Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.47328 | −1.74887 | −0.874436 | − | 0.485142i | \(-0.838768\pi\) | ||||
−0.874436 | + | 0.485142i | \(0.838768\pi\) | |||||||
\(3\) | −1.34586 | −0.777033 | −0.388517 | − | 0.921442i | \(-0.627012\pi\) | ||||
−0.388517 | + | 0.921442i | \(0.627012\pi\) | |||||||
\(4\) | 4.11710 | 2.05855 | ||||||||
\(5\) | 2.94670 | 1.31781 | 0.658903 | − | 0.752228i | \(-0.271021\pi\) | ||||
0.658903 | + | 0.752228i | \(0.271021\pi\) | |||||||
\(6\) | 3.32869 | 1.35893 | ||||||||
\(7\) | −2.85130 | −1.07769 | −0.538845 | − | 0.842405i | \(-0.681139\pi\) | ||||
−0.538845 | + | 0.842405i | \(0.681139\pi\) | |||||||
\(8\) | −5.23618 | −1.85127 | ||||||||
\(9\) | −1.18866 | −0.396219 | ||||||||
\(10\) | −7.28801 | −2.30467 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −5.54105 | −1.59956 | ||||||||
\(13\) | −1.72879 | −0.479479 | −0.239740 | − | 0.970837i | \(-0.577062\pi\) | ||||
−0.239740 | + | 0.970837i | \(0.577062\pi\) | |||||||
\(14\) | 7.05206 | 1.88474 | ||||||||
\(15\) | −3.96585 | −1.02398 | ||||||||
\(16\) | 4.71631 | 1.17908 | ||||||||
\(17\) | −6.02426 | −1.46110 | −0.730549 | − | 0.682861i | \(-0.760736\pi\) | ||||
−0.730549 | + | 0.682861i | \(0.760736\pi\) | |||||||
\(18\) | 2.93988 | 0.692936 | ||||||||
\(19\) | −4.89251 | −1.12242 | −0.561209 | − | 0.827674i | \(-0.689664\pi\) | ||||
−0.561209 | + | 0.827674i | \(0.689664\pi\) | |||||||
\(20\) | 12.1319 | 2.71277 | ||||||||
\(21\) | 3.83746 | 0.837402 | ||||||||
\(22\) | 2.47328 | 0.527304 | ||||||||
\(23\) | 3.06664 | 0.639439 | 0.319720 | − | 0.947512i | \(-0.396411\pi\) | ||||
0.319720 | + | 0.947512i | \(0.396411\pi\) | |||||||
\(24\) | 7.04717 | 1.43850 | ||||||||
\(25\) | 3.68306 | 0.736612 | ||||||||
\(26\) | 4.27577 | 0.838547 | ||||||||
\(27\) | 5.63735 | 1.08491 | ||||||||
\(28\) | −11.7391 | −2.21848 | ||||||||
\(29\) | −9.51723 | −1.76731 | −0.883653 | − | 0.468143i | \(-0.844923\pi\) | ||||
−0.883653 | + | 0.468143i | \(0.844923\pi\) | |||||||
\(30\) | 9.80866 | 1.79081 | ||||||||
\(31\) | −2.12362 | −0.381413 | −0.190707 | − | 0.981647i | \(-0.561078\pi\) | ||||
−0.190707 | + | 0.981647i | \(0.561078\pi\) | |||||||
\(32\) | −1.19240 | −0.210789 | ||||||||
\(33\) | 1.34586 | 0.234284 | ||||||||
\(34\) | 14.8997 | 2.55527 | ||||||||
\(35\) | −8.40194 | −1.42019 | ||||||||
\(36\) | −4.89382 | −0.815637 | ||||||||
\(37\) | −2.03716 | −0.334906 | −0.167453 | − | 0.985880i | \(-0.553554\pi\) | ||||
−0.167453 | + | 0.985880i | \(0.553554\pi\) | |||||||
\(38\) | 12.1005 | 1.96296 | ||||||||
\(39\) | 2.32671 | 0.372571 | ||||||||
\(40\) | −15.4295 | −2.43961 | ||||||||
\(41\) | −2.59459 | −0.405207 | −0.202603 | − | 0.979261i | \(-0.564940\pi\) | ||||
−0.202603 | + | 0.979261i | \(0.564940\pi\) | |||||||
\(42\) | −9.49109 | −1.46451 | ||||||||
\(43\) | −10.3932 | −1.58495 | −0.792476 | − | 0.609904i | \(-0.791208\pi\) | ||||
−0.792476 | + | 0.609904i | \(0.791208\pi\) | |||||||
\(44\) | −4.11710 | −0.620676 | ||||||||
\(45\) | −3.50262 | −0.522140 | ||||||||
\(46\) | −7.58466 | −1.11830 | ||||||||
\(47\) | −4.16877 | −0.608078 | −0.304039 | − | 0.952660i | \(-0.598335\pi\) | ||||
−0.304039 | + | 0.952660i | \(0.598335\pi\) | |||||||
\(48\) | −6.34750 | −0.916183 | ||||||||
\(49\) | 1.12992 | 0.161417 | ||||||||
\(50\) | −9.10923 | −1.28824 | ||||||||
\(51\) | 8.10782 | 1.13532 | ||||||||
\(52\) | −7.11759 | −0.987032 | ||||||||
\(53\) | 10.0709 | 1.38335 | 0.691675 | − | 0.722209i | \(-0.256873\pi\) | ||||
0.691675 | + | 0.722209i | \(0.256873\pi\) | |||||||
\(54\) | −13.9427 | −1.89737 | ||||||||
\(55\) | −2.94670 | −0.397333 | ||||||||
\(56\) | 14.9299 | 1.99509 | ||||||||
\(57\) | 6.58464 | 0.872156 | ||||||||
\(58\) | 23.5388 | 3.09079 | ||||||||
\(59\) | 4.62139 | 0.601653 | 0.300827 | − | 0.953679i | \(-0.402737\pi\) | ||||
0.300827 | + | 0.953679i | \(0.402737\pi\) | |||||||
\(60\) | −16.3278 | −2.10791 | ||||||||
\(61\) | −14.6861 | −1.88037 | −0.940183 | − | 0.340670i | \(-0.889346\pi\) | ||||
−0.940183 | + | 0.340670i | \(0.889346\pi\) | |||||||
\(62\) | 5.25230 | 0.667043 | ||||||||
\(63\) | 3.38922 | 0.427002 | ||||||||
\(64\) | −6.48349 | −0.810436 | ||||||||
\(65\) | −5.09422 | −0.631861 | ||||||||
\(66\) | −3.32869 | −0.409733 | ||||||||
\(67\) | −7.80053 | −0.952987 | −0.476493 | − | 0.879178i | \(-0.658092\pi\) | ||||
−0.476493 | + | 0.879178i | \(0.658092\pi\) | |||||||
\(68\) | −24.8025 | −3.00774 | ||||||||
\(69\) | −4.12728 | −0.496866 | ||||||||
\(70\) | 20.7803 | 2.48372 | ||||||||
\(71\) | −16.5584 | −1.96512 | −0.982560 | − | 0.185946i | \(-0.940465\pi\) | ||||
−0.982560 | + | 0.185946i | \(0.940465\pi\) | |||||||
\(72\) | 6.22402 | 0.733508 | ||||||||
\(73\) | 10.1702 | 1.19033 | 0.595164 | − | 0.803605i | \(-0.297087\pi\) | ||||
0.595164 | + | 0.803605i | \(0.297087\pi\) | |||||||
\(74\) | 5.03845 | 0.585708 | ||||||||
\(75\) | −4.95689 | −0.572372 | ||||||||
\(76\) | −20.1429 | −2.31055 | ||||||||
\(77\) | 2.85130 | 0.324936 | ||||||||
\(78\) | −5.75459 | −0.651579 | ||||||||
\(79\) | 8.61927 | 0.969744 | 0.484872 | − | 0.874585i | \(-0.338866\pi\) | ||||
0.484872 | + | 0.874585i | \(0.338866\pi\) | |||||||
\(80\) | 13.8976 | 1.55380 | ||||||||
\(81\) | −4.02112 | −0.446791 | ||||||||
\(82\) | 6.41714 | 0.708655 | ||||||||
\(83\) | −8.70178 | −0.955144 | −0.477572 | − | 0.878593i | \(-0.658483\pi\) | ||||
−0.477572 | + | 0.878593i | \(0.658483\pi\) | |||||||
\(84\) | 15.7992 | 1.72383 | ||||||||
\(85\) | −17.7517 | −1.92544 | ||||||||
\(86\) | 25.7053 | 2.77188 | ||||||||
\(87\) | 12.8089 | 1.37326 | ||||||||
\(88\) | 5.23618 | 0.558178 | ||||||||
\(89\) | 7.51142 | 0.796208 | 0.398104 | − | 0.917340i | \(-0.369668\pi\) | ||||
0.398104 | + | 0.917340i | \(0.369668\pi\) | |||||||
\(90\) | 8.66295 | 0.913156 | ||||||||
\(91\) | 4.92929 | 0.516730 | ||||||||
\(92\) | 12.6257 | 1.31632 | ||||||||
\(93\) | 2.85810 | 0.296371 | ||||||||
\(94\) | 10.3105 | 1.06345 | ||||||||
\(95\) | −14.4168 | −1.47913 | ||||||||
\(96\) | 1.60481 | 0.163790 | ||||||||
\(97\) | −3.08062 | −0.312790 | −0.156395 | − | 0.987695i | \(-0.549987\pi\) | ||||
−0.156395 | + | 0.987695i | \(0.549987\pi\) | |||||||
\(98\) | −2.79461 | −0.282298 | ||||||||
\(99\) | 1.18866 | 0.119465 | ||||||||
\(100\) | 15.1635 | 1.51635 | ||||||||
\(101\) | −9.37227 | −0.932576 | −0.466288 | − | 0.884633i | \(-0.654409\pi\) | ||||
−0.466288 | + | 0.884633i | \(0.654409\pi\) | |||||||
\(102\) | −20.0529 | −1.98553 | ||||||||
\(103\) | 4.16480 | 0.410370 | 0.205185 | − | 0.978723i | \(-0.434220\pi\) | ||||
0.205185 | + | 0.978723i | \(0.434220\pi\) | |||||||
\(104\) | 9.05223 | 0.887645 | ||||||||
\(105\) | 11.3078 | 1.10353 | ||||||||
\(106\) | −24.9082 | −2.41930 | ||||||||
\(107\) | 9.72118 | 0.939782 | 0.469891 | − | 0.882724i | \(-0.344293\pi\) | ||||
0.469891 | + | 0.882724i | \(0.344293\pi\) | |||||||
\(108\) | 23.2095 | 2.23334 | ||||||||
\(109\) | −2.01684 | −0.193178 | −0.0965891 | − | 0.995324i | \(-0.530793\pi\) | ||||
−0.0965891 | + | 0.995324i | \(0.530793\pi\) | |||||||
\(110\) | 7.28801 | 0.694885 | ||||||||
\(111\) | 2.74173 | 0.260233 | ||||||||
\(112\) | −13.4476 | −1.27068 | ||||||||
\(113\) | −0.484566 | −0.0455842 | −0.0227921 | − | 0.999740i | \(-0.507256\pi\) | ||||
−0.0227921 | + | 0.999740i | \(0.507256\pi\) | |||||||
\(114\) | −16.2856 | −1.52529 | ||||||||
\(115\) | 9.03649 | 0.842657 | ||||||||
\(116\) | −39.1834 | −3.63809 | ||||||||
\(117\) | 2.05494 | 0.189979 | ||||||||
\(118\) | −11.4300 | −1.05221 | ||||||||
\(119\) | 17.1770 | 1.57461 | ||||||||
\(120\) | 20.7659 | 1.89566 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 36.3229 | 3.28852 | ||||||||
\(123\) | 3.49196 | 0.314859 | ||||||||
\(124\) | −8.74315 | −0.785158 | ||||||||
\(125\) | −3.88063 | −0.347094 | ||||||||
\(126\) | −8.38248 | −0.746771 | ||||||||
\(127\) | 19.5778 | 1.73725 | 0.868624 | − | 0.495472i | \(-0.165005\pi\) | ||||
0.868624 | + | 0.495472i | \(0.165005\pi\) | |||||||
\(128\) | 18.4203 | 1.62814 | ||||||||
\(129\) | 13.9878 | 1.23156 | ||||||||
\(130\) | 12.5994 | 1.10504 | ||||||||
\(131\) | 16.6115 | 1.45135 | 0.725677 | − | 0.688036i | \(-0.241527\pi\) | ||||
0.725677 | + | 0.688036i | \(0.241527\pi\) | |||||||
\(132\) | 5.54105 | 0.482286 | ||||||||
\(133\) | 13.9500 | 1.20962 | ||||||||
\(134\) | 19.2929 | 1.66665 | ||||||||
\(135\) | 16.6116 | 1.42970 | ||||||||
\(136\) | 31.5441 | 2.70488 | ||||||||
\(137\) | 3.70035 | 0.316142 | 0.158071 | − | 0.987428i | \(-0.449472\pi\) | ||||
0.158071 | + | 0.987428i | \(0.449472\pi\) | |||||||
\(138\) | 10.2079 | 0.868954 | ||||||||
\(139\) | 12.1430 | 1.02996 | 0.514978 | − | 0.857203i | \(-0.327800\pi\) | ||||
0.514978 | + | 0.857203i | \(0.327800\pi\) | |||||||
\(140\) | −34.5916 | −2.92353 | ||||||||
\(141\) | 5.61059 | 0.472497 | ||||||||
\(142\) | 40.9535 | 3.43674 | ||||||||
\(143\) | 1.72879 | 0.144568 | ||||||||
\(144\) | −5.60608 | −0.467174 | ||||||||
\(145\) | −28.0445 | −2.32897 | ||||||||
\(146\) | −25.1536 | −2.08173 | ||||||||
\(147\) | −1.52072 | −0.125427 | ||||||||
\(148\) | −8.38718 | −0.689422 | ||||||||
\(149\) | −9.58037 | −0.784854 | −0.392427 | − | 0.919783i | \(-0.628365\pi\) | ||||
−0.392427 | + | 0.919783i | \(0.628365\pi\) | |||||||
\(150\) | 12.2598 | 1.00101 | ||||||||
\(151\) | 6.00145 | 0.488391 | 0.244196 | − | 0.969726i | \(-0.421476\pi\) | ||||
0.244196 | + | 0.969726i | \(0.421476\pi\) | |||||||
\(152\) | 25.6180 | 2.07790 | ||||||||
\(153\) | 7.16078 | 0.578915 | ||||||||
\(154\) | −7.05206 | −0.568271 | ||||||||
\(155\) | −6.25768 | −0.502629 | ||||||||
\(156\) | 9.57929 | 0.766957 | ||||||||
\(157\) | 2.85994 | 0.228248 | 0.114124 | − | 0.993467i | \(-0.463594\pi\) | ||||
0.114124 | + | 0.993467i | \(0.463594\pi\) | |||||||
\(158\) | −21.3179 | −1.69596 | ||||||||
\(159\) | −13.5541 | −1.07491 | ||||||||
\(160\) | −3.51365 | −0.277779 | ||||||||
\(161\) | −8.74392 | −0.689118 | ||||||||
\(162\) | 9.94534 | 0.781380 | ||||||||
\(163\) | 4.96638 | 0.388997 | 0.194498 | − | 0.980903i | \(-0.437692\pi\) | ||||
0.194498 | + | 0.980903i | \(0.437692\pi\) | |||||||
\(164\) | −10.6822 | −0.834139 | ||||||||
\(165\) | 3.96585 | 0.308741 | ||||||||
\(166\) | 21.5219 | 1.67042 | ||||||||
\(167\) | 24.2458 | 1.87619 | 0.938097 | − | 0.346372i | \(-0.112587\pi\) | ||||
0.938097 | + | 0.346372i | \(0.112587\pi\) | |||||||
\(168\) | −20.0936 | −1.55025 | ||||||||
\(169\) | −10.0113 | −0.770100 | ||||||||
\(170\) | 43.9049 | 3.36735 | ||||||||
\(171\) | 5.81552 | 0.444724 | ||||||||
\(172\) | −42.7899 | −3.26270 | ||||||||
\(173\) | −14.9495 | −1.13659 | −0.568295 | − | 0.822825i | \(-0.692397\pi\) | ||||
−0.568295 | + | 0.822825i | \(0.692397\pi\) | |||||||
\(174\) | −31.6799 | −2.40165 | ||||||||
\(175\) | −10.5015 | −0.793840 | ||||||||
\(176\) | −4.71631 | −0.355506 | ||||||||
\(177\) | −6.21975 | −0.467505 | ||||||||
\(178\) | −18.5778 | −1.39247 | ||||||||
\(179\) | −19.8200 | −1.48141 | −0.740707 | − | 0.671828i | \(-0.765509\pi\) | ||||
−0.740707 | + | 0.671828i | \(0.765509\pi\) | |||||||
\(180\) | −14.4206 | −1.07485 | ||||||||
\(181\) | −22.3787 | −1.66340 | −0.831698 | − | 0.555229i | \(-0.812631\pi\) | ||||
−0.831698 | + | 0.555229i | \(0.812631\pi\) | |||||||
\(182\) | −12.1915 | −0.903695 | ||||||||
\(183\) | 19.7655 | 1.46111 | ||||||||
\(184\) | −16.0575 | −1.18377 | ||||||||
\(185\) | −6.00290 | −0.441342 | ||||||||
\(186\) | −7.06886 | −0.518314 | ||||||||
\(187\) | 6.02426 | 0.440537 | ||||||||
\(188\) | −17.1633 | −1.25176 | ||||||||
\(189\) | −16.0738 | −1.16920 | ||||||||
\(190\) | 35.6567 | 2.58681 | ||||||||
\(191\) | 24.5052 | 1.77313 | 0.886567 | − | 0.462600i | \(-0.153083\pi\) | ||||
0.886567 | + | 0.462600i | \(0.153083\pi\) | |||||||
\(192\) | 8.72588 | 0.629736 | ||||||||
\(193\) | −11.3225 | −0.815009 | −0.407504 | − | 0.913203i | \(-0.633601\pi\) | ||||
−0.407504 | + | 0.913203i | \(0.633601\pi\) | |||||||
\(194\) | 7.61923 | 0.547029 | ||||||||
\(195\) | 6.85612 | 0.490977 | ||||||||
\(196\) | 4.65200 | 0.332286 | ||||||||
\(197\) | 12.6698 | 0.902686 | 0.451343 | − | 0.892351i | \(-0.350945\pi\) | ||||
0.451343 | + | 0.892351i | \(0.350945\pi\) | |||||||
\(198\) | −2.93988 | −0.208928 | ||||||||
\(199\) | 5.92740 | 0.420182 | 0.210091 | − | 0.977682i | \(-0.432624\pi\) | ||||
0.210091 | + | 0.977682i | \(0.432624\pi\) | |||||||
\(200\) | −19.2852 | −1.36367 | ||||||||
\(201\) | 10.4984 | 0.740502 | ||||||||
\(202\) | 23.1802 | 1.63095 | ||||||||
\(203\) | 27.1365 | 1.90461 | ||||||||
\(204\) | 33.3807 | 2.33712 | ||||||||
\(205\) | −7.64549 | −0.533984 | ||||||||
\(206\) | −10.3007 | −0.717684 | ||||||||
\(207\) | −3.64519 | −0.253358 | ||||||||
\(208\) | −8.15350 | −0.565344 | ||||||||
\(209\) | 4.89251 | 0.338422 | ||||||||
\(210\) | −27.9674 | −1.92994 | ||||||||
\(211\) | −2.85902 | −0.196823 | −0.0984116 | − | 0.995146i | \(-0.531376\pi\) | ||||
−0.0984116 | + | 0.995146i | \(0.531376\pi\) | |||||||
\(212\) | 41.4631 | 2.84769 | ||||||||
\(213\) | 22.2853 | 1.52696 | ||||||||
\(214\) | −24.0432 | −1.64356 | ||||||||
\(215\) | −30.6257 | −2.08866 | ||||||||
\(216\) | −29.5182 | −2.00846 | ||||||||
\(217\) | 6.05508 | 0.411045 | ||||||||
\(218\) | 4.98820 | 0.337844 | ||||||||
\(219\) | −13.6876 | −0.924924 | ||||||||
\(220\) | −12.1319 | −0.817931 | ||||||||
\(221\) | 10.4147 | 0.700566 | ||||||||
\(222\) | −6.78106 | −0.455115 | ||||||||
\(223\) | −11.6398 | −0.779460 | −0.389730 | − | 0.920929i | \(-0.627432\pi\) | ||||
−0.389730 | + | 0.920929i | \(0.627432\pi\) | |||||||
\(224\) | 3.39990 | 0.227165 | ||||||||
\(225\) | −4.37790 | −0.291860 | ||||||||
\(226\) | 1.19847 | 0.0797208 | ||||||||
\(227\) | −9.44804 | −0.627088 | −0.313544 | − | 0.949574i | \(-0.601516\pi\) | ||||
−0.313544 | + | 0.949574i | \(0.601516\pi\) | |||||||
\(228\) | 27.1096 | 1.79538 | ||||||||
\(229\) | 10.0854 | 0.666459 | 0.333230 | − | 0.942846i | \(-0.391862\pi\) | ||||
0.333230 | + | 0.942846i | \(0.391862\pi\) | |||||||
\(230\) | −22.3497 | −1.47370 | ||||||||
\(231\) | −3.83746 | −0.252486 | ||||||||
\(232\) | 49.8339 | 3.27176 | ||||||||
\(233\) | −25.7384 | −1.68618 | −0.843091 | − | 0.537772i | \(-0.819266\pi\) | ||||
−0.843091 | + | 0.537772i | \(0.819266\pi\) | |||||||
\(234\) | −5.08243 | −0.332249 | ||||||||
\(235\) | −12.2841 | −0.801329 | ||||||||
\(236\) | 19.0267 | 1.23853 | ||||||||
\(237\) | −11.6003 | −0.753524 | ||||||||
\(238\) | −42.4834 | −2.75379 | ||||||||
\(239\) | 1.51678 | 0.0981123 | 0.0490561 | − | 0.998796i | \(-0.484379\pi\) | ||||
0.0490561 | + | 0.998796i | \(0.484379\pi\) | |||||||
\(240\) | −18.7042 | −1.20735 | ||||||||
\(241\) | 11.0955 | 0.714723 | 0.357361 | − | 0.933966i | \(-0.383676\pi\) | ||||
0.357361 | + | 0.933966i | \(0.383676\pi\) | |||||||
\(242\) | −2.47328 | −0.158988 | ||||||||
\(243\) | −11.5002 | −0.737737 | ||||||||
\(244\) | −60.4643 | −3.87083 | ||||||||
\(245\) | 3.32954 | 0.212717 | ||||||||
\(246\) | −8.63658 | −0.550648 | ||||||||
\(247\) | 8.45810 | 0.538176 | ||||||||
\(248\) | 11.1196 | 0.706098 | ||||||||
\(249\) | 11.7114 | 0.742179 | ||||||||
\(250\) | 9.59787 | 0.607022 | ||||||||
\(251\) | −26.1803 | −1.65248 | −0.826242 | − | 0.563316i | \(-0.809525\pi\) | ||||
−0.826242 | + | 0.563316i | \(0.809525\pi\) | |||||||
\(252\) | 13.9538 | 0.879005 | ||||||||
\(253\) | −3.06664 | −0.192798 | ||||||||
\(254\) | −48.4213 | −3.03822 | ||||||||
\(255\) | 23.8913 | 1.49613 | ||||||||
\(256\) | −32.5915 | −2.03697 | ||||||||
\(257\) | −9.94390 | −0.620284 | −0.310142 | − | 0.950690i | \(-0.600377\pi\) | ||||
−0.310142 | + | 0.950690i | \(0.600377\pi\) | |||||||
\(258\) | −34.5958 | −2.15384 | ||||||||
\(259\) | 5.80855 | 0.360926 | ||||||||
\(260\) | −20.9734 | −1.30072 | ||||||||
\(261\) | 11.3127 | 0.700241 | ||||||||
\(262\) | −41.0849 | −2.53823 | ||||||||
\(263\) | 11.8030 | 0.727805 | 0.363903 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363903 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(264\) | −7.04717 | −0.433723 | ||||||||
\(265\) | 29.6761 | 1.82299 | ||||||||
\(266\) | −34.5023 | −2.11547 | ||||||||
\(267\) | −10.1093 | −0.618680 | ||||||||
\(268\) | −32.1156 | −1.96177 | ||||||||
\(269\) | −12.3852 | −0.755138 | −0.377569 | − | 0.925982i | \(-0.623240\pi\) | ||||
−0.377569 | + | 0.925982i | \(0.623240\pi\) | |||||||
\(270\) | −41.0851 | −2.50036 | ||||||||
\(271\) | 20.1293 | 1.22277 | 0.611383 | − | 0.791335i | \(-0.290614\pi\) | ||||
0.611383 | + | 0.791335i | \(0.290614\pi\) | |||||||
\(272\) | −28.4123 | −1.72275 | ||||||||
\(273\) | −6.63414 | −0.401517 | ||||||||
\(274\) | −9.15199 | −0.552892 | ||||||||
\(275\) | −3.68306 | −0.222097 | ||||||||
\(276\) | −16.9924 | −1.02282 | ||||||||
\(277\) | −8.40085 | −0.504758 | −0.252379 | − | 0.967628i | \(-0.581213\pi\) | ||||
−0.252379 | + | 0.967628i | \(0.581213\pi\) | |||||||
\(278\) | −30.0330 | −1.80126 | ||||||||
\(279\) | 2.52426 | 0.151123 | ||||||||
\(280\) | 43.9940 | 2.62915 | ||||||||
\(281\) | −11.0582 | −0.659675 | −0.329838 | − | 0.944038i | \(-0.606994\pi\) | ||||
−0.329838 | + | 0.944038i | \(0.606994\pi\) | |||||||
\(282\) | −13.8765 | −0.826336 | ||||||||
\(283\) | −22.2760 | −1.32417 | −0.662087 | − | 0.749427i | \(-0.730329\pi\) | ||||
−0.662087 | + | 0.749427i | \(0.730329\pi\) | |||||||
\(284\) | −68.1726 | −4.04530 | ||||||||
\(285\) | 19.4030 | 1.14933 | ||||||||
\(286\) | −4.27577 | −0.252832 | ||||||||
\(287\) | 7.39796 | 0.436688 | ||||||||
\(288\) | 1.41736 | 0.0835186 | ||||||||
\(289\) | 19.2917 | 1.13481 | ||||||||
\(290\) | 69.3617 | 4.07306 | ||||||||
\(291\) | 4.14609 | 0.243048 | ||||||||
\(292\) | 41.8716 | 2.45035 | ||||||||
\(293\) | 27.4214 | 1.60198 | 0.800989 | − | 0.598680i | \(-0.204308\pi\) | ||||
0.800989 | + | 0.598680i | \(0.204308\pi\) | |||||||
\(294\) | 3.76115 | 0.219355 | ||||||||
\(295\) | 13.6179 | 0.792862 | ||||||||
\(296\) | 10.6669 | 0.620001 | ||||||||
\(297\) | −5.63735 | −0.327112 | ||||||||
\(298\) | 23.6949 | 1.37261 | ||||||||
\(299\) | −5.30157 | −0.306598 | ||||||||
\(300\) | −20.4080 | −1.17826 | ||||||||
\(301\) | 29.6342 | 1.70809 | ||||||||
\(302\) | −14.8433 | −0.854134 | ||||||||
\(303\) | 12.6138 | 0.724642 | ||||||||
\(304\) | −23.0746 | −1.32342 | ||||||||
\(305\) | −43.2757 | −2.47796 | ||||||||
\(306\) | −17.7106 | −1.01245 | ||||||||
\(307\) | 20.9564 | 1.19605 | 0.598023 | − | 0.801479i | \(-0.295953\pi\) | ||||
0.598023 | + | 0.801479i | \(0.295953\pi\) | |||||||
\(308\) | 11.7391 | 0.668897 | ||||||||
\(309\) | −5.60524 | −0.318871 | ||||||||
\(310\) | 15.4770 | 0.879033 | ||||||||
\(311\) | −11.5550 | −0.655227 | −0.327613 | − | 0.944812i | \(-0.606244\pi\) | ||||
−0.327613 | + | 0.944812i | \(0.606244\pi\) | |||||||
\(312\) | −12.1831 | −0.689729 | ||||||||
\(313\) | 30.0546 | 1.69879 | 0.849394 | − | 0.527759i | \(-0.176968\pi\) | ||||
0.849394 | + | 0.527759i | \(0.176968\pi\) | |||||||
\(314\) | −7.07342 | −0.399176 | ||||||||
\(315\) | 9.98703 | 0.562705 | ||||||||
\(316\) | 35.4864 | 1.99627 | ||||||||
\(317\) | −11.0222 | −0.619066 | −0.309533 | − | 0.950889i | \(-0.600173\pi\) | ||||
−0.309533 | + | 0.950889i | \(0.600173\pi\) | |||||||
\(318\) | 33.5230 | 1.87988 | ||||||||
\(319\) | 9.51723 | 0.532863 | ||||||||
\(320\) | −19.1049 | −1.06800 | ||||||||
\(321\) | −13.0834 | −0.730242 | ||||||||
\(322\) | 21.6261 | 1.20518 | ||||||||
\(323\) | 29.4737 | 1.63996 | ||||||||
\(324\) | −16.5554 | −0.919742 | ||||||||
\(325\) | −6.36723 | −0.353190 | ||||||||
\(326\) | −12.2832 | −0.680305 | ||||||||
\(327\) | 2.71439 | 0.150106 | ||||||||
\(328\) | 13.5857 | 0.750146 | ||||||||
\(329\) | 11.8864 | 0.655320 | ||||||||
\(330\) | −9.80866 | −0.539949 | ||||||||
\(331\) | −31.0083 | −1.70437 | −0.852186 | − | 0.523239i | \(-0.824723\pi\) | ||||
−0.852186 | + | 0.523239i | \(0.824723\pi\) | |||||||
\(332\) | −35.8261 | −1.96621 | ||||||||
\(333\) | 2.42148 | 0.132696 | ||||||||
\(334\) | −59.9665 | −3.28122 | ||||||||
\(335\) | −22.9859 | −1.25585 | ||||||||
\(336\) | 18.0987 | 0.987362 | ||||||||
\(337\) | 19.4136 | 1.05753 | 0.528764 | − | 0.848769i | \(-0.322656\pi\) | ||||
0.528764 | + | 0.848769i | \(0.322656\pi\) | |||||||
\(338\) | 24.7607 | 1.34680 | ||||||||
\(339\) | 0.652159 | 0.0354204 | ||||||||
\(340\) | −73.0855 | −3.96362 | ||||||||
\(341\) | 2.12362 | 0.115000 | ||||||||
\(342\) | −14.3834 | −0.777764 | ||||||||
\(343\) | 16.7374 | 0.903733 | ||||||||
\(344\) | 54.4207 | 2.93417 | ||||||||
\(345\) | −12.1619 | −0.654772 | ||||||||
\(346\) | 36.9742 | 1.98775 | ||||||||
\(347\) | 23.0518 | 1.23749 | 0.618744 | − | 0.785593i | \(-0.287642\pi\) | ||||
0.618744 | + | 0.785593i | \(0.287642\pi\) | |||||||
\(348\) | 52.7354 | 2.82692 | ||||||||
\(349\) | −14.5280 | −0.777664 | −0.388832 | − | 0.921309i | \(-0.627121\pi\) | ||||
−0.388832 | + | 0.921309i | \(0.627121\pi\) | |||||||
\(350\) | 25.9732 | 1.38832 | ||||||||
\(351\) | −9.74578 | −0.520191 | ||||||||
\(352\) | 1.19240 | 0.0635552 | ||||||||
\(353\) | −17.6495 | −0.939390 | −0.469695 | − | 0.882829i | \(-0.655636\pi\) | ||||
−0.469695 | + | 0.882829i | \(0.655636\pi\) | |||||||
\(354\) | 15.3832 | 0.817606 | ||||||||
\(355\) | −48.7927 | −2.58965 | ||||||||
\(356\) | 30.9252 | 1.63903 | ||||||||
\(357\) | −23.1178 | −1.22353 | ||||||||
\(358\) | 49.0203 | 2.59080 | ||||||||
\(359\) | −18.5507 | −0.979068 | −0.489534 | − | 0.871984i | \(-0.662833\pi\) | ||||
−0.489534 | + | 0.871984i | \(0.662833\pi\) | |||||||
\(360\) | 18.3403 | 0.966621 | ||||||||
\(361\) | 4.93663 | 0.259822 | ||||||||
\(362\) | 55.3487 | 2.90906 | ||||||||
\(363\) | −1.34586 | −0.0706394 | ||||||||
\(364\) | 20.2944 | 1.06372 | ||||||||
\(365\) | 29.9684 | 1.56862 | ||||||||
\(366\) | −48.8855 | −2.55529 | ||||||||
\(367\) | −14.7257 | −0.768677 | −0.384339 | − | 0.923192i | \(-0.625570\pi\) | ||||
−0.384339 | + | 0.923192i | \(0.625570\pi\) | |||||||
\(368\) | 14.4633 | 0.753949 | ||||||||
\(369\) | 3.08408 | 0.160551 | ||||||||
\(370\) | 14.8468 | 0.771850 | ||||||||
\(371\) | −28.7153 | −1.49082 | ||||||||
\(372\) | 11.7671 | 0.610094 | ||||||||
\(373\) | −6.08274 | −0.314952 | −0.157476 | − | 0.987523i | \(-0.550336\pi\) | ||||
−0.157476 | + | 0.987523i | \(0.550336\pi\) | |||||||
\(374\) | −14.8997 | −0.770443 | ||||||||
\(375\) | 5.22279 | 0.269703 | ||||||||
\(376\) | 21.8284 | 1.12572 | ||||||||
\(377\) | 16.4533 | 0.847387 | ||||||||
\(378\) | 39.7549 | 2.04477 | ||||||||
\(379\) | 16.3669 | 0.840710 | 0.420355 | − | 0.907360i | \(-0.361906\pi\) | ||||
0.420355 | + | 0.907360i | \(0.361906\pi\) | |||||||
\(380\) | −59.3553 | −3.04486 | ||||||||
\(381\) | −26.3490 | −1.34990 | ||||||||
\(382\) | −60.6082 | −3.10098 | ||||||||
\(383\) | −13.3470 | −0.681998 | −0.340999 | − | 0.940064i | \(-0.610765\pi\) | ||||
−0.340999 | + | 0.940064i | \(0.610765\pi\) | |||||||
\(384\) | −24.7911 | −1.26512 | ||||||||
\(385\) | 8.40194 | 0.428203 | ||||||||
\(386\) | 28.0036 | 1.42535 | ||||||||
\(387\) | 12.3540 | 0.627988 | ||||||||
\(388\) | −12.6832 | −0.643893 | ||||||||
\(389\) | 35.5734 | 1.80364 | 0.901822 | − | 0.432107i | \(-0.142230\pi\) | ||||
0.901822 | + | 0.432107i | \(0.142230\pi\) | |||||||
\(390\) | −16.9571 | −0.858655 | ||||||||
\(391\) | −18.4742 | −0.934283 | ||||||||
\(392\) | −5.91646 | −0.298827 | ||||||||
\(393\) | −22.3568 | −1.12775 | ||||||||
\(394\) | −31.3359 | −1.57868 | ||||||||
\(395\) | 25.3984 | 1.27793 | ||||||||
\(396\) | 4.89382 | 0.245924 | ||||||||
\(397\) | −4.96886 | −0.249380 | −0.124690 | − | 0.992196i | \(-0.539794\pi\) | ||||
−0.124690 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(398\) | −14.6601 | −0.734844 | ||||||||
\(399\) | −18.7748 | −0.939915 | ||||||||
\(400\) | 17.3705 | 0.868524 | ||||||||
\(401\) | −22.3891 | −1.11806 | −0.559029 | − | 0.829148i | \(-0.688826\pi\) | ||||
−0.559029 | + | 0.829148i | \(0.688826\pi\) | |||||||
\(402\) | −25.9655 | −1.29504 | ||||||||
\(403\) | 3.67128 | 0.182880 | ||||||||
\(404\) | −38.5866 | −1.91975 | ||||||||
\(405\) | −11.8490 | −0.588784 | ||||||||
\(406\) | −67.1161 | −3.33092 | ||||||||
\(407\) | 2.03716 | 0.100978 | ||||||||
\(408\) | −42.4540 | −2.10178 | ||||||||
\(409\) | 20.7219 | 1.02463 | 0.512316 | − | 0.858797i | \(-0.328788\pi\) | ||||
0.512316 | + | 0.858797i | \(0.328788\pi\) | |||||||
\(410\) | 18.9094 | 0.933869 | ||||||||
\(411\) | −4.98016 | −0.245653 | ||||||||
\(412\) | 17.1469 | 0.844767 | ||||||||
\(413\) | −13.1770 | −0.648396 | ||||||||
\(414\) | 9.01556 | 0.443091 | ||||||||
\(415\) | −25.6416 | −1.25869 | ||||||||
\(416\) | 2.06141 | 0.101069 | ||||||||
\(417\) | −16.3428 | −0.800311 | ||||||||
\(418\) | −12.1005 | −0.591856 | ||||||||
\(419\) | −13.9473 | −0.681373 | −0.340686 | − | 0.940177i | \(-0.610659\pi\) | ||||
−0.340686 | + | 0.940177i | \(0.610659\pi\) | |||||||
\(420\) | 46.5555 | 2.27168 | ||||||||
\(421\) | −25.1352 | −1.22501 | −0.612506 | − | 0.790466i | \(-0.709839\pi\) | ||||
−0.612506 | + | 0.790466i | \(0.709839\pi\) | |||||||
\(422\) | 7.07116 | 0.344219 | ||||||||
\(423\) | 4.95524 | 0.240932 | ||||||||
\(424\) | −52.7332 | −2.56095 | ||||||||
\(425\) | −22.1877 | −1.07626 | ||||||||
\(426\) | −55.1177 | −2.67046 | ||||||||
\(427\) | 41.8746 | 2.02645 | ||||||||
\(428\) | 40.0231 | 1.93459 | ||||||||
\(429\) | −2.32671 | −0.112334 | ||||||||
\(430\) | 75.7459 | 3.65279 | ||||||||
\(431\) | 21.1769 | 1.02006 | 0.510028 | − | 0.860158i | \(-0.329635\pi\) | ||||
0.510028 | + | 0.860158i | \(0.329635\pi\) | |||||||
\(432\) | 26.5875 | 1.27919 | ||||||||
\(433\) | 23.1733 | 1.11364 | 0.556819 | − | 0.830634i | \(-0.312022\pi\) | ||||
0.556819 | + | 0.830634i | \(0.312022\pi\) | |||||||
\(434\) | −14.9759 | −0.718866 | ||||||||
\(435\) | 37.7440 | 1.80968 | ||||||||
\(436\) | −8.30353 | −0.397667 | ||||||||
\(437\) | −15.0036 | −0.717718 | ||||||||
\(438\) | 33.8533 | 1.61757 | ||||||||
\(439\) | −12.2394 | −0.584152 | −0.292076 | − | 0.956395i | \(-0.594346\pi\) | ||||
−0.292076 | + | 0.956395i | \(0.594346\pi\) | |||||||
\(440\) | 15.4295 | 0.735571 | ||||||||
\(441\) | −1.34309 | −0.0639566 | ||||||||
\(442\) | −25.7583 | −1.22520 | ||||||||
\(443\) | 9.69077 | 0.460423 | 0.230211 | − | 0.973141i | \(-0.426058\pi\) | ||||
0.230211 | + | 0.973141i | \(0.426058\pi\) | |||||||
\(444\) | 11.2880 | 0.535704 | ||||||||
\(445\) | 22.1339 | 1.04925 | ||||||||
\(446\) | 28.7885 | 1.36318 | ||||||||
\(447\) | 12.8938 | 0.609858 | ||||||||
\(448\) | 18.4864 | 0.873400 | ||||||||
\(449\) | −21.6836 | −1.02331 | −0.511657 | − | 0.859190i | \(-0.670968\pi\) | ||||
−0.511657 | + | 0.859190i | \(0.670968\pi\) | |||||||
\(450\) | 10.8278 | 0.510425 | ||||||||
\(451\) | 2.59459 | 0.122174 | ||||||||
\(452\) | −1.99501 | −0.0938373 | ||||||||
\(453\) | −8.07712 | −0.379496 | ||||||||
\(454\) | 23.3676 | 1.09670 | ||||||||
\(455\) | 14.5252 | 0.680950 | ||||||||
\(456\) | −34.4783 | −1.61459 | ||||||||
\(457\) | 6.22311 | 0.291105 | 0.145552 | − | 0.989351i | \(-0.453504\pi\) | ||||
0.145552 | + | 0.989351i | \(0.453504\pi\) | |||||||
\(458\) | −24.9439 | −1.16555 | ||||||||
\(459\) | −33.9609 | −1.58516 | ||||||||
\(460\) | 37.2041 | 1.73465 | ||||||||
\(461\) | 12.0412 | 0.560813 | 0.280406 | − | 0.959881i | \(-0.409531\pi\) | ||||
0.280406 | + | 0.959881i | \(0.409531\pi\) | |||||||
\(462\) | 9.49109 | 0.441566 | ||||||||
\(463\) | 25.3485 | 1.17805 | 0.589023 | − | 0.808116i | \(-0.299513\pi\) | ||||
0.589023 | + | 0.808116i | \(0.299513\pi\) | |||||||
\(464\) | −44.8863 | −2.08379 | ||||||||
\(465\) | 8.42196 | 0.390559 | ||||||||
\(466\) | 63.6583 | 2.94891 | ||||||||
\(467\) | −38.0466 | −1.76059 | −0.880293 | − | 0.474430i | \(-0.842654\pi\) | ||||
−0.880293 | + | 0.474430i | \(0.842654\pi\) | |||||||
\(468\) | 8.46038 | 0.391081 | ||||||||
\(469\) | 22.2417 | 1.02702 | ||||||||
\(470\) | 30.3821 | 1.40142 | ||||||||
\(471\) | −3.84908 | −0.177356 | ||||||||
\(472\) | −24.1984 | −1.11382 | ||||||||
\(473\) | 10.3932 | 0.477881 | ||||||||
\(474\) | 28.6909 | 1.31782 | ||||||||
\(475\) | −18.0194 | −0.826787 | ||||||||
\(476\) | 70.7193 | 3.24142 | ||||||||
\(477\) | −11.9709 | −0.548110 | ||||||||
\(478\) | −3.75142 | −0.171586 | ||||||||
\(479\) | −19.3242 | −0.882945 | −0.441472 | − | 0.897275i | \(-0.645544\pi\) | ||||
−0.441472 | + | 0.897275i | \(0.645544\pi\) | |||||||
\(480\) | 4.72889 | 0.215843 | ||||||||
\(481\) | 3.52181 | 0.160581 | ||||||||
\(482\) | −27.4422 | −1.24996 | ||||||||
\(483\) | 11.7681 | 0.535467 | ||||||||
\(484\) | 4.11710 | 0.187141 | ||||||||
\(485\) | −9.07768 | −0.412196 | ||||||||
\(486\) | 28.4431 | 1.29021 | ||||||||
\(487\) | 36.9264 | 1.67330 | 0.836648 | − | 0.547741i | \(-0.184512\pi\) | ||||
0.836648 | + | 0.547741i | \(0.184512\pi\) | |||||||
\(488\) | 76.8992 | 3.48106 | ||||||||
\(489\) | −6.68405 | −0.302263 | ||||||||
\(490\) | −8.23488 | −0.372014 | ||||||||
\(491\) | −1.06706 | −0.0481558 | −0.0240779 | − | 0.999710i | \(-0.507665\pi\) | ||||
−0.0240779 | + | 0.999710i | \(0.507665\pi\) | |||||||
\(492\) | 14.3767 | 0.648153 | ||||||||
\(493\) | 57.3343 | 2.58221 | ||||||||
\(494\) | −20.9192 | −0.941201 | ||||||||
\(495\) | 3.50262 | 0.157431 | ||||||||
\(496\) | −10.0157 | −0.449716 | ||||||||
\(497\) | 47.2130 | 2.11779 | ||||||||
\(498\) | −28.9655 | −1.29798 | ||||||||
\(499\) | 21.8418 | 0.977775 | 0.488888 | − | 0.872347i | \(-0.337403\pi\) | ||||
0.488888 | + | 0.872347i | \(0.337403\pi\) | |||||||
\(500\) | −15.9769 | −0.714510 | ||||||||
\(501\) | −32.6314 | −1.45787 | ||||||||
\(502\) | 64.7510 | 2.88998 | ||||||||
\(503\) | −38.3443 | −1.70969 | −0.854843 | − | 0.518887i | \(-0.826347\pi\) | ||||
−0.854843 | + | 0.518887i | \(0.826347\pi\) | |||||||
\(504\) | −17.7466 | −0.790495 | ||||||||
\(505\) | −27.6173 | −1.22895 | ||||||||
\(506\) | 7.58466 | 0.337179 | ||||||||
\(507\) | 13.4738 | 0.598393 | ||||||||
\(508\) | 80.6037 | 3.57621 | ||||||||
\(509\) | −9.43955 | −0.418401 | −0.209200 | − | 0.977873i | \(-0.567086\pi\) | ||||
−0.209200 | + | 0.977873i | \(0.567086\pi\) | |||||||
\(510\) | −59.0899 | −2.61654 | ||||||||
\(511\) | −28.9982 | −1.28280 | ||||||||
\(512\) | 43.7672 | 1.93425 | ||||||||
\(513\) | −27.5808 | −1.21772 | ||||||||
\(514\) | 24.5940 | 1.08480 | ||||||||
\(515\) | 12.2724 | 0.540788 | ||||||||
\(516\) | 57.5893 | 2.53523 | ||||||||
\(517\) | 4.16877 | 0.183342 | ||||||||
\(518\) | −14.3661 | −0.631212 | ||||||||
\(519\) | 20.1199 | 0.883168 | ||||||||
\(520\) | 26.6742 | 1.16974 | ||||||||
\(521\) | 27.6098 | 1.20961 | 0.604803 | − | 0.796375i | \(-0.293252\pi\) | ||||
0.604803 | + | 0.796375i | \(0.293252\pi\) | |||||||
\(522\) | −27.9795 | −1.22463 | ||||||||
\(523\) | 3.62718 | 0.158605 | 0.0793027 | − | 0.996851i | \(-0.474731\pi\) | ||||
0.0793027 | + | 0.996851i | \(0.474731\pi\) | |||||||
\(524\) | 68.3912 | 2.98768 | ||||||||
\(525\) | 14.1336 | 0.616840 | ||||||||
\(526\) | −29.1921 | −1.27284 | ||||||||
\(527\) | 12.7932 | 0.557282 | ||||||||
\(528\) | 6.34750 | 0.276240 | ||||||||
\(529\) | −13.5957 | −0.591118 | ||||||||
\(530\) | −73.3971 | −3.18817 | ||||||||
\(531\) | −5.49325 | −0.238387 | ||||||||
\(532\) | 57.4336 | 2.49006 | ||||||||
\(533\) | 4.48549 | 0.194288 | ||||||||
\(534\) | 25.0032 | 1.08199 | ||||||||
\(535\) | 28.6454 | 1.23845 | ||||||||
\(536\) | 40.8450 | 1.76423 | ||||||||
\(537\) | 26.6749 | 1.15111 | ||||||||
\(538\) | 30.6320 | 1.32064 | ||||||||
\(539\) | −1.12992 | −0.0486691 | ||||||||
\(540\) | 68.3916 | 2.94311 | ||||||||
\(541\) | 0.119301 | 0.00512916 | 0.00256458 | − | 0.999997i | \(-0.499184\pi\) | ||||
0.00256458 | + | 0.999997i | \(0.499184\pi\) | |||||||
\(542\) | −49.7852 | −2.13846 | ||||||||
\(543\) | 30.1186 | 1.29251 | ||||||||
\(544\) | 7.18333 | 0.307983 | ||||||||
\(545\) | −5.94303 | −0.254571 | ||||||||
\(546\) | 16.4081 | 0.702201 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 15.2347 | 0.650795 | ||||||||
\(549\) | 17.4568 | 0.745037 | ||||||||
\(550\) | 9.10923 | 0.388419 | ||||||||
\(551\) | 46.5631 | 1.98366 | ||||||||
\(552\) | 21.6111 | 0.919831 | ||||||||
\(553\) | −24.5762 | −1.04508 | ||||||||
\(554\) | 20.7776 | 0.882757 | ||||||||
\(555\) | 8.07906 | 0.342937 | ||||||||
\(556\) | 49.9940 | 2.12022 | ||||||||
\(557\) | −17.7576 | −0.752415 | −0.376208 | − | 0.926535i | \(-0.622772\pi\) | ||||
−0.376208 | + | 0.926535i | \(0.622772\pi\) | |||||||
\(558\) | −6.24318 | −0.264295 | ||||||||
\(559\) | 17.9677 | 0.759951 | ||||||||
\(560\) | −39.6262 | −1.67451 | ||||||||
\(561\) | −8.10782 | −0.342312 | ||||||||
\(562\) | 27.3499 | 1.15369 | ||||||||
\(563\) | 10.3785 | 0.437402 | 0.218701 | − | 0.975792i | \(-0.429818\pi\) | ||||
0.218701 | + | 0.975792i | \(0.429818\pi\) | |||||||
\(564\) | 23.0994 | 0.972658 | ||||||||
\(565\) | −1.42787 | −0.0600711 | ||||||||
\(566\) | 55.0948 | 2.31581 | ||||||||
\(567\) | 11.4654 | 0.481503 | ||||||||
\(568\) | 86.7027 | 3.63796 | ||||||||
\(569\) | −4.73917 | −0.198676 | −0.0993381 | − | 0.995054i | \(-0.531673\pi\) | ||||
−0.0993381 | + | 0.995054i | \(0.531673\pi\) | |||||||
\(570\) | −47.9889 | −2.01003 | ||||||||
\(571\) | −4.72994 | −0.197942 | −0.0989709 | − | 0.995090i | \(-0.531555\pi\) | ||||
−0.0989709 | + | 0.995090i | \(0.531555\pi\) | |||||||
\(572\) | 7.11759 | 0.297601 | ||||||||
\(573\) | −32.9806 | −1.37778 | ||||||||
\(574\) | −18.2972 | −0.763710 | ||||||||
\(575\) | 11.2946 | 0.471019 | ||||||||
\(576\) | 7.70665 | 0.321110 | ||||||||
\(577\) | −19.7444 | −0.821971 | −0.410986 | − | 0.911642i | \(-0.634815\pi\) | ||||
−0.410986 | + | 0.911642i | \(0.634815\pi\) | |||||||
\(578\) | −47.7137 | −1.98463 | ||||||||
\(579\) | 15.2385 | 0.633289 | ||||||||
\(580\) | −115.462 | −4.79429 | ||||||||
\(581\) | 24.8114 | 1.02935 | ||||||||
\(582\) | −10.2544 | −0.425060 | ||||||||
\(583\) | −10.0709 | −0.417096 | ||||||||
\(584\) | −53.2527 | −2.20361 | ||||||||
\(585\) | 6.05529 | 0.250355 | ||||||||
\(586\) | −67.8208 | −2.80165 | ||||||||
\(587\) | 20.7071 | 0.854675 | 0.427338 | − | 0.904092i | \(-0.359452\pi\) | ||||
0.427338 | + | 0.904092i | \(0.359452\pi\) | |||||||
\(588\) | −6.26094 | −0.258197 | ||||||||
\(589\) | 10.3898 | 0.428105 | ||||||||
\(590\) | −33.6807 | −1.38661 | ||||||||
\(591\) | −17.0518 | −0.701417 | ||||||||
\(592\) | −9.60787 | −0.394881 | ||||||||
\(593\) | −13.2597 | −0.544510 | −0.272255 | − | 0.962225i | \(-0.587769\pi\) | ||||
−0.272255 | + | 0.962225i | \(0.587769\pi\) | |||||||
\(594\) | 13.9427 | 0.572077 | ||||||||
\(595\) | 50.6155 | 2.07503 | ||||||||
\(596\) | −39.4433 | −1.61566 | ||||||||
\(597\) | −7.97745 | −0.326495 | ||||||||
\(598\) | 13.1123 | 0.536200 | ||||||||
\(599\) | −8.90443 | −0.363825 | −0.181913 | − | 0.983315i | \(-0.558229\pi\) | ||||
−0.181913 | + | 0.983315i | \(0.558229\pi\) | |||||||
\(600\) | 25.9551 | 1.05961 | ||||||||
\(601\) | 23.6532 | 0.964836 | 0.482418 | − | 0.875941i | \(-0.339759\pi\) | ||||
0.482418 | + | 0.875941i | \(0.339759\pi\) | |||||||
\(602\) | −73.2936 | −2.98722 | ||||||||
\(603\) | 9.27216 | 0.377592 | ||||||||
\(604\) | 24.7086 | 1.00538 | ||||||||
\(605\) | 2.94670 | 0.119801 | ||||||||
\(606\) | −31.1974 | −1.26731 | ||||||||
\(607\) | 44.2974 | 1.79797 | 0.898987 | − | 0.437975i | \(-0.144304\pi\) | ||||
0.898987 | + | 0.437975i | \(0.144304\pi\) | |||||||
\(608\) | 5.83383 | 0.236593 | ||||||||
\(609\) | −36.5220 | −1.47994 | ||||||||
\(610\) | 107.033 | 4.33363 | ||||||||
\(611\) | 7.20692 | 0.291561 | ||||||||
\(612\) | 29.4817 | 1.19173 | ||||||||
\(613\) | −11.5228 | −0.465400 | −0.232700 | − | 0.972549i | \(-0.574756\pi\) | ||||
−0.232700 | + | 0.972549i | \(0.574756\pi\) | |||||||
\(614\) | −51.8310 | −2.09173 | ||||||||
\(615\) | 10.2898 | 0.414923 | ||||||||
\(616\) | −14.9299 | −0.601544 | ||||||||
\(617\) | 12.4727 | 0.502132 | 0.251066 | − | 0.967970i | \(-0.419219\pi\) | ||||
0.251066 | + | 0.967970i | \(0.419219\pi\) | |||||||
\(618\) | 13.8633 | 0.557665 | ||||||||
\(619\) | 12.3058 | 0.494614 | 0.247307 | − | 0.968937i | \(-0.420454\pi\) | ||||
0.247307 | + | 0.968937i | \(0.420454\pi\) | |||||||
\(620\) | −25.7635 | −1.03469 | ||||||||
\(621\) | 17.2877 | 0.693733 | ||||||||
\(622\) | 28.5788 | 1.14591 | ||||||||
\(623\) | −21.4173 | −0.858066 | ||||||||
\(624\) | 10.9735 | 0.439291 | ||||||||
\(625\) | −29.8504 | −1.19401 | ||||||||
\(626\) | −74.3334 | −2.97096 | ||||||||
\(627\) | −6.58464 | −0.262965 | ||||||||
\(628\) | 11.7746 | 0.469860 | ||||||||
\(629\) | 12.2724 | 0.489331 | ||||||||
\(630\) | −24.7007 | −0.984099 | ||||||||
\(631\) | 24.5884 | 0.978850 | 0.489425 | − | 0.872045i | \(-0.337207\pi\) | ||||
0.489425 | + | 0.872045i | \(0.337207\pi\) | |||||||
\(632\) | −45.1320 | −1.79526 | ||||||||
\(633\) | 3.84785 | 0.152938 | ||||||||
\(634\) | 27.2608 | 1.08267 | ||||||||
\(635\) | 57.6899 | 2.28936 | ||||||||
\(636\) | −55.8035 | −2.21275 | ||||||||
\(637\) | −1.95339 | −0.0773962 | ||||||||
\(638\) | −23.5388 | −0.931908 | ||||||||
\(639\) | 19.6823 | 0.778618 | ||||||||
\(640\) | 54.2791 | 2.14557 | ||||||||
\(641\) | 17.2955 | 0.683131 | 0.341566 | − | 0.939858i | \(-0.389043\pi\) | ||||
0.341566 | + | 0.939858i | \(0.389043\pi\) | |||||||
\(642\) | 32.3588 | 1.27710 | ||||||||
\(643\) | 13.1943 | 0.520334 | 0.260167 | − | 0.965564i | \(-0.416222\pi\) | ||||
0.260167 | + | 0.965564i | \(0.416222\pi\) | |||||||
\(644\) | −35.9996 | −1.41858 | ||||||||
\(645\) | 41.2180 | 1.62296 | ||||||||
\(646\) | −72.8967 | −2.86808 | ||||||||
\(647\) | 40.6351 | 1.59753 | 0.798765 | − | 0.601643i | \(-0.205487\pi\) | ||||
0.798765 | + | 0.601643i | \(0.205487\pi\) | |||||||
\(648\) | 21.0553 | 0.827130 | ||||||||
\(649\) | −4.62139 | −0.181405 | ||||||||
\(650\) | 15.7479 | 0.617684 | ||||||||
\(651\) | −8.14929 | −0.319396 | ||||||||
\(652\) | 20.4471 | 0.800769 | ||||||||
\(653\) | −26.3499 | −1.03115 | −0.515575 | − | 0.856844i | \(-0.672422\pi\) | ||||
−0.515575 | + | 0.856844i | \(0.672422\pi\) | |||||||
\(654\) | −6.71343 | −0.262516 | ||||||||
\(655\) | 48.9492 | 1.91260 | ||||||||
\(656\) | −12.2369 | −0.477771 | ||||||||
\(657\) | −12.0888 | −0.471631 | ||||||||
\(658\) | −29.3984 | −1.14607 | ||||||||
\(659\) | 38.5793 | 1.50283 | 0.751417 | − | 0.659827i | \(-0.229371\pi\) | ||||
0.751417 | + | 0.659827i | \(0.229371\pi\) | |||||||
\(660\) | 16.3278 | 0.635559 | ||||||||
\(661\) | 12.3498 | 0.480351 | 0.240176 | − | 0.970729i | \(-0.422795\pi\) | ||||
0.240176 | + | 0.970729i | \(0.422795\pi\) | |||||||
\(662\) | 76.6922 | 2.98073 | ||||||||
\(663\) | −14.0167 | −0.544363 | ||||||||
\(664\) | 45.5640 | 1.76823 | ||||||||
\(665\) | 41.1066 | 1.59404 | ||||||||
\(666\) | −5.98899 | −0.232069 | ||||||||
\(667\) | −29.1860 | −1.13008 | ||||||||
\(668\) | 99.8223 | 3.86224 | ||||||||
\(669\) | 15.6656 | 0.605667 | ||||||||
\(670\) | 56.8504 | 2.19632 | ||||||||
\(671\) | 14.6861 | 0.566952 | ||||||||
\(672\) | −4.57579 | −0.176515 | ||||||||
\(673\) | −41.2498 | −1.59006 | −0.795031 | − | 0.606568i | \(-0.792546\pi\) | ||||
−0.795031 | + | 0.606568i | \(0.792546\pi\) | |||||||
\(674\) | −48.0153 | −1.84948 | ||||||||
\(675\) | 20.7627 | 0.799157 | ||||||||
\(676\) | −41.2175 | −1.58529 | ||||||||
\(677\) | 20.4798 | 0.787104 | 0.393552 | − | 0.919302i | \(-0.371246\pi\) | ||||
0.393552 | + | 0.919302i | \(0.371246\pi\) | |||||||
\(678\) | −1.61297 | −0.0619457 | ||||||||
\(679\) | 8.78378 | 0.337090 | ||||||||
\(680\) | 92.9511 | 3.56451 | ||||||||
\(681\) | 12.7157 | 0.487269 | ||||||||
\(682\) | −5.25230 | −0.201121 | ||||||||
\(683\) | −48.8368 | −1.86869 | −0.934344 | − | 0.356371i | \(-0.884014\pi\) | ||||
−0.934344 | + | 0.356371i | \(0.884014\pi\) | |||||||
\(684\) | 23.9431 | 0.915486 | ||||||||
\(685\) | 10.9038 | 0.416614 | ||||||||
\(686\) | −41.3961 | −1.58051 | ||||||||
\(687\) | −13.5735 | −0.517861 | ||||||||
\(688\) | −49.0177 | −1.86878 | ||||||||
\(689\) | −17.4105 | −0.663287 | ||||||||
\(690\) | 30.0796 | 1.14511 | ||||||||
\(691\) | 1.68571 | 0.0641275 | 0.0320637 | − | 0.999486i | \(-0.489792\pi\) | ||||
0.0320637 | + | 0.999486i | \(0.489792\pi\) | |||||||
\(692\) | −61.5486 | −2.33973 | ||||||||
\(693\) | −3.38922 | −0.128746 | ||||||||
\(694\) | −57.0136 | −2.16421 | ||||||||
\(695\) | 35.7819 | 1.35728 | ||||||||
\(696\) | −67.0695 | −2.54226 | ||||||||
\(697\) | 15.6305 | 0.592047 | ||||||||
\(698\) | 35.9317 | 1.36003 | ||||||||
\(699\) | 34.6404 | 1.31022 | ||||||||
\(700\) | −43.2358 | −1.63416 | ||||||||
\(701\) | −45.6853 | −1.72551 | −0.862756 | − | 0.505621i | \(-0.831263\pi\) | ||||
−0.862756 | + | 0.505621i | \(0.831263\pi\) | |||||||
\(702\) | 24.1040 | 0.909748 | ||||||||
\(703\) | 9.96680 | 0.375905 | ||||||||
\(704\) | 6.48349 | 0.244356 | ||||||||
\(705\) | 16.5327 | 0.622659 | ||||||||
\(706\) | 43.6522 | 1.64287 | ||||||||
\(707\) | 26.7232 | 1.00503 | ||||||||
\(708\) | −25.6073 | −0.962382 | ||||||||
\(709\) | −30.4771 | −1.14459 | −0.572296 | − | 0.820047i | \(-0.693947\pi\) | ||||
−0.572296 | + | 0.820047i | \(0.693947\pi\) | |||||||
\(710\) | 120.678 | 4.52896 | ||||||||
\(711\) | −10.2454 | −0.384231 | ||||||||
\(712\) | −39.3311 | −1.47400 | ||||||||
\(713\) | −6.51238 | −0.243891 | ||||||||
\(714\) | 57.1768 | 2.13979 | ||||||||
\(715\) | 5.09422 | 0.190513 | ||||||||
\(716\) | −81.6008 | −3.04957 | ||||||||
\(717\) | −2.04137 | −0.0762365 | ||||||||
\(718\) | 45.8810 | 1.71226 | ||||||||
\(719\) | −35.6273 | −1.32867 | −0.664337 | − | 0.747433i | \(-0.731286\pi\) | ||||
−0.664337 | + | 0.747433i | \(0.731286\pi\) | |||||||
\(720\) | −16.5195 | −0.615644 | ||||||||
\(721\) | −11.8751 | −0.442252 | ||||||||
\(722\) | −12.2096 | −0.454396 | ||||||||
\(723\) | −14.9330 | −0.555364 | ||||||||
\(724\) | −92.1353 | −3.42418 | ||||||||
\(725\) | −35.0526 | −1.30182 | ||||||||
\(726\) | 3.32869 | 0.123539 | ||||||||
\(727\) | −14.8843 | −0.552028 | −0.276014 | − | 0.961154i | \(-0.589014\pi\) | ||||
−0.276014 | + | 0.961154i | \(0.589014\pi\) | |||||||
\(728\) | −25.8106 | −0.956606 | ||||||||
\(729\) | 27.5410 | 1.02004 | ||||||||
\(730\) | −74.1203 | −2.74331 | ||||||||
\(731\) | 62.6115 | 2.31577 | ||||||||
\(732\) | 81.3765 | 3.00776 | ||||||||
\(733\) | 36.0575 | 1.33181 | 0.665907 | − | 0.746035i | \(-0.268045\pi\) | ||||
0.665907 | + | 0.746035i | \(0.268045\pi\) | |||||||
\(734\) | 36.4208 | 1.34432 | ||||||||
\(735\) | −4.48110 | −0.165288 | ||||||||
\(736\) | −3.65667 | −0.134787 | ||||||||
\(737\) | 7.80053 | 0.287336 | ||||||||
\(738\) | −7.62778 | −0.280783 | ||||||||
\(739\) | −24.3289 | −0.894954 | −0.447477 | − | 0.894295i | \(-0.647677\pi\) | ||||
−0.447477 | + | 0.894295i | \(0.647677\pi\) | |||||||
\(740\) | −24.7145 | −0.908524 | ||||||||
\(741\) | −11.3834 | −0.418181 | ||||||||
\(742\) | 71.0208 | 2.60726 | ||||||||
\(743\) | −24.1041 | −0.884293 | −0.442146 | − | 0.896943i | \(-0.645783\pi\) | ||||
−0.442146 | + | 0.896943i | \(0.645783\pi\) | |||||||
\(744\) | −14.9655 | −0.548662 | ||||||||
\(745\) | −28.2305 | −1.03429 | ||||||||
\(746\) | 15.0443 | 0.550811 | ||||||||
\(747\) | 10.3434 | 0.378447 | ||||||||
\(748\) | 24.8025 | 0.906868 | ||||||||
\(749\) | −27.7180 | −1.01279 | ||||||||
\(750\) | −12.9174 | −0.471677 | ||||||||
\(751\) | 47.9202 | 1.74863 | 0.874317 | − | 0.485355i | \(-0.161310\pi\) | ||||
0.874317 | + | 0.485355i | \(0.161310\pi\) | |||||||
\(752\) | −19.6612 | −0.716972 | ||||||||
\(753\) | 35.2350 | 1.28403 | ||||||||
\(754\) | −40.6935 | −1.48197 | ||||||||
\(755\) | 17.6845 | 0.643605 | ||||||||
\(756\) | −66.1774 | −2.40685 | ||||||||
\(757\) | 39.8742 | 1.44925 | 0.724625 | − | 0.689143i | \(-0.242013\pi\) | ||||
0.724625 | + | 0.689143i | \(0.242013\pi\) | |||||||
\(758\) | −40.4798 | −1.47029 | ||||||||
\(759\) | 4.12728 | 0.149811 | ||||||||
\(760\) | 75.4887 | 2.73826 | ||||||||
\(761\) | −16.5601 | −0.600303 | −0.300151 | − | 0.953892i | \(-0.597037\pi\) | ||||
−0.300151 | + | 0.953892i | \(0.597037\pi\) | |||||||
\(762\) | 65.1683 | 2.36080 | ||||||||
\(763\) | 5.75062 | 0.208186 | ||||||||
\(764\) | 100.890 | 3.65009 | ||||||||
\(765\) | 21.1007 | 0.762897 | ||||||||
\(766\) | 33.0107 | 1.19273 | ||||||||
\(767\) | −7.98940 | −0.288480 | ||||||||
\(768\) | 43.8636 | 1.58279 | ||||||||
\(769\) | 12.8474 | 0.463288 | 0.231644 | − | 0.972801i | \(-0.425590\pi\) | ||||
0.231644 | + | 0.972801i | \(0.425590\pi\) | |||||||
\(770\) | −20.7803 | −0.748871 | ||||||||
\(771\) | 13.3831 | 0.481981 | ||||||||
\(772\) | −46.6157 | −1.67774 | ||||||||
\(773\) | 3.37971 | 0.121560 | 0.0607798 | − | 0.998151i | \(-0.480641\pi\) | ||||
0.0607798 | + | 0.998151i | \(0.480641\pi\) | |||||||
\(774\) | −30.5548 | −1.09827 | ||||||||
\(775\) | −7.82142 | −0.280954 | ||||||||
\(776\) | 16.1307 | 0.579057 | ||||||||
\(777\) | −7.81750 | −0.280451 | ||||||||
\(778\) | −87.9830 | −3.15434 | ||||||||
\(779\) | 12.6940 | 0.454811 | ||||||||
\(780\) | 28.2273 | 1.01070 | ||||||||
\(781\) | 16.5584 | 0.592506 | ||||||||
\(782\) | 45.6919 | 1.63394 | ||||||||
\(783\) | −53.6520 | −1.91737 | ||||||||
\(784\) | 5.32906 | 0.190324 | ||||||||
\(785\) | 8.42739 | 0.300786 | ||||||||
\(786\) | 55.2945 | 1.97229 | ||||||||
\(787\) | −46.3437 | −1.65198 | −0.825988 | − | 0.563688i | \(-0.809382\pi\) | ||||
−0.825988 | + | 0.563688i | \(0.809382\pi\) | |||||||
\(788\) | 52.1628 | 1.85822 | ||||||||
\(789\) | −15.8852 | −0.565529 | ||||||||
\(790\) | −62.8174 | −2.23494 | ||||||||
\(791\) | 1.38164 | 0.0491256 | ||||||||
\(792\) | −6.22402 | −0.221161 | ||||||||
\(793\) | 25.3892 | 0.901597 | ||||||||
\(794\) | 12.2894 | 0.436133 | ||||||||
\(795\) | −39.9399 | −1.41652 | ||||||||
\(796\) | 24.4037 | 0.864966 | ||||||||
\(797\) | −31.2883 | −1.10829 | −0.554145 | − | 0.832420i | \(-0.686955\pi\) | ||||
−0.554145 | + | 0.832420i | \(0.686955\pi\) | |||||||
\(798\) | 46.4352 | 1.64379 | ||||||||
\(799\) | 25.1138 | 0.888461 | ||||||||
\(800\) | −4.39169 | −0.155270 | ||||||||
\(801\) | −8.92850 | −0.315473 | ||||||||
\(802\) | 55.3745 | 1.95534 | ||||||||
\(803\) | −10.1702 | −0.358897 | ||||||||
\(804\) | 43.2231 | 1.52436 | ||||||||
\(805\) | −25.7657 | −0.908123 | ||||||||
\(806\) | −9.08011 | −0.319833 | ||||||||
\(807\) | 16.6687 | 0.586767 | ||||||||
\(808\) | 49.0749 | 1.72645 | ||||||||
\(809\) | −2.21503 | −0.0778761 | −0.0389381 | − | 0.999242i | \(-0.512398\pi\) | ||||
−0.0389381 | + | 0.999242i | \(0.512398\pi\) | |||||||
\(810\) | 29.3060 | 1.02971 | ||||||||
\(811\) | −21.2640 | −0.746681 | −0.373340 | − | 0.927694i | \(-0.621788\pi\) | ||||
−0.373340 | + | 0.927694i | \(0.621788\pi\) | |||||||
\(812\) | 111.724 | 3.92073 | ||||||||
\(813\) | −27.0912 | −0.950129 | ||||||||
\(814\) | −5.03845 | −0.176598 | ||||||||
\(815\) | 14.6344 | 0.512622 | ||||||||
\(816\) | 38.2390 | 1.33863 | ||||||||
\(817\) | 50.8489 | 1.77898 | ||||||||
\(818\) | −51.2510 | −1.79195 | ||||||||
\(819\) | −5.85924 | −0.204739 | ||||||||
\(820\) | −31.4772 | −1.09923 | ||||||||
\(821\) | 30.7599 | 1.07353 | 0.536764 | − | 0.843733i | \(-0.319647\pi\) | ||||
0.536764 | + | 0.843733i | \(0.319647\pi\) | |||||||
\(822\) | 12.3173 | 0.429615 | ||||||||
\(823\) | 18.3193 | 0.638570 | 0.319285 | − | 0.947659i | \(-0.396557\pi\) | ||||
0.319285 | + | 0.947659i | \(0.396557\pi\) | |||||||
\(824\) | −21.8076 | −0.759705 | ||||||||
\(825\) | 4.95689 | 0.172577 | ||||||||
\(826\) | 32.5903 | 1.13396 | ||||||||
\(827\) | −20.2249 | −0.703288 | −0.351644 | − | 0.936134i | \(-0.614377\pi\) | ||||
−0.351644 | + | 0.936134i | \(0.614377\pi\) | |||||||
\(828\) | −15.0076 | −0.521550 | ||||||||
\(829\) | 12.8392 | 0.445923 | 0.222962 | − | 0.974827i | \(-0.428428\pi\) | ||||
0.222962 | + | 0.974827i | \(0.428428\pi\) | |||||||
\(830\) | 63.4187 | 2.20129 | ||||||||
\(831\) | 11.3064 | 0.392214 | ||||||||
\(832\) | 11.2086 | 0.388587 | ||||||||
\(833\) | −6.80694 | −0.235846 | ||||||||
\(834\) | 40.4203 | 1.39964 | ||||||||
\(835\) | 71.4451 | 2.47246 | ||||||||
\(836\) | 20.1429 | 0.696658 | ||||||||
\(837\) | −11.9716 | −0.413799 | ||||||||
\(838\) | 34.4957 | 1.19163 | ||||||||
\(839\) | −0.367383 | −0.0126835 | −0.00634173 | − | 0.999980i | \(-0.502019\pi\) | ||||
−0.00634173 | + | 0.999980i | \(0.502019\pi\) | |||||||
\(840\) | −59.2099 | −2.04293 | ||||||||
\(841\) | 61.5777 | 2.12337 | ||||||||
\(842\) | 62.1662 | 2.14239 | ||||||||
\(843\) | 14.8828 | 0.512590 | ||||||||
\(844\) | −11.7709 | −0.405171 | ||||||||
\(845\) | −29.5003 | −1.01484 | ||||||||
\(846\) | −12.2557 | −0.421359 | ||||||||
\(847\) | −2.85130 | −0.0979719 | ||||||||
\(848\) | 47.4977 | 1.63108 | ||||||||
\(849\) | 29.9805 | 1.02893 | ||||||||
\(850\) | 54.8764 | 1.88224 | ||||||||
\(851\) | −6.24723 | −0.214152 | ||||||||
\(852\) | 91.7508 | 3.14333 | ||||||||
\(853\) | 48.0920 | 1.64664 | 0.823319 | − | 0.567578i | \(-0.192120\pi\) | ||||
0.823319 | + | 0.567578i | \(0.192120\pi\) | |||||||
\(854\) | −103.567 | −3.54400 | ||||||||
\(855\) | 17.1366 | 0.586059 | ||||||||
\(856\) | −50.9018 | −1.73979 | ||||||||
\(857\) | 16.9505 | 0.579019 | 0.289510 | − | 0.957175i | \(-0.406508\pi\) | ||||
0.289510 | + | 0.957175i | \(0.406508\pi\) | |||||||
\(858\) | 5.75459 | 0.196459 | ||||||||
\(859\) | 36.1630 | 1.23387 | 0.616933 | − | 0.787016i | \(-0.288375\pi\) | ||||
0.616933 | + | 0.787016i | \(0.288375\pi\) | |||||||
\(860\) | −126.089 | −4.29961 | ||||||||
\(861\) | −9.95662 | −0.339321 | ||||||||
\(862\) | −52.3764 | −1.78395 | ||||||||
\(863\) | −34.4936 | −1.17418 | −0.587089 | − | 0.809523i | \(-0.699726\pi\) | ||||
−0.587089 | + | 0.809523i | \(0.699726\pi\) | |||||||
\(864\) | −6.72199 | −0.228687 | ||||||||
\(865\) | −44.0517 | −1.49780 | ||||||||
\(866\) | −57.3140 | −1.94761 | ||||||||
\(867\) | −25.9639 | −0.881782 | ||||||||
\(868\) | 24.9294 | 0.846158 | ||||||||
\(869\) | −8.61927 | −0.292389 | ||||||||
\(870\) | −93.3513 | −3.16490 | ||||||||
\(871\) | 13.4855 | 0.456937 | ||||||||
\(872\) | 10.5605 | 0.357625 | ||||||||
\(873\) | 3.66180 | 0.123933 | ||||||||
\(874\) | 37.1080 | 1.25520 | ||||||||
\(875\) | 11.0648 | 0.374060 | ||||||||
\(876\) | −56.3533 | −1.90400 | ||||||||
\(877\) | −13.7788 | −0.465277 | −0.232639 | − | 0.972563i | \(-0.574736\pi\) | ||||
−0.232639 | + | 0.972563i | \(0.574736\pi\) | |||||||
\(878\) | 30.2713 | 1.02161 | ||||||||
\(879\) | −36.9054 | −1.24479 | ||||||||
\(880\) | −13.8976 | −0.468487 | ||||||||
\(881\) | 48.3733 | 1.62974 | 0.814868 | − | 0.579646i | \(-0.196809\pi\) | ||||
0.814868 | + | 0.579646i | \(0.196809\pi\) | |||||||
\(882\) | 3.32183 | 0.111852 | ||||||||
\(883\) | 12.5634 | 0.422793 | 0.211396 | − | 0.977400i | \(-0.432199\pi\) | ||||
0.211396 | + | 0.977400i | \(0.432199\pi\) | |||||||
\(884\) | 42.8782 | 1.44215 | ||||||||
\(885\) | −18.3277 | −0.616081 | ||||||||
\(886\) | −23.9680 | −0.805220 | ||||||||
\(887\) | −30.5742 | −1.02658 | −0.513291 | − | 0.858215i | \(-0.671574\pi\) | ||||
−0.513291 | + | 0.858215i | \(0.671574\pi\) | |||||||
\(888\) | −14.3562 | −0.481762 | ||||||||
\(889\) | −55.8222 | −1.87222 | ||||||||
\(890\) | −54.7433 | −1.83500 | ||||||||
\(891\) | 4.02112 | 0.134713 | ||||||||
\(892\) | −47.9223 | −1.60456 | ||||||||
\(893\) | 20.3957 | 0.682518 | ||||||||
\(894\) | −31.8901 | −1.06656 | ||||||||
\(895\) | −58.4036 | −1.95222 | ||||||||
\(896\) | −52.5217 | −1.75463 | ||||||||
\(897\) | 7.13518 | 0.238237 | ||||||||
\(898\) | 53.6296 | 1.78964 | ||||||||
\(899\) | 20.2110 | 0.674074 | ||||||||
\(900\) | −18.0243 | −0.600808 | ||||||||
\(901\) | −60.6699 | −2.02121 | ||||||||
\(902\) | −6.41714 | −0.213667 | ||||||||
\(903\) | −39.8835 | −1.32724 | ||||||||
\(904\) | 2.53727 | 0.0843885 | ||||||||
\(905\) | −65.9434 | −2.19203 | ||||||||
\(906\) | 19.9770 | 0.663690 | ||||||||
\(907\) | 48.3468 | 1.60533 | 0.802665 | − | 0.596430i | \(-0.203415\pi\) | ||||
0.802665 | + | 0.596430i | \(0.203415\pi\) | |||||||
\(908\) | −38.8985 | −1.29089 | ||||||||
\(909\) | 11.1404 | 0.369504 | ||||||||
\(910\) | −35.9248 | −1.19089 | ||||||||
\(911\) | −28.2675 | −0.936544 | −0.468272 | − | 0.883584i | \(-0.655123\pi\) | ||||
−0.468272 | + | 0.883584i | \(0.655123\pi\) | |||||||
\(912\) | 31.0552 | 1.02834 | ||||||||
\(913\) | 8.70178 | 0.287987 | ||||||||
\(914\) | −15.3915 | −0.509105 | ||||||||
\(915\) | 58.2430 | 1.92546 | ||||||||
\(916\) | 41.5224 | 1.37194 | ||||||||
\(917\) | −47.3644 | −1.56411 | ||||||||
\(918\) | 83.9946 | 2.77224 | ||||||||
\(919\) | −35.0627 | −1.15661 | −0.578306 | − | 0.815820i | \(-0.696286\pi\) | ||||
−0.578306 | + | 0.815820i | \(0.696286\pi\) | |||||||
\(920\) | −47.3166 | −1.55998 | ||||||||
\(921\) | −28.2044 | −0.929368 | ||||||||
\(922\) | −29.7811 | −0.980789 | ||||||||
\(923\) | 28.6259 | 0.942234 | ||||||||
\(924\) | −15.7992 | −0.519755 | ||||||||
\(925\) | −7.50297 | −0.246696 | ||||||||
\(926\) | −62.6940 | −2.06025 | ||||||||
\(927\) | −4.95052 | −0.162597 | ||||||||
\(928\) | 11.3484 | 0.372528 | ||||||||
\(929\) | −10.7945 | −0.354155 | −0.177078 | − | 0.984197i | \(-0.556664\pi\) | ||||
−0.177078 | + | 0.984197i | \(0.556664\pi\) | |||||||
\(930\) | −20.8298 | −0.683038 | ||||||||
\(931\) | −5.52815 | −0.181178 | ||||||||
\(932\) | −105.968 | −3.47109 | ||||||||
\(933\) | 15.5515 | 0.509133 | ||||||||
\(934\) | 94.0998 | 3.07904 | ||||||||
\(935\) | 17.7517 | 0.580543 | ||||||||
\(936\) | −10.7600 | −0.351702 | ||||||||
\(937\) | 23.2088 | 0.758199 | 0.379099 | − | 0.925356i | \(-0.376234\pi\) | ||||
0.379099 | + | 0.925356i | \(0.376234\pi\) | |||||||
\(938\) | −55.0098 | −1.79613 | ||||||||
\(939\) | −40.4494 | −1.32001 | ||||||||
\(940\) | −50.5750 | −1.64958 | ||||||||
\(941\) | −43.4382 | −1.41604 | −0.708022 | − | 0.706190i | \(-0.750412\pi\) | ||||
−0.708022 | + | 0.706190i | \(0.750412\pi\) | |||||||
\(942\) | 9.51984 | 0.310173 | ||||||||
\(943\) | −7.95668 | −0.259105 | ||||||||
\(944\) | 21.7959 | 0.709397 | ||||||||
\(945\) | −47.3647 | −1.54077 | ||||||||
\(946\) | −25.7053 | −0.835752 | ||||||||
\(947\) | 5.09549 | 0.165581 | 0.0827905 | − | 0.996567i | \(-0.473617\pi\) | ||||
0.0827905 | + | 0.996567i | \(0.473617\pi\) | |||||||
\(948\) | −47.7598 | −1.55117 | ||||||||
\(949\) | −17.5820 | −0.570737 | ||||||||
\(950\) | 44.5670 | 1.44594 | ||||||||
\(951\) | 14.8343 | 0.481035 | ||||||||
\(952\) | −89.9417 | −2.91503 | ||||||||
\(953\) | 25.1708 | 0.815363 | 0.407682 | − | 0.913124i | \(-0.366337\pi\) | ||||
0.407682 | + | 0.913124i | \(0.366337\pi\) | |||||||
\(954\) | 29.6073 | 0.958573 | ||||||||
\(955\) | 72.2096 | 2.33665 | ||||||||
\(956\) | 6.24473 | 0.201969 | ||||||||
\(957\) | −12.8089 | −0.414052 | ||||||||
\(958\) | 47.7941 | 1.54416 | ||||||||
\(959\) | −10.5508 | −0.340704 | ||||||||
\(960\) | 25.7126 | 0.829870 | ||||||||
\(961\) | −26.4902 | −0.854524 | ||||||||
\(962\) | −8.71041 | −0.280835 | ||||||||
\(963\) | −11.5552 | −0.372360 | ||||||||
\(964\) | 45.6812 | 1.47129 | ||||||||
\(965\) | −33.3639 | −1.07402 | ||||||||
\(966\) | −29.1058 | −0.936463 | ||||||||
\(967\) | 56.1142 | 1.80451 | 0.902256 | − | 0.431200i | \(-0.141910\pi\) | ||||
0.902256 | + | 0.431200i | \(0.141910\pi\) | |||||||
\(968\) | −5.23618 | −0.168297 | ||||||||
\(969\) | −39.6675 | −1.27431 | ||||||||
\(970\) | 22.4516 | 0.720878 | ||||||||
\(971\) | 51.7528 | 1.66083 | 0.830413 | − | 0.557149i | \(-0.188105\pi\) | ||||
0.830413 | + | 0.557149i | \(0.188105\pi\) | |||||||
\(972\) | −47.3474 | −1.51867 | ||||||||
\(973\) | −34.6234 | −1.10997 | ||||||||
\(974\) | −91.3293 | −2.92638 | ||||||||
\(975\) | 8.56941 | 0.274441 | ||||||||
\(976\) | −69.2644 | −2.21710 | ||||||||
\(977\) | −22.7312 | −0.727235 | −0.363618 | − | 0.931548i | \(-0.618458\pi\) | ||||
−0.363618 | + | 0.931548i | \(0.618458\pi\) | |||||||
\(978\) | 16.5315 | 0.528620 | ||||||||
\(979\) | −7.51142 | −0.240066 | ||||||||
\(980\) | 13.7081 | 0.437888 | ||||||||
\(981\) | 2.39733 | 0.0765409 | ||||||||
\(982\) | 2.63914 | 0.0842184 | ||||||||
\(983\) | −7.96890 | −0.254169 | −0.127084 | − | 0.991892i | \(-0.540562\pi\) | ||||
−0.127084 | + | 0.991892i | \(0.540562\pi\) | |||||||
\(984\) | −18.2845 | −0.582889 | ||||||||
\(985\) | 37.3341 | 1.18956 | ||||||||
\(986\) | −141.804 | −4.51595 | ||||||||
\(987\) | −15.9975 | −0.509205 | ||||||||
\(988\) | 34.8229 | 1.10786 | ||||||||
\(989\) | −31.8723 | −1.01348 | ||||||||
\(990\) | −8.66295 | −0.275327 | ||||||||
\(991\) | −41.3921 | −1.31486 | −0.657431 | − | 0.753514i | \(-0.728357\pi\) | ||||
−0.657431 | + | 0.753514i | \(0.728357\pi\) | |||||||
\(992\) | 2.53221 | 0.0803976 | ||||||||
\(993\) | 41.7329 | 1.32435 | ||||||||
\(994\) | −116.771 | −3.70374 | ||||||||
\(995\) | 17.4663 | 0.553718 | ||||||||
\(996\) | 48.2170 | 1.52781 | ||||||||
\(997\) | 37.9007 | 1.20033 | 0.600163 | − | 0.799878i | \(-0.295102\pi\) | ||||
0.600163 | + | 0.799878i | \(0.295102\pi\) | |||||||
\(998\) | −54.0209 | −1.71000 | ||||||||
\(999\) | −11.4842 | −0.363343 |
(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 | 6017.2.a.f.1.11 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.f.1.11 | ✓ | 121 | 1.1 | even | 1 | trivial |