Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9522,2,Mod(1,9522)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9522, 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("9522.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9522 = 2 \cdot 3^{2} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9522.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: | \(76.0335528047\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\Q(\zeta_{22})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.91899\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9522.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.47889 | 0.661380 | 0.330690 | − | 0.943739i | \(-0.392718\pi\) | ||||
0.330690 | + | 0.943739i | \(0.392718\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.20362 | −1.21085 | −0.605426 | − | 0.795901i | \(-0.706997\pi\) | ||||
−0.605426 | + | 0.795901i | \(0.706997\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.47889 | −0.467667 | ||||||||
\(11\) | −0.0552927 | −0.0166714 | −0.00833568 | − | 0.999965i | \(-0.502653\pi\) | ||||
−0.00833568 | + | 0.999965i | \(0.502653\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.805738 | −0.223472 | −0.111736 | − | 0.993738i | \(-0.535641\pi\) | ||||
−0.111736 | + | 0.993738i | \(0.535641\pi\) | |||||||
\(14\) | 3.20362 | 0.856202 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.05954 | −0.499511 | −0.249756 | − | 0.968309i | \(-0.580350\pi\) | ||||
−0.249756 | + | 0.968309i | \(0.580350\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.67657 | −0.843464 | −0.421732 | − | 0.906721i | \(-0.638578\pi\) | ||||
−0.421732 | + | 0.906721i | \(0.638578\pi\) | |||||||
\(20\) | 1.47889 | 0.330690 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0552927 | 0.0117884 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.81288 | −0.562576 | ||||||||
\(26\) | 0.805738 | 0.158018 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.20362 | −0.605426 | ||||||||
\(29\) | −7.34575 | −1.36407 | −0.682036 | − | 0.731319i | \(-0.738905\pi\) | ||||
−0.682036 | + | 0.731319i | \(0.738905\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.95546 | −1.42884 | −0.714422 | − | 0.699715i | \(-0.753310\pi\) | ||||
−0.714422 | + | 0.699715i | \(0.753310\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.05954 | 0.353208 | ||||||||
\(35\) | −4.73780 | −0.800834 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.08816 | −0.507690 | −0.253845 | − | 0.967245i | \(-0.581695\pi\) | ||||
−0.253845 | + | 0.967245i | \(0.581695\pi\) | |||||||
\(38\) | 3.67657 | 0.596419 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.47889 | −0.233833 | ||||||||
\(41\) | 1.45973 | 0.227972 | 0.113986 | − | 0.993482i | \(-0.463638\pi\) | ||||
0.113986 | + | 0.993482i | \(0.463638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.5322 | −1.91115 | −0.955574 | − | 0.294750i | \(-0.904764\pi\) | ||||
−0.955574 | + | 0.294750i | \(0.904764\pi\) | |||||||
\(44\) | −0.0552927 | −0.00833568 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.27459 | 0.185918 | 0.0929591 | − | 0.995670i | \(-0.470367\pi\) | ||||
0.0929591 | + | 0.995670i | \(0.470367\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.26315 | 0.466165 | ||||||||
\(50\) | 2.81288 | 0.397801 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.805738 | −0.111736 | ||||||||
\(53\) | 11.0449 | 1.51713 | 0.758564 | − | 0.651599i | \(-0.225901\pi\) | ||||
0.758564 | + | 0.651599i | \(0.225901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0817718 | −0.0110261 | ||||||||
\(56\) | 3.20362 | 0.428101 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.34575 | 0.964544 | ||||||||
\(59\) | 5.36077 | 0.697913 | 0.348956 | − | 0.937139i | \(-0.386536\pi\) | ||||
0.348956 | + | 0.937139i | \(0.386536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2015 | 1.56224 | 0.781120 | − | 0.624380i | \(-0.214648\pi\) | ||||
0.781120 | + | 0.624380i | \(0.214648\pi\) | |||||||
\(62\) | 7.95546 | 1.01034 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.19160 | −0.147800 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.52116 | 0.552348 | 0.276174 | − | 0.961108i | \(-0.410933\pi\) | ||||
0.276174 | + | 0.961108i | \(0.410933\pi\) | |||||||
\(68\) | −2.05954 | −0.249756 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.73780 | 0.566275 | ||||||||
\(71\) | 14.6029 | 1.73304 | 0.866522 | − | 0.499138i | \(-0.166350\pi\) | ||||
0.866522 | + | 0.499138i | \(0.166350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.86160 | −1.15421 | −0.577106 | − | 0.816669i | \(-0.695818\pi\) | ||||
−0.577106 | + | 0.816669i | \(0.695818\pi\) | |||||||
\(74\) | 3.08816 | 0.358991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.67657 | −0.421732 | ||||||||
\(77\) | 0.177136 | 0.0201866 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.61983 | 0.407262 | 0.203631 | − | 0.979048i | \(-0.434726\pi\) | ||||
0.203631 | + | 0.979048i | \(0.434726\pi\) | |||||||
\(80\) | 1.47889 | 0.165345 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.45973 | −0.161201 | ||||||||
\(83\) | 10.0343 | 1.10140 | 0.550702 | − | 0.834702i | \(-0.314360\pi\) | ||||
0.550702 | + | 0.834702i | \(0.314360\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.04583 | −0.330367 | ||||||||
\(86\) | 12.5322 | 1.35139 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.0552927 | 0.00589422 | ||||||||
\(89\) | 8.25248 | 0.874762 | 0.437381 | − | 0.899276i | \(-0.355906\pi\) | ||||
0.437381 | + | 0.899276i | \(0.355906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.58128 | 0.270591 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.27459 | −0.131464 | ||||||||
\(95\) | −5.43725 | −0.557850 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.01618 | 0.712386 | 0.356193 | − | 0.934412i | \(-0.384075\pi\) | ||||
0.356193 | + | 0.934412i | \(0.384075\pi\) | |||||||
\(98\) | −3.26315 | −0.329628 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.81288 | −0.281288 | ||||||||
\(101\) | −15.3507 | −1.52745 | −0.763725 | − | 0.645542i | \(-0.776632\pi\) | ||||
−0.763725 | + | 0.645542i | \(0.776632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3219 | 1.50971 | 0.754854 | − | 0.655893i | \(-0.227708\pi\) | ||||
0.754854 | + | 0.655893i | \(0.227708\pi\) | |||||||
\(104\) | 0.805738 | 0.0790091 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.0449 | −1.07277 | ||||||||
\(107\) | 9.67542 | 0.935358 | 0.467679 | − | 0.883898i | \(-0.345090\pi\) | ||||
0.467679 | + | 0.883898i | \(0.345090\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4002 | −1.28350 | −0.641752 | − | 0.766912i | \(-0.721792\pi\) | ||||
−0.641752 | + | 0.766912i | \(0.721792\pi\) | |||||||
\(110\) | 0.0817718 | 0.00779664 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.20362 | −0.302713 | ||||||||
\(113\) | −8.22890 | −0.774110 | −0.387055 | − | 0.922057i | \(-0.626508\pi\) | ||||
−0.387055 | + | 0.922057i | \(0.626508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.34575 | −0.682036 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.36077 | −0.493499 | ||||||||
\(119\) | 6.59797 | 0.604835 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9969 | −0.999722 | ||||||||
\(122\) | −12.2015 | −1.10467 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.95546 | −0.714422 | ||||||||
\(125\) | −11.5544 | −1.03346 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.3524 | 1.71725 | 0.858624 | − | 0.512606i | \(-0.171320\pi\) | ||||
0.858624 | + | 0.512606i | \(0.171320\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.19160 | 0.104510 | ||||||||
\(131\) | 20.9028 | 1.82628 | 0.913141 | − | 0.407643i | \(-0.133649\pi\) | ||||
0.913141 | + | 0.407643i | \(0.133649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.7783 | 1.02131 | ||||||||
\(134\) | −4.52116 | −0.390569 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.05954 | 0.176604 | ||||||||
\(137\) | −5.89909 | −0.503993 | −0.251997 | − | 0.967728i | \(-0.581087\pi\) | ||||
−0.251997 | + | 0.967728i | \(0.581087\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.04356 | −0.342971 | −0.171485 | − | 0.985187i | \(-0.554857\pi\) | ||||
−0.171485 | + | 0.985187i | \(0.554857\pi\) | |||||||
\(140\) | −4.73780 | −0.400417 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.6029 | −1.22545 | ||||||||
\(143\) | 0.0445514 | 0.00372558 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.8636 | −0.902170 | ||||||||
\(146\) | 9.86160 | 0.816152 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.08816 | −0.253845 | ||||||||
\(149\) | 8.21355 | 0.672880 | 0.336440 | − | 0.941705i | \(-0.390777\pi\) | ||||
0.336440 | + | 0.941705i | \(0.390777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8490 | −1.04564 | −0.522820 | − | 0.852443i | \(-0.675120\pi\) | ||||
−0.522820 | + | 0.852443i | \(0.675120\pi\) | |||||||
\(152\) | 3.67657 | 0.298209 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.177136 | −0.0142741 | ||||||||
\(155\) | −11.7653 | −0.945009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.91879 | 0.312754 | 0.156377 | − | 0.987697i | \(-0.450019\pi\) | ||||
0.156377 | + | 0.987697i | \(0.450019\pi\) | |||||||
\(158\) | −3.61983 | −0.287978 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.47889 | −0.116917 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7247 | 1.23165 | 0.615825 | − | 0.787883i | \(-0.288823\pi\) | ||||
0.615825 | + | 0.787883i | \(0.288823\pi\) | |||||||
\(164\) | 1.45973 | 0.113986 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.0343 | −0.778810 | ||||||||
\(167\) | 4.01965 | 0.311050 | 0.155525 | − | 0.987832i | \(-0.450293\pi\) | ||||
0.155525 | + | 0.987832i | \(0.450293\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3508 | −0.950060 | ||||||||
\(170\) | 3.04583 | 0.233605 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.5322 | −0.955574 | ||||||||
\(173\) | −5.25447 | −0.399490 | −0.199745 | − | 0.979848i | \(-0.564011\pi\) | ||||
−0.199745 | + | 0.979848i | \(0.564011\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.01139 | 0.681197 | ||||||||
\(176\) | −0.0552927 | −0.00416784 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.25248 | −0.618550 | ||||||||
\(179\) | 2.11290 | 0.157926 | 0.0789629 | − | 0.996878i | \(-0.474839\pi\) | ||||
0.0789629 | + | 0.996878i | \(0.474839\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.230880 | −0.0171612 | −0.00858058 | − | 0.999963i | \(-0.502731\pi\) | ||||
−0.00858058 | + | 0.999963i | \(0.502731\pi\) | |||||||
\(182\) | −2.58128 | −0.191337 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.56705 | −0.335776 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.113877 | 0.00832753 | ||||||||
\(188\) | 1.27459 | 0.0929591 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.43725 | 0.394460 | ||||||||
\(191\) | −4.40318 | −0.318603 | −0.159302 | − | 0.987230i | \(-0.550924\pi\) | ||||
−0.159302 | + | 0.987230i | \(0.550924\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.4973 | 1.54741 | 0.773704 | − | 0.633547i | \(-0.218402\pi\) | ||||
0.773704 | + | 0.633547i | \(0.218402\pi\) | |||||||
\(194\) | −7.01618 | −0.503733 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.26315 | 0.233082 | ||||||||
\(197\) | −8.89209 | −0.633535 | −0.316768 | − | 0.948503i | \(-0.602598\pi\) | ||||
−0.316768 | + | 0.948503i | \(0.602598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.1550 | 1.28698 | 0.643488 | − | 0.765456i | \(-0.277487\pi\) | ||||
0.643488 | + | 0.765456i | \(0.277487\pi\) | |||||||
\(200\) | 2.81288 | 0.198901 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.3507 | 1.08007 | ||||||||
\(203\) | 23.5330 | 1.65169 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.15879 | 0.150776 | ||||||||
\(206\) | −15.3219 | −1.06752 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.805738 | −0.0558679 | ||||||||
\(209\) | 0.203288 | 0.0140617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2040 | 1.18437 | 0.592187 | − | 0.805801i | \(-0.298265\pi\) | ||||
0.592187 | + | 0.805801i | \(0.298265\pi\) | |||||||
\(212\) | 11.0449 | 0.758564 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.67542 | −0.661398 | ||||||||
\(215\) | −18.5338 | −1.26400 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.4862 | 1.73012 | ||||||||
\(218\) | 13.4002 | 0.907575 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0817718 | −0.00551306 | ||||||||
\(221\) | 1.65945 | 0.111627 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.64578 | −0.645929 | −0.322964 | − | 0.946411i | \(-0.604679\pi\) | ||||
−0.322964 | + | 0.946411i | \(0.604679\pi\) | |||||||
\(224\) | 3.20362 | 0.214051 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.22890 | 0.547378 | ||||||||
\(227\) | 13.2879 | 0.881951 | 0.440975 | − | 0.897519i | \(-0.354633\pi\) | ||||
0.440975 | + | 0.897519i | \(0.354633\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3343 | 0.682912 | 0.341456 | − | 0.939898i | \(-0.389080\pi\) | ||||
0.341456 | + | 0.939898i | \(0.389080\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.34575 | 0.482272 | ||||||||
\(233\) | 0.221377 | 0.0145029 | 0.00725144 | − | 0.999974i | \(-0.497692\pi\) | ||||
0.00725144 | + | 0.999974i | \(0.497692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.88498 | 0.122963 | ||||||||
\(236\) | 5.36077 | 0.348956 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.59797 | −0.427683 | ||||||||
\(239\) | −10.0933 | −0.652880 | −0.326440 | − | 0.945218i | \(-0.605849\pi\) | ||||
−0.326440 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.49660 | −0.160820 | −0.0804099 | − | 0.996762i | \(-0.525623\pi\) | ||||
−0.0804099 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(242\) | 10.9969 | 0.706910 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.2015 | 0.781120 | ||||||||
\(245\) | 4.82585 | 0.308312 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.96236 | 0.188490 | ||||||||
\(248\) | 7.95546 | 0.505172 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.5544 | 0.730765 | ||||||||
\(251\) | −14.3756 | −0.907379 | −0.453690 | − | 0.891160i | \(-0.649893\pi\) | ||||
−0.453690 | + | 0.891160i | \(0.649893\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −19.3524 | −1.21428 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.1087 | 1.06721 | 0.533606 | − | 0.845733i | \(-0.320836\pi\) | ||||
0.533606 | + | 0.845733i | \(0.320836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.89326 | 0.614738 | ||||||||
\(260\) | −1.19160 | −0.0738999 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.9028 | −1.29138 | ||||||||
\(263\) | 9.82969 | 0.606125 | 0.303062 | − | 0.952971i | \(-0.401991\pi\) | ||||
0.303062 | + | 0.952971i | \(0.401991\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.3341 | 1.00340 | ||||||||
\(266\) | −11.7783 | −0.722176 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.52116 | 0.276174 | ||||||||
\(269\) | −27.0424 | −1.64881 | −0.824404 | − | 0.566002i | \(-0.808489\pi\) | ||||
−0.824404 | + | 0.566002i | \(0.808489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0124 | 0.851195 | 0.425597 | − | 0.904913i | \(-0.360064\pi\) | ||||
0.425597 | + | 0.904913i | \(0.360064\pi\) | |||||||
\(272\) | −2.05954 | −0.124878 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.89909 | 0.356377 | ||||||||
\(275\) | 0.155532 | 0.00937891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.65528 | −0.399877 | −0.199938 | − | 0.979808i | \(-0.564074\pi\) | ||||
−0.199938 | + | 0.979808i | \(0.564074\pi\) | |||||||
\(278\) | 4.04356 | 0.242517 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.73780 | 0.283138 | ||||||||
\(281\) | 14.7244 | 0.878384 | 0.439192 | − | 0.898393i | \(-0.355265\pi\) | ||||
0.439192 | + | 0.898393i | \(0.355265\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.6907 | −0.813827 | −0.406914 | − | 0.913467i | \(-0.633395\pi\) | ||||
−0.406914 | + | 0.913467i | \(0.633395\pi\) | |||||||
\(284\) | 14.6029 | 0.866522 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0445514 | −0.00263438 | ||||||||
\(287\) | −4.67642 | −0.276041 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.7583 | −0.750489 | ||||||||
\(290\) | 10.8636 | 0.637931 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.86160 | −0.577106 | ||||||||
\(293\) | −29.6195 | −1.73039 | −0.865194 | − | 0.501437i | \(-0.832805\pi\) | ||||
−0.865194 | + | 0.501437i | \(0.832805\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.92800 | 0.461586 | ||||||||
\(296\) | 3.08816 | 0.179495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.21355 | −0.475798 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 40.1485 | 2.31412 | ||||||||
\(302\) | 12.8490 | 0.739380 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.67657 | −0.210866 | ||||||||
\(305\) | 18.0447 | 1.03324 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.12670 | 0.520888 | 0.260444 | − | 0.965489i | \(-0.416131\pi\) | ||||
0.260444 | + | 0.965489i | \(0.416131\pi\) | |||||||
\(308\) | 0.177136 | 0.0100933 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.7653 | 0.668222 | ||||||||
\(311\) | −22.9754 | −1.30281 | −0.651407 | − | 0.758728i | \(-0.725821\pi\) | ||||
−0.651407 | + | 0.758728i | \(0.725821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.7421 | 1.11589 | 0.557946 | − | 0.829877i | \(-0.311590\pi\) | ||||
0.557946 | + | 0.829877i | \(0.311590\pi\) | |||||||
\(314\) | −3.91879 | −0.221150 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.61983 | 0.203631 | ||||||||
\(317\) | 20.8318 | 1.17003 | 0.585016 | − | 0.811022i | \(-0.301088\pi\) | ||||
0.585016 | + | 0.811022i | \(0.301088\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.406166 | 0.0227409 | ||||||||
\(320\) | 1.47889 | 0.0826725 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.57204 | 0.421320 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.26645 | 0.125720 | ||||||||
\(326\) | −15.7247 | −0.870909 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.45973 | −0.0806003 | ||||||||
\(329\) | −4.08330 | −0.225120 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.5468 | −0.854527 | −0.427264 | − | 0.904127i | \(-0.640522\pi\) | ||||
−0.427264 | + | 0.904127i | \(0.640522\pi\) | |||||||
\(332\) | 10.0343 | 0.550702 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.01965 | −0.219945 | ||||||||
\(335\) | 6.68631 | 0.365312 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.07769 | 0.385546 | 0.192773 | − | 0.981243i | \(-0.438252\pi\) | ||||
0.192773 | + | 0.981243i | \(0.438252\pi\) | |||||||
\(338\) | 12.3508 | 0.671794 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.04583 | −0.165183 | ||||||||
\(341\) | 0.439879 | 0.0238208 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.9714 | 0.646396 | ||||||||
\(344\) | 12.5322 | 0.675693 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.25447 | 0.282482 | ||||||||
\(347\) | 25.4158 | 1.36439 | 0.682195 | − | 0.731170i | \(-0.261025\pi\) | ||||
0.682195 | + | 0.731170i | \(0.261025\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1316 | −1.23821 | −0.619104 | − | 0.785309i | \(-0.712504\pi\) | ||||
−0.619104 | + | 0.785309i | \(0.712504\pi\) | |||||||
\(350\) | −9.01139 | −0.481679 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0552927 | 0.00294711 | ||||||||
\(353\) | −24.0678 | −1.28100 | −0.640500 | − | 0.767958i | \(-0.721273\pi\) | ||||
−0.640500 | + | 0.767958i | \(0.721273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.5961 | 1.14620 | ||||||||
\(356\) | 8.25248 | 0.437381 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.11290 | −0.111670 | ||||||||
\(359\) | −19.1724 | −1.01188 | −0.505940 | − | 0.862569i | \(-0.668854\pi\) | ||||
−0.505940 | + | 0.862569i | \(0.668854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.48281 | −0.288569 | ||||||||
\(362\) | 0.230880 | 0.0121348 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.58128 | 0.135296 | ||||||||
\(365\) | −14.5842 | −0.763374 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.2686 | −1.37121 | −0.685606 | − | 0.727973i | \(-0.740463\pi\) | ||||
−0.685606 | + | 0.727973i | \(0.740463\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.56705 | 0.237429 | ||||||||
\(371\) | −35.3835 | −1.83702 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4049 | 1.05653 | 0.528263 | − | 0.849081i | \(-0.322844\pi\) | ||||
0.528263 | + | 0.849081i | \(0.322844\pi\) | |||||||
\(374\) | −0.113877 | −0.00588846 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.27459 | −0.0657320 | ||||||||
\(377\) | 5.91875 | 0.304831 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.99029 | 0.204968 | 0.102484 | − | 0.994735i | \(-0.467321\pi\) | ||||
0.102484 | + | 0.994735i | \(0.467321\pi\) | |||||||
\(380\) | −5.43725 | −0.278925 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.40318 | 0.225286 | ||||||||
\(383\) | −6.32220 | −0.323049 | −0.161525 | − | 0.986869i | \(-0.551641\pi\) | ||||
−0.161525 | + | 0.986869i | \(0.551641\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.261966 | 0.0133510 | ||||||||
\(386\) | −21.4973 | −1.09418 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.01618 | 0.356193 | ||||||||
\(389\) | 25.4165 | 1.28867 | 0.644335 | − | 0.764743i | \(-0.277134\pi\) | ||||
0.644335 | + | 0.764743i | \(0.277134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.26315 | −0.164814 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.89209 | 0.447977 | ||||||||
\(395\) | 5.35333 | 0.269355 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.43509 | −0.172402 | −0.0862011 | − | 0.996278i | \(-0.527473\pi\) | ||||
−0.0862011 | + | 0.996278i | \(0.527473\pi\) | |||||||
\(398\) | −18.1550 | −0.910029 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.81288 | −0.140644 | ||||||||
\(401\) | 8.35498 | 0.417228 | 0.208614 | − | 0.977998i | \(-0.433105\pi\) | ||||
0.208614 | + | 0.977998i | \(0.433105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.41002 | 0.319306 | ||||||||
\(404\) | −15.3507 | −0.763725 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.5330 | −1.16792 | ||||||||
\(407\) | 0.170752 | 0.00846388 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.18657 | −0.207013 | −0.103506 | − | 0.994629i | \(-0.533006\pi\) | ||||
−0.103506 | + | 0.994629i | \(0.533006\pi\) | |||||||
\(410\) | −2.15879 | −0.106615 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.3219 | 0.754854 | ||||||||
\(413\) | −17.1738 | −0.845070 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.8396 | 0.728447 | ||||||||
\(416\) | 0.805738 | 0.0395046 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.203288 | −0.00994312 | ||||||||
\(419\) | −8.98508 | −0.438950 | −0.219475 | − | 0.975618i | \(-0.570434\pi\) | ||||
−0.219475 | + | 0.975618i | \(0.570434\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.75886 | −0.329407 | −0.164703 | − | 0.986343i | \(-0.552667\pi\) | ||||
−0.164703 | + | 0.986343i | \(0.552667\pi\) | |||||||
\(422\) | −17.2040 | −0.837478 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11.0449 | −0.536386 | ||||||||
\(425\) | 5.79323 | 0.281013 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.0889 | −1.89164 | ||||||||
\(428\) | 9.67542 | 0.467679 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.5338 | 0.893780 | ||||||||
\(431\) | 22.6737 | 1.09216 | 0.546078 | − | 0.837734i | \(-0.316120\pi\) | ||||
0.546078 | + | 0.837734i | \(0.316120\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.9541 | 1.43950 | 0.719752 | − | 0.694231i | \(-0.244256\pi\) | ||||
0.719752 | + | 0.694231i | \(0.244256\pi\) | |||||||
\(434\) | −25.4862 | −1.22338 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.4002 | −0.641752 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.50141 | −0.0716585 | −0.0358292 | − | 0.999358i | \(-0.511407\pi\) | ||||
−0.0358292 | + | 0.999358i | \(0.511407\pi\) | |||||||
\(440\) | 0.0817718 | 0.00389832 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.65945 | −0.0789319 | ||||||||
\(443\) | 5.89537 | 0.280097 | 0.140049 | − | 0.990145i | \(-0.455274\pi\) | ||||
0.140049 | + | 0.990145i | \(0.455274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2045 | 0.578550 | ||||||||
\(446\) | 9.64578 | 0.456741 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.20362 | −0.151357 | ||||||||
\(449\) | 36.8587 | 1.73947 | 0.869734 | − | 0.493520i | \(-0.164290\pi\) | ||||
0.869734 | + | 0.493520i | \(0.164290\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0807125 | −0.00380061 | ||||||||
\(452\) | −8.22890 | −0.387055 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.2879 | −0.623633 | ||||||||
\(455\) | 3.81743 | 0.178964 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.79767 | −0.271203 | −0.135602 | − | 0.990763i | \(-0.543297\pi\) | ||||
−0.135602 | + | 0.990763i | \(0.543297\pi\) | |||||||
\(458\) | −10.3343 | −0.482892 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.1277 | 0.890864 | 0.445432 | − | 0.895316i | \(-0.353050\pi\) | ||||
0.445432 | + | 0.895316i | \(0.353050\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.3367 | −0.945126 | −0.472563 | − | 0.881297i | \(-0.656671\pi\) | ||||
−0.472563 | + | 0.881297i | \(0.656671\pi\) | |||||||
\(464\) | −7.34575 | −0.341018 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.221377 | −0.0102551 | ||||||||
\(467\) | −27.1467 | −1.25620 | −0.628101 | − | 0.778132i | \(-0.716167\pi\) | ||||
−0.628101 | + | 0.778132i | \(0.716167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.4841 | −0.668812 | ||||||||
\(470\) | −1.88498 | −0.0869477 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.36077 | −0.246749 | ||||||||
\(473\) | 0.692941 | 0.0318615 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3418 | 0.474512 | ||||||||
\(476\) | 6.59797 | 0.302417 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.0933 | 0.461656 | ||||||||
\(479\) | 3.73359 | 0.170592 | 0.0852961 | − | 0.996356i | \(-0.472816\pi\) | ||||
0.0852961 | + | 0.996356i | \(0.472816\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.48825 | 0.113454 | ||||||||
\(482\) | 2.49660 | 0.113717 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9969 | −0.499861 | ||||||||
\(485\) | 10.3762 | 0.471158 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.0573 | 1.04483 | 0.522413 | − | 0.852693i | \(-0.325032\pi\) | ||||
0.522413 | + | 0.852693i | \(0.325032\pi\) | |||||||
\(488\) | −12.2015 | −0.552336 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.82585 | −0.218010 | ||||||||
\(491\) | 1.12229 | 0.0506483 | 0.0253241 | − | 0.999679i | \(-0.491938\pi\) | ||||
0.0253241 | + | 0.999679i | \(0.491938\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.1288 | 0.681369 | ||||||||
\(494\) | −2.96236 | −0.133283 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.95546 | −0.357211 | ||||||||
\(497\) | −46.7821 | −2.09846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.6576 | 1.77532 | 0.887659 | − | 0.460502i | \(-0.152331\pi\) | ||||
0.887659 | + | 0.460502i | \(0.152331\pi\) | |||||||
\(500\) | −11.5544 | −0.516729 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.3756 | 0.641614 | ||||||||
\(503\) | 34.0385 | 1.51770 | 0.758850 | − | 0.651266i | \(-0.225762\pi\) | ||||
0.758850 | + | 0.651266i | \(0.225762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.7020 | −1.01023 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 19.3524 | 0.858624 | ||||||||
\(509\) | −0.940632 | −0.0416928 | −0.0208464 | − | 0.999783i | \(-0.506636\pi\) | ||||
−0.0208464 | + | 0.999783i | \(0.506636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31.5928 | 1.39758 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.1087 | −0.754633 | ||||||||
\(515\) | 22.6594 | 0.998491 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.0704755 | −0.00309951 | ||||||||
\(518\) | −9.89326 | −0.434685 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.19160 | 0.0522551 | ||||||||
\(521\) | 40.4064 | 1.77024 | 0.885119 | − | 0.465366i | \(-0.154077\pi\) | ||||
0.885119 | + | 0.465366i | \(0.154077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0908 | −0.616146 | −0.308073 | − | 0.951363i | \(-0.599684\pi\) | ||||
−0.308073 | + | 0.951363i | \(0.599684\pi\) | |||||||
\(524\) | 20.9028 | 0.913141 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.82969 | −0.428595 | ||||||||
\(527\) | 16.3846 | 0.713723 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | −16.3341 | −0.709510 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.7783 | 0.510655 | ||||||||
\(533\) | −1.17616 | −0.0509453 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.3089 | 0.618628 | ||||||||
\(536\) | −4.52116 | −0.195285 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 27.0424 | 1.16588 | ||||||||
\(539\) | −0.180428 | −0.00777160 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.0267 | −1.37694 | −0.688468 | − | 0.725267i | \(-0.741716\pi\) | ||||
−0.688468 | + | 0.725267i | \(0.741716\pi\) | |||||||
\(542\) | −14.0124 | −0.601885 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.05954 | 0.0883019 | ||||||||
\(545\) | −19.8174 | −0.848885 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.2269 | −1.46344 | −0.731718 | − | 0.681607i | \(-0.761281\pi\) | ||||
−0.731718 | + | 0.681607i | \(0.761281\pi\) | |||||||
\(548\) | −5.89909 | −0.251997 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.155532 | −0.00663189 | ||||||||
\(551\) | 27.0072 | 1.15054 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.5965 | −0.493135 | ||||||||
\(554\) | 6.65528 | 0.282756 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.04356 | −0.171485 | ||||||||
\(557\) | 11.3076 | 0.479117 | 0.239559 | − | 0.970882i | \(-0.422997\pi\) | ||||
0.239559 | + | 0.970882i | \(0.422997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0977 | 0.427087 | ||||||||
\(560\) | −4.73780 | −0.200209 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.7244 | −0.621111 | ||||||||
\(563\) | −17.2976 | −0.729006 | −0.364503 | − | 0.931202i | \(-0.618761\pi\) | ||||
−0.364503 | + | 0.931202i | \(0.618761\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.1697 | −0.511981 | ||||||||
\(566\) | 13.6907 | 0.575463 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.6029 | −0.612724 | ||||||||
\(569\) | −29.0600 | −1.21826 | −0.609129 | − | 0.793071i | \(-0.708481\pi\) | ||||
−0.609129 | + | 0.793071i | \(0.708481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.14635 | 0.131671 | 0.0658354 | − | 0.997830i | \(-0.479029\pi\) | ||||
0.0658354 | + | 0.997830i | \(0.479029\pi\) | |||||||
\(572\) | 0.0445514 | 0.00186279 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.67642 | 0.195190 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8526 | 0.451799 | 0.225900 | − | 0.974151i | \(-0.427468\pi\) | ||||
0.225900 | + | 0.974151i | \(0.427468\pi\) | |||||||
\(578\) | 12.7583 | 0.530676 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −10.8636 | −0.451085 | ||||||||
\(581\) | −32.1459 | −1.33364 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.610700 | −0.0252926 | ||||||||
\(584\) | 9.86160 | 0.408076 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.6195 | 1.22357 | ||||||||
\(587\) | 32.2820 | 1.33242 | 0.666210 | − | 0.745764i | \(-0.267915\pi\) | ||||
0.666210 | + | 0.745764i | \(0.267915\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.2488 | 1.20518 | ||||||||
\(590\) | −7.92800 | −0.326390 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.08816 | −0.126922 | ||||||||
\(593\) | −35.1225 | −1.44231 | −0.721154 | − | 0.692774i | \(-0.756388\pi\) | ||||
−0.721154 | + | 0.692774i | \(0.756388\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.75768 | 0.400026 | ||||||||
\(596\) | 8.21355 | 0.336440 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.0831 | 1.35174 | 0.675870 | − | 0.737021i | \(-0.263768\pi\) | ||||
0.675870 | + | 0.737021i | \(0.263768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.9247 | −1.66935 | −0.834677 | − | 0.550740i | \(-0.814345\pi\) | ||||
−0.834677 | + | 0.550740i | \(0.814345\pi\) | |||||||
\(602\) | −40.1485 | −1.63633 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.8490 | −0.522820 | ||||||||
\(605\) | −16.2633 | −0.661197 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.867250 | 0.0352006 | 0.0176003 | − | 0.999845i | \(-0.494397\pi\) | ||||
0.0176003 | + | 0.999845i | \(0.494397\pi\) | |||||||
\(608\) | 3.67657 | 0.149105 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0447 | −0.730608 | ||||||||
\(611\) | −1.02699 | −0.0415474 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5982 | 0.549227 | 0.274614 | − | 0.961555i | \(-0.411450\pi\) | ||||
0.274614 | + | 0.961555i | \(0.411450\pi\) | |||||||
\(614\) | −9.12670 | −0.368324 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.177136 | −0.00713703 | ||||||||
\(617\) | 42.6638 | 1.71758 | 0.858790 | − | 0.512328i | \(-0.171217\pi\) | ||||
0.858790 | + | 0.512328i | \(0.171217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.5251 | −1.26710 | −0.633551 | − | 0.773701i | \(-0.718403\pi\) | ||||
−0.633551 | + | 0.773701i | \(0.718403\pi\) | |||||||
\(620\) | −11.7653 | −0.472505 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.9754 | 0.921229 | ||||||||
\(623\) | −26.4378 | −1.05921 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.02331 | −0.120932 | ||||||||
\(626\) | −19.7421 | −0.789054 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.91879 | 0.156377 | ||||||||
\(629\) | 6.36017 | 0.253597 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −48.7324 | −1.94001 | −0.970003 | − | 0.243093i | \(-0.921838\pi\) | ||||
−0.970003 | + | 0.243093i | \(0.921838\pi\) | |||||||
\(632\) | −3.61983 | −0.143989 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.8318 | −0.827337 | ||||||||
\(635\) | 28.6201 | 1.13575 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.62925 | −0.104175 | ||||||||
\(638\) | −0.406166 | −0.0160803 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.47889 | −0.0584583 | ||||||||
\(641\) | −30.1834 | −1.19217 | −0.596086 | − | 0.802920i | \(-0.703278\pi\) | ||||
−0.596086 | + | 0.802920i | \(0.703278\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.4723 | 1.35946 | 0.679728 | − | 0.733464i | \(-0.262098\pi\) | ||||
0.679728 | + | 0.733464i | \(0.262098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.57204 | −0.297918 | ||||||||
\(647\) | −13.9668 | −0.549092 | −0.274546 | − | 0.961574i | \(-0.588528\pi\) | ||||
−0.274546 | + | 0.961574i | \(0.588528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.296411 | −0.0116352 | ||||||||
\(650\) | −2.26645 | −0.0888973 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.7247 | 0.615825 | ||||||||
\(653\) | −36.9272 | −1.44507 | −0.722537 | − | 0.691332i | \(-0.757024\pi\) | ||||
−0.722537 | + | 0.691332i | \(0.757024\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.9129 | 1.20787 | ||||||||
\(656\) | 1.45973 | 0.0569930 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.08330 | 0.159184 | ||||||||
\(659\) | 11.0352 | 0.429872 | 0.214936 | − | 0.976628i | \(-0.431046\pi\) | ||||
0.214936 | + | 0.976628i | \(0.431046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.9751 | 1.32148 | 0.660738 | − | 0.750616i | \(-0.270243\pi\) | ||||
0.660738 | + | 0.750616i | \(0.270243\pi\) | |||||||
\(662\) | 15.5468 | 0.604242 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.0343 | −0.389405 | ||||||||
\(665\) | 17.4189 | 0.675475 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 4.01965 | 0.155525 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.68631 | −0.258315 | ||||||||
\(671\) | −0.674653 | −0.0260447 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.3928 | −1.21010 | −0.605052 | − | 0.796186i | \(-0.706848\pi\) | ||||
−0.605052 | + | 0.796186i | \(0.706848\pi\) | |||||||
\(674\) | −7.07769 | −0.272622 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3508 | −0.475030 | ||||||||
\(677\) | 39.3382 | 1.51189 | 0.755944 | − | 0.654636i | \(-0.227178\pi\) | ||||
0.755944 | + | 0.654636i | \(0.227178\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4772 | −0.862594 | ||||||||
\(680\) | 3.04583 | 0.116802 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.439879 | −0.0168438 | ||||||||
\(683\) | −31.6224 | −1.21000 | −0.604998 | − | 0.796227i | \(-0.706826\pi\) | ||||
−0.604998 | + | 0.796227i | \(0.706826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.72412 | −0.333331 | ||||||||
\(686\) | −11.9714 | −0.457071 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.5322 | −0.477787 | ||||||||
\(689\) | −8.89927 | −0.339035 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.2620 | 0.846886 | 0.423443 | − | 0.905923i | \(-0.360821\pi\) | ||||
0.423443 | + | 0.905923i | \(0.360821\pi\) | |||||||
\(692\) | −5.25447 | −0.199745 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.4158 | −0.964770 | ||||||||
\(695\) | −5.97999 | −0.226834 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.00638 | −0.113875 | ||||||||
\(698\) | 23.1316 | 0.875545 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.01139 | 0.340598 | ||||||||
\(701\) | −13.8462 | −0.522964 | −0.261482 | − | 0.965208i | \(-0.584211\pi\) | ||||
−0.261482 | + | 0.965208i | \(0.584211\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3538 | 0.428218 | ||||||||
\(704\) | −0.0552927 | −0.00208392 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0678 | 0.905804 | ||||||||
\(707\) | 49.1777 | 1.84952 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.1026 | 1.84409 | 0.922043 | − | 0.387087i | \(-0.126519\pi\) | ||||
0.922043 | + | 0.387087i | \(0.126519\pi\) | |||||||
\(710\) | −21.5961 | −0.810487 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.25248 | −0.309275 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0658867 | 0.00246402 | ||||||||
\(716\) | 2.11290 | 0.0789629 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.1724 | 0.715507 | ||||||||
\(719\) | −36.5928 | −1.36468 | −0.682341 | − | 0.731034i | \(-0.739038\pi\) | ||||
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −49.0853 | −1.82803 | ||||||||
\(722\) | 5.48281 | 0.204049 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.230880 | −0.00858058 | ||||||||
\(725\) | 20.6627 | 0.767394 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.6107 | 0.690232 | 0.345116 | − | 0.938560i | \(-0.387840\pi\) | ||||
0.345116 | + | 0.938560i | \(0.387840\pi\) | |||||||
\(728\) | −2.58128 | −0.0956684 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.5842 | 0.539787 | ||||||||
\(731\) | 25.8106 | 0.954640 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.6156 | −0.835327 | −0.417664 | − | 0.908602i | \(-0.637151\pi\) | ||||
−0.417664 | + | 0.908602i | \(0.637151\pi\) | |||||||
\(734\) | 26.2686 | 0.969593 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.249987 | −0.00920840 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.8869 | −0.657982 | −0.328991 | − | 0.944333i | \(-0.606709\pi\) | ||||
−0.328991 | + | 0.944333i | \(0.606709\pi\) | |||||||
\(740\) | −4.56705 | −0.167888 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35.3835 | 1.29897 | ||||||||
\(743\) | 22.4379 | 0.823168 | 0.411584 | − | 0.911372i | \(-0.364976\pi\) | ||||
0.411584 | + | 0.911372i | \(0.364976\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.1469 | 0.445030 | ||||||||
\(746\) | −20.4049 | −0.747076 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.113877 | 0.00416377 | ||||||||
\(749\) | −30.9963 | −1.13258 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.9846 | 1.71449 | 0.857246 | − | 0.514907i | \(-0.172174\pi\) | ||||
0.857246 | + | 0.514907i | \(0.172174\pi\) | |||||||
\(752\) | 1.27459 | 0.0464795 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.91875 | −0.215548 | ||||||||
\(755\) | −19.0023 | −0.691566 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.7306 | 1.04423 | 0.522115 | − | 0.852875i | \(-0.325143\pi\) | ||||
0.522115 | + | 0.852875i | \(0.325143\pi\) | |||||||
\(758\) | −3.99029 | −0.144934 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.43725 | 0.197230 | ||||||||
\(761\) | −15.6869 | −0.568651 | −0.284326 | − | 0.958728i | \(-0.591770\pi\) | ||||
−0.284326 | + | 0.958728i | \(0.591770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.9290 | 1.55413 | ||||||||
\(764\) | −4.40318 | −0.159302 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.32220 | 0.228430 | ||||||||
\(767\) | −4.31938 | −0.155964 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.8140 | −0.714509 | −0.357255 | − | 0.934007i | \(-0.616287\pi\) | ||||
−0.357255 | + | 0.934007i | \(0.616287\pi\) | |||||||
\(770\) | −0.261966 | −0.00944058 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.4973 | 0.773704 | ||||||||
\(773\) | −19.5152 | −0.701915 | −0.350957 | − | 0.936391i | \(-0.614144\pi\) | ||||
−0.350957 | + | 0.936391i | \(0.614144\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.3778 | 0.803833 | ||||||||
\(776\) | −7.01618 | −0.251866 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.4165 | −0.911227 | ||||||||
\(779\) | −5.36682 | −0.192286 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.807433 | −0.0288922 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.26315 | 0.116541 | ||||||||
\(785\) | 5.79547 | 0.206849 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0112 | 0.713321 | 0.356661 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356661 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(788\) | −8.89209 | −0.316768 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.35333 | −0.190463 | ||||||||
\(791\) | 26.3622 | 0.937333 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.83121 | −0.349116 | ||||||||
\(794\) | 3.43509 | 0.121907 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.1550 | 0.643488 | ||||||||
\(797\) | 19.7315 | 0.698927 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.62507 | −0.0928682 | ||||||||
\(800\) | 2.81288 | 0.0994503 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.35498 | −0.295024 | ||||||||
\(803\) | 0.545274 | 0.0192423 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.41002 | −0.225783 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.3507 | 0.540035 | ||||||||
\(809\) | −27.7606 | −0.976009 | −0.488005 | − | 0.872841i | \(-0.662275\pi\) | ||||
−0.488005 | + | 0.872841i | \(0.662275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.4982 | 0.649560 | 0.324780 | − | 0.945790i | \(-0.394710\pi\) | ||||
0.324780 | + | 0.945790i | \(0.394710\pi\) | |||||||
\(812\) | 23.5330 | 0.825845 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.170752 | −0.00598487 | ||||||||
\(815\) | 23.2551 | 0.814590 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 46.0757 | 1.61198 | ||||||||
\(818\) | 4.18657 | 0.146380 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.15879 | 0.0753881 | ||||||||
\(821\) | 3.89872 | 0.136066 | 0.0680332 | − | 0.997683i | \(-0.478328\pi\) | ||||
0.0680332 | + | 0.997683i | \(0.478328\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.6654 | −0.476345 | −0.238173 | − | 0.971223i | \(-0.576548\pi\) | ||||
−0.238173 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(824\) | −15.3219 | −0.533762 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.1738 | 0.597554 | ||||||||
\(827\) | −1.97288 | −0.0686037 | −0.0343019 | − | 0.999412i | \(-0.510921\pi\) | ||||
−0.0343019 | + | 0.999412i | \(0.510921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.37133 | 0.221285 | 0.110643 | − | 0.993860i | \(-0.464709\pi\) | ||||
0.110643 | + | 0.993860i | \(0.464709\pi\) | |||||||
\(830\) | −14.8396 | −0.515090 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.805738 | −0.0279339 | ||||||||
\(833\) | −6.72059 | −0.232855 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.94462 | 0.205722 | ||||||||
\(836\) | 0.203288 | 0.00703085 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.98508 | 0.310384 | ||||||||
\(839\) | 0.347463 | 0.0119957 | 0.00599787 | − | 0.999982i | \(-0.498091\pi\) | ||||
0.00599787 | + | 0.999982i | \(0.498091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.9600 | 0.860691 | ||||||||
\(842\) | 6.75886 | 0.232926 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.2040 | 0.592187 | ||||||||
\(845\) | −18.2655 | −0.628351 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.2300 | 1.21052 | ||||||||
\(848\) | 11.0449 | 0.379282 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.79323 | −0.198706 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.0786 | −0.755958 | −0.377979 | − | 0.925814i | \(-0.623381\pi\) | ||||
−0.377979 | + | 0.925814i | \(0.623381\pi\) | |||||||
\(854\) | 39.0889 | 1.33759 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.67542 | −0.330699 | ||||||||
\(857\) | 19.3638 | 0.661454 | 0.330727 | − | 0.943726i | \(-0.392706\pi\) | ||||
0.330727 | + | 0.943726i | \(0.392706\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1662 | −0.346866 | −0.173433 | − | 0.984846i | \(-0.555486\pi\) | ||||
−0.173433 | + | 0.984846i | \(0.555486\pi\) | |||||||
\(860\) | −18.5338 | −0.631998 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.6737 | −0.772271 | ||||||||
\(863\) | 11.7222 | 0.399027 | 0.199514 | − | 0.979895i | \(-0.436064\pi\) | ||||
0.199514 | + | 0.979895i | \(0.436064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.77079 | −0.264215 | ||||||||
\(866\) | −29.9541 | −1.01788 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 25.4862 | 0.865060 | ||||||||
\(869\) | −0.200150 | −0.00678962 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.64287 | −0.123434 | ||||||||
\(872\) | 13.4002 | 0.453787 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 37.0159 | 1.25136 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.3909 | −1.02623 | −0.513114 | − | 0.858321i | \(-0.671508\pi\) | ||||
−0.513114 | + | 0.858321i | \(0.671508\pi\) | |||||||
\(878\) | 1.50141 | 0.0506702 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0817718 | −0.00275653 | ||||||||
\(881\) | 33.3403 | 1.12326 | 0.561632 | − | 0.827387i | \(-0.310174\pi\) | ||||
0.561632 | + | 0.827387i | \(0.310174\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.16297 | −0.173748 | −0.0868740 | − | 0.996219i | \(-0.527688\pi\) | ||||
−0.0868740 | + | 0.996219i | \(0.527688\pi\) | |||||||
\(884\) | 1.65945 | 0.0558133 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.89537 | −0.198059 | ||||||||
\(887\) | 13.6271 | 0.457555 | 0.228777 | − | 0.973479i | \(-0.426527\pi\) | ||||
0.228777 | + | 0.973479i | \(0.426527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.9977 | −2.07933 | ||||||||
\(890\) | −12.2045 | −0.409097 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.64578 | −0.322964 | ||||||||
\(893\) | −4.68613 | −0.156815 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.12476 | 0.104449 | ||||||||
\(896\) | 3.20362 | 0.107025 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −36.8587 | −1.22999 | ||||||||
\(899\) | 58.4388 | 1.94904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.7473 | −0.757822 | ||||||||
\(902\) | 0.0807125 | 0.00268743 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.22890 | 0.273689 | ||||||||
\(905\) | −0.341446 | −0.0113500 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.2146 | −0.737623 | −0.368811 | − | 0.929504i | \(-0.620235\pi\) | ||||
−0.368811 | + | 0.929504i | \(0.620235\pi\) | |||||||
\(908\) | 13.2879 | 0.440975 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.81743 | −0.126546 | ||||||||
\(911\) | 18.1822 | 0.602402 | 0.301201 | − | 0.953561i | \(-0.402612\pi\) | ||||
0.301201 | + | 0.953561i | \(0.402612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.554821 | −0.0183619 | ||||||||
\(914\) | 5.79767 | 0.191770 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.3343 | 0.341456 | ||||||||
\(917\) | −66.9644 | −2.21136 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.2025 | −0.996289 | −0.498145 | − | 0.867094i | \(-0.665985\pi\) | ||||
−0.498145 | + | 0.867094i | \(0.665985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.1277 | −0.629936 | ||||||||
\(923\) | −11.7661 | −0.387286 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.68661 | 0.285614 | ||||||||
\(926\) | 20.3367 | 0.668305 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.34575 | 0.241136 | ||||||||
\(929\) | 25.8080 | 0.846733 | 0.423366 | − | 0.905959i | \(-0.360848\pi\) | ||||
0.423366 | + | 0.905959i | \(0.360848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.9972 | −0.393193 | ||||||||
\(932\) | 0.221377 | 0.00725144 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.1467 | 0.888268 | ||||||||
\(935\) | 0.168412 | 0.00550767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.1514 | −0.494976 | −0.247488 | − | 0.968891i | \(-0.579605\pi\) | ||||
−0.247488 | + | 0.968891i | \(0.579605\pi\) | |||||||
\(938\) | 14.4841 | 0.472922 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.88498 | 0.0614813 | ||||||||
\(941\) | −25.1968 | −0.821391 | −0.410695 | − | 0.911773i | \(-0.634714\pi\) | ||||
−0.410695 | + | 0.911773i | \(0.634714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 5.36077 | 0.174478 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.692941 | −0.0225295 | ||||||||
\(947\) | 0.612556 | 0.0199054 | 0.00995271 | − | 0.999950i | \(-0.496832\pi\) | ||||
0.00995271 | + | 0.999950i | \(0.496832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.94587 | 0.257934 | ||||||||
\(950\) | −10.3418 | −0.335531 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.59797 | −0.213841 | ||||||||
\(953\) | −34.2779 | −1.11037 | −0.555185 | − | 0.831727i | \(-0.687353\pi\) | ||||
−0.555185 | + | 0.831727i | \(0.687353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.51183 | −0.210718 | ||||||||
\(956\) | −10.0933 | −0.326440 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.73359 | −0.120627 | ||||||||
\(959\) | 18.8984 | 0.610262 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32.2894 | 1.04159 | ||||||||
\(962\) | −2.48825 | −0.0802242 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.49660 | −0.0804099 | ||||||||
\(965\) | 31.7921 | 1.02343 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.9004 | 1.05801 | 0.529003 | − | 0.848620i | \(-0.322566\pi\) | ||||
0.529003 | + | 0.848620i | \(0.322566\pi\) | |||||||
\(968\) | 10.9969 | 0.353455 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.3762 | −0.333159 | ||||||||
\(971\) | 15.3464 | 0.492488 | 0.246244 | − | 0.969208i | \(-0.420803\pi\) | ||||
0.246244 | + | 0.969208i | \(0.420803\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.9540 | 0.415287 | ||||||||
\(974\) | −23.0573 | −0.738804 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.2015 | 0.390560 | ||||||||
\(977\) | 7.59382 | 0.242948 | 0.121474 | − | 0.992595i | \(-0.461238\pi\) | ||||
0.121474 | + | 0.992595i | \(0.461238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.456302 | −0.0145835 | ||||||||
\(980\) | 4.82585 | 0.154156 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.12229 | −0.0358137 | ||||||||
\(983\) | −2.79957 | −0.0892924 | −0.0446462 | − | 0.999003i | \(-0.514216\pi\) | ||||
−0.0446462 | + | 0.999003i | \(0.514216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1504 | −0.419008 | ||||||||
\(986\) | −15.1288 | −0.481801 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.96236 | 0.0942451 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.506808 | 0.0160993 | 0.00804964 | − | 0.999968i | \(-0.497438\pi\) | ||||
0.00804964 | + | 0.999968i | \(0.497438\pi\) | |||||||
\(992\) | 7.95546 | 0.252586 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 46.7821 | 1.48384 | ||||||||
\(995\) | 26.8493 | 0.851181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.1136 | 0.383640 | 0.191820 | − | 0.981430i | \(-0.438561\pi\) | ||||
0.191820 | + | 0.981430i | \(0.438561\pi\) | |||||||
\(998\) | −39.6576 | −1.25534 | ||||||||
\(999\) | 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 | 9522.2.a.bt.1.3 | 5 | ||
3.2 | odd | 2 | 3174.2.a.bc.1.3 | 5 | |||
23.4 | even | 11 | 414.2.i.d.361.1 | 10 | |||
23.6 | even | 11 | 414.2.i.d.289.1 | 10 | |||
23.22 | odd | 2 | 9522.2.a.bq.1.3 | 5 | |||
69.29 | odd | 22 | 138.2.e.a.13.1 | ✓ | 10 | ||
69.50 | odd | 22 | 138.2.e.a.85.1 | yes | 10 | ||
69.68 | even | 2 | 3174.2.a.bd.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.2.e.a.13.1 | ✓ | 10 | 69.29 | odd | 22 | ||
138.2.e.a.85.1 | yes | 10 | 69.50 | odd | 22 | ||
414.2.i.d.289.1 | 10 | 23.6 | even | 11 | |||
414.2.i.d.361.1 | 10 | 23.4 | even | 11 | |||
3174.2.a.bc.1.3 | 5 | 3.2 | odd | 2 | |||
3174.2.a.bd.1.3 | 5 | 69.68 | even | 2 | |||
9522.2.a.bq.1.3 | 5 | 23.22 | odd | 2 | |||
9522.2.a.bt.1.3 | 5 | 1.1 | even | 1 | trivial |