Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.3 | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.e.1601.3 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.295801 | + | 2.62916i | −0.111802 | + | 0.993730i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.570938 | + | 0.329631i | 0.172144 | + | 0.0993876i | 0.583597 | − | 0.812044i | \(-0.301645\pi\) |
−0.411452 | + | 0.911431i | \(0.634978\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.13514i | − | 1.70158i | −0.525504 | − | 0.850791i | \(-0.676123\pi\) | ||
0.525504 | − | 0.850791i | \(-0.323877\pi\) | |||||||
\(14\) | −1.05841 | − | 2.42482i | −0.282872 | − | 0.648061i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.43678 | − | 4.22062i | 0.591005 | − | 1.02365i | −0.403092 | − | 0.915160i | \(-0.632064\pi\) |
0.994097 | − | 0.108492i | \(-0.0346022\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.30208 | + | 3.63851i | −1.44580 | + | 0.834732i | −0.998227 | − | 0.0595173i | \(-0.981044\pi\) |
−0.447570 | + | 0.894249i | \(0.647711\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.659263 | −0.140555 | ||||||||
\(23\) | 3.98266 | − | 2.29939i | 0.830442 | − | 0.479456i | −0.0235617 | − | 0.999722i | \(-0.507501\pi\) |
0.854004 | + | 0.520266i | \(0.174167\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.06757 | + | 5.31319i | 0.601600 | + | 1.04200i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.12902 | + | 1.57075i | 0.402347 | + | 0.296844i | ||||
\(29\) | 8.09526i | 1.50325i | 0.659589 | + | 0.751626i | \(0.270730\pi\) | ||||
−0.659589 | + | 0.751626i | \(0.729270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.759345 | + | 0.438408i | 0.136382 | + | 0.0787404i | 0.566639 | − | 0.823966i | \(-0.308243\pi\) |
−0.430256 | + | 0.902707i | \(0.641577\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.87356i | 0.835808i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.05533 | − | 8.75609i | −0.831092 | − | 1.43949i | −0.897173 | − | 0.441679i | \(-0.854383\pi\) |
0.0660818 | − | 0.997814i | \(-0.478950\pi\) | |||||||
\(38\) | 3.63851 | − | 6.30208i | 0.590244 | − | 1.02233i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.25234 | −0.976451 | −0.488226 | − | 0.872717i | \(-0.662356\pi\) | ||||
−0.488226 | + | 0.872717i | \(0.662356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.03582 | −1.37795 | −0.688975 | − | 0.724785i | \(-0.741939\pi\) | ||||
−0.688975 | + | 0.724785i | \(0.741939\pi\) | |||||||
\(44\) | 0.570938 | − | 0.329631i | 0.0860722 | − | 0.0496938i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.29939 | + | 3.98266i | −0.339027 | + | 0.587211i | ||||
\(47\) | 6.00136 | + | 10.3947i | 0.875388 | + | 1.51622i | 0.856349 | + | 0.516397i | \(0.172727\pi\) |
0.0190383 | + | 0.999819i | \(0.493940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.82500 | − | 1.55542i | −0.975001 | − | 0.222202i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.31319 | − | 3.06757i | −0.736807 | − | 0.425396i | ||||
\(53\) | −10.5749 | − | 6.10540i | −1.45257 | − | 0.838641i | −0.453943 | − | 0.891031i | \(-0.649983\pi\) |
−0.998627 | + | 0.0523897i | \(0.983316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.62916 | − | 0.295801i | −0.351337 | − | 0.0395280i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.04763 | − | 7.01070i | −0.531480 | − | 0.920550i | ||||
\(59\) | 4.06613 | − | 7.04274i | 0.529365 | − | 0.916887i | −0.470049 | − | 0.882640i | \(-0.655764\pi\) |
0.999413 | − | 0.0342461i | \(-0.0109030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0618764 | + | 0.0357243i | −0.00792246 | + | 0.00457403i | −0.503956 | − | 0.863729i | \(-0.668123\pi\) |
0.496034 | + | 0.868303i | \(0.334789\pi\) | |||||||
\(62\) | −0.876816 | −0.111356 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.666965 | + | 1.15522i | −0.0814827 | + | 0.141132i | −0.903887 | − | 0.427771i | \(-0.859299\pi\) |
0.822404 | + | 0.568903i | \(0.192632\pi\) | |||||||
\(68\) | −2.43678 | − | 4.22062i | −0.295503 | − | 0.511826i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.60701i | 0.309395i | 0.987962 | + | 0.154697i | \(0.0494402\pi\) | ||||
−0.987962 | + | 0.154697i | \(0.950560\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.44571 | − | 1.41203i | −0.286249 | − | 0.165266i | 0.350000 | − | 0.936750i | \(-0.386181\pi\) |
−0.636249 | + | 0.771484i | \(0.719515\pi\) | |||||||
\(74\) | 8.75609 | + | 5.05533i | 1.01788 | + | 0.587670i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.27702i | 0.834732i | ||||||||
\(77\) | −1.03554 | + | 1.40359i | −0.118011 | + | 0.159953i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.88837 | − | 5.00280i | −0.324967 | − | 0.562859i | 0.656539 | − | 0.754292i | \(-0.272020\pi\) |
−0.981506 | + | 0.191433i | \(0.938686\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.41468 | − | 3.12617i | 0.597952 | − | 0.345228i | ||||
\(83\) | 7.44660 | 0.817370 | 0.408685 | − | 0.912675i | \(-0.365987\pi\) | ||||
0.408685 | + | 0.912675i | \(0.365987\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.82525 | − | 4.51791i | 0.843819 | − | 0.487179i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.329631 | + | 0.570938i | −0.0351388 | + | 0.0608622i | ||||
\(89\) | −2.66489 | − | 4.61572i | −0.282478 | − | 0.489266i | 0.689517 | − | 0.724270i | \(-0.257823\pi\) |
−0.971994 | + | 0.235004i | \(0.924490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.1303 | + | 1.81478i | 1.69091 | + | 0.190241i | ||||
\(92\) | − | 4.59878i | − | 0.479456i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.3947 | − | 6.00136i | −1.07213 | − | 0.618993i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4792i | 1.16553i | 0.812640 | + | 0.582766i | \(0.198030\pi\) | ||||
−0.812640 | + | 0.582766i | \(0.801970\pi\) | |||||||
\(98\) | 6.68833 | − | 2.06547i | 0.675624 | − | 0.208644i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.74874 | + | 13.4212i | −0.771029 | + | 1.33546i | 0.165971 | + | 0.986131i | \(0.446924\pi\) |
−0.937000 | + | 0.349330i | \(0.886409\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.79131 | + | 1.03422i | −0.176503 | + | 0.101904i | −0.585649 | − | 0.810565i | \(-0.699160\pi\) |
0.409145 | + | 0.912469i | \(0.365827\pi\) | |||||||
\(104\) | 6.13514 | 0.601600 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.2108 | 1.18602 | ||||||||
\(107\) | 9.43331 | − | 5.44632i | 0.911953 | − | 0.526516i | 0.0308937 | − | 0.999523i | \(-0.490165\pi\) |
0.881059 | + | 0.473007i | \(0.156831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.17254 | − | 12.4232i | 0.687005 | − | 1.18993i | −0.285797 | − | 0.958290i | \(-0.592258\pi\) |
0.972802 | − | 0.231637i | \(-0.0744082\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.42482 | − | 1.05841i | 0.229124 | − | 0.100010i | ||||
\(113\) | − | 11.9081i | − | 1.12022i | −0.828420 | − | 0.560108i | \(-0.810760\pi\) | ||
0.828420 | − | 0.560108i | \(-0.189240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.01070 | + | 4.04763i | 0.650927 | + | 0.375813i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.13225i | 0.748635i | ||||||||
\(119\) | 10.3759 | + | 7.65515i | 0.951158 | + | 0.701747i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.28269 | − | 9.14988i | −0.480244 | − | 0.831807i | ||||
\(122\) | 0.0357243 | − | 0.0618764i | 0.00323433 | − | 0.00560202i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.759345 | − | 0.438408i | 0.0681912 | − | 0.0393702i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.6264 | −1.29788 | −0.648941 | − | 0.760839i | \(-0.724788\pi\) | ||||
−0.648941 | + | 0.760839i | \(0.724788\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.64037 | − | 2.84120i | −0.143320 | − | 0.248237i | 0.785425 | − | 0.618957i | \(-0.212444\pi\) |
−0.928745 | + | 0.370720i | \(0.879111\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.70208 | − | 17.6455i | −0.667855 | − | 1.53006i | ||||
\(134\) | − | 1.33393i | − | 0.115234i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.22062 | + | 2.43678i | 0.361915 | + | 0.208952i | ||||
\(137\) | −3.03168 | − | 1.75034i | −0.259014 | − | 0.149542i | 0.364871 | − | 0.931058i | \(-0.381113\pi\) |
−0.623885 | + | 0.781516i | \(0.714447\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.78031i | − | 0.151004i | −0.997146 | − | 0.0755021i | \(-0.975944\pi\) | ||
0.997146 | − | 0.0755021i | \(-0.0240560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.30350 | − | 2.25773i | −0.109388 | − | 0.189465i | ||||
\(143\) | 2.02234 | − | 3.50279i | 0.169116 | − | 0.292918i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.82406 | 0.233721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.1107 | −0.831092 | ||||||||
\(149\) | 7.14910 | − | 4.12754i | 0.585677 | − | 0.338141i | −0.177709 | − | 0.984083i | \(-0.556869\pi\) |
0.763386 | + | 0.645942i | \(0.223535\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.463545 | + | 0.802883i | −0.0377227 | + | 0.0653377i | −0.884270 | − | 0.466975i | \(-0.845344\pi\) |
0.846548 | + | 0.532313i | \(0.178677\pi\) | |||||||
\(152\) | −3.63851 | − | 6.30208i | −0.295122 | − | 0.511167i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.195010 | − | 1.73331i | 0.0157144 | − | 0.139674i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.22480 | − | 4.17124i | −0.576602 | − | 0.332901i | 0.183180 | − | 0.983079i | \(-0.441361\pi\) |
−0.759782 | + | 0.650178i | \(0.774694\pi\) | |||||||
\(158\) | 5.00280 | + | 2.88837i | 0.398001 | + | 0.229786i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.86740 | + | 11.1512i | 0.383605 | + | 0.878840i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.1525 | − | 21.0488i | −0.951858 | − | 1.64867i | −0.741400 | − | 0.671064i | \(-0.765838\pi\) |
−0.210458 | − | 0.977603i | \(-0.567496\pi\) | |||||||
\(164\) | −3.12617 | + | 5.41468i | −0.244113 | + | 0.422816i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.44894 | + | 3.72330i | −0.500535 | + | 0.288984i | ||||
\(167\) | 7.48724 | 0.579380 | 0.289690 | − | 0.957120i | \(-0.406448\pi\) | ||||
0.289690 | + | 0.957120i | \(0.406448\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −24.6400 | −1.89538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.51791 | + | 7.82525i | −0.344487 | + | 0.596670i | ||||
\(173\) | −7.12036 | − | 12.3328i | −0.541351 | − | 0.937647i | −0.998827 | − | 0.0484252i | \(-0.984580\pi\) |
0.457476 | − | 0.889222i | \(-0.348754\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.659263i | − | 0.0496938i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.61572 | + | 2.66489i | 0.345963 | + | 0.199742i | ||||
\(179\) | −11.3826 | − | 6.57176i | −0.850777 | − | 0.491196i | 0.0101362 | − | 0.999949i | \(-0.496774\pi\) |
−0.860913 | + | 0.508752i | \(0.830107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.34537i | 0.471648i | 0.971796 | + | 0.235824i | \(0.0757788\pi\) | ||||
−0.971796 | + | 0.235824i | \(0.924221\pi\) | |||||||
\(182\) | −14.8766 | + | 6.49350i | −1.10273 | + | 0.481331i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.29939 | + | 3.98266i | 0.169513 | + | 0.293606i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.78250 | − | 1.60648i | 0.203477 | − | 0.117477i | ||||
\(188\) | 12.0027 | 0.875388 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8926 | + | 10.9077i | −1.36702 | + | 0.789251i | −0.990547 | − | 0.137175i | \(-0.956198\pi\) |
−0.376477 | + | 0.926426i | \(0.622865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.20933 | + | 2.09462i | −0.0870495 | + | 0.150774i | −0.906263 | − | 0.422715i | \(-0.861077\pi\) |
0.819213 | + | 0.573489i | \(0.194411\pi\) | |||||||
\(194\) | −5.73958 | − | 9.94125i | −0.412078 | − | 0.713740i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.75953 | + | 5.13292i | −0.339967 | + | 0.366637i | ||||
\(197\) | 6.24457i | 0.444907i | 0.974943 | + | 0.222454i | \(0.0714066\pi\) | ||||
−0.974943 | + | 0.222454i | \(0.928593\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.38388 | − | 2.53103i | −0.310765 | − | 0.179420i | 0.336504 | − | 0.941682i | \(-0.390756\pi\) |
−0.647269 | + | 0.762262i | \(0.724089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 15.4975i | − | 1.09040i | ||||||
\(203\) | −21.2838 | − | 2.39458i | −1.49383 | − | 0.168067i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.03422 | − | 1.79131i | 0.0720572 | − | 0.124807i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.31319 | + | 3.06757i | −0.368403 | + | 0.212698i | ||||
\(209\) | −4.79747 | −0.331848 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.72168 | 0.393896 | 0.196948 | − | 0.980414i | \(-0.436897\pi\) | ||||
0.196948 | + | 0.980414i | \(0.436897\pi\) | |||||||
\(212\) | −10.5749 | + | 6.10540i | −0.726285 | + | 0.419321i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.44632 | + | 9.43331i | −0.372303 | + | 0.644848i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.37726 | + | 1.86676i | −0.0934946 | + | 0.126724i | ||||
\(218\) | 14.3451i | 0.971572i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.8941 | − | 14.9500i | −1.74183 | − | 1.00564i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.61006i | 0.442642i | 0.975201 | + | 0.221321i | \(0.0710369\pi\) | ||||
−0.975201 | + | 0.221321i | \(0.928963\pi\) | |||||||
\(224\) | −1.57075 | + | 2.12902i | −0.104950 | + | 0.142251i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.95403 | + | 10.3127i | 0.396056 | + | 0.685989i | ||||
\(227\) | 12.0278 | − | 20.8328i | 0.798314 | − | 1.38272i | −0.122400 | − | 0.992481i | \(-0.539059\pi\) |
0.920714 | − | 0.390239i | \(-0.127608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.39811 | + | 2.53925i | −0.290635 | + | 0.167798i | −0.638228 | − | 0.769847i | \(-0.720332\pi\) |
0.347593 | + | 0.937645i | \(0.386999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.09526 | −0.531480 | ||||||||
\(233\) | 19.1195 | − | 11.0386i | 1.25256 | − | 0.723165i | 0.280941 | − | 0.959725i | \(-0.409353\pi\) |
0.971617 | + | 0.236560i | \(0.0760201\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.06613 | − | 7.04274i | −0.264682 | − | 0.458443i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.8134 | − | 1.44160i | −0.830568 | − | 0.0934451i | ||||
\(239\) | − | 17.8556i | − | 1.15498i | −0.816398 | − | 0.577490i | \(-0.804032\pi\) | ||
0.816398 | − | 0.577490i | \(-0.195968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8401 | + | 10.8773i | 1.21360 | + | 0.700670i | 0.963541 | − | 0.267562i | \(-0.0862179\pi\) |
0.250055 | + | 0.968232i | \(0.419551\pi\) | |||||||
\(242\) | 9.14988 | + | 5.28269i | 0.588177 | + | 0.339584i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.0714487i | 0.00457403i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.3228 | + | 38.6642i | 1.42036 | + | 2.46014i | ||||
\(248\) | −0.438408 | + | 0.759345i | −0.0278390 | + | 0.0482185i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.0445 | −1.01272 | −0.506361 | − | 0.862321i | \(-0.669010\pi\) | ||||
−0.506361 | + | 0.862321i | \(0.669010\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.03181 | 0.190608 | ||||||||
\(254\) | 12.6668 | − | 7.31319i | 0.794787 | − | 0.458870i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.23399 | − | 14.2617i | −0.513622 | − | 0.889620i | −0.999875 | − | 0.0158016i | \(-0.994970\pi\) |
0.486253 | − | 0.873818i | \(-0.338363\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.5166 | − | 10.7012i | 1.52339 | − | 0.664943i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.84120 | + | 1.64037i | 0.175530 | + | 0.101342i | ||||
\(263\) | 4.86760 | + | 2.81031i | 0.300149 | + | 0.173291i | 0.642510 | − | 0.766278i | \(-0.277893\pi\) |
−0.342361 | + | 0.939569i | \(0.611227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 15.4929 | + | 11.4304i | 0.949933 | + | 0.700843i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.666965 | + | 1.15522i | 0.0407414 | + | 0.0705661i | ||||
\(269\) | 3.27081 | − | 5.66521i | 0.199425 | − | 0.345414i | −0.748917 | − | 0.662664i | \(-0.769426\pi\) |
0.948342 | + | 0.317249i | \(0.102759\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0238 | + | 9.25135i | −0.973377 | + | 0.561980i | −0.900264 | − | 0.435344i | \(-0.856627\pi\) |
−0.0731130 | + | 0.997324i | \(0.523293\pi\) | |||||||
\(272\) | −4.87356 | −0.295503 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.50069 | 0.211484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.9572 | − | 22.4426i | 0.778525 | − | 1.34844i | −0.154267 | − | 0.988029i | \(-0.549302\pi\) |
0.932792 | − | 0.360415i | \(-0.117365\pi\) | |||||||
\(278\) | 0.890157 | + | 1.54180i | 0.0533881 | + | 0.0924708i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.24160i | − | 0.551308i | −0.961257 | − | 0.275654i | \(-0.911106\pi\) | ||
0.961257 | − | 0.275654i | \(-0.0888943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.14531 | − | 3.54800i | −0.365301 | − | 0.210907i | 0.306103 | − | 0.951999i | \(-0.400975\pi\) |
−0.671404 | + | 0.741092i | \(0.734308\pi\) | |||||||
\(284\) | 2.25773 | + | 1.30350i | 0.133972 | + | 0.0773486i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.04467i | 0.239166i | ||||||||
\(287\) | 1.84944 | − | 16.4384i | 0.109169 | − | 0.970329i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.37577 | − | 5.84701i | −0.198575 | − | 0.343942i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.44571 | + | 1.41203i | −0.143124 | + | 0.0826328i | ||||
\(293\) | 8.94657 | 0.522664 | 0.261332 | − | 0.965249i | \(-0.415838\pi\) | ||||
0.261332 | + | 0.965249i | \(0.415838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.75609 | − | 5.05533i | 0.508938 | − | 0.293835i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.12754 | + | 7.14910i | −0.239102 | + | 0.414136i | ||||
\(299\) | −14.1071 | − | 24.4342i | −0.815834 | − | 1.41307i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.67280 | − | 23.7567i | 0.154058 | − | 1.36931i | ||||
\(302\) | − | 0.927090i | − | 0.0533480i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.30208 | + | 3.63851i | 0.361449 | + | 0.208683i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.62584i | − | 0.435230i | −0.976035 | − | 0.217615i | \(-0.930172\pi\) | ||
0.976035 | − | 0.217615i | \(-0.0698276\pi\) | |||||||
\(308\) | 0.697771 | + | 1.59860i | 0.0397592 | + | 0.0910884i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.20348 | + | 5.54859i | −0.181653 | + | 0.314632i | −0.942443 | − | 0.334366i | \(-0.891478\pi\) |
0.760791 | + | 0.648997i | \(0.224811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.84360 | + | 4.52850i | −0.443346 | + | 0.255966i | −0.705016 | − | 0.709191i | \(-0.749060\pi\) |
0.261670 | + | 0.965157i | \(0.415727\pi\) | |||||||
\(314\) | 8.34248 | 0.470793 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.77674 | −0.324967 | ||||||||
\(317\) | −24.6876 | + | 14.2534i | −1.38660 | + | 0.800552i | −0.992930 | − | 0.118702i | \(-0.962127\pi\) |
−0.393666 | + | 0.919253i | \(0.628793\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.66845 | + | 4.62189i | −0.149405 | + | 0.258776i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −9.79091 | − | 7.22355i | −0.545626 | − | 0.402553i | ||||
\(323\) | 35.4650i | 1.97332i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.0488 | + | 12.1525i | 1.16578 | + | 0.673065i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.25234i | − | 0.345228i | ||||||
\(329\) | −29.1044 | + | 12.7038i | −1.60458 | + | 0.700383i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.53535 | − | 13.0516i | −0.414180 | − | 0.717381i | 0.581162 | − | 0.813788i | \(-0.302598\pi\) |
−0.995342 | + | 0.0964068i | \(0.969265\pi\) | |||||||
\(332\) | 3.72330 | − | 6.44894i | 0.204343 | − | 0.353932i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.48414 | + | 3.74362i | −0.354797 | + | 0.204842i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.480936 | −0.0261983 | −0.0130991 | − | 0.999914i | \(-0.504170\pi\) | ||||
−0.0130991 | + | 0.999914i | \(0.504170\pi\) | |||||||
\(338\) | 21.3389 | − | 12.3200i | 1.16068 | − | 0.670119i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.289026 | + | 0.500608i | 0.0156516 | + | 0.0271094i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.10828 | − | 17.4840i | 0.329816 | − | 0.944045i | ||||
\(344\) | − | 9.03582i | − | 0.487179i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3328 | + | 7.12036i | 0.663017 | + | 0.382793i | ||||
\(347\) | 3.01081 | + | 1.73829i | 0.161629 | + | 0.0933165i | 0.578633 | − | 0.815588i | \(-0.303586\pi\) |
−0.417004 | + | 0.908905i | \(0.636920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 0.611574i | − | 0.0327368i | −0.999866 | − | 0.0163684i | \(-0.994790\pi\) | ||
0.999866 | − | 0.0163684i | \(-0.00521046\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.329631 | + | 0.570938i | 0.0175694 | + | 0.0304311i | ||||
\(353\) | −10.8916 | + | 18.8649i | −0.579703 | + | 1.00407i | 0.415810 | + | 0.909451i | \(0.363498\pi\) |
−0.995513 | + | 0.0946235i | \(0.969835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.32978 | −0.282478 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.1435 | 0.694656 | ||||||||
\(359\) | −14.0413 | + | 8.10672i | −0.741069 | + | 0.427857i | −0.822458 | − | 0.568826i | \(-0.807398\pi\) |
0.0813887 | + | 0.996682i | \(0.474064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.9775 | − | 29.4059i | 0.893553 | − | 1.54768i | ||||
\(362\) | −3.17268 | − | 5.49525i | −0.166753 | − | 0.288824i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.63679 | − | 13.0619i | 0.505105 | − | 0.684627i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.0615 | − | 10.4278i | −0.942802 | − | 0.544327i | −0.0519641 | − | 0.998649i | \(-0.516548\pi\) |
−0.890837 | + | 0.454322i | \(0.849881\pi\) | |||||||
\(368\) | −3.98266 | − | 2.29939i | −0.207611 | − | 0.119864i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.1801 | − | 25.9971i | 0.995784 | − | 1.34970i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.702477 | + | 1.21673i | 0.0363729 | + | 0.0629997i | 0.883639 | − | 0.468169i | \(-0.155086\pi\) |
−0.847266 | + | 0.531169i | \(0.821753\pi\) | |||||||
\(374\) | −1.60648 | + | 2.78250i | −0.0830689 | + | 0.143880i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.3947 | + | 6.00136i | −0.536063 | + | 0.309496i | ||||
\(377\) | 49.6656 | 2.55791 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.8729 | 1.12353 | 0.561766 | − | 0.827296i | \(-0.310122\pi\) | ||||
0.561766 | + | 0.827296i | \(0.310122\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.9077 | − | 18.8926i | 0.558085 | − | 0.966632i | ||||
\(383\) | −17.2741 | − | 29.9197i | −0.882666 | − | 1.52882i | −0.848365 | − | 0.529411i | \(-0.822413\pi\) |
−0.0343009 | − | 0.999412i | \(-0.510920\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 2.41866i | − | 0.123107i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.94125 | + | 5.73958i | 0.504690 | + | 0.291383i | ||||
\(389\) | 10.0406 | + | 5.79694i | 0.509078 | + | 0.293916i | 0.732455 | − | 0.680816i | \(-0.238375\pi\) |
−0.223376 | + | 0.974732i | \(0.571708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 22.4124i | − | 1.13344i | ||||||
\(392\) | 1.55542 | − | 6.82500i | 0.0785604 | − | 0.344715i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.12229 | − | 5.40796i | −0.157299 | − | 0.272449i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.02400 | + | 2.90061i | −0.252147 | + | 0.145577i | −0.620747 | − | 0.784011i | \(-0.713171\pi\) |
0.368600 | + | 0.929588i | \(0.379837\pi\) | |||||||
\(398\) | 5.06207 | 0.253739 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.7829 | − | 10.2670i | 0.888036 | − | 0.512708i | 0.0147366 | − | 0.999891i | \(-0.495309\pi\) |
0.873300 | + | 0.487183i | \(0.161976\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.68970 | − | 4.65869i | 0.133983 | − | 0.232066i | ||||
\(404\) | 7.74874 | + | 13.4212i | 0.385514 | + | 0.667730i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.6296 | − | 8.56811i | 0.974199 | − | 0.425228i | ||||
\(407\) | − | 6.66558i | − | 0.330401i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.85765 | + | 4.53662i | 0.388536 | + | 0.224321i | 0.681526 | − | 0.731794i | \(-0.261317\pi\) |
−0.292990 | + | 0.956116i | \(0.594650\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.06843i | 0.101904i | ||||||||
\(413\) | 17.3138 | + | 12.7738i | 0.851954 | + | 0.628556i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.06757 | − | 5.31319i | 0.150400 | − | 0.260501i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.15473 | − | 2.39873i | 0.203214 | − | 0.117326i | ||||
\(419\) | 5.30162 | 0.259001 | 0.129501 | − | 0.991579i | \(-0.458663\pi\) | ||||
0.129501 | + | 0.991579i | \(0.458663\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8234 | 1.06361 | 0.531804 | − | 0.846867i | \(-0.321514\pi\) | ||||
0.531804 | + | 0.846867i | \(0.321514\pi\) | |||||||
\(422\) | −4.95512 | + | 2.86084i | −0.241211 | + | 0.139263i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.10540 | − | 10.5749i | 0.296504 | − | 0.513561i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0756221 | − | 0.173250i | −0.00365961 | − | 0.00838417i | ||||
\(428\) | − | 10.8926i | − | 0.526516i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.9922 | + | 7.50107i | 0.625814 | + | 0.361314i | 0.779129 | − | 0.626864i | \(-0.215662\pi\) |
−0.153315 | + | 0.988177i | \(0.548995\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.2578i | 1.69438i | 0.531289 | + | 0.847190i | \(0.321708\pi\) | ||||
−0.531289 | + | 0.847190i | \(0.678292\pi\) | |||||||
\(434\) | 0.259363 | − | 2.30529i | 0.0124498 | − | 0.110658i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.17254 | − | 12.4232i | −0.343502 | − | 0.594964i | ||||
\(437\) | −16.7327 | + | 28.9819i | −0.800434 | + | 1.38639i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4755 | − | 14.7083i | 1.21588 | − | 0.701988i | 0.251846 | − | 0.967767i | \(-0.418962\pi\) |
0.964034 | + | 0.265779i | \(0.0856291\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 29.9000 | 1.42220 | ||||||||
\(443\) | −25.5061 | + | 14.7259i | −1.21183 | + | 0.699651i | −0.963158 | − | 0.268937i | \(-0.913328\pi\) |
−0.248673 | + | 0.968588i | \(0.579994\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.30503 | − | 5.72448i | −0.156498 | − | 0.271062i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.295801 | − | 2.62916i | 0.0139753 | − | 0.124216i | ||||
\(449\) | 29.2408i | 1.37996i | 0.723829 | + | 0.689980i | \(0.242381\pi\) | ||||
−0.723829 | + | 0.689980i | \(0.757619\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.56970 | − | 2.06097i | −0.168091 | − | 0.0970471i | ||||
\(452\) | −10.3127 | − | 5.95403i | −0.485067 | − | 0.280054i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.0556i | 1.12899i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.98679 | + | 6.90532i | 0.186494 | + | 0.323017i | 0.944079 | − | 0.329720i | \(-0.106954\pi\) |
−0.757585 | + | 0.652737i | \(0.773621\pi\) | |||||||
\(458\) | 2.53925 | − | 4.39811i | 0.118651 | − | 0.205510i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.9112 | −1.85885 | −0.929425 | − | 0.369012i | \(-0.879696\pi\) | ||||
−0.929425 | + | 0.369012i | \(0.879696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.6663 | −0.821021 | −0.410511 | − | 0.911856i | \(-0.634650\pi\) | ||||
−0.410511 | + | 0.911856i | \(0.634650\pi\) | |||||||
\(464\) | 7.01070 | − | 4.04763i | 0.325464 | − | 0.187907i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0386 | + | 19.1195i | −0.511355 | + | 0.885692i | ||||
\(467\) | 10.9757 | + | 19.0104i | 0.507894 | + | 0.879698i | 0.999958 | + | 0.00913924i | \(0.00290915\pi\) |
−0.492064 | + | 0.870559i | \(0.663758\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.83997 | − | 2.09527i | −0.131137 | − | 0.0967507i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.04274 | + | 4.06613i | 0.324168 | + | 0.187159i | ||||
\(473\) | −5.15890 | − | 2.97849i | −0.237206 | − | 0.136951i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.8175 | − | 5.15823i | 0.541655 | − | 0.236427i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.92778 | + | 15.4634i | 0.408347 | + | 0.707278i | ||||
\(479\) | 16.9834 | − | 29.4161i | 0.775990 | − | 1.34405i | −0.158246 | − | 0.987400i | \(-0.550584\pi\) |
0.934236 | − | 0.356655i | \(-0.116083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −53.7199 | + | 31.0152i | −2.44942 | + | 1.41417i | ||||
\(482\) | −21.7546 | −0.990897 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.5654 | −0.480244 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.42482 | − | 12.8602i | 0.336451 | − | 0.582750i | −0.647312 | − | 0.762225i | \(-0.724107\pi\) |
0.983762 | + | 0.179476i | \(0.0574401\pi\) | |||||||
\(488\) | −0.0357243 | − | 0.0618764i | −0.00161716 | − | 0.00280101i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.6224i | 0.705029i | 0.935806 | + | 0.352515i | \(0.114673\pi\) | ||||
−0.935806 | + | 0.352515i | \(0.885327\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.1670 | + | 19.7264i | 1.53881 | + | 0.888430i | ||||
\(494\) | −38.6642 | − | 22.3228i | −1.73958 | − | 1.00435i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.876816i | − | 0.0393702i | ||||||
\(497\) | −6.85424 | − | 0.771153i | −0.307455 | − | 0.0345910i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.23416 | − | 15.9940i | −0.413378 | − | 0.715991i | 0.581879 | − | 0.813275i | \(-0.302318\pi\) |
−0.995257 | + | 0.0972842i | \(0.968984\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.8950 | − | 8.02227i | 0.620164 | − | 0.358052i | ||||
\(503\) | −5.46007 | −0.243452 | −0.121726 | − | 0.992564i | \(-0.538843\pi\) | ||||
−0.121726 | + | 0.992564i | \(0.538843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.62562 | + | 1.51590i | −0.116723 | + | 0.0673901i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.31319 | + | 12.6668i | −0.324470 | + | 0.561999i | ||||
\(509\) | 0.412125 | + | 0.713821i | 0.0182671 | + | 0.0316396i | 0.875014 | − | 0.484097i | \(-0.160852\pi\) |
−0.856747 | + | 0.515736i | \(0.827518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.43590 | − | 6.01249i | 0.196233 | − | 0.265977i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.2617 | + | 8.23399i | 0.629056 | + | 0.363186i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.91294i | 0.348011i | ||||||||
\(518\) | −15.8814 | + | 21.5258i | −0.697787 | + | 0.945791i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.2147 | + | 26.3526i | −0.666566 | + | 1.15453i | 0.312292 | + | 0.949986i | \(0.398903\pi\) |
−0.978858 | + | 0.204541i | \(0.934430\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.196400 | + | 0.113392i | −0.00858799 | + | 0.00495828i | −0.504288 | − | 0.863536i | \(-0.668245\pi\) |
0.495700 | + | 0.868494i | \(0.334912\pi\) | |||||||
\(524\) | −3.28074 | −0.143320 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.62062 | −0.245070 | ||||||||
\(527\) | 3.70071 | − | 2.13661i | 0.161206 | − | 0.0930721i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.925602 | + | 1.60319i | −0.0402436 | + | 0.0697039i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −19.1325 | − | 2.15255i | −0.829498 | − | 0.0933247i | ||||
\(533\) | 38.3590i | 1.66151i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.15522 | − | 0.666965i | −0.0498978 | − | 0.0288085i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.54163i | 0.282030i | ||||||||
\(539\) | −3.38394 | − | 3.13778i | −0.145757 | − | 0.135154i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.5678 | − | 32.1603i | −0.798290 | − | 1.38268i | −0.920729 | − | 0.390204i | \(-0.872405\pi\) |
0.122438 | − | 0.992476i | \(-0.460929\pi\) | |||||||
\(542\) | 9.25135 | − | 16.0238i | 0.397380 | − | 0.688282i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.22062 | − | 2.43678i | 0.180958 | − | 0.104476i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.2444 | 0.609047 | 0.304524 | − | 0.952505i | \(-0.401503\pi\) | ||||
0.304524 | + | 0.952505i | \(0.401503\pi\) | |||||||
\(548\) | −3.03168 | + | 1.75034i | −0.129507 | + | 0.0747709i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.4547 | − | 51.0170i | −1.25481 | − | 2.17340i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0076 | − | 6.11416i | 0.595662 | − | 0.260001i | ||||
\(554\) | 25.9145i | 1.10100i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.54180 | − | 0.890157i | −0.0653867 | − | 0.0377511i | ||||
\(557\) | 16.3764 | + | 9.45492i | 0.693890 | + | 0.400618i | 0.805068 | − | 0.593183i | \(-0.202129\pi\) |
−0.111177 | + | 0.993801i | \(0.535462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.4361i | 2.34470i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.62080 | + | 8.00346i | 0.194917 | + | 0.337606i | ||||
\(563\) | −19.6538 | + | 34.0414i | −0.828310 | + | 1.43467i | 0.0710537 | + | 0.997472i | \(0.477364\pi\) |
−0.899363 | + | 0.437202i | \(0.855969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.09599 | 0.298267 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.60701 | −0.109388 | ||||||||
\(569\) | 0.768837 | − | 0.443888i | 0.0322313 | − | 0.0186088i | −0.483798 | − | 0.875180i | \(-0.660743\pi\) |
0.516029 | + | 0.856571i | \(0.327410\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.7120 | + | 22.0178i | −0.531981 | + | 0.921418i | 0.467322 | + | 0.884087i | \(0.345219\pi\) |
−0.999303 | + | 0.0373309i | \(0.988114\pi\) | |||||||
\(572\) | −2.02234 | − | 3.50279i | −0.0845581 | − | 0.146459i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.61754 | + | 15.1608i | 0.276211 | + | 0.632800i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.90681 | − | 5.14235i | −0.370795 | − | 0.214079i | 0.303010 | − | 0.952987i | \(-0.402008\pi\) |
−0.673806 | + | 0.738908i | \(0.735342\pi\) | |||||||
\(578\) | 5.84701 | + | 3.37577i | 0.243204 | + | 0.140414i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.20271 | + | 19.5783i | −0.0913837 | + | 0.812246i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.02506 | − | 6.97161i | −0.166701 | − | 0.288735i | ||||
\(584\) | 1.41203 | − | 2.44571i | 0.0584302 | − | 0.101204i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.74795 | + | 4.47328i | −0.320065 | + | 0.184790i | ||||
\(587\) | −25.1241 | −1.03698 | −0.518490 | − | 0.855083i | \(-0.673506\pi\) | ||||
−0.518490 | + | 0.855083i | \(0.673506\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.38061 | −0.262909 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.05533 | + | 8.75609i | −0.207773 | + | 0.359873i | ||||
\(593\) | −5.05492 | − | 8.75538i | −0.207581 | − | 0.359540i | 0.743371 | − | 0.668879i | \(-0.233226\pi\) |
−0.950952 | + | 0.309339i | \(0.899892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 8.25507i | − | 0.338141i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.4342 | + | 14.1071i | 0.999189 | + | 0.576882i | ||||
\(599\) | 21.6368 | + | 12.4920i | 0.884056 | + | 0.510410i | 0.871994 | − | 0.489517i | \(-0.162827\pi\) |
0.0120624 | + | 0.999927i | \(0.496160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.2936i | 0.623837i | 0.950109 | + | 0.311919i | \(0.100972\pi\) | ||||
−0.950109 | + | 0.311919i | \(0.899028\pi\) | |||||||
\(602\) | 9.56361 | + | 21.9103i | 0.389784 | + | 0.892996i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.463545 | + | 0.802883i | 0.0188614 | + | 0.0326689i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.1973 | − | 19.7438i | 1.38802 | − | 0.801377i | 0.394932 | − | 0.918710i | \(-0.370768\pi\) |
0.993093 | + | 0.117334i | \(0.0374347\pi\) | |||||||
\(608\) | −7.27702 | −0.295122 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 63.7727 | − | 36.8192i | 2.57997 | − | 1.48954i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.55968 | − | 14.8258i | 0.345722 | − | 0.598809i | −0.639762 | − | 0.768573i | \(-0.720967\pi\) |
0.985485 | + | 0.169764i | \(0.0543006\pi\) | |||||||
\(614\) | 3.81292 | + | 6.60417i | 0.153877 | + | 0.266523i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.40359 | − | 1.03554i | −0.0565521 | − | 0.0417230i | ||||
\(617\) | 5.80201i | 0.233580i | 0.993157 | + | 0.116790i | \(0.0372605\pi\) | ||||
−0.993157 | + | 0.116790i | \(0.962740\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5344 | + | 17.0517i | 1.18709 | + | 0.685366i | 0.957644 | − | 0.287956i | \(-0.0929756\pi\) |
0.229445 | + | 0.973322i | \(0.426309\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.40696i | − | 0.256896i | ||||||
\(623\) | 12.9238 | − | 5.64109i | 0.517780 | − | 0.226006i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.52850 | − | 7.84360i | 0.180995 | − | 0.313493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.22480 | + | 4.17124i | −0.288301 | + | 0.166451i | ||||
\(629\) | −49.2749 | −1.96472 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1261 | 1.31873 | 0.659365 | − | 0.751823i | \(-0.270825\pi\) | ||||
0.659365 | + | 0.751823i | \(0.270825\pi\) | |||||||
\(632\) | 5.00280 | − | 2.88837i | 0.199001 | − | 0.114893i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.2534 | − | 24.6876i | 0.566076 | − | 0.980472i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.54270 | + | 41.8724i | −0.378096 | + | 1.65904i | ||||
\(638\) | − | 5.33690i | − | 0.211290i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.72685 | + | 0.997000i | 0.0682067 | + | 0.0393791i | 0.533716 | − | 0.845664i | \(-0.320795\pi\) |
−0.465509 | + | 0.885043i | \(0.654129\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.661676i | 0.0260940i | 0.999915 | + | 0.0130470i | \(0.00415310\pi\) | ||||
−0.999915 | + | 0.0130470i | \(0.995847\pi\) | |||||||
\(644\) | 12.0910 | + | 1.36032i | 0.476450 | + | 0.0536042i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.7325 | − | 30.7136i | −0.697675 | − | 1.20841i | ||||
\(647\) | 9.19276 | − | 15.9223i | 0.361405 | − | 0.625971i | −0.626787 | − | 0.779190i | \(-0.715631\pi\) |
0.988192 | + | 0.153219i | \(0.0489639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.64302 | − | 2.68065i | 0.182254 | − | 0.105225i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.3050 | −0.951858 | ||||||||
\(653\) | 15.0571 | − | 8.69323i | 0.589231 | − | 0.340193i | −0.175562 | − | 0.984468i | \(-0.556174\pi\) |
0.764793 | + | 0.644276i | \(0.222841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.12617 | + | 5.41468i | 0.122056 | + | 0.211408i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.8533 | − | 25.5540i | 0.734978 | − | 0.996200i | ||||
\(659\) | 35.4692i | 1.38168i | 0.723006 | + | 0.690841i | \(0.242760\pi\) | ||||
−0.723006 | + | 0.690841i | \(0.757240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9704 | − | 16.7261i | −1.12682 | − | 0.650568i | −0.183685 | − | 0.982985i | \(-0.558803\pi\) |
−0.943133 | + | 0.332417i | \(0.892136\pi\) | |||||||
\(662\) | 13.0516 | + | 7.53535i | 0.507265 | + | 0.292870i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.44660i | 0.288984i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.6142 | + | 32.2407i | 0.720744 | + | 1.24836i | ||||
\(668\) | 3.74362 | − | 6.48414i | 0.144845 | − | 0.250879i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0471035 | −0.00181841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9964 | 0.847898 | 0.423949 | − | 0.905686i | \(-0.360644\pi\) | ||||
0.423949 | + | 0.905686i | \(0.360644\pi\) | |||||||
\(674\) | 0.416503 | − | 0.240468i | 0.0160431 | − | 0.00926249i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3200 | + | 21.3389i | −0.473846 | + | 0.820725i | ||||
\(677\) | 6.18250 | + | 10.7084i | 0.237613 | + | 0.411557i | 0.960029 | − | 0.279901i | \(-0.0903018\pi\) |
−0.722416 | + | 0.691459i | \(0.756968\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −30.1806 | − | 3.39554i | −1.15823 | − | 0.130309i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.500608 | − | 0.289026i | −0.0191693 | − | 0.0110674i | ||||
\(683\) | −25.9621 | − | 14.9892i | −0.993411 | − | 0.573546i | −0.0871187 | − | 0.996198i | \(-0.527766\pi\) |
−0.906292 | + | 0.422652i | \(0.861099\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.45205 | + | 18.1957i | 0.131800 | + | 0.694715i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.51791 | + | 7.82525i | 0.172244 | + | 0.298335i | ||||
\(689\) | −37.4575 | + | 64.8783i | −1.42702 | + | 2.47167i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.97882 | − | 4.60657i | 0.303529 | − | 0.175242i | −0.340498 | − | 0.940245i | \(-0.610596\pi\) |
0.644027 | + | 0.765003i | \(0.277262\pi\) | |||||||
\(692\) | −14.2407 | −0.541351 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.47659 | −0.131969 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.2356 | + | 26.3888i | −0.577088 | + | 0.999546i | ||||
\(698\) | 0.305787 | + | 0.529638i | 0.0115742 | + | 0.0200471i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 44.9022i | − | 1.69593i | −0.530050 | − | 0.847967i | \(-0.677827\pi\) | ||
0.530050 | − | 0.847967i | \(-0.322173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 63.7183 | + | 36.7878i | 2.40318 | + | 1.38748i | ||||
\(704\) | −0.570938 | − | 0.329631i | −0.0215180 | − | 0.0124234i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 21.7833i | − | 0.819824i | ||||||
\(707\) | −32.9945 | − | 24.3427i | −1.24089 | − | 0.915502i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.39264 | − | 2.41213i | −0.0523019 | − | 0.0905895i | 0.838689 | − | 0.544610i | \(-0.183322\pi\) |
−0.890991 | + | 0.454021i | \(0.849989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.61572 | − | 2.66489i | 0.172981 | − | 0.0998709i | ||||
\(713\) | 4.03229 | 0.151010 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.3826 | + | 6.57176i | −0.425388 | + | 0.245598i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.10672 | − | 14.0413i | 0.302540 | − | 0.524015i | ||||
\(719\) | −13.4818 | − | 23.3511i | −0.502785 | − | 0.870849i | −0.999995 | − | 0.00321841i | \(-0.998976\pi\) |
0.497210 | − | 0.867630i | \(-0.334358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.18925 | − | 5.01558i | −0.0815319 | − | 0.186790i | ||||
\(722\) | 33.9550i | 1.26368i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.49525 | + | 3.17268i | 0.204229 | + | 0.117912i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.6632i | 1.10015i | 0.835116 | + | 0.550074i | \(0.185400\pi\) | ||||
−0.835116 | + | 0.550074i | \(0.814600\pi\) | |||||||
\(728\) | −1.81478 | + | 16.1303i | −0.0672602 | + | 0.597829i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.0183 | + | 38.1368i | −0.814376 | + | 1.41054i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.9455 | − | 11.5155i | 0.736704 | − | 0.425336i | −0.0841657 | − | 0.996452i | \(-0.526823\pi\) |
0.820870 | + | 0.571116i | \(0.193489\pi\) | |||||||
\(734\) | 20.8556 | 0.769794 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.59878 | 0.169513 | ||||||||
\(737\) | −0.761591 | + | 0.439705i | −0.0280536 | + | 0.0161967i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.2029 | + | 29.7964i | −0.632821 | + | 1.09608i | 0.354152 | + | 0.935188i | \(0.384770\pi\) |
−0.986972 | + | 0.160889i | \(0.948564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.61196 | + | 32.1042i | −0.132599 | + | 1.17858i | ||||
\(743\) | 40.6201i | 1.49021i | 0.666950 | + | 0.745103i | \(0.267600\pi\) | ||||
−0.666950 | + | 0.745103i | \(0.732400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.21673 | − | 0.702477i | −0.0445475 | − | 0.0257195i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.21295i | − | 0.117477i | ||||||
\(749\) | 11.5289 | + | 26.4127i | 0.421257 | + | 0.965101i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.8927 | − | 39.6513i | −0.835366 | − | 1.44690i | −0.893732 | − | 0.448601i | \(-0.851922\pi\) |
0.0583658 | − | 0.998295i | \(-0.481411\pi\) | |||||||
\(752\) | 6.00136 | − | 10.3947i | 0.218847 | − | 0.379054i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −43.0117 | + | 24.8328i | −1.56639 | + | 0.904357i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −50.7755 | −1.84547 | −0.922733 | − | 0.385440i | \(-0.874050\pi\) | ||||
−0.922733 | + | 0.385440i | \(0.874050\pi\) | |||||||
\(758\) | −18.9424 | + | 10.9364i | −0.688021 | + | 0.397229i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0315 | + | 31.2316i | 0.653643 | + | 1.13214i | 0.982232 | + | 0.187670i | \(0.0600935\pi\) |
−0.328589 | + | 0.944473i | \(0.606573\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.5410 | + | 22.5326i | 1.10566 | + | 0.815734i | ||||
\(764\) | 21.8153i | 0.789251i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.9197 | + | 17.2741i | 1.08104 | + | 0.624139i | ||||
\(767\) | −43.2082 | − | 24.9463i | −1.56016 | − | 0.900758i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.5798i | − | 0.633943i | −0.948435 | − | 0.316971i | \(-0.897334\pi\) | ||
0.948435 | − | 0.316971i | \(-0.102666\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.20933 | + | 2.09462i | 0.0435248 | + | 0.0753871i | ||||
\(773\) | 24.7318 | − | 42.8367i | 0.889541 | − | 1.54073i | 0.0491225 | − | 0.998793i | \(-0.484358\pi\) |
0.840419 | − | 0.541938i | \(-0.182309\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.4792 | −0.412078 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.5939 | −0.415661 | ||||||||
\(779\) | 39.4028 | − | 22.7492i | 1.41175 | − | 0.815074i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.859351 | + | 1.48844i | −0.0307500 | + | 0.0532605i | ||||
\(782\) | 11.2062 | + | 19.4097i | 0.400733 | + | 0.694090i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.06547 | + | 6.68833i | 0.0737669 | + | 0.238869i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.38310 | − | 4.83998i | −0.298825 | − | 0.172527i | 0.343090 | − | 0.939303i | \(-0.388526\pi\) |
−0.641915 | + | 0.766776i | \(0.721860\pi\) | |||||||
\(788\) | 5.40796 | + | 3.12229i | 0.192651 | + | 0.111227i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.3082 | + | 3.52241i | 1.11319 | + | 0.125242i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.219174 | + | 0.379620i | 0.00778310 | + | 0.0134807i | ||||
\(794\) | 2.90061 | − | 5.02400i | 0.102939 | − | 0.178295i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.38388 | + | 2.53103i | −0.155383 | + | 0.0897101i | ||||
\(797\) | 15.1216 | 0.535636 | 0.267818 | − | 0.963470i | \(-0.413697\pi\) | ||||
0.267818 | + | 0.963470i | \(0.413697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 58.4959 | 2.06944 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.2670 | + | 17.7829i | −0.362539 | + | 0.627937i | ||||
\(803\) | −0.930899 | − | 1.61236i | −0.0328507 | − | 0.0568991i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.37940i | 0.189481i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.4212 | − | 7.74874i | −0.472157 | − | 0.272600i | ||||
\(809\) | 4.53839 | + | 2.62024i | 0.159561 | + | 0.0921228i | 0.577655 | − | 0.816281i | \(-0.303968\pi\) |
−0.418093 | + | 0.908404i | \(0.637301\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.1101i | 1.90006i | 0.312154 | + | 0.950031i | \(0.398949\pi\) | ||||
−0.312154 | + | 0.950031i | \(0.601051\pi\) | |||||||
\(812\) | −12.7157 | + | 17.2350i | −0.446232 | + | 0.604830i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.33279 | + | 5.77257i | 0.116814 | + | 0.202328i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56.9445 | − | 32.8769i | 1.99224 | − | 1.15022i | ||||
\(818\) | −9.07323 | −0.317238 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.3717 | − | 13.4936i | 0.815677 | − | 0.470931i | −0.0332463 | − | 0.999447i | \(-0.510585\pi\) |
0.848924 | + | 0.528516i | \(0.177251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.12999 | + | 5.42130i | −0.109105 | + | 0.188975i | −0.915408 | − | 0.402528i | \(-0.868132\pi\) |
0.806303 | + | 0.591502i | \(0.201465\pi\) | |||||||
\(824\) | −1.03422 | − | 1.79131i | −0.0360286 | − | 0.0624034i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.3810 | − | 2.40553i | −0.743941 | − | 0.0836989i | ||||
\(827\) | 32.0713i | 1.11523i | 0.830100 | + | 0.557615i | \(0.188283\pi\) | ||||
−0.830100 | + | 0.557615i | \(0.811717\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.3975 | + | 6.00303i | 0.361122 | + | 0.208494i | 0.669573 | − | 0.742746i | \(-0.266477\pi\) |
−0.308451 | + | 0.951240i | \(0.599811\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.13514i | 0.212698i | ||||||||
\(833\) | −23.1958 | + | 25.0156i | −0.803688 | + | 0.866738i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.39873 | + | 4.15473i | −0.0829620 | + | 0.143694i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.59134 | + | 2.65081i | −0.158605 | + | 0.0915707i | ||||
\(839\) | 51.4896 | 1.77762 | 0.888809 | − | 0.458278i | \(-0.151534\pi\) | ||||
0.888809 | + | 0.458278i | \(0.151534\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −36.5332 | −1.25977 | ||||||||
\(842\) | −18.8996 | + | 10.9117i | −0.651324 | + | 0.376042i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.86084 | − | 4.95512i | 0.0984741 | − | 0.170562i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.6192 | − | 11.1825i | 0.880285 | − | 0.384236i | ||||
\(848\) | 12.2108i | 0.419321i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.2674 | − | 23.2484i | −1.38035 | − | 0.796944i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.4695i | 1.41989i | 0.704258 | + | 0.709944i | \(0.251280\pi\) | ||||
−0.704258 | + | 0.709944i | \(0.748720\pi\) | |||||||
\(854\) | 0.152116 | + | 0.112228i | 0.00520530 | + | 0.00384037i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.44632 | + | 9.43331i | 0.186152 | + | 0.322424i | ||||
\(857\) | −27.9394 | + | 48.3925i | −0.954393 | + | 1.65306i | −0.218641 | + | 0.975805i | \(0.570163\pi\) |
−0.735751 | + | 0.677252i | \(0.763171\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.0097 | + | 15.0167i | −0.887440 | + | 0.512364i | −0.873104 | − | 0.487534i | \(-0.837897\pi\) |
−0.0143355 | + | 0.999897i | \(0.504563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.0021 | −0.510975 | ||||||||
\(863\) | −1.77218 | + | 1.02317i | −0.0603258 | + | 0.0348291i | −0.529860 | − | 0.848085i | \(-0.677755\pi\) |
0.469534 | + | 0.882915i | \(0.344422\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.6289 | − | 30.5341i | −0.599054 | − | 1.03759i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.928032 | + | 2.12612i | 0.0314995 | + | 0.0721654i | ||||
\(869\) | − | 3.80839i | − | 0.129191i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.08742 | + | 4.09192i | 0.240148 | + | 0.138650i | ||||
\(872\) | 12.4232 | + | 7.17254i | 0.420703 | + | 0.242893i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 33.4654i | − | 1.13199i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.24489 | + | 9.08442i | 0.177107 | + | 0.306759i | 0.940889 | − | 0.338716i | \(-0.109993\pi\) |
−0.763781 | + | 0.645475i | \(0.776659\pi\) | |||||||
\(878\) | −14.7083 | + | 25.4755i | −0.496381 | + | 0.859757i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.2280 | 1.49008 | 0.745039 | − | 0.667021i | \(-0.232431\pi\) | ||||
0.745039 | + | 0.667021i | \(0.232431\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.8143 | 0.801416 | 0.400708 | − | 0.916206i | \(-0.368764\pi\) | ||||
0.400708 | + | 0.916206i | \(0.368764\pi\) | |||||||
\(884\) | −25.8941 | + | 14.9500i | −0.870914 | + | 0.502822i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.7259 | − | 25.5061i | 0.494728 | − | 0.856893i | ||||
\(887\) | 15.6120 | + | 27.0408i | 0.524200 | + | 0.907941i | 0.999603 | + | 0.0281729i | \(0.00896889\pi\) |
−0.475403 | + | 0.879768i | \(0.657698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.32649 | − | 38.4552i | 0.145106 | − | 1.28974i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.72448 | + | 3.30503i | 0.191670 | + | 0.110661i | ||||
\(893\) | −75.6421 | − | 43.6720i | −2.53127 | − | 1.46143i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.05841 | + | 2.42482i | 0.0353590 | + | 0.0810076i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.6204 | − | 25.3233i | −0.487889 | − | 0.845049i | ||||
\(899\) | −3.54903 | + | 6.14710i | −0.118367 | + | 0.205017i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.5372 | + | 29.7550i | −1.71695 | + | 0.991283i | ||||
\(902\) | 4.12193 | 0.137245 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.9081 | 0.396056 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.73076 | − | 13.3901i | 0.256696 | − | 0.444610i | −0.708659 | − | 0.705551i | \(-0.750699\pi\) |
0.965355 | + | 0.260941i | \(0.0840328\pi\) | |||||||
\(908\) | −12.0278 | − | 20.8328i | −0.399157 | − | 0.691360i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.7655i | 0.389810i | 0.980822 | + | 0.194905i | \(0.0624398\pi\) | ||||
−0.980822 | + | 0.194905i | \(0.937560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.25155 | + | 2.45463i | 0.140706 | + | 0.0812365i | ||||
\(914\) | −6.90532 | − | 3.98679i | −0.228408 | − | 0.131871i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.07850i | 0.167798i | ||||||||
\(917\) | 7.95521 | − | 3.47237i | 0.262704 | − | 0.114668i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.4078 | + | 26.6871i | 0.508256 | + | 0.880326i | 0.999954 | + | 0.00955987i | \(0.00304305\pi\) |
−0.491698 | + | 0.870766i | \(0.663624\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.5641 | − | 19.9556i | 1.13831 | − | 0.657203i | ||||
\(923\) | 15.9944 | 0.526460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.2994 | − | 8.83314i | 0.502771 | − | 0.290275i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.04763 | + | 7.01070i | −0.132870 | + | 0.230138i | ||||
\(929\) | 2.44799 | + | 4.24005i | 0.0803160 | + | 0.139111i | 0.903386 | − | 0.428829i | \(-0.141074\pi\) |
−0.823070 | + | 0.567940i | \(0.807740\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.6712 | − | 15.0305i | 1.59513 | − | 0.492604i | ||||
\(932\) | − | 22.0773i | − | 0.723165i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19.0104 | − | 10.9757i | −0.622040 | − | 0.359135i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.7661i | − | 0.939747i | −0.882734 | − | 0.469874i | \(-0.844299\pi\) | ||
0.882734 | − | 0.469874i | \(-0.155701\pi\) | |||||||
\(938\) | 3.50712 | + | 0.394577i | 0.114511 | + | 0.0128834i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.0535167 | + | 0.0926937i | −0.00174460 | + | 0.00302173i | −0.866896 | − | 0.498488i | \(-0.833889\pi\) |
0.865152 | + | 0.501510i | \(0.167222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.9009 | + | 14.3766i | −0.810886 | + | 0.468165i | ||||
\(944\) | −8.13225 | −0.264682 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.95698 | 0.193678 | ||||||||
\(947\) | 12.7502 | − | 7.36136i | 0.414327 | − | 0.239212i | −0.278320 | − | 0.960488i | \(-0.589778\pi\) |
0.692647 | + | 0.721276i | \(0.256444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.66301 | + | 15.0048i | −0.281213 | + | 0.487076i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.65515 | + | 10.3759i | −0.248105 | + | 0.336285i | ||||
\(953\) | − | 10.5168i | − | 0.340672i | −0.985386 | − | 0.170336i | \(-0.945515\pi\) | ||
0.985386 | − | 0.170336i | \(-0.0544852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.4634 | − | 8.92778i | −0.500121 | − | 0.288745i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.9667i | 1.09742i | ||||||||
\(959\) | 5.49871 | − | 7.45304i | 0.177563 | − | 0.240671i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1156 | − | 26.1810i | −0.487600 | − | 0.844548i | ||||
\(962\) | 31.0152 | − | 53.7199i | 0.999970 | − | 1.73200i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 18.8401 | − | 10.8773i | 0.606798 | − | 0.350335i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.51148 | 0.273711 | 0.136855 | − | 0.990591i | \(-0.456300\pi\) | ||||
0.136855 | + | 0.990591i | \(0.456300\pi\) | |||||||
\(968\) | 9.14988 | − | 5.28269i | 0.294088 | − | 0.169792i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.49465 | − | 7.78496i | −0.144240 | − | 0.249831i | 0.784849 | − | 0.619687i | \(-0.212740\pi\) |
−0.929089 | + | 0.369856i | \(0.879407\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.68074 | + | 0.526618i | 0.150057 | + | 0.0168826i | ||||
\(974\) | 14.8496i | 0.475813i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0618764 | + | 0.0357243i | 0.00198061 | + | 0.00114351i | ||||
\(977\) | −39.2963 | − | 22.6877i | −1.25720 | − | 0.725845i | −0.284671 | − | 0.958625i | \(-0.591884\pi\) |
−0.972529 | + | 0.232781i | \(0.925218\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.51372i | − | 0.112299i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.81120 | − | 13.5294i | −0.249266 | − | 0.431741i | ||||
\(983\) | −12.9209 | + | 22.3797i | −0.412114 | + | 0.713802i | −0.995121 | − | 0.0986654i | \(-0.968543\pi\) |
0.583007 | + | 0.812467i | \(0.301876\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −39.4527 | −1.25643 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 44.6456 | 1.42036 | ||||||||
\(989\) | −35.9866 | + | 20.7769i | −1.14431 | + | 0.660667i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.5315 | + | 28.6333i | −0.525139 | + | 0.909568i | 0.474432 | + | 0.880292i | \(0.342654\pi\) |
−0.999571 | + | 0.0292760i | \(0.990680\pi\) | |||||||
\(992\) | 0.438408 | + | 0.759345i | 0.0139195 | + | 0.0241092i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.32153 | − | 2.75928i | 0.200507 | − | 0.0875191i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.2828 | − | 24.9894i | −1.37078 | − | 0.791421i | −0.379755 | − | 0.925087i | \(-0.623992\pi\) |
−0.991026 | + | 0.133666i | \(0.957325\pi\) | |||||||
\(998\) | 15.9940 | + | 9.23416i | 0.506282 | + | 0.292302i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.bf.e.1151.3 | yes | 24 | |
3.2 | odd | 2 | inner | 3150.2.bf.e.1151.10 | yes | 24 | |
5.2 | odd | 4 | 3150.2.bp.g.899.1 | 24 | |||
5.3 | odd | 4 | 3150.2.bp.h.899.12 | 24 | |||
5.4 | even | 2 | 3150.2.bf.d.1151.10 | yes | 24 | ||
7.5 | odd | 6 | inner | 3150.2.bf.e.1601.10 | yes | 24 | |
15.2 | even | 4 | 3150.2.bp.h.899.1 | 24 | |||
15.8 | even | 4 | 3150.2.bp.g.899.12 | 24 | |||
15.14 | odd | 2 | 3150.2.bf.d.1151.3 | ✓ | 24 | ||
21.5 | even | 6 | inner | 3150.2.bf.e.1601.3 | yes | 24 | |
35.12 | even | 12 | 3150.2.bp.g.1349.12 | 24 | |||
35.19 | odd | 6 | 3150.2.bf.d.1601.3 | yes | 24 | ||
35.33 | even | 12 | 3150.2.bp.h.1349.1 | 24 | |||
105.47 | odd | 12 | 3150.2.bp.h.1349.12 | 24 | |||
105.68 | odd | 12 | 3150.2.bp.g.1349.1 | 24 | |||
105.89 | even | 6 | 3150.2.bf.d.1601.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.3 | ✓ | 24 | 15.14 | odd | 2 | ||
3150.2.bf.d.1151.10 | yes | 24 | 5.4 | even | 2 | ||
3150.2.bf.d.1601.3 | yes | 24 | 35.19 | odd | 6 | ||
3150.2.bf.d.1601.10 | yes | 24 | 105.89 | even | 6 | ||
3150.2.bf.e.1151.3 | yes | 24 | 1.1 | even | 1 | trivial | |
3150.2.bf.e.1151.10 | yes | 24 | 3.2 | odd | 2 | inner | |
3150.2.bf.e.1601.3 | yes | 24 | 21.5 | even | 6 | inner | |
3150.2.bf.e.1601.10 | yes | 24 | 7.5 | odd | 6 | inner | |
3150.2.bp.g.899.1 | 24 | 5.2 | odd | 4 | |||
3150.2.bp.g.899.12 | 24 | 15.8 | even | 4 | |||
3150.2.bp.g.1349.1 | 24 | 105.68 | odd | 12 | |||
3150.2.bp.g.1349.12 | 24 | 35.12 | even | 12 | |||
3150.2.bp.h.899.1 | 24 | 15.2 | even | 4 | |||
3150.2.bp.h.899.12 | 24 | 5.3 | odd | 4 | |||
3150.2.bp.h.1349.1 | 24 | 35.33 | even | 12 | |||
3150.2.bp.h.1349.12 | 24 | 105.47 | odd | 12 |