Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3762,2,Mod(1,3762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3762.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: | \(30.0397212404\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.469.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.39138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3762.1 |
$q$-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 | ||||||||
\(5\) | 0.391382 | 0.175032 | 0.0875158 | − | 0.996163i | \(-0.472107\pi\) | ||||
0.0875158 | + | 0.996163i | \(0.472107\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.71871 | −0.649611 | −0.324806 | − | 0.945781i | \(-0.605299\pi\) | ||||
−0.324806 | + | 0.945781i | \(0.605299\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.391382 | −0.123766 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.71871 | 1.03138 | 0.515692 | − | 0.856774i | \(-0.327535\pi\) | ||||
0.515692 | + | 0.856774i | \(0.327535\pi\) | |||||||
\(14\) | 1.71871 | 0.459344 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.43742 | −1.31877 | −0.659384 | − | 0.751806i | \(-0.729183\pi\) | ||||
−0.659384 | + | 0.751806i | \(0.729183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.391382 | 0.0875158 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 3.43742 | 0.716751 | 0.358376 | − | 0.933577i | \(-0.383331\pi\) | ||||
0.358376 | + | 0.933577i | \(0.383331\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.84682 | −0.969364 | ||||||||
\(26\) | −3.71871 | −0.729299 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.71871 | −0.324806 | ||||||||
\(29\) | 3.82880 | 0.710991 | 0.355495 | − | 0.934678i | \(-0.384312\pi\) | ||||
0.355495 | + | 0.934678i | \(0.384312\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.06406 | −0.550321 | −0.275160 | − | 0.961398i | \(-0.588731\pi\) | ||||
−0.275160 | + | 0.961398i | \(0.588731\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.43742 | 0.932510 | ||||||||
\(35\) | −0.672673 | −0.113702 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.65465 | −0.765221 | −0.382610 | − | 0.923910i | \(-0.624975\pi\) | ||||
−0.382610 | + | 0.923910i | \(0.624975\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.391382 | −0.0618830 | ||||||||
\(41\) | −1.06406 | −0.166177 | −0.0830887 | − | 0.996542i | \(-0.526478\pi\) | ||||
−0.0830887 | + | 0.996542i | \(0.526478\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.73673 | −0.569846 | −0.284923 | − | 0.958550i | \(-0.591968\pi\) | ||||
−0.284923 | + | 0.958550i | \(0.591968\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.43742 | −0.506820 | ||||||||
\(47\) | 8.22018 | 1.19904 | 0.599519 | − | 0.800361i | \(-0.295359\pi\) | ||||
0.599519 | + | 0.800361i | \(0.295359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.04604 | −0.578005 | ||||||||
\(50\) | 4.84682 | 0.685444 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.71871 | 0.515692 | ||||||||
\(53\) | 1.21724 | 0.167200 | 0.0836001 | − | 0.996499i | \(-0.473358\pi\) | ||||
0.0836001 | + | 0.996499i | \(0.473358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.391382 | 0.0527740 | ||||||||
\(56\) | 1.71871 | 0.229672 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.82880 | −0.502746 | ||||||||
\(59\) | −12.4404 | −1.61960 | −0.809799 | − | 0.586707i | \(-0.800424\pi\) | ||||
−0.809799 | + | 0.586707i | \(0.800424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 3.06406 | 0.389135 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.45544 | 0.180525 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71871 | −0.209974 | −0.104987 | − | 0.994474i | \(-0.533480\pi\) | ||||
−0.104987 | + | 0.994474i | \(0.533480\pi\) | |||||||
\(68\) | −5.43742 | −0.659384 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.672673 | 0.0803998 | ||||||||
\(71\) | −1.04604 | −0.124142 | −0.0620709 | − | 0.998072i | \(-0.519770\pi\) | ||||
−0.0620709 | + | 0.998072i | \(0.519770\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.6576 | 1.59850 | 0.799251 | − | 0.600998i | \(-0.205230\pi\) | ||||
0.799251 | + | 0.600998i | \(0.205230\pi\) | |||||||
\(74\) | 4.65465 | 0.541093 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −1.71871 | −0.195865 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0029 | 1.46295 | 0.731473 | − | 0.681870i | \(-0.238833\pi\) | ||||
0.731473 | + | 0.681870i | \(0.238833\pi\) | |||||||
\(80\) | 0.391382 | 0.0437579 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.06406 | 0.117505 | ||||||||
\(83\) | −8.51949 | −0.935136 | −0.467568 | − | 0.883957i | \(-0.654870\pi\) | ||||
−0.467568 | + | 0.883957i | \(0.654870\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.12811 | −0.230826 | ||||||||
\(86\) | 3.73673 | 0.402942 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −17.6936 | −1.87552 | −0.937761 | − | 0.347281i | \(-0.887105\pi\) | ||||
−0.937761 | + | 0.347281i | \(0.887105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.39138 | −0.669999 | ||||||||
\(92\) | 3.43742 | 0.358376 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.22018 | −0.847847 | ||||||||
\(95\) | −0.391382 | −0.0401550 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.65465 | −0.472609 | −0.236304 | − | 0.971679i | \(-0.575936\pi\) | ||||
−0.236304 | + | 0.971679i | \(0.575936\pi\) | |||||||
\(98\) | 4.04604 | 0.408711 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.84682 | −0.484682 | ||||||||
\(101\) | 9.65760 | 0.960967 | 0.480484 | − | 0.877004i | \(-0.340461\pi\) | ||||
0.480484 | + | 0.877004i | \(0.340461\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.95396 | −0.685194 | −0.342597 | − | 0.939482i | \(-0.611307\pi\) | ||||
−0.342597 | + | 0.939482i | \(0.611307\pi\) | |||||||
\(104\) | −3.71871 | −0.364649 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.21724 | −0.118228 | ||||||||
\(107\) | −2.65465 | −0.256635 | −0.128318 | − | 0.991733i | \(-0.540958\pi\) | ||||
−0.128318 | + | 0.991733i | \(0.540958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | −0.391382 | −0.0373168 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.71871 | −0.162403 | ||||||||
\(113\) | −7.52949 | −0.708315 | −0.354158 | − | 0.935186i | \(-0.615232\pi\) | ||||
−0.354158 | + | 0.935186i | \(0.615232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.34535 | 0.125454 | ||||||||
\(116\) | 3.82880 | 0.355495 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.4404 | 1.14523 | ||||||||
\(119\) | 9.34535 | 0.856686 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.06406 | −0.275160 | ||||||||
\(125\) | −3.85387 | −0.344701 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00295 | −0.443940 | −0.221970 | − | 0.975054i | \(-0.571249\pi\) | ||||
−0.221970 | + | 0.975054i | \(0.571249\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.45544 | −0.127650 | ||||||||
\(131\) | 6.50147 | 0.568036 | 0.284018 | − | 0.958819i | \(-0.408332\pi\) | ||||
0.284018 | + | 0.958819i | \(0.408332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.71871 | 0.149031 | ||||||||
\(134\) | 1.71871 | 0.148474 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.43742 | 0.466255 | ||||||||
\(137\) | −15.7187 | −1.34294 | −0.671470 | − | 0.741032i | \(-0.734337\pi\) | ||||
−0.671470 | + | 0.741032i | \(0.734337\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.1381 | −0.944722 | −0.472361 | − | 0.881405i | \(-0.656598\pi\) | ||||
−0.472361 | + | 0.881405i | \(0.656598\pi\) | |||||||
\(140\) | −0.672673 | −0.0568512 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.04604 | 0.0877815 | ||||||||
\(143\) | 3.71871 | 0.310974 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.49853 | 0.124446 | ||||||||
\(146\) | −13.6576 | −1.13031 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.65465 | −0.382610 | ||||||||
\(149\) | −11.3453 | −0.929447 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6547 | −1.19258 | −0.596289 | − | 0.802770i | \(-0.703359\pi\) | ||||
−0.596289 | + | 0.802770i | \(0.703359\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.71871 | 0.138498 | ||||||||
\(155\) | −1.19922 | −0.0963234 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4835 | −0.836671 | −0.418335 | − | 0.908293i | \(-0.637386\pi\) | ||||
−0.418335 | + | 0.908293i | \(0.637386\pi\) | |||||||
\(158\) | −13.0029 | −1.03446 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.391382 | −0.0309415 | ||||||||
\(161\) | −5.90793 | −0.465610 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.47346 | −0.272062 | −0.136031 | − | 0.990705i | \(-0.543435\pi\) | ||||
−0.136031 | + | 0.990705i | \(0.543435\pi\) | |||||||
\(164\) | −1.06406 | −0.0830887 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.51949 | 0.661241 | ||||||||
\(167\) | −23.0950 | −1.78715 | −0.893573 | − | 0.448917i | \(-0.851810\pi\) | ||||
−0.893573 | + | 0.448917i | \(0.851810\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.828802 | 0.0637540 | ||||||||
\(170\) | 2.12811 | 0.163219 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.73673 | −0.284923 | ||||||||
\(173\) | 18.1771 | 1.38198 | 0.690990 | − | 0.722865i | \(-0.257175\pi\) | ||||
0.690990 | + | 0.722865i | \(0.257175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.33028 | 0.629710 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.6936 | 1.32619 | ||||||||
\(179\) | −11.2842 | −0.843424 | −0.421712 | − | 0.906730i | \(-0.638571\pi\) | ||||
−0.421712 | + | 0.906730i | \(0.638571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8778 | 1.62616 | 0.813082 | − | 0.582150i | \(-0.197788\pi\) | ||||
0.813082 | + | 0.582150i | \(0.197788\pi\) | |||||||
\(182\) | 6.39138 | 0.473761 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.43742 | −0.253410 | ||||||||
\(185\) | −1.82175 | −0.133938 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.43742 | −0.397623 | ||||||||
\(188\) | 8.22018 | 0.599519 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.391382 | 0.0283939 | ||||||||
\(191\) | 7.09502 | 0.513378 | 0.256689 | − | 0.966494i | \(-0.417368\pi\) | ||||
0.256689 | + | 0.966494i | \(0.417368\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6476 | 0.910394 | 0.455197 | − | 0.890391i | \(-0.349569\pi\) | ||||
0.455197 | + | 0.890391i | \(0.349569\pi\) | |||||||
\(194\) | 4.65465 | 0.334185 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.04604 | −0.289003 | ||||||||
\(197\) | −8.43447 | −0.600931 | −0.300466 | − | 0.953793i | \(-0.597142\pi\) | ||||
−0.300466 | + | 0.953793i | \(0.597142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.09207 | −0.148303 | −0.0741516 | − | 0.997247i | \(-0.523625\pi\) | ||||
−0.0741516 | + | 0.997247i | \(0.523625\pi\) | |||||||
\(200\) | 4.84682 | 0.342722 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.65760 | −0.679507 | ||||||||
\(203\) | −6.58060 | −0.461867 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.416452 | −0.0290863 | ||||||||
\(206\) | 6.95396 | 0.484506 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.71871 | 0.257846 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.09207 | −0.419396 | −0.209698 | − | 0.977766i | \(-0.567248\pi\) | ||||
−0.209698 | + | 0.977766i | \(0.567248\pi\) | |||||||
\(212\) | 1.21724 | 0.0836001 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.65465 | 0.181468 | ||||||||
\(215\) | −1.46249 | −0.0997409 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.26622 | 0.357494 | ||||||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.391382 | 0.0263870 | ||||||||
\(221\) | −20.2202 | −1.36016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8748 | −1.26395 | −0.631976 | − | 0.774988i | \(-0.717756\pi\) | ||||
−0.631976 | + | 0.774988i | \(0.717756\pi\) | |||||||
\(224\) | 1.71871 | 0.114836 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.52949 | 0.500854 | ||||||||
\(227\) | −20.9669 | −1.39162 | −0.695811 | − | 0.718225i | \(-0.744955\pi\) | ||||
−0.695811 | + | 0.718225i | \(0.744955\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8108 | 0.912642 | 0.456321 | − | 0.889815i | \(-0.349167\pi\) | ||||
0.456321 | + | 0.889815i | \(0.349167\pi\) | |||||||
\(230\) | −1.34535 | −0.0887094 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.82880 | −0.251373 | ||||||||
\(233\) | −4.91087 | −0.321722 | −0.160861 | − | 0.986977i | \(-0.551427\pi\) | ||||
−0.160861 | + | 0.986977i | \(0.551427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.21724 | 0.209869 | ||||||||
\(236\) | −12.4404 | −0.809799 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.34535 | −0.605769 | ||||||||
\(239\) | 14.0490 | 0.908753 | 0.454377 | − | 0.890810i | \(-0.349862\pi\) | ||||
0.454377 | + | 0.890810i | \(0.349862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.7397 | 1.46479 | 0.732396 | − | 0.680879i | \(-0.238402\pi\) | ||||
0.732396 | + | 0.680879i | \(0.238402\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −1.58355 | −0.101169 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.71871 | −0.236616 | ||||||||
\(248\) | 3.06406 | 0.194568 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.85387 | 0.243740 | ||||||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.43742 | 0.216109 | ||||||||
\(254\) | 5.00295 | 0.313913 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.4433 | 1.21284 | 0.606420 | − | 0.795144i | \(-0.292605\pi\) | ||||
0.606420 | + | 0.795144i | \(0.292605\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 1.45544 | 0.0902624 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.50147 | −0.401662 | ||||||||
\(263\) | −14.6476 | −0.903210 | −0.451605 | − | 0.892218i | \(-0.649148\pi\) | ||||
−0.451605 | + | 0.892218i | \(0.649148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.476404 | 0.0292653 | ||||||||
\(266\) | −1.71871 | −0.105381 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.71871 | −0.104987 | ||||||||
\(269\) | −8.34829 | −0.509004 | −0.254502 | − | 0.967072i | \(-0.581912\pi\) | ||||
−0.254502 | + | 0.967072i | \(0.581912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.5375 | −0.640108 | −0.320054 | − | 0.947399i | \(-0.603701\pi\) | ||||
−0.320054 | + | 0.947399i | \(0.603701\pi\) | |||||||
\(272\) | −5.43742 | −0.329692 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.7187 | 0.949602 | ||||||||
\(275\) | −4.84682 | −0.292274 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.8807 | −1.37477 | −0.687385 | − | 0.726293i | \(-0.741242\pi\) | ||||
−0.687385 | + | 0.726293i | \(0.741242\pi\) | |||||||
\(278\) | 11.1381 | 0.668020 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.672673 | 0.0401999 | ||||||||
\(281\) | 4.39138 | 0.261968 | 0.130984 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130984 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.0670 | −1.43063 | −0.715317 | − | 0.698800i | \(-0.753718\pi\) | ||||
−0.715317 | + | 0.698800i | \(0.753718\pi\) | |||||||
\(284\) | −1.04604 | −0.0620709 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.71871 | −0.219892 | ||||||||
\(287\) | 1.82880 | 0.107951 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.5655 | 0.739149 | ||||||||
\(290\) | −1.49853 | −0.0879965 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.6576 | 0.799251 | ||||||||
\(293\) | 27.2901 | 1.59431 | 0.797153 | − | 0.603777i | \(-0.206338\pi\) | ||||
0.797153 | + | 0.603777i | \(0.206338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.86894 | −0.283481 | ||||||||
\(296\) | 4.65465 | 0.270546 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.3453 | 0.657218 | ||||||||
\(299\) | 12.7828 | 0.739246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.42235 | 0.370178 | ||||||||
\(302\) | 14.6547 | 0.843281 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0.782765 | 0.0448210 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.22313 | −0.526392 | −0.263196 | − | 0.964742i | \(-0.584777\pi\) | ||||
−0.263196 | + | 0.964742i | \(0.584777\pi\) | |||||||
\(308\) | −1.71871 | −0.0979326 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.19922 | 0.0681110 | ||||||||
\(311\) | −6.34829 | −0.359979 | −0.179989 | − | 0.983669i | \(-0.557606\pi\) | ||||
−0.179989 | + | 0.983669i | \(0.557606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.3943 | 0.757092 | 0.378546 | − | 0.925582i | \(-0.376424\pi\) | ||||
0.378546 | + | 0.925582i | \(0.376424\pi\) | |||||||
\(314\) | 10.4835 | 0.591616 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0029 | 0.731473 | ||||||||
\(317\) | −31.0029 | −1.74130 | −0.870650 | − | 0.491904i | \(-0.836301\pi\) | ||||
−0.870650 | + | 0.491904i | \(0.836301\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.82880 | 0.214372 | ||||||||
\(320\) | 0.391382 | 0.0218789 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.90793 | 0.329236 | ||||||||
\(323\) | 5.43742 | 0.302546 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.0239 | −0.999787 | ||||||||
\(326\) | 3.47346 | 0.192377 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.06406 | 0.0587526 | ||||||||
\(329\) | −14.1281 | −0.778908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.2993 | −0.895891 | −0.447946 | − | 0.894061i | \(-0.647844\pi\) | ||||
−0.447946 | + | 0.894061i | \(0.647844\pi\) | |||||||
\(332\) | −8.51949 | −0.467568 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.0950 | 1.26370 | ||||||||
\(335\) | −0.672673 | −0.0367520 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.19217 | −0.173888 | −0.0869442 | − | 0.996213i | \(-0.527710\pi\) | ||||
−0.0869442 | + | 0.996213i | \(0.527710\pi\) | |||||||
\(338\) | −0.828802 | −0.0450809 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.12811 | −0.115413 | ||||||||
\(341\) | −3.06406 | −0.165928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.9849 | 1.02509 | ||||||||
\(344\) | 3.73673 | 0.201471 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.1771 | −0.977207 | ||||||||
\(347\) | −24.6966 | −1.32578 | −0.662891 | − | 0.748716i | \(-0.730671\pi\) | ||||
−0.662891 | + | 0.748716i | \(0.730671\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.43447 | −0.237372 | −0.118686 | − | 0.992932i | \(-0.537868\pi\) | ||||
−0.118686 | + | 0.992932i | \(0.537868\pi\) | |||||||
\(350\) | −8.33028 | −0.445272 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −25.3152 | −1.34739 | −0.673696 | − | 0.739008i | \(-0.735294\pi\) | ||||
−0.673696 | + | 0.739008i | \(0.735294\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.409400 | −0.0217287 | ||||||||
\(356\) | −17.6936 | −0.937761 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2842 | 0.596391 | ||||||||
\(359\) | 13.9749 | 0.737569 | 0.368784 | − | 0.929515i | \(-0.379774\pi\) | ||||
0.368784 | + | 0.929515i | \(0.379774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −21.8778 | −1.14987 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.39138 | −0.334999 | ||||||||
\(365\) | 5.34535 | 0.279788 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.3453 | −1.32302 | −0.661508 | − | 0.749938i | \(-0.730083\pi\) | ||||
−0.661508 | + | 0.749938i | \(0.730083\pi\) | |||||||
\(368\) | 3.43742 | 0.179188 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.82175 | 0.0947083 | ||||||||
\(371\) | −2.09207 | −0.108615 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.95396 | 0.463619 | 0.231809 | − | 0.972761i | \(-0.425535\pi\) | ||||
0.231809 | + | 0.972761i | \(0.425535\pi\) | |||||||
\(374\) | 5.43742 | 0.281162 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.22018 | −0.423924 | ||||||||
\(377\) | 14.2382 | 0.733305 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.8527 | −1.32796 | −0.663982 | − | 0.747748i | \(-0.731135\pi\) | ||||
−0.663982 | + | 0.747748i | \(0.731135\pi\) | |||||||
\(380\) | −0.391382 | −0.0200775 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.09502 | −0.363013 | ||||||||
\(383\) | 20.6296 | 1.05412 | 0.527061 | − | 0.849827i | \(-0.323294\pi\) | ||||
0.527061 | + | 0.849827i | \(0.323294\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.672673 | −0.0342826 | ||||||||
\(386\) | −12.6476 | −0.643746 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.65465 | −0.236304 | ||||||||
\(389\) | −15.6086 | −0.791388 | −0.395694 | − | 0.918382i | \(-0.629496\pi\) | ||||
−0.395694 | + | 0.918382i | \(0.629496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.6907 | −0.945229 | ||||||||
\(392\) | 4.04604 | 0.204356 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.43447 | 0.424922 | ||||||||
\(395\) | 5.08913 | 0.256062 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.2512 | −1.71902 | −0.859508 | − | 0.511122i | \(-0.829230\pi\) | ||||
−0.859508 | + | 0.511122i | \(0.829230\pi\) | |||||||
\(398\) | 2.09207 | 0.104866 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.84682 | −0.242341 | ||||||||
\(401\) | −4.09207 | −0.204348 | −0.102174 | − | 0.994767i | \(-0.532580\pi\) | ||||
−0.102174 | + | 0.994767i | \(0.532580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.3943 | −0.567592 | ||||||||
\(404\) | 9.65760 | 0.480484 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.58060 | 0.326590 | ||||||||
\(407\) | −4.65465 | −0.230723 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.48346 | 0.122799 | 0.0613995 | − | 0.998113i | \(-0.480444\pi\) | ||||
0.0613995 | + | 0.998113i | \(0.480444\pi\) | |||||||
\(410\) | 0.416452 | 0.0205671 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.95396 | −0.342597 | ||||||||
\(413\) | 21.3814 | 1.05211 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.33438 | −0.163678 | ||||||||
\(416\) | −3.71871 | −0.182325 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.00000 | 0.0489116 | ||||||||
\(419\) | −35.0950 | −1.71450 | −0.857252 | − | 0.514897i | \(-0.827830\pi\) | ||||
−0.857252 | + | 0.514897i | \(0.827830\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.3483 | −0.601819 | −0.300910 | − | 0.953653i | \(-0.597290\pi\) | ||||
−0.300910 | + | 0.953653i | \(0.597290\pi\) | |||||||
\(422\) | 6.09207 | 0.296558 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.21724 | −0.0591142 | ||||||||
\(425\) | 26.3542 | 1.27837 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.43742 | −0.166348 | ||||||||
\(428\) | −2.65465 | −0.128318 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.46249 | 0.0705275 | ||||||||
\(431\) | 6.94691 | 0.334621 | 0.167310 | − | 0.985904i | \(-0.446492\pi\) | ||||
0.167310 | + | 0.985904i | \(0.446492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.2533 | −0.636912 | −0.318456 | − | 0.947938i | \(-0.603164\pi\) | ||||
−0.318456 | + | 0.947938i | \(0.603164\pi\) | |||||||
\(434\) | −5.26622 | −0.252787 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | −3.43742 | −0.164434 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.3152 | 0.730955 | 0.365477 | − | 0.930820i | \(-0.380906\pi\) | ||||
0.365477 | + | 0.930820i | \(0.380906\pi\) | |||||||
\(440\) | −0.391382 | −0.0186584 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.2202 | 0.961776 | ||||||||
\(443\) | 20.8807 | 0.992074 | 0.496037 | − | 0.868301i | \(-0.334788\pi\) | ||||
0.496037 | + | 0.868301i | \(0.334788\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.92498 | −0.328275 | ||||||||
\(446\) | 18.8748 | 0.893750 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.71871 | −0.0812014 | ||||||||
\(449\) | 28.7887 | 1.35862 | 0.679310 | − | 0.733851i | \(-0.262279\pi\) | ||||
0.679310 | + | 0.733851i | \(0.262279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.06406 | −0.0501044 | ||||||||
\(452\) | −7.52949 | −0.354158 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.9669 | 0.984026 | ||||||||
\(455\) | −2.50147 | −0.117271 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.7526 | −1.53210 | −0.766052 | − | 0.642779i | \(-0.777781\pi\) | ||||
−0.766052 | + | 0.642779i | \(0.777781\pi\) | |||||||
\(458\) | −13.8108 | −0.645336 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.34535 | 0.0627271 | ||||||||
\(461\) | −20.2261 | −0.942023 | −0.471011 | − | 0.882127i | \(-0.656111\pi\) | ||||
−0.471011 | + | 0.882127i | \(0.656111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6907 | −0.868630 | −0.434315 | − | 0.900761i | \(-0.643010\pi\) | ||||
−0.434315 | + | 0.900761i | \(0.643010\pi\) | |||||||
\(464\) | 3.82880 | 0.177748 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.91087 | 0.227492 | ||||||||
\(467\) | −34.5685 | −1.59964 | −0.799819 | − | 0.600241i | \(-0.795071\pi\) | ||||
−0.799819 | + | 0.600241i | \(0.795071\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.95396 | 0.136401 | ||||||||
\(470\) | −3.21724 | −0.148400 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.4404 | 0.572614 | ||||||||
\(473\) | −3.73673 | −0.171815 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.84682 | 0.222387 | ||||||||
\(476\) | 9.34535 | 0.428343 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.0490 | −0.642586 | ||||||||
\(479\) | 17.7187 | 0.809589 | 0.404794 | − | 0.914408i | \(-0.367343\pi\) | ||||
0.404794 | + | 0.914408i | \(0.367343\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.3093 | −0.789237 | ||||||||
\(482\) | −22.7397 | −1.03576 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −1.82175 | −0.0827214 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.7426 | 1.71028 | 0.855141 | − | 0.518396i | \(-0.173471\pi\) | ||||
0.855141 | + | 0.518396i | \(0.173471\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.58355 | 0.0715374 | ||||||||
\(491\) | −0.373364 | −0.0168497 | −0.00842485 | − | 0.999965i | \(-0.502682\pi\) | ||||
−0.00842485 | + | 0.999965i | \(0.502682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.8188 | −0.937632 | ||||||||
\(494\) | 3.71871 | 0.167313 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.06406 | −0.137580 | ||||||||
\(497\) | 1.79783 | 0.0806439 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.8388 | −0.664276 | −0.332138 | − | 0.943231i | \(-0.607770\pi\) | ||||
−0.332138 | + | 0.943231i | \(0.607770\pi\) | |||||||
\(500\) | −3.85387 | −0.172350 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | −33.2662 | −1.48327 | −0.741634 | − | 0.670805i | \(-0.765949\pi\) | ||||
−0.741634 | + | 0.670805i | \(0.765949\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.77982 | 0.168200 | ||||||||
\(506\) | −3.43742 | −0.152812 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.00295 | −0.221970 | ||||||||
\(509\) | 8.47051 | 0.375449 | 0.187724 | − | 0.982222i | \(-0.439889\pi\) | ||||
0.187724 | + | 0.982222i | \(0.439889\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.4735 | −1.03840 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.4433 | −0.857608 | ||||||||
\(515\) | −2.72166 | −0.119931 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.22018 | 0.361523 | ||||||||
\(518\) | −8.00000 | −0.351500 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.45544 | −0.0638252 | ||||||||
\(521\) | 37.3152 | 1.63481 | 0.817404 | − | 0.576064i | \(-0.195412\pi\) | ||||
0.817404 | + | 0.576064i | \(0.195412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.6576 | −1.38429 | −0.692145 | − | 0.721758i | \(-0.743334\pi\) | ||||
−0.692145 | + | 0.721758i | \(0.743334\pi\) | |||||||
\(524\) | 6.50147 | 0.284018 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.6476 | 0.638666 | ||||||||
\(527\) | 16.6606 | 0.725745 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.1841 | −0.486267 | ||||||||
\(530\) | −0.476404 | −0.0206937 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.71871 | 0.0745155 | ||||||||
\(533\) | −3.95691 | −0.171393 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.03899 | −0.0449192 | ||||||||
\(536\) | 1.71871 | 0.0742370 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.34829 | 0.359921 | ||||||||
\(539\) | −4.04604 | −0.174275 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0921 | 1.20777 | 0.603886 | − | 0.797070i | \(-0.293618\pi\) | ||||
0.603886 | + | 0.797070i | \(0.293618\pi\) | |||||||
\(542\) | 10.5375 | 0.452625 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.43742 | 0.233127 | ||||||||
\(545\) | 2.34829 | 0.100590 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.1841 | 1.03404 | 0.517020 | − | 0.855973i | \(-0.327041\pi\) | ||||
0.517020 | + | 0.855973i | \(0.327041\pi\) | |||||||
\(548\) | −15.7187 | −0.671470 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.84682 | 0.206669 | ||||||||
\(551\) | −3.82880 | −0.163112 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.3483 | −0.950346 | ||||||||
\(554\) | 22.8807 | 0.972109 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.1381 | −0.472361 | ||||||||
\(557\) | −39.9699 | −1.69358 | −0.846789 | − | 0.531929i | \(-0.821467\pi\) | ||||
−0.846789 | + | 0.531929i | \(0.821467\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.8958 | −0.587730 | ||||||||
\(560\) | −0.672673 | −0.0284256 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.39138 | −0.185239 | ||||||||
\(563\) | −16.4764 | −0.694398 | −0.347199 | − | 0.937792i | \(-0.612867\pi\) | ||||
−0.347199 | + | 0.937792i | \(0.612867\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.94691 | −0.123977 | ||||||||
\(566\) | 24.0670 | 1.01161 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.04604 | 0.0438907 | ||||||||
\(569\) | 24.9418 | 1.04562 | 0.522808 | − | 0.852450i | \(-0.324884\pi\) | ||||
0.522808 | + | 0.852450i | \(0.324884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.50737 | −0.356022 | −0.178011 | − | 0.984028i | \(-0.556966\pi\) | ||||
−0.178011 | + | 0.984028i | \(0.556966\pi\) | |||||||
\(572\) | 3.71871 | 0.155487 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.82880 | −0.0763327 | ||||||||
\(575\) | −16.6606 | −0.694793 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.8527 | 1.32605 | 0.663023 | − | 0.748599i | \(-0.269273\pi\) | ||||
0.663023 | + | 0.748599i | \(0.269273\pi\) | |||||||
\(578\) | −12.5655 | −0.522657 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.49853 | 0.0622229 | ||||||||
\(581\) | 14.6425 | 0.607475 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.21724 | 0.0504127 | ||||||||
\(584\) | −13.6576 | −0.565156 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.2901 | −1.12735 | ||||||||
\(587\) | −2.43447 | −0.100481 | −0.0502407 | − | 0.998737i | \(-0.515999\pi\) | ||||
−0.0502407 | + | 0.998737i | \(0.515999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.06406 | 0.126252 | ||||||||
\(590\) | 4.86894 | 0.200451 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.65465 | −0.191305 | ||||||||
\(593\) | 18.1841 | 0.746733 | 0.373367 | − | 0.927684i | \(-0.378203\pi\) | ||||
0.373367 | + | 0.927684i | \(0.378203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.65760 | 0.149947 | ||||||||
\(596\) | −11.3453 | −0.464723 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.7828 | −0.522726 | ||||||||
\(599\) | −4.33534 | −0.177137 | −0.0885687 | − | 0.996070i | \(-0.528229\pi\) | ||||
−0.0885687 | + | 0.996070i | \(0.528229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.2453 | 0.662658 | 0.331329 | − | 0.943515i | \(-0.392503\pi\) | ||||
0.331329 | + | 0.943515i | \(0.392503\pi\) | |||||||
\(602\) | −6.42235 | −0.261755 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −14.6547 | −0.596289 | ||||||||
\(605\) | 0.391382 | 0.0159120 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.6995 | 1.69253 | 0.846266 | − | 0.532761i | \(-0.178845\pi\) | ||||
0.846266 | + | 0.532761i | \(0.178845\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.782765 | −0.0316932 | ||||||||
\(611\) | 30.5685 | 1.23667 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.1900 | 1.94638 | 0.973189 | − | 0.230008i | \(-0.0738751\pi\) | ||||
0.973189 | + | 0.230008i | \(0.0738751\pi\) | |||||||
\(614\) | 9.22313 | 0.372215 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.71871 | 0.0692488 | ||||||||
\(617\) | −15.7187 | −0.632811 | −0.316406 | − | 0.948624i | \(-0.602476\pi\) | ||||
−0.316406 | + | 0.948624i | \(0.602476\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.6606 | 1.79506 | 0.897530 | − | 0.440954i | \(-0.145360\pi\) | ||||
0.897530 | + | 0.440954i | \(0.145360\pi\) | |||||||
\(620\) | −1.19922 | −0.0481617 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.34829 | 0.254543 | ||||||||
\(623\) | 30.4102 | 1.21836 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.7258 | 0.909030 | ||||||||
\(626\) | −13.3943 | −0.535345 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.4835 | −0.418335 | ||||||||
\(629\) | 25.3093 | 1.00915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.38433 | 0.0949187 | 0.0474593 | − | 0.998873i | \(-0.484888\pi\) | ||||
0.0474593 | + | 0.998873i | \(0.484888\pi\) | |||||||
\(632\) | −13.0029 | −0.517230 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 31.0029 | 1.23128 | ||||||||
\(635\) | −1.95807 | −0.0777035 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0460 | −0.596146 | ||||||||
\(638\) | −3.82880 | −0.151584 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.391382 | −0.0154707 | ||||||||
\(641\) | 45.6936 | 1.80479 | 0.902395 | − | 0.430910i | \(-0.141807\pi\) | ||||
0.902395 | + | 0.430910i | \(0.141807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.2621 | 1.66666 | 0.833328 | − | 0.552779i | \(-0.186433\pi\) | ||||
0.833328 | + | 0.552779i | \(0.186433\pi\) | |||||||
\(644\) | −5.90793 | −0.232805 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.43742 | −0.213932 | ||||||||
\(647\) | 38.7166 | 1.52211 | 0.761053 | − | 0.648690i | \(-0.224683\pi\) | ||||
0.761053 | + | 0.648690i | \(0.224683\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.4404 | −0.488327 | ||||||||
\(650\) | 18.0239 | 0.706956 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.47346 | −0.136031 | ||||||||
\(653\) | −38.6915 | −1.51412 | −0.757058 | − | 0.653348i | \(-0.773364\pi\) | ||||
−0.757058 | + | 0.653348i | \(0.773364\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.54456 | 0.0994243 | ||||||||
\(656\) | −1.06406 | −0.0415444 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.1281 | 0.550771 | ||||||||
\(659\) | −12.7467 | −0.496542 | −0.248271 | − | 0.968691i | \(-0.579862\pi\) | ||||
−0.248271 | + | 0.968691i | \(0.579862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.1671 | −0.823305 | −0.411652 | − | 0.911341i | \(-0.635048\pi\) | ||||
−0.411652 | + | 0.911341i | \(0.635048\pi\) | |||||||
\(662\) | 16.2993 | 0.633491 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.51949 | 0.330620 | ||||||||
\(665\) | 0.672673 | 0.0260851 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.1612 | 0.509604 | ||||||||
\(668\) | −23.0950 | −0.893573 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.672673 | 0.0259876 | ||||||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.25115 | 0.0867755 | 0.0433878 | − | 0.999058i | \(-0.486185\pi\) | ||||
0.0433878 | + | 0.999058i | \(0.486185\pi\) | |||||||
\(674\) | 3.19217 | 0.122958 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.828802 | 0.0318770 | ||||||||
\(677\) | 9.57848 | 0.368131 | 0.184065 | − | 0.982914i | \(-0.441074\pi\) | ||||
0.184065 | + | 0.982914i | \(0.441074\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.00000 | 0.307012 | ||||||||
\(680\) | 2.12811 | 0.0816093 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.06406 | 0.117329 | ||||||||
\(683\) | 32.0118 | 1.22490 | 0.612449 | − | 0.790510i | \(-0.290185\pi\) | ||||
0.612449 | + | 0.790510i | \(0.290185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.15203 | −0.235057 | ||||||||
\(686\) | −18.9849 | −0.724848 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.73673 | −0.142461 | ||||||||
\(689\) | 4.52654 | 0.172448 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.9699 | −0.987940 | −0.493970 | − | 0.869479i | \(-0.664455\pi\) | ||||
−0.493970 | + | 0.869479i | \(0.664455\pi\) | |||||||
\(692\) | 18.1771 | 0.690990 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.6966 | 0.937470 | ||||||||
\(695\) | −4.35926 | −0.165356 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.78571 | 0.219150 | ||||||||
\(698\) | 4.43447 | 0.167847 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.33028 | 0.314855 | ||||||||
\(701\) | 21.0950 | 0.796748 | 0.398374 | − | 0.917223i | \(-0.369575\pi\) | ||||
0.398374 | + | 0.917223i | \(0.369575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.65465 | 0.175554 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 25.3152 | 0.952750 | ||||||||
\(707\) | −16.5986 | −0.624255 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.1981 | 1.09656 | 0.548278 | − | 0.836296i | \(-0.315284\pi\) | ||||
0.548278 | + | 0.836296i | \(0.315284\pi\) | |||||||
\(710\) | 0.409400 | 0.0153645 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17.6936 | 0.663097 | ||||||||
\(713\) | −10.5324 | −0.394443 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.45544 | 0.0544303 | ||||||||
\(716\) | −11.2842 | −0.421712 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.9749 | −0.521540 | ||||||||
\(719\) | 13.9079 | 0.518678 | 0.259339 | − | 0.965786i | \(-0.416495\pi\) | ||||
0.259339 | + | 0.965786i | \(0.416495\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.9518 | 0.445110 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.8778 | 0.813082 | ||||||||
\(725\) | −18.5575 | −0.689209 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0059 | −1.55791 | −0.778956 | − | 0.627078i | \(-0.784251\pi\) | ||||
−0.778956 | + | 0.627078i | \(0.784251\pi\) | |||||||
\(728\) | 6.39138 | 0.236880 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.34535 | −0.197840 | ||||||||
\(731\) | 20.3182 | 0.751494 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.0780 | 1.33257 | 0.666285 | − | 0.745697i | \(-0.267883\pi\) | ||||
0.666285 | + | 0.745697i | \(0.267883\pi\) | |||||||
\(734\) | 25.3453 | 0.935514 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.43742 | −0.126705 | ||||||||
\(737\) | −1.71871 | −0.0633095 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.9988 | 1.83924 | 0.919619 | − | 0.392812i | \(-0.128498\pi\) | ||||
0.919619 | + | 0.392812i | \(0.128498\pi\) | |||||||
\(740\) | −1.82175 | −0.0669689 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.09207 | 0.0768025 | ||||||||
\(743\) | −0.220184 | −0.00807777 | −0.00403889 | − | 0.999992i | \(-0.501286\pi\) | ||||
−0.00403889 | + | 0.999992i | \(0.501286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.44037 | −0.162683 | ||||||||
\(746\) | −8.95396 | −0.327828 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.43742 | −0.198812 | ||||||||
\(749\) | 4.56258 | 0.166713 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.1311 | −0.844064 | −0.422032 | − | 0.906581i | \(-0.638683\pi\) | ||||
−0.422032 | + | 0.906581i | \(0.638683\pi\) | |||||||
\(752\) | 8.22018 | 0.299759 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.2382 | −0.518525 | ||||||||
\(755\) | −5.73557 | −0.208739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.4304 | 1.36043 | 0.680215 | − | 0.733013i | \(-0.261886\pi\) | ||||
0.680215 | + | 0.733013i | \(0.261886\pi\) | |||||||
\(758\) | 25.8527 | 0.939013 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.391382 | 0.0141969 | ||||||||
\(761\) | 33.9499 | 1.23068 | 0.615341 | − | 0.788261i | \(-0.289018\pi\) | ||||
0.615341 | + | 0.788261i | \(0.289018\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.3123 | −0.373329 | ||||||||
\(764\) | 7.09502 | 0.256689 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.6296 | −0.745377 | ||||||||
\(767\) | −46.2621 | −1.67043 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.7025 | −1.61201 | −0.806006 | − | 0.591907i | \(-0.798375\pi\) | ||||
−0.806006 | + | 0.591907i | \(0.798375\pi\) | |||||||
\(770\) | 0.672673 | 0.0242414 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.6476 | 0.455197 | ||||||||
\(773\) | 44.8748 | 1.61404 | 0.807018 | − | 0.590527i | \(-0.201080\pi\) | ||||
0.807018 | + | 0.590527i | \(0.201080\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.8509 | 0.533461 | ||||||||
\(776\) | 4.65465 | 0.167092 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.6086 | 0.559596 | ||||||||
\(779\) | 1.06406 | 0.0381237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04604 | −0.0374301 | ||||||||
\(782\) | 18.6907 | 0.668378 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.04604 | −0.144501 | ||||||||
\(785\) | −4.10304 | −0.146444 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.8418 | 0.422113 | 0.211056 | − | 0.977474i | \(-0.432310\pi\) | ||||
0.211056 | + | 0.977474i | \(0.432310\pi\) | |||||||
\(788\) | −8.43447 | −0.300466 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.08913 | −0.181063 | ||||||||
\(791\) | 12.9410 | 0.460129 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.43742 | 0.264111 | ||||||||
\(794\) | 34.2512 | 1.21553 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.09207 | −0.0741516 | ||||||||
\(797\) | −0.128110 | −0.00453789 | −0.00226895 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226895 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.6966 | −1.58125 | ||||||||
\(800\) | 4.84682 | 0.171361 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.09207 | 0.144496 | ||||||||
\(803\) | 13.6576 | 0.481966 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.31226 | −0.0814964 | ||||||||
\(806\) | 11.3943 | 0.401348 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.65760 | −0.339753 | ||||||||
\(809\) | −17.5354 | −0.616512 | −0.308256 | − | 0.951304i | \(-0.599745\pi\) | ||||
−0.308256 | + | 0.951304i | \(0.599745\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.3512 | −1.38181 | −0.690905 | − | 0.722946i | \(-0.742788\pi\) | ||||
−0.690905 | + | 0.722946i | \(0.742788\pi\) | |||||||
\(812\) | −6.58060 | −0.230934 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.65465 | 0.163146 | ||||||||
\(815\) | −1.35945 | −0.0476194 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.73673 | 0.130732 | ||||||||
\(818\) | −2.48346 | −0.0868320 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.416452 | −0.0145431 | ||||||||
\(821\) | −14.0980 | −0.492023 | −0.246011 | − | 0.969267i | \(-0.579120\pi\) | ||||
−0.246011 | + | 0.969267i | \(0.579120\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.12516 | −0.0392207 | −0.0196103 | − | 0.999808i | \(-0.506243\pi\) | ||||
−0.0196103 | + | 0.999808i | \(0.506243\pi\) | |||||||
\(824\) | 6.95396 | 0.242253 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.3814 | −0.743953 | ||||||||
\(827\) | 33.8217 | 1.17610 | 0.588049 | − | 0.808825i | \(-0.299896\pi\) | ||||
0.588049 | + | 0.808825i | \(0.299896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.1900 | −1.25693 | −0.628466 | − | 0.777837i | \(-0.716317\pi\) | ||||
−0.628466 | + | 0.777837i | \(0.716317\pi\) | |||||||
\(830\) | 3.33438 | 0.115738 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.71871 | 0.128923 | ||||||||
\(833\) | 22.0000 | 0.762255 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.03899 | −0.312807 | ||||||||
\(836\) | −1.00000 | −0.0345857 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35.0950 | 1.21234 | ||||||||
\(839\) | 31.8347 | 1.09906 | 0.549528 | − | 0.835475i | \(-0.314808\pi\) | ||||
0.549528 | + | 0.835475i | \(0.314808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3403 | −0.494492 | ||||||||
\(842\) | 12.3483 | 0.425550 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.09207 | −0.209698 | ||||||||
\(845\) | 0.324378 | 0.0111590 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.71871 | −0.0590556 | ||||||||
\(848\) | 1.21724 | 0.0418000 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −26.3542 | −0.903941 | ||||||||
\(851\) | −16.0000 | −0.548473 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.1009 | −1.06488 | −0.532438 | − | 0.846469i | \(-0.678724\pi\) | ||||
−0.532438 | + | 0.846469i | \(0.678724\pi\) | |||||||
\(854\) | 3.43742 | 0.117626 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.65465 | 0.0907342 | ||||||||
\(857\) | 35.4985 | 1.21261 | 0.606303 | − | 0.795234i | \(-0.292652\pi\) | ||||
0.606303 | + | 0.795234i | \(0.292652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.63760 | −0.192352 | −0.0961762 | − | 0.995364i | \(-0.530661\pi\) | ||||
−0.0961762 | + | 0.995364i | \(0.530661\pi\) | |||||||
\(860\) | −1.46249 | −0.0498705 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.94691 | −0.236613 | ||||||||
\(863\) | −31.9949 | −1.08912 | −0.544560 | − | 0.838722i | \(-0.683303\pi\) | ||||
−0.544560 | + | 0.838722i | \(0.683303\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.11420 | 0.241890 | ||||||||
\(866\) | 13.2533 | 0.450364 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.26622 | 0.178747 | ||||||||
\(869\) | 13.0029 | 0.441095 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.39138 | −0.216564 | ||||||||
\(872\) | −6.00000 | −0.203186 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.43742 | 0.116272 | ||||||||
\(875\) | 6.62369 | 0.223921 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.23019 | −0.109076 | −0.0545378 | − | 0.998512i | \(-0.517369\pi\) | ||||
−0.0545378 | + | 0.998512i | \(0.517369\pi\) | |||||||
\(878\) | −15.3152 | −0.516863 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.391382 | 0.0131935 | ||||||||
\(881\) | 24.7217 | 0.832894 | 0.416447 | − | 0.909160i | \(-0.363275\pi\) | ||||
0.416447 | + | 0.909160i | \(0.363275\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.9138 | 0.400932 | 0.200466 | − | 0.979701i | \(-0.435754\pi\) | ||||
0.200466 | + | 0.979701i | \(0.435754\pi\) | |||||||
\(884\) | −20.2202 | −0.680078 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.8807 | −0.701502 | ||||||||
\(887\) | 12.1841 | 0.409104 | 0.204552 | − | 0.978856i | \(-0.434426\pi\) | ||||
0.204552 | + | 0.978856i | \(0.434426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.59862 | 0.288388 | ||||||||
\(890\) | 6.92498 | 0.232126 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.8748 | −0.631976 | ||||||||
\(893\) | −8.22018 | −0.275078 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.41645 | −0.147626 | ||||||||
\(896\) | 1.71871 | 0.0574181 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.7887 | −0.960690 | ||||||||
\(899\) | −11.7317 | −0.391273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.61862 | −0.220498 | ||||||||
\(902\) | 1.06406 | 0.0354292 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.52949 | 0.250427 | ||||||||
\(905\) | 8.56258 | 0.284630 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.3211 | 1.50486 | 0.752431 | − | 0.658671i | \(-0.228881\pi\) | ||||
0.752431 | + | 0.658671i | \(0.228881\pi\) | |||||||
\(908\) | −20.9669 | −0.695811 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.50147 | 0.0829231 | ||||||||
\(911\) | 13.6376 | 0.451834 | 0.225917 | − | 0.974147i | \(-0.427462\pi\) | ||||
0.225917 | + | 0.974147i | \(0.427462\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.51949 | −0.281954 | ||||||||
\(914\) | 32.7526 | 1.08336 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.8108 | 0.456321 | ||||||||
\(917\) | −11.1741 | −0.369003 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39.5283 | 1.30392 | 0.651960 | − | 0.758254i | \(-0.273947\pi\) | ||||
0.651960 | + | 0.758254i | \(0.273947\pi\) | |||||||
\(920\) | −1.34535 | −0.0443547 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.2261 | 0.666111 | ||||||||
\(923\) | −3.88991 | −0.128038 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.5603 | 0.741777 | ||||||||
\(926\) | 18.6907 | 0.614214 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.82880 | −0.125687 | ||||||||
\(929\) | −6.89991 | −0.226379 | −0.113189 | − | 0.993573i | \(-0.536107\pi\) | ||||
−0.113189 | + | 0.993573i | \(0.536107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.04604 | 0.132604 | ||||||||
\(932\) | −4.91087 | −0.160861 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.5685 | 1.13112 | ||||||||
\(935\) | −2.12811 | −0.0695966 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.3873 | −0.698692 | −0.349346 | − | 0.936994i | \(-0.613596\pi\) | ||||
−0.349346 | + | 0.936994i | \(0.613596\pi\) | |||||||
\(938\) | −2.95396 | −0.0964503 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.21724 | 0.104935 | ||||||||
\(941\) | 27.5655 | 0.898611 | 0.449305 | − | 0.893378i | \(-0.351672\pi\) | ||||
0.449305 | + | 0.893378i | \(0.351672\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.65760 | −0.119108 | ||||||||
\(944\) | −12.4404 | −0.404899 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.73673 | 0.121491 | ||||||||
\(947\) | 9.22313 | 0.299712 | 0.149856 | − | 0.988708i | \(-0.452119\pi\) | ||||
0.149856 | + | 0.988708i | \(0.452119\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 50.7887 | 1.64867 | ||||||||
\(950\) | −4.84682 | −0.157252 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.34535 | −0.302884 | ||||||||
\(953\) | −22.6966 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.77687 | 0.0898573 | ||||||||
\(956\) | 14.0490 | 0.454377 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.7187 | −0.572466 | ||||||||
\(959\) | 27.0159 | 0.872389 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6116 | −0.697147 | ||||||||
\(962\) | 17.3093 | 0.558075 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.7397 | 0.732396 | ||||||||
\(965\) | 4.95005 | 0.159348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.6966 | −1.56598 | −0.782988 | − | 0.622036i | \(-0.786306\pi\) | ||||
−0.782988 | + | 0.622036i | \(0.786306\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.82175 | 0.0584929 | ||||||||
\(971\) | 19.5165 | 0.626316 | 0.313158 | − | 0.949701i | \(-0.398613\pi\) | ||||
0.313158 | + | 0.949701i | \(0.398613\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.1432 | 0.613702 | ||||||||
\(974\) | −37.7426 | −1.20935 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −37.3512 | −1.19497 | −0.597486 | − | 0.801879i | \(-0.703834\pi\) | ||||
−0.597486 | + | 0.801879i | \(0.703834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.6936 | −0.565491 | ||||||||
\(980\) | −1.58355 | −0.0505846 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.373364 | 0.0119145 | ||||||||
\(983\) | 45.8888 | 1.46362 | 0.731812 | − | 0.681507i | \(-0.238675\pi\) | ||||
0.731812 | + | 0.681507i | \(0.238675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.30110 | −0.105182 | ||||||||
\(986\) | 20.8188 | 0.663006 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.71871 | −0.118308 | ||||||||
\(989\) | −12.8447 | −0.408438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.9418 | −0.982900 | −0.491450 | − | 0.870906i | \(-0.663533\pi\) | ||||
−0.491450 | + | 0.870906i | \(0.663533\pi\) | |||||||
\(992\) | 3.06406 | 0.0972838 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.79783 | −0.0570238 | ||||||||
\(995\) | −0.818801 | −0.0259577 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.8418 | 1.57850 | 0.789252 | − | 0.614069i | \(-0.210469\pi\) | ||||
0.789252 | + | 0.614069i | \(0.210469\pi\) | |||||||
\(998\) | 14.8388 | 0.469714 | ||||||||
\(999\) | 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 | 3762.2.a.bd.1.3 | 3 | ||
3.2 | odd | 2 | 418.2.a.h.1.3 | ✓ | 3 | ||
12.11 | even | 2 | 3344.2.a.p.1.1 | 3 | |||
33.32 | even | 2 | 4598.2.a.bm.1.3 | 3 | |||
57.56 | even | 2 | 7942.2.a.bc.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.h.1.3 | ✓ | 3 | 3.2 | odd | 2 | ||
3344.2.a.p.1.1 | 3 | 12.11 | even | 2 | |||
3762.2.a.bd.1.3 | 3 | 1.1 | even | 1 | trivial | ||
4598.2.a.bm.1.3 | 3 | 33.32 | even | 2 | |||
7942.2.a.bc.1.1 | 3 | 57.56 | even | 2 |