Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.81702\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.81702 | 1.28483 | 0.642415 | − | 0.766357i | \(-0.277933\pi\) | ||||
0.642415 | + | 0.766357i | \(0.277933\pi\) | |||||||
\(3\) | 0.177104 | 0.102251 | 0.0511256 | − | 0.998692i | \(-0.483719\pi\) | ||||
0.0511256 | + | 0.998692i | \(0.483719\pi\) | |||||||
\(4\) | 1.30157 | 0.650787 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.321803 | 0.131375 | ||||||||
\(7\) | 1.07346 | 0.405731 | 0.202865 | − | 0.979207i | \(-0.434975\pi\) | ||||
0.202865 | + | 0.979207i | \(0.434975\pi\) | |||||||
\(8\) | −1.26906 | −0.448679 | ||||||||
\(9\) | −2.96863 | −0.989545 | ||||||||
\(10\) | −1.81702 | −0.574593 | ||||||||
\(11\) | −3.31015 | −0.998048 | −0.499024 | − | 0.866588i | \(-0.666308\pi\) | ||||
−0.499024 | + | 0.866588i | \(0.666308\pi\) | |||||||
\(12\) | 0.230514 | 0.0665438 | ||||||||
\(13\) | 2.65763 | 0.737094 | 0.368547 | − | 0.929609i | \(-0.379855\pi\) | ||||
0.368547 | + | 0.929609i | \(0.379855\pi\) | |||||||
\(14\) | 1.95051 | 0.521295 | ||||||||
\(15\) | −0.177104 | −0.0457281 | ||||||||
\(16\) | −4.90905 | −1.22726 | ||||||||
\(17\) | −3.99991 | −0.970120 | −0.485060 | − | 0.874481i | \(-0.661202\pi\) | ||||
−0.485060 | + | 0.874481i | \(0.661202\pi\) | |||||||
\(18\) | −5.39408 | −1.27140 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.30157 | −0.291041 | ||||||||
\(21\) | 0.190115 | 0.0414865 | ||||||||
\(22\) | −6.01462 | −1.28232 | ||||||||
\(23\) | 1.75378 | 0.365689 | 0.182844 | − | 0.983142i | \(-0.441470\pi\) | ||||
0.182844 | + | 0.983142i | \(0.441470\pi\) | |||||||
\(24\) | −0.224755 | −0.0458780 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.82898 | 0.947041 | ||||||||
\(27\) | −1.05707 | −0.203433 | ||||||||
\(28\) | 1.39719 | 0.264044 | ||||||||
\(29\) | 2.25251 | 0.418281 | 0.209140 | − | 0.977886i | \(-0.432933\pi\) | ||||
0.209140 | + | 0.977886i | \(0.432933\pi\) | |||||||
\(30\) | −0.321803 | −0.0587529 | ||||||||
\(31\) | −8.05272 | −1.44631 | −0.723156 | − | 0.690685i | \(-0.757309\pi\) | ||||
−0.723156 | + | 0.690685i | \(0.757309\pi\) | |||||||
\(32\) | −6.38175 | −1.12815 | ||||||||
\(33\) | −0.586242 | −0.102052 | ||||||||
\(34\) | −7.26792 | −1.24644 | ||||||||
\(35\) | −1.07346 | −0.181448 | ||||||||
\(36\) | −3.86390 | −0.643983 | ||||||||
\(37\) | −5.64805 | −0.928534 | −0.464267 | − | 0.885695i | \(-0.653682\pi\) | ||||
−0.464267 | + | 0.885695i | \(0.653682\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.470678 | 0.0753688 | ||||||||
\(40\) | 1.26906 | 0.200655 | ||||||||
\(41\) | −0.896172 | −0.139959 | −0.0699793 | − | 0.997548i | \(-0.522293\pi\) | ||||
−0.0699793 | + | 0.997548i | \(0.522293\pi\) | |||||||
\(42\) | 0.345443 | 0.0533030 | ||||||||
\(43\) | −8.51211 | −1.29808 | −0.649042 | − | 0.760752i | \(-0.724830\pi\) | ||||
−0.649042 | + | 0.760752i | \(0.724830\pi\) | |||||||
\(44\) | −4.30841 | −0.649517 | ||||||||
\(45\) | 2.96863 | 0.442538 | ||||||||
\(46\) | 3.18666 | 0.469848 | ||||||||
\(47\) | −6.29616 | −0.918389 | −0.459194 | − | 0.888336i | \(-0.651862\pi\) | ||||
−0.459194 | + | 0.888336i | \(0.651862\pi\) | |||||||
\(48\) | −0.869414 | −0.125489 | ||||||||
\(49\) | −5.84768 | −0.835382 | ||||||||
\(50\) | 1.81702 | 0.256966 | ||||||||
\(51\) | −0.708401 | −0.0991959 | ||||||||
\(52\) | 3.45911 | 0.479692 | ||||||||
\(53\) | −3.39943 | −0.466947 | −0.233474 | − | 0.972363i | \(-0.575009\pi\) | ||||
−0.233474 | + | 0.972363i | \(0.575009\pi\) | |||||||
\(54\) | −1.92072 | −0.261377 | ||||||||
\(55\) | 3.31015 | 0.446341 | ||||||||
\(56\) | −1.36228 | −0.182043 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.09287 | 0.537420 | ||||||||
\(59\) | −1.48676 | −0.193560 | −0.0967801 | − | 0.995306i | \(-0.530854\pi\) | ||||
−0.0967801 | + | 0.995306i | \(0.530854\pi\) | |||||||
\(60\) | −0.230514 | −0.0297593 | ||||||||
\(61\) | 13.7298 | 1.75792 | 0.878962 | − | 0.476892i | \(-0.158237\pi\) | ||||
0.878962 | + | 0.476892i | \(0.158237\pi\) | |||||||
\(62\) | −14.6320 | −1.85826 | ||||||||
\(63\) | −3.18672 | −0.401489 | ||||||||
\(64\) | −1.77769 | −0.222211 | ||||||||
\(65\) | −2.65763 | −0.329639 | ||||||||
\(66\) | −1.06522 | −0.131119 | ||||||||
\(67\) | 12.8597 | 1.57106 | 0.785531 | − | 0.618822i | \(-0.212390\pi\) | ||||
0.785531 | + | 0.618822i | \(0.212390\pi\) | |||||||
\(68\) | −5.20618 | −0.631342 | ||||||||
\(69\) | 0.310602 | 0.0373921 | ||||||||
\(70\) | −1.95051 | −0.233130 | ||||||||
\(71\) | 11.0262 | 1.30857 | 0.654287 | − | 0.756246i | \(-0.272969\pi\) | ||||
0.654287 | + | 0.756246i | \(0.272969\pi\) | |||||||
\(72\) | 3.76736 | 0.443988 | ||||||||
\(73\) | −2.61065 | −0.305553 | −0.152776 | − | 0.988261i | \(-0.548821\pi\) | ||||
−0.152776 | + | 0.988261i | \(0.548821\pi\) | |||||||
\(74\) | −10.2626 | −1.19301 | ||||||||
\(75\) | 0.177104 | 0.0204502 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.55333 | −0.404939 | ||||||||
\(78\) | 0.855233 | 0.0968360 | ||||||||
\(79\) | −6.57050 | −0.739239 | −0.369619 | − | 0.929183i | \(-0.620512\pi\) | ||||
−0.369619 | + | 0.929183i | \(0.620512\pi\) | |||||||
\(80\) | 4.90905 | 0.548849 | ||||||||
\(81\) | 8.71869 | 0.968743 | ||||||||
\(82\) | −1.62837 | −0.179823 | ||||||||
\(83\) | 2.69888 | 0.296241 | 0.148120 | − | 0.988969i | \(-0.452678\pi\) | ||||
0.148120 | + | 0.988969i | \(0.452678\pi\) | |||||||
\(84\) | 0.247449 | 0.0269989 | ||||||||
\(85\) | 3.99991 | 0.433851 | ||||||||
\(86\) | −15.4667 | −1.66782 | ||||||||
\(87\) | 0.398929 | 0.0427697 | ||||||||
\(88\) | 4.20077 | 0.447803 | ||||||||
\(89\) | 0.789838 | 0.0837227 | 0.0418613 | − | 0.999123i | \(-0.486671\pi\) | ||||
0.0418613 | + | 0.999123i | \(0.486671\pi\) | |||||||
\(90\) | 5.39408 | 0.568586 | ||||||||
\(91\) | 2.85287 | 0.299062 | ||||||||
\(92\) | 2.28268 | 0.237986 | ||||||||
\(93\) | −1.42617 | −0.147887 | ||||||||
\(94\) | −11.4403 | −1.17997 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.13024 | −0.115354 | ||||||||
\(97\) | −18.7179 | −1.90052 | −0.950259 | − | 0.311461i | \(-0.899182\pi\) | ||||
−0.950259 | + | 0.311461i | \(0.899182\pi\) | |||||||
\(98\) | −10.6254 | −1.07332 | ||||||||
\(99\) | 9.82663 | 0.987613 | ||||||||
\(100\) | 1.30157 | 0.130157 | ||||||||
\(101\) | 18.9172 | 1.88233 | 0.941164 | − | 0.337951i | \(-0.109734\pi\) | ||||
0.941164 | + | 0.337951i | \(0.109734\pi\) | |||||||
\(102\) | −1.28718 | −0.127450 | ||||||||
\(103\) | −11.6438 | −1.14730 | −0.573650 | − | 0.819101i | \(-0.694473\pi\) | ||||
−0.573650 | + | 0.819101i | \(0.694473\pi\) | |||||||
\(104\) | −3.37268 | −0.330719 | ||||||||
\(105\) | −0.190115 | −0.0185533 | ||||||||
\(106\) | −6.17684 | −0.599948 | ||||||||
\(107\) | 11.3958 | 1.10168 | 0.550838 | − | 0.834612i | \(-0.314308\pi\) | ||||
0.550838 | + | 0.834612i | \(0.314308\pi\) | |||||||
\(108\) | −1.37586 | −0.132392 | ||||||||
\(109\) | −12.7375 | −1.22003 | −0.610014 | − | 0.792390i | \(-0.708836\pi\) | ||||
−0.610014 | + | 0.792390i | \(0.708836\pi\) | |||||||
\(110\) | 6.01462 | 0.573472 | ||||||||
\(111\) | −1.00029 | −0.0949438 | ||||||||
\(112\) | −5.26969 | −0.497939 | ||||||||
\(113\) | 16.5894 | 1.56060 | 0.780300 | − | 0.625406i | \(-0.215067\pi\) | ||||
0.780300 | + | 0.625406i | \(0.215067\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.75378 | −0.163541 | ||||||||
\(116\) | 2.93181 | 0.272212 | ||||||||
\(117\) | −7.88954 | −0.729388 | ||||||||
\(118\) | −2.70148 | −0.248692 | ||||||||
\(119\) | −4.29375 | −0.393608 | ||||||||
\(120\) | 0.224755 | 0.0205172 | ||||||||
\(121\) | −0.0428972 | −0.00389975 | ||||||||
\(122\) | 24.9474 | 2.25863 | ||||||||
\(123\) | −0.158716 | −0.0143109 | ||||||||
\(124\) | −10.4812 | −0.941241 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.79034 | −0.515845 | ||||||||
\(127\) | −9.72338 | −0.862811 | −0.431405 | − | 0.902158i | \(-0.641982\pi\) | ||||
−0.431405 | + | 0.902158i | \(0.641982\pi\) | |||||||
\(128\) | 9.53340 | 0.842642 | ||||||||
\(129\) | −1.50753 | −0.132731 | ||||||||
\(130\) | −4.82898 | −0.423529 | ||||||||
\(131\) | 14.7903 | 1.29224 | 0.646118 | − | 0.763238i | \(-0.276392\pi\) | ||||
0.646118 | + | 0.763238i | \(0.276392\pi\) | |||||||
\(132\) | −0.763038 | −0.0664139 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 23.3664 | 2.01855 | ||||||||
\(135\) | 1.05707 | 0.0909782 | ||||||||
\(136\) | 5.07610 | 0.435272 | ||||||||
\(137\) | 3.59629 | 0.307252 | 0.153626 | − | 0.988129i | \(-0.450905\pi\) | ||||
0.153626 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(138\) | 0.564372 | 0.0480425 | ||||||||
\(139\) | −5.85467 | −0.496587 | −0.248293 | − | 0.968685i | \(-0.579870\pi\) | ||||
−0.248293 | + | 0.968685i | \(0.579870\pi\) | |||||||
\(140\) | −1.39719 | −0.118084 | ||||||||
\(141\) | −1.11508 | −0.0939063 | ||||||||
\(142\) | 20.0349 | 1.68129 | ||||||||
\(143\) | −8.79716 | −0.735656 | ||||||||
\(144\) | 14.5732 | 1.21443 | ||||||||
\(145\) | −2.25251 | −0.187061 | ||||||||
\(146\) | −4.74360 | −0.392584 | ||||||||
\(147\) | −1.03565 | −0.0854189 | ||||||||
\(148\) | −7.35136 | −0.604278 | ||||||||
\(149\) | 10.0667 | 0.824693 | 0.412347 | − | 0.911027i | \(-0.364709\pi\) | ||||
0.412347 | + | 0.911027i | \(0.364709\pi\) | |||||||
\(150\) | 0.321803 | 0.0262751 | ||||||||
\(151\) | −2.12653 | −0.173054 | −0.0865272 | − | 0.996249i | \(-0.527577\pi\) | ||||
−0.0865272 | + | 0.996249i | \(0.527577\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.8743 | 0.959977 | ||||||||
\(154\) | −6.45648 | −0.520278 | ||||||||
\(155\) | 8.05272 | 0.646810 | ||||||||
\(156\) | 0.612622 | 0.0490490 | ||||||||
\(157\) | −11.5499 | −0.921783 | −0.460891 | − | 0.887457i | \(-0.652470\pi\) | ||||
−0.460891 | + | 0.887457i | \(0.652470\pi\) | |||||||
\(158\) | −11.9388 | −0.949796 | ||||||||
\(159\) | −0.602053 | −0.0477459 | ||||||||
\(160\) | 6.38175 | 0.504522 | ||||||||
\(161\) | 1.88262 | 0.148371 | ||||||||
\(162\) | 15.8421 | 1.24467 | ||||||||
\(163\) | 18.4313 | 1.44365 | 0.721827 | − | 0.692073i | \(-0.243303\pi\) | ||||
0.721827 | + | 0.692073i | \(0.243303\pi\) | |||||||
\(164\) | −1.16643 | −0.0910832 | ||||||||
\(165\) | 0.586242 | 0.0456389 | ||||||||
\(166\) | 4.90393 | 0.380619 | ||||||||
\(167\) | 1.94262 | 0.150324 | 0.0751621 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751621 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(168\) | −0.241266 | −0.0186141 | ||||||||
\(169\) | −5.93699 | −0.456692 | ||||||||
\(170\) | 7.26792 | 0.557424 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −11.0791 | −0.844777 | ||||||||
\(173\) | −12.0515 | −0.916255 | −0.458128 | − | 0.888886i | \(-0.651480\pi\) | ||||
−0.458128 | + | 0.888886i | \(0.651480\pi\) | |||||||
\(174\) | 0.724864 | 0.0549518 | ||||||||
\(175\) | 1.07346 | 0.0811462 | ||||||||
\(176\) | 16.2497 | 1.22487 | ||||||||
\(177\) | −0.263312 | −0.0197918 | ||||||||
\(178\) | 1.43515 | 0.107569 | ||||||||
\(179\) | −18.3104 | −1.36858 | −0.684291 | − | 0.729209i | \(-0.739888\pi\) | ||||
−0.684291 | + | 0.729209i | \(0.739888\pi\) | |||||||
\(180\) | 3.86390 | 0.287998 | ||||||||
\(181\) | −25.6514 | −1.90665 | −0.953327 | − | 0.301941i | \(-0.902365\pi\) | ||||
−0.953327 | + | 0.301941i | \(0.902365\pi\) | |||||||
\(182\) | 5.18373 | 0.384244 | ||||||||
\(183\) | 2.43161 | 0.179750 | ||||||||
\(184\) | −2.22565 | −0.164077 | ||||||||
\(185\) | 5.64805 | 0.415253 | ||||||||
\(186\) | −2.59139 | −0.190010 | ||||||||
\(187\) | 13.2403 | 0.968226 | ||||||||
\(188\) | −8.19492 | −0.597676 | ||||||||
\(189\) | −1.13473 | −0.0825392 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.22171 | 0.667259 | 0.333630 | − | 0.942704i | \(-0.391726\pi\) | ||||
0.333630 | + | 0.942704i | \(0.391726\pi\) | |||||||
\(192\) | −0.314837 | −0.0227214 | ||||||||
\(193\) | 12.0020 | 0.863922 | 0.431961 | − | 0.901892i | \(-0.357822\pi\) | ||||
0.431961 | + | 0.901892i | \(0.357822\pi\) | |||||||
\(194\) | −34.0109 | −2.44184 | ||||||||
\(195\) | −0.470678 | −0.0337059 | ||||||||
\(196\) | −7.61119 | −0.543656 | ||||||||
\(197\) | −26.8972 | −1.91635 | −0.958174 | − | 0.286186i | \(-0.907613\pi\) | ||||
−0.958174 | + | 0.286186i | \(0.907613\pi\) | |||||||
\(198\) | 17.8552 | 1.26891 | ||||||||
\(199\) | −4.57394 | −0.324238 | −0.162119 | − | 0.986771i | \(-0.551833\pi\) | ||||
−0.162119 | + | 0.986771i | \(0.551833\pi\) | |||||||
\(200\) | −1.26906 | −0.0897358 | ||||||||
\(201\) | 2.27751 | 0.160643 | ||||||||
\(202\) | 34.3729 | 2.41847 | ||||||||
\(203\) | 2.41799 | 0.169709 | ||||||||
\(204\) | −0.922036 | −0.0645554 | ||||||||
\(205\) | 0.896172 | 0.0625914 | ||||||||
\(206\) | −21.1571 | −1.47408 | ||||||||
\(207\) | −5.20634 | −0.361865 | ||||||||
\(208\) | −13.0465 | −0.904609 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.345443 | −0.0238378 | ||||||||
\(211\) | −15.5626 | −1.07138 | −0.535688 | − | 0.844416i | \(-0.679948\pi\) | ||||
−0.535688 | + | 0.844416i | \(0.679948\pi\) | |||||||
\(212\) | −4.42461 | −0.303883 | ||||||||
\(213\) | 1.95279 | 0.133803 | ||||||||
\(214\) | 20.7065 | 1.41547 | ||||||||
\(215\) | 8.51211 | 0.580521 | ||||||||
\(216\) | 1.34148 | 0.0912762 | ||||||||
\(217\) | −8.64430 | −0.586813 | ||||||||
\(218\) | −23.1443 | −1.56753 | ||||||||
\(219\) | −0.462357 | −0.0312432 | ||||||||
\(220\) | 4.30841 | 0.290473 | ||||||||
\(221\) | −10.6303 | −0.715070 | ||||||||
\(222\) | −1.81756 | −0.121987 | ||||||||
\(223\) | −20.1284 | −1.34790 | −0.673949 | − | 0.738778i | \(-0.735403\pi\) | ||||
−0.673949 | + | 0.738778i | \(0.735403\pi\) | |||||||
\(224\) | −6.85058 | −0.457723 | ||||||||
\(225\) | −2.96863 | −0.197909 | ||||||||
\(226\) | 30.1433 | 2.00510 | ||||||||
\(227\) | 13.8680 | 0.920453 | 0.460226 | − | 0.887802i | \(-0.347768\pi\) | ||||
0.460226 | + | 0.887802i | \(0.347768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.70352 | 0.575145 | 0.287572 | − | 0.957759i | \(-0.407152\pi\) | ||||
0.287572 | + | 0.957759i | \(0.407152\pi\) | |||||||
\(230\) | −3.18666 | −0.210122 | ||||||||
\(231\) | −0.629309 | −0.0414055 | ||||||||
\(232\) | −2.85856 | −0.187674 | ||||||||
\(233\) | 15.7206 | 1.02989 | 0.514946 | − | 0.857223i | \(-0.327812\pi\) | ||||
0.514946 | + | 0.857223i | \(0.327812\pi\) | |||||||
\(234\) | −14.3355 | −0.937139 | ||||||||
\(235\) | 6.29616 | 0.410716 | ||||||||
\(236\) | −1.93513 | −0.125966 | ||||||||
\(237\) | −1.16366 | −0.0755881 | ||||||||
\(238\) | −7.80185 | −0.505719 | ||||||||
\(239\) | −13.8346 | −0.894887 | −0.447443 | − | 0.894312i | \(-0.647665\pi\) | ||||
−0.447443 | + | 0.894312i | \(0.647665\pi\) | |||||||
\(240\) | 0.869414 | 0.0561204 | ||||||||
\(241\) | 12.1767 | 0.784373 | 0.392187 | − | 0.919886i | \(-0.371719\pi\) | ||||
0.392187 | + | 0.919886i | \(0.371719\pi\) | |||||||
\(242\) | −0.0779453 | −0.00501051 | ||||||||
\(243\) | 4.71533 | 0.302489 | ||||||||
\(244\) | 17.8704 | 1.14403 | ||||||||
\(245\) | 5.84768 | 0.373594 | ||||||||
\(246\) | −0.288390 | −0.0183871 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 10.2194 | 0.648929 | ||||||||
\(249\) | 0.477983 | 0.0302910 | ||||||||
\(250\) | −1.81702 | −0.114919 | ||||||||
\(251\) | 4.38309 | 0.276658 | 0.138329 | − | 0.990386i | \(-0.455827\pi\) | ||||
0.138329 | + | 0.990386i | \(0.455827\pi\) | |||||||
\(252\) | −4.14775 | −0.261284 | ||||||||
\(253\) | −5.80528 | −0.364975 | ||||||||
\(254\) | −17.6676 | −1.10856 | ||||||||
\(255\) | 0.708401 | 0.0443618 | ||||||||
\(256\) | 20.8778 | 1.30486 | ||||||||
\(257\) | 23.1584 | 1.44458 | 0.722290 | − | 0.691590i | \(-0.243090\pi\) | ||||
0.722290 | + | 0.691590i | \(0.243090\pi\) | |||||||
\(258\) | −2.73922 | −0.170536 | ||||||||
\(259\) | −6.06298 | −0.376735 | ||||||||
\(260\) | −3.45911 | −0.214525 | ||||||||
\(261\) | −6.68688 | −0.413908 | ||||||||
\(262\) | 26.8743 | 1.66030 | ||||||||
\(263\) | 32.0083 | 1.97371 | 0.986857 | − | 0.161595i | \(-0.0516639\pi\) | ||||
0.986857 | + | 0.161595i | \(0.0516639\pi\) | |||||||
\(264\) | 0.743974 | 0.0457884 | ||||||||
\(265\) | 3.39943 | 0.208825 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.139884 | 0.00856074 | ||||||||
\(268\) | 16.7378 | 1.02243 | ||||||||
\(269\) | 3.78715 | 0.230907 | 0.115453 | − | 0.993313i | \(-0.463168\pi\) | ||||
0.115453 | + | 0.993313i | \(0.463168\pi\) | |||||||
\(270\) | 1.92072 | 0.116891 | ||||||||
\(271\) | 16.7383 | 1.01678 | 0.508389 | − | 0.861128i | \(-0.330241\pi\) | ||||
0.508389 | + | 0.861128i | \(0.330241\pi\) | |||||||
\(272\) | 19.6358 | 1.19059 | ||||||||
\(273\) | 0.505255 | 0.0305794 | ||||||||
\(274\) | 6.53455 | 0.394767 | ||||||||
\(275\) | −3.31015 | −0.199610 | ||||||||
\(276\) | 0.404272 | 0.0243343 | ||||||||
\(277\) | 11.5892 | 0.696330 | 0.348165 | − | 0.937433i | \(-0.386805\pi\) | ||||
0.348165 | + | 0.937433i | \(0.386805\pi\) | |||||||
\(278\) | −10.6381 | −0.638030 | ||||||||
\(279\) | 23.9056 | 1.43119 | ||||||||
\(280\) | 1.36228 | 0.0814121 | ||||||||
\(281\) | −2.55105 | −0.152183 | −0.0760916 | − | 0.997101i | \(-0.524244\pi\) | ||||
−0.0760916 | + | 0.997101i | \(0.524244\pi\) | |||||||
\(282\) | −2.02612 | −0.120654 | ||||||||
\(283\) | −0.518893 | −0.0308450 | −0.0154225 | − | 0.999881i | \(-0.504909\pi\) | ||||
−0.0154225 | + | 0.999881i | \(0.504909\pi\) | |||||||
\(284\) | 14.3515 | 0.851603 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.9847 | −0.945192 | ||||||||
\(287\) | −0.962007 | −0.0567855 | ||||||||
\(288\) | 18.9451 | 1.11635 | ||||||||
\(289\) | −1.00075 | −0.0588674 | ||||||||
\(290\) | −4.09287 | −0.240341 | ||||||||
\(291\) | −3.31503 | −0.194330 | ||||||||
\(292\) | −3.39795 | −0.198850 | ||||||||
\(293\) | 1.16042 | 0.0677925 | 0.0338963 | − | 0.999425i | \(-0.489208\pi\) | ||||
0.0338963 | + | 0.999425i | \(0.489208\pi\) | |||||||
\(294\) | −1.88180 | −0.109749 | ||||||||
\(295\) | 1.48676 | 0.0865627 | ||||||||
\(296\) | 7.16769 | 0.416614 | ||||||||
\(297\) | 3.49906 | 0.203036 | ||||||||
\(298\) | 18.2914 | 1.05959 | ||||||||
\(299\) | 4.66091 | 0.269547 | ||||||||
\(300\) | 0.230514 | 0.0133088 | ||||||||
\(301\) | −9.13743 | −0.526673 | ||||||||
\(302\) | −3.86395 | −0.222345 | ||||||||
\(303\) | 3.35031 | 0.192470 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.7298 | −0.786168 | ||||||||
\(306\) | 21.5758 | 1.23341 | ||||||||
\(307\) | −14.9713 | −0.854456 | −0.427228 | − | 0.904144i | \(-0.640510\pi\) | ||||
−0.427228 | + | 0.904144i | \(0.640510\pi\) | |||||||
\(308\) | −4.62492 | −0.263529 | ||||||||
\(309\) | −2.06217 | −0.117313 | ||||||||
\(310\) | 14.6320 | 0.831041 | ||||||||
\(311\) | 11.2063 | 0.635452 | 0.317726 | − | 0.948183i | \(-0.397081\pi\) | ||||
0.317726 | + | 0.948183i | \(0.397081\pi\) | |||||||
\(312\) | −0.597316 | −0.0338164 | ||||||||
\(313\) | 13.6242 | 0.770087 | 0.385044 | − | 0.922898i | \(-0.374186\pi\) | ||||
0.385044 | + | 0.922898i | \(0.374186\pi\) | |||||||
\(314\) | −20.9864 | −1.18433 | ||||||||
\(315\) | 3.18672 | 0.179551 | ||||||||
\(316\) | −8.55199 | −0.481087 | ||||||||
\(317\) | −8.68500 | −0.487798 | −0.243899 | − | 0.969801i | \(-0.578427\pi\) | ||||
−0.243899 | + | 0.969801i | \(0.578427\pi\) | |||||||
\(318\) | −1.09394 | −0.0613454 | ||||||||
\(319\) | −7.45615 | −0.417464 | ||||||||
\(320\) | 1.77769 | 0.0993759 | ||||||||
\(321\) | 2.01825 | 0.112648 | ||||||||
\(322\) | 3.42076 | 0.190632 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 11.3480 | 0.630446 | ||||||||
\(325\) | 2.65763 | 0.147419 | ||||||||
\(326\) | 33.4902 | 1.85485 | ||||||||
\(327\) | −2.25586 | −0.124749 | ||||||||
\(328\) | 1.13729 | 0.0627964 | ||||||||
\(329\) | −6.75869 | −0.372619 | ||||||||
\(330\) | 1.06522 | 0.0586382 | ||||||||
\(331\) | −23.3399 | −1.28288 | −0.641439 | − | 0.767174i | \(-0.721662\pi\) | ||||
−0.641439 | + | 0.767174i | \(0.721662\pi\) | |||||||
\(332\) | 3.51279 | 0.192790 | ||||||||
\(333\) | 16.7670 | 0.918826 | ||||||||
\(334\) | 3.52978 | 0.193141 | ||||||||
\(335\) | −12.8597 | −0.702600 | ||||||||
\(336\) | −0.933284 | −0.0509148 | ||||||||
\(337\) | −12.8541 | −0.700206 | −0.350103 | − | 0.936711i | \(-0.613853\pi\) | ||||
−0.350103 | + | 0.936711i | \(0.613853\pi\) | |||||||
\(338\) | −10.7877 | −0.586771 | ||||||||
\(339\) | 2.93805 | 0.159573 | ||||||||
\(340\) | 5.20618 | 0.282345 | ||||||||
\(341\) | 26.6557 | 1.44349 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.7915 | −0.744671 | ||||||||
\(344\) | 10.8023 | 0.582423 | ||||||||
\(345\) | −0.310602 | −0.0167223 | ||||||||
\(346\) | −21.8978 | −1.17723 | ||||||||
\(347\) | −32.4343 | −1.74116 | −0.870581 | − | 0.492025i | \(-0.836257\pi\) | ||||
−0.870581 | + | 0.492025i | \(0.836257\pi\) | |||||||
\(348\) | 0.519236 | 0.0278340 | ||||||||
\(349\) | 12.1085 | 0.648152 | 0.324076 | − | 0.946031i | \(-0.394947\pi\) | ||||
0.324076 | + | 0.946031i | \(0.394947\pi\) | |||||||
\(350\) | 1.95051 | 0.104259 | ||||||||
\(351\) | −2.80930 | −0.149950 | ||||||||
\(352\) | 21.1246 | 1.12594 | ||||||||
\(353\) | −23.0962 | −1.22929 | −0.614643 | − | 0.788805i | \(-0.710700\pi\) | ||||
−0.614643 | + | 0.788805i | \(0.710700\pi\) | |||||||
\(354\) | −0.478444 | −0.0254290 | ||||||||
\(355\) | −11.0262 | −0.585212 | ||||||||
\(356\) | 1.02803 | 0.0544856 | ||||||||
\(357\) | −0.760442 | −0.0402469 | ||||||||
\(358\) | −33.2704 | −1.75839 | ||||||||
\(359\) | −6.44613 | −0.340214 | −0.170107 | − | 0.985426i | \(-0.554411\pi\) | ||||
−0.170107 | + | 0.985426i | \(0.554411\pi\) | |||||||
\(360\) | −3.76736 | −0.198557 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −46.6092 | −2.44972 | ||||||||
\(363\) | −0.00759728 | −0.000398754 0 | ||||||||
\(364\) | 3.71322 | 0.194626 | ||||||||
\(365\) | 2.61065 | 0.136647 | ||||||||
\(366\) | 4.41829 | 0.230948 | ||||||||
\(367\) | −8.61879 | −0.449897 | −0.224949 | − | 0.974371i | \(-0.572221\pi\) | ||||
−0.224949 | + | 0.974371i | \(0.572221\pi\) | |||||||
\(368\) | −8.60941 | −0.448796 | ||||||||
\(369\) | 2.66041 | 0.138495 | ||||||||
\(370\) | 10.2626 | 0.533530 | ||||||||
\(371\) | −3.64916 | −0.189455 | ||||||||
\(372\) | −1.85627 | −0.0962430 | ||||||||
\(373\) | −9.50581 | −0.492192 | −0.246096 | − | 0.969245i | \(-0.579148\pi\) | ||||
−0.246096 | + | 0.969245i | \(0.579148\pi\) | |||||||
\(374\) | 24.0579 | 1.24401 | ||||||||
\(375\) | −0.177104 | −0.00914563 | ||||||||
\(376\) | 7.99017 | 0.412062 | ||||||||
\(377\) | 5.98634 | 0.308312 | ||||||||
\(378\) | −2.06182 | −0.106049 | ||||||||
\(379\) | −11.3635 | −0.583706 | −0.291853 | − | 0.956463i | \(-0.594272\pi\) | ||||
−0.291853 | + | 0.956463i | \(0.594272\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.72205 | −0.0882234 | ||||||||
\(382\) | 16.7561 | 0.857315 | ||||||||
\(383\) | −2.73290 | −0.139644 | −0.0698222 | − | 0.997559i | \(-0.522243\pi\) | ||||
−0.0698222 | + | 0.997559i | \(0.522243\pi\) | |||||||
\(384\) | 1.68841 | 0.0861611 | ||||||||
\(385\) | 3.55333 | 0.181094 | ||||||||
\(386\) | 21.8079 | 1.10999 | ||||||||
\(387\) | 25.2693 | 1.28451 | ||||||||
\(388\) | −24.3628 | −1.23683 | ||||||||
\(389\) | −22.1536 | −1.12323 | −0.561615 | − | 0.827398i | \(-0.689820\pi\) | ||||
−0.561615 | + | 0.827398i | \(0.689820\pi\) | |||||||
\(390\) | −0.855233 | −0.0433064 | ||||||||
\(391\) | −7.01496 | −0.354762 | ||||||||
\(392\) | 7.42103 | 0.374818 | ||||||||
\(393\) | 2.61943 | 0.132133 | ||||||||
\(394\) | −48.8729 | −2.46218 | ||||||||
\(395\) | 6.57050 | 0.330598 | ||||||||
\(396\) | 12.7901 | 0.642726 | ||||||||
\(397\) | 16.9608 | 0.851238 | 0.425619 | − | 0.904903i | \(-0.360056\pi\) | ||||
0.425619 | + | 0.904903i | \(0.360056\pi\) | |||||||
\(398\) | −8.31096 | −0.416591 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.90905 | −0.245453 | ||||||||
\(401\) | 6.61906 | 0.330540 | 0.165270 | − | 0.986248i | \(-0.447150\pi\) | ||||
0.165270 | + | 0.986248i | \(0.447150\pi\) | |||||||
\(402\) | 4.13828 | 0.206399 | ||||||||
\(403\) | −21.4012 | −1.06607 | ||||||||
\(404\) | 24.6221 | 1.22499 | ||||||||
\(405\) | −8.71869 | −0.433235 | ||||||||
\(406\) | 4.39354 | 0.218048 | ||||||||
\(407\) | 18.6959 | 0.926722 | ||||||||
\(408\) | 0.899000 | 0.0445071 | ||||||||
\(409\) | 35.7642 | 1.76842 | 0.884212 | − | 0.467085i | \(-0.154696\pi\) | ||||
0.884212 | + | 0.467085i | \(0.154696\pi\) | |||||||
\(410\) | 1.62837 | 0.0804192 | ||||||||
\(411\) | 0.636919 | 0.0314169 | ||||||||
\(412\) | −15.1553 | −0.746648 | ||||||||
\(413\) | −1.59599 | −0.0785333 | ||||||||
\(414\) | −9.46004 | −0.464935 | ||||||||
\(415\) | −2.69888 | −0.132483 | ||||||||
\(416\) | −16.9603 | −0.831549 | ||||||||
\(417\) | −1.03689 | −0.0507766 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.6681 | −1.44938 | −0.724691 | − | 0.689074i | \(-0.758018\pi\) | ||||
−0.724691 | + | 0.689074i | \(0.758018\pi\) | |||||||
\(420\) | −0.247449 | −0.0120743 | ||||||||
\(421\) | 12.3465 | 0.601733 | 0.300867 | − | 0.953666i | \(-0.402724\pi\) | ||||
0.300867 | + | 0.953666i | \(0.402724\pi\) | |||||||
\(422\) | −28.2777 | −1.37654 | ||||||||
\(423\) | 18.6910 | 0.908787 | ||||||||
\(424\) | 4.31406 | 0.209509 | ||||||||
\(425\) | −3.99991 | −0.194024 | ||||||||
\(426\) | 3.54827 | 0.171914 | ||||||||
\(427\) | 14.7385 | 0.713244 | ||||||||
\(428\) | 14.8325 | 0.716957 | ||||||||
\(429\) | −1.55802 | −0.0752217 | ||||||||
\(430\) | 15.4667 | 0.745871 | ||||||||
\(431\) | −17.0666 | −0.822069 | −0.411035 | − | 0.911620i | \(-0.634832\pi\) | ||||
−0.411035 | + | 0.911620i | \(0.634832\pi\) | |||||||
\(432\) | 5.18922 | 0.249666 | ||||||||
\(433\) | −2.80017 | −0.134568 | −0.0672839 | − | 0.997734i | \(-0.521433\pi\) | ||||
−0.0672839 | + | 0.997734i | \(0.521433\pi\) | |||||||
\(434\) | −15.7069 | −0.753955 | ||||||||
\(435\) | −0.398929 | −0.0191272 | ||||||||
\(436\) | −16.5788 | −0.793979 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.840113 | −0.0401421 | ||||||||
\(439\) | 21.2151 | 1.01254 | 0.506270 | − | 0.862375i | \(-0.331024\pi\) | ||||
0.506270 | + | 0.862375i | \(0.331024\pi\) | |||||||
\(440\) | −4.20077 | −0.200264 | ||||||||
\(441\) | 17.3596 | 0.826648 | ||||||||
\(442\) | −19.3155 | −0.918743 | ||||||||
\(443\) | 22.7790 | 1.08226 | 0.541131 | − | 0.840939i | \(-0.317996\pi\) | ||||
0.541131 | + | 0.840939i | \(0.317996\pi\) | |||||||
\(444\) | −1.30196 | −0.0617882 | ||||||||
\(445\) | −0.789838 | −0.0374419 | ||||||||
\(446\) | −36.5738 | −1.73182 | ||||||||
\(447\) | 1.78285 | 0.0843259 | ||||||||
\(448\) | −1.90828 | −0.0901580 | ||||||||
\(449\) | −29.7698 | −1.40492 | −0.702461 | − | 0.711722i | \(-0.747916\pi\) | ||||
−0.702461 | + | 0.711722i | \(0.747916\pi\) | |||||||
\(450\) | −5.39408 | −0.254279 | ||||||||
\(451\) | 2.96646 | 0.139685 | ||||||||
\(452\) | 21.5923 | 1.01562 | ||||||||
\(453\) | −0.376617 | −0.0176950 | ||||||||
\(454\) | 25.1985 | 1.18262 | ||||||||
\(455\) | −2.85287 | −0.133745 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −36.7666 | −1.71987 | −0.859934 | − | 0.510406i | \(-0.829495\pi\) | ||||
−0.859934 | + | 0.510406i | \(0.829495\pi\) | |||||||
\(458\) | 15.8145 | 0.738963 | ||||||||
\(459\) | 4.22818 | 0.197355 | ||||||||
\(460\) | −2.28268 | −0.106430 | ||||||||
\(461\) | −25.7299 | −1.19836 | −0.599181 | − | 0.800613i | \(-0.704507\pi\) | ||||
−0.599181 | + | 0.800613i | \(0.704507\pi\) | |||||||
\(462\) | −1.14347 | −0.0531990 | ||||||||
\(463\) | −35.5688 | −1.65302 | −0.826511 | − | 0.562920i | \(-0.809678\pi\) | ||||
−0.826511 | + | 0.562920i | \(0.809678\pi\) | |||||||
\(464\) | −11.0577 | −0.513341 | ||||||||
\(465\) | 1.42617 | 0.0661371 | ||||||||
\(466\) | 28.5647 | 1.32324 | ||||||||
\(467\) | −7.11571 | −0.329276 | −0.164638 | − | 0.986354i | \(-0.552646\pi\) | ||||
−0.164638 | + | 0.986354i | \(0.552646\pi\) | |||||||
\(468\) | −10.2688 | −0.474676 | ||||||||
\(469\) | 13.8044 | 0.637428 | ||||||||
\(470\) | 11.4403 | 0.527700 | ||||||||
\(471\) | −2.04554 | −0.0942534 | ||||||||
\(472\) | 1.88679 | 0.0868463 | ||||||||
\(473\) | 28.1764 | 1.29555 | ||||||||
\(474\) | −2.11440 | −0.0971178 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.58864 | −0.256155 | ||||||||
\(477\) | 10.0917 | 0.462065 | ||||||||
\(478\) | −25.1378 | −1.14978 | ||||||||
\(479\) | −8.81275 | −0.402665 | −0.201332 | − | 0.979523i | \(-0.564527\pi\) | ||||
−0.201332 | + | 0.979523i | \(0.564527\pi\) | |||||||
\(480\) | 1.13024 | 0.0515880 | ||||||||
\(481\) | −15.0104 | −0.684417 | ||||||||
\(482\) | 22.1254 | 1.00779 | ||||||||
\(483\) | 0.333420 | 0.0151711 | ||||||||
\(484\) | −0.0558339 | −0.00253791 | ||||||||
\(485\) | 18.7179 | 0.849937 | ||||||||
\(486\) | 8.56786 | 0.388646 | ||||||||
\(487\) | −4.78306 | −0.216741 | −0.108370 | − | 0.994111i | \(-0.534563\pi\) | ||||
−0.108370 | + | 0.994111i | \(0.534563\pi\) | |||||||
\(488\) | −17.4239 | −0.788744 | ||||||||
\(489\) | 3.26427 | 0.147615 | ||||||||
\(490\) | 10.6254 | 0.480005 | ||||||||
\(491\) | 10.0710 | 0.454497 | 0.227248 | − | 0.973837i | \(-0.427027\pi\) | ||||
0.227248 | + | 0.973837i | \(0.427027\pi\) | |||||||
\(492\) | −0.206581 | −0.00931337 | ||||||||
\(493\) | −9.00984 | −0.405783 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.82663 | −0.441674 | ||||||||
\(496\) | 39.5312 | 1.77500 | ||||||||
\(497\) | 11.8363 | 0.530929 | ||||||||
\(498\) | 0.868507 | 0.0389187 | ||||||||
\(499\) | −1.92213 | −0.0860462 | −0.0430231 | − | 0.999074i | \(-0.513699\pi\) | ||||
−0.0430231 | + | 0.999074i | \(0.513699\pi\) | |||||||
\(500\) | −1.30157 | −0.0582082 | ||||||||
\(501\) | 0.344046 | 0.0153708 | ||||||||
\(502\) | 7.96418 | 0.355459 | ||||||||
\(503\) | −16.2293 | −0.723629 | −0.361814 | − | 0.932250i | \(-0.617843\pi\) | ||||
−0.361814 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(504\) | 4.04412 | 0.180140 | ||||||||
\(505\) | −18.9172 | −0.841802 | ||||||||
\(506\) | −10.5483 | −0.468931 | ||||||||
\(507\) | −1.05147 | −0.0466973 | ||||||||
\(508\) | −12.6557 | −0.561506 | ||||||||
\(509\) | −33.8249 | −1.49926 | −0.749631 | − | 0.661856i | \(-0.769769\pi\) | ||||
−0.749631 | + | 0.661856i | \(0.769769\pi\) | |||||||
\(510\) | 1.28718 | 0.0569973 | ||||||||
\(511\) | −2.80243 | −0.123972 | ||||||||
\(512\) | 18.8686 | 0.833884 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 42.0793 | 1.85604 | ||||||||
\(515\) | 11.6438 | 0.513088 | ||||||||
\(516\) | −1.96216 | −0.0863794 | ||||||||
\(517\) | 20.8412 | 0.916596 | ||||||||
\(518\) | −11.0166 | −0.484040 | ||||||||
\(519\) | −2.13436 | −0.0936882 | ||||||||
\(520\) | 3.37268 | 0.147902 | ||||||||
\(521\) | 6.88838 | 0.301785 | 0.150893 | − | 0.988550i | \(-0.451785\pi\) | ||||
0.150893 | + | 0.988550i | \(0.451785\pi\) | |||||||
\(522\) | −12.1502 | −0.531801 | ||||||||
\(523\) | −20.1891 | −0.882809 | −0.441405 | − | 0.897308i | \(-0.645520\pi\) | ||||
−0.441405 | + | 0.897308i | \(0.645520\pi\) | |||||||
\(524\) | 19.2507 | 0.840970 | ||||||||
\(525\) | 0.190115 | 0.00829729 | ||||||||
\(526\) | 58.1598 | 2.53589 | ||||||||
\(527\) | 32.2101 | 1.40310 | ||||||||
\(528\) | 2.87789 | 0.125244 | ||||||||
\(529\) | −19.9242 | −0.866272 | ||||||||
\(530\) | 6.17684 | 0.268305 | ||||||||
\(531\) | 4.41366 | 0.191536 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.38169 | −0.103163 | ||||||||
\(534\) | 0.254172 | 0.0109991 | ||||||||
\(535\) | −11.3958 | −0.492684 | ||||||||
\(536\) | −16.3197 | −0.704902 | ||||||||
\(537\) | −3.24285 | −0.139939 | ||||||||
\(538\) | 6.88135 | 0.296676 | ||||||||
\(539\) | 19.3567 | 0.833752 | ||||||||
\(540\) | 1.37586 | 0.0592074 | ||||||||
\(541\) | 2.62143 | 0.112704 | 0.0563520 | − | 0.998411i | \(-0.482053\pi\) | ||||
0.0563520 | + | 0.998411i | \(0.482053\pi\) | |||||||
\(542\) | 30.4138 | 1.30639 | ||||||||
\(543\) | −4.54297 | −0.194958 | ||||||||
\(544\) | 25.5264 | 1.09444 | ||||||||
\(545\) | 12.7375 | 0.545613 | ||||||||
\(546\) | 0.918061 | 0.0392894 | ||||||||
\(547\) | 26.5701 | 1.13606 | 0.568029 | − | 0.823009i | \(-0.307706\pi\) | ||||
0.568029 | + | 0.823009i | \(0.307706\pi\) | |||||||
\(548\) | 4.68085 | 0.199956 | ||||||||
\(549\) | −40.7588 | −1.73954 | ||||||||
\(550\) | −6.01462 | −0.256464 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.394172 | −0.0167771 | ||||||||
\(553\) | −7.05319 | −0.299932 | ||||||||
\(554\) | 21.0579 | 0.894666 | ||||||||
\(555\) | 1.00029 | 0.0424601 | ||||||||
\(556\) | −7.62029 | −0.323172 | ||||||||
\(557\) | 17.4267 | 0.738394 | 0.369197 | − | 0.929351i | \(-0.379633\pi\) | ||||
0.369197 | + | 0.929351i | \(0.379633\pi\) | |||||||
\(558\) | 43.4370 | 1.83884 | ||||||||
\(559\) | −22.6220 | −0.956811 | ||||||||
\(560\) | 5.26969 | 0.222685 | ||||||||
\(561\) | 2.34491 | 0.0990023 | ||||||||
\(562\) | −4.63533 | −0.195529 | ||||||||
\(563\) | −2.25335 | −0.0949676 | −0.0474838 | − | 0.998872i | \(-0.515120\pi\) | ||||
−0.0474838 | + | 0.998872i | \(0.515120\pi\) | |||||||
\(564\) | −1.45135 | −0.0611131 | ||||||||
\(565\) | −16.5894 | −0.697921 | ||||||||
\(566\) | −0.942840 | −0.0396305 | ||||||||
\(567\) | 9.35919 | 0.393049 | ||||||||
\(568\) | −13.9929 | −0.587130 | ||||||||
\(569\) | −8.49148 | −0.355982 | −0.177991 | − | 0.984032i | \(-0.556960\pi\) | ||||
−0.177991 | + | 0.984032i | \(0.556960\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.29006 | −0.0958359 | −0.0479179 | − | 0.998851i | \(-0.515259\pi\) | ||||
−0.0479179 | + | 0.998851i | \(0.515259\pi\) | |||||||
\(572\) | −11.4502 | −0.478755 | ||||||||
\(573\) | 1.63320 | 0.0682281 | ||||||||
\(574\) | −1.74799 | −0.0729597 | ||||||||
\(575\) | 1.75378 | 0.0731378 | ||||||||
\(576\) | 5.27731 | 0.219888 | ||||||||
\(577\) | −2.00916 | −0.0836426 | −0.0418213 | − | 0.999125i | \(-0.513316\pi\) | ||||
−0.0418213 | + | 0.999125i | \(0.513316\pi\) | |||||||
\(578\) | −1.81838 | −0.0756346 | ||||||||
\(579\) | 2.12560 | 0.0883370 | ||||||||
\(580\) | −2.93181 | −0.121737 | ||||||||
\(581\) | 2.89715 | 0.120194 | ||||||||
\(582\) | −6.02348 | −0.249681 | ||||||||
\(583\) | 11.2526 | 0.466036 | ||||||||
\(584\) | 3.31305 | 0.137095 | ||||||||
\(585\) | 7.88954 | 0.326192 | ||||||||
\(586\) | 2.10851 | 0.0871018 | ||||||||
\(587\) | −7.38929 | −0.304989 | −0.152494 | − | 0.988304i | \(-0.548731\pi\) | ||||
−0.152494 | + | 0.988304i | \(0.548731\pi\) | |||||||
\(588\) | −1.34797 | −0.0555895 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.70148 | 0.111218 | ||||||||
\(591\) | −4.76361 | −0.195949 | ||||||||
\(592\) | 27.7266 | 1.13956 | ||||||||
\(593\) | −23.4755 | −0.964022 | −0.482011 | − | 0.876165i | \(-0.660094\pi\) | ||||
−0.482011 | + | 0.876165i | \(0.660094\pi\) | |||||||
\(594\) | 6.35788 | 0.260867 | ||||||||
\(595\) | 4.29375 | 0.176027 | ||||||||
\(596\) | 13.1025 | 0.536700 | ||||||||
\(597\) | −0.810065 | −0.0331538 | ||||||||
\(598\) | 8.46898 | 0.346322 | ||||||||
\(599\) | −32.2695 | −1.31850 | −0.659249 | − | 0.751925i | \(-0.729126\pi\) | ||||
−0.659249 | + | 0.751925i | \(0.729126\pi\) | |||||||
\(600\) | −0.224755 | −0.00917559 | ||||||||
\(601\) | 29.8357 | 1.21703 | 0.608513 | − | 0.793544i | \(-0.291767\pi\) | ||||
0.608513 | + | 0.793544i | \(0.291767\pi\) | |||||||
\(602\) | −16.6029 | −0.676685 | ||||||||
\(603\) | −38.1757 | −1.55464 | ||||||||
\(604\) | −2.76784 | −0.112622 | ||||||||
\(605\) | 0.0428972 | 0.00174402 | ||||||||
\(606\) | 6.08759 | 0.247291 | ||||||||
\(607\) | −9.11607 | −0.370010 | −0.185005 | − | 0.982738i | \(-0.559230\pi\) | ||||
−0.185005 | + | 0.982738i | \(0.559230\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.428236 | 0.0173530 | ||||||||
\(610\) | −24.9474 | −1.01009 | ||||||||
\(611\) | −16.7329 | −0.676939 | ||||||||
\(612\) | 15.4552 | 0.624741 | ||||||||
\(613\) | 42.0516 | 1.69845 | 0.849224 | − | 0.528033i | \(-0.177070\pi\) | ||||
0.849224 | + | 0.528033i | \(0.177070\pi\) | |||||||
\(614\) | −27.2032 | −1.09783 | ||||||||
\(615\) | 0.158716 | 0.00640004 | ||||||||
\(616\) | 4.50937 | 0.181688 | ||||||||
\(617\) | 33.6832 | 1.35604 | 0.678018 | − | 0.735045i | \(-0.262839\pi\) | ||||
0.678018 | + | 0.735045i | \(0.262839\pi\) | |||||||
\(618\) | −3.74701 | −0.150727 | ||||||||
\(619\) | −41.6917 | −1.67573 | −0.837865 | − | 0.545878i | \(-0.816196\pi\) | ||||
−0.837865 | + | 0.545878i | \(0.816196\pi\) | |||||||
\(620\) | 10.4812 | 0.420936 | ||||||||
\(621\) | −1.85387 | −0.0743933 | ||||||||
\(622\) | 20.3621 | 0.816447 | ||||||||
\(623\) | 0.847862 | 0.0339689 | ||||||||
\(624\) | −2.31058 | −0.0924973 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 24.7556 | 0.989431 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.0331 | −0.599884 | ||||||||
\(629\) | 22.5917 | 0.900790 | ||||||||
\(630\) | 5.79034 | 0.230693 | ||||||||
\(631\) | −8.32410 | −0.331377 | −0.165689 | − | 0.986178i | \(-0.552985\pi\) | ||||
−0.165689 | + | 0.986178i | \(0.552985\pi\) | |||||||
\(632\) | 8.33833 | 0.331681 | ||||||||
\(633\) | −2.75621 | −0.109549 | ||||||||
\(634\) | −15.7808 | −0.626737 | ||||||||
\(635\) | 9.72338 | 0.385861 | ||||||||
\(636\) | −0.783617 | −0.0310724 | ||||||||
\(637\) | −15.5410 | −0.615756 | ||||||||
\(638\) | −13.5480 | −0.536371 | ||||||||
\(639\) | −32.7329 | −1.29489 | ||||||||
\(640\) | −9.53340 | −0.376841 | ||||||||
\(641\) | −7.26032 | −0.286765 | −0.143383 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143383 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(642\) | 3.66721 | 0.144733 | ||||||||
\(643\) | 3.57195 | 0.140864 | 0.0704320 | − | 0.997517i | \(-0.477562\pi\) | ||||
0.0704320 | + | 0.997517i | \(0.477562\pi\) | |||||||
\(644\) | 2.45037 | 0.0965581 | ||||||||
\(645\) | 1.50753 | 0.0593590 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.0229 | 0.826494 | 0.413247 | − | 0.910619i | \(-0.364395\pi\) | ||||
0.413247 | + | 0.910619i | \(0.364395\pi\) | |||||||
\(648\) | −11.0645 | −0.434655 | ||||||||
\(649\) | 4.92141 | 0.193182 | ||||||||
\(650\) | 4.82898 | 0.189408 | ||||||||
\(651\) | −1.53094 | −0.0600024 | ||||||||
\(652\) | 23.9898 | 0.939512 | ||||||||
\(653\) | −23.2646 | −0.910413 | −0.455207 | − | 0.890386i | \(-0.650435\pi\) | ||||
−0.455207 | + | 0.890386i | \(0.650435\pi\) | |||||||
\(654\) | −4.09895 | −0.160282 | ||||||||
\(655\) | −14.7903 | −0.577905 | ||||||||
\(656\) | 4.39936 | 0.171766 | ||||||||
\(657\) | 7.75005 | 0.302358 | ||||||||
\(658\) | −12.2807 | −0.478752 | ||||||||
\(659\) | −23.5264 | −0.916457 | −0.458228 | − | 0.888834i | \(-0.651516\pi\) | ||||
−0.458228 | + | 0.888834i | \(0.651516\pi\) | |||||||
\(660\) | 0.763038 | 0.0297012 | ||||||||
\(661\) | −21.3079 | −0.828781 | −0.414390 | − | 0.910099i | \(-0.636005\pi\) | ||||
−0.414390 | + | 0.910099i | \(0.636005\pi\) | |||||||
\(662\) | −42.4092 | −1.64828 | ||||||||
\(663\) | −1.88267 | −0.0731168 | ||||||||
\(664\) | −3.42503 | −0.132917 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.4660 | 1.18054 | ||||||||
\(667\) | 3.95041 | 0.152961 | ||||||||
\(668\) | 2.52846 | 0.0978291 | ||||||||
\(669\) | −3.56483 | −0.137824 | ||||||||
\(670\) | −23.3664 | −0.902722 | ||||||||
\(671\) | −45.4478 | −1.75449 | ||||||||
\(672\) | −1.21327 | −0.0468028 | ||||||||
\(673\) | 7.74601 | 0.298587 | 0.149293 | − | 0.988793i | \(-0.452300\pi\) | ||||
0.149293 | + | 0.988793i | \(0.452300\pi\) | |||||||
\(674\) | −23.3562 | −0.899645 | ||||||||
\(675\) | −1.05707 | −0.0406867 | ||||||||
\(676\) | −7.72744 | −0.297209 | ||||||||
\(677\) | −3.31146 | −0.127270 | −0.0636348 | − | 0.997973i | \(-0.520269\pi\) | ||||
−0.0636348 | + | 0.997973i | \(0.520269\pi\) | |||||||
\(678\) | 5.33851 | 0.205024 | ||||||||
\(679\) | −20.0930 | −0.771099 | ||||||||
\(680\) | −5.07610 | −0.194660 | ||||||||
\(681\) | 2.45608 | 0.0941174 | ||||||||
\(682\) | 48.4341 | 1.85464 | ||||||||
\(683\) | −4.09964 | −0.156868 | −0.0784342 | − | 0.996919i | \(-0.524992\pi\) | ||||
−0.0784342 | + | 0.996919i | \(0.524992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.59629 | −0.137407 | ||||||||
\(686\) | −25.0595 | −0.956776 | ||||||||
\(687\) | 1.54143 | 0.0588092 | ||||||||
\(688\) | 41.7864 | 1.59309 | ||||||||
\(689\) | −9.03443 | −0.344184 | ||||||||
\(690\) | −0.564372 | −0.0214853 | ||||||||
\(691\) | −22.8437 | −0.869016 | −0.434508 | − | 0.900668i | \(-0.643078\pi\) | ||||
−0.434508 | + | 0.900668i | \(0.643078\pi\) | |||||||
\(692\) | −15.6859 | −0.596287 | ||||||||
\(693\) | 10.5485 | 0.400705 | ||||||||
\(694\) | −58.9338 | −2.23710 | ||||||||
\(695\) | 5.85467 | 0.222080 | ||||||||
\(696\) | −0.506264 | −0.0191899 | ||||||||
\(697\) | 3.58460 | 0.135777 | ||||||||
\(698\) | 22.0014 | 0.832765 | ||||||||
\(699\) | 2.78419 | 0.105308 | ||||||||
\(700\) | 1.39719 | 0.0528089 | ||||||||
\(701\) | −43.1824 | −1.63098 | −0.815488 | − | 0.578774i | \(-0.803531\pi\) | ||||
−0.815488 | + | 0.578774i | \(0.803531\pi\) | |||||||
\(702\) | −5.10457 | −0.192660 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.88442 | 0.221778 | ||||||||
\(705\) | 1.11508 | 0.0419962 | ||||||||
\(706\) | −41.9663 | −1.57942 | ||||||||
\(707\) | 20.3069 | 0.763718 | ||||||||
\(708\) | −0.342720 | −0.0128802 | ||||||||
\(709\) | 12.5505 | 0.471343 | 0.235671 | − | 0.971833i | \(-0.424271\pi\) | ||||
0.235671 | + | 0.971833i | \(0.424271\pi\) | |||||||
\(710\) | −20.0349 | −0.751898 | ||||||||
\(711\) | 19.5054 | 0.731510 | ||||||||
\(712\) | −1.00235 | −0.0375646 | ||||||||
\(713\) | −14.1227 | −0.528900 | ||||||||
\(714\) | −1.38174 | −0.0517103 | ||||||||
\(715\) | 8.79716 | 0.328995 | ||||||||
\(716\) | −23.8323 | −0.890656 | ||||||||
\(717\) | −2.45017 | −0.0915033 | ||||||||
\(718\) | −11.7128 | −0.437117 | ||||||||
\(719\) | 22.4682 | 0.837923 | 0.418961 | − | 0.908004i | \(-0.362394\pi\) | ||||
0.418961 | + | 0.908004i | \(0.362394\pi\) | |||||||
\(720\) | −14.5732 | −0.543110 | ||||||||
\(721\) | −12.4992 | −0.465495 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.15655 | 0.0802031 | ||||||||
\(724\) | −33.3872 | −1.24083 | ||||||||
\(725\) | 2.25251 | 0.0836562 | ||||||||
\(726\) | −0.0138044 | −0.000512331 0 | ||||||||
\(727\) | 29.5868 | 1.09731 | 0.548656 | − | 0.836048i | \(-0.315140\pi\) | ||||
0.548656 | + | 0.836048i | \(0.315140\pi\) | |||||||
\(728\) | −3.62045 | −0.134183 | ||||||||
\(729\) | −25.3210 | −0.937814 | ||||||||
\(730\) | 4.74360 | 0.175569 | ||||||||
\(731\) | 34.0476 | 1.25930 | ||||||||
\(732\) | 3.16492 | 0.116979 | ||||||||
\(733\) | 46.8312 | 1.72975 | 0.864876 | − | 0.501986i | \(-0.167397\pi\) | ||||
0.864876 | + | 0.501986i | \(0.167397\pi\) | |||||||
\(734\) | −15.6605 | −0.578041 | ||||||||
\(735\) | 1.03565 | 0.0382005 | ||||||||
\(736\) | −11.1922 | −0.412550 | ||||||||
\(737\) | −42.5675 | −1.56800 | ||||||||
\(738\) | 4.83402 | 0.177943 | ||||||||
\(739\) | 38.9919 | 1.43434 | 0.717170 | − | 0.696898i | \(-0.245437\pi\) | ||||
0.717170 | + | 0.696898i | \(0.245437\pi\) | |||||||
\(740\) | 7.35136 | 0.270241 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.63061 | −0.243417 | ||||||||
\(743\) | 12.1347 | 0.445177 | 0.222589 | − | 0.974912i | \(-0.428549\pi\) | ||||
0.222589 | + | 0.974912i | \(0.428549\pi\) | |||||||
\(744\) | 1.80989 | 0.0663538 | ||||||||
\(745\) | −10.0667 | −0.368814 | ||||||||
\(746\) | −17.2723 | −0.632383 | ||||||||
\(747\) | −8.01199 | −0.293143 | ||||||||
\(748\) | 17.2332 | 0.630109 | ||||||||
\(749\) | 12.2330 | 0.446984 | ||||||||
\(750\) | −0.321803 | −0.0117506 | ||||||||
\(751\) | −5.31316 | −0.193880 | −0.0969399 | − | 0.995290i | \(-0.530905\pi\) | ||||
−0.0969399 | + | 0.995290i | \(0.530905\pi\) | |||||||
\(752\) | 30.9082 | 1.12710 | ||||||||
\(753\) | 0.776265 | 0.0282887 | ||||||||
\(754\) | 10.8773 | 0.396129 | ||||||||
\(755\) | 2.12653 | 0.0773923 | ||||||||
\(756\) | −1.47693 | −0.0537155 | ||||||||
\(757\) | −21.2441 | −0.772129 | −0.386065 | − | 0.922472i | \(-0.626166\pi\) | ||||
−0.386065 | + | 0.922472i | \(0.626166\pi\) | |||||||
\(758\) | −20.6478 | −0.749963 | ||||||||
\(759\) | −1.02814 | −0.0373191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.4718 | 1.35835 | 0.679176 | − | 0.733975i | \(-0.262337\pi\) | ||||
0.679176 | + | 0.733975i | \(0.262337\pi\) | |||||||
\(762\) | −3.12901 | −0.113352 | ||||||||
\(763\) | −13.6732 | −0.495003 | ||||||||
\(764\) | 12.0027 | 0.434244 | ||||||||
\(765\) | −11.8743 | −0.429315 | ||||||||
\(766\) | −4.96574 | −0.179419 | ||||||||
\(767\) | −3.95127 | −0.142672 | ||||||||
\(768\) | 3.69755 | 0.133424 | ||||||||
\(769\) | −2.99630 | −0.108049 | −0.0540247 | − | 0.998540i | \(-0.517205\pi\) | ||||
−0.0540247 | + | 0.998540i | \(0.517205\pi\) | |||||||
\(770\) | 6.45648 | 0.232675 | ||||||||
\(771\) | 4.10145 | 0.147710 | ||||||||
\(772\) | 15.6215 | 0.562229 | ||||||||
\(773\) | 15.8749 | 0.570981 | 0.285491 | − | 0.958382i | \(-0.407843\pi\) | ||||
0.285491 | + | 0.958382i | \(0.407843\pi\) | |||||||
\(774\) | 45.9150 | 1.65038 | ||||||||
\(775\) | −8.05272 | −0.289262 | ||||||||
\(776\) | 23.7541 | 0.852722 | ||||||||
\(777\) | −1.07378 | −0.0385216 | ||||||||
\(778\) | −40.2536 | −1.44316 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.612622 | −0.0219354 | ||||||||
\(781\) | −36.4985 | −1.30602 | ||||||||
\(782\) | −12.7464 | −0.455809 | ||||||||
\(783\) | −2.38106 | −0.0850923 | ||||||||
\(784\) | 28.7066 | 1.02523 | ||||||||
\(785\) | 11.5499 | 0.412234 | ||||||||
\(786\) | 4.75956 | 0.169768 | ||||||||
\(787\) | 4.85017 | 0.172890 | 0.0864449 | − | 0.996257i | \(-0.472449\pi\) | ||||
0.0864449 | + | 0.996257i | \(0.472449\pi\) | |||||||
\(788\) | −35.0087 | −1.24713 | ||||||||
\(789\) | 5.66880 | 0.201815 | ||||||||
\(790\) | 11.9388 | 0.424762 | ||||||||
\(791\) | 17.8081 | 0.633183 | ||||||||
\(792\) | −12.4705 | −0.443121 | ||||||||
\(793\) | 36.4888 | 1.29576 | ||||||||
\(794\) | 30.8182 | 1.09370 | ||||||||
\(795\) | 0.602053 | 0.0213526 | ||||||||
\(796\) | −5.95333 | −0.211010 | ||||||||
\(797\) | 42.7169 | 1.51311 | 0.756555 | − | 0.653930i | \(-0.226881\pi\) | ||||
0.756555 | + | 0.653930i | \(0.226881\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.1840 | 0.890947 | ||||||||
\(800\) | −6.38175 | −0.225629 | ||||||||
\(801\) | −2.34474 | −0.0828473 | ||||||||
\(802\) | 12.0270 | 0.424688 | ||||||||
\(803\) | 8.64163 | 0.304957 | ||||||||
\(804\) | 2.96434 | 0.104544 | ||||||||
\(805\) | −1.88262 | −0.0663536 | ||||||||
\(806\) | −38.8864 | −1.36972 | ||||||||
\(807\) | 0.670721 | 0.0236105 | ||||||||
\(808\) | −24.0069 | −0.844561 | ||||||||
\(809\) | 15.3572 | 0.539930 | 0.269965 | − | 0.962870i | \(-0.412988\pi\) | ||||
0.269965 | + | 0.962870i | \(0.412988\pi\) | |||||||
\(810\) | −15.8421 | −0.556633 | ||||||||
\(811\) | −28.5751 | −1.00341 | −0.501703 | − | 0.865040i | \(-0.667293\pi\) | ||||
−0.501703 | + | 0.865040i | \(0.667293\pi\) | |||||||
\(812\) | 3.14719 | 0.110445 | ||||||||
\(813\) | 2.96442 | 0.103967 | ||||||||
\(814\) | 33.9709 | 1.19068 | ||||||||
\(815\) | −18.4313 | −0.645622 | ||||||||
\(816\) | 3.47758 | 0.121740 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 64.9843 | 2.27212 | ||||||||
\(819\) | −8.46912 | −0.295935 | ||||||||
\(820\) | 1.16643 | 0.0407337 | ||||||||
\(821\) | −0.898646 | −0.0313630 | −0.0156815 | − | 0.999877i | \(-0.504992\pi\) | ||||
−0.0156815 | + | 0.999877i | \(0.504992\pi\) | |||||||
\(822\) | 1.15730 | 0.0403654 | ||||||||
\(823\) | −36.7102 | −1.27964 | −0.639818 | − | 0.768526i | \(-0.720990\pi\) | ||||
−0.639818 | + | 0.768526i | \(0.720990\pi\) | |||||||
\(824\) | 14.7767 | 0.514769 | ||||||||
\(825\) | −0.586242 | −0.0204103 | ||||||||
\(826\) | −2.89994 | −0.100902 | ||||||||
\(827\) | −42.3584 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(828\) | −6.77643 | −0.235497 | ||||||||
\(829\) | 24.3888 | 0.847059 | 0.423530 | − | 0.905882i | \(-0.360791\pi\) | ||||
0.423530 | + | 0.905882i | \(0.360791\pi\) | |||||||
\(830\) | −4.90393 | −0.170218 | ||||||||
\(831\) | 2.05251 | 0.0712006 | ||||||||
\(832\) | −4.72445 | −0.163791 | ||||||||
\(833\) | 23.3902 | 0.810421 | ||||||||
\(834\) | −1.88405 | −0.0652393 | ||||||||
\(835\) | −1.94262 | −0.0672271 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.51230 | 0.294228 | ||||||||
\(838\) | −53.9077 | −1.86221 | ||||||||
\(839\) | −23.4810 | −0.810653 | −0.405327 | − | 0.914172i | \(-0.632842\pi\) | ||||
−0.405327 | + | 0.914172i | \(0.632842\pi\) | |||||||
\(840\) | 0.241266 | 0.00832448 | ||||||||
\(841\) | −23.9262 | −0.825041 | ||||||||
\(842\) | 22.4339 | 0.773125 | ||||||||
\(843\) | −0.451803 | −0.0155609 | ||||||||
\(844\) | −20.2559 | −0.697238 | ||||||||
\(845\) | 5.93699 | 0.204239 | ||||||||
\(846\) | 33.9620 | 1.16764 | ||||||||
\(847\) | −0.0460486 | −0.00158225 | ||||||||
\(848\) | 16.6880 | 0.573067 | ||||||||
\(849\) | −0.0918981 | −0.00315394 | ||||||||
\(850\) | −7.26792 | −0.249288 | ||||||||
\(851\) | −9.90545 | −0.339555 | ||||||||
\(852\) | 2.54171 | 0.0870775 | ||||||||
\(853\) | 5.83975 | 0.199949 | 0.0999745 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999745 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(854\) | 26.7801 | 0.916397 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.4619 | −0.494299 | ||||||||
\(857\) | −27.0008 | −0.922330 | −0.461165 | − | 0.887314i | \(-0.652568\pi\) | ||||
−0.461165 | + | 0.887314i | \(0.652568\pi\) | |||||||
\(858\) | −2.83095 | −0.0966470 | ||||||||
\(859\) | −3.18654 | −0.108723 | −0.0543617 | − | 0.998521i | \(-0.517312\pi\) | ||||
−0.0543617 | + | 0.998521i | \(0.517312\pi\) | |||||||
\(860\) | 11.0791 | 0.377796 | ||||||||
\(861\) | −0.170376 | −0.00580639 | ||||||||
\(862\) | −31.0104 | −1.05622 | ||||||||
\(863\) | 8.42174 | 0.286679 | 0.143340 | − | 0.989674i | \(-0.454216\pi\) | ||||
0.143340 | + | 0.989674i | \(0.454216\pi\) | |||||||
\(864\) | 6.74596 | 0.229502 | ||||||||
\(865\) | 12.0515 | 0.409762 | ||||||||
\(866\) | −5.08798 | −0.172897 | ||||||||
\(867\) | −0.177236 | −0.00601926 | ||||||||
\(868\) | −11.2512 | −0.381891 | ||||||||
\(869\) | 21.7493 | 0.737796 | ||||||||
\(870\) | −0.724864 | −0.0245752 | ||||||||
\(871\) | 34.1763 | 1.15802 | ||||||||
\(872\) | 16.1646 | 0.547401 | ||||||||
\(873\) | 55.5667 | 1.88065 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.07346 | −0.0362897 | ||||||||
\(876\) | −0.601791 | −0.0203326 | ||||||||
\(877\) | −41.8102 | −1.41183 | −0.705915 | − | 0.708297i | \(-0.749464\pi\) | ||||
−0.705915 | + | 0.708297i | \(0.749464\pi\) | |||||||
\(878\) | 38.5483 | 1.30094 | ||||||||
\(879\) | 0.205516 | 0.00693187 | ||||||||
\(880\) | −16.2497 | −0.547778 | ||||||||
\(881\) | −27.8465 | −0.938173 | −0.469087 | − | 0.883152i | \(-0.655417\pi\) | ||||
−0.469087 | + | 0.883152i | \(0.655417\pi\) | |||||||
\(882\) | 31.5428 | 1.06210 | ||||||||
\(883\) | 28.0898 | 0.945296 | 0.472648 | − | 0.881251i | \(-0.343298\pi\) | ||||
0.472648 | + | 0.881251i | \(0.343298\pi\) | |||||||
\(884\) | −13.8361 | −0.465358 | ||||||||
\(885\) | 0.263312 | 0.00885114 | ||||||||
\(886\) | 41.3899 | 1.39052 | ||||||||
\(887\) | 0.112362 | 0.00377274 | 0.00188637 | − | 0.999998i | \(-0.499400\pi\) | ||||
0.00188637 | + | 0.999998i | \(0.499400\pi\) | |||||||
\(888\) | 1.26943 | 0.0425993 | ||||||||
\(889\) | −10.4377 | −0.350069 | ||||||||
\(890\) | −1.43515 | −0.0481065 | ||||||||
\(891\) | −28.8602 | −0.966853 | ||||||||
\(892\) | −26.1986 | −0.877195 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 3.23948 | 0.108344 | ||||||||
\(895\) | 18.3104 | 0.612049 | ||||||||
\(896\) | 10.2338 | 0.341886 | ||||||||
\(897\) | 0.825466 | 0.0275615 | ||||||||
\(898\) | −54.0924 | −1.80509 | ||||||||
\(899\) | −18.1388 | −0.604964 | ||||||||
\(900\) | −3.86390 | −0.128797 | ||||||||
\(901\) | 13.5974 | 0.452995 | ||||||||
\(902\) | 5.39014 | 0.179472 | ||||||||
\(903\) | −1.61828 | −0.0538529 | ||||||||
\(904\) | −21.0529 | −0.700208 | ||||||||
\(905\) | 25.6514 | 0.852681 | ||||||||
\(906\) | −0.684322 | −0.0227351 | ||||||||
\(907\) | 36.0731 | 1.19779 | 0.598894 | − | 0.800829i | \(-0.295607\pi\) | ||||
0.598894 | + | 0.800829i | \(0.295607\pi\) | |||||||
\(908\) | 18.0503 | 0.599019 | ||||||||
\(909\) | −56.1581 | −1.86265 | ||||||||
\(910\) | −5.18373 | −0.171839 | ||||||||
\(911\) | −51.0528 | −1.69145 | −0.845727 | − | 0.533615i | \(-0.820833\pi\) | ||||
−0.845727 | + | 0.533615i | \(0.820833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.93370 | −0.295662 | ||||||||
\(914\) | −66.8057 | −2.20974 | ||||||||
\(915\) | −2.43161 | −0.0803866 | ||||||||
\(916\) | 11.3283 | 0.374297 | ||||||||
\(917\) | 15.8769 | 0.524300 | ||||||||
\(918\) | 7.68271 | 0.253567 | ||||||||
\(919\) | 41.2224 | 1.35980 | 0.679900 | − | 0.733305i | \(-0.262023\pi\) | ||||
0.679900 | + | 0.733305i | \(0.262023\pi\) | |||||||
\(920\) | 2.22565 | 0.0733774 | ||||||||
\(921\) | −2.65148 | −0.0873692 | ||||||||
\(922\) | −46.7519 | −1.53969 | ||||||||
\(923\) | 29.3037 | 0.964543 | ||||||||
\(924\) | −0.819093 | −0.0269462 | ||||||||
\(925\) | −5.64805 | −0.185707 | ||||||||
\(926\) | −64.6294 | −2.12385 | ||||||||
\(927\) | 34.5662 | 1.13530 | ||||||||
\(928\) | −14.3750 | −0.471882 | ||||||||
\(929\) | 12.9464 | 0.424757 | 0.212378 | − | 0.977187i | \(-0.431879\pi\) | ||||
0.212378 | + | 0.977187i | \(0.431879\pi\) | |||||||
\(930\) | 2.59139 | 0.0849749 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.4616 | 0.670241 | ||||||||
\(933\) | 1.98469 | 0.0649757 | ||||||||
\(934\) | −12.9294 | −0.423063 | ||||||||
\(935\) | −13.2403 | −0.433004 | ||||||||
\(936\) | 10.0123 | 0.327261 | ||||||||
\(937\) | 31.0792 | 1.01531 | 0.507657 | − | 0.861560i | \(-0.330512\pi\) | ||||
0.507657 | + | 0.861560i | \(0.330512\pi\) | |||||||
\(938\) | 25.0829 | 0.818987 | ||||||||
\(939\) | 2.41291 | 0.0787424 | ||||||||
\(940\) | 8.19492 | 0.267289 | ||||||||
\(941\) | 1.69686 | 0.0553160 | 0.0276580 | − | 0.999617i | \(-0.491195\pi\) | ||||
0.0276580 | + | 0.999617i | \(0.491195\pi\) | |||||||
\(942\) | −3.71679 | −0.121100 | ||||||||
\(943\) | −1.57169 | −0.0511813 | ||||||||
\(944\) | 7.29860 | 0.237549 | ||||||||
\(945\) | 1.13473 | 0.0369126 | ||||||||
\(946\) | 51.1971 | 1.66456 | ||||||||
\(947\) | −47.1251 | −1.53136 | −0.765680 | − | 0.643222i | \(-0.777597\pi\) | ||||
−0.765680 | + | 0.643222i | \(0.777597\pi\) | |||||||
\(948\) | −1.51459 | −0.0491917 | ||||||||
\(949\) | −6.93813 | −0.225221 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.53815 | −0.0498779 | ||||||||
\(952\) | 5.44901 | 0.176603 | ||||||||
\(953\) | 51.7089 | 1.67502 | 0.837508 | − | 0.546426i | \(-0.184012\pi\) | ||||
0.837508 | + | 0.546426i | \(0.184012\pi\) | |||||||
\(954\) | 18.3368 | 0.593675 | ||||||||
\(955\) | −9.22171 | −0.298408 | ||||||||
\(956\) | −18.0068 | −0.582381 | ||||||||
\(957\) | −1.32052 | −0.0426862 | ||||||||
\(958\) | −16.0130 | −0.517356 | ||||||||
\(959\) | 3.86049 | 0.124662 | ||||||||
\(960\) | 0.314837 | 0.0101613 | ||||||||
\(961\) | 33.8463 | 1.09182 | ||||||||
\(962\) | −27.2743 | −0.879360 | ||||||||
\(963\) | −33.8300 | −1.09016 | ||||||||
\(964\) | 15.8489 | 0.510460 | ||||||||
\(965\) | −12.0020 | −0.386357 | ||||||||
\(966\) | 0.605832 | 0.0194923 | ||||||||
\(967\) | −11.5790 | −0.372356 | −0.186178 | − | 0.982516i | \(-0.559610\pi\) | ||||
−0.186178 | + | 0.982516i | \(0.559610\pi\) | |||||||
\(968\) | 0.0544390 | 0.00174973 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.0109 | 1.09202 | ||||||||
\(971\) | −59.2842 | −1.90252 | −0.951260 | − | 0.308390i | \(-0.900210\pi\) | ||||
−0.951260 | + | 0.308390i | \(0.900210\pi\) | |||||||
\(972\) | 6.13735 | 0.196856 | ||||||||
\(973\) | −6.28478 | −0.201481 | ||||||||
\(974\) | −8.69093 | −0.278475 | ||||||||
\(975\) | 0.470678 | 0.0150738 | ||||||||
\(976\) | −67.4005 | −2.15744 | ||||||||
\(977\) | 21.9879 | 0.703454 | 0.351727 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351727 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(978\) | 5.93126 | 0.189661 | ||||||||
\(979\) | −2.61448 | −0.0835592 | ||||||||
\(980\) | 7.61119 | 0.243130 | ||||||||
\(981\) | 37.8129 | 1.20727 | ||||||||
\(982\) | 18.2992 | 0.583951 | ||||||||
\(983\) | 19.7062 | 0.628531 | 0.314265 | − | 0.949335i | \(-0.398242\pi\) | ||||
0.314265 | + | 0.949335i | \(0.398242\pi\) | |||||||
\(984\) | 0.201419 | 0.00642101 | ||||||||
\(985\) | 26.8972 | 0.857017 | ||||||||
\(986\) | −16.3711 | −0.521361 | ||||||||
\(987\) | −1.19699 | −0.0381007 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.9284 | −0.474695 | ||||||||
\(990\) | −17.8552 | −0.567476 | ||||||||
\(991\) | −46.7488 | −1.48503 | −0.742513 | − | 0.669832i | \(-0.766366\pi\) | ||||
−0.742513 | + | 0.669832i | \(0.766366\pi\) | |||||||
\(992\) | 51.3905 | 1.63165 | ||||||||
\(993\) | −4.13360 | −0.131176 | ||||||||
\(994\) | 21.5068 | 0.682153 | ||||||||
\(995\) | 4.57394 | 0.145004 | ||||||||
\(996\) | 0.622131 | 0.0197130 | ||||||||
\(997\) | 11.6112 | 0.367729 | 0.183865 | − | 0.982952i | \(-0.441139\pi\) | ||||
0.183865 | + | 0.982952i | \(0.441139\pi\) | |||||||
\(998\) | −3.49255 | −0.110555 | ||||||||
\(999\) | 5.97039 | 0.188895 |
(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 | 1805.2.a.t.1.8 | 9 | ||
5.4 | even | 2 | 9025.2.a.ce.1.2 | 9 | |||
19.4 | even | 9 | 95.2.k.b.16.3 | yes | 18 | ||
19.5 | even | 9 | 95.2.k.b.6.3 | ✓ | 18 | ||
19.18 | odd | 2 | 1805.2.a.u.1.2 | 9 | |||
57.5 | odd | 18 | 855.2.bs.b.766.1 | 18 | |||
57.23 | odd | 18 | 855.2.bs.b.586.1 | 18 | |||
95.4 | even | 18 | 475.2.l.b.301.1 | 18 | |||
95.23 | odd | 36 | 475.2.u.c.149.6 | 36 | |||
95.24 | even | 18 | 475.2.l.b.101.1 | 18 | |||
95.42 | odd | 36 | 475.2.u.c.149.1 | 36 | |||
95.43 | odd | 36 | 475.2.u.c.424.1 | 36 | |||
95.62 | odd | 36 | 475.2.u.c.424.6 | 36 | |||
95.94 | odd | 2 | 9025.2.a.cd.1.8 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.6.3 | ✓ | 18 | 19.5 | even | 9 | ||
95.2.k.b.16.3 | yes | 18 | 19.4 | even | 9 | ||
475.2.l.b.101.1 | 18 | 95.24 | even | 18 | |||
475.2.l.b.301.1 | 18 | 95.4 | even | 18 | |||
475.2.u.c.149.1 | 36 | 95.42 | odd | 36 | |||
475.2.u.c.149.6 | 36 | 95.23 | odd | 36 | |||
475.2.u.c.424.1 | 36 | 95.43 | odd | 36 | |||
475.2.u.c.424.6 | 36 | 95.62 | odd | 36 | |||
855.2.bs.b.586.1 | 18 | 57.23 | odd | 18 | |||
855.2.bs.b.766.1 | 18 | 57.5 | odd | 18 | |||
1805.2.a.t.1.8 | 9 | 1.1 | even | 1 | trivial | ||
1805.2.a.u.1.2 | 9 | 19.18 | odd | 2 | |||
9025.2.a.cd.1.8 | 9 | 95.94 | odd | 2 | |||
9025.2.a.ce.1.2 | 9 | 5.4 | even | 2 |