Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(185,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.185");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.cx (of order \(6\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 185.14 | ||
Character | \(\chi\) | \(=\) | 504.185 |
Dual form | 504.2.cx.a.425.14 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0.310783 | − | 1.70394i | 0.179430 | − | 0.983771i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.76937 | 1.23850 | 0.619249 | − | 0.785195i | \(-0.287437\pi\) | ||||
0.619249 | + | 0.785195i | \(0.287437\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.21939 | − | 2.34800i | −0.460886 | − | 0.887459i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.80683 | − | 1.05911i | −0.935609 | − | 0.353037i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.41924i | − | 0.729429i | −0.931119 | − | 0.364715i | \(-0.881167\pi\) | ||
0.931119 | − | 0.364715i | \(-0.118833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0461613 | + | 0.0266512i | 0.0128028 | + | 0.00739172i | 0.506388 | − | 0.862306i | \(-0.330980\pi\) |
−0.493585 | + | 0.869698i | \(0.664314\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.860670 | − | 4.71884i | 0.222224 | − | 1.21840i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.79727 | + | 3.11297i | −0.435903 | + | 0.755006i | −0.997369 | − | 0.0724940i | \(-0.976904\pi\) |
0.561466 | + | 0.827500i | \(0.310238\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.96978 | − | 2.29195i | 0.910730 | − | 0.525810i | 0.0300639 | − | 0.999548i | \(-0.490429\pi\) |
0.880666 | + | 0.473738i | \(0.157096\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.37981 | + | 1.34805i | −0.955753 | + | 0.294169i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.106917i | 0.0222937i | 0.999938 | + | 0.0111469i | \(0.00354823\pi\) | ||||
−0.999938 | + | 0.0111469i | \(0.996452\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.66939 | 0.533877 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.67697 | + | 4.45352i | −0.515184 | + | 0.857080i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.57376 | − | 3.79536i | 1.22072 | − | 0.704781i | 0.255646 | − | 0.966770i | \(-0.417712\pi\) |
0.965071 | + | 0.261989i | \(0.0843785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.90251 | + | 3.40781i | −1.06012 | + | 0.612062i | −0.925466 | − | 0.378831i | \(-0.876326\pi\) |
−0.134656 | + | 0.990892i | \(0.542993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.12225 | − | 0.751859i | −0.717591 | − | 0.130882i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.37694 | − | 6.50246i | −0.570807 | − | 1.09912i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.06198 | + | 3.57146i | 0.338988 | + | 0.587144i | 0.984243 | − | 0.176823i | \(-0.0565821\pi\) |
−0.645255 | + | 0.763967i | \(0.723249\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0597583 | − | 0.0703734i | 0.00956898 | − | 0.0112688i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.838974 | − | 1.45315i | 0.131026 | − | 0.226943i | −0.793047 | − | 0.609161i | \(-0.791506\pi\) |
0.924072 | + | 0.382218i | \(0.124840\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.74347 | + | 3.01978i | 0.265877 | + | 0.460513i | 0.967793 | − | 0.251747i | \(-0.0810051\pi\) |
−0.701916 | + | 0.712260i | \(0.747672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.77313 | − | 2.93306i | −1.15875 | − | 0.437235i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.59698 | − | 11.4263i | 0.962268 | − | 1.66670i | 0.245484 | − | 0.969401i | \(-0.421053\pi\) |
0.716783 | − | 0.697296i | \(-0.245614\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.02618 | + | 5.72625i | −0.575168 | + | 0.818035i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.74575 | + | 4.02990i | 0.664538 | + | 0.564299i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.27512 | − | 3.04559i | −0.724593 | − | 0.418344i | 0.0918477 | − | 0.995773i | \(-0.470723\pi\) |
−0.816441 | + | 0.577429i | \(0.804056\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.69977i | − | 0.903397i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.67161 | − | 7.47657i | −0.353864 | − | 0.990295i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.72417 | − | 8.18250i | −0.615034 | − | 1.06527i | −0.990379 | − | 0.138385i | \(-0.955809\pi\) |
0.375344 | − | 0.926885i | \(-0.377524\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.29928 | + | 1.32749i | 0.294392 | + | 0.169967i | 0.639921 | − | 0.768441i | \(-0.278967\pi\) |
−0.345529 | + | 0.938408i | \(0.612300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.935832 | + | 7.88189i | 0.117904 | + | 0.993025i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.127838 | + | 0.0738070i | 0.0158563 | + | 0.00915464i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.09356 | + | 12.2864i | 0.866616 | + | 1.50102i | 0.865433 | + | 0.501024i | \(0.167043\pi\) |
0.00118266 | + | 0.999999i | \(0.499624\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.182180 | + | 0.0332279i | 0.0219319 | + | 0.00400017i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.40262i | − | 0.166460i | −0.996530 | − | 0.0832300i | \(-0.973476\pi\) | ||
0.996530 | − | 0.0832300i | \(-0.0265236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.54168 | + | 3.19949i | 0.648605 | + | 0.374472i | 0.787921 | − | 0.615776i | \(-0.211157\pi\) |
−0.139317 | + | 0.990248i | \(0.544491\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.829599 | − | 4.54848i | 0.0957938 | − | 0.525213i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.68038 | + | 2.95000i | −0.647339 | + | 0.336184i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.11067 | + | 3.65578i | −0.237469 | + | 0.411308i | −0.959987 | − | 0.280044i | \(-0.909651\pi\) |
0.722519 | + | 0.691351i | \(0.242984\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.75657 | + | 5.94548i | 0.750730 | + | 0.660609i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.86670 | + | 11.8935i | 0.753719 | + | 1.30548i | 0.946009 | + | 0.324141i | \(0.105075\pi\) |
−0.192290 | + | 0.981338i | \(0.561591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.97731 | + | 8.62095i | −0.539865 | + | 0.935073i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.42406 | − | 12.3808i | −0.474309 | − | 1.32736i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.71724 | + | 9.90254i | 0.606026 | + | 1.04967i | 0.991888 | + | 0.127111i | \(0.0405705\pi\) |
−0.385863 | + | 0.922556i | \(0.626096\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.00628839 | − | 0.140885i | 0.000659203 | − | 0.0147687i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.97232 | + | 11.1166i | 0.411910 | + | 1.15274i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.9938 | − | 6.34726i | 1.12794 | − | 0.651215i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3549 | − | 8.28778i | 1.45751 | − | 0.841496i | 0.458626 | − | 0.888630i | \(-0.348342\pi\) |
0.998889 | + | 0.0471333i | \(0.0150086\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.56224 | + | 6.79040i | −0.257515 | + | 0.682461i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5000 | −1.04479 | −0.522394 | − | 0.852704i | \(-0.674961\pi\) | ||||
−0.522394 | + | 0.852704i | \(0.674961\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4270i | 1.52007i | 0.649884 | + | 0.760033i | \(0.274817\pi\) | ||||
−0.649884 | + | 0.760033i | \(0.725183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −12.1293 | + | 3.73325i | −1.18370 | + | 0.364328i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.76426 | − | 5.63740i | 0.943946 | − | 0.544988i | 0.0527511 | − | 0.998608i | \(-0.483201\pi\) |
0.891195 | + | 0.453620i | \(0.149868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.06307 | + | 13.9657i | −0.772302 | + | 1.33767i | 0.163996 | + | 0.986461i | \(0.447562\pi\) |
−0.936298 | + | 0.351206i | \(0.885772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.72638 | − | 2.40355i | 0.638440 | − | 0.228135i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7542 | + | 6.78629i | 1.10574 | + | 0.638400i | 0.937723 | − | 0.347384i | \(-0.112930\pi\) |
0.168018 | + | 0.985784i | \(0.446263\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.296092i | 0.0276107i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.101340 | − | 0.123695i | −0.00936891 | − | 0.0114356i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.50082 | + | 0.424069i | 0.870938 | + | 0.0388743i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.14726 | 0.467933 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.21533 | − | 1.88117i | −0.199750 | − | 0.169620i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.45432 | −0.577292 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.23056 | −0.819080 | −0.409540 | − | 0.912292i | \(-0.634311\pi\) | ||||
−0.409540 | + | 0.912292i | \(0.634311\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.68737 | − | 2.03228i | 0.500745 | − | 0.178932i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.18879 | −0.278606 | −0.139303 | − | 0.990250i | \(-0.544486\pi\) | ||||
−0.139303 | + | 0.990250i | \(0.544486\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2222 | − | 6.52624i | −0.886378 | − | 0.565897i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.41352 | + | 12.3334i | −0.638054 | + | 1.06149i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.62925i | − | 0.480939i | −0.970657 | − | 0.240470i | \(-0.922699\pi\) | ||
0.970657 | − | 0.240470i | \(-0.0773014\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.6739 | − | 10.7814i | −1.58390 | − | 0.914467i | −0.994282 | − | 0.106786i | \(-0.965944\pi\) |
−0.589620 | − | 0.807680i | \(-0.700723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.4195 | − | 14.7919i | −1.46699 | − | 1.24571i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.0644758 | − | 0.111675i | 0.00539174 | − | 0.00933877i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.2052 | − | 10.5107i | 1.51186 | − | 0.872870i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.50592 | + | 8.63998i | 0.701557 | + | 0.712614i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.1303i | 1.56722i | 0.621254 | + | 0.783609i | \(0.286623\pi\) | ||||
−0.621254 | + | 0.783609i | \(0.713377\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.88100 | −0.641347 | −0.320673 | − | 0.947190i | \(-0.603909\pi\) | ||||
−0.320673 | + | 0.947190i | \(0.603909\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.34161 | − | 6.83406i | 0.674380 | − | 0.552501i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.3462 | + | 9.43748i | −1.31296 | + | 0.758037i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.2853 | − | 9.97966i | 1.37952 | − | 0.796463i | 0.387414 | − | 0.921906i | \(-0.373368\pi\) |
0.992101 | + | 0.125442i | \(0.0400350\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.82892 | + | 8.04197i | −0.541569 | + | 0.637770i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.251041 | − | 0.130373i | 0.0197848 | − | 0.0102749i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0423 | + | 20.8578i | 0.943223 | + | 1.63371i | 0.759271 | + | 0.650774i | \(0.225556\pi\) |
0.183951 | + | 0.982935i | \(0.441111\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.4160 | − | 2.08217i | −0.888735 | − | 0.162097i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.793686 | − | 1.37470i | 0.0614172 | − | 0.106378i | −0.833682 | − | 0.552245i | \(-0.813771\pi\) |
0.895099 | + | 0.445867i | \(0.147105\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.49858 | − | 11.2559i | −0.499891 | − | 0.865836i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.5699 | + | 2.22869i | −1.03772 | + | 0.170432i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.11856 | − | 3.66945i | 0.161071 | − | 0.278983i | −0.774182 | − | 0.632963i | \(-0.781839\pi\) |
0.935253 | + | 0.353980i | \(0.115172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.25502 | − | 6.26771i | −0.246057 | − | 0.473794i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.4107 | + | 5.50672i | −1.15834 | + | 0.413911i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.38034 | − | 1.95164i | −0.252658 | − | 0.145872i | 0.368323 | − | 0.929698i | \(-0.379932\pi\) |
−0.620981 | + | 0.783826i | \(0.713266\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 15.3685i | − | 1.14233i | −0.820835 | − | 0.571166i | \(-0.806491\pi\) | ||
0.820835 | − | 0.571166i | \(-0.193509\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.97654 | − | 3.50527i | 0.220032 | − | 0.259117i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.71038 | + | 9.89067i | 0.419836 | + | 0.727177i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.53103 | + | 4.34804i | 0.550723 | + | 0.317960i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.7211 | + | 0.854952i | 0.998064 | + | 0.0621886i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.28415 | − | 1.31876i | −0.165276 | − | 0.0954219i | 0.415081 | − | 0.909785i | \(-0.363753\pi\) |
−0.580356 | + | 0.814363i | \(0.697087\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.72965 | + | 6.45994i | 0.268466 | + | 0.464997i | 0.968466 | − | 0.249146i | \(-0.0801499\pi\) |
−0.700000 | + | 0.714143i | \(0.746817\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.165492 | − | 0.194890i | 0.0118512 | − | 0.0139563i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.77770i | − | 0.197903i | −0.995092 | − | 0.0989515i | \(-0.968451\pi\) | ||
0.995092 | − | 0.0989515i | \(-0.0315489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.49892 | − | 2.02010i | −0.248032 | − | 0.143201i | 0.370831 | − | 0.928700i | \(-0.379073\pi\) |
−0.618863 | + | 0.785499i | \(0.712406\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.1399 | − | 8.26860i | 1.63216 | − | 0.583222i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.9275 | − | 10.8071i | −1.18808 | − | 0.758513i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.32343 | − | 4.02429i | 0.162275 | − | 0.281069i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.113237 | − | 0.300097i | 0.00787050 | − | 0.0208582i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.54479 | − | 9.60386i | −0.383541 | − | 0.664313i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4855 | + | 18.1614i | −0.721849 | + | 1.25028i | 0.238409 | + | 0.971165i | \(0.423374\pi\) |
−0.960258 | + | 0.279115i | \(0.909959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.38998 | − | 0.435909i | −0.163758 | − | 0.0298680i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.82831 | + | 8.36289i | 0.329288 | + | 0.570344i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.1990 | + | 9.70361i | 1.03178 | + | 0.658724i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.17400 | − | 8.44835i | 0.484774 | − | 0.570887i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.165929 | + | 0.0957991i | −0.0111616 | + | 0.00644415i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.82344 | + | 5.09421i | −0.590861 | + | 0.341134i | −0.765438 | − | 0.643510i | \(-0.777478\pi\) |
0.174577 | + | 0.984644i | \(0.444144\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.49251 | − | 2.82717i | −0.499501 | − | 0.188478i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.0630 | −0.667906 | −0.333953 | − | 0.942590i | \(-0.608383\pi\) | ||||
−0.333953 | + | 0.942590i | \(0.608383\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.9555i | − | 0.988287i | −0.869380 | − | 0.494144i | \(-0.835482\pi\) | ||
0.869380 | − | 0.494144i | \(-0.164518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.26127 | + | 10.5958i | 0.214576 | + | 0.697155i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.3200 | − | 8.26764i | 0.938133 | − | 0.541631i | 0.0487581 | − | 0.998811i | \(-0.484474\pi\) |
0.889374 | + | 0.457180i | \(0.151140\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.2694 | − | 31.6436i | 1.19177 | − | 2.06420i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.57328 | + | 4.73260i | 0.362023 | + | 0.307416i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.02155 | + | 5.20859i | 0.583555 | + | 0.336916i | 0.762545 | − | 0.646935i | \(-0.223950\pi\) |
−0.178990 | + | 0.983851i | \(0.557283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 10.3654i | − | 0.667693i | −0.942627 | − | 0.333846i | \(-0.891653\pi\) | ||
0.942627 | − | 0.333846i | \(-0.108347\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.2306 | − | 9.66505i | 0.784591 | − | 0.620013i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.1500 | + | 15.8581i | −0.712344 | + | 1.01314i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.244334 | 0.0155466 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.3998 | − | 8.00417i | 1.41953 | − | 0.507244i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.1006 | −0.826903 | −0.413452 | − | 0.910526i | \(-0.635677\pi\) | ||||
−0.413452 | + | 0.910526i | \(0.635677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.258658 | 0.0162617 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.1427 | + | 11.1603i | 0.823029 | + | 0.698884i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.886831 | 0.0553190 | 0.0276595 | − | 0.999617i | \(-0.491195\pi\) | ||||
0.0276595 | + | 0.999617i | \(0.491195\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.87141 | − | 9.19653i | 0.364832 | − | 0.571444i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.4711 | + | 3.69060i | −1.39093 | + | 0.228442i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 7.12492i | − | 0.439342i | −0.975574 | − | 0.219671i | \(-0.929502\pi\) | ||
0.975574 | − | 0.219671i | \(-0.0704983\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.6087 | − | 8.43436i | −0.897407 | − | 0.518118i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.6502 | − | 6.66429i | 1.14137 | − | 0.407848i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.7987 | − | 27.3641i | 0.963261 | − | 1.66842i | 0.249045 | − | 0.968492i | \(-0.419883\pi\) |
0.714216 | − | 0.699925i | \(-0.246783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8215 | + | 9.13455i | −0.961088 | + | 0.554884i | −0.896508 | − | 0.443028i | \(-0.853904\pi\) |
−0.0645803 | + | 0.997913i | \(0.520571\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.238105 | − | 0.0544996i | −0.0144108 | − | 0.00329847i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 6.45790i | − | 0.389426i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.5690 | −1.83671 | −0.918357 | − | 0.395753i | \(-0.870484\pi\) | ||||
−0.918357 | + | 0.395753i | \(0.870484\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.1766 | − | 3.31375i | 1.20794 | − | 0.198389i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.92237 | − | 2.26458i | 0.233989 | − | 0.135094i | −0.378422 | − | 0.925633i | \(-0.623533\pi\) |
0.612411 | + | 0.790540i | \(0.290200\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.10730 | + | 4.68075i | −0.481929 | + | 0.278242i | −0.721220 | − | 0.692706i | \(-0.756418\pi\) |
0.239291 | + | 0.970948i | \(0.423085\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.39868 | − | 20.7053i | −0.438260 | − | 1.22648i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.43502 | − | 0.197957i | −0.261791 | − | 0.0116850i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.03962 | + | 3.53272i | 0.119977 | + | 0.207807i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.66064 | − | 27.0355i | −0.566317 | − | 1.58485i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.17267 | + | 14.1555i | −0.477452 | + | 0.826972i | −0.999666 | − | 0.0258430i | \(-0.991773\pi\) |
0.522214 | + | 0.852815i | \(0.325106\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0829 | − | 22.6603i | −0.761719 | − | 1.31934i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.7741 | + | 6.47625i | 0.625179 | + | 0.375790i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.00284947 | + | 0.00493542i | −0.000164789 | + | 0.000285423i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.96447 | − | 7.77596i | 0.286147 | − | 0.448199i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.26321 | + | 17.8914i | −0.187467 | + | 1.02783i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.36754 | + | 3.67630i | 0.364604 | + | 0.210504i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 0.985041i | − | 0.0562193i | −0.999605 | − | 0.0281096i | \(-0.991051\pi\) | ||
0.999605 | − | 0.0281096i | \(-0.00894875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.2867 | + | 4.79444i | 1.49540 | + | 0.272746i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.1302 | − | 22.7422i | −0.744545 | − | 1.28959i | −0.950407 | − | 0.311008i | \(-0.899333\pi\) |
0.205863 | − | 0.978581i | \(-0.434000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.5858 | − | 7.26643i | −0.711393 | − | 0.410723i | 0.100184 | − | 0.994969i | \(-0.468057\pi\) |
−0.811576 | + | 0.584246i | \(0.801390\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.59166 | + | 21.8278i | 0.146024 | + | 1.22986i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.5148 | − | 14.7310i | −1.43306 | − | 0.827375i | −0.435704 | − | 0.900090i | \(-0.643500\pi\) |
−0.997353 | + | 0.0727147i | \(0.976834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.18191 | − | 15.9035i | −0.514088 | − | 0.890427i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.57123 | − | 18.3897i | −0.366770 | − | 1.02641i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.4771i | 0.916808i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.123222 | + | 0.0711425i | 0.00683515 | + | 0.00394627i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.2908 | + | 18.0793i | 1.17738 | + | 0.999787i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −34.8732 | − | 1.55656i | −1.92262 | − | 0.0858162i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.91015 | − | 5.04053i | 0.159956 | − | 0.277052i | −0.774896 | − | 0.632088i | \(-0.782198\pi\) |
0.934853 | + | 0.355036i | \(0.115531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00506 | − | 12.2083i | −0.109877 | − | 0.669013i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.6447 | + | 34.0255i | 1.07330 | + | 1.85901i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4909 | + | 19.9028i | −0.625950 | + | 1.08418i | 0.362407 | + | 0.932020i | \(0.381955\pi\) |
−0.988356 | + | 0.152157i | \(0.951378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.2164 | − | 17.9194i | 0.826443 | − | 0.973248i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.24433 | + | 14.2796i | 0.446456 | + | 0.773284i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3547 | + | 2.47092i | 0.991060 | + | 0.133417i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.504523 | + | 0.0920202i | 0.0271626 | + | 0.00495420i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.9435 | − | 7.47293i | 0.694843 | − | 0.401168i | −0.110581 | − | 0.993867i | \(-0.535271\pi\) |
0.805424 | + | 0.592699i | \(0.201938\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.768588 | + | 0.443744i | −0.0411416 | + | 0.0237531i | −0.520430 | − | 0.853905i | \(-0.674228\pi\) |
0.479288 | + | 0.877658i | \(0.340895\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.242264 | + | 0.134235i | −0.0129311 | + | 0.00716496i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.04996 | 0.268782 | 0.134391 | − | 0.990928i | \(-0.457092\pi\) | ||||
0.134391 | + | 0.990928i | \(0.457092\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.88436i | − | 0.206160i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.67528 | − | 16.0570i | 0.194516 | − | 0.849828i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −30.2467 | + | 17.4629i | −1.59636 | + | 0.921659i | −0.604179 | + | 0.796848i | \(0.706499\pi\) |
−0.992181 | + | 0.124810i | \(0.960168\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00610 | − | 1.74261i | 0.0529524 | − | 0.0917163i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.59968 | − | 8.77063i | 0.0839614 | − | 0.460339i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.3469 | + | 8.86056i | 0.803296 | + | 0.463783i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.0893i | − | 1.20525i | −0.798025 | − | 0.602625i | \(-0.794122\pi\) | ||
0.798025 | − | 0.602625i | \(-0.205878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.89390 | + | 3.19016i | −0.202708 | + | 0.166073i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.718611 | + | 16.0997i | −0.0373084 | + | 0.835856i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.79851 | 0.0931235 | 0.0465617 | − | 0.998915i | \(-0.485174\pi\) | ||||
0.0465617 | + | 0.998915i | \(0.485174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.00589 | + | 10.9978i | −0.103584 | + | 0.567923i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.404605 | 0.0208382 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.34605 | −0.171875 | −0.0859375 | − | 0.996301i | \(-0.527389\pi\) | ||||
−0.0859375 | + | 0.996301i | \(0.527389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.86870 | + | 15.7283i | −0.146968 | + | 0.805787i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.97833 | 0.101088 | 0.0505439 | − | 0.998722i | \(-0.483905\pi\) | ||||
0.0505439 | + | 0.998722i | \(0.483905\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.7310 | + | 8.16963i | −0.801728 | + | 0.416363i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.69535 | − | 10.3225i | −0.0861793 | − | 0.524724i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.9095i | 1.76998i | 0.465609 | + | 0.884990i | \(0.345835\pi\) | ||||
−0.465609 | + | 0.884990i | \(0.654165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.332829 | − | 0.192159i | −0.0168319 | − | 0.00971789i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.991021 | + | 5.43352i | −0.0499904 | + | 0.274085i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.84521 | + | 10.1242i | −0.294104 | + | 0.509404i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.73751 | − | 1.58050i | 0.137392 | − | 0.0793231i | −0.429729 | − | 0.902958i | \(-0.641391\pi\) |
0.567120 | + | 0.823635i | \(0.308057\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −14.2972 | + | 15.3898i | −0.715756 | + | 0.770453i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 33.0291i | − | 1.64940i | −0.565573 | − | 0.824698i | \(-0.691345\pi\) | ||
0.565573 | − | 0.824698i | \(-0.308655\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.363290 | −0.0180968 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.7114 | + | 16.4652i | 0.929778 | + | 0.818163i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.64023 | − | 4.98844i | 0.428280 | − | 0.247268i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.933684 | − | 0.539063i | 0.0461677 | − | 0.0266549i | −0.476739 | − | 0.879045i | \(-0.658181\pi\) |
0.522906 | + | 0.852390i | \(0.324848\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.59190 | − | 1.74947i | −0.473134 | − | 0.0862951i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.4519 | + | 21.0700i | −0.661923 | + | 1.03679i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.0164 | + | 32.9374i | 0.933479 | + | 1.61683i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.1744 | + | 28.4686i | −1.18383 | + | 1.39411i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.2799 | + | 23.0015i | −0.648768 | + | 1.12370i | 0.334650 | + | 0.942343i | \(0.391382\pi\) |
−0.983418 | + | 0.181356i | \(0.941951\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.32791 | + | 5.76411i | 0.162192 | + | 0.280925i | 0.935655 | − | 0.352917i | \(-0.114810\pi\) |
−0.773462 | + | 0.633842i | \(0.781477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.6183 | + | 25.0847i | −1.48871 | + | 1.21966i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.79762 | + | 8.30972i | −0.232719 | + | 0.403081i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.313223 | − | 7.01742i | 0.0151579 | − | 0.339597i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.170250 | − | 0.144570i | −0.00821976 | − | 0.00697989i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.2930 | + | 7.67471i | 0.640300 | + | 0.369678i | 0.784730 | − | 0.619837i | \(-0.212801\pi\) |
−0.144430 | + | 0.989515i | \(0.546135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.9407i | 0.766060i | 0.923736 | + | 0.383030i | \(0.125119\pi\) | ||||
−0.923736 | + | 0.383030i | \(0.874881\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2519 | − | 34.2871i | −0.587431 | − | 1.64394i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.245049 | + | 0.424436i | 0.0117223 | + | 0.0203036i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.8768 | − | 10.3212i | −0.853214 | − | 0.492603i | 0.00852006 | − | 0.999964i | \(-0.497288\pi\) |
−0.861734 | + | 0.507360i | \(0.830621\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.3655 | − | 11.8084i | 0.826929 | − | 0.562306i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.25880 | + | 0.726768i | 0.0598073 | + | 0.0345298i | 0.529605 | − | 0.848244i | \(-0.322340\pi\) |
−0.469798 | + | 0.882774i | \(0.655673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.8331 | + | 27.4238i | 0.750562 | + | 1.30001i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.5970 | + | 5.94537i | 1.54178 | + | 0.281207i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.09933i | 0.429424i | 0.976677 | + | 0.214712i | \(0.0688813\pi\) | ||||
−0.976677 | + | 0.214712i | \(0.931119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.51551 | − | 2.02968i | −0.165539 | − | 0.0955740i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.44928 | + | 13.4288i | −0.115077 | + | 0.630938i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0174149 | − | 0.390162i | 0.000816421 | − | 0.0182911i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.23209 | − | 12.5264i | 0.338303 | − | 0.585958i | −0.645811 | − | 0.763498i | \(-0.723480\pi\) |
0.984114 | + | 0.177540i | \(0.0568138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.05240 | − | 16.3375i | −0.422530 | − | 0.762570i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.2769 | − | 22.9963i | −0.618369 | − | 1.07105i | −0.989783 | − | 0.142579i | \(-0.954461\pi\) |
0.371415 | − | 0.928467i | \(-0.378873\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.4968 | − | 26.8412i | 0.720196 | − | 1.24742i | −0.240725 | − | 0.970593i | \(-0.577385\pi\) |
0.960921 | − | 0.276823i | \(-0.0892816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.0008 | + | 30.7860i | 0.510150 | + | 1.42767i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.1348 | − | 17.5541i | −0.468985 | − | 0.812306i | 0.530387 | − | 0.847756i | \(-0.322047\pi\) |
−0.999371 | + | 0.0354503i | \(0.988713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.1986 | − | 31.6376i | 0.932686 | − | 1.46089i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.6328 | − | 32.5546i | −0.536010 | − | 1.50004i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.30559 | − | 4.21789i | 0.335911 | − | 0.193939i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.5969 | − | 6.11811i | 0.486218 | − | 0.280718i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5807 | + | 14.1354i | 0.530245 | + | 0.647215i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0258 | 0.732236 | 0.366118 | − | 0.930568i | \(-0.380687\pi\) | ||||
0.366118 | + | 0.930568i | \(0.380687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.219817i | 0.0100228i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.144130 | − | 0.468276i | −0.00655812 | − | 0.0213073i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 39.7538 | − | 22.9519i | 1.80513 | − | 1.04219i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.54048 | − | 14.7925i | 0.387006 | − | 0.670314i | −0.605039 | − | 0.796196i | \(-0.706843\pi\) |
0.992045 | + | 0.125881i | \(0.0401759\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 39.2830 | − | 14.0371i | 1.77644 | − | 0.634778i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9745 | + | 7.49082i | 0.585530 | + | 0.338056i | 0.763328 | − | 0.646011i | \(-0.223564\pi\) |
−0.177798 | + | 0.984067i | \(0.556897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.2852i | 1.22886i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.09579 | + | 18.8051i | −0.318932 | + | 0.845227i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.29334 | + | 1.71034i | −0.147726 | + | 0.0767191i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.3276 | 1.13382 | 0.566910 | − | 0.823780i | \(-0.308139\pi\) | ||||
0.566910 | + | 0.823780i | \(0.308139\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.09575 | − | 1.77963i | −0.0936312 | − | 0.0795079i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.95401 | −0.443827 | −0.221914 | − | 0.975066i | \(-0.571230\pi\) | ||||
−0.221914 | + | 0.975066i | \(0.571230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.0783 | −1.29397 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.1990 | + | 7.57507i | −0.941480 | + | 0.336421i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.6595 | −0.516800 | −0.258400 | − | 0.966038i | \(-0.583195\pi\) | ||||
−0.258400 | + | 0.966038i | \(0.583195\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.754924 | − | 16.9133i | 0.0333959 | − | 0.748199i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.419744 | + | 23.8150i | −0.0185321 | + | 1.05146i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 42.7230i | 1.88260i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27.6430 | − | 15.9597i | −1.21574 | − | 0.701906i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.59411 | − | 4.75029i | −0.245554 | − | 0.208515i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.59307 | + | 14.8836i | −0.376469 | + | 0.652064i | −0.990546 | − | 0.137183i | \(-0.956195\pi\) |
0.614077 | + | 0.789246i | \(0.289529\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.1175 | + | 22.0071i | −1.66676 | + | 0.962305i | −0.697394 | + | 0.716688i | \(0.745657\pi\) |
−0.969367 | + | 0.245616i | \(0.921010\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.6914 | + | 3.59847i | −0.510255 | + | 0.157050i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24.4991i | − | 1.06720i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9886 | 0.999503 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.59376 | + | 27.9703i | 0.199352 | + | 1.21381i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0774562 | − | 0.0447194i | 0.00335500 | − | 0.00193701i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.0408 | − | 15.6120i | 1.16908 | − | 0.674966i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.37602 | + | 5.15336i | −0.188839 | + | 0.222384i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.8532 | + | 9.74030i | 0.596699 | + | 0.419544i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.06580 | − | 8.77423i | −0.217796 | − | 0.377234i | 0.736338 | − | 0.676614i | \(-0.236553\pi\) |
−0.954134 | + | 0.299380i | \(0.903220\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.1870 | − | 4.77626i | −1.12379 | − | 0.204969i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.3296 | + | 38.6760i | −0.956495 | + | 1.65670i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0000 | + | 29.4449i | 0.726869 | + | 1.25897i | 0.958200 | + | 0.286099i | \(0.0923585\pi\) |
−0.231331 | + | 0.972875i | \(0.574308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.04772 | − | 6.16122i | −0.215431 | − | 0.262954i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.3976 | − | 30.1335i | 0.741162 | − | 1.28373i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.1575 | + | 0.498014i | 0.474465 | + | 0.0211777i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.6278 | − | 6.65631i | 0.790706 | − | 0.282544i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.88366 | + | 1.08753i | 0.0798133 | + | 0.0460802i | 0.539376 | − | 0.842065i | \(-0.318660\pi\) |
−0.459562 | + | 0.888146i | \(0.651994\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.185863i | 0.00786116i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.74932 | − | 11.4811i | 0.411617 | − | 0.484734i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.24777 | − | 3.89326i | −0.0947324 | − | 0.164081i | 0.814765 | − | 0.579792i | \(-0.196866\pi\) |
−0.909497 | + | 0.415711i | \(0.863533\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.5517 | + | 18.7937i | 1.36946 | + | 0.790657i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.72107 | − | 23.1143i | 0.240262 | − | 0.970708i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.30272 | + | 3.06153i | 0.222302 | + | 0.128346i | 0.607016 | − | 0.794690i | \(-0.292367\pi\) |
−0.384714 | + | 0.923036i | \(0.625700\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.1829 | + | 28.0296i | 0.677233 | + | 1.17300i | 0.975811 | + | 0.218616i | \(0.0701543\pi\) |
−0.298578 | + | 0.954385i | \(0.596512\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.95696 | + | 3.48222i | −0.123529 | + | 0.145472i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.285403i | 0.0119021i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.2034 | − | 19.7473i | −1.42390 | − | 0.822092i | −0.427274 | − | 0.904122i | \(-0.640526\pi\) |
−0.996630 | + | 0.0820304i | \(0.973860\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.1665 | − | 4.34747i | 0.505621 | − | 0.180675i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.5527 | − | 30.6258i | 0.811181 | − | 1.27057i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.36803 | + | 12.7618i | −0.305152 | + | 0.528540i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.280648 | − | 0.342558i | −0.0116034 | − | 0.0141630i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.129711 | + | 0.224667i | 0.00535376 | + | 0.00927298i | 0.868690 | − | 0.495356i | \(-0.164963\pi\) |
−0.863336 | + | 0.504629i | \(0.831629\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6211 | + | 27.0565i | −0.643656 | + | 1.11485i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.73304 | − | 0.863261i | −0.194691 | − | 0.0355098i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.13549 | + | 5.43083i | 0.128759 | + | 0.223017i | 0.923196 | − | 0.384329i | \(-0.125567\pi\) |
−0.794437 | + | 0.607347i | \(0.792234\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.3112 | + | 1.17440i | 1.07866 | + | 0.0481458i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.52954 | + | 5.33414i | −0.185382 | + | 0.218312i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.52001 | − | 3.18698i | 0.225542 | − | 0.130217i | −0.382972 | − | 0.923760i | \(-0.625099\pi\) |
0.608514 | + | 0.793543i | \(0.291766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.0862 | + | 8.71001i | −0.615378 | + | 0.355289i | −0.775067 | − | 0.631879i | \(-0.782284\pi\) |
0.159689 | + | 0.987167i | \(0.448951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.89775 | − | 41.9987i | −0.280898 | − | 1.71032i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.2546 | 0.579534 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.80344i | − | 0.0731996i | −0.999330 | − | 0.0365998i | \(-0.988347\pi\) | ||
0.999330 | − | 0.0365998i | \(-0.0116527\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.6755 | + | 25.4848i | −0.959380 | + | 1.03269i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.609050 | − | 0.351635i | 0.0246395 | − | 0.0142256i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6290 | + | 30.5343i | −0.712028 | + | 1.23327i | 0.252066 | + | 0.967710i | \(0.418890\pi\) |
−0.964095 | + | 0.265559i | \(0.914443\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.13507 | − | 5.20966i | −0.247390 | − | 0.210074i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.73458 | − | 4.46556i | −0.311383 | − | 0.179777i | 0.336162 | − | 0.941804i | \(-0.390871\pi\) |
−0.647545 | + | 0.762027i | \(0.724204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.5146i | 1.54803i | 0.633166 | + | 0.774016i | \(0.281755\pi\) | ||||
−0.633166 | + | 0.774016i | \(0.718245\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.476156 | − | 0.286214i | −0.0191075 | − | 0.0114854i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.2796 | − | 25.4991i | 0.652228 | − | 1.02160i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2213 | −1.24885 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.0876 | + | 6.46329i | −0.722351 | + | 0.258119i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14.8238 | −0.591063 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5826 | −0.978616 | −0.489308 | − | 0.872111i | \(-0.662751\pi\) | ||||
−0.489308 | + | 0.872111i | \(0.662751\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 27.6872 | + | 23.5108i | 1.10047 | + | 0.934472i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.5628 | −1.01443 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.338465 | + | 0.157028i | −0.0134105 | + | 0.00622169i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.48553 | + | 3.93690i | −0.0587665 | + | 0.155742i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 33.6752i | − | 1.33009i | −0.746804 | − | 0.665044i | \(-0.768413\pi\) | ||
0.746804 | − | 0.665044i | \(-0.231587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.02496 | + | 1.16911i | 0.0798567 | + | 0.0461053i | 0.539397 | − | 0.842052i | \(-0.318652\pi\) |
−0.459540 | + | 0.888157i | \(0.651986\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.7504 | − | 5.62812i | 0.620172 | − | 0.221607i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.89769 | − | 3.28689i | 0.0746059 | − | 0.129221i | −0.826309 | − | 0.563217i | \(-0.809563\pi\) |
0.900915 | + | 0.433996i | \(0.142897\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.7955 | + | 11.4289i | −0.777040 | + | 0.448624i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.2580 | − | 22.8825i | 0.833165 | − | 0.896835i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.7151i | 0.458447i | 0.973374 | + | 0.229224i | \(0.0736187\pi\) | ||||
−0.973374 | + | 0.229224i | \(0.926381\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.83094 | −0.345053 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.1659 | − | 14.8497i | −0.474638 | − | 0.579341i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.4962 | − | 12.9882i | 0.876329 | − | 0.505949i | 0.00688257 | − | 0.999976i | \(-0.497809\pi\) |
0.869446 | + | 0.494028i | \(0.164476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.94177 | − | 3.43048i | 0.231108 | − | 0.133430i | −0.379975 | − | 0.924997i | \(-0.624067\pi\) |
0.611083 | + | 0.791566i | \(0.290734\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.111668 | + | 0.312506i | 0.00433683 | + | 0.0121367i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28.3090 | − | 18.0736i | −1.09778 | − | 0.700862i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.405789 | + | 0.702846i | 0.0157122 | + | 0.0272143i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.93807 | + | 16.6178i | 0.229579 | + | 0.642482i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.21152 | − | 5.56251i | 0.123979 | − | 0.214738i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.652179 | − | 1.12961i | −0.0251397 | − | 0.0435432i | 0.853182 | − | 0.521614i | \(-0.174670\pi\) |
−0.878322 | + | 0.478070i | \(0.841336\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.14588 | + | 11.8882i | −0.275045 | + | 0.457575i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.61516 | + | 11.4578i | −0.254241 | + | 0.440359i | −0.964689 | − | 0.263391i | \(-0.915159\pi\) |
0.710448 | + | 0.703750i | \(0.248492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −36.9638 | − | 23.5991i | −1.41854 | − | 0.905651i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.12741 | + | 17.1468i | −0.119843 | + | 0.657067i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.49949 | − | 0.865733i | −0.0573765 | − | 0.0331264i | 0.471037 | − | 0.882113i | \(-0.343880\pi\) |
−0.528414 | + | 0.848987i | \(0.677213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 15.5894i | − | 0.595642i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.4833 | − | 4.64791i | −0.972248 | − | 0.177329i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.162338 | − | 0.281177i | −0.00618457 | − | 0.0107120i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.27541 | − | 4.20046i | −0.276770 | − | 0.159793i | 0.355190 | − | 0.934794i | \(-0.384416\pi\) |
−0.631960 | + | 0.775001i | \(0.717749\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.0682 | − | 2.26401i | 0.724342 | − | 0.0860024i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −51.7150 | − | 29.8576i | −1.96166 | − | 1.13256i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.01573 | + | 5.22340i | 0.114229 | + | 0.197850i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.63717 | − | 26.9698i | −0.364511 | − | 1.02009i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.3493i | − | 0.806353i | −0.915122 | − | 0.403176i | \(-0.867906\pi\) | ||
0.915122 | − | 0.403176i | \(-0.132094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3712 | + | 9.45193i | 0.617452 | + | 0.356486i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −48.2410 | − | 40.9643i | −1.81686 | − | 1.54281i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.8036 | + | 24.6539i | 0.481528 | + | 0.927207i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.63087 | − | 16.6812i | 0.361695 | − | 0.626474i | −0.626545 | − | 0.779385i | \(-0.715532\pi\) |
0.988240 | + | 0.152911i | \(0.0488648\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.79616 | − | 8.02573i | 0.367385 | − | 0.300988i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.364353 | − | 0.631078i | −0.0136451 | − | 0.0236341i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.178557 | − | 0.309270i | 0.00667766 | − | 0.0115660i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.6789 | − | 13.7534i | 0.436155 | − | 0.513632i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.39920 | − | 9.35168i | −0.201356 | − | 0.348759i | 0.747610 | − | 0.664138i | \(-0.231201\pi\) |
−0.948966 | + | 0.315380i | \(0.897868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.2225 | − | 18.8115i | 1.34900 | − | 0.700577i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.6620 | − | 3.22138i | −0.656857 | − | 0.119804i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.5479 | − | 10.1313i | 0.651713 | − | 0.376267i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.9316 | − | 14.9716i | 0.961751 | − | 0.555267i | 0.0650393 | − | 0.997883i | \(-0.479283\pi\) |
0.896711 | + | 0.442616i | \(0.145949\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.6676 | − | 23.8439i | −0.469171 | − | 0.883107i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.5340 | −0.463586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.0355i | 0.592286i | 0.955144 | + | 0.296143i | \(0.0957004\pi\) | ||||
−0.955144 | + | 0.296143i | \(0.904300\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 23.5560 | + | 23.9273i | 0.868876 | + | 0.882571i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.7238 | − | 17.1610i | 1.09489 | − | 0.632135i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5186 | − | 19.9508i | 0.423719 | − | 0.733903i | −0.572581 | − | 0.819848i | \(-0.694058\pi\) |
0.996300 | + | 0.0859453i | \(0.0273910\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0759346 | − | 0.416330i | 0.00278953 | − | 0.0152943i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.2352 | + | 21.4978i | 1.36603 | + | 0.788676i | 0.990418 | − | 0.138102i | \(-0.0441001\pi\) |
0.375609 | + | 0.926778i | \(0.377433\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 52.9789i | 1.94100i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.67716 | − | 40.6556i | −0.244304 | − | 1.48751i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.1430 | − | 16.0523i | −0.918706 | − | 0.586537i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.3800 | 1.29104 | 0.645518 | − | 0.763745i | \(-0.276642\pi\) | ||||
0.645518 | + | 0.763745i | \(0.276642\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.07144 | + | 22.3227i | −0.148372 | + | 0.813483i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.8254 | −0.794307 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.6138 | −0.894604 | −0.447302 | − | 0.894383i | \(-0.647615\pi\) | ||||
−0.447302 | + | 0.894383i | \(0.647615\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0803864 | − | 0.440738i | 0.00291784 | − | 0.0159978i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.7853 | 0.499716 | 0.249858 | − | 0.968283i | \(-0.419616\pi\) | ||||
0.249858 | + | 0.968283i | \(0.419616\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.6233 | + | 1.90249i | 1.54307 | + | 0.0688748i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23.1010 | − | 18.9260i | 0.835218 | − | 0.684271i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.503620i | − | 0.0181847i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.0352 | − | 11.5673i | −0.722486 | − | 0.417128i | 0.0931808 | − | 0.995649i | \(-0.470297\pi\) |
−0.815667 | + | 0.578522i | \(0.803630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.275611 | − | 1.51111i | 0.00992591 | − | 0.0544212i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.5072 | − | 45.9118i | 0.953398 | − | 1.65133i | 0.215405 | − | 0.976525i | \(-0.430893\pi\) |
0.737993 | − | 0.674808i | \(-0.235774\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.7561 | + | 9.09678i | −0.565975 | + | 0.326766i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.8456 | − | 12.8627i | −0.496708 | − | 0.461445i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 7.69155i | − | 0.275578i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.39327 | −0.121421 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.695075 | + | 39.4364i | −0.0248400 | + | 1.40934i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.8693 | − | 27.6373i | 1.70853 | − | 0.986418i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.16436 | − | 2.98164i | 0.184089 | − | 0.106284i | −0.405123 | − | 0.914262i | \(-0.632771\pi\) |
0.589213 | + | 0.807978i | \(0.299438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.1404 | − | 2.21430i | −0.432211 | − | 0.0788312i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.60123 | − | 35.8739i | 0.0569333 | − | 1.27553i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0707584 | + | 0.122557i | 0.00251271 | + | 0.00435213i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.9118 | + | 22.2712i | −0.670732 | + | 0.789877i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.28758 | − | 9.15836i | 0.187296 | − | 0.324406i | −0.757052 | − | 0.653355i | \(-0.773361\pi\) |
0.944348 | + | 0.328949i | \(0.106694\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7131 | + | 41.0724i | 0.838910 | + | 1.45304i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.55942 | − | 33.8499i | −0.196432 | − | 1.19603i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.74035 | − | 13.4067i | 0.273151 | − | 0.473111i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.695223 | − | 0.361052i | 0.0245034 | − | 0.0127254i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −41.7168 | − | 35.4243i | −1.46850 | − | 1.24699i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.1452 | − | 18.5591i | −1.13017 | − | 0.652501i | −0.186189 | − | 0.982514i | \(-0.559614\pi\) |
−0.943977 | + | 0.330012i | \(0.892947\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.02945i | − | 0.246837i | −0.992355 | − | 0.123419i | \(-0.960614\pi\) | ||
0.992355 | − | 0.123419i | \(-0.0393858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.6477 | + | 29.7978i | 0.373431 | + | 1.04505i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.3494 | + | 57.7629i | 1.16818 | + | 2.02335i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8424 | + | 7.99192i | 0.484284 | + | 0.279602i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.166863 | + | 0.388779i | −0.00583066 | + | 0.0135851i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5657 | + | 10.7189i | 0.647947 | + | 0.374092i | 0.787669 | − | 0.616099i | \(-0.211288\pi\) |
−0.139722 | + | 0.990191i | \(0.544621\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.72455 | + | 16.8434i | 0.338977 | + | 0.587125i | 0.984240 | − | 0.176835i | \(-0.0565859\pi\) |
−0.645264 | + | 0.763960i | \(0.723253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.0039 | − | 2.00700i | −0.383106 | − | 0.0698748i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.3789i | 0.569549i | 0.958595 | + | 0.284774i | \(0.0919187\pi\) | ||||
−0.958595 | + | 0.284774i | \(0.908081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.5517 | − | 7.82408i | −0.470670 | − | 0.271741i | 0.245850 | − | 0.969308i | \(-0.420933\pi\) |
−0.716520 | + | 0.697566i | \(0.754266\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.50032 | + | 52.0878i | −0.329562 | + | 1.80691i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.5895 | − | 22.8250i | −0.366904 | − | 0.790839i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.19801 | − | 3.80706i | 0.0760651 | − | 0.131749i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.624100 | − | 35.4095i | 0.0215721 | − | 1.22393i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.260756 | + | 0.451642i | 0.00900229 | + | 0.0155924i | 0.870491 | − | 0.492184i | \(-0.163801\pi\) |
−0.861489 | + | 0.507776i | \(0.830468\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3096 | − | 24.7849i | 0.493433 | − | 0.854652i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.63971 | − | 7.38728i | −0.0909164 | − | 0.254431i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.9969 | − | 31.1716i | −0.619114 | − | 1.07234i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.27652 | − | 12.0858i | −0.215664 | − | 0.415271i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.45612 | + | 15.2691i | 0.187253 | + | 0.524033i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.381849 | + | 0.220461i | −0.0130896 | + | 0.00755730i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.3460 | − | 8.85999i | 0.525436 | − | 0.303360i | −0.213720 | − | 0.976895i | \(-0.568558\pi\) |
0.739156 | + | 0.673535i | \(0.235225\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −37.5801 | + | 6.17205i | −1.28521 | + | 0.211080i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.82727 | −0.0965777 | −0.0482888 | − | 0.998833i | \(-0.515377\pi\) | ||||
−0.0482888 | + | 0.998833i | \(0.515377\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.21152i | − | 0.314293i | −0.987575 | − | 0.157147i | \(-0.949770\pi\) | ||
0.987575 | − | 0.157147i | \(-0.0502295\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.71563 | + | 7.49548i | −0.0584686 | + | 0.255445i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.7016 | + | 9.06534i | −0.534490 | + | 0.308588i | −0.742843 | − | 0.669466i | \(-0.766523\pi\) |
0.208353 | + | 0.978054i | \(0.433190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.86705 | − | 10.1620i | 0.199486 | − | 0.345520i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.65342 | − | 2.37748i | 0.225962 | − | 0.0807434i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.84423 | + | 5.10622i | 0.300020 | + | 0.173217i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.756208i | 0.0256231i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −49.0693 | + | 8.05900i | −1.66074 | + | 0.272756i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.87033 | + | 15.1547i | 0.266066 | + | 0.512323i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2086 | 0.479792 | 0.239896 | − | 0.970799i | \(-0.422887\pi\) | ||||
0.239896 | + | 0.970799i | \(0.422887\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.5802 | + | 18.3250i | 0.727881 | + | 0.618087i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0649 | 1.55197 | 0.775984 | − | 0.630753i | \(-0.217254\pi\) | ||||
0.775984 | + | 0.630753i | \(0.217254\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.16154 | 0.274658 | 0.137329 | − | 0.990526i | \(-0.456148\pi\) | ||||
0.137329 | + | 0.990526i | \(0.456148\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −42.6778 | + | 15.2501i | −1.43460 | + | 0.512628i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.1287 | 0.910893 | 0.455446 | − | 0.890263i | \(-0.349480\pi\) | ||||
0.455446 | + | 0.890263i | \(0.349480\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.2557 | + | 21.6733i | 0.377503 | + | 0.726900i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.3836 | − | 16.3458i | 0.481868 | − | 0.547605i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 60.4798i | − | 2.02388i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.36139 | − | 5.40480i | −0.312917 | − | 0.180662i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.00752410 | + | 0.00638917i | 0.000251223 | + | 0.000213328i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.8678 | + | 44.8043i | −0.862739 | + | 1.49431i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.9617 | − | 10.9475i | 0.631704 | − | 0.364715i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.7069 | − | 10.8758i | −0.389582 | − | 0.361924i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 42.5610i | − | 1.41478i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.5851 | −0.849541 | −0.424770 | − | 0.905301i | \(-0.639645\pi\) | ||||
−0.424770 | + | 0.905301i | \(0.639645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.4717 | + | 11.1206i | 0.977514 | + | 0.368849i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.57426 | − | 2.64095i | 0.151552 | − | 0.0874986i | −0.422306 | − | 0.906453i | \(-0.638779\pi\) |
0.573858 | + | 0.818955i | \(0.305446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.7732 | − | 16.6122i | 0.952255 | − | 0.549785i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.24312 | − | 9.70738i | 0.272509 | − | 0.320916i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.88838 | + | 7.48728i | 0.128406 | + | 0.247252i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7214 | − | 48.0149i | −0.914445 | − | 1.58387i | −0.807712 | − | 0.589578i | \(-0.799294\pi\) |
−0.106733 | − | 0.994288i | \(-0.534039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.67845 | − | 0.306133i | −0.0553069 | − | 0.0100874i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0373815 | − | 0.0647466i | 0.00123043 | − | 0.00213116i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.50423 | + | 9.53360i | 0.180978 | + | 0.313463i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.3389 | − | 43.3009i | 0.536639 | − | 1.42219i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.6004 | + | 30.4849i | −0.577452 | + | 1.00018i | 0.418319 | + | 0.908300i | \(0.362620\pi\) |
−0.995770 | + | 0.0918756i | \(0.970714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.85874 | + | 31.9597i | −0.0936914 | + | 1.04744i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.8319 | + | 15.3052i | −1.40225 | + | 0.501070i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.8562 | + | 12.0413i | 0.682070 | + | 0.393793i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.6315i | 1.55605i | 0.628231 | + | 0.778027i | \(0.283779\pi\) | ||||
−0.628231 | + | 0.778027i | \(0.716221\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.2930 | + | 19.1872i | −0.531702 | + | 0.626151i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.3802 | + | 17.9790i | 0.338384 | + | 0.586098i | 0.984129 | − | 0.177455i | \(-0.0567865\pi\) |
−0.645745 | + | 0.763553i | \(0.723453\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.155366 | + | 0.0897005i | 0.00505941 | + | 0.00292105i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 37.9988 | + | 2.36767i | 1.23610 | + | 0.0770205i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.50667 | − | 3.75663i | −0.211438 | − | 0.122074i | 0.390541 | − | 0.920585i | \(-0.372288\pi\) |
−0.601980 | + | 0.798511i | \(0.705621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.170541 | + | 0.295385i | 0.00553599 | + | 0.00958861i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.0303 | + | 38.8976i | −1.07108 | + | 1.26134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.6047i | 1.73643i | 0.496192 | + | 0.868213i | \(0.334731\pi\) | ||||
−0.496192 | + | 0.868213i | \(0.665269\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.32566 | − | 3.65212i | −0.204694 | − | 0.118180i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.9523 | + | 10.7029i | −0.968219 | + | 0.345975i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.2175 | + | 6.86425i | −0.426814 | + | 0.221658i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.72640 | − | 13.3825i | 0.249239 | − | 0.431694i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.3772 | + | 5.48178i | −1.07557 | + | 0.176648i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.3288 | + | 17.8899i | 0.332495 | + | 0.575898i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.72860 | + | 9.92223i | −0.184220 | + | 0.319078i | −0.943313 | − | 0.331904i | \(-0.892309\pi\) |
0.759094 | + | 0.650981i | \(0.225642\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.0759 | + | 5.12078i | 0.901929 | + | 0.164503i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.02601 | − | 6.97326i | −0.129201 | − | 0.223782i | 0.794166 | − | 0.607700i | \(-0.207908\pi\) |
−0.923367 | + | 0.383918i | \(0.874575\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.54388 | + | 56.9931i | −0.0815532 | + | 1.82711i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.159518 | − | 0.187854i | 0.00510866 | − | 0.00601614i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.4615 | + | 23.9378i | −1.32647 | + | 0.765838i | −0.984752 | − | 0.173965i | \(-0.944342\pi\) |
−0.341718 | + | 0.939802i | \(0.611009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.9567 | − | 13.8314i | 0.765658 | − | 0.442053i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.4228 | − | 30.6595i | 1.19482 | − | 0.978883i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.36180 | 0.0753297 | 0.0376648 | − | 0.999290i | \(-0.488008\pi\) | ||||
0.0376648 | + | 0.999290i | \(0.488008\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 7.69247i | − | 0.245102i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.4903 | + | 58.9381i | −0.429400 | + | 1.87602i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.322866 | + | 0.186407i | −0.0102665 | + | 0.00592739i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8241 | + | 20.4800i | −0.375606 | + | 0.650568i | −0.990417 | − | 0.138106i | \(-0.955899\pi\) |
0.614812 | + | 0.788674i | \(0.289232\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.68434 | − | 6.52523i | −0.243855 | − | 0.207072i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.68979 | − | 5.59440i | −0.307187 | − | 0.177355i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4290i | 1.34374i | 0.740670 | + | 0.671869i | \(0.234508\pi\) | ||||
−0.740670 | + | 0.671869i | \(0.765492\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.4254 | − | 0.377627i | −0.677870 | − | 0.0119476i |
(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 | 504.2.cx.a.185.14 | yes | 48 | |
3.2 | odd | 2 | 1512.2.cx.a.17.4 | 48 | |||
4.3 | odd | 2 | 1008.2.df.e.689.11 | 48 | |||
7.5 | odd | 6 | 504.2.bs.a.257.6 | ✓ | 48 | ||
9.2 | odd | 6 | 504.2.bs.a.353.6 | yes | 48 | ||
9.7 | even | 3 | 1512.2.bs.a.521.4 | 48 | |||
12.11 | even | 2 | 3024.2.df.e.17.4 | 48 | |||
21.5 | even | 6 | 1512.2.bs.a.1097.4 | 48 | |||
28.19 | even | 6 | 1008.2.ca.e.257.19 | 48 | |||
36.7 | odd | 6 | 3024.2.ca.e.2033.4 | 48 | |||
36.11 | even | 6 | 1008.2.ca.e.353.19 | 48 | |||
63.47 | even | 6 | inner | 504.2.cx.a.425.14 | yes | 48 | |
63.61 | odd | 6 | 1512.2.cx.a.89.4 | 48 | |||
84.47 | odd | 6 | 3024.2.ca.e.2609.4 | 48 | |||
252.47 | odd | 6 | 1008.2.df.e.929.11 | 48 | |||
252.187 | even | 6 | 3024.2.df.e.1601.4 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.6 | ✓ | 48 | 7.5 | odd | 6 | ||
504.2.bs.a.353.6 | yes | 48 | 9.2 | odd | 6 | ||
504.2.cx.a.185.14 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.cx.a.425.14 | yes | 48 | 63.47 | even | 6 | inner | |
1008.2.ca.e.257.19 | 48 | 28.19 | even | 6 | |||
1008.2.ca.e.353.19 | 48 | 36.11 | even | 6 | |||
1008.2.df.e.689.11 | 48 | 4.3 | odd | 2 | |||
1008.2.df.e.929.11 | 48 | 252.47 | odd | 6 | |||
1512.2.bs.a.521.4 | 48 | 9.7 | even | 3 | |||
1512.2.bs.a.1097.4 | 48 | 21.5 | even | 6 | |||
1512.2.cx.a.17.4 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.89.4 | 48 | 63.61 | odd | 6 | |||
3024.2.ca.e.2033.4 | 48 | 36.7 | odd | 6 | |||
3024.2.ca.e.2609.4 | 48 | 84.47 | odd | 6 | |||
3024.2.df.e.17.4 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.1601.4 | 48 | 252.187 | even | 6 |