Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(37,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.e (of order \(3\), degree \(2\), not 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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{16} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(-9.84603i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.37 |
Dual form | 108.6.e.a.73.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.1603 | + | 22.7942i | −0.235418 | + | 0.407755i | −0.959394 | − | 0.282069i | \(-0.908979\pi\) |
0.723976 | + | 0.689825i | \(0.242312\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.6287 | − | 54.7826i | −0.243970 | − | 0.422569i | 0.717871 | − | 0.696176i | \(-0.245117\pi\) |
−0.961842 | + | 0.273607i | \(0.911783\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 49.1194 | + | 85.0772i | 0.122397 | + | 0.211998i | 0.920712 | − | 0.390242i | \(-0.127609\pi\) |
−0.798315 | + | 0.602240i | \(0.794275\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 369.143 | − | 639.374i | 0.605809 | − | 1.04929i | −0.386114 | − | 0.922451i | \(-0.626183\pi\) |
0.991923 | − | 0.126841i | \(-0.0404839\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −250.060 | −0.209856 | −0.104928 | − | 0.994480i | \(-0.533461\pi\) | ||||
−0.104928 | + | 0.994480i | \(0.533461\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1102.41 | 0.700579 | 0.350290 | − | 0.936641i | \(-0.386083\pi\) | ||||
0.350290 | + | 0.936641i | \(0.386083\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2204.70 | − | 3818.66i | 0.869022 | − | 1.50519i | 0.00602414 | − | 0.999982i | \(-0.498082\pi\) |
0.862998 | − | 0.505208i | \(-0.168584\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1216.12 | + | 2106.37i | 0.389157 | + | 0.674040i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3941.06 | − | 6826.11i | −0.870197 | − | 1.50723i | −0.861792 | − | 0.507262i | \(-0.830658\pi\) |
−0.00840534 | − | 0.999965i | \(-0.502676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2305.65 | − | 3993.49i | 0.430912 | − | 0.746361i | −0.566040 | − | 0.824377i | \(-0.691525\pi\) |
0.996952 | + | 0.0780167i | \(0.0248587\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1664.97 | 0.229740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11896.3 | 1.42859 | 0.714297 | − | 0.699843i | \(-0.246747\pi\) | ||||
0.714297 | + | 0.699843i | \(0.246747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5040.58 | − | 8730.55i | 0.468297 | − | 0.811114i | −0.531047 | − | 0.847343i | \(-0.678201\pi\) |
0.999344 | + | 0.0362286i | \(0.0115344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3518.99 | − | 6095.07i | −0.290233 | − | 0.502698i | 0.683632 | − | 0.729827i | \(-0.260400\pi\) |
−0.973865 | + | 0.227129i | \(0.927066\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7459.33 | + | 12919.9i | 0.492555 | + | 0.853131i | 0.999963 | − | 0.00857499i | \(-0.00272954\pi\) |
−0.507408 | + | 0.861706i | \(0.669396\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6402.75 | − | 11089.9i | 0.380957 | − | 0.659837i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −22451.7 | −1.09789 | −0.548947 | − | 0.835857i | \(-0.684971\pi\) | ||||
−0.548947 | + | 0.835857i | \(0.684971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2585.69 | −0.115258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5405.25 | − | 9362.17i | 0.202156 | − | 0.350144i | −0.747067 | − | 0.664749i | \(-0.768539\pi\) |
0.949223 | + | 0.314605i | \(0.101872\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 594.647 | + | 1029.96i | 0.0204614 | + | 0.0354401i | 0.876075 | − | 0.482175i | \(-0.160153\pi\) |
−0.855613 | + | 0.517615i | \(0.826820\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9716.02 | + | 16828.6i | 0.285236 | + | 0.494044i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −29590.2 | + | 51251.8i | −0.805307 | + | 1.39483i | 0.110776 | + | 0.993845i | \(0.464666\pi\) |
−0.916084 | + | 0.400988i | \(0.868667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14326.6 | −0.337284 | −0.168642 | − | 0.985677i | \(-0.553938\pi\) | ||||
−0.168642 | + | 0.985677i | \(0.553938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −53098.2 | −1.16620 | −0.583099 | − | 0.812401i | \(-0.698160\pi\) | ||||
−0.583099 | + | 0.812401i | \(0.698160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3107.17 | − | 5381.77i | 0.0597225 | − | 0.103442i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 18695.6 | + | 32381.6i | 0.337032 | + | 0.583756i | 0.983873 | − | 0.178869i | \(-0.0572438\pi\) |
−0.646841 | + | 0.762625i | \(0.723910\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 60439.5 | + | 104684.i | 0.962998 | + | 1.66796i | 0.714900 | + | 0.699226i | \(0.246472\pi\) |
0.248097 | + | 0.968735i | \(0.420195\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3290.85 | − | 5699.93i | 0.0494039 | − | 0.0855701i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −97873.2 | −1.30975 | −0.654875 | − | 0.755737i | \(-0.727279\pi\) | ||||
−0.654875 | + | 0.755737i | \(0.727279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −46702.1 | −0.591198 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −14507.9 | + | 25128.5i | −0.164929 | + | 0.285665i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −53356.7 | − | 92416.4i | −0.575784 | − | 0.997286i | −0.995956 | − | 0.0898422i | \(-0.971364\pi\) |
0.420172 | − | 0.907444i | \(-0.361970\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 48236.1 | + | 83547.3i | 0.470510 | + | 0.814946i | 0.999431 | − | 0.0337242i | \(-0.0107368\pi\) |
−0.528922 | + | 0.848671i | \(0.677403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14972.2 | + | 25932.6i | −0.139057 | + | 0.240854i | −0.927140 | − | 0.374715i | \(-0.877740\pi\) |
0.788083 | + | 0.615569i | \(0.211074\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −22758.9 | −0.192173 | −0.0960865 | − | 0.995373i | \(-0.530633\pi\) | ||||
−0.0960865 | + | 0.995373i | \(0.530633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2671.93 | −0.0215407 | −0.0107703 | − | 0.999942i | \(-0.503428\pi\) | ||||
−0.0107703 | + | 0.999942i | \(0.503428\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 65669.6 | − | 113743.i | 0.483803 | − | 0.837971i | −0.516024 | − | 0.856574i | \(-0.672588\pi\) |
0.999827 | + | 0.0186028i | \(0.00592179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 58028.9 | + | 100509.i | 0.409166 | + | 0.708697i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7909.09 | + | 13698.9i | 0.0511987 | + | 0.0886787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 75700.1 | − | 131116.i | 0.470038 | − | 0.814130i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −146269. | −0.837293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 236012. | 1.29845 | 0.649223 | − | 0.760598i | \(-0.275094\pi\) | ||||
0.649223 | + | 0.760598i | \(0.275094\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 180183. | − | 312086.i | 0.917352 | − | 1.58890i | 0.113930 | − | 0.993489i | \(-0.463656\pi\) |
0.803421 | − | 0.595411i | \(-0.203011\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −34867.7 | − | 60392.6i | −0.170920 | − | 0.296043i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −118833. | − | 205825.i | −0.540923 | − | 0.936906i | −0.998851 | − | 0.0479167i | \(-0.984742\pi\) |
0.457929 | − | 0.888989i | \(-0.348592\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −81673.4 | + | 141462.i | −0.358545 | + | 0.621018i | −0.987718 | − | 0.156247i | \(-0.950060\pi\) |
0.629173 | + | 0.777265i | \(0.283394\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 72528.2 | 0.296597 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 207461. | 0.819440 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 167803. | − | 290644.i | 0.619205 | − | 1.07250i | −0.370426 | − | 0.928862i | \(-0.620788\pi\) |
0.989631 | − | 0.143633i | \(-0.0458785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 67788.5 | + | 117413.i | 0.241943 | + | 0.419058i | 0.961268 | − | 0.275616i | \(-0.0888819\pi\) |
−0.719325 | + | 0.694674i | \(0.755549\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 60685.7 | + | 105111.i | 0.202888 | + | 0.351413i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 212716. | − | 368435.i | 0.688733 | − | 1.19292i | −0.283516 | − | 0.958968i | \(-0.591501\pi\) |
0.972248 | − | 0.233952i | \(-0.0751659\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −278928. | −0.848062 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −158679. | −0.467789 | −0.233895 | − | 0.972262i | \(-0.575147\pi\) | ||||
−0.233895 | + | 0.972262i | \(0.575147\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −259223. | + | 448988.i | −0.719254 | + | 1.24579i | 0.242041 | + | 0.970266i | \(0.422183\pi\) |
−0.961296 | + | 0.275519i | \(0.911150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −86886.2 | − | 150491.i | −0.234010 | − | 0.405317i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −76589.0 | − | 132656.i | −0.194559 | − | 0.336986i | 0.752197 | − | 0.658938i | \(-0.228994\pi\) |
−0.946756 | + | 0.321953i | \(0.895661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 76928.4 | − | 133244.i | 0.189885 | − | 0.328891i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 736845. | 1.71887 | 0.859437 | − | 0.511242i | \(-0.170815\pi\) | ||||
0.859437 | + | 0.511242i | \(0.170815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 28183.8 | 0.0639445 | 0.0319722 | − | 0.999489i | \(-0.489821\pi\) | ||||
0.0319722 | + | 0.999489i | \(0.489821\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −156559. | + | 271168.i | −0.336316 | + | 0.582517i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12282.8 | − | 21274.4i | −0.0256858 | − | 0.0444891i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 49660.5 | + | 86014.5i | 0.0984981 | + | 0.170604i | 0.911063 | − | 0.412267i | \(-0.135263\pi\) |
−0.812565 | + | 0.582870i | \(0.801929\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −208636. | + | 361368.i | −0.403177 | + | 0.698324i | −0.994107 | − | 0.108399i | \(-0.965428\pi\) |
0.590930 | + | 0.806723i | \(0.298761\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −254565. | −0.467340 | −0.233670 | − | 0.972316i | \(-0.575073\pi\) | ||||
−0.233670 | + | 0.972316i | \(0.575073\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −599702. | −1.07350 | −0.536751 | − | 0.843741i | \(-0.680348\pi\) | ||||
−0.536751 | + | 0.843741i | \(0.680348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −249301. | + | 431803.i | −0.424604 | + | 0.735436i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 132671. | + | 229792.i | 0.220491 | + | 0.381901i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 54149.4 | + | 93789.6i | 0.0857488 | + | 0.148521i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −378292. | + | 655221.i | −0.584953 | + | 1.01317i | 0.409928 | + | 0.912118i | \(0.365554\pi\) |
−0.994881 | + | 0.101051i | \(0.967779\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 185243. | 0.273304 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −291699. | −0.420518 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −92307.9 | + | 159882.i | −0.127133 | + | 0.220201i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 55602.4 | + | 96306.2i | 0.0748741 | + | 0.129686i | 0.901032 | − | 0.433754i | \(-0.142811\pi\) |
−0.826157 | + | 0.563439i | \(0.809478\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −245380. | − | 425010.i | −0.316063 | − | 0.547438i | 0.663600 | − | 0.748088i | \(-0.269028\pi\) |
−0.979663 | + | 0.200650i | \(0.935695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −380511. | + | 659064.i | −0.479488 | + | 0.830498i | −0.999723 | − | 0.0235249i | \(-0.992511\pi\) |
0.520235 | + | 0.854023i | \(0.325844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 356267. | 0.429918 | 0.214959 | − | 0.976623i | \(-0.431038\pi\) | ||||
0.214959 | + | 0.976623i | \(0.431038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −392667. | −0.463825 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −453120. | + | 784826.i | −0.513119 | + | 0.888748i | 0.486765 | + | 0.873533i | \(0.338177\pi\) |
−0.999884 | + | 0.0152152i | \(0.995157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −261288. | − | 452564.i | −0.289785 | − | 0.501923i | 0.683973 | − | 0.729507i | \(-0.260251\pi\) |
−0.973758 | + | 0.227584i | \(0.926917\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 168523. | + | 291891.i | 0.179368 | + | 0.310675i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 406945. | − | 704849.i | 0.424417 | − | 0.735113i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 625287. | 0.626462 | 0.313231 | − | 0.949677i | \(-0.398589\pi\) | ||||
0.313231 | + | 0.949677i | \(0.398589\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 433175. | 0.425463 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −651106. | + | 1.12775e6i | −0.614921 | + | 1.06507i | 0.375478 | + | 0.926831i | \(0.377479\pi\) |
−0.990398 | + | 0.138243i | \(0.955855\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −376266. | − | 651712.i | −0.348534 | − | 0.603679i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −716761. | − | 1.24147e6i | −0.638977 | − | 1.10674i | −0.985658 | − | 0.168757i | \(-0.946025\pi\) |
0.346681 | − | 0.937983i | \(-0.387309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 295471. | − | 511770.i | 0.258464 | − | 0.447672i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.52329e6 | 1.28352 | 0.641758 | − | 0.766907i | \(-0.278205\pi\) | ||||
0.641758 | + | 0.766907i | \(0.278205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.60134e6 | 1.32453 | 0.662263 | − | 0.749271i | \(-0.269596\pi\) | ||||
0.662263 | + | 0.749271i | \(0.269596\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −119470. | + | 206927.i | −0.0952633 | + | 0.165001i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 446972. | + | 774178.i | 0.350010 | + | 0.606235i | 0.986251 | − | 0.165255i | \(-0.0528448\pi\) |
−0.636241 | + | 0.771491i | \(0.719511\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14200.0 | − | 24595.2i | −0.0107281 | − | 0.0185817i | 0.860612 | − | 0.509262i | \(-0.170082\pi\) |
−0.871340 | + | 0.490680i | \(0.836748\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 554783. | − | 960912.i | 0.411772 | − | 0.713210i | −0.583312 | − | 0.812248i | \(-0.698243\pi\) |
0.995084 | + | 0.0990384i | \(0.0315767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −637709. | −0.457002 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.35733e6 | −0.955960 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.22884e6 | − | 2.12841e6i | 0.836230 | − | 1.44839i | −0.0567942 | − | 0.998386i | \(-0.518088\pi\) |
0.893025 | − | 0.450008i | \(-0.148579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 142269. | + | 246417.i | 0.0951821 | + | 0.164860i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.62770e6 | − | 2.81926e6i | −1.05292 | − | 1.82372i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −222602. | + | 385559.i | −0.141616 | + | 0.245287i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31302.8 | −0.0192679 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.77336e6 | 1.07387 | 0.536934 | − | 0.843624i | \(-0.319583\pi\) | ||||
0.536934 | + | 0.843624i | \(0.319583\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 752855. | − | 1.30398e6i | 0.441378 | − | 0.764489i | −0.556414 | − | 0.830905i | \(-0.687823\pi\) |
0.997792 | + | 0.0664162i | \(0.0211565\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 406353. | + | 703823.i | 0.234446 | + | 0.406072i | 0.959111 | − | 0.283029i | \(-0.0913392\pi\) |
−0.724666 | + | 0.689100i | \(0.758006\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 523798. | + | 907244.i | 0.292763 | + | 0.507080i | 0.974462 | − | 0.224553i | \(-0.0720921\pi\) |
−0.681699 | + | 0.731632i | \(0.738759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 387164. | − | 670588.i | 0.213019 | − | 0.368960i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −275668. | −0.147021 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.79568e6 | 0.943020 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 471858. | − | 817283.i | 0.240338 | − | 0.416277i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 34002.7 | + | 58894.4i | 0.0170586 | + | 0.0295463i | 0.874429 | − | 0.485154i | \(-0.161236\pi\) |
−0.857370 | + | 0.514700i | \(0.827903\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −778830. | − | 1.34897e6i | −0.379167 | − | 0.656737i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 208236. | − | 360675.i | 0.0998806 | − | 0.172998i | −0.811755 | − | 0.583999i | \(-0.801487\pi\) |
0.911635 | + | 0.411001i | \(0.134821\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 453007. | 0.210969 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.87321e6 | −0.859709 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.40370e6 | + | 2.43128e6i | −0.625822 | + | 1.08396i | 0.362559 | + | 0.931961i | \(0.381903\pi\) |
−0.988381 | + | 0.151995i | \(0.951430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 240986. | + | 417401.i | 0.105908 | + | 0.183438i | 0.914109 | − | 0.405469i | \(-0.132892\pi\) |
−0.808201 | + | 0.588907i | \(0.799558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.00019e6 | + | 3.46442e6i | 0.854346 | + | 1.47977i | 0.877251 | + | 0.480033i | \(0.159375\pi\) |
−0.0229050 | + | 0.999738i | \(0.507292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 188541. | − | 326563.i | 0.0794027 | − | 0.137530i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 800858. | 0.327959 | 0.163979 | − | 0.986464i | \(-0.447567\pi\) | ||||
0.163979 | + | 0.986464i | \(0.447567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.26080e6 | −0.509189 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 698785. | − | 1.21033e6i | 0.274544 | − | 0.475524i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50486e6 | − | 2.60649e6i | −0.583218 | − | 1.01016i | −0.995095 | − | 0.0989236i | \(-0.968460\pi\) |
0.411877 | − | 0.911239i | \(-0.364873\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 710120. | + | 1.22996e6i | 0.267853 | + | 0.463936i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −796653. | + | 1.37984e6i | −0.296481 | + | 0.513520i | −0.975328 | − | 0.220759i | \(-0.929147\pi\) |
0.678847 | + | 0.734280i | \(0.262480\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.81925e6 | −2.10869 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −297930. | −0.106541 | −0.0532703 | − | 0.998580i | \(-0.516965\pi\) | ||||
−0.0532703 | + | 0.998580i | \(0.516965\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −645151. | + | 1.11743e6i | −0.224732 | + | 0.389247i | −0.956239 | − | 0.292587i | \(-0.905484\pi\) |
0.731507 | + | 0.681834i | \(0.238817\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 81782.2 | + | 141651.i | 0.0281194 | + | 0.0487043i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.49937e6 | + | 4.32903e6i | 0.837444 | + | 1.45050i | 0.892025 | + | 0.451986i | \(0.149284\pi\) |
−0.0545807 | + | 0.998509i | \(0.517382\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −551309. | + | 954894.i | −0.182370 | + | 0.315874i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −984153. | −0.317373 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −558980. | −0.178000 | −0.0890000 | − | 0.996032i | \(-0.528367\pi\) | ||||
−0.0890000 | + | 0.996032i | \(0.528367\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 47103.6 | − | 81585.8i | 0.0146283 | − | 0.0253369i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) |
0.873247 | + | 0.487278i | \(0.162010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.70222e6 | − | 2.94834e6i | −0.522101 | − | 0.904305i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 584340. | + | 1.01211e6i | 0.174856 | + | 0.302859i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.73115e6 | + | 4.73049e6i | −0.807304 | + | 1.39829i | 0.107420 | + | 0.994214i | \(0.465741\pi\) |
−0.914724 | + | 0.404078i | \(0.867592\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −683845. | −0.197280 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.18159e6 | −0.906827 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −418486. | + | 724839.i | −0.116452 | + | 0.201700i | −0.918359 | − | 0.395748i | \(-0.870485\pi\) |
0.801907 | + | 0.597448i | \(0.203819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.21404e6 | + | 5.56689e6i | 0.883785 | + | 1.53076i | 0.847100 | + | 0.531433i | \(0.178346\pi\) |
0.0366842 | + | 0.999327i | \(0.488320\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −304102. | − | 526720.i | −0.0816671 | − | 0.141452i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 37615.8 | − | 65152.5i | 0.00998392 | − | 0.0172927i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.11509e6 | 1.32636 | 0.663178 | − | 0.748462i | \(-0.269207\pi\) | ||||
0.663178 | + | 0.748462i | \(0.269207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.39089e6 | −0.356512 | −0.178256 | − | 0.983984i | \(-0.557045\pi\) | ||||
−0.178256 | + | 0.983984i | \(0.557045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.43048e6 | − | 4.20971e6i | 0.608819 | − | 1.05450i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.76266e6 | + | 3.05301e6i | 0.436523 | + | 0.756079i | 0.997419 | − | 0.0718069i | \(-0.0228765\pi\) |
−0.560896 | + | 0.827886i | \(0.689543\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.02216e6 | + | 1.77043e6i | 0.247462 | + | 0.428617i | 0.962821 | − | 0.270140i | \(-0.0870701\pi\) |
−0.715359 | + | 0.698757i | \(0.753737\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.28804e6 | − | 2.23094e6i | 0.308339 | − | 0.534058i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.70508e6 | −1.80369 | −0.901844 | − | 0.432062i | \(-0.857786\pi\) | ||||
−0.901844 | + | 0.432062i | \(0.857786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 990361. | 0.229273 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 614611. | − | 1.06454e6i | 0.139178 | − | 0.241064i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.28846e6 | − | 7.42783e6i | −0.960529 | − | 1.66369i | −0.721175 | − | 0.692753i | \(-0.756397\pi\) |
−0.239355 | − | 0.970932i | \(-0.576936\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 716317. | + | 1.24070e6i | 0.156983 | + | 0.271903i | 0.933779 | − | 0.357849i | \(-0.116490\pi\) |
−0.776796 | + | 0.629752i | \(0.783157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.47223e6 | + | 2.54998e6i | −0.319172 | + | 0.552821i | −0.980315 | − | 0.197438i | \(-0.936738\pi\) |
0.661144 | + | 0.750259i | \(0.270071\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.96160e6 | −1.05276 | −0.526380 | − | 0.850249i | \(-0.676451\pi\) | ||||
−0.526380 | + | 0.850249i | \(0.676451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.74361e6 | 0.785884 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 345701. | − | 598772.i | 0.0710473 | − | 0.123058i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.34065e6 | + | 2.32208e6i | 0.272635 | + | 0.472218i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −120757. | − | 209157.i | −0.0240476 | − | 0.0416517i | 0.853751 | − | 0.520681i | \(-0.174322\pi\) |
−0.877799 | + | 0.479030i | \(0.840989\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.39145e6 | − | 7.60621e6i | 0.865456 | − | 1.49901i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.80875e6 | 0.542199 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 325055. | 0.0621061 | 0.0310530 | − | 0.999518i | \(-0.490114\pi\) | ||||
0.0310530 | + | 0.999518i | \(0.490114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.49023e6 | − | 4.31321e6i | 0.466162 | − | 0.807416i | −0.533091 | − | 0.846058i | \(-0.678970\pi\) |
0.999253 | + | 0.0386419i | \(0.0123032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 985502. | + | 1.70694e6i | 0.182617 | + | 0.316301i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 453131. | + | 784846.i | 0.0822873 | + | 0.142526i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.93247e6 | − | 5.07919e6i | 0.527209 | − | 0.913153i | −0.472288 | − | 0.881444i | \(-0.656572\pi\) |
0.999497 | − | 0.0317085i | \(-0.0100948\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.36396e6 | 0.240370 | 0.120185 | − | 0.992751i | \(-0.461651\pi\) | ||||
0.120185 | + | 0.992751i | \(0.461651\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.53919e6 | −0.443065 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.85023e6 | − | 3.20470e6i | 0.316542 | − | 0.548268i | −0.663222 | − | 0.748423i | \(-0.730811\pi\) |
0.979764 | + | 0.200155i | \(0.0641447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.67943e6 | + | 2.90885e6i | 0.284517 | + | 0.492799i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −394076. | − | 682560.i | −0.0654730 | − | 0.113403i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −732795. | + | 1.26924e6i | −0.120575 | + | 0.208841i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 285260. | 0.0460412 | 0.0230206 | − | 0.999735i | \(-0.492672\pi\) | ||||
0.0230206 | + | 0.999735i | \(0.492672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.28809e6 | 1.32495 | 0.662476 | − | 0.749083i | \(-0.269506\pi\) | ||||
0.662476 | + | 0.749083i | \(0.269506\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −576550. | + | 998614.i | −0.0904296 | + | 0.156629i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50327e6 | − | 1.12640e7i | −1.01040 | − | 1.75006i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.72139e6 | − | 6.44564e6i | −0.567397 | − | 0.982761i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 299513. | − | 518772.i | 0.0452409 | − | 0.0783596i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.25800e6 | 0.186512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.29750e7 | 1.90596 | 0.952982 | − | 0.303028i | \(-0.0979975\pi\) | ||||
0.952982 | + | 0.303028i | \(0.0979975\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35163.3 | − | 60904.6i | 0.00507105 | − | 0.00878332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.65800e6 | + | 8.06790e6i | 0.665628 | + | 1.15290i | 0.979115 | + | 0.203309i | \(0.0651696\pi\) |
−0.313487 | + | 0.949593i | \(0.601497\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.34464e6 | − | 7.52514e6i | −0.609642 | − | 1.05593i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.18263e6 | − | 2.04838e6i | 0.164451 | − | 0.284838i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.18234e6 | 0.571192 | 0.285596 | − | 0.958350i | \(-0.407809\pi\) | ||||
0.285596 | + | 0.958350i | \(0.407809\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.19604e6 | −0.703304 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.65660e6 | + | 2.86931e6i | −0.220265 | + | 0.381511i | −0.954888 | − | 0.296965i | \(-0.904026\pi\) |
0.734623 | + | 0.678475i | \(0.237359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.72846e6 | + | 2.99378e6i | 0.227792 | + | 0.394547i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.92695e6 | − | 5.06963e6i | −0.378996 | − | 0.656441i | 0.611920 | − | 0.790920i | \(-0.290397\pi\) |
−0.990917 | + | 0.134478i | \(0.957064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.75429e6 | + | 1.16988e7i | −0.866941 | + | 1.50159i | −0.00183339 | + | 0.999998i | \(0.500584\pi\) |
−0.865107 | + | 0.501587i | \(0.832750\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.07247e7 | 1.35274 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.12898e7 | −1.41171 | −0.705855 | − | 0.708356i | \(-0.749437\pi\) | ||||
−0.705855 | + | 0.708356i | \(0.749437\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.82325e6 | − | 6.62206e6i | 0.469886 | − | 0.813866i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.10282e6 | − | 1.91013e6i | −0.134379 | − | 0.232751i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 991398. | + | 1.71715e6i | 0.118755 | + | 0.205690i | 0.919275 | − | 0.393617i | \(-0.128776\pi\) |
−0.800519 | + | 0.599307i | \(0.795443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.54176e6 | − | 4.40245e6i | 0.301888 | − | 0.522885i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.22629e7 | −1.43204 | −0.716021 | − | 0.698078i | \(-0.754039\pi\) | ||||
−0.716021 | + | 0.698078i | \(0.754039\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −416342. | −0.0482123 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.84977e6 | + | 1.35962e7i | −0.893902 | + | 1.54828i | −0.0587438 | + | 0.998273i | \(0.518710\pi\) |
−0.835158 | + | 0.550010i | \(0.814624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.65972e6 | + | 4.60677e6i | 0.300366 | + | 0.520248i | 0.976219 | − | 0.216788i | \(-0.0695580\pi\) |
−0.675853 | + | 0.737036i | \(0.736225\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.99246e6 | + | 3.45105e6i | 0.221311 | + | 0.383321i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.18482e6 | + | 3.78422e6i | −0.240682 | + | 0.416874i | −0.960909 | − | 0.276865i | \(-0.910705\pi\) |
0.720226 | + | 0.693739i | \(0.244038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.10142e7 | 1.19358 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.62875e6 | −0.819978 | −0.409989 | − | 0.912091i | \(-0.634467\pi\) | ||||
−0.409989 | + | 0.912091i | \(0.634467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.16498e6 | + | 1.24101e7i | −0.757708 | + | 1.31239i | 0.186309 | + | 0.982491i | \(0.440348\pi\) |
−0.944017 | + | 0.329898i | \(0.892986\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.40907e6 | − | 9.36878e6i | −0.567408 | − | 0.982780i | −0.996821 | − | 0.0796716i | \(-0.974613\pi\) |
0.429413 | − | 0.903108i | \(-0.358720\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.09560e6 | + | 5.36174e6i | 0.319540 | + | 0.553460i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.87542e6 | + | 3.24833e6i | −0.192043 | + | 0.332629i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.97480e6 | −0.299800 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.96579e6 | 0.796444 | 0.398222 | − | 0.917289i | \(-0.369627\pi\) | ||||
0.398222 | + | 0.917289i | \(0.369627\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.10597e6 | + | 5.37970e6i | −0.305677 | + | 0.529448i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.72705e6 | − | 8.18750e6i | −0.461575 | − | 0.799471i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.40224e6 | + | 5.89285e6i | 0.327054 | + | 0.566475i | 0.981926 | − | 0.189266i | \(-0.0606107\pi\) |
−0.654872 | + | 0.755740i | \(0.727277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.66464e6 | − | 4.61530e6i | 0.254163 | − | 0.440223i | −0.710505 | − | 0.703692i | \(-0.751533\pi\) |
0.964668 | + | 0.263469i | \(0.0848668\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.03021e6 | 0.472417 | 0.236208 | − | 0.971702i | \(-0.424095\pi\) | ||||
0.236208 | + | 0.971702i | \(0.424095\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06201e6 | 0.0989731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.66704e6 | + | 9.81560e6i | −0.520084 | + | 0.900811i | 0.479644 | + | 0.877463i | \(0.340766\pi\) |
−0.999727 | + | 0.0233481i | \(0.992567\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.74251e6 | + | 8.21427e6i | 0.431922 | + | 0.748110i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.91003e6 | + | 3.30828e6i | 0.171328 | + | 0.296748i | 0.938884 | − | 0.344233i | \(-0.111861\pi\) |
−0.767557 | + | 0.640981i | \(0.778528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −463286. | + | 802435.i | −0.0412426 | + | 0.0714342i | −0.885910 | − | 0.463857i | \(-0.846465\pi\) |
0.844667 | + | 0.535292i | \(0.179798\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.83547e6 | 0.160951 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.47555e7 | −3.02488 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −58417.3 | + | 101182.i | −0.00500882 | + | 0.00867553i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.45146e6 | − | 4.24605e6i | −0.208635 | − | 0.361366i | 0.742650 | − | 0.669680i | \(-0.233569\pi\) |
−0.951285 | + | 0.308314i | \(0.900235\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.37201e6 | − | 1.27687e7i | −0.618179 | − | 1.07072i | −0.989818 | − | 0.142340i | \(-0.954537\pi\) |
0.371639 | − | 0.928378i | \(-0.378796\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.37521e6 | + | 5.84603e6i | −0.280948 | + | 0.486616i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.53893e6 | 0.536358 | 0.268179 | − | 0.963369i | \(-0.413578\pi\) | ||||
0.268179 | + | 0.963369i | \(0.413578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.25548e6 | 0.509371 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.28790e6 | + | 1.43551e7i | −0.665114 | + | 1.15201i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.45248e6 | + | 9.44397e6i | 0.434409 | + | 0.752419i | 0.997247 | − | 0.0741485i | \(-0.0236239\pi\) |
−0.562838 | + | 0.826567i | \(0.690291\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.14968e6 | − | 3.72336e6i | −0.168816 | − | 0.292397i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.26045e6 | + | 2.18316e6i | −0.0982751 | + | 0.170217i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.89162e7 | 1.45391 | 0.726957 | − | 0.686683i | \(-0.240934\pi\) | ||||
0.726957 | + | 0.686683i | \(0.240934\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.31146e7 | 1.00084 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.05129e6 | − | 5.28499e6i | 0.229581 | − | 0.397645i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.63661e6 | + | 1.66911e7i | 0.719960 | + | 1.24701i | 0.961015 | + | 0.276496i | \(0.0891733\pi\) |
−0.241055 | + | 0.970512i | \(0.577493\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.01665e7 | − | 1.76089e7i | −0.748943 | − | 1.29721i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −954489. | + | 1.65322e6i | −0.0698242 | + | 0.120939i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.42859e7 | −1.03059 | −0.515293 | − | 0.857014i | \(-0.672317\pi\) | ||||
−0.515293 | + | 0.857014i | \(0.672317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.89421e6 | 0.135703 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.58556e6 | − | 1.66027e7i | 0.677287 | − | 1.17310i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.41386e7 | − | 2.44887e7i | −0.992132 | − | 1.71842i | −0.604491 | − | 0.796612i | \(-0.706623\pi\) |
−0.387641 | − | 0.921810i | \(-0.626710\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 879959. | + | 1.52413e6i | 0.0609073 | + | 0.105494i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.93850e6 | + | 8.55373e6i | −0.339496 | + | 0.588025i | −0.984338 | − | 0.176291i | \(-0.943590\pi\) |
0.644842 | + | 0.764316i | \(0.276923\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.81381e6 | −0.394269 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.31081e6 | 0.425083 | 0.212542 | − | 0.977152i | \(-0.431826\pi\) | ||||
0.212542 | + | 0.977152i | \(0.431826\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31529.9 | + | 54611.3i | −0.00209532 | + | 0.00362920i | −0.867071 | − | 0.498184i | \(-0.834000\pi\) |
0.864976 | + | 0.501814i | \(0.167334\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.41667e6 | + | 7.64989e6i | 0.291544 | + | 0.504969i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 719836. | + | 1.24679e6i | 0.0468845 | + | 0.0812063i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.69183e6 | − | 1.50547e7i | 0.562356 | − | 0.974029i | −0.434934 | − | 0.900462i | \(-0.643228\pi\) |
0.997290 | − | 0.0735670i | \(-0.0234383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.56845e6 | −0.227831 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.43592e6 | 0.598473 | 0.299237 | − | 0.954179i | \(-0.403268\pi\) | ||||
0.299237 | + | 0.954179i | \(0.403268\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.06409e6 | − | 1.39674e7i | 0.504771 | − | 0.874288i | −0.495214 | − | 0.868771i | \(-0.664910\pi\) |
0.999985 | − | 0.00551731i | \(-0.00175622\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 84509.8 | + | 146375.i | 0.00525528 | + | 0.00910241i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.99062e6 | − | 6.91196e6i | −0.244936 | − | 0.424241i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.28431e7 | − | 2.22450e7i | 0.783169 | − | 1.35649i | −0.146918 | − | 0.989149i | \(-0.546935\pi\) |
0.930087 | − | 0.367339i | \(-0.119731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.01235e7 | 1.21131 | 0.605654 | − | 0.795728i | \(-0.292912\pi\) | ||||
0.605654 | + | 0.795728i | \(0.292912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.12157e7 | 0.670769 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.55677e6 | − | 9.62460e6i | 0.328079 | − | 0.568250i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −703712. | − | 1.21886e6i | −0.0412826 | − | 0.0715036i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.59879e6 | + | 9.69738e6i | 0.324280 | + | 0.561669i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.87640e6 | + | 4.98208e6i | −0.165544 | + | 0.286730i | −0.936848 | − | 0.349736i | \(-0.886271\pi\) |
0.771304 | + | 0.636466i | \(0.219605\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.30819e6 | −0.472134 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 878038. | 0.0495827 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.09822e6 | + | 8.83038e6i | −0.284298 | + | 0.492418i | −0.972439 | − | 0.233159i | \(-0.925094\pi\) |
0.688141 | + | 0.725577i | \(0.258427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.86528e6 | − | 3.23076e6i | −0.103366 | − | 0.179035i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.60815e6 | − | 4.51744e6i | −0.142739 | − | 0.247232i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.67076e6 | − | 6.35795e6i | 0.199649 | − | 0.345802i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00420e6 | −0.322540 | −0.161270 | − | 0.986910i | \(-0.551559\pi\) | ||||
−0.161270 | + | 0.986910i | \(0.551559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.23880e7 | 1.72915 | 0.864574 | − | 0.502506i | \(-0.167589\pi\) | ||||
0.864574 | + | 0.502506i | \(0.167589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.08826e6 | − | 3.61696e6i | 0.110126 | − | 0.190744i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.87935e6 | − | 6.71924e6i | −0.203331 | − | 0.352180i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.83736e6 | + | 1.35747e7i | 0.405800 | + | 0.702866i | 0.994414 | − | 0.105548i | \(-0.0336596\pi\) |
−0.588614 | + | 0.808414i | \(0.700326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.35733e7 | − | 2.35097e7i | 0.698532 | − | 1.20989i | −0.270443 | − | 0.962736i | \(-0.587170\pi\) |
0.968975 | − | 0.247157i | \(-0.0794964\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.28543e7 | −1.16199 | −0.580997 | − | 0.813906i | \(-0.697337\pi\) | ||||
−0.580997 | + | 0.813906i | \(0.697337\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.05418e7 | −1.03813 | −0.519066 | − | 0.854734i | \(-0.673720\pi\) | ||||
−0.519066 | + | 0.854734i | \(0.673720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.60107e6 | + | 2.77314e6i | −0.0799463 | + | 0.138471i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.82288e6 | − | 1.18176e7i | −0.338650 | − | 0.586560i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.39436e6 | − | 1.28074e7i | −0.362657 | − | 0.628140i | 0.625740 | − | 0.780031i | \(-0.284797\pi\) |
−0.988397 | + | 0.151891i | \(0.951464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.08083e7 | + | 3.60410e7i | −1.01449 | + | 1.75714i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.57378e6 | 0.220360 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.57719e6 | −0.458701 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.62279e7 | − | 4.54280e7i | 1.24148 | − | 2.15031i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.26223e6 | + | 9.11445e6i | 0.247627 | + | 0.428902i | 0.962867 | − | 0.269977i | \(-0.0870161\pi\) |
−0.715240 | + | 0.698879i | \(0.753683\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.43357e6 | + | 1.28753e7i | 0.345736 | + | 0.598833i | 0.985487 | − | 0.169749i | \(-0.0542958\pi\) |
−0.639751 | + | 0.768582i | \(0.720962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.32340e6 | − | 7.48834e6i | 0.199913 | − | 0.346260i | −0.748587 | − | 0.663037i | \(-0.769267\pi\) |
0.948500 | + | 0.316777i | \(0.102601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.38401e7 | −1.08964 | −0.544818 | − | 0.838555i | \(-0.683401\pi\) | ||||
−0.544818 | + | 0.838555i | \(0.683401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.03172e6 | 0.183210 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.83663e6 | + | 3.18113e6i | −0.0825033 | + | 0.142900i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.18460e7 | + | 3.78385e7i | 0.975725 | + | 1.69001i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.62631e6 | + | 8.01300e6i | 0.204275 | + | 0.353814i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19157.8 | − | 33182.4i | 0.000841100 | − | 0.00145683i | −0.865605 | − | 0.500728i | \(-0.833066\pi\) |
0.866446 | + | 0.499271i | \(0.166399\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.55072e7 | 1.10719 | 0.553596 | − | 0.832785i | \(-0.313255\pi\) | ||||
0.553596 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.37096e7 | −1.45496 | −0.727482 | − | 0.686127i | \(-0.759309\pi\) | ||||
−0.727482 | + | 0.686127i | \(0.759309\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.32111e6 | + | 2.28823e6i | −0.0563806 | + | 0.0976540i | −0.892838 | − | 0.450378i | \(-0.851289\pi\) |
0.836458 | + | 0.548032i | \(0.184623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.46475e6 | − | 1.29293e7i | −0.316782 | − | 0.548683i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.22320e6 | + | 1.42430e7i | 0.345074 | + | 0.597686i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.69707e6 | + | 1.67958e7i | −0.404653 | + | 0.700880i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.63467e7 | −1.49991 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.61429e6 | 0.230400 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −370906. | + | 642428.i | −0.0150537 | + | 0.0260737i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.56509e6 | − | 6.17492e6i | −0.143897 | − | 0.249237i | 0.785064 | − | 0.619415i | \(-0.212630\pi\) |
−0.928961 | + | 0.370178i | \(0.879297\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.56577e7 | + | 2.71200e7i | 0.625075 | + | 1.08266i | 0.988526 | + | 0.151049i | \(0.0482651\pi\) |
−0.363451 | + | 0.931613i | \(0.618402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.93749e6 | + | 1.02840e7i | −0.235736 | + | 0.408307i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.27959e7 | −0.895226 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.28042e6 | 0.0890687 | 0.0445344 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445344 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.28855e6 | + | 9.16003e6i | −0.204330 | + | 0.353910i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.44673e7 | + | 2.50581e7i | 0.555947 | + | 0.962929i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.28625e6 | + | 9.15605e6i | 0.200959 | + | 0.348072i | 0.948838 | − | 0.315764i | \(-0.102261\pi\) |
−0.747879 | + | 0.663836i | \(0.768927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.05842e6 | − | 1.22255e7i | 0.266891 | − | 0.462268i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 646579. | 0.0241876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.99327e7 | −1.48587 | −0.742934 | − | 0.669365i | \(-0.766566\pi\) | ||||
−0.742934 | + | 0.669365i | \(0.766566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.16316e6 | + | 7.21080e6i | −0.153267 | + | 0.265466i | −0.932427 | − | 0.361359i | \(-0.882313\pi\) |
0.779160 | + | 0.626826i | \(0.215646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.22260e7 | − | 3.84965e7i | −0.813920 | − | 1.40975i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.37834e7 | + | 2.38735e7i | 0.499437 | + | 0.865050i | 1.00000 | 0.000650313i | \(-0.000207001\pi\) | |
−0.500563 | + | 0.865700i | \(0.666874\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.96008e7 | + | 3.39496e7i | −0.706493 | + | 1.22368i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.81280e7 | 1.35992 | 0.679958 | − | 0.733251i | \(-0.261998\pi\) | ||||
0.679958 | + | 0.733251i | \(0.261998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.61418e6 | −0.0927528 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.51707e6 | + | 1.30199e7i | −0.263938 | + | 0.457154i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.68258e6 | + | 6.37841e6i | 0.128630 | + | 0.222794i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.49141e6 | − | 9.51139e6i | −0.189830 | − | 0.328796i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.36356e6 | − | 2.36175e6i | 0.0468928 | − | 0.0812208i | −0.841626 | − | 0.540060i | \(-0.818401\pi\) |
0.888519 | + | 0.458840i | \(0.151735\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.26521e7 | −0.430641 | −0.215320 | − | 0.976543i | \(-0.569080\pi\) | ||||
−0.215320 | + | 0.976543i | \(0.569080\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.03329e7 | 0.349897 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.68626e7 | + | 2.92069e7i | −0.565182 | + | 0.978923i | 0.431851 | + | 0.901945i | \(0.357861\pi\) |
−0.997033 | + | 0.0769784i | \(0.975473\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.80747e6 | − | 8.32678e6i | −0.160310 | − | 0.277664i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.93714e6 | + | 1.02834e7i | 0.195972 | + | 0.339433i | 0.947219 | − | 0.320588i | \(-0.103881\pi\) |
−0.751247 | + | 0.660021i | \(0.770547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.35014e6 | − | 5.80260e6i | 0.110020 | − | 0.190560i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.10333e7 | −1.00888 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.31910e7 | −0.750128 | −0.375064 | − | 0.926999i | \(-0.622379\pi\) | ||||
−0.375064 | + | 0.926999i | \(0.622379\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.89223e6 | − | 1.36697e7i | 0.252721 | − | 0.437726i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.93132e7 | − | 3.34515e7i | −0.615342 | − | 1.06580i | −0.990324 | − | 0.138772i | \(-0.955685\pi\) |
0.374982 | − | 0.927032i | \(-0.377649\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 108.6.e.a.37.2 | 10 | ||
3.2 | odd | 2 | 36.6.e.a.13.4 | ✓ | 10 | ||
4.3 | odd | 2 | 432.6.i.d.145.2 | 10 | |||
9.2 | odd | 6 | 36.6.e.a.25.4 | yes | 10 | ||
9.4 | even | 3 | 324.6.a.d.1.4 | 5 | |||
9.5 | odd | 6 | 324.6.a.e.1.2 | 5 | |||
9.7 | even | 3 | inner | 108.6.e.a.73.2 | 10 | ||
12.11 | even | 2 | 144.6.i.d.49.2 | 10 | |||
36.7 | odd | 6 | 432.6.i.d.289.2 | 10 | |||
36.11 | even | 6 | 144.6.i.d.97.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.e.a.13.4 | ✓ | 10 | 3.2 | odd | 2 | ||
36.6.e.a.25.4 | yes | 10 | 9.2 | odd | 6 | ||
108.6.e.a.37.2 | 10 | 1.1 | even | 1 | trivial | ||
108.6.e.a.73.2 | 10 | 9.7 | even | 3 | inner | ||
144.6.i.d.49.2 | 10 | 12.11 | even | 2 | |||
144.6.i.d.97.2 | 10 | 36.11 | even | 6 | |||
324.6.a.d.1.4 | 5 | 9.4 | even | 3 | |||
324.6.a.e.1.2 | 5 | 9.5 | odd | 6 | |||
432.6.i.d.145.2 | 10 | 4.3 | odd | 2 | |||
432.6.i.d.289.2 | 10 | 36.7 | odd | 6 |