Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5 x^{13} - 9 x^{12} + 76 x^{11} - 12 x^{10} - 414 x^{9} + 331 x^{8} + 959 x^{7} - 1067 x^{6} - 875 x^{5} + 1134 x^{4} + 301 x^{3} - 418 x^{2} - 42 x + 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 2667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.477041\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.477041 | −0.337319 | −0.168660 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168660 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.77243 | −0.886216 | ||||||||
\(5\) | 1.98652 | 0.888398 | 0.444199 | − | 0.895928i | \(-0.353488\pi\) | ||||
0.444199 | + | 0.895928i | \(0.353488\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.79961 | 0.636257 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.947652 | −0.299674 | ||||||||
\(11\) | 0.129110 | 0.0389283 | 0.0194641 | − | 0.999811i | \(-0.493804\pi\) | ||||
0.0194641 | + | 0.999811i | \(0.493804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.16963 | 1.43380 | 0.716898 | − | 0.697178i | \(-0.245561\pi\) | ||||
0.716898 | + | 0.697178i | \(0.245561\pi\) | |||||||
\(14\) | 0.477041 | 0.127495 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.68638 | 0.671594 | ||||||||
\(17\) | 2.68090 | 0.650213 | 0.325106 | − | 0.945677i | \(-0.394600\pi\) | ||||
0.325106 | + | 0.945677i | \(0.394600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.39995 | 1.00942 | 0.504709 | − | 0.863289i | \(-0.331600\pi\) | ||||
0.504709 | + | 0.863289i | \(0.331600\pi\) | |||||||
\(20\) | −3.52097 | −0.787313 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0615910 | −0.0131312 | ||||||||
\(23\) | 2.43926 | 0.508621 | 0.254310 | − | 0.967123i | \(-0.418151\pi\) | ||||
0.254310 | + | 0.967123i | \(0.418151\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.05374 | −0.210748 | ||||||||
\(26\) | −2.46613 | −0.483647 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.77243 | 0.334958 | ||||||||
\(29\) | −5.32140 | −0.988158 | −0.494079 | − | 0.869417i | \(-0.664495\pi\) | ||||
−0.494079 | + | 0.869417i | \(0.664495\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.06047 | 0.370071 | 0.185036 | − | 0.982732i | \(-0.440760\pi\) | ||||
0.185036 | + | 0.982732i | \(0.440760\pi\) | |||||||
\(32\) | −4.88072 | −0.862798 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.27890 | −0.219329 | ||||||||
\(35\) | −1.98652 | −0.335783 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.29275 | 0.376925 | 0.188463 | − | 0.982080i | \(-0.439650\pi\) | ||||
0.188463 | + | 0.982080i | \(0.439650\pi\) | |||||||
\(38\) | −2.09896 | −0.340496 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.57495 | 0.565249 | ||||||||
\(41\) | 3.69549 | 0.577139 | 0.288570 | − | 0.957459i | \(-0.406820\pi\) | ||||
0.288570 | + | 0.957459i | \(0.406820\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.38263 | 0.973342 | 0.486671 | − | 0.873585i | \(-0.338211\pi\) | ||||
0.486671 | + | 0.873585i | \(0.338211\pi\) | |||||||
\(44\) | −0.228839 | −0.0344988 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.16363 | −0.171568 | ||||||||
\(47\) | 11.8866 | 1.73384 | 0.866918 | − | 0.498451i | \(-0.166098\pi\) | ||||
0.866918 | + | 0.498451i | \(0.166098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.502678 | 0.0710894 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.16281 | −1.27065 | ||||||||
\(53\) | 7.84774 | 1.07797 | 0.538985 | − | 0.842316i | \(-0.318808\pi\) | ||||
0.538985 | + | 0.842316i | \(0.318808\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.256480 | 0.0345838 | ||||||||
\(56\) | −1.79961 | −0.240482 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.53853 | 0.333325 | ||||||||
\(59\) | −8.58540 | −1.11772 | −0.558862 | − | 0.829261i | \(-0.688762\pi\) | ||||
−0.558862 | + | 0.829261i | \(0.688762\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.08167 | 0.394567 | 0.197284 | − | 0.980346i | \(-0.436788\pi\) | ||||
0.197284 | + | 0.980346i | \(0.436788\pi\) | |||||||
\(62\) | −0.982930 | −0.124832 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.04445 | −0.380556 | ||||||||
\(65\) | 10.2696 | 1.27378 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.38959 | −0.658444 | −0.329222 | − | 0.944253i | \(-0.606786\pi\) | ||||
−0.329222 | + | 0.944253i | \(0.606786\pi\) | |||||||
\(68\) | −4.75171 | −0.576229 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.947652 | 0.113266 | ||||||||
\(71\) | −0.409103 | −0.0485516 | −0.0242758 | − | 0.999705i | \(-0.507728\pi\) | ||||
−0.0242758 | + | 0.999705i | \(0.507728\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.61874 | −1.12579 | −0.562894 | − | 0.826529i | \(-0.690312\pi\) | ||||
−0.562894 | + | 0.826529i | \(0.690312\pi\) | |||||||
\(74\) | −1.09373 | −0.127144 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.79862 | −0.894563 | ||||||||
\(77\) | −0.129110 | −0.0147135 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.71224 | 0.530168 | 0.265084 | − | 0.964225i | \(-0.414600\pi\) | ||||
0.265084 | + | 0.964225i | \(0.414600\pi\) | |||||||
\(80\) | 5.33654 | 0.596643 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.76290 | −0.194680 | ||||||||
\(83\) | 7.35722 | 0.807560 | 0.403780 | − | 0.914856i | \(-0.367696\pi\) | ||||
0.403780 | + | 0.914856i | \(0.367696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.32565 | 0.577648 | ||||||||
\(86\) | −3.04478 | −0.328327 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.232348 | 0.0247684 | ||||||||
\(89\) | −0.833032 | −0.0883013 | −0.0441506 | − | 0.999025i | \(-0.514058\pi\) | ||||
−0.0441506 | + | 0.999025i | \(0.514058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.16963 | −0.541924 | ||||||||
\(92\) | −4.32342 | −0.450748 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.67039 | −0.584856 | ||||||||
\(95\) | 8.74059 | 0.896766 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.28385 | 0.231890 | 0.115945 | − | 0.993256i | \(-0.463010\pi\) | ||||
0.115945 | + | 0.993256i | \(0.463010\pi\) | |||||||
\(98\) | −0.477041 | −0.0481885 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.86768 | 0.186768 | ||||||||
\(101\) | 4.38532 | 0.436356 | 0.218178 | − | 0.975909i | \(-0.429989\pi\) | ||||
0.218178 | + | 0.975909i | \(0.429989\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.21117 | −0.612005 | −0.306003 | − | 0.952031i | \(-0.598992\pi\) | ||||
−0.306003 | + | 0.952031i | \(0.598992\pi\) | |||||||
\(104\) | 9.30329 | 0.912263 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.74369 | −0.363620 | ||||||||
\(107\) | 7.71277 | 0.745621 | 0.372811 | − | 0.927907i | \(-0.378394\pi\) | ||||
0.372811 | + | 0.927907i | \(0.378394\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.1046 | −1.82989 | −0.914943 | − | 0.403582i | \(-0.867765\pi\) | ||||
−0.914943 | + | 0.403582i | \(0.867765\pi\) | |||||||
\(110\) | −0.122352 | −0.0116658 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.68638 | −0.253839 | ||||||||
\(113\) | 9.12949 | 0.858830 | 0.429415 | − | 0.903107i | \(-0.358720\pi\) | ||||
0.429415 | + | 0.903107i | \(0.358720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.84564 | 0.451858 | ||||||||
\(116\) | 9.43181 | 0.875722 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.09559 | 0.377029 | ||||||||
\(119\) | −2.68090 | −0.245757 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9833 | −0.998485 | ||||||||
\(122\) | −1.47008 | −0.133095 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.65204 | −0.327963 | ||||||||
\(125\) | −12.0259 | −1.07563 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 11.2138 | 0.991167 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.89901 | −0.429671 | ||||||||
\(131\) | −6.03668 | −0.527428 | −0.263714 | − | 0.964601i | \(-0.584947\pi\) | ||||
−0.263714 | + | 0.964601i | \(0.584947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.39995 | −0.381524 | ||||||||
\(134\) | 2.57106 | 0.222106 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.82456 | 0.413702 | ||||||||
\(137\) | 5.11663 | 0.437143 | 0.218572 | − | 0.975821i | \(-0.429860\pi\) | ||||
0.218572 | + | 0.975821i | \(0.429860\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1869 | −0.864038 | −0.432019 | − | 0.901865i | \(-0.642199\pi\) | ||||
−0.432019 | + | 0.901865i | \(0.642199\pi\) | |||||||
\(140\) | 3.52097 | 0.297576 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.195159 | 0.0163774 | ||||||||
\(143\) | 0.667453 | 0.0558152 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.5711 | −0.877878 | ||||||||
\(146\) | 4.58853 | 0.379750 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.06374 | −0.334037 | ||||||||
\(149\) | −12.4575 | −1.02056 | −0.510278 | − | 0.860009i | \(-0.670458\pi\) | ||||
−0.510278 | + | 0.860009i | \(0.670458\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.2748 | −1.08029 | −0.540145 | − | 0.841572i | \(-0.681630\pi\) | ||||
−0.540145 | + | 0.841572i | \(0.681630\pi\) | |||||||
\(152\) | 7.91818 | 0.642249 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.0615910 | 0.00496315 | ||||||||
\(155\) | 4.09316 | 0.328771 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.59894 | −0.526653 | −0.263326 | − | 0.964707i | \(-0.584820\pi\) | ||||
−0.263326 | + | 0.964707i | \(0.584820\pi\) | |||||||
\(158\) | −2.24793 | −0.178836 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.69565 | −0.766509 | ||||||||
\(161\) | −2.43926 | −0.192241 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.5374 | 1.06033 | 0.530166 | − | 0.847894i | \(-0.322130\pi\) | ||||
0.530166 | + | 0.847894i | \(0.322130\pi\) | |||||||
\(164\) | −6.55001 | −0.511470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.50970 | −0.272405 | ||||||||
\(167\) | −16.6771 | −1.29051 | −0.645256 | − | 0.763966i | \(-0.723249\pi\) | ||||
−0.645256 | + | 0.763966i | \(0.723249\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.7250 | 1.05577 | ||||||||
\(170\) | −2.54056 | −0.194852 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.3128 | −0.862591 | ||||||||
\(173\) | 0.0899016 | 0.00683509 | 0.00341754 | − | 0.999994i | \(-0.498912\pi\) | ||||
0.00341754 | + | 0.999994i | \(0.498912\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.05374 | 0.0796553 | ||||||||
\(176\) | 0.346839 | 0.0261440 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.397391 | 0.0297857 | ||||||||
\(179\) | −2.08901 | −0.156140 | −0.0780698 | − | 0.996948i | \(-0.524876\pi\) | ||||
−0.0780698 | + | 0.996948i | \(0.524876\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.62613 | 0.715505 | 0.357752 | − | 0.933817i | \(-0.383543\pi\) | ||||
0.357752 | + | 0.933817i | \(0.383543\pi\) | |||||||
\(182\) | 2.46613 | 0.182801 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.38971 | 0.323613 | ||||||||
\(185\) | 4.55459 | 0.334860 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.346132 | 0.0253117 | ||||||||
\(188\) | −21.0681 | −1.53655 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.16962 | −0.302496 | ||||||||
\(191\) | 8.89822 | 0.643853 | 0.321926 | − | 0.946765i | \(-0.395670\pi\) | ||||
0.321926 | + | 0.946765i | \(0.395670\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.73789 | −0.485004 | −0.242502 | − | 0.970151i | \(-0.577968\pi\) | ||||
−0.242502 | + | 0.970151i | \(0.577968\pi\) | |||||||
\(194\) | −1.08949 | −0.0782209 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.77243 | −0.126602 | ||||||||
\(197\) | 18.1025 | 1.28975 | 0.644874 | − | 0.764289i | \(-0.276910\pi\) | ||||
0.644874 | + | 0.764289i | \(0.276910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.6429 | 1.32156 | 0.660778 | − | 0.750581i | \(-0.270226\pi\) | ||||
0.660778 | + | 0.750581i | \(0.270226\pi\) | |||||||
\(200\) | −1.89632 | −0.134090 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.09198 | −0.147191 | ||||||||
\(203\) | 5.32140 | 0.373489 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.34117 | 0.512729 | ||||||||
\(206\) | 2.96299 | 0.206441 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.8876 | 0.962929 | ||||||||
\(209\) | 0.568080 | 0.0392949 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.51918 | −0.448799 | −0.224399 | − | 0.974497i | \(-0.572042\pi\) | ||||
−0.224399 | + | 0.974497i | \(0.572042\pi\) | |||||||
\(212\) | −13.9096 | −0.955313 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.67931 | −0.251512 | ||||||||
\(215\) | 12.6792 | 0.864716 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.06047 | −0.139874 | ||||||||
\(218\) | 9.11367 | 0.617256 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.454594 | −0.0306487 | ||||||||
\(221\) | 13.8592 | 0.932273 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.81814 | −0.188717 | −0.0943584 | − | 0.995538i | \(-0.530080\pi\) | ||||
−0.0943584 | + | 0.995538i | \(0.530080\pi\) | |||||||
\(224\) | 4.88072 | 0.326107 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.35514 | −0.289700 | ||||||||
\(227\) | −2.68150 | −0.177977 | −0.0889887 | − | 0.996033i | \(-0.528363\pi\) | ||||
−0.0889887 | + | 0.996033i | \(0.528363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6506 | −1.23246 | −0.616232 | − | 0.787565i | \(-0.711341\pi\) | ||||
−0.616232 | + | 0.787565i | \(0.711341\pi\) | |||||||
\(230\) | −2.31157 | −0.152420 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.57642 | −0.628722 | ||||||||
\(233\) | 20.0572 | 1.31399 | 0.656994 | − | 0.753895i | \(-0.271827\pi\) | ||||
0.656994 | + | 0.753895i | \(0.271827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.6129 | 1.54034 | ||||||||
\(236\) | 15.2170 | 0.990544 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.27890 | 0.0828987 | ||||||||
\(239\) | 11.2371 | 0.726865 | 0.363432 | − | 0.931621i | \(-0.381605\pi\) | ||||
0.363432 | + | 0.931621i | \(0.381605\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.6209 | 1.45714 | 0.728572 | − | 0.684970i | \(-0.240185\pi\) | ||||
0.728572 | + | 0.684970i | \(0.240185\pi\) | |||||||
\(242\) | 5.23950 | 0.336808 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.46205 | −0.349672 | ||||||||
\(245\) | 1.98652 | 0.126914 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.7461 | 1.44730 | ||||||||
\(248\) | 3.70803 | 0.235460 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.73684 | 0.362830 | ||||||||
\(251\) | −16.1825 | −1.02143 | −0.510717 | − | 0.859749i | \(-0.670620\pi\) | ||||
−0.510717 | + | 0.859749i | \(0.670620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.314934 | 0.0197997 | ||||||||
\(254\) | 0.477041 | 0.0299322 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.739459 | 0.0462162 | ||||||||
\(257\) | −18.2153 | −1.13624 | −0.568119 | − | 0.822947i | \(-0.692329\pi\) | ||||
−0.568119 | + | 0.822947i | \(0.692329\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.29275 | −0.142464 | ||||||||
\(260\) | −18.2021 | −1.12885 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.87975 | 0.177911 | ||||||||
\(263\) | 27.6166 | 1.70291 | 0.851457 | − | 0.524425i | \(-0.175720\pi\) | ||||
0.851457 | + | 0.524425i | \(0.175720\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.5897 | 0.957666 | ||||||||
\(266\) | 2.09896 | 0.128695 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.55269 | 0.583523 | ||||||||
\(269\) | 1.60396 | 0.0977951 | 0.0488975 | − | 0.998804i | \(-0.484429\pi\) | ||||
0.0488975 | + | 0.998804i | \(0.484429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.86194 | 0.416833 | 0.208417 | − | 0.978040i | \(-0.433169\pi\) | ||||
0.208417 | + | 0.978040i | \(0.433169\pi\) | |||||||
\(272\) | 7.20190 | 0.436679 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.44084 | −0.147457 | ||||||||
\(275\) | −0.136049 | −0.00820406 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.6146 | 0.697854 | 0.348927 | − | 0.937150i | \(-0.386546\pi\) | ||||
0.348927 | + | 0.937150i | \(0.386546\pi\) | |||||||
\(278\) | 4.85955 | 0.291456 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.57495 | −0.213644 | ||||||||
\(281\) | 22.9259 | 1.36764 | 0.683821 | − | 0.729650i | \(-0.260317\pi\) | ||||
0.683821 | + | 0.729650i | \(0.260317\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.19161 | −0.130277 | −0.0651387 | − | 0.997876i | \(-0.520749\pi\) | ||||
−0.0651387 | + | 0.997876i | \(0.520749\pi\) | |||||||
\(284\) | 0.725107 | 0.0430272 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.318403 | −0.0188275 | ||||||||
\(287\) | −3.69549 | −0.218138 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.81279 | −0.577223 | ||||||||
\(290\) | 5.04283 | 0.296125 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.0486 | 0.997691 | ||||||||
\(293\) | −11.8079 | −0.689826 | −0.344913 | − | 0.938635i | \(-0.612092\pi\) | ||||
−0.344913 | + | 0.938635i | \(0.612092\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.0551 | −0.992984 | ||||||||
\(296\) | 4.12604 | 0.239821 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.94274 | 0.344253 | ||||||||
\(299\) | 12.6101 | 0.729259 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.38263 | −0.367889 | ||||||||
\(302\) | 6.33264 | 0.364402 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.8199 | 0.677920 | ||||||||
\(305\) | 6.12180 | 0.350533 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2456 | 1.49791 | 0.748957 | − | 0.662619i | \(-0.230555\pi\) | ||||
0.748957 | + | 0.662619i | \(0.230555\pi\) | |||||||
\(308\) | 0.228839 | 0.0130393 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.95261 | −0.110901 | ||||||||
\(311\) | 7.30728 | 0.414358 | 0.207179 | − | 0.978303i | \(-0.433572\pi\) | ||||
0.207179 | + | 0.978303i | \(0.433572\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.1419 | −0.629778 | −0.314889 | − | 0.949128i | \(-0.601967\pi\) | ||||
−0.314889 | + | 0.949128i | \(0.601967\pi\) | |||||||
\(314\) | 3.14797 | 0.177650 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.35212 | −0.469843 | ||||||||
\(317\) | 10.9722 | 0.616257 | 0.308129 | − | 0.951345i | \(-0.400297\pi\) | ||||
0.308129 | + | 0.951345i | \(0.400297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.687048 | −0.0384673 | ||||||||
\(320\) | −6.04785 | −0.338085 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.16363 | 0.0648464 | ||||||||
\(323\) | 11.7958 | 0.656337 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.44745 | −0.302170 | ||||||||
\(326\) | −6.45791 | −0.357670 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.65043 | 0.367209 | ||||||||
\(329\) | −11.8866 | −0.655328 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.64958 | −0.310529 | −0.155264 | − | 0.987873i | \(-0.549623\pi\) | ||||
−0.155264 | + | 0.987873i | \(0.549623\pi\) | |||||||
\(332\) | −13.0402 | −0.715672 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.95566 | 0.435314 | ||||||||
\(335\) | −10.7065 | −0.584960 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.559535 | −0.0304798 | −0.0152399 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152399 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(338\) | −6.54741 | −0.356132 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.43936 | −0.511921 | ||||||||
\(341\) | 0.266028 | 0.0144062 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.4862 | 0.619295 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0428868 | −0.00230561 | ||||||||
\(347\) | −2.34374 | −0.125819 | −0.0629094 | − | 0.998019i | \(-0.520038\pi\) | ||||
−0.0629094 | + | 0.998019i | \(0.520038\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.675167 | −0.0361409 | −0.0180704 | − | 0.999837i | \(-0.505752\pi\) | ||||
−0.0180704 | + | 0.999837i | \(0.505752\pi\) | |||||||
\(350\) | −0.502678 | −0.0268693 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.630152 | −0.0335872 | ||||||||
\(353\) | 21.4329 | 1.14076 | 0.570379 | − | 0.821381i | \(-0.306796\pi\) | ||||
0.570379 | + | 0.821381i | \(0.306796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.812691 | −0.0431332 | ||||||||
\(356\) | 1.47649 | 0.0782540 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.996542 | 0.0526689 | ||||||||
\(359\) | 3.26825 | 0.172492 | 0.0862459 | − | 0.996274i | \(-0.472513\pi\) | ||||
0.0862459 | + | 0.996274i | \(0.472513\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.359596 | 0.0189261 | ||||||||
\(362\) | −4.59206 | −0.241353 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.16281 | 0.480262 | ||||||||
\(365\) | −19.1078 | −1.00015 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.41540 | −0.387081 | −0.193540 | − | 0.981092i | \(-0.561997\pi\) | ||||
−0.193540 | + | 0.981092i | \(0.561997\pi\) | |||||||
\(368\) | 6.55277 | 0.341587 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.17273 | −0.112955 | ||||||||
\(371\) | −7.84774 | −0.407434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.75369 | 0.194358 | 0.0971792 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971792 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(374\) | −0.165119 | −0.00853811 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.3912 | 1.10316 | ||||||||
\(377\) | −27.5096 | −1.41682 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.35309 | −0.274970 | −0.137485 | − | 0.990504i | \(-0.543902\pi\) | ||||
−0.137485 | + | 0.990504i | \(0.543902\pi\) | |||||||
\(380\) | −15.4921 | −0.794728 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.24482 | −0.217184 | ||||||||
\(383\) | 9.90859 | 0.506305 | 0.253153 | − | 0.967426i | \(-0.418533\pi\) | ||||
0.253153 | + | 0.967426i | \(0.418533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.256480 | −0.0130714 | ||||||||
\(386\) | 3.21425 | 0.163601 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.04797 | −0.205505 | ||||||||
\(389\) | −26.0393 | −1.32025 | −0.660123 | − | 0.751157i | \(-0.729496\pi\) | ||||
−0.660123 | + | 0.751157i | \(0.729496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.53940 | 0.330712 | ||||||||
\(392\) | 1.79961 | 0.0908938 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.63562 | −0.435056 | ||||||||
\(395\) | 9.36095 | 0.471000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.39700 | 0.471622 | 0.235811 | − | 0.971799i | \(-0.424225\pi\) | ||||
0.235811 | + | 0.971799i | \(0.424225\pi\) | |||||||
\(398\) | −8.89341 | −0.445786 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.83075 | −0.141537 | ||||||||
\(401\) | 14.1417 | 0.706204 | 0.353102 | − | 0.935585i | \(-0.385127\pi\) | ||||
0.353102 | + | 0.935585i | \(0.385127\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.6519 | 0.530607 | ||||||||
\(404\) | −7.77269 | −0.386706 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.53853 | −0.125985 | ||||||||
\(407\) | 0.296018 | 0.0146730 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.11432 | −0.351781 | −0.175890 | − | 0.984410i | \(-0.556280\pi\) | ||||
−0.175890 | + | 0.984410i | \(0.556280\pi\) | |||||||
\(410\) | −3.50204 | −0.172953 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.0089 | 0.542369 | ||||||||
\(413\) | 8.58540 | 0.422460 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.6153 | 0.717435 | ||||||||
\(416\) | −25.2315 | −1.23708 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.270998 | −0.0132549 | ||||||||
\(419\) | 22.3886 | 1.09376 | 0.546879 | − | 0.837212i | \(-0.315816\pi\) | ||||
0.546879 | + | 0.837212i | \(0.315816\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.5919 | −1.68591 | −0.842954 | − | 0.537986i | \(-0.819186\pi\) | ||||
−0.842954 | + | 0.537986i | \(0.819186\pi\) | |||||||
\(422\) | 3.10992 | 0.151388 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 14.1228 | 0.685865 | ||||||||
\(425\) | −2.82497 | −0.137031 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.08167 | −0.149132 | ||||||||
\(428\) | −13.6704 | −0.660781 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.04851 | −0.291685 | ||||||||
\(431\) | −14.9139 | −0.718376 | −0.359188 | − | 0.933265i | \(-0.616946\pi\) | ||||
−0.359188 | + | 0.933265i | \(0.616946\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.1174 | −0.630381 | −0.315190 | − | 0.949028i | \(-0.602068\pi\) | ||||
−0.315190 | + | 0.949028i | \(0.602068\pi\) | |||||||
\(434\) | 0.982930 | 0.0471821 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.8616 | 1.62167 | ||||||||
\(437\) | 10.7326 | 0.513411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3284 | −0.731584 | −0.365792 | − | 0.930697i | \(-0.619202\pi\) | ||||
−0.365792 | + | 0.930697i | \(0.619202\pi\) | |||||||
\(440\) | 0.461564 | 0.0220042 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.61143 | −0.314474 | ||||||||
\(443\) | 30.4768 | 1.44800 | 0.723999 | − | 0.689801i | \(-0.242302\pi\) | ||||
0.723999 | + | 0.689801i | \(0.242302\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.65483 | −0.0784467 | ||||||||
\(446\) | 1.34437 | 0.0636578 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.04445 | 0.143837 | ||||||||
\(449\) | −13.9932 | −0.660382 | −0.330191 | − | 0.943914i | \(-0.607113\pi\) | ||||
−0.330191 | + | 0.943914i | \(0.607113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.477127 | 0.0224670 | ||||||||
\(452\) | −16.1814 | −0.761109 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.27919 | 0.0600352 | ||||||||
\(455\) | −10.2696 | −0.481445 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.6734 | 1.62196 | 0.810978 | − | 0.585077i | \(-0.198936\pi\) | ||||
0.810978 | + | 0.585077i | \(0.198936\pi\) | |||||||
\(458\) | 8.89708 | 0.415733 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.58856 | −0.400444 | ||||||||
\(461\) | 36.2406 | 1.68789 | 0.843945 | − | 0.536429i | \(-0.180227\pi\) | ||||
0.843945 | + | 0.536429i | \(0.180227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1365 | 1.02877 | 0.514385 | − | 0.857559i | \(-0.328020\pi\) | ||||
0.514385 | + | 0.857559i | \(0.328020\pi\) | |||||||
\(464\) | −14.2953 | −0.663642 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.56810 | −0.443234 | ||||||||
\(467\) | 2.49566 | 0.115486 | 0.0577428 | − | 0.998331i | \(-0.481610\pi\) | ||||
0.0577428 | + | 0.998331i | \(0.481610\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.38959 | 0.248868 | ||||||||
\(470\) | −11.2643 | −0.519585 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.4503 | −0.711159 | ||||||||
\(473\) | 0.824064 | 0.0378905 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.63641 | −0.212733 | ||||||||
\(476\) | 4.75171 | 0.217794 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.36054 | −0.245185 | ||||||||
\(479\) | 15.8007 | 0.721952 | 0.360976 | − | 0.932575i | \(-0.382444\pi\) | ||||
0.360976 | + | 0.932575i | \(0.382444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.8526 | 0.540434 | ||||||||
\(482\) | −10.7911 | −0.491522 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.4672 | 0.884873 | ||||||||
\(485\) | 4.53692 | 0.206011 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.2573 | −1.37109 | −0.685545 | − | 0.728030i | \(-0.740436\pi\) | ||||
−0.685545 | + | 0.728030i | \(0.740436\pi\) | |||||||
\(488\) | 5.54579 | 0.251046 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.947652 | −0.0428105 | ||||||||
\(491\) | −5.79434 | −0.261495 | −0.130747 | − | 0.991416i | \(-0.541738\pi\) | ||||
−0.130747 | + | 0.991416i | \(0.541738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2661 | −0.642513 | ||||||||
\(494\) | −10.8508 | −0.488202 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.53520 | 0.248538 | ||||||||
\(497\) | 0.409103 | 0.0183508 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.3151 | 1.49139 | 0.745695 | − | 0.666288i | \(-0.232118\pi\) | ||||
0.745695 | + | 0.666288i | \(0.232118\pi\) | |||||||
\(500\) | 21.3150 | 0.953237 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.71974 | 0.344549 | ||||||||
\(503\) | −26.8954 | −1.19920 | −0.599602 | − | 0.800298i | \(-0.704675\pi\) | ||||
−0.599602 | + | 0.800298i | \(0.704675\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.71153 | 0.387658 | ||||||||
\(506\) | −0.150237 | −0.00667883 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.77243 | 0.0786389 | ||||||||
\(509\) | −10.0142 | −0.443874 | −0.221937 | − | 0.975061i | \(-0.571238\pi\) | ||||
−0.221937 | + | 0.975061i | \(0.571238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.61874 | 0.425508 | ||||||||
\(512\) | −22.7803 | −1.00676 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.68944 | 0.383275 | ||||||||
\(515\) | −12.3386 | −0.543704 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.53468 | 0.0674952 | ||||||||
\(518\) | 1.09373 | 0.0480560 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.4812 | 0.810453 | ||||||||
\(521\) | 33.9433 | 1.48708 | 0.743541 | − | 0.668690i | \(-0.233145\pi\) | ||||
0.743541 | + | 0.668690i | \(0.233145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.8700 | 1.17494 | 0.587471 | − | 0.809246i | \(-0.300124\pi\) | ||||
0.587471 | + | 0.809246i | \(0.300124\pi\) | |||||||
\(524\) | 10.6996 | 0.467415 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.1743 | −0.574425 | ||||||||
\(527\) | 5.52391 | 0.240625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.0500 | −0.741305 | ||||||||
\(530\) | −7.43692 | −0.323039 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.79862 | 0.338113 | ||||||||
\(533\) | 19.1043 | 0.827500 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.3216 | 0.662409 | ||||||||
\(536\) | −9.69914 | −0.418939 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.765154 | −0.0329881 | ||||||||
\(539\) | 0.129110 | 0.00556118 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.8389 | 1.58383 | 0.791914 | − | 0.610632i | \(-0.209085\pi\) | ||||
0.791914 | + | 0.610632i | \(0.209085\pi\) | |||||||
\(542\) | −3.27343 | −0.140606 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.0847 | −0.561003 | ||||||||
\(545\) | −37.9516 | −1.62567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.1644 | −1.76006 | −0.880031 | − | 0.474917i | \(-0.842478\pi\) | ||||
−0.880031 | + | 0.474917i | \(0.842478\pi\) | |||||||
\(548\) | −9.06888 | −0.387403 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0649010 | 0.00276739 | ||||||||
\(551\) | −23.4139 | −0.997466 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.71224 | −0.200385 | ||||||||
\(554\) | −5.54065 | −0.235399 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.0555 | 0.765724 | ||||||||
\(557\) | 41.8639 | 1.77383 | 0.886915 | − | 0.461933i | \(-0.152844\pi\) | ||||
0.886915 | + | 0.461933i | \(0.152844\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.9958 | 1.39557 | ||||||||
\(560\) | −5.33654 | −0.225510 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.9366 | −0.461332 | ||||||||
\(563\) | 11.9735 | 0.504624 | 0.252312 | − | 0.967646i | \(-0.418809\pi\) | ||||
0.252312 | + | 0.967646i | \(0.418809\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.1359 | 0.762983 | ||||||||
\(566\) | 1.04549 | 0.0439451 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.736224 | −0.0308913 | ||||||||
\(569\) | −15.6036 | −0.654138 | −0.327069 | − | 0.945001i | \(-0.606061\pi\) | ||||
−0.327069 | + | 0.945001i | \(0.606061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.18440 | 0.216960 | 0.108480 | − | 0.994099i | \(-0.465402\pi\) | ||||
0.108480 | + | 0.994099i | \(0.465402\pi\) | |||||||
\(572\) | −1.18301 | −0.0494643 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.76290 | 0.0735821 | ||||||||
\(575\) | −2.57035 | −0.107191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.288300 | 0.0120021 | 0.00600105 | − | 0.999982i | \(-0.498090\pi\) | ||||
0.00600105 | + | 0.999982i | \(0.498090\pi\) | |||||||
\(578\) | 4.68111 | 0.194708 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 18.7365 | 0.777990 | ||||||||
\(581\) | −7.35722 | −0.305229 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.01322 | 0.0419635 | ||||||||
\(584\) | −17.3099 | −0.716290 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.63287 | 0.232692 | ||||||||
\(587\) | 1.34227 | 0.0554013 | 0.0277006 | − | 0.999616i | \(-0.491181\pi\) | ||||
0.0277006 | + | 0.999616i | \(0.491181\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.06598 | 0.373557 | ||||||||
\(590\) | 8.13597 | 0.334952 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.15918 | 0.253141 | ||||||||
\(593\) | 25.2541 | 1.03706 | 0.518530 | − | 0.855060i | \(-0.326480\pi\) | ||||
0.518530 | + | 0.855060i | \(0.326480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.32565 | −0.218330 | ||||||||
\(596\) | 22.0800 | 0.904434 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.01552 | −0.245993 | ||||||||
\(599\) | 35.6941 | 1.45842 | 0.729211 | − | 0.684289i | \(-0.239887\pi\) | ||||
0.729211 | + | 0.684289i | \(0.239887\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.21440 | 0.0495364 | 0.0247682 | − | 0.999693i | \(-0.492115\pi\) | ||||
0.0247682 | + | 0.999693i | \(0.492115\pi\) | |||||||
\(602\) | 3.04478 | 0.124096 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 23.5287 | 0.957369 | ||||||||
\(605\) | −21.8186 | −0.887052 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.81330 | −0.154777 | −0.0773886 | − | 0.997001i | \(-0.524658\pi\) | ||||
−0.0773886 | + | 0.997001i | \(0.524658\pi\) | |||||||
\(608\) | −21.4750 | −0.870925 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.92035 | −0.118242 | ||||||||
\(611\) | 61.4492 | 2.48597 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.3128 | −1.26471 | −0.632357 | − | 0.774677i | \(-0.717912\pi\) | ||||
−0.632357 | + | 0.774677i | \(0.717912\pi\) | |||||||
\(614\) | −12.5202 | −0.505275 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.232348 | −0.00936156 | ||||||||
\(617\) | 18.9750 | 0.763904 | 0.381952 | − | 0.924182i | \(-0.375252\pi\) | ||||
0.381952 | + | 0.924182i | \(0.375252\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.4920 | −1.14519 | −0.572596 | − | 0.819838i | \(-0.694064\pi\) | ||||
−0.572596 | + | 0.819838i | \(0.694064\pi\) | |||||||
\(620\) | −7.25485 | −0.291362 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.48587 | −0.139771 | ||||||||
\(623\) | 0.833032 | 0.0333747 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.6209 | −0.744837 | ||||||||
\(626\) | 5.31515 | 0.212436 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.6962 | 0.466728 | ||||||||
\(629\) | 6.14662 | 0.245082 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.7097 | −0.505966 | −0.252983 | − | 0.967471i | \(-0.581412\pi\) | ||||
−0.252983 | + | 0.967471i | \(0.581412\pi\) | |||||||
\(632\) | 8.48017 | 0.337323 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.23417 | −0.207875 | ||||||||
\(635\) | −1.98652 | −0.0788326 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.16963 | 0.204828 | ||||||||
\(638\) | 0.327750 | 0.0129758 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 22.2764 | 0.880551 | ||||||||
\(641\) | −5.36641 | −0.211961 | −0.105980 | − | 0.994368i | \(-0.533798\pi\) | ||||
−0.105980 | + | 0.994368i | \(0.533798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.99046 | 0.315113 | 0.157557 | − | 0.987510i | \(-0.449638\pi\) | ||||
0.157557 | + | 0.987510i | \(0.449638\pi\) | |||||||
\(644\) | 4.32342 | 0.170367 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.62709 | −0.221395 | ||||||||
\(647\) | 3.76942 | 0.148191 | 0.0740956 | − | 0.997251i | \(-0.476393\pi\) | ||||
0.0740956 | + | 0.997251i | \(0.476393\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.10846 | −0.0435110 | ||||||||
\(650\) | 2.59866 | 0.101928 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.9941 | −0.939683 | ||||||||
\(653\) | 17.1656 | 0.671742 | 0.335871 | − | 0.941908i | \(-0.390969\pi\) | ||||
0.335871 | + | 0.941908i | \(0.390969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.9920 | −0.468566 | ||||||||
\(656\) | 9.92749 | 0.387603 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.67039 | 0.221055 | ||||||||
\(659\) | −20.9072 | −0.814430 | −0.407215 | − | 0.913332i | \(-0.633500\pi\) | ||||
−0.407215 | + | 0.913332i | \(0.633500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.9980 | −1.20568 | −0.602841 | − | 0.797862i | \(-0.705965\pi\) | ||||
−0.602841 | + | 0.797862i | \(0.705965\pi\) | |||||||
\(662\) | 2.69508 | 0.104747 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.2401 | 0.513815 | ||||||||
\(665\) | −8.74059 | −0.338946 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.9803 | −0.502598 | ||||||||
\(668\) | 29.5590 | 1.14367 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.10746 | 0.197318 | ||||||||
\(671\) | 0.397876 | 0.0153598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7276 | −0.567707 | −0.283853 | − | 0.958868i | \(-0.591613\pi\) | ||||
−0.283853 | + | 0.958868i | \(0.591613\pi\) | |||||||
\(674\) | 0.266922 | 0.0102814 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.3267 | −0.935642 | ||||||||
\(677\) | −35.4202 | −1.36131 | −0.680654 | − | 0.732605i | \(-0.738304\pi\) | ||||
−0.680654 | + | 0.732605i | \(0.738304\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.28385 | −0.0876462 | ||||||||
\(680\) | 9.58408 | 0.367533 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.126906 | −0.00485950 | ||||||||
\(683\) | 25.0084 | 0.956920 | 0.478460 | − | 0.878109i | \(-0.341195\pi\) | ||||
0.478460 | + | 0.878109i | \(0.341195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1643 | 0.388357 | ||||||||
\(686\) | 0.477041 | 0.0182135 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.1462 | 0.653691 | ||||||||
\(689\) | 40.5699 | 1.54559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.3999 | 1.27059 | 0.635295 | − | 0.772269i | \(-0.280878\pi\) | ||||
0.635295 | + | 0.772269i | \(0.280878\pi\) | |||||||
\(692\) | −0.159344 | −0.00605736 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.11806 | 0.0424411 | ||||||||
\(695\) | −20.2364 | −0.767610 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.90724 | 0.375263 | ||||||||
\(698\) | 0.322083 | 0.0121910 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.86768 | −0.0705918 | ||||||||
\(701\) | −3.96654 | −0.149814 | −0.0749070 | − | 0.997191i | \(-0.523866\pi\) | ||||
−0.0749070 | + | 0.997191i | \(0.523866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.0880 | 0.380475 | ||||||||
\(704\) | −0.393070 | −0.0148144 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.2244 | −0.384800 | ||||||||
\(707\) | −4.38532 | −0.164927 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7457 | −1.07957 | −0.539783 | − | 0.841804i | \(-0.681494\pi\) | ||||
−0.539783 | + | 0.841804i | \(0.681494\pi\) | |||||||
\(710\) | 0.387687 | 0.0145496 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.49913 | −0.0561823 | ||||||||
\(713\) | 5.02602 | 0.188226 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.32591 | 0.0495861 | ||||||||
\(716\) | 3.70262 | 0.138373 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.55909 | −0.0581848 | ||||||||
\(719\) | −25.8862 | −0.965391 | −0.482696 | − | 0.875788i | \(-0.660342\pi\) | ||||
−0.482696 | + | 0.875788i | \(0.660342\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.21117 | 0.231316 | ||||||||
\(722\) | −0.171542 | −0.00638413 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.0617 | −0.634091 | ||||||||
\(725\) | 5.60737 | 0.208253 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.6071 | 1.28350 | 0.641752 | − | 0.766912i | \(-0.278208\pi\) | ||||
0.641752 | + | 0.766912i | \(0.278208\pi\) | |||||||
\(728\) | −9.30329 | −0.344803 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.11521 | 0.337369 | ||||||||
\(731\) | 17.1112 | 0.632880 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.4119 | −1.16023 | −0.580113 | − | 0.814536i | \(-0.696992\pi\) | ||||
−0.580113 | + | 0.814536i | \(0.696992\pi\) | |||||||
\(734\) | 3.53745 | 0.130570 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.9054 | −0.438837 | ||||||||
\(737\) | −0.695853 | −0.0256321 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.6874 | 1.60707 | 0.803534 | − | 0.595259i | \(-0.202951\pi\) | ||||
0.803534 | + | 0.595259i | \(0.202951\pi\) | |||||||
\(740\) | −8.07269 | −0.296758 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.74369 | 0.137435 | ||||||||
\(743\) | 35.4888 | 1.30196 | 0.650978 | − | 0.759097i | \(-0.274359\pi\) | ||||
0.650978 | + | 0.759097i | \(0.274359\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −24.7470 | −0.906661 | ||||||||
\(746\) | −1.79066 | −0.0655608 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.613495 | −0.0224316 | ||||||||
\(749\) | −7.71277 | −0.281818 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.8825 | 1.52831 | 0.764157 | − | 0.645030i | \(-0.223155\pi\) | ||||
0.764157 | + | 0.645030i | \(0.223155\pi\) | |||||||
\(752\) | 31.9318 | 1.16443 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.1232 | 0.477920 | ||||||||
\(755\) | −26.3707 | −0.959727 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.1857 | 1.02443 | 0.512213 | − | 0.858858i | \(-0.328826\pi\) | ||||
0.512213 | + | 0.858858i | \(0.328826\pi\) | |||||||
\(758\) | 2.55364 | 0.0927525 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15.7296 | 0.570573 | ||||||||
\(761\) | −21.1198 | −0.765591 | −0.382796 | − | 0.923833i | \(-0.625039\pi\) | ||||
−0.382796 | + | 0.923833i | \(0.625039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.1046 | 0.691632 | ||||||||
\(764\) | −15.7715 | −0.570593 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.72681 | −0.170786 | ||||||||
\(767\) | −44.3833 | −1.60259 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.2389 | −1.48711 | −0.743556 | − | 0.668673i | \(-0.766862\pi\) | ||||
−0.743556 | + | 0.668673i | \(0.766862\pi\) | |||||||
\(770\) | 0.122352 | 0.00440925 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.9425 | 0.429818 | ||||||||
\(773\) | −10.8885 | −0.391631 | −0.195815 | − | 0.980641i | \(-0.562735\pi\) | ||||
−0.195815 | + | 0.980641i | \(0.562735\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.17120 | −0.0779919 | ||||||||
\(776\) | 4.11003 | 0.147542 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.4218 | 0.445345 | ||||||||
\(779\) | 16.2600 | 0.582575 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0528195 | −0.00189003 | ||||||||
\(782\) | −3.11957 | −0.111555 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.68638 | 0.0959420 | ||||||||
\(785\) | −13.1089 | −0.467877 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.3691 | 1.79546 | 0.897732 | − | 0.440542i | \(-0.145214\pi\) | ||||
0.897732 | + | 0.440542i | \(0.145214\pi\) | |||||||
\(788\) | −32.0854 | −1.14299 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.46556 | −0.158877 | ||||||||
\(791\) | −9.12949 | −0.324607 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.9311 | 0.565729 | ||||||||
\(794\) | −4.48276 | −0.159087 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.0432 | −1.17118 | ||||||||
\(797\) | −19.5899 | −0.693909 | −0.346954 | − | 0.937882i | \(-0.612784\pi\) | ||||
−0.346954 | + | 0.937882i | \(0.612784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.8667 | 1.12736 | ||||||||
\(800\) | 5.14302 | 0.181833 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.74618 | −0.238216 | ||||||||
\(803\) | −1.24188 | −0.0438250 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.84564 | −0.170786 | ||||||||
\(806\) | −5.08138 | −0.178984 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.89185 | 0.277634 | ||||||||
\(809\) | −3.78018 | −0.132904 | −0.0664520 | − | 0.997790i | \(-0.521168\pi\) | ||||
−0.0664520 | + | 0.997790i | \(0.521168\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.20558 | −0.182793 | −0.0913963 | − | 0.995815i | \(-0.529133\pi\) | ||||
−0.0913963 | + | 0.995815i | \(0.529133\pi\) | |||||||
\(812\) | −9.43181 | −0.330992 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.141213 | −0.00494950 | ||||||||
\(815\) | 26.8923 | 0.941997 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0833 | 0.982510 | ||||||||
\(818\) | 3.39383 | 0.118662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.0117 | −0.454389 | ||||||||
\(821\) | 9.88339 | 0.344933 | 0.172466 | − | 0.985015i | \(-0.444826\pi\) | ||||
0.172466 | + | 0.985015i | \(0.444826\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.4906 | 1.27198 | 0.635991 | − | 0.771697i | \(-0.280592\pi\) | ||||
0.635991 | + | 0.771697i | \(0.280592\pi\) | |||||||
\(824\) | −11.1777 | −0.389392 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.09559 | −0.142504 | ||||||||
\(827\) | 11.6976 | 0.406765 | 0.203383 | − | 0.979099i | \(-0.434806\pi\) | ||||
0.203383 | + | 0.979099i | \(0.434806\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.0192 | 0.417443 | 0.208722 | − | 0.977975i | \(-0.433070\pi\) | ||||
0.208722 | + | 0.977975i | \(0.433070\pi\) | |||||||
\(830\) | −6.97208 | −0.242005 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.7387 | −0.545640 | ||||||||
\(833\) | 2.68090 | 0.0928876 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.1294 | −1.14649 | ||||||||
\(836\) | −1.00688 | −0.0348238 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.6803 | −0.368945 | ||||||||
\(839\) | −15.6959 | −0.541883 | −0.270941 | − | 0.962596i | \(-0.587335\pi\) | ||||
−0.270941 | + | 0.962596i | \(0.587335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.682742 | −0.0235428 | ||||||||
\(842\) | 16.5018 | 0.568689 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 11.5548 | 0.397733 | ||||||||
\(845\) | 27.2651 | 0.937947 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.9833 | 0.377392 | ||||||||
\(848\) | 21.0820 | 0.723958 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.34763 | 0.0462233 | ||||||||
\(851\) | 5.59261 | 0.191712 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −56.3980 | −1.93103 | −0.965515 | − | 0.260346i | \(-0.916163\pi\) | ||||
−0.965515 | + | 0.260346i | \(0.916163\pi\) | |||||||
\(854\) | 1.47008 | 0.0503052 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.8799 | 0.474407 | ||||||||
\(857\) | 4.53943 | 0.155064 | 0.0775320 | − | 0.996990i | \(-0.475296\pi\) | ||||
0.0775320 | + | 0.996990i | \(0.475296\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.6839 | −0.705726 | −0.352863 | − | 0.935675i | \(-0.614792\pi\) | ||||
−0.352863 | + | 0.935675i | \(0.614792\pi\) | |||||||
\(860\) | −22.4730 | −0.766325 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.11453 | 0.242322 | ||||||||
\(863\) | 3.53249 | 0.120247 | 0.0601237 | − | 0.998191i | \(-0.480850\pi\) | ||||
0.0601237 | + | 0.998191i | \(0.480850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.178591 | 0.00607228 | ||||||||
\(866\) | 6.25753 | 0.212640 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.65204 | 0.123958 | ||||||||
\(869\) | 0.608399 | 0.0206385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.8622 | −0.944074 | ||||||||
\(872\) | −34.3807 | −1.16428 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.11991 | −0.173184 | ||||||||
\(875\) | 12.0259 | 0.406549 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.7631 | 1.61285 | 0.806423 | − | 0.591340i | \(-0.201401\pi\) | ||||
0.806423 | + | 0.591340i | \(0.201401\pi\) | |||||||
\(878\) | 7.31227 | 0.246777 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.689003 | 0.0232263 | ||||||||
\(881\) | −9.77071 | −0.329184 | −0.164592 | − | 0.986362i | \(-0.552631\pi\) | ||||
−0.164592 | + | 0.986362i | \(0.552631\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.4589 | −0.553886 | −0.276943 | − | 0.960886i | \(-0.589321\pi\) | ||||
−0.276943 | + | 0.960886i | \(0.589321\pi\) | |||||||
\(884\) | −24.5645 | −0.826195 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.5387 | −0.488437 | ||||||||
\(887\) | −16.5289 | −0.554985 | −0.277493 | − | 0.960728i | \(-0.589503\pi\) | ||||
−0.277493 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 0.789425 | 0.0264616 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.99497 | 0.167244 | ||||||||
\(893\) | 52.3004 | 1.75017 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.14985 | −0.138714 | ||||||||
\(896\) | −11.2138 | −0.374626 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.67535 | 0.222759 | ||||||||
\(899\) | −10.9646 | −0.365689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.0390 | 0.700910 | ||||||||
\(902\) | −0.227609 | −0.00757856 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.4295 | 0.546436 | ||||||||
\(905\) | 19.1225 | 0.635653 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.12502 | 0.170173 | 0.0850867 | − | 0.996374i | \(-0.472883\pi\) | ||||
0.0850867 | + | 0.996374i | \(0.472883\pi\) | |||||||
\(908\) | 4.75277 | 0.157726 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.89901 | 0.162400 | ||||||||
\(911\) | 49.3661 | 1.63557 | 0.817787 | − | 0.575521i | \(-0.195201\pi\) | ||||
0.817787 | + | 0.575521i | \(0.195201\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.949894 | 0.0314369 | ||||||||
\(914\) | −16.5407 | −0.547117 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.0568 | 1.09223 | ||||||||
\(917\) | 6.03668 | 0.199349 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.9866 | 0.692283 | 0.346141 | − | 0.938182i | \(-0.387492\pi\) | ||||
0.346141 | + | 0.938182i | \(0.387492\pi\) | |||||||
\(920\) | 8.72024 | 0.287498 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.2882 | −0.569358 | ||||||||
\(923\) | −2.11491 | −0.0696131 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.41596 | −0.0794363 | ||||||||
\(926\) | −10.5600 | −0.347024 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 25.9723 | 0.852581 | ||||||||
\(929\) | 42.3000 | 1.38782 | 0.693910 | − | 0.720062i | \(-0.255887\pi\) | ||||
0.693910 | + | 0.720062i | \(0.255887\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.39995 | 0.144203 | ||||||||
\(932\) | −35.5500 | −1.16448 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.19054 | −0.0389555 | ||||||||
\(935\) | 0.687597 | 0.0224868 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.8141 | 1.07199 | 0.535996 | − | 0.844221i | \(-0.319936\pi\) | ||||
0.535996 | + | 0.844221i | \(0.319936\pi\) | |||||||
\(938\) | −2.57106 | −0.0839480 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −41.8523 | −1.36507 | ||||||||
\(941\) | −13.6694 | −0.445609 | −0.222805 | − | 0.974863i | \(-0.571521\pi\) | ||||
−0.222805 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.01427 | 0.293545 | ||||||||
\(944\) | −23.0636 | −0.750656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.393113 | −0.0127812 | ||||||||
\(947\) | 38.3611 | 1.24657 | 0.623283 | − | 0.781996i | \(-0.285798\pi\) | ||||
0.623283 | + | 0.781996i | \(0.285798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.7253 | −1.61415 | ||||||||
\(950\) | 2.21176 | 0.0717590 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.82456 | −0.156365 | ||||||||
\(953\) | −26.1473 | −0.846993 | −0.423497 | − | 0.905898i | \(-0.639197\pi\) | ||||
−0.423497 | + | 0.905898i | \(0.639197\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.6765 | 0.571998 | ||||||||
\(956\) | −19.9169 | −0.644159 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.53759 | −0.243528 | ||||||||
\(959\) | −5.11663 | −0.165225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7545 | −0.863047 | ||||||||
\(962\) | −5.65420 | −0.182299 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −40.0941 | −1.29134 | ||||||||
\(965\) | −13.3850 | −0.430877 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.229274 | −0.00737297 | −0.00368648 | − | 0.999993i | \(-0.501173\pi\) | ||||
−0.00368648 | + | 0.999993i | \(0.501173\pi\) | |||||||
\(968\) | −19.7657 | −0.635293 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.16430 | −0.0694914 | ||||||||
\(971\) | 35.4274 | 1.13692 | 0.568460 | − | 0.822711i | \(-0.307539\pi\) | ||||
0.568460 | + | 0.822711i | \(0.307539\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.1869 | 0.326576 | ||||||||
\(974\) | 14.4340 | 0.462495 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.27853 | 0.264989 | ||||||||
\(977\) | −45.0167 | −1.44021 | −0.720105 | − | 0.693865i | \(-0.755907\pi\) | ||||
−0.720105 | + | 0.693865i | \(0.755907\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.107553 | −0.00343741 | ||||||||
\(980\) | −3.52097 | −0.112473 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.76414 | 0.0882072 | ||||||||
\(983\) | 36.6478 | 1.16888 | 0.584441 | − | 0.811436i | \(-0.301314\pi\) | ||||
0.584441 | + | 0.811436i | \(0.301314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35.9609 | 1.14581 | ||||||||
\(986\) | 6.80553 | 0.216732 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −40.3159 | −1.28262 | ||||||||
\(989\) | 15.5689 | 0.495062 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.3587 | 0.519650 | 0.259825 | − | 0.965656i | \(-0.416335\pi\) | ||||
0.259825 | + | 0.965656i | \(0.416335\pi\) | |||||||
\(992\) | −10.0566 | −0.319297 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.195159 | −0.00619007 | ||||||||
\(995\) | 37.0344 | 1.17407 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.2285 | −1.05236 | −0.526178 | − | 0.850374i | \(-0.676376\pi\) | ||||
−0.526178 | + | 0.850374i | \(0.676376\pi\) | |||||||
\(998\) | −15.8927 | −0.503074 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.p.1.6 | 14 | ||
3.2 | odd | 2 | 2667.2.a.m.1.9 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.m.1.9 | ✓ | 14 | 3.2 | odd | 2 | ||
8001.2.a.p.1.6 | 14 | 1.1 | even | 1 | trivial |