Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 625.1 | ||
Character | \(\chi\) | \(=\) | 1008.625 |
Dual form | 1008.2.q.k.529.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −1.73195 | − | 0.0184869i | −0.999943 | − | 0.0106734i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.790938 | + | 1.36994i | 0.353718 | + | 0.612658i | 0.986898 | − | 0.161347i | \(-0.0515839\pi\) |
−0.633180 | + | 0.774005i | \(0.718251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.57645 | + | 0.601597i | −0.973806 | + | 0.227382i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.99932 | + | 0.0640368i | 0.999772 | + | 0.0213456i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.58569 | − | 4.47855i | 0.779616 | − | 1.35033i | −0.152548 | − | 0.988296i | \(-0.548748\pi\) |
0.932163 | − | 0.362038i | \(-0.117919\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.681985 | + | 1.18123i | −0.189149 | + | 0.327615i | −0.944967 | − | 0.327167i | \(-0.893906\pi\) |
0.755818 | + | 0.654782i | \(0.227239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.34454 | − | 2.38730i | −0.347159 | − | 0.616398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.30781 | − | 3.99724i | −0.559726 | − | 0.969473i | −0.997519 | − | 0.0703975i | \(-0.977573\pi\) |
0.437794 | − | 0.899076i | \(-0.355760\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0321742 | + | 0.0557274i | −0.00738128 | + | 0.0127847i | −0.869692 | − | 0.493594i | \(-0.835683\pi\) |
0.862311 | + | 0.506379i | \(0.169016\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.47341 | − | 0.994307i | 0.976177 | − | 0.216976i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.37197 | + | 5.84043i | 0.703105 | + | 1.21781i | 0.967371 | + | 0.253364i | \(0.0815370\pi\) |
−0.264266 | + | 0.964450i | \(0.585130\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.24883 | − | 2.16305i | 0.249767 | − | 0.432609i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19349 | − | 0.166357i | −0.999487 | − | 0.0320154i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.70787 | + | 8.15427i | 0.874229 | + | 1.51421i | 0.857582 | + | 0.514348i | \(0.171966\pi\) |
0.0166475 | + | 0.999861i | \(0.494701\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.66278 | 0.478250 | 0.239125 | − | 0.970989i | \(-0.423139\pi\) | ||||
0.239125 | + | 0.970989i | \(0.423139\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.56109 | + | 7.70884i | −0.793984 | + | 1.34194i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.86196 | − | 3.05376i | −0.483760 | − | 0.516180i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.880766 | − | 1.52553i | 0.144797 | − | 0.250796i | −0.784500 | − | 0.620129i | \(-0.787080\pi\) |
0.929297 | + | 0.369333i | \(0.120414\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.20300 | − | 2.03323i | 0.192635 | − | 0.325578i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.858924 | + | 1.48770i | −0.134141 | + | 0.232340i | −0.925269 | − | 0.379311i | \(-0.876161\pi\) |
0.791128 | + | 0.611651i | \(0.209494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.12012 | + | 8.86831i | 0.780811 | + | 1.35240i | 0.931470 | + | 0.363819i | \(0.118527\pi\) |
−0.150658 | + | 0.988586i | \(0.548139\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.28455 | + | 4.15955i | 0.340560 | + | 0.620068i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.20834 | −0.759715 | −0.379857 | − | 0.925045i | \(-0.624027\pi\) | ||||
−0.379857 | + | 0.925045i | \(0.624027\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.27616 | − | 3.09997i | 0.896594 | − | 0.442853i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.92312 | + | 6.96569i | 0.549346 | + | 0.975392i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.479996 | − | 0.831377i | −0.0659325 | − | 0.114198i | 0.831175 | − | 0.556011i | \(-0.187669\pi\) |
−0.897107 | + | 0.441813i | \(0.854336\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.18049 | 1.10306 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0567545 | − | 0.0959224i | 0.00751732 | − | 0.0127052i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.33353 | 1.21512 | 0.607561 | − | 0.794273i | \(-0.292148\pi\) | ||||
0.607561 | + | 0.794273i | \(0.292148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.3902 | 1.84248 | 0.921241 | − | 0.388993i | \(-0.127177\pi\) | ||||
0.921241 | + | 0.388993i | \(0.127177\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.76611 | + | 1.63939i | −0.978437 | + | 0.206544i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.15763 | −0.267621 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4981 | 1.52688 | 0.763441 | − | 0.645878i | \(-0.223509\pi\) | ||||
0.763441 | + | 0.645878i | \(0.223509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.73213 | − | 10.1777i | −0.690067 | − | 1.22525i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.49160 | 0.533055 | 0.266527 | − | 0.963827i | \(-0.414124\pi\) | ||||
0.266527 | + | 0.963827i | \(0.414124\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.941655 | − | 1.63099i | −0.110212 | − | 0.190893i | 0.805643 | − | 0.592401i | \(-0.201820\pi\) |
−0.915856 | + | 0.401507i | \(0.868486\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.20291 | + | 3.72320i | −0.254370 | + | 0.429919i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.96762 | + | 13.0943i | −0.452152 | + | 1.49223i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.53504 | −0.735250 | −0.367625 | − | 0.929974i | \(-0.619829\pi\) | ||||
−0.367625 | + | 0.929974i | \(0.619829\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99180 | + | 0.384134i | 0.999089 | + | 0.0426815i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.08661 | + | 8.81026i | 0.558328 | + | 0.967052i | 0.997636 | + | 0.0687156i | \(0.0218901\pi\) |
−0.439309 | + | 0.898336i | \(0.644777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65066 | − | 6.32314i | 0.395970 | − | 0.685840i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.00306 | − | 14.2098i | −0.858018 | − | 1.52345i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.12369 | + | 7.14243i | −0.437110 | + | 0.757096i | −0.997465 | − | 0.0711559i | \(-0.977331\pi\) |
0.560355 | + | 0.828252i | \(0.310665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.04647 | − | 3.45366i | 0.109700 | − | 0.362042i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.61181 | − | 0.0492266i | −0.478223 | − | 0.00510456i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.101791 | −0.0104436 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.26638 | − | 12.5857i | −0.737789 | − | 1.27789i | −0.953489 | − | 0.301428i | \(-0.902537\pi\) |
0.215700 | − | 0.976460i | \(-0.430797\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.04210 | − | 13.2670i | 0.808262 | − | 1.33339i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.12310 | + | 5.40937i | −0.310760 | + | 0.538252i | −0.978527 | − | 0.206118i | \(-0.933917\pi\) |
0.667767 | + | 0.744370i | \(0.267250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.88881 | − | 5.00357i | −0.284643 | − | 0.493016i | 0.687879 | − | 0.725825i | \(-0.258542\pi\) |
−0.972523 | + | 0.232809i | \(0.925208\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.90033 | + | 5.34188i | 0.478223 | + | 0.521314i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.251126 | − | 0.434963i | 0.0242773 | − | 0.0420494i | −0.853632 | − | 0.520877i | \(-0.825605\pi\) |
0.877909 | + | 0.478828i | \(0.158938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.37218 | − | 4.10874i | −0.227214 | − | 0.393546i | 0.729767 | − | 0.683696i | \(-0.239628\pi\) |
−0.956981 | + | 0.290149i | \(0.906295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.55365 | + | 2.62587i | −0.147466 | + | 0.249236i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.11328 | + | 1.92825i | −0.104728 | + | 0.181395i | −0.913627 | − | 0.406553i | \(-0.866731\pi\) |
0.808899 | + | 0.587948i | \(0.200064\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.33404 | + | 9.23883i | −0.497402 | + | 0.861526i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.12113 | + | 3.49922i | −0.196099 | + | 0.323503i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.35067 | + | 8.91031i | 0.765505 | + | 0.816806i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.87162 | − | 13.6340i | −0.715601 | − | 1.23946i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.51512 | − | 2.56075i | 0.136614 | − | 0.230895i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8604 | 1.06082 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.6057 | 1.65099 | 0.825494 | − | 0.564410i | \(-0.190896\pi\) | ||||
0.825494 | + | 0.564410i | \(0.190896\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.70386 | − | 15.4541i | −0.766332 | − | 1.36066i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.77020 | + | 11.7263i | 0.591515 | + | 1.02453i | 0.994029 | + | 0.109120i | \(0.0348032\pi\) |
−0.402514 | + | 0.915414i | \(0.631863\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0493698 | − | 0.162935i | 0.00428090 | − | 0.0141282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.87983 | − | 7.24637i | −0.333922 | − | 0.623668i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.87100 | + | 11.9009i | −0.587029 | + | 1.01676i | 0.407590 | + | 0.913165i | \(0.366369\pi\) |
−0.994619 | + | 0.103599i | \(0.966964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.79328 | + | 11.7663i | −0.576198 | + | 0.998005i | 0.419712 | + | 0.907657i | \(0.362131\pi\) |
−0.995910 | + | 0.0903476i | \(0.971202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.02060 | + | 0.0962861i | 0.759671 | + | 0.00810875i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.52681 | + | 6.10861i | 0.294927 | + | 0.510828i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.44726 | + | 12.8990i | −0.618461 | + | 1.07121i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.9273 | + | 5.25297i | −0.901270 | + | 0.433258i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.98033 | − | 5.16209i | −0.244158 | − | 0.422895i | 0.717736 | − | 0.696315i | \(-0.245178\pi\) |
−0.961895 | + | 0.273420i | \(0.911845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.27071 | − | 7.39709i | 0.347546 | − | 0.601967i | −0.638267 | − | 0.769815i | \(-0.720349\pi\) |
0.985813 | + | 0.167848i | \(0.0536819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.66587 | − | 12.1368i | −0.538904 | − | 0.981200i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.10610 | + | 3.64786i | 0.169166 | + | 0.293004i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.63992 | −0.210688 | −0.105344 | − | 0.994436i | \(-0.533594\pi\) | ||||
−0.105344 | + | 0.994436i | \(0.533594\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.815960 | + | 1.44878i | 0.0647099 | + | 0.114896i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.2013 | − | 13.0190i | −0.961597 | − | 1.02604i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.87875 | − | 15.3785i | 0.695438 | − | 1.20453i | −0.274595 | − | 0.961560i | \(-0.588544\pi\) |
0.970033 | − | 0.242973i | \(-0.0781228\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.1682 | − | 0.151232i | −1.10299 | − | 0.0117734i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.98937 | + | 6.90979i | −0.308706 | + | 0.534695i | −0.978080 | − | 0.208231i | \(-0.933229\pi\) |
0.669373 | + | 0.742926i | \(0.266563\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.56979 | + | 9.64716i | 0.428446 | + | 0.742090i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.100069 | + | 0.165084i | −0.00765250 | + | 0.0126243i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.66341 | 0.582638 | 0.291319 | − | 0.956626i | \(-0.405906\pi\) | ||||
0.291319 | + | 0.956626i | \(0.405906\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.91627 | + | 6.32427i | −0.144857 | + | 0.478070i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.1652 | − | 0.172548i | −1.21505 | − | 0.0129695i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7864 | − | 20.4147i | −0.880958 | − | 1.52586i | −0.850277 | − | 0.526335i | \(-0.823566\pi\) |
−0.0306808 | − | 0.999529i | \(-0.509768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3700 | 1.29110 | 0.645551 | − | 0.763717i | \(-0.276628\pi\) | ||||
0.645551 | + | 0.763717i | \(0.276628\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.9232 | − | 0.266031i | −1.84238 | − | 0.0196656i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.78653 | 0.204869 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.8691 | −1.74548 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.4808 | − | 2.69578i | 0.980586 | − | 0.196089i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.84660 | −0.350687 | −0.175344 | − | 0.984507i | \(-0.556104\pi\) | ||||
−0.175344 | + | 0.984507i | \(0.556104\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.6418 | −1.05394 | −0.526970 | − | 0.849884i | \(-0.676672\pi\) | ||||
−0.526970 | + | 0.849884i | \(0.676672\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.73691 | + | 0.0398879i | 0.267606 | + | 0.00285643i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.1996 | −1.36791 | −0.683957 | − | 0.729522i | \(-0.739743\pi\) | ||||
−0.683957 | + | 0.729522i | \(0.739743\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.50796 | − | 11.2721i | −0.461337 | − | 0.799060i | 0.537691 | − | 0.843142i | \(-0.319297\pi\) |
−0.999028 | + | 0.0440825i | \(0.985964\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.6460 | − | 0.231050i | −1.52679 | − | 0.0162970i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.0352 | − | 18.1768i | −1.19563 | − | 1.27576i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.71742 | −0.189793 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.73961 | + | 17.7332i | 0.676950 | + | 1.23254i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.166385 | + | 0.288188i | 0.0115091 | + | 0.0199344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43389 | − | 12.8759i | 0.511770 | − | 0.886412i | −0.488137 | − | 0.872767i | \(-0.662323\pi\) |
0.999907 | − | 0.0136450i | \(-0.00434348\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.77923 | − | 0.0830357i | −0.533024 | − | 0.00568951i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.09940 | + | 14.0286i | −0.552374 | + | 0.956740i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.86052 | + | 1.60192i | −0.465722 | + | 0.108746i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.60075 | + | 2.84221i | 0.108169 | + | 0.192059i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.29556 | 0.423485 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.2085 | − | 19.4136i | −0.750574 | − | 1.30003i | −0.947545 | − | 0.319623i | \(-0.896444\pi\) |
0.196971 | − | 0.980409i | \(-0.436890\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.88417 | − | 6.40769i | 0.258944 | − | 0.427179i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.94725 | − | 3.37273i | 0.129243 | − | 0.223856i | −0.794140 | − | 0.607735i | \(-0.792078\pi\) |
0.923384 | + | 0.383878i | \(0.125412\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.693586 | + | 1.20133i | 0.0458334 | + | 0.0793858i | 0.888032 | − | 0.459782i | \(-0.152072\pi\) |
−0.842199 | + | 0.539167i | \(0.818739\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.11379 | − | 22.6053i | 0.468053 | − | 1.48732i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.99057 | − | 15.5721i | 0.588992 | − | 1.02016i | −0.405373 | − | 0.914151i | \(-0.632858\pi\) |
0.994365 | − | 0.106013i | \(-0.0338084\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.11947 | − | 7.13514i | −0.268725 | − | 0.465445i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3184 | + | 0.120813i | 0.735208 | + | 0.00784763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.68043 | − | 4.64264i | 0.173382 | − | 0.300307i | −0.766218 | − | 0.642581i | \(-0.777864\pi\) |
0.939600 | + | 0.342274i | \(0.111197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.208296 | + | 0.360779i | −0.0134175 | + | 0.0232398i | −0.872656 | − | 0.488335i | \(-0.837604\pi\) |
0.859239 | + | 0.511575i | \(0.170938\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5663 | − | 0.831531i | −0.998576 | − | 0.0533428i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.21084 | + | 6.14611i | 0.588459 | + | 0.392661i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.0438847 | − | 0.0760106i | −0.00279232 | − | 0.00483644i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.64688 | − | 15.3530i | −0.547974 | − | 0.972956i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.5606 | −1.42401 | −0.712006 | − | 0.702173i | \(-0.752213\pi\) | ||||
−0.712006 | + | 0.702173i | \(0.752213\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.8756 | 2.19261 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.43967 | + | 10.8839i | −0.403268 | + | 0.681575i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.52307 | + | 9.56624i | 0.344520 | + | 0.596726i | 0.985266 | − | 0.171027i | \(-0.0547084\pi\) |
−0.640747 | + | 0.767752i | \(0.721375\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.35149 | + | 4.46032i | −0.0839776 | + | 0.277151i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.5982 | + | 24.7587i | 0.841708 | + | 1.53253i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7310 | + | 22.0508i | −0.785028 | + | 1.35971i | 0.143954 | + | 0.989584i | \(0.454018\pi\) |
−0.928982 | + | 0.370124i | \(0.879315\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.759294 | − | 1.31514i | 0.0466430 | − | 0.0807881i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.27407 | − | 12.2941i | 0.445166 | − | 0.752388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.78957 | + | 4.83168i | 0.170083 | + | 0.294593i | 0.938449 | − | 0.345419i | \(-0.112263\pi\) |
−0.768366 | + | 0.640011i | \(0.778930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.46645 | − | 2.53997i | 0.0890806 | − | 0.154292i | −0.818042 | − | 0.575158i | \(-0.804940\pi\) |
0.907123 | + | 0.420866i | \(0.138274\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.87629 | + | 5.96224i | −0.113558 | + | 0.360851i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.45821 | − | 11.1859i | −0.389445 | − | 0.674538i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0458 | + | 19.1320i | −0.663680 | + | 1.14953i | 0.315961 | + | 0.948772i | \(0.397673\pi\) |
−0.979641 | + | 0.200756i | \(0.935660\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.98653 | + | 0.170516i | 0.478141 | + | 0.0102085i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.81009 | − | 4.86721i | −0.167636 | − | 0.290354i | 0.769952 | − | 0.638101i | \(-0.220280\pi\) |
−0.937588 | + | 0.347748i | \(0.886947\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.3003 | −1.26617 | −0.633086 | − | 0.774082i | \(-0.718212\pi\) | ||||
−0.633086 | + | 0.774082i | \(0.718212\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.176298 | + | 0.00188181i | 0.0104430 | + | 0.000111469i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.31798 | − | 4.34971i | 0.0777977 | − | 0.256755i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.15195 | + | 3.72729i | −0.126585 | + | 0.219252i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.3524 | + | 21.9322i | 0.724108 | + | 1.28569i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1128 | − | 24.4440i | 0.824477 | − | 1.42804i | −0.0778418 | − | 0.996966i | \(-0.524803\pi\) |
0.902319 | − | 0.431070i | \(-0.141864\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.38224 | + | 12.7864i | 0.429811 | + | 0.744454i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.1738 | + | 22.8292i | −0.822448 | + | 1.32468i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.19854 | −0.531966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.5269 | − | 19.7685i | −1.06787 | − | 1.13944i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.50906 | − | 9.31103i | 0.316487 | − | 0.534905i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.3818 | + | 19.7138i | 0.651719 | + | 1.12881i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.41329 | 0.137734 | 0.0688669 | − | 0.997626i | \(-0.478062\pi\) | ||||
0.0688669 | + | 0.997626i | \(0.478062\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.91078 | + | 8.71935i | 0.279365 | + | 0.496026i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.53680 | −0.540782 | −0.270391 | − | 0.962751i | \(-0.587153\pi\) | ||||
−0.270391 | + | 0.962751i | \(0.587153\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.6020 | 1.84277 | 0.921386 | − | 0.388650i | \(-0.127058\pi\) | ||||
0.921386 | + | 0.388650i | \(0.127058\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.38838 | − | 9.34247i | −0.472632 | − | 0.526389i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.09954 | −0.174088 | −0.0870438 | − | 0.996204i | \(-0.527742\pi\) | ||||
−0.0870438 | + | 0.996204i | \(0.527742\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.6924 | 2.72625 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.442979 | + | 0.748692i | −0.0247247 | + | 0.0417879i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.297008 | 0.0165260 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.70337 | + | 2.95033i | 0.0944862 | + | 0.163655i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.03255 | + | 7.16000i | 0.223001 | + | 0.395949i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.4190 | − | 3.13332i | 0.739814 | − | 0.172746i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.67650 | 0.202079 | 0.101039 | − | 0.994882i | \(-0.467783\pi\) | ||||
0.101039 | + | 0.994882i | \(0.467783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.73939 | − | 4.51915i | 0.150117 | − | 0.247648i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.88519 | + | 17.1216i | 0.540086 | + | 0.935456i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.15866 | − | 10.6671i | 0.335483 | − | 0.581074i | −0.648094 | − | 0.761560i | \(-0.724434\pi\) |
0.983578 | + | 0.180486i | \(0.0577670\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.96379 | − | 3.31906i | 0.106658 | − | 0.180266i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.88514 | − | 11.9254i | 0.372851 | − | 0.645797i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.3053 | + | 11.7626i | −0.772412 | + | 0.635122i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.40910 | − | 15.9026i | 0.506569 | − | 0.856168i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.7016 | 0.950269 | 0.475135 | − | 0.879913i | \(-0.342399\pi\) | ||||
0.475135 | + | 0.879913i | \(0.342399\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.562639 | + | 0.974519i | 0.0301174 | + | 0.0521648i | 0.880691 | − | 0.473691i | \(-0.157079\pi\) |
−0.850574 | + | 0.525856i | \(0.823745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.73839 | − | 6.02127i | 0.199540 | − | 0.321391i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.48125 | − | 9.49381i | 0.291738 | − | 0.505304i | −0.682483 | − | 0.730901i | \(-0.739100\pi\) |
0.974221 | + | 0.225597i | \(0.0724332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.55257 | + | 6.15324i | 0.188551 | + | 0.326580i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.2982 | − | 15.5866i | −0.756743 | − | 0.824930i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.4733 | − | 23.3364i | 0.711092 | − | 1.23165i | −0.253356 | − | 0.967373i | \(-0.581534\pi\) |
0.964448 | − | 0.264274i | \(-0.0851324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49793 | + | 16.4509i | 0.499891 | + | 0.865837i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.3812 | + | 23.7590i | 0.702331 | + | 1.24703i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.48958 | − | 2.58003i | 0.0779682 | − | 0.135045i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4137 | − | 30.1614i | 0.908986 | − | 1.57441i | 0.0935112 | − | 0.995618i | \(-0.470191\pi\) |
0.815475 | − | 0.578792i | \(-0.196476\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.67145 | + | 4.40708i | −0.139070 | + | 0.229424i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.73684 | + | 1.85324i | 0.0901722 | + | 0.0962152i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5793 | + | 20.0559i | 0.599551 | + | 1.03845i | 0.992887 | + | 0.119058i | \(0.0379876\pi\) |
−0.393336 | + | 0.919395i | \(0.628679\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.5416 | − | 0.219262i | −1.06076 | − | 0.0113226i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.8428 | −0.661437 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.7259 | −1.16735 | −0.583676 | − | 0.811987i | \(-0.698386\pi\) | ||||
−0.583676 | + | 0.811987i | \(0.698386\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −32.2242 | − | 0.343962i | −1.65089 | − | 0.0176217i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.6021 | + | 20.0954i | 0.592837 | + | 1.02682i | 0.993848 | + | 0.110751i | \(0.0353257\pi\) |
−0.401011 | + | 0.916073i | \(0.631341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −21.0766 | + | 4.92136i | −1.07416 | + | 0.250816i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.7890 | + | 26.9267i | 0.751765 | + | 1.36876i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.56737 | − | 7.91091i | 0.231575 | − | 0.401099i | −0.726697 | − | 0.686958i | \(-0.758946\pi\) |
0.958272 | + | 0.285859i | \(0.0922789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.5637 | − | 26.9572i | 0.787092 | − | 1.36328i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.5089 | − | 20.4346i | −0.580546 | − | 1.03079i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.16881 | − | 8.95265i | −0.260071 | − | 0.450456i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2126 | + | 33.2773i | −0.964255 | + | 1.67014i | −0.252652 | + | 0.967557i | \(0.581303\pi\) |
−0.711603 | + | 0.702582i | \(0.752031\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0885182 | + | 0.281282i | −0.00443145 | + | 0.0140817i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.47348 | − | 2.55214i | −0.0735821 | − | 0.127448i | 0.826887 | − | 0.562369i | \(-0.190110\pi\) |
−0.900469 | + | 0.434921i | \(0.856776\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.81598 | + | 3.14537i | −0.0904603 | + | 0.156682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.58571 | + | 12.6221i | 0.327247 | + | 0.627197i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.55478 | − | 7.88912i | −0.225772 | − | 0.391049i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.60591 | 0.326641 | 0.163321 | − | 0.986573i | \(-0.447779\pi\) | ||||
0.163321 | + | 0.986573i | \(0.447779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.1202 | − | 20.4848i | 0.597848 | − | 1.01044i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.0473 | + | 5.61503i | −1.18329 | + | 0.276297i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.04638 | + | 13.9367i | −0.394981 | + | 0.684127i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.9832 | − | 20.2531i | 0.586818 | − | 0.991798i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.381961 | − | 0.661576i | 0.0186600 | − | 0.0323201i | −0.856545 | − | 0.516073i | \(-0.827393\pi\) |
0.875205 | + | 0.483753i | \(0.160727\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.48798 | − | 4.30931i | −0.121257 | − | 0.210023i | 0.799007 | − | 0.601322i | \(-0.205359\pi\) |
−0.920264 | + | 0.391299i | \(0.872026\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.6215 | − | 0.333526i | −0.759542 | − | 0.0162166i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.5283 | −0.559204 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −37.0757 | + | 8.65713i | −1.79422 | + | 0.418948i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.99533 | − | 10.6450i | −0.289457 | − | 0.513946i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.01856 | + | 6.96035i | 0.193567 | + | 0.335268i | 0.946430 | − | 0.322909i | \(-0.104661\pi\) |
−0.752863 | + | 0.658178i | \(0.771328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.8006 | −0.519043 | −0.259522 | − | 0.965737i | \(-0.583565\pi\) | ||||
−0.259522 | + | 0.965737i | \(0.583565\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.1368 | − | 22.2028i | 0.629860 | − | 1.06454i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.433963 | −0.0207593 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.1194 | 0.960244 | 0.480122 | − | 0.877202i | \(-0.340592\pi\) | ||||
0.480122 | + | 0.877202i | \(0.340592\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.0227 | − | 8.89588i | 0.905843 | − | 0.423613i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.21245 | 0.437697 | 0.218848 | − | 0.975759i | \(-0.429770\pi\) | ||||
0.218848 | + | 0.975759i | \(0.429770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.0463 | −0.618455 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.06636 | + | 8.99558i | 0.239631 | + | 0.425476i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.4840 | −1.06109 | −0.530544 | − | 0.847658i | \(-0.678012\pi\) | ||||
−0.530544 | + | 0.847658i | \(0.678012\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.44183 | + | 7.69347i | 0.209158 | + | 0.362271i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.53342 | + | 12.7325i | −0.353951 | + | 0.598223i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.55902 | − | 1.29803i | 0.260611 | − | 0.0608524i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7955 | 0.879218 | 0.439609 | − | 0.898189i | \(-0.355117\pi\) | ||||
0.439609 | + | 0.898189i | \(0.355117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.3206 | + | 21.1435i | 0.528401 | + | 0.986896i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3773 | + | 17.9739i | 0.483317 | + | 0.837129i | 0.999816 | − | 0.0191582i | \(-0.00609862\pi\) |
−0.516500 | + | 0.856287i | \(0.672765\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0414 | + | 17.3922i | −0.466663 | + | 0.808284i | −0.999275 | − | 0.0380753i | \(-0.987877\pi\) |
0.532612 | + | 0.846360i | \(0.321211\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.58022 | − | 6.35686i | −0.166029 | − | 0.294792i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.6015 | + | 25.2905i | −0.675676 | + | 1.17030i | 0.300595 | + | 0.953752i | \(0.402815\pi\) |
−0.976271 | + | 0.216553i | \(0.930519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.2006 | + | 7.51880i | −1.48689 | + | 0.347186i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.57221 | + | 0.0488039i | 0.210676 | + | 0.00224876i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.9563 | 2.43493 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0803606 | + | 0.139189i | 0.00368720 | + | 0.00638642i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.38642 | − | 2.52430i | −0.0634798 | − | 0.115580i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0327 | + | 34.6977i | −0.915319 | + | 1.58538i | −0.108884 | + | 0.994054i | \(0.534728\pi\) |
−0.806434 | + | 0.591324i | \(0.798606\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.20134 | + | 2.08078i | 0.0547763 | + | 0.0948754i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.8914 | + | 22.7738i | 0.950591 | + | 1.03625i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.4945 | − | 19.9091i | 0.521939 | − | 0.904024i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.32801 | − | 16.1566i | −0.422692 | − | 0.732125i | 0.573509 | − | 0.819199i | \(-0.305582\pi\) |
−0.996202 | + | 0.0870742i | \(0.972248\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.6619 | + | 26.4706i | −0.708254 | + | 1.19704i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.285132 | − | 0.493864i | 0.0128678 | − | 0.0222878i | −0.859520 | − | 0.511102i | \(-0.829237\pi\) |
0.872388 | + | 0.488815i | \(0.162571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.7297 | − | 37.6370i | 0.978657 | − | 1.69508i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 24.5359 | + | 0.523853i | 1.10281 | + | 0.0235454i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.5724 | + | 2.70213i | −0.519092 | + | 0.121207i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.464297 | − | 0.804185i | −0.0207848 | − | 0.0360003i | 0.855446 | − | 0.517892i | \(-0.173283\pi\) |
−0.876231 | + | 0.481892i | \(0.839950\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.03713 | − | 11.8937i | 0.314396 | − | 0.531370i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.27170 | 0.145878 | 0.0729389 | − | 0.997336i | \(-0.476762\pi\) | ||||
0.0729389 | + | 0.997336i | \(0.476762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.88071 | −0.439686 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.46827 | − | 16.8114i | −0.420501 | − | 0.746620i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.48391 | − | 7.76635i | −0.198746 | − | 0.344238i | 0.749376 | − | 0.662144i | \(-0.230353\pi\) |
−0.948122 | + | 0.317907i | \(0.897020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.40733 | + | 3.63567i | 0.150731 | + | 0.160833i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.176367 | − | 0.284067i | 0.00778680 | − | 0.0125419i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.56974 | − | 7.91502i | 0.201367 | − | 0.348778i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4672 | + | 23.3258i | −0.592286 | + | 1.02587i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.2727 | − | 0.141673i | −0.582605 | − | 0.00621874i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.37649 | − | 9.31235i | −0.235548 | − | 0.407982i | 0.723884 | − | 0.689922i | \(-0.242355\pi\) |
−0.959432 | + | 0.281940i | \(0.909022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.2796 | − | 28.1970i | 0.711856 | − | 1.23297i | −0.252304 | − | 0.967648i | \(-0.581188\pi\) |
0.964160 | − | 0.265322i | \(-0.0854784\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.43581 | − | 10.9179i | 0.149951 | − | 0.476496i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.14519 | − | 10.6438i | −0.267689 | − | 0.463650i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2404 | + | 19.4690i | −0.488714 | + | 0.846477i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.9942 | + | 0.597690i | 1.21484 | + | 0.0259375i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.17155 | − | 2.02918i | −0.0507453 | − | 0.0878935i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.794500 | 0.0343492 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.0361 | + | 35.5751i | 0.864622 | + | 1.53518i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.34486 | − | 36.1237i | 0.101000 | − | 1.55596i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.46359 | + | 5.99911i | −0.148911 | + | 0.257922i | −0.930825 | − | 0.365464i | \(-0.880910\pi\) |
0.781914 | + | 0.623386i | \(0.214244\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.0840 | − | 0.321118i | −1.29103 | − | 0.0137805i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.75250 | − | 6.49952i | 0.160739 | − | 0.278409i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8974 | + | 27.5351i | 0.679725 | + | 1.17732i | 0.975064 | + | 0.221925i | \(0.0712340\pi\) |
−0.295339 | + | 0.955392i | \(0.595433\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 43.1609 | + | 0.921505i | 1.84206 | + | 0.0393289i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.605888 | −0.0258117 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.8372 | − | 3.93147i | 0.715990 | − | 0.167183i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.82613 | − | 0.0515142i | −0.204858 | − | 0.00218666i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.1679 | + | 24.5395i | 0.600314 | + | 1.03977i | 0.992773 | + | 0.120005i | \(0.0382909\pi\) |
−0.392460 | + | 0.919769i | \(0.628376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.9674 | −0.590758 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 41.3402 | + | 0.441266i | 1.74538 | + | 0.0186303i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.6541 | 1.88194 | 0.940972 | − | 0.338484i | \(-0.109914\pi\) | ||||
0.940972 | + | 0.338484i | \(0.109914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.52213 | −0.148177 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.3980 | + | 4.41974i | −0.982623 | + | 0.185612i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.2205 | −0.889608 | −0.444804 | − | 0.895628i | \(-0.646727\pi\) | ||||
−0.444804 | + | 0.895628i | \(0.646727\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.8957 | −0.497820 | −0.248910 | − | 0.968527i | \(-0.580072\pi\) | ||||
−0.248910 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.39407 | + | 0.0895985i | 0.350667 | + | 0.00374303i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.8442 | 0.702450 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.3490 | − | 33.5135i | −0.805511 | − | 1.39519i | −0.915946 | − | 0.401302i | \(-0.868558\pi\) |
0.110435 | − | 0.993883i | \(-0.464776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.3589 | + | 0.270682i | 1.05388 | + | 0.0112491i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.4056 | − | 19.6391i | −0.763593 | − | 0.814766i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.96449 | −0.205608 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.47142 | − | 0.138168i | −0.267560 | − | 0.00571254i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.92138 | − | 17.1843i | −0.409499 | − | 0.709274i | 0.585334 | − | 0.810792i | \(-0.300963\pi\) |
−0.994834 | + | 0.101518i | \(0.967630\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0856730 | + | 0.148390i | −0.00353010 | + | 0.00611431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 33.2528 | + | 0.354941i | 1.36784 | + | 0.0146003i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9566 | − | 18.9774i | 0.449933 | − | 0.779307i | −0.548448 | − | 0.836185i | \(-0.684781\pi\) |
0.998381 | + | 0.0568775i | \(0.0181144\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.60176 | + | 18.4875i | −0.229650 | + | 0.757912i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0631 | + | 19.6431i | 0.452782 | + | 0.803938i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.0445 | −1.35016 | −0.675081 | − | 0.737743i | \(-0.735892\pi\) | ||||
−0.675081 | + | 0.737743i | \(0.735892\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4951 | + | 19.9100i | 0.468893 | + | 0.812147i | 0.999368 | − | 0.0355541i | \(-0.0113196\pi\) |
−0.530475 | + | 0.847701i | \(0.677986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.4856 | + | 0.800336i | 1.52653 | + | 0.0325922i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12.4519 | − | 21.5674i | 0.506242 | − | 0.876838i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8282 | + | 23.9511i | 0.561269 | + | 0.972146i | 0.997386 | + | 0.0722559i | \(0.0230198\pi\) |
−0.436118 | + | 0.899890i | \(0.643647\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 29.1680 | + | 31.7963i | 1.18195 | + | 1.28845i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.55201 | − | 6.15226i | 0.143699 | − | 0.248894i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.7684 | − | 27.3116i | −0.636879 | − | 1.10311i | −0.986114 | − | 0.166072i | \(-0.946892\pi\) |
0.349235 | − | 0.937035i | \(-0.386442\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.70645 | + | 0.0502367i | 0.189782 | + | 0.00202574i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.7513 | + | 18.6217i | −0.432830 | + | 0.749683i | −0.997116 | − | 0.0758961i | \(-0.975818\pi\) |
0.564286 | + | 0.825580i | \(0.309152\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.1261 | − | 24.4671i | 0.567776 | − | 0.983417i | −0.429009 | − | 0.903300i | \(-0.641137\pi\) |
0.996785 | − | 0.0801169i | \(-0.0255294\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.5407 | − | 30.8932i | −0.663756 | − | 1.23970i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.32759 | − | 20.8829i | 0.253509 | − | 0.836656i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.13665 | + | 5.43283i | 0.125466 | + | 0.217313i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.282844 | − | 0.502204i | −0.0112957 | − | 0.0200561i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.13056 | −0.324187 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.12550 | 0.363281 | 0.181640 | − | 0.983365i | \(-0.441859\pi\) | ||||
0.181640 | + | 0.983365i | \(0.441859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.1132 | + | 22.1630i | −0.521202 | + | 0.880899i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.7159 | + | 25.4888i | 0.583985 | + | 1.01149i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.618464 | + | 9.52774i | −0.0245044 | + | 0.377503i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.4717 | + | 0.287628i | 0.532933 | + | 0.0113784i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.4489 | + | 28.4904i | −0.649693 | + | 1.12530i | 0.333503 | + | 0.942749i | \(0.391769\pi\) |
−0.983196 | + | 0.182552i | \(0.941564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1276 | + | 17.5415i | −0.399392 | + | 0.691767i | −0.993651 | − | 0.112506i | \(-0.964112\pi\) |
0.594259 | + | 0.804274i | \(0.297445\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.2871 | − | 24.1471i | 0.562554 | − | 0.950790i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.67441 | + | 9.82837i | 0.223084 | + | 0.386393i | 0.955743 | − | 0.294203i | \(-0.0950542\pi\) |
−0.732659 | + | 0.680596i | \(0.761721\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.1336 | − | 41.8007i | 0.947328 | − | 1.64082i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.9117 | − | 2.64762i | 0.466857 | − | 0.103769i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.79018 | − | 3.10069i | −0.0700552 | − | 0.121339i | 0.828870 | − | 0.559441i | \(-0.188984\pi\) |
−0.898925 | + | 0.438102i | \(0.855651\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7096 | + | 18.5496i | −0.418459 | + | 0.724792i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.71988 | − | 4.95217i | −0.106113 | − | 0.193203i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.13582 | − | 15.8237i | −0.355881 | − | 0.616404i | 0.631387 | − | 0.775468i | \(-0.282486\pi\) |
−0.987268 | + | 0.159064i | \(0.949152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.23391 | 0.0868891 | 0.0434446 | − | 0.999056i | \(-0.486167\pi\) | ||||
0.0434446 | + | 0.999056i | \(0.486167\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.9036 | − | 0.116385i | −0.423461 | − | 0.00452003i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.262260 | − | 0.0612374i | 0.0101700 | − | 0.00237468i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.7496 | + | 54.9919i | −1.22935 | + | 2.12930i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.0536 | + | 33.8307i | 0.736655 | + | 1.30797i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.2087 | − | 64.4474i | 1.43643 | − | 2.48797i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4804 | − | 21.6166i | −0.481083 | − | 0.833260i | 0.518681 | − | 0.854968i | \(-0.326423\pi\) |
−0.999764 | + | 0.0217074i | \(0.993090\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.84565 | + | 11.0260i | −0.263489 | + | 0.424391i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.8127 | −0.761463 | −0.380731 | − | 0.924686i | \(-0.624328\pi\) | ||||
−0.380731 | + | 0.924686i | \(0.624328\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.2930 | + | 28.0551i | 1.00903 | + | 1.07665i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.43489 | + | 5.80541i | −0.131625 | + | 0.222464i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.72871 | − | 9.92242i | −0.219203 | − | 0.379671i | 0.735361 | − | 0.677675i | \(-0.237012\pi\) |
−0.954565 | + | 0.298004i | \(0.903679\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.7381 | −0.830571 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.17905 | − | 2.09346i | −0.0449835 | − | 0.0798705i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.30940 | 0.0498842 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.5105 | −1.54109 | −0.770545 | − | 0.637385i | \(-0.780016\pi\) | ||||
−0.770545 | + | 0.637385i | \(0.780016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.7387 | + | 39.0199i | −0.483901 | + | 1.48224i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.4922 | −0.815247 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.92893 | 0.300330 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.8591 | + | 26.8040i | −0.599847 | + | 1.01382i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.5416 | −1.11577 | −0.557885 | − | 0.829918i | \(-0.688387\pi\) | ||||
−0.557885 | + | 0.829918i | \(0.688387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0566760 | + | 0.0981657i | 0.00213758 | + | 0.00370239i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.00283 | + | 12.4339i | 0.263742 | + | 0.468287i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.79224 | − | 15.8158i | 0.180231 | − | 0.594814i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.4814 | −1.40764 | −0.703822 | − | 0.710376i | \(-0.748525\pi\) | ||||
−0.703822 | + | 0.710376i | \(0.748525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19.6007 | − | 0.418484i | −0.735082 | − | 0.0156944i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.97883 | + | 15.5518i | 0.336260 | + | 0.582419i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.57897 | + | 9.66306i | −0.208642 | + | 0.361378i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.72820 | + | 7.99127i | −0.176578 | + | 0.298439i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.35418 | + | 11.0058i | −0.236971 | + | 0.410445i | −0.959844 | − | 0.280536i | \(-0.909488\pi\) |
0.722873 | + | 0.690981i | \(0.242821\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4530 | + | 11.1535i | 0.389290 | + | 0.415379i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.367429 | − | 0.621002i | 0.0136648 | − | 0.0230953i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 23.5174 | 0.873414 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9463 | − | 34.5480i | −0.739768 | − | 1.28132i | −0.952600 | − | 0.304227i | \(-0.901602\pi\) |
0.212832 | − | 0.977089i | \(-0.431731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9447 | + | 1.72794i | 0.997950 | + | 0.0639979i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.6325 | − | 40.9327i | 0.874080 | − | 1.51395i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.4091 | + | 38.8137i | 0.827699 | + | 1.43362i | 0.899839 | + | 0.436222i | \(0.143684\pi\) |
−0.0721400 | + | 0.997395i | \(0.522983\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.8391 | − | 10.8150i | −0.584234 | − | 0.398919i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.3162 | − | 55.9732i | 1.19038 | − | 2.06180i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.64954 | + | 11.5173i | 0.244607 | + | 0.423672i | 0.962021 | − | 0.272975i | \(-0.0880076\pi\) |
−0.717414 | + | 0.696647i | \(0.754674\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0746010 | + | 0.132458i | 0.00274054 | + | 0.00486596i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.15562 | + | 3.73365i | −0.0790822 | + | 0.136974i | −0.902854 | − | 0.429947i | \(-0.858532\pi\) |
0.823772 | + | 0.566921i | \(0.191866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.71451 | − | 8.16578i | 0.172726 | − | 0.299171i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.6922 | + | 26.7505i | 0.537558 | + | 0.978749i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.385340 | + | 1.27174i | −0.0140800 | + | 0.0464682i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.7651 | − | 37.6983i | −0.794221 | − | 1.37563i | −0.923333 | − | 0.384001i | \(-0.874546\pi\) |
0.129112 | − | 0.991630i | \(-0.458787\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39.0739 | + | 0.417076i | 1.42393 | + | 0.0151991i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13.5115 | 0.491733 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.6790 | 1.26043 | 0.630215 | − | 0.776420i | \(-0.282967\pi\) | ||||
0.630215 | + | 0.776420i | \(0.282967\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −60.4028 | − | 0.644741i | −2.19248 | − | 0.0234026i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.75973 | + | 3.04794i | 0.0637902 | + | 0.110488i | 0.896157 | − | 0.443738i | \(-0.146348\pi\) |
−0.832367 | + | 0.554226i | \(0.813014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.58362 | + | 9.15886i | 0.310748 | + | 0.331573i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.3544 | − | 18.7313i | 0.410520 | − | 0.677232i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.36533 | + | 11.0251i | −0.229839 | + | 0.398092i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5075 | + | 33.7879i | −0.703457 | + | 1.21842i | 0.263788 | + | 0.964581i | \(0.415028\pi\) |
−0.967245 | + | 0.253843i | \(0.918305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.38884 | − | 16.6704i | −0.338131 | − | 0.600369i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.2169 | + | 40.2128i | 0.835054 | + | 1.44636i | 0.893987 | + | 0.448094i | \(0.147897\pi\) |
−0.0589329 | + | 0.998262i | \(0.518770\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.32538 | − | 5.75972i | 0.119451 | − | 0.206895i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.42318 | − | 7.70008i | 0.0869310 | − | 0.276239i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0552705 | − | 0.0957313i | −0.00198027 | − | 0.00342993i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.6139 | − | 20.1159i | 0.415578 | − | 0.719802i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23.0937 | − | 43.1323i | −0.825303 | − | 1.54142i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.08801 | − | 3.61654i | −0.0745242 | − | 0.129080i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.4424 | −1.69114 | −0.845569 | − | 0.533866i | \(-0.820739\pi\) | ||||
−0.845569 | + | 0.533866i | \(0.820739\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.4572 | − | 37.9555i | 0.799496 | − | 1.35125i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.70827 | − | 5.63778i | 0.0607390 | − | 0.200456i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.81393 | + | 16.9982i | −0.348503 | + | 0.603625i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.33937 | + | 2.26371i | −0.0475027 | + | 0.0802857i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.69773 | − | 13.3329i | 0.272668 | − | 0.472274i | −0.696876 | − | 0.717191i | \(-0.745427\pi\) |
0.969544 | + | 0.244917i | \(0.0787607\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0198 | + | 20.8190i | 0.425232 | + | 0.736523i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.8256 | + | 21.1583i | −0.453171 | + | 0.747593i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.73932 | −0.343693 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.18482 | − | 27.0123i | 0.288477 | − | 0.952059i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.74208 | − | 8.41981i | −0.166929 | − | 0.296391i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0433 | − | 26.0557i | −0.528893 | − | 0.916069i | −0.999432 | − | 0.0336903i | \(-0.989274\pi\) |
0.470539 | − | 0.882379i | \(-0.344059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2821 | 0.396170 | 0.198085 | − | 0.980185i | \(-0.436528\pi\) | ||||
0.198085 | + | 0.980185i | \(0.436528\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.58678 | + | 4.37200i | −0.0907224 | + | 0.153333i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.0902 | 0.983955 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.658944 | −0.0230535 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.35986 | − | 10.2916i | 0.117403 | − | 0.359618i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.25266 | 0.113519 | 0.0567593 | − | 0.998388i | \(-0.481923\pi\) | ||||
0.0567593 | + | 0.998388i | \(0.481923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.5968 | −0.508814 | −0.254407 | − | 0.967097i | \(-0.581880\pi\) | ||||
−0.254407 | + | 0.967097i | \(0.581880\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.9785 | + | 19.4929i | 0.382223 | + | 0.678656i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.7500 | −1.48656 | −0.743282 | − | 0.668978i | \(-0.766732\pi\) | ||||
−0.743282 | + | 0.668978i | \(0.766732\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.6799 | − | 30.6225i | −0.614049 | − | 1.06356i | −0.990551 | − | 0.137148i | \(-0.956207\pi\) |
0.376502 | − | 0.926416i | \(-0.377127\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.4846 | − | 32.9314i | 0.675912 | − | 1.14238i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.8755 | − | 17.9332i | −0.931180 | − | 0.621348i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.6214 | −0.436780 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.8291 | − | 0.442972i | −0.478005 | − | 0.0153114i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0886 | − | 26.1343i | −0.520917 | − | 0.902255i | −0.999704 | − | 0.0243242i | \(-0.992257\pi\) |
0.478787 | − | 0.877931i | \(-0.341077\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.8280 | + | 51.6637i | −1.02855 | + | 1.78151i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.77696 | + | 8.48173i | 0.164527 | + | 0.292126i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.81072 | + | 15.2606i | −0.303098 | + | 0.524981i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.4830 | + | 30.3918i | 0.978688 | + | 1.04428i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 36.8911 | + | 0.393777i | 1.26610 | + | 0.0135144i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.8797 | 0.407230 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.4789 | − | 35.4705i | −0.701184 | − | 1.21449i | −0.968051 | − | 0.250753i | \(-0.919322\pi\) |
0.266867 | − | 0.963733i | \(-0.414011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.305304 | − | 0.00651839i | −0.0104412 | − | 0.000222924i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.2283 | + | 26.3762i | −0.520190 | + | 0.900995i | 0.479535 | + | 0.877523i | \(0.340805\pi\) |
−0.999724 | + | 0.0234720i | \(0.992528\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.59467 | + | 2.76206i | 0.0544096 | + | 0.0942401i | 0.891947 | − | 0.452139i | \(-0.149339\pi\) |
−0.837538 | + | 0.546379i | \(0.816006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.36308 | + | 7.50912i | −0.0805337 | + | 0.255910i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.5498 | + | 20.0049i | −0.393161 | + | 0.680975i | −0.992865 | − | 0.119247i | \(-0.961952\pi\) |
0.599703 | + | 0.800222i | \(0.295285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.06128 | + | 10.4984i | 0.206090 | + | 0.356958i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.79598 | − | 6.41570i | 0.128918 | − | 0.217889i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.8976 | + | 29.2675i | −0.573212 | + | 0.992833i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.52349 | + | 14.7631i | −0.288808 | + | 0.500229i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.9882 | − | 38.2139i | −0.710344 | − | 1.29335i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −30.5576 | + | 7.13517i | −1.03304 | + | 0.241213i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.64469 | + | 2.84868i | 0.0555372 | + | 0.0961932i | 0.892457 | − | 0.451132i | \(-0.148980\pi\) |
−0.836920 | + | 0.547325i | \(0.815646\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.8945 | + | 42.0750i | −0.839672 | + | 1.41915i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.4835 | 1.73452 | 0.867262 | − | 0.497852i | \(-0.165878\pi\) | ||||
0.867262 | + | 0.497852i | \(0.165878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.359433 | −0.0120959 | −0.00604794 | − | 0.999982i | \(-0.501925\pi\) | ||||
−0.00604794 | + | 0.999982i | \(0.501925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.5493 | − | 22.2819i | −0.421840 | − | 0.748999i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.79998 | + | 10.0459i | 0.194744 | + | 0.337307i | 0.946817 | − | 0.321774i | \(-0.104279\pi\) |
−0.752072 | + | 0.659080i | \(0.770946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.9366 | + | 11.1931i | −1.60774 | + | 0.375406i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.9704 | − | 39.2770i | 0.836540 | − | 1.31583i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.167574 | − | 0.290247i | 0.00560767 | − | 0.00971276i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.6446 | − | 32.2935i | 0.623222 | − | 1.07945i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.9314 | + | 0.170053i | 0.531935 | + | 0.00567789i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.5360 | + | 21.7130i | 0.418100 | + | 0.724170i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.21548 | + | 3.83732i | −0.0738082 | + | 0.127840i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.7222 | + | 34.5806i | 1.05565 | + | 1.15077i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.7386 | + | 23.7960i | 0.456686 | + | 0.791004i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2895 | − | 21.2861i | 0.408067 | − | 0.706793i | −0.586606 | − | 0.809873i | \(-0.699536\pi\) |
0.994673 | + | 0.103079i | \(0.0328695\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.71356 | + | 16.0244i | −0.322179 | + | 0.531496i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.1678 | + | 34.9317i | 0.668190 | + | 1.15734i | 0.978410 | + | 0.206675i | \(0.0662642\pi\) |
−0.310219 | + | 0.950665i | \(0.600402\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.6096 | 1.74112 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.3483 | − | 34.3538i | −0.639634 | − | 1.13570i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.4976 | − | 26.1393i | −0.808981 | − | 0.863197i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.8377 | + | 18.7714i | −0.357501 | + | 0.619210i | −0.987543 | − | 0.157351i | \(-0.949705\pi\) |
0.630041 | + | 0.776562i | \(0.283038\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.17970 | − | 0.0446143i | −0.137726 | − | 0.00147009i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.06320 | + | 5.30562i | −0.100827 | + | 0.174637i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.19986 | − | 3.81028i | −0.0723311 | − | 0.125281i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.34405 | − | 15.1923i | −0.274055 | − | 0.498980i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.92818 | −0.260115 | −0.130058 | − | 0.991506i | \(-0.541516\pi\) | ||||
−0.130058 | + | 0.991506i | \(0.541516\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0291775 | + | 0.449493i | −0.000956254 | + | 0.0147316i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.5173 | + | 0.176306i | 0.540751 | + | 0.00577199i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18.8790 | − | 32.6994i | −0.617409 | − | 1.06938i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.84549 | 0.190964 | 0.0954819 | − | 0.995431i | \(-0.469561\pi\) | ||||
0.0954819 | + | 0.995431i | \(0.469561\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −56.4650 | − | 0.602709i | −1.84267 | − | 0.0196687i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39.0091 | −1.27166 | −0.635831 | − | 0.771829i | \(-0.719342\pi\) | ||||
−0.635831 | + | 0.771829i | \(0.719342\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.5851 | −0.377262 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.3556 | + | 16.3358i | 0.466987 | + | 0.531403i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.04371 | 0.228890 | 0.114445 | − | 0.993430i | \(-0.463491\pi\) | ||||
0.114445 | + | 0.993430i | \(0.463491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.56878 | 0.0833861 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.36826 | + | 0.0573009i | 0.174078 | + | 0.00185811i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.2379 | 0.914716 | 0.457358 | − | 0.889283i | \(-0.348796\pi\) | ||||
0.457358 | + | 0.889283i | \(0.348796\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.83336 | − | 6.63957i | −0.124044 | − | 0.214851i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −84.3329 | − | 0.900172i | −2.72610 | − | 0.0290984i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5432 | − | 34.7957i | 0.340458 | − | 1.12361i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9096 | −0.771277 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.781059 | − | 1.28851i | 0.0251693 | − | 0.0415216i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.5808 | − | 20.0585i | −0.372798 | − | 0.645705i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.430925 | − | 0.746384i | 0.0138576 | − | 0.0240021i | −0.859013 | − | 0.511953i | \(-0.828922\pi\) |
0.872871 | + | 0.487951i | \(0.162256\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.514403 | − | 0.00549075i | −0.0165250 | − | 0.000176388i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.6403 | − | 34.0181i | 0.630288 | − | 1.09169i | −0.357204 | − | 0.934026i | \(-0.616270\pi\) |
0.987493 | − | 0.157665i | \(-0.0503967\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.4239 | − | 34.4021i | 0.334176 | − | 1.10288i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.89562 | − | 5.14132i | −0.0927340 | − | 0.164654i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.5478 | −1.10528 | −0.552641 | − | 0.833419i | \(-0.686380\pi\) | ||||
−0.552641 | + | 0.833419i | \(0.686380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.3252 | + | 36.9363i | 0.681555 | + | 1.18049i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.85182 | − | 12.4753i | −0.218762 | − | 0.398307i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.0096 | + | 17.3372i | −0.319258 | + | 0.552971i | −0.980333 | − | 0.197349i | \(-0.936767\pi\) |
0.661076 | + | 0.750319i | \(0.270100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15.1857 | − | 26.3024i | −0.483856 | − | 0.838063i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.2990 | + | 5.17869i | −0.741616 | + | 0.164840i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.5298 | + | 59.8074i | −1.09798 | + | 1.90177i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.27853 | − | 3.94653i | −0.0723799 | − | 0.125366i | 0.827564 | − | 0.561371i | \(-0.189726\pi\) |
−0.899944 | + | 0.436006i | \(0.856393\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.36752 | − | 0.0679670i | −0.202067 | − | 0.00215687i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.2948 | − | 17.8311i | 0.326367 | − | 0.565284i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.8662 | + | 18.8207i | −0.344135 | + | 0.596059i | −0.985196 | − | 0.171431i | \(-0.945161\pi\) |
0.641061 | + | 0.767490i | \(0.278494\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.82803 | + | 7.77631i | −0.152752 | + | 0.246032i |
(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 | 1008.2.q.k.625.1 | 22 | ||
3.2 | odd | 2 | 3024.2.q.k.2305.5 | 22 | |||
4.3 | odd | 2 | 504.2.q.d.121.11 | yes | 22 | ||
7.4 | even | 3 | 1008.2.t.k.193.8 | 22 | |||
9.2 | odd | 6 | 3024.2.t.l.289.7 | 22 | |||
9.7 | even | 3 | 1008.2.t.k.961.8 | 22 | |||
12.11 | even | 2 | 1512.2.q.c.793.5 | 22 | |||
21.11 | odd | 6 | 3024.2.t.l.1873.7 | 22 | |||
28.11 | odd | 6 | 504.2.t.d.193.4 | yes | 22 | ||
36.7 | odd | 6 | 504.2.t.d.457.4 | yes | 22 | ||
36.11 | even | 6 | 1512.2.t.d.289.7 | 22 | |||
63.11 | odd | 6 | 3024.2.q.k.2881.5 | 22 | |||
63.25 | even | 3 | inner | 1008.2.q.k.529.1 | 22 | ||
84.11 | even | 6 | 1512.2.t.d.361.7 | 22 | |||
252.11 | even | 6 | 1512.2.q.c.1369.5 | 22 | |||
252.151 | odd | 6 | 504.2.q.d.25.11 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.11 | ✓ | 22 | 252.151 | odd | 6 | ||
504.2.q.d.121.11 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.d.193.4 | yes | 22 | 28.11 | odd | 6 | ||
504.2.t.d.457.4 | yes | 22 | 36.7 | odd | 6 | ||
1008.2.q.k.529.1 | 22 | 63.25 | even | 3 | inner | ||
1008.2.q.k.625.1 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.k.193.8 | 22 | 7.4 | even | 3 | |||
1008.2.t.k.961.8 | 22 | 9.7 | even | 3 | |||
1512.2.q.c.793.5 | 22 | 12.11 | even | 2 | |||
1512.2.q.c.1369.5 | 22 | 252.11 | even | 6 | |||
1512.2.t.d.289.7 | 22 | 36.11 | even | 6 | |||
1512.2.t.d.361.7 | 22 | 84.11 | even | 6 | |||
3024.2.q.k.2305.5 | 22 | 3.2 | odd | 2 | |||
3024.2.q.k.2881.5 | 22 | 63.11 | odd | 6 | |||
3024.2.t.l.289.7 | 22 | 9.2 | odd | 6 | |||
3024.2.t.l.1873.7 | 22 | 21.11 | odd | 6 |