Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.70716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70716 | −1.20714 | −0.603572 | − | 0.797309i | \(-0.706256\pi\) | ||||
−0.603572 | + | 0.797309i | \(0.706256\pi\) | |||||||
\(3\) | 2.29155 | 1.32303 | 0.661515 | − | 0.749932i | \(-0.269914\pi\) | ||||
0.661515 | + | 0.749932i | \(0.269914\pi\) | |||||||
\(4\) | 0.914391 | 0.457196 | ||||||||
\(5\) | 4.06637 | 1.81854 | 0.909268 | − | 0.416211i | \(-0.136642\pi\) | ||||
0.909268 | + | 0.416211i | \(0.136642\pi\) | |||||||
\(6\) | −3.91205 | −1.59709 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.85331 | 0.655243 | ||||||||
\(9\) | 2.25122 | 0.750407 | ||||||||
\(10\) | −6.94194 | −2.19523 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.09538 | 0.604883 | ||||||||
\(13\) | 3.27792 | 0.909132 | 0.454566 | − | 0.890713i | \(-0.349794\pi\) | ||||
0.454566 | + | 0.890713i | \(0.349794\pi\) | |||||||
\(14\) | −1.70716 | −0.456257 | ||||||||
\(15\) | 9.31831 | 2.40598 | ||||||||
\(16\) | −4.99267 | −1.24817 | ||||||||
\(17\) | −1.32088 | −0.320361 | −0.160180 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160180 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(18\) | −3.84319 | −0.905849 | ||||||||
\(19\) | 2.16175 | 0.495939 | 0.247969 | − | 0.968768i | \(-0.420237\pi\) | ||||
0.247969 | + | 0.968768i | \(0.420237\pi\) | |||||||
\(20\) | 3.71825 | 0.831427 | ||||||||
\(21\) | 2.29155 | 0.500058 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.86611 | −0.389112 | −0.194556 | − | 0.980891i | \(-0.562327\pi\) | ||||
−0.194556 | + | 0.980891i | \(0.562327\pi\) | |||||||
\(24\) | 4.24695 | 0.866905 | ||||||||
\(25\) | 11.5354 | 2.30707 | ||||||||
\(26\) | −5.59593 | −1.09745 | ||||||||
\(27\) | −1.71587 | −0.330219 | ||||||||
\(28\) | 0.914391 | 0.172804 | ||||||||
\(29\) | −0.244102 | −0.0453286 | −0.0226643 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226643 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(30\) | −15.9078 | −2.90436 | ||||||||
\(31\) | −6.86988 | −1.23387 | −0.616933 | − | 0.787015i | \(-0.711625\pi\) | ||||
−0.616933 | + | 0.787015i | \(0.711625\pi\) | |||||||
\(32\) | 4.81667 | 0.851475 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.25495 | 0.386721 | ||||||||
\(35\) | 4.06637 | 0.687342 | ||||||||
\(36\) | 2.05850 | 0.343083 | ||||||||
\(37\) | 0.255619 | 0.0420236 | 0.0210118 | − | 0.999779i | \(-0.493311\pi\) | ||||
0.0210118 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(38\) | −3.69045 | −0.598669 | ||||||||
\(39\) | 7.51153 | 1.20281 | ||||||||
\(40\) | 7.53623 | 1.19158 | ||||||||
\(41\) | −5.73233 | −0.895239 | −0.447620 | − | 0.894224i | \(-0.647728\pi\) | ||||
−0.447620 | + | 0.894224i | \(0.647728\pi\) | |||||||
\(42\) | −3.91205 | −0.603642 | ||||||||
\(43\) | −8.01781 | −1.22270 | −0.611352 | − | 0.791358i | \(-0.709374\pi\) | ||||
−0.611352 | + | 0.791358i | \(0.709374\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.15429 | 1.36464 | ||||||||
\(46\) | 3.18575 | 0.469714 | ||||||||
\(47\) | −4.06768 | −0.593332 | −0.296666 | − | 0.954981i | \(-0.595875\pi\) | ||||
−0.296666 | + | 0.954981i | \(0.595875\pi\) | |||||||
\(48\) | −11.4410 | −1.65136 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −19.6927 | −2.78497 | ||||||||
\(51\) | −3.02687 | −0.423847 | ||||||||
\(52\) | 2.99730 | 0.415651 | ||||||||
\(53\) | −5.00585 | −0.687607 | −0.343803 | − | 0.939042i | \(-0.611715\pi\) | ||||
−0.343803 | + | 0.939042i | \(0.611715\pi\) | |||||||
\(54\) | 2.92926 | 0.398622 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.85331 | 0.247658 | ||||||||
\(57\) | 4.95376 | 0.656142 | ||||||||
\(58\) | 0.416720 | 0.0547181 | ||||||||
\(59\) | −0.983592 | −0.128053 | −0.0640264 | − | 0.997948i | \(-0.520394\pi\) | ||||
−0.0640264 | + | 0.997948i | \(0.520394\pi\) | |||||||
\(60\) | 8.52058 | 1.10000 | ||||||||
\(61\) | 1.84671 | 0.236447 | 0.118223 | − | 0.992987i | \(-0.462280\pi\) | ||||
0.118223 | + | 0.992987i | \(0.462280\pi\) | |||||||
\(62\) | 11.7280 | 1.48945 | ||||||||
\(63\) | 2.25122 | 0.283627 | ||||||||
\(64\) | 1.76252 | 0.220315 | ||||||||
\(65\) | 13.3292 | 1.65329 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.00700 | −0.367364 | −0.183682 | − | 0.982986i | \(-0.558802\pi\) | ||||
−0.183682 | + | 0.982986i | \(0.558802\pi\) | |||||||
\(68\) | −1.20780 | −0.146468 | ||||||||
\(69\) | −4.27630 | −0.514806 | ||||||||
\(70\) | −6.94194 | −0.829720 | ||||||||
\(71\) | 6.47642 | 0.768609 | 0.384305 | − | 0.923206i | \(-0.374441\pi\) | ||||
0.384305 | + | 0.923206i | \(0.374441\pi\) | |||||||
\(72\) | 4.17220 | 0.491699 | ||||||||
\(73\) | −9.65164 | −1.12964 | −0.564820 | − | 0.825214i | \(-0.691054\pi\) | ||||
−0.564820 | + | 0.825214i | \(0.691054\pi\) | |||||||
\(74\) | −0.436383 | −0.0507285 | ||||||||
\(75\) | 26.4339 | 3.05233 | ||||||||
\(76\) | 1.97668 | 0.226741 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −12.8234 | −1.45196 | ||||||||
\(79\) | −5.53450 | −0.622680 | −0.311340 | − | 0.950299i | \(-0.600778\pi\) | ||||
−0.311340 | + | 0.950299i | \(0.600778\pi\) | |||||||
\(80\) | −20.3020 | −2.26984 | ||||||||
\(81\) | −10.6857 | −1.18730 | ||||||||
\(82\) | 9.78600 | 1.08068 | ||||||||
\(83\) | 2.07023 | 0.227237 | 0.113618 | − | 0.993524i | \(-0.463756\pi\) | ||||
0.113618 | + | 0.993524i | \(0.463756\pi\) | |||||||
\(84\) | 2.09538 | 0.228624 | ||||||||
\(85\) | −5.37119 | −0.582588 | ||||||||
\(86\) | 13.6877 | 1.47598 | ||||||||
\(87\) | −0.559372 | −0.0599710 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.6306 | 1.76284 | 0.881421 | − | 0.472331i | \(-0.156587\pi\) | ||||
0.881421 | + | 0.472331i | \(0.156587\pi\) | |||||||
\(90\) | −15.6278 | −1.64732 | ||||||||
\(91\) | 3.27792 | 0.343620 | ||||||||
\(92\) | −1.70636 | −0.177900 | ||||||||
\(93\) | −15.7427 | −1.63244 | ||||||||
\(94\) | 6.94417 | 0.716237 | ||||||||
\(95\) | 8.79046 | 0.901883 | ||||||||
\(96\) | 11.0377 | 1.12653 | ||||||||
\(97\) | −2.58559 | −0.262527 | −0.131264 | − | 0.991348i | \(-0.541903\pi\) | ||||
−0.131264 | + | 0.991348i | \(0.541903\pi\) | |||||||
\(98\) | −1.70716 | −0.172449 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10.5478 | 1.05478 | ||||||||
\(101\) | 10.5686 | 1.05162 | 0.525808 | − | 0.850604i | \(-0.323763\pi\) | ||||
0.525808 | + | 0.850604i | \(0.323763\pi\) | |||||||
\(102\) | 5.16735 | 0.511644 | ||||||||
\(103\) | 13.8489 | 1.36457 | 0.682286 | − | 0.731086i | \(-0.260986\pi\) | ||||
0.682286 | + | 0.731086i | \(0.260986\pi\) | |||||||
\(104\) | 6.07499 | 0.595702 | ||||||||
\(105\) | 9.31831 | 0.909374 | ||||||||
\(106\) | 8.54578 | 0.830040 | ||||||||
\(107\) | 12.4286 | 1.20152 | 0.600761 | − | 0.799428i | \(-0.294864\pi\) | ||||
0.600761 | + | 0.799428i | \(0.294864\pi\) | |||||||
\(108\) | −1.56898 | −0.150975 | ||||||||
\(109\) | −7.36748 | −0.705676 | −0.352838 | − | 0.935684i | \(-0.614783\pi\) | ||||
−0.352838 | + | 0.935684i | \(0.614783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.585766 | 0.0555984 | ||||||||
\(112\) | −4.99267 | −0.471763 | ||||||||
\(113\) | 11.4083 | 1.07320 | 0.536600 | − | 0.843837i | \(-0.319708\pi\) | ||||
0.536600 | + | 0.843837i | \(0.319708\pi\) | |||||||
\(114\) | −8.45686 | −0.792057 | ||||||||
\(115\) | −7.58831 | −0.707614 | ||||||||
\(116\) | −0.223205 | −0.0207240 | ||||||||
\(117\) | 7.37932 | 0.682219 | ||||||||
\(118\) | 1.67915 | 0.154578 | ||||||||
\(119\) | −1.32088 | −0.121085 | ||||||||
\(120\) | 17.2697 | 1.57650 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.15263 | −0.285425 | ||||||||
\(123\) | −13.1359 | −1.18443 | ||||||||
\(124\) | −6.28176 | −0.564119 | ||||||||
\(125\) | 26.5752 | 2.37696 | ||||||||
\(126\) | −3.84319 | −0.342379 | ||||||||
\(127\) | −8.74845 | −0.776300 | −0.388150 | − | 0.921596i | \(-0.626886\pi\) | ||||
−0.388150 | + | 0.921596i | \(0.626886\pi\) | |||||||
\(128\) | −12.6422 | −1.11743 | ||||||||
\(129\) | −18.3732 | −1.61767 | ||||||||
\(130\) | −22.7551 | −1.99576 | ||||||||
\(131\) | −12.5516 | −1.09664 | −0.548319 | − | 0.836269i | \(-0.684732\pi\) | ||||
−0.548319 | + | 0.836269i | \(0.684732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.16175 | 0.187447 | ||||||||
\(134\) | 5.13343 | 0.443461 | ||||||||
\(135\) | −6.97736 | −0.600516 | ||||||||
\(136\) | −2.44800 | −0.209914 | ||||||||
\(137\) | −6.32819 | −0.540654 | −0.270327 | − | 0.962769i | \(-0.587132\pi\) | ||||
−0.270327 | + | 0.962769i | \(0.587132\pi\) | |||||||
\(138\) | 7.30033 | 0.621445 | ||||||||
\(139\) | 14.4429 | 1.22503 | 0.612517 | − | 0.790457i | \(-0.290157\pi\) | ||||
0.612517 | + | 0.790457i | \(0.290157\pi\) | |||||||
\(140\) | 3.71825 | 0.314250 | ||||||||
\(141\) | −9.32130 | −0.784995 | ||||||||
\(142\) | −11.0563 | −0.927822 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −11.2396 | −0.936633 | ||||||||
\(145\) | −0.992608 | −0.0824316 | ||||||||
\(146\) | 16.4769 | 1.36364 | ||||||||
\(147\) | 2.29155 | 0.189004 | ||||||||
\(148\) | 0.233736 | 0.0192130 | ||||||||
\(149\) | 24.0592 | 1.97101 | 0.985504 | − | 0.169653i | \(-0.0542648\pi\) | ||||
0.985504 | + | 0.169653i | \(0.0542648\pi\) | |||||||
\(150\) | −45.1269 | −3.68460 | ||||||||
\(151\) | −1.32418 | −0.107760 | −0.0538802 | − | 0.998547i | \(-0.517159\pi\) | ||||
−0.0538802 | + | 0.998547i | \(0.517159\pi\) | |||||||
\(152\) | 4.00638 | 0.324960 | ||||||||
\(153\) | −2.97359 | −0.240401 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.9355 | −2.24383 | ||||||||
\(156\) | 6.86848 | 0.549919 | ||||||||
\(157\) | 14.6141 | 1.16633 | 0.583165 | − | 0.812354i | \(-0.301814\pi\) | ||||
0.583165 | + | 0.812354i | \(0.301814\pi\) | |||||||
\(158\) | 9.44827 | 0.751664 | ||||||||
\(159\) | −11.4712 | −0.909724 | ||||||||
\(160\) | 19.5864 | 1.54844 | ||||||||
\(161\) | −1.86611 | −0.147070 | ||||||||
\(162\) | 18.2421 | 1.43324 | ||||||||
\(163\) | −20.9215 | −1.63870 | −0.819349 | − | 0.573296i | \(-0.805665\pi\) | ||||
−0.819349 | + | 0.573296i | \(0.805665\pi\) | |||||||
\(164\) | −5.24159 | −0.409300 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.53421 | −0.274308 | ||||||||
\(167\) | 4.91335 | 0.380206 | 0.190103 | − | 0.981764i | \(-0.439118\pi\) | ||||
0.190103 | + | 0.981764i | \(0.439118\pi\) | |||||||
\(168\) | 4.24695 | 0.327659 | ||||||||
\(169\) | −2.25523 | −0.173479 | ||||||||
\(170\) | 9.16948 | 0.703267 | ||||||||
\(171\) | 4.86657 | 0.372156 | ||||||||
\(172\) | −7.33142 | −0.559015 | ||||||||
\(173\) | 19.6578 | 1.49456 | 0.747279 | − | 0.664511i | \(-0.231360\pi\) | ||||
0.747279 | + | 0.664511i | \(0.231360\pi\) | |||||||
\(174\) | 0.954937 | 0.0723936 | ||||||||
\(175\) | 11.5354 | 0.871992 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.25395 | −0.169418 | ||||||||
\(178\) | −28.3911 | −2.12800 | ||||||||
\(179\) | −25.3588 | −1.89541 | −0.947705 | − | 0.319149i | \(-0.896603\pi\) | ||||
−0.947705 | + | 0.319149i | \(0.896603\pi\) | |||||||
\(180\) | 8.37061 | 0.623908 | ||||||||
\(181\) | −1.97569 | −0.146852 | −0.0734258 | − | 0.997301i | \(-0.523393\pi\) | ||||
−0.0734258 | + | 0.997301i | \(0.523393\pi\) | |||||||
\(182\) | −5.59593 | −0.414798 | ||||||||
\(183\) | 4.23184 | 0.312826 | ||||||||
\(184\) | −3.45848 | −0.254963 | ||||||||
\(185\) | 1.03944 | 0.0764214 | ||||||||
\(186\) | 26.8753 | 1.97059 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.71945 | −0.271269 | ||||||||
\(189\) | −1.71587 | −0.124811 | ||||||||
\(190\) | −15.0067 | −1.08870 | ||||||||
\(191\) | 0.972995 | 0.0704035 | 0.0352017 | − | 0.999380i | \(-0.488793\pi\) | ||||
0.0352017 | + | 0.999380i | \(0.488793\pi\) | |||||||
\(192\) | 4.03891 | 0.291484 | ||||||||
\(193\) | −23.1326 | −1.66512 | −0.832562 | − | 0.553932i | \(-0.813127\pi\) | ||||
−0.832562 | + | 0.553932i | \(0.813127\pi\) | |||||||
\(194\) | 4.41402 | 0.316908 | ||||||||
\(195\) | 30.5447 | 2.18735 | ||||||||
\(196\) | 0.914391 | 0.0653137 | ||||||||
\(197\) | −9.91237 | −0.706227 | −0.353114 | − | 0.935580i | \(-0.614877\pi\) | ||||
−0.353114 | + | 0.935580i | \(0.614877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3847 | 0.736154 | 0.368077 | − | 0.929795i | \(-0.380016\pi\) | ||||
0.368077 | + | 0.929795i | \(0.380016\pi\) | |||||||
\(200\) | 21.3786 | 1.51169 | ||||||||
\(201\) | −6.89070 | −0.486033 | ||||||||
\(202\) | −18.0423 | −1.26945 | ||||||||
\(203\) | −0.244102 | −0.0171326 | ||||||||
\(204\) | −2.76774 | −0.193781 | ||||||||
\(205\) | −23.3098 | −1.62803 | ||||||||
\(206\) | −23.6422 | −1.64723 | ||||||||
\(207\) | −4.20103 | −0.291992 | ||||||||
\(208\) | −16.3656 | −1.13475 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −15.9078 | −1.09774 | ||||||||
\(211\) | −12.9916 | −0.894378 | −0.447189 | − | 0.894439i | \(-0.647575\pi\) | ||||
−0.447189 | + | 0.894439i | \(0.647575\pi\) | |||||||
\(212\) | −4.57731 | −0.314371 | ||||||||
\(213\) | 14.8411 | 1.01689 | ||||||||
\(214\) | −21.2177 | −1.45041 | ||||||||
\(215\) | −32.6034 | −2.22353 | ||||||||
\(216\) | −3.18003 | −0.216374 | ||||||||
\(217\) | −6.86988 | −0.466358 | ||||||||
\(218\) | 12.5775 | 0.851853 | ||||||||
\(219\) | −22.1173 | −1.49455 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.32975 | −0.291250 | ||||||||
\(222\) | −0.999995 | −0.0671153 | ||||||||
\(223\) | −14.3527 | −0.961127 | −0.480563 | − | 0.876960i | \(-0.659568\pi\) | ||||
−0.480563 | + | 0.876960i | \(0.659568\pi\) | |||||||
\(224\) | 4.81667 | 0.321827 | ||||||||
\(225\) | 25.9686 | 1.73124 | ||||||||
\(226\) | −19.4757 | −1.29551 | ||||||||
\(227\) | 6.37479 | 0.423110 | 0.211555 | − | 0.977366i | \(-0.432147\pi\) | ||||
0.211555 | + | 0.977366i | \(0.432147\pi\) | |||||||
\(228\) | 4.52968 | 0.299985 | ||||||||
\(229\) | −8.00237 | −0.528812 | −0.264406 | − | 0.964412i | \(-0.585176\pi\) | ||||
−0.264406 | + | 0.964412i | \(0.585176\pi\) | |||||||
\(230\) | 12.9545 | 0.854191 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.452395 | −0.0297012 | ||||||||
\(233\) | −10.8022 | −0.707675 | −0.353837 | − | 0.935307i | \(-0.615123\pi\) | ||||
−0.353837 | + | 0.935307i | \(0.615123\pi\) | |||||||
\(234\) | −12.5977 | −0.823536 | ||||||||
\(235\) | −16.5407 | −1.07900 | ||||||||
\(236\) | −0.899388 | −0.0585452 | ||||||||
\(237\) | −12.6826 | −0.823824 | ||||||||
\(238\) | 2.25495 | 0.146167 | ||||||||
\(239\) | 25.1583 | 1.62735 | 0.813676 | − | 0.581318i | \(-0.197463\pi\) | ||||
0.813676 | + | 0.581318i | \(0.197463\pi\) | |||||||
\(240\) | −46.5232 | −3.00306 | ||||||||
\(241\) | −18.2462 | −1.17534 | −0.587669 | − | 0.809101i | \(-0.699954\pi\) | ||||
−0.587669 | + | 0.809101i | \(0.699954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.3392 | −1.24061 | ||||||||
\(244\) | 1.68862 | 0.108103 | ||||||||
\(245\) | 4.06637 | 0.259791 | ||||||||
\(246\) | 22.4251 | 1.42977 | ||||||||
\(247\) | 7.08604 | 0.450874 | ||||||||
\(248\) | −12.7320 | −0.808482 | ||||||||
\(249\) | 4.74404 | 0.300641 | ||||||||
\(250\) | −45.3681 | −2.86933 | ||||||||
\(251\) | 15.3284 | 0.967520 | 0.483760 | − | 0.875201i | \(-0.339271\pi\) | ||||
0.483760 | + | 0.875201i | \(0.339271\pi\) | |||||||
\(252\) | 2.05850 | 0.129673 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 14.9350 | 0.937105 | ||||||||
\(255\) | −12.3084 | −0.770780 | ||||||||
\(256\) | 18.0573 | 1.12858 | ||||||||
\(257\) | 2.67980 | 0.167161 | 0.0835805 | − | 0.996501i | \(-0.473364\pi\) | ||||
0.0835805 | + | 0.996501i | \(0.473364\pi\) | |||||||
\(258\) | 31.3661 | 1.95277 | ||||||||
\(259\) | 0.255619 | 0.0158834 | ||||||||
\(260\) | 12.1881 | 0.755877 | ||||||||
\(261\) | −0.549527 | −0.0340149 | ||||||||
\(262\) | 21.4276 | 1.32380 | ||||||||
\(263\) | −9.97733 | −0.615229 | −0.307614 | − | 0.951511i | \(-0.599531\pi\) | ||||
−0.307614 | + | 0.951511i | \(0.599531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.3556 | −1.25044 | ||||||||
\(266\) | −3.69045 | −0.226276 | ||||||||
\(267\) | 38.1100 | 2.33229 | ||||||||
\(268\) | −2.74958 | −0.167957 | ||||||||
\(269\) | −21.5774 | −1.31560 | −0.657798 | − | 0.753194i | \(-0.728512\pi\) | ||||
−0.657798 | + | 0.753194i | \(0.728512\pi\) | |||||||
\(270\) | 11.9115 | 0.724909 | ||||||||
\(271\) | −14.9862 | −0.910349 | −0.455175 | − | 0.890402i | \(-0.650423\pi\) | ||||
−0.455175 | + | 0.890402i | \(0.650423\pi\) | |||||||
\(272\) | 6.59473 | 0.399864 | ||||||||
\(273\) | 7.51153 | 0.454619 | ||||||||
\(274\) | 10.8032 | 0.652647 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.91021 | −0.235367 | ||||||||
\(277\) | 5.20640 | 0.312822 | 0.156411 | − | 0.987692i | \(-0.450008\pi\) | ||||
0.156411 | + | 0.987692i | \(0.450008\pi\) | |||||||
\(278\) | −24.6564 | −1.47879 | ||||||||
\(279\) | −15.4656 | −0.925902 | ||||||||
\(280\) | 7.53623 | 0.450376 | ||||||||
\(281\) | 15.1601 | 0.904374 | 0.452187 | − | 0.891923i | \(-0.350644\pi\) | ||||
0.452187 | + | 0.891923i | \(0.350644\pi\) | |||||||
\(282\) | 15.9129 | 0.947602 | ||||||||
\(283\) | −5.66559 | −0.336784 | −0.168392 | − | 0.985720i | \(-0.553857\pi\) | ||||
−0.168392 | + | 0.985720i | \(0.553857\pi\) | |||||||
\(284\) | 5.92198 | 0.351405 | ||||||||
\(285\) | 20.1438 | 1.19322 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.73233 | −0.338369 | ||||||||
\(288\) | 10.8434 | 0.638952 | ||||||||
\(289\) | −15.2553 | −0.897369 | ||||||||
\(290\) | 1.69454 | 0.0995068 | ||||||||
\(291\) | −5.92502 | −0.347331 | ||||||||
\(292\) | −8.82538 | −0.516466 | ||||||||
\(293\) | −26.9403 | −1.57387 | −0.786935 | − | 0.617035i | \(-0.788334\pi\) | ||||
−0.786935 | + | 0.617035i | \(0.788334\pi\) | |||||||
\(294\) | −3.91205 | −0.228155 | ||||||||
\(295\) | −3.99965 | −0.232869 | ||||||||
\(296\) | 0.473741 | 0.0275356 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −41.0729 | −2.37929 | ||||||||
\(299\) | −6.11698 | −0.353754 | ||||||||
\(300\) | 24.1709 | 1.39551 | ||||||||
\(301\) | −8.01781 | −0.462139 | ||||||||
\(302\) | 2.26059 | 0.130082 | ||||||||
\(303\) | 24.2185 | 1.39132 | ||||||||
\(304\) | −10.7929 | −0.619015 | ||||||||
\(305\) | 7.50941 | 0.429987 | ||||||||
\(306\) | 5.07640 | 0.290198 | ||||||||
\(307\) | 24.6157 | 1.40489 | 0.702447 | − | 0.711736i | \(-0.252091\pi\) | ||||
0.702447 | + | 0.711736i | \(0.252091\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.7355 | 1.80537 | ||||||||
\(310\) | 47.6903 | 2.70863 | ||||||||
\(311\) | −10.2131 | −0.579132 | −0.289566 | − | 0.957158i | \(-0.593511\pi\) | ||||
−0.289566 | + | 0.957158i | \(0.593511\pi\) | |||||||
\(312\) | 13.9212 | 0.788131 | ||||||||
\(313\) | 22.4003 | 1.26614 | 0.633069 | − | 0.774096i | \(-0.281795\pi\) | ||||
0.633069 | + | 0.774096i | \(0.281795\pi\) | |||||||
\(314\) | −24.9485 | −1.40793 | ||||||||
\(315\) | 9.15429 | 0.515786 | ||||||||
\(316\) | −5.06070 | −0.284687 | ||||||||
\(317\) | 23.3595 | 1.31200 | 0.656000 | − | 0.754761i | \(-0.272247\pi\) | ||||
0.656000 | + | 0.754761i | \(0.272247\pi\) | |||||||
\(318\) | 19.5831 | 1.09817 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7.16707 | 0.400651 | ||||||||
\(321\) | 28.4809 | 1.58965 | ||||||||
\(322\) | 3.18575 | 0.177535 | ||||||||
\(323\) | −2.85541 | −0.158879 | ||||||||
\(324\) | −9.77088 | −0.542827 | ||||||||
\(325\) | 37.8120 | 2.09743 | ||||||||
\(326\) | 35.7163 | 1.97814 | ||||||||
\(327\) | −16.8830 | −0.933631 | ||||||||
\(328\) | −10.6238 | −0.586599 | ||||||||
\(329\) | −4.06768 | −0.224258 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.6444 | 0.859892 | 0.429946 | − | 0.902855i | \(-0.358533\pi\) | ||||
0.429946 | + | 0.902855i | \(0.358533\pi\) | |||||||
\(332\) | 1.89300 | 0.103892 | ||||||||
\(333\) | 0.575455 | 0.0315348 | ||||||||
\(334\) | −8.38787 | −0.458964 | ||||||||
\(335\) | −12.2276 | −0.668064 | ||||||||
\(336\) | −11.4410 | −0.624156 | ||||||||
\(337\) | 32.5910 | 1.77534 | 0.887672 | − | 0.460477i | \(-0.152322\pi\) | ||||
0.887672 | + | 0.460477i | \(0.152322\pi\) | |||||||
\(338\) | 3.85004 | 0.209414 | ||||||||
\(339\) | 26.1427 | 1.41988 | ||||||||
\(340\) | −4.91137 | −0.266356 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −8.30801 | −0.449245 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −14.8595 | −0.801169 | ||||||||
\(345\) | −17.3890 | −0.936194 | ||||||||
\(346\) | −33.5590 | −1.80415 | ||||||||
\(347\) | 5.75284 | 0.308829 | 0.154414 | − | 0.988006i | \(-0.450651\pi\) | ||||
0.154414 | + | 0.988006i | \(0.450651\pi\) | |||||||
\(348\) | −0.511485 | −0.0274185 | ||||||||
\(349\) | −0.183939 | −0.00984606 | −0.00492303 | − | 0.999988i | \(-0.501567\pi\) | ||||
−0.00492303 | + | 0.999988i | \(0.501567\pi\) | |||||||
\(350\) | −19.6927 | −1.05262 | ||||||||
\(351\) | −5.62449 | −0.300213 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0211 | 1.01239 | 0.506195 | − | 0.862419i | \(-0.331052\pi\) | ||||
0.506195 | + | 0.862419i | \(0.331052\pi\) | |||||||
\(354\) | 3.84786 | 0.204511 | ||||||||
\(355\) | 26.3355 | 1.39774 | ||||||||
\(356\) | 15.2069 | 0.805964 | ||||||||
\(357\) | −3.02687 | −0.160199 | ||||||||
\(358\) | 43.2916 | 2.28803 | ||||||||
\(359\) | −0.718928 | −0.0379435 | −0.0189718 | − | 0.999820i | \(-0.506039\pi\) | ||||
−0.0189718 | + | 0.999820i | \(0.506039\pi\) | |||||||
\(360\) | 16.9657 | 0.894172 | ||||||||
\(361\) | −14.3268 | −0.754045 | ||||||||
\(362\) | 3.37281 | 0.177271 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.99730 | 0.157101 | ||||||||
\(365\) | −39.2471 | −2.05429 | ||||||||
\(366\) | −7.22442 | −0.377626 | ||||||||
\(367\) | −7.89295 | −0.412009 | −0.206004 | − | 0.978551i | \(-0.566046\pi\) | ||||
−0.206004 | + | 0.978551i | \(0.566046\pi\) | |||||||
\(368\) | 9.31689 | 0.485677 | ||||||||
\(369\) | −12.9047 | −0.671794 | ||||||||
\(370\) | −1.77449 | −0.0922516 | ||||||||
\(371\) | −5.00585 | −0.259891 | ||||||||
\(372\) | −14.3950 | −0.746345 | ||||||||
\(373\) | 15.6686 | 0.811292 | 0.405646 | − | 0.914030i | \(-0.367047\pi\) | ||||
0.405646 | + | 0.914030i | \(0.367047\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 60.8985 | 3.14479 | ||||||||
\(376\) | −7.53865 | −0.388776 | ||||||||
\(377\) | −0.800146 | −0.0412096 | ||||||||
\(378\) | 2.92926 | 0.150665 | ||||||||
\(379\) | −13.3144 | −0.683914 | −0.341957 | − | 0.939716i | \(-0.611090\pi\) | ||||
−0.341957 | + | 0.939716i | \(0.611090\pi\) | |||||||
\(380\) | 8.03792 | 0.412337 | ||||||||
\(381\) | −20.0476 | −1.02707 | ||||||||
\(382\) | −1.66106 | −0.0849871 | ||||||||
\(383\) | 11.8484 | 0.605426 | 0.302713 | − | 0.953082i | \(-0.402108\pi\) | ||||
0.302713 | + | 0.953082i | \(0.402108\pi\) | |||||||
\(384\) | −28.9704 | −1.47839 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 39.4911 | 2.01004 | ||||||||
\(387\) | −18.0499 | −0.917526 | ||||||||
\(388\) | −2.36424 | −0.120026 | ||||||||
\(389\) | −6.04972 | −0.306733 | −0.153366 | − | 0.988169i | \(-0.549011\pi\) | ||||
−0.153366 | + | 0.988169i | \(0.549011\pi\) | |||||||
\(390\) | −52.1446 | −2.64045 | ||||||||
\(391\) | 2.46491 | 0.124656 | ||||||||
\(392\) | 1.85331 | 0.0936061 | ||||||||
\(393\) | −28.7627 | −1.45089 | ||||||||
\(394\) | 16.9220 | 0.852518 | ||||||||
\(395\) | −22.5053 | −1.13237 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5763 | −0.580996 | −0.290498 | − | 0.956876i | \(-0.593821\pi\) | ||||
−0.290498 | + | 0.956876i | \(0.593821\pi\) | |||||||
\(398\) | −17.7284 | −0.888643 | ||||||||
\(399\) | 4.95376 | 0.247998 | ||||||||
\(400\) | −57.5923 | −2.87961 | ||||||||
\(401\) | 33.7924 | 1.68751 | 0.843755 | − | 0.536728i | \(-0.180340\pi\) | ||||
0.843755 | + | 0.536728i | \(0.180340\pi\) | |||||||
\(402\) | 11.7635 | 0.586711 | ||||||||
\(403\) | −22.5189 | −1.12175 | ||||||||
\(404\) | 9.66384 | 0.480794 | ||||||||
\(405\) | −43.4519 | −2.15914 | ||||||||
\(406\) | 0.416720 | 0.0206815 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.60972 | −0.277722 | ||||||||
\(409\) | 18.0520 | 0.892613 | 0.446306 | − | 0.894880i | \(-0.352739\pi\) | ||||
0.446306 | + | 0.894880i | \(0.352739\pi\) | |||||||
\(410\) | 39.7935 | 1.96526 | ||||||||
\(411\) | −14.5014 | −0.715301 | ||||||||
\(412\) | 12.6633 | 0.623876 | ||||||||
\(413\) | −0.983592 | −0.0483994 | ||||||||
\(414\) | 7.17183 | 0.352476 | ||||||||
\(415\) | 8.41831 | 0.413239 | ||||||||
\(416\) | 15.7887 | 0.774103 | ||||||||
\(417\) | 33.0968 | 1.62076 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.58559 | 0.126314 | 0.0631571 | − | 0.998004i | \(-0.479883\pi\) | ||||
0.0631571 | + | 0.998004i | \(0.479883\pi\) | |||||||
\(420\) | 8.52058 | 0.415762 | ||||||||
\(421\) | 13.9948 | 0.682064 | 0.341032 | − | 0.940052i | \(-0.389224\pi\) | ||||
0.341032 | + | 0.940052i | \(0.389224\pi\) | |||||||
\(422\) | 22.1787 | 1.07964 | ||||||||
\(423\) | −9.15724 | −0.445240 | ||||||||
\(424\) | −9.27738 | −0.450549 | ||||||||
\(425\) | −15.2368 | −0.739096 | ||||||||
\(426\) | −25.3360 | −1.22754 | ||||||||
\(427\) | 1.84671 | 0.0893686 | ||||||||
\(428\) | 11.3646 | 0.549331 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 55.6592 | 2.68412 | ||||||||
\(431\) | −33.6682 | −1.62174 | −0.810870 | − | 0.585227i | \(-0.801005\pi\) | ||||
−0.810870 | + | 0.585227i | \(0.801005\pi\) | |||||||
\(432\) | 8.56677 | 0.412169 | ||||||||
\(433\) | 7.52292 | 0.361529 | 0.180764 | − | 0.983526i | \(-0.442143\pi\) | ||||
0.180764 | + | 0.983526i | \(0.442143\pi\) | |||||||
\(434\) | 11.7280 | 0.562961 | ||||||||
\(435\) | −2.27461 | −0.109059 | ||||||||
\(436\) | −6.73676 | −0.322632 | ||||||||
\(437\) | −4.03407 | −0.192976 | ||||||||
\(438\) | 37.7577 | 1.80413 | ||||||||
\(439\) | −22.0123 | −1.05059 | −0.525294 | − | 0.850921i | \(-0.676045\pi\) | ||||
−0.525294 | + | 0.850921i | \(0.676045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.25122 | 0.107201 | ||||||||
\(442\) | 7.39156 | 0.351581 | ||||||||
\(443\) | 23.6893 | 1.12551 | 0.562756 | − | 0.826623i | \(-0.309741\pi\) | ||||
0.562756 | + | 0.826623i | \(0.309741\pi\) | |||||||
\(444\) | 0.535619 | 0.0254194 | ||||||||
\(445\) | 67.6263 | 3.20579 | ||||||||
\(446\) | 24.5023 | 1.16022 | ||||||||
\(447\) | 55.1330 | 2.60770 | ||||||||
\(448\) | 1.76252 | 0.0832713 | ||||||||
\(449\) | 2.27513 | 0.107370 | 0.0536851 | − | 0.998558i | \(-0.482903\pi\) | ||||
0.0536851 | + | 0.998558i | \(0.482903\pi\) | |||||||
\(450\) | −44.3326 | −2.08986 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 10.4316 | 0.490663 | ||||||||
\(453\) | −3.03443 | −0.142570 | ||||||||
\(454\) | −10.8828 | −0.510754 | ||||||||
\(455\) | 13.3292 | 0.624885 | ||||||||
\(456\) | 9.18084 | 0.429932 | ||||||||
\(457\) | −27.3134 | −1.27767 | −0.638833 | − | 0.769345i | \(-0.720583\pi\) | ||||
−0.638833 | + | 0.769345i | \(0.720583\pi\) | |||||||
\(458\) | 13.6613 | 0.638351 | ||||||||
\(459\) | 2.26646 | 0.105789 | ||||||||
\(460\) | −6.93868 | −0.323518 | ||||||||
\(461\) | −8.21908 | −0.382801 | −0.191400 | − | 0.981512i | \(-0.561303\pi\) | ||||
−0.191400 | + | 0.981512i | \(0.561303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.9839 | −1.30052 | −0.650261 | − | 0.759711i | \(-0.725340\pi\) | ||||
−0.650261 | + | 0.759711i | \(0.725340\pi\) | |||||||
\(464\) | 1.21872 | 0.0565776 | ||||||||
\(465\) | −64.0156 | −2.96865 | ||||||||
\(466\) | 18.4411 | 0.854265 | ||||||||
\(467\) | 26.6745 | 1.23435 | 0.617175 | − | 0.786826i | \(-0.288277\pi\) | ||||
0.617175 | + | 0.786826i | \(0.288277\pi\) | |||||||
\(468\) | 6.74759 | 0.311907 | ||||||||
\(469\) | −3.00700 | −0.138850 | ||||||||
\(470\) | 28.2376 | 1.30250 | ||||||||
\(471\) | 33.4889 | 1.54309 | ||||||||
\(472\) | −1.82290 | −0.0839057 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 21.6512 | 0.994474 | ||||||||
\(475\) | 24.9365 | 1.14417 | ||||||||
\(476\) | −1.20780 | −0.0553595 | ||||||||
\(477\) | −11.2693 | −0.515985 | ||||||||
\(478\) | −42.9491 | −1.96445 | ||||||||
\(479\) | −23.2240 | −1.06113 | −0.530566 | − | 0.847644i | \(-0.678020\pi\) | ||||
−0.530566 | + | 0.847644i | \(0.678020\pi\) | |||||||
\(480\) | 44.8832 | 2.04863 | ||||||||
\(481\) | 0.837900 | 0.0382050 | ||||||||
\(482\) | 31.1491 | 1.41880 | ||||||||
\(483\) | −4.27630 | −0.194578 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.5140 | −0.477415 | ||||||||
\(486\) | 33.0150 | 1.49759 | ||||||||
\(487\) | −18.7920 | −0.851548 | −0.425774 | − | 0.904830i | \(-0.639998\pi\) | ||||
−0.425774 | + | 0.904830i | \(0.639998\pi\) | |||||||
\(488\) | 3.42252 | 0.154930 | ||||||||
\(489\) | −47.9427 | −2.16804 | ||||||||
\(490\) | −6.94194 | −0.313605 | ||||||||
\(491\) | 7.40573 | 0.334216 | 0.167108 | − | 0.985939i | \(-0.446557\pi\) | ||||
0.167108 | + | 0.985939i | \(0.446557\pi\) | |||||||
\(492\) | −12.0114 | −0.541515 | ||||||||
\(493\) | 0.322429 | 0.0145215 | ||||||||
\(494\) | −12.0970 | −0.544269 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.2991 | 1.54007 | ||||||||
\(497\) | 6.47642 | 0.290507 | ||||||||
\(498\) | −8.09882 | −0.362917 | ||||||||
\(499\) | 23.6703 | 1.05963 | 0.529815 | − | 0.848113i | \(-0.322261\pi\) | ||||
0.529815 | + | 0.848113i | \(0.322261\pi\) | |||||||
\(500\) | 24.3001 | 1.08674 | ||||||||
\(501\) | 11.2592 | 0.503024 | ||||||||
\(502\) | −26.1680 | −1.16794 | ||||||||
\(503\) | −8.39731 | −0.374418 | −0.187209 | − | 0.982320i | \(-0.559944\pi\) | ||||
−0.187209 | + | 0.982320i | \(0.559944\pi\) | |||||||
\(504\) | 4.17220 | 0.185845 | ||||||||
\(505\) | 42.9758 | 1.91240 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.16798 | −0.229518 | ||||||||
\(508\) | −7.99951 | −0.354921 | ||||||||
\(509\) | 14.3065 | 0.634123 | 0.317061 | − | 0.948405i | \(-0.397304\pi\) | ||||
0.317061 | + | 0.948405i | \(0.397304\pi\) | |||||||
\(510\) | 21.0124 | 0.930443 | ||||||||
\(511\) | −9.65164 | −0.426963 | ||||||||
\(512\) | −5.54215 | −0.244931 | ||||||||
\(513\) | −3.70928 | −0.163769 | ||||||||
\(514\) | −4.57484 | −0.201787 | ||||||||
\(515\) | 56.3147 | 2.48152 | ||||||||
\(516\) | −16.8003 | −0.739594 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.436383 | −0.0191736 | ||||||||
\(519\) | 45.0470 | 1.97734 | ||||||||
\(520\) | 24.7032 | 1.08331 | ||||||||
\(521\) | −33.3684 | −1.46189 | −0.730947 | − | 0.682434i | \(-0.760921\pi\) | ||||
−0.730947 | + | 0.682434i | \(0.760921\pi\) | |||||||
\(522\) | 0.938129 | 0.0410608 | ||||||||
\(523\) | 13.3817 | 0.585143 | 0.292571 | − | 0.956244i | \(-0.405489\pi\) | ||||
0.292571 | + | 0.956244i | \(0.405489\pi\) | |||||||
\(524\) | −11.4771 | −0.501378 | ||||||||
\(525\) | 26.4339 | 1.15367 | ||||||||
\(526\) | 17.0329 | 0.742669 | ||||||||
\(527\) | 9.07430 | 0.395283 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.5176 | −0.848592 | ||||||||
\(530\) | 34.7503 | 1.50946 | ||||||||
\(531\) | −2.21428 | −0.0960917 | ||||||||
\(532\) | 1.97668 | 0.0857001 | ||||||||
\(533\) | −18.7901 | −0.813891 | ||||||||
\(534\) | −65.0598 | −2.81541 | ||||||||
\(535\) | 50.5395 | 2.18501 | ||||||||
\(536\) | −5.57289 | −0.240712 | ||||||||
\(537\) | −58.1112 | −2.50768 | ||||||||
\(538\) | 36.8360 | 1.58811 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.38004 | −0.274553 | ||||||||
\(541\) | −34.0639 | −1.46452 | −0.732262 | − | 0.681023i | \(-0.761535\pi\) | ||||
−0.732262 | + | 0.681023i | \(0.761535\pi\) | |||||||
\(542\) | 25.5839 | 1.09892 | ||||||||
\(543\) | −4.52739 | −0.194289 | ||||||||
\(544\) | −6.36225 | −0.272779 | ||||||||
\(545\) | −29.9589 | −1.28330 | ||||||||
\(546\) | −12.8234 | −0.548790 | ||||||||
\(547\) | −15.7614 | −0.673909 | −0.336954 | − | 0.941521i | \(-0.609397\pi\) | ||||
−0.336954 | + | 0.941521i | \(0.609397\pi\) | |||||||
\(548\) | −5.78644 | −0.247185 | ||||||||
\(549\) | 4.15735 | 0.177431 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.527686 | −0.0224802 | ||||||||
\(552\) | −7.92530 | −0.337323 | ||||||||
\(553\) | −5.53450 | −0.235351 | ||||||||
\(554\) | −8.88815 | −0.377621 | ||||||||
\(555\) | 2.38194 | 0.101108 | ||||||||
\(556\) | 13.2065 | 0.560080 | ||||||||
\(557\) | 16.1024 | 0.682282 | 0.341141 | − | 0.940012i | \(-0.389187\pi\) | ||||
0.341141 | + | 0.940012i | \(0.389187\pi\) | |||||||
\(558\) | 26.4023 | 1.11770 | ||||||||
\(559\) | −26.2818 | −1.11160 | ||||||||
\(560\) | −20.3020 | −0.857918 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −25.8806 | −1.09171 | ||||||||
\(563\) | −17.2305 | −0.726177 | −0.363089 | − | 0.931755i | \(-0.618278\pi\) | ||||
−0.363089 | + | 0.931755i | \(0.618278\pi\) | |||||||
\(564\) | −8.52332 | −0.358896 | ||||||||
\(565\) | 46.3903 | 1.95165 | ||||||||
\(566\) | 9.67206 | 0.406547 | ||||||||
\(567\) | −10.6857 | −0.448756 | ||||||||
\(568\) | 12.0028 | 0.503626 | ||||||||
\(569\) | −35.6143 | −1.49303 | −0.746514 | − | 0.665370i | \(-0.768274\pi\) | ||||
−0.746514 | + | 0.665370i | \(0.768274\pi\) | |||||||
\(570\) | −34.3887 | −1.44038 | ||||||||
\(571\) | 26.6026 | 1.11329 | 0.556643 | − | 0.830752i | \(-0.312089\pi\) | ||||
0.556643 | + | 0.830752i | \(0.312089\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.22967 | 0.0931459 | ||||||||
\(574\) | 9.78600 | 0.408460 | ||||||||
\(575\) | −21.5263 | −0.897709 | ||||||||
\(576\) | 3.96783 | 0.165326 | ||||||||
\(577\) | 28.8725 | 1.20198 | 0.600989 | − | 0.799257i | \(-0.294773\pi\) | ||||
0.600989 | + | 0.799257i | \(0.294773\pi\) | |||||||
\(578\) | 26.0432 | 1.08325 | ||||||||
\(579\) | −53.0097 | −2.20301 | ||||||||
\(580\) | −0.907632 | −0.0376874 | ||||||||
\(581\) | 2.07023 | 0.0858875 | ||||||||
\(582\) | 10.1150 | 0.419278 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −17.8874 | −0.740188 | ||||||||
\(585\) | 30.0071 | 1.24064 | ||||||||
\(586\) | 45.9914 | 1.89989 | ||||||||
\(587\) | 2.43414 | 0.100468 | 0.0502339 | − | 0.998737i | \(-0.484003\pi\) | ||||
0.0502339 | + | 0.998737i | \(0.484003\pi\) | |||||||
\(588\) | 2.09538 | 0.0864119 | ||||||||
\(589\) | −14.8509 | −0.611922 | ||||||||
\(590\) | 6.82804 | 0.281106 | ||||||||
\(591\) | −22.7147 | −0.934359 | ||||||||
\(592\) | −1.27622 | −0.0524525 | ||||||||
\(593\) | 15.6870 | 0.644187 | 0.322093 | − | 0.946708i | \(-0.395613\pi\) | ||||
0.322093 | + | 0.946708i | \(0.395613\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.37119 | −0.220197 | ||||||||
\(596\) | 21.9995 | 0.901136 | ||||||||
\(597\) | 23.7972 | 0.973953 | ||||||||
\(598\) | 10.4426 | 0.427032 | ||||||||
\(599\) | −13.2218 | −0.540229 | −0.270115 | − | 0.962828i | \(-0.587062\pi\) | ||||
−0.270115 | + | 0.962828i | \(0.587062\pi\) | |||||||
\(600\) | 48.9901 | 2.00001 | ||||||||
\(601\) | −11.2303 | −0.458093 | −0.229047 | − | 0.973415i | \(-0.573561\pi\) | ||||
−0.229047 | + | 0.973415i | \(0.573561\pi\) | |||||||
\(602\) | 13.6877 | 0.557868 | ||||||||
\(603\) | −6.76942 | −0.275672 | ||||||||
\(604\) | −1.21082 | −0.0492676 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −41.3449 | −1.67952 | ||||||||
\(607\) | 19.3477 | 0.785298 | 0.392649 | − | 0.919688i | \(-0.371559\pi\) | ||||
0.392649 | + | 0.919688i | \(0.371559\pi\) | |||||||
\(608\) | 10.4124 | 0.422279 | ||||||||
\(609\) | −0.559372 | −0.0226669 | ||||||||
\(610\) | −12.8197 | −0.519056 | ||||||||
\(611\) | −13.3335 | −0.539417 | ||||||||
\(612\) | −2.71903 | −0.109910 | ||||||||
\(613\) | 21.0549 | 0.850398 | 0.425199 | − | 0.905100i | \(-0.360204\pi\) | ||||
0.425199 | + | 0.905100i | \(0.360204\pi\) | |||||||
\(614\) | −42.0230 | −1.69591 | ||||||||
\(615\) | −53.4156 | −2.15392 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.1496 | −0.972228 | −0.486114 | − | 0.873895i | \(-0.661586\pi\) | ||||
−0.486114 | + | 0.873895i | \(0.661586\pi\) | |||||||
\(618\) | −54.1775 | −2.17934 | ||||||||
\(619\) | 2.62475 | 0.105497 | 0.0527487 | − | 0.998608i | \(-0.483202\pi\) | ||||
0.0527487 | + | 0.998608i | \(0.483202\pi\) | |||||||
\(620\) | −25.5440 | −1.02587 | ||||||||
\(621\) | 3.20201 | 0.128492 | ||||||||
\(622\) | 17.4354 | 0.699095 | ||||||||
\(623\) | 16.6306 | 0.666292 | ||||||||
\(624\) | −37.5026 | −1.50131 | ||||||||
\(625\) | 50.3878 | 2.01551 | ||||||||
\(626\) | −38.2408 | −1.52841 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.3630 | 0.533241 | ||||||||
\(629\) | −0.337643 | −0.0134627 | ||||||||
\(630\) | −15.6278 | −0.622628 | ||||||||
\(631\) | −25.1176 | −0.999914 | −0.499957 | − | 0.866050i | \(-0.666651\pi\) | ||||
−0.499957 | + | 0.866050i | \(0.666651\pi\) | |||||||
\(632\) | −10.2571 | −0.408006 | ||||||||
\(633\) | −29.7709 | −1.18329 | ||||||||
\(634\) | −39.8784 | −1.58377 | ||||||||
\(635\) | −35.5744 | −1.41173 | ||||||||
\(636\) | −10.4891 | −0.415922 | ||||||||
\(637\) | 3.27792 | 0.129876 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.5798 | 0.576770 | ||||||||
\(640\) | −51.4080 | −2.03208 | ||||||||
\(641\) | 20.6584 | 0.815958 | 0.407979 | − | 0.912991i | \(-0.366234\pi\) | ||||
0.407979 | + | 0.912991i | \(0.366234\pi\) | |||||||
\(642\) | −48.6214 | −1.91894 | ||||||||
\(643\) | 16.4632 | 0.649246 | 0.324623 | − | 0.945844i | \(-0.394763\pi\) | ||||
0.324623 | + | 0.945844i | \(0.394763\pi\) | |||||||
\(644\) | −1.70636 | −0.0672399 | ||||||||
\(645\) | −74.7124 | −2.94180 | ||||||||
\(646\) | 4.87464 | 0.191790 | ||||||||
\(647\) | −34.9584 | −1.37435 | −0.687177 | − | 0.726490i | \(-0.741150\pi\) | ||||
−0.687177 | + | 0.726490i | \(0.741150\pi\) | |||||||
\(648\) | −19.8038 | −0.777967 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −64.5511 | −2.53190 | ||||||||
\(651\) | −15.7427 | −0.617005 | ||||||||
\(652\) | −19.1304 | −0.749205 | ||||||||
\(653\) | 2.41649 | 0.0945645 | 0.0472823 | − | 0.998882i | \(-0.484944\pi\) | ||||
0.0472823 | + | 0.998882i | \(0.484944\pi\) | |||||||
\(654\) | 28.8219 | 1.12703 | ||||||||
\(655\) | −51.0395 | −1.99428 | ||||||||
\(656\) | 28.6196 | 1.11741 | ||||||||
\(657\) | −21.7280 | −0.847689 | ||||||||
\(658\) | 6.94417 | 0.270712 | ||||||||
\(659\) | 16.9733 | 0.661186 | 0.330593 | − | 0.943773i | \(-0.392751\pi\) | ||||
0.330593 | + | 0.943773i | \(0.392751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.96946 | 0.309976 | 0.154988 | − | 0.987916i | \(-0.450466\pi\) | ||||
0.154988 | + | 0.987916i | \(0.450466\pi\) | |||||||
\(662\) | −26.7074 | −1.03801 | ||||||||
\(663\) | −9.92184 | −0.385333 | ||||||||
\(664\) | 3.83677 | 0.148895 | ||||||||
\(665\) | 8.79046 | 0.340880 | ||||||||
\(666\) | −0.982394 | −0.0380670 | ||||||||
\(667\) | 0.455522 | 0.0176379 | ||||||||
\(668\) | 4.49272 | 0.173829 | ||||||||
\(669\) | −32.8899 | −1.27160 | ||||||||
\(670\) | 20.8744 | 0.806449 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 11.0377 | 0.425787 | ||||||||
\(673\) | 16.0250 | 0.617717 | 0.308859 | − | 0.951108i | \(-0.400053\pi\) | ||||
0.308859 | + | 0.951108i | \(0.400053\pi\) | |||||||
\(674\) | −55.6380 | −2.14309 | ||||||||
\(675\) | −19.7932 | −0.761840 | ||||||||
\(676\) | −2.06216 | −0.0793140 | ||||||||
\(677\) | 15.2366 | 0.585589 | 0.292794 | − | 0.956175i | \(-0.405415\pi\) | ||||
0.292794 | + | 0.956175i | \(0.405415\pi\) | |||||||
\(678\) | −44.6297 | −1.71399 | ||||||||
\(679\) | −2.58559 | −0.0992259 | ||||||||
\(680\) | −9.95446 | −0.381736 | ||||||||
\(681\) | 14.6082 | 0.559787 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.3742 | 0.550013 | 0.275007 | − | 0.961442i | \(-0.411320\pi\) | ||||
0.275007 | + | 0.961442i | \(0.411320\pi\) | |||||||
\(684\) | 4.44995 | 0.170148 | ||||||||
\(685\) | −25.7328 | −0.983198 | ||||||||
\(686\) | −1.70716 | −0.0651796 | ||||||||
\(687\) | −18.3379 | −0.699633 | ||||||||
\(688\) | 40.0303 | 1.52614 | ||||||||
\(689\) | −16.4088 | −0.625125 | ||||||||
\(690\) | 29.6858 | 1.13012 | ||||||||
\(691\) | −44.7978 | −1.70419 | −0.852095 | − | 0.523387i | \(-0.824668\pi\) | ||||
−0.852095 | + | 0.523387i | \(0.824668\pi\) | |||||||
\(692\) | 17.9750 | 0.683305 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.82101 | −0.372800 | ||||||||
\(695\) | 58.7303 | 2.22777 | ||||||||
\(696\) | −1.03669 | −0.0392956 | ||||||||
\(697\) | 7.57173 | 0.286800 | ||||||||
\(698\) | 0.314014 | 0.0118856 | ||||||||
\(699\) | −24.7538 | −0.936275 | ||||||||
\(700\) | 10.5478 | 0.398671 | ||||||||
\(701\) | −0.240330 | −0.00907713 | −0.00453857 | − | 0.999990i | \(-0.501445\pi\) | ||||
−0.00453857 | + | 0.999990i | \(0.501445\pi\) | |||||||
\(702\) | 9.60189 | 0.362400 | ||||||||
\(703\) | 0.552584 | 0.0208411 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −37.9039 | −1.42754 | ||||||||
\(706\) | −32.4720 | −1.22210 | ||||||||
\(707\) | 10.5686 | 0.397473 | ||||||||
\(708\) | −2.06100 | −0.0774570 | ||||||||
\(709\) | 10.7534 | 0.403852 | 0.201926 | − | 0.979401i | \(-0.435280\pi\) | ||||
0.201926 | + | 0.979401i | \(0.435280\pi\) | |||||||
\(710\) | −44.9589 | −1.68728 | ||||||||
\(711\) | −12.4594 | −0.467263 | ||||||||
\(712\) | 30.8216 | 1.15509 | ||||||||
\(713\) | 12.8200 | 0.480112 | ||||||||
\(714\) | 5.16735 | 0.193383 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.1879 | −0.866573 | ||||||||
\(717\) | 57.6515 | 2.15304 | ||||||||
\(718\) | 1.22732 | 0.0458033 | ||||||||
\(719\) | −25.7748 | −0.961239 | −0.480620 | − | 0.876929i | \(-0.659588\pi\) | ||||
−0.480620 | + | 0.876929i | \(0.659588\pi\) | |||||||
\(720\) | −45.7044 | −1.70330 | ||||||||
\(721\) | 13.8489 | 0.515759 | ||||||||
\(722\) | 24.4582 | 0.910240 | ||||||||
\(723\) | −41.8120 | −1.55501 | ||||||||
\(724\) | −1.80655 | −0.0671399 | ||||||||
\(725\) | −2.81580 | −0.104576 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.47160 | −0.202930 | −0.101465 | − | 0.994839i | \(-0.532353\pi\) | ||||
−0.101465 | + | 0.994839i | \(0.532353\pi\) | |||||||
\(728\) | 6.07499 | 0.225154 | ||||||||
\(729\) | −12.2598 | −0.454065 | ||||||||
\(730\) | 67.0011 | 2.47982 | ||||||||
\(731\) | 10.5906 | 0.391707 | ||||||||
\(732\) | 3.86955 | 0.143023 | ||||||||
\(733\) | −19.8563 | −0.733411 | −0.366705 | − | 0.930337i | \(-0.619514\pi\) | ||||
−0.366705 | + | 0.930337i | \(0.619514\pi\) | |||||||
\(734\) | 13.4745 | 0.497354 | ||||||||
\(735\) | 9.31831 | 0.343711 | ||||||||
\(736\) | −8.98845 | −0.331319 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 22.0304 | 0.810951 | ||||||||
\(739\) | 1.80077 | 0.0662423 | 0.0331212 | − | 0.999451i | \(-0.489455\pi\) | ||||
0.0331212 | + | 0.999451i | \(0.489455\pi\) | |||||||
\(740\) | 0.950458 | 0.0349395 | ||||||||
\(741\) | 16.2380 | 0.596519 | ||||||||
\(742\) | 8.54578 | 0.313726 | ||||||||
\(743\) | 48.0579 | 1.76307 | 0.881537 | − | 0.472115i | \(-0.156509\pi\) | ||||
0.881537 | + | 0.472115i | \(0.156509\pi\) | |||||||
\(744\) | −29.1760 | −1.06965 | ||||||||
\(745\) | 97.8337 | 3.58435 | ||||||||
\(746\) | −26.7489 | −0.979346 | ||||||||
\(747\) | 4.66054 | 0.170520 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.4286 | 0.454133 | ||||||||
\(750\) | −103.963 | −3.79621 | ||||||||
\(751\) | −25.0465 | −0.913961 | −0.456980 | − | 0.889477i | \(-0.651069\pi\) | ||||
−0.456980 | + | 0.889477i | \(0.651069\pi\) | |||||||
\(752\) | 20.3086 | 0.740578 | ||||||||
\(753\) | 35.1259 | 1.28006 | ||||||||
\(754\) | 1.36598 | 0.0497459 | ||||||||
\(755\) | −5.38461 | −0.195966 | ||||||||
\(756\) | −1.56898 | −0.0570631 | ||||||||
\(757\) | 10.6487 | 0.387032 | 0.193516 | − | 0.981097i | \(-0.438011\pi\) | ||||
0.193516 | + | 0.981097i | \(0.438011\pi\) | |||||||
\(758\) | 22.7298 | 0.825583 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 16.2914 | 0.590952 | ||||||||
\(761\) | −29.8160 | −1.08083 | −0.540414 | − | 0.841399i | \(-0.681732\pi\) | ||||
−0.540414 | + | 0.841399i | \(0.681732\pi\) | |||||||
\(762\) | 34.2244 | 1.23982 | ||||||||
\(763\) | −7.36748 | −0.266721 | ||||||||
\(764\) | 0.889698 | 0.0321882 | ||||||||
\(765\) | −12.0917 | −0.437178 | ||||||||
\(766\) | −20.2271 | −0.730836 | ||||||||
\(767\) | −3.22414 | −0.116417 | ||||||||
\(768\) | 41.3792 | 1.49314 | ||||||||
\(769\) | −28.3115 | −1.02094 | −0.510470 | − | 0.859896i | \(-0.670529\pi\) | ||||
−0.510470 | + | 0.859896i | \(0.670529\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.14090 | 0.221159 | ||||||||
\(772\) | −21.1523 | −0.761287 | ||||||||
\(773\) | 13.2564 | 0.476800 | 0.238400 | − | 0.971167i | \(-0.423377\pi\) | ||||
0.238400 | + | 0.971167i | \(0.423377\pi\) | |||||||
\(774\) | 30.8140 | 1.10759 | ||||||||
\(775\) | −79.2466 | −2.84662 | ||||||||
\(776\) | −4.79189 | −0.172019 | ||||||||
\(777\) | 0.585766 | 0.0210142 | ||||||||
\(778\) | 10.3278 | 0.370271 | ||||||||
\(779\) | −12.3918 | −0.443984 | ||||||||
\(780\) | 27.9298 | 1.00005 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −4.20800 | −0.150478 | ||||||||
\(783\) | 0.418847 | 0.0149684 | ||||||||
\(784\) | −4.99267 | −0.178310 | ||||||||
\(785\) | 59.4262 | 2.12101 | ||||||||
\(786\) | 49.1025 | 1.75143 | ||||||||
\(787\) | 52.6771 | 1.87774 | 0.938868 | − | 0.344279i | \(-0.111876\pi\) | ||||
0.938868 | + | 0.344279i | \(0.111876\pi\) | |||||||
\(788\) | −9.06379 | −0.322884 | ||||||||
\(789\) | −22.8636 | −0.813965 | ||||||||
\(790\) | 38.4202 | 1.36693 | ||||||||
\(791\) | 11.4083 | 0.405632 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.05337 | 0.214961 | ||||||||
\(794\) | 19.7625 | 0.701346 | ||||||||
\(795\) | −46.6461 | −1.65437 | ||||||||
\(796\) | 9.49570 | 0.336566 | ||||||||
\(797\) | −7.33480 | −0.259812 | −0.129906 | − | 0.991526i | \(-0.541468\pi\) | ||||
−0.129906 | + | 0.991526i | \(0.541468\pi\) | |||||||
\(798\) | −8.45686 | −0.299369 | ||||||||
\(799\) | 5.37292 | 0.190080 | ||||||||
\(800\) | 55.5620 | 1.96442 | ||||||||
\(801\) | 37.4392 | 1.32285 | ||||||||
\(802\) | −57.6890 | −2.03707 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −6.30080 | −0.222212 | ||||||||
\(805\) | −7.58831 | −0.267453 | ||||||||
\(806\) | 38.4434 | 1.35411 | ||||||||
\(807\) | −49.4458 | −1.74057 | ||||||||
\(808\) | 19.5869 | 0.689063 | ||||||||
\(809\) | 8.66809 | 0.304754 | 0.152377 | − | 0.988322i | \(-0.451307\pi\) | ||||
0.152377 | + | 0.988322i | \(0.451307\pi\) | |||||||
\(810\) | 74.1793 | 2.60639 | ||||||||
\(811\) | 19.9487 | 0.700494 | 0.350247 | − | 0.936657i | \(-0.386098\pi\) | ||||
0.350247 | + | 0.936657i | \(0.386098\pi\) | |||||||
\(812\) | −0.223205 | −0.00783294 | ||||||||
\(813\) | −34.3418 | −1.20442 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −85.0745 | −2.98003 | ||||||||
\(816\) | 15.1122 | 0.529032 | ||||||||
\(817\) | −17.3325 | −0.606387 | ||||||||
\(818\) | −30.8176 | −1.07751 | ||||||||
\(819\) | 7.37932 | 0.257854 | ||||||||
\(820\) | −21.3143 | −0.744326 | ||||||||
\(821\) | 53.5648 | 1.86943 | 0.934713 | − | 0.355404i | \(-0.115657\pi\) | ||||
0.934713 | + | 0.355404i | \(0.115657\pi\) | |||||||
\(822\) | 24.7562 | 0.863471 | ||||||||
\(823\) | −8.44842 | −0.294493 | −0.147247 | − | 0.989100i | \(-0.547041\pi\) | ||||
−0.147247 | + | 0.989100i | \(0.547041\pi\) | |||||||
\(824\) | 25.6662 | 0.894125 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.67915 | 0.0584250 | ||||||||
\(827\) | −3.18260 | −0.110670 | −0.0553349 | − | 0.998468i | \(-0.517623\pi\) | ||||
−0.0553349 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(828\) | −3.84139 | −0.133497 | ||||||||
\(829\) | 57.5089 | 1.99737 | 0.998684 | − | 0.0512831i | \(-0.0163311\pi\) | ||||
0.998684 | + | 0.0512831i | \(0.0163311\pi\) | |||||||
\(830\) | −14.3714 | −0.498838 | ||||||||
\(831\) | 11.9307 | 0.413873 | ||||||||
\(832\) | 5.77741 | 0.200296 | ||||||||
\(833\) | −1.32088 | −0.0457658 | ||||||||
\(834\) | −56.5015 | −1.95649 | ||||||||
\(835\) | 19.9795 | 0.691419 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.7878 | 0.407447 | ||||||||
\(838\) | −4.41401 | −0.152479 | ||||||||
\(839\) | 12.5594 | 0.433600 | 0.216800 | − | 0.976216i | \(-0.430438\pi\) | ||||
0.216800 | + | 0.976216i | \(0.430438\pi\) | |||||||
\(840\) | 17.2697 | 0.595861 | ||||||||
\(841\) | −28.9404 | −0.997945 | ||||||||
\(842\) | −23.8913 | −0.823349 | ||||||||
\(843\) | 34.7401 | 1.19651 | ||||||||
\(844\) | −11.8794 | −0.408906 | ||||||||
\(845\) | −9.17060 | −0.315478 | ||||||||
\(846\) | 15.6329 | 0.537469 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.9926 | 0.858248 | ||||||||
\(849\) | −12.9830 | −0.445575 | ||||||||
\(850\) | 26.0117 | 0.892195 | ||||||||
\(851\) | −0.477015 | −0.0163519 | ||||||||
\(852\) | 13.5705 | 0.464919 | ||||||||
\(853\) | 33.3315 | 1.14125 | 0.570625 | − | 0.821211i | \(-0.306701\pi\) | ||||
0.570625 | + | 0.821211i | \(0.306701\pi\) | |||||||
\(854\) | −3.15263 | −0.107881 | ||||||||
\(855\) | 19.7893 | 0.676779 | ||||||||
\(856\) | 23.0341 | 0.787289 | ||||||||
\(857\) | 54.0291 | 1.84560 | 0.922800 | − | 0.385279i | \(-0.125895\pi\) | ||||
0.922800 | + | 0.385279i | \(0.125895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.8624 | −0.438860 | −0.219430 | − | 0.975628i | \(-0.570420\pi\) | ||||
−0.219430 | + | 0.975628i | \(0.570420\pi\) | |||||||
\(860\) | −29.8123 | −1.01659 | ||||||||
\(861\) | −13.1359 | −0.447672 | ||||||||
\(862\) | 57.4769 | 1.95767 | ||||||||
\(863\) | −33.2271 | −1.13106 | −0.565531 | − | 0.824727i | \(-0.691329\pi\) | ||||
−0.565531 | + | 0.824727i | \(0.691329\pi\) | |||||||
\(864\) | −8.26478 | −0.281173 | ||||||||
\(865\) | 79.9360 | 2.71791 | ||||||||
\(866\) | −12.8428 | −0.436417 | ||||||||
\(867\) | −34.9583 | −1.18725 | ||||||||
\(868\) | −6.28176 | −0.213217 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.88313 | 0.131650 | ||||||||
\(871\) | −9.85671 | −0.333982 | ||||||||
\(872\) | −13.6542 | −0.462389 | ||||||||
\(873\) | −5.82074 | −0.197002 | ||||||||
\(874\) | 6.88679 | 0.232949 | ||||||||
\(875\) | 26.5752 | 0.898406 | ||||||||
\(876\) | −20.2238 | −0.683300 | ||||||||
\(877\) | 27.6709 | 0.934379 | 0.467189 | − | 0.884157i | \(-0.345267\pi\) | ||||
0.467189 | + | 0.884157i | \(0.345267\pi\) | |||||||
\(878\) | 37.5784 | 1.26821 | ||||||||
\(879\) | −61.7352 | −2.08228 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.9636 | 1.64963 | 0.824813 | − | 0.565406i | \(-0.191280\pi\) | ||||
0.824813 | + | 0.565406i | \(0.191280\pi\) | |||||||
\(882\) | −3.84319 | −0.129407 | ||||||||
\(883\) | 21.3223 | 0.717554 | 0.358777 | − | 0.933423i | \(-0.383194\pi\) | ||||
0.358777 | + | 0.933423i | \(0.383194\pi\) | |||||||
\(884\) | −3.95908 | −0.133158 | ||||||||
\(885\) | −9.16541 | −0.308092 | ||||||||
\(886\) | −40.4414 | −1.35865 | ||||||||
\(887\) | −45.2483 | −1.51929 | −0.759645 | − | 0.650338i | \(-0.774627\pi\) | ||||
−0.759645 | + | 0.650338i | \(0.774627\pi\) | |||||||
\(888\) | 1.08560 | 0.0364305 | ||||||||
\(889\) | −8.74845 | −0.293414 | ||||||||
\(890\) | −115.449 | −3.86985 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.1240 | −0.439423 | ||||||||
\(893\) | −8.79329 | −0.294256 | ||||||||
\(894\) | −94.1208 | −3.14787 | ||||||||
\(895\) | −103.118 | −3.44687 | ||||||||
\(896\) | −12.6422 | −0.422348 | ||||||||
\(897\) | −14.0174 | −0.468027 | ||||||||
\(898\) | −3.88401 | −0.129611 | ||||||||
\(899\) | 1.67695 | 0.0559294 | ||||||||
\(900\) | 23.7455 | 0.791517 | ||||||||
\(901\) | 6.61213 | 0.220282 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −18.3732 | −0.611423 | ||||||||
\(904\) | 21.1430 | 0.703207 | ||||||||
\(905\) | −8.03388 | −0.267055 | ||||||||
\(906\) | 5.18026 | 0.172103 | ||||||||
\(907\) | −45.0665 | −1.49641 | −0.748205 | − | 0.663468i | \(-0.769084\pi\) | ||||
−0.748205 | + | 0.663468i | \(0.769084\pi\) | |||||||
\(908\) | 5.82906 | 0.193444 | ||||||||
\(909\) | 23.7922 | 0.789139 | ||||||||
\(910\) | −22.7551 | −0.754325 | ||||||||
\(911\) | −9.21469 | −0.305296 | −0.152648 | − | 0.988281i | \(-0.548780\pi\) | ||||
−0.152648 | + | 0.988281i | \(0.548780\pi\) | |||||||
\(912\) | −24.7325 | −0.818975 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 46.6283 | 1.54233 | ||||||||
\(915\) | 17.2082 | 0.568886 | ||||||||
\(916\) | −7.31730 | −0.241770 | ||||||||
\(917\) | −12.5516 | −0.414491 | ||||||||
\(918\) | −3.86921 | −0.127703 | ||||||||
\(919\) | 49.7144 | 1.63993 | 0.819963 | − | 0.572417i | \(-0.193994\pi\) | ||||
0.819963 | + | 0.572417i | \(0.193994\pi\) | |||||||
\(920\) | −14.0635 | −0.463659 | ||||||||
\(921\) | 56.4083 | 1.85872 | ||||||||
\(922\) | 14.0313 | 0.462095 | ||||||||
\(923\) | 21.2292 | 0.698767 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.94866 | 0.0969514 | ||||||||
\(926\) | 47.7729 | 1.56992 | ||||||||
\(927\) | 31.1769 | 1.02398 | ||||||||
\(928\) | −1.17576 | −0.0385961 | ||||||||
\(929\) | 49.5105 | 1.62439 | 0.812193 | − | 0.583389i | \(-0.198274\pi\) | ||||
0.812193 | + | 0.583389i | \(0.198274\pi\) | |||||||
\(930\) | 109.285 | 3.58359 | ||||||||
\(931\) | 2.16175 | 0.0708484 | ||||||||
\(932\) | −9.87743 | −0.323546 | ||||||||
\(933\) | −23.4039 | −0.766208 | ||||||||
\(934\) | −45.5377 | −1.49004 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.6761 | 0.447019 | ||||||||
\(937\) | 6.98790 | 0.228285 | 0.114142 | − | 0.993464i | \(-0.463588\pi\) | ||||
0.114142 | + | 0.993464i | \(0.463588\pi\) | |||||||
\(938\) | 5.13343 | 0.167612 | ||||||||
\(939\) | 51.3314 | 1.67514 | ||||||||
\(940\) | −15.1247 | −0.493312 | ||||||||
\(941\) | 46.8241 | 1.52642 | 0.763211 | − | 0.646150i | \(-0.223622\pi\) | ||||
0.763211 | + | 0.646150i | \(0.223622\pi\) | |||||||
\(942\) | −57.1709 | −1.86273 | ||||||||
\(943\) | 10.6972 | 0.348348 | ||||||||
\(944\) | 4.91075 | 0.159831 | ||||||||
\(945\) | −6.97736 | −0.226974 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.1286 | 0.491614 | 0.245807 | − | 0.969319i | \(-0.420947\pi\) | ||||
0.245807 | + | 0.969319i | \(0.420947\pi\) | |||||||
\(948\) | −11.5969 | −0.376649 | ||||||||
\(949\) | −31.6373 | −1.02699 | ||||||||
\(950\) | −42.5706 | −1.38117 | ||||||||
\(951\) | 53.5295 | 1.73581 | ||||||||
\(952\) | −2.44800 | −0.0793401 | ||||||||
\(953\) | −56.2273 | −1.82138 | −0.910690 | − | 0.413090i | \(-0.864450\pi\) | ||||
−0.910690 | + | 0.413090i | \(0.864450\pi\) | |||||||
\(954\) | 19.2384 | 0.622867 | ||||||||
\(955\) | 3.95656 | 0.128031 | ||||||||
\(956\) | 23.0045 | 0.744019 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.6470 | 1.28094 | ||||||||
\(959\) | −6.32819 | −0.204348 | ||||||||
\(960\) | 16.4237 | 0.530073 | ||||||||
\(961\) | 16.1952 | 0.522427 | ||||||||
\(962\) | −1.43043 | −0.0461189 | ||||||||
\(963\) | 27.9796 | 0.901631 | ||||||||
\(964\) | −16.6841 | −0.537359 | ||||||||
\(965\) | −94.0658 | −3.02809 | ||||||||
\(966\) | 7.30033 | 0.234884 | ||||||||
\(967\) | 46.3761 | 1.49136 | 0.745678 | − | 0.666307i | \(-0.232126\pi\) | ||||
0.745678 | + | 0.666307i | \(0.232126\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.54333 | −0.210202 | ||||||||
\(970\) | 17.9490 | 0.576308 | ||||||||
\(971\) | 15.5400 | 0.498701 | 0.249351 | − | 0.968413i | \(-0.419783\pi\) | ||||
0.249351 | + | 0.968413i | \(0.419783\pi\) | |||||||
\(972\) | −17.6836 | −0.567201 | ||||||||
\(973\) | 14.4429 | 0.463019 | ||||||||
\(974\) | 32.0810 | 1.02794 | ||||||||
\(975\) | 86.6483 | 2.77497 | ||||||||
\(976\) | −9.22002 | −0.295125 | ||||||||
\(977\) | 32.8287 | 1.05028 | 0.525141 | − | 0.851015i | \(-0.324012\pi\) | ||||
0.525141 | + | 0.851015i | \(0.324012\pi\) | |||||||
\(978\) | 81.8458 | 2.61714 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.71825 | 0.118775 | ||||||||
\(981\) | −16.5858 | −0.529544 | ||||||||
\(982\) | −12.6428 | −0.403447 | ||||||||
\(983\) | 24.3184 | 0.775635 | 0.387817 | − | 0.921736i | \(-0.373229\pi\) | ||||
0.387817 | + | 0.921736i | \(0.373229\pi\) | |||||||
\(984\) | −24.3449 | −0.776088 | ||||||||
\(985\) | −40.3074 | −1.28430 | ||||||||
\(986\) | −0.550438 | −0.0175295 | ||||||||
\(987\) | −9.32130 | −0.296700 | ||||||||
\(988\) | 6.47941 | 0.206138 | ||||||||
\(989\) | 14.9622 | 0.475769 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.7104 | −1.51557 | −0.757786 | − | 0.652503i | \(-0.773719\pi\) | ||||
−0.757786 | + | 0.652503i | \(0.773719\pi\) | |||||||
\(992\) | −33.0899 | −1.05061 | ||||||||
\(993\) | 35.8499 | 1.13766 | ||||||||
\(994\) | −11.0563 | −0.350684 | ||||||||
\(995\) | 42.2281 | 1.33872 | ||||||||
\(996\) | 4.33791 | 0.137452 | ||||||||
\(997\) | 19.8449 | 0.628494 | 0.314247 | − | 0.949341i | \(-0.398248\pi\) | ||||
0.314247 | + | 0.949341i | \(0.398248\pi\) | |||||||
\(998\) | −40.4090 | −1.27913 | ||||||||
\(999\) | −0.438610 | −0.0138770 |
(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 | 847.2.a.p.1.2 | 8 | ||
3.2 | odd | 2 | 7623.2.a.ct.1.7 | 8 | |||
7.6 | odd | 2 | 5929.2.a.bt.1.2 | 8 | |||
11.2 | odd | 10 | 847.2.f.x.323.1 | 16 | |||
11.3 | even | 5 | 847.2.f.w.372.1 | 16 | |||
11.4 | even | 5 | 847.2.f.w.148.1 | 16 | |||
11.5 | even | 5 | 77.2.f.b.36.4 | yes | 16 | ||
11.6 | odd | 10 | 847.2.f.x.729.1 | 16 | |||
11.7 | odd | 10 | 847.2.f.v.148.4 | 16 | |||
11.8 | odd | 10 | 847.2.f.v.372.4 | 16 | |||
11.9 | even | 5 | 77.2.f.b.15.4 | ✓ | 16 | ||
11.10 | odd | 2 | 847.2.a.o.1.7 | 8 | |||
33.5 | odd | 10 | 693.2.m.i.190.1 | 16 | |||
33.20 | odd | 10 | 693.2.m.i.631.1 | 16 | |||
33.32 | even | 2 | 7623.2.a.cw.1.2 | 8 | |||
77.5 | odd | 30 | 539.2.q.f.410.1 | 32 | |||
77.9 | even | 15 | 539.2.q.g.312.4 | 32 | |||
77.16 | even | 15 | 539.2.q.g.410.1 | 32 | |||
77.20 | odd | 10 | 539.2.f.e.246.4 | 16 | |||
77.27 | odd | 10 | 539.2.f.e.344.4 | 16 | |||
77.31 | odd | 30 | 539.2.q.f.422.1 | 32 | |||
77.38 | odd | 30 | 539.2.q.f.520.4 | 32 | |||
77.53 | even | 15 | 539.2.q.g.422.1 | 32 | |||
77.60 | even | 15 | 539.2.q.g.520.4 | 32 | |||
77.75 | odd | 30 | 539.2.q.f.312.4 | 32 | |||
77.76 | even | 2 | 5929.2.a.bs.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.4 | ✓ | 16 | 11.9 | even | 5 | ||
77.2.f.b.36.4 | yes | 16 | 11.5 | even | 5 | ||
539.2.f.e.246.4 | 16 | 77.20 | odd | 10 | |||
539.2.f.e.344.4 | 16 | 77.27 | odd | 10 | |||
539.2.q.f.312.4 | 32 | 77.75 | odd | 30 | |||
539.2.q.f.410.1 | 32 | 77.5 | odd | 30 | |||
539.2.q.f.422.1 | 32 | 77.31 | odd | 30 | |||
539.2.q.f.520.4 | 32 | 77.38 | odd | 30 | |||
539.2.q.g.312.4 | 32 | 77.9 | even | 15 | |||
539.2.q.g.410.1 | 32 | 77.16 | even | 15 | |||
539.2.q.g.422.1 | 32 | 77.53 | even | 15 | |||
539.2.q.g.520.4 | 32 | 77.60 | even | 15 | |||
693.2.m.i.190.1 | 16 | 33.5 | odd | 10 | |||
693.2.m.i.631.1 | 16 | 33.20 | odd | 10 | |||
847.2.a.o.1.7 | 8 | 11.10 | odd | 2 | |||
847.2.a.p.1.2 | 8 | 1.1 | even | 1 | trivial | ||
847.2.f.v.148.4 | 16 | 11.7 | odd | 10 | |||
847.2.f.v.372.4 | 16 | 11.8 | odd | 10 | |||
847.2.f.w.148.1 | 16 | 11.4 | even | 5 | |||
847.2.f.w.372.1 | 16 | 11.3 | even | 5 | |||
847.2.f.x.323.1 | 16 | 11.2 | odd | 10 | |||
847.2.f.x.729.1 | 16 | 11.6 | odd | 10 | |||
5929.2.a.bs.1.7 | 8 | 77.76 | even | 2 | |||
5929.2.a.bt.1.2 | 8 | 7.6 | odd | 2 | |||
7623.2.a.ct.1.7 | 8 | 3.2 | odd | 2 | |||
7623.2.a.cw.1.2 | 8 | 33.32 | even | 2 |