Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,3,Mod(557,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.557");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.s (of order \(6\), 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: | \(24.0327593166\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12745506816.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 863.2 | ||
Root | \(2.23256 - 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.863 |
Dual form | 882.3.s.e.557.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.250000 | + | 0.433013i | ||||
\(5\) | 7.70549 | + | 4.44876i | 1.54110 | + | 0.889753i | 0.998770 | + | 0.0495855i | \(0.0157900\pi\) |
0.542327 | + | 0.840167i | \(0.317543\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −6.29150 | − | 10.8972i | −0.629150 | − | 1.08972i | ||||
\(11\) | −15.4110 | + | 8.89753i | −1.40100 | + | 0.808866i | −0.994495 | − | 0.104784i | \(-0.966585\pi\) |
−0.406502 | + | 0.913650i | \(0.633252\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.58301 | 0.198693 | 0.0993464 | − | 0.995053i | \(-0.468325\pi\) | ||||
0.0993464 | + | 0.995053i | \(0.468325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | 22.4024 | − | 12.9340i | 1.31779 | − | 0.760826i | 0.334417 | − | 0.942425i | \(-0.391461\pi\) |
0.983373 | + | 0.181599i | \(0.0581273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.0000 | + | 17.3205i | −0.526316 | + | 0.911606i | 0.473214 | + | 0.880947i | \(0.343094\pi\) |
−0.999530 | + | 0.0306583i | \(0.990240\pi\) | |||||||
\(20\) | 17.7951i | 0.889753i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 25.1660 | 1.14391 | ||||||||
\(23\) | 15.4110 | + | 8.89753i | 0.670042 | + | 0.386849i | 0.796093 | − | 0.605175i | \(-0.206897\pi\) |
−0.126050 | + | 0.992024i | \(0.540230\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 27.0830 | + | 46.9091i | 1.08332 | + | 1.87637i | ||||
\(26\) | −3.16352 | − | 1.82646i | −0.121674 | − | 0.0702485i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 11.9034i | − | 0.410463i | −0.978713 | − | 0.205232i | \(-0.934205\pi\) | ||
0.978713 | − | 0.205232i | \(-0.0657947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.58301 | + | 14.8662i | 0.276871 | + | 0.479555i | 0.970605 | − | 0.240676i | \(-0.0773692\pi\) |
−0.693734 | + | 0.720231i | \(0.744036\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −36.5830 | −1.07597 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.0000 | + | 32.9090i | −0.513514 | + | 0.889431i | 0.486364 | + | 0.873757i | \(0.338323\pi\) |
−0.999877 | + | 0.0156750i | \(0.995010\pi\) | |||||||
\(38\) | 24.4949 | − | 14.1421i | 0.644603 | − | 0.372161i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.5830 | − | 21.7944i | 0.314575 | − | 0.544860i | ||||
\(41\) | 15.7338i | 0.383752i | 0.981419 | + | 0.191876i | \(0.0614571\pi\) | ||||
−0.981419 | + | 0.191876i | \(0.938543\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −43.4980 | −1.01158 | −0.505791 | − | 0.862656i | \(-0.668799\pi\) | ||||
−0.505791 | + | 0.862656i | \(0.668799\pi\) | |||||||
\(44\) | −30.8219 | − | 17.7951i | −0.700499 | − | 0.404433i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.5830 | − | 21.7944i | −0.273544 | − | 0.473791i | ||||
\(47\) | −14.6969 | − | 8.48528i | −0.312701 | − | 0.180538i | 0.335434 | − | 0.942064i | \(-0.391117\pi\) |
−0.648134 | + | 0.761526i | \(0.724451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 76.6023i | − | 1.53205i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.58301 | + | 4.47390i | 0.0496732 | + | 0.0860365i | ||||
\(53\) | 74.0947 | − | 42.7786i | 1.39801 | − | 0.807143i | 0.403828 | − | 0.914835i | \(-0.367679\pi\) |
0.994184 | + | 0.107692i | \(0.0343461\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −158.332 | −2.87876 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.41699 | + | 14.5787i | −0.145121 | + | 0.251356i | ||||
\(59\) | −1.42807 | + | 0.824494i | −0.0242045 | + | 0.0139745i | −0.512053 | − | 0.858954i | \(-0.671115\pi\) |
0.487849 | + | 0.872928i | \(0.337782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −50.1660 | + | 86.8901i | −0.822394 | + | 1.42443i | 0.0815014 | + | 0.996673i | \(0.474028\pi\) |
−0.903895 | + | 0.427754i | \(0.859305\pi\) | |||||||
\(62\) | − | 24.2764i | − | 0.391555i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 19.9033 | + | 11.4912i | 0.306205 | + | 0.176787i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −18.3320 | − | 31.7520i | −0.273612 | − | 0.473910i | 0.696172 | − | 0.717875i | \(-0.254885\pi\) |
−0.969784 | + | 0.243965i | \(0.921552\pi\) | |||||||
\(68\) | 44.8048 | + | 25.8681i | 0.658895 | + | 0.380413i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 17.7951i | − | 0.250635i | −0.992117 | − | 0.125317i | \(-0.960005\pi\) | ||
0.992117 | − | 0.125317i | \(-0.0399949\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.4575 | − | 25.0411i | −0.198048 | − | 0.343029i | 0.749847 | − | 0.661611i | \(-0.230127\pi\) |
−0.947895 | + | 0.318581i | \(0.896794\pi\) | |||||||
\(74\) | 46.5403 | − | 26.8701i | 0.628923 | − | 0.363109i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −40.0000 | −0.526316 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −59.1660 | + | 102.479i | −0.748937 | + | 1.29720i | 0.199396 | + | 0.979919i | \(0.436102\pi\) |
−0.948333 | + | 0.317278i | \(0.897231\pi\) | |||||||
\(80\) | −30.8219 | + | 17.7951i | −0.385274 | + | 0.222438i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 11.1255 | − | 19.2699i | 0.135677 | − | 0.234999i | ||||
\(83\) | 120.443i | 1.45112i | 0.688159 | + | 0.725560i | \(0.258419\pi\) | ||||
−0.688159 | + | 0.725560i | \(0.741581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 230.162 | 2.70779 | ||||||||
\(86\) | 53.2740 | + | 30.7578i | 0.619465 | + | 0.357648i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 25.1660 | + | 43.5888i | 0.285977 | + | 0.495327i | ||||
\(89\) | −120.789 | − | 69.7374i | −1.35718 | − | 0.783566i | −0.367934 | − | 0.929852i | \(-0.619935\pi\) |
−0.989242 | + | 0.146286i | \(0.953268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 35.5901i | 0.386849i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0000 | + | 20.7846i | 0.127660 | + | 0.221113i | ||||
\(95\) | −154.110 | + | 88.9753i | −1.62221 | + | 0.936582i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 44.4131 | 0.457867 | 0.228933 | − | 0.973442i | \(-0.426476\pi\) | ||||
0.228933 | + | 0.973442i | \(0.426476\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −54.1660 | + | 93.8183i | −0.541660 | + | 0.938183i | ||||
\(101\) | −27.6088 | + | 15.9399i | −0.273354 | + | 0.157821i | −0.630411 | − | 0.776261i | \(-0.717114\pi\) |
0.357057 | + | 0.934083i | \(0.383780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.25098 | + | 3.89882i | −0.0218542 | + | 0.0378526i | −0.876746 | − | 0.480954i | \(-0.840290\pi\) |
0.854891 | + | 0.518807i | \(0.173624\pi\) | |||||||
\(104\) | − | 7.30584i | − | 0.0702485i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −120.996 | −1.14147 | ||||||||
\(107\) | 149.111 | + | 86.0896i | 1.39357 | + | 0.804575i | 0.993708 | − | 0.112002i | \(-0.0357263\pi\) |
0.399857 | + | 0.916577i | \(0.369060\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 88.9150 | + | 154.005i | 0.815734 | + | 1.41289i | 0.908800 | + | 0.417233i | \(0.137000\pi\) |
−0.0930653 | + | 0.995660i | \(0.529667\pi\) | |||||||
\(110\) | 193.916 | + | 111.958i | 1.76288 | + | 1.01780i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 31.3475i | − | 0.277411i | −0.990334 | − | 0.138706i | \(-0.955706\pi\) | ||
0.990334 | − | 0.138706i | \(-0.0442942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 79.1660 | + | 137.120i | 0.688400 | + | 1.19234i | ||||
\(116\) | 20.6173 | − | 11.9034i | 0.177736 | − | 0.102616i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.33202 | 0.0197629 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 97.8320 | − | 169.450i | 0.808529 | − | 1.40041i | ||||
\(122\) | 122.881 | − | 70.9455i | 1.00722 | − | 0.581520i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −17.1660 | + | 29.7324i | −0.138436 | + | 0.239777i | ||||
\(125\) | 259.505i | 2.07604i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 214.332 | 1.68765 | 0.843827 | − | 0.536616i | \(-0.180297\pi\) | ||||
0.843827 | + | 0.536616i | \(0.180297\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −16.2510 | − | 28.1475i | −0.125008 | − | 0.216519i | ||||
\(131\) | 79.1970 | + | 45.7244i | 0.604557 | + | 0.349041i | 0.770832 | − | 0.637038i | \(-0.219841\pi\) |
−0.166275 | + | 0.986079i | \(0.553174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 51.8508i | 0.386946i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −36.5830 | − | 63.3636i | −0.268993 | − | 0.465909i | ||||
\(137\) | 92.5699 | − | 53.4453i | 0.675693 | − | 0.390111i | −0.122537 | − | 0.992464i | \(-0.539103\pi\) |
0.798230 | + | 0.602353i | \(0.205770\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −121.328 | −0.872864 | −0.436432 | − | 0.899737i | \(-0.643758\pi\) | ||||
−0.436432 | + | 0.899737i | \(0.643758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.5830 | + | 21.7944i | −0.0886127 | + | 0.153482i | ||||
\(143\) | −39.8066 | + | 22.9824i | −0.278368 | + | 0.160716i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 52.9555 | − | 91.7217i | 0.365211 | − | 0.632563i | ||||
\(146\) | 40.8920i | 0.280082i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −76.0000 | −0.513514 | ||||||||
\(149\) | −15.3069 | − | 8.83744i | −0.102731 | − | 0.0593117i | 0.447754 | − | 0.894157i | \(-0.352224\pi\) |
−0.550485 | + | 0.834845i | \(0.685557\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 25.4170 | + | 44.0235i | 0.168324 | + | 0.291547i | 0.937831 | − | 0.347093i | \(-0.112831\pi\) |
−0.769506 | + | 0.638639i | \(0.779498\pi\) | |||||||
\(152\) | 48.9898 | + | 28.2843i | 0.322301 | + | 0.186081i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 152.735i | 0.985388i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −34.4980 | − | 59.7523i | −0.219733 | − | 0.380588i | 0.734994 | − | 0.678074i | \(-0.237185\pi\) |
−0.954726 | + | 0.297486i | \(0.903852\pi\) | |||||||
\(158\) | 144.927 | − | 83.6734i | 0.917257 | − | 0.529578i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 50.3320 | 0.314575 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 83.4980 | − | 144.623i | 0.512258 | − | 0.887257i | −0.487641 | − | 0.873044i | \(-0.662143\pi\) |
0.999899 | − | 0.0142125i | \(-0.00452412\pi\) | |||||||
\(164\) | −27.2518 | + | 15.7338i | −0.166169 | + | 0.0959379i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 85.1660 | − | 147.512i | 0.513048 | − | 0.888626i | ||||
\(167\) | − | 120.443i | − | 0.721215i | −0.932718 | − | 0.360608i | \(-0.882569\pi\) | ||
0.932718 | − | 0.360608i | \(-0.117431\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −162.328 | −0.960521 | ||||||||
\(170\) | −281.890 | − | 162.749i | −1.65818 | − | 0.957348i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −43.4980 | − | 75.3408i | −0.252896 | − | 0.438028i | ||||
\(173\) | −79.5540 | − | 45.9305i | −0.459850 | − | 0.265494i | 0.252131 | − | 0.967693i | \(-0.418868\pi\) |
−0.711981 | + | 0.702199i | \(0.752202\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 71.1802i | − | 0.404433i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 98.6235 | + | 170.821i | 0.554065 | + | 0.959668i | ||||
\(179\) | −115.433 | + | 66.6455i | −0.644879 | + | 0.372321i | −0.786492 | − | 0.617601i | \(-0.788105\pi\) |
0.141612 | + | 0.989922i | \(0.454771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 83.0850 | 0.459033 | 0.229517 | − | 0.973305i | \(-0.426286\pi\) | ||||
0.229517 | + | 0.973305i | \(0.426286\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 25.1660 | − | 43.5888i | 0.136772 | − | 0.236896i | ||||
\(185\) | −292.808 | + | 169.053i | −1.58275 | + | 0.913800i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −230.162 | + | 398.652i | −1.23081 | + | 2.13183i | ||||
\(188\) | − | 33.9411i | − | 0.180538i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 251.660 | 1.32453 | ||||||||
\(191\) | 35.8202 | + | 20.6808i | 0.187540 | + | 0.108276i | 0.590830 | − | 0.806796i | \(-0.298800\pi\) |
−0.403290 | + | 0.915072i | \(0.632134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −67.0000 | − | 116.047i | −0.347150 | − | 0.601282i | 0.638592 | − | 0.769546i | \(-0.279517\pi\) |
−0.985742 | + | 0.168264i | \(0.946184\pi\) | |||||||
\(194\) | −54.3947 | − | 31.4048i | −0.280385 | − | 0.161880i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 68.8269i | 0.349375i | 0.984624 | + | 0.174688i | \(0.0558916\pi\) | ||||
−0.984624 | + | 0.174688i | \(0.944108\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 139.247 | + | 241.183i | 0.699734 | + | 1.21197i | 0.968559 | + | 0.248786i | \(0.0800314\pi\) |
−0.268825 | + | 0.963189i | \(0.586635\pi\) | |||||||
\(200\) | 132.679 | − | 76.6023i | 0.663395 | − | 0.383012i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 45.0850 | 0.223193 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −69.9961 | + | 121.237i | −0.341444 | + | 0.591399i | ||||
\(206\) | 5.51376 | − | 3.18337i | 0.0267658 | − | 0.0154533i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.16601 | + | 8.94779i | −0.0248366 | + | 0.0430182i | ||||
\(209\) | − | 355.901i | − | 1.70288i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −211.498 | −1.00236 | −0.501180 | − | 0.865343i | \(-0.667101\pi\) | ||||
−0.501180 | + | 0.865343i | \(0.667101\pi\) | |||||||
\(212\) | 148.189 | + | 85.5571i | 0.699006 | + | 0.403571i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −121.749 | − | 210.875i | −0.568921 | − | 0.985399i | ||||
\(215\) | −335.173 | − | 193.512i | −1.55895 | − | 0.900058i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 251.490i | − | 1.15362i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −158.332 | − | 274.239i | −0.719691 | − | 1.24654i | ||||
\(221\) | 57.8656 | − | 33.4087i | 0.261835 | − | 0.151171i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 222.494 | 0.997731 | 0.498866 | − | 0.866679i | \(-0.333750\pi\) | ||||
0.498866 | + | 0.866679i | \(0.333750\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −22.1660 | + | 38.3927i | −0.0980797 | + | 0.169879i | ||||
\(227\) | −88.1816 | + | 50.9117i | −0.388465 | + | 0.224281i | −0.681495 | − | 0.731823i | \(-0.738670\pi\) |
0.293030 | + | 0.956103i | \(0.405337\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 81.5425 | − | 141.236i | 0.356081 | − | 0.616750i | −0.631222 | − | 0.775603i | \(-0.717446\pi\) |
0.987302 | + | 0.158853i | \(0.0507795\pi\) | |||||||
\(230\) | − | 223.915i | − | 0.973545i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −33.6680 | −0.145121 | ||||||||
\(233\) | 314.244 | + | 181.429i | 1.34869 | + | 0.778664i | 0.988063 | − | 0.154047i | \(-0.0492308\pi\) |
0.360623 | + | 0.932712i | \(0.382564\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −75.4980 | − | 130.766i | −0.321268 | − | 0.556453i | ||||
\(236\) | −2.85613 | − | 1.64899i | −0.0121022 | − | 0.00698724i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 177.126i | 0.741113i | 0.928810 | + | 0.370557i | \(0.120833\pi\) | ||||
−0.928810 | + | 0.370557i | \(0.879167\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −76.3765 | − | 132.288i | −0.316915 | − | 0.548913i | 0.662928 | − | 0.748683i | \(-0.269314\pi\) |
−0.979843 | + | 0.199771i | \(0.935980\pi\) | |||||||
\(242\) | −239.639 | + | 138.355i | −0.990242 | + | 0.571716i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −200.664 | −0.822394 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.8301 | + | 44.7390i | −0.104575 | + | 0.181129i | ||||
\(248\) | 42.0480 | − | 24.2764i | 0.169548 | − | 0.0978887i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 183.498 | − | 317.828i | 0.733992 | − | 1.27131i | ||||
\(251\) | − | 356.382i | − | 1.41985i | −0.704278 | − | 0.709924i | \(-0.748729\pi\) | ||
0.704278 | − | 0.709924i | \(-0.251271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −316.664 | −1.25164 | ||||||||
\(254\) | −262.502 | − | 151.556i | −1.03347 | − | 0.596676i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 51.5882 | + | 29.7844i | 0.200732 | + | 0.115893i | 0.596997 | − | 0.802244i | \(-0.296360\pi\) |
−0.396265 | + | 0.918136i | \(0.629694\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 45.9647i | 0.176787i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −64.6640 | − | 112.001i | −0.246809 | − | 0.427486i | ||||
\(263\) | 6.42629 | − | 3.71022i | 0.0244346 | − | 0.0141073i | −0.487733 | − | 0.872993i | \(-0.662176\pi\) |
0.512168 | + | 0.858886i | \(0.328843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 761.247 | 2.87263 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 36.6640 | − | 63.5040i | 0.136806 | − | 0.236955i | ||||
\(269\) | 372.571 | − | 215.104i | 1.38502 | − | 0.799642i | 0.392272 | − | 0.919849i | \(-0.371689\pi\) |
0.992749 | + | 0.120207i | \(0.0383559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.5830 | − | 35.6508i | 0.0759520 | − | 0.131553i | −0.825548 | − | 0.564332i | \(-0.809134\pi\) |
0.901500 | + | 0.432779i | \(0.142467\pi\) | |||||||
\(272\) | 103.472i | 0.380413i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −151.166 | −0.551701 | ||||||||
\(275\) | −834.751 | − | 481.944i | −3.03546 | − | 1.75252i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.0000 | − | 27.7128i | −0.0577617 | − | 0.100046i | 0.835699 | − | 0.549188i | \(-0.185063\pi\) |
−0.893460 | + | 0.449142i | \(0.851730\pi\) | |||||||
\(278\) | 148.596 | + | 85.7919i | 0.534518 | + | 0.308604i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.0907i | − | 0.0608211i | −0.999537 | − | 0.0304106i | \(-0.990319\pi\) | ||
0.999537 | − | 0.0304106i | \(-0.00968147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −219.830 | − | 380.757i | −0.776785 | − | 1.34543i | −0.933786 | − | 0.357832i | \(-0.883516\pi\) |
0.157001 | − | 0.987598i | \(-0.449817\pi\) | |||||||
\(284\) | 30.8219 | − | 17.7951i | 0.108528 | − | 0.0626587i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 65.0039 | 0.227286 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 190.079 | − | 329.227i | 0.657713 | − | 1.13919i | ||||
\(290\) | −129.714 | + | 74.8904i | −0.447290 | + | 0.258243i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 28.9150 | − | 50.0823i | 0.0990241 | − | 0.171515i | ||||
\(293\) | 394.377i | 1.34600i | 0.739644 | + | 0.672998i | \(0.234994\pi\) | ||||
−0.739644 | + | 0.672998i | \(0.765006\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.6719 | −0.0497353 | ||||||||
\(296\) | 93.0806 | + | 53.7401i | 0.314462 | + | 0.181554i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.4980 | + | 21.6472i | 0.0419397 | + | 0.0726417i | ||||
\(299\) | 39.8066 | + | 22.9824i | 0.133133 | + | 0.0768641i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 71.8901i | − | 0.238047i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −40.0000 | − | 69.2820i | −0.131579 | − | 0.227901i | ||||
\(305\) | −773.107 | + | 446.353i | −2.53478 | + | 1.46345i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.3360 | −0.0760129 | −0.0380064 | − | 0.999277i | \(-0.512101\pi\) | ||||
−0.0380064 | + | 0.999277i | \(0.512101\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 108.000 | − | 187.061i | 0.348387 | − | 0.603424i | ||||
\(311\) | 456.617 | − | 263.628i | 1.46822 | − | 0.847678i | 0.468855 | − | 0.883275i | \(-0.344667\pi\) |
0.999366 | + | 0.0355970i | \(0.0113333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 147.664 | − | 255.762i | 0.471770 | − | 0.817130i | −0.527708 | − | 0.849426i | \(-0.676949\pi\) |
0.999478 | + | 0.0322959i | \(0.0102819\pi\) | |||||||
\(314\) | 97.5752i | 0.310749i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −236.664 | −0.748937 | ||||||||
\(317\) | 93.0758 | + | 53.7373i | 0.293614 | + | 0.169518i | 0.639571 | − | 0.768732i | \(-0.279112\pi\) |
−0.345956 | + | 0.938251i | \(0.612445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 105.911 | + | 183.443i | 0.332010 | + | 0.575058i | ||||
\(320\) | −61.6439 | − | 35.5901i | −0.192637 | − | 0.111219i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 517.362i | 1.60174i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 69.9555 | + | 121.167i | 0.215248 | + | 0.372820i | ||||
\(326\) | −204.528 | + | 118.084i | −0.627385 | + | 0.362221i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 44.5020 | 0.135677 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 136.745 | − | 236.849i | 0.413127 | − | 0.715557i | −0.582103 | − | 0.813115i | \(-0.697770\pi\) |
0.995230 | + | 0.0975581i | \(0.0311032\pi\) | |||||||
\(332\) | −208.613 | + | 120.443i | −0.628353 | + | 0.362780i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −85.1660 | + | 147.512i | −0.254988 | + | 0.441652i | ||||
\(335\) | − | 326.219i | − | 0.973789i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −341.166 | −1.01236 | −0.506181 | − | 0.862427i | \(-0.668943\pi\) | ||||
−0.506181 | + | 0.862427i | \(0.668943\pi\) | |||||||
\(338\) | 198.810 | + | 114.783i | 0.588197 | + | 0.339596i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 230.162 | + | 398.652i | 0.676947 | + | 1.17251i | ||||
\(341\) | −264.545 | − | 152.735i | −0.775791 | − | 0.447903i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 123.031i | 0.357648i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 64.9555 | + | 112.506i | 0.187733 | + | 0.325163i | ||||
\(347\) | −100.736 | + | 58.1602i | −0.290307 | + | 0.167609i | −0.638080 | − | 0.769970i | \(-0.720271\pi\) |
0.347773 | + | 0.937579i | \(0.386938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −158.324 | −0.453651 | −0.226825 | − | 0.973935i | \(-0.572835\pi\) | ||||
−0.226825 | + | 0.973935i | \(0.572835\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −50.3320 | + | 87.1776i | −0.142989 | + | 0.247664i | ||||
\(353\) | 199.480 | − | 115.170i | 0.565098 | − | 0.326260i | −0.190091 | − | 0.981766i | \(-0.560878\pi\) |
0.755189 | + | 0.655507i | \(0.227545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 79.1660 | − | 137.120i | 0.223003 | − | 0.386252i | ||||
\(356\) | − | 278.949i | − | 0.783566i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 188.502 | 0.526542 | ||||||||
\(359\) | 148.695 | + | 85.8492i | 0.414193 | + | 0.239134i | 0.692590 | − | 0.721332i | \(-0.256470\pi\) |
−0.278397 | + | 0.960466i | \(0.589803\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.5000 | − | 33.7750i | −0.0540166 | − | 0.0935595i | ||||
\(362\) | −101.758 | − | 58.7499i | −0.281099 | − | 0.162293i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 257.272i | − | 0.704856i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −258.745 | − | 448.160i | −0.705027 | − | 1.22114i | −0.966682 | − | 0.255982i | \(-0.917601\pi\) |
0.261654 | − | 0.965162i | \(-0.415732\pi\) | |||||||
\(368\) | −61.6439 | + | 35.5901i | −0.167511 | + | 0.0967123i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 478.154 | 1.29231 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 116.668 | − | 202.075i | 0.312783 | − | 0.541756i | −0.666181 | − | 0.745790i | \(-0.732072\pi\) |
0.978964 | + | 0.204035i | \(0.0654055\pi\) | |||||||
\(374\) | 563.780 | − | 325.498i | 1.50743 | − | 0.870316i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | + | 41.5692i | −0.0638298 | + | 0.110556i | ||||
\(377\) | − | 30.7466i | − | 0.0815560i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 441.166 | 1.16403 | 0.582013 | − | 0.813179i | \(-0.302265\pi\) | ||||
0.582013 | + | 0.813179i | \(0.302265\pi\) | |||||||
\(380\) | −308.219 | − | 177.951i | −0.811104 | − | 0.468291i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −29.2470 | − | 50.6574i | −0.0765630 | − | 0.132611i | ||||
\(383\) | −184.515 | − | 106.530i | −0.481763 | − | 0.278146i | 0.239388 | − | 0.970924i | \(-0.423053\pi\) |
−0.721151 | + | 0.692778i | \(0.756387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 189.505i | 0.490945i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 44.4131 | + | 76.9257i | 0.114467 | + | 0.198262i | ||||
\(389\) | 489.387 | − | 282.548i | 1.25806 | − | 0.726344i | 0.285367 | − | 0.958418i | \(-0.407885\pi\) |
0.972698 | + | 0.232074i | \(0.0745512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 460.324 | 1.17730 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 48.6680 | − | 84.2954i | 0.123523 | − | 0.213948i | ||||
\(395\) | −911.806 | + | 526.431i | −2.30837 | + | 1.33274i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −249.162 | + | 431.561i | −0.627612 | + | 1.08706i | 0.360417 | + | 0.932791i | \(0.382634\pi\) |
−0.988029 | + | 0.154265i | \(0.950699\pi\) | |||||||
\(398\) | − | 393.850i | − | 0.989573i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −216.664 | −0.541660 | ||||||||
\(401\) | −167.483 | − | 96.6962i | −0.417662 | − | 0.241138i | 0.276414 | − | 0.961039i | \(-0.410854\pi\) |
−0.694077 | + | 0.719901i | \(0.744187\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.1699 | + | 38.3995i | 0.0550123 | + | 0.0952841i | ||||
\(404\) | −55.2176 | − | 31.8799i | −0.136677 | − | 0.0789106i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 676.212i | − | 1.66145i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 227.122 | + | 393.386i | 0.555309 | + | 0.961824i | 0.997879 | + | 0.0650902i | \(0.0207335\pi\) |
−0.442570 | + | 0.896734i | \(0.645933\pi\) | |||||||
\(410\) | 171.455 | − | 98.9894i | 0.418182 | − | 0.241438i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.00394 | −0.0218542 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −535.822 | + | 928.071i | −1.29114 | + | 2.23632i | ||||
\(416\) | 12.6541 | − | 7.30584i | 0.0304185 | − | 0.0175621i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −251.660 | + | 435.888i | −0.602058 | + | 1.04279i | ||||
\(419\) | − | 339.411i | − | 0.810051i | −0.914305 | − | 0.405025i | \(-0.867263\pi\) | ||
0.914305 | − | 0.405025i | \(-0.132737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 247.320 | 0.587459 | 0.293729 | − | 0.955889i | \(-0.405104\pi\) | ||||
0.293729 | + | 0.955889i | \(0.405104\pi\) | |||||||
\(422\) | 259.031 | + | 149.552i | 0.613818 | + | 0.354388i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −120.996 | − | 209.571i | −0.285368 | − | 0.494272i | ||||
\(425\) | 1213.45 | + | 700.586i | 2.85518 | + | 1.64844i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 344.358i | 0.804575i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 273.668 | + | 474.007i | 0.636437 | + | 1.10234i | ||||
\(431\) | 395.271 | − | 228.210i | 0.917101 | − | 0.529489i | 0.0343923 | − | 0.999408i | \(-0.489050\pi\) |
0.882709 | + | 0.469920i | \(0.155717\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −637.984 | −1.47340 | −0.736702 | − | 0.676217i | \(-0.763618\pi\) | ||||
−0.736702 | + | 0.676217i | \(0.763618\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −177.830 | + | 308.011i | −0.407867 | + | 0.706447i | ||||
\(437\) | −308.219 | + | 177.951i | −0.705308 | + | 0.407210i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 392.073 | − | 679.091i | 0.893105 | − | 1.54690i | 0.0569728 | − | 0.998376i | \(-0.481855\pi\) |
0.836132 | − | 0.548528i | \(-0.184812\pi\) | |||||||
\(440\) | 447.831i | 1.01780i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −94.4941 | −0.213788 | ||||||||
\(443\) | −408.956 | − | 236.111i | −0.923151 | − | 0.532981i | −0.0385120 | − | 0.999258i | \(-0.512262\pi\) |
−0.884639 | + | 0.466277i | \(0.845595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −620.490 | − | 1074.72i | −1.39436 | − | 2.41510i | ||||
\(446\) | −272.499 | − | 157.327i | −0.610983 | − | 0.352751i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 739.852i | − | 1.64778i | −0.566752 | − | 0.823888i | \(-0.691800\pi\) | ||
0.566752 | − | 0.823888i | \(-0.308200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −139.992 | − | 242.473i | −0.310404 | − | 0.537635i | ||||
\(452\) | 54.2954 | − | 31.3475i | 0.120123 | − | 0.0693528i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 144.000 | 0.317181 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 124.162 | − | 215.055i | 0.271689 | − | 0.470580i | −0.697605 | − | 0.716482i | \(-0.745751\pi\) |
0.969295 | + | 0.245903i | \(0.0790843\pi\) | |||||||
\(458\) | −199.737 | + | 115.318i | −0.436108 | + | 0.251787i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −158.332 | + | 274.239i | −0.344200 | + | 0.596172i | ||||
\(461\) | 355.970i | 0.772168i | 0.922464 | + | 0.386084i | \(0.126173\pi\) | ||||
−0.922464 | + | 0.386084i | \(0.873827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33202 | −0.0136761 | −0.00683804 | − | 0.999977i | \(-0.502177\pi\) | ||||
−0.00683804 | + | 0.999977i | \(0.502177\pi\) | |||||||
\(464\) | 41.2347 | + | 23.8069i | 0.0888679 | + | 0.0513079i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −256.579 | − | 444.408i | −0.550599 | − | 0.953665i | ||||
\(467\) | −760.968 | − | 439.345i | −1.62948 | − | 0.940782i | −0.984247 | − | 0.176799i | \(-0.943426\pi\) |
−0.645236 | − | 0.763984i | \(-0.723241\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 213.541i | 0.454342i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.33202 | + | 4.03918i | 0.00494072 | + | 0.00855758i | ||||
\(473\) | 670.347 | − | 387.025i | 1.41722 | − | 0.818235i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1083.32 | −2.28067 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 125.247 | − | 216.934i | 0.262023 | − | 0.453837i | ||||
\(479\) | 194.333 | − | 112.198i | 0.405705 | − | 0.234234i | −0.283238 | − | 0.959050i | \(-0.591409\pi\) |
0.688943 | + | 0.724816i | \(0.258075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −49.0771 | + | 85.0040i | −0.102031 | + | 0.176724i | ||||
\(482\) | 216.025i | 0.448185i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 391.328 | 0.808529 | ||||||||
\(485\) | 342.224 | + | 197.583i | 0.705617 | + | 0.407388i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 358.745 | + | 621.365i | 0.736643 | + | 1.27590i | 0.953999 | + | 0.299810i | \(0.0969234\pi\) |
−0.217356 | + | 0.976092i | \(0.569743\pi\) | |||||||
\(488\) | 245.762 | + | 141.891i | 0.503611 | + | 0.290760i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 274.002i | 0.558050i | 0.960284 | + | 0.279025i | \(0.0900112\pi\) | ||||
−0.960284 | + | 0.279025i | \(0.909989\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −153.959 | − | 266.666i | −0.312291 | − | 0.540904i | ||||
\(494\) | 63.2704 | − | 36.5292i | 0.128078 | − | 0.0739458i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −68.6640 | −0.138436 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 364.405 | − | 631.168i | 0.730271 | − | 1.26487i | −0.226496 | − | 0.974012i | \(-0.572727\pi\) |
0.956767 | − | 0.290854i | \(-0.0939395\pi\) | |||||||
\(500\) | −449.477 | + | 259.505i | −0.898953 | + | 0.519011i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −252.000 | + | 436.477i | −0.501992 | + | 0.869476i | ||||
\(503\) | − | 594.657i | − | 1.18222i | −0.806590 | − | 0.591111i | \(-0.798690\pi\) | ||
0.806590 | − | 0.591111i | \(-0.201310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −283.652 | −0.561688 | ||||||||
\(506\) | 387.833 | + | 223.915i | 0.766468 | + | 0.442520i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 214.332 | + | 371.234i | 0.421913 | + | 0.730775i | ||||
\(509\) | 860.842 | + | 497.007i | 1.69124 | + | 0.976439i | 0.953518 | + | 0.301336i | \(0.0974325\pi\) |
0.737723 | + | 0.675103i | \(0.235901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −42.1216 | − | 72.9567i | −0.0819486 | − | 0.141939i | ||||
\(515\) | −34.6899 | + | 20.0282i | −0.0673589 | + | 0.0388897i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 301.992 | 0.584124 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 32.5020 | − | 56.2951i | 0.0625038 | − | 0.108260i | ||||
\(521\) | −35.3735 | + | 20.4229i | −0.0678955 | + | 0.0391995i | −0.533563 | − | 0.845760i | \(-0.679147\pi\) |
0.465668 | + | 0.884960i | \(0.345814\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 116.000 | − | 200.918i | 0.221797 | − | 0.384164i | −0.733556 | − | 0.679629i | \(-0.762141\pi\) |
0.955354 | + | 0.295464i | \(0.0954743\pi\) | |||||||
\(524\) | 182.898i | 0.349041i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.4941 | −0.0199507 | ||||||||
\(527\) | 384.560 | + | 222.026i | 0.729716 | + | 0.421302i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −106.168 | − | 183.888i | −0.200696 | − | 0.347615i | ||||
\(530\) | −932.333 | − | 538.283i | −1.75912 | − | 1.01563i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.6405i | 0.0762487i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 765.984 | + | 1326.72i | 1.43175 | + | 2.47986i | ||||
\(536\) | −89.8082 | + | 51.8508i | −0.167553 | + | 0.0967365i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −608.405 | −1.13086 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −125.166 | + | 216.794i | −0.231360 | + | 0.400728i | −0.958209 | − | 0.286070i | \(-0.907651\pi\) |
0.726848 | + | 0.686798i | \(0.240984\pi\) | |||||||
\(542\) | −50.4179 | + | 29.1088i | −0.0930219 | + | 0.0537062i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 73.1660 | − | 126.727i | 0.134496 | − | 0.232954i | ||||
\(545\) | 1582.25i | 2.90321i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 888.324 | 1.62399 | 0.811996 | − | 0.583662i | \(-0.198381\pi\) | ||||
0.811996 | + | 0.583662i | \(0.198381\pi\) | |||||||
\(548\) | 185.140 | + | 106.891i | 0.337846 | + | 0.195056i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 681.571 | + | 1180.52i | 1.23922 | + | 2.14639i | ||||
\(551\) | 206.173 | + | 119.034i | 0.374180 | + | 0.216033i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 45.2548i | 0.0816874i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −121.328 | − | 210.146i | −0.218216 | − | 0.377961i | ||||
\(557\) | −273.931 | + | 158.154i | −0.491798 | + | 0.283940i | −0.725320 | − | 0.688412i | \(-0.758308\pi\) |
0.233522 | + | 0.972351i | \(0.424975\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −112.356 | −0.200994 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0850 | + | 20.9318i | −0.0215035 | + | 0.0372452i | ||||
\(563\) | −50.6356 | + | 29.2345i | −0.0899390 | + | 0.0519263i | −0.544295 | − | 0.838894i | \(-0.683203\pi\) |
0.454356 | + | 0.890820i | \(0.349869\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 139.458 | − | 241.547i | 0.246827 | − | 0.427518i | ||||
\(566\) | 621.773i | 1.09854i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −50.3320 | −0.0886127 | ||||||||
\(569\) | 191.968 | + | 110.833i | 0.337378 | + | 0.194785i | 0.659112 | − | 0.752045i | \(-0.270932\pi\) |
−0.321734 | + | 0.946830i | \(0.604266\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 243.822 | + | 422.312i | 0.427009 | + | 0.739601i | 0.996606 | − | 0.0823230i | \(-0.0262339\pi\) |
−0.569597 | + | 0.821924i | \(0.692901\pi\) | |||||||
\(572\) | −79.6132 | − | 45.9647i | −0.139184 | − | 0.0803579i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 963.887i | 1.67633i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 243.664 | + | 422.039i | 0.422295 | + | 0.731436i | 0.996164 | − | 0.0875114i | \(-0.0278914\pi\) |
−0.573869 | + | 0.818947i | \(0.694558\pi\) | |||||||
\(578\) | −465.597 | + | 268.812i | −0.805531 | + | 0.465073i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 211.822 | 0.365211 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −761.247 | + | 1318.52i | −1.30574 | + | 2.26161i | ||||
\(584\) | −70.8271 | + | 40.8920i | −0.121279 | + | 0.0700206i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 278.867 | − | 483.011i | 0.475882 | − | 0.824251i | ||||
\(587\) | 445.701i | 0.759286i | 0.925133 | + | 0.379643i | \(0.123953\pi\) | ||||
−0.925133 | + | 0.379643i | \(0.876047\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −343.320 | −0.582887 | ||||||||
\(590\) | 17.9694 | + | 10.3746i | 0.0304565 | + | 0.0175841i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −76.0000 | − | 131.636i | −0.128378 | − | 0.222358i | ||||
\(593\) | −239.584 | − | 138.324i | −0.404020 | − | 0.233261i | 0.284197 | − | 0.958766i | \(-0.408273\pi\) |
−0.688217 | + | 0.725505i | \(0.741606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 35.3498i | − | 0.0593117i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −32.5020 | − | 56.2951i | −0.0543511 | − | 0.0941389i | ||||
\(599\) | 71.3426 | − | 41.1897i | 0.119103 | − | 0.0687641i | −0.439265 | − | 0.898358i | \(-0.644761\pi\) |
0.558368 | + | 0.829593i | \(0.311428\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −418.000 | −0.695507 | −0.347754 | − | 0.937586i | \(-0.613055\pi\) | ||||
−0.347754 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −50.8340 | + | 88.0471i | −0.0841622 | + | 0.145773i | ||||
\(605\) | 1507.69 | − | 870.463i | 2.49204 | − | 1.43878i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −38.4209 | + | 66.5470i | −0.0632964 | + | 0.109633i | −0.895937 | − | 0.444181i | \(-0.853495\pi\) |
0.832641 | + | 0.553814i | \(0.186828\pi\) | |||||||
\(608\) | 113.137i | 0.186081i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1262.48 | 2.06964 | ||||||||
\(611\) | −37.9623 | − | 21.9175i | −0.0621314 | − | 0.0358716i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.6640 | − | 51.3796i | −0.0483916 | − | 0.0838167i | 0.840815 | − | 0.541323i | \(-0.182076\pi\) |
−0.889207 | + | 0.457506i | \(0.848743\pi\) | |||||||
\(614\) | 28.5806 | + | 16.5010i | 0.0465482 | + | 0.0268746i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 29.1143i | − | 0.0471869i | −0.999722 | − | 0.0235935i | \(-0.992489\pi\) | ||
0.999722 | − | 0.0235935i | \(-0.00751073\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −227.822 | − | 394.600i | −0.368049 | − | 0.637479i | 0.621212 | − | 0.783643i | \(-0.286641\pi\) |
−0.989260 | + | 0.146164i | \(0.953307\pi\) | |||||||
\(620\) | −264.545 | + | 152.735i | −0.426685 | + | 0.246347i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −745.652 | −1.19880 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −477.403 | + | 826.887i | −0.763845 | + | 1.32302i | ||||
\(626\) | −361.702 | + | 208.828i | −0.577798 | + | 0.333592i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 68.9961 | − | 119.505i | 0.109866 | − | 0.190294i | ||||
\(629\) | 982.987i | 1.56278i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.0039 | −0.0713216 | −0.0356608 | − | 0.999364i | \(-0.511354\pi\) | ||||
−0.0356608 | + | 0.999364i | \(0.511354\pi\) | |||||||
\(632\) | 289.853 | + | 167.347i | 0.458628 | + | 0.264789i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −75.9961 | − | 131.629i | −0.119868 | − | 0.207617i | ||||
\(635\) | 1651.53 | + | 953.513i | 2.60084 | + | 1.50159i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 299.562i | − | 0.469533i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 50.3320 | + | 87.1776i | 0.0786438 | + | 0.136215i | ||||
\(641\) | 555.315 | − | 320.611i | 0.866327 | − | 0.500174i | 0.000200774 | − | 1.00000i | \(-0.499936\pi\) |
0.866126 | + | 0.499826i | \(0.166603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −604.000 | −0.939347 | −0.469673 | − | 0.882840i | \(-0.655628\pi\) | ||||
−0.469673 | + | 0.882840i | \(0.655628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 365.830 | − | 633.636i | 0.566300 | − | 0.980861i | ||||
\(647\) | 155.538 | − | 89.7998i | 0.240398 | − | 0.138794i | −0.374961 | − | 0.927040i | \(-0.622344\pi\) |
0.615360 | + | 0.788246i | \(0.289011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.6719 | − | 25.4125i | 0.0226070 | − | 0.0391564i | ||||
\(650\) | − | 197.864i | − | 0.304406i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 333.992 | 0.512258 | ||||||||
\(653\) | 339.562 | + | 196.046i | 0.520003 | + | 0.300224i | 0.736936 | − | 0.675963i | \(-0.236272\pi\) |
−0.216933 | + | 0.976186i | \(0.569605\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 406.834 | + | 704.657i | 0.621121 | + | 1.07581i | ||||
\(656\) | −54.5036 | − | 31.4676i | −0.0830847 | − | 0.0479690i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1266.54i | − | 1.92191i | −0.276701 | − | 0.960956i | \(-0.589241\pi\) | ||
0.276701 | − | 0.960956i | \(-0.410759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −458.822 | − | 794.703i | −0.694133 | − | 1.20227i | −0.970472 | − | 0.241214i | \(-0.922454\pi\) |
0.276339 | − | 0.961060i | \(-0.410879\pi\) | |||||||
\(662\) | −334.956 | + | 193.387i | −0.505975 | + | 0.292125i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 340.664 | 0.513048 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 105.911 | − | 183.443i | 0.158787 | − | 0.275028i | ||||
\(668\) | 208.613 | − | 120.443i | 0.312295 | − | 0.180304i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −230.672 | + | 399.535i | −0.344286 | + | 0.596322i | ||||
\(671\) | − | 1785.41i | − | 2.66083i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −152.008 | −0.225866 | −0.112933 | − | 0.993603i | \(-0.536025\pi\) | ||||
−0.112933 | + | 0.993603i | \(0.536025\pi\) | |||||||
\(674\) | 417.841 | + | 241.241i | 0.619943 | + | 0.357924i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −162.328 | − | 281.160i | −0.240130 | − | 0.415918i | ||||
\(677\) | 141.316 | + | 81.5891i | 0.208739 | + | 0.120516i | 0.600725 | − | 0.799456i | \(-0.294879\pi\) |
−0.391986 | + | 0.919971i | \(0.628212\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 650.997i | − | 0.957348i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 216.000 | + | 374.123i | 0.316716 | + | 0.548567i | ||||
\(683\) | 281.384 | − | 162.457i | 0.411982 | − | 0.237858i | −0.279659 | − | 0.960099i | \(-0.590221\pi\) |
0.691641 | + | 0.722241i | \(0.256888\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 951.061 | 1.38841 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 86.9961 | − | 150.682i | 0.126448 | − | 0.219014i | ||||
\(689\) | 191.387 | − | 110.497i | 0.277775 | − | 0.160373i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −609.490 | + | 1055.67i | −0.882041 | + | 1.52774i | −0.0329725 | + | 0.999456i | \(0.510497\pi\) |
−0.849068 | + | 0.528283i | \(0.822836\pi\) | |||||||
\(692\) | − | 183.722i | − | 0.265494i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 164.502 | 0.237035 | ||||||||
\(695\) | −934.892 | − | 539.760i | −1.34517 | − | 0.776633i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 203.502 | + | 352.476i | 0.291968 | + | 0.505704i | ||||
\(698\) | 193.907 | + | 111.952i | 0.277803 | + | 0.160390i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 427.202i | 0.609417i | 0.952446 | + | 0.304709i | \(0.0985591\pi\) | ||||
−0.952446 | + | 0.304709i | \(0.901441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −380.000 | − | 658.179i | −0.540541 | − | 0.936244i | ||||
\(704\) | 123.288 | − | 71.1802i | 0.175125 | − | 0.101108i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −325.749 | −0.461401 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.7490 | + | 61.9191i | −0.0504217 | + | 0.0873330i | −0.890135 | − | 0.455697i | \(-0.849390\pi\) |
0.839713 | + | 0.543031i | \(0.182723\pi\) | |||||||
\(710\) | −193.916 | + | 111.958i | −0.273122 | + | 0.157687i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −197.247 | + | 341.642i | −0.277032 | + | 0.479834i | ||||
\(713\) | 305.470i | 0.428429i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −408.972 | −0.571989 | ||||||||
\(716\) | −230.867 | − | 133.291i | −0.322440 | − | 0.186161i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −121.409 | − | 210.287i | −0.169093 | − | 0.292879i | ||||
\(719\) | −96.1545 | − | 55.5148i | −0.133734 | − | 0.0772112i | 0.431641 | − | 0.902046i | \(-0.357935\pi\) |
−0.565374 | + | 0.824835i | \(0.691268\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 55.1543i | 0.0763910i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 83.0850 | + | 143.907i | 0.114758 | + | 0.198767i | ||||
\(725\) | 558.380 | − | 322.381i | 0.770179 | − | 0.444663i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1338.82 | −1.84157 | −0.920783 | − | 0.390076i | \(-0.872449\pi\) | ||||
−0.920783 | + | 0.390076i | \(0.872449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −181.919 | + | 315.093i | −0.249204 | + | 0.431634i | ||||
\(731\) | −974.461 | + | 562.606i | −1.33305 | + | 0.769638i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.5385 | + | 42.5020i | −0.0334769 | + | 0.0579836i | −0.882278 | − | 0.470728i | \(-0.843991\pi\) |
0.848802 | + | 0.528712i | \(0.177325\pi\) | |||||||
\(734\) | 731.842i | 0.997059i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 100.664 | 0.136772 | ||||||||
\(737\) | 565.028 | + | 326.219i | 0.766660 | + | 0.442631i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −715.158 | − | 1238.69i | −0.967738 | − | 1.67617i | −0.702073 | − | 0.712105i | \(-0.747742\pi\) |
−0.265665 | − | 0.964065i | \(-0.585592\pi\) | |||||||
\(740\) | −585.617 | − | 338.106i | −0.791374 | − | 0.456900i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 875.736i | − | 1.17865i | −0.807896 | − | 0.589325i | \(-0.799394\pi\) | ||
0.807896 | − | 0.589325i | \(-0.200606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −78.6314 | − | 136.194i | −0.105546 | − | 0.182810i | ||||
\(746\) | −285.777 | + | 164.993i | −0.383079 | + | 0.221171i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −920.648 | −1.23081 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −160.413 | + | 277.844i | −0.213599 | + | 0.369965i | −0.952838 | − | 0.303478i | \(-0.901852\pi\) |
0.739239 | + | 0.673443i | \(0.235185\pi\) | |||||||
\(752\) | 58.7878 | − | 33.9411i | 0.0781752 | − | 0.0451345i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21.7411 | + | 37.6568i | −0.0288344 | + | 0.0499427i | ||||
\(755\) | 452.297i | 0.599069i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 289.830 | 0.382867 | 0.191433 | − | 0.981506i | \(-0.438686\pi\) | ||||
0.191433 | + | 0.981506i | \(0.438686\pi\) | |||||||
\(758\) | −540.316 | − | 311.951i | −0.712818 | − | 0.411545i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 251.660 | + | 435.888i | 0.331132 | + | 0.573537i | ||||
\(761\) | −610.251 | − | 352.329i | −0.801907 | − | 0.462981i | 0.0422307 | − | 0.999108i | \(-0.486554\pi\) |
−0.844137 | + | 0.536127i | \(0.819887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 82.7231i | 0.108276i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 150.656 | + | 260.944i | 0.196679 | + | 0.340658i | ||||
\(767\) | −3.68870 | + | 2.12967i | −0.00480926 | + | 0.00277663i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −117.320 | −0.152562 | −0.0762810 | − | 0.997086i | \(-0.524305\pi\) | ||||
−0.0762810 | + | 0.997086i | \(0.524305\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 134.000 | − | 232.095i | 0.173575 | − | 0.300641i | ||||
\(773\) | −569.849 | + | 329.002i | −0.737191 | + | 0.425618i | −0.821047 | − | 0.570860i | \(-0.806610\pi\) |
0.0838559 | + | 0.996478i | \(0.473276\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −464.907 | + | 805.243i | −0.599880 | + | 1.03902i | ||||
\(776\) | − | 125.619i | − | 0.161880i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −799.166 | −1.02721 | ||||||||
\(779\) | −272.518 | − | 157.338i | −0.349830 | − | 0.201975i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 158.332 | + | 274.239i | 0.202730 | + | 0.351138i | ||||
\(782\) | −563.780 | − | 325.498i | −0.720946 | − | 0.416238i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 613.894i | − | 0.782031i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 600.324 | + | 1039.79i | 0.762801 | + | 1.32121i | 0.941402 | + | 0.337288i | \(0.109510\pi\) |
−0.178601 | + | 0.983922i | \(0.557157\pi\) | |||||||
\(788\) | −119.212 | + | 68.8269i | −0.151284 | + | 0.0873438i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1488.97 | 1.88478 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −129.579 | + | 224.438i | −0.163404 | + | 0.283023i | ||||
\(794\) | 610.320 | − | 352.368i | 0.768665 | − | 0.443789i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −278.494 | + | 482.366i | −0.349867 | + | 0.605987i | ||||
\(797\) | − | 797.411i | − | 1.00052i | −0.865876 | − | 0.500258i | \(-0.833239\pi\) | ||
0.865876 | − | 0.500258i | \(-0.166761\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −438.996 | −0.549432 | ||||||||
\(800\) | 265.358 | + | 153.205i | 0.331698 | + | 0.191506i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 136.749 | + | 236.856i | 0.170510 | + | 0.295332i | ||||
\(803\) | 445.609 | + | 257.272i | 0.554930 | + | 0.320389i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 62.7061i | − | 0.0777991i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 45.0850 | + | 78.0895i | 0.0557982 | + | 0.0966454i | ||||
\(809\) | 135.114 | − | 78.0082i | 0.167014 | − | 0.0964254i | −0.414163 | − | 0.910203i | \(-0.635926\pi\) |
0.581177 | + | 0.813777i | \(0.302592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −598.316 | −0.737751 | −0.368876 | − | 0.929479i | \(-0.620257\pi\) | ||||
−0.368876 | + | 0.929479i | \(0.620257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −478.154 | + | 828.187i | −0.587413 | + | 1.01743i | ||||
\(815\) | 1286.79 | − | 742.926i | 1.57888 | − | 0.911566i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 434.980 | − | 753.408i | 0.532412 | − | 0.922164i | ||||
\(818\) | − | 642.397i | − | 0.785326i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −279.984 | −0.341444 | ||||||||
\(821\) | −849.552 | − | 490.489i | −1.03478 | − | 0.597429i | −0.116427 | − | 0.993199i | \(-0.537144\pi\) |
−0.918349 | + | 0.395770i | \(0.870478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 215.668 | + | 373.548i | 0.262051 | + | 0.453886i | 0.966787 | − | 0.255584i | \(-0.0822678\pi\) |
−0.704736 | + | 0.709470i | \(0.748934\pi\) | |||||||
\(824\) | 11.0275 | + | 6.36674i | 0.0133829 | + | 0.00772663i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1219.41i | 1.47449i | 0.675623 | + | 0.737247i | \(0.263875\pi\) | ||||
−0.675623 | + | 0.737247i | \(0.736125\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 385.041 | + | 666.910i | 0.464464 | + | 0.804475i | 0.999177 | − | 0.0405586i | \(-0.0129137\pi\) |
−0.534713 | + | 0.845034i | \(0.679580\pi\) | |||||||
\(830\) | 1312.49 | − | 757.767i | 1.58131 | − | 0.912972i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −20.6640 | −0.0248366 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 535.822 | − | 928.071i | 0.641703 | − | 1.11146i | ||||
\(836\) | 616.439 | − | 355.901i | 0.737367 | − | 0.425719i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −240.000 | + | 415.692i | −0.286396 | + | 0.496053i | ||||
\(839\) | − | 1310.03i | − | 1.56142i | −0.624894 | − | 0.780710i | \(-0.714858\pi\) | ||
0.624894 | − | 0.780710i | \(-0.285142\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 699.308 | 0.831520 | ||||||||
\(842\) | −302.904 | − | 174.882i | −0.359744 | − | 0.207698i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −211.498 | − | 366.325i | −0.250590 | − | 0.434035i | ||||
\(845\) | −1250.82 | − | 722.159i | −1.48026 | − | 0.854626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 342.229i | 0.403571i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −990.778 | − | 1716.08i | −1.16562 | − | 2.01891i | ||||
\(851\) | −585.617 | + | 338.106i | −0.688151 | + | 0.397304i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 898.988 | 1.05391 | 0.526957 | − | 0.849892i | \(-0.323333\pi\) | ||||
0.526957 | + | 0.849892i | \(0.323333\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 243.498 | − | 421.751i | 0.284460 | − | 0.492700i | ||||
\(857\) | 646.190 | − | 373.078i | 0.754014 | − | 0.435330i | −0.0731286 | − | 0.997323i | \(-0.523298\pi\) |
0.827142 | + | 0.561993i | \(0.189965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 495.992 | − | 859.084i | 0.577406 | − | 1.00010i | −0.418369 | − | 0.908277i | \(-0.637398\pi\) |
0.995776 | − | 0.0918202i | \(-0.0292685\pi\) | |||||||
\(860\) | − | 774.050i | − | 0.900058i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −645.474 | −0.748810 | ||||||||
\(863\) | −181.361 | − | 104.709i | −0.210152 | − | 0.121332i | 0.391230 | − | 0.920293i | \(-0.372050\pi\) |
−0.601382 | + | 0.798961i | \(0.705383\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −408.668 | − | 707.834i | −0.472449 | − | 0.818305i | ||||
\(866\) | 781.368 | + | 451.123i | 0.902272 | + | 0.520927i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2105.73i | − | 2.42316i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.3517 | − | 82.0156i | −0.0543648 | − | 0.0941625i | ||||
\(872\) | 435.593 | − | 251.490i | 0.499533 | − | 0.288406i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 503.320 | 0.575881 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 432.652 | − | 749.376i | 0.493332 | − | 0.854476i | −0.506638 | − | 0.862159i | \(-0.669112\pi\) |
0.999970 | + | 0.00768242i | \(0.00244541\pi\) | |||||||
\(878\) | −960.379 | + | 554.475i | −1.09383 | + | 0.631521i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 316.664 | − | 548.478i | 0.359846 | − | 0.623271i | ||||
\(881\) | 995.046i | 1.12945i | 0.825279 | + | 0.564725i | \(0.191018\pi\) | ||||
−0.825279 | + | 0.564725i | \(0.808982\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 101.474 | 0.114920 | 0.0574600 | − | 0.998348i | \(-0.481700\pi\) | ||||
0.0574600 | + | 0.998348i | \(0.481700\pi\) | |||||||
\(884\) | 115.731 | + | 66.8174i | 0.130918 | + | 0.0755853i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 333.911 | + | 578.351i | 0.376875 | + | 0.652766i | ||||
\(887\) | −930.191 | − | 537.046i | −1.04869 | − | 0.605464i | −0.126410 | − | 0.991978i | \(-0.540346\pi\) |
−0.922283 | + | 0.386514i | \(0.873679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1755.01i | 1.97192i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 222.494 | + | 385.371i | 0.249433 | + | 0.432030i | ||||
\(893\) | 293.939 | − | 169.706i | 0.329159 | − | 0.190040i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1185.96 | −1.32510 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −523.154 | + | 906.130i | −0.582577 | + | 1.00905i | ||||
\(899\) | 176.959 | − | 102.167i | 0.196840 | − | 0.113645i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1106.60 | − | 1916.69i | 1.22819 | − | 2.12729i | ||||
\(902\) | 395.958i | 0.438977i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −88.6640 | −0.0980797 | ||||||||
\(905\) | 640.210 | + | 369.625i | 0.707414 | + | 0.408426i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 216.081 | + | 374.263i | 0.238237 | + | 0.412639i | 0.960209 | − | 0.279284i | \(-0.0900971\pi\) |
−0.721971 | + | 0.691923i | \(0.756764\pi\) | |||||||
\(908\) | −176.363 | − | 101.823i | −0.194233 | − | 0.112140i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 104.984i | − | 0.115241i | −0.998339 | − | 0.0576205i | \(-0.981649\pi\) | ||
0.998339 | − | 0.0576205i | \(-0.0183513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1071.64 | − | 1856.14i | −1.17376 | − | 2.03301i | ||||
\(914\) | −304.134 | + | 175.592i | −0.332750 | + | 0.192113i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 326.170 | 0.356081 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.9190 | − | 79.5340i | 0.0499662 | − | 0.0865440i | −0.839961 | − | 0.542647i | \(-0.817422\pi\) |
0.889927 | + | 0.456103i | \(0.150755\pi\) | |||||||
\(920\) | 387.833 | − | 223.915i | 0.421557 | − | 0.243386i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 251.708 | − | 435.972i | 0.273003 | − | 0.472855i | ||||
\(923\) | − | 45.9647i | − | 0.0497993i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2058.31 | −2.22520 | ||||||||
\(926\) | 7.75511 | + | 4.47741i | 0.00837485 | + | 0.00483522i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −33.6680 | − | 58.3147i | −0.0362801 | − | 0.0628391i | ||||
\(929\) | 1133.63 | + | 654.501i | 1.22027 | + | 0.704522i | 0.964975 | − | 0.262342i | \(-0.0844949\pi\) |
0.255293 | + | 0.966864i | \(0.417828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 725.715i | 0.778664i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 621.328 | + | 1076.17i | 0.665233 | + | 1.15222i | ||||
\(935\) | −3547.02 | + | 2047.87i | −3.79361 | + | 2.19024i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1262.00 | 1.34685 | 0.673426 | − | 0.739255i | \(-0.264822\pi\) | ||||
0.673426 | + | 0.739255i | \(0.264822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 150.996 | − | 261.533i | 0.160634 | − | 0.278226i | ||||
\(941\) | −1139.67 | + | 657.987i | −1.21112 | + | 0.699243i | −0.963004 | − | 0.269487i | \(-0.913146\pi\) |
−0.248120 | + | 0.968729i | \(0.579813\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −139.992 | + | 242.473i | −0.148454 | + | 0.257130i | ||||
\(944\) | − | 6.59595i | − | 0.00698724i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1094.67 | −1.15716 | ||||||||
\(947\) | −421.392 | − | 243.291i | −0.444976 | − | 0.256907i | 0.260730 | − | 0.965412i | \(-0.416037\pi\) |
−0.705706 | + | 0.708505i | \(0.749370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.3438 | − | 64.6814i | −0.0393507 | − | 0.0681574i | ||||
\(950\) | 1326.79 | + | 766.023i | 1.39662 | + | 0.806340i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.3711i | 0.0455100i | 0.999741 | + | 0.0227550i | \(0.00724377\pi\) | ||||
−0.999741 | + | 0.0227550i | \(0.992756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 184.008 | + | 318.711i | 0.192678 | + | 0.333729i | ||||
\(956\) | −306.791 | + | 177.126i | −0.320911 | + | 0.185278i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −317.344 | −0.331257 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 333.164 | − | 577.057i | 0.346685 | − | 0.600476i | ||||
\(962\) | 120.214 | − | 69.4055i | 0.124962 | − | 0.0721471i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 152.753 | − | 264.576i | 0.158457 | − | 0.274456i | ||||
\(965\) | − | 1192.27i | − | 1.23551i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1648.99 | 1.70526 | 0.852631 | − | 0.522514i | \(-0.175006\pi\) | ||||
0.852631 | + | 0.522514i | \(0.175006\pi\) | |||||||
\(968\) | −479.277 | − | 276.711i | −0.495121 | − | 0.285858i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −279.425 | − | 483.978i | −0.288067 | − | 0.498946i | ||||
\(971\) | −448.881 | − | 259.162i | −0.462287 | − | 0.266902i | 0.250718 | − | 0.968060i | \(-0.419333\pi\) |
−0.713006 | + | 0.701158i | \(0.752667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 1014.68i | − | 1.04177i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −200.664 | − | 347.560i | −0.205598 | − | 0.356107i | ||||
\(977\) | 95.2179 | − | 54.9741i | 0.0974595 | − | 0.0562682i | −0.450478 | − | 0.892787i | \(-0.648746\pi\) |
0.547938 | + | 0.836519i | \(0.315413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2481.96 | 2.53520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 193.749 | − | 335.583i | 0.197300 | − | 0.341734i | ||||
\(983\) | −510.704 | + | 294.855i | −0.519536 | + | 0.299954i | −0.736745 | − | 0.676171i | \(-0.763638\pi\) |
0.217209 | + | 0.976125i | \(0.430305\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −306.195 | + | 530.345i | −0.310858 | + | 0.538421i | ||||
\(986\) | 435.463i | 0.441646i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −103.320 | −0.104575 | ||||||||
\(989\) | −670.347 | − | 387.025i | −0.677803 | − | 0.391330i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −356.737 | − | 617.887i | −0.359977 | − | 0.623498i | 0.627980 | − | 0.778230i | \(-0.283882\pi\) |
−0.987957 | + | 0.154731i | \(0.950549\pi\) | |||||||
\(992\) | 84.0959 | + | 48.5528i | 0.0847741 | + | 0.0489444i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2477.91i | 2.49036i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −611.494 | − | 1059.14i | −0.613334 | − | 1.06233i | −0.990674 | − | 0.136251i | \(-0.956495\pi\) |
0.377340 | − | 0.926075i | \(-0.376839\pi\) | |||||||
\(998\) | −892.607 | + | 515.347i | −0.894396 | + | 0.516380i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 882.3.s.e.863.2 | 8 | ||
3.2 | odd | 2 | inner | 882.3.s.e.863.3 | 8 | ||
7.2 | even | 3 | 126.3.b.a.71.3 | yes | 4 | ||
7.3 | odd | 6 | 882.3.s.i.557.4 | 8 | |||
7.4 | even | 3 | inner | 882.3.s.e.557.3 | 8 | ||
7.5 | odd | 6 | 882.3.b.f.197.4 | 4 | |||
7.6 | odd | 2 | 882.3.s.i.863.1 | 8 | |||
21.2 | odd | 6 | 126.3.b.a.71.2 | ✓ | 4 | ||
21.5 | even | 6 | 882.3.b.f.197.1 | 4 | |||
21.11 | odd | 6 | inner | 882.3.s.e.557.2 | 8 | ||
21.17 | even | 6 | 882.3.s.i.557.1 | 8 | |||
21.20 | even | 2 | 882.3.s.i.863.4 | 8 | |||
28.23 | odd | 6 | 1008.3.d.a.449.1 | 4 | |||
35.2 | odd | 12 | 3150.3.c.b.449.3 | 8 | |||
35.9 | even | 6 | 3150.3.e.e.701.1 | 4 | |||
35.23 | odd | 12 | 3150.3.c.b.449.5 | 8 | |||
56.37 | even | 6 | 4032.3.d.i.449.4 | 4 | |||
56.51 | odd | 6 | 4032.3.d.j.449.4 | 4 | |||
63.2 | odd | 6 | 1134.3.q.c.701.1 | 8 | |||
63.16 | even | 3 | 1134.3.q.c.701.4 | 8 | |||
63.23 | odd | 6 | 1134.3.q.c.1079.4 | 8 | |||
63.58 | even | 3 | 1134.3.q.c.1079.1 | 8 | |||
84.23 | even | 6 | 1008.3.d.a.449.4 | 4 | |||
105.2 | even | 12 | 3150.3.c.b.449.8 | 8 | |||
105.23 | even | 12 | 3150.3.c.b.449.2 | 8 | |||
105.44 | odd | 6 | 3150.3.e.e.701.3 | 4 | |||
168.107 | even | 6 | 4032.3.d.j.449.1 | 4 | |||
168.149 | odd | 6 | 4032.3.d.i.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.b.a.71.2 | ✓ | 4 | 21.2 | odd | 6 | ||
126.3.b.a.71.3 | yes | 4 | 7.2 | even | 3 | ||
882.3.b.f.197.1 | 4 | 21.5 | even | 6 | |||
882.3.b.f.197.4 | 4 | 7.5 | odd | 6 | |||
882.3.s.e.557.2 | 8 | 21.11 | odd | 6 | inner | ||
882.3.s.e.557.3 | 8 | 7.4 | even | 3 | inner | ||
882.3.s.e.863.2 | 8 | 1.1 | even | 1 | trivial | ||
882.3.s.e.863.3 | 8 | 3.2 | odd | 2 | inner | ||
882.3.s.i.557.1 | 8 | 21.17 | even | 6 | |||
882.3.s.i.557.4 | 8 | 7.3 | odd | 6 | |||
882.3.s.i.863.1 | 8 | 7.6 | odd | 2 | |||
882.3.s.i.863.4 | 8 | 21.20 | even | 2 | |||
1008.3.d.a.449.1 | 4 | 28.23 | odd | 6 | |||
1008.3.d.a.449.4 | 4 | 84.23 | even | 6 | |||
1134.3.q.c.701.1 | 8 | 63.2 | odd | 6 | |||
1134.3.q.c.701.4 | 8 | 63.16 | even | 3 | |||
1134.3.q.c.1079.1 | 8 | 63.58 | even | 3 | |||
1134.3.q.c.1079.4 | 8 | 63.23 | odd | 6 | |||
3150.3.c.b.449.2 | 8 | 105.23 | even | 12 | |||
3150.3.c.b.449.3 | 8 | 35.2 | odd | 12 | |||
3150.3.c.b.449.5 | 8 | 35.23 | odd | 12 | |||
3150.3.c.b.449.8 | 8 | 105.2 | even | 12 | |||
3150.3.e.e.701.1 | 4 | 35.9 | even | 6 | |||
3150.3.e.e.701.3 | 4 | 105.44 | odd | 6 | |||
4032.3.d.i.449.1 | 4 | 168.149 | odd | 6 | |||
4032.3.d.i.449.4 | 4 | 56.37 | even | 6 | |||
4032.3.d.j.449.1 | 4 | 168.107 | even | 6 | |||
4032.3.d.j.449.4 | 4 | 56.51 | odd | 6 |