Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
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, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.t (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 | 961.8 | ||
Character | \(\chi\) | \(=\) | 1008.961 |
Dual form | 1008.2.t.k.193.8 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0.849966 | − | 1.50916i | 0.490728 | − | 0.871313i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58188 | −0.707436 | −0.353718 | − | 0.935352i | \(-0.615083\pi\) | ||||
−0.353718 | + | 0.935352i | \(0.615083\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.80922 | + | 1.93047i | 0.683822 | + | 0.729649i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.55512 | − | 2.56547i | −0.518372 | − | 0.855155i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.17139 | −1.55923 | −0.779616 | − | 0.626258i | \(-0.784586\pi\) | ||||
−0.779616 | + | 0.626258i | \(0.784586\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.681985 | − | 1.18123i | −0.189149 | − | 0.327615i | 0.755818 | − | 0.654782i | \(-0.227239\pi\) |
−0.944967 | + | 0.327167i | \(0.893906\pi\) | |||||||
\(14\) | 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 | ||||||||
\(21\) | 4.45116 | − | 1.08957i | 0.971323 | − | 0.237763i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.74395 | −1.40621 | −0.703105 | − | 0.711086i | \(-0.748204\pi\) | ||||
−0.703105 | + | 0.711086i | \(0.748204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.49767 | −0.499534 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19349 | + | 0.166357i | −0.999487 | + | 0.0320154i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.70787 | − | 8.15427i | 0.874229 | − | 1.51421i | 0.0166475 | − | 0.999861i | \(-0.494701\pi\) |
0.857582 | − | 0.514348i | \(-0.171966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.33139 | + | 2.30604i | −0.239125 | + | 0.414177i | −0.960463 | − | 0.278406i | \(-0.910194\pi\) |
0.721339 | + | 0.692583i | \(0.243527\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.39550 | + | 7.80444i | −0.765159 | + | 1.35858i | ||||
\(34\) | 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 | ||||||||
\(39\) | −2.36233 | + | 0.0252156i | −0.378276 | + | 0.00403772i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.858924 | − | 1.48770i | −0.134141 | − | 0.232340i | 0.791128 | − | 0.611651i | \(-0.209494\pi\) |
−0.925269 | + | 0.379311i | \(0.876161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.12012 | − | 8.86831i | 0.780811 | − | 1.35240i | −0.150658 | − | 0.988586i | \(-0.548139\pi\) |
0.931470 | − | 0.363819i | \(-0.118527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.46000 | + | 4.05825i | 0.366715 | + | 0.604968i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.60417 | + | 4.51056i | 0.379857 | + | 0.657932i | 0.991041 | − | 0.133556i | \(-0.0426397\pi\) |
−0.611184 | + | 0.791489i | \(0.709306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.453429 | + | 6.98530i | −0.0647756 | + | 0.997900i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.99402 | + | 0.0853284i | −1.11939 | + | 0.0119484i | ||||
\(52\) | 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 | ||||||||
\(59\) | −4.66676 | + | 8.08307i | −0.607561 | + | 1.05233i | 0.384080 | + | 0.923300i | \(0.374519\pi\) |
−0.991641 | + | 0.129027i | \(0.958815\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.19512 | − | 12.4623i | −0.921241 | − | 1.59564i | −0.797498 | − | 0.603321i | \(-0.793844\pi\) |
−0.123742 | − | 0.992314i | \(-0.539490\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.13900 | − | 7.64360i | 0.269489 | − | 0.963003i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.07882 | + | 1.86856i | 0.133811 | + | 0.231767i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.24903 | + | 10.8236i | −0.763441 | + | 1.32232i | 0.177626 | + | 0.984098i | \(0.443158\pi\) |
−0.941067 | + | 0.338220i | \(0.890175\pi\) | |||||||
\(68\) | 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 | ||||||||
\(75\) | −2.12293 | + | 3.76938i | −0.245135 | + | 0.435250i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.35619 | − | 9.98321i | −1.06624 | − | 1.13769i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26752 | + | 5.65951i | 0.367625 | + | 0.636745i | 0.989194 | − | 0.146615i | \(-0.0468377\pi\) |
−0.621569 | + | 0.783360i | \(0.713504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.16323 | + | 7.97919i | −0.462581 | + | 0.886577i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.08661 | − | 8.81026i | 0.558328 | − | 0.967052i | −0.439309 | − | 0.898336i | \(-0.644777\pi\) |
0.997636 | − | 0.0687156i | \(-0.0218901\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65066 | + | 6.32314i | 0.395970 | + | 0.685840i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.30455 | − | 14.0358i | −0.890341 | − | 1.50479i | ||||
\(88\) | 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 | ||||||||
\(93\) | 2.34854 | + | 3.96933i | 0.243532 | + | 0.411601i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0508957 | − | 0.0881539i | 0.00522178 | − | 0.00904440i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.26638 | + | 12.5857i | −0.737789 | + | 1.27789i | 0.215700 | + | 0.976460i | \(0.430797\pi\) |
−0.953489 | + | 0.301428i | \(0.902537\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.04210 | + | 13.2670i | 0.808262 | + | 1.33339i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.24620 | 0.621520 | 0.310760 | − | 0.950488i | \(-0.399416\pi\) | ||||
0.310760 | + | 0.950488i | \(0.399416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.77762 | 0.569286 | 0.284643 | − | 0.958634i | \(-0.408125\pi\) | ||||
0.284643 | + | 0.958634i | \(0.408125\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.04118 | + | 1.72356i | −0.687149 | + | 0.168202i | ||||
\(106\) | 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 | 0.808899 | − | 0.587948i | \(-0.200064\pi\) |
−0.913627 | + | 0.406553i | \(0.866731\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.6681 | 0.994804 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.96985 | + | 3.58656i | −0.182112 | + | 0.331578i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.54121 | − | 11.6870i | 0.324623 | − | 1.07135i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.7432 | 1.43120 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.97523 | + | 0.0317577i | −0.268268 | + | 0.00286349i | ||||
\(124\) | 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 | ||||||||
\(129\) | −9.03175 | − | 15.2648i | −0.795202 | − | 1.34399i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.5404 | −1.18303 | −0.591515 | − | 0.806294i | \(-0.701470\pi\) | ||||
−0.591515 | + | 0.806294i | \(0.701470\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.165791 | + | 0.0387119i | −0.0143759 | + | 0.00335675i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.21545 | − | 0.263156i | 0.707074 | − | 0.0226488i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.7420 | 1.17406 | 0.587029 | − | 0.809566i | \(-0.300298\pi\) | ||||
0.587029 | + | 0.809566i | \(0.300298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.79328 | − | 11.7663i | −0.576198 | − | 0.998005i | −0.995910 | − | 0.0903476i | \(-0.971202\pi\) |
0.419712 | − | 0.907657i | \(-0.362131\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 10.1565 | + | 6.62156i | 0.837696 | + | 0.546137i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.96066 | 0.488317 | 0.244158 | − | 0.969735i | \(-0.421488\pi\) | ||||
0.244158 | + | 0.969735i | \(0.421488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.54142 | −0.695091 | −0.347546 | − | 0.937663i | \(-0.612985\pi\) | ||||
−0.347546 | + | 0.937663i | \(0.612985\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | 1.31996 | − | 2.28623i | 0.105344 | − | 0.182461i | −0.808535 | − | 0.588449i | \(-0.799739\pi\) |
0.913879 | + | 0.405987i | \(0.133072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.66266 | + | 0.0177473i | −0.131857 | + | 0.00140745i | ||||
\(160\) | 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 | ||||||||
\(165\) | 6.95314 | − | 12.3457i | 0.541301 | − | 0.961108i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.98937 | − | 6.90979i | −0.308706 | − | 0.534695i | 0.669373 | − | 0.742926i | \(-0.266563\pi\) |
−0.978080 | + | 0.208231i | \(0.933229\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.56979 | − | 9.64716i | 0.428446 | − | 0.742090i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.193002 | − | 0.00412067i | 0.0147592 | − | 0.000315116i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.83170 | − | 6.63670i | −0.291319 | − | 0.504579i | 0.682803 | − | 0.730603i | \(-0.260761\pi\) |
−0.974122 | + | 0.226023i | \(0.927427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.51884 | − | 4.82168i | −0.341592 | − | 0.364485i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.23204 | + | 13.9132i | 0.618758 | + | 1.04578i | ||||
\(178\) | 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 | ||||||||
\(185\) | −1.39326 | + | 2.41320i | −0.102435 | + | 0.177422i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.9346 | + | 20.6713i | 0.872742 | + | 1.51163i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.71732 | − | 9.72490i | −0.706831 | − | 0.707382i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.42330 | + | 4.19728i | 0.175344 | + | 0.303704i | 0.940280 | − | 0.340402i | \(-0.110563\pi\) |
−0.764936 | + | 0.644106i | \(0.777230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.32091 | − | 12.6802i | 0.526970 | − | 0.912739i | −0.472536 | − | 0.881312i | \(-0.656661\pi\) |
0.999506 | − | 0.0314278i | \(-0.0100054\pi\) | |||||||
\(194\) | 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 | ||||||||
\(201\) | 11.0231 | + | 18.6305i | 0.777511 | + | 1.31409i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.2591 | − | 5.66448i | 1.70266 | − | 0.397569i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.35871 | + | 2.35336i | 0.0948965 | + | 0.164366i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.4876 | + | 17.3014i | 0.728940 | + | 1.20253i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.166385 | − | 0.288188i | 0.0115091 | − | 0.0199344i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43389 | + | 12.8759i | 0.511770 | + | 0.886412i | 0.999907 | + | 0.0136450i | \(0.00434348\pi\) |
−0.488137 | + | 0.872767i | \(0.662323\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.81771 | − | 6.77853i | 0.261585 | − | 0.464457i | ||||
\(214\) | 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 | ||||||||
\(219\) | −3.26180 | + | 0.0348166i | −0.220412 | + | 0.00235269i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.14778 | + | 5.45212i | −0.211743 | + | 0.366749i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.2085 | + | 19.4136i | −0.750574 | + | 1.30003i | 0.196971 | + | 0.980409i | \(0.436890\pi\) |
−0.947545 | + | 0.319623i | \(0.896444\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.88417 | + | 6.40769i | 0.258944 | + | 0.427179i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.89450 | −0.258487 | −0.129243 | − | 0.991613i | \(-0.541255\pi\) | ||||
−0.129243 | + | 0.991613i | \(0.541255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.38717 | −0.0916669 | −0.0458334 | − | 0.998949i | \(-0.514594\pi\) | ||||
−0.0458334 | + | 0.998949i | \(0.514594\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.0187 | + | 5.63458i | −1.51452 | + | 0.370728i | ||||
\(232\) | 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 | 0.939600 | − | 0.342274i | \(-0.111197\pi\) |
−0.766218 | + | 0.642581i | \(0.777864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.416592 | 0.0268351 | 0.0134175 | − | 0.999910i | \(-0.495729\pi\) | ||||
0.0134175 | + | 0.999910i | \(0.495729\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.50326 | + | 13.0650i | 0.545484 | + | 0.838121i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.717269 | − | 11.0499i | 0.0458246 | − | 0.705951i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0877694 | 0.00558464 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.97263 | − | 15.1649i | −0.568618 | − | 0.961037i | ||||
\(250\) | 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 | ||||||||
\(255\) | 12.6456 | − | 0.134979i | 0.791895 | − | 0.00845271i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0461 | −0.689039 | −0.344520 | − | 0.938779i | \(-0.611958\pi\) | ||||
−0.344520 | + | 0.938779i | \(0.611958\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.53850 | − | 1.05973i | 0.282008 | − | 0.0658486i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −28.2408 | + | 0.602954i | −1.74806 | + | 0.0373219i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.4620 | 1.57006 | 0.785028 | − | 0.619460i | \(-0.212648\pi\) | ||||
0.785028 | + | 0.619460i | \(0.212648\pi\) | |||||||
\(264\) | 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 | ||||||||
\(273\) | −4.32266 | − | 4.51479i | −0.261619 | − | 0.273247i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.9164 | 0.778889 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.0917 | 1.32736 | 0.663680 | − | 0.748016i | \(-0.268993\pi\) | ||||
0.663680 | + | 0.748016i | \(0.268993\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.98653 | − | 0.170516i | 0.478141 | − | 0.0102085i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.81009 | + | 4.86721i | −0.167636 | + | 0.290354i | −0.937588 | − | 0.347748i | \(-0.886947\pi\) |
0.769952 | + | 0.638101i | \(0.220280\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6502 | − | 18.4466i | 0.633086 | − | 1.09654i | −0.353831 | − | 0.935309i | \(-0.615121\pi\) |
0.986917 | − | 0.161228i | \(-0.0515454\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0897785 | − | 0.151737i | −0.00531802 | − | 0.00898815i | ||||
\(286\) | 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 | ||||||||
\(291\) | 12.8177 | + | 21.6636i | 0.751387 | + | 1.26994i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.1128 | + | 24.4440i | 0.824477 | + | 1.42804i | 0.902319 | + | 0.431070i | \(0.141864\pi\) |
−0.0778418 | + | 0.996966i | \(0.524803\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.38224 | − | 12.7864i | 0.429811 | − | 0.744454i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.8575 | − | 0.860295i | 1.55843 | − | 0.0499194i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.59927 | + | 7.96617i | 0.265983 | + | 0.460696i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3834 | − | 6.16050i | 1.52072 | − | 0.355086i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.30906 | − | 9.42650i | 0.304997 | − | 0.541538i | ||||
\(304\) | 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 | ||||||||
\(311\) | 4.76840 | − | 8.25911i | 0.270391 | − | 0.468331i | −0.698571 | − | 0.715541i | \(-0.746180\pi\) |
0.968962 | + | 0.247210i | \(0.0795137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.3010 | − | 28.2341i | −0.921386 | − | 1.59589i | −0.797273 | − | 0.603619i | \(-0.793725\pi\) |
−0.124112 | − | 0.992268i | \(-0.539608\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.38364 | + | 12.0912i | −0.190646 | + | 0.681263i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.54977 | + | 2.68428i | 0.0870438 | + | 0.150764i | 0.906260 | − | 0.422720i | \(-0.138925\pi\) |
−0.819216 | + | 0.573484i | \(0.805591\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.3462 | + | 42.1689i | −1.36313 | + | 2.36100i | ||||
\(320\) | 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 | ||||||||
\(327\) | −8.21702 | + | 0.0877087i | −0.454402 | + | 0.00485030i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.99597 | + | 13.1879i | −0.220305 | + | 0.727071i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.83825 | − | 3.18394i | −0.101039 | − | 0.175005i | 0.811074 | − | 0.584944i | \(-0.198883\pi\) |
−0.912113 | + | 0.409939i | \(0.865550\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.28339 | + | 0.112803i | −0.289528 | + | 0.00618157i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.88519 | − | 17.1216i | 0.540086 | − | 0.935456i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.15866 | + | 10.6671i | 0.335483 | + | 0.581074i | 0.983578 | − | 0.180486i | \(-0.0577670\pi\) |
−0.648094 | + | 0.761560i | \(0.724434\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.85628 | + | 0.0411620i | −0.209444 | + | 0.00223562i | ||||
\(340\) | 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 | ||||||||
\(345\) | 9.06751 | − | 16.0998i | 0.488178 | − | 0.866786i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.85078 | + | 15.3300i | −0.475135 | + | 0.822958i | −0.999594 | − | 0.0284778i | \(-0.990934\pi\) |
0.524460 | + | 0.851435i | \(0.324267\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.562639 | − | 0.974519i | 0.0301174 | − | 0.0521648i | −0.850574 | − | 0.525856i | \(-0.823745\pi\) |
0.880691 | + | 0.473691i | \(0.157079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.73839 | + | 6.02127i | 0.199540 | + | 0.321391i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9625 | −0.583475 | −0.291738 | − | 0.956498i | \(-0.594233\pi\) | ||||
−0.291738 | + | 0.956498i | \(0.594233\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.10515 | −0.377102 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −14.6277 | − | 15.2778i | −0.774179 | − | 0.808589i | ||||
\(358\) | 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 | ||||||||
\(367\) | −34.8273 | −1.81797 | −0.908986 | − | 0.416826i | \(-0.863142\pi\) | ||||
−0.908986 | + | 0.416826i | \(0.863142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.48092 | + | 4.51709i | −0.129151 | + | 0.235150i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.736530 | − | 2.43076i | 0.0382387 | − | 0.126199i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.1585 | −1.19910 | −0.599551 | − | 0.800336i | \(-0.704654\pi\) | ||||
−0.599551 | + | 0.800336i | \(0.704654\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.0809 | − | 17.8992i | 0.520576 | − | 0.924310i | ||||
\(376\) | 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 | ||||||||
\(381\) | 15.8142 | − | 28.0789i | 0.810186 | − | 1.43853i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.2041 | −1.18567 | −0.592837 | − | 0.805322i | \(-0.701992\pi\) | ||||
−0.592837 | + | 0.805322i | \(0.701992\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.8003 | + | 15.7922i | 0.754294 | + | 0.804844i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.7137 | + | 0.655753i | −1.56127 | + | 0.0333338i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.13474 | −0.463149 | −0.231575 | − | 0.972817i | \(-0.574388\pi\) | ||||
−0.231575 | + | 0.972817i | \(0.574388\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | −0.0824939 | + | 0.283108i | −0.00412986 | + | 0.0141731i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.94696 | 0.147164 | 0.0735821 | − | 0.997289i | \(-0.476557\pi\) | ||||
0.0735821 | + | 0.997289i | \(0.476557\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.63196 | 0.180921 | ||||||||
\(404\) | 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 | ||||||||
\(409\) | −3.30296 | + | 5.72089i | −0.163321 | + | 0.282880i | −0.936058 | − | 0.351847i | \(-0.885554\pi\) |
0.772737 | + | 0.634726i | \(0.218887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.6802 | − | 20.7388i | 0.576143 | − | 1.02297i | ||||
\(412\) | 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 | ||||||||
\(417\) | −23.5313 | + | 0.251173i | −1.15233 | + | 0.0123000i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.381961 | + | 0.661576i | 0.0186600 | + | 0.0323201i | 0.875205 | − | 0.483753i | \(-0.160727\pi\) |
−0.856545 | + | 0.516073i | \(0.827393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.48798 | + | 4.30931i | −0.121257 | + | 0.210023i | −0.920264 | − | 0.391299i | \(-0.872026\pi\) |
0.799007 | + | 0.601322i | \(0.205359\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.52189 | − | 13.6953i | 0.365727 | − | 0.665891i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.76414 | + | 9.98378i | 0.279602 | + | 0.484285i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.0406 | − | 36.4371i | 0.534290 | − | 1.76331i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.2165 | − | 0.130399i | 0.589819 | − | 0.00629575i | ||||
\(430\) | 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 | ||||||||
\(437\) | 0.216981 | − | 0.375823i | 0.0103796 | − | 0.0179780i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0597 | − | 17.4239i | −0.480122 | − | 0.831596i | 0.519618 | − | 0.854399i | \(-0.326074\pi\) |
−0.999740 | + | 0.0228028i | \(0.992741\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.6257 | − | 9.69969i | 0.886937 | − | 0.461890i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.60623 | − | 7.97822i | −0.218848 | − | 0.379057i | 0.735608 | − | 0.677408i | \(-0.236897\pi\) |
−0.954456 | + | 0.298351i | \(0.903563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.52316 | − | 11.2984i | 0.309227 | − | 0.535597i | ||||
\(446\) | 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 | ||||||||
\(453\) | −7.25992 | + | 12.8904i | −0.341101 | + | 0.605642i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.65539 | + | 5.46327i | −0.0776058 | + | 0.256122i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.39776 | − | 16.2774i | −0.439609 | − | 0.761425i | 0.558050 | − | 0.829807i | \(-0.311550\pi\) |
−0.997659 | + | 0.0683823i | \(0.978216\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.6505 | + | 20.3757i | 0.590477 | + | 0.951056i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3773 | − | 17.9739i | 0.483317 | − | 0.837129i | −0.516500 | − | 0.856287i | \(-0.672765\pi\) |
0.999816 | + | 0.0191582i | \(0.00609862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0414 | − | 17.3922i | −0.466663 | − | 0.808284i | 0.532612 | − | 0.846360i | \(-0.321211\pi\) |
−0.999275 | + | 0.0380753i | \(0.987877\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.71509 | − | 6.27899i | −0.172283 | − | 0.291181i | ||||
\(466\) | 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 | ||||||||
\(471\) | −2.32837 | − | 3.93525i | −0.107286 | − | 0.181327i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −26.4781 | + | 45.8615i | −1.21747 | + | 2.10871i | ||||
\(474\) | 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 | ||||||||
\(479\) | 40.0654 | 1.83064 | 0.915319 | − | 0.402731i | \(-0.131939\pi\) | ||||
0.915319 | + | 0.402731i | \(0.131939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.40268 | −0.109553 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.0184 | + | 7.34799i | −1.36588 | + | 0.334345i | ||||
\(484\) | 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 | 0.872388 | − | 0.488815i | \(-0.162571\pi\) |
−0.859520 | + | 0.511102i | \(0.829237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −43.4594 | −1.95731 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.7216 | − | 20.9868i | −0.571794 | − | 0.943285i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.12630 | + | 8.67090i | 0.364514 | + | 0.388943i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.928593 | 0.0415695 | 0.0207848 | − | 0.999784i | \(-0.493384\pi\) | ||||
0.0207848 | + | 0.999784i | \(0.493384\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.8188 | + | 0.147502i | −0.617378 | + | 0.00658990i | ||||
\(502\) | 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 | ||||||||
\(507\) | −9.82496 | − | 16.6055i | −0.436342 | − | 0.737474i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.96781 | 0.397491 | 0.198746 | − | 0.980051i | \(-0.436313\pi\) | ||||
0.198746 | + | 0.980051i | \(0.436313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.44492 | − | 4.76867i | 0.0639196 | − | 0.210953i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.157826 | − | 0.294772i | 0.00696819 | − | 0.0130145i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.13948 | −0.402734 | ||||||||
\(516\) | 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 | ||||||||
\(525\) | −11.1175 | + | 2.72138i | −0.485209 | + | 0.118771i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.2904 | 0.535377 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.4808 | 0.977427 | ||||||||
\(530\) | 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 | ||||||||
\(535\) | −0.397250 | + | 0.688057i | −0.0171746 | + | 0.0297473i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40.8270 | + | 0.435789i | −1.76182 | + | 0.0188057i | ||||
\(538\) | 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 | ||||||||
\(543\) | 14.7639 | − | 26.2141i | 0.633580 | − | 1.12495i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.75250 | + | 6.49952i | 0.160739 | + | 0.278409i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.8974 | − | 27.5351i | 0.679725 | − | 1.17732i | −0.295339 | − | 0.955392i | \(-0.595433\pi\) |
0.975064 | − | 0.221925i | \(-0.0712340\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.7824 | + | 37.8392i | −0.886971 | + | 1.61494i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.302944 | + | 0.524715i | 0.0129059 | + | 0.0223536i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.01385 | + | 16.5472i | −0.213211 | + | 0.703657i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.45768 | + | 4.15379i | 0.104323 | + | 0.176319i | ||||
\(556\) | 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 | ||||||||
\(563\) | −22.3270 | + | 38.6715i | −0.940972 | + | 1.62981i | −0.177350 | + | 0.984148i | \(0.556752\pi\) |
−0.763622 | + | 0.645664i | \(0.776581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.76106 | + | 3.05025i | 0.0740885 | + | 0.128325i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.9358 | + | 6.39914i | −0.963213 | + | 0.268739i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.6102 | + | 18.3775i | 0.444804 | + | 0.770423i | 0.998039 | − | 0.0626026i | \(-0.0199401\pi\) |
−0.553235 | + | 0.833025i | \(0.686607\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.94786 | − | 10.3020i | 0.248910 | − | 0.431125i | −0.714313 | − | 0.699826i | \(-0.753261\pi\) |
0.963224 | + | 0.268701i | \(0.0865943\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | −12.9139 | − | 21.8261i | −0.536682 | − | 0.907063i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.2107 | − | 6.12018i | 1.08741 | − | 0.253908i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.48224 | + | 4.29937i | 0.102804 | + | 0.178062i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.11605 | − | 5.67350i | 0.128833 | − | 0.234570i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.92138 | + | 17.1843i | −0.409499 | + | 0.709274i | −0.994834 | − | 0.101518i | \(-0.967630\pi\) |
0.585334 | + | 0.810792i | \(0.300963\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0856730 | − | 0.148390i | −0.00353010 | − | 0.00611431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.3190 | + | 28.9752i | −0.671274 | + | 1.19188i | ||||
\(592\) | 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 | ||||||||
\(597\) | −22.5430 | + | 0.240624i | −0.922622 | + | 0.00984809i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.5223 | − | 28.6174i | 0.675081 | − | 1.16928i | −0.301364 | − | 0.953509i | \(-0.597442\pi\) |
0.976445 | − | 0.215766i | \(-0.0692248\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4951 | − | 19.9100i | 0.468893 | − | 0.812147i | −0.530475 | − | 0.847701i | \(-0.677986\pi\) |
0.999368 | + | 0.0355541i | \(0.0113196\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37.4856 | − | 0.800336i | 1.52653 | − | 0.0325922i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −24.9038 | −1.01248 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.6564 | −1.12254 | −0.561269 | − | 0.827634i | \(-0.689686\pi\) | ||||
−0.561269 | + | 0.827634i | \(0.689686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0709 | − | 41.4255i | 0.489136 | − | 1.67865i | ||||
\(610\) | 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 | 0.564286 | − | 0.825580i | \(-0.309152\pi\) |
−0.997116 | + | 0.0758961i | \(0.975818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.2522 | −1.13555 | −0.567776 | − | 0.823183i | \(-0.692196\pi\) | ||||
−0.567776 | + | 0.823183i | \(0.692196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.0246 | − | 1.12190i | 1.40549 | − | 0.0450204i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −21.2489 | + | 4.96160i | −0.851320 | + | 0.198782i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.27330 | −0.250932 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.293499 | − | 0.496052i | −0.0117212 | − | 0.0198104i | ||||
\(628\) | 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 | ||||||||
\(633\) | 25.7503 | − | 0.274859i | 1.02348 | − | 0.0109247i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.4319 | −1.16797 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.56050 | − | 4.22826i | 0.339179 | − | 0.167530i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.98496 | − | 11.5230i | −0.276321 | − | 0.455844i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.8978 | 1.29939 | 0.649693 | − | 0.760197i | \(-0.274897\pi\) | ||||
0.649693 | + | 0.760197i | \(0.274897\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1276 | − | 17.5415i | −0.399392 | − | 0.691767i | 0.594259 | − | 0.804274i | \(-0.297445\pi\) |
−0.993651 | + | 0.112506i | \(0.964112\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −3.41365 | + | 11.7152i | −0.133792 | + | 0.459154i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.58036 | 0.140110 | 0.0700552 | − | 0.997543i | \(-0.477682\pi\) | ||||
0.0700552 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.4192 | 0.836918 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.71988 | + | 4.95217i | −0.106113 | + | 0.193203i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.13582 | + | 15.8237i | −0.355881 | + | 0.616404i | −0.987268 | − | 0.159064i | \(-0.949152\pi\) |
0.631387 | + | 0.775468i | \(0.282486\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.11696 | + | 1.93462i | −0.0434446 | + | 0.0752482i | −0.886930 | − | 0.461904i | \(-0.847167\pi\) |
0.843485 | + | 0.537152i | \(0.180500\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.55260 | + | 9.38461i | 0.215645 | + | 0.364468i | ||||
\(664\) | 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 | ||||||||
\(669\) | 19.7714 | + | 33.4163i | 0.764407 | + | 1.29195i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.2087 | + | 64.4474i | 1.43643 | + | 2.48797i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4804 | + | 21.6166i | −0.481083 | + | 0.833260i | −0.999764 | − | 0.0217074i | \(-0.993090\pi\) |
0.518681 | + | 0.854968i | \(0.326423\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.9716 | − | 0.415504i | 0.499278 | − | 0.0159928i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.90633 | + | 17.1583i | 0.380731 | + | 0.659446i | 0.991167 | − | 0.132620i | \(-0.0423389\pi\) |
−0.610436 | + | 0.792066i | \(0.709006\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.4429 | + | 8.74287i | −1.43693 | + | 0.335521i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.31019 | + | 5.87741i | −0.126847 | + | 0.225223i | ||||
\(682\) | 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 | ||||||||
\(689\) | −0.654700 | + | 1.13397i | −0.0249421 | + | 0.0432010i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2552 | + | 35.0831i | 0.770545 | + | 1.33462i | 0.937265 | + | 0.348619i | \(0.113349\pi\) |
−0.166719 | + | 0.986004i | \(0.553317\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.0616 | + | 39.5280i | −0.420196 | + | 1.50155i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.7461 | + | 18.6128i | 0.407624 | + | 0.706025i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.96446 | + | 6.86665i | −0.150165 | + | 0.260093i | ||||
\(698\) | 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 | ||||||||
\(705\) | −14.2695 | + | 0.152313i | −0.537419 | + | 0.00573642i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.3008 | + | 12.0581i | 0.425009 | + | 0.453492i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.7407 | + | 32.4599i | 0.703822 | + | 1.21906i | 0.967115 | + | 0.254340i | \(0.0818581\pi\) |
−0.263293 | + | 0.964716i | \(0.584809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.43791 | − | 17.1839i | 0.353949 | − | 0.644447i | ||||
\(712\) | 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 | ||||||||
\(717\) | 9.28474 | − | 0.0991056i | 0.346745 | − | 0.00370116i | ||||
\(718\) | 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 | ||||||||
\(723\) | 0.354089 | − | 0.628703i | 0.0131687 | − | 0.0233817i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.7587 | + | 20.3667i | −0.436707 | + | 0.756399i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9463 | + | 34.5480i | −0.739768 | + | 1.28132i | 0.212832 | + | 0.977089i | \(0.431731\pi\) |
−0.952600 | + | 0.304227i | \(0.901602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.9447 | − | 1.72794i | 0.997950 | − | 0.0639979i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.2650 | −1.74816 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.8182 | −1.65540 | −0.827699 | − | 0.561172i | \(-0.810350\pi\) | ||||
−0.827699 | + | 0.561172i | \(0.810350\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.0664 | − | 10.4745i | −0.592616 | − | 0.386357i | ||||
\(736\) | 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 | 0.823772 | − | 0.566921i | \(-0.191866\pi\) |
−0.902854 | + | 0.429947i | \(0.858532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.42903 | −0.345453 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.5127 | + | 0.651460i | −1.11640 | + | 0.0238357i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.29402 | − | 0.302153i | 0.0472826 | − | 0.0110404i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.5303 | 1.58844 | 0.794221 | − | 0.607629i | \(-0.207879\pi\) | ||||
0.794221 | + | 0.607629i | \(0.207879\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.1757 | + | 34.0475i | −0.698803 | + | 1.24076i | ||||
\(754\) | 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 | ||||||||
\(759\) | 29.6430 | − | 52.6327i | 1.07597 | − | 1.91045i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.51946 | −0.127580 | −0.0637902 | − | 0.997963i | \(-0.520319\pi\) | ||||
−0.0637902 | + | 0.997963i | \(0.520319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.64000 | − | 12.0131i | 0.131777 | − | 0.434902i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.5446 | − | 19.1989i | 0.381240 | − | 0.694136i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.7307 | 0.459677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.5075 | − | 33.7879i | −0.703457 | − | 1.21842i | −0.967245 | − | 0.253843i | \(-0.918305\pi\) |
0.263788 | − | 0.964581i | \(-0.415028\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | 2.25826 | − | 7.75005i | 0.0810147 | − | 0.278031i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.110541 | 0.00396054 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.2278 | −0.831156 | ||||||||
\(782\) | 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 | ||||||||
\(787\) | 23.7212 | − | 41.0863i | 0.845569 | − | 1.46457i | −0.0395575 | − | 0.999217i | \(-0.512595\pi\) |
0.885126 | − | 0.465351i | \(-0.154072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.6419 | − | 38.4262i | 0.770471 | − | 1.36801i | ||||
\(790\) | 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 | ||||||||
\(795\) | 2.63012 | − | 0.0280740i | 0.0932808 | − | 0.000995681i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.69773 | + | 13.3329i | 0.272668 | + | 0.472274i | 0.969544 | − | 0.244917i | \(-0.0787607\pi\) |
−0.696876 | + | 0.717191i | \(0.745427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0198 | − | 20.8190i | 0.425232 | − | 0.736523i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.7365 | − | 0.528136i | 0.874020 | − | 0.0186608i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.86966 | + | 8.43450i | 0.171847 | + | 0.297647i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.3009 | + | 20.5944i | 0.680269 | + | 0.725858i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.66281 | − | 0.103141i | 0.340147 | − | 0.00363074i | ||||
\(808\) | 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 | ||||||||
\(815\) | −14.0451 | + | 24.3268i | −0.491978 | + | 0.852130i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.329472 | + | 0.570662i | 0.0115268 | + | 0.0199650i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.4876 | + | 2.68616i | −0.366468 | + | 0.0938620i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.62633 | − | 2.81688i | −0.0567593 | − | 0.0983099i | 0.836250 | − | 0.548349i | \(-0.184743\pi\) |
−0.893009 | + | 0.450039i | \(0.851410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.29842 | − | 12.6412i | 0.254407 | − | 0.440645i | −0.710327 | − | 0.703871i | \(-0.751453\pi\) |
0.964734 | + | 0.263226i | \(0.0847865\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | 18.7772 | − | 33.3398i | 0.651373 | − | 1.15655i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.9683 | − | 14.3083i | 1.00369 | − | 0.495752i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.31068 | + | 10.9304i | 0.218390 | + | 0.378263i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.53094 | − | 12.1979i | 0.225742 | − | 0.421620i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.0886 | + | 26.1343i | −0.520917 | + | 0.902255i | 0.478787 | + | 0.877931i | \(0.341077\pi\) |
−0.999704 | + | 0.0243242i | \(0.992257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.8280 | − | 51.6637i | −1.02855 | − | 1.78151i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.95692 | + | 8.37783i | 0.170725 | + | 0.288548i | ||||
\(844\) | 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 | ||||||||
\(849\) | −18.7866 | − | 31.7518i | −0.644754 | − | 1.08972i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.93984 | + | 10.2881i | −0.203615 | + | 0.352672i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.4789 | + | 35.4705i | −0.701184 | + | 1.21449i | 0.266867 | + | 0.963733i | \(0.414011\pi\) |
−0.968051 | + | 0.250753i | \(0.919322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.305304 | + | 0.00651839i | −0.0104412 | + | 0.000222924i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.4566 | 1.04038 | 0.520190 | − | 0.854051i | \(-0.325861\pi\) | ||||
0.520190 | + | 0.854051i | \(0.325861\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.18935 | −0.108819 | −0.0544096 | − | 0.998519i | \(-0.517328\pi\) | ||||
−0.0544096 | + | 0.998519i | \(0.517328\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.44416 | − | 5.68614i | −0.185537 | − | 0.193783i | ||||
\(862\) | 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 | ||||||||
\(871\) | 17.0470 | 0.577615 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 43.5883 | − | 0.930632i | 1.47524 | − | 0.0314971i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21.4581 | + | 22.8961i | 0.725415 | + | 0.774030i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.28938 | −0.111074 | −0.0555372 | − | 0.998457i | \(-0.517687\pi\) | ||||
−0.0555372 | + | 0.998457i | \(0.517687\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 48.8853 | − | 0.521803i | 1.64886 | − | 0.0176000i | ||||
\(880\) | 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 | ||||||||
\(885\) | −13.0221 | − | 22.0090i | −0.437732 | − | 0.739824i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.6000 | −0.389488 | −0.194744 | − | 0.980854i | \(-0.562388\pi\) | ||||
−0.194744 | + | 0.980854i | \(0.562388\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.6618 | + | 35.9177i | 1.12898 | + | 1.20464i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.5297 | − | 41.2635i | 0.721271 | − | 1.38238i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.335149 | −0.0112153 | ||||||||
\(894\) | 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 | ||||||||
\(903\) | 13.1279 | − | 45.0530i | 0.436868 | − | 1.49927i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.4772 | −0.913373 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5791 | −0.816135 | −0.408067 | − | 0.912952i | \(-0.633797\pi\) | ||||
−0.408067 | + | 0.912952i | \(0.633797\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.71356 | − | 16.0244i | −0.322179 | − | 0.531496i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.1678 | − | 34.9317i | 0.668190 | − | 1.15734i | −0.310219 | − | 0.950665i | \(-0.600402\pi\) |
0.978410 | − | 0.206675i | \(-0.0662642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.3048 | + | 45.5613i | −0.870562 | + | 1.50786i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 39.4254 | − | 0.420828i | 1.30336 | − | 0.0139121i | ||||
\(916\) | 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 | ||||||||
\(921\) | 2.05122 | − | 3.64204i | 0.0675898 | − | 0.120009i | ||||
\(922\) | 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 | ||||||||
\(927\) | −8.98487 | − | 14.8223i | −0.295102 | − | 0.486828i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.96409 | + | 6.86601i | 0.130058 | + | 0.225266i | 0.923699 | − | 0.383120i | \(-0.125150\pi\) |
−0.793641 | + | 0.608386i | \(0.791817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.374684 | − | 0.250015i | −0.0122798 | − | 0.00819392i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.41132 | − | 14.2162i | −0.275374 | − | 0.465418i | ||||
\(934\) | 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 | ||||||||
\(941\) | 19.5046 | − | 33.7829i | 0.635831 | − | 1.10129i | −0.350508 | − | 0.936560i | \(-0.613991\pi\) |
0.986339 | − | 0.164731i | \(-0.0526756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.79254 | + | 10.0330i | 0.188631 | + | 0.326719i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 15.3716 | + | 15.3836i | 0.500038 | + | 0.500428i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.52185 | − | 6.10003i | −0.114445 | − | 0.198224i | 0.803113 | − | 0.595827i | \(-0.203176\pi\) |
−0.917558 | + | 0.397603i | \(0.869842\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.28439 | + | 2.22463i | −0.0416930 | + | 0.0722145i | ||||
\(950\) | 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 | ||||||||
\(957\) | 42.9460 | + | 72.5844i | 1.38825 | + | 2.34632i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.8623 | + | 26.5285i | 0.802846 | + | 0.856650i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.9548 | + | 20.7063i | 0.385639 | + | 0.667946i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.50641 | + | 0.0321626i | −0.0485434 | + | 0.00103643i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11.5808 | + | 20.0585i | −0.372798 | + | 0.645705i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.430925 | + | 0.746384i | 0.0138576 | + | 0.0240021i | 0.872871 | − | 0.487951i | \(-0.162256\pi\) |
−0.859013 | + | 0.511953i | \(0.828922\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.252447 | − | 0.448232i | 0.00810975 | − | 0.0143993i | ||||
\(970\) | 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 | ||||||||
\(975\) | 5.90032 | − | 0.0629802i | 0.188962 | − | 0.00201698i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.2739 | − | 29.9193i | 0.552641 | − | 0.957202i | −0.445442 | − | 0.895311i | \(-0.646953\pi\) |
0.998083 | − | 0.0618913i | \(-0.0197132\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 20.0193 | 0.638516 | 0.319258 | − | 0.947668i | \(-0.396566\pi\) | ||||
0.319258 | + | 0.947668i | \(0.396566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.3714 | 0.967712 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.5061 | + | 17.2398i | 0.525396 | + | 0.548749i | ||||
\(988\) | 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 | ||||||||
\(997\) | 21.7323 | 0.688270 | 0.344135 | − | 0.938920i | \(-0.388172\pi\) | ||||
0.344135 | + | 0.938920i | \(0.388172\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.32047 | + | 8.06936i | −0.136694 | + | 0.255303i |
(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.t.k.961.8 | 22 | ||
3.2 | odd | 2 | 3024.2.t.l.289.7 | 22 | |||
4.3 | odd | 2 | 504.2.t.d.457.4 | yes | 22 | ||
7.4 | even | 3 | 1008.2.q.k.529.1 | 22 | |||
9.4 | even | 3 | 1008.2.q.k.625.1 | 22 | |||
9.5 | odd | 6 | 3024.2.q.k.2305.5 | 22 | |||
12.11 | even | 2 | 1512.2.t.d.289.7 | 22 | |||
21.11 | odd | 6 | 3024.2.q.k.2881.5 | 22 | |||
28.11 | odd | 6 | 504.2.q.d.25.11 | ✓ | 22 | ||
36.23 | even | 6 | 1512.2.q.c.793.5 | 22 | |||
36.31 | odd | 6 | 504.2.q.d.121.11 | yes | 22 | ||
63.4 | even | 3 | inner | 1008.2.t.k.193.8 | 22 | ||
63.32 | odd | 6 | 3024.2.t.l.1873.7 | 22 | |||
84.11 | even | 6 | 1512.2.q.c.1369.5 | 22 | |||
252.67 | odd | 6 | 504.2.t.d.193.4 | yes | 22 | ||
252.95 | even | 6 | 1512.2.t.d.361.7 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.11 | ✓ | 22 | 28.11 | odd | 6 | ||
504.2.q.d.121.11 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.d.193.4 | yes | 22 | 252.67 | odd | 6 | ||
504.2.t.d.457.4 | yes | 22 | 4.3 | odd | 2 | ||
1008.2.q.k.529.1 | 22 | 7.4 | even | 3 | |||
1008.2.q.k.625.1 | 22 | 9.4 | even | 3 | |||
1008.2.t.k.193.8 | 22 | 63.4 | even | 3 | inner | ||
1008.2.t.k.961.8 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.q.c.793.5 | 22 | 36.23 | even | 6 | |||
1512.2.q.c.1369.5 | 22 | 84.11 | even | 6 | |||
1512.2.t.d.289.7 | 22 | 12.11 | even | 2 | |||
1512.2.t.d.361.7 | 22 | 252.95 | even | 6 | |||
3024.2.q.k.2305.5 | 22 | 9.5 | odd | 6 | |||
3024.2.q.k.2881.5 | 22 | 21.11 | odd | 6 | |||
3024.2.t.l.289.7 | 22 | 3.2 | odd | 2 | |||
3024.2.t.l.1873.7 | 22 | 63.32 | odd | 6 |