Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56155 | −1.81129 | −0.905646 | − | 0.424035i | \(-0.860613\pi\) | ||||
−0.905646 | + | 0.424035i | \(0.860613\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.56155 | 2.28078 | ||||||||
\(5\) | −0.561553 | −0.251134 | −0.125567 | − | 0.992085i | \(-0.540075\pi\) | ||||
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | −2.56155 | −1.04575 | ||||||||
\(7\) | 3.56155 | 1.34614 | 0.673070 | − | 0.739579i | \(-0.264975\pi\) | ||||
0.673070 | + | 0.739579i | \(0.264975\pi\) | |||||||
\(8\) | −6.56155 | −2.31986 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.43845 | 0.454877 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 4.56155 | 1.31681 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −9.12311 | −2.43825 | ||||||||
\(15\) | −0.561553 | −0.144992 | ||||||||
\(16\) | 7.68466 | 1.92116 | ||||||||
\(17\) | 2.56155 | 0.621268 | 0.310634 | − | 0.950530i | \(-0.399459\pi\) | ||||
0.310634 | + | 0.950530i | \(0.399459\pi\) | |||||||
\(18\) | −2.56155 | −0.603764 | ||||||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | −2.56155 | −0.572781 | ||||||||
\(21\) | 3.56155 | 0.777195 | ||||||||
\(22\) | −5.12311 | −1.09225 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | −6.56155 | −1.33937 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 16.2462 | 3.07025 | ||||||||
\(29\) | −5.68466 | −1.05561 | −0.527807 | − | 0.849364i | \(-0.676986\pi\) | ||||
−0.527807 | + | 0.849364i | \(0.676986\pi\) | |||||||
\(30\) | 1.43845 | 0.262623 | ||||||||
\(31\) | 1.56155 | 0.280463 | 0.140232 | − | 0.990119i | \(-0.455215\pi\) | ||||
0.140232 | + | 0.990119i | \(0.455215\pi\) | |||||||
\(32\) | −6.56155 | −1.15993 | ||||||||
\(33\) | 2.00000 | 0.348155 | ||||||||
\(34\) | −6.56155 | −1.12530 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 4.56155 | 0.760259 | ||||||||
\(37\) | −3.43845 | −0.565277 | −0.282639 | − | 0.959226i | \(-0.591210\pi\) | ||||
−0.282639 | + | 0.959226i | \(0.591210\pi\) | |||||||
\(38\) | −2.87689 | −0.466694 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.68466 | 0.582596 | ||||||||
\(41\) | −2.56155 | −0.400047 | −0.200024 | − | 0.979791i | \(-0.564102\pi\) | ||||
−0.200024 | + | 0.979791i | \(0.564102\pi\) | |||||||
\(42\) | −9.12311 | −1.40773 | ||||||||
\(43\) | 0.438447 | 0.0668626 | 0.0334313 | − | 0.999441i | \(-0.489357\pi\) | ||||
0.0334313 | + | 0.999441i | \(0.489357\pi\) | |||||||
\(44\) | 9.12311 | 1.37536 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | −5.12311 | −0.755361 | ||||||||
\(47\) | 8.24621 | 1.20283 | 0.601417 | − | 0.798935i | \(-0.294603\pi\) | ||||
0.601417 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(48\) | 7.68466 | 1.10918 | ||||||||
\(49\) | 5.68466 | 0.812094 | ||||||||
\(50\) | 12.0000 | 1.69706 | ||||||||
\(51\) | 2.56155 | 0.358689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6847 | 1.60501 | 0.802506 | − | 0.596645i | \(-0.203500\pi\) | ||||
0.802506 | + | 0.596645i | \(0.203500\pi\) | |||||||
\(54\) | −2.56155 | −0.348583 | ||||||||
\(55\) | −1.12311 | −0.151440 | ||||||||
\(56\) | −23.3693 | −3.12286 | ||||||||
\(57\) | 1.12311 | 0.148759 | ||||||||
\(58\) | 14.5616 | 1.91203 | ||||||||
\(59\) | 11.1231 | 1.44811 | 0.724053 | − | 0.689745i | \(-0.242277\pi\) | ||||
0.724053 | + | 0.689745i | \(0.242277\pi\) | |||||||
\(60\) | −2.56155 | −0.330695 | ||||||||
\(61\) | 12.1231 | 1.55220 | 0.776102 | − | 0.630607i | \(-0.217194\pi\) | ||||
0.776102 | + | 0.630607i | \(0.217194\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 3.56155 | 0.448713 | ||||||||
\(64\) | 1.43845 | 0.179806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.12311 | −0.630611 | ||||||||
\(67\) | −0.438447 | −0.0535648 | −0.0267824 | − | 0.999641i | \(-0.508526\pi\) | ||||
−0.0267824 | + | 0.999641i | \(0.508526\pi\) | |||||||
\(68\) | 11.6847 | 1.41697 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 5.12311 | 0.612328 | ||||||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | −6.56155 | −0.773286 | ||||||||
\(73\) | 1.87689 | 0.219674 | 0.109837 | − | 0.993950i | \(-0.464967\pi\) | ||||
0.109837 | + | 0.993950i | \(0.464967\pi\) | |||||||
\(74\) | 8.80776 | 1.02388 | ||||||||
\(75\) | −4.68466 | −0.540938 | ||||||||
\(76\) | 5.12311 | 0.587661 | ||||||||
\(77\) | 7.12311 | 0.811753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.56155 | 1.07576 | 0.537879 | − | 0.843022i | \(-0.319226\pi\) | ||||
0.537879 | + | 0.843022i | \(0.319226\pi\) | |||||||
\(80\) | −4.31534 | −0.482470 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.56155 | 0.724602 | ||||||||
\(83\) | 9.12311 | 1.00139 | 0.500695 | − | 0.865624i | \(-0.333078\pi\) | ||||
0.500695 | + | 0.865624i | \(0.333078\pi\) | |||||||
\(84\) | 16.2462 | 1.77261 | ||||||||
\(85\) | −1.43845 | −0.156022 | ||||||||
\(86\) | −1.12311 | −0.121108 | ||||||||
\(87\) | −5.68466 | −0.609459 | ||||||||
\(88\) | −13.1231 | −1.39893 | ||||||||
\(89\) | −13.1231 | −1.39105 | −0.695523 | − | 0.718504i | \(-0.744827\pi\) | ||||
−0.695523 | + | 0.718504i | \(0.744827\pi\) | |||||||
\(90\) | 1.43845 | 0.151626 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.12311 | 0.951150 | ||||||||
\(93\) | 1.56155 | 0.161925 | ||||||||
\(94\) | −21.1231 | −2.17868 | ||||||||
\(95\) | −0.630683 | −0.0647067 | ||||||||
\(96\) | −6.56155 | −0.669686 | ||||||||
\(97\) | 4.43845 | 0.450656 | 0.225328 | − | 0.974283i | \(-0.427655\pi\) | ||||
0.225328 | + | 0.974283i | \(0.427655\pi\) | |||||||
\(98\) | −14.5616 | −1.47094 | ||||||||
\(99\) | 2.00000 | 0.201008 | ||||||||
\(100\) | −21.3693 | −2.13693 | ||||||||
\(101\) | −3.43845 | −0.342138 | −0.171069 | − | 0.985259i | \(-0.554722\pi\) | ||||
−0.171069 | + | 0.985259i | \(0.554722\pi\) | |||||||
\(102\) | −6.56155 | −0.649691 | ||||||||
\(103\) | −7.56155 | −0.745062 | −0.372531 | − | 0.928020i | \(-0.621510\pi\) | ||||
−0.372531 | + | 0.928020i | \(0.621510\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | −29.9309 | −2.90714 | ||||||||
\(107\) | 8.24621 | 0.797191 | 0.398596 | − | 0.917127i | \(-0.369498\pi\) | ||||
0.398596 | + | 0.917127i | \(0.369498\pi\) | |||||||
\(108\) | 4.56155 | 0.438936 | ||||||||
\(109\) | −17.8078 | −1.70567 | −0.852837 | − | 0.522177i | \(-0.825120\pi\) | ||||
−0.852837 | + | 0.522177i | \(0.825120\pi\) | |||||||
\(110\) | 2.87689 | 0.274301 | ||||||||
\(111\) | −3.43845 | −0.326363 | ||||||||
\(112\) | 27.3693 | 2.58616 | ||||||||
\(113\) | −14.8078 | −1.39300 | −0.696499 | − | 0.717558i | \(-0.745260\pi\) | ||||
−0.696499 | + | 0.717558i | \(0.745260\pi\) | |||||||
\(114\) | −2.87689 | −0.269446 | ||||||||
\(115\) | −1.12311 | −0.104730 | ||||||||
\(116\) | −25.9309 | −2.40762 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −28.4924 | −2.62294 | ||||||||
\(119\) | 9.12311 | 0.836314 | ||||||||
\(120\) | 3.68466 | 0.336362 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −31.0540 | −2.81149 | ||||||||
\(123\) | −2.56155 | −0.230967 | ||||||||
\(124\) | 7.12311 | 0.639674 | ||||||||
\(125\) | 5.43845 | 0.486430 | ||||||||
\(126\) | −9.12311 | −0.812751 | ||||||||
\(127\) | 9.56155 | 0.848451 | 0.424225 | − | 0.905557i | \(-0.360546\pi\) | ||||
0.424225 | + | 0.905557i | \(0.360546\pi\) | |||||||
\(128\) | 9.43845 | 0.834249 | ||||||||
\(129\) | 0.438447 | 0.0386031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3693 | −1.51756 | −0.758782 | − | 0.651345i | \(-0.774205\pi\) | ||||
−0.758782 | + | 0.651345i | \(0.774205\pi\) | |||||||
\(132\) | 9.12311 | 0.794064 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 1.12311 | 0.0970215 | ||||||||
\(135\) | −0.561553 | −0.0483308 | ||||||||
\(136\) | −16.8078 | −1.44125 | ||||||||
\(137\) | 1.43845 | 0.122895 | 0.0614474 | − | 0.998110i | \(-0.480428\pi\) | ||||
0.0614474 | + | 0.998110i | \(0.480428\pi\) | |||||||
\(138\) | −5.12311 | −0.436108 | ||||||||
\(139\) | 10.9309 | 0.927144 | 0.463572 | − | 0.886059i | \(-0.346567\pi\) | ||||
0.463572 | + | 0.886059i | \(0.346567\pi\) | |||||||
\(140\) | −9.12311 | −0.771043 | ||||||||
\(141\) | 8.24621 | 0.694456 | ||||||||
\(142\) | 35.8617 | 3.00945 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.68466 | 0.640388 | ||||||||
\(145\) | 3.19224 | 0.265101 | ||||||||
\(146\) | −4.80776 | −0.397893 | ||||||||
\(147\) | 5.68466 | 0.468863 | ||||||||
\(148\) | −15.6847 | −1.28927 | ||||||||
\(149\) | 6.56155 | 0.537543 | 0.268772 | − | 0.963204i | \(-0.413382\pi\) | ||||
0.268772 | + | 0.963204i | \(0.413382\pi\) | |||||||
\(150\) | 12.0000 | 0.979796 | ||||||||
\(151\) | −15.3693 | −1.25074 | −0.625369 | − | 0.780329i | \(-0.715051\pi\) | ||||
−0.625369 | + | 0.780329i | \(0.715051\pi\) | |||||||
\(152\) | −7.36932 | −0.597731 | ||||||||
\(153\) | 2.56155 | 0.207089 | ||||||||
\(154\) | −18.2462 | −1.47032 | ||||||||
\(155\) | −0.876894 | −0.0704339 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.36932 | −0.348709 | −0.174355 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174355 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(158\) | −24.4924 | −1.94851 | ||||||||
\(159\) | 11.6847 | 0.926654 | ||||||||
\(160\) | 3.68466 | 0.291298 | ||||||||
\(161\) | 7.12311 | 0.561379 | ||||||||
\(162\) | −2.56155 | −0.201255 | ||||||||
\(163\) | −15.8078 | −1.23816 | −0.619080 | − | 0.785328i | \(-0.712494\pi\) | ||||
−0.619080 | + | 0.785328i | \(0.712494\pi\) | |||||||
\(164\) | −11.6847 | −0.912419 | ||||||||
\(165\) | −1.12311 | −0.0874337 | ||||||||
\(166\) | −23.3693 | −1.81381 | ||||||||
\(167\) | 6.24621 | 0.483346 | 0.241673 | − | 0.970358i | \(-0.422304\pi\) | ||||
0.241673 | + | 0.970358i | \(0.422304\pi\) | |||||||
\(168\) | −23.3693 | −1.80298 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.68466 | 0.282600 | ||||||||
\(171\) | 1.12311 | 0.0858860 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 3.75379 | 0.285395 | 0.142698 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142698 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(174\) | 14.5616 | 1.10391 | ||||||||
\(175\) | −16.6847 | −1.26124 | ||||||||
\(176\) | 15.3693 | 1.15851 | ||||||||
\(177\) | 11.1231 | 0.836064 | ||||||||
\(178\) | 33.6155 | 2.51959 | ||||||||
\(179\) | −13.1231 | −0.980867 | −0.490433 | − | 0.871479i | \(-0.663162\pi\) | ||||
−0.490433 | + | 0.871479i | \(0.663162\pi\) | |||||||
\(180\) | −2.56155 | −0.190927 | ||||||||
\(181\) | 9.68466 | 0.719855 | 0.359927 | − | 0.932980i | \(-0.382801\pi\) | ||||
0.359927 | + | 0.932980i | \(0.382801\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.1231 | 0.896166 | ||||||||
\(184\) | −13.1231 | −0.967448 | ||||||||
\(185\) | 1.93087 | 0.141960 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 5.12311 | 0.374639 | ||||||||
\(188\) | 37.6155 | 2.74339 | ||||||||
\(189\) | 3.56155 | 0.259065 | ||||||||
\(190\) | 1.61553 | 0.117203 | ||||||||
\(191\) | −0.876894 | −0.0634499 | −0.0317249 | − | 0.999497i | \(-0.510100\pi\) | ||||
−0.0317249 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(192\) | 1.43845 | 0.103811 | ||||||||
\(193\) | −19.4924 | −1.40310 | −0.701548 | − | 0.712623i | \(-0.747507\pi\) | ||||
−0.701548 | + | 0.712623i | \(0.747507\pi\) | |||||||
\(194\) | −11.3693 | −0.816269 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 25.9309 | 1.85220 | ||||||||
\(197\) | 11.3693 | 0.810030 | 0.405015 | − | 0.914310i | \(-0.367266\pi\) | ||||
0.405015 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(198\) | −5.12311 | −0.364083 | ||||||||
\(199\) | −23.1771 | −1.64298 | −0.821490 | − | 0.570223i | \(-0.806857\pi\) | ||||
−0.821490 | + | 0.570223i | \(0.806857\pi\) | |||||||
\(200\) | 30.7386 | 2.17355 | ||||||||
\(201\) | −0.438447 | −0.0309257 | ||||||||
\(202\) | 8.80776 | 0.619712 | ||||||||
\(203\) | −20.2462 | −1.42101 | ||||||||
\(204\) | 11.6847 | 0.818090 | ||||||||
\(205\) | 1.43845 | 0.100466 | ||||||||
\(206\) | 19.3693 | 1.34952 | ||||||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.24621 | 0.155374 | ||||||||
\(210\) | 5.12311 | 0.353528 | ||||||||
\(211\) | 7.31534 | 0.503609 | 0.251804 | − | 0.967778i | \(-0.418976\pi\) | ||||
0.251804 | + | 0.967778i | \(0.418976\pi\) | |||||||
\(212\) | 53.3002 | 3.66067 | ||||||||
\(213\) | −14.0000 | −0.959264 | ||||||||
\(214\) | −21.1231 | −1.44395 | ||||||||
\(215\) | −0.246211 | −0.0167915 | ||||||||
\(216\) | −6.56155 | −0.446457 | ||||||||
\(217\) | 5.56155 | 0.377543 | ||||||||
\(218\) | 45.6155 | 3.08947 | ||||||||
\(219\) | 1.87689 | 0.126829 | ||||||||
\(220\) | −5.12311 | −0.345400 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 8.80776 | 0.591138 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | −23.3693 | −1.56143 | ||||||||
\(225\) | −4.68466 | −0.312311 | ||||||||
\(226\) | 37.9309 | 2.52312 | ||||||||
\(227\) | 1.12311 | 0.0745431 | 0.0372716 | − | 0.999305i | \(-0.488133\pi\) | ||||
0.0372716 | + | 0.999305i | \(0.488133\pi\) | |||||||
\(228\) | 5.12311 | 0.339286 | ||||||||
\(229\) | −0.246211 | −0.0162701 | −0.00813505 | − | 0.999967i | \(-0.502589\pi\) | ||||
−0.00813505 | + | 0.999967i | \(0.502589\pi\) | |||||||
\(230\) | 2.87689 | 0.189697 | ||||||||
\(231\) | 7.12311 | 0.468666 | ||||||||
\(232\) | 37.3002 | 2.44888 | ||||||||
\(233\) | 26.0000 | 1.70332 | 0.851658 | − | 0.524097i | \(-0.175597\pi\) | ||||
0.851658 | + | 0.524097i | \(0.175597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.63068 | −0.302072 | ||||||||
\(236\) | 50.7386 | 3.30280 | ||||||||
\(237\) | 9.56155 | 0.621090 | ||||||||
\(238\) | −23.3693 | −1.51481 | ||||||||
\(239\) | 0.630683 | 0.0407955 | 0.0203977 | − | 0.999792i | \(-0.493507\pi\) | ||||
0.0203977 | + | 0.999792i | \(0.493507\pi\) | |||||||
\(240\) | −4.31534 | −0.278554 | ||||||||
\(241\) | −2.80776 | −0.180864 | −0.0904320 | − | 0.995903i | \(-0.528825\pi\) | ||||
−0.0904320 | + | 0.995903i | \(0.528825\pi\) | |||||||
\(242\) | 17.9309 | 1.15264 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 55.3002 | 3.54023 | ||||||||
\(245\) | −3.19224 | −0.203944 | ||||||||
\(246\) | 6.56155 | 0.418349 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.2462 | −0.650635 | ||||||||
\(249\) | 9.12311 | 0.578153 | ||||||||
\(250\) | −13.9309 | −0.881066 | ||||||||
\(251\) | −30.7386 | −1.94021 | −0.970103 | − | 0.242695i | \(-0.921969\pi\) | ||||
−0.970103 | + | 0.242695i | \(0.921969\pi\) | |||||||
\(252\) | 16.2462 | 1.02342 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | −24.4924 | −1.53679 | ||||||||
\(255\) | −1.43845 | −0.0900791 | ||||||||
\(256\) | −27.0540 | −1.69087 | ||||||||
\(257\) | −16.1771 | −1.00910 | −0.504549 | − | 0.863383i | \(-0.668341\pi\) | ||||
−0.504549 | + | 0.863383i | \(0.668341\pi\) | |||||||
\(258\) | −1.12311 | −0.0699215 | ||||||||
\(259\) | −12.2462 | −0.760943 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.68466 | −0.351872 | ||||||||
\(262\) | 44.4924 | 2.74875 | ||||||||
\(263\) | −15.3693 | −0.947713 | −0.473856 | − | 0.880602i | \(-0.657138\pi\) | ||||
−0.473856 | + | 0.880602i | \(0.657138\pi\) | |||||||
\(264\) | −13.1231 | −0.807671 | ||||||||
\(265\) | −6.56155 | −0.403073 | ||||||||
\(266\) | −10.2462 | −0.628236 | ||||||||
\(267\) | −13.1231 | −0.803121 | ||||||||
\(268\) | −2.00000 | −0.122169 | ||||||||
\(269\) | 3.36932 | 0.205431 | 0.102715 | − | 0.994711i | \(-0.467247\pi\) | ||||
0.102715 | + | 0.994711i | \(0.467247\pi\) | |||||||
\(270\) | 1.43845 | 0.0875411 | ||||||||
\(271\) | 1.06913 | 0.0649450 | 0.0324725 | − | 0.999473i | \(-0.489662\pi\) | ||||
0.0324725 | + | 0.999473i | \(0.489662\pi\) | |||||||
\(272\) | 19.6847 | 1.19356 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.68466 | −0.222598 | ||||||||
\(275\) | −9.36932 | −0.564991 | ||||||||
\(276\) | 9.12311 | 0.549146 | ||||||||
\(277\) | 17.6847 | 1.06257 | 0.531284 | − | 0.847194i | \(-0.321710\pi\) | ||||
0.531284 | + | 0.847194i | \(0.321710\pi\) | |||||||
\(278\) | −28.0000 | −1.67933 | ||||||||
\(279\) | 1.56155 | 0.0934877 | ||||||||
\(280\) | 13.1231 | 0.784256 | ||||||||
\(281\) | 2.80776 | 0.167497 | 0.0837486 | − | 0.996487i | \(-0.473311\pi\) | ||||
0.0837486 | + | 0.996487i | \(0.473311\pi\) | |||||||
\(282\) | −21.1231 | −1.25786 | ||||||||
\(283\) | −1.31534 | −0.0781889 | −0.0390945 | − | 0.999236i | \(-0.512447\pi\) | ||||
−0.0390945 | + | 0.999236i | \(0.512447\pi\) | |||||||
\(284\) | −63.8617 | −3.78950 | ||||||||
\(285\) | −0.630683 | −0.0373584 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.12311 | −0.538520 | ||||||||
\(288\) | −6.56155 | −0.386643 | ||||||||
\(289\) | −10.4384 | −0.614026 | ||||||||
\(290\) | −8.17708 | −0.480175 | ||||||||
\(291\) | 4.43845 | 0.260186 | ||||||||
\(292\) | 8.56155 | 0.501027 | ||||||||
\(293\) | −24.5616 | −1.43490 | −0.717451 | − | 0.696609i | \(-0.754691\pi\) | ||||
−0.717451 | + | 0.696609i | \(0.754691\pi\) | |||||||
\(294\) | −14.5616 | −0.849247 | ||||||||
\(295\) | −6.24621 | −0.363668 | ||||||||
\(296\) | 22.5616 | 1.31136 | ||||||||
\(297\) | 2.00000 | 0.116052 | ||||||||
\(298\) | −16.8078 | −0.973648 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −21.3693 | −1.23376 | ||||||||
\(301\) | 1.56155 | 0.0900064 | ||||||||
\(302\) | 39.3693 | 2.26545 | ||||||||
\(303\) | −3.43845 | −0.197534 | ||||||||
\(304\) | 8.63068 | 0.495004 | ||||||||
\(305\) | −6.80776 | −0.389811 | ||||||||
\(306\) | −6.56155 | −0.375099 | ||||||||
\(307\) | −10.1922 | −0.581702 | −0.290851 | − | 0.956768i | \(-0.593938\pi\) | ||||
−0.290851 | + | 0.956768i | \(0.593938\pi\) | |||||||
\(308\) | 32.4924 | 1.85143 | ||||||||
\(309\) | −7.56155 | −0.430162 | ||||||||
\(310\) | 2.24621 | 0.127576 | ||||||||
\(311\) | −10.8769 | −0.616772 | −0.308386 | − | 0.951261i | \(-0.599789\pi\) | ||||
−0.308386 | + | 0.951261i | \(0.599789\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.31534 | −0.0743475 | −0.0371738 | − | 0.999309i | \(-0.511835\pi\) | ||||
−0.0371738 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(314\) | 11.1922 | 0.631614 | ||||||||
\(315\) | −2.00000 | −0.112687 | ||||||||
\(316\) | 43.6155 | 2.45357 | ||||||||
\(317\) | 23.0540 | 1.29484 | 0.647420 | − | 0.762133i | \(-0.275848\pi\) | ||||
0.647420 | + | 0.762133i | \(0.275848\pi\) | |||||||
\(318\) | −29.9309 | −1.67844 | ||||||||
\(319\) | −11.3693 | −0.636560 | ||||||||
\(320\) | −0.807764 | −0.0451554 | ||||||||
\(321\) | 8.24621 | 0.460259 | ||||||||
\(322\) | −18.2462 | −1.01682 | ||||||||
\(323\) | 2.87689 | 0.160075 | ||||||||
\(324\) | 4.56155 | 0.253420 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 40.4924 | 2.24267 | ||||||||
\(327\) | −17.8078 | −0.984772 | ||||||||
\(328\) | 16.8078 | 0.928054 | ||||||||
\(329\) | 29.3693 | 1.61918 | ||||||||
\(330\) | 2.87689 | 0.158368 | ||||||||
\(331\) | 23.8078 | 1.30859 | 0.654297 | − | 0.756238i | \(-0.272965\pi\) | ||||
0.654297 | + | 0.756238i | \(0.272965\pi\) | |||||||
\(332\) | 41.6155 | 2.28395 | ||||||||
\(333\) | −3.43845 | −0.188426 | ||||||||
\(334\) | −16.0000 | −0.875481 | ||||||||
\(335\) | 0.246211 | 0.0134520 | ||||||||
\(336\) | 27.3693 | 1.49312 | ||||||||
\(337\) | 2.12311 | 0.115653 | 0.0578265 | − | 0.998327i | \(-0.481583\pi\) | ||||
0.0578265 | + | 0.998327i | \(0.481583\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.8078 | −0.804247 | ||||||||
\(340\) | −6.56155 | −0.355850 | ||||||||
\(341\) | 3.12311 | 0.169126 | ||||||||
\(342\) | −2.87689 | −0.155565 | ||||||||
\(343\) | −4.68466 | −0.252948 | ||||||||
\(344\) | −2.87689 | −0.155112 | ||||||||
\(345\) | −1.12311 | −0.0604660 | ||||||||
\(346\) | −9.61553 | −0.516934 | ||||||||
\(347\) | −13.6155 | −0.730920 | −0.365460 | − | 0.930827i | \(-0.619088\pi\) | ||||
−0.365460 | + | 0.930827i | \(0.619088\pi\) | |||||||
\(348\) | −25.9309 | −1.39004 | ||||||||
\(349\) | 13.8078 | 0.739113 | 0.369556 | − | 0.929208i | \(-0.379510\pi\) | ||||
0.369556 | + | 0.929208i | \(0.379510\pi\) | |||||||
\(350\) | 42.7386 | 2.28448 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.1231 | −0.699464 | ||||||||
\(353\) | −17.6847 | −0.941259 | −0.470630 | − | 0.882331i | \(-0.655973\pi\) | ||||
−0.470630 | + | 0.882331i | \(0.655973\pi\) | |||||||
\(354\) | −28.4924 | −1.51436 | ||||||||
\(355\) | 7.86174 | 0.417258 | ||||||||
\(356\) | −59.8617 | −3.17267 | ||||||||
\(357\) | 9.12311 | 0.482846 | ||||||||
\(358\) | 33.6155 | 1.77664 | ||||||||
\(359\) | −15.3693 | −0.811162 | −0.405581 | − | 0.914059i | \(-0.632931\pi\) | ||||
−0.405581 | + | 0.914059i | \(0.632931\pi\) | |||||||
\(360\) | 3.68466 | 0.194199 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | −24.8078 | −1.30387 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.05398 | −0.0551676 | ||||||||
\(366\) | −31.0540 | −1.62322 | ||||||||
\(367\) | 20.0540 | 1.04681 | 0.523404 | − | 0.852084i | \(-0.324662\pi\) | ||||
0.523404 | + | 0.852084i | \(0.324662\pi\) | |||||||
\(368\) | 15.3693 | 0.801181 | ||||||||
\(369\) | −2.56155 | −0.133349 | ||||||||
\(370\) | −4.94602 | −0.257132 | ||||||||
\(371\) | 41.6155 | 2.16057 | ||||||||
\(372\) | 7.12311 | 0.369316 | ||||||||
\(373\) | 3.63068 | 0.187990 | 0.0939948 | − | 0.995573i | \(-0.470036\pi\) | ||||
0.0939948 | + | 0.995573i | \(0.470036\pi\) | |||||||
\(374\) | −13.1231 | −0.678580 | ||||||||
\(375\) | 5.43845 | 0.280840 | ||||||||
\(376\) | −54.1080 | −2.79040 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −9.12311 | −0.469242 | ||||||||
\(379\) | −11.3153 | −0.581230 | −0.290615 | − | 0.956840i | \(-0.593860\pi\) | ||||
−0.290615 | + | 0.956840i | \(0.593860\pi\) | |||||||
\(380\) | −2.87689 | −0.147582 | ||||||||
\(381\) | 9.56155 | 0.489853 | ||||||||
\(382\) | 2.24621 | 0.114926 | ||||||||
\(383\) | −26.7386 | −1.36628 | −0.683140 | − | 0.730287i | \(-0.739386\pi\) | ||||
−0.683140 | + | 0.730287i | \(0.739386\pi\) | |||||||
\(384\) | 9.43845 | 0.481654 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 49.9309 | 2.54141 | ||||||||
\(387\) | 0.438447 | 0.0222875 | ||||||||
\(388\) | 20.2462 | 1.02785 | ||||||||
\(389\) | −3.05398 | −0.154843 | −0.0774213 | − | 0.996998i | \(-0.524669\pi\) | ||||
−0.0774213 | + | 0.996998i | \(0.524669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.12311 | 0.259087 | ||||||||
\(392\) | −37.3002 | −1.88394 | ||||||||
\(393\) | −17.3693 | −0.876166 | ||||||||
\(394\) | −29.1231 | −1.46720 | ||||||||
\(395\) | −5.36932 | −0.270160 | ||||||||
\(396\) | 9.12311 | 0.458453 | ||||||||
\(397\) | 12.0540 | 0.604972 | 0.302486 | − | 0.953154i | \(-0.402184\pi\) | ||||
0.302486 | + | 0.953154i | \(0.402184\pi\) | |||||||
\(398\) | 59.3693 | 2.97591 | ||||||||
\(399\) | 4.00000 | 0.200250 | ||||||||
\(400\) | −36.0000 | −1.80000 | ||||||||
\(401\) | −18.5616 | −0.926920 | −0.463460 | − | 0.886118i | \(-0.653392\pi\) | ||||
−0.463460 | + | 0.886118i | \(0.653392\pi\) | |||||||
\(402\) | 1.12311 | 0.0560154 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −15.6847 | −0.780341 | ||||||||
\(405\) | −0.561553 | −0.0279038 | ||||||||
\(406\) | 51.8617 | 2.57385 | ||||||||
\(407\) | −6.87689 | −0.340875 | ||||||||
\(408\) | −16.8078 | −0.832108 | ||||||||
\(409\) | 18.3693 | 0.908304 | 0.454152 | − | 0.890924i | \(-0.349942\pi\) | ||||
0.454152 | + | 0.890924i | \(0.349942\pi\) | |||||||
\(410\) | −3.68466 | −0.181972 | ||||||||
\(411\) | 1.43845 | 0.0709534 | ||||||||
\(412\) | −34.4924 | −1.69932 | ||||||||
\(413\) | 39.6155 | 1.94935 | ||||||||
\(414\) | −5.12311 | −0.251787 | ||||||||
\(415\) | −5.12311 | −0.251483 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.9309 | 0.535287 | ||||||||
\(418\) | −5.75379 | −0.281427 | ||||||||
\(419\) | −17.7538 | −0.867329 | −0.433665 | − | 0.901074i | \(-0.642780\pi\) | ||||
−0.433665 | + | 0.901074i | \(0.642780\pi\) | |||||||
\(420\) | −9.12311 | −0.445162 | ||||||||
\(421\) | −14.7538 | −0.719056 | −0.359528 | − | 0.933134i | \(-0.617062\pi\) | ||||
−0.359528 | + | 0.933134i | \(0.617062\pi\) | |||||||
\(422\) | −18.7386 | −0.912182 | ||||||||
\(423\) | 8.24621 | 0.400945 | ||||||||
\(424\) | −76.6695 | −3.72340 | ||||||||
\(425\) | −12.0000 | −0.582086 | ||||||||
\(426\) | 35.8617 | 1.73751 | ||||||||
\(427\) | 43.1771 | 2.08949 | ||||||||
\(428\) | 37.6155 | 1.81822 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.630683 | 0.0304142 | ||||||||
\(431\) | 2.87689 | 0.138575 | 0.0692876 | − | 0.997597i | \(-0.477927\pi\) | ||||
0.0692876 | + | 0.997597i | \(0.477927\pi\) | |||||||
\(432\) | 7.68466 | 0.369728 | ||||||||
\(433\) | 25.2462 | 1.21326 | 0.606628 | − | 0.794986i | \(-0.292522\pi\) | ||||
0.606628 | + | 0.794986i | \(0.292522\pi\) | |||||||
\(434\) | −14.2462 | −0.683840 | ||||||||
\(435\) | 3.19224 | 0.153056 | ||||||||
\(436\) | −81.2311 | −3.89026 | ||||||||
\(437\) | 2.24621 | 0.107451 | ||||||||
\(438\) | −4.80776 | −0.229724 | ||||||||
\(439\) | −1.31534 | −0.0627778 | −0.0313889 | − | 0.999507i | \(-0.509993\pi\) | ||||
−0.0313889 | + | 0.999507i | \(0.509993\pi\) | |||||||
\(440\) | 7.36932 | 0.351318 | ||||||||
\(441\) | 5.68466 | 0.270698 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.7386 | 0.700254 | 0.350127 | − | 0.936702i | \(-0.386138\pi\) | ||||
0.350127 | + | 0.936702i | \(0.386138\pi\) | |||||||
\(444\) | −15.6847 | −0.744361 | ||||||||
\(445\) | 7.36932 | 0.349339 | ||||||||
\(446\) | 20.4924 | 0.970344 | ||||||||
\(447\) | 6.56155 | 0.310351 | ||||||||
\(448\) | 5.12311 | 0.242044 | ||||||||
\(449\) | −8.24621 | −0.389163 | −0.194581 | − | 0.980886i | \(-0.562335\pi\) | ||||
−0.194581 | + | 0.980886i | \(0.562335\pi\) | |||||||
\(450\) | 12.0000 | 0.565685 | ||||||||
\(451\) | −5.12311 | −0.241238 | ||||||||
\(452\) | −67.5464 | −3.17712 | ||||||||
\(453\) | −15.3693 | −0.722113 | ||||||||
\(454\) | −2.87689 | −0.135019 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.36932 | −0.345100 | ||||||||
\(457\) | 28.6155 | 1.33858 | 0.669289 | − | 0.743002i | \(-0.266599\pi\) | ||||
0.669289 | + | 0.743002i | \(0.266599\pi\) | |||||||
\(458\) | 0.630683 | 0.0294699 | ||||||||
\(459\) | 2.56155 | 0.119563 | ||||||||
\(460\) | −5.12311 | −0.238866 | ||||||||
\(461\) | 36.8078 | 1.71431 | 0.857154 | − | 0.515060i | \(-0.172230\pi\) | ||||
0.857154 | + | 0.515060i | \(0.172230\pi\) | |||||||
\(462\) | −18.2462 | −0.848891 | ||||||||
\(463\) | 26.6847 | 1.24014 | 0.620071 | − | 0.784546i | \(-0.287104\pi\) | ||||
0.620071 | + | 0.784546i | \(0.287104\pi\) | |||||||
\(464\) | −43.6847 | −2.02801 | ||||||||
\(465\) | −0.876894 | −0.0406650 | ||||||||
\(466\) | −66.6004 | −3.08520 | ||||||||
\(467\) | −26.0000 | −1.20314 | −0.601568 | − | 0.798821i | \(-0.705457\pi\) | ||||
−0.601568 | + | 0.798821i | \(0.705457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.56155 | −0.0721058 | ||||||||
\(470\) | 11.8617 | 0.547141 | ||||||||
\(471\) | −4.36932 | −0.201327 | ||||||||
\(472\) | −72.9848 | −3.35940 | ||||||||
\(473\) | 0.876894 | 0.0403196 | ||||||||
\(474\) | −24.4924 | −1.12497 | ||||||||
\(475\) | −5.26137 | −0.241408 | ||||||||
\(476\) | 41.6155 | 1.90744 | ||||||||
\(477\) | 11.6847 | 0.535004 | ||||||||
\(478\) | −1.61553 | −0.0738925 | ||||||||
\(479\) | 6.24621 | 0.285397 | 0.142698 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142698 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(480\) | 3.68466 | 0.168181 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.19224 | 0.327597 | ||||||||
\(483\) | 7.12311 | 0.324113 | ||||||||
\(484\) | −31.9309 | −1.45140 | ||||||||
\(485\) | −2.49242 | −0.113175 | ||||||||
\(486\) | −2.56155 | −0.116194 | ||||||||
\(487\) | 1.12311 | 0.0508928 | 0.0254464 | − | 0.999676i | \(-0.491899\pi\) | ||||
0.0254464 | + | 0.999676i | \(0.491899\pi\) | |||||||
\(488\) | −79.5464 | −3.60090 | ||||||||
\(489\) | −15.8078 | −0.714852 | ||||||||
\(490\) | 8.17708 | 0.369403 | ||||||||
\(491\) | −19.7538 | −0.891476 | −0.445738 | − | 0.895163i | \(-0.647059\pi\) | ||||
−0.445738 | + | 0.895163i | \(0.647059\pi\) | |||||||
\(492\) | −11.6847 | −0.526785 | ||||||||
\(493\) | −14.5616 | −0.655819 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.12311 | −0.0504798 | ||||||||
\(496\) | 12.0000 | 0.538816 | ||||||||
\(497\) | −49.8617 | −2.23660 | ||||||||
\(498\) | −23.3693 | −1.04720 | ||||||||
\(499\) | 28.4924 | 1.27550 | 0.637748 | − | 0.770245i | \(-0.279866\pi\) | ||||
0.637748 | + | 0.770245i | \(0.279866\pi\) | |||||||
\(500\) | 24.8078 | 1.10944 | ||||||||
\(501\) | 6.24621 | 0.279060 | ||||||||
\(502\) | 78.7386 | 3.51428 | ||||||||
\(503\) | −11.7538 | −0.524076 | −0.262038 | − | 0.965058i | \(-0.584395\pi\) | ||||
−0.262038 | + | 0.965058i | \(0.584395\pi\) | |||||||
\(504\) | −23.3693 | −1.04095 | ||||||||
\(505\) | 1.93087 | 0.0859226 | ||||||||
\(506\) | −10.2462 | −0.455500 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 43.6155 | 1.93513 | ||||||||
\(509\) | −6.80776 | −0.301749 | −0.150874 | − | 0.988553i | \(-0.548209\pi\) | ||||
−0.150874 | + | 0.988553i | \(0.548209\pi\) | |||||||
\(510\) | 3.68466 | 0.163159 | ||||||||
\(511\) | 6.68466 | 0.295712 | ||||||||
\(512\) | 50.4233 | 2.22842 | ||||||||
\(513\) | 1.12311 | 0.0495863 | ||||||||
\(514\) | 41.4384 | 1.82777 | ||||||||
\(515\) | 4.24621 | 0.187110 | ||||||||
\(516\) | 2.00000 | 0.0880451 | ||||||||
\(517\) | 16.4924 | 0.725336 | ||||||||
\(518\) | 31.3693 | 1.37829 | ||||||||
\(519\) | 3.75379 | 0.164773 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.9309 | −1.66178 | −0.830891 | − | 0.556436i | \(-0.812169\pi\) | ||||
−0.830891 | + | 0.556436i | \(0.812169\pi\) | |||||||
\(522\) | 14.5616 | 0.637342 | ||||||||
\(523\) | −23.8617 | −1.04340 | −0.521701 | − | 0.853129i | \(-0.674702\pi\) | ||||
−0.521701 | + | 0.853129i | \(0.674702\pi\) | |||||||
\(524\) | −79.2311 | −3.46122 | ||||||||
\(525\) | −16.6847 | −0.728178 | ||||||||
\(526\) | 39.3693 | 1.71658 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | 15.3693 | 0.668864 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 16.8078 | 0.730083 | ||||||||
\(531\) | 11.1231 | 0.482702 | ||||||||
\(532\) | 18.2462 | 0.791074 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 33.6155 | 1.45469 | ||||||||
\(535\) | −4.63068 | −0.200202 | ||||||||
\(536\) | 2.87689 | 0.124263 | ||||||||
\(537\) | −13.1231 | −0.566304 | ||||||||
\(538\) | −8.63068 | −0.372095 | ||||||||
\(539\) | 11.3693 | 0.489711 | ||||||||
\(540\) | −2.56155 | −0.110232 | ||||||||
\(541\) | 29.7386 | 1.27856 | 0.639282 | − | 0.768972i | \(-0.279232\pi\) | ||||
0.639282 | + | 0.768972i | \(0.279232\pi\) | |||||||
\(542\) | −2.73863 | −0.117634 | ||||||||
\(543\) | 9.68466 | 0.415608 | ||||||||
\(544\) | −16.8078 | −0.720627 | ||||||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.9309 | −1.06597 | −0.532984 | − | 0.846126i | \(-0.678929\pi\) | ||||
−0.532984 | + | 0.846126i | \(0.678929\pi\) | |||||||
\(548\) | 6.56155 | 0.280296 | ||||||||
\(549\) | 12.1231 | 0.517402 | ||||||||
\(550\) | 24.0000 | 1.02336 | ||||||||
\(551\) | −6.38447 | −0.271988 | ||||||||
\(552\) | −13.1231 | −0.558556 | ||||||||
\(553\) | 34.0540 | 1.44812 | ||||||||
\(554\) | −45.3002 | −1.92462 | ||||||||
\(555\) | 1.93087 | 0.0819609 | ||||||||
\(556\) | 49.8617 | 2.11461 | ||||||||
\(557\) | 14.0691 | 0.596128 | 0.298064 | − | 0.954546i | \(-0.403659\pi\) | ||||
0.298064 | + | 0.954546i | \(0.403659\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −15.3693 | −0.649472 | ||||||||
\(561\) | 5.12311 | 0.216298 | ||||||||
\(562\) | −7.19224 | −0.303386 | ||||||||
\(563\) | 1.36932 | 0.0577098 | 0.0288549 | − | 0.999584i | \(-0.490814\pi\) | ||||
0.0288549 | + | 0.999584i | \(0.490814\pi\) | |||||||
\(564\) | 37.6155 | 1.58390 | ||||||||
\(565\) | 8.31534 | 0.349829 | ||||||||
\(566\) | 3.36932 | 0.141623 | ||||||||
\(567\) | 3.56155 | 0.149571 | ||||||||
\(568\) | 91.8617 | 3.85443 | ||||||||
\(569\) | 40.7386 | 1.70785 | 0.853926 | − | 0.520394i | \(-0.174215\pi\) | ||||
0.853926 | + | 0.520394i | \(0.174215\pi\) | |||||||
\(570\) | 1.61553 | 0.0676670 | ||||||||
\(571\) | 19.3693 | 0.810581 | 0.405290 | − | 0.914188i | \(-0.367170\pi\) | ||||
0.405290 | + | 0.914188i | \(0.367170\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.876894 | −0.0366328 | ||||||||
\(574\) | 23.3693 | 0.975416 | ||||||||
\(575\) | −9.36932 | −0.390728 | ||||||||
\(576\) | 1.43845 | 0.0599353 | ||||||||
\(577\) | 29.6847 | 1.23579 | 0.617894 | − | 0.786261i | \(-0.287986\pi\) | ||||
0.617894 | + | 0.786261i | \(0.287986\pi\) | |||||||
\(578\) | 26.7386 | 1.11218 | ||||||||
\(579\) | −19.4924 | −0.810077 | ||||||||
\(580\) | 14.5616 | 0.604636 | ||||||||
\(581\) | 32.4924 | 1.34801 | ||||||||
\(582\) | −11.3693 | −0.471273 | ||||||||
\(583\) | 23.3693 | 0.967858 | ||||||||
\(584\) | −12.3153 | −0.509612 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 62.9157 | 2.59902 | ||||||||
\(587\) | −14.6307 | −0.603873 | −0.301936 | − | 0.953328i | \(-0.597633\pi\) | ||||
−0.301936 | + | 0.953328i | \(0.597633\pi\) | |||||||
\(588\) | 25.9309 | 1.06937 | ||||||||
\(589\) | 1.75379 | 0.0722636 | ||||||||
\(590\) | 16.0000 | 0.658710 | ||||||||
\(591\) | 11.3693 | 0.467671 | ||||||||
\(592\) | −26.4233 | −1.08599 | ||||||||
\(593\) | −44.4233 | −1.82425 | −0.912123 | − | 0.409917i | \(-0.865558\pi\) | ||||
−0.912123 | + | 0.409917i | \(0.865558\pi\) | |||||||
\(594\) | −5.12311 | −0.210204 | ||||||||
\(595\) | −5.12311 | −0.210027 | ||||||||
\(596\) | 29.9309 | 1.22602 | ||||||||
\(597\) | −23.1771 | −0.948575 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.384472 | −0.0157091 | −0.00785455 | − | 0.999969i | \(-0.502500\pi\) | ||||
−0.00785455 | + | 0.999969i | \(0.502500\pi\) | |||||||
\(600\) | 30.7386 | 1.25490 | ||||||||
\(601\) | −35.9309 | −1.46565 | −0.732825 | − | 0.680417i | \(-0.761799\pi\) | ||||
−0.732825 | + | 0.680417i | \(0.761799\pi\) | |||||||
\(602\) | −4.00000 | −0.163028 | ||||||||
\(603\) | −0.438447 | −0.0178549 | ||||||||
\(604\) | −70.1080 | −2.85265 | ||||||||
\(605\) | 3.93087 | 0.159813 | ||||||||
\(606\) | 8.80776 | 0.357791 | ||||||||
\(607\) | −16.0000 | −0.649420 | −0.324710 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324710 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(608\) | −7.36932 | −0.298865 | ||||||||
\(609\) | −20.2462 | −0.820418 | ||||||||
\(610\) | 17.4384 | 0.706062 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 11.6847 | 0.472324 | ||||||||
\(613\) | −22.8617 | −0.923377 | −0.461688 | − | 0.887042i | \(-0.652756\pi\) | ||||
−0.461688 | + | 0.887042i | \(0.652756\pi\) | |||||||
\(614\) | 26.1080 | 1.05363 | ||||||||
\(615\) | 1.43845 | 0.0580038 | ||||||||
\(616\) | −46.7386 | −1.88315 | ||||||||
\(617\) | 10.8078 | 0.435104 | 0.217552 | − | 0.976049i | \(-0.430193\pi\) | ||||
0.217552 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(618\) | 19.3693 | 0.779148 | ||||||||
\(619\) | 24.3002 | 0.976707 | 0.488353 | − | 0.872646i | \(-0.337598\pi\) | ||||
0.488353 | + | 0.872646i | \(0.337598\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | 2.00000 | 0.0802572 | ||||||||
\(622\) | 27.8617 | 1.11715 | ||||||||
\(623\) | −46.7386 | −1.87254 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 3.36932 | 0.134665 | ||||||||
\(627\) | 2.24621 | 0.0897050 | ||||||||
\(628\) | −19.9309 | −0.795328 | ||||||||
\(629\) | −8.80776 | −0.351189 | ||||||||
\(630\) | 5.12311 | 0.204109 | ||||||||
\(631\) | 14.4384 | 0.574786 | 0.287393 | − | 0.957813i | \(-0.407212\pi\) | ||||
0.287393 | + | 0.957813i | \(0.407212\pi\) | |||||||
\(632\) | −62.7386 | −2.49561 | ||||||||
\(633\) | 7.31534 | 0.290759 | ||||||||
\(634\) | −59.0540 | −2.34533 | ||||||||
\(635\) | −5.36932 | −0.213075 | ||||||||
\(636\) | 53.3002 | 2.11349 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 29.1231 | 1.15299 | ||||||||
\(639\) | −14.0000 | −0.553831 | ||||||||
\(640\) | −5.30019 | −0.209508 | ||||||||
\(641\) | 26.1771 | 1.03393 | 0.516966 | − | 0.856006i | \(-0.327061\pi\) | ||||
0.516966 | + | 0.856006i | \(0.327061\pi\) | |||||||
\(642\) | −21.1231 | −0.833662 | ||||||||
\(643\) | −38.5464 | −1.52012 | −0.760061 | − | 0.649852i | \(-0.774831\pi\) | ||||
−0.760061 | + | 0.649852i | \(0.774831\pi\) | |||||||
\(644\) | 32.4924 | 1.28038 | ||||||||
\(645\) | −0.246211 | −0.00969456 | ||||||||
\(646\) | −7.36932 | −0.289942 | ||||||||
\(647\) | −47.6155 | −1.87196 | −0.935980 | − | 0.352054i | \(-0.885483\pi\) | ||||
−0.935980 | + | 0.352054i | \(0.885483\pi\) | |||||||
\(648\) | −6.56155 | −0.257762 | ||||||||
\(649\) | 22.2462 | 0.873240 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.56155 | 0.217974 | ||||||||
\(652\) | −72.1080 | −2.82397 | ||||||||
\(653\) | 14.8769 | 0.582178 | 0.291089 | − | 0.956696i | \(-0.405982\pi\) | ||||
0.291089 | + | 0.956696i | \(0.405982\pi\) | |||||||
\(654\) | 45.6155 | 1.78371 | ||||||||
\(655\) | 9.75379 | 0.381112 | ||||||||
\(656\) | −19.6847 | −0.768557 | ||||||||
\(657\) | 1.87689 | 0.0732246 | ||||||||
\(658\) | −75.2311 | −2.93281 | ||||||||
\(659\) | 14.2462 | 0.554954 | 0.277477 | − | 0.960732i | \(-0.410502\pi\) | ||||
0.277477 | + | 0.960732i | \(0.410502\pi\) | |||||||
\(660\) | −5.12311 | −0.199417 | ||||||||
\(661\) | −30.3693 | −1.18123 | −0.590615 | − | 0.806954i | \(-0.701115\pi\) | ||||
−0.590615 | + | 0.806954i | \(0.701115\pi\) | |||||||
\(662\) | −60.9848 | −2.37024 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −59.8617 | −2.32309 | ||||||||
\(665\) | −2.24621 | −0.0871043 | ||||||||
\(666\) | 8.80776 | 0.341294 | ||||||||
\(667\) | −11.3693 | −0.440222 | ||||||||
\(668\) | 28.4924 | 1.10240 | ||||||||
\(669\) | −8.00000 | −0.309298 | ||||||||
\(670\) | −0.630683 | −0.0243654 | ||||||||
\(671\) | 24.2462 | 0.936015 | ||||||||
\(672\) | −23.3693 | −0.901491 | ||||||||
\(673\) | −6.75379 | −0.260339 | −0.130170 | − | 0.991492i | \(-0.541552\pi\) | ||||
−0.130170 | + | 0.991492i | \(0.541552\pi\) | |||||||
\(674\) | −5.43845 | −0.209481 | ||||||||
\(675\) | −4.68466 | −0.180313 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25.6155 | 0.984485 | 0.492242 | − | 0.870458i | \(-0.336177\pi\) | ||||
0.492242 | + | 0.870458i | \(0.336177\pi\) | |||||||
\(678\) | 37.9309 | 1.45673 | ||||||||
\(679\) | 15.8078 | 0.606646 | ||||||||
\(680\) | 9.43845 | 0.361948 | ||||||||
\(681\) | 1.12311 | 0.0430375 | ||||||||
\(682\) | −8.00000 | −0.306336 | ||||||||
\(683\) | −36.1080 | −1.38163 | −0.690816 | − | 0.723030i | \(-0.742749\pi\) | ||||
−0.690816 | + | 0.723030i | \(0.742749\pi\) | |||||||
\(684\) | 5.12311 | 0.195887 | ||||||||
\(685\) | −0.807764 | −0.0308631 | ||||||||
\(686\) | 12.0000 | 0.458162 | ||||||||
\(687\) | −0.246211 | −0.00939355 | ||||||||
\(688\) | 3.36932 | 0.128454 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 2.87689 | 0.109521 | ||||||||
\(691\) | −2.30019 | −0.0875032 | −0.0437516 | − | 0.999042i | \(-0.513931\pi\) | ||||
−0.0437516 | + | 0.999042i | \(0.513931\pi\) | |||||||
\(692\) | 17.1231 | 0.650923 | ||||||||
\(693\) | 7.12311 | 0.270584 | ||||||||
\(694\) | 34.8769 | 1.32391 | ||||||||
\(695\) | −6.13826 | −0.232837 | ||||||||
\(696\) | 37.3002 | 1.41386 | ||||||||
\(697\) | −6.56155 | −0.248537 | ||||||||
\(698\) | −35.3693 | −1.33875 | ||||||||
\(699\) | 26.0000 | 0.983410 | ||||||||
\(700\) | −76.1080 | −2.87661 | ||||||||
\(701\) | 19.3693 | 0.731569 | 0.365785 | − | 0.930700i | \(-0.380801\pi\) | ||||
0.365785 | + | 0.930700i | \(0.380801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.86174 | −0.145648 | ||||||||
\(704\) | 2.87689 | 0.108427 | ||||||||
\(705\) | −4.63068 | −0.174402 | ||||||||
\(706\) | 45.3002 | 1.70490 | ||||||||
\(707\) | −12.2462 | −0.460566 | ||||||||
\(708\) | 50.7386 | 1.90687 | ||||||||
\(709\) | −25.4924 | −0.957388 | −0.478694 | − | 0.877982i | \(-0.658890\pi\) | ||||
−0.478694 | + | 0.877982i | \(0.658890\pi\) | |||||||
\(710\) | −20.1383 | −0.755775 | ||||||||
\(711\) | 9.56155 | 0.358586 | ||||||||
\(712\) | 86.1080 | 3.22703 | ||||||||
\(713\) | 3.12311 | 0.116961 | ||||||||
\(714\) | −23.3693 | −0.874575 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −59.8617 | −2.23714 | ||||||||
\(717\) | 0.630683 | 0.0235533 | ||||||||
\(718\) | 39.3693 | 1.46925 | ||||||||
\(719\) | 1.36932 | 0.0510669 | 0.0255335 | − | 0.999674i | \(-0.491872\pi\) | ||||
0.0255335 | + | 0.999674i | \(0.491872\pi\) | |||||||
\(720\) | −4.31534 | −0.160823 | ||||||||
\(721\) | −26.9309 | −1.00296 | ||||||||
\(722\) | 45.4384 | 1.69104 | ||||||||
\(723\) | −2.80776 | −0.104422 | ||||||||
\(724\) | 44.1771 | 1.64183 | ||||||||
\(725\) | 26.6307 | 0.989039 | ||||||||
\(726\) | 17.9309 | 0.665477 | ||||||||
\(727\) | 39.6695 | 1.47126 | 0.735630 | − | 0.677383i | \(-0.236886\pi\) | ||||
0.735630 | + | 0.677383i | \(0.236886\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.69981 | 0.0999246 | ||||||||
\(731\) | 1.12311 | 0.0415396 | ||||||||
\(732\) | 55.3002 | 2.04395 | ||||||||
\(733\) | −53.4924 | −1.97579 | −0.987894 | − | 0.155131i | \(-0.950420\pi\) | ||||
−0.987894 | + | 0.155131i | \(0.950420\pi\) | |||||||
\(734\) | −51.3693 | −1.89608 | ||||||||
\(735\) | −3.19224 | −0.117747 | ||||||||
\(736\) | −13.1231 | −0.483724 | ||||||||
\(737\) | −0.876894 | −0.0323008 | ||||||||
\(738\) | 6.56155 | 0.241534 | ||||||||
\(739\) | 6.24621 | 0.229771 | 0.114885 | − | 0.993379i | \(-0.463350\pi\) | ||||
0.114885 | + | 0.993379i | \(0.463350\pi\) | |||||||
\(740\) | 8.80776 | 0.323780 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −106.600 | −3.91342 | ||||||||
\(743\) | 37.3693 | 1.37095 | 0.685474 | − | 0.728097i | \(-0.259595\pi\) | ||||
0.685474 | + | 0.728097i | \(0.259595\pi\) | |||||||
\(744\) | −10.2462 | −0.375644 | ||||||||
\(745\) | −3.68466 | −0.134995 | ||||||||
\(746\) | −9.30019 | −0.340504 | ||||||||
\(747\) | 9.12311 | 0.333797 | ||||||||
\(748\) | 23.3693 | 0.854467 | ||||||||
\(749\) | 29.3693 | 1.07313 | ||||||||
\(750\) | −13.9309 | −0.508683 | ||||||||
\(751\) | −30.1080 | −1.09865 | −0.549327 | − | 0.835607i | \(-0.685116\pi\) | ||||
−0.549327 | + | 0.835607i | \(0.685116\pi\) | |||||||
\(752\) | 63.3693 | 2.31084 | ||||||||
\(753\) | −30.7386 | −1.12018 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.63068 | 0.314103 | ||||||||
\(756\) | 16.2462 | 0.590869 | ||||||||
\(757\) | 30.0000 | 1.09037 | 0.545184 | − | 0.838316i | \(-0.316460\pi\) | ||||
0.545184 | + | 0.838316i | \(0.316460\pi\) | |||||||
\(758\) | 28.9848 | 1.05278 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 4.13826 | 0.150110 | ||||||||
\(761\) | 15.3693 | 0.557137 | 0.278569 | − | 0.960416i | \(-0.410140\pi\) | ||||
0.278569 | + | 0.960416i | \(0.410140\pi\) | |||||||
\(762\) | −24.4924 | −0.887267 | ||||||||
\(763\) | −63.4233 | −2.29608 | ||||||||
\(764\) | −4.00000 | −0.144715 | ||||||||
\(765\) | −1.43845 | −0.0520072 | ||||||||
\(766\) | 68.4924 | 2.47473 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.0540 | −0.976226 | ||||||||
\(769\) | 18.0000 | 0.649097 | 0.324548 | − | 0.945869i | \(-0.394788\pi\) | ||||
0.324548 | + | 0.945869i | \(0.394788\pi\) | |||||||
\(770\) | 10.2462 | 0.369248 | ||||||||
\(771\) | −16.1771 | −0.582603 | ||||||||
\(772\) | −88.9157 | −3.20015 | ||||||||
\(773\) | 7.75379 | 0.278884 | 0.139442 | − | 0.990230i | \(-0.455469\pi\) | ||||
0.139442 | + | 0.990230i | \(0.455469\pi\) | |||||||
\(774\) | −1.12311 | −0.0403692 | ||||||||
\(775\) | −7.31534 | −0.262775 | ||||||||
\(776\) | −29.1231 | −1.04546 | ||||||||
\(777\) | −12.2462 | −0.439330 | ||||||||
\(778\) | 7.82292 | 0.280465 | ||||||||
\(779\) | −2.87689 | −0.103075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.0000 | −1.00192 | ||||||||
\(782\) | −13.1231 | −0.469281 | ||||||||
\(783\) | −5.68466 | −0.203153 | ||||||||
\(784\) | 43.6847 | 1.56017 | ||||||||
\(785\) | 2.45360 | 0.0875728 | ||||||||
\(786\) | 44.4924 | 1.58699 | ||||||||
\(787\) | 1.17708 | 0.0419584 | 0.0209792 | − | 0.999780i | \(-0.493322\pi\) | ||||
0.0209792 | + | 0.999780i | \(0.493322\pi\) | |||||||
\(788\) | 51.8617 | 1.84750 | ||||||||
\(789\) | −15.3693 | −0.547162 | ||||||||
\(790\) | 13.7538 | 0.489338 | ||||||||
\(791\) | −52.7386 | −1.87517 | ||||||||
\(792\) | −13.1231 | −0.466309 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −30.8769 | −1.09578 | ||||||||
\(795\) | −6.56155 | −0.232714 | ||||||||
\(796\) | −105.723 | −3.74727 | ||||||||
\(797\) | −41.6155 | −1.47410 | −0.737049 | − | 0.675840i | \(-0.763781\pi\) | ||||
−0.737049 | + | 0.675840i | \(0.763781\pi\) | |||||||
\(798\) | −10.2462 | −0.362712 | ||||||||
\(799\) | 21.1231 | 0.747282 | ||||||||
\(800\) | 30.7386 | 1.08677 | ||||||||
\(801\) | −13.1231 | −0.463682 | ||||||||
\(802\) | 47.5464 | 1.67892 | ||||||||
\(803\) | 3.75379 | 0.132468 | ||||||||
\(804\) | −2.00000 | −0.0705346 | ||||||||
\(805\) | −4.00000 | −0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.36932 | 0.118606 | ||||||||
\(808\) | 22.5616 | 0.793713 | ||||||||
\(809\) | 37.3002 | 1.31140 | 0.655702 | − | 0.755019i | \(-0.272373\pi\) | ||||
0.655702 | + | 0.755019i | \(0.272373\pi\) | |||||||
\(810\) | 1.43845 | 0.0505419 | ||||||||
\(811\) | 1.56155 | 0.0548335 | 0.0274168 | − | 0.999624i | \(-0.491272\pi\) | ||||
0.0274168 | + | 0.999624i | \(0.491272\pi\) | |||||||
\(812\) | −92.3542 | −3.24100 | ||||||||
\(813\) | 1.06913 | 0.0374960 | ||||||||
\(814\) | 17.6155 | 0.617424 | ||||||||
\(815\) | 8.87689 | 0.310944 | ||||||||
\(816\) | 19.6847 | 0.689101 | ||||||||
\(817\) | 0.492423 | 0.0172277 | ||||||||
\(818\) | −47.0540 | −1.64520 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.56155 | 0.229139 | ||||||||
\(821\) | 26.4924 | 0.924592 | 0.462296 | − | 0.886726i | \(-0.347026\pi\) | ||||
0.462296 | + | 0.886726i | \(0.347026\pi\) | |||||||
\(822\) | −3.68466 | −0.128517 | ||||||||
\(823\) | 8.00000 | 0.278862 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(824\) | 49.6155 | 1.72844 | ||||||||
\(825\) | −9.36932 | −0.326198 | ||||||||
\(826\) | −101.477 | −3.53085 | ||||||||
\(827\) | −34.7386 | −1.20798 | −0.603990 | − | 0.796992i | \(-0.706423\pi\) | ||||
−0.603990 | + | 0.796992i | \(0.706423\pi\) | |||||||
\(828\) | 9.12311 | 0.317050 | ||||||||
\(829\) | −19.4924 | −0.677000 | −0.338500 | − | 0.940966i | \(-0.609919\pi\) | ||||
−0.338500 | + | 0.940966i | \(0.609919\pi\) | |||||||
\(830\) | 13.1231 | 0.455510 | ||||||||
\(831\) | 17.6847 | 0.613474 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.5616 | 0.504528 | ||||||||
\(834\) | −28.0000 | −0.969561 | ||||||||
\(835\) | −3.50758 | −0.121385 | ||||||||
\(836\) | 10.2462 | 0.354373 | ||||||||
\(837\) | 1.56155 | 0.0539752 | ||||||||
\(838\) | 45.4773 | 1.57099 | ||||||||
\(839\) | 19.6155 | 0.677203 | 0.338602 | − | 0.940930i | \(-0.390046\pi\) | ||||
0.338602 | + | 0.940930i | \(0.390046\pi\) | |||||||
\(840\) | 13.1231 | 0.452790 | ||||||||
\(841\) | 3.31534 | 0.114322 | ||||||||
\(842\) | 37.7926 | 1.30242 | ||||||||
\(843\) | 2.80776 | 0.0967045 | ||||||||
\(844\) | 33.3693 | 1.14862 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21.1231 | −0.726227 | ||||||||
\(847\) | −24.9309 | −0.856635 | ||||||||
\(848\) | 89.7926 | 3.08349 | ||||||||
\(849\) | −1.31534 | −0.0451424 | ||||||||
\(850\) | 30.7386 | 1.05433 | ||||||||
\(851\) | −6.87689 | −0.235737 | ||||||||
\(852\) | −63.8617 | −2.18787 | ||||||||
\(853\) | 6.12311 | 0.209651 | 0.104826 | − | 0.994491i | \(-0.466572\pi\) | ||||
0.104826 | + | 0.994491i | \(0.466572\pi\) | |||||||
\(854\) | −110.600 | −3.78467 | ||||||||
\(855\) | −0.630683 | −0.0215689 | ||||||||
\(856\) | −54.1080 | −1.84937 | ||||||||
\(857\) | 31.4384 | 1.07392 | 0.536958 | − | 0.843609i | \(-0.319573\pi\) | ||||
0.536958 | + | 0.843609i | \(0.319573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.4384 | 0.697351 | 0.348675 | − | 0.937244i | \(-0.386632\pi\) | ||||
0.348675 | + | 0.937244i | \(0.386632\pi\) | |||||||
\(860\) | −1.12311 | −0.0382976 | ||||||||
\(861\) | −9.12311 | −0.310915 | ||||||||
\(862\) | −7.36932 | −0.251000 | ||||||||
\(863\) | 2.49242 | 0.0848430 | 0.0424215 | − | 0.999100i | \(-0.486493\pi\) | ||||
0.0424215 | + | 0.999100i | \(0.486493\pi\) | |||||||
\(864\) | −6.56155 | −0.223229 | ||||||||
\(865\) | −2.10795 | −0.0716725 | ||||||||
\(866\) | −64.6695 | −2.19756 | ||||||||
\(867\) | −10.4384 | −0.354508 | ||||||||
\(868\) | 25.3693 | 0.861091 | ||||||||
\(869\) | 19.1231 | 0.648707 | ||||||||
\(870\) | −8.17708 | −0.277229 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 116.847 | 3.95692 | ||||||||
\(873\) | 4.43845 | 0.150219 | ||||||||
\(874\) | −5.75379 | −0.194625 | ||||||||
\(875\) | 19.3693 | 0.654802 | ||||||||
\(876\) | 8.56155 | 0.289268 | ||||||||
\(877\) | −19.4384 | −0.656390 | −0.328195 | − | 0.944610i | \(-0.606440\pi\) | ||||
−0.328195 | + | 0.944610i | \(0.606440\pi\) | |||||||
\(878\) | 3.36932 | 0.113709 | ||||||||
\(879\) | −24.5616 | −0.828441 | ||||||||
\(880\) | −8.63068 | −0.290940 | ||||||||
\(881\) | −37.9309 | −1.27792 | −0.638962 | − | 0.769239i | \(-0.720636\pi\) | ||||
−0.638962 | + | 0.769239i | \(0.720636\pi\) | |||||||
\(882\) | −14.5616 | −0.490313 | ||||||||
\(883\) | −11.8078 | −0.397363 | −0.198681 | − | 0.980064i | \(-0.563666\pi\) | ||||
−0.198681 | + | 0.980064i | \(0.563666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.24621 | −0.209964 | ||||||||
\(886\) | −37.7538 | −1.26836 | ||||||||
\(887\) | 49.3693 | 1.65766 | 0.828830 | − | 0.559501i | \(-0.189007\pi\) | ||||
0.828830 | + | 0.559501i | \(0.189007\pi\) | |||||||
\(888\) | 22.5616 | 0.757116 | ||||||||
\(889\) | 34.0540 | 1.14213 | ||||||||
\(890\) | −18.8769 | −0.632755 | ||||||||
\(891\) | 2.00000 | 0.0670025 | ||||||||
\(892\) | −36.4924 | −1.22186 | ||||||||
\(893\) | 9.26137 | 0.309920 | ||||||||
\(894\) | −16.8078 | −0.562136 | ||||||||
\(895\) | 7.36932 | 0.246329 | ||||||||
\(896\) | 33.6155 | 1.12302 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.1231 | 0.704887 | ||||||||
\(899\) | −8.87689 | −0.296061 | ||||||||
\(900\) | −21.3693 | −0.712311 | ||||||||
\(901\) | 29.9309 | 0.997142 | ||||||||
\(902\) | 13.1231 | 0.436952 | ||||||||
\(903\) | 1.56155 | 0.0519652 | ||||||||
\(904\) | 97.1619 | 3.23156 | ||||||||
\(905\) | −5.43845 | −0.180780 | ||||||||
\(906\) | 39.3693 | 1.30796 | ||||||||
\(907\) | 28.0000 | 0.929725 | 0.464862 | − | 0.885383i | \(-0.346104\pi\) | ||||
0.464862 | + | 0.885383i | \(0.346104\pi\) | |||||||
\(908\) | 5.12311 | 0.170016 | ||||||||
\(909\) | −3.43845 | −0.114046 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.7386 | −0.355787 | −0.177893 | − | 0.984050i | \(-0.556928\pi\) | ||||
−0.177893 | + | 0.984050i | \(0.556928\pi\) | |||||||
\(912\) | 8.63068 | 0.285790 | ||||||||
\(913\) | 18.2462 | 0.603861 | ||||||||
\(914\) | −73.3002 | −2.42455 | ||||||||
\(915\) | −6.80776 | −0.225058 | ||||||||
\(916\) | −1.12311 | −0.0371085 | ||||||||
\(917\) | −61.8617 | −2.04285 | ||||||||
\(918\) | −6.56155 | −0.216564 | ||||||||
\(919\) | 44.4924 | 1.46767 | 0.733835 | − | 0.679328i | \(-0.237729\pi\) | ||||
0.733835 | + | 0.679328i | \(0.237729\pi\) | |||||||
\(920\) | 7.36932 | 0.242959 | ||||||||
\(921\) | −10.1922 | −0.335846 | ||||||||
\(922\) | −94.2850 | −3.10511 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 32.4924 | 1.06892 | ||||||||
\(925\) | 16.1080 | 0.529626 | ||||||||
\(926\) | −68.3542 | −2.24626 | ||||||||
\(927\) | −7.56155 | −0.248354 | ||||||||
\(928\) | 37.3002 | 1.22444 | ||||||||
\(929\) | −12.8078 | −0.420209 | −0.210105 | − | 0.977679i | \(-0.567380\pi\) | ||||
−0.210105 | + | 0.977679i | \(0.567380\pi\) | |||||||
\(930\) | 2.24621 | 0.0736562 | ||||||||
\(931\) | 6.38447 | 0.209243 | ||||||||
\(932\) | 118.600 | 3.88488 | ||||||||
\(933\) | −10.8769 | −0.356094 | ||||||||
\(934\) | 66.6004 | 2.17923 | ||||||||
\(935\) | −2.87689 | −0.0940845 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.43845 | −0.112329 | −0.0561646 | − | 0.998422i | \(-0.517887\pi\) | ||||
−0.0561646 | + | 0.998422i | \(0.517887\pi\) | |||||||
\(938\) | 4.00000 | 0.130605 | ||||||||
\(939\) | −1.31534 | −0.0429245 | ||||||||
\(940\) | −21.1231 | −0.688960 | ||||||||
\(941\) | 2.49242 | 0.0812507 | 0.0406253 | − | 0.999174i | \(-0.487065\pi\) | ||||
0.0406253 | + | 0.999174i | \(0.487065\pi\) | |||||||
\(942\) | 11.1922 | 0.364663 | ||||||||
\(943\) | −5.12311 | −0.166831 | ||||||||
\(944\) | 85.4773 | 2.78205 | ||||||||
\(945\) | −2.00000 | −0.0650600 | ||||||||
\(946\) | −2.24621 | −0.0730306 | ||||||||
\(947\) | −10.7386 | −0.348959 | −0.174479 | − | 0.984661i | \(-0.555824\pi\) | ||||
−0.174479 | + | 0.984661i | \(0.555824\pi\) | |||||||
\(948\) | 43.6155 | 1.41657 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 13.4773 | 0.437260 | ||||||||
\(951\) | 23.0540 | 0.747576 | ||||||||
\(952\) | −59.8617 | −1.94013 | ||||||||
\(953\) | −34.9848 | −1.13327 | −0.566635 | − | 0.823969i | \(-0.691755\pi\) | ||||
−0.566635 | + | 0.823969i | \(0.691755\pi\) | |||||||
\(954\) | −29.9309 | −0.969048 | ||||||||
\(955\) | 0.492423 | 0.0159344 | ||||||||
\(956\) | 2.87689 | 0.0930454 | ||||||||
\(957\) | −11.3693 | −0.367518 | ||||||||
\(958\) | −16.0000 | −0.516937 | ||||||||
\(959\) | 5.12311 | 0.165434 | ||||||||
\(960\) | −0.807764 | −0.0260705 | ||||||||
\(961\) | −28.5616 | −0.921340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.24621 | 0.265730 | ||||||||
\(964\) | −12.8078 | −0.412510 | ||||||||
\(965\) | 10.9460 | 0.352365 | ||||||||
\(966\) | −18.2462 | −0.587062 | ||||||||
\(967\) | 9.12311 | 0.293379 | 0.146690 | − | 0.989183i | \(-0.453138\pi\) | ||||
0.146690 | + | 0.989183i | \(0.453138\pi\) | |||||||
\(968\) | 45.9309 | 1.47627 | ||||||||
\(969\) | 2.87689 | 0.0924192 | ||||||||
\(970\) | 6.38447 | 0.204993 | ||||||||
\(971\) | 52.9848 | 1.70036 | 0.850182 | − | 0.526488i | \(-0.176492\pi\) | ||||
0.850182 | + | 0.526488i | \(0.176492\pi\) | |||||||
\(972\) | 4.56155 | 0.146312 | ||||||||
\(973\) | 38.9309 | 1.24807 | ||||||||
\(974\) | −2.87689 | −0.0921816 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 93.1619 | 2.98204 | ||||||||
\(977\) | −15.8229 | −0.506220 | −0.253110 | − | 0.967438i | \(-0.581453\pi\) | ||||
−0.253110 | + | 0.967438i | \(0.581453\pi\) | |||||||
\(978\) | 40.4924 | 1.29480 | ||||||||
\(979\) | −26.2462 | −0.838833 | ||||||||
\(980\) | −14.5616 | −0.465152 | ||||||||
\(981\) | −17.8078 | −0.568558 | ||||||||
\(982\) | 50.6004 | 1.61472 | ||||||||
\(983\) | 27.6155 | 0.880799 | 0.440399 | − | 0.897802i | \(-0.354837\pi\) | ||||
0.440399 | + | 0.897802i | \(0.354837\pi\) | |||||||
\(984\) | 16.8078 | 0.535812 | ||||||||
\(985\) | −6.38447 | −0.203426 | ||||||||
\(986\) | 37.3002 | 1.18788 | ||||||||
\(987\) | 29.3693 | 0.934836 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.876894 | 0.0278836 | ||||||||
\(990\) | 2.87689 | 0.0914337 | ||||||||
\(991\) | 40.3542 | 1.28189 | 0.640946 | − | 0.767586i | \(-0.278542\pi\) | ||||
0.640946 | + | 0.767586i | \(0.278542\pi\) | |||||||
\(992\) | −10.2462 | −0.325318 | ||||||||
\(993\) | 23.8078 | 0.755517 | ||||||||
\(994\) | 127.723 | 4.05114 | ||||||||
\(995\) | 13.0152 | 0.412608 | ||||||||
\(996\) | 41.6155 | 1.31864 | ||||||||
\(997\) | 20.6155 | 0.652900 | 0.326450 | − | 0.945214i | \(-0.394147\pi\) | ||||
0.326450 | + | 0.945214i | \(0.394147\pi\) | |||||||
\(998\) | −72.9848 | −2.31029 | ||||||||
\(999\) | −3.43845 | −0.108788 |
(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 | 507.2.a.d.1.1 | 2 | ||
3.2 | odd | 2 | 1521.2.a.m.1.2 | 2 | |||
4.3 | odd | 2 | 8112.2.a.bo.1.1 | 2 | |||
13.2 | odd | 12 | 507.2.j.g.316.1 | 8 | |||
13.3 | even | 3 | 507.2.e.g.22.2 | 4 | |||
13.4 | even | 6 | 39.2.e.b.16.1 | ✓ | 4 | ||
13.5 | odd | 4 | 507.2.b.d.337.4 | 4 | |||
13.6 | odd | 12 | 507.2.j.g.361.4 | 8 | |||
13.7 | odd | 12 | 507.2.j.g.361.1 | 8 | |||
13.8 | odd | 4 | 507.2.b.d.337.1 | 4 | |||
13.9 | even | 3 | 507.2.e.g.484.2 | 4 | |||
13.10 | even | 6 | 39.2.e.b.22.1 | yes | 4 | ||
13.11 | odd | 12 | 507.2.j.g.316.4 | 8 | |||
13.12 | even | 2 | 507.2.a.g.1.2 | 2 | |||
39.5 | even | 4 | 1521.2.b.h.1351.1 | 4 | |||
39.8 | even | 4 | 1521.2.b.h.1351.4 | 4 | |||
39.17 | odd | 6 | 117.2.g.c.55.2 | 4 | |||
39.23 | odd | 6 | 117.2.g.c.100.2 | 4 | |||
39.38 | odd | 2 | 1521.2.a.g.1.1 | 2 | |||
52.23 | odd | 6 | 624.2.q.h.529.2 | 4 | |||
52.43 | odd | 6 | 624.2.q.h.289.2 | 4 | |||
52.51 | odd | 2 | 8112.2.a.bk.1.2 | 2 | |||
65.4 | even | 6 | 975.2.i.k.601.2 | 4 | |||
65.17 | odd | 12 | 975.2.bb.i.874.4 | 8 | |||
65.23 | odd | 12 | 975.2.bb.i.724.4 | 8 | |||
65.43 | odd | 12 | 975.2.bb.i.874.1 | 8 | |||
65.49 | even | 6 | 975.2.i.k.451.2 | 4 | |||
65.62 | odd | 12 | 975.2.bb.i.724.1 | 8 | |||
156.23 | even | 6 | 1872.2.t.r.1153.1 | 4 | |||
156.95 | even | 6 | 1872.2.t.r.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.2.e.b.16.1 | ✓ | 4 | 13.4 | even | 6 | ||
39.2.e.b.22.1 | yes | 4 | 13.10 | even | 6 | ||
117.2.g.c.55.2 | 4 | 39.17 | odd | 6 | |||
117.2.g.c.100.2 | 4 | 39.23 | odd | 6 | |||
507.2.a.d.1.1 | 2 | 1.1 | even | 1 | trivial | ||
507.2.a.g.1.2 | 2 | 13.12 | even | 2 | |||
507.2.b.d.337.1 | 4 | 13.8 | odd | 4 | |||
507.2.b.d.337.4 | 4 | 13.5 | odd | 4 | |||
507.2.e.g.22.2 | 4 | 13.3 | even | 3 | |||
507.2.e.g.484.2 | 4 | 13.9 | even | 3 | |||
507.2.j.g.316.1 | 8 | 13.2 | odd | 12 | |||
507.2.j.g.316.4 | 8 | 13.11 | odd | 12 | |||
507.2.j.g.361.1 | 8 | 13.7 | odd | 12 | |||
507.2.j.g.361.4 | 8 | 13.6 | odd | 12 | |||
624.2.q.h.289.2 | 4 | 52.43 | odd | 6 | |||
624.2.q.h.529.2 | 4 | 52.23 | odd | 6 | |||
975.2.i.k.451.2 | 4 | 65.49 | even | 6 | |||
975.2.i.k.601.2 | 4 | 65.4 | even | 6 | |||
975.2.bb.i.724.1 | 8 | 65.62 | odd | 12 | |||
975.2.bb.i.724.4 | 8 | 65.23 | odd | 12 | |||
975.2.bb.i.874.1 | 8 | 65.43 | odd | 12 | |||
975.2.bb.i.874.4 | 8 | 65.17 | odd | 12 | |||
1521.2.a.g.1.1 | 2 | 39.38 | odd | 2 | |||
1521.2.a.m.1.2 | 2 | 3.2 | odd | 2 | |||
1521.2.b.h.1351.1 | 4 | 39.5 | even | 4 | |||
1521.2.b.h.1351.4 | 4 | 39.8 | even | 4 | |||
1872.2.t.r.289.1 | 4 | 156.95 | even | 6 | |||
1872.2.t.r.1153.1 | 4 | 156.23 | even | 6 | |||
8112.2.a.bk.1.2 | 2 | 52.51 | odd | 2 | |||
8112.2.a.bo.1.1 | 2 | 4.3 | odd | 2 |