Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,3,Mod(41,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 17]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.41");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.u (of order \(18\), degree \(6\), 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: | \(5.88557371018\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 41.6 | ||
Character | \(\chi\) | \(=\) | 216.41 |
Dual form | 216.3.u.a.137.6 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{17}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.45288 | + | 2.62471i | −0.484295 | + | 0.874905i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.32440 | − | 5.15362i | 0.864879 | − | 1.03072i | −0.134329 | − | 0.990937i | \(-0.542888\pi\) |
0.999208 | − | 0.0397864i | \(-0.0126677\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.87984 | − | 2.50406i | −0.982835 | − | 0.357723i | −0.199893 | − | 0.979818i | \(-0.564059\pi\) |
−0.782942 | + | 0.622095i | \(0.786282\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.77825 | − | 7.62682i | −0.530917 | − | 0.847424i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.56973 | − | 4.25424i | −0.324521 | − | 0.386749i | 0.578975 | − | 0.815345i | \(-0.303453\pi\) |
−0.903496 | + | 0.428596i | \(0.859008\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.53915 | − | 14.4002i | 0.195319 | − | 1.10771i | −0.716645 | − | 0.697439i | \(-0.754323\pi\) |
0.911964 | − | 0.410271i | \(-0.134566\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.24392 | + | 18.8379i | 0.482928 | + | 1.25586i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.8419 | + | 6.83690i | 0.696580 | + | 0.402170i | 0.806072 | − | 0.591817i | \(-0.201589\pi\) |
−0.109493 | + | 0.993988i | \(0.534923\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.69299 | − | 6.39644i | −0.194368 | − | 0.336655i | 0.752325 | − | 0.658792i | \(-0.228932\pi\) |
−0.946693 | + | 0.322137i | \(0.895599\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.5681 | − | 14.4195i | 0.788955 | − | 0.686643i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.92992 | − | 24.5347i | −0.388257 | − | 1.06673i | −0.967786 | − | 0.251776i | \(-0.918985\pi\) |
0.579528 | − | 0.814952i | \(-0.303237\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.51814 | − | 19.9524i | −0.140726 | − | 0.798095i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.9605 | − | 1.46066i | 0.998536 | − | 0.0540985i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.4508 | + | 1.84276i | −0.360374 | + | 0.0635436i | −0.350904 | − | 0.936412i | \(-0.614126\pi\) |
−0.00947000 | + | 0.999955i | \(0.503014\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.9860 | − | 21.1052i | 1.87052 | − | 0.680813i | 0.902072 | − | 0.431585i | \(-0.142046\pi\) |
0.968445 | − | 0.249228i | \(-0.0801767\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.3526 | − | 3.18861i | 0.495533 | − | 0.0966244i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −42.6561 | + | 24.6275i | −1.21875 | + | 0.703643i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 22.3400 | − | 38.6941i | 0.603785 | − | 1.04579i | −0.388458 | − | 0.921467i | \(-0.626992\pi\) |
0.992242 | − | 0.124319i | \(-0.0396746\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 34.1074 | + | 27.5864i | 0.874548 | + | 0.707344i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −62.6507 | − | 11.0470i | −1.52807 | − | 0.269439i | −0.654468 | − | 0.756089i | \(-0.727107\pi\) |
−0.873597 | + | 0.486650i | \(0.838219\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −29.5293 | + | 24.7781i | −0.686729 | + | 0.576234i | −0.917964 | − | 0.396664i | \(-0.870168\pi\) |
0.231235 | + | 0.972898i | \(0.425723\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −59.9687 | − | 8.35611i | −1.33264 | − | 0.185691i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.9363 | + | 32.7947i | −0.253964 | + | 0.697759i | 0.745546 | + | 0.666454i | \(0.232189\pi\) |
−0.999510 | + | 0.0313055i | \(0.990034\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.52574 | + | 2.95845i | 0.0719539 | + | 0.0603765i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −35.1497 | + | 21.1483i | −0.689211 | + | 0.414672i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 88.5126i | 1.67005i | 0.550213 | + | 0.835025i | \(0.314547\pi\) | ||||
−0.550213 | + | 0.835025i | \(0.685453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −37.3617 | −0.679303 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 22.1543 | − | 0.399744i | 0.388672 | − | 0.00701305i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.4934 | + | 12.5056i | −0.177854 | + | 0.211959i | −0.847605 | − | 0.530627i | \(-0.821956\pi\) |
0.669751 | + | 0.742586i | \(0.266401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.2822 | + | 8.47404i | 0.381676 | + | 0.138919i | 0.525731 | − | 0.850651i | \(-0.323792\pi\) |
−0.144055 | + | 0.989570i | \(0.546014\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.7756 | + | 64.4363i | 0.218661 | + | 1.02280i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −63.2329 | − | 75.3581i | −0.972814 | − | 1.15936i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2794 | + | 69.6399i | −0.183274 | + | 1.03940i | 0.744878 | + | 0.667201i | \(0.232508\pi\) |
−0.928152 | + | 0.372200i | \(0.878603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 77.3708 | + | 12.2077i | 1.12132 | + | 0.176923i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.0730 | − | 9.27975i | −0.226380 | − | 0.130701i | 0.382521 | − | 0.923947i | \(-0.375056\pi\) |
−0.608901 | + | 0.793246i | \(0.708389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.35792 | − | 7.54814i | −0.0596976 | − | 0.103399i | 0.834632 | − | 0.550808i | \(-0.185680\pi\) |
−0.894330 | + | 0.447409i | \(0.852347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 57.4807 | + | 19.7544i | 0.766410 | + | 0.263392i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.9063 | + | 38.2073i | 0.180602 | + | 0.496199i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −24.7889 | − | 140.585i | −0.313783 | − | 1.77955i | −0.578962 | − | 0.815354i | \(-0.696542\pi\) |
0.265179 | − | 0.964199i | \(-0.414569\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −35.3366 | + | 72.8857i | −0.436255 | + | 0.899823i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 132.285 | − | 23.3254i | 1.59380 | − | 0.281029i | 0.694872 | − | 0.719133i | \(-0.255461\pi\) |
0.898924 | + | 0.438104i | \(0.144350\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 86.4436 | − | 31.4629i | 1.01698 | − | 0.370152i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3471 | − | 30.1078i | 0.118933 | − | 0.346067i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 19.5901 | − | 11.3103i | 0.220113 | − | 0.127082i | −0.385889 | − | 0.922545i | \(-0.626105\pi\) |
0.606003 | + | 0.795463i | \(0.292772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −53.5279 | + | 92.7131i | −0.588219 | + | 1.01883i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28.8519 | + | 182.860i | −0.310236 | + | 1.96624i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −48.9347 | − | 8.62851i | −0.515102 | − | 0.0908264i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 124.652 | − | 104.596i | 1.28507 | − | 1.07830i | 0.292550 | − | 0.956250i | \(-0.405496\pi\) |
0.992523 | − | 0.122054i | \(-0.0389482\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.3892 | + | 47.5535i | −0.155447 | + | 0.480339i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −44.5503 | + | 122.401i | −0.441092 | + | 1.21189i | 0.497683 | + | 0.867359i | \(0.334184\pi\) |
−0.938775 | + | 0.344531i | \(0.888038\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −58.6095 | − | 49.1792i | −0.569024 | − | 0.477468i | 0.312298 | − | 0.949984i | \(-0.398901\pi\) |
−0.881322 | + | 0.472516i | \(0.843346\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.66578 | − | 147.741i | −0.0253884 | − | 1.40706i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 62.4824i | − | 0.583948i | −0.956426 | − | 0.291974i | \(-0.905688\pi\) | ||
0.956426 | − | 0.291974i | \(-0.0943120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −85.3182 | −0.782736 | −0.391368 | − | 0.920234i | \(-0.627998\pi\) | ||||
−0.391368 | + | 0.920234i | \(0.627998\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 69.1034 | + | 114.854i | 0.622553 | + | 1.03472i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −96.6078 | + | 115.133i | −0.854936 | + | 1.01887i | 0.144632 | + | 0.989486i | \(0.453800\pi\) |
−0.999568 | + | 0.0293876i | \(0.990644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −165.059 | − | 60.0766i | −1.43530 | − | 0.522405i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −121.961 | + | 49.4423i | −1.04240 | + | 0.422584i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −64.3501 | − | 76.6894i | −0.540757 | − | 0.644449i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.6558 | − | 88.7887i | 0.129387 | − | 0.733791i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 120.019 | − | 148.390i | 0.975768 | − | 1.20642i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 27.6154 | + | 15.9438i | 0.220923 | + | 0.127550i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 100.956 | + | 174.860i | 0.794925 | + | 1.37685i | 0.922886 | + | 0.385072i | \(0.125823\pi\) |
−0.127961 | + | 0.991779i | \(0.540843\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.1326 | − | 113.506i | −0.171571 | − | 0.879890i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −34.1892 | − | 93.9341i | −0.260987 | − | 0.717055i | −0.999102 | − | 0.0423797i | \(-0.986506\pi\) |
0.738115 | − | 0.674675i | \(-0.235716\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.39011 | + | 53.2539i | 0.0706023 | + | 0.400406i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 109.060 | − | 145.260i | 0.807852 | − | 1.07600i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 264.589 | − | 46.6542i | 1.93131 | − | 0.340542i | 0.931574 | − | 0.363551i | \(-0.118436\pi\) |
0.999735 | + | 0.0230094i | \(0.00732478\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.8860 | − | 5.41806i | 0.107093 | − | 0.0389788i | −0.287918 | − | 0.957655i | \(-0.592963\pi\) |
0.395011 | + | 0.918676i | \(0.370741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −68.7346 | − | 78.9763i | −0.487480 | − | 0.560115i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −70.3261 | + | 40.6028i | −0.491791 | + | 0.283936i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35.6967 | + | 61.8284i | −0.246184 | + | 0.426403i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.8876 | + | 4.95578i | −0.0876705 | + | 0.0337128i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −126.776 | − | 22.3541i | −0.850848 | − | 0.150027i | −0.268814 | − | 0.963192i | \(-0.586632\pi\) |
−0.582034 | + | 0.813165i | \(0.697743\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 155.738 | − | 130.679i | 1.03138 | − | 0.865427i | 0.0403614 | − | 0.999185i | \(-0.487149\pi\) |
0.991014 | + | 0.133758i | \(0.0427046\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.43960 | − | 122.984i | −0.0290170 | − | 0.803817i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 141.987 | − | 390.105i | 0.916043 | − | 2.51681i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 180.484 | + | 151.444i | 1.14958 | + | 0.964611i | 0.999710 | − | 0.0240954i | \(-0.00767056\pi\) |
0.149868 | + | 0.988706i | \(0.452115\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −232.320 | − | 128.599i | −1.46113 | − | 0.808796i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 191.156i | 1.18731i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −70.3599 | −0.431656 | −0.215828 | − | 0.976431i | \(-0.569245\pi\) | ||||
−0.215828 | + | 0.976431i | \(0.569245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 54.2822 | − | 98.0637i | 0.328983 | − | 0.594326i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 34.9973 | − | 41.7082i | 0.209565 | − | 0.249750i | −0.651015 | − | 0.759064i | \(-0.725657\pi\) |
0.860580 | + | 0.509315i | \(0.170101\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −42.1111 | − | 15.3272i | −0.249178 | − | 0.0906935i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −31.1384 | + | 58.7295i | −0.182096 | + | 0.343447i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 174.881 | + | 208.415i | 1.01087 | + | 1.20471i | 0.978715 | + | 0.205226i | \(0.0657929\pi\) |
0.0321559 | + | 0.999483i | \(0.489763\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.7576 | + | 146.079i | −0.147186 | + | 0.834736i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.5778 | − | 45.7113i | −0.0993096 | − | 0.258256i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 37.9838 | + | 21.9300i | 0.212200 | + | 0.122514i | 0.602333 | − | 0.798245i | \(-0.294238\pi\) |
−0.390133 | + | 0.920758i | \(0.627571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 139.053 | + | 240.847i | 0.768249 | + | 1.33065i | 0.938511 | + | 0.345248i | \(0.112205\pi\) |
−0.170262 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −56.0684 | + | 48.7974i | −0.306384 | + | 0.266653i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −102.807 | − | 282.460i | −0.555715 | − | 1.52681i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.1864 | − | 74.7840i | −0.0705157 | − | 0.399915i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.141 | − | 57.4614i | −1.00075 | − | 0.304029i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 212.171 | − | 37.4115i | 1.11084 | − | 0.195872i | 0.412026 | − | 0.911172i | \(-0.364821\pi\) |
0.698817 | + | 0.715301i | \(0.253710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 63.8460 | − | 23.2380i | 0.330808 | − | 0.120404i | −0.171276 | − | 0.985223i | \(-0.554789\pi\) |
0.502084 | + | 0.864819i | \(0.332567\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 289.664 | − | 56.4818i | 1.48545 | − | 0.289650i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 100.437 | − | 57.9874i | 0.509833 | − | 0.294352i | −0.222932 | − | 0.974834i | \(-0.571563\pi\) |
0.732765 | + | 0.680482i | \(0.238229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1274 | − | 33.1296i | 0.0961175 | − | 0.166480i | −0.813957 | − | 0.580925i | \(-0.802691\pi\) |
0.910074 | + | 0.414445i | \(0.136024\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −164.944 | − | 133.409i | −0.820618 | − | 0.663724i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 76.5145 | + | 13.4916i | 0.376919 | + | 0.0664609i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −327.858 | + | 275.106i | −1.59931 | + | 1.34198i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −144.453 | + | 185.340i | −0.697839 | + | 0.895362i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.0290 | + | 38.5444i | −0.0671245 | + | 0.184423i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 53.1484 | + | 44.5968i | 0.251888 | + | 0.211359i | 0.759985 | − | 0.649941i | \(-0.225206\pi\) |
−0.508097 | + | 0.861300i | \(0.669651\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 47.7089 | − | 28.7046i | 0.223985 | − | 0.134763i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 259.333i | 1.20620i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −451.783 | −2.08195 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.1433 | − | 0.471719i | 0.119376 | − | 0.00215397i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 128.521 | − | 153.165i | 0.581543 | − | 0.693056i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −115.775 | − | 42.1388i | −0.519173 | − | 0.188963i | 0.0691248 | − | 0.997608i | \(-0.477979\pi\) |
−0.588297 | + | 0.808645i | \(0.700202\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −135.362 | + | 122.170i | −0.601611 | + | 0.542976i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −44.9299 | − | 53.5454i | −0.197929 | − | 0.235883i | 0.657946 | − | 0.753065i | \(-0.271425\pi\) |
−0.855875 | + | 0.517182i | \(0.826981\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 62.3612 | − | 353.668i | 0.272320 | − | 1.54440i | −0.475030 | − | 0.879970i | \(-0.657563\pi\) |
0.747350 | − | 0.664431i | \(-0.231326\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −120.488 | − | 19.0107i | −0.521592 | − | 0.0822974i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 272.110 | + | 157.103i | 1.16785 | + | 0.674260i | 0.953173 | − | 0.302425i | \(-0.0977960\pi\) |
0.214679 | + | 0.976685i | \(0.431129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 117.394 | + | 203.332i | 0.499549 | + | 0.865244i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 405.010 | + | 139.190i | 1.70890 | + | 0.587298i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 64.4222 | + | 176.999i | 0.269549 | + | 0.740580i | 0.998434 | + | 0.0559437i | \(0.0178167\pi\) |
−0.728885 | + | 0.684636i | \(0.759961\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6689 | − | 134.233i | −0.0982114 | − | 0.556984i | −0.993716 | − | 0.111932i | \(-0.964296\pi\) |
0.895505 | − | 0.445052i | \(-0.146815\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −139.964 | − | 198.643i | −0.575984 | − | 0.817461i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 30.4934 | − | 5.37681i | 0.124463 | − | 0.0219462i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −101.487 | + | 36.9383i | −0.410879 | + | 0.149548i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −130.972 | + | 381.100i | −0.525994 | + | 1.53052i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −191.634 | + | 110.640i | −0.763483 | + | 0.440797i | −0.830545 | − | 0.556952i | \(-0.811971\pi\) |
0.0670621 | + | 0.997749i | \(0.478637\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −72.4993 | + | 125.573i | −0.286559 | + | 0.496334i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −43.0115 | + | 272.602i | −0.168672 | + | 1.06903i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −81.1382 | − | 14.3069i | −0.315713 | − | 0.0556687i | 0.0135464 | − | 0.999908i | \(-0.495688\pi\) |
−0.329259 | + | 0.944240i | \(0.606799\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −250.588 | + | 210.268i | −0.967521 | + | 0.811847i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 63.9912 | + | 70.9014i | 0.245177 | + | 0.271653i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 37.7946 | − | 103.840i | 0.143706 | − | 0.394828i | −0.846869 | − | 0.531801i | \(-0.821515\pi\) |
0.990575 | + | 0.136973i | \(0.0437375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 456.160 | + | 382.764i | 1.72136 | + | 1.44439i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.22428 | + | 67.8510i | 0.00458531 | + | 0.254124i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 95.6029i | − | 0.355401i | −0.984085 | − | 0.177701i | \(-0.943134\pi\) | ||
0.984085 | − | 0.177701i | \(-0.0568659\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −118.872 | −0.438644 | −0.219322 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219322 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −165.575 | − | 275.197i | −0.606504 | − | 1.00805i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −72.3234 | + | 86.1917i | −0.262994 | + | 0.313424i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −48.0056 | − | 17.4726i | −0.173305 | − | 0.0630780i | 0.253910 | − | 0.967228i | \(-0.418283\pi\) |
−0.427216 | + | 0.904150i | \(0.640505\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −438.037 | − | 341.403i | −1.57003 | − | 1.22367i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −124.350 | − | 148.195i | −0.442527 | − | 0.527383i | 0.497966 | − | 0.867196i | \(-0.334080\pi\) |
−0.940493 | + | 0.339814i | \(0.889636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −83.3308 | + | 472.592i | −0.294455 | + | 1.66994i | 0.374953 | + | 0.927044i | \(0.377659\pi\) |
−0.669409 | + | 0.742894i | \(0.733452\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 93.7439 | − | 115.903i | 0.328926 | − | 0.406679i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 403.364 | + | 232.883i | 1.40545 | + | 0.811437i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −51.0137 | − | 88.3583i | −0.176518 | − | 0.305738i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 93.4283 | + | 479.142i | 0.321059 | + | 1.64653i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −89.4582 | − | 245.784i | −0.305318 | − | 0.838855i | −0.993553 | − | 0.113367i | \(-0.963836\pi\) |
0.688235 | − | 0.725488i | \(-0.258386\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.0712 | + | 108.158i | 0.0646481 | + | 0.366637i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −102.456 | − | 109.482i | −0.344969 | − | 0.368627i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −375.980 | + | 66.2955i | −1.25746 | + | 0.221724i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 265.203 | − | 96.5260i | 0.881073 | − | 0.320684i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −256.541 | − | 294.766i | −0.846670 | − | 0.972826i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 144.354 | − | 83.3426i | 0.473291 | − | 0.273254i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 195.394 | − | 338.433i | 0.636463 | − | 1.10239i | −0.349740 | − | 0.936847i | \(-0.613730\pi\) |
0.986203 | − | 0.165540i | \(-0.0529367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 214.234 | − | 82.3814i | 0.693314 | − | 0.266607i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33.3803 | + | 5.88584i | 0.107332 | + | 0.0189255i | 0.227056 | − | 0.973882i | \(-0.427090\pi\) |
−0.119724 | + | 0.992807i | \(0.538201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 142.198 | − | 119.319i | 0.454308 | − | 0.381209i | −0.386724 | − | 0.922196i | \(-0.626393\pi\) |
0.841031 | + | 0.540986i | \(0.181949\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 391.651 | + | 207.654i | 1.24334 | + | 0.659219i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −70.8562 | + | 194.676i | −0.223521 | + | 0.614119i | −0.999869 | − | 0.0161853i | \(-0.994848\pi\) |
0.776348 | + | 0.630305i | \(0.217070\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 45.1463 | + | 37.8822i | 0.141524 | + | 0.118753i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 163.998 | + | 90.7797i | 0.510899 | + | 0.282803i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 100.994i | − | 0.312676i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −296.252 | −0.911544 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 123.958 | − | 223.936i | 0.379075 | − | 0.684819i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 164.240 | − | 195.733i | 0.499209 | − | 0.594934i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 230.402 | + | 83.8595i | 0.696079 | + | 0.253352i | 0.665736 | − | 0.746188i | \(-0.268118\pi\) |
0.0303430 | + | 0.999540i | \(0.490340\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −401.859 | + | 14.5067i | −1.20678 | + | 0.0435636i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 305.796 | + | 364.434i | 0.912825 | + | 1.08786i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 46.2391 | − | 262.235i | 0.137208 | − | 0.778146i | −0.836088 | − | 0.548595i | \(-0.815163\pi\) |
0.973297 | − | 0.229551i | \(-0.0737259\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −161.830 | − | 420.842i | −0.477376 | − | 1.24142i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −296.781 | − | 171.347i | −0.870326 | − | 0.502483i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 162.525 | + | 281.502i | 0.473835 | + | 0.820706i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 397.496 | − | 345.949i | 1.15216 | − | 1.00275i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 137.584 | + | 378.008i | 0.396495 | + | 1.08936i | 0.963980 | + | 0.265976i | \(0.0856943\pi\) |
−0.567485 | + | 0.823384i | \(0.692084\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.3889 | + | 155.330i | 0.0784781 | + | 0.445071i | 0.998574 | + | 0.0533790i | \(0.0169991\pi\) |
−0.920096 | + | 0.391692i | \(0.871890\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 47.4228 | − | 391.946i | 0.135108 | − | 1.11665i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −478.960 | + | 84.4536i | −1.35683 | + | 0.239245i | −0.804287 | − | 0.594241i | \(-0.797453\pi\) |
−0.552540 | + | 0.833486i | \(0.686341\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −117.330 | + | 42.7047i | −0.330508 | + | 0.120295i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 294.781 | − | 57.4797i | 0.825718 | − | 0.161007i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.72147 | + | 1.57124i | −0.00758069 | + | 0.00437671i | −0.503786 | − | 0.863829i | \(-0.668060\pi\) |
0.496205 | + | 0.868205i | \(0.334726\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 153.224 | − | 265.391i | 0.424442 | − | 0.735156i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 210.299 | + | 170.092i | 0.579336 | + | 0.468573i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −57.7456 | − | 10.1821i | −0.158207 | − | 0.0278962i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 489.134 | − | 410.432i | 1.33279 | − | 1.11834i | 0.349374 | − | 0.936983i | \(-0.386394\pi\) |
0.983417 | − | 0.181361i | \(-0.0580503\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 215.107 | + | 530.610i | 0.582946 | + | 1.43797i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 221.641 | − | 608.953i | 0.597414 | − | 1.64138i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −366.702 | − | 307.699i | −0.983115 | − | 0.824931i | 0.00144181 | − | 0.999999i | \(-0.499541\pi\) |
−0.984556 | + | 0.175068i | \(0.943986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −81.9698 | + | 49.3181i | −0.218586 | + | 0.131515i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 155.173i | 0.411601i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −47.1034 | −0.124283 | −0.0621417 | − | 0.998067i | \(-0.519793\pi\) | ||||
−0.0621417 | + | 0.998067i | \(0.519793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −605.635 | + | 10.9278i | −1.58959 | + | 0.0286820i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −219.042 | + | 261.044i | −0.571912 | + | 0.681578i | −0.972022 | − | 0.234889i | \(-0.924527\pi\) |
0.400111 | + | 0.916467i | \(0.368972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 257.042 | + | 93.5558i | 0.667643 | + | 0.243002i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 330.076 | + | 106.819i | 0.852910 | + | 0.276018i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −50.7155 | − | 60.4404i | −0.130374 | − | 0.155374i | 0.696908 | − | 0.717161i | \(-0.254559\pi\) |
−0.827282 | + | 0.561787i | \(0.810114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.9948 | − | 351.590i | 0.158554 | − | 0.899207i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 296.223 | + | 46.7385i | 0.753749 | + | 0.118928i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −831.717 | − | 480.192i | −2.10561 | − | 1.21568i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −40.7252 | − | 70.5382i | −0.102582 | − | 0.177678i | 0.810165 | − | 0.586201i | \(-0.199377\pi\) |
−0.912748 | + | 0.408523i | \(0.866044\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −153.419 | − | 52.7255i | −0.384509 | − | 0.132144i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −151.072 | − | 415.066i | −0.376737 | − | 1.03508i | −0.972700 | − | 0.232066i | \(-0.925452\pi\) |
0.595963 | − | 0.803012i | \(-0.296771\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −156.684 | − | 888.601i | −0.388795 | − | 2.20497i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 222.815 | + | 497.298i | 0.550161 | + | 1.22790i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −244.362 | + | 43.0876i | −0.600398 | + | 0.105866i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −739.504 | + | 269.157i | −1.80808 | + | 0.658087i | −0.810721 | + | 0.585433i | \(0.800924\pi\) |
−0.997357 | + | 0.0726533i | \(0.976853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −261.964 | + | 762.255i | −0.637382 | + | 1.85463i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 103.508 | − | 59.7602i | 0.250624 | − | 0.144698i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 451.843 | − | 782.615i | 1.08878 | − | 1.88582i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.40677 | + | 46.9433i | −0.0177620 | + | 0.112574i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −439.072 | − | 77.4203i | −1.04791 | − | 0.184774i | −0.376921 | − | 0.926245i | \(-0.623017\pi\) |
−0.670984 | + | 0.741472i | \(0.734128\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0380 | + | 18.4921i | −0.0523468 | + | 0.0439242i | −0.668586 | − | 0.743635i | \(-0.733100\pi\) |
0.616239 | + | 0.787559i | \(0.288656\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 307.154 | − | 65.6654i | 0.726132 | − | 0.155237i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 94.7510 | − | 260.326i | 0.222944 | − | 0.612532i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −138.959 | − | 116.600i | −0.325430 | − | 0.273068i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.39501 | − | 243.577i | −0.0102448 | − | 0.567779i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 196.699i | 0.456379i | 0.973617 | + | 0.228189i | \(0.0732805\pi\) | ||||
−0.973617 | + | 0.228189i | \(0.926719\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −501.062 | −1.15719 | −0.578593 | − | 0.815616i | \(-0.696398\pi\) | ||||
−0.578593 | + | 0.815616i | \(0.696398\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −110.419 | − | 183.523i | −0.253836 | − | 0.421892i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −123.957 | + | 147.726i | −0.283654 | + | 0.338046i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −235.846 | − | 85.8407i | −0.537234 | − | 0.195537i | 0.0591318 | − | 0.998250i | \(-0.481167\pi\) |
−0.596365 | + | 0.802713i | \(0.703389\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.71666 | − | 41.0264i | 0.0129629 | − | 0.0930303i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 322.537 | + | 384.385i | 0.728074 | + | 0.867685i | 0.995389 | − | 0.0959243i | \(-0.0305807\pi\) |
−0.267314 | + | 0.963609i | \(0.586136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.4261 | − | 149.870i | 0.0593846 | − | 0.336787i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 242.865 | − | 300.274i | 0.543321 | − | 0.671753i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 329.004 | + | 189.950i | 0.732748 | + | 0.423052i | 0.819427 | − | 0.573184i | \(-0.194292\pi\) |
−0.0866787 | + | 0.996236i | \(0.527625\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 176.650 | + | 305.966i | 0.391684 | + | 0.678417i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 116.727 | + | 598.629i | 0.257676 | + | 1.32148i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 246.332 | + | 676.791i | 0.541388 | + | 1.48745i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 72.5062 | + | 411.203i | 0.158657 | + | 0.899788i | 0.955366 | + | 0.295425i | \(0.0954612\pi\) |
−0.796709 | + | 0.604363i | \(0.793428\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 329.248 | + | 167.029i | 0.717316 | + | 0.363898i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 256.854 | − | 45.2902i | 0.557166 | − | 0.0982435i | 0.112028 | − | 0.993705i | \(-0.464265\pi\) |
0.445139 | + | 0.895462i | \(0.353154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 601.134 | − | 218.795i | 1.29835 | − | 0.472559i | 0.401888 | − | 0.915689i | \(-0.368354\pi\) |
0.896458 | + | 0.443130i | \(0.146132\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 817.624 | + | 939.452i | 1.75833 | + | 2.02033i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −135.572 | + | 78.2725i | −0.290304 | + | 0.167607i | −0.638079 | − | 0.769971i | \(-0.720271\pi\) |
0.347775 | + | 0.937578i | \(0.386937\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 258.863 | − | 448.363i | 0.551946 | − | 0.955998i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −659.719 | + | 253.688i | −1.40068 | + | 0.538615i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 210.824 | + | 37.1739i | 0.445716 | + | 0.0785918i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −114.632 | + | 96.1874i | −0.241330 | + | 0.202500i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 675.069 | − | 422.935i | 1.41524 | − | 0.886657i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −53.8684 | + | 148.002i | −0.112460 | + | 0.308982i | −0.983136 | − | 0.182875i | \(-0.941460\pi\) |
0.870676 | + | 0.491857i | \(0.163682\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −500.479 | − | 419.951i | −1.04050 | − | 0.873080i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −501.730 | − | 277.728i | −1.03878 | − | 0.575006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 1094.72i | − | 2.25716i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 511.013 | 1.04931 | 0.524654 | − | 0.851316i | \(-0.324195\pi\) | ||||
0.524654 | + | 0.851316i | \(0.324195\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 102.225 | − | 184.675i | 0.209049 | − | 0.377658i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 152.561 | − | 181.816i | 0.310716 | − | 0.370296i | −0.587975 | − | 0.808879i | \(-0.700075\pi\) |
0.898691 | + | 0.438582i | \(0.144519\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −136.356 | − | 49.6295i | −0.276584 | − | 0.100668i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 178.523 | + | 284.951i | 0.360654 | + | 0.575658i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 87.3426 | + | 104.091i | 0.175740 | + | 0.209438i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 57.8365 | − | 328.007i | 0.115905 | − | 0.657328i | −0.870394 | − | 0.492357i | \(-0.836136\pi\) |
0.986298 | − | 0.164972i | \(-0.0527533\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 58.6250 | + | 152.455i | 0.117016 | + | 0.304302i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −853.503 | − | 492.770i | −1.69682 | − | 0.979662i | −0.948739 | − | 0.316060i | \(-0.897640\pi\) |
−0.748086 | − | 0.663602i | \(-0.769027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 438.154 | + | 758.906i | 0.867632 | + | 1.50278i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 101.412 | − | 88.2611i | 0.200024 | − | 0.174085i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 198.478 | + | 545.315i | 0.389938 | + | 1.07135i | 0.967029 | + | 0.254666i | \(0.0819654\pi\) |
−0.577091 | + | 0.816680i | \(0.695812\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0808 | + | 62.8425i | 0.0216846 | + | 0.122980i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −108.908 | − | 167.057i | −0.212296 | − | 0.325647i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −506.901 | + | 89.3804i | −0.984274 | + | 0.173554i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 182.126 | − | 66.2884i | 0.352275 | − | 0.128217i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −801.110 | + | 156.209i | −1.54356 | + | 0.300981i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −256.933 | + | 148.340i | −0.493154 | + | 0.284722i | −0.725882 | − | 0.687819i | \(-0.758568\pi\) |
0.232728 | + | 0.972542i | \(0.425235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.93376 | − | 5.08142i | 0.00560948 | − | 0.00971590i | −0.863207 | − | 0.504850i | \(-0.831548\pi\) |
0.868817 | + | 0.495134i | \(0.164881\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −345.992 | − | 279.842i | −0.659033 | − | 0.533033i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 830.956 | + | 146.520i | 1.57677 | + | 0.278027i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −116.973 | + | 98.1519i | −0.221121 | + | 0.185542i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 145.518 | + | 20.2766i | 0.274045 | + | 0.0381857i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −318.159 | + | 874.134i | −0.596921 | + | 1.64003i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −322.010 | − | 270.199i | −0.601888 | − | 0.505044i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −112.746 | + | 67.8350i | −0.209955 | + | 0.126322i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 25.5602i | − | 0.0474215i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −177.850 | −0.328744 | −0.164372 | − | 0.986398i | \(-0.552560\pi\) | ||||
−0.164372 | + | 0.986398i | \(0.552560\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −834.183 | + | 15.0517i | −1.53625 | + | 0.0277195i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −368.950 | + | 439.697i | −0.676972 | + | 0.806784i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 382.051 | + | 139.055i | 0.698447 | + | 0.254214i | 0.666748 | − | 0.745284i | \(-0.267686\pi\) |
0.0316993 | + | 0.999497i | \(0.489908\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −46.6184 | − | 218.060i | −0.0849152 | − | 0.397196i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.3819 | + | 60.0428i | 0.0914372 | + | 0.108971i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −181.489 | + | 1029.27i | −0.328189 | + | 1.86125i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 890.745 | + | 140.543i | 1.60495 | + | 0.253231i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 237.957 | + | 137.385i | 0.427212 | + | 0.246651i | 0.698158 | − | 0.715944i | \(-0.254003\pi\) |
−0.270946 | + | 0.962594i | \(0.587337\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 281.830 | + | 488.144i | 0.504169 | + | 0.873246i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 215.445 | + | 74.0419i | 0.384038 | + | 0.131982i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −255.595 | − | 702.241i | −0.453987 | − | 1.24732i | −0.929895 | − | 0.367825i | \(-0.880103\pi\) |
0.475908 | − | 0.879495i | \(-0.342120\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 175.579 | + | 995.759i | 0.310760 | + | 1.76240i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 425.620 | − | 412.957i | 0.750653 | − | 0.728319i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −690.640 | + | 121.778i | −1.21378 | + | 0.214022i | −0.743646 | − | 0.668574i | \(-0.766905\pi\) |
−0.470133 | + | 0.882596i | \(0.655794\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −647.093 | + | 235.522i | −1.13326 | + | 0.412474i | −0.839476 | − | 0.543397i | \(-0.817138\pi\) |
−0.293786 | + | 0.955871i | \(0.594915\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −210.066 | + | 611.243i | −0.366607 | + | 1.06674i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −458.110 | + | 264.490i | −0.796713 | + | 0.459982i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 117.684 | − | 203.835i | 0.203959 | − | 0.353267i | −0.745842 | − | 0.666123i | \(-0.767953\pi\) |
0.949800 | + | 0.312856i | \(0.101286\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.7677 | + | 201.340i | −0.0548664 | + | 0.347737i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −968.509 | − | 170.774i | −1.66697 | − | 0.293932i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 376.554 | − | 315.966i | 0.645890 | − | 0.541966i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −272.599 | + | 842.346i | −0.465982 | + | 1.43991i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −62.8426 | + | 172.659i | −0.107057 | + | 0.294137i | −0.981641 | − | 0.190737i | \(-0.938912\pi\) |
0.874584 | + | 0.484874i | \(0.161135\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −349.140 | − | 292.963i | −0.592767 | − | 0.497390i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.27679 | + | 347.868i | 0.0106206 | + | 0.588609i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 124.761i | − | 0.210389i | −0.994452 | − | 0.105195i | \(-0.966453\pi\) | ||
0.994452 | − | 0.105195i | \(-0.0335466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −673.503 | −1.13194 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 59.1658 | + | 98.3374i | 0.0991052 | + | 0.164719i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −149.073 | + | 177.659i | −0.248870 | + | 0.296592i | −0.875988 | − | 0.482332i | \(-0.839790\pi\) |
0.627118 | + | 0.778924i | \(0.284234\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 403.490 | + | 146.858i | 0.671365 | + | 0.244357i | 0.655135 | − | 0.755512i | \(-0.272612\pi\) |
0.0162293 | + | 0.999868i | \(0.494834\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 589.805 | − | 239.104i | 0.978117 | − | 0.396524i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −389.881 | − | 464.642i | −0.644431 | − | 0.768003i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −54.3580 | + | 308.280i | −0.0895519 | + | 0.507874i | 0.906729 | + | 0.421713i | \(0.138571\pi\) |
−0.996281 | + | 0.0861611i | \(0.972540\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −146.578 | + | 181.227i | −0.240687 | + | 0.297581i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 441.943 | + | 255.156i | 0.723311 | + | 0.417604i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −515.576 | − | 893.004i | −0.841071 | − | 1.45678i | −0.888990 | − | 0.457926i | \(-0.848593\pi\) |
0.0479199 | − | 0.998851i | \(-0.484741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −245.734 | − | 1260.23i | −0.399567 | − | 2.04916i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 115.102 | + | 316.240i | 0.186551 | + | 0.512544i | 0.997348 | − | 0.0727832i | \(-0.0231881\pi\) |
−0.810797 | + | 0.585328i | \(0.800966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 148.838 | + | 844.101i | 0.240449 | + | 1.36365i | 0.830829 | + | 0.556527i | \(0.187867\pi\) |
−0.590381 | + | 0.807125i | \(0.701022\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −276.592 | − | 648.425i | −0.445397 | − | 1.04416i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −163.098 | + | 28.7586i | −0.261795 | + | 0.0461615i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 677.546 | − | 246.607i | 1.08407 | − | 0.394571i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −80.7856 | − | 92.8228i | −0.128845 | − | 0.148043i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 529.095 | − | 305.473i | 0.841168 | − | 0.485649i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 611.855 | − | 1059.76i | 0.969659 | − | 1.67950i | 0.273120 | − | 0.961980i | \(-0.411945\pi\) |
0.696539 | − | 0.717519i | \(-0.254722\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −194.272 | + | 74.7053i | −0.306907 | + | 0.118018i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1337.73 | + | 235.879i | 2.10667 | + | 0.371462i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51.5547 | − | 43.2595i | 0.0809335 | − | 0.0679113i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.02588 | + | 166.927i | 0.00943018 | + | 0.261231i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −298.440 | + | 819.958i | −0.465585 | + | 1.27918i | 0.455643 | + | 0.890163i | \(0.349409\pi\) |
−0.921228 | + | 0.389022i | \(0.872813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.3105 | + | 37.1809i | 0.0689121 | + | 0.0578241i | 0.676593 | − | 0.736357i | \(-0.263456\pi\) |
−0.607681 | + | 0.794181i | \(0.707900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −680.675 | − | 376.781i | −1.05531 | − | 0.584157i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 193.571i | 0.299183i | 0.988748 | + | 0.149592i | \(0.0477959\pi\) | ||||
−0.988748 | + | 0.149592i | \(0.952204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 90.6604 | 0.139692 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 656.389 | − | 1185.80i | 1.00828 | − | 1.82151i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 640.303 | − | 763.083i | 0.980556 | − | 1.16858i | −0.00512976 | − | 0.999987i | \(-0.501633\pi\) |
0.985686 | − | 0.168594i | \(-0.0539227\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −631.948 | − | 230.010i | −0.964807 | − | 0.351161i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.7450 | + | 69.3040i | −0.0559285 | + | 0.105486i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −113.438 | − | 135.191i | −0.172137 | − | 0.205145i | 0.673078 | − | 0.739572i | \(-0.264972\pi\) |
−0.845215 | + | 0.534427i | \(0.820528\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −72.9433 | + | 413.682i | −0.110353 | + | 0.625843i | 0.878594 | + | 0.477570i | \(0.158482\pi\) |
−0.988947 | + | 0.148273i | \(0.952629\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 215.289 | + | 559.863i | 0.324720 | + | 0.844439i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 315.057 | + | 181.898i | 0.473770 | + | 0.273531i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 138.537 | + | 239.953i | 0.207701 | + | 0.359749i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 278.811 | − | 242.655i | 0.416758 | − | 0.362713i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −47.0608 | − | 129.298i | −0.0701353 | − | 0.192695i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.47264 | − | 19.6943i | −0.00515994 | − | 0.0292635i | 0.982119 | − | 0.188261i | \(-0.0602850\pi\) |
−0.987279 | + | 0.158997i | \(0.949174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −123.994 | − | 532.786i | −0.183695 | − | 0.789313i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 847.445 | − | 149.427i | 1.25176 | − | 0.220720i | 0.491814 | − | 0.870700i | \(-0.336334\pi\) |
0.759951 | + | 0.649980i | \(0.225223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1119.50 | + | 407.465i | −1.64875 | + | 0.600095i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 205.819 | − | 40.1329i | 0.302231 | − | 0.0589323i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 912.242 | − | 526.683i | 1.33564 | − | 0.771132i | 0.349482 | − | 0.936943i | \(-0.386358\pi\) |
0.986157 | + | 0.165812i | \(0.0530244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 903.752 | − | 1565.34i | 1.31935 | − | 2.28517i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 837.673 | + | 677.519i | 1.21932 | + | 0.986199i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1274.60 | + | 224.747i | 1.84993 | + | 0.326192i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −535.800 | + | 449.589i | −0.775398 | + | 0.650636i | −0.942085 | − | 0.335374i | \(-0.891137\pi\) |
0.166687 | + | 0.986010i | \(0.446693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 224.952 | − | 288.625i | 0.324607 | − | 0.416487i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 36.4503 | − | 100.146i | 0.0524465 | − | 0.144096i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −666.373 | − | 559.153i | −0.956059 | − | 0.802228i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −807.693 | + | 485.958i | −1.15550 | + | 0.695219i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 501.304i | − | 0.715128i | −0.933889 | − | 0.357564i | \(-0.883607\pi\) | ||
0.933889 | − | 0.357564i | \(-0.116393\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −330.006 | −0.469425 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −704.249 | + | 12.7072i | −0.998935 | + | 0.0180244i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 612.998 | − | 730.543i | 0.867041 | − | 1.03330i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 604.269 | + | 219.936i | 0.852284 | + | 0.310206i | 0.730971 | − | 0.682408i | \(-0.239067\pi\) |
0.121313 | + | 0.992614i | \(0.461290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −953.766 | + | 860.809i | −1.34144 | + | 1.21070i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1035.62 | − | 1234.21i | −1.45248 | − | 1.73100i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −94.8668 | + | 538.017i | −0.132681 | + | 0.752471i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −558.169 | − | 88.0687i | −0.778478 | − | 0.122829i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −62.7071 | − | 36.2040i | −0.0872143 | − | 0.0503532i | 0.455759 | − | 0.890103i | \(-0.349368\pi\) |
−0.542973 | + | 0.839750i | \(0.682701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 280.076 | + | 485.106i | 0.388455 | + | 0.672824i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 386.712 | + | 132.901i | 0.534871 | + | 0.183819i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 73.5351 | + | 202.036i | 0.101428 | + | 0.278670i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 81.4433 | + | 461.888i | 0.112027 | + | 0.635334i | 0.988180 | + | 0.153301i | \(0.0489905\pi\) |
−0.876153 | + | 0.482033i | \(0.839898\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 724.733 | − | 78.7602i | 0.994147 | − | 0.108039i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −519.087 | + | 91.5291i | −0.710106 | + | 0.125211i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 607.808 | − | 221.224i | 0.829207 | − | 0.301807i | 0.107673 | − | 0.994186i | \(-0.465660\pi\) |
0.721533 | + | 0.692380i | \(0.243438\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30.1908 | + | 87.8483i | −0.0410759 | + | 0.119522i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 340.099 | − | 196.356i | 0.461464 | − | 0.266426i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −326.379 | + | 565.305i | −0.441650 | + | 0.764960i | −0.997812 | − | 0.0661137i | \(-0.978940\pi\) |
0.556162 | + | 0.831074i | \(0.312273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 50.4967 | − | 320.042i | 0.0681467 | − | 0.431906i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 509.113 | + | 89.7704i | 0.685213 | + | 0.120822i | 0.505408 | − | 0.862881i | \(-0.331342\pi\) |
0.179805 | + | 0.983702i | \(0.442453\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −663.436 | + | 556.689i | −0.890518 | + | 0.747233i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −809.990 | − | 897.460i | −1.08432 | − | 1.20142i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −156.460 | + | 429.869i | −0.208891 | + | 0.573924i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1039.45 | + | 872.204i | 1.38409 | + | 1.16139i | 0.967671 | + | 0.252217i | \(0.0811598\pi\) |
0.416420 | + | 0.909172i | \(0.363285\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.9761 | − | 663.732i | −0.0159045 | − | 0.881450i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1367.72i | − | 1.81155i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1412.28 | −1.86562 | −0.932812 | − | 0.360365i | \(-0.882652\pi\) | ||||
−0.932812 | + | 0.360365i | \(0.882652\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −224.259 | − | 372.733i | −0.295466 | − | 0.491084i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 405.626 | − | 483.406i | 0.533017 | − | 0.635225i | −0.430590 | − | 0.902548i | \(-0.641695\pi\) |
0.963607 | + | 0.267323i | \(0.0861390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 586.976 | + | 213.642i | 0.769300 | + | 0.280002i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −653.011 | − | 508.952i | −0.853609 | − | 0.665297i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 153.439 | + | 182.861i | 0.200050 | + | 0.238411i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 66.3741 | − | 376.426i | 0.0863122 | − | 0.489501i | −0.910753 | − | 0.412951i | \(-0.864498\pi\) |
0.997066 | − | 0.0765505i | \(-0.0243907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 155.436 | − | 192.178i | 0.201603 | − | 0.249259i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −430.599 | − | 248.606i | −0.557049 | − | 0.321612i | 0.194911 | − | 0.980821i | \(-0.437558\pi\) |
−0.751960 | + | 0.659208i | \(0.770891\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −625.102 | − | 1082.71i | −0.806583 | − | 1.39704i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −187.819 | − | 963.218i | −0.241723 | − | 1.23966i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 160.707 | + | 441.538i | 0.206299 | + | 0.566801i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.8980 | + | 101.505i | 0.0229168 | + | 0.129968i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −279.068 | + | 64.9469i | −0.356408 | + | 0.0829462i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1560.97 | − | 275.241i | 1.98849 | − | 0.350625i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −883.966 | + | 321.737i | −1.12321 | + | 0.408815i | −0.835822 | − | 0.549000i | \(-0.815009\pi\) |
−0.287387 | + | 0.957815i | \(0.592786\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 217.638 | + | 250.067i | 0.275841 | + | 0.316942i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 952.945 | − | 550.183i | 1.20473 | − | 0.695554i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 181.145 | − | 313.753i | 0.228430 | − | 0.395653i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1667.39 | + | 641.178i | −2.09735 | + | 0.806513i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −61.1087 | − | 10.7751i | −0.0766734 | − | 0.0135196i | 0.135180 | − | 0.990821i | \(-0.456839\pi\) |
−0.211853 | + | 0.977301i | \(0.567950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −365.562 | + | 306.743i | −0.457524 | + | 0.383908i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −179.868 | − | 95.3663i | −0.224555 | − | 0.119059i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.5550 | + | 45.4845i | −0.0206165 | + | 0.0566432i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 985.146 | + | 826.635i | 1.22378 | + | 1.02688i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 250.930 | + | 138.900i | 0.310942 | + | 0.172119i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 276.515i | 0.341799i | 0.985288 | + | 0.170899i | \(0.0546673\pi\) | ||||
−0.985288 | + | 0.170899i | \(0.945333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 273.208 | 0.336878 | 0.168439 | − | 0.985712i | \(-0.446127\pi\) | ||||
0.168439 | + | 0.985712i | \(0.446127\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 172.708 | − | 312.006i | 0.212433 | − | 0.383771i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −304.264 | + | 362.608i | −0.373330 | + | 0.444918i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 267.543 | + | 97.3776i | 0.327470 | + | 0.119189i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 962.876 | − | 34.7588i | 1.17567 | − | 0.0424406i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 157.600 | + | 187.821i | 0.191961 | + | 0.228771i | 0.853437 | − | 0.521196i | \(-0.174514\pi\) |
−0.661476 | + | 0.749967i | \(0.730069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 171.074 | − | 970.208i | 0.207866 | − | 1.17887i | −0.684999 | − | 0.728544i | \(-0.740197\pi\) |
0.892865 | − | 0.450324i | \(-0.148691\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −121.151 | − | 315.055i | −0.146850 | − | 0.381885i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 724.427 | + | 418.248i | 0.875970 | + | 0.505741i | 0.869327 | − | 0.494237i | \(-0.164552\pi\) |
0.00664222 | + | 0.999978i | \(0.497886\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 238.896 | + | 413.780i | 0.288174 | + | 0.499132i | 0.973374 | − | 0.229223i | \(-0.0736185\pi\) |
−0.685200 | + | 0.728355i | \(0.740285\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 115.607 | − | 100.615i | 0.139118 | − | 0.121077i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.5247 | + | 59.1386i | 0.0258400 | + | 0.0709947i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −63.6056 | − | 360.725i | −0.0761744 | − | 0.432006i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1532.50 | − | 653.704i | 1.83095 | − | 0.781008i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −775.758 | + | 136.787i | −0.924622 | + | 0.163036i | −0.615636 | − | 0.788031i | \(-0.711101\pi\) |
−0.308986 | + | 0.951067i | \(0.599990\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −684.457 | + | 249.122i | −0.813861 | + | 0.296221i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 569.634 | − | 111.074i | 0.675723 | − | 0.131760i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −261.096 | + | 150.744i | −0.308989 | + | 0.178395i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −330.042 | + | 571.649i | −0.389660 | + | 0.674910i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1119.35 | − | 905.342i | −1.31843 | − | 1.06636i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1148.84 | − | 202.572i | −1.34999 | − | 0.238040i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −533.403 | + | 447.578i | −0.625326 | + | 0.524710i | −0.899472 | − | 0.436977i | \(-0.856049\pi\) |
0.274147 | + | 0.961688i | \(0.411605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 168.014 | + | 414.445i | 0.196508 | + | 0.484731i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −560.564 | + | 1540.14i | −0.654100 | + | 1.79713i | −0.0520817 | + | 0.998643i | \(0.516586\pi\) |
−0.602018 | + | 0.798482i | \(0.705637\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −683.464 | − | 573.495i | −0.795651 | − | 0.667631i | 0.151486 | − | 0.988459i | \(-0.451594\pi\) |
−0.947137 | + | 0.320829i | \(0.896039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1197.29 | + | 720.365i | −1.39058 | + | 0.836661i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 623.038i | 0.721945i | 0.932577 | + | 0.360972i | \(0.117555\pi\) | ||||
−0.932577 | + | 0.360972i | \(0.882445\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1830.34 | 2.11600 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 306.032 | − | 5.52193i | 0.352978 | − | 0.00636901i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −509.592 | + | 607.308i | −0.586412 | + | 0.698858i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 971.651 | + | 353.652i | 1.11556 | + | 0.406030i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1393.35 | − | 450.915i | −1.59605 | − | 0.516512i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −150.066 | − | 178.841i | −0.171503 | − | 0.204390i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −105.739 | + | 599.677i | −0.120569 | + | 0.683783i | 0.863272 | + | 0.504739i | \(0.168411\pi\) |
−0.983841 | + | 0.179043i | \(0.942700\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 775.086 | + | 122.294i | 0.881782 | + | 0.139129i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1266.00 | − | 730.926i | −1.43700 | − | 0.829655i | −0.439363 | − | 0.898309i | \(-0.644796\pi\) |
−0.997640 | + | 0.0686548i | \(0.978129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 711.593 | + | 1232.52i | 0.805881 | + | 1.39583i | 0.915694 | + | 0.401875i | \(0.131641\pi\) |
−0.109813 | + | 0.993952i | \(0.535025\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −311.592 | − | 107.085i | −0.352081 | − | 0.121000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.5597 | − | 105.942i | −0.0434720 | − | 0.119438i | 0.916057 | − | 0.401048i | \(-0.131354\pi\) |
−0.959529 | + | 0.281610i | \(0.909132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −256.698 | − | 1455.81i | −0.288749 | − | 1.63758i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 436.216 | − | 109.852i | 0.489580 | − | 0.123291i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 253.850 | − | 44.7606i | 0.284266 | − | 0.0501238i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 277.276 | − | 100.920i | 0.309805 | − | 0.112760i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 372.249 | − | 1083.16i | 0.414994 | − | 1.20754i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −567.111 | + | 327.422i | −0.630824 | + | 0.364206i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −605.152 | + | 1048.15i | −0.671644 | + | 1.16332i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −131.956 | + | 836.323i | −0.146131 | + | 0.926160i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1842.55 | + | 324.892i | 2.03597 | + | 0.358997i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −800.032 | + | 671.307i | −0.882064 | + | 0.740140i | −0.966602 | − | 0.256280i | \(-0.917503\pi\) |
0.0845382 | + | 0.996420i | \(0.473058\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1146.40 | − | 245.086i | 1.26117 | − | 0.269621i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 397.869 | − | 1093.14i | 0.436739 | − | 1.19993i | −0.504862 | − | 0.863200i | \(-0.668457\pi\) |
0.941601 | − | 0.336731i | \(-0.109321\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −571.455 | − | 479.508i | −0.625909 | − | 0.525200i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.02134 | + | 499.974i | 0.00985939 | + | 0.546420i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 731.864i | 0.798107i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −256.079 | −0.278650 | −0.139325 | − | 0.990247i | \(-0.544493\pi\) | ||||
−0.139325 | + | 0.990247i | \(0.544493\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 604.404 | + | 1004.56i | 0.656248 | + | 1.09073i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −174.442 | + | 207.892i | −0.188995 | + | 0.225235i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −850.634 | − | 309.605i | −0.919604 | − | 0.334708i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −95.0298 | + | 681.994i | −0.102513 | + | 0.735700i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 147.158 | + | 175.375i | 0.158404 | + | 0.188779i | 0.839409 | − | 0.543500i | \(-0.182901\pi\) |
−0.681005 | + | 0.732279i | \(0.738457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.90302 | − | 33.4777i | 0.00634051 | − | 0.0359588i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −63.9463 | + | 79.0622i | −0.0685384 | + | 0.0847398i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −442.432 | − | 255.438i | −0.473189 | − | 0.273196i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 854.276 | + | 1479.65i | 0.911714 | + | 1.57913i | 0.811643 | + | 0.584154i | \(0.198574\pi\) |
0.100071 | + | 0.994980i | \(0.468093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 106.579 | + | 546.586i | 0.113503 | + | 0.582094i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 253.810 | + | 697.338i | 0.269724 | + | 0.741061i | 0.998418 | + | 0.0562218i | \(0.0179054\pi\) |
−0.728694 | + | 0.684839i | \(0.759872\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 288.430 | + | 1635.77i | 0.305864 | + | 1.73464i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1114.06 | + | 726.275i | −1.17890 | + | 0.768545i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 762.068 | − | 134.373i | 0.804719 | − | 0.141894i | 0.243866 | − | 0.969809i | \(-0.421584\pi\) |
0.560853 | + | 0.827915i | \(0.310473\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −119.760 | + | 43.5892i | −0.126196 | + | 0.0459317i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −408.023 | − | 468.819i | −0.429046 | − | 0.492975i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1464.55 | + | 845.558i | −1.53678 | + | 0.887259i | −0.537752 | + | 0.843103i | \(0.680727\pi\) |
−0.999025 | + | 0.0441559i | \(0.985940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 724.707 | − | 1255.23i | 0.758856 | − | 1.31438i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −165.022 | + | 63.4576i | −0.172437 | + | 0.0663088i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1937.16 | − | 341.573i | −2.01998 | − | 0.356176i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2180.78 | − | 1829.89i | 2.26928 | − | 1.90416i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −476.542 | + | 298.557i | −0.494851 | + | 0.310028i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 156.336 | − | 429.528i | 0.162006 | − | 0.445107i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −356.079 | − | 298.785i | −0.368230 | − | 0.308982i | 0.439831 | − | 0.898081i | \(-0.355038\pi\) |
−0.808061 | + | 0.589099i | \(0.799483\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 265.081 | + | 146.733i | 0.273561 | + | 0.151427i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 410.975i | − | 0.423249i | −0.977351 | − | 0.211624i | \(-0.932125\pi\) | ||
0.977351 | − | 0.211624i | \(-0.0678753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −115.980 | −0.119199 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 430.420 | − | 777.576i | 0.441456 | − | 0.797514i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 376.733 | − | 448.972i | 0.385601 | − | 0.459542i | −0.537972 | − | 0.842962i | \(-0.680810\pi\) |
0.923574 | + | 0.383421i | \(0.125254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −118.048 | − | 42.9661i | −0.120580 | − | 0.0438877i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 407.672 | + | 650.706i | 0.415568 | + | 0.663309i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 588.023 | + | 700.778i | 0.598192 | + | 0.712898i | 0.977158 | − | 0.212513i | \(-0.0681648\pi\) |
−0.378966 | + | 0.925411i | \(0.623720\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 135.485 | − | 768.375i | 0.137548 | − | 0.780076i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 275.122 | + | 715.460i | 0.278746 | + | 0.724883i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 871.618 | + | 503.229i | 0.881312 | + | 0.508826i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −188.018 | − | 325.658i | −0.189726 | − | 0.328615i | 0.755433 | − | 0.655226i | \(-0.227427\pi\) |
−0.945159 | + | 0.326611i | \(0.894093\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −554.855 | + | 482.901i | −0.558766 | + | 0.486306i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −88.0228 | − | 241.841i | −0.0884651 | − | 0.243056i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.0542 | − | 198.802i | −0.0351597 | − | 0.199401i | 0.962168 | − | 0.272456i | \(-0.0878360\pi\) |
−0.997328 | + | 0.0730558i | \(0.976725\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 545.779 | − | 1075.84i | 0.546325 | − | 1.07692i |
(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 | 216.3.u.a.41.6 | ✓ | 108 | |
4.3 | odd | 2 | 432.3.bc.d.257.13 | 108 | |||
27.2 | odd | 18 | inner | 216.3.u.a.137.6 | yes | 108 | |
108.83 | even | 18 | 432.3.bc.d.353.13 | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.3.u.a.41.6 | ✓ | 108 | 1.1 | even | 1 | trivial | |
216.3.u.a.137.6 | yes | 108 | 27.2 | odd | 18 | inner | |
432.3.bc.d.257.13 | 108 | 4.3 | odd | 2 | |||
432.3.bc.d.353.13 | 108 | 108.83 | even | 18 |