Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61751 | −1.85086 | −0.925431 | − | 0.378916i | \(-0.876297\pi\) | ||||
−0.925431 | + | 0.378916i | \(0.876297\pi\) | |||||||
\(3\) | −2.91594 | −1.68352 | −0.841760 | − | 0.539851i | \(-0.818480\pi\) | ||||
−0.841760 | + | 0.539851i | \(0.818480\pi\) | |||||||
\(4\) | 4.85138 | 2.42569 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 7.63252 | 3.11596 | ||||||||
\(7\) | 2.00988 | 0.759664 | 0.379832 | − | 0.925055i | \(-0.375982\pi\) | ||||
0.379832 | + | 0.925055i | \(0.375982\pi\) | |||||||
\(8\) | −7.46353 | −2.63876 | ||||||||
\(9\) | 5.50273 | 1.83424 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.47720 | −0.445393 | −0.222697 | − | 0.974888i | \(-0.571486\pi\) | ||||
−0.222697 | + | 0.974888i | \(0.571486\pi\) | |||||||
\(12\) | −14.1463 | −4.08370 | ||||||||
\(13\) | −0.967484 | −0.268332 | −0.134166 | − | 0.990959i | \(-0.542836\pi\) | ||||
−0.134166 | + | 0.990959i | \(0.542836\pi\) | |||||||
\(14\) | −5.26090 | −1.40603 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.83313 | 2.45828 | ||||||||
\(17\) | −6.02295 | −1.46078 | −0.730391 | − | 0.683030i | \(-0.760662\pi\) | ||||
−0.730391 | + | 0.683030i | \(0.760662\pi\) | |||||||
\(18\) | −14.4035 | −3.39493 | ||||||||
\(19\) | 0.541650 | 0.124263 | 0.0621315 | − | 0.998068i | \(-0.480210\pi\) | ||||
0.0621315 | + | 0.998068i | \(0.480210\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.86070 | −1.27891 | ||||||||
\(22\) | 3.86660 | 0.824362 | ||||||||
\(23\) | 1.49200 | 0.311104 | 0.155552 | − | 0.987828i | \(-0.450284\pi\) | ||||
0.155552 | + | 0.987828i | \(0.450284\pi\) | |||||||
\(24\) | 21.7632 | 4.44240 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.53240 | 0.496645 | ||||||||
\(27\) | −7.29781 | −1.40446 | ||||||||
\(28\) | 9.75070 | 1.84271 | ||||||||
\(29\) | −6.69224 | −1.24272 | −0.621359 | − | 0.783526i | \(-0.713419\pi\) | ||||
−0.621359 | + | 0.783526i | \(0.713419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.96085 | 1.25021 | 0.625103 | − | 0.780542i | \(-0.285057\pi\) | ||||
0.625103 | + | 0.780542i | \(0.285057\pi\) | |||||||
\(32\) | −10.8113 | −1.91119 | ||||||||
\(33\) | 4.30744 | 0.749829 | ||||||||
\(34\) | 15.7652 | 2.70370 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 26.6958 | 4.44930 | ||||||||
\(37\) | 7.43384 | 1.22212 | 0.611058 | − | 0.791586i | \(-0.290744\pi\) | ||||
0.611058 | + | 0.791586i | \(0.290744\pi\) | |||||||
\(38\) | −1.41778 | −0.229994 | ||||||||
\(39\) | 2.82113 | 0.451742 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.91426 | 1.07983 | 0.539913 | − | 0.841721i | \(-0.318457\pi\) | ||||
0.539913 | + | 0.841721i | \(0.318457\pi\) | |||||||
\(42\) | 15.3405 | 2.36709 | ||||||||
\(43\) | 8.06903 | 1.23052 | 0.615258 | − | 0.788326i | \(-0.289052\pi\) | ||||
0.615258 | + | 0.788326i | \(0.289052\pi\) | |||||||
\(44\) | −7.16647 | −1.08039 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.90534 | −0.575811 | ||||||||
\(47\) | −4.13499 | −0.603150 | −0.301575 | − | 0.953442i | \(-0.597512\pi\) | ||||
−0.301575 | + | 0.953442i | \(0.597512\pi\) | |||||||
\(48\) | −28.6728 | −4.13857 | ||||||||
\(49\) | −2.96037 | −0.422910 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 17.5626 | 2.45926 | ||||||||
\(52\) | −4.69363 | −0.650890 | ||||||||
\(53\) | −5.72513 | −0.786407 | −0.393203 | − | 0.919452i | \(-0.628633\pi\) | ||||
−0.393203 | + | 0.919452i | \(0.628633\pi\) | |||||||
\(54\) | 19.1021 | 2.59947 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −15.0008 | −2.00457 | ||||||||
\(57\) | −1.57942 | −0.209199 | ||||||||
\(58\) | 17.5170 | 2.30010 | ||||||||
\(59\) | −4.68972 | −0.610550 | −0.305275 | − | 0.952264i | \(-0.598748\pi\) | ||||
−0.305275 | + | 0.952264i | \(0.598748\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.80442 | −0.487106 | −0.243553 | − | 0.969888i | \(-0.578313\pi\) | ||||
−0.243553 | + | 0.969888i | \(0.578313\pi\) | |||||||
\(62\) | −18.2201 | −2.31396 | ||||||||
\(63\) | 11.0598 | 1.39341 | ||||||||
\(64\) | 8.63246 | 1.07906 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.2748 | −1.38783 | ||||||||
\(67\) | −2.54318 | −0.310698 | −0.155349 | − | 0.987860i | \(-0.549650\pi\) | ||||
−0.155349 | + | 0.987860i | \(0.549650\pi\) | |||||||
\(68\) | −29.2196 | −3.54340 | ||||||||
\(69\) | −4.35060 | −0.523751 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.73886 | 0.325043 | 0.162522 | − | 0.986705i | \(-0.448037\pi\) | ||||
0.162522 | + | 0.986705i | \(0.448037\pi\) | |||||||
\(72\) | −41.0697 | −4.84012 | ||||||||
\(73\) | −4.42334 | −0.517712 | −0.258856 | − | 0.965916i | \(-0.583346\pi\) | ||||
−0.258856 | + | 0.965916i | \(0.583346\pi\) | |||||||
\(74\) | −19.4582 | −2.26197 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.62775 | 0.301424 | ||||||||
\(77\) | −2.96900 | −0.338349 | ||||||||
\(78\) | −7.38435 | −0.836113 | ||||||||
\(79\) | −4.05640 | −0.456381 | −0.228190 | − | 0.973617i | \(-0.573281\pi\) | ||||
−0.228190 | + | 0.973617i | \(0.573281\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.77182 | 0.530202 | ||||||||
\(82\) | −18.0982 | −1.99861 | ||||||||
\(83\) | 1.66433 | 0.182684 | 0.0913419 | − | 0.995820i | \(-0.470884\pi\) | ||||
0.0913419 | + | 0.995820i | \(0.470884\pi\) | |||||||
\(84\) | −28.4325 | −3.10224 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −21.1208 | −2.27751 | ||||||||
\(87\) | 19.5142 | 2.09214 | ||||||||
\(88\) | 11.0251 | 1.17528 | ||||||||
\(89\) | −2.78206 | −0.294898 | −0.147449 | − | 0.989070i | \(-0.547106\pi\) | ||||
−0.147449 | + | 0.989070i | \(0.547106\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.94453 | −0.203842 | ||||||||
\(92\) | 7.23828 | 0.754643 | ||||||||
\(93\) | −20.2974 | −2.10475 | ||||||||
\(94\) | 10.8234 | 1.11635 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 31.5251 | 3.21752 | ||||||||
\(97\) | 14.3639 | 1.45843 | 0.729214 | − | 0.684285i | \(-0.239886\pi\) | ||||
0.729214 | + | 0.684285i | \(0.239886\pi\) | |||||||
\(98\) | 7.74882 | 0.782749 | ||||||||
\(99\) | −8.12864 | −0.816959 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.14294 | 0.611245 | 0.305623 | − | 0.952153i | \(-0.401135\pi\) | ||||
0.305623 | + | 0.952153i | \(0.401135\pi\) | |||||||
\(102\) | −45.9703 | −4.55174 | ||||||||
\(103\) | −18.4803 | −1.82092 | −0.910461 | − | 0.413595i | \(-0.864273\pi\) | ||||
−0.910461 | + | 0.413595i | \(0.864273\pi\) | |||||||
\(104\) | 7.22085 | 0.708062 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.9856 | 1.45553 | ||||||||
\(107\) | 17.5663 | 1.69820 | 0.849100 | − | 0.528231i | \(-0.177145\pi\) | ||||
0.849100 | + | 0.528231i | \(0.177145\pi\) | |||||||
\(108\) | −35.4044 | −3.40679 | ||||||||
\(109\) | 6.62056 | 0.634134 | 0.317067 | − | 0.948403i | \(-0.397302\pi\) | ||||
0.317067 | + | 0.948403i | \(0.397302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.6767 | −2.05746 | ||||||||
\(112\) | 19.7634 | 1.86747 | ||||||||
\(113\) | 9.32887 | 0.877587 | 0.438793 | − | 0.898588i | \(-0.355406\pi\) | ||||
0.438793 | + | 0.898588i | \(0.355406\pi\) | |||||||
\(114\) | 4.13416 | 0.387199 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32.4666 | −3.01445 | ||||||||
\(117\) | −5.32380 | −0.492186 | ||||||||
\(118\) | 12.2754 | 1.13004 | ||||||||
\(119\) | −12.1054 | −1.10970 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.81787 | −0.801625 | ||||||||
\(122\) | 9.95813 | 0.901567 | ||||||||
\(123\) | −20.1616 | −1.81791 | ||||||||
\(124\) | 33.7697 | 3.03261 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −28.9493 | −2.57901 | ||||||||
\(127\) | −16.3798 | −1.45347 | −0.726735 | − | 0.686918i | \(-0.758963\pi\) | ||||
−0.726735 | + | 0.686918i | \(0.758963\pi\) | |||||||
\(128\) | −0.973005 | −0.0860023 | ||||||||
\(129\) | −23.5288 | −2.07160 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.4491 | −1.34980 | −0.674899 | − | 0.737910i | \(-0.735813\pi\) | ||||
−0.674899 | + | 0.737910i | \(0.735813\pi\) | |||||||
\(132\) | 20.8970 | 1.81885 | ||||||||
\(133\) | 1.08865 | 0.0943982 | ||||||||
\(134\) | 6.65680 | 0.575060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 44.9525 | 3.85464 | ||||||||
\(137\) | 13.4896 | 1.15250 | 0.576249 | − | 0.817274i | \(-0.304516\pi\) | ||||
0.576249 | + | 0.817274i | \(0.304516\pi\) | |||||||
\(138\) | 11.3878 | 0.969391 | ||||||||
\(139\) | 21.9276 | 1.85988 | 0.929939 | − | 0.367714i | \(-0.119860\pi\) | ||||
0.929939 | + | 0.367714i | \(0.119860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0574 | 1.01542 | ||||||||
\(142\) | −7.16901 | −0.601610 | ||||||||
\(143\) | 1.42917 | 0.119513 | ||||||||
\(144\) | 54.1090 | 4.50908 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.5781 | 0.958214 | ||||||||
\(147\) | 8.63228 | 0.711978 | ||||||||
\(148\) | 36.0644 | 2.96447 | ||||||||
\(149\) | 4.70327 | 0.385307 | 0.192653 | − | 0.981267i | \(-0.438291\pi\) | ||||
0.192653 | + | 0.981267i | \(0.438291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.9686 | −1.54364 | −0.771822 | − | 0.635839i | \(-0.780654\pi\) | ||||
−0.771822 | + | 0.635839i | \(0.780654\pi\) | |||||||
\(152\) | −4.04262 | −0.327900 | ||||||||
\(153\) | −33.1427 | −2.67943 | ||||||||
\(154\) | 7.77141 | 0.626238 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.6864 | 1.09579 | ||||||||
\(157\) | 5.58592 | 0.445805 | 0.222902 | − | 0.974841i | \(-0.428447\pi\) | ||||
0.222902 | + | 0.974841i | \(0.428447\pi\) | |||||||
\(158\) | 10.6177 | 0.844698 | ||||||||
\(159\) | 16.6941 | 1.32393 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.99875 | 0.236335 | ||||||||
\(162\) | −12.4903 | −0.981330 | ||||||||
\(163\) | 3.66298 | 0.286907 | 0.143453 | − | 0.989657i | \(-0.454179\pi\) | ||||
0.143453 | + | 0.989657i | \(0.454179\pi\) | |||||||
\(164\) | 33.5437 | 2.61932 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.35640 | −0.338123 | ||||||||
\(167\) | 1.70255 | 0.131748 | 0.0658738 | − | 0.997828i | \(-0.479017\pi\) | ||||
0.0658738 | + | 0.997828i | \(0.479017\pi\) | |||||||
\(168\) | 43.7415 | 3.37473 | ||||||||
\(169\) | −12.0640 | −0.927998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.98055 | 0.227929 | ||||||||
\(172\) | 39.1459 | 2.98485 | ||||||||
\(173\) | −10.3525 | −0.787086 | −0.393543 | − | 0.919306i | \(-0.628751\pi\) | ||||
−0.393543 | + | 0.919306i | \(0.628751\pi\) | |||||||
\(174\) | −51.0787 | −3.87227 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.5255 | −1.09490 | ||||||||
\(177\) | 13.6750 | 1.02787 | ||||||||
\(178\) | 7.28208 | 0.545815 | ||||||||
\(179\) | 1.43819 | 0.107495 | 0.0537477 | − | 0.998555i | \(-0.482883\pi\) | ||||
0.0537477 | + | 0.998555i | \(0.482883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.65171 | 0.494418 | 0.247209 | − | 0.968962i | \(-0.420487\pi\) | ||||
0.247209 | + | 0.968962i | \(0.420487\pi\) | |||||||
\(182\) | 5.08983 | 0.377284 | ||||||||
\(183\) | 11.0935 | 0.820054 | ||||||||
\(184\) | −11.1356 | −0.820929 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 53.1288 | 3.89560 | ||||||||
\(187\) | 8.89712 | 0.650622 | ||||||||
\(188\) | −20.0604 | −1.46306 | ||||||||
\(189\) | −14.6677 | −1.06692 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.4229 | −1.55011 | −0.775054 | − | 0.631896i | \(-0.782277\pi\) | ||||
−0.775054 | + | 0.631896i | \(0.782277\pi\) | |||||||
\(192\) | −25.1718 | −1.81662 | ||||||||
\(193\) | −9.46494 | −0.681302 | −0.340651 | − | 0.940190i | \(-0.610647\pi\) | ||||
−0.340651 | + | 0.940190i | \(0.610647\pi\) | |||||||
\(194\) | −37.5976 | −2.69935 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.3619 | −1.02585 | ||||||||
\(197\) | −10.8006 | −0.769513 | −0.384757 | − | 0.923018i | \(-0.625715\pi\) | ||||
−0.384757 | + | 0.923018i | \(0.625715\pi\) | |||||||
\(198\) | 21.2768 | 1.51208 | ||||||||
\(199\) | −11.5501 | −0.818768 | −0.409384 | − | 0.912362i | \(-0.634256\pi\) | ||||
−0.409384 | + | 0.912362i | \(0.634256\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.41576 | 0.523067 | ||||||||
\(202\) | −16.0792 | −1.13133 | ||||||||
\(203\) | −13.4506 | −0.944048 | ||||||||
\(204\) | 85.2028 | 5.96539 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 48.3725 | 3.37027 | ||||||||
\(207\) | 8.21009 | 0.570641 | ||||||||
\(208\) | −9.51340 | −0.659635 | ||||||||
\(209\) | −0.800127 | −0.0553460 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7769 | 1.22381 | 0.611907 | − | 0.790930i | \(-0.290403\pi\) | ||||
0.611907 | + | 0.790930i | \(0.290403\pi\) | |||||||
\(212\) | −27.7748 | −1.90758 | ||||||||
\(213\) | −7.98637 | −0.547217 | ||||||||
\(214\) | −45.9801 | −3.14314 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 54.4674 | 3.70604 | ||||||||
\(217\) | 13.9905 | 0.949736 | ||||||||
\(218\) | −17.3294 | −1.17370 | ||||||||
\(219\) | 12.8982 | 0.871579 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.82711 | 0.391974 | ||||||||
\(222\) | 56.7390 | 3.80807 | ||||||||
\(223\) | −6.39477 | −0.428226 | −0.214113 | − | 0.976809i | \(-0.568686\pi\) | ||||
−0.214113 | + | 0.976809i | \(0.568686\pi\) | |||||||
\(224\) | −21.7294 | −1.45186 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.4185 | −1.62429 | ||||||||
\(227\) | 28.9636 | 1.92238 | 0.961190 | − | 0.275888i | \(-0.0889720\pi\) | ||||
0.961190 | + | 0.275888i | \(0.0889720\pi\) | |||||||
\(228\) | −7.66237 | −0.507453 | ||||||||
\(229\) | 14.0844 | 0.930727 | 0.465363 | − | 0.885120i | \(-0.345924\pi\) | ||||
0.465363 | + | 0.885120i | \(0.345924\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.65745 | 0.569618 | ||||||||
\(232\) | 49.9477 | 3.27923 | ||||||||
\(233\) | −2.80871 | −0.184005 | −0.0920024 | − | 0.995759i | \(-0.529327\pi\) | ||||
−0.0920024 | + | 0.995759i | \(0.529327\pi\) | |||||||
\(234\) | 13.9351 | 0.910968 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −22.7516 | −1.48101 | ||||||||
\(237\) | 11.8282 | 0.768326 | ||||||||
\(238\) | 31.6861 | 2.05391 | ||||||||
\(239\) | −14.0335 | −0.907754 | −0.453877 | − | 0.891064i | \(-0.649960\pi\) | ||||
−0.453877 | + | 0.891064i | \(0.649960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 23.0809 | 1.48370 | ||||||||
\(243\) | 7.97908 | 0.511858 | ||||||||
\(244\) | −18.4567 | −1.18157 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 52.7732 | 3.36470 | ||||||||
\(247\) | −0.524038 | −0.0333437 | ||||||||
\(248\) | −51.9525 | −3.29899 | ||||||||
\(249\) | −4.85309 | −0.307552 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.2508 | 1.21510 | 0.607550 | − | 0.794282i | \(-0.292152\pi\) | ||||
0.607550 | + | 0.794282i | \(0.292152\pi\) | |||||||
\(252\) | 53.6554 | 3.37998 | ||||||||
\(253\) | −2.20399 | −0.138564 | ||||||||
\(254\) | 42.8743 | 2.69017 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.7181 | −0.919880 | ||||||||
\(257\) | 3.03581 | 0.189369 | 0.0946843 | − | 0.995507i | \(-0.469816\pi\) | ||||
0.0946843 | + | 0.995507i | \(0.469816\pi\) | |||||||
\(258\) | 61.5870 | 3.83424 | ||||||||
\(259\) | 14.9411 | 0.928398 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −36.8256 | −2.27945 | ||||||||
\(262\) | 40.4383 | 2.49829 | ||||||||
\(263\) | 0.703973 | 0.0434089 | 0.0217044 | − | 0.999764i | \(-0.493091\pi\) | ||||
0.0217044 | + | 0.999764i | \(0.493091\pi\) | |||||||
\(264\) | −32.1487 | −1.97862 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.84957 | −0.174718 | ||||||||
\(267\) | 8.11232 | 0.496466 | ||||||||
\(268\) | −12.3379 | −0.753658 | ||||||||
\(269\) | 30.7423 | 1.87439 | 0.937195 | − | 0.348807i | \(-0.113413\pi\) | ||||
0.937195 | + | 0.348807i | \(0.113413\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2233 | 1.22848 | 0.614238 | − | 0.789121i | \(-0.289463\pi\) | ||||
0.614238 | + | 0.789121i | \(0.289463\pi\) | |||||||
\(272\) | −59.2245 | −3.59101 | ||||||||
\(273\) | 5.67014 | 0.343172 | ||||||||
\(274\) | −35.3093 | −2.13312 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −21.1064 | −1.27046 | ||||||||
\(277\) | 2.84379 | 0.170867 | 0.0854335 | − | 0.996344i | \(-0.472772\pi\) | ||||
0.0854335 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(278\) | −57.3959 | −3.44238 | ||||||||
\(279\) | 38.3036 | 2.29318 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.30607 | 0.555154 | 0.277577 | − | 0.960703i | \(-0.410469\pi\) | ||||
0.277577 | + | 0.960703i | \(0.410469\pi\) | |||||||
\(282\) | −31.5604 | −1.87940 | ||||||||
\(283\) | −19.9804 | −1.18771 | −0.593856 | − | 0.804571i | \(-0.702395\pi\) | ||||
−0.593856 | + | 0.804571i | \(0.702395\pi\) | |||||||
\(284\) | 13.2873 | 0.788454 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.74087 | −0.221203 | ||||||||
\(287\) | 13.8968 | 0.820305 | ||||||||
\(288\) | −59.4916 | −3.50558 | ||||||||
\(289\) | 19.2760 | 1.13388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −41.8842 | −2.45530 | ||||||||
\(292\) | −21.4593 | −1.25581 | ||||||||
\(293\) | 10.9840 | 0.641691 | 0.320845 | − | 0.947132i | \(-0.396033\pi\) | ||||
0.320845 | + | 0.947132i | \(0.396033\pi\) | |||||||
\(294\) | −22.5951 | −1.31777 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −55.4827 | −3.22487 | ||||||||
\(297\) | 10.7803 | 0.625539 | ||||||||
\(298\) | −12.3109 | −0.713150 | ||||||||
\(299\) | −1.44349 | −0.0834793 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.2178 | 0.934778 | ||||||||
\(302\) | 49.6506 | 2.85707 | ||||||||
\(303\) | −17.9125 | −1.02904 | ||||||||
\(304\) | 5.32612 | 0.305474 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 86.7514 | 4.95925 | ||||||||
\(307\) | 33.8904 | 1.93423 | 0.967114 | − | 0.254343i | \(-0.0818593\pi\) | ||||
0.967114 | + | 0.254343i | \(0.0818593\pi\) | |||||||
\(308\) | −14.4038 | −0.820731 | ||||||||
\(309\) | 53.8876 | 3.06556 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.38229 | 0.418611 | 0.209306 | − | 0.977850i | \(-0.432880\pi\) | ||||
0.209306 | + | 0.977850i | \(0.432880\pi\) | |||||||
\(312\) | −21.0556 | −1.19204 | ||||||||
\(313\) | 17.8476 | 1.00880 | 0.504402 | − | 0.863469i | \(-0.331713\pi\) | ||||
0.504402 | + | 0.863469i | \(0.331713\pi\) | |||||||
\(314\) | −14.6212 | −0.825123 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6791 | −1.10704 | ||||||||
\(317\) | −12.6525 | −0.710634 | −0.355317 | − | 0.934746i | \(-0.615627\pi\) | ||||
−0.355317 | + | 0.934746i | \(0.615627\pi\) | |||||||
\(318\) | −43.6972 | −2.45041 | ||||||||
\(319\) | 9.88580 | 0.553498 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −51.2224 | −2.85896 | ||||||||
\(322\) | −7.84928 | −0.437423 | ||||||||
\(323\) | −3.26233 | −0.181521 | ||||||||
\(324\) | 23.1499 | 1.28611 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.58790 | −0.531024 | ||||||||
\(327\) | −19.3052 | −1.06758 | ||||||||
\(328\) | −51.6047 | −2.84940 | ||||||||
\(329\) | −8.31085 | −0.458192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7774 | −1.03210 | −0.516049 | − | 0.856559i | \(-0.672598\pi\) | ||||
−0.516049 | + | 0.856559i | \(0.672598\pi\) | |||||||
\(332\) | 8.07429 | 0.443134 | ||||||||
\(333\) | 40.9064 | 2.24166 | ||||||||
\(334\) | −4.45646 | −0.243847 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −57.6290 | −3.14392 | ||||||||
\(337\) | 11.1758 | 0.608787 | 0.304394 | − | 0.952546i | \(-0.401546\pi\) | ||||
0.304394 | + | 0.952546i | \(0.401546\pi\) | |||||||
\(338\) | 31.5776 | 1.71760 | ||||||||
\(339\) | −27.2025 | −1.47744 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.2826 | −0.556833 | ||||||||
\(342\) | −7.80164 | −0.421864 | ||||||||
\(343\) | −20.0192 | −1.08093 | ||||||||
\(344\) | −60.2234 | −3.24703 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.0978 | 1.45679 | ||||||||
\(347\) | 7.56445 | 0.406081 | 0.203040 | − | 0.979170i | \(-0.434918\pi\) | ||||
0.203040 | + | 0.979170i | \(0.434918\pi\) | |||||||
\(348\) | 94.6708 | 5.07489 | ||||||||
\(349\) | −22.5350 | −1.20627 | −0.603135 | − | 0.797639i | \(-0.706082\pi\) | ||||
−0.603135 | + | 0.797639i | \(0.706082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.06052 | 0.376862 | ||||||||
\(352\) | 15.9705 | 0.851229 | ||||||||
\(353\) | 17.3041 | 0.921002 | 0.460501 | − | 0.887659i | \(-0.347670\pi\) | ||||
0.460501 | + | 0.887659i | \(0.347670\pi\) | |||||||
\(354\) | −35.7944 | −1.90245 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.4968 | −0.715330 | ||||||||
\(357\) | 35.2987 | 1.86821 | ||||||||
\(358\) | −3.76449 | −0.198959 | ||||||||
\(359\) | −8.06827 | −0.425827 | −0.212914 | − | 0.977071i | \(-0.568295\pi\) | ||||
−0.212914 | + | 0.977071i | \(0.568295\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7066 | −0.984559 | ||||||||
\(362\) | −17.4109 | −0.915099 | ||||||||
\(363\) | 25.7124 | 1.34955 | ||||||||
\(364\) | −9.43365 | −0.494458 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −29.0373 | −1.51781 | ||||||||
\(367\) | −30.8104 | −1.60829 | −0.804144 | − | 0.594435i | \(-0.797376\pi\) | ||||
−0.804144 | + | 0.594435i | \(0.797376\pi\) | |||||||
\(368\) | 14.6711 | 0.764783 | ||||||||
\(369\) | 38.0473 | 1.98066 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5068 | −0.597405 | ||||||||
\(372\) | −98.4706 | −5.10546 | ||||||||
\(373\) | 10.1247 | 0.524237 | 0.262118 | − | 0.965036i | \(-0.415579\pi\) | ||||
0.262118 | + | 0.965036i | \(0.415579\pi\) | |||||||
\(374\) | −23.2883 | −1.20421 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.8616 | 1.59157 | ||||||||
\(377\) | 6.47464 | 0.333461 | ||||||||
\(378\) | 38.3930 | 1.97472 | ||||||||
\(379\) | 19.5232 | 1.00284 | 0.501419 | − | 0.865205i | \(-0.332812\pi\) | ||||
0.501419 | + | 0.865205i | \(0.332812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 47.7625 | 2.44695 | ||||||||
\(382\) | 56.0748 | 2.86903 | ||||||||
\(383\) | −31.0185 | −1.58497 | −0.792484 | − | 0.609892i | \(-0.791213\pi\) | ||||
−0.792484 | + | 0.609892i | \(0.791213\pi\) | |||||||
\(384\) | 2.83723 | 0.144787 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.7746 | 1.26100 | ||||||||
\(387\) | 44.4017 | 2.25706 | ||||||||
\(388\) | 69.6845 | 3.53770 | ||||||||
\(389\) | −26.0860 | −1.32261 | −0.661307 | − | 0.750115i | \(-0.729998\pi\) | ||||
−0.661307 | + | 0.750115i | \(0.729998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.98628 | −0.454456 | ||||||||
\(392\) | 22.0948 | 1.11596 | ||||||||
\(393\) | 45.0488 | 2.27241 | ||||||||
\(394\) | 28.2708 | 1.42426 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −39.4351 | −1.98169 | ||||||||
\(397\) | 7.96047 | 0.399524 | 0.199762 | − | 0.979844i | \(-0.435983\pi\) | ||||
0.199762 | + | 0.979844i | \(0.435983\pi\) | |||||||
\(398\) | 30.2326 | 1.51543 | ||||||||
\(399\) | −3.17445 | −0.158921 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0082 | 1.04910 | 0.524551 | − | 0.851379i | \(-0.324233\pi\) | ||||
0.524551 | + | 0.851379i | \(0.324233\pi\) | |||||||
\(402\) | −19.4108 | −0.968125 | ||||||||
\(403\) | −6.73451 | −0.335470 | ||||||||
\(404\) | 29.8017 | 1.48269 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35.2072 | 1.74730 | ||||||||
\(407\) | −10.9813 | −0.544322 | ||||||||
\(408\) | −131.079 | −6.48937 | ||||||||
\(409\) | 11.2395 | 0.555757 | 0.277878 | − | 0.960616i | \(-0.410369\pi\) | ||||
0.277878 | + | 0.960616i | \(0.410369\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −39.3351 | −1.94026 | ||||||||
\(412\) | −89.6551 | −4.41699 | ||||||||
\(413\) | −9.42579 | −0.463813 | ||||||||
\(414\) | −21.4900 | −1.05618 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.4598 | 0.512832 | ||||||||
\(417\) | −63.9397 | −3.13114 | ||||||||
\(418\) | 2.09434 | 0.102438 | ||||||||
\(419\) | −39.6052 | −1.93484 | −0.967420 | − | 0.253178i | \(-0.918524\pi\) | ||||
−0.967420 | + | 0.253178i | \(0.918524\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.34705 | −0.309337 | −0.154668 | − | 0.987966i | \(-0.549431\pi\) | ||||
−0.154668 | + | 0.987966i | \(0.549431\pi\) | |||||||
\(422\) | −46.5313 | −2.26511 | ||||||||
\(423\) | −22.7537 | −1.10632 | ||||||||
\(424\) | 42.7296 | 2.07513 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20.9044 | 1.01282 | ||||||||
\(427\) | −7.64644 | −0.370037 | ||||||||
\(428\) | 85.2209 | 4.11931 | ||||||||
\(429\) | −4.16738 | −0.201203 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5452 | 0.796954 | 0.398477 | − | 0.917178i | \(-0.369539\pi\) | ||||
0.398477 | + | 0.917178i | \(0.369539\pi\) | |||||||
\(432\) | −71.7603 | −3.45257 | ||||||||
\(433\) | −12.7015 | −0.610397 | −0.305199 | − | 0.952289i | \(-0.598723\pi\) | ||||
−0.305199 | + | 0.952289i | \(0.598723\pi\) | |||||||
\(434\) | −36.6203 | −1.75783 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 32.1188 | 1.53821 | ||||||||
\(437\) | 0.808145 | 0.0386588 | ||||||||
\(438\) | −33.7612 | −1.61317 | ||||||||
\(439\) | −16.4422 | −0.784742 | −0.392371 | − | 0.919807i | \(-0.628345\pi\) | ||||
−0.392371 | + | 0.919807i | \(0.628345\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.2901 | −0.775720 | ||||||||
\(442\) | −15.2526 | −0.725490 | ||||||||
\(443\) | −38.2619 | −1.81788 | −0.908940 | − | 0.416927i | \(-0.863107\pi\) | ||||
−0.908940 | + | 0.416927i | \(0.863107\pi\) | |||||||
\(444\) | −105.162 | −4.99075 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.7384 | 0.792587 | ||||||||
\(447\) | −13.7145 | −0.648672 | ||||||||
\(448\) | 17.3502 | 0.819722 | ||||||||
\(449\) | −21.0276 | −0.992355 | −0.496178 | − | 0.868221i | \(-0.665263\pi\) | ||||
−0.496178 | + | 0.868221i | \(0.665263\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.2138 | −0.480947 | ||||||||
\(452\) | 45.2579 | 2.12875 | ||||||||
\(453\) | 55.3114 | 2.59876 | ||||||||
\(454\) | −75.8125 | −3.55806 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.7881 | 0.552026 | ||||||||
\(457\) | 28.5200 | 1.33411 | 0.667055 | − | 0.745008i | \(-0.267554\pi\) | ||||
0.667055 | + | 0.745008i | \(0.267554\pi\) | |||||||
\(458\) | −36.8662 | −1.72265 | ||||||||
\(459\) | 43.9544 | 2.05161 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.4782 | 1.60581 | 0.802905 | − | 0.596107i | \(-0.203286\pi\) | ||||
0.802905 | + | 0.596107i | \(0.203286\pi\) | |||||||
\(462\) | −22.6610 | −1.05428 | ||||||||
\(463\) | −9.61723 | −0.446951 | −0.223475 | − | 0.974710i | \(-0.571740\pi\) | ||||
−0.223475 | + | 0.974710i | \(0.571740\pi\) | |||||||
\(464\) | −65.8057 | −3.05495 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.35184 | 0.340568 | ||||||||
\(467\) | −36.4956 | −1.68882 | −0.844408 | − | 0.535701i | \(-0.820047\pi\) | ||||
−0.844408 | + | 0.535701i | \(0.820047\pi\) | |||||||
\(468\) | −25.8278 | −1.19389 | ||||||||
\(469\) | −5.11148 | −0.236026 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.2882 | −0.750521 | ||||||||
\(472\) | 35.0019 | 1.61109 | ||||||||
\(473\) | −11.9196 | −0.548063 | ||||||||
\(474\) | −30.9606 | −1.42207 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −58.7280 | −2.69180 | ||||||||
\(477\) | −31.5038 | −1.44246 | ||||||||
\(478\) | 36.7330 | 1.68013 | ||||||||
\(479\) | 14.4680 | 0.661058 | 0.330529 | − | 0.943796i | \(-0.392773\pi\) | ||||
0.330529 | + | 0.943796i | \(0.392773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.19213 | −0.327933 | ||||||||
\(482\) | −2.61751 | −0.119224 | ||||||||
\(483\) | −8.74420 | −0.397875 | ||||||||
\(484\) | −42.7789 | −1.94449 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −20.8853 | −0.947379 | ||||||||
\(487\) | −1.90549 | −0.0863461 | −0.0431730 | − | 0.999068i | \(-0.513747\pi\) | ||||
−0.0431730 | + | 0.999068i | \(0.513747\pi\) | |||||||
\(488\) | 28.3944 | 1.28535 | ||||||||
\(489\) | −10.6810 | −0.483013 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0041 | −0.451480 | −0.225740 | − | 0.974188i | \(-0.572480\pi\) | ||||
−0.225740 | + | 0.974188i | \(0.572480\pi\) | |||||||
\(492\) | −97.8115 | −4.40968 | ||||||||
\(493\) | 40.3071 | 1.81534 | ||||||||
\(494\) | 1.37168 | 0.0617147 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 68.4469 | 3.07336 | ||||||||
\(497\) | 5.50479 | 0.246924 | ||||||||
\(498\) | 12.7030 | 0.569236 | ||||||||
\(499\) | 15.8138 | 0.707921 | 0.353961 | − | 0.935260i | \(-0.384835\pi\) | ||||
0.353961 | + | 0.935260i | \(0.384835\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.96455 | −0.221800 | ||||||||
\(502\) | −50.3892 | −2.24898 | ||||||||
\(503\) | −22.2704 | −0.992989 | −0.496495 | − | 0.868040i | \(-0.665380\pi\) | ||||
−0.496495 | + | 0.868040i | \(0.665380\pi\) | |||||||
\(504\) | −82.5454 | −3.67686 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.76898 | 0.256463 | ||||||||
\(507\) | 35.1779 | 1.56230 | ||||||||
\(508\) | −79.4645 | −3.52567 | ||||||||
\(509\) | −4.30285 | −0.190721 | −0.0953603 | − | 0.995443i | \(-0.530400\pi\) | ||||
−0.0953603 | + | 0.995443i | \(0.530400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.89038 | −0.393287 | ||||||||
\(512\) | 40.4708 | 1.78857 | ||||||||
\(513\) | −3.95286 | −0.174523 | ||||||||
\(514\) | −7.94627 | −0.350495 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −114.147 | −5.02505 | ||||||||
\(517\) | 6.10822 | 0.268639 | ||||||||
\(518\) | −39.1087 | −1.71834 | ||||||||
\(519\) | 30.1873 | 1.32508 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0258 | 1.57832 | 0.789160 | − | 0.614187i | \(-0.210516\pi\) | ||||
0.789160 | + | 0.614187i | \(0.210516\pi\) | |||||||
\(522\) | 96.3915 | 4.21894 | ||||||||
\(523\) | 26.7740 | 1.17074 | 0.585372 | − | 0.810764i | \(-0.300948\pi\) | ||||
0.585372 | + | 0.810764i | \(0.300948\pi\) | |||||||
\(524\) | −74.9496 | −3.27419 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.84266 | −0.0803438 | ||||||||
\(527\) | −41.9249 | −1.82628 | ||||||||
\(528\) | 42.3556 | 1.84329 | ||||||||
\(529\) | −20.7739 | −0.903214 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25.8063 | −1.11990 | ||||||||
\(532\) | 5.28147 | 0.228981 | ||||||||
\(533\) | −6.68944 | −0.289752 | ||||||||
\(534\) | −21.2341 | −0.918890 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18.9811 | 0.819857 | ||||||||
\(537\) | −4.19368 | −0.180971 | ||||||||
\(538\) | −80.4683 | −3.46924 | ||||||||
\(539\) | 4.37307 | 0.188361 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.20360 | −0.0517468 | −0.0258734 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258734 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(542\) | −52.9347 | −2.27374 | ||||||||
\(543\) | −19.3960 | −0.832362 | ||||||||
\(544\) | 65.1159 | 2.79182 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −14.8417 | −0.635165 | ||||||||
\(547\) | −11.1103 | −0.475043 | −0.237522 | − | 0.971382i | \(-0.576335\pi\) | ||||
−0.237522 | + | 0.971382i | \(0.576335\pi\) | |||||||
\(548\) | 65.4434 | 2.79560 | ||||||||
\(549\) | −20.9347 | −0.893471 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.62485 | −0.154424 | ||||||||
\(552\) | 32.4708 | 1.38205 | ||||||||
\(553\) | −8.15289 | −0.346696 | ||||||||
\(554\) | −7.44367 | −0.316251 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 106.379 | 4.51149 | ||||||||
\(557\) | −41.9026 | −1.77547 | −0.887735 | − | 0.460354i | \(-0.847722\pi\) | ||||
−0.887735 | + | 0.460354i | \(0.847722\pi\) | |||||||
\(558\) | −100.260 | −4.24436 | ||||||||
\(559\) | −7.80666 | −0.330187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.9435 | −1.09534 | ||||||||
\(562\) | −24.3588 | −1.02751 | ||||||||
\(563\) | −20.0207 | −0.843771 | −0.421886 | − | 0.906649i | \(-0.638632\pi\) | ||||
−0.421886 | + | 0.906649i | \(0.638632\pi\) | |||||||
\(564\) | 58.4950 | 2.46309 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 52.2990 | 2.19829 | ||||||||
\(567\) | 9.59079 | 0.402775 | ||||||||
\(568\) | −20.4416 | −0.857709 | ||||||||
\(569\) | −40.1123 | −1.68159 | −0.840797 | − | 0.541351i | \(-0.817913\pi\) | ||||
−0.840797 | + | 0.541351i | \(0.817913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.44389 | 0.227820 | 0.113910 | − | 0.993491i | \(-0.463663\pi\) | ||||
0.113910 | + | 0.993491i | \(0.463663\pi\) | |||||||
\(572\) | 6.93345 | 0.289902 | ||||||||
\(573\) | 62.4680 | 2.60964 | ||||||||
\(574\) | −36.3752 | −1.51827 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 47.5021 | 1.97925 | ||||||||
\(577\) | −5.96992 | −0.248531 | −0.124266 | − | 0.992249i | \(-0.539657\pi\) | ||||
−0.124266 | + | 0.992249i | \(0.539657\pi\) | |||||||
\(578\) | −50.4552 | −2.09866 | ||||||||
\(579\) | 27.5992 | 1.14699 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.34511 | 0.138778 | ||||||||
\(582\) | 109.632 | 4.54441 | ||||||||
\(583\) | 8.45717 | 0.350260 | ||||||||
\(584\) | 33.0137 | 1.36612 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.7507 | −1.18768 | ||||||||
\(587\) | 46.9038 | 1.93593 | 0.967964 | − | 0.251091i | \(-0.0807892\pi\) | ||||
0.967964 | + | 0.251091i | \(0.0807892\pi\) | |||||||
\(588\) | 41.8785 | 1.72704 | ||||||||
\(589\) | 3.77035 | 0.155354 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.4940 | 1.29549 | ||||||||
\(592\) | 73.0979 | 3.00431 | ||||||||
\(593\) | 5.55227 | 0.228004 | 0.114002 | − | 0.993481i | \(-0.463633\pi\) | ||||
0.114002 | + | 0.993481i | \(0.463633\pi\) | |||||||
\(594\) | −28.2177 | −1.15779 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.8174 | 0.934635 | ||||||||
\(597\) | 33.6795 | 1.37841 | ||||||||
\(598\) | 3.77836 | 0.154509 | ||||||||
\(599\) | −36.3540 | −1.48538 | −0.742691 | − | 0.669634i | \(-0.766451\pi\) | ||||
−0.742691 | + | 0.669634i | \(0.766451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.6980 | 1.74169 | 0.870844 | − | 0.491559i | \(-0.163573\pi\) | ||||
0.870844 | + | 0.491559i | \(0.163573\pi\) | |||||||
\(602\) | −42.4503 | −1.73015 | ||||||||
\(603\) | −13.9944 | −0.569896 | ||||||||
\(604\) | −92.0239 | −3.74440 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 46.8861 | 1.90462 | ||||||||
\(607\) | −16.5312 | −0.670981 | −0.335490 | − | 0.942044i | \(-0.608902\pi\) | ||||
−0.335490 | + | 0.942044i | \(0.608902\pi\) | |||||||
\(608\) | −5.85594 | −0.237490 | ||||||||
\(609\) | 39.2212 | 1.58933 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.00054 | 0.161845 | ||||||||
\(612\) | −160.788 | −6.49946 | ||||||||
\(613\) | 17.8745 | 0.721945 | 0.360973 | − | 0.932576i | \(-0.382445\pi\) | ||||
0.360973 | + | 0.932576i | \(0.382445\pi\) | |||||||
\(614\) | −88.7086 | −3.57999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.1592 | 0.892821 | ||||||||
\(617\) | 1.22431 | 0.0492888 | 0.0246444 | − | 0.999696i | \(-0.492155\pi\) | ||||
0.0246444 | + | 0.999696i | \(0.492155\pi\) | |||||||
\(618\) | −141.052 | −5.67393 | ||||||||
\(619\) | 34.6297 | 1.39189 | 0.695943 | − | 0.718097i | \(-0.254987\pi\) | ||||
0.695943 | + | 0.718097i | \(0.254987\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.8884 | −0.436935 | ||||||||
\(622\) | −19.3233 | −0.774792 | ||||||||
\(623\) | −5.59161 | −0.224023 | ||||||||
\(624\) | 27.7405 | 1.11051 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −46.7163 | −1.86716 | ||||||||
\(627\) | 2.33313 | 0.0931761 | ||||||||
\(628\) | 27.0994 | 1.08138 | ||||||||
\(629\) | −44.7737 | −1.78524 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.85881 | 0.233236 | 0.116618 | − | 0.993177i | \(-0.462795\pi\) | ||||
0.116618 | + | 0.993177i | \(0.462795\pi\) | |||||||
\(632\) | 30.2751 | 1.20428 | ||||||||
\(633\) | −51.8365 | −2.06032 | ||||||||
\(634\) | 33.1180 | 1.31528 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 80.9896 | 3.21145 | ||||||||
\(637\) | 2.86411 | 0.113480 | ||||||||
\(638\) | −25.8762 | −1.02445 | ||||||||
\(639\) | 15.0712 | 0.596208 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.10916 | −0.241297 | −0.120649 | − | 0.992695i | \(-0.538497\pi\) | ||||
−0.120649 | + | 0.992695i | \(0.538497\pi\) | |||||||
\(642\) | 134.075 | 5.29153 | ||||||||
\(643\) | −23.2044 | −0.915092 | −0.457546 | − | 0.889186i | \(-0.651272\pi\) | ||||
−0.457546 | + | 0.889186i | \(0.651272\pi\) | |||||||
\(644\) | 14.5481 | 0.573275 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.53921 | 0.335971 | ||||||||
\(647\) | −38.1244 | −1.49883 | −0.749413 | − | 0.662103i | \(-0.769664\pi\) | ||||
−0.749413 | + | 0.662103i | \(0.769664\pi\) | |||||||
\(648\) | −35.6146 | −1.39907 | ||||||||
\(649\) | 6.92767 | 0.271935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.7955 | −1.59890 | ||||||||
\(652\) | 17.7705 | 0.695946 | ||||||||
\(653\) | 14.8821 | 0.582383 | 0.291191 | − | 0.956665i | \(-0.405948\pi\) | ||||
0.291191 | + | 0.956665i | \(0.405948\pi\) | |||||||
\(654\) | 50.5316 | 1.97594 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 67.9888 | 2.65452 | ||||||||
\(657\) | −24.3404 | −0.949610 | ||||||||
\(658\) | 21.7538 | 0.848050 | ||||||||
\(659\) | 9.15991 | 0.356820 | 0.178410 | − | 0.983956i | \(-0.442905\pi\) | ||||
0.178410 | + | 0.983956i | \(0.442905\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.23056 | 0.359027 | 0.179514 | − | 0.983755i | \(-0.442548\pi\) | ||||
0.179514 | + | 0.983755i | \(0.442548\pi\) | |||||||
\(662\) | 49.1500 | 1.91027 | ||||||||
\(663\) | −16.9915 | −0.659897 | ||||||||
\(664\) | −12.4218 | −0.482058 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −107.073 | −4.14900 | ||||||||
\(667\) | −9.98486 | −0.386615 | ||||||||
\(668\) | 8.25974 | 0.319579 | ||||||||
\(669\) | 18.6468 | 0.720927 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.61990 | 0.216954 | ||||||||
\(672\) | 63.3618 | 2.44423 | ||||||||
\(673\) | 16.0187 | 0.617476 | 0.308738 | − | 0.951147i | \(-0.400093\pi\) | ||||
0.308738 | + | 0.951147i | \(0.400093\pi\) | |||||||
\(674\) | −29.2529 | −1.12678 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −58.5269 | −2.25104 | ||||||||
\(677\) | 36.7022 | 1.41058 | 0.705290 | − | 0.708919i | \(-0.250817\pi\) | ||||
0.705290 | + | 0.708919i | \(0.250817\pi\) | |||||||
\(678\) | 71.2029 | 2.73453 | ||||||||
\(679\) | 28.8697 | 1.10792 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −84.4561 | −3.23637 | ||||||||
\(682\) | 26.9148 | 1.03062 | ||||||||
\(683\) | −31.1207 | −1.19080 | −0.595400 | − | 0.803430i | \(-0.703006\pi\) | ||||
−0.595400 | + | 0.803430i | \(0.703006\pi\) | |||||||
\(684\) | 14.4598 | 0.552884 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 52.4005 | 2.00066 | ||||||||
\(687\) | −41.0695 | −1.56690 | ||||||||
\(688\) | 79.3438 | 3.02495 | ||||||||
\(689\) | 5.53897 | 0.211018 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.5540 | 0.591703 | 0.295852 | − | 0.955234i | \(-0.404397\pi\) | ||||
0.295852 | + | 0.955234i | \(0.404397\pi\) | |||||||
\(692\) | −50.2239 | −1.90923 | ||||||||
\(693\) | −16.3376 | −0.620615 | ||||||||
\(694\) | −19.8000 | −0.751599 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −145.645 | −5.52065 | ||||||||
\(697\) | −41.6443 | −1.57739 | ||||||||
\(698\) | 58.9856 | 2.23264 | ||||||||
\(699\) | 8.19004 | 0.309776 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.2977 | −1.55979 | −0.779896 | − | 0.625909i | \(-0.784728\pi\) | ||||
−0.779896 | + | 0.625909i | \(0.784728\pi\) | |||||||
\(702\) | −18.4810 | −0.697520 | ||||||||
\(703\) | 4.02654 | 0.151864 | ||||||||
\(704\) | −12.7519 | −0.480605 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.2936 | −1.70465 | ||||||||
\(707\) | 12.3466 | 0.464341 | ||||||||
\(708\) | 66.3425 | 2.49330 | ||||||||
\(709\) | −4.14082 | −0.155512 | −0.0777559 | − | 0.996972i | \(-0.524775\pi\) | ||||
−0.0777559 | + | 0.996972i | \(0.524775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.3213 | −0.837113 | ||||||||
\(712\) | 20.7640 | 0.778162 | ||||||||
\(713\) | 10.3856 | 0.388945 | ||||||||
\(714\) | −92.3950 | −3.45780 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.97721 | 0.260751 | ||||||||
\(717\) | 40.9210 | 1.52822 | ||||||||
\(718\) | 21.1188 | 0.788147 | ||||||||
\(719\) | −7.26334 | −0.270877 | −0.135438 | − | 0.990786i | \(-0.543244\pi\) | ||||
−0.135438 | + | 0.990786i | \(0.543244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.1433 | −1.38329 | ||||||||
\(722\) | 48.9648 | 1.82228 | ||||||||
\(723\) | −2.91594 | −0.108445 | ||||||||
\(724\) | 32.2700 | 1.19930 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −67.3026 | −2.49783 | ||||||||
\(727\) | −27.5563 | −1.02201 | −0.511004 | − | 0.859578i | \(-0.670726\pi\) | ||||
−0.511004 | + | 0.859578i | \(0.670726\pi\) | |||||||
\(728\) | 14.5131 | 0.537889 | ||||||||
\(729\) | −37.5820 | −1.39193 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.5994 | −1.79751 | ||||||||
\(732\) | 53.8187 | 1.98920 | ||||||||
\(733\) | 22.2034 | 0.820103 | 0.410051 | − | 0.912062i | \(-0.365511\pi\) | ||||
0.410051 | + | 0.912062i | \(0.365511\pi\) | |||||||
\(734\) | 80.6466 | 2.97672 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.1305 | −0.594578 | ||||||||
\(737\) | 3.75679 | 0.138383 | ||||||||
\(738\) | −99.5892 | −3.66593 | ||||||||
\(739\) | 17.1110 | 0.629440 | 0.314720 | − | 0.949185i | \(-0.398089\pi\) | ||||
0.314720 | + | 0.949185i | \(0.398089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.52807 | 0.0561349 | ||||||||
\(742\) | 30.1193 | 1.10571 | ||||||||
\(743\) | −34.8194 | −1.27740 | −0.638700 | − | 0.769456i | \(-0.720528\pi\) | ||||
−0.638700 | + | 0.769456i | \(0.720528\pi\) | |||||||
\(744\) | 151.491 | 5.55391 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −26.5015 | −0.970290 | ||||||||
\(747\) | 9.15835 | 0.335086 | ||||||||
\(748\) | 43.1633 | 1.57821 | ||||||||
\(749\) | 35.3063 | 1.29006 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −51.9686 | −1.89636 | −0.948180 | − | 0.317733i | \(-0.897078\pi\) | ||||
−0.948180 | + | 0.317733i | \(0.897078\pi\) | |||||||
\(752\) | −40.6599 | −1.48271 | ||||||||
\(753\) | −56.1342 | −2.04565 | ||||||||
\(754\) | −16.9475 | −0.617190 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −71.1588 | −2.58802 | ||||||||
\(757\) | 12.7291 | 0.462647 | 0.231323 | − | 0.972877i | \(-0.425694\pi\) | ||||
0.231323 | + | 0.972877i | \(0.425694\pi\) | |||||||
\(758\) | −51.1021 | −1.85611 | ||||||||
\(759\) | 6.42672 | 0.233275 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.108092 | 0.00391832 | 0.00195916 | − | 0.999998i | \(-0.499376\pi\) | ||||
0.00195916 | + | 0.999998i | \(0.499376\pi\) | |||||||
\(762\) | −125.019 | −4.52896 | ||||||||
\(763\) | 13.3065 | 0.481729 | ||||||||
\(764\) | −103.931 | −3.76008 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 81.1912 | 2.93356 | ||||||||
\(767\) | 4.53723 | 0.163830 | ||||||||
\(768\) | 42.9171 | 1.54864 | ||||||||
\(769\) | −36.3976 | −1.31253 | −0.656266 | − | 0.754530i | \(-0.727865\pi\) | ||||
−0.656266 | + | 0.754530i | \(0.727865\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.85224 | −0.318806 | ||||||||
\(772\) | −45.9180 | −1.65263 | ||||||||
\(773\) | −8.06503 | −0.290079 | −0.145039 | − | 0.989426i | \(-0.546331\pi\) | ||||
−0.145039 | + | 0.989426i | \(0.546331\pi\) | |||||||
\(774\) | −116.222 | −4.17751 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −107.205 | −3.84844 | ||||||||
\(777\) | −43.5675 | −1.56298 | ||||||||
\(778\) | 68.2805 | 2.44798 | ||||||||
\(779\) | 3.74511 | 0.134182 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.04585 | −0.144772 | ||||||||
\(782\) | 23.5217 | 0.841135 | ||||||||
\(783\) | 48.8387 | 1.74535 | ||||||||
\(784\) | −29.1097 | −1.03963 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −117.916 | −4.20592 | ||||||||
\(787\) | −20.5415 | −0.732226 | −0.366113 | − | 0.930570i | \(-0.619312\pi\) | ||||
−0.366113 | + | 0.930570i | \(0.619312\pi\) | |||||||
\(788\) | −52.3980 | −1.86660 | ||||||||
\(789\) | −2.05275 | −0.0730797 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.7499 | 0.666671 | ||||||||
\(792\) | 60.6683 | 2.15576 | ||||||||
\(793\) | 3.68072 | 0.130706 | ||||||||
\(794\) | −20.8366 | −0.739465 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −56.0341 | −1.98608 | ||||||||
\(797\) | 2.56805 | 0.0909649 | 0.0454825 | − | 0.998965i | \(-0.485517\pi\) | ||||
0.0454825 | + | 0.998965i | \(0.485517\pi\) | |||||||
\(798\) | 8.30917 | 0.294141 | ||||||||
\(799\) | 24.9049 | 0.881071 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.3089 | −0.540913 | ||||||||
\(802\) | −54.9894 | −1.94174 | ||||||||
\(803\) | 6.53416 | 0.230586 | ||||||||
\(804\) | 35.9767 | 1.26880 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.6277 | 0.620909 | ||||||||
\(807\) | −89.6427 | −3.15557 | ||||||||
\(808\) | −45.8480 | −1.61293 | ||||||||
\(809\) | 17.4707 | 0.614237 | 0.307119 | − | 0.951671i | \(-0.400635\pi\) | ||||
0.307119 | + | 0.951671i | \(0.400635\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.3292 | −0.889427 | −0.444713 | − | 0.895673i | \(-0.646694\pi\) | ||||
−0.444713 | + | 0.895673i | \(0.646694\pi\) | |||||||
\(812\) | −65.2541 | −2.28997 | ||||||||
\(813\) | −58.9699 | −2.06817 | ||||||||
\(814\) | 28.7437 | 1.00747 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 172.695 | 6.04554 | ||||||||
\(817\) | 4.37059 | 0.152908 | ||||||||
\(818\) | −29.4195 | −1.02863 | ||||||||
\(819\) | −10.7002 | −0.373896 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.554175 | 0.0193408 | 0.00967042 | − | 0.999953i | \(-0.496922\pi\) | ||||
0.00967042 | + | 0.999953i | \(0.496922\pi\) | |||||||
\(822\) | 102.960 | 3.59114 | ||||||||
\(823\) | −50.8525 | −1.77261 | −0.886304 | − | 0.463105i | \(-0.846735\pi\) | ||||
−0.886304 | + | 0.463105i | \(0.846735\pi\) | |||||||
\(824\) | 137.929 | 4.80497 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.6721 | 0.858454 | ||||||||
\(827\) | 52.2652 | 1.81744 | 0.908719 | − | 0.417409i | \(-0.137062\pi\) | ||||
0.908719 | + | 0.417409i | \(0.137062\pi\) | |||||||
\(828\) | 39.8303 | 1.38420 | ||||||||
\(829\) | 19.2786 | 0.669574 | 0.334787 | − | 0.942294i | \(-0.391336\pi\) | ||||
0.334787 | + | 0.942294i | \(0.391336\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.29234 | −0.287658 | ||||||||
\(832\) | −8.35177 | −0.289546 | ||||||||
\(833\) | 17.8302 | 0.617780 | ||||||||
\(834\) | 167.363 | 5.79531 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.88172 | −0.134252 | ||||||||
\(837\) | −50.7989 | −1.75587 | ||||||||
\(838\) | 103.667 | 3.58112 | ||||||||
\(839\) | 52.3553 | 1.80751 | 0.903753 | − | 0.428055i | \(-0.140801\pi\) | ||||
0.903753 | + | 0.428055i | \(0.140801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.7861 | 0.544349 | ||||||||
\(842\) | 16.6135 | 0.572539 | ||||||||
\(843\) | −27.1360 | −0.934613 | ||||||||
\(844\) | 86.2426 | 2.96859 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 59.5582 | 2.04765 | ||||||||
\(847\) | −17.7229 | −0.608966 | ||||||||
\(848\) | −56.2959 | −1.93321 | ||||||||
\(849\) | 58.2617 | 1.99954 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.0913 | 0.380206 | ||||||||
\(852\) | −38.7449 | −1.32738 | ||||||||
\(853\) | −46.7427 | −1.60044 | −0.800219 | − | 0.599708i | \(-0.795284\pi\) | ||||
−0.800219 | + | 0.599708i | \(0.795284\pi\) | |||||||
\(854\) | 20.0147 | 0.684888 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −131.107 | −4.48114 | ||||||||
\(857\) | −32.2371 | −1.10120 | −0.550599 | − | 0.834770i | \(-0.685601\pi\) | ||||
−0.550599 | + | 0.834770i | \(0.685601\pi\) | |||||||
\(858\) | 10.9082 | 0.372399 | ||||||||
\(859\) | −49.6830 | −1.69516 | −0.847581 | − | 0.530666i | \(-0.821942\pi\) | ||||
−0.847581 | + | 0.530666i | \(0.821942\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −40.5224 | −1.38100 | ||||||||
\(862\) | −43.3073 | −1.47505 | ||||||||
\(863\) | −19.4871 | −0.663349 | −0.331675 | − | 0.943394i | \(-0.607614\pi\) | ||||
−0.331675 | + | 0.943394i | \(0.607614\pi\) | |||||||
\(864\) | 78.8988 | 2.68419 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 33.2465 | 1.12976 | ||||||||
\(867\) | −56.2077 | −1.90891 | ||||||||
\(868\) | 67.8732 | 2.30377 | ||||||||
\(869\) | 5.99213 | 0.203269 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.46048 | 0.0833703 | ||||||||
\(872\) | −49.4127 | −1.67333 | ||||||||
\(873\) | 79.0404 | 2.67511 | ||||||||
\(874\) | −2.11533 | −0.0715521 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 62.5741 | 2.11418 | ||||||||
\(877\) | −33.5686 | −1.13353 | −0.566766 | − | 0.823879i | \(-0.691806\pi\) | ||||
−0.566766 | + | 0.823879i | \(0.691806\pi\) | |||||||
\(878\) | 43.0376 | 1.45245 | ||||||||
\(879\) | −32.0287 | −1.08030 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.8009 | 0.801872 | 0.400936 | − | 0.916106i | \(-0.368685\pi\) | ||||
0.400936 | + | 0.916106i | \(0.368685\pi\) | |||||||
\(882\) | 42.6396 | 1.43575 | ||||||||
\(883\) | −17.8466 | −0.600585 | −0.300293 | − | 0.953847i | \(-0.597084\pi\) | ||||
−0.300293 | + | 0.953847i | \(0.597084\pi\) | |||||||
\(884\) | 28.2695 | 0.950808 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 100.151 | 3.36464 | ||||||||
\(887\) | 47.4414 | 1.59292 | 0.796462 | − | 0.604688i | \(-0.206702\pi\) | ||||
0.796462 | + | 0.604688i | \(0.206702\pi\) | |||||||
\(888\) | 161.784 | 5.42913 | ||||||||
\(889\) | −32.9214 | −1.10415 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.04894 | −0.236148 | ||||||||
\(892\) | −31.0235 | −1.03874 | ||||||||
\(893\) | −2.23972 | −0.0749493 | ||||||||
\(894\) | 35.8978 | 1.20060 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.95563 | −0.0653329 | ||||||||
\(897\) | 4.20914 | 0.140539 | ||||||||
\(898\) | 55.0401 | 1.83671 | ||||||||
\(899\) | −46.5837 | −1.55365 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.4822 | 1.14877 | ||||||||
\(902\) | 26.7347 | 0.890167 | ||||||||
\(903\) | −47.2902 | −1.57372 | ||||||||
\(904\) | −69.6263 | −2.31574 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −144.778 | −4.80994 | ||||||||
\(907\) | −2.24706 | −0.0746123 | −0.0373061 | − | 0.999304i | \(-0.511878\pi\) | ||||
−0.0373061 | + | 0.999304i | \(0.511878\pi\) | |||||||
\(908\) | 140.513 | 4.66310 | ||||||||
\(909\) | 33.8029 | 1.12117 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.2694 | 1.36732 | 0.683658 | − | 0.729803i | \(-0.260388\pi\) | ||||
0.683658 | + | 0.729803i | \(0.260388\pi\) | |||||||
\(912\) | −15.5307 | −0.514271 | ||||||||
\(913\) | −2.45855 | −0.0813662 | ||||||||
\(914\) | −74.6516 | −2.46925 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 68.3290 | 2.25765 | ||||||||
\(917\) | −31.0509 | −1.02539 | ||||||||
\(918\) | −115.051 | −3.79725 | ||||||||
\(919\) | 50.0566 | 1.65121 | 0.825607 | − | 0.564246i | \(-0.190833\pi\) | ||||
0.825607 | + | 0.564246i | \(0.190833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −98.8225 | −3.25631 | ||||||||
\(922\) | −90.2472 | −2.97213 | ||||||||
\(923\) | −2.64981 | −0.0872195 | ||||||||
\(924\) | 42.0006 | 1.38172 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25.1732 | 0.827244 | ||||||||
\(927\) | −101.692 | −3.34001 | ||||||||
\(928\) | 72.3518 | 2.37506 | ||||||||
\(929\) | 2.57944 | 0.0846288 | 0.0423144 | − | 0.999104i | \(-0.486527\pi\) | ||||
0.0423144 | + | 0.999104i | \(0.486527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.60349 | −0.0525522 | ||||||||
\(932\) | −13.6261 | −0.446339 | ||||||||
\(933\) | −21.5263 | −0.704741 | ||||||||
\(934\) | 95.5278 | 3.12576 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 39.7343 | 1.29876 | ||||||||
\(937\) | 39.6842 | 1.29643 | 0.648213 | − | 0.761459i | \(-0.275517\pi\) | ||||
0.648213 | + | 0.761459i | \(0.275517\pi\) | |||||||
\(938\) | 13.3794 | 0.436852 | ||||||||
\(939\) | −52.0425 | −1.69834 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.1641 | −0.331339 | −0.165669 | − | 0.986181i | \(-0.552978\pi\) | ||||
−0.165669 | + | 0.986181i | \(0.552978\pi\) | |||||||
\(942\) | 42.6346 | 1.38911 | ||||||||
\(943\) | 10.3161 | 0.335939 | ||||||||
\(944\) | −46.1147 | −1.50090 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.1997 | 1.01439 | ||||||||
\(947\) | 2.33651 | 0.0759263 | 0.0379631 | − | 0.999279i | \(-0.487913\pi\) | ||||
0.0379631 | + | 0.999279i | \(0.487913\pi\) | |||||||
\(948\) | 57.3833 | 1.86372 | ||||||||
\(949\) | 4.27951 | 0.138919 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.8939 | 1.19637 | ||||||||
\(952\) | 90.3492 | 2.92823 | ||||||||
\(953\) | 6.62319 | 0.214546 | 0.107273 | − | 0.994230i | \(-0.465788\pi\) | ||||
0.107273 | + | 0.994230i | \(0.465788\pi\) | |||||||
\(954\) | 82.4616 | 2.66979 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −68.0820 | −2.20193 | ||||||||
\(957\) | −28.8264 | −0.931826 | ||||||||
\(958\) | −37.8701 | −1.22353 | ||||||||
\(959\) | 27.1126 | 0.875512 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.4534 | 0.563014 | ||||||||
\(962\) | 18.8255 | 0.606958 | ||||||||
\(963\) | 96.6627 | 3.11491 | ||||||||
\(964\) | 4.85138 | 0.156252 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 22.8881 | 0.736411 | ||||||||
\(967\) | −27.1899 | −0.874369 | −0.437184 | − | 0.899372i | \(-0.644024\pi\) | ||||
−0.437184 | + | 0.899372i | \(0.644024\pi\) | |||||||
\(968\) | 65.8124 | 2.11529 | ||||||||
\(969\) | 9.51278 | 0.305595 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.9802 | 0.577011 | 0.288506 | − | 0.957478i | \(-0.406842\pi\) | ||||
0.288506 | + | 0.957478i | \(0.406842\pi\) | |||||||
\(972\) | 38.7095 | 1.24161 | ||||||||
\(973\) | 44.0720 | 1.41288 | ||||||||
\(974\) | 4.98765 | 0.159815 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.4094 | −1.19745 | ||||||||
\(977\) | −11.9489 | −0.382280 | −0.191140 | − | 0.981563i | \(-0.561218\pi\) | ||||
−0.191140 | + | 0.981563i | \(0.561218\pi\) | |||||||
\(978\) | 27.9578 | 0.893991 | ||||||||
\(979\) | 4.10966 | 0.131345 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.4311 | 1.16316 | ||||||||
\(982\) | 26.1859 | 0.835626 | ||||||||
\(983\) | −6.03967 | −0.192636 | −0.0963178 | − | 0.995351i | \(-0.530707\pi\) | ||||
−0.0963178 | + | 0.995351i | \(0.530707\pi\) | |||||||
\(984\) | 150.477 | 4.79702 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −105.504 | −3.35994 | ||||||||
\(987\) | 24.2340 | 0.771375 | ||||||||
\(988\) | −2.54231 | −0.0808816 | ||||||||
\(989\) | 12.0390 | 0.382819 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.2454 | 1.24667 | 0.623336 | − | 0.781954i | \(-0.285777\pi\) | ||||
0.623336 | + | 0.781954i | \(0.285777\pi\) | |||||||
\(992\) | −75.2558 | −2.38937 | ||||||||
\(993\) | 54.7538 | 1.73756 | ||||||||
\(994\) | −14.4089 | −0.457022 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −23.5442 | −0.746026 | ||||||||
\(997\) | −45.7163 | −1.44785 | −0.723925 | − | 0.689878i | \(-0.757664\pi\) | ||||
−0.723925 | + | 0.689878i | \(0.757664\pi\) | |||||||
\(998\) | −41.3927 | −1.31026 | ||||||||
\(999\) | −54.2507 | −1.71642 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6025.2.a.m.1.4 | ✓ | 40 | |
5.4 | even | 2 | 6025.2.a.n.1.37 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.m.1.4 | ✓ | 40 | 1.1 | even | 1 | trivial | |
6025.2.a.n.1.37 | yes | 40 | 5.4 | even | 2 |