Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7595,2,Mod(1,7595)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7595, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7595.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7595 = 5 \cdot 7^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7595.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: | \(60.6463803352\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 1085) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 7595.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.628452 | −0.444383 | −0.222191 | − | 0.975003i | \(-0.571321\pi\) | ||||
−0.222191 | + | 0.975003i | \(0.571321\pi\) | |||||||
\(3\) | −1.52512 | −0.880530 | −0.440265 | − | 0.897868i | \(-0.645115\pi\) | ||||
−0.440265 | + | 0.897868i | \(0.645115\pi\) | |||||||
\(4\) | −1.60505 | −0.802524 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.958466 | 0.391292 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.26560 | 0.801010 | ||||||||
\(9\) | −0.674002 | −0.224667 | ||||||||
\(10\) | −0.628452 | −0.198734 | ||||||||
\(11\) | −4.48476 | −1.35220 | −0.676102 | − | 0.736808i | \(-0.736332\pi\) | ||||
−0.676102 | + | 0.736808i | \(0.736332\pi\) | |||||||
\(12\) | 2.44789 | 0.706646 | ||||||||
\(13\) | −3.10381 | −0.860842 | −0.430421 | − | 0.902628i | \(-0.641635\pi\) | ||||
−0.430421 | + | 0.902628i | \(0.641635\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.52512 | −0.393785 | ||||||||
\(16\) | 1.78628 | 0.446569 | ||||||||
\(17\) | 0.893389 | 0.216679 | 0.108339 | − | 0.994114i | \(-0.465447\pi\) | ||||
0.108339 | + | 0.994114i | \(0.465447\pi\) | |||||||
\(18\) | 0.423578 | 0.0998382 | ||||||||
\(19\) | −6.74349 | −1.54706 | −0.773531 | − | 0.633758i | \(-0.781511\pi\) | ||||
−0.773531 | + | 0.633758i | \(0.781511\pi\) | |||||||
\(20\) | −1.60505 | −0.358900 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.81845 | 0.600897 | ||||||||
\(23\) | 5.95926 | 1.24259 | 0.621296 | − | 0.783576i | \(-0.286607\pi\) | ||||
0.621296 | + | 0.783576i | \(0.286607\pi\) | |||||||
\(24\) | −3.45532 | −0.705314 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.95060 | 0.382543 | ||||||||
\(27\) | 5.60330 | 1.07836 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05255 | 0.381150 | 0.190575 | − | 0.981673i | \(-0.438965\pi\) | ||||
0.190575 | + | 0.981673i | \(0.438965\pi\) | |||||||
\(30\) | 0.958466 | 0.174991 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −5.65379 | −0.999458 | ||||||||
\(33\) | 6.83980 | 1.19066 | ||||||||
\(34\) | −0.561452 | −0.0962882 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.08180 | 0.180301 | ||||||||
\(37\) | −4.09693 | −0.673532 | −0.336766 | − | 0.941588i | \(-0.609333\pi\) | ||||
−0.336766 | + | 0.941588i | \(0.609333\pi\) | |||||||
\(38\) | 4.23796 | 0.687488 | ||||||||
\(39\) | 4.73369 | 0.757997 | ||||||||
\(40\) | 2.26560 | 0.358223 | ||||||||
\(41\) | 7.42574 | 1.15971 | 0.579853 | − | 0.814721i | \(-0.303110\pi\) | ||||
0.579853 | + | 0.814721i | \(0.303110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.56997 | 0.849413 | 0.424706 | − | 0.905331i | \(-0.360377\pi\) | ||||
0.424706 | + | 0.905331i | \(0.360377\pi\) | |||||||
\(44\) | 7.19825 | 1.08518 | ||||||||
\(45\) | −0.674002 | −0.100474 | ||||||||
\(46\) | −3.74511 | −0.552186 | ||||||||
\(47\) | 11.0066 | 1.60548 | 0.802741 | − | 0.596328i | \(-0.203374\pi\) | ||||
0.802741 | + | 0.596328i | \(0.203374\pi\) | |||||||
\(48\) | −2.72429 | −0.393217 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.628452 | −0.0888765 | ||||||||
\(51\) | −1.36253 | −0.190792 | ||||||||
\(52\) | 4.98177 | 0.690847 | ||||||||
\(53\) | −4.30252 | −0.590997 | −0.295498 | − | 0.955343i | \(-0.595486\pi\) | ||||
−0.295498 | + | 0.955343i | \(0.595486\pi\) | |||||||
\(54\) | −3.52141 | −0.479203 | ||||||||
\(55\) | −4.48476 | −0.604724 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.2846 | 1.36223 | ||||||||
\(58\) | −1.28993 | −0.169376 | ||||||||
\(59\) | −9.91053 | −1.29024 | −0.645121 | − | 0.764081i | \(-0.723193\pi\) | ||||
−0.645121 | + | 0.764081i | \(0.723193\pi\) | |||||||
\(60\) | 2.44789 | 0.316022 | ||||||||
\(61\) | 6.58024 | 0.842513 | 0.421257 | − | 0.906942i | \(-0.361589\pi\) | ||||
0.421257 | + | 0.906942i | \(0.361589\pi\) | |||||||
\(62\) | 0.628452 | 0.0798135 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.0194157 | −0.00242697 | ||||||||
\(65\) | −3.10381 | −0.384980 | ||||||||
\(66\) | −4.29849 | −0.529107 | ||||||||
\(67\) | 10.0098 | 1.22289 | 0.611444 | − | 0.791288i | \(-0.290589\pi\) | ||||
0.611444 | + | 0.791288i | \(0.290589\pi\) | |||||||
\(68\) | −1.43393 | −0.173890 | ||||||||
\(69\) | −9.08860 | −1.09414 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.0016 | −1.54301 | −0.771505 | − | 0.636223i | \(-0.780496\pi\) | ||||
−0.771505 | + | 0.636223i | \(0.780496\pi\) | |||||||
\(72\) | −1.52702 | −0.179961 | ||||||||
\(73\) | 1.93156 | 0.226072 | 0.113036 | − | 0.993591i | \(-0.463942\pi\) | ||||
0.113036 | + | 0.993591i | \(0.463942\pi\) | |||||||
\(74\) | 2.57473 | 0.299306 | ||||||||
\(75\) | −1.52512 | −0.176106 | ||||||||
\(76\) | 10.8236 | 1.24155 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.97490 | −0.336841 | ||||||||
\(79\) | 6.89495 | 0.775742 | 0.387871 | − | 0.921714i | \(-0.373211\pi\) | ||||
0.387871 | + | 0.921714i | \(0.373211\pi\) | |||||||
\(80\) | 1.78628 | 0.199712 | ||||||||
\(81\) | −6.52372 | −0.724857 | ||||||||
\(82\) | −4.66672 | −0.515353 | ||||||||
\(83\) | −0.685851 | −0.0752819 | −0.0376409 | − | 0.999291i | \(-0.511984\pi\) | ||||
−0.0376409 | + | 0.999291i | \(0.511984\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.893389 | 0.0969016 | ||||||||
\(86\) | −3.50046 | −0.377464 | ||||||||
\(87\) | −3.13040 | −0.335614 | ||||||||
\(88\) | −10.1607 | −1.08313 | ||||||||
\(89\) | 16.0205 | 1.69817 | 0.849084 | − | 0.528257i | \(-0.177154\pi\) | ||||
0.849084 | + | 0.528257i | \(0.177154\pi\) | |||||||
\(90\) | 0.423578 | 0.0446490 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −9.56489 | −0.997209 | ||||||||
\(93\) | 1.52512 | 0.158148 | ||||||||
\(94\) | −6.91714 | −0.713449 | ||||||||
\(95\) | −6.74349 | −0.691867 | ||||||||
\(96\) | 8.62272 | 0.880053 | ||||||||
\(97\) | 4.21722 | 0.428193 | 0.214097 | − | 0.976812i | \(-0.431319\pi\) | ||||
0.214097 | + | 0.976812i | \(0.431319\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.02273 | 0.303796 | ||||||||
\(100\) | −1.60505 | −0.160505 | ||||||||
\(101\) | −17.8697 | −1.77810 | −0.889052 | − | 0.457806i | \(-0.848635\pi\) | ||||
−0.889052 | + | 0.457806i | \(0.848635\pi\) | |||||||
\(102\) | 0.856283 | 0.0847847 | ||||||||
\(103\) | −3.88759 | −0.383055 | −0.191528 | − | 0.981487i | \(-0.561344\pi\) | ||||
−0.191528 | + | 0.981487i | \(0.561344\pi\) | |||||||
\(104\) | −7.03199 | −0.689544 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.70393 | 0.262629 | ||||||||
\(107\) | −0.402701 | −0.0389305 | −0.0194653 | − | 0.999811i | \(-0.506196\pi\) | ||||
−0.0194653 | + | 0.999811i | \(0.506196\pi\) | |||||||
\(108\) | −8.99357 | −0.865407 | ||||||||
\(109\) | −8.51377 | −0.815472 | −0.407736 | − | 0.913100i | \(-0.633682\pi\) | ||||
−0.407736 | + | 0.913100i | \(0.633682\pi\) | |||||||
\(110\) | 2.81845 | 0.268729 | ||||||||
\(111\) | 6.24833 | 0.593065 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.7872 | −1.20292 | −0.601461 | − | 0.798902i | \(-0.705415\pi\) | ||||
−0.601461 | + | 0.798902i | \(0.705415\pi\) | |||||||
\(114\) | −6.46341 | −0.605354 | ||||||||
\(115\) | 5.95926 | 0.555704 | ||||||||
\(116\) | −3.29445 | −0.305882 | ||||||||
\(117\) | 2.09197 | 0.193403 | ||||||||
\(118\) | 6.22830 | 0.573361 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.45532 | −0.315426 | ||||||||
\(121\) | 9.11304 | 0.828458 | ||||||||
\(122\) | −4.13536 | −0.374398 | ||||||||
\(123\) | −11.3252 | −1.02116 | ||||||||
\(124\) | 1.60505 | 0.144138 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.3099 | 1.89095 | 0.945476 | − | 0.325691i | \(-0.105597\pi\) | ||||
0.945476 | + | 0.325691i | \(0.105597\pi\) | |||||||
\(128\) | 11.3198 | 1.00054 | ||||||||
\(129\) | −8.49489 | −0.747933 | ||||||||
\(130\) | 1.95060 | 0.171079 | ||||||||
\(131\) | −0.227315 | −0.0198606 | −0.00993030 | − | 0.999951i | \(-0.503161\pi\) | ||||
−0.00993030 | + | 0.999951i | \(0.503161\pi\) | |||||||
\(132\) | −10.9782 | −0.955531 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.29066 | −0.543430 | ||||||||
\(135\) | 5.60330 | 0.482255 | ||||||||
\(136\) | 2.02406 | 0.173562 | ||||||||
\(137\) | 21.1273 | 1.80503 | 0.902514 | − | 0.430661i | \(-0.141720\pi\) | ||||
0.902514 | + | 0.430661i | \(0.141720\pi\) | |||||||
\(138\) | 5.71175 | 0.486216 | ||||||||
\(139\) | 7.10186 | 0.602372 | 0.301186 | − | 0.953565i | \(-0.402617\pi\) | ||||
0.301186 | + | 0.953565i | \(0.402617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.7865 | −1.41368 | ||||||||
\(142\) | 8.17090 | 0.685687 | ||||||||
\(143\) | 13.9198 | 1.16404 | ||||||||
\(144\) | −1.20395 | −0.100329 | ||||||||
\(145\) | 2.05255 | 0.170455 | ||||||||
\(146\) | −1.21390 | −0.100463 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.57578 | 0.540525 | ||||||||
\(149\) | −16.9951 | −1.39229 | −0.696145 | − | 0.717902i | \(-0.745103\pi\) | ||||
−0.696145 | + | 0.717902i | \(0.745103\pi\) | |||||||
\(150\) | 0.958466 | 0.0782584 | ||||||||
\(151\) | 9.40602 | 0.765451 | 0.382725 | − | 0.923862i | \(-0.374986\pi\) | ||||
0.382725 | + | 0.923862i | \(0.374986\pi\) | |||||||
\(152\) | −15.2780 | −1.23921 | ||||||||
\(153\) | −0.602145 | −0.0486806 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | −7.59780 | −0.608311 | ||||||||
\(157\) | −5.76050 | −0.459738 | −0.229869 | − | 0.973222i | \(-0.573830\pi\) | ||||
−0.229869 | + | 0.973222i | \(0.573830\pi\) | |||||||
\(158\) | −4.33314 | −0.344726 | ||||||||
\(159\) | 6.56187 | 0.520390 | ||||||||
\(160\) | −5.65379 | −0.446971 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.09984 | 0.322114 | ||||||||
\(163\) | 14.7931 | 1.15869 | 0.579344 | − | 0.815083i | \(-0.303309\pi\) | ||||
0.579344 | + | 0.815083i | \(0.303309\pi\) | |||||||
\(164\) | −11.9187 | −0.930691 | ||||||||
\(165\) | 6.83980 | 0.532478 | ||||||||
\(166\) | 0.431024 | 0.0334540 | ||||||||
\(167\) | −13.1759 | −1.01958 | −0.509792 | − | 0.860298i | \(-0.670278\pi\) | ||||
−0.509792 | + | 0.860298i | \(0.670278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.36635 | −0.258950 | ||||||||
\(170\) | −0.561452 | −0.0430614 | ||||||||
\(171\) | 4.54512 | 0.347574 | ||||||||
\(172\) | −8.94007 | −0.681674 | ||||||||
\(173\) | −13.6830 | −1.04030 | −0.520150 | − | 0.854075i | \(-0.674124\pi\) | ||||
−0.520150 | + | 0.854075i | \(0.674124\pi\) | |||||||
\(174\) | 1.96730 | 0.149141 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.01101 | −0.603853 | ||||||||
\(177\) | 15.1148 | 1.13610 | ||||||||
\(178\) | −10.0681 | −0.754637 | ||||||||
\(179\) | 14.2212 | 1.06295 | 0.531473 | − | 0.847076i | \(-0.321639\pi\) | ||||
0.531473 | + | 0.847076i | \(0.321639\pi\) | |||||||
\(180\) | 1.08180 | 0.0806330 | ||||||||
\(181\) | −14.7671 | −1.09763 | −0.548816 | − | 0.835943i | \(-0.684921\pi\) | ||||
−0.548816 | + | 0.835943i | \(0.684921\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0357 | −0.741858 | ||||||||
\(184\) | 13.5013 | 0.995328 | ||||||||
\(185\) | −4.09693 | −0.301213 | ||||||||
\(186\) | −0.958466 | −0.0702782 | ||||||||
\(187\) | −4.00663 | −0.292994 | ||||||||
\(188\) | −17.6662 | −1.28844 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.23796 | 0.307454 | ||||||||
\(191\) | 22.1209 | 1.60061 | 0.800306 | − | 0.599591i | \(-0.204670\pi\) | ||||
0.800306 | + | 0.599591i | \(0.204670\pi\) | |||||||
\(192\) | 0.0296114 | 0.00213702 | ||||||||
\(193\) | 21.5583 | 1.55180 | 0.775899 | − | 0.630858i | \(-0.217297\pi\) | ||||
0.775899 | + | 0.630858i | \(0.217297\pi\) | |||||||
\(194\) | −2.65032 | −0.190282 | ||||||||
\(195\) | 4.73369 | 0.338987 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.87476 | 0.347312 | 0.173656 | − | 0.984806i | \(-0.444442\pi\) | ||||
0.173656 | + | 0.984806i | \(0.444442\pi\) | |||||||
\(198\) | −1.89964 | −0.135002 | ||||||||
\(199\) | −13.5023 | −0.957150 | −0.478575 | − | 0.878047i | \(-0.658847\pi\) | ||||
−0.478575 | + | 0.878047i | \(0.658847\pi\) | |||||||
\(200\) | 2.26560 | 0.160202 | ||||||||
\(201\) | −15.2661 | −1.07679 | ||||||||
\(202\) | 11.2303 | 0.790159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.18692 | 0.153115 | ||||||||
\(205\) | 7.42574 | 0.518636 | ||||||||
\(206\) | 2.44316 | 0.170223 | ||||||||
\(207\) | −4.01655 | −0.279169 | ||||||||
\(208\) | −5.54426 | −0.384425 | ||||||||
\(209\) | 30.2429 | 2.09195 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.9410 | 1.37280 | 0.686398 | − | 0.727226i | \(-0.259191\pi\) | ||||
0.686398 | + | 0.727226i | \(0.259191\pi\) | |||||||
\(212\) | 6.90576 | 0.474289 | ||||||||
\(213\) | 19.8291 | 1.35867 | ||||||||
\(214\) | 0.253078 | 0.0173001 | ||||||||
\(215\) | 5.56997 | 0.379869 | ||||||||
\(216\) | 12.6948 | 0.863774 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.35050 | 0.362381 | ||||||||
\(219\) | −2.94587 | −0.199064 | ||||||||
\(220\) | 7.19825 | 0.485306 | ||||||||
\(221\) | −2.77291 | −0.186526 | ||||||||
\(222\) | −3.92677 | −0.263548 | ||||||||
\(223\) | −28.4148 | −1.90280 | −0.951399 | − | 0.307961i | \(-0.900353\pi\) | ||||
−0.951399 | + | 0.307961i | \(0.900353\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.674002 | −0.0449334 | ||||||||
\(226\) | 8.03617 | 0.534558 | ||||||||
\(227\) | −7.83410 | −0.519967 | −0.259984 | − | 0.965613i | \(-0.583717\pi\) | ||||
−0.259984 | + | 0.965613i | \(0.583717\pi\) | |||||||
\(228\) | −16.5074 | −1.09323 | ||||||||
\(229\) | −15.6446 | −1.03382 | −0.516911 | − | 0.856039i | \(-0.672918\pi\) | ||||
−0.516911 | + | 0.856039i | \(0.672918\pi\) | |||||||
\(230\) | −3.74511 | −0.246945 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.65027 | 0.305305 | ||||||||
\(233\) | 11.4393 | 0.749414 | 0.374707 | − | 0.927143i | \(-0.377743\pi\) | ||||
0.374707 | + | 0.927143i | \(0.377743\pi\) | |||||||
\(234\) | −1.31471 | −0.0859450 | ||||||||
\(235\) | 11.0066 | 0.717993 | ||||||||
\(236\) | 15.9069 | 1.03545 | ||||||||
\(237\) | −10.5156 | −0.683064 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.52378 | −0.227934 | −0.113967 | − | 0.993485i | \(-0.536356\pi\) | ||||
−0.113967 | + | 0.993485i | \(0.536356\pi\) | |||||||
\(240\) | −2.72429 | −0.175852 | ||||||||
\(241\) | 23.4335 | 1.50948 | 0.754741 | − | 0.656023i | \(-0.227762\pi\) | ||||
0.754741 | + | 0.656023i | \(0.227762\pi\) | |||||||
\(242\) | −5.72711 | −0.368153 | ||||||||
\(243\) | −6.86044 | −0.440097 | ||||||||
\(244\) | −10.5616 | −0.676137 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.11732 | 0.453784 | ||||||||
\(247\) | 20.9305 | 1.33178 | ||||||||
\(248\) | −2.26560 | −0.143866 | ||||||||
\(249\) | 1.04601 | 0.0662879 | ||||||||
\(250\) | −0.628452 | −0.0397468 | ||||||||
\(251\) | 17.5688 | 1.10894 | 0.554468 | − | 0.832205i | \(-0.312922\pi\) | ||||
0.554468 | + | 0.832205i | \(0.312922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.7258 | −1.68024 | ||||||||
\(254\) | −13.3923 | −0.840306 | ||||||||
\(255\) | −1.36253 | −0.0853248 | ||||||||
\(256\) | −7.07511 | −0.442194 | ||||||||
\(257\) | −15.6731 | −0.977659 | −0.488829 | − | 0.872379i | \(-0.662576\pi\) | ||||
−0.488829 | + | 0.872379i | \(0.662576\pi\) | |||||||
\(258\) | 5.33863 | 0.332369 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.98177 | 0.308956 | ||||||||
\(261\) | −1.38342 | −0.0856319 | ||||||||
\(262\) | 0.142857 | 0.00882571 | ||||||||
\(263\) | 3.28965 | 0.202849 | 0.101424 | − | 0.994843i | \(-0.467660\pi\) | ||||
0.101424 | + | 0.994843i | \(0.467660\pi\) | |||||||
\(264\) | 15.4963 | 0.953729 | ||||||||
\(265\) | −4.30252 | −0.264302 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −24.4332 | −1.49529 | ||||||||
\(268\) | −16.0662 | −0.981397 | ||||||||
\(269\) | −20.5142 | −1.25077 | −0.625386 | − | 0.780315i | \(-0.715059\pi\) | ||||
−0.625386 | + | 0.780315i | \(0.715059\pi\) | |||||||
\(270\) | −3.52141 | −0.214306 | ||||||||
\(271\) | −14.1700 | −0.860768 | −0.430384 | − | 0.902646i | \(-0.641622\pi\) | ||||
−0.430384 | + | 0.902646i | \(0.641622\pi\) | |||||||
\(272\) | 1.59584 | 0.0967619 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.2775 | −0.802123 | ||||||||
\(275\) | −4.48476 | −0.270441 | ||||||||
\(276\) | 14.5876 | 0.878072 | ||||||||
\(277\) | −15.5823 | −0.936250 | −0.468125 | − | 0.883662i | \(-0.655070\pi\) | ||||
−0.468125 | + | 0.883662i | \(0.655070\pi\) | |||||||
\(278\) | −4.46318 | −0.267684 | ||||||||
\(279\) | 0.674002 | 0.0403514 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.37454 | 0.320618 | 0.160309 | − | 0.987067i | \(-0.448751\pi\) | ||||
0.160309 | + | 0.987067i | \(0.448751\pi\) | |||||||
\(282\) | 10.5495 | 0.628213 | ||||||||
\(283\) | 22.6902 | 1.34879 | 0.674397 | − | 0.738368i | \(-0.264403\pi\) | ||||
0.674397 | + | 0.738368i | \(0.264403\pi\) | |||||||
\(284\) | 20.8682 | 1.23830 | ||||||||
\(285\) | 10.2846 | 0.609210 | ||||||||
\(286\) | −8.74795 | −0.517277 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.81066 | 0.224545 | ||||||||
\(289\) | −16.2019 | −0.953050 | ||||||||
\(290\) | −1.28993 | −0.0757474 | ||||||||
\(291\) | −6.43177 | −0.377037 | ||||||||
\(292\) | −3.10025 | −0.181429 | ||||||||
\(293\) | 11.6084 | 0.678170 | 0.339085 | − | 0.940756i | \(-0.389882\pi\) | ||||
0.339085 | + | 0.940756i | \(0.389882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.91053 | −0.577014 | ||||||||
\(296\) | −9.28201 | −0.539506 | ||||||||
\(297\) | −25.1294 | −1.45816 | ||||||||
\(298\) | 10.6806 | 0.618709 | ||||||||
\(299\) | −18.4964 | −1.06968 | ||||||||
\(300\) | 2.44789 | 0.141329 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.91123 | −0.340153 | ||||||||
\(303\) | 27.2535 | 1.56567 | ||||||||
\(304\) | −12.0457 | −0.690870 | ||||||||
\(305\) | 6.58024 | 0.376783 | ||||||||
\(306\) | 0.378420 | 0.0216328 | ||||||||
\(307\) | −15.7237 | −0.897398 | −0.448699 | − | 0.893683i | \(-0.648112\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648112\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.92904 | 0.337292 | ||||||||
\(310\) | 0.628452 | 0.0356937 | ||||||||
\(311\) | 25.8444 | 1.46550 | 0.732750 | − | 0.680498i | \(-0.238236\pi\) | ||||
0.732750 | + | 0.680498i | \(0.238236\pi\) | |||||||
\(312\) | 10.7247 | 0.607164 | ||||||||
\(313\) | −15.4473 | −0.873136 | −0.436568 | − | 0.899671i | \(-0.643806\pi\) | ||||
−0.436568 | + | 0.899671i | \(0.643806\pi\) | |||||||
\(314\) | 3.62020 | 0.204300 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.0667 | −0.622552 | ||||||||
\(317\) | −18.3025 | −1.02797 | −0.513986 | − | 0.857799i | \(-0.671832\pi\) | ||||
−0.513986 | + | 0.857799i | \(0.671832\pi\) | |||||||
\(318\) | −4.12382 | −0.231253 | ||||||||
\(319\) | −9.20521 | −0.515393 | ||||||||
\(320\) | −0.0194157 | −0.00108537 | ||||||||
\(321\) | 0.614168 | 0.0342795 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.02456 | −0.335215 | ||||||||
\(324\) | 10.4709 | 0.581716 | ||||||||
\(325\) | −3.10381 | −0.172168 | ||||||||
\(326\) | −9.29677 | −0.514901 | ||||||||
\(327\) | 12.9845 | 0.718047 | ||||||||
\(328\) | 16.8237 | 0.928936 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.29849 | −0.236624 | ||||||||
\(331\) | 3.48343 | 0.191466 | 0.0957332 | − | 0.995407i | \(-0.469480\pi\) | ||||
0.0957332 | + | 0.995407i | \(0.469480\pi\) | |||||||
\(332\) | 1.10082 | 0.0604155 | ||||||||
\(333\) | 2.76134 | 0.151320 | ||||||||
\(334\) | 8.28044 | 0.453085 | ||||||||
\(335\) | 10.0098 | 0.546892 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2942 | 0.669706 | 0.334853 | − | 0.942270i | \(-0.391313\pi\) | ||||
0.334853 | + | 0.942270i | \(0.391313\pi\) | |||||||
\(338\) | 2.11559 | 0.115073 | ||||||||
\(339\) | 19.5021 | 1.05921 | ||||||||
\(340\) | −1.43393 | −0.0777659 | ||||||||
\(341\) | 4.48476 | 0.242863 | ||||||||
\(342\) | −2.85639 | −0.154456 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.6193 | 0.680389 | ||||||||
\(345\) | −9.08860 | −0.489314 | ||||||||
\(346\) | 8.59912 | 0.462291 | ||||||||
\(347\) | 8.12139 | 0.435979 | 0.217989 | − | 0.975951i | \(-0.430050\pi\) | ||||
0.217989 | + | 0.975951i | \(0.430050\pi\) | |||||||
\(348\) | 5.02444 | 0.269338 | ||||||||
\(349\) | 36.4917 | 1.95335 | 0.976677 | − | 0.214715i | \(-0.0688823\pi\) | ||||
0.976677 | + | 0.214715i | \(0.0688823\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.3916 | −0.928295 | ||||||||
\(352\) | 25.3559 | 1.35147 | ||||||||
\(353\) | −25.0330 | −1.33237 | −0.666186 | − | 0.745785i | \(-0.732075\pi\) | ||||
−0.666186 | + | 0.745785i | \(0.732075\pi\) | |||||||
\(354\) | −9.49891 | −0.504862 | ||||||||
\(355\) | −13.0016 | −0.690055 | ||||||||
\(356\) | −25.7137 | −1.36282 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.93737 | −0.472354 | ||||||||
\(359\) | 3.09086 | 0.163129 | 0.0815646 | − | 0.996668i | \(-0.474008\pi\) | ||||
0.0815646 | + | 0.996668i | \(0.474008\pi\) | |||||||
\(360\) | −1.52702 | −0.0804809 | ||||||||
\(361\) | 26.4746 | 1.39340 | ||||||||
\(362\) | 9.28042 | 0.487768 | ||||||||
\(363\) | −13.8985 | −0.729482 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.93156 | 0.101103 | ||||||||
\(366\) | 6.30694 | 0.329669 | ||||||||
\(367\) | −19.9819 | −1.04305 | −0.521524 | − | 0.853236i | \(-0.674636\pi\) | ||||
−0.521524 | + | 0.853236i | \(0.674636\pi\) | |||||||
\(368\) | 10.6449 | 0.554902 | ||||||||
\(369\) | −5.00496 | −0.260548 | ||||||||
\(370\) | 2.57473 | 0.133854 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.44789 | −0.126917 | ||||||||
\(373\) | −17.2769 | −0.894564 | −0.447282 | − | 0.894393i | \(-0.647608\pi\) | ||||
−0.447282 | + | 0.894393i | \(0.647608\pi\) | |||||||
\(374\) | 2.51798 | 0.130201 | ||||||||
\(375\) | −1.52512 | −0.0787570 | ||||||||
\(376\) | 24.9366 | 1.28601 | ||||||||
\(377\) | −6.37074 | −0.328110 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.4735 | −0.640720 | −0.320360 | − | 0.947296i | \(-0.603804\pi\) | ||||
−0.320360 | + | 0.947296i | \(0.603804\pi\) | |||||||
\(380\) | 10.8236 | 0.555240 | ||||||||
\(381\) | −32.5003 | −1.66504 | ||||||||
\(382\) | −13.9019 | −0.711285 | ||||||||
\(383\) | 9.09317 | 0.464639 | 0.232320 | − | 0.972640i | \(-0.425368\pi\) | ||||
0.232320 | + | 0.972640i | \(0.425368\pi\) | |||||||
\(384\) | −17.2640 | −0.881002 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.5483 | −0.689592 | ||||||||
\(387\) | −3.75417 | −0.190835 | ||||||||
\(388\) | −6.76883 | −0.343635 | ||||||||
\(389\) | −26.2233 | −1.32958 | −0.664788 | − | 0.747032i | \(-0.731478\pi\) | ||||
−0.664788 | + | 0.747032i | \(0.731478\pi\) | |||||||
\(390\) | −2.97490 | −0.150640 | ||||||||
\(391\) | 5.32393 | 0.269243 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.346683 | 0.0174878 | ||||||||
\(394\) | −3.06355 | −0.154339 | ||||||||
\(395\) | 6.89495 | 0.346922 | ||||||||
\(396\) | −4.85163 | −0.243804 | ||||||||
\(397\) | 22.0450 | 1.10641 | 0.553204 | − | 0.833046i | \(-0.313405\pi\) | ||||
0.553204 | + | 0.833046i | \(0.313405\pi\) | |||||||
\(398\) | 8.48553 | 0.425341 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.78628 | 0.0893138 | ||||||||
\(401\) | 4.42019 | 0.220734 | 0.110367 | − | 0.993891i | \(-0.464797\pi\) | ||||
0.110367 | + | 0.993891i | \(0.464797\pi\) | |||||||
\(402\) | 9.59403 | 0.478506 | ||||||||
\(403\) | 3.10381 | 0.154612 | ||||||||
\(404\) | 28.6818 | 1.42697 | ||||||||
\(405\) | −6.52372 | −0.324166 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.3737 | 0.910753 | ||||||||
\(408\) | −3.08694 | −0.152826 | ||||||||
\(409\) | −16.5367 | −0.817689 | −0.408844 | − | 0.912604i | \(-0.634068\pi\) | ||||
−0.408844 | + | 0.912604i | \(0.634068\pi\) | |||||||
\(410\) | −4.66672 | −0.230473 | ||||||||
\(411\) | −32.2217 | −1.58938 | ||||||||
\(412\) | 6.23976 | 0.307411 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.52421 | 0.124058 | ||||||||
\(415\) | −0.685851 | −0.0336671 | ||||||||
\(416\) | 17.5483 | 0.860376 | ||||||||
\(417\) | −10.8312 | −0.530407 | ||||||||
\(418\) | −19.0062 | −0.929624 | ||||||||
\(419\) | −21.7783 | −1.06394 | −0.531970 | − | 0.846763i | \(-0.678548\pi\) | ||||
−0.531970 | + | 0.846763i | \(0.678548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.5816 | 0.710666 | 0.355333 | − | 0.934740i | \(-0.384368\pi\) | ||||
0.355333 | + | 0.934740i | \(0.384368\pi\) | |||||||
\(422\) | −12.5320 | −0.610047 | ||||||||
\(423\) | −7.41849 | −0.360699 | ||||||||
\(424\) | −9.74780 | −0.473395 | ||||||||
\(425\) | 0.893389 | 0.0433357 | ||||||||
\(426\) | −12.4616 | −0.603768 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.646354 | 0.0312427 | ||||||||
\(429\) | −21.2295 | −1.02497 | ||||||||
\(430\) | −3.50046 | −0.168807 | ||||||||
\(431\) | −21.5009 | −1.03566 | −0.517830 | − | 0.855483i | \(-0.673260\pi\) | ||||
−0.517830 | + | 0.855483i | \(0.673260\pi\) | |||||||
\(432\) | 10.0090 | 0.481560 | ||||||||
\(433\) | −15.8270 | −0.760597 | −0.380298 | − | 0.924864i | \(-0.624179\pi\) | ||||
−0.380298 | + | 0.924864i | \(0.624179\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.13040 | −0.150091 | ||||||||
\(436\) | 13.6650 | 0.654435 | ||||||||
\(437\) | −40.1862 | −1.92237 | ||||||||
\(438\) | 1.85134 | 0.0884604 | ||||||||
\(439\) | −22.0465 | −1.05222 | −0.526112 | − | 0.850415i | \(-0.676351\pi\) | ||||
−0.526112 | + | 0.850415i | \(0.676351\pi\) | |||||||
\(440\) | −10.1607 | −0.484391 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.74264 | 0.0828890 | ||||||||
\(443\) | −29.1921 | −1.38696 | −0.693480 | − | 0.720475i | \(-0.743924\pi\) | ||||
−0.693480 | + | 0.720475i | \(0.743924\pi\) | |||||||
\(444\) | −10.0289 | −0.475949 | ||||||||
\(445\) | 16.0205 | 0.759444 | ||||||||
\(446\) | 17.8574 | 0.845571 | ||||||||
\(447\) | 25.9195 | 1.22595 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.3294 | 1.24256 | 0.621280 | − | 0.783589i | \(-0.286613\pi\) | ||||
0.621280 | + | 0.783589i | \(0.286613\pi\) | |||||||
\(450\) | 0.423578 | 0.0199676 | ||||||||
\(451\) | −33.3026 | −1.56816 | ||||||||
\(452\) | 20.5241 | 0.965374 | ||||||||
\(453\) | −14.3453 | −0.674002 | ||||||||
\(454\) | 4.92336 | 0.231065 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 23.3009 | 1.09116 | ||||||||
\(457\) | 14.2530 | 0.666728 | 0.333364 | − | 0.942798i | \(-0.391816\pi\) | ||||
0.333364 | + | 0.942798i | \(0.391816\pi\) | |||||||
\(458\) | 9.83187 | 0.459413 | ||||||||
\(459\) | 5.00593 | 0.233657 | ||||||||
\(460\) | −9.56489 | −0.445965 | ||||||||
\(461\) | −1.88451 | −0.0877704 | −0.0438852 | − | 0.999037i | \(-0.513974\pi\) | ||||
−0.0438852 | + | 0.999037i | \(0.513974\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.3234 | −1.78104 | −0.890519 | − | 0.454945i | \(-0.849659\pi\) | ||||
−0.890519 | + | 0.454945i | \(0.849659\pi\) | |||||||
\(464\) | 3.66643 | 0.170210 | ||||||||
\(465\) | 1.52512 | 0.0707259 | ||||||||
\(466\) | −7.18906 | −0.333027 | ||||||||
\(467\) | −5.88209 | −0.272191 | −0.136095 | − | 0.990696i | \(-0.543455\pi\) | ||||
−0.136095 | + | 0.990696i | \(0.543455\pi\) | |||||||
\(468\) | −3.35772 | −0.155211 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.91714 | −0.319064 | ||||||||
\(471\) | 8.78548 | 0.404813 | ||||||||
\(472\) | −22.4533 | −1.03350 | ||||||||
\(473\) | −24.9800 | −1.14858 | ||||||||
\(474\) | 6.60857 | 0.303542 | ||||||||
\(475\) | −6.74349 | −0.309413 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.89991 | 0.132778 | ||||||||
\(478\) | 2.21453 | 0.101290 | ||||||||
\(479\) | 18.8916 | 0.863180 | 0.431590 | − | 0.902070i | \(-0.357953\pi\) | ||||
0.431590 | + | 0.902070i | \(0.357953\pi\) | |||||||
\(480\) | 8.62272 | 0.393571 | ||||||||
\(481\) | 12.7161 | 0.579805 | ||||||||
\(482\) | −14.7268 | −0.670788 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.6269 | −0.664858 | ||||||||
\(485\) | 4.21722 | 0.191494 | ||||||||
\(486\) | 4.31146 | 0.195572 | ||||||||
\(487\) | −14.1560 | −0.641471 | −0.320735 | − | 0.947169i | \(-0.603930\pi\) | ||||
−0.320735 | + | 0.947169i | \(0.603930\pi\) | |||||||
\(488\) | 14.9082 | 0.674862 | ||||||||
\(489\) | −22.5613 | −1.02026 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.2203 | −1.45408 | −0.727040 | − | 0.686595i | \(-0.759104\pi\) | ||||
−0.727040 | + | 0.686595i | \(0.759104\pi\) | |||||||
\(492\) | 18.1774 | 0.819501 | ||||||||
\(493\) | 1.83373 | 0.0825870 | ||||||||
\(494\) | −13.1538 | −0.591819 | ||||||||
\(495\) | 3.02273 | 0.135862 | ||||||||
\(496\) | −1.78628 | −0.0802061 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.657365 | −0.0294572 | ||||||||
\(499\) | −1.13745 | −0.0509191 | −0.0254595 | − | 0.999676i | \(-0.508105\pi\) | ||||
−0.0254595 | + | 0.999676i | \(0.508105\pi\) | |||||||
\(500\) | −1.60505 | −0.0717799 | ||||||||
\(501\) | 20.0949 | 0.897774 | ||||||||
\(502\) | −11.0412 | −0.492792 | ||||||||
\(503\) | −29.6040 | −1.31998 | −0.659990 | − | 0.751275i | \(-0.729439\pi\) | ||||
−0.659990 | + | 0.751275i | \(0.729439\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.8697 | −0.795192 | ||||||||
\(506\) | 16.7959 | 0.746669 | ||||||||
\(507\) | 5.13410 | 0.228013 | ||||||||
\(508\) | −34.2035 | −1.51753 | ||||||||
\(509\) | −7.51171 | −0.332951 | −0.166475 | − | 0.986046i | \(-0.553239\pi\) | ||||
−0.166475 | + | 0.986046i | \(0.553239\pi\) | |||||||
\(510\) | 0.856283 | 0.0379168 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −18.1932 | −0.804033 | ||||||||
\(513\) | −37.7858 | −1.66828 | ||||||||
\(514\) | 9.84977 | 0.434455 | ||||||||
\(515\) | −3.88759 | −0.171308 | ||||||||
\(516\) | 13.6347 | 0.600234 | ||||||||
\(517\) | −49.3621 | −2.17094 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.8683 | 0.916015 | ||||||||
\(520\) | −7.03199 | −0.308373 | ||||||||
\(521\) | −21.1550 | −0.926817 | −0.463409 | − | 0.886145i | \(-0.653374\pi\) | ||||
−0.463409 | + | 0.886145i | \(0.653374\pi\) | |||||||
\(522\) | 0.869416 | 0.0380533 | ||||||||
\(523\) | 7.08430 | 0.309775 | 0.154887 | − | 0.987932i | \(-0.450498\pi\) | ||||
0.154887 | + | 0.987932i | \(0.450498\pi\) | |||||||
\(524\) | 0.364851 | 0.0159386 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.06739 | −0.0901424 | ||||||||
\(527\) | −0.893389 | −0.0389166 | ||||||||
\(528\) | 12.2178 | 0.531710 | ||||||||
\(529\) | 12.5127 | 0.544032 | ||||||||
\(530\) | 2.70393 | 0.117451 | ||||||||
\(531\) | 6.67972 | 0.289875 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.0481 | −0.998323 | ||||||||
\(534\) | 15.3551 | 0.664480 | ||||||||
\(535\) | −0.402701 | −0.0174103 | ||||||||
\(536\) | 22.6781 | 0.979546 | ||||||||
\(537\) | −21.6891 | −0.935955 | ||||||||
\(538\) | 12.8922 | 0.555822 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.99357 | −0.387022 | ||||||||
\(541\) | 20.9831 | 0.902133 | 0.451066 | − | 0.892490i | \(-0.351044\pi\) | ||||
0.451066 | + | 0.892490i | \(0.351044\pi\) | |||||||
\(542\) | 8.90519 | 0.382511 | ||||||||
\(543\) | 22.5217 | 0.966497 | ||||||||
\(544\) | −5.05103 | −0.216561 | ||||||||
\(545\) | −8.51377 | −0.364690 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.43394 | 0.317853 | 0.158926 | − | 0.987290i | \(-0.449197\pi\) | ||||
0.158926 | + | 0.987290i | \(0.449197\pi\) | |||||||
\(548\) | −33.9103 | −1.44858 | ||||||||
\(549\) | −4.43509 | −0.189285 | ||||||||
\(550\) | 2.81845 | 0.120179 | ||||||||
\(551\) | −13.8414 | −0.589663 | ||||||||
\(552\) | −20.5911 | −0.876416 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.79274 | 0.416053 | ||||||||
\(555\) | 6.24833 | 0.265227 | ||||||||
\(556\) | −11.3988 | −0.483418 | ||||||||
\(557\) | −16.4996 | −0.699109 | −0.349555 | − | 0.936916i | \(-0.613667\pi\) | ||||
−0.349555 | + | 0.936916i | \(0.613667\pi\) | |||||||
\(558\) | −0.423578 | −0.0179315 | ||||||||
\(559\) | −17.2881 | −0.731211 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.11060 | 0.257990 | ||||||||
\(562\) | −3.37764 | −0.142477 | ||||||||
\(563\) | 1.70528 | 0.0718691 | 0.0359345 | − | 0.999354i | \(-0.488559\pi\) | ||||
0.0359345 | + | 0.999354i | \(0.488559\pi\) | |||||||
\(564\) | 26.9431 | 1.13451 | ||||||||
\(565\) | −12.7872 | −0.537963 | ||||||||
\(566\) | −14.2597 | −0.599381 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.4565 | −1.23597 | ||||||||
\(569\) | 31.9978 | 1.34142 | 0.670709 | − | 0.741721i | \(-0.265990\pi\) | ||||
0.670709 | + | 0.741721i | \(0.265990\pi\) | |||||||
\(570\) | −6.46341 | −0.270722 | ||||||||
\(571\) | 4.90648 | 0.205330 | 0.102665 | − | 0.994716i | \(-0.467263\pi\) | ||||
0.102665 | + | 0.994716i | \(0.467263\pi\) | |||||||
\(572\) | −22.3420 | −0.934166 | ||||||||
\(573\) | −33.7371 | −1.40939 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.95926 | 0.248518 | ||||||||
\(576\) | 0.0130862 | 0.000545260 0 | ||||||||
\(577\) | 12.2116 | 0.508377 | 0.254189 | − | 0.967155i | \(-0.418192\pi\) | ||||
0.254189 | + | 0.967155i | \(0.418192\pi\) | |||||||
\(578\) | 10.1821 | 0.423519 | ||||||||
\(579\) | −32.8790 | −1.36640 | ||||||||
\(580\) | −3.29445 | −0.136795 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.04206 | 0.167549 | ||||||||
\(583\) | 19.2958 | 0.799149 | ||||||||
\(584\) | 4.37615 | 0.181086 | ||||||||
\(585\) | 2.09197 | 0.0864925 | ||||||||
\(586\) | −7.29533 | −0.301367 | ||||||||
\(587\) | −6.18296 | −0.255198 | −0.127599 | − | 0.991826i | \(-0.540727\pi\) | ||||
−0.127599 | + | 0.991826i | \(0.540727\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.74349 | 0.277861 | ||||||||
\(590\) | 6.22830 | 0.256415 | ||||||||
\(591\) | −7.43460 | −0.305819 | ||||||||
\(592\) | −7.31825 | −0.300778 | ||||||||
\(593\) | −40.2425 | −1.65256 | −0.826281 | − | 0.563258i | \(-0.809548\pi\) | ||||
−0.826281 | + | 0.563258i | \(0.809548\pi\) | |||||||
\(594\) | 15.7927 | 0.647980 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 27.2779 | 1.11735 | ||||||||
\(597\) | 20.5926 | 0.842800 | ||||||||
\(598\) | 11.6241 | 0.475345 | ||||||||
\(599\) | 36.3748 | 1.48623 | 0.743117 | − | 0.669161i | \(-0.233346\pi\) | ||||
0.743117 | + | 0.669161i | \(0.233346\pi\) | |||||||
\(600\) | −3.45532 | −0.141063 | ||||||||
\(601\) | −24.2045 | −0.987321 | −0.493661 | − | 0.869655i | \(-0.664341\pi\) | ||||
−0.493661 | + | 0.869655i | \(0.664341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.74660 | −0.274743 | ||||||||
\(604\) | −15.0971 | −0.614293 | ||||||||
\(605\) | 9.11304 | 0.370498 | ||||||||
\(606\) | −17.1275 | −0.695758 | ||||||||
\(607\) | −23.1734 | −0.940579 | −0.470290 | − | 0.882512i | \(-0.655851\pi\) | ||||
−0.470290 | + | 0.882512i | \(0.655851\pi\) | |||||||
\(608\) | 38.1263 | 1.54622 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.13536 | −0.167436 | ||||||||
\(611\) | −34.1625 | −1.38207 | ||||||||
\(612\) | 0.966472 | 0.0390673 | ||||||||
\(613\) | −44.7988 | −1.80941 | −0.904703 | − | 0.426043i | \(-0.859907\pi\) | ||||
−0.904703 | + | 0.426043i | \(0.859907\pi\) | |||||||
\(614\) | 9.88158 | 0.398788 | ||||||||
\(615\) | −11.3252 | −0.456674 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.36822 | 0.135600 | 0.0677998 | − | 0.997699i | \(-0.478402\pi\) | ||||
0.0677998 | + | 0.997699i | \(0.478402\pi\) | |||||||
\(618\) | −3.72612 | −0.149887 | ||||||||
\(619\) | 13.6575 | 0.548943 | 0.274472 | − | 0.961595i | \(-0.411497\pi\) | ||||
0.274472 | + | 0.961595i | \(0.411497\pi\) | |||||||
\(620\) | 1.60505 | 0.0644603 | ||||||||
\(621\) | 33.3915 | 1.33996 | ||||||||
\(622\) | −16.2420 | −0.651243 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.45568 | 0.338498 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.70792 | 0.388006 | ||||||||
\(627\) | −46.1241 | −1.84202 | ||||||||
\(628\) | 9.24589 | 0.368951 | ||||||||
\(629\) | −3.66015 | −0.145940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.2207 | −1.16326 | −0.581628 | − | 0.813455i | \(-0.697584\pi\) | ||||
−0.581628 | + | 0.813455i | \(0.697584\pi\) | |||||||
\(632\) | 15.6212 | 0.621378 | ||||||||
\(633\) | −30.4125 | −1.20879 | ||||||||
\(634\) | 11.5022 | 0.456813 | ||||||||
\(635\) | 21.3099 | 0.845660 | ||||||||
\(636\) | −10.5321 | −0.417626 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.78503 | 0.229032 | ||||||||
\(639\) | 8.76312 | 0.346664 | ||||||||
\(640\) | 11.3198 | 0.447454 | ||||||||
\(641\) | −18.9049 | −0.746700 | −0.373350 | − | 0.927690i | \(-0.621791\pi\) | ||||
−0.373350 | + | 0.927690i | \(0.621791\pi\) | |||||||
\(642\) | −0.385975 | −0.0152332 | ||||||||
\(643\) | −6.81626 | −0.268807 | −0.134403 | − | 0.990927i | \(-0.542912\pi\) | ||||
−0.134403 | + | 0.990927i | \(0.542912\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.49489 | −0.334486 | ||||||||
\(646\) | 3.78615 | 0.148964 | ||||||||
\(647\) | 1.83008 | 0.0719479 | 0.0359740 | − | 0.999353i | \(-0.488547\pi\) | ||||
0.0359740 | + | 0.999353i | \(0.488547\pi\) | |||||||
\(648\) | −14.7801 | −0.580618 | ||||||||
\(649\) | 44.4463 | 1.74467 | ||||||||
\(650\) | 1.95060 | 0.0765087 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −23.7437 | −0.929875 | ||||||||
\(653\) | −30.7795 | −1.20450 | −0.602248 | − | 0.798309i | \(-0.705728\pi\) | ||||
−0.602248 | + | 0.798309i | \(0.705728\pi\) | |||||||
\(654\) | −8.16016 | −0.319088 | ||||||||
\(655\) | −0.227315 | −0.00888193 | ||||||||
\(656\) | 13.2644 | 0.517888 | ||||||||
\(657\) | −1.30188 | −0.0507911 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.1721 | 0.941610 | 0.470805 | − | 0.882237i | \(-0.343964\pi\) | ||||
0.470805 | + | 0.882237i | \(0.343964\pi\) | |||||||
\(660\) | −10.9782 | −0.427326 | ||||||||
\(661\) | −20.9786 | −0.815972 | −0.407986 | − | 0.912988i | \(-0.633769\pi\) | ||||
−0.407986 | + | 0.912988i | \(0.633769\pi\) | |||||||
\(662\) | −2.18917 | −0.0850844 | ||||||||
\(663\) | 4.22903 | 0.164242 | ||||||||
\(664\) | −1.55386 | −0.0603016 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.73537 | −0.0672442 | ||||||||
\(667\) | 12.2317 | 0.473613 | ||||||||
\(668\) | 21.1480 | 0.818240 | ||||||||
\(669\) | 43.3361 | 1.67547 | ||||||||
\(670\) | −6.29066 | −0.243029 | ||||||||
\(671\) | −29.5108 | −1.13925 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3613 | −0.399397 | −0.199699 | − | 0.979857i | \(-0.563996\pi\) | ||||
−0.199699 | + | 0.979857i | \(0.563996\pi\) | |||||||
\(674\) | −7.72630 | −0.297606 | ||||||||
\(675\) | 5.60330 | 0.215671 | ||||||||
\(676\) | 5.40316 | 0.207814 | ||||||||
\(677\) | 25.1326 | 0.965924 | 0.482962 | − | 0.875641i | \(-0.339561\pi\) | ||||
0.482962 | + | 0.875641i | \(0.339561\pi\) | |||||||
\(678\) | −12.2561 | −0.470694 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.02406 | 0.0776192 | ||||||||
\(681\) | 11.9480 | 0.457847 | ||||||||
\(682\) | −2.81845 | −0.107924 | ||||||||
\(683\) | −0.460467 | −0.0176193 | −0.00880964 | − | 0.999961i | \(-0.502804\pi\) | ||||
−0.00880964 | + | 0.999961i | \(0.502804\pi\) | |||||||
\(684\) | −7.29514 | −0.278937 | ||||||||
\(685\) | 21.1273 | 0.807233 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.8599 | 0.910312 | ||||||||
\(688\) | 9.94950 | 0.379321 | ||||||||
\(689\) | 13.3542 | 0.508755 | ||||||||
\(690\) | 5.71175 | 0.217443 | ||||||||
\(691\) | 11.9224 | 0.453550 | 0.226775 | − | 0.973947i | \(-0.427182\pi\) | ||||
0.226775 | + | 0.973947i | \(0.427182\pi\) | |||||||
\(692\) | 21.9619 | 0.834866 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.10390 | −0.193741 | ||||||||
\(695\) | 7.10186 | 0.269389 | ||||||||
\(696\) | −7.09223 | −0.268830 | ||||||||
\(697\) | 6.63407 | 0.251283 | ||||||||
\(698\) | −22.9333 | −0.868037 | ||||||||
\(699\) | −17.4463 | −0.659881 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.5297 | 0.435472 | 0.217736 | − | 0.976008i | \(-0.430133\pi\) | ||||
0.217736 | + | 0.976008i | \(0.430133\pi\) | |||||||
\(702\) | 10.9298 | 0.412518 | ||||||||
\(703\) | 27.6276 | 1.04200 | ||||||||
\(704\) | 0.0870749 | 0.00328176 | ||||||||
\(705\) | −16.7865 | −0.632215 | ||||||||
\(706\) | 15.7320 | 0.592083 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24.2599 | −0.911745 | ||||||||
\(709\) | −46.2350 | −1.73639 | −0.868196 | − | 0.496221i | \(-0.834720\pi\) | ||||
−0.868196 | + | 0.496221i | \(0.834720\pi\) | |||||||
\(710\) | 8.17090 | 0.306649 | ||||||||
\(711\) | −4.64720 | −0.174284 | ||||||||
\(712\) | 36.2960 | 1.36025 | ||||||||
\(713\) | −5.95926 | −0.223176 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.9198 | 0.520572 | ||||||||
\(716\) | −22.8258 | −0.853039 | ||||||||
\(717\) | 5.37420 | 0.200703 | ||||||||
\(718\) | −1.94246 | −0.0724918 | ||||||||
\(719\) | −21.8789 | −0.815945 | −0.407973 | − | 0.912994i | \(-0.633764\pi\) | ||||
−0.407973 | + | 0.912994i | \(0.633764\pi\) | |||||||
\(720\) | −1.20395 | −0.0448687 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −16.6380 | −0.619204 | ||||||||
\(723\) | −35.7389 | −1.32914 | ||||||||
\(724\) | 23.7019 | 0.880875 | ||||||||
\(725\) | 2.05255 | 0.0762300 | ||||||||
\(726\) | 8.73454 | 0.324169 | ||||||||
\(727\) | −5.93195 | −0.220004 | −0.110002 | − | 0.993931i | \(-0.535086\pi\) | ||||
−0.110002 | + | 0.993931i | \(0.535086\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30.0342 | 1.11238 | ||||||||
\(730\) | −1.21390 | −0.0449283 | ||||||||
\(731\) | 4.97615 | 0.184050 | ||||||||
\(732\) | 16.1077 | 0.595359 | ||||||||
\(733\) | −20.1307 | −0.743544 | −0.371772 | − | 0.928324i | \(-0.621250\pi\) | ||||
−0.371772 | + | 0.928324i | \(0.621250\pi\) | |||||||
\(734\) | 12.5577 | 0.463513 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.6924 | −1.24192 | ||||||||
\(737\) | −44.8914 | −1.65359 | ||||||||
\(738\) | 3.14538 | 0.115783 | ||||||||
\(739\) | −40.7240 | −1.49806 | −0.749028 | − | 0.662538i | \(-0.769479\pi\) | ||||
−0.749028 | + | 0.662538i | \(0.769479\pi\) | |||||||
\(740\) | 6.57578 | 0.241730 | ||||||||
\(741\) | −31.9216 | −1.17267 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.1651 | 0.666414 | 0.333207 | − | 0.942854i | \(-0.391869\pi\) | ||||
0.333207 | + | 0.942854i | \(0.391869\pi\) | |||||||
\(744\) | 3.45532 | 0.126678 | ||||||||
\(745\) | −16.9951 | −0.622651 | ||||||||
\(746\) | 10.8577 | 0.397529 | ||||||||
\(747\) | 0.462264 | 0.0169134 | ||||||||
\(748\) | 6.43083 | 0.235135 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.958466 | 0.0349982 | ||||||||
\(751\) | 26.0999 | 0.952400 | 0.476200 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476200 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(752\) | 19.6609 | 0.716958 | ||||||||
\(753\) | −26.7946 | −0.976451 | ||||||||
\(754\) | 4.00371 | 0.145806 | ||||||||
\(755\) | 9.40602 | 0.342320 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.2988 | 1.24661 | 0.623305 | − | 0.781979i | \(-0.285789\pi\) | ||||
0.623305 | + | 0.781979i | \(0.285789\pi\) | |||||||
\(758\) | 7.83899 | 0.284725 | ||||||||
\(759\) | 40.7601 | 1.47950 | ||||||||
\(760\) | −15.2780 | −0.554193 | ||||||||
\(761\) | −12.6136 | −0.457242 | −0.228621 | − | 0.973516i | \(-0.573422\pi\) | ||||
−0.228621 | + | 0.973516i | \(0.573422\pi\) | |||||||
\(762\) | 20.4249 | 0.739915 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −35.5051 | −1.28453 | ||||||||
\(765\) | −0.602145 | −0.0217706 | ||||||||
\(766\) | −5.71462 | −0.206478 | ||||||||
\(767\) | 30.7604 | 1.11069 | ||||||||
\(768\) | 10.7904 | 0.389365 | ||||||||
\(769\) | 35.4076 | 1.27683 | 0.638416 | − | 0.769691i | \(-0.279590\pi\) | ||||
0.638416 | + | 0.769691i | \(0.279590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.9033 | 0.860858 | ||||||||
\(772\) | −34.6020 | −1.24535 | ||||||||
\(773\) | −51.8408 | −1.86458 | −0.932291 | − | 0.361709i | \(-0.882194\pi\) | ||||
−0.932291 | + | 0.361709i | \(0.882194\pi\) | |||||||
\(774\) | 2.35932 | 0.0848039 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 9.55452 | 0.342987 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.4801 | 0.590840 | ||||||||
\(779\) | −50.0754 | −1.79414 | ||||||||
\(780\) | −7.59780 | −0.272045 | ||||||||
\(781\) | 58.3092 | 2.08647 | ||||||||
\(782\) | −3.34584 | −0.119647 | ||||||||
\(783\) | 11.5011 | 0.411015 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.76050 | −0.205601 | ||||||||
\(786\) | −0.217874 | −0.00777130 | ||||||||
\(787\) | 6.72042 | 0.239557 | 0.119779 | − | 0.992801i | \(-0.461782\pi\) | ||||
0.119779 | + | 0.992801i | \(0.461782\pi\) | |||||||
\(788\) | −7.82422 | −0.278726 | ||||||||
\(789\) | −5.01712 | −0.178614 | ||||||||
\(790\) | −4.33314 | −0.154166 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.84830 | 0.243344 | ||||||||
\(793\) | −20.4238 | −0.725271 | ||||||||
\(794\) | −13.8542 | −0.491669 | ||||||||
\(795\) | 6.56187 | 0.232726 | ||||||||
\(796\) | 21.6718 | 0.768136 | ||||||||
\(797\) | 5.36374 | 0.189994 | 0.0949968 | − | 0.995478i | \(-0.469716\pi\) | ||||
0.0949968 | + | 0.995478i | \(0.469716\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.83320 | 0.347874 | ||||||||
\(800\) | −5.65379 | −0.199892 | ||||||||
\(801\) | −10.7978 | −0.381523 | ||||||||
\(802\) | −2.77788 | −0.0980903 | ||||||||
\(803\) | −8.66259 | −0.305696 | ||||||||
\(804\) | 24.5029 | 0.864149 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.95060 | −0.0687068 | ||||||||
\(807\) | 31.2867 | 1.10134 | ||||||||
\(808\) | −40.4856 | −1.42428 | ||||||||
\(809\) | −10.8740 | −0.382311 | −0.191155 | − | 0.981560i | \(-0.561223\pi\) | ||||
−0.191155 | + | 0.981560i | \(0.561223\pi\) | |||||||
\(810\) | 4.09984 | 0.144054 | ||||||||
\(811\) | 44.2555 | 1.55402 | 0.777010 | − | 0.629489i | \(-0.216736\pi\) | ||||
0.777010 | + | 0.629489i | \(0.216736\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.6110 | 0.757932 | ||||||||
\(814\) | −11.5470 | −0.404723 | ||||||||
\(815\) | 14.7931 | 0.518181 | ||||||||
\(816\) | −2.43385 | −0.0852017 | ||||||||
\(817\) | −37.5610 | −1.31409 | ||||||||
\(818\) | 10.3925 | 0.363367 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.9187 | −0.416218 | ||||||||
\(821\) | 7.87797 | 0.274943 | 0.137471 | − | 0.990506i | \(-0.456102\pi\) | ||||
0.137471 | + | 0.990506i | \(0.456102\pi\) | |||||||
\(822\) | 20.2498 | 0.706293 | ||||||||
\(823\) | −16.5354 | −0.576389 | −0.288194 | − | 0.957572i | \(-0.593055\pi\) | ||||
−0.288194 | + | 0.957572i | \(0.593055\pi\) | |||||||
\(824\) | −8.80771 | −0.306831 | ||||||||
\(825\) | 6.83980 | 0.238131 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.58315 | 0.333239 | 0.166619 | − | 0.986021i | \(-0.446715\pi\) | ||||
0.166619 | + | 0.986021i | \(0.446715\pi\) | |||||||
\(828\) | 6.44675 | 0.224040 | ||||||||
\(829\) | −6.49447 | −0.225562 | −0.112781 | − | 0.993620i | \(-0.535976\pi\) | ||||
−0.112781 | + | 0.993620i | \(0.535976\pi\) | |||||||
\(830\) | 0.431024 | 0.0149611 | ||||||||
\(831\) | 23.7649 | 0.824396 | ||||||||
\(832\) | 0.0602628 | 0.00208924 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.80690 | 0.235704 | ||||||||
\(835\) | −13.1759 | −0.455972 | ||||||||
\(836\) | −48.5413 | −1.67884 | ||||||||
\(837\) | −5.60330 | −0.193678 | ||||||||
\(838\) | 13.6866 | 0.472796 | ||||||||
\(839\) | −5.38547 | −0.185927 | −0.0929636 | − | 0.995670i | \(-0.529634\pi\) | ||||
−0.0929636 | + | 0.995670i | \(0.529634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7870 | −0.854725 | ||||||||
\(842\) | −9.16386 | −0.315807 | ||||||||
\(843\) | −8.19682 | −0.282314 | ||||||||
\(844\) | −32.0063 | −1.10170 | ||||||||
\(845\) | −3.36635 | −0.115806 | ||||||||
\(846\) | 4.66216 | 0.160288 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.68549 | −0.263921 | ||||||||
\(849\) | −34.6054 | −1.18765 | ||||||||
\(850\) | −0.561452 | −0.0192576 | ||||||||
\(851\) | −24.4147 | −0.836924 | ||||||||
\(852\) | −31.8266 | −1.09036 | ||||||||
\(853\) | −46.7475 | −1.60060 | −0.800302 | − | 0.599597i | \(-0.795328\pi\) | ||||
−0.800302 | + | 0.599597i | \(0.795328\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.54512 | 0.155440 | ||||||||
\(856\) | −0.912358 | −0.0311838 | ||||||||
\(857\) | −5.95898 | −0.203555 | −0.101777 | − | 0.994807i | \(-0.532453\pi\) | ||||
−0.101777 | + | 0.994807i | \(0.532453\pi\) | |||||||
\(858\) | 13.3417 | 0.455478 | ||||||||
\(859\) | −24.0132 | −0.819320 | −0.409660 | − | 0.912238i | \(-0.634353\pi\) | ||||
−0.409660 | + | 0.912238i | \(0.634353\pi\) | |||||||
\(860\) | −8.94007 | −0.304854 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.5123 | 0.460230 | ||||||||
\(863\) | 33.6969 | 1.14706 | 0.573528 | − | 0.819186i | \(-0.305574\pi\) | ||||
0.573528 | + | 0.819186i | \(0.305574\pi\) | |||||||
\(864\) | −31.6799 | −1.07777 | ||||||||
\(865\) | −13.6830 | −0.465236 | ||||||||
\(866\) | 9.94651 | 0.337996 | ||||||||
\(867\) | 24.7098 | 0.839189 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.9222 | −1.04896 | ||||||||
\(870\) | 1.96730 | 0.0666979 | ||||||||
\(871\) | −31.0684 | −1.05271 | ||||||||
\(872\) | −19.2888 | −0.653201 | ||||||||
\(873\) | −2.84241 | −0.0962010 | ||||||||
\(874\) | 25.2551 | 0.854266 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.72826 | 0.159753 | ||||||||
\(877\) | −41.2781 | −1.39386 | −0.696931 | − | 0.717138i | \(-0.745452\pi\) | ||||
−0.696931 | + | 0.717138i | \(0.745452\pi\) | |||||||
\(878\) | 13.8552 | 0.467590 | ||||||||
\(879\) | −17.7042 | −0.597149 | ||||||||
\(880\) | −8.01101 | −0.270051 | ||||||||
\(881\) | 17.8003 | 0.599708 | 0.299854 | − | 0.953985i | \(-0.403062\pi\) | ||||
0.299854 | + | 0.953985i | \(0.403062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.7816 | 1.60798 | 0.803989 | − | 0.594644i | \(-0.202707\pi\) | ||||
0.803989 | + | 0.594644i | \(0.202707\pi\) | |||||||
\(884\) | 4.45065 | 0.149692 | ||||||||
\(885\) | 15.1148 | 0.508078 | ||||||||
\(886\) | 18.3459 | 0.616341 | ||||||||
\(887\) | 23.5587 | 0.791025 | 0.395512 | − | 0.918461i | \(-0.370567\pi\) | ||||
0.395512 | + | 0.918461i | \(0.370567\pi\) | |||||||
\(888\) | 14.1562 | 0.475051 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −10.0681 | −0.337484 | ||||||||
\(891\) | 29.2573 | 0.980156 | ||||||||
\(892\) | 45.6072 | 1.52704 | ||||||||
\(893\) | −74.2231 | −2.48378 | ||||||||
\(894\) | −16.2892 | −0.544792 | ||||||||
\(895\) | 14.2212 | 0.475364 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.2093 | 0.941881 | ||||||||
\(898\) | −16.5468 | −0.552172 | ||||||||
\(899\) | −2.05255 | −0.0684565 | ||||||||
\(900\) | 1.08180 | 0.0360602 | ||||||||
\(901\) | −3.84383 | −0.128056 | ||||||||
\(902\) | 20.9291 | 0.696863 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.9708 | −0.963554 | ||||||||
\(905\) | −14.7671 | −0.490876 | ||||||||
\(906\) | 9.01535 | 0.299515 | ||||||||
\(907\) | 52.2289 | 1.73423 | 0.867116 | − | 0.498107i | \(-0.165971\pi\) | ||||
0.867116 | + | 0.498107i | \(0.165971\pi\) | |||||||
\(908\) | 12.5741 | 0.417286 | ||||||||
\(909\) | 12.0442 | 0.399482 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.8910 | 0.625886 | 0.312943 | − | 0.949772i | \(-0.398685\pi\) | ||||
0.312943 | + | 0.949772i | \(0.398685\pi\) | |||||||
\(912\) | 18.3712 | 0.608332 | ||||||||
\(913\) | 3.07587 | 0.101797 | ||||||||
\(914\) | −8.95734 | −0.296282 | ||||||||
\(915\) | −10.0357 | −0.331769 | ||||||||
\(916\) | 25.1103 | 0.829668 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.14599 | −0.103833 | ||||||||
\(919\) | 24.9938 | 0.824468 | 0.412234 | − | 0.911078i | \(-0.364749\pi\) | ||||
0.412234 | + | 0.911078i | \(0.364749\pi\) | |||||||
\(920\) | 13.5013 | 0.445124 | ||||||||
\(921\) | 23.9805 | 0.790186 | ||||||||
\(922\) | 1.18432 | 0.0390036 | ||||||||
\(923\) | 40.3546 | 1.32829 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.09693 | −0.134706 | ||||||||
\(926\) | 24.0844 | 0.791463 | ||||||||
\(927\) | 2.62024 | 0.0860599 | ||||||||
\(928\) | −11.6047 | −0.380943 | ||||||||
\(929\) | −57.1220 | −1.87411 | −0.937057 | − | 0.349177i | \(-0.886461\pi\) | ||||
−0.937057 | + | 0.349177i | \(0.886461\pi\) | |||||||
\(930\) | −0.958466 | −0.0314293 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −18.3606 | −0.601423 | ||||||||
\(933\) | −39.4158 | −1.29042 | ||||||||
\(934\) | 3.69661 | 0.120957 | ||||||||
\(935\) | −4.00663 | −0.131031 | ||||||||
\(936\) | 4.73958 | 0.154918 | ||||||||
\(937\) | −5.48542 | −0.179201 | −0.0896004 | − | 0.995978i | \(-0.528559\pi\) | ||||
−0.0896004 | + | 0.995978i | \(0.528559\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 23.5591 | 0.768822 | ||||||||
\(940\) | −17.6662 | −0.576207 | ||||||||
\(941\) | −19.8486 | −0.647045 | −0.323523 | − | 0.946220i | \(-0.604867\pi\) | ||||
−0.323523 | + | 0.946220i | \(0.604867\pi\) | |||||||
\(942\) | −5.52125 | −0.179892 | ||||||||
\(943\) | 44.2519 | 1.44104 | ||||||||
\(944\) | −17.7029 | −0.576182 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.6987 | 0.510409 | ||||||||
\(947\) | 33.2459 | 1.08035 | 0.540173 | − | 0.841554i | \(-0.318359\pi\) | ||||
0.540173 | + | 0.841554i | \(0.318359\pi\) | |||||||
\(948\) | 16.8781 | 0.548175 | ||||||||
\(949\) | −5.99521 | −0.194613 | ||||||||
\(950\) | 4.23796 | 0.137498 | ||||||||
\(951\) | 27.9136 | 0.905159 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.8889 | −0.611871 | −0.305936 | − | 0.952052i | \(-0.598969\pi\) | ||||
−0.305936 | + | 0.952052i | \(0.598969\pi\) | |||||||
\(954\) | −1.82245 | −0.0590041 | ||||||||
\(955\) | 22.1209 | 0.715816 | ||||||||
\(956\) | 5.65584 | 0.182923 | ||||||||
\(957\) | 14.0391 | 0.453819 | ||||||||
\(958\) | −11.8725 | −0.383582 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0296114 | 0.000955703 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −7.99147 | −0.257655 | ||||||||
\(963\) | 0.271421 | 0.00874641 | ||||||||
\(964\) | −37.6118 | −1.21140 | ||||||||
\(965\) | 21.5583 | 0.693985 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.2574 | −0.554960 | −0.277480 | − | 0.960731i | \(-0.589499\pi\) | ||||
−0.277480 | + | 0.960731i | \(0.589499\pi\) | |||||||
\(968\) | 20.6465 | 0.663604 | ||||||||
\(969\) | 9.18819 | 0.295167 | ||||||||
\(970\) | −2.65032 | −0.0850966 | ||||||||
\(971\) | −23.9709 | −0.769262 | −0.384631 | − | 0.923070i | \(-0.625671\pi\) | ||||
−0.384631 | + | 0.923070i | \(0.625671\pi\) | |||||||
\(972\) | 11.0113 | 0.353189 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.89639 | 0.285059 | ||||||||
\(975\) | 4.73369 | 0.151599 | ||||||||
\(976\) | 11.7541 | 0.376240 | ||||||||
\(977\) | 12.5674 | 0.402067 | 0.201034 | − | 0.979584i | \(-0.435570\pi\) | ||||
0.201034 | + | 0.979584i | \(0.435570\pi\) | |||||||
\(978\) | 14.1787 | 0.453385 | ||||||||
\(979\) | −71.8480 | −2.29627 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.73830 | 0.183210 | ||||||||
\(982\) | 20.2489 | 0.646168 | ||||||||
\(983\) | −21.6759 | −0.691355 | −0.345677 | − | 0.938353i | \(-0.612351\pi\) | ||||
−0.345677 | + | 0.938353i | \(0.612351\pi\) | |||||||
\(984\) | −25.6583 | −0.817956 | ||||||||
\(985\) | 4.87476 | 0.155323 | ||||||||
\(986\) | −1.15241 | −0.0367002 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.5945 | −1.06878 | ||||||||
\(989\) | 33.1929 | 1.05547 | ||||||||
\(990\) | −1.89964 | −0.0603746 | ||||||||
\(991\) | −39.7085 | −1.26138 | −0.630691 | − | 0.776034i | \(-0.717228\pi\) | ||||
−0.630691 | + | 0.776034i | \(0.717228\pi\) | |||||||
\(992\) | 5.65379 | 0.179508 | ||||||||
\(993\) | −5.31265 | −0.168592 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.5023 | −0.428051 | ||||||||
\(996\) | −1.67889 | −0.0531977 | ||||||||
\(997\) | 9.53611 | 0.302012 | 0.151006 | − | 0.988533i | \(-0.451749\pi\) | ||||
0.151006 | + | 0.988533i | \(0.451749\pi\) | |||||||
\(998\) | 0.714830 | 0.0226276 | ||||||||
\(999\) | −22.9564 | −0.726307 |
(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 | 7595.2.a.bf.1.10 | 21 | ||
7.3 | odd | 6 | 1085.2.j.d.156.12 | ✓ | 42 | ||
7.5 | odd | 6 | 1085.2.j.d.466.12 | yes | 42 | ||
7.6 | odd | 2 | 7595.2.a.bg.1.10 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1085.2.j.d.156.12 | ✓ | 42 | 7.3 | odd | 6 | ||
1085.2.j.d.466.12 | yes | 42 | 7.5 | odd | 6 | ||
7595.2.a.bf.1.10 | 21 | 1.1 | even | 1 | trivial | ||
7595.2.a.bg.1.10 | 21 | 7.6 | odd | 2 |