Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 5 x^{19} - 19 x^{18} + 127 x^{17} + 95 x^{16} - 1293 x^{15} + 329 x^{14} + 6765 x^{13} + \cdots - 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-1.59121\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59121 | −1.12516 | −0.562578 | − | 0.826744i | \(-0.690191\pi\) | ||||
−0.562578 | + | 0.826744i | \(0.690191\pi\) | |||||||
\(3\) | −2.69692 | −1.55707 | −0.778534 | − | 0.627602i | \(-0.784036\pi\) | ||||
−0.778534 | + | 0.627602i | \(0.784036\pi\) | |||||||
\(4\) | 0.531955 | 0.265977 | ||||||||
\(5\) | −1.39893 | −0.625621 | −0.312811 | − | 0.949815i | \(-0.601271\pi\) | ||||
−0.312811 | + | 0.949815i | \(0.601271\pi\) | |||||||
\(6\) | 4.29137 | 1.75195 | ||||||||
\(7\) | −3.40103 | −1.28547 | −0.642734 | − | 0.766090i | \(-0.722200\pi\) | ||||
−0.642734 | + | 0.766090i | \(0.722200\pi\) | |||||||
\(8\) | 2.33597 | 0.825890 | ||||||||
\(9\) | 4.27339 | 1.42446 | ||||||||
\(10\) | 2.22600 | 0.703922 | ||||||||
\(11\) | 3.00388 | 0.905705 | 0.452852 | − | 0.891586i | \(-0.350406\pi\) | ||||
0.452852 | + | 0.891586i | \(0.350406\pi\) | |||||||
\(12\) | −1.43464 | −0.414145 | ||||||||
\(13\) | 4.01281 | 1.11295 | 0.556477 | − | 0.830863i | \(-0.312153\pi\) | ||||
0.556477 | + | 0.830863i | \(0.312153\pi\) | |||||||
\(14\) | 5.41176 | 1.44635 | ||||||||
\(15\) | 3.77281 | 0.974135 | ||||||||
\(16\) | −4.78093 | −1.19523 | ||||||||
\(17\) | −5.59257 | −1.35640 | −0.678199 | − | 0.734878i | \(-0.737239\pi\) | ||||
−0.678199 | + | 0.734878i | \(0.737239\pi\) | |||||||
\(18\) | −6.79986 | −1.60274 | ||||||||
\(19\) | 4.72532 | 1.08406 | 0.542032 | − | 0.840358i | \(-0.317655\pi\) | ||||
0.542032 | + | 0.840358i | \(0.317655\pi\) | |||||||
\(20\) | −0.744168 | −0.166401 | ||||||||
\(21\) | 9.17231 | 2.00156 | ||||||||
\(22\) | −4.77981 | −1.01906 | ||||||||
\(23\) | −2.45986 | −0.512917 | −0.256459 | − | 0.966555i | \(-0.582556\pi\) | ||||
−0.256459 | + | 0.966555i | \(0.582556\pi\) | |||||||
\(24\) | −6.29993 | −1.28597 | ||||||||
\(25\) | −3.04299 | −0.608598 | ||||||||
\(26\) | −6.38523 | −1.25225 | ||||||||
\(27\) | −3.43422 | −0.660916 | ||||||||
\(28\) | −1.80919 | −0.341905 | ||||||||
\(29\) | 0.534027 | 0.0991664 | 0.0495832 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495832 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(30\) | −6.00334 | −1.09605 | ||||||||
\(31\) | −8.47342 | −1.52187 | −0.760936 | − | 0.648828i | \(-0.775260\pi\) | ||||
−0.760936 | + | 0.648828i | \(0.775260\pi\) | |||||||
\(32\) | 2.93554 | 0.518934 | ||||||||
\(33\) | −8.10123 | −1.41024 | ||||||||
\(34\) | 8.89897 | 1.52616 | ||||||||
\(35\) | 4.75781 | 0.804216 | ||||||||
\(36\) | 2.27325 | 0.378874 | ||||||||
\(37\) | −4.64697 | −0.763957 | −0.381978 | − | 0.924171i | \(-0.624757\pi\) | ||||
−0.381978 | + | 0.924171i | \(0.624757\pi\) | |||||||
\(38\) | −7.51899 | −1.21974 | ||||||||
\(39\) | −10.8222 | −1.73295 | ||||||||
\(40\) | −3.26786 | −0.516695 | ||||||||
\(41\) | −2.25975 | −0.352913 | −0.176456 | − | 0.984308i | \(-0.556463\pi\) | ||||
−0.176456 | + | 0.984308i | \(0.556463\pi\) | |||||||
\(42\) | −14.5951 | −2.25207 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 1.59793 | 0.240897 | ||||||||
\(45\) | −5.97818 | −0.891174 | ||||||||
\(46\) | 3.91416 | 0.577112 | ||||||||
\(47\) | −0.893285 | −0.130299 | −0.0651495 | − | 0.997876i | \(-0.520752\pi\) | ||||
−0.0651495 | + | 0.997876i | \(0.520752\pi\) | |||||||
\(48\) | 12.8938 | 1.86106 | ||||||||
\(49\) | 4.56699 | 0.652427 | ||||||||
\(50\) | 4.84204 | 0.684768 | ||||||||
\(51\) | 15.0827 | 2.11200 | ||||||||
\(52\) | 2.13463 | 0.296020 | ||||||||
\(53\) | −9.68307 | −1.33007 | −0.665036 | − | 0.746811i | \(-0.731584\pi\) | ||||
−0.665036 | + | 0.746811i | \(0.731584\pi\) | |||||||
\(54\) | 5.46457 | 0.743634 | ||||||||
\(55\) | −4.20223 | −0.566628 | ||||||||
\(56\) | −7.94470 | −1.06166 | ||||||||
\(57\) | −12.7438 | −1.68796 | ||||||||
\(58\) | −0.849750 | −0.111578 | ||||||||
\(59\) | 10.3383 | 1.34593 | 0.672966 | − | 0.739673i | \(-0.265020\pi\) | ||||
0.672966 | + | 0.739673i | \(0.265020\pi\) | |||||||
\(60\) | 2.00696 | 0.259098 | ||||||||
\(61\) | 2.23249 | 0.285841 | 0.142921 | − | 0.989734i | \(-0.454351\pi\) | ||||
0.142921 | + | 0.989734i | \(0.454351\pi\) | |||||||
\(62\) | 13.4830 | 1.71234 | ||||||||
\(63\) | −14.5339 | −1.83110 | ||||||||
\(64\) | 4.89081 | 0.611351 | ||||||||
\(65\) | −5.61365 | −0.696288 | ||||||||
\(66\) | 12.8908 | 1.58675 | ||||||||
\(67\) | 3.27528 | 0.400139 | 0.200070 | − | 0.979782i | \(-0.435883\pi\) | ||||
0.200070 | + | 0.979782i | \(0.435883\pi\) | |||||||
\(68\) | −2.97499 | −0.360771 | ||||||||
\(69\) | 6.63406 | 0.798647 | ||||||||
\(70\) | −7.57068 | −0.904869 | ||||||||
\(71\) | −7.07450 | −0.839589 | −0.419795 | − | 0.907619i | \(-0.637898\pi\) | ||||
−0.419795 | + | 0.907619i | \(0.637898\pi\) | |||||||
\(72\) | 9.98250 | 1.17645 | ||||||||
\(73\) | −12.7026 | −1.48673 | −0.743366 | − | 0.668885i | \(-0.766772\pi\) | ||||
−0.743366 | + | 0.668885i | \(0.766772\pi\) | |||||||
\(74\) | 7.39431 | 0.859571 | ||||||||
\(75\) | 8.20670 | 0.947628 | ||||||||
\(76\) | 2.51366 | 0.288336 | ||||||||
\(77\) | −10.2163 | −1.16425 | ||||||||
\(78\) | 17.2205 | 1.94983 | ||||||||
\(79\) | 2.34826 | 0.264200 | 0.132100 | − | 0.991236i | \(-0.457828\pi\) | ||||
0.132100 | + | 0.991236i | \(0.457828\pi\) | |||||||
\(80\) | 6.68820 | 0.747764 | ||||||||
\(81\) | −3.55833 | −0.395370 | ||||||||
\(82\) | 3.59573 | 0.397082 | ||||||||
\(83\) | 3.50210 | 0.384406 | 0.192203 | − | 0.981355i | \(-0.438437\pi\) | ||||
0.192203 | + | 0.981355i | \(0.438437\pi\) | |||||||
\(84\) | 4.87925 | 0.532370 | ||||||||
\(85\) | 7.82363 | 0.848592 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.44023 | −0.154409 | ||||||||
\(88\) | 7.01698 | 0.748013 | ||||||||
\(89\) | 0.915547 | 0.0970477 | 0.0485239 | − | 0.998822i | \(-0.484548\pi\) | ||||
0.0485239 | + | 0.998822i | \(0.484548\pi\) | |||||||
\(90\) | 9.51254 | 1.00271 | ||||||||
\(91\) | −13.6477 | −1.43067 | ||||||||
\(92\) | −1.30854 | −0.136424 | ||||||||
\(93\) | 22.8521 | 2.36966 | ||||||||
\(94\) | 1.42141 | 0.146607 | ||||||||
\(95\) | −6.61041 | −0.678213 | ||||||||
\(96\) | −7.91691 | −0.808016 | ||||||||
\(97\) | 1.91917 | 0.194862 | 0.0974309 | − | 0.995242i | \(-0.468938\pi\) | ||||
0.0974309 | + | 0.995242i | \(0.468938\pi\) | |||||||
\(98\) | −7.26705 | −0.734083 | ||||||||
\(99\) | 12.8367 | 1.29014 | ||||||||
\(100\) | −1.61873 | −0.161873 | ||||||||
\(101\) | 7.67146 | 0.763339 | 0.381670 | − | 0.924299i | \(-0.375349\pi\) | ||||
0.381670 | + | 0.924299i | \(0.375349\pi\) | |||||||
\(102\) | −23.9998 | −2.37634 | ||||||||
\(103\) | −0.699112 | −0.0688855 | −0.0344428 | − | 0.999407i | \(-0.510966\pi\) | ||||
−0.0344428 | + | 0.999407i | \(0.510966\pi\) | |||||||
\(104\) | 9.37381 | 0.919178 | ||||||||
\(105\) | −12.8314 | −1.25222 | ||||||||
\(106\) | 15.4078 | 1.49654 | ||||||||
\(107\) | 12.7477 | 1.23236 | 0.616181 | − | 0.787604i | \(-0.288679\pi\) | ||||
0.616181 | + | 0.787604i | \(0.288679\pi\) | |||||||
\(108\) | −1.82685 | −0.175789 | ||||||||
\(109\) | −7.83181 | −0.750151 | −0.375076 | − | 0.926994i | \(-0.622383\pi\) | ||||
−0.375076 | + | 0.926994i | \(0.622383\pi\) | |||||||
\(110\) | 6.68663 | 0.637545 | ||||||||
\(111\) | 12.5325 | 1.18953 | ||||||||
\(112\) | 16.2601 | 1.53643 | ||||||||
\(113\) | −7.54717 | −0.709978 | −0.354989 | − | 0.934871i | \(-0.615515\pi\) | ||||
−0.354989 | + | 0.934871i | \(0.615515\pi\) | |||||||
\(114\) | 20.2781 | 1.89922 | ||||||||
\(115\) | 3.44118 | 0.320892 | ||||||||
\(116\) | 0.284078 | 0.0263760 | ||||||||
\(117\) | 17.1483 | 1.58536 | ||||||||
\(118\) | −16.4504 | −1.51439 | ||||||||
\(119\) | 19.0205 | 1.74361 | ||||||||
\(120\) | 8.81317 | 0.804529 | ||||||||
\(121\) | −1.97669 | −0.179699 | ||||||||
\(122\) | −3.55237 | −0.321616 | ||||||||
\(123\) | 6.09435 | 0.549509 | ||||||||
\(124\) | −4.50747 | −0.404783 | ||||||||
\(125\) | 11.2516 | 1.00637 | ||||||||
\(126\) | 23.1265 | 2.06027 | ||||||||
\(127\) | −3.05508 | −0.271094 | −0.135547 | − | 0.990771i | \(-0.543279\pi\) | ||||
−0.135547 | + | 0.990771i | \(0.543279\pi\) | |||||||
\(128\) | −13.6534 | −1.20680 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.93251 | 0.783433 | ||||||||
\(131\) | −10.9528 | −0.956948 | −0.478474 | − | 0.878102i | \(-0.658810\pi\) | ||||
−0.478474 | + | 0.878102i | \(0.658810\pi\) | |||||||
\(132\) | −4.30949 | −0.375093 | ||||||||
\(133\) | −16.0710 | −1.39353 | ||||||||
\(134\) | −5.21166 | −0.450219 | ||||||||
\(135\) | 4.80424 | 0.413483 | ||||||||
\(136\) | −13.0641 | −1.12024 | ||||||||
\(137\) | −18.3639 | −1.56894 | −0.784468 | − | 0.620170i | \(-0.787064\pi\) | ||||
−0.784468 | + | 0.620170i | \(0.787064\pi\) | |||||||
\(138\) | −10.5562 | −0.898603 | ||||||||
\(139\) | −20.6344 | −1.75019 | −0.875093 | − | 0.483955i | \(-0.839200\pi\) | ||||
−0.875093 | + | 0.483955i | \(0.839200\pi\) | |||||||
\(140\) | 2.53094 | 0.213903 | ||||||||
\(141\) | 2.40912 | 0.202884 | ||||||||
\(142\) | 11.2570 | 0.944669 | ||||||||
\(143\) | 12.0540 | 1.00801 | ||||||||
\(144\) | −20.4308 | −1.70256 | ||||||||
\(145\) | −0.747068 | −0.0620406 | ||||||||
\(146\) | 20.2126 | 1.67281 | ||||||||
\(147\) | −12.3168 | −1.01587 | ||||||||
\(148\) | −2.47198 | −0.203195 | ||||||||
\(149\) | 11.5188 | 0.943658 | 0.471829 | − | 0.881690i | \(-0.343594\pi\) | ||||
0.471829 | + | 0.881690i | \(0.343594\pi\) | |||||||
\(150\) | −13.0586 | −1.06623 | ||||||||
\(151\) | 19.1074 | 1.55494 | 0.777470 | − | 0.628920i | \(-0.216503\pi\) | ||||
0.777470 | + | 0.628920i | \(0.216503\pi\) | |||||||
\(152\) | 11.0382 | 0.895318 | ||||||||
\(153\) | −23.8992 | −1.93214 | ||||||||
\(154\) | 16.2563 | 1.30997 | ||||||||
\(155\) | 11.8537 | 0.952115 | ||||||||
\(156\) | −5.75694 | −0.460924 | ||||||||
\(157\) | −2.95930 | −0.236178 | −0.118089 | − | 0.993003i | \(-0.537677\pi\) | ||||
−0.118089 | + | 0.993003i | \(0.537677\pi\) | |||||||
\(158\) | −3.73658 | −0.297267 | ||||||||
\(159\) | 26.1145 | 2.07101 | ||||||||
\(160\) | −4.10661 | −0.324656 | ||||||||
\(161\) | 8.36607 | 0.659338 | ||||||||
\(162\) | 5.66206 | 0.444854 | ||||||||
\(163\) | 12.5553 | 0.983410 | 0.491705 | − | 0.870762i | \(-0.336374\pi\) | ||||
0.491705 | + | 0.870762i | \(0.336374\pi\) | |||||||
\(164\) | −1.20208 | −0.0938668 | ||||||||
\(165\) | 11.3331 | 0.882279 | ||||||||
\(166\) | −5.57259 | −0.432517 | ||||||||
\(167\) | 5.30051 | 0.410166 | 0.205083 | − | 0.978745i | \(-0.434254\pi\) | ||||
0.205083 | + | 0.978745i | \(0.434254\pi\) | |||||||
\(168\) | 21.4262 | 1.65307 | ||||||||
\(169\) | 3.10266 | 0.238666 | ||||||||
\(170\) | −12.4490 | −0.954798 | ||||||||
\(171\) | 20.1931 | 1.54421 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.59027 | −0.348992 | −0.174496 | − | 0.984658i | \(-0.555830\pi\) | ||||
−0.174496 | + | 0.984658i | \(0.555830\pi\) | |||||||
\(174\) | 2.29171 | 0.173734 | ||||||||
\(175\) | 10.3493 | 0.782333 | ||||||||
\(176\) | −14.3614 | −1.08253 | ||||||||
\(177\) | −27.8816 | −2.09571 | ||||||||
\(178\) | −1.45683 | −0.109194 | ||||||||
\(179\) | 1.69814 | 0.126925 | 0.0634624 | − | 0.997984i | \(-0.479786\pi\) | ||||
0.0634624 | + | 0.997984i | \(0.479786\pi\) | |||||||
\(180\) | −3.18012 | −0.237032 | ||||||||
\(181\) | 21.6860 | 1.61191 | 0.805953 | − | 0.591979i | \(-0.201653\pi\) | ||||
0.805953 | + | 0.591979i | \(0.201653\pi\) | |||||||
\(182\) | 21.7164 | 1.60972 | ||||||||
\(183\) | −6.02086 | −0.445075 | ||||||||
\(184\) | −5.74617 | −0.423613 | ||||||||
\(185\) | 6.50079 | 0.477948 | ||||||||
\(186\) | −36.3626 | −2.66624 | ||||||||
\(187\) | −16.7994 | −1.22850 | ||||||||
\(188\) | −0.475187 | −0.0346566 | ||||||||
\(189\) | 11.6799 | 0.849586 | ||||||||
\(190\) | 10.5186 | 0.763096 | ||||||||
\(191\) | 14.5080 | 1.04976 | 0.524881 | − | 0.851176i | \(-0.324110\pi\) | ||||
0.524881 | + | 0.851176i | \(0.324110\pi\) | |||||||
\(192\) | −13.1901 | −0.951916 | ||||||||
\(193\) | −12.7206 | −0.915647 | −0.457824 | − | 0.889043i | \(-0.651371\pi\) | ||||
−0.457824 | + | 0.889043i | \(0.651371\pi\) | |||||||
\(194\) | −3.05380 | −0.219250 | ||||||||
\(195\) | 15.1396 | 1.08417 | ||||||||
\(196\) | 2.42943 | 0.173531 | ||||||||
\(197\) | 15.2633 | 1.08746 | 0.543732 | − | 0.839259i | \(-0.317011\pi\) | ||||
0.543732 | + | 0.839259i | \(0.317011\pi\) | |||||||
\(198\) | −20.4260 | −1.45161 | ||||||||
\(199\) | 19.2754 | 1.36640 | 0.683199 | − | 0.730232i | \(-0.260588\pi\) | ||||
0.683199 | + | 0.730232i | \(0.260588\pi\) | |||||||
\(200\) | −7.10834 | −0.502635 | ||||||||
\(201\) | −8.83317 | −0.623044 | ||||||||
\(202\) | −12.2069 | −0.858876 | ||||||||
\(203\) | −1.81624 | −0.127475 | ||||||||
\(204\) | 8.02333 | 0.561745 | ||||||||
\(205\) | 3.16123 | 0.220790 | ||||||||
\(206\) | 1.11243 | 0.0775070 | ||||||||
\(207\) | −10.5119 | −0.730631 | ||||||||
\(208\) | −19.1850 | −1.33024 | ||||||||
\(209\) | 14.1943 | 0.981842 | ||||||||
\(210\) | 20.4175 | 1.40894 | ||||||||
\(211\) | −21.3719 | −1.47130 | −0.735649 | − | 0.677362i | \(-0.763123\pi\) | ||||
−0.735649 | + | 0.677362i | \(0.763123\pi\) | |||||||
\(212\) | −5.15095 | −0.353769 | ||||||||
\(213\) | 19.0794 | 1.30730 | ||||||||
\(214\) | −20.2842 | −1.38660 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.02224 | −0.545844 | ||||||||
\(217\) | 28.8183 | 1.95632 | ||||||||
\(218\) | 12.4621 | 0.844038 | ||||||||
\(219\) | 34.2580 | 2.31494 | ||||||||
\(220\) | −2.23539 | −0.150710 | ||||||||
\(221\) | −22.4419 | −1.50961 | ||||||||
\(222\) | −19.9419 | −1.33841 | ||||||||
\(223\) | −13.3355 | −0.893012 | −0.446506 | − | 0.894781i | \(-0.647332\pi\) | ||||
−0.446506 | + | 0.894781i | \(0.647332\pi\) | |||||||
\(224\) | −9.98384 | −0.667073 | ||||||||
\(225\) | −13.0039 | −0.866924 | ||||||||
\(226\) | 12.0091 | 0.798836 | ||||||||
\(227\) | 5.05601 | 0.335579 | 0.167790 | − | 0.985823i | \(-0.446337\pi\) | ||||
0.167790 | + | 0.985823i | \(0.446337\pi\) | |||||||
\(228\) | −6.77914 | −0.448959 | ||||||||
\(229\) | 22.0663 | 1.45818 | 0.729092 | − | 0.684415i | \(-0.239942\pi\) | ||||
0.729092 | + | 0.684415i | \(0.239942\pi\) | |||||||
\(230\) | −5.47565 | −0.361054 | ||||||||
\(231\) | 27.5525 | 1.81282 | ||||||||
\(232\) | 1.24747 | 0.0819006 | ||||||||
\(233\) | 9.68779 | 0.634668 | 0.317334 | − | 0.948314i | \(-0.397212\pi\) | ||||
0.317334 | + | 0.948314i | \(0.397212\pi\) | |||||||
\(234\) | −27.2866 | −1.78378 | ||||||||
\(235\) | 1.24965 | 0.0815179 | ||||||||
\(236\) | 5.49951 | 0.357988 | ||||||||
\(237\) | −6.33308 | −0.411378 | ||||||||
\(238\) | −30.2656 | −1.96183 | ||||||||
\(239\) | 11.0134 | 0.712395 | 0.356197 | − | 0.934411i | \(-0.384073\pi\) | ||||
0.356197 | + | 0.934411i | \(0.384073\pi\) | |||||||
\(240\) | −18.0376 | −1.16432 | ||||||||
\(241\) | −13.5694 | −0.874081 | −0.437040 | − | 0.899442i | \(-0.643973\pi\) | ||||
−0.437040 | + | 0.899442i | \(0.643973\pi\) | |||||||
\(242\) | 3.14533 | 0.202190 | ||||||||
\(243\) | 19.8992 | 1.27653 | ||||||||
\(244\) | 1.18758 | 0.0760273 | ||||||||
\(245\) | −6.38891 | −0.408173 | ||||||||
\(246\) | −9.69741 | −0.618284 | ||||||||
\(247\) | 18.9618 | 1.20651 | ||||||||
\(248\) | −19.7937 | −1.25690 | ||||||||
\(249\) | −9.44490 | −0.598546 | ||||||||
\(250\) | −17.9037 | −1.13233 | ||||||||
\(251\) | 19.8413 | 1.25237 | 0.626186 | − | 0.779673i | \(-0.284615\pi\) | ||||
0.626186 | + | 0.779673i | \(0.284615\pi\) | |||||||
\(252\) | −7.73138 | −0.487031 | ||||||||
\(253\) | −7.38914 | −0.464551 | ||||||||
\(254\) | 4.86127 | 0.305023 | ||||||||
\(255\) | −21.0997 | −1.32132 | ||||||||
\(256\) | 11.9438 | 0.746488 | ||||||||
\(257\) | 15.2857 | 0.953497 | 0.476749 | − | 0.879040i | \(-0.341815\pi\) | ||||
0.476749 | + | 0.879040i | \(0.341815\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.8045 | 0.982042 | ||||||||
\(260\) | −2.98621 | −0.185197 | ||||||||
\(261\) | 2.28210 | 0.141259 | ||||||||
\(262\) | 17.4282 | 1.07672 | ||||||||
\(263\) | 19.2163 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(264\) | −18.9243 | −1.16471 | ||||||||
\(265\) | 13.5460 | 0.832122 | ||||||||
\(266\) | 25.5723 | 1.56794 | ||||||||
\(267\) | −2.46916 | −0.151110 | ||||||||
\(268\) | 1.74230 | 0.106428 | ||||||||
\(269\) | −20.6980 | −1.26198 | −0.630988 | − | 0.775792i | \(-0.717350\pi\) | ||||
−0.630988 | + | 0.775792i | \(0.717350\pi\) | |||||||
\(270\) | −7.64456 | −0.465233 | ||||||||
\(271\) | −19.8545 | −1.20607 | −0.603037 | − | 0.797713i | \(-0.706043\pi\) | ||||
−0.603037 | + | 0.797713i | \(0.706043\pi\) | |||||||
\(272\) | 26.7377 | 1.62121 | ||||||||
\(273\) | 36.8067 | 2.22765 | ||||||||
\(274\) | 29.2209 | 1.76530 | ||||||||
\(275\) | −9.14078 | −0.551210 | ||||||||
\(276\) | 3.52902 | 0.212422 | ||||||||
\(277\) | −3.79499 | −0.228019 | −0.114009 | − | 0.993480i | \(-0.536369\pi\) | ||||
−0.114009 | + | 0.993480i | \(0.536369\pi\) | |||||||
\(278\) | 32.8337 | 1.96923 | ||||||||
\(279\) | −36.2102 | −2.16785 | ||||||||
\(280\) | 11.1141 | 0.664194 | ||||||||
\(281\) | 6.63552 | 0.395842 | 0.197921 | − | 0.980218i | \(-0.436581\pi\) | ||||
0.197921 | + | 0.980218i | \(0.436581\pi\) | |||||||
\(282\) | −3.83342 | −0.228277 | ||||||||
\(283\) | −27.9623 | −1.66218 | −0.831092 | − | 0.556134i | \(-0.812284\pi\) | ||||
−0.831092 | + | 0.556134i | \(0.812284\pi\) | |||||||
\(284\) | −3.76331 | −0.223312 | ||||||||
\(285\) | 17.8277 | 1.05602 | ||||||||
\(286\) | −19.1805 | −1.13417 | ||||||||
\(287\) | 7.68546 | 0.453658 | ||||||||
\(288\) | 12.5447 | 0.739202 | ||||||||
\(289\) | 14.2769 | 0.839816 | ||||||||
\(290\) | 1.18874 | 0.0698054 | ||||||||
\(291\) | −5.17584 | −0.303413 | ||||||||
\(292\) | −6.75723 | −0.395437 | ||||||||
\(293\) | 6.14946 | 0.359255 | 0.179628 | − | 0.983735i | \(-0.442511\pi\) | ||||
0.179628 | + | 0.983735i | \(0.442511\pi\) | |||||||
\(294\) | 19.5987 | 1.14302 | ||||||||
\(295\) | −14.4626 | −0.842044 | ||||||||
\(296\) | −10.8552 | −0.630945 | ||||||||
\(297\) | −10.3160 | −0.598595 | ||||||||
\(298\) | −18.3289 | −1.06176 | ||||||||
\(299\) | −9.87097 | −0.570853 | ||||||||
\(300\) | 4.36559 | 0.252048 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −30.4040 | −1.74955 | ||||||||
\(303\) | −20.6893 | −1.18857 | ||||||||
\(304\) | −22.5915 | −1.29571 | ||||||||
\(305\) | −3.12311 | −0.178829 | ||||||||
\(306\) | 38.0287 | 2.17396 | ||||||||
\(307\) | 16.6202 | 0.948566 | 0.474283 | − | 0.880372i | \(-0.342707\pi\) | ||||
0.474283 | + | 0.880372i | \(0.342707\pi\) | |||||||
\(308\) | −5.43460 | −0.309665 | ||||||||
\(309\) | 1.88545 | 0.107259 | ||||||||
\(310\) | −18.8618 | −1.07128 | ||||||||
\(311\) | 29.7732 | 1.68828 | 0.844141 | − | 0.536121i | \(-0.180111\pi\) | ||||
0.844141 | + | 0.536121i | \(0.180111\pi\) | |||||||
\(312\) | −25.2804 | −1.43122 | ||||||||
\(313\) | −6.59385 | −0.372707 | −0.186353 | − | 0.982483i | \(-0.559667\pi\) | ||||
−0.186353 | + | 0.982483i | \(0.559667\pi\) | |||||||
\(314\) | 4.70888 | 0.265737 | ||||||||
\(315\) | 20.3319 | 1.14558 | ||||||||
\(316\) | 1.24917 | 0.0702713 | ||||||||
\(317\) | 5.30076 | 0.297720 | 0.148860 | − | 0.988858i | \(-0.452440\pi\) | ||||
0.148860 | + | 0.988858i | \(0.452440\pi\) | |||||||
\(318\) | −41.5537 | −2.33021 | ||||||||
\(319\) | 1.60415 | 0.0898154 | ||||||||
\(320\) | −6.84191 | −0.382474 | ||||||||
\(321\) | −34.3794 | −1.91887 | ||||||||
\(322\) | −13.3122 | −0.741859 | ||||||||
\(323\) | −26.4267 | −1.47042 | ||||||||
\(324\) | −1.89287 | −0.105160 | ||||||||
\(325\) | −12.2109 | −0.677341 | ||||||||
\(326\) | −19.9782 | −1.10649 | ||||||||
\(327\) | 21.1218 | 1.16804 | ||||||||
\(328\) | −5.27870 | −0.291467 | ||||||||
\(329\) | 3.03809 | 0.167495 | ||||||||
\(330\) | −18.0333 | −0.992702 | ||||||||
\(331\) | −29.5150 | −1.62229 | −0.811146 | − | 0.584843i | \(-0.801156\pi\) | ||||
−0.811146 | + | 0.584843i | \(0.801156\pi\) | |||||||
\(332\) | 1.86296 | 0.102243 | ||||||||
\(333\) | −19.8583 | −1.08823 | ||||||||
\(334\) | −8.43424 | −0.461501 | ||||||||
\(335\) | −4.58189 | −0.250336 | ||||||||
\(336\) | −43.8522 | −2.39233 | ||||||||
\(337\) | −30.3713 | −1.65443 | −0.827215 | − | 0.561885i | \(-0.810076\pi\) | ||||
−0.827215 | + | 0.561885i | \(0.810076\pi\) | |||||||
\(338\) | −4.93699 | −0.268537 | ||||||||
\(339\) | 20.3541 | 1.10548 | ||||||||
\(340\) | 4.16181 | 0.225706 | ||||||||
\(341\) | −25.4532 | −1.37837 | ||||||||
\(342\) | −32.1315 | −1.73748 | ||||||||
\(343\) | 8.27473 | 0.446793 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.28060 | −0.499651 | ||||||||
\(346\) | 7.30410 | 0.392671 | ||||||||
\(347\) | −9.38404 | −0.503762 | −0.251881 | − | 0.967758i | \(-0.581049\pi\) | ||||
−0.251881 | + | 0.967758i | \(0.581049\pi\) | |||||||
\(348\) | −0.766137 | −0.0410692 | ||||||||
\(349\) | −10.8935 | −0.583114 | −0.291557 | − | 0.956554i | \(-0.594173\pi\) | ||||
−0.291557 | + | 0.956554i | \(0.594173\pi\) | |||||||
\(350\) | −16.4679 | −0.880247 | ||||||||
\(351\) | −13.7809 | −0.735569 | ||||||||
\(352\) | 8.81800 | 0.470001 | ||||||||
\(353\) | 28.7437 | 1.52987 | 0.764935 | − | 0.644107i | \(-0.222771\pi\) | ||||
0.764935 | + | 0.644107i | \(0.222771\pi\) | |||||||
\(354\) | 44.3655 | 2.35800 | ||||||||
\(355\) | 9.89675 | 0.525265 | ||||||||
\(356\) | 0.487029 | 0.0258125 | ||||||||
\(357\) | −51.2968 | −2.71491 | ||||||||
\(358\) | −2.70210 | −0.142810 | ||||||||
\(359\) | −9.21850 | −0.486534 | −0.243267 | − | 0.969959i | \(-0.578219\pi\) | ||||
−0.243267 | + | 0.969959i | \(0.578219\pi\) | |||||||
\(360\) | −13.9648 | −0.736012 | ||||||||
\(361\) | 3.32869 | 0.175194 | ||||||||
\(362\) | −34.5070 | −1.81365 | ||||||||
\(363\) | 5.33098 | 0.279804 | ||||||||
\(364\) | −7.25995 | −0.380525 | ||||||||
\(365\) | 17.7701 | 0.930132 | ||||||||
\(366\) | 9.58046 | 0.500779 | ||||||||
\(367\) | −18.3320 | −0.956921 | −0.478460 | − | 0.878109i | \(-0.658805\pi\) | ||||
−0.478460 | + | 0.878109i | \(0.658805\pi\) | |||||||
\(368\) | 11.7604 | 0.613056 | ||||||||
\(369\) | −9.65676 | −0.502711 | ||||||||
\(370\) | −10.3441 | −0.537766 | ||||||||
\(371\) | 32.9324 | 1.70976 | ||||||||
\(372\) | 12.1563 | 0.630275 | ||||||||
\(373\) | −27.5423 | −1.42609 | −0.713043 | − | 0.701121i | \(-0.752683\pi\) | ||||
−0.713043 | + | 0.701121i | \(0.752683\pi\) | |||||||
\(374\) | 26.7314 | 1.38225 | ||||||||
\(375\) | −30.3447 | −1.56699 | ||||||||
\(376\) | −2.08669 | −0.107613 | ||||||||
\(377\) | 2.14295 | 0.110368 | ||||||||
\(378\) | −18.5852 | −0.955917 | ||||||||
\(379\) | 9.09979 | 0.467425 | 0.233713 | − | 0.972306i | \(-0.424913\pi\) | ||||
0.233713 | + | 0.972306i | \(0.424913\pi\) | |||||||
\(380\) | −3.51644 | −0.180389 | ||||||||
\(381\) | 8.23930 | 0.422112 | ||||||||
\(382\) | −23.0853 | −1.18115 | ||||||||
\(383\) | 18.1462 | 0.927225 | 0.463613 | − | 0.886038i | \(-0.346553\pi\) | ||||
0.463613 | + | 0.886038i | \(0.346553\pi\) | |||||||
\(384\) | 36.8221 | 1.87907 | ||||||||
\(385\) | 14.2919 | 0.728382 | ||||||||
\(386\) | 20.2411 | 1.03025 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.02091 | 0.0518288 | ||||||||
\(389\) | −12.4180 | −0.629618 | −0.314809 | − | 0.949155i | \(-0.601940\pi\) | ||||
−0.314809 | + | 0.949155i | \(0.601940\pi\) | |||||||
\(390\) | −24.0903 | −1.21986 | ||||||||
\(391\) | 13.7570 | 0.695720 | ||||||||
\(392\) | 10.6684 | 0.538834 | ||||||||
\(393\) | 29.5387 | 1.49003 | ||||||||
\(394\) | −24.2871 | −1.22357 | ||||||||
\(395\) | −3.28506 | −0.165289 | ||||||||
\(396\) | 6.82857 | 0.343148 | ||||||||
\(397\) | 32.5998 | 1.63614 | 0.818068 | − | 0.575121i | \(-0.195045\pi\) | ||||
0.818068 | + | 0.575121i | \(0.195045\pi\) | |||||||
\(398\) | −30.6713 | −1.53741 | ||||||||
\(399\) | 43.3421 | 2.16982 | ||||||||
\(400\) | 14.5483 | 0.727417 | ||||||||
\(401\) | −28.4192 | −1.41919 | −0.709594 | − | 0.704611i | \(-0.751122\pi\) | ||||
−0.709594 | + | 0.704611i | \(0.751122\pi\) | |||||||
\(402\) | 14.0554 | 0.701022 | ||||||||
\(403\) | −34.0022 | −1.69377 | ||||||||
\(404\) | 4.08087 | 0.203031 | ||||||||
\(405\) | 4.97787 | 0.247352 | ||||||||
\(406\) | 2.89002 | 0.143430 | ||||||||
\(407\) | −13.9589 | −0.691919 | ||||||||
\(408\) | 35.2328 | 1.74428 | ||||||||
\(409\) | 23.6424 | 1.16904 | 0.584521 | − | 0.811379i | \(-0.301282\pi\) | ||||
0.584521 | + | 0.811379i | \(0.301282\pi\) | |||||||
\(410\) | −5.03019 | −0.248423 | ||||||||
\(411\) | 49.5260 | 2.44294 | ||||||||
\(412\) | −0.371896 | −0.0183220 | ||||||||
\(413\) | −35.1609 | −1.73015 | ||||||||
\(414\) | 16.7267 | 0.822074 | ||||||||
\(415\) | −4.89920 | −0.240493 | ||||||||
\(416\) | 11.7798 | 0.577550 | ||||||||
\(417\) | 55.6493 | 2.72516 | ||||||||
\(418\) | −22.5862 | −1.10473 | ||||||||
\(419\) | −3.07048 | −0.150003 | −0.0750014 | − | 0.997183i | \(-0.523896\pi\) | ||||
−0.0750014 | + | 0.997183i | \(0.523896\pi\) | |||||||
\(420\) | −6.82574 | −0.333062 | ||||||||
\(421\) | −7.88852 | −0.384463 | −0.192231 | − | 0.981350i | \(-0.561572\pi\) | ||||
−0.192231 | + | 0.981350i | \(0.561572\pi\) | |||||||
\(422\) | 34.0071 | 1.65544 | ||||||||
\(423\) | −3.81735 | −0.185606 | ||||||||
\(424\) | −22.6194 | −1.09849 | ||||||||
\(425\) | 17.0181 | 0.825501 | ||||||||
\(426\) | −30.3593 | −1.47091 | ||||||||
\(427\) | −7.59277 | −0.367440 | ||||||||
\(428\) | 6.78117 | 0.327780 | ||||||||
\(429\) | −32.5087 | −1.56954 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.7332 | 1.23952 | 0.619762 | − | 0.784790i | \(-0.287229\pi\) | ||||
0.619762 | + | 0.784790i | \(0.287229\pi\) | |||||||
\(432\) | 16.4188 | 0.789949 | ||||||||
\(433\) | 9.31965 | 0.447874 | 0.223937 | − | 0.974604i | \(-0.428109\pi\) | ||||
0.223937 | + | 0.974604i | \(0.428109\pi\) | |||||||
\(434\) | −45.8561 | −2.20116 | ||||||||
\(435\) | 2.01478 | 0.0966014 | ||||||||
\(436\) | −4.16617 | −0.199523 | ||||||||
\(437\) | −11.6237 | −0.556035 | ||||||||
\(438\) | −54.5118 | −2.60467 | ||||||||
\(439\) | −11.5668 | −0.552051 | −0.276025 | − | 0.961150i | \(-0.589017\pi\) | ||||
−0.276025 | + | 0.961150i | \(0.589017\pi\) | |||||||
\(440\) | −9.81628 | −0.467973 | ||||||||
\(441\) | 19.5165 | 0.929358 | ||||||||
\(442\) | 35.7099 | 1.69855 | ||||||||
\(443\) | 38.9254 | 1.84940 | 0.924701 | − | 0.380694i | \(-0.124315\pi\) | ||||
0.924701 | + | 0.380694i | \(0.124315\pi\) | |||||||
\(444\) | 6.66673 | 0.316389 | ||||||||
\(445\) | −1.28079 | −0.0607151 | ||||||||
\(446\) | 21.2196 | 1.00478 | ||||||||
\(447\) | −31.0653 | −1.46934 | ||||||||
\(448\) | −16.6338 | −0.785872 | ||||||||
\(449\) | 16.2249 | 0.765701 | 0.382850 | − | 0.923810i | \(-0.374943\pi\) | ||||
0.382850 | + | 0.923810i | \(0.374943\pi\) | |||||||
\(450\) | 20.6919 | 0.975426 | ||||||||
\(451\) | −6.78801 | −0.319635 | ||||||||
\(452\) | −4.01475 | −0.188838 | ||||||||
\(453\) | −51.5312 | −2.42115 | ||||||||
\(454\) | −8.04519 | −0.377579 | ||||||||
\(455\) | 19.0922 | 0.895055 | ||||||||
\(456\) | −29.7692 | −1.39407 | ||||||||
\(457\) | −32.0054 | −1.49715 | −0.748574 | − | 0.663051i | \(-0.769261\pi\) | ||||
−0.748574 | + | 0.663051i | \(0.769261\pi\) | |||||||
\(458\) | −35.1122 | −1.64069 | ||||||||
\(459\) | 19.2061 | 0.896465 | ||||||||
\(460\) | 1.83055 | 0.0853499 | ||||||||
\(461\) | 31.3240 | 1.45890 | 0.729451 | − | 0.684033i | \(-0.239775\pi\) | ||||
0.729451 | + | 0.684033i | \(0.239775\pi\) | |||||||
\(462\) | −43.8419 | −2.03971 | ||||||||
\(463\) | −19.9993 | −0.929448 | −0.464724 | − | 0.885456i | \(-0.653846\pi\) | ||||
−0.464724 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(464\) | −2.55315 | −0.118527 | ||||||||
\(465\) | −31.9686 | −1.48251 | ||||||||
\(466\) | −15.4153 | −0.714101 | ||||||||
\(467\) | −3.31678 | −0.153482 | −0.0767412 | − | 0.997051i | \(-0.524452\pi\) | ||||
−0.0767412 | + | 0.997051i | \(0.524452\pi\) | |||||||
\(468\) | 9.12211 | 0.421670 | ||||||||
\(469\) | −11.1393 | −0.514366 | ||||||||
\(470\) | −1.98845 | −0.0917203 | ||||||||
\(471\) | 7.98101 | 0.367746 | ||||||||
\(472\) | 24.1500 | 1.11159 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 10.0773 | 0.462865 | ||||||||
\(475\) | −14.3791 | −0.659759 | ||||||||
\(476\) | 10.1180 | 0.463760 | ||||||||
\(477\) | −41.3795 | −1.89464 | ||||||||
\(478\) | −17.5246 | −0.801555 | ||||||||
\(479\) | 21.1522 | 0.966468 | 0.483234 | − | 0.875491i | \(-0.339462\pi\) | ||||
0.483234 | + | 0.875491i | \(0.339462\pi\) | |||||||
\(480\) | 11.0752 | 0.505512 | ||||||||
\(481\) | −18.6474 | −0.850249 | ||||||||
\(482\) | 21.5918 | 0.983478 | ||||||||
\(483\) | −22.5626 | −1.02663 | ||||||||
\(484\) | −1.05151 | −0.0477959 | ||||||||
\(485\) | −2.68478 | −0.121910 | ||||||||
\(486\) | −31.6639 | −1.43630 | ||||||||
\(487\) | 19.1829 | 0.869260 | 0.434630 | − | 0.900609i | \(-0.356879\pi\) | ||||
0.434630 | + | 0.900609i | \(0.356879\pi\) | |||||||
\(488\) | 5.21504 | 0.236074 | ||||||||
\(489\) | −33.8608 | −1.53124 | ||||||||
\(490\) | 10.1661 | 0.459258 | ||||||||
\(491\) | 11.3550 | 0.512442 | 0.256221 | − | 0.966618i | \(-0.417522\pi\) | ||||
0.256221 | + | 0.966618i | \(0.417522\pi\) | |||||||
\(492\) | 3.24192 | 0.146157 | ||||||||
\(493\) | −2.98659 | −0.134509 | ||||||||
\(494\) | −30.1723 | −1.35752 | ||||||||
\(495\) | −17.9577 | −0.807140 | ||||||||
\(496\) | 40.5109 | 1.81899 | ||||||||
\(497\) | 24.0606 | 1.07926 | ||||||||
\(498\) | 15.0288 | 0.673458 | ||||||||
\(499\) | 32.2406 | 1.44329 | 0.721643 | − | 0.692265i | \(-0.243387\pi\) | ||||
0.721643 | + | 0.692265i | \(0.243387\pi\) | |||||||
\(500\) | 5.98534 | 0.267672 | ||||||||
\(501\) | −14.2951 | −0.638656 | ||||||||
\(502\) | −31.5717 | −1.40912 | ||||||||
\(503\) | 29.2740 | 1.30526 | 0.652632 | − | 0.757675i | \(-0.273665\pi\) | ||||
0.652632 | + | 0.757675i | \(0.273665\pi\) | |||||||
\(504\) | −33.9508 | −1.51229 | ||||||||
\(505\) | −10.7319 | −0.477561 | ||||||||
\(506\) | 11.7577 | 0.522693 | ||||||||
\(507\) | −8.36764 | −0.371620 | ||||||||
\(508\) | −1.62516 | −0.0721049 | ||||||||
\(509\) | −19.8904 | −0.881628 | −0.440814 | − | 0.897599i | \(-0.645310\pi\) | ||||
−0.440814 | + | 0.897599i | \(0.645310\pi\) | |||||||
\(510\) | 33.5741 | 1.48669 | ||||||||
\(511\) | 43.2021 | 1.91115 | ||||||||
\(512\) | 8.30165 | 0.366884 | ||||||||
\(513\) | −16.2278 | −0.716475 | ||||||||
\(514\) | −24.3228 | −1.07283 | ||||||||
\(515\) | 0.978009 | 0.0430962 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.68332 | −0.118012 | ||||||||
\(518\) | −25.1483 | −1.10495 | ||||||||
\(519\) | 12.3796 | 0.543405 | ||||||||
\(520\) | −13.1133 | −0.575057 | ||||||||
\(521\) | 38.3269 | 1.67913 | 0.839566 | − | 0.543257i | \(-0.182809\pi\) | ||||
0.839566 | + | 0.543257i | \(0.182809\pi\) | |||||||
\(522\) | −3.63131 | −0.158938 | ||||||||
\(523\) | −3.95763 | −0.173055 | −0.0865275 | − | 0.996249i | \(-0.527577\pi\) | ||||
−0.0865275 | + | 0.996249i | \(0.527577\pi\) | |||||||
\(524\) | −5.82637 | −0.254526 | ||||||||
\(525\) | −27.9112 | −1.21815 | ||||||||
\(526\) | −30.5772 | −1.33323 | ||||||||
\(527\) | 47.3882 | 2.06426 | ||||||||
\(528\) | 38.7315 | 1.68557 | ||||||||
\(529\) | −16.9491 | −0.736916 | ||||||||
\(530\) | −21.5545 | −0.936267 | ||||||||
\(531\) | 44.1796 | 1.91723 | ||||||||
\(532\) | −8.54902 | −0.370647 | ||||||||
\(533\) | −9.06793 | −0.392776 | ||||||||
\(534\) | 3.92895 | 0.170022 | ||||||||
\(535\) | −17.8331 | −0.770992 | ||||||||
\(536\) | 7.65096 | 0.330471 | ||||||||
\(537\) | −4.57974 | −0.197631 | ||||||||
\(538\) | 32.9348 | 1.41992 | ||||||||
\(539\) | 13.7187 | 0.590907 | ||||||||
\(540\) | 2.55564 | 0.109977 | ||||||||
\(541\) | 27.3590 | 1.17626 | 0.588128 | − | 0.808768i | \(-0.299865\pi\) | ||||
0.588128 | + | 0.808768i | \(0.299865\pi\) | |||||||
\(542\) | 31.5927 | 1.35702 | ||||||||
\(543\) | −58.4854 | −2.50985 | ||||||||
\(544\) | −16.4172 | −0.703881 | ||||||||
\(545\) | 10.9562 | 0.469311 | ||||||||
\(546\) | −58.5673 | −2.50645 | ||||||||
\(547\) | −18.6376 | −0.796885 | −0.398443 | − | 0.917193i | \(-0.630449\pi\) | ||||
−0.398443 | + | 0.917193i | \(0.630449\pi\) | |||||||
\(548\) | −9.76877 | −0.417301 | ||||||||
\(549\) | 9.54030 | 0.407170 | ||||||||
\(550\) | 14.5449 | 0.620197 | ||||||||
\(551\) | 2.52345 | 0.107503 | ||||||||
\(552\) | 15.4970 | 0.659595 | ||||||||
\(553\) | −7.98651 | −0.339621 | ||||||||
\(554\) | 6.03863 | 0.256557 | ||||||||
\(555\) | −17.5321 | −0.744197 | ||||||||
\(556\) | −10.9766 | −0.465510 | ||||||||
\(557\) | 33.3451 | 1.41288 | 0.706439 | − | 0.707774i | \(-0.250300\pi\) | ||||
0.706439 | + | 0.707774i | \(0.250300\pi\) | |||||||
\(558\) | 57.6181 | 2.43917 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −22.7468 | −0.961226 | ||||||||
\(561\) | 45.3067 | 1.91285 | ||||||||
\(562\) | −10.5585 | −0.445384 | ||||||||
\(563\) | −34.3483 | −1.44761 | −0.723805 | − | 0.690005i | \(-0.757608\pi\) | ||||
−0.723805 | + | 0.690005i | \(0.757608\pi\) | |||||||
\(564\) | 1.28154 | 0.0539627 | ||||||||
\(565\) | 10.5580 | 0.444177 | ||||||||
\(566\) | 44.4939 | 1.87022 | ||||||||
\(567\) | 12.1020 | 0.508236 | ||||||||
\(568\) | −16.5258 | −0.693409 | ||||||||
\(569\) | 2.84152 | 0.119123 | 0.0595613 | − | 0.998225i | \(-0.481030\pi\) | ||||
0.0595613 | + | 0.998225i | \(0.481030\pi\) | |||||||
\(570\) | −28.3677 | −1.18819 | ||||||||
\(571\) | 23.0580 | 0.964948 | 0.482474 | − | 0.875910i | \(-0.339738\pi\) | ||||
0.482474 | + | 0.875910i | \(0.339738\pi\) | |||||||
\(572\) | 6.41219 | 0.268107 | ||||||||
\(573\) | −39.1269 | −1.63455 | ||||||||
\(574\) | −12.2292 | −0.510436 | ||||||||
\(575\) | 7.48534 | 0.312160 | ||||||||
\(576\) | 20.9003 | 0.870846 | ||||||||
\(577\) | 20.8477 | 0.867900 | 0.433950 | − | 0.900937i | \(-0.357119\pi\) | ||||
0.433950 | + | 0.900937i | \(0.357119\pi\) | |||||||
\(578\) | −22.7175 | −0.944924 | ||||||||
\(579\) | 34.3064 | 1.42573 | ||||||||
\(580\) | −0.397406 | −0.0165014 | ||||||||
\(581\) | −11.9108 | −0.494141 | ||||||||
\(582\) | 8.23586 | 0.341387 | ||||||||
\(583\) | −29.0868 | −1.20465 | ||||||||
\(584\) | −29.6730 | −1.22788 | ||||||||
\(585\) | −23.9893 | −0.991835 | ||||||||
\(586\) | −9.78509 | −0.404218 | ||||||||
\(587\) | 26.6929 | 1.10173 | 0.550867 | − | 0.834593i | \(-0.314297\pi\) | ||||
0.550867 | + | 0.834593i | \(0.314297\pi\) | |||||||
\(588\) | −6.55199 | −0.270199 | ||||||||
\(589\) | −40.0397 | −1.64981 | ||||||||
\(590\) | 23.0130 | 0.947432 | ||||||||
\(591\) | −41.1639 | −1.69326 | ||||||||
\(592\) | 22.2168 | 0.913107 | ||||||||
\(593\) | −42.3372 | −1.73858 | −0.869290 | − | 0.494302i | \(-0.835424\pi\) | ||||
−0.869290 | + | 0.494302i | \(0.835424\pi\) | |||||||
\(594\) | 16.4149 | 0.673513 | ||||||||
\(595\) | −26.6084 | −1.09084 | ||||||||
\(596\) | 6.12749 | 0.250992 | ||||||||
\(597\) | −51.9843 | −2.12758 | ||||||||
\(598\) | 15.7068 | 0.642299 | ||||||||
\(599\) | 6.44069 | 0.263159 | 0.131580 | − | 0.991306i | \(-0.457995\pi\) | ||||
0.131580 | + | 0.991306i | \(0.457995\pi\) | |||||||
\(600\) | 19.1706 | 0.782637 | ||||||||
\(601\) | 20.6424 | 0.842023 | 0.421012 | − | 0.907055i | \(-0.361675\pi\) | ||||
0.421012 | + | 0.907055i | \(0.361675\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.9965 | 0.569983 | ||||||||
\(604\) | 10.1643 | 0.413579 | ||||||||
\(605\) | 2.76526 | 0.112424 | ||||||||
\(606\) | 32.9211 | 1.33733 | ||||||||
\(607\) | 20.7341 | 0.841570 | 0.420785 | − | 0.907160i | \(-0.361755\pi\) | ||||
0.420785 | + | 0.907160i | \(0.361755\pi\) | |||||||
\(608\) | 13.8714 | 0.562558 | ||||||||
\(609\) | 4.89826 | 0.198488 | ||||||||
\(610\) | 4.96952 | 0.201210 | ||||||||
\(611\) | −3.58459 | −0.145017 | ||||||||
\(612\) | −12.7133 | −0.513905 | ||||||||
\(613\) | 31.9337 | 1.28979 | 0.644895 | − | 0.764271i | \(-0.276901\pi\) | ||||
0.644895 | + | 0.764271i | \(0.276901\pi\) | |||||||
\(614\) | −26.4463 | −1.06729 | ||||||||
\(615\) | −8.52559 | −0.343785 | ||||||||
\(616\) | −23.8650 | −0.961546 | ||||||||
\(617\) | −43.3901 | −1.74682 | −0.873410 | − | 0.486986i | \(-0.838096\pi\) | ||||
−0.873410 | + | 0.486986i | \(0.838096\pi\) | |||||||
\(618\) | −3.00015 | −0.120684 | ||||||||
\(619\) | 13.5577 | 0.544930 | 0.272465 | − | 0.962166i | \(-0.412161\pi\) | ||||
0.272465 | + | 0.962166i | \(0.412161\pi\) | |||||||
\(620\) | 6.30565 | 0.253241 | ||||||||
\(621\) | 8.44771 | 0.338995 | ||||||||
\(622\) | −47.3754 | −1.89958 | ||||||||
\(623\) | −3.11380 | −0.124752 | ||||||||
\(624\) | 51.7404 | 2.07127 | ||||||||
\(625\) | −0.525268 | −0.0210107 | ||||||||
\(626\) | 10.4922 | 0.419353 | ||||||||
\(627\) | −38.2810 | −1.52879 | ||||||||
\(628\) | −1.57422 | −0.0628180 | ||||||||
\(629\) | 25.9885 | 1.03623 | ||||||||
\(630\) | −32.3524 | −1.28895 | ||||||||
\(631\) | 28.9685 | 1.15322 | 0.576608 | − | 0.817021i | \(-0.304376\pi\) | ||||
0.576608 | + | 0.817021i | \(0.304376\pi\) | |||||||
\(632\) | 5.48548 | 0.218201 | ||||||||
\(633\) | 57.6382 | 2.29091 | ||||||||
\(634\) | −8.43463 | −0.334982 | ||||||||
\(635\) | 4.27384 | 0.169602 | ||||||||
\(636\) | 13.8917 | 0.550842 | ||||||||
\(637\) | 18.3265 | 0.726122 | ||||||||
\(638\) | −2.55255 | −0.101056 | ||||||||
\(639\) | −30.2321 | −1.19596 | ||||||||
\(640\) | 19.1002 | 0.755000 | ||||||||
\(641\) | −14.1942 | −0.560636 | −0.280318 | − | 0.959907i | \(-0.590440\pi\) | ||||
−0.280318 | + | 0.959907i | \(0.590440\pi\) | |||||||
\(642\) | 54.7049 | 2.15903 | ||||||||
\(643\) | −0.787730 | −0.0310650 | −0.0155325 | − | 0.999879i | \(-0.504944\pi\) | ||||
−0.0155325 | + | 0.999879i | \(0.504944\pi\) | |||||||
\(644\) | 4.45037 | 0.175369 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 42.0505 | 1.65445 | ||||||||
\(647\) | 1.14447 | 0.0449937 | 0.0224969 | − | 0.999747i | \(-0.492838\pi\) | ||||
0.0224969 | + | 0.999747i | \(0.492838\pi\) | |||||||
\(648\) | −8.31217 | −0.326533 | ||||||||
\(649\) | 31.0551 | 1.21902 | ||||||||
\(650\) | 19.4302 | 0.762115 | ||||||||
\(651\) | −77.7208 | −3.04612 | ||||||||
\(652\) | 6.67887 | 0.261565 | ||||||||
\(653\) | 41.8841 | 1.63905 | 0.819525 | − | 0.573044i | \(-0.194237\pi\) | ||||
0.819525 | + | 0.573044i | \(0.194237\pi\) | |||||||
\(654\) | −33.6092 | −1.31422 | ||||||||
\(655\) | 15.3222 | 0.598687 | ||||||||
\(656\) | 10.8037 | 0.421813 | ||||||||
\(657\) | −54.2833 | −2.11779 | ||||||||
\(658\) | −4.83424 | −0.188458 | ||||||||
\(659\) | 26.2488 | 1.02251 | 0.511255 | − | 0.859429i | \(-0.329181\pi\) | ||||
0.511255 | + | 0.859429i | \(0.329181\pi\) | |||||||
\(660\) | 6.02868 | 0.234666 | ||||||||
\(661\) | 12.1269 | 0.471682 | 0.235841 | − | 0.971792i | \(-0.424216\pi\) | ||||
0.235841 | + | 0.971792i | \(0.424216\pi\) | |||||||
\(662\) | 46.9647 | 1.82533 | ||||||||
\(663\) | 60.5242 | 2.35056 | ||||||||
\(664\) | 8.18081 | 0.317477 | ||||||||
\(665\) | 22.4822 | 0.871822 | ||||||||
\(666\) | 31.5987 | 1.22443 | ||||||||
\(667\) | −1.31363 | −0.0508641 | ||||||||
\(668\) | 2.81963 | 0.109095 | ||||||||
\(669\) | 35.9648 | 1.39048 | ||||||||
\(670\) | 7.29076 | 0.281667 | ||||||||
\(671\) | 6.70615 | 0.258888 | ||||||||
\(672\) | 26.9256 | 1.03868 | ||||||||
\(673\) | 29.0911 | 1.12138 | 0.560689 | − | 0.828027i | \(-0.310536\pi\) | ||||
0.560689 | + | 0.828027i | \(0.310536\pi\) | |||||||
\(674\) | 48.3272 | 1.86149 | ||||||||
\(675\) | 10.4503 | 0.402232 | ||||||||
\(676\) | 1.65048 | 0.0634798 | ||||||||
\(677\) | 2.47305 | 0.0950469 | 0.0475235 | − | 0.998870i | \(-0.484867\pi\) | ||||
0.0475235 | + | 0.998870i | \(0.484867\pi\) | |||||||
\(678\) | −32.3877 | −1.24384 | ||||||||
\(679\) | −6.52714 | −0.250489 | ||||||||
\(680\) | 18.2758 | 0.700844 | ||||||||
\(681\) | −13.6357 | −0.522520 | ||||||||
\(682\) | 40.5014 | 1.55088 | ||||||||
\(683\) | −5.38825 | −0.206176 | −0.103088 | − | 0.994672i | \(-0.532872\pi\) | ||||
−0.103088 | + | 0.994672i | \(0.532872\pi\) | |||||||
\(684\) | 10.7418 | 0.410724 | ||||||||
\(685\) | 25.6899 | 0.981559 | ||||||||
\(686\) | −13.1668 | −0.502712 | ||||||||
\(687\) | −59.5112 | −2.27049 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38.8563 | −1.48031 | ||||||||
\(690\) | 14.7674 | 0.562185 | ||||||||
\(691\) | 4.72188 | 0.179629 | 0.0898143 | − | 0.995959i | \(-0.471373\pi\) | ||||
0.0898143 | + | 0.995959i | \(0.471373\pi\) | |||||||
\(692\) | −2.44182 | −0.0928240 | ||||||||
\(693\) | −43.6581 | −1.65844 | ||||||||
\(694\) | 14.9320 | 0.566811 | ||||||||
\(695\) | 28.8661 | 1.09495 | ||||||||
\(696\) | −3.36433 | −0.127525 | ||||||||
\(697\) | 12.6378 | 0.478690 | ||||||||
\(698\) | 17.3338 | 0.656094 | ||||||||
\(699\) | −26.1272 | −0.988222 | ||||||||
\(700\) | 5.50535 | 0.208083 | ||||||||
\(701\) | −26.8815 | −1.01530 | −0.507650 | − | 0.861564i | \(-0.669486\pi\) | ||||
−0.507650 | + | 0.861564i | \(0.669486\pi\) | |||||||
\(702\) | 21.9283 | 0.827630 | ||||||||
\(703\) | −21.9584 | −0.828178 | ||||||||
\(704\) | 14.6914 | 0.553704 | ||||||||
\(705\) | −3.37019 | −0.126929 | ||||||||
\(706\) | −45.7373 | −1.72134 | ||||||||
\(707\) | −26.0909 | −0.981248 | ||||||||
\(708\) | −14.8317 | −0.557411 | ||||||||
\(709\) | −7.05891 | −0.265103 | −0.132551 | − | 0.991176i | \(-0.542317\pi\) | ||||
−0.132551 | + | 0.991176i | \(0.542317\pi\) | |||||||
\(710\) | −15.7478 | −0.591005 | ||||||||
\(711\) | 10.0350 | 0.376343 | ||||||||
\(712\) | 2.13869 | 0.0801508 | ||||||||
\(713\) | 20.8435 | 0.780594 | ||||||||
\(714\) | 81.6240 | 3.05470 | ||||||||
\(715\) | −16.8627 | −0.630631 | ||||||||
\(716\) | 0.903332 | 0.0337591 | ||||||||
\(717\) | −29.7021 | −1.10925 | ||||||||
\(718\) | 14.6686 | 0.547426 | ||||||||
\(719\) | −21.3692 | −0.796936 | −0.398468 | − | 0.917182i | \(-0.630458\pi\) | ||||
−0.398468 | + | 0.917182i | \(0.630458\pi\) | |||||||
\(720\) | 28.5813 | 1.06516 | ||||||||
\(721\) | 2.37770 | 0.0885501 | ||||||||
\(722\) | −5.29665 | −0.197121 | ||||||||
\(723\) | 36.5956 | 1.36100 | ||||||||
\(724\) | 11.5360 | 0.428730 | ||||||||
\(725\) | −1.62504 | −0.0603524 | ||||||||
\(726\) | −8.48272 | −0.314823 | ||||||||
\(727\) | 5.21292 | 0.193336 | 0.0966682 | − | 0.995317i | \(-0.469181\pi\) | ||||
0.0966682 | + | 0.995317i | \(0.469181\pi\) | |||||||
\(728\) | −31.8806 | −1.18157 | ||||||||
\(729\) | −42.9916 | −1.59228 | ||||||||
\(730\) | −28.2761 | −1.04654 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −3.20282 | −0.118380 | ||||||||
\(733\) | 25.3899 | 0.937796 | 0.468898 | − | 0.883252i | \(-0.344651\pi\) | ||||
0.468898 | + | 0.883252i | \(0.344651\pi\) | |||||||
\(734\) | 29.1700 | 1.07669 | ||||||||
\(735\) | 17.2304 | 0.635553 | ||||||||
\(736\) | −7.22102 | −0.266170 | ||||||||
\(737\) | 9.83855 | 0.362408 | ||||||||
\(738\) | 15.3660 | 0.565628 | ||||||||
\(739\) | −7.02353 | −0.258365 | −0.129182 | − | 0.991621i | \(-0.541235\pi\) | ||||
−0.129182 | + | 0.991621i | \(0.541235\pi\) | |||||||
\(740\) | 3.45813 | 0.127123 | ||||||||
\(741\) | −51.1386 | −1.87862 | ||||||||
\(742\) | −52.4024 | −1.92375 | ||||||||
\(743\) | −34.9579 | −1.28248 | −0.641240 | − | 0.767341i | \(-0.721580\pi\) | ||||
−0.641240 | + | 0.767341i | \(0.721580\pi\) | |||||||
\(744\) | 53.3820 | 1.95708 | ||||||||
\(745\) | −16.1140 | −0.590373 | ||||||||
\(746\) | 43.8256 | 1.60457 | ||||||||
\(747\) | 14.9658 | 0.547571 | ||||||||
\(748\) | −8.93653 | −0.326752 | ||||||||
\(749\) | −43.3551 | −1.58416 | ||||||||
\(750\) | 48.2848 | 1.76311 | ||||||||
\(751\) | 10.8777 | 0.396934 | 0.198467 | − | 0.980108i | \(-0.436404\pi\) | ||||
0.198467 | + | 0.980108i | \(0.436404\pi\) | |||||||
\(752\) | 4.27074 | 0.155738 | ||||||||
\(753\) | −53.5105 | −1.95003 | ||||||||
\(754\) | −3.40989 | −0.124181 | ||||||||
\(755\) | −26.7300 | −0.972804 | ||||||||
\(756\) | 6.21316 | 0.225971 | ||||||||
\(757\) | 3.07537 | 0.111776 | 0.0558881 | − | 0.998437i | \(-0.482201\pi\) | ||||
0.0558881 | + | 0.998437i | \(0.482201\pi\) | |||||||
\(758\) | −14.4797 | −0.525926 | ||||||||
\(759\) | 19.9279 | 0.723338 | ||||||||
\(760\) | −15.4417 | −0.560130 | ||||||||
\(761\) | 20.2784 | 0.735090 | 0.367545 | − | 0.930006i | \(-0.380198\pi\) | ||||
0.367545 | + | 0.930006i | \(0.380198\pi\) | |||||||
\(762\) | −13.1105 | −0.474942 | ||||||||
\(763\) | 26.6362 | 0.964295 | ||||||||
\(764\) | 7.71759 | 0.279213 | ||||||||
\(765\) | 33.4334 | 1.20879 | ||||||||
\(766\) | −28.8744 | −1.04327 | ||||||||
\(767\) | 41.4857 | 1.49796 | ||||||||
\(768\) | −32.2115 | −1.16233 | ||||||||
\(769\) | −19.6319 | −0.707946 | −0.353973 | − | 0.935256i | \(-0.615169\pi\) | ||||
−0.353973 | + | 0.935256i | \(0.615169\pi\) | |||||||
\(770\) | −22.7414 | −0.819544 | ||||||||
\(771\) | −41.2244 | −1.48466 | ||||||||
\(772\) | −6.76677 | −0.243541 | ||||||||
\(773\) | 15.6254 | 0.562006 | 0.281003 | − | 0.959707i | \(-0.409333\pi\) | ||||
0.281003 | + | 0.959707i | \(0.409333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.7845 | 0.926208 | ||||||||
\(776\) | 4.48312 | 0.160935 | ||||||||
\(777\) | −42.6234 | −1.52911 | ||||||||
\(778\) | 19.7597 | 0.708419 | ||||||||
\(779\) | −10.6780 | −0.382580 | ||||||||
\(780\) | 8.05357 | 0.288364 | ||||||||
\(781\) | −21.2510 | −0.760420 | ||||||||
\(782\) | −21.8902 | −0.782794 | ||||||||
\(783\) | −1.83397 | −0.0655406 | ||||||||
\(784\) | −21.8345 | −0.779803 | ||||||||
\(785\) | 4.13987 | 0.147758 | ||||||||
\(786\) | −47.0024 | −1.67652 | ||||||||
\(787\) | 23.8861 | 0.851448 | 0.425724 | − | 0.904853i | \(-0.360019\pi\) | ||||
0.425724 | + | 0.904853i | \(0.360019\pi\) | |||||||
\(788\) | 8.11938 | 0.289241 | ||||||||
\(789\) | −51.8249 | −1.84501 | ||||||||
\(790\) | 5.22723 | 0.185976 | ||||||||
\(791\) | 25.6681 | 0.912654 | ||||||||
\(792\) | 29.9863 | 1.06552 | ||||||||
\(793\) | 8.95858 | 0.318128 | ||||||||
\(794\) | −51.8732 | −1.84091 | ||||||||
\(795\) | −36.5324 | −1.29567 | ||||||||
\(796\) | 10.2536 | 0.363431 | ||||||||
\(797\) | −6.40006 | −0.226702 | −0.113351 | − | 0.993555i | \(-0.536158\pi\) | ||||
−0.113351 | + | 0.993555i | \(0.536158\pi\) | |||||||
\(798\) | −68.9665 | −2.44139 | ||||||||
\(799\) | 4.99576 | 0.176737 | ||||||||
\(800\) | −8.93280 | −0.315822 | ||||||||
\(801\) | 3.91248 | 0.138241 | ||||||||
\(802\) | 45.2210 | 1.59681 | ||||||||
\(803\) | −38.1573 | −1.34654 | ||||||||
\(804\) | −4.69885 | −0.165716 | ||||||||
\(805\) | −11.7036 | −0.412496 | ||||||||
\(806\) | 54.1048 | 1.90576 | ||||||||
\(807\) | 55.8208 | 1.96498 | ||||||||
\(808\) | 17.9203 | 0.630435 | ||||||||
\(809\) | −37.6885 | −1.32506 | −0.662528 | − | 0.749037i | \(-0.730517\pi\) | ||||
−0.662528 | + | 0.749037i | \(0.730517\pi\) | |||||||
\(810\) | −7.92084 | −0.278310 | ||||||||
\(811\) | 3.96460 | 0.139216 | 0.0696079 | − | 0.997574i | \(-0.477825\pi\) | ||||
0.0696079 | + | 0.997574i | \(0.477825\pi\) | |||||||
\(812\) | −0.966158 | −0.0339055 | ||||||||
\(813\) | 53.5460 | 1.87794 | ||||||||
\(814\) | 22.2116 | 0.778518 | ||||||||
\(815\) | −17.5641 | −0.615242 | ||||||||
\(816\) | −72.1095 | −2.52434 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −37.6201 | −1.31536 | ||||||||
\(819\) | −58.3218 | −2.03793 | ||||||||
\(820\) | 1.68163 | 0.0587251 | ||||||||
\(821\) | −5.50054 | −0.191970 | −0.0959851 | − | 0.995383i | \(-0.530600\pi\) | ||||
−0.0959851 | + | 0.995383i | \(0.530600\pi\) | |||||||
\(822\) | −78.8064 | −2.74869 | ||||||||
\(823\) | −17.2937 | −0.602820 | −0.301410 | − | 0.953495i | \(-0.597457\pi\) | ||||
−0.301410 | + | 0.953495i | \(0.597457\pi\) | |||||||
\(824\) | −1.63310 | −0.0568919 | ||||||||
\(825\) | 24.6520 | 0.858272 | ||||||||
\(826\) | 55.9484 | 1.94669 | ||||||||
\(827\) | 23.1815 | 0.806101 | 0.403051 | − | 0.915178i | \(-0.367950\pi\) | ||||
0.403051 | + | 0.915178i | \(0.367950\pi\) | |||||||
\(828\) | −5.59188 | −0.194331 | ||||||||
\(829\) | 37.8108 | 1.31322 | 0.656611 | − | 0.754229i | \(-0.271989\pi\) | ||||
0.656611 | + | 0.754229i | \(0.271989\pi\) | |||||||
\(830\) | 7.79567 | 0.270592 | ||||||||
\(831\) | 10.2348 | 0.355041 | ||||||||
\(832\) | 19.6259 | 0.680406 | ||||||||
\(833\) | −25.5412 | −0.884951 | ||||||||
\(834\) | −88.5498 | −3.06623 | ||||||||
\(835\) | −7.41505 | −0.256609 | ||||||||
\(836\) | 7.55073 | 0.261148 | ||||||||
\(837\) | 29.0996 | 1.00583 | ||||||||
\(838\) | 4.88579 | 0.168777 | ||||||||
\(839\) | −39.5304 | −1.36474 | −0.682370 | − | 0.731007i | \(-0.739051\pi\) | ||||
−0.682370 | + | 0.731007i | \(0.739051\pi\) | |||||||
\(840\) | −29.9739 | −1.03420 | ||||||||
\(841\) | −28.7148 | −0.990166 | ||||||||
\(842\) | 12.5523 | 0.432581 | ||||||||
\(843\) | −17.8955 | −0.616353 | ||||||||
\(844\) | −11.3689 | −0.391332 | ||||||||
\(845\) | −4.34041 | −0.149315 | ||||||||
\(846\) | 6.07421 | 0.208836 | ||||||||
\(847\) | 6.72278 | 0.230997 | ||||||||
\(848\) | 46.2941 | 1.58975 | ||||||||
\(849\) | 75.4121 | 2.58814 | ||||||||
\(850\) | −27.0795 | −0.928818 | ||||||||
\(851\) | 11.4309 | 0.391847 | ||||||||
\(852\) | 10.1494 | 0.347712 | ||||||||
\(853\) | 53.1969 | 1.82143 | 0.910713 | − | 0.413040i | \(-0.135533\pi\) | ||||
0.910713 | + | 0.413040i | \(0.135533\pi\) | |||||||
\(854\) | 12.0817 | 0.413427 | ||||||||
\(855\) | −28.2488 | −0.966089 | ||||||||
\(856\) | 29.7782 | 1.01780 | ||||||||
\(857\) | 32.7837 | 1.11987 | 0.559935 | − | 0.828536i | \(-0.310826\pi\) | ||||
0.559935 | + | 0.828536i | \(0.310826\pi\) | |||||||
\(858\) | 51.7283 | 1.76597 | ||||||||
\(859\) | −18.7249 | −0.638885 | −0.319442 | − | 0.947606i | \(-0.603496\pi\) | ||||
−0.319442 | + | 0.947606i | \(0.603496\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.7271 | −0.706377 | ||||||||
\(862\) | −40.9469 | −1.39466 | ||||||||
\(863\) | 18.8899 | 0.643019 | 0.321510 | − | 0.946906i | \(-0.395810\pi\) | ||||
0.321510 | + | 0.946906i | \(0.395810\pi\) | |||||||
\(864\) | −10.0813 | −0.342972 | ||||||||
\(865\) | 6.42148 | 0.218337 | ||||||||
\(866\) | −14.8295 | −0.503928 | ||||||||
\(867\) | −38.5036 | −1.30765 | ||||||||
\(868\) | 15.3300 | 0.520336 | ||||||||
\(869\) | 7.05391 | 0.239287 | ||||||||
\(870\) | −3.20595 | −0.108692 | ||||||||
\(871\) | 13.1431 | 0.445336 | ||||||||
\(872\) | −18.2949 | −0.619543 | ||||||||
\(873\) | 8.20134 | 0.277573 | ||||||||
\(874\) | 18.4957 | 0.625626 | ||||||||
\(875\) | −38.2670 | −1.29366 | ||||||||
\(876\) | 18.2237 | 0.615722 | ||||||||
\(877\) | 22.6957 | 0.766378 | 0.383189 | − | 0.923670i | \(-0.374826\pi\) | ||||
0.383189 | + | 0.923670i | \(0.374826\pi\) | |||||||
\(878\) | 18.4052 | 0.621144 | ||||||||
\(879\) | −16.5846 | −0.559385 | ||||||||
\(880\) | 20.0906 | 0.677253 | ||||||||
\(881\) | 37.8496 | 1.27519 | 0.637593 | − | 0.770373i | \(-0.279930\pi\) | ||||
0.637593 | + | 0.770373i | \(0.279930\pi\) | |||||||
\(882\) | −31.0549 | −1.04567 | ||||||||
\(883\) | 6.97263 | 0.234648 | 0.117324 | − | 0.993094i | \(-0.462568\pi\) | ||||
0.117324 | + | 0.993094i | \(0.462568\pi\) | |||||||
\(884\) | −11.9381 | −0.401522 | ||||||||
\(885\) | 39.0045 | 1.31112 | ||||||||
\(886\) | −61.9386 | −2.08087 | ||||||||
\(887\) | −12.7605 | −0.428456 | −0.214228 | − | 0.976784i | \(-0.568723\pi\) | ||||
−0.214228 | + | 0.976784i | \(0.568723\pi\) | |||||||
\(888\) | 29.2756 | 0.982424 | ||||||||
\(889\) | 10.3904 | 0.348483 | ||||||||
\(890\) | 2.03800 | 0.0683140 | ||||||||
\(891\) | −10.6888 | −0.358089 | ||||||||
\(892\) | −7.09389 | −0.237521 | ||||||||
\(893\) | −4.22106 | −0.141252 | ||||||||
\(894\) | 49.4315 | 1.65324 | ||||||||
\(895\) | −2.37558 | −0.0794068 | ||||||||
\(896\) | 46.4355 | 1.55130 | ||||||||
\(897\) | 26.6212 | 0.888857 | ||||||||
\(898\) | −25.8173 | −0.861533 | ||||||||
\(899\) | −4.52504 | −0.150918 | ||||||||
\(900\) | −6.91747 | −0.230582 | ||||||||
\(901\) | 54.1533 | 1.80411 | ||||||||
\(902\) | 10.8012 | 0.359639 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.6300 | −0.586364 | ||||||||
\(905\) | −30.3372 | −1.00844 | ||||||||
\(906\) | 81.9971 | 2.72417 | ||||||||
\(907\) | 32.6147 | 1.08295 | 0.541476 | − | 0.840716i | \(-0.317866\pi\) | ||||
0.541476 | + | 0.840716i | \(0.317866\pi\) | |||||||
\(908\) | 2.68957 | 0.0892565 | ||||||||
\(909\) | 32.7831 | 1.08735 | ||||||||
\(910\) | −30.3797 | −1.00708 | ||||||||
\(911\) | −16.9707 | −0.562264 | −0.281132 | − | 0.959669i | \(-0.590710\pi\) | ||||
−0.281132 | + | 0.959669i | \(0.590710\pi\) | |||||||
\(912\) | 60.9274 | 2.01751 | ||||||||
\(913\) | 10.5199 | 0.348158 | ||||||||
\(914\) | 50.9273 | 1.68453 | ||||||||
\(915\) | 8.42277 | 0.278448 | ||||||||
\(916\) | 11.7383 | 0.387844 | ||||||||
\(917\) | 37.2507 | 1.23013 | ||||||||
\(918\) | −30.5610 | −1.00866 | ||||||||
\(919\) | −20.0436 | −0.661178 | −0.330589 | − | 0.943775i | \(-0.607247\pi\) | ||||
−0.330589 | + | 0.943775i | \(0.607247\pi\) | |||||||
\(920\) | 8.03850 | 0.265022 | ||||||||
\(921\) | −44.8234 | −1.47698 | ||||||||
\(922\) | −49.8431 | −1.64149 | ||||||||
\(923\) | −28.3887 | −0.934424 | ||||||||
\(924\) | 14.6567 | 0.482170 | ||||||||
\(925\) | 14.1407 | 0.464943 | ||||||||
\(926\) | 31.8232 | 1.04577 | ||||||||
\(927\) | −2.98757 | −0.0981248 | ||||||||
\(928\) | 1.56766 | 0.0514608 | ||||||||
\(929\) | −39.5173 | −1.29652 | −0.648260 | − | 0.761419i | \(-0.724503\pi\) | ||||
−0.648260 | + | 0.761419i | \(0.724503\pi\) | |||||||
\(930\) | 50.8688 | 1.66805 | ||||||||
\(931\) | 21.5805 | 0.707273 | ||||||||
\(932\) | 5.15346 | 0.168807 | ||||||||
\(933\) | −80.2959 | −2.62877 | ||||||||
\(934\) | 5.27770 | 0.172692 | ||||||||
\(935\) | 23.5013 | 0.768573 | ||||||||
\(936\) | 40.0579 | 1.30933 | ||||||||
\(937\) | 32.5538 | 1.06349 | 0.531744 | − | 0.846905i | \(-0.321537\pi\) | ||||
0.531744 | + | 0.846905i | \(0.321537\pi\) | |||||||
\(938\) | 17.7250 | 0.578742 | ||||||||
\(939\) | 17.7831 | 0.580330 | ||||||||
\(940\) | 0.664754 | 0.0216819 | ||||||||
\(941\) | 33.7288 | 1.09953 | 0.549764 | − | 0.835320i | \(-0.314718\pi\) | ||||
0.549764 | + | 0.835320i | \(0.314718\pi\) | |||||||
\(942\) | −12.6995 | −0.413771 | ||||||||
\(943\) | 5.55866 | 0.181015 | ||||||||
\(944\) | −49.4268 | −1.60870 | ||||||||
\(945\) | −16.3394 | −0.531519 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.2833 | 1.34153 | 0.670763 | − | 0.741672i | \(-0.265967\pi\) | ||||
0.670763 | + | 0.741672i | \(0.265967\pi\) | |||||||
\(948\) | −3.36891 | −0.109417 | ||||||||
\(949\) | −50.9733 | −1.65466 | ||||||||
\(950\) | 22.8802 | 0.742332 | ||||||||
\(951\) | −14.2957 | −0.463571 | ||||||||
\(952\) | 44.4313 | 1.44003 | ||||||||
\(953\) | −37.8902 | −1.22738 | −0.613692 | − | 0.789546i | \(-0.710316\pi\) | ||||
−0.613692 | + | 0.789546i | \(0.710316\pi\) | |||||||
\(954\) | 65.8435 | 2.13176 | ||||||||
\(955\) | −20.2957 | −0.656753 | ||||||||
\(956\) | 5.85860 | 0.189481 | ||||||||
\(957\) | −4.32628 | −0.139849 | ||||||||
\(958\) | −33.6576 | −1.08743 | ||||||||
\(959\) | 62.4562 | 2.01682 | ||||||||
\(960\) | 18.4521 | 0.595539 | ||||||||
\(961\) | 40.7988 | 1.31609 | ||||||||
\(962\) | 29.6720 | 0.956663 | ||||||||
\(963\) | 54.4756 | 1.75545 | ||||||||
\(964\) | −7.21829 | −0.232486 | ||||||||
\(965\) | 17.7952 | 0.572849 | ||||||||
\(966\) | 35.9019 | 1.15512 | ||||||||
\(967\) | 39.6951 | 1.27651 | 0.638254 | − | 0.769826i | \(-0.279657\pi\) | ||||
0.638254 | + | 0.769826i | \(0.279657\pi\) | |||||||
\(968\) | −4.61749 | −0.148412 | ||||||||
\(969\) | 71.2708 | 2.28955 | ||||||||
\(970\) | 4.27206 | 0.137168 | ||||||||
\(971\) | 3.14256 | 0.100849 | 0.0504247 | − | 0.998728i | \(-0.483942\pi\) | ||||
0.0504247 | + | 0.998728i | \(0.483942\pi\) | |||||||
\(972\) | 10.5855 | 0.339529 | ||||||||
\(973\) | 70.1781 | 2.24981 | ||||||||
\(974\) | −30.5241 | −0.978054 | ||||||||
\(975\) | 32.9320 | 1.05467 | ||||||||
\(976\) | −10.6734 | −0.341647 | ||||||||
\(977\) | 18.1280 | 0.579966 | 0.289983 | − | 0.957032i | \(-0.406350\pi\) | ||||
0.289983 | + | 0.957032i | \(0.406350\pi\) | |||||||
\(978\) | 53.8796 | 1.72288 | ||||||||
\(979\) | 2.75019 | 0.0878966 | ||||||||
\(980\) | −3.39861 | −0.108565 | ||||||||
\(981\) | −33.4683 | −1.06856 | ||||||||
\(982\) | −18.0681 | −0.576578 | ||||||||
\(983\) | 0.540449 | 0.0172376 | 0.00861882 | − | 0.999963i | \(-0.497257\pi\) | ||||
0.00861882 | + | 0.999963i | \(0.497257\pi\) | |||||||
\(984\) | 14.2362 | 0.453835 | ||||||||
\(985\) | −21.3523 | −0.680341 | ||||||||
\(986\) | 4.75229 | 0.151344 | ||||||||
\(987\) | −8.19348 | −0.260801 | ||||||||
\(988\) | 10.0868 | 0.320905 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 28.5746 | 0.908159 | ||||||||
\(991\) | 2.80194 | 0.0890065 | 0.0445032 | − | 0.999009i | \(-0.485829\pi\) | ||||
0.0445032 | + | 0.999009i | \(0.485829\pi\) | |||||||
\(992\) | −24.8740 | −0.789751 | ||||||||
\(993\) | 79.5997 | 2.52602 | ||||||||
\(994\) | −38.2855 | −1.21434 | ||||||||
\(995\) | −26.9650 | −0.854848 | ||||||||
\(996\) | −5.02426 | −0.159200 | ||||||||
\(997\) | −6.73119 | −0.213179 | −0.106590 | − | 0.994303i | \(-0.533993\pi\) | ||||
−0.106590 | + | 0.994303i | \(0.533993\pi\) | |||||||
\(998\) | −51.3016 | −1.62392 | ||||||||
\(999\) | 15.9587 | 0.504911 |
(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 | 1849.2.a.r.1.5 | yes | 20 | |
43.42 | odd | 2 | 1849.2.a.p.1.16 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.2.a.p.1.16 | ✓ | 20 | 43.42 | odd | 2 | ||
1849.2.a.r.1.5 | yes | 20 | 1.1 | even | 1 | trivial |