Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,6,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (of order \(4\), degree \(2\), 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: | \(36.0863594579\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.3 | ||
Character | \(\chi\) | \(=\) | 225.143 |
Dual form | 225.6.f.c.107.3 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.41913 | − | 5.41913i | −0.957975 | − | 0.957975i | 0.0411767 | − | 0.999152i | \(-0.486889\pi\) |
−0.999152 | + | 0.0411767i | \(0.986889\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 26.7338i | 0.835433i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.9755 | + | 10.9755i | −0.0846601 | + | 0.0846601i | −0.748169 | − | 0.663509i | \(-0.769067\pi\) |
0.663509 | + | 0.748169i | \(0.269067\pi\) | |||||||
\(8\) | −28.5379 | + | 28.5379i | −0.157651 | + | 0.157651i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 194.798i | 0.485402i | 0.970101 | + | 0.242701i | \(0.0780334\pi\) | ||||
−0.970101 | + | 0.242701i | \(0.921967\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 194.671 | + | 194.671i | 0.319479 | + | 0.319479i | 0.848567 | − | 0.529088i | \(-0.177466\pi\) |
−0.529088 | + | 0.848567i | \(0.677466\pi\) | |||||||
\(14\) | 118.955 | 0.162205 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1164.78 | 1.13748 | ||||||||
\(17\) | −1427.43 | − | 1427.43i | −1.19794 | − | 1.19794i | −0.974783 | − | 0.223154i | \(-0.928365\pi\) |
−0.223154 | − | 0.974783i | \(-0.571635\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2273.37i | 1.44473i | 0.691513 | + | 0.722364i | \(0.256944\pi\) | ||||
−0.691513 | + | 0.722364i | \(0.743056\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1055.63 | − | 1055.63i | 0.465003 | − | 0.465003i | ||||
\(23\) | 354.348 | − | 354.348i | 0.139672 | − | 0.139672i | −0.633813 | − | 0.773486i | \(-0.718511\pi\) |
0.773486 | + | 0.633813i | \(0.218511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 2109.89i | − | 0.612106i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −293.417 | − | 293.417i | −0.0707278 | − | 0.0707278i | ||||
\(29\) | 3373.99 | 0.744987 | 0.372494 | − | 0.928035i | \(-0.378503\pi\) | ||||
0.372494 | + | 0.928035i | \(0.378503\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4493.52 | 0.839813 | 0.419906 | − | 0.907567i | \(-0.362063\pi\) | ||||
0.419906 | + | 0.907567i | \(0.362063\pi\) | |||||||
\(32\) | −5398.90 | − | 5398.90i | −0.932031 | − | 0.932031i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 15470.9i | 2.29519i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9731.76 | − | 9731.76i | 1.16866 | − | 1.16866i | 0.186132 | − | 0.982525i | \(-0.440405\pi\) |
0.982525 | − | 0.186132i | \(-0.0595953\pi\) | |||||||
\(38\) | 12319.7 | − | 12319.7i | 1.38401 | − | 1.38401i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 16191.0i | − | 1.50423i | −0.659033 | − | 0.752114i | \(-0.729034\pi\) | ||
0.659033 | − | 0.752114i | \(-0.270966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6182.12 | − | 6182.12i | −0.509878 | − | 0.509878i | 0.404611 | − | 0.914489i | \(-0.367407\pi\) |
−0.914489 | + | 0.404611i | \(0.867407\pi\) | |||||||
\(44\) | −5207.69 | −0.405521 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3840.52 | −0.267606 | ||||||||
\(47\) | −5123.99 | − | 5123.99i | −0.338348 | − | 0.338348i | 0.517397 | − | 0.855745i | \(-0.326901\pi\) |
−0.855745 | + | 0.517397i | \(0.826901\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 16566.1i | 0.985665i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5204.30 | + | 5204.30i | −0.266903 | + | 0.266903i | ||||
\(53\) | 11304.4 | − | 11304.4i | 0.552787 | − | 0.552787i | −0.374457 | − | 0.927244i | \(-0.622171\pi\) |
0.927244 | + | 0.374457i | \(0.122171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 626.435i | − | 0.0266935i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18284.1 | − | 18284.1i | −0.713679 | − | 0.713679i | ||||
\(59\) | −32365.9 | −1.21048 | −0.605240 | − | 0.796043i | \(-0.706923\pi\) | ||||
−0.605240 | + | 0.796043i | \(0.706923\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5599.54 | 0.192676 | 0.0963379 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963379 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(62\) | −24351.0 | − | 24351.0i | −0.804520 | − | 0.804520i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 21241.5i | 0.648240i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −40504.9 | + | 40504.9i | −1.10235 | + | 1.10235i | −0.108226 | + | 0.994126i | \(0.534517\pi\) |
−0.994126 | + | 0.108226i | \(0.965483\pi\) | |||||||
\(68\) | 38160.8 | − | 38160.8i | 1.00080 | − | 1.00080i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 22026.4i | 0.518557i | 0.965803 | + | 0.259279i | \(0.0834848\pi\) | ||||
−0.965803 | + | 0.259279i | \(0.916515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −26237.5 | − | 26237.5i | −0.576255 | − | 0.576255i | 0.357614 | − | 0.933869i | \(-0.383590\pi\) |
−0.933869 | + | 0.357614i | \(0.883590\pi\) | |||||||
\(74\) | −105475. | −2.23909 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −60775.9 | −1.20697 | ||||||||
\(77\) | −2138.00 | − | 2138.00i | −0.0410942 | − | 0.0410942i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 70839.5i | − | 1.27705i | −0.769601 | − | 0.638525i | \(-0.779545\pi\) | ||
0.769601 | − | 0.638525i | \(-0.220455\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −87741.0 | + | 87741.0i | −1.44101 | + | 1.44101i | ||||
\(83\) | −12450.6 | + | 12450.6i | −0.198378 | + | 0.198378i | −0.799304 | − | 0.600926i | \(-0.794799\pi\) |
0.600926 | + | 0.799304i | \(0.294799\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 67003.4i | 0.976901i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5559.12 | − | 5559.12i | −0.0765243 | − | 0.0765243i | ||||
\(89\) | −91155.9 | −1.21986 | −0.609930 | − | 0.792456i | \(-0.708802\pi\) | ||||
−0.609930 | + | 0.792456i | \(0.708802\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4273.21 | −0.0540942 | ||||||||
\(92\) | 9473.10 | + | 9473.10i | 0.116687 | + | 0.116687i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 55535.1i | 0.648258i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1795.86 | − | 1795.86i | 0.0193796 | − | 0.0193796i | −0.697351 | − | 0.716730i | \(-0.745638\pi\) |
0.716730 | + | 0.697351i | \(0.245638\pi\) | |||||||
\(98\) | 89773.7 | − | 89773.7i | 0.944243 | − | 0.944243i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 129300.i | − | 1.26123i | −0.776094 | − | 0.630617i | \(-0.782802\pi\) | ||
0.776094 | − | 0.630617i | \(-0.217198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −138191. | − | 138191.i | −1.28347 | − | 1.28347i | −0.938680 | − | 0.344789i | \(-0.887950\pi\) |
−0.344789 | − | 0.938680i | \(-0.612050\pi\) | |||||||
\(104\) | −11111.0 | −0.100732 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −122520. | −1.05911 | ||||||||
\(107\) | 69822.5 | + | 69822.5i | 0.589571 | + | 0.589571i | 0.937515 | − | 0.347944i | \(-0.113120\pi\) |
−0.347944 | + | 0.937515i | \(0.613120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 131350.i | − | 1.05893i | −0.848333 | − | 0.529463i | \(-0.822394\pi\) | ||
0.848333 | − | 0.529463i | \(-0.177606\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12784.1 | + | 12784.1i | −0.0962996 | + | 0.0962996i | ||||
\(113\) | −26187.1 | + | 26187.1i | −0.192926 | + | 0.192926i | −0.796959 | − | 0.604033i | \(-0.793559\pi\) |
0.604033 | + | 0.796959i | \(0.293559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 90199.8i | 0.622387i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 175395. | + | 175395.i | 1.15961 | + | 1.15961i | ||||
\(119\) | 31333.6 | 0.202835 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 123105. | 0.764385 | ||||||||
\(122\) | −30344.6 | − | 30344.6i | −0.184579 | − | 0.184579i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 120129.i | 0.701607i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 218514. | − | 218514.i | 1.20218 | − | 1.20218i | 0.228683 | − | 0.973501i | \(-0.426558\pi\) |
0.973501 | − | 0.228683i | \(-0.0734419\pi\) | |||||||
\(128\) | −57654.3 | + | 57654.3i | −0.311033 | + | 0.311033i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 273444.i | − | 1.39216i | −0.717962 | − | 0.696082i | \(-0.754925\pi\) | ||
0.717962 | − | 0.696082i | \(-0.245075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24951.3 | − | 24951.3i | −0.122311 | − | 0.122311i | ||||
\(134\) | 439002. | 2.11205 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 81472.1 | 0.377713 | ||||||||
\(137\) | −74124.9 | − | 74124.9i | −0.337414 | − | 0.337414i | 0.517979 | − | 0.855393i | \(-0.326684\pi\) |
−0.855393 | + | 0.517979i | \(0.826684\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 224787.i | 0.986811i | 0.869799 | + | 0.493406i | \(0.164248\pi\) | ||||
−0.869799 | + | 0.493406i | \(0.835752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 119364. | − | 119364.i | 0.496765 | − | 0.496765i | ||||
\(143\) | −37921.4 | + | 37921.4i | −0.155076 | + | 0.155076i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 284368.i | 1.10408i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 260167. | + | 260167.i | 0.976334 | + | 0.976334i | ||||
\(149\) | 164888. | 0.608449 | 0.304224 | − | 0.952600i | \(-0.401603\pi\) | ||||
0.304224 | + | 0.952600i | \(0.401603\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 392244. | 1.39996 | 0.699978 | − | 0.714165i | \(-0.253193\pi\) | ||||
0.699978 | + | 0.714165i | \(0.253193\pi\) | |||||||
\(152\) | −64877.2 | − | 64877.2i | −0.227763 | − | 0.227763i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 23172.2i | 0.0787344i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 107211. | − | 107211.i | 0.347129 | − | 0.347129i | −0.511910 | − | 0.859039i | \(-0.671062\pi\) |
0.859039 | + | 0.511910i | \(0.171062\pi\) | |||||||
\(158\) | −383888. | + | 383888.i | −1.22338 | + | 1.22338i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7778.29i | 0.0236494i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 72934.4 | + | 72934.4i | 0.215012 | + | 0.215012i | 0.806393 | − | 0.591380i | \(-0.201417\pi\) |
−0.591380 | + | 0.806393i | \(0.701417\pi\) | |||||||
\(164\) | 432847. | 1.25668 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 134942. | 0.380083 | ||||||||
\(167\) | 39616.8 | + | 39616.8i | 0.109923 | + | 0.109923i | 0.759929 | − | 0.650006i | \(-0.225234\pi\) |
−0.650006 | + | 0.759929i | \(0.725234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 295500.i | − | 0.795867i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 165272. | − | 165272.i | 0.425969 | − | 0.425969i | ||||
\(173\) | −303757. | + | 303757.i | −0.771633 | + | 0.771633i | −0.978392 | − | 0.206759i | \(-0.933708\pi\) |
0.206759 | + | 0.978392i | \(0.433708\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 226897.i | 0.552138i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 493985. | + | 493985.i | 1.16859 | + | 1.16859i | ||||
\(179\) | 337098. | 0.786363 | 0.393181 | − | 0.919461i | \(-0.371374\pi\) | ||||
0.393181 | + | 0.919461i | \(0.371374\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 45494.0 | 0.103219 | 0.0516093 | − | 0.998667i | \(-0.483565\pi\) | ||||
0.0516093 | + | 0.998667i | \(0.483565\pi\) | |||||||
\(182\) | 23157.1 | + | 23157.1i | 0.0518209 | + | 0.0518209i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 20224.7i | 0.0440391i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 278061. | − | 278061.i | 0.581481 | − | 0.581481i | ||||
\(188\) | 136984. | − | 136984.i | 0.282667 | − | 0.282667i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 843927.i | − | 1.67387i | −0.547303 | − | 0.836935i | \(-0.684345\pi\) | ||
0.547303 | − | 0.836935i | \(-0.315655\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −454404. | − | 454404.i | −0.878111 | − | 0.878111i | 0.115228 | − | 0.993339i | \(-0.463240\pi\) |
−0.993339 | + | 0.115228i | \(0.963240\pi\) | |||||||
\(194\) | −19464.0 | −0.0371303 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −442875. | −0.823457 | ||||||||
\(197\) | 725036. | + | 725036.i | 1.33105 | + | 1.33105i | 0.904433 | + | 0.426617i | \(0.140295\pi\) |
0.426617 | + | 0.904433i | \(0.359705\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 838663.i | − | 1.50126i | −0.660725 | − | 0.750628i | \(-0.729751\pi\) | ||
0.660725 | − | 0.750628i | \(-0.270249\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −700694. | + | 700694.i | −1.20823 | + | 1.20823i | ||||
\(203\) | −37031.2 | + | 37031.2i | −0.0630707 | + | 0.0630707i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.49774e6i | 2.45906i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 226749. | + | 226749.i | 0.363402 | + | 0.363402i | ||||
\(209\) | −442846. | −0.701274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −781145. | −1.20788 | −0.603942 | − | 0.797028i | \(-0.706404\pi\) | ||||
−0.603942 | + | 0.797028i | \(0.706404\pi\) | |||||||
\(212\) | 302210. | + | 302210.i | 0.461817 | + | 0.461817i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 756754.i | − | 1.12959i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −49318.6 | + | 49318.6i | −0.0710986 | + | 0.0710986i | ||||
\(218\) | −711804. | + | 711804.i | −1.01442 | + | 1.01442i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 555759.i | − | 0.765431i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −323966. | − | 323966.i | −0.436252 | − | 0.436252i | 0.454496 | − | 0.890749i | \(-0.349819\pi\) |
−0.890749 | + | 0.454496i | \(0.849819\pi\) | |||||||
\(224\) | 118511. | 0.157812 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 283822. | 0.369637 | ||||||||
\(227\) | 531318. | + | 531318.i | 0.684368 | + | 0.684368i | 0.960981 | − | 0.276613i | \(-0.0892121\pi\) |
−0.276613 | + | 0.960981i | \(0.589212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 242575.i | − | 0.305673i | −0.988251 | − | 0.152837i | \(-0.951159\pi\) | ||
0.988251 | − | 0.152837i | \(-0.0488408\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −96286.7 | + | 96286.7i | −0.117448 | + | 0.117448i | ||||
\(233\) | 1.07761e6 | − | 1.07761e6i | 1.30038 | − | 1.30038i | 0.372244 | − | 0.928135i | \(-0.378589\pi\) |
0.928135 | − | 0.372244i | \(-0.121411\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 865265.i | − | 1.01127i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −169801. | − | 169801.i | −0.194311 | − | 0.194311i | ||||
\(239\) | −876668. | −0.992752 | −0.496376 | − | 0.868108i | \(-0.665336\pi\) | ||||
−0.496376 | + | 0.868108i | \(0.665336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.17411e6 | −1.30217 | −0.651085 | − | 0.759005i | \(-0.725686\pi\) | ||||
−0.651085 | + | 0.759005i | \(0.725686\pi\) | |||||||
\(242\) | −667121. | − | 667121.i | −0.732262 | − | 0.732262i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 149697.i | 0.160968i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −442558. | + | 442558.i | −0.461560 | + | 0.461560i | ||||
\(248\) | −128236. | + | 128236.i | −0.132398 | + | 0.132398i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.72668e6i | 1.72993i | 0.501835 | + | 0.864963i | \(0.332658\pi\) | ||||
−0.501835 | + | 0.864963i | \(0.667342\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 69026.2 | + | 69026.2i | 0.0677973 | + | 0.0677973i | ||||
\(254\) | −2.36832e6 | −2.30332 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.30460e6 | 1.24416 | ||||||||
\(257\) | −54001.3 | − | 54001.3i | −0.0510001 | − | 0.0510001i | 0.681147 | − | 0.732147i | \(-0.261482\pi\) |
−0.732147 | + | 0.681147i | \(0.761482\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 213622.i | 0.197877i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.48183e6 | + | 1.48183e6i | −1.33366 | + | 1.33366i | ||||
\(263\) | −131461. | + | 131461.i | −0.117195 | + | 0.117195i | −0.763272 | − | 0.646077i | \(-0.776408\pi\) |
0.646077 | + | 0.763272i | \(0.276408\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 270429.i | 0.234341i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.08285e6 | − | 1.08285e6i | −0.920941 | − | 0.920941i | ||||
\(269\) | 1.47111e6 | 1.23955 | 0.619774 | − | 0.784781i | \(-0.287224\pi\) | ||||
0.619774 | + | 0.784781i | \(0.287224\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −206507. | −0.170809 | −0.0854047 | − | 0.996346i | \(-0.527218\pi\) | ||||
−0.0854047 | + | 0.996346i | \(0.527218\pi\) | |||||||
\(272\) | −1.66265e6 | − | 1.66265e6i | −1.36264 | − | 1.36264i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 803384.i | 0.646468i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 872040. | − | 872040.i | 0.682869 | − | 0.682869i | −0.277777 | − | 0.960646i | \(-0.589598\pi\) |
0.960646 | + | 0.277777i | \(0.0895976\pi\) | |||||||
\(278\) | 1.21815e6 | − | 1.21815e6i | 0.945341 | − | 0.945341i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.61973e6i | − | 1.22371i | −0.790971 | − | 0.611854i | \(-0.790424\pi\) | ||
0.790971 | − | 0.611854i | \(-0.209576\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 786552. | + | 786552.i | 0.583796 | + | 0.583796i | 0.935944 | − | 0.352148i | \(-0.114549\pi\) |
−0.352148 | + | 0.935944i | \(0.614549\pi\) | |||||||
\(284\) | −588849. | −0.433220 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 411001. | 0.297117 | ||||||||
\(287\) | 177704. | + | 177704.i | 0.127348 | + | 0.127348i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.65528e6i | 1.87011i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 701429. | − | 701429.i | 0.481423 | − | 0.481423i | ||||
\(293\) | 852510. | − | 852510.i | 0.580137 | − | 0.580137i | −0.354804 | − | 0.934941i | \(-0.615452\pi\) |
0.934941 | + | 0.354804i | \(0.115452\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 555449.i | 0.368481i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −893550. | − | 893550.i | −0.582879 | − | 0.582879i | ||||
\(299\) | 137962. | 0.0892448 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 135704. | 0.0863327 | ||||||||
\(302\) | −2.12562e6 | − | 2.12562e6i | −1.34112 | − | 1.34112i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.64798e6i | 1.64336i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 642741. | − | 642741.i | 0.389216 | − | 0.389216i | −0.485192 | − | 0.874408i | \(-0.661250\pi\) |
0.874408 | + | 0.485192i | \(0.161250\pi\) | |||||||
\(308\) | 57156.9 | − | 57156.9i | 0.0343314 | − | 0.0343314i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.78173e6i | − | 1.63085i | −0.578863 | − | 0.815425i | \(-0.696503\pi\) | ||
0.578863 | − | 0.815425i | \(-0.303497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −751913. | − | 751913.i | −0.433817 | − | 0.433817i | 0.456107 | − | 0.889925i | \(-0.349243\pi\) |
−0.889925 | + | 0.456107i | \(0.849243\pi\) | |||||||
\(314\) | −1.16198e6 | −0.665082 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.89381e6 | 1.06689 | ||||||||
\(317\) | 4557.50 | + | 4557.50i | 0.00254729 | + | 0.00254729i | 0.708379 | − | 0.705832i | \(-0.249427\pi\) |
−0.705832 | + | 0.708379i | \(0.749427\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 657245.i | 0.361618i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42151.5 | − | 42151.5i | 0.0226555 | − | 0.0226555i | ||||
\(323\) | 3.24509e6 | − | 3.24509e6i | 1.73069 | − | 1.73069i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 790481.i | − | 0.411953i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 462057. | + | 462057.i | 0.237143 | + | 0.237143i | ||||
\(329\) | 112477. | 0.0572891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.75226e6 | −1.38076 | −0.690382 | − | 0.723445i | \(-0.742557\pi\) | ||||
−0.690382 | + | 0.723445i | \(0.742557\pi\) | |||||||
\(332\) | −332852. | − | 332852.i | −0.165732 | − | 0.165732i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 429377.i | − | 0.210607i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 949071. | − | 949071.i | 0.455223 | − | 0.455223i | −0.441861 | − | 0.897084i | \(-0.645682\pi\) |
0.897084 | + | 0.441861i | \(0.145682\pi\) | |||||||
\(338\) | −1.60135e6 | + | 1.60135e6i | −0.762420 | + | 0.762420i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 875327.i | 0.407647i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −366286. | − | 366286.i | −0.168107 | − | 0.168107i | ||||
\(344\) | 352850. | 0.160766 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.29219e6 | 1.47841 | ||||||||
\(347\) | 1.15265e6 | + | 1.15265e6i | 0.513895 | + | 0.513895i | 0.915717 | − | 0.401823i | \(-0.131623\pi\) |
−0.401823 | + | 0.915717i | \(0.631623\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.38647e6i | 0.609320i | 0.952461 | + | 0.304660i | \(0.0985429\pi\) | ||||
−0.952461 | + | 0.304660i | \(0.901457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.05169e6 | − | 1.05169e6i | 0.452410 | − | 0.452410i | ||||
\(353\) | 336957. | − | 336957.i | 0.143925 | − | 0.143925i | −0.631473 | − | 0.775398i | \(-0.717549\pi\) |
0.775398 | + | 0.631473i | \(0.217549\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 2.43695e6i | − | 1.01911i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.82677e6 | − | 1.82677e6i | −0.753316 | − | 0.753316i | ||||
\(359\) | 3.85085e6 | 1.57696 | 0.788480 | − | 0.615061i | \(-0.210869\pi\) | ||||
0.788480 | + | 0.615061i | \(0.210869\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.69210e6 | −1.08724 | ||||||||
\(362\) | −246538. | − | 246538.i | −0.0988808 | − | 0.0988808i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 114239.i | − | 0.0451921i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.08759e6 | − | 1.08759e6i | 0.421501 | − | 0.421501i | −0.464219 | − | 0.885720i | \(-0.653665\pi\) |
0.885720 | + | 0.464219i | \(0.153665\pi\) | |||||||
\(368\) | 412740. | − | 412740.i | 0.158875 | − | 0.158875i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 248143.i | 0.0935981i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.46018e6 | + | 2.46018e6i | 0.915575 | + | 0.915575i | 0.996704 | − | 0.0811283i | \(-0.0258524\pi\) |
−0.0811283 | + | 0.996704i | \(0.525852\pi\) | |||||||
\(374\) | −3.01369e6 | −1.11409 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 292456. | 0.106682 | ||||||||
\(377\) | 656817. | + | 656817.i | 0.238008 | + | 0.238008i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 236094.i | 0.0844282i | 0.999109 | + | 0.0422141i | \(0.0134412\pi\) | ||||
−0.999109 | + | 0.0422141i | \(0.986559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.57335e6 | + | 4.57335e6i | −1.60352 | + | 1.60352i | ||||
\(383\) | −1.14707e6 | + | 1.14707e6i | −0.399570 | + | 0.399570i | −0.878081 | − | 0.478511i | \(-0.841177\pi\) |
0.478511 | + | 0.878081i | \(0.341177\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.92495e6i | 1.68242i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 48010.3 | + | 48010.3i | 0.0161903 | + | 0.0161903i | ||||
\(389\) | −4.13785e6 | −1.38644 | −0.693219 | − | 0.720727i | \(-0.743808\pi\) | ||||
−0.693219 | + | 0.720727i | \(0.743808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.01162e6 | −0.334638 | ||||||||
\(392\) | −472762. | − | 472762.i | −0.155391 | − | 0.155391i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 7.85812e6i | − | 2.55022i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.87558e6 | + | 3.87558e6i | −1.23413 | + | 1.23413i | −0.271766 | + | 0.962363i | \(0.587608\pi\) |
−0.962363 | + | 0.271766i | \(0.912392\pi\) | |||||||
\(398\) | −4.54482e6 | + | 4.54482e6i | −1.43817 | + | 1.43817i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.46163e6i | 1.07503i | 0.843255 | + | 0.537514i | \(0.180637\pi\) | ||||
−0.843255 | + | 0.537514i | \(0.819363\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 874756. | + | 874756.i | 0.268302 | + | 0.268302i | ||||
\(404\) | 3.45669e6 | 1.05368 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 401353. | 0.120840 | ||||||||
\(407\) | 1.89572e6 | + | 1.89572e6i | 0.567269 | + | 0.567269i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.21009e6i | − | 1.54006i | −0.638009 | − | 0.770029i | \(-0.720242\pi\) | ||
0.638009 | − | 0.770029i | \(-0.279758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.69437e6 | − | 3.69437e6i | 1.07225 | − | 1.07225i | ||||
\(413\) | 355231. | − | 355231.i | 0.102479 | − | 0.102479i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 2.10201e6i | − | 0.595528i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.39984e6 | + | 2.39984e6i | 0.671803 | + | 0.671803i | ||||
\(419\) | 1.98439e6 | 0.552195 | 0.276097 | − | 0.961130i | \(-0.410959\pi\) | ||||
0.276097 | + | 0.961130i | \(0.410959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.18296e6 | −0.875236 | −0.437618 | − | 0.899161i | \(-0.644178\pi\) | ||||
−0.437618 | + | 0.899161i | \(0.644178\pi\) | |||||||
\(422\) | 4.23312e6 | + | 4.23312e6i | 1.15712 | + | 1.15712i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 645209.i | 0.174295i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −61457.6 | + | 61457.6i | −0.0163120 | + | 0.0163120i | ||||
\(428\) | −1.86662e6 | + | 1.86662e6i | −0.492547 | + | 0.492547i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.76453e6i | 0.976153i | 0.872801 | + | 0.488077i | \(0.162301\pi\) | ||||
−0.872801 | + | 0.488077i | \(0.837699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −116515. | − | 116515.i | −0.0298651 | − | 0.0298651i | 0.692017 | − | 0.721882i | \(-0.256723\pi\) |
−0.721882 | + | 0.692017i | \(0.756723\pi\) | |||||||
\(434\) | 534527. | 0.136221 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.51150e6 | 0.884661 | ||||||||
\(437\) | 805565. | + | 805565.i | 0.201789 | + | 0.201789i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.35575e6i | − | 0.583403i | −0.956509 | − | 0.291701i | \(-0.905779\pi\) | ||
0.956509 | − | 0.291701i | \(-0.0942213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.01173e6 | + | 3.01173e6i | −0.733264 | + | 0.733264i | ||||
\(443\) | −4.26536e6 | + | 4.26536e6i | −1.03263 | + | 1.03263i | −0.0331846 | + | 0.999449i | \(0.510565\pi\) |
−0.999449 | + | 0.0331846i | \(0.989435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.51123e6i | 0.835837i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −233136. | − | 233136.i | −0.0548801 | − | 0.0548801i | ||||
\(449\) | −1.38214e6 | −0.323546 | −0.161773 | − | 0.986828i | \(-0.551721\pi\) | ||||
−0.161773 | + | 0.986828i | \(0.551721\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.15396e6 | 0.730155 | ||||||||
\(452\) | −700082. | − | 700082.i | −0.161177 | − | 0.161177i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 5.75856e6i | − | 1.31122i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.05756e6 | − | 1.05756e6i | 0.236872 | − | 0.236872i | −0.578682 | − | 0.815554i | \(-0.696433\pi\) |
0.815554 | + | 0.578682i | \(0.196433\pi\) | |||||||
\(458\) | −1.31454e6 | + | 1.31454e6i | −0.292827 | + | 0.292827i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.58869e6i | − | 1.00563i | −0.864395 | − | 0.502813i | \(-0.832298\pi\) | ||
0.864395 | − | 0.502813i | \(-0.167702\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 65050.0 | + | 65050.0i | 0.0141025 | + | 0.0141025i | 0.714123 | − | 0.700020i | \(-0.246826\pi\) |
−0.700020 | + | 0.714123i | \(0.746826\pi\) | |||||||
\(464\) | 3.92997e6 | 0.847412 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.16794e7 | −2.49146 | ||||||||
\(467\) | 1.59074e6 | + | 1.59074e6i | 0.337525 | + | 0.337525i | 0.855435 | − | 0.517910i | \(-0.173290\pi\) |
−0.517910 | + | 0.855435i | \(0.673290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 889122.i | − | 0.186650i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 923656. | − | 923656.i | 0.190834 | − | 0.190834i | ||||
\(473\) | 1.20426e6 | − | 1.20426e6i | 0.247496 | − | 0.247496i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 837667.i | 0.169455i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.75078e6 | + | 4.75078e6i | 0.951031 | + | 0.951031i | ||||
\(479\) | 2.60690e6 | 0.519141 | 0.259570 | − | 0.965724i | \(-0.416419\pi\) | ||||
0.259570 | + | 0.965724i | \(0.416419\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.78898e6 | 0.746722 | ||||||||
\(482\) | 6.36268e6 | + | 6.36268e6i | 1.24745 | + | 1.24745i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.29107e6i | 0.638592i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.21227e6 | − | 2.21227e6i | 0.422683 | − | 0.422683i | −0.463443 | − | 0.886127i | \(-0.653386\pi\) |
0.886127 | + | 0.463443i | \(0.153386\pi\) | |||||||
\(488\) | −159799. | + | 159799.i | −0.0303756 | + | 0.0303756i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.58021e6i | − | 1.04459i | −0.852764 | − | 0.522297i | \(-0.825075\pi\) | ||
0.852764 | − | 0.522297i | \(-0.174925\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.81615e6 | − | 4.81615e6i | −0.892448 | − | 0.892448i | ||||
\(494\) | 4.79656e6 | 0.884325 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.23398e6 | 0.955274 | ||||||||
\(497\) | −241750. | − | 241750.i | −0.0439011 | − | 0.0439011i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.39810e6i | 0.251354i | 0.992071 | + | 0.125677i | \(0.0401104\pi\) | ||||
−0.992071 | + | 0.125677i | \(0.959890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9.35710e6 | − | 9.35710e6i | 1.65723 | − | 1.65723i | ||||
\(503\) | −471587. | + | 471587.i | −0.0831078 | + | 0.0831078i | −0.747439 | − | 0.664331i | \(-0.768717\pi\) |
0.664331 | + | 0.747439i | \(0.268717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 748123.i | − | 0.129896i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.84173e6 | + | 5.84173e6i | 1.00434 | + | 1.00434i | ||||
\(509\) | 3.97703e6 | 0.680399 | 0.340200 | − | 0.940353i | \(-0.389505\pi\) | ||||
0.340200 | + | 0.940353i | \(0.389505\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 575938. | 0.0975717 | ||||||||
\(512\) | −5.22486e6 | − | 5.22486e6i | −0.880845 | − | 0.880845i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 585280.i | 0.0977137i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 998140. | − | 998140.i | 0.164235 | − | 0.164235i | ||||
\(518\) | 1.15764e6 | − | 1.15764e6i | 0.189561 | − | 0.189561i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.70745e6i | − | 0.275585i | −0.990461 | − | 0.137792i | \(-0.955999\pi\) | ||
0.990461 | − | 0.137792i | \(-0.0440006\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.03074e6 | + | 3.03074e6i | 0.484501 | + | 0.484501i | 0.906566 | − | 0.422065i | \(-0.138695\pi\) |
−0.422065 | + | 0.906566i | \(0.638695\pi\) | |||||||
\(524\) | 7.31022e6 | 1.16306 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.42481e6 | 0.224539 | ||||||||
\(527\) | −6.41421e6 | − | 6.41421e6i | −1.00604 | − | 1.00604i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.18522e6i | 0.960983i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 667045. | − | 667045.i | 0.102182 | − | 0.102182i | ||||
\(533\) | 3.15191e6 | − | 3.15191e6i | 0.480569 | − | 0.480569i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 2.31185e6i | − | 0.347574i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.97211e6 | − | 7.97211e6i | −1.18746 | − | 1.18746i | ||||
\(539\) | −3.22703e6 | −0.478444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.93011e6 | 1.16489 | 0.582446 | − | 0.812869i | \(-0.302096\pi\) | ||||
0.582446 | + | 0.812869i | \(0.302096\pi\) | |||||||
\(542\) | 1.11909e6 | + | 1.11909e6i | 0.163631 | + | 0.163631i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.54132e7i | 2.23303i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 347229. | − | 347229.i | 0.0496189 | − | 0.0496189i | −0.681862 | − | 0.731481i | \(-0.738830\pi\) |
0.731481 | + | 0.681862i | \(0.238830\pi\) | |||||||
\(548\) | 1.98164e6 | − | 1.98164e6i | 0.281886 | − | 0.281886i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.67032e6i | 1.07630i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 777498. | + | 777498.i | 0.108115 | + | 0.108115i | ||||
\(554\) | −9.45139e6 | −1.30834 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.00942e6 | −0.824414 | ||||||||
\(557\) | −5.98254e6 | − | 5.98254e6i | −0.817048 | − | 0.817048i | 0.168631 | − | 0.985679i | \(-0.446065\pi\) |
−0.985679 | + | 0.168631i | \(0.946065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.40696e6i | − | 0.325791i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.77754e6 | + | 8.77754e6i | −1.17228 | + | 1.17228i | ||||
\(563\) | −8.86463e6 | + | 8.86463e6i | −1.17866 | + | 1.17866i | −0.198577 | + | 0.980085i | \(0.563632\pi\) |
−0.980085 | + | 0.198577i | \(0.936368\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 8.52485e6i | − | 1.11852i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −628586. | − | 628586.i | −0.0817512 | − | 0.0817512i | ||||
\(569\) | −263589. | −0.0341308 | −0.0170654 | − | 0.999854i | \(-0.505432\pi\) | ||||
−0.0170654 | + | 0.999854i | \(0.505432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.24926e7 | 1.60347 | 0.801737 | − | 0.597677i | \(-0.203910\pi\) | ||||
0.801737 | + | 0.597677i | \(0.203910\pi\) | |||||||
\(572\) | −1.01378e6 | − | 1.01378e6i | −0.129555 | − | 0.129555i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1.92600e6i | − | 0.243992i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.28115e6 | − | 3.28115e6i | 0.410286 | − | 0.410286i | −0.471552 | − | 0.881838i | \(-0.656306\pi\) |
0.881838 | + | 0.471552i | \(0.156306\pi\) | |||||||
\(578\) | 1.43893e7 | − | 1.43893e7i | 1.79152 | − | 1.79152i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 273302.i | − | 0.0335894i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.20207e6 | + | 2.20207e6i | 0.268324 | + | 0.268324i | ||||
\(584\) | 1.49753e6 | 0.181695 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.23972e6 | −1.11151 | ||||||||
\(587\) | −3.85645e6 | − | 3.85645e6i | −0.461948 | − | 0.461948i | 0.437346 | − | 0.899293i | \(-0.355919\pi\) |
−0.899293 | + | 0.437346i | \(0.855919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.02154e7i | 1.21330i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.13354e7 | − | 1.13354e7i | 1.32933 | − | 1.32933i | ||||
\(593\) | −7.34203e6 | + | 7.34203e6i | −0.857392 | + | 0.857392i | −0.991030 | − | 0.133638i | \(-0.957334\pi\) |
0.133638 | + | 0.991030i | \(0.457334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.40810e6i | 0.508318i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −747636. | − | 747636.i | −0.0854943 | − | 0.0854943i | ||||
\(599\) | −2.16225e6 | −0.246228 | −0.123114 | − | 0.992393i | \(-0.539288\pi\) | ||||
−0.123114 | + | 0.992393i | \(0.539288\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.31939e6 | 0.487793 | 0.243897 | − | 0.969801i | \(-0.421574\pi\) | ||||
0.243897 | + | 0.969801i | \(0.421574\pi\) | |||||||
\(602\) | −735395. | − | 735395.i | −0.0827046 | − | 0.0827046i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.04862e7i | 1.16957i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.11920e7 | + | 1.11920e7i | −1.23292 | + | 1.23292i | −0.270082 | + | 0.962837i | \(0.587051\pi\) |
−0.962837 | + | 0.270082i | \(0.912949\pi\) | |||||||
\(608\) | 1.22737e7 | − | 1.22737e7i | 1.34653 | − | 1.34653i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.99498e6i | − | 0.216190i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.40080e6 | − | 9.40080e6i | −1.01045 | − | 1.01045i | −0.999945 | − | 0.0105019i | \(-0.996657\pi\) |
−0.0105019 | − | 0.999945i | \(-0.503343\pi\) | |||||||
\(614\) | −6.96619e6 | −0.745718 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 122028. | 0.0129571 | ||||||||
\(617\) | −9.23092e6 | − | 9.23092e6i | −0.976185 | − | 0.976185i | 0.0235377 | − | 0.999723i | \(-0.492507\pi\) |
−0.999723 | + | 0.0235377i | \(0.992507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.66306e7i | − | 1.74454i | −0.489027 | − | 0.872269i | \(-0.662648\pi\) | ||
0.489027 | − | 0.872269i | \(-0.337352\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.50745e7 | + | 1.50745e7i | −1.56231 | + | 1.56231i | ||||
\(623\) | 1.00048e6 | − | 1.00048e6i | 0.103273 | − | 0.103273i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.14942e6i | 0.831172i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.86617e6 | + | 2.86617e6i | 0.290003 | + | 0.290003i | ||||
\(629\) | −2.77829e7 | −2.79995 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −872532. | −0.0872385 | −0.0436192 | − | 0.999048i | \(-0.513889\pi\) | ||||
−0.0436192 | + | 0.999048i | \(0.513889\pi\) | |||||||
\(632\) | 2.02161e6 | + | 2.02161e6i | 0.201328 | + | 0.201328i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 49395.4i | − | 0.00488049i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.22493e6 | + | 3.22493e6i | −0.314899 | + | 0.314899i | ||||
\(638\) | 3.56169e6 | − | 3.56169e6i | 0.346422 | − | 0.346422i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.87418e6i | 0.276292i | 0.990412 | + | 0.138146i | \(0.0441143\pi\) | ||||
−0.990412 | + | 0.138146i | \(0.955886\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.25870e7 | − | 1.25870e7i | −1.20059 | − | 1.20059i | −0.973988 | − | 0.226599i | \(-0.927239\pi\) |
−0.226599 | − | 0.973988i | \(-0.572761\pi\) | |||||||
\(644\) | −207944. | −0.0197575 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.51711e7 | −3.31592 | ||||||||
\(647\) | 1.15062e7 | + | 1.15062e7i | 1.08062 | + | 1.08062i | 0.996452 | + | 0.0841657i | \(0.0268225\pi\) |
0.0841657 | + | 0.996452i | \(0.473178\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.30479e6i | − | 0.587569i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.94982e6 | + | 1.94982e6i | −0.179628 | + | 0.179628i | ||||
\(653\) | 1.10167e7 | − | 1.10167e7i | 1.01104 | − | 1.01104i | 0.0111059 | − | 0.999938i | \(-0.496465\pi\) |
0.999938 | − | 0.0111059i | \(-0.00353519\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.88590e7i | − | 1.71104i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −609525. | − | 609525.i | −0.0548816 | − | 0.0548816i | ||||
\(659\) | −3.56502e6 | −0.319778 | −0.159889 | − | 0.987135i | \(-0.551114\pi\) | ||||
−0.159889 | + | 0.987135i | \(0.551114\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 609051. | 0.0542188 | 0.0271094 | − | 0.999632i | \(-0.491370\pi\) | ||||
0.0271094 | + | 0.999632i | \(0.491370\pi\) | |||||||
\(662\) | 1.49148e7 | + | 1.49148e7i | 1.32274 | + | 1.32274i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 710627.i | − | 0.0625492i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.19557e6 | − | 1.19557e6i | 0.104054 | − | 0.104054i | ||||
\(668\) | −1.05911e6 | + | 1.05911e6i | −0.0918332 | + | 0.0918332i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.09078e6i | 0.0935253i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.32688e6 | − | 6.32688e6i | −0.538458 | − | 0.538458i | 0.384618 | − | 0.923076i | \(-0.374333\pi\) |
−0.923076 | + | 0.384618i | \(0.874333\pi\) | |||||||
\(674\) | −1.02863e7 | −0.872184 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.89984e6 | 0.664893 | ||||||||
\(677\) | −4.90614e6 | − | 4.90614e6i | −0.411404 | − | 0.411404i | 0.470824 | − | 0.882227i | \(-0.343957\pi\) |
−0.882227 | + | 0.470824i | \(0.843957\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39420.9i | 0.00328135i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.74350e6 | − | 4.74350e6i | 0.390516 | − | 0.390516i | ||||
\(683\) | −1.03107e7 | + | 1.03107e7i | −0.845741 | + | 0.845741i | −0.989598 | − | 0.143857i | \(-0.954049\pi\) |
0.143857 | + | 0.989598i | \(0.454049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.96990e6i | 0.322084i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.20084e6 | − | 7.20084e6i | −0.579979 | − | 0.579979i | ||||
\(689\) | 4.40127e6 | 0.353208 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.75927e6 | −0.379180 | −0.189590 | − | 0.981863i | \(-0.560716\pi\) | ||||
−0.189590 | + | 0.981863i | \(0.560716\pi\) | |||||||
\(692\) | −8.12059e6 | − | 8.12059e6i | −0.644648 | − | 0.644648i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 1.24927e7i | − | 0.984597i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.31116e7 | + | 2.31116e7i | −1.80197 | + | 1.80197i | ||||
\(698\) | 7.51343e6 | − | 7.51343e6i | 0.583714 | − | 0.583714i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.82391e6i | − | 0.140187i | −0.997540 | − | 0.0700937i | \(-0.977670\pi\) | ||
0.997540 | − | 0.0700937i | \(-0.0223298\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.21239e7 | + | 2.21239e7i | 1.68839 | + | 1.68839i | ||||
\(704\) | −4.13780e6 | −0.314657 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.65202e6 | −0.275754 | ||||||||
\(707\) | 1.41913e6 | + | 1.41913e6i | 0.106776 | + | 0.106776i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.24106e6i | 0.167432i | 0.996490 | + | 0.0837158i | \(0.0266788\pi\) | ||||
−0.996490 | + | 0.0837158i | \(0.973321\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.60140e6 | − | 2.60140e6i | 0.192312 | − | 0.192312i | ||||
\(713\) | 1.59227e6 | − | 1.59227e6i | 0.117299 | − | 0.117299i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.01191e6i | 0.656953i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.08682e7 | − | 2.08682e7i | −1.51069 | − | 1.51069i | ||||
\(719\) | 1.26499e6 | 0.0912565 | 0.0456283 | − | 0.998958i | \(-0.485471\pi\) | ||||
0.0456283 | + | 0.998958i | \(0.485471\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.03342e6 | 0.217317 | ||||||||
\(722\) | 1.45889e7 | + | 1.45889e7i | 1.04155 | + | 1.04155i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.21623e6i | 0.0862322i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.55230e7 | − | 1.55230e7i | 1.08928 | − | 1.08928i | 0.0936761 | − | 0.995603i | \(-0.470138\pi\) |
0.995603 | − | 0.0936761i | \(-0.0298618\pi\) | |||||||
\(728\) | 121949. | − | 121949.i | 0.00852802 | − | 0.00852802i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.76492e7i | 1.22160i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.63098e6 | + | 6.63098e6i | 0.455846 | + | 0.455846i | 0.897289 | − | 0.441443i | \(-0.145533\pi\) |
−0.441443 | + | 0.897289i | \(0.645533\pi\) | |||||||
\(734\) | −1.17875e7 | −0.807576 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.82618e6 | −0.260358 | ||||||||
\(737\) | −7.89025e6 | − | 7.89025e6i | −0.535084 | − | 0.535084i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.71487e6i | − | 0.452300i | −0.974092 | − | 0.226150i | \(-0.927386\pi\) | ||
0.974092 | − | 0.226150i | \(-0.0726140\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.34472e6 | − | 1.34472e6i | 0.0896646 | − | 0.0896646i | ||||
\(743\) | −7.01273e6 | + | 7.01273e6i | −0.466031 | + | 0.466031i | −0.900626 | − | 0.434595i | \(-0.856892\pi\) |
0.434595 | + | 0.900626i | \(0.356892\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 2.66640e7i | − | 1.75420i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7.43363e6 | + | 7.43363e6i | 0.485788 | + | 0.485788i | ||||
\(749\) | −1.53267e6 | −0.0998262 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.08177e7 | 0.699896 | 0.349948 | − | 0.936769i | \(-0.386199\pi\) | ||||
0.349948 | + | 0.936769i | \(0.386199\pi\) | |||||||
\(752\) | −5.96834e6 | − | 5.96834e6i | −0.384866 | − | 0.384866i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 7.11875e6i | − | 0.456011i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.46756e7 | + | 1.46756e7i | −0.930798 | + | 0.930798i | −0.997756 | − | 0.0669581i | \(-0.978671\pi\) |
0.0669581 | + | 0.997756i | \(0.478671\pi\) | |||||||
\(758\) | 1.27943e6 | − | 1.27943e6i | 0.0808802 | − | 0.0808802i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.75265e7i | 1.09707i | 0.836127 | + | 0.548535i | \(0.184814\pi\) | ||||
−0.836127 | + | 0.548535i | \(0.815186\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.44163e6 | + | 1.44163e6i | 0.0896487 | + | 0.0896487i | ||||
\(764\) | 2.25614e7 | 1.39841 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.24322e7 | 0.765556 | ||||||||
\(767\) | −6.30069e6 | − | 6.30069e6i | −0.386723 | − | 0.386723i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.48329e7i | 0.904501i | 0.891891 | + | 0.452251i | \(0.149379\pi\) | ||||
−0.891891 | + | 0.452251i | \(0.850621\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.21480e7 | − | 1.21480e7i | 0.733602 | − | 0.733602i | ||||
\(773\) | −1.30854e7 | + | 1.30854e7i | −0.787658 | + | 0.787658i | −0.981110 | − | 0.193451i | \(-0.938032\pi\) |
0.193451 | + | 0.981110i | \(0.438032\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 102500.i | 0.00611042i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.24235e7 | + | 2.24235e7i | 1.32817 | + | 1.32817i | ||||
\(779\) | 3.68081e7 | 2.17320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.29068e6 | −0.251709 | ||||||||
\(782\) | 5.48209e6 | + | 5.48209e6i | 0.320575 | + | 0.320575i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.92959e7i | 1.12118i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.07428e7 | − | 1.07428e7i | 0.618273 | − | 0.618273i | −0.326815 | − | 0.945088i | \(-0.605975\pi\) |
0.945088 | + | 0.326815i | \(0.105975\pi\) | |||||||
\(788\) | −1.93830e7 | + | 1.93830e7i | −1.11200 | + | 1.11200i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 574832.i | − | 0.0326663i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.09007e6 | + | 1.09007e6i | 0.0615559 | + | 0.0615559i | ||||
\(794\) | 4.20045e7 | 2.36453 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.24207e7 | 1.25420 | ||||||||
\(797\) | −1.18496e7 | − | 1.18496e7i | −0.660780 | − | 0.660780i | 0.294784 | − | 0.955564i | \(-0.404752\pi\) |
−0.955564 | + | 0.294784i | \(0.904752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.46283e7i | 0.810639i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.87590e7 | − | 1.87590e7i | 1.02985 | − | 1.02985i | ||||
\(803\) | 5.11100e6 | − | 5.11100e6i | 0.279716 | − | 0.279716i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 9.48083e6i | − | 0.514054i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.68996e6 | + | 3.68996e6i | 0.198835 | + | 0.198835i | ||||
\(809\) | −2.70325e7 | −1.45216 | −0.726081 | − | 0.687610i | \(-0.758660\pi\) | ||||
−0.726081 | + | 0.687610i | \(0.758660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.53514e7 | 1.35347 | 0.676737 | − | 0.736225i | \(-0.263394\pi\) | ||||
0.676737 | + | 0.736225i | \(0.263394\pi\) | |||||||
\(812\) | −989986. | − | 989986.i | −0.0526913 | − | 0.0526913i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 2.05463e7i | − | 1.08686i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.40542e7 | − | 1.40542e7i | 0.736635 | − | 0.736635i | ||||
\(818\) | −2.82341e7 | + | 2.82341e7i | −1.47534 | + | 1.47534i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.15371e7i | 0.597366i | 0.954352 | + | 0.298683i | \(0.0965472\pi\) | ||||
−0.954352 | + | 0.298683i | \(0.903453\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.30562e7 | + | 1.30562e7i | 0.671918 | + | 0.671918i | 0.958158 | − | 0.286240i | \(-0.0924055\pi\) |
−0.286240 | + | 0.958158i | \(0.592405\pi\) | |||||||
\(824\) | 7.88735e6 | 0.404681 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.85009e6 | −0.196345 | ||||||||
\(827\) | −6.81499e6 | − | 6.81499e6i | −0.346499 | − | 0.346499i | 0.512305 | − | 0.858804i | \(-0.328792\pi\) |
−0.858804 | + | 0.512305i | \(0.828792\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.23963e7i | 0.626476i | 0.949675 | + | 0.313238i | \(0.101414\pi\) | ||||
−0.949675 | + | 0.313238i | \(0.898586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.13510e6 | + | 4.13510e6i | −0.207099 | + | 0.207099i | ||||
\(833\) | 2.36470e7 | − | 2.36470e7i | 1.18077 | − | 1.18077i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 1.18390e7i | − | 0.585867i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.07537e7 | − | 1.07537e7i | −0.528989 | − | 0.528989i | ||||
\(839\) | 3.23818e7 | 1.58817 | 0.794083 | − | 0.607809i | \(-0.207951\pi\) | ||||
0.794083 | + | 0.607809i | \(0.207951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.12733e6 | −0.444994 | ||||||||
\(842\) | 1.72488e7 | + | 1.72488e7i | 0.838455 | + | 0.838455i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 2.08830e7i | − | 1.00911i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.35114e6 | + | 1.35114e6i | −0.0647129 | + | 0.0647129i | ||||
\(848\) | 1.31672e7 | − | 1.31672e7i | 0.628787 | − | 0.628787i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.89687e6i | − | 0.326458i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.39744e6 | + | 3.39744e6i | 0.159875 | + | 0.159875i | 0.782511 | − | 0.622636i | \(-0.213938\pi\) |
−0.622636 | + | 0.782511i | \(0.713938\pi\) | |||||||
\(854\) | 666093. | 0.0312529 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.98518e6 | −0.185893 | ||||||||
\(857\) | 1.93484e7 | + | 1.93484e7i | 0.899897 | + | 0.899897i | 0.995427 | − | 0.0955295i | \(-0.0304544\pi\) |
−0.0955295 | + | 0.995427i | \(0.530454\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.39307e6i | 0.110656i | 0.998468 | + | 0.0553278i | \(0.0176204\pi\) | ||||
−0.998468 | + | 0.0553278i | \(0.982380\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.04005e7 | − | 2.04005e7i | 0.935130 | − | 0.935130i | ||||
\(863\) | −2.53145e7 | + | 2.53145e7i | −1.15702 | + | 1.15702i | −0.171909 | + | 0.985113i | \(0.554994\pi\) |
−0.985113 | + | 0.171909i | \(0.945006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.26282e6i | 0.0572200i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.31848e6 | − | 1.31848e6i | −0.0593981 | − | 0.0593981i | ||||
\(869\) | 1.37994e7 | 0.619882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.57702e7 | −0.704356 | ||||||||
\(872\) | 3.74847e6 | + | 3.74847e6i | 0.166941 | + | 0.166941i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 8.73091e6i | − | 0.386617i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.14638e7 | − | 2.14638e7i | 0.942339 | − | 0.942339i | −0.0560871 | − | 0.998426i | \(-0.517862\pi\) |
0.998426 | + | 0.0560871i | \(0.0178625\pi\) | |||||||
\(878\) | −1.27661e7 | + | 1.27661e7i | −0.558885 | + | 0.558885i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.01600e7i | − | 1.30916i | −0.755994 | − | 0.654578i | \(-0.772846\pi\) | ||
0.755994 | − | 0.654578i | \(-0.227154\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.03899e7 | + | 2.03899e7i | 0.880061 | + | 0.880061i | 0.993540 | − | 0.113480i | \(-0.0361996\pi\) |
−0.113480 | + | 0.993540i | \(0.536200\pi\) | |||||||
\(884\) | 1.48576e7 | 0.639466 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.62290e7 | 1.97848 | ||||||||
\(887\) | 6.74195e6 | + | 6.74195e6i | 0.287724 | + | 0.287724i | 0.836180 | − | 0.548455i | \(-0.184784\pi\) |
−0.548455 | + | 0.836180i | \(0.684784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.79661e6i | 0.203554i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.66086e6 | − | 8.66086e6i | 0.364459 | − | 0.364459i | ||||
\(893\) | 1.16487e7 | − | 1.16487e7i | 0.488820 | − | 0.488820i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.26557e6i | − | 0.0526642i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.48998e6 | + | 7.48998e6i | 0.309949 | + | 0.309949i | ||||
\(899\) | 1.51611e7 | 0.625650 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.22726e7 | −1.32441 | ||||||||
\(902\) | −1.70917e7 | − | 1.70917e7i | −0.699471 | − | 0.699471i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 1.49465e6i | − | 0.0608301i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.01745e7 | + | 2.01745e7i | −0.814301 | + | 0.814301i | −0.985276 | − | 0.170974i | \(-0.945309\pi\) |
0.170974 | + | 0.985276i | \(0.445309\pi\) | |||||||
\(908\) | −1.42042e7 | + | 1.42042e7i | −0.571744 | + | 0.571744i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.76912e7i | 1.90389i | 0.306266 | + | 0.951946i | \(0.400920\pi\) | ||||
−0.306266 | + | 0.951946i | \(0.599080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.42534e6 | − | 2.42534e6i | −0.0962932 | − | 0.0962932i | ||||
\(914\) | −1.14621e7 | −0.453835 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.48496e6 | 0.255369 | ||||||||
\(917\) | 3.00118e6 | + | 3.00118e6i | 0.117861 | + | 0.117861i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.43195e7i | − | 0.559293i | −0.960103 | − | 0.279646i | \(-0.909783\pi\) | ||
0.960103 | − | 0.279646i | \(-0.0902172\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.48667e7 | + | 2.48667e7i | −0.963365 | + | 0.963365i | ||||
\(923\) | −4.28788e6 | + | 4.28788e6i | −0.165668 | + | 0.165668i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 705028.i | − | 0.0270196i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.82158e7 | − | 1.82158e7i | −0.694351 | − | 0.694351i | ||||
\(929\) | −2.60483e7 | −0.990241 | −0.495120 | − | 0.868824i | \(-0.664876\pi\) | ||||
−0.495120 | + | 0.868824i | \(0.664876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.76608e7 | −1.42402 | ||||||||
\(932\) | 2.88085e7 | + | 2.88085e7i | 1.08638 | + | 1.08638i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 1.72408e7i | − | 0.646681i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.81854e7 | + | 1.81854e7i | −0.676665 | + | 0.676665i | −0.959244 | − | 0.282579i | \(-0.908810\pi\) |
0.282579 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(938\) | −4.81826e6 | + | 4.81826e6i | −0.178806 | + | 0.178806i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.70102e6i | 0.0626231i | 0.999510 | + | 0.0313115i | \(0.00996840\pi\) | ||||
−0.999510 | + | 0.0313115i | \(0.990032\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.73725e6 | − | 5.73725e6i | −0.210099 | − | 0.210099i | ||||
\(944\) | −3.76993e7 | −1.37690 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.30521e7 | −0.474190 | ||||||||
\(947\) | 3.59453e7 | + | 3.59453e7i | 1.30247 | + | 1.30247i | 0.926724 | + | 0.375744i | \(0.122613\pi\) |
0.375744 | + | 0.926724i | \(0.377387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.02153e7i | − | 0.368203i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −894196. | + | 894196.i | −0.0319772 | + | 0.0319772i | ||||
\(953\) | 3.75538e7 | − | 3.75538e7i | 1.33943 | − | 1.33943i | 0.442827 | − | 0.896607i | \(-0.353976\pi\) |
0.896607 | − | 0.442827i | \(-0.146024\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.34367e7i | − | 0.829377i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.41271e7 | − | 1.41271e7i | −0.497324 | − | 0.497324i | ||||
\(959\) | 1.62711e6 | 0.0571309 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.43743e6 | −0.294715 | ||||||||
\(962\) | −2.05329e7 | − | 2.05329e7i | −0.715341 | − | 0.715341i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 3.13886e7i | − | 1.08788i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.16001e6 | + | 7.16001e6i | −0.246234 | + | 0.246234i | −0.819423 | − | 0.573189i | \(-0.805706\pi\) |
0.573189 | + | 0.819423i | \(0.305706\pi\) | |||||||
\(968\) | −3.51316e6 | + | 3.51316e6i | −0.120506 | + | 0.120506i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.40544e7i | 0.818740i | 0.912368 | + | 0.409370i | \(0.134252\pi\) | ||||
−0.912368 | + | 0.409370i | \(0.865748\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.46715e6 | − | 2.46715e6i | −0.0835435 | − | 0.0835435i | ||||
\(974\) | −2.39771e7 | −0.809840 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.52225e6 | 0.219166 | ||||||||
\(977\) | −3.64967e7 | − | 3.64967e7i | −1.22326 | − | 1.22326i | −0.966467 | − | 0.256789i | \(-0.917335\pi\) |
−0.256789 | − | 0.966467i | \(-0.582665\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.77569e7i | − | 0.592122i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.02399e7 | + | 3.02399e7i | −1.00069 | + | 1.00069i | ||||
\(983\) | −2.25567e7 | + | 2.25567e7i | −0.744546 | + | 0.744546i | −0.973449 | − | 0.228903i | \(-0.926486\pi\) |
0.228903 | + | 0.973449i | \(0.426486\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.21987e7i | 1.70989i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.18313e7 | − | 1.18313e7i | −0.385602 | − | 0.385602i | ||||
\(989\) | −4.38125e6 | −0.142432 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.40802e6 | 0.110235 | 0.0551173 | − | 0.998480i | \(-0.482447\pi\) | ||||
0.0551173 | + | 0.998480i | \(0.482447\pi\) | |||||||
\(992\) | −2.42601e7 | − | 2.42601e7i | −0.782731 | − | 0.782731i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.62015e6i | 0.0841123i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.74529e7 | + | 2.74529e7i | −0.874684 | + | 0.874684i | −0.992979 | − | 0.118295i | \(-0.962257\pi\) |
0.118295 | + | 0.992979i | \(0.462257\pi\) | |||||||
\(998\) | 7.57647e6 | − | 7.57647e6i | 0.240791 | − | 0.240791i | ||||
\(999\) | 0 | 0 |
(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 | 225.6.f.c.143.3 | yes | 24 | |
3.2 | odd | 2 | inner | 225.6.f.c.143.10 | yes | 24 | |
5.2 | odd | 4 | inner | 225.6.f.c.107.10 | yes | 24 | |
5.3 | odd | 4 | inner | 225.6.f.c.107.4 | yes | 24 | |
5.4 | even | 2 | inner | 225.6.f.c.143.9 | yes | 24 | |
15.2 | even | 4 | inner | 225.6.f.c.107.3 | ✓ | 24 | |
15.8 | even | 4 | inner | 225.6.f.c.107.9 | yes | 24 | |
15.14 | odd | 2 | inner | 225.6.f.c.143.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.6.f.c.107.3 | ✓ | 24 | 15.2 | even | 4 | inner | |
225.6.f.c.107.4 | yes | 24 | 5.3 | odd | 4 | inner | |
225.6.f.c.107.9 | yes | 24 | 15.8 | even | 4 | inner | |
225.6.f.c.107.10 | yes | 24 | 5.2 | odd | 4 | inner | |
225.6.f.c.143.3 | yes | 24 | 1.1 | even | 1 | trivial | |
225.6.f.c.143.4 | yes | 24 | 15.14 | odd | 2 | inner | |
225.6.f.c.143.9 | yes | 24 | 5.4 | even | 2 | inner | |
225.6.f.c.143.10 | yes | 24 | 3.2 | odd | 2 | inner |