Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(1,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1815.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.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: | \(14.4928479669\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.469.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.39138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39138 | −1.69096 | −0.845481 | − | 0.534005i | \(-0.820686\pi\) | ||||
−0.845481 | + | 0.534005i | \(0.820686\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.71871 | 1.85935 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.39138 | −0.976278 | ||||||||
\(7\) | −5.11009 | −1.93143 | −0.965717 | − | 0.259599i | \(-0.916410\pi\) | ||||
−0.965717 | + | 0.259599i | \(0.916410\pi\) | |||||||
\(8\) | −4.11009 | −1.45314 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.39138 | −0.756222 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.71871 | 1.07350 | ||||||||
\(13\) | 5.43742 | 1.50807 | 0.754034 | − | 0.656835i | \(-0.228105\pi\) | ||||
0.754034 | + | 0.656835i | \(0.228105\pi\) | |||||||
\(14\) | 12.2202 | 3.26598 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 2.39138 | 0.597846 | ||||||||
\(17\) | 1.32733 | 0.321924 | 0.160962 | − | 0.986961i | \(-0.448540\pi\) | ||||
0.160962 | + | 0.986961i | \(0.448540\pi\) | |||||||
\(18\) | −2.39138 | −0.563654 | ||||||||
\(19\) | 1.67267 | 0.383737 | 0.191869 | − | 0.981421i | \(-0.438545\pi\) | ||||
0.191869 | + | 0.981421i | \(0.438545\pi\) | |||||||
\(20\) | 3.71871 | 0.831529 | ||||||||
\(21\) | −5.11009 | −1.11511 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.11009 | −0.439985 | −0.219992 | − | 0.975502i | \(-0.570603\pi\) | ||||
−0.219992 | + | 0.975502i | \(0.570603\pi\) | |||||||
\(24\) | −4.11009 | −0.838969 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −13.0029 | −2.55009 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −19.0029 | −3.59122 | ||||||||
\(29\) | 0.782765 | 0.145356 | 0.0726779 | − | 0.997355i | \(-0.476845\pi\) | ||||
0.0726779 | + | 0.997355i | \(0.476845\pi\) | |||||||
\(30\) | −2.39138 | −0.436605 | ||||||||
\(31\) | −4.43742 | −0.796984 | −0.398492 | − | 0.917172i | \(-0.630466\pi\) | ||||
−0.398492 | + | 0.917172i | \(0.630466\pi\) | |||||||
\(32\) | 2.50147 | 0.442202 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.17415 | −0.544362 | ||||||||
\(35\) | −5.11009 | −0.863763 | ||||||||
\(36\) | 3.71871 | 0.619785 | ||||||||
\(37\) | −11.3303 | −1.86269 | −0.931343 | − | 0.364143i | \(-0.881362\pi\) | ||||
−0.931343 | + | 0.364143i | \(0.881362\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 5.43742 | 0.870684 | ||||||||
\(40\) | −4.11009 | −0.649863 | ||||||||
\(41\) | 11.5655 | 1.80623 | 0.903116 | − | 0.429396i | \(-0.141274\pi\) | ||||
0.903116 | + | 0.429396i | \(0.141274\pi\) | |||||||
\(42\) | 12.2202 | 1.88562 | ||||||||
\(43\) | −4.78276 | −0.729365 | −0.364682 | − | 0.931132i | \(-0.618822\pi\) | ||||
−0.364682 | + | 0.931132i | \(0.618822\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 5.04604 | 0.743998 | ||||||||
\(47\) | 9.45544 | 1.37922 | 0.689609 | − | 0.724182i | \(-0.257783\pi\) | ||||
0.689609 | + | 0.724182i | \(0.257783\pi\) | |||||||
\(48\) | 2.39138 | 0.345166 | ||||||||
\(49\) | 19.1130 | 2.73043 | ||||||||
\(50\) | −2.39138 | −0.338193 | ||||||||
\(51\) | 1.32733 | 0.185863 | ||||||||
\(52\) | 20.2202 | 2.80404 | ||||||||
\(53\) | −8.23820 | −1.13160 | −0.565802 | − | 0.824541i | \(-0.691433\pi\) | ||||
−0.565802 | + | 0.824541i | \(0.691433\pi\) | |||||||
\(54\) | −2.39138 | −0.325426 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 21.0029 | 2.80664 | ||||||||
\(57\) | 1.67267 | 0.221551 | ||||||||
\(58\) | −1.87189 | −0.245791 | ||||||||
\(59\) | 10.0921 | 1.31388 | 0.656938 | − | 0.753945i | \(-0.271851\pi\) | ||||
0.656938 | + | 0.753945i | \(0.271851\pi\) | |||||||
\(60\) | 3.71871 | 0.480083 | ||||||||
\(61\) | −0.779816 | −0.0998452 | −0.0499226 | − | 0.998753i | \(-0.515897\pi\) | ||||
−0.0499226 | + | 0.998753i | \(0.515897\pi\) | |||||||
\(62\) | 10.6116 | 1.34767 | ||||||||
\(63\) | −5.11009 | −0.643811 | ||||||||
\(64\) | −10.7647 | −1.34559 | ||||||||
\(65\) | 5.43742 | 0.674429 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.45544 | −0.544318 | −0.272159 | − | 0.962252i | \(-0.587738\pi\) | ||||
−0.272159 | + | 0.962252i | \(0.587738\pi\) | |||||||
\(68\) | 4.93594 | 0.598571 | ||||||||
\(69\) | −2.11009 | −0.254025 | ||||||||
\(70\) | 12.2202 | 1.46059 | ||||||||
\(71\) | 12.9109 | 1.53224 | 0.766119 | − | 0.642698i | \(-0.222185\pi\) | ||||
0.766119 | + | 0.642698i | \(0.222185\pi\) | |||||||
\(72\) | −4.11009 | −0.484379 | ||||||||
\(73\) | 2.32733 | 0.272393 | 0.136197 | − | 0.990682i | \(-0.456512\pi\) | ||||
0.136197 | + | 0.990682i | \(0.456512\pi\) | |||||||
\(74\) | 27.0950 | 3.14973 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 6.22018 | 0.713504 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −13.0029 | −1.47229 | ||||||||
\(79\) | 1.12811 | 0.126922 | 0.0634612 | − | 0.997984i | \(-0.479786\pi\) | ||||
0.0634612 | + | 0.997984i | \(0.479786\pi\) | |||||||
\(80\) | 2.39138 | 0.267365 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −27.6576 | −3.05427 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | −19.0029 | −2.07339 | ||||||||
\(85\) | 1.32733 | 0.143969 | ||||||||
\(86\) | 11.4374 | 1.23333 | ||||||||
\(87\) | 0.782765 | 0.0839212 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7828 | 1.56697 | 0.783485 | − | 0.621411i | \(-0.213440\pi\) | ||||
0.783485 | + | 0.621411i | \(0.213440\pi\) | |||||||
\(90\) | −2.39138 | −0.252074 | ||||||||
\(91\) | −27.7857 | −2.91273 | ||||||||
\(92\) | −7.84682 | −0.818088 | ||||||||
\(93\) | −4.43742 | −0.460139 | ||||||||
\(94\) | −22.6116 | −2.33221 | ||||||||
\(95\) | 1.67267 | 0.171613 | ||||||||
\(96\) | 2.50147 | 0.255306 | ||||||||
\(97\) | 4.45544 | 0.452381 | 0.226191 | − | 0.974083i | \(-0.427373\pi\) | ||||
0.226191 | + | 0.974083i | \(0.427373\pi\) | |||||||
\(98\) | −45.7066 | −4.61706 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.71871 | 0.371871 | ||||||||
\(101\) | −6.87484 | −0.684072 | −0.342036 | − | 0.939687i | \(-0.611116\pi\) | ||||
−0.342036 | + | 0.939687i | \(0.611116\pi\) | |||||||
\(102\) | −3.17415 | −0.314287 | ||||||||
\(103\) | 10.5835 | 1.04283 | 0.521414 | − | 0.853304i | \(-0.325405\pi\) | ||||
0.521414 | + | 0.853304i | \(0.325405\pi\) | |||||||
\(104\) | −22.3483 | −2.19143 | ||||||||
\(105\) | −5.11009 | −0.498694 | ||||||||
\(106\) | 19.7007 | 1.91350 | ||||||||
\(107\) | −1.41940 | −0.137219 | −0.0686094 | − | 0.997644i | \(-0.521856\pi\) | ||||
−0.0686094 | + | 0.997644i | \(0.521856\pi\) | |||||||
\(108\) | 3.71871 | 0.357833 | ||||||||
\(109\) | 15.2022 | 1.45610 | 0.728052 | − | 0.685522i | \(-0.240426\pi\) | ||||
0.728052 | + | 0.685522i | \(0.240426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.3303 | −1.07542 | ||||||||
\(112\) | −12.2202 | −1.15470 | ||||||||
\(113\) | 2.01802 | 0.189839 | 0.0949196 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949196 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | −2.11009 | −0.196767 | ||||||||
\(116\) | 2.91087 | 0.270268 | ||||||||
\(117\) | 5.43742 | 0.502690 | ||||||||
\(118\) | −24.1340 | −2.22172 | ||||||||
\(119\) | −6.78276 | −0.621775 | ||||||||
\(120\) | −4.11009 | −0.375198 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.86484 | 0.168834 | ||||||||
\(123\) | 11.5655 | 1.04283 | ||||||||
\(124\) | −16.5015 | −1.48188 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 12.2202 | 1.08866 | ||||||||
\(127\) | −9.98493 | −0.886019 | −0.443010 | − | 0.896517i | \(-0.646089\pi\) | ||||
−0.443010 | + | 0.896517i | \(0.646089\pi\) | |||||||
\(128\) | 20.7397 | 1.83315 | ||||||||
\(129\) | −4.78276 | −0.421099 | ||||||||
\(130\) | −13.0029 | −1.14043 | ||||||||
\(131\) | −4.87484 | −0.425917 | −0.212958 | − | 0.977061i | \(-0.568310\pi\) | ||||
−0.212958 | + | 0.977061i | \(0.568310\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.54751 | −0.741163 | ||||||||
\(134\) | 10.6547 | 0.920422 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −5.45544 | −0.467800 | ||||||||
\(137\) | 19.7677 | 1.68887 | 0.844434 | − | 0.535659i | \(-0.179937\pi\) | ||||
0.844434 | + | 0.535659i | \(0.179937\pi\) | |||||||
\(138\) | 5.04604 | 0.429547 | ||||||||
\(139\) | −6.76475 | −0.573778 | −0.286889 | − | 0.957964i | \(-0.592621\pi\) | ||||
−0.286889 | + | 0.957964i | \(0.592621\pi\) | |||||||
\(140\) | −19.0029 | −1.60604 | ||||||||
\(141\) | 9.45544 | 0.796291 | ||||||||
\(142\) | −30.8748 | −2.59096 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.39138 | 0.199282 | ||||||||
\(145\) | 0.782765 | 0.0650051 | ||||||||
\(146\) | −5.56553 | −0.460607 | ||||||||
\(147\) | 19.1130 | 1.57642 | ||||||||
\(148\) | −42.1340 | −3.46339 | ||||||||
\(149\) | 0.128110 | 0.0104952 | 0.00524760 | − | 0.999986i | \(-0.498330\pi\) | ||||
0.00524760 | + | 0.999986i | \(0.498330\pi\) | |||||||
\(150\) | −2.39138 | −0.195256 | ||||||||
\(151\) | 5.45544 | 0.443957 | 0.221979 | − | 0.975052i | \(-0.428748\pi\) | ||||
0.221979 | + | 0.975052i | \(0.428748\pi\) | |||||||
\(152\) | −6.87484 | −0.557623 | ||||||||
\(153\) | 1.32733 | 0.107308 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.43742 | −0.356422 | ||||||||
\(156\) | 20.2202 | 1.61891 | ||||||||
\(157\) | 11.9849 | 0.956502 | 0.478251 | − | 0.878223i | \(-0.341271\pi\) | ||||
0.478251 | + | 0.878223i | \(0.341271\pi\) | |||||||
\(158\) | −2.69774 | −0.214621 | ||||||||
\(159\) | −8.23820 | −0.653332 | ||||||||
\(160\) | 2.50147 | 0.197759 | ||||||||
\(161\) | 10.7828 | 0.849801 | ||||||||
\(162\) | −2.39138 | −0.187885 | ||||||||
\(163\) | 9.98493 | 0.782080 | 0.391040 | − | 0.920374i | \(-0.372115\pi\) | ||||
0.391040 | + | 0.920374i | \(0.372115\pi\) | |||||||
\(164\) | 43.0088 | 3.35843 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.56553 | 0.742429 | ||||||||
\(167\) | 7.67562 | 0.593957 | 0.296979 | − | 0.954884i | \(-0.404021\pi\) | ||||
0.296979 | + | 0.954884i | \(0.404021\pi\) | |||||||
\(168\) | 21.0029 | 1.62041 | ||||||||
\(169\) | 16.5655 | 1.27427 | ||||||||
\(170\) | −3.17415 | −0.243446 | ||||||||
\(171\) | 1.67267 | 0.127912 | ||||||||
\(172\) | −17.7857 | −1.35615 | ||||||||
\(173\) | −4.69069 | −0.356627 | −0.178313 | − | 0.983974i | \(-0.557064\pi\) | ||||
−0.178313 | + | 0.983974i | \(0.557064\pi\) | |||||||
\(174\) | −1.87189 | −0.141908 | ||||||||
\(175\) | −5.11009 | −0.386287 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.0921 | 0.758567 | ||||||||
\(178\) | −35.3512 | −2.64969 | ||||||||
\(179\) | 11.4374 | 0.854873 | 0.427436 | − | 0.904045i | \(-0.359417\pi\) | ||||
0.427436 | + | 0.904045i | \(0.359417\pi\) | |||||||
\(180\) | 3.71871 | 0.277176 | ||||||||
\(181\) | −8.11304 | −0.603038 | −0.301519 | − | 0.953460i | \(-0.597494\pi\) | ||||
−0.301519 | + | 0.953460i | \(0.597494\pi\) | |||||||
\(182\) | 66.4463 | 4.92532 | ||||||||
\(183\) | −0.779816 | −0.0576456 | ||||||||
\(184\) | 8.67267 | 0.639358 | ||||||||
\(185\) | −11.3303 | −0.833018 | ||||||||
\(186\) | 10.6116 | 0.778078 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 35.1620 | 2.56445 | ||||||||
\(189\) | −5.11009 | −0.371705 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −1.00295 | −0.0725708 | −0.0362854 | − | 0.999341i | \(-0.511553\pi\) | ||||
−0.0362854 | + | 0.999341i | \(0.511553\pi\) | |||||||
\(192\) | −10.7647 | −0.776879 | ||||||||
\(193\) | 15.9849 | 1.15062 | 0.575310 | − | 0.817935i | \(-0.304881\pi\) | ||||
0.575310 | + | 0.817935i | \(0.304881\pi\) | |||||||
\(194\) | −10.6547 | −0.764960 | ||||||||
\(195\) | 5.43742 | 0.389382 | ||||||||
\(196\) | 71.0759 | 5.07685 | ||||||||
\(197\) | 16.2202 | 1.15564 | 0.577820 | − | 0.816164i | \(-0.303904\pi\) | ||||
0.577820 | + | 0.816164i | \(0.303904\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.34240 | −0.0951600 | −0.0475800 | − | 0.998867i | \(-0.515151\pi\) | ||||
−0.0475800 | + | 0.998867i | \(0.515151\pi\) | |||||||
\(200\) | −4.11009 | −0.290627 | ||||||||
\(201\) | −4.45544 | −0.314262 | ||||||||
\(202\) | 16.4404 | 1.15674 | ||||||||
\(203\) | −4.00000 | −0.280745 | ||||||||
\(204\) | 4.93594 | 0.345585 | ||||||||
\(205\) | 11.5655 | 0.807772 | ||||||||
\(206\) | −25.3093 | −1.76338 | ||||||||
\(207\) | −2.11009 | −0.146662 | ||||||||
\(208\) | 13.0029 | 0.901592 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 12.2202 | 0.843273 | ||||||||
\(211\) | 12.2231 | 0.841475 | 0.420738 | − | 0.907182i | \(-0.361771\pi\) | ||||
0.420738 | + | 0.907182i | \(0.361771\pi\) | |||||||
\(212\) | −30.6355 | −2.10405 | ||||||||
\(213\) | 12.9109 | 0.884639 | ||||||||
\(214\) | 3.39433 | 0.232032 | ||||||||
\(215\) | −4.78276 | −0.326182 | ||||||||
\(216\) | −4.11009 | −0.279656 | ||||||||
\(217\) | 22.6756 | 1.53932 | ||||||||
\(218\) | −36.3542 | −2.46222 | ||||||||
\(219\) | 2.32733 | 0.157266 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.21724 | 0.485484 | ||||||||
\(222\) | 27.0950 | 1.81850 | ||||||||
\(223\) | 11.2022 | 0.750153 | 0.375076 | − | 0.926994i | \(-0.377617\pi\) | ||||
0.375076 | + | 0.926994i | \(0.377617\pi\) | |||||||
\(224\) | −12.7828 | −0.854084 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −4.82585 | −0.321011 | ||||||||
\(227\) | −14.5446 | −0.965357 | −0.482678 | − | 0.875798i | \(-0.660336\pi\) | ||||
−0.482678 | + | 0.875798i | \(0.660336\pi\) | |||||||
\(228\) | 6.22018 | 0.411942 | ||||||||
\(229\) | −14.9289 | −0.986529 | −0.493265 | − | 0.869879i | \(-0.664197\pi\) | ||||
−0.493265 | + | 0.869879i | \(0.664197\pi\) | |||||||
\(230\) | 5.04604 | 0.332726 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.21724 | −0.211222 | ||||||||
\(233\) | 27.5475 | 1.80470 | 0.902349 | − | 0.431007i | \(-0.141841\pi\) | ||||
0.902349 | + | 0.431007i | \(0.141841\pi\) | |||||||
\(234\) | −13.0029 | −0.850029 | ||||||||
\(235\) | 9.45544 | 0.616805 | ||||||||
\(236\) | 37.5295 | 2.44296 | ||||||||
\(237\) | 1.12811 | 0.0732786 | ||||||||
\(238\) | 16.2202 | 1.05140 | ||||||||
\(239\) | 3.21724 | 0.208106 | 0.104053 | − | 0.994572i | \(-0.466819\pi\) | ||||
0.104053 | + | 0.994572i | \(0.466819\pi\) | |||||||
\(240\) | 2.39138 | 0.154363 | ||||||||
\(241\) | 21.5835 | 1.39032 | 0.695159 | − | 0.718856i | \(-0.255334\pi\) | ||||
0.695159 | + | 0.718856i | \(0.255334\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.89991 | −0.185648 | ||||||||
\(245\) | 19.1130 | 1.22109 | ||||||||
\(246\) | −27.6576 | −1.76338 | ||||||||
\(247\) | 9.09502 | 0.578702 | ||||||||
\(248\) | 18.2382 | 1.15813 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | −2.39138 | −0.151244 | ||||||||
\(251\) | −5.43742 | −0.343207 | −0.171603 | − | 0.985166i | \(-0.554895\pi\) | ||||
−0.171603 | + | 0.985166i | \(0.554895\pi\) | |||||||
\(252\) | −19.0029 | −1.19707 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 23.8778 | 1.49823 | ||||||||
\(255\) | 1.32733 | 0.0831205 | ||||||||
\(256\) | −28.0670 | −1.75419 | ||||||||
\(257\) | −12.2022 | −0.761150 | −0.380575 | − | 0.924750i | \(-0.624274\pi\) | ||||
−0.380575 | + | 0.924750i | \(0.624274\pi\) | |||||||
\(258\) | 11.4374 | 0.712063 | ||||||||
\(259\) | 57.8988 | 3.59765 | ||||||||
\(260\) | 20.2202 | 1.25400 | ||||||||
\(261\) | 0.782765 | 0.0484519 | ||||||||
\(262\) | 11.6576 | 0.720209 | ||||||||
\(263\) | 1.85387 | 0.114315 | 0.0571573 | − | 0.998365i | \(-0.481796\pi\) | ||||
0.0571573 | + | 0.998365i | \(0.481796\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.23820 | −0.506069 | ||||||||
\(266\) | 20.4404 | 1.25328 | ||||||||
\(267\) | 14.7828 | 0.904691 | ||||||||
\(268\) | −16.5685 | −1.01208 | ||||||||
\(269\) | −9.74968 | −0.594448 | −0.297224 | − | 0.954808i | \(-0.596061\pi\) | ||||
−0.297224 | + | 0.954808i | \(0.596061\pi\) | |||||||
\(270\) | −2.39138 | −0.145535 | ||||||||
\(271\) | −15.2051 | −0.923645 | −0.461822 | − | 0.886972i | \(-0.652804\pi\) | ||||
−0.461822 | + | 0.886972i | \(0.652804\pi\) | |||||||
\(272\) | 3.17415 | 0.192461 | ||||||||
\(273\) | −27.7857 | −1.68167 | ||||||||
\(274\) | −47.2721 | −2.85581 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.84682 | −0.472323 | ||||||||
\(277\) | 12.3332 | 0.741032 | 0.370516 | − | 0.928826i | \(-0.379181\pi\) | ||||
0.370516 | + | 0.928826i | \(0.379181\pi\) | |||||||
\(278\) | 16.1771 | 0.970238 | ||||||||
\(279\) | −4.43742 | −0.265661 | ||||||||
\(280\) | 21.0029 | 1.25517 | ||||||||
\(281\) | −14.7828 | −0.881866 | −0.440933 | − | 0.897540i | \(-0.645352\pi\) | ||||
−0.440933 | + | 0.897540i | \(0.645352\pi\) | |||||||
\(282\) | −22.6116 | −1.34650 | ||||||||
\(283\) | −29.0239 | −1.72529 | −0.862646 | − | 0.505808i | \(-0.831195\pi\) | ||||
−0.862646 | + | 0.505808i | \(0.831195\pi\) | |||||||
\(284\) | 48.0118 | 2.84898 | ||||||||
\(285\) | 1.67267 | 0.0990806 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −59.1009 | −3.48862 | ||||||||
\(288\) | 2.50147 | 0.147401 | ||||||||
\(289\) | −15.2382 | −0.896365 | ||||||||
\(290\) | −1.87189 | −0.109921 | ||||||||
\(291\) | 4.45544 | 0.261182 | ||||||||
\(292\) | 8.65465 | 0.506475 | ||||||||
\(293\) | −9.32733 | −0.544908 | −0.272454 | − | 0.962169i | \(-0.587835\pi\) | ||||
−0.272454 | + | 0.962169i | \(0.587835\pi\) | |||||||
\(294\) | −45.7066 | −2.66566 | ||||||||
\(295\) | 10.0921 | 0.587583 | ||||||||
\(296\) | 46.5685 | 2.70674 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.306360 | −0.0177470 | ||||||||
\(299\) | −11.4735 | −0.663527 | ||||||||
\(300\) | 3.71871 | 0.214700 | ||||||||
\(301\) | 24.4404 | 1.40872 | ||||||||
\(302\) | −13.0460 | −0.750715 | ||||||||
\(303\) | −6.87484 | −0.394949 | ||||||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | −0.779816 | −0.0446521 | ||||||||
\(306\) | −3.17415 | −0.181454 | ||||||||
\(307\) | 13.2382 | 0.755544 | 0.377772 | − | 0.925899i | \(-0.376690\pi\) | ||||
0.377772 | + | 0.925899i | \(0.376690\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.5835 | 0.602077 | ||||||||
\(310\) | 10.6116 | 0.602696 | ||||||||
\(311\) | 2.78276 | 0.157796 | 0.0788981 | − | 0.996883i | \(-0.474860\pi\) | ||||
0.0788981 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(312\) | −22.3483 | −1.26522 | ||||||||
\(313\) | 3.87189 | 0.218852 | 0.109426 | − | 0.993995i | \(-0.465099\pi\) | ||||
0.109426 | + | 0.993995i | \(0.465099\pi\) | |||||||
\(314\) | −28.6606 | −1.61741 | ||||||||
\(315\) | −5.11009 | −0.287921 | ||||||||
\(316\) | 4.19511 | 0.235994 | ||||||||
\(317\) | −9.10714 | −0.511508 | −0.255754 | − | 0.966742i | \(-0.582324\pi\) | ||||
−0.255754 | + | 0.966742i | \(0.582324\pi\) | |||||||
\(318\) | 19.7007 | 1.10476 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.7647 | −0.601768 | ||||||||
\(321\) | −1.41940 | −0.0792233 | ||||||||
\(322\) | −25.7857 | −1.43698 | ||||||||
\(323\) | 2.22018 | 0.123534 | ||||||||
\(324\) | 3.71871 | 0.206595 | ||||||||
\(325\) | 5.43742 | 0.301614 | ||||||||
\(326\) | −23.8778 | −1.32247 | ||||||||
\(327\) | 15.2022 | 0.840682 | ||||||||
\(328\) | −47.5354 | −2.62470 | ||||||||
\(329\) | −48.3182 | −2.66387 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.21724 | −0.341730 | −0.170865 | − | 0.985294i | \(-0.554656\pi\) | ||||
−0.170865 | + | 0.985294i | \(0.554656\pi\) | |||||||
\(332\) | −14.8748 | −0.816363 | ||||||||
\(333\) | −11.3303 | −0.620895 | ||||||||
\(334\) | −18.3553 | −1.00436 | ||||||||
\(335\) | −4.45544 | −0.243427 | ||||||||
\(336\) | −12.2202 | −0.666666 | ||||||||
\(337\) | 26.9879 | 1.47012 | 0.735062 | − | 0.678000i | \(-0.237153\pi\) | ||||
0.735062 | + | 0.678000i | \(0.237153\pi\) | |||||||
\(338\) | −39.6145 | −2.15475 | ||||||||
\(339\) | 2.01802 | 0.109604 | ||||||||
\(340\) | 4.93594 | 0.267689 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | −61.8988 | −3.34222 | ||||||||
\(344\) | 19.6576 | 1.05987 | ||||||||
\(345\) | −2.11009 | −0.113604 | ||||||||
\(346\) | 11.2172 | 0.603042 | ||||||||
\(347\) | −12.1160 | −0.650420 | −0.325210 | − | 0.945642i | \(-0.605435\pi\) | ||||
−0.325210 | + | 0.945642i | \(0.605435\pi\) | |||||||
\(348\) | 2.91087 | 0.156039 | ||||||||
\(349\) | 23.4764 | 1.25666 | 0.628332 | − | 0.777946i | \(-0.283738\pi\) | ||||
0.628332 | + | 0.777946i | \(0.283738\pi\) | |||||||
\(350\) | 12.2202 | 0.653196 | ||||||||
\(351\) | 5.43742 | 0.290228 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.5115 | 0.932042 | 0.466021 | − | 0.884774i | \(-0.345687\pi\) | ||||
0.466021 | + | 0.884774i | \(0.345687\pi\) | |||||||
\(354\) | −24.1340 | −1.28271 | ||||||||
\(355\) | 12.9109 | 0.685238 | ||||||||
\(356\) | 54.9728 | 2.91355 | ||||||||
\(357\) | −6.78276 | −0.358982 | ||||||||
\(358\) | −27.3512 | −1.44556 | ||||||||
\(359\) | 12.8388 | 0.677606 | 0.338803 | − | 0.940857i | \(-0.389978\pi\) | ||||
0.338803 | + | 0.940857i | \(0.389978\pi\) | |||||||
\(360\) | −4.11009 | −0.216621 | ||||||||
\(361\) | −16.2022 | −0.852746 | ||||||||
\(362\) | 19.4014 | 1.01971 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −103.327 | −5.41581 | ||||||||
\(365\) | 2.32733 | 0.121818 | ||||||||
\(366\) | 1.86484 | 0.0974766 | ||||||||
\(367\) | −4.81880 | −0.251539 | −0.125770 | − | 0.992059i | \(-0.540140\pi\) | ||||
−0.125770 | + | 0.992059i | \(0.540140\pi\) | |||||||
\(368\) | −5.04604 | −0.263043 | ||||||||
\(369\) | 11.5655 | 0.602077 | ||||||||
\(370\) | 27.0950 | 1.40860 | ||||||||
\(371\) | 42.0980 | 2.18562 | ||||||||
\(372\) | −16.5015 | −0.855562 | ||||||||
\(373\) | 16.1071 | 0.833996 | 0.416998 | − | 0.908907i | \(-0.363082\pi\) | ||||
0.416998 | + | 0.908907i | \(0.363082\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −38.8627 | −2.00419 | ||||||||
\(377\) | 4.25622 | 0.219206 | ||||||||
\(378\) | 12.2202 | 0.628538 | ||||||||
\(379\) | 8.36631 | 0.429749 | 0.214874 | − | 0.976642i | \(-0.431066\pi\) | ||||
0.214874 | + | 0.976642i | \(0.431066\pi\) | |||||||
\(380\) | 6.22018 | 0.319089 | ||||||||
\(381\) | −9.98493 | −0.511544 | ||||||||
\(382\) | 2.39843 | 0.122715 | ||||||||
\(383\) | −11.3453 | −0.579720 | −0.289860 | − | 0.957069i | \(-0.593609\pi\) | ||||
−0.289860 | + | 0.957069i | \(0.593609\pi\) | |||||||
\(384\) | 20.7397 | 1.05837 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −38.2261 | −1.94566 | ||||||||
\(387\) | −4.78276 | −0.243122 | ||||||||
\(388\) | 16.5685 | 0.841137 | ||||||||
\(389\) | 5.18120 | 0.262697 | 0.131349 | − | 0.991336i | \(-0.458069\pi\) | ||||
0.131349 | + | 0.991336i | \(0.458069\pi\) | |||||||
\(390\) | −13.0029 | −0.658430 | ||||||||
\(391\) | −2.80078 | −0.141642 | ||||||||
\(392\) | −78.5564 | −3.96770 | ||||||||
\(393\) | −4.87484 | −0.245903 | ||||||||
\(394\) | −38.7887 | −1.95414 | ||||||||
\(395\) | 1.12811 | 0.0567614 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.767696 | 0.0385295 | 0.0192648 | − | 0.999814i | \(-0.493867\pi\) | ||||
0.0192648 | + | 0.999814i | \(0.493867\pi\) | |||||||
\(398\) | 3.21018 | 0.160912 | ||||||||
\(399\) | −8.54751 | −0.427911 | ||||||||
\(400\) | 2.39138 | 0.119569 | ||||||||
\(401\) | 18.0360 | 0.900677 | 0.450338 | − | 0.892858i | \(-0.351303\pi\) | ||||
0.450338 | + | 0.892858i | \(0.351303\pi\) | |||||||
\(402\) | 10.6547 | 0.531406 | ||||||||
\(403\) | −24.1281 | −1.20191 | ||||||||
\(404\) | −25.5655 | −1.27193 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 9.56553 | 0.474729 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.45544 | −0.270084 | ||||||||
\(409\) | −2.55963 | −0.126566 | −0.0632828 | − | 0.997996i | \(-0.520157\pi\) | ||||
−0.0632828 | + | 0.997996i | \(0.520157\pi\) | |||||||
\(410\) | −27.6576 | −1.36591 | ||||||||
\(411\) | 19.7677 | 0.975069 | ||||||||
\(412\) | 39.3571 | 1.93899 | ||||||||
\(413\) | −51.5714 | −2.53766 | ||||||||
\(414\) | 5.04604 | 0.247999 | ||||||||
\(415\) | −4.00000 | −0.196352 | ||||||||
\(416\) | 13.6016 | 0.666872 | ||||||||
\(417\) | −6.76475 | −0.331271 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0950 | 0.542027 | 0.271014 | − | 0.962575i | \(-0.412641\pi\) | ||||
0.271014 | + | 0.962575i | \(0.412641\pi\) | |||||||
\(420\) | −19.0029 | −0.927249 | ||||||||
\(421\) | 15.3332 | 0.747296 | 0.373648 | − | 0.927571i | \(-0.378107\pi\) | ||||
0.373648 | + | 0.927571i | \(0.378107\pi\) | |||||||
\(422\) | −29.2302 | −1.42290 | ||||||||
\(423\) | 9.45544 | 0.459739 | ||||||||
\(424\) | 33.8598 | 1.64438 | ||||||||
\(425\) | 1.32733 | 0.0643848 | ||||||||
\(426\) | −30.8748 | −1.49589 | ||||||||
\(427\) | 3.98493 | 0.192844 | ||||||||
\(428\) | −5.27834 | −0.255138 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.4374 | 0.551561 | ||||||||
\(431\) | −3.68774 | −0.177632 | −0.0888161 | − | 0.996048i | \(-0.528308\pi\) | ||||
−0.0888161 | + | 0.996048i | \(0.528308\pi\) | |||||||
\(432\) | 2.39138 | 0.115055 | ||||||||
\(433\) | 27.9489 | 1.34314 | 0.671569 | − | 0.740942i | \(-0.265621\pi\) | ||||
0.671569 | + | 0.740942i | \(0.265621\pi\) | |||||||
\(434\) | −54.2261 | −2.60294 | ||||||||
\(435\) | 0.782765 | 0.0375307 | ||||||||
\(436\) | 56.5324 | 2.70741 | ||||||||
\(437\) | −3.52949 | −0.168839 | ||||||||
\(438\) | −5.56553 | −0.265931 | ||||||||
\(439\) | −24.0029 | −1.14560 | −0.572799 | − | 0.819696i | \(-0.694142\pi\) | ||||
−0.572799 | + | 0.819696i | \(0.694142\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.1130 | 0.910145 | ||||||||
\(442\) | −17.2592 | −0.820935 | ||||||||
\(443\) | −6.22018 | −0.295530 | −0.147765 | − | 0.989023i | \(-0.547208\pi\) | ||||
−0.147765 | + | 0.989023i | \(0.547208\pi\) | |||||||
\(444\) | −42.1340 | −1.99959 | ||||||||
\(445\) | 14.7828 | 0.700770 | ||||||||
\(446\) | −26.7887 | −1.26848 | ||||||||
\(447\) | 0.128110 | 0.00605940 | ||||||||
\(448\) | 55.0088 | 2.59892 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | −2.39138 | −0.112731 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.50442 | 0.352978 | ||||||||
\(453\) | 5.45544 | 0.256319 | ||||||||
\(454\) | 34.7816 | 1.63238 | ||||||||
\(455\) | −27.7857 | −1.30261 | ||||||||
\(456\) | −6.87484 | −0.321944 | ||||||||
\(457\) | −16.8748 | −0.789372 | −0.394686 | − | 0.918816i | \(-0.629147\pi\) | ||||
−0.394686 | + | 0.918816i | \(0.629147\pi\) | |||||||
\(458\) | 35.7007 | 1.66818 | ||||||||
\(459\) | 1.32733 | 0.0619543 | ||||||||
\(460\) | −7.84682 | −0.365860 | ||||||||
\(461\) | 23.8719 | 1.11182 | 0.555912 | − | 0.831241i | \(-0.312369\pi\) | ||||
0.555912 | + | 0.831241i | \(0.312369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.2261 | 1.21883 | 0.609415 | − | 0.792852i | \(-0.291404\pi\) | ||||
0.609415 | + | 0.792852i | \(0.291404\pi\) | |||||||
\(464\) | 1.87189 | 0.0869003 | ||||||||
\(465\) | −4.43742 | −0.205780 | ||||||||
\(466\) | −65.8766 | −3.05168 | ||||||||
\(467\) | −34.5505 | −1.59880 | −0.799402 | − | 0.600796i | \(-0.794850\pi\) | ||||
−0.799402 | + | 0.600796i | \(0.794850\pi\) | |||||||
\(468\) | 20.2202 | 0.934678 | ||||||||
\(469\) | 22.7677 | 1.05131 | ||||||||
\(470\) | −22.6116 | −1.04299 | ||||||||
\(471\) | 11.9849 | 0.552236 | ||||||||
\(472\) | −41.4794 | −1.90924 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.69774 | −0.123911 | ||||||||
\(475\) | 1.67267 | 0.0767475 | ||||||||
\(476\) | −25.2231 | −1.15610 | ||||||||
\(477\) | −8.23820 | −0.377201 | ||||||||
\(478\) | −7.69364 | −0.351899 | ||||||||
\(479\) | −35.2290 | −1.60966 | −0.804828 | − | 0.593508i | \(-0.797742\pi\) | ||||
−0.804828 | + | 0.593508i | \(0.797742\pi\) | |||||||
\(480\) | 2.50147 | 0.114176 | ||||||||
\(481\) | −61.6075 | −2.80906 | ||||||||
\(482\) | −51.6145 | −2.35098 | ||||||||
\(483\) | 10.7828 | 0.490633 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.45544 | 0.202311 | ||||||||
\(486\) | −2.39138 | −0.108475 | ||||||||
\(487\) | −19.6576 | −0.890771 | −0.445386 | − | 0.895339i | \(-0.646933\pi\) | ||||
−0.445386 | + | 0.895339i | \(0.646933\pi\) | |||||||
\(488\) | 3.20511 | 0.145089 | ||||||||
\(489\) | 9.98493 | 0.451534 | ||||||||
\(490\) | −45.7066 | −2.06481 | ||||||||
\(491\) | −0.470507 | −0.0212337 | −0.0106168 | − | 0.999944i | \(-0.503380\pi\) | ||||
−0.0106168 | + | 0.999944i | \(0.503380\pi\) | |||||||
\(492\) | 43.0088 | 1.93899 | ||||||||
\(493\) | 1.03899 | 0.0467935 | ||||||||
\(494\) | −21.7497 | −0.978564 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.6116 | −0.476473 | ||||||||
\(497\) | −65.9758 | −2.95942 | ||||||||
\(498\) | 9.56553 | 0.428642 | ||||||||
\(499\) | −29.8568 | −1.33657 | −0.668287 | − | 0.743903i | \(-0.732972\pi\) | ||||
−0.668287 | + | 0.743903i | \(0.732972\pi\) | |||||||
\(500\) | 3.71871 | 0.166306 | ||||||||
\(501\) | 7.67562 | 0.342921 | ||||||||
\(502\) | 13.0029 | 0.580350 | ||||||||
\(503\) | 25.8598 | 1.15303 | 0.576515 | − | 0.817087i | \(-0.304412\pi\) | ||||
0.576515 | + | 0.817087i | \(0.304412\pi\) | |||||||
\(504\) | 21.0029 | 0.935546 | ||||||||
\(505\) | −6.87484 | −0.305926 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.5655 | 0.735701 | ||||||||
\(508\) | −37.1311 | −1.64742 | ||||||||
\(509\) | −25.4433 | −1.12776 | −0.563878 | − | 0.825858i | \(-0.690691\pi\) | ||||
−0.563878 | + | 0.825858i | \(0.690691\pi\) | |||||||
\(510\) | −3.17415 | −0.140554 | ||||||||
\(511\) | −11.8929 | −0.526109 | ||||||||
\(512\) | 25.6396 | 1.13312 | ||||||||
\(513\) | 1.67267 | 0.0738503 | ||||||||
\(514\) | 29.1800 | 1.28708 | ||||||||
\(515\) | 10.5835 | 0.466367 | ||||||||
\(516\) | −17.7857 | −0.782972 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −138.458 | −6.08350 | ||||||||
\(519\) | −4.69069 | −0.205898 | ||||||||
\(520\) | −22.3483 | −0.980038 | ||||||||
\(521\) | −40.5383 | −1.77602 | −0.888008 | − | 0.459827i | \(-0.847911\pi\) | ||||
−0.888008 | + | 0.459827i | \(0.847911\pi\) | |||||||
\(522\) | −1.87189 | −0.0819304 | ||||||||
\(523\) | 35.3303 | 1.54489 | 0.772443 | − | 0.635085i | \(-0.219035\pi\) | ||||
0.772443 | + | 0.635085i | \(0.219035\pi\) | |||||||
\(524\) | −18.1281 | −0.791930 | ||||||||
\(525\) | −5.11009 | −0.223023 | ||||||||
\(526\) | −4.43332 | −0.193302 | ||||||||
\(527\) | −5.88991 | −0.256568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5475 | −0.806414 | ||||||||
\(530\) | 19.7007 | 0.855743 | ||||||||
\(531\) | 10.0921 | 0.437959 | ||||||||
\(532\) | −31.7857 | −1.37809 | ||||||||
\(533\) | 62.8866 | 2.72392 | ||||||||
\(534\) | −35.3512 | −1.52980 | ||||||||
\(535\) | −1.41940 | −0.0613661 | ||||||||
\(536\) | 18.3123 | 0.790969 | ||||||||
\(537\) | 11.4374 | 0.493561 | ||||||||
\(538\) | 23.3152 | 1.00519 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.71871 | 0.160028 | ||||||||
\(541\) | −22.6966 | −0.975803 | −0.487901 | − | 0.872899i | \(-0.662237\pi\) | ||||
−0.487901 | + | 0.872899i | \(0.662237\pi\) | |||||||
\(542\) | 36.3612 | 1.56185 | ||||||||
\(543\) | −8.11304 | −0.348164 | ||||||||
\(544\) | 3.32028 | 0.142356 | ||||||||
\(545\) | 15.2022 | 0.651189 | ||||||||
\(546\) | 66.4463 | 2.84364 | ||||||||
\(547\) | 7.47346 | 0.319542 | 0.159771 | − | 0.987154i | \(-0.448924\pi\) | ||||
0.159771 | + | 0.987154i | \(0.448924\pi\) | |||||||
\(548\) | 73.5103 | 3.14021 | ||||||||
\(549\) | −0.779816 | −0.0332817 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.30931 | 0.0557784 | ||||||||
\(552\) | 8.67267 | 0.369133 | ||||||||
\(553\) | −5.76475 | −0.245142 | ||||||||
\(554\) | −29.4935 | −1.25306 | ||||||||
\(555\) | −11.3303 | −0.480943 | ||||||||
\(556\) | −25.1561 | −1.06686 | ||||||||
\(557\) | −25.8037 | −1.09334 | −0.546670 | − | 0.837348i | \(-0.684105\pi\) | ||||
−0.546670 | + | 0.837348i | \(0.684105\pi\) | |||||||
\(558\) | 10.6116 | 0.449223 | ||||||||
\(559\) | −26.0059 | −1.09993 | ||||||||
\(560\) | −12.2202 | −0.516397 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 35.3512 | 1.49120 | ||||||||
\(563\) | −9.74968 | −0.410900 | −0.205450 | − | 0.978668i | \(-0.565866\pi\) | ||||
−0.205450 | + | 0.978668i | \(0.565866\pi\) | |||||||
\(564\) | 35.1620 | 1.48059 | ||||||||
\(565\) | 2.01802 | 0.0848987 | ||||||||
\(566\) | 69.4073 | 2.91741 | ||||||||
\(567\) | −5.11009 | −0.214604 | ||||||||
\(568\) | −53.0649 | −2.22655 | ||||||||
\(569\) | −21.2231 | −0.889720 | −0.444860 | − | 0.895600i | \(-0.646747\pi\) | ||||
−0.444860 | + | 0.895600i | \(0.646747\pi\) | |||||||
\(570\) | −4.00000 | −0.167542 | ||||||||
\(571\) | −1.81880 | −0.0761144 | −0.0380572 | − | 0.999276i | \(-0.512117\pi\) | ||||
−0.0380572 | + | 0.999276i | \(0.512117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.00295 | −0.0418988 | ||||||||
\(574\) | 141.333 | 5.89912 | ||||||||
\(575\) | −2.11009 | −0.0879969 | ||||||||
\(576\) | −10.7647 | −0.448531 | ||||||||
\(577\) | −39.4643 | −1.64292 | −0.821460 | − | 0.570266i | \(-0.806840\pi\) | ||||
−0.821460 | + | 0.570266i | \(0.806840\pi\) | |||||||
\(578\) | 36.4404 | 1.51572 | ||||||||
\(579\) | 15.9849 | 0.664311 | ||||||||
\(580\) | 2.91087 | 0.120868 | ||||||||
\(581\) | 20.4404 | 0.848009 | ||||||||
\(582\) | −10.6547 | −0.441650 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −9.56553 | −0.395824 | ||||||||
\(585\) | 5.43742 | 0.224810 | ||||||||
\(586\) | 22.3052 | 0.921420 | ||||||||
\(587\) | 29.6396 | 1.22336 | 0.611678 | − | 0.791107i | \(-0.290495\pi\) | ||||
0.611678 | + | 0.791107i | \(0.290495\pi\) | |||||||
\(588\) | 71.0759 | 2.93112 | ||||||||
\(589\) | −7.42235 | −0.305833 | ||||||||
\(590\) | −24.1340 | −0.993581 | ||||||||
\(591\) | 16.2202 | 0.667209 | ||||||||
\(592\) | −27.0950 | −1.11360 | ||||||||
\(593\) | −29.1311 | −1.19627 | −0.598135 | − | 0.801396i | \(-0.704091\pi\) | ||||
−0.598135 | + | 0.801396i | \(0.704091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.78276 | −0.278066 | ||||||||
\(596\) | 0.476404 | 0.0195143 | ||||||||
\(597\) | −1.34240 | −0.0549406 | ||||||||
\(598\) | 27.4374 | 1.12200 | ||||||||
\(599\) | 44.1039 | 1.80204 | 0.901018 | − | 0.433782i | \(-0.142821\pi\) | ||||
0.901018 | + | 0.433782i | \(0.142821\pi\) | |||||||
\(600\) | −4.11009 | −0.167794 | ||||||||
\(601\) | −34.5174 | −1.40799 | −0.703997 | − | 0.710203i | \(-0.748603\pi\) | ||||
−0.703997 | + | 0.710203i | \(0.748603\pi\) | |||||||
\(602\) | −58.4463 | −2.38209 | ||||||||
\(603\) | −4.45544 | −0.181439 | ||||||||
\(604\) | 20.2872 | 0.825474 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.4404 | 0.667844 | ||||||||
\(607\) | 2.99705 | 0.121647 | 0.0608233 | − | 0.998149i | \(-0.480627\pi\) | ||||
0.0608233 | + | 0.998149i | \(0.480627\pi\) | |||||||
\(608\) | 4.18415 | 0.169690 | ||||||||
\(609\) | −4.00000 | −0.162088 | ||||||||
\(610\) | 1.86484 | 0.0755051 | ||||||||
\(611\) | 51.4132 | 2.07995 | ||||||||
\(612\) | 4.93594 | 0.199524 | ||||||||
\(613\) | −0.761798 | −0.0307687 | −0.0153844 | − | 0.999882i | \(-0.504897\pi\) | ||||
−0.0153844 | + | 0.999882i | \(0.504897\pi\) | |||||||
\(614\) | −31.6576 | −1.27760 | ||||||||
\(615\) | 11.5655 | 0.466367 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.8217 | −0.959028 | −0.479514 | − | 0.877534i | \(-0.659187\pi\) | ||||
−0.479514 | + | 0.877534i | \(0.659187\pi\) | |||||||
\(618\) | −25.3093 | −1.01809 | ||||||||
\(619\) | −30.4463 | −1.22374 | −0.611869 | − | 0.790959i | \(-0.709582\pi\) | ||||
−0.611869 | + | 0.790959i | \(0.709582\pi\) | |||||||
\(620\) | −16.5015 | −0.662715 | ||||||||
\(621\) | −2.11009 | −0.0846751 | ||||||||
\(622\) | −6.65465 | −0.266827 | ||||||||
\(623\) | −75.5413 | −3.02650 | ||||||||
\(624\) | 13.0029 | 0.520535 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.25917 | −0.370071 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.5685 | 1.77848 | ||||||||
\(629\) | −15.0390 | −0.599644 | ||||||||
\(630\) | 12.2202 | 0.486864 | ||||||||
\(631\) | −10.5446 | −0.419772 | −0.209886 | − | 0.977726i | \(-0.567309\pi\) | ||||
−0.209886 | + | 0.977726i | \(0.567309\pi\) | |||||||
\(632\) | −4.63664 | −0.184435 | ||||||||
\(633\) | 12.2231 | 0.485826 | ||||||||
\(634\) | 21.7787 | 0.864941 | ||||||||
\(635\) | −9.98493 | −0.396240 | ||||||||
\(636\) | −30.6355 | −1.21478 | ||||||||
\(637\) | 103.926 | 4.11768 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.9109 | 0.510746 | ||||||||
\(640\) | 20.7397 | 0.819808 | ||||||||
\(641\) | 17.4014 | 0.687313 | 0.343657 | − | 0.939095i | \(-0.388334\pi\) | ||||
0.343657 | + | 0.939095i | \(0.388334\pi\) | |||||||
\(642\) | 3.39433 | 0.133964 | ||||||||
\(643\) | −32.3693 | −1.27652 | −0.638260 | − | 0.769821i | \(-0.720345\pi\) | ||||
−0.638260 | + | 0.769821i | \(0.720345\pi\) | |||||||
\(644\) | 40.0980 | 1.58008 | ||||||||
\(645\) | −4.78276 | −0.188321 | ||||||||
\(646\) | −5.30931 | −0.208892 | ||||||||
\(647\) | 38.3362 | 1.50715 | 0.753575 | − | 0.657362i | \(-0.228328\pi\) | ||||
0.753575 | + | 0.657362i | \(0.228328\pi\) | |||||||
\(648\) | −4.11009 | −0.161460 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −13.0029 | −0.510018 | ||||||||
\(651\) | 22.6756 | 0.888728 | ||||||||
\(652\) | 37.1311 | 1.45416 | ||||||||
\(653\) | 3.74968 | 0.146736 | 0.0733681 | − | 0.997305i | \(-0.476625\pi\) | ||||
0.0733681 | + | 0.997305i | \(0.476625\pi\) | |||||||
\(654\) | −36.3542 | −1.42156 | ||||||||
\(655\) | −4.87484 | −0.190476 | ||||||||
\(656\) | 27.6576 | 1.07985 | ||||||||
\(657\) | 2.32733 | 0.0907977 | ||||||||
\(658\) | 115.547 | 4.50450 | ||||||||
\(659\) | −15.9079 | −0.619685 | −0.309842 | − | 0.950788i | \(-0.600276\pi\) | ||||
−0.309842 | + | 0.950788i | \(0.600276\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.2382 | 0.670488 | 0.335244 | − | 0.942131i | \(-0.391181\pi\) | ||||
0.335244 | + | 0.942131i | \(0.391181\pi\) | |||||||
\(662\) | 14.8678 | 0.577853 | ||||||||
\(663\) | 7.21724 | 0.280294 | ||||||||
\(664\) | 16.4404 | 0.638010 | ||||||||
\(665\) | −8.54751 | −0.331458 | ||||||||
\(666\) | 27.0950 | 1.04991 | ||||||||
\(667\) | −1.65171 | −0.0639543 | ||||||||
\(668\) | 28.5434 | 1.10438 | ||||||||
\(669\) | 11.2022 | 0.433101 | ||||||||
\(670\) | 10.6547 | 0.411625 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −12.7828 | −0.493106 | ||||||||
\(673\) | 21.2942 | 0.820833 | 0.410416 | − | 0.911898i | \(-0.365383\pi\) | ||||
0.410416 | + | 0.911898i | \(0.365383\pi\) | |||||||
\(674\) | −64.5383 | −2.48592 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 61.6024 | 2.36932 | ||||||||
\(677\) | −38.0419 | −1.46207 | −0.731035 | − | 0.682340i | \(-0.760962\pi\) | ||||
−0.731035 | + | 0.682340i | \(0.760962\pi\) | |||||||
\(678\) | −4.82585 | −0.185336 | ||||||||
\(679\) | −22.7677 | −0.873744 | ||||||||
\(680\) | −5.45544 | −0.209206 | ||||||||
\(681\) | −14.5446 | −0.557349 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.0950 | 1.26635 | 0.633173 | − | 0.774010i | \(-0.281752\pi\) | ||||
0.633173 | + | 0.774010i | \(0.281752\pi\) | |||||||
\(684\) | 6.22018 | 0.237835 | ||||||||
\(685\) | 19.7677 | 0.755285 | ||||||||
\(686\) | 148.024 | 5.65157 | ||||||||
\(687\) | −14.9289 | −0.569573 | ||||||||
\(688\) | −11.4374 | −0.436048 | ||||||||
\(689\) | −44.7946 | −1.70654 | ||||||||
\(690\) | 5.04604 | 0.192099 | ||||||||
\(691\) | −32.8778 | −1.25073 | −0.625365 | − | 0.780332i | \(-0.715050\pi\) | ||||
−0.625365 | + | 0.780332i | \(0.715050\pi\) | |||||||
\(692\) | −17.4433 | −0.663095 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.9740 | 1.09984 | ||||||||
\(695\) | −6.76475 | −0.256601 | ||||||||
\(696\) | −3.21724 | −0.121949 | ||||||||
\(697\) | 15.3512 | 0.581470 | ||||||||
\(698\) | −56.1411 | −2.12497 | ||||||||
\(699\) | 27.5475 | 1.04194 | ||||||||
\(700\) | −19.0029 | −0.718244 | ||||||||
\(701\) | −35.2231 | −1.33036 | −0.665180 | − | 0.746683i | \(-0.731645\pi\) | ||||
−0.665180 | + | 0.746683i | \(0.731645\pi\) | |||||||
\(702\) | −13.0029 | −0.490765 | ||||||||
\(703\) | −18.9518 | −0.714782 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.45544 | 0.356112 | ||||||||
\(706\) | −41.8766 | −1.57605 | ||||||||
\(707\) | 35.1311 | 1.32124 | ||||||||
\(708\) | 37.5295 | 1.41044 | ||||||||
\(709\) | 1.14318 | 0.0429330 | 0.0214665 | − | 0.999770i | \(-0.493166\pi\) | ||||
0.0214665 | + | 0.999770i | \(0.493166\pi\) | |||||||
\(710\) | −30.8748 | −1.15871 | ||||||||
\(711\) | 1.12811 | 0.0423074 | ||||||||
\(712\) | −60.7585 | −2.27702 | ||||||||
\(713\) | 9.36336 | 0.350661 | ||||||||
\(714\) | 16.2202 | 0.607025 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.5324 | 1.58951 | ||||||||
\(717\) | 3.21724 | 0.120150 | ||||||||
\(718\) | −30.7025 | −1.14581 | ||||||||
\(719\) | 1.16120 | 0.0433054 | 0.0216527 | − | 0.999766i | \(-0.493107\pi\) | ||||
0.0216527 | + | 0.999766i | \(0.493107\pi\) | |||||||
\(720\) | 2.39138 | 0.0891216 | ||||||||
\(721\) | −54.0829 | −2.01415 | ||||||||
\(722\) | 38.7456 | 1.44196 | ||||||||
\(723\) | 21.5835 | 0.802701 | ||||||||
\(724\) | −30.1700 | −1.12126 | ||||||||
\(725\) | 0.782765 | 0.0290712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.65465 | 0.246807 | 0.123404 | − | 0.992357i | \(-0.460619\pi\) | ||||
0.123404 | + | 0.992357i | \(0.460619\pi\) | |||||||
\(728\) | 114.202 | 4.23260 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.56553 | −0.205989 | ||||||||
\(731\) | −6.34829 | −0.234800 | ||||||||
\(732\) | −2.89991 | −0.107184 | ||||||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | 11.5236 | 0.425344 | ||||||||
\(735\) | 19.1130 | 0.704995 | ||||||||
\(736\) | −5.27834 | −0.194562 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −27.6576 | −1.01809 | ||||||||
\(739\) | 4.47346 | 0.164559 | 0.0822794 | − | 0.996609i | \(-0.473780\pi\) | ||||
0.0822794 | + | 0.996609i | \(0.473780\pi\) | |||||||
\(740\) | −42.1340 | −1.54888 | ||||||||
\(741\) | 9.09502 | 0.334114 | ||||||||
\(742\) | −100.672 | −3.69580 | ||||||||
\(743\) | 24.3303 | 0.892591 | 0.446296 | − | 0.894886i | \(-0.352743\pi\) | ||||
0.446296 | + | 0.894886i | \(0.352743\pi\) | |||||||
\(744\) | 18.2382 | 0.668645 | ||||||||
\(745\) | 0.128110 | 0.00469359 | ||||||||
\(746\) | −38.5183 | −1.41026 | ||||||||
\(747\) | −4.00000 | −0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.25327 | 0.265029 | ||||||||
\(750\) | −2.39138 | −0.0873209 | ||||||||
\(751\) | 32.6635 | 1.19191 | 0.595954 | − | 0.803019i | \(-0.296774\pi\) | ||||
0.595954 | + | 0.803019i | \(0.296774\pi\) | |||||||
\(752\) | 22.6116 | 0.824559 | ||||||||
\(753\) | −5.43742 | −0.198151 | ||||||||
\(754\) | −10.1783 | −0.370670 | ||||||||
\(755\) | 5.45544 | 0.198544 | ||||||||
\(756\) | −19.0029 | −0.691131 | ||||||||
\(757\) | −12.0711 | −0.438732 | −0.219366 | − | 0.975643i | \(-0.570399\pi\) | ||||
−0.219366 | + | 0.975643i | \(0.570399\pi\) | |||||||
\(758\) | −20.0071 | −0.726689 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.87484 | −0.249377 | ||||||||
\(761\) | 16.3123 | 0.591319 | 0.295659 | − | 0.955293i | \(-0.404461\pi\) | ||||
0.295659 | + | 0.955293i | \(0.404461\pi\) | |||||||
\(762\) | 23.8778 | 0.865001 | ||||||||
\(763\) | −77.6845 | −2.81237 | ||||||||
\(764\) | −3.72968 | −0.134935 | ||||||||
\(765\) | 1.32733 | 0.0479896 | ||||||||
\(766\) | 27.1311 | 0.980285 | ||||||||
\(767\) | 54.8748 | 1.98142 | ||||||||
\(768\) | −28.0670 | −1.01278 | ||||||||
\(769\) | −14.6016 | −0.526546 | −0.263273 | − | 0.964721i | \(-0.584802\pi\) | ||||
−0.263273 | + | 0.964721i | \(0.584802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.2022 | −0.439450 | ||||||||
\(772\) | 59.4433 | 2.13941 | ||||||||
\(773\) | −26.2742 | −0.945019 | −0.472509 | − | 0.881326i | \(-0.656652\pi\) | ||||
−0.472509 | + | 0.881326i | \(0.656652\pi\) | |||||||
\(774\) | 11.4374 | 0.411110 | ||||||||
\(775\) | −4.43742 | −0.159397 | ||||||||
\(776\) | −18.3123 | −0.657372 | ||||||||
\(777\) | 57.8988 | 2.07711 | ||||||||
\(778\) | −12.3902 | −0.444211 | ||||||||
\(779\) | 19.3453 | 0.693119 | ||||||||
\(780\) | 20.2202 | 0.723999 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 6.69774 | 0.239511 | ||||||||
\(783\) | 0.782765 | 0.0279737 | ||||||||
\(784\) | 45.7066 | 1.63238 | ||||||||
\(785\) | 11.9849 | 0.427761 | ||||||||
\(786\) | 11.6576 | 0.415813 | ||||||||
\(787\) | 44.8807 | 1.59983 | 0.799913 | − | 0.600116i | \(-0.204879\pi\) | ||||
0.799913 | + | 0.600116i | \(0.204879\pi\) | |||||||
\(788\) | 60.3182 | 2.14875 | ||||||||
\(789\) | 1.85387 | 0.0659996 | ||||||||
\(790\) | −2.69774 | −0.0959814 | ||||||||
\(791\) | −10.3123 | −0.366662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.24019 | −0.150573 | ||||||||
\(794\) | −1.83585 | −0.0651520 | ||||||||
\(795\) | −8.23820 | −0.292179 | ||||||||
\(796\) | −4.99198 | −0.176936 | ||||||||
\(797\) | −38.5124 | −1.36418 | −0.682090 | − | 0.731268i | \(-0.738929\pi\) | ||||
−0.682090 | + | 0.731268i | \(0.738929\pi\) | |||||||
\(798\) | 20.4404 | 0.723581 | ||||||||
\(799\) | 12.5505 | 0.444003 | ||||||||
\(800\) | 2.50147 | 0.0884405 | ||||||||
\(801\) | 14.7828 | 0.522323 | ||||||||
\(802\) | −43.1311 | −1.52301 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −16.5685 | −0.584325 | ||||||||
\(805\) | 10.7828 | 0.380043 | ||||||||
\(806\) | 57.6995 | 2.03238 | ||||||||
\(807\) | −9.74968 | −0.343205 | ||||||||
\(808\) | 28.2562 | 0.994050 | ||||||||
\(809\) | 9.09502 | 0.319764 | 0.159882 | − | 0.987136i | \(-0.448889\pi\) | ||||
0.159882 | + | 0.987136i | \(0.448889\pi\) | |||||||
\(810\) | −2.39138 | −0.0840246 | ||||||||
\(811\) | −16.7297 | −0.587458 | −0.293729 | − | 0.955889i | \(-0.594896\pi\) | ||||
−0.293729 | + | 0.955889i | \(0.594896\pi\) | |||||||
\(812\) | −14.8748 | −0.522005 | ||||||||
\(813\) | −15.2051 | −0.533267 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.98493 | 0.349757 | ||||||||
\(816\) | 3.17415 | 0.111117 | ||||||||
\(817\) | −8.00000 | −0.279885 | ||||||||
\(818\) | 6.12106 | 0.214018 | ||||||||
\(819\) | −27.7857 | −0.970911 | ||||||||
\(820\) | 43.0088 | 1.50193 | ||||||||
\(821\) | −7.38138 | −0.257612 | −0.128806 | − | 0.991670i | \(-0.541114\pi\) | ||||
−0.128806 | + | 0.991670i | \(0.541114\pi\) | |||||||
\(822\) | −47.2721 | −1.64880 | ||||||||
\(823\) | −38.0410 | −1.32602 | −0.663012 | − | 0.748608i | \(-0.730722\pi\) | ||||
−0.663012 | + | 0.748608i | \(0.730722\pi\) | |||||||
\(824\) | −43.4994 | −1.51537 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 123.327 | 4.29110 | ||||||||
\(827\) | 46.1900 | 1.60619 | 0.803093 | − | 0.595854i | \(-0.203186\pi\) | ||||
0.803093 | + | 0.595854i | \(0.203186\pi\) | |||||||
\(828\) | −7.84682 | −0.272696 | ||||||||
\(829\) | 8.55963 | 0.297288 | 0.148644 | − | 0.988891i | \(-0.452509\pi\) | ||||
0.148644 | + | 0.988891i | \(0.452509\pi\) | |||||||
\(830\) | 9.56553 | 0.332024 | ||||||||
\(831\) | 12.3332 | 0.427835 | ||||||||
\(832\) | −58.5324 | −2.02925 | ||||||||
\(833\) | 25.3693 | 0.878993 | ||||||||
\(834\) | 16.1771 | 0.560167 | ||||||||
\(835\) | 7.67562 | 0.265626 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.43742 | −0.153380 | ||||||||
\(838\) | −26.5324 | −0.916548 | ||||||||
\(839\) | 55.7556 | 1.92490 | 0.962448 | − | 0.271466i | \(-0.0875084\pi\) | ||||
0.962448 | + | 0.271466i | \(0.0875084\pi\) | |||||||
\(840\) | 21.0029 | 0.724671 | ||||||||
\(841\) | −28.3873 | −0.978872 | ||||||||
\(842\) | −36.6676 | −1.26365 | ||||||||
\(843\) | −14.7828 | −0.509145 | ||||||||
\(844\) | 45.4543 | 1.56460 | ||||||||
\(845\) | 16.5655 | 0.569872 | ||||||||
\(846\) | −22.6116 | −0.777402 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.7007 | −0.676525 | ||||||||
\(849\) | −29.0239 | −0.996098 | ||||||||
\(850\) | −3.17415 | −0.108872 | ||||||||
\(851\) | 23.9079 | 0.819553 | ||||||||
\(852\) | 48.0118 | 1.64486 | ||||||||
\(853\) | −12.7258 | −0.435722 | −0.217861 | − | 0.975980i | \(-0.569908\pi\) | ||||
−0.217861 | + | 0.975980i | \(0.569908\pi\) | |||||||
\(854\) | −9.52949 | −0.326093 | ||||||||
\(855\) | 1.67267 | 0.0572042 | ||||||||
\(856\) | 5.83387 | 0.199398 | ||||||||
\(857\) | 13.5835 | 0.464005 | 0.232003 | − | 0.972715i | \(-0.425472\pi\) | ||||
0.232003 | + | 0.972715i | \(0.425472\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0239 | 0.376131 | 0.188066 | − | 0.982156i | \(-0.439778\pi\) | ||||
0.188066 | + | 0.982156i | \(0.439778\pi\) | |||||||
\(860\) | −17.7857 | −0.606488 | ||||||||
\(861\) | −59.1009 | −2.01415 | ||||||||
\(862\) | 8.81880 | 0.300370 | ||||||||
\(863\) | −46.1900 | −1.57233 | −0.786164 | − | 0.618018i | \(-0.787936\pi\) | ||||
−0.786164 | + | 0.618018i | \(0.787936\pi\) | |||||||
\(864\) | 2.50147 | 0.0851019 | ||||||||
\(865\) | −4.69069 | −0.159488 | ||||||||
\(866\) | −66.8365 | −2.27120 | ||||||||
\(867\) | −15.2382 | −0.517516 | ||||||||
\(868\) | 84.3241 | 2.86214 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.87189 | −0.0634630 | ||||||||
\(871\) | −24.2261 | −0.820869 | ||||||||
\(872\) | −62.4823 | −2.11592 | ||||||||
\(873\) | 4.45544 | 0.150794 | ||||||||
\(874\) | 8.44037 | 0.285500 | ||||||||
\(875\) | −5.11009 | −0.172753 | ||||||||
\(876\) | 8.65465 | 0.292414 | ||||||||
\(877\) | −22.3634 | −0.755157 | −0.377579 | − | 0.925978i | \(-0.623243\pi\) | ||||
−0.377579 | + | 0.925978i | \(0.623243\pi\) | |||||||
\(878\) | 57.4002 | 1.93716 | ||||||||
\(879\) | −9.32733 | −0.314603 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.5124 | 1.23014 | 0.615068 | − | 0.788474i | \(-0.289129\pi\) | ||||
0.615068 | + | 0.788474i | \(0.289129\pi\) | |||||||
\(882\) | −45.7066 | −1.53902 | ||||||||
\(883\) | −42.4672 | −1.42914 | −0.714568 | − | 0.699566i | \(-0.753377\pi\) | ||||
−0.714568 | + | 0.699566i | \(0.753377\pi\) | |||||||
\(884\) | 26.8388 | 0.902687 | ||||||||
\(885\) | 10.0921 | 0.339241 | ||||||||
\(886\) | 14.8748 | 0.499730 | ||||||||
\(887\) | 17.5354 | 0.588781 | 0.294390 | − | 0.955685i | \(-0.404883\pi\) | ||||
0.294390 | + | 0.955685i | \(0.404883\pi\) | |||||||
\(888\) | 46.5685 | 1.56274 | ||||||||
\(889\) | 51.0239 | 1.71129 | ||||||||
\(890\) | −35.3512 | −1.18498 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 41.6576 | 1.39480 | ||||||||
\(893\) | 15.8159 | 0.529257 | ||||||||
\(894\) | −0.306360 | −0.0102462 | ||||||||
\(895\) | 11.4374 | 0.382311 | ||||||||
\(896\) | −105.982 | −3.54060 | ||||||||
\(897\) | −11.4735 | −0.383088 | ||||||||
\(898\) | −52.6104 | −1.75563 | ||||||||
\(899\) | −3.47346 | −0.115846 | ||||||||
\(900\) | 3.71871 | 0.123957 | ||||||||
\(901\) | −10.9348 | −0.364291 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.4404 | 0.813325 | ||||||||
\(904\) | −8.29424 | −0.275862 | ||||||||
\(905\) | −8.11304 | −0.269687 | ||||||||
\(906\) | −13.0460 | −0.433426 | ||||||||
\(907\) | −24.5835 | −0.816283 | −0.408142 | − | 0.912919i | \(-0.633823\pi\) | ||||
−0.408142 | + | 0.912919i | \(0.633823\pi\) | |||||||
\(908\) | −54.0870 | −1.79494 | ||||||||
\(909\) | −6.87484 | −0.228024 | ||||||||
\(910\) | 66.4463 | 2.20267 | ||||||||
\(911\) | −42.5685 | −1.41036 | −0.705178 | − | 0.709030i | \(-0.749133\pi\) | ||||
−0.705178 | + | 0.709030i | \(0.749133\pi\) | |||||||
\(912\) | 4.00000 | 0.132453 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 40.3542 | 1.33480 | ||||||||
\(915\) | −0.779816 | −0.0257799 | ||||||||
\(916\) | −55.5162 | −1.83431 | ||||||||
\(917\) | 24.9109 | 0.822630 | ||||||||
\(918\) | −3.17415 | −0.104762 | ||||||||
\(919\) | 32.1491 | 1.06050 | 0.530250 | − | 0.847841i | \(-0.322098\pi\) | ||||
0.530250 | + | 0.847841i | \(0.322098\pi\) | |||||||
\(920\) | 8.67267 | 0.285930 | ||||||||
\(921\) | 13.2382 | 0.436214 | ||||||||
\(922\) | −57.0868 | −1.88005 | ||||||||
\(923\) | 70.2018 | 2.31072 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.3303 | −0.372537 | ||||||||
\(926\) | −62.7166 | −2.06100 | ||||||||
\(927\) | 10.5835 | 0.347609 | ||||||||
\(928\) | 1.95807 | 0.0642767 | ||||||||
\(929\) | 8.17825 | 0.268320 | 0.134160 | − | 0.990960i | \(-0.457166\pi\) | ||||
0.134160 | + | 0.990960i | \(0.457166\pi\) | |||||||
\(930\) | 10.6116 | 0.347967 | ||||||||
\(931\) | 31.9699 | 1.04777 | ||||||||
\(932\) | 102.441 | 3.35557 | ||||||||
\(933\) | 2.78276 | 0.0911036 | ||||||||
\(934\) | 82.6234 | 2.70352 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −22.3483 | −0.730477 | ||||||||
\(937\) | −19.0741 | −0.623122 | −0.311561 | − | 0.950226i | \(-0.600852\pi\) | ||||
−0.311561 | + | 0.950226i | \(0.600852\pi\) | |||||||
\(938\) | −54.4463 | −1.77773 | ||||||||
\(939\) | 3.87189 | 0.126354 | ||||||||
\(940\) | 35.1620 | 1.14686 | ||||||||
\(941\) | −31.0029 | −1.01067 | −0.505334 | − | 0.862924i | \(-0.668631\pi\) | ||||
−0.505334 | + | 0.862924i | \(0.668631\pi\) | |||||||
\(942\) | −28.6606 | −0.933811 | ||||||||
\(943\) | −24.4043 | −0.794714 | ||||||||
\(944\) | 24.1340 | 0.785495 | ||||||||
\(945\) | −5.11009 | −0.166231 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.3604 | 0.466651 | 0.233325 | − | 0.972399i | \(-0.425039\pi\) | ||||
0.233325 | + | 0.972399i | \(0.425039\pi\) | |||||||
\(948\) | 4.19511 | 0.136251 | ||||||||
\(949\) | 12.6547 | 0.410787 | ||||||||
\(950\) | −4.00000 | −0.129777 | ||||||||
\(951\) | −9.10714 | −0.295319 | ||||||||
\(952\) | 27.8778 | 0.903524 | ||||||||
\(953\) | 50.0000 | 1.61966 | 0.809829 | − | 0.586665i | \(-0.199560\pi\) | ||||
0.809829 | + | 0.586665i | \(0.199560\pi\) | |||||||
\(954\) | 19.7007 | 0.637833 | ||||||||
\(955\) | −1.00295 | −0.0324547 | ||||||||
\(956\) | 11.9640 | 0.386942 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 84.2461 | 2.72187 | ||||||||
\(959\) | −101.015 | −3.26194 | ||||||||
\(960\) | −10.7647 | −0.347431 | ||||||||
\(961\) | −11.3093 | −0.364816 | ||||||||
\(962\) | 147.327 | 4.75001 | ||||||||
\(963\) | −1.41940 | −0.0457396 | ||||||||
\(964\) | 80.2629 | 2.58510 | ||||||||
\(965\) | 15.9849 | 0.514573 | ||||||||
\(966\) | −25.7857 | −0.829642 | ||||||||
\(967\) | −21.4165 | −0.688707 | −0.344353 | − | 0.938840i | \(-0.611902\pi\) | ||||
−0.344353 | + | 0.938840i | \(0.611902\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.22018 | 0.0713226 | ||||||||
\(970\) | −10.6547 | −0.342100 | ||||||||
\(971\) | −3.61567 | −0.116032 | −0.0580162 | − | 0.998316i | \(-0.518477\pi\) | ||||
−0.0580162 | + | 0.998316i | \(0.518477\pi\) | |||||||
\(972\) | 3.71871 | 0.119278 | ||||||||
\(973\) | 34.5685 | 1.10821 | ||||||||
\(974\) | 47.0088 | 1.50626 | ||||||||
\(975\) | 5.43742 | 0.174137 | ||||||||
\(976\) | −1.86484 | −0.0596920 | ||||||||
\(977\) | 20.2022 | 0.646325 | 0.323162 | − | 0.946344i | \(-0.395254\pi\) | ||||
0.323162 | + | 0.946344i | \(0.395254\pi\) | |||||||
\(978\) | −23.8778 | −0.763527 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 71.0759 | 2.27043 | ||||||||
\(981\) | 15.2022 | 0.485368 | ||||||||
\(982\) | 1.12516 | 0.0359053 | ||||||||
\(983\) | −46.8067 | −1.49290 | −0.746451 | − | 0.665441i | \(-0.768244\pi\) | ||||
−0.746451 | + | 0.665441i | \(0.768244\pi\) | |||||||
\(984\) | −47.5354 | −1.51537 | ||||||||
\(985\) | 16.2202 | 0.516818 | ||||||||
\(986\) | −2.48461 | −0.0791261 | ||||||||
\(987\) | −48.3182 | −1.53798 | ||||||||
\(988\) | 33.8217 | 1.07601 | ||||||||
\(989\) | 10.0921 | 0.320909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.3893 | −1.50537 | −0.752685 | − | 0.658381i | \(-0.771242\pi\) | ||||
−0.752685 | + | 0.658381i | \(0.771242\pi\) | |||||||
\(992\) | −11.1001 | −0.352428 | ||||||||
\(993\) | −6.21724 | −0.197298 | ||||||||
\(994\) | 157.773 | 5.00426 | ||||||||
\(995\) | −1.34240 | −0.0425568 | ||||||||
\(996\) | −14.8748 | −0.471327 | ||||||||
\(997\) | 30.4554 | 0.964533 | 0.482267 | − | 0.876024i | \(-0.339814\pi\) | ||||
0.482267 | + | 0.876024i | \(0.339814\pi\) | |||||||
\(998\) | 71.3991 | 2.26010 | ||||||||
\(999\) | −11.3303 | −0.358474 |
(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 | 1815.2.a.l.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 5445.2.a.bc.1.3 | 3 | |||
5.4 | even | 2 | 9075.2.a.ci.1.3 | 3 | |||
11.10 | odd | 2 | 1815.2.a.n.1.3 | yes | 3 | ||
33.32 | even | 2 | 5445.2.a.ba.1.1 | 3 | |||
55.54 | odd | 2 | 9075.2.a.ce.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.a.l.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1815.2.a.n.1.3 | yes | 3 | 11.10 | odd | 2 | ||
5445.2.a.ba.1.1 | 3 | 33.32 | even | 2 | |||
5445.2.a.bc.1.3 | 3 | 3.2 | odd | 2 | |||
9075.2.a.ce.1.1 | 3 | 55.54 | odd | 2 | |||
9075.2.a.ci.1.3 | 3 | 5.4 | even | 2 |