Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.324000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 26x^{4} + 24x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.1 | ||
Root | \(0.209057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.d.1249.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.95630i | − 1.38331i | −0.722228 | − | 0.691655i | \(-0.756882\pi\) | ||||
0.722228 | − | 0.691655i | \(-0.243118\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.82709 | −0.913545 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.95630 | 0.798654 | ||||||||
\(7\) | 4.57433i | 1.72893i | 0.502690 | + | 0.864467i | \(0.332344\pi\) | ||||
−0.502690 | + | 0.864467i | \(0.667656\pi\) | |||||||
\(8\) | − 0.338261i | − 0.119593i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.16535 | −1.25590 | −0.627950 | − | 0.778253i | \(-0.716106\pi\) | ||||
−0.627950 | + | 0.778253i | \(0.716106\pi\) | |||||||
\(12\) | − 1.82709i | − 0.527436i | ||||||||
\(13\) | − 3.75638i | − 1.04183i | −0.853608 | − | 0.520915i | \(-0.825591\pi\) | ||||
0.853608 | − | 0.520915i | \(-0.174409\pi\) | |||||||
\(14\) | 8.94874 | 2.39165 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.31592 | −1.07898 | ||||||||
\(17\) | − 3.26755i | − 0.792496i | −0.918143 | − | 0.396248i | \(-0.870312\pi\) | ||||
0.918143 | − | 0.396248i | \(-0.129688\pi\) | |||||||
\(18\) | 1.95630i | 0.461103i | ||||||||
\(19\) | 0.243625 | 0.0558914 | 0.0279457 | − | 0.999609i | \(-0.491103\pi\) | ||||
0.0279457 | + | 0.999609i | \(0.491103\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.57433 | −0.998200 | ||||||||
\(22\) | 8.14866i | 1.73730i | ||||||||
\(23\) | 0.654182i | 0.136406i | 0.997671 | + | 0.0682032i | \(0.0217266\pi\) | ||||
−0.997671 | + | 0.0682032i | \(0.978273\pi\) | |||||||
\(24\) | 0.338261 | 0.0690473 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.34858 | −1.44117 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 8.35772i | − 1.57946i | ||||||||
\(29\) | 8.54732 | 1.58720 | 0.793599 | − | 0.608442i | \(-0.208205\pi\) | ||||
0.793599 | + | 0.608442i | \(0.208205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.90694 | −0.701708 | −0.350854 | − | 0.936430i | \(-0.614109\pi\) | ||||
−0.350854 | + | 0.936430i | \(0.614109\pi\) | |||||||
\(32\) | 7.76669i | 1.37297i | ||||||||
\(33\) | − 4.16535i | − 0.725095i | ||||||||
\(34\) | −6.39228 | −1.09627 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.82709 | 0.304515 | ||||||||
\(37\) | − 10.6151i | − 1.74512i | −0.488507 | − | 0.872560i | \(-0.662458\pi\) | ||||
0.488507 | − | 0.872560i | \(-0.337542\pi\) | |||||||
\(38\) | − 0.476602i | − 0.0773151i | ||||||||
\(39\) | 3.75638 | 0.601501 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.769579 | 0.120188 | 0.0600940 | − | 0.998193i | \(-0.480860\pi\) | ||||
0.0600940 | + | 0.998193i | \(0.480860\pi\) | |||||||
\(42\) | 8.94874i | 1.38082i | ||||||||
\(43\) | 3.90345i | 0.595271i | 0.954680 | + | 0.297636i | \(0.0961980\pi\) | ||||
−0.954680 | + | 0.297636i | \(0.903802\pi\) | |||||||
\(44\) | 7.61048 | 1.14732 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.27977 | 0.188692 | ||||||||
\(47\) | − 7.67555i | − 1.11959i | −0.828630 | − | 0.559797i | \(-0.810879\pi\) | ||||
0.828630 | − | 0.559797i | \(-0.189121\pi\) | |||||||
\(48\) | − 4.31592i | − 0.622949i | ||||||||
\(49\) | −13.9245 | −1.98921 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.26755 | 0.457548 | ||||||||
\(52\) | 6.86324i | 0.951760i | ||||||||
\(53\) | − 12.1197i | − 1.66477i | −0.554195 | − | 0.832387i | \(-0.686974\pi\) | ||||
0.554195 | − | 0.832387i | \(-0.313026\pi\) | |||||||
\(54\) | −1.95630 | −0.266218 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.54732 | 0.206769 | ||||||||
\(57\) | 0.243625i | 0.0322689i | ||||||||
\(58\) | − 16.7211i | − 2.19559i | ||||||||
\(59\) | −4.90248 | −0.638248 | −0.319124 | − | 0.947713i | \(-0.603389\pi\) | ||||
−0.319124 | + | 0.947713i | \(0.603389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.7035 | −1.88259 | −0.941297 | − | 0.337579i | \(-0.890392\pi\) | ||||
−0.941297 | + | 0.337579i | \(0.890392\pi\) | |||||||
\(62\) | 7.64313i | 0.970679i | ||||||||
\(63\) | − 4.57433i | − 0.576311i | ||||||||
\(64\) | 6.56210 | 0.820263 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.14866 | −1.00303 | ||||||||
\(67\) | − 0.316897i | − 0.0387151i | −0.999813 | − | 0.0193576i | \(-0.993838\pi\) | ||||
0.999813 | − | 0.0193576i | \(-0.00616209\pi\) | |||||||
\(68\) | 5.97010i | 0.723981i | ||||||||
\(69\) | −0.654182 | −0.0787542 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.446705 | 0.0530141 | 0.0265070 | − | 0.999649i | \(-0.491562\pi\) | ||||
0.0265070 | + | 0.999649i | \(0.491562\pi\) | |||||||
\(72\) | 0.338261i | 0.0398645i | ||||||||
\(73\) | − 11.1172i | − 1.30117i | −0.759434 | − | 0.650584i | \(-0.774524\pi\) | ||||
0.759434 | − | 0.650584i | \(-0.225476\pi\) | |||||||
\(74\) | −20.7664 | −2.41404 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.445125 | −0.0510593 | ||||||||
\(77\) | − 19.0537i | − 2.17137i | ||||||||
\(78\) | − 7.34858i | − 0.832063i | ||||||||
\(79\) | −9.80731 | −1.10341 | −0.551704 | − | 0.834040i | \(-0.686022\pi\) | ||||
−0.551704 | + | 0.834040i | \(0.686022\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 1.50552i | − 0.166257i | ||||||||
\(83\) | − 8.86482i | − 0.973040i | −0.873669 | − | 0.486520i | \(-0.838266\pi\) | ||||
0.873669 | − | 0.486520i | \(-0.161734\pi\) | |||||||
\(84\) | 8.35772 | 0.911902 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.63631 | 0.823444 | ||||||||
\(87\) | 8.54732i | 0.916369i | ||||||||
\(88\) | 1.40898i | 0.150197i | ||||||||
\(89\) | 7.81040 | 0.827900 | 0.413950 | − | 0.910300i | \(-0.364149\pi\) | ||||
0.413950 | + | 0.910300i | \(0.364149\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.1829 | 1.80126 | ||||||||
\(92\) | − 1.19525i | − 0.124613i | ||||||||
\(93\) | − 3.90694i | − 0.405131i | ||||||||
\(94\) | −15.0156 | −1.54874 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −7.76669 | −0.792685 | ||||||||
\(97\) | − 8.15938i | − 0.828459i | −0.910172 | − | 0.414230i | \(-0.864051\pi\) | ||||
0.910172 | − | 0.414230i | \(-0.135949\pi\) | |||||||
\(98\) | 27.2404i | 2.75170i | ||||||||
\(99\) | 4.16535 | 0.418634 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.54383 | −0.949646 | −0.474823 | − | 0.880081i | \(-0.657488\pi\) | ||||
−0.474823 | + | 0.880081i | \(0.657488\pi\) | |||||||
\(102\) | − 6.39228i | − 0.632930i | ||||||||
\(103\) | 9.86698i | 0.972222i | 0.873897 | + | 0.486111i | \(0.161585\pi\) | ||||
−0.873897 | + | 0.486111i | \(0.838415\pi\) | |||||||
\(104\) | −1.27064 | −0.124596 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.7098 | −2.30290 | ||||||||
\(107\) | − 16.1273i | − 1.55908i | −0.626350 | − | 0.779542i | \(-0.715452\pi\) | ||||
0.626350 | − | 0.779542i | \(-0.284548\pi\) | |||||||
\(108\) | 1.82709i | 0.175812i | ||||||||
\(109\) | 2.44236 | 0.233936 | 0.116968 | − | 0.993136i | \(-0.462682\pi\) | ||||
0.116968 | + | 0.993136i | \(0.462682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.6151 | 1.00755 | ||||||||
\(112\) | − 19.7424i | − 1.86549i | ||||||||
\(113\) | 10.9293i | 1.02814i | 0.857748 | + | 0.514070i | \(0.171863\pi\) | ||||
−0.857748 | + | 0.514070i | \(0.828137\pi\) | |||||||
\(114\) | 0.476602 | 0.0446379 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −15.6167 | −1.44998 | ||||||||
\(117\) | 3.75638i | 0.347277i | ||||||||
\(118\) | 9.59069i | 0.882895i | ||||||||
\(119\) | 14.9468 | 1.37017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.35016 | 0.577287 | ||||||||
\(122\) | 28.7645i | 2.60421i | ||||||||
\(123\) | 0.769579i | 0.0693906i | ||||||||
\(124\) | 7.13834 | 0.641042 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.94874 | −0.797217 | ||||||||
\(127\) | 12.8613i | 1.14126i | 0.821208 | + | 0.570629i | \(0.193301\pi\) | ||||
−0.821208 | + | 0.570629i | \(0.806699\pi\) | |||||||
\(128\) | 2.69598i | 0.238293i | ||||||||
\(129\) | −3.90345 | −0.343680 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.37441 | 0.207453 | 0.103727 | − | 0.994606i | \(-0.466923\pi\) | ||||
0.103727 | + | 0.994606i | \(0.466923\pi\) | |||||||
\(132\) | 7.61048i | 0.662407i | ||||||||
\(133\) | 1.11442i | 0.0966325i | ||||||||
\(134\) | −0.619944 | −0.0535550 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.10528 | −0.0947773 | ||||||||
\(137\) | 12.5026i | 1.06817i | 0.845430 | + | 0.534086i | \(0.179344\pi\) | ||||
−0.845430 | + | 0.534086i | \(0.820656\pi\) | |||||||
\(138\) | 1.27977i | 0.108941i | ||||||||
\(139\) | 0.356135 | 0.0302070 | 0.0151035 | − | 0.999886i | \(-0.495192\pi\) | ||||
0.0151035 | + | 0.999886i | \(0.495192\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.67555 | 0.646398 | ||||||||
\(142\) | − 0.873886i | − 0.0733349i | ||||||||
\(143\) | 15.6466i | 1.30844i | ||||||||
\(144\) | 4.31592 | 0.359660 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −21.7485 | −1.79992 | ||||||||
\(147\) | − 13.9245i | − 1.14847i | ||||||||
\(148\) | 19.3948i | 1.59425i | ||||||||
\(149\) | 15.0317 | 1.23144 | 0.615722 | − | 0.787964i | \(-0.288865\pi\) | ||||
0.615722 | + | 0.787964i | \(0.288865\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.65576 | −0.460259 | −0.230130 | − | 0.973160i | \(-0.573915\pi\) | ||||
−0.230130 | + | 0.973160i | \(0.573915\pi\) | |||||||
\(152\) | − 0.0824089i | − 0.00668424i | ||||||||
\(153\) | 3.26755i | 0.264165i | ||||||||
\(154\) | −37.2746 | −3.00368 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.86324 | −0.549499 | ||||||||
\(157\) | 6.69480i | 0.534303i | 0.963655 | + | 0.267151i | \(0.0860824\pi\) | ||||
−0.963655 | + | 0.267151i | \(0.913918\pi\) | |||||||
\(158\) | 19.1860i | 1.52636i | ||||||||
\(159\) | 12.1197 | 0.961158 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.99244 | −0.235838 | ||||||||
\(162\) | − 1.95630i | − 0.153701i | ||||||||
\(163\) | 13.8314i | 1.08336i | 0.840584 | + | 0.541681i | \(0.182212\pi\) | ||||
−0.840584 | + | 0.541681i | \(0.817788\pi\) | |||||||
\(164\) | −1.40609 | −0.109797 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.3422 | −1.34602 | ||||||||
\(167\) | − 13.5017i | − 1.04479i | −0.852703 | − | 0.522397i | \(-0.825038\pi\) | ||||
0.852703 | − | 0.522397i | \(-0.174962\pi\) | |||||||
\(168\) | 1.54732i | 0.119378i | ||||||||
\(169\) | −1.11035 | −0.0854118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.243625 | −0.0186305 | ||||||||
\(172\) | − 7.13196i | − 0.543807i | ||||||||
\(173\) | − 13.7259i | − 1.04356i | −0.853080 | − | 0.521779i | \(-0.825268\pi\) | ||||
0.853080 | − | 0.521779i | \(-0.174732\pi\) | |||||||
\(174\) | 16.7211 | 1.26762 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.9773 | 1.35509 | ||||||||
\(177\) | − 4.90248i | − 0.368493i | ||||||||
\(178\) | − 15.2794i | − 1.14524i | ||||||||
\(179\) | −4.46491 | −0.333723 | −0.166861 | − | 0.985980i | \(-0.553363\pi\) | ||||
−0.166861 | + | 0.985980i | \(0.553363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0032 | −1.04085 | −0.520423 | − | 0.853908i | \(-0.674226\pi\) | ||||
−0.520423 | + | 0.853908i | \(0.674226\pi\) | |||||||
\(182\) | − 33.6148i | − 2.49170i | ||||||||
\(183\) | − 14.7035i | − 1.08692i | ||||||||
\(184\) | 0.221284 | 0.0163133 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.64313 | −0.560422 | ||||||||
\(187\) | 13.6105i | 0.995297i | ||||||||
\(188\) | 14.0239i | 1.02280i | ||||||||
\(189\) | 4.57433 | 0.332733 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.29614 | −0.310858 | −0.155429 | − | 0.987847i | \(-0.549676\pi\) | ||||
−0.155429 | + | 0.987847i | \(0.549676\pi\) | |||||||
\(192\) | 6.56210i | 0.473579i | ||||||||
\(193\) | − 13.0436i | − 0.938897i | −0.882960 | − | 0.469449i | \(-0.844453\pi\) | ||||
0.882960 | − | 0.469449i | \(-0.155547\pi\) | |||||||
\(194\) | −15.9621 | −1.14602 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 25.4413 | 1.81724 | ||||||||
\(197\) | − 9.17856i | − 0.653945i | −0.945034 | − | 0.326973i | \(-0.893972\pi\) | ||||
0.945034 | − | 0.326973i | \(-0.106028\pi\) | |||||||
\(198\) | − 8.14866i | − 0.579100i | ||||||||
\(199\) | −0.677499 | −0.0480266 | −0.0240133 | − | 0.999712i | \(-0.507644\pi\) | ||||
−0.0240133 | + | 0.999712i | \(0.507644\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.316897 | 0.0223522 | ||||||||
\(202\) | 18.6705i | 1.31365i | ||||||||
\(203\) | 39.0982i | 2.74416i | ||||||||
\(204\) | −5.97010 | −0.417991 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 19.3027 | 1.34488 | ||||||||
\(207\) | − 0.654182i | − 0.0454688i | ||||||||
\(208\) | 16.2122i | 1.12411i | ||||||||
\(209\) | −1.01478 | −0.0701941 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.1662 | −1.11293 | −0.556464 | − | 0.830872i | \(-0.687842\pi\) | ||||
−0.556464 | + | 0.830872i | \(0.687842\pi\) | |||||||
\(212\) | 22.1439i | 1.52085i | ||||||||
\(213\) | 0.446705i | 0.0306077i | ||||||||
\(214\) | −31.5497 | −2.15670 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.338261 | −0.0230158 | ||||||||
\(217\) | − 17.8716i | − 1.21321i | ||||||||
\(218\) | − 4.77799i | − 0.323606i | ||||||||
\(219\) | 11.1172 | 0.751229 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.2741 | −0.825647 | ||||||||
\(222\) | − 20.7664i | − 1.39375i | ||||||||
\(223\) | 9.96064i | 0.667013i | 0.942748 | + | 0.333507i | \(0.108232\pi\) | ||||
−0.942748 | + | 0.333507i | \(0.891768\pi\) | |||||||
\(224\) | −35.5274 | −2.37377 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.3809 | 1.42224 | ||||||||
\(227\) | 24.0646i | 1.59722i | 0.601846 | + | 0.798612i | \(0.294432\pi\) | ||||
−0.601846 | + | 0.798612i | \(0.705568\pi\) | |||||||
\(228\) | − 0.445125i | − 0.0294791i | ||||||||
\(229\) | 15.3847 | 1.01665 | 0.508326 | − | 0.861165i | \(-0.330265\pi\) | ||||
0.508326 | + | 0.861165i | \(0.330265\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.0537 | 1.25364 | ||||||||
\(232\) | − 2.89123i | − 0.189818i | ||||||||
\(233\) | − 6.58907i | − 0.431664i | −0.976430 | − | 0.215832i | \(-0.930754\pi\) | ||||
0.976430 | − | 0.215832i | \(-0.0692464\pi\) | |||||||
\(234\) | 7.34858 | 0.480392 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.95727 | 0.583069 | ||||||||
\(237\) | − 9.80731i | − 0.637053i | ||||||||
\(238\) | − 29.2404i | − 1.89537i | ||||||||
\(239\) | −17.8874 | −1.15704 | −0.578520 | − | 0.815668i | \(-0.696370\pi\) | ||||
−0.578520 | + | 0.815668i | \(0.696370\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.22404 | 0.400926 | 0.200463 | − | 0.979701i | \(-0.435755\pi\) | ||||
0.200463 | + | 0.979701i | \(0.435755\pi\) | |||||||
\(242\) | − 12.4228i | − 0.798567i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 26.8647 | 1.71984 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.50552 | 0.0959887 | ||||||||
\(247\) | − 0.915147i | − 0.0582294i | ||||||||
\(248\) | 1.32157i | 0.0839196i | ||||||||
\(249\) | 8.86482 | 0.561785 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.11580 | −0.449145 | −0.224573 | − | 0.974457i | \(-0.572099\pi\) | ||||
−0.224573 | + | 0.974457i | \(0.572099\pi\) | |||||||
\(252\) | 8.35772i | 0.526487i | ||||||||
\(253\) | − 2.72490i | − 0.171313i | ||||||||
\(254\) | 25.1606 | 1.57871 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 18.3983 | 1.14990 | ||||||||
\(257\) | 7.15589i | 0.446372i | 0.974776 | + | 0.223186i | \(0.0716457\pi\) | ||||
−0.974776 | + | 0.223186i | \(0.928354\pi\) | |||||||
\(258\) | 7.63631i | 0.475416i | ||||||||
\(259\) | 48.5572 | 3.01720 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.54732 | −0.529066 | ||||||||
\(262\) | − 4.64505i | − 0.286972i | ||||||||
\(263\) | 1.30967i | 0.0807577i | 0.999184 | + | 0.0403789i | \(0.0128565\pi\) | ||||
−0.999184 | + | 0.0403789i | \(0.987144\pi\) | |||||||
\(264\) | −1.40898 | −0.0867165 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.18014 | 0.133673 | ||||||||
\(267\) | 7.81040i | 0.477989i | ||||||||
\(268\) | 0.579000i | 0.0353680i | ||||||||
\(269\) | 20.9745 | 1.27884 | 0.639418 | − | 0.768859i | \(-0.279175\pi\) | ||||
0.639418 | + | 0.768859i | \(0.279175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.65260 | 0.586354 | 0.293177 | − | 0.956058i | \(-0.405288\pi\) | ||||
0.293177 | + | 0.956058i | \(0.405288\pi\) | |||||||
\(272\) | 14.1025i | 0.855088i | ||||||||
\(273\) | 17.1829i | 1.03996i | ||||||||
\(274\) | 24.4588 | 1.47761 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.19525 | 0.0719456 | ||||||||
\(277\) | 20.0455i | 1.20442i | 0.798338 | + | 0.602210i | \(0.205713\pi\) | ||||
−0.798338 | + | 0.602210i | \(0.794287\pi\) | |||||||
\(278\) | − 0.696706i | − 0.0417857i | ||||||||
\(279\) | 3.90694 | 0.233903 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.42685 | −0.264084 | −0.132042 | − | 0.991244i | \(-0.542153\pi\) | ||||
−0.132042 | + | 0.991244i | \(0.542153\pi\) | |||||||
\(282\) | − 15.0156i | − 0.894168i | ||||||||
\(283\) | − 11.2028i | − 0.665938i | −0.942938 | − | 0.332969i | \(-0.891950\pi\) | ||||
0.942938 | − | 0.332969i | \(-0.108050\pi\) | |||||||
\(284\) | −0.816170 | −0.0484308 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 30.6094 | 1.80997 | ||||||||
\(287\) | 3.52031i | 0.207797i | ||||||||
\(288\) | − 7.76669i | − 0.457657i | ||||||||
\(289\) | 6.32315 | 0.371950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.15938 | 0.478311 | ||||||||
\(292\) | 20.3121i | 1.18868i | ||||||||
\(293\) | 26.6504i | 1.55693i | 0.627688 | + | 0.778465i | \(0.284002\pi\) | ||||
−0.627688 | + | 0.778465i | \(0.715998\pi\) | |||||||
\(294\) | −27.2404 | −1.58869 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.59069 | −0.208705 | ||||||||
\(297\) | 4.16535i | 0.241698i | ||||||||
\(298\) | − 29.4064i | − 1.70347i | ||||||||
\(299\) | 2.45735 | 0.142112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.8557 | −1.02918 | ||||||||
\(302\) | 11.0643i | 0.636681i | ||||||||
\(303\) | − 9.54383i | − 0.548279i | ||||||||
\(304\) | −1.05147 | −0.0603057 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.39228 | 0.365423 | ||||||||
\(307\) | − 9.48870i | − 0.541549i | −0.962643 | − | 0.270774i | \(-0.912720\pi\) | ||||
0.962643 | − | 0.270774i | \(-0.0872798\pi\) | |||||||
\(308\) | 34.8128i | 1.98364i | ||||||||
\(309\) | −9.86698 | −0.561313 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5152 | 0.652969 | 0.326485 | − | 0.945203i | \(-0.394136\pi\) | ||||
0.326485 | + | 0.945203i | \(0.394136\pi\) | |||||||
\(312\) | − 1.27064i | − 0.0719356i | ||||||||
\(313\) | 2.14459i | 0.121219i | 0.998162 | + | 0.0606097i | \(0.0193045\pi\) | ||||
−0.998162 | + | 0.0606097i | \(0.980695\pi\) | |||||||
\(314\) | 13.0970 | 0.739106 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.9188 | 1.00801 | ||||||||
\(317\) | − 0.735614i | − 0.0413162i | −0.999787 | − | 0.0206581i | \(-0.993424\pi\) | ||||
0.999787 | − | 0.0206581i | \(-0.00657615\pi\) | |||||||
\(318\) | − 23.7098i | − 1.32958i | ||||||||
\(319\) | −35.6026 | −1.99336 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.1273 | 0.900138 | ||||||||
\(322\) | 5.85410i | 0.326236i | ||||||||
\(323\) | − 0.796056i | − 0.0442937i | ||||||||
\(324\) | −1.82709 | −0.101505 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 27.0584 | 1.49862 | ||||||||
\(327\) | 2.44236i | 0.135063i | ||||||||
\(328\) | − 0.260319i | − 0.0143737i | ||||||||
\(329\) | 35.1105 | 1.93570 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.1178 | 0.611089 | 0.305544 | − | 0.952178i | \(-0.401162\pi\) | ||||
0.305544 | + | 0.952178i | \(0.401162\pi\) | |||||||
\(332\) | 16.1968i | 0.888917i | ||||||||
\(333\) | 10.6151i | 0.581706i | ||||||||
\(334\) | −26.4133 | −1.44527 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 19.7424 | 1.07704 | ||||||||
\(337\) | − 14.2506i | − 0.776282i | −0.921600 | − | 0.388141i | \(-0.873117\pi\) | ||||
0.921600 | − | 0.388141i | \(-0.126883\pi\) | |||||||
\(338\) | 2.17218i | 0.118151i | ||||||||
\(339\) | −10.9293 | −0.593597 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.2738 | 0.881275 | ||||||||
\(342\) | 0.476602i | 0.0257717i | ||||||||
\(343\) | − 31.6749i | − 1.71028i | ||||||||
\(344\) | 1.32039 | 0.0711905 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −26.8519 | −1.44357 | ||||||||
\(347\) | − 0.174615i | − 0.00937383i | −0.999989 | − | 0.00468691i | \(-0.998508\pi\) | ||||
0.999989 | − | 0.00468691i | \(-0.00149190\pi\) | |||||||
\(348\) | − 15.6167i | − 0.837144i | ||||||||
\(349\) | 18.6640 | 0.999059 | 0.499530 | − | 0.866297i | \(-0.333506\pi\) | ||||
0.499530 | + | 0.866297i | \(0.333506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.75638 | −0.200500 | ||||||||
\(352\) | − 32.3510i | − 1.72431i | ||||||||
\(353\) | 8.67239i | 0.461585i | 0.973003 | + | 0.230792i | \(0.0741318\pi\) | ||||
−0.973003 | + | 0.230792i | \(0.925868\pi\) | |||||||
\(354\) | −9.59069 | −0.509740 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.2703 | −0.756325 | ||||||||
\(357\) | 14.9468i | 0.791070i | ||||||||
\(358\) | 8.73468i | 0.461642i | ||||||||
\(359\) | −13.7180 | −0.724008 | −0.362004 | − | 0.932177i | \(-0.617907\pi\) | ||||
−0.362004 | + | 0.932177i | \(0.617907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9406 | −0.996876 | ||||||||
\(362\) | 27.3943i | 1.43981i | ||||||||
\(363\) | 6.35016i | 0.333297i | ||||||||
\(364\) | −31.3947 | −1.64553 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −28.7645 | −1.50354 | ||||||||
\(367\) | 0.530351i | 0.0276841i | 0.999904 | + | 0.0138421i | \(0.00440620\pi\) | ||||
−0.999904 | + | 0.0138421i | \(0.995594\pi\) | |||||||
\(368\) | − 2.82340i | − 0.147180i | ||||||||
\(369\) | −0.769579 | −0.0400627 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 55.4397 | 2.87828 | ||||||||
\(372\) | 7.13834i | 0.370106i | ||||||||
\(373\) | − 29.3489i | − 1.51963i | −0.650142 | − | 0.759813i | \(-0.725290\pi\) | ||||
0.650142 | − | 0.759813i | \(-0.274710\pi\) | |||||||
\(374\) | 26.6261 | 1.37680 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.59634 | −0.133896 | ||||||||
\(377\) | − 32.1069i | − 1.65359i | ||||||||
\(378\) | − 8.94874i | − 0.460273i | ||||||||
\(379\) | −4.84634 | −0.248940 | −0.124470 | − | 0.992223i | \(-0.539723\pi\) | ||||
−0.124470 | + | 0.992223i | \(0.539723\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.8613 | −0.658906 | ||||||||
\(382\) | 8.40451i | 0.430012i | ||||||||
\(383\) | 21.3587i | 1.09138i | 0.837988 | + | 0.545689i | \(0.183732\pi\) | ||||
−0.837988 | + | 0.545689i | \(0.816268\pi\) | |||||||
\(384\) | −2.69598 | −0.137578 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.5171 | −1.29879 | ||||||||
\(387\) | − 3.90345i | − 0.198424i | ||||||||
\(388\) | 14.9079i | 0.756835i | ||||||||
\(389\) | −10.4329 | −0.528971 | −0.264486 | − | 0.964390i | \(-0.585202\pi\) | ||||
−0.264486 | + | 0.964390i | \(0.585202\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.13757 | 0.108102 | ||||||||
\(392\) | 4.71011i | 0.237897i | ||||||||
\(393\) | 2.37441i | 0.119773i | ||||||||
\(394\) | −17.9560 | −0.904608 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.61048 | −0.382441 | ||||||||
\(397\) | − 16.3146i | − 0.818806i | −0.912354 | − | 0.409403i | \(-0.865737\pi\) | ||||
0.912354 | − | 0.409403i | \(-0.134263\pi\) | |||||||
\(398\) | 1.32539i | 0.0664357i | ||||||||
\(399\) | −1.11442 | −0.0557908 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3272 | 0.515718 | 0.257859 | − | 0.966183i | \(-0.416983\pi\) | ||||
0.257859 | + | 0.966183i | \(0.416983\pi\) | |||||||
\(402\) | − 0.619944i | − 0.0309200i | ||||||||
\(403\) | 14.6759i | 0.731061i | ||||||||
\(404\) | 17.4374 | 0.867545 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 76.4877 | 3.79602 | ||||||||
\(407\) | 44.2158i | 2.19170i | ||||||||
\(408\) | − 1.10528i | − 0.0547197i | ||||||||
\(409\) | −26.8421 | −1.32726 | −0.663629 | − | 0.748062i | \(-0.730985\pi\) | ||||
−0.663629 | + | 0.748062i | \(0.730985\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.5026 | −0.616710 | ||||||||
\(412\) | − 18.0279i | − 0.888169i | ||||||||
\(413\) | − 22.4255i | − 1.10349i | ||||||||
\(414\) | −1.27977 | −0.0628974 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 29.1746 | 1.43040 | ||||||||
\(417\) | 0.356135i | 0.0174400i | ||||||||
\(418\) | 1.98522i | 0.0971001i | ||||||||
\(419\) | −5.04882 | −0.246651 | −0.123325 | − | 0.992366i | \(-0.539356\pi\) | ||||
−0.123325 | + | 0.992366i | \(0.539356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.2026 | −1.13082 | −0.565412 | − | 0.824809i | \(-0.691283\pi\) | ||||
−0.565412 | + | 0.824809i | \(0.691283\pi\) | |||||||
\(422\) | 31.6259i | 1.53952i | ||||||||
\(423\) | 7.67555i | 0.373198i | ||||||||
\(424\) | −4.09964 | −0.199096 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.873886 | 0.0423399 | ||||||||
\(427\) | − 67.2588i | − 3.25488i | ||||||||
\(428\) | 29.4660i | 1.42429i | ||||||||
\(429\) | −15.6466 | −0.755426 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −39.7692 | −1.91561 | −0.957807 | − | 0.287413i | \(-0.907205\pi\) | ||||
−0.957807 | + | 0.287413i | \(0.907205\pi\) | |||||||
\(432\) | 4.31592i | 0.207650i | ||||||||
\(433\) | 18.3272i | 0.880750i | 0.897814 | + | 0.440375i | \(0.145154\pi\) | ||||
−0.897814 | + | 0.440375i | \(0.854846\pi\) | |||||||
\(434\) | −34.9622 | −1.67824 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.46242 | −0.213711 | ||||||||
\(437\) | 0.159375i | 0.00762394i | ||||||||
\(438\) | − 21.7485i | − 1.03918i | ||||||||
\(439\) | 37.2170 | 1.77627 | 0.888135 | − | 0.459582i | \(-0.152001\pi\) | ||||
0.888135 | + | 0.459582i | \(0.152001\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.9245 | 0.663071 | ||||||||
\(442\) | 24.0118i | 1.14213i | ||||||||
\(443\) | − 8.41969i | − 0.400032i | −0.979793 | − | 0.200016i | \(-0.935901\pi\) | ||||
0.979793 | − | 0.200016i | \(-0.0640994\pi\) | |||||||
\(444\) | −19.3948 | −0.920438 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 19.4859 | 0.922686 | ||||||||
\(447\) | 15.0317i | 0.710974i | ||||||||
\(448\) | 30.0172i | 1.41818i | ||||||||
\(449\) | −3.31527 | −0.156457 | −0.0782287 | − | 0.996935i | \(-0.524926\pi\) | ||||
−0.0782287 | + | 0.996935i | \(0.524926\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.20557 | −0.150944 | ||||||||
\(452\) | − 19.9688i | − 0.939253i | ||||||||
\(453\) | − 5.65576i | − 0.265731i | ||||||||
\(454\) | 47.0775 | 2.20946 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.0824089 | 0.00385915 | ||||||||
\(457\) | − 2.57124i | − 0.120277i | −0.998190 | − | 0.0601387i | \(-0.980846\pi\) | ||||
0.998190 | − | 0.0601387i | \(-0.0191543\pi\) | |||||||
\(458\) | − 30.0971i | − 1.40634i | ||||||||
\(459\) | −3.26755 | −0.152516 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.8861 | 1.62481 | 0.812404 | − | 0.583095i | \(-0.198159\pi\) | ||||
0.812404 | + | 0.583095i | \(0.198159\pi\) | |||||||
\(462\) | − 37.2746i | − 1.73417i | ||||||||
\(463\) | − 8.24992i | − 0.383406i | −0.981453 | − | 0.191703i | \(-0.938599\pi\) | ||||
0.981453 | − | 0.191703i | \(-0.0614011\pi\) | |||||||
\(464\) | −36.8895 | −1.71255 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.8902 | −0.597125 | ||||||||
\(467\) | − 24.4499i | − 1.13140i | −0.824609 | − | 0.565702i | \(-0.808605\pi\) | ||||
0.824609 | − | 0.565702i | \(-0.191395\pi\) | |||||||
\(468\) | − 6.86324i | − 0.317253i | ||||||||
\(469\) | 1.44959 | 0.0669359 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.69480 | −0.308480 | ||||||||
\(472\) | 1.65832i | 0.0763303i | ||||||||
\(473\) | − 16.2593i | − 0.747602i | ||||||||
\(474\) | −19.1860 | −0.881242 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −27.3092 | −1.25172 | ||||||||
\(477\) | 12.1197i | 0.554925i | ||||||||
\(478\) | 34.9930i | 1.60054i | ||||||||
\(479\) | −4.79732 | −0.219195 | −0.109598 | − | 0.993976i | \(-0.534956\pi\) | ||||
−0.109598 | + | 0.993976i | \(0.534956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.8745 | −1.81812 | ||||||||
\(482\) | − 12.1761i | − 0.554605i | ||||||||
\(483\) | − 2.99244i | − 0.136161i | ||||||||
\(484\) | −11.6023 | −0.527378 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.95630 | 0.0887394 | ||||||||
\(487\) | 20.2715i | 0.918589i | 0.888284 | + | 0.459294i | \(0.151898\pi\) | ||||
−0.888284 | + | 0.459294i | \(0.848102\pi\) | |||||||
\(488\) | 4.97364i | 0.225146i | ||||||||
\(489\) | −13.8314 | −0.625479 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.2638 | 1.63656 | 0.818281 | − | 0.574818i | \(-0.194927\pi\) | ||||
0.818281 | + | 0.574818i | \(0.194927\pi\) | |||||||
\(492\) | − 1.40609i | − 0.0633915i | ||||||||
\(493\) | − 27.9287i | − 1.25785i | ||||||||
\(494\) | −1.79030 | −0.0805493 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.8621 | 0.757129 | ||||||||
\(497\) | 2.04337i | 0.0916579i | ||||||||
\(498\) | − 17.3422i | − 0.777123i | ||||||||
\(499\) | −2.39550 | −0.107237 | −0.0536187 | − | 0.998561i | \(-0.517076\pi\) | ||||
−0.0536187 | + | 0.998561i | \(0.517076\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.5017 | 0.603212 | ||||||||
\(502\) | 13.9206i | 0.621307i | ||||||||
\(503\) | − 22.7079i | − 1.01249i | −0.862389 | − | 0.506247i | \(-0.831032\pi\) | ||||
0.862389 | − | 0.506247i | \(-0.168968\pi\) | |||||||
\(504\) | −1.54732 | −0.0689230 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.33070 | −0.236979 | ||||||||
\(507\) | − 1.11035i | − 0.0493125i | ||||||||
\(508\) | − 23.4988i | − 1.04259i | ||||||||
\(509\) | −14.9257 | −0.661569 | −0.330784 | − | 0.943706i | \(-0.607313\pi\) | ||||
−0.330784 | + | 0.943706i | \(0.607313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 50.8536 | 2.24963 | ||||||||
\(512\) | − 30.6006i | − 1.35237i | ||||||||
\(513\) | − 0.243625i | − 0.0107563i | ||||||||
\(514\) | 13.9990 | 0.617470 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.13196 | 0.313967 | ||||||||
\(517\) | 31.9714i | 1.40610i | ||||||||
\(518\) | − 94.9922i | − 4.17372i | ||||||||
\(519\) | 13.7259 | 0.602499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.56462 | −0.243790 | −0.121895 | − | 0.992543i | \(-0.538897\pi\) | ||||
−0.121895 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(522\) | 16.7211i | 0.731862i | ||||||||
\(523\) | − 22.6133i | − 0.988811i | −0.869231 | − | 0.494405i | \(-0.835386\pi\) | ||||
0.869231 | − | 0.494405i | \(-0.164614\pi\) | |||||||
\(524\) | −4.33826 | −0.189518 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.56210 | 0.111713 | ||||||||
\(527\) | 12.7661i | 0.556101i | ||||||||
\(528\) | 17.9773i | 0.782363i | ||||||||
\(529\) | 22.5720 | 0.981393 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.90248 | 0.212749 | ||||||||
\(532\) | − 2.03615i | − 0.0882782i | ||||||||
\(533\) | − 2.89083i | − 0.125216i | ||||||||
\(534\) | 15.2794 | 0.661206 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.107194 | −0.00463007 | ||||||||
\(537\) | − 4.46491i | − 0.192675i | ||||||||
\(538\) | − 41.0323i | − 1.76903i | ||||||||
\(539\) | 58.0004 | 2.49825 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5382 | −0.539059 | −0.269529 | − | 0.962992i | \(-0.586868\pi\) | ||||
−0.269529 | + | 0.962992i | \(0.586868\pi\) | |||||||
\(542\) | − 18.8833i | − 0.811109i | ||||||||
\(543\) | − 14.0032i | − 0.600933i | ||||||||
\(544\) | 25.3780 | 1.08807 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 33.6148 | 1.43858 | ||||||||
\(547\) | − 5.45889i | − 0.233405i | −0.993167 | − | 0.116703i | \(-0.962768\pi\) | ||||
0.993167 | − | 0.116703i | \(-0.0372324\pi\) | |||||||
\(548\) | − 22.8435i | − 0.975824i | ||||||||
\(549\) | 14.7035 | 0.627532 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.08234 | 0.0887107 | ||||||||
\(552\) | 0.221284i | 0.00941849i | ||||||||
\(553\) | − 44.8618i | − 1.90772i | ||||||||
\(554\) | 39.2150 | 1.66608 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.650692 | −0.0275955 | ||||||||
\(557\) | − 4.84648i | − 0.205352i | −0.994715 | − | 0.102676i | \(-0.967260\pi\) | ||||
0.994715 | − | 0.102676i | \(-0.0327404\pi\) | |||||||
\(558\) | − 7.64313i | − 0.323560i | ||||||||
\(559\) | 14.6628 | 0.620172 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.6105 | −0.574635 | ||||||||
\(562\) | 8.66023i | 0.365310i | ||||||||
\(563\) | − 37.5755i | − 1.58362i | −0.610769 | − | 0.791809i | \(-0.709139\pi\) | ||||
0.610769 | − | 0.791809i | \(-0.290861\pi\) | |||||||
\(564\) | −14.0239 | −0.590514 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.9160 | −0.921198 | ||||||||
\(567\) | 4.57433i | 0.192104i | ||||||||
\(568\) | − 0.151103i | − 0.00634014i | ||||||||
\(569\) | −17.0619 | −0.715272 | −0.357636 | − | 0.933861i | \(-0.616417\pi\) | ||||
−0.357636 | + | 0.933861i | \(0.616417\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.6234 | −1.19785 | −0.598925 | − | 0.800805i | \(-0.704405\pi\) | ||||
−0.598925 | + | 0.800805i | \(0.704405\pi\) | |||||||
\(572\) | − 28.5878i | − 1.19532i | ||||||||
\(573\) | − 4.29614i | − 0.179474i | ||||||||
\(574\) | 6.88676 | 0.287448 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.56210 | −0.273421 | ||||||||
\(577\) | 2.22388i | 0.0925815i | 0.998928 | + | 0.0462907i | \(0.0147401\pi\) | ||||
−0.998928 | + | 0.0462907i | \(0.985260\pi\) | |||||||
\(578\) | − 12.3699i | − 0.514522i | ||||||||
\(579\) | 13.0436 | 0.542073 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 40.5506 | 1.68232 | ||||||||
\(582\) | − 15.9621i | − 0.661652i | ||||||||
\(583\) | 50.4830i | 2.09079i | ||||||||
\(584\) | −3.76051 | −0.155611 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 52.1360 | 2.15372 | ||||||||
\(587\) | − 29.8085i | − 1.23033i | −0.788399 | − | 0.615164i | \(-0.789090\pi\) | ||||
0.788399 | − | 0.615164i | \(-0.210910\pi\) | |||||||
\(588\) | 25.4413i | 1.04918i | ||||||||
\(589\) | −0.951829 | −0.0392194 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.17856 | 0.377555 | ||||||||
\(592\) | 45.8141i | 1.88295i | ||||||||
\(593\) | 43.9251i | 1.80379i | 0.431956 | + | 0.901895i | \(0.357823\pi\) | ||||
−0.431956 | + | 0.901895i | \(0.642177\pi\) | |||||||
\(594\) | 8.14866 | 0.334344 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −27.4642 | −1.12498 | ||||||||
\(597\) | − 0.677499i | − 0.0277282i | ||||||||
\(598\) | − 4.80731i | − 0.196585i | ||||||||
\(599\) | −43.1539 | −1.76322 | −0.881610 | − | 0.471978i | \(-0.843540\pi\) | ||||
−0.881610 | + | 0.471978i | \(0.843540\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.7365 | 1.53931 | 0.769653 | − | 0.638463i | \(-0.220429\pi\) | ||||
0.769653 | + | 0.638463i | \(0.220429\pi\) | |||||||
\(602\) | 34.9310i | 1.42368i | ||||||||
\(603\) | 0.316897i | 0.0129050i | ||||||||
\(604\) | 10.3336 | 0.420468 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.6705 | −0.758439 | ||||||||
\(607\) | 45.6549i | 1.85308i | 0.376202 | + | 0.926538i | \(0.377230\pi\) | ||||
−0.376202 | + | 0.926538i | \(0.622770\pi\) | |||||||
\(608\) | 1.89216i | 0.0767372i | ||||||||
\(609\) | −39.0982 | −1.58434 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.8322 | −1.16643 | ||||||||
\(612\) | − 5.97010i | − 0.241327i | ||||||||
\(613\) | 39.0685i | 1.57796i | 0.614418 | + | 0.788980i | \(0.289391\pi\) | ||||
−0.614418 | + | 0.788980i | \(0.710609\pi\) | |||||||
\(614\) | −18.5627 | −0.749130 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.44512 | −0.259681 | ||||||||
\(617\) | − 27.4125i | − 1.10359i | −0.833981 | − | 0.551794i | \(-0.813944\pi\) | ||||
0.833981 | − | 0.551794i | \(-0.186056\pi\) | |||||||
\(618\) | 19.3027i | 0.776469i | ||||||||
\(619\) | 22.8242 | 0.917384 | 0.458692 | − | 0.888595i | \(-0.348318\pi\) | ||||
0.458692 | + | 0.888595i | \(0.348318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.654182 | 0.0262514 | ||||||||
\(622\) | − 22.5272i | − 0.903259i | ||||||||
\(623\) | 35.7273i | 1.43139i | ||||||||
\(624\) | −16.2122 | −0.649008 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.19545 | 0.167684 | ||||||||
\(627\) | − 1.01478i | − 0.0405266i | ||||||||
\(628\) | − 12.2320i | − 0.488110i | ||||||||
\(629\) | −34.6855 | −1.38300 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.0638 | 0.400632 | 0.200316 | − | 0.979731i | \(-0.435803\pi\) | ||||
0.200316 | + | 0.979731i | \(0.435803\pi\) | |||||||
\(632\) | 3.31743i | 0.131960i | ||||||||
\(633\) | − 16.1662i | − 0.642549i | ||||||||
\(634\) | −1.43908 | −0.0571531 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −22.1439 | −0.878061 | ||||||||
\(637\) | 52.3056i | 2.07242i | ||||||||
\(638\) | 69.6492i | 2.75744i | ||||||||
\(639\) | −0.446705 | −0.0176714 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −42.7831 | −1.68983 | −0.844916 | − | 0.534899i | \(-0.820350\pi\) | ||||
−0.844916 | + | 0.534899i | \(0.820350\pi\) | |||||||
\(642\) | − 31.5497i | − 1.24517i | ||||||||
\(643\) | − 10.1067i | − 0.398571i | −0.979941 | − | 0.199285i | \(-0.936138\pi\) | ||||
0.979941 | − | 0.199285i | \(-0.0638621\pi\) | |||||||
\(644\) | 5.46747 | 0.215448 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.55732 | −0.0612719 | ||||||||
\(647\) | − 16.7580i | − 0.658826i | −0.944186 | − | 0.329413i | \(-0.893149\pi\) | ||||
0.944186 | − | 0.329413i | \(-0.106851\pi\) | |||||||
\(648\) | − 0.338261i | − 0.0132882i | ||||||||
\(649\) | 20.4205 | 0.801576 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.8716 | 0.700445 | ||||||||
\(652\) | − 25.2713i | − 0.989700i | ||||||||
\(653\) | − 20.7798i | − 0.813175i | −0.913612 | − | 0.406588i | \(-0.866719\pi\) | ||||
0.913612 | − | 0.406588i | \(-0.133281\pi\) | |||||||
\(654\) | 4.77799 | 0.186834 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.32144 | −0.129680 | ||||||||
\(657\) | 11.1172i | 0.433723i | ||||||||
\(658\) | − 68.6865i | − 2.67768i | ||||||||
\(659\) | 15.9362 | 0.620785 | 0.310393 | − | 0.950608i | \(-0.399539\pi\) | ||||
0.310393 | + | 0.950608i | \(0.399539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.37323 | 0.131203 | 0.0656017 | − | 0.997846i | \(-0.479103\pi\) | ||||
0.0656017 | + | 0.997846i | \(0.479103\pi\) | |||||||
\(662\) | − 21.7497i | − 0.845325i | ||||||||
\(663\) | − 12.2741i | − 0.476688i | ||||||||
\(664\) | −2.99862 | −0.116369 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 20.7664 | 0.804680 | ||||||||
\(667\) | 5.59150i | 0.216504i | ||||||||
\(668\) | 24.6688i | 0.954466i | ||||||||
\(669\) | −9.96064 | −0.385100 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 61.2454 | 2.36435 | ||||||||
\(672\) | − 35.5274i | − 1.37050i | ||||||||
\(673\) | 35.2852i | 1.36015i | 0.733144 | + | 0.680073i | \(0.238052\pi\) | ||||
−0.733144 | + | 0.680073i | \(0.761948\pi\) | |||||||
\(674\) | −27.8785 | −1.07384 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.02872 | 0.0780276 | ||||||||
\(677\) | − 31.2943i | − 1.20274i | −0.798971 | − | 0.601369i | \(-0.794622\pi\) | ||||
0.798971 | − | 0.601369i | \(-0.205378\pi\) | |||||||
\(678\) | 21.3809i | 0.821129i | ||||||||
\(679\) | 37.3237 | 1.43235 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.0646 | −0.922158 | ||||||||
\(682\) | − 31.8363i | − 1.21908i | ||||||||
\(683\) | − 10.8131i | − 0.413751i | −0.978367 | − | 0.206876i | \(-0.933670\pi\) | ||||
0.978367 | − | 0.206876i | \(-0.0663296\pi\) | |||||||
\(684\) | 0.445125 | 0.0170198 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −61.9654 | −2.36585 | ||||||||
\(687\) | 15.3847i | 0.586964i | ||||||||
\(688\) | − 16.8470i | − 0.642286i | ||||||||
\(689\) | −45.5263 | −1.73441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.9819 | −1.93944 | −0.969722 | − | 0.244210i | \(-0.921471\pi\) | ||||
−0.969722 | + | 0.244210i | \(0.921471\pi\) | |||||||
\(692\) | 25.0784i | 0.953338i | ||||||||
\(693\) | 19.0537i | 0.723790i | ||||||||
\(694\) | −0.341599 | −0.0129669 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.89123 | 0.109592 | ||||||||
\(697\) | − 2.51463i | − 0.0952485i | ||||||||
\(698\) | − 36.5122i | − 1.38201i | ||||||||
\(699\) | 6.58907 | 0.249222 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.20728 | 0.196676 | 0.0983382 | − | 0.995153i | \(-0.468647\pi\) | ||||
0.0983382 | + | 0.995153i | \(0.468647\pi\) | |||||||
\(702\) | 7.34858i | 0.277354i | ||||||||
\(703\) | − 2.58611i | − 0.0975372i | ||||||||
\(704\) | −27.3335 | −1.03017 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.9657 | 0.638514 | ||||||||
\(707\) | − 43.6566i | − 1.64188i | ||||||||
\(708\) | 8.95727i | 0.336635i | ||||||||
\(709\) | 37.4108 | 1.40499 | 0.702497 | − | 0.711687i | \(-0.252069\pi\) | ||||
0.702497 | + | 0.711687i | \(0.252069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.80731 | 0.367803 | ||||||||
\(712\) | − 2.64195i | − 0.0990114i | ||||||||
\(713\) | − 2.55585i | − 0.0957174i | ||||||||
\(714\) | 29.2404 | 1.09429 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.15780 | 0.304871 | ||||||||
\(717\) | − 17.8874i | − 0.668017i | ||||||||
\(718\) | 26.8364i | 1.00153i | ||||||||
\(719\) | −31.2527 | −1.16553 | −0.582764 | − | 0.812641i | \(-0.698029\pi\) | ||||
−0.582764 | + | 0.812641i | \(0.698029\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −45.1348 | −1.68091 | ||||||||
\(722\) | 37.0535i | 1.37899i | ||||||||
\(723\) | 6.22404i | 0.231475i | ||||||||
\(724\) | 25.5850 | 0.950861 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.4228 | 0.461053 | ||||||||
\(727\) | 1.21933i | 0.0452225i | 0.999744 | + | 0.0226113i | \(0.00719800\pi\) | ||||
−0.999744 | + | 0.0226113i | \(0.992802\pi\) | |||||||
\(728\) | − 5.81231i | − 0.215418i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7547 | 0.471750 | ||||||||
\(732\) | 26.8647i | 0.992948i | ||||||||
\(733\) | 13.3535i | 0.493221i | 0.969115 | + | 0.246611i | \(0.0793168\pi\) | ||||
−0.969115 | + | 0.246611i | \(0.920683\pi\) | |||||||
\(734\) | 1.03752 | 0.0382957 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.08083 | −0.187282 | ||||||||
\(737\) | 1.31999i | 0.0486224i | ||||||||
\(738\) | 1.50552i | 0.0554191i | ||||||||
\(739\) | 5.24691 | 0.193011 | 0.0965054 | − | 0.995332i | \(-0.469234\pi\) | ||||
0.0965054 | + | 0.995332i | \(0.469234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.915147 | 0.0336188 | ||||||||
\(742\) | − 108.456i | − 3.98156i | ||||||||
\(743\) | − 42.9203i | − 1.57459i | −0.616575 | − | 0.787296i | \(-0.711480\pi\) | ||||
0.616575 | − | 0.787296i | \(-0.288520\pi\) | |||||||
\(744\) | −1.32157 | −0.0484510 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −57.4150 | −2.10211 | ||||||||
\(747\) | 8.86482i | 0.324347i | ||||||||
\(748\) | − 24.8676i | − 0.909249i | ||||||||
\(749\) | 73.7716 | 2.69555 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.2461 | −0.738792 | −0.369396 | − | 0.929272i | \(-0.620435\pi\) | ||||
−0.369396 | + | 0.929272i | \(0.620435\pi\) | |||||||
\(752\) | 33.1270i | 1.20802i | ||||||||
\(753\) | − 7.11580i | − 0.259314i | ||||||||
\(754\) | −62.8106 | −2.28743 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.35772 | −0.303967 | ||||||||
\(757\) | 10.3260i | 0.375306i | 0.982235 | + | 0.187653i | \(0.0600881\pi\) | ||||
−0.982235 | + | 0.187653i | \(0.939912\pi\) | |||||||
\(758\) | 9.48087i | 0.344361i | ||||||||
\(759\) | 2.72490 | 0.0989075 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.2923 | 1.06185 | 0.530923 | − | 0.847420i | \(-0.321845\pi\) | ||||
0.530923 | + | 0.847420i | \(0.321845\pi\) | |||||||
\(762\) | 25.1606i | 0.911471i | ||||||||
\(763\) | 11.1722i | 0.404460i | ||||||||
\(764\) | 7.84943 | 0.283982 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41.7839 | 1.50971 | ||||||||
\(767\) | 18.4155i | 0.664947i | ||||||||
\(768\) | 18.3983i | 0.663893i | ||||||||
\(769\) | 22.9834 | 0.828803 | 0.414402 | − | 0.910094i | \(-0.363991\pi\) | ||||
0.414402 | + | 0.910094i | \(0.363991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.15589 | −0.257713 | ||||||||
\(772\) | 23.8318i | 0.857725i | ||||||||
\(773\) | 54.2216i | 1.95022i | 0.221732 | + | 0.975108i | \(0.428829\pi\) | ||||
−0.221732 | + | 0.975108i | \(0.571171\pi\) | |||||||
\(774\) | −7.63631 | −0.274481 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.76000 | −0.0990782 | ||||||||
\(777\) | 48.5572i | 1.74198i | ||||||||
\(778\) | 20.4099i | 0.731731i | ||||||||
\(779\) | 0.187489 | 0.00671748 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.86068 | −0.0665805 | ||||||||
\(782\) | − 4.18172i | − 0.149538i | ||||||||
\(783\) | − 8.54732i | − 0.305456i | ||||||||
\(784\) | 60.0970 | 2.14632 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.64505 | 0.165683 | ||||||||
\(787\) | 6.60711i | 0.235518i | 0.993042 | + | 0.117759i | \(0.0375711\pi\) | ||||
−0.993042 | + | 0.117759i | \(0.962429\pi\) | |||||||
\(788\) | 16.7701i | 0.597409i | ||||||||
\(789\) | −1.30967 | −0.0466255 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −49.9941 | −1.77759 | ||||||||
\(792\) | − 1.40898i | − 0.0500658i | ||||||||
\(793\) | 55.2320i | 1.96135i | ||||||||
\(794\) | −31.9161 | −1.13266 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.23785 | 0.0438745 | ||||||||
\(797\) | − 2.34163i | − 0.0829446i | −0.999140 | − | 0.0414723i | \(-0.986795\pi\) | ||||
0.999140 | − | 0.0414723i | \(-0.0132048\pi\) | |||||||
\(798\) | 2.18014i | 0.0771760i | ||||||||
\(799\) | −25.0802 | −0.887274 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.81040 | −0.275967 | ||||||||
\(802\) | − 20.2031i | − 0.713397i | ||||||||
\(803\) | 46.3070i | 1.63414i | ||||||||
\(804\) | −0.579000 | −0.0204197 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.7105 | 1.01128 | ||||||||
\(807\) | 20.9745i | 0.738337i | ||||||||
\(808\) | 3.22831i | 0.113571i | ||||||||
\(809\) | 53.7248 | 1.88886 | 0.944432 | − | 0.328707i | \(-0.106613\pi\) | ||||
0.944432 | + | 0.328707i | \(0.106613\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.5877 | −1.03897 | −0.519483 | − | 0.854481i | \(-0.673875\pi\) | ||||
−0.519483 | + | 0.854481i | \(0.673875\pi\) | |||||||
\(812\) | − 71.4361i | − 2.50691i | ||||||||
\(813\) | 9.65260i | 0.338532i | ||||||||
\(814\) | 86.4992 | 3.03180 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.1025 | −0.493685 | ||||||||
\(817\) | 0.950979i | 0.0332705i | ||||||||
\(818\) | 52.5112i | 1.83601i | ||||||||
\(819\) | −17.1829 | −0.600419 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.3855 | 1.16516 | 0.582580 | − | 0.812773i | \(-0.302043\pi\) | ||||
0.582580 | + | 0.812773i | \(0.302043\pi\) | |||||||
\(822\) | 24.4588i | 0.853100i | ||||||||
\(823\) | 17.5383i | 0.611345i | 0.952137 | + | 0.305672i | \(0.0988813\pi\) | ||||
−0.952137 | + | 0.305672i | \(0.901119\pi\) | |||||||
\(824\) | 3.33762 | 0.116271 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −43.8710 | −1.52647 | ||||||||
\(827\) | 26.6114i | 0.925369i | 0.886523 | + | 0.462684i | \(0.153114\pi\) | ||||
−0.886523 | + | 0.462684i | \(0.846886\pi\) | |||||||
\(828\) | 1.19525i | 0.0415378i | ||||||||
\(829\) | −20.3212 | −0.705784 | −0.352892 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352892 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.0455 | −0.695372 | ||||||||
\(832\) | − 24.6497i | − 0.854575i | ||||||||
\(833\) | 45.4989i | 1.57644i | ||||||||
\(834\) | 0.696706 | 0.0241250 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.85410 | 0.0641255 | ||||||||
\(837\) | 3.90694i | 0.135044i | ||||||||
\(838\) | 9.87698i | 0.341195i | ||||||||
\(839\) | 23.3881 | 0.807448 | 0.403724 | − | 0.914881i | \(-0.367716\pi\) | ||||
0.403724 | + | 0.914881i | \(0.367716\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.0566 | 1.51919 | ||||||||
\(842\) | 45.3910i | 1.56428i | ||||||||
\(843\) | − 4.42685i | − 0.152469i | ||||||||
\(844\) | 29.5371 | 1.01671 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.0156 | 0.516248 | ||||||||
\(847\) | 29.0477i | 0.998091i | ||||||||
\(848\) | 52.3078i | 1.79626i | ||||||||
\(849\) | 11.2028 | 0.384479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.94424 | 0.238045 | ||||||||
\(852\) | − 0.816170i | − 0.0279615i | ||||||||
\(853\) | 9.81934i | 0.336208i | 0.985769 | + | 0.168104i | \(0.0537644\pi\) | ||||
−0.985769 | + | 0.168104i | \(0.946236\pi\) | |||||||
\(854\) | −131.578 | −4.50251 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.45524 | −0.186456 | ||||||||
\(857\) | − 15.9866i | − 0.546093i | −0.962001 | − | 0.273047i | \(-0.911969\pi\) | ||||
0.962001 | − | 0.273047i | \(-0.0880313\pi\) | |||||||
\(858\) | 30.6094i | 1.04499i | ||||||||
\(859\) | 20.5913 | 0.702567 | 0.351284 | − | 0.936269i | \(-0.385745\pi\) | ||||
0.351284 | + | 0.936269i | \(0.385745\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.52031 | −0.119972 | ||||||||
\(862\) | 77.8002i | 2.64989i | ||||||||
\(863\) | − 51.5169i | − 1.75366i | −0.480803 | − | 0.876828i | \(-0.659655\pi\) | ||||
0.480803 | − | 0.876828i | \(-0.340345\pi\) | |||||||
\(864\) | 7.76669 | 0.264228 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.8534 | 1.21835 | ||||||||
\(867\) | 6.32315i | 0.214745i | ||||||||
\(868\) | 32.6531i | 1.10832i | ||||||||
\(869\) | 40.8509 | 1.38577 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.19038 | −0.0403346 | ||||||||
\(872\) | − 0.826157i | − 0.0279772i | ||||||||
\(873\) | 8.15938i | 0.276153i | ||||||||
\(874\) | 0.311785 | 0.0105463 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.3121 | −0.686282 | ||||||||
\(877\) | 17.6050i | 0.594480i | 0.954803 | + | 0.297240i | \(0.0960661\pi\) | ||||
−0.954803 | + | 0.297240i | \(0.903934\pi\) | |||||||
\(878\) | − 72.8075i | − 2.45713i | ||||||||
\(879\) | −26.6504 | −0.898894 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.1453 | −1.58837 | −0.794183 | − | 0.607679i | \(-0.792101\pi\) | ||||
−0.794183 | + | 0.607679i | \(0.792101\pi\) | |||||||
\(882\) | − 27.2404i | − 0.917232i | ||||||||
\(883\) | − 23.2300i | − 0.781751i | −0.920444 | − | 0.390875i | \(-0.872172\pi\) | ||||
0.920444 | − | 0.390875i | \(-0.127828\pi\) | |||||||
\(884\) | 22.4259 | 0.754266 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.4714 | −0.553368 | ||||||||
\(887\) | − 20.5226i | − 0.689082i | −0.938771 | − | 0.344541i | \(-0.888035\pi\) | ||||
0.938771 | − | 0.344541i | \(-0.111965\pi\) | |||||||
\(888\) | − 3.59069i | − 0.120496i | ||||||||
\(889\) | −58.8320 | −1.97316 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.16535 | −0.139545 | ||||||||
\(892\) | − 18.1990i | − 0.609347i | ||||||||
\(893\) | − 1.86995i | − 0.0625756i | ||||||||
\(894\) | 29.4064 | 0.983497 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.3323 | −0.411993 | ||||||||
\(897\) | 2.45735i | 0.0820486i | ||||||||
\(898\) | 6.48566i | 0.216429i | ||||||||
\(899\) | −33.3939 | −1.11375 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.6018 | −1.31933 | ||||||||
\(902\) | 6.27104i | 0.208803i | ||||||||
\(903\) | − 17.8557i | − 0.594200i | ||||||||
\(904\) | 3.69695 | 0.122959 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.0643 | −0.367588 | ||||||||
\(907\) | 13.1950i | 0.438133i | 0.975710 | + | 0.219066i | \(0.0703011\pi\) | ||||
−0.975710 | + | 0.219066i | \(0.929699\pi\) | |||||||
\(908\) | − 43.9682i | − 1.45914i | ||||||||
\(909\) | 9.54383 | 0.316549 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.1021 | 0.897932 | 0.448966 | − | 0.893549i | \(-0.351792\pi\) | ||||
0.448966 | + | 0.893549i | \(0.351792\pi\) | |||||||
\(912\) | − 1.05147i | − 0.0348175i | ||||||||
\(913\) | 36.9251i | 1.22204i | ||||||||
\(914\) | −5.03010 | −0.166381 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −28.1093 | −0.928757 | ||||||||
\(917\) | 10.8613i | 0.358673i | ||||||||
\(918\) | 6.39228i | 0.210977i | ||||||||
\(919\) | 3.80568 | 0.125538 | 0.0627690 | − | 0.998028i | \(-0.480007\pi\) | ||||
0.0627690 | + | 0.998028i | \(0.480007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.48870 | 0.312663 | ||||||||
\(922\) | − 68.2475i | − 2.24761i | ||||||||
\(923\) | − 1.67799i | − 0.0552317i | ||||||||
\(924\) | −34.8128 | −1.14526 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.1393 | −0.530369 | ||||||||
\(927\) | − 9.86698i | − 0.324074i | ||||||||
\(928\) | 66.3844i | 2.17917i | ||||||||
\(929\) | −41.8941 | −1.37450 | −0.687250 | − | 0.726421i | \(-0.741182\pi\) | ||||
−0.687250 | + | 0.726421i | \(0.741182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.39235 | −0.111180 | ||||||||
\(932\) | 12.0388i | 0.394345i | ||||||||
\(933\) | 11.5152i | 0.376992i | ||||||||
\(934\) | −47.8312 | −1.56508 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.27064 | 0.0415320 | ||||||||
\(937\) | 8.55321i | 0.279421i | 0.990192 | + | 0.139711i | \(0.0446172\pi\) | ||||
−0.990192 | + | 0.139711i | \(0.955383\pi\) | |||||||
\(938\) | − 2.83583i | − 0.0925931i | ||||||||
\(939\) | −2.14459 | −0.0699861 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.3669 | −1.57672 | −0.788358 | − | 0.615216i | \(-0.789069\pi\) | ||||
−0.788358 | + | 0.615216i | \(0.789069\pi\) | |||||||
\(942\) | 13.0970i | 0.426723i | ||||||||
\(943\) | 0.503445i | 0.0163944i | ||||||||
\(944\) | 21.1587 | 0.688657 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.8079 | −1.03416 | ||||||||
\(947\) | − 8.71018i | − 0.283043i | −0.989935 | − | 0.141521i | \(-0.954801\pi\) | ||||
0.989935 | − | 0.141521i | \(-0.0451994\pi\) | |||||||
\(948\) | 17.9188i | 0.581977i | ||||||||
\(949\) | −41.7603 | −1.35560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.735614 | 0.0238539 | ||||||||
\(952\) | − 5.05593i | − 0.163864i | ||||||||
\(953\) | − 43.4534i | − 1.40760i | −0.710401 | − | 0.703798i | \(-0.751486\pi\) | ||||
0.710401 | − | 0.703798i | \(-0.248514\pi\) | |||||||
\(954\) | 23.7098 | 0.767633 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 32.6819 | 1.05701 | ||||||||
\(957\) | − 35.6026i | − 1.15087i | ||||||||
\(958\) | 9.38497i | 0.303215i | ||||||||
\(959\) | −57.1912 | −1.84680 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7358 | −0.507606 | ||||||||
\(962\) | 78.0062i | 2.51502i | ||||||||
\(963\) | 16.1273i | 0.519695i | ||||||||
\(964\) | −11.3719 | −0.366264 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.85410 | −0.188353 | ||||||||
\(967\) | 60.2789i | 1.93844i | 0.246197 | + | 0.969220i | \(0.420819\pi\) | ||||
−0.246197 | + | 0.969220i | \(0.579181\pi\) | |||||||
\(968\) | − 2.14801i | − 0.0690397i | ||||||||
\(969\) | 0.796056 | 0.0255730 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.42583 | 0.174123 | 0.0870616 | − | 0.996203i | \(-0.472252\pi\) | ||||
0.0870616 | + | 0.996203i | \(0.472252\pi\) | |||||||
\(972\) | − 1.82709i | − 0.0586040i | ||||||||
\(973\) | 1.62908i | 0.0522259i | ||||||||
\(974\) | 39.6570 | 1.27069 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 63.4593 | 2.03128 | ||||||||
\(977\) | 36.5741i | 1.17011i | 0.810994 | + | 0.585054i | \(0.198927\pi\) | ||||
−0.810994 | + | 0.585054i | \(0.801073\pi\) | |||||||
\(978\) | 27.0584i | 0.865231i | ||||||||
\(979\) | −32.5331 | −1.03976 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.44236 | −0.0779787 | ||||||||
\(982\) | − 70.9427i | − 2.26387i | ||||||||
\(983\) | − 41.0896i | − 1.31056i | −0.755388 | − | 0.655278i | \(-0.772551\pi\) | ||||
0.755388 | − | 0.655278i | \(-0.227449\pi\) | |||||||
\(984\) | 0.260319 | 0.00829866 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −54.6369 | −1.73999 | ||||||||
\(987\) | 35.1105i | 1.11758i | ||||||||
\(988\) | 1.67206i | 0.0531952i | ||||||||
\(989\) | −2.55357 | −0.0811988 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.20264 | −0.133501 | −0.0667506 | − | 0.997770i | \(-0.521263\pi\) | ||||
−0.0667506 | + | 0.997770i | \(0.521263\pi\) | |||||||
\(992\) | − 30.3440i | − 0.963424i | ||||||||
\(993\) | 11.1178i | 0.352812i | ||||||||
\(994\) | 3.99744 | 0.126791 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −16.1968 | −0.513216 | ||||||||
\(997\) | 10.1577i | 0.321698i | 0.986979 | + | 0.160849i | \(0.0514233\pi\) | ||||
−0.986979 | + | 0.160849i | \(0.948577\pi\) | |||||||
\(998\) | 4.68631i | 0.148342i | ||||||||
\(999\) | −10.6151 | −0.335848 |
(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 | 1875.2.b.d.1249.1 | 8 | ||
5.2 | odd | 4 | 1875.2.a.f.1.4 | ✓ | 4 | ||
5.3 | odd | 4 | 1875.2.a.g.1.1 | yes | 4 | ||
5.4 | even | 2 | inner | 1875.2.b.d.1249.8 | 8 | ||
15.2 | even | 4 | 5625.2.a.m.1.1 | 4 | |||
15.8 | even | 4 | 5625.2.a.j.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.f.1.4 | ✓ | 4 | 5.2 | odd | 4 | ||
1875.2.a.g.1.1 | yes | 4 | 5.3 | odd | 4 | ||
1875.2.b.d.1249.1 | 8 | 1.1 | even | 1 | trivial | ||
1875.2.b.d.1249.8 | 8 | 5.4 | even | 2 | inner | ||
5625.2.a.j.1.4 | 4 | 15.8 | even | 4 | |||
5625.2.a.m.1.1 | 4 | 15.2 | even | 4 |