Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 625.2 | ||
Character | \(\chi\) | \(=\) | 1008.625 |
Dual form | 1008.2.q.k.529.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.57901 | + | 0.711841i | −0.911644 | + | 0.410982i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.92048 | − | 3.32636i | −0.858863 | − | 1.48759i | −0.873014 | − | 0.487694i | \(-0.837838\pi\) |
0.0141515 | − | 0.999900i | \(-0.495495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55336 | + | 0.693065i | 0.965080 | + | 0.261954i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.98656 | − | 2.24801i | 0.662188 | − | 0.749337i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.903316 | − | 1.56459i | 0.272360 | − | 0.471741i | −0.697106 | − | 0.716968i | \(-0.745529\pi\) |
0.969466 | + | 0.245227i | \(0.0788625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.692713 | + | 1.19981i | −0.192124 | + | 0.332769i | −0.945954 | − | 0.324301i | \(-0.894871\pi\) |
0.753830 | + | 0.657070i | \(0.228204\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.40030 | + | 3.88530i | 1.39435 | + | 1.00318i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.833405 | − | 1.44350i | −0.202130 | − | 0.350100i | 0.747084 | − | 0.664729i | \(-0.231453\pi\) |
−0.949215 | + | 0.314629i | \(0.898120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0802084 | − | 0.138925i | 0.0184011 | − | 0.0318716i | −0.856678 | − | 0.515851i | \(-0.827476\pi\) |
0.875079 | + | 0.483980i | \(0.160809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.52515 | + | 0.723229i | −0.987468 | + | 0.157822i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.60019 | + | 2.77161i | 0.333663 | + | 0.577921i | 0.983227 | − | 0.182386i | \(-0.0583819\pi\) |
−0.649564 | + | 0.760307i | \(0.725049\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.87646 | + | 8.44627i | −0.975291 | + | 1.68925i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.53658 | + | 4.96376i | −0.295716 | + | 0.955276i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.78000 | − | 6.54716i | −0.701929 | − | 1.21578i | −0.967788 | − | 0.251765i | \(-0.918989\pi\) |
0.265859 | − | 0.964012i | \(-0.414344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.22021 | −0.578367 | −0.289184 | − | 0.957274i | \(-0.593384\pi\) | ||||
−0.289184 | + | 0.957274i | \(0.593384\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.312609 | + | 3.11352i | −0.0544182 | + | 0.541995i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.59829 | − | 9.82442i | −0.439190 | − | 1.66063i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.58395 | − | 2.74348i | 0.260399 | − | 0.451025i | −0.705949 | − | 0.708263i | \(-0.749479\pi\) |
0.966348 | + | 0.257238i | \(0.0828124\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.239726 | − | 2.38762i | 0.0383869 | − | 0.382326i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00329 | − | 10.3980i | 0.937556 | − | 1.62389i | 0.167545 | − | 0.985864i | \(-0.446416\pi\) |
0.770011 | − | 0.638030i | \(-0.220250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.45480 | − | 5.98389i | −0.526852 | − | 0.912535i | −0.999510 | − | 0.0312891i | \(-0.990039\pi\) |
0.472658 | − | 0.881246i | \(-0.343295\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.2929 | − | 2.29078i | −1.68344 | − | 0.341489i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.4384 | −1.66846 | −0.834232 | − | 0.551414i | \(-0.814089\pi\) | ||||
−0.834232 | + | 0.551414i | \(0.814089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.03932 | + | 3.53929i | 0.862760 | + | 0.505613i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.34350 | + | 1.68605i | 0.328156 | + | 0.236095i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37450 | + | 2.38071i | 0.188802 | + | 0.327015i | 0.944851 | − | 0.327500i | \(-0.106206\pi\) |
−0.756049 | + | 0.654515i | \(0.772873\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.93918 | −0.935679 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0277576 | + | 0.276460i | −0.00367658 | + | 0.0366180i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −15.0705 | −1.96202 | −0.981009 | − | 0.193964i | \(-0.937866\pi\) | ||||
−0.981009 | + | 0.193964i | \(0.937866\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.20285 | −1.17830 | −0.589152 | − | 0.808022i | \(-0.700538\pi\) | ||||
−0.589152 | + | 0.808022i | \(0.700538\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.63044 | − | 4.36317i | 0.835357 | − | 0.549708i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.32136 | 0.660033 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3366 | 1.50716 | 0.753578 | − | 0.657359i | \(-0.228326\pi\) | ||||
0.753578 | + | 0.657359i | \(0.228326\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.49967 | − | 3.23733i | −0.541697 | − | 0.389729i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.93289 | 0.822783 | 0.411391 | − | 0.911459i | \(-0.365043\pi\) | ||||
0.411391 | + | 0.911459i | \(0.365043\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.22457 | − | 10.7813i | −0.728531 | − | 1.26185i | −0.957504 | − | 0.288420i | \(-0.906870\pi\) |
0.228973 | − | 0.973433i | \(-0.426463\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.68759 | − | 16.8080i | 0.194866 | − | 1.94082i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.39085 | − | 3.36891i | 0.386424 | − | 0.383922i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.0743 | −1.80850 | −0.904251 | − | 0.427001i | \(-0.859570\pi\) | ||||
−0.904251 | + | 0.427001i | \(0.859570\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10712 | − | 8.93165i | −0.123013 | − | 0.992405i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.45280 | + | 2.51633i | 0.159466 | + | 0.276203i | 0.934676 | − | 0.355500i | \(-0.115689\pi\) |
−0.775210 | + | 0.631703i | \(0.782356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.20107 | + | 5.54441i | −0.347205 | + | 0.601376i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.6292 | + | 7.64729i | 1.13957 | + | 0.819875i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.04034 | − | 8.73012i | 0.534275 | − | 0.925391i | −0.464923 | − | 0.885351i | \(-0.653918\pi\) |
0.999198 | − | 0.0400399i | \(-0.0127485\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.60030 | + | 2.58347i | −0.272585 | + | 0.270821i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.08476 | − | 2.29228i | 0.527265 | − | 0.237698i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.616153 | −0.0632160 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.18830 | + | 7.25435i | 0.425257 | + | 0.736567i | 0.996444 | − | 0.0842527i | \(-0.0268503\pi\) |
−0.571187 | + | 0.820820i | \(0.693517\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.72272 | − | 5.13882i | −0.173140 | − | 0.516471i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.05750 | + | 7.02780i | −0.403736 | + | 0.699292i | −0.994173 | − | 0.107792i | \(-0.965622\pi\) |
0.590437 | + | 0.807084i | \(0.298955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.76891 | − | 6.52794i | −0.371362 | − | 0.643217i | 0.618414 | − | 0.785853i | \(-0.287776\pi\) |
−0.989775 | + | 0.142635i | \(0.954442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.0962 | + | 13.6633i | 1.08287 | + | 1.33340i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.95731 | − | 5.12221i | 0.285894 | − | 0.495183i | −0.686932 | − | 0.726722i | \(-0.741043\pi\) |
0.972826 | + | 0.231539i | \(0.0743762\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.48409 | − | 7.76668i | −0.429498 | − | 0.743913i | 0.567331 | − | 0.823490i | \(-0.307976\pi\) |
−0.996829 | + | 0.0795776i | \(0.974643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.548154 | + | 5.45951i | −0.0520285 | + | 0.518193i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.98131 | + | 13.8240i | −0.750819 | + | 1.30046i | 0.196608 | + | 0.980482i | \(0.437007\pi\) |
−0.947426 | + | 0.319974i | \(0.896326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.14626 | − | 10.6456i | 0.573142 | − | 0.992710i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.32108 | + | 3.94074i | 0.122134 | + | 0.364321i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.12755 | − | 4.26338i | −0.103362 | − | 0.390824i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.86804 | + | 6.69964i | 0.351640 | + | 0.609059i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.07755 | + | 20.6920i | −0.187326 | + | 1.86573i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.2557 | 1.63284 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.60913 | −0.763937 | −0.381968 | − | 0.924175i | \(-0.624754\pi\) | ||||
−0.381968 | + | 0.924175i | \(0.624754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.71476 | + | 6.98937i | 0.855337 | + | 0.615380i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.964831 | − | 1.67114i | −0.0842976 | − | 0.146008i | 0.820794 | − | 0.571224i | \(-0.193531\pi\) |
−0.905092 | + | 0.425216i | \(0.860198\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.301085 | − | 0.299136i | 0.0261074 | − | 0.0259384i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.4622 | − | 4.42154i | 1.67504 | − | 0.380546i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.85442 | − | 3.21195i | 0.158434 | − | 0.274416i | −0.775870 | − | 0.630893i | \(-0.782689\pi\) |
0.934304 | + | 0.356477i | \(0.116022\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.134568 | + | 0.233079i | −0.0114139 | + | 0.0197695i | −0.871676 | − | 0.490083i | \(-0.836967\pi\) |
0.860262 | + | 0.509852i | \(0.170300\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.0614 | − | 8.14233i | 1.52104 | − | 0.685708i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.25148 | + | 2.16762i | 0.104654 | + | 0.181266i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.5188 | + | 25.1473i | −1.20572 | + | 2.08837i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0556 | − | 1.28955i | −0.994328 | − | 0.106361i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.15880 | − | 7.20325i | −0.340702 | − | 0.590113i | 0.643861 | − | 0.765142i | \(-0.277331\pi\) |
−0.984563 | + | 0.175029i | \(0.943998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.87069 | − | 8.43628i | 0.396371 | − | 0.686535i | −0.596904 | − | 0.802313i | \(-0.703603\pi\) |
0.993275 | + | 0.115778i | \(0.0369360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.90062 | − | 0.994101i | −0.396192 | − | 0.0803683i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.18434 | + | 10.7116i | 0.496738 | + | 0.860376i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.2580 | 1.93600 | 0.968001 | − | 0.250947i | \(-0.0807420\pi\) | ||||
0.968001 | + | 0.250947i | \(0.0807420\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.86504 | − | 2.78074i | −0.306518 | − | 0.220527i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.16496 | + | 8.18597i | 0.170623 | + | 0.645145i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.91401 | + | 6.77927i | −0.306569 | + | 0.530993i | −0.977609 | − | 0.210428i | \(-0.932514\pi\) |
0.671040 | + | 0.741421i | \(0.265848\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.9571 | − | 4.93960i | 0.853006 | − | 0.384547i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.15395 | − | 3.73076i | 0.166678 | − | 0.288695i | −0.770572 | − | 0.637353i | \(-0.780029\pi\) |
0.937250 | + | 0.348658i | \(0.113363\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.54030 | + | 9.59608i | 0.426177 | + | 0.738160i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.152966 | − | 0.456293i | −0.0116976 | − | 0.0348936i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.3359 | −1.31803 | −0.659014 | − | 0.752131i | \(-0.729026\pi\) | ||||
−0.659014 | + | 0.752131i | \(0.729026\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.3052 | + | 18.1867i | −1.38374 | + | 1.37478i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.7966 | − | 10.7278i | 1.78866 | − | 0.806353i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.68644 | + | 16.7774i | 0.723998 | + | 1.25400i | 0.959385 | + | 0.282100i | \(0.0910310\pi\) |
−0.235387 | + | 0.971902i | \(0.575636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.89036 | 0.214839 | 0.107420 | − | 0.994214i | \(-0.465741\pi\) | ||||
0.107420 | + | 0.994214i | \(0.465741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.5314 | − | 6.55097i | 1.07419 | − | 0.484261i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.1677 | −0.894590 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.01131 | −0.220209 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.36367 | + | 11.6093i | −0.535628 | + | 0.844454i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.70044 | −0.267755 | −0.133877 | − | 0.990998i | \(-0.542743\pi\) | ||||
−0.133877 | + | 0.990998i | \(0.542743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.7670 | −0.918991 | −0.459495 | − | 0.888180i | \(-0.651970\pi\) | ||||
−0.459495 | + | 0.888180i | \(0.651970\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.40249 | + | 3.78796i | −0.601715 | + | 0.271261i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.44715 | 0.174352 | 0.0871762 | − | 0.996193i | \(-0.472216\pi\) | ||||
0.0871762 | + | 0.996193i | \(0.472216\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.24829 | − | 3.89415i | −0.159377 | − | 0.276049i | 0.775267 | − | 0.631633i | \(-0.217615\pi\) |
−0.934644 | + | 0.355584i | \(0.884282\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.4797 | + | 8.78170i | −1.37399 | + | 0.619413i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.11411 | − | 19.3371i | −0.358940 | − | 1.35720i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −46.1167 | −3.22093 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.40950 | + | 1.90874i | 0.654006 | + | 0.132666i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.144907 | − | 0.250986i | −0.0100234 | − | 0.0173611i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.09087 | + | 1.88945i | −0.0750987 | + | 0.130075i | −0.901129 | − | 0.433551i | \(-0.857261\pi\) |
0.826030 | + | 0.563625i | \(0.190594\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.9471 | + | 4.93512i | −0.750085 | + | 0.338149i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.2697 | + | 22.9838i | −0.904988 | + | 1.56749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.22237 | − | 2.23182i | −0.558171 | − | 0.151506i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.5032 | + | 12.5929i | 1.18276 | + | 0.850947i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.30924 | 0.155336 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.87967 | + | 4.98773i | 0.192837 | + | 0.334003i | 0.946189 | − | 0.323614i | \(-0.104898\pi\) |
−0.753352 | + | 0.657617i | \(0.771564\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.29992 | + | 27.7414i | 0.619995 | + | 1.84943i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.29135 | − | 14.3610i | 0.550316 | − | 0.953175i | −0.447935 | − | 0.894066i | \(-0.647841\pi\) |
0.998252 | − | 0.0591094i | \(-0.0188261\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.29688 | + | 12.6386i | 0.482191 | + | 0.835180i | 0.999791 | − | 0.0204432i | \(-0.00650771\pi\) |
−0.517600 | + | 0.855623i | \(0.673174\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.95608 | + | 7.73329i | −0.194496 | + | 0.508813i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.949438 | − | 1.64448i | 0.0621998 | − | 0.107733i | −0.833249 | − | 0.552898i | \(-0.813522\pi\) |
0.895448 | + | 0.445165i | \(0.146855\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.9672 | + | 38.0483i | 1.43298 | + | 2.48200i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.3816 | − | 11.4424i | 1.64871 | − | 0.743261i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.46351 | − | 7.73103i | 0.288721 | − | 0.500079i | −0.684784 | − | 0.728746i | \(-0.740103\pi\) |
0.973505 | + | 0.228667i | \(0.0734368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1465 | − | 21.0383i | 0.782423 | − | 1.35520i | −0.148104 | − | 0.988972i | \(-0.547317\pi\) |
0.930527 | − | 0.366224i | \(-0.119350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.10607 | + | 13.3151i | 0.520005 | + | 0.854164i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.174600 | − | 26.8861i | 0.0111548 | − | 1.71769i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.111123 | + | 0.192470i | 0.00707057 | + | 0.0122466i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.08522 | − | 2.93915i | −0.258890 | − | 0.186261i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.64873 | 0.356545 | 0.178272 | − | 0.983981i | \(-0.442949\pi\) | ||||
0.178272 | + | 0.983981i | \(0.442949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.78191 | 0.363506 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.10779 | − | 11.0334i | 0.0693724 | − | 0.690935i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.7856 | + | 20.4132i | 0.735163 | + | 1.27334i | 0.954652 | + | 0.297724i | \(0.0962275\pi\) |
−0.219489 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.94580 | − | 5.90731i | 0.369454 | − | 0.367063i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −22.2273 | − | 4.50886i | −1.37584 | − | 0.279091i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.8203 | − | 22.2053i | 0.790531 | − | 1.36924i | −0.135108 | − | 0.990831i | \(-0.543138\pi\) |
0.925639 | − | 0.378409i | \(-0.123529\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.27940 | − | 9.14419i | 0.324311 | − | 0.561723i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.74430 | + | 17.3729i | −0.106749 | + | 1.06320i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.27239 | − | 14.3282i | −0.504376 | − | 0.873606i | −0.999987 | − | 0.00506090i | \(-0.998389\pi\) |
0.495611 | − | 0.868545i | \(-0.334944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.90748 | + | 15.4282i | −0.541091 | + | 0.937197i | 0.457751 | + | 0.889081i | \(0.348655\pi\) |
−0.998842 | + | 0.0481166i | \(0.984678\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.26689 | − | 5.93032i | 0.137198 | − | 0.358920i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.80996 | + | 15.2593i | 0.531260 | + | 0.920170i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.92191 | − | 5.06089i | 0.175560 | − | 0.304080i | −0.764795 | − | 0.644274i | \(-0.777160\pi\) |
0.940355 | + | 0.340194i | \(0.110493\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.39716 | + | 7.23908i | −0.382988 | + | 0.433392i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.5591 | − | 18.2889i | −0.629905 | − | 1.09103i | −0.987570 | − | 0.157177i | \(-0.949761\pi\) |
0.357666 | − | 0.933850i | \(-0.383573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.7762 | 0.759468 | 0.379734 | − | 0.925096i | \(-0.376016\pi\) | ||||
0.379734 | + | 0.925096i | \(0.376016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.972914 | − | 0.438603i | 0.0576304 | − | 0.0259806i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.5351 | − | 22.3892i | 1.33020 | − | 1.32159i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.11087 | − | 12.3164i | 0.418287 | − | 0.724494i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.7773 | − | 8.47330i | −0.690399 | − | 0.496714i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.93828 | − | 10.2854i | 0.346918 | − | 0.600880i | −0.638782 | − | 0.769388i | \(-0.720561\pi\) |
0.985700 | + | 0.168508i | \(0.0538948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.9426 | + | 50.1301i | 1.68510 | + | 2.91869i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.37822 | + | 6.88796i | 0.370102 | + | 0.399680i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.43389 | −0.256419 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.67413 | − | 17.6734i | −0.269413 | − | 1.01868i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.40417 | − | 13.9853i | 0.0806676 | − | 0.803433i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 17.6739 | + | 30.6120i | 1.01200 | + | 1.75284i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.93298 | 0.224467 | 0.112234 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112234 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.5980 | + | 7.62484i | 0.602900 | + | 0.433762i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.98221 | −0.112401 | −0.0562005 | − | 0.998420i | \(-0.517899\pi\) | ||||
−0.0562005 | + | 0.998420i | \(0.517899\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.4995 | 1.15870 | 0.579349 | − | 0.815080i | \(-0.303307\pi\) | ||||
0.579349 | + | 0.815080i | \(0.303307\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −27.2471 | − | 13.6759i | −1.53520 | − | 0.770548i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.51416 | 0.534369 | 0.267184 | − | 0.963645i | \(-0.413907\pi\) | ||||
0.267184 | + | 0.963645i | \(0.413907\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.6581 | −0.764709 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.02343 | + | 10.1932i | −0.0571224 | + | 0.568927i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.267384 | −0.0148777 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.75597 | − | 11.7017i | −0.374754 | − | 0.649093i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.6091 | + | 9.07172i | 0.697284 | + | 0.501667i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −29.2064 | − | 7.92756i | −1.61020 | − | 0.437061i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.52986 | −0.0840886 | −0.0420443 | − | 0.999116i | \(-0.513387\pi\) | ||||
−0.0420443 | + | 0.999116i | \(0.513387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.02076 | − | 9.01083i | −0.165536 | − | 0.493790i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.6921 | − | 41.0360i | −1.29444 | − | 2.24204i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.6972 | − | 18.5281i | 0.582714 | − | 1.00929i | −0.412442 | − | 0.910984i | \(-0.635324\pi\) |
0.995156 | − | 0.0983063i | \(-0.0313425\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.76208 | − | 27.5098i | 0.150016 | − | 1.49413i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.90887 | + | 5.03831i | −0.157524 | + | 0.272840i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.9676 | + | 13.2227i | 0.700185 | + | 0.713961i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.12703 | + | 21.1848i | −0.114515 | + | 1.14055i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.14381 | −0.276134 | −0.138067 | − | 0.990423i | \(-0.544089\pi\) | ||||
−0.138067 | + | 0.990423i | \(0.544089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.207526 | + | 0.359446i | 0.0111086 | + | 0.0192407i | 0.871526 | − | 0.490349i | \(-0.163131\pi\) |
−0.860418 | + | 0.509590i | \(0.829797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.89118 | − | 5.28208i | −0.261072 | − | 0.281936i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.04122 | − | 10.4637i | 0.321542 | − | 0.556926i | −0.659265 | − | 0.751911i | \(-0.729132\pi\) |
0.980806 | + | 0.194985i | \(0.0624657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.3145 | − | 23.0613i | −0.706658 | − | 1.22397i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.81526 | + | 5.92930i | 0.254851 | + | 0.313812i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.14926 | − | 14.1149i | 0.430102 | − | 0.744958i | −0.566780 | − | 0.823869i | \(-0.691811\pi\) |
0.996882 | + | 0.0789113i | \(0.0251444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.48713 | + | 16.4322i | 0.499323 | + | 0.864852i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.8768 | − | 7.82540i | −0.570882 | − | 0.410727i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.9083 | + | 41.4104i | −1.25142 | + | 2.16752i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3500 | − | 30.0511i | 0.905664 | − | 1.56866i | 0.0856404 | − | 0.996326i | \(-0.472706\pi\) |
0.820024 | − | 0.572330i | \(-0.193960\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.4489 | − | 34.1518i | −0.596007 | − | 1.77787i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.85962 | + | 7.03143i | 0.0965465 | + | 0.365054i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.75329 | + | 13.4291i | 0.401450 | + | 0.695332i | 0.993901 | − | 0.110274i | \(-0.0351730\pi\) |
−0.592451 | + | 0.805606i | \(0.701840\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.8260 | + | 12.9952i | −1.48857 | + | 0.671067i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4738 | 0.539430 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1820 | 0.831214 | 0.415607 | − | 0.909544i | \(-0.363569\pi\) | ||||
0.415607 | + | 0.909544i | \(0.363569\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.5939 | − | 6.12833i | 0.696438 | − | 0.313964i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.17027 | + | 3.75902i | 0.110896 | + | 0.192077i | 0.916132 | − | 0.400877i | \(-0.131295\pi\) |
−0.805236 | + | 0.592955i | \(0.797961\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.7183 | − | 4.80931i | −0.903006 | − | 0.245105i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.3151 | − | 4.12095i | −1.03267 | − | 0.209480i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7731 | + | 22.1237i | −0.647624 | + | 1.12172i | 0.336065 | + | 0.941839i | \(0.390904\pi\) |
−0.983689 | + | 0.179879i | \(0.942429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.66722 | − | 4.61975i | 0.134887 | − | 0.233631i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.71306 | + | 1.95194i | 0.136856 | + | 0.0984623i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.8703 | + | 53.4690i | 1.55326 | + | 2.69032i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.28225 | − | 3.95297i | 0.114543 | − | 0.198394i | −0.803054 | − | 0.595906i | \(-0.796793\pi\) |
0.917597 | + | 0.397512i | \(0.130126\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.262480 | + | 0.686665i | −0.0131404 | + | 0.0343762i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.668128 | − | 1.15723i | −0.0333647 | − | 0.0577894i | 0.848861 | − | 0.528616i | \(-0.177289\pi\) |
−0.882226 | + | 0.470827i | \(0.843956\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.23068 | − | 3.86366i | 0.111118 | − | 0.192463i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −27.5837 | + | 20.8357i | −1.37064 | + | 1.03533i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.86161 | − | 4.95645i | −0.141845 | − | 0.245682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.6664 | 1.02189 | 0.510944 | − | 0.859614i | \(-0.329296\pi\) | ||||
0.510944 | + | 0.859614i | \(0.329296\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.641757 | + | 6.39177i | −0.0316555 | + | 0.315283i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −38.4806 | − | 10.4449i | −1.89350 | − | 0.513958i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.58015 | − | 9.66510i | 0.273919 | − | 0.474441i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.0465699 | − | 0.463826i | 0.00228054 | − | 0.0227137i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5227 | + | 18.2259i | −0.514069 | + | 0.890394i | 0.485797 | + | 0.874071i | \(0.338529\pi\) |
−0.999867 | + | 0.0163228i | \(0.994804\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.51630 | − | 14.7507i | −0.415059 | − | 0.718903i | 0.580376 | − | 0.814349i | \(-0.302906\pi\) |
−0.995435 | + | 0.0954456i | \(0.969572\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.7231 | + | 25.7137i | −1.10484 | + | 1.25024i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.2563 | 0.788544 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.4982 | − | 6.37818i | −1.13716 | − | 0.308662i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.51910 | − | 2.53185i | −0.169904 | − | 0.122239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.2925 | − | 31.6836i | −0.881121 | − | 1.52615i | −0.850096 | − | 0.526627i | \(-0.823456\pi\) |
−0.0310244 | − | 0.999519i | \(-0.509877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.6571 | −1.13689 | −0.568444 | − | 0.822722i | \(-0.692454\pi\) | ||||
−0.568444 | + | 0.822722i | \(0.692454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.02450 | − | 50.0430i | 0.240906 | − | 2.39938i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.513395 | 0.0245590 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.7864 | −0.992082 | −0.496041 | − | 0.868299i | \(-0.665213\pi\) | ||||
−0.496041 | + | 0.868299i | \(0.665213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.9539 | − | 6.54543i | 0.950185 | − | 0.311687i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.42807 | −0.352918 | −0.176459 | − | 0.984308i | \(-0.556464\pi\) | ||||
−0.176459 | + | 0.984308i | \(0.556464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.7194 | −1.83547 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.6944 | + | 8.41363i | 0.553125 | + | 0.397951i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.15800 | −0.385000 | −0.192500 | − | 0.981297i | \(-0.561660\pi\) | ||||
−0.192500 | + | 0.981297i | \(0.561660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8457 | − | 18.7854i | −0.510705 | − | 0.884568i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.68559 | + | 16.7882i | −0.0791960 | + | 0.788776i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.5873 | + | 3.68805i | 0.636985 | + | 0.172898i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3058 | 0.669199 | 0.334600 | − | 0.942360i | \(-0.391399\pi\) | ||||
0.334600 | + | 0.942360i | \(0.391399\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.44578 | − | 1.91876i | 0.394215 | − | 0.0895602i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.71961 | + | 13.3708i | 0.359538 | + | 0.622738i | 0.987884 | − | 0.155196i | \(-0.0496009\pi\) |
−0.628346 | + | 0.777934i | \(0.716268\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.5531 | + | 18.2785i | −0.490444 | + | 0.849474i | −0.999940 | − | 0.0109995i | \(-0.996499\pi\) |
0.509496 | + | 0.860473i | \(0.329832\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.3901 | − | 12.5115i | −0.806447 | − | 0.580206i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.49896 | + | 6.06037i | −0.161912 | + | 0.280440i | −0.935555 | − | 0.353182i | \(-0.885100\pi\) |
0.773642 | + | 0.633623i | \(0.218433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 31.4998 | + | 8.55007i | 1.45453 | + | 0.394805i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −38.3037 | + | 17.2679i | −1.76494 | + | 0.795661i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.4831 | −0.573974 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.782265 | + | 1.35492i | 0.0358928 | + | 0.0621681i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.08240 | + | 1.63953i | 0.370068 | + | 0.0750691i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.54406 | − | 2.67440i | 0.0705500 | − | 0.122196i | −0.828592 | − | 0.559852i | \(-0.810858\pi\) |
0.899142 | + | 0.437656i | \(0.144191\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.19444 | + | 3.80089i | 0.100058 | + | 0.173305i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.24561 | − | 11.3846i | −0.420690 | − | 0.518019i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0871 | − | 27.8636i | 0.730475 | − | 1.26522i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.90011 | − | 8.48725i | −0.222045 | − | 0.384594i | 0.733384 | − | 0.679815i | \(-0.237940\pi\) |
−0.955429 | + | 0.295221i | \(0.904607\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.35452 | − | 13.4907i | 0.0612533 | − | 0.610071i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.98641 | + | 17.2970i | −0.450680 | + | 0.780601i | −0.998428 | − | 0.0560419i | \(-0.982152\pi\) |
0.547748 | + | 0.836643i | \(0.315485\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.30055 | + | 10.9129i | −0.283762 | + | 0.491491i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.7851 | + | 15.5994i | −0.619596 | + | 0.701140i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.7022 | + | 4.80495i | 0.794052 | + | 0.215531i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.1650 | − | 17.6062i | −0.455046 | − | 0.788163i | 0.543645 | − | 0.839315i | \(-0.317044\pi\) |
−0.998691 | + | 0.0511526i | \(0.983710\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.745415 | + | 7.42419i | −0.0333027 | + | 0.331688i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.9595 | 1.06830 | 0.534151 | − | 0.845389i | \(-0.320631\pi\) | ||||
0.534151 | + | 0.845389i | \(0.320631\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.1693 | 1.38702 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.5791 | − | 11.2085i | −0.691891 | − | 0.497788i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.03046 | − | 8.71302i | −0.222971 | − | 0.386198i | 0.732737 | − | 0.680511i | \(-0.238242\pi\) |
−0.955709 | + | 0.294314i | \(0.904909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.42146 | − | 31.8425i | −0.372544 | − | 1.40863i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.566343 | + | 0.611605i | 0.0250047 | + | 0.0270030i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14.4762 | + | 25.0735i | −0.637898 | + | 1.10487i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3325 | + | 17.8964i | −0.454423 | + | 0.787083i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.3737 | − | 12.3404i | 1.20157 | − | 0.541685i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.99821 | + | 13.8533i | 0.350408 | + | 0.606924i | 0.986321 | − | 0.164836i | \(-0.0527096\pi\) |
−0.635913 | + | 0.771761i | \(0.719376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.7103 | − | 32.4072i | 0.818146 | − | 1.41707i | −0.0889016 | − | 0.996040i | \(-0.528336\pi\) |
0.907047 | − | 0.421029i | \(-0.138331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.9581 | − | 41.7474i | 0.696468 | − | 1.82201i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.68374 | + | 4.64838i | 0.116906 | + | 0.202487i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.37877 | − | 11.0484i | 0.277338 | − | 0.480364i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.9386 | + | 33.8788i | −1.29922 | + | 1.47021i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.31711 | + | 14.4057i | 0.360254 | + | 0.623978i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.7178 | −0.982175 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.2379 | − | 19.5965i | −1.17540 | − | 0.845653i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.9930 | − | 6.25195i | 0.473500 | − | 0.269291i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.229159 | − | 0.396916i | 0.00985233 | − | 0.0170647i | −0.861057 | − | 0.508508i | \(-0.830197\pi\) |
0.870910 | + | 0.491443i | \(0.163531\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.56392 | + | 2.05748i | −0.195857 | + | 0.0882949i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.2232 | + | 29.8314i | −0.737760 | + | 1.27784i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2013 | + | 19.4011i | 0.478931 | + | 0.829533i | 0.999708 | − | 0.0241596i | \(-0.00769098\pi\) |
−0.520777 | + | 0.853693i | \(0.674358\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.2821 | + | 20.6881i | −0.780259 | + | 0.882948i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.21275 | −0.0516650 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.0436 | − | 11.1405i | −1.74535 | − | 0.473744i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.2130 | − | 8.66149i | 0.815547 | − | 0.367660i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.4155 | + | 18.0401i | 0.441317 | + | 0.764383i | 0.997787 | − | 0.0664841i | \(-0.0211782\pi\) |
−0.556471 | + | 0.830867i | \(0.687845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.57275 | 0.404884 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.75490 | − | 2.14357i | 0.200752 | − | 0.0905018i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.80605 | −0.371131 | −0.185565 | − | 0.982632i | \(-0.559412\pi\) | ||||
−0.185565 | + | 0.982632i | \(0.559412\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.3117 | 2.57940 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.36333 | − | 23.5730i | 0.141247 | − | 0.989974i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9857 | 0.795923 | 0.397962 | − | 0.917402i | \(-0.369718\pi\) | ||||
0.397962 | + | 0.917402i | \(0.369718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.7597 | 0.659523 | 0.329762 | − | 0.944064i | \(-0.393032\pi\) | ||||
0.329762 | + | 0.944064i | \(0.393032\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.84305 | − | 2.63413i | 0.244097 | − | 0.110042i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.2131 | −1.30167 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.9306 | − | 27.5927i | −0.663201 | − | 1.14870i | −0.979770 | − | 0.200128i | \(-0.935864\pi\) |
0.316569 | − | 0.948570i | \(-0.397469\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.1593 | − | 9.08809i | 0.837792 | − | 0.377688i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.96555 | + | 7.43199i | 0.0815449 | + | 0.308331i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.96644 | 0.205689 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.5712 | − | 11.9625i | 0.437066 | − | 0.494587i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.3597 | + | 35.2640i | 0.840333 | + | 1.45550i | 0.889613 | + | 0.456715i | \(0.150974\pi\) |
−0.0492799 | + | 0.998785i | \(0.515693\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.258288 | + | 0.447368i | −0.0106426 | + | 0.0184335i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.86409 | + | 1.74198i | −0.158947 | + | 0.0716557i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0693 | + | 24.3688i | −0.577759 | + | 1.00071i | 0.417977 | + | 0.908458i | \(0.362739\pi\) |
−0.995736 | + | 0.0922500i | \(0.970594\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0161 | + | 11.9383i | −0.492613 | + | 0.489425i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.32209 | + | 4.54849i | 0.258746 | + | 0.186157i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.9926 | −1.34804 | −0.674020 | − | 0.738713i | \(-0.735434\pi\) | ||||
−0.674020 | + | 0.738713i | \(0.735434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.98103 | − | 3.43124i | −0.0808079 | − | 0.139963i | 0.822789 | − | 0.568347i | \(-0.192417\pi\) |
−0.903597 | + | 0.428383i | \(0.859083\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.5075 | − | 27.7328i | 0.998021 | − | 1.12937i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.8570 | − | 25.7330i | 0.604021 | − | 1.04620i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.0132 | + | 29.4676i | 0.690543 | + | 1.19605i | 0.971660 | + | 0.236382i | \(0.0759615\pi\) |
−0.281118 | + | 0.959673i | \(0.590705\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.8402 | + | 26.8930i | 0.885008 | + | 1.08976i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.92354 | − | 13.7240i | 0.320552 | − | 0.555212i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.2967 | − | 26.4946i | −0.617827 | − | 1.07011i | −0.989881 | − | 0.141897i | \(-0.954680\pi\) |
0.372054 | − | 0.928211i | \(-0.378654\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 72.8188 | − | 32.8277i | 2.93634 | − | 1.32374i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.7646 | − | 32.5013i | 0.755435 | − | 1.30845i | −0.189723 | − | 0.981838i | \(-0.560759\pi\) |
0.945158 | − | 0.326614i | \(-0.105908\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.92302 | + | 5.06282i | −0.117486 | + | 0.203492i | −0.918771 | − | 0.394791i | \(-0.870817\pi\) |
0.801285 | + | 0.598283i | \(0.204150\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.2164 | + | 3.68415i | −0.650744 | + | 0.147840i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18.9203 | − | 18.7979i | 0.758028 | − | 0.753121i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.6774 | − | 18.4937i | −0.427095 | − | 0.739749i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.407472 | + | 0.293160i | 0.0162729 | + | 0.0117077i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.28028 | −0.210539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6347 | −1.02050 | −0.510251 | − | 0.860025i | \(-0.670448\pi\) | ||||
−0.510251 | + | 0.860025i | \(0.670448\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.377516 | − | 3.75999i | 0.0150049 | − | 0.149446i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.5336 | + | 28.6371i | 0.656117 | + | 1.13643i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.43001 | + | 4.79435i | −0.334009 | + | 0.189959i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.7726 | − | 15.5852i | 0.544837 | − | 0.616542i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.9824 | + | 22.4861i | −0.512772 | + | 0.888147i | 0.487118 | + | 0.873336i | \(0.338048\pi\) |
−0.999890 | + | 0.0148113i | \(0.995285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.5634 | − | 39.0809i | 0.889812 | − | 1.54120i | 0.0497151 | − | 0.998763i | \(-0.484169\pi\) |
0.840097 | − | 0.542436i | \(-0.182498\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.59223 | − | 45.7377i | 0.180819 | − | 1.80092i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.70324 | − | 4.68215i | −0.106275 | − | 0.184074i | 0.807983 | − | 0.589206i | \(-0.200559\pi\) |
−0.914259 | + | 0.405131i | \(0.867226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6135 | + | 23.5792i | −0.534375 | + | 0.925564i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.5719 | − | 2.32895i | 0.571119 | − | 0.0912788i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.9515 | + | 27.6288i | 0.624231 | + | 1.08120i | 0.988689 | + | 0.149980i | \(0.0479211\pi\) |
−0.364458 | + | 0.931220i | \(0.618746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.70587 | + | 6.41875i | −0.144800 | + | 0.250801i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.6020 | − | 7.42479i | −1.42798 | − | 0.289669i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.50215 | − | 4.33385i | −0.0974699 | − | 0.168823i | 0.813167 | − | 0.582031i | \(-0.197742\pi\) |
−0.910637 | + | 0.413208i | \(0.864408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.63406 | 0.374721 | 0.187361 | − | 0.982291i | \(-0.440007\pi\) | ||||
0.187361 | + | 0.982291i | \(0.440007\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.64632 | + | 1.64381i | −0.141611 | + | 0.0638404i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.57326 | − | 0.427034i | −0.0610085 | − | 0.0165597i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.0975 | − | 20.9534i | 0.468415 | − | 0.811319i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.09751 | − | 5.82583i | −0.313068 | − | 0.225240i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.31308 | + | 14.3987i | −0.320923 | + | 0.555855i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5885 | + | 23.5359i | 0.523797 | + | 0.907243i | 0.999616 | + | 0.0276998i | \(0.00881825\pi\) |
−0.475819 | + | 0.879543i | \(0.657848\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −34.4322 | − | 37.1840i | −1.32529 | − | 1.43121i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.0502 | −1.46239 | −0.731194 | − | 0.682169i | \(-0.761037\pi\) | ||||
−0.731194 | + | 0.682169i | \(0.761037\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.66651 | + | 21.4257i | 0.217461 | + | 0.822244i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.86937 | + | 28.5784i | −0.109955 | + | 1.09513i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.0571 | − | 26.0797i | −0.576146 | − | 0.997913i | −0.995916 | − | 0.0902831i | \(-0.971223\pi\) |
0.419771 | − | 0.907630i | \(-0.362111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2455 | −0.544293 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.5185 | − | 14.7622i | −0.782830 | − | 0.563215i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.80854 | −0.145094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.3902 | −0.547429 | −0.273714 | − | 0.961811i | \(-0.588252\pi\) | ||||
−0.273714 | + | 0.961811i | \(0.588252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.837189 | − | 14.3152i | −0.0318022 | − | 0.543791i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.03374 | 0.0392120 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.0127 | −0.758034 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.328571 | + | 3.27250i | −0.0124277 | + | 0.123777i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.4170 | 0.544521 | 0.272261 | − | 0.962224i | \(-0.412229\pi\) | ||||
0.272261 | + | 0.962224i | \(0.412229\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.254092 | − | 0.440100i | −0.00958325 | − | 0.0165987i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −61.7708 | − | 44.4416i | −2.32642 | − | 1.67377i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.2310 | + | 15.1324i | −0.572820 | + | 0.569113i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.4882 | 0.431448 | 0.215724 | − | 0.976454i | \(-0.430789\pi\) | ||||
0.215724 | + | 0.976454i | \(0.430789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −31.9327 | + | 36.1353i | −1.19757 | + | 1.35518i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.15296 | − | 8.92519i | −0.192980 | − | 0.334251i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.80686 | − | 8.32573i | 0.179766 | − | 0.311365i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.54468 | + | 15.3847i | −0.0576871 | + | 0.574552i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.9451 | + | 31.0818i | −0.669240 | + | 1.15916i | 0.308877 | + | 0.951102i | \(0.400047\pi\) |
−0.978117 | + | 0.208055i | \(0.933287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.09910 | − | 19.2803i | −0.189901 | − | 0.718036i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.20351 | + | 41.8661i | −0.156330 | + | 1.55702i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 73.7321 | 2.73834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.03060 | + | 8.71326i | 0.186575 | + | 0.323157i | 0.944106 | − | 0.329642i | \(-0.106928\pi\) |
−0.757531 | + | 0.652799i | \(0.773595\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.2778 | − | 15.2545i | −0.825104 | − | 0.564980i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.75850 | + | 9.97401i | −0.212986 | + | 0.368902i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.5690 | − | 28.6984i | −0.611992 | − | 1.06000i | −0.990904 | − | 0.134568i | \(-0.957035\pi\) |
0.378913 | − | 0.925432i | \(-0.376298\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.8629 | + | 42.5778i | 0.695770 | + | 1.57051i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.1438 | − | 19.3017i | 0.410489 | − | 0.710987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9237 | − | 37.9729i | −0.806475 | − | 1.39686i | −0.915291 | − | 0.402793i | \(-0.868039\pi\) |
0.108816 | − | 0.994062i | \(-0.465294\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.312473 | − | 0.224811i | −0.0114790 | − | 0.00825865i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.50115 | + | 7.79622i | −0.165131 | + | 0.286016i | −0.936702 | − | 0.350128i | \(-0.886138\pi\) |
0.771571 | + | 0.636144i | \(0.219471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.9738 | + | 27.6673i | −0.585233 | + | 1.01365i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.54283 | + | 1.73293i | 0.312566 | + | 0.0634046i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.1011 | − | 11.0293i | 0.405626 | − | 0.403000i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.59141 | + | 9.68460i | 0.204033 | + | 0.353396i | 0.949824 | − | 0.312784i | \(-0.101262\pi\) |
−0.745791 | + | 0.666180i | \(0.767928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.91942 | + | 4.02100i | −0.325042 | + | 0.146533i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.4162 | −1.36171 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.1431 | 1.53172 | 0.765859 | − | 0.643009i | \(-0.222314\pi\) | ||||
0.765859 | + | 0.643009i | \(0.222314\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.12971 | + | 4.11580i | −0.331388 | + | 0.149394i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.14155 | − | 1.97721i | −0.0413810 | − | 0.0716740i | 0.844593 | − | 0.535409i | \(-0.179842\pi\) |
−0.885974 | + | 0.463735i | \(0.846509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.06670 | − | 22.9389i | −0.219629 | − | 0.830444i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.10478 | + | 18.2104i | 0.220719 | + | 0.658398i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.4396 | − | 18.0819i | 0.376951 | − | 0.652898i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.96676 | − | 15.5309i | 0.323350 | − | 0.560058i | −0.657827 | − | 0.753169i | \(-0.728524\pi\) |
0.981177 | + | 0.193111i | \(0.0618577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.1405 | − | 23.8432i | −1.19353 | − | 0.858693i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.4807 | + | 30.2775i | 0.628737 | + | 1.08901i | 0.987805 | + | 0.155694i | \(0.0497613\pi\) |
−0.359068 | + | 0.933311i | \(0.616905\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.7032 | − | 27.1988i | 0.564077 | − | 0.977009i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.18343 | + | 13.5602i | −0.185955 | + | 0.486469i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.963028 | − | 1.66801i | −0.0345041 | − | 0.0597628i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.26259 | − | 10.8471i | 0.224093 | − | 0.388141i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 38.3068 | − | 8.70277i | 1.36897 | − | 0.311011i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −46.5870 | − | 80.6910i | −1.66276 | − | 2.87998i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.3564 | 1.01079 | 0.505397 | − | 0.862887i | \(-0.331346\pi\) | ||||
0.505397 | + | 0.862887i | \(0.331346\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.43668 | + | 44.1885i | −0.157950 | + | 1.57315i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.9601 | + | 29.7662i | −1.06526 | + | 1.05836i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.37494 | − | 11.0417i | 0.226381 | − | 0.392103i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.82703 | + | 18.1969i | −0.0647982 | + | 0.645377i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.51922 | + | 16.4878i | −0.337188 | + | 0.584027i | −0.983903 | − | 0.178705i | \(-0.942809\pi\) |
0.646715 | + | 0.762732i | \(0.276143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.53283 | + | 16.5113i | 0.337247 | + | 0.584129i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.61246 | − | 28.6737i | −0.339640 | − | 1.01313i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.4910 | −0.793691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.0717 | − | 22.9224i | 0.813172 | − | 0.807908i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 23.2616 | + | 16.7358i | 0.818847 | + | 0.589128i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4529 | − | 18.1050i | −0.367505 | − | 0.636538i | 0.621670 | − | 0.783280i | \(-0.286455\pi\) |
−0.989175 | + | 0.146742i | \(0.953121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.5392 | −0.615884 | −0.307942 | − | 0.951405i | \(-0.599640\pi\) | ||||
−0.307942 | + | 0.951405i | \(0.599640\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.08260 | − | 30.7021i | 0.108111 | − | 1.07677i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.0671 | 1.05320 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.10842 | −0.0387786 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.642004 | + | 10.9777i | 0.0224334 | + | 0.383593i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.9762 | −1.22068 | −0.610339 | − | 0.792140i | \(-0.708967\pi\) | ||||
−0.610339 | + | 0.792140i | \(0.708967\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.4235 | 1.06050 | 0.530249 | − | 0.847842i | \(-0.322099\pi\) | ||||
0.530249 | + | 0.847842i | \(0.322099\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −24.7732 | − | 17.8233i | −0.862493 | − | 0.620529i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.6276 | 0.891158 | 0.445579 | − | 0.895243i | \(-0.352998\pi\) | ||||
0.445579 | + | 0.895243i | \(0.352998\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9403 | + | 41.4658i | 0.831481 | + | 1.44017i | 0.896864 | + | 0.442307i | \(0.145840\pi\) |
−0.0653833 | + | 0.997860i | \(0.520827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.01118 | + | 10.0712i | −0.0350775 | + | 0.349364i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0757689 | − | 11.6674i | 0.00262524 | − | 0.404252i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.5465 | −0.572614 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.94813 | − | 15.9844i | 0.171032 | − | 0.552501i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.8466 | + | 37.8394i | 0.754227 | + | 1.30636i | 0.945758 | + | 0.324873i | \(0.105322\pi\) |
−0.191530 | + | 0.981487i | \(0.561345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.0769 | + | 24.3818i | −0.485409 | + | 0.840753i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.6918 | + | 21.3621i | 1.02264 | + | 0.735749i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.2800 | − | 36.8581i | 0.732055 | − | 1.26796i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.23322 | + | 19.7874i | 0.179816 | + | 0.679904i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.1738 | + | 9.09464i | −0.692364 | + | 0.312127i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.1385 | 0.347543 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.33994 | + | 14.4452i | 0.285554 | + | 0.494594i | 0.972743 | − | 0.231884i | \(-0.0744890\pi\) |
−0.687189 | + | 0.726478i | \(0.741156\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.22403 | + | 1.38512i | −0.0418609 | + | 0.0473701i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.21452 | + | 12.4959i | −0.246443 | + | 0.426852i | −0.962536 | − | 0.271152i | \(-0.912595\pi\) |
0.716093 | + | 0.698005i | \(0.245929\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.3867 | + | 19.7223i | 0.388508 | + | 0.672915i | 0.992249 | − | 0.124265i | \(-0.0396573\pi\) |
−0.603741 | + | 0.797180i | \(0.706324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.6456 | + | 51.3942i | −0.669521 | + | 1.75151i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.97266 | − | 10.3450i | 0.203312 | − | 0.352146i | −0.746282 | − | 0.665630i | \(-0.768163\pi\) |
0.949594 | + | 0.313484i | \(0.101496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 33.2933 | + | 57.6656i | 1.13200 | + | 1.96069i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.46085 | + | 24.5096i | −0.0835748 | + | 0.832388i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.5202 | + | 25.1497i | −0.492563 | + | 0.853145i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.54572 | + | 14.8016i | −0.289561 | + | 0.501534i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.6282 | + | 4.99588i | 0.833538 | + | 0.169085i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 46.6134 | + | 12.6524i | 1.57582 | + | 0.427729i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.3099 | + | 49.0342i | 0.955957 | + | 1.65577i | 0.732163 | + | 0.681130i | \(0.238511\pi\) |
0.223794 | + | 0.974636i | \(0.428156\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.05505 | + | 20.4679i | −0.0693152 | + | 0.690365i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.41130 | −0.216002 | −0.108001 | − | 0.994151i | \(-0.534445\pi\) | ||||
−0.108001 | + | 0.994151i | \(0.534445\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.7180 | 0.865481 | 0.432741 | − | 0.901518i | \(-0.357547\pi\) | ||||
0.432741 | + | 0.901518i | \(0.357547\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −81.3854 | − | 58.5535i | −2.73574 | − | 1.96825i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.99472 | + | 17.3114i | 0.335590 | + | 0.581259i | 0.983598 | − | 0.180375i | \(-0.0577311\pi\) |
−0.648008 | + | 0.761633i | \(0.724398\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.9822 | − | 5.96669i | −0.737261 | − | 0.200116i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.9744 | − | 6.33591i | −0.501662 | − | 0.212261i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.917456 | + | 1.58908i | −0.0307015 | + | 0.0531766i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.2051 | − | 64.4412i | 1.24363 | − | 2.15403i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.00118 | − | 3.15623i | 0.233762 | − | 0.105383i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.1724 | + | 21.0832i | 0.405973 | + | 0.703166i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.29104 | − | 3.96819i | 0.0763254 | − | 0.132200i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19.9612 | + | 24.5794i | 0.664267 | + | 0.817950i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.55087 | − | 9.61439i | −0.184517 | − | 0.319593i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.1517 | − | 21.0474i | 0.403491 | − | 0.698866i | −0.590654 | − | 0.806925i | \(-0.701130\pi\) |
0.994145 | + | 0.108059i | \(0.0344635\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.73809 | + | 23.0825i | 0.256656 | + | 0.765598i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7871 | − | 34.2723i | −0.655577 | − | 1.13549i | −0.981749 | − | 0.190183i | \(-0.939092\pi\) |
0.326171 | − | 0.945311i | \(-0.394241\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.24936 | 0.173728 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −49.6981 | − | 35.7558i | −1.64297 | − | 1.18205i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.30536 | − | 4.93571i | −0.0431067 | − | 0.162991i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9220 | − | 22.3815i | 0.426257 | − | 0.738298i | −0.570280 | − | 0.821450i | \(-0.693165\pi\) |
0.996537 | + | 0.0831519i | \(0.0264987\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.21023 | + | 2.79966i | −0.204634 | + | 0.0922518i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.80251 | + | 8.31818i | −0.158076 | + | 0.273796i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4481 | + | 26.7569i | 0.507930 | + | 0.879761i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.1621 | − | 4.49563i | −0.727898 | − | 0.147656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.8506 | 1.66836 | 0.834178 | − | 0.551496i | \(-0.185943\pi\) | ||||
0.834178 | + | 0.551496i | \(0.185943\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.976100 | − | 0.555132i | 0.0319904 | − | 0.0181937i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.12994 | − | 1.41102i | 0.102470 | − | 0.0461948i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.78315 | + | 10.0167i | 0.189129 | + | 0.327581i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.7623 | 1.07030 | 0.535149 | − | 0.844758i | \(-0.320256\pi\) | ||||
0.535149 | + | 0.844758i | \(0.320256\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.3689 | + | 14.5923i | −1.05632 | + | 0.476203i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50.6793 | 1.65210 | 0.826048 | − | 0.563599i | \(-0.190584\pi\) | ||||
0.826048 | + | 0.563599i | \(0.190584\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.4256 | 1.25131 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 52.7586 | + | 2.19879i | 1.71624 | + | 0.0715267i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.5255 | 0.374530 | 0.187265 | − | 0.982309i | \(-0.440038\pi\) | ||||
0.187265 | + | 0.982309i | \(0.440038\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.2474 | 0.559873 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.0230 | + | 6.77257i | −0.487154 | + | 0.219616i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45.7747 | −1.48279 | −0.741395 | − | 0.671069i | \(-0.765835\pi\) | ||||
−0.741395 | + | 0.671069i | \(0.765835\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.10661 | + | 12.3090i | 0.229965 | + | 0.398310i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 21.5664 | − | 9.72243i | 0.697142 | − | 0.314281i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.96111 | − | 6.91605i | 0.224786 | − | 0.223331i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.6302 | −0.665491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.63990 | − | 16.8237i | −0.181743 | − | 0.542135i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.5188 | + | 42.4678i | 0.789287 | + | 1.36709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.07666 | − | 7.06098i | 0.131097 | − | 0.227066i | −0.793003 | − | 0.609218i | \(-0.791484\pi\) |
0.924100 | + | 0.382152i | \(0.124817\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.422203 | − | 0.190335i | 0.0135631 | − | 0.00611444i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.1137 | + | 24.4457i | −0.452932 | + | 0.784501i | −0.998567 | − | 0.0535223i | \(-0.982955\pi\) |
0.545635 | + | 0.838023i | \(0.316288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.505141 | + | 0.501871i | −0.0161941 | + | 0.0160893i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.9975 | + | 13.6679i | 0.608407 | + | 0.437724i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.6502 | −0.500694 | −0.250347 | − | 0.968156i | \(-0.580545\pi\) | ||||
−0.250347 | + | 0.968156i | \(0.580545\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.10603 | − | 15.7721i | −0.291030 | − | 0.504079i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.3675 | − | 5.34871i | −0.841850 | − | 0.170771i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.47581 | − | 2.55617i | 0.0470710 | − | 0.0815293i | −0.841530 | − | 0.540210i | \(-0.818345\pi\) |
0.888601 | + | 0.458681i | \(0.151678\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.69970 | − | 8.14012i | −0.149745 | − | 0.259366i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 51.7605 | − | 8.27259i | 1.64755 | − | 0.263319i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0567 | − | 19.1507i | 0.351582 | − | 0.608958i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.8182 | − | 27.3979i | −0.502482 | − | 0.870324i | −0.999996 | − | 0.00286819i | \(-0.999087\pi\) |
0.497514 | − | 0.867456i | \(-0.334246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.41567 | − | 1.08902i | 0.0766588 | − | 0.0345589i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.63557 | + | 14.9572i | −0.273766 | + | 0.474176i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.792608 | − | 1.37284i | 0.0251021 | − | 0.0434782i | −0.853201 | − | 0.521582i | \(-0.825342\pi\) |
0.878304 | + | 0.478103i | \(0.158676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.1841 | + | 12.0779i | 0.353849 | + | 0.382129i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.2.q.k.625.2 | 22 | ||
3.2 | odd | 2 | 3024.2.q.k.2305.11 | 22 | |||
4.3 | odd | 2 | 504.2.q.d.121.10 | yes | 22 | ||
7.4 | even | 3 | 1008.2.t.k.193.10 | 22 | |||
9.2 | odd | 6 | 3024.2.t.l.289.1 | 22 | |||
9.7 | even | 3 | 1008.2.t.k.961.10 | 22 | |||
12.11 | even | 2 | 1512.2.q.c.793.11 | 22 | |||
21.11 | odd | 6 | 3024.2.t.l.1873.1 | 22 | |||
28.11 | odd | 6 | 504.2.t.d.193.2 | yes | 22 | ||
36.7 | odd | 6 | 504.2.t.d.457.2 | yes | 22 | ||
36.11 | even | 6 | 1512.2.t.d.289.1 | 22 | |||
63.11 | odd | 6 | 3024.2.q.k.2881.11 | 22 | |||
63.25 | even | 3 | inner | 1008.2.q.k.529.2 | 22 | ||
84.11 | even | 6 | 1512.2.t.d.361.1 | 22 | |||
252.11 | even | 6 | 1512.2.q.c.1369.11 | 22 | |||
252.151 | odd | 6 | 504.2.q.d.25.10 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.10 | ✓ | 22 | 252.151 | odd | 6 | ||
504.2.q.d.121.10 | yes | 22 | 4.3 | odd | 2 | ||
504.2.t.d.193.2 | yes | 22 | 28.11 | odd | 6 | ||
504.2.t.d.457.2 | yes | 22 | 36.7 | odd | 6 | ||
1008.2.q.k.529.2 | 22 | 63.25 | even | 3 | inner | ||
1008.2.q.k.625.2 | 22 | 1.1 | even | 1 | trivial | ||
1008.2.t.k.193.10 | 22 | 7.4 | even | 3 | |||
1008.2.t.k.961.10 | 22 | 9.7 | even | 3 | |||
1512.2.q.c.793.11 | 22 | 12.11 | even | 2 | |||
1512.2.q.c.1369.11 | 22 | 252.11 | even | 6 | |||
1512.2.t.d.289.1 | 22 | 36.11 | even | 6 | |||
1512.2.t.d.361.1 | 22 | 84.11 | even | 6 | |||
3024.2.q.k.2305.11 | 22 | 3.2 | odd | 2 | |||
3024.2.q.k.2881.11 | 22 | 63.11 | odd | 6 | |||
3024.2.t.l.289.1 | 22 | 9.2 | odd | 6 | |||
3024.2.t.l.1873.1 | 22 | 21.11 | odd | 6 |