Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), 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: | \(48.6765757547\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.a.199.2 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 5.00000i | − 1.76777i | −0.467707 | − | 0.883883i | \(-0.654920\pi\) | ||||
0.467707 | − | 0.883883i | \(-0.345080\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −17.0000 | −2.12500 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −15.0000 | −1.02062 | ||||||||
\(7\) | − 32.0000i | − 1.72784i | −0.503631 | − | 0.863919i | \(-0.668003\pi\) | ||||
0.503631 | − | 0.863919i | \(-0.331997\pi\) | |||||||
\(8\) | 45.0000i | 1.98874i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 51.0000i | 1.22687i | ||||||||
\(13\) | 38.0000i | 0.810716i | 0.914158 | + | 0.405358i | \(0.132853\pi\) | ||||
−0.914158 | + | 0.405358i | \(0.867147\pi\) | |||||||
\(14\) | −160.000 | −3.05441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | − 2.00000i | − 0.0285336i | −0.999898 | − | 0.0142668i | \(-0.995459\pi\) | ||||
0.999898 | − | 0.0142668i | \(-0.00454142\pi\) | |||||||
\(18\) | 45.0000i | 0.589256i | ||||||||
\(19\) | −72.0000 | −0.869365 | −0.434682 | − | 0.900584i | \(-0.643139\pi\) | ||||
−0.434682 | + | 0.900584i | \(0.643139\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −96.0000 | −0.997567 | ||||||||
\(22\) | 55.0000i | 0.533002i | ||||||||
\(23\) | − 68.0000i | − 0.616477i | −0.951309 | − | 0.308239i | \(-0.900260\pi\) | ||||
0.951309 | − | 0.308239i | \(-0.0997395\pi\) | |||||||
\(24\) | 135.000 | 1.14820 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 190.000 | 1.43316 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 544.000i | 3.67165i | ||||||||
\(29\) | 54.0000 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −152.000 | −0.880645 | −0.440323 | − | 0.897840i | \(-0.645136\pi\) | ||||
−0.440323 | + | 0.897840i | \(0.645136\pi\) | |||||||
\(32\) | − 85.0000i | − 0.469563i | ||||||||
\(33\) | 33.0000i | 0.174078i | ||||||||
\(34\) | −10.0000 | −0.0504408 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 153.000 | 0.708333 | ||||||||
\(37\) | 174.000i | 0.773120i | 0.922264 | + | 0.386560i | \(0.126337\pi\) | ||||
−0.922264 | + | 0.386560i | \(0.873663\pi\) | |||||||
\(38\) | 360.000i | 1.53683i | ||||||||
\(39\) | 114.000 | 0.468067 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 94.0000 | 0.358057 | 0.179028 | − | 0.983844i | \(-0.442705\pi\) | ||||
0.179028 | + | 0.983844i | \(0.442705\pi\) | |||||||
\(42\) | 480.000i | 1.76347i | ||||||||
\(43\) | 528.000i | 1.87254i | 0.351280 | + | 0.936270i | \(0.385746\pi\) | ||||
−0.351280 | + | 0.936270i | \(0.614254\pi\) | |||||||
\(44\) | 187.000 | 0.640712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −340.000 | −1.08979 | ||||||||
\(47\) | − 340.000i | − 1.05519i | −0.849495 | − | 0.527597i | \(-0.823093\pi\) | ||||
0.849495 | − | 0.527597i | \(-0.176907\pi\) | |||||||
\(48\) | − 267.000i | − 0.802878i | ||||||||
\(49\) | −681.000 | −1.98542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | −0.0164739 | ||||||||
\(52\) | − 646.000i | − 1.72277i | ||||||||
\(53\) | 438.000i | 1.13517i | 0.823315 | + | 0.567584i | \(0.192122\pi\) | ||||
−0.823315 | + | 0.567584i | \(0.807878\pi\) | |||||||
\(54\) | 135.000 | 0.340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1440.00 | 3.43622 | ||||||||
\(57\) | 216.000i | 0.501928i | ||||||||
\(58\) | − 270.000i | − 0.611254i | ||||||||
\(59\) | −20.0000 | −0.0441318 | −0.0220659 | − | 0.999757i | \(-0.507024\pi\) | ||||
−0.0220659 | + | 0.999757i | \(0.507024\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 570.000 | 1.19641 | 0.598205 | − | 0.801343i | \(-0.295881\pi\) | ||||
0.598205 | + | 0.801343i | \(0.295881\pi\) | |||||||
\(62\) | 760.000i | 1.55678i | ||||||||
\(63\) | 288.000i | 0.575946i | ||||||||
\(64\) | 287.000 | 0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 165.000 | 0.307729 | ||||||||
\(67\) | − 460.000i | − 0.838775i | −0.907807 | − | 0.419388i | \(-0.862245\pi\) | ||||
0.907807 | − | 0.419388i | \(-0.137755\pi\) | |||||||
\(68\) | 34.0000i | 0.0606339i | ||||||||
\(69\) | −204.000 | −0.355923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1092.00 | −1.82530 | −0.912652 | − | 0.408738i | \(-0.865969\pi\) | ||||
−0.912652 | + | 0.408738i | \(0.865969\pi\) | |||||||
\(72\) | − 405.000i | − 0.662913i | ||||||||
\(73\) | − 562.000i | − 0.901057i | −0.892762 | − | 0.450528i | \(-0.851236\pi\) | ||||
0.892762 | − | 0.450528i | \(-0.148764\pi\) | |||||||
\(74\) | 870.000 | 1.36670 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1224.00 | 1.84740 | ||||||||
\(77\) | 352.000i | 0.520963i | ||||||||
\(78\) | − 570.000i | − 0.827433i | ||||||||
\(79\) | 16.0000 | 0.0227866 | 0.0113933 | − | 0.999935i | \(-0.496373\pi\) | ||||
0.0113933 | + | 0.999935i | \(0.496373\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 470.000i | − 0.632961i | ||||||||
\(83\) | − 372.000i | − 0.491955i | −0.969275 | − | 0.245978i | \(-0.920891\pi\) | ||||
0.969275 | − | 0.245978i | \(-0.0791090\pi\) | |||||||
\(84\) | 1632.00 | 2.11983 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2640.00 | 3.31022 | ||||||||
\(87\) | − 162.000i | − 0.199635i | ||||||||
\(88\) | − 495.000i | − 0.599627i | ||||||||
\(89\) | 966.000 | 1.15051 | 0.575257 | − | 0.817973i | \(-0.304902\pi\) | ||||
0.575257 | + | 0.817973i | \(0.304902\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1216.00 | 1.40079 | ||||||||
\(92\) | 1156.00i | 1.31001i | ||||||||
\(93\) | 456.000i | 0.508441i | ||||||||
\(94\) | −1700.00 | −1.86534 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −255.000 | −0.271102 | ||||||||
\(97\) | − 526.000i | − 0.550590i | −0.961360 | − | 0.275295i | \(-0.911225\pi\) | ||||
0.961360 | − | 0.275295i | \(-0.0887755\pi\) | |||||||
\(98\) | 3405.00i | 3.50976i | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.0000 | 0.0492593 | 0.0246296 | − | 0.999697i | \(-0.492159\pi\) | ||||
0.0246296 | + | 0.999697i | \(0.492159\pi\) | |||||||
\(102\) | 30.0000i | 0.0291220i | ||||||||
\(103\) | − 944.000i | − 0.903059i | −0.892256 | − | 0.451530i | \(-0.850879\pi\) | ||||
0.892256 | − | 0.451530i | \(-0.149121\pi\) | |||||||
\(104\) | −1710.00 | −1.61230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2190.00 | 2.00671 | ||||||||
\(107\) | 468.000i | 0.422834i | 0.977396 | + | 0.211417i | \(0.0678079\pi\) | ||||
−0.977396 | + | 0.211417i | \(0.932192\pi\) | |||||||
\(108\) | − 459.000i | − 0.408956i | ||||||||
\(109\) | −154.000 | −0.135326 | −0.0676630 | − | 0.997708i | \(-0.521554\pi\) | ||||
−0.0676630 | + | 0.997708i | \(0.521554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 522.000 | 0.446361 | ||||||||
\(112\) | − 2848.00i | − 2.40277i | ||||||||
\(113\) | 54.0000i | 0.0449548i | 0.999747 | + | 0.0224774i | \(0.00715538\pi\) | ||||
−0.999747 | + | 0.0224774i | \(0.992845\pi\) | |||||||
\(114\) | 1080.00 | 0.887292 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −918.000 | −0.734777 | ||||||||
\(117\) | − 342.000i | − 0.270239i | ||||||||
\(118\) | 100.000i | 0.0780148i | ||||||||
\(119\) | −64.0000 | −0.0493014 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | − 2850.00i | − 2.11497i | ||||||||
\(123\) | − 282.000i | − 0.206724i | ||||||||
\(124\) | 2584.00 | 1.87137 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1440.00 | 1.01814 | ||||||||
\(127\) | − 2224.00i | − 1.55392i | −0.629549 | − | 0.776961i | \(-0.716760\pi\) | ||||
0.629549 | − | 0.776961i | \(-0.283240\pi\) | |||||||
\(128\) | − 2115.00i | − 1.46048i | ||||||||
\(129\) | 1584.00 | 1.08111 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2772.00 | −1.84878 | −0.924392 | − | 0.381443i | \(-0.875427\pi\) | ||||
−0.924392 | + | 0.381443i | \(0.875427\pi\) | |||||||
\(132\) | − 561.000i | − 0.369915i | ||||||||
\(133\) | 2304.00i | 1.50212i | ||||||||
\(134\) | −2300.00 | −1.48276 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 90.0000 | 0.0567459 | ||||||||
\(137\) | 1130.00i | 0.704689i | 0.935870 | + | 0.352345i | \(0.114615\pi\) | ||||
−0.935870 | + | 0.352345i | \(0.885385\pi\) | |||||||
\(138\) | 1020.00i | 0.629190i | ||||||||
\(139\) | 1616.00 | 0.986096 | 0.493048 | − | 0.870002i | \(-0.335883\pi\) | ||||
0.493048 | + | 0.870002i | \(0.335883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1020.00 | −0.609216 | ||||||||
\(142\) | 5460.00i | 3.22671i | ||||||||
\(143\) | − 418.000i | − 0.244440i | ||||||||
\(144\) | −801.000 | −0.463542 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2810.00 | −1.59286 | ||||||||
\(147\) | 2043.00i | 1.14628i | ||||||||
\(148\) | − 2958.00i | − 1.64288i | ||||||||
\(149\) | −2066.00 | −1.13593 | −0.567964 | − | 0.823053i | \(-0.692269\pi\) | ||||
−0.567964 | + | 0.823053i | \(0.692269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 248.000 | 0.133655 | 0.0668277 | − | 0.997765i | \(-0.478712\pi\) | ||||
0.0668277 | + | 0.997765i | \(0.478712\pi\) | |||||||
\(152\) | − 3240.00i | − 1.72894i | ||||||||
\(153\) | 18.0000i | 0.00951120i | ||||||||
\(154\) | 1760.00 | 0.920941 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1938.00 | −0.994642 | ||||||||
\(157\) | 2366.00i | 1.20272i | 0.798977 | + | 0.601361i | \(0.205375\pi\) | ||||
−0.798977 | + | 0.601361i | \(0.794625\pi\) | |||||||
\(158\) | − 80.0000i | − 0.0402814i | ||||||||
\(159\) | 1314.00 | 0.655390 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2176.00 | −1.06517 | ||||||||
\(162\) | − 405.000i | − 0.196419i | ||||||||
\(163\) | 284.000i | 0.136470i | 0.997669 | + | 0.0682350i | \(0.0217368\pi\) | ||||
−0.997669 | + | 0.0682350i | \(0.978263\pi\) | |||||||
\(164\) | −1598.00 | −0.760871 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1860.00 | −0.869663 | ||||||||
\(167\) | 600.000i | 0.278020i | 0.990291 | + | 0.139010i | \(0.0443921\pi\) | ||||
−0.990291 | + | 0.139010i | \(0.955608\pi\) | |||||||
\(168\) | − 4320.00i | − 1.98390i | ||||||||
\(169\) | 753.000 | 0.342740 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 648.000 | 0.289788 | ||||||||
\(172\) | − 8976.00i | − 3.97915i | ||||||||
\(173\) | − 138.000i | − 0.0606471i | −0.999540 | − | 0.0303235i | \(-0.990346\pi\) | ||||
0.999540 | − | 0.0303235i | \(-0.00965376\pi\) | |||||||
\(174\) | −810.000 | −0.352908 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −979.000 | −0.419289 | ||||||||
\(177\) | 60.0000i | 0.0254795i | ||||||||
\(178\) | − 4830.00i | − 2.03384i | ||||||||
\(179\) | −3972.00 | −1.65855 | −0.829277 | − | 0.558838i | \(-0.811248\pi\) | ||||
−0.829277 | + | 0.558838i | \(0.811248\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2230.00 | 0.915771 | 0.457886 | − | 0.889011i | \(-0.348607\pi\) | ||||
0.457886 | + | 0.889011i | \(0.348607\pi\) | |||||||
\(182\) | − 6080.00i | − 2.47626i | ||||||||
\(183\) | − 1710.00i | − 0.690748i | ||||||||
\(184\) | 3060.00 | 1.22601 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2280.00 | 0.898805 | ||||||||
\(187\) | 22.0000i | 0.00860320i | ||||||||
\(188\) | 5780.00i | 2.24229i | ||||||||
\(189\) | 864.000 | 0.332522 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −772.000 | −0.292461 | −0.146230 | − | 0.989251i | \(-0.546714\pi\) | ||||
−0.146230 | + | 0.989251i | \(0.546714\pi\) | |||||||
\(192\) | − 861.000i | − 0.323632i | ||||||||
\(193\) | − 394.000i | − 0.146947i | −0.997297 | − | 0.0734734i | \(-0.976592\pi\) | ||||
0.997297 | − | 0.0734734i | \(-0.0234084\pi\) | |||||||
\(194\) | −2630.00 | −0.973314 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11577.0 | 4.21902 | ||||||||
\(197\) | 3058.00i | 1.10596i | 0.833196 | + | 0.552978i | \(0.186509\pi\) | ||||
−0.833196 | + | 0.552978i | \(0.813491\pi\) | |||||||
\(198\) | − 495.000i | − 0.177667i | ||||||||
\(199\) | −2664.00 | −0.948975 | −0.474487 | − | 0.880262i | \(-0.657367\pi\) | ||||
−0.474487 | + | 0.880262i | \(0.657367\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1380.00 | −0.484267 | ||||||||
\(202\) | − 250.000i | − 0.0870789i | ||||||||
\(203\) | − 1728.00i | − 0.597447i | ||||||||
\(204\) | 102.000 | 0.0350070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4720.00 | −1.59640 | ||||||||
\(207\) | 612.000i | 0.205492i | ||||||||
\(208\) | 3382.00i | 1.12740i | ||||||||
\(209\) | 792.000 | 0.262123 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6000.00 | −1.95762 | −0.978808 | − | 0.204779i | \(-0.934352\pi\) | ||||
−0.978808 | + | 0.204779i | \(0.934352\pi\) | |||||||
\(212\) | − 7446.00i | − 2.41223i | ||||||||
\(213\) | 3276.00i | 1.05384i | ||||||||
\(214\) | 2340.00 | 0.747472 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1215.00 | −0.382733 | ||||||||
\(217\) | 4864.00i | 1.52161i | ||||||||
\(218\) | 770.000i | 0.239225i | ||||||||
\(219\) | −1686.00 | −0.520225 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 76.0000 | 0.0231326 | ||||||||
\(222\) | − 2610.00i | − 0.789062i | ||||||||
\(223\) | 560.000i | 0.168163i | 0.996459 | + | 0.0840816i | \(0.0267956\pi\) | ||||
−0.996459 | + | 0.0840816i | \(0.973204\pi\) | |||||||
\(224\) | −2720.00 | −0.811329 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 270.000 | 0.0794696 | ||||||||
\(227\) | 5292.00i | 1.54732i | 0.633599 | + | 0.773662i | \(0.281577\pi\) | ||||
−0.633599 | + | 0.773662i | \(0.718423\pi\) | |||||||
\(228\) | − 3672.00i | − 1.06660i | ||||||||
\(229\) | 5322.00 | 1.53575 | 0.767877 | − | 0.640597i | \(-0.221313\pi\) | ||||
0.767877 | + | 0.640597i | \(0.221313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1056.00 | 0.300778 | ||||||||
\(232\) | 2430.00i | 0.687661i | ||||||||
\(233\) | 3954.00i | 1.11174i | 0.831270 | + | 0.555869i | \(0.187615\pi\) | ||||
−0.831270 | + | 0.555869i | \(0.812385\pi\) | |||||||
\(234\) | −1710.00 | −0.477719 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 340.000 | 0.0937801 | ||||||||
\(237\) | − 48.0000i | − 0.0131558i | ||||||||
\(238\) | 320.000i | 0.0871534i | ||||||||
\(239\) | 3360.00 | 0.909374 | 0.454687 | − | 0.890651i | \(-0.349751\pi\) | ||||
0.454687 | + | 0.890651i | \(0.349751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3278.00 | −0.876160 | −0.438080 | − | 0.898936i | \(-0.644341\pi\) | ||||
−0.438080 | + | 0.898936i | \(0.644341\pi\) | |||||||
\(242\) | − 605.000i | − 0.160706i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | −9690.00 | −2.54237 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1410.00 | −0.365440 | ||||||||
\(247\) | − 2736.00i | − 0.704808i | ||||||||
\(248\) | − 6840.00i | − 1.75137i | ||||||||
\(249\) | −1116.00 | −0.284031 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2092.00 | 0.526079 | 0.263040 | − | 0.964785i | \(-0.415275\pi\) | ||||
0.263040 | + | 0.964785i | \(0.415275\pi\) | |||||||
\(252\) | − 4896.00i | − 1.22388i | ||||||||
\(253\) | 748.000i | 0.185875i | ||||||||
\(254\) | −11120.0 | −2.74697 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | 658.000i | 0.159708i | 0.996807 | + | 0.0798539i | \(0.0254454\pi\) | ||||
−0.996807 | + | 0.0798539i | \(0.974555\pi\) | |||||||
\(258\) | − 7920.00i | − 1.91115i | ||||||||
\(259\) | 5568.00 | 1.33583 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −486.000 | −0.115259 | ||||||||
\(262\) | 13860.0i | 3.26822i | ||||||||
\(263\) | 5104.00i | 1.19668i | 0.801243 | + | 0.598339i | \(0.204172\pi\) | ||||
−0.801243 | + | 0.598339i | \(0.795828\pi\) | |||||||
\(264\) | −1485.00 | −0.346195 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11520.0 | 2.65540 | ||||||||
\(267\) | − 2898.00i | − 0.664250i | ||||||||
\(268\) | 7820.00i | 1.78240i | ||||||||
\(269\) | 4238.00 | 0.960578 | 0.480289 | − | 0.877110i | \(-0.340532\pi\) | ||||
0.480289 | + | 0.877110i | \(0.340532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3376.00 | −0.756743 | −0.378372 | − | 0.925654i | \(-0.623516\pi\) | ||||
−0.378372 | + | 0.925654i | \(0.623516\pi\) | |||||||
\(272\) | − 178.000i | − 0.0396795i | ||||||||
\(273\) | − 3648.00i | − 0.808744i | ||||||||
\(274\) | 5650.00 | 1.24573 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3468.00 | 0.756337 | ||||||||
\(277\) | 2074.00i | 0.449872i | 0.974374 | + | 0.224936i | \(0.0722173\pi\) | ||||
−0.974374 | + | 0.224936i | \(0.927783\pi\) | |||||||
\(278\) | − 8080.00i | − 1.74319i | ||||||||
\(279\) | 1368.00 | 0.293548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 702.000 | 0.149031 | 0.0745157 | − | 0.997220i | \(-0.476259\pi\) | ||||
0.0745157 | + | 0.997220i | \(0.476259\pi\) | |||||||
\(282\) | 5100.00i | 1.07695i | ||||||||
\(283\) | − 4912.00i | − 1.03176i | −0.856661 | − | 0.515880i | \(-0.827465\pi\) | ||||
0.856661 | − | 0.515880i | \(-0.172535\pi\) | |||||||
\(284\) | 18564.0 | 3.87877 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2090.00 | −0.432113 | ||||||||
\(287\) | − 3008.00i | − 0.618664i | ||||||||
\(288\) | 765.000i | 0.156521i | ||||||||
\(289\) | 4909.00 | 0.999186 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1578.00 | −0.317883 | ||||||||
\(292\) | 9554.00i | 1.91475i | ||||||||
\(293\) | 3486.00i | 0.695066i | 0.937668 | + | 0.347533i | \(0.112981\pi\) | ||||
−0.937668 | + | 0.347533i | \(0.887019\pi\) | |||||||
\(294\) | 10215.0 | 2.02636 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7830.00 | −1.53753 | ||||||||
\(297\) | − 297.000i | − 0.0580259i | ||||||||
\(298\) | 10330.0i | 2.00806i | ||||||||
\(299\) | 2584.00 | 0.499788 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16896.0 | 3.23545 | ||||||||
\(302\) | − 1240.00i | − 0.236271i | ||||||||
\(303\) | − 150.000i | − 0.0284399i | ||||||||
\(304\) | −6408.00 | −1.20896 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 90.0000 | 0.0168136 | ||||||||
\(307\) | 8360.00i | 1.55417i | 0.629395 | + | 0.777085i | \(0.283303\pi\) | ||||
−0.629395 | + | 0.777085i | \(0.716697\pi\) | |||||||
\(308\) | − 5984.00i | − 1.10705i | ||||||||
\(309\) | −2832.00 | −0.521381 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5532.00 | −1.00865 | −0.504326 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504326 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(312\) | 5130.00i | 0.930862i | ||||||||
\(313\) | − 4826.00i | − 0.871507i | −0.900066 | − | 0.435753i | \(-0.856482\pi\) | ||||
0.900066 | − | 0.435753i | \(-0.143518\pi\) | |||||||
\(314\) | 11830.0 | 2.12613 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −272.000 | −0.0484215 | ||||||||
\(317\) | 7570.00i | 1.34124i | 0.741800 | + | 0.670621i | \(0.233972\pi\) | ||||
−0.741800 | + | 0.670621i | \(0.766028\pi\) | |||||||
\(318\) | − 6570.00i | − 1.15858i | ||||||||
\(319\) | −594.000 | −0.104256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1404.00 | 0.244123 | ||||||||
\(322\) | 10880.0i | 1.88298i | ||||||||
\(323\) | 144.000i | 0.0248061i | ||||||||
\(324\) | −1377.00 | −0.236111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1420.00 | 0.241247 | ||||||||
\(327\) | 462.000i | 0.0781305i | ||||||||
\(328\) | 4230.00i | 0.712081i | ||||||||
\(329\) | −10880.0 | −1.82320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3676.00 | 0.610427 | 0.305213 | − | 0.952284i | \(-0.401272\pi\) | ||||
0.305213 | + | 0.952284i | \(0.401272\pi\) | |||||||
\(332\) | 6324.00i | 1.04541i | ||||||||
\(333\) | − 1566.00i | − 0.257707i | ||||||||
\(334\) | 3000.00 | 0.491475 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −8544.00 | −1.38724 | ||||||||
\(337\) | − 5686.00i | − 0.919098i | −0.888152 | − | 0.459549i | \(-0.848011\pi\) | ||||
0.888152 | − | 0.459549i | \(-0.151989\pi\) | |||||||
\(338\) | − 3765.00i | − 0.605885i | ||||||||
\(339\) | 162.000 | 0.0259547 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1672.00 | 0.265525 | ||||||||
\(342\) | − 3240.00i | − 0.512278i | ||||||||
\(343\) | 10816.0i | 1.70265i | ||||||||
\(344\) | −23760.0 | −3.72399 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −690.000 | −0.107210 | ||||||||
\(347\) | − 1652.00i | − 0.255574i | −0.991802 | − | 0.127787i | \(-0.959213\pi\) | ||||
0.991802 | − | 0.127787i | \(-0.0407873\pi\) | |||||||
\(348\) | 2754.00i | 0.424224i | ||||||||
\(349\) | 6990.00 | 1.07211 | 0.536055 | − | 0.844183i | \(-0.319914\pi\) | ||||
0.536055 | + | 0.844183i | \(0.319914\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1026.00 | −0.156022 | ||||||||
\(352\) | 935.000i | 0.141579i | ||||||||
\(353\) | 8094.00i | 1.22040i | 0.792249 | + | 0.610199i | \(0.208910\pi\) | ||||
−0.792249 | + | 0.610199i | \(0.791090\pi\) | |||||||
\(354\) | 300.000 | 0.0450419 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16422.0 | −2.44484 | ||||||||
\(357\) | 192.000i | 0.0284642i | ||||||||
\(358\) | 19860.0i | 2.93194i | ||||||||
\(359\) | −1024.00 | −0.150542 | −0.0752711 | − | 0.997163i | \(-0.523982\pi\) | ||||
−0.0752711 | + | 0.997163i | \(0.523982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1675.00 | −0.244205 | ||||||||
\(362\) | − 11150.0i | − 1.61887i | ||||||||
\(363\) | − 363.000i | − 0.0524864i | ||||||||
\(364\) | −20672.0 | −2.97667 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8550.00 | −1.22108 | ||||||||
\(367\) | − 13664.0i | − 1.94347i | −0.236066 | − | 0.971737i | \(-0.575858\pi\) | ||||
0.236066 | − | 0.971737i | \(-0.424142\pi\) | |||||||
\(368\) | − 6052.00i | − 0.857289i | ||||||||
\(369\) | −846.000 | −0.119352 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14016.0 | 1.96139 | ||||||||
\(372\) | − 7752.00i | − 1.08044i | ||||||||
\(373\) | 1958.00i | 0.271800i | 0.990723 | + | 0.135900i | \(0.0433926\pi\) | ||||
−0.990723 | + | 0.135900i | \(0.956607\pi\) | |||||||
\(374\) | 110.000 | 0.0152085 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15300.0 | 2.09850 | ||||||||
\(377\) | 2052.00i | 0.280327i | ||||||||
\(378\) | − 4320.00i | − 0.587822i | ||||||||
\(379\) | −6124.00 | −0.829997 | −0.414998 | − | 0.909822i | \(-0.636218\pi\) | ||||
−0.414998 | + | 0.909822i | \(0.636218\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6672.00 | −0.897157 | ||||||||
\(382\) | 3860.00i | 0.517002i | ||||||||
\(383\) | − 5612.00i | − 0.748720i | −0.927283 | − | 0.374360i | \(-0.877862\pi\) | ||||
0.927283 | − | 0.374360i | \(-0.122138\pi\) | |||||||
\(384\) | −6345.00 | −0.843208 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1970.00 | −0.259768 | ||||||||
\(387\) | − 4752.00i | − 0.624180i | ||||||||
\(388\) | 8942.00i | 1.17000i | ||||||||
\(389\) | −12450.0 | −1.62273 | −0.811363 | − | 0.584543i | \(-0.801274\pi\) | ||||
−0.811363 | + | 0.584543i | \(0.801274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −136.000 | −0.0175903 | ||||||||
\(392\) | − 30645.0i | − 3.94849i | ||||||||
\(393\) | 8316.00i | 1.06740i | ||||||||
\(394\) | 15290.0 | 1.95507 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1683.00 | −0.213571 | ||||||||
\(397\) | 14830.0i | 1.87480i | 0.348252 | + | 0.937401i | \(0.386775\pi\) | ||||
−0.348252 | + | 0.937401i | \(0.613225\pi\) | |||||||
\(398\) | 13320.0i | 1.67757i | ||||||||
\(399\) | 6912.00 | 0.867250 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3358.00 | −0.418181 | −0.209090 | − | 0.977896i | \(-0.567050\pi\) | ||||
−0.209090 | + | 0.977896i | \(0.567050\pi\) | |||||||
\(402\) | 6900.00i | 0.856071i | ||||||||
\(403\) | − 5776.00i | − 0.713953i | ||||||||
\(404\) | −850.000 | −0.104676 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8640.00 | −1.05615 | ||||||||
\(407\) | − 1914.00i | − 0.233104i | ||||||||
\(408\) | − 270.000i | − 0.0327622i | ||||||||
\(409\) | −10698.0 | −1.29335 | −0.646677 | − | 0.762764i | \(-0.723842\pi\) | ||||
−0.646677 | + | 0.762764i | \(0.723842\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3390.00 | 0.406852 | ||||||||
\(412\) | 16048.0i | 1.91900i | ||||||||
\(413\) | 640.000i | 0.0762526i | ||||||||
\(414\) | 3060.00 | 0.363263 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3230.00 | 0.380682 | ||||||||
\(417\) | − 4848.00i | − 0.569323i | ||||||||
\(418\) | − 3960.00i | − 0.463373i | ||||||||
\(419\) | 2044.00 | 0.238320 | 0.119160 | − | 0.992875i | \(-0.461980\pi\) | ||||
0.119160 | + | 0.992875i | \(0.461980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3070.00 | 0.355398 | 0.177699 | − | 0.984085i | \(-0.443135\pi\) | ||||
0.177699 | + | 0.984085i | \(0.443135\pi\) | |||||||
\(422\) | 30000.0i | 3.46061i | ||||||||
\(423\) | 3060.00i | 0.351731i | ||||||||
\(424\) | −19710.0 | −2.25755 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 16380.0 | 1.86294 | ||||||||
\(427\) | − 18240.0i | − 2.06720i | ||||||||
\(428\) | − 7956.00i | − 0.898523i | ||||||||
\(429\) | −1254.00 | −0.141127 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12600.0 | −1.40817 | −0.704084 | − | 0.710116i | \(-0.748642\pi\) | ||||
−0.704084 | + | 0.710116i | \(0.748642\pi\) | |||||||
\(432\) | 2403.00i | 0.267626i | ||||||||
\(433\) | 9902.00i | 1.09898i | 0.835499 | + | 0.549492i | \(0.185179\pi\) | ||||
−0.835499 | + | 0.549492i | \(0.814821\pi\) | |||||||
\(434\) | 24320.0 | 2.68986 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2618.00 | 0.287568 | ||||||||
\(437\) | 4896.00i | 0.535944i | ||||||||
\(438\) | 8430.00i | 0.919637i | ||||||||
\(439\) | −11440.0 | −1.24374 | −0.621869 | − | 0.783121i | \(-0.713627\pi\) | ||||
−0.621869 | + | 0.783121i | \(0.713627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6129.00 | 0.661808 | ||||||||
\(442\) | − 380.000i | − 0.0408931i | ||||||||
\(443\) | 5180.00i | 0.555551i | 0.960646 | + | 0.277776i | \(0.0895972\pi\) | ||||
−0.960646 | + | 0.277776i | \(0.910403\pi\) | |||||||
\(444\) | −8874.00 | −0.948517 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2800.00 | 0.297273 | ||||||||
\(447\) | 6198.00i | 0.655829i | ||||||||
\(448\) | − 9184.00i | − 0.968534i | ||||||||
\(449\) | −10826.0 | −1.13789 | −0.568943 | − | 0.822377i | \(-0.692647\pi\) | ||||
−0.568943 | + | 0.822377i | \(0.692647\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1034.00 | −0.107958 | ||||||||
\(452\) | − 918.000i | − 0.0955290i | ||||||||
\(453\) | − 744.000i | − 0.0771659i | ||||||||
\(454\) | 26460.0 | 2.73531 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9720.00 | −0.998203 | ||||||||
\(457\) | − 15798.0i | − 1.61707i | −0.588451 | − | 0.808533i | \(-0.700262\pi\) | ||||
0.588451 | − | 0.808533i | \(-0.299738\pi\) | |||||||
\(458\) | − 26610.0i | − 2.71486i | ||||||||
\(459\) | 54.0000 | 0.00549129 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3894.00 | −0.393409 | −0.196705 | − | 0.980463i | \(-0.563024\pi\) | ||||
−0.196705 | + | 0.980463i | \(0.563024\pi\) | |||||||
\(462\) | − 5280.00i | − 0.531705i | ||||||||
\(463\) | 15992.0i | 1.60521i | 0.596512 | + | 0.802604i | \(0.296553\pi\) | ||||
−0.596512 | + | 0.802604i | \(0.703447\pi\) | |||||||
\(464\) | 4806.00 | 0.480847 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19770.0 | 1.96530 | ||||||||
\(467\) | 11844.0i | 1.17361i | 0.809729 | + | 0.586804i | \(0.199614\pi\) | ||||
−0.809729 | + | 0.586804i | \(0.800386\pi\) | |||||||
\(468\) | 5814.00i | 0.574257i | ||||||||
\(469\) | −14720.0 | −1.44927 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7098.00 | 0.694392 | ||||||||
\(472\) | − 900.000i | − 0.0877666i | ||||||||
\(473\) | − 5808.00i | − 0.564592i | ||||||||
\(474\) | −240.000 | −0.0232565 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1088.00 | 0.104766 | ||||||||
\(477\) | − 3942.00i | − 0.378389i | ||||||||
\(478\) | − 16800.0i | − 1.60756i | ||||||||
\(479\) | −14936.0 | −1.42472 | −0.712362 | − | 0.701812i | \(-0.752375\pi\) | ||||
−0.712362 | + | 0.701812i | \(0.752375\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6612.00 | −0.626780 | ||||||||
\(482\) | 16390.0i | 1.54885i | ||||||||
\(483\) | 6528.00i | 0.614978i | ||||||||
\(484\) | −2057.00 | −0.193182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1215.00 | −0.113402 | ||||||||
\(487\) | − 2056.00i | − 0.191306i | −0.995415 | − | 0.0956532i | \(-0.969506\pi\) | ||||
0.995415 | − | 0.0956532i | \(-0.0304940\pi\) | |||||||
\(488\) | 25650.0i | 2.37935i | ||||||||
\(489\) | 852.000 | 0.0787909 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17852.0 | −1.64083 | −0.820417 | − | 0.571766i | \(-0.806259\pi\) | ||||
−0.820417 | + | 0.571766i | \(0.806259\pi\) | |||||||
\(492\) | 4794.00i | 0.439289i | ||||||||
\(493\) | − 108.000i | − 0.00986628i | ||||||||
\(494\) | −13680.0 | −1.24594 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −13528.0 | −1.22465 | ||||||||
\(497\) | 34944.0i | 3.15383i | ||||||||
\(498\) | 5580.00i | 0.502100i | ||||||||
\(499\) | −4508.00 | −0.404420 | −0.202210 | − | 0.979342i | \(-0.564812\pi\) | ||||
−0.202210 | + | 0.979342i | \(0.564812\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1800.00 | 0.160515 | ||||||||
\(502\) | − 10460.0i | − 0.929985i | ||||||||
\(503\) | 5912.00i | 0.524062i | 0.965059 | + | 0.262031i | \(0.0843922\pi\) | ||||
−0.965059 | + | 0.262031i | \(0.915608\pi\) | |||||||
\(504\) | −12960.0 | −1.14541 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3740.00 | 0.328584 | ||||||||
\(507\) | − 2259.00i | − 0.197881i | ||||||||
\(508\) | 37808.0i | 3.30208i | ||||||||
\(509\) | 11406.0 | 0.993246 | 0.496623 | − | 0.867966i | \(-0.334573\pi\) | ||||
0.496623 | + | 0.867966i | \(0.334573\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17984.0 | −1.55688 | ||||||||
\(512\) | 24475.0i | 2.11260i | ||||||||
\(513\) | − 1944.00i | − 0.167309i | ||||||||
\(514\) | 3290.00 | 0.282326 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −26928.0 | −2.29736 | ||||||||
\(517\) | 3740.00i | 0.318153i | ||||||||
\(518\) | − 27840.0i | − 2.36143i | ||||||||
\(519\) | −414.000 | −0.0350146 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1542.00 | −0.129667 | −0.0648333 | − | 0.997896i | \(-0.520652\pi\) | ||||
−0.0648333 | + | 0.997896i | \(0.520652\pi\) | |||||||
\(522\) | 2430.00i | 0.203751i | ||||||||
\(523\) | 7504.00i | 0.627394i | 0.949523 | + | 0.313697i | \(0.101568\pi\) | ||||
−0.949523 | + | 0.313697i | \(0.898432\pi\) | |||||||
\(524\) | 47124.0 | 3.92867 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25520.0 | 2.11545 | ||||||||
\(527\) | 304.000i | 0.0251280i | ||||||||
\(528\) | 2937.00i | 0.242077i | ||||||||
\(529\) | 7543.00 | 0.619956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 180.000 | 0.0147106 | ||||||||
\(532\) | − 39168.0i | − 3.19201i | ||||||||
\(533\) | 3572.00i | 0.290282i | ||||||||
\(534\) | −14490.0 | −1.17424 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20700.0 | 1.66810 | ||||||||
\(537\) | 11916.0i | 0.957567i | ||||||||
\(538\) | − 21190.0i | − 1.69808i | ||||||||
\(539\) | 7491.00 | 0.598627 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1018.00 | 0.0809006 | 0.0404503 | − | 0.999182i | \(-0.487121\pi\) | ||||
0.0404503 | + | 0.999182i | \(0.487121\pi\) | |||||||
\(542\) | 16880.0i | 1.33775i | ||||||||
\(543\) | − 6690.00i | − 0.528721i | ||||||||
\(544\) | −170.000 | −0.0133983 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −18240.0 | −1.42967 | ||||||||
\(547\) | 7904.00i | 0.617826i | 0.951090 | + | 0.308913i | \(0.0999651\pi\) | ||||
−0.951090 | + | 0.308913i | \(0.900035\pi\) | |||||||
\(548\) | − 19210.0i | − 1.49746i | ||||||||
\(549\) | −5130.00 | −0.398803 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3888.00 | −0.300607 | ||||||||
\(552\) | − 9180.00i | − 0.707838i | ||||||||
\(553\) | − 512.000i | − 0.0393715i | ||||||||
\(554\) | 10370.0 | 0.795269 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −27472.0 | −2.09545 | ||||||||
\(557\) | − 22934.0i | − 1.74460i | −0.488967 | − | 0.872302i | \(-0.662626\pi\) | ||||
0.488967 | − | 0.872302i | \(-0.337374\pi\) | |||||||
\(558\) | − 6840.00i | − 0.518925i | ||||||||
\(559\) | −20064.0 | −1.51810 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 66.0000 | 0.00496706 | ||||||||
\(562\) | − 3510.00i | − 0.263453i | ||||||||
\(563\) | − 14020.0i | − 1.04951i | −0.851254 | − | 0.524754i | \(-0.824157\pi\) | ||||
0.851254 | − | 0.524754i | \(-0.175843\pi\) | |||||||
\(564\) | 17340.0 | 1.29458 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −24560.0 | −1.82391 | ||||||||
\(567\) | − 2592.00i | − 0.191982i | ||||||||
\(568\) | − 49140.0i | − 3.63005i | ||||||||
\(569\) | −4230.00 | −0.311653 | −0.155827 | − | 0.987784i | \(-0.549804\pi\) | ||||
−0.155827 | + | 0.987784i | \(0.549804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8536.00 | −0.625605 | −0.312803 | − | 0.949818i | \(-0.601268\pi\) | ||||
−0.312803 | + | 0.949818i | \(0.601268\pi\) | |||||||
\(572\) | 7106.00i | 0.519435i | ||||||||
\(573\) | 2316.00i | 0.168852i | ||||||||
\(574\) | −15040.0 | −1.09365 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2583.00 | −0.186849 | ||||||||
\(577\) | − 11982.0i | − 0.864501i | −0.901754 | − | 0.432251i | \(-0.857720\pi\) | ||||
0.901754 | − | 0.432251i | \(-0.142280\pi\) | |||||||
\(578\) | − 24545.0i | − 1.76633i | ||||||||
\(579\) | −1182.00 | −0.0848398 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11904.0 | −0.850019 | ||||||||
\(582\) | 7890.00i | 0.561943i | ||||||||
\(583\) | − 4818.00i | − 0.342266i | ||||||||
\(584\) | 25290.0 | 1.79197 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17430.0 | 1.22871 | ||||||||
\(587\) | − 20396.0i | − 1.43413i | −0.697007 | − | 0.717064i | \(-0.745486\pi\) | ||||
0.697007 | − | 0.717064i | \(-0.254514\pi\) | |||||||
\(588\) | − 34731.0i | − 2.43585i | ||||||||
\(589\) | 10944.0 | 0.765602 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9174.00 | 0.638524 | ||||||||
\(592\) | 15486.0i | 1.07512i | ||||||||
\(593\) | − 12518.0i | − 0.866868i | −0.901185 | − | 0.433434i | \(-0.857302\pi\) | ||||
0.901185 | − | 0.433434i | \(-0.142698\pi\) | |||||||
\(594\) | −1485.00 | −0.102576 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 35122.0 | 2.41385 | ||||||||
\(597\) | 7992.00i | 0.547891i | ||||||||
\(598\) | − 12920.0i | − 0.883509i | ||||||||
\(599\) | 25292.0 | 1.72521 | 0.862607 | − | 0.505875i | \(-0.168830\pi\) | ||||
0.862607 | + | 0.505875i | \(0.168830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15962.0 | 1.08337 | 0.541683 | − | 0.840583i | \(-0.317787\pi\) | ||||
0.541683 | + | 0.840583i | \(0.317787\pi\) | |||||||
\(602\) | − 84480.0i | − 5.71951i | ||||||||
\(603\) | 4140.00i | 0.279592i | ||||||||
\(604\) | −4216.00 | −0.284018 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −750.000 | −0.0502750 | ||||||||
\(607\) | − 1600.00i | − 0.106988i | −0.998568 | − | 0.0534942i | \(-0.982964\pi\) | ||||
0.998568 | − | 0.0534942i | \(-0.0170359\pi\) | |||||||
\(608\) | 6120.00i | 0.408222i | ||||||||
\(609\) | −5184.00 | −0.344936 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12920.0 | 0.855462 | ||||||||
\(612\) | − 306.000i | − 0.0202113i | ||||||||
\(613\) | − 2162.00i | − 0.142451i | −0.997460 | − | 0.0712254i | \(-0.977309\pi\) | ||||
0.997460 | − | 0.0712254i | \(-0.0226910\pi\) | |||||||
\(614\) | 41800.0 | 2.74741 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15840.0 | −1.03606 | ||||||||
\(617\) | − 18126.0i | − 1.18270i | −0.806415 | − | 0.591350i | \(-0.798595\pi\) | ||||
0.806415 | − | 0.591350i | \(-0.201405\pi\) | |||||||
\(618\) | 14160.0i | 0.921681i | ||||||||
\(619\) | −17348.0 | −1.12645 | −0.563227 | − | 0.826302i | \(-0.690440\pi\) | ||||
−0.563227 | + | 0.826302i | \(0.690440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1836.00 | 0.118641 | ||||||||
\(622\) | 27660.0i | 1.78306i | ||||||||
\(623\) | − 30912.0i | − 1.98790i | ||||||||
\(624\) | 10146.0 | 0.650906 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −24130.0 | −1.54062 | ||||||||
\(627\) | − 2376.00i | − 0.151337i | ||||||||
\(628\) | − 40222.0i | − 2.55578i | ||||||||
\(629\) | 348.000 | 0.0220599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10096.0 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 720.000i | 0.0453166i | ||||||||
\(633\) | 18000.0i | 1.13023i | ||||||||
\(634\) | 37850.0 | 2.37100 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −22338.0 | −1.39270 | ||||||||
\(637\) | − 25878.0i | − 1.60961i | ||||||||
\(638\) | 2970.00i | 0.184300i | ||||||||
\(639\) | 9828.00 | 0.608435 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8922.00 | 0.549763 | 0.274881 | − | 0.961478i | \(-0.411361\pi\) | ||||
0.274881 | + | 0.961478i | \(0.411361\pi\) | |||||||
\(642\) | − 7020.00i | − 0.431553i | ||||||||
\(643\) | 14644.0i | 0.898138i | 0.893497 | + | 0.449069i | \(0.148244\pi\) | ||||
−0.893497 | + | 0.449069i | \(0.851756\pi\) | |||||||
\(644\) | 36992.0 | 2.26349 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 720.000 | 0.0438514 | ||||||||
\(647\) | 6932.00i | 0.421213i | 0.977571 | + | 0.210607i | \(0.0675439\pi\) | ||||
−0.977571 | + | 0.210607i | \(0.932456\pi\) | |||||||
\(648\) | 3645.00i | 0.220971i | ||||||||
\(649\) | 220.000 | 0.0133062 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14592.0 | 0.878503 | ||||||||
\(652\) | − 4828.00i | − 0.289999i | ||||||||
\(653\) | 5942.00i | 0.356093i | 0.984022 | + | 0.178046i | \(0.0569777\pi\) | ||||
−0.984022 | + | 0.178046i | \(0.943022\pi\) | |||||||
\(654\) | 2310.00 | 0.138116 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8366.00 | 0.497923 | ||||||||
\(657\) | 5058.00i | 0.300352i | ||||||||
\(658\) | 54400.0i | 3.22300i | ||||||||
\(659\) | −484.000 | −0.0286100 | −0.0143050 | − | 0.999898i | \(-0.504554\pi\) | ||||
−0.0143050 | + | 0.999898i | \(0.504554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17114.0 | −1.00705 | −0.503523 | − | 0.863982i | \(-0.667963\pi\) | ||||
−0.503523 | + | 0.863982i | \(0.667963\pi\) | |||||||
\(662\) | − 18380.0i | − 1.07909i | ||||||||
\(663\) | − 228.000i | − 0.0133556i | ||||||||
\(664\) | 16740.0 | 0.978370 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7830.00 | −0.455565 | ||||||||
\(667\) | − 3672.00i | − 0.213164i | ||||||||
\(668\) | − 10200.0i | − 0.590793i | ||||||||
\(669\) | 1680.00 | 0.0970890 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6270.00 | −0.360731 | ||||||||
\(672\) | 8160.00i | 0.468421i | ||||||||
\(673\) | − 16154.0i | − 0.925247i | −0.886555 | − | 0.462623i | \(-0.846908\pi\) | ||||
0.886555 | − | 0.462623i | \(-0.153092\pi\) | |||||||
\(674\) | −28430.0 | −1.62475 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12801.0 | −0.728323 | ||||||||
\(677\) | − 3390.00i | − 0.192449i | −0.995360 | − | 0.0962247i | \(-0.969323\pi\) | ||||
0.995360 | − | 0.0962247i | \(-0.0306767\pi\) | |||||||
\(678\) | − 810.000i | − 0.0458818i | ||||||||
\(679\) | −16832.0 | −0.951330 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15876.0 | 0.893347 | ||||||||
\(682\) | − 8360.00i | − 0.469386i | ||||||||
\(683\) | 25540.0i | 1.43084i | 0.698697 | + | 0.715418i | \(0.253764\pi\) | ||||
−0.698697 | + | 0.715418i | \(0.746236\pi\) | |||||||
\(684\) | −11016.0 | −0.615800 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 54080.0 | 3.00989 | ||||||||
\(687\) | − 15966.0i | − 0.886668i | ||||||||
\(688\) | 46992.0i | 2.60400i | ||||||||
\(689\) | −16644.0 | −0.920299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12476.0 | 0.686844 | 0.343422 | − | 0.939181i | \(-0.388414\pi\) | ||||
0.343422 | + | 0.939181i | \(0.388414\pi\) | |||||||
\(692\) | 2346.00i | 0.128875i | ||||||||
\(693\) | − 3168.00i | − 0.173654i | ||||||||
\(694\) | −8260.00 | −0.451794 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7290.00 | 0.397021 | ||||||||
\(697\) | − 188.000i | − 0.0102167i | ||||||||
\(698\) | − 34950.0i | − 1.89524i | ||||||||
\(699\) | 11862.0 | 0.641863 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20806.0 | −1.12102 | −0.560508 | − | 0.828149i | \(-0.689394\pi\) | ||||
−0.560508 | + | 0.828149i | \(0.689394\pi\) | |||||||
\(702\) | 5130.00i | 0.275811i | ||||||||
\(703\) | − 12528.0i | − 0.672123i | ||||||||
\(704\) | −3157.00 | −0.169011 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40470.0 | 2.15738 | ||||||||
\(707\) | − 1600.00i | − 0.0851120i | ||||||||
\(708\) | − 1020.00i | − 0.0541440i | ||||||||
\(709\) | −14198.0 | −0.752069 | −0.376035 | − | 0.926606i | \(-0.622713\pi\) | ||||
−0.376035 | + | 0.926606i | \(0.622713\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −144.000 | −0.00759553 | ||||||||
\(712\) | 43470.0i | 2.28807i | ||||||||
\(713\) | 10336.0i | 0.542898i | ||||||||
\(714\) | 960.000 | 0.0503181 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 67524.0 | 3.52443 | ||||||||
\(717\) | − 10080.0i | − 0.525027i | ||||||||
\(718\) | 5120.00i | 0.266124i | ||||||||
\(719\) | −4596.00 | −0.238389 | −0.119195 | − | 0.992871i | \(-0.538031\pi\) | ||||
−0.119195 | + | 0.992871i | \(0.538031\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30208.0 | −1.56034 | ||||||||
\(722\) | 8375.00i | 0.431697i | ||||||||
\(723\) | 9834.00i | 0.505851i | ||||||||
\(724\) | −37910.0 | −1.94601 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1815.00 | −0.0927837 | ||||||||
\(727\) | 19560.0i | 0.997855i | 0.866644 | + | 0.498927i | \(0.166273\pi\) | ||||
−0.866644 | + | 0.498927i | \(0.833727\pi\) | |||||||
\(728\) | 54720.0i | 2.78579i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1056.00 | 0.0534303 | ||||||||
\(732\) | 29070.0i | 1.46784i | ||||||||
\(733\) | 1638.00i | 0.0825388i | 0.999148 | + | 0.0412694i | \(0.0131402\pi\) | ||||
−0.999148 | + | 0.0412694i | \(0.986860\pi\) | |||||||
\(734\) | −68320.0 | −3.43561 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5780.00 | −0.289475 | ||||||||
\(737\) | 5060.00i | 0.252900i | ||||||||
\(738\) | 4230.00i | 0.210987i | ||||||||
\(739\) | 15592.0 | 0.776131 | 0.388066 | − | 0.921632i | \(-0.373143\pi\) | ||||
0.388066 | + | 0.921632i | \(0.373143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8208.00 | −0.406921 | ||||||||
\(742\) | − 70080.0i | − 3.46727i | ||||||||
\(743\) | − 592.000i | − 0.0292307i | −0.999893 | − | 0.0146153i | \(-0.995348\pi\) | ||||
0.999893 | − | 0.0146153i | \(-0.00465237\pi\) | |||||||
\(744\) | −20520.0 | −1.01116 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9790.00 | 0.480479 | ||||||||
\(747\) | 3348.00i | 0.163985i | ||||||||
\(748\) | − 374.000i | − 0.0182818i | ||||||||
\(749\) | 14976.0 | 0.730589 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 39832.0 | 1.93541 | 0.967703 | − | 0.252092i | \(-0.0811186\pi\) | ||||
0.967703 | + | 0.252092i | \(0.0811186\pi\) | |||||||
\(752\) | − 30260.0i | − 1.46738i | ||||||||
\(753\) | − 6276.00i | − 0.303732i | ||||||||
\(754\) | 10260.0 | 0.495553 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −14688.0 | −0.706610 | ||||||||
\(757\) | 10958.0i | 0.526123i | 0.964779 | + | 0.263062i | \(0.0847323\pi\) | ||||
−0.964779 | + | 0.263062i | \(0.915268\pi\) | |||||||
\(758\) | 30620.0i | 1.46724i | ||||||||
\(759\) | 2244.00 | 0.107315 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8970.00 | −0.427283 | −0.213641 | − | 0.976912i | \(-0.568532\pi\) | ||||
−0.213641 | + | 0.976912i | \(0.568532\pi\) | |||||||
\(762\) | 33360.0i | 1.58596i | ||||||||
\(763\) | 4928.00i | 0.233821i | ||||||||
\(764\) | 13124.0 | 0.621479 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28060.0 | −1.32356 | ||||||||
\(767\) | − 760.000i | − 0.0357784i | ||||||||
\(768\) | 24837.0i | 1.16696i | ||||||||
\(769\) | 10054.0 | 0.471465 | 0.235732 | − | 0.971818i | \(-0.424251\pi\) | ||||
0.235732 | + | 0.971818i | \(0.424251\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1974.00 | 0.0922074 | ||||||||
\(772\) | 6698.00i | 0.312262i | ||||||||
\(773\) | − 26346.0i | − 1.22587i | −0.790132 | − | 0.612936i | \(-0.789988\pi\) | ||||
0.790132 | − | 0.612936i | \(-0.210012\pi\) | |||||||
\(774\) | −23760.0 | −1.10341 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23670.0 | 1.09498 | ||||||||
\(777\) | − 16704.0i | − 0.771239i | ||||||||
\(778\) | 62250.0i | 2.86860i | ||||||||
\(779\) | −6768.00 | −0.311282 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12012.0 | 0.550350 | ||||||||
\(782\) | 680.000i | 0.0310956i | ||||||||
\(783\) | 1458.00i | 0.0665449i | ||||||||
\(784\) | −60609.0 | −2.76098 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 41580.0 | 1.88691 | ||||||||
\(787\) | − 16040.0i | − 0.726511i | −0.931690 | − | 0.363256i | \(-0.881665\pi\) | ||||
0.931690 | − | 0.363256i | \(-0.118335\pi\) | |||||||
\(788\) | − 51986.0i | − 2.35016i | ||||||||
\(789\) | 15312.0 | 0.690902 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1728.00 | 0.0776746 | ||||||||
\(792\) | 4455.00i | 0.199876i | ||||||||
\(793\) | 21660.0i | 0.969948i | ||||||||
\(794\) | 74150.0 | 3.31421 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45288.0 | 2.01657 | ||||||||
\(797\) | 32810.0i | 1.45821i | 0.684404 | + | 0.729103i | \(0.260062\pi\) | ||||
−0.684404 | + | 0.729103i | \(0.739938\pi\) | |||||||
\(798\) | − 34560.0i | − 1.53310i | ||||||||
\(799\) | −680.000 | −0.0301085 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8694.00 | −0.383505 | ||||||||
\(802\) | 16790.0i | 0.739246i | ||||||||
\(803\) | 6182.00i | 0.271679i | ||||||||
\(804\) | 23460.0 | 1.02907 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28880.0 | −1.26210 | ||||||||
\(807\) | − 12714.0i | − 0.554590i | ||||||||
\(808\) | 2250.00i | 0.0979638i | ||||||||
\(809\) | −18918.0 | −0.822153 | −0.411076 | − | 0.911601i | \(-0.634847\pi\) | ||||
−0.411076 | + | 0.911601i | \(0.634847\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8552.00 | −0.370285 | −0.185143 | − | 0.982712i | \(-0.559275\pi\) | ||||
−0.185143 | + | 0.982712i | \(0.559275\pi\) | |||||||
\(812\) | 29376.0i | 1.26958i | ||||||||
\(813\) | 10128.0i | 0.436906i | ||||||||
\(814\) | −9570.00 | −0.412074 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −534.000 | −0.0229090 | ||||||||
\(817\) | − 38016.0i | − 1.62792i | ||||||||
\(818\) | 53490.0i | 2.28635i | ||||||||
\(819\) | −10944.0 | −0.466928 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46430.0 | −1.97371 | −0.986856 | − | 0.161600i | \(-0.948335\pi\) | ||||
−0.986856 | + | 0.161600i | \(0.948335\pi\) | |||||||
\(822\) | − 16950.0i | − 0.719220i | ||||||||
\(823\) | − 16392.0i | − 0.694276i | −0.937814 | − | 0.347138i | \(-0.887154\pi\) | ||||
0.937814 | − | 0.347138i | \(-0.112846\pi\) | |||||||
\(824\) | 42480.0 | 1.79595 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3200.00 | 0.134797 | ||||||||
\(827\) | − 13876.0i | − 0.583453i | −0.956502 | − | 0.291727i | \(-0.905770\pi\) | ||||
0.956502 | − | 0.291727i | \(-0.0942297\pi\) | |||||||
\(828\) | − 10404.0i | − 0.436671i | ||||||||
\(829\) | 24554.0 | 1.02870 | 0.514352 | − | 0.857579i | \(-0.328032\pi\) | ||||
0.514352 | + | 0.857579i | \(0.328032\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6222.00 | 0.259734 | ||||||||
\(832\) | 10906.0i | 0.454444i | ||||||||
\(833\) | 1362.00i | 0.0566513i | ||||||||
\(834\) | −24240.0 | −1.00643 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −13464.0 | −0.557012 | ||||||||
\(837\) | − 4104.00i | − 0.169480i | ||||||||
\(838\) | − 10220.0i | − 0.421294i | ||||||||
\(839\) | −19900.0 | −0.818861 | −0.409430 | − | 0.912341i | \(-0.634273\pi\) | ||||
−0.409430 | + | 0.912341i | \(0.634273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | − 15350.0i | − 0.628261i | ||||||||
\(843\) | − 2106.00i | − 0.0860433i | ||||||||
\(844\) | 102000. | 4.15993 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15300.0 | 0.621779 | ||||||||
\(847\) | − 3872.00i | − 0.157076i | ||||||||
\(848\) | 38982.0i | 1.57859i | ||||||||
\(849\) | −14736.0 | −0.595687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11832.0 | 0.476611 | ||||||||
\(852\) | − 55692.0i | − 2.23941i | ||||||||
\(853\) | − 41138.0i | − 1.65128i | −0.564200 | − | 0.825638i | \(-0.690815\pi\) | ||||
0.564200 | − | 0.825638i | \(-0.309185\pi\) | |||||||
\(854\) | −91200.0 | −3.65433 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21060.0 | −0.840907 | ||||||||
\(857\) | 19910.0i | 0.793597i | 0.917906 | + | 0.396799i | \(0.129879\pi\) | ||||
−0.917906 | + | 0.396799i | \(0.870121\pi\) | |||||||
\(858\) | 6270.00i | 0.249481i | ||||||||
\(859\) | −42924.0 | −1.70495 | −0.852473 | − | 0.522772i | \(-0.824898\pi\) | ||||
−0.852473 | + | 0.522772i | \(0.824898\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9024.00 | −0.357186 | ||||||||
\(862\) | 63000.0i | 2.48931i | ||||||||
\(863\) | 46236.0i | 1.82374i | 0.410474 | + | 0.911872i | \(0.365363\pi\) | ||||
−0.410474 | + | 0.911872i | \(0.634637\pi\) | |||||||
\(864\) | 2295.00 | 0.0903675 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 49510.0 | 1.94275 | ||||||||
\(867\) | − 14727.0i | − 0.576880i | ||||||||
\(868\) | − 82688.0i | − 3.23343i | ||||||||
\(869\) | −176.000 | −0.00687042 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17480.0 | 0.680008 | ||||||||
\(872\) | − 6930.00i | − 0.269128i | ||||||||
\(873\) | 4734.00i | 0.183530i | ||||||||
\(874\) | 24480.0 | 0.947424 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28662.0 | 1.10548 | ||||||||
\(877\) | 25746.0i | 0.991312i | 0.868519 | + | 0.495656i | \(0.165072\pi\) | ||||
−0.868519 | + | 0.495656i | \(0.834928\pi\) | |||||||
\(878\) | 57200.0i | 2.19864i | ||||||||
\(879\) | 10458.0 | 0.401296 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24550.0 | −0.938831 | −0.469416 | − | 0.882977i | \(-0.655535\pi\) | ||||
−0.469416 | + | 0.882977i | \(0.655535\pi\) | |||||||
\(882\) | − 30645.0i | − 1.16992i | ||||||||
\(883\) | 19436.0i | 0.740740i | 0.928884 | + | 0.370370i | \(0.120769\pi\) | ||||
−0.928884 | + | 0.370370i | \(0.879231\pi\) | |||||||
\(884\) | −1292.00 | −0.0491569 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25900.0 | 0.982085 | ||||||||
\(887\) | − 22912.0i | − 0.867316i | −0.901077 | − | 0.433658i | \(-0.857223\pi\) | ||||
0.901077 | − | 0.433658i | \(-0.142777\pi\) | |||||||
\(888\) | 23490.0i | 0.887695i | ||||||||
\(889\) | −71168.0 | −2.68492 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | − 9520.00i | − 0.357347i | ||||||||
\(893\) | 24480.0i | 0.917348i | ||||||||
\(894\) | 30990.0 | 1.15935 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −67680.0 | −2.52347 | ||||||||
\(897\) | − 7752.00i | − 0.288553i | ||||||||
\(898\) | 54130.0i | 2.01152i | ||||||||
\(899\) | −8208.00 | −0.304507 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 876.000 | 0.0323904 | ||||||||
\(902\) | 5170.00i | 0.190845i | ||||||||
\(903\) | − 50688.0i | − 1.86799i | ||||||||
\(904\) | −2430.00 | −0.0894033 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3720.00 | −0.136411 | ||||||||
\(907\) | − 39900.0i | − 1.46070i | −0.683071 | − | 0.730352i | \(-0.739356\pi\) | ||||
0.683071 | − | 0.730352i | \(-0.260644\pi\) | |||||||
\(908\) | − 89964.0i | − 3.28806i | ||||||||
\(909\) | −450.000 | −0.0164198 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29460.0 | 1.07141 | 0.535704 | − | 0.844406i | \(-0.320046\pi\) | ||||
0.535704 | + | 0.844406i | \(0.320046\pi\) | |||||||
\(912\) | 19224.0i | 0.697994i | ||||||||
\(913\) | 4092.00i | 0.148330i | ||||||||
\(914\) | −78990.0 | −2.85860 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −90474.0 | −3.26348 | ||||||||
\(917\) | 88704.0i | 3.19440i | ||||||||
\(918\) | − 270.000i | − 0.00970733i | ||||||||
\(919\) | −29368.0 | −1.05415 | −0.527073 | − | 0.849820i | \(-0.676711\pi\) | ||||
−0.527073 | + | 0.849820i | \(0.676711\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25080.0 | 0.897301 | ||||||||
\(922\) | 19470.0i | 0.695456i | ||||||||
\(923\) | − 41496.0i | − 1.47980i | ||||||||
\(924\) | −17952.0 | −0.639153 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 79960.0 | 2.83763 | ||||||||
\(927\) | 8496.00i | 0.301020i | ||||||||
\(928\) | − 4590.00i | − 0.162364i | ||||||||
\(929\) | −33954.0 | −1.19913 | −0.599567 | − | 0.800325i | \(-0.704660\pi\) | ||||
−0.599567 | + | 0.800325i | \(0.704660\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49032.0 | 1.72606 | ||||||||
\(932\) | − 67218.0i | − 2.36245i | ||||||||
\(933\) | 16596.0i | 0.582346i | ||||||||
\(934\) | 59220.0 | 2.07467 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15390.0 | 0.537434 | ||||||||
\(937\) | − 2854.00i | − 0.0995049i | −0.998762 | − | 0.0497525i | \(-0.984157\pi\) | ||||
0.998762 | − | 0.0497525i | \(-0.0158432\pi\) | |||||||
\(938\) | 73600.0i | 2.56197i | ||||||||
\(939\) | −14478.0 | −0.503165 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6294.00 | −0.218043 | −0.109022 | − | 0.994039i | \(-0.534772\pi\) | ||||
−0.109022 | + | 0.994039i | \(0.534772\pi\) | |||||||
\(942\) | − 35490.0i | − 1.22752i | ||||||||
\(943\) | − 6392.00i | − 0.220734i | ||||||||
\(944\) | −1780.00 | −0.0613708 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29040.0 | −0.998067 | ||||||||
\(947\) | 2268.00i | 0.0778248i | 0.999243 | + | 0.0389124i | \(0.0123893\pi\) | ||||
−0.999243 | + | 0.0389124i | \(0.987611\pi\) | |||||||
\(948\) | 816.000i | 0.0279562i | ||||||||
\(949\) | 21356.0 | 0.730501 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22710.0 | 0.774366 | ||||||||
\(952\) | − 2880.00i | − 0.0980476i | ||||||||
\(953\) | − 26566.0i | − 0.902998i | −0.892272 | − | 0.451499i | \(-0.850889\pi\) | ||||
0.892272 | − | 0.451499i | \(-0.149111\pi\) | |||||||
\(954\) | −19710.0 | −0.668904 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −57120.0 | −1.93242 | ||||||||
\(957\) | 1782.00i | 0.0601921i | ||||||||
\(958\) | 74680.0i | 2.51858i | ||||||||
\(959\) | 36160.0 | 1.21759 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6687.00 | −0.224464 | ||||||||
\(962\) | 33060.0i | 1.10800i | ||||||||
\(963\) | − 4212.00i | − 0.140945i | ||||||||
\(964\) | 55726.0 | 1.86184 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 32640.0 | 1.08714 | ||||||||
\(967\) | 11176.0i | 0.371661i | 0.982582 | + | 0.185830i | \(0.0594975\pi\) | ||||
−0.982582 | + | 0.185830i | \(0.940503\pi\) | |||||||
\(968\) | 5445.00i | 0.180794i | ||||||||
\(969\) | 432.000 | 0.0143218 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42316.0 | −1.39854 | −0.699271 | − | 0.714856i | \(-0.746492\pi\) | ||||
−0.699271 | + | 0.714856i | \(0.746492\pi\) | |||||||
\(972\) | 4131.00i | 0.136319i | ||||||||
\(973\) | − 51712.0i | − 1.70381i | ||||||||
\(974\) | −10280.0 | −0.338185 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 50730.0 | 1.66376 | ||||||||
\(977\) | − 45054.0i | − 1.47534i | −0.675163 | − | 0.737669i | \(-0.735927\pi\) | ||||
0.675163 | − | 0.737669i | \(-0.264073\pi\) | |||||||
\(978\) | − 4260.00i | − 0.139284i | ||||||||
\(979\) | −10626.0 | −0.346893 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1386.00 | 0.0451086 | ||||||||
\(982\) | 89260.0i | 2.90061i | ||||||||
\(983\) | 12300.0i | 0.399094i | 0.979888 | + | 0.199547i | \(0.0639470\pi\) | ||||
−0.979888 | + | 0.199547i | \(0.936053\pi\) | |||||||
\(984\) | 12690.0 | 0.411120 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −540.000 | −0.0174413 | ||||||||
\(987\) | 32640.0i | 1.05263i | ||||||||
\(988\) | 46512.0i | 1.49772i | ||||||||
\(989\) | 35904.0 | 1.15438 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36280.0 | 1.16294 | 0.581469 | − | 0.813568i | \(-0.302478\pi\) | ||||
0.581469 | + | 0.813568i | \(0.302478\pi\) | |||||||
\(992\) | 12920.0i | 0.413519i | ||||||||
\(993\) | − 11028.0i | − 0.352430i | ||||||||
\(994\) | 174720. | 5.57523 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18972.0 | 0.603565 | ||||||||
\(997\) | 3290.00i | 0.104509i | 0.998634 | + | 0.0522544i | \(0.0166407\pi\) | ||||
−0.998634 | + | 0.0522544i | \(0.983359\pi\) | |||||||
\(998\) | 22540.0i | 0.714921i | ||||||||
\(999\) | −4698.00 | −0.148787 |
(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 | 825.4.c.a.199.1 | 2 | ||
5.2 | odd | 4 | 825.4.a.i.1.1 | 1 | |||
5.3 | odd | 4 | 33.4.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 825.4.c.a.199.2 | 2 | ||
15.2 | even | 4 | 2475.4.a.b.1.1 | 1 | |||
15.8 | even | 4 | 99.4.a.b.1.1 | 1 | |||
20.3 | even | 4 | 528.4.a.a.1.1 | 1 | |||
35.13 | even | 4 | 1617.4.a.a.1.1 | 1 | |||
40.3 | even | 4 | 2112.4.a.y.1.1 | 1 | |||
40.13 | odd | 4 | 2112.4.a.l.1.1 | 1 | |||
55.43 | even | 4 | 363.4.a.h.1.1 | 1 | |||
60.23 | odd | 4 | 1584.4.a.t.1.1 | 1 | |||
165.98 | odd | 4 | 1089.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
99.4.a.b.1.1 | 1 | 15.8 | even | 4 | |||
363.4.a.h.1.1 | 1 | 55.43 | even | 4 | |||
528.4.a.a.1.1 | 1 | 20.3 | even | 4 | |||
825.4.a.i.1.1 | 1 | 5.2 | odd | 4 | |||
825.4.c.a.199.1 | 2 | 1.1 | even | 1 | trivial | ||
825.4.c.a.199.2 | 2 | 5.4 | even | 2 | inner | ||
1089.4.a.a.1.1 | 1 | 165.98 | odd | 4 | |||
1584.4.a.t.1.1 | 1 | 60.23 | odd | 4 | |||
1617.4.a.a.1.1 | 1 | 35.13 | even | 4 | |||
2112.4.a.l.1.1 | 1 | 40.13 | odd | 4 | |||
2112.4.a.y.1.1 | 1 | 40.3 | even | 4 | |||
2475.4.a.b.1.1 | 1 | 15.2 | even | 4 |