i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.31534 | −0.189680 | −0.0948401 | − | 0.995493i | \(-0.530234\pi\) | ||||
−0.0948401 | + | 0.995493i | \(0.530234\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1231 | −1.06794 | −0.533972 | − | 0.845502i | \(-0.679301\pi\) | ||||
−0.533972 | + | 0.845502i | \(0.679301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8078i | 1.18179i | 0.806749 | + | 0.590894i | \(0.201225\pi\) | ||||
−0.806749 | + | 0.590894i | \(0.798775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.6847 | −0.926654 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.1231 | −1.03425 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.19224i | 0.250035i | 0.992155 | + | 0.125018i | \(0.0398987\pi\) | ||||
−0.992155 | + | 0.125018i | \(0.960101\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.5616i | 0.817277i | 0.912696 | + | 0.408639i | \(0.133996\pi\) | ||||
−0.912696 | + | 0.408639i | \(0.866004\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.12311 | −0.697661 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4.24621i | − 0.322833i | −0.986886 | − | 0.161417i | \(-0.948394\pi\) | ||||
0.986886 | − | 0.161417i | \(-0.0516063\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 2.87689i | − 0.216241i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.24621 | −0.466864 | −0.233432 | − | 0.972373i | \(-0.574996\pi\) | ||||
−0.233432 | + | 0.972373i | \(0.574996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.24621 | −0.315618 | −0.157809 | − | 0.987470i | \(-0.550443\pi\) | ||||
−0.157809 | + | 0.987470i | \(0.550443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 5.93087i | − 0.438423i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.561553i | 0.0410648i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.68466 | −0.268019 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.2462 | −0.741390 | −0.370695 | − | 0.928755i | \(-0.620880\pi\) | ||||
−0.370695 | + | 0.928755i | \(0.620880\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 5.19224i | − 0.373745i | −0.982384 | − | 0.186873i | \(-0.940165\pi\) | ||||
0.982384 | − | 0.186873i | \(-0.0598352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 5.36932i | − 0.382548i | −0.981537 | − | 0.191274i | \(-0.938738\pi\) | ||||
0.981537 | − | 0.191274i | \(-0.0612619\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.807764 | −0.0572609 | −0.0286304 | − | 0.999590i | \(-0.509115\pi\) | ||||
−0.0286304 | + | 0.999590i | \(0.509115\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0000 | −1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 24.8078i | − 1.74116i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 18.2462i | − 1.26820i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.56155 | −0.177186 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.31534 | −0.572452 | −0.286226 | − | 0.958162i | \(-0.592401\pi\) | ||||
−0.286226 | + | 0.958162i | \(0.592401\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.43845i | 0.646712i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 16.8078i | − 1.14099i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.12311 | 0.346187 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.12311 | −0.0755483 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.1231i | 0.878788i | 0.898294 | + | 0.439394i | \(0.144807\pi\) | ||||
−0.898294 | + | 0.439394i | \(0.855193\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.87689i | − 0.190946i | −0.995432 | − | 0.0954731i | \(-0.969564\pi\) | ||||
0.995432 | − | 0.0954731i | \(-0.0304364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.7386 | 1.63477 | 0.817387 | − | 0.576088i | \(-0.195422\pi\) | ||||
0.817387 | + | 0.576088i | \(0.195422\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.56155 | −0.431718 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 19.9309i | − 1.30571i | −0.757481 | − | 0.652857i | \(-0.773570\pi\) | ||||
0.757481 | − | 0.652857i | \(-0.226430\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 39.3693i | 2.55731i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6155 | 1.65693 | 0.828465 | − | 0.560040i | \(-0.189214\pi\) | ||||
0.828465 | + | 0.560040i | \(0.189214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.2462 | −1.04651 | −0.523255 | − | 0.852176i | \(-0.675283\pi\) | ||||
−0.523255 | + | 0.852176i | \(0.675283\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462i | 1.42710i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 5.12311i | − 0.325975i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.1231 | 0.831643 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.6155 | 1.86932 | 0.934658 | − | 0.355549i | \(-0.115706\pi\) | ||||
0.934658 | + | 0.355549i | \(0.115706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.12311i | − 0.322087i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 28.7386i | − 1.79267i | −0.443381 | − | 0.896333i | \(-0.646221\pi\) | ||||
0.443381 | − | 0.896333i | \(-0.353779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.5616 | 0.904811 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 34.4924 | 2.13503 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.80776i | 0.296459i | 0.988953 | + | 0.148230i | \(0.0473575\pi\) | ||||
−0.988953 | + | 0.148230i | \(0.952643\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 32.1771i | − 1.96921i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.6155 | 1.19598 | 0.597990 | − | 0.801504i | \(-0.295966\pi\) | ||||
0.597990 | + | 0.801504i | \(0.295966\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.4924 | −1.73079 | −0.865396 | − | 0.501089i | \(-0.832933\pi\) | ||||
−0.865396 | + | 0.501089i | \(0.832933\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 13.1231i | − 0.794246i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.12311i | 0.427986i | 0.976835 | + | 0.213993i | \(0.0686470\pi\) | ||||
−0.976835 | + | 0.213993i | \(0.931353\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.3693 | 1.39908 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.24621 | −0.491928 | −0.245964 | − | 0.969279i | \(-0.579104\pi\) | ||||
−0.245964 | + | 0.969279i | \(0.579104\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.3693i | − 1.38916i | −0.719415 | − | 0.694581i | \(-0.755590\pi\) | ||||
0.719415 | − | 0.694581i | \(-0.244410\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.12311i | 0.302407i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6847 | 0.981450 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.2462 | 1.06961 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 14.4924i | − 0.846656i | −0.905976 | − | 0.423328i | \(-0.860862\pi\) | ||||
0.905976 | − | 0.423328i | \(-0.139138\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1.43845i | − 0.0834672i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.2462 | 0.592554 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.2462 | −1.51281 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.8769i | 0.624861i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.6155i | 1.46196i | 0.682401 | + | 0.730978i | \(0.260936\pi\) | ||||
−0.682401 | + | 0.730978i | \(0.739064\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.2462 | 1.49309 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.4384 | 1.44248 | 0.721241 | − | 0.692684i | \(-0.243572\pi\) | ||||
0.721241 | + | 0.692684i | \(0.243572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 30.4924i | − 1.72353i | −0.507305 | − | 0.861767i | \(-0.669358\pi\) | ||||
0.507305 | − | 0.861767i | \(-0.330642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.1922i | 0.740950i | 0.928842 | + | 0.370475i | \(0.120805\pi\) | ||||
−0.928842 | + | 0.370475i | \(0.879195\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.68466 | 0.542237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 40.9848 | 2.28755 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.43845i | − 0.0800373i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 47.3693i | 2.61953i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −33.6155 | −1.85328 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.49242 | 0.466786 | 0.233393 | − | 0.972383i | \(-0.425017\pi\) | ||||
0.233393 | + | 0.972383i | \(0.425017\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.2462i | 1.10949i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.31534i | 0.126125i | 0.998010 | + | 0.0630623i | \(0.0200867\pi\) | ||||
−0.998010 | + | 0.0630623i | \(0.979913\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 48.9848 | 2.66049 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.56155 | 0.355328 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0540i | 1.02882i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8769i | 1.01336i | 0.862133 | + | 0.506682i | \(0.169128\pi\) | ||||
−0.862133 | + | 0.506682i | \(0.830872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.4924 | −0.561646 | −0.280823 | − | 0.959760i | \(-0.590607\pi\) | ||||
−0.280823 | + | 0.959760i | \(0.590607\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.87689 | 0.153557 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.4924i | 1.83585i | 0.396758 | + | 0.917923i | \(0.370135\pi\) | ||||
−0.396758 | + | 0.917923i | \(0.629865\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.68466i | − 0.195013i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.2462 | 1.38522 | 0.692611 | − | 0.721311i | \(-0.256460\pi\) | ||||
0.692611 | + | 0.721311i | \(0.256460\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4384 | −0.654655 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 2.56155i | − 0.134447i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.7386i | 0.769350i | 0.923052 | + | 0.384675i | \(0.125687\pi\) | ||||
−0.923052 | + | 0.384675i | \(0.874313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.12311 | −0.370814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.6847 | 0.606637 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 2.00000i | − 0.103556i | −0.998659 | − | 0.0517780i | \(-0.983511\pi\) | ||||
0.998659 | − | 0.0517780i | \(-0.0164888\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.3693i | 0.997571i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.1231 | −1.29049 | −0.645244 | − | 0.763977i | \(-0.723244\pi\) | ||||
−0.645244 | + | 0.763977i | \(0.723244\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.4924 | −1.86956 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 31.3693i | − 1.60290i | −0.598064 | − | 0.801449i | \(-0.704063\pi\) | ||||
0.598064 | − | 0.801449i | \(-0.295937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 36.4924i | − 1.85501i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.2462 | −1.63495 | −0.817474 | − | 0.575966i | \(-0.804626\pi\) | ||||
−0.817474 | + | 0.575966i | \(0.804626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.87689 | 0.145491 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 19.6847i | − 0.992960i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 18.0000i | − 0.903394i | −0.892171 | − | 0.451697i | \(-0.850819\pi\) | ||||
0.892171 | − | 0.451697i | \(-0.149181\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.8078 | 0.841441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.43845 | −0.371458 | −0.185729 | − | 0.982601i | \(-0.559465\pi\) | ||||
−0.185729 | + | 0.982601i | \(0.559465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.1231i | 0.653708i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.68466i | 0.281778i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.12311 | −0.352215 | −0.176107 | − | 0.984371i | \(-0.556351\pi\) | ||||
−0.176107 | + | 0.984371i | \(0.556351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 50.2462 | 2.47846 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.87689i | 0.141563i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 30.7386i | − 1.50528i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.7386 | −1.30627 | −0.653134 | − | 0.757242i | \(-0.726546\pi\) | ||||
−0.653134 | + | 0.757242i | \(0.726546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.61553 | 0.371158 | 0.185579 | − | 0.982629i | \(-0.440584\pi\) | ||||
0.185579 | + | 0.982629i | \(0.440584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 46.7386i | − 2.27251i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.93087i | 0.287015i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.12311 | 0.247346 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 33.3693i | − 1.60363i | −0.597574 | − | 0.801814i | \(-0.703869\pi\) | ||||
0.597574 | − | 0.801814i | \(-0.296131\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1231i | 0.627763i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.2462 | −1.63448 | −0.817241 | − | 0.576296i | \(-0.804498\pi\) | ||||
−0.817241 | + | 0.576296i | \(0.804498\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.56155 | −0.0743597 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 4.00000i | − 0.190046i | −0.995475 | − | 0.0950229i | \(-0.969708\pi\) | ||||
0.995475 | − | 0.0950229i | \(-0.0302924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.93087i | 0.280521i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.00000 | −0.0941763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.6155i | 1.57940i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.5616i | 1.33605i | 0.744137 | + | 0.668027i | \(0.232861\pi\) | ||||
−0.744137 | + | 0.668027i | \(0.767139\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.807764 | 0.0377032 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.5616 | 0.957647 | 0.478823 | − | 0.877911i | \(-0.341063\pi\) | ||||
0.478823 | + | 0.877911i | \(0.341063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 7.36932i | − 0.342481i | −0.985229 | − | 0.171241i | \(-0.945222\pi\) | ||||
0.985229 | − | 0.171241i | \(-0.0547775\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 9.93087i | − 0.459546i | −0.973244 | − | 0.229773i | \(-0.926202\pi\) | ||||
0.973244 | − | 0.229773i | \(-0.0737984\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.9309 | 1.74776 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 10.2462i | − 0.471121i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.2462i | 0.743863i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.9848 | −1.50712 | −0.753558 | − | 0.657381i | \(-0.771664\pi\) | ||||
−0.753558 | + | 0.657381i | \(0.771664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.3693 | −0.518396 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 33.6155i | 1.52956i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.24621i | 0.101786i | 0.998704 | + | 0.0508928i | \(0.0162067\pi\) | ||||
−0.998704 | + | 0.0508928i | \(0.983793\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.17708 | 0.369780 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.05398 | −0.318341 | −0.159171 | − | 0.987251i | \(-0.550882\pi\) | ||||
−0.159171 | + | 0.987251i | \(0.550882\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.43845i | 0.244935i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 9.43845i | − 0.423372i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4924 | 0.738302 | 0.369151 | − | 0.929369i | \(-0.379648\pi\) | ||||
0.369151 | + | 0.929369i | \(0.379648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.0540 | 1.20868 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 14.2462i | − 0.635207i | −0.948224 | − | 0.317604i | \(-0.897122\pi\) | ||||
0.948224 | − | 0.317604i | \(-0.102878\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 23.0540i | − 1.02386i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.3693 | −0.947178 | −0.473589 | − | 0.880746i | \(-0.657042\pi\) | ||||
−0.473589 | + | 0.880746i | \(0.657042\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.12311 | −0.226633 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.68466i | 0.162682i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 13.1231i | − 0.577154i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.8769 | −0.477443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.73863 | 0.382846 | 0.191423 | − | 0.981508i | \(-0.438690\pi\) | ||||
0.191423 | + | 0.981508i | \(0.438690\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 3.50758i | − 0.153376i | −0.997055 | − | 0.0766878i | \(-0.975566\pi\) | ||||
0.997055 | − | 0.0766878i | \(-0.0244345\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.68466i | 0.160506i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.24621 | −0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 4.00000i | − 0.173259i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.0000i | 0.690451i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.438447 | −0.0188853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.5464 | −1.44227 | −0.721136 | − | 0.692793i | \(-0.756380\pi\) | ||||
−0.721136 | + | 0.692793i | \(0.756380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.8769i | 0.466772i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.0000i | 0.684111i | 0.939680 | + | 0.342055i | \(0.111123\pi\) | ||||
−0.939680 | + | 0.342055i | \(0.888877\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.24621 | −0.351940 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.8078 | −1.05685 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 39.3693i | − 1.67415i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 46.4924i | 1.96995i | 0.172705 | + | 0.984974i | \(0.444749\pi\) | ||||
−0.172705 | + | 0.984974i | \(0.555251\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.4924 | 0.866737 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.43845 | 0.0607313 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 2.87689i | − 0.121247i | −0.998161 | − | 0.0606233i | \(-0.980691\pi\) | ||||
0.998161 | − | 0.0606233i | \(-0.0193088\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 17.9309i | − 0.753026i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.1080 | 1.17835 | 0.589173 | − | 0.808007i | \(-0.299454\pi\) | ||||
0.589173 | + | 0.808007i | \(0.299454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.4233 | −1.27318 | −0.636588 | − | 0.771204i | \(-0.719655\pi\) | ||||
−0.636588 | + | 0.771204i | \(0.719655\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.2462i | 1.09645i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.7386i | 1.02988i | 0.857225 | + | 0.514941i | \(0.172186\pi\) | ||||
−0.857225 | + | 0.514941i | \(0.827814\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3002 | −0.552737 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.1231 | −0.544438 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.56155i | 0.188920i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 32.3153i | − 1.33380i | −0.745149 | − | 0.666898i | \(-0.767621\pi\) | ||||
0.745149 | − | 0.666898i | \(-0.232379\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.8078 | −0.692552 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.7538 | −0.565755 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.50758i | − 0.0619088i | −0.999521 | − | 0.0309544i | \(-0.990145\pi\) | ||||
0.999521 | − | 0.0309544i | \(-0.00985466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.06913i | 0.0846839i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4384 | −0.712516 | −0.356258 | − | 0.934388i | \(-0.615948\pi\) | ||||
−0.356258 | + | 0.934388i | \(0.615948\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0000 | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.2462i | 0.905936i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 20.8078i | − 0.844561i | −0.906465 | − | 0.422281i | \(-0.861230\pi\) | ||||
0.906465 | − | 0.422281i | \(-0.138770\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −63.5464 | −2.57503 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.2462 | 1.06181 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 16.7386i | − 0.676067i | −0.941134 | − | 0.338034i | \(-0.890238\pi\) | ||||
0.941134 | − | 0.338034i | \(-0.109762\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 6.63068i | − 0.266941i | −0.991053 | − | 0.133471i | \(-0.957388\pi\) | ||||
0.991053 | − | 0.133471i | \(-0.0426122\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.49242 | −0.341339 | −0.170670 | − | 0.985328i | \(-0.554593\pi\) | ||||
−0.170670 | + | 0.985328i | \(0.554593\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.36932 | −0.295720 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32.1771i | 1.28915i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.56155i | 0.262043i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.19224 | −0.127283 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.8078 | 0.669107 | 0.334553 | − | 0.942377i | \(-0.391415\pi\) | ||||
0.334553 | + | 0.942377i | \(0.391415\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.3002i | 0.846606i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 0.876894i | − 0.0347438i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1231 | 0.519142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.1771 | −1.50790 | −0.753952 | − | 0.656929i | \(-0.771855\pi\) | ||||
−0.753952 | + | 0.656929i | \(0.771855\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.6847i | 0.934032i | 0.884249 | + | 0.467016i | \(0.154671\pi\) | ||||
−0.884249 | + | 0.467016i | \(0.845329\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.1231i | 0.515923i | 0.966155 | + | 0.257961i | \(0.0830507\pi\) | ||||
−0.966155 | + | 0.257961i | \(0.916949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.12311 | −0.0440858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −43.0540 | −1.68742 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.8078i | 0.422940i | 0.977384 | + | 0.211470i | \(0.0678251\pi\) | ||||
−0.977384 | + | 0.211470i | \(0.932175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 7.12311i | − 0.277899i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.1922 | 0.747623 | 0.373812 | − | 0.927505i | \(-0.378051\pi\) | ||||
0.373812 | + | 0.927505i | \(0.378051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2462 | 0.631904 | 0.315952 | − | 0.948775i | \(-0.397676\pi\) | ||||
0.315952 | + | 0.948775i | \(0.397676\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.87689i | 0.111729i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 49.6155i | − 1.92112i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 33.6155 | 1.29965 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.31534 | −0.0893828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7926i | 1.37970i | 0.723951 | + | 0.689852i | \(0.242324\pi\) | ||||
−0.723951 | + | 0.689852i | \(0.757676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.6155i | 1.06135i | 0.847575 | + | 0.530675i | \(0.178062\pi\) | ||||
−0.847575 | + | 0.530675i | \(0.821938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.2462 | −0.700225 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.36932 | −0.282393 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 25.9309i | − 0.992217i | −0.868260 | − | 0.496109i | \(-0.834762\pi\) | ||||
0.868260 | − | 0.496109i | \(-0.165238\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 63.3693i | − 2.41769i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.12311 | −0.347563 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.36932 | −0.128175 | −0.0640874 | − | 0.997944i | \(-0.520414\pi\) | ||||
−0.0640874 | + | 0.997944i | \(0.520414\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.12311i | 0.346558i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.12311i | − 0.0425407i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −51.0540 | −1.93104 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.3153 | 1.29607 | 0.648036 | − | 0.761609i | \(-0.275591\pi\) | ||||
0.648036 | + | 0.761609i | \(0.275591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 14.5616i | − 0.549199i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 10.8769i | − 0.409068i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.50758 | −0.0566183 | −0.0283091 | − | 0.999599i | \(-0.509012\pi\) | ||||
−0.0283091 | + | 0.999599i | \(0.509012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 54.7386 | 2.05286 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 33.6155i | − 1.25891i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 65.6155i | − 2.45046i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.82292 | 0.291746 | 0.145873 | − | 0.989303i | \(-0.453401\pi\) | ||||
0.145873 | + | 0.989303i | \(0.453401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.2462 | −0.977460 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 41.6155i | 1.54770i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 17.6155i | − 0.653324i | −0.945141 | − | 0.326662i | \(-0.894076\pi\) | ||||
0.945141 | − | 0.326662i | \(-0.105924\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35.9848 | 1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.75379 | 0.212812 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.1231i | 0.706328i | 0.935561 | + | 0.353164i | \(0.114894\pi\) | ||||
−0.935561 | + | 0.353164i | \(0.885106\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.24621i | 0.230082i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −42.7386 | −1.57217 | −0.786083 | − | 0.618121i | \(-0.787894\pi\) | ||||
−0.786083 | + | 0.618121i | \(0.787894\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.1231 | −0.482089 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.56155i | − 0.0939743i | −0.998895 | − | 0.0469871i | \(-0.985038\pi\) | ||||
0.998895 | − | 0.0469871i | \(-0.0149620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 18.2462i | − 0.667594i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40.9848 | −1.49755 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.1771 | 0.590310 | 0.295155 | − | 0.955449i | \(-0.404629\pi\) | ||||
0.295155 | + | 0.955449i | \(0.404629\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 75.8617i | − 2.76456i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 26.0000i | − 0.944986i | −0.881334 | − | 0.472493i | \(-0.843354\pi\) | ||||
0.881334 | − | 0.472493i | \(-0.156646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.1231 | −0.476339 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.7386 | −1.33177 | −0.665887 | − | 0.746052i | \(-0.731947\pi\) | ||||
−0.665887 | + | 0.746052i | \(0.731947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 47.3693i | − 1.71488i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 2.24621i | − 0.0811060i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.7386 | −0.892098 | −0.446049 | − | 0.895009i | \(-0.647169\pi\) | ||||
−0.446049 | + | 0.895009i | \(0.647169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −73.6155 | −2.65120 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.6847i | 1.35542i | 0.735328 | + | 0.677711i | \(0.237028\pi\) | ||||
−0.735328 | + | 0.677711i | \(0.762972\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 37.3002i | − 1.33814i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.12311 | 0.183554 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.68466 | 0.131847 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 13.9309i | − 0.497849i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.7386i | 1.95122i | 0.219508 | + | 0.975611i | \(0.429555\pi\) | ||||
−0.219508 | + | 0.975611i | \(0.570445\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.3153 | 0.438438 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.9848 | −1.74170 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 4.63068i | − 0.164440i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 23.7538i | − 0.841402i | −0.907199 | − | 0.420701i | \(-0.861784\pi\) | ||||
0.907199 | − | 0.420701i | \(-0.138216\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.36932 | 0.260708 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.7386 | −1.58076 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.00000i | − 0.0705785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 50.2462i | − 1.76875i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.49242 | −0.228261 | −0.114131 | − | 0.993466i | \(-0.536408\pi\) | ||||
−0.114131 | + | 0.993466i | \(0.536408\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.1922 | −0.954849 | −0.477424 | − | 0.878673i | \(-0.658430\pi\) | ||||
−0.477424 | + | 0.878673i | \(0.658430\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 72.9848i | 2.55969i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.2462i | 0.918239i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.2462 | −0.637574 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.00000 | −0.0698005 | −0.0349002 | − | 0.999391i | \(-0.511111\pi\) | ||||
−0.0349002 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 52.4924i | − 1.82977i | −0.403714 | − | 0.914885i | \(-0.632281\pi\) | ||||
0.403714 | − | 0.914885i | \(-0.367719\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.49242i | 0.156217i | 0.996945 | + | 0.0781084i | \(0.0248880\pi\) | ||||
−0.996945 | + | 0.0781084i | \(0.975112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.36932 | −0.186484 | −0.0932420 | − | 0.995643i | \(-0.529723\pi\) | ||||
−0.0932420 | + | 0.995643i | \(0.529723\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.2462 | 0.632954 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.246211i | − 0.00853071i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 9.43845i | − 0.326240i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.5076 | 0.397286 | 0.198643 | − | 0.980072i | \(-0.436347\pi\) | ||||
0.198643 | + | 0.980072i | \(0.436347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64.7926 | 2.23423 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.1231i | 0.727518i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.56155i | 0.0880160i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −59.8617 | −2.05445 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29.1231 | 0.998327 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.75379i | 0.128527i | 0.997933 | + | 0.0642636i | \(0.0204699\pi\) | ||||
−0.997933 | + | 0.0642636i | \(0.979530\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.4233i | 1.10756i | 0.832664 | + | 0.553779i | \(0.186815\pi\) | ||||
−0.832664 | + | 0.553779i | \(0.813185\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.8769 | −1.32646 | −0.663231 | − | 0.748415i | \(-0.730815\pi\) | ||||
−0.663231 | + | 0.748415i | \(0.730815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.1231 | 0.447234 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.61553i | 0.327316i | 0.986517 | + | 0.163658i | \(0.0523294\pi\) | ||||
−0.986517 | + | 0.163658i | \(0.947671\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 42.7386i | − 1.45148i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.3693 | 0.521368 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.4924 | −0.423290 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 25.3693i | − 0.858621i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 32.2462i | − 1.08888i | −0.838801 | − | 0.544439i | \(-0.816743\pi\) | ||||
0.838801 | − | 0.544439i | \(-0.183257\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.1231 | −1.25213 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.06913i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.2462i | 1.01557i | 0.861484 | + | 0.507784i | \(0.169535\pi\) | ||||
−0.861484 | + | 0.507784i | \(0.830465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.4924 | 1.22392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.00000 | 0.234509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.6155i | 1.12490i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 26.2462i | − 0.876335i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 63.5464 | 2.11939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.56155 | −0.0853377 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 67.2311i | 2.23731i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8.94602i | − 0.297048i | −0.988909 | − | 0.148524i | \(-0.952548\pi\) | ||||
0.988909 | − | 0.148524i | \(-0.0474522\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1231 | 0.501602 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.06913 | 0.0685533 | 0.0342767 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342767 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 5.12311i | − 0.169550i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.6847i | 0.650045i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | 0.263896 | 0.131948 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131948 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 65.6155 | 2.16211 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.36932i | 0.242564i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 36.4924i | − 1.19857i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.0540 | −1.47817 | −0.739086 | − | 0.673611i | \(-0.764743\pi\) | ||||
−0.739086 | + | 0.673611i | \(0.764743\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.12311 | 0.0368083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 65.1619i | − 2.13331i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 42.0000i | − 1.37208i | −0.727564 | − | 0.686040i | \(-0.759347\pi\) | ||||
0.727564 | − | 0.686040i | \(-0.240653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −78.1080 | −2.54896 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.06913 | −0.132650 | −0.0663249 | − | 0.997798i | \(-0.521127\pi\) | ||||
−0.0663249 | + | 0.997798i | \(0.521127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.2462i | 0.333663i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 39.6847i | 1.28958i | 0.764361 | + | 0.644789i | \(0.223055\pi\) | ||||
−0.764361 | + | 0.644789i | \(0.776945\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.7926 | 1.09580 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.1771i | 1.10710i | 0.832815 | + | 0.553552i | \(0.186728\pi\) | ||||
−0.832815 | + | 0.553552i | \(0.813272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 24.8078i | − 0.801921i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −50.2462 | −1.62253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0540 | 0.388838 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 56.9848i | − 1.83631i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 11.5464i | − 0.371307i | −0.982615 | − | 0.185654i | \(-0.940560\pi\) | ||||
0.982615 | − | 0.185654i | \(-0.0594402\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.68466 | −0.118368 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.24621 | −0.200450 | −0.100225 | − | 0.994965i | \(-0.531956\pi\) | ||||
−0.100225 | + | 0.994965i | \(0.531956\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30.7386i | 0.985435i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 24.8769i | − 0.795882i | −0.917411 | − | 0.397941i | \(-0.869725\pi\) | ||||
0.917411 | − | 0.397941i | \(-0.130275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.5616 | −0.401469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 65.8617 | 2.10280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.8769i | 0.602079i | 0.953612 | + | 0.301040i | \(0.0973337\pi\) | ||||
−0.953612 | + | 0.301040i | \(0.902666\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 86.1080i | 2.74085i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −52.4924 | −1.66916 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 21.7538i | − 0.690336i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.8617i | 0.439006i | 0.975612 | + | 0.219503i | \(0.0704435\pi\) | ||||
−0.975612 | + | 0.219503i | \(0.929556\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.17708 | 0.258711 |
(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 | 4400.2.b.t.4049.1 | 4 | ||
4.3 | odd | 2 | 2200.2.b.i.1849.4 | 4 | |||
5.2 | odd | 4 | 4400.2.a.bj.1.1 | 2 | |||
5.3 | odd | 4 | 880.2.a.o.1.2 | 2 | |||
5.4 | even | 2 | inner | 4400.2.b.t.4049.4 | 4 | ||
15.8 | even | 4 | 7920.2.a.bu.1.2 | 2 | |||
20.3 | even | 4 | 440.2.a.e.1.1 | ✓ | 2 | ||
20.7 | even | 4 | 2200.2.a.s.1.2 | 2 | |||
20.19 | odd | 2 | 2200.2.b.i.1849.1 | 4 | |||
40.3 | even | 4 | 3520.2.a.bp.1.2 | 2 | |||
40.13 | odd | 4 | 3520.2.a.bk.1.1 | 2 | |||
55.43 | even | 4 | 9680.2.a.bs.1.2 | 2 | |||
60.23 | odd | 4 | 3960.2.a.w.1.1 | 2 | |||
220.43 | odd | 4 | 4840.2.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.a.e.1.1 | ✓ | 2 | 20.3 | even | 4 | ||
880.2.a.o.1.2 | 2 | 5.3 | odd | 4 | |||
2200.2.a.s.1.2 | 2 | 20.7 | even | 4 | |||
2200.2.b.i.1849.1 | 4 | 20.19 | odd | 2 | |||
2200.2.b.i.1849.4 | 4 | 4.3 | odd | 2 | |||
3520.2.a.bk.1.1 | 2 | 40.13 | odd | 4 | |||
3520.2.a.bp.1.2 | 2 | 40.3 | even | 4 | |||
3960.2.a.w.1.1 | 2 | 60.23 | odd | 4 | |||
4400.2.a.bj.1.1 | 2 | 5.2 | odd | 4 | |||
4400.2.b.t.4049.1 | 4 | 1.1 | even | 1 | trivial | ||
4400.2.b.t.4049.4 | 4 | 5.4 | even | 2 | inner | ||
4840.2.a.j.1.1 | 2 | 220.43 | odd | 4 | |||
7920.2.a.bu.1.2 | 2 | 15.8 | even | 4 | |||
9680.2.a.bs.1.2 | 2 | 55.43 | even | 4 |