Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1537,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("3072.1537");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.d (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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 768) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1537.2 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1537 |
Dual form | 3072.2.d.h.1537.7 |
$q$-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 \(\left(\mathbb{Z}/3072\mathbb{Z}\right)^\times\).
\(n\) | \(1025\) | \(2047\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.03528i | − 0.462990i | −0.972836 | − | 0.231495i | \(-0.925638\pi\) | ||||
0.972836 | − | 0.231495i | \(-0.0743616\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | −0.925820 | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.46410i | 1.64749i | 0.566961 | + | 0.823744i | \(0.308119\pi\) | ||||
−0.566961 | + | 0.823744i | \(0.691881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.24264i | − 1.17670i | −0.808608 | − | 0.588348i | \(-0.799778\pi\) | ||||
0.808608 | − | 0.588348i | \(-0.200222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.03528 | −0.267307 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.535898i | − 0.122944i | −0.998109 | − | 0.0614718i | \(-0.980421\pi\) | ||||
0.998109 | − | 0.0614718i | \(-0.0195794\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.44949i | 0.534522i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.92820 | 0.785641 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.93426i | 1.10196i | 0.834517 | + | 0.550982i | \(0.185747\pi\) | ||||
−0.834517 | + | 0.550982i | \(0.814253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34847 | 1.31982 | 0.659912 | − | 0.751343i | \(-0.270594\pi\) | ||||
0.659912 | + | 0.751343i | \(0.270594\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.46410 | 0.951178 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53590i | 0.428645i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 9.14162i | − 1.50287i | −0.659805 | − | 0.751437i | \(-0.729361\pi\) | ||||
0.659805 | − | 0.751437i | \(-0.270639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.24264 | −0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4641 | −1.79039 | −0.895196 | − | 0.445673i | \(-0.852964\pi\) | ||||
−0.895196 | + | 0.445673i | \(0.852964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410i | 0.528271i | 0.964486 | + | 0.264135i | \(0.0850865\pi\) | ||||
−0.964486 | + | 0.264135i | \(0.914913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.03528i | 0.154330i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.46410i | − 0.485071i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.52056i | − 1.30775i | −0.756603 | − | 0.653875i | \(-0.773142\pi\) | ||||
0.756603 | − | 0.653875i | \(-0.226858\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.535898 | −0.0709815 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 13.8564i | − 1.80395i | −0.431788 | − | 0.901975i | \(-0.642117\pi\) | ||||
0.431788 | − | 0.901975i | \(-0.357883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 9.14162i | − 1.17046i | −0.810866 | − | 0.585232i | \(-0.801003\pi\) | ||||
0.810866 | − | 0.585232i | \(-0.198997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.44949 | 0.308607 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.39230 | −0.544798 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 1.07180i | − 0.130941i | −0.997855 | − | 0.0654704i | \(-0.979145\pi\) | ||||
0.997855 | − | 0.0654704i | \(-0.0208548\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.82843i | − 0.340503i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2127 | 1.92409 | 0.962046 | − | 0.272887i | \(-0.0879786\pi\) | ||||
0.962046 | + | 0.272887i | \(0.0879786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 3.92820i | − 0.453590i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 13.3843i | − 1.52528i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.44949 | −0.275589 | −0.137795 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137795 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.46410i | 0.160706i | 0.996766 | + | 0.0803530i | \(0.0256048\pi\) | ||||
−0.996766 | + | 0.0803530i | \(0.974395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 3.58630i | − 0.388989i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.93426 | 0.636219 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.92820 | −0.946388 | −0.473194 | − | 0.880958i | \(-0.656899\pi\) | ||||
−0.473194 | + | 0.880958i | \(0.656899\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3923i | 1.08941i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 7.34847i | − 0.762001i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.554803 | −0.0569216 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9282 | 1.51573 | 0.757865 | − | 0.652412i | \(-0.226243\pi\) | ||||
0.757865 | + | 0.652412i | \(0.226243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 5.46410i | − 0.549163i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.277401i | 0.0276025i | 0.999905 | + | 0.0138012i | \(0.00439321\pi\) | ||||
−0.999905 | + | 0.0138012i | \(0.995607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.10634 | −0.798742 | −0.399371 | − | 0.916789i | \(-0.630771\pi\) | ||||
−0.399371 | + | 0.916789i | \(0.630771\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.53590 | 0.247478 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.00000i | − 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1.41421i | − 0.135457i | −0.997704 | − | 0.0677285i | \(-0.978425\pi\) | ||||
0.997704 | − | 0.0677285i | \(-0.0215752\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.14162 | −0.867684 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.92820i | − 0.273056i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.24264i | 0.392232i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.48528 | −0.777844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.8564 | −1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4641i | 1.03368i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 9.24316i | − 0.826733i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.4201 | −1.72325 | −0.861625 | − | 0.507545i | \(-0.830553\pi\) | ||||
−0.861625 | + | 0.507545i | \(0.830553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.46410 | 0.304997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.07180i | 0.0936433i | 0.998903 | + | 0.0468217i | \(0.0149092\pi\) | ||||
−0.998903 | + | 0.0468217i | \(0.985091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.31268i | 0.113824i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.03528 | 0.0891024 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.39230 | 0.546131 | 0.273066 | − | 0.961995i | \(-0.411962\pi\) | ||||
0.273066 | + | 0.961995i | \(0.411962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 6.92820i | − 0.587643i | −0.955860 | − | 0.293821i | \(-0.905073\pi\) | ||||
0.955860 | − | 0.293821i | \(-0.0949270\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.82843i | − 0.238197i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.1822 | 1.93859 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.14359 | 0.510198 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 20.0764i | − 1.64472i | −0.568966 | − | 0.822361i | \(-0.692656\pi\) | ||||
0.568966 | − | 0.822361i | \(-0.307344\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.9043 | −1.45703 | −0.728516 | − | 0.685029i | \(-0.759789\pi\) | ||||
−0.728516 | + | 0.685029i | \(0.759789\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.46410 | −0.280056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 7.60770i | − 0.611065i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 11.9700i | − 0.955314i | −0.878546 | − | 0.477657i | \(-0.841486\pi\) | ||||
0.878546 | − | 0.477657i | \(-0.158514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.52056 | −0.755029 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.92820 | −0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 11.4641i | − 0.897938i | −0.893547 | − | 0.448969i | \(-0.851791\pi\) | ||||
0.893547 | − | 0.448969i | \(-0.148209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 5.65685i | − 0.440386i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.07055 | 0.160224 | 0.0801121 | − | 0.996786i | \(-0.474472\pi\) | ||||
0.0801121 | + | 0.996786i | \(0.474472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.535898i | 0.0409812i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.55103i | 0.193951i | 0.995287 | + | 0.0969754i | \(0.0309168\pi\) | ||||
−0.995287 | + | 0.0969754i | \(0.969083\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.62209 | −0.727362 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.8564 | −1.04151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.07180i | 0.379084i | 0.981873 | + | 0.189542i | \(0.0607003\pi\) | ||||
−0.981873 | + | 0.189542i | \(0.939300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.07107i | 0.525588i | 0.964852 | + | 0.262794i | \(0.0846440\pi\) | ||||
−0.964852 | + | 0.262794i | \(0.915356\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.14162 | −0.675768 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.46410 | −0.695815 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.9282i | 1.38417i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 2.44949i | − 0.178174i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.07055 | −0.149820 | −0.0749100 | − | 0.997190i | \(-0.523867\pi\) | ||||
−0.0749100 | + | 0.997190i | \(0.523867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.39230i | 0.314539i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.93426i | 0.422798i | 0.977400 | + | 0.211399i | \(0.0678020\pi\) | ||||
−0.977400 | + | 0.211399i | \(0.932198\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.96524 | 0.281088 | 0.140544 | − | 0.990074i | \(-0.455115\pi\) | ||||
0.140544 | + | 0.990074i | \(0.455115\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.07180 | −0.0755987 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 14.5359i | − 1.02022i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8685i | 0.828933i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.92820 | 0.202548 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.92820i | 0.476957i | 0.971148 | + | 0.238479i | \(0.0766487\pi\) | ||||
−0.971148 | + | 0.238479i | \(0.923351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 16.2127i | − 1.11088i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.58630 | 0.244584 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18.0000 | −1.22192 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.00000i | 0.270295i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 14.6969i | − 0.988623i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.4201 | 1.30046 | 0.650231 | − | 0.759736i | \(-0.274672\pi\) | ||||
0.650231 | + | 0.759736i | \(0.274672\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.92820 | −0.261880 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.3205i | 1.54784i | 0.633286 | + | 0.773918i | \(0.281706\pi\) | ||||
−0.633286 | + | 0.773918i | \(0.718294\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.72689i | 0.180198i | 0.995933 | + | 0.0900990i | \(0.0287184\pi\) | ||||
−0.995933 | + | 0.0900990i | \(0.971282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.3843 | −0.880620 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.928203 | 0.0608086 | 0.0304043 | − | 0.999538i | \(-0.490321\pi\) | ||||
0.0304043 | + | 0.999538i | \(0.490321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.92820i | − 0.191015i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.44949i | 0.159111i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.07055 | 0.133933 | 0.0669664 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669664 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7846 | 0.952360 | 0.476180 | − | 0.879348i | \(-0.342021\pi\) | ||||
0.476180 | + | 0.879348i | \(0.342021\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.03528i | 0.0661414i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.27362 | −0.144667 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.46410 | 0.0927837 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 13.4641i | − 0.849847i | −0.905229 | − | 0.424923i | \(-0.860301\pi\) | ||||
0.905229 | − | 0.424923i | \(-0.139699\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4548i | 0.971636i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.58630 | −0.224583 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.7846 | 1.17175 | 0.585876 | − | 0.810401i | \(-0.300751\pi\) | ||||
0.585876 | + | 0.810401i | \(0.300751\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.3923i | 1.39139i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 5.93426i | − 0.367321i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.6274 | 1.39527 | 0.697633 | − | 0.716455i | \(-0.254237\pi\) | ||||
0.697633 | + | 0.716455i | \(0.254237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.85641 | −0.605474 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.92820i | 0.546397i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 15.1774i | − 0.925383i | −0.886519 | − | 0.462692i | \(-0.846884\pi\) | ||||
0.886519 | − | 0.462692i | \(-0.153116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.10634 | 0.492425 | 0.246213 | − | 0.969216i | \(-0.420814\pi\) | ||||
0.246213 | + | 0.969216i | \(0.420814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.3923 | 0.628971 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.4641i | 1.29433i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 26.6670i | − 1.60226i | −0.598488 | − | 0.801132i | \(-0.704231\pi\) | ||||
0.598488 | − | 0.801132i | \(-0.295769\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.34847 | −0.439941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9282 | 0.771232 | 0.385616 | − | 0.922659i | \(-0.373989\pi\) | ||||
0.385616 | + | 0.922659i | \(0.373989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.8564i | − 1.06145i | −0.847543 | − | 0.530727i | \(-0.821919\pi\) | ||||
0.847543 | − | 0.530727i | \(-0.178081\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.554803i | 0.0328637i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 28.0812 | 1.65758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 14.9282i | − 0.875107i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 13.6617i | − 0.798123i | −0.916924 | − | 0.399061i | \(-0.869336\pi\) | ||||
0.916924 | − | 0.399061i | \(-0.130664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.3452 | −0.835210 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.46410 | −0.317059 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 12.0000i | − 0.693978i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.48528i | − 0.489083i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.277401 | 0.0159363 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.46410 | −0.541913 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 9.07180i | − 0.517755i | −0.965910 | − | 0.258877i | \(-0.916647\pi\) | ||||
0.965910 | − | 0.258877i | \(-0.0833526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.10634i | 0.461154i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.8295 | 0.727492 | 0.363746 | − | 0.931498i | \(-0.381498\pi\) | ||||
0.363746 | + | 0.931498i | \(0.381498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.8564 | 1.34844 | 0.674222 | − | 0.738529i | \(-0.264479\pi\) | ||||
0.674222 | + | 0.738529i | \(0.264479\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.53590i | − 0.142882i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.79315i | − 0.100713i | −0.998731 | − | 0.0503567i | \(-0.983964\pi\) | ||||
0.998731 | − | 0.0503567i | \(-0.0160358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.4254 | −1.81547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.85641i | − 0.103293i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 16.6660i | − 0.924461i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.41421 | −0.0782062 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.92820 | −0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.9282i | 0.820528i | 0.911967 | + | 0.410264i | \(0.134563\pi\) | ||||
−0.911967 | + | 0.410264i | \(0.865437\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.14162i | 0.500958i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.10961 | −0.0606242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.8564 | −0.972700 | −0.486350 | − | 0.873764i | \(-0.661672\pi\) | ||||
−0.486350 | + | 0.873764i | \(0.661672\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 18.0000i | − 0.977626i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.1528i | 2.17440i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959 | 1.05808 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.92820 | −0.157649 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.46410i | 0.508060i | 0.967196 | + | 0.254030i | \(0.0817561\pi\) | ||||
−0.967196 | + | 0.254030i | \(0.918244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.96902i | 0.105399i | 0.998610 | + | 0.0526995i | \(0.0167826\pi\) | ||||
−0.998610 | + | 0.0526995i | \(0.983217\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9282 | 0.688099 | 0.344049 | − | 0.938952i | \(-0.388201\pi\) | ||||
0.344049 | + | 0.938952i | \(0.388201\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 16.7846i | − 0.890835i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.48528i | 0.449089i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.1518 | −1.59135 | −0.795674 | − | 0.605725i | \(-0.792883\pi\) | ||||
−0.795674 | + | 0.605725i | \(0.792883\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.7128 | 0.984885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.8564i | 0.989705i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.14110i | 0.216755i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.7023 | −1.44605 | −0.723023 | − | 0.690824i | \(-0.757248\pi\) | ||||
−0.723023 | + | 0.690824i | \(0.757248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.4641 | 0.596797 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.3205i | 1.21074i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.1112i | 0.834204i | 0.908860 | + | 0.417102i | \(0.136954\pi\) | ||||
−0.908860 | + | 0.417102i | \(0.863046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.24316 | −0.477315 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.1769 | 1.29668 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 21.3205i | − 1.09516i | −0.836753 | − | 0.547580i | \(-0.815549\pi\) | ||||
0.836753 | − | 0.547580i | \(-0.184451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.4201i | 0.994919i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.554803 | 0.0283491 | 0.0141746 | − | 0.999900i | \(-0.495488\pi\) | ||||
0.0141746 | + | 0.999900i | \(0.495488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.8564 | −0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 3.46410i | − 0.176090i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.62158i | 0.234323i | 0.993113 | + | 0.117162i | \(0.0373796\pi\) | ||||
−0.993113 | + | 0.117162i | \(0.962620\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.79796 | 0.495504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.07180 | 0.0540650 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.53590i | 0.127595i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 25.9091i | − 1.30034i | −0.759788 | − | 0.650171i | \(-0.774697\pi\) | ||||
0.759788 | − | 0.650171i | \(-0.225303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.31268 | 0.0657161 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.39230 | 0.119466 | 0.0597330 | − | 0.998214i | \(-0.480975\pi\) | ||||
0.0597330 | + | 0.998214i | \(0.480975\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 31.1769i | − 1.55303i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 1.03528i | − 0.0514433i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 49.9507 | 2.47597 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.9282 | 1.13373 | 0.566863 | − | 0.823812i | \(-0.308157\pi\) | ||||
0.566863 | + | 0.823812i | \(0.308157\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 6.39230i | − 0.315309i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.9411i | 1.67013i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.51575 | 0.0744052 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.92820 | −0.339276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.3923i | 0.996229i | 0.867111 | + | 0.498115i | \(0.165974\pi\) | ||||
−0.867111 | + | 0.498115i | \(0.834026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.101536i | 0.00494856i | 0.999997 | + | 0.00247428i | \(0.000787589\pi\) | ||||
−0.999997 | + | 0.00247428i | \(0.999212\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.82843 | −0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.6077 | 0.660070 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.3923i | 1.08364i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 23.1822i | − 1.11925i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.9401 | −1.15315 | −0.576577 | − | 0.817043i | \(-0.695612\pi\) | ||||
−0.576577 | + | 0.817043i | \(0.695612\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.14359 | −0.103015 | −0.0515073 | − | 0.998673i | \(-0.516403\pi\) | ||||
−0.0515073 | + | 0.998673i | \(0.516403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 6.14359i | − 0.294563i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.51575i | − 0.0725081i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.4601 | −1.35833 | −0.679164 | − | 0.733986i | \(-0.737658\pi\) | ||||
−0.679164 | + | 0.733986i | \(0.737658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 0.679492i | − 0.0322836i | −0.999870 | − | 0.0161418i | \(-0.994862\pi\) | ||||
0.999870 | − | 0.0161418i | \(-0.00513832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.24316i | 0.438168i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.0764 | −0.949581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3923 | 0.679215 | 0.339607 | − | 0.940567i | \(-0.389706\pi\) | ||||
0.339607 | + | 0.940567i | \(0.389706\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 62.6410i | − 2.94965i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.9043i | 0.841218i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.7589 | 0.504385 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7846 | −0.972263 | −0.486132 | − | 0.873886i | \(-0.661592\pi\) | ||||
−0.486132 | + | 0.873886i | \(0.661592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.46410i | 0.161690i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.7017i | 1.05733i | 0.848832 | + | 0.528663i | \(0.177306\pi\) | ||||
−0.848832 | + | 0.528663i | \(0.822694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.72311 | 0.219502 | 0.109751 | − | 0.993959i | \(-0.464995\pi\) | ||||
0.109751 | + | 0.993959i | \(0.464995\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.60770 | −0.352798 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 18.2487i | − 0.844450i | −0.906491 | − | 0.422225i | \(-0.861249\pi\) | ||||
0.906491 | − | 0.422225i | \(-0.138751\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.62536i | 0.121228i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.9700 | −0.551551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.9282 | −0.870320 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.10512i | − 0.0965894i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.52056i | 0.435916i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.8401 | 1.77465 | 0.887325 | − | 0.461145i | \(-0.152561\pi\) | ||||
0.887325 | + | 0.461145i | \(0.152561\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.7846 | −1.76843 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.92820i | 0.315244i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 15.4548i | − 0.701767i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.8033 | −1.03332 | −0.516658 | − | 0.856192i | \(-0.672824\pi\) | ||||
−0.516658 | + | 0.856192i | \(0.672824\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.4641 | −0.518425 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 21.8564i | − 0.986366i | −0.869926 | − | 0.493183i | \(-0.835833\pi\) | ||||
0.869926 | − | 0.493183i | \(-0.164167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.5569i | 0.925835i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65685 | −0.254257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −39.7128 | −1.78136 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 4.00000i | − 0.179065i | −0.995984 | − | 0.0895323i | \(-0.971463\pi\) | ||||
0.995984 | − | 0.0895323i | \(-0.0285372\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 2.07055i | − 0.0925055i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.1833 | 1.47957 | 0.739784 | − | 0.672844i | \(-0.234928\pi\) | ||||
0.739784 | + | 0.672844i | \(0.234928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.287187 | 0.0127797 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.00000i | 0.222058i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 27.0459i | − 1.19879i | −0.800454 | − | 0.599395i | \(-0.795408\pi\) | ||||
0.800454 | − | 0.599395i | \(-0.204592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79796 | 0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.535898 | 0.0236605 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.39230i | 0.369809i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.4548i | 0.679702i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.55103 | 0.111978 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3205 | −0.583582 | −0.291791 | − | 0.956482i | \(-0.594251\pi\) | ||||
−0.291791 | + | 0.956482i | \(0.594251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.5359i | 1.07288i | 0.843938 | + | 0.536440i | \(0.180231\pi\) | ||||
−0.843938 | + | 0.536440i | \(0.819769\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.62209i | 0.419943i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4558 | 1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.8564i | 0.601317i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 48.6381i | 2.10675i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.14110 | −0.179036 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.07180 | 0.218864 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.46410i | − 0.235356i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.58682i | 0.369176i | 0.982816 | + | 0.184588i | \(0.0590951\pi\) | ||||
−0.982816 | + | 0.184588i | \(0.940905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.07107 | 0.303449 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.46410 | −0.0627152 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.1769i | 1.67508i | 0.546373 | + | 0.837542i | \(0.316008\pi\) | ||||
−0.546373 | + | 0.837542i | \(0.683992\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.14162i | 0.390155i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.18016 | 0.135479 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | 0.255146 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.46410i | 0.401729i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.7038i | 1.80942i | 0.426030 | + | 0.904709i | \(0.359912\pi\) | ||||
−0.426030 | + | 0.904709i | \(0.640088\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.6969 | 0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.9282 | 0.799149 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.46410i | 0.230284i | 0.993349 | + | 0.115142i | \(0.0367324\pi\) | ||||
−0.993349 | + | 0.115142i | \(0.963268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 18.6350i | − 0.783979i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.44949 | −0.102869 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.46410 | −0.145223 | −0.0726113 | − | 0.997360i | \(-0.523133\pi\) | ||||
−0.0726113 | + | 0.997360i | \(0.523133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.7128i | 0.992350i | 0.868222 | + | 0.496175i | \(0.165263\pi\) | ||||
−0.868222 | + | 0.496175i | \(0.834737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.07055i | 0.0864986i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.1106 | 0.463346 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.85641 | 0.243805 | 0.121903 | − | 0.992542i | \(-0.461100\pi\) | ||||
0.121903 | + | 0.992542i | \(0.461100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 6.00000i | − 0.249351i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 3.58630i | − 0.148785i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 52.0213 | 2.15450 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.39230 | 0.181599 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 29.0718i | − 1.19992i | −0.800029 | − | 0.599961i | \(-0.795183\pi\) | ||||
0.800029 | − | 0.599961i | \(-0.204817\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 3.93803i | − 0.162264i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.93426 | 0.244103 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.7128 | −0.727378 | −0.363689 | − | 0.931520i | \(-0.618483\pi\) | ||||
−0.363689 | + | 0.931520i | \(0.618483\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.78461i | 0.360134i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.96524i | − 0.162286i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.6264 | −0.515900 | −0.257950 | − | 0.966158i | \(-0.583047\pi\) | ||||
−0.257950 | + | 0.966158i | \(0.583047\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.7128 | 1.45676 | 0.728378 | − | 0.685176i | \(-0.240275\pi\) | ||||
0.728378 | + | 0.685176i | \(0.240275\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.07180i | 0.0436469i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19.5216i | 0.793665i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8434 | −1.29248 | −0.646241 | − | 0.763133i | \(-0.723660\pi\) | ||||
−0.646241 | + | 0.763133i | \(0.723660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.5359 | −0.589024 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 12.0000i | − 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.8797i | 1.73189i | 0.500136 | + | 0.865947i | \(0.333283\pi\) | ||||
−0.500136 | + | 0.865947i | \(0.666717\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.8685 | 0.478585 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1436 | 0.488883 | 0.244441 | − | 0.969664i | \(-0.421395\pi\) | ||||
0.244441 | + | 0.969664i | \(0.421395\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 12.0000i | − 0.482321i | −0.970485 | − | 0.241160i | \(-0.922472\pi\) | ||||
0.970485 | − | 0.241160i | \(-0.0775280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82843i | 0.113501i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.8695 | 0.876185 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.92820i | − 0.116941i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 31.6675i | − 1.26267i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.933740 | 0.0371716 | 0.0185858 | − | 0.999827i | \(-0.494084\pi\) | ||||
0.0185858 | + | 0.999827i | \(0.494084\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.92820 | 0.275371 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.1051i | 0.797847i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.24264i | 0.168100i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.2127 | −0.641364 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −46.3923 | −1.83239 | −0.916193 | − | 0.400737i | \(-0.868754\pi\) | ||||
−0.916193 | + | 0.400737i | \(0.868754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.4641i | 1.39857i | 0.714844 | + | 0.699284i | \(0.246498\pi\) | ||||
−0.714844 | + | 0.699284i | \(0.753502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3.58630i | − 0.141210i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.3147 | 0.837969 | 0.418984 | − | 0.907993i | \(-0.362386\pi\) | ||||
0.418984 | + | 0.907993i | \(0.362386\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 75.7128 | 2.97199 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.0000i | 0.705476i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.480473i | 0.0188024i | 0.999956 | + | 0.00940119i | \(0.00299254\pi\) | ||||
−0.999956 | + | 0.00940119i | \(0.997007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.10961 | 0.0433559 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000i | 0.934907i | 0.884018 | + | 0.467454i | \(0.154829\pi\) | ||||
−0.884018 | + | 0.467454i | \(0.845171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.9101i | 1.39674i | 0.715736 | + | 0.698371i | \(0.246092\pi\) | ||||
−0.715736 | + | 0.698371i | \(0.753908\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.6969 | −0.570782 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.35898 | 0.0526991 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.7846i | 0.649903i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 19.4201i | − 0.750823i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 49.9507 | 1.92833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.92820i | 0.151197i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.8038i | 1.06859i | 0.845299 | + | 0.534293i | \(0.179422\pi\) | ||||
−0.845299 | + | 0.534293i | \(0.820578\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.5665 | −1.40329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.3205 | 0.893644 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 37.1769i | − 1.42254i | −0.702921 | − | 0.711268i | \(-0.748121\pi\) | ||||
0.702921 | − | 0.711268i | \(-0.251879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 6.61780i | − 0.252853i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.72689 | 0.104037 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −40.3923 | −1.53882 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 5.60770i | − 0.213327i | −0.994295 | − | 0.106663i | \(-0.965983\pi\) | ||||
0.994295 | − | 0.106663i | \(-0.0340167\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.3843i | 0.508426i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.17260 | −0.272072 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −39.7128 | −1.50423 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 0.928203i | − 0.0351079i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 29.1165i | − 1.09971i | −0.835259 | − | 0.549857i | \(-0.814682\pi\) | ||||
0.835259 | − | 0.549857i | \(-0.185318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.89898 | −0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.92820 | −0.110283 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 0.679492i | − 0.0255549i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.2923i | 1.10010i | 0.835133 | + | 0.550048i | \(0.185391\pi\) | ||||
−0.835133 | + | 0.550048i | \(0.814609\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.44949 | 0.0918630 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7846 | 0.778390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 24.0000i | − 0.897549i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.07055i | − 0.0773262i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.6675 | 1.18100 | 0.590499 | − | 0.807038i | \(-0.298931\pi\) | ||||
0.590499 | + | 0.807038i | \(0.298931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.8564 | 0.739491 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 14.7846i | − 0.549846i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.3110i | 0.865747i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.20736 | −0.118955 | −0.0594773 | − | 0.998230i | \(-0.518943\pi\) | ||||
−0.0594773 | + | 0.998230i | \(0.518943\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000i | 0.443836i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 7.07107i | − 0.261176i | −0.991437 | − | 0.130588i | \(-0.958314\pi\) | ||||
0.991437 | − | 0.130588i | \(-0.0416865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.03528 | 0.0381867 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.85641 | 0.215724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 36.0000i | − 1.32428i | −0.749380 | − | 0.662141i | \(-0.769648\pi\) | ||||
0.749380 | − | 0.662141i | \(-0.230352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.27362i | 0.0835237i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.6665 | −0.794866 | −0.397433 | − | 0.917631i | \(-0.630099\pi\) | ||||
−0.397433 | + | 0.917631i | \(0.630099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.7846 | −0.761489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 1.46410i | − 0.0535687i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.79796i | 0.358010i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6937 | −0.791614 | −0.395807 | − | 0.918334i | \(-0.629535\pi\) | ||||
−0.395807 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.4641 | −0.490659 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.5359i | 0.674590i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1512i | 0.914137i | 0.889431 | + | 0.457069i | \(0.151101\pi\) | ||||
−0.889431 | + | 0.457069i | \(0.848899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.4548 | 0.560974 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.75129 | 0.135984 | 0.0679921 | − | 0.997686i | \(-0.478341\pi\) | ||||
0.0679921 | + | 0.997686i | \(0.478341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.46410i | 0.125409i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.58630i | 0.129663i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −58.7878 | −2.12270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 18.7846i | − 0.676511i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.82465i | 0.173531i | 0.996229 | + | 0.0867653i | \(0.0276530\pi\) | ||||
−0.996229 | + | 0.0867653i | \(0.972347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.8663 | 1.03691 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.3923 | 0.803319 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.14359i | 0.220117i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 88.5878i | 3.16992i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.93426 | −0.212073 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.3923 | −0.442300 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.5359i | 0.589441i | 0.955583 | + | 0.294721i | \(0.0952266\pi\) | ||||
−0.955583 | + | 0.294721i | \(0.904773\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 22.6274i | − 0.805557i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.0908 | −1.56769 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.7846 | −1.37728 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.85641i | 0.349571i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.7429i | 1.47861i | 0.673372 | + | 0.739304i | \(0.264845\pi\) | ||||
−0.673372 | + | 0.739304i | \(0.735155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.79796 | 0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.92820 | 0.315463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 21.8564i | − 0.771296i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.17260i | 0.252801i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.1774 | −0.534270 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.3205 | 1.45275 | 0.726376 | − | 0.687298i | \(-0.241203\pi\) | ||||
0.726376 | + | 0.687298i | \(0.241203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.6077i | 1.18013i | 0.807357 | + | 0.590063i | \(0.200897\pi\) | ||||
−0.807357 | + | 0.590063i | \(0.799103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 8.10634i | − 0.284302i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.8685 | −0.415736 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.85641 | 0.0649474 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 10.3923i | − 0.363137i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 39.8754i | − 1.39166i | −0.718206 | − | 0.695830i | \(-0.755037\pi\) | ||||
0.718206 | − | 0.695830i | \(-0.244963\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.9149 | −1.53078 | −0.765389 | − | 0.643567i | \(-0.777454\pi\) | ||||
−0.765389 | + | 0.643567i | \(0.777454\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21.4641 | 0.747284 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.21539i | 0.111810i | 0.998436 | + | 0.0559050i | \(0.0178044\pi\) | ||||
−0.998436 | + | 0.0559050i | \(0.982196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.8091i | 1.41736i | 0.705530 | + | 0.708680i | \(0.250709\pi\) | ||||
−0.705530 | + | 0.708680i | \(0.749291\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.6670 | −0.925067 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.46410 | −0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 2.14359i | − 0.0741821i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.34847i | 0.254000i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.38323 | 0.116802 | 0.0584010 | − | 0.998293i | \(-0.481400\pi\) | ||||
0.0584010 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.21539 | −0.214324 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 12.9282i | − 0.445271i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.17638i | 0.178073i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.1886 | 1.58706 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.8564 | −0.612830 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 25.8564i | − 0.886346i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 21.5649i | − 0.738369i | −0.929356 | − | 0.369185i | \(-0.879637\pi\) | ||||
0.929356 | − | 0.369185i | \(-0.120363\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.554803 | 0.0189739 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.1769 | 0.655071 | 0.327535 | − | 0.944839i | \(-0.393782\pi\) | ||||
0.327535 | + | 0.944839i | \(0.393782\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2487i | 0.554399i | 0.960812 | + | 0.277199i | \(0.0894063\pi\) | ||||
−0.960812 | + | 0.277199i | \(0.910594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 28.0812i | − 0.957005i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.4644 | −1.07106 | −0.535531 | − | 0.844516i | \(-0.679888\pi\) | ||||
−0.535531 | + | 0.844516i | \(0.679888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.64102 | 0.0897972 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.00000i | 0.169809i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 13.3843i | − 0.454030i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.54725 | −0.154078 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14.9282 | −0.505243 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.6410i | 0.765406i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 32.8786i | − 1.11023i | −0.831773 | − | 0.555116i | \(-0.812674\pi\) | ||||
0.831773 | − | 0.555116i | \(-0.187326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.6617 | −0.460796 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.6410 | 1.09970 | 0.549852 | − | 0.835262i | \(-0.314684\pi\) | ||||
0.549852 | + | 0.835262i | \(0.314684\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3923i | 0.888172i | 0.895984 | + | 0.444086i | \(0.146471\pi\) | ||||
−0.895984 | + | 0.444086i | \(0.853529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 14.3452i | 0.482209i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.62536 | 0.0881508 | 0.0440754 | − | 0.999028i | \(-0.485966\pi\) | ||||
0.0440754 | + | 0.999028i | \(0.485966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.5692 | 1.59542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.46410i | 0.183054i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1.51575i | − 0.0507226i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.25071 | 0.175512 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.6077i | 1.45440i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 32.9802i | − 1.09873i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.48528 | −0.282372 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.32051 | 0.243342 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 21.6077i | − 0.717472i | −0.933439 | − | 0.358736i | \(-0.883208\pi\) | ||||
0.933439 | − | 0.358736i | \(-0.116792\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 0.277401i | − 0.00920082i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.4665 | −1.70516 | −0.852580 | − | 0.522596i | \(-0.824964\pi\) | ||||
−0.852580 | + | 0.522596i | \(0.824964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.46410i | 0.312874i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.62536i | − 0.0866969i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.6728 | 1.47362 | 0.736810 | − | 0.676100i | \(-0.236331\pi\) | ||||
0.736810 | + | 0.676100i | \(0.236331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.07180 | −0.298926 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 68.7846i | − 2.26407i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 35.9101i | − 1.18072i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.10634 | 0.266247 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.6795 | −0.350383 | −0.175191 | − | 0.984534i | \(-0.556054\pi\) | ||||
−0.175191 | + | 0.984534i | \(0.556054\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.535898i | 0.0175634i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 12.8295i | − 0.420018i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959 | 0.640855 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 23.8564i | − 0.778524i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7942i | 0.384479i | 0.981348 | + | 0.192240i | \(0.0615751\pi\) | ||||
−0.981348 | + | 0.192240i | \(0.938425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.4254 | −1.05592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.53590 | −0.0824928 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 42.9282i | − 1.39498i | −0.716595 | − | 0.697490i | \(-0.754300\pi\) | ||||
0.716595 | − | 0.697490i | \(-0.245700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.9706i | 0.550888i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.79315 | −0.0581469 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25.6077 | −0.829515 | −0.414757 | − | 0.909932i | \(-0.636134\pi\) | ||||
−0.414757 | + | 0.909932i | \(0.636134\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.14359i | 0.0693651i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.4254i | 1.04816i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.6579 | −0.505619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 6.21166i | − 0.199960i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.8749 | −1.12150 | −0.560750 | − | 0.827985i | \(-0.689487\pi\) | ||||
−0.560750 | + | 0.827985i | \(0.689487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.85641 | −0.0596364 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 26.2487i | − 0.842361i | −0.906977 | − | 0.421181i | \(-0.861616\pi\) | ||||
0.906977 | − | 0.421181i | \(-0.138384\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9706i | 0.544051i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −16.6660 | −0.533738 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.1769 | 0.869467 | 0.434733 | − | 0.900559i | \(-0.356843\pi\) | ||||
0.434733 | + | 0.900559i | \(0.356843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 48.7846i | − 1.55916i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.41421i | 0.0451524i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.0507 | 1.11794 | 0.558972 | − | 0.829186i | \(-0.311196\pi\) | ||||
0.558972 | + | 0.829186i | \(0.311196\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.14359 | 0.195751 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.92820i | 0.220527i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.79796i | 0.311557i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.2474 | 0.389053 | 0.194527 | − | 0.980897i | \(-0.437683\pi\) | ||||
0.194527 | + | 0.980897i | \(0.437683\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.9282 | 0.473732 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 4.10512i | − 0.130141i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.82894i | 0.247945i | 0.992286 | + | 0.123973i | \(0.0395635\pi\) | ||||
−0.992286 | + | 0.123973i | \(0.960437\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.14162 | 0.289228 |
(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 | 3072.2.d.h.1537.2 | 8 | ||
4.3 | odd | 2 | inner | 3072.2.d.h.1537.6 | 8 | ||
8.3 | odd | 2 | inner | 3072.2.d.h.1537.3 | 8 | ||
8.5 | even | 2 | inner | 3072.2.d.h.1537.7 | 8 | ||
16.3 | odd | 4 | 3072.2.a.l.1.2 | 4 | |||
16.5 | even | 4 | 3072.2.a.l.1.3 | 4 | |||
16.11 | odd | 4 | 3072.2.a.r.1.3 | 4 | |||
16.13 | even | 4 | 3072.2.a.r.1.2 | 4 | |||
32.3 | odd | 8 | 768.2.j.e.193.2 | ✓ | 8 | ||
32.5 | even | 8 | 768.2.j.e.577.4 | yes | 8 | ||
32.11 | odd | 8 | 768.2.j.f.577.3 | yes | 8 | ||
32.13 | even | 8 | 768.2.j.f.193.1 | yes | 8 | ||
32.19 | odd | 8 | 768.2.j.f.193.3 | yes | 8 | ||
32.21 | even | 8 | 768.2.j.f.577.1 | yes | 8 | ||
32.27 | odd | 8 | 768.2.j.e.577.2 | yes | 8 | ||
32.29 | even | 8 | 768.2.j.e.193.4 | yes | 8 | ||
48.5 | odd | 4 | 9216.2.a.bi.1.2 | 4 | |||
48.11 | even | 4 | 9216.2.a.bc.1.2 | 4 | |||
48.29 | odd | 4 | 9216.2.a.bc.1.3 | 4 | |||
48.35 | even | 4 | 9216.2.a.bi.1.3 | 4 | |||
96.5 | odd | 8 | 2304.2.k.l.577.1 | 8 | |||
96.11 | even | 8 | 2304.2.k.e.577.4 | 8 | |||
96.29 | odd | 8 | 2304.2.k.l.1729.2 | 8 | |||
96.35 | even | 8 | 2304.2.k.l.1729.1 | 8 | |||
96.53 | odd | 8 | 2304.2.k.e.577.3 | 8 | |||
96.59 | even | 8 | 2304.2.k.l.577.2 | 8 | |||
96.77 | odd | 8 | 2304.2.k.e.1729.4 | 8 | |||
96.83 | even | 8 | 2304.2.k.e.1729.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.2 | ✓ | 8 | 32.3 | odd | 8 | ||
768.2.j.e.193.4 | yes | 8 | 32.29 | even | 8 | ||
768.2.j.e.577.2 | yes | 8 | 32.27 | odd | 8 | ||
768.2.j.e.577.4 | yes | 8 | 32.5 | even | 8 | ||
768.2.j.f.193.1 | yes | 8 | 32.13 | even | 8 | ||
768.2.j.f.193.3 | yes | 8 | 32.19 | odd | 8 | ||
768.2.j.f.577.1 | yes | 8 | 32.21 | even | 8 | ||
768.2.j.f.577.3 | yes | 8 | 32.11 | odd | 8 | ||
2304.2.k.e.577.3 | 8 | 96.53 | odd | 8 | |||
2304.2.k.e.577.4 | 8 | 96.11 | even | 8 | |||
2304.2.k.e.1729.3 | 8 | 96.83 | even | 8 | |||
2304.2.k.e.1729.4 | 8 | 96.77 | odd | 8 | |||
2304.2.k.l.577.1 | 8 | 96.5 | odd | 8 | |||
2304.2.k.l.577.2 | 8 | 96.59 | even | 8 | |||
2304.2.k.l.1729.1 | 8 | 96.35 | even | 8 | |||
2304.2.k.l.1729.2 | 8 | 96.29 | odd | 8 | |||
3072.2.a.l.1.2 | 4 | 16.3 | odd | 4 | |||
3072.2.a.l.1.3 | 4 | 16.5 | even | 4 | |||
3072.2.a.r.1.2 | 4 | 16.13 | even | 4 | |||
3072.2.a.r.1.3 | 4 | 16.11 | odd | 4 | |||
3072.2.d.h.1537.2 | 8 | 1.1 | even | 1 | trivial | ||
3072.2.d.h.1537.3 | 8 | 8.3 | odd | 2 | inner | ||
3072.2.d.h.1537.6 | 8 | 4.3 | odd | 2 | inner | ||
3072.2.d.h.1537.7 | 8 | 8.5 | even | 2 | inner | ||
9216.2.a.bc.1.2 | 4 | 48.11 | even | 4 | |||
9216.2.a.bc.1.3 | 4 | 48.29 | odd | 4 | |||
9216.2.a.bi.1.2 | 4 | 48.5 | odd | 4 | |||
9216.2.a.bi.1.3 | 4 | 48.35 | even | 4 |