Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(17,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 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("336.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bc (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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(1.60841 + 0.642670i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.257 |
Dual form | 336.2.bc.f.17.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.642670 | + | 1.60841i | −0.371046 | + | 0.928615i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.28955 | − | 2.23357i | 0.576704 | − | 0.998881i | −0.419150 | − | 0.907917i | \(-0.637672\pi\) |
0.995854 | − | 0.0909641i | \(-0.0289949\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.203402 | − | 2.63792i | 0.0768787 | − | 0.997040i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.17395 | − | 2.06735i | −0.724650 | − | 0.689117i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.43199 | − | 0.826762i | 0.431763 | − | 0.249278i | −0.268335 | − | 0.963326i | \(-0.586473\pi\) |
0.700097 | + | 0.714048i | \(0.253140\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.71177i | − | 1.58416i | −0.610418 | − | 0.792080i | \(-0.708998\pi\) | ||
0.610418 | − | 0.792080i | \(-0.291002\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.76373 | + | 3.50957i | 0.713592 | + | 0.906167i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.79313 | + | 6.56990i | 0.919970 | + | 1.59343i | 0.799458 | + | 0.600722i | \(0.205120\pi\) |
0.120512 | + | 0.992712i | \(0.461547\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.58961 | − | 1.49511i | −0.594097 | − | 0.343002i | 0.172619 | − | 0.984989i | \(-0.444777\pi\) |
−0.766716 | + | 0.641987i | \(0.778110\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.11213 | + | 2.02247i | 0.897341 | + | 0.441338i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.249340 | + | 0.143957i | 0.0519910 | + | 0.0300170i | 0.525770 | − | 0.850627i | \(-0.323777\pi\) |
−0.473779 | + | 0.880644i | \(0.657111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.825879 | − | 1.43046i | −0.165176 | − | 0.286093i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.72227 | − | 2.16798i | 0.908802 | − | 0.417227i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.05856i | 0.382265i | 0.981564 | + | 0.191133i | \(0.0612161\pi\) | ||||
−0.981564 | + | 0.191133i | \(0.938784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.21209 | − | 3.00920i | 0.936118 | − | 0.540468i | 0.0473770 | − | 0.998877i | \(-0.484914\pi\) |
0.888741 | + | 0.458409i | \(0.151580\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.409472 | + | 2.83457i | 0.0712798 | + | 0.493435i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.62967 | − | 3.85604i | −0.951589 | − | 0.651790i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.877523 | + | 1.51991i | −0.144264 | + | 0.249872i | −0.929098 | − | 0.369833i | \(-0.879415\pi\) |
0.784834 | + | 0.619706i | \(0.212748\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.18685 | + | 3.67078i | 1.47107 | + | 0.587795i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.28635 | 0.669415 | 0.334708 | − | 0.942322i | \(-0.391362\pi\) | ||||
0.334708 | + | 0.942322i | \(0.391362\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.46537 | −0.375965 | −0.187982 | − | 0.982172i | \(-0.560195\pi\) | ||||
−0.187982 | + | 0.982172i | \(0.560195\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.42098 | + | 2.18971i | −1.10625 | + | 0.326423i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.186586 | − | 0.323176i | 0.0272163 | − | 0.0471401i | −0.852096 | − | 0.523385i | \(-0.824669\pi\) |
0.879313 | + | 0.476245i | \(0.158002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.91726 | − | 1.07312i | −0.988179 | − | 0.153302i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.0048 | + | 1.87863i | −1.82104 | + | 0.263061i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.73264 | + | 3.88709i | −0.924799 | + | 0.533933i | −0.885163 | − | 0.465281i | \(-0.845953\pi\) |
−0.0396361 | + | 0.999214i | \(0.512620\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.26461i | − | 0.575039i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.06901 | − | 3.20429i | 0.538954 | − | 0.424418i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.89610 | − | 8.48029i | −0.637417 | − | 1.10404i | −0.985997 | − | 0.166760i | \(-0.946669\pi\) |
0.348580 | − | 0.937279i | \(-0.386664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.889794 | + | 0.513723i | 0.113926 | + | 0.0657755i | 0.555880 | − | 0.831262i | \(-0.312381\pi\) |
−0.441954 | + | 0.897038i | \(0.645715\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.89569 | + | 5.31421i | −0.742787 | + | 0.669527i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.7576 | − | 7.36561i | −1.58239 | − | 0.913592i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.18281 | + | 2.04868i | 0.144503 | + | 0.250286i | 0.929187 | − | 0.369609i | \(-0.120508\pi\) |
−0.784685 | + | 0.619895i | \(0.787175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.391784 | + | 0.308524i | −0.0471653 | + | 0.0371419i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.6655i | 1.85915i | 0.368631 | + | 0.929576i | \(0.379826\pi\) | ||||
−0.368631 | + | 0.929576i | \(0.620174\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.30170 | + | 1.90624i | −0.386434 | + | 0.223108i | −0.680614 | − | 0.732642i | \(-0.738287\pi\) |
0.294180 | + | 0.955750i | \(0.404954\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.83154 | − | 0.409034i | 0.326958 | − | 0.0472312i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.88966 | − | 3.94565i | −0.215347 | − | 0.449649i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.56033 | + | 7.89872i | −0.513077 | + | 0.888676i | 0.486808 | + | 0.873509i | \(0.338161\pi\) |
−0.999885 | + | 0.0151665i | \(0.995172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.452128 | + | 8.98864i | 0.0502364 | + | 0.998737i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.65166 | 0.730114 | 0.365057 | − | 0.930985i | \(-0.381049\pi\) | ||||
0.365057 | + | 0.930985i | \(0.381049\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.5657 | 2.12220 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.31101 | − | 1.32298i | −0.354977 | − | 0.141838i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.25723 | − | 12.5699i | 0.769265 | − | 1.33241i | −0.168697 | − | 0.985668i | \(-0.553956\pi\) |
0.937962 | − | 0.346738i | \(-0.112711\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.0672 | − | 1.16179i | −1.57947 | − | 0.121788i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.49037 | + | 10.3171i | 0.154544 | + | 1.06983i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.67886 | + | 3.85604i | −0.685237 | + | 0.395622i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.43739i | 0.450548i | 0.974295 | + | 0.225274i | \(0.0723278\pi\) | ||||
−0.974295 | + | 0.225274i | \(0.927672\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.82229 | − | 1.16309i | −0.484659 | − | 0.116895i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.03628 | − | 3.52694i | −0.202617 | − | 0.350943i | 0.746754 | − | 0.665101i | \(-0.231611\pi\) |
−0.949371 | + | 0.314157i | \(0.898278\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.30346 | + | 4.21666i | 0.719632 | + | 0.415479i | 0.814617 | − | 0.579999i | \(-0.196947\pi\) |
−0.0949855 | + | 0.995479i | \(0.530280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.82011 | − | 6.57665i | 0.958345 | − | 0.641815i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.6334 | + | 7.29389i | 1.22132 | + | 0.705127i | 0.965199 | − | 0.261518i | \(-0.0842231\pi\) |
0.256118 | + | 0.966646i | \(0.417556\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.64994 | − | 14.9821i | −0.828514 | − | 1.43503i | −0.899204 | − | 0.437530i | \(-0.855853\pi\) |
0.0706901 | − | 0.997498i | \(-0.477480\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.88068 | − | 2.38822i | −0.178507 | − | 0.226680i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.643073 | − | 0.371279i | 0.0599669 | − | 0.0346219i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.8082 | + | 12.4171i | −1.09167 | + | 1.14796i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.1024 | − | 8.66965i | 1.65944 | − | 0.794746i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.13293 | + | 7.15844i | −0.375721 | + | 0.650767i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.75471 | + | 6.89420i | −0.248384 | + | 0.621629i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.63545 | 0.772378 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.6481 | 1.47728 | 0.738641 | − | 0.674099i | \(-0.235468\pi\) | ||||
0.738641 | + | 0.674099i | \(0.235468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.58442 | − | 3.96531i | 0.139500 | − | 0.349126i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.29744 | + | 14.3716i | −0.724951 | + | 1.25565i | 0.234043 | + | 0.972226i | \(0.424804\pi\) |
−0.958994 | + | 0.283426i | \(0.908529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.47072 | + | 6.52708i | −0.387660 | + | 0.565969i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.24729 | − | 13.3432i | 0.107350 | − | 1.14840i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.61684 | + | 4.97493i | −0.736186 | + | 0.425037i | −0.820681 | − | 0.571387i | \(-0.806406\pi\) |
0.0844948 | + | 0.996424i | \(0.473072\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 3.11952i | − | 0.264594i | −0.991210 | − | 0.132297i | \(-0.957765\pi\) | ||
0.991210 | − | 0.132297i | \(-0.0422353\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.399886 | + | 0.507801i | 0.0336765 | + | 0.0427646i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.72227 | − | 8.17922i | −0.394896 | − | 0.683981i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.59794 | + | 2.65462i | 0.381838 | + | 0.220454i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.17152 | − | 10.4361i | 0.509018 | − | 0.860756i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.987090 | + | 0.569897i | 0.0808655 | + | 0.0466877i | 0.539888 | − | 0.841737i | \(-0.318467\pi\) |
−0.459022 | + | 0.888425i | \(0.651800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.38621 | − | 11.0612i | −0.519702 | − | 0.900151i | −0.999738 | − | 0.0229016i | \(-0.992710\pi\) |
0.480036 | − | 0.877249i | \(-0.340624\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.33619 | − | 22.1244i | 0.431406 | − | 1.78865i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 15.5221i | − | 1.24676i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.82053 | − | 4.51518i | 0.624146 | − | 0.360351i | −0.154335 | − | 0.988019i | \(-0.549324\pi\) |
0.778481 | + | 0.627668i | \(0.215990\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.92516 | − | 13.3269i | −0.152675 | − | 1.05690i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.430463 | − | 0.628459i | 0.0339252 | − | 0.0495295i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0498774 | − | 0.0863903i | 0.00390670 | − | 0.00676661i | −0.864065 | − | 0.503379i | \(-0.832090\pi\) |
0.867972 | + | 0.496613i | \(0.165423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.85922 | + | 2.74073i | 0.533990 | + | 0.213366i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.08612 | −0.238811 | −0.119406 | − | 0.992846i | \(-0.538099\pi\) | ||||
−0.119406 | + | 0.992846i | \(0.538099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.6243 | −1.50956 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.53877 | + | 8.60393i | 0.194144 | + | 0.657959i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.73038 | + | 6.46120i | −0.283615 | + | 0.491236i | −0.972272 | − | 0.233851i | \(-0.924867\pi\) |
0.688657 | + | 0.725087i | \(0.258201\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.94144 | + | 1.88764i | −0.297945 | + | 0.142693i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.7863 | − | 2.42490i | 1.26174 | − | 0.182266i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.61465 | + | 1.50957i | −0.195428 | + | 0.112830i | −0.594521 | − | 0.804080i | \(-0.702658\pi\) |
0.399093 | + | 0.916910i | \(0.369325\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.762552i | − | 0.0566801i | −0.999598 | − | 0.0283400i | \(-0.990978\pi\) | ||
0.999598 | − | 0.0283400i | \(-0.00902212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.39812 | + | 1.10100i | −0.103352 | + | 0.0813881i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.26322 | + | 3.92001i | 0.166395 | + | 0.288205i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.8635 | + | 6.27204i | 0.794417 | + | 0.458657i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.75843 | − | 12.8980i | −0.346125 | − | 0.938188i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.05844 | − | 0.611089i | −0.0765859 | − | 0.0442169i | 0.461218 | − | 0.887287i | \(-0.347413\pi\) |
−0.537804 | + | 0.843070i | \(0.680746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7587 | + | 20.3666i | 0.846409 | + | 1.46602i | 0.884392 | + | 0.466744i | \(0.154573\pi\) |
−0.0379837 | + | 0.999278i | \(0.512093\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.0458 | − | 15.7858i | 1.43551 | − | 1.13044i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.7312i | 1.04956i | 0.851239 | + | 0.524778i | \(0.175852\pi\) | ||||
−0.851239 | + | 0.524778i | \(0.824148\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.96032 | + | 3.44119i | −0.422516 | + | 0.243940i | −0.696153 | − | 0.717893i | \(-0.745107\pi\) |
0.273637 | + | 0.961833i | \(0.411773\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.05527 | + | 0.585810i | −0.286036 | + | 0.0413198i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.43032 | + | 0.418716i | 0.381134 | + | 0.0293881i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.52746 | − | 9.57384i | 0.386055 | − | 0.668666i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.244445 | − | 0.828428i | −0.0169901 | − | 0.0575797i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.94441 | −0.342012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0897 | 1.31419 | 0.657093 | − | 0.753809i | \(-0.271786\pi\) | ||||
0.657093 | + | 0.753809i | \(0.271786\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.1965 | − | 10.0677i | −1.72644 | − | 0.689830i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.17921 | + | 5.50656i | −0.216821 | + | 0.375544i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.87788 | − | 14.3612i | −0.466901 | − | 0.974898i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.944103 | − | 6.53555i | −0.0637966 | − | 0.441632i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.5257 | − | 21.6655i | 2.52425 | − | 1.45738i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.9876i | 0.735785i | 0.929868 | + | 0.367892i | \(0.119921\pi\) | ||||
−0.929868 | + | 0.367892i | \(0.880079\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.16185 | + | 4.81714i | −0.0774567 | + | 0.321143i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.45418 | + | 16.3751i | 0.627496 | + | 1.08686i | 0.988052 | + | 0.154118i | \(0.0492535\pi\) |
−0.360556 | + | 0.932737i | \(0.617413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9744 | + | 8.64545i | 0.989533 | + | 0.571307i | 0.905135 | − | 0.425125i | \(-0.139770\pi\) |
0.0843986 | + | 0.996432i | \(0.473103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.56065 | − | 0.503597i | 0.497454 | − | 0.0331343i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.45119 | + | 2.56990i | 0.291607 | + | 0.168360i | 0.638666 | − | 0.769484i | \(-0.279486\pi\) |
−0.347059 | + | 0.937843i | \(0.612820\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.481223 | − | 0.833503i | −0.0313916 | − | 0.0543718i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −9.77358 | − | 12.4111i | −0.634862 | − | 0.806190i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.67983i | − | 0.367398i | −0.982983 | − | 0.183699i | \(-0.941193\pi\) | ||
0.982983 | − | 0.183699i | \(-0.0588071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.1604 | − | 11.6396i | 1.29864 | − | 0.749773i | 0.318475 | − | 0.947931i | \(-0.396829\pi\) |
0.980170 | + | 0.198158i | \(0.0634960\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7480 | − | 5.04952i | −0.946082 | − | 0.323927i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.3170 | + | 14.0663i | −0.723018 | + | 0.898664i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.53973 | + | 14.7913i | −0.543370 | + | 0.941145i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.27482 | + | 10.6986i | −0.270906 | + | 0.677995i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.3799 | −1.34949 | −0.674744 | − | 0.738052i | \(-0.735746\pi\) | ||||
−0.674744 | + | 0.738052i | \(0.735746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.476072 | 0.0299304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.5743 | + | 31.4697i | −0.787433 | + | 1.97071i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.09305 | + | 12.2855i | −0.442452 | + | 0.766349i | −0.997871 | − | 0.0652214i | \(-0.979225\pi\) |
0.555419 | + | 0.831571i | \(0.312558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.83092 | + | 2.62399i | 0.238042 | + | 0.163047i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.25577 | − | 4.47521i | 0.263425 | − | 0.277009i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.90698 | − | 1.10100i | 0.117590 | − | 0.0678904i | −0.440052 | − | 0.897973i | \(-0.645040\pi\) |
0.557641 | + | 0.830082i | \(0.311707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.0504i | 1.23169i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.5535 | + | 19.7509i | 0.951860 | + | 1.20873i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.33275 | − | 12.7007i | −0.447086 | − | 0.774375i | 0.551109 | − | 0.834433i | \(-0.314205\pi\) |
−0.998195 | + | 0.0600579i | \(0.980871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.6687 | − | 10.2010i | −1.07330 | − | 0.619669i | −0.144217 | − | 0.989546i | \(-0.546066\pi\) |
−0.929081 | + | 0.369877i | \(0.879400\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.5519 | − | 23.4875i | 0.699150 | − | 1.42153i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.36531 | − | 1.36561i | −0.142633 | − | 0.0823495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.00535275 | − | 0.00927123i | −0.000321615 | − | 0.000557054i | 0.865865 | − | 0.500279i | \(-0.166769\pi\) |
−0.866186 | + | 0.499721i | \(0.833436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.5519 | − | 4.23335i | −1.05080 | − | 0.253444i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.11712i | − | 0.484227i | −0.970248 | − | 0.242114i | \(-0.922159\pi\) | ||
0.970248 | − | 0.242114i | \(-0.0778406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.34466 | − | 1.93104i | 0.198819 | − | 0.114788i | −0.397285 | − | 0.917695i | \(-0.630048\pi\) |
0.596105 | + | 0.802907i | \(0.296714\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.90979 | − | 13.2205i | −0.113126 | − | 0.783115i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.871852 | − | 11.3070i | 0.0514638 | − | 0.667434i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.2757 | + | 35.1185i | −1.19269 | + | 2.06580i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.13713 | − | 2.85177i | −0.418386 | − | 0.167174i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.75351 | 0.336123 | 0.168062 | − | 0.985776i | \(-0.446249\pi\) | ||||
0.168062 | + | 0.985776i | \(0.446249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.2550 | −1.47041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.96987 | − | 7.00873i | 0.288381 | − | 0.406688i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.822247 | − | 1.42417i | 0.0475518 | − | 0.0823621i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.501460 | + | 6.50344i | −0.0289037 | + | 0.374852i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.98141 | − | 1.00851i | 0.401071 | − | 0.0579374i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.29487 | − | 1.32494i | 0.131404 | − | 0.0758660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.9041i | 1.36428i | 0.731221 | + | 0.682140i | \(0.238951\pi\) | ||||
−0.731221 | + | 0.682140i | \(0.761049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4758 | + | 9.03703i | −0.652836 | + | 0.514099i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5789 | − | 18.3232i | −0.599874 | − | 1.03901i | −0.992839 | − | 0.119459i | \(-0.961884\pi\) |
0.392965 | − | 0.919553i | \(-0.371449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2861 | − | 10.5575i | −1.03359 | − | 0.596746i | −0.115582 | − | 0.993298i | \(-0.536873\pi\) |
−0.918012 | + | 0.396552i | \(0.870207\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.26685 | + | 20.0214i | 0.240410 | + | 1.12808i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8698 | − | 8.00775i | −0.779007 | − | 0.449760i | 0.0570712 | − | 0.998370i | \(-0.481824\pi\) |
−0.836078 | + | 0.548610i | \(0.815157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.70194 | + | 2.94785i | 0.0952904 | + | 0.165048i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.8507 | + | 15.6321i | −1.10796 | + | 0.872498i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 22.6846i | − | 1.26221i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.17048 | + | 4.71723i | −0.453217 | + | 0.261665i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.6564 | − | 4.28406i | 1.64000 | − | 0.236909i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.814561 | − | 0.557933i | −0.0449082 | − | 0.0307599i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.48985 | − | 16.4369i | 0.521610 | − | 0.903454i | −0.478074 | − | 0.878319i | \(-0.658665\pi\) |
0.999684 | − | 0.0251350i | \(-0.00800157\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.04989 | − | 1.49007i | 0.276732 | − | 0.0816555i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.10115 | 0.333341 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.151144 | 0.00823337 | 0.00411668 | − | 0.999992i | \(-0.498690\pi\) | ||||
0.00411668 | + | 0.999992i | \(0.498690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.43363 | − | 2.57068i | −0.349427 | − | 0.139620i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.97579 | − | 8.61831i | 0.269454 | − | 0.466708i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.23778 | + | 18.0289i | −0.228819 | + | 0.973469i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.183884 | + | 1.27293i | 0.00989996 | + | 0.0685325i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.5977 | + | 6.69596i | −0.622599 | + | 0.359458i | −0.777880 | − | 0.628412i | \(-0.783705\pi\) |
0.155281 | + | 0.987870i | \(0.450372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4025i | 0.717421i | 0.933449 | + | 0.358710i | \(0.116783\pi\) | ||||
−0.933449 | + | 0.358710i | \(0.883217\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3830 | − | 26.9725i | −0.660955 | − | 1.43969i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.7469 | + | 18.6141i | 0.571998 | + | 0.990729i | 0.996361 | + | 0.0852371i | \(0.0271648\pi\) |
−0.424363 | + | 0.905492i | \(0.639502\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 34.9899 | + | 20.2014i | 1.85707 | + | 1.07218i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.31047 | + | 34.6878i | 0.122283 | + | 1.83587i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4173 | − | 14.0974i | −1.28870 | − | 0.744030i | −0.310276 | − | 0.950647i | \(-0.600421\pi\) |
−0.978422 | + | 0.206616i | \(0.933755\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.02928 | − | 8.71097i | −0.264699 | − | 0.458472i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.85759 | − | 11.2479i | −0.464903 | − | 0.590364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.83274i | 0.514669i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.6810 | − | 11.3628i | 1.02734 | − | 0.593135i | 0.111118 | − | 0.993807i | \(-0.464557\pi\) |
0.916221 | + | 0.400673i | \(0.131224\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.31831 | − | 8.86138i | −0.485092 | − | 0.461305i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.88441 | + | 18.5508i | 0.461255 | + | 0.963110i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.95699 | − | 12.0499i | 0.360219 | − | 0.623918i | −0.627778 | − | 0.778393i | \(-0.716035\pi\) |
0.987997 | + | 0.154475i | \(0.0493686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.54974 | + | 13.8893i | −0.286588 | + | 0.717242i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.7580 | 0.605569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8656 | −1.07179 | −0.535897 | − | 0.844283i | \(-0.680027\pi\) | ||||
−0.535897 | + | 0.844283i | \(0.680027\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.6992 | + | 26.7770i | −0.548139 | + | 1.37183i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.23577 | − | 2.14042i | 0.0631451 | − | 0.109371i | −0.832725 | − | 0.553687i | \(-0.813220\pi\) |
0.895870 | + | 0.444317i | \(0.146554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.2497 | − | 0.867429i | −0.573337 | − | 0.0442083i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.35959 | + | 5.09677i | 0.272443 | + | 0.259084i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.4245 | + | 11.7921i | −1.03556 | + | 0.597882i | −0.918573 | − | 0.395251i | \(-0.870658\pi\) |
−0.116989 | + | 0.993133i | \(0.537324\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.18419i | 0.110459i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.7829 | − | 22.5819i | −0.897027 | − | 1.13910i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.7615 | + | 20.3716i | 0.591788 | + | 1.02501i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.79160 | − | 1.03438i | −0.0899181 | − | 0.0519142i | 0.454367 | − | 0.890815i | \(-0.349866\pi\) |
−0.544285 | + | 0.838901i | \(0.683199\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.62501 | − | 11.3855i | −0.381728 | − | 0.569988i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.46052 | − | 3.72998i | −0.322623 | − | 0.186266i | 0.329938 | − | 0.944003i | \(-0.392972\pi\) |
−0.652561 | + | 0.757736i | \(0.726305\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.1879 | − | 29.7702i | −0.856188 | − | 1.48296i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.6598 | + | 10.5814i | 1.02659 | + | 0.525796i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.90201i | 0.143847i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.2897 | − | 16.9104i | 1.44828 | − | 0.836166i | 0.449902 | − | 0.893078i | \(-0.351459\pi\) |
0.998379 | + | 0.0569122i | \(0.0181255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.46394 | − | 17.0566i | −0.121537 | − | 0.841342i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.3662 | + | 11.1906i | −1.14978 | + | 0.550654i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.57764 | − | 14.8569i | 0.421060 | − | 0.729297i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.01746 | + | 2.00482i | 0.245706 | + | 0.0981765i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.2980 | 0.747358 | 0.373679 | − | 0.927558i | \(-0.378096\pi\) | ||||
0.373679 | + | 0.927558i | \(0.378096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8931 | 0.579633 | 0.289816 | − | 0.957082i | \(-0.406406\pi\) | ||||
0.289816 | + | 0.957082i | \(0.406406\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.07375 | + | 0.316831i | −0.0522073 | + | 0.0154048i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.26534 | − | 10.8519i | 0.303913 | − | 0.526393i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.53615 | − | 2.24271i | 0.0743393 | − | 0.108533i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.1904 | − | 2.33881i | 0.781679 | − | 0.112919i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9148 | − | 8.61109i | 0.718423 | − | 0.414782i | −0.0957491 | − | 0.995405i | \(-0.530525\pi\) |
0.814172 | + | 0.580624i | \(0.197191\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.55093i | 0.0745329i | 0.999305 | + | 0.0372664i | \(0.0118650\pi\) | ||||
−0.999305 | + | 0.0372664i | \(0.988135\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.22466 | + | 5.68931i | −0.346396 | + | 0.272782i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.430463 | − | 0.745583i | −0.0205918 | − | 0.0356661i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.8278 | − | 9.71551i | −0.803145 | − | 0.463696i | 0.0414249 | − | 0.999142i | \(-0.486810\pi\) |
−0.844570 | + | 0.535446i | \(0.820144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.8193 | + | 16.6333i | 0.610441 | + | 0.792062i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.08964 | + | 1.78380i | 0.146793 | + | 0.0847510i | 0.571598 | − | 0.820534i | \(-0.306324\pi\) |
−0.424805 | + | 0.905285i | \(0.639657\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.7171 | − | 32.4190i | −0.887277 | − | 1.53681i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.55100 | + | 1.22139i | −0.0733597 | + | 0.0577697i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.5796i | − | 1.39595i | −0.716124 | − | 0.697973i | \(-0.754085\pi\) | ||
0.716124 | − | 0.697973i | \(-0.245915\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.13803 | − | 3.54379i | 0.289028 | − | 0.166871i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.8952 | − | 3.16290i | 1.02873 | − | 0.148606i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −22.0248 | + | 32.1554i | −1.03254 | + | 1.50747i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2312 | − | 19.4530i | 0.525374 | − | 0.909975i | −0.474189 | − | 0.880423i | \(-0.657259\pi\) |
0.999563 | − | 0.0295520i | \(-0.00940807\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 32.1556 | + | 22.8014i | 1.50089 | + | 1.06428i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.31904 | −0.434031 | −0.217015 | − | 0.976168i | \(-0.569632\pi\) | ||||
−0.217015 | + | 0.976168i | \(0.569632\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6243 | 0.772597 | 0.386298 | − | 0.922374i | \(-0.373754\pi\) | ||||
0.386298 | + | 0.922374i | \(0.373754\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.9658 | + | 9.97556i | 1.15776 | + | 0.462605i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.06560 | − | 10.5059i | 0.280683 | − | 0.486156i | −0.690871 | − | 0.722979i | \(-0.742773\pi\) |
0.971553 | + | 0.236822i | \(0.0761059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.64484 | − | 2.70344i | 0.260654 | − | 0.124833i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.23624 | + | 15.4804i | 0.103040 | + | 0.713298i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.53039 | + | 2.03827i | −0.162328 | + | 0.0937198i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.93913i | 0.226623i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.6724 | + | 5.46838i | 1.03810 | + | 0.250380i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.2594 | + | 22.9660i | 0.605839 | + | 1.04934i | 0.991918 | + | 0.126878i | \(0.0404956\pi\) |
−0.386080 | + | 0.922465i | \(0.626171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.68140 | + | 5.01221i | 0.395838 | + | 0.228537i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.734173 | + | 1.09625i | 0.0334060 | + | 0.0498811i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.91120 | + | 5.72223i | 0.450044 | + | 0.259833i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.5986 | − | 30.4817i | −0.797469 | − | 1.38126i | −0.921260 | − | 0.388948i | \(-0.872839\pi\) |
0.123791 | − | 0.992308i | \(-0.460495\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.106896 | + | 0.135744i | 0.00483401 | + | 0.00613854i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.5795i | 1.47029i | 0.677910 | + | 0.735145i | \(0.262886\pi\) | ||||
−0.677910 | + | 0.735145i | \(0.737114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.5245 | + | 7.80840i | −0.609115 | + | 0.351673i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.81643 | + | 9.27104i | −0.396269 | + | 0.416702i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.3243 | + | 3.18639i | 1.85365 | + | 0.142929i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.46895 | − | 4.27635i | 0.110525 | − | 0.191436i | −0.805457 | − | 0.592655i | \(-0.798080\pi\) |
0.915982 | + | 0.401219i | \(0.131413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.98336 | − | 4.96374i | 0.0886099 | − | 0.221764i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.7907 | 0.748661 | 0.374331 | − | 0.927295i | \(-0.377873\pi\) | ||||
0.374331 | + | 0.927295i | \(0.377873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.5035 | −0.467401 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.6119 | − | 31.5639i | 0.560116 | − | 1.40180i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.631490 | + | 1.09377i | −0.0279903 | + | 0.0484806i | −0.879681 | − | 0.475564i | \(-0.842244\pi\) |
0.851691 | + | 0.524044i | \(0.175577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.35693 | + | 9.09735i | 0.192739 | + | 0.402443i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.4702 | − | 1.44611i | −0.683027 | − | 0.0638475i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.8364 | − | 10.8752i | 0.830029 | − | 0.479218i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.617048i | − | 0.0271378i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.99485 | − | 10.1524i | −0.350935 | − | 0.445640i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.9945 | − | 25.9713i | −0.656922 | − | 1.13782i | −0.981408 | − | 0.191932i | \(-0.938525\pi\) |
0.324486 | − | 0.945891i | \(-0.394809\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.7587 | − | 17.7586i | −1.34499 | − | 0.776528i | −0.357451 | − | 0.933932i | \(-0.616354\pi\) |
−0.987534 | + | 0.157404i | \(0.949688\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.503059 | − | 7.55257i | −0.0219553 | − | 0.329621i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.5403 | + | 22.8286i | 1.72240 | + | 0.994429i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4586 | − | 19.8468i | −0.498198 | − | 0.862904i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.88785 | + | 28.5577i | −0.298907 | + | 1.23930i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 24.4826i | − | 1.06046i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.5828 | − | 18.8117i | 1.40868 | − | 0.813300i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.747645 | − | 5.17557i | −0.0322633 | − | 0.223343i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.7927 | + | 4.18223i | −0.464874 | + | 0.180141i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.9158 | − | 20.6388i | 0.512300 | − | 0.887330i | −0.487598 | − | 0.873068i | \(-0.662127\pi\) |
0.999898 | − | 0.0142616i | \(-0.00453975\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.22649 | + | 0.490069i | 0.0526339 | + | 0.0210309i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −44.6181 | −1.91123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.1040 | −0.902342 | −0.451171 | − | 0.892437i | \(-0.648994\pi\) | ||||
−0.451171 | + | 0.892437i | \(0.648994\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.872324 | − | 2.95632i | −0.0372299 | − | 0.126173i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.07778 | − | 5.33087i | 0.131118 | − | 0.227103i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.9086 | + | 13.6364i | 0.846601 | + | 0.579879i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.75948 | + | 1.12091i | −0.329372 | + | 0.0475799i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.3020 | − | 11.1440i | 0.817852 | − | 0.472187i | −0.0318235 | − | 0.999494i | \(-0.510131\pi\) |
0.849675 | + | 0.527307i | \(0.176798\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0816i | 0.595588i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0696 | + | 13.4421i | −0.720680 | + | 0.567525i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.2197 | − | 35.0215i | −0.852157 | − | 1.47598i | −0.879258 | − | 0.476347i | \(-0.841961\pi\) |
0.0271005 | − | 0.999633i | \(-0.491373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.93427 | + | 5.15820i | 0.375867 | + | 0.217007i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.8033 | + | 0.635629i | 0.999644 | + | 0.0266939i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.7717 | + | 12.5699i | 0.912717 | + | 0.526957i | 0.881304 | − | 0.472549i | \(-0.156666\pi\) |
0.0314127 | + | 0.999506i | \(0.489999\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.655344 | + | 1.13509i | 0.0274253 | + | 0.0475020i | 0.879412 | − | 0.476061i | \(-0.157936\pi\) |
−0.851987 | + | 0.523563i | \(0.824602\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.66311 | − | 1.30967i | 0.0694773 | − | 0.0547123i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.475563i | − | 0.0198324i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.21739 | − | 3.01226i | 0.217203 | − | 0.125402i | −0.387452 | − | 0.921890i | \(-0.626645\pi\) |
0.604654 | + | 0.796488i | \(0.293311\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.3148 | + | 5.82374i | −1.67543 | + | 0.242026i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.35296 | − | 17.5465i | 0.0561303 | − | 0.727953i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.42740 | + | 11.1326i | −0.266196 | + | 0.461065i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.5071 | + | 42.3869i | 0.517106 | + | 1.75248i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.5131 | −1.63088 | −0.815439 | − | 0.578843i | \(-0.803504\pi\) | ||||
−0.815439 | + | 0.578843i | \(0.803504\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.9964 | −0.741527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.6938 | − | 9.46731i | −0.974633 | − | 0.389433i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.75855 | + | 11.7062i | −0.277540 | + | 0.480714i | −0.970773 | − | 0.240000i | \(-0.922853\pi\) |
0.693232 | + | 0.720714i | \(0.256186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.97971 | − | 51.6129i | 0.163152 | − | 2.11592i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.70432 | − | 11.7982i | −0.0697533 | − | 0.482867i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.68762 | − | 3.28375i | 0.232390 | − | 0.134170i | −0.379284 | − | 0.925280i | \(-0.623830\pi\) |
0.611674 | + | 0.791110i | \(0.290496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.0499i | − | 0.409946i | −0.978768 | − | 0.204973i | \(-0.934289\pi\) | ||
0.978768 | − | 0.204973i | \(-0.0657106\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.66398 | − | 6.89900i | 0.0677623 | − | 0.280949i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.6592 | + | 18.4623i | 0.433360 | + | 0.750601i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.673920 | + | 0.389088i | 0.0273536 | + | 0.0157926i | 0.513614 | − | 0.858021i | \(-0.328306\pi\) |
−0.486261 | + | 0.873814i | \(0.661640\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.16337 | + | 8.46508i | −0.168708 | + | 0.343022i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.84591 | − | 1.06573i | −0.0746774 | − | 0.0431150i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.3349 | − | 33.4890i | −0.780928 | − | 1.35261i | −0.931402 | − | 0.363993i | \(-0.881413\pi\) |
0.150474 | − | 0.988614i | \(-0.451920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.8463 | + | 15.0432i | 0.477689 | + | 0.606602i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.83523i | − | 0.315434i | −0.987484 | − | 0.157717i | \(-0.949587\pi\) | ||
0.987484 | − | 0.157717i | \(-0.0504134\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.9235 | + | 10.3481i | −0.720407 | + | 0.415927i | −0.814902 | − | 0.579598i | \(-0.803209\pi\) |
0.0944957 | + | 0.995525i | \(0.469876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.48955 | + | 0.139239i | 0.0597735 | + | 0.00558747i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −31.6823 | − | 21.7008i | −1.26932 | − | 0.869422i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.2652 | − | 26.4402i | 0.610610 | − | 1.05761i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.17762 | − | 7.95263i | 0.126902 | − | 0.317597i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.3142 | −0.530874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.21022 | 0.287034 | 0.143517 | − | 0.989648i | \(-0.454159\pi\) | ||||
0.143517 | + | 0.989648i | \(0.454159\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.2683 | + | 30.7040i | −0.487623 | + | 1.22037i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.4686 | − | 37.1847i | 0.851955 | − | 1.47563i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.12940 | + | 39.5098i | −0.242855 | + | 1.56543i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.3860 | − | 34.0560i | 1.28117 | − | 1.34723i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.9156 | + | 18.4265i | −1.26059 | + | 0.727802i | −0.973189 | − | 0.230009i | \(-0.926124\pi\) |
−0.287401 | + | 0.957810i | \(0.592791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5183i | 0.414801i | 0.978256 | + | 0.207400i | \(0.0665003\pi\) | ||||
−0.978256 | + | 0.207400i | \(0.933500\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.81361 | − | 8.65237i | −0.268286 | − | 0.340687i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.2057 | + | 17.6768i | 0.401228 | + | 0.694948i | 0.993874 | − | 0.110515i | \(-0.0352501\pi\) |
−0.592646 | + | 0.805463i | \(0.701917\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.0224 | − | 8.09581i | −0.550426 | − | 0.317789i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.5188 | − | 1.83296i | 1.07855 | − | 0.0718395i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.7382 | + | 16.5920i | 1.12461 | + | 0.649295i | 0.942574 | − | 0.333996i | \(-0.108397\pi\) |
0.182038 | + | 0.983291i | \(0.441731\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.3999 | + | 37.0658i | 0.836165 | + | 1.44828i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.1186 | + | 2.68170i | 0.433777 | + | 0.104623i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 7.18286i | − | 0.279804i | −0.990165 | − | 0.139902i | \(-0.955321\pi\) | ||
0.990165 | − | 0.139902i | \(-0.0446788\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.2360 | + | 10.5285i | −0.709297 | + | 0.409513i | −0.810801 | − | 0.585323i | \(-0.800968\pi\) |
0.101504 | + | 0.994835i | \(0.467635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.7303 | + | 74.2804i | 0.416730 | + | 2.88481i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.81344 | + | 18.4026i | 0.341771 | + | 0.713624i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.296344 | + | 0.513282i | −0.0114745 | + | 0.0198744i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.6726 | − | 7.06140i | −0.683261 | − | 0.273010i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.69891 | 0.0655856 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.5441 | −0.830464 | −0.415232 | − | 0.909715i | \(-0.636300\pi\) | ||||
−0.415232 | + | 0.909715i | \(0.636300\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7.00124 | − | 4.96456i | −0.269478 | − | 0.191086i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.69876 | − | 4.67439i | 0.103722 | − | 0.179651i | −0.809493 | − | 0.587129i | \(-0.800258\pi\) |
0.913215 | + | 0.407477i | \(0.133592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.7055 | + | 0.902573i | 0.449215 | + | 0.0346376i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.4138 | + | 4.68238i | −1.24210 | + | 0.179429i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.9007 | − | 16.6858i | 1.10585 | − | 0.638465i | 0.168101 | − | 0.985770i | \(-0.446236\pi\) |
0.937752 | + | 0.347305i | \(0.112903\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.6617i | 0.980483i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.5290 | + | 18.5287i | −0.897686 | + | 0.706914i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.2022 | + | 38.4553i | 0.845835 | + | 1.46503i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.4696 | + | 19.9010i | 1.31128 | + | 0.757070i | 0.982309 | − | 0.187268i | \(-0.0599634\pi\) |
0.328975 | + | 0.944339i | \(0.393297\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.04901 | + | 12.4843i | −0.153809 | + | 0.474238i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.96765 | − | 4.02278i | −0.264298 | − | 0.152593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.2587 | + | 28.1609i | 0.615842 | + | 1.06667i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.99409 | + | 5.50774i | −0.264541 | + | 0.208322i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.6583i | 0.402559i | 0.979534 | + | 0.201280i | \(0.0645100\pi\) | ||||
−0.979534 | + | 0.201280i | \(0.935490\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.54488 | − | 2.62399i | 0.171414 | − | 0.0989657i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.64988 | − | 0.238336i | 0.0621381 | − | 0.00897626i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.71797 | + | 4.65416i | −0.365482 | + | 0.175038i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5727 | + | 30.4367i | −0.659955 | + | 1.14308i | 0.320672 | + | 0.947190i | \(0.396091\pi\) |
−0.980627 | + | 0.195885i | \(0.937242\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.2434 | − | 7.74364i | 0.984203 | − | 0.290409i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.73278 | 0.0648930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.3584 | −0.910954 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.13549 | + | 3.65026i | 0.341171 | + | 0.136321i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.6309 | + | 27.0734i | −0.582932 | + | 1.00967i | 0.412197 | + | 0.911095i | \(0.364761\pi\) |
−0.995130 | + | 0.0985739i | \(0.968572\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6087 | − | 18.4083i | 0.469574 | − | 0.685560i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.76476 | + | 39.9066i | 0.214394 | + | 1.48414i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.94470 | − | 1.70012i | 0.109363 | − | 0.0631410i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.7975i | − | 1.47601i | −0.674797 | − | 0.738003i | \(-0.735769\pi\) | ||
0.674797 | − | 0.738003i | \(-0.264231\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.5998 | − | 20.4756i | 0.651843 | − | 0.758354i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.35146 | − | 16.1972i | −0.345876 | − | 0.599075i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5878 | + | 6.11289i | 0.391071 | + | 0.225785i | 0.682624 | − | 0.730770i | \(-0.260839\pi\) |
−0.291553 | + | 0.956555i | \(0.594172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.3513 | − | 27.2424i | −0.566240 | − | 1.00485i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.38754 | + | 1.95580i | 0.124782 | + | 0.0720428i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5001 | + | 25.1148i | 0.533393 | + | 0.923864i | 0.999239 | + | 0.0389981i | \(0.0124166\pi\) |
−0.465846 | + | 0.884866i | \(0.654250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.3021 | − | 23.2413i | −0.672346 | − | 0.853789i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 33.4864i | − | 1.22850i | −0.789113 | − | 0.614248i | \(-0.789459\pi\) | ||
0.789113 | − | 0.614248i | \(-0.210541\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.54580 | − | 1.46982i | 0.0932710 | − | 0.0538501i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.4604 | − | 13.7513i | −0.529078 | − | 0.503134i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.8104 | − | 31.8423i | 0.796934 | − | 1.16349i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.86021 | − | 10.1502i | 0.213842 | − | 0.370385i | −0.739072 | − | 0.673627i | \(-0.764736\pi\) |
0.952914 | + | 0.303242i | \(0.0980689\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.7402 | − | 34.3876i | 0.500722 | − | 1.25315i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.9413 | −1.19886 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.2688 | 0.409571 | 0.204785 | − | 0.978807i | \(-0.434350\pi\) | ||||
0.204785 | + | 0.978807i | \(0.434350\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.305957 | + | 0.765717i | −0.0111055 | + | 0.0277938i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0633 | + | 17.4301i | −0.364793 | + | 0.631841i | −0.988743 | − | 0.149624i | \(-0.952194\pi\) |
0.623950 | + | 0.781465i | \(0.285527\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.2811 | + | 19.7705i | −1.49448 | + | 0.715739i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −42.5349 | − | 40.4492i | −1.53785 | − | 1.46244i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.4374 | + | 27.9654i | −1.74897 | + | 1.00977i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.95157i | 0.286741i | 0.989669 | + | 0.143370i | \(0.0457940\pi\) | ||||
−0.989669 | + | 0.143370i | \(0.954206\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2016 | − | 19.3040i | −0.547473 | − | 0.695218i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.8927 | − | 27.5269i | −0.571620 | − | 0.990075i | −0.996400 | − | 0.0847784i | \(-0.972982\pi\) |
0.424780 | − | 0.905297i | \(-0.360352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.60911 | − | 4.97047i | −0.309248 | − | 0.178545i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.68246 | + | 4.47533i | −0.239732 | + | 0.160552i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.1000 | − | 6.40857i | −0.397698 | − | 0.229611i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.9516 | + | 22.4329i | 0.463446 | + | 0.802712i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.46291 | + | 9.72110i | 0.159492 | + | 0.347404i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 23.2902i | − | 0.831264i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.3569 | + | 15.2172i | −0.939523 | + | 0.542434i | −0.889811 | − | 0.456330i | \(-0.849164\pi\) |
−0.0497122 | + | 0.998764i | \(0.515830\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.545292 | + | 3.77478i | 0.0194129 | + | 0.134386i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.5517 | + | 0.813608i | 0.375175 | + | 0.0289286i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.93427 | − | 5.08230i | 0.104199 | − | 0.180478i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −32.2492 | − | 12.8858i | −1.14376 | − | 0.457012i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.0924 | −1.42015 | −0.710074 | − | 0.704127i | \(-0.751338\pi\) | ||||
−0.710074 | + | 0.704127i | \(0.751338\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.83098 | 0.100153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −41.7632 | + | 12.3231i | −1.47563 | + | 0.435415i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.15201 | + | 5.45944i | −0.111232 | + | 0.192659i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.848601 | − | 1.77190i | −0.0299093 | − | 0.0624511i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.1404 | − | 3.63170i | 0.884985 | − | 0.127842i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34.0306 | + | 19.6476i | −1.19645 | + | 0.690773i | −0.959763 | − | 0.280812i | \(-0.909396\pi\) |
−0.236691 | + | 0.971585i | \(0.576063\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.6789i | 0.831480i | 0.909484 | + | 0.415740i | \(0.136477\pi\) | ||||
−0.909484 | + | 0.415740i | \(0.863523\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.7626 | − | 21.8626i | 0.973676 | − | 0.766755i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.128639 | − | 0.222809i | −0.00450602 | − | 0.00780466i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.38434 | + | 3.68600i | 0.223360 | + | 0.128957i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 30.3535 | + | 33.6748i | 1.06064 | + | 1.17669i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.4772 | + | 21.6374i | 1.30796 | + | 0.755152i | 0.981756 | − | 0.190146i | \(-0.0608963\pi\) |
0.326206 | + | 0.945299i | \(0.394230\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.484756 | − | 0.839623i | −0.0168975 | − | 0.0292674i | 0.857453 | − | 0.514562i | \(-0.172046\pi\) |
−0.874351 | + | 0.485295i | \(0.838712\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.71657 | − | 2.92674i | 0.129394 | − | 0.101896i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.9510i | 1.52833i | 0.645023 | + | 0.764163i | \(0.276848\pi\) | ||||
−0.645023 | + | 0.764163i | \(0.723152\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.57119 | + | 3.79388i | −0.228227 | + | 0.131767i | −0.609754 | − | 0.792591i | \(-0.708732\pi\) |
0.381527 | + | 0.924358i | \(0.375398\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0183520 | − | 0.00265106i | 0.000636622 | − | 9.19643e-5i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.1878 | − | 49.5161i | −0.664818 | − | 1.71563i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.97971 | + | 6.89306i | −0.137724 | + | 0.238544i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.0890 | − | 25.5099i | 0.625248 | − | 0.881753i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.87477 | −0.306391 | −0.153196 | − | 0.988196i | \(-0.548956\pi\) | ||||
−0.153196 | + | 0.988196i | \(0.548956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.7623 | 0.853873 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.0556 | + | 5.21663i | 0.449660 | + | 0.179670i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.3065 | + | 43.8322i | −0.870570 | + | 1.50787i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.0428 | + | 12.3584i | 0.619957 | + | 0.424639i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.956387 | + | 6.62059i | 0.0328231 | + | 0.227218i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.437604 | + | 0.252651i | −0.0150009 | + | 0.00866075i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.208510i | − | 0.00713924i | −0.999994 | − | 0.00356962i | \(-0.998864\pi\) | ||
0.999994 | − | 0.00356962i | \(-0.00113625\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.4913 | + | 5.42470i | 0.769187 | + | 0.185521i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.9945 | − | 25.9713i | −0.512204 | − | 0.887163i | −0.999900 | − | 0.0141492i | \(-0.995496\pi\) |
0.487696 | − | 0.873013i | \(-0.337837\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.9227 | − | 10.3477i | −0.611513 | − | 0.353057i | 0.162044 | − | 0.986783i | \(-0.448191\pi\) |
−0.773557 | + | 0.633726i | \(0.781525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.6260 | + | 8.66899i | 0.600694 | + | 0.295438i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.8134 | − | 8.55253i | −0.504254 | − | 0.291131i | 0.226214 | − | 0.974078i | \(-0.427365\pi\) |
−0.730469 | + | 0.682946i | \(0.760698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.62102 | + | 16.6641i | 0.327124 | + | 0.566596i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.4543 | − | 55.1812i | −1.47579 | − | 1.87405i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.0812i | 0.511596i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7016 | − | 6.75591i | 0.396493 | − | 0.228915i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.17363 | − | 9.64666i | 0.310480 | − | 0.326490i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.75647 | − | 22.7796i | 0.0593795 | − | 0.770092i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.71713 | + | 16.8306i | −0.328124 | + | 0.568328i | −0.982140 | − | 0.188153i | \(-0.939750\pi\) |
0.654015 | + | 0.756481i | \(0.273083\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.69760 | + | 9.25398i | −0.124717 | + | 0.312129i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0526 | 1.01250 | 0.506249 | − | 0.862387i | \(-0.331032\pi\) | ||||
0.506249 | + | 0.862387i | \(0.331032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.8382 | 0.566649 | 0.283324 | − | 0.959024i | \(-0.408563\pi\) | ||||
0.283324 | + | 0.959024i | \(0.408563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 16.2307 | − | 40.6204i | 0.545587 | − | 1.36544i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.3283 | − | 23.0853i | 0.447520 | − | 0.775128i | −0.550704 | − | 0.834701i | \(-0.685641\pi\) |
0.998224 | + | 0.0595728i | \(0.0189738\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.38626 | − | 43.9164i | 0.113572 | − | 1.47291i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.07891 | + | 12.4979i | 0.270654 | + | 0.418695i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.966369 | + | 0.557933i | −0.0323383 | + | 0.0186705i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.78665i | 0.260279i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.76222 | + | 2.23778i | 0.0588388 | + | 0.0747174i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.19462 | + | 10.7294i | 0.206602 | + | 0.357846i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.0756 | − | 29.4885i | −1.70157 | − | 0.982404i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.1379 | − | 4.98612i | −0.337369 | − | 0.165928i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.70321 | − | 0.983349i | −0.0566166 | − | 0.0326876i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.22753 | + | 7.32230i | 0.140373 | + | 0.243133i | 0.927637 | − | 0.373483i | \(-0.121837\pi\) |
−0.787264 | + | 0.616616i | \(0.788503\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.86464 | + | 11.8771i | −0.0950143 | + | 0.393938i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.4171i | 0.510792i | 0.966837 | + | 0.255396i | \(0.0822058\pi\) | ||||
−0.966837 | + | 0.255396i | \(0.917794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.52513 | − | 5.49934i | 0.315236 | − | 0.182002i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.656206 | + | 4.54258i | 0.0216935 | + | 0.150173i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.2234 | + | 24.8112i | 1.19620 | + | 0.819338i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.7933 | + | 49.8714i | −0.949802 | + | 1.64511i | −0.203964 | + | 0.978978i | \(0.565383\pi\) |
−0.745838 | + | 0.666127i | \(0.767951\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −38.4476 | − | 15.3625i | −1.26689 | − | 0.506210i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 89.4776 | 2.94519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.89891 | 0.0953156 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.16007 | − | 24.2656i | −0.235167 | − | 0.796988i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.6879 | − | 41.0287i | 0.777176 | − | 1.34611i | −0.156388 | − | 0.987696i | \(-0.549985\pi\) |
0.933563 | − | 0.358412i | \(-0.116682\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.3086 | + | 13.1210i | 0.534492 | + | 0.430024i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.2699 | − | 5.23942i | 1.18742 | − | 0.171531i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.0180 | − | 16.1762i | 0.916287 | − | 0.529019i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.6136i | 1.32679i | 0.748270 | + | 0.663394i | \(0.230885\pi\) | ||||
−0.748270 | + | 0.663394i | \(0.769115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.7327 | − | 22.6266i | 0.937657 | − | 0.738391i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.9142 | − | 25.8322i | −0.486189 | − | 0.842105i | 0.513685 | − | 0.857979i | \(-0.328280\pi\) |
−0.999874 | + | 0.0158745i | \(0.994947\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.06876 | + | 0.617048i | 0.0348036 | + | 0.0200939i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −34.9447 | − | 6.00429i | −1.13675 | − | 0.195320i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.1139 | − | 20.2730i | −1.14105 | − | 0.658785i | −0.194359 | − | 0.980930i | \(-0.562263\pi\) |
−0.946690 | + | 0.322145i | \(0.895596\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.8880 | + | 18.8585i | 0.353439 | + | 0.612174i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.7934 | − | 17.1620i | 0.706701 | − | 0.556516i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.7169i | 1.18938i | 0.803956 | + | 0.594688i | \(0.202724\pi\) | ||||
−0.803956 | + | 0.594688i | \(0.797276\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.72982 | + | 1.57606i | −0.0883348 | + | 0.0510001i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.83513 | + | 0.842923i | −0.188623 | + | 0.0272478i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.3708 | + | 23.7425i | 0.367182 | + | 0.766684i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.61057 | − | 4.52163i | 0.0842118 | − | 0.145859i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.3854 | − | 41.9742i | −0.399112 | − | 1.35260i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 60.6536 | 1.95251 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.1106 | −0.968290 | −0.484145 | − | 0.874988i | \(-0.660869\pi\) | ||||
−0.484145 | + | 0.874988i | \(0.660869\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.4861 | + | 14.5787i | 1.17210 | + | 0.468336i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.1290 | − | 19.2760i | 0.357147 | − | 0.618597i | −0.630336 | − | 0.776322i | \(-0.717083\pi\) |
0.987483 | + | 0.157726i | \(0.0504162\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.22904 | − | 0.634516i | −0.263811 | − | 0.0203417i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.33631 | − | 16.1731i | −0.0748217 | − | 0.517953i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.3918 | − | 27.9390i | 1.54819 | − | 0.893849i | 0.549912 | − | 0.835223i | \(-0.314661\pi\) |
0.998280 | − | 0.0586266i | \(-0.0186721\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 24.0000i | − | 0.767044i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1688 | + | 50.4529i | −0.388519 | + | 1.61084i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.8878 | + | 37.9109i | 0.698114 | + | 1.20917i | 0.969120 | + | 0.246591i | \(0.0793104\pi\) |
−0.271006 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.9032 | + | 18.9966i | 1.04838 | + | 0.605284i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.42088 | − | 0.951579i | 0.0452270 | − | 0.0302891i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.614715 | − | 0.354906i | −0.0195468 | − | 0.0112853i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.7736 | − | 20.3924i | −0.374000 | − | 0.647787i | 0.616177 | − | 0.787608i | \(-0.288681\pi\) |
−0.990177 | + | 0.139821i | \(0.955347\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.3384 | + | 25.8271i | 0.645420 | + | 0.819597i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.7504i | 0.562724i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.4923 | + | 9.52186i | −0.522318 | + | 0.301560i | −0.737882 | − | 0.674929i | \(-0.764174\pi\) |
0.215565 | + | 0.976490i | \(0.430841\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.848765 | + | 9.07990i | −0.0268537 | + | 0.287275i |
(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 | 336.2.bc.f.257.3 | 16 | ||
3.2 | odd | 2 | inner | 336.2.bc.f.257.1 | 16 | ||
4.3 | odd | 2 | 168.2.u.a.89.6 | yes | 16 | ||
7.2 | even | 3 | 2352.2.k.i.881.5 | 16 | |||
7.3 | odd | 6 | inner | 336.2.bc.f.17.1 | 16 | ||
7.5 | odd | 6 | 2352.2.k.i.881.12 | 16 | |||
12.11 | even | 2 | 168.2.u.a.89.8 | yes | 16 | ||
21.2 | odd | 6 | 2352.2.k.i.881.11 | 16 | |||
21.5 | even | 6 | 2352.2.k.i.881.6 | 16 | |||
21.17 | even | 6 | inner | 336.2.bc.f.17.3 | 16 | ||
28.3 | even | 6 | 168.2.u.a.17.8 | yes | 16 | ||
28.11 | odd | 6 | 1176.2.u.b.521.1 | 16 | |||
28.19 | even | 6 | 1176.2.k.a.881.5 | 16 | |||
28.23 | odd | 6 | 1176.2.k.a.881.12 | 16 | |||
28.27 | even | 2 | 1176.2.u.b.1097.3 | 16 | |||
84.11 | even | 6 | 1176.2.u.b.521.3 | 16 | |||
84.23 | even | 6 | 1176.2.k.a.881.6 | 16 | |||
84.47 | odd | 6 | 1176.2.k.a.881.11 | 16 | |||
84.59 | odd | 6 | 168.2.u.a.17.6 | ✓ | 16 | ||
84.83 | odd | 2 | 1176.2.u.b.1097.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.6 | ✓ | 16 | 84.59 | odd | 6 | ||
168.2.u.a.17.8 | yes | 16 | 28.3 | even | 6 | ||
168.2.u.a.89.6 | yes | 16 | 4.3 | odd | 2 | ||
168.2.u.a.89.8 | yes | 16 | 12.11 | even | 2 | ||
336.2.bc.f.17.1 | 16 | 7.3 | odd | 6 | inner | ||
336.2.bc.f.17.3 | 16 | 21.17 | even | 6 | inner | ||
336.2.bc.f.257.1 | 16 | 3.2 | odd | 2 | inner | ||
336.2.bc.f.257.3 | 16 | 1.1 | even | 1 | trivial | ||
1176.2.k.a.881.5 | 16 | 28.19 | even | 6 | |||
1176.2.k.a.881.6 | 16 | 84.23 | even | 6 | |||
1176.2.k.a.881.11 | 16 | 84.47 | odd | 6 | |||
1176.2.k.a.881.12 | 16 | 28.23 | odd | 6 | |||
1176.2.u.b.521.1 | 16 | 28.11 | odd | 6 | |||
1176.2.u.b.521.3 | 16 | 84.11 | even | 6 | |||
1176.2.u.b.1097.1 | 16 | 84.83 | odd | 2 | |||
1176.2.u.b.1097.3 | 16 | 28.27 | even | 2 | |||
2352.2.k.i.881.5 | 16 | 7.2 | even | 3 | |||
2352.2.k.i.881.6 | 16 | 21.5 | even | 6 | |||
2352.2.k.i.881.11 | 16 | 21.2 | odd | 6 | |||
2352.2.k.i.881.12 | 16 | 7.5 | odd | 6 |