Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.74673 | −1.58583 | −0.792914 | − | 0.609334i | \(-0.791437\pi\) | ||||
−0.792914 | + | 0.609334i | \(0.791437\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.35693 | −0.890835 | −0.445417 | − | 0.895323i | \(-0.646945\pi\) | ||||
−0.445417 | + | 0.895323i | \(0.646945\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.54455 | 1.51485 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.675516 | −0.203676 | −0.101838 | − | 0.994801i | \(-0.532472\pi\) | ||||
−0.101838 | + | 0.994801i | \(0.532472\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.24160 | 1.45376 | 0.726880 | − | 0.686765i | \(-0.240970\pi\) | ||||
0.726880 | + | 0.686765i | \(0.240970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.74673 | −0.709204 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.157089 | 0.0380997 | 0.0190499 | − | 0.999819i | \(-0.493936\pi\) | ||||
0.0190499 | + | 0.999819i | \(0.493936\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.38382 | 0.776303 | 0.388151 | − | 0.921596i | \(-0.373114\pi\) | ||||
0.388151 | + | 0.921596i | \(0.373114\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.47385 | 1.41271 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.83745 | −1.63422 | −0.817110 | − | 0.576481i | \(-0.804425\pi\) | ||||
−0.817110 | + | 0.576481i | \(0.804425\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.24247 | −0.816464 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.03674 | −0.378212 | −0.189106 | − | 0.981957i | \(-0.560559\pi\) | ||||
−0.189106 | + | 0.981957i | \(0.560559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.89059 | −0.519166 | −0.259583 | − | 0.965721i | \(-0.583585\pi\) | ||||
−0.259583 | + | 0.965721i | \(0.583585\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.85546 | 0.322995 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.35693 | −0.398393 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.10459 | 1.00359 | 0.501794 | − | 0.864987i | \(-0.332673\pi\) | ||||
0.501794 | + | 0.864987i | \(0.332673\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.3973 | −2.30541 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.90724 | −0.297860 | −0.148930 | − | 0.988848i | \(-0.547583\pi\) | ||||
−0.148930 | + | 0.988848i | \(0.547583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.82206 | 1.49785 | 0.748925 | − | 0.662654i | \(-0.230570\pi\) | ||||
0.748925 | + | 0.662654i | \(0.230570\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.54455 | 0.677462 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.3241 | 1.79765 | 0.898827 | − | 0.438304i | \(-0.144421\pi\) | ||||
0.898827 | + | 0.438304i | \(0.144421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.44490 | −0.206414 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.431482 | −0.0604196 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.83339 | 0.801278 | 0.400639 | − | 0.916236i | \(-0.368788\pi\) | ||||
0.400639 | + | 0.916236i | \(0.368788\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.675516 | −0.0910866 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.29447 | −1.23108 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.257517 | −0.0335258 | −0.0167629 | − | 0.999859i | \(-0.505336\pi\) | ||||
−0.0167629 | + | 0.999859i | \(0.505336\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.24169 | 0.927203 | 0.463602 | − | 0.886044i | \(-0.346557\pi\) | ||||
0.463602 | + | 0.886044i | \(0.346557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.7112 | −1.34948 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.24160 | 0.650141 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.7233 | −1.79873 | −0.899367 | − | 0.437195i | \(-0.855972\pi\) | ||||
−0.899367 | + | 0.437195i | \(0.855972\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.5274 | 2.59159 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.19249 | −0.378879 | −0.189439 | − | 0.981892i | \(-0.560667\pi\) | ||||
−0.189439 | + | 0.981892i | \(0.560667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.56610 | 0.534422 | 0.267211 | − | 0.963638i | \(-0.413898\pi\) | ||||
0.267211 | + | 0.963638i | \(0.413898\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.74673 | −0.317166 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.59214 | 0.181442 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.5784 | −1.86521 | −0.932606 | − | 0.360896i | \(-0.882471\pi\) | ||||
−0.932606 | + | 0.360896i | \(0.882471\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.98071 | −0.220079 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.8412 | 1.51927 | 0.759634 | − | 0.650351i | \(-0.225378\pi\) | ||||
0.759634 | + | 0.650351i | \(0.225378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.157089 | 0.0170387 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.59437 | 0.599780 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.93737 | −0.417360 | −0.208680 | − | 0.977984i | \(-0.566917\pi\) | ||||
−0.208680 | + | 0.977984i | \(0.566917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.3541 | −1.29506 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.93969 | 0.823307 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.38382 | 0.347173 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.95434 | 0.401503 | 0.200751 | − | 0.979642i | \(-0.435662\pi\) | ||||
0.200751 | + | 0.979642i | \(0.435662\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.06992 | −0.308538 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.13165 | −0.112603 | −0.0563015 | − | 0.998414i | \(-0.517931\pi\) | ||||
−0.0563015 | + | 0.998414i | \(0.517931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.92119 | −0.977564 | −0.488782 | − | 0.872406i | \(-0.662559\pi\) | ||||
−0.488782 | + | 0.872406i | \(0.662559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.47385 | 0.631783 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.206483 | −0.0199614 | −0.00998072 | − | 0.999950i | \(-0.503177\pi\) | ||||
−0.00998072 | + | 0.999950i | \(0.503177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.7094 | −1.69626 | −0.848128 | − | 0.529792i | \(-0.822270\pi\) | ||||
−0.848128 | + | 0.529792i | \(0.822270\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.7677 | −1.59152 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.33331 | −0.125427 | −0.0627135 | − | 0.998032i | \(-0.519975\pi\) | ||||
−0.0627135 | + | 0.998032i | \(0.519975\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.83745 | −0.730846 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.8207 | 2.20223 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.370248 | −0.0339406 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5437 | −0.958516 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.23867 | 0.472355 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.47071 | 0.485447 | 0.242723 | − | 0.970096i | \(-0.421959\pi\) | ||||
0.242723 | + | 0.970096i | \(0.421959\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −26.9786 | −2.37533 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.84144 | −0.160887 | −0.0804437 | − | 0.996759i | \(-0.525634\pi\) | ||||
−0.0804437 | + | 0.996759i | \(0.525634\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.97543 | −0.691557 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.24247 | −0.365134 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6340 | 1.16483 | 0.582416 | − | 0.812891i | \(-0.302108\pi\) | ||||
0.582416 | + | 0.812891i | \(0.302108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.18219 | 0.694005 | 0.347002 | − | 0.937864i | \(-0.387200\pi\) | ||||
0.347002 | + | 0.937864i | \(0.387200\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.8510 | −2.85077 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.54079 | −0.296096 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.03674 | −0.169142 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.96874 | 0.327336 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3172 | 1.09099 | 0.545495 | − | 0.838114i | \(-0.316342\pi\) | ||||
0.545495 | + | 0.838114i | \(0.316342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0377 | 0.816854 | 0.408427 | − | 0.912791i | \(-0.366077\pi\) | ||||
0.408427 | + | 0.912791i | \(0.366077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.713900 | 0.0577154 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.89059 | −0.232178 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.44926 | −0.275281 | −0.137641 | − | 0.990482i | \(-0.543952\pi\) | ||||
−0.137641 | + | 0.990482i | \(0.543952\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.0228 | −1.27069 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.4723 | 1.45582 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.25398 | 0.333198 | 0.166599 | − | 0.986025i | \(-0.446722\pi\) | ||||
0.166599 | + | 0.986025i | \(0.446722\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.85546 | 0.144448 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.2554 | −1.49003 | −0.745013 | − | 0.667050i | \(-0.767557\pi\) | ||||
−0.745013 | + | 0.667050i | \(0.767557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.4744 | 1.11342 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.3780 | 1.17598 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.949945 | −0.0722230 | −0.0361115 | − | 0.999348i | \(-0.511497\pi\) | ||||
−0.0361115 | + | 0.999348i | \(0.511497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.35693 | −0.178167 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.707330 | 0.0531662 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.8555 | −1.03561 | −0.517805 | − | 0.855499i | \(-0.673251\pi\) | ||||
−0.517805 | + | 0.855499i | \(0.673251\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.7508 | −1.61672 | −0.808362 | − | 0.588686i | \(-0.799645\pi\) | ||||
−0.808362 | + | 0.588686i | \(0.799645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.8910 | −1.47038 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.10459 | 0.448818 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.106116 | −0.00776000 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.99919 | 0.727334 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.89030 | −0.209135 | −0.104567 | − | 0.994518i | \(-0.533346\pi\) | ||||
−0.104567 | + | 0.994518i | \(0.533346\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.0936 | −1.23043 | −0.615213 | − | 0.788361i | \(-0.710930\pi\) | ||||
−0.615213 | + | 0.788361i | \(0.710930\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.3973 | −1.03101 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8684 | 1.55806 | 0.779030 | − | 0.626987i | \(-0.215712\pi\) | ||||
0.779030 | + | 0.626987i | \(0.215712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1016 | 0.716083 | 0.358041 | − | 0.933706i | \(-0.383445\pi\) | ||||
0.358041 | + | 0.933706i | \(0.383445\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 40.4409 | 2.85248 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.80044 | 0.336925 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.90724 | −0.133207 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −35.6177 | −2.47560 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.28583 | −0.158114 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7501 | −1.35965 | −0.679827 | − | 0.733372i | \(-0.737945\pi\) | ||||
−0.679827 | + | 0.733372i | \(0.737945\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.76892 | 0.600836 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.82206 | 0.669859 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.81291 | 0.462491 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.5419 | −0.847501 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.823399 | 0.0553878 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1607 | −1.48399 | −0.741994 | − | 0.670406i | \(-0.766120\pi\) | ||||
−0.741994 | + | 0.670406i | \(0.766120\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.54455 | 0.302970 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.61799 | −0.107390 | −0.0536949 | − | 0.998557i | \(-0.517100\pi\) | ||||
−0.0536949 | + | 0.998557i | \(0.517100\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.3177 | 1.80520 | 0.902602 | − | 0.430475i | \(-0.141654\pi\) | ||||
0.902602 | + | 0.430475i | \(0.141654\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.37319 | −0.287735 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.8665 | 1.56355 | 0.781773 | − | 0.623563i | \(-0.214315\pi\) | ||||
0.781773 | + | 0.623563i | \(0.214315\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3241 | 0.803935 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 45.5364 | 2.95791 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.85642 | 0.443505 | 0.221752 | − | 0.975103i | \(-0.428822\pi\) | ||||
0.221752 | + | 0.975103i | \(0.428822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8260 | −1.08386 | −0.541930 | − | 0.840423i | \(-0.682306\pi\) | ||||
−0.541930 | + | 0.840423i | \(0.682306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.1679 | 1.16547 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.44490 | −0.0923110 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.7367 | 1.12856 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −38.0181 | −2.40930 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.0167 | 1.64216 | 0.821081 | − | 0.570811i | \(-0.193371\pi\) | ||||
0.821081 | + | 0.570811i | \(0.193371\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.29432 | 0.332851 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.431482 | −0.0270205 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.00335 | 0.436857 | 0.218429 | − | 0.975853i | \(-0.429907\pi\) | ||||
0.218429 | + | 0.975853i | \(0.429907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.3881 | −0.894031 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.25605 | −0.572935 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.64211 | 0.286245 | 0.143122 | − | 0.989705i | \(-0.454286\pi\) | ||||
0.143122 | + | 0.989705i | \(0.454286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.83339 | 0.358343 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.8149 | 0.661862 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.7875 | 1.02355 | 0.511774 | − | 0.859120i | \(-0.328988\pi\) | ||||
0.511774 | + | 0.859120i | \(0.328988\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1380 | 0.919565 | 0.459783 | − | 0.888032i | \(-0.347927\pi\) | ||||
0.459783 | + | 0.888032i | \(0.347927\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 33.9334 | 2.05374 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.675516 | −0.0407352 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.4382 | 0.747338 | 0.373669 | − | 0.927562i | \(-0.378100\pi\) | ||||
0.373669 | + | 0.927562i | \(0.378100\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.1364 | −0.786458 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.2324 | 0.729725 | 0.364863 | − | 0.931061i | \(-0.381116\pi\) | ||||
0.364863 | + | 0.931061i | \(0.381116\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.20676 | 0.547285 | 0.273643 | − | 0.961831i | \(-0.411771\pi\) | ||||
0.273643 | + | 0.961831i | \(0.411771\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.29447 | −0.550557 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.49522 | 0.265344 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9753 | −0.998548 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.8615 | −0.636714 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.5556 | 1.37613 | 0.688067 | − | 0.725647i | \(-0.258459\pi\) | ||||
0.688067 | + | 0.725647i | \(0.258459\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.257517 | −0.0149932 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.86586 | 0.166294 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −41.0808 | −2.37576 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.1499 | −1.33434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.10833 | 0.178569 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.24169 | 0.414658 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.4008 | 1.62092 | 0.810461 | − | 0.585793i | \(-0.199217\pi\) | ||||
0.810461 | + | 0.585793i | \(0.199217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.2509 | 1.55025 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1693 | 0.803467 | 0.401733 | − | 0.915757i | \(-0.368408\pi\) | ||||
0.401733 | + | 0.915757i | \(0.368408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.7246 | −1.51056 | −0.755282 | − | 0.655400i | \(-0.772500\pi\) | ||||
−0.755282 | + | 0.655400i | \(0.772500\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.7112 | −0.603506 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.6263 | −1.15849 | −0.579244 | − | 0.815154i | \(-0.696652\pi\) | ||||
−0.579244 | + | 0.815154i | \(0.696652\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.37585 | 0.0770327 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.567153 | 0.0316554 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.531562 | 0.0295769 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.24160 | 0.290752 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 48.6431 | 2.68997 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.0470 | −1.60141 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.1479 | 1.10743 | 0.553715 | − | 0.832706i | \(-0.313210\pi\) | ||||
0.553715 | + | 0.832706i | \(0.313210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 27.7426 | 1.52029 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.7233 | −0.804418 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.77718 | 0.260229 | 0.130115 | − | 0.991499i | \(-0.458465\pi\) | ||||
0.130115 | + | 0.991499i | \(0.458465\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.66224 | 0.198906 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.95264 | 0.105742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.9040 | 1.07472 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.5274 | 1.15900 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.1422 | −1.02761 | −0.513803 | − | 0.857908i | \(-0.671764\pi\) | ||||
−0.513803 | + | 0.857908i | \(0.671764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.80676 | 0.524944 | 0.262472 | − | 0.964940i | \(-0.415462\pi\) | ||||
0.262472 | + | 0.964940i | \(0.415462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.2373 | −1.18694 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.8820 | −0.579191 | −0.289596 | − | 0.957149i | \(-0.593521\pi\) | ||||
−0.289596 | + | 0.957149i | \(0.593521\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.19249 | −0.169440 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.01697 | 0.0538239 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.58874 | −0.347740 | −0.173870 | − | 0.984769i | \(-0.555627\pi\) | ||||
−0.173870 | + | 0.984769i | \(0.555627\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.54973 | −0.397354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.9607 | 1.52004 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.56610 | 0.239001 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4470 | 0.597529 | 0.298764 | − | 0.954327i | \(-0.403426\pi\) | ||||
0.298764 | + | 0.954327i | \(0.403426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.66753 | −0.451214 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.7489 | −0.713807 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.8529 | −1.70106 | −0.850529 | − | 0.525928i | \(-0.823718\pi\) | ||||
−0.850529 | + | 0.525928i | \(0.823718\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.74673 | −0.141841 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.6758 | −0.549830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.6223 | −0.853831 | −0.426916 | − | 0.904291i | \(-0.640400\pi\) | ||||
−0.426916 | + | 0.904291i | \(0.640400\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.0266 | −0.769835 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.3113 | 1.39554 | 0.697771 | − | 0.716320i | \(-0.254175\pi\) | ||||
0.697771 | + | 0.716320i | \(0.254175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.59214 | 0.0811431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 44.6369 | 2.26902 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.869264 | −0.0440734 | −0.0220367 | − | 0.999757i | \(-0.507015\pi\) | ||||
−0.0220367 | + | 0.999757i | \(0.507015\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.23118 | −0.0622634 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.05795 | 0.255140 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.5784 | −0.834148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.64722 | −0.0826717 | −0.0413359 | − | 0.999145i | \(-0.513161\pi\) | ||||
−0.0413359 | + | 0.999145i | \(0.513161\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.9064 | 1.09669 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.1513 | −0.754742 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.98071 | −0.0984224 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.12375 | −0.204407 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.9538 | 1.58001 | 0.790007 | − | 0.613098i | \(-0.210077\pi\) | ||||
0.790007 | + | 0.613098i | \(0.210077\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −37.4490 | −1.84722 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.606948 | 0.0298660 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.8412 | 0.679437 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.4743 | −1.10057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.5057 | 1.00177 | 0.500885 | − | 0.865514i | \(-0.333008\pi\) | ||||
0.500885 | + | 0.865514i | \(0.333008\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.5213 | 1.29257 | 0.646285 | − | 0.763096i | \(-0.276322\pi\) | ||||
0.646285 | + | 0.763096i | \(0.276322\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 56.0075 | 2.72318 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.157089 | 0.00761995 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.0681 | −0.825985 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.72561 | 0.469557 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.89089 | 0.428259 | 0.214130 | − | 0.976805i | \(-0.431309\pi\) | ||||
0.214130 | + | 0.976805i | \(0.431309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.33574 | −0.160305 | −0.0801527 | − | 0.996783i | \(-0.525541\pi\) | ||||
−0.0801527 | + | 0.996783i | \(0.525541\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.59437 | 0.268230 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.5205 | −1.26865 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.57491 | 0.218349 | 0.109174 | − | 0.994023i | \(-0.465179\pi\) | ||||
0.109174 | + | 0.994023i | \(0.465179\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.56640 | −0.312686 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.66705 | −0.221738 | −0.110869 | − | 0.993835i | \(-0.535363\pi\) | ||||
−0.110869 | + | 0.993835i | \(0.535363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.93737 | −0.186649 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.5789 | −1.73012 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.0697 | 1.60785 | 0.803925 | − | 0.594731i | \(-0.202741\pi\) | ||||
0.803925 | + | 0.594731i | \(0.202741\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.28837 | 0.0606669 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −27.5708 | −1.29539 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.3541 | −0.579168 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.8840 | 1.16402 | 0.582011 | − | 0.813181i | \(-0.302266\pi\) | ||||
0.582011 | + | 0.813181i | \(0.302266\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.666446 | −0.0311070 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.37550 | 0.0640635 | 0.0320318 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320318 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.4902 | 1.09168 | 0.545840 | − | 0.837889i | \(-0.316210\pi\) | ||||
0.545840 | + | 0.837889i | \(0.316210\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.93969 | 0.368194 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.7970 | 0.638450 | 0.319225 | − | 0.947679i | \(-0.396577\pi\) | ||||
0.319225 | + | 0.947679i | \(0.396577\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34.7017 | 1.60237 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.47421 | 0.436549 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.63497 | −0.305076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.38382 | 0.155261 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.5102 | 1.21382 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.65571 | 0.0756515 | 0.0378258 | − | 0.999284i | \(-0.487957\pi\) | ||||
0.0378258 | + | 0.999284i | \(0.487957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.9978 | 1.45898 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −50.7385 | −2.30868 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.95434 | 0.179558 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0482 | 0.908470 | 0.454235 | − | 0.890882i | \(-0.349913\pi\) | ||||
0.454235 | + | 0.890882i | \(0.349913\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.6846 | −0.528394 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.5603 | −1.24378 | −0.621888 | − | 0.783106i | \(-0.713634\pi\) | ||||
−0.621888 | + | 0.783106i | \(0.713634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.319949 | −0.0144098 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.06992 | −0.137983 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.52446 | 0.337518 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 42.5205 | 1.90348 | 0.951739 | − | 0.306909i | \(-0.0992946\pi\) | ||||
0.951739 | + | 0.306909i | \(0.0992946\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 52.8894 | 2.36292 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.8194 | −1.06206 | −0.531028 | − | 0.847354i | \(-0.678194\pi\) | ||||
−0.531028 | + | 0.847354i | \(0.678194\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.13165 | −0.0503576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −39.7573 | −1.76569 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.1383 | 1.86775 | 0.933873 | − | 0.357605i | \(-0.116406\pi\) | ||||
0.933873 | + | 0.357605i | \(0.116406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.7620 | −0.476081 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.3558 | −0.633823 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.92119 | −0.437180 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.32513 | −0.366139 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.60925 | 0.114533 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.8252 | 1.08761 | 0.543806 | − | 0.839211i | \(-0.316983\pi\) | ||||
0.543806 | + | 0.839211i | \(0.316983\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.29873 | −0.100516 | −0.0502582 | − | 0.998736i | \(-0.516004\pi\) | ||||
−0.0502582 | + | 0.998736i | \(0.516004\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.47385 | 0.282542 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.454081 | −0.0197801 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.4256 | 1.67068 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.17030 | −0.0507866 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.99697 | −0.433017 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.206483 | −0.00892703 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 38.0574 | 1.64230 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.976051 | 0.0420415 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.97452 | −0.342851 | −0.171426 | − | 0.985197i | \(-0.554837\pi\) | ||||
−0.171426 | + | 0.985197i | \(0.554837\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 59.7436 | 2.56385 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.7094 | −0.758589 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.69184 | −0.286122 | −0.143061 | − | 0.989714i | \(-0.545695\pi\) | ||||
−0.143061 | + | 0.989714i | \(0.545695\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 32.9102 | 1.40457 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.89196 | −0.293607 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 39.0740 | 1.66160 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.7677 | −0.711749 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22.1841 | −0.939972 | −0.469986 | − | 0.882674i | \(-0.655741\pi\) | ||||
−0.469986 | + | 0.882674i | \(0.655741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.4834 | 2.17751 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.291473 | 0.0123060 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.4256 | 0.860838 | 0.430419 | − | 0.902629i | \(-0.358366\pi\) | ||||
0.430419 | + | 0.902629i | \(0.358366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.33331 | −0.0560927 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.66840 | 0.196054 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.9291 | −1.50622 | −0.753112 | − | 0.657892i | \(-0.771448\pi\) | ||||
−0.753112 | + | 0.657892i | \(0.771448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.0430 | −0.964319 | −0.482160 | − | 0.876083i | \(-0.660147\pi\) | ||||
−0.482160 | + | 0.876083i | \(0.660147\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.93889 | 0.331652 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.83745 | −0.326844 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.07596 | −0.128054 | −0.0640269 | − | 0.997948i | \(-0.520394\pi\) | ||||
−0.0640269 | + | 0.997948i | \(0.520394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 46.9516 | 1.95124 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.6227 | −1.35342 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.94055 | −0.163201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 23.8207 | 0.984866 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 27.6217 | 1.14007 | 0.570034 | − | 0.821621i | \(-0.306930\pi\) | ||||
0.570034 | + | 0.821621i | \(0.306930\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.78126 | −0.403030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −60.0667 | −2.47081 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.67058 | −0.356058 | −0.178029 | − | 0.984025i | \(-0.556972\pi\) | ||||
−0.178029 | + | 0.984025i | \(0.556972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.370248 | −0.0151787 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.7464 | −1.13558 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5487 | 1.12561 | 0.562805 | − | 0.826590i | \(-0.309722\pi\) | ||||
0.562805 | + | 0.826590i | \(0.309722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.1909 | −1.10914 | −0.554569 | − | 0.832138i | \(-0.687117\pi\) | ||||
−0.554569 | + | 0.832138i | \(0.687117\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −66.9106 | −2.72481 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.5437 | −0.428661 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.75401 | −0.314726 | −0.157363 | − | 0.987541i | \(-0.550299\pi\) | ||||
−0.157363 | + | 0.987541i | \(0.550299\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.1855 | −0.534305 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 64.5980 | 2.61336 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.1104 | 0.529525 | 0.264762 | − | 0.964314i | \(-0.414706\pi\) | ||||
0.264762 | + | 0.964314i | \(0.414706\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.23867 | 0.211244 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.4737 | 0.582689 | 0.291344 | − | 0.956618i | \(-0.405897\pi\) | ||||
0.291344 | + | 0.956618i | \(0.405897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.72697 | 0.189993 | 0.0949966 | − | 0.995478i | \(-0.469716\pi\) | ||||
0.0949966 | + | 0.995478i | \(0.469716\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 33.2501 | 1.33428 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.28009 | 0.371799 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.27857 | 0.250742 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.958965 | 0.0382365 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4211 | −0.494475 | −0.247237 | − | 0.968955i | \(-0.579523\pi\) | ||||
−0.247237 | + | 0.968955i | \(0.579523\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 54.2484 | 2.15618 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.47071 | 0.217098 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.57357 | −0.300076 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.5084 | −0.573944 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.7557 | −1.41227 | −0.706133 | − | 0.708079i | \(-0.749562\pi\) | ||||
−0.706133 | + | 0.708079i | \(0.749562\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.62857 | 0.143097 | 0.0715483 | − | 0.997437i | \(-0.477206\pi\) | ||||
0.0715483 | + | 0.997437i | \(0.477206\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26.9786 | −1.06228 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.23846 | −0.284573 | −0.142287 | − | 0.989825i | \(-0.545445\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545445\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.173957 | 0.00682840 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.7133 | −0.733431 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.7184 | 1.04557 | 0.522787 | − | 0.852463i | \(-0.324892\pi\) | ||||
0.522787 | + | 0.852463i | \(0.324892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.84144 | −0.0719510 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.7509 | 0.809569 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.2410 | −0.398932 | −0.199466 | − | 0.979905i | \(-0.563921\pi\) | ||||
−0.199466 | + | 0.979905i | \(0.563921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.3705 | −1.29796 | −0.648981 | − | 0.760804i | \(-0.724805\pi\) | ||||
−0.648981 | + | 0.760804i | \(0.724805\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.26166 | −0.0878356 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.97543 | −0.309274 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.9628 | 0.618082 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 60.8695 | 2.35335 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.89188 | −0.188849 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.1827 | 1.20201 | 0.601003 | − | 0.799247i | \(-0.294768\pi\) | ||||
0.601003 | + | 0.799247i | \(0.294768\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.24247 | −0.163293 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.9394 | 1.34283 | 0.671415 | − | 0.741082i | \(-0.265687\pi\) | ||||
0.671415 | + | 0.741082i | \(0.265687\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.32010 | −0.357673 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.44419 | 0.170302 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.69137 | 0.370830 | 0.185415 | − | 0.982660i | \(-0.440637\pi\) | ||||
0.185415 | + | 0.982660i | \(0.440637\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6340 | 0.520929 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −75.0345 | −2.86274 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 30.5763 | 1.16487 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.59884 | 0.0988647 | 0.0494324 | − | 0.998777i | \(-0.484259\pi\) | ||||
0.0494324 | + | 0.998777i | \(0.484259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.23557 | 0.274857 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.18219 | 0.310368 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.299606 | −0.0113484 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −65.5550 | −2.47952 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.36879 | 0.202776 | 0.101388 | − | 0.994847i | \(-0.467672\pi\) | ||||
0.101388 | + | 0.994847i | \(0.467672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.6569 | 0.779088 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.8510 | −1.27490 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.66721 | 0.100311 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.3711 | 0.727497 | 0.363748 | − | 0.931497i | \(-0.381497\pi\) | ||||
0.363748 | + | 0.931497i | \(0.381497\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −75.3412 | −2.82552 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.6549 | 0.848431 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.54079 | −0.132418 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.8328 | −0.703322 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.2067 | 0.529821 | 0.264911 | − | 0.964273i | \(-0.414658\pi\) | ||||
0.264911 | + | 0.964273i | \(0.414658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.3835 | 0.870848 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 46.2167 | 1.71882 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.03674 | −0.0756425 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.92275 | 0.256751 | 0.128375 | − | 0.991726i | \(-0.459024\pi\) | ||||
0.128375 | + | 0.991726i | \(0.459024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.9603 | −1.62816 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.54294 | 0.0570677 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −41.2470 | −1.52349 | −0.761747 | − | 0.647875i | \(-0.775658\pi\) | ||||
−0.761747 | + | 0.647875i | \(0.775658\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.96874 | 0.146389 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.94581 | 0.366359 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.2304 | −1.73740 | −0.868699 | − | 0.495341i | \(-0.835043\pi\) | ||||
−0.868699 | + | 0.495341i | \(0.835043\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −48.7179 | −1.78970 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.5974 | 1.81955 | 0.909777 | − | 0.415098i | \(-0.136253\pi\) | ||||
0.909777 | + | 0.415098i | \(0.136253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3172 | 0.487905 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 62.9020 | 2.30146 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.486665 | 0.0177823 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 41.3945 | 1.51051 | 0.755254 | − | 0.655432i | \(-0.227514\pi\) | ||||
0.755254 | + | 0.655432i | \(0.227514\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −71.4611 | −2.60419 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.0377 | 0.365308 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.3215 | −0.774943 | −0.387472 | − | 0.921882i | \(-0.626652\pi\) | ||||
−0.387472 | + | 0.921882i | \(0.626652\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −14.5421 | −0.527845 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39.4007 | 1.42827 | 0.714136 | − | 0.700007i | \(-0.246820\pi\) | ||||
0.714136 | + | 0.700007i | \(0.246820\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.7398 | 1.51108 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.713900 | 0.0258111 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.34980 | −0.0487385 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.9959 | 1.83896 | 0.919479 | − | 0.393138i | \(-0.128611\pi\) | ||||
0.919479 | + | 0.393138i | \(0.128611\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2363 | −0.692780 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0573 | −0.397705 | −0.198852 | − | 0.980029i | \(-0.563721\pi\) | ||||
−0.198852 | + | 0.980029i | \(0.563721\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.89059 | −0.103833 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 39.5202 | 1.41778 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.45375 | −0.231230 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.15658 | 0.0771684 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.64079 | 0.308797 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.44926 | −0.123110 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.1182 | −0.824073 | −0.412037 | − | 0.911167i | \(-0.635182\pi\) | ||||
−0.412037 | + | 0.911167i | \(0.635182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.7506 | −0.453935 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.14251 | 0.111735 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.9581 | 1.34793 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.0228 | −0.568270 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.7864 | −0.877978 | −0.438989 | − | 0.898492i | \(-0.644663\pi\) | ||||
−0.438989 | + | 0.898492i | \(0.644663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.93598 | 0.0684901 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.8936 | −0.632238 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.08448 | −0.108849 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.4723 | 0.651063 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −46.1107 | −1.62317 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.5187 | 0.756557 | 0.378279 | − | 0.925692i | \(-0.376516\pi\) | ||||
0.378279 | + | 0.925692i | \(0.376516\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0224 | 0.387050 | 0.193525 | − | 0.981095i | \(-0.438008\pi\) | ||||
0.193525 | + | 0.981095i | \(0.438008\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −41.5799 | −1.45827 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.25398 | 0.149011 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.2361 | 1.16279 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −56.1437 | −1.96182 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −53.0765 | −1.85238 | −0.926191 | − | 0.377055i | \(-0.876937\pi\) | ||||
−0.926191 | + | 0.377055i | \(0.876937\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.7220 | 0.548035 | 0.274018 | − | 0.961725i | \(-0.411647\pi\) | ||||
0.274018 | + | 0.961725i | \(0.411647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.85546 | 0.0645990 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.15905 | 0.0750774 | 0.0375387 | − | 0.999295i | \(-0.488048\pi\) | ||||
0.0375387 | + | 0.999295i | \(0.488048\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.3343 | 1.81764 | 0.908822 | − | 0.417184i | \(-0.136983\pi\) | ||||
0.908822 | + | 0.417184i | \(0.136983\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.1644 | −1.18515 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.226978 | −0.00786430 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.2554 | −0.666360 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2632 | 0.423880 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.2239 | 0.456539 | 0.228269 | − | 0.973598i | \(-0.426693\pi\) | ||||
0.228269 | + | 0.973598i | \(0.426693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.8517 | −0.856955 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −33.5992 | −1.15722 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.4744 | 0.497935 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.8507 | 0.853879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.2885 | −0.867900 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.8444 | −1.64008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.4094 | 1.28087 | 0.640436 | − | 0.768011i | \(-0.278754\pi\) | ||||
0.640436 | + | 0.768011i | \(0.278754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.3780 | 0.525915 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.587197 | −0.0200583 | −0.0100291 | − | 0.999950i | \(-0.503192\pi\) | ||||
−0.0100291 | + | 0.999950i | \(0.503192\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.6017 | 1.18060 | 0.590298 | − | 0.807186i | \(-0.299010\pi\) | ||||
0.590298 | + | 0.807186i | \(0.299010\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.3472 | −0.420790 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.56387 | 0.325558 | 0.162779 | − | 0.986663i | \(-0.447954\pi\) | ||||
0.162779 | + | 0.986663i | \(0.447954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.949945 | −0.0322991 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 46.6267 | 1.58353 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.1990 | 0.379899 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −77.1735 | −2.61493 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.9707 | 0.608217 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.35693 | −0.0796787 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.59274 | −0.188853 | −0.0944266 | − | 0.995532i | \(-0.530102\pi\) | ||||
−0.0944266 | + | 0.995532i | \(0.530102\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −64.7011 | −2.18231 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.9843 | 1.01020 | 0.505098 | − | 0.863062i | \(-0.331456\pi\) | ||||
0.505098 | + | 0.863062i | \(0.331456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.2756 | 0.951551 | 0.475775 | − | 0.879567i | \(-0.342168\pi\) | ||||
0.475775 | + | 0.879567i | \(0.342168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.707330 | 0.0237766 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.5686 | 0.892087 | 0.446044 | − | 0.895011i | \(-0.352833\pi\) | ||||
0.446044 | + | 0.895011i | \(0.352833\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.8941 | −0.432453 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.33800 | 0.0448248 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 41.7026 | 1.39552 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.8555 | −0.463139 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 112.838 | 3.76755 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.88737 | 0.196355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.916364 | 0.0305285 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 63.5866 | 2.11603 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.7508 | −0.723021 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.9310 | 0.728205 | 0.364103 | − | 0.931359i | \(-0.381376\pi\) | ||||
0.364103 | + | 0.931359i | \(0.381376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.14283 | −0.170577 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.1605 | 0.966130 | 0.483065 | − | 0.875585i | \(-0.339524\pi\) | ||||
0.483065 | + | 0.875585i | \(0.339524\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.34995 | −0.309438 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.8910 | −0.657576 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.34014 | 0.143324 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.8207 | 1.01668 | 0.508341 | − | 0.861156i | \(-0.330259\pi\) | ||||
0.508341 | + | 0.861156i | \(0.330259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −78.0096 | −2.57050 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.7338 | −0.550798 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.10459 | 0.200718 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.0873 | −1.48086 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.0881 | −1.51210 | −0.756050 | − | 0.654514i | \(-0.772873\pi\) | ||||
−0.756050 | + | 0.654514i | \(0.772873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.88927 | −0.160239 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.9193 | −1.27416 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.106116 | −0.00347038 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −41.5416 | −1.35711 | −0.678553 | − | 0.734551i | \(-0.737393\pi\) | ||||
−0.678553 | + | 0.734551i | \(0.737393\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 73.4054 | 2.39549 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.82853 | −0.320401 | −0.160201 | − | 0.987084i | \(-0.551214\pi\) | ||||
−0.160201 | + | 0.987084i | \(0.551214\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.9479 | 0.486769 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.99919 | 0.325274 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.1718 | 0.980453 | 0.490226 | − | 0.871595i | \(-0.336914\pi\) | ||||
0.490226 | + | 0.871595i | \(0.336914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.9337 | 0.776920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 56.6550 | 1.83716 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.4222 | 1.08265 | 0.541326 | − | 0.840813i | \(-0.317922\pi\) | ||||
0.541326 | + | 0.840813i | \(0.317922\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.89030 | −0.0935280 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.77909 | −0.122161 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.1344 | −1.03767 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.6445 | −0.730467 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.938372 | −0.0302386 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.0936 | −0.550263 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.1891 | 0.938659 | 0.469329 | − | 0.883023i | \(-0.344496\pi\) | ||||
0.469329 | + | 0.883023i | \(0.344496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.46006 | −0.0469039 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.2958 | −1.71034 | −0.855172 | − | 0.518344i | \(-0.826549\pi\) | ||||
−0.855172 | + | 0.518344i | \(0.826549\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.2848 | −0.618243 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.3973 | −0.461082 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.7273 | −1.23900 | −0.619499 | − | 0.784998i | \(-0.712664\pi\) | ||||
−0.619499 | + | 0.784998i | \(0.712664\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.65976 | 0.0850063 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −80.4814 | −2.56957 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59.0720 | 1.88410 | 0.942052 | − | 0.335468i | \(-0.108894\pi\) | ||||
0.942052 | + | 0.335468i | \(0.108894\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.8684 | 0.696785 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 79.7843 | 2.53956 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −76.9799 | −2.44782 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.7595 | −1.23124 | −0.615618 | − | 0.788045i | \(-0.711093\pi\) | ||||
−0.615618 | + | 0.788045i | \(0.711093\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −55.3410 | −1.75619 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.1016 | 0.320242 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4228 | −0.520115 | −0.260058 | − | 0.965593i | \(-0.583742\pi\) | ||||
−0.260058 | + | 0.965593i | \(0.583742\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25.8985 | −0.819394 |
(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 | 8020.2.a.f.1.4 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.f.1.4 | ✓ | 37 | 1.1 | even | 1 | trivial |