Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3025,2,Mod(1,3025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, 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("3025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3025 = 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3025.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: | \(24.1547466114\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 7x^{6} + 18x^{5} + 16x^{4} - 30x^{3} - 12x^{2} + 12x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 275) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.95882\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.958815 | 0.677985 | 0.338992 | − | 0.940789i | \(-0.389914\pi\) | ||||
0.338992 | + | 0.940789i | \(0.389914\pi\) | |||||||
\(3\) | 0.899342 | 0.519235 | 0.259618 | − | 0.965711i | \(-0.416403\pi\) | ||||
0.259618 | + | 0.965711i | \(0.416403\pi\) | |||||||
\(4\) | −1.08067 | −0.540337 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.862303 | 0.352034 | ||||||||
\(7\) | 0.761645 | 0.287875 | 0.143937 | − | 0.989587i | \(-0.454024\pi\) | ||||
0.143937 | + | 0.989587i | \(0.454024\pi\) | |||||||
\(8\) | −2.95380 | −1.04432 | ||||||||
\(9\) | −2.19118 | −0.730395 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.971895 | −0.280562 | ||||||||
\(13\) | 3.25819 | 0.903658 | 0.451829 | − | 0.892104i | \(-0.350772\pi\) | ||||
0.451829 | + | 0.892104i | \(0.350772\pi\) | |||||||
\(14\) | 0.730277 | 0.195175 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.670799 | −0.167700 | ||||||||
\(17\) | 0.782845 | 0.189868 | 0.0949339 | − | 0.995484i | \(-0.469736\pi\) | ||||
0.0949339 | + | 0.995484i | \(0.469736\pi\) | |||||||
\(18\) | −2.10094 | −0.495196 | ||||||||
\(19\) | −4.59787 | −1.05482 | −0.527412 | − | 0.849609i | \(-0.676838\pi\) | ||||
−0.527412 | + | 0.849609i | \(0.676838\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.684980 | 0.149475 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.51720 | 0.524873 | 0.262436 | − | 0.964949i | \(-0.415474\pi\) | ||||
0.262436 | + | 0.964949i | \(0.415474\pi\) | |||||||
\(24\) | −2.65647 | −0.542251 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.12400 | 0.612667 | ||||||||
\(27\) | −4.66865 | −0.898482 | ||||||||
\(28\) | −0.823090 | −0.155549 | ||||||||
\(29\) | −3.37985 | −0.627623 | −0.313812 | − | 0.949485i | \(-0.601606\pi\) | ||||
−0.313812 | + | 0.949485i | \(0.601606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.90481 | −0.880930 | −0.440465 | − | 0.897770i | \(-0.645186\pi\) | ||||
−0.440465 | + | 0.897770i | \(0.645186\pi\) | |||||||
\(32\) | 5.26442 | 0.930627 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.750604 | 0.128728 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.36795 | 0.394659 | ||||||||
\(37\) | −5.69215 | −0.935784 | −0.467892 | − | 0.883786i | \(-0.654986\pi\) | ||||
−0.467892 | + | 0.883786i | \(0.654986\pi\) | |||||||
\(38\) | −4.40851 | −0.715155 | ||||||||
\(39\) | 2.93022 | 0.469211 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.44874 | 0.850950 | 0.425475 | − | 0.904970i | \(-0.360107\pi\) | ||||
0.425475 | + | 0.904970i | \(0.360107\pi\) | |||||||
\(42\) | 0.656769 | 0.101342 | ||||||||
\(43\) | −10.5601 | −1.61040 | −0.805200 | − | 0.593003i | \(-0.797942\pi\) | ||||
−0.805200 | + | 0.593003i | \(0.797942\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.41353 | 0.355856 | ||||||||
\(47\) | −3.00667 | −0.438568 | −0.219284 | − | 0.975661i | \(-0.570372\pi\) | ||||
−0.219284 | + | 0.975661i | \(0.570372\pi\) | |||||||
\(48\) | −0.603278 | −0.0870757 | ||||||||
\(49\) | −6.41990 | −0.917128 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.704046 | 0.0985861 | ||||||||
\(52\) | −3.52103 | −0.488280 | ||||||||
\(53\) | 13.8424 | 1.90140 | 0.950699 | − | 0.310115i | \(-0.100368\pi\) | ||||
0.950699 | + | 0.310115i | \(0.100368\pi\) | |||||||
\(54\) | −4.47637 | −0.609157 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.24975 | −0.300635 | ||||||||
\(57\) | −4.13506 | −0.547702 | ||||||||
\(58\) | −3.24066 | −0.425519 | ||||||||
\(59\) | −14.2468 | −1.85478 | −0.927389 | − | 0.374100i | \(-0.877952\pi\) | ||||
−0.927389 | + | 0.374100i | \(0.877952\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.44700 | −1.20956 | −0.604782 | − | 0.796391i | \(-0.706740\pi\) | ||||
−0.604782 | + | 0.796391i | \(0.706740\pi\) | |||||||
\(62\) | −4.70281 | −0.597257 | ||||||||
\(63\) | −1.66890 | −0.210262 | ||||||||
\(64\) | 6.38921 | 0.798651 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.8555 | 1.44838 | 0.724189 | − | 0.689601i | \(-0.242214\pi\) | ||||
0.724189 | + | 0.689601i | \(0.242214\pi\) | |||||||
\(68\) | −0.846000 | −0.102593 | ||||||||
\(69\) | 2.26383 | 0.272533 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.18239 | −0.259002 | −0.129501 | − | 0.991579i | \(-0.541338\pi\) | ||||
−0.129501 | + | 0.991579i | \(0.541338\pi\) | |||||||
\(72\) | 6.47231 | 0.762769 | ||||||||
\(73\) | −14.4991 | −1.69699 | −0.848494 | − | 0.529205i | \(-0.822490\pi\) | ||||
−0.848494 | + | 0.529205i | \(0.822490\pi\) | |||||||
\(74\) | −5.45772 | −0.634447 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.96880 | 0.569960 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.80954 | 0.318118 | ||||||||
\(79\) | −7.34554 | −0.826438 | −0.413219 | − | 0.910632i | \(-0.635596\pi\) | ||||
−0.413219 | + | 0.910632i | \(0.635596\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.37484 | 0.263871 | ||||||||
\(82\) | 5.22433 | 0.576931 | ||||||||
\(83\) | −0.788913 | −0.0865944 | −0.0432972 | − | 0.999062i | \(-0.513786\pi\) | ||||
−0.0432972 | + | 0.999062i | \(0.513786\pi\) | |||||||
\(84\) | −0.740239 | −0.0807667 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.1252 | −1.09183 | ||||||||
\(87\) | −3.03965 | −0.325884 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.41895 | 0.256408 | 0.128204 | − | 0.991748i | \(-0.459079\pi\) | ||||
0.128204 | + | 0.991748i | \(0.459079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.48158 | 0.260141 | ||||||||
\(92\) | −2.72027 | −0.283608 | ||||||||
\(93\) | −4.41110 | −0.457410 | ||||||||
\(94\) | −2.88284 | −0.297342 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.73452 | 0.483214 | ||||||||
\(97\) | −1.80480 | −0.183249 | −0.0916247 | − | 0.995794i | \(-0.529206\pi\) | ||||
−0.0916247 | + | 0.995794i | \(0.529206\pi\) | |||||||
\(98\) | −6.15550 | −0.621799 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.0478 | −1.09930 | −0.549648 | − | 0.835396i | \(-0.685238\pi\) | ||||
−0.549648 | + | 0.835396i | \(0.685238\pi\) | |||||||
\(102\) | 0.675050 | 0.0668399 | ||||||||
\(103\) | −14.1500 | −1.39424 | −0.697119 | − | 0.716956i | \(-0.745535\pi\) | ||||
−0.697119 | + | 0.716956i | \(0.745535\pi\) | |||||||
\(104\) | −9.62402 | −0.943713 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.2723 | 1.28912 | ||||||||
\(107\) | −11.3577 | −1.09799 | −0.548997 | − | 0.835824i | \(-0.684990\pi\) | ||||
−0.548997 | + | 0.835824i | \(0.684990\pi\) | |||||||
\(108\) | 5.04529 | 0.485483 | ||||||||
\(109\) | 10.6108 | 1.01634 | 0.508168 | − | 0.861258i | \(-0.330323\pi\) | ||||
0.508168 | + | 0.861258i | \(0.330323\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.11919 | −0.485892 | ||||||||
\(112\) | −0.510911 | −0.0482766 | ||||||||
\(113\) | 10.6727 | 1.00400 | 0.502001 | − | 0.864867i | \(-0.332598\pi\) | ||||
0.502001 | + | 0.864867i | \(0.332598\pi\) | |||||||
\(114\) | −3.96476 | −0.371334 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.65252 | 0.339128 | ||||||||
\(117\) | −7.13928 | −0.660027 | ||||||||
\(118\) | −13.6601 | −1.25751 | ||||||||
\(119\) | 0.596251 | 0.0546582 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.05793 | −0.820066 | ||||||||
\(123\) | 4.90028 | 0.441843 | ||||||||
\(124\) | 5.30050 | 0.475999 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.60017 | −0.142555 | ||||||||
\(127\) | −6.91796 | −0.613869 | −0.306935 | − | 0.951731i | \(-0.599303\pi\) | ||||
−0.306935 | + | 0.951731i | \(0.599303\pi\) | |||||||
\(128\) | −4.40277 | −0.389154 | ||||||||
\(129\) | −9.49714 | −0.836177 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.01744 | 0.613117 | 0.306558 | − | 0.951852i | \(-0.400823\pi\) | ||||
0.306558 | + | 0.951852i | \(0.400823\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.50195 | −0.303658 | ||||||||
\(134\) | 11.3672 | 0.981979 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.31237 | −0.198284 | ||||||||
\(137\) | −7.95932 | −0.680011 | −0.340005 | − | 0.940423i | \(-0.610429\pi\) | ||||
−0.340005 | + | 0.940423i | \(0.610429\pi\) | |||||||
\(138\) | 2.17059 | 0.184773 | ||||||||
\(139\) | −13.8450 | −1.17432 | −0.587158 | − | 0.809473i | \(-0.699753\pi\) | ||||
−0.587158 | + | 0.809473i | \(0.699753\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.70403 | −0.227720 | ||||||||
\(142\) | −2.09251 | −0.175600 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.46984 | 0.122487 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.9019 | −1.15053 | ||||||||
\(147\) | −5.77368 | −0.476205 | ||||||||
\(148\) | 6.15136 | 0.505638 | ||||||||
\(149\) | 6.94056 | 0.568593 | 0.284297 | − | 0.958736i | \(-0.408240\pi\) | ||||
0.284297 | + | 0.958736i | \(0.408240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0162 | 0.977862 | 0.488931 | − | 0.872322i | \(-0.337387\pi\) | ||||
0.488931 | + | 0.872322i | \(0.337387\pi\) | |||||||
\(152\) | 13.5812 | 1.10158 | ||||||||
\(153\) | −1.71536 | −0.138678 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.16662 | −0.253532 | ||||||||
\(157\) | 17.7526 | 1.41681 | 0.708405 | − | 0.705806i | \(-0.249415\pi\) | ||||
0.708405 | + | 0.705806i | \(0.249415\pi\) | |||||||
\(158\) | −7.04302 | −0.560313 | ||||||||
\(159\) | 12.4490 | 0.987273 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.91721 | 0.151098 | ||||||||
\(162\) | 2.27703 | 0.178900 | ||||||||
\(163\) | 8.59091 | 0.672892 | 0.336446 | − | 0.941703i | \(-0.390775\pi\) | ||||
0.336446 | + | 0.941703i | \(0.390775\pi\) | |||||||
\(164\) | −5.88831 | −0.459799 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.756422 | −0.0587097 | ||||||||
\(167\) | 0.747673 | 0.0578567 | 0.0289283 | − | 0.999581i | \(-0.490791\pi\) | ||||
0.0289283 | + | 0.999581i | \(0.490791\pi\) | |||||||
\(168\) | −2.02329 | −0.156100 | ||||||||
\(169\) | −2.38422 | −0.183402 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.0748 | 0.770438 | ||||||||
\(172\) | 11.4120 | 0.870158 | ||||||||
\(173\) | −25.9204 | −1.97069 | −0.985346 | − | 0.170565i | \(-0.945441\pi\) | ||||
−0.985346 | + | 0.170565i | \(0.945441\pi\) | |||||||
\(174\) | −2.91446 | −0.220945 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.8128 | −0.963066 | ||||||||
\(178\) | 2.31933 | 0.173841 | ||||||||
\(179\) | −6.44765 | −0.481920 | −0.240960 | − | 0.970535i | \(-0.577462\pi\) | ||||
−0.240960 | + | 0.970535i | \(0.577462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.8187 | 1.62177 | 0.810887 | − | 0.585202i | \(-0.198985\pi\) | ||||
0.810887 | + | 0.585202i | \(0.198985\pi\) | |||||||
\(182\) | 2.37938 | 0.176371 | ||||||||
\(183\) | −8.49609 | −0.628049 | ||||||||
\(184\) | −7.43530 | −0.548138 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.22943 | −0.310117 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.24923 | 0.236974 | ||||||||
\(189\) | −3.55586 | −0.258650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9374 | 1.22555 | 0.612775 | − | 0.790258i | \(-0.290053\pi\) | ||||
0.612775 | + | 0.790258i | \(0.290053\pi\) | |||||||
\(192\) | 5.74608 | 0.414688 | ||||||||
\(193\) | 7.46517 | 0.537354 | 0.268677 | − | 0.963230i | \(-0.413414\pi\) | ||||
0.268677 | + | 0.963230i | \(0.413414\pi\) | |||||||
\(194\) | −1.73047 | −0.124240 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.93781 | 0.495558 | ||||||||
\(197\) | −18.8091 | −1.34009 | −0.670045 | − | 0.742320i | \(-0.733725\pi\) | ||||
−0.670045 | + | 0.742320i | \(0.733725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7708 | 0.976187 | 0.488094 | − | 0.872791i | \(-0.337692\pi\) | ||||
0.488094 | + | 0.872791i | \(0.337692\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6621 | 0.752049 | ||||||||
\(202\) | −10.5928 | −0.745306 | ||||||||
\(203\) | −2.57425 | −0.180677 | ||||||||
\(204\) | −0.760843 | −0.0532697 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.5672 | −0.945272 | ||||||||
\(207\) | −5.51565 | −0.383364 | ||||||||
\(208\) | −2.18559 | −0.151543 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0376 | 1.17291 | 0.586457 | − | 0.809980i | \(-0.300522\pi\) | ||||
0.586457 | + | 0.809980i | \(0.300522\pi\) | |||||||
\(212\) | −14.9591 | −1.02739 | ||||||||
\(213\) | −1.96272 | −0.134483 | ||||||||
\(214\) | −10.8900 | −0.744424 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.7902 | 0.938307 | ||||||||
\(217\) | −3.73573 | −0.253598 | ||||||||
\(218\) | 10.1738 | 0.689060 | ||||||||
\(219\) | −13.0396 | −0.881136 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.55066 | 0.171576 | ||||||||
\(222\) | −4.90836 | −0.329428 | ||||||||
\(223\) | −7.19470 | −0.481793 | −0.240896 | − | 0.970551i | \(-0.577441\pi\) | ||||
−0.240896 | + | 0.970551i | \(0.577441\pi\) | |||||||
\(224\) | 4.00962 | 0.267904 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.2331 | 0.680698 | ||||||||
\(227\) | −13.5046 | −0.896330 | −0.448165 | − | 0.893951i | \(-0.647922\pi\) | ||||
−0.448165 | + | 0.893951i | \(0.647922\pi\) | |||||||
\(228\) | 4.46865 | 0.295944 | ||||||||
\(229\) | 24.5209 | 1.62038 | 0.810192 | − | 0.586164i | \(-0.199363\pi\) | ||||
0.810192 | + | 0.586164i | \(0.199363\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.98340 | 0.655442 | ||||||||
\(233\) | −6.17558 | −0.404576 | −0.202288 | − | 0.979326i | \(-0.564838\pi\) | ||||
−0.202288 | + | 0.979326i | \(0.564838\pi\) | |||||||
\(234\) | −6.84526 | −0.447488 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.3961 | 1.00220 | ||||||||
\(237\) | −6.60616 | −0.429116 | ||||||||
\(238\) | 0.571694 | 0.0370574 | ||||||||
\(239\) | 12.0519 | 0.779574 | 0.389787 | − | 0.920905i | \(-0.372549\pi\) | ||||
0.389787 | + | 0.920905i | \(0.372549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.38650 | 0.346975 | 0.173488 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173488 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1417 | 1.03549 | ||||||||
\(244\) | 10.2091 | 0.653572 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.69846 | 0.299563 | ||||||||
\(247\) | −14.9807 | −0.953201 | ||||||||
\(248\) | 14.4878 | 0.919977 | ||||||||
\(249\) | −0.709502 | −0.0449629 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.54538 | −0.286902 | −0.143451 | − | 0.989657i | \(-0.545820\pi\) | ||||
−0.143451 | + | 0.989657i | \(0.545820\pi\) | |||||||
\(252\) | 1.80354 | 0.113612 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −6.63304 | −0.416194 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.9999 | −1.06249 | ||||||||
\(257\) | 21.9515 | 1.36930 | 0.684648 | − | 0.728874i | \(-0.259956\pi\) | ||||
0.684648 | + | 0.728874i | \(0.259956\pi\) | |||||||
\(258\) | −9.10601 | −0.566915 | ||||||||
\(259\) | −4.33540 | −0.269389 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.40588 | 0.458413 | ||||||||
\(262\) | 6.72843 | 0.415684 | ||||||||
\(263\) | −1.42036 | −0.0875834 | −0.0437917 | − | 0.999041i | \(-0.513944\pi\) | ||||
−0.0437917 | + | 0.999041i | \(0.513944\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.35772 | −0.205875 | ||||||||
\(267\) | 2.17546 | 0.133136 | ||||||||
\(268\) | −12.8119 | −0.782612 | ||||||||
\(269\) | 6.86809 | 0.418755 | 0.209377 | − | 0.977835i | \(-0.432856\pi\) | ||||
0.209377 | + | 0.977835i | \(0.432856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3452 | −0.992900 | −0.496450 | − | 0.868065i | \(-0.665363\pi\) | ||||
−0.496450 | + | 0.868065i | \(0.665363\pi\) | |||||||
\(272\) | −0.525132 | −0.0318408 | ||||||||
\(273\) | 2.23179 | 0.135074 | ||||||||
\(274\) | −7.63152 | −0.461037 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.44646 | −0.147259 | ||||||||
\(277\) | 9.95773 | 0.598302 | 0.299151 | − | 0.954206i | \(-0.403297\pi\) | ||||
0.299151 | + | 0.954206i | \(0.403297\pi\) | |||||||
\(278\) | −13.2748 | −0.796168 | ||||||||
\(279\) | 10.7473 | 0.643426 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6466 | −1.29133 | −0.645663 | − | 0.763623i | \(-0.723419\pi\) | ||||
−0.645663 | + | 0.763623i | \(0.723419\pi\) | |||||||
\(282\) | −2.59266 | −0.154391 | ||||||||
\(283\) | 6.61565 | 0.393260 | 0.196630 | − | 0.980478i | \(-0.437000\pi\) | ||||
0.196630 | + | 0.980478i | \(0.437000\pi\) | |||||||
\(284\) | 2.35845 | 0.139948 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.15001 | 0.244967 | ||||||||
\(288\) | −11.5353 | −0.679725 | ||||||||
\(289\) | −16.3872 | −0.963950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.62313 | −0.0951495 | ||||||||
\(292\) | 15.6688 | 0.916944 | ||||||||
\(293\) | 10.4738 | 0.611885 | 0.305943 | − | 0.952050i | \(-0.401028\pi\) | ||||
0.305943 | + | 0.952050i | \(0.401028\pi\) | |||||||
\(294\) | −5.53590 | −0.322860 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 16.8135 | 0.977263 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.65472 | 0.385498 | ||||||||
\(299\) | 8.20151 | 0.474306 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.04305 | −0.463594 | ||||||||
\(302\) | 11.5213 | 0.662976 | ||||||||
\(303\) | −9.93574 | −0.570793 | ||||||||
\(304\) | 3.08425 | 0.176894 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.64471 | −0.0940219 | ||||||||
\(307\) | −13.0191 | −0.743041 | −0.371520 | − | 0.928425i | \(-0.621163\pi\) | ||||
−0.371520 | + | 0.928425i | \(0.621163\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.7257 | −0.723938 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.2791 | 0.979807 | 0.489904 | − | 0.871777i | \(-0.337032\pi\) | ||||
0.489904 | + | 0.871777i | \(0.337032\pi\) | |||||||
\(312\) | −8.65529 | −0.490009 | ||||||||
\(313\) | −10.0540 | −0.568286 | −0.284143 | − | 0.958782i | \(-0.591709\pi\) | ||||
−0.284143 | + | 0.958782i | \(0.591709\pi\) | |||||||
\(314\) | 17.0214 | 0.960575 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.93813 | 0.446555 | ||||||||
\(317\) | −1.99347 | −0.111964 | −0.0559822 | − | 0.998432i | \(-0.517829\pi\) | ||||
−0.0559822 | + | 0.998432i | \(0.517829\pi\) | |||||||
\(318\) | 11.9363 | 0.669356 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.2145 | −0.570118 | ||||||||
\(322\) | 1.83826 | 0.102442 | ||||||||
\(323\) | −3.59942 | −0.200277 | ||||||||
\(324\) | −2.56642 | −0.142579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.23710 | 0.456211 | ||||||||
\(327\) | 9.54279 | 0.527717 | ||||||||
\(328\) | −16.0945 | −0.888668 | ||||||||
\(329\) | −2.29002 | −0.126253 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4300 | −0.573283 | −0.286642 | − | 0.958038i | \(-0.592539\pi\) | ||||
−0.286642 | + | 0.958038i | \(0.592539\pi\) | |||||||
\(332\) | 0.852557 | 0.0467901 | ||||||||
\(333\) | 12.4726 | 0.683492 | ||||||||
\(334\) | 0.716881 | 0.0392260 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.459484 | −0.0250669 | ||||||||
\(337\) | −11.6395 | −0.634044 | −0.317022 | − | 0.948418i | \(-0.602683\pi\) | ||||
−0.317022 | + | 0.948418i | \(0.602683\pi\) | |||||||
\(338\) | −2.28603 | −0.124343 | ||||||||
\(339\) | 9.59839 | 0.521313 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 9.65986 | 0.522345 | ||||||||
\(343\) | −10.2212 | −0.551893 | ||||||||
\(344\) | 31.1924 | 1.68178 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.8529 | −1.33610 | ||||||||
\(347\) | −34.1016 | −1.83067 | −0.915334 | − | 0.402695i | \(-0.868074\pi\) | ||||
−0.915334 | + | 0.402695i | \(0.868074\pi\) | |||||||
\(348\) | 3.28486 | 0.176087 | ||||||||
\(349\) | 6.32525 | 0.338583 | 0.169291 | − | 0.985566i | \(-0.445852\pi\) | ||||
0.169291 | + | 0.985566i | \(0.445852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.2113 | −0.811921 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.5776 | −1.62748 | −0.813742 | − | 0.581226i | \(-0.802573\pi\) | ||||
−0.813742 | + | 0.581226i | \(0.802573\pi\) | |||||||
\(354\) | −12.2851 | −0.652944 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.61409 | −0.138547 | ||||||||
\(357\) | 0.536233 | 0.0283805 | ||||||||
\(358\) | −6.18211 | −0.326734 | ||||||||
\(359\) | 14.4505 | 0.762668 | 0.381334 | − | 0.924437i | \(-0.375465\pi\) | ||||
0.381334 | + | 0.924437i | \(0.375465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.14045 | 0.112655 | ||||||||
\(362\) | 20.9201 | 1.09954 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.68178 | −0.140563 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.14618 | −0.425808 | ||||||||
\(367\) | 29.0792 | 1.51792 | 0.758962 | − | 0.651135i | \(-0.225707\pi\) | ||||
0.758962 | + | 0.651135i | \(0.225707\pi\) | |||||||
\(368\) | −1.68854 | −0.0880211 | ||||||||
\(369\) | −11.9392 | −0.621529 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.5430 | 0.547365 | ||||||||
\(372\) | 4.76696 | 0.247155 | ||||||||
\(373\) | 12.1992 | 0.631653 | 0.315826 | − | 0.948817i | \(-0.397718\pi\) | ||||
0.315826 | + | 0.948817i | \(0.397718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.88109 | 0.458007 | ||||||||
\(377\) | −11.0122 | −0.567157 | ||||||||
\(378\) | −3.40941 | −0.175361 | ||||||||
\(379\) | 27.0350 | 1.38869 | 0.694346 | − | 0.719641i | \(-0.255694\pi\) | ||||
0.694346 | + | 0.719641i | \(0.255694\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.22161 | −0.318743 | ||||||||
\(382\) | 16.2399 | 0.830904 | ||||||||
\(383\) | −26.9866 | −1.37895 | −0.689477 | − | 0.724308i | \(-0.742159\pi\) | ||||
−0.689477 | + | 0.724308i | \(0.742159\pi\) | |||||||
\(384\) | −3.95960 | −0.202062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.15772 | 0.364318 | ||||||||
\(387\) | 23.1391 | 1.17623 | ||||||||
\(388\) | 1.95040 | 0.0990163 | ||||||||
\(389\) | 10.3178 | 0.523133 | 0.261567 | − | 0.965185i | \(-0.415761\pi\) | ||||
0.261567 | + | 0.965185i | \(0.415761\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.97058 | 0.0996565 | ||||||||
\(392\) | 18.9631 | 0.957780 | ||||||||
\(393\) | 6.31108 | 0.318352 | ||||||||
\(394\) | −18.0344 | −0.908561 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.63508 | 0.383194 | 0.191597 | − | 0.981474i | \(-0.438633\pi\) | ||||
0.191597 | + | 0.981474i | \(0.438633\pi\) | |||||||
\(398\) | 13.2037 | 0.661840 | ||||||||
\(399\) | −3.14945 | −0.157670 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.3039 | −1.01393 | −0.506964 | − | 0.861967i | \(-0.669232\pi\) | ||||
−0.506964 | + | 0.861967i | \(0.669232\pi\) | |||||||
\(402\) | 10.2230 | 0.509878 | ||||||||
\(403\) | −15.9808 | −0.796060 | ||||||||
\(404\) | 11.9390 | 0.593990 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.46823 | −0.122496 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2.07961 | −0.102956 | ||||||||
\(409\) | 16.4461 | 0.813208 | 0.406604 | − | 0.913605i | \(-0.366713\pi\) | ||||
0.406604 | + | 0.913605i | \(0.366713\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.15816 | −0.353086 | ||||||||
\(412\) | 15.2915 | 0.753358 | ||||||||
\(413\) | −10.8510 | −0.533944 | ||||||||
\(414\) | −5.28849 | −0.259915 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17.1525 | 0.840969 | ||||||||
\(417\) | −12.4514 | −0.609746 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.536621 | 0.0262157 | 0.0131078 | − | 0.999914i | \(-0.495828\pi\) | ||||
0.0131078 | + | 0.999914i | \(0.495828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.94084 | −0.387013 | −0.193506 | − | 0.981099i | \(-0.561986\pi\) | ||||
−0.193506 | + | 0.981099i | \(0.561986\pi\) | |||||||
\(422\) | 16.3359 | 0.795219 | ||||||||
\(423\) | 6.58817 | 0.320328 | ||||||||
\(424\) | −40.8876 | −1.98568 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.88188 | −0.0911776 | ||||||||
\(427\) | −7.19527 | −0.348203 | ||||||||
\(428\) | 12.2740 | 0.593287 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.97717 | −0.239742 | −0.119871 | − | 0.992789i | \(-0.538248\pi\) | ||||
−0.119871 | + | 0.992789i | \(0.538248\pi\) | |||||||
\(432\) | 3.13173 | 0.150675 | ||||||||
\(433\) | 15.5489 | 0.747230 | 0.373615 | − | 0.927584i | \(-0.378118\pi\) | ||||
0.373615 | + | 0.927584i | \(0.378118\pi\) | |||||||
\(434\) | −3.58187 | −0.171935 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.4669 | −0.549163 | ||||||||
\(437\) | −11.5738 | −0.553649 | ||||||||
\(438\) | −12.5026 | −0.597397 | ||||||||
\(439\) | 13.4404 | 0.641476 | 0.320738 | − | 0.947168i | \(-0.396069\pi\) | ||||
0.320738 | + | 0.947168i | \(0.396069\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.0672 | 0.669865 | ||||||||
\(442\) | 2.44561 | 0.116326 | ||||||||
\(443\) | 17.6173 | 0.837023 | 0.418511 | − | 0.908212i | \(-0.362552\pi\) | ||||
0.418511 | + | 0.908212i | \(0.362552\pi\) | |||||||
\(444\) | 5.53217 | 0.262545 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.89839 | −0.326648 | ||||||||
\(447\) | 6.24194 | 0.295234 | ||||||||
\(448\) | 4.86631 | 0.229912 | ||||||||
\(449\) | 1.16048 | 0.0547665 | 0.0273833 | − | 0.999625i | \(-0.491283\pi\) | ||||
0.0273833 | + | 0.999625i | \(0.491283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −11.5337 | −0.542499 | ||||||||
\(453\) | 10.8067 | 0.507741 | ||||||||
\(454\) | −12.9484 | −0.607698 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.2141 | 0.571979 | ||||||||
\(457\) | 21.7498 | 1.01741 | 0.508705 | − | 0.860941i | \(-0.330124\pi\) | ||||
0.508705 | + | 0.860941i | \(0.330124\pi\) | |||||||
\(458\) | 23.5110 | 1.09860 | ||||||||
\(459\) | −3.65483 | −0.170593 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.7416 | −1.61808 | −0.809040 | − | 0.587754i | \(-0.800012\pi\) | ||||
−0.809040 | + | 0.587754i | \(0.800012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.01443 | 0.186566 | 0.0932832 | − | 0.995640i | \(-0.470264\pi\) | ||||
0.0932832 | + | 0.995640i | \(0.470264\pi\) | |||||||
\(464\) | 2.26720 | 0.105252 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.92124 | −0.274296 | ||||||||
\(467\) | −2.64795 | −0.122533 | −0.0612663 | − | 0.998121i | \(-0.519514\pi\) | ||||
−0.0612663 | + | 0.998121i | \(0.519514\pi\) | |||||||
\(468\) | 7.71523 | 0.356637 | ||||||||
\(469\) | 9.02968 | 0.416952 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.9656 | 0.735658 | ||||||||
\(472\) | 42.0822 | 1.93699 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.33409 | −0.290934 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.644352 | −0.0295338 | ||||||||
\(477\) | −30.3312 | −1.38877 | ||||||||
\(478\) | 11.5556 | 0.528539 | ||||||||
\(479\) | 15.9127 | 0.727068 | 0.363534 | − | 0.931581i | \(-0.381570\pi\) | ||||
0.363534 | + | 0.931581i | \(0.381570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5461 | −0.845629 | ||||||||
\(482\) | 5.16466 | 0.235244 | ||||||||
\(483\) | 1.72423 | 0.0784553 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15.4770 | 0.702049 | ||||||||
\(487\) | 5.71235 | 0.258851 | 0.129426 | − | 0.991589i | \(-0.458687\pi\) | ||||
0.129426 | + | 0.991589i | \(0.458687\pi\) | |||||||
\(488\) | 27.9045 | 1.26318 | ||||||||
\(489\) | 7.72617 | 0.349389 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.24698 | −0.236793 | −0.118396 | − | 0.992966i | \(-0.537775\pi\) | ||||
−0.118396 | + | 0.992966i | \(0.537775\pi\) | |||||||
\(492\) | −5.29560 | −0.238744 | ||||||||
\(493\) | −2.64590 | −0.119165 | ||||||||
\(494\) | −14.3638 | −0.646256 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.29014 | 0.147732 | ||||||||
\(497\) | −1.66221 | −0.0745603 | ||||||||
\(498\) | −0.680282 | −0.0304842 | ||||||||
\(499\) | 15.8703 | 0.710451 | 0.355225 | − | 0.934781i | \(-0.384404\pi\) | ||||
0.355225 | + | 0.934781i | \(0.384404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.672414 | 0.0300412 | ||||||||
\(502\) | −4.35818 | −0.194515 | ||||||||
\(503\) | 36.2385 | 1.61579 | 0.807897 | − | 0.589323i | \(-0.200606\pi\) | ||||
0.807897 | + | 0.589323i | \(0.200606\pi\) | |||||||
\(504\) | 4.92961 | 0.219582 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.14423 | −0.0952286 | ||||||||
\(508\) | 7.47605 | 0.331696 | ||||||||
\(509\) | 17.8023 | 0.789075 | 0.394537 | − | 0.918880i | \(-0.370905\pi\) | ||||
0.394537 | + | 0.918880i | \(0.370905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.0431 | −0.488520 | ||||||||
\(512\) | −7.49418 | −0.331199 | ||||||||
\(513\) | 21.4659 | 0.947741 | ||||||||
\(514\) | 21.0474 | 0.928362 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.2633 | 0.451817 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.15685 | −0.182642 | ||||||||
\(519\) | −23.3113 | −1.02325 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.2701 | 1.36997 | 0.684984 | − | 0.728558i | \(-0.259809\pi\) | ||||
0.684984 | + | 0.728558i | \(0.259809\pi\) | |||||||
\(522\) | 7.10087 | 0.310797 | ||||||||
\(523\) | −3.14554 | −0.137545 | −0.0687723 | − | 0.997632i | \(-0.521908\pi\) | ||||
−0.0687723 | + | 0.997632i | \(0.521908\pi\) | |||||||
\(524\) | −7.58356 | −0.331289 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.36187 | −0.0593802 | ||||||||
\(527\) | −3.83971 | −0.167260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6637 | −0.724509 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.2174 | 1.35472 | ||||||||
\(532\) | 3.78446 | 0.164077 | ||||||||
\(533\) | 17.7530 | 0.768968 | ||||||||
\(534\) | 2.08587 | 0.0902643 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −35.0187 | −1.51258 | ||||||||
\(537\) | −5.79864 | −0.250230 | ||||||||
\(538\) | 6.58523 | 0.283909 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.2469 | 1.12844 | 0.564221 | − | 0.825624i | \(-0.309177\pi\) | ||||
0.564221 | + | 0.825624i | \(0.309177\pi\) | |||||||
\(542\) | −15.6720 | −0.673171 | ||||||||
\(543\) | 19.6225 | 0.842083 | ||||||||
\(544\) | 4.12123 | 0.176696 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.13988 | 0.0915783 | ||||||||
\(547\) | 34.1455 | 1.45996 | 0.729979 | − | 0.683470i | \(-0.239530\pi\) | ||||
0.729979 | + | 0.683470i | \(0.239530\pi\) | |||||||
\(548\) | 8.60143 | 0.367435 | ||||||||
\(549\) | 20.7001 | 0.883459 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5401 | 0.662032 | ||||||||
\(552\) | −6.68688 | −0.284613 | ||||||||
\(553\) | −5.59470 | −0.237911 | ||||||||
\(554\) | 9.54762 | 0.405640 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.9619 | 0.634525 | ||||||||
\(557\) | 34.6084 | 1.46640 | 0.733202 | − | 0.680010i | \(-0.238025\pi\) | ||||
0.733202 | + | 0.680010i | \(0.238025\pi\) | |||||||
\(558\) | 10.3047 | 0.436233 | ||||||||
\(559\) | −34.4068 | −1.45525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.7550 | −0.875499 | ||||||||
\(563\) | −25.9394 | −1.09322 | −0.546608 | − | 0.837389i | \(-0.684081\pi\) | ||||
−0.546608 | + | 0.837389i | \(0.684081\pi\) | |||||||
\(564\) | 2.92217 | 0.123045 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.34319 | 0.266624 | ||||||||
\(567\) | 1.80878 | 0.0759617 | ||||||||
\(568\) | 6.44634 | 0.270482 | ||||||||
\(569\) | 16.3801 | 0.686691 | 0.343346 | − | 0.939209i | \(-0.388440\pi\) | ||||
0.343346 | + | 0.939209i | \(0.388440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.8503 | −0.621465 | −0.310733 | − | 0.950497i | \(-0.600574\pi\) | ||||
−0.310733 | + | 0.950497i | \(0.600574\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2325 | 0.636349 | ||||||||
\(574\) | 3.97909 | 0.166084 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −13.9999 | −0.583330 | ||||||||
\(577\) | −34.2715 | −1.42674 | −0.713370 | − | 0.700788i | \(-0.752832\pi\) | ||||
−0.713370 | + | 0.700788i | \(0.752832\pi\) | |||||||
\(578\) | −15.7123 | −0.653544 | ||||||||
\(579\) | 6.71374 | 0.279013 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.600872 | −0.0249284 | ||||||||
\(582\) | −1.55628 | −0.0645100 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 42.8273 | 1.77221 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.0424 | 0.414849 | ||||||||
\(587\) | 6.32594 | 0.261100 | 0.130550 | − | 0.991442i | \(-0.458326\pi\) | ||||
0.130550 | + | 0.991442i | \(0.458326\pi\) | |||||||
\(588\) | 6.23946 | 0.257311 | ||||||||
\(589\) | 22.5517 | 0.929227 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.9158 | −0.695822 | ||||||||
\(592\) | 3.81829 | 0.156931 | ||||||||
\(593\) | −18.3276 | −0.752623 | −0.376311 | − | 0.926493i | \(-0.622808\pi\) | ||||
−0.376311 | + | 0.926493i | \(0.622808\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.50048 | −0.307232 | ||||||||
\(597\) | 12.3847 | 0.506871 | ||||||||
\(598\) | 7.86374 | 0.321572 | ||||||||
\(599\) | −18.9096 | −0.772627 | −0.386313 | − | 0.922368i | \(-0.626252\pi\) | ||||
−0.386313 | + | 0.922368i | \(0.626252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.9804 | −1.87558 | −0.937790 | − | 0.347202i | \(-0.887132\pi\) | ||||
−0.937790 | + | 0.347202i | \(0.887132\pi\) | |||||||
\(602\) | −7.71180 | −0.314310 | ||||||||
\(603\) | −25.9776 | −1.05789 | ||||||||
\(604\) | −12.9856 | −0.528375 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.52654 | −0.386989 | ||||||||
\(607\) | −35.0051 | −1.42081 | −0.710406 | − | 0.703792i | \(-0.751489\pi\) | ||||
−0.710406 | + | 0.703792i | \(0.751489\pi\) | |||||||
\(608\) | −24.2051 | −0.981648 | ||||||||
\(609\) | −2.31513 | −0.0938139 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.79629 | −0.396316 | ||||||||
\(612\) | 1.85374 | 0.0749330 | ||||||||
\(613\) | 41.0877 | 1.65951 | 0.829757 | − | 0.558124i | \(-0.188479\pi\) | ||||
0.829757 | + | 0.558124i | \(0.188479\pi\) | |||||||
\(614\) | −12.4829 | −0.503770 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.1082 | −0.447201 | −0.223600 | − | 0.974681i | \(-0.571781\pi\) | ||||
−0.223600 | + | 0.974681i | \(0.571781\pi\) | |||||||
\(618\) | −12.2016 | −0.490819 | ||||||||
\(619\) | −24.0771 | −0.967741 | −0.483870 | − | 0.875140i | \(-0.660769\pi\) | ||||
−0.483870 | + | 0.875140i | \(0.660769\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7519 | −0.471589 | ||||||||
\(622\) | 16.5675 | 0.664295 | ||||||||
\(623\) | 1.84238 | 0.0738135 | ||||||||
\(624\) | −1.96559 | −0.0786867 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.63993 | −0.385289 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.1847 | −0.765554 | ||||||||
\(629\) | −4.45608 | −0.177675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.6944 | −1.73945 | −0.869724 | − | 0.493538i | \(-0.835703\pi\) | ||||
−0.869724 | + | 0.493538i | \(0.835703\pi\) | |||||||
\(632\) | 21.6972 | 0.863070 | ||||||||
\(633\) | 15.3226 | 0.609019 | ||||||||
\(634\) | −1.91137 | −0.0759101 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.4533 | −0.533460 | ||||||||
\(637\) | −20.9172 | −0.828770 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.78202 | 0.189174 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.7544 | −0.661760 | −0.330880 | − | 0.943673i | \(-0.607346\pi\) | ||||
−0.330880 | + | 0.943673i | \(0.607346\pi\) | |||||||
\(642\) | −9.79382 | −0.386531 | ||||||||
\(643\) | −4.18868 | −0.165186 | −0.0825928 | − | 0.996583i | \(-0.526320\pi\) | ||||
−0.0825928 | + | 0.996583i | \(0.526320\pi\) | |||||||
\(644\) | −2.07188 | −0.0816436 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.45118 | −0.135785 | ||||||||
\(647\) | −14.6389 | −0.575516 | −0.287758 | − | 0.957703i | \(-0.592910\pi\) | ||||
−0.287758 | + | 0.957703i | \(0.592910\pi\) | |||||||
\(648\) | −7.01478 | −0.275567 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.35970 | −0.131677 | ||||||||
\(652\) | −9.28397 | −0.363588 | ||||||||
\(653\) | 22.5629 | 0.882954 | 0.441477 | − | 0.897273i | \(-0.354455\pi\) | ||||
0.441477 | + | 0.897273i | \(0.354455\pi\) | |||||||
\(654\) | 9.14977 | 0.357784 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.65501 | −0.142704 | ||||||||
\(657\) | 31.7701 | 1.23947 | ||||||||
\(658\) | −2.19570 | −0.0855974 | ||||||||
\(659\) | 42.3114 | 1.64822 | 0.824110 | − | 0.566430i | \(-0.191676\pi\) | ||||
0.824110 | + | 0.566430i | \(0.191676\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.6525 | −0.414334 | −0.207167 | − | 0.978306i | \(-0.566424\pi\) | ||||
−0.207167 | + | 0.978306i | \(0.566424\pi\) | |||||||
\(662\) | −10.0004 | −0.388677 | ||||||||
\(663\) | 2.29391 | 0.0890882 | ||||||||
\(664\) | 2.33029 | 0.0904327 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.9589 | 0.463397 | ||||||||
\(667\) | −8.50777 | −0.329422 | ||||||||
\(668\) | −0.807990 | −0.0312621 | ||||||||
\(669\) | −6.47050 | −0.250164 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.60602 | 0.139105 | ||||||||
\(673\) | 18.7484 | 0.722696 | 0.361348 | − | 0.932431i | \(-0.382317\pi\) | ||||
0.361348 | + | 0.932431i | \(0.382317\pi\) | |||||||
\(674\) | −11.1601 | −0.429872 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.57656 | 0.0990986 | ||||||||
\(677\) | −46.0553 | −1.77005 | −0.885025 | − | 0.465543i | \(-0.845859\pi\) | ||||
−0.885025 | + | 0.465543i | \(0.845859\pi\) | |||||||
\(678\) | 9.20308 | 0.353442 | ||||||||
\(679\) | −1.37461 | −0.0527529 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.1452 | −0.465406 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.99721 | 0.306005 | 0.153002 | − | 0.988226i | \(-0.451106\pi\) | ||||
0.153002 | + | 0.988226i | \(0.451106\pi\) | |||||||
\(684\) | −10.8876 | −0.416296 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.80025 | −0.374175 | ||||||||
\(687\) | 22.0527 | 0.841361 | ||||||||
\(688\) | 7.08371 | 0.270064 | ||||||||
\(689\) | 45.1011 | 1.71821 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.14408 | 0.233732 | 0.116866 | − | 0.993148i | \(-0.462715\pi\) | ||||
0.116866 | + | 0.993148i | \(0.462715\pi\) | |||||||
\(692\) | 28.0115 | 1.06484 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.6971 | −1.24117 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 8.97850 | 0.340329 | ||||||||
\(697\) | 4.26552 | 0.161568 | ||||||||
\(698\) | 6.06475 | 0.229554 | ||||||||
\(699\) | −5.55396 | −0.210070 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.5075 | −0.850096 | −0.425048 | − | 0.905171i | \(-0.639743\pi\) | ||||
−0.425048 | + | 0.905171i | \(0.639743\pi\) | |||||||
\(702\) | −14.5849 | −0.550470 | ||||||||
\(703\) | 26.1718 | 0.987088 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.3183 | −1.10341 | ||||||||
\(707\) | −8.41449 | −0.316460 | ||||||||
\(708\) | 13.8464 | 0.520380 | ||||||||
\(709\) | −6.00326 | −0.225457 | −0.112729 | − | 0.993626i | \(-0.535959\pi\) | ||||
−0.112729 | + | 0.993626i | \(0.535959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.0954 | 0.603626 | ||||||||
\(712\) | −7.14509 | −0.267773 | ||||||||
\(713\) | −12.3464 | −0.462376 | ||||||||
\(714\) | 0.514149 | 0.0192415 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.96780 | 0.260399 | ||||||||
\(717\) | 10.8388 | 0.404782 | ||||||||
\(718\) | 13.8554 | 0.517077 | ||||||||
\(719\) | −26.2179 | −0.977762 | −0.488881 | − | 0.872351i | \(-0.662595\pi\) | ||||
−0.488881 | + | 0.872351i | \(0.662595\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7773 | −0.401366 | ||||||||
\(722\) | 2.05230 | 0.0763786 | ||||||||
\(723\) | 4.84431 | 0.180162 | ||||||||
\(724\) | −23.5789 | −0.876304 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.86669 | 0.180495 | 0.0902477 | − | 0.995919i | \(-0.471234\pi\) | ||||
0.0902477 | + | 0.995919i | \(0.471234\pi\) | |||||||
\(728\) | −7.33009 | −0.271671 | ||||||||
\(729\) | 7.39244 | 0.273794 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.26693 | −0.305763 | ||||||||
\(732\) | 9.18149 | 0.339358 | ||||||||
\(733\) | 37.0900 | 1.36995 | 0.684975 | − | 0.728566i | \(-0.259813\pi\) | ||||
0.684975 | + | 0.728566i | \(0.259813\pi\) | |||||||
\(734\) | 27.8816 | 1.02913 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.2516 | 0.488461 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −11.4475 | −0.421387 | ||||||||
\(739\) | 0.723750 | 0.0266236 | 0.0133118 | − | 0.999911i | \(-0.495763\pi\) | ||||
0.0133118 | + | 0.999911i | \(0.495763\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.4728 | −0.494936 | ||||||||
\(742\) | 10.1088 | 0.371105 | ||||||||
\(743\) | −34.6512 | −1.27123 | −0.635614 | − | 0.772007i | \(-0.719253\pi\) | ||||
−0.635614 | + | 0.772007i | \(0.719253\pi\) | |||||||
\(744\) | 13.0295 | 0.477685 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.6968 | 0.428251 | ||||||||
\(747\) | 1.72865 | 0.0632481 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.65057 | −0.316085 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.49256 | 0.236917 | 0.118458 | − | 0.992959i | \(-0.462205\pi\) | ||||
0.118458 | + | 0.992959i | \(0.462205\pi\) | |||||||
\(752\) | 2.01687 | 0.0735478 | ||||||||
\(753\) | −4.08785 | −0.148970 | ||||||||
\(754\) | −10.5587 | −0.384524 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.84272 | 0.139758 | ||||||||
\(757\) | −34.8773 | −1.26764 | −0.633818 | − | 0.773482i | \(-0.718513\pi\) | ||||
−0.633818 | + | 0.773482i | \(0.718513\pi\) | |||||||
\(758\) | 25.9215 | 0.941512 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.3602 | −1.60806 | −0.804029 | − | 0.594591i | \(-0.797314\pi\) | ||||
−0.804029 | + | 0.594591i | \(0.797314\pi\) | |||||||
\(762\) | −5.96538 | −0.216103 | ||||||||
\(763\) | 8.08170 | 0.292577 | ||||||||
\(764\) | −18.3038 | −0.662209 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −25.8752 | −0.934909 | ||||||||
\(767\) | −46.4188 | −1.67608 | ||||||||
\(768\) | −15.2887 | −0.551683 | ||||||||
\(769\) | 17.0854 | 0.616117 | 0.308058 | − | 0.951367i | \(-0.400321\pi\) | ||||
0.308058 | + | 0.951367i | \(0.400321\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.7419 | 0.710987 | ||||||||
\(772\) | −8.06740 | −0.290352 | ||||||||
\(773\) | −12.6914 | −0.456477 | −0.228239 | − | 0.973605i | \(-0.573297\pi\) | ||||
−0.228239 | + | 0.973605i | \(0.573297\pi\) | |||||||
\(774\) | 22.1861 | 0.797464 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.33100 | 0.191372 | ||||||||
\(777\) | −3.89901 | −0.139876 | ||||||||
\(778\) | 9.89286 | 0.354676 | ||||||||
\(779\) | −25.0526 | −0.897603 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.88942 | 0.0675656 | ||||||||
\(783\) | 15.7794 | 0.563908 | ||||||||
\(784\) | 4.30646 | 0.153802 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.05116 | 0.215838 | ||||||||
\(787\) | 35.8290 | 1.27717 | 0.638584 | − | 0.769552i | \(-0.279521\pi\) | ||||
0.638584 | + | 0.769552i | \(0.279521\pi\) | |||||||
\(788\) | 20.3264 | 0.724100 | ||||||||
\(789\) | −1.27739 | −0.0454764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.12880 | 0.289027 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.7801 | −1.09303 | ||||||||
\(794\) | 7.32063 | 0.259800 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.8817 | −0.527470 | ||||||||
\(797\) | −4.70921 | −0.166809 | −0.0834043 | − | 0.996516i | \(-0.526579\pi\) | ||||
−0.0834043 | + | 0.996516i | \(0.526579\pi\) | |||||||
\(798\) | −3.01974 | −0.106898 | ||||||||
\(799\) | −2.35376 | −0.0832700 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.30036 | −0.187279 | ||||||||
\(802\) | −19.4677 | −0.687428 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −11.5223 | −0.406360 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −15.3226 | −0.539717 | ||||||||
\(807\) | 6.17676 | 0.217432 | ||||||||
\(808\) | 32.6329 | 1.14802 | ||||||||
\(809\) | 18.6284 | 0.654940 | 0.327470 | − | 0.944862i | \(-0.393804\pi\) | ||||
0.327470 | + | 0.944862i | \(0.393804\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.8626 | 0.557012 | 0.278506 | − | 0.960435i | \(-0.410161\pi\) | ||||
0.278506 | + | 0.960435i | \(0.410161\pi\) | |||||||
\(812\) | 2.78192 | 0.0976264 | ||||||||
\(813\) | −14.6999 | −0.515549 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.472274 | −0.0165329 | ||||||||
\(817\) | 48.5540 | 1.69869 | ||||||||
\(818\) | 15.7688 | 0.551342 | ||||||||
\(819\) | −5.43760 | −0.190005 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.685709 | −0.0239314 | −0.0119657 | − | 0.999928i | \(-0.503809\pi\) | ||||
−0.0119657 | + | 0.999928i | \(0.503809\pi\) | |||||||
\(822\) | −6.86335 | −0.239387 | ||||||||
\(823\) | −24.5414 | −0.855460 | −0.427730 | − | 0.903907i | \(-0.640687\pi\) | ||||
−0.427730 | + | 0.903907i | \(0.640687\pi\) | |||||||
\(824\) | 41.7961 | 1.45604 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.4041 | −0.362006 | ||||||||
\(827\) | −30.4322 | −1.05823 | −0.529116 | − | 0.848550i | \(-0.677476\pi\) | ||||
−0.529116 | + | 0.848550i | \(0.677476\pi\) | |||||||
\(828\) | 5.96062 | 0.207146 | ||||||||
\(829\) | −10.0715 | −0.349797 | −0.174899 | − | 0.984586i | \(-0.555960\pi\) | ||||
−0.174899 | + | 0.984586i | \(0.555960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.95541 | 0.310660 | ||||||||
\(832\) | 20.8172 | 0.721707 | ||||||||
\(833\) | −5.02579 | −0.174133 | ||||||||
\(834\) | −11.9386 | −0.413399 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.8988 | 0.791500 | ||||||||
\(838\) | 0.514521 | 0.0177738 | ||||||||
\(839\) | 34.8027 | 1.20152 | 0.600762 | − | 0.799428i | \(-0.294864\pi\) | ||||
0.600762 | + | 0.799428i | \(0.294864\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5766 | −0.606089 | ||||||||
\(842\) | −7.61380 | −0.262389 | ||||||||
\(843\) | −19.4677 | −0.670502 | ||||||||
\(844\) | −18.4120 | −0.633769 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.31683 | 0.217177 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.28547 | −0.318864 | ||||||||
\(849\) | 5.94973 | 0.204194 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.3283 | −0.491168 | ||||||||
\(852\) | 2.12106 | 0.0726662 | ||||||||
\(853\) | −27.1822 | −0.930699 | −0.465350 | − | 0.885127i | \(-0.654071\pi\) | ||||
−0.465350 | + | 0.885127i | \(0.654071\pi\) | |||||||
\(854\) | −6.89893 | −0.236077 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33.5485 | 1.14666 | ||||||||
\(857\) | 31.7263 | 1.08375 | 0.541875 | − | 0.840459i | \(-0.317715\pi\) | ||||
0.541875 | + | 0.840459i | \(0.317715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.649871 | −0.0221733 | −0.0110867 | − | 0.999939i | \(-0.503529\pi\) | ||||
−0.0110867 | + | 0.999939i | \(0.503529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.73228 | 0.127196 | ||||||||
\(862\) | −4.77219 | −0.162541 | ||||||||
\(863\) | 29.6096 | 1.00792 | 0.503961 | − | 0.863727i | \(-0.331876\pi\) | ||||
0.503961 | + | 0.863727i | \(0.331876\pi\) | |||||||
\(864\) | −24.5777 | −0.836152 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.9085 | 0.506611 | ||||||||
\(867\) | −14.7377 | −0.500517 | ||||||||
\(868\) | 4.03710 | 0.137028 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.6274 | 1.30884 | ||||||||
\(872\) | −31.3423 | −1.06138 | ||||||||
\(873\) | 3.95464 | 0.133844 | ||||||||
\(874\) | −11.0971 | −0.375366 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.0916 | 0.476110 | ||||||||
\(877\) | 11.1676 | 0.377104 | 0.188552 | − | 0.982063i | \(-0.439621\pi\) | ||||
0.188552 | + | 0.982063i | \(0.439621\pi\) | |||||||
\(878\) | 12.8869 | 0.434911 | ||||||||
\(879\) | 9.41952 | 0.317713 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.2369 | −1.18716 | −0.593581 | − | 0.804774i | \(-0.702286\pi\) | ||||
−0.593581 | + | 0.804774i | \(0.702286\pi\) | |||||||
\(882\) | 13.4878 | 0.454159 | ||||||||
\(883\) | −8.91151 | −0.299896 | −0.149948 | − | 0.988694i | \(-0.547911\pi\) | ||||
−0.149948 | + | 0.988694i | \(0.547911\pi\) | |||||||
\(884\) | −2.75643 | −0.0927086 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.8917 | 0.567489 | ||||||||
\(887\) | −35.3317 | −1.18632 | −0.593161 | − | 0.805084i | \(-0.702120\pi\) | ||||
−0.593161 | + | 0.805084i | \(0.702120\pi\) | |||||||
\(888\) | 15.1211 | 0.507429 | ||||||||
\(889\) | −5.26903 | −0.176718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.77512 | 0.260330 | ||||||||
\(893\) | 13.8243 | 0.462612 | ||||||||
\(894\) | 5.98487 | 0.200164 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.35335 | −0.112028 | ||||||||
\(897\) | 7.37597 | 0.246276 | ||||||||
\(898\) | 1.11269 | 0.0371309 | ||||||||
\(899\) | 16.5775 | 0.552892 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.8364 | 0.361014 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.23346 | −0.240714 | ||||||||
\(904\) | −31.5249 | −1.04850 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.3616 | 0.344241 | ||||||||
\(907\) | −12.0851 | −0.401280 | −0.200640 | − | 0.979665i | \(-0.564302\pi\) | ||||
−0.200640 | + | 0.979665i | \(0.564302\pi\) | |||||||
\(908\) | 14.5940 | 0.484320 | ||||||||
\(909\) | 24.2077 | 0.802919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.3913 | 1.30509 | 0.652546 | − | 0.757749i | \(-0.273701\pi\) | ||||
0.652546 | + | 0.757749i | \(0.273701\pi\) | |||||||
\(912\) | 2.77380 | 0.0918496 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 20.8540 | 0.689789 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.4990 | −0.875553 | ||||||||
\(917\) | 5.34480 | 0.176501 | ||||||||
\(918\) | −3.50431 | −0.115659 | ||||||||
\(919\) | 12.2124 | 0.402849 | 0.201424 | − | 0.979504i | \(-0.435443\pi\) | ||||
0.201424 | + | 0.979504i | \(0.435443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.7087 | −0.385813 | ||||||||
\(922\) | −33.3108 | −1.09703 | ||||||||
\(923\) | −7.11064 | −0.234050 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.84910 | 0.126489 | ||||||||
\(927\) | 31.0052 | 1.01834 | ||||||||
\(928\) | −17.7930 | −0.584083 | ||||||||
\(929\) | 36.5892 | 1.20045 | 0.600227 | − | 0.799830i | \(-0.295077\pi\) | ||||
0.600227 | + | 0.799830i | \(0.295077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.5179 | 0.967409 | ||||||||
\(932\) | 6.67378 | 0.218607 | ||||||||
\(933\) | 15.5398 | 0.508751 | ||||||||
\(934\) | −2.53890 | −0.0830753 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 21.0880 | 0.689283 | ||||||||
\(937\) | 38.6598 | 1.26296 | 0.631481 | − | 0.775391i | \(-0.282447\pi\) | ||||
0.631481 | + | 0.775391i | \(0.282447\pi\) | |||||||
\(938\) | 8.65779 | 0.282687 | ||||||||
\(939\) | −9.04199 | −0.295074 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.4244 | −0.828811 | −0.414405 | − | 0.910092i | \(-0.636010\pi\) | ||||
−0.414405 | + | 0.910092i | \(0.636010\pi\) | |||||||
\(942\) | 15.3081 | 0.498765 | ||||||||
\(943\) | 13.7156 | 0.446641 | ||||||||
\(944\) | 9.55675 | 0.311046 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.6579 | −1.61367 | −0.806833 | − | 0.590780i | \(-0.798820\pi\) | ||||
−0.806833 | + | 0.590780i | \(0.798820\pi\) | |||||||
\(948\) | 7.13910 | 0.231867 | ||||||||
\(949\) | −47.2407 | −1.53350 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.79281 | −0.0581358 | ||||||||
\(952\) | −1.76120 | −0.0570809 | ||||||||
\(953\) | 34.4689 | 1.11656 | 0.558279 | − | 0.829654i | \(-0.311462\pi\) | ||||
0.558279 | + | 0.829654i | \(0.311462\pi\) | |||||||
\(954\) | −29.0820 | −0.941565 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.0242 | −0.421232 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.2573 | 0.492941 | ||||||||
\(959\) | −6.06218 | −0.195758 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.94283 | −0.223962 | ||||||||
\(962\) | −17.7823 | −0.573324 | ||||||||
\(963\) | 24.8869 | 0.801969 | ||||||||
\(964\) | −5.82105 | −0.187483 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.65322 | 0.0531915 | ||||||||
\(967\) | −9.89492 | −0.318199 | −0.159100 | − | 0.987263i | \(-0.550859\pi\) | ||||
−0.159100 | + | 0.987263i | \(0.550859\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.23711 | −0.103991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.28258 | −0.233709 | −0.116855 | − | 0.993149i | \(-0.537281\pi\) | ||||
−0.116855 | + | 0.993149i | \(0.537281\pi\) | |||||||
\(972\) | −17.4439 | −0.559515 | ||||||||
\(973\) | −10.5450 | −0.338056 | ||||||||
\(974\) | 5.47709 | 0.175497 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.33704 | 0.202844 | ||||||||
\(977\) | 51.9849 | 1.66315 | 0.831573 | − | 0.555416i | \(-0.187441\pi\) | ||||
0.831573 | + | 0.555416i | \(0.187441\pi\) | |||||||
\(978\) | 7.40797 | 0.236881 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.2503 | −0.742326 | ||||||||
\(982\) | −5.03088 | −0.160542 | ||||||||
\(983\) | 51.2712 | 1.63530 | 0.817648 | − | 0.575719i | \(-0.195278\pi\) | ||||
0.817648 | + | 0.575719i | \(0.195278\pi\) | |||||||
\(984\) | −14.4744 | −0.461428 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.53693 | −0.0807924 | ||||||||
\(987\) | −2.05951 | −0.0655549 | ||||||||
\(988\) | 16.1893 | 0.515049 | ||||||||
\(989\) | −26.5819 | −0.845255 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.14987 | −0.163591 | −0.0817955 | − | 0.996649i | \(-0.526065\pi\) | ||||
−0.0817955 | + | 0.996649i | \(0.526065\pi\) | |||||||
\(992\) | −25.8210 | −0.819817 | ||||||||
\(993\) | −9.38012 | −0.297669 | ||||||||
\(994\) | −1.59375 | −0.0505507 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.766740 | 0.0242951 | ||||||||
\(997\) | 29.4832 | 0.933743 | 0.466871 | − | 0.884325i | \(-0.345381\pi\) | ||||
0.466871 | + | 0.884325i | \(0.345381\pi\) | |||||||
\(998\) | 15.2167 | 0.481675 | ||||||||
\(999\) | 26.5747 | 0.840785 |
(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 | 3025.2.a.bj.1.7 | 8 | ||
5.4 | even | 2 | 3025.2.a.bm.1.2 | 8 | |||
11.7 | odd | 10 | 275.2.h.e.126.1 | yes | 16 | ||
11.8 | odd | 10 | 275.2.h.e.251.1 | yes | 16 | ||
11.10 | odd | 2 | 3025.2.a.bn.1.2 | 8 | |||
55.7 | even | 20 | 275.2.z.c.49.6 | 32 | |||
55.8 | even | 20 | 275.2.z.c.174.6 | 32 | |||
55.18 | even | 20 | 275.2.z.c.49.3 | 32 | |||
55.19 | odd | 10 | 275.2.h.c.251.4 | yes | 16 | ||
55.29 | odd | 10 | 275.2.h.c.126.4 | ✓ | 16 | ||
55.52 | even | 20 | 275.2.z.c.174.3 | 32 | |||
55.54 | odd | 2 | 3025.2.a.bi.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.h.c.126.4 | ✓ | 16 | 55.29 | odd | 10 | ||
275.2.h.c.251.4 | yes | 16 | 55.19 | odd | 10 | ||
275.2.h.e.126.1 | yes | 16 | 11.7 | odd | 10 | ||
275.2.h.e.251.1 | yes | 16 | 11.8 | odd | 10 | ||
275.2.z.c.49.3 | 32 | 55.18 | even | 20 | |||
275.2.z.c.49.6 | 32 | 55.7 | even | 20 | |||
275.2.z.c.174.3 | 32 | 55.52 | even | 20 | |||
275.2.z.c.174.6 | 32 | 55.8 | even | 20 | |||
3025.2.a.bi.1.7 | 8 | 55.54 | odd | 2 | |||
3025.2.a.bj.1.7 | 8 | 1.1 | even | 1 | trivial | ||
3025.2.a.bm.1.2 | 8 | 5.4 | even | 2 | |||
3025.2.a.bn.1.2 | 8 | 11.10 | odd | 2 |