Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
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, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
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.bp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
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 | 899.12 | ||
Character | \(\chi\) | \(=\) | 3150.899 |
Dual form | 3150.2.bp.g.1349.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62916 | + | 0.295801i | 0.993730 | + | 0.111802i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.570938 | − | 0.329631i | −0.172144 | − | 0.0993876i | 0.411452 | − | 0.911431i | \(-0.365022\pi\) |
−0.583597 | + | 0.812044i | \(0.698355\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.13514 | 1.70158 | 0.850791 | − | 0.525504i | \(-0.176123\pi\) | ||||
0.850791 | + | 0.525504i | \(0.176123\pi\) | |||||||
\(14\) | −1.05841 | − | 2.42482i | −0.282872 | − | 0.648061i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.22062 | + | 2.43678i | 1.02365 | + | 0.591005i | 0.915160 | − | 0.403092i | \(-0.132064\pi\) |
0.108492 | + | 0.994097i | \(0.465398\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.30208 | − | 3.63851i | 1.44580 | − | 0.834732i | 0.447570 | − | 0.894249i | \(-0.352289\pi\) |
0.998227 | + | 0.0595173i | \(0.0189562\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.659263i | 0.140555i | ||||||||
\(23\) | −2.29939 | − | 3.98266i | −0.479456 | − | 0.830442i | 0.520266 | − | 0.854004i | \(-0.325833\pi\) |
−0.999722 | + | 0.0235617i | \(0.992499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.06757 | − | 5.31319i | −0.601600 | − | 1.04200i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.57075 | + | 2.12902i | −0.296844 | + | 0.402347i | ||||
\(29\) | 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 | \(0.641577\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.87356i | − | 0.835808i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.75609 | + | 5.05533i | −1.43949 | + | 0.831092i | −0.997814 | − | 0.0660818i | \(-0.978950\pi\) |
−0.441679 | + | 0.897173i | \(0.645617\pi\) | |||||||
\(38\) | −6.30208 | − | 3.63851i | −1.02233 | − | 0.590244i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.25234 | 0.976451 | 0.488226 | − | 0.872717i | \(-0.337644\pi\) | ||||
0.488226 | + | 0.872717i | \(0.337644\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.03582i | − | 1.37795i | −0.724785 | − | 0.688975i | \(-0.758061\pi\) | ||
0.724785 | − | 0.688975i | \(-0.241939\pi\) | |||||||
\(44\) | 0.570938 | − | 0.329631i | 0.0860722 | − | 0.0496938i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.29939 | + | 3.98266i | −0.339027 | + | 0.587211i | ||||
\(47\) | −10.3947 | + | 6.00136i | −1.51622 | + | 0.875388i | −0.516397 | + | 0.856349i | \(0.672727\pi\) |
−0.999819 | + | 0.0190383i | \(0.993940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.82500 | + | 1.55542i | 0.975001 | + | 0.222202i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.06757 | + | 5.31319i | −0.425396 | + | 0.736807i | ||||
\(53\) | −6.10540 | + | 10.5749i | −0.838641 | + | 1.45257i | 0.0523897 | + | 0.998627i | \(0.483316\pi\) |
−0.891031 | + | 0.453943i | \(0.850017\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.62916 | + | 0.295801i | 0.351337 | + | 0.0395280i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.01070 | − | 4.04763i | 0.920550 | − | 0.531480i | ||||
\(59\) | 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 | \(0.334789\pi\) | |||||||
\(62\) | − | 0.876816i | − | 0.111356i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.15522 | + | 0.666965i | 0.141132 | + | 0.0814827i | 0.568903 | − | 0.822404i | \(-0.307368\pi\) |
−0.427771 | + | 0.903887i | \(0.640701\pi\) | |||||||
\(68\) | −4.22062 | + | 2.43678i | −0.511826 | + | 0.295503i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.60701i | − | 0.309395i | −0.987962 | − | 0.154697i | \(-0.950560\pi\) | ||
0.987962 | − | 0.154697i | \(-0.0494402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.41203 | − | 2.44571i | 0.165266 | − | 0.286249i | −0.771484 | − | 0.636249i | \(-0.780485\pi\) |
0.936750 | + | 0.350000i | \(0.113819\pi\) | |||||||
\(74\) | 8.75609 | + | 5.05533i | 1.01788 | + | 0.587670i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.27702i | 0.834732i | ||||||||
\(77\) | −1.40359 | − | 1.03554i | −0.159953 | − | 0.118011i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.88837 | + | 5.00280i | 0.324967 | + | 0.562859i | 0.981506 | − | 0.191433i | \(-0.0613136\pi\) |
−0.656539 | + | 0.754292i | \(0.727980\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.12617 | − | 5.41468i | −0.345228 | − | 0.597952i | ||||
\(83\) | − | 7.44660i | − | 0.817370i | −0.912675 | − | 0.408685i | \(-0.865987\pi\) | ||
0.912675 | − | 0.408685i | \(-0.134013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.82525 | + | 4.51791i | −0.843819 | + | 0.487179i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.570938 | − | 0.329631i | −0.0608622 | − | 0.0351388i | ||||
\(89\) | −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 | ||||
\(92\) | 4.59878 | 0.479456 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.3947 | + | 6.00136i | 1.07213 | + | 0.618993i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4792 | 1.16553 | 0.582766 | − | 0.812640i | \(-0.301970\pi\) | ||||
0.582766 | + | 0.812640i | \(0.301970\pi\) | |||||||
\(98\) | −2.06547 | − | 6.68833i | −0.208644 | − | 0.675624i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.74874 | − | 13.4212i | 0.771029 | − | 1.33546i | −0.165971 | − | 0.986131i | \(-0.553076\pi\) |
0.937000 | − | 0.349330i | \(-0.113591\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.03422 | − | 1.79131i | −0.101904 | − | 0.176503i | 0.810565 | − | 0.585649i | \(-0.199160\pi\) |
−0.912469 | + | 0.409145i | \(0.865827\pi\) | |||||||
\(104\) | 6.13514 | 0.601600 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.2108 | 1.18602 | ||||||||
\(107\) | 5.44632 | + | 9.43331i | 0.526516 | + | 0.911953i | 0.999523 | + | 0.0308937i | \(0.00983533\pi\) |
−0.473007 | + | 0.881059i | \(0.656831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.17254 | + | 12.4232i | −0.687005 | + | 1.18993i | 0.285797 | + | 0.958290i | \(0.407742\pi\) |
−0.972802 | + | 0.231637i | \(0.925592\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.05841 | − | 2.42482i | −0.100010 | − | 0.229124i | ||||
\(113\) | −11.9081 | −1.12022 | −0.560108 | − | 0.828420i | \(-0.689240\pi\) | ||||
−0.560108 | + | 0.828420i | \(0.689240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.01070 | − | 4.04763i | −0.650927 | − | 0.375813i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.13225 | −0.748635 | ||||||||
\(119\) | 10.3759 | + | 7.65515i | 0.951158 | + | 0.701747i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.28269 | − | 9.14988i | −0.480244 | − | 0.831807i | ||||
\(122\) | 0.0618764 | + | 0.0357243i | 0.00560202 | + | 0.00323433i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.759345 | + | 0.438408i | −0.0681912 | + | 0.0393702i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6264i | 1.29788i | 0.760839 | + | 0.648941i | \(0.224788\pi\) | ||||
−0.760839 | + | 0.648941i | \(0.775212\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.64037 | + | 2.84120i | 0.143320 | + | 0.248237i | 0.928745 | − | 0.370720i | \(-0.120889\pi\) |
−0.785425 | + | 0.618957i | \(0.787556\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.6455 | − | 7.70208i | 1.53006 | − | 0.667855i | ||||
\(134\) | − | 1.33393i | − | 0.115234i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.22062 | + | 2.43678i | 0.361915 | + | 0.208952i | ||||
\(137\) | 1.75034 | − | 3.03168i | 0.149542 | − | 0.259014i | −0.781516 | − | 0.623885i | \(-0.785553\pi\) |
0.931058 | + | 0.364871i | \(0.118887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.78031i | 0.151004i | 0.997146 | + | 0.0755021i | \(0.0240560\pi\) | ||||
−0.997146 | + | 0.0755021i | \(0.975944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.25773 | + | 1.30350i | −0.189465 | + | 0.109388i | ||||
\(143\) | −3.50279 | − | 2.02234i | −0.292918 | − | 0.169116i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.82406 | −0.233721 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 10.1107i | − | 0.831092i | ||||||
\(149\) | 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 | \(0.178677\pi\) | |||||||
\(152\) | 6.30208 | − | 3.63851i | 0.511167 | − | 0.295122i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.195010 | + | 1.73331i | −0.0157144 | + | 0.139674i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.17124 | + | 7.22480i | −0.332901 | + | 0.576602i | −0.983079 | − | 0.183180i | \(-0.941361\pi\) |
0.650178 | + | 0.759782i | \(0.274694\pi\) | |||||||
\(158\) | 2.88837 | − | 5.00280i | 0.229786 | − | 0.398001i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.86740 | − | 11.1512i | −0.383605 | − | 0.878840i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0488 | − | 12.1525i | 1.64867 | − | 0.951858i | 0.671064 | − | 0.741400i | \(-0.265838\pi\) |
0.977603 | − | 0.210458i | \(-0.0674956\pi\) | |||||||
\(164\) | −3.12617 | + | 5.41468i | −0.244113 | + | 0.422816i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.44894 | + | 3.72330i | −0.500535 | + | 0.288984i | ||||
\(167\) | 7.48724i | 0.579380i | 0.957120 | + | 0.289690i | \(0.0935523\pi\) | ||||
−0.957120 | + | 0.289690i | \(0.906448\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.6400 | 1.89538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.82525 | + | 4.51791i | 0.596670 | + | 0.344487i | ||||
\(173\) | −12.3328 | + | 7.12036i | −0.937647 | + | 0.541351i | −0.889222 | − | 0.457476i | \(-0.848754\pi\) |
−0.0484252 | + | 0.998827i | \(0.515420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.659263i | 0.0496938i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.66489 | + | 4.61572i | −0.199742 | + | 0.345963i | ||||
\(179\) | −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 | \(0.924221\pi\) | |||||||
\(182\) | −6.49350 | − | 14.8766i | −0.481331 | − | 1.10273i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.29939 | − | 3.98266i | −0.169513 | − | 0.293606i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.60648 | − | 2.78250i | −0.117477 | − | 0.203477i | ||||
\(188\) | − | 12.0027i | − | 0.875388i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.8926 | − | 10.9077i | 1.36702 | − | 0.789251i | 0.376477 | − | 0.926426i | \(-0.377135\pi\) |
0.990547 | + | 0.137175i | \(0.0438022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.09462 | − | 1.20933i | −0.150774 | − | 0.0870495i | 0.422715 | − | 0.906263i | \(-0.361077\pi\) |
−0.573489 | + | 0.819213i | \(0.694411\pi\) | |||||||
\(194\) | −5.73958 | − | 9.94125i | −0.412078 | − | 0.713740i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.75953 | + | 5.13292i | −0.339967 | + | 0.366637i | ||||
\(197\) | −6.24457 | −0.444907 | −0.222454 | − | 0.974943i | \(-0.571407\pi\) | ||||
−0.222454 | + | 0.974943i | \(0.571407\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.38388 | + | 2.53103i | 0.310765 | + | 0.179420i | 0.647269 | − | 0.762262i | \(-0.275911\pi\) |
−0.336504 | + | 0.941682i | \(0.609244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.4975 | −1.09040 | ||||||||
\(203\) | −2.39458 | + | 21.2838i | −0.168067 | + | 1.49383i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.03422 | + | 1.79131i | −0.0720572 | + | 0.124807i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.06757 | − | 5.31319i | −0.212698 | − | 0.368403i | ||||
\(209\) | −4.79747 | −0.331848 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.72168 | 0.393896 | 0.196948 | − | 0.980414i | \(-0.436897\pi\) | ||||
0.196948 | + | 0.980414i | \(0.436897\pi\) | |||||||
\(212\) | −6.10540 | − | 10.5749i | −0.419321 | − | 0.726285i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.44632 | − | 9.43331i | 0.372303 | − | 0.644848i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.86676 | + | 1.37726i | 0.126724 | + | 0.0934946i | ||||
\(218\) | 14.3451 | 0.971572 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.8941 | + | 14.9500i | 1.74183 | + | 1.00564i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.61006 | −0.442642 | −0.221321 | − | 0.975201i | \(-0.571037\pi\) | ||||
−0.221321 | + | 0.975201i | \(0.571037\pi\) | |||||||
\(224\) | −1.57075 | + | 2.12902i | −0.104950 | + | 0.142251i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.95403 | + | 10.3127i | 0.396056 | + | 0.685989i | ||||
\(227\) | 20.8328 | + | 12.0278i | 1.38272 | + | 0.798314i | 0.992481 | − | 0.122400i | \(-0.0390590\pi\) |
0.390239 | + | 0.920714i | \(0.372392\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.39811 | − | 2.53925i | 0.290635 | − | 0.167798i | −0.347593 | − | 0.937645i | \(-0.613001\pi\) |
0.638228 | + | 0.769847i | \(0.279668\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.09526i | 0.531480i | ||||||||
\(233\) | −11.0386 | − | 19.1195i | −0.723165 | − | 1.25256i | −0.959725 | − | 0.280941i | \(-0.909353\pi\) |
0.236560 | − | 0.971617i | \(-0.423980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.06613 | + | 7.04274i | 0.264682 | + | 0.458443i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.44160 | − | 12.8134i | 0.0934451 | − | 0.830568i | ||||
\(239\) | − | 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 | \(0.419551\pi\) | |||||||
\(242\) | −5.28269 | + | 9.14988i | −0.339584 | + | 0.588177i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 0.0714487i | − | 0.00457403i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 38.6642 | − | 22.3228i | 2.46014 | − | 1.42036i | ||||
\(248\) | 0.759345 | + | 0.438408i | 0.0482185 | + | 0.0278390i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0445 | 1.01272 | 0.506361 | − | 0.862321i | \(-0.330990\pi\) | ||||
0.506361 | + | 0.862321i | \(0.330990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.03181i | 0.190608i | ||||||||
\(254\) | 12.6668 | − | 7.31319i | 0.794787 | − | 0.458870i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.2617 | − | 8.23399i | 0.889620 | − | 0.513622i | 0.0158016 | − | 0.999875i | \(-0.494970\pi\) |
0.873818 | + | 0.486253i | \(0.161637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.5166 | + | 10.7012i | −1.52339 | + | 0.664943i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.64037 | − | 2.84120i | 0.101342 | − | 0.175530i | ||||
\(263\) | 2.81031 | − | 4.86760i | 0.173291 | − | 0.300149i | −0.766278 | − | 0.642510i | \(-0.777893\pi\) |
0.939569 | + | 0.342361i | \(0.111227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.4929 | − | 11.4304i | −0.949933 | − | 0.700843i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.15522 | + | 0.666965i | −0.0705661 | + | 0.0407414i | ||||
\(269\) | 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 | \(0.523293\pi\) | |||||||
\(272\) | − | 4.87356i | − | 0.295503i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.50069 | −0.211484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.4426 | − | 12.9572i | −1.34844 | − | 0.778525i | −0.360415 | − | 0.932792i | \(-0.617365\pi\) |
−0.988029 | + | 0.154267i | \(0.950698\pi\) | |||||||
\(278\) | 1.54180 | − | 0.890157i | 0.0924708 | − | 0.0533881i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.24160i | 0.551308i | 0.961257 | + | 0.275654i | \(0.0888943\pi\) | ||||
−0.961257 | + | 0.275654i | \(0.911106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.54800 | − | 6.14531i | 0.210907 | − | 0.365301i | −0.741092 | − | 0.671404i | \(-0.765692\pi\) |
0.951999 | + | 0.306103i | \(0.0990251\pi\) | |||||||
\(284\) | 2.25773 | + | 1.30350i | 0.133972 | + | 0.0773486i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.04467i | 0.239166i | ||||||||
\(287\) | 16.4384 | + | 1.84944i | 0.970329 | + | 0.109169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.37577 | + | 5.84701i | 0.198575 | + | 0.343942i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.41203 | + | 2.44571i | 0.0826328 | + | 0.143124i | ||||
\(293\) | − | 8.94657i | − | 0.522664i | −0.965249 | − | 0.261332i | \(-0.915838\pi\) | ||
0.965249 | − | 0.261332i | \(-0.0841617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.75609 | + | 5.05533i | −0.508938 | + | 0.293835i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.14910 | − | 4.12754i | −0.414136 | − | 0.239102i | ||||
\(299\) | −14.1071 | − | 24.4342i | −0.815834 | − | 1.41307i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.67280 | − | 23.7567i | 0.154058 | − | 1.36931i | ||||
\(302\) | 0.927090 | 0.0533480 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.30208 | − | 3.63851i | −0.361449 | − | 0.208683i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.62584 | −0.435230 | −0.217615 | − | 0.976035i | \(-0.569828\pi\) | ||||
−0.217615 | + | 0.976035i | \(0.569828\pi\) | |||||||
\(308\) | 1.59860 | − | 0.697771i | 0.0910884 | − | 0.0397592i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.20348 | − | 5.54859i | 0.181653 | − | 0.314632i | −0.760791 | − | 0.648997i | \(-0.775189\pi\) |
0.942443 | + | 0.334366i | \(0.108522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.52850 | − | 7.84360i | −0.255966 | − | 0.443346i | 0.709191 | − | 0.705016i | \(-0.249060\pi\) |
−0.965157 | + | 0.261670i | \(0.915727\pi\) | |||||||
\(314\) | 8.34248 | 0.470793 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.77674 | −0.324967 | ||||||||
\(317\) | −14.2534 | − | 24.6876i | −0.800552 | − | 1.38660i | −0.919253 | − | 0.393666i | \(-0.871207\pi\) |
0.118702 | − | 0.992930i | \(-0.462127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.66845 | − | 4.62189i | 0.149405 | − | 0.258776i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.22355 | + | 9.79091i | −0.402553 | + | 0.545626i | ||||
\(323\) | 35.4650 | 1.97332 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.0488 | − | 12.1525i | −1.16578 | − | 0.673065i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.25234 | 0.345228 | ||||||||
\(329\) | −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 | \(0.969265\pi\) | |||||||
\(332\) | 6.44894 | + | 3.72330i | 0.353932 | + | 0.204343i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.48414 | − | 3.74362i | 0.354797 | − | 0.204842i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.480936i | 0.0261983i | 0.999914 | + | 0.0130991i | \(0.00416970\pi\) | ||||
−0.999914 | + | 0.0130991i | \(0.995830\pi\) | |||||||
\(338\) | −12.3200 | − | 21.3389i | −0.670119 | − | 1.16068i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.289026 | − | 0.500608i | −0.0156516 | − | 0.0271094i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4840 | + | 6.10828i | 0.944045 | + | 0.329816i | ||||
\(344\) | − | 9.03582i | − | 0.487179i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3328 | + | 7.12036i | 0.663017 | + | 0.382793i | ||||
\(347\) | −1.73829 | + | 3.01081i | −0.0933165 | + | 0.161629i | −0.908905 | − | 0.417004i | \(-0.863080\pi\) |
0.815588 | + | 0.578633i | \(0.196414\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.611574i | 0.0327368i | 0.999866 | + | 0.0163684i | \(0.00521046\pi\) | ||||
−0.999866 | + | 0.0163684i | \(0.994790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.570938 | − | 0.329631i | 0.0304311 | − | 0.0175694i | ||||
\(353\) | 18.8649 | + | 10.8916i | 1.00407 | + | 0.579703i | 0.909451 | − | 0.415810i | \(-0.136502\pi\) |
0.0946235 | + | 0.995513i | \(0.469835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.32978 | 0.282478 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.1435i | 0.694656i | ||||||||
\(359\) | −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 | ||||
\(362\) | 5.49525 | − | 3.17268i | 0.288824 | − | 0.166753i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.63679 | + | 13.0619i | −0.505105 | + | 0.684627i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4278 | + | 18.0615i | −0.544327 | + | 0.942802i | 0.454322 | + | 0.890837i | \(0.349881\pi\) |
−0.998649 | + | 0.0519641i | \(0.983452\pi\) | |||||||
\(368\) | −2.29939 | + | 3.98266i | −0.119864 | + | 0.207611i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.1801 | + | 25.9971i | −0.995784 | + | 1.34970i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.21673 | + | 0.702477i | −0.0629997 | + | 0.0363729i | −0.531169 | − | 0.847266i | \(-0.678247\pi\) |
0.468169 | + | 0.883639i | \(0.344914\pi\) | |||||||
\(374\) | −1.60648 | + | 2.78250i | −0.0830689 | + | 0.143880i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.3947 | + | 6.00136i | −0.536063 | + | 0.309496i | ||||
\(377\) | 49.6656i | 2.55791i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.8729 | −1.12353 | −0.561766 | − | 0.827296i | \(-0.689878\pi\) | ||||
−0.561766 | + | 0.827296i | \(0.689878\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.8926 | − | 10.9077i | −0.966632 | − | 0.558085i | ||||
\(383\) | −29.9197 | + | 17.2741i | −1.52882 | + | 0.882666i | −0.529411 | + | 0.848365i | \(0.677587\pi\) |
−0.999412 | + | 0.0343009i | \(0.989080\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.41866i | 0.123107i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.73958 | + | 9.94125i | −0.291383 | + | 0.504690i | ||||
\(389\) | 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 | ||||||
\(392\) | 6.82500 | + | 1.55542i | 0.344715 | + | 0.0785604i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.12229 | + | 5.40796i | 0.157299 | + | 0.272449i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.90061 | + | 5.02400i | 0.145577 | + | 0.252147i | 0.929588 | − | 0.368600i | \(-0.120163\pi\) |
−0.784011 | + | 0.620747i | \(0.786829\pi\) | |||||||
\(398\) | − | 5.06207i | − | 0.253739i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.7829 | + | 10.2670i | −0.888036 | + | 0.512708i | −0.873300 | − | 0.487183i | \(-0.838024\pi\) |
−0.0147366 | + | 0.999891i | \(0.504691\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.65869 | + | 2.68970i | 0.232066 | + | 0.133983i | ||||
\(404\) | 7.74874 | + | 13.4212i | 0.385514 | + | 0.667730i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.6296 | − | 8.56811i | 0.974199 | − | 0.425228i | ||||
\(407\) | 6.66558 | 0.330401 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.85765 | − | 4.53662i | −0.388536 | − | 0.224321i | 0.292990 | − | 0.956116i | \(-0.405350\pi\) |
−0.681526 | + | 0.731794i | \(0.738683\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.06843 | 0.101904 | ||||||||
\(413\) | 12.7738 | − | 17.3138i | 0.628556 | − | 0.851954i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.06757 | + | 5.31319i | −0.150400 | + | 0.260501i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.39873 | + | 4.15473i | 0.117326 | + | 0.203214i | ||||
\(419\) | 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 | \(0.321514\pi\) | |||||||
\(422\) | −2.86084 | − | 4.95512i | −0.139263 | − | 0.241211i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.10540 | + | 10.5749i | −0.296504 | + | 0.513561i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.173250 | + | 0.0756221i | −0.00838417 | + | 0.00365961i | ||||
\(428\) | −10.8926 | −0.526516 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.9922 | − | 7.50107i | −0.625814 | − | 0.361314i | 0.153315 | − | 0.988177i | \(-0.451005\pi\) |
−0.779129 | + | 0.626864i | \(0.784338\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.2578 | −1.69438 | −0.847190 | − | 0.531289i | \(-0.821708\pi\) | ||||
−0.847190 | + | 0.531289i | \(0.821708\pi\) | |||||||
\(434\) | 0.259363 | − | 2.30529i | 0.0124498 | − | 0.110658i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.17254 | − | 12.4232i | −0.343502 | − | 0.594964i | ||||
\(437\) | −28.9819 | − | 16.7327i | −1.38639 | − | 0.800434i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4755 | + | 14.7083i | −1.21588 | + | 0.701988i | −0.964034 | − | 0.265779i | \(-0.914371\pi\) |
−0.251846 | + | 0.967767i | \(0.581038\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 29.9000i | − | 1.42220i | ||||||
\(443\) | 14.7259 | + | 25.5061i | 0.699651 | + | 1.21183i | 0.968588 | + | 0.248673i | \(0.0799943\pi\) |
−0.268937 | + | 0.963158i | \(0.586672\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.30503 | + | 5.72448i | 0.156498 | + | 0.271062i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.62916 | + | 0.295801i | 0.124216 | + | 0.0139753i | ||||
\(449\) | 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 | ||||
\(452\) | 5.95403 | − | 10.3127i | 0.280054 | − | 0.485067i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 24.0556i | − | 1.12899i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.90532 | − | 3.98679i | 0.323017 | − | 0.186494i | −0.329720 | − | 0.944079i | \(-0.606954\pi\) |
0.652737 | + | 0.757585i | \(0.273621\pi\) | |||||||
\(458\) | −4.39811 | − | 2.53925i | −0.205510 | − | 0.118651i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.9112 | 1.85885 | 0.929425 | − | 0.369012i | \(-0.120304\pi\) | ||||
0.929425 | + | 0.369012i | \(0.120304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.6663i | − | 0.821021i | −0.911856 | − | 0.410511i | \(-0.865350\pi\) | ||
0.911856 | − | 0.410511i | \(-0.134650\pi\) | |||||||
\(464\) | 7.01070 | − | 4.04763i | 0.325464 | − | 0.187907i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.0386 | + | 19.1195i | −0.511355 | + | 0.885692i | ||||
\(467\) | −19.0104 | + | 10.9757i | −0.879698 | + | 0.507894i | −0.870559 | − | 0.492064i | \(-0.836242\pi\) |
−0.00913924 | + | 0.999958i | \(0.502909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.83997 | + | 2.09527i | 0.131137 | + | 0.0967507i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.06613 | − | 7.04274i | 0.187159 | − | 0.324168i | ||||
\(473\) | −2.97849 | + | 5.15890i | −0.136951 | + | 0.237206i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −11.8175 | + | 5.15823i | −0.541655 | + | 0.236427i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −15.4634 | + | 8.92778i | −0.707278 | + | 0.408347i | ||||
\(479\) | 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 | ||||
\(482\) | − | 21.7546i | − | 0.990897i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.5654 | 0.480244 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.8602 | − | 7.42482i | −0.582750 | − | 0.336451i | 0.179476 | − | 0.983762i | \(-0.442560\pi\) |
−0.762225 | + | 0.647312i | \(0.775893\pi\) | |||||||
\(488\) | −0.0618764 | + | 0.0357243i | −0.00280101 | + | 0.00161716i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.6224i | − | 0.705029i | −0.935806 | − | 0.352515i | \(-0.885327\pi\) | ||
0.935806 | − | 0.352515i | \(-0.114673\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.7264 | + | 34.1670i | −0.888430 | + | 1.53881i | ||||
\(494\) | −38.6642 | − | 22.3228i | −1.73958 | − | 1.00435i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.876816i | − | 0.0393702i | ||||||
\(497\) | 0.771153 | − | 6.85424i | 0.0345910 | − | 0.307455i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.23416 | + | 15.9940i | 0.413378 | + | 0.715991i | 0.995257 | − | 0.0972842i | \(-0.0310156\pi\) |
−0.581879 | + | 0.813275i | \(0.697682\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.02227 | − | 13.8950i | −0.358052 | − | 0.620164i | ||||
\(503\) | 5.46007i | 0.243452i | 0.992564 | + | 0.121726i | \(0.0388430\pi\) | ||||
−0.992564 | + | 0.121726i | \(0.961157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.62562 | − | 1.51590i | 0.116723 | − | 0.0673901i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.6668 | − | 7.31319i | −0.561999 | − | 0.324470i | ||||
\(509\) | 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 | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.2617 | − | 8.23399i | −0.629056 | − | 0.363186i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.91294 | 0.348011 | ||||||||
\(518\) | 21.5258 | + | 15.8814i | 0.945791 | + | 0.697787i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.2147 | − | 26.3526i | 0.666566 | − | 1.15453i | −0.312292 | − | 0.949986i | \(-0.601097\pi\) |
0.978858 | − | 0.204541i | \(-0.0655701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.113392 | − | 0.196400i | −0.00495828 | − | 0.00858799i | 0.863536 | − | 0.504288i | \(-0.168245\pi\) |
−0.868494 | + | 0.495700i | \(0.834912\pi\) | |||||||
\(524\) | −3.28074 | −0.143320 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.62062 | −0.245070 | ||||||||
\(527\) | 2.13661 | + | 3.70071i | 0.0930721 | + | 0.161206i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.925602 | − | 1.60319i | 0.0402436 | − | 0.0697039i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.15255 | + | 19.1325i | −0.0933247 | + | 0.829498i | ||||
\(533\) | 38.3590 | 1.66151 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.15522 | + | 0.666965i | 0.0498978 | + | 0.0288085i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.54163 | −0.282030 | ||||||||
\(539\) | −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 | \(-0.460929\pi\) | |||||||
\(542\) | 16.0238 | + | 9.25135i | 0.688282 | + | 0.397380i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.22062 | + | 2.43678i | −0.180958 | + | 0.104476i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.2444i | − | 0.609047i | −0.952505 | − | 0.304524i | \(-0.901503\pi\) | ||
0.952505 | − | 0.304524i | \(-0.0984972\pi\) | |||||||
\(548\) | 1.75034 | + | 3.03168i | 0.0747709 | + | 0.129507i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.4547 | + | 51.0170i | 1.25481 | + | 2.17340i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.11416 | + | 14.0076i | 0.260001 | + | 0.595662i | ||||
\(554\) | 25.9145i | 1.10100i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.54180 | − | 0.890157i | −0.0653867 | − | 0.0377511i | ||||
\(557\) | −9.45492 | + | 16.3764i | −0.400618 | + | 0.693890i | −0.993801 | − | 0.111177i | \(-0.964538\pi\) |
0.593183 | + | 0.805068i | \(0.297871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 55.4361i | − | 2.34470i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.00346 | − | 4.62080i | 0.337606 | − | 0.194917i | ||||
\(563\) | 34.0414 | + | 19.6538i | 1.43467 | + | 0.828310i | 0.997472 | − | 0.0710537i | \(-0.0226362\pi\) |
0.437202 | + | 0.899363i | \(0.355969\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.09599 | −0.298267 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.60701i | − | 0.109388i | ||||||
\(569\) | 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 | \(0.988114\pi\) | |||||||
\(572\) | 3.50279 | − | 2.02234i | 0.146459 | − | 0.0845581i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.61754 | − | 15.1608i | −0.276211 | − | 0.632800i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.14235 | + | 8.90681i | −0.214079 | + | 0.370795i | −0.952987 | − | 0.303010i | \(-0.902008\pi\) |
0.738908 | + | 0.673806i | \(0.235342\pi\) | |||||||
\(578\) | 3.37577 | − | 5.84701i | 0.140414 | − | 0.243204i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.20271 | − | 19.5783i | 0.0913837 | − | 0.812246i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.97161 | − | 4.02506i | 0.288735 | − | 0.166701i | ||||
\(584\) | 1.41203 | − | 2.44571i | 0.0584302 | − | 0.101204i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.74795 | + | 4.47328i | −0.320065 | + | 0.184790i | ||||
\(587\) | − | 25.1241i | − | 1.03698i | −0.855083 | − | 0.518490i | \(-0.826494\pi\) | ||
0.855083 | − | 0.518490i | \(-0.173506\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.38061 | 0.262909 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.75609 | + | 5.05533i | 0.359873 | + | 0.207773i | ||||
\(593\) | −8.75538 | + | 5.05492i | −0.359540 | + | 0.207581i | −0.668879 | − | 0.743371i | \(-0.733226\pi\) |
0.309339 | + | 0.950952i | \(0.399892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.25507i | 0.338141i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.1071 | + | 24.4342i | −0.576882 | + | 0.999189i | ||||
\(599\) | 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 | \(0.899028\pi\) | |||||||
\(602\) | −21.9103 | + | 9.56361i | −0.892996 | + | 0.389784i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.463545 | − | 0.802883i | −0.0188614 | − | 0.0326689i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.7438 | − | 34.1973i | −0.801377 | − | 1.38802i | −0.918710 | − | 0.394932i | \(-0.870768\pi\) |
0.117334 | − | 0.993093i | \(-0.462565\pi\) | |||||||
\(608\) | 7.27702i | 0.295122i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −63.7727 | + | 36.8192i | −2.57997 | + | 1.48954i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.8258 | + | 8.55968i | 0.598809 | + | 0.345722i | 0.768573 | − | 0.639762i | \(-0.220967\pi\) |
−0.169764 | + | 0.985485i | \(0.554301\pi\) | |||||||
\(614\) | 3.81292 | + | 6.60417i | 0.153877 | + | 0.266523i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.40359 | − | 1.03554i | −0.0565521 | − | 0.0417230i | ||||
\(617\) | −5.80201 | −0.233580 | −0.116790 | − | 0.993157i | \(-0.537260\pi\) | ||||
−0.116790 | + | 0.993157i | \(0.537260\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.5344 | − | 17.0517i | −1.18709 | − | 0.685366i | −0.229445 | − | 0.973322i | \(-0.573691\pi\) |
−0.957644 | + | 0.287956i | \(0.907024\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.40696 | −0.256896 | ||||||||
\(623\) | −5.64109 | − | 12.9238i | −0.226006 | − | 0.517780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.52850 | + | 7.84360i | −0.180995 | + | 0.313493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.17124 | − | 7.22480i | −0.166451 | − | 0.288301i | ||||
\(629\) | −49.2749 | −1.96472 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1261 | 1.31873 | 0.659365 | − | 0.751823i | \(-0.270825\pi\) | ||||
0.659365 | + | 0.751823i | \(0.270825\pi\) | |||||||
\(632\) | 2.88837 | + | 5.00280i | 0.114893 | + | 0.199001i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.2534 | + | 24.6876i | −0.566076 | + | 0.980472i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 41.8724 | + | 9.54270i | 1.65904 | + | 0.378096i | ||||
\(638\) | −5.33690 | −0.211290 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.72685 | − | 0.997000i | −0.0682067 | − | 0.0393791i | 0.465509 | − | 0.885043i | \(-0.345871\pi\) |
−0.533716 | + | 0.845664i | \(0.679205\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.661676 | −0.0260940 | −0.0130470 | − | 0.999915i | \(-0.504153\pi\) | ||||
−0.0130470 | + | 0.999915i | \(0.504153\pi\) | |||||||
\(644\) | 12.0910 | + | 1.36032i | 0.476450 | + | 0.0536042i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.7325 | − | 30.7136i | −0.697675 | − | 1.20841i | ||||
\(647\) | 15.9223 | + | 9.19276i | 0.625971 | + | 0.361405i | 0.779190 | − | 0.626787i | \(-0.215631\pi\) |
−0.153219 | + | 0.988192i | \(0.548964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.64302 | + | 2.68065i | −0.182254 | + | 0.105225i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.3050i | 0.951858i | ||||||||
\(653\) | −8.69323 | − | 15.0571i | −0.340193 | − | 0.589231i | 0.644276 | − | 0.764793i | \(-0.277159\pi\) |
−0.984468 | + | 0.175562i | \(0.943826\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.12617 | − | 5.41468i | −0.122056 | − | 0.211408i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25.5540 | + | 18.8533i | 0.996200 | + | 0.734978i | ||||
\(659\) | 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 | \(0.892136\pi\) | |||||||
\(662\) | −7.53535 | + | 13.0516i | −0.292870 | + | 0.507265i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 7.44660i | − | 0.288984i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.2407 | − | 18.6142i | 1.24836 | − | 0.720744i | ||||
\(668\) | −6.48414 | − | 3.74362i | −0.250879 | − | 0.144845i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0471035 | 0.00181841 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9964i | 0.847898i | 0.905686 | + | 0.423949i | \(0.139356\pi\) | ||||
−0.905686 | + | 0.423949i | \(0.860644\pi\) | |||||||
\(674\) | 0.416503 | − | 0.240468i | 0.0160431 | − | 0.00926249i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3200 | + | 21.3389i | −0.473846 | + | 0.820725i | ||||
\(677\) | −10.7084 | + | 6.18250i | −0.411557 | + | 0.237613i | −0.691459 | − | 0.722416i | \(-0.743032\pi\) |
0.279901 | + | 0.960029i | \(0.409698\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 30.1806 | + | 3.39554i | 1.15823 | + | 0.130309i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.289026 | + | 0.500608i | −0.0110674 | + | 0.0191693i | ||||
\(683\) | −14.9892 | + | 25.9621i | −0.573546 | + | 0.993411i | 0.422652 | + | 0.906292i | \(0.361099\pi\) |
−0.996198 | + | 0.0871187i | \(0.972234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.45205 | − | 18.1957i | −0.131800 | − | 0.694715i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.82525 | + | 4.51791i | −0.298335 | + | 0.172244i | ||||
\(689\) | −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 | \(0.277262\pi\) | |||||||
\(692\) | − | 14.2407i | − | 0.541351i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.47659 | 0.131969 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.3888 | + | 15.2356i | 0.999546 | + | 0.577088i | ||||
\(698\) | 0.529638 | − | 0.305787i | 0.0200471 | − | 0.0115742i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.9022i | 1.69593i | 0.530050 | + | 0.847967i | \(0.322173\pi\) | ||||
−0.530050 | + | 0.847967i | \(0.677827\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.7878 | + | 63.7183i | −1.38748 | + | 2.40318i | ||||
\(704\) | −0.570938 | − | 0.329631i | −0.0215180 | − | 0.0124234i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 21.7833i | − | 0.819824i | ||||||
\(707\) | 24.3427 | − | 32.9945i | 0.915502 | − | 1.24089i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.39264 | + | 2.41213i | 0.0523019 | + | 0.0905895i | 0.890991 | − | 0.454021i | \(-0.150011\pi\) |
−0.838689 | + | 0.544610i | \(0.816678\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.66489 | − | 4.61572i | −0.0998709 | − | 0.172981i | ||||
\(713\) | − | 4.03229i | − | 0.151010i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.3826 | − | 6.57176i | 0.425388 | − | 0.245598i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.0413 | + | 8.10672i | 0.524015 | + | 0.302540i | ||||
\(719\) | −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 | ||||
\(722\) | −33.9550 | −1.26368 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.49525 | − | 3.17268i | −0.204229 | − | 0.117912i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.6632 | 1.10015 | 0.550074 | − | 0.835116i | \(-0.314600\pi\) | ||||
0.550074 | + | 0.835116i | \(0.314600\pi\) | |||||||
\(728\) | 16.1303 | + | 1.81478i | 0.597829 | + | 0.0672602i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.0183 | − | 38.1368i | 0.814376 | − | 1.41054i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.5155 | + | 19.9455i | 0.425336 | + | 0.736704i | 0.996452 | − | 0.0841657i | \(-0.0268225\pi\) |
−0.571116 | + | 0.820870i | \(0.693489\pi\) | |||||||
\(734\) | 20.8556 | 0.769794 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.59878 | 0.169513 | ||||||||
\(737\) | −0.439705 | − | 0.761591i | −0.0161967 | − | 0.0280536i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.2029 | − | 29.7964i | 0.632821 | − | 1.09608i | −0.354152 | − | 0.935188i | \(-0.615230\pi\) |
0.986972 | − | 0.160889i | \(-0.0514363\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 32.1042 | + | 3.61196i | 1.17858 | + | 0.132599i | ||||
\(743\) | 40.6201 | 1.49021 | 0.745103 | − | 0.666950i | \(-0.232400\pi\) | ||||
0.745103 | + | 0.666950i | \(0.232400\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.21673 | + | 0.702477i | 0.0445475 | + | 0.0257195i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.21295 | 0.117477 | ||||||||
\(749\) | 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 | \(-0.481411\pi\) | |||||||
\(752\) | 10.3947 | + | 6.00136i | 0.379054 | + | 0.218847i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 43.0117 | − | 24.8328i | 1.56639 | − | 0.904357i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.7755i | 1.84547i | 0.385440 | + | 0.922733i | \(0.374050\pi\) | ||||
−0.385440 | + | 0.922733i | \(0.625950\pi\) | |||||||
\(758\) | 10.9364 | + | 18.9424i | 0.397229 | + | 0.688021i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0315 | − | 31.2316i | −0.653643 | − | 1.13214i | −0.982232 | − | 0.187670i | \(-0.939906\pi\) |
0.328589 | − | 0.944473i | \(-0.393427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.5326 | + | 30.5410i | −0.815734 | + | 1.10566i | ||||
\(764\) | 21.8153i | 0.789251i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.9197 | + | 17.2741i | 1.08104 | + | 0.624139i | ||||
\(767\) | 24.9463 | − | 43.2082i | 0.900758 | − | 1.56016i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5798i | 0.633943i | 0.948435 | + | 0.316971i | \(0.102666\pi\) | ||||
−0.948435 | + | 0.316971i | \(0.897334\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.09462 | − | 1.20933i | 0.0753871 | − | 0.0435248i | ||||
\(773\) | −42.8367 | − | 24.7318i | −1.54073 | − | 0.889541i | −0.998793 | − | 0.0491225i | \(-0.984358\pi\) |
−0.541938 | − | 0.840419i | \(-0.682309\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.4792 | 0.412078 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 11.5939i | − | 0.415661i | ||||||
\(779\) | 39.4028 | − | 22.7492i | 1.41175 | − | 0.815074i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.859351 | + | 1.48844i | −0.0307500 | + | 0.0532605i | ||||
\(782\) | −19.4097 | + | 11.2062i | −0.694090 | + | 0.400733i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.06547 | − | 6.68833i | −0.0737669 | − | 0.238869i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.83998 | + | 8.38310i | −0.172527 | + | 0.298825i | −0.939303 | − | 0.343090i | \(-0.888526\pi\) |
0.766776 | + | 0.641915i | \(0.221860\pi\) | |||||||
\(788\) | 3.12229 | − | 5.40796i | 0.111227 | − | 0.192651i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.3082 | − | 3.52241i | −1.11319 | − | 0.125242i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.379620 | + | 0.219174i | −0.0134807 | + | 0.00778310i | ||||
\(794\) | 2.90061 | − | 5.02400i | 0.102939 | − | 0.178295i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.38388 | + | 2.53103i | −0.155383 | + | 0.0897101i | ||||
\(797\) | 15.1216i | 0.535636i | 0.963470 | + | 0.267818i | \(0.0863026\pi\) | ||||
−0.963470 | + | 0.267818i | \(0.913697\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58.4959 | −2.06944 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.7829 | + | 10.2670i | 0.627937 | + | 0.362539i | ||||
\(803\) | −1.61236 | + | 0.930899i | −0.0568991 | + | 0.0328507i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 5.37940i | − | 0.189481i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.74874 | − | 13.4212i | 0.272600 | − | 0.472157i | ||||
\(809\) | 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 | \(0.601051\pi\) | |||||||
\(812\) | −17.2350 | − | 12.7157i | −0.604830 | − | 0.446232i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.33279 | − | 5.77257i | −0.116814 | − | 0.202328i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.8769 | − | 56.9445i | −1.15022 | − | 1.99224i | ||||
\(818\) | 9.07323i | 0.317238i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.3717 | + | 13.4936i | −0.815677 | + | 0.470931i | −0.848924 | − | 0.528516i | \(-0.822749\pi\) |
0.0332463 | + | 0.999447i | \(0.489415\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.42130 | − | 3.12999i | −0.188975 | − | 0.109105i | 0.402528 | − | 0.915408i | \(-0.368132\pi\) |
−0.591502 | + | 0.806303i | \(0.701465\pi\) | |||||||
\(824\) | −1.03422 | − | 1.79131i | −0.0360286 | − | 0.0624034i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.3810 | − | 2.40553i | −0.743941 | − | 0.0836989i | ||||
\(827\) | −32.0713 | −1.11523 | −0.557615 | − | 0.830100i | \(-0.688283\pi\) | ||||
−0.557615 | + | 0.830100i | \(0.688283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.3975 | − | 6.00303i | −0.361122 | − | 0.208494i | 0.308451 | − | 0.951240i | \(-0.400189\pi\) |
−0.669573 | + | 0.742746i | \(0.733523\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.13514 | 0.212698 | ||||||||
\(833\) | 25.0156 | + | 23.1958i | 0.866738 | + | 0.803688i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.39873 | − | 4.15473i | 0.0829620 | − | 0.143694i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.65081 | − | 4.59134i | −0.0915707 | − | 0.158605i | ||||
\(839\) | 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 | ||||||||
\(842\) | −10.9117 | − | 18.8996i | −0.376042 | − | 0.651324i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.86084 | + | 4.95512i | −0.0984741 | + | 0.170562i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.1825 | − | 25.6192i | −0.384236 | − | 0.880285i | ||||
\(848\) | 12.2108 | 0.419321 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.2674 | + | 23.2484i | 1.38035 | + | 0.796944i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.4695 | −1.41989 | −0.709944 | − | 0.704258i | \(-0.751280\pi\) | ||||
−0.709944 | + | 0.704258i | \(0.751280\pi\) | |||||||
\(854\) | 0.152116 | + | 0.112228i | 0.00520530 | + | 0.00384037i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.44632 | + | 9.43331i | 0.186152 | + | 0.322424i | ||||
\(857\) | −48.3925 | − | 27.9394i | −1.65306 | − | 0.954393i | −0.975805 | − | 0.218641i | \(-0.929837\pi\) |
−0.677252 | − | 0.735751i | \(-0.736829\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0097 | − | 15.0167i | 0.887440 | − | 0.512364i | 0.0143355 | − | 0.999897i | \(-0.495437\pi\) |
0.873104 | + | 0.487534i | \(0.162103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.0021i | 0.510975i | ||||||||
\(863\) | 1.02317 | + | 1.77218i | 0.0348291 | + | 0.0603258i | 0.882915 | − | 0.469534i | \(-0.155578\pi\) |
−0.848085 | + | 0.529860i | \(0.822245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.6289 | + | 30.5341i | 0.599054 | + | 1.03759i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.12612 | + | 0.928032i | −0.0721654 | + | 0.0314995i | ||||
\(869\) | − | 3.80839i | − | 0.129191i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.08742 | + | 4.09192i | 0.240148 | + | 0.138650i | ||||
\(872\) | −7.17254 | + | 12.4232i | −0.242893 | + | 0.420703i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 33.4654i | 1.13199i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.08442 | − | 5.24489i | 0.306759 | − | 0.177107i | −0.338716 | − | 0.940889i | \(-0.609993\pi\) |
0.645475 | + | 0.763781i | \(0.276659\pi\) | |||||||
\(878\) | 25.4755 | + | 14.7083i | 0.859757 | + | 0.496381i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.2280 | −1.49008 | −0.745039 | − | 0.667021i | \(-0.767569\pi\) | ||||
−0.745039 | + | 0.667021i | \(0.767569\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.8143i | 0.801416i | 0.916206 | + | 0.400708i | \(0.131236\pi\) | ||||
−0.916206 | + | 0.400708i | \(0.868764\pi\) | |||||||
\(884\) | −25.8941 | + | 14.9500i | −0.870914 | + | 0.502822i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.7259 | − | 25.5061i | 0.494728 | − | 0.856893i | ||||
\(887\) | −27.0408 | + | 15.6120i | −0.907941 | + | 0.524200i | −0.879768 | − | 0.475403i | \(-0.842302\pi\) |
−0.0281729 | + | 0.999603i | \(0.508969\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.32649 | + | 38.4552i | −0.145106 | + | 1.28974i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.30503 | − | 5.72448i | 0.110661 | − | 0.191670i | ||||
\(893\) | −43.6720 | + | 75.6421i | −1.46143 | + | 2.53127i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.05841 | − | 2.42482i | −0.0353590 | − | 0.0810076i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 25.3233 | − | 14.6204i | 0.845049 | − | 0.487889i | ||||
\(899\) | −3.54903 | + | 6.14710i | −0.118367 | + | 0.205017i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.5372 | + | 29.7550i | −1.71695 | + | 0.991283i | ||||
\(902\) | 4.12193i | 0.137245i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.9081 | −0.396056 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3901 | − | 7.73076i | −0.444610 | − | 0.256696i | 0.260941 | − | 0.965355i | \(-0.415967\pi\) |
−0.705551 | + | 0.708659i | \(0.749301\pi\) | |||||||
\(908\) | −20.8328 | + | 12.0278i | −0.691360 | + | 0.399157i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 11.7655i | − | 0.389810i | −0.980822 | − | 0.194905i | \(-0.937560\pi\) | ||
0.980822 | − | 0.194905i | \(-0.0624398\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.45463 | + | 4.25155i | −0.0812365 | + | 0.140706i | ||||
\(914\) | −6.90532 | − | 3.98679i | −0.228408 | − | 0.131871i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.07850i | 0.167798i | ||||||||
\(917\) | 3.47237 | + | 7.95521i | 0.114668 | + | 0.262704i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.4078 | − | 26.6871i | −0.508256 | − | 0.880326i | −0.999954 | − | 0.00955987i | \(-0.996957\pi\) |
0.491698 | − | 0.870766i | \(-0.336376\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −19.9556 | − | 34.5641i | −0.657203 | − | 1.13831i | ||||
\(923\) | − | 15.9944i | − | 0.526460i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.2994 | + | 8.83314i | −0.502771 | + | 0.290275i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.01070 | − | 4.04763i | −0.230138 | − | 0.132870i | ||||
\(929\) | 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 | ||||
\(932\) | 22.0773 | 0.723165 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.0104 | + | 10.9757i | 0.622040 | + | 0.359135i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.7661 | −0.939747 | −0.469874 | − | 0.882734i | \(-0.655701\pi\) | ||||
−0.469874 | + | 0.882734i | \(0.655701\pi\) | |||||||
\(938\) | 0.394577 | − | 3.50712i | 0.0128834 | − | 0.114511i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.0535167 | − | 0.0926937i | 0.00174460 | − | 0.00302173i | −0.865152 | − | 0.501510i | \(-0.832778\pi\) |
0.866896 | + | 0.498488i | \(0.166111\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.3766 | − | 24.9009i | −0.468165 | − | 0.810886i | ||||
\(944\) | −8.13225 | −0.264682 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.95698 | 0.193678 | ||||||||
\(947\) | 7.36136 | + | 12.7502i | 0.239212 | + | 0.414327i | 0.960488 | − | 0.278320i | \(-0.0897776\pi\) |
−0.721276 | + | 0.692647i | \(0.756444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.66301 | − | 15.0048i | 0.281213 | − | 0.487076i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.3759 | + | 7.65515i | 0.336285 | + | 0.248105i | ||||
\(953\) | −10.5168 | −0.340672 | −0.170336 | − | 0.985386i | \(-0.554485\pi\) | ||||
−0.170336 | + | 0.985386i | \(0.554485\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.4634 | + | 8.92778i | 0.500121 | + | 0.288745i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33.9667 | −1.09742 | ||||||||
\(959\) | 5.49871 | − | 7.45304i | 0.177563 | − | 0.240671i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1156 | − | 26.1810i | −0.487600 | − | 0.844548i | ||||
\(962\) | 53.7199 | + | 31.0152i | 1.73200 | + | 0.999970i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.8401 | + | 10.8773i | −0.606798 | + | 0.350335i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.51148i | − | 0.273711i | −0.990591 | − | 0.136855i | \(-0.956300\pi\) | ||
0.990591 | − | 0.136855i | \(-0.0436995\pi\) | |||||||
\(968\) | −5.28269 | − | 9.14988i | −0.169792 | − | 0.294088i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.49465 | + | 7.78496i | 0.144240 | + | 0.249831i | 0.929089 | − | 0.369856i | \(-0.120593\pi\) |
−0.784849 | + | 0.619687i | \(0.787260\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.526618 | + | 4.68074i | −0.0168826 | + | 0.150057i | ||||
\(974\) | 14.8496i | 0.475813i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0618764 | + | 0.0357243i | 0.00198061 | + | 0.00114351i | ||||
\(977\) | 22.6877 | − | 39.2963i | 0.725845 | − | 1.25720i | −0.232781 | − | 0.972529i | \(-0.574782\pi\) |
0.958625 | − | 0.284671i | \(-0.0918843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.51372i | 0.112299i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.5294 | + | 7.81120i | −0.431741 | + | 0.249266i | ||||
\(983\) | 22.3797 | + | 12.9209i | 0.713802 | + | 0.412114i | 0.812467 | − | 0.583007i | \(-0.198124\pi\) |
−0.0986654 | + | 0.995121i | \(0.531457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 39.4527 | 1.25643 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 44.6456i | 1.42036i | ||||||||
\(989\) | −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 | \(0.990680\pi\) | |||||||
\(992\) | −0.759345 | + | 0.438408i | −0.0241092 | + | 0.0139195i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.32153 | + | 2.75928i | −0.200507 | + | 0.0875191i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.9894 | + | 43.2828i | −0.791421 | + | 1.37078i | 0.133666 | + | 0.991026i | \(0.457325\pi\) |
−0.925087 | + | 0.379755i | \(0.876008\pi\) | |||||||
\(998\) | 9.23416 | − | 15.9940i | 0.292302 | − | 0.506282i | ||||
\(999\) | 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.bp.g.899.12 | 24 | ||
3.2 | odd | 2 | 3150.2.bp.h.899.12 | 24 | |||
5.2 | odd | 4 | 3150.2.bf.e.1151.10 | yes | 24 | ||
5.3 | odd | 4 | 3150.2.bf.d.1151.3 | ✓ | 24 | ||
5.4 | even | 2 | 3150.2.bp.h.899.1 | 24 | |||
7.5 | odd | 6 | inner | 3150.2.bp.g.1349.1 | 24 | ||
15.2 | even | 4 | 3150.2.bf.e.1151.3 | yes | 24 | ||
15.8 | even | 4 | 3150.2.bf.d.1151.10 | yes | 24 | ||
15.14 | odd | 2 | inner | 3150.2.bp.g.899.1 | 24 | ||
21.5 | even | 6 | 3150.2.bp.h.1349.1 | 24 | |||
35.12 | even | 12 | 3150.2.bf.e.1601.3 | yes | 24 | ||
35.19 | odd | 6 | 3150.2.bp.h.1349.12 | 24 | |||
35.33 | even | 12 | 3150.2.bf.d.1601.10 | yes | 24 | ||
105.47 | odd | 12 | 3150.2.bf.e.1601.10 | yes | 24 | ||
105.68 | odd | 12 | 3150.2.bf.d.1601.3 | yes | 24 | ||
105.89 | even | 6 | inner | 3150.2.bp.g.1349.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.3 | ✓ | 24 | 5.3 | odd | 4 | ||
3150.2.bf.d.1151.10 | yes | 24 | 15.8 | even | 4 | ||
3150.2.bf.d.1601.3 | yes | 24 | 105.68 | odd | 12 | ||
3150.2.bf.d.1601.10 | yes | 24 | 35.33 | even | 12 | ||
3150.2.bf.e.1151.3 | yes | 24 | 15.2 | even | 4 | ||
3150.2.bf.e.1151.10 | yes | 24 | 5.2 | odd | 4 | ||
3150.2.bf.e.1601.3 | yes | 24 | 35.12 | even | 12 | ||
3150.2.bf.e.1601.10 | yes | 24 | 105.47 | odd | 12 | ||
3150.2.bp.g.899.1 | 24 | 15.14 | odd | 2 | inner | ||
3150.2.bp.g.899.12 | 24 | 1.1 | even | 1 | trivial | ||
3150.2.bp.g.1349.1 | 24 | 7.5 | odd | 6 | inner | ||
3150.2.bp.g.1349.12 | 24 | 105.89 | even | 6 | inner | ||
3150.2.bp.h.899.1 | 24 | 5.4 | even | 2 | |||
3150.2.bp.h.899.12 | 24 | 3.2 | odd | 2 | |||
3150.2.bp.h.1349.1 | 24 | 21.5 | even | 6 | |||
3150.2.bp.h.1349.12 | 24 | 35.19 | odd | 6 |