Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.19462 | −1.55183 | −0.775917 | − | 0.630835i | \(-0.782712\pi\) | ||||
−0.775917 | + | 0.630835i | \(0.782712\pi\) | |||||||
\(3\) | −2.47425 | −1.42851 | −0.714253 | − | 0.699887i | \(-0.753233\pi\) | ||||
−0.714253 | + | 0.699887i | \(0.753233\pi\) | |||||||
\(4\) | 2.81638 | 1.40819 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 5.43004 | 2.21680 | ||||||||
\(7\) | 3.64013 | 1.37584 | 0.687919 | − | 0.725787i | \(-0.258524\pi\) | ||||
0.687919 | + | 0.725787i | \(0.258524\pi\) | |||||||
\(8\) | −1.79164 | −0.633442 | ||||||||
\(9\) | 3.12189 | 1.04063 | ||||||||
\(10\) | 2.19462 | 0.694001 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −6.96841 | −2.01161 | ||||||||
\(13\) | −2.80642 | −0.778362 | −0.389181 | − | 0.921161i | \(-0.627242\pi\) | ||||
−0.389181 | + | 0.921161i | \(0.627242\pi\) | |||||||
\(14\) | −7.98871 | −2.13507 | ||||||||
\(15\) | 2.47425 | 0.638847 | ||||||||
\(16\) | −1.70077 | −0.425193 | ||||||||
\(17\) | 4.66302 | 1.13095 | 0.565475 | − | 0.824766i | \(-0.308693\pi\) | ||||
0.565475 | + | 0.824766i | \(0.308693\pi\) | |||||||
\(18\) | −6.85138 | −1.61489 | ||||||||
\(19\) | −4.34117 | −0.995933 | −0.497966 | − | 0.867196i | \(-0.665920\pi\) | ||||
−0.497966 | + | 0.867196i | \(0.665920\pi\) | |||||||
\(20\) | −2.81638 | −0.629761 | ||||||||
\(21\) | −9.00657 | −1.96539 | ||||||||
\(22\) | −2.19462 | −0.467896 | ||||||||
\(23\) | −5.74058 | −1.19699 | −0.598497 | − | 0.801125i | \(-0.704235\pi\) | ||||
−0.598497 | + | 0.801125i | \(0.704235\pi\) | |||||||
\(24\) | 4.43297 | 0.904876 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.15904 | 1.20789 | ||||||||
\(27\) | −0.301589 | −0.0580409 | ||||||||
\(28\) | 10.2520 | 1.93744 | ||||||||
\(29\) | 4.06241 | 0.754371 | 0.377185 | − | 0.926138i | \(-0.376892\pi\) | ||||
0.377185 | + | 0.926138i | \(0.376892\pi\) | |||||||
\(30\) | −5.43004 | −0.991385 | ||||||||
\(31\) | −4.88222 | −0.876872 | −0.438436 | − | 0.898762i | \(-0.644467\pi\) | ||||
−0.438436 | + | 0.898762i | \(0.644467\pi\) | |||||||
\(32\) | 7.31584 | 1.29327 | ||||||||
\(33\) | −2.47425 | −0.430711 | ||||||||
\(34\) | −10.2336 | −1.75505 | ||||||||
\(35\) | −3.64013 | −0.615294 | ||||||||
\(36\) | 8.79243 | 1.46540 | ||||||||
\(37\) | 9.96750 | 1.63865 | 0.819323 | − | 0.573332i | \(-0.194349\pi\) | ||||
0.819323 | + | 0.573332i | \(0.194349\pi\) | |||||||
\(38\) | 9.52724 | 1.54552 | ||||||||
\(39\) | 6.94378 | 1.11189 | ||||||||
\(40\) | 1.79164 | 0.283284 | ||||||||
\(41\) | −1.64330 | −0.256641 | −0.128320 | − | 0.991733i | \(-0.540959\pi\) | ||||
−0.128320 | + | 0.991733i | \(0.540959\pi\) | |||||||
\(42\) | 19.7660 | 3.04997 | ||||||||
\(43\) | 5.70250 | 0.869624 | 0.434812 | − | 0.900521i | \(-0.356815\pi\) | ||||
0.434812 | + | 0.900521i | \(0.356815\pi\) | |||||||
\(44\) | 2.81638 | 0.424585 | ||||||||
\(45\) | −3.12189 | −0.465384 | ||||||||
\(46\) | 12.5984 | 1.85754 | ||||||||
\(47\) | 12.0297 | 1.75471 | 0.877353 | − | 0.479845i | \(-0.159307\pi\) | ||||
0.877353 | + | 0.479845i | \(0.159307\pi\) | |||||||
\(48\) | 4.20812 | 0.607390 | ||||||||
\(49\) | 6.25052 | 0.892932 | ||||||||
\(50\) | −2.19462 | −0.310367 | ||||||||
\(51\) | −11.5375 | −1.61557 | ||||||||
\(52\) | −7.90395 | −1.09608 | ||||||||
\(53\) | −1.44311 | −0.198227 | −0.0991134 | − | 0.995076i | \(-0.531601\pi\) | ||||
−0.0991134 | + | 0.995076i | \(0.531601\pi\) | |||||||
\(54\) | 0.661876 | 0.0900699 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −6.52181 | −0.871514 | ||||||||
\(57\) | 10.7411 | 1.42270 | ||||||||
\(58\) | −8.91546 | −1.17066 | ||||||||
\(59\) | 3.08475 | 0.401600 | 0.200800 | − | 0.979632i | \(-0.435646\pi\) | ||||
0.200800 | + | 0.979632i | \(0.435646\pi\) | |||||||
\(60\) | 6.96841 | 0.899618 | ||||||||
\(61\) | −4.34581 | −0.556424 | −0.278212 | − | 0.960520i | \(-0.589742\pi\) | ||||
−0.278212 | + | 0.960520i | \(0.589742\pi\) | |||||||
\(62\) | 10.7146 | 1.36076 | ||||||||
\(63\) | 11.3641 | 1.43174 | ||||||||
\(64\) | −12.6540 | −1.58175 | ||||||||
\(65\) | 2.80642 | 0.348094 | ||||||||
\(66\) | 5.43004 | 0.668392 | ||||||||
\(67\) | −11.9606 | −1.46122 | −0.730609 | − | 0.682796i | \(-0.760764\pi\) | ||||
−0.730609 | + | 0.682796i | \(0.760764\pi\) | |||||||
\(68\) | 13.1328 | 1.59259 | ||||||||
\(69\) | 14.2036 | 1.70991 | ||||||||
\(70\) | 7.98871 | 0.954834 | ||||||||
\(71\) | 3.21937 | 0.382069 | 0.191035 | − | 0.981583i | \(-0.438816\pi\) | ||||
0.191035 | + | 0.981583i | \(0.438816\pi\) | |||||||
\(72\) | −5.59332 | −0.659179 | ||||||||
\(73\) | −1.00000 | −0.117041 | ||||||||
\(74\) | −21.8749 | −2.54291 | ||||||||
\(75\) | −2.47425 | −0.285701 | ||||||||
\(76\) | −12.2264 | −1.40246 | ||||||||
\(77\) | 3.64013 | 0.414831 | ||||||||
\(78\) | −15.2390 | −1.72548 | ||||||||
\(79\) | −0.195611 | −0.0220080 | −0.0110040 | − | 0.999939i | \(-0.503503\pi\) | ||||
−0.0110040 | + | 0.999939i | \(0.503503\pi\) | |||||||
\(80\) | 1.70077 | 0.190152 | ||||||||
\(81\) | −8.61947 | −0.957719 | ||||||||
\(82\) | 3.60643 | 0.398264 | ||||||||
\(83\) | −3.05395 | −0.335214 | −0.167607 | − | 0.985854i | \(-0.553604\pi\) | ||||
−0.167607 | + | 0.985854i | \(0.553604\pi\) | |||||||
\(84\) | −25.3659 | −2.76765 | ||||||||
\(85\) | −4.66302 | −0.505776 | ||||||||
\(86\) | −12.5149 | −1.34951 | ||||||||
\(87\) | −10.0514 | −1.07762 | ||||||||
\(88\) | −1.79164 | −0.190990 | ||||||||
\(89\) | 7.36450 | 0.780636 | 0.390318 | − | 0.920680i | \(-0.372365\pi\) | ||||
0.390318 | + | 0.920680i | \(0.372365\pi\) | |||||||
\(90\) | 6.85138 | 0.722199 | ||||||||
\(91\) | −10.2157 | −1.07090 | ||||||||
\(92\) | −16.1676 | −1.68559 | ||||||||
\(93\) | 12.0798 | 1.25262 | ||||||||
\(94\) | −26.4006 | −2.72301 | ||||||||
\(95\) | 4.34117 | 0.445395 | ||||||||
\(96\) | −18.1012 | −1.84744 | ||||||||
\(97\) | 12.4554 | 1.26466 | 0.632329 | − | 0.774700i | \(-0.282099\pi\) | ||||
0.632329 | + | 0.774700i | \(0.282099\pi\) | |||||||
\(98\) | −13.7175 | −1.38568 | ||||||||
\(99\) | 3.12189 | 0.313762 | ||||||||
\(100\) | 2.81638 | 0.281638 | ||||||||
\(101\) | −1.09557 | −0.109013 | −0.0545066 | − | 0.998513i | \(-0.517359\pi\) | ||||
−0.0545066 | + | 0.998513i | \(0.517359\pi\) | |||||||
\(102\) | 25.3204 | 2.50709 | ||||||||
\(103\) | −0.294190 | −0.0289874 | −0.0144937 | − | 0.999895i | \(-0.504614\pi\) | ||||
−0.0144937 | + | 0.999895i | \(0.504614\pi\) | |||||||
\(104\) | 5.02811 | 0.493047 | ||||||||
\(105\) | 9.00657 | 0.878951 | ||||||||
\(106\) | 3.16709 | 0.307615 | ||||||||
\(107\) | −9.35533 | −0.904414 | −0.452207 | − | 0.891913i | \(-0.649363\pi\) | ||||
−0.452207 | + | 0.891913i | \(0.649363\pi\) | |||||||
\(108\) | −0.849390 | −0.0817326 | ||||||||
\(109\) | −9.39473 | −0.899852 | −0.449926 | − | 0.893066i | \(-0.648550\pi\) | ||||
−0.449926 | + | 0.893066i | \(0.648550\pi\) | |||||||
\(110\) | 2.19462 | 0.209249 | ||||||||
\(111\) | −24.6620 | −2.34082 | ||||||||
\(112\) | −6.19102 | −0.584996 | ||||||||
\(113\) | 5.74075 | 0.540044 | 0.270022 | − | 0.962854i | \(-0.412969\pi\) | ||||
0.270022 | + | 0.962854i | \(0.412969\pi\) | |||||||
\(114\) | −23.5727 | −2.20779 | ||||||||
\(115\) | 5.74058 | 0.535312 | ||||||||
\(116\) | 11.4413 | 1.06230 | ||||||||
\(117\) | −8.76135 | −0.809987 | ||||||||
\(118\) | −6.76987 | −0.623217 | ||||||||
\(119\) | 16.9740 | 1.55600 | ||||||||
\(120\) | −4.43297 | −0.404673 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 9.53742 | 0.863477 | ||||||||
\(123\) | 4.06593 | 0.366613 | ||||||||
\(124\) | −13.7502 | −1.23480 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −24.9399 | −2.22182 | ||||||||
\(127\) | 14.7636 | 1.31006 | 0.655030 | − | 0.755603i | \(-0.272656\pi\) | ||||
0.655030 | + | 0.755603i | \(0.272656\pi\) | |||||||
\(128\) | 13.1391 | 1.16134 | ||||||||
\(129\) | −14.1094 | −1.24226 | ||||||||
\(130\) | −6.15904 | −0.540184 | ||||||||
\(131\) | −4.12655 | −0.360539 | −0.180269 | − | 0.983617i | \(-0.557697\pi\) | ||||
−0.180269 | + | 0.983617i | \(0.557697\pi\) | |||||||
\(132\) | −6.96841 | −0.606522 | ||||||||
\(133\) | −15.8024 | −1.37024 | ||||||||
\(134\) | 26.2490 | 2.26757 | ||||||||
\(135\) | 0.301589 | 0.0259567 | ||||||||
\(136\) | −8.35448 | −0.716391 | ||||||||
\(137\) | 0.921093 | 0.0786943 | 0.0393472 | − | 0.999226i | \(-0.487472\pi\) | ||||
0.0393472 | + | 0.999226i | \(0.487472\pi\) | |||||||
\(138\) | −31.1716 | −2.65350 | ||||||||
\(139\) | −6.81597 | −0.578123 | −0.289061 | − | 0.957311i | \(-0.593343\pi\) | ||||
−0.289061 | + | 0.957311i | \(0.593343\pi\) | |||||||
\(140\) | −10.2520 | −0.866450 | ||||||||
\(141\) | −29.7643 | −2.50661 | ||||||||
\(142\) | −7.06532 | −0.592908 | ||||||||
\(143\) | −2.80642 | −0.234685 | ||||||||
\(144\) | −5.30962 | −0.442468 | ||||||||
\(145\) | −4.06241 | −0.337365 | ||||||||
\(146\) | 2.19462 | 0.181628 | ||||||||
\(147\) | −15.4653 | −1.27556 | ||||||||
\(148\) | 28.0722 | 2.30752 | ||||||||
\(149\) | −3.85111 | −0.315495 | −0.157748 | − | 0.987479i | \(-0.550423\pi\) | ||||
−0.157748 | + | 0.987479i | \(0.550423\pi\) | |||||||
\(150\) | 5.43004 | 0.443361 | ||||||||
\(151\) | −2.47794 | −0.201652 | −0.100826 | − | 0.994904i | \(-0.532149\pi\) | ||||
−0.100826 | + | 0.994904i | \(0.532149\pi\) | |||||||
\(152\) | 7.77783 | 0.630866 | ||||||||
\(153\) | 14.5575 | 1.17690 | ||||||||
\(154\) | −7.98871 | −0.643749 | ||||||||
\(155\) | 4.88222 | 0.392149 | ||||||||
\(156\) | 19.5563 | 1.56576 | ||||||||
\(157\) | −17.7582 | −1.41726 | −0.708629 | − | 0.705581i | \(-0.750686\pi\) | ||||
−0.708629 | + | 0.705581i | \(0.750686\pi\) | |||||||
\(158\) | 0.429293 | 0.0341527 | ||||||||
\(159\) | 3.57061 | 0.283168 | ||||||||
\(160\) | −7.31584 | −0.578368 | ||||||||
\(161\) | −20.8964 | −1.64687 | ||||||||
\(162\) | 18.9165 | 1.48622 | ||||||||
\(163\) | −6.72566 | −0.526795 | −0.263397 | − | 0.964687i | \(-0.584843\pi\) | ||||
−0.263397 | + | 0.964687i | \(0.584843\pi\) | |||||||
\(164\) | −4.62816 | −0.361399 | ||||||||
\(165\) | 2.47425 | 0.192620 | ||||||||
\(166\) | 6.70227 | 0.520197 | ||||||||
\(167\) | 11.4657 | 0.887239 | 0.443620 | − | 0.896215i | \(-0.353694\pi\) | ||||
0.443620 | + | 0.896215i | \(0.353694\pi\) | |||||||
\(168\) | 16.1366 | 1.24496 | ||||||||
\(169\) | −5.12399 | −0.394153 | ||||||||
\(170\) | 10.2336 | 0.784880 | ||||||||
\(171\) | −13.5527 | −1.03640 | ||||||||
\(172\) | 16.0604 | 1.22459 | ||||||||
\(173\) | 21.0607 | 1.60122 | 0.800608 | − | 0.599188i | \(-0.204510\pi\) | ||||
0.800608 | + | 0.599188i | \(0.204510\pi\) | |||||||
\(174\) | 22.0591 | 1.67229 | ||||||||
\(175\) | 3.64013 | 0.275168 | ||||||||
\(176\) | −1.70077 | −0.128200 | ||||||||
\(177\) | −7.63243 | −0.573688 | ||||||||
\(178\) | −16.1623 | −1.21142 | ||||||||
\(179\) | −8.24694 | −0.616406 | −0.308203 | − | 0.951321i | \(-0.599728\pi\) | ||||
−0.308203 | + | 0.951321i | \(0.599728\pi\) | |||||||
\(180\) | −8.79243 | −0.655349 | ||||||||
\(181\) | 20.1422 | 1.49716 | 0.748580 | − | 0.663044i | \(-0.230736\pi\) | ||||
0.748580 | + | 0.663044i | \(0.230736\pi\) | |||||||
\(182\) | 22.4197 | 1.66186 | ||||||||
\(183\) | 10.7526 | 0.794855 | ||||||||
\(184\) | 10.2851 | 0.758226 | ||||||||
\(185\) | −9.96750 | −0.732825 | ||||||||
\(186\) | −26.5106 | −1.94385 | ||||||||
\(187\) | 4.66302 | 0.340994 | ||||||||
\(188\) | 33.8801 | 2.47096 | ||||||||
\(189\) | −1.09782 | −0.0798549 | ||||||||
\(190\) | −9.52724 | −0.691179 | ||||||||
\(191\) | 10.0721 | 0.728792 | 0.364396 | − | 0.931244i | \(-0.381275\pi\) | ||||
0.364396 | + | 0.931244i | \(0.381275\pi\) | |||||||
\(192\) | 31.3091 | 2.25954 | ||||||||
\(193\) | −18.6235 | −1.34055 | −0.670275 | − | 0.742113i | \(-0.733824\pi\) | ||||
−0.670275 | + | 0.742113i | \(0.733824\pi\) | |||||||
\(194\) | −27.3350 | −1.96254 | ||||||||
\(195\) | −6.94378 | −0.497254 | ||||||||
\(196\) | 17.6038 | 1.25742 | ||||||||
\(197\) | −4.27797 | −0.304793 | −0.152396 | − | 0.988319i | \(-0.548699\pi\) | ||||
−0.152396 | + | 0.988319i | \(0.548699\pi\) | |||||||
\(198\) | −6.85138 | −0.486906 | ||||||||
\(199\) | 6.41209 | 0.454541 | 0.227270 | − | 0.973832i | \(-0.427020\pi\) | ||||
0.227270 | + | 0.973832i | \(0.427020\pi\) | |||||||
\(200\) | −1.79164 | −0.126688 | ||||||||
\(201\) | 29.5934 | 2.08736 | ||||||||
\(202\) | 2.40436 | 0.169170 | ||||||||
\(203\) | 14.7877 | 1.03789 | ||||||||
\(204\) | −32.4939 | −2.27503 | ||||||||
\(205\) | 1.64330 | 0.114773 | ||||||||
\(206\) | 0.645636 | 0.0449836 | ||||||||
\(207\) | −17.9215 | −1.24563 | ||||||||
\(208\) | 4.77308 | 0.330954 | ||||||||
\(209\) | −4.34117 | −0.300285 | ||||||||
\(210\) | −19.7660 | −1.36399 | ||||||||
\(211\) | −13.7589 | −0.947201 | −0.473600 | − | 0.880740i | \(-0.657046\pi\) | ||||
−0.473600 | + | 0.880740i | \(0.657046\pi\) | |||||||
\(212\) | −4.06435 | −0.279141 | ||||||||
\(213\) | −7.96552 | −0.545788 | ||||||||
\(214\) | 20.5314 | 1.40350 | ||||||||
\(215\) | −5.70250 | −0.388908 | ||||||||
\(216\) | 0.540341 | 0.0367655 | ||||||||
\(217\) | −17.7719 | −1.20643 | ||||||||
\(218\) | 20.6179 | 1.39642 | ||||||||
\(219\) | 2.47425 | 0.167194 | ||||||||
\(220\) | −2.81638 | −0.189880 | ||||||||
\(221\) | −13.0864 | −0.880288 | ||||||||
\(222\) | 54.1239 | 3.63256 | ||||||||
\(223\) | 1.61027 | 0.107831 | 0.0539157 | − | 0.998545i | \(-0.482830\pi\) | ||||
0.0539157 | + | 0.998545i | \(0.482830\pi\) | |||||||
\(224\) | 26.6306 | 1.77933 | ||||||||
\(225\) | 3.12189 | 0.208126 | ||||||||
\(226\) | −12.5988 | −0.838059 | ||||||||
\(227\) | 10.6625 | 0.707697 | 0.353848 | − | 0.935303i | \(-0.384873\pi\) | ||||
0.353848 | + | 0.935303i | \(0.384873\pi\) | |||||||
\(228\) | 30.2511 | 2.00343 | ||||||||
\(229\) | −14.1419 | −0.934523 | −0.467262 | − | 0.884119i | \(-0.654759\pi\) | ||||
−0.467262 | + | 0.884119i | \(0.654759\pi\) | |||||||
\(230\) | −12.5984 | −0.830715 | ||||||||
\(231\) | −9.00657 | −0.592589 | ||||||||
\(232\) | −7.27839 | −0.477850 | ||||||||
\(233\) | −10.0006 | −0.655160 | −0.327580 | − | 0.944824i | \(-0.606233\pi\) | ||||
−0.327580 | + | 0.944824i | \(0.606233\pi\) | |||||||
\(234\) | 19.2279 | 1.25697 | ||||||||
\(235\) | −12.0297 | −0.784729 | ||||||||
\(236\) | 8.68782 | 0.565529 | ||||||||
\(237\) | 0.483990 | 0.0314385 | ||||||||
\(238\) | −37.2516 | −2.41466 | ||||||||
\(239\) | −15.9358 | −1.03080 | −0.515401 | − | 0.856949i | \(-0.672357\pi\) | ||||
−0.515401 | + | 0.856949i | \(0.672357\pi\) | |||||||
\(240\) | −4.20812 | −0.271633 | ||||||||
\(241\) | −9.68288 | −0.623729 | −0.311865 | − | 0.950127i | \(-0.600954\pi\) | ||||
−0.311865 | + | 0.950127i | \(0.600954\pi\) | |||||||
\(242\) | −2.19462 | −0.141076 | ||||||||
\(243\) | 22.2314 | 1.42615 | ||||||||
\(244\) | −12.2394 | −0.783550 | ||||||||
\(245\) | −6.25052 | −0.399331 | ||||||||
\(246\) | −8.92320 | −0.568922 | ||||||||
\(247\) | 12.1832 | 0.775196 | ||||||||
\(248\) | 8.74719 | 0.555447 | ||||||||
\(249\) | 7.55621 | 0.478856 | ||||||||
\(250\) | 2.19462 | 0.138800 | ||||||||
\(251\) | 20.1970 | 1.27483 | 0.637413 | − | 0.770523i | \(-0.280005\pi\) | ||||
0.637413 | + | 0.770523i | \(0.280005\pi\) | |||||||
\(252\) | 32.0055 | 2.01616 | ||||||||
\(253\) | −5.74058 | −0.360907 | ||||||||
\(254\) | −32.4006 | −2.03300 | ||||||||
\(255\) | 11.5375 | 0.722504 | ||||||||
\(256\) | −3.52736 | −0.220460 | ||||||||
\(257\) | 17.1357 | 1.06890 | 0.534448 | − | 0.845201i | \(-0.320519\pi\) | ||||
0.534448 | + | 0.845201i | \(0.320519\pi\) | |||||||
\(258\) | 30.9648 | 1.92779 | ||||||||
\(259\) | 36.2829 | 2.25451 | ||||||||
\(260\) | 7.90395 | 0.490182 | ||||||||
\(261\) | 12.6824 | 0.785021 | ||||||||
\(262\) | 9.05624 | 0.559496 | ||||||||
\(263\) | 27.0099 | 1.66550 | 0.832752 | − | 0.553647i | \(-0.186764\pi\) | ||||
0.832752 | + | 0.553647i | \(0.186764\pi\) | |||||||
\(264\) | 4.43297 | 0.272830 | ||||||||
\(265\) | 1.44311 | 0.0886497 | ||||||||
\(266\) | 34.6804 | 2.12639 | ||||||||
\(267\) | −18.2216 | −1.11514 | ||||||||
\(268\) | −33.6855 | −2.05767 | ||||||||
\(269\) | 9.73801 | 0.593737 | 0.296868 | − | 0.954918i | \(-0.404058\pi\) | ||||
0.296868 | + | 0.954918i | \(0.404058\pi\) | |||||||
\(270\) | −0.661876 | −0.0402805 | ||||||||
\(271\) | 6.01256 | 0.365237 | 0.182619 | − | 0.983184i | \(-0.441543\pi\) | ||||
0.182619 | + | 0.983184i | \(0.441543\pi\) | |||||||
\(272\) | −7.93073 | −0.480871 | ||||||||
\(273\) | 25.2762 | 1.52979 | ||||||||
\(274\) | −2.02145 | −0.122121 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 40.0027 | 2.40788 | ||||||||
\(277\) | −15.5173 | −0.932344 | −0.466172 | − | 0.884694i | \(-0.654367\pi\) | ||||
−0.466172 | + | 0.884694i | \(0.654367\pi\) | |||||||
\(278\) | 14.9585 | 0.897151 | ||||||||
\(279\) | −15.2417 | −0.912499 | ||||||||
\(280\) | 6.52181 | 0.389753 | ||||||||
\(281\) | 20.5454 | 1.22563 | 0.612817 | − | 0.790225i | \(-0.290036\pi\) | ||||
0.612817 | + | 0.790225i | \(0.290036\pi\) | |||||||
\(282\) | 65.3216 | 3.88984 | ||||||||
\(283\) | −7.51200 | −0.446542 | −0.223271 | − | 0.974756i | \(-0.571674\pi\) | ||||
−0.223271 | + | 0.974756i | \(0.571674\pi\) | |||||||
\(284\) | 9.06697 | 0.538026 | ||||||||
\(285\) | −10.7411 | −0.636249 | ||||||||
\(286\) | 6.15904 | 0.364192 | ||||||||
\(287\) | −5.98183 | −0.353096 | ||||||||
\(288\) | 22.8393 | 1.34582 | ||||||||
\(289\) | 4.74380 | 0.279047 | ||||||||
\(290\) | 8.91546 | 0.523534 | ||||||||
\(291\) | −30.8178 | −1.80657 | ||||||||
\(292\) | −2.81638 | −0.164816 | ||||||||
\(293\) | 0.356672 | 0.0208370 | 0.0104185 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104185 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(294\) | 33.9406 | 1.97946 | ||||||||
\(295\) | −3.08475 | −0.179601 | ||||||||
\(296\) | −17.8582 | −1.03799 | ||||||||
\(297\) | −0.301589 | −0.0175000 | ||||||||
\(298\) | 8.45174 | 0.489596 | ||||||||
\(299\) | 16.1105 | 0.931694 | ||||||||
\(300\) | −6.96841 | −0.402321 | ||||||||
\(301\) | 20.7578 | 1.19646 | ||||||||
\(302\) | 5.43815 | 0.312930 | ||||||||
\(303\) | 2.71071 | 0.155726 | ||||||||
\(304\) | 7.38334 | 0.423463 | ||||||||
\(305\) | 4.34581 | 0.248840 | ||||||||
\(306\) | −31.9482 | −1.82635 | ||||||||
\(307\) | −8.18397 | −0.467084 | −0.233542 | − | 0.972347i | \(-0.575032\pi\) | ||||
−0.233542 | + | 0.972347i | \(0.575032\pi\) | |||||||
\(308\) | 10.2520 | 0.584160 | ||||||||
\(309\) | 0.727898 | 0.0414086 | ||||||||
\(310\) | −10.7146 | −0.608550 | ||||||||
\(311\) | −0.203576 | −0.0115438 | −0.00577188 | − | 0.999983i | \(-0.501837\pi\) | ||||
−0.00577188 | + | 0.999983i | \(0.501837\pi\) | |||||||
\(312\) | −12.4408 | −0.704320 | ||||||||
\(313\) | −10.2880 | −0.581514 | −0.290757 | − | 0.956797i | \(-0.593907\pi\) | ||||
−0.290757 | + | 0.956797i | \(0.593907\pi\) | |||||||
\(314\) | 38.9726 | 2.19935 | ||||||||
\(315\) | −11.3641 | −0.640293 | ||||||||
\(316\) | −0.550915 | −0.0309914 | ||||||||
\(317\) | 22.4822 | 1.26273 | 0.631363 | − | 0.775487i | \(-0.282496\pi\) | ||||
0.631363 | + | 0.775487i | \(0.282496\pi\) | |||||||
\(318\) | −7.83616 | −0.439430 | ||||||||
\(319\) | 4.06241 | 0.227451 | ||||||||
\(320\) | 12.6540 | 0.707379 | ||||||||
\(321\) | 23.1474 | 1.29196 | ||||||||
\(322\) | 45.8598 | 2.55567 | ||||||||
\(323\) | −20.2430 | −1.12635 | ||||||||
\(324\) | −24.2757 | −1.34865 | ||||||||
\(325\) | −2.80642 | −0.155672 | ||||||||
\(326\) | 14.7603 | 0.817498 | ||||||||
\(327\) | 23.2449 | 1.28544 | ||||||||
\(328\) | 2.94421 | 0.162567 | ||||||||
\(329\) | 43.7895 | 2.41419 | ||||||||
\(330\) | −5.43004 | −0.298914 | ||||||||
\(331\) | −7.78673 | −0.427997 | −0.213999 | − | 0.976834i | \(-0.568649\pi\) | ||||
−0.213999 | + | 0.976834i | \(0.568649\pi\) | |||||||
\(332\) | −8.60107 | −0.472045 | ||||||||
\(333\) | 31.1174 | 1.70523 | ||||||||
\(334\) | −25.1628 | −1.37685 | ||||||||
\(335\) | 11.9606 | 0.653476 | ||||||||
\(336\) | 15.3181 | 0.835671 | ||||||||
\(337\) | 17.8175 | 0.970580 | 0.485290 | − | 0.874353i | \(-0.338714\pi\) | ||||
0.485290 | + | 0.874353i | \(0.338714\pi\) | |||||||
\(338\) | 11.2452 | 0.611660 | ||||||||
\(339\) | −14.2040 | −0.771457 | ||||||||
\(340\) | −13.1328 | −0.712228 | ||||||||
\(341\) | −4.88222 | −0.264387 | ||||||||
\(342\) | 29.7430 | 1.60832 | ||||||||
\(343\) | −2.72820 | −0.147309 | ||||||||
\(344\) | −10.2169 | −0.550856 | ||||||||
\(345\) | −14.2036 | −0.764696 | ||||||||
\(346\) | −46.2204 | −2.48482 | ||||||||
\(347\) | −17.3513 | −0.931465 | −0.465732 | − | 0.884926i | \(-0.654209\pi\) | ||||
−0.465732 | + | 0.884926i | \(0.654209\pi\) | |||||||
\(348\) | −28.3085 | −1.51750 | ||||||||
\(349\) | −2.02662 | −0.108483 | −0.0542413 | − | 0.998528i | \(-0.517274\pi\) | ||||
−0.0542413 | + | 0.998528i | \(0.517274\pi\) | |||||||
\(350\) | −7.98871 | −0.427015 | ||||||||
\(351\) | 0.846387 | 0.0451768 | ||||||||
\(352\) | 7.31584 | 0.389936 | ||||||||
\(353\) | −9.44223 | −0.502559 | −0.251280 | − | 0.967915i | \(-0.580851\pi\) | ||||
−0.251280 | + | 0.967915i | \(0.580851\pi\) | |||||||
\(354\) | 16.7503 | 0.890269 | ||||||||
\(355\) | −3.21937 | −0.170867 | ||||||||
\(356\) | 20.7412 | 1.09928 | ||||||||
\(357\) | −41.9978 | −2.22276 | ||||||||
\(358\) | 18.0989 | 0.956559 | ||||||||
\(359\) | −13.5248 | −0.713813 | −0.356907 | − | 0.934140i | \(-0.616169\pi\) | ||||
−0.356907 | + | 0.934140i | \(0.616169\pi\) | |||||||
\(360\) | 5.59332 | 0.294794 | ||||||||
\(361\) | −0.154232 | −0.00811746 | ||||||||
\(362\) | −44.2047 | −2.32334 | ||||||||
\(363\) | −2.47425 | −0.129864 | ||||||||
\(364\) | −28.7714 | −1.50803 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −23.5979 | −1.23348 | ||||||||
\(367\) | −18.8315 | −0.982999 | −0.491499 | − | 0.870878i | \(-0.663551\pi\) | ||||
−0.491499 | + | 0.870878i | \(0.663551\pi\) | |||||||
\(368\) | 9.76341 | 0.508953 | ||||||||
\(369\) | −5.13021 | −0.267068 | ||||||||
\(370\) | 21.8749 | 1.13722 | ||||||||
\(371\) | −5.25311 | −0.272728 | ||||||||
\(372\) | 34.0213 | 1.76392 | ||||||||
\(373\) | 32.9971 | 1.70852 | 0.854262 | − | 0.519842i | \(-0.174009\pi\) | ||||
0.854262 | + | 0.519842i | \(0.174009\pi\) | |||||||
\(374\) | −10.2336 | −0.529166 | ||||||||
\(375\) | 2.47425 | 0.127769 | ||||||||
\(376\) | −21.5529 | −1.11150 | ||||||||
\(377\) | −11.4008 | −0.587173 | ||||||||
\(378\) | 2.40931 | 0.123922 | ||||||||
\(379\) | 27.7488 | 1.42536 | 0.712680 | − | 0.701489i | \(-0.247481\pi\) | ||||
0.712680 | + | 0.701489i | \(0.247481\pi\) | |||||||
\(380\) | 12.2264 | 0.627200 | ||||||||
\(381\) | −36.5289 | −1.87143 | ||||||||
\(382\) | −22.1045 | −1.13096 | ||||||||
\(383\) | −4.45851 | −0.227819 | −0.113910 | − | 0.993491i | \(-0.536337\pi\) | ||||
−0.113910 | + | 0.993491i | \(0.536337\pi\) | |||||||
\(384\) | −32.5093 | −1.65898 | ||||||||
\(385\) | −3.64013 | −0.185518 | ||||||||
\(386\) | 40.8716 | 2.08031 | ||||||||
\(387\) | 17.8026 | 0.904957 | ||||||||
\(388\) | 35.0792 | 1.78088 | ||||||||
\(389\) | −29.5097 | −1.49620 | −0.748101 | − | 0.663584i | \(-0.769034\pi\) | ||||
−0.748101 | + | 0.663584i | \(0.769034\pi\) | |||||||
\(390\) | 15.2390 | 0.771656 | ||||||||
\(391\) | −26.7685 | −1.35374 | ||||||||
\(392\) | −11.1987 | −0.565620 | ||||||||
\(393\) | 10.2101 | 0.515032 | ||||||||
\(394\) | 9.38854 | 0.472988 | ||||||||
\(395\) | 0.195611 | 0.00984226 | ||||||||
\(396\) | 8.79243 | 0.441836 | ||||||||
\(397\) | 1.85205 | 0.0929517 | 0.0464759 | − | 0.998919i | \(-0.485201\pi\) | ||||
0.0464759 | + | 0.998919i | \(0.485201\pi\) | |||||||
\(398\) | −14.0721 | −0.705372 | ||||||||
\(399\) | 39.0991 | 1.95740 | ||||||||
\(400\) | −1.70077 | −0.0850385 | ||||||||
\(401\) | 23.0963 | 1.15338 | 0.576688 | − | 0.816965i | \(-0.304345\pi\) | ||||
0.576688 | + | 0.816965i | \(0.304345\pi\) | |||||||
\(402\) | −64.9464 | −3.23923 | ||||||||
\(403\) | 13.7016 | 0.682523 | ||||||||
\(404\) | −3.08554 | −0.153511 | ||||||||
\(405\) | 8.61947 | 0.428305 | ||||||||
\(406\) | −32.4534 | −1.61064 | ||||||||
\(407\) | 9.96750 | 0.494070 | ||||||||
\(408\) | 20.6710 | 1.02337 | ||||||||
\(409\) | 4.35359 | 0.215271 | 0.107635 | − | 0.994190i | \(-0.465672\pi\) | ||||
0.107635 | + | 0.994190i | \(0.465672\pi\) | |||||||
\(410\) | −3.60643 | −0.178109 | ||||||||
\(411\) | −2.27901 | −0.112415 | ||||||||
\(412\) | −0.828550 | −0.0408197 | ||||||||
\(413\) | 11.2289 | 0.552537 | ||||||||
\(414\) | 39.3309 | 1.93301 | ||||||||
\(415\) | 3.05395 | 0.149912 | ||||||||
\(416\) | −20.5313 | −1.00663 | ||||||||
\(417\) | 16.8644 | 0.825852 | ||||||||
\(418\) | 9.52724 | 0.465993 | ||||||||
\(419\) | −8.52259 | −0.416356 | −0.208178 | − | 0.978091i | \(-0.566753\pi\) | ||||
−0.208178 | + | 0.978091i | \(0.566753\pi\) | |||||||
\(420\) | 25.3659 | 1.23773 | ||||||||
\(421\) | 27.5755 | 1.34395 | 0.671974 | − | 0.740575i | \(-0.265447\pi\) | ||||
0.671974 | + | 0.740575i | \(0.265447\pi\) | |||||||
\(422\) | 30.1956 | 1.46990 | ||||||||
\(423\) | 37.5553 | 1.82600 | ||||||||
\(424\) | 2.58554 | 0.125565 | ||||||||
\(425\) | 4.66302 | 0.226190 | ||||||||
\(426\) | 17.4813 | 0.846973 | ||||||||
\(427\) | −15.8193 | −0.765549 | ||||||||
\(428\) | −26.3481 | −1.27359 | ||||||||
\(429\) | 6.94378 | 0.335249 | ||||||||
\(430\) | 12.5149 | 0.603520 | ||||||||
\(431\) | −4.24124 | −0.204293 | −0.102147 | − | 0.994769i | \(-0.532571\pi\) | ||||
−0.102147 | + | 0.994769i | \(0.532571\pi\) | |||||||
\(432\) | 0.512934 | 0.0246786 | ||||||||
\(433\) | 20.8649 | 1.00270 | 0.501351 | − | 0.865244i | \(-0.332836\pi\) | ||||
0.501351 | + | 0.865244i | \(0.332836\pi\) | |||||||
\(434\) | 39.0026 | 1.87219 | ||||||||
\(435\) | 10.0514 | 0.481928 | ||||||||
\(436\) | −26.4591 | −1.26716 | ||||||||
\(437\) | 24.9208 | 1.19213 | ||||||||
\(438\) | −5.43004 | −0.259457 | ||||||||
\(439\) | 40.6450 | 1.93988 | 0.969940 | − | 0.243343i | \(-0.0782441\pi\) | ||||
0.969940 | + | 0.243343i | \(0.0782441\pi\) | |||||||
\(440\) | 1.79164 | 0.0854133 | ||||||||
\(441\) | 19.5134 | 0.929212 | ||||||||
\(442\) | 28.7198 | 1.36606 | ||||||||
\(443\) | 17.3800 | 0.825750 | 0.412875 | − | 0.910788i | \(-0.364525\pi\) | ||||
0.412875 | + | 0.910788i | \(0.364525\pi\) | |||||||
\(444\) | −69.4576 | −3.29631 | ||||||||
\(445\) | −7.36450 | −0.349111 | ||||||||
\(446\) | −3.53393 | −0.167337 | ||||||||
\(447\) | 9.52859 | 0.450687 | ||||||||
\(448\) | −46.0621 | −2.17623 | ||||||||
\(449\) | −4.04946 | −0.191106 | −0.0955530 | − | 0.995424i | \(-0.530462\pi\) | ||||
−0.0955530 | + | 0.995424i | \(0.530462\pi\) | |||||||
\(450\) | −6.85138 | −0.322977 | ||||||||
\(451\) | −1.64330 | −0.0773801 | ||||||||
\(452\) | 16.1681 | 0.760485 | ||||||||
\(453\) | 6.13103 | 0.288061 | ||||||||
\(454\) | −23.4002 | −1.09823 | ||||||||
\(455\) | 10.2157 | 0.478921 | ||||||||
\(456\) | −19.2443 | −0.901195 | ||||||||
\(457\) | 1.55809 | 0.0728842 | 0.0364421 | − | 0.999336i | \(-0.488398\pi\) | ||||
0.0364421 | + | 0.999336i | \(0.488398\pi\) | |||||||
\(458\) | 31.0362 | 1.45023 | ||||||||
\(459\) | −1.40632 | −0.0656413 | ||||||||
\(460\) | 16.1676 | 0.753820 | ||||||||
\(461\) | 36.6604 | 1.70745 | 0.853723 | − | 0.520728i | \(-0.174339\pi\) | ||||
0.853723 | + | 0.520728i | \(0.174339\pi\) | |||||||
\(462\) | 19.7660 | 0.919599 | ||||||||
\(463\) | −33.4585 | −1.55495 | −0.777474 | − | 0.628915i | \(-0.783500\pi\) | ||||
−0.777474 | + | 0.628915i | \(0.783500\pi\) | |||||||
\(464\) | −6.90923 | −0.320753 | ||||||||
\(465\) | −12.0798 | −0.560187 | ||||||||
\(466\) | 21.9475 | 1.01670 | ||||||||
\(467\) | −24.1951 | −1.11962 | −0.559809 | − | 0.828622i | \(-0.689125\pi\) | ||||
−0.559809 | + | 0.828622i | \(0.689125\pi\) | |||||||
\(468\) | −24.6753 | −1.14061 | ||||||||
\(469\) | −43.5380 | −2.01040 | ||||||||
\(470\) | 26.4006 | 1.21777 | ||||||||
\(471\) | 43.9382 | 2.02456 | ||||||||
\(472\) | −5.52677 | −0.254390 | ||||||||
\(473\) | 5.70250 | 0.262201 | ||||||||
\(474\) | −1.06218 | −0.0487874 | ||||||||
\(475\) | −4.34117 | −0.199187 | ||||||||
\(476\) | 47.8052 | 2.19115 | ||||||||
\(477\) | −4.50524 | −0.206281 | ||||||||
\(478\) | 34.9731 | 1.59963 | ||||||||
\(479\) | 23.6600 | 1.08105 | 0.540527 | − | 0.841326i | \(-0.318225\pi\) | ||||
0.540527 | + | 0.841326i | \(0.318225\pi\) | |||||||
\(480\) | 18.1012 | 0.826202 | ||||||||
\(481\) | −27.9730 | −1.27546 | ||||||||
\(482\) | 21.2503 | 0.967924 | ||||||||
\(483\) | 51.7029 | 2.35256 | ||||||||
\(484\) | 2.81638 | 0.128017 | ||||||||
\(485\) | −12.4554 | −0.565572 | ||||||||
\(486\) | −48.7897 | −2.21315 | ||||||||
\(487\) | 18.7526 | 0.849763 | 0.424881 | − | 0.905249i | \(-0.360316\pi\) | ||||
0.424881 | + | 0.905249i | \(0.360316\pi\) | |||||||
\(488\) | 7.78614 | 0.352462 | ||||||||
\(489\) | 16.6409 | 0.752530 | ||||||||
\(490\) | 13.7175 | 0.619696 | ||||||||
\(491\) | −22.0103 | −0.993311 | −0.496656 | − | 0.867948i | \(-0.665439\pi\) | ||||
−0.496656 | + | 0.867948i | \(0.665439\pi\) | |||||||
\(492\) | 11.4512 | 0.516260 | ||||||||
\(493\) | 18.9431 | 0.853155 | ||||||||
\(494\) | −26.7375 | −1.20298 | ||||||||
\(495\) | −3.12189 | −0.140319 | ||||||||
\(496\) | 8.30353 | 0.372839 | ||||||||
\(497\) | 11.7189 | 0.525666 | ||||||||
\(498\) | −16.5831 | −0.743104 | ||||||||
\(499\) | −31.3218 | −1.40216 | −0.701078 | − | 0.713085i | \(-0.747297\pi\) | ||||
−0.701078 | + | 0.713085i | \(0.747297\pi\) | |||||||
\(500\) | −2.81638 | −0.125952 | ||||||||
\(501\) | −28.3689 | −1.26743 | ||||||||
\(502\) | −44.3249 | −1.97832 | ||||||||
\(503\) | 29.9817 | 1.33682 | 0.668409 | − | 0.743794i | \(-0.266975\pi\) | ||||
0.668409 | + | 0.743794i | \(0.266975\pi\) | |||||||
\(504\) | −20.3604 | −0.906924 | ||||||||
\(505\) | 1.09557 | 0.0487522 | ||||||||
\(506\) | 12.5984 | 0.560068 | ||||||||
\(507\) | 12.6780 | 0.563050 | ||||||||
\(508\) | 41.5800 | 1.84481 | ||||||||
\(509\) | 37.8795 | 1.67898 | 0.839491 | − | 0.543374i | \(-0.182854\pi\) | ||||
0.839491 | + | 0.543374i | \(0.182854\pi\) | |||||||
\(510\) | −25.3204 | −1.12121 | ||||||||
\(511\) | −3.64013 | −0.161030 | ||||||||
\(512\) | −18.5369 | −0.819224 | ||||||||
\(513\) | 1.30925 | 0.0578049 | ||||||||
\(514\) | −37.6065 | −1.65875 | ||||||||
\(515\) | 0.294190 | 0.0129635 | ||||||||
\(516\) | −39.7374 | −1.74934 | ||||||||
\(517\) | 12.0297 | 0.529064 | ||||||||
\(518\) | −79.6275 | −3.49863 | ||||||||
\(519\) | −52.1094 | −2.28735 | ||||||||
\(520\) | −5.02811 | −0.220497 | ||||||||
\(521\) | 23.3971 | 1.02505 | 0.512524 | − | 0.858673i | \(-0.328711\pi\) | ||||
0.512524 | + | 0.858673i | \(0.328711\pi\) | |||||||
\(522\) | −27.8331 | −1.21822 | ||||||||
\(523\) | −16.3607 | −0.715404 | −0.357702 | − | 0.933836i | \(-0.616440\pi\) | ||||
−0.357702 | + | 0.933836i | \(0.616440\pi\) | |||||||
\(524\) | −11.6219 | −0.507707 | ||||||||
\(525\) | −9.00657 | −0.393079 | ||||||||
\(526\) | −59.2767 | −2.58459 | ||||||||
\(527\) | −22.7659 | −0.991698 | ||||||||
\(528\) | 4.20812 | 0.183135 | ||||||||
\(529\) | 9.95424 | 0.432793 | ||||||||
\(530\) | −3.16709 | −0.137570 | ||||||||
\(531\) | 9.63025 | 0.417917 | ||||||||
\(532\) | −44.5056 | −1.92956 | ||||||||
\(533\) | 4.61180 | 0.199759 | ||||||||
\(534\) | 39.9895 | 1.73052 | ||||||||
\(535\) | 9.35533 | 0.404466 | ||||||||
\(536\) | 21.4291 | 0.925596 | ||||||||
\(537\) | 20.4050 | 0.880539 | ||||||||
\(538\) | −21.3713 | −0.921381 | ||||||||
\(539\) | 6.25052 | 0.269229 | ||||||||
\(540\) | 0.849390 | 0.0365519 | ||||||||
\(541\) | 6.15317 | 0.264545 | 0.132273 | − | 0.991213i | \(-0.457773\pi\) | ||||
0.132273 | + | 0.991213i | \(0.457773\pi\) | |||||||
\(542\) | −13.1953 | −0.566788 | ||||||||
\(543\) | −49.8368 | −2.13870 | ||||||||
\(544\) | 34.1139 | 1.46262 | ||||||||
\(545\) | 9.39473 | 0.402426 | ||||||||
\(546\) | −55.4719 | −2.37398 | ||||||||
\(547\) | 3.83976 | 0.164176 | 0.0820881 | − | 0.996625i | \(-0.473841\pi\) | ||||
0.0820881 | + | 0.996625i | \(0.473841\pi\) | |||||||
\(548\) | 2.59415 | 0.110816 | ||||||||
\(549\) | −13.5671 | −0.579031 | ||||||||
\(550\) | −2.19462 | −0.0935791 | ||||||||
\(551\) | −17.6356 | −0.751302 | ||||||||
\(552\) | −25.4478 | −1.08313 | ||||||||
\(553\) | −0.712049 | −0.0302794 | ||||||||
\(554\) | 34.0546 | 1.44684 | ||||||||
\(555\) | 24.6620 | 1.04685 | ||||||||
\(556\) | −19.1963 | −0.814106 | ||||||||
\(557\) | −1.40081 | −0.0593542 | −0.0296771 | − | 0.999560i | \(-0.509448\pi\) | ||||
−0.0296771 | + | 0.999560i | \(0.509448\pi\) | |||||||
\(558\) | 33.4499 | 1.41605 | ||||||||
\(559\) | −16.0036 | −0.676882 | ||||||||
\(560\) | 6.19102 | 0.261618 | ||||||||
\(561\) | −11.5375 | −0.487112 | ||||||||
\(562\) | −45.0894 | −1.90198 | ||||||||
\(563\) | 24.9166 | 1.05011 | 0.525056 | − | 0.851068i | \(-0.324045\pi\) | ||||
0.525056 | + | 0.851068i | \(0.324045\pi\) | |||||||
\(564\) | −83.8276 | −3.52978 | ||||||||
\(565\) | −5.74075 | −0.241515 | ||||||||
\(566\) | 16.4860 | 0.692960 | ||||||||
\(567\) | −31.3760 | −1.31767 | ||||||||
\(568\) | −5.76797 | −0.242019 | ||||||||
\(569\) | −21.3975 | −0.897031 | −0.448516 | − | 0.893775i | \(-0.648047\pi\) | ||||
−0.448516 | + | 0.893775i | \(0.648047\pi\) | |||||||
\(570\) | 23.5727 | 0.987353 | ||||||||
\(571\) | 30.2271 | 1.26496 | 0.632482 | − | 0.774575i | \(-0.282036\pi\) | ||||
0.632482 | + | 0.774575i | \(0.282036\pi\) | |||||||
\(572\) | −7.90395 | −0.330481 | ||||||||
\(573\) | −24.9209 | −1.04108 | ||||||||
\(574\) | 13.1279 | 0.547947 | ||||||||
\(575\) | −5.74058 | −0.239399 | ||||||||
\(576\) | −39.5044 | −1.64602 | ||||||||
\(577\) | 29.9408 | 1.24645 | 0.623226 | − | 0.782042i | \(-0.285822\pi\) | ||||
0.623226 | + | 0.782042i | \(0.285822\pi\) | |||||||
\(578\) | −10.4109 | −0.433034 | ||||||||
\(579\) | 46.0792 | 1.91498 | ||||||||
\(580\) | −11.4413 | −0.475073 | ||||||||
\(581\) | −11.1167 | −0.461200 | ||||||||
\(582\) | 67.6335 | 2.80350 | ||||||||
\(583\) | −1.44311 | −0.0597676 | ||||||||
\(584\) | 1.79164 | 0.0741387 | ||||||||
\(585\) | 8.76135 | 0.362237 | ||||||||
\(586\) | −0.782762 | −0.0323356 | ||||||||
\(587\) | −2.46650 | −0.101803 | −0.0509017 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509017 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(588\) | −43.5562 | −1.79623 | ||||||||
\(589\) | 21.1945 | 0.873305 | ||||||||
\(590\) | 6.76987 | 0.278711 | ||||||||
\(591\) | 10.5847 | 0.435398 | ||||||||
\(592\) | −16.9524 | −0.696740 | ||||||||
\(593\) | 20.8216 | 0.855041 | 0.427520 | − | 0.904006i | \(-0.359387\pi\) | ||||
0.427520 | + | 0.904006i | \(0.359387\pi\) | |||||||
\(594\) | 0.661876 | 0.0271571 | ||||||||
\(595\) | −16.9740 | −0.695866 | ||||||||
\(596\) | −10.8462 | −0.444277 | ||||||||
\(597\) | −15.8651 | −0.649315 | ||||||||
\(598\) | −35.3565 | −1.44583 | ||||||||
\(599\) | −28.8207 | −1.17758 | −0.588792 | − | 0.808285i | \(-0.700396\pi\) | ||||
−0.588792 | + | 0.808285i | \(0.700396\pi\) | |||||||
\(600\) | 4.43297 | 0.180975 | ||||||||
\(601\) | 3.36972 | 0.137454 | 0.0687269 | − | 0.997636i | \(-0.478106\pi\) | ||||
0.0687269 | + | 0.997636i | \(0.478106\pi\) | |||||||
\(602\) | −45.5557 | −1.85671 | ||||||||
\(603\) | −37.3396 | −1.52059 | ||||||||
\(604\) | −6.97881 | −0.283964 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −5.94899 | −0.241661 | ||||||||
\(607\) | 10.7172 | 0.434998 | 0.217499 | − | 0.976061i | \(-0.430210\pi\) | ||||
0.217499 | + | 0.976061i | \(0.430210\pi\) | |||||||
\(608\) | −31.7593 | −1.28801 | ||||||||
\(609\) | −36.5884 | −1.48264 | ||||||||
\(610\) | −9.53742 | −0.386159 | ||||||||
\(611\) | −33.7603 | −1.36580 | ||||||||
\(612\) | 40.9993 | 1.65730 | ||||||||
\(613\) | −26.2977 | −1.06215 | −0.531077 | − | 0.847324i | \(-0.678212\pi\) | ||||
−0.531077 | + | 0.847324i | \(0.678212\pi\) | |||||||
\(614\) | 17.9608 | 0.724837 | ||||||||
\(615\) | −4.06593 | −0.163954 | ||||||||
\(616\) | −6.52181 | −0.262771 | ||||||||
\(617\) | 10.4666 | 0.421368 | 0.210684 | − | 0.977554i | \(-0.432431\pi\) | ||||
0.210684 | + | 0.977554i | \(0.432431\pi\) | |||||||
\(618\) | −1.59746 | −0.0642594 | ||||||||
\(619\) | 20.3956 | 0.819770 | 0.409885 | − | 0.912137i | \(-0.365569\pi\) | ||||
0.409885 | + | 0.912137i | \(0.365569\pi\) | |||||||
\(620\) | 13.7502 | 0.552220 | ||||||||
\(621\) | 1.73130 | 0.0694746 | ||||||||
\(622\) | 0.446774 | 0.0179140 | ||||||||
\(623\) | 26.8077 | 1.07403 | ||||||||
\(624\) | −11.8098 | −0.472769 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 22.5784 | 0.902414 | ||||||||
\(627\) | 10.7411 | 0.428959 | ||||||||
\(628\) | −50.0138 | −1.99577 | ||||||||
\(629\) | 46.4787 | 1.85323 | ||||||||
\(630\) | 24.9399 | 0.993629 | ||||||||
\(631\) | 25.1243 | 1.00018 | 0.500090 | − | 0.865973i | \(-0.333300\pi\) | ||||
0.500090 | + | 0.865973i | \(0.333300\pi\) | |||||||
\(632\) | 0.350465 | 0.0139408 | ||||||||
\(633\) | 34.0429 | 1.35308 | ||||||||
\(634\) | −49.3400 | −1.95954 | ||||||||
\(635\) | −14.7636 | −0.585877 | ||||||||
\(636\) | 10.0562 | 0.398754 | ||||||||
\(637\) | −17.5416 | −0.695024 | ||||||||
\(638\) | −8.91546 | −0.352967 | ||||||||
\(639\) | 10.0505 | 0.397593 | ||||||||
\(640\) | −13.1391 | −0.519367 | ||||||||
\(641\) | −35.2324 | −1.39160 | −0.695799 | − | 0.718237i | \(-0.744949\pi\) | ||||
−0.695799 | + | 0.718237i | \(0.744949\pi\) | |||||||
\(642\) | −50.7998 | −2.00491 | ||||||||
\(643\) | −26.6067 | −1.04927 | −0.524634 | − | 0.851328i | \(-0.675798\pi\) | ||||
−0.524634 | + | 0.851328i | \(0.675798\pi\) | |||||||
\(644\) | −58.8523 | −2.31910 | ||||||||
\(645\) | 14.1094 | 0.555557 | ||||||||
\(646\) | 44.4258 | 1.74791 | ||||||||
\(647\) | 35.9696 | 1.41411 | 0.707055 | − | 0.707158i | \(-0.250023\pi\) | ||||
0.707055 | + | 0.707158i | \(0.250023\pi\) | |||||||
\(648\) | 15.4430 | 0.606659 | ||||||||
\(649\) | 3.08475 | 0.121087 | ||||||||
\(650\) | 6.15904 | 0.241578 | ||||||||
\(651\) | 43.9720 | 1.72340 | ||||||||
\(652\) | −18.9420 | −0.741826 | ||||||||
\(653\) | 43.3096 | 1.69484 | 0.847418 | − | 0.530926i | \(-0.178156\pi\) | ||||
0.847418 | + | 0.530926i | \(0.178156\pi\) | |||||||
\(654\) | −51.0137 | −1.99480 | ||||||||
\(655\) | 4.12655 | 0.161238 | ||||||||
\(656\) | 2.79488 | 0.109122 | ||||||||
\(657\) | −3.12189 | −0.121797 | ||||||||
\(658\) | −96.1015 | −3.74643 | ||||||||
\(659\) | 25.4710 | 0.992209 | 0.496105 | − | 0.868263i | \(-0.334763\pi\) | ||||
0.496105 | + | 0.868263i | \(0.334763\pi\) | |||||||
\(660\) | 6.96841 | 0.271245 | ||||||||
\(661\) | 45.1553 | 1.75634 | 0.878169 | − | 0.478350i | \(-0.158765\pi\) | ||||
0.878169 | + | 0.478350i | \(0.158765\pi\) | |||||||
\(662\) | 17.0889 | 0.664181 | ||||||||
\(663\) | 32.3790 | 1.25750 | ||||||||
\(664\) | 5.47158 | 0.212339 | ||||||||
\(665\) | 15.8024 | 0.612791 | ||||||||
\(666\) | −68.2911 | −2.64623 | ||||||||
\(667\) | −23.3206 | −0.902977 | ||||||||
\(668\) | 32.2916 | 1.24940 | ||||||||
\(669\) | −3.98420 | −0.154038 | ||||||||
\(670\) | −26.2490 | −1.01409 | ||||||||
\(671\) | −4.34581 | −0.167768 | ||||||||
\(672\) | −65.8906 | −2.54179 | ||||||||
\(673\) | 42.2888 | 1.63011 | 0.815057 | − | 0.579381i | \(-0.196706\pi\) | ||||
0.815057 | + | 0.579381i | \(0.196706\pi\) | |||||||
\(674\) | −39.1027 | −1.50618 | ||||||||
\(675\) | −0.301589 | −0.0116082 | ||||||||
\(676\) | −14.4311 | −0.555042 | ||||||||
\(677\) | −43.8186 | −1.68409 | −0.842043 | − | 0.539411i | \(-0.818647\pi\) | ||||
−0.842043 | + | 0.539411i | \(0.818647\pi\) | |||||||
\(678\) | 31.1725 | 1.19717 | ||||||||
\(679\) | 45.3393 | 1.73996 | ||||||||
\(680\) | 8.35448 | 0.320380 | ||||||||
\(681\) | −26.3817 | −1.01095 | ||||||||
\(682\) | 10.7146 | 0.410284 | ||||||||
\(683\) | 22.4666 | 0.859662 | 0.429831 | − | 0.902909i | \(-0.358573\pi\) | ||||
0.429831 | + | 0.902909i | \(0.358573\pi\) | |||||||
\(684\) | −38.1694 | −1.45944 | ||||||||
\(685\) | −0.921093 | −0.0351932 | ||||||||
\(686\) | 5.98737 | 0.228599 | ||||||||
\(687\) | 34.9905 | 1.33497 | ||||||||
\(688\) | −9.69865 | −0.369758 | ||||||||
\(689\) | 4.04998 | 0.154292 | ||||||||
\(690\) | 31.1716 | 1.18668 | ||||||||
\(691\) | 6.92332 | 0.263376 | 0.131688 | − | 0.991291i | \(-0.457960\pi\) | ||||
0.131688 | + | 0.991291i | \(0.457960\pi\) | |||||||
\(692\) | 59.3149 | 2.25482 | ||||||||
\(693\) | 11.3641 | 0.431686 | ||||||||
\(694\) | 38.0795 | 1.44548 | ||||||||
\(695\) | 6.81597 | 0.258544 | ||||||||
\(696\) | 18.0085 | 0.682611 | ||||||||
\(697\) | −7.66276 | −0.290248 | ||||||||
\(698\) | 4.44768 | 0.168347 | ||||||||
\(699\) | 24.7439 | 0.935900 | ||||||||
\(700\) | 10.2520 | 0.387488 | ||||||||
\(701\) | 18.3795 | 0.694183 | 0.347092 | − | 0.937831i | \(-0.387169\pi\) | ||||
0.347092 | + | 0.937831i | \(0.387169\pi\) | |||||||
\(702\) | −1.85750 | −0.0701069 | ||||||||
\(703\) | −43.2706 | −1.63198 | ||||||||
\(704\) | −12.6540 | −0.476915 | ||||||||
\(705\) | 29.7643 | 1.12099 | ||||||||
\(706\) | 20.7222 | 0.779889 | ||||||||
\(707\) | −3.98801 | −0.149985 | ||||||||
\(708\) | −21.4958 | −0.807862 | ||||||||
\(709\) | 3.37053 | 0.126583 | 0.0632915 | − | 0.997995i | \(-0.479840\pi\) | ||||
0.0632915 | + | 0.997995i | \(0.479840\pi\) | |||||||
\(710\) | 7.06532 | 0.265157 | ||||||||
\(711\) | −0.610676 | −0.0229022 | ||||||||
\(712\) | −13.1946 | −0.494487 | ||||||||
\(713\) | 28.0267 | 1.04961 | ||||||||
\(714\) | 92.1695 | 3.44936 | ||||||||
\(715\) | 2.80642 | 0.104954 | ||||||||
\(716\) | −23.2265 | −0.868016 | ||||||||
\(717\) | 39.4291 | 1.47251 | ||||||||
\(718\) | 29.6819 | 1.10772 | ||||||||
\(719\) | −27.3627 | −1.02045 | −0.510227 | − | 0.860039i | \(-0.670439\pi\) | ||||
−0.510227 | + | 0.860039i | \(0.670439\pi\) | |||||||
\(720\) | 5.30962 | 0.197878 | ||||||||
\(721\) | −1.07089 | −0.0398819 | ||||||||
\(722\) | 0.338481 | 0.0125970 | ||||||||
\(723\) | 23.9578 | 0.891001 | ||||||||
\(724\) | 56.7282 | 2.10829 | ||||||||
\(725\) | 4.06241 | 0.150874 | ||||||||
\(726\) | 5.43004 | 0.201528 | ||||||||
\(727\) | −18.6057 | −0.690048 | −0.345024 | − | 0.938594i | \(-0.612129\pi\) | ||||
−0.345024 | + | 0.938594i | \(0.612129\pi\) | |||||||
\(728\) | 18.3030 | 0.678353 | ||||||||
\(729\) | −29.1477 | −1.07954 | ||||||||
\(730\) | −2.19462 | −0.0812267 | ||||||||
\(731\) | 26.5909 | 0.983501 | ||||||||
\(732\) | 30.2834 | 1.11931 | ||||||||
\(733\) | 23.0238 | 0.850405 | 0.425203 | − | 0.905098i | \(-0.360203\pi\) | ||||
0.425203 | + | 0.905098i | \(0.360203\pi\) | |||||||
\(734\) | 41.3282 | 1.52545 | ||||||||
\(735\) | 15.4653 | 0.570447 | ||||||||
\(736\) | −41.9972 | −1.54804 | ||||||||
\(737\) | −11.9606 | −0.440574 | ||||||||
\(738\) | 11.2589 | 0.414445 | ||||||||
\(739\) | 44.1029 | 1.62235 | 0.811175 | − | 0.584804i | \(-0.198828\pi\) | ||||
0.811175 | + | 0.584804i | \(0.198828\pi\) | |||||||
\(740\) | −28.0722 | −1.03196 | ||||||||
\(741\) | −30.1441 | −1.10737 | ||||||||
\(742\) | 11.5286 | 0.423229 | ||||||||
\(743\) | −21.4811 | −0.788067 | −0.394033 | − | 0.919096i | \(-0.628921\pi\) | ||||
−0.394033 | + | 0.919096i | \(0.628921\pi\) | |||||||
\(744\) | −21.6427 | −0.793460 | ||||||||
\(745\) | 3.85111 | 0.141094 | ||||||||
\(746\) | −72.4162 | −2.65135 | ||||||||
\(747\) | −9.53409 | −0.348834 | ||||||||
\(748\) | 13.1328 | 0.480184 | ||||||||
\(749\) | −34.0546 | −1.24433 | ||||||||
\(750\) | −5.43004 | −0.198277 | ||||||||
\(751\) | −32.4913 | −1.18563 | −0.592813 | − | 0.805340i | \(-0.701983\pi\) | ||||
−0.592813 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(752\) | −20.4597 | −0.746088 | ||||||||
\(753\) | −49.9724 | −1.82110 | ||||||||
\(754\) | 25.0206 | 0.911195 | ||||||||
\(755\) | 2.47794 | 0.0901814 | ||||||||
\(756\) | −3.09189 | −0.112451 | ||||||||
\(757\) | −10.0855 | −0.366563 | −0.183282 | − | 0.983060i | \(-0.558672\pi\) | ||||
−0.183282 | + | 0.983060i | \(0.558672\pi\) | |||||||
\(758\) | −60.8982 | −2.21192 | ||||||||
\(759\) | 14.2036 | 0.515558 | ||||||||
\(760\) | −7.77783 | −0.282132 | ||||||||
\(761\) | 2.99779 | 0.108670 | 0.0543349 | − | 0.998523i | \(-0.482696\pi\) | ||||
0.0543349 | + | 0.998523i | \(0.482696\pi\) | |||||||
\(762\) | 80.1671 | 2.90415 | ||||||||
\(763\) | −34.1980 | −1.23805 | ||||||||
\(764\) | 28.3669 | 1.02628 | ||||||||
\(765\) | −14.5575 | −0.526326 | ||||||||
\(766\) | 9.78475 | 0.353537 | ||||||||
\(767\) | −8.65711 | −0.312590 | ||||||||
\(768\) | 8.72754 | 0.314928 | ||||||||
\(769\) | 28.2696 | 1.01943 | 0.509714 | − | 0.860344i | \(-0.329751\pi\) | ||||
0.509714 | + | 0.860344i | \(0.329751\pi\) | |||||||
\(770\) | 7.98871 | 0.287893 | ||||||||
\(771\) | −42.3980 | −1.52693 | ||||||||
\(772\) | −52.4509 | −1.88775 | ||||||||
\(773\) | −44.3826 | −1.59633 | −0.798166 | − | 0.602437i | \(-0.794196\pi\) | ||||
−0.798166 | + | 0.602437i | \(0.794196\pi\) | |||||||
\(774\) | −39.0700 | −1.40434 | ||||||||
\(775\) | −4.88222 | −0.175374 | ||||||||
\(776\) | −22.3157 | −0.801087 | ||||||||
\(777\) | −89.7729 | −3.22059 | ||||||||
\(778\) | 64.7628 | 2.32186 | ||||||||
\(779\) | 7.13386 | 0.255597 | ||||||||
\(780\) | −19.5563 | −0.700228 | ||||||||
\(781\) | 3.21937 | 0.115198 | ||||||||
\(782\) | 58.7467 | 2.10078 | ||||||||
\(783\) | −1.22518 | −0.0437844 | ||||||||
\(784\) | −10.6307 | −0.379668 | ||||||||
\(785\) | 17.7582 | 0.633817 | ||||||||
\(786\) | −22.4074 | −0.799244 | ||||||||
\(787\) | 50.1514 | 1.78770 | 0.893852 | − | 0.448362i | \(-0.147992\pi\) | ||||
0.893852 | + | 0.448362i | \(0.147992\pi\) | |||||||
\(788\) | −12.0484 | −0.429206 | ||||||||
\(789\) | −66.8292 | −2.37918 | ||||||||
\(790\) | −0.429293 | −0.0152736 | ||||||||
\(791\) | 20.8971 | 0.743014 | ||||||||
\(792\) | −5.59332 | −0.198750 | ||||||||
\(793\) | 12.1962 | 0.433099 | ||||||||
\(794\) | −4.06456 | −0.144246 | ||||||||
\(795\) | −3.57061 | −0.126637 | ||||||||
\(796\) | 18.0589 | 0.640080 | ||||||||
\(797\) | −20.1489 | −0.713711 | −0.356855 | − | 0.934160i | \(-0.616151\pi\) | ||||
−0.356855 | + | 0.934160i | \(0.616151\pi\) | |||||||
\(798\) | −85.8077 | −3.03756 | ||||||||
\(799\) | 56.0946 | 1.98448 | ||||||||
\(800\) | 7.31584 | 0.258654 | ||||||||
\(801\) | 22.9912 | 0.812353 | ||||||||
\(802\) | −50.6878 | −1.78985 | ||||||||
\(803\) | −1.00000 | −0.0352892 | ||||||||
\(804\) | 83.3462 | 2.93940 | ||||||||
\(805\) | 20.8964 | 0.736502 | ||||||||
\(806\) | −30.0698 | −1.05916 | ||||||||
\(807\) | −24.0942 | −0.848157 | ||||||||
\(808\) | 1.96287 | 0.0690535 | ||||||||
\(809\) | 53.8212 | 1.89225 | 0.946126 | − | 0.323798i | \(-0.104960\pi\) | ||||
0.946126 | + | 0.323798i | \(0.104960\pi\) | |||||||
\(810\) | −18.9165 | −0.664658 | ||||||||
\(811\) | −28.4447 | −0.998830 | −0.499415 | − | 0.866363i | \(-0.666452\pi\) | ||||
−0.499415 | + | 0.866363i | \(0.666452\pi\) | |||||||
\(812\) | 41.6477 | 1.46155 | ||||||||
\(813\) | −14.8766 | −0.521744 | ||||||||
\(814\) | −21.8749 | −0.766715 | ||||||||
\(815\) | 6.72566 | 0.235590 | ||||||||
\(816\) | 19.6226 | 0.686928 | ||||||||
\(817\) | −24.7555 | −0.866087 | ||||||||
\(818\) | −9.55449 | −0.334065 | ||||||||
\(819\) | −31.8924 | −1.11441 | ||||||||
\(820\) | 4.62816 | 0.161622 | ||||||||
\(821\) | −47.5293 | −1.65878 | −0.829391 | − | 0.558668i | \(-0.811313\pi\) | ||||
−0.829391 | + | 0.558668i | \(0.811313\pi\) | |||||||
\(822\) | 5.00158 | 0.174450 | ||||||||
\(823\) | 40.4250 | 1.40913 | 0.704564 | − | 0.709640i | \(-0.251143\pi\) | ||||
0.704564 | + | 0.709640i | \(0.251143\pi\) | |||||||
\(824\) | 0.527083 | 0.0183618 | ||||||||
\(825\) | −2.47425 | −0.0861422 | ||||||||
\(826\) | −24.6432 | −0.857446 | ||||||||
\(827\) | 42.4552 | 1.47631 | 0.738156 | − | 0.674630i | \(-0.235697\pi\) | ||||
0.738156 | + | 0.674630i | \(0.235697\pi\) | |||||||
\(828\) | −50.4736 | −1.75408 | ||||||||
\(829\) | 47.8975 | 1.66355 | 0.831774 | − | 0.555114i | \(-0.187325\pi\) | ||||
0.831774 | + | 0.555114i | \(0.187325\pi\) | |||||||
\(830\) | −6.70227 | −0.232639 | ||||||||
\(831\) | 38.3936 | 1.33186 | ||||||||
\(832\) | 35.5124 | 1.23117 | ||||||||
\(833\) | 29.1463 | 1.00986 | ||||||||
\(834\) | −37.0110 | −1.28159 | ||||||||
\(835\) | −11.4657 | −0.396785 | ||||||||
\(836\) | −12.2264 | −0.422858 | ||||||||
\(837\) | 1.47242 | 0.0508944 | ||||||||
\(838\) | 18.7039 | 0.646115 | ||||||||
\(839\) | 2.59083 | 0.0894453 | 0.0447227 | − | 0.998999i | \(-0.485760\pi\) | ||||
0.0447227 | + | 0.998999i | \(0.485760\pi\) | |||||||
\(840\) | −16.1366 | −0.556764 | ||||||||
\(841\) | −12.4968 | −0.430925 | ||||||||
\(842\) | −60.5179 | −2.08558 | ||||||||
\(843\) | −50.8343 | −1.75083 | ||||||||
\(844\) | −38.7502 | −1.33384 | ||||||||
\(845\) | 5.12399 | 0.176271 | ||||||||
\(846\) | −82.4198 | −2.83365 | ||||||||
\(847\) | 3.64013 | 0.125076 | ||||||||
\(848\) | 2.45440 | 0.0842845 | ||||||||
\(849\) | 18.5865 | 0.637889 | ||||||||
\(850\) | −10.2336 | −0.351009 | ||||||||
\(851\) | −57.2192 | −1.96145 | ||||||||
\(852\) | −22.4339 | −0.768573 | ||||||||
\(853\) | 48.1761 | 1.64952 | 0.824760 | − | 0.565483i | \(-0.191310\pi\) | ||||
0.824760 | + | 0.565483i | \(0.191310\pi\) | |||||||
\(854\) | 34.7174 | 1.18801 | ||||||||
\(855\) | 13.5527 | 0.463491 | ||||||||
\(856\) | 16.7614 | 0.572893 | ||||||||
\(857\) | 41.9844 | 1.43416 | 0.717080 | − | 0.696991i | \(-0.245478\pi\) | ||||
0.717080 | + | 0.696991i | \(0.245478\pi\) | |||||||
\(858\) | −15.2390 | −0.520251 | ||||||||
\(859\) | 42.2777 | 1.44250 | 0.721248 | − | 0.692677i | \(-0.243569\pi\) | ||||
0.721248 | + | 0.692677i | \(0.243569\pi\) | |||||||
\(860\) | −16.0604 | −0.547655 | ||||||||
\(861\) | 14.8005 | 0.504400 | ||||||||
\(862\) | 9.30792 | 0.317029 | ||||||||
\(863\) | −6.26259 | −0.213181 | −0.106591 | − | 0.994303i | \(-0.533993\pi\) | ||||
−0.106591 | + | 0.994303i | \(0.533993\pi\) | |||||||
\(864\) | −2.20638 | −0.0750626 | ||||||||
\(865\) | −21.0607 | −0.716086 | ||||||||
\(866\) | −45.7906 | −1.55603 | ||||||||
\(867\) | −11.7373 | −0.398620 | ||||||||
\(868\) | −50.0523 | −1.69889 | ||||||||
\(869\) | −0.195611 | −0.00663565 | ||||||||
\(870\) | −22.0591 | −0.747872 | ||||||||
\(871\) | 33.5664 | 1.13736 | ||||||||
\(872\) | 16.8320 | 0.570004 | ||||||||
\(873\) | 38.8845 | 1.31604 | ||||||||
\(874\) | −54.6919 | −1.84998 | ||||||||
\(875\) | −3.64013 | −0.123059 | ||||||||
\(876\) | 6.96841 | 0.235441 | ||||||||
\(877\) | −12.6290 | −0.426450 | −0.213225 | − | 0.977003i | \(-0.568397\pi\) | ||||
−0.213225 | + | 0.977003i | \(0.568397\pi\) | |||||||
\(878\) | −89.2005 | −3.01037 | ||||||||
\(879\) | −0.882495 | −0.0297658 | ||||||||
\(880\) | 1.70077 | 0.0573330 | ||||||||
\(881\) | 23.0629 | 0.777009 | 0.388505 | − | 0.921447i | \(-0.372992\pi\) | ||||
0.388505 | + | 0.921447i | \(0.372992\pi\) | |||||||
\(882\) | −42.8247 | −1.44198 | ||||||||
\(883\) | 47.0786 | 1.58432 | 0.792161 | − | 0.610312i | \(-0.208956\pi\) | ||||
0.792161 | + | 0.610312i | \(0.208956\pi\) | |||||||
\(884\) | −36.8563 | −1.23961 | ||||||||
\(885\) | 7.63243 | 0.256561 | ||||||||
\(886\) | −38.1427 | −1.28143 | ||||||||
\(887\) | −25.6178 | −0.860161 | −0.430081 | − | 0.902791i | \(-0.641515\pi\) | ||||
−0.430081 | + | 0.902791i | \(0.641515\pi\) | |||||||
\(888\) | 44.1856 | 1.48277 | ||||||||
\(889\) | 53.7415 | 1.80243 | ||||||||
\(890\) | 16.1623 | 0.541762 | ||||||||
\(891\) | −8.61947 | −0.288763 | ||||||||
\(892\) | 4.53512 | 0.151847 | ||||||||
\(893\) | −52.2228 | −1.74757 | ||||||||
\(894\) | −20.9117 | −0.699391 | ||||||||
\(895\) | 8.24694 | 0.275665 | ||||||||
\(896\) | 47.8279 | 1.59782 | ||||||||
\(897\) | −39.8613 | −1.33093 | ||||||||
\(898\) | 8.88705 | 0.296565 | ||||||||
\(899\) | −19.8336 | −0.661486 | ||||||||
\(900\) | 8.79243 | 0.293081 | ||||||||
\(901\) | −6.72927 | −0.224184 | ||||||||
\(902\) | 3.60643 | 0.120081 | ||||||||
\(903\) | −51.3600 | −1.70915 | ||||||||
\(904\) | −10.2854 | −0.342087 | ||||||||
\(905\) | −20.1422 | −0.669551 | ||||||||
\(906\) | −13.4553 | −0.447023 | ||||||||
\(907\) | −40.7122 | −1.35183 | −0.675914 | − | 0.736981i | \(-0.736251\pi\) | ||||
−0.675914 | + | 0.736981i | \(0.736251\pi\) | |||||||
\(908\) | 30.0297 | 0.996571 | ||||||||
\(909\) | −3.42025 | −0.113442 | ||||||||
\(910\) | −22.4197 | −0.743206 | ||||||||
\(911\) | −2.66730 | −0.0883717 | −0.0441859 | − | 0.999023i | \(-0.514069\pi\) | ||||
−0.0441859 | + | 0.999023i | \(0.514069\pi\) | |||||||
\(912\) | −18.2682 | −0.604920 | ||||||||
\(913\) | −3.05395 | −0.101071 | ||||||||
\(914\) | −3.41941 | −0.113104 | ||||||||
\(915\) | −10.7526 | −0.355470 | ||||||||
\(916\) | −39.8289 | −1.31599 | ||||||||
\(917\) | −15.0212 | −0.496043 | ||||||||
\(918\) | 3.08634 | 0.101864 | ||||||||
\(919\) | −12.8028 | −0.422326 | −0.211163 | − | 0.977451i | \(-0.567725\pi\) | ||||
−0.211163 | + | 0.977451i | \(0.567725\pi\) | |||||||
\(920\) | −10.2851 | −0.339089 | ||||||||
\(921\) | 20.2492 | 0.667233 | ||||||||
\(922\) | −80.4559 | −2.64967 | ||||||||
\(923\) | −9.03492 | −0.297388 | ||||||||
\(924\) | −25.3659 | −0.834477 | ||||||||
\(925\) | 9.96750 | 0.327729 | ||||||||
\(926\) | 73.4289 | 2.41302 | ||||||||
\(927\) | −0.918428 | −0.0301651 | ||||||||
\(928\) | 29.7199 | 0.975605 | ||||||||
\(929\) | −35.2716 | −1.15722 | −0.578612 | − | 0.815603i | \(-0.696405\pi\) | ||||
−0.578612 | + | 0.815603i | \(0.696405\pi\) | |||||||
\(930\) | 26.5106 | 0.869318 | ||||||||
\(931\) | −27.1346 | −0.889300 | ||||||||
\(932\) | −28.1654 | −0.922588 | ||||||||
\(933\) | 0.503698 | 0.0164903 | ||||||||
\(934\) | 53.0992 | 1.73746 | ||||||||
\(935\) | −4.66302 | −0.152497 | ||||||||
\(936\) | 15.6972 | 0.513079 | ||||||||
\(937\) | 26.5731 | 0.868106 | 0.434053 | − | 0.900887i | \(-0.357083\pi\) | ||||
0.434053 | + | 0.900887i | \(0.357083\pi\) | |||||||
\(938\) | 95.5496 | 3.11981 | ||||||||
\(939\) | 25.4551 | 0.830697 | ||||||||
\(940\) | −33.8801 | −1.10505 | ||||||||
\(941\) | 28.2273 | 0.920183 | 0.460092 | − | 0.887871i | \(-0.347817\pi\) | ||||
0.460092 | + | 0.887871i | \(0.347817\pi\) | |||||||
\(942\) | −96.4278 | −3.14179 | ||||||||
\(943\) | 9.43351 | 0.307197 | ||||||||
\(944\) | −5.24645 | −0.170757 | ||||||||
\(945\) | 1.09782 | 0.0357122 | ||||||||
\(946\) | −12.5149 | −0.406893 | ||||||||
\(947\) | −24.8105 | −0.806234 | −0.403117 | − | 0.915148i | \(-0.632073\pi\) | ||||
−0.403117 | + | 0.915148i | \(0.632073\pi\) | |||||||
\(948\) | 1.36310 | 0.0442714 | ||||||||
\(949\) | 2.80642 | 0.0911003 | ||||||||
\(950\) | 9.52724 | 0.309105 | ||||||||
\(951\) | −55.6265 | −1.80381 | ||||||||
\(952\) | −30.4114 | −0.985638 | ||||||||
\(953\) | −0.650393 | −0.0210683 | −0.0105341 | − | 0.999945i | \(-0.503353\pi\) | ||||
−0.0105341 | + | 0.999945i | \(0.503353\pi\) | |||||||
\(954\) | 9.88731 | 0.320114 | ||||||||
\(955\) | −10.0721 | −0.325926 | ||||||||
\(956\) | −44.8813 | −1.45156 | ||||||||
\(957\) | −10.0514 | −0.324916 | ||||||||
\(958\) | −51.9249 | −1.67762 | ||||||||
\(959\) | 3.35290 | 0.108271 | ||||||||
\(960\) | −31.3091 | −1.01050 | ||||||||
\(961\) | −7.16398 | −0.231096 | ||||||||
\(962\) | 61.3903 | 1.97930 | ||||||||
\(963\) | −29.2063 | −0.941160 | ||||||||
\(964\) | −27.2706 | −0.878328 | ||||||||
\(965\) | 18.6235 | 0.599512 | ||||||||
\(966\) | −113.468 | −3.65079 | ||||||||
\(967\) | −43.1429 | −1.38738 | −0.693691 | − | 0.720273i | \(-0.744017\pi\) | ||||
−0.693691 | + | 0.720273i | \(0.744017\pi\) | |||||||
\(968\) | −1.79164 | −0.0575856 | ||||||||
\(969\) | 50.0861 | 1.60900 | ||||||||
\(970\) | 27.3350 | 0.877674 | ||||||||
\(971\) | −55.2874 | −1.77426 | −0.887129 | − | 0.461521i | \(-0.847304\pi\) | ||||
−0.887129 | + | 0.461521i | \(0.847304\pi\) | |||||||
\(972\) | 62.6122 | 2.00829 | ||||||||
\(973\) | −24.8110 | −0.795404 | ||||||||
\(974\) | −41.1550 | −1.31869 | ||||||||
\(975\) | 6.94378 | 0.222379 | ||||||||
\(976\) | 7.39122 | 0.236587 | ||||||||
\(977\) | 3.59426 | 0.114991 | 0.0574954 | − | 0.998346i | \(-0.481689\pi\) | ||||
0.0574954 | + | 0.998346i | \(0.481689\pi\) | |||||||
\(978\) | −36.5206 | −1.16780 | ||||||||
\(979\) | 7.36450 | 0.235371 | ||||||||
\(980\) | −17.6038 | −0.562334 | ||||||||
\(981\) | −29.3293 | −0.936413 | ||||||||
\(982\) | 48.3044 | 1.54145 | ||||||||
\(983\) | −26.7667 | −0.853725 | −0.426863 | − | 0.904317i | \(-0.640381\pi\) | ||||
−0.426863 | + | 0.904317i | \(0.640381\pi\) | |||||||
\(984\) | −7.28471 | −0.232228 | ||||||||
\(985\) | 4.27797 | 0.136307 | ||||||||
\(986\) | −41.5730 | −1.32396 | ||||||||
\(987\) | −108.346 | −3.44869 | ||||||||
\(988\) | 34.3124 | 1.09162 | ||||||||
\(989\) | −32.7357 | −1.04093 | ||||||||
\(990\) | 6.85138 | 0.217751 | ||||||||
\(991\) | −47.1497 | −1.49776 | −0.748881 | − | 0.662705i | \(-0.769408\pi\) | ||||
−0.748881 | + | 0.662705i | \(0.769408\pi\) | |||||||
\(992\) | −35.7175 | −1.13403 | ||||||||
\(993\) | 19.2663 | 0.611397 | ||||||||
\(994\) | −25.7186 | −0.815746 | ||||||||
\(995\) | −6.41209 | −0.203277 | ||||||||
\(996\) | 21.2812 | 0.674319 | ||||||||
\(997\) | −43.3273 | −1.37219 | −0.686094 | − | 0.727513i | \(-0.740676\pi\) | ||||
−0.686094 | + | 0.727513i | \(0.740676\pi\) | |||||||
\(998\) | 68.7395 | 2.17591 | ||||||||
\(999\) | −3.00609 | −0.0951085 |
(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 | 4015.2.a.e.1.4 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.e.1.4 | ✓ | 27 | 1.1 | even | 1 | trivial |