Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(226,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.1223810289.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.4 | ||
Root | \(1.31686 + 2.28087i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.226 |
Dual form | 675.2.e.e.451.4 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31686 | + | 2.28087i | 0.931162 | + | 1.61282i | 0.781339 | + | 0.624107i | \(0.214537\pi\) |
0.149823 | + | 0.988713i | \(0.452130\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.46825 | + | 4.27513i | −1.23412 | + | 2.13757i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.898714 | + | 1.55662i | 0.339682 | + | 0.588346i | 0.984373 | − | 0.176097i | \(-0.0563473\pi\) |
−0.644691 | + | 0.764443i | \(0.723014\pi\) | |||||||
\(8\) | −7.73393 | −2.73436 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.904062 | + | 1.56588i | 0.272585 | + | 0.472131i | 0.969523 | − | 0.245000i | \(-0.0787881\pi\) |
−0.696938 | + | 0.717131i | \(0.745455\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.985914 | + | 1.70765i | −0.273443 | + | 0.473618i | −0.969741 | − | 0.244135i | \(-0.921496\pi\) |
0.696298 | + | 0.717753i | \(0.254829\pi\) | |||||||
\(14\) | −2.36696 | + | 4.09970i | −0.632598 | + | 1.09569i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.24801 | − | 9.08982i | −1.31200 | − | 2.27246i | ||||
\(17\) | −4.80812 | −1.16614 | −0.583071 | − | 0.812421i | \(-0.698149\pi\) | ||||
−0.583071 | + | 0.812421i | \(0.698149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.96467 | 0.680142 | 0.340071 | − | 0.940400i | \(-0.389549\pi\) | ||||
0.340071 | + | 0.940400i | \(0.389549\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.38105 | + | 4.12410i | −0.507641 | + | 0.879261i | ||||
\(23\) | −0.866963 | + | 1.50162i | −0.180774 | + | 0.313110i | −0.942144 | − | 0.335207i | \(-0.891194\pi\) |
0.761370 | + | 0.648317i | \(0.224527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.19325 | −1.01848 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.87300 | −1.67684 | ||||||||
\(29\) | −3.68382 | − | 6.38057i | −0.684069 | − | 1.18484i | −0.973728 | − | 0.227713i | \(-0.926875\pi\) |
0.289659 | − | 0.957130i | \(-0.406458\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.31151 | − | 2.27161i | 0.235555 | − | 0.407993i | −0.723879 | − | 0.689927i | \(-0.757643\pi\) |
0.959434 | + | 0.281934i | \(0.0909760\pi\) | |||||||
\(32\) | 6.08789 | − | 10.5445i | 1.07620 | − | 1.86403i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.33163 | − | 10.9667i | −1.08587 | − | 1.88078i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6351 | 1.91280 | 0.956399 | − | 0.292063i | \(-0.0943417\pi\) | ||||
0.956399 | + | 0.292063i | \(0.0943417\pi\) | |||||||
\(38\) | 3.90406 | + | 6.76203i | 0.633322 | + | 1.09695i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.23324 | + | 2.13603i | −0.192600 | + | 0.333592i | −0.946111 | − | 0.323842i | \(-0.895025\pi\) |
0.753511 | + | 0.657435i | \(0.228359\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.63907 | + | 6.30306i | 0.554953 | + | 0.961207i | 0.997907 | + | 0.0646628i | \(0.0205972\pi\) |
−0.442954 | + | 0.896544i | \(0.646069\pi\) | |||||||
\(44\) | −8.92580 | −1.34562 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.56668 | −0.673321 | ||||||||
\(47\) | 3.14604 | + | 5.44910i | 0.458897 | + | 0.794833i | 0.998903 | − | 0.0468283i | \(-0.0149113\pi\) |
−0.540006 | + | 0.841661i | \(0.681578\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.88463 | − | 3.26427i | 0.269233 | − | 0.466324i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.86696 | − | 8.42983i | −0.674926 | − | 1.16901i | ||||
\(53\) | −1.72540 | −0.237001 | −0.118501 | − | 0.992954i | \(-0.537809\pi\) | ||||
−0.118501 | + | 0.992954i | \(0.537809\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.95059 | − | 12.0388i | −0.928811 | − | 1.60875i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.70218 | − | 16.8047i | 1.27396 | − | 2.20656i | ||||
\(59\) | 5.51300 | − | 9.54880i | 0.717732 | − | 1.24315i | −0.244165 | − | 0.969734i | \(-0.578514\pi\) |
0.961896 | − | 0.273414i | \(-0.0881529\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.33521 | + | 10.9729i | 0.811141 | + | 1.40494i | 0.912066 | + | 0.410043i | \(0.134486\pi\) |
−0.100925 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(62\) | 6.90833 | 0.877358 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.0756 | 1.38445 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.55187 | + | 7.88407i | −0.556100 | + | 0.963193i | 0.441717 | + | 0.897154i | \(0.354369\pi\) |
−0.997817 | + | 0.0660386i | \(0.978964\pi\) | |||||||
\(68\) | 11.8676 | − | 20.5554i | 1.43916 | − | 2.49271i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.27460 | −0.151268 | −0.0756338 | − | 0.997136i | \(-0.524098\pi\) | ||||
−0.0756338 | + | 0.997136i | \(0.524098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.58770 | −0.419908 | −0.209954 | − | 0.977711i | \(-0.567331\pi\) | ||||
−0.209954 | + | 0.977711i | \(0.567331\pi\) | |||||||
\(74\) | 15.3218 | + | 26.5382i | 1.78112 | + | 3.08500i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.31755 | + | 12.6744i | −0.839380 | + | 1.45385i | ||||
\(77\) | −1.62499 | + | 2.81456i | −0.185184 | + | 0.320749i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.05545 | − | 1.82809i | −0.118747 | − | 0.205676i | 0.800524 | − | 0.599300i | \(-0.204555\pi\) |
−0.919272 | + | 0.393624i | \(0.871221\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.49602 | −0.717366 | ||||||||
\(83\) | 0.549415 | + | 0.951614i | 0.0603061 | + | 0.104453i | 0.894602 | − | 0.446863i | \(-0.147459\pi\) |
−0.834296 | + | 0.551317i | \(0.814126\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.58431 | + | 16.6005i | −1.03350 | + | 1.79008i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.99195 | − | 12.1104i | −0.745344 | − | 1.29097i | ||||
\(89\) | 13.2935 | 1.40910 | 0.704552 | − | 0.709653i | \(-0.251148\pi\) | ||||
0.704552 | + | 0.709653i | \(0.251148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.54422 | −0.371535 | ||||||||
\(92\) | −4.27976 | − | 7.41277i | −0.446196 | − | 0.772834i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.28580 | + | 14.3514i | −0.854615 | + | 1.48024i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.91638 | + | 3.31926i | 0.194579 | + | 0.337020i | 0.946762 | − | 0.321933i | \(-0.104333\pi\) |
−0.752184 | + | 0.658954i | \(0.770999\pi\) | |||||||
\(98\) | 9.92718 | 1.00280 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.27618 | + | 5.67452i | 0.325993 | + | 0.564636i | 0.981713 | − | 0.190368i | \(-0.0609682\pi\) |
−0.655720 | + | 0.755004i | \(0.727635\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.03779 | − | 6.99365i | 0.397855 | − | 0.689105i | −0.595606 | − | 0.803277i | \(-0.703088\pi\) |
0.993461 | + | 0.114172i | \(0.0364214\pi\) | |||||||
\(104\) | 7.62499 | − | 13.2069i | 0.747691 | − | 1.29504i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.27211 | − | 3.93541i | −0.220687 | − | 0.382241i | ||||
\(107\) | 8.97674 | 0.867814 | 0.433907 | − | 0.900958i | \(-0.357135\pi\) | ||||
0.433907 | + | 0.900958i | \(0.357135\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.34164 | −0.607419 | −0.303710 | − | 0.952765i | \(-0.598225\pi\) | ||||
−0.303710 | + | 0.952765i | \(0.598225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.43292 | − | 16.3383i | 0.891327 | − | 1.54382i | ||||
\(113\) | −7.45127 | + | 12.9060i | −0.700957 | + | 1.21409i | 0.267174 | + | 0.963648i | \(0.413910\pi\) |
−0.968131 | + | 0.250444i | \(0.919423\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 36.3704 | 3.37691 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 29.0394 | 2.67330 | ||||||||
\(119\) | −4.32113 | − | 7.48441i | −0.396117 | − | 0.686095i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86534 | − | 6.69497i | 0.351395 | − | 0.608634i | ||||
\(122\) | −16.6852 | + | 28.8996i | −1.51061 | + | 2.61645i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.47428 | + | 11.2138i | 0.581408 | + | 1.00703i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.62303 | 0.321492 | 0.160746 | − | 0.986996i | \(-0.448610\pi\) | ||||
0.160746 | + | 0.986996i | \(0.448610\pi\) | |||||||
\(128\) | 2.40922 | + | 4.17289i | 0.212947 | + | 0.368835i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.64673 | − | 6.31631i | 0.318616 | − | 0.551859i | −0.661584 | − | 0.749871i | \(-0.730115\pi\) |
0.980200 | + | 0.198012i | \(0.0634486\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.66439 | + | 4.61486i | 0.231032 | + | 0.400159i | ||||
\(134\) | −23.9767 | −2.07127 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 37.1857 | 3.18865 | ||||||||
\(137\) | −3.56310 | − | 6.17148i | −0.304417 | − | 0.527265i | 0.672715 | − | 0.739902i | \(-0.265128\pi\) |
−0.977131 | + | 0.212637i | \(0.931795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.35533 | − | 12.7398i | 0.623871 | − | 1.08058i | −0.364887 | − | 0.931052i | \(-0.618892\pi\) |
0.988758 | − | 0.149525i | \(-0.0477744\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.67848 | − | 2.90721i | −0.140855 | − | 0.243967i | ||||
\(143\) | −3.56531 | −0.298146 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.72450 | − | 8.18308i | −0.391003 | − | 0.677236i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −28.7183 | + | 49.7416i | −2.36063 | + | 4.08873i | ||||
\(149\) | −0.282655 | + | 0.489572i | −0.0231560 | + | 0.0401073i | −0.877371 | − | 0.479812i | \(-0.840705\pi\) |
0.854215 | + | 0.519920i | \(0.174038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0766925 | − | 0.132835i | −0.00624115 | − | 0.0108100i | 0.862888 | − | 0.505395i | \(-0.168653\pi\) |
−0.869129 | + | 0.494585i | \(0.835320\pi\) | |||||||
\(152\) | −22.9285 | −1.85975 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.55953 | −0.689746 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.73035 | − | 9.92525i | 0.457332 | − | 0.792121i | −0.541487 | − | 0.840709i | \(-0.682139\pi\) |
0.998819 | + | 0.0485874i | \(0.0154719\pi\) | |||||||
\(158\) | 2.77976 | − | 4.81469i | 0.221146 | − | 0.383036i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.11661 | −0.245623 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0595 | −1.72783 | −0.863915 | − | 0.503637i | \(-0.831995\pi\) | ||||
−0.863915 | + | 0.503637i | \(0.831995\pi\) | |||||||
\(164\) | −6.08789 | − | 10.5445i | −0.475384 | − | 0.823389i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.44701 | + | 2.50629i | −0.112310 | + | 0.194526i | ||||
\(167\) | 8.53421 | − | 14.7817i | 0.660397 | − | 1.14384i | −0.320115 | − | 0.947379i | \(-0.603721\pi\) |
0.980511 | − | 0.196462i | \(-0.0629452\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.55595 | + | 7.89113i | 0.350457 | + | 0.607010i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −35.9285 | −2.73953 | ||||||||
\(173\) | 5.97233 | + | 10.3444i | 0.454067 | + | 0.786468i | 0.998634 | − | 0.0522497i | \(-0.0166392\pi\) |
−0.544567 | + | 0.838718i | \(0.683306\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.48906 | − | 16.4355i | 0.715265 | − | 1.23887i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.5056 | + | 30.3207i | 1.31210 | + | 2.27263i | ||||
\(179\) | −8.54921 | −0.638998 | −0.319499 | − | 0.947587i | \(-0.603515\pi\) | ||||
−0.319499 | + | 0.947587i | \(0.603515\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5524 | −0.784351 | −0.392176 | − | 0.919890i | \(-0.628277\pi\) | ||||
−0.392176 | + | 0.919890i | \(0.628277\pi\) | |||||||
\(182\) | −4.66724 | − | 8.08390i | −0.345959 | − | 0.599219i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.70503 | − | 11.6135i | 0.494301 | − | 0.856155i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.34684 | − | 7.52895i | −0.317873 | − | 0.550571i | ||||
\(188\) | −31.0608 | −2.26534 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.66862 | − | 15.0145i | −0.627239 | − | 1.08641i | −0.988103 | − | 0.153792i | \(-0.950852\pi\) |
0.360864 | − | 0.932618i | \(-0.382482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.779763 | + | 1.35059i | −0.0561286 | + | 0.0972175i | −0.892724 | − | 0.450603i | \(-0.851209\pi\) |
0.836596 | + | 0.547821i | \(0.184542\pi\) | |||||||
\(194\) | −5.04721 | + | 8.74202i | −0.362369 | + | 0.627641i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.30346 | + | 16.1141i | 0.664533 | + | 1.15100i | ||||
\(197\) | −17.9767 | −1.28079 | −0.640395 | − | 0.768046i | \(-0.721229\pi\) | ||||
−0.640395 | + | 0.768046i | \(0.721229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0225 | 0.781362 | 0.390681 | − | 0.920526i | \(-0.372240\pi\) | ||||
0.390681 | + | 0.920526i | \(0.372240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.62856 | + | 14.9451i | −0.607104 | + | 1.05153i | ||||
\(203\) | 6.62141 | − | 11.4686i | 0.464732 | − | 0.804939i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 21.2688 | 1.48187 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.6964 | 1.43503 | ||||||||
\(209\) | 2.68025 | + | 4.64232i | 0.185397 | + | 0.321116i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9643 | − | 20.7227i | 0.823655 | − | 1.42661i | −0.0792886 | − | 0.996852i | \(-0.525265\pi\) |
0.902943 | − | 0.429760i | \(-0.141402\pi\) | |||||||
\(212\) | 4.25871 | − | 7.37630i | 0.292489 | − | 0.506606i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.8211 | + | 20.4748i | 0.808076 | + | 1.39963i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.71470 | 0.320055 | ||||||||
\(218\) | −8.35107 | − | 14.4645i | −0.565606 | − | 0.979658i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.74040 | − | 8.21061i | 0.318874 | − | 0.552305i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.8553 | − | 18.8020i | −0.726927 | − | 1.25907i | −0.958176 | − | 0.286180i | \(-0.907615\pi\) |
0.231249 | − | 0.972895i | \(-0.425719\pi\) | |||||||
\(224\) | 21.8851 | 1.46226 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −39.2492 | −2.61082 | ||||||||
\(227\) | 7.05010 | + | 12.2111i | 0.467932 | + | 0.810481i | 0.999328 | − | 0.0366416i | \(-0.0116660\pi\) |
−0.531397 | + | 0.847123i | \(0.678333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.83879 | + | 3.18488i | −0.121511 | + | 0.210463i | −0.920364 | − | 0.391064i | \(-0.872107\pi\) |
0.798853 | + | 0.601526i | \(0.205441\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 28.4904 | + | 49.3469i | 1.87049 | + | 3.23978i | ||||
\(233\) | 5.34164 | 0.349943 | 0.174971 | − | 0.984574i | \(-0.444017\pi\) | ||||
0.174971 | + | 0.984574i | \(0.444017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 27.2149 | + | 47.1376i | 1.77154 | + | 3.06840i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.3807 | − | 19.7119i | 0.737698 | − | 1.27773i | ||||
\(239\) | −11.0167 | + | 19.0815i | −0.712613 | + | 1.23428i | 0.251260 | + | 0.967920i | \(0.419155\pi\) |
−0.963873 | + | 0.266362i | \(0.914178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.32358 | + | 16.1489i | 0.600585 | + | 1.04024i | 0.992733 | + | 0.120341i | \(0.0383988\pi\) |
−0.392148 | + | 0.919902i | \(0.628268\pi\) | |||||||
\(242\) | 20.3605 | 1.30882 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −62.5475 | −4.00420 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.92291 | + | 5.06263i | −0.185980 | + | 0.322127i | ||||
\(248\) | −10.1431 | + | 17.5684i | −0.644091 | + | 1.11560i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6929 | −0.927407 | −0.463704 | − | 0.885990i | \(-0.653480\pi\) | ||||
−0.463704 | + | 0.885990i | \(0.653480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.13515 | −0.197105 | ||||||||
\(254\) | 4.77103 | + | 8.26366i | 0.299361 | + | 0.518508i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.73035 | − | 8.19320i | 0.295647 | − | 0.512075i | ||||
\(257\) | 11.1045 | − | 19.2335i | 0.692678 | − | 1.19975i | −0.278280 | − | 0.960500i | \(-0.589764\pi\) |
0.970957 | − | 0.239253i | \(-0.0769025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.4566 | + | 18.1114i | 0.649743 | + | 1.12539i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.2089 | 1.18673 | ||||||||
\(263\) | 2.87001 | + | 4.97100i | 0.176972 | + | 0.306525i | 0.940842 | − | 0.338846i | \(-0.110036\pi\) |
−0.763870 | + | 0.645370i | \(0.776703\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.01727 | + | 12.1543i | −0.430256 | + | 0.745226i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −22.4703 | − | 38.9197i | −1.37259 | − | 2.37740i | ||||
\(269\) | 15.6162 | 0.952139 | 0.476070 | − | 0.879408i | \(-0.342061\pi\) | ||||
0.476070 | + | 0.879408i | \(0.342061\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.75315 | −0.410225 | −0.205112 | − | 0.978738i | \(-0.565756\pi\) | ||||
−0.205112 | + | 0.978738i | \(0.565756\pi\) | |||||||
\(272\) | 25.2331 | + | 43.7050i | 1.52998 | + | 2.65000i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.38423 | − | 16.2540i | 0.566922 | − | 0.981938i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.1483 | − | 26.2376i | −0.910172 | − | 1.57646i | −0.813820 | − | 0.581118i | \(-0.802616\pi\) |
−0.0963529 | − | 0.995347i | \(-0.530718\pi\) | |||||||
\(278\) | 38.7438 | 2.32370 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.31755 | + | 16.1385i | 0.555838 | + | 0.962740i | 0.997838 | + | 0.0657249i | \(0.0209360\pi\) |
−0.441999 | + | 0.897015i | \(0.645731\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.83683 | − | 4.91354i | 0.168632 | − | 0.292079i | −0.769307 | − | 0.638879i | \(-0.779398\pi\) |
0.937939 | + | 0.346800i | \(0.112732\pi\) | |||||||
\(284\) | 3.14604 | − | 5.44910i | 0.186683 | − | 0.323345i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.69502 | − | 8.13201i | −0.277622 | − | 0.480856i | ||||
\(287\) | −4.43332 | −0.261690 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.11806 | 0.359886 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.85533 | − | 15.3379i | 0.518219 | − | 0.897582i | ||||
\(293\) | 9.13867 | − | 15.8286i | 0.533887 | − | 0.924720i | −0.465329 | − | 0.885138i | \(-0.654064\pi\) |
0.999216 | − | 0.0395819i | \(-0.0126026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −89.9850 | −5.23027 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.48887 | −0.0862478 | ||||||||
\(299\) | −1.70950 | − | 2.96094i | −0.0988631 | − | 0.171236i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.54097 | + | 11.3293i | −0.377015 | + | 0.653009i | ||||
\(302\) | 0.201987 | − | 0.349852i | 0.0116230 | − | 0.0201317i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.5586 | − | 26.9483i | −0.892349 | − | 1.54559i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5050 | −0.884915 | −0.442458 | − | 0.896789i | \(-0.645893\pi\) | ||||
−0.442458 | + | 0.896789i | \(0.645893\pi\) | |||||||
\(308\) | −8.02174 | − | 13.8941i | −0.457081 | − | 0.791688i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.2232 | − | 26.3673i | 0.863228 | − | 1.49515i | −0.00556798 | − | 0.999984i | \(-0.501772\pi\) |
0.868796 | − | 0.495170i | \(-0.164894\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.47468 | + | 6.01832i | 0.196401 | + | 0.340176i | 0.947359 | − | 0.320174i | \(-0.103741\pi\) |
−0.750958 | + | 0.660350i | \(0.770408\pi\) | |||||||
\(314\) | 30.1843 | 1.70340 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4205 | 0.586196 | ||||||||
\(317\) | −8.07253 | − | 13.9820i | −0.453398 | − | 0.785309i | 0.545196 | − | 0.838308i | \(-0.316455\pi\) |
−0.998595 | + | 0.0529995i | \(0.983122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.66081 | − | 11.5369i | 0.372934 | − | 0.645940i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.10414 | − | 7.10858i | −0.228715 | − | 0.396146i | ||||
\(323\) | −14.2545 | −0.793142 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −29.0493 | − | 50.3148i | −1.60889 | − | 2.78668i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.53779 | − | 16.5199i | 0.526636 | − | 0.912160i | ||||
\(329\) | −5.65478 | + | 9.79436i | −0.311758 | + | 0.539981i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.31112 | − | 10.9312i | −0.346890 | − | 0.600832i | 0.638805 | − | 0.769369i | \(-0.279429\pi\) |
−0.985695 | + | 0.168537i | \(0.946096\pi\) | |||||||
\(332\) | −5.42437 | −0.297701 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 44.9535 | 2.45975 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.46020 | − | 5.99324i | 0.188489 | − | 0.326473i | −0.756258 | − | 0.654274i | \(-0.772974\pi\) |
0.944747 | + | 0.327801i | \(0.106308\pi\) | |||||||
\(338\) | −11.9991 | + | 20.7831i | −0.652665 | + | 1.13045i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.74276 | 0.256835 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3570 | 1.04518 | ||||||||
\(344\) | −28.1443 | − | 48.7474i | −1.51744 | − | 2.62828i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.7295 | + | 27.2442i | −0.845621 | + | 1.46466i | ||||
\(347\) | 6.90317 | − | 11.9566i | 0.370581 | − | 0.641866i | −0.619074 | − | 0.785333i | \(-0.712492\pi\) |
0.989655 | + | 0.143467i | \(0.0458251\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.28384 | − | 5.68778i | −0.175780 | − | 0.304460i | 0.764651 | − | 0.644445i | \(-0.222911\pi\) |
−0.940431 | + | 0.339985i | \(0.889578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.0153 | 1.17342 | ||||||||
\(353\) | −1.76250 | − | 3.05273i | −0.0938082 | − | 0.162481i | 0.815302 | − | 0.579035i | \(-0.196571\pi\) |
−0.909111 | + | 0.416555i | \(0.863237\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −32.8116 | + | 56.8313i | −1.73901 | + | 3.01205i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.2581 | − | 19.4996i | −0.595010 | − | 1.03059i | ||||
\(359\) | −22.9285 | −1.21012 | −0.605061 | − | 0.796179i | \(-0.706851\pi\) | ||||
−0.605061 | + | 0.796179i | \(0.706851\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2107 | −0.537407 | ||||||||
\(362\) | −13.8960 | − | 24.0686i | −0.730358 | − | 1.26502i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.74801 | − | 15.1520i | 0.458520 | − | 0.794181i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.08966 | − | 3.61939i | −0.109079 | − | 0.188931i | 0.806318 | − | 0.591482i | \(-0.201457\pi\) |
−0.915397 | + | 0.402551i | \(0.868124\pi\) | |||||||
\(368\) | 18.1993 | 0.948706 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.55064 | − | 2.68578i | −0.0805051 | − | 0.139439i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.42045 | + | 5.92440i | −0.177104 | + | 0.306754i | −0.940888 | − | 0.338719i | \(-0.890006\pi\) |
0.763783 | + | 0.645473i | \(0.223340\pi\) | |||||||
\(374\) | 11.4484 | − | 19.8292i | 0.591982 | − | 1.02534i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.3312 | − | 42.1429i | −1.25479 | − | 2.17336i | ||||
\(377\) | 14.5277 | 0.748217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.7764 | −0.656280 | −0.328140 | − | 0.944629i | \(-0.606422\pi\) | ||||
−0.328140 | + | 0.944629i | \(0.606422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.8307 | − | 39.5440i | 1.16812 | − | 2.02325i | ||||
\(383\) | 3.76730 | − | 6.52515i | 0.192500 | − | 0.333420i | −0.753578 | − | 0.657358i | \(-0.771674\pi\) |
0.946078 | + | 0.323939i | \(0.105007\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.10736 | −0.209059 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.9204 | −0.960538 | ||||||||
\(389\) | 2.72588 | + | 4.72135i | 0.138207 | + | 0.239382i | 0.926818 | − | 0.375511i | \(-0.122533\pi\) |
−0.788611 | + | 0.614893i | \(0.789199\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.16847 | − | 7.22000i | 0.210808 | − | 0.365131i | ||||
\(392\) | −14.5756 | + | 25.2456i | −0.736177 | + | 1.27510i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.6729 | − | 41.0026i | −1.19262 | − | 2.06568i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.64549 | −0.283339 | −0.141670 | − | 0.989914i | \(-0.545247\pi\) | ||||
−0.141670 | + | 0.989914i | \(0.545247\pi\) | |||||||
\(398\) | 14.5151 | + | 25.1408i | 0.727574 | + | 1.26020i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.75209 | + | 4.76676i | −0.137433 | + | 0.238040i | −0.926524 | − | 0.376235i | \(-0.877218\pi\) |
0.789091 | + | 0.614276i | \(0.210552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.58608 | + | 4.47922i | 0.128822 | + | 0.223126i | ||||
\(404\) | −32.3458 | −1.60926 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.8779 | 1.73096 | ||||||||
\(407\) | 10.5188 | + | 18.2192i | 0.521400 | + | 0.903091i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.4265 | + | 28.4515i | −0.812238 | + | 1.40684i | 0.0990570 | + | 0.995082i | \(0.468417\pi\) |
−0.911295 | + | 0.411755i | \(0.864916\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 19.9325 | + | 34.5241i | 0.982005 | + | 1.70088i | ||||
\(413\) | 19.8184 | 0.975202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.0043 | + | 20.7920i | 0.588558 | + | 1.01941i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.05903 | + | 12.2266i | −0.345268 | + | 0.598022i | ||||
\(419\) | 11.4295 | − | 19.7965i | 0.558369 | − | 0.967124i | −0.439264 | − | 0.898358i | \(-0.644761\pi\) |
0.997633 | − | 0.0687656i | \(-0.0219060\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.97071 | − | 15.5377i | −0.437205 | − | 0.757262i | 0.560267 | − | 0.828312i | \(-0.310698\pi\) |
−0.997473 | + | 0.0710498i | \(0.977365\pi\) | |||||||
\(422\) | 63.0212 | 3.06782 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.3441 | 0.648046 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.3871 | + | 19.7230i | −0.551060 | + | 0.954463i | ||||
\(428\) | −22.1568 | + | 38.3768i | −1.07099 | + | 1.85501i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.18871 | 0.298100 | 0.149050 | − | 0.988830i | \(-0.452378\pi\) | ||||
0.149050 | + | 0.988830i | \(0.452378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.11806 | −0.149844 | −0.0749221 | − | 0.997189i | \(-0.523871\pi\) | ||||
−0.0749221 | + | 0.997189i | \(0.523871\pi\) | |||||||
\(434\) | 6.20861 | + | 10.7536i | 0.298023 | + | 0.516190i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.6528 | − | 27.1114i | 0.749631 | − | 1.29840i | ||||
\(437\) | −2.57026 | + | 4.45182i | −0.122952 | + | 0.212960i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.75494 | − | 11.6999i | −0.322396 | − | 0.558406i | 0.658586 | − | 0.752505i | \(-0.271155\pi\) |
−0.980982 | + | 0.194100i | \(0.937822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.9698 | 1.18769 | ||||||||
\(443\) | −12.1387 | − | 21.0248i | −0.576726 | − | 0.998918i | −0.995852 | − | 0.0909904i | \(-0.970997\pi\) |
0.419126 | − | 0.907928i | \(-0.362337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 28.5899 | − | 49.5192i | 1.35377 | − | 2.34480i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.95377 | + | 17.2404i | 0.470271 | + | 0.814534i | ||||
\(449\) | 24.1437 | 1.13941 | 0.569705 | − | 0.821849i | \(-0.307057\pi\) | ||||
0.569705 | + | 0.821849i | \(0.307057\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.45970 | −0.209999 | ||||||||
\(452\) | −36.7832 | − | 63.7104i | −1.73014 | − | 2.99668i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.5680 | + | 32.1607i | −0.871440 | + | 1.50938i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.41078 | + | 2.44355i | 0.0659937 | + | 0.114304i | 0.897134 | − | 0.441758i | \(-0.145645\pi\) |
−0.831141 | + | 0.556062i | \(0.812312\pi\) | |||||||
\(458\) | −9.68573 | −0.452585 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7286 | + | 18.5825i | 0.499681 | + | 0.865474i | 1.00000 | 0.000367761i | \(-0.000117062\pi\) | |
−0.500318 | + | 0.865841i | \(0.666784\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.90167 | − | 17.1502i | 0.460170 | − | 0.797037i | −0.538799 | − | 0.842434i | \(-0.681122\pi\) |
0.998969 | + | 0.0453970i | \(0.0144553\pi\) | |||||||
\(464\) | −38.6655 | + | 66.9706i | −1.79500 | + | 3.10903i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.03421 | + | 12.1836i | 0.325853 | + | 0.564395i | ||||
\(467\) | −22.7210 | −1.05140 | −0.525701 | − | 0.850669i | \(-0.676197\pi\) | ||||
−0.525701 | + | 0.850669i | \(0.676197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3633 | −0.755588 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −42.6372 | + | 73.8497i | −1.96253 | + | 3.39921i | ||||
\(473\) | −6.57989 | + | 11.3967i | −0.302544 | + | 0.524021i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 42.6625 | 1.95543 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −58.0300 | −2.65423 | ||||||||
\(479\) | 10.6440 | + | 18.4359i | 0.486336 | + | 0.842359i | 0.999877 | − | 0.0157065i | \(-0.00499974\pi\) |
−0.513541 | + | 0.858065i | \(0.671666\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.4712 | + | 19.8687i | −0.523042 | + | 0.905935i | ||||
\(482\) | −24.5557 | + | 42.5318i | −1.11848 | + | 1.93727i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.0813 | + | 33.0497i | 0.867330 | + | 1.50226i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.58690 | −0.434424 | −0.217212 | − | 0.976124i | \(-0.569696\pi\) | ||||
−0.217212 | + | 0.976124i | \(0.569696\pi\) | |||||||
\(488\) | −48.9961 | − | 84.8637i | −2.21795 | − | 3.84160i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.9222 | + | 32.7742i | −0.853945 | + | 1.47908i | 0.0236745 | + | 0.999720i | \(0.492463\pi\) |
−0.877620 | + | 0.479357i | \(0.840870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.7123 | + | 30.6786i | 0.797721 | + | 1.38169i | ||||
\(494\) | −15.3963 | −0.692711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −27.5314 | −1.23619 | ||||||||
\(497\) | −1.14550 | − | 1.98407i | −0.0513829 | − | 0.0889977i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.46266 | + | 14.6577i | −0.378840 | + | 0.656171i | −0.990894 | − | 0.134646i | \(-0.957010\pi\) |
0.612053 | + | 0.790816i | \(0.290344\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −19.3485 | − | 33.5126i | −0.863566 | − | 1.49574i | ||||
\(503\) | −40.4168 | −1.80210 | −0.901048 | − | 0.433719i | \(-0.857201\pi\) | ||||
−0.901048 | + | 0.433719i | \(0.857201\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.12856 | − | 7.15088i | −0.183537 | − | 0.317896i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.94253 | + | 15.4889i | −0.396761 | + | 0.687210i | ||||
\(509\) | −20.7034 | + | 35.8593i | −0.917660 | + | 1.58943i | −0.114701 | + | 0.993400i | \(0.536591\pi\) |
−0.802959 | + | 0.596034i | \(0.796742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.22431 | − | 5.58467i | −0.142635 | − | 0.247051i | ||||
\(512\) | 34.5537 | 1.52707 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 58.4922 | 2.57998 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.68843 | + | 9.85265i | −0.250177 | + | 0.433319i | ||||
\(518\) | −27.5398 | + | 47.7004i | −1.21003 | + | 2.09584i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0301 | 0.746103 | 0.373052 | − | 0.927811i | \(-0.378311\pi\) | ||||
0.373052 | + | 0.927811i | \(0.378311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.57651 | 0.418751 | 0.209376 | − | 0.977835i | \(-0.432857\pi\) | ||||
0.209376 | + | 0.977835i | \(0.432857\pi\) | |||||||
\(524\) | 18.0021 | + | 31.1805i | 0.786424 | + | 1.36213i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.55880 | + | 13.0922i | −0.329579 | + | 0.570848i | ||||
\(527\) | −6.30592 | + | 10.9222i | −0.274690 | + | 0.475777i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.99675 | + | 17.3149i | 0.434641 | + | 0.752821i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.3055 | −1.14049 | ||||||||
\(533\) | −2.43174 | − | 4.21189i | −0.105330 | − | 0.182437i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 35.2038 | − | 60.9748i | 1.52057 | − | 2.63371i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.5644 | + | 35.6187i | 0.886596 | + | 1.53563i | ||||
\(539\) | 6.81528 | 0.293555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.833751 | −0.0358458 | −0.0179229 | − | 0.999839i | \(-0.505705\pi\) | ||||
−0.0179229 | + | 0.999839i | \(0.505705\pi\) | |||||||
\(542\) | −8.89297 | − | 15.4031i | −0.381986 | − | 0.661619i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −29.2713 | + | 50.6994i | −1.25500 | + | 2.17372i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.1635 | + | 24.5319i | 0.605587 | + | 1.04891i | 0.991958 | + | 0.126565i | \(0.0403951\pi\) |
−0.386371 | + | 0.922343i | \(0.626272\pi\) | |||||||
\(548\) | 35.1785 | 1.50275 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9213 | − | 18.9163i | −0.465264 | − | 0.805861i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.89709 | − | 3.28586i | 0.0806727 | − | 0.139729i | ||||
\(554\) | 39.8964 | − | 69.1026i | 1.69504 | − | 2.93589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 36.3096 | + | 62.8901i | 1.53987 | + | 2.66713i | ||||
\(557\) | −11.5042 | −0.487448 | −0.243724 | − | 0.969845i | \(-0.578369\pi\) | ||||
−0.243724 | + | 0.969845i | \(0.578369\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.3512 | −0.606993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.5398 | + | 42.5043i | −1.03515 | + | 1.79293i | ||||
\(563\) | 16.5030 | − | 28.5840i | 0.695517 | − | 1.20467i | −0.274490 | − | 0.961590i | \(-0.588509\pi\) |
0.970006 | − | 0.243080i | \(-0.0781578\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.9429 | 0.628095 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.85769 | 0.413619 | ||||||||
\(569\) | −13.5044 | − | 23.3903i | −0.566135 | − | 0.980574i | −0.996943 | − | 0.0781305i | \(-0.975105\pi\) |
0.430809 | − | 0.902443i | \(-0.358228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2122 | − | 21.1521i | 0.511064 | − | 0.885189i | −0.488854 | − | 0.872366i | \(-0.662585\pi\) |
0.999918 | − | 0.0128232i | \(-0.00408185\pi\) | |||||||
\(572\) | 8.80007 | − | 15.2422i | 0.367950 | − | 0.637307i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.83807 | − | 10.1118i | −0.243676 | − | 0.422060i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.7976 | 0.616033 | 0.308017 | − | 0.951381i | \(-0.400335\pi\) | ||||
0.308017 | + | 0.951381i | \(0.400335\pi\) | |||||||
\(578\) | 8.05663 | + | 13.9545i | 0.335112 | + | 0.580431i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.987533 | + | 1.71046i | −0.0409698 | + | 0.0709617i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.55987 | − | 2.70177i | −0.0646030 | − | 0.111896i | ||||
\(584\) | 27.7470 | 1.14818 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.1375 | 1.98854 | ||||||||
\(587\) | 15.2890 | + | 26.4813i | 0.631044 | + | 1.09300i | 0.987339 | + | 0.158626i | \(0.0507065\pi\) |
−0.356295 | + | 0.934374i | \(0.615960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.88821 | − | 6.73457i | 0.160211 | − | 0.277493i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −61.0611 | − | 105.761i | −2.50960 | − | 4.34675i | ||||
\(593\) | 5.09990 | 0.209428 | 0.104714 | − | 0.994502i | \(-0.466607\pi\) | ||||
0.104714 | + | 0.994502i | \(0.466607\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.39532 | − | 2.41677i | −0.0571547 | − | 0.0989949i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.50236 | − | 7.79831i | 0.184115 | − | 0.318897i | ||||
\(599\) | −0.282655 | + | 0.489572i | −0.0115490 | + | 0.0200034i | −0.871742 | − | 0.489965i | \(-0.837010\pi\) |
0.860193 | + | 0.509968i | \(0.170343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50480 | + | 9.53459i | 0.224546 | + | 0.388924i | 0.956183 | − | 0.292770i | \(-0.0945769\pi\) |
−0.731637 | + | 0.681694i | \(0.761244\pi\) | |||||||
\(602\) | −34.4542 | −1.40425 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.757185 | 0.0308094 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.54913 | − | 16.5396i | 0.387587 | − | 0.671321i | −0.604537 | − | 0.796577i | \(-0.706642\pi\) |
0.992124 | + | 0.125256i | \(0.0399753\pi\) | |||||||
\(608\) | 18.0486 | − | 31.2611i | 0.731967 | − | 1.26780i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.4069 | −0.501929 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.33918 | 0.377206 | 0.188603 | − | 0.982053i | \(-0.439604\pi\) | ||||
0.188603 | + | 0.982053i | \(0.439604\pi\) | |||||||
\(614\) | −20.4179 | − | 35.3648i | −0.823999 | − | 1.42721i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.5675 | − | 21.7676i | 0.506360 | − | 0.877041i | ||||
\(617\) | −12.2077 | + | 21.1444i | −0.491464 | + | 0.851241i | −0.999952 | − | 0.00982861i | \(-0.996871\pi\) |
0.508488 | + | 0.861069i | \(0.330205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.7431 | − | 34.1961i | −0.793544 | − | 1.37446i | −0.923760 | − | 0.382973i | \(-0.874900\pi\) |
0.130216 | − | 0.991486i | \(-0.458433\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 80.1874 | 3.21522 | ||||||||
\(623\) | 11.9470 | + | 20.6928i | 0.478647 | + | 0.829040i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.15135 | + | 15.8506i | −0.365761 | + | 0.633517i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 28.2879 | + | 48.9960i | 1.12881 | + | 1.95515i | ||||
\(629\) | −55.9430 | −2.23059 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1634 | 1.67850 | 0.839249 | − | 0.543747i | \(-0.182995\pi\) | ||||
0.839249 | + | 0.543747i | \(0.182995\pi\) | |||||||
\(632\) | 8.16277 | + | 14.1383i | 0.324698 | + | 0.562393i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 21.2608 | − | 36.8248i | 0.844375 | − | 1.46250i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.71616 | + | 6.43658i | 0.147240 | + | 0.255027i | ||||
\(638\) | 35.0855 | 1.38905 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.6577 | + | 30.5841i | 0.697438 | + | 1.20800i | 0.969352 | + | 0.245677i | \(0.0790103\pi\) |
−0.271913 | + | 0.962322i | \(0.587656\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.09771 | + | 12.2936i | −0.279906 | + | 0.484812i | −0.971361 | − | 0.237608i | \(-0.923637\pi\) |
0.691455 | + | 0.722420i | \(0.256970\pi\) | |||||||
\(644\) | 7.69256 | − | 13.3239i | 0.303129 | − | 0.525036i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.7712 | − | 32.5127i | −0.738544 | − | 1.27919i | ||||
\(647\) | −17.4897 | −0.687593 | −0.343796 | − | 0.939044i | \(-0.611713\pi\) | ||||
−0.343796 | + | 0.939044i | \(0.611713\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.9364 | 0.782572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 54.4483 | − | 94.3072i | 2.13236 | − | 3.69335i | ||||
\(653\) | −5.48858 | + | 9.50650i | −0.214785 | + | 0.372018i | −0.953206 | − | 0.302322i | \(-0.902238\pi\) |
0.738421 | + | 0.674340i | \(0.235572\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 25.8882 | 1.01077 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.7862 | −1.16119 | ||||||||
\(659\) | −7.89381 | − | 13.6725i | −0.307499 | − | 0.532604i | 0.670316 | − | 0.742076i | \(-0.266159\pi\) |
−0.977815 | + | 0.209472i | \(0.932825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.9466 | + | 43.2088i | −0.970311 | + | 1.68063i | −0.275697 | + | 0.961245i | \(0.588909\pi\) |
−0.694614 | + | 0.719383i | \(0.744425\pi\) | |||||||
\(662\) | 16.6217 | − | 28.7897i | 0.646022 | − | 1.11894i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.24913 | − | 7.35972i | −0.164898 | − | 0.285612i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.7750 | 0.494649 | ||||||||
\(668\) | 42.1291 | + | 72.9698i | 1.63002 | + | 2.82328i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.4549 | + | 19.8404i | −0.442210 | + | 0.765929i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.4197 | − | 24.9757i | −0.555840 | − | 0.962743i | −0.997838 | − | 0.0657266i | \(-0.979063\pi\) |
0.441998 | − | 0.897016i | \(-0.354270\pi\) | |||||||
\(674\) | 18.2264 | 0.702055 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −44.9809 | −1.73003 | ||||||||
\(677\) | 5.23181 | + | 9.06176i | 0.201075 | + | 0.348272i | 0.948875 | − | 0.315652i | \(-0.102223\pi\) |
−0.747800 | + | 0.663924i | \(0.768890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.44455 | + | 5.96614i | −0.132190 | + | 0.228959i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.24556 | + | 10.8176i | 0.239155 | + | 0.414228i | ||||
\(683\) | 16.1875 | 0.619396 | 0.309698 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 25.4904 | + | 44.1507i | 0.973229 | + | 1.68568i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 38.1958 | − | 66.1570i | 1.45620 | − | 2.52221i | ||||
\(689\) | 1.70109 | − | 2.94638i | 0.0648065 | − | 0.112248i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.94181 | − | 8.55946i | −0.187995 | − | 0.325617i | 0.756586 | − | 0.653894i | \(-0.226866\pi\) |
−0.944582 | + | 0.328276i | \(0.893532\pi\) | |||||||
\(692\) | −58.9648 | −2.24150 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.3621 | 1.38029 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.92957 | − | 10.2703i | 0.224598 | − | 0.389016i | ||||
\(698\) | 8.64872 | − | 14.9800i | 0.327359 | − | 0.567002i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.9692 | −1.66069 | −0.830346 | − | 0.557248i | \(-0.811857\pi\) | ||||
−0.830346 | + | 0.557248i | \(0.811857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.4942 | 1.30097 | ||||||||
\(704\) | 10.0130 | + | 17.3430i | 0.377379 | + | 0.653640i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.64193 | − | 8.04005i | 0.174701 | − | 0.302591i | ||||
\(707\) | −5.88870 | + | 10.1995i | −0.221467 | + | 0.383593i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.6130 | − | 21.8464i | −0.473692 | − | 0.820458i | 0.525855 | − | 0.850574i | \(-0.323746\pi\) |
−0.999546 | + | 0.0301162i | \(0.990412\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −102.811 | −3.85299 | ||||||||
\(713\) | 2.27407 | + | 3.93880i | 0.0851645 | + | 0.147509i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 21.1016 | − | 36.5490i | 0.788603 | − | 1.36590i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30.1937 | − | 52.2971i | −1.12682 | − | 1.95171i | ||||
\(719\) | 36.8600 | 1.37465 | 0.687323 | − | 0.726352i | \(-0.258786\pi\) | ||||
0.687323 | + | 0.726352i | \(0.258786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5153 | 0.540576 | ||||||||
\(722\) | −13.4461 | − | 23.2893i | −0.500412 | − | 0.866740i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.0459 | − | 45.1128i | 0.967988 | − | 1.67660i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.1226 | + | 33.1213i | 0.709217 | + | 1.22840i | 0.965148 | + | 0.261705i | \(0.0842847\pi\) |
−0.255931 | + | 0.966695i | \(0.582382\pi\) | |||||||
\(728\) | 27.4107 | 1.01591 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4971 | − | 30.3059i | −0.647154 | − | 1.12090i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.7916 | + | 34.2801i | −0.731020 | + | 1.26616i | 0.225428 | + | 0.974260i | \(0.427622\pi\) |
−0.956448 | + | 0.291903i | \(0.905711\pi\) | |||||||
\(734\) | 5.50358 | − | 9.53248i | 0.203141 | − | 0.351850i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.5559 | + | 18.2834i | 0.389097 | + | 0.673936i | ||||
\(737\) | −16.4607 | −0.606338 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.24773 | −0.303398 | −0.151699 | − | 0.988427i | \(-0.548474\pi\) | ||||
−0.151699 | + | 0.988427i | \(0.548474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.08395 | − | 7.07361i | 0.149927 | − | 0.259680i | ||||
\(743\) | 0.654091 | − | 1.13292i | 0.0239963 | − | 0.0415627i | −0.853778 | − | 0.520637i | \(-0.825694\pi\) |
0.877774 | + | 0.479075i | \(0.159028\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18.0171 | −0.659651 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 42.9164 | 1.56918 | ||||||||
\(749\) | 8.06752 | + | 13.9734i | 0.294781 | + | 0.510575i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.2234 | + | 24.6357i | −0.519020 | + | 0.898969i | 0.480736 | + | 0.876866i | \(0.340370\pi\) |
−0.999756 | + | 0.0221034i | \(0.992964\pi\) | |||||||
\(752\) | 33.0209 | − | 57.1939i | 1.20415 | − | 2.08565i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.1310 | + | 33.1359i | 0.696711 | + | 1.20674i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.2012 | −1.38845 | −0.694223 | − | 0.719760i | \(-0.744252\pi\) | ||||
−0.694223 | + | 0.719760i | \(0.744252\pi\) | |||||||
\(758\) | −16.8248 | − | 29.1414i | −0.611103 | − | 1.05846i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.0952 | − | 19.2174i | 0.402200 | − | 0.696632i | −0.591791 | − | 0.806092i | \(-0.701579\pi\) |
0.993991 | + | 0.109460i | \(0.0349121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.69932 | − | 9.87152i | −0.206329 | − | 0.357373i | ||||
\(764\) | 85.5852 | 3.09637 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.8440 | 0.716994 | ||||||||
\(767\) | 10.8707 | + | 18.8286i | 0.392518 | + | 0.679861i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.45652 | − | 14.6471i | 0.304950 | − | 0.528189i | −0.672300 | − | 0.740279i | \(-0.734694\pi\) |
0.977250 | + | 0.212090i | \(0.0680270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.84930 | − | 6.66718i | −0.138539 | − | 0.239957i | ||||
\(773\) | 38.6464 | 1.39001 | 0.695007 | − | 0.719003i | \(-0.255401\pi\) | ||||
0.695007 | + | 0.719003i | \(0.255401\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.8211 | − | 25.6709i | −0.532047 | − | 0.921533i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.17920 | + | 12.4347i | −0.257387 | + | 0.445807i | ||||
\(779\) | −3.65615 | + | 6.33264i | −0.130995 | + | 0.226890i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.15232 | − | 1.99588i | −0.0412333 | − | 0.0714181i | ||||
\(782\) | 21.9572 | 0.785187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −39.5622 | −1.41294 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.45734 | + | 9.45240i | −0.194533 | + | 0.336942i | −0.946747 | − | 0.321977i | \(-0.895653\pi\) |
0.752214 | + | 0.658919i | \(0.228986\pi\) | |||||||
\(788\) | 44.3711 | − | 76.8530i | 1.58065 | − | 2.73777i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.7862 | −0.952409 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.9839 | −0.887204 | ||||||||
\(794\) | −7.43433 | − | 12.8766i | −0.263835 | − | 0.456975i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.2062 | + | 47.1225i | −0.964298 | + | 1.67021i | ||||
\(797\) | −1.46275 | + | 2.53356i | −0.0518133 | + | 0.0897432i | −0.890769 | − | 0.454457i | \(-0.849833\pi\) |
0.838956 | + | 0.544200i | \(0.183167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.1265 | − | 26.1999i | −0.535139 | − | 0.926888i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.4965 | −0.511888 | ||||||||
\(803\) | −3.24350 | − | 5.61791i | −0.114461 | − | 0.198252i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.81102 | + | 11.7970i | −0.239908 | + | 0.415532i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −25.3378 | − | 43.8863i | −0.891380 | − | 1.54391i | ||||
\(809\) | 37.9241 | 1.33334 | 0.666671 | − | 0.745352i | \(-0.267719\pi\) | ||||
0.666671 | + | 0.745352i | \(0.267719\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5050 | 0.684912 | 0.342456 | − | 0.939534i | \(-0.388741\pi\) | ||||
0.342456 | + | 0.939534i | \(0.388741\pi\) | |||||||
\(812\) | 32.6866 | + | 56.6148i | 1.14707 | + | 1.98679i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.7037 | + | 47.9843i | −0.971016 | + | 1.68185i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7887 | + | 18.6865i | 0.377447 | + | 0.653758i | ||||
\(818\) | −86.5257 | −3.02530 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3762 | + | 38.7567i | 0.780934 | + | 1.35262i | 0.931398 | + | 0.364002i | \(0.118590\pi\) |
−0.150464 | + | 0.988615i | \(0.548077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.9497 | − | 31.0898i | 0.625687 | − | 1.08372i | −0.362721 | − | 0.931898i | \(-0.618152\pi\) |
0.988408 | − | 0.151824i | \(-0.0485146\pi\) | |||||||
\(824\) | −31.2279 | + | 54.0884i | −1.08788 | + | 1.88426i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.0981 | + | 45.2033i | 0.908071 | + | 1.57282i | ||||
\(827\) | 16.2717 | 0.565822 | 0.282911 | − | 0.959146i | \(-0.408700\pi\) | ||||
0.282911 | + | 0.959146i | \(0.408700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.6592 | −0.717525 | −0.358762 | − | 0.933429i | \(-0.616801\pi\) | ||||
−0.358762 | + | 0.933429i | \(0.616801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.9196 | + | 18.9132i | −0.378568 | + | 0.655698i | ||||
\(833\) | −9.06152 | + | 15.6950i | −0.313963 | + | 0.543800i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −26.4621 | −0.915210 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 60.2044 | 2.07973 | ||||||||
\(839\) | −6.11836 | − | 10.5973i | −0.211229 | − | 0.365860i | 0.740870 | − | 0.671648i | \(-0.234413\pi\) |
−0.952100 | + | 0.305788i | \(0.901080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.6411 | + | 21.8951i | −0.435901 | + | 0.755003i | ||||
\(842\) | 23.6264 | − | 40.9221i | 0.814218 | − | 1.41027i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 59.0616 | + | 102.298i | 2.03299 | + | 3.52123i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.8953 | 0.477450 | ||||||||
\(848\) | 9.05490 | + | 15.6836i | 0.310947 | + | 0.538575i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0872 | + | 17.4715i | −0.345785 | + | 0.598917i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.21464 | − | 14.2282i | −0.281264 | − | 0.487164i | 0.690432 | − | 0.723397i | \(-0.257420\pi\) |
−0.971696 | + | 0.236233i | \(0.924087\pi\) | |||||||
\(854\) | −59.9809 | −2.05250 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −69.4255 | −2.37291 | ||||||||
\(857\) | 24.5449 | + | 42.5129i | 0.838436 | + | 1.45221i | 0.891202 | + | 0.453607i | \(0.149863\pi\) |
−0.0527655 | + | 0.998607i | \(0.516804\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5454 | + | 35.5856i | −0.700999 | + | 1.21417i | 0.267117 | + | 0.963664i | \(0.413929\pi\) |
−0.968116 | + | 0.250502i | \(0.919404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.14968 | + | 14.1157i | 0.277579 | + | 0.480781i | ||||
\(863\) | −47.8366 | −1.62838 | −0.814188 | − | 0.580601i | \(-0.802817\pi\) | ||||
−0.814188 | + | 0.580601i | \(0.802817\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.10605 | − | 7.11189i | −0.139529 | − | 0.241672i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.6371 | + | 20.1560i | −0.394987 | + | 0.684138i | ||||
\(869\) | 1.90838 | − | 3.30542i | 0.0647375 | − | 0.112129i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.97551 | − | 15.5460i | −0.304123 | − | 0.526757i | ||||
\(872\) | 49.0458 | 1.66090 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.5387 | −0.457954 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.68859 | − | 9.85292i | 0.192090 | − | 0.332710i | −0.753853 | − | 0.657043i | \(-0.771807\pi\) |
0.945943 | + | 0.324334i | \(0.105140\pi\) | |||||||
\(878\) | 17.7906 | − | 30.8143i | 0.600405 | − | 1.03993i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.9924 | 1.48214 | 0.741071 | − | 0.671426i | \(-0.234318\pi\) | ||||
0.741071 | + | 0.671426i | \(0.234318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.6820 | 1.26810 | 0.634051 | − | 0.773291i | \(-0.281391\pi\) | ||||
0.634051 | + | 0.773291i | \(0.281391\pi\) | |||||||
\(884\) | 23.4010 | + | 40.5317i | 0.787060 | + | 1.36323i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.9699 | − | 55.3735i | 1.07405 | − | 1.86031i | ||||
\(887\) | −16.6416 | + | 28.8241i | −0.558771 | + | 0.967820i | 0.438828 | + | 0.898571i | \(0.355394\pi\) |
−0.997599 | + | 0.0692492i | \(0.977940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.25606 | + | 5.63967i | 0.109205 | + | 0.189148i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 107.175 | 3.58847 | ||||||||
\(893\) | 9.32697 | + | 16.1548i | 0.312115 | + | 0.540599i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.33040 | + | 7.50047i | −0.144669 | + | 0.250573i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.7939 | + | 55.0686i | 1.06098 | + | 1.83766i | ||||
\(899\) | −19.3255 | −0.644543 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.29592 | 0.276377 | ||||||||
\(902\) | −5.87281 | − | 10.1720i | −0.195543 | − | 0.338691i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 57.6276 | − | 99.8139i | 1.91667 | − | 3.31976i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.03918 | + | 12.1922i | 0.233732 | + | 0.404836i | 0.958903 | − | 0.283733i | \(-0.0915728\pi\) |
−0.725171 | + | 0.688568i | \(0.758239\pi\) | |||||||
\(908\) | −69.6056 | −2.30994 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.65761 | + | 6.33517i | 0.121182 | + | 0.209894i | 0.920234 | − | 0.391368i | \(-0.127998\pi\) |
−0.799052 | + | 0.601262i | \(0.794665\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.993410 | + | 1.72064i | −0.0328771 | + | 0.0569448i | ||||
\(914\) | −3.71561 | + | 6.43563i | −0.122902 | + | 0.212872i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.07719 | − | 15.7222i | −0.299919 | − | 0.519475i | ||||
\(917\) | 13.1094 | 0.432912 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.44684 | 0.146688 | 0.0733438 | − | 0.997307i | \(-0.476633\pi\) | ||||
0.0733438 | + | 0.997307i | \(0.476633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.2562 | + | 48.9412i | −0.930569 | + | 1.61179i | ||||
\(923\) | 1.25665 | − | 2.17658i | 0.0413631 | − | 0.0716430i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 52.1565 | 1.71397 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −89.7068 | −2.94477 | ||||||||
\(929\) | 6.55663 | + | 11.3564i | 0.215116 | + | 0.372592i | 0.953309 | − | 0.301998i | \(-0.0976536\pi\) |
−0.738192 | + | 0.674590i | \(0.764320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.58730 | − | 9.67749i | 0.183116 | − | 0.317167i | ||||
\(932\) | −13.1845 | + | 22.8362i | −0.431873 | + | 0.748026i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.9204 | − | 51.8236i | −0.979025 | − | 1.69572i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.5187 | −1.09501 | −0.547504 | − | 0.836803i | \(-0.684422\pi\) | ||||
−0.547504 | + | 0.836803i | \(0.684422\pi\) | |||||||
\(938\) | −21.5482 | − | 37.3226i | −0.703574 | − | 1.21863i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.895381 | − | 1.55085i | 0.0291886 | − | 0.0505561i | −0.851062 | − | 0.525065i | \(-0.824041\pi\) |
0.880251 | + | 0.474509i | \(0.157374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.13835 | − | 3.70373i | −0.0696342 | − | 0.120610i | ||||
\(944\) | −115.729 | −3.76667 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.6592 | −1.12687 | ||||||||
\(947\) | −26.3175 | − | 45.5832i | −0.855204 | − | 1.48126i | −0.876456 | − | 0.481482i | \(-0.840099\pi\) |
0.0212525 | − | 0.999774i | \(-0.493235\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.53716 | − | 6.12654i | 0.114821 | − | 0.198876i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 33.4193 | + | 57.8839i | 1.08312 | + | 1.87603i | ||||
\(953\) | 18.4072 | 0.596268 | 0.298134 | − | 0.954524i | \(-0.403636\pi\) | ||||
0.298134 | + | 0.954524i | \(0.403636\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −54.3841 | − | 94.1960i | −1.75891 | − | 3.04652i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.0333 | + | 48.5551i | −0.905715 | + | 1.56874i | ||||
\(959\) | 6.40442 | − | 11.0928i | 0.206810 | − | 0.358205i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0599 | + | 20.8883i | 0.389028 | + | 0.673816i | ||||
\(962\) | −60.4240 | −1.94815 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −92.0517 | −2.96479 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.04790 | − | 5.27911i | 0.0980137 | − | 0.169765i | −0.812849 | − | 0.582475i | \(-0.802084\pi\) |
0.910862 | + | 0.412710i | \(0.135418\pi\) | |||||||
\(968\) | −29.8943 | + | 51.7784i | −0.960839 | + | 1.66422i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.1077 | 1.09457 | 0.547283 | − | 0.836947i | \(-0.315662\pi\) | ||||
0.547283 | + | 0.836947i | \(0.315662\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.4414 | 0.847671 | ||||||||
\(974\) | −12.6246 | − | 21.8665i | −0.404519 | − | 0.700648i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 66.4945 | − | 115.172i | 2.12844 | − | 3.68656i | ||||
\(977\) | 24.3957 | − | 42.2546i | 0.780488 | − | 1.35184i | −0.151170 | − | 0.988508i | \(-0.548304\pi\) |
0.931658 | − | 0.363337i | \(-0.118363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0181 | + | 20.8160i | 0.384100 | + | 0.665281i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −99.6715 | −3.18065 | ||||||||
\(983\) | 16.7086 | + | 28.9402i | 0.532922 | + | 0.923048i | 0.999261 | + | 0.0384416i | \(0.0122394\pi\) |
−0.466339 | + | 0.884606i | \(0.654427\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −46.6493 | + | 80.7989i | −1.48562 | + | 2.57316i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.4289 | − | 24.9917i | −0.459046 | − | 0.795091i | ||||
\(989\) | −12.6198 | −0.401285 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3512 | −0.614713 | −0.307356 | − | 0.951595i | \(-0.599444\pi\) | ||||
−0.307356 | + | 0.951595i | \(0.599444\pi\) | |||||||
\(992\) | −15.9687 | − | 27.6586i | −0.507006 | − | 0.878161i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.01694 | − | 5.22549i | 0.0956915 | − | 0.165743i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.7721 | − | 34.2463i | −0.626189 | − | 1.08459i | −0.988310 | − | 0.152460i | \(-0.951281\pi\) |
0.362121 | − | 0.932131i | \(-0.382053\pi\) | |||||||
\(998\) | −44.5766 | −1.41105 | ||||||||
\(999\) | 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 | 675.2.e.e.226.4 | 8 | ||
3.2 | odd | 2 | 225.2.e.c.76.1 | ✓ | 8 | ||
5.2 | odd | 4 | 675.2.k.c.199.1 | 16 | |||
5.3 | odd | 4 | 675.2.k.c.199.8 | 16 | |||
5.4 | even | 2 | 675.2.e.c.226.1 | 8 | |||
9.2 | odd | 6 | 225.2.e.c.151.1 | yes | 8 | ||
9.4 | even | 3 | 2025.2.a.p.1.1 | 4 | |||
9.5 | odd | 6 | 2025.2.a.y.1.4 | 4 | |||
9.7 | even | 3 | inner | 675.2.e.e.451.4 | 8 | ||
15.2 | even | 4 | 225.2.k.c.49.8 | 16 | |||
15.8 | even | 4 | 225.2.k.c.49.1 | 16 | |||
15.14 | odd | 2 | 225.2.e.e.76.4 | yes | 8 | ||
45.2 | even | 12 | 225.2.k.c.124.1 | 16 | |||
45.4 | even | 6 | 2025.2.a.z.1.4 | 4 | |||
45.7 | odd | 12 | 675.2.k.c.424.8 | 16 | |||
45.13 | odd | 12 | 2025.2.b.o.649.8 | 8 | |||
45.14 | odd | 6 | 2025.2.a.q.1.1 | 4 | |||
45.22 | odd | 12 | 2025.2.b.o.649.1 | 8 | |||
45.23 | even | 12 | 2025.2.b.n.649.1 | 8 | |||
45.29 | odd | 6 | 225.2.e.e.151.4 | yes | 8 | ||
45.32 | even | 12 | 2025.2.b.n.649.8 | 8 | |||
45.34 | even | 6 | 675.2.e.c.451.1 | 8 | |||
45.38 | even | 12 | 225.2.k.c.124.8 | 16 | |||
45.43 | odd | 12 | 675.2.k.c.424.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.1 | ✓ | 8 | 3.2 | odd | 2 | ||
225.2.e.c.151.1 | yes | 8 | 9.2 | odd | 6 | ||
225.2.e.e.76.4 | yes | 8 | 15.14 | odd | 2 | ||
225.2.e.e.151.4 | yes | 8 | 45.29 | odd | 6 | ||
225.2.k.c.49.1 | 16 | 15.8 | even | 4 | |||
225.2.k.c.49.8 | 16 | 15.2 | even | 4 | |||
225.2.k.c.124.1 | 16 | 45.2 | even | 12 | |||
225.2.k.c.124.8 | 16 | 45.38 | even | 12 | |||
675.2.e.c.226.1 | 8 | 5.4 | even | 2 | |||
675.2.e.c.451.1 | 8 | 45.34 | even | 6 | |||
675.2.e.e.226.4 | 8 | 1.1 | even | 1 | trivial | ||
675.2.e.e.451.4 | 8 | 9.7 | even | 3 | inner | ||
675.2.k.c.199.1 | 16 | 5.2 | odd | 4 | |||
675.2.k.c.199.8 | 16 | 5.3 | odd | 4 | |||
675.2.k.c.424.1 | 16 | 45.43 | odd | 12 | |||
675.2.k.c.424.8 | 16 | 45.7 | odd | 12 | |||
2025.2.a.p.1.1 | 4 | 9.4 | even | 3 | |||
2025.2.a.q.1.1 | 4 | 45.14 | odd | 6 | |||
2025.2.a.y.1.4 | 4 | 9.5 | odd | 6 | |||
2025.2.a.z.1.4 | 4 | 45.4 | even | 6 | |||
2025.2.b.n.649.1 | 8 | 45.23 | even | 12 | |||
2025.2.b.n.649.8 | 8 | 45.32 | even | 12 | |||
2025.2.b.o.649.1 | 8 | 45.22 | odd | 12 | |||
2025.2.b.o.649.8 | 8 | 45.13 | odd | 12 |