Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.88286 | −1.33138 | −0.665692 | − | 0.746227i | \(-0.731863\pi\) | ||||
−0.665692 | + | 0.746227i | \(0.731863\pi\) | |||||||
\(3\) | −2.55671 | −1.47612 | −0.738058 | − | 0.674737i | \(-0.764257\pi\) | ||||
−0.738058 | + | 0.674737i | \(0.764257\pi\) | |||||||
\(4\) | 1.54517 | 0.772583 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.81392 | 1.96528 | ||||||||
\(7\) | 3.51799 | 1.32967 | 0.664837 | − | 0.746988i | \(-0.268501\pi\) | ||||
0.664837 | + | 0.746988i | \(0.268501\pi\) | |||||||
\(8\) | 0.856390 | 0.302780 | ||||||||
\(9\) | 3.53675 | 1.17892 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.11714 | −0.336829 | −0.168414 | − | 0.985716i | \(-0.553865\pi\) | ||||
−0.168414 | + | 0.985716i | \(0.553865\pi\) | |||||||
\(12\) | −3.95054 | −1.14042 | ||||||||
\(13\) | 0.230541 | 0.0639405 | 0.0319702 | − | 0.999489i | \(-0.489822\pi\) | ||||
0.0319702 | + | 0.999489i | \(0.489822\pi\) | |||||||
\(14\) | −6.62388 | −1.77031 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.70279 | −1.17570 | ||||||||
\(17\) | 4.35003 | 1.05504 | 0.527519 | − | 0.849543i | \(-0.323123\pi\) | ||||
0.527519 | + | 0.849543i | \(0.323123\pi\) | |||||||
\(18\) | −6.65921 | −1.56959 | ||||||||
\(19\) | 3.14602 | 0.721746 | 0.360873 | − | 0.932615i | \(-0.382479\pi\) | ||||
0.360873 | + | 0.932615i | \(0.382479\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.99446 | −1.96275 | ||||||||
\(22\) | 2.10341 | 0.448449 | ||||||||
\(23\) | 6.36510 | 1.32722 | 0.663608 | − | 0.748081i | \(-0.269024\pi\) | ||||
0.663608 | + | 0.748081i | \(0.269024\pi\) | |||||||
\(24\) | −2.18954 | −0.446938 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.434076 | −0.0851293 | ||||||||
\(27\) | −1.37232 | −0.264103 | ||||||||
\(28\) | 5.43587 | 1.02728 | ||||||||
\(29\) | −0.0527009 | −0.00978631 | −0.00489315 | − | 0.999988i | \(-0.501558\pi\) | ||||
−0.00489315 | + | 0.999988i | \(0.501558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.55850 | −0.818730 | −0.409365 | − | 0.912371i | \(-0.634250\pi\) | ||||
−0.409365 | + | 0.912371i | \(0.634250\pi\) | |||||||
\(32\) | 7.14193 | 1.26253 | ||||||||
\(33\) | 2.85619 | 0.497199 | ||||||||
\(34\) | −8.19050 | −1.40466 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.46487 | 0.910811 | ||||||||
\(37\) | 6.27282 | 1.03125 | 0.515623 | − | 0.856816i | \(-0.327561\pi\) | ||||
0.515623 | + | 0.856816i | \(0.327561\pi\) | |||||||
\(38\) | −5.92351 | −0.960921 | ||||||||
\(39\) | −0.589425 | −0.0943835 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.79348 | −1.37331 | −0.686655 | − | 0.726983i | \(-0.740922\pi\) | ||||
−0.686655 | + | 0.726983i | \(0.740922\pi\) | |||||||
\(42\) | 16.9353 | 2.61318 | ||||||||
\(43\) | −2.95908 | −0.451256 | −0.225628 | − | 0.974214i | \(-0.572443\pi\) | ||||
−0.225628 | + | 0.974214i | \(0.572443\pi\) | |||||||
\(44\) | −1.72616 | −0.260228 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11.9846 | −1.76703 | ||||||||
\(47\) | −10.3334 | −1.50729 | −0.753643 | − | 0.657284i | \(-0.771705\pi\) | ||||
−0.753643 | + | 0.657284i | \(0.771705\pi\) | |||||||
\(48\) | 12.0237 | 1.73547 | ||||||||
\(49\) | 5.37623 | 0.768033 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.1218 | −1.55736 | ||||||||
\(52\) | 0.356224 | 0.0493993 | ||||||||
\(53\) | −6.03035 | −0.828332 | −0.414166 | − | 0.910201i | \(-0.635927\pi\) | ||||
−0.414166 | + | 0.910201i | \(0.635927\pi\) | |||||||
\(54\) | 2.58389 | 0.351622 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.01277 | 0.402598 | ||||||||
\(57\) | −8.04344 | −1.06538 | ||||||||
\(58\) | 0.0992284 | 0.0130293 | ||||||||
\(59\) | 6.43499 | 0.837765 | 0.418882 | − | 0.908041i | \(-0.362422\pi\) | ||||
0.418882 | + | 0.908041i | \(0.362422\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.8995 | −1.52358 | −0.761789 | − | 0.647825i | \(-0.775679\pi\) | ||||
−0.761789 | + | 0.647825i | \(0.775679\pi\) | |||||||
\(62\) | 8.58302 | 1.09004 | ||||||||
\(63\) | 12.4423 | 1.56758 | ||||||||
\(64\) | −4.04167 | −0.505209 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.37781 | −0.661962 | ||||||||
\(67\) | −2.08295 | −0.254473 | −0.127236 | − | 0.991872i | \(-0.540611\pi\) | ||||
−0.127236 | + | 0.991872i | \(0.540611\pi\) | |||||||
\(68\) | 6.72152 | 0.815104 | ||||||||
\(69\) | −16.2737 | −1.95912 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.17552 | −0.614222 | −0.307111 | − | 0.951674i | \(-0.599362\pi\) | ||||
−0.307111 | + | 0.951674i | \(0.599362\pi\) | |||||||
\(72\) | 3.02884 | 0.356952 | ||||||||
\(73\) | −1.25992 | −0.147463 | −0.0737313 | − | 0.997278i | \(-0.523491\pi\) | ||||
−0.0737313 | + | 0.997278i | \(0.523491\pi\) | |||||||
\(74\) | −11.8109 | −1.37298 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.86112 | 0.557608 | ||||||||
\(77\) | −3.93007 | −0.447873 | ||||||||
\(78\) | 1.10981 | 0.125661 | ||||||||
\(79\) | −0.749786 | −0.0843575 | −0.0421788 | − | 0.999110i | \(-0.513430\pi\) | ||||
−0.0421788 | + | 0.999110i | \(0.513430\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.10164 | −0.789071 | ||||||||
\(82\) | 16.5569 | 1.82840 | ||||||||
\(83\) | −11.1374 | −1.22249 | −0.611244 | − | 0.791442i | \(-0.709331\pi\) | ||||
−0.611244 | + | 0.791442i | \(0.709331\pi\) | |||||||
\(84\) | −13.8979 | −1.51639 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.57154 | 0.600795 | ||||||||
\(87\) | 0.134741 | 0.0144457 | ||||||||
\(88\) | −0.956703 | −0.101985 | ||||||||
\(89\) | −8.15389 | −0.864310 | −0.432155 | − | 0.901799i | \(-0.642247\pi\) | ||||
−0.432155 | + | 0.901799i | \(0.642247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.811039 | 0.0850200 | ||||||||
\(92\) | 9.83514 | 1.02538 | ||||||||
\(93\) | 11.6547 | 1.20854 | ||||||||
\(94\) | 19.4564 | 2.00678 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −18.2598 | −1.86364 | ||||||||
\(97\) | 7.78090 | 0.790031 | 0.395016 | − | 0.918674i | \(-0.370739\pi\) | ||||
0.395016 | + | 0.918674i | \(0.370739\pi\) | |||||||
\(98\) | −10.1227 | −1.02255 | ||||||||
\(99\) | −3.95103 | −0.397094 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.17087 | 0.614025 | 0.307012 | − | 0.951706i | \(-0.400671\pi\) | ||||
0.307012 | + | 0.951706i | \(0.400671\pi\) | |||||||
\(102\) | 20.9407 | 2.07344 | ||||||||
\(103\) | −12.4124 | −1.22303 | −0.611513 | − | 0.791235i | \(-0.709439\pi\) | ||||
−0.611513 | + | 0.791235i | \(0.709439\pi\) | |||||||
\(104\) | 0.197433 | 0.0193599 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.3543 | 1.10283 | ||||||||
\(107\) | −7.65910 | −0.740433 | −0.370216 | − | 0.928946i | \(-0.620716\pi\) | ||||
−0.370216 | + | 0.928946i | \(0.620716\pi\) | |||||||
\(108\) | −2.12046 | −0.204041 | ||||||||
\(109\) | −0.837327 | −0.0802014 | −0.0401007 | − | 0.999196i | \(-0.512768\pi\) | ||||
−0.0401007 | + | 0.999196i | \(0.512768\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.0378 | −1.52224 | ||||||||
\(112\) | −16.5444 | −1.56330 | ||||||||
\(113\) | −14.1036 | −1.32676 | −0.663378 | − | 0.748285i | \(-0.730878\pi\) | ||||
−0.663378 | + | 0.748285i | \(0.730878\pi\) | |||||||
\(114\) | 15.1447 | 1.41843 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.0814316 | −0.00756073 | ||||||||
\(117\) | 0.815365 | 0.0753805 | ||||||||
\(118\) | −12.1162 | −1.11539 | ||||||||
\(119\) | 15.3033 | 1.40286 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.75201 | −0.886546 | ||||||||
\(122\) | 22.4052 | 2.02847 | ||||||||
\(123\) | 22.4824 | 2.02717 | ||||||||
\(124\) | −7.04363 | −0.632537 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −23.4270 | −2.08705 | ||||||||
\(127\) | −16.6119 | −1.47407 | −0.737033 | − | 0.675857i | \(-0.763774\pi\) | ||||
−0.737033 | + | 0.675857i | \(0.763774\pi\) | |||||||
\(128\) | −6.67395 | −0.589900 | ||||||||
\(129\) | 7.56551 | 0.666106 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.55100 | −0.135512 | −0.0677558 | − | 0.997702i | \(-0.521584\pi\) | ||||
−0.0677558 | + | 0.997702i | \(0.521584\pi\) | |||||||
\(132\) | 4.41328 | 0.384127 | ||||||||
\(133\) | 11.0676 | 0.959687 | ||||||||
\(134\) | 3.92190 | 0.338801 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.72532 | 0.319444 | ||||||||
\(137\) | 1.06515 | 0.0910016 | 0.0455008 | − | 0.998964i | \(-0.485512\pi\) | ||||
0.0455008 | + | 0.998964i | \(0.485512\pi\) | |||||||
\(138\) | 30.6411 | 2.60835 | ||||||||
\(139\) | 10.1224 | 0.858570 | 0.429285 | − | 0.903169i | \(-0.358766\pi\) | ||||
0.429285 | + | 0.903169i | \(0.358766\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.4196 | 2.22493 | ||||||||
\(142\) | 9.74479 | 0.817765 | ||||||||
\(143\) | −0.257545 | −0.0215370 | ||||||||
\(144\) | −16.6326 | −1.38605 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.37226 | 0.196329 | ||||||||
\(147\) | −13.7455 | −1.13371 | ||||||||
\(148\) | 9.69255 | 0.796723 | ||||||||
\(149\) | −18.6972 | −1.53173 | −0.765867 | − | 0.642999i | \(-0.777690\pi\) | ||||
−0.765867 | + | 0.642999i | \(0.777690\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.48916 | 0.365323 | 0.182661 | − | 0.983176i | \(-0.441529\pi\) | ||||
0.182661 | + | 0.983176i | \(0.441529\pi\) | |||||||
\(152\) | 2.69422 | 0.218530 | ||||||||
\(153\) | 15.3850 | 1.24380 | ||||||||
\(154\) | 7.39977 | 0.596291 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.910759 | −0.0729191 | ||||||||
\(157\) | 2.73158 | 0.218003 | 0.109002 | − | 0.994042i | \(-0.465235\pi\) | ||||
0.109002 | + | 0.994042i | \(0.465235\pi\) | |||||||
\(158\) | 1.41174 | 0.112312 | ||||||||
\(159\) | 15.4178 | 1.22271 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 22.3923 | 1.76476 | ||||||||
\(162\) | 13.3714 | 1.05056 | ||||||||
\(163\) | 19.3913 | 1.51884 | 0.759421 | − | 0.650600i | \(-0.225483\pi\) | ||||
0.759421 | + | 0.650600i | \(0.225483\pi\) | |||||||
\(164\) | −13.5874 | −1.06100 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 20.9702 | 1.62760 | ||||||||
\(167\) | 14.3680 | 1.11183 | 0.555913 | − | 0.831241i | \(-0.312369\pi\) | ||||
0.555913 | + | 0.831241i | \(0.312369\pi\) | |||||||
\(168\) | −7.70277 | −0.594281 | ||||||||
\(169\) | −12.9469 | −0.995912 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.1267 | 0.850879 | ||||||||
\(172\) | −4.57227 | −0.348632 | ||||||||
\(173\) | 15.0237 | 1.14223 | 0.571114 | − | 0.820871i | \(-0.306512\pi\) | ||||
0.571114 | + | 0.820871i | \(0.306512\pi\) | |||||||
\(174\) | −0.253698 | −0.0192328 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.25366 | 0.396009 | ||||||||
\(177\) | −16.4524 | −1.23664 | ||||||||
\(178\) | 15.3526 | 1.15073 | ||||||||
\(179\) | −12.9071 | −0.964719 | −0.482360 | − | 0.875973i | \(-0.660220\pi\) | ||||
−0.482360 | + | 0.875973i | \(0.660220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.0476 | 1.56446 | 0.782229 | − | 0.622991i | \(-0.214083\pi\) | ||||
0.782229 | + | 0.622991i | \(0.214083\pi\) | |||||||
\(182\) | −1.52707 | −0.113194 | ||||||||
\(183\) | 30.4236 | 2.24898 | ||||||||
\(184\) | 5.45101 | 0.401854 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −21.9443 | −1.60903 | ||||||||
\(187\) | −4.85957 | −0.355367 | ||||||||
\(188\) | −15.9669 | −1.16450 | ||||||||
\(189\) | −4.82780 | −0.351171 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.3891 | −0.896442 | −0.448221 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448221 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(192\) | 10.3334 | 0.745747 | ||||||||
\(193\) | 12.3460 | 0.888684 | 0.444342 | − | 0.895857i | \(-0.353438\pi\) | ||||
0.444342 | + | 0.895857i | \(0.353438\pi\) | |||||||
\(194\) | −14.6504 | −1.05183 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.30717 | 0.593369 | ||||||||
\(197\) | −7.55643 | −0.538373 | −0.269187 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269187 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(198\) | 7.43924 | 0.528684 | ||||||||
\(199\) | −19.3457 | −1.37138 | −0.685689 | − | 0.727895i | \(-0.740499\pi\) | ||||
−0.685689 | + | 0.727895i | \(0.740499\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.32549 | 0.375631 | ||||||||
\(202\) | −11.6189 | −0.817503 | ||||||||
\(203\) | −0.185401 | −0.0130126 | ||||||||
\(204\) | −17.1850 | −1.20319 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 23.3707 | 1.62832 | ||||||||
\(207\) | 22.5118 | 1.56468 | ||||||||
\(208\) | −1.08419 | −0.0751747 | ||||||||
\(209\) | −3.51453 | −0.243105 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8658 | 1.71183 | 0.855915 | − | 0.517116i | \(-0.172994\pi\) | ||||
0.855915 | + | 0.517116i | \(0.172994\pi\) | |||||||
\(212\) | −9.31788 | −0.639955 | ||||||||
\(213\) | 13.2323 | 0.906662 | ||||||||
\(214\) | 14.4210 | 0.985800 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.17524 | −0.0799650 | ||||||||
\(217\) | −16.0367 | −1.08864 | ||||||||
\(218\) | 1.57657 | 0.106779 | ||||||||
\(219\) | 3.22125 | 0.217672 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00286 | 0.0674596 | ||||||||
\(222\) | 30.1969 | 2.02668 | ||||||||
\(223\) | 1.62890 | 0.109079 | 0.0545396 | − | 0.998512i | \(-0.482631\pi\) | ||||
0.0545396 | + | 0.998512i | \(0.482631\pi\) | |||||||
\(224\) | 25.1252 | 1.67875 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 26.5551 | 1.76642 | ||||||||
\(227\) | −11.5071 | −0.763751 | −0.381876 | − | 0.924214i | \(-0.624722\pi\) | ||||
−0.381876 | + | 0.924214i | \(0.624722\pi\) | |||||||
\(228\) | −12.4285 | −0.823094 | ||||||||
\(229\) | 21.7531 | 1.43749 | 0.718743 | − | 0.695276i | \(-0.244718\pi\) | ||||
0.718743 | + | 0.695276i | \(0.244718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.0480 | 0.661112 | ||||||||
\(232\) | −0.0451325 | −0.00296309 | ||||||||
\(233\) | −6.93311 | −0.454203 | −0.227102 | − | 0.973871i | \(-0.572925\pi\) | ||||
−0.227102 | + | 0.973871i | \(0.572925\pi\) | |||||||
\(234\) | −1.53522 | −0.100360 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.94313 | 0.647243 | ||||||||
\(237\) | 1.91698 | 0.124521 | ||||||||
\(238\) | −28.8141 | −1.86774 | ||||||||
\(239\) | 13.0493 | 0.844087 | 0.422044 | − | 0.906576i | \(-0.361313\pi\) | ||||
0.422044 | + | 0.906576i | \(0.361313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 18.3617 | 1.18033 | ||||||||
\(243\) | 22.2738 | 1.42886 | ||||||||
\(244\) | −18.3867 | −1.17709 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −42.3312 | −2.69894 | ||||||||
\(247\) | 0.725285 | 0.0461488 | ||||||||
\(248\) | −3.90385 | −0.247895 | ||||||||
\(249\) | 28.4751 | 1.80453 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.8117 | −1.81858 | −0.909291 | − | 0.416162i | \(-0.863375\pi\) | ||||
−0.909291 | + | 0.416162i | \(0.863375\pi\) | |||||||
\(252\) | 19.2253 | 1.21108 | ||||||||
\(253\) | −7.11068 | −0.447045 | ||||||||
\(254\) | 31.2778 | 1.96255 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.6495 | 1.29059 | ||||||||
\(257\) | 15.3709 | 0.958809 | 0.479404 | − | 0.877594i | \(-0.340853\pi\) | ||||
0.479404 | + | 0.877594i | \(0.340853\pi\) | |||||||
\(258\) | −14.2448 | −0.886842 | ||||||||
\(259\) | 22.0677 | 1.37122 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.186390 | −0.0115372 | ||||||||
\(262\) | 2.92032 | 0.180418 | ||||||||
\(263\) | 7.75814 | 0.478387 | 0.239194 | − | 0.970972i | \(-0.423117\pi\) | ||||
0.239194 | + | 0.970972i | \(0.423117\pi\) | |||||||
\(264\) | 2.44601 | 0.150542 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −20.8388 | −1.27771 | ||||||||
\(267\) | 20.8471 | 1.27582 | ||||||||
\(268\) | −3.21850 | −0.196601 | ||||||||
\(269\) | −26.5185 | −1.61686 | −0.808430 | − | 0.588592i | \(-0.799682\pi\) | ||||
−0.808430 | + | 0.588592i | \(0.799682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.7841 | −1.56627 | −0.783137 | − | 0.621849i | \(-0.786382\pi\) | ||||
−0.783137 | + | 0.621849i | \(0.786382\pi\) | |||||||
\(272\) | −20.4573 | −1.24041 | ||||||||
\(273\) | −2.07359 | −0.125499 | ||||||||
\(274\) | −2.00552 | −0.121158 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −25.1456 | −1.51359 | ||||||||
\(277\) | 16.8051 | 1.00972 | 0.504860 | − | 0.863201i | \(-0.331544\pi\) | ||||
0.504860 | + | 0.863201i | \(0.331544\pi\) | |||||||
\(278\) | −19.0591 | −1.14309 | ||||||||
\(279\) | −16.1223 | −0.965215 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.13034 | 0.425360 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(282\) | −49.7444 | −2.96223 | ||||||||
\(283\) | −1.50077 | −0.0892114 | −0.0446057 | − | 0.999005i | \(-0.514203\pi\) | ||||
−0.0446057 | + | 0.999005i | \(0.514203\pi\) | |||||||
\(284\) | −7.99704 | −0.474537 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.484922 | 0.0286740 | ||||||||
\(287\) | −30.9354 | −1.82606 | ||||||||
\(288\) | 25.2592 | 1.48841 | ||||||||
\(289\) | 1.92276 | 0.113103 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.8935 | −1.16618 | ||||||||
\(292\) | −1.94679 | −0.113927 | ||||||||
\(293\) | 27.0432 | 1.57988 | 0.789939 | − | 0.613186i | \(-0.210112\pi\) | ||||
0.789939 | + | 0.613186i | \(0.210112\pi\) | |||||||
\(294\) | 25.8808 | 1.50940 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.37198 | 0.312240 | ||||||||
\(297\) | 1.53307 | 0.0889575 | ||||||||
\(298\) | 35.2042 | 2.03933 | ||||||||
\(299\) | 1.46741 | 0.0848628 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.4100 | −0.600023 | ||||||||
\(302\) | −8.45247 | −0.486385 | ||||||||
\(303\) | −15.7771 | −0.906371 | ||||||||
\(304\) | −14.7951 | −0.848555 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −28.9678 | −1.65598 | ||||||||
\(307\) | −1.85072 | −0.105626 | −0.0528130 | − | 0.998604i | \(-0.516819\pi\) | ||||
−0.0528130 | + | 0.998604i | \(0.516819\pi\) | |||||||
\(308\) | −6.07261 | −0.346019 | ||||||||
\(309\) | 31.7347 | 1.80533 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.609280 | 0.0345491 | 0.0172745 | − | 0.999851i | \(-0.494501\pi\) | ||||
0.0172745 | + | 0.999851i | \(0.494501\pi\) | |||||||
\(312\) | −0.504778 | −0.0285774 | ||||||||
\(313\) | −22.9454 | −1.29695 | −0.648476 | − | 0.761236i | \(-0.724593\pi\) | ||||
−0.648476 | + | 0.761236i | \(0.724593\pi\) | |||||||
\(314\) | −5.14318 | −0.290246 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.15854 | −0.0651732 | ||||||||
\(317\) | −2.44078 | −0.137088 | −0.0685439 | − | 0.997648i | \(-0.521835\pi\) | ||||
−0.0685439 | + | 0.997648i | \(0.521835\pi\) | |||||||
\(318\) | −29.0296 | −1.62790 | ||||||||
\(319\) | 0.0588740 | 0.00329631 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.5821 | 1.09296 | ||||||||
\(322\) | −42.1617 | −2.34958 | ||||||||
\(323\) | 13.6853 | 0.761469 | ||||||||
\(324\) | −10.9732 | −0.609623 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −36.5111 | −2.02216 | ||||||||
\(327\) | 2.14080 | 0.118387 | ||||||||
\(328\) | −7.53065 | −0.415810 | ||||||||
\(329\) | −36.3529 | −2.00420 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.91377 | 0.380015 | 0.190008 | − | 0.981783i | \(-0.439149\pi\) | ||||
0.190008 | + | 0.981783i | \(0.439149\pi\) | |||||||
\(332\) | −17.2091 | −0.944473 | ||||||||
\(333\) | 22.1854 | 1.21575 | ||||||||
\(334\) | −27.0529 | −1.48027 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 42.2991 | 2.30761 | ||||||||
\(337\) | 14.0181 | 0.763616 | 0.381808 | − | 0.924242i | \(-0.375302\pi\) | ||||
0.381808 | + | 0.924242i | \(0.375302\pi\) | |||||||
\(338\) | 24.3771 | 1.32594 | ||||||||
\(339\) | 36.0588 | 1.95845 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.09246 | 0.275772 | ||||||||
\(342\) | −20.9500 | −1.13285 | ||||||||
\(343\) | −5.71239 | −0.308440 | ||||||||
\(344\) | −2.53413 | −0.136631 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.2874 | −1.52074 | ||||||||
\(347\) | −25.2046 | −1.35305 | −0.676526 | − | 0.736419i | \(-0.736515\pi\) | ||||
−0.676526 | + | 0.736419i | \(0.736515\pi\) | |||||||
\(348\) | 0.208197 | 0.0111605 | ||||||||
\(349\) | 0.543622 | 0.0290994 | 0.0145497 | − | 0.999894i | \(-0.495369\pi\) | ||||
0.0145497 | + | 0.999894i | \(0.495369\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.316375 | −0.0168869 | ||||||||
\(352\) | −7.97850 | −0.425256 | ||||||||
\(353\) | −7.06140 | −0.375840 | −0.187920 | − | 0.982184i | \(-0.560175\pi\) | ||||
−0.187920 | + | 0.982184i | \(0.560175\pi\) | |||||||
\(354\) | 30.9776 | 1.64644 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.5991 | −0.667751 | ||||||||
\(357\) | −39.1262 | −2.07078 | ||||||||
\(358\) | 24.3022 | 1.28441 | ||||||||
\(359\) | −32.0985 | −1.69409 | −0.847047 | − | 0.531519i | \(-0.821622\pi\) | ||||
−0.847047 | + | 0.531519i | \(0.821622\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.10258 | −0.479083 | ||||||||
\(362\) | −39.6298 | −2.08289 | ||||||||
\(363\) | 24.9330 | 1.30864 | ||||||||
\(364\) | 1.25319 | 0.0656850 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −57.2834 | −2.99425 | ||||||||
\(367\) | 15.2909 | 0.798176 | 0.399088 | − | 0.916913i | \(-0.369327\pi\) | ||||
0.399088 | + | 0.916913i | \(0.369327\pi\) | |||||||
\(368\) | −29.9338 | −1.56041 | ||||||||
\(369\) | −31.1004 | −1.61902 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.2147 | −1.10141 | ||||||||
\(372\) | 18.0085 | 0.933698 | ||||||||
\(373\) | −15.6074 | −0.808122 | −0.404061 | − | 0.914732i | \(-0.632402\pi\) | ||||
−0.404061 | + | 0.914732i | \(0.632402\pi\) | |||||||
\(374\) | 9.14990 | 0.473130 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.84945 | −0.456375 | ||||||||
\(377\) | −0.0121497 | −0.000625741 0 | ||||||||
\(378\) | 9.09008 | 0.467543 | ||||||||
\(379\) | 18.5818 | 0.954484 | 0.477242 | − | 0.878772i | \(-0.341637\pi\) | ||||
0.477242 | + | 0.878772i | \(0.341637\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.4717 | 2.17589 | ||||||||
\(382\) | 23.3269 | 1.19351 | ||||||||
\(383\) | −31.3371 | −1.60125 | −0.800626 | − | 0.599165i | \(-0.795499\pi\) | ||||
−0.800626 | + | 0.599165i | \(0.795499\pi\) | |||||||
\(384\) | 17.0633 | 0.870760 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.2458 | −1.18318 | ||||||||
\(387\) | −10.4655 | −0.531993 | ||||||||
\(388\) | 12.0228 | 0.610364 | ||||||||
\(389\) | −24.3977 | −1.23701 | −0.618506 | − | 0.785780i | \(-0.712262\pi\) | ||||
−0.618506 | + | 0.785780i | \(0.712262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.6884 | 1.40026 | ||||||||
\(392\) | 4.60415 | 0.232545 | ||||||||
\(393\) | 3.96545 | 0.200031 | ||||||||
\(394\) | 14.2277 | 0.716781 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.10500 | −0.306788 | ||||||||
\(397\) | −9.32624 | −0.468071 | −0.234035 | − | 0.972228i | \(-0.575193\pi\) | ||||
−0.234035 | + | 0.972228i | \(0.575193\pi\) | |||||||
\(398\) | 36.4252 | 1.82583 | ||||||||
\(399\) | −28.2967 | −1.41661 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.9440 | −0.546518 | −0.273259 | − | 0.961940i | \(-0.588102\pi\) | ||||
−0.273259 | + | 0.961940i | \(0.588102\pi\) | |||||||
\(402\) | −10.0272 | −0.500109 | ||||||||
\(403\) | −1.05092 | −0.0523500 | ||||||||
\(404\) | 9.53502 | 0.474385 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.349084 | 0.0173248 | ||||||||
\(407\) | −7.00759 | −0.347353 | ||||||||
\(408\) | −9.52456 | −0.471536 | ||||||||
\(409\) | 29.3280 | 1.45017 | 0.725087 | − | 0.688657i | \(-0.241799\pi\) | ||||
0.725087 | + | 0.688657i | \(0.241799\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.72327 | −0.134329 | ||||||||
\(412\) | −19.1791 | −0.944888 | ||||||||
\(413\) | 22.6382 | 1.11395 | ||||||||
\(414\) | −42.3866 | −2.08319 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.64650 | 0.0807265 | ||||||||
\(417\) | −25.8800 | −1.26735 | ||||||||
\(418\) | 6.61737 | 0.323666 | ||||||||
\(419\) | 28.6323 | 1.39878 | 0.699391 | − | 0.714740i | \(-0.253455\pi\) | ||||
0.699391 | + | 0.714740i | \(0.253455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0637058 | −0.00310483 | −0.00155241 | − | 0.999999i | \(-0.500494\pi\) | ||||
−0.00155241 | + | 0.999999i | \(0.500494\pi\) | |||||||
\(422\) | −46.8188 | −2.27910 | ||||||||
\(423\) | −36.5468 | −1.77697 | ||||||||
\(424\) | −5.16433 | −0.250802 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −24.9146 | −1.20712 | ||||||||
\(427\) | −41.8624 | −2.02586 | ||||||||
\(428\) | −11.8346 | −0.572046 | ||||||||
\(429\) | 0.658468 | 0.0317911 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7098 | −1.23840 | −0.619199 | − | 0.785234i | \(-0.712543\pi\) | ||||
−0.619199 | + | 0.785234i | \(0.712543\pi\) | |||||||
\(432\) | 6.45374 | 0.310506 | ||||||||
\(433\) | −22.4971 | −1.08114 | −0.540570 | − | 0.841299i | \(-0.681791\pi\) | ||||
−0.540570 | + | 0.841299i | \(0.681791\pi\) | |||||||
\(434\) | 30.1949 | 1.44940 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.29381 | −0.0619622 | ||||||||
\(437\) | 20.0247 | 0.957912 | ||||||||
\(438\) | −6.06516 | −0.289805 | ||||||||
\(439\) | −17.3064 | −0.825989 | −0.412995 | − | 0.910733i | \(-0.635517\pi\) | ||||
−0.412995 | + | 0.910733i | \(0.635517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.0144 | 0.905448 | ||||||||
\(442\) | −1.88824 | −0.0898146 | ||||||||
\(443\) | −35.4484 | −1.68421 | −0.842103 | − | 0.539317i | \(-0.818682\pi\) | ||||
−0.842103 | + | 0.539317i | \(0.818682\pi\) | |||||||
\(444\) | −24.7810 | −1.17605 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.06699 | −0.145226 | ||||||||
\(447\) | 47.8032 | 2.26102 | ||||||||
\(448\) | −14.2185 | −0.671763 | ||||||||
\(449\) | 15.9564 | 0.753031 | 0.376516 | − | 0.926410i | \(-0.377122\pi\) | ||||
0.376516 | + | 0.926410i | \(0.377122\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.82351 | 0.462571 | ||||||||
\(452\) | −21.7924 | −1.02503 | ||||||||
\(453\) | −11.4775 | −0.539259 | ||||||||
\(454\) | 21.6662 | 1.01685 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.88832 | −0.322575 | ||||||||
\(457\) | 8.07516 | 0.377740 | 0.188870 | − | 0.982002i | \(-0.439518\pi\) | ||||
0.188870 | + | 0.982002i | \(0.439518\pi\) | |||||||
\(458\) | −40.9581 | −1.91384 | ||||||||
\(459\) | −5.96963 | −0.278638 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.1354 | −1.26382 | −0.631912 | − | 0.775040i | \(-0.717730\pi\) | ||||
−0.631912 | + | 0.775040i | \(0.717730\pi\) | |||||||
\(462\) | −18.9191 | −0.880194 | ||||||||
\(463\) | 29.4190 | 1.36721 | 0.683607 | − | 0.729850i | \(-0.260410\pi\) | ||||
0.683607 | + | 0.729850i | \(0.260410\pi\) | |||||||
\(464\) | 0.247841 | 0.0115057 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 13.0541 | 0.604719 | ||||||||
\(467\) | 2.70008 | 0.124945 | 0.0624724 | − | 0.998047i | \(-0.480101\pi\) | ||||
0.0624724 | + | 0.998047i | \(0.480101\pi\) | |||||||
\(468\) | 1.25987 | 0.0582377 | ||||||||
\(469\) | −7.32779 | −0.338366 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.98384 | −0.321798 | ||||||||
\(472\) | 5.51086 | 0.253658 | ||||||||
\(473\) | 3.30570 | 0.151996 | ||||||||
\(474\) | −3.60941 | −0.165786 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 23.6462 | 1.08382 | ||||||||
\(477\) | −21.3278 | −0.976535 | ||||||||
\(478\) | −24.5700 | −1.12380 | ||||||||
\(479\) | −24.4078 | −1.11522 | −0.557609 | − | 0.830103i | \(-0.688281\pi\) | ||||
−0.557609 | + | 0.830103i | \(0.688281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.44614 | 0.0659383 | ||||||||
\(482\) | −1.88286 | −0.0857620 | ||||||||
\(483\) | −57.2507 | −2.60500 | ||||||||
\(484\) | −15.0685 | −0.684930 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −41.9384 | −1.90237 | ||||||||
\(487\) | −19.3677 | −0.877633 | −0.438817 | − | 0.898577i | \(-0.644602\pi\) | ||||
−0.438817 | + | 0.898577i | \(0.644602\pi\) | |||||||
\(488\) | −10.1906 | −0.461308 | ||||||||
\(489\) | −49.5778 | −2.24199 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.3025 | 0.645462 | 0.322731 | − | 0.946491i | \(-0.395399\pi\) | ||||
0.322731 | + | 0.946491i | \(0.395399\pi\) | |||||||
\(492\) | 34.7390 | 1.56615 | ||||||||
\(493\) | −0.229250 | −0.0103249 | ||||||||
\(494\) | −1.36561 | −0.0614417 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.4377 | 0.962580 | ||||||||
\(497\) | −18.2074 | −0.816715 | ||||||||
\(498\) | −53.6146 | −2.40253 | ||||||||
\(499\) | −22.6504 | −1.01397 | −0.506987 | − | 0.861954i | \(-0.669241\pi\) | ||||
−0.506987 | + | 0.861954i | \(0.669241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.7347 | −1.64118 | ||||||||
\(502\) | 54.2485 | 2.42123 | ||||||||
\(503\) | −33.2011 | −1.48036 | −0.740181 | − | 0.672407i | \(-0.765260\pi\) | ||||
−0.740181 | + | 0.672407i | \(0.765260\pi\) | |||||||
\(504\) | 10.6554 | 0.474630 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13.3884 | 0.595188 | ||||||||
\(507\) | 33.1013 | 1.47008 | ||||||||
\(508\) | −25.6681 | −1.13884 | ||||||||
\(509\) | 26.1038 | 1.15703 | 0.578515 | − | 0.815671i | \(-0.303632\pi\) | ||||
0.578515 | + | 0.815671i | \(0.303632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.43239 | −0.196077 | ||||||||
\(512\) | −25.5322 | −1.12837 | ||||||||
\(513\) | −4.31734 | −0.190615 | ||||||||
\(514\) | −28.9412 | −1.27654 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 11.6900 | 0.514622 | ||||||||
\(517\) | 11.5438 | 0.507698 | ||||||||
\(518\) | −41.5504 | −1.82562 | ||||||||
\(519\) | −38.4111 | −1.68606 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1582 | 0.488849 | 0.244425 | − | 0.969668i | \(-0.421401\pi\) | ||||
0.244425 | + | 0.969668i | \(0.421401\pi\) | |||||||
\(522\) | 0.350946 | 0.0153605 | ||||||||
\(523\) | 21.4491 | 0.937902 | 0.468951 | − | 0.883224i | \(-0.344632\pi\) | ||||
0.468951 | + | 0.883224i | \(0.344632\pi\) | |||||||
\(524\) | −2.39655 | −0.104694 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.6075 | −0.636917 | ||||||||
\(527\) | −19.8296 | −0.863791 | ||||||||
\(528\) | −13.4321 | −0.584556 | ||||||||
\(529\) | 17.5145 | 0.761501 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.7590 | 0.987655 | ||||||||
\(532\) | 17.1013 | 0.741437 | ||||||||
\(533\) | −2.02725 | −0.0878102 | ||||||||
\(534\) | −39.2522 | −1.69861 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.78382 | −0.0770491 | ||||||||
\(537\) | 32.9996 | 1.42404 | ||||||||
\(538\) | 49.9306 | 2.15266 | ||||||||
\(539\) | −6.00598 | −0.258696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.9845 | 1.63308 | 0.816541 | − | 0.577288i | \(-0.195889\pi\) | ||||
0.816541 | + | 0.577288i | \(0.195889\pi\) | |||||||
\(542\) | 48.5479 | 2.08531 | ||||||||
\(543\) | −53.8126 | −2.30932 | ||||||||
\(544\) | 31.0676 | 1.33201 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.90428 | 0.167088 | ||||||||
\(547\) | 12.5760 | 0.537711 | 0.268856 | − | 0.963180i | \(-0.413355\pi\) | ||||
0.268856 | + | 0.963180i | \(0.413355\pi\) | |||||||
\(548\) | 1.64583 | 0.0703063 | ||||||||
\(549\) | −42.0857 | −1.79617 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.165798 | −0.00706322 | ||||||||
\(552\) | −13.9366 | −0.593183 | ||||||||
\(553\) | −2.63774 | −0.112168 | ||||||||
\(554\) | −31.6417 | −1.34433 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.6408 | 0.663316 | ||||||||
\(557\) | −17.7488 | −0.752039 | −0.376020 | − | 0.926612i | \(-0.622707\pi\) | ||||
−0.376020 | + | 0.926612i | \(0.622707\pi\) | |||||||
\(558\) | 30.3560 | 1.28507 | ||||||||
\(559\) | −0.682189 | −0.0288535 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.4245 | 0.524563 | ||||||||
\(562\) | −13.4254 | −0.566318 | ||||||||
\(563\) | 19.5515 | 0.823999 | 0.411999 | − | 0.911184i | \(-0.364831\pi\) | ||||
0.411999 | + | 0.911184i | \(0.364831\pi\) | |||||||
\(564\) | 40.8226 | 1.71894 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.82574 | 0.118775 | ||||||||
\(567\) | −24.9835 | −1.04921 | ||||||||
\(568\) | −4.43227 | −0.185974 | ||||||||
\(569\) | 41.0771 | 1.72204 | 0.861021 | − | 0.508570i | \(-0.169826\pi\) | ||||
0.861021 | + | 0.508570i | \(0.169826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.8425 | −1.45811 | −0.729057 | − | 0.684453i | \(-0.760041\pi\) | ||||
−0.729057 | + | 0.684453i | \(0.760041\pi\) | |||||||
\(572\) | −0.397950 | −0.0166391 | ||||||||
\(573\) | 31.6752 | 1.32325 | ||||||||
\(574\) | 58.2470 | 2.43118 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −14.2944 | −0.595599 | ||||||||
\(577\) | −2.25604 | −0.0939202 | −0.0469601 | − | 0.998897i | \(-0.514953\pi\) | ||||
−0.0469601 | + | 0.998897i | \(0.514953\pi\) | |||||||
\(578\) | −3.62029 | −0.150584 | ||||||||
\(579\) | −31.5651 | −1.31180 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.1812 | −1.62551 | ||||||||
\(582\) | 37.4567 | 1.55263 | ||||||||
\(583\) | 6.73671 | 0.279006 | ||||||||
\(584\) | −1.07898 | −0.0446487 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −50.9185 | −2.10342 | ||||||||
\(587\) | 27.6141 | 1.13976 | 0.569879 | − | 0.821729i | \(-0.306990\pi\) | ||||
0.569879 | + | 0.821729i | \(0.306990\pi\) | |||||||
\(588\) | −21.2390 | −0.875882 | ||||||||
\(589\) | −14.3411 | −0.590915 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.3196 | 0.794701 | ||||||||
\(592\) | −29.4998 | −1.21243 | ||||||||
\(593\) | −32.2396 | −1.32392 | −0.661961 | − | 0.749538i | \(-0.730276\pi\) | ||||
−0.661961 | + | 0.749538i | \(0.730276\pi\) | |||||||
\(594\) | −2.88655 | −0.118437 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.8903 | −1.18339 | ||||||||
\(597\) | 49.4612 | 2.02431 | ||||||||
\(598\) | −2.76294 | −0.112985 | ||||||||
\(599\) | 23.7981 | 0.972365 | 0.486183 | − | 0.873857i | \(-0.338389\pi\) | ||||
0.486183 | + | 0.873857i | \(0.338389\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.59760 | 0.350703 | 0.175352 | − | 0.984506i | \(-0.443894\pi\) | ||||
0.175352 | + | 0.984506i | \(0.443894\pi\) | |||||||
\(602\) | 19.6006 | 0.798861 | ||||||||
\(603\) | −7.36687 | −0.300002 | ||||||||
\(604\) | 6.93650 | 0.282242 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 29.7061 | 1.20673 | ||||||||
\(607\) | 13.7016 | 0.556130 | 0.278065 | − | 0.960562i | \(-0.410307\pi\) | ||||
0.278065 | + | 0.960562i | \(0.410307\pi\) | |||||||
\(608\) | 22.4686 | 0.911223 | ||||||||
\(609\) | 0.474016 | 0.0192081 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.38228 | −0.0963766 | ||||||||
\(612\) | 23.7723 | 0.960940 | ||||||||
\(613\) | −44.7325 | −1.80673 | −0.903365 | − | 0.428873i | \(-0.858911\pi\) | ||||
−0.903365 | + | 0.428873i | \(0.858911\pi\) | |||||||
\(614\) | 3.48464 | 0.140629 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.36567 | −0.135607 | ||||||||
\(617\) | −11.8716 | −0.477931 | −0.238965 | − | 0.971028i | \(-0.576808\pi\) | ||||
−0.238965 | + | 0.971028i | \(0.576808\pi\) | |||||||
\(618\) | −59.7521 | −2.40358 | ||||||||
\(619\) | −30.7196 | −1.23472 | −0.617362 | − | 0.786679i | \(-0.711799\pi\) | ||||
−0.617362 | + | 0.786679i | \(0.711799\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.73495 | −0.350522 | ||||||||
\(622\) | −1.14719 | −0.0459981 | ||||||||
\(623\) | −28.6853 | −1.14925 | ||||||||
\(624\) | 2.77194 | 0.110967 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 43.2030 | 1.72674 | ||||||||
\(627\) | 8.98562 | 0.358851 | ||||||||
\(628\) | 4.22074 | 0.168426 | ||||||||
\(629\) | 27.2870 | 1.08800 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5309 | −0.896943 | −0.448471 | − | 0.893797i | \(-0.648031\pi\) | ||||
−0.448471 | + | 0.893797i | \(0.648031\pi\) | |||||||
\(632\) | −0.642109 | −0.0255417 | ||||||||
\(633\) | −63.5745 | −2.52686 | ||||||||
\(634\) | 4.59565 | 0.182517 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 23.8231 | 0.944647 | ||||||||
\(637\) | 1.23944 | 0.0491084 | ||||||||
\(638\) | −0.110852 | −0.00438866 | ||||||||
\(639\) | −18.3045 | −0.724117 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.9732 | 1.26287 | 0.631433 | − | 0.775430i | \(-0.282467\pi\) | ||||
0.631433 | + | 0.775430i | \(0.282467\pi\) | |||||||
\(642\) | −36.8703 | −1.45516 | ||||||||
\(643\) | −1.68365 | −0.0663968 | −0.0331984 | − | 0.999449i | \(-0.510569\pi\) | ||||
−0.0331984 | + | 0.999449i | \(0.510569\pi\) | |||||||
\(644\) | 34.5999 | 1.36343 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.7675 | −1.01381 | ||||||||
\(647\) | −4.78774 | −0.188225 | −0.0941127 | − | 0.995562i | \(-0.530001\pi\) | ||||
−0.0941127 | + | 0.995562i | \(0.530001\pi\) | |||||||
\(648\) | −6.08177 | −0.238915 | ||||||||
\(649\) | −7.18876 | −0.282183 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.0012 | 1.60697 | ||||||||
\(652\) | 29.9627 | 1.17343 | ||||||||
\(653\) | 17.3077 | 0.677301 | 0.338650 | − | 0.940912i | \(-0.390030\pi\) | ||||
0.338650 | + | 0.940912i | \(0.390030\pi\) | |||||||
\(654\) | −4.03083 | −0.157618 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 41.3539 | 1.61460 | ||||||||
\(657\) | −4.45603 | −0.173846 | ||||||||
\(658\) | 68.4474 | 2.66836 | ||||||||
\(659\) | −6.27035 | −0.244258 | −0.122129 | − | 0.992514i | \(-0.538972\pi\) | ||||
−0.122129 | + | 0.992514i | \(0.538972\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.20469 | −0.241334 | −0.120667 | − | 0.992693i | \(-0.538503\pi\) | ||||
−0.120667 | + | 0.992693i | \(0.538503\pi\) | |||||||
\(662\) | −13.0177 | −0.505946 | ||||||||
\(663\) | −2.56402 | −0.0995781 | ||||||||
\(664\) | −9.53795 | −0.370144 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −41.7721 | −1.61863 | ||||||||
\(667\) | −0.335446 | −0.0129885 | ||||||||
\(668\) | 22.2009 | 0.858977 | ||||||||
\(669\) | −4.16462 | −0.161013 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.2934 | 0.513185 | ||||||||
\(672\) | −64.2378 | −2.47803 | ||||||||
\(673\) | −32.2078 | −1.24152 | −0.620759 | − | 0.784001i | \(-0.713176\pi\) | ||||
−0.620759 | + | 0.784001i | \(0.713176\pi\) | |||||||
\(674\) | −26.3942 | −1.01667 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.0050 | −0.769424 | ||||||||
\(677\) | 16.1123 | 0.619245 | 0.309622 | − | 0.950860i | \(-0.399797\pi\) | ||||
0.309622 | + | 0.950860i | \(0.399797\pi\) | |||||||
\(678\) | −67.8937 | −2.60744 | ||||||||
\(679\) | 27.3731 | 1.05048 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.4202 | 1.12739 | ||||||||
\(682\) | −9.58839 | −0.367158 | ||||||||
\(683\) | 15.1853 | 0.581048 | 0.290524 | − | 0.956868i | \(-0.406170\pi\) | ||||
0.290524 | + | 0.956868i | \(0.406170\pi\) | |||||||
\(684\) | 17.1926 | 0.657374 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.7556 | 0.410652 | ||||||||
\(687\) | −55.6163 | −2.12189 | ||||||||
\(688\) | 13.9160 | 0.530541 | ||||||||
\(689\) | −1.39024 | −0.0529639 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.7865 | 0.600547 | 0.300274 | − | 0.953853i | \(-0.402922\pi\) | ||||
0.300274 | + | 0.953853i | \(0.402922\pi\) | |||||||
\(692\) | 23.2140 | 0.882465 | ||||||||
\(693\) | −13.8997 | −0.528005 | ||||||||
\(694\) | 47.4567 | 1.80143 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.115391 | 0.00437387 | ||||||||
\(697\) | −38.2519 | −1.44889 | ||||||||
\(698\) | −1.02357 | −0.0387425 | ||||||||
\(699\) | 17.7259 | 0.670456 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.3713 | 0.391717 | 0.195859 | − | 0.980632i | \(-0.437251\pi\) | ||||
0.195859 | + | 0.980632i | \(0.437251\pi\) | |||||||
\(702\) | 0.595691 | 0.0224829 | ||||||||
\(703\) | 19.7344 | 0.744297 | ||||||||
\(704\) | 4.51509 | 0.170169 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.2956 | 0.500387 | ||||||||
\(707\) | 21.7090 | 0.816453 | ||||||||
\(708\) | −25.4217 | −0.955405 | ||||||||
\(709\) | 17.6528 | 0.662966 | 0.331483 | − | 0.943461i | \(-0.392451\pi\) | ||||
0.331483 | + | 0.943461i | \(0.392451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.65181 | −0.0994506 | ||||||||
\(712\) | −6.98291 | −0.261696 | ||||||||
\(713\) | −29.0153 | −1.08663 | ||||||||
\(714\) | 73.6692 | 2.75700 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −19.9435 | −0.745325 | ||||||||
\(717\) | −33.3632 | −1.24597 | ||||||||
\(718\) | 60.4370 | 2.25549 | ||||||||
\(719\) | −20.1461 | −0.751324 | −0.375662 | − | 0.926757i | \(-0.622585\pi\) | ||||
−0.375662 | + | 0.926757i | \(0.622585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.6665 | −1.62623 | ||||||||
\(722\) | 17.1389 | 0.637843 | ||||||||
\(723\) | −2.55671 | −0.0950850 | ||||||||
\(724\) | 32.5221 | 1.20867 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −46.9454 | −1.74231 | ||||||||
\(727\) | 49.4317 | 1.83332 | 0.916661 | − | 0.399666i | \(-0.130874\pi\) | ||||
0.916661 | + | 0.399666i | \(0.130874\pi\) | |||||||
\(728\) | 0.694566 | 0.0257423 | ||||||||
\(729\) | −35.6426 | −1.32010 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.8721 | −0.476092 | ||||||||
\(732\) | 47.0095 | 1.73752 | ||||||||
\(733\) | 31.2375 | 1.15378 | 0.576891 | − | 0.816821i | \(-0.304266\pi\) | ||||
0.576891 | + | 0.816821i | \(0.304266\pi\) | |||||||
\(734\) | −28.7905 | −1.06268 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 45.4591 | 1.67564 | ||||||||
\(737\) | 2.32694 | 0.0857138 | ||||||||
\(738\) | 58.5577 | 2.15554 | ||||||||
\(739\) | −0.931126 | −0.0342520 | −0.0171260 | − | 0.999853i | \(-0.505452\pi\) | ||||
−0.0171260 | + | 0.999853i | \(0.505452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.85434 | −0.0681209 | ||||||||
\(742\) | 39.9443 | 1.46640 | ||||||||
\(743\) | 50.7530 | 1.86195 | 0.930974 | − | 0.365085i | \(-0.118960\pi\) | ||||
0.930974 | + | 0.365085i | \(0.118960\pi\) | |||||||
\(744\) | 9.98100 | 0.365921 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29.3866 | 1.07592 | ||||||||
\(747\) | −39.3902 | −1.44121 | ||||||||
\(748\) | −7.50884 | −0.274551 | ||||||||
\(749\) | −26.9446 | −0.984534 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.6990 | −0.390412 | −0.195206 | − | 0.980762i | \(-0.562538\pi\) | ||||
−0.195206 | + | 0.980762i | \(0.562538\pi\) | |||||||
\(752\) | 48.5960 | 1.77211 | ||||||||
\(753\) | 73.6632 | 2.68444 | ||||||||
\(754\) | 0.0228762 | 0.000833101 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.45975 | −0.271309 | ||||||||
\(757\) | 3.26326 | 0.118605 | 0.0593027 | − | 0.998240i | \(-0.481112\pi\) | ||||
0.0593027 | + | 0.998240i | \(0.481112\pi\) | |||||||
\(758\) | −34.9870 | −1.27078 | ||||||||
\(759\) | 18.1799 | 0.659890 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.3419 | −1.57114 | −0.785572 | − | 0.618771i | \(-0.787631\pi\) | ||||
−0.785572 | + | 0.618771i | \(0.787631\pi\) | |||||||
\(762\) | −79.9683 | −2.89695 | ||||||||
\(763\) | −2.94571 | −0.106642 | ||||||||
\(764\) | −19.1432 | −0.692576 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 59.0034 | 2.13188 | ||||||||
\(767\) | 1.48353 | 0.0535671 | ||||||||
\(768\) | −52.7946 | −1.90506 | ||||||||
\(769\) | 26.6436 | 0.960793 | 0.480396 | − | 0.877051i | \(-0.340493\pi\) | ||||
0.480396 | + | 0.877051i | \(0.340493\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −39.2988 | −1.41531 | ||||||||
\(772\) | 19.0766 | 0.686582 | ||||||||
\(773\) | −40.7749 | −1.46657 | −0.733285 | − | 0.679922i | \(-0.762014\pi\) | ||||
−0.733285 | + | 0.679922i | \(0.762014\pi\) | |||||||
\(774\) | 19.7052 | 0.708287 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.66349 | 0.239205 | ||||||||
\(777\) | −56.4207 | −2.02408 | ||||||||
\(778\) | 45.9375 | 1.64694 | ||||||||
\(779\) | −27.6644 | −0.991181 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.78176 | 0.206888 | ||||||||
\(782\) | −52.1334 | −1.86429 | ||||||||
\(783\) | 0.0723224 | 0.00258459 | ||||||||
\(784\) | −25.2833 | −0.902976 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.46640 | −0.266318 | ||||||||
\(787\) | 13.2146 | 0.471051 | 0.235525 | − | 0.971868i | \(-0.424319\pi\) | ||||
0.235525 | + | 0.971868i | \(0.424319\pi\) | |||||||
\(788\) | −11.6759 | −0.415938 | ||||||||
\(789\) | −19.8353 | −0.706155 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −49.6163 | −1.76415 | ||||||||
\(792\) | −3.38362 | −0.120232 | ||||||||
\(793\) | −2.74333 | −0.0974183 | ||||||||
\(794\) | 17.5600 | 0.623182 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29.8923 | −1.05950 | ||||||||
\(797\) | −3.31174 | −0.117308 | −0.0586539 | − | 0.998278i | \(-0.518681\pi\) | ||||
−0.0586539 | + | 0.998278i | \(0.518681\pi\) | |||||||
\(798\) | 53.2788 | 1.88605 | ||||||||
\(799\) | −44.9507 | −1.59024 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.8383 | −1.01895 | ||||||||
\(802\) | 20.6061 | 0.727626 | ||||||||
\(803\) | 1.40750 | 0.0496697 | ||||||||
\(804\) | 8.22876 | 0.290206 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.97873 | 0.0696979 | ||||||||
\(807\) | 67.8000 | 2.38667 | ||||||||
\(808\) | 5.28467 | 0.185914 | ||||||||
\(809\) | 22.5759 | 0.793727 | 0.396864 | − | 0.917878i | \(-0.370099\pi\) | ||||
0.396864 | + | 0.917878i | \(0.370099\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.1034 | 0.600581 | 0.300291 | − | 0.953848i | \(-0.402916\pi\) | ||||
0.300291 | + | 0.953848i | \(0.402916\pi\) | |||||||
\(812\) | −0.286475 | −0.0100533 | ||||||||
\(813\) | 65.9225 | 2.31200 | ||||||||
\(814\) | 13.1943 | 0.462461 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 52.3033 | 1.83098 | ||||||||
\(817\) | −9.30932 | −0.325692 | ||||||||
\(818\) | −55.2205 | −1.93074 | ||||||||
\(819\) | 2.86844 | 0.100232 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.57786 | −0.264469 | −0.132235 | − | 0.991218i | \(-0.542215\pi\) | ||||
−0.132235 | + | 0.991218i | \(0.542215\pi\) | |||||||
\(822\) | 5.12754 | 0.178843 | ||||||||
\(823\) | 43.7880 | 1.52635 | 0.763177 | − | 0.646190i | \(-0.223639\pi\) | ||||
0.763177 | + | 0.646190i | \(0.223639\pi\) | |||||||
\(824\) | −10.6298 | −0.370307 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42.6246 | −1.48310 | ||||||||
\(827\) | 12.9806 | 0.451379 | 0.225690 | − | 0.974199i | \(-0.427536\pi\) | ||||
0.225690 | + | 0.974199i | \(0.427536\pi\) | |||||||
\(828\) | 34.7844 | 1.20884 | ||||||||
\(829\) | −2.03755 | −0.0707669 | −0.0353834 | − | 0.999374i | \(-0.511265\pi\) | ||||
−0.0353834 | + | 0.999374i | \(0.511265\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.9657 | −1.49046 | ||||||||
\(832\) | −0.931769 | −0.0323033 | ||||||||
\(833\) | 23.3868 | 0.810304 | ||||||||
\(834\) | 48.7284 | 1.68733 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.43053 | −0.187819 | ||||||||
\(837\) | 6.25571 | 0.216229 | ||||||||
\(838\) | −53.9107 | −1.86231 | ||||||||
\(839\) | −27.3908 | −0.945635 | −0.472817 | − | 0.881160i | \(-0.656763\pi\) | ||||
−0.472817 | + | 0.881160i | \(0.656763\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9972 | −0.999904 | ||||||||
\(842\) | 0.119949 | 0.00413372 | ||||||||
\(843\) | −18.2302 | −0.627881 | ||||||||
\(844\) | 38.4217 | 1.32253 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 68.8125 | 2.36582 | ||||||||
\(847\) | −34.3074 | −1.17882 | ||||||||
\(848\) | 28.3595 | 0.973868 | ||||||||
\(849\) | 3.83703 | 0.131686 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.9271 | 1.36869 | ||||||||
\(852\) | 20.4461 | 0.700472 | ||||||||
\(853\) | 26.0906 | 0.893325 | 0.446663 | − | 0.894702i | \(-0.352612\pi\) | ||||
0.446663 | + | 0.894702i | \(0.352612\pi\) | |||||||
\(854\) | 78.8211 | 2.69720 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.55917 | −0.224188 | ||||||||
\(857\) | 17.1819 | 0.586922 | 0.293461 | − | 0.955971i | \(-0.405193\pi\) | ||||
0.293461 | + | 0.955971i | \(0.405193\pi\) | |||||||
\(858\) | −1.23980 | −0.0423262 | ||||||||
\(859\) | 2.77639 | 0.0947292 | 0.0473646 | − | 0.998878i | \(-0.484918\pi\) | ||||
0.0473646 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 79.0926 | 2.69547 | ||||||||
\(862\) | 48.4080 | 1.64878 | ||||||||
\(863\) | −11.5989 | −0.394832 | −0.197416 | − | 0.980320i | \(-0.563255\pi\) | ||||
−0.197416 | + | 0.980320i | \(0.563255\pi\) | |||||||
\(864\) | −9.80101 | −0.333437 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 42.3588 | 1.43941 | ||||||||
\(867\) | −4.91593 | −0.166954 | ||||||||
\(868\) | −24.7794 | −0.841068 | ||||||||
\(869\) | 0.837613 | 0.0284141 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.480204 | −0.0162711 | ||||||||
\(872\) | −0.717078 | −0.0242833 | ||||||||
\(873\) | 27.5191 | 0.931381 | ||||||||
\(874\) | −37.7038 | −1.27535 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.97736 | 0.168170 | ||||||||
\(877\) | 19.8014 | 0.668647 | 0.334323 | − | 0.942458i | \(-0.391492\pi\) | ||||
0.334323 | + | 0.942458i | \(0.391492\pi\) | |||||||
\(878\) | 32.5855 | 1.09971 | ||||||||
\(879\) | −69.1414 | −2.33208 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 50.1717 | 1.69033 | 0.845164 | − | 0.534508i | \(-0.179503\pi\) | ||||
0.845164 | + | 0.534508i | \(0.179503\pi\) | |||||||
\(882\) | −35.8015 | −1.20550 | ||||||||
\(883\) | 13.0038 | 0.437614 | 0.218807 | − | 0.975768i | \(-0.429784\pi\) | ||||
0.218807 | + | 0.975768i | \(0.429784\pi\) | |||||||
\(884\) | 1.54958 | 0.0521181 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 66.7444 | 2.24232 | ||||||||
\(887\) | 14.2467 | 0.478358 | 0.239179 | − | 0.970975i | \(-0.423122\pi\) | ||||
0.239179 | + | 0.970975i | \(0.423122\pi\) | |||||||
\(888\) | −13.7346 | −0.460902 | ||||||||
\(889\) | −58.4403 | −1.96003 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.93349 | 0.265782 | ||||||||
\(892\) | 2.51692 | 0.0842727 | ||||||||
\(893\) | −32.5091 | −1.08788 | ||||||||
\(894\) | −90.0069 | −3.01028 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −23.4789 | −0.784374 | ||||||||
\(897\) | −3.75175 | −0.125267 | ||||||||
\(898\) | −30.0438 | −1.00257 | ||||||||
\(899\) | 0.240237 | 0.00801234 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.2322 | −0.873921 | ||||||||
\(902\) | −18.4963 | −0.615859 | ||||||||
\(903\) | 26.6154 | 0.885704 | ||||||||
\(904\) | −12.0782 | −0.401715 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 21.6105 | 0.717960 | ||||||||
\(907\) | −15.5109 | −0.515032 | −0.257516 | − | 0.966274i | \(-0.582904\pi\) | ||||
−0.257516 | + | 0.966274i | \(0.582904\pi\) | |||||||
\(908\) | −17.7803 | −0.590061 | ||||||||
\(909\) | 21.8248 | 0.723884 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.4743 | −1.87108 | −0.935538 | − | 0.353225i | \(-0.885085\pi\) | ||||
−0.935538 | + | 0.353225i | \(0.885085\pi\) | |||||||
\(912\) | 37.8267 | 1.25257 | ||||||||
\(913\) | 12.4420 | 0.411769 | ||||||||
\(914\) | −15.2044 | −0.502917 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.6121 | 1.11058 | ||||||||
\(917\) | −5.45640 | −0.180186 | ||||||||
\(918\) | 11.2400 | 0.370975 | ||||||||
\(919\) | 50.4305 | 1.66355 | 0.831774 | − | 0.555115i | \(-0.187326\pi\) | ||||
0.831774 | + | 0.555115i | \(0.187326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.73174 | 0.155916 | ||||||||
\(922\) | 51.0923 | 1.68263 | ||||||||
\(923\) | −1.19317 | −0.0392736 | ||||||||
\(924\) | 15.5259 | 0.510764 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −55.3918 | −1.82029 | ||||||||
\(927\) | −43.8994 | −1.44185 | ||||||||
\(928\) | −0.376386 | −0.0123555 | ||||||||
\(929\) | 38.0255 | 1.24757 | 0.623787 | − | 0.781594i | \(-0.285593\pi\) | ||||
0.623787 | + | 0.781594i | \(0.285593\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.9137 | 0.554325 | ||||||||
\(932\) | −10.7128 | −0.350909 | ||||||||
\(933\) | −1.55775 | −0.0509984 | ||||||||
\(934\) | −5.08388 | −0.166349 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.698271 | 0.0228237 | ||||||||
\(937\) | 4.68279 | 0.152980 | 0.0764900 | − | 0.997070i | \(-0.475629\pi\) | ||||
0.0764900 | + | 0.997070i | \(0.475629\pi\) | |||||||
\(938\) | 13.7972 | 0.450495 | ||||||||
\(939\) | 58.6647 | 1.91445 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.3443 | −1.67378 | −0.836889 | − | 0.547373i | \(-0.815628\pi\) | ||||
−0.836889 | + | 0.547373i | \(0.815628\pi\) | |||||||
\(942\) | 13.1496 | 0.428437 | ||||||||
\(943\) | −55.9714 | −1.82268 | ||||||||
\(944\) | −30.2624 | −0.984959 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.22417 | −0.202365 | ||||||||
\(947\) | −29.5601 | −0.960575 | −0.480288 | − | 0.877111i | \(-0.659468\pi\) | ||||
−0.480288 | + | 0.877111i | \(0.659468\pi\) | |||||||
\(948\) | 2.96206 | 0.0962032 | ||||||||
\(949\) | −0.290463 | −0.00942883 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.24036 | 0.202357 | ||||||||
\(952\) | 13.1056 | 0.424756 | ||||||||
\(953\) | −46.8102 | −1.51633 | −0.758166 | − | 0.652062i | \(-0.773904\pi\) | ||||
−0.758166 | + | 0.652062i | \(0.773904\pi\) | |||||||
\(954\) | 40.1574 | 1.30014 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.1633 | 0.652127 | ||||||||
\(957\) | −0.150524 | −0.00486574 | ||||||||
\(958\) | 45.9564 | 1.48478 | ||||||||
\(959\) | 3.74717 | 0.121003 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.2201 | −0.329681 | ||||||||
\(962\) | −2.72288 | −0.0877892 | ||||||||
\(963\) | −27.0883 | −0.872909 | ||||||||
\(964\) | 1.54517 | 0.0497664 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 107.795 | 3.46825 | ||||||||
\(967\) | −37.6906 | −1.21205 | −0.606024 | − | 0.795446i | \(-0.707237\pi\) | ||||
−0.606024 | + | 0.795446i | \(0.707237\pi\) | |||||||
\(968\) | −8.35152 | −0.268428 | ||||||||
\(969\) | −34.9892 | −1.12402 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.4295 | −1.71464 | −0.857318 | − | 0.514788i | \(-0.827871\pi\) | ||||
−0.857318 | + | 0.514788i | \(0.827871\pi\) | |||||||
\(972\) | 34.4167 | 1.10392 | ||||||||
\(973\) | 35.6104 | 1.14162 | ||||||||
\(974\) | 36.4667 | 1.16847 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 55.9610 | 1.79127 | ||||||||
\(977\) | −9.03874 | −0.289175 | −0.144587 | − | 0.989492i | \(-0.546186\pi\) | ||||
−0.144587 | + | 0.989492i | \(0.546186\pi\) | |||||||
\(978\) | 93.3481 | 2.98494 | ||||||||
\(979\) | 9.10900 | 0.291125 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.96142 | −0.0945508 | ||||||||
\(982\) | −26.9296 | −0.859357 | ||||||||
\(983\) | 39.4162 | 1.25718 | 0.628590 | − | 0.777737i | \(-0.283632\pi\) | ||||
0.628590 | + | 0.777737i | \(0.283632\pi\) | |||||||
\(984\) | 19.2537 | 0.613784 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.431647 | 0.0137464 | ||||||||
\(987\) | 92.9437 | 2.95843 | ||||||||
\(988\) | 1.12069 | 0.0356537 | ||||||||
\(989\) | −18.8349 | −0.598914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.5302 | −1.60515 | −0.802573 | − | 0.596554i | \(-0.796536\pi\) | ||||
−0.802573 | + | 0.596554i | \(0.796536\pi\) | |||||||
\(992\) | −32.5565 | −1.03367 | ||||||||
\(993\) | −17.6765 | −0.560946 | ||||||||
\(994\) | 34.2820 | 1.08736 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 43.9987 | 1.39415 | ||||||||
\(997\) | 31.8629 | 1.00911 | 0.504553 | − | 0.863380i | \(-0.331657\pi\) | ||||
0.504553 | + | 0.863380i | \(0.331657\pi\) | |||||||
\(998\) | 42.6476 | 1.34999 | ||||||||
\(999\) | −8.60832 | −0.272355 |
(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 | 6025.2.a.p.1.8 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.8 | ✓ | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.39 | yes | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.39 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.8 | ✓ | 46 | 5.2 | odd | 4 | ||
1205.2.b.c.724.39 | yes | 46 | 5.3 | odd | 4 | ||
6025.2.a.p.1.8 | 46 | 1.1 | even | 1 | trivial | ||
6025.2.a.p.1.39 | 46 | 5.4 | even | 2 | inner |