Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,2,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, 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("1441.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(11.5064429313\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13757 | 0.804381 | 0.402190 | − | 0.915556i | \(-0.368249\pi\) | ||||
0.402190 | + | 0.915556i | \(0.368249\pi\) | |||||||
\(3\) | −1.95057 | −1.12616 | −0.563082 | − | 0.826401i | \(-0.690384\pi\) | ||||
−0.563082 | + | 0.826401i | \(0.690384\pi\) | |||||||
\(4\) | −0.705942 | −0.352971 | ||||||||
\(5\) | 1.75766 | 0.786047 | 0.393024 | − | 0.919528i | \(-0.371429\pi\) | ||||
0.393024 | + | 0.919528i | \(0.371429\pi\) | |||||||
\(6\) | −2.21891 | −0.905865 | ||||||||
\(7\) | 1.09174 | 0.412641 | 0.206320 | − | 0.978485i | \(-0.433851\pi\) | ||||
0.206320 | + | 0.978485i | \(0.433851\pi\) | |||||||
\(8\) | −3.07819 | −1.08830 | ||||||||
\(9\) | 0.804735 | 0.268245 | ||||||||
\(10\) | 1.99945 | 0.632282 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 1.37699 | 0.397503 | ||||||||
\(13\) | 2.00061 | 0.554870 | 0.277435 | − | 0.960744i | \(-0.410516\pi\) | ||||
0.277435 | + | 0.960744i | \(0.410516\pi\) | |||||||
\(14\) | 1.24193 | 0.331920 | ||||||||
\(15\) | −3.42844 | −0.885218 | ||||||||
\(16\) | −2.08976 | −0.522440 | ||||||||
\(17\) | 3.43459 | 0.833011 | 0.416506 | − | 0.909133i | \(-0.363255\pi\) | ||||
0.416506 | + | 0.909133i | \(0.363255\pi\) | |||||||
\(18\) | 0.915439 | 0.215771 | ||||||||
\(19\) | −2.69464 | −0.618194 | −0.309097 | − | 0.951031i | \(-0.600027\pi\) | ||||
−0.309097 | + | 0.951031i | \(0.600027\pi\) | |||||||
\(20\) | −1.24080 | −0.277452 | ||||||||
\(21\) | −2.12953 | −0.464701 | ||||||||
\(22\) | −1.13757 | −0.242530 | ||||||||
\(23\) | 4.47210 | 0.932498 | 0.466249 | − | 0.884654i | \(-0.345605\pi\) | ||||
0.466249 | + | 0.884654i | \(0.345605\pi\) | |||||||
\(24\) | 6.00423 | 1.22561 | ||||||||
\(25\) | −1.91065 | −0.382130 | ||||||||
\(26\) | 2.27583 | 0.446327 | ||||||||
\(27\) | 4.28202 | 0.824076 | ||||||||
\(28\) | −0.770709 | −0.145650 | ||||||||
\(29\) | −6.09860 | −1.13248 | −0.566241 | − | 0.824240i | \(-0.691603\pi\) | ||||
−0.566241 | + | 0.824240i | \(0.691603\pi\) | |||||||
\(30\) | −3.90007 | −0.712053 | ||||||||
\(31\) | 6.39697 | 1.14893 | 0.574465 | − | 0.818529i | \(-0.305210\pi\) | ||||
0.574465 | + | 0.818529i | \(0.305210\pi\) | |||||||
\(32\) | 3.77914 | 0.668063 | ||||||||
\(33\) | 1.95057 | 0.339551 | ||||||||
\(34\) | 3.90708 | 0.670058 | ||||||||
\(35\) | 1.91891 | 0.324355 | ||||||||
\(36\) | −0.568096 | −0.0946827 | ||||||||
\(37\) | 9.61513 | 1.58072 | 0.790359 | − | 0.612644i | \(-0.209894\pi\) | ||||
0.790359 | + | 0.612644i | \(0.209894\pi\) | |||||||
\(38\) | −3.06534 | −0.497263 | ||||||||
\(39\) | −3.90234 | −0.624874 | ||||||||
\(40\) | −5.41040 | −0.855459 | ||||||||
\(41\) | −7.70692 | −1.20362 | −0.601809 | − | 0.798640i | \(-0.705553\pi\) | ||||
−0.601809 | + | 0.798640i | \(0.705553\pi\) | |||||||
\(42\) | −2.42248 | −0.373797 | ||||||||
\(43\) | 5.45427 | 0.831768 | 0.415884 | − | 0.909418i | \(-0.363472\pi\) | ||||
0.415884 | + | 0.909418i | \(0.363472\pi\) | |||||||
\(44\) | 0.705942 | 0.106425 | ||||||||
\(45\) | 1.41445 | 0.210853 | ||||||||
\(46\) | 5.08731 | 0.750083 | ||||||||
\(47\) | 11.4366 | 1.66820 | 0.834101 | − | 0.551611i | \(-0.185987\pi\) | ||||
0.834101 | + | 0.551611i | \(0.185987\pi\) | |||||||
\(48\) | 4.07623 | 0.588353 | ||||||||
\(49\) | −5.80809 | −0.829728 | ||||||||
\(50\) | −2.17349 | −0.307378 | ||||||||
\(51\) | −6.69942 | −0.938107 | ||||||||
\(52\) | −1.41232 | −0.195853 | ||||||||
\(53\) | 0.811524 | 0.111471 | 0.0557357 | − | 0.998446i | \(-0.482250\pi\) | ||||
0.0557357 | + | 0.998446i | \(0.482250\pi\) | |||||||
\(54\) | 4.87109 | 0.662871 | ||||||||
\(55\) | −1.75766 | −0.237002 | ||||||||
\(56\) | −3.36060 | −0.449079 | ||||||||
\(57\) | 5.25610 | 0.696187 | ||||||||
\(58\) | −6.93756 | −0.910947 | ||||||||
\(59\) | 15.0522 | 1.95962 | 0.979812 | − | 0.199923i | \(-0.0640694\pi\) | ||||
0.979812 | + | 0.199923i | \(0.0640694\pi\) | |||||||
\(60\) | 2.42028 | 0.312457 | ||||||||
\(61\) | 5.64667 | 0.722982 | 0.361491 | − | 0.932376i | \(-0.382268\pi\) | ||||
0.361491 | + | 0.932376i | \(0.382268\pi\) | |||||||
\(62\) | 7.27698 | 0.924178 | ||||||||
\(63\) | 0.878565 | 0.110689 | ||||||||
\(64\) | 8.47854 | 1.05982 | ||||||||
\(65\) | 3.51639 | 0.436154 | ||||||||
\(66\) | 2.21891 | 0.273128 | ||||||||
\(67\) | −11.0074 | −1.34476 | −0.672382 | − | 0.740204i | \(-0.734729\pi\) | ||||
−0.672382 | + | 0.740204i | \(0.734729\pi\) | |||||||
\(68\) | −2.42463 | −0.294029 | ||||||||
\(69\) | −8.72316 | −1.05015 | ||||||||
\(70\) | 2.18289 | 0.260905 | ||||||||
\(71\) | 5.93400 | 0.704236 | 0.352118 | − | 0.935956i | \(-0.385462\pi\) | ||||
0.352118 | + | 0.935956i | \(0.385462\pi\) | |||||||
\(72\) | −2.47713 | −0.291932 | ||||||||
\(73\) | 8.69955 | 1.01821 | 0.509103 | − | 0.860706i | \(-0.329977\pi\) | ||||
0.509103 | + | 0.860706i | \(0.329977\pi\) | |||||||
\(74\) | 10.9379 | 1.27150 | ||||||||
\(75\) | 3.72686 | 0.430340 | ||||||||
\(76\) | 1.90226 | 0.218205 | ||||||||
\(77\) | −1.09174 | −0.124416 | ||||||||
\(78\) | −4.43917 | −0.502637 | ||||||||
\(79\) | 1.30616 | 0.146954 | 0.0734771 | − | 0.997297i | \(-0.476590\pi\) | ||||
0.0734771 | + | 0.997297i | \(0.476590\pi\) | |||||||
\(80\) | −3.67308 | −0.410663 | ||||||||
\(81\) | −10.7666 | −1.19629 | ||||||||
\(82\) | −8.76713 | −0.968168 | ||||||||
\(83\) | 14.3500 | 1.57511 | 0.787557 | − | 0.616242i | \(-0.211346\pi\) | ||||
0.787557 | + | 0.616242i | \(0.211346\pi\) | |||||||
\(84\) | 1.50332 | 0.164026 | ||||||||
\(85\) | 6.03683 | 0.654786 | ||||||||
\(86\) | 6.20459 | 0.669058 | ||||||||
\(87\) | 11.8958 | 1.27536 | ||||||||
\(88\) | 3.07819 | 0.328136 | ||||||||
\(89\) | 5.83903 | 0.618936 | 0.309468 | − | 0.950910i | \(-0.399849\pi\) | ||||
0.309468 | + | 0.950910i | \(0.399849\pi\) | |||||||
\(90\) | 1.60903 | 0.169606 | ||||||||
\(91\) | 2.18416 | 0.228962 | ||||||||
\(92\) | −3.15705 | −0.329145 | ||||||||
\(93\) | −12.4778 | −1.29388 | ||||||||
\(94\) | 13.0099 | 1.34187 | ||||||||
\(95\) | −4.73625 | −0.485929 | ||||||||
\(96\) | −7.37148 | −0.752349 | ||||||||
\(97\) | 7.73029 | 0.784892 | 0.392446 | − | 0.919775i | \(-0.371629\pi\) | ||||
0.392446 | + | 0.919775i | \(0.371629\pi\) | |||||||
\(98\) | −6.60709 | −0.667417 | ||||||||
\(99\) | −0.804735 | −0.0808789 | ||||||||
\(100\) | 1.34881 | 0.134881 | ||||||||
\(101\) | −11.7973 | −1.17387 | −0.586937 | − | 0.809632i | \(-0.699667\pi\) | ||||
−0.586937 | + | 0.809632i | \(0.699667\pi\) | |||||||
\(102\) | −7.62104 | −0.754596 | ||||||||
\(103\) | 4.45932 | 0.439390 | 0.219695 | − | 0.975569i | \(-0.429494\pi\) | ||||
0.219695 | + | 0.975569i | \(0.429494\pi\) | |||||||
\(104\) | −6.15826 | −0.603867 | ||||||||
\(105\) | −3.74297 | −0.365277 | ||||||||
\(106\) | 0.923163 | 0.0896655 | ||||||||
\(107\) | −3.65710 | −0.353545 | −0.176773 | − | 0.984252i | \(-0.556566\pi\) | ||||
−0.176773 | + | 0.984252i | \(0.556566\pi\) | |||||||
\(108\) | −3.02286 | −0.290875 | ||||||||
\(109\) | 1.87716 | 0.179799 | 0.0898996 | − | 0.995951i | \(-0.471345\pi\) | ||||
0.0898996 | + | 0.995951i | \(0.471345\pi\) | |||||||
\(110\) | −1.99945 | −0.190640 | ||||||||
\(111\) | −18.7550 | −1.78015 | ||||||||
\(112\) | −2.28148 | −0.215580 | ||||||||
\(113\) | −8.95939 | −0.842829 | −0.421414 | − | 0.906868i | \(-0.638466\pi\) | ||||
−0.421414 | + | 0.906868i | \(0.638466\pi\) | |||||||
\(114\) | 5.97916 | 0.560000 | ||||||||
\(115\) | 7.86041 | 0.732987 | ||||||||
\(116\) | 4.30526 | 0.399734 | ||||||||
\(117\) | 1.60996 | 0.148841 | ||||||||
\(118\) | 17.1228 | 1.57628 | ||||||||
\(119\) | 3.74970 | 0.343734 | ||||||||
\(120\) | 10.5534 | 0.963387 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.42346 | 0.581553 | ||||||||
\(123\) | 15.0329 | 1.35547 | ||||||||
\(124\) | −4.51590 | −0.405539 | ||||||||
\(125\) | −12.1465 | −1.08642 | ||||||||
\(126\) | 0.999426 | 0.0890359 | ||||||||
\(127\) | 9.18504 | 0.815040 | 0.407520 | − | 0.913196i | \(-0.366394\pi\) | ||||
0.407520 | + | 0.913196i | \(0.366394\pi\) | |||||||
\(128\) | 2.08663 | 0.184434 | ||||||||
\(129\) | −10.6389 | −0.936707 | ||||||||
\(130\) | 4.00012 | 0.350834 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −1.37699 | −0.119852 | ||||||||
\(133\) | −2.94186 | −0.255092 | ||||||||
\(134\) | −12.5216 | −1.08170 | ||||||||
\(135\) | 7.52632 | 0.647763 | ||||||||
\(136\) | −10.5723 | −0.906570 | ||||||||
\(137\) | 15.8488 | 1.35405 | 0.677025 | − | 0.735960i | \(-0.263269\pi\) | ||||
0.677025 | + | 0.735960i | \(0.263269\pi\) | |||||||
\(138\) | −9.92318 | −0.844717 | ||||||||
\(139\) | −17.8990 | −1.51818 | −0.759088 | − | 0.650988i | \(-0.774355\pi\) | ||||
−0.759088 | + | 0.650988i | \(0.774355\pi\) | |||||||
\(140\) | −1.35464 | −0.114488 | ||||||||
\(141\) | −22.3080 | −1.87867 | ||||||||
\(142\) | 6.75031 | 0.566474 | ||||||||
\(143\) | −2.00061 | −0.167300 | ||||||||
\(144\) | −1.68170 | −0.140142 | ||||||||
\(145\) | −10.7192 | −0.890184 | ||||||||
\(146\) | 9.89632 | 0.819025 | ||||||||
\(147\) | 11.3291 | 0.934409 | ||||||||
\(148\) | −6.78773 | −0.557948 | ||||||||
\(149\) | −5.65189 | −0.463021 | −0.231510 | − | 0.972832i | \(-0.574367\pi\) | ||||
−0.231510 | + | 0.972832i | \(0.574367\pi\) | |||||||
\(150\) | 4.23955 | 0.346158 | ||||||||
\(151\) | −22.8834 | −1.86222 | −0.931112 | − | 0.364734i | \(-0.881160\pi\) | ||||
−0.931112 | + | 0.364734i | \(0.881160\pi\) | |||||||
\(152\) | 8.29462 | 0.672783 | ||||||||
\(153\) | 2.76394 | 0.223451 | ||||||||
\(154\) | −1.24193 | −0.100078 | ||||||||
\(155\) | 11.2437 | 0.903114 | ||||||||
\(156\) | 2.75483 | 0.220563 | ||||||||
\(157\) | 4.45835 | 0.355815 | 0.177908 | − | 0.984047i | \(-0.443067\pi\) | ||||
0.177908 | + | 0.984047i | \(0.443067\pi\) | |||||||
\(158\) | 1.48584 | 0.118207 | ||||||||
\(159\) | −1.58294 | −0.125535 | ||||||||
\(160\) | 6.64242 | 0.525130 | ||||||||
\(161\) | 4.88239 | 0.384786 | ||||||||
\(162\) | −12.2477 | −0.962273 | ||||||||
\(163\) | 0.308265 | 0.0241452 | 0.0120726 | − | 0.999927i | \(-0.496157\pi\) | ||||
0.0120726 | + | 0.999927i | \(0.496157\pi\) | |||||||
\(164\) | 5.44064 | 0.424843 | ||||||||
\(165\) | 3.42844 | 0.266903 | ||||||||
\(166\) | 16.3240 | 1.26699 | ||||||||
\(167\) | 18.4166 | 1.42512 | 0.712561 | − | 0.701610i | \(-0.247535\pi\) | ||||
0.712561 | + | 0.701610i | \(0.247535\pi\) | |||||||
\(168\) | 6.55509 | 0.505736 | ||||||||
\(169\) | −8.99755 | −0.692120 | ||||||||
\(170\) | 6.86730 | 0.526698 | ||||||||
\(171\) | −2.16847 | −0.165827 | ||||||||
\(172\) | −3.85040 | −0.293590 | ||||||||
\(173\) | −13.8103 | −1.04998 | −0.524989 | − | 0.851109i | \(-0.675931\pi\) | ||||
−0.524989 | + | 0.851109i | \(0.675931\pi\) | |||||||
\(174\) | 13.5322 | 1.02588 | ||||||||
\(175\) | −2.08594 | −0.157682 | ||||||||
\(176\) | 2.08976 | 0.157522 | ||||||||
\(177\) | −29.3603 | −2.20686 | ||||||||
\(178\) | 6.64229 | 0.497861 | ||||||||
\(179\) | 15.6504 | 1.16977 | 0.584884 | − | 0.811117i | \(-0.301140\pi\) | ||||
0.584884 | + | 0.811117i | \(0.301140\pi\) | |||||||
\(180\) | −0.998518 | −0.0744251 | ||||||||
\(181\) | −7.04581 | −0.523711 | −0.261855 | − | 0.965107i | \(-0.584334\pi\) | ||||
−0.261855 | + | 0.965107i | \(0.584334\pi\) | |||||||
\(182\) | 2.48462 | 0.184172 | ||||||||
\(183\) | −11.0142 | −0.814196 | ||||||||
\(184\) | −13.7660 | −1.01484 | ||||||||
\(185\) | 16.9001 | 1.24252 | ||||||||
\(186\) | −14.1943 | −1.04078 | ||||||||
\(187\) | −3.43459 | −0.251162 | ||||||||
\(188\) | −8.07360 | −0.588828 | ||||||||
\(189\) | 4.67488 | 0.340047 | ||||||||
\(190\) | −5.38780 | −0.390872 | ||||||||
\(191\) | −8.39998 | −0.607801 | −0.303901 | − | 0.952704i | \(-0.598289\pi\) | ||||
−0.303901 | + | 0.952704i | \(0.598289\pi\) | |||||||
\(192\) | −16.5380 | −1.19353 | ||||||||
\(193\) | −3.92772 | −0.282724 | −0.141362 | − | 0.989958i | \(-0.545148\pi\) | ||||
−0.141362 | + | 0.989958i | \(0.545148\pi\) | |||||||
\(194\) | 8.79372 | 0.631353 | ||||||||
\(195\) | −6.85897 | −0.491181 | ||||||||
\(196\) | 4.10018 | 0.292870 | ||||||||
\(197\) | −15.4093 | −1.09787 | −0.548934 | − | 0.835866i | \(-0.684966\pi\) | ||||
−0.548934 | + | 0.835866i | \(0.684966\pi\) | |||||||
\(198\) | −0.915439 | −0.0650574 | ||||||||
\(199\) | 21.9965 | 1.55929 | 0.779647 | − | 0.626220i | \(-0.215399\pi\) | ||||
0.779647 | + | 0.626220i | \(0.215399\pi\) | |||||||
\(200\) | 5.88134 | 0.415873 | ||||||||
\(201\) | 21.4707 | 1.51443 | ||||||||
\(202\) | −13.4202 | −0.944242 | ||||||||
\(203\) | −6.65811 | −0.467308 | ||||||||
\(204\) | 4.72941 | 0.331125 | ||||||||
\(205\) | −13.5461 | −0.946101 | ||||||||
\(206\) | 5.07278 | 0.353437 | ||||||||
\(207\) | 3.59886 | 0.250138 | ||||||||
\(208\) | −4.18080 | −0.289886 | ||||||||
\(209\) | 2.69464 | 0.186392 | ||||||||
\(210\) | −4.25788 | −0.293822 | ||||||||
\(211\) | 19.0523 | 1.31162 | 0.655808 | − | 0.754928i | \(-0.272328\pi\) | ||||
0.655808 | + | 0.754928i | \(0.272328\pi\) | |||||||
\(212\) | −0.572889 | −0.0393462 | ||||||||
\(213\) | −11.5747 | −0.793085 | ||||||||
\(214\) | −4.16020 | −0.284385 | ||||||||
\(215\) | 9.58672 | 0.653809 | ||||||||
\(216\) | −13.1809 | −0.896846 | ||||||||
\(217\) | 6.98386 | 0.474095 | ||||||||
\(218\) | 2.13539 | 0.144627 | ||||||||
\(219\) | −16.9691 | −1.14667 | ||||||||
\(220\) | 1.24080 | 0.0836550 | ||||||||
\(221\) | 6.87129 | 0.462213 | ||||||||
\(222\) | −21.3351 | −1.43192 | ||||||||
\(223\) | −24.2701 | −1.62525 | −0.812624 | − | 0.582788i | \(-0.801962\pi\) | ||||
−0.812624 | + | 0.582788i | \(0.801962\pi\) | |||||||
\(224\) | 4.12585 | 0.275670 | ||||||||
\(225\) | −1.53756 | −0.102504 | ||||||||
\(226\) | −10.1919 | −0.677956 | ||||||||
\(227\) | 14.5859 | 0.968102 | 0.484051 | − | 0.875040i | \(-0.339165\pi\) | ||||
0.484051 | + | 0.875040i | \(0.339165\pi\) | |||||||
\(228\) | −3.71050 | −0.245734 | ||||||||
\(229\) | −6.10368 | −0.403343 | −0.201671 | − | 0.979453i | \(-0.564637\pi\) | ||||
−0.201671 | + | 0.979453i | \(0.564637\pi\) | |||||||
\(230\) | 8.94174 | 0.589601 | ||||||||
\(231\) | 2.12953 | 0.140113 | ||||||||
\(232\) | 18.7727 | 1.23248 | ||||||||
\(233\) | −28.0101 | −1.83500 | −0.917501 | − | 0.397734i | \(-0.869797\pi\) | ||||
−0.917501 | + | 0.397734i | \(0.869797\pi\) | |||||||
\(234\) | 1.83144 | 0.119725 | ||||||||
\(235\) | 20.1016 | 1.31129 | ||||||||
\(236\) | −10.6260 | −0.691691 | ||||||||
\(237\) | −2.54775 | −0.165494 | ||||||||
\(238\) | 4.26553 | 0.276493 | ||||||||
\(239\) | −7.23726 | −0.468139 | −0.234070 | − | 0.972220i | \(-0.575204\pi\) | ||||
−0.234070 | + | 0.972220i | \(0.575204\pi\) | |||||||
\(240\) | 7.16461 | 0.462473 | ||||||||
\(241\) | 14.0898 | 0.907606 | 0.453803 | − | 0.891102i | \(-0.350067\pi\) | ||||
0.453803 | + | 0.891102i | \(0.350067\pi\) | |||||||
\(242\) | 1.13757 | 0.0731255 | ||||||||
\(243\) | 8.15498 | 0.523142 | ||||||||
\(244\) | −3.98622 | −0.255192 | ||||||||
\(245\) | −10.2086 | −0.652205 | ||||||||
\(246\) | 17.1009 | 1.09032 | ||||||||
\(247\) | −5.39093 | −0.343017 | ||||||||
\(248\) | −19.6911 | −1.25039 | ||||||||
\(249\) | −27.9907 | −1.77384 | ||||||||
\(250\) | −13.8175 | −0.873895 | ||||||||
\(251\) | −26.7069 | −1.68572 | −0.842861 | − | 0.538131i | \(-0.819131\pi\) | ||||
−0.842861 | + | 0.538131i | \(0.819131\pi\) | |||||||
\(252\) | −0.620216 | −0.0390699 | ||||||||
\(253\) | −4.47210 | −0.281159 | ||||||||
\(254\) | 10.4486 | 0.655603 | ||||||||
\(255\) | −11.7753 | −0.737397 | ||||||||
\(256\) | −14.5834 | −0.911463 | ||||||||
\(257\) | −19.9317 | −1.24330 | −0.621652 | − | 0.783294i | \(-0.713538\pi\) | ||||
−0.621652 | + | 0.783294i | \(0.713538\pi\) | |||||||
\(258\) | −12.1025 | −0.753469 | ||||||||
\(259\) | 10.4973 | 0.652269 | ||||||||
\(260\) | −2.48237 | −0.153950 | ||||||||
\(261\) | −4.90776 | −0.303783 | ||||||||
\(262\) | 1.13757 | 0.0702791 | ||||||||
\(263\) | −8.57035 | −0.528470 | −0.264235 | − | 0.964458i | \(-0.585120\pi\) | ||||
−0.264235 | + | 0.964458i | \(0.585120\pi\) | |||||||
\(264\) | −6.00423 | −0.369535 | ||||||||
\(265\) | 1.42638 | 0.0876218 | ||||||||
\(266\) | −3.34656 | −0.205191 | ||||||||
\(267\) | −11.3895 | −0.697024 | ||||||||
\(268\) | 7.77057 | 0.474663 | ||||||||
\(269\) | 0.525731 | 0.0320544 | 0.0160272 | − | 0.999872i | \(-0.494898\pi\) | ||||
0.0160272 | + | 0.999872i | \(0.494898\pi\) | |||||||
\(270\) | 8.56169 | 0.521048 | ||||||||
\(271\) | 23.0570 | 1.40061 | 0.700307 | − | 0.713842i | \(-0.253047\pi\) | ||||
0.700307 | + | 0.713842i | \(0.253047\pi\) | |||||||
\(272\) | −7.17748 | −0.435198 | ||||||||
\(273\) | −4.26036 | −0.257848 | ||||||||
\(274\) | 18.0290 | 1.08917 | ||||||||
\(275\) | 1.91065 | 0.115216 | ||||||||
\(276\) | 6.15805 | 0.370671 | ||||||||
\(277\) | 27.3092 | 1.64085 | 0.820426 | − | 0.571752i | \(-0.193736\pi\) | ||||
0.820426 | + | 0.571752i | \(0.193736\pi\) | |||||||
\(278\) | −20.3613 | −1.22119 | ||||||||
\(279\) | 5.14787 | 0.308195 | ||||||||
\(280\) | −5.90677 | −0.352997 | ||||||||
\(281\) | 3.75780 | 0.224172 | 0.112086 | − | 0.993699i | \(-0.464247\pi\) | ||||
0.112086 | + | 0.993699i | \(0.464247\pi\) | |||||||
\(282\) | −25.3768 | −1.51117 | ||||||||
\(283\) | −30.2194 | −1.79636 | −0.898178 | − | 0.439631i | \(-0.855109\pi\) | ||||
−0.898178 | + | 0.439631i | \(0.855109\pi\) | |||||||
\(284\) | −4.18906 | −0.248575 | ||||||||
\(285\) | 9.23841 | 0.547236 | ||||||||
\(286\) | −2.27583 | −0.134573 | ||||||||
\(287\) | −8.41399 | −0.496662 | ||||||||
\(288\) | 3.04120 | 0.179205 | ||||||||
\(289\) | −5.20357 | −0.306092 | ||||||||
\(290\) | −12.1938 | −0.716047 | ||||||||
\(291\) | −15.0785 | −0.883917 | ||||||||
\(292\) | −6.14138 | −0.359397 | ||||||||
\(293\) | −5.98282 | −0.349520 | −0.174760 | − | 0.984611i | \(-0.555915\pi\) | ||||
−0.174760 | + | 0.984611i | \(0.555915\pi\) | |||||||
\(294\) | 12.8876 | 0.751621 | ||||||||
\(295\) | 26.4565 | 1.54036 | ||||||||
\(296\) | −29.5972 | −1.72030 | ||||||||
\(297\) | −4.28202 | −0.248468 | ||||||||
\(298\) | −6.42940 | −0.372445 | ||||||||
\(299\) | 8.94694 | 0.517415 | ||||||||
\(300\) | −2.63095 | −0.151898 | ||||||||
\(301\) | 5.95467 | 0.343221 | ||||||||
\(302\) | −26.0314 | −1.49794 | ||||||||
\(303\) | 23.0115 | 1.32198 | ||||||||
\(304\) | 5.63116 | 0.322969 | ||||||||
\(305\) | 9.92489 | 0.568298 | ||||||||
\(306\) | 3.14416 | 0.179740 | ||||||||
\(307\) | −22.6542 | −1.29294 | −0.646472 | − | 0.762938i | \(-0.723756\pi\) | ||||
−0.646472 | + | 0.762938i | \(0.723756\pi\) | |||||||
\(308\) | 0.770709 | 0.0439152 | ||||||||
\(309\) | −8.69823 | −0.494825 | ||||||||
\(310\) | 12.7904 | 0.726448 | ||||||||
\(311\) | 19.4225 | 1.10135 | 0.550675 | − | 0.834720i | \(-0.314370\pi\) | ||||
0.550675 | + | 0.834720i | \(0.314370\pi\) | |||||||
\(312\) | 12.0121 | 0.680053 | ||||||||
\(313\) | 10.8276 | 0.612009 | 0.306005 | − | 0.952030i | \(-0.401008\pi\) | ||||
0.306005 | + | 0.952030i | \(0.401008\pi\) | |||||||
\(314\) | 5.07167 | 0.286211 | ||||||||
\(315\) | 1.54421 | 0.0870066 | ||||||||
\(316\) | −0.922072 | −0.0518706 | ||||||||
\(317\) | 12.1650 | 0.683253 | 0.341627 | − | 0.939836i | \(-0.389022\pi\) | ||||
0.341627 | + | 0.939836i | \(0.389022\pi\) | |||||||
\(318\) | −1.80070 | −0.100978 | ||||||||
\(319\) | 6.09860 | 0.341456 | ||||||||
\(320\) | 14.9024 | 0.833067 | ||||||||
\(321\) | 7.13344 | 0.398150 | ||||||||
\(322\) | 5.55405 | 0.309515 | ||||||||
\(323\) | −9.25500 | −0.514962 | ||||||||
\(324\) | 7.60060 | 0.422256 | ||||||||
\(325\) | −3.82246 | −0.212032 | ||||||||
\(326\) | 0.350672 | 0.0194219 | ||||||||
\(327\) | −3.66153 | −0.202483 | ||||||||
\(328\) | 23.7234 | 1.30990 | ||||||||
\(329\) | 12.4859 | 0.688368 | ||||||||
\(330\) | 3.90007 | 0.214692 | ||||||||
\(331\) | −24.6957 | −1.35740 | −0.678700 | − | 0.734416i | \(-0.737456\pi\) | ||||
−0.678700 | + | 0.734416i | \(0.737456\pi\) | |||||||
\(332\) | −10.1303 | −0.555970 | ||||||||
\(333\) | 7.73763 | 0.424020 | ||||||||
\(334\) | 20.9502 | 1.14634 | ||||||||
\(335\) | −19.3472 | −1.05705 | ||||||||
\(336\) | 4.45020 | 0.242778 | ||||||||
\(337\) | 15.9721 | 0.870054 | 0.435027 | − | 0.900417i | \(-0.356739\pi\) | ||||
0.435027 | + | 0.900417i | \(0.356739\pi\) | |||||||
\(338\) | −10.2353 | −0.556728 | ||||||||
\(339\) | 17.4760 | 0.949163 | ||||||||
\(340\) | −4.26166 | −0.231121 | ||||||||
\(341\) | −6.39697 | −0.346416 | ||||||||
\(342\) | −2.46678 | −0.133388 | ||||||||
\(343\) | −13.9832 | −0.755020 | ||||||||
\(344\) | −16.7893 | −0.905217 | ||||||||
\(345\) | −15.3323 | −0.825464 | ||||||||
\(346\) | −15.7101 | −0.844583 | ||||||||
\(347\) | 35.1138 | 1.88501 | 0.942503 | − | 0.334199i | \(-0.108466\pi\) | ||||
0.942503 | + | 0.334199i | \(0.108466\pi\) | |||||||
\(348\) | −8.39773 | −0.450165 | ||||||||
\(349\) | 16.1312 | 0.863481 | 0.431741 | − | 0.901998i | \(-0.357900\pi\) | ||||
0.431741 | + | 0.901998i | \(0.357900\pi\) | |||||||
\(350\) | −2.37289 | −0.126837 | ||||||||
\(351\) | 8.56667 | 0.457255 | ||||||||
\(352\) | −3.77914 | −0.201429 | ||||||||
\(353\) | −3.12868 | −0.166523 | −0.0832613 | − | 0.996528i | \(-0.526534\pi\) | ||||
−0.0832613 | + | 0.996528i | \(0.526534\pi\) | |||||||
\(354\) | −33.3993 | −1.77515 | ||||||||
\(355\) | 10.4299 | 0.553563 | ||||||||
\(356\) | −4.12202 | −0.218467 | ||||||||
\(357\) | −7.31406 | −0.387101 | ||||||||
\(358\) | 17.8034 | 0.940939 | ||||||||
\(359\) | −0.0215923 | −0.00113960 | −0.000569800 | − | 1.00000i | \(-0.500181\pi\) | ||||
−0.000569800 | 1.00000i | \(0.500181\pi\) | ||||||||
\(360\) | −4.35393 | −0.229472 | ||||||||
\(361\) | −11.7389 | −0.617837 | ||||||||
\(362\) | −8.01508 | −0.421263 | ||||||||
\(363\) | −1.95057 | −0.102379 | ||||||||
\(364\) | −1.54189 | −0.0808169 | ||||||||
\(365\) | 15.2908 | 0.800358 | ||||||||
\(366\) | −12.5294 | −0.654924 | ||||||||
\(367\) | 18.4828 | 0.964795 | 0.482398 | − | 0.875952i | \(-0.339766\pi\) | ||||
0.482398 | + | 0.875952i | \(0.339766\pi\) | |||||||
\(368\) | −9.34562 | −0.487174 | ||||||||
\(369\) | −6.20203 | −0.322865 | ||||||||
\(370\) | 19.2250 | 0.999459 | ||||||||
\(371\) | 0.885977 | 0.0459976 | ||||||||
\(372\) | 8.80858 | 0.456704 | ||||||||
\(373\) | −2.87353 | −0.148785 | −0.0743927 | − | 0.997229i | \(-0.523702\pi\) | ||||
−0.0743927 | + | 0.997229i | \(0.523702\pi\) | |||||||
\(374\) | −3.90708 | −0.202030 | ||||||||
\(375\) | 23.6927 | 1.22349 | ||||||||
\(376\) | −35.2041 | −1.81551 | ||||||||
\(377\) | −12.2009 | −0.628380 | ||||||||
\(378\) | 5.31798 | 0.273528 | ||||||||
\(379\) | −29.2177 | −1.50081 | −0.750406 | − | 0.660977i | \(-0.770142\pi\) | ||||
−0.750406 | + | 0.660977i | \(0.770142\pi\) | |||||||
\(380\) | 3.34352 | 0.171519 | ||||||||
\(381\) | −17.9161 | −0.917869 | ||||||||
\(382\) | −9.55554 | −0.488904 | ||||||||
\(383\) | −38.2620 | −1.95510 | −0.977549 | − | 0.210709i | \(-0.932423\pi\) | ||||
−0.977549 | + | 0.210709i | \(0.932423\pi\) | |||||||
\(384\) | −4.07012 | −0.207703 | ||||||||
\(385\) | −1.91891 | −0.0977967 | ||||||||
\(386\) | −4.46805 | −0.227418 | ||||||||
\(387\) | 4.38924 | 0.223118 | ||||||||
\(388\) | −5.45714 | −0.277044 | ||||||||
\(389\) | 20.5669 | 1.04278 | 0.521392 | − | 0.853317i | \(-0.325413\pi\) | ||||
0.521392 | + | 0.853317i | \(0.325413\pi\) | |||||||
\(390\) | −7.80253 | −0.395096 | ||||||||
\(391\) | 15.3599 | 0.776781 | ||||||||
\(392\) | 17.8784 | 0.902996 | ||||||||
\(393\) | −1.95057 | −0.0983934 | ||||||||
\(394\) | −17.5291 | −0.883104 | ||||||||
\(395\) | 2.29577 | 0.115513 | ||||||||
\(396\) | 0.568096 | 0.0285479 | ||||||||
\(397\) | −15.8314 | −0.794556 | −0.397278 | − | 0.917698i | \(-0.630045\pi\) | ||||
−0.397278 | + | 0.917698i | \(0.630045\pi\) | |||||||
\(398\) | 25.0225 | 1.25427 | ||||||||
\(399\) | 5.73832 | 0.287275 | ||||||||
\(400\) | 3.99280 | 0.199640 | ||||||||
\(401\) | 19.3481 | 0.966196 | 0.483098 | − | 0.875566i | \(-0.339511\pi\) | ||||
0.483098 | + | 0.875566i | \(0.339511\pi\) | |||||||
\(402\) | 24.4243 | 1.21817 | ||||||||
\(403\) | 12.7979 | 0.637507 | ||||||||
\(404\) | 8.32821 | 0.414344 | ||||||||
\(405\) | −18.9240 | −0.940340 | ||||||||
\(406\) | −7.57405 | −0.375894 | ||||||||
\(407\) | −9.61513 | −0.476605 | ||||||||
\(408\) | 20.6221 | 1.02095 | ||||||||
\(409\) | 25.4854 | 1.26017 | 0.630086 | − | 0.776525i | \(-0.283020\pi\) | ||||
0.630086 | + | 0.776525i | \(0.283020\pi\) | |||||||
\(410\) | −15.4096 | −0.761026 | ||||||||
\(411\) | −30.9142 | −1.52488 | ||||||||
\(412\) | −3.14803 | −0.155092 | ||||||||
\(413\) | 16.4331 | 0.808620 | ||||||||
\(414\) | 4.09394 | 0.201206 | ||||||||
\(415\) | 25.2223 | 1.23811 | ||||||||
\(416\) | 7.56059 | 0.370688 | ||||||||
\(417\) | 34.9134 | 1.70971 | ||||||||
\(418\) | 3.06534 | 0.149930 | ||||||||
\(419\) | 31.9263 | 1.55970 | 0.779851 | − | 0.625965i | \(-0.215295\pi\) | ||||
0.779851 | + | 0.625965i | \(0.215295\pi\) | |||||||
\(420\) | 2.64232 | 0.128932 | ||||||||
\(421\) | 5.41374 | 0.263849 | 0.131925 | − | 0.991260i | \(-0.457884\pi\) | ||||
0.131925 | + | 0.991260i | \(0.457884\pi\) | |||||||
\(422\) | 21.6733 | 1.05504 | ||||||||
\(423\) | 9.20345 | 0.447487 | ||||||||
\(424\) | −2.49803 | −0.121315 | ||||||||
\(425\) | −6.56230 | −0.318318 | ||||||||
\(426\) | −13.1670 | −0.637942 | ||||||||
\(427\) | 6.16472 | 0.298332 | ||||||||
\(428\) | 2.58170 | 0.124791 | ||||||||
\(429\) | 3.90234 | 0.188407 | ||||||||
\(430\) | 10.9055 | 0.525912 | ||||||||
\(431\) | −7.71959 | −0.371840 | −0.185920 | − | 0.982565i | \(-0.559526\pi\) | ||||
−0.185920 | + | 0.982565i | \(0.559526\pi\) | |||||||
\(432\) | −8.94841 | −0.430530 | ||||||||
\(433\) | 33.1543 | 1.59329 | 0.796647 | − | 0.604445i | \(-0.206605\pi\) | ||||
0.796647 | + | 0.604445i | \(0.206605\pi\) | |||||||
\(434\) | 7.94461 | 0.381353 | ||||||||
\(435\) | 20.9087 | 1.00249 | ||||||||
\(436\) | −1.32517 | −0.0634639 | ||||||||
\(437\) | −12.0507 | −0.576464 | ||||||||
\(438\) | −19.3035 | −0.922356 | ||||||||
\(439\) | 21.7082 | 1.03607 | 0.518037 | − | 0.855358i | \(-0.326663\pi\) | ||||
0.518037 | + | 0.855358i | \(0.326663\pi\) | |||||||
\(440\) | 5.41040 | 0.257931 | ||||||||
\(441\) | −4.67398 | −0.222570 | ||||||||
\(442\) | 7.81655 | 0.371795 | ||||||||
\(443\) | 19.4593 | 0.924539 | 0.462270 | − | 0.886739i | \(-0.347035\pi\) | ||||
0.462270 | + | 0.886739i | \(0.347035\pi\) | |||||||
\(444\) | 13.2400 | 0.628341 | ||||||||
\(445\) | 10.2630 | 0.486513 | ||||||||
\(446\) | −27.6089 | −1.30732 | ||||||||
\(447\) | 11.0244 | 0.521437 | ||||||||
\(448\) | 9.25640 | 0.437324 | ||||||||
\(449\) | 23.6281 | 1.11508 | 0.557540 | − | 0.830150i | \(-0.311745\pi\) | ||||
0.557540 | + | 0.830150i | \(0.311745\pi\) | |||||||
\(450\) | −1.74908 | −0.0824525 | ||||||||
\(451\) | 7.70692 | 0.362905 | ||||||||
\(452\) | 6.32482 | 0.297494 | ||||||||
\(453\) | 44.6357 | 2.09717 | ||||||||
\(454\) | 16.5925 | 0.778723 | ||||||||
\(455\) | 3.83899 | 0.179975 | ||||||||
\(456\) | −16.1793 | −0.757664 | ||||||||
\(457\) | 39.2363 | 1.83540 | 0.917698 | − | 0.397279i | \(-0.130045\pi\) | ||||
0.917698 | + | 0.397279i | \(0.130045\pi\) | |||||||
\(458\) | −6.94335 | −0.324441 | ||||||||
\(459\) | 14.7070 | 0.686465 | ||||||||
\(460\) | −5.54900 | −0.258723 | ||||||||
\(461\) | −15.3999 | −0.717244 | −0.358622 | − | 0.933483i | \(-0.616753\pi\) | ||||
−0.358622 | + | 0.933483i | \(0.616753\pi\) | |||||||
\(462\) | 2.42248 | 0.112704 | ||||||||
\(463\) | 13.9125 | 0.646569 | 0.323284 | − | 0.946302i | \(-0.395213\pi\) | ||||
0.323284 | + | 0.946302i | \(0.395213\pi\) | |||||||
\(464\) | 12.7446 | 0.591654 | ||||||||
\(465\) | −21.9316 | −1.01705 | ||||||||
\(466\) | −31.8633 | −1.47604 | ||||||||
\(467\) | −10.2319 | −0.473477 | −0.236738 | − | 0.971573i | \(-0.576078\pi\) | ||||
−0.236738 | + | 0.971573i | \(0.576078\pi\) | |||||||
\(468\) | −1.13654 | −0.0525366 | ||||||||
\(469\) | −12.0172 | −0.554904 | ||||||||
\(470\) | 22.8670 | 1.05477 | ||||||||
\(471\) | −8.69634 | −0.400706 | ||||||||
\(472\) | −46.3334 | −2.13267 | ||||||||
\(473\) | −5.45427 | −0.250788 | ||||||||
\(474\) | −2.89824 | −0.133121 | ||||||||
\(475\) | 5.14851 | 0.236230 | ||||||||
\(476\) | −2.64707 | −0.121328 | ||||||||
\(477\) | 0.653062 | 0.0299016 | ||||||||
\(478\) | −8.23287 | −0.376563 | ||||||||
\(479\) | −40.0909 | −1.83180 | −0.915900 | − | 0.401407i | \(-0.868521\pi\) | ||||
−0.915900 | + | 0.401407i | \(0.868521\pi\) | |||||||
\(480\) | −12.9565 | −0.591382 | ||||||||
\(481\) | 19.2361 | 0.877093 | ||||||||
\(482\) | 16.0281 | 0.730061 | ||||||||
\(483\) | −9.52346 | −0.433332 | ||||||||
\(484\) | −0.705942 | −0.0320883 | ||||||||
\(485\) | 13.5872 | 0.616963 | ||||||||
\(486\) | 9.27683 | 0.420805 | ||||||||
\(487\) | −26.1046 | −1.18291 | −0.591456 | − | 0.806337i | \(-0.701447\pi\) | ||||
−0.591456 | + | 0.806337i | \(0.701447\pi\) | |||||||
\(488\) | −17.3815 | −0.786824 | ||||||||
\(489\) | −0.601293 | −0.0271914 | ||||||||
\(490\) | −11.6130 | −0.524622 | ||||||||
\(491\) | −18.8564 | −0.850975 | −0.425488 | − | 0.904964i | \(-0.639897\pi\) | ||||
−0.425488 | + | 0.904964i | \(0.639897\pi\) | |||||||
\(492\) | −10.6124 | −0.478443 | ||||||||
\(493\) | −20.9462 | −0.943370 | ||||||||
\(494\) | −6.13255 | −0.275916 | ||||||||
\(495\) | −1.41445 | −0.0635746 | ||||||||
\(496\) | −13.3681 | −0.600247 | ||||||||
\(497\) | 6.47841 | 0.290596 | ||||||||
\(498\) | −31.8412 | −1.42684 | ||||||||
\(499\) | 3.48327 | 0.155933 | 0.0779663 | − | 0.996956i | \(-0.475157\pi\) | ||||
0.0779663 | + | 0.996956i | \(0.475157\pi\) | |||||||
\(500\) | 8.57476 | 0.383475 | ||||||||
\(501\) | −35.9230 | −1.60492 | ||||||||
\(502\) | −30.3808 | −1.35596 | ||||||||
\(503\) | 39.6260 | 1.76684 | 0.883418 | − | 0.468586i | \(-0.155237\pi\) | ||||
0.883418 | + | 0.468586i | \(0.155237\pi\) | |||||||
\(504\) | −2.70439 | −0.120463 | ||||||||
\(505\) | −20.7356 | −0.922721 | ||||||||
\(506\) | −5.08731 | −0.226159 | ||||||||
\(507\) | 17.5504 | 0.779440 | ||||||||
\(508\) | −6.48411 | −0.287686 | ||||||||
\(509\) | 37.4963 | 1.66200 | 0.830998 | − | 0.556276i | \(-0.187770\pi\) | ||||
0.830998 | + | 0.556276i | \(0.187770\pi\) | |||||||
\(510\) | −13.3952 | −0.593148 | ||||||||
\(511\) | 9.49768 | 0.420153 | ||||||||
\(512\) | −20.7628 | −0.917597 | ||||||||
\(513\) | −11.5385 | −0.509439 | ||||||||
\(514\) | −22.6736 | −1.00009 | ||||||||
\(515\) | 7.83795 | 0.345381 | ||||||||
\(516\) | 7.51048 | 0.330631 | ||||||||
\(517\) | −11.4366 | −0.502982 | ||||||||
\(518\) | 11.9413 | 0.524672 | ||||||||
\(519\) | 26.9380 | 1.18245 | ||||||||
\(520\) | −10.8241 | −0.474668 | ||||||||
\(521\) | 34.6407 | 1.51764 | 0.758818 | − | 0.651302i | \(-0.225777\pi\) | ||||
0.758818 | + | 0.651302i | \(0.225777\pi\) | |||||||
\(522\) | −5.58290 | −0.244357 | ||||||||
\(523\) | −4.87646 | −0.213233 | −0.106616 | − | 0.994300i | \(-0.534002\pi\) | ||||
−0.106616 | + | 0.994300i | \(0.534002\pi\) | |||||||
\(524\) | −0.705942 | −0.0308392 | ||||||||
\(525\) | 4.06878 | 0.177576 | ||||||||
\(526\) | −9.74934 | −0.425092 | ||||||||
\(527\) | 21.9710 | 0.957072 | ||||||||
\(528\) | −4.07623 | −0.177395 | ||||||||
\(529\) | −3.00031 | −0.130448 | ||||||||
\(530\) | 1.62260 | 0.0704813 | ||||||||
\(531\) | 12.1130 | 0.525659 | ||||||||
\(532\) | 2.07678 | 0.0900400 | ||||||||
\(533\) | −15.4186 | −0.667852 | ||||||||
\(534\) | −12.9563 | −0.560673 | ||||||||
\(535\) | −6.42792 | −0.277903 | ||||||||
\(536\) | 33.8828 | 1.46351 | ||||||||
\(537\) | −30.5273 | −1.31735 | ||||||||
\(538\) | 0.598054 | 0.0257840 | ||||||||
\(539\) | 5.80809 | 0.250172 | ||||||||
\(540\) | −5.31315 | −0.228642 | ||||||||
\(541\) | 10.5127 | 0.451978 | 0.225989 | − | 0.974130i | \(-0.427439\pi\) | ||||
0.225989 | + | 0.974130i | \(0.427439\pi\) | |||||||
\(542\) | 26.2289 | 1.12663 | ||||||||
\(543\) | 13.7434 | 0.589784 | ||||||||
\(544\) | 12.9798 | 0.556504 | ||||||||
\(545\) | 3.29940 | 0.141331 | ||||||||
\(546\) | −4.84644 | −0.207408 | ||||||||
\(547\) | 18.1230 | 0.774884 | 0.387442 | − | 0.921894i | \(-0.373359\pi\) | ||||
0.387442 | + | 0.921894i | \(0.373359\pi\) | |||||||
\(548\) | −11.1883 | −0.477941 | ||||||||
\(549\) | 4.54407 | 0.193936 | ||||||||
\(550\) | 2.17349 | 0.0926779 | ||||||||
\(551\) | 16.4336 | 0.700093 | ||||||||
\(552\) | 26.8515 | 1.14288 | ||||||||
\(553\) | 1.42599 | 0.0606392 | ||||||||
\(554\) | 31.0661 | 1.31987 | ||||||||
\(555\) | −32.9649 | −1.39928 | ||||||||
\(556\) | 12.6357 | 0.535872 | ||||||||
\(557\) | 2.00993 | 0.0851634 | 0.0425817 | − | 0.999093i | \(-0.486442\pi\) | ||||
0.0425817 | + | 0.999093i | \(0.486442\pi\) | |||||||
\(558\) | 5.85604 | 0.247906 | ||||||||
\(559\) | 10.9119 | 0.461523 | ||||||||
\(560\) | −4.01006 | −0.169456 | ||||||||
\(561\) | 6.69942 | 0.282850 | ||||||||
\(562\) | 4.27475 | 0.180319 | ||||||||
\(563\) | 13.6203 | 0.574027 | 0.287013 | − | 0.957927i | \(-0.407338\pi\) | ||||
0.287013 | + | 0.957927i | \(0.407338\pi\) | |||||||
\(564\) | 15.7481 | 0.663116 | ||||||||
\(565\) | −15.7475 | −0.662503 | ||||||||
\(566\) | −34.3766 | −1.44496 | ||||||||
\(567\) | −11.7544 | −0.493638 | ||||||||
\(568\) | −18.2660 | −0.766423 | ||||||||
\(569\) | 13.2879 | 0.557059 | 0.278529 | − | 0.960428i | \(-0.410153\pi\) | ||||
0.278529 | + | 0.960428i | \(0.410153\pi\) | |||||||
\(570\) | 10.5093 | 0.440186 | ||||||||
\(571\) | −4.46627 | −0.186908 | −0.0934538 | − | 0.995624i | \(-0.529791\pi\) | ||||
−0.0934538 | + | 0.995624i | \(0.529791\pi\) | |||||||
\(572\) | 1.41232 | 0.0590519 | ||||||||
\(573\) | 16.3848 | 0.684484 | ||||||||
\(574\) | −9.57147 | −0.399505 | ||||||||
\(575\) | −8.54461 | −0.356335 | ||||||||
\(576\) | 6.82298 | 0.284291 | ||||||||
\(577\) | −33.7833 | −1.40642 | −0.703208 | − | 0.710985i | \(-0.748250\pi\) | ||||
−0.703208 | + | 0.710985i | \(0.748250\pi\) | |||||||
\(578\) | −5.91940 | −0.246215 | ||||||||
\(579\) | 7.66131 | 0.318393 | ||||||||
\(580\) | 7.56717 | 0.314209 | ||||||||
\(581\) | 15.6665 | 0.649956 | ||||||||
\(582\) | −17.1528 | −0.711006 | ||||||||
\(583\) | −0.811524 | −0.0336099 | ||||||||
\(584\) | −26.7789 | −1.10812 | ||||||||
\(585\) | 2.82976 | 0.116996 | ||||||||
\(586\) | −6.80585 | −0.281147 | ||||||||
\(587\) | −8.60283 | −0.355077 | −0.177538 | − | 0.984114i | \(-0.556813\pi\) | ||||
−0.177538 | + | 0.984114i | \(0.556813\pi\) | |||||||
\(588\) | −7.99770 | −0.329820 | ||||||||
\(589\) | −17.2376 | −0.710261 | ||||||||
\(590\) | 30.0960 | 1.23903 | ||||||||
\(591\) | 30.0570 | 1.23638 | ||||||||
\(592\) | −20.0933 | −0.825831 | ||||||||
\(593\) | 7.82861 | 0.321482 | 0.160741 | − | 0.986997i | \(-0.448612\pi\) | ||||
0.160741 | + | 0.986997i | \(0.448612\pi\) | |||||||
\(594\) | −4.87109 | −0.199863 | ||||||||
\(595\) | 6.59068 | 0.270191 | ||||||||
\(596\) | 3.98991 | 0.163433 | ||||||||
\(597\) | −42.9059 | −1.75602 | ||||||||
\(598\) | 10.1777 | 0.416199 | ||||||||
\(599\) | −11.8346 | −0.483550 | −0.241775 | − | 0.970332i | \(-0.577730\pi\) | ||||
−0.241775 | + | 0.970332i | \(0.577730\pi\) | |||||||
\(600\) | −11.4720 | −0.468341 | ||||||||
\(601\) | −17.9521 | −0.732279 | −0.366140 | − | 0.930560i | \(-0.619321\pi\) | ||||
−0.366140 | + | 0.930560i | \(0.619321\pi\) | |||||||
\(602\) | 6.77383 | 0.276081 | ||||||||
\(603\) | −8.85802 | −0.360726 | ||||||||
\(604\) | 16.1544 | 0.657311 | ||||||||
\(605\) | 1.75766 | 0.0714589 | ||||||||
\(606\) | 26.1771 | 1.06337 | ||||||||
\(607\) | −12.6055 | −0.511640 | −0.255820 | − | 0.966724i | \(-0.582345\pi\) | ||||
−0.255820 | + | 0.966724i | \(0.582345\pi\) | |||||||
\(608\) | −10.1834 | −0.412993 | ||||||||
\(609\) | 12.9871 | 0.526265 | ||||||||
\(610\) | 11.2902 | 0.457128 | ||||||||
\(611\) | 22.8802 | 0.925635 | ||||||||
\(612\) | −1.95118 | −0.0788718 | ||||||||
\(613\) | −27.4558 | −1.10893 | −0.554465 | − | 0.832207i | \(-0.687077\pi\) | ||||
−0.554465 | + | 0.832207i | \(0.687077\pi\) | |||||||
\(614\) | −25.7707 | −1.04002 | ||||||||
\(615\) | 26.4227 | 1.06547 | ||||||||
\(616\) | 3.36060 | 0.135402 | ||||||||
\(617\) | −3.30308 | −0.132977 | −0.0664884 | − | 0.997787i | \(-0.521180\pi\) | ||||
−0.0664884 | + | 0.997787i | \(0.521180\pi\) | |||||||
\(618\) | −9.89482 | −0.398028 | ||||||||
\(619\) | −24.0139 | −0.965201 | −0.482601 | − | 0.875841i | \(-0.660308\pi\) | ||||
−0.482601 | + | 0.875841i | \(0.660308\pi\) | |||||||
\(620\) | −7.93739 | −0.318773 | ||||||||
\(621\) | 19.1497 | 0.768449 | ||||||||
\(622\) | 22.0944 | 0.885906 | ||||||||
\(623\) | 6.37473 | 0.255398 | ||||||||
\(624\) | 8.15495 | 0.326459 | ||||||||
\(625\) | −11.7962 | −0.471848 | ||||||||
\(626\) | 12.3171 | 0.492289 | ||||||||
\(627\) | −5.25610 | −0.209908 | ||||||||
\(628\) | −3.14734 | −0.125593 | ||||||||
\(629\) | 33.0241 | 1.31676 | ||||||||
\(630\) | 1.75665 | 0.0699864 | ||||||||
\(631\) | −17.9033 | −0.712717 | −0.356359 | − | 0.934349i | \(-0.615982\pi\) | ||||
−0.356359 | + | 0.934349i | \(0.615982\pi\) | |||||||
\(632\) | −4.02060 | −0.159931 | ||||||||
\(633\) | −37.1629 | −1.47709 | ||||||||
\(634\) | 13.8385 | 0.549596 | ||||||||
\(635\) | 16.1441 | 0.640660 | ||||||||
\(636\) | 1.11746 | 0.0443103 | ||||||||
\(637\) | −11.6197 | −0.460391 | ||||||||
\(638\) | 6.93756 | 0.274661 | ||||||||
\(639\) | 4.77529 | 0.188908 | ||||||||
\(640\) | 3.66757 | 0.144974 | ||||||||
\(641\) | 34.7303 | 1.37177 | 0.685883 | − | 0.727712i | \(-0.259416\pi\) | ||||
0.685883 | + | 0.727712i | \(0.259416\pi\) | |||||||
\(642\) | 8.11476 | 0.320264 | ||||||||
\(643\) | 15.2374 | 0.600905 | 0.300453 | − | 0.953797i | \(-0.402862\pi\) | ||||
0.300453 | + | 0.953797i | \(0.402862\pi\) | |||||||
\(644\) | −3.44669 | −0.135819 | ||||||||
\(645\) | −18.6996 | −0.736296 | ||||||||
\(646\) | −10.5282 | −0.414226 | ||||||||
\(647\) | 31.7613 | 1.24867 | 0.624333 | − | 0.781159i | \(-0.285371\pi\) | ||||
0.624333 | + | 0.781159i | \(0.285371\pi\) | |||||||
\(648\) | 33.1417 | 1.30193 | ||||||||
\(649\) | −15.0522 | −0.590849 | ||||||||
\(650\) | −4.34831 | −0.170555 | ||||||||
\(651\) | −13.6225 | −0.533909 | ||||||||
\(652\) | −0.217617 | −0.00852255 | ||||||||
\(653\) | 8.28279 | 0.324131 | 0.162065 | − | 0.986780i | \(-0.448184\pi\) | ||||
0.162065 | + | 0.986780i | \(0.448184\pi\) | |||||||
\(654\) | −4.16524 | −0.162874 | ||||||||
\(655\) | 1.75766 | 0.0686773 | ||||||||
\(656\) | 16.1056 | 0.628819 | ||||||||
\(657\) | 7.00083 | 0.273128 | ||||||||
\(658\) | 14.2035 | 0.553710 | ||||||||
\(659\) | −2.57352 | −0.100250 | −0.0501250 | − | 0.998743i | \(-0.515962\pi\) | ||||
−0.0501250 | + | 0.998743i | \(0.515962\pi\) | |||||||
\(660\) | −2.42028 | −0.0942092 | ||||||||
\(661\) | −39.8325 | −1.54930 | −0.774652 | − | 0.632388i | \(-0.782075\pi\) | ||||
−0.774652 | + | 0.632388i | \(0.782075\pi\) | |||||||
\(662\) | −28.0930 | −1.09187 | ||||||||
\(663\) | −13.4029 | −0.520527 | ||||||||
\(664\) | −44.1719 | −1.71420 | ||||||||
\(665\) | −5.17078 | −0.200514 | ||||||||
\(666\) | 8.80207 | 0.341073 | ||||||||
\(667\) | −27.2736 | −1.05604 | ||||||||
\(668\) | −13.0011 | −0.503027 | ||||||||
\(669\) | 47.3407 | 1.83030 | ||||||||
\(670\) | −22.0087 | −0.850270 | ||||||||
\(671\) | −5.64667 | −0.217987 | ||||||||
\(672\) | −8.04778 | −0.310450 | ||||||||
\(673\) | −1.57525 | −0.0607213 | −0.0303607 | − | 0.999539i | \(-0.509666\pi\) | ||||
−0.0303607 | + | 0.999539i | \(0.509666\pi\) | |||||||
\(674\) | 18.1693 | 0.699855 | ||||||||
\(675\) | −8.18144 | −0.314904 | ||||||||
\(676\) | 6.35176 | 0.244298 | ||||||||
\(677\) | −47.2379 | −1.81550 | −0.907750 | − | 0.419511i | \(-0.862202\pi\) | ||||
−0.907750 | + | 0.419511i | \(0.862202\pi\) | |||||||
\(678\) | 19.8801 | 0.763489 | ||||||||
\(679\) | 8.43950 | 0.323878 | ||||||||
\(680\) | −18.5825 | −0.712607 | ||||||||
\(681\) | −28.4509 | −1.09024 | ||||||||
\(682\) | −7.27698 | −0.278650 | ||||||||
\(683\) | 14.3977 | 0.550912 | 0.275456 | − | 0.961314i | \(-0.411171\pi\) | ||||
0.275456 | + | 0.961314i | \(0.411171\pi\) | |||||||
\(684\) | 1.53082 | 0.0585323 | ||||||||
\(685\) | 27.8567 | 1.06435 | ||||||||
\(686\) | −15.9068 | −0.607324 | ||||||||
\(687\) | 11.9057 | 0.454230 | ||||||||
\(688\) | −11.3981 | −0.434549 | ||||||||
\(689\) | 1.62354 | 0.0618521 | ||||||||
\(690\) | −17.4415 | −0.663987 | ||||||||
\(691\) | −17.9227 | −0.681810 | −0.340905 | − | 0.940098i | \(-0.610734\pi\) | ||||
−0.340905 | + | 0.940098i | \(0.610734\pi\) | |||||||
\(692\) | 9.74928 | 0.370612 | ||||||||
\(693\) | −0.878565 | −0.0333739 | ||||||||
\(694\) | 39.9442 | 1.51626 | ||||||||
\(695\) | −31.4603 | −1.19336 | ||||||||
\(696\) | −36.6174 | −1.38798 | ||||||||
\(697\) | −26.4701 | −1.00263 | ||||||||
\(698\) | 18.3503 | 0.694568 | ||||||||
\(699\) | 54.6357 | 2.06651 | ||||||||
\(700\) | 1.47255 | 0.0556573 | ||||||||
\(701\) | −43.4718 | −1.64191 | −0.820953 | − | 0.570995i | \(-0.806557\pi\) | ||||
−0.820953 | + | 0.570995i | \(0.806557\pi\) | |||||||
\(702\) | 9.74515 | 0.367807 | ||||||||
\(703\) | −25.9094 | −0.977190 | ||||||||
\(704\) | −8.47854 | −0.319547 | ||||||||
\(705\) | −39.2097 | −1.47672 | ||||||||
\(706\) | −3.55908 | −0.133948 | ||||||||
\(707\) | −12.8796 | −0.484388 | ||||||||
\(708\) | 20.7267 | 0.778957 | ||||||||
\(709\) | −37.1979 | −1.39700 | −0.698499 | − | 0.715611i | \(-0.746148\pi\) | ||||
−0.698499 | + | 0.715611i | \(0.746148\pi\) | |||||||
\(710\) | 11.8647 | 0.445275 | ||||||||
\(711\) | 1.05111 | 0.0394197 | ||||||||
\(712\) | −17.9737 | −0.673591 | ||||||||
\(713\) | 28.6079 | 1.07138 | ||||||||
\(714\) | −8.32023 | −0.311377 | ||||||||
\(715\) | −3.51639 | −0.131505 | ||||||||
\(716\) | −11.0483 | −0.412894 | ||||||||
\(717\) | 14.1168 | 0.527202 | ||||||||
\(718\) | −0.0245627 | −0.000916672 0 | ||||||||
\(719\) | −26.3528 | −0.982793 | −0.491397 | − | 0.870936i | \(-0.663513\pi\) | ||||
−0.491397 | + | 0.870936i | \(0.663513\pi\) | |||||||
\(720\) | −2.95585 | −0.110158 | ||||||||
\(721\) | 4.86844 | 0.181310 | ||||||||
\(722\) | −13.3538 | −0.496976 | ||||||||
\(723\) | −27.4833 | −1.02211 | ||||||||
\(724\) | 4.97394 | 0.184855 | ||||||||
\(725\) | 11.6523 | 0.432755 | ||||||||
\(726\) | −2.21891 | −0.0823513 | ||||||||
\(727\) | 49.5107 | 1.83625 | 0.918126 | − | 0.396289i | \(-0.129702\pi\) | ||||
0.918126 | + | 0.396289i | \(0.129702\pi\) | |||||||
\(728\) | −6.72325 | −0.249180 | ||||||||
\(729\) | 16.3929 | 0.607146 | ||||||||
\(730\) | 17.3943 | 0.643792 | ||||||||
\(731\) | 18.7332 | 0.692872 | ||||||||
\(732\) | 7.77542 | 0.287388 | ||||||||
\(733\) | −20.2404 | −0.747596 | −0.373798 | − | 0.927510i | \(-0.621945\pi\) | ||||
−0.373798 | + | 0.927510i | \(0.621945\pi\) | |||||||
\(734\) | 21.0254 | 0.776063 | ||||||||
\(735\) | 19.9127 | 0.734490 | ||||||||
\(736\) | 16.9007 | 0.622968 | ||||||||
\(737\) | 11.0074 | 0.405462 | ||||||||
\(738\) | −7.05522 | −0.259706 | ||||||||
\(739\) | 16.5128 | 0.607434 | 0.303717 | − | 0.952762i | \(-0.401772\pi\) | ||||
0.303717 | + | 0.952762i | \(0.401772\pi\) | |||||||
\(740\) | −11.9305 | −0.438574 | ||||||||
\(741\) | 10.5154 | 0.386293 | ||||||||
\(742\) | 1.00786 | 0.0369996 | ||||||||
\(743\) | 48.0271 | 1.76194 | 0.880972 | − | 0.473169i | \(-0.156890\pi\) | ||||
0.880972 | + | 0.473169i | \(0.156890\pi\) | |||||||
\(744\) | 38.4089 | 1.40814 | ||||||||
\(745\) | −9.93407 | −0.363956 | ||||||||
\(746\) | −3.26883 | −0.119680 | ||||||||
\(747\) | 11.5479 | 0.422516 | ||||||||
\(748\) | 2.42463 | 0.0886531 | ||||||||
\(749\) | −3.99262 | −0.145887 | ||||||||
\(750\) | 26.9520 | 0.984149 | ||||||||
\(751\) | −22.2433 | −0.811668 | −0.405834 | − | 0.913947i | \(-0.633019\pi\) | ||||
−0.405834 | + | 0.913947i | \(0.633019\pi\) | |||||||
\(752\) | −23.8998 | −0.871536 | ||||||||
\(753\) | 52.0937 | 1.89840 | ||||||||
\(754\) | −13.8794 | −0.505457 | ||||||||
\(755\) | −40.2211 | −1.46380 | ||||||||
\(756\) | −3.30019 | −0.120027 | ||||||||
\(757\) | −27.5235 | −1.00036 | −0.500180 | − | 0.865921i | \(-0.666733\pi\) | ||||
−0.500180 | + | 0.865921i | \(0.666733\pi\) | |||||||
\(758\) | −33.2371 | −1.20722 | ||||||||
\(759\) | 8.72316 | 0.316631 | ||||||||
\(760\) | 14.5791 | 0.528839 | ||||||||
\(761\) | −10.9265 | −0.396084 | −0.198042 | − | 0.980194i | \(-0.563458\pi\) | ||||
−0.198042 | + | 0.980194i | \(0.563458\pi\) | |||||||
\(762\) | −20.3807 | −0.738316 | ||||||||
\(763\) | 2.04938 | 0.0741924 | ||||||||
\(764\) | 5.92990 | 0.214536 | ||||||||
\(765\) | 4.85805 | 0.175643 | ||||||||
\(766\) | −43.5256 | −1.57264 | ||||||||
\(767\) | 30.1135 | 1.08734 | ||||||||
\(768\) | 28.4460 | 1.02646 | ||||||||
\(769\) | −44.5038 | −1.60485 | −0.802424 | − | 0.596755i | \(-0.796457\pi\) | ||||
−0.802424 | + | 0.596755i | \(0.796457\pi\) | |||||||
\(770\) | −2.18289 | −0.0786658 | ||||||||
\(771\) | 38.8782 | 1.40016 | ||||||||
\(772\) | 2.77275 | 0.0997933 | ||||||||
\(773\) | 36.0813 | 1.29775 | 0.648876 | − | 0.760894i | \(-0.275239\pi\) | ||||
0.648876 | + | 0.760894i | \(0.275239\pi\) | |||||||
\(774\) | 4.99305 | 0.179472 | ||||||||
\(775\) | −12.2224 | −0.439040 | ||||||||
\(776\) | −23.7953 | −0.854202 | ||||||||
\(777\) | −20.4757 | −0.734561 | ||||||||
\(778\) | 23.3963 | 0.838796 | ||||||||
\(779\) | 20.7674 | 0.744069 | ||||||||
\(780\) | 4.84204 | 0.173373 | ||||||||
\(781\) | −5.93400 | −0.212335 | ||||||||
\(782\) | 17.4729 | 0.624828 | ||||||||
\(783\) | −26.1144 | −0.933251 | ||||||||
\(784\) | 12.1375 | 0.433483 | ||||||||
\(785\) | 7.83625 | 0.279688 | ||||||||
\(786\) | −2.21891 | −0.0791458 | ||||||||
\(787\) | −38.4177 | −1.36944 | −0.684722 | − | 0.728804i | \(-0.740077\pi\) | ||||
−0.684722 | + | 0.728804i | \(0.740077\pi\) | |||||||
\(788\) | 10.8781 | 0.387516 | ||||||||
\(789\) | 16.7171 | 0.595144 | ||||||||
\(790\) | 2.61160 | 0.0929164 | ||||||||
\(791\) | −9.78137 | −0.347785 | ||||||||
\(792\) | 2.47713 | 0.0880208 | ||||||||
\(793\) | 11.2968 | 0.401161 | ||||||||
\(794\) | −18.0093 | −0.639126 | ||||||||
\(795\) | −2.78226 | −0.0986765 | ||||||||
\(796\) | −15.5283 | −0.550386 | ||||||||
\(797\) | −40.8412 | −1.44667 | −0.723335 | − | 0.690497i | \(-0.757392\pi\) | ||||
−0.723335 | + | 0.690497i | \(0.757392\pi\) | |||||||
\(798\) | 6.52772 | 0.231079 | ||||||||
\(799\) | 39.2802 | 1.38963 | ||||||||
\(800\) | −7.22060 | −0.255287 | ||||||||
\(801\) | 4.69887 | 0.166027 | ||||||||
\(802\) | 22.0097 | 0.777190 | ||||||||
\(803\) | −8.69955 | −0.307000 | ||||||||
\(804\) | −15.1571 | −0.534549 | ||||||||
\(805\) | 8.58156 | 0.302460 | ||||||||
\(806\) | 14.5584 | 0.512798 | ||||||||
\(807\) | −1.02548 | −0.0360985 | ||||||||
\(808\) | 36.3143 | 1.27753 | ||||||||
\(809\) | −21.8674 | −0.768815 | −0.384408 | − | 0.923163i | \(-0.625594\pi\) | ||||
−0.384408 | + | 0.923163i | \(0.625594\pi\) | |||||||
\(810\) | −21.5273 | −0.756392 | ||||||||
\(811\) | −0.0669815 | −0.00235204 | −0.00117602 | − | 0.999999i | \(-0.500374\pi\) | ||||
−0.00117602 | + | 0.999999i | \(0.500374\pi\) | |||||||
\(812\) | 4.70025 | 0.164946 | ||||||||
\(813\) | −44.9744 | −1.57732 | ||||||||
\(814\) | −10.9379 | −0.383372 | ||||||||
\(815\) | 0.541824 | 0.0189793 | ||||||||
\(816\) | 14.0002 | 0.490105 | ||||||||
\(817\) | −14.6973 | −0.514194 | ||||||||
\(818\) | 28.9913 | 1.01366 | ||||||||
\(819\) | 1.75767 | 0.0614178 | ||||||||
\(820\) | 9.56277 | 0.333947 | ||||||||
\(821\) | 16.2689 | 0.567787 | 0.283894 | − | 0.958856i | \(-0.408374\pi\) | ||||
0.283894 | + | 0.958856i | \(0.408374\pi\) | |||||||
\(822\) | −35.1669 | −1.22659 | ||||||||
\(823\) | −16.7175 | −0.582736 | −0.291368 | − | 0.956611i | \(-0.594110\pi\) | ||||
−0.291368 | + | 0.956611i | \(0.594110\pi\) | |||||||
\(824\) | −13.7266 | −0.478190 | ||||||||
\(825\) | −3.72686 | −0.129753 | ||||||||
\(826\) | 18.6937 | 0.650439 | ||||||||
\(827\) | 49.7206 | 1.72896 | 0.864478 | − | 0.502671i | \(-0.167649\pi\) | ||||
0.864478 | + | 0.502671i | \(0.167649\pi\) | |||||||
\(828\) | −2.54058 | −0.0882914 | ||||||||
\(829\) | −6.97007 | −0.242081 | −0.121040 | − | 0.992648i | \(-0.538623\pi\) | ||||
−0.121040 | + | 0.992648i | \(0.538623\pi\) | |||||||
\(830\) | 28.6920 | 0.995915 | ||||||||
\(831\) | −53.2687 | −1.84787 | ||||||||
\(832\) | 16.9623 | 0.588061 | ||||||||
\(833\) | −19.9484 | −0.691173 | ||||||||
\(834\) | 39.7163 | 1.37526 | ||||||||
\(835\) | 32.3701 | 1.12021 | ||||||||
\(836\) | −1.90226 | −0.0657911 | ||||||||
\(837\) | 27.3920 | 0.946806 | ||||||||
\(838\) | 36.3183 | 1.25459 | ||||||||
\(839\) | 21.0361 | 0.726246 | 0.363123 | − | 0.931741i | \(-0.381711\pi\) | ||||
0.363123 | + | 0.931741i | \(0.381711\pi\) | |||||||
\(840\) | 11.5216 | 0.397532 | ||||||||
\(841\) | 8.19294 | 0.282515 | ||||||||
\(842\) | 6.15849 | 0.212235 | ||||||||
\(843\) | −7.32986 | −0.252454 | ||||||||
\(844\) | −13.4498 | −0.462962 | ||||||||
\(845\) | −15.8146 | −0.544039 | ||||||||
\(846\) | 10.4695 | 0.359950 | ||||||||
\(847\) | 1.09174 | 0.0375128 | ||||||||
\(848\) | −1.69589 | −0.0582371 | ||||||||
\(849\) | 58.9451 | 2.02299 | ||||||||
\(850\) | −7.46505 | −0.256049 | ||||||||
\(851\) | 42.9999 | 1.47402 | ||||||||
\(852\) | 8.17107 | 0.279936 | ||||||||
\(853\) | −35.9630 | −1.23135 | −0.615674 | − | 0.788001i | \(-0.711116\pi\) | ||||
−0.615674 | + | 0.788001i | \(0.711116\pi\) | |||||||
\(854\) | 7.01277 | 0.239972 | ||||||||
\(855\) | −3.81143 | −0.130348 | ||||||||
\(856\) | 11.2572 | 0.384765 | ||||||||
\(857\) | 18.6464 | 0.636949 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(858\) | 4.43917 | 0.151551 | ||||||||
\(859\) | −48.0131 | −1.63819 | −0.819093 | − | 0.573661i | \(-0.805523\pi\) | ||||
−0.819093 | + | 0.573661i | \(0.805523\pi\) | |||||||
\(860\) | −6.76768 | −0.230776 | ||||||||
\(861\) | 16.4121 | 0.559323 | ||||||||
\(862\) | −8.78155 | −0.299101 | ||||||||
\(863\) | 14.8925 | 0.506945 | 0.253473 | − | 0.967343i | \(-0.418427\pi\) | ||||
0.253473 | + | 0.967343i | \(0.418427\pi\) | |||||||
\(864\) | 16.1824 | 0.550535 | ||||||||
\(865\) | −24.2738 | −0.825333 | ||||||||
\(866\) | 37.7152 | 1.28162 | ||||||||
\(867\) | 10.1499 | 0.344710 | ||||||||
\(868\) | −4.93020 | −0.167342 | ||||||||
\(869\) | −1.30616 | −0.0443083 | ||||||||
\(870\) | 23.7850 | 0.806387 | ||||||||
\(871\) | −22.0215 | −0.746169 | ||||||||
\(872\) | −5.77825 | −0.195676 | ||||||||
\(873\) | 6.22084 | 0.210543 | ||||||||
\(874\) | −13.7085 | −0.463697 | ||||||||
\(875\) | −13.2609 | −0.448301 | ||||||||
\(876\) | 11.9792 | 0.404740 | ||||||||
\(877\) | −14.3643 | −0.485047 | −0.242523 | − | 0.970146i | \(-0.577975\pi\) | ||||
−0.242523 | + | 0.970146i | \(0.577975\pi\) | |||||||
\(878\) | 24.6945 | 0.833398 | ||||||||
\(879\) | 11.6699 | 0.393617 | ||||||||
\(880\) | 3.67308 | 0.123819 | ||||||||
\(881\) | 40.9924 | 1.38107 | 0.690534 | − | 0.723300i | \(-0.257376\pi\) | ||||
0.690534 | + | 0.723300i | \(0.257376\pi\) | |||||||
\(882\) | −5.31696 | −0.179031 | ||||||||
\(883\) | 45.6966 | 1.53781 | 0.768907 | − | 0.639361i | \(-0.220801\pi\) | ||||
0.768907 | + | 0.639361i | \(0.220801\pi\) | |||||||
\(884\) | −4.85073 | −0.163148 | ||||||||
\(885\) | −51.6053 | −1.73469 | ||||||||
\(886\) | 22.1362 | 0.743682 | ||||||||
\(887\) | −52.8359 | −1.77406 | −0.887029 | − | 0.461714i | \(-0.847235\pi\) | ||||
−0.887029 | + | 0.461714i | \(0.847235\pi\) | |||||||
\(888\) | 57.7315 | 1.93734 | ||||||||
\(889\) | 10.0277 | 0.336319 | ||||||||
\(890\) | 11.6749 | 0.391342 | ||||||||
\(891\) | 10.7666 | 0.360695 | ||||||||
\(892\) | 17.1333 | 0.573666 | ||||||||
\(893\) | −30.8176 | −1.03127 | ||||||||
\(894\) | 12.5410 | 0.419434 | ||||||||
\(895\) | 27.5080 | 0.919493 | ||||||||
\(896\) | 2.27807 | 0.0761048 | ||||||||
\(897\) | −17.4517 | −0.582694 | ||||||||
\(898\) | 26.8785 | 0.896949 | ||||||||
\(899\) | −39.0126 | −1.30114 | ||||||||
\(900\) | 1.08543 | 0.0361811 | ||||||||
\(901\) | 2.78726 | 0.0928570 | ||||||||
\(902\) | 8.76713 | 0.291914 | ||||||||
\(903\) | −11.6150 | −0.386523 | ||||||||
\(904\) | 27.5787 | 0.917254 | ||||||||
\(905\) | −12.3841 | −0.411662 | ||||||||
\(906\) | 50.7761 | 1.68692 | ||||||||
\(907\) | 16.6522 | 0.552927 | 0.276463 | − | 0.961024i | \(-0.410838\pi\) | ||||
0.276463 | + | 0.961024i | \(0.410838\pi\) | |||||||
\(908\) | −10.2968 | −0.341712 | ||||||||
\(909\) | −9.49369 | −0.314886 | ||||||||
\(910\) | 4.36711 | 0.144768 | ||||||||
\(911\) | −10.8575 | −0.359724 | −0.179862 | − | 0.983692i | \(-0.557565\pi\) | ||||
−0.179862 | + | 0.983692i | \(0.557565\pi\) | |||||||
\(912\) | −10.9840 | −0.363716 | ||||||||
\(913\) | −14.3500 | −0.474915 | ||||||||
\(914\) | 44.6339 | 1.47636 | ||||||||
\(915\) | −19.3592 | −0.639996 | ||||||||
\(916\) | 4.30885 | 0.142368 | ||||||||
\(917\) | 1.09174 | 0.0360526 | ||||||||
\(918\) | 16.7302 | 0.552179 | ||||||||
\(919\) | 16.5230 | 0.545043 | 0.272522 | − | 0.962150i | \(-0.412142\pi\) | ||||
0.272522 | + | 0.962150i | \(0.412142\pi\) | |||||||
\(920\) | −24.1958 | −0.797713 | ||||||||
\(921\) | 44.1887 | 1.45607 | ||||||||
\(922\) | −17.5184 | −0.576937 | ||||||||
\(923\) | 11.8716 | 0.390759 | ||||||||
\(924\) | −1.50332 | −0.0494557 | ||||||||
\(925\) | −18.3711 | −0.604039 | ||||||||
\(926\) | 15.8264 | 0.520088 | ||||||||
\(927\) | 3.58857 | 0.117864 | ||||||||
\(928\) | −23.0475 | −0.756570 | ||||||||
\(929\) | −0.831142 | −0.0272689 | −0.0136344 | − | 0.999907i | \(-0.504340\pi\) | ||||
−0.0136344 | + | 0.999907i | \(0.504340\pi\) | |||||||
\(930\) | −24.9487 | −0.818099 | ||||||||
\(931\) | 15.6507 | 0.512932 | ||||||||
\(932\) | 19.7735 | 0.647703 | ||||||||
\(933\) | −37.8851 | −1.24030 | ||||||||
\(934\) | −11.6395 | −0.380856 | ||||||||
\(935\) | −6.03683 | −0.197426 | ||||||||
\(936\) | −4.95577 | −0.161984 | ||||||||
\(937\) | −49.4188 | −1.61444 | −0.807221 | − | 0.590250i | \(-0.799029\pi\) | ||||
−0.807221 | + | 0.590250i | \(0.799029\pi\) | |||||||
\(938\) | −13.6704 | −0.446355 | ||||||||
\(939\) | −21.1199 | −0.689223 | ||||||||
\(940\) | −14.1906 | −0.462846 | ||||||||
\(941\) | 2.08939 | 0.0681120 | 0.0340560 | − | 0.999420i | \(-0.489158\pi\) | ||||
0.0340560 | + | 0.999420i | \(0.489158\pi\) | |||||||
\(942\) | −9.89267 | −0.322320 | ||||||||
\(943\) | −34.4661 | −1.12237 | ||||||||
\(944\) | −31.4554 | −1.02379 | ||||||||
\(945\) | 8.21682 | 0.267293 | ||||||||
\(946\) | −6.20459 | −0.201729 | ||||||||
\(947\) | 37.7122 | 1.22548 | 0.612741 | − | 0.790284i | \(-0.290067\pi\) | ||||
0.612741 | + | 0.790284i | \(0.290067\pi\) | |||||||
\(948\) | 1.79857 | 0.0584148 | ||||||||
\(949\) | 17.4044 | 0.564971 | ||||||||
\(950\) | 5.85678 | 0.190019 | ||||||||
\(951\) | −23.7287 | −0.769455 | ||||||||
\(952\) | −11.5423 | −0.374087 | ||||||||
\(953\) | −6.84925 | −0.221869 | −0.110935 | − | 0.993828i | \(-0.535384\pi\) | ||||
−0.110935 | + | 0.993828i | \(0.535384\pi\) | |||||||
\(954\) | 0.742901 | 0.0240523 | ||||||||
\(955\) | −14.7643 | −0.477761 | ||||||||
\(956\) | 5.10909 | 0.165240 | ||||||||
\(957\) | −11.8958 | −0.384536 | ||||||||
\(958\) | −45.6061 | −1.47346 | ||||||||
\(959\) | 17.3028 | 0.558736 | ||||||||
\(960\) | −29.0681 | −0.938170 | ||||||||
\(961\) | 9.92129 | 0.320041 | ||||||||
\(962\) | 21.8824 | 0.705517 | ||||||||
\(963\) | −2.94300 | −0.0948367 | ||||||||
\(964\) | −9.94662 | −0.320359 | ||||||||
\(965\) | −6.90358 | −0.222234 | ||||||||
\(966\) | −10.8336 | −0.348564 | ||||||||
\(967\) | −5.21500 | −0.167703 | −0.0838516 | − | 0.996478i | \(-0.526722\pi\) | ||||
−0.0838516 | + | 0.996478i | \(0.526722\pi\) | |||||||
\(968\) | −3.07819 | −0.0989368 | ||||||||
\(969\) | 18.0526 | 0.579932 | ||||||||
\(970\) | 15.4563 | 0.496273 | ||||||||
\(971\) | 31.2824 | 1.00390 | 0.501949 | − | 0.864897i | \(-0.332616\pi\) | ||||
0.501949 | + | 0.864897i | \(0.332616\pi\) | |||||||
\(972\) | −5.75694 | −0.184654 | ||||||||
\(973\) | −19.5412 | −0.626461 | ||||||||
\(974\) | −29.6957 | −0.951513 | ||||||||
\(975\) | 7.45599 | 0.238783 | ||||||||
\(976\) | −11.8002 | −0.377715 | ||||||||
\(977\) | 35.1493 | 1.12453 | 0.562263 | − | 0.826959i | \(-0.309931\pi\) | ||||
0.562263 | + | 0.826959i | \(0.309931\pi\) | |||||||
\(978\) | −0.684011 | −0.0218723 | ||||||||
\(979\) | −5.83903 | −0.186616 | ||||||||
\(980\) | 7.20670 | 0.230210 | ||||||||
\(981\) | 1.51061 | 0.0482302 | ||||||||
\(982\) | −21.4504 | −0.684508 | ||||||||
\(983\) | −25.3641 | −0.808989 | −0.404495 | − | 0.914540i | \(-0.632553\pi\) | ||||
−0.404495 | + | 0.914540i | \(0.632553\pi\) | |||||||
\(984\) | −46.2741 | −1.47517 | ||||||||
\(985\) | −27.0843 | −0.862976 | ||||||||
\(986\) | −23.8277 | −0.758829 | ||||||||
\(987\) | −24.3546 | −0.775215 | ||||||||
\(988\) | 3.80569 | 0.121075 | ||||||||
\(989\) | 24.3920 | 0.775622 | ||||||||
\(990\) | −1.60903 | −0.0511382 | ||||||||
\(991\) | −1.31764 | −0.0418562 | −0.0209281 | − | 0.999781i | \(-0.506662\pi\) | ||||
−0.0209281 | + | 0.999781i | \(0.506662\pi\) | |||||||
\(992\) | 24.1750 | 0.767559 | ||||||||
\(993\) | 48.1708 | 1.52865 | ||||||||
\(994\) | 7.36962 | 0.233750 | ||||||||
\(995\) | 38.6623 | 1.22568 | ||||||||
\(996\) | 19.7598 | 0.626113 | ||||||||
\(997\) | 13.5819 | 0.430143 | 0.215072 | − | 0.976598i | \(-0.431001\pi\) | ||||
0.215072 | + | 0.976598i | \(0.431001\pi\) | |||||||
\(998\) | 3.96245 | 0.125429 | ||||||||
\(999\) | 41.1722 | 1.30263 |
(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 | 1441.2.a.f.1.20 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.2.a.f.1.20 | ✓ | 31 | 1.1 | even | 1 | trivial |