Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (of order \(2\), degree \(1\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.5 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.c.323.6 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30241 | − | 0.551119i | −0.920942 | − | 0.389700i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.39253 | + | 1.43556i | 0.696267 | + | 0.717782i | ||||
\(5\) | 3.61017 | 1.61452 | 0.807259 | − | 0.590198i | \(-0.200950\pi\) | ||||
0.807259 | + | 0.590198i | \(0.200950\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −1.02248 | − | 2.63714i | −0.361502 | − | 0.932371i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.70192 | − | 1.98963i | −1.48688 | − | 0.629178i | ||||
\(11\) | − | 2.00899i | − | 0.605734i | −0.953033 | − | 0.302867i | \(-0.902056\pi\) | ||
0.953033 | − | 0.302867i | \(-0.0979438\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.59265i | 0.441722i | 0.975305 | + | 0.220861i | \(0.0708867\pi\) | ||||
−0.975305 | + | 0.220861i | \(0.929113\pi\) | |||||||
\(14\) | 0.551119 | − | 1.30241i | 0.147293 | − | 0.348083i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.121693 | + | 3.99815i | −0.0304232 | + | 0.999537i | ||||
\(17\) | 7.79257i | 1.88998i | 0.327106 | + | 0.944988i | \(0.393926\pi\) | ||||
−0.327106 | + | 0.944988i | \(0.606074\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.05480 | −1.15965 | −0.579825 | − | 0.814741i | \(-0.696879\pi\) | ||||
−0.579825 | + | 0.814741i | \(0.696879\pi\) | |||||||
\(20\) | 5.02729 | + | 5.18263i | 1.12414 | + | 1.15887i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.10719 | + | 2.61653i | −0.236055 | + | 0.557846i | ||||
\(23\) | 7.14612 | 1.49007 | 0.745034 | − | 0.667026i | \(-0.232433\pi\) | ||||
0.745034 | + | 0.667026i | \(0.232433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.03333 | 1.60667 | ||||||||
\(26\) | 0.877741 | − | 2.07428i | 0.172139 | − | 0.406800i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.43556 | + | 1.39253i | −0.271296 | + | 0.263164i | ||||
\(29\) | 4.94298 | 0.917889 | 0.458945 | − | 0.888465i | \(-0.348228\pi\) | ||||
0.458945 | + | 0.888465i | \(0.348228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.53252i | − | 0.454853i | −0.973795 | − | 0.227427i | \(-0.926969\pi\) | ||
0.973795 | − | 0.227427i | \(-0.0730312\pi\) | |||||||
\(32\) | 2.36195 | − | 5.14015i | 0.417538 | − | 0.908660i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.29463 | − | 10.1491i | 0.736524 | − | 1.74056i | ||||
\(35\) | 3.61017i | 0.610230i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.76592i | 0.783512i | 0.920069 | + | 0.391756i | \(0.128132\pi\) | ||||
−0.920069 | + | 0.391756i | \(0.871868\pi\) | |||||||
\(38\) | 6.58341 | + | 2.78580i | 1.06797 | + | 0.451916i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.69133 | − | 9.52054i | −0.583651 | − | 1.50533i | ||||
\(41\) | − | 0.836835i | − | 0.130692i | −0.997863 | − | 0.0653458i | \(-0.979185\pi\) | ||
0.997863 | − | 0.0653458i | \(-0.0208151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.151434 | 0.0230934 | 0.0115467 | − | 0.999933i | \(-0.496324\pi\) | ||||
0.0115467 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(44\) | 2.88404 | − | 2.79759i | 0.434785 | − | 0.421753i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.30717 | − | 3.93836i | −1.37227 | − | 0.580680i | ||||
\(47\) | 0.795430 | 0.116025 | 0.0580127 | − | 0.998316i | \(-0.481524\pi\) | ||||
0.0580127 | + | 0.998316i | \(0.481524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −10.4627 | − | 4.42732i | −1.47965 | − | 0.626118i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.28635 | + | 2.21782i | −0.317060 | + | 0.307557i | ||||
\(53\) | 1.05980 | 0.145575 | 0.0727873 | − | 0.997347i | \(-0.476811\pi\) | ||||
0.0727873 | + | 0.997347i | \(0.476811\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.25280i | − | 0.977968i | ||||||
\(56\) | 2.63714 | − | 1.02248i | 0.352403 | − | 0.136635i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.43778 | − | 2.72417i | −0.845322 | − | 0.357702i | ||||
\(59\) | 8.34506i | 1.08643i | 0.839592 | + | 0.543217i | \(0.182794\pi\) | ||||
−0.839592 | + | 0.543217i | \(0.817206\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2367i | 1.31067i | 0.755336 | + | 0.655337i | \(0.227474\pi\) | ||||
−0.755336 | + | 0.655337i | \(0.772526\pi\) | |||||||
\(62\) | −1.39572 | + | 3.29837i | −0.177256 | + | 0.418893i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.90906 | + | 5.39286i | −0.738633 | + | 0.674108i | ||||
\(65\) | 5.74974i | 0.713168i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.655357 | 0.0800646 | 0.0400323 | − | 0.999198i | \(-0.487254\pi\) | ||||
0.0400323 | + | 0.999198i | \(0.487254\pi\) | |||||||
\(68\) | −11.1867 | + | 10.8514i | −1.35659 | + | 1.31593i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.98963 | − | 4.70192i | 0.237807 | − | 0.561986i | ||||
\(71\) | 11.3675 | 1.34907 | 0.674536 | − | 0.738242i | \(-0.264344\pi\) | ||||
0.674536 | + | 0.738242i | \(0.264344\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.3835 | −1.68346 | −0.841728 | − | 0.539901i | \(-0.818462\pi\) | ||||
−0.841728 | + | 0.539901i | \(0.818462\pi\) | |||||||
\(74\) | 2.62659 | − | 6.20717i | 0.305335 | − | 0.721569i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.03899 | − | 7.25649i | −0.807427 | − | 0.832377i | ||||
\(77\) | 2.00899 | 0.228946 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.81177i | 0.428858i | 0.976740 | + | 0.214429i | \(0.0687890\pi\) | ||||
−0.976740 | + | 0.214429i | \(0.931211\pi\) | |||||||
\(80\) | −0.439332 | + | 14.4340i | −0.0491188 | + | 1.61377i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.461196 | + | 1.08990i | −0.0509306 | + | 0.120359i | ||||
\(83\) | − | 14.9522i | − | 1.64121i | −0.571494 | − | 0.820606i | \(-0.693636\pi\) | ||
0.571494 | − | 0.820606i | \(-0.306364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 28.1325i | 3.05140i | ||||||||
\(86\) | −0.197228 | − | 0.0834580i | −0.0212677 | − | 0.00899951i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.29800 | + | 2.05416i | −0.564769 | + | 0.218974i | ||||
\(89\) | − | 0.0444167i | − | 0.00470816i | −0.999997 | − | 0.00235408i | \(-0.999251\pi\) | ||
0.999997 | − | 0.00235408i | \(-0.000749328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.59265 | −0.166955 | ||||||||
\(92\) | 9.95122 | + | 10.2587i | 1.03749 | + | 1.06955i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.03597 | − | 0.438377i | −0.106853 | − | 0.0452151i | ||||
\(95\) | −18.2487 | −1.87228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.87000 | 1.00215 | 0.501073 | − | 0.865405i | \(-0.332939\pi\) | ||||
0.501073 | + | 0.865405i | \(0.332939\pi\) | |||||||
\(98\) | 1.30241 | + | 0.551119i | 0.131563 | + | 0.0556715i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.1867 | + | 11.5324i | 1.11867 | + | 1.15324i | ||||
\(101\) | −4.43029 | −0.440830 | −0.220415 | − | 0.975406i | \(-0.570741\pi\) | ||||
−0.220415 | + | 0.975406i | \(0.570741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.2939i | − | 1.11282i | −0.830906 | − | 0.556412i | \(-0.812177\pi\) | ||
0.830906 | − | 0.556412i | \(-0.187823\pi\) | |||||||
\(104\) | 4.20005 | − | 1.62846i | 0.411849 | − | 0.159683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.38029 | − | 0.584076i | −0.134066 | − | 0.0567304i | ||||
\(107\) | − | 8.60018i | − | 0.831411i | −0.909499 | − | 0.415705i | \(-0.863535\pi\) | ||
0.909499 | − | 0.415705i | \(-0.136465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 19.9155i | − | 1.90756i | −0.300512 | − | 0.953778i | \(-0.597158\pi\) | ||
0.300512 | − | 0.953778i | \(-0.402842\pi\) | |||||||
\(110\) | −3.99716 | + | 9.44611i | −0.381114 | + | 0.900651i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.99815 | − | 0.121693i | −0.377790 | − | 0.0114989i | ||||
\(113\) | 3.81372i | 0.358764i | 0.983779 | + | 0.179382i | \(0.0574098\pi\) | ||||
−0.983779 | + | 0.179382i | \(0.942590\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.7987 | 2.40574 | ||||||||
\(116\) | 6.88328 | + | 7.09597i | 0.639096 | + | 0.658845i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.59912 | − | 10.8687i | 0.423384 | − | 1.00054i | ||||
\(119\) | −7.79257 | −0.714343 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.96395 | 0.633086 | ||||||||
\(122\) | 5.64164 | − | 13.3324i | 0.510770 | − | 1.20706i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.63559 | − | 3.52662i | 0.326486 | − | 0.316700i | ||||
\(125\) | 10.9508 | 0.979472 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.9943i | 1.41926i | 0.704574 | + | 0.709630i | \(0.251138\pi\) | ||||
−0.704574 | + | 0.709630i | \(0.748862\pi\) | |||||||
\(128\) | 10.6681 | − | 3.76711i | 0.942938 | − | 0.332969i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.16879 | − | 7.48851i | 0.277922 | − | 0.656786i | ||||
\(131\) | − | 19.8839i | − | 1.73726i | −0.495460 | − | 0.868631i | \(-0.665000\pi\) | ||
0.495460 | − | 0.868631i | \(-0.335000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.05480i | − | 0.438307i | ||||||
\(134\) | −0.853543 | − | 0.361180i | −0.0737348 | − | 0.0312012i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.5501 | − | 7.96776i | 1.76216 | − | 0.683229i | ||||
\(137\) | 8.93576i | 0.763433i | 0.924279 | + | 0.381717i | \(0.124667\pi\) | ||||
−0.924279 | + | 0.381717i | \(0.875333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.20344 | 0.102074 | 0.0510372 | − | 0.998697i | \(-0.483747\pi\) | ||||
0.0510372 | + | 0.998697i | \(0.483747\pi\) | |||||||
\(140\) | −5.18263 | + | 5.02729i | −0.438012 | + | 0.424883i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.8051 | − | 6.26484i | −1.24242 | − | 0.525733i | ||||
\(143\) | 3.19962 | 0.267566 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 17.8450 | 1.48195 | ||||||||
\(146\) | 18.7331 | + | 7.92700i | 1.55037 | + | 0.656044i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.84179 | + | 6.63671i | −0.562391 | + | 0.545534i | ||||
\(149\) | −12.6791 | −1.03871 | −0.519355 | − | 0.854559i | \(-0.673828\pi\) | ||||
−0.519355 | + | 0.854559i | \(0.673828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5094i | 1.42489i | 0.701727 | + | 0.712446i | \(0.252412\pi\) | ||||
−0.701727 | + | 0.712446i | \(0.747588\pi\) | |||||||
\(152\) | 5.16844 | + | 13.3302i | 0.419216 | + | 1.08123i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.61653 | − | 1.10719i | −0.210846 | − | 0.0892203i | ||||
\(155\) | − | 9.14281i | − | 0.734368i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2891i | 1.22020i | 0.792324 | + | 0.610100i | \(0.208871\pi\) | ||||
−0.792324 | + | 0.610100i | \(0.791129\pi\) | |||||||
\(158\) | 2.10074 | − | 4.96448i | 0.167126 | − | 0.394953i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.52704 | − | 18.5568i | 0.674122 | − | 1.46705i | ||||
\(161\) | 7.14612i | 0.563193i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.5634 | 1.37567 | 0.687835 | − | 0.725867i | \(-0.258561\pi\) | ||||
0.687835 | + | 0.725867i | \(0.258561\pi\) | |||||||
\(164\) | 1.20133 | − | 1.16532i | 0.0938082 | − | 0.0909964i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.24042 | + | 19.4738i | −0.639581 | + | 1.51146i | ||||
\(167\) | −4.20290 | −0.325230 | −0.162615 | − | 0.986690i | \(-0.551993\pi\) | ||||
−0.162615 | + | 0.986690i | \(0.551993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4635 | 0.804882 | ||||||||
\(170\) | 15.5044 | − | 36.6400i | 1.18913 | − | 2.81016i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.210877 | + | 0.217393i | 0.0160792 | + | 0.0165761i | ||||
\(173\) | 18.0074 | 1.36907 | 0.684537 | − | 0.728978i | \(-0.260005\pi\) | ||||
0.684537 | + | 0.728978i | \(0.260005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.03333i | 0.607263i | ||||||||
\(176\) | 8.03225 | + | 0.244480i | 0.605454 | + | 0.0184284i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.0244789 | + | 0.0578487i | −0.00183477 | + | 0.00433594i | ||||
\(179\) | − | 0.886091i | − | 0.0662295i | −0.999452 | − | 0.0331148i | \(-0.989457\pi\) | ||
0.999452 | − | 0.0331148i | \(-0.0105427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.47338i | − | 0.629821i | −0.949121 | − | 0.314911i | \(-0.898025\pi\) | ||
0.949121 | − | 0.314911i | \(-0.101975\pi\) | |||||||
\(182\) | 2.07428 | + | 0.877741i | 0.153756 | + | 0.0650625i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.30678 | − | 18.8454i | −0.538663 | − | 1.38930i | ||||
\(185\) | 17.2058i | 1.26499i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.6552 | 1.14482 | ||||||||
\(188\) | 1.10766 | + | 1.14189i | 0.0807847 | + | 0.0832809i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 23.7672 | + | 10.0572i | 1.72426 | + | 0.729626i | ||||
\(191\) | −20.6102 | −1.49130 | −0.745652 | − | 0.666335i | \(-0.767862\pi\) | ||||
−0.745652 | + | 0.666335i | \(0.767862\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.2972 | 1.31706 | 0.658530 | − | 0.752555i | \(-0.271179\pi\) | ||||
0.658530 | + | 0.752555i | \(0.271179\pi\) | |||||||
\(194\) | −12.8548 | − | 5.43955i | −0.922918 | − | 0.390537i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.39253 | − | 1.43556i | −0.0994668 | − | 0.102540i | ||||
\(197\) | 10.6580 | 0.759353 | 0.379677 | − | 0.925119i | \(-0.376035\pi\) | ||||
0.379677 | + | 0.925119i | \(0.376035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.1305i | 1.85234i | 0.377108 | + | 0.926169i | \(0.376919\pi\) | ||||
−0.377108 | + | 0.926169i | \(0.623081\pi\) | |||||||
\(200\) | −8.21393 | − | 21.1850i | −0.580813 | − | 1.49801i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.77004 | + | 2.44162i | 0.405979 | + | 0.171792i | ||||
\(203\) | 4.94298i | 0.346929i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 3.02112i | − | 0.211004i | ||||||
\(206\) | −6.22431 | + | 14.7093i | −0.433668 | + | 1.02485i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.36766 | − | 0.193814i | −0.441518 | − | 0.0134386i | ||||
\(209\) | 10.1551i | 0.702440i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.1542 | −1.45632 | −0.728159 | − | 0.685409i | \(-0.759624\pi\) | ||||
−0.728159 | + | 0.685409i | \(0.759624\pi\) | |||||||
\(212\) | 1.47581 | + | 1.52141i | 0.101359 | + | 0.104491i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.73972 | + | 11.2009i | −0.324001 | + | 0.765681i | ||||
\(215\) | 0.546701 | 0.0372847 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.53252 | 0.171918 | ||||||||
\(218\) | −10.9758 | + | 25.9381i | −0.743375 | + | 1.75675i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.4119 | − | 10.0998i | 0.701968 | − | 0.680927i | ||||
\(221\) | −12.4108 | −0.834844 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.04274i | − | 0.404652i | −0.979318 | − | 0.202326i | \(-0.935150\pi\) | ||
0.979318 | − | 0.202326i | \(-0.0648500\pi\) | |||||||
\(224\) | 5.14015 | + | 2.36195i | 0.343441 | + | 0.157814i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.10181 | − | 4.96702i | 0.139811 | − | 0.330401i | ||||
\(227\) | − | 20.0726i | − | 1.33227i | −0.745832 | − | 0.666134i | \(-0.767948\pi\) | ||
0.745832 | − | 0.666134i | \(-0.232052\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 18.5176i | − | 1.22368i | −0.790983 | − | 0.611838i | \(-0.790430\pi\) | ||
0.790983 | − | 0.611838i | \(-0.209570\pi\) | |||||||
\(230\) | −33.6005 | − | 14.2182i | −2.21555 | − | 0.937518i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.05411 | − | 13.0354i | −0.331819 | − | 0.855814i | ||||
\(233\) | − | 17.1203i | − | 1.12159i | −0.827956 | − | 0.560793i | \(-0.810496\pi\) | ||
0.827956 | − | 0.560793i | \(-0.189504\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.87164 | 0.187325 | ||||||||
\(236\) | −11.9799 | + | 11.6208i | −0.779823 | + | 0.756449i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.1491 | + | 4.29463i | 0.657869 | + | 0.278380i | ||||
\(239\) | −3.95612 | −0.255900 | −0.127950 | − | 0.991781i | \(-0.540840\pi\) | ||||
−0.127950 | + | 0.991781i | \(0.540840\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.3726 | −0.990235 | −0.495117 | − | 0.868826i | \(-0.664875\pi\) | ||||
−0.495117 | + | 0.868826i | \(0.664875\pi\) | |||||||
\(242\) | −9.06991 | − | 3.83797i | −0.583036 | − | 0.246714i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.6954 | + | 14.2550i | −0.940779 | + | 0.912580i | ||||
\(245\) | −3.61017 | −0.230645 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 8.05054i | − | 0.512243i | ||||||
\(248\) | −6.67861 | + | 2.58945i | −0.424092 | + | 0.164430i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.2625 | − | 6.03522i | −0.902037 | − | 0.381701i | ||||
\(251\) | 13.1732i | 0.831482i | 0.909483 | + | 0.415741i | \(0.136478\pi\) | ||||
−0.909483 | + | 0.415741i | \(0.863522\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.3565i | − | 0.902585i | ||||||
\(254\) | 8.81474 | − | 20.8310i | 0.553086 | − | 1.30706i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9704 | − | 0.973093i | −0.998149 | − | 0.0608183i | ||||
\(257\) | − | 26.9072i | − | 1.67843i | −0.543802 | − | 0.839213i | \(-0.683016\pi\) | ||
0.543802 | − | 0.839213i | \(-0.316984\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.76592 | −0.296140 | ||||||||
\(260\) | −8.25413 | + | 8.00672i | −0.511899 | + | 0.496556i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.9584 | + | 25.8969i | −0.677011 | + | 1.59992i | ||||
\(263\) | 8.15057 | 0.502586 | 0.251293 | − | 0.967911i | \(-0.419144\pi\) | ||||
0.251293 | + | 0.967911i | \(0.419144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.82605 | 0.235033 | ||||||||
\(266\) | −2.78580 | + | 6.58341i | −0.170808 | + | 0.403655i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.912608 | + | 0.940808i | 0.0557464 | + | 0.0574690i | ||||
\(269\) | −3.84304 | −0.234314 | −0.117157 | − | 0.993113i | \(-0.537378\pi\) | ||||
−0.117157 | + | 0.993113i | \(0.537378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.8705i | − | 0.781829i | −0.920427 | − | 0.390914i | \(-0.872159\pi\) | ||
0.920427 | − | 0.390914i | \(-0.127841\pi\) | |||||||
\(272\) | −31.1558 | − | 0.948300i | −1.88910 | − | 0.0574991i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.92467 | − | 11.6380i | 0.297510 | − | 0.703078i | ||||
\(275\) | − | 16.1389i | − | 0.973212i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.72420i | 0.163682i | 0.996645 | + | 0.0818408i | \(0.0260799\pi\) | ||||
−0.996645 | + | 0.0818408i | \(0.973920\pi\) | |||||||
\(278\) | −1.56737 | − | 0.663239i | −0.0940046 | − | 0.0397784i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.52054 | − | 3.69133i | 0.568961 | − | 0.220599i | ||||
\(281\) | 8.91234i | 0.531666i | 0.964019 | + | 0.265833i | \(0.0856469\pi\) | ||||
−0.964019 | + | 0.265833i | \(0.914353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.90080 | 0.291322 | 0.145661 | − | 0.989335i | \(-0.453469\pi\) | ||||
0.145661 | + | 0.989335i | \(0.453469\pi\) | |||||||
\(284\) | 15.8296 | + | 16.3188i | 0.939315 | + | 0.968340i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.16722 | − | 1.76338i | −0.246413 | − | 0.104271i | ||||
\(287\) | 0.836835 | 0.0493968 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −43.7241 | −2.57201 | ||||||||
\(290\) | −23.2415 | − | 9.83473i | −1.36479 | − | 0.577515i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −20.0295 | − | 20.6484i | −1.17214 | − | 1.20836i | ||||
\(293\) | 26.1386 | 1.52704 | 0.763518 | − | 0.645786i | \(-0.223470\pi\) | ||||
0.763518 | + | 0.645786i | \(0.223470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 30.1271i | 1.75407i | ||||||||
\(296\) | 12.5684 | − | 4.87307i | 0.730525 | − | 0.283241i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.5133 | + | 6.98768i | 0.956592 | + | 0.404786i | ||||
\(299\) | 11.3813i | 0.658196i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.151434i | 0.00872849i | ||||||||
\(302\) | 9.64975 | − | 22.8043i | 0.555280 | − | 1.31224i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.615133 | − | 20.2098i | 0.0352803 | − | 1.15911i | ||||
\(305\) | 36.9562i | 2.11611i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.4257 | −1.33697 | −0.668487 | − | 0.743724i | \(-0.733058\pi\) | ||||
−0.668487 | + | 0.743724i | \(0.733058\pi\) | |||||||
\(308\) | 2.79759 | + | 2.88404i | 0.159408 | + | 0.164333i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.03878 | + | 11.9077i | −0.286184 | + | 0.676310i | ||||
\(311\) | −15.4333 | −0.875143 | −0.437571 | − | 0.899184i | \(-0.644161\pi\) | ||||
−0.437571 | + | 0.899184i | \(0.644161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.1894 | −1.76293 | −0.881464 | − | 0.472251i | \(-0.843442\pi\) | ||||
−0.881464 | + | 0.472251i | \(0.843442\pi\) | |||||||
\(314\) | 8.42610 | − | 19.9126i | 0.475513 | − | 1.12373i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.47205 | + | 5.30803i | −0.307827 | + | 0.298600i | ||||
\(317\) | 30.7471 | 1.72693 | 0.863466 | − | 0.504407i | \(-0.168289\pi\) | ||||
0.863466 | + | 0.504407i | \(0.168289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.93042i | − | 0.555997i | ||||||
\(320\) | −21.3327 | + | 19.4692i | −1.19254 | + | 1.08836i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.93836 | − | 9.30717i | 0.219476 | − | 0.518668i | ||||
\(323\) | − | 39.3899i | − | 2.19171i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7943i | 0.709700i | ||||||||
\(326\) | −22.8747 | − | 9.67952i | −1.26691 | − | 0.536099i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.20685 | + | 0.855648i | −0.121853 | + | 0.0472453i | ||||
\(329\) | 0.795430i | 0.0438535i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00125 | 0.0550339 | 0.0275169 | − | 0.999621i | \(-0.491240\pi\) | ||||
0.0275169 | + | 0.999621i | \(0.491240\pi\) | |||||||
\(332\) | 21.4648 | − | 20.8214i | 1.17803 | − | 1.14272i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.47389 | + | 2.31630i | 0.299518 | + | 0.126742i | ||||
\(335\) | 2.36595 | 0.129266 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.1818 | 1.53516 | 0.767580 | − | 0.640953i | \(-0.221461\pi\) | ||||
0.767580 | + | 0.640953i | \(0.221461\pi\) | |||||||
\(338\) | −13.6277 | − | 5.76662i | −0.741249 | − | 0.313663i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −40.3860 | + | 39.1755i | −2.19024 | + | 2.12459i | ||||
\(341\) | −5.08780 | −0.275520 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −0.154838 | − | 0.399352i | −0.00834831 | − | 0.0215316i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.4529 | − | 9.92420i | −1.26084 | − | 0.533528i | ||||
\(347\) | 19.6496i | 1.05485i | 0.849602 | + | 0.527424i | \(0.176842\pi\) | ||||
−0.849602 | + | 0.527424i | \(0.823158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2275i | 0.600993i | 0.953783 | + | 0.300497i | \(0.0971524\pi\) | ||||
−0.953783 | + | 0.300497i | \(0.902848\pi\) | |||||||
\(350\) | 4.42732 | − | 10.4627i | 0.236650 | − | 0.559253i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.3265 | − | 4.74514i | −0.550406 | − | 0.252917i | ||||
\(353\) | 32.2047i | 1.71408i | 0.515249 | + | 0.857041i | \(0.327700\pi\) | ||||
−0.515249 | + | 0.857041i | \(0.672300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 41.0385 | 2.17810 | ||||||||
\(356\) | 0.0637631 | − | 0.0618518i | 0.00337944 | − | 0.00327814i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.488342 | + | 1.15405i | −0.0258097 | + | 0.0609935i | ||||
\(359\) | −20.1918 | −1.06568 | −0.532842 | − | 0.846215i | \(-0.678876\pi\) | ||||
−0.532842 | + | 0.846215i | \(0.678876\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.55100 | 0.344790 | ||||||||
\(362\) | −4.66984 | + | 11.0358i | −0.245442 | + | 0.580029i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.21782 | − | 2.28635i | −0.116246 | − | 0.119838i | ||||
\(365\) | −51.9267 | −2.71797 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.42641i | − | 0.0744578i | −0.999307 | − | 0.0372289i | \(-0.988147\pi\) | ||
0.999307 | − | 0.0372289i | \(-0.0118531\pi\) | |||||||
\(368\) | −0.869632 | + | 28.5712i | −0.0453327 | + | 1.48938i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9.48244 | − | 22.4090i | 0.492969 | − | 1.16499i | ||||
\(371\) | 1.05980i | 0.0550220i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.80760i | − | 0.507818i | −0.967228 | − | 0.253909i | \(-0.918284\pi\) | ||
0.967228 | − | 0.253909i | \(-0.0817165\pi\) | |||||||
\(374\) | −20.3895 | − | 8.62789i | −1.05431 | − | 0.446137i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.813312 | − | 2.09766i | −0.0419434 | − | 0.108179i | ||||
\(377\) | 7.87245i | 0.405452i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.5378 | −0.900857 | −0.450428 | − | 0.892813i | \(-0.648729\pi\) | ||||
−0.450428 | + | 0.892813i | \(0.648729\pi\) | |||||||
\(380\) | −25.4119 | − | 26.1972i | −1.30360 | − | 1.34389i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.8429 | + | 11.3587i | 1.37340 | + | 0.581162i | ||||
\(383\) | −8.32355 | −0.425313 | −0.212657 | − | 0.977127i | \(-0.568212\pi\) | ||||
−0.212657 | + | 0.977127i | \(0.568212\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.25280 | 0.369637 | ||||||||
\(386\) | −23.8304 | − | 10.0839i | −1.21293 | − | 0.513258i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.7443 | + | 14.1690i | 0.697762 | + | 0.719323i | ||||
\(389\) | −8.79829 | −0.446091 | −0.223045 | − | 0.974808i | \(-0.571600\pi\) | ||||
−0.223045 | + | 0.974808i | \(0.571600\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 55.6866i | 2.81619i | ||||||||
\(392\) | 1.02248 | + | 2.63714i | 0.0516431 | + | 0.133196i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.8811 | − | 5.87385i | −0.699320 | − | 0.295920i | ||||
\(395\) | 13.7611i | 0.692398i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 31.5495i | − | 1.58342i | −0.610896 | − | 0.791711i | \(-0.709190\pi\) | ||
0.610896 | − | 0.791711i | \(-0.290810\pi\) | |||||||
\(398\) | 14.4010 | − | 34.0325i | 0.721857 | − | 1.70590i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.977599 | + | 32.1184i | −0.0488800 | + | 1.60592i | ||||
\(401\) | − | 8.99955i | − | 0.449416i | −0.974426 | − | 0.224708i | \(-0.927857\pi\) | ||
0.974426 | − | 0.224708i | \(-0.0721428\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.03341 | 0.200919 | ||||||||
\(404\) | −6.16933 | − | 6.35996i | −0.306936 | − | 0.316420i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.72417 | − | 6.43778i | 0.135199 | − | 0.319502i | ||||
\(407\) | 9.57470 | 0.474600 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −35.7330 | −1.76688 | −0.883441 | − | 0.468542i | \(-0.844779\pi\) | ||||
−0.883441 | + | 0.468542i | \(0.844779\pi\) | |||||||
\(410\) | −1.66500 | + | 3.93473i | −0.0822283 | + | 0.194322i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.2132 | − | 15.7272i | 0.798766 | − | 0.774824i | ||||
\(413\) | −8.34506 | −0.410633 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 53.9798i | − | 2.64976i | ||||||
\(416\) | 8.18648 | + | 3.76176i | 0.401375 | + | 0.184436i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.59665 | − | 13.2260i | 0.273741 | − | 0.646906i | ||||
\(419\) | − | 35.1521i | − | 1.71729i | −0.512569 | − | 0.858646i | \(-0.671306\pi\) | ||
0.512569 | − | 0.858646i | \(-0.328694\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.7156i | − | 1.10709i | −0.832819 | − | 0.553546i | \(-0.813274\pi\) | ||
0.832819 | − | 0.553546i | \(-0.186726\pi\) | |||||||
\(422\) | 27.5514 | + | 11.6585i | 1.34118 | + | 0.567527i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.08362 | − | 2.79484i | −0.0526255 | − | 0.135730i | ||||
\(425\) | 62.6002i | 3.03656i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2367 | −0.495388 | ||||||||
\(428\) | 12.3461 | − | 11.9760i | 0.596772 | − | 0.578884i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.712028 | − | 0.301298i | −0.0343371 | − | 0.0145299i | ||||
\(431\) | −1.00587 | −0.0484511 | −0.0242256 | − | 0.999707i | \(-0.507712\pi\) | ||||
−0.0242256 | + | 0.999707i | \(0.507712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.8256 | −1.62555 | −0.812776 | − | 0.582576i | \(-0.802045\pi\) | ||||
−0.812776 | + | 0.582576i | \(0.802045\pi\) | |||||||
\(434\) | −3.29837 | − | 1.39572i | −0.158327 | − | 0.0669966i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.5899 | − | 27.7330i | 1.36921 | − | 1.32817i | ||||
\(437\) | −36.1222 | −1.72796 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9514i | 0.570411i | 0.958466 | + | 0.285206i | \(0.0920619\pi\) | ||||
−0.958466 | + | 0.285206i | \(0.907938\pi\) | |||||||
\(440\) | −19.1267 | + | 7.41586i | −0.911829 | + | 0.353537i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.1640 | + | 6.83986i | 0.768842 | + | 0.325339i | ||||
\(443\) | − | 17.6849i | − | 0.840234i | −0.907470 | − | 0.420117i | \(-0.861989\pi\) | ||
0.907470 | − | 0.420117i | \(-0.138011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 0.160352i | − | 0.00760141i | ||||||
\(446\) | −3.33027 | + | 7.87011i | −0.157693 | + | 0.372661i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.39286 | − | 5.90906i | −0.254789 | − | 0.279177i | ||||
\(449\) | − | 33.4546i | − | 1.57882i | −0.613867 | − | 0.789409i | \(-0.710387\pi\) | ||
0.613867 | − | 0.789409i | \(-0.289613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.68120 | −0.0791644 | ||||||||
\(452\) | −5.47484 | + | 5.31073i | −0.257515 | + | 0.249796i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.0624 | + | 26.1428i | −0.519185 | + | 1.22694i | ||||
\(455\) | −5.74974 | −0.269552 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.7127 | 1.62379 | 0.811896 | − | 0.583802i | \(-0.198436\pi\) | ||||
0.811896 | + | 0.583802i | \(0.198436\pi\) | |||||||
\(458\) | −10.2054 | + | 24.1174i | −0.476867 | + | 1.12693i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 35.9256 | + | 37.0357i | 1.67504 | + | 1.72680i | ||||
\(461\) | 9.30870 | 0.433549 | 0.216775 | − | 0.976222i | \(-0.430446\pi\) | ||||
0.216775 | + | 0.976222i | \(0.430446\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.56421i | − | 0.0726950i | −0.999339 | − | 0.0363475i | \(-0.988428\pi\) | ||
0.999339 | − | 0.0363475i | \(-0.0115723\pi\) | |||||||
\(464\) | −0.601526 | + | 19.7628i | −0.0279252 | + | 0.917464i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.43531 | + | 22.2976i | −0.437082 | + | 1.03292i | ||||
\(467\) | − | 2.47725i | − | 0.114633i | −0.998356 | − | 0.0573167i | \(-0.981746\pi\) | ||
0.998356 | − | 0.0573167i | \(-0.0182545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.655357i | 0.0302616i | ||||||||
\(470\) | −3.74004 | − | 1.58261i | −0.172515 | − | 0.0730006i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22.0071 | − | 8.53267i | 1.01296 | − | 0.392748i | ||||
\(473\) | − | 0.304229i | − | 0.0139885i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −40.6069 | −1.86317 | ||||||||
\(476\) | −10.8514 | − | 11.1867i | −0.497374 | − | 0.512743i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.15248 | + | 2.18029i | 0.235669 | + | 0.0997243i | ||||
\(479\) | −4.20750 | −0.192245 | −0.0961227 | − | 0.995369i | \(-0.530644\pi\) | ||||
−0.0961227 | + | 0.995369i | \(0.530644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.59045 | −0.346095 | ||||||||
\(482\) | 20.0214 | + | 8.47212i | 0.911949 | + | 0.385895i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.69754 | + | 9.99720i | 0.440797 | + | 0.454418i | ||||
\(485\) | 35.6324 | 1.61798 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 29.7159i | − | 1.34656i | −0.739389 | − | 0.673278i | \(-0.764886\pi\) | ||
0.739389 | − | 0.673278i | \(-0.235114\pi\) | |||||||
\(488\) | 26.9956 | − | 10.4668i | 1.22204 | − | 0.473811i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.70192 | + | 1.98963i | 0.212411 | + | 0.0898825i | ||||
\(491\) | 6.98629i | 0.315287i | 0.987496 | + | 0.157643i | \(0.0503896\pi\) | ||||
−0.987496 | + | 0.157643i | \(0.949610\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.5185i | 1.73479i | ||||||||
\(494\) | −4.43681 | + | 10.4851i | −0.199621 | + | 0.471746i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.1254 | + | 0.308189i | 0.454643 | + | 0.0138381i | ||||
\(497\) | 11.3675i | 0.509901i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.65859 | 0.432378 | 0.216189 | − | 0.976352i | \(-0.430637\pi\) | ||||
0.216189 | + | 0.976352i | \(0.430637\pi\) | |||||||
\(500\) | 15.2494 | + | 15.7206i | 0.681975 | + | 0.703048i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.25998 | − | 17.1568i | 0.324029 | − | 0.765747i | ||||
\(503\) | −33.8339 | −1.50858 | −0.754290 | − | 0.656542i | \(-0.772019\pi\) | ||||
−0.754290 | + | 0.656542i | \(0.772019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.9941 | −0.711728 | ||||||||
\(506\) | −7.91214 | + | 18.6980i | −0.351738 | + | 0.831229i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −22.9608 | + | 22.2726i | −1.01872 | + | 0.988185i | ||||
\(509\) | 12.8961 | 0.571611 | 0.285806 | − | 0.958288i | \(-0.407739\pi\) | ||||
0.285806 | + | 0.958288i | \(0.407739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.3835i | − | 0.636287i | ||||||
\(512\) | 20.2637 | + | 10.0690i | 0.895536 | + | 0.444989i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.8291 | + | 35.0442i | −0.654083 | + | 1.54573i | ||||
\(515\) | − | 40.7730i | − | 1.79667i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.59801i | − | 0.0702805i | ||||||
\(518\) | 6.20717 | + | 2.62659i | 0.272728 | + | 0.115406i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.1629 | − | 5.87901i | 0.664937 | − | 0.257811i | ||||
\(521\) | − | 15.4735i | − | 0.677905i | −0.940803 | − | 0.338953i | \(-0.889927\pi\) | ||
0.940803 | − | 0.338953i | \(-0.110073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.0632 | −0.877301 | −0.438651 | − | 0.898658i | \(-0.644543\pi\) | ||||
−0.438651 | + | 0.898658i | \(0.644543\pi\) | |||||||
\(524\) | 28.5446 | − | 27.6890i | 1.24698 | − | 1.20960i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.6154 | − | 4.49194i | −0.462852 | − | 0.195858i | ||||
\(527\) | 19.7348 | 0.859661 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 28.0670 | 1.22031 | ||||||||
\(530\) | −4.98309 | − | 2.10861i | −0.216451 | − | 0.0915923i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.25649 | − | 7.03899i | 0.314609 | − | 0.305179i | ||||
\(533\) | 1.33279 | 0.0577294 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 31.0481i | − | 1.34233i | ||||||
\(536\) | −0.670091 | − | 1.72827i | −0.0289435 | − | 0.0746500i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.00520 | + | 2.11797i | 0.215790 | + | 0.0913123i | ||||
\(539\) | 2.00899i | 0.0865334i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.5169i | 0.796103i | 0.917363 | + | 0.398052i | \(0.130313\pi\) | ||||
−0.917363 | + | 0.398052i | \(0.869687\pi\) | |||||||
\(542\) | −7.09320 | + | 16.7627i | −0.304679 | + | 0.720019i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 40.0550 | + | 18.4057i | 1.71734 | + | 0.789136i | ||||
\(545\) | − | 71.8982i | − | 3.07978i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.8132 | −1.06094 | −0.530468 | − | 0.847705i | \(-0.677984\pi\) | ||||
−0.530468 | + | 0.847705i | \(0.677984\pi\) | |||||||
\(548\) | −12.8279 | + | 12.4434i | −0.547979 | + | 0.531554i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.89446 | + | 21.0194i | −0.379261 | + | 0.896272i | ||||
\(551\) | −24.9858 | −1.06443 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.81177 | −0.162093 | ||||||||
\(554\) | 1.50136 | − | 3.54803i | 0.0637867 | − | 0.150741i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.67583 | + | 1.72762i | 0.0710711 | + | 0.0732672i | ||||
\(557\) | −19.4177 | −0.822756 | −0.411378 | − | 0.911465i | \(-0.634952\pi\) | ||||
−0.411378 | + | 0.911465i | \(0.634952\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.241181i | 0.0102009i | ||||||||
\(560\) | −14.4340 | − | 0.439332i | −0.609948 | − | 0.0185652i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.91176 | − | 11.6075i | 0.207190 | − | 0.489633i | ||||
\(563\) | 14.6696i | 0.618252i | 0.951021 | + | 0.309126i | \(0.100036\pi\) | ||||
−0.951021 | + | 0.309126i | \(0.899964\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.7682i | 0.579231i | ||||||||
\(566\) | −6.38284 | − | 2.70093i | −0.268291 | − | 0.113528i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.6230 | − | 29.9777i | −0.487692 | − | 1.25784i | ||||
\(569\) | − | 17.3133i | − | 0.725809i | −0.931826 | − | 0.362905i | \(-0.881785\pi\) | ||
0.931826 | − | 0.362905i | \(-0.118215\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7082 | 0.489975 | 0.244987 | − | 0.969526i | \(-0.421216\pi\) | ||||
0.244987 | + | 0.969526i | \(0.421216\pi\) | |||||||
\(572\) | 4.45559 | + | 4.59327i | 0.186298 | + | 0.192054i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.08990 | − | 0.461196i | −0.0454916 | − | 0.0192499i | ||||
\(575\) | 57.4071 | 2.39404 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.79465 | 0.199604 | 0.0998020 | − | 0.995007i | \(-0.468179\pi\) | ||||
0.0998020 | + | 0.995007i | \(0.468179\pi\) | |||||||
\(578\) | 56.9466 | + | 24.0972i | 2.36867 | + | 1.00231i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 24.8498 | + | 25.6177i | 1.03183 | + | 1.06372i | ||||
\(581\) | 14.9522 | 0.620320 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.12913i | − | 0.0881795i | ||||||
\(584\) | 14.7068 | + | 37.9313i | 0.608573 | + | 1.56961i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34.0432 | − | 14.4055i | −1.40631 | − | 0.595086i | ||||
\(587\) | − | 30.1643i | − | 1.24501i | −0.782615 | − | 0.622506i | \(-0.786114\pi\) | ||
0.782615 | − | 0.622506i | \(-0.213886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.8014i | 0.527471i | ||||||||
\(590\) | 16.6036 | − | 39.2378i | 0.683560 | − | 1.61539i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.0549 | − | 0.579979i | −0.783150 | − | 0.0238370i | ||||
\(593\) | 2.60974i | 0.107169i | 0.998563 | + | 0.0535847i | \(0.0170647\pi\) | ||||
−0.998563 | + | 0.0535847i | \(0.982935\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.1325 | −1.15332 | ||||||||
\(596\) | −17.6561 | − | 18.2016i | −0.723220 | − | 0.745568i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.27244 | − | 14.8231i | 0.256499 | − | 0.606160i | ||||
\(599\) | 27.6903 | 1.13139 | 0.565697 | − | 0.824613i | \(-0.308607\pi\) | ||||
0.565697 | + | 0.824613i | \(0.308607\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.3291 | 0.666079 | 0.333039 | − | 0.942913i | \(-0.391926\pi\) | ||||
0.333039 | + | 0.942913i | \(0.391926\pi\) | |||||||
\(602\) | 0.0834580 | − | 0.197228i | 0.00340150 | − | 0.00803843i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.1358 | + | 24.3824i | −1.02276 | + | 0.992105i | ||||
\(605\) | 25.1410 | 1.02213 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 12.9385i | − | 0.525159i | −0.964910 | − | 0.262580i | \(-0.915427\pi\) | ||
0.964910 | − | 0.262580i | \(-0.0845732\pi\) | |||||||
\(608\) | −11.9392 | + | 25.9825i | −0.484198 | + | 1.05373i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.3673 | − | 48.1321i | 0.824647 | − | 1.94881i | ||||
\(611\) | 1.26684i | 0.0512509i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 21.7992i | − | 0.880463i | −0.897884 | − | 0.440231i | \(-0.854896\pi\) | ||
0.897884 | − | 0.440231i | \(-0.145104\pi\) | |||||||
\(614\) | 30.5098 | + | 12.9103i | 1.23127 | + | 0.521019i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.05416 | − | 5.29800i | −0.0827644 | − | 0.213463i | ||||
\(617\) | 41.8226i | 1.68371i | 0.539700 | + | 0.841857i | \(0.318538\pi\) | ||||
−0.539700 | + | 0.841857i | \(0.681462\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.82763 | −0.194039 | −0.0970193 | − | 0.995282i | \(-0.530931\pi\) | ||||
−0.0970193 | + | 0.995282i | \(0.530931\pi\) | |||||||
\(620\) | 13.1251 | − | 12.7317i | 0.527117 | − | 0.511317i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 20.1005 | + | 8.50560i | 0.805955 | + | 0.341043i | ||||
\(623\) | 0.0444167 | 0.00177952 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.632276 | −0.0252911 | ||||||||
\(626\) | 40.6213 | + | 17.1891i | 1.62355 | + | 0.687014i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.9485 | + | 21.2906i | −0.875839 | + | 0.849586i | ||||
\(629\) | −37.1388 | −1.48082 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.3929i | − | 0.811830i | −0.913911 | − | 0.405915i | \(-0.866953\pi\) | ||
0.913911 | − | 0.405915i | \(-0.133047\pi\) | |||||||
\(632\) | 10.0522 | − | 3.89747i | 0.399855 | − | 0.155033i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −40.0453 | − | 16.9453i | −1.59040 | − | 0.672986i | ||||
\(635\) | 57.7420i | 2.29142i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.59265i | − | 0.0631032i | ||||||
\(638\) | −5.47285 | + | 12.9335i | −0.216672 | + | 0.512041i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 38.5137 | − | 13.5999i | 1.52239 | − | 0.537584i | ||||
\(641\) | 9.42755i | 0.372366i | 0.982515 | + | 0.186183i | \(0.0596117\pi\) | ||||
−0.982515 | + | 0.186183i | \(0.940388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.2077 | −1.07297 | −0.536484 | − | 0.843911i | \(-0.680248\pi\) | ||||
−0.536484 | + | 0.843911i | \(0.680248\pi\) | |||||||
\(644\) | −10.2587 | + | 9.95122i | −0.404250 | + | 0.392133i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.7085 | + | 51.3017i | −0.854110 | + | 2.01844i | ||||
\(647\) | −7.24081 | −0.284666 | −0.142333 | − | 0.989819i | \(-0.545460\pi\) | ||||
−0.142333 | + | 0.989819i | \(0.545460\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.7652 | 0.658090 | ||||||||
\(650\) | 7.05118 | − | 16.6634i | 0.276570 | − | 0.653592i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.4576 | + | 25.2134i | 0.957834 | + | 0.987432i | ||||
\(653\) | 30.0954 | 1.17772 | 0.588861 | − | 0.808234i | \(-0.299576\pi\) | ||||
0.588861 | + | 0.808234i | \(0.299576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 71.7842i | − | 2.80484i | ||||||
\(656\) | 3.34579 | + | 0.101837i | 0.130631 | + | 0.00397606i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.438377 | − | 1.03597i | 0.0170897 | − | 0.0403865i | ||||
\(659\) | − | 41.9316i | − | 1.63342i | −0.577045 | − | 0.816712i | \(-0.695794\pi\) | ||
0.577045 | − | 0.816712i | \(-0.304206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 0.735053i | − | 0.0285903i | −0.999898 | − | 0.0142951i | \(-0.995450\pi\) | ||
0.999898 | − | 0.0142951i | \(-0.00455044\pi\) | |||||||
\(662\) | −1.30404 | − | 0.551810i | −0.0506830 | − | 0.0214467i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −39.4310 | + | 15.2883i | −1.53022 | + | 0.593301i | ||||
\(665\) | − | 18.2487i | − | 0.707654i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.3232 | 1.36772 | ||||||||
\(668\) | −5.85268 | − | 6.03353i | −0.226447 | − | 0.233444i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.08143 | − | 1.30392i | −0.119046 | − | 0.0503749i | ||||
\(671\) | 20.5654 | 0.793920 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.6142 | −0.833165 | −0.416582 | − | 0.909098i | \(-0.636772\pi\) | ||||
−0.416582 | + | 0.909098i | \(0.636772\pi\) | |||||||
\(674\) | −36.7042 | − | 15.5315i | −1.41379 | − | 0.598252i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.5707 | + | 15.0210i | 0.560413 | + | 0.577730i | ||||
\(677\) | −0.631879 | −0.0242851 | −0.0121425 | − | 0.999926i | \(-0.503865\pi\) | ||||
−0.0121425 | + | 0.999926i | \(0.503865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.87000i | 0.378776i | ||||||||
\(680\) | 74.1894 | − | 28.7650i | 2.84504 | − | 1.10309i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.62640 | + | 2.80399i | 0.253738 | + | 0.107370i | ||||
\(683\) | 22.4241i | 0.858033i | 0.903297 | + | 0.429017i | \(0.141140\pi\) | ||||
−0.903297 | + | 0.429017i | \(0.858860\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.2596i | 1.23258i | ||||||||
\(686\) | −0.551119 | + | 1.30241i | −0.0210418 | + | 0.0497262i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0184284 | + | 0.605454i | −0.000702576 | + | 0.0230827i | ||||
\(689\) | 1.68789i | 0.0643035i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.69349 | −0.102465 | −0.0512325 | − | 0.998687i | \(-0.516315\pi\) | ||||
−0.0512325 | + | 0.998687i | \(0.516315\pi\) | |||||||
\(692\) | 25.0759 | + | 25.8507i | 0.953241 | + | 0.982697i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.8293 | − | 25.5918i | 0.411074 | − | 0.971453i | ||||
\(695\) | 4.34462 | 0.164801 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.52109 | 0.247004 | ||||||||
\(698\) | 6.18768 | − | 14.6228i | 0.234207 | − | 0.553480i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.5324 | + | 11.1867i | −0.435882 | + | 0.422817i | ||||
\(701\) | −28.4555 | −1.07475 | −0.537375 | − | 0.843344i | \(-0.680584\pi\) | ||||
−0.537375 | + | 0.843344i | \(0.680584\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24.0908i | − | 0.908601i | ||||||
\(704\) | 10.8342 | + | 11.8713i | 0.408330 | + | 0.447415i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.7486 | − | 41.9436i | 0.667978 | − | 1.57857i | ||||
\(707\) | − | 4.43029i | − | 0.166618i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 13.4255i | − | 0.504204i | −0.967701 | − | 0.252102i | \(-0.918878\pi\) | ||
0.967701 | − | 0.252102i | \(-0.0811218\pi\) | |||||||
\(710\) | −53.4489 | − | 22.6171i | −2.00590 | − | 0.848806i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.117133 | + | 0.0454153i | −0.00438976 | + | 0.00170201i | ||||
\(713\) | − | 18.0977i | − | 0.677763i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.5512 | 0.431990 | ||||||||
\(716\) | 1.27204 | − | 1.23391i | 0.0475384 | − | 0.0461135i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 26.2980 | + | 11.1281i | 0.981433 | + | 0.415297i | ||||
\(719\) | −49.4437 | −1.84394 | −0.921969 | − | 0.387264i | \(-0.873420\pi\) | ||||
−0.921969 | + | 0.387264i | \(0.873420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.2939 | 0.420608 | ||||||||
\(722\) | −8.53208 | − | 3.61039i | −0.317531 | − | 0.134365i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.1641 | − | 11.7995i | 0.452075 | − | 0.438524i | ||||
\(725\) | 39.7086 | 1.47474 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.65644i | 0.209786i | 0.994484 | + | 0.104893i | \(0.0334500\pi\) | ||||
−0.994484 | + | 0.104893i | \(0.966550\pi\) | |||||||
\(728\) | 1.62846 | + | 4.20005i | 0.0603546 | + | 0.155664i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 67.6298 | + | 28.6178i | 2.50309 | + | 1.05919i | ||||
\(731\) | 1.18006i | 0.0436460i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 42.3705i | − | 1.56499i | −0.622656 | − | 0.782495i | \(-0.713946\pi\) | ||
0.622656 | − | 0.782495i | \(-0.286054\pi\) | |||||||
\(734\) | −0.786120 | + | 1.85776i | −0.0290162 | + | 0.0685713i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.8788 | − | 36.7322i | 0.622160 | − | 1.35397i | ||||
\(737\) | − | 1.31661i | − | 0.0484979i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −41.5942 | −1.53007 | −0.765034 | − | 0.643989i | \(-0.777278\pi\) | ||||
−0.765034 | + | 0.643989i | \(0.777278\pi\) | |||||||
\(740\) | −24.7000 | + | 23.9597i | −0.907991 | + | 0.880774i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.584076 | − | 1.38029i | 0.0214421 | − | 0.0506721i | ||||
\(743\) | −16.5821 | −0.608338 | −0.304169 | − | 0.952618i | \(-0.598379\pi\) | ||||
−0.304169 | + | 0.952618i | \(0.598379\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45.7736 | −1.67702 | ||||||||
\(746\) | −5.40516 | + | 12.7735i | −0.197897 | + | 0.467671i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 21.8004 | + | 22.4741i | 0.797102 | + | 0.821733i | ||||
\(749\) | 8.60018 | 0.314244 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.26395i | 0.155594i | 0.996969 | + | 0.0777968i | \(0.0247886\pi\) | ||||
−0.996969 | + | 0.0777968i | \(0.975211\pi\) | |||||||
\(752\) | −0.0967982 | + | 3.18025i | −0.00352987 | + | 0.115972i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.33866 | − | 10.2531i | 0.158005 | − | 0.373398i | ||||
\(755\) | 63.2118i | 2.30051i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 19.5706i | − | 0.711305i | −0.934618 | − | 0.355653i | \(-0.884259\pi\) | ||
0.934618 | − | 0.355653i | \(-0.115741\pi\) | |||||||
\(758\) | 22.8414 | + | 9.66542i | 0.829636 | + | 0.351064i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18.6589 | + | 48.1244i | 0.676831 | + | 1.74566i | ||||
\(761\) | 22.1256i | 0.802053i | 0.916066 | + | 0.401027i | \(0.131347\pi\) | ||||
−0.916066 | + | 0.401027i | \(0.868653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.9155 | 0.720988 | ||||||||
\(764\) | −28.7005 | − | 29.5873i | −1.03835 | − | 1.07043i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.8407 | + | 4.58727i | 0.391689 | + | 0.165745i | ||||
\(767\) | −13.2908 | −0.479902 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.1961 | −0.584046 | −0.292023 | − | 0.956411i | \(-0.594328\pi\) | ||||
−0.292023 | + | 0.956411i | \(0.594328\pi\) | |||||||
\(770\) | −9.44611 | − | 3.99716i | −0.340414 | − | 0.144048i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.4794 | + | 26.2668i | 0.917025 | + | 0.945362i | ||||
\(773\) | −2.34825 | −0.0844608 | −0.0422304 | − | 0.999108i | \(-0.513446\pi\) | ||||
−0.0422304 | + | 0.999108i | \(0.513446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 20.3445i | − | 0.730797i | ||||||
\(776\) | −10.0919 | − | 26.0286i | −0.362278 | − | 0.934373i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.4590 | + | 4.84891i | 0.410824 | + | 0.173842i | ||||
\(779\) | 4.23003i | 0.151557i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 22.8372i | − | 0.817179i | ||||||
\(782\) | 30.6900 | − | 72.5267i | 1.09747 | − | 2.59355i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.121693 | − | 3.99815i | 0.00434618 | − | 0.142791i | ||||
\(785\) | 55.1962i | 1.97004i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9012 | 0.388586 | 0.194293 | − | 0.980943i | \(-0.437759\pi\) | ||||
0.194293 | + | 0.980943i | \(0.437759\pi\) | |||||||
\(788\) | 14.8417 | + | 15.3003i | 0.528713 | + | 0.545050i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.58403 | − | 17.9226i | 0.269828 | − | 0.637659i | ||||
\(791\) | −3.81372 | −0.135600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.3035 | −0.578954 | ||||||||
\(794\) | −17.3875 | + | 41.0903i | −0.617060 | + | 1.45824i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −37.5120 | + | 36.3876i | −1.32958 | + | 1.28972i | ||||
\(797\) | 5.08600 | 0.180155 | 0.0900776 | − | 0.995935i | \(-0.471288\pi\) | ||||
0.0900776 | + | 0.995935i | \(0.471288\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.19844i | 0.219285i | ||||||||
\(800\) | 18.9743 | − | 41.2925i | 0.670844 | − | 1.45991i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −4.95982 | + | 11.7211i | −0.175137 | + | 0.413886i | ||||
\(803\) | 28.8963i | 1.01973i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.7987i | 0.909285i | ||||||||
\(806\) | −5.25315 | − | 2.22289i | −0.185034 | − | 0.0782981i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.52989 | + | 11.6833i | 0.159361 | + | 0.411017i | ||||
\(809\) | − | 26.8140i | − | 0.942729i | −0.881938 | − | 0.471365i | \(-0.843762\pi\) | ||
0.881938 | − | 0.471365i | \(-0.156238\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.8383 | 1.36380 | 0.681899 | − | 0.731446i | \(-0.261154\pi\) | ||||
0.681899 | + | 0.731446i | \(0.261154\pi\) | |||||||
\(812\) | −7.09597 | + | 6.88328i | −0.249020 | + | 0.241556i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.4702 | − | 5.27680i | −0.437079 | − | 0.184952i | ||||
\(815\) | 63.4068 | 2.22104 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.765467 | −0.0267803 | ||||||||
\(818\) | 46.5389 | + | 19.6931i | 1.62720 | + | 0.688554i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.33701 | − | 4.20701i | 0.151455 | − | 0.146915i | ||||
\(821\) | −29.3421 | −1.02405 | −0.512023 | − | 0.858972i | \(-0.671104\pi\) | ||||
−0.512023 | + | 0.858972i | \(0.671104\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.9770i | 0.835784i | 0.908497 | + | 0.417892i | \(0.137231\pi\) | ||||
−0.908497 | + | 0.417892i | \(0.862769\pi\) | |||||||
\(824\) | −29.7837 | + | 11.5478i | −1.03757 | + | 0.402288i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8687 | + | 4.59912i | 0.378169 | + | 0.160024i | ||||
\(827\) | − | 4.92468i | − | 0.171248i | −0.996328 | − | 0.0856239i | \(-0.972712\pi\) | ||
0.996328 | − | 0.0856239i | \(-0.0272883\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.00324i | 0.277964i | 0.990295 | + | 0.138982i | \(0.0443830\pi\) | ||||
−0.990295 | + | 0.138982i | \(0.955617\pi\) | |||||||
\(830\) | −29.7493 | + | 70.3038i | −1.03261 | + | 2.44028i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.58895 | − | 9.41108i | −0.297768 | − | 0.326270i | ||||
\(833\) | − | 7.79257i | − | 0.269996i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.1732 | −0.525089 | ||||||||
\(836\) | −14.5782 | + | 14.1413i | −0.504199 | + | 0.489086i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19.3730 | + | 45.7824i | −0.669229 | + | 1.58153i | ||||
\(839\) | −31.4595 | −1.08610 | −0.543051 | − | 0.839700i | \(-0.682731\pi\) | ||||
−0.543051 | + | 0.839700i | \(0.682731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.56691 | −0.157479 | ||||||||
\(842\) | −12.5190 | + | 29.5850i | −0.431434 | + | 1.01957i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −29.4580 | − | 30.3683i | −1.01399 | − | 1.04532i | ||||
\(845\) | 37.7749 | 1.29950 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.96395i | 0.239284i | ||||||||
\(848\) | −0.128970 | + | 4.23723i | −0.00442885 | + | 0.145507i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34.5002 | − | 81.5311i | 1.18335 | − | 2.79649i | ||||
\(851\) | 34.0578i | 1.16749i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.31213i | 0.0449263i | 0.999748 | + | 0.0224632i | \(0.00715085\pi\) | ||||
−0.999748 | + | 0.0224632i | \(0.992849\pi\) | |||||||
\(854\) | 13.3324 | + | 5.64164i | 0.456224 | + | 0.193053i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.6799 | + | 8.79352i | −0.775183 | + | 0.300556i | ||||
\(857\) | − | 24.2200i | − | 0.827341i | −0.910427 | − | 0.413670i | \(-0.864247\pi\) | ||
0.910427 | − | 0.413670i | \(-0.135753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.49401 | 0.289812 | 0.144906 | − | 0.989445i | \(-0.453712\pi\) | ||||
0.144906 | + | 0.989445i | \(0.453712\pi\) | |||||||
\(860\) | 0.761301 | + | 0.784825i | 0.0259601 | + | 0.0267623i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.31006 | + | 0.554355i | 0.0446207 | + | 0.0188814i | ||||
\(863\) | 30.8759 | 1.05103 | 0.525513 | − | 0.850785i | \(-0.323873\pi\) | ||||
0.525513 | + | 0.850785i | \(0.323873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 65.0096 | 2.21039 | ||||||||
\(866\) | 44.0547 | + | 18.6419i | 1.49704 | + | 0.633478i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.52662 | + | 3.63559i | 0.119701 | + | 0.123400i | ||||
\(869\) | 7.65782 | 0.259774 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.04376i | 0.0353663i | ||||||||
\(872\) | −52.5200 | + | 20.3632i | −1.77855 | + | 0.689585i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 47.0459 | + | 19.9076i | 1.59135 | + | 0.673386i | ||||
\(875\) | 10.9508i | 0.370206i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 33.4689i | − | 1.13016i | −0.825035 | − | 0.565082i | \(-0.808845\pi\) | ||
0.825035 | − | 0.565082i | \(-0.191155\pi\) | |||||||
\(878\) | 6.58667 | − | 15.5657i | 0.222289 | − | 0.525316i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28.9978 | + | 0.882615i | 0.977515 | + | 0.0297529i | ||||
\(881\) | 33.7535i | 1.13719i | 0.822619 | + | 0.568593i | \(0.192512\pi\) | ||||
−0.822619 | + | 0.568593i | \(0.807488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.59496 | 0.0536746 | 0.0268373 | − | 0.999640i | \(-0.491456\pi\) | ||||
0.0268373 | + | 0.999640i | \(0.491456\pi\) | |||||||
\(884\) | −17.2825 | − | 17.8166i | −0.581275 | − | 0.599236i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.74649 | + | 23.0329i | −0.327440 | + | 0.773807i | ||||
\(887\) | 17.9639 | 0.603167 | 0.301584 | − | 0.953440i | \(-0.402485\pi\) | ||||
0.301584 | + | 0.953440i | \(0.402485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.9943 | −0.536430 | ||||||||
\(890\) | −0.0883730 | + | 0.208844i | −0.00296227 | + | 0.00700045i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.67474 | − | 8.41473i | 0.290452 | − | 0.281746i | ||||
\(893\) | −4.02074 | −0.134549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.19894i | − | 0.106929i | ||||||
\(896\) | 3.76711 | + | 10.6681i | 0.125850 | + | 0.356397i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.4375 | + | 43.5715i | −0.615266 | + | 1.45400i | ||||
\(899\) | − | 12.5182i | − | 0.417505i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.25855i | 0.275132i | ||||||||
\(902\) | 2.18960 | + | 0.926539i | 0.0729058 | + | 0.0308504i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.0573 | − | 3.89945i | 0.334502 | − | 0.129694i | ||||
\(905\) | − | 30.5903i | − | 1.01686i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.9653 | 1.75868 | 0.879342 | − | 0.476190i | \(-0.157983\pi\) | ||||
0.879342 | + | 0.476190i | \(0.157983\pi\) | |||||||
\(908\) | 28.8156 | − | 27.9518i | 0.956278 | − | 0.927614i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.48851 | + | 3.16879i | 0.248242 | + | 0.105045i | ||||
\(911\) | 52.6435 | 1.74416 | 0.872079 | − | 0.489365i | \(-0.162771\pi\) | ||||
0.872079 | + | 0.489365i | \(0.162771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.0388 | −0.994138 | ||||||||
\(914\) | −45.2101 | − | 19.1308i | −1.49542 | − | 0.632792i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.5832 | − | 25.7864i | 0.878333 | − | 0.852006i | ||||
\(917\) | 19.8839 | 0.656623 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.5794i | 1.20664i | 0.797498 | + | 0.603322i | \(0.206157\pi\) | ||||
−0.797498 | + | 0.603322i | \(0.793843\pi\) | |||||||
\(920\) | −26.3787 | − | 68.0349i | −0.869680 | − | 2.24304i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.1237 | − | 5.13020i | −0.399274 | − | 0.168954i | ||||
\(923\) | 18.1044i | 0.595915i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.2862i | 1.25884i | ||||||||
\(926\) | −0.862067 | + | 2.03724i | −0.0283293 | + | 0.0669479i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.6751 | − | 25.4077i | 0.383253 | − | 0.834049i | ||||
\(929\) | − | 24.8413i | − | 0.815018i | −0.913201 | − | 0.407509i | \(-0.866398\pi\) | ||
0.913201 | − | 0.407509i | \(-0.133602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.05480 | 0.165664 | ||||||||
\(932\) | 24.5773 | − | 23.8406i | 0.805055 | − | 0.780924i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.36526 | + | 3.22639i | −0.0446727 | + | 0.105571i | ||||
\(935\) | 56.5180 | 1.84833 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.904448 | 0.0295470 | 0.0147735 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147735 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(938\) | 0.361180 | − | 0.853543i | 0.0117929 | − | 0.0278692i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.99885 | + | 4.12242i | 0.130428 | + | 0.134459i | ||||
\(941\) | −8.11337 | −0.264488 | −0.132244 | − | 0.991217i | \(-0.542218\pi\) | ||||
−0.132244 | + | 0.991217i | \(0.542218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.98012i | − | 0.194740i | ||||||
\(944\) | −33.3648 | − | 1.01553i | −1.08593 | − | 0.0330528i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.167667 | + | 0.396231i | −0.00545131 | + | 0.0128826i | ||||
\(947\) | − | 34.2396i | − | 1.11264i | −0.830969 | − | 0.556319i | \(-0.812213\pi\) | ||
0.830969 | − | 0.556319i | \(-0.187787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 22.9078i | − | 0.743620i | ||||||
\(950\) | 52.8867 | + | 22.3792i | 1.71587 | + | 0.726078i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.96776 | + | 20.5501i | 0.258236 | + | 0.666033i | ||||
\(953\) | − | 5.47739i | − | 0.177430i | −0.996057 | − | 0.0887151i | \(-0.971724\pi\) | ||
0.996057 | − | 0.0887151i | \(-0.0282761\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −74.4065 | −2.40774 | ||||||||
\(956\) | −5.50903 | − | 5.67926i | −0.178175 | − | 0.183680i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.47988 | + | 2.31883i | 0.177047 | + | 0.0749181i | ||||
\(959\) | −8.93576 | −0.288551 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.5864 | 0.793109 | ||||||||
\(962\) | 9.88587 | + | 4.18324i | 0.318733 | + | 0.134873i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.4069 | − | 22.0683i | −0.689468 | − | 0.710773i | ||||
\(965\) | 66.0559 | 2.12641 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.0597i | 1.44902i | 0.689262 | + | 0.724512i | \(0.257935\pi\) | ||||
−0.689262 | + | 0.724512i | \(0.742065\pi\) | |||||||
\(968\) | −7.12051 | − | 18.3649i | −0.228862 | − | 0.590272i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −46.4079 | − | 19.6377i | −1.49007 | − | 0.630528i | ||||
\(971\) | 28.4013i | 0.911442i | 0.890123 | + | 0.455721i | \(0.150618\pi\) | ||||
−0.890123 | + | 0.455721i | \(0.849382\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.20344i | 0.0385805i | ||||||||
\(974\) | −16.3770 | + | 38.7022i | −0.524753 | + | 1.24010i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −40.9278 | − | 1.24573i | −1.31007 | − | 0.0398750i | ||||
\(977\) | 4.06448i | 0.130034i | 0.997884 | + | 0.0650171i | \(0.0207102\pi\) | ||||
−0.997884 | + | 0.0650171i | \(0.979290\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0892328 | −0.00285189 | ||||||||
\(980\) | −5.02729 | − | 5.18263i | −0.160591 | − | 0.165553i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.85028 | − | 9.09900i | 0.122867 | − | 0.290361i | ||||
\(983\) | 13.0487 | 0.416189 | 0.208094 | − | 0.978109i | \(-0.433274\pi\) | ||||
0.208094 | + | 0.978109i | \(0.433274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.4773 | 1.22599 | ||||||||
\(986\) | 21.2283 | − | 50.1669i | 0.676047 | − | 1.59764i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.5571 | − | 11.2107i | 0.367679 | − | 0.356658i | ||||
\(989\) | 1.08216 | 0.0344108 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.598647i | 0.0190166i | 0.999955 | + | 0.00950832i | \(0.00302664\pi\) | ||||
−0.999955 | + | 0.00950832i | \(0.996973\pi\) | |||||||
\(992\) | −13.0175 | − | 5.98168i | −0.413307 | − | 0.189918i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.26484 | − | 14.8051i | 0.198709 | − | 0.469589i | ||||
\(995\) | 94.3354i | 2.99063i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.04553i | 0.128123i | 0.997946 | + | 0.0640616i | \(0.0204054\pi\) | ||||
−0.997946 | + | 0.0640616i | \(0.979595\pi\) | |||||||
\(998\) | −12.5794 | − | 5.32304i | −0.398195 | − | 0.168498i | ||||
\(999\) | 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 | 1512.2.j.c.323.5 | ✓ | 32 | |
3.2 | odd | 2 | inner | 1512.2.j.c.323.28 | yes | 32 | |
4.3 | odd | 2 | 6048.2.j.c.5615.31 | 32 | |||
8.3 | odd | 2 | inner | 1512.2.j.c.323.27 | yes | 32 | |
8.5 | even | 2 | 6048.2.j.c.5615.1 | 32 | |||
12.11 | even | 2 | 6048.2.j.c.5615.2 | 32 | |||
24.5 | odd | 2 | 6048.2.j.c.5615.32 | 32 | |||
24.11 | even | 2 | inner | 1512.2.j.c.323.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.c.323.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
1512.2.j.c.323.6 | yes | 32 | 24.11 | even | 2 | inner | |
1512.2.j.c.323.27 | yes | 32 | 8.3 | odd | 2 | inner | |
1512.2.j.c.323.28 | yes | 32 | 3.2 | odd | 2 | inner | |
6048.2.j.c.5615.1 | 32 | 8.5 | even | 2 | |||
6048.2.j.c.5615.2 | 32 | 12.11 | even | 2 | |||
6048.2.j.c.5615.31 | 32 | 4.3 | odd | 2 | |||
6048.2.j.c.5615.32 | 32 | 24.5 | odd | 2 |