Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 65.11 | ||
Character | \(\chi\) | \(=\) | 108.65 |
Dual form | 108.5.k.a.5.11 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 8.08622 | − | 3.95134i | 0.898469 | − | 0.439038i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.7879 | + | 29.6395i | −0.431515 | + | 1.18558i | 0.513367 | + | 0.858169i | \(0.328398\pi\) |
−0.944883 | + | 0.327409i | \(0.893824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.2291 | − | 86.3688i | 0.310799 | − | 1.76263i | −0.284068 | − | 0.958804i | \(-0.591684\pi\) |
0.594867 | − | 0.803824i | \(-0.297205\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 49.7738 | − | 63.9028i | 0.614492 | − | 0.788923i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 46.1813 | + | 126.882i | 0.381664 | + | 1.04861i | 0.970656 | + | 0.240473i | \(0.0773027\pi\) |
−0.588992 | + | 0.808139i | \(0.700475\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 215.694 | − | 180.988i | 1.27629 | − | 1.07094i | 0.282549 | − | 0.959253i | \(-0.408820\pi\) |
0.993744 | − | 0.111684i | \(-0.0356245\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 29.8824 | + | 282.298i | 0.132811 | + | 1.25466i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 300.316 | − | 173.387i | 1.03915 | − | 0.599956i | 0.119561 | − | 0.992827i | \(-0.461851\pi\) |
0.919594 | + | 0.392871i | \(0.128518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −113.736 | + | 196.996i | −0.315058 | + | 0.545696i | −0.979450 | − | 0.201688i | \(-0.935357\pi\) |
0.664392 | + | 0.747384i | \(0.268690\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −218.126 | − | 758.572i | −0.494617 | − | 1.72012i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −187.562 | + | 33.0723i | −0.354560 | + | 0.0625185i | −0.348091 | − | 0.937461i | \(-0.613170\pi\) |
−0.00646861 | + | 0.999979i | \(0.502059\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −283.341 | − | 237.752i | −0.453346 | − | 0.380403i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 149.980 | − | 713.405i | 0.205734 | − | 0.978608i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 429.966 | − | 512.413i | 0.511256 | − | 0.609291i | −0.447234 | − | 0.894417i | \(-0.647591\pi\) |
0.958490 | + | 0.285126i | \(0.0920355\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35.8536 | − | 203.336i | −0.0373087 | − | 0.211588i | 0.960454 | − | 0.278437i | \(-0.0898164\pi\) |
−0.997763 | + | 0.0668493i | \(0.978705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 874.786 | + | 843.518i | 0.803293 | + | 0.774580i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2395.63 | + | 1383.12i | 1.95562 | + | 1.12908i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 987.943 | + | 1711.17i | 0.721653 | + | 1.24994i | 0.960337 | + | 0.278842i | \(0.0899507\pi\) |
−0.238684 | + | 0.971097i | \(0.576716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1029.00 | − | 2315.79i | 0.676528 | − | 1.52254i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1257.73 | − | 1498.90i | −0.748203 | − | 0.891673i | 0.248838 | − | 0.968545i | \(-0.419951\pi\) |
−0.997041 | + | 0.0768719i | \(0.975507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −793.064 | + | 288.652i | −0.428915 | + | 0.156112i | −0.547452 | − | 0.836837i | \(-0.684402\pi\) |
0.118536 | + | 0.992950i | \(0.462180\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1357.09 | + | 2164.64i | 0.670168 | + | 1.06896i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1802.00 | − | 317.741i | −0.815754 | − | 0.143839i | −0.249822 | − | 0.968292i | \(-0.580372\pi\) |
−0.565932 | + | 0.824452i | \(0.691483\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4971.44 | − | 1809.45i | −2.07057 | − | 0.753626i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1743.31 | − | 2588.70i | 0.670244 | − | 0.995270i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2964.60i | 1.05539i | 0.849432 | + | 0.527697i | \(0.176944\pi\) | ||||
−0.849432 | + | 0.527697i | \(0.823056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4258.91 | −1.40791 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −141.294 | + | 2042.36i | −0.0434883 | + | 0.628613i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1888.83 | + | 5189.52i | −0.542612 | + | 1.49081i | 0.300875 | + | 0.953664i | \(0.402721\pi\) |
−0.843487 | + | 0.537150i | \(0.819501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 680.783 | − | 3860.91i | 0.182957 | − | 1.03760i | −0.745595 | − | 0.666399i | \(-0.767835\pi\) |
0.928552 | − | 0.371202i | \(-0.121054\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4761.19 | − | 5272.09i | −1.19959 | − | 1.32832i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3037.52 | + | 8345.52i | 0.718940 | + | 1.97527i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3957.28 | + | 3320.55i | −0.881549 | + | 0.739708i | −0.966497 | − | 0.256678i | \(-0.917372\pi\) |
0.0849477 | + | 0.996385i | \(0.472928\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1385.99 | + | 1008.55i | −0.291113 | + | 0.211836i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1162.57 | + | 671.209i | −0.230622 | + | 0.133150i | −0.610859 | − | 0.791739i | \(-0.709176\pi\) |
0.380237 | + | 0.924889i | \(0.375843\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1153.91 | + | 1998.62i | −0.216533 | + | 0.375047i | −0.953746 | − | 0.300614i | \(-0.902808\pi\) |
0.737213 | + | 0.675661i | \(0.236142\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3230.60 | − | 802.933i | −0.574328 | − | 0.142744i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11662.0 | − | 2056.32i | 1.96693 | − | 0.346824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6080.80 | + | 5102.39i | 0.974330 | + | 0.817560i | 0.983224 | − | 0.182400i | \(-0.0583867\pi\) |
−0.00889403 | + | 0.999960i | \(0.502831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1606.13 | − | 6361.37i | −0.244800 | − | 0.969574i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −879.339 | + | 1047.96i | −0.127644 | + | 0.152120i | −0.826081 | − | 0.563551i | \(-0.809435\pi\) |
0.698437 | + | 0.715671i | \(0.253879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1899.34 | + | 10771.7i | 0.262884 | + | 1.49089i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1452.08 | − | 5842.43i | 0.191846 | − | 0.771889i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2800.19 | − | 1616.69i | −0.353515 | − | 0.204102i | 0.312717 | − | 0.949846i | \(-0.398761\pi\) |
−0.666232 | + | 0.745744i | \(0.732094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12346.9 | − | 21385.5i | −1.49099 | − | 2.58248i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1093.37 | − | 1502.55i | −0.126416 | − | 0.173725i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4611.89 | − | 5496.24i | −0.511013 | − | 0.609001i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10325.5 | + | 3758.17i | −1.09741 | + | 0.399423i | −0.826359 | − | 0.563143i | \(-0.809592\pi\) |
−0.271046 | + | 0.962566i | \(0.587370\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10406.7 | + | 3364.29i | 1.06180 | + | 0.343260i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17983.3 | + | 3170.94i | 1.76289 | + | 0.310846i | 0.958890 | − | 0.283777i | \(-0.0915876\pi\) |
0.804005 | + | 0.594623i | \(0.202699\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2539.01 | + | 924.124i | 0.239326 | + | 0.0871075i | 0.458899 | − | 0.888489i | \(-0.348244\pi\) |
−0.219573 | + | 0.975596i | \(0.570466\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 24836.8 | + | 1718.25i | 2.25277 | + | 0.155850i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6516.08i | 0.569140i | 0.958655 | + | 0.284570i | \(0.0918508\pi\) | ||||
−0.958655 | + | 0.284570i | \(0.908149\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1020.46 | −0.0858901 | −0.0429451 | − | 0.999077i | \(-0.513674\pi\) | ||||
−0.0429451 | + | 0.999077i | \(0.513674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14750.1 | + | 9933.17i | 1.19715 | + | 0.806199i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6393.36 | + | 17565.6i | −0.500694 | + | 1.37564i | 0.389905 | + | 0.920855i | \(0.372508\pi\) |
−0.890599 | + | 0.454790i | \(0.849714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1043.15 | − | 5916.02i | 0.0788775 | − | 0.447336i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −829.767 | − | 22791.9i | −0.0606156 | − | 1.66498i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10401.7 | − | 28578.4i | −0.734532 | − | 2.01811i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2750.69 | + | 2308.10i | −0.187876 | + | 0.157647i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16092.9 | − | 7150.74i | −1.06371 | − | 0.472651i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6968.94 | + | 4023.52i | −0.446012 | + | 0.257505i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8405.05 | − | 14558.0i | 0.521114 | − | 0.902597i | −0.478584 | − | 0.878042i | \(-0.658850\pi\) |
0.999698 | − | 0.0245549i | \(-0.00781687\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5272.33 | + | 5467.77i | −0.316828 | + | 0.328572i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14033.3 | + | 2474.46i | −0.817746 | + | 0.144191i | −0.566848 | − | 0.823823i | \(-0.691837\pi\) |
−0.250899 | + | 0.968013i | \(0.580726\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15282.2 | + | 12823.3i | 0.863939 | + | 0.724931i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19527.0 | + | 12141.5i | 1.07144 | + | 0.666199i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 23405.4 | − | 27893.5i | 1.24702 | − | 1.48615i | 0.437321 | − | 0.899306i | \(-0.355927\pi\) |
0.809703 | − | 0.586840i | \(-0.199628\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1462.43 | − | 8293.86i | −0.0756913 | − | 0.429267i | −0.998980 | − | 0.0451595i | \(-0.985620\pi\) |
0.923288 | − | 0.384107i | \(-0.125491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15826.9 | + | 4550.99i | −0.796080 | + | 0.228912i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 32925.2 | + | 19009.4i | 1.61011 | + | 0.929599i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10549.2 | + | 18271.8i | 0.501747 | + | 0.869052i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −47349.9 | + | 5012.19i | −2.19121 | + | 0.231949i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15321.1 | − | 18259.0i | −0.690108 | − | 0.822439i | 0.301261 | − | 0.953542i | \(-0.402593\pi\) |
−0.991369 | + | 0.131103i | \(0.958148\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7165.12 | − | 2607.89i | 0.314246 | − | 0.114376i | −0.180082 | − | 0.983652i | \(-0.557636\pi\) |
0.494328 | + | 0.869275i | \(0.335414\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3867.93 | − | 27821.2i | 0.165233 | − | 1.18848i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6413.55 | + | 1130.88i | 0.266953 | + | 0.0470711i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 30590.5 | + | 11134.0i | 1.24104 | + | 0.451703i | 0.877366 | − | 0.479821i | \(-0.159299\pi\) |
0.363678 | + | 0.931525i | \(0.381521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11714.2 | + | 23972.4i | 0.463358 | + | 0.948239i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16703.2i | 0.644388i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11743.8 | −0.442013 | −0.221007 | − | 0.975272i | \(-0.570934\pi\) | ||||
−0.221007 | + | 0.975272i | \(0.570934\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −34438.5 | + | 16828.4i | −1.26496 | + | 0.618124i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2258.54 | − | 6205.28i | 0.0809830 | − | 0.222499i | −0.892592 | − | 0.450864i | \(-0.851116\pi\) |
0.973576 | + | 0.228365i | \(0.0733380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8807.35 | − | 49948.9i | 0.308370 | − | 1.74885i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6927.54 | + | 17073.3i | 0.236912 | + | 0.583882i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11089.4 | − | 30467.9i | −0.370524 | − | 1.01801i | −0.975159 | − | 0.221505i | \(-0.928903\pi\) |
0.604635 | − | 0.796503i | \(-0.293319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24849.4 | + | 20851.1i | −0.811408 | + | 0.680852i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5232.06 | + | 49427.0i | 0.167004 | + | 1.57768i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20902.8 | + | 12068.2i | −0.652377 | + | 0.376650i | −0.789366 | − | 0.613923i | \(-0.789591\pi\) |
0.136989 | + | 0.990573i | \(0.456257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3335.92 | + | 5777.98i | −0.101826 | + | 0.176368i | −0.912437 | − | 0.409217i | \(-0.865802\pi\) |
0.810611 | + | 0.585585i | \(0.199135\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9750.82 | − | 33910.2i | −0.291165 | − | 1.01258i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −61375.9 | + | 10822.2i | −1.79331 | + | 0.316208i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35868.7 | + | 30097.4i | 1.02573 | + | 0.860689i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −59331.9 | − | 23818.2i | −1.66098 | − | 0.666784i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18122.1 | + | 21597.0i | −0.496753 | + | 0.592008i | −0.954922 | − | 0.296858i | \(-0.904061\pi\) |
0.458168 | + | 0.888865i | \(0.348506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5929.51 | + | 33627.9i | 0.159186 | + | 0.902788i | 0.954859 | + | 0.297061i | \(0.0960065\pi\) |
−0.795673 | + | 0.605727i | \(0.792882\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 57538.0 | + | 55481.4i | 1.51316 | + | 1.45908i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4567.28 | − | 2636.92i | −0.117686 | − | 0.0679461i | 0.440001 | − | 0.897997i | \(-0.354978\pi\) |
−0.557688 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24297.3 | − | 42084.1i | −0.613553 | − | 1.06270i | −0.990637 | − | 0.136525i | \(-0.956407\pi\) |
0.377084 | − | 0.926179i | \(-0.376927\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18878.8 | + | 42487.2i | −0.467285 | + | 1.05164i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −37708.5 | − | 44939.3i | −0.915055 | − | 1.09052i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57994.9 | − | 21108.4i | 1.38001 | − | 0.502282i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7222.28 | + | 13631.9i | −0.168552 | + | 0.318138i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −30247.7 | − | 5333.49i | −0.692469 | − | 0.122101i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14002.0 | − | 5096.30i | −0.314503 | − | 0.114470i | 0.179946 | − | 0.983677i | \(-0.442408\pi\) |
−0.494449 | + | 0.869207i | \(0.664630\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6748.60 | + | 10021.2i | −0.148749 | + | 0.220883i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 26619.9i | − | 0.575878i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −18107.9 | −0.384546 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1433.49 | + | 20720.8i | −0.0298887 | + | 0.432034i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33395.1 | − | 91752.2i | 0.683751 | − | 1.87859i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1567.49 | + | 8889.65i | −0.0315206 | + | 0.178762i | −0.996504 | − | 0.0835505i | \(-0.973374\pi\) |
0.964983 | + | 0.262312i | \(0.0844851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29296.0 | + | 6272.49i | −0.578686 | + | 0.123901i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20863.3 | + | 57321.4i | 0.404885 | + | 1.11241i | 0.959844 | + | 0.280534i | \(0.0905115\pi\) |
−0.554960 | + | 0.831877i | \(0.687266\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −45065.7 | + | 37814.6i | −0.859361 | + | 0.721089i | −0.961830 | − | 0.273647i | \(-0.911770\pi\) |
0.102470 | + | 0.994736i | \(0.467326\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 86175.9 | − | 62708.2i | 1.61496 | − | 1.17517i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25541.4 | − | 14746.3i | 0.470470 | − | 0.271626i | −0.245966 | − | 0.969278i | \(-0.579105\pi\) |
0.716437 | + | 0.697652i | \(0.245772\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28857.4 | − | 49982.6i | 0.522543 | − | 0.905071i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 69331.9 | + | 17231.8i | 1.23435 | + | 0.306784i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −91549.5 | + | 16142.6i | −1.60273 | + | 0.282604i | −0.902297 | − | 0.431115i | \(-0.858120\pi\) |
−0.700432 | + | 0.713719i | \(0.747009\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 75263.3 | + | 63153.4i | 1.29583 | + | 1.08733i | 0.990849 | + | 0.134976i | \(0.0430957\pi\) |
0.304985 | + | 0.952357i | \(0.401349\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −38123.5 | − | 45093.1i | −0.645624 | − | 0.763655i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 107263. | − | 127831.i | 1.78696 | − | 2.12962i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11121.9 | + | 63075.6i | 0.182300 | + | 1.03387i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2969.70 | + | 11948.6i | −0.0478976 | + | 0.192716i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 67645.6 | + | 39055.2i | 1.07372 | + | 0.619914i | 0.929196 | − | 0.369587i | \(-0.120501\pi\) |
0.144527 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12858.2 | − | 22271.0i | −0.200880 | − | 0.347935i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 57921.0 | + | 79597.2i | 0.890750 | + | 1.22410i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 35744.0 | + | 42598.0i | 0.541174 | + | 0.644946i | 0.965450 | − | 0.260587i | \(-0.0839160\pi\) |
−0.424277 | + | 0.905533i | \(0.639472\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 162837. | − | 59267.8i | 2.42747 | − | 0.883526i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11343.6 | − | 52980.8i | −0.166521 | − | 0.777746i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 38052.4 | + | 6709.66i | 0.550136 | + | 0.0970038i | 0.441805 | − | 0.897111i | \(-0.354338\pi\) |
0.108331 | + | 0.994115i | \(0.465449\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −87869.3 | − | 31981.8i | −1.25125 | − | 0.455419i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −29031.0 | − | 2008.41i | −0.407230 | − | 0.0281728i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26971.5i | 0.372735i | 0.982480 | + | 0.186367i | \(0.0596715\pi\) | ||||
−0.982480 | + | 0.186367i | \(0.940329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15106.5 | 0.205696 | 0.102848 | − | 0.994697i | \(-0.467204\pi\) | ||||
0.102848 | + | 0.994697i | \(0.467204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −184341. | − | 124141.i | −2.47342 | − | 1.66567i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17081.3 | − | 46930.6i | 0.225869 | − | 0.620570i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1864.45 | + | 10573.8i | −0.0242991 | + | 0.137807i | −0.994544 | − | 0.104319i | \(-0.966734\pi\) |
0.970245 | + | 0.242126i | \(0.0778448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14778.3 | − | 7829.67i | −0.189853 | − | 0.100585i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3060.57 | − | 8408.86i | −0.0387606 | − | 0.106494i | 0.918803 | − | 0.394718i | \(-0.129158\pi\) |
−0.957563 | + | 0.288224i | \(0.906935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 47874.3 | − | 40171.3i | 0.597764 | − | 0.501584i | −0.292962 | − | 0.956124i | \(-0.594641\pi\) |
0.890726 | + | 0.454540i | \(0.150196\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −59010.3 | − | 26220.6i | −0.726504 | − | 0.322815i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −148613. | + | 85801.5i | −1.80423 | + | 1.04167i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18365.8 | − | 31810.6i | 0.219895 | − | 0.380869i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −68644.4 | + | 71188.9i | −0.810623 | + | 0.840672i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19021.2 | + | 3353.96i | −0.221566 | + | 0.0390681i | −0.283329 | − | 0.959023i | \(-0.591439\pi\) |
0.0617628 | + | 0.998091i | \(0.480328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −133438. | − | 111968.i | −1.53333 | − | 1.28662i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 97444.6 | − | 13916.1i | 1.10470 | − | 0.157763i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −34470.3 | + | 41080.1i | −0.385569 | + | 0.459503i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12852.8 | + | 72891.9i | 0.141862 | + | 0.804538i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 157946. | − | 45417.2i | 1.72038 | − | 0.494692i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 107091. | + | 61829.1i | 1.15121 | + | 0.664651i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −73229.0 | − | 126836.i | −0.776974 | − | 1.34576i | −0.933678 | − | 0.358113i | \(-0.883420\pi\) |
0.156704 | − | 0.987646i | \(-0.449913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 24182.5 | − | 2559.82i | 0.253270 | − | 0.0268098i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 76390.5 | + | 91038.6i | 0.789802 | + | 0.941250i | 0.999332 | − | 0.0365526i | \(-0.0116377\pi\) |
−0.209529 | + | 0.977802i | \(0.567193\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −128096. | + | 46623.1i | −1.30752 | + | 0.475897i | −0.899437 | − | 0.437050i | \(-0.856023\pi\) |
−0.408078 | + | 0.912947i | \(0.633801\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 207625. | − | 84244.5i | 2.09247 | − | 0.849025i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2046.11 | + | 360.784i | 0.0203615 | + | 0.00359028i | 0.183820 | − | 0.982960i | \(-0.441154\pi\) |
−0.163458 | + | 0.986550i | \(0.552265\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 84872.5 | + | 30891.1i | 0.834037 | + | 0.303565i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25747.2 | + | 52690.4i | 0.249874 | + | 0.511354i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 78881.4i | 0.756083i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −104145. | −0.985990 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8251.66 | + | 4032.19i | −0.0771696 | + | 0.0377090i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −54885.9 | + | 150798.i | −0.507071 | + | 1.39317i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13925.1 | + | 78973.4i | −0.127099 | + | 0.720817i | 0.852939 | + | 0.522010i | \(0.174818\pi\) |
−0.980039 | + | 0.198807i | \(0.936293\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 158522. | + | 22039.1i | 1.42956 | + | 0.198749i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −55728.6 | − | 153113.i | −0.496579 | − | 1.36434i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −41768.0 | + | 35047.5i | −0.367777 | + | 0.308601i | −0.807881 | − | 0.589345i | \(-0.799386\pi\) |
0.440105 | + | 0.897946i | \(0.354941\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17709.6 | + | 167302.i | 0.154102 | + | 1.45580i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24143.9 | − | 13939.5i | 0.207634 | − | 0.119878i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −126706. | + | 219461.i | −1.07698 | + | 1.86539i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14941.0 | − | 51960.1i | −0.125529 | − | 0.436548i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23633.6 | + | 4167.25i | −0.196278 | + | 0.0346091i | −0.270923 | − | 0.962601i | \(-0.587329\pi\) |
0.0746448 | + | 0.997210i | \(0.476218\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −124185. | − | 104204.i | −1.01957 | − | 0.855524i | −0.0300003 | − | 0.999550i | \(-0.509551\pi\) |
−0.989574 | + | 0.144025i | \(0.953995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −96768.2 | − | 181022.i | −0.785450 | − | 1.46932i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 67927.0 | − | 80952.2i | 0.545121 | − | 0.649650i | −0.421207 | − | 0.906965i | \(-0.638393\pi\) |
0.966328 | + | 0.257315i | \(0.0828378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7352.62 | − | 41698.8i | −0.0583426 | − | 0.330877i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −197034. | − | 189991.i | −1.54598 | − | 1.49072i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 961.228 | + | 554.965i | 0.00745826 | + | 0.00430603i | 0.503724 | − | 0.863864i | \(-0.331963\pi\) |
−0.496266 | + | 0.868170i | \(0.665296\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39288.8 | + | 68050.3i | 0.301477 | + | 0.522174i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13122.6 | + | 29532.8i | −0.0995878 | + | 0.224125i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −46789.9 | − | 55762.1i | −0.351210 | − | 0.418555i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −75284.8 | + | 27401.4i | −0.558952 | + | 0.203442i | −0.606020 | − | 0.795450i | \(-0.707235\pi\) |
0.0470672 | + | 0.998892i | \(0.485013\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −158386. | + | 5766.23i | −1.16323 | + | 0.0423486i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 256049. | + | 45148.4i | 1.86027 | + | 0.328016i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24455.5 | + | 8901.06i | 0.175776 | + | 0.0639771i | 0.428409 | − | 0.903585i | \(-0.359074\pi\) |
−0.252633 | + | 0.967562i | \(0.581297\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −40454.1 | + | 60071.7i | −0.287673 | + | 0.427176i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 188343.i | − | 1.32516i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33218.9 | −0.231263 | −0.115632 | − | 0.993292i | \(-0.536889\pi\) | ||||
−0.115632 | + | 0.993292i | \(0.536889\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10441.6 | − | 150930.i | 0.0719310 | − | 1.03974i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −72532.8 | + | 199282.i | −0.494467 | + | 1.35854i | 0.402087 | + | 0.915601i | \(0.368285\pi\) |
−0.896554 | + | 0.442934i | \(0.853937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −64859.6 | + | 367837.i | −0.437575 | + | 2.48161i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21028.2 | + | 65046.3i | −0.140404 | + | 0.434311i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 39859.9 | + | 109514.i | 0.263413 | + | 0.723721i | 0.998931 | + | 0.0462165i | \(0.0147164\pi\) |
−0.735519 | + | 0.677505i | \(0.763061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −50593.6 | + | 42453.1i | −0.330934 | + | 0.277687i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −103699. | + | 75459.5i | −0.671414 | + | 0.488572i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −216831. | + | 125187.i | −1.38972 | + | 0.802355i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 105374. | − | 182513.i | 0.668580 | − | 1.15801i | −0.309722 | − | 0.950827i | \(-0.600236\pi\) |
0.978301 | − | 0.207187i | \(-0.0664307\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 174245. | + | 43306.8i | 1.09449 | + | 0.272026i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18741.2 | − | 3304.59i | 0.116549 | − | 0.0205508i | −0.115069 | − | 0.993357i | \(-0.536709\pi\) |
0.231619 | + | 0.972807i | \(0.425598\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −44534.8 | − | 37369.2i | −0.274214 | − | 0.230093i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 205874. | + | 21020.9i | 1.25514 | + | 0.128156i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −171492. | + | 204376.i | −1.03527 | + | 1.23379i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17268.1 | − | 97932.2i | −0.103228 | − | 0.585435i | −0.991913 | − | 0.126918i | \(-0.959492\pi\) |
0.888685 | − | 0.458518i | \(-0.151619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 79044.6 | − | 318035.i | 0.467938 | − | 1.88275i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 419448. | + | 242168.i | 2.45911 | + | 1.41977i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21574.6 | − | 37368.4i | −0.125270 | − | 0.216974i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −44597.4 | − | 61287.4i | −0.256471 | − | 0.352451i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −77933.2 | − | 92877.2i | −0.443910 | − | 0.529031i | 0.496972 | − | 0.867767i | \(-0.334445\pi\) |
−0.940882 | + | 0.338736i | \(0.890001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 203870. | − | 74202.8i | 1.15024 | − | 0.418655i | 0.304641 | − | 0.952467i | \(-0.401463\pi\) |
0.845603 | + | 0.533812i | \(0.179241\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −109997. | + | 99337.6i | −0.614752 | + | 0.555179i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −126315. | − | 22272.7i | −0.699322 | − | 0.123309i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −323095. | − | 117597.i | −1.77204 | − | 0.644971i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 341353. | + | 23615.3i | 1.85476 | + | 0.128315i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 234878.i | − | 1.26441i | −0.774802 | − | 0.632204i | \(-0.782150\pi\) | ||
0.774802 | − | 0.632204i | \(-0.217850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21782.0 | −0.116177 | −0.0580887 | − | 0.998311i | \(-0.518501\pi\) | ||||
−0.0580887 | + | 0.998311i | \(0.518501\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 157502. | + | 106066.i | 0.832351 | + | 0.560530i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 14817.4 | − | 40710.6i | 0.0775908 | − | 0.213179i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 65390.8 | − | 370850.i | 0.339303 | − | 1.92428i | −0.0404229 | − | 0.999183i | \(-0.512871\pi\) |
0.379726 | − | 0.925099i | \(-0.376018\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −363077. | + | 227625.i | −1.86690 | + | 1.17042i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 31232.3 | + | 85809.9i | 0.159146 | + | 0.437250i | 0.993480 | − | 0.114010i | \(-0.0363695\pi\) |
−0.834334 | + | 0.551260i | \(0.814147\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 78125.9 | − | 65555.4i | 0.394526 | − | 0.331046i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −196037. | − | 87107.1i | −0.981122 | − | 0.435952i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −107735. | + | 62201.0i | −0.534399 | + | 0.308535i | −0.742806 | − | 0.669507i | \(-0.766505\pi\) |
0.208407 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 132100. | − | 228804.i | 0.649458 | − | 1.12489i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 47634.1 | − | 49399.8i | 0.232125 | − | 0.240729i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 767051. | − | 135252.i | 3.70511 | − | 0.653312i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 103503. | + | 86849.0i | 0.495586 | + | 0.415846i | 0.856023 | − | 0.516938i | \(-0.172928\pi\) |
−0.360437 | + | 0.932783i | \(0.617372\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −78653.9 | − | 240251.i | −0.373332 | − | 1.14036i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −168200. | + | 200453.i | −0.791450 | + | 0.943213i | −0.999390 | − | 0.0349284i | \(-0.988880\pi\) |
0.207940 | + | 0.978142i | \(0.433324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26468.5 | − | 150110.i | −0.123472 | − | 0.700242i | −0.982204 | − | 0.187818i | \(-0.939859\pi\) |
0.858732 | − | 0.512424i | \(-0.171253\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 56329.9 | − | 16197.6i | 0.260515 | − | 0.0749107i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −310052. | − | 179009.i | −1.42168 | − | 0.820806i | −0.425235 | − | 0.905083i | \(-0.639809\pi\) |
−0.996442 | + | 0.0842767i | \(0.973142\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 226526. | + | 392354.i | 1.02985 | + | 1.78374i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 291356. | − | 30841.3i | 1.31335 | − | 0.139024i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −73249.5 | − | 87295.3i | −0.327403 | − | 0.390183i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 79062.2 | − | 28776.3i | 0.350414 | − | 0.127540i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 189446. | + | 147560.i | 0.832626 | + | 0.648531i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −147754. | − | 26053.1i | −0.643976 | − | 0.113550i | −0.157883 | − | 0.987458i | \(-0.550467\pi\) |
−0.486092 | + | 0.873908i | \(0.661578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 522794. | + | 190282.i | 2.25965 | + | 0.822444i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 66000.0 | + | 135066.i | 0.282911 | + | 0.578963i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 346585.i | − | 1.47342i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 191423. | 0.807117 | 0.403559 | − | 0.914954i | \(-0.367773\pi\) | ||||
0.403559 | + | 0.914954i | \(0.367773\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −94963.3 | + | 46403.9i | −0.397135 | + | 0.194060i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 96829.2 | − | 266036.i | 0.401646 | − | 1.10351i | −0.559826 | − | 0.828610i | \(-0.689132\pi\) |
0.961472 | − | 0.274903i | \(-0.0886457\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40279.5 | − | 228436.i | 0.165726 | − | 0.939878i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −211982. | + | 272156.i | −0.865146 | + | 1.11073i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40266.6 | + | 110631.i | 0.163017 | + | 0.447884i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −216992. | + | 182078.i | −0.871450 | + | 0.731233i | −0.964403 | − | 0.264437i | \(-0.914814\pi\) |
0.0929533 | + | 0.995670i | \(0.470369\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6256.14 | − | 59101.5i | −0.0249248 | − | 0.235463i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 176203. | − | 101731.i | 0.696429 | − | 0.402083i | −0.109587 | − | 0.993977i | \(-0.534953\pi\) |
0.806016 | + | 0.591894i | \(0.201620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −287986. | + | 498807.i | −1.12925 | + | 1.95592i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −126147. | − | 438699.i | −0.490751 | − | 1.70667i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 54374.6 | − | 9587.70i | 0.209875 | − | 0.0370066i | −0.0677222 | − | 0.997704i | \(-0.521573\pi\) |
0.277597 | + | 0.960698i | \(0.410462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 155046. | + | 130099.i | 0.593769 | + | 0.498232i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 123480. | + | 110685.i | 0.469204 | + | 0.420586i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −54781.1 | + | 65285.5i | −0.206546 | + | 0.246151i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42903.0 | − | 243315.i | −0.160512 | − | 0.910308i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −210061. | − | 202552.i | −0.779848 | − | 0.751973i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23227.7 | + | 13410.5i | 0.0855719 | + | 0.0494050i | 0.542175 | − | 0.840265i | \(-0.317601\pi\) |
−0.456603 | + | 0.889670i | \(0.650934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25930.8 | + | 44913.4i | 0.0948009 | + | 0.164200i | 0.909525 | − | 0.415648i | \(-0.136445\pi\) |
−0.814725 | + | 0.579848i | \(0.803112\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −118548. | + | 266795.i | −0.430105 | + | 0.967963i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −46023.3 | − | 54848.4i | −0.165713 | − | 0.197489i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −228879. | + | 83305.0i | −0.817888 | + | 0.297687i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 237611. | + | 379004.i | 0.842707 | + | 1.34417i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −542568. | − | 95669.3i | −1.90985 | − | 0.336758i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −193133. | − | 70294.7i | −0.674760 | − | 0.245592i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −121339. | + | 180181.i | −0.420777 | + | 0.624826i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 714349.i | − | 2.45886i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 237828. | 0.812585 | 0.406292 | − | 0.913743i | \(-0.366821\pi\) | ||||
0.406292 | + | 0.913743i | \(0.366821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4144.20 | + | 59903.4i | −0.0140553 | + | 0.203166i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11008.6 | − | 30245.9i | 0.0370629 | − | 0.101829i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −69204.9 | + | 392480.i | −0.231293 | + | 1.31173i | 0.618989 | + | 0.785399i | \(0.287542\pi\) |
−0.850282 | + | 0.526327i | \(0.823569\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −212838. | − | 235676.i | −0.706162 | − | 0.781937i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52041.0 | + | 142981.i | 0.171412 | + | 0.470952i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 533293. | − | 447486.i | 1.74388 | − | 1.46329i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −453537. | + | 330028.i | −1.47240 | + | 1.07143i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −338329. | + | 195334.i | −1.09051 | + | 0.629605i | −0.933712 | − | 0.358026i | \(-0.883450\pi\) |
−0.156797 | + | 0.987631i | \(0.550117\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −118816. | + | 205796.i | −0.380235 | + | 0.658587i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 408967. | + | 101645.i | 1.29946 | + | 0.322968i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −502288. | + | 88566.9i | −1.58466 | + | 0.279418i | −0.895456 | − | 0.445151i | \(-0.853150\pi\) |
−0.689203 | + | 0.724569i | \(0.742039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −451664. | − | 378991.i | −1.41488 | − | 1.18722i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −573884. | + | 41841.3i | −1.78508 | + | 0.130149i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 338791. | − | 403756.i | 1.04642 | − | 1.24708i | 0.0782149 | − | 0.996937i | \(-0.475078\pi\) |
0.968209 | − | 0.250143i | \(-0.0804776\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13409.5 | + | 76049.2i | 0.0411284 | + | 0.233250i | 0.998442 | − | 0.0558010i | \(-0.0177712\pi\) |
−0.957314 | + | 0.289051i | \(0.906660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −61201.7 | + | 246245.i | −0.186404 | + | 0.749994i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 61007.1 | + | 35222.5i | 0.184521 | + | 0.106533i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 82412.6 | + | 142743.i | 0.247538 | + | 0.428748i | 0.962842 | − | 0.270065i | \(-0.0870452\pi\) |
−0.715304 | + | 0.698813i | \(0.753712\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 180823. | + | 248493.i | 0.539381 | + | 0.741238i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 77119.1 | + | 91906.9i | 0.228460 | + | 0.272268i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −376155. | + | 136909.i | −1.10670 | + | 0.402806i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 684491. | + | 221282.i | 2.00012 | + | 0.646599i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −146970. | − | 25914.7i | −0.426532 | − | 0.0752090i | −0.0437382 | − | 0.999043i | \(-0.513927\pi\) |
−0.382793 | + | 0.923834i | \(0.625038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44134.2 | + | 16063.6i | 0.127217 | + | 0.0463032i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47351.4 | − | 3275.84i | −0.135568 | − | 0.00937880i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 87964.7i | − | 0.250149i | −0.992147 | − | 0.125075i | \(-0.960083\pi\) | ||
0.992147 | − | 0.125075i | \(-0.0399170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 959262. | 2.70959 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −362762. | − | 244295.i | −1.01782 | − | 0.685434i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −236836. | + | 650702.i | −0.660077 | + | 1.81355i | −0.0834914 | + | 0.996508i | \(0.526607\pi\) |
−0.576585 | + | 0.817037i | \(0.695615\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8308.99 | − | 47122.6i | 0.0230038 | − | 0.130461i | −0.971143 | − | 0.238497i | \(-0.923345\pi\) |
0.994147 | + | 0.108036i | \(0.0344563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15223.5 | + | 418157.i | 0.0418678 | + | 1.15002i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −38736.8 | − | 106429.i | −0.105831 | − | 0.290769i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 533429. | − | 447600.i | 1.44777 | − | 1.21482i | 0.513582 | − | 0.858041i | \(-0.328318\pi\) |
0.934188 | − | 0.356782i | \(-0.116126\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −482489. | − | 214389.i | −1.30093 | − | 0.578055i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −446187. | + | 257606.i | −1.19518 | + | 0.690040i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 242238. | − | 419569.i | 0.644646 | − | 1.11656i | −0.339737 | − | 0.940521i | \(-0.610338\pi\) |
0.984383 | − | 0.176040i | \(-0.0563287\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 385553. | − | 399845.i | 1.01937 | − | 1.05716i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15518.7 | + | 2736.36i | −0.0407647 | + | 0.00718792i | −0.193993 | − | 0.981003i | \(-0.562144\pi\) |
0.153229 | + | 0.988191i | \(0.451033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 534132. | + | 448190.i | 1.39402 | + | 1.16972i | 0.963683 | + | 0.267047i | \(0.0860480\pi\) |
0.430332 | + | 0.902671i | \(0.358396\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4536.73 | + | 138768.i | −0.0117641 | + | 0.359838i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −182276. | + | 217228.i | −0.469628 | + | 0.559680i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −84217.5 | − | 477621.i | −0.215597 | − | 1.22271i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −265664. | + | 76391.3i | −0.675769 | + | 0.194316i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 593390. | + | 342594.i | 1.49982 | + | 0.865921i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −125378. | − | 217160.i | −0.314892 | − | 0.545408i | 0.664523 | − | 0.747268i | \(-0.268635\pi\) |
−0.979414 | + | 0.201860i | \(0.935302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −133360. | + | 14116.8i | −0.332827 | + | 0.0352312i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 340818. | + | 406171.i | 0.845230 | + | 1.00731i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.39980e6 | + | 509484.i | −3.44974 | + | 1.25560i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14973.3 | + | 107700.i | −0.0366705 | + | 0.263763i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 128403. | + | 22641.0i | 0.312507 | + | 0.0551034i | 0.327702 | − | 0.944781i | \(-0.393726\pi\) |
−0.0151950 | + | 0.999885i | \(0.504837\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 508983. | + | 185255.i | 1.23107 | + | 0.448072i | 0.873963 | − | 0.485993i | \(-0.161542\pi\) |
0.357104 | + | 0.934065i | \(0.383764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −105184. | − | 215255.i | −0.252832 | − | 0.517408i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 667818.i | − | 1.59533i | −0.603102 | − | 0.797664i | \(-0.706069\pi\) | ||
0.603102 | − | 0.797664i | \(-0.293931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −745686. | −1.77038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −146424. | + | 71550.5i | −0.345503 | + | 0.168830i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 121288. | − | 333237.i | 0.284441 | − | 0.781496i | −0.712378 | − | 0.701796i | \(-0.752382\pi\) |
0.996819 | − | 0.0796995i | \(-0.0253961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 78048.5 | − | 442635.i | 0.181921 | − | 1.03172i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 70283.3 | + | 173217.i | 0.162825 | + | 0.401291i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −177897. | − | 488767.i | −0.409635 | − | 1.12546i | −0.957384 | − | 0.288819i | \(-0.906737\pi\) |
0.547749 | − | 0.836643i | \(-0.315485\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 432970. | − | 363305.i | 0.990957 | − | 0.831512i | 0.00525099 | − | 0.999986i | \(-0.498329\pi\) |
0.985706 | + | 0.168475i | \(0.0538841\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −92504.3 | − | 873883.i | −0.210443 | − | 1.98805i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −544938. | + | 314620.i | −1.23227 | + | 0.711449i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −63698.7 | + | 110329.i | −0.143179 | + | 0.247993i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22451.0 | + | 78077.3i | 0.0501630 | + | 0.174451i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 521320. | − | 91922.8i | 1.15787 | − | 0.204164i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −289892. | − | 243249.i | −0.640039 | − | 0.537057i | 0.263991 | − | 0.964525i | \(-0.414961\pi\) |
−0.904030 | + | 0.427468i | \(0.859406\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −212109. | + | 166479.i | −0.465534 | + | 0.365386i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −241740. | + | 288095.i | −0.527438 | + | 0.628576i | −0.962323 | − | 0.271910i | \(-0.912345\pi\) |
0.434884 | + | 0.900486i | \(0.356789\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 167340. | + | 949034.i | 0.362962 | + | 2.05846i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 395202. | + | 381076.i | 0.852167 | + | 0.821707i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −56691.2 | − | 32730.7i | −0.121527 | − | 0.0701639i | 0.438004 | − | 0.898973i | \(-0.355686\pi\) |
−0.559531 | + | 0.828809i | \(0.689019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 574252. | + | 994634.i | 1.22383 | + | 2.11974i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −214993. | + | 483847.i | −0.455523 | + | 1.02517i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 536559. | + | 639446.i | 1.13026 | + | 1.34699i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 353222. | − | 128562.i | 0.739761 | − | 0.269251i | 0.0554705 | − | 0.998460i | \(-0.482334\pi\) |
0.684291 | + | 0.729209i | \(0.260112\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 449056. | − | 847582.i | 0.935048 | − | 1.76488i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 261602. | + | 46127.5i | 0.541591 | + | 0.0954972i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −637606. | − | 232070.i | −1.31246 | − | 0.477697i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 148265. | − | 220165.i | 0.303449 | − | 0.450602i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 960237.i | − | 1.95408i | −0.213055 | − | 0.977040i | \(-0.568341\pi\) | ||
0.213055 | − | 0.977040i | \(-0.431659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −449458. | −0.909449 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 35849.5 | − | 518195.i | 0.0721282 | − | 1.04259i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 547740. | − | 1.50490e6i | 1.09581 | − | 3.01072i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28749.5 | − | 163047.i | 0.0571924 | − | 0.324354i | −0.942766 | − | 0.333455i | \(-0.891786\pi\) |
0.999959 | + | 0.00910028i | \(0.00289675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 628722. | − | 134614.i | 1.24371 | − | 0.266288i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13449.6 | + | 36952.4i | 0.0264563 | + | 0.0726882i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −918620. | + | 770814.i | −1.79690 | + | 1.50778i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −676504. | + | 492276.i | −1.31593 | + | 0.957570i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 243132. | − | 140372.i | 0.470310 | − | 0.271534i | −0.246059 | − | 0.969255i | \(-0.579136\pi\) |
0.716370 | + | 0.697721i | \(0.245802\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 118482. | − | 205218.i | 0.227920 | − | 0.394770i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 858136. | + | 213281.i | 1.64165 | + | 0.408015i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −243654. | + | 42962.8i | −0.463552 | + | 0.0817366i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 299480. | + | 251294.i | 0.566630 | + | 0.475459i | 0.880526 | − | 0.473998i | \(-0.157190\pi\) |
−0.313896 | + | 0.949458i | \(0.601634\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −486453. | − | 213994.i | −0.915347 | − | 0.402667i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −188121. | + | 224194.i | −0.352049 | + | 0.419555i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −63621.7 | − | 360816.i | −0.118412 | − | 0.671550i | −0.985004 | − | 0.172532i | \(-0.944805\pi\) |
0.866592 | − | 0.499018i | \(-0.166306\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 362246. | − | 1.45750e6i | 0.670547 | − | 2.69794i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −604070. | − | 348760.i | −1.11212 | − | 0.642084i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −269023. | − | 465962.i | −0.492607 | − | 0.853221i | 0.507356 | − | 0.861736i | \(-0.330623\pi\) |
−0.999964 | + | 0.00851547i | \(0.997289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 339168. | + | 466097.i | 0.617701 | + | 0.848867i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 569499. | + | 678702.i | 1.03161 | + | 1.22942i | 0.972919 | + | 0.231147i | \(0.0742479\pi\) |
0.0586901 | + | 0.998276i | \(0.481308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 706468. | − | 257133.i | 1.27286 | − | 0.463282i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23199.2 | + | 108353.i | 0.0415750 | + | 0.194178i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 562786. | + | 99234.3i | 1.00318 | + | 0.176888i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −321565. | − | 117040.i | −0.570149 | − | 0.207517i | 0.0408271 | − | 0.999166i | \(-0.487001\pi\) |
−0.610976 | + | 0.791649i | \(0.709223\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 701317. | + | 48518.2i | 1.23687 | + | 0.0855686i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 240504.i | 0.421918i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 360278. | 0.628704 | 0.314352 | − | 0.949307i | \(-0.398213\pi\) | ||||
0.314352 | + | 0.949307i | \(0.398213\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −191974. | − | 129281.i | −0.333241 | − | 0.224415i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −212386. | + | 583525.i | −0.366738 | + | 1.00761i | 0.609855 | + | 0.792513i | \(0.291228\pi\) |
−0.976594 | + | 0.215093i | \(0.930995\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15540.7 | + | 88135.9i | −0.0266945 | + | 0.151392i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 782877. | + | 414775.i | 1.33774 | + | 0.708744i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 531835. | + | 1.46120e6i | 0.904036 | + | 2.48382i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 296424. | − | 248729.i | 0.501257 | − | 0.420604i | −0.356783 | − | 0.934187i | \(-0.616127\pi\) |
0.858040 | + | 0.513583i | \(0.171682\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 457353. | + | 203220.i | 0.769383 | + | 0.341868i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −599094. | + | 345887.i | −1.00262 | + | 0.578862i | −0.909022 | − | 0.416748i | \(-0.863170\pi\) |
−0.0935968 | + | 0.995610i | \(0.529836\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −38184.6 | + | 66137.8i | −0.0635749 | + | 0.110115i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.08255e6 | − | 1.12268e6i | 1.79310 | − | 1.85957i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 438327. | − | 77288.8i | 0.722309 | − | 0.127363i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −138853. | − | 116512.i | −0.227643 | − | 0.191015i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −301072. | − | 383592.i | −0.491074 | − | 0.625671i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −660013. | + | 786573.i | −1.07106 | + | 1.27644i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −111937. | − | 634824.i | −0.180727 | − | 1.02495i | −0.931324 | − | 0.364193i | \(-0.881345\pi\) |
0.750597 | − | 0.660760i | \(-0.229766\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 334212. | − | 96102.0i | 0.536868 | − | 0.154376i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.41975e6 | + | 819696.i | 2.26914 | + | 1.31009i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −551940. | − | 955988.i | −0.877699 | − | 1.52022i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −836901. | + | 88589.5i | −1.32416 | + | 0.140168i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −415691. | − | 495401.i | −0.654416 | − | 0.779903i | 0.332157 | − | 0.943224i | \(-0.392224\pi\) |
−0.986573 | + | 0.163321i | \(0.947779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −596261. | + | 217021.i | −0.933992 | + | 0.339945i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −242687. | + | 98471.1i | −0.378253 | + | 0.153477i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −306878. | − | 54110.9i | −0.475921 | − | 0.0839178i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −495073. | − | 180192.i | −0.763973 | − | 0.278063i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 106573. | + | 218097.i | 0.163645 | + | 0.334891i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 380154.i | 0.580849i | 0.956898 | + | 0.290424i | \(0.0937964\pi\) | ||||
−0.956898 | + | 0.290424i | \(0.906204\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −854020. | −1.29845 | −0.649227 | − | 0.760595i | \(-0.724907\pi\) | ||||
−0.649227 | + | 0.760595i | \(0.724907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 122155. | − | 59691.1i | 0.184812 | − | 0.0903084i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 126691. | − | 348081.i | 0.190735 | − | 0.524041i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33336.5 | − | 189061.i | 0.0499431 | − | 0.283242i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.98115e6 | − | 275435.i | −2.95358 | − | 0.410631i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −339289. | − | 932188.i | −0.503365 | − | 1.38298i | −0.887969 | − | 0.459903i | \(-0.847884\pi\) |
0.384604 | − | 0.923082i | \(-0.374338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −832429. | + | 698491.i | −1.22899 | + | 1.03124i | −0.230683 | + | 0.973029i | \(0.574096\pi\) |
−0.998304 | + | 0.0582138i | \(0.981459\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −47315.3 | − | 446985.i | −0.0695174 | − | 0.656728i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −227618. | + | 131416.i | −0.332810 | + | 0.192148i | −0.657088 | − | 0.753814i | \(-0.728212\pi\) |
0.324278 | + | 0.945962i | \(0.394879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −297967. | + | 516093.i | −0.433569 | + | 0.750964i | −0.997178 | − | 0.0750780i | \(-0.976079\pi\) |
0.563608 | + | 0.826042i | \(0.309413\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26704.4 | + | 92869.1i | 0.0386705 | + | 0.134484i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.80674e6 | + | 318576.i | −2.60378 | + | 0.459117i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 159556. | + | 133884.i | 0.228845 | + | 0.192023i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −150438. | − | 4918.26i | −0.214737 | − | 0.00702039i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 362259. | − | 431724.i | 0.514630 | − | 0.613313i | −0.444672 | − | 0.895693i | \(-0.646680\pi\) |
0.959302 | + | 0.282381i | \(0.0911242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45121.2 | + | 255895.i | 0.0637953 | + | 0.361801i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −57974.7 | − | 55902.5i | −0.0815800 | − | 0.0786640i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.38545e6 | + | 799888.i | 1.94033 | + | 1.12025i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 157457. | + | 272724.i | 0.219481 | + | 0.380152i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 228392. | − | 514002.i | 0.316858 | − | 0.713098i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −241893. | − | 288277.i | −0.334014 | − | 0.398062i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 279796. | − | 101838.i | 0.384542 | − | 0.139962i | −0.142513 | − | 0.989793i | \(-0.545518\pi\) |
0.527055 | + | 0.849831i | \(0.323296\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −580776. | + | 21143.9i | −0.794469 | + | 0.0289236i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 585082. | + | 103166.i | 0.796628 | + | 0.140467i | 0.557125 | − | 0.830429i | \(-0.311904\pi\) |
0.239503 | + | 0.970896i | \(0.423016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 807932. | + | 294063.i | 1.09494 | + | 0.398524i | 0.825447 | − | 0.564480i | \(-0.190923\pi\) |
0.269488 | + | 0.963004i | \(0.413145\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −862682. | + | 1.28103e6i | −1.16371 | + | 1.72803i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 395978.i | − | 0.531679i | −0.964017 | − | 0.265839i | \(-0.914351\pi\) | ||
0.964017 | − | 0.265839i | \(-0.0856491\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.02268e6 | 1.36681 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22815.8 | − | 329797.i | 0.0303528 | − | 0.438741i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −366583. | + | 1.00718e6i | −0.485437 | + | 1.33373i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −252578. | + | 1.43244e6i | −0.332935 | + | 1.88817i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −273782. | + | 846886.i | −0.359233 | + | 1.11121i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 241375. | + | 663173.i | 0.315266 | + | 0.866186i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −952713. | + | 799421.i | −1.23869 | + | 1.03938i | −0.241065 | + | 0.970509i | \(0.577497\pi\) |
−0.997625 | + | 0.0688758i | \(0.978059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −140557. | + | 102280.i | −0.181918 | + | 0.132377i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 725858. | − | 419074.i | 0.935190 | − | 0.539932i | 0.0467407 | − | 0.998907i | \(-0.485117\pi\) |
0.888449 | + | 0.458975i | \(0.151783\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34200.8 | + | 59237.6i | −0.0438647 | + | 0.0759759i | −0.887124 | − | 0.461531i | \(-0.847300\pi\) |
0.843259 | + | 0.537507i | \(0.180634\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.52143e6 | − | 378137.i | −1.94252 | − | 0.482795i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 752766. | − | 132733.i | 0.956781 | − | 0.168706i | 0.326607 | − | 0.945160i | \(-0.394095\pi\) |
0.630174 | + | 0.776454i | \(0.282983\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.12935e6 | − | 947640.i | −1.42898 | − | 1.19906i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 732971. | − | 497566.i | 0.923276 | − | 0.626751i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 267546. | − | 318849.i | 0.335502 | − | 0.399836i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −132199. | − | 749739.i | −0.165037 | − | 0.935974i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −116413. | + | 468386.i | −0.144682 | + | 0.582129i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −119608. | − | 69055.7i | −0.147993 | − | 0.0854437i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 514025. | + | 890317.i | 0.633191 | + | 1.09672i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 391951. | + | 538634.i | 0.480681 | + | 0.660569i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −135269. | − | 161207.i | −0.165158 | − | 0.196828i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 674332. | − | 245437.i | 0.819709 | − | 0.298349i | 0.102081 | − | 0.994776i | \(-0.467450\pi\) |
0.717628 | + | 0.696427i | \(0.245228\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.09773e6 | − | 991352.i | 1.32852 | − | 1.19978i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −258709. | − | 45617.4i | −0.311727 | − | 0.0549659i | 0.0155960 | − | 0.999878i | \(-0.495035\pi\) |
−0.327323 | + | 0.944912i | \(0.606147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −173576. | − | 63176.4i | −0.208232 | − | 0.0757903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.11027e6 | + | 76810.1i | 1.32613 | + | 0.0917437i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.24973e6i | 1.48620i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.20587e6 | −1.42781 | −0.713904 | − | 0.700244i | \(-0.753074\pi\) | ||||
−0.713904 | + | 0.700244i | \(0.753074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.09332e6 | − | 736274.i | −1.28893 | − | 0.868001i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −129277. | + | 355187.i | −0.151747 | + | 0.416920i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 126908. | − | 719730.i | 0.148322 | − | 0.841174i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 185430. | − | 116253.i | 0.215785 | − | 0.135283i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −379238. | − | 1.04195e6i | −0.439421 | − | 1.20730i | −0.939870 | − | 0.341533i | \(-0.889054\pi\) |
0.500449 | − | 0.865766i | \(-0.333168\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 921886. | − | 773554.i | 1.06360 | − | 0.892465i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 977434. | + | 434313.i | 1.12286 | + | 0.498930i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.27902e6 | + | 738442.i | −1.46303 | + | 0.844682i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −236877. | + | 410283.i | −0.269801 | + | 0.467309i | −0.968810 | − | 0.247804i | \(-0.920291\pi\) |
0.699009 | + | 0.715112i | \(0.253625\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −851588. | + | 883155.i | −0.965825 | + | 1.00163i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −672157. | + | 118519.i | −0.759087 | + | 0.133847i | −0.539777 | − | 0.841808i | \(-0.681492\pi\) |
−0.219309 | + | 0.975655i | \(0.570380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 285475. | + | 239542.i | 0.321029 | + | 0.269375i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.34602e6 | − | 1.50162e6i | 1.50726 | − | 1.68149i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 500158. | − | 596065.i | 0.557709 | − | 0.664651i | −0.411351 | − | 0.911477i | \(-0.634943\pi\) |
0.969060 | + | 0.246826i | \(0.0793875\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 112838. | + | 639934.i | 0.125291 | + | 0.710563i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17970.9 | − | 5167.49i | 0.0198705 | − | 0.00571372i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 772825. | + | 446190.i | 0.850932 | + | 0.491286i | 0.860965 | − | 0.508664i | \(-0.169860\pi\) |
−0.0100329 | + | 0.999950i | \(0.503194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −444626. | − | 770114.i | −0.487515 | − | 0.844400i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 808358. | − | 85568.2i | 0.882633 | − | 0.0934304i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.05268e6 | − | 2.44629e6i | −2.23195 | − | 2.65993i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 827766. | − | 301282.i | 0.896315 | − | 0.326232i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 416396. | + | 324330.i | 0.449007 | + | 0.349732i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.06068e6 | − | 187027.i | −1.13902 | − | 0.200839i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 76770.3 | + | 27942.1i | 0.0820995 | + | 0.0298818i | 0.382743 | − | 0.923855i | \(-0.374979\pi\) |
−0.300644 | + | 0.953736i | \(0.597202\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 311687. | + | 637852.i | 0.331949 | + | 0.679317i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.56203e6i | − | 1.65673i | −0.560190 | − | 0.828364i | \(-0.689272\pi\) | ||
0.560190 | − | 0.828364i | \(-0.310728\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −738603. | −0.780163 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −842140. | + | 411513.i | −0.885881 | + | 0.432887i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −397237. | + | 1.09140e6i | −0.416160 | + | 1.14339i | 0.537700 | + | 0.843136i | \(0.319293\pi\) |
−0.953860 | + | 0.300253i | \(0.902929\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75812.6 | − | 429955.i | 0.0790999 | − | 0.448598i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −50792.2 | + | 65210.3i | −0.0527788 | + | 0.0677607i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 195388. | + | 536825.i | 0.202205 | + | 0.555554i | 0.998801 | − | 0.0489587i | \(-0.0155903\pi\) |
−0.796596 | + | 0.604512i | \(0.793368\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 127428. | − | 106925.i | 0.131339 | − | 0.110206i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 152034. | + | 1.43626e6i | 0.156065 | + | 1.47434i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 139203. | − | 80368.7i | 0.142316 | − | 0.0821664i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 240431. | − | 416439.i | 0.244818 | − | 0.424037i | −0.717262 | − | 0.696803i | \(-0.754605\pi\) |
0.962080 | + | 0.272766i | \(0.0879384\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 199449. | + | 693619.i | 0.202271 | + | 0.703432i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.50947e6 | − | 266160.i | 1.52468 | − | 0.268842i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 427974. | + | 359113.i | 0.430554 | + | 0.361277i | 0.832161 | − | 0.554535i | \(-0.187104\pi\) |
−0.401607 | + | 0.915812i | \(0.631548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.36893e6 | − | 448162.i | 1.37167 | − | 0.449060i |
(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 | 108.5.k.a.65.11 | yes | 72 | |
3.2 | odd | 2 | 324.5.k.a.197.11 | 72 | |||
27.5 | odd | 18 | inner | 108.5.k.a.5.11 | ✓ | 72 | |
27.22 | even | 9 | 324.5.k.a.125.11 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.5.11 | ✓ | 72 | 27.5 | odd | 18 | inner | |
108.5.k.a.65.11 | yes | 72 | 1.1 | even | 1 | trivial | |
324.5.k.a.125.11 | 72 | 27.22 | even | 9 | |||
324.5.k.a.197.11 | 72 | 3.2 | odd | 2 |