Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.2597.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.878468\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.878468 | 0.507184 | 0.253592 | − | 0.967311i | \(-0.418388\pi\) | ||||
0.253592 | + | 0.967311i | \(0.418388\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.121532 | 0.0459347 | 0.0229674 | − | 0.999736i | \(-0.492689\pi\) | ||||
0.0229674 | + | 0.999736i | \(0.492689\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.22829 | −0.742765 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.87847 | −0.867891 | −0.433945 | − | 0.900939i | \(-0.642879\pi\) | ||||
−0.433945 | + | 0.900939i | \(0.642879\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.22829 | −1.45007 | −0.725034 | − | 0.688713i | \(-0.758176\pi\) | ||||
−0.725034 | + | 0.688713i | \(0.758176\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.22829 | 0.540441 | 0.270220 | − | 0.962799i | \(-0.412903\pi\) | ||||
0.270220 | + | 0.962799i | \(0.412903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.22829 | −0.281790 | −0.140895 | − | 0.990025i | \(-0.544998\pi\) | ||||
−0.140895 | + | 0.990025i | \(0.544998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.106762 | 0.0232974 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.59289 | −0.883902 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.34983 | 1.73622 | 0.868110 | − | 0.496373i | \(-0.165335\pi\) | ||||
0.868110 | + | 0.496373i | \(0.165335\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.12153 | 0.381038 | 0.190519 | − | 0.981683i | \(-0.438983\pi\) | ||||
0.190519 | + | 0.981683i | \(0.438983\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.52864 | −0.440180 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.59289 | −0.919465 | −0.459733 | − | 0.888057i | \(-0.652055\pi\) | ||||
−0.459733 | + | 0.888057i | \(0.652055\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.59289 | −0.735451 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.22829 | 1.28504 | 0.642522 | − | 0.766267i | \(-0.277888\pi\) | ||||
0.642522 | + | 0.766267i | \(0.277888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.4566 | −1.52525 | −0.762625 | − | 0.646841i | \(-0.776090\pi\) | ||||
−0.762625 | + | 0.646841i | \(0.776090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.98523 | −0.997890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.95749 | 0.274103 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.59289 | 0.493521 | 0.246761 | − | 0.969076i | \(-0.420634\pi\) | ||||
0.246761 | + | 0.969076i | \(0.420634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.07902 | −0.142919 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.650174 | 0.0846455 | 0.0423227 | − | 0.999104i | \(-0.486524\pi\) | ||||
0.0423227 | + | 0.999104i | \(0.486524\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.33506 | −0.939158 | −0.469579 | − | 0.882891i | \(-0.655594\pi\) | ||||
−0.469579 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.270809 | −0.0341187 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.59289 | 0.683280 | 0.341640 | − | 0.939831i | \(-0.389018\pi\) | ||||
0.341640 | + | 0.939831i | \(0.389018\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.878468 | 0.105755 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9852 | 1.65974 | 0.829871 | − | 0.557956i | \(-0.188414\pi\) | ||||
0.829871 | + | 0.557956i | \(0.188414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.9427 | −1.51483 | −0.757415 | − | 0.652934i | \(-0.773538\pi\) | ||||
−0.757415 | + | 0.652934i | \(0.773538\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.349826 | −0.0398663 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.51387 | 0.395342 | 0.197671 | − | 0.980268i | \(-0.436662\pi\) | ||||
0.197671 | + | 0.980268i | \(0.436662\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.65017 | 0.294464 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.1068 | −1.21913 | −0.609563 | − | 0.792738i | \(-0.708655\pi\) | ||||
−0.609563 | + | 0.792738i | \(0.708655\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.21352 | 0.880582 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.486128 | −0.0515294 | −0.0257647 | − | 0.999668i | \(-0.508202\pi\) | ||||
−0.0257647 | + | 0.999668i | \(0.508202\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.635404 | −0.0666085 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.86370 | 0.193256 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.635404 | −0.0645155 | −0.0322578 | − | 0.999480i | \(-0.510270\pi\) | ||||
−0.0322578 | + | 0.999480i | \(0.510270\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.41407 | 0.644639 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3498 | 1.32836 | 0.664179 | − | 0.747574i | \(-0.268781\pi\) | ||||
0.664179 | + | 0.747574i | \(0.268781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.33506 | −0.722745 | −0.361372 | − | 0.932422i | \(-0.617692\pi\) | ||||
−0.361372 | + | 0.932422i | \(0.617692\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0495 | 1.55156 | 0.775781 | − | 0.631003i | \(-0.217356\pi\) | ||||
0.775781 | + | 0.631003i | \(0.217356\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.01477 | 0.0971973 | 0.0485987 | − | 0.998818i | \(-0.484524\pi\) | ||||
0.0485987 | + | 0.998818i | \(0.484524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.91318 | −0.466338 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.3203 | −1.62936 | −0.814678 | − | 0.579914i | \(-0.803086\pi\) | ||||
−0.814678 | + | 0.579914i | \(0.803086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.6502 | 1.07706 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.270809 | 0.0248250 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.71442 | −0.246766 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.22829 | 0.651753 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.75694 | 0.155903 | 0.0779514 | − | 0.996957i | \(-0.475162\pi\) | ||||
0.0779514 | + | 0.996957i | \(0.475162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.02774 | 0.618758 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.2135 | 1.76606 | 0.883032 | − | 0.469313i | \(-0.155498\pi\) | ||||
0.883032 | + | 0.469313i | \(0.155498\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.149277 | −0.0129439 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.9279 | 1.53169 | 0.765844 | − | 0.643027i | \(-0.222322\pi\) | ||||
0.765844 | + | 0.643027i | \(0.222322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8637 | 0.921447 | 0.460723 | − | 0.887544i | \(-0.347590\pi\) | ||||
0.460723 | + | 0.887544i | \(0.347590\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.18578 | −0.773582 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.0495 | 1.25850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.13630 | −0.506114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.7144 | −1.28738 | −0.643688 | − | 0.765288i | \(-0.722596\pi\) | ||||
−0.643688 | + | 0.765288i | \(0.722596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.39234 | 0.682959 | 0.341479 | − | 0.939889i | \(-0.389072\pi\) | ||||
0.341479 | + | 0.939889i | \(0.389072\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.96529 | −0.401420 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.5633 | 1.56133 | 0.780663 | − | 0.624953i | \(-0.214882\pi\) | ||||
0.780663 | + | 0.624953i | \(0.214882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.15624 | 0.250306 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.121532 | 0.00957805 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.01477 | 0.0794829 | 0.0397415 | − | 0.999210i | \(-0.487347\pi\) | ||||
0.0397415 | + | 0.999210i | \(0.487347\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.3351 | 1.10270 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.73700 | 0.209304 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.63540 | 0.200366 | 0.100183 | − | 0.994969i | \(-0.468057\pi\) | ||||
0.100183 | + | 0.994969i | \(0.468057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.571157 | 0.0429308 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.4566 | 1.08054 | 0.540268 | − | 0.841493i | \(-0.318323\pi\) | ||||
0.540268 | + | 0.841493i | \(0.318323\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7422 | 0.798459 | 0.399229 | − | 0.916851i | \(-0.369278\pi\) | ||||
0.399229 | + | 0.916851i | \(0.369278\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.44361 | −0.476326 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.41407 | −0.469043 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.558182 | −0.0406018 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6701 | 1.64035 | 0.820176 | − | 0.572112i | \(-0.193876\pi\) | ||||
0.820176 | + | 0.572112i | \(0.193876\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.24306 | −0.161459 | −0.0807296 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807296 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.57812 | 0.539919 | 0.269959 | − | 0.962872i | \(-0.412990\pi\) | ||||
0.269959 | + | 0.962872i | \(0.412990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.91318 | 0.346549 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.13630 | 0.0797528 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.22829 | −0.154877 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.53560 | 0.244563 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.10676 | 0.213878 | 0.106939 | − | 0.994266i | \(-0.465895\pi\) | ||||
0.106939 | + | 0.994266i | \(0.465895\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 12.2856 | 0.841794 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.257834 | 0.0175029 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.3698 | −0.768297 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.6502 | −0.783676 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.2135 | 1.21967 | 0.609834 | − | 0.792529i | \(-0.291236\pi\) | ||||
0.609834 | + | 0.792529i | \(0.291236\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.9705 | 0.927252 | 0.463626 | − | 0.886031i | \(-0.346548\pi\) | ||||
0.463626 | + | 0.886031i | \(0.346548\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.2135 | 0.807092 | 0.403546 | − | 0.914959i | \(-0.367777\pi\) | ||||
0.403546 | + | 0.914959i | \(0.367777\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.307311 | −0.0202196 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.75694 | −0.639198 | −0.319599 | − | 0.947553i | \(-0.603548\pi\) | ||||
−0.319599 | + | 0.947553i | \(0.603548\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.08682 | 0.200511 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.62063 | −0.557622 | −0.278811 | − | 0.960346i | \(-0.589940\pi\) | ||||
−0.278811 | + | 0.960346i | \(0.589940\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.18578 | 0.205214 | 0.102607 | − | 0.994722i | \(-0.467282\pi\) | ||||
0.102607 | + | 0.994722i | \(0.467282\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1068 | 1.03325 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.42188 | 0.408614 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.75694 | −0.618321 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.2283 | 1.59240 | 0.796198 | − | 0.605036i | \(-0.206841\pi\) | ||||
0.796198 | + | 0.605036i | \(0.206841\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.87847 | −0.180968 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.6701 | 0.665583 | 0.332792 | − | 0.943000i | \(-0.392009\pi\) | ||||
0.332792 | + | 0.943000i | \(0.392009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.679714 | −0.0422354 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.8342 | −1.28960 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.6849 | −1.15216 | −0.576080 | − | 0.817394i | \(-0.695418\pi\) | ||||
−0.576080 | + | 0.817394i | \(0.695418\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.427048 | −0.0261349 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.8637 | −1.51597 | −0.757983 | − | 0.652274i | \(-0.773815\pi\) | ||||
−0.757983 | + | 0.652274i | \(0.773815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.578119 | −0.0351183 | −0.0175591 | − | 0.999846i | \(-0.505590\pi\) | ||||
−0.0175591 | + | 0.999846i | \(0.505590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.558182 | −0.0337827 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.51387 | 0.571633 | 0.285817 | − | 0.958284i | \(-0.407735\pi\) | ||||
0.285817 | + | 0.958284i | \(0.407735\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.72740 | −0.283022 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.1562 | −0.784835 | −0.392418 | − | 0.919787i | \(-0.628361\pi\) | ||||
−0.392418 | + | 0.919787i | \(0.628361\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.5061 | 1.45673 | 0.728367 | − | 0.685187i | \(-0.240280\pi\) | ||||
0.728367 | + | 0.685187i | \(0.240280\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0347 | −0.707924 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.558182 | −0.0327212 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.29254 | 0.367614 | 0.183807 | − | 0.982962i | \(-0.441158\pi\) | ||||
0.183807 | + | 0.982962i | \(0.441158\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.2205 | 0.767130 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.22829 | −0.302360 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.972255 | 0.0560398 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.7274 | 0.673721 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.3351 | 0.761072 | 0.380536 | − | 0.924766i | \(-0.375740\pi\) | ||||
0.380536 | + | 0.924766i | \(0.375740\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.44361 | −0.366564 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.4270 | 1.38513 | 0.692565 | − | 0.721355i | \(-0.256480\pi\) | ||||
0.692565 | + | 0.721355i | \(0.256480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.5486 | −1.50061 | −0.750307 | − | 0.661089i | \(-0.770094\pi\) | ||||
−0.750307 | + | 0.661089i | \(0.770094\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.9852 | 0.953986 | 0.476993 | − | 0.878907i | \(-0.341727\pi\) | ||||
0.476993 | + | 0.878907i | \(0.341727\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −26.9132 | −1.50685 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.0990 | 0.786927 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.73700 | −0.152291 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.891443 | 0.0492969 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.27081 | −0.0700620 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8914 | −0.983403 | −0.491701 | − | 0.870764i | \(-0.663625\pi\) | ||||
−0.491701 | + | 0.870764i | \(0.663625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.4626 | 0.682946 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.52864 | 0.246691 | 0.123345 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123345 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.2153 | −0.826383 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.10676 | −0.330700 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.69965 | −0.0917725 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.0937869 | −0.00503475 | −0.00251737 | − | 0.999997i | \(-0.500801\pi\) | ||||
−0.00251737 | + | 0.999997i | \(0.500801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.07902 | 0.432460 | 0.216230 | − | 0.976342i | \(-0.430624\pi\) | ||||
0.216230 | + | 0.976342i | \(0.430624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0130 | 1.28172 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.00000 | 0.425797 | 0.212899 | − | 0.977074i | \(-0.431710\pi\) | ||||
0.212899 | + | 0.977074i | \(0.431710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.237897 | 0.0125908 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.69965 | −0.459150 | −0.229575 | − | 0.973291i | \(-0.573734\pi\) | ||||
−0.229575 | + | 0.973291i | \(0.573734\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4913 | −0.920594 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.38453 | −0.125156 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.8064 | 1.66028 | 0.830141 | − | 0.557554i | \(-0.188260\pi\) | ||||
0.830141 | + | 0.557554i | \(0.188260\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.3351 | −0.954485 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.436651 | 0.0226698 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.4288 | 0.695319 | 0.347660 | − | 0.937621i | \(-0.386977\pi\) | ||||
0.347660 | + | 0.937621i | \(0.386977\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −48.8836 | −2.51764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.8212 | −1.63454 | −0.817272 | − | 0.576252i | \(-0.804515\pi\) | ||||
−0.817272 | + | 0.576252i | \(0.804515\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.54341 | 0.0790714 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.3480 | 1.75510 | 0.877551 | − | 0.479483i | \(-0.159176\pi\) | ||||
0.877551 | + | 0.479483i | \(0.159176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.8264 | −0.906164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.14928 | 0.413185 | 0.206592 | − | 0.978427i | \(-0.433763\pi\) | ||||
0.206592 | + | 0.978427i | \(0.433763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.22829 | 0.112690 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7569 | 0.895719 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0625 | −0.956717 | −0.478359 | − | 0.878165i | \(-0.658768\pi\) | ||||
−0.478359 | + | 0.878165i | \(0.658768\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.131135 | −0.00656496 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9705 | 0.997277 | 0.498639 | − | 0.866810i | \(-0.333833\pi\) | ||||
0.498639 | + | 0.866810i | \(0.333833\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0920 | −0.552531 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.0990 | 0.797996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.3351 | −0.511036 | −0.255518 | − | 0.966804i | \(-0.582246\pi\) | ||||
−0.255518 | + | 0.966804i | \(0.582246\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.7491 | 0.776847 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.0790169 | 0.00388817 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.54341 | 0.467343 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.72740 | −0.279802 | −0.139901 | − | 0.990166i | \(-0.544678\pi\) | ||||
−0.139901 | + | 0.990166i | \(0.544678\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.44361 | −0.411516 | −0.205758 | − | 0.978603i | \(-0.565966\pi\) | ||||
−0.205758 | + | 0.978603i | \(0.565966\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 23.3003 | 1.13290 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.891443 | −0.0431400 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.2205 | 0.638291 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.3698 | −1.70370 | −0.851851 | − | 0.523785i | \(-0.824520\pi\) | ||||
−0.851851 | + | 0.523785i | \(0.824520\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.3923 | −0.643595 | −0.321797 | − | 0.946809i | \(-0.604287\pi\) | ||||
−0.321797 | + | 0.946809i | \(0.604287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.22829 | −0.0587573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1137 | 1.00770 | 0.503852 | − | 0.863790i | \(-0.331916\pi\) | ||||
0.503852 | + | 0.863790i | \(0.331916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.5651 | 0.741197 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.1692 | −1.48089 | −0.740447 | − | 0.672115i | \(-0.765386\pi\) | ||||
−0.740447 | + | 0.672115i | \(0.765386\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.8046 | −0.652936 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.09199 | −0.287499 | −0.143749 | − | 0.989614i | \(-0.545916\pi\) | ||||
−0.143749 | + | 0.989614i | \(0.545916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.6849 | −1.11528 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.37240 | 0.346386 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.1345 | −1.03541 | −0.517704 | − | 0.855560i | \(-0.673213\pi\) | ||||
−0.517704 | + | 0.855560i | \(0.673213\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.2343 | −0.477697 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5434 | −0.537630 | −0.268815 | − | 0.963192i | \(-0.586632\pi\) | ||||
−0.268815 | + | 0.963192i | \(0.586632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.4270 | 1.41406 | 0.707032 | − | 0.707181i | \(-0.250033\pi\) | ||||
0.707032 | + | 0.707181i | \(0.250033\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.3776 | 0.480217 | 0.240108 | − | 0.970746i | \(-0.422817\pi\) | ||||
0.240108 | + | 0.970746i | \(0.422817\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.679714 | 0.0313863 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.1858 | 0.791879 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.0277 | −1.05882 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.00601 | −0.366570 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.6128 | 1.35304 | 0.676522 | − | 0.736422i | \(-0.263486\pi\) | ||||
0.676522 | + | 0.736422i | \(0.263486\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.2413 | 1.33329 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.106762 | 0.00485783 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.1562 | 0.505537 | 0.252769 | − | 0.967527i | \(-0.418659\pi\) | ||||
0.252769 | + | 0.967527i | \(0.418659\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.891443 | 0.0403125 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.2630 | −1.72679 | −0.863393 | − | 0.504533i | \(-0.831665\pi\) | ||||
−0.863393 | + | 0.504533i | \(0.831665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.8342 | 0.938323 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.69965 | 0.0762398 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.40711 | −0.286822 | −0.143411 | − | 0.989663i | \(-0.545807\pi\) | ||||
−0.143411 | + | 0.989663i | \(0.545807\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.02774 | −0.313976 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.0920 | −0.806682 | −0.403341 | − | 0.915050i | \(-0.632151\pi\) | ||||
−0.403341 | + | 0.915050i | \(0.632151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5929 | 0.559270 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.1285 | −1.51272 | −0.756359 | − | 0.654156i | \(-0.773024\pi\) | ||||
−0.756359 | + | 0.654156i | \(0.773024\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.57295 | −0.0695833 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.64142 | 0.249075 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.0990 | 1.32375 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.31512 | 0.101622 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.8854 | 1.57217 | 0.786085 | − | 0.618119i | \(-0.212105\pi\) | ||||
0.786085 | + | 0.618119i | \(0.212105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.7865 | 0.515387 | 0.257693 | − | 0.966227i | \(-0.417038\pi\) | ||||
0.257693 | + | 0.966227i | \(0.417038\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.72740 | 0.205929 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.44878 | −0.0628717 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.0199 | −1.86340 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.6997 | 0.548030 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.1068 | 0.866060 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.2413 | −0.741260 | −0.370630 | − | 0.928781i | \(-0.620858\pi\) | ||||
−0.370630 | + | 0.928781i | \(0.620858\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.43665 | 0.404965 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6571 | 0.626694 | 0.313347 | − | 0.949639i | \(-0.398550\pi\) | ||||
0.313347 | + | 0.949639i | \(0.398550\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.3447 | 0.697573 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.4843 | −0.489249 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.427048 | 0.0181599 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.07902 | −0.0880908 | −0.0440454 | − | 0.999030i | \(-0.514025\pi\) | ||||
−0.0440454 | + | 0.999030i | \(0.514025\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.8264 | −1.76907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.63456 | −0.237891 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.10676 | −0.215224 | −0.107612 | − | 0.994193i | \(-0.534320\pi\) | ||||
−0.107612 | + | 0.994193i | \(0.534320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.322081 | 0.0135261 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0642 | −0.421176 | −0.210588 | − | 0.977575i | \(-0.567538\pi\) | ||||
−0.210588 | + | 0.977575i | \(0.567538\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.9150 | 0.831960 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.7274 | 0.654740 | 0.327370 | − | 0.944896i | \(-0.393838\pi\) | ||||
0.327370 | + | 0.944896i | \(0.393838\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.97046 | −0.0818895 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.34983 | −0.0560002 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.3420 | −0.428323 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.7344 | −0.773250 | −0.386625 | − | 0.922237i | \(-0.626359\pi\) | ||||
−0.386625 | + | 0.922237i | \(0.626359\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.60586 | −0.107373 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.65714 | 0.273838 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.21532 | 0.132037 | 0.0660187 | − | 0.997818i | \(-0.478970\pi\) | ||||
0.0660187 | + | 0.997818i | \(0.478970\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.2986 | 0.503346 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.7639 | −0.930108 | −0.465054 | − | 0.885282i | \(-0.653965\pi\) | ||||
−0.465054 | + | 0.885282i | \(0.653965\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.30552 | 0.175626 | 0.0878128 | − | 0.996137i | \(-0.472012\pi\) | ||||
0.0878128 | + | 0.996137i | \(0.472012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.4626 | −0.507516 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.0868 | 0.450000 | 0.225000 | − | 0.974359i | \(-0.427762\pi\) | ||||
0.225000 | + | 0.974359i | \(0.427762\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.998205 | 0.0404493 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 54.6701 | 2.21172 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.9409 | −1.20930 | −0.604651 | − | 0.796490i | \(-0.706687\pi\) | ||||
−0.604651 | + | 0.796490i | \(0.706687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.0130 | −1.40957 | −0.704785 | − | 0.709421i | \(-0.748956\pi\) | ||||
−0.704785 | + | 0.709421i | \(0.748956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.98523 | −0.200373 | −0.100187 | − | 0.994969i | \(-0.531944\pi\) | ||||
−0.100187 | + | 0.994969i | \(0.531944\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.59289 | −0.184306 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0590800 | −0.00236699 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.10592 | 0.124038 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.4626 | −0.496916 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.64237 | 0.145000 | 0.0725002 | − | 0.997368i | \(-0.476902\pi\) | ||||
0.0725002 | + | 0.997368i | \(0.476902\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.72919 | 0.108476 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.5208 | 1.44701 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.1632 | −1.23280 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.6997 | 1.52854 | 0.764272 | − | 0.644894i | \(-0.223098\pi\) | ||||
0.764272 | + | 0.644894i | \(0.223098\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.8637 | −1.13827 | −0.569137 | − | 0.822243i | \(-0.692722\pi\) | ||||
−0.569137 | + | 0.822243i | \(0.692722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.8854 | −0.781777 | −0.390888 | − | 0.920438i | \(-0.627832\pi\) | ||||
−0.390888 | + | 0.920438i | \(0.627832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.87151 | −0.0734630 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.226499 | 0.00887719 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.1988 | 1.06437 | 0.532185 | − | 0.846628i | \(-0.321371\pi\) | ||||
0.532185 | + | 0.846628i | \(0.321371\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.8402 | 1.12516 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.7274 | 0.690561 | 0.345281 | − | 0.938499i | \(-0.387784\pi\) | ||||
0.345281 | + | 0.938499i | \(0.387784\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.7048 | 1.58323 | 0.791617 | − | 0.611018i | \(-0.209240\pi\) | ||||
0.791617 | + | 0.611018i | \(0.209240\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.2343 | −0.397468 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.34983 | 0.362027 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.0000 | 0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1137 | 0.815086 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.2135 | −0.470797 | −0.235398 | − | 0.971899i | \(-0.575639\pi\) | ||||
−0.235398 | + | 0.971899i | \(0.575639\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.5061 | −0.634380 | −0.317190 | − | 0.948362i | \(-0.602739\pi\) | ||||
−0.317190 | + | 0.948362i | \(0.602739\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0772219 | −0.00296350 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.2726 | 0.470287 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.1988 | −1.11726 | −0.558630 | − | 0.829417i | \(-0.688673\pi\) | ||||
−0.558630 | + | 0.829417i | \(0.688673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.7292 | 0.409344 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.7847 | −0.715639 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.9150 | 0.605434 | 0.302717 | − | 0.953080i | \(-0.402106\pi\) | ||||
0.302717 | + | 0.953080i | \(0.402106\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.779514 | 0.0296113 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.3351 | 0.694490 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.57116 | −0.324191 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.5981 | 1.30675 | 0.653375 | − | 0.757034i | \(-0.273352\pi\) | ||||
0.653375 | + | 0.757034i | \(0.273352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.86971 | 0.259096 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.62243 | 0.0610177 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.8212 | 1.34529 | 0.672646 | − | 0.739964i | \(-0.265158\pi\) | ||||
0.672646 | + | 0.739964i | \(0.265158\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.82994 | −0.293646 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.12153 | 0.0794520 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.57295 | −0.282817 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32.5781 | 1.21496 | 0.607479 | − | 0.794335i | \(-0.292181\pi\) | ||||
0.607479 | + | 0.794335i | \(0.292181\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.891443 | −0.0331991 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.79861 | 0.104081 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.9557 | −1.18517 | −0.592585 | − | 0.805508i | \(-0.701893\pi\) | ||||
−0.592585 | + | 0.805508i | \(0.701893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.19875 | 0.229583 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.8264 | 0.659331 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.19359 | 0.0810220 | 0.0405110 | − | 0.999179i | \(-0.487101\pi\) | ||||
0.0405110 | + | 0.999179i | \(0.487101\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.0990 | −0.593013 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.7473 | 1.90356 | 0.951778 | − | 0.306787i | \(-0.0992539\pi\) | ||||
0.951778 | + | 0.306787i | \(0.0992539\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.64142 | 0.207243 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.4436 | −0.529885 | −0.264942 | − | 0.964264i | \(-0.585353\pi\) | ||||
−0.264942 | + | 0.964264i | \(0.585353\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.7491 | 0.905523 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.95052 | 0.0712706 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4288 | −0.635987 | −0.317994 | − | 0.948093i | \(-0.603009\pi\) | ||||
−0.317994 | + | 0.948093i | \(0.603009\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 22.1623 | 0.807637 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.9331 | 1.26967 | 0.634833 | − | 0.772650i | \(-0.281069\pi\) | ||||
0.634833 | + | 0.772650i | \(0.281069\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.52864 | −0.0917839 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.2482 | −0.842748 | −0.421374 | − | 0.906887i | \(-0.638452\pi\) | ||||
−0.421374 | + | 0.906887i | \(0.638452\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.123327 | 0.00446473 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.39930 | −0.122742 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.6997 | −1.75615 | −0.878077 | − | 0.478519i | \(-0.841174\pi\) | ||||
−0.878077 | + | 0.478519i | \(0.841174\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.37335 | 0.337573 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6128 | 0.561554 | 0.280777 | − | 0.959773i | \(-0.409408\pi\) | ||||
0.280777 | + | 0.959773i | \(0.409408\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.597107 | −0.0214211 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.1068 | −0.362112 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.2560 | −1.44047 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.9427 | −1.53465 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.2630 | 0.864883 | 0.432441 | − | 0.901662i | \(-0.357652\pi\) | ||||
0.432441 | + | 0.901662i | \(0.357652\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.4141 | −0.584356 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.10497 | −0.0748440 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.3498 | 1.36184 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.5911 | −1.57950 | −0.789749 | − | 0.613430i | \(-0.789789\pi\) | ||||
−0.789749 | + | 0.613430i | \(0.789789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.3003 | −0.824307 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.08323 | 0.0382742 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.2552 | 1.31471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.8420 | −0.768874 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.7144 | −1.57208 | −0.786038 | − | 0.618179i | \(-0.787871\pi\) | ||||
−0.786038 | + | 0.618179i | \(0.787871\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.19179 | −0.0418495 | −0.0209247 | − | 0.999781i | \(-0.506661\pi\) | ||||
−0.0209247 | + | 0.999781i | \(0.506661\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.507859 | −0.0178114 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.82635 | −0.343780 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.41587 | 0.0494744 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0000 | 0.349002 | 0.174501 | − | 0.984657i | \(-0.444169\pi\) | ||||
0.174501 | + | 0.984657i | \(0.444169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.7551 | 0.932626 | 0.466313 | − | 0.884620i | \(-0.345582\pi\) | ||||
0.466313 | + | 0.884620i | \(0.345582\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.2907 | −0.948992 | −0.474496 | − | 0.880258i | \(-0.657370\pi\) | ||||
−0.474496 | + | 0.880258i | \(0.657370\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.2925 | 1.19103 | 0.595515 | − | 0.803344i | \(-0.296948\pi\) | ||||
0.595515 | + | 0.803344i | \(0.296948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.35763 | 0.289923 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.5651 | −0.539300 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.74396 | −0.336801 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.6701 | 1.40409 | 0.702044 | − | 0.712133i | \(-0.252271\pi\) | ||||
0.702044 | + | 0.712133i | \(0.252271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.4192 | 2.01446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.5573 | −0.398056 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.329889 | −0.0113351 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.5278 | 0.738832 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.59289 | −0.191722 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.6276 | 1.18563 | 0.592813 | − | 0.805340i | \(-0.298017\pi\) | ||||
0.592813 | + | 0.805340i | \(0.298017\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.4861 | −0.904749 | −0.452374 | − | 0.891828i | \(-0.649423\pi\) | ||||
−0.452374 | + | 0.891828i | \(0.649423\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.9627 | −1.39763 | −0.698814 | − | 0.715304i | \(-0.746288\pi\) | ||||
−0.698814 | + | 0.715304i | \(0.746288\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.878468 | 0.0299381 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.5712 | −0.632170 | −0.316085 | − | 0.948731i | \(-0.602368\pi\) | ||||
−0.316085 | + | 0.948731i | \(0.602368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −10.5721 | −0.359048 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1146 | −0.343113 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.2413 | −0.990803 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.41587 | 0.0479199 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.4913 | 0.962083 | 0.481041 | − | 0.876698i | \(-0.340259\pi\) | ||||
0.481041 | + | 0.876698i | \(0.340259\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.52780 | 0.186448 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.91318 | −0.165529 | −0.0827645 | − | 0.996569i | \(-0.526375\pi\) | ||||
−0.0827645 | + | 0.996569i | \(0.526375\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.1710 | 1.01534 | 0.507668 | − | 0.861553i | \(-0.330508\pi\) | ||||
0.507668 | + | 0.861553i | \(0.330508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.7865 | 0.865825 | 0.432913 | − | 0.901436i | \(-0.357486\pi\) | ||||
0.432913 | + | 0.901436i | \(0.357486\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.213524 | 0.00716136 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.62844 | −0.255562 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.8438 | 0.429800 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.59289 | −0.153352 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.8360 | 0.661566 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00601 | 0.266719 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.854095 | 0.0284225 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.3776 | −1.47353 | −0.736767 | − | 0.676147i | \(-0.763648\pi\) | ||||
−0.736767 | + | 0.676147i | \(0.763648\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −29.7473 | −0.986657 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.7968 | −1.58358 | −0.791789 | − | 0.610794i | \(-0.790850\pi\) | ||||
−0.791789 | + | 0.610794i | \(0.790850\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.9705 | 1.05807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.45659 | 0.0811237 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7144 | 0.386003 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −73.1189 | −2.40674 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.3447 | 0.536829 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0199 | 0.788069 | 0.394034 | − | 0.919096i | \(-0.371079\pi\) | ||||
0.394034 | + | 0.919096i | \(0.371079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.57991 | 0.281195 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.4584 | 0.702516 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.384533 | −0.0125621 | −0.00628107 | − | 0.999980i | \(-0.501999\pi\) | ||||
−0.00628107 | + | 0.999980i | \(0.501999\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.3221 | −0.761087 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.0920 | 0.817976 | 0.408988 | − | 0.912540i | \(-0.365882\pi\) | ||||
0.408988 | + | 0.912540i | \(0.365882\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.22829 | 0.267950 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.7126 | 1.45297 | 0.726483 | − | 0.687185i | \(-0.241154\pi\) | ||||
0.726483 | + | 0.687185i | \(0.241154\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 67.6683 | 2.19661 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.9210 | 0.483846 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2500 | 0.688356 | 0.344178 | − | 0.938904i | \(-0.388158\pi\) | ||||
0.344178 | + | 0.938904i | \(0.388158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.6424 | −0.764249 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.17882 | 0.0703577 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.4991 | −0.854810 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −35.7629 | −1.15244 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.0417 | −1.31981 | −0.659906 | − | 0.751349i | \(-0.729404\pi\) | ||||
−0.659906 | + | 0.751349i | \(0.729404\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.40437 | −0.0772394 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.2760 | −1.13206 | −0.566030 | − | 0.824385i | \(-0.691521\pi\) | ||||
−0.566030 | + | 0.824385i | \(0.691521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.32029 | 0.0423264 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.79164 | 0.217284 | 0.108642 | − | 0.994081i | \(-0.465350\pi\) | ||||
0.108642 | + | 0.994081i | \(0.465350\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.39930 | 0.0447219 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.26121 | −0.0721947 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.5981 | 0.625081 | 0.312540 | − | 0.949904i | \(-0.398820\pi\) | ||||
0.312540 | + | 0.949904i | \(0.398820\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.11636 | −0.0355343 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.2995 | 1.18486 | 0.592429 | − | 0.805623i | \(-0.298169\pi\) | ||||
0.592429 | + | 0.805623i | \(0.298169\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −15.7171 | −0.498766 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.7274 | 0.624773 | 0.312386 | − | 0.949955i | \(-0.398872\pi\) | ||||
0.312386 | + | 0.949955i | \(0.398872\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.6875 | 0.812717 |
(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 | 9200.2.a.ce.1.2 | 3 | ||
4.3 | odd | 2 | 4600.2.a.x.1.2 | 3 | |||
5.4 | even | 2 | 1840.2.a.s.1.2 | 3 | |||
20.3 | even | 4 | 4600.2.e.p.4049.3 | 6 | |||
20.7 | even | 4 | 4600.2.e.p.4049.4 | 6 | |||
20.19 | odd | 2 | 920.2.a.h.1.2 | ✓ | 3 | ||
40.19 | odd | 2 | 7360.2.a.by.1.2 | 3 | |||
40.29 | even | 2 | 7360.2.a.cc.1.2 | 3 | |||
60.59 | even | 2 | 8280.2.a.bj.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.h.1.2 | ✓ | 3 | 20.19 | odd | 2 | ||
1840.2.a.s.1.2 | 3 | 5.4 | even | 2 | |||
4600.2.a.x.1.2 | 3 | 4.3 | odd | 2 | |||
4600.2.e.p.4049.3 | 6 | 20.3 | even | 4 | |||
4600.2.e.p.4049.4 | 6 | 20.7 | even | 4 | |||
7360.2.a.by.1.2 | 3 | 40.19 | odd | 2 | |||
7360.2.a.cc.1.2 | 3 | 40.29 | even | 2 | |||
8280.2.a.bj.1.2 | 3 | 60.59 | even | 2 | |||
9200.2.a.ce.1.2 | 3 | 1.1 | even | 1 | trivial |