Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6021,2,Mod(1,6021)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6021, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6021.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6021 = 3^{3} \cdot 223 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6021.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: | \(48.0779270570\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 20x^{8} + 139x^{6} - 384x^{4} + 331x^{2} - 63 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.31657\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6021.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31657 | −1.63806 | −0.819031 | − | 0.573750i | \(-0.805488\pi\) | ||||
−0.819031 | + | 0.573750i | \(0.805488\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.36649 | 1.68325 | ||||||||
\(5\) | −1.78959 | −0.800327 | −0.400164 | − | 0.916444i | \(-0.631047\pi\) | ||||
−0.400164 | + | 0.916444i | \(0.631047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.694189 | 0.262379 | 0.131189 | − | 0.991357i | \(-0.458120\pi\) | ||||
0.131189 | + | 0.991357i | \(0.458120\pi\) | |||||||
\(8\) | −3.16557 | −1.11920 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.14570 | 1.31099 | ||||||||
\(11\) | −5.07293 | −1.52955 | −0.764773 | − | 0.644299i | \(-0.777149\pi\) | ||||
−0.764773 | + | 0.644299i | \(0.777149\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.67900 | 1.29772 | 0.648860 | − | 0.760908i | \(-0.275246\pi\) | ||||
0.648860 | + | 0.760908i | \(0.275246\pi\) | |||||||
\(14\) | −1.60814 | −0.429793 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.600282 | 0.150071 | ||||||||
\(17\) | 0.374011 | 0.0907110 | 0.0453555 | − | 0.998971i | \(-0.485558\pi\) | ||||
0.0453555 | + | 0.998971i | \(0.485558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.67230 | 0.842484 | 0.421242 | − | 0.906948i | \(-0.361594\pi\) | ||||
0.421242 | + | 0.906948i | \(0.361594\pi\) | |||||||
\(20\) | −6.02463 | −1.34715 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 11.7518 | 2.50549 | ||||||||
\(23\) | 9.24219 | 1.92713 | 0.963565 | − | 0.267474i | \(-0.0861891\pi\) | ||||
0.963565 | + | 0.267474i | \(0.0861891\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79738 | −0.359476 | ||||||||
\(26\) | −10.8392 | −2.12575 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.33698 | 0.441648 | ||||||||
\(29\) | −9.13260 | −1.69588 | −0.847941 | − | 0.530091i | \(-0.822158\pi\) | ||||
−0.847941 | + | 0.530091i | \(0.822158\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.920410 | 0.165311 | 0.0826553 | − | 0.996578i | \(-0.473660\pi\) | ||||
0.0826553 | + | 0.996578i | \(0.473660\pi\) | |||||||
\(32\) | 4.94055 | 0.873374 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.866423 | −0.148590 | ||||||||
\(35\) | −1.24231 | −0.209989 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.16978 | 0.685508 | 0.342754 | − | 0.939425i | \(-0.388640\pi\) | ||||
0.342754 | + | 0.939425i | \(0.388640\pi\) | |||||||
\(38\) | −8.50714 | −1.38004 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.66507 | 0.895725 | ||||||||
\(41\) | 5.53413 | 0.864286 | 0.432143 | − | 0.901805i | \(-0.357758\pi\) | ||||
0.432143 | + | 0.901805i | \(0.357758\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.34832 | 0.205617 | 0.102809 | − | 0.994701i | \(-0.467217\pi\) | ||||
0.102809 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(44\) | −17.0780 | −2.57460 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −21.4102 | −3.15676 | ||||||||
\(47\) | 11.4169 | 1.66533 | 0.832663 | − | 0.553780i | \(-0.186815\pi\) | ||||
0.832663 | + | 0.553780i | \(0.186815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.51810 | −0.931157 | ||||||||
\(50\) | 4.16375 | 0.588844 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 15.7518 | 2.18438 | ||||||||
\(53\) | 2.04525 | 0.280937 | 0.140468 | − | 0.990085i | \(-0.455139\pi\) | ||||
0.140468 | + | 0.990085i | \(0.455139\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.07845 | 1.22414 | ||||||||
\(56\) | −2.19751 | −0.293654 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 21.1563 | 2.77796 | ||||||||
\(59\) | −12.3267 | −1.60479 | −0.802397 | − | 0.596791i | \(-0.796442\pi\) | ||||
−0.802397 | + | 0.596791i | \(0.796442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.40231 | 0.435621 | 0.217810 | − | 0.975991i | \(-0.430109\pi\) | ||||
0.217810 | + | 0.975991i | \(0.430109\pi\) | |||||||
\(62\) | −2.13219 | −0.270789 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.6457 | −1.58071 | ||||||||
\(65\) | −8.37347 | −1.03860 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.22157 | −0.149239 | −0.0746196 | − | 0.997212i | \(-0.523774\pi\) | ||||
−0.0746196 | + | 0.997212i | \(0.523774\pi\) | |||||||
\(68\) | 1.25911 | 0.152689 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.87790 | 0.343975 | ||||||||
\(71\) | −12.3816 | −1.46942 | −0.734711 | − | 0.678380i | \(-0.762682\pi\) | ||||
−0.734711 | + | 0.678380i | \(0.762682\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.34539 | −0.625630 | −0.312815 | − | 0.949814i | \(-0.601272\pi\) | ||||
−0.312815 | + | 0.949814i | \(0.601272\pi\) | |||||||
\(74\) | −9.65958 | −1.12290 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.3628 | 1.41811 | ||||||||
\(77\) | −3.52157 | −0.401321 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.37909 | −0.380178 | −0.190089 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190089 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(80\) | −1.07426 | −0.120106 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.8202 | −1.41575 | ||||||||
\(83\) | 11.4450 | 1.25625 | 0.628124 | − | 0.778114i | \(-0.283823\pi\) | ||||
0.628124 | + | 0.778114i | \(0.283823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.669325 | −0.0725985 | ||||||||
\(86\) | −3.12348 | −0.336813 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 16.0587 | 1.71187 | ||||||||
\(89\) | 3.41759 | 0.362264 | 0.181132 | − | 0.983459i | \(-0.442024\pi\) | ||||
0.181132 | + | 0.983459i | \(0.442024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.24811 | 0.340494 | ||||||||
\(92\) | 31.1138 | 3.24383 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −26.4480 | −2.72791 | ||||||||
\(95\) | −6.57190 | −0.674263 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.83863 | −0.998961 | −0.499481 | − | 0.866325i | \(-0.666476\pi\) | ||||
−0.499481 | + | 0.866325i | \(0.666476\pi\) | |||||||
\(98\) | 15.0996 | 1.52529 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.05086 | −0.605086 | ||||||||
\(101\) | 0.412606 | 0.0410558 | 0.0205279 | − | 0.999789i | \(-0.493465\pi\) | ||||
0.0205279 | + | 0.999789i | \(0.493465\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.70719 | 0.660879 | 0.330439 | − | 0.943827i | \(-0.392803\pi\) | ||||
0.330439 | + | 0.943827i | \(0.392803\pi\) | |||||||
\(104\) | −14.8117 | −1.45241 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.73796 | −0.460192 | ||||||||
\(107\) | −2.67071 | −0.258187 | −0.129094 | − | 0.991632i | \(-0.541207\pi\) | ||||
−0.129094 | + | 0.991632i | \(0.541207\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.77178 | 0.744401 | 0.372201 | − | 0.928152i | \(-0.378603\pi\) | ||||
0.372201 | + | 0.928152i | \(0.378603\pi\) | |||||||
\(110\) | −21.0309 | −2.00521 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.416710 | 0.0393753 | ||||||||
\(113\) | 16.3605 | 1.53907 | 0.769534 | − | 0.638605i | \(-0.220488\pi\) | ||||
0.769534 | + | 0.638605i | \(0.220488\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.5397 | −1.54234 | ||||||||
\(116\) | −30.7448 | −2.85459 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 28.5555 | 2.62875 | ||||||||
\(119\) | 0.259634 | 0.0238006 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.7347 | 1.33951 | ||||||||
\(122\) | −7.88168 | −0.713574 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.09855 | 0.278258 | ||||||||
\(125\) | 12.1645 | 1.08803 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.45416 | −0.838921 | −0.419460 | − | 0.907774i | \(-0.637781\pi\) | ||||
−0.419460 | + | 0.907774i | \(0.637781\pi\) | |||||||
\(128\) | 19.4135 | 1.71593 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 19.3977 | 1.70129 | ||||||||
\(131\) | −14.9905 | −1.30972 | −0.654862 | − | 0.755749i | \(-0.727273\pi\) | ||||
−0.654862 | + | 0.755749i | \(0.727273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.54927 | 0.221050 | ||||||||
\(134\) | 2.82986 | 0.244463 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.18396 | −0.101524 | ||||||||
\(137\) | −9.22476 | −0.788124 | −0.394062 | − | 0.919084i | \(-0.628930\pi\) | ||||
−0.394062 | + | 0.919084i | \(0.628930\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.70631 | −0.399184 | −0.199592 | − | 0.979879i | \(-0.563962\pi\) | ||||
−0.199592 | + | 0.979879i | \(0.563962\pi\) | |||||||
\(140\) | −4.18223 | −0.353463 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 28.6828 | 2.40700 | ||||||||
\(143\) | −23.7362 | −1.98492 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.3436 | 1.35726 | ||||||||
\(146\) | 12.3830 | 1.02482 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.0375 | 1.15388 | ||||||||
\(149\) | −0.872272 | −0.0714593 | −0.0357296 | − | 0.999361i | \(-0.511376\pi\) | ||||
−0.0357296 | + | 0.999361i | \(0.511376\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.663895 | 0.0540270 | 0.0270135 | − | 0.999635i | \(-0.491400\pi\) | ||||
0.0270135 | + | 0.999635i | \(0.491400\pi\) | |||||||
\(152\) | −11.6249 | −0.942907 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.15797 | 0.657388 | ||||||||
\(155\) | −1.64715 | −0.132303 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.60531 | 0.766588 | 0.383294 | − | 0.923626i | \(-0.374790\pi\) | ||||
0.383294 | + | 0.923626i | \(0.374790\pi\) | |||||||
\(158\) | 7.82790 | 0.622755 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.84154 | −0.698985 | ||||||||
\(161\) | 6.41583 | 0.505638 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.6592 | −0.913216 | −0.456608 | − | 0.889668i | \(-0.650936\pi\) | ||||
−0.456608 | + | 0.889668i | \(0.650936\pi\) | |||||||
\(164\) | 18.6306 | 1.45481 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −26.5130 | −2.05781 | ||||||||
\(167\) | −15.0364 | −1.16355 | −0.581775 | − | 0.813350i | \(-0.697642\pi\) | ||||
−0.581775 | + | 0.813350i | \(0.697642\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.89300 | 0.684077 | ||||||||
\(170\) | 1.55054 | 0.118921 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.53911 | 0.346104 | ||||||||
\(173\) | 11.7444 | 0.892912 | 0.446456 | − | 0.894806i | \(-0.352686\pi\) | ||||
0.446456 | + | 0.894806i | \(0.352686\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.24772 | −0.0943189 | ||||||||
\(176\) | −3.04519 | −0.229540 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.91709 | −0.593411 | ||||||||
\(179\) | 9.06429 | 0.677497 | 0.338748 | − | 0.940877i | \(-0.389996\pi\) | ||||
0.338748 | + | 0.940877i | \(0.389996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.0468 | 0.895433 | 0.447716 | − | 0.894176i | \(-0.352237\pi\) | ||||
0.447716 | + | 0.894176i | \(0.352237\pi\) | |||||||
\(182\) | −7.52447 | −0.557750 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −29.2568 | −2.15684 | ||||||||
\(185\) | −7.46218 | −0.548631 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.89733 | −0.138747 | ||||||||
\(188\) | 38.4349 | 2.80315 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 15.2243 | 1.10448 | ||||||||
\(191\) | −8.99893 | −0.651140 | −0.325570 | − | 0.945518i | \(-0.605556\pi\) | ||||
−0.325570 | + | 0.945518i | \(0.605556\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.51054 | 0.108731 | 0.0543656 | − | 0.998521i | \(-0.482686\pi\) | ||||
0.0543656 | + | 0.998521i | \(0.482686\pi\) | |||||||
\(194\) | 22.7919 | 1.63636 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.9431 | −1.56737 | ||||||||
\(197\) | 22.6144 | 1.61121 | 0.805604 | − | 0.592455i | \(-0.201841\pi\) | ||||
0.805604 | + | 0.592455i | \(0.201841\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5611 | 1.03221 | 0.516103 | − | 0.856526i | \(-0.327382\pi\) | ||||
0.516103 | + | 0.856526i | \(0.327382\pi\) | |||||||
\(200\) | 5.68973 | 0.402325 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.955829 | −0.0672519 | ||||||||
\(203\) | −6.33975 | −0.444963 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.90381 | −0.691712 | ||||||||
\(206\) | −15.5377 | −1.08256 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.80872 | 0.194750 | ||||||||
\(209\) | −18.6293 | −1.28862 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.0830 | 1.52025 | 0.760127 | − | 0.649775i | \(-0.225137\pi\) | ||||
0.760127 | + | 0.649775i | \(0.225137\pi\) | |||||||
\(212\) | 6.88532 | 0.472885 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.18688 | 0.422927 | ||||||||
\(215\) | −2.41294 | −0.164561 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.638939 | 0.0433740 | ||||||||
\(218\) | −18.0039 | −1.21938 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 30.5625 | 2.06053 | ||||||||
\(221\) | 1.75000 | 0.117718 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.00000 | −0.0669650 | ||||||||
\(224\) | 3.42967 | 0.229155 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −37.9003 | −2.52109 | ||||||||
\(227\) | 17.6360 | 1.17054 | 0.585270 | − | 0.810839i | \(-0.300989\pi\) | ||||
0.585270 | + | 0.810839i | \(0.300989\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.09312 | −0.534809 | −0.267404 | − | 0.963584i | \(-0.586166\pi\) | ||||
−0.267404 | + | 0.963584i | \(0.586166\pi\) | |||||||
\(230\) | 38.3154 | 2.52644 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 28.9099 | 1.89803 | ||||||||
\(233\) | −11.4724 | −0.751584 | −0.375792 | − | 0.926704i | \(-0.622629\pi\) | ||||
−0.375792 | + | 0.926704i | \(0.622629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.4315 | −1.33281 | ||||||||
\(236\) | −41.4976 | −2.70126 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.601461 | −0.0389869 | ||||||||
\(239\) | −15.0997 | −0.976721 | −0.488360 | − | 0.872642i | \(-0.662405\pi\) | ||||
−0.488360 | + | 0.872642i | \(0.662405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.00743 | 0.193726 | 0.0968629 | − | 0.995298i | \(-0.469119\pi\) | ||||
0.0968629 | + | 0.995298i | \(0.469119\pi\) | |||||||
\(242\) | −34.1338 | −2.19421 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.4538 | 0.733257 | ||||||||
\(245\) | 11.6647 | 0.745231 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.1827 | 1.09331 | ||||||||
\(248\) | −2.91362 | −0.185015 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −28.1799 | −1.78225 | ||||||||
\(251\) | −12.9343 | −0.816407 | −0.408204 | − | 0.912891i | \(-0.633845\pi\) | ||||
−0.408204 | + | 0.912891i | \(0.633845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −46.8850 | −2.94764 | ||||||||
\(254\) | 21.9012 | 1.37420 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −19.6814 | −1.23008 | ||||||||
\(257\) | 12.9167 | 0.805724 | 0.402862 | − | 0.915261i | \(-0.368015\pi\) | ||||
0.402862 | + | 0.915261i | \(0.368015\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.89462 | 0.179863 | ||||||||
\(260\) | −28.1892 | −1.74822 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 34.7264 | 2.14541 | ||||||||
\(263\) | −14.7541 | −0.909777 | −0.454888 | − | 0.890548i | \(-0.650321\pi\) | ||||
−0.454888 | + | 0.890548i | \(0.650321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.66015 | −0.224841 | ||||||||
\(266\) | −5.90556 | −0.362093 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.11242 | −0.251206 | ||||||||
\(269\) | −5.78037 | −0.352435 | −0.176218 | − | 0.984351i | \(-0.556386\pi\) | ||||
−0.176218 | + | 0.984351i | \(0.556386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.11744 | −0.310862 | −0.155431 | − | 0.987847i | \(-0.549677\pi\) | ||||
−0.155431 | + | 0.987847i | \(0.549677\pi\) | |||||||
\(272\) | 0.224512 | 0.0136131 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.3698 | 1.29100 | ||||||||
\(275\) | 9.11799 | 0.549835 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.9271 | 1.19730 | 0.598652 | − | 0.801009i | \(-0.295703\pi\) | ||||
0.598652 | + | 0.801009i | \(0.295703\pi\) | |||||||
\(278\) | 10.9025 | 0.653888 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.93263 | 0.235019 | ||||||||
\(281\) | −16.6653 | −0.994166 | −0.497083 | − | 0.867703i | \(-0.665595\pi\) | ||||
−0.497083 | + | 0.867703i | \(0.665595\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.2883 | −1.68157 | −0.840783 | − | 0.541372i | \(-0.817905\pi\) | ||||
−0.840783 | + | 0.541372i | \(0.817905\pi\) | |||||||
\(284\) | −41.6824 | −2.47340 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 54.9866 | 3.25143 | ||||||||
\(287\) | 3.84173 | 0.226770 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8601 | −0.991772 | ||||||||
\(290\) | −37.8610 | −2.22328 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.9952 | −1.05309 | ||||||||
\(293\) | −18.9266 | −1.10570 | −0.552852 | − | 0.833279i | \(-0.686461\pi\) | ||||
−0.552852 | + | 0.833279i | \(0.686461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.0596 | 1.28436 | ||||||||
\(296\) | −13.1997 | −0.767219 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.02068 | 0.117055 | ||||||||
\(299\) | 43.2442 | 2.50087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.935990 | 0.0539495 | ||||||||
\(302\) | −1.53796 | −0.0884996 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.20442 | 0.126432 | ||||||||
\(305\) | −6.08873 | −0.348639 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.6545 | 0.722232 | 0.361116 | − | 0.932521i | \(-0.382396\pi\) | ||||
0.361116 | + | 0.932521i | \(0.382396\pi\) | |||||||
\(308\) | −11.8554 | −0.675521 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.81574 | 0.216720 | ||||||||
\(311\) | 32.7411 | 1.85658 | 0.928288 | − | 0.371861i | \(-0.121280\pi\) | ||||
0.928288 | + | 0.371861i | \(0.121280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.7729 | −1.17415 | −0.587076 | − | 0.809532i | \(-0.699721\pi\) | ||||
−0.587076 | + | 0.809532i | \(0.699721\pi\) | |||||||
\(314\) | −22.2514 | −1.25572 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.3757 | −0.639933 | ||||||||
\(317\) | 26.1965 | 1.47134 | 0.735670 | − | 0.677340i | \(-0.236867\pi\) | ||||
0.735670 | + | 0.677340i | \(0.236867\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.3291 | 2.59393 | ||||||||
\(320\) | 22.6305 | 1.26509 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −14.8627 | −0.828266 | ||||||||
\(323\) | 1.37348 | 0.0764226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.40993 | −0.466499 | ||||||||
\(326\) | 27.0092 | 1.49590 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −17.5187 | −0.967308 | ||||||||
\(329\) | 7.92549 | 0.436946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.7778 | 1.36191 | 0.680955 | − | 0.732325i | \(-0.261565\pi\) | ||||
0.680955 | + | 0.732325i | \(0.261565\pi\) | |||||||
\(332\) | 38.5293 | 2.11457 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 34.8328 | 1.90597 | ||||||||
\(335\) | 2.18611 | 0.119440 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.55094 | −0.302379 | −0.151190 | − | 0.988505i | \(-0.548310\pi\) | ||||
−0.151190 | + | 0.988505i | \(0.548310\pi\) | |||||||
\(338\) | −20.6012 | −1.12056 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.25328 | −0.122201 | ||||||||
\(341\) | −4.66918 | −0.252850 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.38412 | −0.506695 | ||||||||
\(344\) | −4.26821 | −0.230126 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −27.2068 | −1.46264 | ||||||||
\(347\) | 32.4295 | 1.74090 | 0.870452 | − | 0.492252i | \(-0.163826\pi\) | ||||
0.870452 | + | 0.492252i | \(0.163826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.02169 | 0.161748 | 0.0808738 | − | 0.996724i | \(-0.474229\pi\) | ||||
0.0808738 | + | 0.996724i | \(0.474229\pi\) | |||||||
\(350\) | 2.89043 | 0.154500 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −25.0631 | −1.33587 | ||||||||
\(353\) | −7.25508 | −0.386149 | −0.193074 | − | 0.981184i | \(-0.561846\pi\) | ||||
−0.193074 | + | 0.981184i | \(0.561846\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.1579 | 1.17602 | ||||||||
\(356\) | 11.5053 | 0.609780 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.9981 | −1.10978 | ||||||||
\(359\) | 3.29124 | 0.173705 | 0.0868525 | − | 0.996221i | \(-0.472319\pi\) | ||||
0.0868525 | + | 0.996221i | \(0.472319\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.51419 | −0.290221 | ||||||||
\(362\) | −27.9073 | −1.46677 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.9347 | 0.573135 | ||||||||
\(365\) | 9.56604 | 0.500709 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.67488 | 0.191827 | 0.0959136 | − | 0.995390i | \(-0.469423\pi\) | ||||
0.0959136 | + | 0.995390i | \(0.469423\pi\) | |||||||
\(368\) | 5.54793 | 0.289206 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.2867 | 0.898691 | ||||||||
\(371\) | 1.41979 | 0.0737118 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.1309 | 0.990560 | 0.495280 | − | 0.868733i | \(-0.335065\pi\) | ||||
0.495280 | + | 0.868733i | \(0.335065\pi\) | |||||||
\(374\) | 4.39530 | 0.227276 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −36.1410 | −1.86383 | ||||||||
\(377\) | −42.7314 | −2.20078 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.62044 | 0.494169 | 0.247084 | − | 0.968994i | \(-0.420528\pi\) | ||||
0.247084 | + | 0.968994i | \(0.420528\pi\) | |||||||
\(380\) | −22.1243 | −1.13495 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 20.8466 | 1.06661 | ||||||||
\(383\) | 5.99657 | 0.306411 | 0.153205 | − | 0.988194i | \(-0.451040\pi\) | ||||
0.153205 | + | 0.988194i | \(0.451040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.30216 | 0.321188 | ||||||||
\(386\) | −3.49928 | −0.178109 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −33.1217 | −1.68150 | ||||||||
\(389\) | 25.4826 | 1.29202 | 0.646009 | − | 0.763330i | \(-0.276437\pi\) | ||||
0.646009 | + | 0.763330i | \(0.276437\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.45668 | 0.174812 | ||||||||
\(392\) | 20.6335 | 1.04215 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −52.3878 | −2.63926 | ||||||||
\(395\) | 6.04718 | 0.304267 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.8521 | 1.24729 | 0.623645 | − | 0.781708i | \(-0.285651\pi\) | ||||
0.623645 | + | 0.781708i | \(0.285651\pi\) | |||||||
\(398\) | −33.7317 | −1.69082 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.07894 | −0.0539468 | ||||||||
\(401\) | 15.9426 | 0.796135 | 0.398067 | − | 0.917356i | \(-0.369681\pi\) | ||||
0.398067 | + | 0.917356i | \(0.369681\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.30659 | 0.214527 | ||||||||
\(404\) | 1.38903 | 0.0691070 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 14.6865 | 0.728877 | ||||||||
\(407\) | −21.1530 | −1.04852 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.1882 | −0.800457 | −0.400229 | − | 0.916415i | \(-0.631069\pi\) | ||||
−0.400229 | + | 0.916415i | \(0.631069\pi\) | |||||||
\(410\) | 22.9429 | 1.13307 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.5797 | 1.11242 | ||||||||
\(413\) | −8.55703 | −0.421064 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.4817 | −1.00541 | ||||||||
\(416\) | 23.1168 | 1.13339 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 43.1562 | 2.11084 | ||||||||
\(419\) | −21.4969 | −1.05019 | −0.525096 | − | 0.851043i | \(-0.675970\pi\) | ||||
−0.525096 | + | 0.851043i | \(0.675970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.1847 | −1.56858 | −0.784292 | − | 0.620392i | \(-0.786974\pi\) | ||||
−0.784292 | + | 0.620392i | \(0.786974\pi\) | |||||||
\(422\) | −51.1567 | −2.49027 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.47439 | −0.314424 | ||||||||
\(425\) | −0.672240 | −0.0326084 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.36185 | 0.114298 | ||||||||
\(428\) | −8.99092 | −0.434593 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.58974 | 0.269561 | ||||||||
\(431\) | 17.9042 | 0.862413 | 0.431207 | − | 0.902253i | \(-0.358088\pi\) | ||||
0.431207 | + | 0.902253i | \(0.358088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.9371 | −1.53480 | −0.767399 | − | 0.641170i | \(-0.778450\pi\) | ||||
−0.767399 | + | 0.641170i | \(0.778450\pi\) | |||||||
\(434\) | −1.48015 | −0.0710492 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.1636 | 1.25301 | ||||||||
\(437\) | 33.9401 | 1.62358 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.81237 | 0.229682 | 0.114841 | − | 0.993384i | \(-0.463364\pi\) | ||||
0.114841 | + | 0.993384i | \(0.463364\pi\) | |||||||
\(440\) | −28.7385 | −1.37005 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.05399 | −0.192829 | ||||||||
\(443\) | 14.0761 | 0.668775 | 0.334387 | − | 0.942436i | \(-0.391471\pi\) | ||||
0.334387 | + | 0.942436i | \(0.391471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.11608 | −0.289930 | ||||||||
\(446\) | 2.31657 | 0.109693 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.77850 | −0.414745 | ||||||||
\(449\) | −7.73708 | −0.365135 | −0.182568 | − | 0.983193i | \(-0.558441\pi\) | ||||
−0.182568 | + | 0.983193i | \(0.558441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.0743 | −1.32197 | ||||||||
\(452\) | 55.0776 | 2.59063 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −40.8549 | −1.91742 | ||||||||
\(455\) | −5.81277 | −0.272507 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.42234 | 0.113312 | 0.0566562 | − | 0.998394i | \(-0.481956\pi\) | ||||
0.0566562 | + | 0.998394i | \(0.481956\pi\) | |||||||
\(458\) | 18.7483 | 0.876049 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −55.6808 | −2.59613 | ||||||||
\(461\) | 3.14473 | 0.146465 | 0.0732324 | − | 0.997315i | \(-0.476669\pi\) | ||||
0.0732324 | + | 0.997315i | \(0.476669\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6304 | 0.679931 | 0.339966 | − | 0.940438i | \(-0.389585\pi\) | ||||
0.339966 | + | 0.940438i | \(0.389585\pi\) | |||||||
\(464\) | −5.48214 | −0.254502 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.5767 | 1.23114 | ||||||||
\(467\) | −37.7571 | −1.74719 | −0.873594 | − | 0.486655i | \(-0.838217\pi\) | ||||
−0.873594 | + | 0.486655i | \(0.838217\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.848004 | −0.0391572 | ||||||||
\(470\) | 47.3311 | 2.18322 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 39.0209 | 1.79608 | ||||||||
\(473\) | −6.83994 | −0.314501 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.60052 | −0.302853 | ||||||||
\(476\) | 0.874057 | 0.0400623 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 34.9796 | 1.59993 | ||||||||
\(479\) | −11.2029 | −0.511875 | −0.255938 | − | 0.966693i | \(-0.582384\pi\) | ||||
−0.255938 | + | 0.966693i | \(0.582384\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.5104 | 0.889597 | ||||||||
\(482\) | −6.96692 | −0.317335 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 49.6041 | 2.25473 | ||||||||
\(485\) | 17.6071 | 0.799496 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.8101 | 1.57740 | 0.788698 | − | 0.614781i | \(-0.210756\pi\) | ||||
0.788698 | + | 0.614781i | \(0.210756\pi\) | |||||||
\(488\) | −10.7703 | −0.487546 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −27.0221 | −1.22073 | ||||||||
\(491\) | 31.4656 | 1.42002 | 0.710012 | − | 0.704190i | \(-0.248690\pi\) | ||||
0.710012 | + | 0.704190i | \(0.248690\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.41569 | −0.153835 | ||||||||
\(494\) | −39.8049 | −1.79091 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.552506 | 0.0248083 | ||||||||
\(497\) | −8.59515 | −0.385545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.05596 | −0.136804 | −0.0684018 | − | 0.997658i | \(-0.521790\pi\) | ||||
−0.0684018 | + | 0.997658i | \(0.521790\pi\) | |||||||
\(500\) | 40.9517 | 1.83142 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.9632 | 1.33733 | ||||||||
\(503\) | 40.4444 | 1.80333 | 0.901664 | − | 0.432437i | \(-0.142346\pi\) | ||||
0.901664 | + | 0.432437i | \(0.142346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.738393 | −0.0328581 | ||||||||
\(506\) | 108.612 | 4.82841 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −31.8273 | −1.41211 | ||||||||
\(509\) | 41.1229 | 1.82274 | 0.911370 | − | 0.411589i | \(-0.135026\pi\) | ||||
0.911370 | + | 0.411589i | \(0.135026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.71071 | −0.164152 | ||||||||
\(512\) | 6.76620 | 0.299027 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −29.9225 | −1.31983 | ||||||||
\(515\) | −12.0031 | −0.528920 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −57.9172 | −2.54719 | ||||||||
\(518\) | −6.70558 | −0.294626 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 26.5068 | 1.16240 | ||||||||
\(521\) | −20.0545 | −0.878603 | −0.439302 | − | 0.898340i | \(-0.644774\pi\) | ||||
−0.439302 | + | 0.898340i | \(0.644774\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.05018 | −0.177102 | −0.0885510 | − | 0.996072i | \(-0.528224\pi\) | ||||
−0.0885510 | + | 0.996072i | \(0.528224\pi\) | |||||||
\(524\) | −50.4653 | −2.20459 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.1789 | 1.49027 | ||||||||
\(527\) | 0.344244 | 0.0149955 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 62.4181 | 2.71383 | ||||||||
\(530\) | 8.47899 | 0.368304 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.58210 | 0.372081 | ||||||||
\(533\) | 25.8942 | 1.12160 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.77947 | 0.206634 | ||||||||
\(536\) | 3.86698 | 0.167028 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.3906 | 0.577311 | ||||||||
\(539\) | 33.0659 | 1.42425 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.7203 | 1.92268 | 0.961338 | − | 0.275372i | \(-0.0888011\pi\) | ||||
0.961338 | + | 0.275372i | \(0.0888011\pi\) | |||||||
\(542\) | 11.8549 | 0.509212 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.84782 | 0.0792246 | ||||||||
\(545\) | −13.9083 | −0.595765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.1122 | −1.15923 | −0.579617 | − | 0.814889i | \(-0.696798\pi\) | ||||
−0.579617 | + | 0.814889i | \(0.696798\pi\) | |||||||
\(548\) | −31.0551 | −1.32661 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.1224 | −0.900664 | ||||||||
\(551\) | −33.5377 | −1.42875 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.34573 | −0.0997506 | ||||||||
\(554\) | −46.1625 | −1.96126 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.8438 | −0.671925 | ||||||||
\(557\) | 39.8298 | 1.68764 | 0.843822 | − | 0.536624i | \(-0.180301\pi\) | ||||
0.843822 | + | 0.536624i | \(0.180301\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.30879 | 0.266833 | ||||||||
\(560\) | −0.745738 | −0.0315132 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 38.6062 | 1.62850 | ||||||||
\(563\) | 20.2614 | 0.853918 | 0.426959 | − | 0.904271i | \(-0.359585\pi\) | ||||
0.426959 | + | 0.904271i | \(0.359585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.2786 | −1.23176 | ||||||||
\(566\) | 65.5319 | 2.75451 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 39.1947 | 1.64458 | ||||||||
\(569\) | −12.2600 | −0.513966 | −0.256983 | − | 0.966416i | \(-0.582728\pi\) | ||||
−0.256983 | + | 0.966416i | \(0.582728\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.3009 | −1.60284 | −0.801422 | − | 0.598100i | \(-0.795923\pi\) | ||||
−0.801422 | + | 0.598100i | \(0.795923\pi\) | |||||||
\(572\) | −79.9078 | −3.34111 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.89964 | −0.371464 | ||||||||
\(575\) | −16.6117 | −0.692757 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.10968 | −0.295980 | −0.147990 | − | 0.988989i | \(-0.547280\pi\) | ||||
−0.147990 | + | 0.988989i | \(0.547280\pi\) | |||||||
\(578\) | 39.0576 | 1.62458 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 55.0205 | 2.28460 | ||||||||
\(581\) | 7.94496 | 0.329613 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.3754 | −0.429706 | ||||||||
\(584\) | 16.9212 | 0.700205 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.8448 | 1.81121 | ||||||||
\(587\) | 35.2035 | 1.45300 | 0.726502 | − | 0.687165i | \(-0.241145\pi\) | ||||
0.726502 | + | 0.687165i | \(0.241145\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.38002 | 0.139271 | ||||||||
\(590\) | −51.1026 | −2.10386 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.50305 | 0.102875 | ||||||||
\(593\) | −40.5533 | −1.66533 | −0.832663 | − | 0.553780i | \(-0.813185\pi\) | ||||
−0.832663 | + | 0.553780i | \(0.813185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.464638 | −0.0190483 | ||||||||
\(596\) | −2.93649 | −0.120284 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −100.178 | −4.09659 | ||||||||
\(599\) | 30.7944 | 1.25822 | 0.629112 | − | 0.777314i | \(-0.283419\pi\) | ||||
0.629112 | + | 0.777314i | \(0.283419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.1844 | −0.945711 | −0.472855 | − | 0.881140i | \(-0.656777\pi\) | ||||
−0.472855 | + | 0.881140i | \(0.656777\pi\) | |||||||
\(602\) | −2.16828 | −0.0883727 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.23500 | 0.0909408 | ||||||||
\(605\) | −26.3689 | −1.07205 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.78635 | −0.397216 | −0.198608 | − | 0.980079i | \(-0.563642\pi\) | ||||
−0.198608 | + | 0.980079i | \(0.563642\pi\) | |||||||
\(608\) | 18.1432 | 0.735803 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.1050 | 0.571093 | ||||||||
\(611\) | 53.4196 | 2.16113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.39778 | −0.339183 | −0.169592 | − | 0.985514i | \(-0.554245\pi\) | ||||
−0.169592 | + | 0.985514i | \(0.554245\pi\) | |||||||
\(614\) | −29.3151 | −1.18306 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1478 | 0.449158 | ||||||||
\(617\) | 35.2055 | 1.41732 | 0.708660 | − | 0.705550i | \(-0.249300\pi\) | ||||
0.708660 | + | 0.705550i | \(0.249300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.5728 | −1.02786 | −0.513928 | − | 0.857833i | \(-0.671810\pi\) | ||||
−0.513928 | + | 0.857833i | \(0.671810\pi\) | |||||||
\(620\) | −5.54513 | −0.222698 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −75.8470 | −3.04119 | ||||||||
\(623\) | 2.37246 | 0.0950505 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.7825 | −0.511301 | ||||||||
\(626\) | 48.1218 | 1.92333 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.3362 | 1.29036 | ||||||||
\(629\) | 1.55954 | 0.0621831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.2488 | 1.84114 | 0.920568 | − | 0.390583i | \(-0.127726\pi\) | ||||
0.920568 | + | 0.390583i | \(0.127726\pi\) | |||||||
\(632\) | 10.6968 | 0.425494 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −60.6859 | −2.41015 | ||||||||
\(635\) | 16.9190 | 0.671411 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −30.4982 | −1.20838 | ||||||||
\(638\) | −107.325 | −4.24902 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −34.7421 | −1.37330 | ||||||||
\(641\) | 5.89743 | 0.232934 | 0.116467 | − | 0.993195i | \(-0.462843\pi\) | ||||
0.116467 | + | 0.993195i | \(0.462843\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.507148 | −0.0200000 | −0.00999999 | − | 0.999950i | \(-0.503183\pi\) | ||||
−0.00999999 | + | 0.999950i | \(0.503183\pi\) | |||||||
\(644\) | 21.5988 | 0.851113 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.18177 | −0.125185 | ||||||||
\(647\) | 46.6012 | 1.83208 | 0.916041 | − | 0.401085i | \(-0.131367\pi\) | ||||
0.916041 | + | 0.401085i | \(0.131367\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 62.5323 | 2.45461 | ||||||||
\(650\) | 19.4822 | 0.764154 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −39.2505 | −1.53717 | ||||||||
\(653\) | 28.1513 | 1.10165 | 0.550823 | − | 0.834622i | \(-0.314314\pi\) | ||||
0.550823 | + | 0.834622i | \(0.314314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.8267 | 1.04821 | ||||||||
\(656\) | 3.32204 | 0.129704 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.3599 | −0.715745 | ||||||||
\(659\) | 15.5857 | 0.607134 | 0.303567 | − | 0.952810i | \(-0.401822\pi\) | ||||
0.303567 | + | 0.952810i | \(0.401822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.81367 | −0.109439 | −0.0547195 | − | 0.998502i | \(-0.517426\pi\) | ||||
−0.0547195 | + | 0.998502i | \(0.517426\pi\) | |||||||
\(662\) | −57.3995 | −2.23089 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36.2298 | −1.40599 | ||||||||
\(665\) | −4.56214 | −0.176912 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −84.4052 | −3.26818 | ||||||||
\(668\) | −50.6198 | −1.95854 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.06428 | −0.195650 | ||||||||
\(671\) | −17.2597 | −0.666303 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0542 | 0.618842 | 0.309421 | − | 0.950925i | \(-0.399865\pi\) | ||||
0.309421 | + | 0.950925i | \(0.399865\pi\) | |||||||
\(674\) | 12.8591 | 0.495315 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 29.9382 | 1.15147 | ||||||||
\(677\) | 31.0430 | 1.19308 | 0.596540 | − | 0.802583i | \(-0.296542\pi\) | ||||
0.596540 | + | 0.802583i | \(0.296542\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.82987 | −0.262106 | ||||||||
\(680\) | 2.11880 | 0.0812522 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.8165 | 0.414184 | ||||||||
\(683\) | −12.0994 | −0.462970 | −0.231485 | − | 0.972838i | \(-0.574358\pi\) | ||||
−0.231485 | + | 0.972838i | \(0.574358\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.5085 | 0.630757 | ||||||||
\(686\) | 21.7390 | 0.829997 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.809373 | 0.0308571 | ||||||||
\(689\) | 9.56971 | 0.364577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.9787 | 1.36869 | 0.684346 | − | 0.729157i | \(-0.260088\pi\) | ||||
0.684346 | + | 0.729157i | \(0.260088\pi\) | |||||||
\(692\) | 39.5375 | 1.50299 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −75.1251 | −2.85171 | ||||||||
\(695\) | 8.42235 | 0.319478 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.06983 | 0.0784003 | ||||||||
\(698\) | −6.99996 | −0.264953 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.20044 | −0.158762 | ||||||||
\(701\) | −17.6047 | −0.664919 | −0.332459 | − | 0.943118i | \(-0.607878\pi\) | ||||
−0.332459 | + | 0.943118i | \(0.607878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3127 | 0.577529 | ||||||||
\(704\) | 64.1507 | 2.41777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.8069 | 0.632535 | ||||||||
\(707\) | 0.286426 | 0.0107722 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.06306 | 0.265259 | 0.132629 | − | 0.991166i | \(-0.457658\pi\) | ||||
0.132629 | + | 0.991166i | \(0.457658\pi\) | |||||||
\(710\) | −51.3303 | −1.92639 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.8186 | −0.405446 | ||||||||
\(713\) | 8.50661 | 0.318575 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.4780 | 1.58859 | ||||||||
\(716\) | 30.5149 | 1.14039 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.62438 | −0.284539 | ||||||||
\(719\) | 0.00798484 | 0.000297784 0 | 0.000148892 | − | 1.00000i | \(-0.499953\pi\) | ||||
0.000148892 | 1.00000i | \(0.499953\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.65606 | 0.173401 | ||||||||
\(722\) | 12.7740 | 0.475399 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 40.5555 | 1.50723 | ||||||||
\(725\) | 16.4148 | 0.609629 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.1360 | 1.89653 | 0.948265 | − | 0.317479i | \(-0.102836\pi\) | ||||
0.948265 | + | 0.317479i | \(0.102836\pi\) | |||||||
\(728\) | −10.2821 | −0.381081 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −22.1604 | −0.820193 | ||||||||
\(731\) | 0.504287 | 0.0186517 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.8058 | 1.10090 | 0.550451 | − | 0.834868i | \(-0.314456\pi\) | ||||
0.550451 | + | 0.834868i | \(0.314456\pi\) | |||||||
\(734\) | −8.51312 | −0.314225 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 45.6615 | 1.68310 | ||||||||
\(737\) | 6.19697 | 0.228268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.3189 | 1.59351 | 0.796756 | − | 0.604302i | \(-0.206548\pi\) | ||||
0.796756 | + | 0.604302i | \(0.206548\pi\) | |||||||
\(740\) | −25.1214 | −0.923480 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.28904 | −0.120745 | ||||||||
\(743\) | 21.6495 | 0.794244 | 0.397122 | − | 0.917766i | \(-0.370009\pi\) | ||||
0.397122 | + | 0.917766i | \(0.370009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.56101 | 0.0571908 | ||||||||
\(746\) | −44.3180 | −1.62260 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.38736 | −0.233545 | ||||||||
\(749\) | −1.85398 | −0.0677429 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.21926 | −0.226944 | −0.113472 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113472 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(752\) | 6.85337 | 0.249917 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 98.9902 | 3.60501 | ||||||||
\(755\) | −1.18810 | −0.0432393 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.3786 | 1.21317 | 0.606583 | − | 0.795020i | \(-0.292540\pi\) | ||||
0.606583 | + | 0.795020i | \(0.292540\pi\) | |||||||
\(758\) | −22.2864 | −0.809479 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.8038 | 0.754634 | ||||||||
\(761\) | −15.1807 | −0.550301 | −0.275151 | − | 0.961401i | \(-0.588728\pi\) | ||||
−0.275151 | + | 0.961401i | \(0.588728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.39508 | 0.195315 | ||||||||
\(764\) | −30.2948 | −1.09603 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.8915 | −0.501919 | ||||||||
\(767\) | −57.6764 | −2.08257 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.5453 | 0.993310 | 0.496655 | − | 0.867948i | \(-0.334561\pi\) | ||||
0.496655 | + | 0.867948i | \(0.334561\pi\) | |||||||
\(770\) | −14.5994 | −0.526126 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.08523 | 0.183021 | ||||||||
\(773\) | −31.5503 | −1.13479 | −0.567393 | − | 0.823447i | \(-0.692048\pi\) | ||||
−0.567393 | + | 0.823447i | \(0.692048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.65433 | −0.0594252 | ||||||||
\(776\) | 31.1449 | 1.11804 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −59.0322 | −2.11641 | ||||||||
\(779\) | 20.3230 | 0.728147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 62.8109 | 2.24755 | ||||||||
\(782\) | −8.00764 | −0.286353 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.91270 | −0.139739 | ||||||||
\(785\) | −17.1895 | −0.613521 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.566008 | −0.0201760 | −0.0100880 | − | 0.999949i | \(-0.503211\pi\) | ||||
−0.0100880 | + | 0.999949i | \(0.503211\pi\) | |||||||
\(788\) | 76.1311 | 2.71206 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.0087 | −0.498408 | ||||||||
\(791\) | 11.3573 | 0.403819 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.9194 | 0.565314 | ||||||||
\(794\) | −57.5716 | −2.04314 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 49.0197 | 1.73746 | ||||||||
\(797\) | 26.6443 | 0.943789 | 0.471894 | − | 0.881655i | \(-0.343570\pi\) | ||||
0.471894 | + | 0.881655i | \(0.343570\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.27005 | 0.151063 | ||||||||
\(800\) | −8.88004 | −0.313957 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.9321 | −1.30412 | ||||||||
\(803\) | 27.1168 | 0.956931 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.4817 | −0.404676 | ||||||||
\(806\) | −9.97652 | −0.351408 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.30613 | −0.0459496 | ||||||||
\(809\) | 35.8890 | 1.26179 | 0.630895 | − | 0.775868i | \(-0.282688\pi\) | ||||
0.630895 | + | 0.775868i | \(0.282688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.5695 | 1.14367 | 0.571835 | − | 0.820369i | \(-0.306232\pi\) | ||||
0.571835 | + | 0.820369i | \(0.306232\pi\) | |||||||
\(812\) | −21.3427 | −0.748983 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 49.0024 | 1.71753 | ||||||||
\(815\) | 20.8651 | 0.730872 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.95144 | 0.173229 | ||||||||
\(818\) | 37.5012 | 1.31120 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33.3411 | −1.16432 | ||||||||
\(821\) | −0.800013 | −0.0279206 | −0.0139603 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139603 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4706 | −0.887850 | −0.443925 | − | 0.896064i | \(-0.646414\pi\) | ||||
−0.443925 | + | 0.896064i | \(0.646414\pi\) | |||||||
\(824\) | −21.2321 | −0.739655 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.8229 | 0.689728 | ||||||||
\(827\) | 19.3649 | 0.673385 | 0.336692 | − | 0.941615i | \(-0.390692\pi\) | ||||
0.336692 | + | 0.941615i | \(0.390692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.7068 | −1.10122 | −0.550612 | − | 0.834761i | \(-0.685606\pi\) | ||||
−0.550612 | + | 0.834761i | \(0.685606\pi\) | |||||||
\(830\) | 47.4474 | 1.64692 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −59.1691 | −2.05132 | ||||||||
\(833\) | −2.43784 | −0.0844662 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 26.9089 | 0.931221 | ||||||||
\(836\) | −62.7155 | −2.16906 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 49.7990 | 1.72028 | ||||||||
\(839\) | −33.4750 | −1.15568 | −0.577842 | − | 0.816149i | \(-0.696105\pi\) | ||||
−0.577842 | + | 0.816149i | \(0.696105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.4044 | 1.87601 | ||||||||
\(842\) | 74.5580 | 2.56944 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 74.3421 | 2.55896 | ||||||||
\(845\) | −15.9148 | −0.547486 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.2286 | 0.351460 | ||||||||
\(848\) | 1.22773 | 0.0421603 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.55729 | 0.0534146 | ||||||||
\(851\) | 38.5379 | 1.32106 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.7066 | 0.777460 | 0.388730 | − | 0.921352i | \(-0.372914\pi\) | ||||
0.388730 | + | 0.921352i | \(0.372914\pi\) | |||||||
\(854\) | −5.47138 | −0.187227 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.45432 | 0.288963 | ||||||||
\(857\) | 35.4417 | 1.21067 | 0.605333 | − | 0.795973i | \(-0.293040\pi\) | ||||
0.605333 | + | 0.795973i | \(0.293040\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.3038 | 1.81870 | 0.909351 | − | 0.416029i | \(-0.136579\pi\) | ||||
0.909351 | + | 0.416029i | \(0.136579\pi\) | |||||||
\(860\) | −8.12313 | −0.276997 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.4762 | −1.41269 | ||||||||
\(863\) | 33.0046 | 1.12349 | 0.561745 | − | 0.827310i | \(-0.310130\pi\) | ||||
0.561745 | + | 0.827310i | \(0.310130\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0177 | −0.714622 | ||||||||
\(866\) | 73.9845 | 2.51409 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.15098 | 0.0730091 | ||||||||
\(869\) | 17.1419 | 0.581500 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.71574 | −0.193671 | ||||||||
\(872\) | −24.6021 | −0.833133 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −78.6246 | −2.65952 | ||||||||
\(875\) | 8.44446 | 0.285475 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.0251686 | −0.000849883 0 | −0.000424942 | − | 1.00000i | \(-0.500135\pi\) | ||||
−0.000424942 | 1.00000i | \(0.500135\pi\) | ||||||||
\(878\) | −11.1482 | −0.376233 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.44964 | 0.183707 | ||||||||
\(881\) | 8.28965 | 0.279286 | 0.139643 | − | 0.990202i | \(-0.455405\pi\) | ||||
0.139643 | + | 0.990202i | \(0.455405\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.4759 | 1.79961 | 0.899803 | − | 0.436296i | \(-0.143710\pi\) | ||||
0.899803 | + | 0.436296i | \(0.143710\pi\) | |||||||
\(884\) | 5.89135 | 0.198147 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.6082 | −1.09549 | ||||||||
\(887\) | 17.2857 | 0.580399 | 0.290199 | − | 0.956966i | \(-0.406278\pi\) | ||||
0.290199 | + | 0.956966i | \(0.406278\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.56297 | −0.220115 | ||||||||
\(890\) | 14.1683 | 0.474923 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.36649 | −0.112718 | ||||||||
\(893\) | 41.9263 | 1.40301 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.2213 | −0.542219 | ||||||||
\(896\) | 13.4766 | 0.450223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.9235 | 0.598114 | ||||||||
\(899\) | −8.40574 | −0.280347 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.764946 | 0.0254841 | ||||||||
\(902\) | 65.0360 | 2.16546 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −51.7904 | −1.72252 | ||||||||
\(905\) | −21.5588 | −0.716639 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.0950 | 0.700447 | 0.350223 | − | 0.936666i | \(-0.386106\pi\) | ||||
0.350223 | + | 0.936666i | \(0.386106\pi\) | |||||||
\(908\) | 59.3713 | 1.97031 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.4657 | 0.446383 | ||||||||
\(911\) | −38.3792 | −1.27156 | −0.635780 | − | 0.771870i | \(-0.719322\pi\) | ||||
−0.635780 | + | 0.771870i | \(0.719322\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58.0595 | −1.92149 | ||||||||
\(914\) | −5.61152 | −0.185613 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.2454 | −0.900214 | ||||||||
\(917\) | −10.4062 | −0.343644 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.6007 | −1.66916 | −0.834582 | − | 0.550884i | \(-0.814291\pi\) | ||||
−0.834582 | + | 0.550884i | \(0.814291\pi\) | |||||||
\(920\) | 52.3576 | 1.72618 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −7.28499 | −0.239918 | ||||||||
\(923\) | −57.9333 | −1.90690 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.49468 | −0.246424 | ||||||||
\(926\) | −33.8923 | −1.11377 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −45.1201 | −1.48114 | ||||||||
\(929\) | −42.1910 | −1.38424 | −0.692121 | − | 0.721781i | \(-0.743324\pi\) | ||||
−0.692121 | + | 0.721781i | \(0.743324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.9364 | −0.784485 | ||||||||
\(932\) | −38.6219 | −1.26510 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 87.4668 | 2.86200 | ||||||||
\(935\) | 3.39544 | 0.111043 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.8880 | 0.813056 | 0.406528 | − | 0.913638i | \(-0.366739\pi\) | ||||
0.406528 | + | 0.913638i | \(0.366739\pi\) | |||||||
\(938\) | 1.96446 | 0.0641419 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −68.7826 | −2.24344 | ||||||||
\(941\) | 55.5293 | 1.81020 | 0.905101 | − | 0.425197i | \(-0.139795\pi\) | ||||
0.905101 | + | 0.425197i | \(0.139795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51.1475 | 1.66559 | ||||||||
\(944\) | −7.39947 | −0.240832 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.8452 | 0.515172 | ||||||||
\(947\) | −51.7979 | −1.68321 | −0.841603 | − | 0.540096i | \(-0.818388\pi\) | ||||
−0.841603 | + | 0.540096i | \(0.818388\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.0111 | −0.811893 | ||||||||
\(950\) | 15.2906 | 0.496091 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.821891 | −0.0266377 | ||||||||
\(953\) | −45.4715 | −1.47297 | −0.736484 | − | 0.676455i | \(-0.763515\pi\) | ||||
−0.736484 | + | 0.676455i | \(0.763515\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.1044 | 0.521125 | ||||||||
\(956\) | −50.8331 | −1.64406 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25.9524 | 0.838483 | ||||||||
\(959\) | −6.40372 | −0.206787 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1528 | −0.972672 | ||||||||
\(962\) | −45.1972 | −1.45721 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.1245 | 0.326088 | ||||||||
\(965\) | −2.70325 | −0.0870206 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.52027 | 0.0810463 | 0.0405232 | − | 0.999179i | \(-0.487098\pi\) | ||||
0.0405232 | + | 0.999179i | \(0.487098\pi\) | |||||||
\(968\) | −46.6436 | −1.49918 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.7880 | −1.30962 | ||||||||
\(971\) | 37.2035 | 1.19392 | 0.596958 | − | 0.802273i | \(-0.296376\pi\) | ||||
0.596958 | + | 0.802273i | \(0.296376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.26707 | −0.104737 | ||||||||
\(974\) | −80.6400 | −2.58387 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.04235 | 0.0653739 | ||||||||
\(977\) | 31.3860 | 1.00413 | 0.502064 | − | 0.864830i | \(-0.332574\pi\) | ||||
0.502064 | + | 0.864830i | \(0.332574\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.3372 | −0.554100 | ||||||||
\(980\) | 39.2691 | 1.25441 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −72.8923 | −2.32609 | ||||||||
\(983\) | 23.1176 | 0.737337 | 0.368668 | − | 0.929561i | \(-0.379814\pi\) | ||||
0.368668 | + | 0.929561i | \(0.379814\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −40.4704 | −1.28949 | ||||||||
\(986\) | 7.91269 | 0.251991 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 57.8454 | 1.84031 | ||||||||
\(989\) | 12.4614 | 0.396251 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.6114 | 0.654743 | 0.327371 | − | 0.944896i | \(-0.393837\pi\) | ||||
0.327371 | + | 0.944896i | \(0.393837\pi\) | |||||||
\(992\) | 4.54733 | 0.144378 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.9113 | 0.631547 | ||||||||
\(995\) | −26.0583 | −0.826103 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.3446 | 1.65777 | 0.828885 | − | 0.559419i | \(-0.188976\pi\) | ||||
0.828885 | + | 0.559419i | \(0.188976\pi\) | |||||||
\(998\) | 7.07935 | 0.224093 | ||||||||
\(999\) | 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 | 6021.2.a.l.1.3 | ✓ | 10 | |
3.2 | odd | 2 | inner | 6021.2.a.l.1.8 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6021.2.a.l.1.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
6021.2.a.l.1.8 | yes | 10 | 3.2 | odd | 2 | inner |