Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, 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("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.20648 | −1.56022 | −0.780108 | − | 0.625645i | \(-0.784836\pi\) | ||||
−0.780108 | + | 0.625645i | \(0.784836\pi\) | |||||||
\(3\) | −1.66546 | −0.961552 | −0.480776 | − | 0.876843i | \(-0.659645\pi\) | ||||
−0.480776 | + | 0.876843i | \(0.659645\pi\) | |||||||
\(4\) | 2.86855 | 1.43427 | ||||||||
\(5\) | 2.85921 | 1.27868 | 0.639338 | − | 0.768926i | \(-0.279209\pi\) | ||||
0.639338 | + | 0.768926i | \(0.279209\pi\) | |||||||
\(6\) | 3.67480 | 1.50023 | ||||||||
\(7\) | −0.996345 | −0.376583 | −0.188291 | − | 0.982113i | \(-0.560295\pi\) | ||||
−0.188291 | + | 0.982113i | \(0.560295\pi\) | |||||||
\(8\) | −1.91643 | −0.677562 | ||||||||
\(9\) | −0.226251 | −0.0754171 | ||||||||
\(10\) | −6.30878 | −1.99501 | ||||||||
\(11\) | 4.63930 | 1.39880 | 0.699402 | − | 0.714729i | \(-0.253450\pi\) | ||||
0.699402 | + | 0.714729i | \(0.253450\pi\) | |||||||
\(12\) | −4.77745 | −1.37913 | ||||||||
\(13\) | 1.51057 | 0.418956 | 0.209478 | − | 0.977813i | \(-0.432824\pi\) | ||||
0.209478 | + | 0.977813i | \(0.432824\pi\) | |||||||
\(14\) | 2.19841 | 0.587551 | ||||||||
\(15\) | −4.76189 | −1.22951 | ||||||||
\(16\) | −1.50853 | −0.377131 | ||||||||
\(17\) | 2.86077 | 0.693838 | 0.346919 | − | 0.937895i | \(-0.387228\pi\) | ||||
0.346919 | + | 0.937895i | \(0.387228\pi\) | |||||||
\(18\) | 0.499218 | 0.117667 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 8.20177 | 1.83397 | ||||||||
\(21\) | 1.65937 | 0.362104 | ||||||||
\(22\) | −10.2365 | −2.18244 | ||||||||
\(23\) | −4.55077 | −0.948902 | −0.474451 | − | 0.880282i | \(-0.657353\pi\) | ||||
−0.474451 | + | 0.880282i | \(0.657353\pi\) | |||||||
\(24\) | 3.19174 | 0.651511 | ||||||||
\(25\) | 3.17506 | 0.635012 | ||||||||
\(26\) | −3.33304 | −0.653662 | ||||||||
\(27\) | 5.37318 | 1.03407 | ||||||||
\(28\) | −2.85806 | −0.540123 | ||||||||
\(29\) | −8.47482 | −1.57373 | −0.786867 | − | 0.617122i | \(-0.788298\pi\) | ||||
−0.786867 | + | 0.617122i | \(0.788298\pi\) | |||||||
\(30\) | 10.5070 | 1.91831 | ||||||||
\(31\) | 9.31539 | 1.67309 | 0.836547 | − | 0.547895i | \(-0.184571\pi\) | ||||
0.836547 | + | 0.547895i | \(0.184571\pi\) | |||||||
\(32\) | 7.16140 | 1.26597 | ||||||||
\(33\) | −7.72657 | −1.34502 | ||||||||
\(34\) | −6.31222 | −1.08254 | ||||||||
\(35\) | −2.84875 | −0.481527 | ||||||||
\(36\) | −0.649012 | −0.108169 | ||||||||
\(37\) | 3.67526 | 0.604210 | 0.302105 | − | 0.953275i | \(-0.402311\pi\) | ||||
0.302105 | + | 0.953275i | \(0.402311\pi\) | |||||||
\(38\) | 2.20648 | 0.357938 | ||||||||
\(39\) | −2.51579 | −0.402848 | ||||||||
\(40\) | −5.47948 | −0.866382 | ||||||||
\(41\) | 4.17881 | 0.652621 | 0.326310 | − | 0.945263i | \(-0.394195\pi\) | ||||
0.326310 | + | 0.945263i | \(0.394195\pi\) | |||||||
\(42\) | −3.66136 | −0.564961 | ||||||||
\(43\) | −10.4376 | −1.59171 | −0.795857 | − | 0.605484i | \(-0.792980\pi\) | ||||
−0.795857 | + | 0.605484i | \(0.792980\pi\) | |||||||
\(44\) | 13.3081 | 2.00627 | ||||||||
\(45\) | −0.646899 | −0.0964340 | ||||||||
\(46\) | 10.0412 | 1.48049 | ||||||||
\(47\) | −10.5636 | −1.54087 | −0.770433 | − | 0.637521i | \(-0.779960\pi\) | ||||
−0.770433 | + | 0.637521i | \(0.779960\pi\) | |||||||
\(48\) | 2.51239 | 0.362632 | ||||||||
\(49\) | −6.00730 | −0.858185 | ||||||||
\(50\) | −7.00570 | −0.990756 | ||||||||
\(51\) | −4.76449 | −0.667161 | ||||||||
\(52\) | 4.33314 | 0.600898 | ||||||||
\(53\) | −7.87956 | −1.08234 | −0.541170 | − | 0.840913i | \(-0.682019\pi\) | ||||
−0.541170 | + | 0.840913i | \(0.682019\pi\) | |||||||
\(54\) | −11.8558 | −1.61337 | ||||||||
\(55\) | 13.2647 | 1.78862 | ||||||||
\(56\) | 1.90943 | 0.255158 | ||||||||
\(57\) | 1.66546 | 0.220595 | ||||||||
\(58\) | 18.6995 | 2.45537 | ||||||||
\(59\) | 4.45425 | 0.579894 | 0.289947 | − | 0.957043i | \(-0.406362\pi\) | ||||
0.289947 | + | 0.957043i | \(0.406362\pi\) | |||||||
\(60\) | −13.6597 | −1.76346 | ||||||||
\(61\) | 0.678642 | 0.0868911 | 0.0434456 | − | 0.999056i | \(-0.486166\pi\) | ||||
0.0434456 | + | 0.999056i | \(0.486166\pi\) | |||||||
\(62\) | −20.5542 | −2.61039 | ||||||||
\(63\) | 0.225424 | 0.0284008 | ||||||||
\(64\) | −12.7844 | −1.59805 | ||||||||
\(65\) | 4.31902 | 0.535709 | ||||||||
\(66\) | 17.0485 | 2.09853 | ||||||||
\(67\) | 10.1411 | 1.23894 | 0.619469 | − | 0.785021i | \(-0.287348\pi\) | ||||
0.619469 | + | 0.785021i | \(0.287348\pi\) | |||||||
\(68\) | 8.20625 | 0.995154 | ||||||||
\(69\) | 7.57912 | 0.912418 | ||||||||
\(70\) | 6.28572 | 0.751287 | ||||||||
\(71\) | −1.30386 | −0.154739 | −0.0773696 | − | 0.997002i | \(-0.524652\pi\) | ||||
−0.0773696 | + | 0.997002i | \(0.524652\pi\) | |||||||
\(72\) | 0.433595 | 0.0510997 | ||||||||
\(73\) | −5.52882 | −0.647100 | −0.323550 | − | 0.946211i | \(-0.604876\pi\) | ||||
−0.323550 | + | 0.946211i | \(0.604876\pi\) | |||||||
\(74\) | −8.10939 | −0.942698 | ||||||||
\(75\) | −5.28793 | −0.610597 | ||||||||
\(76\) | −2.86855 | −0.329045 | ||||||||
\(77\) | −4.62235 | −0.526765 | ||||||||
\(78\) | 5.55103 | 0.628530 | ||||||||
\(79\) | −9.51275 | −1.07027 | −0.535134 | − | 0.844767i | \(-0.679739\pi\) | ||||
−0.535134 | + | 0.844767i | \(0.679739\pi\) | |||||||
\(80\) | −4.31319 | −0.482229 | ||||||||
\(81\) | −8.27006 | −0.918895 | ||||||||
\(82\) | −9.22046 | −1.01823 | ||||||||
\(83\) | −4.61347 | −0.506394 | −0.253197 | − | 0.967415i | \(-0.581482\pi\) | ||||
−0.253197 | + | 0.967415i | \(0.581482\pi\) | |||||||
\(84\) | 4.75998 | 0.519357 | ||||||||
\(85\) | 8.17952 | 0.887194 | ||||||||
\(86\) | 23.0303 | 2.48342 | ||||||||
\(87\) | 14.1145 | 1.51323 | ||||||||
\(88\) | −8.89092 | −0.947776 | ||||||||
\(89\) | −6.53101 | −0.692286 | −0.346143 | − | 0.938182i | \(-0.612509\pi\) | ||||
−0.346143 | + | 0.938182i | \(0.612509\pi\) | |||||||
\(90\) | 1.42737 | 0.150458 | ||||||||
\(91\) | −1.50505 | −0.157772 | ||||||||
\(92\) | −13.0541 | −1.36099 | ||||||||
\(93\) | −15.5144 | −1.60877 | ||||||||
\(94\) | 23.3085 | 2.40408 | ||||||||
\(95\) | −2.85921 | −0.293348 | ||||||||
\(96\) | −11.9270 | −1.21729 | ||||||||
\(97\) | −3.54978 | −0.360425 | −0.180213 | − | 0.983628i | \(-0.557679\pi\) | ||||
−0.180213 | + | 0.983628i | \(0.557679\pi\) | |||||||
\(98\) | 13.2550 | 1.33895 | ||||||||
\(99\) | −1.04965 | −0.105494 | ||||||||
\(100\) | 9.10781 | 0.910781 | ||||||||
\(101\) | 3.19030 | 0.317447 | 0.158724 | − | 0.987323i | \(-0.449262\pi\) | ||||
0.158724 | + | 0.987323i | \(0.449262\pi\) | |||||||
\(102\) | 10.5127 | 1.04092 | ||||||||
\(103\) | −6.81128 | −0.671136 | −0.335568 | − | 0.942016i | \(-0.608928\pi\) | ||||
−0.335568 | + | 0.942016i | \(0.608928\pi\) | |||||||
\(104\) | −2.89490 | −0.283869 | ||||||||
\(105\) | 4.74448 | 0.463014 | ||||||||
\(106\) | 17.3861 | 1.68869 | ||||||||
\(107\) | −9.82688 | −0.950000 | −0.475000 | − | 0.879986i | \(-0.657552\pi\) | ||||
−0.475000 | + | 0.879986i | \(0.657552\pi\) | |||||||
\(108\) | 15.4132 | 1.48314 | ||||||||
\(109\) | −14.5679 | −1.39536 | −0.697678 | − | 0.716411i | \(-0.745783\pi\) | ||||
−0.697678 | + | 0.716411i | \(0.745783\pi\) | |||||||
\(110\) | −29.2683 | −2.79063 | ||||||||
\(111\) | −6.12100 | −0.580979 | ||||||||
\(112\) | 1.50301 | 0.142021 | ||||||||
\(113\) | −5.41146 | −0.509067 | −0.254533 | − | 0.967064i | \(-0.581922\pi\) | ||||
−0.254533 | + | 0.967064i | \(0.581922\pi\) | |||||||
\(114\) | −3.67480 | −0.344176 | ||||||||
\(115\) | −13.0116 | −1.21334 | ||||||||
\(116\) | −24.3104 | −2.25717 | ||||||||
\(117\) | −0.341768 | −0.0315964 | ||||||||
\(118\) | −9.82821 | −0.904760 | ||||||||
\(119\) | −2.85031 | −0.261287 | ||||||||
\(120\) | 9.12584 | 0.833072 | ||||||||
\(121\) | 10.5231 | 0.956650 | ||||||||
\(122\) | −1.49741 | −0.135569 | ||||||||
\(123\) | −6.95963 | −0.627529 | ||||||||
\(124\) | 26.7217 | 2.39968 | ||||||||
\(125\) | −5.21788 | −0.466702 | ||||||||
\(126\) | −0.497394 | −0.0443113 | ||||||||
\(127\) | 2.67749 | 0.237589 | 0.118795 | − | 0.992919i | \(-0.462097\pi\) | ||||
0.118795 | + | 0.992919i | \(0.462097\pi\) | |||||||
\(128\) | 13.8858 | 1.22734 | ||||||||
\(129\) | 17.3833 | 1.53052 | ||||||||
\(130\) | −9.52984 | −0.835822 | ||||||||
\(131\) | −3.51171 | −0.306820 | −0.153410 | − | 0.988163i | \(-0.549025\pi\) | ||||
−0.153410 | + | 0.988163i | \(0.549025\pi\) | |||||||
\(132\) | −22.1640 | −1.92913 | ||||||||
\(133\) | 0.996345 | 0.0863940 | ||||||||
\(134\) | −22.3762 | −1.93301 | ||||||||
\(135\) | 15.3630 | 1.32224 | ||||||||
\(136\) | −5.48247 | −0.470118 | ||||||||
\(137\) | −7.90848 | −0.675667 | −0.337833 | − | 0.941206i | \(-0.609694\pi\) | ||||
−0.337833 | + | 0.941206i | \(0.609694\pi\) | |||||||
\(138\) | −16.7232 | −1.42357 | ||||||||
\(139\) | −13.9366 | −1.18208 | −0.591042 | − | 0.806641i | \(-0.701283\pi\) | ||||
−0.591042 | + | 0.806641i | \(0.701283\pi\) | |||||||
\(140\) | −8.17179 | −0.690642 | ||||||||
\(141\) | 17.5933 | 1.48162 | ||||||||
\(142\) | 2.87693 | 0.241427 | ||||||||
\(143\) | 7.00798 | 0.586037 | ||||||||
\(144\) | 0.341306 | 0.0284421 | ||||||||
\(145\) | −24.2313 | −2.01230 | ||||||||
\(146\) | 12.1992 | 1.00962 | ||||||||
\(147\) | 10.0049 | 0.825190 | ||||||||
\(148\) | 10.5427 | 0.866602 | ||||||||
\(149\) | 1.10069 | 0.0901718 | 0.0450859 | − | 0.998983i | \(-0.485644\pi\) | ||||
0.0450859 | + | 0.998983i | \(0.485644\pi\) | |||||||
\(150\) | 11.6677 | 0.952663 | ||||||||
\(151\) | 22.0629 | 1.79545 | 0.897726 | − | 0.440554i | \(-0.145218\pi\) | ||||
0.897726 | + | 0.440554i | \(0.145218\pi\) | |||||||
\(152\) | 1.91643 | 0.155443 | ||||||||
\(153\) | −0.647252 | −0.0523272 | ||||||||
\(154\) | 10.1991 | 0.821868 | ||||||||
\(155\) | 26.6346 | 2.13934 | ||||||||
\(156\) | −7.21666 | −0.577795 | ||||||||
\(157\) | −22.8750 | −1.82563 | −0.912814 | − | 0.408376i | \(-0.866095\pi\) | ||||
−0.912814 | + | 0.408376i | \(0.866095\pi\) | |||||||
\(158\) | 20.9897 | 1.66985 | ||||||||
\(159\) | 13.1231 | 1.04073 | ||||||||
\(160\) | 20.4759 | 1.61876 | ||||||||
\(161\) | 4.53414 | 0.357340 | ||||||||
\(162\) | 18.2477 | 1.43368 | ||||||||
\(163\) | 11.6444 | 0.912060 | 0.456030 | − | 0.889965i | \(-0.349271\pi\) | ||||
0.456030 | + | 0.889965i | \(0.349271\pi\) | |||||||
\(164\) | 11.9871 | 0.936037 | ||||||||
\(165\) | −22.0918 | −1.71985 | ||||||||
\(166\) | 10.1795 | 0.790083 | ||||||||
\(167\) | −1.69408 | −0.131092 | −0.0655460 | − | 0.997850i | \(-0.520879\pi\) | ||||
−0.0655460 | + | 0.997850i | \(0.520879\pi\) | |||||||
\(168\) | −3.18007 | −0.245348 | ||||||||
\(169\) | −10.7182 | −0.824476 | ||||||||
\(170\) | −18.0479 | −1.38421 | ||||||||
\(171\) | 0.226251 | 0.0173019 | ||||||||
\(172\) | −29.9407 | −2.28296 | ||||||||
\(173\) | −5.03574 | −0.382860 | −0.191430 | − | 0.981506i | \(-0.561312\pi\) | ||||
−0.191430 | + | 0.981506i | \(0.561312\pi\) | |||||||
\(174\) | −31.1432 | −2.36096 | ||||||||
\(175\) | −3.16345 | −0.239135 | ||||||||
\(176\) | −6.99851 | −0.527533 | ||||||||
\(177\) | −7.41836 | −0.557598 | ||||||||
\(178\) | 14.4105 | 1.08012 | ||||||||
\(179\) | 11.1998 | 0.837111 | 0.418555 | − | 0.908191i | \(-0.362537\pi\) | ||||
0.418555 | + | 0.908191i | \(0.362537\pi\) | |||||||
\(180\) | −1.85566 | −0.138313 | ||||||||
\(181\) | 21.3420 | 1.58634 | 0.793168 | − | 0.609003i | \(-0.208430\pi\) | ||||
0.793168 | + | 0.609003i | \(0.208430\pi\) | |||||||
\(182\) | 3.32085 | 0.246158 | ||||||||
\(183\) | −1.13025 | −0.0835504 | ||||||||
\(184\) | 8.72126 | 0.642939 | ||||||||
\(185\) | 10.5083 | 0.772588 | ||||||||
\(186\) | 34.2322 | 2.51003 | ||||||||
\(187\) | 13.2720 | 0.970543 | ||||||||
\(188\) | −30.3023 | −2.21002 | ||||||||
\(189\) | −5.35354 | −0.389413 | ||||||||
\(190\) | 6.30878 | 0.457687 | ||||||||
\(191\) | −19.8342 | −1.43515 | −0.717577 | − | 0.696480i | \(-0.754749\pi\) | ||||
−0.717577 | + | 0.696480i | \(0.754749\pi\) | |||||||
\(192\) | 21.2919 | 1.53661 | ||||||||
\(193\) | −8.97106 | −0.645751 | −0.322876 | − | 0.946441i | \(-0.604650\pi\) | ||||
−0.322876 | + | 0.946441i | \(0.604650\pi\) | |||||||
\(194\) | 7.83251 | 0.562342 | ||||||||
\(195\) | −7.19315 | −0.515112 | ||||||||
\(196\) | −17.2322 | −1.23087 | ||||||||
\(197\) | −6.82131 | −0.485998 | −0.242999 | − | 0.970027i | \(-0.578131\pi\) | ||||
−0.242999 | + | 0.970027i | \(0.578131\pi\) | |||||||
\(198\) | 2.31603 | 0.164593 | ||||||||
\(199\) | 4.42136 | 0.313422 | 0.156711 | − | 0.987645i | \(-0.449911\pi\) | ||||
0.156711 | + | 0.987645i | \(0.449911\pi\) | |||||||
\(200\) | −6.08479 | −0.430260 | ||||||||
\(201\) | −16.8896 | −1.19130 | ||||||||
\(202\) | −7.03934 | −0.495286 | ||||||||
\(203\) | 8.44384 | 0.592641 | ||||||||
\(204\) | −13.6672 | −0.956893 | ||||||||
\(205\) | 11.9481 | 0.834490 | ||||||||
\(206\) | 15.0289 | 1.04712 | ||||||||
\(207\) | 1.02962 | 0.0715634 | ||||||||
\(208\) | −2.27873 | −0.158002 | ||||||||
\(209\) | −4.63930 | −0.320907 | ||||||||
\(210\) | −10.4686 | −0.722402 | ||||||||
\(211\) | 9.62297 | 0.662473 | 0.331236 | − | 0.943548i | \(-0.392534\pi\) | ||||
0.331236 | + | 0.943548i | \(0.392534\pi\) | |||||||
\(212\) | −22.6029 | −1.55237 | ||||||||
\(213\) | 2.17152 | 0.148790 | ||||||||
\(214\) | 21.6828 | 1.48221 | ||||||||
\(215\) | −29.8432 | −2.03529 | ||||||||
\(216\) | −10.2974 | −0.700646 | ||||||||
\(217\) | −9.28134 | −0.630059 | ||||||||
\(218\) | 32.1439 | 2.17706 | ||||||||
\(219\) | 9.20802 | 0.622220 | ||||||||
\(220\) | 38.0505 | 2.56537 | ||||||||
\(221\) | 4.32138 | 0.290688 | ||||||||
\(222\) | 13.5058 | 0.906453 | ||||||||
\(223\) | −5.62330 | −0.376564 | −0.188282 | − | 0.982115i | \(-0.560292\pi\) | ||||
−0.188282 | + | 0.982115i | \(0.560292\pi\) | |||||||
\(224\) | −7.13522 | −0.476742 | ||||||||
\(225\) | −0.718361 | −0.0478907 | ||||||||
\(226\) | 11.9403 | 0.794255 | ||||||||
\(227\) | 14.0935 | 0.935416 | 0.467708 | − | 0.883883i | \(-0.345080\pi\) | ||||
0.467708 | + | 0.883883i | \(0.345080\pi\) | |||||||
\(228\) | 4.77745 | 0.316394 | ||||||||
\(229\) | 14.4900 | 0.957525 | 0.478763 | − | 0.877944i | \(-0.341085\pi\) | ||||
0.478763 | + | 0.877944i | \(0.341085\pi\) | |||||||
\(230\) | 28.7098 | 1.89307 | ||||||||
\(231\) | 7.69832 | 0.506512 | ||||||||
\(232\) | 16.2414 | 1.06630 | ||||||||
\(233\) | 17.1006 | 1.12030 | 0.560149 | − | 0.828392i | \(-0.310744\pi\) | ||||
0.560149 | + | 0.828392i | \(0.310744\pi\) | |||||||
\(234\) | 0.754103 | 0.0492973 | ||||||||
\(235\) | −30.2036 | −1.97027 | ||||||||
\(236\) | 12.7772 | 0.831727 | ||||||||
\(237\) | 15.8431 | 1.02912 | ||||||||
\(238\) | 6.28915 | 0.407665 | ||||||||
\(239\) | 23.7055 | 1.53338 | 0.766692 | − | 0.642015i | \(-0.221901\pi\) | ||||
0.766692 | + | 0.642015i | \(0.221901\pi\) | |||||||
\(240\) | 7.18343 | 0.463688 | ||||||||
\(241\) | 26.0845 | 1.68025 | 0.840126 | − | 0.542391i | \(-0.182481\pi\) | ||||
0.840126 | + | 0.542391i | \(0.182481\pi\) | |||||||
\(242\) | −23.2191 | −1.49258 | ||||||||
\(243\) | −2.34612 | −0.150504 | ||||||||
\(244\) | 1.94672 | 0.124626 | ||||||||
\(245\) | −17.1761 | −1.09734 | ||||||||
\(246\) | 15.3563 | 0.979081 | ||||||||
\(247\) | −1.51057 | −0.0961151 | ||||||||
\(248\) | −17.8523 | −1.13362 | ||||||||
\(249\) | 7.68353 | 0.486924 | ||||||||
\(250\) | 11.5131 | 0.728155 | ||||||||
\(251\) | 4.41109 | 0.278426 | 0.139213 | − | 0.990262i | \(-0.455543\pi\) | ||||
0.139213 | + | 0.990262i | \(0.455543\pi\) | |||||||
\(252\) | 0.646640 | 0.0407345 | ||||||||
\(253\) | −21.1124 | −1.32733 | ||||||||
\(254\) | −5.90783 | −0.370690 | ||||||||
\(255\) | −13.6226 | −0.853083 | ||||||||
\(256\) | −5.06979 | −0.316862 | ||||||||
\(257\) | −22.3700 | −1.39540 | −0.697701 | − | 0.716389i | \(-0.745794\pi\) | ||||
−0.697701 | + | 0.716389i | \(0.745794\pi\) | |||||||
\(258\) | −38.3560 | −2.38794 | ||||||||
\(259\) | −3.66183 | −0.227535 | ||||||||
\(260\) | 12.3893 | 0.768354 | ||||||||
\(261\) | 1.91744 | 0.118686 | ||||||||
\(262\) | 7.74852 | 0.478705 | ||||||||
\(263\) | −6.67943 | −0.411872 | −0.205936 | − | 0.978566i | \(-0.566024\pi\) | ||||
−0.205936 | + | 0.978566i | \(0.566024\pi\) | |||||||
\(264\) | 14.8075 | 0.911336 | ||||||||
\(265\) | −22.5293 | −1.38396 | ||||||||
\(266\) | −2.19841 | −0.134793 | ||||||||
\(267\) | 10.8771 | 0.665669 | ||||||||
\(268\) | 29.0904 | 1.77698 | ||||||||
\(269\) | −5.93768 | −0.362027 | −0.181014 | − | 0.983481i | \(-0.557938\pi\) | ||||
−0.181014 | + | 0.983481i | \(0.557938\pi\) | |||||||
\(270\) | −33.8982 | −2.06298 | ||||||||
\(271\) | −28.2007 | −1.71307 | −0.856536 | − | 0.516087i | \(-0.827388\pi\) | ||||
−0.856536 | + | 0.516087i | \(0.827388\pi\) | |||||||
\(272\) | −4.31554 | −0.261668 | ||||||||
\(273\) | 2.50659 | 0.151706 | ||||||||
\(274\) | 17.4499 | 1.05419 | ||||||||
\(275\) | 14.7301 | 0.888256 | ||||||||
\(276\) | 21.7411 | 1.30866 | ||||||||
\(277\) | 11.5208 | 0.692218 | 0.346109 | − | 0.938194i | \(-0.387503\pi\) | ||||
0.346109 | + | 0.938194i | \(0.387503\pi\) | |||||||
\(278\) | 30.7507 | 1.84431 | ||||||||
\(279\) | −2.10762 | −0.126180 | ||||||||
\(280\) | 5.45945 | 0.326265 | ||||||||
\(281\) | 6.25471 | 0.373125 | 0.186562 | − | 0.982443i | \(-0.440265\pi\) | ||||
0.186562 | + | 0.982443i | \(0.440265\pi\) | |||||||
\(282\) | −38.8193 | −2.31165 | ||||||||
\(283\) | 26.6041 | 1.58145 | 0.790724 | − | 0.612172i | \(-0.209704\pi\) | ||||
0.790724 | + | 0.612172i | \(0.209704\pi\) | |||||||
\(284\) | −3.74017 | −0.221939 | ||||||||
\(285\) | 4.76189 | 0.282070 | ||||||||
\(286\) | −15.4630 | −0.914344 | ||||||||
\(287\) | −4.16354 | −0.245766 | ||||||||
\(288\) | −1.62027 | −0.0954756 | ||||||||
\(289\) | −8.81601 | −0.518589 | ||||||||
\(290\) | 53.4658 | 3.13962 | ||||||||
\(291\) | 5.91201 | 0.346568 | ||||||||
\(292\) | −15.8597 | −0.928118 | ||||||||
\(293\) | −9.19726 | −0.537310 | −0.268655 | − | 0.963236i | \(-0.586579\pi\) | ||||
−0.268655 | + | 0.963236i | \(0.586579\pi\) | |||||||
\(294\) | −22.0756 | −1.28747 | ||||||||
\(295\) | 12.7356 | 0.741496 | ||||||||
\(296\) | −7.04340 | −0.409389 | ||||||||
\(297\) | 24.9278 | 1.44646 | ||||||||
\(298\) | −2.42864 | −0.140687 | ||||||||
\(299\) | −6.87425 | −0.397548 | ||||||||
\(300\) | −15.1687 | −0.875764 | ||||||||
\(301\) | 10.3994 | 0.599413 | ||||||||
\(302\) | −48.6813 | −2.80129 | ||||||||
\(303\) | −5.31332 | −0.305242 | ||||||||
\(304\) | 1.50853 | 0.0865199 | ||||||||
\(305\) | 1.94038 | 0.111106 | ||||||||
\(306\) | 1.42815 | 0.0816418 | ||||||||
\(307\) | 25.2512 | 1.44116 | 0.720582 | − | 0.693370i | \(-0.243875\pi\) | ||||
0.720582 | + | 0.693370i | \(0.243875\pi\) | |||||||
\(308\) | −13.2594 | −0.755526 | ||||||||
\(309\) | 11.3439 | 0.645332 | ||||||||
\(310\) | −58.7687 | −3.33784 | ||||||||
\(311\) | 19.0851 | 1.08222 | 0.541109 | − | 0.840953i | \(-0.318005\pi\) | ||||
0.541109 | + | 0.840953i | \(0.318005\pi\) | |||||||
\(312\) | 4.82134 | 0.272955 | ||||||||
\(313\) | −1.50541 | −0.0850907 | −0.0425453 | − | 0.999095i | \(-0.513547\pi\) | ||||
−0.0425453 | + | 0.999095i | \(0.513547\pi\) | |||||||
\(314\) | 50.4733 | 2.84837 | ||||||||
\(315\) | 0.644534 | 0.0363154 | ||||||||
\(316\) | −27.2878 | −1.53506 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | −28.9558 | −1.62376 | ||||||||
\(319\) | −39.3173 | −2.20134 | ||||||||
\(320\) | −36.5533 | −2.04339 | ||||||||
\(321\) | 16.3663 | 0.913475 | ||||||||
\(322\) | −10.0045 | −0.557528 | ||||||||
\(323\) | −2.86077 | −0.159177 | ||||||||
\(324\) | −23.7231 | −1.31795 | ||||||||
\(325\) | 4.79614 | 0.266042 | ||||||||
\(326\) | −25.6931 | −1.42301 | ||||||||
\(327\) | 24.2623 | 1.34171 | ||||||||
\(328\) | −8.00842 | −0.442191 | ||||||||
\(329\) | 10.5250 | 0.580264 | ||||||||
\(330\) | 48.7452 | 2.68333 | ||||||||
\(331\) | −26.1955 | −1.43984 | −0.719918 | − | 0.694059i | \(-0.755821\pi\) | ||||
−0.719918 | + | 0.694059i | \(0.755821\pi\) | |||||||
\(332\) | −13.2339 | −0.726307 | ||||||||
\(333\) | −0.831533 | −0.0455677 | ||||||||
\(334\) | 3.73795 | 0.204532 | ||||||||
\(335\) | 28.9956 | 1.58420 | ||||||||
\(336\) | −2.50320 | −0.136561 | ||||||||
\(337\) | 33.3015 | 1.81405 | 0.907024 | − | 0.421080i | \(-0.138349\pi\) | ||||
0.907024 | + | 0.421080i | \(0.138349\pi\) | |||||||
\(338\) | 23.6494 | 1.28636 | ||||||||
\(339\) | 9.01255 | 0.489495 | ||||||||
\(340\) | 23.4634 | 1.27248 | ||||||||
\(341\) | 43.2170 | 2.34033 | ||||||||
\(342\) | −0.499218 | −0.0269946 | ||||||||
\(343\) | 12.9598 | 0.699761 | ||||||||
\(344\) | 20.0029 | 1.07849 | ||||||||
\(345\) | 21.6703 | 1.16669 | ||||||||
\(346\) | 11.1112 | 0.597344 | ||||||||
\(347\) | −1.93502 | −0.103877 | −0.0519387 | − | 0.998650i | \(-0.516540\pi\) | ||||
−0.0519387 | + | 0.998650i | \(0.516540\pi\) | |||||||
\(348\) | 40.4880 | 2.17038 | ||||||||
\(349\) | −8.13301 | −0.435350 | −0.217675 | − | 0.976021i | \(-0.569847\pi\) | ||||
−0.217675 | + | 0.976021i | \(0.569847\pi\) | |||||||
\(350\) | 6.98009 | 0.373102 | ||||||||
\(351\) | 8.11656 | 0.433230 | ||||||||
\(352\) | 33.2239 | 1.77084 | ||||||||
\(353\) | 12.7288 | 0.677488 | 0.338744 | − | 0.940879i | \(-0.389998\pi\) | ||||
0.338744 | + | 0.940879i | \(0.389998\pi\) | |||||||
\(354\) | 16.3685 | 0.869974 | ||||||||
\(355\) | −3.72799 | −0.197861 | ||||||||
\(356\) | −18.7345 | −0.992927 | ||||||||
\(357\) | 4.74707 | 0.251242 | ||||||||
\(358\) | −24.7121 | −1.30607 | ||||||||
\(359\) | 25.0364 | 1.32137 | 0.660686 | − | 0.750663i | \(-0.270266\pi\) | ||||
0.660686 | + | 0.750663i | \(0.270266\pi\) | |||||||
\(360\) | 1.23974 | 0.0653400 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −47.0906 | −2.47503 | ||||||||
\(363\) | −17.5259 | −0.919869 | ||||||||
\(364\) | −4.31730 | −0.226288 | ||||||||
\(365\) | −15.8080 | −0.827431 | ||||||||
\(366\) | 2.49387 | 0.130357 | ||||||||
\(367\) | −32.2111 | −1.68141 | −0.840704 | − | 0.541495i | \(-0.817859\pi\) | ||||
−0.840704 | + | 0.541495i | \(0.817859\pi\) | |||||||
\(368\) | 6.86496 | 0.357861 | ||||||||
\(369\) | −0.945461 | −0.0492187 | ||||||||
\(370\) | −23.1864 | −1.20540 | ||||||||
\(371\) | 7.85076 | 0.407591 | ||||||||
\(372\) | −44.5038 | −2.30741 | ||||||||
\(373\) | −33.9916 | −1.76002 | −0.880010 | − | 0.474955i | \(-0.842464\pi\) | ||||
−0.880010 | + | 0.474955i | \(0.842464\pi\) | |||||||
\(374\) | −29.2843 | −1.51426 | ||||||||
\(375\) | 8.69016 | 0.448758 | ||||||||
\(376\) | 20.2445 | 1.04403 | ||||||||
\(377\) | −12.8018 | −0.659326 | ||||||||
\(378\) | 11.8125 | 0.607568 | ||||||||
\(379\) | −20.7053 | −1.06356 | −0.531779 | − | 0.846883i | \(-0.678476\pi\) | ||||
−0.531779 | + | 0.846883i | \(0.678476\pi\) | |||||||
\(380\) | −8.20177 | −0.420742 | ||||||||
\(381\) | −4.45925 | −0.228454 | ||||||||
\(382\) | 43.7638 | 2.23915 | ||||||||
\(383\) | −3.48169 | −0.177906 | −0.0889531 | − | 0.996036i | \(-0.528352\pi\) | ||||
−0.0889531 | + | 0.996036i | \(0.528352\pi\) | |||||||
\(384\) | −23.1261 | −1.18015 | ||||||||
\(385\) | −13.2162 | −0.673562 | ||||||||
\(386\) | 19.7945 | 1.00751 | ||||||||
\(387\) | 2.36151 | 0.120042 | ||||||||
\(388\) | −10.1827 | −0.516949 | ||||||||
\(389\) | 34.3179 | 1.73999 | 0.869993 | − | 0.493064i | \(-0.164123\pi\) | ||||
0.869993 | + | 0.493064i | \(0.164123\pi\) | |||||||
\(390\) | 15.8715 | 0.803686 | ||||||||
\(391\) | −13.0187 | −0.658384 | ||||||||
\(392\) | 11.5126 | 0.581474 | ||||||||
\(393\) | 5.84861 | 0.295023 | ||||||||
\(394\) | 15.0511 | 0.758262 | ||||||||
\(395\) | −27.1989 | −1.36853 | ||||||||
\(396\) | −3.01097 | −0.151307 | ||||||||
\(397\) | −18.9587 | −0.951509 | −0.475755 | − | 0.879578i | \(-0.657825\pi\) | ||||
−0.475755 | + | 0.879578i | \(0.657825\pi\) | |||||||
\(398\) | −9.75563 | −0.489006 | ||||||||
\(399\) | −1.65937 | −0.0830724 | ||||||||
\(400\) | −4.78966 | −0.239483 | ||||||||
\(401\) | −11.1614 | −0.557374 | −0.278687 | − | 0.960382i | \(-0.589899\pi\) | ||||
−0.278687 | + | 0.960382i | \(0.589899\pi\) | |||||||
\(402\) | 37.2667 | 1.85869 | ||||||||
\(403\) | 14.0715 | 0.700953 | ||||||||
\(404\) | 9.15154 | 0.455306 | ||||||||
\(405\) | −23.6458 | −1.17497 | ||||||||
\(406\) | −18.6312 | −0.924649 | ||||||||
\(407\) | 17.0507 | 0.845170 | ||||||||
\(408\) | 9.13082 | 0.452043 | ||||||||
\(409\) | −32.2735 | −1.59582 | −0.797910 | − | 0.602776i | \(-0.794061\pi\) | ||||
−0.797910 | + | 0.602776i | \(0.794061\pi\) | |||||||
\(410\) | −26.3632 | −1.30199 | ||||||||
\(411\) | 13.1712 | 0.649689 | ||||||||
\(412\) | −19.5385 | −0.962593 | ||||||||
\(413\) | −4.43797 | −0.218378 | ||||||||
\(414\) | −2.27183 | −0.111654 | ||||||||
\(415\) | −13.1908 | −0.647513 | ||||||||
\(416\) | 10.8178 | 0.530385 | ||||||||
\(417\) | 23.2107 | 1.13663 | ||||||||
\(418\) | 10.2365 | 0.500685 | ||||||||
\(419\) | 18.5806 | 0.907721 | 0.453861 | − | 0.891073i | \(-0.350046\pi\) | ||||
0.453861 | + | 0.891073i | \(0.350046\pi\) | |||||||
\(420\) | 13.6098 | 0.664089 | ||||||||
\(421\) | 20.2117 | 0.985057 | 0.492528 | − | 0.870296i | \(-0.336073\pi\) | ||||
0.492528 | + | 0.870296i | \(0.336073\pi\) | |||||||
\(422\) | −21.2329 | −1.03360 | ||||||||
\(423\) | 2.39004 | 0.116208 | ||||||||
\(424\) | 15.1007 | 0.733353 | ||||||||
\(425\) | 9.08310 | 0.440595 | ||||||||
\(426\) | −4.79141 | −0.232144 | ||||||||
\(427\) | −0.676161 | −0.0327217 | ||||||||
\(428\) | −28.1889 | −1.36256 | ||||||||
\(429\) | −11.6715 | −0.563505 | ||||||||
\(430\) | 65.8483 | 3.17549 | ||||||||
\(431\) | 20.6809 | 0.996162 | 0.498081 | − | 0.867130i | \(-0.334038\pi\) | ||||
0.498081 | + | 0.867130i | \(0.334038\pi\) | |||||||
\(432\) | −8.10559 | −0.389980 | ||||||||
\(433\) | −34.2036 | −1.64372 | −0.821861 | − | 0.569688i | \(-0.807064\pi\) | ||||
−0.821861 | + | 0.569688i | \(0.807064\pi\) | |||||||
\(434\) | 20.4791 | 0.983028 | ||||||||
\(435\) | 40.3561 | 1.93493 | ||||||||
\(436\) | −41.7889 | −2.00132 | ||||||||
\(437\) | 4.55077 | 0.217693 | ||||||||
\(438\) | −20.3173 | −0.970798 | ||||||||
\(439\) | 4.94993 | 0.236247 | 0.118124 | − | 0.992999i | \(-0.462312\pi\) | ||||
0.118124 | + | 0.992999i | \(0.462312\pi\) | |||||||
\(440\) | −25.4210 | −1.21190 | ||||||||
\(441\) | 1.35916 | 0.0647218 | ||||||||
\(442\) | −9.53504 | −0.453536 | ||||||||
\(443\) | 15.1771 | 0.721086 | 0.360543 | − | 0.932743i | \(-0.382591\pi\) | ||||
0.360543 | + | 0.932743i | \(0.382591\pi\) | |||||||
\(444\) | −17.5584 | −0.833284 | ||||||||
\(445\) | −18.6735 | −0.885209 | ||||||||
\(446\) | 12.4077 | 0.587521 | ||||||||
\(447\) | −1.83315 | −0.0867049 | ||||||||
\(448\) | 12.7377 | 0.601799 | ||||||||
\(449\) | 15.6330 | 0.737767 | 0.368884 | − | 0.929476i | \(-0.379740\pi\) | ||||
0.368884 | + | 0.929476i | \(0.379740\pi\) | |||||||
\(450\) | 1.58505 | 0.0747199 | ||||||||
\(451\) | 19.3868 | 0.912888 | ||||||||
\(452\) | −15.5230 | −0.730142 | ||||||||
\(453\) | −36.7448 | −1.72642 | ||||||||
\(454\) | −31.0969 | −1.45945 | ||||||||
\(455\) | −4.30324 | −0.201739 | ||||||||
\(456\) | −3.19174 | −0.149467 | ||||||||
\(457\) | −19.6187 | −0.917726 | −0.458863 | − | 0.888507i | \(-0.651743\pi\) | ||||
−0.458863 | + | 0.888507i | \(0.651743\pi\) | |||||||
\(458\) | −31.9719 | −1.49395 | ||||||||
\(459\) | 15.3714 | 0.717477 | ||||||||
\(460\) | −37.3244 | −1.74026 | ||||||||
\(461\) | −19.2375 | −0.895980 | −0.447990 | − | 0.894038i | \(-0.647860\pi\) | ||||
−0.447990 | + | 0.894038i | \(0.647860\pi\) | |||||||
\(462\) | −16.9862 | −0.790269 | ||||||||
\(463\) | 32.2853 | 1.50043 | 0.750213 | − | 0.661196i | \(-0.229951\pi\) | ||||
0.750213 | + | 0.661196i | \(0.229951\pi\) | |||||||
\(464\) | 12.7845 | 0.593505 | ||||||||
\(465\) | −44.3588 | −2.05709 | ||||||||
\(466\) | −37.7321 | −1.74791 | ||||||||
\(467\) | −21.9740 | −1.01683 | −0.508417 | − | 0.861111i | \(-0.669769\pi\) | ||||
−0.508417 | + | 0.861111i | \(0.669769\pi\) | |||||||
\(468\) | −0.980377 | −0.0453180 | ||||||||
\(469\) | −10.1041 | −0.466563 | ||||||||
\(470\) | 66.6437 | 3.07404 | ||||||||
\(471\) | 38.0974 | 1.75544 | ||||||||
\(472\) | −8.53628 | −0.392914 | ||||||||
\(473\) | −48.4231 | −2.22650 | ||||||||
\(474\) | −34.9574 | −1.60565 | ||||||||
\(475\) | −3.17506 | −0.145682 | ||||||||
\(476\) | −8.17625 | −0.374758 | ||||||||
\(477\) | 1.78276 | 0.0816270 | ||||||||
\(478\) | −52.3058 | −2.39241 | ||||||||
\(479\) | −0.636927 | −0.0291020 | −0.0145510 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145510 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(480\) | −34.1018 | −1.55653 | ||||||||
\(481\) | 5.55174 | 0.253137 | ||||||||
\(482\) | −57.5550 | −2.62156 | ||||||||
\(483\) | −7.55141 | −0.343601 | ||||||||
\(484\) | 30.1862 | 1.37210 | ||||||||
\(485\) | −10.1495 | −0.460867 | ||||||||
\(486\) | 5.17667 | 0.234819 | ||||||||
\(487\) | −21.5537 | −0.976693 | −0.488346 | − | 0.872650i | \(-0.662400\pi\) | ||||
−0.488346 | + | 0.872650i | \(0.662400\pi\) | |||||||
\(488\) | −1.30057 | −0.0588741 | ||||||||
\(489\) | −19.3932 | −0.876993 | ||||||||
\(490\) | 37.8987 | 1.71209 | ||||||||
\(491\) | 14.1894 | 0.640359 | 0.320180 | − | 0.947357i | \(-0.396257\pi\) | ||||
0.320180 | + | 0.947357i | \(0.396257\pi\) | |||||||
\(492\) | −19.9640 | −0.900049 | ||||||||
\(493\) | −24.2445 | −1.09192 | ||||||||
\(494\) | 3.33304 | 0.149960 | ||||||||
\(495\) | −3.00116 | −0.134892 | ||||||||
\(496\) | −14.0525 | −0.630976 | ||||||||
\(497\) | 1.29909 | 0.0582722 | ||||||||
\(498\) | −16.9535 | −0.759707 | ||||||||
\(499\) | −9.38643 | −0.420194 | −0.210097 | − | 0.977681i | \(-0.567378\pi\) | ||||
−0.210097 | + | 0.977681i | \(0.567378\pi\) | |||||||
\(500\) | −14.9678 | −0.669378 | ||||||||
\(501\) | 2.82142 | 0.126052 | ||||||||
\(502\) | −9.73298 | −0.434404 | ||||||||
\(503\) | −24.5717 | −1.09560 | −0.547800 | − | 0.836609i | \(-0.684535\pi\) | ||||
−0.547800 | + | 0.836609i | \(0.684535\pi\) | |||||||
\(504\) | −0.432011 | −0.0192433 | ||||||||
\(505\) | 9.12174 | 0.405912 | ||||||||
\(506\) | 46.5841 | 2.07092 | ||||||||
\(507\) | 17.8507 | 0.792777 | ||||||||
\(508\) | 7.68052 | 0.340768 | ||||||||
\(509\) | 12.6386 | 0.560197 | 0.280099 | − | 0.959971i | \(-0.409633\pi\) | ||||
0.280099 | + | 0.959971i | \(0.409633\pi\) | |||||||
\(510\) | 30.0581 | 1.33099 | ||||||||
\(511\) | 5.50861 | 0.243687 | ||||||||
\(512\) | −16.5851 | −0.732966 | ||||||||
\(513\) | −5.37318 | −0.237232 | ||||||||
\(514\) | 49.3589 | 2.17713 | ||||||||
\(515\) | −19.4749 | −0.858165 | ||||||||
\(516\) | 49.8649 | 2.19518 | ||||||||
\(517\) | −49.0080 | −2.15537 | ||||||||
\(518\) | 8.07975 | 0.355004 | ||||||||
\(519\) | 8.38681 | 0.368140 | ||||||||
\(520\) | −8.27713 | −0.362976 | ||||||||
\(521\) | 0.204005 | 0.00893761 | 0.00446880 | − | 0.999990i | \(-0.498578\pi\) | ||||
0.00446880 | + | 0.999990i | \(0.498578\pi\) | |||||||
\(522\) | −4.23079 | −0.185176 | ||||||||
\(523\) | −10.9746 | −0.479885 | −0.239943 | − | 0.970787i | \(-0.577129\pi\) | ||||
−0.239943 | + | 0.970787i | \(0.577129\pi\) | |||||||
\(524\) | −10.0735 | −0.440064 | ||||||||
\(525\) | 5.26860 | 0.229940 | ||||||||
\(526\) | 14.7380 | 0.642609 | ||||||||
\(527\) | 26.6492 | 1.16086 | ||||||||
\(528\) | 11.6557 | 0.507250 | ||||||||
\(529\) | −2.29048 | −0.0995859 | ||||||||
\(530\) | 49.7104 | 2.15928 | ||||||||
\(531\) | −1.00778 | −0.0437339 | ||||||||
\(532\) | 2.85806 | 0.123913 | ||||||||
\(533\) | 6.31238 | 0.273419 | ||||||||
\(534\) | −24.0001 | −1.03859 | ||||||||
\(535\) | −28.0971 | −1.21474 | ||||||||
\(536\) | −19.4348 | −0.839457 | ||||||||
\(537\) | −18.6528 | −0.804926 | ||||||||
\(538\) | 13.1014 | 0.564840 | ||||||||
\(539\) | −27.8697 | −1.20043 | ||||||||
\(540\) | 44.0696 | 1.89645 | ||||||||
\(541\) | −32.5754 | −1.40053 | −0.700263 | − | 0.713885i | \(-0.746934\pi\) | ||||
−0.700263 | + | 0.713885i | \(0.746934\pi\) | |||||||
\(542\) | 62.2243 | 2.67276 | ||||||||
\(543\) | −35.5441 | −1.52535 | ||||||||
\(544\) | 20.4871 | 0.878377 | ||||||||
\(545\) | −41.6528 | −1.78421 | ||||||||
\(546\) | −5.53074 | −0.236694 | ||||||||
\(547\) | −16.9940 | −0.726612 | −0.363306 | − | 0.931670i | \(-0.618352\pi\) | ||||
−0.363306 | + | 0.931670i | \(0.618352\pi\) | |||||||
\(548\) | −22.6858 | −0.969091 | ||||||||
\(549\) | −0.153543 | −0.00655307 | ||||||||
\(550\) | −32.5016 | −1.38587 | ||||||||
\(551\) | 8.47482 | 0.361039 | ||||||||
\(552\) | −14.5249 | −0.618220 | ||||||||
\(553\) | 9.47797 | 0.403044 | ||||||||
\(554\) | −25.4204 | −1.08001 | ||||||||
\(555\) | −17.5012 | −0.742884 | ||||||||
\(556\) | −39.9777 | −1.69543 | ||||||||
\(557\) | −6.23451 | −0.264165 | −0.132082 | − | 0.991239i | \(-0.542166\pi\) | ||||
−0.132082 | + | 0.991239i | \(0.542166\pi\) | |||||||
\(558\) | 4.65042 | 0.196868 | ||||||||
\(559\) | −15.7667 | −0.666859 | ||||||||
\(560\) | 4.29742 | 0.181599 | ||||||||
\(561\) | −22.1039 | −0.933227 | ||||||||
\(562\) | −13.8009 | −0.582155 | ||||||||
\(563\) | −21.3677 | −0.900540 | −0.450270 | − | 0.892892i | \(-0.648672\pi\) | ||||
−0.450270 | + | 0.892892i | \(0.648672\pi\) | |||||||
\(564\) | 50.4673 | 2.12505 | ||||||||
\(565\) | −15.4725 | −0.650932 | ||||||||
\(566\) | −58.7013 | −2.46740 | ||||||||
\(567\) | 8.23983 | 0.346040 | ||||||||
\(568\) | 2.49875 | 0.104845 | ||||||||
\(569\) | −25.5911 | −1.07283 | −0.536417 | − | 0.843953i | \(-0.680223\pi\) | ||||
−0.536417 | + | 0.843953i | \(0.680223\pi\) | |||||||
\(570\) | −10.5070 | −0.440090 | ||||||||
\(571\) | −25.0555 | −1.04854 | −0.524271 | − | 0.851552i | \(-0.675662\pi\) | ||||
−0.524271 | + | 0.851552i | \(0.675662\pi\) | |||||||
\(572\) | 20.1027 | 0.840538 | ||||||||
\(573\) | 33.0330 | 1.37997 | ||||||||
\(574\) | 9.18675 | 0.383448 | ||||||||
\(575\) | −14.4490 | −0.602564 | ||||||||
\(576\) | 2.89249 | 0.120520 | ||||||||
\(577\) | −11.0713 | −0.460906 | −0.230453 | − | 0.973083i | \(-0.574021\pi\) | ||||
−0.230453 | + | 0.973083i | \(0.574021\pi\) | |||||||
\(578\) | 19.4523 | 0.809111 | ||||||||
\(579\) | 14.9409 | 0.620923 | ||||||||
\(580\) | −69.5085 | −2.88618 | ||||||||
\(581\) | 4.59660 | 0.190699 | ||||||||
\(582\) | −13.0447 | −0.540721 | ||||||||
\(583\) | −36.5557 | −1.51398 | ||||||||
\(584\) | 10.5956 | 0.438450 | ||||||||
\(585\) | −0.977184 | −0.0404016 | ||||||||
\(586\) | 20.2936 | 0.838319 | ||||||||
\(587\) | −15.4232 | −0.636582 | −0.318291 | − | 0.947993i | \(-0.603109\pi\) | ||||
−0.318291 | + | 0.947993i | \(0.603109\pi\) | |||||||
\(588\) | 28.6995 | 1.18355 | ||||||||
\(589\) | −9.31539 | −0.383834 | ||||||||
\(590\) | −28.1009 | −1.15689 | ||||||||
\(591\) | 11.3606 | 0.467313 | ||||||||
\(592\) | −5.54423 | −0.227866 | ||||||||
\(593\) | −35.7808 | −1.46934 | −0.734670 | − | 0.678425i | \(-0.762663\pi\) | ||||
−0.734670 | + | 0.678425i | \(0.762663\pi\) | |||||||
\(594\) | −55.0027 | −2.25679 | ||||||||
\(595\) | −8.14962 | −0.334102 | ||||||||
\(596\) | 3.15737 | 0.129331 | ||||||||
\(597\) | −7.36358 | −0.301371 | ||||||||
\(598\) | 15.1679 | 0.620261 | ||||||||
\(599\) | 26.4128 | 1.07920 | 0.539598 | − | 0.841923i | \(-0.318576\pi\) | ||||
0.539598 | + | 0.841923i | \(0.318576\pi\) | |||||||
\(600\) | 10.1340 | 0.413717 | ||||||||
\(601\) | 9.40049 | 0.383454 | 0.191727 | − | 0.981448i | \(-0.438591\pi\) | ||||
0.191727 | + | 0.981448i | \(0.438591\pi\) | |||||||
\(602\) | −22.9461 | −0.935213 | ||||||||
\(603\) | −2.29445 | −0.0934371 | ||||||||
\(604\) | 63.2885 | 2.57517 | ||||||||
\(605\) | 30.0878 | 1.22325 | ||||||||
\(606\) | 11.7237 | 0.476244 | ||||||||
\(607\) | 37.0366 | 1.50327 | 0.751634 | − | 0.659580i | \(-0.229266\pi\) | ||||
0.751634 | + | 0.659580i | \(0.229266\pi\) | |||||||
\(608\) | −7.16140 | −0.290433 | ||||||||
\(609\) | −14.0629 | −0.569856 | ||||||||
\(610\) | −4.28140 | −0.173349 | ||||||||
\(611\) | −15.9571 | −0.645555 | ||||||||
\(612\) | −1.85667 | −0.0750516 | ||||||||
\(613\) | −14.8900 | −0.601400 | −0.300700 | − | 0.953719i | \(-0.597220\pi\) | ||||
−0.300700 | + | 0.953719i | \(0.597220\pi\) | |||||||
\(614\) | −55.7163 | −2.24853 | ||||||||
\(615\) | −19.8990 | −0.802406 | ||||||||
\(616\) | 8.85842 | 0.356916 | ||||||||
\(617\) | 0.394863 | 0.0158966 | 0.00794830 | − | 0.999968i | \(-0.497470\pi\) | ||||
0.00794830 | + | 0.999968i | \(0.497470\pi\) | |||||||
\(618\) | −25.0301 | −1.00686 | ||||||||
\(619\) | −25.5070 | −1.02521 | −0.512607 | − | 0.858623i | \(-0.671320\pi\) | ||||
−0.512607 | + | 0.858623i | \(0.671320\pi\) | |||||||
\(620\) | 76.4027 | 3.06841 | ||||||||
\(621\) | −24.4521 | −0.981230 | ||||||||
\(622\) | −42.1109 | −1.68849 | ||||||||
\(623\) | 6.50714 | 0.260703 | ||||||||
\(624\) | 3.79513 | 0.151927 | ||||||||
\(625\) | −30.7943 | −1.23177 | ||||||||
\(626\) | 3.32165 | 0.132760 | ||||||||
\(627\) | 7.72657 | 0.308569 | ||||||||
\(628\) | −65.6182 | −2.61845 | ||||||||
\(629\) | 10.5141 | 0.419224 | ||||||||
\(630\) | −1.42215 | −0.0566598 | ||||||||
\(631\) | −20.9015 | −0.832075 | −0.416038 | − | 0.909347i | \(-0.636581\pi\) | ||||
−0.416038 | + | 0.909347i | \(0.636581\pi\) | |||||||
\(632\) | 18.2306 | 0.725172 | ||||||||
\(633\) | −16.0267 | −0.637002 | ||||||||
\(634\) | 2.20648 | 0.0876305 | ||||||||
\(635\) | 7.65551 | 0.303799 | ||||||||
\(636\) | 37.6442 | 1.49269 | ||||||||
\(637\) | −9.07443 | −0.359542 | ||||||||
\(638\) | 86.7527 | 3.43457 | ||||||||
\(639\) | 0.294999 | 0.0116700 | ||||||||
\(640\) | 39.7023 | 1.56937 | ||||||||
\(641\) | −4.44033 | −0.175383 | −0.0876913 | − | 0.996148i | \(-0.527949\pi\) | ||||
−0.0876913 | + | 0.996148i | \(0.527949\pi\) | |||||||
\(642\) | −36.1118 | −1.42522 | ||||||||
\(643\) | −37.3499 | −1.47294 | −0.736468 | − | 0.676472i | \(-0.763508\pi\) | ||||
−0.736468 | + | 0.676472i | \(0.763508\pi\) | |||||||
\(644\) | 13.0064 | 0.512524 | ||||||||
\(645\) | 49.7025 | 1.95704 | ||||||||
\(646\) | 6.31222 | 0.248351 | ||||||||
\(647\) | 39.7561 | 1.56297 | 0.781487 | − | 0.623921i | \(-0.214461\pi\) | ||||
0.781487 | + | 0.623921i | \(0.214461\pi\) | |||||||
\(648\) | 15.8490 | 0.622608 | ||||||||
\(649\) | 20.6646 | 0.811157 | ||||||||
\(650\) | −10.5826 | −0.415083 | ||||||||
\(651\) | 15.4577 | 0.605834 | ||||||||
\(652\) | 33.4025 | 1.30814 | ||||||||
\(653\) | 16.2165 | 0.634603 | 0.317301 | − | 0.948325i | \(-0.397223\pi\) | ||||
0.317301 | + | 0.948325i | \(0.397223\pi\) | |||||||
\(654\) | −53.5342 | −2.09335 | ||||||||
\(655\) | −10.0407 | −0.392323 | ||||||||
\(656\) | −6.30384 | −0.246124 | ||||||||
\(657\) | 1.25090 | 0.0488023 | ||||||||
\(658\) | −23.2233 | −0.905337 | ||||||||
\(659\) | −1.23004 | −0.0479155 | −0.0239577 | − | 0.999713i | \(-0.507627\pi\) | ||||
−0.0239577 | + | 0.999713i | \(0.507627\pi\) | |||||||
\(660\) | −63.3715 | −2.46673 | ||||||||
\(661\) | −7.46481 | −0.290347 | −0.145174 | − | 0.989406i | \(-0.546374\pi\) | ||||
−0.145174 | + | 0.989406i | \(0.546374\pi\) | |||||||
\(662\) | 57.7999 | 2.24646 | ||||||||
\(663\) | −7.19708 | −0.279511 | ||||||||
\(664\) | 8.84140 | 0.343113 | ||||||||
\(665\) | 2.84875 | 0.110470 | ||||||||
\(666\) | 1.83476 | 0.0710955 | ||||||||
\(667\) | 38.5670 | 1.49332 | ||||||||
\(668\) | −4.85955 | −0.188022 | ||||||||
\(669\) | 9.36537 | 0.362086 | ||||||||
\(670\) | −63.9782 | −2.47169 | ||||||||
\(671\) | 3.14842 | 0.121544 | ||||||||
\(672\) | 11.8834 | 0.458412 | ||||||||
\(673\) | −37.0945 | −1.42989 | −0.714943 | − | 0.699183i | \(-0.753547\pi\) | ||||
−0.714943 | + | 0.699183i | \(0.753547\pi\) | |||||||
\(674\) | −73.4790 | −2.83031 | ||||||||
\(675\) | 17.0602 | 0.656647 | ||||||||
\(676\) | −30.7456 | −1.18252 | ||||||||
\(677\) | −6.67528 | −0.256552 | −0.128276 | − | 0.991739i | \(-0.540944\pi\) | ||||
−0.128276 | + | 0.991739i | \(0.540944\pi\) | |||||||
\(678\) | −19.8860 | −0.763717 | ||||||||
\(679\) | 3.53680 | 0.135730 | ||||||||
\(680\) | −15.6755 | −0.601129 | ||||||||
\(681\) | −23.4721 | −0.899452 | ||||||||
\(682\) | −95.3573 | −3.65142 | ||||||||
\(683\) | 15.0637 | 0.576398 | 0.288199 | − | 0.957571i | \(-0.406944\pi\) | ||||
0.288199 | + | 0.957571i | \(0.406944\pi\) | |||||||
\(684\) | 0.649012 | 0.0248156 | ||||||||
\(685\) | −22.6120 | −0.863959 | ||||||||
\(686\) | −28.5954 | −1.09178 | ||||||||
\(687\) | −24.1325 | −0.920711 | ||||||||
\(688\) | 15.7453 | 0.600286 | ||||||||
\(689\) | −11.9026 | −0.453453 | ||||||||
\(690\) | −47.8150 | −1.82028 | ||||||||
\(691\) | −44.5274 | −1.69390 | −0.846951 | − | 0.531671i | \(-0.821564\pi\) | ||||
−0.846951 | + | 0.531671i | \(0.821564\pi\) | |||||||
\(692\) | −14.4453 | −0.549126 | ||||||||
\(693\) | 1.04581 | 0.0397271 | ||||||||
\(694\) | 4.26958 | 0.162071 | ||||||||
\(695\) | −39.8475 | −1.51150 | ||||||||
\(696\) | −27.0494 | −1.02531 | ||||||||
\(697\) | 11.9546 | 0.452813 | ||||||||
\(698\) | 17.9453 | 0.679240 | ||||||||
\(699\) | −28.4803 | −1.07723 | ||||||||
\(700\) | −9.07452 | −0.342985 | ||||||||
\(701\) | −0.767459 | −0.0289865 | −0.0144933 | − | 0.999895i | \(-0.504614\pi\) | ||||
−0.0144933 | + | 0.999895i | \(0.504614\pi\) | |||||||
\(702\) | −17.9090 | −0.675932 | ||||||||
\(703\) | −3.67526 | −0.138615 | ||||||||
\(704\) | −59.3108 | −2.23536 | ||||||||
\(705\) | 50.3029 | 1.89452 | ||||||||
\(706\) | −28.0859 | −1.05703 | ||||||||
\(707\) | −3.17864 | −0.119545 | ||||||||
\(708\) | −21.2799 | −0.799749 | ||||||||
\(709\) | 38.0543 | 1.42916 | 0.714580 | − | 0.699553i | \(-0.246618\pi\) | ||||
0.714580 | + | 0.699553i | \(0.246618\pi\) | |||||||
\(710\) | 8.22574 | 0.308706 | ||||||||
\(711\) | 2.15227 | 0.0807164 | ||||||||
\(712\) | 12.5162 | 0.469066 | ||||||||
\(713\) | −42.3922 | −1.58760 | ||||||||
\(714\) | −10.4743 | −0.391991 | ||||||||
\(715\) | 20.0373 | 0.749351 | ||||||||
\(716\) | 32.1271 | 1.20065 | ||||||||
\(717\) | −39.4806 | −1.47443 | ||||||||
\(718\) | −55.2423 | −2.06163 | ||||||||
\(719\) | 24.9985 | 0.932288 | 0.466144 | − | 0.884709i | \(-0.345643\pi\) | ||||
0.466144 | + | 0.884709i | \(0.345643\pi\) | |||||||
\(720\) | 0.975863 | 0.0363683 | ||||||||
\(721\) | 6.78638 | 0.252738 | ||||||||
\(722\) | −2.20648 | −0.0821166 | ||||||||
\(723\) | −43.4427 | −1.61565 | ||||||||
\(724\) | 61.2205 | 2.27524 | ||||||||
\(725\) | −26.9081 | −0.999340 | ||||||||
\(726\) | 38.6704 | 1.43519 | ||||||||
\(727\) | −14.8519 | −0.550827 | −0.275413 | − | 0.961326i | \(-0.588815\pi\) | ||||
−0.275413 | + | 0.961326i | \(0.588815\pi\) | |||||||
\(728\) | 2.88432 | 0.106900 | ||||||||
\(729\) | 28.7175 | 1.06361 | ||||||||
\(730\) | 34.8801 | 1.29097 | ||||||||
\(731\) | −29.8595 | −1.10439 | ||||||||
\(732\) | −3.24217 | −0.119834 | ||||||||
\(733\) | −28.9854 | −1.07060 | −0.535300 | − | 0.844662i | \(-0.679801\pi\) | ||||
−0.535300 | + | 0.844662i | \(0.679801\pi\) | |||||||
\(734\) | 71.0732 | 2.62336 | ||||||||
\(735\) | 28.6061 | 1.05515 | ||||||||
\(736\) | −32.5899 | −1.20128 | ||||||||
\(737\) | 47.0479 | 1.73303 | ||||||||
\(738\) | 2.08614 | 0.0767919 | ||||||||
\(739\) | −9.66230 | −0.355434 | −0.177717 | − | 0.984082i | \(-0.556871\pi\) | ||||
−0.177717 | + | 0.984082i | \(0.556871\pi\) | |||||||
\(740\) | 30.1437 | 1.10810 | ||||||||
\(741\) | 2.51579 | 0.0924197 | ||||||||
\(742\) | −17.3225 | −0.635930 | ||||||||
\(743\) | 43.4995 | 1.59584 | 0.797922 | − | 0.602761i | \(-0.205933\pi\) | ||||
0.797922 | + | 0.602761i | \(0.205933\pi\) | |||||||
\(744\) | 29.7323 | 1.09004 | ||||||||
\(745\) | 3.14709 | 0.115300 | ||||||||
\(746\) | 75.0018 | 2.74601 | ||||||||
\(747\) | 1.04380 | 0.0381907 | ||||||||
\(748\) | 38.0713 | 1.39202 | ||||||||
\(749\) | 9.79096 | 0.357754 | ||||||||
\(750\) | −19.1747 | −0.700160 | ||||||||
\(751\) | 22.0101 | 0.803159 | 0.401580 | − | 0.915824i | \(-0.368461\pi\) | ||||
0.401580 | + | 0.915824i | \(0.368461\pi\) | |||||||
\(752\) | 15.9355 | 0.581109 | ||||||||
\(753\) | −7.34649 | −0.267721 | ||||||||
\(754\) | 28.2469 | 1.02869 | ||||||||
\(755\) | 63.0823 | 2.29580 | ||||||||
\(756\) | −15.3569 | −0.558525 | ||||||||
\(757\) | −26.2899 | −0.955521 | −0.477761 | − | 0.878490i | \(-0.658551\pi\) | ||||
−0.477761 | + | 0.878490i | \(0.658551\pi\) | |||||||
\(758\) | 45.6857 | 1.65938 | ||||||||
\(759\) | 35.1618 | 1.27629 | ||||||||
\(760\) | 5.47948 | 0.198762 | ||||||||
\(761\) | 48.1510 | 1.74547 | 0.872736 | − | 0.488193i | \(-0.162344\pi\) | ||||
0.872736 | + | 0.488193i | \(0.162344\pi\) | |||||||
\(762\) | 9.83925 | 0.356438 | ||||||||
\(763\) | 14.5147 | 0.525467 | ||||||||
\(764\) | −56.8954 | −2.05840 | ||||||||
\(765\) | −1.85063 | −0.0669095 | ||||||||
\(766\) | 7.68228 | 0.277572 | ||||||||
\(767\) | 6.72844 | 0.242950 | ||||||||
\(768\) | 8.44352 | 0.304679 | ||||||||
\(769\) | −0.670309 | −0.0241720 | −0.0120860 | − | 0.999927i | \(-0.503847\pi\) | ||||
−0.0120860 | + | 0.999927i | \(0.503847\pi\) | |||||||
\(770\) | 29.1614 | 1.05090 | ||||||||
\(771\) | 37.2563 | 1.34175 | ||||||||
\(772\) | −25.7339 | −0.926184 | ||||||||
\(773\) | −26.1415 | −0.940243 | −0.470122 | − | 0.882602i | \(-0.655790\pi\) | ||||
−0.470122 | + | 0.882602i | \(0.655790\pi\) | |||||||
\(774\) | −5.21063 | −0.187292 | ||||||||
\(775\) | 29.5769 | 1.06243 | ||||||||
\(776\) | 6.80292 | 0.244211 | ||||||||
\(777\) | 6.09862 | 0.218787 | ||||||||
\(778\) | −75.7217 | −2.71476 | ||||||||
\(779\) | −4.17881 | −0.149721 | ||||||||
\(780\) | −20.6339 | −0.738812 | ||||||||
\(781\) | −6.04899 | −0.216450 | ||||||||
\(782\) | 28.7255 | 1.02722 | ||||||||
\(783\) | −45.5368 | −1.62735 | ||||||||
\(784\) | 9.06216 | 0.323649 | ||||||||
\(785\) | −65.4045 | −2.33439 | ||||||||
\(786\) | −12.9048 | −0.460300 | ||||||||
\(787\) | 21.9967 | 0.784097 | 0.392049 | − | 0.919945i | \(-0.371767\pi\) | ||||
0.392049 | + | 0.919945i | \(0.371767\pi\) | |||||||
\(788\) | −19.5673 | −0.697055 | ||||||||
\(789\) | 11.1243 | 0.396036 | ||||||||
\(790\) | 60.0138 | 2.13520 | ||||||||
\(791\) | 5.39168 | 0.191706 | ||||||||
\(792\) | 2.01158 | 0.0714784 | ||||||||
\(793\) | 1.02513 | 0.0364036 | ||||||||
\(794\) | 41.8319 | 1.48456 | ||||||||
\(795\) | 37.5216 | 1.33075 | ||||||||
\(796\) | 12.6829 | 0.449533 | ||||||||
\(797\) | −17.2647 | −0.611548 | −0.305774 | − | 0.952104i | \(-0.598915\pi\) | ||||
−0.305774 | + | 0.952104i | \(0.598915\pi\) | |||||||
\(798\) | 3.66136 | 0.129611 | ||||||||
\(799\) | −30.2201 | −1.06911 | ||||||||
\(800\) | 22.7379 | 0.803905 | ||||||||
\(801\) | 1.47765 | 0.0522101 | ||||||||
\(802\) | 24.6274 | 0.869623 | ||||||||
\(803\) | −25.6499 | −0.905165 | ||||||||
\(804\) | −48.4488 | −1.70866 | ||||||||
\(805\) | 12.9640 | 0.456922 | ||||||||
\(806\) | −31.0485 | −1.09364 | ||||||||
\(807\) | 9.88896 | 0.348108 | ||||||||
\(808\) | −6.11401 | −0.215090 | ||||||||
\(809\) | 44.4877 | 1.56411 | 0.782053 | − | 0.623212i | \(-0.214173\pi\) | ||||
0.782053 | + | 0.623212i | \(0.214173\pi\) | |||||||
\(810\) | 52.1739 | 1.83321 | ||||||||
\(811\) | −40.3191 | −1.41580 | −0.707898 | − | 0.706315i | \(-0.750356\pi\) | ||||
−0.707898 | + | 0.706315i | \(0.750356\pi\) | |||||||
\(812\) | 24.2216 | 0.850010 | ||||||||
\(813\) | 46.9671 | 1.64721 | ||||||||
\(814\) | −37.6219 | −1.31865 | ||||||||
\(815\) | 33.2937 | 1.16623 | ||||||||
\(816\) | 7.18735 | 0.251608 | ||||||||
\(817\) | 10.4376 | 0.365164 | ||||||||
\(818\) | 71.2107 | 2.48982 | ||||||||
\(819\) | 0.340518 | 0.0118987 | ||||||||
\(820\) | 34.2737 | 1.19689 | ||||||||
\(821\) | 3.49194 | 0.121869 | 0.0609347 | − | 0.998142i | \(-0.480592\pi\) | ||||
0.0609347 | + | 0.998142i | \(0.480592\pi\) | |||||||
\(822\) | −29.0620 | −1.01366 | ||||||||
\(823\) | −11.3787 | −0.396636 | −0.198318 | − | 0.980138i | \(-0.563548\pi\) | ||||
−0.198318 | + | 0.980138i | \(0.563548\pi\) | |||||||
\(824\) | 13.0534 | 0.454736 | ||||||||
\(825\) | −24.5323 | −0.854105 | ||||||||
\(826\) | 9.79228 | 0.340717 | ||||||||
\(827\) | −25.2499 | −0.878025 | −0.439012 | − | 0.898481i | \(-0.644672\pi\) | ||||
−0.439012 | + | 0.898481i | \(0.644672\pi\) | |||||||
\(828\) | 2.95351 | 0.102641 | ||||||||
\(829\) | −25.8734 | −0.898620 | −0.449310 | − | 0.893376i | \(-0.648330\pi\) | ||||
−0.449310 | + | 0.893376i | \(0.648330\pi\) | |||||||
\(830\) | 29.1053 | 1.01026 | ||||||||
\(831\) | −19.1874 | −0.665604 | ||||||||
\(832\) | −19.3117 | −0.669514 | ||||||||
\(833\) | −17.1855 | −0.595442 | ||||||||
\(834\) | −51.2140 | −1.77340 | ||||||||
\(835\) | −4.84373 | −0.167624 | ||||||||
\(836\) | −13.3081 | −0.460269 | ||||||||
\(837\) | 50.0533 | 1.73010 | ||||||||
\(838\) | −40.9977 | −1.41624 | ||||||||
\(839\) | 48.0672 | 1.65946 | 0.829732 | − | 0.558162i | \(-0.188493\pi\) | ||||
0.829732 | + | 0.558162i | \(0.188493\pi\) | |||||||
\(840\) | −9.09248 | −0.313720 | ||||||||
\(841\) | 42.8226 | 1.47664 | ||||||||
\(842\) | −44.5966 | −1.53690 | ||||||||
\(843\) | −10.4170 | −0.358779 | ||||||||
\(844\) | 27.6040 | 0.950168 | ||||||||
\(845\) | −30.6455 | −1.05424 | ||||||||
\(846\) | −5.27357 | −0.181309 | ||||||||
\(847\) | −10.4847 | −0.360258 | ||||||||
\(848\) | 11.8865 | 0.408185 | ||||||||
\(849\) | −44.3080 | −1.52065 | ||||||||
\(850\) | −20.0417 | −0.687424 | ||||||||
\(851\) | −16.7253 | −0.573335 | ||||||||
\(852\) | 6.22910 | 0.213406 | ||||||||
\(853\) | −4.01704 | −0.137541 | −0.0687704 | − | 0.997633i | \(-0.521908\pi\) | ||||
−0.0687704 | + | 0.997633i | \(0.521908\pi\) | |||||||
\(854\) | 1.49193 | 0.0510530 | ||||||||
\(855\) | 0.646899 | 0.0221235 | ||||||||
\(856\) | 18.8326 | 0.643684 | ||||||||
\(857\) | 5.40918 | 0.184774 | 0.0923870 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923870 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(858\) | 25.7529 | 0.879190 | ||||||||
\(859\) | 34.5560 | 1.17904 | 0.589518 | − | 0.807755i | \(-0.299318\pi\) | ||||
0.589518 | + | 0.807755i | \(0.299318\pi\) | |||||||
\(860\) | −85.6066 | −2.91916 | ||||||||
\(861\) | 6.93419 | 0.236317 | ||||||||
\(862\) | −45.6319 | −1.55423 | ||||||||
\(863\) | 19.5155 | 0.664316 | 0.332158 | − | 0.943224i | \(-0.392223\pi\) | ||||
0.332158 | + | 0.943224i | \(0.392223\pi\) | |||||||
\(864\) | 38.4795 | 1.30910 | ||||||||
\(865\) | −14.3982 | −0.489554 | ||||||||
\(866\) | 75.4696 | 2.56456 | ||||||||
\(867\) | 14.6827 | 0.498650 | ||||||||
\(868\) | −26.6240 | −0.903677 | ||||||||
\(869\) | −44.1325 | −1.49709 | ||||||||
\(870\) | −89.0449 | −3.01891 | ||||||||
\(871\) | 15.3189 | 0.519061 | ||||||||
\(872\) | 27.9185 | 0.945440 | ||||||||
\(873\) | 0.803142 | 0.0271822 | ||||||||
\(874\) | −10.0412 | −0.339648 | ||||||||
\(875\) | 5.19881 | 0.175752 | ||||||||
\(876\) | 26.4136 | 0.892434 | ||||||||
\(877\) | 9.27680 | 0.313255 | 0.156628 | − | 0.987658i | \(-0.449938\pi\) | ||||
0.156628 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(878\) | −10.9219 | −0.368596 | ||||||||
\(879\) | 15.3176 | 0.516651 | ||||||||
\(880\) | −20.0102 | −0.674543 | ||||||||
\(881\) | −12.5957 | −0.424359 | −0.212179 | − | 0.977231i | \(-0.568056\pi\) | ||||
−0.212179 | + | 0.977231i | \(0.568056\pi\) | |||||||
\(882\) | −2.99895 | −0.100980 | ||||||||
\(883\) | −22.2634 | −0.749224 | −0.374612 | − | 0.927182i | \(-0.622224\pi\) | ||||
−0.374612 | + | 0.927182i | \(0.622224\pi\) | |||||||
\(884\) | 12.3961 | 0.416926 | ||||||||
\(885\) | −21.2106 | −0.712987 | ||||||||
\(886\) | −33.4880 | −1.12505 | ||||||||
\(887\) | −25.6123 | −0.859978 | −0.429989 | − | 0.902834i | \(-0.641483\pi\) | ||||
−0.429989 | + | 0.902834i | \(0.641483\pi\) | |||||||
\(888\) | 11.7305 | 0.393649 | ||||||||
\(889\) | −2.66771 | −0.0894720 | ||||||||
\(890\) | 41.2027 | 1.38112 | ||||||||
\(891\) | −38.3673 | −1.28535 | ||||||||
\(892\) | −16.1307 | −0.540096 | ||||||||
\(893\) | 10.5636 | 0.353499 | ||||||||
\(894\) | 4.04480 | 0.135278 | ||||||||
\(895\) | 32.0225 | 1.07039 | ||||||||
\(896\) | −13.8350 | −0.462195 | ||||||||
\(897\) | 11.4488 | 0.382263 | ||||||||
\(898\) | −34.4939 | −1.15108 | ||||||||
\(899\) | −78.9463 | −2.63301 | ||||||||
\(900\) | −2.06065 | −0.0686884 | ||||||||
\(901\) | −22.5416 | −0.750969 | ||||||||
\(902\) | −42.7765 | −1.42430 | ||||||||
\(903\) | −17.3198 | −0.576367 | ||||||||
\(904\) | 10.3707 | 0.344924 | ||||||||
\(905\) | 61.0211 | 2.02841 | ||||||||
\(906\) | 81.0766 | 2.69359 | ||||||||
\(907\) | 11.8235 | 0.392594 | 0.196297 | − | 0.980544i | \(-0.437108\pi\) | ||||
0.196297 | + | 0.980544i | \(0.437108\pi\) | |||||||
\(908\) | 40.4278 | 1.34164 | ||||||||
\(909\) | −0.721810 | −0.0239409 | ||||||||
\(910\) | 9.49500 | 0.314756 | ||||||||
\(911\) | −33.8940 | −1.12296 | −0.561479 | − | 0.827491i | \(-0.689767\pi\) | ||||
−0.561479 | + | 0.827491i | \(0.689767\pi\) | |||||||
\(912\) | −2.51239 | −0.0831934 | ||||||||
\(913\) | −21.4033 | −0.708345 | ||||||||
\(914\) | 43.2883 | 1.43185 | ||||||||
\(915\) | −3.23161 | −0.106834 | ||||||||
\(916\) | 41.5652 | 1.37335 | ||||||||
\(917\) | 3.49888 | 0.115543 | ||||||||
\(918\) | −33.9167 | −1.11942 | ||||||||
\(919\) | 49.0190 | 1.61699 | 0.808493 | − | 0.588505i | \(-0.200283\pi\) | ||||
0.808493 | + | 0.588505i | \(0.200283\pi\) | |||||||
\(920\) | 24.9359 | 0.822111 | ||||||||
\(921\) | −42.0548 | −1.38575 | ||||||||
\(922\) | 42.4472 | 1.39792 | ||||||||
\(923\) | −1.96956 | −0.0648290 | ||||||||
\(924\) | 22.0830 | 0.726478 | ||||||||
\(925\) | 11.6692 | 0.383680 | ||||||||
\(926\) | −71.2369 | −2.34099 | ||||||||
\(927\) | 1.54106 | 0.0506151 | ||||||||
\(928\) | −60.6916 | −1.99230 | ||||||||
\(929\) | −34.9824 | −1.14774 | −0.573868 | − | 0.818948i | \(-0.694558\pi\) | ||||
−0.573868 | + | 0.818948i | \(0.694558\pi\) | |||||||
\(930\) | 97.8769 | 3.20951 | ||||||||
\(931\) | 6.00730 | 0.196881 | ||||||||
\(932\) | 49.0539 | 1.60681 | ||||||||
\(933\) | −31.7855 | −1.04061 | ||||||||
\(934\) | 48.4851 | 1.58648 | ||||||||
\(935\) | 37.9473 | 1.24101 | ||||||||
\(936\) | 0.654975 | 0.0214085 | ||||||||
\(937\) | 60.6607 | 1.98170 | 0.990849 | − | 0.134973i | \(-0.0430946\pi\) | ||||
0.990849 | + | 0.134973i | \(0.0430946\pi\) | |||||||
\(938\) | 22.2944 | 0.727939 | ||||||||
\(939\) | 2.50719 | 0.0818192 | ||||||||
\(940\) | −86.6406 | −2.82591 | ||||||||
\(941\) | −25.9431 | −0.845722 | −0.422861 | − | 0.906194i | \(-0.638974\pi\) | ||||
−0.422861 | + | 0.906194i | \(0.638974\pi\) | |||||||
\(942\) | −84.0611 | −2.73886 | ||||||||
\(943\) | −19.0168 | −0.619273 | ||||||||
\(944\) | −6.71935 | −0.218696 | ||||||||
\(945\) | −15.3069 | −0.497933 | ||||||||
\(946\) | 106.844 | 3.47381 | ||||||||
\(947\) | 5.97264 | 0.194085 | 0.0970423 | − | 0.995280i | \(-0.469062\pi\) | ||||
0.0970423 | + | 0.995280i | \(0.469062\pi\) | |||||||
\(948\) | 45.4466 | 1.47604 | ||||||||
\(949\) | −8.35166 | −0.271106 | ||||||||
\(950\) | 7.00570 | 0.227295 | ||||||||
\(951\) | 1.66546 | 0.0540062 | ||||||||
\(952\) | 5.46243 | 0.177038 | ||||||||
\(953\) | −25.9103 | −0.839317 | −0.419658 | − | 0.907682i | \(-0.637850\pi\) | ||||
−0.419658 | + | 0.907682i | \(0.637850\pi\) | |||||||
\(954\) | −3.93362 | −0.127356 | ||||||||
\(955\) | −56.7101 | −1.83510 | ||||||||
\(956\) | 68.0005 | 2.19929 | ||||||||
\(957\) | 65.4812 | 2.11671 | ||||||||
\(958\) | 1.40537 | 0.0454053 | ||||||||
\(959\) | 7.87957 | 0.254445 | ||||||||
\(960\) | 60.8780 | 1.96483 | ||||||||
\(961\) | 55.7766 | 1.79924 | ||||||||
\(962\) | −12.2498 | −0.394949 | ||||||||
\(963\) | 2.22334 | 0.0716462 | ||||||||
\(964\) | 74.8247 | 2.40994 | ||||||||
\(965\) | −25.6501 | −0.825706 | ||||||||
\(966\) | 16.6620 | 0.536092 | ||||||||
\(967\) | 32.1479 | 1.03381 | 0.516904 | − | 0.856043i | \(-0.327084\pi\) | ||||
0.516904 | + | 0.856043i | \(0.327084\pi\) | |||||||
\(968\) | −20.1669 | −0.648189 | ||||||||
\(969\) | 4.76449 | 0.153057 | ||||||||
\(970\) | 22.3948 | 0.719053 | ||||||||
\(971\) | −48.5836 | −1.55912 | −0.779561 | − | 0.626327i | \(-0.784558\pi\) | ||||
−0.779561 | + | 0.626327i | \(0.784558\pi\) | |||||||
\(972\) | −6.72997 | −0.215864 | ||||||||
\(973\) | 13.8856 | 0.445152 | ||||||||
\(974\) | 47.5578 | 1.52385 | ||||||||
\(975\) | −7.98777 | −0.255813 | ||||||||
\(976\) | −1.02375 | −0.0327694 | ||||||||
\(977\) | −21.2550 | −0.680009 | −0.340004 | − | 0.940424i | \(-0.610429\pi\) | ||||
−0.340004 | + | 0.940424i | \(0.610429\pi\) | |||||||
\(978\) | 42.7908 | 1.36830 | ||||||||
\(979\) | −30.2993 | −0.968371 | ||||||||
\(980\) | −49.2705 | −1.57389 | ||||||||
\(981\) | 3.29601 | 0.105234 | ||||||||
\(982\) | −31.3086 | −0.999099 | ||||||||
\(983\) | 37.4467 | 1.19436 | 0.597181 | − | 0.802106i | \(-0.296287\pi\) | ||||
0.597181 | + | 0.802106i | \(0.296287\pi\) | |||||||
\(984\) | 13.3377 | 0.425190 | ||||||||
\(985\) | −19.5035 | −0.621434 | ||||||||
\(986\) | 53.4949 | 1.70363 | ||||||||
\(987\) | −17.5290 | −0.557954 | ||||||||
\(988\) | −4.33314 | −0.137855 | ||||||||
\(989\) | 47.4990 | 1.51038 | ||||||||
\(990\) | 6.62200 | 0.210461 | ||||||||
\(991\) | 48.0090 | 1.52506 | 0.762528 | − | 0.646956i | \(-0.223958\pi\) | ||||
0.762528 | + | 0.646956i | \(0.223958\pi\) | |||||||
\(992\) | 66.7113 | 2.11808 | ||||||||
\(993\) | 43.6275 | 1.38448 | ||||||||
\(994\) | −2.86641 | −0.0909172 | ||||||||
\(995\) | 12.6416 | 0.400765 | ||||||||
\(996\) | 22.0406 | 0.698383 | ||||||||
\(997\) | −47.6187 | −1.50810 | −0.754050 | − | 0.656817i | \(-0.771902\pi\) | ||||
−0.754050 | + | 0.656817i | \(0.771902\pi\) | |||||||
\(998\) | 20.7110 | 0.655594 | ||||||||
\(999\) | 19.7479 | 0.624795 |
(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 | 6023.2.a.b.1.14 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.14 | ✓ | 99 | 1.1 | even | 1 | trivial |