Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(0\) |
Dimension: | \(41\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.352298 | −0.203399 | −0.101700 | − | 0.994815i | \(-0.532428\pi\) | ||||
−0.101700 | + | 0.994815i | \(0.532428\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.51534 | −0.677679 | −0.338839 | − | 0.940844i | \(-0.610034\pi\) | ||||
−0.338839 | + | 0.940844i | \(0.610034\pi\) | |||||||
\(6\) | −0.352298 | −0.143825 | ||||||||
\(7\) | −1.04103 | −0.393472 | −0.196736 | − | 0.980457i | \(-0.563034\pi\) | ||||
−0.196736 | + | 0.980457i | \(0.563034\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.87589 | −0.958629 | ||||||||
\(10\) | −1.51534 | −0.479191 | ||||||||
\(11\) | 3.44169 | 1.03771 | 0.518855 | − | 0.854863i | \(-0.326359\pi\) | ||||
0.518855 | + | 0.854863i | \(0.326359\pi\) | |||||||
\(12\) | −0.352298 | −0.101700 | ||||||||
\(13\) | −5.23410 | −1.45168 | −0.725839 | − | 0.687865i | \(-0.758548\pi\) | ||||
−0.725839 | + | 0.687865i | \(0.758548\pi\) | |||||||
\(14\) | −1.04103 | −0.278227 | ||||||||
\(15\) | 0.533849 | 0.137839 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.458447 | −0.111190 | −0.0555949 | − | 0.998453i | \(-0.517706\pi\) | ||||
−0.0555949 | + | 0.998453i | \(0.517706\pi\) | |||||||
\(18\) | −2.87589 | −0.677853 | ||||||||
\(19\) | 0.0118520 | 0.00271904 | 0.00135952 | − | 0.999999i | \(-0.499567\pi\) | ||||
0.00135952 | + | 0.999999i | \(0.499567\pi\) | |||||||
\(20\) | −1.51534 | −0.338839 | ||||||||
\(21\) | 0.366752 | 0.0800319 | ||||||||
\(22\) | 3.44169 | 0.733771 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −0.352298 | −0.0719125 | ||||||||
\(25\) | −2.70376 | −0.540751 | ||||||||
\(26\) | −5.23410 | −1.02649 | ||||||||
\(27\) | 2.07006 | 0.398384 | ||||||||
\(28\) | −1.04103 | −0.196736 | ||||||||
\(29\) | 5.71753 | 1.06172 | 0.530860 | − | 0.847460i | \(-0.321869\pi\) | ||||
0.530860 | + | 0.847460i | \(0.321869\pi\) | |||||||
\(30\) | 0.533849 | 0.0974671 | ||||||||
\(31\) | −7.95942 | −1.42955 | −0.714777 | − | 0.699352i | \(-0.753472\pi\) | ||||
−0.714777 | + | 0.699352i | \(0.753472\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.21250 | −0.211069 | ||||||||
\(34\) | −0.458447 | −0.0786231 | ||||||||
\(35\) | 1.57751 | 0.266648 | ||||||||
\(36\) | −2.87589 | −0.479314 | ||||||||
\(37\) | 3.61468 | 0.594249 | 0.297125 | − | 0.954839i | \(-0.403972\pi\) | ||||
0.297125 | + | 0.954839i | \(0.403972\pi\) | |||||||
\(38\) | 0.0118520 | 0.00192265 | ||||||||
\(39\) | 1.84396 | 0.295270 | ||||||||
\(40\) | −1.51534 | −0.239596 | ||||||||
\(41\) | −4.81763 | −0.752387 | −0.376194 | − | 0.926541i | \(-0.622767\pi\) | ||||
−0.376194 | + | 0.926541i | \(0.622767\pi\) | |||||||
\(42\) | 0.366752 | 0.0565911 | ||||||||
\(43\) | 10.3818 | 1.58321 | 0.791603 | − | 0.611035i | \(-0.209247\pi\) | ||||
0.791603 | + | 0.611035i | \(0.209247\pi\) | |||||||
\(44\) | 3.44169 | 0.518855 | ||||||||
\(45\) | 4.35793 | 0.649642 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 8.16294 | 1.19069 | 0.595344 | − | 0.803471i | \(-0.297016\pi\) | ||||
0.595344 | + | 0.803471i | \(0.297016\pi\) | |||||||
\(48\) | −0.352298 | −0.0508498 | ||||||||
\(49\) | −5.91626 | −0.845180 | ||||||||
\(50\) | −2.70376 | −0.382369 | ||||||||
\(51\) | 0.161510 | 0.0226159 | ||||||||
\(52\) | −5.23410 | −0.725839 | ||||||||
\(53\) | 0.539296 | 0.0740779 | 0.0370390 | − | 0.999314i | \(-0.488207\pi\) | ||||
0.0370390 | + | 0.999314i | \(0.488207\pi\) | |||||||
\(54\) | 2.07006 | 0.281700 | ||||||||
\(55\) | −5.21532 | −0.703234 | ||||||||
\(56\) | −1.04103 | −0.139113 | ||||||||
\(57\) | −0.00417544 | −0.000553051 0 | ||||||||
\(58\) | 5.71753 | 0.750749 | ||||||||
\(59\) | 12.5348 | 1.63190 | 0.815948 | − | 0.578126i | \(-0.196216\pi\) | ||||
0.815948 | + | 0.578126i | \(0.196216\pi\) | |||||||
\(60\) | 0.533849 | 0.0689197 | ||||||||
\(61\) | 2.65629 | 0.340104 | 0.170052 | − | 0.985435i | \(-0.445607\pi\) | ||||
0.170052 | + | 0.985435i | \(0.445607\pi\) | |||||||
\(62\) | −7.95942 | −1.01085 | ||||||||
\(63\) | 2.99388 | 0.377193 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.93142 | 0.983771 | ||||||||
\(66\) | −1.21250 | −0.149248 | ||||||||
\(67\) | 7.91446 | 0.966905 | 0.483453 | − | 0.875371i | \(-0.339383\pi\) | ||||
0.483453 | + | 0.875371i | \(0.339383\pi\) | |||||||
\(68\) | −0.458447 | −0.0555949 | ||||||||
\(69\) | −0.352298 | −0.0424117 | ||||||||
\(70\) | 1.57751 | 0.188548 | ||||||||
\(71\) | −2.66119 | −0.315825 | −0.157912 | − | 0.987453i | \(-0.550476\pi\) | ||||
−0.157912 | + | 0.987453i | \(0.550476\pi\) | |||||||
\(72\) | −2.87589 | −0.338926 | ||||||||
\(73\) | −15.3570 | −1.79740 | −0.898701 | − | 0.438563i | \(-0.855488\pi\) | ||||
−0.898701 | + | 0.438563i | \(0.855488\pi\) | |||||||
\(74\) | 3.61468 | 0.420198 | ||||||||
\(75\) | 0.952528 | 0.109988 | ||||||||
\(76\) | 0.0118520 | 0.00135952 | ||||||||
\(77\) | −3.58290 | −0.408309 | ||||||||
\(78\) | 1.84396 | 0.208788 | ||||||||
\(79\) | 3.78651 | 0.426016 | 0.213008 | − | 0.977050i | \(-0.431674\pi\) | ||||
0.213008 | + | 0.977050i | \(0.431674\pi\) | |||||||
\(80\) | −1.51534 | −0.169420 | ||||||||
\(81\) | 7.89838 | 0.877598 | ||||||||
\(82\) | −4.81763 | −0.532018 | ||||||||
\(83\) | 13.5375 | 1.48594 | 0.742968 | − | 0.669327i | \(-0.233418\pi\) | ||||
0.742968 | + | 0.669327i | \(0.233418\pi\) | |||||||
\(84\) | 0.366752 | 0.0400159 | ||||||||
\(85\) | 0.694702 | 0.0753510 | ||||||||
\(86\) | 10.3818 | 1.11950 | ||||||||
\(87\) | −2.01427 | −0.215953 | ||||||||
\(88\) | 3.44169 | 0.366886 | ||||||||
\(89\) | −1.83019 | −0.194000 | −0.0970000 | − | 0.995284i | \(-0.530925\pi\) | ||||
−0.0970000 | + | 0.995284i | \(0.530925\pi\) | |||||||
\(90\) | 4.35793 | 0.459367 | ||||||||
\(91\) | 5.44885 | 0.571194 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 2.80409 | 0.290770 | ||||||||
\(94\) | 8.16294 | 0.841943 | ||||||||
\(95\) | −0.0179598 | −0.00184264 | ||||||||
\(96\) | −0.352298 | −0.0359562 | ||||||||
\(97\) | −7.88491 | −0.800592 | −0.400296 | − | 0.916386i | \(-0.631093\pi\) | ||||
−0.400296 | + | 0.916386i | \(0.631093\pi\) | |||||||
\(98\) | −5.91626 | −0.597632 | ||||||||
\(99\) | −9.89791 | −0.994778 | ||||||||
\(100\) | −2.70376 | −0.270376 | ||||||||
\(101\) | 14.3080 | 1.42369 | 0.711847 | − | 0.702334i | \(-0.247859\pi\) | ||||
0.711847 | + | 0.702334i | \(0.247859\pi\) | |||||||
\(102\) | 0.161510 | 0.0159919 | ||||||||
\(103\) | 17.6647 | 1.74055 | 0.870275 | − | 0.492566i | \(-0.163941\pi\) | ||||
0.870275 | + | 0.492566i | \(0.163941\pi\) | |||||||
\(104\) | −5.23410 | −0.513246 | ||||||||
\(105\) | −0.555753 | −0.0542359 | ||||||||
\(106\) | 0.539296 | 0.0523810 | ||||||||
\(107\) | −0.999157 | −0.0965922 | −0.0482961 | − | 0.998833i | \(-0.515379\pi\) | ||||
−0.0482961 | + | 0.998833i | \(0.515379\pi\) | |||||||
\(108\) | 2.07006 | 0.199192 | ||||||||
\(109\) | −6.65393 | −0.637331 | −0.318666 | − | 0.947867i | \(-0.603235\pi\) | ||||
−0.318666 | + | 0.947867i | \(0.603235\pi\) | |||||||
\(110\) | −5.21532 | −0.497261 | ||||||||
\(111\) | −1.27344 | −0.120870 | ||||||||
\(112\) | −1.04103 | −0.0983680 | ||||||||
\(113\) | −13.5888 | −1.27833 | −0.639163 | − | 0.769072i | \(-0.720719\pi\) | ||||
−0.639163 | + | 0.769072i | \(0.720719\pi\) | |||||||
\(114\) | −0.00417544 | −0.000391066 0 | ||||||||
\(115\) | −1.51534 | −0.141306 | ||||||||
\(116\) | 5.71753 | 0.530860 | ||||||||
\(117\) | 15.0527 | 1.39162 | ||||||||
\(118\) | 12.5348 | 1.15392 | ||||||||
\(119\) | 0.477257 | 0.0437501 | ||||||||
\(120\) | 0.533849 | 0.0487336 | ||||||||
\(121\) | 0.845244 | 0.0768403 | ||||||||
\(122\) | 2.65629 | 0.240490 | ||||||||
\(123\) | 1.69724 | 0.153035 | ||||||||
\(124\) | −7.95942 | −0.714777 | ||||||||
\(125\) | 11.6738 | 1.04413 | ||||||||
\(126\) | 2.99388 | 0.266716 | ||||||||
\(127\) | 3.40953 | 0.302547 | 0.151273 | − | 0.988492i | \(-0.451663\pi\) | ||||
0.151273 | + | 0.988492i | \(0.451663\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.65748 | −0.322023 | ||||||||
\(130\) | 7.93142 | 0.695631 | ||||||||
\(131\) | 1.00000 | 0.0873704 | ||||||||
\(132\) | −1.21250 | −0.105535 | ||||||||
\(133\) | −0.0123383 | −0.00106987 | ||||||||
\(134\) | 7.91446 | 0.683705 | ||||||||
\(135\) | −3.13684 | −0.269976 | ||||||||
\(136\) | −0.458447 | −0.0393115 | ||||||||
\(137\) | 18.4716 | 1.57814 | 0.789069 | − | 0.614305i | \(-0.210563\pi\) | ||||
0.789069 | + | 0.614305i | \(0.210563\pi\) | |||||||
\(138\) | −0.352298 | −0.0299896 | ||||||||
\(139\) | −7.10422 | −0.602572 | −0.301286 | − | 0.953534i | \(-0.597416\pi\) | ||||
−0.301286 | + | 0.953534i | \(0.597416\pi\) | |||||||
\(140\) | 1.57751 | 0.133324 | ||||||||
\(141\) | −2.87579 | −0.242185 | ||||||||
\(142\) | −2.66119 | −0.223322 | ||||||||
\(143\) | −18.0142 | −1.50642 | ||||||||
\(144\) | −2.87589 | −0.239657 | ||||||||
\(145\) | −8.66398 | −0.719505 | ||||||||
\(146\) | −15.3570 | −1.27095 | ||||||||
\(147\) | 2.08428 | 0.171909 | ||||||||
\(148\) | 3.61468 | 0.297125 | ||||||||
\(149\) | 12.8693 | 1.05429 | 0.527146 | − | 0.849775i | \(-0.323262\pi\) | ||||
0.527146 | + | 0.849775i | \(0.323262\pi\) | |||||||
\(150\) | 0.952528 | 0.0777736 | ||||||||
\(151\) | −14.7178 | −1.19772 | −0.598860 | − | 0.800853i | \(-0.704380\pi\) | ||||
−0.598860 | + | 0.800853i | \(0.704380\pi\) | |||||||
\(152\) | 0.0118520 | 0.000961326 0 | ||||||||
\(153\) | 1.31844 | 0.106590 | ||||||||
\(154\) | −3.58290 | −0.288718 | ||||||||
\(155\) | 12.0612 | 0.968779 | ||||||||
\(156\) | 1.84396 | 0.147635 | ||||||||
\(157\) | 17.4726 | 1.39447 | 0.697233 | − | 0.716845i | \(-0.254414\pi\) | ||||
0.697233 | + | 0.716845i | \(0.254414\pi\) | |||||||
\(158\) | 3.78651 | 0.301239 | ||||||||
\(159\) | −0.189993 | −0.0150674 | ||||||||
\(160\) | −1.51534 | −0.119798 | ||||||||
\(161\) | −1.04103 | −0.0820446 | ||||||||
\(162\) | 7.89838 | 0.620555 | ||||||||
\(163\) | 7.29343 | 0.571265 | 0.285633 | − | 0.958339i | \(-0.407796\pi\) | ||||
0.285633 | + | 0.958339i | \(0.407796\pi\) | |||||||
\(164\) | −4.81763 | −0.376194 | ||||||||
\(165\) | 1.83735 | 0.143037 | ||||||||
\(166\) | 13.5375 | 1.05071 | ||||||||
\(167\) | 7.28136 | 0.563448 | 0.281724 | − | 0.959495i | \(-0.409094\pi\) | ||||
0.281724 | + | 0.959495i | \(0.409094\pi\) | |||||||
\(168\) | 0.366752 | 0.0282955 | ||||||||
\(169\) | 14.3958 | 1.10737 | ||||||||
\(170\) | 0.694702 | 0.0532812 | ||||||||
\(171\) | −0.0340851 | −0.00260655 | ||||||||
\(172\) | 10.3818 | 0.791603 | ||||||||
\(173\) | −22.0643 | −1.67751 | −0.838757 | − | 0.544505i | \(-0.816717\pi\) | ||||
−0.838757 | + | 0.544505i | \(0.816717\pi\) | |||||||
\(174\) | −2.01427 | −0.152702 | ||||||||
\(175\) | 2.81469 | 0.212770 | ||||||||
\(176\) | 3.44169 | 0.259427 | ||||||||
\(177\) | −4.41599 | −0.331926 | ||||||||
\(178\) | −1.83019 | −0.137179 | ||||||||
\(179\) | 24.9774 | 1.86690 | 0.933448 | − | 0.358711i | \(-0.116784\pi\) | ||||
0.933448 | + | 0.358711i | \(0.116784\pi\) | |||||||
\(180\) | 4.35793 | 0.324821 | ||||||||
\(181\) | −8.10577 | −0.602497 | −0.301248 | − | 0.953546i | \(-0.597403\pi\) | ||||
−0.301248 | + | 0.953546i | \(0.597403\pi\) | |||||||
\(182\) | 5.44885 | 0.403896 | ||||||||
\(183\) | −0.935806 | −0.0691768 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −5.47745 | −0.402710 | ||||||||
\(186\) | 2.80409 | 0.205606 | ||||||||
\(187\) | −1.57783 | −0.115383 | ||||||||
\(188\) | 8.16294 | 0.595344 | ||||||||
\(189\) | −2.15499 | −0.156753 | ||||||||
\(190\) | −0.0179598 | −0.00130294 | ||||||||
\(191\) | 17.2642 | 1.24920 | 0.624598 | − | 0.780946i | \(-0.285263\pi\) | ||||
0.624598 | + | 0.780946i | \(0.285263\pi\) | |||||||
\(192\) | −0.352298 | −0.0254249 | ||||||||
\(193\) | 1.60663 | 0.115648 | 0.0578240 | − | 0.998327i | \(-0.481584\pi\) | ||||
0.0578240 | + | 0.998327i | \(0.481584\pi\) | |||||||
\(194\) | −7.88491 | −0.566104 | ||||||||
\(195\) | −2.79422 | −0.200098 | ||||||||
\(196\) | −5.91626 | −0.422590 | ||||||||
\(197\) | 9.97120 | 0.710418 | 0.355209 | − | 0.934787i | \(-0.384410\pi\) | ||||
0.355209 | + | 0.934787i | \(0.384410\pi\) | |||||||
\(198\) | −9.89791 | −0.703414 | ||||||||
\(199\) | −14.3287 | −1.01574 | −0.507869 | − | 0.861435i | \(-0.669566\pi\) | ||||
−0.507869 | + | 0.861435i | \(0.669566\pi\) | |||||||
\(200\) | −2.70376 | −0.191185 | ||||||||
\(201\) | −2.78825 | −0.196668 | ||||||||
\(202\) | 14.3080 | 1.00670 | ||||||||
\(203\) | −5.95212 | −0.417757 | ||||||||
\(204\) | 0.161510 | 0.0113080 | ||||||||
\(205\) | 7.30033 | 0.509877 | ||||||||
\(206\) | 17.6647 | 1.23075 | ||||||||
\(207\) | −2.87589 | −0.199888 | ||||||||
\(208\) | −5.23410 | −0.362920 | ||||||||
\(209\) | 0.0407910 | 0.00282157 | ||||||||
\(210\) | −0.555753 | −0.0383506 | ||||||||
\(211\) | 25.1471 | 1.73120 | 0.865600 | − | 0.500736i | \(-0.166937\pi\) | ||||
0.865600 | + | 0.500736i | \(0.166937\pi\) | |||||||
\(212\) | 0.539296 | 0.0370390 | ||||||||
\(213\) | 0.937530 | 0.0642385 | ||||||||
\(214\) | −0.999157 | −0.0683010 | ||||||||
\(215\) | −15.7319 | −1.07291 | ||||||||
\(216\) | 2.07006 | 0.140850 | ||||||||
\(217\) | 8.28599 | 0.562490 | ||||||||
\(218\) | −6.65393 | −0.450661 | ||||||||
\(219\) | 5.41024 | 0.365590 | ||||||||
\(220\) | −5.21532 | −0.351617 | ||||||||
\(221\) | 2.39956 | 0.161412 | ||||||||
\(222\) | −1.27344 | −0.0854679 | ||||||||
\(223\) | 13.8372 | 0.926605 | 0.463303 | − | 0.886200i | \(-0.346664\pi\) | ||||
0.463303 | + | 0.886200i | \(0.346664\pi\) | |||||||
\(224\) | −1.04103 | −0.0695567 | ||||||||
\(225\) | 7.77570 | 0.518380 | ||||||||
\(226\) | −13.5888 | −0.903912 | ||||||||
\(227\) | −2.71032 | −0.179890 | −0.0899450 | − | 0.995947i | \(-0.528669\pi\) | ||||
−0.0899450 | + | 0.995947i | \(0.528669\pi\) | |||||||
\(228\) | −0.00417544 | −0.000276525 0 | ||||||||
\(229\) | −12.8284 | −0.847724 | −0.423862 | − | 0.905727i | \(-0.639326\pi\) | ||||
−0.423862 | + | 0.905727i | \(0.639326\pi\) | |||||||
\(230\) | −1.51534 | −0.0999183 | ||||||||
\(231\) | 1.26225 | 0.0830498 | ||||||||
\(232\) | 5.71753 | 0.375374 | ||||||||
\(233\) | 2.43023 | 0.159210 | 0.0796049 | − | 0.996826i | \(-0.474634\pi\) | ||||
0.0796049 | + | 0.996826i | \(0.474634\pi\) | |||||||
\(234\) | 15.0527 | 0.984024 | ||||||||
\(235\) | −12.3696 | −0.806903 | ||||||||
\(236\) | 12.5348 | 0.815948 | ||||||||
\(237\) | −1.33398 | −0.0866513 | ||||||||
\(238\) | 0.477257 | 0.0309360 | ||||||||
\(239\) | −15.5872 | −1.00825 | −0.504126 | − | 0.863630i | \(-0.668185\pi\) | ||||
−0.504126 | + | 0.863630i | \(0.668185\pi\) | |||||||
\(240\) | 0.533849 | 0.0344598 | ||||||||
\(241\) | 14.0684 | 0.906226 | 0.453113 | − | 0.891453i | \(-0.350313\pi\) | ||||
0.453113 | + | 0.891453i | \(0.350313\pi\) | |||||||
\(242\) | 0.845244 | 0.0543343 | ||||||||
\(243\) | −8.99277 | −0.576886 | ||||||||
\(244\) | 2.65629 | 0.170052 | ||||||||
\(245\) | 8.96512 | 0.572760 | ||||||||
\(246\) | 1.69724 | 0.108212 | ||||||||
\(247\) | −0.0620347 | −0.00394717 | ||||||||
\(248\) | −7.95942 | −0.505424 | ||||||||
\(249\) | −4.76924 | −0.302238 | ||||||||
\(250\) | 11.6738 | 0.738315 | ||||||||
\(251\) | 26.5809 | 1.67777 | 0.838885 | − | 0.544308i | \(-0.183208\pi\) | ||||
0.838885 | + | 0.544308i | \(0.183208\pi\) | |||||||
\(252\) | 2.99388 | 0.188597 | ||||||||
\(253\) | 3.44169 | 0.216377 | ||||||||
\(254\) | 3.40953 | 0.213933 | ||||||||
\(255\) | −0.244742 | −0.0153263 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.2214 | −1.32376 | −0.661879 | − | 0.749611i | \(-0.730241\pi\) | ||||
−0.661879 | + | 0.749611i | \(0.730241\pi\) | |||||||
\(258\) | −3.65748 | −0.227705 | ||||||||
\(259\) | −3.76298 | −0.233820 | ||||||||
\(260\) | 7.93142 | 0.491886 | ||||||||
\(261\) | −16.4430 | −1.01779 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | 18.7421 | 1.15569 | 0.577843 | − | 0.816148i | \(-0.303895\pi\) | ||||
0.577843 | + | 0.816148i | \(0.303895\pi\) | |||||||
\(264\) | −1.21250 | −0.0746242 | ||||||||
\(265\) | −0.817214 | −0.0502011 | ||||||||
\(266\) | −0.0123383 | −0.000756510 0 | ||||||||
\(267\) | 0.644773 | 0.0394594 | ||||||||
\(268\) | 7.91446 | 0.483453 | ||||||||
\(269\) | −0.923774 | −0.0563235 | −0.0281617 | − | 0.999603i | \(-0.508965\pi\) | ||||
−0.0281617 | + | 0.999603i | \(0.508965\pi\) | |||||||
\(270\) | −3.13684 | −0.190902 | ||||||||
\(271\) | −4.53739 | −0.275627 | −0.137813 | − | 0.990458i | \(-0.544007\pi\) | ||||
−0.137813 | + | 0.990458i | \(0.544007\pi\) | |||||||
\(272\) | −0.458447 | −0.0277974 | ||||||||
\(273\) | −1.91962 | −0.116181 | ||||||||
\(274\) | 18.4716 | 1.11591 | ||||||||
\(275\) | −9.30550 | −0.561143 | ||||||||
\(276\) | −0.352298 | −0.0212058 | ||||||||
\(277\) | 22.6030 | 1.35808 | 0.679042 | − | 0.734100i | \(-0.262396\pi\) | ||||
0.679042 | + | 0.734100i | \(0.262396\pi\) | |||||||
\(278\) | −7.10422 | −0.426083 | ||||||||
\(279\) | 22.8904 | 1.37041 | ||||||||
\(280\) | 1.57751 | 0.0942741 | ||||||||
\(281\) | −10.3379 | −0.616707 | −0.308354 | − | 0.951272i | \(-0.599778\pi\) | ||||
−0.308354 | + | 0.951272i | \(0.599778\pi\) | |||||||
\(282\) | −2.87579 | −0.171251 | ||||||||
\(283\) | −20.7533 | −1.23365 | −0.616827 | − | 0.787098i | \(-0.711582\pi\) | ||||
−0.616827 | + | 0.787098i | \(0.711582\pi\) | |||||||
\(284\) | −2.66119 | −0.157912 | ||||||||
\(285\) | 0.00632720 | 0.000374791 0 | ||||||||
\(286\) | −18.0142 | −1.06520 | ||||||||
\(287\) | 5.01529 | 0.296043 | ||||||||
\(288\) | −2.87589 | −0.169463 | ||||||||
\(289\) | −16.7898 | −0.987637 | ||||||||
\(290\) | −8.66398 | −0.508767 | ||||||||
\(291\) | 2.77784 | 0.162840 | ||||||||
\(292\) | −15.3570 | −0.898701 | ||||||||
\(293\) | 7.78476 | 0.454791 | 0.227395 | − | 0.973803i | \(-0.426979\pi\) | ||||
0.227395 | + | 0.973803i | \(0.426979\pi\) | |||||||
\(294\) | 2.08428 | 0.121558 | ||||||||
\(295\) | −18.9945 | −1.10590 | ||||||||
\(296\) | 3.61468 | 0.210099 | ||||||||
\(297\) | 7.12451 | 0.413406 | ||||||||
\(298\) | 12.8693 | 0.745496 | ||||||||
\(299\) | −5.23410 | −0.302696 | ||||||||
\(300\) | 0.952528 | 0.0549942 | ||||||||
\(301\) | −10.8077 | −0.622947 | ||||||||
\(302\) | −14.7178 | −0.846917 | ||||||||
\(303\) | −5.04066 | −0.289578 | ||||||||
\(304\) | 0.0118520 | 0.000679760 0 | ||||||||
\(305\) | −4.02518 | −0.230481 | ||||||||
\(306\) | 1.31844 | 0.0753703 | ||||||||
\(307\) | −1.97831 | −0.112908 | −0.0564540 | − | 0.998405i | \(-0.517979\pi\) | ||||
−0.0564540 | + | 0.998405i | \(0.517979\pi\) | |||||||
\(308\) | −3.58290 | −0.204155 | ||||||||
\(309\) | −6.22322 | −0.354027 | ||||||||
\(310\) | 12.0612 | 0.685030 | ||||||||
\(311\) | 31.0217 | 1.75908 | 0.879540 | − | 0.475825i | \(-0.157850\pi\) | ||||
0.879540 | + | 0.475825i | \(0.157850\pi\) | |||||||
\(312\) | 1.84396 | 0.104394 | ||||||||
\(313\) | −14.2749 | −0.806863 | −0.403432 | − | 0.915010i | \(-0.632183\pi\) | ||||
−0.403432 | + | 0.915010i | \(0.632183\pi\) | |||||||
\(314\) | 17.4726 | 0.986036 | ||||||||
\(315\) | −4.53673 | −0.255616 | ||||||||
\(316\) | 3.78651 | 0.213008 | ||||||||
\(317\) | −1.91311 | −0.107451 | −0.0537256 | − | 0.998556i | \(-0.517110\pi\) | ||||
−0.0537256 | + | 0.998556i | \(0.517110\pi\) | |||||||
\(318\) | −0.189993 | −0.0106543 | ||||||||
\(319\) | 19.6780 | 1.10176 | ||||||||
\(320\) | −1.51534 | −0.0847098 | ||||||||
\(321\) | 0.352001 | 0.0196468 | ||||||||
\(322\) | −1.04103 | −0.0580143 | ||||||||
\(323\) | −0.00543353 | −0.000302330 0 | ||||||||
\(324\) | 7.89838 | 0.438799 | ||||||||
\(325\) | 14.1517 | 0.784997 | ||||||||
\(326\) | 7.29343 | 0.403946 | ||||||||
\(327\) | 2.34417 | 0.129633 | ||||||||
\(328\) | −4.81763 | −0.266009 | ||||||||
\(329\) | −8.49785 | −0.468502 | ||||||||
\(330\) | 1.83735 | 0.101143 | ||||||||
\(331\) | −19.5088 | −1.07230 | −0.536149 | − | 0.844123i | \(-0.680122\pi\) | ||||
−0.536149 | + | 0.844123i | \(0.680122\pi\) | |||||||
\(332\) | 13.5375 | 0.742968 | ||||||||
\(333\) | −10.3954 | −0.569665 | ||||||||
\(334\) | 7.28136 | 0.398418 | ||||||||
\(335\) | −11.9931 | −0.655251 | ||||||||
\(336\) | 0.366752 | 0.0200080 | ||||||||
\(337\) | −16.7671 | −0.913364 | −0.456682 | − | 0.889630i | \(-0.650962\pi\) | ||||
−0.456682 | + | 0.889630i | \(0.650962\pi\) | |||||||
\(338\) | 14.3958 | 0.783028 | ||||||||
\(339\) | 4.78730 | 0.260010 | ||||||||
\(340\) | 0.694702 | 0.0376755 | ||||||||
\(341\) | −27.3939 | −1.48346 | ||||||||
\(342\) | −0.0340851 | −0.00184311 | ||||||||
\(343\) | 13.4462 | 0.726026 | ||||||||
\(344\) | 10.3818 | 0.559748 | ||||||||
\(345\) | 0.533849 | 0.0287415 | ||||||||
\(346\) | −22.0643 | −1.18618 | ||||||||
\(347\) | 20.5624 | 1.10385 | 0.551924 | − | 0.833894i | \(-0.313894\pi\) | ||||
0.551924 | + | 0.833894i | \(0.313894\pi\) | |||||||
\(348\) | −2.01427 | −0.107976 | ||||||||
\(349\) | 4.23107 | 0.226484 | 0.113242 | − | 0.993567i | \(-0.463876\pi\) | ||||
0.113242 | + | 0.993567i | \(0.463876\pi\) | |||||||
\(350\) | 2.81469 | 0.150451 | ||||||||
\(351\) | −10.8349 | −0.578325 | ||||||||
\(352\) | 3.44169 | 0.183443 | ||||||||
\(353\) | 10.0342 | 0.534068 | 0.267034 | − | 0.963687i | \(-0.413956\pi\) | ||||
0.267034 | + | 0.963687i | \(0.413956\pi\) | |||||||
\(354\) | −4.41599 | −0.234707 | ||||||||
\(355\) | 4.03259 | 0.214028 | ||||||||
\(356\) | −1.83019 | −0.0970000 | ||||||||
\(357\) | −0.168136 | −0.00889873 | ||||||||
\(358\) | 24.9774 | 1.32010 | ||||||||
\(359\) | 18.4158 | 0.971951 | 0.485976 | − | 0.873972i | \(-0.338464\pi\) | ||||
0.485976 | + | 0.873972i | \(0.338464\pi\) | |||||||
\(360\) | 4.35793 | 0.229683 | ||||||||
\(361\) | −18.9999 | −0.999993 | ||||||||
\(362\) | −8.10577 | −0.426030 | ||||||||
\(363\) | −0.297777 | −0.0156293 | ||||||||
\(364\) | 5.44885 | 0.285597 | ||||||||
\(365\) | 23.2710 | 1.21806 | ||||||||
\(366\) | −0.935806 | −0.0489154 | ||||||||
\(367\) | 15.9241 | 0.831233 | 0.415617 | − | 0.909540i | \(-0.363566\pi\) | ||||
0.415617 | + | 0.909540i | \(0.363566\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 13.8550 | 0.721260 | ||||||||
\(370\) | −5.47745 | −0.284759 | ||||||||
\(371\) | −0.561422 | −0.0291476 | ||||||||
\(372\) | 2.80409 | 0.145385 | ||||||||
\(373\) | 18.5232 | 0.959096 | 0.479548 | − | 0.877516i | \(-0.340801\pi\) | ||||
0.479548 | + | 0.877516i | \(0.340801\pi\) | |||||||
\(374\) | −1.57783 | −0.0815879 | ||||||||
\(375\) | −4.11265 | −0.212376 | ||||||||
\(376\) | 8.16294 | 0.420971 | ||||||||
\(377\) | −29.9261 | −1.54127 | ||||||||
\(378\) | −2.15499 | −0.110841 | ||||||||
\(379\) | 16.2185 | 0.833086 | 0.416543 | − | 0.909116i | \(-0.363241\pi\) | ||||
0.416543 | + | 0.909116i | \(0.363241\pi\) | |||||||
\(380\) | −0.0179598 | −0.000921318 0 | ||||||||
\(381\) | −1.20117 | −0.0615378 | ||||||||
\(382\) | 17.2642 | 0.883315 | ||||||||
\(383\) | −14.9956 | −0.766242 | −0.383121 | − | 0.923698i | \(-0.625151\pi\) | ||||
−0.383121 | + | 0.923698i | \(0.625151\pi\) | |||||||
\(384\) | −0.352298 | −0.0179781 | ||||||||
\(385\) | 5.42930 | 0.276703 | ||||||||
\(386\) | 1.60663 | 0.0817755 | ||||||||
\(387\) | −29.8568 | −1.51771 | ||||||||
\(388\) | −7.88491 | −0.400296 | ||||||||
\(389\) | −17.4007 | −0.882249 | −0.441125 | − | 0.897446i | \(-0.645420\pi\) | ||||
−0.441125 | + | 0.897446i | \(0.645420\pi\) | |||||||
\(390\) | −2.79422 | −0.141491 | ||||||||
\(391\) | −0.458447 | −0.0231847 | ||||||||
\(392\) | −5.91626 | −0.298816 | ||||||||
\(393\) | −0.352298 | −0.0177711 | ||||||||
\(394\) | 9.97120 | 0.502342 | ||||||||
\(395\) | −5.73784 | −0.288702 | ||||||||
\(396\) | −9.89791 | −0.497389 | ||||||||
\(397\) | −4.57924 | −0.229825 | −0.114913 | − | 0.993376i | \(-0.536659\pi\) | ||||
−0.114913 | + | 0.993376i | \(0.536659\pi\) | |||||||
\(398\) | −14.3287 | −0.718235 | ||||||||
\(399\) | 0.00434676 | 0.000217610 0 | ||||||||
\(400\) | −2.70376 | −0.135188 | ||||||||
\(401\) | 5.29946 | 0.264642 | 0.132321 | − | 0.991207i | \(-0.457757\pi\) | ||||
0.132321 | + | 0.991207i | \(0.457757\pi\) | |||||||
\(402\) | −2.78825 | −0.139065 | ||||||||
\(403\) | 41.6604 | 2.07525 | ||||||||
\(404\) | 14.3080 | 0.711847 | ||||||||
\(405\) | −11.9687 | −0.594729 | ||||||||
\(406\) | −5.95212 | −0.295399 | ||||||||
\(407\) | 12.4406 | 0.616658 | ||||||||
\(408\) | 0.161510 | 0.00799593 | ||||||||
\(409\) | 37.8084 | 1.86950 | 0.934752 | − | 0.355301i | \(-0.115622\pi\) | ||||
0.934752 | + | 0.355301i | \(0.115622\pi\) | |||||||
\(410\) | 7.30033 | 0.360537 | ||||||||
\(411\) | −6.50751 | −0.320992 | ||||||||
\(412\) | 17.6647 | 0.870275 | ||||||||
\(413\) | −13.0491 | −0.642105 | ||||||||
\(414\) | −2.87589 | −0.141342 | ||||||||
\(415\) | −20.5139 | −1.00699 | ||||||||
\(416\) | −5.23410 | −0.256623 | ||||||||
\(417\) | 2.50280 | 0.122563 | ||||||||
\(418\) | 0.0407910 | 0.00199515 | ||||||||
\(419\) | 6.59183 | 0.322032 | 0.161016 | − | 0.986952i | \(-0.448523\pi\) | ||||
0.161016 | + | 0.986952i | \(0.448523\pi\) | |||||||
\(420\) | −0.555753 | −0.0271179 | ||||||||
\(421\) | −26.7028 | −1.30141 | −0.650707 | − | 0.759329i | \(-0.725527\pi\) | ||||
−0.650707 | + | 0.759329i | \(0.725527\pi\) | |||||||
\(422\) | 25.1471 | 1.22414 | ||||||||
\(423\) | −23.4757 | −1.14143 | ||||||||
\(424\) | 0.539296 | 0.0261905 | ||||||||
\(425\) | 1.23953 | 0.0601260 | ||||||||
\(426\) | 0.937530 | 0.0454235 | ||||||||
\(427\) | −2.76528 | −0.133821 | ||||||||
\(428\) | −0.999157 | −0.0482961 | ||||||||
\(429\) | 6.34635 | 0.306405 | ||||||||
\(430\) | −15.7319 | −0.758659 | ||||||||
\(431\) | −22.9331 | −1.10465 | −0.552324 | − | 0.833629i | \(-0.686259\pi\) | ||||
−0.552324 | + | 0.833629i | \(0.686259\pi\) | |||||||
\(432\) | 2.07006 | 0.0995959 | ||||||||
\(433\) | −36.7661 | −1.76687 | −0.883433 | − | 0.468558i | \(-0.844774\pi\) | ||||
−0.883433 | + | 0.468558i | \(0.844774\pi\) | |||||||
\(434\) | 8.28599 | 0.397740 | ||||||||
\(435\) | 3.05230 | 0.146347 | ||||||||
\(436\) | −6.65393 | −0.318666 | ||||||||
\(437\) | 0.0118520 | 0.000566959 0 | ||||||||
\(438\) | 5.41024 | 0.258511 | ||||||||
\(439\) | 8.54496 | 0.407829 | 0.203914 | − | 0.978989i | \(-0.434634\pi\) | ||||
0.203914 | + | 0.978989i | \(0.434634\pi\) | |||||||
\(440\) | −5.21532 | −0.248631 | ||||||||
\(441\) | 17.0145 | 0.810214 | ||||||||
\(442\) | 2.39956 | 0.114135 | ||||||||
\(443\) | 20.9058 | 0.993263 | 0.496631 | − | 0.867962i | \(-0.334570\pi\) | ||||
0.496631 | + | 0.867962i | \(0.334570\pi\) | |||||||
\(444\) | −1.27344 | −0.0604349 | ||||||||
\(445\) | 2.77336 | 0.131470 | ||||||||
\(446\) | 13.8372 | 0.655209 | ||||||||
\(447\) | −4.53381 | −0.214442 | ||||||||
\(448\) | −1.04103 | −0.0491840 | ||||||||
\(449\) | −22.2619 | −1.05060 | −0.525301 | − | 0.850917i | \(-0.676047\pi\) | ||||
−0.525301 | + | 0.850917i | \(0.676047\pi\) | |||||||
\(450\) | 7.77570 | 0.366550 | ||||||||
\(451\) | −16.5808 | −0.780759 | ||||||||
\(452\) | −13.5888 | −0.639163 | ||||||||
\(453\) | 5.18506 | 0.243615 | ||||||||
\(454\) | −2.71032 | −0.127201 | ||||||||
\(455\) | −8.25684 | −0.387086 | ||||||||
\(456\) | −0.00417544 | −0.000195533 0 | ||||||||
\(457\) | 30.7283 | 1.43741 | 0.718705 | − | 0.695315i | \(-0.244735\pi\) | ||||
0.718705 | + | 0.695315i | \(0.244735\pi\) | |||||||
\(458\) | −12.8284 | −0.599431 | ||||||||
\(459\) | −0.949014 | −0.0442962 | ||||||||
\(460\) | −1.51534 | −0.0706529 | ||||||||
\(461\) | 1.84511 | 0.0859352 | 0.0429676 | − | 0.999076i | \(-0.486319\pi\) | ||||
0.0429676 | + | 0.999076i | \(0.486319\pi\) | |||||||
\(462\) | 1.26225 | 0.0587251 | ||||||||
\(463\) | −18.9409 | −0.880258 | −0.440129 | − | 0.897935i | \(-0.645067\pi\) | ||||
−0.440129 | + | 0.897935i | \(0.645067\pi\) | |||||||
\(464\) | 5.71753 | 0.265430 | ||||||||
\(465\) | −4.24913 | −0.197049 | ||||||||
\(466\) | 2.43023 | 0.112578 | ||||||||
\(467\) | −27.4815 | −1.27169 | −0.635846 | − | 0.771816i | \(-0.719349\pi\) | ||||
−0.635846 | + | 0.771816i | \(0.719349\pi\) | |||||||
\(468\) | 15.0527 | 0.695810 | ||||||||
\(469\) | −8.23918 | −0.380450 | ||||||||
\(470\) | −12.3696 | −0.570567 | ||||||||
\(471\) | −6.15556 | −0.283633 | ||||||||
\(472\) | 12.5348 | 0.576962 | ||||||||
\(473\) | 35.7309 | 1.64291 | ||||||||
\(474\) | −1.33398 | −0.0612717 | ||||||||
\(475\) | −0.0320450 | −0.00147033 | ||||||||
\(476\) | 0.477257 | 0.0218750 | ||||||||
\(477\) | −1.55095 | −0.0710132 | ||||||||
\(478\) | −15.5872 | −0.712942 | ||||||||
\(479\) | 31.3647 | 1.43309 | 0.716545 | − | 0.697541i | \(-0.245722\pi\) | ||||
0.716545 | + | 0.697541i | \(0.245722\pi\) | |||||||
\(480\) | 0.533849 | 0.0243668 | ||||||||
\(481\) | −18.9196 | −0.862659 | ||||||||
\(482\) | 14.0684 | 0.640799 | ||||||||
\(483\) | 0.366752 | 0.0166878 | ||||||||
\(484\) | 0.845244 | 0.0384202 | ||||||||
\(485\) | 11.9483 | 0.542544 | ||||||||
\(486\) | −8.99277 | −0.407920 | ||||||||
\(487\) | 17.6248 | 0.798655 | 0.399328 | − | 0.916808i | \(-0.369244\pi\) | ||||
0.399328 | + | 0.916808i | \(0.369244\pi\) | |||||||
\(488\) | 2.65629 | 0.120245 | ||||||||
\(489\) | −2.56946 | −0.116195 | ||||||||
\(490\) | 8.96512 | 0.405003 | ||||||||
\(491\) | 24.4755 | 1.10456 | 0.552282 | − | 0.833658i | \(-0.313757\pi\) | ||||
0.552282 | + | 0.833658i | \(0.313757\pi\) | |||||||
\(492\) | 1.69724 | 0.0765175 | ||||||||
\(493\) | −2.62119 | −0.118052 | ||||||||
\(494\) | −0.0620347 | −0.00279107 | ||||||||
\(495\) | 14.9987 | 0.674140 | ||||||||
\(496\) | −7.95942 | −0.357389 | ||||||||
\(497\) | 2.77037 | 0.124268 | ||||||||
\(498\) | −4.76924 | −0.213715 | ||||||||
\(499\) | 31.3949 | 1.40543 | 0.702713 | − | 0.711473i | \(-0.251972\pi\) | ||||
0.702713 | + | 0.711473i | \(0.251972\pi\) | |||||||
\(500\) | 11.6738 | 0.522067 | ||||||||
\(501\) | −2.56521 | −0.114605 | ||||||||
\(502\) | 26.5809 | 1.18636 | ||||||||
\(503\) | 15.5797 | 0.694665 | 0.347333 | − | 0.937742i | \(-0.387087\pi\) | ||||
0.347333 | + | 0.937742i | \(0.387087\pi\) | |||||||
\(504\) | 2.99388 | 0.133358 | ||||||||
\(505\) | −21.6814 | −0.964808 | ||||||||
\(506\) | 3.44169 | 0.153002 | ||||||||
\(507\) | −5.07161 | −0.225238 | ||||||||
\(508\) | 3.40953 | 0.151273 | ||||||||
\(509\) | −11.8461 | −0.525070 | −0.262535 | − | 0.964923i | \(-0.584558\pi\) | ||||
−0.262535 | + | 0.964923i | \(0.584558\pi\) | |||||||
\(510\) | −0.244742 | −0.0108373 | ||||||||
\(511\) | 15.9871 | 0.707227 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.0245344 | 0.00108322 | ||||||||
\(514\) | −21.2214 | −0.936038 | ||||||||
\(515\) | −26.7679 | −1.17953 | ||||||||
\(516\) | −3.65748 | −0.161012 | ||||||||
\(517\) | 28.0943 | 1.23559 | ||||||||
\(518\) | −3.76298 | −0.165336 | ||||||||
\(519\) | 7.77319 | 0.341205 | ||||||||
\(520\) | 7.93142 | 0.347816 | ||||||||
\(521\) | −27.8162 | −1.21865 | −0.609324 | − | 0.792921i | \(-0.708559\pi\) | ||||
−0.609324 | + | 0.792921i | \(0.708559\pi\) | |||||||
\(522\) | −16.4430 | −0.719690 | ||||||||
\(523\) | −15.9098 | −0.695689 | −0.347844 | − | 0.937552i | \(-0.613086\pi\) | ||||
−0.347844 | + | 0.937552i | \(0.613086\pi\) | |||||||
\(524\) | 1.00000 | 0.0436852 | ||||||||
\(525\) | −0.991609 | −0.0432773 | ||||||||
\(526\) | 18.7421 | 0.817193 | ||||||||
\(527\) | 3.64898 | 0.158952 | ||||||||
\(528\) | −1.21250 | −0.0527673 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.817214 | −0.0354975 | ||||||||
\(531\) | −36.0487 | −1.56438 | ||||||||
\(532\) | −0.0123383 | −0.000534933 0 | ||||||||
\(533\) | 25.2160 | 1.09222 | ||||||||
\(534\) | 0.644773 | 0.0279020 | ||||||||
\(535\) | 1.51406 | 0.0654585 | ||||||||
\(536\) | 7.91446 | 0.341853 | ||||||||
\(537\) | −8.79948 | −0.379725 | ||||||||
\(538\) | −0.923774 | −0.0398267 | ||||||||
\(539\) | −20.3619 | −0.877051 | ||||||||
\(540\) | −3.13684 | −0.134988 | ||||||||
\(541\) | 30.0126 | 1.29034 | 0.645172 | − | 0.764037i | \(-0.276786\pi\) | ||||
0.645172 | + | 0.764037i | \(0.276786\pi\) | |||||||
\(542\) | −4.53739 | −0.194898 | ||||||||
\(543\) | 2.85564 | 0.122547 | ||||||||
\(544\) | −0.458447 | −0.0196558 | ||||||||
\(545\) | 10.0829 | 0.431906 | ||||||||
\(546\) | −1.91962 | −0.0821520 | ||||||||
\(547\) | −43.2762 | −1.85035 | −0.925177 | − | 0.379535i | \(-0.876084\pi\) | ||||
−0.925177 | + | 0.379535i | \(0.876084\pi\) | |||||||
\(548\) | 18.4716 | 0.789069 | ||||||||
\(549\) | −7.63920 | −0.326033 | ||||||||
\(550\) | −9.30550 | −0.396788 | ||||||||
\(551\) | 0.0677644 | 0.00288686 | ||||||||
\(552\) | −0.352298 | −0.0149948 | ||||||||
\(553\) | −3.94187 | −0.167625 | ||||||||
\(554\) | 22.6030 | 0.960310 | ||||||||
\(555\) | 1.92969 | 0.0819109 | ||||||||
\(556\) | −7.10422 | −0.301286 | ||||||||
\(557\) | 13.3302 | 0.564820 | 0.282410 | − | 0.959294i | \(-0.408866\pi\) | ||||
0.282410 | + | 0.959294i | \(0.408866\pi\) | |||||||
\(558\) | 22.8904 | 0.969028 | ||||||||
\(559\) | −54.3393 | −2.29831 | ||||||||
\(560\) | 1.57751 | 0.0666619 | ||||||||
\(561\) | 0.555867 | 0.0234687 | ||||||||
\(562\) | −10.3379 | −0.436078 | ||||||||
\(563\) | −26.2627 | −1.10684 | −0.553420 | − | 0.832903i | \(-0.686677\pi\) | ||||
−0.553420 | + | 0.832903i | \(0.686677\pi\) | |||||||
\(564\) | −2.87579 | −0.121092 | ||||||||
\(565\) | 20.5916 | 0.866294 | ||||||||
\(566\) | −20.7533 | −0.872326 | ||||||||
\(567\) | −8.22244 | −0.345310 | ||||||||
\(568\) | −2.66119 | −0.111661 | ||||||||
\(569\) | 26.0421 | 1.09174 | 0.545871 | − | 0.837869i | \(-0.316199\pi\) | ||||
0.545871 | + | 0.837869i | \(0.316199\pi\) | |||||||
\(570\) | 0.00632720 | 0.000265017 0 | ||||||||
\(571\) | −45.9614 | −1.92342 | −0.961712 | − | 0.274062i | \(-0.911633\pi\) | ||||
−0.961712 | + | 0.274062i | \(0.911633\pi\) | |||||||
\(572\) | −18.0142 | −0.753210 | ||||||||
\(573\) | −6.08215 | −0.254086 | ||||||||
\(574\) | 5.01529 | 0.209334 | ||||||||
\(575\) | −2.70376 | −0.112754 | ||||||||
\(576\) | −2.87589 | −0.119829 | ||||||||
\(577\) | −27.5783 | −1.14810 | −0.574050 | − | 0.818821i | \(-0.694628\pi\) | ||||
−0.574050 | + | 0.818821i | \(0.694628\pi\) | |||||||
\(578\) | −16.7898 | −0.698365 | ||||||||
\(579\) | −0.566013 | −0.0235227 | ||||||||
\(580\) | −8.66398 | −0.359752 | ||||||||
\(581\) | −14.0929 | −0.584674 | ||||||||
\(582\) | 2.77784 | 0.115145 | ||||||||
\(583\) | 1.85609 | 0.0768714 | ||||||||
\(584\) | −15.3570 | −0.635477 | ||||||||
\(585\) | −22.8099 | −0.943072 | ||||||||
\(586\) | 7.78476 | 0.321586 | ||||||||
\(587\) | −18.8978 | −0.779997 | −0.389999 | − | 0.920815i | \(-0.627524\pi\) | ||||
−0.389999 | + | 0.920815i | \(0.627524\pi\) | |||||||
\(588\) | 2.08428 | 0.0859545 | ||||||||
\(589\) | −0.0943353 | −0.00388702 | ||||||||
\(590\) | −18.9945 | −0.781990 | ||||||||
\(591\) | −3.51283 | −0.144499 | ||||||||
\(592\) | 3.61468 | 0.148562 | ||||||||
\(593\) | 1.83243 | 0.0752491 | 0.0376245 | − | 0.999292i | \(-0.488021\pi\) | ||||
0.0376245 | + | 0.999292i | \(0.488021\pi\) | |||||||
\(594\) | 7.12451 | 0.292322 | ||||||||
\(595\) | −0.723204 | −0.0296485 | ||||||||
\(596\) | 12.8693 | 0.527146 | ||||||||
\(597\) | 5.04798 | 0.206600 | ||||||||
\(598\) | −5.23410 | −0.214038 | ||||||||
\(599\) | 2.05151 | 0.0838225 | 0.0419113 | − | 0.999121i | \(-0.486655\pi\) | ||||
0.0419113 | + | 0.999121i | \(0.486655\pi\) | |||||||
\(600\) | 0.952528 | 0.0388868 | ||||||||
\(601\) | 1.95094 | 0.0795805 | 0.0397903 | − | 0.999208i | \(-0.487331\pi\) | ||||
0.0397903 | + | 0.999208i | \(0.487331\pi\) | |||||||
\(602\) | −10.8077 | −0.440490 | ||||||||
\(603\) | −22.7611 | −0.926903 | ||||||||
\(604\) | −14.7178 | −0.598860 | ||||||||
\(605\) | −1.28083 | −0.0520731 | ||||||||
\(606\) | −5.04066 | −0.204763 | ||||||||
\(607\) | −23.4770 | −0.952902 | −0.476451 | − | 0.879201i | \(-0.658077\pi\) | ||||
−0.476451 | + | 0.879201i | \(0.658077\pi\) | |||||||
\(608\) | 0.0118520 | 0.000480663 0 | ||||||||
\(609\) | 2.09692 | 0.0849714 | ||||||||
\(610\) | −4.02518 | −0.162975 | ||||||||
\(611\) | −42.7256 | −1.72849 | ||||||||
\(612\) | 1.31844 | 0.0532949 | ||||||||
\(613\) | −43.5415 | −1.75862 | −0.879312 | − | 0.476247i | \(-0.841997\pi\) | ||||
−0.879312 | + | 0.476247i | \(0.841997\pi\) | |||||||
\(614\) | −1.97831 | −0.0798380 | ||||||||
\(615\) | −2.57189 | −0.103709 | ||||||||
\(616\) | −3.58290 | −0.144359 | ||||||||
\(617\) | 14.4099 | 0.580120 | 0.290060 | − | 0.957008i | \(-0.406325\pi\) | ||||
0.290060 | + | 0.957008i | \(0.406325\pi\) | |||||||
\(618\) | −6.22322 | −0.250335 | ||||||||
\(619\) | 47.8848 | 1.92465 | 0.962327 | − | 0.271895i | \(-0.0876504\pi\) | ||||
0.962327 | + | 0.271895i | \(0.0876504\pi\) | |||||||
\(620\) | 12.0612 | 0.484390 | ||||||||
\(621\) | 2.07006 | 0.0830687 | ||||||||
\(622\) | 31.0217 | 1.24386 | ||||||||
\(623\) | 1.90528 | 0.0763335 | ||||||||
\(624\) | 1.84396 | 0.0738175 | ||||||||
\(625\) | −4.17091 | −0.166836 | ||||||||
\(626\) | −14.2749 | −0.570538 | ||||||||
\(627\) | −0.0143706 | −0.000573906 0 | ||||||||
\(628\) | 17.4726 | 0.697233 | ||||||||
\(629\) | −1.65714 | −0.0660745 | ||||||||
\(630\) | −4.53673 | −0.180748 | ||||||||
\(631\) | 13.0687 | 0.520256 | 0.260128 | − | 0.965574i | \(-0.416235\pi\) | ||||
0.260128 | + | 0.965574i | \(0.416235\pi\) | |||||||
\(632\) | 3.78651 | 0.150619 | ||||||||
\(633\) | −8.85928 | −0.352125 | ||||||||
\(634\) | −1.91311 | −0.0759794 | ||||||||
\(635\) | −5.16658 | −0.205030 | ||||||||
\(636\) | −0.189993 | −0.00753370 | ||||||||
\(637\) | 30.9663 | 1.22693 | ||||||||
\(638\) | 19.6780 | 0.779059 | ||||||||
\(639\) | 7.65327 | 0.302759 | ||||||||
\(640\) | −1.51534 | −0.0598989 | ||||||||
\(641\) | −21.8563 | −0.863271 | −0.431635 | − | 0.902048i | \(-0.642063\pi\) | ||||
−0.431635 | + | 0.902048i | \(0.642063\pi\) | |||||||
\(642\) | 0.352001 | 0.0138924 | ||||||||
\(643\) | 21.2264 | 0.837088 | 0.418544 | − | 0.908196i | \(-0.362541\pi\) | ||||
0.418544 | + | 0.908196i | \(0.362541\pi\) | |||||||
\(644\) | −1.04103 | −0.0410223 | ||||||||
\(645\) | 5.54231 | 0.218228 | ||||||||
\(646\) | −0.00543353 | −0.000213779 0 | ||||||||
\(647\) | −43.9680 | −1.72856 | −0.864281 | − | 0.503010i | \(-0.832226\pi\) | ||||
−0.864281 | + | 0.503010i | \(0.832226\pi\) | |||||||
\(648\) | 7.89838 | 0.310278 | ||||||||
\(649\) | 43.1410 | 1.69343 | ||||||||
\(650\) | 14.1517 | 0.555077 | ||||||||
\(651\) | −2.91914 | −0.114410 | ||||||||
\(652\) | 7.29343 | 0.285633 | ||||||||
\(653\) | 37.9204 | 1.48394 | 0.741970 | − | 0.670433i | \(-0.233892\pi\) | ||||
0.741970 | + | 0.670433i | \(0.233892\pi\) | |||||||
\(654\) | 2.34417 | 0.0916641 | ||||||||
\(655\) | −1.51534 | −0.0592091 | ||||||||
\(656\) | −4.81763 | −0.188097 | ||||||||
\(657\) | 44.1650 | 1.72304 | ||||||||
\(658\) | −8.49785 | −0.331281 | ||||||||
\(659\) | 2.91481 | 0.113545 | 0.0567725 | − | 0.998387i | \(-0.481919\pi\) | ||||
0.0567725 | + | 0.998387i | \(0.481919\pi\) | |||||||
\(660\) | 1.83735 | 0.0715186 | ||||||||
\(661\) | 12.7634 | 0.496439 | 0.248219 | − | 0.968704i | \(-0.420155\pi\) | ||||
0.248219 | + | 0.968704i | \(0.420155\pi\) | |||||||
\(662\) | −19.5088 | −0.758230 | ||||||||
\(663\) | −0.845359 | −0.0328310 | ||||||||
\(664\) | 13.5375 | 0.525357 | ||||||||
\(665\) | 0.0186967 | 0.000725026 0 | ||||||||
\(666\) | −10.3954 | −0.402814 | ||||||||
\(667\) | 5.71753 | 0.221384 | ||||||||
\(668\) | 7.28136 | 0.281724 | ||||||||
\(669\) | −4.87480 | −0.188471 | ||||||||
\(670\) | −11.9931 | −0.463333 | ||||||||
\(671\) | 9.14214 | 0.352929 | ||||||||
\(672\) | 0.366752 | 0.0141478 | ||||||||
\(673\) | −12.7395 | −0.491071 | −0.245536 | − | 0.969388i | \(-0.578964\pi\) | ||||
−0.245536 | + | 0.969388i | \(0.578964\pi\) | |||||||
\(674\) | −16.7671 | −0.645846 | ||||||||
\(675\) | −5.59694 | −0.215426 | ||||||||
\(676\) | 14.3958 | 0.553685 | ||||||||
\(677\) | −41.6208 | −1.59962 | −0.799808 | − | 0.600256i | \(-0.795066\pi\) | ||||
−0.799808 | + | 0.600256i | \(0.795066\pi\) | |||||||
\(678\) | 4.78730 | 0.183855 | ||||||||
\(679\) | 8.20842 | 0.315010 | ||||||||
\(680\) | 0.694702 | 0.0266406 | ||||||||
\(681\) | 0.954839 | 0.0365895 | ||||||||
\(682\) | −27.3939 | −1.04897 | ||||||||
\(683\) | −23.2670 | −0.890286 | −0.445143 | − | 0.895460i | \(-0.646847\pi\) | ||||
−0.445143 | + | 0.895460i | \(0.646847\pi\) | |||||||
\(684\) | −0.0340851 | −0.00130328 | ||||||||
\(685\) | −27.9907 | −1.06947 | ||||||||
\(686\) | 13.4462 | 0.513378 | ||||||||
\(687\) | 4.51941 | 0.172426 | ||||||||
\(688\) | 10.3818 | 0.395802 | ||||||||
\(689\) | −2.82273 | −0.107537 | ||||||||
\(690\) | 0.533849 | 0.0203233 | ||||||||
\(691\) | 21.1975 | 0.806391 | 0.403196 | − | 0.915114i | \(-0.367899\pi\) | ||||
0.403196 | + | 0.915114i | \(0.367899\pi\) | |||||||
\(692\) | −22.0643 | −0.838757 | ||||||||
\(693\) | 10.3040 | 0.391417 | ||||||||
\(694\) | 20.5624 | 0.780539 | ||||||||
\(695\) | 10.7653 | 0.408350 | ||||||||
\(696\) | −2.01427 | −0.0763509 | ||||||||
\(697\) | 2.20863 | 0.0836578 | ||||||||
\(698\) | 4.23107 | 0.160148 | ||||||||
\(699\) | −0.856166 | −0.0323832 | ||||||||
\(700\) | 2.81469 | 0.106385 | ||||||||
\(701\) | 44.6793 | 1.68752 | 0.843758 | − | 0.536724i | \(-0.180338\pi\) | ||||
0.843758 | + | 0.536724i | \(0.180338\pi\) | |||||||
\(702\) | −10.8349 | −0.408937 | ||||||||
\(703\) | 0.0428413 | 0.00161579 | ||||||||
\(704\) | 3.44169 | 0.129714 | ||||||||
\(705\) | 4.35778 | 0.164124 | ||||||||
\(706\) | 10.0342 | 0.377643 | ||||||||
\(707\) | −14.8950 | −0.560184 | ||||||||
\(708\) | −4.41599 | −0.165963 | ||||||||
\(709\) | −1.11972 | −0.0420520 | −0.0210260 | − | 0.999779i | \(-0.506693\pi\) | ||||
−0.0210260 | + | 0.999779i | \(0.506693\pi\) | |||||||
\(710\) | 4.03259 | 0.151340 | ||||||||
\(711\) | −10.8896 | −0.408391 | ||||||||
\(712\) | −1.83019 | −0.0685893 | ||||||||
\(713\) | −7.95942 | −0.298083 | ||||||||
\(714\) | −0.168136 | −0.00629235 | ||||||||
\(715\) | 27.2975 | 1.02087 | ||||||||
\(716\) | 24.9774 | 0.933448 | ||||||||
\(717\) | 5.49134 | 0.205078 | ||||||||
\(718\) | 18.4158 | 0.687273 | ||||||||
\(719\) | −12.6106 | −0.470298 | −0.235149 | − | 0.971959i | \(-0.575558\pi\) | ||||
−0.235149 | + | 0.971959i | \(0.575558\pi\) | |||||||
\(720\) | 4.35793 | 0.162411 | ||||||||
\(721\) | −18.3894 | −0.684858 | ||||||||
\(722\) | −18.9999 | −0.707102 | ||||||||
\(723\) | −4.95627 | −0.184326 | ||||||||
\(724\) | −8.10577 | −0.301248 | ||||||||
\(725\) | −15.4588 | −0.574126 | ||||||||
\(726\) | −0.297777 | −0.0110516 | ||||||||
\(727\) | −0.00700972 | −0.000259976 0 | −0.000129988 | − | 1.00000i | \(-0.500041\pi\) | ||||
−0.000129988 | 1.00000i | \(0.500041\pi\) | ||||||||
\(728\) | 5.44885 | 0.201948 | ||||||||
\(729\) | −20.5270 | −0.760260 | ||||||||
\(730\) | 23.2710 | 0.861299 | ||||||||
\(731\) | −4.75950 | −0.176036 | ||||||||
\(732\) | −0.935806 | −0.0345884 | ||||||||
\(733\) | 8.83525 | 0.326337 | 0.163169 | − | 0.986598i | \(-0.447829\pi\) | ||||
0.163169 | + | 0.986598i | \(0.447829\pi\) | |||||||
\(734\) | 15.9241 | 0.587771 | ||||||||
\(735\) | −3.15839 | −0.116499 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 27.2391 | 1.00337 | ||||||||
\(738\) | 13.8550 | 0.510008 | ||||||||
\(739\) | 8.14061 | 0.299457 | 0.149729 | − | 0.988727i | \(-0.452160\pi\) | ||||
0.149729 | + | 0.988727i | \(0.452160\pi\) | |||||||
\(740\) | −5.47745 | −0.201355 | ||||||||
\(741\) | 0.0218547 | 0.000802852 0 | ||||||||
\(742\) | −0.561422 | −0.0206105 | ||||||||
\(743\) | −8.30326 | −0.304617 | −0.152309 | − | 0.988333i | \(-0.548671\pi\) | ||||
−0.152309 | + | 0.988333i | \(0.548671\pi\) | |||||||
\(744\) | 2.80409 | 0.102803 | ||||||||
\(745\) | −19.5013 | −0.714471 | ||||||||
\(746\) | 18.5232 | 0.678183 | ||||||||
\(747\) | −38.9324 | −1.42446 | ||||||||
\(748\) | −1.57783 | −0.0576913 | ||||||||
\(749\) | 1.04015 | 0.0380063 | ||||||||
\(750\) | −4.11265 | −0.150173 | ||||||||
\(751\) | 45.6034 | 1.66409 | 0.832045 | − | 0.554708i | \(-0.187170\pi\) | ||||
0.832045 | + | 0.554708i | \(0.187170\pi\) | |||||||
\(752\) | 8.16294 | 0.297672 | ||||||||
\(753\) | −9.36439 | −0.341257 | ||||||||
\(754\) | −29.9261 | −1.08985 | ||||||||
\(755\) | 22.3025 | 0.811670 | ||||||||
\(756\) | −2.15499 | −0.0783764 | ||||||||
\(757\) | 29.8653 | 1.08547 | 0.542737 | − | 0.839903i | \(-0.317388\pi\) | ||||
0.542737 | + | 0.839903i | \(0.317388\pi\) | |||||||
\(758\) | 16.2185 | 0.589081 | ||||||||
\(759\) | −1.21250 | −0.0440110 | ||||||||
\(760\) | −0.0179598 | −0.000651470 0 | ||||||||
\(761\) | 22.4368 | 0.813334 | 0.406667 | − | 0.913576i | \(-0.366691\pi\) | ||||
0.406667 | + | 0.913576i | \(0.366691\pi\) | |||||||
\(762\) | −1.20117 | −0.0435138 | ||||||||
\(763\) | 6.92693 | 0.250772 | ||||||||
\(764\) | 17.2642 | 0.624598 | ||||||||
\(765\) | −1.99788 | −0.0722336 | ||||||||
\(766\) | −14.9956 | −0.541815 | ||||||||
\(767\) | −65.6085 | −2.36899 | ||||||||
\(768\) | −0.352298 | −0.0127125 | ||||||||
\(769\) | 0.992382 | 0.0357862 | 0.0178931 | − | 0.999840i | \(-0.494304\pi\) | ||||
0.0178931 | + | 0.999840i | \(0.494304\pi\) | |||||||
\(770\) | 5.42930 | 0.195658 | ||||||||
\(771\) | 7.47627 | 0.269251 | ||||||||
\(772\) | 1.60663 | 0.0578240 | ||||||||
\(773\) | −6.05231 | −0.217687 | −0.108843 | − | 0.994059i | \(-0.534715\pi\) | ||||
−0.108843 | + | 0.994059i | \(0.534715\pi\) | |||||||
\(774\) | −29.8568 | −1.07318 | ||||||||
\(775\) | 21.5204 | 0.773034 | ||||||||
\(776\) | −7.88491 | −0.283052 | ||||||||
\(777\) | 1.32569 | 0.0475589 | ||||||||
\(778\) | −17.4007 | −0.623844 | ||||||||
\(779\) | −0.0570987 | −0.00204577 | ||||||||
\(780\) | −2.79422 | −0.100049 | ||||||||
\(781\) | −9.15898 | −0.327734 | ||||||||
\(782\) | −0.458447 | −0.0163940 | ||||||||
\(783\) | 11.8356 | 0.422972 | ||||||||
\(784\) | −5.91626 | −0.211295 | ||||||||
\(785\) | −26.4769 | −0.945000 | ||||||||
\(786\) | −0.352298 | −0.0125660 | ||||||||
\(787\) | −46.0925 | −1.64302 | −0.821511 | − | 0.570193i | \(-0.806868\pi\) | ||||
−0.821511 | + | 0.570193i | \(0.806868\pi\) | |||||||
\(788\) | 9.97120 | 0.355209 | ||||||||
\(789\) | −6.60279 | −0.235065 | ||||||||
\(790\) | −5.73784 | −0.204143 | ||||||||
\(791\) | 14.1463 | 0.502985 | ||||||||
\(792\) | −9.89791 | −0.351707 | ||||||||
\(793\) | −13.9033 | −0.493721 | ||||||||
\(794\) | −4.57924 | −0.162511 | ||||||||
\(795\) | 0.287903 | 0.0102109 | ||||||||
\(796\) | −14.3287 | −0.507869 | ||||||||
\(797\) | 2.66924 | 0.0945494 | 0.0472747 | − | 0.998882i | \(-0.484946\pi\) | ||||
0.0472747 | + | 0.998882i | \(0.484946\pi\) | |||||||
\(798\) | 0.00434676 | 0.000153873 0 | ||||||||
\(799\) | −3.74228 | −0.132392 | ||||||||
\(800\) | −2.70376 | −0.0955923 | ||||||||
\(801\) | 5.26342 | 0.185974 | ||||||||
\(802\) | 5.29946 | 0.187130 | ||||||||
\(803\) | −52.8541 | −1.86518 | ||||||||
\(804\) | −2.78825 | −0.0983339 | ||||||||
\(805\) | 1.57751 | 0.0555999 | ||||||||
\(806\) | 41.6604 | 1.46743 | ||||||||
\(807\) | 0.325443 | 0.0114562 | ||||||||
\(808\) | 14.3080 | 0.503352 | ||||||||
\(809\) | 19.3720 | 0.681084 | 0.340542 | − | 0.940229i | \(-0.389390\pi\) | ||||
0.340542 | + | 0.940229i | \(0.389390\pi\) | |||||||
\(810\) | −11.9687 | −0.420537 | ||||||||
\(811\) | 16.0883 | 0.564938 | 0.282469 | − | 0.959276i | \(-0.408847\pi\) | ||||
0.282469 | + | 0.959276i | \(0.408847\pi\) | |||||||
\(812\) | −5.95212 | −0.208878 | ||||||||
\(813\) | 1.59851 | 0.0560623 | ||||||||
\(814\) | 12.4406 | 0.436043 | ||||||||
\(815\) | −11.0520 | −0.387134 | ||||||||
\(816\) | 0.161510 | 0.00565398 | ||||||||
\(817\) | 0.123045 | 0.00430480 | ||||||||
\(818\) | 37.8084 | 1.32194 | ||||||||
\(819\) | −15.6703 | −0.547563 | ||||||||
\(820\) | 7.30033 | 0.254938 | ||||||||
\(821\) | −31.6776 | −1.10555 | −0.552777 | − | 0.833329i | \(-0.686432\pi\) | ||||
−0.552777 | + | 0.833329i | \(0.686432\pi\) | |||||||
\(822\) | −6.50751 | −0.226976 | ||||||||
\(823\) | 11.4619 | 0.399537 | 0.199769 | − | 0.979843i | \(-0.435981\pi\) | ||||
0.199769 | + | 0.979843i | \(0.435981\pi\) | |||||||
\(824\) | 17.6647 | 0.615377 | ||||||||
\(825\) | 3.27831 | 0.114136 | ||||||||
\(826\) | −13.0491 | −0.454037 | ||||||||
\(827\) | −42.9348 | −1.49299 | −0.746495 | − | 0.665391i | \(-0.768265\pi\) | ||||
−0.746495 | + | 0.665391i | \(0.768265\pi\) | |||||||
\(828\) | −2.87589 | −0.0999440 | ||||||||
\(829\) | −8.00365 | −0.277978 | −0.138989 | − | 0.990294i | \(-0.544385\pi\) | ||||
−0.138989 | + | 0.990294i | \(0.544385\pi\) | |||||||
\(830\) | −20.5139 | −0.712047 | ||||||||
\(831\) | −7.96299 | −0.276233 | ||||||||
\(832\) | −5.23410 | −0.181460 | ||||||||
\(833\) | 2.71229 | 0.0939754 | ||||||||
\(834\) | 2.50280 | 0.0866649 | ||||||||
\(835\) | −11.0337 | −0.381837 | ||||||||
\(836\) | 0.0407910 | 0.00141079 | ||||||||
\(837\) | −16.4765 | −0.569511 | ||||||||
\(838\) | 6.59183 | 0.227711 | ||||||||
\(839\) | 17.7537 | 0.612926 | 0.306463 | − | 0.951883i | \(-0.400854\pi\) | ||||
0.306463 | + | 0.951883i | \(0.400854\pi\) | |||||||
\(840\) | −0.555753 | −0.0191753 | ||||||||
\(841\) | 3.69019 | 0.127248 | ||||||||
\(842\) | −26.7028 | −0.920238 | ||||||||
\(843\) | 3.64202 | 0.125438 | ||||||||
\(844\) | 25.1471 | 0.865600 | ||||||||
\(845\) | −21.8145 | −0.750441 | ||||||||
\(846\) | −23.4757 | −0.807111 | ||||||||
\(847\) | −0.879923 | −0.0302345 | ||||||||
\(848\) | 0.539296 | 0.0185195 | ||||||||
\(849\) | 7.31134 | 0.250924 | ||||||||
\(850\) | 1.23953 | 0.0425155 | ||||||||
\(851\) | 3.61468 | 0.123910 | ||||||||
\(852\) | 0.937530 | 0.0321192 | ||||||||
\(853\) | 3.05897 | 0.104737 | 0.0523685 | − | 0.998628i | \(-0.483323\pi\) | ||||
0.0523685 | + | 0.998628i | \(0.483323\pi\) | |||||||
\(854\) | −2.76528 | −0.0946259 | ||||||||
\(855\) | 0.0516503 | 0.00176640 | ||||||||
\(856\) | −0.999157 | −0.0341505 | ||||||||
\(857\) | 4.03841 | 0.137949 | 0.0689747 | − | 0.997618i | \(-0.478027\pi\) | ||||
0.0689747 | + | 0.997618i | \(0.478027\pi\) | |||||||
\(858\) | 6.34635 | 0.216661 | ||||||||
\(859\) | 12.8894 | 0.439780 | 0.219890 | − | 0.975525i | \(-0.429430\pi\) | ||||
0.219890 | + | 0.975525i | \(0.429430\pi\) | |||||||
\(860\) | −15.7319 | −0.536453 | ||||||||
\(861\) | −1.76688 | −0.0602150 | ||||||||
\(862\) | −22.9331 | −0.781104 | ||||||||
\(863\) | 34.8251 | 1.18546 | 0.592730 | − | 0.805401i | \(-0.298050\pi\) | ||||
0.592730 | + | 0.805401i | \(0.298050\pi\) | |||||||
\(864\) | 2.07006 | 0.0704249 | ||||||||
\(865\) | 33.4348 | 1.13682 | ||||||||
\(866\) | −36.7661 | −1.24936 | ||||||||
\(867\) | 5.91502 | 0.200885 | ||||||||
\(868\) | 8.28599 | 0.281245 | ||||||||
\(869\) | 13.0320 | 0.442081 | ||||||||
\(870\) | 3.05230 | 0.103483 | ||||||||
\(871\) | −41.4251 | −1.40364 | ||||||||
\(872\) | −6.65393 | −0.225331 | ||||||||
\(873\) | 22.6761 | 0.767470 | ||||||||
\(874\) | 0.0118520 | 0.000400901 0 | ||||||||
\(875\) | −12.1527 | −0.410838 | ||||||||
\(876\) | 5.41024 | 0.182795 | ||||||||
\(877\) | 15.4051 | 0.520192 | 0.260096 | − | 0.965583i | \(-0.416246\pi\) | ||||
0.260096 | + | 0.965583i | \(0.416246\pi\) | |||||||
\(878\) | 8.54496 | 0.288378 | ||||||||
\(879\) | −2.74255 | −0.0925041 | ||||||||
\(880\) | −5.21532 | −0.175808 | ||||||||
\(881\) | −17.7793 | −0.599000 | −0.299500 | − | 0.954096i | \(-0.596820\pi\) | ||||
−0.299500 | + | 0.954096i | \(0.596820\pi\) | |||||||
\(882\) | 17.0145 | 0.572908 | ||||||||
\(883\) | 8.30671 | 0.279543 | 0.139772 | − | 0.990184i | \(-0.455363\pi\) | ||||
0.139772 | + | 0.990184i | \(0.455363\pi\) | |||||||
\(884\) | 2.39956 | 0.0807059 | ||||||||
\(885\) | 6.69171 | 0.224939 | ||||||||
\(886\) | 20.9058 | 0.702343 | ||||||||
\(887\) | −32.9362 | −1.10589 | −0.552944 | − | 0.833218i | \(-0.686496\pi\) | ||||
−0.552944 | + | 0.833218i | \(0.686496\pi\) | |||||||
\(888\) | −1.27344 | −0.0427339 | ||||||||
\(889\) | −3.54942 | −0.119044 | ||||||||
\(890\) | 2.77336 | 0.0929631 | ||||||||
\(891\) | 27.1838 | 0.910691 | ||||||||
\(892\) | 13.8372 | 0.463303 | ||||||||
\(893\) | 0.0967474 | 0.00323753 | ||||||||
\(894\) | −4.53381 | −0.151633 | ||||||||
\(895\) | −37.8491 | −1.26516 | ||||||||
\(896\) | −1.04103 | −0.0347783 | ||||||||
\(897\) | 1.84396 | 0.0615681 | ||||||||
\(898\) | −22.2619 | −0.742888 | ||||||||
\(899\) | −45.5083 | −1.51779 | ||||||||
\(900\) | 7.77570 | 0.259190 | ||||||||
\(901\) | −0.247239 | −0.00823671 | ||||||||
\(902\) | −16.5808 | −0.552080 | ||||||||
\(903\) | 3.80754 | 0.126707 | ||||||||
\(904\) | −13.5888 | −0.451956 | ||||||||
\(905\) | 12.2830 | 0.408299 | ||||||||
\(906\) | 5.18506 | 0.172262 | ||||||||
\(907\) | −37.8218 | −1.25585 | −0.627927 | − | 0.778272i | \(-0.716096\pi\) | ||||
−0.627927 | + | 0.778272i | \(0.716096\pi\) | |||||||
\(908\) | −2.71032 | −0.0899450 | ||||||||
\(909\) | −41.1481 | −1.36479 | ||||||||
\(910\) | −8.25684 | −0.273711 | ||||||||
\(911\) | −32.5061 | −1.07697 | −0.538487 | − | 0.842634i | \(-0.681004\pi\) | ||||
−0.538487 | + | 0.842634i | \(0.681004\pi\) | |||||||
\(912\) | −0.00417544 | −0.000138263 0 | ||||||||
\(913\) | 46.5920 | 1.54197 | ||||||||
\(914\) | 30.7283 | 1.01640 | ||||||||
\(915\) | 1.41806 | 0.0468796 | ||||||||
\(916\) | −12.8284 | −0.423862 | ||||||||
\(917\) | −1.04103 | −0.0343778 | ||||||||
\(918\) | −0.949014 | −0.0313221 | ||||||||
\(919\) | 29.7529 | 0.981456 | 0.490728 | − | 0.871313i | \(-0.336731\pi\) | ||||
0.490728 | + | 0.871313i | \(0.336731\pi\) | |||||||
\(920\) | −1.51534 | −0.0499591 | ||||||||
\(921\) | 0.696954 | 0.0229654 | ||||||||
\(922\) | 1.84511 | 0.0607653 | ||||||||
\(923\) | 13.9289 | 0.458476 | ||||||||
\(924\) | 1.26225 | 0.0415249 | ||||||||
\(925\) | −9.77321 | −0.321341 | ||||||||
\(926\) | −18.9409 | −0.622436 | ||||||||
\(927\) | −50.8015 | −1.66854 | ||||||||
\(928\) | 5.71753 | 0.187687 | ||||||||
\(929\) | 25.3941 | 0.833152 | 0.416576 | − | 0.909101i | \(-0.363230\pi\) | ||||
0.416576 | + | 0.909101i | \(0.363230\pi\) | |||||||
\(930\) | −4.24913 | −0.139335 | ||||||||
\(931\) | −0.0701197 | −0.00229808 | ||||||||
\(932\) | 2.43023 | 0.0796049 | ||||||||
\(933\) | −10.9289 | −0.357795 | ||||||||
\(934\) | −27.4815 | −0.899223 | ||||||||
\(935\) | 2.39095 | 0.0781924 | ||||||||
\(936\) | 15.0527 | 0.492012 | ||||||||
\(937\) | −46.1233 | −1.50678 | −0.753391 | − | 0.657573i | \(-0.771583\pi\) | ||||
−0.753391 | + | 0.657573i | \(0.771583\pi\) | |||||||
\(938\) | −8.23918 | −0.269019 | ||||||||
\(939\) | 5.02900 | 0.164115 | ||||||||
\(940\) | −12.3696 | −0.403452 | ||||||||
\(941\) | 28.6549 | 0.934123 | 0.467061 | − | 0.884225i | \(-0.345313\pi\) | ||||
0.467061 | + | 0.884225i | \(0.345313\pi\) | |||||||
\(942\) | −6.15556 | −0.200559 | ||||||||
\(943\) | −4.81763 | −0.156884 | ||||||||
\(944\) | 12.5348 | 0.407974 | ||||||||
\(945\) | 3.26554 | 0.106228 | ||||||||
\(946\) | 35.7309 | 1.16171 | ||||||||
\(947\) | −49.8271 | −1.61916 | −0.809582 | − | 0.587007i | \(-0.800306\pi\) | ||||
−0.809582 | + | 0.587007i | \(0.800306\pi\) | |||||||
\(948\) | −1.33398 | −0.0433256 | ||||||||
\(949\) | 80.3801 | 2.60925 | ||||||||
\(950\) | −0.0320450 | −0.00103968 | ||||||||
\(951\) | 0.673985 | 0.0218555 | ||||||||
\(952\) | 0.477257 | 0.0154680 | ||||||||
\(953\) | 24.3678 | 0.789350 | 0.394675 | − | 0.918821i | \(-0.370857\pi\) | ||||
0.394675 | + | 0.918821i | \(0.370857\pi\) | |||||||
\(954\) | −1.55095 | −0.0502139 | ||||||||
\(955\) | −26.1611 | −0.846554 | ||||||||
\(956\) | −15.5872 | −0.504126 | ||||||||
\(957\) | −6.93251 | −0.224096 | ||||||||
\(958\) | 31.3647 | 1.01335 | ||||||||
\(959\) | −19.2295 | −0.620953 | ||||||||
\(960\) | 0.533849 | 0.0172299 | ||||||||
\(961\) | 32.3524 | 1.04363 | ||||||||
\(962\) | −18.9196 | −0.609992 | ||||||||
\(963\) | 2.87346 | 0.0925960 | ||||||||
\(964\) | 14.0684 | 0.453113 | ||||||||
\(965\) | −2.43459 | −0.0783722 | ||||||||
\(966\) | 0.366752 | 0.0118001 | ||||||||
\(967\) | −47.1092 | −1.51493 | −0.757465 | − | 0.652875i | \(-0.773562\pi\) | ||||
−0.757465 | + | 0.652875i | \(0.773562\pi\) | |||||||
\(968\) | 0.845244 | 0.0271672 | ||||||||
\(969\) | 0.00191422 | 6.14936e−5 0 | ||||||||
\(970\) | 11.9483 | 0.383637 | ||||||||
\(971\) | 18.4833 | 0.593156 | 0.296578 | − | 0.955009i | \(-0.404154\pi\) | ||||
0.296578 | + | 0.955009i | \(0.404154\pi\) | |||||||
\(972\) | −8.99277 | −0.288443 | ||||||||
\(973\) | 7.39570 | 0.237095 | ||||||||
\(974\) | 17.6248 | 0.564735 | ||||||||
\(975\) | −4.98562 | −0.159668 | ||||||||
\(976\) | 2.65629 | 0.0850259 | ||||||||
\(977\) | −8.44066 | −0.270041 | −0.135020 | − | 0.990843i | \(-0.543110\pi\) | ||||
−0.135020 | + | 0.990843i | \(0.543110\pi\) | |||||||
\(978\) | −2.56946 | −0.0821622 | ||||||||
\(979\) | −6.29896 | −0.201316 | ||||||||
\(980\) | 8.96512 | 0.286380 | ||||||||
\(981\) | 19.1360 | 0.610964 | ||||||||
\(982\) | 24.4755 | 0.781044 | ||||||||
\(983\) | 30.8450 | 0.983803 | 0.491901 | − | 0.870651i | \(-0.336302\pi\) | ||||
0.491901 | + | 0.870651i | \(0.336302\pi\) | |||||||
\(984\) | 1.69724 | 0.0541060 | ||||||||
\(985\) | −15.1097 | −0.481435 | ||||||||
\(986\) | −2.62119 | −0.0834756 | ||||||||
\(987\) | 2.99378 | 0.0952929 | ||||||||
\(988\) | −0.0620347 | −0.00197359 | ||||||||
\(989\) | 10.3818 | 0.330121 | ||||||||
\(990\) | 14.9987 | 0.476689 | ||||||||
\(991\) | −12.7016 | −0.403479 | −0.201739 | − | 0.979439i | \(-0.564659\pi\) | ||||
−0.201739 | + | 0.979439i | \(0.564659\pi\) | |||||||
\(992\) | −7.95942 | −0.252712 | ||||||||
\(993\) | 6.87290 | 0.218105 | ||||||||
\(994\) | 2.77037 | 0.0878708 | ||||||||
\(995\) | 21.7129 | 0.688344 | ||||||||
\(996\) | −4.76924 | −0.151119 | ||||||||
\(997\) | −49.9103 | −1.58067 | −0.790337 | − | 0.612672i | \(-0.790095\pi\) | ||||
−0.790337 | + | 0.612672i | \(0.790095\pi\) | |||||||
\(998\) | 31.3949 | 0.993787 | ||||||||
\(999\) | 7.48261 | 0.236739 |
(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 | 6026.2.a.m.1.19 | ✓ | 41 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.m.1.19 | ✓ | 41 | 1.1 | even | 1 | trivial |