Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(2.13862\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.13862 | 1.51223 | 0.756115 | − | 0.654439i | \(-0.227095\pi\) | ||||
0.756115 | + | 0.654439i | \(0.227095\pi\) | |||||||
\(3\) | 3.19578 | 1.84508 | 0.922541 | − | 0.385899i | \(-0.126109\pi\) | ||||
0.922541 | + | 0.385899i | \(0.126109\pi\) | |||||||
\(4\) | 2.57368 | 1.28684 | ||||||||
\(5\) | −0.343330 | −0.153542 | −0.0767709 | − | 0.997049i | \(-0.524461\pi\) | ||||
−0.0767709 | + | 0.997049i | \(0.524461\pi\) | |||||||
\(6\) | 6.83454 | 2.79019 | ||||||||
\(7\) | −2.49131 | −0.941625 | −0.470812 | − | 0.882233i | \(-0.656039\pi\) | ||||
−0.470812 | + | 0.882233i | \(0.656039\pi\) | |||||||
\(8\) | 1.22687 | 0.433765 | ||||||||
\(9\) | 7.21299 | 2.40433 | ||||||||
\(10\) | −0.734251 | −0.232191 | ||||||||
\(11\) | 0.158588 | 0.0478161 | 0.0239080 | − | 0.999714i | \(-0.492389\pi\) | ||||
0.0239080 | + | 0.999714i | \(0.492389\pi\) | |||||||
\(12\) | 8.22489 | 2.37432 | ||||||||
\(13\) | −0.313547 | −0.0869624 | −0.0434812 | − | 0.999054i | \(-0.513845\pi\) | ||||
−0.0434812 | + | 0.999054i | \(0.513845\pi\) | |||||||
\(14\) | −5.32794 | −1.42395 | ||||||||
\(15\) | −1.09721 | −0.283297 | ||||||||
\(16\) | −2.52354 | −0.630886 | ||||||||
\(17\) | −4.67587 | −1.13406 | −0.567032 | − | 0.823696i | \(-0.691908\pi\) | ||||
−0.567032 | + | 0.823696i | \(0.691908\pi\) | |||||||
\(18\) | 15.4258 | 3.63590 | ||||||||
\(19\) | −4.91384 | −1.12731 | −0.563656 | − | 0.826010i | \(-0.690606\pi\) | ||||
−0.563656 | + | 0.826010i | \(0.690606\pi\) | |||||||
\(20\) | −0.883620 | −0.197584 | ||||||||
\(21\) | −7.96165 | −1.73738 | ||||||||
\(22\) | 0.339159 | 0.0723089 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 3.92081 | 0.800332 | ||||||||
\(25\) | −4.88212 | −0.976425 | ||||||||
\(26\) | −0.670557 | −0.131507 | ||||||||
\(27\) | 13.4638 | 2.59110 | ||||||||
\(28\) | −6.41181 | −1.21172 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −2.34650 | −0.428411 | ||||||||
\(31\) | 8.73283 | 1.56846 | 0.784232 | − | 0.620468i | \(-0.213057\pi\) | ||||
0.784232 | + | 0.620468i | \(0.213057\pi\) | |||||||
\(32\) | −7.85063 | −1.38781 | ||||||||
\(33\) | 0.506812 | 0.0882246 | ||||||||
\(34\) | −9.99988 | −1.71497 | ||||||||
\(35\) | 0.855340 | 0.144579 | ||||||||
\(36\) | 18.5639 | 3.09398 | ||||||||
\(37\) | 7.70294 | 1.26636 | 0.633178 | − | 0.774006i | \(-0.281750\pi\) | ||||
0.633178 | + | 0.774006i | \(0.281750\pi\) | |||||||
\(38\) | −10.5088 | −1.70475 | ||||||||
\(39\) | −1.00203 | −0.160453 | ||||||||
\(40\) | −0.421222 | −0.0666011 | ||||||||
\(41\) | 7.50928 | 1.17275 | 0.586376 | − | 0.810039i | \(-0.300554\pi\) | ||||
0.586376 | + | 0.810039i | \(0.300554\pi\) | |||||||
\(42\) | −17.0269 | −2.62731 | ||||||||
\(43\) | 4.03395 | 0.615171 | 0.307585 | − | 0.951520i | \(-0.400479\pi\) | ||||
0.307585 | + | 0.951520i | \(0.400479\pi\) | |||||||
\(44\) | 0.408154 | 0.0615316 | ||||||||
\(45\) | −2.47644 | −0.369165 | ||||||||
\(46\) | 2.13862 | 0.315322 | ||||||||
\(47\) | 3.87949 | 0.565882 | 0.282941 | − | 0.959137i | \(-0.408690\pi\) | ||||
0.282941 | + | 0.959137i | \(0.408690\pi\) | |||||||
\(48\) | −8.06468 | −1.16404 | ||||||||
\(49\) | −0.793397 | −0.113342 | ||||||||
\(50\) | −10.4410 | −1.47658 | ||||||||
\(51\) | −14.9430 | −2.09244 | ||||||||
\(52\) | −0.806969 | −0.111907 | ||||||||
\(53\) | 5.89609 | 0.809890 | 0.404945 | − | 0.914341i | \(-0.367291\pi\) | ||||
0.404945 | + | 0.914341i | \(0.367291\pi\) | |||||||
\(54\) | 28.7938 | 3.91834 | ||||||||
\(55\) | −0.0544481 | −0.00734177 | ||||||||
\(56\) | −3.05651 | −0.408444 | ||||||||
\(57\) | −15.7035 | −2.07998 | ||||||||
\(58\) | −2.13862 | −0.280814 | ||||||||
\(59\) | −7.19090 | −0.936175 | −0.468088 | − | 0.883682i | \(-0.655057\pi\) | ||||
−0.468088 | + | 0.883682i | \(0.655057\pi\) | |||||||
\(60\) | −2.82385 | −0.364558 | ||||||||
\(61\) | 10.4921 | 1.34337 | 0.671686 | − | 0.740836i | \(-0.265571\pi\) | ||||
0.671686 | + | 0.740836i | \(0.265571\pi\) | |||||||
\(62\) | 18.6762 | 2.37188 | ||||||||
\(63\) | −17.9698 | −2.26398 | ||||||||
\(64\) | −11.7424 | −1.46780 | ||||||||
\(65\) | 0.107650 | 0.0133524 | ||||||||
\(66\) | 1.08388 | 0.133416 | ||||||||
\(67\) | −5.79686 | −0.708199 | −0.354100 | − | 0.935208i | \(-0.615213\pi\) | ||||
−0.354100 | + | 0.935208i | \(0.615213\pi\) | |||||||
\(68\) | −12.0342 | −1.45936 | ||||||||
\(69\) | 3.19578 | 0.384726 | ||||||||
\(70\) | 1.82924 | 0.218636 | ||||||||
\(71\) | −0.837052 | −0.0993398 | −0.0496699 | − | 0.998766i | \(-0.515817\pi\) | ||||
−0.0496699 | + | 0.998766i | \(0.515817\pi\) | |||||||
\(72\) | 8.84941 | 1.04291 | ||||||||
\(73\) | −13.4130 | −1.56987 | −0.784936 | − | 0.619576i | \(-0.787304\pi\) | ||||
−0.784936 | + | 0.619576i | \(0.787304\pi\) | |||||||
\(74\) | 16.4736 | 1.91502 | ||||||||
\(75\) | −15.6022 | −1.80158 | ||||||||
\(76\) | −12.6466 | −1.45067 | ||||||||
\(77\) | −0.395091 | −0.0450248 | ||||||||
\(78\) | −2.14295 | −0.242641 | ||||||||
\(79\) | 6.13553 | 0.690301 | 0.345151 | − | 0.938547i | \(-0.387828\pi\) | ||||
0.345151 | + | 0.938547i | \(0.387828\pi\) | |||||||
\(80\) | 0.866409 | 0.0968674 | ||||||||
\(81\) | 21.3882 | 2.37647 | ||||||||
\(82\) | 16.0595 | 1.77347 | ||||||||
\(83\) | −10.3618 | −1.13735 | −0.568677 | − | 0.822561i | \(-0.692545\pi\) | ||||
−0.568677 | + | 0.822561i | \(0.692545\pi\) | |||||||
\(84\) | −20.4907 | −2.23572 | ||||||||
\(85\) | 1.60537 | 0.174126 | ||||||||
\(86\) | 8.62706 | 0.930280 | ||||||||
\(87\) | −3.19578 | −0.342623 | ||||||||
\(88\) | 0.194567 | 0.0207409 | ||||||||
\(89\) | 3.81659 | 0.404557 | 0.202279 | − | 0.979328i | \(-0.435165\pi\) | ||||
0.202279 | + | 0.979328i | \(0.435165\pi\) | |||||||
\(90\) | −5.29614 | −0.558262 | ||||||||
\(91\) | 0.781142 | 0.0818860 | ||||||||
\(92\) | 2.57368 | 0.268324 | ||||||||
\(93\) | 27.9082 | 2.89394 | ||||||||
\(94\) | 8.29673 | 0.855743 | ||||||||
\(95\) | 1.68707 | 0.173090 | ||||||||
\(96\) | −25.0889 | −2.56062 | ||||||||
\(97\) | 15.2047 | 1.54380 | 0.771902 | − | 0.635741i | \(-0.219306\pi\) | ||||
0.771902 | + | 0.635741i | \(0.219306\pi\) | |||||||
\(98\) | −1.69677 | −0.171400 | ||||||||
\(99\) | 1.14389 | 0.114966 | ||||||||
\(100\) | −12.5650 | −1.25650 | ||||||||
\(101\) | −1.28519 | −0.127882 | −0.0639408 | − | 0.997954i | \(-0.520367\pi\) | ||||
−0.0639408 | + | 0.997954i | \(0.520367\pi\) | |||||||
\(102\) | −31.9574 | −3.16425 | ||||||||
\(103\) | −0.696939 | −0.0686714 | −0.0343357 | − | 0.999410i | \(-0.510932\pi\) | ||||
−0.0343357 | + | 0.999410i | \(0.510932\pi\) | |||||||
\(104\) | −0.384683 | −0.0377212 | ||||||||
\(105\) | 2.73348 | 0.266760 | ||||||||
\(106\) | 12.6095 | 1.22474 | ||||||||
\(107\) | 1.07960 | 0.104369 | 0.0521846 | − | 0.998637i | \(-0.483382\pi\) | ||||
0.0521846 | + | 0.998637i | \(0.483382\pi\) | |||||||
\(108\) | 34.6514 | 3.33433 | ||||||||
\(109\) | −14.2835 | −1.36811 | −0.684054 | − | 0.729431i | \(-0.739785\pi\) | ||||
−0.684054 | + | 0.729431i | \(0.739785\pi\) | |||||||
\(110\) | −0.116443 | −0.0111024 | ||||||||
\(111\) | 24.6169 | 2.33653 | ||||||||
\(112\) | 6.28692 | 0.594058 | ||||||||
\(113\) | −7.25184 | −0.682196 | −0.341098 | − | 0.940028i | \(-0.610799\pi\) | ||||
−0.341098 | + | 0.940028i | \(0.610799\pi\) | |||||||
\(114\) | −33.5838 | −3.14541 | ||||||||
\(115\) | −0.343330 | −0.0320157 | ||||||||
\(116\) | −2.57368 | −0.238960 | ||||||||
\(117\) | −2.26161 | −0.209086 | ||||||||
\(118\) | −15.3786 | −1.41571 | ||||||||
\(119\) | 11.6490 | 1.06786 | ||||||||
\(120\) | −1.34613 | −0.122884 | ||||||||
\(121\) | −10.9748 | −0.997714 | ||||||||
\(122\) | 22.4385 | 2.03149 | ||||||||
\(123\) | 23.9980 | 2.16382 | ||||||||
\(124\) | 22.4755 | 2.01836 | ||||||||
\(125\) | 3.39283 | 0.303464 | ||||||||
\(126\) | −38.4304 | −3.42365 | ||||||||
\(127\) | −15.9435 | −1.41475 | −0.707377 | − | 0.706837i | \(-0.750122\pi\) | ||||
−0.707377 | + | 0.706837i | \(0.750122\pi\) | |||||||
\(128\) | −9.41121 | −0.831841 | ||||||||
\(129\) | 12.8916 | 1.13504 | ||||||||
\(130\) | 0.230222 | 0.0201918 | ||||||||
\(131\) | 0.774574 | 0.0676748 | 0.0338374 | − | 0.999427i | \(-0.489227\pi\) | ||||
0.0338374 | + | 0.999427i | \(0.489227\pi\) | |||||||
\(132\) | 1.30437 | 0.113531 | ||||||||
\(133\) | 12.2419 | 1.06150 | ||||||||
\(134\) | −12.3973 | −1.07096 | ||||||||
\(135\) | −4.62251 | −0.397843 | ||||||||
\(136\) | −5.73669 | −0.491917 | ||||||||
\(137\) | 4.83204 | 0.412829 | 0.206415 | − | 0.978465i | \(-0.433820\pi\) | ||||
0.206415 | + | 0.978465i | \(0.433820\pi\) | |||||||
\(138\) | 6.83454 | 0.581794 | ||||||||
\(139\) | 9.99495 | 0.847761 | 0.423880 | − | 0.905718i | \(-0.360668\pi\) | ||||
0.423880 | + | 0.905718i | \(0.360668\pi\) | |||||||
\(140\) | 2.20137 | 0.186050 | ||||||||
\(141\) | 12.3980 | 1.04410 | ||||||||
\(142\) | −1.79013 | −0.150225 | ||||||||
\(143\) | −0.0497249 | −0.00415820 | ||||||||
\(144\) | −18.2023 | −1.51686 | ||||||||
\(145\) | 0.343330 | 0.0285120 | ||||||||
\(146\) | −28.6852 | −2.37401 | ||||||||
\(147\) | −2.53552 | −0.209126 | ||||||||
\(148\) | 19.8249 | 1.62960 | ||||||||
\(149\) | −16.7051 | −1.36854 | −0.684269 | − | 0.729230i | \(-0.739879\pi\) | ||||
−0.684269 | + | 0.729230i | \(0.739879\pi\) | |||||||
\(150\) | −33.3671 | −2.72441 | ||||||||
\(151\) | 4.53234 | 0.368837 | 0.184418 | − | 0.982848i | \(-0.440960\pi\) | ||||
0.184418 | + | 0.982848i | \(0.440960\pi\) | |||||||
\(152\) | −6.02865 | −0.488988 | ||||||||
\(153\) | −33.7270 | −2.72666 | ||||||||
\(154\) | −0.844948 | −0.0680879 | ||||||||
\(155\) | −2.99824 | −0.240825 | ||||||||
\(156\) | −2.57889 | −0.206477 | ||||||||
\(157\) | 19.0521 | 1.52052 | 0.760260 | − | 0.649619i | \(-0.225072\pi\) | ||||
0.760260 | + | 0.649619i | \(0.225072\pi\) | |||||||
\(158\) | 13.1215 | 1.04389 | ||||||||
\(159\) | 18.8426 | 1.49431 | ||||||||
\(160\) | 2.69536 | 0.213087 | ||||||||
\(161\) | −2.49131 | −0.196342 | ||||||||
\(162\) | 45.7411 | 3.59376 | ||||||||
\(163\) | 0.657843 | 0.0515263 | 0.0257631 | − | 0.999668i | \(-0.491798\pi\) | ||||
0.0257631 | + | 0.999668i | \(0.491798\pi\) | |||||||
\(164\) | 19.3264 | 1.50914 | ||||||||
\(165\) | −0.174004 | −0.0135462 | ||||||||
\(166\) | −22.1599 | −1.71994 | ||||||||
\(167\) | 10.5082 | 0.813149 | 0.406575 | − | 0.913618i | \(-0.366723\pi\) | ||||
0.406575 | + | 0.913618i | \(0.366723\pi\) | |||||||
\(168\) | −9.76793 | −0.753612 | ||||||||
\(169\) | −12.9017 | −0.992438 | ||||||||
\(170\) | 3.43326 | 0.263319 | ||||||||
\(171\) | −35.4434 | −2.71043 | ||||||||
\(172\) | 10.3821 | 0.791625 | ||||||||
\(173\) | 16.1298 | 1.22633 | 0.613164 | − | 0.789955i | \(-0.289896\pi\) | ||||
0.613164 | + | 0.789955i | \(0.289896\pi\) | |||||||
\(174\) | −6.83454 | −0.518125 | ||||||||
\(175\) | 12.1629 | 0.919426 | ||||||||
\(176\) | −0.400204 | −0.0301665 | ||||||||
\(177\) | −22.9805 | −1.72732 | ||||||||
\(178\) | 8.16221 | 0.611783 | ||||||||
\(179\) | 4.86868 | 0.363903 | 0.181951 | − | 0.983308i | \(-0.441759\pi\) | ||||
0.181951 | + | 0.983308i | \(0.441759\pi\) | |||||||
\(180\) | −6.37354 | −0.475056 | ||||||||
\(181\) | −2.00349 | −0.148918 | −0.0744592 | − | 0.997224i | \(-0.523723\pi\) | ||||
−0.0744592 | + | 0.997224i | \(0.523723\pi\) | |||||||
\(182\) | 1.67056 | 0.123830 | ||||||||
\(183\) | 33.5303 | 2.47863 | ||||||||
\(184\) | 1.22687 | 0.0904462 | ||||||||
\(185\) | −2.64465 | −0.194439 | ||||||||
\(186\) | 59.6849 | 4.37631 | ||||||||
\(187\) | −0.741537 | −0.0542265 | ||||||||
\(188\) | 9.98454 | 0.728198 | ||||||||
\(189\) | −33.5423 | −2.43985 | ||||||||
\(190\) | 3.60799 | 0.261751 | ||||||||
\(191\) | 14.9101 | 1.07886 | 0.539429 | − | 0.842031i | \(-0.318640\pi\) | ||||
0.539429 | + | 0.842031i | \(0.318640\pi\) | |||||||
\(192\) | −37.5261 | −2.70821 | ||||||||
\(193\) | −3.17142 | −0.228283 | −0.114142 | − | 0.993464i | \(-0.536412\pi\) | ||||
−0.114142 | + | 0.993464i | \(0.536412\pi\) | |||||||
\(194\) | 32.5170 | 2.33459 | ||||||||
\(195\) | 0.344026 | 0.0246362 | ||||||||
\(196\) | −2.04195 | −0.145853 | ||||||||
\(197\) | 20.3560 | 1.45030 | 0.725151 | − | 0.688590i | \(-0.241770\pi\) | ||||
0.725151 | + | 0.688590i | \(0.241770\pi\) | |||||||
\(198\) | 2.44635 | 0.173854 | ||||||||
\(199\) | −15.6500 | −1.10940 | −0.554700 | − | 0.832050i | \(-0.687167\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(200\) | −5.98974 | −0.423539 | ||||||||
\(201\) | −18.5255 | −1.30669 | ||||||||
\(202\) | −2.74854 | −0.193386 | ||||||||
\(203\) | 2.49131 | 0.174855 | ||||||||
\(204\) | −38.4585 | −2.69263 | ||||||||
\(205\) | −2.57816 | −0.180067 | ||||||||
\(206\) | −1.49048 | −0.103847 | ||||||||
\(207\) | 7.21299 | 0.501337 | ||||||||
\(208\) | 0.791251 | 0.0548634 | ||||||||
\(209\) | −0.779276 | −0.0539036 | ||||||||
\(210\) | 5.84585 | 0.403402 | ||||||||
\(211\) | 17.4505 | 1.20134 | 0.600670 | − | 0.799497i | \(-0.294901\pi\) | ||||
0.600670 | + | 0.799497i | \(0.294901\pi\) | |||||||
\(212\) | 15.1746 | 1.04220 | ||||||||
\(213\) | −2.67503 | −0.183290 | ||||||||
\(214\) | 2.30886 | 0.157830 | ||||||||
\(215\) | −1.38497 | −0.0944545 | ||||||||
\(216\) | 16.5183 | 1.12393 | ||||||||
\(217\) | −21.7562 | −1.47690 | ||||||||
\(218\) | −30.5468 | −2.06889 | ||||||||
\(219\) | −42.8649 | −2.89654 | ||||||||
\(220\) | −0.140132 | −0.00944767 | ||||||||
\(221\) | 1.46611 | 0.0986210 | ||||||||
\(222\) | 52.6461 | 3.53337 | ||||||||
\(223\) | −13.4605 | −0.901379 | −0.450690 | − | 0.892681i | \(-0.648822\pi\) | ||||
−0.450690 | + | 0.892681i | \(0.648822\pi\) | |||||||
\(224\) | 19.5583 | 1.30680 | ||||||||
\(225\) | −35.2147 | −2.34765 | ||||||||
\(226\) | −15.5089 | −1.03164 | ||||||||
\(227\) | −28.0083 | −1.85898 | −0.929488 | − | 0.368853i | \(-0.879751\pi\) | ||||
−0.929488 | + | 0.368853i | \(0.879751\pi\) | |||||||
\(228\) | −40.4158 | −2.67660 | ||||||||
\(229\) | −15.2203 | −1.00578 | −0.502892 | − | 0.864349i | \(-0.667731\pi\) | ||||
−0.502892 | + | 0.864349i | \(0.667731\pi\) | |||||||
\(230\) | −0.734251 | −0.0484151 | ||||||||
\(231\) | −1.26262 | −0.0830745 | ||||||||
\(232\) | −1.22687 | −0.0805481 | ||||||||
\(233\) | 22.7178 | 1.48829 | 0.744147 | − | 0.668016i | \(-0.232856\pi\) | ||||
0.744147 | + | 0.668016i | \(0.232856\pi\) | |||||||
\(234\) | −4.83672 | −0.316186 | ||||||||
\(235\) | −1.33195 | −0.0868865 | ||||||||
\(236\) | −18.5070 | −1.20471 | ||||||||
\(237\) | 19.6078 | 1.27366 | ||||||||
\(238\) | 24.9128 | 1.61485 | ||||||||
\(239\) | −24.6833 | −1.59663 | −0.798315 | − | 0.602240i | \(-0.794275\pi\) | ||||
−0.798315 | + | 0.602240i | \(0.794275\pi\) | |||||||
\(240\) | 2.76885 | 0.178728 | ||||||||
\(241\) | −13.6625 | −0.880081 | −0.440040 | − | 0.897978i | \(-0.645036\pi\) | ||||
−0.440040 | + | 0.897978i | \(0.645036\pi\) | |||||||
\(242\) | −23.4710 | −1.50877 | ||||||||
\(243\) | 27.9606 | 1.79368 | ||||||||
\(244\) | 27.0032 | 1.72870 | ||||||||
\(245\) | 0.272397 | 0.0174028 | ||||||||
\(246\) | 51.3224 | 3.27220 | ||||||||
\(247\) | 1.54072 | 0.0980337 | ||||||||
\(248\) | 10.7141 | 0.680344 | ||||||||
\(249\) | −33.1140 | −2.09851 | ||||||||
\(250\) | 7.25596 | 0.458907 | ||||||||
\(251\) | 8.55413 | 0.539932 | 0.269966 | − | 0.962870i | \(-0.412988\pi\) | ||||
0.269966 | + | 0.962870i | \(0.412988\pi\) | |||||||
\(252\) | −46.2483 | −2.91337 | ||||||||
\(253\) | 0.158588 | 0.00997034 | ||||||||
\(254\) | −34.0969 | −2.13943 | ||||||||
\(255\) | 5.13039 | 0.321278 | ||||||||
\(256\) | 3.35785 | 0.209865 | ||||||||
\(257\) | 11.8392 | 0.738509 | 0.369255 | − | 0.929328i | \(-0.379613\pi\) | ||||
0.369255 | + | 0.929328i | \(0.379613\pi\) | |||||||
\(258\) | 27.5701 | 1.71644 | ||||||||
\(259\) | −19.1904 | −1.19243 | ||||||||
\(260\) | 0.277057 | 0.0171823 | ||||||||
\(261\) | −7.21299 | −0.446473 | ||||||||
\(262\) | 1.65652 | 0.102340 | ||||||||
\(263\) | 21.8415 | 1.34681 | 0.673403 | − | 0.739276i | \(-0.264832\pi\) | ||||
0.673403 | + | 0.739276i | \(0.264832\pi\) | |||||||
\(264\) | 0.621793 | 0.0382687 | ||||||||
\(265\) | −2.02431 | −0.124352 | ||||||||
\(266\) | 26.1807 | 1.60524 | ||||||||
\(267\) | 12.1970 | 0.746442 | ||||||||
\(268\) | −14.9192 | −0.911337 | ||||||||
\(269\) | −28.5894 | −1.74313 | −0.871564 | − | 0.490282i | \(-0.836894\pi\) | ||||
−0.871564 | + | 0.490282i | \(0.836894\pi\) | |||||||
\(270\) | −9.88578 | −0.601629 | ||||||||
\(271\) | 21.7801 | 1.32305 | 0.661525 | − | 0.749923i | \(-0.269910\pi\) | ||||
0.661525 | + | 0.749923i | \(0.269910\pi\) | |||||||
\(272\) | 11.7998 | 0.715465 | ||||||||
\(273\) | 2.49636 | 0.151086 | ||||||||
\(274\) | 10.3339 | 0.624293 | ||||||||
\(275\) | −0.774247 | −0.0466888 | ||||||||
\(276\) | 8.22489 | 0.495080 | ||||||||
\(277\) | 9.32234 | 0.560125 | 0.280063 | − | 0.959982i | \(-0.409645\pi\) | ||||
0.280063 | + | 0.959982i | \(0.409645\pi\) | |||||||
\(278\) | 21.3754 | 1.28201 | ||||||||
\(279\) | 62.9898 | 3.77110 | ||||||||
\(280\) | 1.04939 | 0.0627132 | ||||||||
\(281\) | −8.41066 | −0.501738 | −0.250869 | − | 0.968021i | \(-0.580716\pi\) | ||||
−0.250869 | + | 0.968021i | \(0.580716\pi\) | |||||||
\(282\) | 26.5145 | 1.57892 | ||||||||
\(283\) | 14.7994 | 0.879734 | 0.439867 | − | 0.898063i | \(-0.355026\pi\) | ||||
0.439867 | + | 0.898063i | \(0.355026\pi\) | |||||||
\(284\) | −2.15430 | −0.127834 | ||||||||
\(285\) | 5.39149 | 0.319365 | ||||||||
\(286\) | −0.106342 | −0.00628816 | ||||||||
\(287\) | −18.7079 | −1.10429 | ||||||||
\(288\) | −56.6265 | −3.33675 | ||||||||
\(289\) | 4.86373 | 0.286102 | ||||||||
\(290\) | 0.734251 | 0.0431167 | ||||||||
\(291\) | 48.5908 | 2.84845 | ||||||||
\(292\) | −34.5207 | −2.02017 | ||||||||
\(293\) | −10.9419 | −0.639230 | −0.319615 | − | 0.947547i | \(-0.603554\pi\) | ||||
−0.319615 | + | 0.947547i | \(0.603554\pi\) | |||||||
\(294\) | −5.42250 | −0.316247 | ||||||||
\(295\) | 2.46885 | 0.143742 | ||||||||
\(296\) | 9.45053 | 0.549301 | ||||||||
\(297\) | 2.13519 | 0.123896 | ||||||||
\(298\) | −35.7259 | −2.06954 | ||||||||
\(299\) | −0.313547 | −0.0181329 | ||||||||
\(300\) | −40.1549 | −2.31835 | ||||||||
\(301\) | −10.0498 | −0.579260 | ||||||||
\(302\) | 9.69294 | 0.557766 | ||||||||
\(303\) | −4.10719 | −0.235952 | ||||||||
\(304\) | 12.4003 | 0.711205 | ||||||||
\(305\) | −3.60224 | −0.206264 | ||||||||
\(306\) | −72.1290 | −4.12334 | ||||||||
\(307\) | −4.26400 | −0.243359 | −0.121680 | − | 0.992569i | \(-0.538828\pi\) | ||||
−0.121680 | + | 0.992569i | \(0.538828\pi\) | |||||||
\(308\) | −1.01684 | −0.0579397 | ||||||||
\(309\) | −2.22726 | −0.126704 | ||||||||
\(310\) | −6.41209 | −0.364182 | ||||||||
\(311\) | −10.4457 | −0.592324 | −0.296162 | − | 0.955138i | \(-0.595707\pi\) | ||||
−0.296162 | + | 0.955138i | \(0.595707\pi\) | |||||||
\(312\) | −1.22936 | −0.0695988 | ||||||||
\(313\) | 33.4362 | 1.88992 | 0.944962 | − | 0.327180i | \(-0.106098\pi\) | ||||
0.944962 | + | 0.327180i | \(0.106098\pi\) | |||||||
\(314\) | 40.7450 | 2.29937 | ||||||||
\(315\) | 6.16956 | 0.347615 | ||||||||
\(316\) | 15.7909 | 0.888306 | ||||||||
\(317\) | 18.9342 | 1.06345 | 0.531726 | − | 0.846917i | \(-0.321544\pi\) | ||||
0.531726 | + | 0.846917i | \(0.321544\pi\) | |||||||
\(318\) | 40.2970 | 2.25975 | ||||||||
\(319\) | −0.158588 | −0.00887923 | ||||||||
\(320\) | 4.03152 | 0.225369 | ||||||||
\(321\) | 3.45017 | 0.192570 | ||||||||
\(322\) | −5.32794 | −0.296915 | ||||||||
\(323\) | 22.9765 | 1.27844 | ||||||||
\(324\) | 55.0463 | 3.05813 | ||||||||
\(325\) | 1.53078 | 0.0849122 | ||||||||
\(326\) | 1.40687 | 0.0779195 | ||||||||
\(327\) | −45.6468 | −2.52427 | ||||||||
\(328\) | 9.21292 | 0.508698 | ||||||||
\(329\) | −9.66499 | −0.532848 | ||||||||
\(330\) | −0.372127 | −0.0204849 | ||||||||
\(331\) | −28.4961 | −1.56629 | −0.783143 | − | 0.621842i | \(-0.786385\pi\) | ||||
−0.783143 | + | 0.621842i | \(0.786385\pi\) | |||||||
\(332\) | −26.6679 | −1.46359 | ||||||||
\(333\) | 55.5612 | 3.04474 | ||||||||
\(334\) | 22.4730 | 1.22967 | ||||||||
\(335\) | 1.99024 | 0.108738 | ||||||||
\(336\) | 20.0916 | 1.09609 | ||||||||
\(337\) | −20.4501 | −1.11399 | −0.556994 | − | 0.830517i | \(-0.688045\pi\) | ||||
−0.556994 | + | 0.830517i | \(0.688045\pi\) | |||||||
\(338\) | −27.5917 | −1.50079 | ||||||||
\(339\) | −23.1753 | −1.25871 | ||||||||
\(340\) | 4.13169 | 0.224072 | ||||||||
\(341\) | 1.38492 | 0.0749978 | ||||||||
\(342\) | −75.7999 | −4.09879 | ||||||||
\(343\) | 19.4157 | 1.04835 | ||||||||
\(344\) | 4.94913 | 0.266839 | ||||||||
\(345\) | −1.09721 | −0.0590716 | ||||||||
\(346\) | 34.4955 | 1.85449 | ||||||||
\(347\) | −23.1503 | −1.24277 | −0.621387 | − | 0.783504i | \(-0.713430\pi\) | ||||
−0.621387 | + | 0.783504i | \(0.713430\pi\) | |||||||
\(348\) | −8.22489 | −0.440901 | ||||||||
\(349\) | 4.68704 | 0.250892 | 0.125446 | − | 0.992100i | \(-0.459964\pi\) | ||||
0.125446 | + | 0.992100i | \(0.459964\pi\) | |||||||
\(350\) | 26.0117 | 1.39038 | ||||||||
\(351\) | −4.22153 | −0.225328 | ||||||||
\(352\) | −1.24502 | −0.0663596 | ||||||||
\(353\) | 13.2422 | 0.704809 | 0.352404 | − | 0.935848i | \(-0.385364\pi\) | ||||
0.352404 | + | 0.935848i | \(0.385364\pi\) | |||||||
\(354\) | −49.1465 | −2.61210 | ||||||||
\(355\) | 0.287385 | 0.0152528 | ||||||||
\(356\) | 9.82266 | 0.520600 | ||||||||
\(357\) | 37.2276 | 1.97030 | ||||||||
\(358\) | 10.4122 | 0.550304 | ||||||||
\(359\) | −7.78491 | −0.410872 | −0.205436 | − | 0.978671i | \(-0.565861\pi\) | ||||
−0.205436 | + | 0.978671i | \(0.565861\pi\) | |||||||
\(360\) | −3.03827 | −0.160131 | ||||||||
\(361\) | 5.14581 | 0.270832 | ||||||||
\(362\) | −4.28470 | −0.225199 | ||||||||
\(363\) | −35.0732 | −1.84086 | ||||||||
\(364\) | 2.01041 | 0.105374 | ||||||||
\(365\) | 4.60509 | 0.241041 | ||||||||
\(366\) | 71.7084 | 3.74826 | ||||||||
\(367\) | −7.69335 | −0.401590 | −0.200795 | − | 0.979633i | \(-0.564352\pi\) | ||||
−0.200795 | + | 0.979633i | \(0.564352\pi\) | |||||||
\(368\) | −2.52354 | −0.131549 | ||||||||
\(369\) | 54.1643 | 2.81968 | ||||||||
\(370\) | −5.65589 | −0.294036 | ||||||||
\(371\) | −14.6890 | −0.762613 | ||||||||
\(372\) | 71.8266 | 3.72404 | ||||||||
\(373\) | −10.7967 | −0.559032 | −0.279516 | − | 0.960141i | \(-0.590174\pi\) | ||||
−0.279516 | + | 0.960141i | \(0.590174\pi\) | |||||||
\(374\) | −1.58586 | −0.0820030 | ||||||||
\(375\) | 10.8427 | 0.559916 | ||||||||
\(376\) | 4.75964 | 0.245459 | ||||||||
\(377\) | 0.313547 | 0.0161485 | ||||||||
\(378\) | −71.7342 | −3.68961 | ||||||||
\(379\) | 21.1883 | 1.08837 | 0.544184 | − | 0.838966i | \(-0.316839\pi\) | ||||
0.544184 | + | 0.838966i | \(0.316839\pi\) | |||||||
\(380\) | 4.34197 | 0.222738 | ||||||||
\(381\) | −50.9517 | −2.61034 | ||||||||
\(382\) | 31.8870 | 1.63148 | ||||||||
\(383\) | −24.7991 | −1.26717 | −0.633587 | − | 0.773671i | \(-0.718418\pi\) | ||||
−0.633587 | + | 0.773671i | \(0.718418\pi\) | |||||||
\(384\) | −30.0761 | −1.53482 | ||||||||
\(385\) | 0.135647 | 0.00691320 | ||||||||
\(386\) | −6.78244 | −0.345217 | ||||||||
\(387\) | 29.0968 | 1.47907 | ||||||||
\(388\) | 39.1320 | 1.98663 | ||||||||
\(389\) | 32.3160 | 1.63849 | 0.819243 | − | 0.573447i | \(-0.194394\pi\) | ||||
0.819243 | + | 0.573447i | \(0.194394\pi\) | |||||||
\(390\) | 0.735740 | 0.0372556 | ||||||||
\(391\) | −4.67587 | −0.236469 | ||||||||
\(392\) | −0.973397 | −0.0491640 | ||||||||
\(393\) | 2.47536 | 0.124866 | ||||||||
\(394\) | 43.5336 | 2.19319 | ||||||||
\(395\) | −2.10651 | −0.105990 | ||||||||
\(396\) | 2.94401 | 0.147942 | ||||||||
\(397\) | −23.1437 | −1.16155 | −0.580774 | − | 0.814065i | \(-0.697250\pi\) | ||||
−0.580774 | + | 0.814065i | \(0.697250\pi\) | |||||||
\(398\) | −33.4694 | −1.67767 | ||||||||
\(399\) | 39.1223 | 1.95856 | ||||||||
\(400\) | 12.3203 | 0.616013 | ||||||||
\(401\) | 30.6044 | 1.52831 | 0.764156 | − | 0.645031i | \(-0.223156\pi\) | ||||
0.764156 | + | 0.645031i | \(0.223156\pi\) | |||||||
\(402\) | −39.6188 | −1.97601 | ||||||||
\(403\) | −2.73816 | −0.136397 | ||||||||
\(404\) | −3.30767 | −0.164563 | ||||||||
\(405\) | −7.34322 | −0.364887 | ||||||||
\(406\) | 5.32794 | 0.264421 | ||||||||
\(407\) | 1.22159 | 0.0605522 | ||||||||
\(408\) | −18.3332 | −0.907628 | ||||||||
\(409\) | 29.2880 | 1.44820 | 0.724100 | − | 0.689695i | \(-0.242255\pi\) | ||||
0.724100 | + | 0.689695i | \(0.242255\pi\) | |||||||
\(410\) | −5.51369 | −0.272302 | ||||||||
\(411\) | 15.4421 | 0.761704 | ||||||||
\(412\) | −1.79369 | −0.0883690 | ||||||||
\(413\) | 17.9147 | 0.881526 | ||||||||
\(414\) | 15.4258 | 0.758137 | ||||||||
\(415\) | 3.55751 | 0.174632 | ||||||||
\(416\) | 2.46155 | 0.120687 | ||||||||
\(417\) | 31.9416 | 1.56419 | ||||||||
\(418\) | −1.66657 | −0.0815147 | ||||||||
\(419\) | −0.0155271 | −0.000758550 0 | −0.000379275 | − | 1.00000i | \(-0.500121\pi\) | ||||
−0.000379275 | 1.00000i | \(0.500121\pi\) | ||||||||
\(420\) | 7.03508 | 0.343277 | ||||||||
\(421\) | −6.96739 | −0.339570 | −0.169785 | − | 0.985481i | \(-0.554307\pi\) | ||||
−0.169785 | + | 0.985481i | \(0.554307\pi\) | |||||||
\(422\) | 37.3198 | 1.81670 | ||||||||
\(423\) | 27.9827 | 1.36057 | ||||||||
\(424\) | 7.23375 | 0.351302 | ||||||||
\(425\) | 22.8282 | 1.10733 | ||||||||
\(426\) | −5.72086 | −0.277177 | ||||||||
\(427\) | −26.1389 | −1.26495 | ||||||||
\(428\) | 2.77855 | 0.134306 | ||||||||
\(429\) | −0.158910 | −0.00767222 | ||||||||
\(430\) | −2.96193 | −0.142837 | ||||||||
\(431\) | −13.7066 | −0.660222 | −0.330111 | − | 0.943942i | \(-0.607086\pi\) | ||||
−0.330111 | + | 0.943942i | \(0.607086\pi\) | |||||||
\(432\) | −33.9764 | −1.63469 | ||||||||
\(433\) | −38.4571 | −1.84813 | −0.924065 | − | 0.382235i | \(-0.875155\pi\) | ||||
−0.924065 | + | 0.382235i | \(0.875155\pi\) | |||||||
\(434\) | −46.5281 | −2.23342 | ||||||||
\(435\) | 1.09721 | 0.0526070 | ||||||||
\(436\) | −36.7610 | −1.76053 | ||||||||
\(437\) | −4.91384 | −0.235061 | ||||||||
\(438\) | −91.6716 | −4.38024 | ||||||||
\(439\) | −12.7407 | −0.608082 | −0.304041 | − | 0.952659i | \(-0.598336\pi\) | ||||
−0.304041 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(440\) | −0.0668008 | −0.00318460 | ||||||||
\(441\) | −5.72276 | −0.272512 | ||||||||
\(442\) | 3.13544 | 0.149138 | ||||||||
\(443\) | −11.6666 | −0.554296 | −0.277148 | − | 0.960827i | \(-0.589389\pi\) | ||||
−0.277148 | + | 0.960827i | \(0.589389\pi\) | |||||||
\(444\) | 63.3559 | 3.00674 | ||||||||
\(445\) | −1.31035 | −0.0621165 | ||||||||
\(446\) | −28.7868 | −1.36309 | ||||||||
\(447\) | −53.3859 | −2.52507 | ||||||||
\(448\) | 29.2539 | 1.38212 | ||||||||
\(449\) | 25.7849 | 1.21686 | 0.608432 | − | 0.793606i | \(-0.291799\pi\) | ||||
0.608432 | + | 0.793606i | \(0.291799\pi\) | |||||||
\(450\) | −75.3107 | −3.55018 | ||||||||
\(451\) | 1.19088 | 0.0560764 | ||||||||
\(452\) | −18.6639 | −0.877876 | ||||||||
\(453\) | 14.4844 | 0.680534 | ||||||||
\(454\) | −59.8990 | −2.81120 | ||||||||
\(455\) | −0.268190 | −0.0125729 | ||||||||
\(456\) | −19.2662 | −0.902223 | ||||||||
\(457\) | −34.4433 | −1.61119 | −0.805594 | − | 0.592468i | \(-0.798154\pi\) | ||||
−0.805594 | + | 0.592468i | \(0.798154\pi\) | |||||||
\(458\) | −32.5503 | −1.52098 | ||||||||
\(459\) | −62.9548 | −2.93848 | ||||||||
\(460\) | −0.883620 | −0.0411990 | ||||||||
\(461\) | −14.4672 | −0.673805 | −0.336902 | − | 0.941540i | \(-0.609379\pi\) | ||||
−0.336902 | + | 0.941540i | \(0.609379\pi\) | |||||||
\(462\) | −2.70027 | −0.125628 | ||||||||
\(463\) | −8.72685 | −0.405571 | −0.202786 | − | 0.979223i | \(-0.564999\pi\) | ||||
−0.202786 | + | 0.979223i | \(0.564999\pi\) | |||||||
\(464\) | 2.52354 | 0.117153 | ||||||||
\(465\) | −9.58172 | −0.444342 | ||||||||
\(466\) | 48.5847 | 2.25064 | ||||||||
\(467\) | 14.1065 | 0.652773 | 0.326386 | − | 0.945236i | \(-0.394169\pi\) | ||||
0.326386 | + | 0.945236i | \(0.394169\pi\) | |||||||
\(468\) | −5.82066 | −0.269060 | ||||||||
\(469\) | 14.4417 | 0.666858 | ||||||||
\(470\) | −2.84852 | −0.131392 | ||||||||
\(471\) | 60.8861 | 2.80548 | ||||||||
\(472\) | −8.82231 | −0.406080 | ||||||||
\(473\) | 0.639735 | 0.0294151 | ||||||||
\(474\) | 41.9335 | 1.92607 | ||||||||
\(475\) | 23.9900 | 1.10074 | ||||||||
\(476\) | 29.9808 | 1.37417 | ||||||||
\(477\) | 42.5284 | 1.94724 | ||||||||
\(478\) | −52.7881 | −2.41447 | ||||||||
\(479\) | 0.449722 | 0.0205483 | 0.0102742 | − | 0.999947i | \(-0.496730\pi\) | ||||
0.0102742 | + | 0.999947i | \(0.496730\pi\) | |||||||
\(480\) | 8.61377 | 0.393163 | ||||||||
\(481\) | −2.41524 | −0.110125 | ||||||||
\(482\) | −29.2189 | −1.33088 | ||||||||
\(483\) | −7.96165 | −0.362268 | ||||||||
\(484\) | −28.2457 | −1.28390 | ||||||||
\(485\) | −5.22023 | −0.237039 | ||||||||
\(486\) | 59.7971 | 2.71245 | ||||||||
\(487\) | 17.8669 | 0.809627 | 0.404813 | − | 0.914399i | \(-0.367337\pi\) | ||||
0.404813 | + | 0.914399i | \(0.367337\pi\) | |||||||
\(488\) | 12.8724 | 0.582707 | ||||||||
\(489\) | 2.10232 | 0.0950702 | ||||||||
\(490\) | 0.582553 | 0.0263170 | ||||||||
\(491\) | −0.575247 | −0.0259605 | −0.0129803 | − | 0.999916i | \(-0.504132\pi\) | ||||
−0.0129803 | + | 0.999916i | \(0.504132\pi\) | |||||||
\(492\) | 61.7630 | 2.78449 | ||||||||
\(493\) | 4.67587 | 0.210590 | ||||||||
\(494\) | 3.29501 | 0.148250 | ||||||||
\(495\) | −0.392733 | −0.0176520 | ||||||||
\(496\) | −22.0377 | −0.989522 | ||||||||
\(497\) | 2.08535 | 0.0935408 | ||||||||
\(498\) | −70.8180 | −3.17343 | ||||||||
\(499\) | −10.9754 | −0.491327 | −0.245663 | − | 0.969355i | \(-0.579006\pi\) | ||||
−0.245663 | + | 0.969355i | \(0.579006\pi\) | |||||||
\(500\) | 8.73205 | 0.390509 | ||||||||
\(501\) | 33.5819 | 1.50033 | ||||||||
\(502\) | 18.2940 | 0.816501 | ||||||||
\(503\) | 40.4773 | 1.80479 | 0.902396 | − | 0.430907i | \(-0.141806\pi\) | ||||
0.902396 | + | 0.430907i | \(0.141806\pi\) | |||||||
\(504\) | −22.0466 | −0.982033 | ||||||||
\(505\) | 0.441246 | 0.0196352 | ||||||||
\(506\) | 0.339159 | 0.0150774 | ||||||||
\(507\) | −41.2309 | −1.83113 | ||||||||
\(508\) | −41.0333 | −1.82056 | ||||||||
\(509\) | 24.3146 | 1.07772 | 0.538862 | − | 0.842394i | \(-0.318854\pi\) | ||||
0.538862 | + | 0.842394i | \(0.318854\pi\) | |||||||
\(510\) | 10.9719 | 0.485845 | ||||||||
\(511\) | 33.4159 | 1.47823 | ||||||||
\(512\) | 26.0036 | 1.14921 | ||||||||
\(513\) | −66.1587 | −2.92098 | ||||||||
\(514\) | 25.3195 | 1.11680 | ||||||||
\(515\) | 0.239280 | 0.0105439 | ||||||||
\(516\) | 33.1788 | 1.46061 | ||||||||
\(517\) | 0.615240 | 0.0270582 | ||||||||
\(518\) | −41.0409 | −1.80323 | ||||||||
\(519\) | 51.5473 | 2.26268 | ||||||||
\(520\) | 0.132073 | 0.00579179 | ||||||||
\(521\) | 40.6841 | 1.78240 | 0.891202 | − | 0.453607i | \(-0.149863\pi\) | ||||
0.891202 | + | 0.453607i | \(0.149863\pi\) | |||||||
\(522\) | −15.4258 | −0.675169 | ||||||||
\(523\) | −22.5315 | −0.985233 | −0.492616 | − | 0.870247i | \(-0.663959\pi\) | ||||
−0.492616 | + | 0.870247i | \(0.663959\pi\) | |||||||
\(524\) | 1.99350 | 0.0870865 | ||||||||
\(525\) | 38.8698 | 1.69642 | ||||||||
\(526\) | 46.7106 | 2.03668 | ||||||||
\(527\) | −40.8336 | −1.77874 | ||||||||
\(528\) | −1.27896 | −0.0556597 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.32921 | −0.188049 | ||||||||
\(531\) | −51.8679 | −2.25087 | ||||||||
\(532\) | 31.5066 | 1.36598 | ||||||||
\(533\) | −2.35451 | −0.101985 | ||||||||
\(534\) | 26.0846 | 1.12879 | ||||||||
\(535\) | −0.370661 | −0.0160251 | ||||||||
\(536\) | −7.11200 | −0.307192 | ||||||||
\(537\) | 15.5592 | 0.671430 | ||||||||
\(538\) | −61.1418 | −2.63601 | ||||||||
\(539\) | −0.125823 | −0.00541959 | ||||||||
\(540\) | −11.8969 | −0.511959 | ||||||||
\(541\) | −43.3803 | −1.86506 | −0.932532 | − | 0.361088i | \(-0.882406\pi\) | ||||
−0.932532 | + | 0.361088i | \(0.882406\pi\) | |||||||
\(542\) | 46.5794 | 2.00075 | ||||||||
\(543\) | −6.40271 | −0.274767 | ||||||||
\(544\) | 36.7085 | 1.57387 | ||||||||
\(545\) | 4.90394 | 0.210062 | ||||||||
\(546\) | 5.33875 | 0.228477 | ||||||||
\(547\) | −33.1997 | −1.41952 | −0.709758 | − | 0.704446i | \(-0.751196\pi\) | ||||
−0.709758 | + | 0.704446i | \(0.751196\pi\) | |||||||
\(548\) | 12.4361 | 0.531244 | ||||||||
\(549\) | 75.6791 | 3.22991 | ||||||||
\(550\) | −1.65582 | −0.0706042 | ||||||||
\(551\) | 4.91384 | 0.209337 | ||||||||
\(552\) | 3.92081 | 0.166881 | ||||||||
\(553\) | −15.2855 | −0.650005 | ||||||||
\(554\) | 19.9369 | 0.847038 | ||||||||
\(555\) | −8.45172 | −0.358755 | ||||||||
\(556\) | 25.7238 | 1.09093 | ||||||||
\(557\) | −4.50127 | −0.190725 | −0.0953625 | − | 0.995443i | \(-0.530401\pi\) | ||||
−0.0953625 | + | 0.995443i | \(0.530401\pi\) | |||||||
\(558\) | 134.711 | 5.70277 | ||||||||
\(559\) | −1.26483 | −0.0534967 | ||||||||
\(560\) | −2.15849 | −0.0912128 | ||||||||
\(561\) | −2.36979 | −0.100052 | ||||||||
\(562\) | −17.9872 | −0.758743 | ||||||||
\(563\) | 46.9636 | 1.97928 | 0.989641 | − | 0.143568i | \(-0.0458575\pi\) | ||||
0.989641 | + | 0.143568i | \(0.0458575\pi\) | |||||||
\(564\) | 31.9084 | 1.34358 | ||||||||
\(565\) | 2.48978 | 0.104746 | ||||||||
\(566\) | 31.6502 | 1.33036 | ||||||||
\(567\) | −53.2846 | −2.23774 | ||||||||
\(568\) | −1.02696 | −0.0430901 | ||||||||
\(569\) | −0.207925 | −0.00871668 | −0.00435834 | − | 0.999991i | \(-0.501387\pi\) | ||||
−0.00435834 | + | 0.999991i | \(0.501387\pi\) | |||||||
\(570\) | 11.5303 | 0.482952 | ||||||||
\(571\) | −11.0902 | −0.464111 | −0.232055 | − | 0.972703i | \(-0.574545\pi\) | ||||
−0.232055 | + | 0.972703i | \(0.574545\pi\) | |||||||
\(572\) | −0.127976 | −0.00535093 | ||||||||
\(573\) | 47.6494 | 1.99058 | ||||||||
\(574\) | −40.0090 | −1.66994 | ||||||||
\(575\) | −4.88212 | −0.203599 | ||||||||
\(576\) | −84.6978 | −3.52907 | ||||||||
\(577\) | 33.8313 | 1.40841 | 0.704207 | − | 0.709994i | \(-0.251303\pi\) | ||||
0.704207 | + | 0.709994i | \(0.251303\pi\) | |||||||
\(578\) | 10.4017 | 0.432652 | ||||||||
\(579\) | −10.1351 | −0.421202 | ||||||||
\(580\) | 0.883620 | 0.0366903 | ||||||||
\(581\) | 25.8144 | 1.07096 | ||||||||
\(582\) | 103.917 | 4.30750 | ||||||||
\(583\) | 0.935049 | 0.0387258 | ||||||||
\(584\) | −16.4560 | −0.680956 | ||||||||
\(585\) | 0.776480 | 0.0321035 | ||||||||
\(586\) | −23.4004 | −0.966663 | ||||||||
\(587\) | 10.3629 | 0.427723 | 0.213862 | − | 0.976864i | \(-0.431396\pi\) | ||||
0.213862 | + | 0.976864i | \(0.431396\pi\) | |||||||
\(588\) | −6.52561 | −0.269111 | ||||||||
\(589\) | −42.9117 | −1.76815 | ||||||||
\(590\) | 5.27993 | 0.217371 | ||||||||
\(591\) | 65.0531 | 2.67593 | ||||||||
\(592\) | −19.4387 | −0.798926 | ||||||||
\(593\) | 13.5687 | 0.557200 | 0.278600 | − | 0.960407i | \(-0.410130\pi\) | ||||
0.278600 | + | 0.960407i | \(0.410130\pi\) | |||||||
\(594\) | 4.56635 | 0.187360 | ||||||||
\(595\) | −3.99946 | −0.163962 | ||||||||
\(596\) | −42.9936 | −1.76109 | ||||||||
\(597\) | −50.0139 | −2.04693 | ||||||||
\(598\) | −0.670557 | −0.0274211 | ||||||||
\(599\) | −27.9553 | −1.14222 | −0.571110 | − | 0.820873i | \(-0.693487\pi\) | ||||
−0.571110 | + | 0.820873i | \(0.693487\pi\) | |||||||
\(600\) | −19.1419 | −0.781464 | ||||||||
\(601\) | −33.7230 | −1.37559 | −0.687796 | − | 0.725904i | \(-0.741422\pi\) | ||||
−0.687796 | + | 0.725904i | \(0.741422\pi\) | |||||||
\(602\) | −21.4926 | −0.875974 | ||||||||
\(603\) | −41.8127 | −1.70274 | ||||||||
\(604\) | 11.6648 | 0.474633 | ||||||||
\(605\) | 3.76800 | 0.153191 | ||||||||
\(606\) | −8.78371 | −0.356814 | ||||||||
\(607\) | −46.2277 | −1.87633 | −0.938163 | − | 0.346194i | \(-0.887474\pi\) | ||||
−0.938163 | + | 0.346194i | \(0.887474\pi\) | |||||||
\(608\) | 38.5768 | 1.56449 | ||||||||
\(609\) | 7.96165 | 0.322623 | ||||||||
\(610\) | −7.70381 | −0.311918 | ||||||||
\(611\) | −1.21640 | −0.0492104 | ||||||||
\(612\) | −86.8023 | −3.50877 | ||||||||
\(613\) | 5.12758 | 0.207101 | 0.103550 | − | 0.994624i | \(-0.466980\pi\) | ||||
0.103550 | + | 0.994624i | \(0.466980\pi\) | |||||||
\(614\) | −9.11905 | −0.368015 | ||||||||
\(615\) | −8.23922 | −0.332238 | ||||||||
\(616\) | −0.484726 | −0.0195302 | ||||||||
\(617\) | −12.8558 | −0.517553 | −0.258777 | − | 0.965937i | \(-0.583319\pi\) | ||||
−0.258777 | + | 0.965937i | \(0.583319\pi\) | |||||||
\(618\) | −4.76325 | −0.191606 | ||||||||
\(619\) | −4.23277 | −0.170129 | −0.0850647 | − | 0.996375i | \(-0.527110\pi\) | ||||
−0.0850647 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(620\) | −7.71651 | −0.309903 | ||||||||
\(621\) | 13.4638 | 0.540282 | ||||||||
\(622\) | −22.3394 | −0.895729 | ||||||||
\(623\) | −9.50828 | −0.380941 | ||||||||
\(624\) | 2.52866 | 0.101227 | ||||||||
\(625\) | 23.2458 | 0.929830 | ||||||||
\(626\) | 71.5071 | 2.85800 | ||||||||
\(627\) | −2.49039 | −0.0994567 | ||||||||
\(628\) | 49.0338 | 1.95666 | ||||||||
\(629\) | −36.0179 | −1.43613 | ||||||||
\(630\) | 13.1943 | 0.525674 | ||||||||
\(631\) | −41.8169 | −1.66470 | −0.832351 | − | 0.554248i | \(-0.813006\pi\) | ||||
−0.832351 | + | 0.554248i | \(0.813006\pi\) | |||||||
\(632\) | 7.52751 | 0.299428 | ||||||||
\(633\) | 55.7678 | 2.21657 | ||||||||
\(634\) | 40.4930 | 1.60818 | ||||||||
\(635\) | 5.47387 | 0.217224 | ||||||||
\(636\) | 48.4947 | 1.92294 | ||||||||
\(637\) | 0.248768 | 0.00985653 | ||||||||
\(638\) | −0.339159 | −0.0134274 | ||||||||
\(639\) | −6.03764 | −0.238845 | ||||||||
\(640\) | 3.23115 | 0.127722 | ||||||||
\(641\) | −32.2839 | −1.27514 | −0.637569 | − | 0.770393i | \(-0.720060\pi\) | ||||
−0.637569 | + | 0.770393i | \(0.720060\pi\) | |||||||
\(642\) | 7.37859 | 0.291210 | ||||||||
\(643\) | −39.3651 | −1.55241 | −0.776203 | − | 0.630483i | \(-0.782857\pi\) | ||||
−0.776203 | + | 0.630483i | \(0.782857\pi\) | |||||||
\(644\) | −6.41181 | −0.252661 | ||||||||
\(645\) | −4.42607 | −0.174276 | ||||||||
\(646\) | 49.1378 | 1.93330 | ||||||||
\(647\) | −22.0399 | −0.866479 | −0.433239 | − | 0.901279i | \(-0.642630\pi\) | ||||
−0.433239 | + | 0.901279i | \(0.642630\pi\) | |||||||
\(648\) | 26.2406 | 1.03083 | ||||||||
\(649\) | −1.14039 | −0.0447642 | ||||||||
\(650\) | 3.27374 | 0.128407 | ||||||||
\(651\) | −69.5278 | −2.72501 | ||||||||
\(652\) | 1.69308 | 0.0663059 | ||||||||
\(653\) | −5.30012 | −0.207410 | −0.103705 | − | 0.994608i | \(-0.533070\pi\) | ||||
−0.103705 | + | 0.994608i | \(0.533070\pi\) | |||||||
\(654\) | −97.6209 | −3.81728 | ||||||||
\(655\) | −0.265934 | −0.0103909 | ||||||||
\(656\) | −18.9500 | −0.739873 | ||||||||
\(657\) | −96.7478 | −3.77449 | ||||||||
\(658\) | −20.6697 | −0.805789 | ||||||||
\(659\) | 0.638640 | 0.0248779 | 0.0124389 | − | 0.999923i | \(-0.496040\pi\) | ||||
0.0124389 | + | 0.999923i | \(0.496040\pi\) | |||||||
\(660\) | −0.447829 | −0.0174317 | ||||||||
\(661\) | 22.0446 | 0.857434 | 0.428717 | − | 0.903439i | \(-0.358966\pi\) | ||||
0.428717 | + | 0.903439i | \(0.358966\pi\) | |||||||
\(662\) | −60.9421 | −2.36858 | ||||||||
\(663\) | 4.68535 | 0.181964 | ||||||||
\(664\) | −12.7126 | −0.493344 | ||||||||
\(665\) | −4.20300 | −0.162985 | ||||||||
\(666\) | 118.824 | 4.60434 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 27.0447 | 1.04639 | ||||||||
\(669\) | −43.0166 | −1.66312 | ||||||||
\(670\) | 4.25635 | 0.164437 | ||||||||
\(671\) | 1.66392 | 0.0642348 | ||||||||
\(672\) | 62.5040 | 2.41115 | ||||||||
\(673\) | −0.261282 | −0.0100717 | −0.00503584 | − | 0.999987i | \(-0.501603\pi\) | ||||
−0.00503584 | + | 0.999987i | \(0.501603\pi\) | |||||||
\(674\) | −43.7349 | −1.68460 | ||||||||
\(675\) | −65.7318 | −2.53002 | ||||||||
\(676\) | −33.2048 | −1.27711 | ||||||||
\(677\) | 28.9774 | 1.11369 | 0.556846 | − | 0.830616i | \(-0.312011\pi\) | ||||
0.556846 | + | 0.830616i | \(0.312011\pi\) | |||||||
\(678\) | −49.5630 | −1.90345 | ||||||||
\(679\) | −37.8796 | −1.45368 | ||||||||
\(680\) | 1.96958 | 0.0755299 | ||||||||
\(681\) | −89.5082 | −3.42996 | ||||||||
\(682\) | 2.96182 | 0.113414 | ||||||||
\(683\) | 17.6353 | 0.674797 | 0.337399 | − | 0.941362i | \(-0.390453\pi\) | ||||
0.337399 | + | 0.941362i | \(0.390453\pi\) | |||||||
\(684\) | −91.2199 | −3.48788 | ||||||||
\(685\) | −1.65899 | −0.0633866 | ||||||||
\(686\) | 41.5228 | 1.58535 | ||||||||
\(687\) | −48.6406 | −1.85575 | ||||||||
\(688\) | −10.1798 | −0.388103 | ||||||||
\(689\) | −1.84870 | −0.0704300 | ||||||||
\(690\) | −2.34650 | −0.0893298 | ||||||||
\(691\) | −23.7385 | −0.903053 | −0.451527 | − | 0.892258i | \(-0.649120\pi\) | ||||
−0.451527 | + | 0.892258i | \(0.649120\pi\) | |||||||
\(692\) | 41.5130 | 1.57809 | ||||||||
\(693\) | −2.84979 | −0.108254 | ||||||||
\(694\) | −49.5096 | −1.87936 | ||||||||
\(695\) | −3.43157 | −0.130167 | ||||||||
\(696\) | −3.92081 | −0.148618 | ||||||||
\(697\) | −35.1124 | −1.32998 | ||||||||
\(698\) | 10.0238 | 0.379406 | ||||||||
\(699\) | 72.6010 | 2.74602 | ||||||||
\(700\) | 31.3033 | 1.18315 | ||||||||
\(701\) | −19.1584 | −0.723603 | −0.361802 | − | 0.932255i | \(-0.617838\pi\) | ||||
−0.361802 | + | 0.932255i | \(0.617838\pi\) | |||||||
\(702\) | −9.02822 | −0.340748 | ||||||||
\(703\) | −37.8510 | −1.42758 | ||||||||
\(704\) | −1.86220 | −0.0701845 | ||||||||
\(705\) | −4.25660 | −0.160313 | ||||||||
\(706\) | 28.3199 | 1.06583 | ||||||||
\(707\) | 3.20181 | 0.120417 | ||||||||
\(708\) | −59.1444 | −2.22278 | ||||||||
\(709\) | −24.5942 | −0.923654 | −0.461827 | − | 0.886970i | \(-0.652806\pi\) | ||||
−0.461827 | + | 0.886970i | \(0.652806\pi\) | |||||||
\(710\) | 0.614606 | 0.0230658 | ||||||||
\(711\) | 44.2555 | 1.65971 | ||||||||
\(712\) | 4.68246 | 0.175483 | ||||||||
\(713\) | 8.73283 | 0.327047 | ||||||||
\(714\) | 79.6156 | 2.97954 | ||||||||
\(715\) | 0.0170720 | 0.000638458 0 | ||||||||
\(716\) | 12.5304 | 0.468284 | ||||||||
\(717\) | −78.8823 | −2.94592 | ||||||||
\(718\) | −16.6489 | −0.621333 | ||||||||
\(719\) | −51.5016 | −1.92068 | −0.960342 | − | 0.278825i | \(-0.910055\pi\) | ||||
−0.960342 | + | 0.278825i | \(0.910055\pi\) | |||||||
\(720\) | 6.24939 | 0.232901 | ||||||||
\(721\) | 1.73629 | 0.0646627 | ||||||||
\(722\) | 11.0049 | 0.409560 | ||||||||
\(723\) | −43.6624 | −1.62382 | ||||||||
\(724\) | −5.15634 | −0.191634 | ||||||||
\(725\) | 4.88212 | 0.181318 | ||||||||
\(726\) | −75.0080 | −2.78381 | ||||||||
\(727\) | 41.4085 | 1.53575 | 0.767877 | − | 0.640597i | \(-0.221313\pi\) | ||||
0.767877 | + | 0.640597i | \(0.221313\pi\) | |||||||
\(728\) | 0.958362 | 0.0355192 | ||||||||
\(729\) | 25.1913 | 0.933013 | ||||||||
\(730\) | 9.84851 | 0.364510 | ||||||||
\(731\) | −18.8622 | −0.697643 | ||||||||
\(732\) | 86.2961 | 3.18960 | ||||||||
\(733\) | 27.7842 | 1.02623 | 0.513116 | − | 0.858319i | \(-0.328491\pi\) | ||||
0.513116 | + | 0.858319i | \(0.328491\pi\) | |||||||
\(734\) | −16.4531 | −0.607296 | ||||||||
\(735\) | 0.870520 | 0.0321096 | ||||||||
\(736\) | −7.85063 | −0.289378 | ||||||||
\(737\) | −0.919313 | −0.0338633 | ||||||||
\(738\) | 115.837 | 4.26400 | ||||||||
\(739\) | −7.26062 | −0.267086 | −0.133543 | − | 0.991043i | \(-0.542635\pi\) | ||||
−0.133543 | + | 0.991043i | \(0.542635\pi\) | |||||||
\(740\) | −6.80648 | −0.250211 | ||||||||
\(741\) | 4.92380 | 0.180880 | ||||||||
\(742\) | −31.4140 | −1.15325 | ||||||||
\(743\) | 39.0845 | 1.43387 | 0.716936 | − | 0.697139i | \(-0.245544\pi\) | ||||
0.716936 | + | 0.697139i | \(0.245544\pi\) | |||||||
\(744\) | 34.2398 | 1.25529 | ||||||||
\(745\) | 5.73538 | 0.210128 | ||||||||
\(746\) | −23.0900 | −0.845384 | ||||||||
\(747\) | −74.7394 | −2.73457 | ||||||||
\(748\) | −1.90847 | −0.0697808 | ||||||||
\(749\) | −2.68962 | −0.0982767 | ||||||||
\(750\) | 23.1884 | 0.846722 | ||||||||
\(751\) | −5.12605 | −0.187052 | −0.0935261 | − | 0.995617i | \(-0.529814\pi\) | ||||
−0.0935261 | + | 0.995617i | \(0.529814\pi\) | |||||||
\(752\) | −9.79006 | −0.357007 | ||||||||
\(753\) | 27.3371 | 0.996218 | ||||||||
\(754\) | 0.670557 | 0.0244203 | ||||||||
\(755\) | −1.55609 | −0.0566319 | ||||||||
\(756\) | −86.3271 | −3.13969 | ||||||||
\(757\) | −31.1220 | −1.13115 | −0.565574 | − | 0.824697i | \(-0.691345\pi\) | ||||
−0.565574 | + | 0.824697i | \(0.691345\pi\) | |||||||
\(758\) | 45.3136 | 1.64586 | ||||||||
\(759\) | 0.506812 | 0.0183961 | ||||||||
\(760\) | 2.06982 | 0.0750802 | ||||||||
\(761\) | 11.1825 | 0.405366 | 0.202683 | − | 0.979244i | \(-0.435034\pi\) | ||||
0.202683 | + | 0.979244i | \(0.435034\pi\) | |||||||
\(762\) | −108.966 | −3.94743 | ||||||||
\(763\) | 35.5845 | 1.28824 | ||||||||
\(764\) | 38.3738 | 1.38832 | ||||||||
\(765\) | 11.5795 | 0.418657 | ||||||||
\(766\) | −53.0357 | −1.91626 | ||||||||
\(767\) | 2.25469 | 0.0814120 | ||||||||
\(768\) | 10.7309 | 0.387219 | ||||||||
\(769\) | 36.8803 | 1.32994 | 0.664970 | − | 0.746870i | \(-0.268444\pi\) | ||||
0.664970 | + | 0.746870i | \(0.268444\pi\) | |||||||
\(770\) | 0.290096 | 0.0104543 | ||||||||
\(771\) | 37.8355 | 1.36261 | ||||||||
\(772\) | −8.16220 | −0.293764 | ||||||||
\(773\) | 52.2607 | 1.87969 | 0.939843 | − | 0.341605i | \(-0.110971\pi\) | ||||
0.939843 | + | 0.341605i | \(0.110971\pi\) | |||||||
\(774\) | 62.2268 | 2.23670 | ||||||||
\(775\) | −42.6348 | −1.53149 | ||||||||
\(776\) | 18.6542 | 0.669648 | ||||||||
\(777\) | −61.3282 | −2.20014 | ||||||||
\(778\) | 69.1115 | 2.47777 | ||||||||
\(779\) | −36.8994 | −1.32206 | ||||||||
\(780\) | 0.885412 | 0.0317028 | ||||||||
\(781\) | −0.132746 | −0.00475004 | ||||||||
\(782\) | −9.99988 | −0.357595 | ||||||||
\(783\) | −13.4638 | −0.481156 | ||||||||
\(784\) | 2.00217 | 0.0715062 | ||||||||
\(785\) | −6.54114 | −0.233463 | ||||||||
\(786\) | 5.29385 | 0.188825 | ||||||||
\(787\) | −26.7116 | −0.952167 | −0.476083 | − | 0.879400i | \(-0.657944\pi\) | ||||
−0.476083 | + | 0.879400i | \(0.657944\pi\) | |||||||
\(788\) | 52.3897 | 1.86630 | ||||||||
\(789\) | 69.8006 | 2.48497 | ||||||||
\(790\) | −4.50502 | −0.160281 | ||||||||
\(791\) | 18.0666 | 0.642373 | ||||||||
\(792\) | 1.40341 | 0.0498680 | ||||||||
\(793\) | −3.28976 | −0.116823 | ||||||||
\(794\) | −49.4954 | −1.75653 | ||||||||
\(795\) | −6.46923 | −0.229440 | ||||||||
\(796\) | −40.2781 | −1.42762 | ||||||||
\(797\) | 27.4579 | 0.972610 | 0.486305 | − | 0.873789i | \(-0.338344\pi\) | ||||
0.486305 | + | 0.873789i | \(0.338344\pi\) | |||||||
\(798\) | 83.6675 | 2.96180 | ||||||||
\(799\) | −18.1400 | −0.641746 | ||||||||
\(800\) | 38.3278 | 1.35509 | ||||||||
\(801\) | 27.5290 | 0.972689 | ||||||||
\(802\) | 65.4511 | 2.31116 | ||||||||
\(803\) | −2.12714 | −0.0750652 | ||||||||
\(804\) | −47.6785 | −1.68149 | ||||||||
\(805\) | 0.855340 | 0.0301468 | ||||||||
\(806\) | −5.85586 | −0.206264 | ||||||||
\(807\) | −91.3654 | −3.21621 | ||||||||
\(808\) | −1.57677 | −0.0554705 | ||||||||
\(809\) | 20.1703 | 0.709149 | 0.354575 | − | 0.935028i | \(-0.384626\pi\) | ||||
0.354575 | + | 0.935028i | \(0.384626\pi\) | |||||||
\(810\) | −15.7043 | −0.551793 | ||||||||
\(811\) | 39.3120 | 1.38043 | 0.690216 | − | 0.723604i | \(-0.257516\pi\) | ||||
0.690216 | + | 0.723604i | \(0.257516\pi\) | |||||||
\(812\) | 6.41181 | 0.225011 | ||||||||
\(813\) | 69.6045 | 2.44114 | ||||||||
\(814\) | 2.61252 | 0.0915688 | ||||||||
\(815\) | −0.225857 | −0.00791144 | ||||||||
\(816\) | 37.7094 | 1.32009 | ||||||||
\(817\) | −19.8222 | −0.693489 | ||||||||
\(818\) | 62.6358 | 2.19001 | ||||||||
\(819\) | 5.63437 | 0.196881 | ||||||||
\(820\) | −6.63535 | −0.231716 | ||||||||
\(821\) | −31.6601 | −1.10494 | −0.552472 | − | 0.833531i | \(-0.686315\pi\) | ||||
−0.552472 | + | 0.833531i | \(0.686315\pi\) | |||||||
\(822\) | 33.0248 | 1.15187 | ||||||||
\(823\) | −9.48598 | −0.330661 | −0.165330 | − | 0.986238i | \(-0.552869\pi\) | ||||
−0.165330 | + | 0.986238i | \(0.552869\pi\) | |||||||
\(824\) | −0.855055 | −0.0297872 | ||||||||
\(825\) | −2.47432 | −0.0861447 | ||||||||
\(826\) | 38.3127 | 1.33307 | ||||||||
\(827\) | −16.0595 | −0.558444 | −0.279222 | − | 0.960227i | \(-0.590076\pi\) | ||||
−0.279222 | + | 0.960227i | \(0.590076\pi\) | |||||||
\(828\) | 18.5639 | 0.645140 | ||||||||
\(829\) | 39.9655 | 1.38806 | 0.694030 | − | 0.719946i | \(-0.255834\pi\) | ||||
0.694030 | + | 0.719946i | \(0.255834\pi\) | |||||||
\(830\) | 7.60815 | 0.264083 | ||||||||
\(831\) | 29.7921 | 1.03348 | ||||||||
\(832\) | 3.68180 | 0.127643 | ||||||||
\(833\) | 3.70982 | 0.128538 | ||||||||
\(834\) | 68.3109 | 2.36541 | ||||||||
\(835\) | −3.60778 | −0.124852 | ||||||||
\(836\) | −2.00560 | −0.0693653 | ||||||||
\(837\) | 117.577 | 4.06405 | ||||||||
\(838\) | −0.0332065 | −0.00114710 | ||||||||
\(839\) | 3.17049 | 0.109457 | 0.0547287 | − | 0.998501i | \(-0.482571\pi\) | ||||
0.0547287 | + | 0.998501i | \(0.482571\pi\) | |||||||
\(840\) | 3.35363 | 0.115711 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −14.9006 | −0.513507 | ||||||||
\(843\) | −26.8786 | −0.925747 | ||||||||
\(844\) | 44.9118 | 1.54593 | ||||||||
\(845\) | 4.42954 | 0.152381 | ||||||||
\(846\) | 59.8442 | 2.05749 | ||||||||
\(847\) | 27.3417 | 0.939472 | ||||||||
\(848\) | −14.8790 | −0.510948 | ||||||||
\(849\) | 47.2956 | 1.62318 | ||||||||
\(850\) | 48.8207 | 1.67454 | ||||||||
\(851\) | 7.70294 | 0.264054 | ||||||||
\(852\) | −6.88466 | −0.235865 | ||||||||
\(853\) | −32.5145 | −1.11328 | −0.556638 | − | 0.830755i | \(-0.687909\pi\) | ||||
−0.556638 | + | 0.830755i | \(0.687909\pi\) | |||||||
\(854\) | −55.9011 | −1.91290 | ||||||||
\(855\) | 12.1688 | 0.416164 | ||||||||
\(856\) | 1.32454 | 0.0452717 | ||||||||
\(857\) | 24.1199 | 0.823918 | 0.411959 | − | 0.911202i | \(-0.364845\pi\) | ||||
0.411959 | + | 0.911202i | \(0.364845\pi\) | |||||||
\(858\) | −0.339846 | −0.0116022 | ||||||||
\(859\) | −46.6111 | −1.59035 | −0.795174 | − | 0.606381i | \(-0.792621\pi\) | ||||
−0.795174 | + | 0.606381i | \(0.792621\pi\) | |||||||
\(860\) | −3.56448 | −0.121548 | ||||||||
\(861\) | −59.7863 | −2.03751 | ||||||||
\(862\) | −29.3131 | −0.998407 | ||||||||
\(863\) | −18.7605 | −0.638614 | −0.319307 | − | 0.947651i | \(-0.603450\pi\) | ||||
−0.319307 | + | 0.947651i | \(0.603450\pi\) | |||||||
\(864\) | −105.699 | −3.59596 | ||||||||
\(865\) | −5.53786 | −0.188293 | ||||||||
\(866\) | −82.2450 | −2.79480 | ||||||||
\(867\) | 15.5434 | 0.527882 | ||||||||
\(868\) | −55.9933 | −1.90054 | ||||||||
\(869\) | 0.973022 | 0.0330075 | ||||||||
\(870\) | 2.34650 | 0.0795539 | ||||||||
\(871\) | 1.81759 | 0.0615867 | ||||||||
\(872\) | −17.5240 | −0.593437 | ||||||||
\(873\) | 109.671 | 3.71181 | ||||||||
\(874\) | −10.5088 | −0.355466 | ||||||||
\(875\) | −8.45258 | −0.285749 | ||||||||
\(876\) | −110.320 | −3.72738 | ||||||||
\(877\) | 3.96746 | 0.133972 | 0.0669858 | − | 0.997754i | \(-0.478662\pi\) | ||||
0.0669858 | + | 0.997754i | \(0.478662\pi\) | |||||||
\(878\) | −27.2475 | −0.919559 | ||||||||
\(879\) | −34.9677 | −1.17943 | ||||||||
\(880\) | 0.137402 | 0.00463182 | ||||||||
\(881\) | 43.8307 | 1.47669 | 0.738346 | − | 0.674422i | \(-0.235607\pi\) | ||||
0.738346 | + | 0.674422i | \(0.235607\pi\) | |||||||
\(882\) | −12.2388 | −0.412101 | ||||||||
\(883\) | −40.1624 | −1.35157 | −0.675786 | − | 0.737098i | \(-0.736196\pi\) | ||||
−0.675786 | + | 0.737098i | \(0.736196\pi\) | |||||||
\(884\) | 3.77328 | 0.126909 | ||||||||
\(885\) | 7.88990 | 0.265216 | ||||||||
\(886\) | −24.9504 | −0.838223 | ||||||||
\(887\) | 44.7250 | 1.50172 | 0.750860 | − | 0.660462i | \(-0.229639\pi\) | ||||
0.750860 | + | 0.660462i | \(0.229639\pi\) | |||||||
\(888\) | 30.2018 | 1.01351 | ||||||||
\(889\) | 39.7200 | 1.33217 | ||||||||
\(890\) | −2.80233 | −0.0939344 | ||||||||
\(891\) | 3.39191 | 0.113633 | ||||||||
\(892\) | −34.6429 | −1.15993 | ||||||||
\(893\) | −19.0632 | −0.637925 | ||||||||
\(894\) | −114.172 | −3.81848 | ||||||||
\(895\) | −1.67157 | −0.0558743 | ||||||||
\(896\) | 23.4462 | 0.783282 | ||||||||
\(897\) | −1.00203 | −0.0334567 | ||||||||
\(898\) | 55.1440 | 1.84018 | ||||||||
\(899\) | −8.73283 | −0.291256 | ||||||||
\(900\) | −90.6312 | −3.02104 | ||||||||
\(901\) | −27.5693 | −0.918468 | ||||||||
\(902\) | 2.54684 | 0.0848004 | ||||||||
\(903\) | −32.1169 | −1.06878 | ||||||||
\(904\) | −8.89708 | −0.295913 | ||||||||
\(905\) | 0.687859 | 0.0228652 | ||||||||
\(906\) | 30.9765 | 1.02912 | ||||||||
\(907\) | 1.46051 | 0.0484955 | 0.0242477 | − | 0.999706i | \(-0.492281\pi\) | ||||
0.0242477 | + | 0.999706i | \(0.492281\pi\) | |||||||
\(908\) | −72.0843 | −2.39220 | ||||||||
\(909\) | −9.27009 | −0.307469 | ||||||||
\(910\) | −0.573555 | −0.0190131 | ||||||||
\(911\) | 3.68832 | 0.122199 | 0.0610997 | − | 0.998132i | \(-0.480539\pi\) | ||||
0.0610997 | + | 0.998132i | \(0.480539\pi\) | |||||||
\(912\) | 39.6285 | 1.31223 | ||||||||
\(913\) | −1.64326 | −0.0543838 | ||||||||
\(914\) | −73.6609 | −2.43649 | ||||||||
\(915\) | −11.5120 | −0.380574 | ||||||||
\(916\) | −39.1720 | −1.29428 | ||||||||
\(917\) | −1.92970 | −0.0637243 | ||||||||
\(918\) | −134.636 | −4.44365 | ||||||||
\(919\) | 37.3186 | 1.23103 | 0.615514 | − | 0.788126i | \(-0.288948\pi\) | ||||
0.615514 | + | 0.788126i | \(0.288948\pi\) | |||||||
\(920\) | −0.421222 | −0.0138873 | ||||||||
\(921\) | −13.6268 | −0.449018 | ||||||||
\(922\) | −30.9398 | −1.01895 | ||||||||
\(923\) | 0.262455 | 0.00863883 | ||||||||
\(924\) | −3.24958 | −0.106903 | ||||||||
\(925\) | −37.6067 | −1.23650 | ||||||||
\(926\) | −18.6634 | −0.613317 | ||||||||
\(927\) | −5.02701 | −0.165109 | ||||||||
\(928\) | 7.85063 | 0.257710 | ||||||||
\(929\) | 30.7613 | 1.00925 | 0.504623 | − | 0.863340i | \(-0.331631\pi\) | ||||
0.504623 | + | 0.863340i | \(0.331631\pi\) | |||||||
\(930\) | −20.4916 | −0.671946 | ||||||||
\(931\) | 3.89863 | 0.127772 | ||||||||
\(932\) | 58.4683 | 1.91519 | ||||||||
\(933\) | −33.3823 | −1.09289 | ||||||||
\(934\) | 30.1685 | 0.987142 | ||||||||
\(935\) | 0.254592 | 0.00832604 | ||||||||
\(936\) | −2.77471 | −0.0906942 | ||||||||
\(937\) | 3.14121 | 0.102619 | 0.0513095 | − | 0.998683i | \(-0.483661\pi\) | ||||
0.0513095 | + | 0.998683i | \(0.483661\pi\) | |||||||
\(938\) | 30.8853 | 1.00844 | ||||||||
\(939\) | 106.855 | 3.48707 | ||||||||
\(940\) | −3.42799 | −0.111809 | ||||||||
\(941\) | 31.4897 | 1.02654 | 0.513268 | − | 0.858229i | \(-0.328435\pi\) | ||||
0.513268 | + | 0.858229i | \(0.328435\pi\) | |||||||
\(942\) | 130.212 | 4.24254 | ||||||||
\(943\) | 7.50928 | 0.244536 | ||||||||
\(944\) | 18.1466 | 0.590620 | ||||||||
\(945\) | 11.5161 | 0.374619 | ||||||||
\(946\) | 1.36815 | 0.0444823 | ||||||||
\(947\) | −29.8197 | −0.969010 | −0.484505 | − | 0.874789i | \(-0.661000\pi\) | ||||
−0.484505 | + | 0.874789i | \(0.661000\pi\) | |||||||
\(948\) | 50.4641 | 1.63900 | ||||||||
\(949\) | 4.20561 | 0.136520 | ||||||||
\(950\) | 51.3053 | 1.66456 | ||||||||
\(951\) | 60.5095 | 1.96216 | ||||||||
\(952\) | 14.2918 | 0.463202 | ||||||||
\(953\) | 49.6273 | 1.60759 | 0.803793 | − | 0.594910i | \(-0.202812\pi\) | ||||
0.803793 | + | 0.594910i | \(0.202812\pi\) | |||||||
\(954\) | 90.9519 | 2.94468 | ||||||||
\(955\) | −5.11909 | −0.165650 | ||||||||
\(956\) | −63.5268 | −2.05460 | ||||||||
\(957\) | −0.506812 | −0.0163829 | ||||||||
\(958\) | 0.961782 | 0.0310738 | ||||||||
\(959\) | −12.0381 | −0.388730 | ||||||||
\(960\) | 12.8838 | 0.415824 | ||||||||
\(961\) | 45.2624 | 1.46008 | ||||||||
\(962\) | −5.16526 | −0.166535 | ||||||||
\(963\) | 7.78717 | 0.250938 | ||||||||
\(964\) | −35.1629 | −1.13252 | ||||||||
\(965\) | 1.08884 | 0.0350511 | ||||||||
\(966\) | −17.0269 | −0.547832 | ||||||||
\(967\) | 19.1279 | 0.615111 | 0.307555 | − | 0.951530i | \(-0.400489\pi\) | ||||
0.307555 | + | 0.951530i | \(0.400489\pi\) | |||||||
\(968\) | −13.4647 | −0.432773 | ||||||||
\(969\) | 73.4276 | 2.35883 | ||||||||
\(970\) | −11.1641 | −0.358457 | ||||||||
\(971\) | −3.01449 | −0.0967394 | −0.0483697 | − | 0.998830i | \(-0.515403\pi\) | ||||
−0.0483697 | + | 0.998830i | \(0.515403\pi\) | |||||||
\(972\) | 71.9616 | 2.30817 | ||||||||
\(973\) | −24.9005 | −0.798273 | ||||||||
\(974\) | 38.2104 | 1.22434 | ||||||||
\(975\) | 4.89202 | 0.156670 | ||||||||
\(976\) | −26.4772 | −0.847514 | ||||||||
\(977\) | −17.9958 | −0.575736 | −0.287868 | − | 0.957670i | \(-0.592947\pi\) | ||||
−0.287868 | + | 0.957670i | \(0.592947\pi\) | |||||||
\(978\) | 4.49605 | 0.143768 | ||||||||
\(979\) | 0.605265 | 0.0193444 | ||||||||
\(980\) | 0.701062 | 0.0223946 | ||||||||
\(981\) | −103.026 | −3.28938 | ||||||||
\(982\) | −1.23023 | −0.0392583 | ||||||||
\(983\) | 36.1164 | 1.15193 | 0.575967 | − | 0.817473i | \(-0.304625\pi\) | ||||
0.575967 | + | 0.817473i | \(0.304625\pi\) | |||||||
\(984\) | 29.4424 | 0.938590 | ||||||||
\(985\) | −6.98882 | −0.222682 | ||||||||
\(986\) | 9.99988 | 0.318461 | ||||||||
\(987\) | −30.8871 | −0.983149 | ||||||||
\(988\) | 3.96532 | 0.126154 | ||||||||
\(989\) | 4.03395 | 0.128272 | ||||||||
\(990\) | −0.839905 | −0.0266939 | ||||||||
\(991\) | 57.0453 | 1.81210 | 0.906052 | − | 0.423165i | \(-0.139081\pi\) | ||||
0.906052 | + | 0.423165i | \(0.139081\pi\) | |||||||
\(992\) | −68.5583 | −2.17673 | ||||||||
\(993\) | −91.0670 | −2.88993 | ||||||||
\(994\) | 4.45977 | 0.141455 | ||||||||
\(995\) | 5.37312 | 0.170339 | ||||||||
\(996\) | −85.2246 | −2.70044 | ||||||||
\(997\) | 27.0324 | 0.856124 | 0.428062 | − | 0.903749i | \(-0.359196\pi\) | ||||
0.428062 | + | 0.903749i | \(0.359196\pi\) | |||||||
\(998\) | −23.4722 | −0.742999 | ||||||||
\(999\) | 103.711 | 3.28126 |
(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 | 667.2.a.d.1.13 | ✓ | 16 | |
3.2 | odd | 2 | 6003.2.a.q.1.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.d.1.13 | ✓ | 16 | 1.1 | even | 1 | trivial | |
6003.2.a.q.1.4 | 16 | 3.2 | odd | 2 |