Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,3,Mod(21,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.21");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(0.599456581593\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.21 |
Dual form | 22.3.b.a.21.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).
\(n\) | \(13\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 1.00000 | 0.333333 | 0.166667 | − | 0.986013i | \(-0.446700\pi\) | ||||
0.166667 | + | 0.986013i | \(0.446700\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.200000 | −0.100000 | − | 0.994987i | \(-0.531884\pi\) | ||||
−0.100000 | + | 0.994987i | \(0.531884\pi\) | |||||||
\(6\) | − | 1.41421i | − | 0.235702i | ||||||
\(7\) | 8.48528i | 1.21218i | 0.795395 | + | 0.606092i | \(0.207263\pi\) | ||||
−0.795395 | + | 0.606092i | \(0.792737\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −8.00000 | −0.888889 | ||||||||
\(10\) | 1.41421i | 0.141421i | ||||||||
\(11\) | 7.00000 | − | 8.48528i | 0.636364 | − | 0.771389i | ||||
\(12\) | −2.00000 | −0.166667 | ||||||||
\(13\) | − | 8.48528i | − | 0.652714i | −0.945247 | − | 0.326357i | \(-0.894179\pi\) | ||
0.945247 | − | 0.326357i | \(-0.105821\pi\) | |||||||
\(14\) | 12.0000 | 0.857143 | ||||||||
\(15\) | −1.00000 | −0.0666667 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 25.4558i | − | 1.49740i | −0.662908 | − | 0.748701i | \(-0.730678\pi\) | ||
0.662908 | − | 0.748701i | \(-0.269322\pi\) | |||||||
\(18\) | 11.3137i | 0.628539i | ||||||||
\(19\) | 25.4558i | 1.33978i | 0.742460 | + | 0.669891i | \(0.233659\pi\) | ||||
−0.742460 | + | 0.669891i | \(0.766341\pi\) | |||||||
\(20\) | 2.00000 | 0.100000 | ||||||||
\(21\) | 8.48528i | 0.404061i | ||||||||
\(22\) | −12.0000 | − | 9.89949i | −0.545455 | − | 0.449977i | ||||
\(23\) | 17.0000 | 0.739130 | 0.369565 | − | 0.929205i | \(-0.379507\pi\) | ||||
0.369565 | + | 0.929205i | \(0.379507\pi\) | |||||||
\(24\) | 2.82843i | 0.117851i | ||||||||
\(25\) | −24.0000 | −0.960000 | ||||||||
\(26\) | −12.0000 | −0.461538 | ||||||||
\(27\) | −17.0000 | −0.629630 | ||||||||
\(28\) | − | 16.9706i | − | 0.606092i | ||||||
\(29\) | 33.9411i | 1.17038i | 0.810895 | + | 0.585192i | \(0.198981\pi\) | ||||
−0.810895 | + | 0.585192i | \(0.801019\pi\) | |||||||
\(30\) | 1.41421i | 0.0471405i | ||||||||
\(31\) | 17.0000 | 0.548387 | 0.274194 | − | 0.961675i | \(-0.411589\pi\) | ||||
0.274194 | + | 0.961675i | \(0.411589\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 7.00000 | − | 8.48528i | 0.212121 | − | 0.257130i | ||||
\(34\) | −36.0000 | −1.05882 | ||||||||
\(35\) | − | 8.48528i | − | 0.242437i | ||||||
\(36\) | 16.0000 | 0.444444 | ||||||||
\(37\) | 47.0000 | 1.27027 | 0.635135 | − | 0.772401i | \(-0.280944\pi\) | ||||
0.635135 | + | 0.772401i | \(0.280944\pi\) | |||||||
\(38\) | 36.0000 | 0.947368 | ||||||||
\(39\) | − | 8.48528i | − | 0.217571i | ||||||
\(40\) | − | 2.82843i | − | 0.0707107i | ||||||
\(41\) | − | 8.48528i | − | 0.206958i | −0.994632 | − | 0.103479i | \(-0.967003\pi\) | ||
0.994632 | − | 0.103479i | \(-0.0329975\pi\) | |||||||
\(42\) | 12.0000 | 0.285714 | ||||||||
\(43\) | − | 16.9706i | − | 0.394664i | −0.980337 | − | 0.197332i | \(-0.936772\pi\) | ||
0.980337 | − | 0.197332i | \(-0.0632277\pi\) | |||||||
\(44\) | −14.0000 | + | 16.9706i | −0.318182 | + | 0.385695i | ||||
\(45\) | 8.00000 | 0.177778 | ||||||||
\(46\) | − | 24.0416i | − | 0.522644i | ||||||
\(47\) | −58.0000 | −1.23404 | −0.617021 | − | 0.786946i | \(-0.711661\pi\) | ||||
−0.617021 | + | 0.786946i | \(0.711661\pi\) | |||||||
\(48\) | 4.00000 | 0.0833333 | ||||||||
\(49\) | −23.0000 | −0.469388 | ||||||||
\(50\) | 33.9411i | 0.678823i | ||||||||
\(51\) | − | 25.4558i | − | 0.499134i | ||||||
\(52\) | 16.9706i | 0.326357i | ||||||||
\(53\) | 2.00000 | 0.0377358 | 0.0188679 | − | 0.999822i | \(-0.493994\pi\) | ||||
0.0188679 | + | 0.999822i | \(0.493994\pi\) | |||||||
\(54\) | 24.0416i | 0.445215i | ||||||||
\(55\) | −7.00000 | + | 8.48528i | −0.127273 | + | 0.154278i | ||||
\(56\) | −24.0000 | −0.428571 | ||||||||
\(57\) | 25.4558i | 0.446594i | ||||||||
\(58\) | 48.0000 | 0.827586 | ||||||||
\(59\) | −55.0000 | −0.932203 | −0.466102 | − | 0.884731i | \(-0.654342\pi\) | ||||
−0.466102 | + | 0.884731i | \(0.654342\pi\) | |||||||
\(60\) | 2.00000 | 0.0333333 | ||||||||
\(61\) | 84.8528i | 1.39103i | 0.718512 | + | 0.695515i | \(0.244824\pi\) | ||||
−0.718512 | + | 0.695515i | \(0.755176\pi\) | |||||||
\(62\) | − | 24.0416i | − | 0.387768i | ||||||
\(63\) | − | 67.8823i | − | 1.07750i | ||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 8.48528i | 0.130543i | ||||||||
\(66\) | −12.0000 | − | 9.89949i | −0.181818 | − | 0.149992i | ||||
\(67\) | 89.0000 | 1.32836 | 0.664179 | − | 0.747573i | \(-0.268781\pi\) | ||||
0.664179 | + | 0.747573i | \(0.268781\pi\) | |||||||
\(68\) | 50.9117i | 0.748701i | ||||||||
\(69\) | 17.0000 | 0.246377 | ||||||||
\(70\) | −12.0000 | −0.171429 | ||||||||
\(71\) | −7.00000 | −0.0985915 | −0.0492958 | − | 0.998784i | \(-0.515698\pi\) | ||||
−0.0492958 | + | 0.998784i | \(0.515698\pi\) | |||||||
\(72\) | − | 22.6274i | − | 0.314270i | ||||||
\(73\) | − | 127.279i | − | 1.74355i | −0.489906 | − | 0.871775i | \(-0.662969\pi\) | ||
0.489906 | − | 0.871775i | \(-0.337031\pi\) | |||||||
\(74\) | − | 66.4680i | − | 0.898217i | ||||||
\(75\) | −24.0000 | −0.320000 | ||||||||
\(76\) | − | 50.9117i | − | 0.669891i | ||||||
\(77\) | 72.0000 | + | 59.3970i | 0.935065 | + | 0.771389i | ||||
\(78\) | −12.0000 | −0.153846 | ||||||||
\(79\) | 33.9411i | 0.429634i | 0.976654 | + | 0.214817i | \(0.0689156\pi\) | ||||
−0.976654 | + | 0.214817i | \(0.931084\pi\) | |||||||
\(80\) | −4.00000 | −0.0500000 | ||||||||
\(81\) | 55.0000 | 0.679012 | ||||||||
\(82\) | −12.0000 | −0.146341 | ||||||||
\(83\) | 33.9411i | 0.408929i | 0.978874 | + | 0.204465i | \(0.0655453\pi\) | ||||
−0.978874 | + | 0.204465i | \(0.934455\pi\) | |||||||
\(84\) | − | 16.9706i | − | 0.202031i | ||||||
\(85\) | 25.4558i | 0.299481i | ||||||||
\(86\) | −24.0000 | −0.279070 | ||||||||
\(87\) | 33.9411i | 0.390128i | ||||||||
\(88\) | 24.0000 | + | 19.7990i | 0.272727 | + | 0.224989i | ||||
\(89\) | −97.0000 | −1.08989 | −0.544944 | − | 0.838473i | \(-0.683449\pi\) | ||||
−0.544944 | + | 0.838473i | \(0.683449\pi\) | |||||||
\(90\) | − | 11.3137i | − | 0.125708i | ||||||
\(91\) | 72.0000 | 0.791209 | ||||||||
\(92\) | −34.0000 | −0.369565 | ||||||||
\(93\) | 17.0000 | 0.182796 | ||||||||
\(94\) | 82.0244i | 0.872600i | ||||||||
\(95\) | − | 25.4558i | − | 0.267956i | ||||||
\(96\) | − | 5.65685i | − | 0.0589256i | ||||||
\(97\) | −121.000 | −1.24742 | −0.623711 | − | 0.781655i | \(-0.714376\pi\) | ||||
−0.623711 | + | 0.781655i | \(0.714376\pi\) | |||||||
\(98\) | 32.5269i | 0.331907i | ||||||||
\(99\) | −56.0000 | + | 67.8823i | −0.565657 | + | 0.685679i | ||||
\(100\) | 48.0000 | 0.480000 | ||||||||
\(101\) | 8.48528i | 0.0840127i | 0.999117 | + | 0.0420063i | \(0.0133750\pi\) | ||||
−0.999117 | + | 0.0420063i | \(0.986625\pi\) | |||||||
\(102\) | −36.0000 | −0.352941 | ||||||||
\(103\) | −82.0000 | −0.796117 | −0.398058 | − | 0.917360i | \(-0.630316\pi\) | ||||
−0.398058 | + | 0.917360i | \(0.630316\pi\) | |||||||
\(104\) | 24.0000 | 0.230769 | ||||||||
\(105\) | − | 8.48528i | − | 0.0808122i | ||||||
\(106\) | − | 2.82843i | − | 0.0266833i | ||||||
\(107\) | − | 76.3675i | − | 0.713715i | −0.934159 | − | 0.356858i | \(-0.883848\pi\) | ||
0.934159 | − | 0.356858i | \(-0.116152\pi\) | |||||||
\(108\) | 34.0000 | 0.314815 | ||||||||
\(109\) | − | 152.735i | − | 1.40124i | −0.713535 | − | 0.700620i | \(-0.752907\pi\) | ||
0.713535 | − | 0.700620i | \(-0.247093\pi\) | |||||||
\(110\) | 12.0000 | + | 9.89949i | 0.109091 | + | 0.0899954i | ||||
\(111\) | 47.0000 | 0.423423 | ||||||||
\(112\) | 33.9411i | 0.303046i | ||||||||
\(113\) | −1.00000 | −0.00884956 | −0.00442478 | − | 0.999990i | \(-0.501408\pi\) | ||||
−0.00442478 | + | 0.999990i | \(0.501408\pi\) | |||||||
\(114\) | 36.0000 | 0.315789 | ||||||||
\(115\) | −17.0000 | −0.147826 | ||||||||
\(116\) | − | 67.8823i | − | 0.585192i | ||||||
\(117\) | 67.8823i | 0.580190i | ||||||||
\(118\) | 77.7817i | 0.659167i | ||||||||
\(119\) | 216.000 | 1.81513 | ||||||||
\(120\) | − | 2.82843i | − | 0.0235702i | ||||||
\(121\) | −23.0000 | − | 118.794i | −0.190083 | − | 0.981768i | ||||
\(122\) | 120.000 | 0.983607 | ||||||||
\(123\) | − | 8.48528i | − | 0.0689860i | ||||||
\(124\) | −34.0000 | −0.274194 | ||||||||
\(125\) | 49.0000 | 0.392000 | ||||||||
\(126\) | −96.0000 | −0.761905 | ||||||||
\(127\) | 25.4558i | 0.200440i | 0.994965 | + | 0.100220i | \(0.0319546\pi\) | ||||
−0.994965 | + | 0.100220i | \(0.968045\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | − | 16.9706i | − | 0.131555i | ||||||
\(130\) | 12.0000 | 0.0923077 | ||||||||
\(131\) | 93.3381i | 0.712505i | 0.934390 | + | 0.356252i | \(0.115946\pi\) | ||||
−0.934390 | + | 0.356252i | \(0.884054\pi\) | |||||||
\(132\) | −14.0000 | + | 16.9706i | −0.106061 | + | 0.128565i | ||||
\(133\) | −216.000 | −1.62406 | ||||||||
\(134\) | − | 125.865i | − | 0.939291i | ||||||
\(135\) | 17.0000 | 0.125926 | ||||||||
\(136\) | 72.0000 | 0.529412 | ||||||||
\(137\) | 167.000 | 1.21898 | 0.609489 | − | 0.792794i | \(-0.291375\pi\) | ||||
0.609489 | + | 0.792794i | \(0.291375\pi\) | |||||||
\(138\) | − | 24.0416i | − | 0.174215i | ||||||
\(139\) | 93.3381i | 0.671497i | 0.941952 | + | 0.335749i | \(0.108989\pi\) | ||||
−0.941952 | + | 0.335749i | \(0.891011\pi\) | |||||||
\(140\) | 16.9706i | 0.121218i | ||||||||
\(141\) | −58.0000 | −0.411348 | ||||||||
\(142\) | 9.89949i | 0.0697148i | ||||||||
\(143\) | −72.0000 | − | 59.3970i | −0.503497 | − | 0.415363i | ||||
\(144\) | −32.0000 | −0.222222 | ||||||||
\(145\) | − | 33.9411i | − | 0.234077i | ||||||
\(146\) | −180.000 | −1.23288 | ||||||||
\(147\) | −23.0000 | −0.156463 | ||||||||
\(148\) | −94.0000 | −0.635135 | ||||||||
\(149\) | − | 161.220i | − | 1.08202i | −0.841018 | − | 0.541008i | \(-0.818043\pi\) | ||
0.841018 | − | 0.541008i | \(-0.181957\pi\) | |||||||
\(150\) | 33.9411i | 0.226274i | ||||||||
\(151\) | 288.500i | 1.91059i | 0.295649 | + | 0.955297i | \(0.404464\pi\) | ||||
−0.295649 | + | 0.955297i | \(0.595536\pi\) | |||||||
\(152\) | −72.0000 | −0.473684 | ||||||||
\(153\) | 203.647i | 1.33102i | ||||||||
\(154\) | 84.0000 | − | 101.823i | 0.545455 | − | 0.661191i | ||||
\(155\) | −17.0000 | −0.109677 | ||||||||
\(156\) | 16.9706i | 0.108786i | ||||||||
\(157\) | −1.00000 | −0.00636943 | −0.00318471 | − | 0.999995i | \(-0.501014\pi\) | ||||
−0.00318471 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(158\) | 48.0000 | 0.303797 | ||||||||
\(159\) | 2.00000 | 0.0125786 | ||||||||
\(160\) | 5.65685i | 0.0353553i | ||||||||
\(161\) | 144.250i | 0.895961i | ||||||||
\(162\) | − | 77.7817i | − | 0.480134i | ||||||
\(163\) | 110.000 | 0.674847 | 0.337423 | − | 0.941353i | \(-0.390445\pi\) | ||||
0.337423 | + | 0.941353i | \(0.390445\pi\) | |||||||
\(164\) | 16.9706i | 0.103479i | ||||||||
\(165\) | −7.00000 | + | 8.48528i | −0.0424242 | + | 0.0514259i | ||||
\(166\) | 48.0000 | 0.289157 | ||||||||
\(167\) | − | 110.309i | − | 0.660531i | −0.943888 | − | 0.330265i | \(-0.892862\pi\) | ||
0.943888 | − | 0.330265i | \(-0.107138\pi\) | |||||||
\(168\) | −24.0000 | −0.142857 | ||||||||
\(169\) | 97.0000 | 0.573964 | ||||||||
\(170\) | 36.0000 | 0.211765 | ||||||||
\(171\) | − | 203.647i | − | 1.19092i | ||||||
\(172\) | 33.9411i | 0.197332i | ||||||||
\(173\) | − | 16.9706i | − | 0.0980957i | −0.998796 | − | 0.0490479i | \(-0.984381\pi\) | ||
0.998796 | − | 0.0490479i | \(-0.0156187\pi\) | |||||||
\(174\) | 48.0000 | 0.275862 | ||||||||
\(175\) | − | 203.647i | − | 1.16370i | ||||||
\(176\) | 28.0000 | − | 33.9411i | 0.159091 | − | 0.192847i | ||||
\(177\) | −55.0000 | −0.310734 | ||||||||
\(178\) | 137.179i | 0.770667i | ||||||||
\(179\) | 209.000 | 1.16760 | 0.583799 | − | 0.811898i | \(-0.301566\pi\) | ||||
0.583799 | + | 0.811898i | \(0.301566\pi\) | |||||||
\(180\) | −16.0000 | −0.0888889 | ||||||||
\(181\) | 119.000 | 0.657459 | 0.328729 | − | 0.944424i | \(-0.393380\pi\) | ||||
0.328729 | + | 0.944424i | \(0.393380\pi\) | |||||||
\(182\) | − | 101.823i | − | 0.559469i | ||||||
\(183\) | 84.8528i | 0.463677i | ||||||||
\(184\) | 48.0833i | 0.261322i | ||||||||
\(185\) | −47.0000 | −0.254054 | ||||||||
\(186\) | − | 24.0416i | − | 0.129256i | ||||||
\(187\) | −216.000 | − | 178.191i | −1.15508 | − | 0.952893i | ||||
\(188\) | 116.000 | 0.617021 | ||||||||
\(189\) | − | 144.250i | − | 0.763226i | ||||||
\(190\) | −36.0000 | −0.189474 | ||||||||
\(191\) | −319.000 | −1.67016 | −0.835079 | − | 0.550131i | \(-0.814578\pi\) | ||||
−0.835079 | + | 0.550131i | \(0.814578\pi\) | |||||||
\(192\) | −8.00000 | −0.0416667 | ||||||||
\(193\) | 16.9706i | 0.0879304i | 0.999033 | + | 0.0439652i | \(0.0139991\pi\) | ||||
−0.999033 | + | 0.0439652i | \(0.986001\pi\) | |||||||
\(194\) | 171.120i | 0.882061i | ||||||||
\(195\) | 8.48528i | 0.0435143i | ||||||||
\(196\) | 46.0000 | 0.234694 | ||||||||
\(197\) | 101.823i | 0.516870i | 0.966029 | + | 0.258435i | \(0.0832068\pi\) | ||||
−0.966029 | + | 0.258435i | \(0.916793\pi\) | |||||||
\(198\) | 96.0000 | + | 79.1960i | 0.484848 | + | 0.399980i | ||||
\(199\) | 182.000 | 0.914573 | 0.457286 | − | 0.889319i | \(-0.348821\pi\) | ||||
0.457286 | + | 0.889319i | \(0.348821\pi\) | |||||||
\(200\) | − | 67.8823i | − | 0.339411i | ||||||
\(201\) | 89.0000 | 0.442786 | ||||||||
\(202\) | 12.0000 | 0.0594059 | ||||||||
\(203\) | −288.000 | −1.41872 | ||||||||
\(204\) | 50.9117i | 0.249567i | ||||||||
\(205\) | 8.48528i | 0.0413916i | ||||||||
\(206\) | 115.966i | 0.562939i | ||||||||
\(207\) | −136.000 | −0.657005 | ||||||||
\(208\) | − | 33.9411i | − | 0.163178i | ||||||
\(209\) | 216.000 | + | 178.191i | 1.03349 | + | 0.852588i | ||||
\(210\) | −12.0000 | −0.0571429 | ||||||||
\(211\) | 118.794i | 0.563004i | 0.959561 | + | 0.281502i | \(0.0908327\pi\) | ||||
−0.959561 | + | 0.281502i | \(0.909167\pi\) | |||||||
\(212\) | −4.00000 | −0.0188679 | ||||||||
\(213\) | −7.00000 | −0.0328638 | ||||||||
\(214\) | −108.000 | −0.504673 | ||||||||
\(215\) | 16.9706i | 0.0789328i | ||||||||
\(216\) | − | 48.0833i | − | 0.222608i | ||||||
\(217\) | 144.250i | 0.664746i | ||||||||
\(218\) | −216.000 | −0.990826 | ||||||||
\(219\) | − | 127.279i | − | 0.581184i | ||||||
\(220\) | 14.0000 | − | 16.9706i | 0.0636364 | − | 0.0771389i | ||||
\(221\) | −216.000 | −0.977376 | ||||||||
\(222\) | − | 66.4680i | − | 0.299406i | ||||||
\(223\) | −31.0000 | −0.139013 | −0.0695067 | − | 0.997581i | \(-0.522143\pi\) | ||||
−0.0695067 | + | 0.997581i | \(0.522143\pi\) | |||||||
\(224\) | 48.0000 | 0.214286 | ||||||||
\(225\) | 192.000 | 0.853333 | ||||||||
\(226\) | 1.41421i | 0.00625758i | ||||||||
\(227\) | − | 93.3381i | − | 0.411181i | −0.978638 | − | 0.205591i | \(-0.934089\pi\) | ||
0.978638 | − | 0.205591i | \(-0.0659115\pi\) | |||||||
\(228\) | − | 50.9117i | − | 0.223297i | ||||||
\(229\) | −73.0000 | −0.318777 | −0.159389 | − | 0.987216i | \(-0.550952\pi\) | ||||
−0.159389 | + | 0.987216i | \(0.550952\pi\) | |||||||
\(230\) | 24.0416i | 0.104529i | ||||||||
\(231\) | 72.0000 | + | 59.3970i | 0.311688 | + | 0.257130i | ||||
\(232\) | −96.0000 | −0.413793 | ||||||||
\(233\) | 203.647i | 0.874020i | 0.899457 | + | 0.437010i | \(0.143963\pi\) | ||||
−0.899457 | + | 0.437010i | \(0.856037\pi\) | |||||||
\(234\) | 96.0000 | 0.410256 | ||||||||
\(235\) | 58.0000 | 0.246809 | ||||||||
\(236\) | 110.000 | 0.466102 | ||||||||
\(237\) | 33.9411i | 0.143211i | ||||||||
\(238\) | − | 305.470i | − | 1.28349i | ||||||
\(239\) | − | 288.500i | − | 1.20711i | −0.797321 | − | 0.603556i | \(-0.793750\pi\) | ||
0.797321 | − | 0.603556i | \(-0.206250\pi\) | |||||||
\(240\) | −4.00000 | −0.0166667 | ||||||||
\(241\) | − | 118.794i | − | 0.492921i | −0.969153 | − | 0.246460i | \(-0.920732\pi\) | ||
0.969153 | − | 0.246460i | \(-0.0792675\pi\) | |||||||
\(242\) | −168.000 | + | 32.5269i | −0.694215 | + | 0.134409i | ||||
\(243\) | 208.000 | 0.855967 | ||||||||
\(244\) | − | 169.706i | − | 0.695515i | ||||||
\(245\) | 23.0000 | 0.0938776 | ||||||||
\(246\) | −12.0000 | −0.0487805 | ||||||||
\(247\) | 216.000 | 0.874494 | ||||||||
\(248\) | 48.0833i | 0.193884i | ||||||||
\(249\) | 33.9411i | 0.136310i | ||||||||
\(250\) | − | 69.2965i | − | 0.277186i | ||||||
\(251\) | 65.0000 | 0.258964 | 0.129482 | − | 0.991582i | \(-0.458669\pi\) | ||||
0.129482 | + | 0.991582i | \(0.458669\pi\) | |||||||
\(252\) | 135.765i | 0.538748i | ||||||||
\(253\) | 119.000 | − | 144.250i | 0.470356 | − | 0.570157i | ||||
\(254\) | 36.0000 | 0.141732 | ||||||||
\(255\) | 25.4558i | 0.0998268i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 170.000 | 0.661479 | 0.330739 | − | 0.943722i | \(-0.392702\pi\) | ||||
0.330739 | + | 0.943722i | \(0.392702\pi\) | |||||||
\(258\) | −24.0000 | −0.0930233 | ||||||||
\(259\) | 398.808i | 1.53980i | ||||||||
\(260\) | − | 16.9706i | − | 0.0652714i | ||||||
\(261\) | − | 271.529i | − | 1.04034i | ||||||
\(262\) | 132.000 | 0.503817 | ||||||||
\(263\) | 313.955i | 1.19375i | 0.802335 | + | 0.596873i | \(0.203591\pi\) | ||||
−0.802335 | + | 0.596873i | \(0.796409\pi\) | |||||||
\(264\) | 24.0000 | + | 19.7990i | 0.0909091 | + | 0.0749962i | ||||
\(265\) | −2.00000 | −0.00754717 | ||||||||
\(266\) | 305.470i | 1.14838i | ||||||||
\(267\) | −97.0000 | −0.363296 | ||||||||
\(268\) | −178.000 | −0.664179 | ||||||||
\(269\) | −430.000 | −1.59851 | −0.799257 | − | 0.600990i | \(-0.794773\pi\) | ||||
−0.799257 | + | 0.600990i | \(0.794773\pi\) | |||||||
\(270\) | − | 24.0416i | − | 0.0890431i | ||||||
\(271\) | − | 381.838i | − | 1.40900i | −0.709706 | − | 0.704498i | \(-0.751172\pi\) | ||
0.709706 | − | 0.704498i | \(-0.248828\pi\) | |||||||
\(272\) | − | 101.823i | − | 0.374351i | ||||||
\(273\) | 72.0000 | 0.263736 | ||||||||
\(274\) | − | 236.174i | − | 0.861948i | ||||||
\(275\) | −168.000 | + | 203.647i | −0.610909 | + | 0.740534i | ||||
\(276\) | −34.0000 | −0.123188 | ||||||||
\(277\) | 84.8528i | 0.306328i | 0.988201 | + | 0.153164i | \(0.0489463\pi\) | ||||
−0.988201 | + | 0.153164i | \(0.951054\pi\) | |||||||
\(278\) | 132.000 | 0.474820 | ||||||||
\(279\) | −136.000 | −0.487455 | ||||||||
\(280\) | 24.0000 | 0.0857143 | ||||||||
\(281\) | 135.765i | 0.483148i | 0.970382 | + | 0.241574i | \(0.0776636\pi\) | ||||
−0.970382 | + | 0.241574i | \(0.922336\pi\) | |||||||
\(282\) | 82.0244i | 0.290867i | ||||||||
\(283\) | 67.8823i | 0.239867i | 0.992782 | + | 0.119933i | \(0.0382681\pi\) | ||||
−0.992782 | + | 0.119933i | \(0.961732\pi\) | |||||||
\(284\) | 14.0000 | 0.0492958 | ||||||||
\(285\) | − | 25.4558i | − | 0.0893188i | ||||||
\(286\) | −84.0000 | + | 101.823i | −0.293706 | + | 0.356026i | ||||
\(287\) | 72.0000 | 0.250871 | ||||||||
\(288\) | 45.2548i | 0.157135i | ||||||||
\(289\) | −359.000 | −1.24221 | ||||||||
\(290\) | −48.0000 | −0.165517 | ||||||||
\(291\) | −121.000 | −0.415808 | ||||||||
\(292\) | 254.558i | 0.871775i | ||||||||
\(293\) | − | 517.602i | − | 1.76656i | −0.468846 | − | 0.883280i | \(-0.655330\pi\) | ||
0.468846 | − | 0.883280i | \(-0.344670\pi\) | |||||||
\(294\) | 32.5269i | 0.110636i | ||||||||
\(295\) | 55.0000 | 0.186441 | ||||||||
\(296\) | 132.936i | 0.449108i | ||||||||
\(297\) | −119.000 | + | 144.250i | −0.400673 | + | 0.485690i | ||||
\(298\) | −228.000 | −0.765101 | ||||||||
\(299\) | − | 144.250i | − | 0.482441i | ||||||
\(300\) | 48.0000 | 0.160000 | ||||||||
\(301\) | 144.000 | 0.478405 | ||||||||
\(302\) | 408.000 | 1.35099 | ||||||||
\(303\) | 8.48528i | 0.0280042i | ||||||||
\(304\) | 101.823i | 0.334945i | ||||||||
\(305\) | − | 84.8528i | − | 0.278206i | ||||||
\(306\) | 288.000 | 0.941176 | ||||||||
\(307\) | − | 25.4558i | − | 0.0829181i | −0.999140 | − | 0.0414590i | \(-0.986799\pi\) | ||
0.999140 | − | 0.0414590i | \(-0.0132006\pi\) | |||||||
\(308\) | −144.000 | − | 118.794i | −0.467532 | − | 0.385695i | ||||
\(309\) | −82.0000 | −0.265372 | ||||||||
\(310\) | 24.0416i | 0.0775536i | ||||||||
\(311\) | −154.000 | −0.495177 | −0.247588 | − | 0.968865i | \(-0.579638\pi\) | ||||
−0.247588 | + | 0.968865i | \(0.579638\pi\) | |||||||
\(312\) | 24.0000 | 0.0769231 | ||||||||
\(313\) | 95.0000 | 0.303514 | 0.151757 | − | 0.988418i | \(-0.451507\pi\) | ||||
0.151757 | + | 0.988418i | \(0.451507\pi\) | |||||||
\(314\) | 1.41421i | 0.00450386i | ||||||||
\(315\) | 67.8823i | 0.215499i | ||||||||
\(316\) | − | 67.8823i | − | 0.214817i | ||||||
\(317\) | 23.0000 | 0.0725552 | 0.0362776 | − | 0.999342i | \(-0.488450\pi\) | ||||
0.0362776 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(318\) | − | 2.82843i | − | 0.00889442i | ||||||
\(319\) | 288.000 | + | 237.588i | 0.902821 | + | 0.744790i | ||||
\(320\) | 8.00000 | 0.0250000 | ||||||||
\(321\) | − | 76.3675i | − | 0.237905i | ||||||
\(322\) | 204.000 | 0.633540 | ||||||||
\(323\) | 648.000 | 2.00619 | ||||||||
\(324\) | −110.000 | −0.339506 | ||||||||
\(325\) | 203.647i | 0.626605i | ||||||||
\(326\) | − | 155.563i | − | 0.477189i | ||||||
\(327\) | − | 152.735i | − | 0.467080i | ||||||
\(328\) | 24.0000 | 0.0731707 | ||||||||
\(329\) | − | 492.146i | − | 1.49589i | ||||||
\(330\) | 12.0000 | + | 9.89949i | 0.0363636 | + | 0.0299985i | ||||
\(331\) | 185.000 | 0.558912 | 0.279456 | − | 0.960158i | \(-0.409846\pi\) | ||||
0.279456 | + | 0.960158i | \(0.409846\pi\) | |||||||
\(332\) | − | 67.8823i | − | 0.204465i | ||||||
\(333\) | −376.000 | −1.12913 | ||||||||
\(334\) | −156.000 | −0.467066 | ||||||||
\(335\) | −89.0000 | −0.265672 | ||||||||
\(336\) | 33.9411i | 0.101015i | ||||||||
\(337\) | − | 8.48528i | − | 0.0251789i | −0.999921 | − | 0.0125894i | \(-0.995993\pi\) | ||
0.999921 | − | 0.0125894i | \(-0.00400745\pi\) | |||||||
\(338\) | − | 137.179i | − | 0.405854i | ||||||
\(339\) | −1.00000 | −0.00294985 | ||||||||
\(340\) | − | 50.9117i | − | 0.149740i | ||||||
\(341\) | 119.000 | − | 144.250i | 0.348974 | − | 0.423020i | ||||
\(342\) | −288.000 | −0.842105 | ||||||||
\(343\) | 220.617i | 0.643199i | ||||||||
\(344\) | 48.0000 | 0.139535 | ||||||||
\(345\) | −17.0000 | −0.0492754 | ||||||||
\(346\) | −24.0000 | −0.0693642 | ||||||||
\(347\) | − | 212.132i | − | 0.611332i | −0.952139 | − | 0.305666i | \(-0.901121\pi\) | ||
0.952139 | − | 0.305666i | \(-0.0988790\pi\) | |||||||
\(348\) | − | 67.8823i | − | 0.195064i | ||||||
\(349\) | 263.044i | 0.753707i | 0.926273 | + | 0.376853i | \(0.122994\pi\) | ||||
−0.926273 | + | 0.376853i | \(0.877006\pi\) | |||||||
\(350\) | −288.000 | −0.822857 | ||||||||
\(351\) | 144.250i | 0.410968i | ||||||||
\(352\) | −48.0000 | − | 39.5980i | −0.136364 | − | 0.112494i | ||||
\(353\) | 167.000 | 0.473088 | 0.236544 | − | 0.971621i | \(-0.423985\pi\) | ||||
0.236544 | + | 0.971621i | \(0.423985\pi\) | |||||||
\(354\) | 77.7817i | 0.219722i | ||||||||
\(355\) | 7.00000 | 0.0197183 | ||||||||
\(356\) | 194.000 | 0.544944 | ||||||||
\(357\) | 216.000 | 0.605042 | ||||||||
\(358\) | − | 295.571i | − | 0.825616i | ||||||
\(359\) | 636.396i | 1.77269i | 0.463024 | + | 0.886346i | \(0.346764\pi\) | ||||
−0.463024 | + | 0.886346i | \(0.653236\pi\) | |||||||
\(360\) | 22.6274i | 0.0628539i | ||||||||
\(361\) | −287.000 | −0.795014 | ||||||||
\(362\) | − | 168.291i | − | 0.464893i | ||||||
\(363\) | −23.0000 | − | 118.794i | −0.0633609 | − | 0.327256i | ||||
\(364\) | −144.000 | −0.395604 | ||||||||
\(365\) | 127.279i | 0.348710i | ||||||||
\(366\) | 120.000 | 0.327869 | ||||||||
\(367\) | −607.000 | −1.65395 | −0.826975 | − | 0.562238i | \(-0.809940\pi\) | ||||
−0.826975 | + | 0.562238i | \(0.809940\pi\) | |||||||
\(368\) | 68.0000 | 0.184783 | ||||||||
\(369\) | 67.8823i | 0.183963i | ||||||||
\(370\) | 66.4680i | 0.179643i | ||||||||
\(371\) | 16.9706i | 0.0457428i | ||||||||
\(372\) | −34.0000 | −0.0913978 | ||||||||
\(373\) | 347.897i | 0.932698i | 0.884601 | + | 0.466349i | \(0.154431\pi\) | ||||
−0.884601 | + | 0.466349i | \(0.845569\pi\) | |||||||
\(374\) | −252.000 | + | 305.470i | −0.673797 | + | 0.816765i | ||||
\(375\) | 49.0000 | 0.130667 | ||||||||
\(376\) | − | 164.049i | − | 0.436300i | ||||||
\(377\) | 288.000 | 0.763926 | ||||||||
\(378\) | −204.000 | −0.539683 | ||||||||
\(379\) | −295.000 | −0.778364 | −0.389182 | − | 0.921161i | \(-0.627242\pi\) | ||||
−0.389182 | + | 0.921161i | \(0.627242\pi\) | |||||||
\(380\) | 50.9117i | 0.133978i | ||||||||
\(381\) | 25.4558i | 0.0668132i | ||||||||
\(382\) | 451.134i | 1.18098i | ||||||||
\(383\) | 377.000 | 0.984334 | 0.492167 | − | 0.870501i | \(-0.336205\pi\) | ||||
0.492167 | + | 0.870501i | \(0.336205\pi\) | |||||||
\(384\) | 11.3137i | 0.0294628i | ||||||||
\(385\) | −72.0000 | − | 59.3970i | −0.187013 | − | 0.154278i | ||||
\(386\) | 24.0000 | 0.0621762 | ||||||||
\(387\) | 135.765i | 0.350813i | ||||||||
\(388\) | 242.000 | 0.623711 | ||||||||
\(389\) | −121.000 | −0.311054 | −0.155527 | − | 0.987832i | \(-0.549708\pi\) | ||||
−0.155527 | + | 0.987832i | \(0.549708\pi\) | |||||||
\(390\) | 12.0000 | 0.0307692 | ||||||||
\(391\) | − | 432.749i | − | 1.10678i | ||||||
\(392\) | − | 65.0538i | − | 0.165954i | ||||||
\(393\) | 93.3381i | 0.237502i | ||||||||
\(394\) | 144.000 | 0.365482 | ||||||||
\(395\) | − | 33.9411i | − | 0.0859269i | ||||||
\(396\) | 112.000 | − | 135.765i | 0.282828 | − | 0.342840i | ||||
\(397\) | 578.000 | 1.45592 | 0.727960 | − | 0.685620i | \(-0.240469\pi\) | ||||
0.727960 | + | 0.685620i | \(0.240469\pi\) | |||||||
\(398\) | − | 257.387i | − | 0.646701i | ||||||
\(399\) | −216.000 | −0.541353 | ||||||||
\(400\) | −96.0000 | −0.240000 | ||||||||
\(401\) | −550.000 | −1.37157 | −0.685786 | − | 0.727804i | \(-0.740541\pi\) | ||||
−0.685786 | + | 0.727804i | \(0.740541\pi\) | |||||||
\(402\) | − | 125.865i | − | 0.313097i | ||||||
\(403\) | − | 144.250i | − | 0.357940i | ||||||
\(404\) | − | 16.9706i | − | 0.0420063i | ||||||
\(405\) | −55.0000 | −0.135802 | ||||||||
\(406\) | 407.294i | 1.00319i | ||||||||
\(407\) | 329.000 | − | 398.808i | 0.808354 | − | 0.979873i | ||||
\(408\) | 72.0000 | 0.176471 | ||||||||
\(409\) | − | 593.970i | − | 1.45225i | −0.687563 | − | 0.726124i | \(-0.741320\pi\) | ||
0.687563 | − | 0.726124i | \(-0.258680\pi\) | |||||||
\(410\) | 12.0000 | 0.0292683 | ||||||||
\(411\) | 167.000 | 0.406326 | ||||||||
\(412\) | 164.000 | 0.398058 | ||||||||
\(413\) | − | 466.690i | − | 1.13000i | ||||||
\(414\) | 192.333i | 0.464573i | ||||||||
\(415\) | − | 33.9411i | − | 0.0817858i | ||||||
\(416\) | −48.0000 | −0.115385 | ||||||||
\(417\) | 93.3381i | 0.223832i | ||||||||
\(418\) | 252.000 | − | 305.470i | 0.602871 | − | 0.730790i | ||||
\(419\) | −370.000 | −0.883055 | −0.441527 | − | 0.897248i | \(-0.645563\pi\) | ||||
−0.441527 | + | 0.897248i | \(0.645563\pi\) | |||||||
\(420\) | 16.9706i | 0.0404061i | ||||||||
\(421\) | 338.000 | 0.802850 | 0.401425 | − | 0.915892i | \(-0.368515\pi\) | ||||
0.401425 | + | 0.915892i | \(0.368515\pi\) | |||||||
\(422\) | 168.000 | 0.398104 | ||||||||
\(423\) | 464.000 | 1.09693 | ||||||||
\(424\) | 5.65685i | 0.0133416i | ||||||||
\(425\) | 610.940i | 1.43751i | ||||||||
\(426\) | 9.89949i | 0.0232383i | ||||||||
\(427\) | −720.000 | −1.68618 | ||||||||
\(428\) | 152.735i | 0.356858i | ||||||||
\(429\) | −72.0000 | − | 59.3970i | −0.167832 | − | 0.138454i | ||||
\(430\) | 24.0000 | 0.0558140 | ||||||||
\(431\) | − | 229.103i | − | 0.531561i | −0.964034 | − | 0.265780i | \(-0.914370\pi\) | ||
0.964034 | − | 0.265780i | \(-0.0856296\pi\) | |||||||
\(432\) | −68.0000 | −0.157407 | ||||||||
\(433\) | −25.0000 | −0.0577367 | −0.0288684 | − | 0.999583i | \(-0.509190\pi\) | ||||
−0.0288684 | + | 0.999583i | \(0.509190\pi\) | |||||||
\(434\) | 204.000 | 0.470046 | ||||||||
\(435\) | − | 33.9411i | − | 0.0780256i | ||||||
\(436\) | 305.470i | 0.700620i | ||||||||
\(437\) | 432.749i | 0.990273i | ||||||||
\(438\) | −180.000 | −0.410959 | ||||||||
\(439\) | − | 373.352i | − | 0.850461i | −0.905085 | − | 0.425231i | \(-0.860193\pi\) | ||
0.905085 | − | 0.425231i | \(-0.139807\pi\) | |||||||
\(440\) | −24.0000 | − | 19.7990i | −0.0545455 | − | 0.0449977i | ||||
\(441\) | 184.000 | 0.417234 | ||||||||
\(442\) | 305.470i | 0.691109i | ||||||||
\(443\) | 257.000 | 0.580135 | 0.290068 | − | 0.957006i | \(-0.406322\pi\) | ||||
0.290068 | + | 0.957006i | \(0.406322\pi\) | |||||||
\(444\) | −94.0000 | −0.211712 | ||||||||
\(445\) | 97.0000 | 0.217978 | ||||||||
\(446\) | 43.8406i | 0.0982974i | ||||||||
\(447\) | − | 161.220i | − | 0.360672i | ||||||
\(448\) | − | 67.8823i | − | 0.151523i | ||||||
\(449\) | 47.0000 | 0.104677 | 0.0523385 | − | 0.998629i | \(-0.483333\pi\) | ||||
0.0523385 | + | 0.998629i | \(0.483333\pi\) | |||||||
\(450\) | − | 271.529i | − | 0.603398i | ||||||
\(451\) | −72.0000 | − | 59.3970i | −0.159645 | − | 0.131701i | ||||
\(452\) | 2.00000 | 0.00442478 | ||||||||
\(453\) | 288.500i | 0.636864i | ||||||||
\(454\) | −132.000 | −0.290749 | ||||||||
\(455\) | −72.0000 | −0.158242 | ||||||||
\(456\) | −72.0000 | −0.157895 | ||||||||
\(457\) | − | 271.529i | − | 0.594155i | −0.954853 | − | 0.297078i | \(-0.903988\pi\) | ||
0.954853 | − | 0.297078i | \(-0.0960120\pi\) | |||||||
\(458\) | 103.238i | 0.225410i | ||||||||
\(459\) | 432.749i | 0.942809i | ||||||||
\(460\) | 34.0000 | 0.0739130 | ||||||||
\(461\) | 492.146i | 1.06756i | 0.845623 | + | 0.533781i | \(0.179229\pi\) | ||||
−0.845623 | + | 0.533781i | \(0.820771\pi\) | |||||||
\(462\) | 84.0000 | − | 101.823i | 0.181818 | − | 0.220397i | ||||
\(463\) | −631.000 | −1.36285 | −0.681425 | − | 0.731887i | \(-0.738640\pi\) | ||||
−0.681425 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(464\) | 135.765i | 0.292596i | ||||||||
\(465\) | −17.0000 | −0.0365591 | ||||||||
\(466\) | 288.000 | 0.618026 | ||||||||
\(467\) | −367.000 | −0.785867 | −0.392934 | − | 0.919567i | \(-0.628540\pi\) | ||||
−0.392934 | + | 0.919567i | \(0.628540\pi\) | |||||||
\(468\) | − | 135.765i | − | 0.290095i | ||||||
\(469\) | 755.190i | 1.61021i | ||||||||
\(470\) | − | 82.0244i | − | 0.174520i | ||||||
\(471\) | −1.00000 | −0.00212314 | ||||||||
\(472\) | − | 155.563i | − | 0.329584i | ||||||
\(473\) | −144.000 | − | 118.794i | −0.304440 | − | 0.251150i | ||||
\(474\) | 48.0000 | 0.101266 | ||||||||
\(475\) | − | 610.940i | − | 1.28619i | ||||||
\(476\) | −432.000 | −0.907563 | ||||||||
\(477\) | −16.0000 | −0.0335430 | ||||||||
\(478\) | −408.000 | −0.853556 | ||||||||
\(479\) | 466.690i | 0.974302i | 0.873318 | + | 0.487151i | \(0.161964\pi\) | ||||
−0.873318 | + | 0.487151i | \(0.838036\pi\) | |||||||
\(480\) | 5.65685i | 0.0117851i | ||||||||
\(481\) | − | 398.808i | − | 0.829123i | ||||||
\(482\) | −168.000 | −0.348548 | ||||||||
\(483\) | 144.250i | 0.298654i | ||||||||
\(484\) | 46.0000 | + | 237.588i | 0.0950413 | + | 0.490884i | ||||
\(485\) | 121.000 | 0.249485 | ||||||||
\(486\) | − | 294.156i | − | 0.605260i | ||||||
\(487\) | −511.000 | −1.04928 | −0.524641 | − | 0.851324i | \(-0.675800\pi\) | ||||
−0.524641 | + | 0.851324i | \(0.675800\pi\) | |||||||
\(488\) | −240.000 | −0.491803 | ||||||||
\(489\) | 110.000 | 0.224949 | ||||||||
\(490\) | − | 32.5269i | − | 0.0663815i | ||||||
\(491\) | − | 33.9411i | − | 0.0691265i | −0.999403 | − | 0.0345633i | \(-0.988996\pi\) | ||
0.999403 | − | 0.0345633i | \(-0.0110040\pi\) | |||||||
\(492\) | 16.9706i | 0.0344930i | ||||||||
\(493\) | 864.000 | 1.75254 | ||||||||
\(494\) | − | 305.470i | − | 0.618361i | ||||||
\(495\) | 56.0000 | − | 67.8823i | 0.113131 | − | 0.137136i | ||||
\(496\) | 68.0000 | 0.137097 | ||||||||
\(497\) | − | 59.3970i | − | 0.119511i | ||||||
\(498\) | 48.0000 | 0.0963855 | ||||||||
\(499\) | 494.000 | 0.989980 | 0.494990 | − | 0.868899i | \(-0.335172\pi\) | ||||
0.494990 | + | 0.868899i | \(0.335172\pi\) | |||||||
\(500\) | −98.0000 | −0.196000 | ||||||||
\(501\) | − | 110.309i | − | 0.220177i | ||||||
\(502\) | − | 91.9239i | − | 0.183115i | ||||||
\(503\) | 661.852i | 1.31581i | 0.753101 | + | 0.657905i | \(0.228557\pi\) | ||||
−0.753101 | + | 0.657905i | \(0.771443\pi\) | |||||||
\(504\) | 192.000 | 0.380952 | ||||||||
\(505\) | − | 8.48528i | − | 0.0168025i | ||||||
\(506\) | −204.000 | − | 168.291i | −0.403162 | − | 0.332592i | ||||
\(507\) | 97.0000 | 0.191321 | ||||||||
\(508\) | − | 50.9117i | − | 0.100220i | ||||||
\(509\) | 503.000 | 0.988212 | 0.494106 | − | 0.869402i | \(-0.335495\pi\) | ||||
0.494106 | + | 0.869402i | \(0.335495\pi\) | |||||||
\(510\) | 36.0000 | 0.0705882 | ||||||||
\(511\) | 1080.00 | 2.11350 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | − | 432.749i | − | 0.843566i | ||||||
\(514\) | − | 240.416i | − | 0.467736i | ||||||
\(515\) | 82.0000 | 0.159223 | ||||||||
\(516\) | 33.9411i | 0.0657774i | ||||||||
\(517\) | −406.000 | + | 492.146i | −0.785300 | + | 0.951927i | ||||
\(518\) | 564.000 | 1.08880 | ||||||||
\(519\) | − | 16.9706i | − | 0.0326986i | ||||||
\(520\) | −24.0000 | −0.0461538 | ||||||||
\(521\) | −745.000 | −1.42994 | −0.714971 | − | 0.699154i | \(-0.753560\pi\) | ||||
−0.714971 | + | 0.699154i | \(0.753560\pi\) | |||||||
\(522\) | −384.000 | −0.735632 | ||||||||
\(523\) | − | 330.926i | − | 0.632746i | −0.948635 | − | 0.316373i | \(-0.897535\pi\) | ||
0.948635 | − | 0.316373i | \(-0.102465\pi\) | |||||||
\(524\) | − | 186.676i | − | 0.356252i | ||||||
\(525\) | − | 203.647i | − | 0.387899i | ||||||
\(526\) | 444.000 | 0.844106 | ||||||||
\(527\) | − | 432.749i | − | 0.821156i | ||||||
\(528\) | 28.0000 | − | 33.9411i | 0.0530303 | − | 0.0642824i | ||||
\(529\) | −240.000 | −0.453686 | ||||||||
\(530\) | 2.82843i | 0.00533665i | ||||||||
\(531\) | 440.000 | 0.828625 | ||||||||
\(532\) | 432.000 | 0.812030 | ||||||||
\(533\) | −72.0000 | −0.135084 | ||||||||
\(534\) | 137.179i | 0.256889i | ||||||||
\(535\) | 76.3675i | 0.142743i | ||||||||
\(536\) | 251.730i | 0.469646i | ||||||||
\(537\) | 209.000 | 0.389199 | ||||||||
\(538\) | 608.112i | 1.13032i | ||||||||
\(539\) | −161.000 | + | 195.161i | −0.298701 | + | 0.362081i | ||||
\(540\) | −34.0000 | −0.0629630 | ||||||||
\(541\) | 687.308i | 1.27044i | 0.772331 | + | 0.635220i | \(0.219090\pi\) | ||||
−0.772331 | + | 0.635220i | \(0.780910\pi\) | |||||||
\(542\) | −540.000 | −0.996310 | ||||||||
\(543\) | 119.000 | 0.219153 | ||||||||
\(544\) | −144.000 | −0.264706 | ||||||||
\(545\) | 152.735i | 0.280248i | ||||||||
\(546\) | − | 101.823i | − | 0.186490i | ||||||
\(547\) | − | 831.558i | − | 1.52021i | −0.649797 | − | 0.760107i | \(-0.725146\pi\) | ||
0.649797 | − | 0.760107i | \(-0.274854\pi\) | |||||||
\(548\) | −334.000 | −0.609489 | ||||||||
\(549\) | − | 678.823i | − | 1.23647i | ||||||
\(550\) | 288.000 | + | 237.588i | 0.523636 | + | 0.431978i | ||||
\(551\) | −864.000 | −1.56806 | ||||||||
\(552\) | 48.0833i | 0.0871074i | ||||||||
\(553\) | −288.000 | −0.520796 | ||||||||
\(554\) | 120.000 | 0.216606 | ||||||||
\(555\) | −47.0000 | −0.0846847 | ||||||||
\(556\) | − | 186.676i | − | 0.335749i | ||||||
\(557\) | − | 636.396i | − | 1.14254i | −0.820761 | − | 0.571271i | \(-0.806450\pi\) | ||
0.820761 | − | 0.571271i | \(-0.193550\pi\) | |||||||
\(558\) | 192.333i | 0.344683i | ||||||||
\(559\) | −144.000 | −0.257603 | ||||||||
\(560\) | − | 33.9411i | − | 0.0606092i | ||||||
\(561\) | −216.000 | − | 178.191i | −0.385027 | − | 0.317631i | ||||
\(562\) | 192.000 | 0.341637 | ||||||||
\(563\) | 780.646i | 1.38658i | 0.720658 | + | 0.693291i | \(0.243840\pi\) | ||||
−0.720658 | + | 0.693291i | \(0.756160\pi\) | |||||||
\(564\) | 116.000 | 0.205674 | ||||||||
\(565\) | 1.00000 | 0.00176991 | ||||||||
\(566\) | 96.0000 | 0.169611 | ||||||||
\(567\) | 466.690i | 0.823087i | ||||||||
\(568\) | − | 19.7990i | − | 0.0348574i | ||||||
\(569\) | − | 576.999i | − | 1.01406i | −0.861929 | − | 0.507029i | \(-0.830744\pi\) | ||
0.861929 | − | 0.507029i | \(-0.169256\pi\) | |||||||
\(570\) | −36.0000 | −0.0631579 | ||||||||
\(571\) | 627.911i | 1.09967i | 0.835274 | + | 0.549834i | \(0.185309\pi\) | ||||
−0.835274 | + | 0.549834i | \(0.814691\pi\) | |||||||
\(572\) | 144.000 | + | 118.794i | 0.251748 | + | 0.207682i | ||||
\(573\) | −319.000 | −0.556719 | ||||||||
\(574\) | − | 101.823i | − | 0.177393i | ||||||
\(575\) | −408.000 | −0.709565 | ||||||||
\(576\) | 64.0000 | 0.111111 | ||||||||
\(577\) | −385.000 | −0.667244 | −0.333622 | − | 0.942707i | \(-0.608271\pi\) | ||||
−0.333622 | + | 0.942707i | \(0.608271\pi\) | |||||||
\(578\) | 507.703i | 0.878378i | ||||||||
\(579\) | 16.9706i | 0.0293101i | ||||||||
\(580\) | 67.8823i | 0.117038i | ||||||||
\(581\) | −288.000 | −0.495697 | ||||||||
\(582\) | 171.120i | 0.294020i | ||||||||
\(583\) | 14.0000 | − | 16.9706i | 0.0240137 | − | 0.0291090i | ||||
\(584\) | 360.000 | 0.616438 | ||||||||
\(585\) | − | 67.8823i | − | 0.116038i | ||||||
\(586\) | −732.000 | −1.24915 | ||||||||
\(587\) | 806.000 | 1.37308 | 0.686542 | − | 0.727090i | \(-0.259128\pi\) | ||||
0.686542 | + | 0.727090i | \(0.259128\pi\) | |||||||
\(588\) | 46.0000 | 0.0782313 | ||||||||
\(589\) | 432.749i | 0.734719i | ||||||||
\(590\) | − | 77.7817i | − | 0.131833i | ||||||
\(591\) | 101.823i | 0.172290i | ||||||||
\(592\) | 188.000 | 0.317568 | ||||||||
\(593\) | 152.735i | 0.257563i | 0.991673 | + | 0.128782i | \(0.0411066\pi\) | ||||
−0.991673 | + | 0.128782i | \(0.958893\pi\) | |||||||
\(594\) | 204.000 | + | 168.291i | 0.343434 | + | 0.283319i | ||||
\(595\) | −216.000 | −0.363025 | ||||||||
\(596\) | 322.441i | 0.541008i | ||||||||
\(597\) | 182.000 | 0.304858 | ||||||||
\(598\) | −204.000 | −0.341137 | ||||||||
\(599\) | 998.000 | 1.66611 | 0.833055 | − | 0.553190i | \(-0.186590\pi\) | ||||
0.833055 | + | 0.553190i | \(0.186590\pi\) | |||||||
\(600\) | − | 67.8823i | − | 0.113137i | ||||||
\(601\) | − | 755.190i | − | 1.25656i | −0.777989 | − | 0.628278i | \(-0.783760\pi\) | ||
0.777989 | − | 0.628278i | \(-0.216240\pi\) | |||||||
\(602\) | − | 203.647i | − | 0.338284i | ||||||
\(603\) | −712.000 | −1.18076 | ||||||||
\(604\) | − | 576.999i | − | 0.955297i | ||||||
\(605\) | 23.0000 | + | 118.794i | 0.0380165 | + | 0.196354i | ||||
\(606\) | 12.0000 | 0.0198020 | ||||||||
\(607\) | 373.352i | 0.615078i | 0.951535 | + | 0.307539i | \(0.0995055\pi\) | ||||
−0.951535 | + | 0.307539i | \(0.900495\pi\) | |||||||
\(608\) | 144.000 | 0.236842 | ||||||||
\(609\) | −288.000 | −0.472906 | ||||||||
\(610\) | −120.000 | −0.196721 | ||||||||
\(611\) | 492.146i | 0.805477i | ||||||||
\(612\) | − | 407.294i | − | 0.665512i | ||||||
\(613\) | − | 356.382i | − | 0.581373i | −0.956818 | − | 0.290687i | \(-0.906116\pi\) | ||
0.956818 | − | 0.290687i | \(-0.0938837\pi\) | |||||||
\(614\) | −36.0000 | −0.0586319 | ||||||||
\(615\) | 8.48528i | 0.0137972i | ||||||||
\(616\) | −168.000 | + | 203.647i | −0.272727 | + | 0.330595i | ||||
\(617\) | 314.000 | 0.508914 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(618\) | 115.966i | 0.187646i | ||||||||
\(619\) | 1193.00 | 1.92730 | 0.963651 | − | 0.267164i | \(-0.0860866\pi\) | ||||
0.963651 | + | 0.267164i | \(0.0860866\pi\) | |||||||
\(620\) | 34.0000 | 0.0548387 | ||||||||
\(621\) | −289.000 | −0.465378 | ||||||||
\(622\) | 217.789i | 0.350143i | ||||||||
\(623\) | − | 823.072i | − | 1.32114i | ||||||
\(624\) | − | 33.9411i | − | 0.0543928i | ||||||
\(625\) | 551.000 | 0.881600 | ||||||||
\(626\) | − | 134.350i | − | 0.214617i | ||||||
\(627\) | 216.000 | + | 178.191i | 0.344498 | + | 0.284196i | ||||
\(628\) | 2.00000 | 0.00318471 | ||||||||
\(629\) | − | 1196.42i | − | 1.90211i | ||||||
\(630\) | 96.0000 | 0.152381 | ||||||||
\(631\) | −439.000 | −0.695721 | −0.347861 | − | 0.937546i | \(-0.613092\pi\) | ||||
−0.347861 | + | 0.937546i | \(0.613092\pi\) | |||||||
\(632\) | −96.0000 | −0.151899 | ||||||||
\(633\) | 118.794i | 0.187668i | ||||||||
\(634\) | − | 32.5269i | − | 0.0513043i | ||||||
\(635\) | − | 25.4558i | − | 0.0400879i | ||||||
\(636\) | −4.00000 | −0.00628931 | ||||||||
\(637\) | 195.161i | 0.306376i | ||||||||
\(638\) | 336.000 | − | 407.294i | 0.526646 | − | 0.638391i | ||||
\(639\) | 56.0000 | 0.0876369 | ||||||||
\(640\) | − | 11.3137i | − | 0.0176777i | ||||||
\(641\) | 671.000 | 1.04680 | 0.523401 | − | 0.852087i | \(-0.324663\pi\) | ||||
0.523401 | + | 0.852087i | \(0.324663\pi\) | |||||||
\(642\) | −108.000 | −0.168224 | ||||||||
\(643\) | −487.000 | −0.757387 | −0.378694 | − | 0.925522i | \(-0.623627\pi\) | ||||
−0.378694 | + | 0.925522i | \(0.623627\pi\) | |||||||
\(644\) | − | 288.500i | − | 0.447981i | ||||||
\(645\) | 16.9706i | 0.0263109i | ||||||||
\(646\) | − | 916.410i | − | 1.41859i | ||||||
\(647\) | 569.000 | 0.879444 | 0.439722 | − | 0.898134i | \(-0.355077\pi\) | ||||
0.439722 | + | 0.898134i | \(0.355077\pi\) | |||||||
\(648\) | 155.563i | 0.240067i | ||||||||
\(649\) | −385.000 | + | 466.690i | −0.593220 | + | 0.719092i | ||||
\(650\) | 288.000 | 0.443077 | ||||||||
\(651\) | 144.250i | 0.221582i | ||||||||
\(652\) | −220.000 | −0.337423 | ||||||||
\(653\) | −1081.00 | −1.65544 | −0.827718 | − | 0.561144i | \(-0.810361\pi\) | ||||
−0.827718 | + | 0.561144i | \(0.810361\pi\) | |||||||
\(654\) | −216.000 | −0.330275 | ||||||||
\(655\) | − | 93.3381i | − | 0.142501i | ||||||
\(656\) | − | 33.9411i | − | 0.0517395i | ||||||
\(657\) | 1018.23i | 1.54982i | ||||||||
\(658\) | −696.000 | −1.05775 | ||||||||
\(659\) | − | 780.646i | − | 1.18459i | −0.805721 | − | 0.592296i | \(-0.798222\pi\) | ||
0.805721 | − | 0.592296i | \(-0.201778\pi\) | |||||||
\(660\) | 14.0000 | − | 16.9706i | 0.0212121 | − | 0.0257130i | ||||
\(661\) | 1007.00 | 1.52345 | 0.761725 | − | 0.647901i | \(-0.224353\pi\) | ||||
0.761725 | + | 0.647901i | \(0.224353\pi\) | |||||||
\(662\) | − | 261.630i | − | 0.395211i | ||||||
\(663\) | −216.000 | −0.325792 | ||||||||
\(664\) | −96.0000 | −0.144578 | ||||||||
\(665\) | 216.000 | 0.324812 | ||||||||
\(666\) | 531.744i | 0.798415i | ||||||||
\(667\) | 576.999i | 0.865066i | ||||||||
\(668\) | 220.617i | 0.330265i | ||||||||
\(669\) | −31.0000 | −0.0463378 | ||||||||
\(670\) | 125.865i | 0.187858i | ||||||||
\(671\) | 720.000 | + | 593.970i | 1.07303 | + | 0.885201i | ||||
\(672\) | 48.0000 | 0.0714286 | ||||||||
\(673\) | 644.881i | 0.958219i | 0.877755 | + | 0.479109i | \(0.159040\pi\) | ||||
−0.877755 | + | 0.479109i | \(0.840960\pi\) | |||||||
\(674\) | −12.0000 | −0.0178042 | ||||||||
\(675\) | 408.000 | 0.604444 | ||||||||
\(676\) | −194.000 | −0.286982 | ||||||||
\(677\) | 873.984i | 1.29097i | 0.763775 | + | 0.645483i | \(0.223344\pi\) | ||||
−0.763775 | + | 0.645483i | \(0.776656\pi\) | |||||||
\(678\) | 1.41421i | 0.00208586i | ||||||||
\(679\) | − | 1026.72i | − | 1.51210i | ||||||
\(680\) | −72.0000 | −0.105882 | ||||||||
\(681\) | − | 93.3381i | − | 0.137060i | ||||||
\(682\) | −204.000 | − | 168.291i | −0.299120 | − | 0.246762i | ||||
\(683\) | −610.000 | −0.893119 | −0.446559 | − | 0.894754i | \(-0.647351\pi\) | ||||
−0.446559 | + | 0.894754i | \(0.647351\pi\) | |||||||
\(684\) | 407.294i | 0.595458i | ||||||||
\(685\) | −167.000 | −0.243796 | ||||||||
\(686\) | 312.000 | 0.454810 | ||||||||
\(687\) | −73.0000 | −0.106259 | ||||||||
\(688\) | − | 67.8823i | − | 0.0986661i | ||||||
\(689\) | − | 16.9706i | − | 0.0246307i | ||||||
\(690\) | 24.0416i | 0.0348429i | ||||||||
\(691\) | −1255.00 | −1.81621 | −0.908104 | − | 0.418744i | \(-0.862470\pi\) | ||||
−0.908104 | + | 0.418744i | \(0.862470\pi\) | |||||||
\(692\) | 33.9411i | 0.0490479i | ||||||||
\(693\) | −576.000 | − | 475.176i | −0.831169 | − | 0.685679i | ||||
\(694\) | −300.000 | −0.432277 | ||||||||
\(695\) | − | 93.3381i | − | 0.134299i | ||||||
\(696\) | −96.0000 | −0.137931 | ||||||||
\(697\) | −216.000 | −0.309900 | ||||||||
\(698\) | 372.000 | 0.532951 | ||||||||
\(699\) | 203.647i | 0.291340i | ||||||||
\(700\) | 407.294i | 0.581848i | ||||||||
\(701\) | 76.3675i | 0.108941i | 0.998515 | + | 0.0544704i | \(0.0173471\pi\) | ||||
−0.998515 | + | 0.0544704i | \(0.982653\pi\) | |||||||
\(702\) | 204.000 | 0.290598 | ||||||||
\(703\) | 1196.42i | 1.70188i | ||||||||
\(704\) | −56.0000 | + | 67.8823i | −0.0795455 | + | 0.0964237i | ||||
\(705\) | 58.0000 | 0.0822695 | ||||||||
\(706\) | − | 236.174i | − | 0.334524i | ||||||
\(707\) | −72.0000 | −0.101839 | ||||||||
\(708\) | 110.000 | 0.155367 | ||||||||
\(709\) | 455.000 | 0.641749 | 0.320874 | − | 0.947122i | \(-0.396023\pi\) | ||||
0.320874 | + | 0.947122i | \(0.396023\pi\) | |||||||
\(710\) | − | 9.89949i | − | 0.0139430i | ||||||
\(711\) | − | 271.529i | − | 0.381897i | ||||||
\(712\) | − | 274.357i | − | 0.385333i | ||||||
\(713\) | 289.000 | 0.405330 | ||||||||
\(714\) | − | 305.470i | − | 0.427829i | ||||||
\(715\) | 72.0000 | + | 59.3970i | 0.100699 | + | 0.0830727i | ||||
\(716\) | −418.000 | −0.583799 | ||||||||
\(717\) | − | 288.500i | − | 0.402370i | ||||||
\(718\) | 900.000 | 1.25348 | ||||||||
\(719\) | −223.000 | −0.310153 | −0.155076 | − | 0.987902i | \(-0.549562\pi\) | ||||
−0.155076 | + | 0.987902i | \(0.549562\pi\) | |||||||
\(720\) | 32.0000 | 0.0444444 | ||||||||
\(721\) | − | 695.793i | − | 0.965039i | ||||||
\(722\) | 405.879i | 0.562160i | ||||||||
\(723\) | − | 118.794i | − | 0.164307i | ||||||
\(724\) | −238.000 | −0.328729 | ||||||||
\(725\) | − | 814.587i | − | 1.12357i | ||||||
\(726\) | −168.000 | + | 32.5269i | −0.231405 | + | 0.0448029i | ||||
\(727\) | −535.000 | −0.735901 | −0.367950 | − | 0.929845i | \(-0.619940\pi\) | ||||
−0.367950 | + | 0.929845i | \(0.619940\pi\) | |||||||
\(728\) | 203.647i | 0.279735i | ||||||||
\(729\) | −287.000 | −0.393690 | ||||||||
\(730\) | 180.000 | 0.246575 | ||||||||
\(731\) | −432.000 | −0.590971 | ||||||||
\(732\) | − | 169.706i | − | 0.231838i | ||||||
\(733\) | 627.911i | 0.856631i | 0.903629 | + | 0.428316i | \(0.140893\pi\) | ||||
−0.903629 | + | 0.428316i | \(0.859107\pi\) | |||||||
\(734\) | 858.428i | 1.16952i | ||||||||
\(735\) | 23.0000 | 0.0312925 | ||||||||
\(736\) | − | 96.1665i | − | 0.130661i | ||||||
\(737\) | 623.000 | − | 755.190i | 0.845319 | − | 1.02468i | ||||
\(738\) | 96.0000 | 0.130081 | ||||||||
\(739\) | − | 865.499i | − | 1.17118i | −0.810609 | − | 0.585588i | \(-0.800864\pi\) | ||
0.810609 | − | 0.585588i | \(-0.199136\pi\) | |||||||
\(740\) | 94.0000 | 0.127027 | ||||||||
\(741\) | 216.000 | 0.291498 | ||||||||
\(742\) | 24.0000 | 0.0323450 | ||||||||
\(743\) | − | 1154.00i | − | 1.55316i | −0.630018 | − | 0.776580i | \(-0.716953\pi\) | ||
0.630018 | − | 0.776580i | \(-0.283047\pi\) | |||||||
\(744\) | 48.0833i | 0.0646280i | ||||||||
\(745\) | 161.220i | 0.216403i | ||||||||
\(746\) | 492.000 | 0.659517 | ||||||||
\(747\) | − | 271.529i | − | 0.363493i | ||||||
\(748\) | 432.000 | + | 356.382i | 0.577540 | + | 0.476446i | ||||
\(749\) | 648.000 | 0.865154 | ||||||||
\(750\) | − | 69.2965i | − | 0.0923953i | ||||||
\(751\) | −55.0000 | −0.0732357 | −0.0366178 | − | 0.999329i | \(-0.511658\pi\) | ||||
−0.0366178 | + | 0.999329i | \(0.511658\pi\) | |||||||
\(752\) | −232.000 | −0.308511 | ||||||||
\(753\) | 65.0000 | 0.0863214 | ||||||||
\(754\) | − | 407.294i | − | 0.540177i | ||||||
\(755\) | − | 288.500i | − | 0.382119i | ||||||
\(756\) | 288.500i | 0.381613i | ||||||||
\(757\) | 2.00000 | 0.00264201 | 0.00132100 | − | 0.999999i | \(-0.499580\pi\) | ||||
0.00132100 | + | 0.999999i | \(0.499580\pi\) | |||||||
\(758\) | 417.193i | 0.550387i | ||||||||
\(759\) | 119.000 | − | 144.250i | 0.156785 | − | 0.190052i | ||||
\(760\) | 72.0000 | 0.0947368 | ||||||||
\(761\) | 1264.31i | 1.66138i | 0.556738 | + | 0.830688i | \(0.312053\pi\) | ||||
−0.556738 | + | 0.830688i | \(0.687947\pi\) | |||||||
\(762\) | 36.0000 | 0.0472441 | ||||||||
\(763\) | 1296.00 | 1.69856 | ||||||||
\(764\) | 638.000 | 0.835079 | ||||||||
\(765\) | − | 203.647i | − | 0.266205i | ||||||
\(766\) | − | 533.159i | − | 0.696029i | ||||||
\(767\) | 466.690i | 0.608462i | ||||||||
\(768\) | 16.0000 | 0.0208333 | ||||||||
\(769\) | 602.455i | 0.783426i | 0.920087 | + | 0.391713i | \(0.128117\pi\) | ||||
−0.920087 | + | 0.391713i | \(0.871883\pi\) | |||||||
\(770\) | −84.0000 | + | 101.823i | −0.109091 | + | 0.132238i | ||||
\(771\) | 170.000 | 0.220493 | ||||||||
\(772\) | − | 33.9411i | − | 0.0439652i | ||||||
\(773\) | −1222.00 | −1.58085 | −0.790427 | − | 0.612556i | \(-0.790141\pi\) | ||||
−0.790427 | + | 0.612556i | \(0.790141\pi\) | |||||||
\(774\) | 192.000 | 0.248062 | ||||||||
\(775\) | −408.000 | −0.526452 | ||||||||
\(776\) | − | 342.240i | − | 0.441031i | ||||||
\(777\) | 398.808i | 0.513267i | ||||||||
\(778\) | 171.120i | 0.219948i | ||||||||
\(779\) | 216.000 | 0.277279 | ||||||||
\(780\) | − | 16.9706i | − | 0.0217571i | ||||||
\(781\) | −49.0000 | + | 59.3970i | −0.0627401 | + | 0.0760525i | ||||
\(782\) | −612.000 | −0.782609 | ||||||||
\(783\) | − | 576.999i | − | 0.736908i | ||||||
\(784\) | −92.0000 | −0.117347 | ||||||||
\(785\) | 1.00000 | 0.00127389 | ||||||||
\(786\) | 132.000 | 0.167939 | ||||||||
\(787\) | − | 899.440i | − | 1.14287i | −0.820647 | − | 0.571436i | \(-0.806387\pi\) | ||
0.820647 | − | 0.571436i | \(-0.193613\pi\) | |||||||
\(788\) | − | 203.647i | − | 0.258435i | ||||||
\(789\) | 313.955i | 0.397916i | ||||||||
\(790\) | −48.0000 | −0.0607595 | ||||||||
\(791\) | − | 8.48528i | − | 0.0107273i | ||||||
\(792\) | −192.000 | − | 158.392i | −0.242424 | − | 0.199990i | ||||
\(793\) | 720.000 | 0.907945 | ||||||||
\(794\) | − | 817.415i | − | 1.02949i | ||||||
\(795\) | −2.00000 | −0.00251572 | ||||||||
\(796\) | −364.000 | −0.457286 | ||||||||
\(797\) | −289.000 | −0.362610 | −0.181305 | − | 0.983427i | \(-0.558032\pi\) | ||||
−0.181305 | + | 0.983427i | \(0.558032\pi\) | |||||||
\(798\) | 305.470i | 0.382795i | ||||||||
\(799\) | 1476.44i | 1.84786i | ||||||||
\(800\) | 135.765i | 0.169706i | ||||||||
\(801\) | 776.000 | 0.968789 | ||||||||
\(802\) | 777.817i | 0.969847i | ||||||||
\(803\) | −1080.00 | − | 890.955i | −1.34496 | − | 1.10953i | ||||
\(804\) | −178.000 | −0.221393 | ||||||||
\(805\) | − | 144.250i | − | 0.179192i | ||||||
\(806\) | −204.000 | −0.253102 | ||||||||
\(807\) | −430.000 | −0.532838 | ||||||||
\(808\) | −24.0000 | −0.0297030 | ||||||||
\(809\) | 229.103i | 0.283192i | 0.989925 | + | 0.141596i | \(0.0452234\pi\) | ||||
−0.989925 | + | 0.141596i | \(0.954777\pi\) | |||||||
\(810\) | 77.7817i | 0.0960268i | ||||||||
\(811\) | 763.675i | 0.941647i | 0.882228 | + | 0.470823i | \(0.156043\pi\) | ||||
−0.882228 | + | 0.470823i | \(0.843957\pi\) | |||||||
\(812\) | 576.000 | 0.709360 | ||||||||
\(813\) | − | 381.838i | − | 0.469665i | ||||||
\(814\) | −564.000 | − | 465.276i | −0.692875 | − | 0.571592i | ||||
\(815\) | −110.000 | −0.134969 | ||||||||
\(816\) | − | 101.823i | − | 0.124784i | ||||||
\(817\) | 432.000 | 0.528764 | ||||||||
\(818\) | −840.000 | −1.02689 | ||||||||
\(819\) | −576.000 | −0.703297 | ||||||||
\(820\) | − | 16.9706i | − | 0.0206958i | ||||||
\(821\) | 593.970i | 0.723471i | 0.932281 | + | 0.361736i | \(0.117816\pi\) | ||||
−0.932281 | + | 0.361736i | \(0.882184\pi\) | |||||||
\(822\) | − | 236.174i | − | 0.287316i | ||||||
\(823\) | 305.000 | 0.370595 | 0.185298 | − | 0.982682i | \(-0.440675\pi\) | ||||
0.185298 | + | 0.982682i | \(0.440675\pi\) | |||||||
\(824\) | − | 231.931i | − | 0.281470i | ||||||
\(825\) | −168.000 | + | 203.647i | −0.203636 | + | 0.246845i | ||||
\(826\) | −660.000 | −0.799031 | ||||||||
\(827\) | 585.484i | 0.707962i | 0.935253 | + | 0.353981i | \(0.115172\pi\) | ||||
−0.935253 | + | 0.353981i | \(0.884828\pi\) | |||||||
\(828\) | 272.000 | 0.328502 | ||||||||
\(829\) | 119.000 | 0.143546 | 0.0717732 | − | 0.997421i | \(-0.477134\pi\) | ||||
0.0717732 | + | 0.997421i | \(0.477134\pi\) | |||||||
\(830\) | −48.0000 | −0.0578313 | ||||||||
\(831\) | 84.8528i | 0.102109i | ||||||||
\(832\) | 67.8823i | 0.0815892i | ||||||||
\(833\) | 585.484i | 0.702862i | ||||||||
\(834\) | 132.000 | 0.158273 | ||||||||
\(835\) | 110.309i | 0.132106i | ||||||||
\(836\) | −432.000 | − | 356.382i | −0.516746 | − | 0.426294i | ||||
\(837\) | −289.000 | −0.345281 | ||||||||
\(838\) | 523.259i | 0.624414i | ||||||||
\(839\) | −1615.00 | −1.92491 | −0.962455 | − | 0.271440i | \(-0.912500\pi\) | ||||
−0.962455 | + | 0.271440i | \(0.912500\pi\) | |||||||
\(840\) | 24.0000 | 0.0285714 | ||||||||
\(841\) | −311.000 | −0.369798 | ||||||||
\(842\) | − | 478.004i | − | 0.567701i | ||||||
\(843\) | 135.765i | 0.161049i | ||||||||
\(844\) | − | 237.588i | − | 0.281502i | ||||||
\(845\) | −97.0000 | −0.114793 | ||||||||
\(846\) | − | 656.195i | − | 0.775644i | ||||||
\(847\) | 1008.00 | − | 195.161i | 1.19008 | − | 0.230415i | ||||
\(848\) | 8.00000 | 0.00943396 | ||||||||
\(849\) | 67.8823i | 0.0799555i | ||||||||
\(850\) | 864.000 | 1.01647 | ||||||||
\(851\) | 799.000 | 0.938895 | ||||||||
\(852\) | 14.0000 | 0.0164319 | ||||||||
\(853\) | − | 1086.12i | − | 1.27329i | −0.771157 | − | 0.636645i | \(-0.780322\pi\) | ||
0.771157 | − | 0.636645i | \(-0.219678\pi\) | |||||||
\(854\) | 1018.23i | 1.19231i | ||||||||
\(855\) | 203.647i | 0.238183i | ||||||||
\(856\) | 216.000 | 0.252336 | ||||||||
\(857\) | 1001.26i | 1.16834i | 0.811633 | + | 0.584168i | \(0.198579\pi\) | ||||
−0.811633 | + | 0.584168i | \(0.801421\pi\) | |||||||
\(858\) | −84.0000 | + | 101.823i | −0.0979021 | + | 0.118675i | ||||
\(859\) | 593.000 | 0.690338 | 0.345169 | − | 0.938541i | \(-0.387822\pi\) | ||||
0.345169 | + | 0.938541i | \(0.387822\pi\) | |||||||
\(860\) | − | 33.9411i | − | 0.0394664i | ||||||
\(861\) | 72.0000 | 0.0836237 | ||||||||
\(862\) | −324.000 | −0.375870 | ||||||||
\(863\) | 1190.00 | 1.37891 | 0.689455 | − | 0.724328i | \(-0.257850\pi\) | ||||
0.689455 | + | 0.724328i | \(0.257850\pi\) | |||||||
\(864\) | 96.1665i | 0.111304i | ||||||||
\(865\) | 16.9706i | 0.0196191i | ||||||||
\(866\) | 35.3553i | 0.0408260i | ||||||||
\(867\) | −359.000 | −0.414072 | ||||||||
\(868\) | − | 288.500i | − | 0.332373i | ||||||
\(869\) | 288.000 | + | 237.588i | 0.331415 | + | 0.273404i | ||||
\(870\) | −48.0000 | −0.0551724 | ||||||||
\(871\) | − | 755.190i | − | 0.867038i | ||||||
\(872\) | 432.000 | 0.495413 | ||||||||
\(873\) | 968.000 | 1.10882 | ||||||||
\(874\) | 612.000 | 0.700229 | ||||||||
\(875\) | 415.779i | 0.475176i | ||||||||
\(876\) | 254.558i | 0.290592i | ||||||||
\(877\) | − | 924.896i | − | 1.05461i | −0.849675 | − | 0.527307i | \(-0.823202\pi\) | ||
0.849675 | − | 0.527307i | \(-0.176798\pi\) | |||||||
\(878\) | −528.000 | −0.601367 | ||||||||
\(879\) | − | 517.602i | − | 0.588853i | ||||||
\(880\) | −28.0000 | + | 33.9411i | −0.0318182 | + | 0.0385695i | ||||
\(881\) | 263.000 | 0.298524 | 0.149262 | − | 0.988798i | \(-0.452310\pi\) | ||||
0.149262 | + | 0.988798i | \(0.452310\pi\) | |||||||
\(882\) | − | 260.215i | − | 0.295029i | ||||||
\(883\) | −394.000 | −0.446206 | −0.223103 | − | 0.974795i | \(-0.571619\pi\) | ||||
−0.223103 | + | 0.974795i | \(0.571619\pi\) | |||||||
\(884\) | 432.000 | 0.488688 | ||||||||
\(885\) | 55.0000 | 0.0621469 | ||||||||
\(886\) | − | 363.453i | − | 0.410218i | ||||||
\(887\) | 16.9706i | 0.0191325i | 0.999954 | + | 0.00956627i | \(0.00304508\pi\) | ||||
−0.999954 | + | 0.00956627i | \(0.996955\pi\) | |||||||
\(888\) | 132.936i | 0.149703i | ||||||||
\(889\) | −216.000 | −0.242970 | ||||||||
\(890\) | − | 137.179i | − | 0.154133i | ||||||
\(891\) | 385.000 | − | 466.690i | 0.432099 | − | 0.523783i | ||||
\(892\) | 62.0000 | 0.0695067 | ||||||||
\(893\) | − | 1476.44i | − | 1.65335i | ||||||
\(894\) | −228.000 | −0.255034 | ||||||||
\(895\) | −209.000 | −0.233520 | ||||||||
\(896\) | −96.0000 | −0.107143 | ||||||||
\(897\) | − | 144.250i | − | 0.160814i | ||||||
\(898\) | − | 66.4680i | − | 0.0740179i | ||||||
\(899\) | 576.999i | 0.641823i | ||||||||
\(900\) | −384.000 | −0.426667 | ||||||||
\(901\) | − | 50.9117i | − | 0.0565058i | ||||||
\(902\) | −84.0000 | + | 101.823i | −0.0931264 | + | 0.112886i | ||||
\(903\) | 144.000 | 0.159468 | ||||||||
\(904\) | − | 2.82843i | − | 0.00312879i | ||||||
\(905\) | −119.000 | −0.131492 | ||||||||
\(906\) | 408.000 | 0.450331 | ||||||||
\(907\) | −418.000 | −0.460860 | −0.230430 | − | 0.973089i | \(-0.574013\pi\) | ||||
−0.230430 | + | 0.973089i | \(0.574013\pi\) | |||||||
\(908\) | 186.676i | 0.205591i | ||||||||
\(909\) | − | 67.8823i | − | 0.0746779i | ||||||
\(910\) | 101.823i | 0.111894i | ||||||||
\(911\) | −490.000 | −0.537870 | −0.268935 | − | 0.963158i | \(-0.586672\pi\) | ||||
−0.268935 | + | 0.963158i | \(0.586672\pi\) | |||||||
\(912\) | 101.823i | 0.111648i | ||||||||
\(913\) | 288.000 | + | 237.588i | 0.315444 | + | 0.260228i | ||||
\(914\) | −384.000 | −0.420131 | ||||||||
\(915\) | − | 84.8528i | − | 0.0927353i | ||||||
\(916\) | 146.000 | 0.159389 | ||||||||
\(917\) | −792.000 | −0.863686 | ||||||||
\(918\) | 612.000 | 0.666667 | ||||||||
\(919\) | 610.940i | 0.664788i | 0.943141 | + | 0.332394i | \(0.107856\pi\) | ||||
−0.943141 | + | 0.332394i | \(0.892144\pi\) | |||||||
\(920\) | − | 48.0833i | − | 0.0522644i | ||||||
\(921\) | − | 25.4558i | − | 0.0276394i | ||||||
\(922\) | 696.000 | 0.754881 | ||||||||
\(923\) | 59.3970i | 0.0643521i | ||||||||
\(924\) | −144.000 | − | 118.794i | −0.155844 | − | 0.128565i | ||||
\(925\) | −1128.00 | −1.21946 | ||||||||
\(926\) | 892.369i | 0.963681i | ||||||||
\(927\) | 656.000 | 0.707659 | ||||||||
\(928\) | 192.000 | 0.206897 | ||||||||
\(929\) | −742.000 | −0.798708 | −0.399354 | − | 0.916797i | \(-0.630766\pi\) | ||||
−0.399354 | + | 0.916797i | \(0.630766\pi\) | |||||||
\(930\) | 24.0416i | 0.0258512i | ||||||||
\(931\) | − | 585.484i | − | 0.628877i | ||||||
\(932\) | − | 407.294i | − | 0.437010i | ||||||
\(933\) | −154.000 | −0.165059 | ||||||||
\(934\) | 519.016i | 0.555692i | ||||||||
\(935\) | 216.000 | + | 178.191i | 0.231016 | + | 0.190579i | ||||
\(936\) | −192.000 | −0.205128 | ||||||||
\(937\) | − | 1196.42i | − | 1.27687i | −0.769677 | − | 0.638434i | \(-0.779583\pi\) | ||
0.769677 | − | 0.638434i | \(-0.220417\pi\) | |||||||
\(938\) | 1068.00 | 1.13859 | ||||||||
\(939\) | 95.0000 | 0.101171 | ||||||||
\(940\) | −116.000 | −0.123404 | ||||||||
\(941\) | − | 135.765i | − | 0.144277i | −0.997395 | − | 0.0721384i | \(-0.977018\pi\) | ||
0.997395 | − | 0.0721384i | \(-0.0229823\pi\) | |||||||
\(942\) | 1.41421i | 0.00150129i | ||||||||
\(943\) | − | 144.250i | − | 0.152969i | ||||||
\(944\) | −220.000 | −0.233051 | ||||||||
\(945\) | 144.250i | 0.152645i | ||||||||
\(946\) | −168.000 | + | 203.647i | −0.177590 | + | 0.215271i | ||||
\(947\) | 113.000 | 0.119324 | 0.0596621 | − | 0.998219i | \(-0.480998\pi\) | ||||
0.0596621 | + | 0.998219i | \(0.480998\pi\) | |||||||
\(948\) | − | 67.8823i | − | 0.0716057i | ||||||
\(949\) | −1080.00 | −1.13804 | ||||||||
\(950\) | −864.000 | −0.909474 | ||||||||
\(951\) | 23.0000 | 0.0241851 | ||||||||
\(952\) | 610.940i | 0.641744i | ||||||||
\(953\) | 25.4558i | 0.0267113i | 0.999911 | + | 0.0133556i | \(0.00425136\pi\) | ||||
−0.999911 | + | 0.0133556i | \(0.995749\pi\) | |||||||
\(954\) | 22.6274i | 0.0237185i | ||||||||
\(955\) | 319.000 | 0.334031 | ||||||||
\(956\) | 576.999i | 0.603556i | ||||||||
\(957\) | 288.000 | + | 237.588i | 0.300940 | + | 0.248263i | ||||
\(958\) | 660.000 | 0.688935 | ||||||||
\(959\) | 1417.04i | 1.47762i | ||||||||
\(960\) | 8.00000 | 0.00833333 | ||||||||
\(961\) | −672.000 | −0.699272 | ||||||||
\(962\) | −564.000 | −0.586279 | ||||||||
\(963\) | 610.940i | 0.634414i | ||||||||
\(964\) | 237.588i | 0.246460i | ||||||||
\(965\) | − | 16.9706i | − | 0.0175861i | ||||||
\(966\) | 204.000 | 0.211180 | ||||||||
\(967\) | − | 339.411i | − | 0.350994i | −0.984480 | − | 0.175497i | \(-0.943847\pi\) | ||
0.984480 | − | 0.175497i | \(-0.0561532\pi\) | |||||||
\(968\) | 336.000 | − | 65.0538i | 0.347107 | − | 0.0672044i | ||||
\(969\) | 648.000 | 0.668731 | ||||||||
\(970\) | − | 171.120i | − | 0.176412i | ||||||
\(971\) | 569.000 | 0.585994 | 0.292997 | − | 0.956113i | \(-0.405347\pi\) | ||||
0.292997 | + | 0.956113i | \(0.405347\pi\) | |||||||
\(972\) | −416.000 | −0.427984 | ||||||||
\(973\) | −792.000 | −0.813977 | ||||||||
\(974\) | 722.663i | 0.741954i | ||||||||
\(975\) | 203.647i | 0.208868i | ||||||||
\(976\) | 339.411i | 0.347757i | ||||||||
\(977\) | −649.000 | −0.664278 | −0.332139 | − | 0.943230i | \(-0.607770\pi\) | ||||
−0.332139 | + | 0.943230i | \(0.607770\pi\) | |||||||
\(978\) | − | 155.563i | − | 0.159063i | ||||||
\(979\) | −679.000 | + | 823.072i | −0.693565 | + | 0.840728i | ||||
\(980\) | −46.0000 | −0.0469388 | ||||||||
\(981\) | 1221.88i | 1.24555i | ||||||||
\(982\) | −48.0000 | −0.0488798 | ||||||||
\(983\) | −175.000 | −0.178026 | −0.0890132 | − | 0.996030i | \(-0.528371\pi\) | ||||
−0.0890132 | + | 0.996030i | \(0.528371\pi\) | |||||||
\(984\) | 24.0000 | 0.0243902 | ||||||||
\(985\) | − | 101.823i | − | 0.103374i | ||||||
\(986\) | − | 1221.88i | − | 1.23923i | ||||||
\(987\) | − | 492.146i | − | 0.498628i | ||||||
\(988\) | −432.000 | −0.437247 | ||||||||
\(989\) | − | 288.500i | − | 0.291708i | ||||||
\(990\) | −96.0000 | − | 79.1960i | −0.0969697 | − | 0.0799959i | ||||
\(991\) | 1334.00 | 1.34612 | 0.673058 | − | 0.739590i | \(-0.264981\pi\) | ||||
0.673058 | + | 0.739590i | \(0.264981\pi\) | |||||||
\(992\) | − | 96.1665i | − | 0.0969421i | ||||||
\(993\) | 185.000 | 0.186304 | ||||||||
\(994\) | −84.0000 | −0.0845070 | ||||||||
\(995\) | −182.000 | −0.182915 | ||||||||
\(996\) | − | 67.8823i | − | 0.0681549i | ||||||
\(997\) | − | 1111.57i | − | 1.11492i | −0.830205 | − | 0.557458i | \(-0.811777\pi\) | ||
0.830205 | − | 0.557458i | \(-0.188223\pi\) | |||||||
\(998\) | − | 698.621i | − | 0.700022i | ||||||
\(999\) | −799.000 | −0.799800 |
(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 | 22.3.b.a.21.1 | ✓ | 2 | |
3.2 | odd | 2 | 198.3.d.b.109.2 | 2 | |||
4.3 | odd | 2 | 176.3.h.c.65.1 | 2 | |||
5.2 | odd | 4 | 550.3.c.a.549.3 | 4 | |||
5.3 | odd | 4 | 550.3.c.a.549.2 | 4 | |||
5.4 | even | 2 | 550.3.d.a.351.2 | 2 | |||
7.6 | odd | 2 | 1078.3.d.a.197.1 | 2 | |||
8.3 | odd | 2 | 704.3.h.e.65.1 | 2 | |||
8.5 | even | 2 | 704.3.h.d.65.2 | 2 | |||
11.2 | odd | 10 | 242.3.d.b.161.2 | 8 | |||
11.3 | even | 5 | 242.3.d.b.233.1 | 8 | |||
11.4 | even | 5 | 242.3.d.b.215.2 | 8 | |||
11.5 | even | 5 | 242.3.d.b.239.2 | 8 | |||
11.6 | odd | 10 | 242.3.d.b.239.1 | 8 | |||
11.7 | odd | 10 | 242.3.d.b.215.1 | 8 | |||
11.8 | odd | 10 | 242.3.d.b.233.2 | 8 | |||
11.9 | even | 5 | 242.3.d.b.161.1 | 8 | |||
11.10 | odd | 2 | inner | 22.3.b.a.21.2 | yes | 2 | |
12.11 | even | 2 | 1584.3.j.d.1297.1 | 2 | |||
33.32 | even | 2 | 198.3.d.b.109.1 | 2 | |||
44.43 | even | 2 | 176.3.h.c.65.2 | 2 | |||
55.32 | even | 4 | 550.3.c.a.549.1 | 4 | |||
55.43 | even | 4 | 550.3.c.a.549.4 | 4 | |||
55.54 | odd | 2 | 550.3.d.a.351.1 | 2 | |||
77.76 | even | 2 | 1078.3.d.a.197.2 | 2 | |||
88.21 | odd | 2 | 704.3.h.d.65.1 | 2 | |||
88.43 | even | 2 | 704.3.h.e.65.2 | 2 | |||
132.131 | odd | 2 | 1584.3.j.d.1297.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.3.b.a.21.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
22.3.b.a.21.2 | yes | 2 | 11.10 | odd | 2 | inner | |
176.3.h.c.65.1 | 2 | 4.3 | odd | 2 | |||
176.3.h.c.65.2 | 2 | 44.43 | even | 2 | |||
198.3.d.b.109.1 | 2 | 33.32 | even | 2 | |||
198.3.d.b.109.2 | 2 | 3.2 | odd | 2 | |||
242.3.d.b.161.1 | 8 | 11.9 | even | 5 | |||
242.3.d.b.161.2 | 8 | 11.2 | odd | 10 | |||
242.3.d.b.215.1 | 8 | 11.7 | odd | 10 | |||
242.3.d.b.215.2 | 8 | 11.4 | even | 5 | |||
242.3.d.b.233.1 | 8 | 11.3 | even | 5 | |||
242.3.d.b.233.2 | 8 | 11.8 | odd | 10 | |||
242.3.d.b.239.1 | 8 | 11.6 | odd | 10 | |||
242.3.d.b.239.2 | 8 | 11.5 | even | 5 | |||
550.3.c.a.549.1 | 4 | 55.32 | even | 4 | |||
550.3.c.a.549.2 | 4 | 5.3 | odd | 4 | |||
550.3.c.a.549.3 | 4 | 5.2 | odd | 4 | |||
550.3.c.a.549.4 | 4 | 55.43 | even | 4 | |||
550.3.d.a.351.1 | 2 | 55.54 | odd | 2 | |||
550.3.d.a.351.2 | 2 | 5.4 | even | 2 | |||
704.3.h.d.65.1 | 2 | 88.21 | odd | 2 | |||
704.3.h.d.65.2 | 2 | 8.5 | even | 2 | |||
704.3.h.e.65.1 | 2 | 8.3 | odd | 2 | |||
704.3.h.e.65.2 | 2 | 88.43 | even | 2 | |||
1078.3.d.a.197.1 | 2 | 7.6 | odd | 2 | |||
1078.3.d.a.197.2 | 2 | 77.76 | even | 2 | |||
1584.3.j.d.1297.1 | 2 | 12.11 | even | 2 | |||
1584.3.j.d.1297.2 | 2 | 132.131 | odd | 2 |