Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(257,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.ca (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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.11 | ||
Character | \(\chi\) | \(=\) | 1008.353 |
Dual form | 1008.2.ca.e.257.11 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.589575 | − | 1.62862i | −0.340392 | − | 0.940284i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.11415 | − | 1.92977i | 0.498263 | − | 0.863017i | −0.501735 | − | 0.865022i | \(-0.667305\pi\) |
0.999998 | + | 0.00200427i | \(0.000637980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.553477 | + | 2.58721i | 0.209195 | + | 0.977874i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.30480 | + | 1.92039i | −0.768267 | + | 0.640129i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.83714 | + | 1.06068i | −0.553920 | + | 0.319806i | −0.750701 | − | 0.660642i | \(-0.770284\pi\) |
0.196782 | + | 0.980447i | \(0.436951\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.10339 | − | 2.94644i | 1.41542 | − | 0.817196i | 0.419533 | − | 0.907740i | \(-0.362194\pi\) |
0.995892 | + | 0.0905443i | \(0.0288607\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.79973 | − | 0.676785i | −0.981086 | − | 0.174745i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.34020 | − | 4.05335i | 0.567583 | − | 0.983082i | −0.429222 | − | 0.903199i | \(-0.641212\pi\) |
0.996804 | − | 0.0798828i | \(-0.0254546\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.54550 | − | 2.62435i | 1.04281 | − | 0.602066i | 0.122181 | − | 0.992508i | \(-0.461011\pi\) |
0.920628 | + | 0.390442i | \(0.127678\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.88727 | − | 2.42676i | 0.848271 | − | 0.529563i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.77916 | − | 2.18190i | −0.788010 | − | 0.454958i | 0.0512518 | − | 0.998686i | \(-0.483679\pi\) |
−0.839261 | + | 0.543728i | \(0.817012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0173374 | + | 0.0300292i | 0.00346748 | + | 0.00600585i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.48644 | + | 2.62143i | 0.863415 | + | 0.504495i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.25182 | − | 1.30009i | −0.418152 | − | 0.241420i | 0.276134 | − | 0.961119i | \(-0.410947\pi\) |
−0.694286 | + | 0.719699i | \(0.744280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.61221i | − | 1.36719i | −0.729860 | − | 0.683597i | \(-0.760415\pi\) | ||
0.729860 | − | 0.683597i | \(-0.239585\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.81057 | + | 2.36666i | 0.489258 | + | 0.411983i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.60937 | + | 1.81446i | 0.948156 | + | 0.306700i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.80274 | − | 3.12244i | −0.296369 | − | 0.513326i | 0.678934 | − | 0.734200i | \(-0.262442\pi\) |
−0.975302 | + | 0.220874i | \(0.929109\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.80746 | − | 6.57433i | −1.25019 | − | 1.05273i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0395039 | − | 0.0684228i | −0.00616948 | − | 0.0106858i | 0.862924 | − | 0.505333i | \(-0.168630\pi\) |
−0.869094 | + | 0.494648i | \(0.835297\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.24922 | − | 2.16371i | 0.190504 | − | 0.329962i | −0.754914 | − | 0.655824i | \(-0.772321\pi\) |
0.945417 | + | 0.325862i | \(0.105655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.13800 | + | 6.58733i | 0.169643 | + | 0.981981i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.79674 | −0.553811 | −0.276905 | − | 0.960897i | \(-0.589309\pi\) | ||||
−0.276905 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.38733 | + | 2.86393i | −0.912475 | + | 0.409132i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.98109 | − | 1.42154i | −1.11758 | − | 0.199056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.08014 | + | 2.35567i | 0.560451 | + | 0.323576i | 0.753326 | − | 0.657647i | \(-0.228448\pi\) |
−0.192876 | + | 0.981223i | \(0.561781\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.72701i | 0.637390i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.95397 | − | 5.85564i | −0.921076 | − | 0.775598i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.1939 | −1.71770 | −0.858849 | − | 0.512229i | \(-0.828820\pi\) | ||||
−0.858849 | + | 0.512229i | \(0.828820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.15939i | 1.04470i | 0.852730 | + | 0.522352i | \(0.174945\pi\) | ||||
−0.852730 | + | 0.522352i | \(0.825055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.24410 | − | 4.90012i | −0.786683 | − | 0.617357i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 13.1311i | − | 1.62871i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.75228 | 0.580583 | 0.290292 | − | 0.956938i | \(-0.406248\pi\) | ||||
0.290292 | + | 0.956938i | \(0.406248\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.32538 | + | 7.44121i | −0.159557 | + | 0.895816i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0325i | 1.19064i | 0.803490 | + | 0.595318i | \(0.202974\pi\) | ||||
−0.803490 | + | 0.595318i | \(0.797026\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.6610 | − | 7.30986i | −1.48186 | − | 0.855554i | −0.482075 | − | 0.876130i | \(-0.660117\pi\) |
−0.999788 | + | 0.0205755i | \(0.993450\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.0386845 | − | 0.0459405i | 0.00446690 | − | 0.00530475i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.76101 | − | 4.16602i | −0.428607 | − | 0.474762i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.5483 | 1.63681 | 0.818405 | − | 0.574642i | \(-0.194859\pi\) | ||||
0.818405 | + | 0.574642i | \(0.194859\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.62422 | − | 8.85223i | 0.180469 | − | 0.983581i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.41294 | − | 11.1075i | 0.703911 | − | 1.21921i | −0.263172 | − | 0.964749i | \(-0.584769\pi\) |
0.967083 | − | 0.254461i | \(-0.0818982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.21468 | − | 9.03209i | −0.565611 | − | 0.979667i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.789732 | + | 4.43386i | −0.0846681 | + | 0.475359i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.73464 | − | 4.73654i | −0.289871 | − | 0.502072i | 0.683907 | − | 0.729569i | \(-0.260279\pi\) |
−0.973779 | + | 0.227497i | \(0.926946\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.4477 | + | 11.5728i | 1.09521 | + | 1.21315i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.3974 | + | 4.48797i | −1.28555 | + | 0.465381i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 11.6957i | − | 1.19995i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.9290 | + | 7.46454i | 1.31274 | + | 0.757909i | 0.982549 | − | 0.186006i | \(-0.0595544\pi\) |
0.330188 | + | 0.943915i | \(0.392888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.19734 | − | 5.97268i | 0.220841 | − | 0.600277i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.63302 | − | 2.82847i | −0.162492 | − | 0.281444i | 0.773270 | − | 0.634077i | \(-0.218620\pi\) |
−0.935762 | + | 0.352633i | \(0.885286\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.12945 | − | 2.38414i | −0.406887 | − | 0.234916i | 0.282564 | − | 0.959248i | \(-0.408815\pi\) |
−0.689451 | + | 0.724332i | \(0.742148\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.352079 | − | 10.2053i | −0.0343594 | − | 0.995934i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.39655 | − | 3.69305i | 0.618378 | − | 0.357021i | −0.157859 | − | 0.987462i | \(-0.550459\pi\) |
0.776237 | + | 0.630441i | \(0.217126\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.17349 | + | 2.03254i | −0.112400 | + | 0.194682i | −0.916737 | − | 0.399490i | \(-0.869187\pi\) |
0.804338 | + | 0.594173i | \(0.202520\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.02241 | + | 4.77689i | −0.381790 | + | 0.453402i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.8961 | − | 6.86824i | 1.11909 | − | 0.646109i | 0.177925 | − | 0.984044i | \(-0.443062\pi\) |
0.941170 | + | 0.337935i | \(0.109728\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.42111 | + | 4.86193i | −0.785272 | + | 0.453377i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.10398 | + | 16.5914i | −0.564314 | + | 1.53388i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.7821 | + | 3.81116i | 1.08007 | + | 0.349369i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.24993 | + | 5.62905i | −0.295449 | + | 0.511732i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0881442 | + | 0.104677i | −0.00794769 | + | 0.00943843i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.2188 | 1.00344 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.97913 | 0.530562 | 0.265281 | − | 0.964171i | \(-0.414535\pi\) | ||||
0.265281 | + | 0.964171i | \(0.414535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.26036 | − | 0.758830i | −0.375104 | − | 0.0668112i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4792 | − | 18.1506i | 0.915576 | − | 1.58582i | 0.109519 | − | 0.993985i | \(-0.465069\pi\) |
0.806056 | − | 0.591839i | \(-0.201598\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.30557 | + | 10.3077i | 0.806895 | + | 0.893787i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.0573 | − | 5.73710i | 0.865595 | − | 0.493771i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00063 | + | 1.73242i | −0.256361 | + | 0.148010i | −0.622674 | − | 0.782482i | \(-0.713954\pi\) |
0.366312 | + | 0.930492i | \(0.380620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.379607 | + | 0.219166i | −0.0321979 | + | 0.0185895i | −0.516013 | − | 0.856581i | \(-0.672584\pi\) |
0.483815 | + | 0.875170i | \(0.339251\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.23846 | + | 6.18344i | 0.188512 | + | 0.520739i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.25044 | + | 10.8261i | −0.522688 | + | 0.905322i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.01773 | + | 2.89699i | −0.416700 | + | 0.240582i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.43006 | + | 8.71402i | 0.695299 | + | 0.718720i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.1560 | − | 8.75030i | −1.24162 | − | 0.716852i | −0.272200 | − | 0.962241i | \(-0.587751\pi\) |
−0.969425 | + | 0.245388i | \(0.921085\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.187420 | − | 0.324621i | −0.0152520 | − | 0.0264172i | 0.858299 | − | 0.513150i | \(-0.171522\pi\) |
−0.873551 | + | 0.486733i | \(0.838188\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.39030 | + | 13.8363i | 0.193244 | + | 1.11860i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.6898 | − | 8.48115i | −1.17991 | − | 0.681223i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.3549i | 1.62450i | 0.583311 | + | 0.812249i | \(0.301757\pi\) | ||||
−0.583311 | + | 0.812249i | \(0.698243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.43094 | − | 8.03385i | 0.113481 | − | 0.637126i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.55336 | − | 10.9851i | 0.280044 | − | 0.865749i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.25400 | + | 12.5643i | 0.568177 | + | 0.984112i | 0.996746 | + | 0.0806027i | \(0.0256845\pi\) |
−0.428569 | + | 0.903509i | \(0.640982\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.69850 | − | 2.78693i | 0.599327 | − | 0.216962i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.62510 | + | 13.2071i | 0.590048 | + | 1.02199i | 0.994225 | + | 0.107313i | \(0.0342246\pi\) |
−0.404177 | + | 0.914681i | \(0.632442\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8630 | − | 18.8153i | 0.835619 | − | 1.44733i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.43671 | + | 14.7777i | −0.415756 | + | 1.13008i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.88136 | 0.143037 | 0.0715185 | − | 0.997439i | \(-0.477215\pi\) | ||||
0.0715185 | + | 0.997439i | \(0.477215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0680961 | + | 0.0614760i | −0.00514758 | + | 0.00464715i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.77879 | + | 21.4878i | 0.584690 | + | 1.61512i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.64064 | − | 4.98867i | −0.645831 | − | 0.372871i | 0.141026 | − | 0.990006i | \(-0.454960\pi\) |
−0.786857 | + | 0.617135i | \(0.788293\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2828i | 0.838641i | 0.907838 | + | 0.419320i | \(0.137732\pi\) | ||||
−0.907838 | + | 0.419320i | \(0.862268\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.2885 | − | 4.81058i | 0.982318 | − | 0.355608i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.03410 | −0.590679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.92879i | 0.726065i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.29906 | + | 13.0583i | −0.312710 | + | 0.949849i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.8654i | 0.930907i | 0.885072 | + | 0.465454i | \(0.154109\pi\) | ||||
−0.885072 | + | 0.465454i | \(0.845891\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0372 | −0.866458 | −0.433229 | − | 0.901284i | \(-0.642626\pi\) | ||||
−0.433229 | + | 0.901284i | \(0.642626\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.3856 | + | 7.74179i | −1.53145 | + | 0.554401i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 27.7262i | 1.97541i | 0.156339 | + | 0.987703i | \(0.450031\pi\) | ||||
−0.156339 | + | 0.987703i | \(0.549969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.382862 | − | 0.221045i | −0.0271404 | − | 0.0156695i | 0.486368 | − | 0.873754i | \(-0.338321\pi\) |
−0.513509 | + | 0.858084i | \(0.671655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.80183 | − | 7.73965i | −0.197626 | − | 0.545913i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.11727 | − | 6.54550i | 0.148603 | − | 0.459404i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.176053 | −0.0122961 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.9003 | − | 2.22861i | 0.896634 | − | 0.154899i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.56716 | + | 9.64260i | −0.385088 | + | 0.666993i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.219300 | + | 0.379839i | 0.0150972 | + | 0.0261492i | 0.873475 | − | 0.486868i | \(-0.161861\pi\) |
−0.858378 | + | 0.513018i | \(0.828528\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.3391 | − | 5.91490i | 1.11954 | − | 0.405282i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.78363 | − | 4.82139i | −0.189842 | − | 0.328816i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.6944 | − | 4.21319i | 1.33694 | − | 0.286010i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.44034 | + | 24.9297i | −0.300050 | + | 1.68460i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.5811i | − | 1.85531i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.6417 | − | 10.1854i | −1.18137 | − | 0.682066i | −0.225041 | − | 0.974349i | \(-0.572252\pi\) |
−0.956332 | + | 0.292284i | \(0.905585\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0976270 | − | 0.0359169i | −0.00650847 | − | 0.00239446i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.754935 | − | 1.30759i | −0.0501068 | − | 0.0867875i | 0.839884 | − | 0.542766i | \(-0.182623\pi\) |
−0.889991 | + | 0.455978i | \(0.849290\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3899 | + | 10.6174i | 1.21524 | + | 0.701617i | 0.963895 | − | 0.266281i | \(-0.0857950\pi\) |
0.251341 | + | 0.967899i | \(0.419128\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.56746 | + | 8.58144i | −0.300517 | + | 0.564617i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.85938 | + | 5.69231i | −0.645909 | + | 0.372916i | −0.786887 | − | 0.617097i | \(-0.788309\pi\) |
0.140978 | + | 0.990013i | \(0.454975\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.23013 | + | 7.32681i | −0.275944 | + | 0.477948i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.57731 | − | 23.6936i | −0.557156 | − | 1.53907i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.1401 | + | 8.16380i | −0.914648 | + | 0.528072i | −0.881924 | − | 0.471392i | \(-0.843752\pi\) |
−0.0327241 | + | 0.999464i | \(0.510418\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.7592 | − | 11.9853i | 1.33722 | − | 0.772042i | 0.350822 | − | 0.936442i | \(-0.385902\pi\) |
0.986394 | + | 0.164400i | \(0.0525688\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3745 | + | 2.57382i | −0.986275 | + | 0.165110i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.58974 | + | 15.5169i | −0.101564 | + | 0.991337i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.4650 | − | 26.7861i | 0.984012 | − | 1.70436i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.8709 | − | 3.89551i | −1.38601 | − | 0.246868i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.9828 | 1.64002 | 0.820009 | − | 0.572351i | \(-0.193969\pi\) | ||||
0.820009 | + | 0.572351i | \(0.193969\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.25715 | 0.581992 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.6354 | + | 13.8178i | −0.728636 | + | 0.865305i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.979785 | + | 1.69704i | −0.0611173 | + | 0.105858i | −0.894965 | − | 0.446136i | \(-0.852800\pi\) |
0.833848 | + | 0.551994i | \(0.186133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.08063 | − | 6.39227i | 0.439969 | − | 0.397196i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.68667 | − | 1.32792i | 0.475793 | − | 0.0821962i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.11722 | − | 1.79973i | 0.192216 | − | 0.110976i | −0.400804 | − | 0.916164i | \(-0.631269\pi\) |
0.593019 | + | 0.805188i | \(0.297936\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.09179 | − | 5.24915i | 0.558504 | − | 0.322453i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.10174 | + | 7.24623i | −0.373420 | + | 0.443462i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.06967 | − | 7.04888i | 0.248132 | − | 0.429778i | −0.714875 | − | 0.699252i | \(-0.753517\pi\) |
0.963008 | + | 0.269474i | \(0.0868499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.3378 | + | 9.43265i | −0.992452 | + | 0.572992i | −0.906006 | − | 0.423264i | \(-0.860884\pi\) |
−0.0864458 | + | 0.996257i | \(0.527551\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.6879 | − | 23.8383i | 0.767907 | − | 1.44276i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0637026 | − | 0.0367787i | −0.00384141 | − | 0.00221784i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8340 | − | 18.7650i | −0.650950 | − | 1.12748i | −0.982893 | − | 0.184179i | \(-0.941037\pi\) |
0.331943 | − | 0.943300i | \(-0.392296\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.6184 | + | 17.5446i | 0.875181 | + | 1.05037i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.6851 | + | 6.74642i | 0.697077 | + | 0.402457i | 0.806258 | − | 0.591564i | \(-0.201489\pi\) |
−0.109181 | + | 0.994022i | \(0.534823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.03256i | 0.120823i | 0.998174 | + | 0.0604115i | \(0.0192413\pi\) | ||||
−0.998174 | + | 0.0604115i | \(0.980759\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.0478 | + | 6.89548i | −1.12829 | + | 0.408453i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.155160 | − | 0.140075i | 0.00915879 | − | 0.00826839i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.45310 | − | 4.24890i | −0.144300 | − | 0.249935i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.53429 | − | 25.4573i | 0.265805 | − | 1.49233i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.8661 | + | 27.4809i | 0.926908 | + | 1.60545i | 0.788463 | + | 0.615083i | \(0.210877\pi\) |
0.138446 | + | 0.990370i | \(0.455789\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.7000 | + | 25.4611i | −0.855866 | + | 1.48240i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.0227 | − | 0.0572942i | −0.639603 | − | 0.00332454i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.7154 | −1.48716 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.28938 | + | 2.03442i | 0.362514 | + | 0.117262i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.64372 | + | 4.32717i | −0.209326 | + | 0.248589i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.7457 | + | 9.09079i | 0.901597 | + | 0.520537i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.266045i | 0.0151840i | 0.999971 | + | 0.00759200i | \(0.00241663\pi\) | ||||
−0.999971 | + | 0.00759200i | \(0.997583\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.44823 | + | 8.13094i | −0.0823872 | + | 0.462553i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.36245 | −0.247372 | −0.123686 | − | 0.992321i | \(-0.539472\pi\) | ||||
−0.123686 | + | 0.992321i | \(0.539472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4386i | 0.872640i | 0.899792 | + | 0.436320i | \(0.143718\pi\) | ||||
−0.899792 | + | 0.436320i | \(0.856282\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.4129 | + | 6.59019i | −0.924765 | + | 0.371315i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.7248i | 1.22019i | 0.792329 | + | 0.610094i | \(0.208868\pi\) | ||||
−0.792329 | + | 0.610094i | \(0.791132\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.51589 | 0.308831 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.78582 | − | 8.24021i | −0.546191 | − | 0.459924i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 24.5660i | − | 1.36689i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.176959 | + | 0.102167i | 0.00981591 | + | 0.00566722i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.00210 | + | 0.712830i | 0.221317 | + | 0.0394196i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.10141 | − | 9.82296i | −0.115854 | − | 0.541557i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.1462 | 0.832511 | 0.416255 | − | 0.909248i | \(-0.363342\pi\) | ||||
0.416255 | + | 0.909248i | \(0.363342\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1513 | + | 3.73464i | 0.556285 | + | 0.204657i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.29475 | − | 9.17078i | 0.289283 | − | 0.501053i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.75166 | + | 6.49807i | 0.204366 | + | 0.353973i | 0.949931 | − | 0.312461i | \(-0.101153\pi\) |
−0.745564 | + | 0.666434i | \(0.767820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.1994 | − | 15.3249i | −0.988456 | − | 0.832336i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.07409 | + | 13.9847i | 0.437237 | + | 0.757316i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.9448 | − | 14.9402i | −0.590965 | − | 0.806697i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.8831 | + | 10.8483i | 0.693603 | + | 0.584053i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.89571i | 0.262816i | 0.991328 | + | 0.131408i | \(0.0419497\pi\) | ||||
−0.991328 | + | 0.131408i | \(0.958050\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.64213 | + | 1.52543i | 0.141430 | + | 0.0816546i | 0.569045 | − | 0.822306i | \(-0.307313\pi\) |
−0.427615 | + | 0.903961i | \(0.640646\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30.6199 | + | 0.159157i | 1.63437 | + | 0.00849517i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.51890 | − | 14.7552i | −0.453415 | − | 0.785338i | 0.545180 | − | 0.838319i | \(-0.316461\pi\) |
−0.998596 | + | 0.0529806i | \(0.983128\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.3603 | + | 11.1777i | 1.02754 | + | 0.593250i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.739520 | − | 21.4356i | −0.0391395 | − | 1.13449i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.27682 | + | 1.31452i | −0.120166 | + | 0.0693778i | −0.558878 | − | 0.829250i | \(-0.688768\pi\) |
0.438712 | + | 0.898628i | \(0.355435\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.27438 | − | 7.40344i | 0.224967 | − | 0.389655i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.0837 | + | 1.97416i | 0.581741 | + | 0.103616i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.2126 | + | 16.2886i | −1.47672 | + | 0.852583i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.2436 | + | 9.37824i | −0.847908 | + | 0.489540i | −0.859945 | − | 0.510387i | \(-0.829502\pi\) |
0.0120362 | + | 0.999928i | \(0.496169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.222447 | + | 0.0818381i | 0.0115801 | + | 0.00426032i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.83635 | + | 11.8600i | −0.199174 | + | 0.615741i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.42980 | + | 4.20853i | −0.125810 | + | 0.217910i | −0.922049 | − | 0.387072i | \(-0.873486\pi\) |
0.796239 | + | 0.604982i | \(0.206820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.61431 | − | 18.2711i | −0.341562 | − | 0.943516i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.3225 | −0.789151 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.46902 | 0.178192 | 0.0890959 | − | 0.996023i | \(-0.471602\pi\) | ||||
0.0890959 | + | 0.996023i | \(0.471602\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.52515 | − | 9.73773i | −0.180599 | − | 0.498879i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.30298 | − | 16.1132i | 0.475360 | − | 0.823348i | −0.524241 | − | 0.851570i | \(-0.675651\pi\) |
0.999602 | + | 0.0282216i | \(0.00898441\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.2298 | + | 2.61629i | −0.623287 | + | 0.133339i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.27596 | + | 7.38589i | 0.0648606 | + | 0.375446i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4613 | − | 7.77186i | 0.682513 | − | 0.394049i | −0.118288 | − | 0.992979i | \(-0.537741\pi\) |
0.800801 | + | 0.598930i | \(0.204407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.6880 | + | 10.2122i | −0.894521 | + | 0.516452i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −35.7387 | − | 6.36556i | −1.80278 | − | 0.321100i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.2090 | − | 28.0748i | 0.815562 | − | 1.41260i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0507 | + | 7.53483i | −0.654996 | + | 0.378162i | −0.790368 | − | 0.612633i | \(-0.790111\pi\) |
0.135371 | + | 0.990795i | \(0.456777\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.3009 | − | 21.2324i | 0.565753 | − | 1.06295i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.74463 | − | 3.89401i | −0.336811 | − | 0.194458i | 0.322050 | − | 0.946723i | \(-0.395628\pi\) |
−0.658861 | + | 0.752265i | \(0.728961\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.4289 | − | 38.8481i | −1.11727 | − | 1.93516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15.2731 | − | 12.9971i | −0.758926 | − | 0.645830i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.62379 | + | 3.82425i | 0.328329 | + | 0.189561i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.99874i | − | 0.444959i | −0.974937 | − | 0.222480i | \(-0.928585\pi\) | ||
0.974937 | − | 0.222480i | \(-0.0714151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.59055 | + | 3.86550i | 0.226435 | + | 0.190671i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.30252 | − | 34.1354i | −0.359334 | − | 1.67969i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2900 | − | 24.7509i | −0.701466 | − | 1.21498i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.580746 | + | 0.489021i | 0.0284392 | + | 0.0239474i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.70022 | − | 11.6051i | −0.327327 | − | 0.566947i | 0.654653 | − | 0.755929i | \(-0.272815\pi\) |
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.44700 | − | 16.3627i | 0.460419 | − | 0.797469i | −0.538563 | − | 0.842585i | \(-0.681033\pi\) |
0.998982 | + | 0.0451166i | \(0.0143659\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.75072 | − | 7.29120i | 0.425475 | − | 0.354510i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.162292 | 0.00787232 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.1101 | + | 4.51604i | −1.02159 | + | 0.218547i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21.3167 | + | 3.79680i | 1.02918 | + | 0.183311i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.4056 | + | 14.6679i | 1.22375 | + | 0.706530i | 0.965714 | − | 0.259607i | \(-0.0835931\pi\) |
0.258031 | + | 0.966137i | \(0.416926\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.41744i | 0.452573i | 0.974061 | + | 0.226287i | \(0.0726586\pi\) | ||||
−0.974061 | + | 0.226287i | \(0.927341\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.67642 | + | 6.46398i | 0.368056 | + | 0.309924i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.9042 | −1.09566 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.7980i | 1.51764i | 0.651302 | + | 0.758819i | \(0.274223\pi\) | ||||
−0.651302 | + | 0.758819i | \(0.725777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.22167 | − | 18.8669i | 0.439127 | − | 0.898425i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.0295i | 1.75932i | 0.475600 | + | 0.879662i | \(0.342231\pi\) | ||||
−0.475600 | + | 0.879662i | \(0.657769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.1872 | −0.577729 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.31532 | + | 29.8423i | −0.251406 | + | 1.41149i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.3840i | 0.914789i | 0.889264 | + | 0.457394i | \(0.151217\pi\) | ||||
−0.889264 | + | 0.457394i | \(0.848783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.145149 | + | 0.0838017i | 0.00683479 | + | 0.00394607i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.418185 | + | 0.496624i | −0.0196481 | + | 0.0233334i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.9730 | − | 7.26778i | 1.59268 | − | 0.340719i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5349 | 0.492803 | 0.246401 | − | 0.969168i | \(-0.420752\pi\) | ||||
0.246401 | + | 0.969168i | \(0.420752\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.1247 | − | 12.0504i | 0.986019 | − | 0.562465i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.09138 | + | 12.2826i | −0.330278 | + | 0.572059i | −0.982566 | − | 0.185912i | \(-0.940476\pi\) |
0.652288 | + | 0.757971i | \(0.273809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.05071 | − | 8.74808i | −0.234726 | − | 0.406558i | 0.724467 | − | 0.689310i | \(-0.242086\pi\) |
−0.959193 | + | 0.282752i | \(0.908753\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.15183 | + | 28.9243i | −0.238910 | + | 1.34133i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.1047 | + | 19.2340i | 0.513866 | + | 0.890042i | 0.999871 | + | 0.0160858i | \(0.00512048\pi\) |
−0.486005 | + | 0.873956i | \(0.661546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.63028 | + | 12.2951i | 0.121455 | + | 0.567737i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.1504 | − | 12.0008i | 1.52749 | − | 0.552965i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.30005i | 0.243697i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.157614 | + | 0.0909986i | 0.00723184 | + | 0.00417530i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.9277 | + | 2.40610i | −0.637707 | + | 0.110168i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.71275 | + | 8.16272i | 0.215331 | + | 0.372964i | 0.953375 | − | 0.301788i | \(-0.0975836\pi\) |
−0.738044 | + | 0.674753i | \(0.764250\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.4002 | − | 10.6233i | −0.838975 | − | 0.484383i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.9856 | + | 0.689495i | −0.909374 | + | 0.0313731i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.8096 | − | 16.6332i | 1.30818 | − | 0.755276i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.6113 | + | 25.3076i | −0.662103 | + | 1.14680i | 0.317959 | + | 0.948104i | \(0.397003\pi\) |
−0.980062 | + | 0.198692i | \(0.936331\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.1857 | − | 19.2216i | 0.731942 | − | 0.869231i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.31308 | + | 3.64486i | −0.284905 | + | 0.164490i | −0.635642 | − | 0.771984i | \(-0.719265\pi\) |
0.350737 | + | 0.936474i | \(0.385931\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.5394 | + | 6.08494i | −0.474672 | + | 0.274052i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.07769 | − | 10.8948i | −0.408012 | − | 0.489686i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.9561 | + | 5.55275i | −1.16429 | + | 0.249075i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.80996 | − | 13.5272i | 0.349622 | − | 0.605563i | −0.636561 | − | 0.771227i | \(-0.719643\pi\) |
0.986182 | + | 0.165664i | \(0.0529768\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.0137 | − | 20.2049i | 0.760116 | − | 0.902690i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.09425 | −0.271729 | −0.135865 | − | 0.990727i | \(-0.543381\pi\) | ||||
−0.135865 | + | 0.990727i | \(0.543381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.27772 | −0.323854 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.0476 | − | 6.59870i | −1.64534 | − | 0.293058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.1799 | − | 24.5604i | 0.628515 | − | 1.08862i | −0.359335 | − | 0.933208i | \(-0.616997\pi\) |
0.987850 | − | 0.155411i | \(-0.0496701\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9045 | − | 36.8026i | 0.526626 | − | 1.62805i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 27.2726 | + | 0.141758i | 1.20412 | + | 0.00625879i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.20167 | + | 5.31258i | −0.405474 | + | 0.234100i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.97515 | − | 4.02710i | 0.306767 | − | 0.177112i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.10920 | − | 3.06402i | −0.0486886 | − | 0.134495i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.2896 | + | 33.4105i | −0.845091 | + | 1.46374i | 0.0404517 | + | 0.999181i | \(0.487120\pi\) |
−0.885542 | + | 0.464559i | \(0.846213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.1399 | − | 13.9372i | 1.05556 | − | 0.609429i | 0.131361 | − | 0.991335i | \(-0.458065\pi\) |
0.924201 | + | 0.381905i | \(0.124732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.140269 | + | 0.0746579i | 0.00612183 | + | 0.00325834i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −30.8550 | − | 17.8141i | −1.34406 | − | 0.775996i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.97863 | − | 3.42708i | −0.0860273 | − | 0.149004i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.4093 | − | 25.3374i | 1.31965 | − | 1.09955i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.403208 | − | 0.232792i | −0.0174649 | − | 0.0100833i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.4585i | − | 0.711561i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.03034 | + | 17.0135i | −0.130769 | + | 0.734187i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.69674 | − | 12.0363i | 0.374595 | − | 0.518441i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.9182 | − | 18.9109i | −0.469410 | − | 0.813041i | 0.529979 | − | 0.848011i | \(-0.322200\pi\) |
−0.999388 | + | 0.0349697i | \(0.988867\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.3753 | − | 6.65204i | 0.788560 | − | 0.285466i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.61489 | + | 4.52912i | 0.112009 | + | 0.194006i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5173 | + | 21.6806i | −0.535201 | + | 0.926995i | 0.463953 | + | 0.885860i | \(0.346431\pi\) |
−0.999154 | + | 0.0411350i | \(0.986903\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.6692 | − | 18.8058i | −0.668745 | − | 0.802611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6475 | −0.581404 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.05215 | + | 37.6395i | 0.342412 | + | 1.60059i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.73671 | + | 13.0845i | 0.201062 | + | 0.555406i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.1937 | + | 6.46267i | 0.474291 | + | 0.273832i | 0.718034 | − | 0.696008i | \(-0.245042\pi\) |
−0.243743 | + | 0.969840i | \(0.578375\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14.7230i | − | 0.622715i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.1702 | − | 5.85377i | 0.682707 | − | 0.247146i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6211 | 0.658352 | 0.329176 | − | 0.944269i | \(-0.393229\pi\) | ||||
0.329176 | + | 0.944269i | \(0.393229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 30.6090i | − | 1.28773i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.8015 | − | 0.697304i | 0.999571 | − | 0.0292840i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 42.6069i | − | 1.78617i | −0.449884 | − | 0.893087i | \(-0.648535\pi\) | ||
0.449884 | − | 0.893087i | \(-0.351465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.7970 | 0.828477 | 0.414239 | − | 0.910168i | \(-0.364048\pi\) | ||||
0.414239 | + | 0.910168i | \(0.364048\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.9528 | − | 7.58512i | 0.875317 | − | 0.316873i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.151314i | − | 0.00631022i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.6443 | − | 23.4660i | −1.69204 | − | 0.976902i | −0.952866 | − | 0.303391i | \(-0.901881\pi\) |
−0.739178 | − | 0.673511i | \(-0.764786\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.09685 | + | 19.6040i | 0.294935 | + | 0.814716i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.2870 | + | 10.4439i | 1.33949 | + | 0.433284i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.99442 | −0.413927 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 25.2168 | + | 30.2646i | 1.04259 | + | 1.25129i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.18063 | − | 3.77696i | 0.0900041 | − | 0.155892i | −0.817509 | − | 0.575917i | \(-0.804645\pi\) |
0.907513 | + | 0.420025i | \(0.137979\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.9771 | − | 34.6013i | −0.823141 | − | 1.42572i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 45.1554 | − | 16.3467i | 1.85744 | − | 0.672412i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.31077 | + | 4.00236i | 0.0948918 | + | 0.164357i | 0.909563 | − | 0.415565i | \(-0.136416\pi\) |
−0.814672 | + | 0.579922i | \(0.803083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.4817 | − | 18.4905i | 0.839668 | − | 0.758038i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.134273 | + | 0.753859i | −0.00549542 | + | 0.0308534i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.5173i | 1.04261i | 0.853371 | + | 0.521304i | \(0.174554\pi\) | ||||
−0.853371 | + | 0.521304i | \(0.825446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6824 | − | 13.0957i | −0.925235 | − | 0.534185i | −0.0399336 | − | 0.999202i | \(-0.512715\pi\) |
−0.885301 | + | 0.465018i | \(0.846048\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9531 | + | 9.12622i | −0.446043 | + | 0.371648i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.24183 | + | 12.5432i | 0.294422 | + | 0.509954i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.08757 | + | 2.93731i | 0.206498 | + | 0.119222i | 0.599683 | − | 0.800238i | \(-0.295293\pi\) |
−0.393185 | + | 0.919459i | \(0.628627\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.9084 | + | 0.410836i | −0.482554 | + | 0.0166479i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.3762 | + | 11.1869i | −0.783878 | + | 0.452572i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.4511 | − | 21.5660i | 0.502896 | − | 0.871041i | −0.497099 | − | 0.867694i | \(-0.665601\pi\) |
0.999994 | − | 0.00334675i | \(-0.00106531\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.103797 | + | 0.286724i | 0.00418549 | + | 0.0115618i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.1105 | − | 15.0749i | 1.05117 | − | 0.606894i | 0.128194 | − | 0.991749i | \(-0.459082\pi\) |
0.922977 | + | 0.384855i | \(0.125749\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5953 | − | 17.0869i | 1.18954 | − | 0.686779i | 0.231334 | − | 0.972874i | \(-0.425691\pi\) |
0.958201 | + | 0.286096i | \(0.0923575\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.2353 | − | 19.6958i | −0.450855 | − | 0.790364i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.7409 | − | 9.69666i | 0.430323 | − | 0.388489i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.4127 | − | 21.4994i | 0.496508 | − | 0.859978i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.9864 | + | 3.38174i | 0.758243 | + | 0.135054i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16.8751 | −0.672855 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.55990 | −0.340764 | −0.170382 | − | 0.985378i | \(-0.554500\pi\) | ||||
−0.170382 | + | 0.985378i | \(0.554500\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.489319 | − | 0.581100i | 0.0194487 | − | 0.0230967i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.66165 | − | 11.5383i | 0.264360 | − | 0.457884i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.1586 | + | 33.4356i | −0.957199 | + | 1.32477i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.2662 | − | 23.1229i | −0.762161 | − | 0.914726i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.0737 | + | 20.2498i | −1.38533 | + | 0.799818i | −0.992784 | − | 0.119916i | \(-0.961738\pi\) |
−0.392542 | + | 0.919734i | \(0.628404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.8435 | + | 18.3849i | −1.25579 | + | 0.725028i | −0.972252 | − | 0.233935i | \(-0.924840\pi\) |
−0.283533 | + | 0.958963i | \(0.591507\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.21105 | + | 7.37604i | −0.244560 | + | 0.290431i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.5492 | + | 40.7884i | −0.925815 | + | 1.60356i | −0.135569 | + | 0.990768i | \(0.543286\pi\) |
−0.790246 | + | 0.612790i | \(0.790047\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.2391 | − | 13.9944i | 0.951467 | − | 0.549330i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.4730 | − | 29.5907i | −0.724015 | − | 1.15975i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.16748 | − | 1.25139i | −0.0848199 | − | 0.0489708i | 0.456990 | − | 0.889472i | \(-0.348927\pi\) |
−0.541810 | + | 0.840501i | \(0.682261\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.3509 | − | 40.4450i | −0.912395 | − | 1.58032i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 43.2190 | − | 7.46635i | 1.68613 | − | 0.291290i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.2490 | − | 20.9284i | −1.41206 | − | 0.815254i | −0.416479 | − | 0.909146i | \(-0.636736\pi\) |
−0.995582 | + | 0.0938917i | \(0.970069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.49304i | 0.330341i | 0.986265 | + | 0.165170i | \(0.0528174\pi\) | ||||
−0.986265 | + | 0.165170i | \(0.947183\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −44.9191 | + | 16.2611i | −1.74451 | + | 0.631530i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.2592 | − | 6.47329i | 1.17340 | − | 0.251023i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.67333 | + | 9.82649i | 0.219672 | + | 0.380483i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.18708 | + | 34.7366i | −0.239206 | + | 1.34299i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.65447 | − | 14.9900i | −0.334102 | − | 0.578682i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9974 | + | 29.4403i | −0.655201 | + | 1.13484i | 0.326642 | + | 0.945148i | \(0.394083\pi\) |
−0.981843 | + | 0.189694i | \(0.939251\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.000936508 | 0.180173i | −3.60462e−5 | 0.00693486i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.0351 | −1.50024 | −0.750121 | − | 0.661301i | \(-0.770005\pi\) | ||||
−0.750121 | + | 0.661301i | \(0.770005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.1564 | + | 37.5814i | −0.466522 | + | 1.44224i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.68447 | + | 2.00042i | −0.0645490 | + | 0.0766564i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.91400 | + | 1.10505i | 0.0732373 | + | 0.0422836i | 0.536171 | − | 0.844109i | \(-0.319870\pi\) |
−0.462934 | + | 0.886393i | \(0.653203\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.72069i | 0.294992i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.44948 | − | 36.2099i | 0.246063 | − | 1.38149i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 27.7634 | 1.05770 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.41836i | 0.130041i | 0.997884 | + | 0.0650203i | \(0.0207112\pi\) | ||||
−0.997884 | + | 0.0650203i | \(0.979289\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.6688 | + | 2.37925i | 0.633194 | + | 0.0903803i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.976737i | 0.0370498i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.369789 | −0.0140068 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.0835 | + | 12.7011i | 0.570509 | + | 0.480401i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 37.5732i | − | 1.41912i | −0.704645 | − | 0.709560i | \(-0.748894\pi\) | ||
0.704645 | − | 0.709560i | \(-0.251106\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.3887 | − | 9.46203i | −0.618112 | − | 0.356867i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.4266 | + | 2.56957i | 0.543336 | + | 0.0967757i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.41402 | − | 5.79046i | 0.241224 | − | 0.217773i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.8780 | −1.00942 | −0.504712 | − | 0.863288i | \(-0.668401\pi\) | ||||
−0.504712 | + | 0.863288i | \(0.668401\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.5309 | + | 27.9384i | −1.25751 | + | 1.04777i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.6091 | + | 28.7678i | −0.622015 | + | 1.07736i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.9279 | + | 24.1238i | 0.520872 | + | 0.902177i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.6324 | + | 18.2157i | 0.807876 | + | 0.680277i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.41278 | − | 2.44701i | −0.0526879 | − | 0.0912580i | 0.838479 | − | 0.544935i | \(-0.183446\pi\) |
−0.891166 | + | 0.453676i | \(0.850112\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.88272 | − | 12.0033i | 0.144600 | − | 0.447028i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.7586 | − | 26.7425i | −1.18112 | − | 0.994566i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 0.0901606i | − | 0.00334848i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.622076 | + | 0.359156i | 0.0230715 | + | 0.0133203i | 0.511491 | − | 0.859288i | \(-0.329093\pi\) |
−0.488420 | + | 0.872609i | \(0.662427\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.2562 | + | 23.5218i | 0.490970 | + | 0.871176i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.84684 | − | 10.1270i | −0.216253 | − | 0.374561i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.4490 | + | 19.3118i | 1.23547 | + | 0.713297i | 0.968164 | − | 0.250315i | \(-0.0805343\pi\) |
0.267303 | + | 0.963613i | \(0.413868\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26.2084 | − | 6.55930i | 0.966710 | − | 0.241943i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.73062 | + | 5.04063i | −0.321596 | + | 0.185674i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.9491 | + | 20.6965i | −0.439556 | + | 0.761334i | −0.997655 | − | 0.0684405i | \(-0.978198\pi\) |
0.558099 | + | 0.829775i | \(0.311531\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −52.7421 | − | 9.39411i | −1.93753 | − | 0.345101i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.5325 | + | 11.8544i | −0.753264 | + | 0.434897i | −0.826872 | − | 0.562390i | \(-0.809882\pi\) |
0.0736078 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.7720 | + | 19.4983i | −1.23731 | + | 0.714362i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.55022 | + | 37.9160i | 0.239660 | + | 1.38727i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.0950 | + | 14.5052i | 0.478483 | + | 0.530009i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.89344 | − | 11.9398i | 0.251545 | − | 0.435689i | −0.712406 | − | 0.701767i | \(-0.752395\pi\) |
0.963951 | + | 0.266078i | \(0.0857279\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.3188 | − | 42.3160i | −0.558248 | − | 1.54208i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.835255 | −0.0303981 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.6447 | −0.714000 | −0.357000 | − | 0.934104i | \(-0.616200\pi\) | ||||
−0.357000 | + | 0.934104i | \(0.616200\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.45779 | − | 15.0764i | −0.198105 | − | 0.547238i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.4732 | − | 45.8529i | 0.959653 | − | 1.66217i | 0.236312 | − | 0.971677i | \(-0.424061\pi\) |
0.723341 | − | 0.690491i | \(-0.242605\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.90812 | − | 1.91110i | −0.213888 | − | 0.0691864i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 29.3639 | + | 10.8030i | 1.06165 | + | 0.390582i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −67.3335 | + | 38.8750i | −2.43127 | + | 1.40370i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.6774 | + | 10.2060i | −0.637462 | + | 0.368039i | −0.783636 | − | 0.621220i | \(-0.786637\pi\) |
0.146174 | + | 0.989259i | \(0.453304\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.34149 | + | 0.595165i | 0.120341 | + | 0.0214344i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.07789 | + | 1.86697i | −0.0387692 | + | 0.0671501i | −0.884759 | − | 0.466049i | \(-0.845677\pi\) |
0.845990 | + | 0.533199i | \(0.179010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.228589 | − | 0.131976i | 0.00821116 | − | 0.00474072i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.5851 | − | 7.76293i | −0.523239 | − | 0.278494i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.359130 | − | 0.207344i | −0.0128672 | − | 0.00742887i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.6412 | − | 18.4311i | −0.380772 | − | 0.659517i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.69455 | − | 11.7358i | −0.239244 | − | 0.419402i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.2802 | + | 22.6784i | 1.40197 | + | 0.809428i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.8939i | − | 0.744786i | −0.928075 | − | 0.372393i | \(-0.878537\pi\) | ||
0.928075 | − | 0.372393i | \(-0.121463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.76890 | − | 4.01569i | −0.169777 | − | 0.142962i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.3538 | + | 26.9764i | 0.865922 | + | 0.959170i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0412 | + | 41.6405i | 0.853727 | + | 1.47870i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.9092 | − | 11.7123i | −0.493307 | − | 0.415392i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.9964 | − | 24.2424i | −0.495777 | − | 0.858710i | 0.504211 | − | 0.863580i | \(-0.331783\pi\) |
−0.999988 | + | 0.00486976i | \(0.998450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.88513 | + | 15.3895i | −0.314333 | + | 0.544441i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.3988 | + | 5.66521i | 0.544090 | + | 0.200170i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.0136 | 1.09444 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.2397 | − | 19.0962i | −0.607621 | − | 0.673053i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.8793 | − | 2.47210i | −0.488575 | − | 0.0870221i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.1345 | + | 21.4396i | 1.30558 | + | 0.753777i | 0.981355 | − | 0.192203i | \(-0.0615633\pi\) |
0.324225 | + | 0.945980i | \(0.394897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.7421i | − | 0.833699i | −0.908976 | − | 0.416849i | \(-0.863134\pi\) | ||
0.908976 | − | 0.416849i | \(-0.136866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 24.9946 | + | 21.0468i | 0.876598 | + | 0.738145i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.3282 | 1.13241 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 13.1135i | − | 0.458783i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −46.3040 | − | 6.60930i | −1.61799 | − | 0.230948i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.58699i | 0.0553863i | 0.999616 | + | 0.0276932i | \(0.00881614\pi\) | ||||
−0.999616 | + | 0.0276932i | \(0.991184\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.08203 | −0.107433 | −0.0537164 | − | 0.998556i | \(-0.517107\pi\) | ||||
−0.0537164 | + | 0.998556i | \(0.517107\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0223410 | + | 0.125431i | −0.000777815 | + | 0.00436695i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7448i | 0.721369i | 0.932688 | + | 0.360685i | \(0.117457\pi\) | ||||
−0.932688 | + | 0.360685i | \(0.882543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.917576 | − | 0.529763i | −0.0318687 | − | 0.0183994i | 0.483981 | − | 0.875079i | \(-0.339190\pi\) |
−0.515850 | + | 0.856679i | \(0.672524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.1736 | + | 28.7078i | −0.838572 | + | 0.995862i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.33914 | + | 32.5922i | −0.115694 | + | 1.12925i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.9820 | 1.17600 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.9549 | − | 34.1517i | 0.689742 | − | 1.18046i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2137 | + | 33.2792i | −0.663332 | + | 1.14892i | 0.316403 | + | 0.948625i | \(0.397525\pi\) |
−0.979735 | + | 0.200299i | \(0.935809\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1195 | − | 19.2596i | −0.383432 | − | 0.664124i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.09807 | − | 23.0082i | 0.141145 | − | 0.792443i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.2061 | − | 41.9262i | −0.832716 | − | 1.44231i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.3623 | − | 5.29271i | −0.562216 | − | 0.181860i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.31026 | − | 1.19835i | 0.113608 | − | 0.0411271i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.7336i | 0.539341i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0659 | + | 6.96626i | 0.413129 | + | 0.238520i | 0.692133 | − | 0.721770i | \(-0.256671\pi\) |
−0.279004 | + | 0.960290i | \(0.590004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.4602 | + | 26.9562i | 0.768123 | + | 0.921882i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.4632 | − | 23.3189i | −0.459894 | − | 0.796560i | 0.539061 | − | 0.842267i | \(-0.318779\pi\) |
−0.998955 | + | 0.0457070i | \(0.985446\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4938 | + | 10.1000i | 0.596880 | + | 0.344609i | 0.767813 | − | 0.640674i | \(-0.221345\pi\) |
−0.170933 | + | 0.985283i | \(0.554678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.319608 | − | 0.170111i | −0.0108922 | − | 0.00579737i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38.1427 | + | 22.0217i | −1.29839 | + | 0.749627i | −0.980126 | − | 0.198374i | \(-0.936434\pi\) |
−0.318266 | + | 0.948001i | \(0.603101\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.09612 | − | 3.63058i | 0.0712701 | − | 0.123443i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.47355 | + | 6.50022i | −0.185891 | + | 0.220759i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.7273 | + | 15.4310i | −0.906662 | + | 0.523461i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.2527 | − | 14.0023i | 0.821772 | − | 0.474450i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −44.1335 | + | 7.62434i | −1.49369 | + | 0.258045i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.20934 | + | 29.0253i | 0.209914 | + | 0.981235i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.0436 | − | 46.8409i | 0.913198 | − | 1.58170i | 0.103678 | − | 0.994611i | \(-0.466939\pi\) |
0.809519 | − | 0.587094i | \(-0.199728\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.4017 | − | 42.0419i | 1.19407 | − | 1.41804i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.82593 | −0.229972 | −0.114986 | − | 0.993367i | \(-0.536682\pi\) | ||||
−0.114986 | + | 0.993367i | \(0.536682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.87685 | 0.332382 | 0.166191 | − | 0.986094i | \(-0.446853\pi\) | ||||
0.166191 | + | 0.986094i | \(0.446853\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 50.1332 | + | 8.92943i | 1.68521 | + | 0.300159i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.5412 | + | 30.3823i | −0.588977 | + | 1.02014i | 0.405390 | + | 0.914144i | \(0.367136\pi\) |
−0.994367 | + | 0.105994i | \(0.966198\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.30931 | + | 15.4693i | 0.110991 | + | 0.518823i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.40541 | + | 17.9856i | 0.214589 | + | 0.602540i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17.2581 | + | 9.96395i | −0.577519 | + | 0.333431i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.2539 | + | 11.1163i | −0.643588 | + | 0.371576i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.1611 | + | 41.8805i | 0.506216 | + | 1.39835i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.89655 | + | 17.1413i | −0.330069 | + | 0.571695i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.0967 | − | 11.0255i | 0.636204 | − | 0.367313i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.394760 | − | 11.4424i | −0.0131368 | − | 0.380781i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.7731 | + | 12.5707i | 0.723761 | + | 0.417864i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.2231 | + | 29.8313i | 0.571885 | + | 0.990533i | 0.996372 | + | 0.0850994i | \(0.0271208\pi\) |
−0.424488 | + | 0.905434i | \(0.639546\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.19555 | + | 3.38304i | 0.304997 | + | 0.112208i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.9046 | + | 26.5030i | 1.52089 | + | 0.878084i | 0.999696 | + | 0.0246430i | \(0.00784490\pi\) |
0.521190 | + | 0.853441i | \(0.325488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.2082i | 0.900460i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.52215 | − | 31.0035i | 0.182557 | − | 1.02494i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.7594 | + | 17.0661i | 1.74227 | + | 0.563571i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.73193 | − | 9.92799i | −0.189079 | − | 0.327494i | 0.755865 | − | 0.654728i | \(-0.227217\pi\) |
−0.944943 | + | 0.327234i | \(0.893884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.433286 | − | 0.156854i | 0.0142773 | − | 0.00516850i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.5601 | + | 51.1996i | 0.972983 | + | 1.68526i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0625096 | − | 0.108270i | 0.00205530 | − | 0.00355989i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.0960 | − | 2.43518i | 0.462975 | − | 0.0799818i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.7866 | 1.14131 | 0.570656 | − | 0.821189i | \(-0.306689\pi\) | ||||
0.570656 | + | 0.821189i | \(0.306689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.5177 | + | 29.7805i | −0.705213 | + | 0.976017i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.57199 | + | 7.10477i | 0.0842033 | + | 0.232600i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.1602 | + | 11.0622i | 0.626606 | + | 0.361771i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5180i | 0.604956i | 0.953156 | + | 0.302478i | \(0.0978139\pi\) | ||||
−0.953156 | + | 0.302478i | \(0.902186\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.1436 | − | 9.10221i | 0.820529 | − | 0.297039i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.78447 | −0.318965 | −0.159482 | − | 0.987201i | \(-0.550983\pi\) | ||||
−0.159482 | + | 0.987201i | \(0.550983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.344774i | 0.0112274i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 20.4096 | + | 22.8450i | 0.663924 | + | 0.743149i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 33.5503i | − | 1.09024i | −0.838359 | − | 0.545119i | \(-0.816484\pi\) | ||
0.838359 | − | 0.545119i | \(-0.183516\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −86.1523 | −2.79662 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.3815 | − | 12.8084i | 1.14732 | − | 0.415342i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.8871i | − | 0.352668i | −0.984330 | − | 0.176334i | \(-0.943576\pi\) | ||
0.984330 | − | 0.176334i | \(-0.0564239\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.8272 | + | 14.3340i | 0.803389 | + | 0.463837i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.25203 | − | 8.98328i | −0.105123 | − | 0.290388i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.14291 | − | 6.80442i | −0.198365 | − | 0.219726i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.9458 | −0.869220 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.65069 | + | 20.7956i | −0.246540 | + | 0.670129i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.4113 | + | 23.2290i | −0.431724 | + | 0.747768i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.3931 | − | 45.7142i | −0.848746 | − | 1.47007i | −0.882328 | − | 0.470635i | \(-0.844025\pi\) |
0.0335826 | − | 0.999436i | \(-0.489308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.0087 | + | 14.4835i | −1.28526 | + | 0.465278i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.7931 | − | 27.3544i | −0.506824 | − | 0.877844i | −0.999969 | − | 0.00789735i | \(-0.997486\pi\) |
0.493145 | − | 0.869947i | \(-0.335847\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.777134 | − | 0.860821i | −0.0249138 | − | 0.0275966i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.0620609 | − | 0.348434i | 0.00198754 | − | 0.0111588i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.2654i | 1.25621i | 0.778128 | + | 0.628106i | \(0.216169\pi\) | ||||
−0.778128 | + | 0.628106i | \(0.783831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.0479 | + | 5.80113i | 0.321131 | + | 0.185405i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.19861 | − | 6.93816i | −0.0382687 | − | 0.221519i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.9170 | + | 34.4973i | 0.635255 | + | 1.10029i | 0.986461 | + | 0.163996i | \(0.0524383\pi\) |
−0.351206 | + | 0.936298i | \(0.614228\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.5050 | + | 30.8911i | 1.70481 | + | 0.984273i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.7589 | + | 9.21377i | −0.469782 | + | 0.293277i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.44198 | + | 5.45133i | −0.300237 | + | 0.173342i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.9472 | − | 34.5496i | 0.633645 | − | 1.09750i | −0.353156 | − | 0.935565i | \(-0.614891\pi\) |
0.986801 | − | 0.161940i | \(-0.0517752\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.92983 | − | 24.6674i | −0.283380 | − | 0.782796i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.853132 | + | 0.492556i | −0.0270461 | + | 0.0156151i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.6084 | − | 14.7850i | 0.811026 | − | 0.468246i | −0.0362863 | − | 0.999341i | \(-0.511553\pi\) |
0.847312 | + | 0.531096i | \(0.178219\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.0973781 | − | 18.7344i | 0.00308091 | − | 0.592729i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.2.ca.e.353.11 | 48 | ||
3.2 | odd | 2 | 3024.2.ca.e.2033.6 | 48 | |||
4.3 | odd | 2 | 504.2.bs.a.353.14 | yes | 48 | ||
7.5 | odd | 6 | 1008.2.df.e.929.3 | 48 | |||
9.4 | even | 3 | 3024.2.df.e.17.6 | 48 | |||
9.5 | odd | 6 | 1008.2.df.e.689.3 | 48 | |||
12.11 | even | 2 | 1512.2.bs.a.521.6 | 48 | |||
21.5 | even | 6 | 3024.2.df.e.1601.6 | 48 | |||
28.19 | even | 6 | 504.2.cx.a.425.22 | yes | 48 | ||
36.23 | even | 6 | 504.2.cx.a.185.22 | yes | 48 | ||
36.31 | odd | 6 | 1512.2.cx.a.17.6 | 48 | |||
63.5 | even | 6 | inner | 1008.2.ca.e.257.11 | 48 | ||
63.40 | odd | 6 | 3024.2.ca.e.2609.6 | 48 | |||
84.47 | odd | 6 | 1512.2.cx.a.89.6 | 48 | |||
252.103 | even | 6 | 1512.2.bs.a.1097.6 | 48 | |||
252.131 | odd | 6 | 504.2.bs.a.257.14 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.14 | ✓ | 48 | 252.131 | odd | 6 | ||
504.2.bs.a.353.14 | yes | 48 | 4.3 | odd | 2 | ||
504.2.cx.a.185.22 | yes | 48 | 36.23 | even | 6 | ||
504.2.cx.a.425.22 | yes | 48 | 28.19 | even | 6 | ||
1008.2.ca.e.257.11 | 48 | 63.5 | even | 6 | inner | ||
1008.2.ca.e.353.11 | 48 | 1.1 | even | 1 | trivial | ||
1008.2.df.e.689.3 | 48 | 9.5 | odd | 6 | |||
1008.2.df.e.929.3 | 48 | 7.5 | odd | 6 | |||
1512.2.bs.a.521.6 | 48 | 12.11 | even | 2 | |||
1512.2.bs.a.1097.6 | 48 | 252.103 | even | 6 | |||
1512.2.cx.a.17.6 | 48 | 36.31 | odd | 6 | |||
1512.2.cx.a.89.6 | 48 | 84.47 | odd | 6 | |||
3024.2.ca.e.2033.6 | 48 | 3.2 | odd | 2 | |||
3024.2.ca.e.2609.6 | 48 | 63.40 | odd | 6 | |||
3024.2.df.e.17.6 | 48 | 9.4 | even | 3 | |||
3024.2.df.e.1601.6 | 48 | 21.5 | even | 6 |