Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.98476 | −1.72325 | −0.861626 | − | 0.507544i | \(-0.830554\pi\) | ||||
−0.861626 | + | 0.507544i | \(0.830554\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.57995 | 0.706577 | 0.353288 | − | 0.935514i | \(-0.385063\pi\) | ||||
0.353288 | + | 0.935514i | \(0.385063\pi\) | |||||||
\(6\) | 2.98476 | 1.21852 | ||||||||
\(7\) | 2.90984 | 1.09982 | 0.549909 | − | 0.835225i | \(-0.314662\pi\) | ||||
0.549909 | + | 0.835225i | \(0.314662\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.90879 | 1.96960 | ||||||||
\(10\) | −1.57995 | −0.499625 | ||||||||
\(11\) | −4.95802 | −1.49490 | −0.747450 | − | 0.664318i | \(-0.768722\pi\) | ||||
−0.747450 | + | 0.664318i | \(0.768722\pi\) | |||||||
\(12\) | −2.98476 | −0.861626 | ||||||||
\(13\) | −4.16275 | −1.15454 | −0.577270 | − | 0.816553i | \(-0.695882\pi\) | ||||
−0.577270 | + | 0.816553i | \(0.695882\pi\) | |||||||
\(14\) | −2.90984 | −0.777689 | ||||||||
\(15\) | −4.71578 | −1.21761 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.92081 | 0.708400 | 0.354200 | − | 0.935170i | \(-0.384753\pi\) | ||||
0.354200 | + | 0.935170i | \(0.384753\pi\) | |||||||
\(18\) | −5.90879 | −1.39272 | ||||||||
\(19\) | 2.68824 | 0.616725 | 0.308362 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308362 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(20\) | 1.57995 | 0.353288 | ||||||||
\(21\) | −8.68519 | −1.89526 | ||||||||
\(22\) | 4.95802 | 1.05705 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.98476 | 0.609262 | ||||||||
\(25\) | −2.50375 | −0.500749 | ||||||||
\(26\) | 4.16275 | 0.816383 | ||||||||
\(27\) | −8.68205 | −1.67086 | ||||||||
\(28\) | 2.90984 | 0.549909 | ||||||||
\(29\) | 5.30982 | 0.986009 | 0.493005 | − | 0.870027i | \(-0.335899\pi\) | ||||
0.493005 | + | 0.870027i | \(0.335899\pi\) | |||||||
\(30\) | 4.71578 | 0.860980 | ||||||||
\(31\) | −3.13133 | −0.562404 | −0.281202 | − | 0.959649i | \(-0.590733\pi\) | ||||
−0.281202 | + | 0.959649i | \(0.590733\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 14.7985 | 2.57609 | ||||||||
\(34\) | −2.92081 | −0.500914 | ||||||||
\(35\) | 4.59742 | 0.777106 | ||||||||
\(36\) | 5.90879 | 0.984799 | ||||||||
\(37\) | 4.98422 | 0.819401 | 0.409700 | − | 0.912220i | \(-0.365633\pi\) | ||||
0.409700 | + | 0.912220i | \(0.365633\pi\) | |||||||
\(38\) | −2.68824 | −0.436090 | ||||||||
\(39\) | 12.4248 | 1.98956 | ||||||||
\(40\) | −1.57995 | −0.249813 | ||||||||
\(41\) | 6.04686 | 0.944361 | 0.472180 | − | 0.881502i | \(-0.343467\pi\) | ||||
0.472180 | + | 0.881502i | \(0.343467\pi\) | |||||||
\(42\) | 8.68519 | 1.34015 | ||||||||
\(43\) | −0.659532 | −0.100578 | −0.0502889 | − | 0.998735i | \(-0.516014\pi\) | ||||
−0.0502889 | + | 0.998735i | \(0.516014\pi\) | |||||||
\(44\) | −4.95802 | −0.747450 | ||||||||
\(45\) | 9.33562 | 1.39167 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −6.46454 | −0.942950 | −0.471475 | − | 0.881879i | \(-0.656278\pi\) | ||||
−0.471475 | + | 0.881879i | \(0.656278\pi\) | |||||||
\(48\) | −2.98476 | −0.430813 | ||||||||
\(49\) | 1.46720 | 0.209599 | ||||||||
\(50\) | 2.50375 | 0.354083 | ||||||||
\(51\) | −8.71791 | −1.22075 | ||||||||
\(52\) | −4.16275 | −0.577270 | ||||||||
\(53\) | 1.53961 | 0.211481 | 0.105741 | − | 0.994394i | \(-0.466279\pi\) | ||||
0.105741 | + | 0.994394i | \(0.466279\pi\) | |||||||
\(54\) | 8.68205 | 1.18148 | ||||||||
\(55\) | −7.83345 | −1.05626 | ||||||||
\(56\) | −2.90984 | −0.388844 | ||||||||
\(57\) | −8.02376 | −1.06277 | ||||||||
\(58\) | −5.30982 | −0.697214 | ||||||||
\(59\) | −3.36081 | −0.437540 | −0.218770 | − | 0.975776i | \(-0.570204\pi\) | ||||
−0.218770 | + | 0.975776i | \(0.570204\pi\) | |||||||
\(60\) | −4.71578 | −0.608805 | ||||||||
\(61\) | −8.26073 | −1.05768 | −0.528839 | − | 0.848722i | \(-0.677373\pi\) | ||||
−0.528839 | + | 0.848722i | \(0.677373\pi\) | |||||||
\(62\) | 3.13133 | 0.397680 | ||||||||
\(63\) | 17.1937 | 2.16620 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.57696 | −0.815771 | ||||||||
\(66\) | −14.7985 | −1.82157 | ||||||||
\(67\) | −4.81120 | −0.587782 | −0.293891 | − | 0.955839i | \(-0.594950\pi\) | ||||
−0.293891 | + | 0.955839i | \(0.594950\pi\) | |||||||
\(68\) | 2.92081 | 0.354200 | ||||||||
\(69\) | −2.98476 | −0.359323 | ||||||||
\(70\) | −4.59742 | −0.549497 | ||||||||
\(71\) | −13.2195 | −1.56887 | −0.784434 | − | 0.620212i | \(-0.787047\pi\) | ||||
−0.784434 | + | 0.620212i | \(0.787047\pi\) | |||||||
\(72\) | −5.90879 | −0.696358 | ||||||||
\(73\) | 1.36743 | 0.160046 | 0.0800229 | − | 0.996793i | \(-0.474501\pi\) | ||||
0.0800229 | + | 0.996793i | \(0.474501\pi\) | |||||||
\(74\) | −4.98422 | −0.579404 | ||||||||
\(75\) | 7.47308 | 0.862917 | ||||||||
\(76\) | 2.68824 | 0.308362 | ||||||||
\(77\) | −14.4271 | −1.64412 | ||||||||
\(78\) | −12.4248 | −1.40683 | ||||||||
\(79\) | −1.09845 | −0.123586 | −0.0617929 | − | 0.998089i | \(-0.519682\pi\) | ||||
−0.0617929 | + | 0.998089i | \(0.519682\pi\) | |||||||
\(80\) | 1.57995 | 0.176644 | ||||||||
\(81\) | 8.18746 | 0.909718 | ||||||||
\(82\) | −6.04686 | −0.667764 | ||||||||
\(83\) | −5.31930 | −0.583869 | −0.291934 | − | 0.956438i | \(-0.594299\pi\) | ||||
−0.291934 | + | 0.956438i | \(0.594299\pi\) | |||||||
\(84\) | −8.68519 | −0.947632 | ||||||||
\(85\) | 4.61474 | 0.500539 | ||||||||
\(86\) | 0.659532 | 0.0711192 | ||||||||
\(87\) | −15.8485 | −1.69914 | ||||||||
\(88\) | 4.95802 | 0.528527 | ||||||||
\(89\) | 9.76882 | 1.03549 | 0.517746 | − | 0.855534i | \(-0.326771\pi\) | ||||
0.517746 | + | 0.855534i | \(0.326771\pi\) | |||||||
\(90\) | −9.33562 | −0.984061 | ||||||||
\(91\) | −12.1130 | −1.26978 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 9.34627 | 0.969163 | ||||||||
\(94\) | 6.46454 | 0.666766 | ||||||||
\(95\) | 4.24730 | 0.435764 | ||||||||
\(96\) | 2.98476 | 0.304631 | ||||||||
\(97\) | 0.168734 | 0.0171324 | 0.00856620 | − | 0.999963i | \(-0.497273\pi\) | ||||
0.00856620 | + | 0.999963i | \(0.497273\pi\) | |||||||
\(98\) | −1.46720 | −0.148209 | ||||||||
\(99\) | −29.2959 | −2.94435 | ||||||||
\(100\) | −2.50375 | −0.250375 | ||||||||
\(101\) | −7.93894 | −0.789954 | −0.394977 | − | 0.918691i | \(-0.629247\pi\) | ||||
−0.394977 | + | 0.918691i | \(0.629247\pi\) | |||||||
\(102\) | 8.71791 | 0.863202 | ||||||||
\(103\) | 11.7967 | 1.16236 | 0.581180 | − | 0.813775i | \(-0.302591\pi\) | ||||
0.581180 | + | 0.813775i | \(0.302591\pi\) | |||||||
\(104\) | 4.16275 | 0.408191 | ||||||||
\(105\) | −13.7222 | −1.33915 | ||||||||
\(106\) | −1.53961 | −0.149540 | ||||||||
\(107\) | 5.22241 | 0.504869 | 0.252435 | − | 0.967614i | \(-0.418769\pi\) | ||||
0.252435 | + | 0.967614i | \(0.418769\pi\) | |||||||
\(108\) | −8.68205 | −0.835431 | ||||||||
\(109\) | −7.46020 | −0.714557 | −0.357279 | − | 0.933998i | \(-0.616295\pi\) | ||||
−0.357279 | + | 0.933998i | \(0.616295\pi\) | |||||||
\(110\) | 7.83345 | 0.746890 | ||||||||
\(111\) | −14.8767 | −1.41203 | ||||||||
\(112\) | 2.90984 | 0.274954 | ||||||||
\(113\) | 12.0064 | 1.12946 | 0.564732 | − | 0.825274i | \(-0.308979\pi\) | ||||
0.564732 | + | 0.825274i | \(0.308979\pi\) | |||||||
\(114\) | 8.02376 | 0.751494 | ||||||||
\(115\) | 1.57995 | 0.147331 | ||||||||
\(116\) | 5.30982 | 0.493005 | ||||||||
\(117\) | −24.5968 | −2.27398 | ||||||||
\(118\) | 3.36081 | 0.309388 | ||||||||
\(119\) | 8.49910 | 0.779111 | ||||||||
\(120\) | 4.71578 | 0.430490 | ||||||||
\(121\) | 13.5820 | 1.23473 | ||||||||
\(122\) | 8.26073 | 0.747891 | ||||||||
\(123\) | −18.0484 | −1.62737 | ||||||||
\(124\) | −3.13133 | −0.281202 | ||||||||
\(125\) | −11.8556 | −1.06039 | ||||||||
\(126\) | −17.1937 | −1.53173 | ||||||||
\(127\) | 10.4798 | 0.929930 | 0.464965 | − | 0.885329i | \(-0.346067\pi\) | ||||
0.464965 | + | 0.885329i | \(0.346067\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.96855 | 0.173321 | ||||||||
\(130\) | 6.57696 | 0.576837 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | 14.7985 | 1.28804 | ||||||||
\(133\) | 7.82237 | 0.678285 | ||||||||
\(134\) | 4.81120 | 0.415624 | ||||||||
\(135\) | −13.7172 | −1.18059 | ||||||||
\(136\) | −2.92081 | −0.250457 | ||||||||
\(137\) | −9.48217 | −0.810116 | −0.405058 | − | 0.914291i | \(-0.632749\pi\) | ||||
−0.405058 | + | 0.914291i | \(0.632749\pi\) | |||||||
\(138\) | 2.98476 | 0.254080 | ||||||||
\(139\) | 17.1336 | 1.45325 | 0.726625 | − | 0.687034i | \(-0.241088\pi\) | ||||
0.726625 | + | 0.687034i | \(0.241088\pi\) | |||||||
\(140\) | 4.59742 | 0.388553 | ||||||||
\(141\) | 19.2951 | 1.62494 | ||||||||
\(142\) | 13.2195 | 1.10936 | ||||||||
\(143\) | 20.6390 | 1.72592 | ||||||||
\(144\) | 5.90879 | 0.492399 | ||||||||
\(145\) | 8.38927 | 0.696691 | ||||||||
\(146\) | −1.36743 | −0.113169 | ||||||||
\(147\) | −4.37923 | −0.361193 | ||||||||
\(148\) | 4.98422 | 0.409700 | ||||||||
\(149\) | 16.0611 | 1.31578 | 0.657890 | − | 0.753114i | \(-0.271449\pi\) | ||||
0.657890 | + | 0.753114i | \(0.271449\pi\) | |||||||
\(150\) | −7.47308 | −0.610174 | ||||||||
\(151\) | −5.62376 | −0.457655 | −0.228828 | − | 0.973467i | \(-0.573489\pi\) | ||||
−0.228828 | + | 0.973467i | \(0.573489\pi\) | |||||||
\(152\) | −2.68824 | −0.218045 | ||||||||
\(153\) | 17.2585 | 1.39526 | ||||||||
\(154\) | 14.4271 | 1.16257 | ||||||||
\(155\) | −4.94736 | −0.397382 | ||||||||
\(156\) | 12.4248 | 0.994782 | ||||||||
\(157\) | 2.63971 | 0.210672 | 0.105336 | − | 0.994437i | \(-0.466408\pi\) | ||||
0.105336 | + | 0.994437i | \(0.466408\pi\) | |||||||
\(158\) | 1.09845 | 0.0873883 | ||||||||
\(159\) | −4.59536 | −0.364435 | ||||||||
\(160\) | −1.57995 | −0.124906 | ||||||||
\(161\) | 2.90984 | 0.229328 | ||||||||
\(162\) | −8.18746 | −0.643268 | ||||||||
\(163\) | −12.1135 | −0.948803 | −0.474402 | − | 0.880309i | \(-0.657336\pi\) | ||||
−0.474402 | + | 0.880309i | \(0.657336\pi\) | |||||||
\(164\) | 6.04686 | 0.472180 | ||||||||
\(165\) | 23.3810 | 1.82021 | ||||||||
\(166\) | 5.31930 | 0.412857 | ||||||||
\(167\) | 7.22648 | 0.559202 | 0.279601 | − | 0.960116i | \(-0.409798\pi\) | ||||
0.279601 | + | 0.960116i | \(0.409798\pi\) | |||||||
\(168\) | 8.68519 | 0.670077 | ||||||||
\(169\) | 4.32851 | 0.332962 | ||||||||
\(170\) | −4.61474 | −0.353935 | ||||||||
\(171\) | 15.8843 | 1.21470 | ||||||||
\(172\) | −0.659532 | −0.0502889 | ||||||||
\(173\) | 10.6149 | 0.807035 | 0.403517 | − | 0.914972i | \(-0.367787\pi\) | ||||
0.403517 | + | 0.914972i | \(0.367787\pi\) | |||||||
\(174\) | 15.8485 | 1.20148 | ||||||||
\(175\) | −7.28551 | −0.550733 | ||||||||
\(176\) | −4.95802 | −0.373725 | ||||||||
\(177\) | 10.0312 | 0.753992 | ||||||||
\(178\) | −9.76882 | −0.732204 | ||||||||
\(179\) | −9.66447 | −0.722357 | −0.361178 | − | 0.932497i | \(-0.617625\pi\) | ||||
−0.361178 | + | 0.932497i | \(0.617625\pi\) | |||||||
\(180\) | 9.33562 | 0.695836 | ||||||||
\(181\) | −15.4462 | −1.14811 | −0.574053 | − | 0.818818i | \(-0.694630\pi\) | ||||
−0.574053 | + | 0.818818i | \(0.694630\pi\) | |||||||
\(182\) | 12.1130 | 0.897873 | ||||||||
\(183\) | 24.6563 | 1.82265 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 7.87484 | 0.578970 | ||||||||
\(186\) | −9.34627 | −0.685302 | ||||||||
\(187\) | −14.4814 | −1.05899 | ||||||||
\(188\) | −6.46454 | −0.471475 | ||||||||
\(189\) | −25.2634 | −1.83764 | ||||||||
\(190\) | −4.24730 | −0.308131 | ||||||||
\(191\) | 0.917679 | 0.0664009 | 0.0332005 | − | 0.999449i | \(-0.489430\pi\) | ||||
0.0332005 | + | 0.999449i | \(0.489430\pi\) | |||||||
\(192\) | −2.98476 | −0.215407 | ||||||||
\(193\) | −22.1129 | −1.59172 | −0.795859 | − | 0.605482i | \(-0.792980\pi\) | ||||
−0.795859 | + | 0.605482i | \(0.792980\pi\) | |||||||
\(194\) | −0.168734 | −0.0121144 | ||||||||
\(195\) | 19.6306 | 1.40578 | ||||||||
\(196\) | 1.46720 | 0.104800 | ||||||||
\(197\) | 4.11730 | 0.293345 | 0.146673 | − | 0.989185i | \(-0.453144\pi\) | ||||
0.146673 | + | 0.989185i | \(0.453144\pi\) | |||||||
\(198\) | 29.2959 | 2.08197 | ||||||||
\(199\) | −8.82532 | −0.625610 | −0.312805 | − | 0.949817i | \(-0.601269\pi\) | ||||
−0.312805 | + | 0.949817i | \(0.601269\pi\) | |||||||
\(200\) | 2.50375 | 0.177042 | ||||||||
\(201\) | 14.3603 | 1.01290 | ||||||||
\(202\) | 7.93894 | 0.558582 | ||||||||
\(203\) | 15.4508 | 1.08443 | ||||||||
\(204\) | −8.71791 | −0.610376 | ||||||||
\(205\) | 9.55376 | 0.667264 | ||||||||
\(206\) | −11.7967 | −0.821913 | ||||||||
\(207\) | 5.90879 | 0.410690 | ||||||||
\(208\) | −4.16275 | −0.288635 | ||||||||
\(209\) | −13.3284 | −0.921942 | ||||||||
\(210\) | 13.7222 | 0.946922 | ||||||||
\(211\) | −2.67508 | −0.184160 | −0.0920802 | − | 0.995752i | \(-0.529352\pi\) | ||||
−0.0920802 | + | 0.995752i | \(0.529352\pi\) | |||||||
\(212\) | 1.53961 | 0.105741 | ||||||||
\(213\) | 39.4571 | 2.70356 | ||||||||
\(214\) | −5.22241 | −0.356996 | ||||||||
\(215\) | −1.04203 | −0.0710659 | ||||||||
\(216\) | 8.68205 | 0.590739 | ||||||||
\(217\) | −9.11169 | −0.618542 | ||||||||
\(218\) | 7.46020 | 0.505268 | ||||||||
\(219\) | −4.08146 | −0.275799 | ||||||||
\(220\) | −7.83345 | −0.528131 | ||||||||
\(221\) | −12.1586 | −0.817876 | ||||||||
\(222\) | 14.8767 | 0.998459 | ||||||||
\(223\) | −18.3835 | −1.23105 | −0.615527 | − | 0.788116i | \(-0.711057\pi\) | ||||
−0.615527 | + | 0.788116i | \(0.711057\pi\) | |||||||
\(224\) | −2.90984 | −0.194422 | ||||||||
\(225\) | −14.7941 | −0.986274 | ||||||||
\(226\) | −12.0064 | −0.798652 | ||||||||
\(227\) | −23.7503 | −1.57636 | −0.788182 | − | 0.615442i | \(-0.788978\pi\) | ||||
−0.788182 | + | 0.615442i | \(0.788978\pi\) | |||||||
\(228\) | −8.02376 | −0.531386 | ||||||||
\(229\) | −1.46778 | −0.0969936 | −0.0484968 | − | 0.998823i | \(-0.515443\pi\) | ||||
−0.0484968 | + | 0.998823i | \(0.515443\pi\) | |||||||
\(230\) | −1.57995 | −0.104179 | ||||||||
\(231\) | 43.0614 | 2.83323 | ||||||||
\(232\) | −5.30982 | −0.348607 | ||||||||
\(233\) | 0.0638321 | 0.00418178 | 0.00209089 | − | 0.999998i | \(-0.499334\pi\) | ||||
0.00209089 | + | 0.999998i | \(0.499334\pi\) | |||||||
\(234\) | 24.5968 | 1.60795 | ||||||||
\(235\) | −10.2137 | −0.666267 | ||||||||
\(236\) | −3.36081 | −0.218770 | ||||||||
\(237\) | 3.27862 | 0.212969 | ||||||||
\(238\) | −8.49910 | −0.550915 | ||||||||
\(239\) | 6.88773 | 0.445530 | 0.222765 | − | 0.974872i | \(-0.428492\pi\) | ||||
0.222765 | + | 0.974872i | \(0.428492\pi\) | |||||||
\(240\) | −4.71578 | −0.304403 | ||||||||
\(241\) | −6.04018 | −0.389082 | −0.194541 | − | 0.980894i | \(-0.562322\pi\) | ||||
−0.194541 | + | 0.980894i | \(0.562322\pi\) | |||||||
\(242\) | −13.5820 | −0.873083 | ||||||||
\(243\) | 1.60854 | 0.103188 | ||||||||
\(244\) | −8.26073 | −0.528839 | ||||||||
\(245\) | 2.31810 | 0.148098 | ||||||||
\(246\) | 18.0484 | 1.15073 | ||||||||
\(247\) | −11.1905 | −0.712034 | ||||||||
\(248\) | 3.13133 | 0.198840 | ||||||||
\(249\) | 15.8768 | 1.00615 | ||||||||
\(250\) | 11.8556 | 0.749812 | ||||||||
\(251\) | −13.1367 | −0.829180 | −0.414590 | − | 0.910008i | \(-0.636075\pi\) | ||||
−0.414590 | + | 0.910008i | \(0.636075\pi\) | |||||||
\(252\) | 17.1937 | 1.08310 | ||||||||
\(253\) | −4.95802 | −0.311708 | ||||||||
\(254\) | −10.4798 | −0.657560 | ||||||||
\(255\) | −13.7739 | −0.862555 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.6320 | 0.850338 | 0.425169 | − | 0.905114i | \(-0.360215\pi\) | ||||
0.425169 | + | 0.905114i | \(0.360215\pi\) | |||||||
\(258\) | −1.96855 | −0.122556 | ||||||||
\(259\) | 14.5033 | 0.901192 | ||||||||
\(260\) | −6.57696 | −0.407886 | ||||||||
\(261\) | 31.3746 | 1.94204 | ||||||||
\(262\) | −1.00000 | −0.0617802 | ||||||||
\(263\) | 25.0039 | 1.54181 | 0.770903 | − | 0.636953i | \(-0.219805\pi\) | ||||
0.770903 | + | 0.636953i | \(0.219805\pi\) | |||||||
\(264\) | −14.7985 | −0.910785 | ||||||||
\(265\) | 2.43251 | 0.149428 | ||||||||
\(266\) | −7.82237 | −0.479620 | ||||||||
\(267\) | −29.1576 | −1.78441 | ||||||||
\(268\) | −4.81120 | −0.293891 | ||||||||
\(269\) | 23.5338 | 1.43488 | 0.717440 | − | 0.696621i | \(-0.245314\pi\) | ||||
0.717440 | + | 0.696621i | \(0.245314\pi\) | |||||||
\(270\) | 13.7172 | 0.834805 | ||||||||
\(271\) | −3.11828 | −0.189422 | −0.0947110 | − | 0.995505i | \(-0.530193\pi\) | ||||
−0.0947110 | + | 0.995505i | \(0.530193\pi\) | |||||||
\(272\) | 2.92081 | 0.177100 | ||||||||
\(273\) | 36.1543 | 2.18816 | ||||||||
\(274\) | 9.48217 | 0.572839 | ||||||||
\(275\) | 12.4136 | 0.748570 | ||||||||
\(276\) | −2.98476 | −0.179661 | ||||||||
\(277\) | −25.9233 | −1.55758 | −0.778792 | − | 0.627283i | \(-0.784167\pi\) | ||||
−0.778792 | + | 0.627283i | \(0.784167\pi\) | |||||||
\(278\) | −17.1336 | −1.02760 | ||||||||
\(279\) | −18.5024 | −1.10771 | ||||||||
\(280\) | −4.59742 | −0.274748 | ||||||||
\(281\) | 23.3456 | 1.39268 | 0.696342 | − | 0.717710i | \(-0.254810\pi\) | ||||
0.696342 | + | 0.717710i | \(0.254810\pi\) | |||||||
\(282\) | −19.2951 | −1.14901 | ||||||||
\(283\) | −8.89929 | −0.529008 | −0.264504 | − | 0.964385i | \(-0.585208\pi\) | ||||
−0.264504 | + | 0.964385i | \(0.585208\pi\) | |||||||
\(284\) | −13.2195 | −0.784434 | ||||||||
\(285\) | −12.6772 | −0.750931 | ||||||||
\(286\) | −20.6390 | −1.22041 | ||||||||
\(287\) | 17.5954 | 1.03862 | ||||||||
\(288\) | −5.90879 | −0.348179 | ||||||||
\(289\) | −8.46888 | −0.498170 | ||||||||
\(290\) | −8.38927 | −0.492635 | ||||||||
\(291\) | −0.503632 | −0.0295234 | ||||||||
\(292\) | 1.36743 | 0.0800229 | ||||||||
\(293\) | −16.9497 | −0.990210 | −0.495105 | − | 0.868833i | \(-0.664870\pi\) | ||||
−0.495105 | + | 0.868833i | \(0.664870\pi\) | |||||||
\(294\) | 4.37923 | 0.255402 | ||||||||
\(295\) | −5.30992 | −0.309156 | ||||||||
\(296\) | −4.98422 | −0.289702 | ||||||||
\(297\) | 43.0458 | 2.49777 | ||||||||
\(298\) | −16.0611 | −0.930397 | ||||||||
\(299\) | −4.16275 | −0.240738 | ||||||||
\(300\) | 7.47308 | 0.431458 | ||||||||
\(301\) | −1.91914 | −0.110617 | ||||||||
\(302\) | 5.62376 | 0.323611 | ||||||||
\(303\) | 23.6958 | 1.36129 | ||||||||
\(304\) | 2.68824 | 0.154181 | ||||||||
\(305\) | −13.0516 | −0.747331 | ||||||||
\(306\) | −17.2585 | −0.986600 | ||||||||
\(307\) | −1.38029 | −0.0787775 | −0.0393888 | − | 0.999224i | \(-0.512541\pi\) | ||||
−0.0393888 | + | 0.999224i | \(0.512541\pi\) | |||||||
\(308\) | −14.4271 | −0.822059 | ||||||||
\(309\) | −35.2102 | −2.00304 | ||||||||
\(310\) | 4.94736 | 0.280991 | ||||||||
\(311\) | 0.482578 | 0.0273645 | 0.0136822 | − | 0.999906i | \(-0.495645\pi\) | ||||
0.0136822 | + | 0.999906i | \(0.495645\pi\) | |||||||
\(312\) | −12.4248 | −0.703417 | ||||||||
\(313\) | 8.07664 | 0.456519 | 0.228259 | − | 0.973600i | \(-0.426697\pi\) | ||||
0.228259 | + | 0.973600i | \(0.426697\pi\) | |||||||
\(314\) | −2.63971 | −0.148967 | ||||||||
\(315\) | 27.1652 | 1.53059 | ||||||||
\(316\) | −1.09845 | −0.0617929 | ||||||||
\(317\) | 4.82347 | 0.270913 | 0.135457 | − | 0.990783i | \(-0.456750\pi\) | ||||
0.135457 | + | 0.990783i | \(0.456750\pi\) | |||||||
\(318\) | 4.59536 | 0.257695 | ||||||||
\(319\) | −26.3262 | −1.47399 | ||||||||
\(320\) | 1.57995 | 0.0883221 | ||||||||
\(321\) | −15.5876 | −0.870017 | ||||||||
\(322\) | −2.90984 | −0.162159 | ||||||||
\(323\) | 7.85184 | 0.436888 | ||||||||
\(324\) | 8.18746 | 0.454859 | ||||||||
\(325\) | 10.4225 | 0.578135 | ||||||||
\(326\) | 12.1135 | 0.670905 | ||||||||
\(327\) | 22.2669 | 1.23136 | ||||||||
\(328\) | −6.04686 | −0.333882 | ||||||||
\(329\) | −18.8108 | −1.03707 | ||||||||
\(330\) | −23.3810 | −1.28708 | ||||||||
\(331\) | 3.07731 | 0.169144 | 0.0845721 | − | 0.996417i | \(-0.473048\pi\) | ||||
0.0845721 | + | 0.996417i | \(0.473048\pi\) | |||||||
\(332\) | −5.31930 | −0.291934 | ||||||||
\(333\) | 29.4507 | 1.61389 | ||||||||
\(334\) | −7.22648 | −0.395415 | ||||||||
\(335\) | −7.60147 | −0.415313 | ||||||||
\(336\) | −8.68519 | −0.473816 | ||||||||
\(337\) | 34.3457 | 1.87093 | 0.935466 | − | 0.353416i | \(-0.114980\pi\) | ||||
0.935466 | + | 0.353416i | \(0.114980\pi\) | |||||||
\(338\) | −4.32851 | −0.235440 | ||||||||
\(339\) | −35.8361 | −1.94635 | ||||||||
\(340\) | 4.61474 | 0.250270 | ||||||||
\(341\) | 15.5252 | 0.840737 | ||||||||
\(342\) | −15.8843 | −0.858923 | ||||||||
\(343\) | −16.0996 | −0.869297 | ||||||||
\(344\) | 0.659532 | 0.0355596 | ||||||||
\(345\) | −4.71578 | −0.253889 | ||||||||
\(346\) | −10.6149 | −0.570660 | ||||||||
\(347\) | −0.367674 | −0.0197378 | −0.00986888 | − | 0.999951i | \(-0.503141\pi\) | ||||
−0.00986888 | + | 0.999951i | \(0.503141\pi\) | |||||||
\(348\) | −15.8485 | −0.849571 | ||||||||
\(349\) | −0.894177 | −0.0478642 | −0.0239321 | − | 0.999714i | \(-0.507619\pi\) | ||||
−0.0239321 | + | 0.999714i | \(0.507619\pi\) | |||||||
\(350\) | 7.28551 | 0.389427 | ||||||||
\(351\) | 36.1412 | 1.92908 | ||||||||
\(352\) | 4.95802 | 0.264263 | ||||||||
\(353\) | 8.63781 | 0.459744 | 0.229872 | − | 0.973221i | \(-0.426169\pi\) | ||||
0.229872 | + | 0.973221i | \(0.426169\pi\) | |||||||
\(354\) | −10.0312 | −0.533153 | ||||||||
\(355\) | −20.8862 | −1.10853 | ||||||||
\(356\) | 9.76882 | 0.517746 | ||||||||
\(357\) | −25.3678 | −1.34260 | ||||||||
\(358\) | 9.66447 | 0.510783 | ||||||||
\(359\) | −19.1586 | −1.01115 | −0.505577 | − | 0.862781i | \(-0.668720\pi\) | ||||
−0.505577 | + | 0.862781i | \(0.668720\pi\) | |||||||
\(360\) | −9.33562 | −0.492031 | ||||||||
\(361\) | −11.7734 | −0.619650 | ||||||||
\(362\) | 15.4462 | 0.811833 | ||||||||
\(363\) | −40.5390 | −2.12774 | ||||||||
\(364\) | −12.1130 | −0.634892 | ||||||||
\(365\) | 2.16048 | 0.113085 | ||||||||
\(366\) | −24.6563 | −1.28881 | ||||||||
\(367\) | 17.2141 | 0.898569 | 0.449284 | − | 0.893389i | \(-0.351679\pi\) | ||||
0.449284 | + | 0.893389i | \(0.351679\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 35.7296 | 1.86001 | ||||||||
\(370\) | −7.87484 | −0.409393 | ||||||||
\(371\) | 4.48002 | 0.232591 | ||||||||
\(372\) | 9.34627 | 0.484582 | ||||||||
\(373\) | 0.494841 | 0.0256219 | 0.0128110 | − | 0.999918i | \(-0.495922\pi\) | ||||
0.0128110 | + | 0.999918i | \(0.495922\pi\) | |||||||
\(374\) | 14.4814 | 0.748817 | ||||||||
\(375\) | 35.3860 | 1.82733 | ||||||||
\(376\) | 6.46454 | 0.333383 | ||||||||
\(377\) | −22.1035 | −1.13839 | ||||||||
\(378\) | 25.2634 | 1.29941 | ||||||||
\(379\) | −11.2343 | −0.577067 | −0.288533 | − | 0.957470i | \(-0.593168\pi\) | ||||
−0.288533 | + | 0.957470i | \(0.593168\pi\) | |||||||
\(380\) | 4.24730 | 0.217882 | ||||||||
\(381\) | −31.2796 | −1.60250 | ||||||||
\(382\) | −0.917679 | −0.0469525 | ||||||||
\(383\) | 12.7838 | 0.653219 | 0.326610 | − | 0.945159i | \(-0.394094\pi\) | ||||
0.326610 | + | 0.945159i | \(0.394094\pi\) | |||||||
\(384\) | 2.98476 | 0.152315 | ||||||||
\(385\) | −22.7941 | −1.16170 | ||||||||
\(386\) | 22.1129 | 1.12551 | ||||||||
\(387\) | −3.89704 | −0.198098 | ||||||||
\(388\) | 0.168734 | 0.00856620 | ||||||||
\(389\) | −25.2337 | −1.27940 | −0.639699 | − | 0.768626i | \(-0.720941\pi\) | ||||
−0.639699 | + | 0.768626i | \(0.720941\pi\) | |||||||
\(390\) | −19.6306 | −0.994036 | ||||||||
\(391\) | 2.92081 | 0.147712 | ||||||||
\(392\) | −1.46720 | −0.0741046 | ||||||||
\(393\) | −2.98476 | −0.150561 | ||||||||
\(394\) | −4.11730 | −0.207427 | ||||||||
\(395\) | −1.73551 | −0.0873228 | ||||||||
\(396\) | −29.2959 | −1.47218 | ||||||||
\(397\) | −2.61143 | −0.131064 | −0.0655318 | − | 0.997850i | \(-0.520874\pi\) | ||||
−0.0655318 | + | 0.997850i | \(0.520874\pi\) | |||||||
\(398\) | 8.82532 | 0.442373 | ||||||||
\(399\) | −23.3479 | −1.16886 | ||||||||
\(400\) | −2.50375 | −0.125187 | ||||||||
\(401\) | 6.70995 | 0.335079 | 0.167539 | − | 0.985865i | \(-0.446418\pi\) | ||||
0.167539 | + | 0.985865i | \(0.446418\pi\) | |||||||
\(402\) | −14.3603 | −0.716226 | ||||||||
\(403\) | 13.0350 | 0.649318 | ||||||||
\(404\) | −7.93894 | −0.394977 | ||||||||
\(405\) | 12.9358 | 0.642786 | ||||||||
\(406\) | −15.4508 | −0.766808 | ||||||||
\(407\) | −24.7119 | −1.22492 | ||||||||
\(408\) | 8.71791 | 0.431601 | ||||||||
\(409\) | −14.4763 | −0.715805 | −0.357903 | − | 0.933759i | \(-0.616508\pi\) | ||||
−0.357903 | + | 0.933759i | \(0.616508\pi\) | |||||||
\(410\) | −9.55376 | −0.471827 | ||||||||
\(411\) | 28.3020 | 1.39603 | ||||||||
\(412\) | 11.7967 | 0.581180 | ||||||||
\(413\) | −9.77943 | −0.481214 | ||||||||
\(414\) | −5.90879 | −0.290401 | ||||||||
\(415\) | −8.40424 | −0.412548 | ||||||||
\(416\) | 4.16275 | 0.204096 | ||||||||
\(417\) | −51.1396 | −2.50432 | ||||||||
\(418\) | 13.3284 | 0.651912 | ||||||||
\(419\) | −25.0401 | −1.22329 | −0.611646 | − | 0.791132i | \(-0.709492\pi\) | ||||
−0.611646 | + | 0.791132i | \(0.709492\pi\) | |||||||
\(420\) | −13.7222 | −0.669575 | ||||||||
\(421\) | −33.5078 | −1.63307 | −0.816536 | − | 0.577294i | \(-0.804109\pi\) | ||||
−0.816536 | + | 0.577294i | \(0.804109\pi\) | |||||||
\(422\) | 2.67508 | 0.130221 | ||||||||
\(423\) | −38.1976 | −1.85723 | ||||||||
\(424\) | −1.53961 | −0.0747699 | ||||||||
\(425\) | −7.31296 | −0.354731 | ||||||||
\(426\) | −39.4571 | −1.91170 | ||||||||
\(427\) | −24.0374 | −1.16325 | ||||||||
\(428\) | 5.22241 | 0.252435 | ||||||||
\(429\) | −61.6025 | −2.97420 | ||||||||
\(430\) | 1.04203 | 0.0502512 | ||||||||
\(431\) | −12.3898 | −0.596796 | −0.298398 | − | 0.954442i | \(-0.596452\pi\) | ||||
−0.298398 | + | 0.954442i | \(0.596452\pi\) | |||||||
\(432\) | −8.68205 | −0.417715 | ||||||||
\(433\) | 20.4285 | 0.981733 | 0.490867 | − | 0.871235i | \(-0.336680\pi\) | ||||
0.490867 | + | 0.871235i | \(0.336680\pi\) | |||||||
\(434\) | 9.11169 | 0.437375 | ||||||||
\(435\) | −25.0400 | −1.20057 | ||||||||
\(436\) | −7.46020 | −0.357279 | ||||||||
\(437\) | 2.68824 | 0.128596 | ||||||||
\(438\) | 4.08146 | 0.195020 | ||||||||
\(439\) | 9.67055 | 0.461550 | 0.230775 | − | 0.973007i | \(-0.425874\pi\) | ||||
0.230775 | + | 0.973007i | \(0.425874\pi\) | |||||||
\(440\) | 7.83345 | 0.373445 | ||||||||
\(441\) | 8.66936 | 0.412826 | ||||||||
\(442\) | 12.1586 | 0.578326 | ||||||||
\(443\) | 26.6064 | 1.26411 | 0.632053 | − | 0.774925i | \(-0.282212\pi\) | ||||
0.632053 | + | 0.774925i | \(0.282212\pi\) | |||||||
\(444\) | −14.8767 | −0.706017 | ||||||||
\(445\) | 15.4343 | 0.731655 | ||||||||
\(446\) | 18.3835 | 0.870486 | ||||||||
\(447\) | −47.9387 | −2.26742 | ||||||||
\(448\) | 2.90984 | 0.137477 | ||||||||
\(449\) | −10.3336 | −0.487674 | −0.243837 | − | 0.969816i | \(-0.578406\pi\) | ||||
−0.243837 | + | 0.969816i | \(0.578406\pi\) | |||||||
\(450\) | 14.7941 | 0.697401 | ||||||||
\(451\) | −29.9805 | −1.41173 | ||||||||
\(452\) | 12.0064 | 0.564732 | ||||||||
\(453\) | 16.7856 | 0.788655 | ||||||||
\(454\) | 23.7503 | 1.11466 | ||||||||
\(455\) | −19.1379 | −0.897200 | ||||||||
\(456\) | 8.02376 | 0.375747 | ||||||||
\(457\) | 1.45972 | 0.0682827 | 0.0341414 | − | 0.999417i | \(-0.489130\pi\) | ||||
0.0341414 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(458\) | 1.46778 | 0.0685848 | ||||||||
\(459\) | −25.3586 | −1.18364 | ||||||||
\(460\) | 1.57995 | 0.0736657 | ||||||||
\(461\) | −5.60953 | −0.261262 | −0.130631 | − | 0.991431i | \(-0.541700\pi\) | ||||
−0.130631 | + | 0.991431i | \(0.541700\pi\) | |||||||
\(462\) | −43.0614 | −2.00340 | ||||||||
\(463\) | 0.661601 | 0.0307472 | 0.0153736 | − | 0.999882i | \(-0.495106\pi\) | ||||
0.0153736 | + | 0.999882i | \(0.495106\pi\) | |||||||
\(464\) | 5.30982 | 0.246502 | ||||||||
\(465\) | 14.7667 | 0.684789 | ||||||||
\(466\) | −0.0638321 | −0.00295697 | ||||||||
\(467\) | −20.9449 | −0.969214 | −0.484607 | − | 0.874732i | \(-0.661037\pi\) | ||||
−0.484607 | + | 0.874732i | \(0.661037\pi\) | |||||||
\(468\) | −24.5968 | −1.13699 | ||||||||
\(469\) | −13.9998 | −0.646453 | ||||||||
\(470\) | 10.2137 | 0.471122 | ||||||||
\(471\) | −7.87890 | −0.363040 | ||||||||
\(472\) | 3.36081 | 0.154694 | ||||||||
\(473\) | 3.26998 | 0.150354 | ||||||||
\(474\) | −3.27862 | −0.150592 | ||||||||
\(475\) | −6.73067 | −0.308824 | ||||||||
\(476\) | 8.49910 | 0.389555 | ||||||||
\(477\) | 9.09722 | 0.416533 | ||||||||
\(478\) | −6.88773 | −0.315037 | ||||||||
\(479\) | −25.4412 | −1.16244 | −0.581219 | − | 0.813747i | \(-0.697424\pi\) | ||||
−0.581219 | + | 0.813747i | \(0.697424\pi\) | |||||||
\(480\) | 4.71578 | 0.215245 | ||||||||
\(481\) | −20.7481 | −0.946031 | ||||||||
\(482\) | 6.04018 | 0.275123 | ||||||||
\(483\) | −8.68519 | −0.395190 | ||||||||
\(484\) | 13.5820 | 0.617363 | ||||||||
\(485\) | 0.266593 | 0.0121054 | ||||||||
\(486\) | −1.60854 | −0.0729649 | ||||||||
\(487\) | −33.4736 | −1.51683 | −0.758417 | − | 0.651770i | \(-0.774027\pi\) | ||||
−0.758417 | + | 0.651770i | \(0.774027\pi\) | |||||||
\(488\) | 8.26073 | 0.373946 | ||||||||
\(489\) | 36.1559 | 1.63503 | ||||||||
\(490\) | −2.31810 | −0.104721 | ||||||||
\(491\) | −9.23297 | −0.416678 | −0.208339 | − | 0.978057i | \(-0.566806\pi\) | ||||
−0.208339 | + | 0.978057i | \(0.566806\pi\) | |||||||
\(492\) | −18.0484 | −0.813686 | ||||||||
\(493\) | 15.5090 | 0.698489 | ||||||||
\(494\) | 11.1905 | 0.503484 | ||||||||
\(495\) | −46.2862 | −2.08041 | ||||||||
\(496\) | −3.13133 | −0.140601 | ||||||||
\(497\) | −38.4668 | −1.72547 | ||||||||
\(498\) | −15.8768 | −0.711457 | ||||||||
\(499\) | −31.5925 | −1.41427 | −0.707136 | − | 0.707077i | \(-0.750013\pi\) | ||||
−0.707136 | + | 0.707077i | \(0.750013\pi\) | |||||||
\(500\) | −11.8556 | −0.530197 | ||||||||
\(501\) | −21.5693 | −0.963645 | ||||||||
\(502\) | 13.1367 | 0.586319 | ||||||||
\(503\) | 16.3391 | 0.728523 | 0.364261 | − | 0.931297i | \(-0.381321\pi\) | ||||
0.364261 | + | 0.931297i | \(0.381321\pi\) | |||||||
\(504\) | −17.1937 | −0.765867 | ||||||||
\(505\) | −12.5432 | −0.558163 | ||||||||
\(506\) | 4.95802 | 0.220411 | ||||||||
\(507\) | −12.9196 | −0.573778 | ||||||||
\(508\) | 10.4798 | 0.464965 | ||||||||
\(509\) | 19.6485 | 0.870903 | 0.435452 | − | 0.900212i | \(-0.356589\pi\) | ||||
0.435452 | + | 0.900212i | \(0.356589\pi\) | |||||||
\(510\) | 13.7739 | 0.609918 | ||||||||
\(511\) | 3.97901 | 0.176021 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −23.3395 | −1.03046 | ||||||||
\(514\) | −13.6320 | −0.601280 | ||||||||
\(515\) | 18.6382 | 0.821297 | ||||||||
\(516\) | 1.96855 | 0.0866604 | ||||||||
\(517\) | 32.0513 | 1.40962 | ||||||||
\(518\) | −14.5033 | −0.637239 | ||||||||
\(519\) | −31.6829 | −1.39072 | ||||||||
\(520\) | 6.57696 | 0.288419 | ||||||||
\(521\) | −7.98997 | −0.350047 | −0.175024 | − | 0.984564i | \(-0.556000\pi\) | ||||
−0.175024 | + | 0.984564i | \(0.556000\pi\) | |||||||
\(522\) | −31.3746 | −1.37323 | ||||||||
\(523\) | −42.3639 | −1.85245 | −0.926223 | − | 0.376976i | \(-0.876964\pi\) | ||||
−0.926223 | + | 0.376976i | \(0.876964\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | 21.7455 | 0.949051 | ||||||||
\(526\) | −25.0039 | −1.09022 | ||||||||
\(527\) | −9.14602 | −0.398407 | ||||||||
\(528\) | 14.7985 | 0.644022 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.43251 | −0.105661 | ||||||||
\(531\) | −19.8583 | −0.861778 | ||||||||
\(532\) | 7.82237 | 0.339143 | ||||||||
\(533\) | −25.1716 | −1.09030 | ||||||||
\(534\) | 29.1576 | 1.26177 | ||||||||
\(535\) | 8.25116 | 0.356729 | ||||||||
\(536\) | 4.81120 | 0.207812 | ||||||||
\(537\) | 28.8461 | 1.24480 | ||||||||
\(538\) | −23.5338 | −1.01461 | ||||||||
\(539\) | −7.27439 | −0.313330 | ||||||||
\(540\) | −13.7172 | −0.590296 | ||||||||
\(541\) | −31.3746 | −1.34890 | −0.674449 | − | 0.738321i | \(-0.735619\pi\) | ||||
−0.674449 | + | 0.738321i | \(0.735619\pi\) | |||||||
\(542\) | 3.11828 | 0.133942 | ||||||||
\(543\) | 46.1032 | 1.97848 | ||||||||
\(544\) | −2.92081 | −0.125229 | ||||||||
\(545\) | −11.7868 | −0.504890 | ||||||||
\(546\) | −36.1543 | −1.54726 | ||||||||
\(547\) | −33.5092 | −1.43275 | −0.716375 | − | 0.697716i | \(-0.754200\pi\) | ||||
−0.716375 | + | 0.697716i | \(0.754200\pi\) | |||||||
\(548\) | −9.48217 | −0.405058 | ||||||||
\(549\) | −48.8110 | −2.08320 | ||||||||
\(550\) | −12.4136 | −0.529319 | ||||||||
\(551\) | 14.2741 | 0.608096 | ||||||||
\(552\) | 2.98476 | 0.127040 | ||||||||
\(553\) | −3.19633 | −0.135922 | ||||||||
\(554\) | 25.9233 | 1.10138 | ||||||||
\(555\) | −23.5045 | −0.997711 | ||||||||
\(556\) | 17.1336 | 0.726625 | ||||||||
\(557\) | 37.1042 | 1.57216 | 0.786078 | − | 0.618127i | \(-0.212108\pi\) | ||||
0.786078 | + | 0.618127i | \(0.212108\pi\) | |||||||
\(558\) | 18.5024 | 0.783269 | ||||||||
\(559\) | 2.74547 | 0.116121 | ||||||||
\(560\) | 4.59742 | 0.194276 | ||||||||
\(561\) | 43.2236 | 1.82490 | ||||||||
\(562\) | −23.3456 | −0.984776 | ||||||||
\(563\) | −18.6130 | −0.784443 | −0.392222 | − | 0.919871i | \(-0.628293\pi\) | ||||
−0.392222 | + | 0.919871i | \(0.628293\pi\) | |||||||
\(564\) | 19.2951 | 0.812470 | ||||||||
\(565\) | 18.9695 | 0.798053 | ||||||||
\(566\) | 8.89929 | 0.374065 | ||||||||
\(567\) | 23.8242 | 1.00052 | ||||||||
\(568\) | 13.2195 | 0.554679 | ||||||||
\(569\) | 6.11142 | 0.256204 | 0.128102 | − | 0.991761i | \(-0.459112\pi\) | ||||
0.128102 | + | 0.991761i | \(0.459112\pi\) | |||||||
\(570\) | 12.6772 | 0.530988 | ||||||||
\(571\) | 33.1298 | 1.38644 | 0.693219 | − | 0.720727i | \(-0.256192\pi\) | ||||
0.693219 | + | 0.720727i | \(0.256192\pi\) | |||||||
\(572\) | 20.6390 | 0.862961 | ||||||||
\(573\) | −2.73905 | −0.114426 | ||||||||
\(574\) | −17.5954 | −0.734419 | ||||||||
\(575\) | −2.50375 | −0.104413 | ||||||||
\(576\) | 5.90879 | 0.246200 | ||||||||
\(577\) | 12.5125 | 0.520902 | 0.260451 | − | 0.965487i | \(-0.416129\pi\) | ||||
0.260451 | + | 0.965487i | \(0.416129\pi\) | |||||||
\(578\) | 8.46888 | 0.352259 | ||||||||
\(579\) | 66.0016 | 2.74293 | ||||||||
\(580\) | 8.38927 | 0.348346 | ||||||||
\(581\) | −15.4783 | −0.642149 | ||||||||
\(582\) | 0.503632 | 0.0208762 | ||||||||
\(583\) | −7.63340 | −0.316143 | ||||||||
\(584\) | −1.36743 | −0.0565847 | ||||||||
\(585\) | −38.8619 | −1.60674 | ||||||||
\(586\) | 16.9497 | 0.700184 | ||||||||
\(587\) | −8.60823 | −0.355299 | −0.177650 | − | 0.984094i | \(-0.556849\pi\) | ||||
−0.177650 | + | 0.984094i | \(0.556849\pi\) | |||||||
\(588\) | −4.37923 | −0.180596 | ||||||||
\(589\) | −8.41778 | −0.346848 | ||||||||
\(590\) | 5.30992 | 0.218606 | ||||||||
\(591\) | −12.2891 | −0.505508 | ||||||||
\(592\) | 4.98422 | 0.204850 | ||||||||
\(593\) | −32.8502 | −1.34900 | −0.674498 | − | 0.738277i | \(-0.735640\pi\) | ||||
−0.674498 | + | 0.738277i | \(0.735640\pi\) | |||||||
\(594\) | −43.0458 | −1.76619 | ||||||||
\(595\) | 13.4282 | 0.550502 | ||||||||
\(596\) | 16.0611 | 0.657890 | ||||||||
\(597\) | 26.3415 | 1.07808 | ||||||||
\(598\) | 4.16275 | 0.170228 | ||||||||
\(599\) | −32.4045 | −1.32401 | −0.662006 | − | 0.749498i | \(-0.730295\pi\) | ||||
−0.662006 | + | 0.749498i | \(0.730295\pi\) | |||||||
\(600\) | −7.47308 | −0.305087 | ||||||||
\(601\) | 26.5066 | 1.08123 | 0.540614 | − | 0.841271i | \(-0.318192\pi\) | ||||
0.540614 | + | 0.841271i | \(0.318192\pi\) | |||||||
\(602\) | 1.91914 | 0.0782181 | ||||||||
\(603\) | −28.4284 | −1.15769 | ||||||||
\(604\) | −5.62376 | −0.228828 | ||||||||
\(605\) | 21.4589 | 0.872429 | ||||||||
\(606\) | −23.6958 | −0.962578 | ||||||||
\(607\) | 1.31780 | 0.0534877 | 0.0267439 | − | 0.999642i | \(-0.491486\pi\) | ||||
0.0267439 | + | 0.999642i | \(0.491486\pi\) | |||||||
\(608\) | −2.68824 | −0.109023 | ||||||||
\(609\) | −46.1168 | −1.86875 | ||||||||
\(610\) | 13.0516 | 0.528443 | ||||||||
\(611\) | 26.9103 | 1.08867 | ||||||||
\(612\) | 17.2585 | 0.697631 | ||||||||
\(613\) | 27.4062 | 1.10693 | 0.553463 | − | 0.832874i | \(-0.313306\pi\) | ||||
0.553463 | + | 0.832874i | \(0.313306\pi\) | |||||||
\(614\) | 1.38029 | 0.0557041 | ||||||||
\(615\) | −28.5157 | −1.14986 | ||||||||
\(616\) | 14.4271 | 0.581283 | ||||||||
\(617\) | −0.0454317 | −0.00182901 | −0.000914505 | − | 1.00000i | \(-0.500291\pi\) | ||||
−0.000914505 | 1.00000i | \(0.500291\pi\) | ||||||||
\(618\) | 35.2102 | 1.41636 | ||||||||
\(619\) | −39.0324 | −1.56884 | −0.784422 | − | 0.620228i | \(-0.787040\pi\) | ||||
−0.784422 | + | 0.620228i | \(0.787040\pi\) | |||||||
\(620\) | −4.94736 | −0.198691 | ||||||||
\(621\) | −8.68205 | −0.348399 | ||||||||
\(622\) | −0.482578 | −0.0193496 | ||||||||
\(623\) | 28.4257 | 1.13885 | ||||||||
\(624\) | 12.4248 | 0.497391 | ||||||||
\(625\) | −6.21254 | −0.248501 | ||||||||
\(626\) | −8.07664 | −0.322807 | ||||||||
\(627\) | 39.7820 | 1.58874 | ||||||||
\(628\) | 2.63971 | 0.105336 | ||||||||
\(629\) | 14.5580 | 0.580464 | ||||||||
\(630\) | −27.1652 | −1.08229 | ||||||||
\(631\) | −16.7170 | −0.665493 | −0.332746 | − | 0.943016i | \(-0.607975\pi\) | ||||
−0.332746 | + | 0.943016i | \(0.607975\pi\) | |||||||
\(632\) | 1.09845 | 0.0436941 | ||||||||
\(633\) | 7.98449 | 0.317355 | ||||||||
\(634\) | −4.82347 | −0.191565 | ||||||||
\(635\) | 16.5576 | 0.657067 | ||||||||
\(636\) | −4.59536 | −0.182218 | ||||||||
\(637\) | −6.10757 | −0.241991 | ||||||||
\(638\) | 26.3262 | 1.04226 | ||||||||
\(639\) | −78.1114 | −3.09004 | ||||||||
\(640\) | −1.57995 | −0.0624532 | ||||||||
\(641\) | 16.8115 | 0.664012 | 0.332006 | − | 0.943277i | \(-0.392275\pi\) | ||||
0.332006 | + | 0.943277i | \(0.392275\pi\) | |||||||
\(642\) | 15.5876 | 0.615195 | ||||||||
\(643\) | −32.8091 | −1.29386 | −0.646932 | − | 0.762548i | \(-0.723948\pi\) | ||||
−0.646932 | + | 0.762548i | \(0.723948\pi\) | |||||||
\(644\) | 2.90984 | 0.114664 | ||||||||
\(645\) | 3.11021 | 0.122464 | ||||||||
\(646\) | −7.85184 | −0.308926 | ||||||||
\(647\) | −5.86103 | −0.230421 | −0.115210 | − | 0.993341i | \(-0.536754\pi\) | ||||
−0.115210 | + | 0.993341i | \(0.536754\pi\) | |||||||
\(648\) | −8.18746 | −0.321634 | ||||||||
\(649\) | 16.6630 | 0.654079 | ||||||||
\(650\) | −10.4225 | −0.408803 | ||||||||
\(651\) | 27.1962 | 1.06590 | ||||||||
\(652\) | −12.1135 | −0.474402 | ||||||||
\(653\) | 27.0456 | 1.05838 | 0.529188 | − | 0.848505i | \(-0.322497\pi\) | ||||
0.529188 | + | 0.848505i | \(0.322497\pi\) | |||||||
\(654\) | −22.2669 | −0.870705 | ||||||||
\(655\) | 1.57995 | 0.0617339 | ||||||||
\(656\) | 6.04686 | 0.236090 | ||||||||
\(657\) | 8.07987 | 0.315226 | ||||||||
\(658\) | 18.8108 | 0.733322 | ||||||||
\(659\) | −1.48147 | −0.0577099 | −0.0288550 | − | 0.999584i | \(-0.509186\pi\) | ||||
−0.0288550 | + | 0.999584i | \(0.509186\pi\) | |||||||
\(660\) | 23.3810 | 0.910103 | ||||||||
\(661\) | −32.4112 | −1.26065 | −0.630324 | − | 0.776332i | \(-0.717078\pi\) | ||||
−0.630324 | + | 0.776332i | \(0.717078\pi\) | |||||||
\(662\) | −3.07731 | −0.119603 | ||||||||
\(663\) | 36.2905 | 1.40941 | ||||||||
\(664\) | 5.31930 | 0.206429 | ||||||||
\(665\) | 12.3590 | 0.479261 | ||||||||
\(666\) | −29.4507 | −1.14119 | ||||||||
\(667\) | 5.30982 | 0.205597 | ||||||||
\(668\) | 7.22648 | 0.279601 | ||||||||
\(669\) | 54.8705 | 2.12142 | ||||||||
\(670\) | 7.60147 | 0.293671 | ||||||||
\(671\) | 40.9569 | 1.58112 | ||||||||
\(672\) | 8.68519 | 0.335038 | ||||||||
\(673\) | 44.5513 | 1.71733 | 0.858664 | − | 0.512540i | \(-0.171295\pi\) | ||||
0.858664 | + | 0.512540i | \(0.171295\pi\) | |||||||
\(674\) | −34.3457 | −1.32295 | ||||||||
\(675\) | 21.7376 | 0.836682 | ||||||||
\(676\) | 4.32851 | 0.166481 | ||||||||
\(677\) | −32.8608 | −1.26294 | −0.631471 | − | 0.775400i | \(-0.717549\pi\) | ||||
−0.631471 | + | 0.775400i | \(0.717549\pi\) | |||||||
\(678\) | 35.8361 | 1.37628 | ||||||||
\(679\) | 0.490991 | 0.0188425 | ||||||||
\(680\) | −4.61474 | −0.176967 | ||||||||
\(681\) | 70.8891 | 2.71647 | ||||||||
\(682\) | −15.5252 | −0.594491 | ||||||||
\(683\) | −34.5906 | −1.32357 | −0.661787 | − | 0.749692i | \(-0.730202\pi\) | ||||
−0.661787 | + | 0.749692i | \(0.730202\pi\) | |||||||
\(684\) | 15.8843 | 0.607350 | ||||||||
\(685\) | −14.9814 | −0.572410 | ||||||||
\(686\) | 16.0996 | 0.614686 | ||||||||
\(687\) | 4.38097 | 0.167144 | ||||||||
\(688\) | −0.659532 | −0.0251444 | ||||||||
\(689\) | −6.40900 | −0.244163 | ||||||||
\(690\) | 4.71578 | 0.179527 | ||||||||
\(691\) | −46.8383 | −1.78181 | −0.890906 | − | 0.454187i | \(-0.849930\pi\) | ||||
−0.890906 | + | 0.454187i | \(0.849930\pi\) | |||||||
\(692\) | 10.6149 | 0.403517 | ||||||||
\(693\) | −85.2466 | −3.23825 | ||||||||
\(694\) | 0.367674 | 0.0139567 | ||||||||
\(695\) | 27.0703 | 1.02683 | ||||||||
\(696\) | 15.8485 | 0.600738 | ||||||||
\(697\) | 17.6617 | 0.668985 | ||||||||
\(698\) | 0.894177 | 0.0338451 | ||||||||
\(699\) | −0.190524 | −0.00720626 | ||||||||
\(700\) | −7.28551 | −0.275366 | ||||||||
\(701\) | −33.9576 | −1.28256 | −0.641281 | − | 0.767306i | \(-0.721597\pi\) | ||||
−0.641281 | + | 0.767306i | \(0.721597\pi\) | |||||||
\(702\) | −36.1412 | −1.36406 | ||||||||
\(703\) | 13.3988 | 0.505345 | ||||||||
\(704\) | −4.95802 | −0.186863 | ||||||||
\(705\) | 30.4854 | 1.14815 | ||||||||
\(706\) | −8.63781 | −0.325088 | ||||||||
\(707\) | −23.1011 | −0.868806 | ||||||||
\(708\) | 10.0312 | 0.376996 | ||||||||
\(709\) | −13.9892 | −0.525374 | −0.262687 | − | 0.964881i | \(-0.584609\pi\) | ||||
−0.262687 | + | 0.964881i | \(0.584609\pi\) | |||||||
\(710\) | 20.8862 | 0.783847 | ||||||||
\(711\) | −6.49054 | −0.243414 | ||||||||
\(712\) | −9.76882 | −0.366102 | ||||||||
\(713\) | −3.13133 | −0.117269 | ||||||||
\(714\) | 25.3678 | 0.949365 | ||||||||
\(715\) | 32.6087 | 1.21950 | ||||||||
\(716\) | −9.66447 | −0.361178 | ||||||||
\(717\) | −20.5582 | −0.767761 | ||||||||
\(718\) | 19.1586 | 0.714994 | ||||||||
\(719\) | 7.46332 | 0.278335 | 0.139167 | − | 0.990269i | \(-0.455557\pi\) | ||||
0.139167 | + | 0.990269i | \(0.455557\pi\) | |||||||
\(720\) | 9.33562 | 0.347918 | ||||||||
\(721\) | 34.3265 | 1.27838 | ||||||||
\(722\) | 11.7734 | 0.438159 | ||||||||
\(723\) | 18.0285 | 0.670487 | ||||||||
\(724\) | −15.4462 | −0.574053 | ||||||||
\(725\) | −13.2944 | −0.493743 | ||||||||
\(726\) | 40.5390 | 1.50454 | ||||||||
\(727\) | 17.2487 | 0.639720 | 0.319860 | − | 0.947465i | \(-0.396364\pi\) | ||||
0.319860 | + | 0.947465i | \(0.396364\pi\) | |||||||
\(728\) | 12.1130 | 0.448936 | ||||||||
\(729\) | −29.3635 | −1.08754 | ||||||||
\(730\) | −2.16048 | −0.0799629 | ||||||||
\(731\) | −1.92637 | −0.0712492 | ||||||||
\(732\) | 24.6563 | 0.911323 | ||||||||
\(733\) | 36.3583 | 1.34293 | 0.671463 | − | 0.741038i | \(-0.265666\pi\) | ||||
0.671463 | + | 0.741038i | \(0.265666\pi\) | |||||||
\(734\) | −17.2141 | −0.635384 | ||||||||
\(735\) | −6.91898 | −0.255210 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 23.8540 | 0.878675 | ||||||||
\(738\) | −35.7296 | −1.31523 | ||||||||
\(739\) | −29.9814 | −1.10288 | −0.551442 | − | 0.834213i | \(-0.685922\pi\) | ||||
−0.551442 | + | 0.834213i | \(0.685922\pi\) | |||||||
\(740\) | 7.87484 | 0.289485 | ||||||||
\(741\) | 33.4009 | 1.22701 | ||||||||
\(742\) | −4.48002 | −0.164467 | ||||||||
\(743\) | −33.9101 | −1.24404 | −0.622020 | − | 0.783001i | \(-0.713688\pi\) | ||||
−0.622020 | + | 0.783001i | \(0.713688\pi\) | |||||||
\(744\) | −9.34627 | −0.342651 | ||||||||
\(745\) | 25.3759 | 0.929700 | ||||||||
\(746\) | −0.494841 | −0.0181174 | ||||||||
\(747\) | −31.4306 | −1.14999 | ||||||||
\(748\) | −14.4814 | −0.529494 | ||||||||
\(749\) | 15.1964 | 0.555264 | ||||||||
\(750\) | −35.3860 | −1.29212 | ||||||||
\(751\) | 35.0857 | 1.28029 | 0.640147 | − | 0.768252i | \(-0.278873\pi\) | ||||
0.640147 | + | 0.768252i | \(0.278873\pi\) | |||||||
\(752\) | −6.46454 | −0.235738 | ||||||||
\(753\) | 39.2098 | 1.42889 | ||||||||
\(754\) | 22.1035 | 0.804961 | ||||||||
\(755\) | −8.88528 | −0.323369 | ||||||||
\(756\) | −25.2634 | −0.918822 | ||||||||
\(757\) | −23.0994 | −0.839561 | −0.419781 | − | 0.907626i | \(-0.637893\pi\) | ||||
−0.419781 | + | 0.907626i | \(0.637893\pi\) | |||||||
\(758\) | 11.2343 | 0.408048 | ||||||||
\(759\) | 14.7985 | 0.537152 | ||||||||
\(760\) | −4.24730 | −0.154066 | ||||||||
\(761\) | −29.9840 | −1.08692 | −0.543459 | − | 0.839436i | \(-0.682886\pi\) | ||||
−0.543459 | + | 0.839436i | \(0.682886\pi\) | |||||||
\(762\) | 31.2796 | 1.13314 | ||||||||
\(763\) | −21.7080 | −0.785883 | ||||||||
\(764\) | 0.917679 | 0.0332005 | ||||||||
\(765\) | 27.2676 | 0.985861 | ||||||||
\(766\) | −12.7838 | −0.461896 | ||||||||
\(767\) | 13.9902 | 0.505157 | ||||||||
\(768\) | −2.98476 | −0.107703 | ||||||||
\(769\) | −30.0495 | −1.08361 | −0.541806 | − | 0.840503i | \(-0.682259\pi\) | ||||
−0.541806 | + | 0.840503i | \(0.682259\pi\) | |||||||
\(770\) | 22.7941 | 0.821443 | ||||||||
\(771\) | −40.6881 | −1.46535 | ||||||||
\(772\) | −22.1129 | −0.795859 | ||||||||
\(773\) | 37.4894 | 1.34840 | 0.674200 | − | 0.738549i | \(-0.264489\pi\) | ||||
0.674200 | + | 0.738549i | \(0.264489\pi\) | |||||||
\(774\) | 3.89704 | 0.140076 | ||||||||
\(775\) | 7.84006 | 0.281623 | ||||||||
\(776\) | −0.168734 | −0.00605722 | ||||||||
\(777\) | −43.2889 | −1.55298 | ||||||||
\(778\) | 25.2337 | 0.904671 | ||||||||
\(779\) | 16.2554 | 0.582411 | ||||||||
\(780\) | 19.6306 | 0.702890 | ||||||||
\(781\) | 65.5427 | 2.34530 | ||||||||
\(782\) | −2.92081 | −0.104448 | ||||||||
\(783\) | −46.1002 | −1.64749 | ||||||||
\(784\) | 1.46720 | 0.0523998 | ||||||||
\(785\) | 4.17062 | 0.148856 | ||||||||
\(786\) | 2.98476 | 0.106463 | ||||||||
\(787\) | 11.2174 | 0.399857 | 0.199929 | − | 0.979810i | \(-0.435929\pi\) | ||||
0.199929 | + | 0.979810i | \(0.435929\pi\) | |||||||
\(788\) | 4.11730 | 0.146673 | ||||||||
\(789\) | −74.6306 | −2.65692 | ||||||||
\(790\) | 1.73551 | 0.0617466 | ||||||||
\(791\) | 34.9367 | 1.24220 | ||||||||
\(792\) | 29.2959 | 1.04099 | ||||||||
\(793\) | 34.3874 | 1.22113 | ||||||||
\(794\) | 2.61143 | 0.0926760 | ||||||||
\(795\) | −7.26045 | −0.257502 | ||||||||
\(796\) | −8.82532 | −0.312805 | ||||||||
\(797\) | −15.1338 | −0.536068 | −0.268034 | − | 0.963409i | \(-0.586374\pi\) | ||||
−0.268034 | + | 0.963409i | \(0.586374\pi\) | |||||||
\(798\) | 23.3479 | 0.826506 | ||||||||
\(799\) | −18.8817 | −0.667986 | ||||||||
\(800\) | 2.50375 | 0.0885208 | ||||||||
\(801\) | 57.7219 | 2.03950 | ||||||||
\(802\) | −6.70995 | −0.236936 | ||||||||
\(803\) | −6.77976 | −0.239252 | ||||||||
\(804\) | 14.3603 | 0.506448 | ||||||||
\(805\) | 4.59742 | 0.162038 | ||||||||
\(806\) | −13.0350 | −0.459137 | ||||||||
\(807\) | −70.2427 | −2.47266 | ||||||||
\(808\) | 7.93894 | 0.279291 | ||||||||
\(809\) | −10.9435 | −0.384752 | −0.192376 | − | 0.981321i | \(-0.561619\pi\) | ||||
−0.192376 | + | 0.981321i | \(0.561619\pi\) | |||||||
\(810\) | −12.9358 | −0.454518 | ||||||||
\(811\) | 0.376068 | 0.0132055 | 0.00660276 | − | 0.999978i | \(-0.497898\pi\) | ||||
0.00660276 | + | 0.999978i | \(0.497898\pi\) | |||||||
\(812\) | 15.4508 | 0.542215 | ||||||||
\(813\) | 9.30732 | 0.326422 | ||||||||
\(814\) | 24.7119 | 0.866151 | ||||||||
\(815\) | −19.1388 | −0.670402 | ||||||||
\(816\) | −8.71791 | −0.305188 | ||||||||
\(817\) | −1.77298 | −0.0620288 | ||||||||
\(818\) | 14.4763 | 0.506151 | ||||||||
\(819\) | −71.5730 | −2.50096 | ||||||||
\(820\) | 9.55376 | 0.333632 | ||||||||
\(821\) | 28.4953 | 0.994493 | 0.497246 | − | 0.867609i | \(-0.334345\pi\) | ||||
0.497246 | + | 0.867609i | \(0.334345\pi\) | |||||||
\(822\) | −28.3020 | −0.987146 | ||||||||
\(823\) | −2.03754 | −0.0710241 | −0.0355121 | − | 0.999369i | \(-0.511306\pi\) | ||||
−0.0355121 | + | 0.999369i | \(0.511306\pi\) | |||||||
\(824\) | −11.7967 | −0.410956 | ||||||||
\(825\) | −37.0517 | −1.28997 | ||||||||
\(826\) | 9.77943 | 0.340270 | ||||||||
\(827\) | −25.1963 | −0.876161 | −0.438080 | − | 0.898936i | \(-0.644342\pi\) | ||||
−0.438080 | + | 0.898936i | \(0.644342\pi\) | |||||||
\(828\) | 5.90879 | 0.205345 | ||||||||
\(829\) | −12.0311 | −0.417858 | −0.208929 | − | 0.977931i | \(-0.566998\pi\) | ||||
−0.208929 | + | 0.977931i | \(0.566998\pi\) | |||||||
\(830\) | 8.40424 | 0.291716 | ||||||||
\(831\) | 77.3750 | 2.68411 | ||||||||
\(832\) | −4.16275 | −0.144317 | ||||||||
\(833\) | 4.28540 | 0.148480 | ||||||||
\(834\) | 51.1396 | 1.77082 | ||||||||
\(835\) | 11.4175 | 0.395119 | ||||||||
\(836\) | −13.3284 | −0.460971 | ||||||||
\(837\) | 27.1864 | 0.939699 | ||||||||
\(838\) | 25.0401 | 0.864998 | ||||||||
\(839\) | 6.72287 | 0.232099 | 0.116050 | − | 0.993243i | \(-0.462977\pi\) | ||||
0.116050 | + | 0.993243i | \(0.462977\pi\) | |||||||
\(840\) | 13.7222 | 0.473461 | ||||||||
\(841\) | −0.805792 | −0.0277859 | ||||||||
\(842\) | 33.5078 | 1.15476 | ||||||||
\(843\) | −69.6811 | −2.39995 | ||||||||
\(844\) | −2.67508 | −0.0920802 | ||||||||
\(845\) | 6.83884 | 0.235263 | ||||||||
\(846\) | 38.1976 | 1.31326 | ||||||||
\(847\) | 39.5215 | 1.35797 | ||||||||
\(848\) | 1.53961 | 0.0528703 | ||||||||
\(849\) | 26.5622 | 0.911613 | ||||||||
\(850\) | 7.31296 | 0.250832 | ||||||||
\(851\) | 4.98422 | 0.170857 | ||||||||
\(852\) | 39.4571 | 1.35178 | ||||||||
\(853\) | 23.7875 | 0.814467 | 0.407234 | − | 0.913324i | \(-0.366493\pi\) | ||||
0.407234 | + | 0.913324i | \(0.366493\pi\) | |||||||
\(854\) | 24.0374 | 0.822544 | ||||||||
\(855\) | 25.0964 | 0.858279 | ||||||||
\(856\) | −5.22241 | −0.178498 | ||||||||
\(857\) | 39.1973 | 1.33895 | 0.669477 | − | 0.742833i | \(-0.266518\pi\) | ||||
0.669477 | + | 0.742833i | \(0.266518\pi\) | |||||||
\(858\) | 61.6025 | 2.10308 | ||||||||
\(859\) | −42.1297 | −1.43745 | −0.718723 | − | 0.695296i | \(-0.755273\pi\) | ||||
−0.718723 | + | 0.695296i | \(0.755273\pi\) | |||||||
\(860\) | −1.04203 | −0.0355329 | ||||||||
\(861\) | −52.5181 | −1.78981 | ||||||||
\(862\) | 12.3898 | 0.421999 | ||||||||
\(863\) | 41.9476 | 1.42791 | 0.713957 | − | 0.700189i | \(-0.246901\pi\) | ||||
0.713957 | + | 0.700189i | \(0.246901\pi\) | |||||||
\(864\) | 8.68205 | 0.295369 | ||||||||
\(865\) | 16.7710 | 0.570232 | ||||||||
\(866\) | −20.4285 | −0.694190 | ||||||||
\(867\) | 25.2776 | 0.858472 | ||||||||
\(868\) | −9.11169 | −0.309271 | ||||||||
\(869\) | 5.44616 | 0.184748 | ||||||||
\(870\) | 25.0400 | 0.848935 | ||||||||
\(871\) | 20.0278 | 0.678617 | ||||||||
\(872\) | 7.46020 | 0.252634 | ||||||||
\(873\) | 0.997017 | 0.0337439 | ||||||||
\(874\) | −2.68824 | −0.0909311 | ||||||||
\(875\) | −34.4979 | −1.16624 | ||||||||
\(876\) | −4.08146 | −0.137900 | ||||||||
\(877\) | −3.78112 | −0.127679 | −0.0638397 | − | 0.997960i | \(-0.520335\pi\) | ||||
−0.0638397 | + | 0.997960i | \(0.520335\pi\) | |||||||
\(878\) | −9.67055 | −0.326365 | ||||||||
\(879\) | 50.5907 | 1.70638 | ||||||||
\(880\) | −7.83345 | −0.264065 | ||||||||
\(881\) | −9.42863 | −0.317659 | −0.158829 | − | 0.987306i | \(-0.550772\pi\) | ||||
−0.158829 | + | 0.987306i | \(0.550772\pi\) | |||||||
\(882\) | −8.66936 | −0.291912 | ||||||||
\(883\) | −40.0826 | −1.34889 | −0.674443 | − | 0.738327i | \(-0.735616\pi\) | ||||
−0.674443 | + | 0.738327i | \(0.735616\pi\) | |||||||
\(884\) | −12.1586 | −0.408938 | ||||||||
\(885\) | 15.8488 | 0.532753 | ||||||||
\(886\) | −26.6064 | −0.893859 | ||||||||
\(887\) | 15.3085 | 0.514008 | 0.257004 | − | 0.966410i | \(-0.417265\pi\) | ||||
0.257004 | + | 0.966410i | \(0.417265\pi\) | |||||||
\(888\) | 14.8767 | 0.499230 | ||||||||
\(889\) | 30.4945 | 1.02275 | ||||||||
\(890\) | −15.4343 | −0.517358 | ||||||||
\(891\) | −40.5936 | −1.35994 | ||||||||
\(892\) | −18.3835 | −0.615527 | ||||||||
\(893\) | −17.3782 | −0.581541 | ||||||||
\(894\) | 47.9387 | 1.60331 | ||||||||
\(895\) | −15.2694 | −0.510401 | ||||||||
\(896\) | −2.90984 | −0.0972111 | ||||||||
\(897\) | 12.4248 | 0.414853 | ||||||||
\(898\) | 10.3336 | 0.344838 | ||||||||
\(899\) | −16.6268 | −0.554535 | ||||||||
\(900\) | −14.7941 | −0.493137 | ||||||||
\(901\) | 4.49689 | 0.149813 | ||||||||
\(902\) | 29.9805 | 0.998240 | ||||||||
\(903\) | 5.72816 | 0.190621 | ||||||||
\(904\) | −12.0064 | −0.399326 | ||||||||
\(905\) | −24.4043 | −0.811225 | ||||||||
\(906\) | −16.7856 | −0.557663 | ||||||||
\(907\) | −27.7325 | −0.920844 | −0.460422 | − | 0.887700i | \(-0.652302\pi\) | ||||
−0.460422 | + | 0.887700i | \(0.652302\pi\) | |||||||
\(908\) | −23.7503 | −0.788182 | ||||||||
\(909\) | −46.9096 | −1.55589 | ||||||||
\(910\) | 19.1379 | 0.634416 | ||||||||
\(911\) | −28.5947 | −0.947383 | −0.473692 | − | 0.880691i | \(-0.657079\pi\) | ||||
−0.473692 | + | 0.880691i | \(0.657079\pi\) | |||||||
\(912\) | −8.02376 | −0.265693 | ||||||||
\(913\) | 26.3732 | 0.872825 | ||||||||
\(914\) | −1.45972 | −0.0482832 | ||||||||
\(915\) | 38.9558 | 1.28784 | ||||||||
\(916\) | −1.46778 | −0.0484968 | ||||||||
\(917\) | 2.90984 | 0.0960915 | ||||||||
\(918\) | 25.3586 | 0.836959 | ||||||||
\(919\) | −4.07715 | −0.134493 | −0.0672464 | − | 0.997736i | \(-0.521421\pi\) | ||||
−0.0672464 | + | 0.997736i | \(0.521421\pi\) | |||||||
\(920\) | −1.57995 | −0.0520895 | ||||||||
\(921\) | 4.11984 | 0.135754 | ||||||||
\(922\) | 5.60953 | 0.184740 | ||||||||
\(923\) | 55.0296 | 1.81132 | ||||||||
\(924\) | 43.0614 | 1.41661 | ||||||||
\(925\) | −12.4792 | −0.410314 | ||||||||
\(926\) | −0.661601 | −0.0217415 | ||||||||
\(927\) | 69.7041 | 2.28938 | ||||||||
\(928\) | −5.30982 | −0.174303 | ||||||||
\(929\) | −36.9161 | −1.21118 | −0.605589 | − | 0.795778i | \(-0.707062\pi\) | ||||
−0.605589 | + | 0.795778i | \(0.707062\pi\) | |||||||
\(930\) | −14.7667 | −0.484219 | ||||||||
\(931\) | 3.94418 | 0.129265 | ||||||||
\(932\) | 0.0638321 | 0.00209089 | ||||||||
\(933\) | −1.44038 | −0.0471559 | ||||||||
\(934\) | 20.9449 | 0.685338 | ||||||||
\(935\) | −22.8800 | −0.748256 | ||||||||
\(936\) | 24.5968 | 0.803973 | ||||||||
\(937\) | −19.7459 | −0.645072 | −0.322536 | − | 0.946557i | \(-0.604535\pi\) | ||||
−0.322536 | + | 0.946557i | \(0.604535\pi\) | |||||||
\(938\) | 13.9998 | 0.457111 | ||||||||
\(939\) | −24.1068 | −0.786697 | ||||||||
\(940\) | −10.2137 | −0.333133 | ||||||||
\(941\) | −18.8650 | −0.614981 | −0.307491 | − | 0.951551i | \(-0.599489\pi\) | ||||
−0.307491 | + | 0.951551i | \(0.599489\pi\) | |||||||
\(942\) | 7.87890 | 0.256708 | ||||||||
\(943\) | 6.04686 | 0.196913 | ||||||||
\(944\) | −3.36081 | −0.109385 | ||||||||
\(945\) | −39.9151 | −1.29844 | ||||||||
\(946\) | −3.26998 | −0.106316 | ||||||||
\(947\) | −20.2305 | −0.657404 | −0.328702 | − | 0.944434i | \(-0.606611\pi\) | ||||
−0.328702 | + | 0.944434i | \(0.606611\pi\) | |||||||
\(948\) | 3.27862 | 0.106485 | ||||||||
\(949\) | −5.69228 | −0.184779 | ||||||||
\(950\) | 6.73067 | 0.218372 | ||||||||
\(951\) | −14.3969 | −0.466852 | ||||||||
\(952\) | −8.49910 | −0.275457 | ||||||||
\(953\) | −48.5232 | −1.57182 | −0.785910 | − | 0.618341i | \(-0.787805\pi\) | ||||
−0.785910 | + | 0.618341i | \(0.787805\pi\) | |||||||
\(954\) | −9.09722 | −0.294533 | ||||||||
\(955\) | 1.44989 | 0.0469174 | ||||||||
\(956\) | 6.88773 | 0.222765 | ||||||||
\(957\) | 78.5774 | 2.54005 | ||||||||
\(958\) | 25.4412 | 0.821968 | ||||||||
\(959\) | −27.5916 | −0.890981 | ||||||||
\(960\) | −4.71578 | −0.152201 | ||||||||
\(961\) | −21.1948 | −0.683702 | ||||||||
\(962\) | 20.7481 | 0.668945 | ||||||||
\(963\) | 30.8581 | 0.994389 | ||||||||
\(964\) | −6.04018 | −0.194541 | ||||||||
\(965\) | −34.9373 | −1.12467 | ||||||||
\(966\) | 8.68519 | 0.279441 | ||||||||
\(967\) | −35.1041 | −1.12887 | −0.564436 | − | 0.825477i | \(-0.690906\pi\) | ||||
−0.564436 | + | 0.825477i | \(0.690906\pi\) | |||||||
\(968\) | −13.5820 | −0.436542 | ||||||||
\(969\) | −23.4359 | −0.752868 | ||||||||
\(970\) | −0.266593 | −0.00855978 | ||||||||
\(971\) | −39.0796 | −1.25412 | −0.627062 | − | 0.778969i | \(-0.715743\pi\) | ||||
−0.627062 | + | 0.778969i | \(0.715743\pi\) | |||||||
\(972\) | 1.60854 | 0.0515940 | ||||||||
\(973\) | 49.8560 | 1.59831 | ||||||||
\(974\) | 33.4736 | 1.07256 | ||||||||
\(975\) | −31.1086 | −0.996272 | ||||||||
\(976\) | −8.26073 | −0.264420 | ||||||||
\(977\) | 18.3768 | 0.587925 | 0.293962 | − | 0.955817i | \(-0.405026\pi\) | ||||
0.293962 | + | 0.955817i | \(0.405026\pi\) | |||||||
\(978\) | −36.1559 | −1.15614 | ||||||||
\(979\) | −48.4340 | −1.54796 | ||||||||
\(980\) | 2.31810 | 0.0740490 | ||||||||
\(981\) | −44.0808 | −1.40739 | ||||||||
\(982\) | 9.23297 | 0.294636 | ||||||||
\(983\) | 36.2338 | 1.15568 | 0.577840 | − | 0.816150i | \(-0.303896\pi\) | ||||
0.577840 | + | 0.816150i | \(0.303896\pi\) | |||||||
\(984\) | 18.0484 | 0.575363 | ||||||||
\(985\) | 6.50514 | 0.207271 | ||||||||
\(986\) | −15.5090 | −0.493906 | ||||||||
\(987\) | 56.1458 | 1.78714 | ||||||||
\(988\) | −11.1905 | −0.356017 | ||||||||
\(989\) | −0.659532 | −0.0209719 | ||||||||
\(990\) | 46.2862 | 1.47107 | ||||||||
\(991\) | −11.2022 | −0.355848 | −0.177924 | − | 0.984044i | \(-0.556938\pi\) | ||||
−0.177924 | + | 0.984044i | \(0.556938\pi\) | |||||||
\(992\) | 3.13133 | 0.0994199 | ||||||||
\(993\) | −9.18503 | −0.291478 | ||||||||
\(994\) | 38.4668 | 1.22009 | ||||||||
\(995\) | −13.9436 | −0.442042 | ||||||||
\(996\) | 15.8768 | 0.503076 | ||||||||
\(997\) | −15.2277 | −0.482265 | −0.241133 | − | 0.970492i | \(-0.577519\pi\) | ||||
−0.241133 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(998\) | 31.5925 | 1.00004 | ||||||||
\(999\) | −43.2733 | −1.36911 |
(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 | 6026.2.a.i.1.1 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.i.1.1 | ✓ | 25 | 1.1 | even | 1 | trivial |