Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.m.361.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 11.0000 | − | 19.0526i | 0.983870 | − | 1.70411i | 0.337016 | − | 0.941499i | \(-0.390582\pi\) |
0.646854 | − | 0.762614i | \(-0.276084\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 22.0000 | + | 38.1051i | 0.695701 | + | 1.20499i | ||||
\(11\) | 13.0000 | + | 22.5167i | 0.356332 | + | 0.617184i | 0.987345 | − | 0.158588i | \(-0.0506940\pi\) |
−0.631013 | + | 0.775772i | \(0.717361\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −54.0000 | −1.15207 | −0.576035 | − | 0.817425i | \(-0.695401\pi\) | ||||
−0.576035 | + | 0.817425i | \(0.695401\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 37.0000 | + | 64.0859i | 0.527872 | + | 0.914301i | 0.999472 | + | 0.0324882i | \(0.0103431\pi\) |
−0.471600 | + | 0.881812i | \(0.656324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −58.0000 | + | 100.459i | −0.700322 | + | 1.21299i | 0.268032 | + | 0.963410i | \(0.413627\pi\) |
−0.968353 | + | 0.249583i | \(0.919707\pi\) | |||||||
\(20\) | −88.0000 | −0.983870 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −52.0000 | −0.503929 | ||||||||
\(23\) | −29.0000 | + | 50.2295i | −0.262909 | + | 0.455373i | −0.967014 | − | 0.254724i | \(-0.918015\pi\) |
0.704104 | + | 0.710097i | \(0.251349\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −179.500 | − | 310.903i | −1.43600 | − | 2.48722i | ||||
\(26\) | 54.0000 | − | 93.5307i | 0.407318 | − | 0.705496i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −208.000 | −1.33188 | −0.665942 | − | 0.746004i | \(-0.731970\pi\) | ||||
−0.665942 | + | 0.746004i | \(0.731970\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 126.000 | + | 218.238i | 0.730009 | + | 1.26441i | 0.956879 | + | 0.290487i | \(0.0938173\pi\) |
−0.226870 | + | 0.973925i | \(0.572849\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −148.000 | −0.746523 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −25.0000 | + | 43.3013i | −0.111080 | + | 0.192397i | −0.916206 | − | 0.400707i | \(-0.868764\pi\) |
0.805126 | + | 0.593104i | \(0.202098\pi\) | |||||||
\(38\) | −116.000 | − | 200.918i | −0.495202 | − | 0.857715i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 88.0000 | − | 152.420i | 0.347851 | − | 0.602495i | ||||
\(41\) | −126.000 | −0.479949 | −0.239974 | − | 0.970779i | \(-0.577139\pi\) | ||||
−0.239974 | + | 0.970779i | \(0.577139\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 164.000 | 0.581622 | 0.290811 | − | 0.956780i | \(-0.406075\pi\) | ||||
0.290811 | + | 0.956780i | \(0.406075\pi\) | |||||||
\(44\) | 52.0000 | − | 90.0666i | 0.178166 | − | 0.308592i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −58.0000 | − | 100.459i | −0.185905 | − | 0.321997i | ||||
\(47\) | −222.000 | + | 384.515i | −0.688979 | + | 1.19335i | 0.283189 | + | 0.959064i | \(0.408608\pi\) |
−0.972168 | + | 0.234283i | \(0.924726\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 718.000 | 2.03081 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 108.000 | + | 187.061i | 0.288017 | + | 0.498861i | ||||
\(53\) | 6.00000 | + | 10.3923i | 0.0155503 | + | 0.0269338i | 0.873696 | − | 0.486473i | \(-0.161717\pi\) |
−0.858146 | + | 0.513406i | \(0.828383\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 572.000 | 1.40234 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 208.000 | − | 360.267i | 0.470892 | − | 0.815609i | ||||
\(59\) | 62.0000 | + | 107.387i | 0.136809 | + | 0.236960i | 0.926287 | − | 0.376819i | \(-0.122982\pi\) |
−0.789478 | + | 0.613779i | \(0.789649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 81.0000 | − | 140.296i | 0.170016 | − | 0.294477i | −0.768409 | − | 0.639959i | \(-0.778951\pi\) |
0.938425 | + | 0.345482i | \(0.112285\pi\) | |||||||
\(62\) | −504.000 | −1.03239 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −594.000 | + | 1028.84i | −1.13349 | + | 1.96326i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 430.000 | + | 744.782i | 0.784073 | + | 1.35805i | 0.929552 | + | 0.368692i | \(0.120194\pi\) |
−0.145479 | + | 0.989361i | \(0.546472\pi\) | |||||||
\(68\) | 148.000 | − | 256.344i | 0.263936 | − | 0.457150i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 238.000 | 0.397823 | 0.198911 | − | 0.980017i | \(-0.436259\pi\) | ||||
0.198911 | + | 0.980017i | \(0.436259\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 73.0000 | + | 126.440i | 0.117041 | + | 0.202721i | 0.918594 | − | 0.395203i | \(-0.129326\pi\) |
−0.801553 | + | 0.597924i | \(0.795992\pi\) | |||||||
\(74\) | −50.0000 | − | 86.6025i | −0.0785457 | − | 0.136045i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 464.000 | 0.700322 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 492.000 | − | 852.169i | 0.700688 | − | 1.21363i | −0.267538 | − | 0.963547i | \(-0.586210\pi\) |
0.968225 | − | 0.250079i | \(-0.0804567\pi\) | |||||||
\(80\) | 176.000 | + | 304.841i | 0.245967 | + | 0.426028i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 126.000 | − | 218.238i | 0.169687 | − | 0.293907i | ||||
\(83\) | −656.000 | −0.867534 | −0.433767 | − | 0.901025i | \(-0.642816\pi\) | ||||
−0.433767 | + | 0.901025i | \(0.642816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1628.00 | 2.07743 | ||||||||
\(86\) | −164.000 | + | 284.056i | −0.205635 | + | 0.356170i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 104.000 | + | 180.133i | 0.125982 | + | 0.218208i | ||||
\(89\) | −477.000 | + | 826.188i | −0.568111 | + | 0.983998i | 0.428642 | + | 0.903475i | \(0.358992\pi\) |
−0.996753 | + | 0.0805229i | \(0.974341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 232.000 | 0.262909 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −444.000 | − | 769.031i | −0.487182 | − | 0.843824i | ||||
\(95\) | 1276.00 | + | 2210.10i | 1.37805 | + | 2.38685i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 526.000 | 0.550590 | 0.275295 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275295 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −718.000 | + | 1243.61i | −0.718000 | + | 1.24361i | ||||
\(101\) | 653.000 | + | 1131.03i | 0.643326 | + | 1.11427i | 0.984685 | + | 0.174341i | \(0.0557793\pi\) |
−0.341359 | + | 0.939933i | \(0.610887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 254.000 | − | 439.941i | 0.242984 | − | 0.420861i | −0.718579 | − | 0.695446i | \(-0.755207\pi\) |
0.961563 | + | 0.274585i | \(0.0885404\pi\) | |||||||
\(104\) | −432.000 | −0.407318 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −24.0000 | −0.0219914 | ||||||||
\(107\) | 249.000 | − | 431.281i | 0.224970 | − | 0.389659i | −0.731341 | − | 0.682012i | \(-0.761105\pi\) |
0.956310 | + | 0.292354i | \(0.0944384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 307.000 | + | 531.740i | 0.269773 | + | 0.467261i | 0.968803 | − | 0.247832i | \(-0.0797180\pi\) |
−0.699030 | + | 0.715092i | \(0.746385\pi\) | |||||||
\(110\) | −572.000 | + | 990.733i | −0.495801 | + | 0.858752i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1232.00 | 1.02564 | 0.512818 | − | 0.858498i | \(-0.328602\pi\) | ||||
0.512818 | + | 0.858498i | \(0.328602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 638.000 | + | 1105.05i | 0.517337 | + | 0.896055i | ||||
\(116\) | 416.000 | + | 720.533i | 0.332971 | + | 0.576723i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −248.000 | −0.193477 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 327.500 | − | 567.247i | 0.246056 | − | 0.426181i | ||||
\(122\) | 162.000 | + | 280.592i | 0.120220 | + | 0.208226i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 504.000 | − | 872.954i | 0.365004 | − | 0.632206i | ||||
\(125\) | −5148.00 | −3.68361 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2808.00 | −1.96197 | −0.980983 | − | 0.194093i | \(-0.937824\pi\) | ||||
−0.980983 | + | 0.194093i | \(0.937824\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1188.00 | − | 2057.68i | −0.801496 | − | 1.38823i | ||||
\(131\) | 260.000 | − | 450.333i | 0.173407 | − | 0.300350i | −0.766202 | − | 0.642600i | \(-0.777856\pi\) |
0.939609 | + | 0.342250i | \(0.111189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1720.00 | −1.10885 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 296.000 | + | 512.687i | 0.186631 | + | 0.323254i | ||||
\(137\) | −1258.00 | − | 2178.92i | −0.784512 | − | 1.35882i | −0.929290 | − | 0.369351i | \(-0.879580\pi\) |
0.144778 | − | 0.989464i | \(-0.453753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2672.00 | −1.63048 | −0.815238 | − | 0.579126i | \(-0.803394\pi\) | ||||
−0.815238 | + | 0.579126i | \(0.803394\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −238.000 | + | 412.228i | −0.140652 | + | 0.243616i | ||||
\(143\) | −702.000 | − | 1215.90i | −0.410519 | − | 0.711039i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2288.00 | + | 3962.93i | −1.31040 | + | 2.26968i | ||||
\(146\) | −292.000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 200.000 | 0.111080 | ||||||||
\(149\) | −582.000 | + | 1008.05i | −0.319995 | + | 0.554248i | −0.980487 | − | 0.196586i | \(-0.937015\pi\) |
0.660491 | + | 0.750834i | \(0.270348\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −836.000 | − | 1447.99i | −0.450548 | − | 0.780372i | 0.547872 | − | 0.836562i | \(-0.315438\pi\) |
−0.998420 | + | 0.0561903i | \(0.982105\pi\) | |||||||
\(152\) | −464.000 | + | 803.672i | −0.247601 | + | 0.428858i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5544.00 | 2.87293 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −223.000 | − | 386.247i | −0.113359 | − | 0.196343i | 0.803764 | − | 0.594949i | \(-0.202828\pi\) |
−0.917123 | + | 0.398605i | \(0.869494\pi\) | |||||||
\(158\) | 984.000 | + | 1704.34i | 0.495461 | + | 0.858164i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −704.000 | −0.347851 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −214.000 | + | 370.659i | −0.102833 | + | 0.178112i | −0.912851 | − | 0.408293i | \(-0.866124\pi\) |
0.810018 | + | 0.586405i | \(0.199457\pi\) | |||||||
\(164\) | 252.000 | + | 436.477i | 0.119987 | + | 0.207824i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 656.000 | − | 1136.23i | 0.306720 | − | 0.531254i | ||||
\(167\) | −4.00000 | −0.00185347 | −0.000926734 | − | 1.00000i | \(-0.500295\pi\) | ||||
−0.000926734 | 1.00000i | \(0.500295\pi\) | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 719.000 | 0.327264 | ||||||||
\(170\) | −1628.00 | + | 2819.78i | −0.734482 | + | 1.27216i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −328.000 | − | 568.113i | −0.145406 | − | 0.251850i | ||||
\(173\) | −295.000 | + | 510.955i | −0.129644 | + | 0.224550i | −0.923539 | − | 0.383505i | \(-0.874717\pi\) |
0.793895 | + | 0.608055i | \(0.208050\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −416.000 | −0.178166 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −954.000 | − | 1652.38i | −0.401715 | − | 0.695791i | ||||
\(179\) | 1767.00 | + | 3060.53i | 0.737831 | + | 1.27796i | 0.953470 | + | 0.301488i | \(0.0974833\pi\) |
−0.215639 | + | 0.976473i | \(0.569183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1098.00 | 0.450904 | 0.225452 | − | 0.974254i | \(-0.427614\pi\) | ||||
0.225452 | + | 0.974254i | \(0.427614\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −232.000 | + | 401.836i | −0.0929525 | + | 0.160999i | ||||
\(185\) | 550.000 | + | 952.628i | 0.218577 | + | 0.378587i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −962.000 | + | 1666.23i | −0.376195 | + | 0.651588i | ||||
\(188\) | 1776.00 | 0.688979 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5104.00 | −1.94886 | ||||||||
\(191\) | −2427.00 | + | 4203.69i | −0.919432 | + | 1.59250i | −0.119153 | + | 0.992876i | \(0.538018\pi\) |
−0.800279 | + | 0.599627i | \(0.795315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 749.000 | + | 1297.31i | 0.279348 | + | 0.483845i | 0.971223 | − | 0.238172i | \(-0.0765483\pi\) |
−0.691875 | + | 0.722018i | \(0.743215\pi\) | |||||||
\(194\) | −526.000 | + | 911.059i | −0.194663 | + | 0.337166i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −620.000 | −0.224229 | −0.112115 | − | 0.993695i | \(-0.535762\pi\) | ||||
−0.112115 | + | 0.993695i | \(0.535762\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | − | 27.7128i | −0.00569955 | − | 0.00987191i | 0.863162 | − | 0.504928i | \(-0.168481\pi\) |
−0.868861 | + | 0.495056i | \(0.835148\pi\) | |||||||
\(200\) | −1436.00 | − | 2487.22i | −0.507703 | − | 0.879367i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2612.00 | −0.909800 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1386.00 | + | 2400.62i | −0.472207 | + | 0.817887i | ||||
\(206\) | 508.000 | + | 879.882i | 0.171816 | + | 0.297594i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 432.000 | − | 748.246i | 0.144009 | − | 0.249430i | ||||
\(209\) | −3016.00 | −0.998187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4268.00 | 1.39252 | 0.696259 | − | 0.717791i | \(-0.254847\pi\) | ||||
0.696259 | + | 0.717791i | \(0.254847\pi\) | |||||||
\(212\) | 24.0000 | − | 41.5692i | 0.00777513 | − | 0.0134669i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 498.000 | + | 862.561i | 0.159077 | + | 0.275530i | ||||
\(215\) | 1804.00 | − | 3124.62i | 0.572241 | − | 0.991150i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1228.00 | −0.381517 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1144.00 | − | 1981.47i | −0.350584 | − | 0.607229i | ||||
\(221\) | −1998.00 | − | 3460.64i | −0.608145 | − | 1.05334i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3464.00 | 1.04021 | 0.520104 | − | 0.854103i | \(-0.325893\pi\) | ||||
0.520104 | + | 0.854103i | \(0.325893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1232.00 | + | 2133.89i | −0.362617 | + | 0.628071i | ||||
\(227\) | −1626.00 | − | 2816.31i | −0.475425 | − | 0.823460i | 0.524179 | − | 0.851608i | \(-0.324372\pi\) |
−0.999604 | + | 0.0281483i | \(0.991039\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −209.000 | + | 361.999i | −0.0603105 | + | 0.104461i | −0.894604 | − | 0.446859i | \(-0.852542\pi\) |
0.834294 | + | 0.551320i | \(0.185876\pi\) | |||||||
\(230\) | −2552.00 | −0.731626 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1664.00 | −0.470892 | ||||||||
\(233\) | 1042.00 | − | 1804.80i | 0.292977 | − | 0.507451i | −0.681535 | − | 0.731785i | \(-0.738687\pi\) |
0.974512 | + | 0.224334i | \(0.0720207\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4884.00 | + | 8459.34i | 1.35573 | + | 2.34820i | ||||
\(236\) | 248.000 | − | 429.549i | 0.0684043 | − | 0.118480i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1662.00 | −0.449815 | −0.224908 | − | 0.974380i | \(-0.572208\pi\) | ||||
−0.224908 | + | 0.974380i | \(0.572208\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3091.00 | − | 5353.77i | −0.826178 | − | 1.43098i | −0.901016 | − | 0.433786i | \(-0.857177\pi\) |
0.0748383 | − | 0.997196i | \(-0.476156\pi\) | |||||||
\(242\) | 655.000 | + | 1134.49i | 0.173988 | + | 0.301355i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −648.000 | −0.170016 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3132.00 | − | 5424.78i | 0.806819 | − | 1.39745i | ||||
\(248\) | 1008.00 | + | 1745.91i | 0.258097 | + | 0.447037i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5148.00 | − | 8916.60i | 1.30235 | − | 2.25574i | ||||
\(251\) | 996.000 | 0.250466 | 0.125233 | − | 0.992127i | \(-0.460032\pi\) | ||||
0.125233 | + | 0.992127i | \(0.460032\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1508.00 | −0.374732 | ||||||||
\(254\) | 2808.00 | − | 4863.60i | 0.693660 | − | 1.20145i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2997.00 | + | 5190.96i | −0.727423 | + | 1.25993i | 0.230546 | + | 0.973061i | \(0.425949\pi\) |
−0.957969 | + | 0.286872i | \(0.907384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4752.00 | 1.13349 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 520.000 | + | 900.666i | 0.122617 | + | 0.212379i | ||||
\(263\) | 3207.00 | + | 5554.69i | 0.751909 | + | 1.30234i | 0.946896 | + | 0.321539i | \(0.104200\pi\) |
−0.194987 | + | 0.980806i | \(0.562467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 264.000 | 0.0611977 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1720.00 | − | 2979.13i | 0.392036 | − | 0.679027i | ||||
\(269\) | 1343.00 | + | 2326.14i | 0.304402 | + | 0.527240i | 0.977128 | − | 0.212652i | \(-0.0682100\pi\) |
−0.672726 | + | 0.739892i | \(0.734877\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2550.00 | + | 4416.73i | −0.571592 | + | 0.990027i | 0.424811 | + | 0.905282i | \(0.360341\pi\) |
−0.996403 | + | 0.0847444i | \(0.972993\pi\) | |||||||
\(272\) | −1184.00 | −0.263936 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5032.00 | 1.10947 | ||||||||
\(275\) | 4667.00 | − | 8083.48i | 1.02338 | − | 1.77255i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2213.00 | + | 3833.03i | 0.480023 | + | 0.831424i | 0.999737 | − | 0.0229162i | \(-0.00729509\pi\) |
−0.519715 | + | 0.854340i | \(0.673962\pi\) | |||||||
\(278\) | 2672.00 | − | 4628.04i | 0.576460 | − | 0.998458i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7508.00 | −1.59391 | −0.796957 | − | 0.604036i | \(-0.793558\pi\) | ||||
−0.796957 | + | 0.604036i | \(0.793558\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1706.00 | − | 2954.88i | −0.358343 | − | 0.620669i | 0.629341 | − | 0.777129i | \(-0.283325\pi\) |
−0.987684 | + | 0.156460i | \(0.949992\pi\) | |||||||
\(284\) | −476.000 | − | 824.456i | −0.0994556 | − | 0.172262i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2808.00 | 0.580561 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −281.500 | + | 487.572i | −0.0572970 | + | 0.0992413i | ||||
\(290\) | −4576.00 | − | 7925.86i | −0.926593 | − | 1.60491i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 292.000 | − | 505.759i | 0.0585206 | − | 0.101361i | ||||
\(293\) | 4734.00 | 0.943902 | 0.471951 | − | 0.881625i | \(-0.343550\pi\) | ||||
0.471951 | + | 0.881625i | \(0.343550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2728.00 | 0.538408 | ||||||||
\(296\) | −200.000 | + | 346.410i | −0.0392729 | + | 0.0680226i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1164.00 | − | 2016.11i | −0.226271 | − | 0.391913i | ||||
\(299\) | 1566.00 | − | 2712.39i | 0.302890 | − | 0.524621i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3344.00 | 0.637171 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −928.000 | − | 1607.34i | −0.175080 | − | 0.303248i | ||||
\(305\) | −1782.00 | − | 3086.51i | −0.334548 | − | 0.579453i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5836.00 | 1.08494 | 0.542472 | − | 0.840074i | \(-0.317488\pi\) | ||||
0.542472 | + | 0.840074i | \(0.317488\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5544.00 | + | 9602.49i | −1.01574 | + | 1.75931i | ||||
\(311\) | 2810.00 | + | 4867.06i | 0.512349 | + | 0.887414i | 0.999897 | + | 0.0143184i | \(0.00455783\pi\) |
−0.487549 | + | 0.873096i | \(0.662109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3041.00 | + | 5267.17i | −0.549161 | + | 0.951175i | 0.449171 | + | 0.893446i | \(0.351719\pi\) |
−0.998332 | + | 0.0577294i | \(0.981614\pi\) | |||||||
\(314\) | 892.000 | 0.160314 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3936.00 | −0.700688 | ||||||||
\(317\) | −3654.00 | + | 6328.91i | −0.647410 | + | 1.12135i | 0.336329 | + | 0.941745i | \(0.390815\pi\) |
−0.983739 | + | 0.179603i | \(0.942519\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2704.00 | − | 4683.47i | −0.474592 | − | 0.822018i | ||||
\(320\) | 704.000 | − | 1219.36i | 0.122984 | − | 0.213014i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8584.00 | −1.47872 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9693.00 | + | 16788.8i | 1.65437 | + | 2.86546i | ||||
\(326\) | −428.000 | − | 741.318i | −0.0727139 | − | 0.125944i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1008.00 | −0.169687 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4010.00 | − | 6945.52i | 0.665890 | − | 1.15336i | −0.313153 | − | 0.949703i | \(-0.601385\pi\) |
0.979043 | − | 0.203652i | \(-0.0652813\pi\) | |||||||
\(332\) | 1312.00 | + | 2272.45i | 0.216884 | + | 0.375653i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.00000 | − | 6.92820i | 0.000655300 | − | 0.00113501i | ||||
\(335\) | 18920.0 | 3.08570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4590.00 | 0.741938 | 0.370969 | − | 0.928645i | \(-0.379026\pi\) | ||||
0.370969 | + | 0.928645i | \(0.379026\pi\) | |||||||
\(338\) | −719.000 | + | 1245.34i | −0.115705 | + | 0.200408i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3256.00 | − | 5639.56i | −0.519357 | − | 0.899553i | ||||
\(341\) | −3276.00 | + | 5674.20i | −0.520250 | + | 0.901100i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1312.00 | 0.205635 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −590.000 | − | 1021.91i | −0.0916722 | − | 0.158781i | ||||
\(347\) | −3273.00 | − | 5669.00i | −0.506351 | − | 0.877026i | −0.999973 | − | 0.00734926i | \(-0.997661\pi\) |
0.493622 | − | 0.869677i | \(-0.335673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7994.00 | −1.22610 | −0.613050 | − | 0.790044i | \(-0.710058\pi\) | ||||
−0.613050 | + | 0.790044i | \(0.710058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 416.000 | − | 720.533i | 0.0629911 | − | 0.109104i | ||||
\(353\) | 2325.00 | + | 4027.02i | 0.350559 | + | 0.607186i | 0.986347 | − | 0.164678i | \(-0.0526583\pi\) |
−0.635789 | + | 0.771863i | \(0.719325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2618.00 | − | 4534.51i | 0.391406 | − | 0.677935i | ||||
\(356\) | 3816.00 | 0.568111 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7068.00 | −1.04345 | ||||||||
\(359\) | 173.000 | − | 299.645i | 0.0254334 | − | 0.0440519i | −0.853029 | − | 0.521864i | \(-0.825237\pi\) |
0.878462 | + | 0.477812i | \(0.158570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3298.50 | − | 5713.17i | −0.480901 | − | 0.832945i | ||||
\(362\) | −1098.00 | + | 1901.79i | −0.159419 | + | 0.276121i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3212.00 | 0.460613 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3392.00 | + | 5875.12i | 0.482455 | + | 0.835636i | 0.999797 | − | 0.0201422i | \(-0.00641189\pi\) |
−0.517342 | + | 0.855779i | \(0.673079\pi\) | |||||||
\(368\) | −464.000 | − | 803.672i | −0.0657274 | − | 0.113843i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2200.00 | −0.309115 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3049.00 | − | 5281.02i | 0.423247 | − | 0.733086i | −0.573008 | − | 0.819550i | \(-0.694223\pi\) |
0.996255 | + | 0.0864642i | \(0.0275568\pi\) | |||||||
\(374\) | −1924.00 | − | 3332.47i | −0.266010 | − | 0.460743i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1776.00 | + | 3076.12i | −0.243591 | + | 0.421912i | ||||
\(377\) | 11232.0 | 1.53442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2660.00 | −0.360515 | −0.180257 | − | 0.983619i | \(-0.557693\pi\) | ||||
−0.180257 | + | 0.983619i | \(0.557693\pi\) | |||||||
\(380\) | 5104.00 | − | 8840.39i | 0.689025 | − | 1.19343i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4854.00 | − | 8407.37i | −0.650137 | − | 1.12607i | ||||
\(383\) | −380.000 | + | 658.179i | −0.0506974 | + | 0.0878104i | −0.890260 | − | 0.455452i | \(-0.849478\pi\) |
0.839563 | + | 0.543262i | \(0.182811\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2996.00 | −0.395058 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1052.00 | − | 1822.12i | −0.137647 | − | 0.238412i | ||||
\(389\) | −52.0000 | − | 90.0666i | −0.00677765 | − | 0.0117392i | 0.862617 | − | 0.505858i | \(-0.168824\pi\) |
−0.869394 | + | 0.494119i | \(0.835491\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4292.00 | −0.555130 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 620.000 | − | 1073.87i | 0.0792770 | − | 0.137312i | ||||
\(395\) | −10824.0 | − | 18747.7i | −1.37877 | − | 2.38810i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2199.00 | + | 3808.78i | −0.277997 | + | 0.481504i | −0.970887 | − | 0.239539i | \(-0.923004\pi\) |
0.692890 | + | 0.721043i | \(0.256337\pi\) | |||||||
\(398\) | 64.0000 | 0.00806038 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5744.00 | 0.718000 | ||||||||
\(401\) | 6618.00 | − | 11462.7i | 0.824157 | − | 1.42748i | −0.0784040 | − | 0.996922i | \(-0.524982\pi\) |
0.902561 | − | 0.430561i | \(-0.141684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6804.00 | − | 11784.9i | −0.841021 | − | 1.45669i | ||||
\(404\) | 2612.00 | − | 4524.12i | 0.321663 | − | 0.557137i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1300.00 | −0.158326 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4745.00 | + | 8218.58i | 0.573656 | + | 0.993601i | 0.996186 | + | 0.0872520i | \(0.0278085\pi\) |
−0.422531 | + | 0.906349i | \(0.638858\pi\) | |||||||
\(410\) | −2772.00 | − | 4801.24i | −0.333901 | − | 0.578333i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2032.00 | −0.242984 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7216.00 | + | 12498.5i | −0.853541 | + | 1.47838i | ||||
\(416\) | 864.000 | + | 1496.49i | 0.101830 | + | 0.176374i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3016.00 | − | 5223.87i | 0.352912 | − | 0.611262i | ||||
\(419\) | −4236.00 | −0.493895 | −0.246948 | − | 0.969029i | \(-0.579428\pi\) | ||||
−0.246948 | + | 0.969029i | \(0.579428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 918.000 | 0.106272 | 0.0531361 | − | 0.998587i | \(-0.483078\pi\) | ||||
0.0531361 | + | 0.998587i | \(0.483078\pi\) | |||||||
\(422\) | −4268.00 | + | 7392.39i | −0.492329 | + | 0.852739i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 48.0000 | + | 83.1384i | 0.00549784 | + | 0.00952255i | ||||
\(425\) | 13283.0 | − | 23006.8i | 1.51605 | − | 2.62587i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1992.00 | −0.224970 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3608.00 | + | 6249.24i | 0.404635 | + | 0.700849i | ||||
\(431\) | −5907.00 | − | 10231.2i | −0.660163 | − | 1.14344i | −0.980573 | − | 0.196157i | \(-0.937154\pi\) |
0.320410 | − | 0.947279i | \(-0.396179\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8374.00 | −0.929397 | −0.464698 | − | 0.885469i | \(-0.653837\pi\) | ||||
−0.464698 | + | 0.885469i | \(0.653837\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1228.00 | − | 2126.96i | 0.134887 | − | 0.233630i | ||||
\(437\) | −3364.00 | − | 5826.62i | −0.368242 | − | 0.637815i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1920.00 | + | 3325.54i | −0.208739 | + | 0.361547i | −0.951318 | − | 0.308212i | \(-0.900269\pi\) |
0.742578 | + | 0.669759i | \(0.233603\pi\) | |||||||
\(440\) | 4576.00 | 0.495801 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7992.00 | 0.860047 | ||||||||
\(443\) | 5083.00 | − | 8804.01i | 0.545148 | − | 0.944224i | −0.453449 | − | 0.891282i | \(-0.649807\pi\) |
0.998598 | − | 0.0529423i | \(-0.0168599\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10494.0 | + | 18176.1i | 1.11790 | + | 1.93625i | ||||
\(446\) | −3464.00 | + | 5999.82i | −0.367769 | + | 0.636995i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8200.00 | −0.861875 | −0.430938 | − | 0.902382i | \(-0.641817\pi\) | ||||
−0.430938 | + | 0.902382i | \(0.641817\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1638.00 | − | 2837.10i | −0.171021 | − | 0.296217i | ||||
\(452\) | −2464.00 | − | 4267.77i | −0.256409 | − | 0.444113i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6504.00 | 0.672352 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3037.00 | − | 5260.24i | 0.310864 | − | 0.538432i | −0.667686 | − | 0.744443i | \(-0.732715\pi\) |
0.978550 | + | 0.206011i | \(0.0660483\pi\) | |||||||
\(458\) | −418.000 | − | 723.997i | −0.0426460 | − | 0.0738650i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2552.00 | − | 4420.19i | 0.258669 | − | 0.448027i | ||||
\(461\) | 2006.00 | 0.202665 | 0.101333 | − | 0.994853i | \(-0.467689\pi\) | ||||
0.101333 | + | 0.994853i | \(0.467689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3728.00 | −0.374201 | −0.187100 | − | 0.982341i | \(-0.559909\pi\) | ||||
−0.187100 | + | 0.982341i | \(0.559909\pi\) | |||||||
\(464\) | 1664.00 | − | 2882.13i | 0.166485 | − | 0.288361i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2084.00 | + | 3609.59i | 0.207166 | + | 0.358822i | ||||
\(467\) | −3190.00 | + | 5525.24i | −0.316093 | + | 0.547490i | −0.979669 | − | 0.200619i | \(-0.935705\pi\) |
0.663576 | + | 0.748109i | \(0.269038\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −19536.0 | −1.91729 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 496.000 | + | 859.097i | 0.0483692 | + | 0.0837779i | ||||
\(473\) | 2132.00 | + | 3692.73i | 0.207250 | + | 0.358968i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41644.0 | 4.02265 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1662.00 | − | 2878.67i | 0.159034 | − | 0.275454i | ||||
\(479\) | 8590.00 | + | 14878.3i | 0.819389 | + | 1.41922i | 0.906133 | + | 0.422992i | \(0.139020\pi\) |
−0.0867448 | + | 0.996231i | \(0.527646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1350.00 | − | 2338.27i | 0.127972 | − | 0.221655i | ||||
\(482\) | 12364.0 | 1.16839 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2620.00 | −0.246056 | ||||||||
\(485\) | 5786.00 | − | 10021.6i | 0.541709 | − | 0.938267i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1364.00 | + | 2362.52i | 0.126917 | + | 0.219827i | 0.922481 | − | 0.386043i | \(-0.126158\pi\) |
−0.795563 | + | 0.605870i | \(0.792825\pi\) | |||||||
\(488\) | 648.000 | − | 1122.37i | 0.0601098 | − | 0.104113i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2574.00 | −0.236585 | −0.118292 | − | 0.992979i | \(-0.537742\pi\) | ||||
−0.118292 | + | 0.992979i | \(0.537742\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7696.00 | − | 13329.9i | −0.703064 | − | 1.21774i | ||||
\(494\) | 6264.00 | + | 10849.6i | 0.570507 | + | 0.988148i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4032.00 | −0.365004 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3742.00 | − | 6481.33i | 0.335701 | − | 0.581452i | −0.647918 | − | 0.761710i | \(-0.724360\pi\) |
0.983619 | + | 0.180258i | \(0.0576934\pi\) | |||||||
\(500\) | 10296.0 | + | 17833.2i | 0.920902 | + | 1.59505i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −996.000 | + | 1725.12i | −0.0885531 | + | 0.153378i | ||||
\(503\) | −7920.00 | −0.702058 | −0.351029 | − | 0.936365i | \(-0.614168\pi\) | ||||
−0.351029 | + | 0.936365i | \(0.614168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28732.0 | 2.53180 | ||||||||
\(506\) | 1508.00 | − | 2611.93i | 0.132488 | − | 0.229475i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5616.00 | + | 9727.20i | 0.490492 | + | 0.849556i | ||||
\(509\) | 3627.00 | − | 6282.15i | 0.315843 | − | 0.547056i | −0.663774 | − | 0.747934i | \(-0.731046\pi\) |
0.979616 | + | 0.200878i | \(0.0643795\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5994.00 | − | 10381.9i | −0.514366 | − | 0.890908i | ||||
\(515\) | −5588.00 | − | 9678.70i | −0.478130 | − | 0.828145i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11544.0 | −0.982020 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4752.00 | + | 8230.71i | −0.400748 | + | 0.694116i | ||||
\(521\) | −8931.00 | − | 15468.9i | −0.751006 | − | 1.30078i | −0.947335 | − | 0.320243i | \(-0.896235\pi\) |
0.196329 | − | 0.980538i | \(-0.437098\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 296.000 | − | 512.687i | 0.0247479 | − | 0.0428647i | −0.853386 | − | 0.521279i | \(-0.825455\pi\) |
0.878134 | + | 0.478415i | \(0.158788\pi\) | |||||||
\(524\) | −2080.00 | −0.173407 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12828.0 | −1.06336 | ||||||||
\(527\) | −9324.00 | + | 16149.6i | −0.770702 | + | 1.33489i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4401.50 | + | 7623.62i | 0.361757 | + | 0.626582i | ||||
\(530\) | −264.000 | + | 457.261i | −0.0216367 | + | 0.0374758i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6804.00 | 0.552934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5478.00 | − | 9488.17i | −0.442681 | − | 0.766747i | ||||
\(536\) | 3440.00 | + | 5958.25i | 0.277212 | + | 0.480144i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5372.00 | −0.430490 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3201.00 | − | 5544.29i | 0.254384 | − | 0.440606i | −0.710344 | − | 0.703855i | \(-0.751461\pi\) |
0.964728 | + | 0.263249i | \(0.0847940\pi\) | |||||||
\(542\) | −5100.00 | − | 8833.46i | −0.404177 | − | 0.700055i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1184.00 | − | 2050.75i | 0.0933154 | − | 0.161627i | ||||
\(545\) | 13508.0 | 1.06169 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8988.00 | −0.702558 | −0.351279 | − | 0.936271i | \(-0.614253\pi\) | ||||
−0.351279 | + | 0.936271i | \(0.614253\pi\) | |||||||
\(548\) | −5032.00 | + | 8715.68i | −0.392256 | + | 0.679408i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9334.00 | + | 16167.0i | 0.723642 | + | 1.25338i | ||||
\(551\) | 12064.0 | − | 20895.5i | 0.932747 | − | 1.61557i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8852.00 | −0.678855 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5344.00 | + | 9256.08i | 0.407619 | + | 0.706017i | ||||
\(557\) | 1622.00 | + | 2809.39i | 0.123387 | + | 0.213712i | 0.921101 | − | 0.389323i | \(-0.127291\pi\) |
−0.797715 | + | 0.603035i | \(0.793958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8856.00 | −0.670070 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7508.00 | − | 13004.2i | 0.563534 | − | 0.976069i | ||||
\(563\) | 4906.00 | + | 8497.44i | 0.367253 | + | 0.636100i | 0.989135 | − | 0.147010i | \(-0.0469651\pi\) |
−0.621882 | + | 0.783111i | \(0.713632\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13552.0 | − | 23472.8i | 1.00909 | − | 1.74780i | ||||
\(566\) | 6824.00 | 0.506774 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1904.00 | 0.140652 | ||||||||
\(569\) | −6078.00 | + | 10527.4i | −0.447808 | + | 0.775627i | −0.998243 | − | 0.0592513i | \(-0.981129\pi\) |
0.550435 | + | 0.834878i | \(0.314462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3438.00 | − | 5954.79i | −0.251972 | − | 0.436428i | 0.712097 | − | 0.702081i | \(-0.247746\pi\) |
−0.964069 | + | 0.265653i | \(0.914412\pi\) | |||||||
\(572\) | −2808.00 | + | 4863.60i | −0.205259 | + | 0.355520i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20822.0 | 1.51015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10001.0 | − | 17322.2i | −0.721572 | − | 1.24980i | −0.960369 | − | 0.278730i | \(-0.910087\pi\) |
0.238797 | − | 0.971069i | \(-0.423247\pi\) | |||||||
\(578\) | −563.000 | − | 975.145i | −0.0405151 | − | 0.0701742i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 18304.0 | 1.31040 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −156.000 | + | 270.200i | −0.0110821 | + | 0.0191947i | ||||
\(584\) | 584.000 | + | 1011.52i | 0.0413803 | + | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4734.00 | + | 8199.53i | −0.333720 | + | 0.578019i | ||||
\(587\) | −18404.0 | −1.29406 | −0.647031 | − | 0.762464i | \(-0.723990\pi\) | ||||
−0.647031 | + | 0.762464i | \(0.723990\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29232.0 | −2.04496 | ||||||||
\(590\) | −2728.00 | + | 4725.03i | −0.190356 | + | 0.329706i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −400.000 | − | 692.820i | −0.0277701 | − | 0.0480992i | ||||
\(593\) | −4923.00 | + | 8526.89i | −0.340916 | + | 0.590484i | −0.984603 | − | 0.174805i | \(-0.944071\pi\) |
0.643687 | + | 0.765289i | \(0.277404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4656.00 | 0.319995 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3132.00 | + | 5424.78i | 0.214176 | + | 0.370963i | ||||
\(599\) | 4617.00 | + | 7996.88i | 0.314934 | + | 0.545482i | 0.979423 | − | 0.201816i | \(-0.0646843\pi\) |
−0.664489 | + | 0.747298i | \(0.731351\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1510.00 | −0.102486 | −0.0512431 | − | 0.998686i | \(-0.516318\pi\) | ||||
−0.0512431 | + | 0.998686i | \(0.516318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3344.00 | + | 5791.98i | −0.225274 | + | 0.390186i | ||||
\(605\) | −7205.00 | − | 12479.4i | −0.484173 | − | 0.838613i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8772.00 | + | 15193.5i | −0.586564 | + | 1.01596i | 0.408114 | + | 0.912931i | \(0.366187\pi\) |
−0.994678 | + | 0.103028i | \(0.967147\pi\) | |||||||
\(608\) | 3712.00 | 0.247601 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7128.00 | 0.473122 | ||||||||
\(611\) | 11988.0 | − | 20763.8i | 0.793752 | − | 1.37482i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4623.00 | − | 8007.27i | −0.304602 | − | 0.527587i | 0.672570 | − | 0.740033i | \(-0.265190\pi\) |
−0.977173 | + | 0.212446i | \(0.931857\pi\) | |||||||
\(614\) | −5836.00 | + | 10108.2i | −0.383586 | + | 0.664390i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29212.0 | 1.90605 | 0.953023 | − | 0.302897i | \(-0.0979537\pi\) | ||||
0.953023 | + | 0.302897i | \(0.0979537\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3548.00 | − | 6145.32i | −0.230382 | − | 0.399032i | 0.727539 | − | 0.686066i | \(-0.240664\pi\) |
−0.957920 | + | 0.287034i | \(0.907331\pi\) | |||||||
\(620\) | −11088.0 | − | 19205.0i | −0.718234 | − | 1.24402i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11240.0 | −0.724571 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −34190.5 | + | 59219.7i | −2.18819 | + | 3.79006i | ||||
\(626\) | −6082.00 | − | 10534.3i | −0.388316 | − | 0.672582i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −892.000 | + | 1544.99i | −0.0566794 | + | 0.0981716i | ||||
\(629\) | −3700.00 | −0.234545 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 488.000 | 0.0307876 | 0.0153938 | − | 0.999882i | \(-0.495100\pi\) | ||||
0.0153938 | + | 0.999882i | \(0.495100\pi\) | |||||||
\(632\) | 3936.00 | − | 6817.35i | 0.247730 | − | 0.429082i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7308.00 | − | 12657.8i | −0.457788 | − | 0.792913i | ||||
\(635\) | −30888.0 | + | 53499.6i | −1.93032 | + | 3.34341i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10816.0 | 0.671175 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1408.00 | + | 2438.73i | 0.0869626 | + | 0.150624i | ||||
\(641\) | 4378.00 | + | 7582.92i | 0.269767 | + | 0.467250i | 0.968802 | − | 0.247838i | \(-0.0797200\pi\) |
−0.699035 | + | 0.715088i | \(0.746387\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3364.00 | −0.206319 | −0.103160 | − | 0.994665i | \(-0.532895\pi\) | ||||
−0.103160 | + | 0.994665i | \(0.532895\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8584.00 | − | 14867.9i | 0.522806 | − | 0.905527i | ||||
\(647\) | 10902.0 | + | 18882.8i | 0.662445 | + | 1.14739i | 0.979971 | + | 0.199139i | \(0.0638145\pi\) |
−0.317526 | + | 0.948249i | \(0.602852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1612.00 | + | 2792.07i | −0.0974985 | + | 0.168872i | ||||
\(650\) | −38772.0 | −2.33964 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1712.00 | 0.102833 | ||||||||
\(653\) | 6744.00 | − | 11681.0i | 0.404155 | − | 0.700017i | −0.590068 | − | 0.807354i | \(-0.700899\pi\) |
0.994223 | + | 0.107337i | \(0.0342324\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5720.00 | − | 9907.33i | −0.341220 | − | 0.591010i | ||||
\(656\) | 1008.00 | − | 1745.91i | 0.0599936 | − | 0.103912i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28946.0 | −1.71104 | −0.855521 | − | 0.517769i | \(-0.826763\pi\) | ||||
−0.855521 | + | 0.517769i | \(0.826763\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10321.0 | + | 17876.5i | 0.607323 | + | 1.05191i | 0.991680 | + | 0.128729i | \(0.0410899\pi\) |
−0.384357 | + | 0.923185i | \(0.625577\pi\) | |||||||
\(662\) | 8020.00 | + | 13891.0i | 0.470855 | + | 0.815545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5248.00 | −0.306720 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6032.00 | − | 10447.7i | 0.350165 | − | 0.606503i | ||||
\(668\) | 8.00000 | + | 13.8564i | 0.000463367 | + | 0.000802576i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18920.0 | + | 32770.4i | −1.09096 | + | 1.88960i | ||||
\(671\) | 4212.00 | 0.242329 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17602.0 | −1.00818 | −0.504092 | − | 0.863650i | \(-0.668173\pi\) | ||||
−0.504092 | + | 0.863650i | \(0.668173\pi\) | |||||||
\(674\) | −4590.00 | + | 7950.11i | −0.262315 | + | 0.454343i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1438.00 | − | 2490.69i | −0.0818161 | − | 0.141710i | ||||
\(677\) | 2133.00 | − | 3694.46i | 0.121090 | − | 0.209734i | −0.799108 | − | 0.601188i | \(-0.794694\pi\) |
0.920198 | + | 0.391454i | \(0.128028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 13024.0 | 0.734482 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6552.00 | − | 11348.4i | −0.367873 | − | 0.637174i | ||||
\(683\) | −13437.0 | − | 23273.6i | −0.752786 | − | 1.30386i | −0.946468 | − | 0.322798i | \(-0.895376\pi\) |
0.193682 | − | 0.981064i | \(-0.437957\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55352.0 | −3.08743 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1312.00 | + | 2272.45i | −0.0727028 | + | 0.125925i | ||||
\(689\) | −324.000 | − | 561.184i | −0.0179150 | − | 0.0310296i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8564.00 | − | 14833.3i | 0.471476 | − | 0.816620i | −0.527992 | − | 0.849250i | \(-0.677055\pi\) |
0.999468 | + | 0.0326293i | \(0.0103881\pi\) | |||||||
\(692\) | 2360.00 | 0.129644 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13092.0 | 0.716089 | ||||||||
\(695\) | −29392.0 | + | 50908.4i | −1.60418 | + | 2.77851i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4662.00 | − | 8074.82i | −0.253351 | − | 0.438817i | ||||
\(698\) | 7994.00 | − | 13846.0i | 0.433492 | − | 0.750830i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11968.0 | −0.644829 | −0.322414 | − | 0.946599i | \(-0.604494\pi\) | ||||
−0.322414 | + | 0.946599i | \(0.604494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2900.00 | − | 5022.95i | −0.155584 | − | 0.269479i | ||||
\(704\) | 832.000 | + | 1441.07i | 0.0445414 | + | 0.0771481i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9300.00 | −0.495765 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2639.00 | − | 4570.88i | 0.139788 | − | 0.242120i | −0.787628 | − | 0.616151i | \(-0.788691\pi\) |
0.927416 | + | 0.374031i | \(0.122025\pi\) | |||||||
\(710\) | 5236.00 | + | 9069.02i | 0.276766 | + | 0.479372i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3816.00 | + | 6609.51i | −0.200858 | + | 0.347896i | ||||
\(713\) | −14616.0 | −0.767705 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −30888.0 | −1.61559 | ||||||||
\(716\) | 7068.00 | − | 12242.1i | 0.368916 | − | 0.638981i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 346.000 | + | 599.290i | 0.0179841 | + | 0.0311494i | ||||
\(719\) | 3360.00 | − | 5819.69i | 0.174279 | − | 0.301861i | −0.765632 | − | 0.643278i | \(-0.777574\pi\) |
0.939912 | + | 0.341418i | \(0.110907\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13194.0 | 0.680097 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2196.00 | − | 3803.58i | −0.112726 | − | 0.195247i | ||||
\(725\) | 37336.0 | + | 64667.8i | 1.91259 | + | 3.31269i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16804.0 | 0.857257 | 0.428629 | − | 0.903481i | \(-0.358997\pi\) | ||||
0.428629 | + | 0.903481i | \(0.358997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3212.00 | + | 5563.35i | −0.162851 | + | 0.282067i | ||||
\(731\) | 6068.00 | + | 10510.1i | 0.307022 | + | 0.531778i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13761.0 | + | 23834.8i | −0.693416 | + | 1.20103i | 0.277295 | + | 0.960785i | \(0.410562\pi\) |
−0.970712 | + | 0.240248i | \(0.922771\pi\) | |||||||
\(734\) | −13568.0 | −0.682294 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1856.00 | 0.0929525 | ||||||||
\(737\) | −11180.0 | + | 19364.3i | −0.558780 | + | 0.967835i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10566.0 | − | 18300.8i | −0.525949 | − | 0.910971i | −0.999543 | − | 0.0302276i | \(-0.990377\pi\) |
0.473594 | − | 0.880743i | \(-0.342957\pi\) | |||||||
\(740\) | 2200.00 | − | 3810.51i | 0.109289 | − | 0.189294i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000 | 0.00148128 | 0.000740641 | − | 1.00000i | \(-0.499764\pi\) | ||||
0.000740641 | 1.00000i | \(0.499764\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12804.0 | + | 22177.2i | 0.629667 | + | 1.09062i | ||||
\(746\) | 6098.00 | + | 10562.0i | 0.299281 | + | 0.518370i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7696.00 | 0.376195 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7740.00 | − | 13406.1i | 0.376081 | − | 0.651391i | −0.614407 | − | 0.788989i | \(-0.710605\pi\) |
0.990488 | + | 0.137598i | \(0.0439382\pi\) | |||||||
\(752\) | −3552.00 | − | 6152.24i | −0.172245 | − | 0.298337i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11232.0 | + | 19454.4i | −0.542500 | + | 0.939638i | ||||
\(755\) | −36784.0 | −1.77312 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28770.0 | 1.38133 | 0.690663 | − | 0.723177i | \(-0.257319\pi\) | ||||
0.690663 | + | 0.723177i | \(0.257319\pi\) | |||||||
\(758\) | 2660.00 | − | 4607.26i | 0.127461 | − | 0.220769i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10208.0 | + | 17680.8i | 0.487215 | + | 0.843880i | ||||
\(761\) | −6209.00 | + | 10754.3i | −0.295764 | + | 0.512278i | −0.975162 | − | 0.221492i | \(-0.928907\pi\) |
0.679399 | + | 0.733769i | \(0.262241\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19416.0 | 0.919432 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −760.000 | − | 1316.36i | −0.0358485 | − | 0.0620913i | ||||
\(767\) | −3348.00 | − | 5798.91i | −0.157613 | − | 0.272994i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12346.0 | 0.578944 | 0.289472 | − | 0.957186i | \(-0.406520\pi\) | ||||
0.289472 | + | 0.957186i | \(0.406520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2996.00 | − | 5189.22i | 0.139674 | − | 0.241923i | ||||
\(773\) | 19049.0 | + | 32993.8i | 0.886345 | + | 1.53520i | 0.844164 | + | 0.536085i | \(0.180097\pi\) |
0.0421813 | + | 0.999110i | \(0.486569\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45234.0 | − | 78347.6i | 2.09658 | − | 3.63139i | ||||
\(776\) | 4208.00 | 0.194663 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 208.000 | 0.00958504 | ||||||||
\(779\) | 7308.00 | − | 12657.8i | 0.336118 | − | 0.582174i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3094.00 | + | 5358.97i | 0.141757 | + | 0.245530i | ||||
\(782\) | 4292.00 | − | 7433.96i | 0.196268 | − | 0.339946i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9812.00 | −0.446121 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6912.00 | − | 11971.9i | −0.313070 | − | 0.542253i | 0.665955 | − | 0.745992i | \(-0.268024\pi\) |
−0.979025 | + | 0.203738i | \(0.934691\pi\) | |||||||
\(788\) | 1240.00 | + | 2147.74i | 0.0560573 | + | 0.0970941i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 43296.0 | 1.94988 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4374.00 | + | 7575.99i | −0.195870 | + | 0.339258i | ||||
\(794\) | −4398.00 | − | 7617.56i | −0.196573 | − | 0.340475i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −64.0000 | + | 110.851i | −0.00284977 | + | 0.00493595i | ||||
\(797\) | −22170.0 | −0.985322 | −0.492661 | − | 0.870221i | \(-0.663976\pi\) | ||||
−0.492661 | + | 0.870221i | \(0.663976\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32856.0 | −1.45477 | ||||||||
\(800\) | −5744.00 | + | 9948.90i | −0.253851 | + | 0.439683i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13236.0 | + | 22925.4i | 0.582767 | + | 1.00938i | ||||
\(803\) | −1898.00 | + | 3287.43i | −0.0834109 | + | 0.144472i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27216.0 | 1.18938 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5224.00 | + | 9048.23i | 0.227450 | + | 0.393955i | ||||
\(809\) | 8144.00 | + | 14105.8i | 0.353928 | + | 0.613021i | 0.986934 | − | 0.161126i | \(-0.0515124\pi\) |
−0.633006 | + | 0.774147i | \(0.718179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8720.00 | −0.377559 | −0.188780 | − | 0.982019i | \(-0.560453\pi\) | ||||
−0.188780 | + | 0.982019i | \(0.560453\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1300.00 | − | 2251.67i | 0.0559766 | − | 0.0969544i | ||||
\(815\) | 4708.00 | + | 8154.50i | 0.202349 | + | 0.350478i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9512.00 | + | 16475.3i | −0.407323 | + | 0.705504i | ||||
\(818\) | −18980.0 | −0.811272 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11088.0 | 0.472207 | ||||||||
\(821\) | −15686.0 | + | 27168.9i | −0.666803 | + | 1.15494i | 0.311990 | + | 0.950085i | \(0.399004\pi\) |
−0.978793 | + | 0.204851i | \(0.934329\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8824.00 | + | 15283.6i | 0.373737 | + | 0.647331i | 0.990137 | − | 0.140102i | \(-0.0447430\pi\) |
−0.616400 | + | 0.787433i | \(0.711410\pi\) | |||||||
\(824\) | 2032.00 | − | 3519.53i | 0.0859079 | − | 0.148797i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2382.00 | 0.100158 | 0.0500788 | − | 0.998745i | \(-0.484053\pi\) | ||||
0.0500788 | + | 0.998745i | \(0.484053\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13325.0 | − | 23079.6i | −0.558259 | − | 0.966932i | −0.997642 | − | 0.0686326i | \(-0.978136\pi\) |
0.439383 | − | 0.898300i | \(-0.355197\pi\) | |||||||
\(830\) | −14432.0 | − | 24997.0i | −0.603545 | − | 1.04537i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3456.00 | −0.144009 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.0000 | + | 76.2102i | −0.00182357 | + | 0.00315852i | ||||
\(836\) | 6032.00 | + | 10447.7i | 0.249547 | + | 0.432228i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4236.00 | − | 7336.97i | 0.174618 | − | 0.302448i | ||||
\(839\) | −24092.0 | −0.991357 | −0.495678 | − | 0.868506i | \(-0.665080\pi\) | ||||
−0.495678 | + | 0.868506i | \(0.665080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18875.0 | 0.773914 | ||||||||
\(842\) | −918.000 | + | 1590.02i | −0.0375729 | + | 0.0650781i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8536.00 | − | 14784.8i | −0.348129 | − | 0.602978i | ||||
\(845\) | 7909.00 | − | 13698.8i | 0.321986 | − | 0.557695i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −192.000 | −0.00777513 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26566.0 | + | 46013.7i | 1.07201 | + | 1.85677i | ||||
\(851\) | −1450.00 | − | 2511.47i | −0.0584082 | − | 0.101166i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8194.00 | −0.328906 | −0.164453 | − | 0.986385i | \(-0.552586\pi\) | ||||
−0.164453 | + | 0.986385i | \(0.552586\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1992.00 | − | 3450.25i | 0.0795387 | − | 0.137765i | ||||
\(857\) | −8481.00 | − | 14689.5i | −0.338046 | − | 0.585513i | 0.646019 | − | 0.763321i | \(-0.276433\pi\) |
−0.984065 | + | 0.177808i | \(0.943099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24278.0 | − | 42050.7i | 0.964324 | − | 1.67026i | 0.252905 | − | 0.967491i | \(-0.418614\pi\) |
0.711419 | − | 0.702768i | \(-0.248053\pi\) | |||||||
\(860\) | −14432.0 | −0.572241 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23628.0 | 0.933611 | ||||||||
\(863\) | −17137.0 | + | 29682.2i | −0.675956 | + | 1.17079i | 0.300232 | + | 0.953866i | \(0.402936\pi\) |
−0.976188 | + | 0.216924i | \(0.930397\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6490.00 | + | 11241.0i | 0.255106 | + | 0.441856i | ||||
\(866\) | 8374.00 | − | 14504.2i | 0.328591 | − | 0.569137i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25584.0 | 0.998709 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23220.0 | − | 40218.2i | −0.903306 | − | 1.56457i | ||||
\(872\) | 2456.00 | + | 4253.92i | 0.0953792 | + | 0.165202i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13456.0 | 0.520773 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3563.00 | + | 6171.30i | −0.137188 | + | 0.237617i | −0.926431 | − | 0.376464i | \(-0.877140\pi\) |
0.789243 | + | 0.614081i | \(0.210473\pi\) | |||||||
\(878\) | −3840.00 | − | 6651.08i | −0.147601 | − | 0.255653i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4576.00 | + | 7925.86i | −0.175292 | + | 0.303615i | ||||
\(881\) | 9222.00 | 0.352664 | 0.176332 | − | 0.984331i | \(-0.443577\pi\) | ||||
0.176332 | + | 0.984331i | \(0.443577\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37652.0 | 1.43498 | 0.717492 | − | 0.696567i | \(-0.245290\pi\) | ||||
0.717492 | + | 0.696567i | \(0.245290\pi\) | |||||||
\(884\) | −7992.00 | + | 13842.6i | −0.304072 | + | 0.526669i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10166.0 | + | 17608.0i | 0.385478 | + | 0.667667i | ||||
\(887\) | −10998.0 | + | 19049.1i | −0.416321 | + | 0.721089i | −0.995566 | − | 0.0940643i | \(-0.970014\pi\) |
0.579245 | + | 0.815153i | \(0.303347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −41976.0 | −1.58094 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6928.00 | − | 11999.6i | −0.260052 | − | 0.450424i | ||||
\(893\) | −25752.0 | − | 44603.8i | −0.965014 | − | 1.67145i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 77748.0 | 2.90372 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8200.00 | − | 14202.8i | 0.304719 | − | 0.527789i | ||||
\(899\) | −26208.0 | − | 45393.6i | −0.972287 | − | 1.68405i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −444.000 | + | 769.031i | −0.0164171 | + | 0.0284352i | ||||
\(902\) | 6552.00 | 0.241860 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9856.00 | 0.362617 | ||||||||
\(905\) | 12078.0 | − | 20919.7i | 0.443631 | − | 0.768392i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7422.00 | − | 12855.3i | −0.271713 | − | 0.470620i | 0.697588 | − | 0.716499i | \(-0.254257\pi\) |
−0.969301 | + | 0.245879i | \(0.920923\pi\) | |||||||
\(908\) | −6504.00 | + | 11265.3i | −0.237712 | + | 0.411730i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19446.0 | 0.707217 | 0.353609 | − | 0.935394i | \(-0.384955\pi\) | ||||
0.353609 | + | 0.935394i | \(0.384955\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8528.00 | − | 14770.9i | −0.309130 | − | 0.535429i | ||||
\(914\) | 6074.00 | + | 10520.5i | 0.219814 | + | 0.380729i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1672.00 | 0.0603105 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19600.0 | − | 33948.2i | 0.703530 | − | 1.21855i | −0.263689 | − | 0.964608i | \(-0.584939\pi\) |
0.967219 | − | 0.253942i | \(-0.0817274\pi\) | |||||||
\(920\) | 5104.00 | + | 8840.39i | 0.182906 | + | 0.316803i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2006.00 | + | 3474.49i | −0.0716530 | + | 0.124107i | ||||
\(923\) | −12852.0 | −0.458319 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17950.0 | 0.638046 | ||||||||
\(926\) | 3728.00 | − | 6457.09i | 0.132300 | − | 0.229150i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3328.00 | + | 5764.27i | 0.117723 | + | 0.203902i | ||||
\(929\) | −7977.00 | + | 13816.6i | −0.281719 | + | 0.487951i | −0.971808 | − | 0.235773i | \(-0.924238\pi\) |
0.690089 | + | 0.723724i | \(0.257571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −8336.00 | −0.292977 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6380.00 | − | 11050.5i | −0.223512 | − | 0.387134i | ||||
\(935\) | 21164.0 | + | 36657.1i | 0.740253 | + | 1.28216i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2546.00 | 0.0887665 | 0.0443832 | − | 0.999015i | \(-0.485868\pi\) | ||||
0.0443832 | + | 0.999015i | \(0.485868\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19536.0 | − | 33837.3i | 0.677866 | − | 1.17410i | ||||
\(941\) | 215.000 | + | 372.391i | 0.00744825 | + | 0.0129007i | 0.869726 | − | 0.493536i | \(-0.164296\pi\) |
−0.862277 | + | 0.506437i | \(0.830962\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3654.00 | − | 6328.91i | 0.126183 | − | 0.218555i | ||||
\(944\) | −1984.00 | −0.0684043 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8528.00 | −0.293096 | ||||||||
\(947\) | 19133.0 | − | 33139.3i | 0.656535 | − | 1.13715i | −0.324971 | − | 0.945724i | \(-0.605355\pi\) |
0.981507 | − | 0.191429i | \(-0.0613121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3942.00 | − | 6827.74i | −0.134840 | − | 0.233549i | ||||
\(950\) | −41644.0 | + | 72129.5i | −1.42222 | + | 2.46336i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28216.0 | 0.959083 | 0.479541 | − | 0.877519i | \(-0.340803\pi\) | ||||
0.479541 | + | 0.877519i | \(0.340803\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53394.0 | + | 92481.1i | 1.80920 | + | 3.13363i | ||||
\(956\) | 3324.00 | + | 5757.34i | 0.112454 | + | 0.194776i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34360.0 | −1.15879 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16856.5 | + | 29196.3i | −0.565825 | + | 0.980038i | ||||
\(962\) | 2700.00 | + | 4676.54i | 0.0904901 | + | 0.156733i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12364.0 | + | 21415.1i | −0.413089 | + | 0.715491i | ||||
\(965\) | 32956.0 | 1.09937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27712.0 | −0.921570 | −0.460785 | − | 0.887512i | \(-0.652432\pi\) | ||||
−0.460785 | + | 0.887512i | \(0.652432\pi\) | |||||||
\(968\) | 2620.00 | − | 4537.97i | 0.0869938 | − | 0.150678i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11572.0 | + | 20043.3i | 0.383046 | + | 0.663455i | ||||
\(971\) | 16488.0 | − | 28558.1i | 0.544928 | − | 0.943843i | −0.453683 | − | 0.891163i | \(-0.649890\pi\) |
0.998611 | − | 0.0526801i | \(-0.0167764\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5456.00 | −0.179488 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1296.00 | + | 2244.74i | 0.0425040 | + | 0.0736192i | ||||
\(977\) | −4470.00 | − | 7742.27i | −0.146375 | − | 0.253528i | 0.783510 | − | 0.621379i | \(-0.213427\pi\) |
−0.929885 | + | 0.367851i | \(0.880094\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24804.0 | −0.809744 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2574.00 | − | 4458.30i | 0.0836453 | − | 0.144878i | ||||
\(983\) | −1644.00 | − | 2847.49i | −0.0533423 | − | 0.0923915i | 0.838121 | − | 0.545484i | \(-0.183654\pi\) |
−0.891464 | + | 0.453092i | \(0.850321\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6820.00 | + | 11812.6i | −0.220612 | + | 0.382112i | ||||
\(986\) | 30784.0 | 0.994282 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25056.0 | −0.806819 | ||||||||
\(989\) | −4756.00 | + | 8237.63i | −0.152914 | + | 0.264855i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16972.0 | − | 29396.4i | −0.544030 | − | 0.942287i | −0.998667 | − | 0.0516105i | \(-0.983565\pi\) |
0.454638 | − | 0.890676i | \(-0.349769\pi\) | |||||||
\(992\) | 4032.00 | − | 6983.63i | 0.129049 | − | 0.223519i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −704.000 | −0.0224305 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27281.0 | + | 47252.1i | 0.866598 | + | 1.50099i | 0.865452 | + | 0.500992i | \(0.167031\pi\) |
0.00114579 | + | 0.999999i | \(0.499635\pi\) | |||||||
\(998\) | 7484.00 | + | 12962.7i | 0.237377 | + | 0.411148i | ||||
\(999\) | 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 | 882.4.g.m.667.1 | 2 | ||
3.2 | odd | 2 | 882.4.g.n.667.1 | 2 | |||
7.2 | even | 3 | 126.4.a.f.1.1 | yes | 1 | ||
7.3 | odd | 6 | 882.4.g.a.361.1 | 2 | |||
7.4 | even | 3 | inner | 882.4.g.m.361.1 | 2 | ||
7.5 | odd | 6 | 882.4.a.s.1.1 | 1 | |||
7.6 | odd | 2 | 882.4.g.a.667.1 | 2 | |||
21.2 | odd | 6 | 126.4.a.e.1.1 | ✓ | 1 | ||
21.5 | even | 6 | 882.4.a.a.1.1 | 1 | |||
21.11 | odd | 6 | 882.4.g.n.361.1 | 2 | |||
21.17 | even | 6 | 882.4.g.x.361.1 | 2 | |||
21.20 | even | 2 | 882.4.g.x.667.1 | 2 | |||
28.23 | odd | 6 | 1008.4.a.a.1.1 | 1 | |||
84.23 | even | 6 | 1008.4.a.w.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.a.e.1.1 | ✓ | 1 | 21.2 | odd | 6 | ||
126.4.a.f.1.1 | yes | 1 | 7.2 | even | 3 | ||
882.4.a.a.1.1 | 1 | 21.5 | even | 6 | |||
882.4.a.s.1.1 | 1 | 7.5 | odd | 6 | |||
882.4.g.a.361.1 | 2 | 7.3 | odd | 6 | |||
882.4.g.a.667.1 | 2 | 7.6 | odd | 2 | |||
882.4.g.m.361.1 | 2 | 7.4 | even | 3 | inner | ||
882.4.g.m.667.1 | 2 | 1.1 | even | 1 | trivial | ||
882.4.g.n.361.1 | 2 | 21.11 | odd | 6 | |||
882.4.g.n.667.1 | 2 | 3.2 | odd | 2 | |||
882.4.g.x.361.1 | 2 | 21.17 | even | 6 | |||
882.4.g.x.667.1 | 2 | 21.20 | even | 2 | |||
1008.4.a.a.1.1 | 1 | 28.23 | odd | 6 | |||
1008.4.a.w.1.1 | 1 | 84.23 | even | 6 |