Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,2,Mod(17,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, 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("168.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.u (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.34148675396\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.8 | ||
Root | \(1.60841 + 0.642670i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.89 |
Dual form | 168.2.u.a.17.8 |
$q$-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 \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.71426 | + | 0.247636i | 0.989727 | + | 0.142972i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.28955 | + | 2.23357i | −0.576704 | + | 0.998881i | 0.419150 | + | 0.907917i | \(0.362328\pi\) |
−0.995854 | + | 0.0909641i | \(0.971005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.203402 | + | 2.63792i | −0.0768787 | + | 0.997040i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.87735 | + | 0.849022i | 0.959118 | + | 0.283007i | ||||
\(10\) | 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 | \(-0.794880\pi\) |
−0.120512 | − | 0.992712i | \(-0.538453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.58961 | + | 1.49511i | 0.594097 | + | 0.343002i | 0.766716 | − | 0.641987i | \(-0.221890\pi\) |
−0.172619 | + | 0.984989i | \(0.555223\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00193 | + | 4.47170i | −0.218638 | + | 0.975806i | ||||
\(22\) | 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 | \(-0.938784\pi\) | ||
0.981564 | − | 0.191133i | \(-0.0612161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.21209 | + | 3.00920i | −0.936118 | + | 0.540468i | −0.888741 | − | 0.458409i | \(-0.848420\pi\) |
−0.0473770 | + | 0.998877i | \(0.515086\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.65954 | − | 1.06267i | 0.462967 | − | 0.184987i | ||||
\(34\) | 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 | ||||||||
\(39\) | 1.41444 | − | 9.79144i | 0.226491 | − | 1.56788i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.28635 | −0.669415 | −0.334708 | − | 0.942322i | \(-0.608638\pi\) | ||||
−0.334708 | + | 0.942322i | \(0.608638\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.46537 | 0.375965 | 0.187982 | − | 0.982172i | \(-0.439805\pi\) | ||||
0.187982 | + | 0.982172i | \(0.439805\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.60684 | + | 5.33190i | −0.835818 | + | 0.794833i | ||||
\(46\) | 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 | ||||||||
\(51\) | −4.87546 | − | 12.2018i | −0.682701 | − | 1.70859i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.73264 | − | 3.88709i | 0.924799 | − | 0.533933i | 0.0396361 | − | 0.999214i | \(-0.487380\pi\) |
0.885163 | + | 0.465281i | \(0.154047\pi\) | |||||||
\(54\) | 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 | ||||||||
\(63\) | −2.82491 | + | 7.41754i | −0.355906 | + | 0.934522i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.7576 | + | 7.36561i | 1.58239 | + | 0.913592i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.18281 | − | 2.04868i | −0.144503 | − | 0.250286i | 0.784685 | − | 0.619895i | \(-0.212825\pi\) |
−0.929187 | + | 0.369609i | \(0.879492\pi\) | |||||||
\(68\) | 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 | ||||||||
\(75\) | −1.06153 | − | 2.65670i | −0.122575 | − | 0.306769i | ||||
\(76\) | 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 | \(-0.661839\pi\) |
0.999885 | − | 0.0151665i | \(-0.00482783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.55832 | + | 4.88587i | 0.839814 | + | 0.542875i | ||||
\(82\) | 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 | ||||||||
\(87\) | 0.509773 | − | 3.52890i | 0.0546534 | − | 0.378338i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.25723 | + | 12.5699i | −0.769265 | + | 1.33241i | 0.168697 | + | 0.985668i | \(0.446044\pi\) |
−0.937962 | + | 0.346738i | \(0.887289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.0672 | + | 1.16179i | 1.57947 | + | 0.121788i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.68004 | + | 3.86784i | −1.00377 | + | 0.401077i | ||||
\(94\) | 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 | 0.949371 | − | 0.314157i | \(-0.101722\pi\) |
−0.746754 | + | 0.665101i | \(0.768389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.30346 | − | 4.21666i | −0.719632 | − | 0.415479i | 0.0949855 | − | 0.995479i | \(-0.469720\pi\) |
−0.814617 | + | 0.579999i | \(0.803053\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.69581 | − | 8.00436i | −0.848625 | − | 0.781145i | ||||
\(106\) | 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 | \(-0.939753\pi\) | ||
0.982141 | − | 0.188144i | \(-0.0602472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.643073 | + | 0.371279i | −0.0599669 | + | 0.0346219i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.84942 | − | 16.4348i | 0.448329 | − | 1.51940i | ||||
\(118\) | 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 | ||||||||
\(123\) | −7.34790 | − | 1.06145i | −0.662538 | − | 0.0957079i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.63545 | −0.772378 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.6481 | −1.47728 | −0.738641 | − | 0.674099i | \(-0.764532\pi\) | ||||
−0.738641 | + | 0.674099i | \(0.764532\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.22627 | + | 0.610512i | 0.372102 | + | 0.0537526i | ||||
\(130\) | 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 | ||||||||
\(135\) | −10.9319 | + | 7.75180i | −0.940871 | + | 0.667169i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.61684 | − | 4.97493i | 0.736186 | − | 0.425037i | −0.0844948 | − | 0.996424i | \(-0.526928\pi\) |
0.820681 | + | 0.571387i | \(0.193594\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.11952i | 0.264594i | 0.991210 | + | 0.132297i | \(0.0422353\pi\) | ||||
−0.991210 | + | 0.132297i | \(0.957765\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −11.5922 | − | 3.55256i | −0.956109 | − | 0.293010i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.987090 | − | 0.569897i | −0.0808655 | − | 0.0466877i | 0.459022 | − | 0.888425i | \(-0.348200\pi\) |
−0.539888 | + | 0.841737i | \(0.681533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.38621 | + | 11.0612i | 0.519702 | + | 0.900151i | 0.999738 | + | 0.0229016i | \(0.00729044\pi\) |
−0.480036 | + | 0.877249i | \(0.659376\pi\) | |||||||
\(152\) | 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 | ||||||||
\(159\) | 12.5041 | − | 4.99623i | 0.991636 | − | 0.396227i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.430463 | + | 0.628459i | −0.0339252 | + | 0.0495295i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0498774 | + | 0.0863903i | −0.00390670 | + | 0.00676661i | −0.867972 | − | 0.496613i | \(-0.834577\pi\) |
0.864065 | + | 0.503379i | \(0.167910\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.05607 | + | 7.31063i | −0.0822148 | + | 0.569132i | ||||
\(166\) | 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 | ||||||||
\(171\) | 6.18184 | + | 6.50060i | 0.472737 | + | 0.497113i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.73038 | − | 6.46120i | 0.283615 | − | 0.491236i | −0.688657 | − | 0.725087i | \(-0.741799\pi\) |
0.972272 | + | 0.233851i | \(0.0751328\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.94144 | − | 1.88764i | 0.297945 | − | 0.142693i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.29315 | − | 15.7498i | −0.473022 | − | 1.18383i | ||||
\(178\) | 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 | ||||||||
\(189\) | −6.67947 | + | 12.0160i | −0.485860 | + | 0.874037i | ||||
\(190\) | 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 | \(-0.824148\pi\) | ||
0.851239 | − | 0.524778i | \(-0.175852\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.96032 | − | 3.44119i | 0.422516 | − | 0.243940i | −0.273637 | − | 0.961833i | \(-0.588227\pi\) |
0.696153 | + | 0.717893i | \(0.254893\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.52031 | − | 3.80487i | −0.107234 | − | 0.268375i | ||||
\(202\) | 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 | ||||||||
\(207\) | 0.595218 | + | 0.625909i | 0.0413705 | + | 0.0435037i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.94441 | 0.342012 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.0897 | −1.31419 | −0.657093 | − | 0.753809i | \(-0.728214\pi\) | ||||
−0.657093 | + | 0.753809i | \(0.728214\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.87933 | + | 26.8547i | −0.265807 | + | 1.84005i | ||||
\(214\) | 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 | ||||||||
\(219\) | −6.13201 | + | 2.45016i | −0.414363 | + | 0.165566i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37.5257 | + | 21.6655i | −2.52425 | + | 1.45738i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.9876i | − | 0.735785i | −0.929868 | − | 0.367892i | \(-0.880079\pi\) | ||
0.929868 | − | 0.367892i | \(-0.119921\pi\) | |||||||
\(224\) | 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 | ||||||||
\(231\) | 2.26228 | + | 7.23181i | 0.148847 | + | 0.475818i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.45119 | − | 2.56990i | −0.291607 | − | 0.168360i | 0.347059 | − | 0.937843i | \(-0.387180\pi\) |
−0.638666 | + | 0.769484i | \(0.720514\pi\) | |||||||
\(234\) | 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 | ||||||||
\(243\) | 11.7470 | + | 10.2473i | 0.753570 | + | 0.657368i | ||||
\(244\) | 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 | ||||||||
\(249\) | 11.4026 | + | 1.64719i | 0.722613 | + | 0.104386i | ||||
\(250\) | 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 | ||||||||
\(255\) | 33.5407 | + | 4.84517i | 2.10040 | + | 0.303416i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.09305 | − | 12.2855i | 0.442452 | − | 0.766349i | −0.555419 | − | 0.831571i | \(-0.687442\pi\) |
0.997871 | + | 0.0652214i | \(0.0207753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.83092 | − | 2.62399i | −0.238042 | − | 0.163047i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.74776 | − | 5.92321i | 0.108184 | − | 0.366638i | ||||
\(262\) | 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 | 0.998195 | − | 0.0600579i | \(-0.0191285\pi\) |
−0.551109 | + | 0.834433i | \(0.685795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.6687 | + | 10.2010i | 1.07330 | + | 0.619669i | 0.929081 | − | 0.369877i | \(-0.120600\pi\) |
0.144217 | + | 0.989546i | \(0.453934\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.5413 | + | 5.72277i | 1.54583 | + | 0.346358i | ||||
\(274\) | 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 | \(0.0778406\pi\) | ||||
−0.970248 | + | 0.242114i | \(0.922159\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.34466 | + | 1.93104i | −0.198819 | + | 0.114788i | −0.596105 | − | 0.802907i | \(-0.703286\pi\) |
0.397285 | + | 0.917695i | \(0.369952\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.4042 | + | 4.95632i | −0.734760 | + | 0.293587i | ||||
\(286\) | 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 | ||||||||
\(291\) | −1.09885 | + | 7.60682i | −0.0644160 | + | 0.445920i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.75351 | −0.336123 | −0.168062 | − | 0.985776i | \(-0.553751\pi\) | ||||
−0.168062 | + | 0.985776i | \(0.553751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.2550 | 1.47041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.55467 | − | 0.799668i | 0.496392 | − | 0.0464015i | ||||
\(298\) | 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 | ||||||||
\(303\) | 2.61731 | + | 6.55033i | 0.150360 | + | 0.376307i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.29487 | + | 1.32494i | −0.131404 | + | 0.0758660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.9041i | − | 1.36428i | −0.731221 | − | 0.682140i | \(-0.761049\pi\) | ||
0.731221 | − | 0.682140i | \(-0.238951\pi\) | |||||||
\(308\) | 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 | ||||||||
\(315\) | −12.9247 | − | 15.8749i | −0.728224 | − | 0.894450i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.8698 | + | 8.00775i | 0.779007 | + | 0.449760i | 0.836078 | − | 0.548610i | \(-0.184843\pi\) |
−0.0570712 | + | 0.998370i | \(0.518176\pi\) | |||||||
\(318\) | 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 | ||||||||
\(327\) | −11.1181 | − | 27.8253i | −0.614833 | − | 1.53874i | ||||
\(328\) | 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 | \(0.341335\pi\) |
−0.999684 | + | 0.0251350i | \(0.991998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.81538 | + | 3.62829i | −0.209082 | + | 0.198829i | ||||
\(334\) | 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 | ||||||||
\(339\) | 0.990542 | − | 6.85703i | 0.0537989 | − | 0.372423i | ||||
\(340\) | 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 | ||||||||
\(345\) | −1.19433 | + | 0.477219i | −0.0643008 | + | 0.0256926i | ||||
\(346\) | 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 | \(-0.972835\pi\) |
0.424363 | − | 0.905492i | \(-0.360498\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.9899 | − | 20.2014i | −1.85707 | − | 1.07218i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 33.1791 | − | 10.3792i | 1.75602 | − | 0.549326i | ||||
\(358\) | 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 | −0.916221 | − | 0.400673i | \(-0.868776\pi\) |
−0.111118 | + | 0.993807i | \(0.535443\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.3333 | − | 3.63920i | −0.642048 | − | 0.189449i | ||||
\(370\) | 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 | ||||||||
\(375\) | −14.8034 | − | 2.13845i | −0.764443 | − | 0.110429i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.7580 | −0.605569 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.8656 | 1.07179 | 0.535897 | − | 0.844283i | \(-0.319973\pi\) | ||||
0.535897 | + | 0.844283i | \(0.319973\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.5392 | − | 4.12267i | −1.46211 | − | 0.211211i | ||||
\(382\) | 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 | ||||||||
\(387\) | 7.09373 | + | 2.09315i | 0.360595 | + | 0.106401i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 20.4245 | − | 11.7921i | 1.03556 | − | 0.597882i | 0.116989 | − | 0.993133i | \(-0.462676\pi\) |
0.918573 | + | 0.395251i | \(0.129342\pi\) | |||||||
\(390\) | 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 | ||||||||
\(399\) | −9.28030 | + | 10.0820i | −0.464596 | + | 0.504730i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.46052 | + | 3.72998i | 0.322623 | + | 0.186266i | 0.652561 | − | 0.757736i | \(-0.273695\pi\) |
−0.329938 | + | 0.944003i | \(0.607028\pi\) | |||||||
\(402\) | 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 | ||||||||
\(411\) | 16.0034 | − | 6.39448i | 0.789392 | − | 0.315416i | ||||
\(412\) | 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 | ||||||||
\(417\) | −0.772504 | + | 5.34766i | −0.0378297 | + | 0.261876i | ||||
\(418\) | 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 | ||||||||
\(423\) | 0.811257 | − | 0.771476i | 0.0394447 | − | 0.0375105i | ||||
\(424\) | 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 | ||||||||
\(429\) | −6.06973 | − | 15.1907i | −0.293049 | − | 0.733413i | ||||
\(430\) | 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 | 0.844570 | − | 0.535446i | \(-0.179856\pi\) |
−0.0414249 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.9923 | − | 8.96064i | −0.904395 | − | 0.426697i | ||||
\(442\) | 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 | \(0.245915\pi\) | ||||
−0.716124 | + | 0.697973i | \(0.754085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.13803 | + | 3.54379i | −0.289028 | + | 0.166871i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.20844 | + | 20.5433i | 0.385666 | + | 0.965206i | ||||
\(454\) | 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 | ||||||||
\(459\) | −3.66883 | − | 39.2483i | −0.171246 | − | 1.83195i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.31904 | 0.434031 | 0.217015 | − | 0.976168i | \(-0.430368\pi\) | ||||
0.217015 | + | 0.976168i | \(0.430368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.6243 | −0.772597 | −0.386298 | − | 0.922374i | \(-0.626246\pi\) | ||||
−0.386298 | + | 0.922374i | \(0.626246\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.84381 | − | 26.6088i | 0.178253 | − | 1.23395i | ||||
\(466\) | 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 | ||||||||
\(471\) | 14.5245 | − | 5.80354i | 0.669254 | − | 0.267413i | ||||
\(472\) | 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 | ||||||||
\(483\) | −0.893552 | + | 0.970742i | −0.0406580 | + | 0.0441703i | ||||
\(484\) | 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 | \(0.127161\pi\) |
−0.123791 | + | 0.992308i | \(0.539505\pi\) | |||||||
\(488\) | 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 | ||||||||
\(495\) | −3.62074 | + | 12.2708i | −0.162740 | + | 0.551530i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −41.3243 | − | 3.18639i | −1.85365 | − | 0.142929i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.46895 | + | 4.27635i | −0.110525 | + | 0.191436i | −0.915982 | − | 0.401219i | \(-0.868587\pi\) |
0.805457 | + | 0.592655i | \(0.201920\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.29041 | − | 0.764234i | −0.236358 | − | 0.0341434i | ||||
\(502\) | 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 | ||||||||
\(507\) | −33.6411 | − | 4.85967i | −1.49405 | − | 0.215826i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.631490 | − | 1.09377i | 0.0279903 | − | 0.0484806i | −0.851691 | − | 0.524044i | \(-0.824423\pi\) |
0.879681 | + | 0.475564i | \(0.157756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.35693 | − | 9.09735i | −0.192739 | − | 0.402443i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.98748 | + | 12.6745i | 0.396807 | + | 0.559595i | ||||
\(514\) | 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 | \(0.0614755\pi\) |
−0.324486 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.7587 | + | 17.7586i | 1.34499 | + | 0.776528i | 0.987534 | − | 0.157404i | \(-0.0503125\pi\) |
0.357451 | + | 0.933932i | \(0.383646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7.22408 | − | 2.25987i | 0.315285 | − | 0.0986287i | ||||
\(526\) | 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 | ||||||||
\(537\) | −4.85600 | + | 1.94031i | −0.209552 | + | 0.0837304i | ||||
\(538\) | 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 | ||||||||
\(543\) | 0.188835 | − | 1.30721i | 0.00810369 | − | 0.0560978i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 44.6181 | 1.91123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.1040 | 0.902342 | 0.451171 | − | 0.892437i | \(-0.351006\pi\) | ||||
0.451171 | + | 0.892437i | \(0.351006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.12409 | + | 2.23362i | 0.0906539 | + | 0.0953284i | ||||
\(550\) | 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 | ||||||||
\(555\) | −2.90901 | − | 7.28036i | −0.123480 | − | 0.309034i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.3020 | + | 11.1440i | −0.817852 | + | 0.472187i | −0.849675 | − | 0.527307i | \(-0.823202\pi\) |
0.0318235 | + | 0.999494i | \(0.489869\pi\) | |||||||
\(558\) | 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 | ||||||||
\(567\) | −14.4259 | + | 18.9445i | −0.605832 | + | 0.795593i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7717 | − | 12.5699i | −0.912717 | − | 0.526957i | −0.0314127 | − | 0.999506i | \(-0.510001\pi\) |
−0.881304 | + | 0.472549i | \(0.843334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.655344 | − | 1.13509i | −0.0274253 | − | 0.0475020i | 0.851987 | − | 0.523563i | \(-0.175398\pi\) |
−0.879412 | + | 0.476061i | \(0.842064\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | 15.1139 | + | 37.8255i | 0.628112 | + | 1.57197i | ||||
\(580\) | 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 | ||||||||
\(585\) | 30.4546 | + | 32.0250i | 1.25914 | + | 1.32407i | ||||
\(586\) | 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 | ||||||||
\(591\) | 3.64797 | − | 25.2531i | 0.150058 | − | 1.03877i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.75855 | − | 11.7062i | 0.277540 | − | 0.480714i | −0.693232 | − | 0.720714i | \(-0.743814\pi\) |
0.970773 | + | 0.240000i | \(0.0771474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.97971 | + | 51.6129i | −0.163152 | + | 2.11592i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.0697 | − | 4.42310i | 0.453052 | − | 0.181025i | ||||
\(598\) | 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 | 0.486261 | − | 0.873814i | \(-0.338360\pi\) |
−0.513614 | + | 0.858021i | \(0.671694\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.20528 | + | 2.06253i | 0.373017 | + | 0.0835778i | ||||
\(610\) | 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 | \(0.0504134\pi\) | ||||
−0.987484 | + | 0.157717i | \(0.949587\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.9235 | − | 10.3481i | 0.720407 | − | 0.415927i | −0.0944957 | − | 0.995525i | \(-0.530124\pi\) |
0.814902 | + | 0.579598i | \(0.196791\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.865358 | + | 1.22037i | 0.0347256 | + | 0.0489716i | ||||
\(622\) | 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 | ||||||||
\(627\) | 8.47599 | + | 1.22441i | 0.338498 | + | 0.0488983i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.3142 | 0.530874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.21022 | −0.287034 | −0.143517 | − | 0.989648i | \(-0.545841\pi\) | ||||
−0.143517 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.7246 | − | 4.72728i | −1.30069 | − | 0.187892i | ||||
\(634\) | 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 | ||||||||
\(639\) | −13.3003 | + | 45.0751i | −0.526153 | + | 1.78315i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.9156 | − | 18.4265i | 1.26059 | − | 0.727802i | 0.287401 | − | 0.957810i | \(-0.407209\pi\) |
0.973189 | + | 0.230009i | \(0.0738755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.5183i | − | 0.414801i | −0.978256 | − | 0.207400i | \(-0.933500\pi\) | ||
0.978256 | − | 0.207400i | \(-0.0665003\pi\) | |||||||
\(644\) | 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 | ||||||||
\(651\) | −8.23413 | − | 26.3219i | −0.322721 | − | 1.03164i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.7382 | − | 16.5920i | −1.12461 | − | 0.649295i | −0.182038 | − | 0.983291i | \(-0.558269\pi\) |
−0.942574 | + | 0.333996i | \(0.891603\pi\) | |||||||
\(654\) | 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 | ||||||||
\(663\) | −69.6939 | + | 27.8475i | −2.70669 | + | 1.08151i | ||||
\(664\) | 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 | ||||||||
\(669\) | 2.72092 | − | 18.8356i | 0.105197 | − | 0.728226i | ||||
\(670\) | 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 | ||||||||
\(675\) | −0.798814 | − | 8.54553i | −0.0307464 | − | 0.328918i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.69876 | + | 4.67439i | −0.103722 | + | 0.179651i | −0.913215 | − | 0.407477i | \(-0.866408\pi\) |
0.809493 | + | 0.587129i | \(0.199742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.7055 | − | 0.902573i | −0.449215 | − | 0.0346376i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.1518 | + | 30.4124i | 0.465659 | + | 1.16540i | ||||
\(682\) | 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 | −0.328975 | − | 0.944339i | \(-0.606703\pi\) |
−0.982309 | + | 0.187268i | \(0.940037\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.08728 | + | 12.9574i | 0.0792893 | + | 0.492211i | ||||
\(694\) | 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 | \(-0.935490\pi\) | ||
0.979534 | − | 0.201280i | \(-0.0645100\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.54488 | + | 2.62399i | −0.171414 | + | 0.0989657i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.618535 | + | 1.54801i | 0.0232954 | + | 0.0583013i | ||||
\(706\) | 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 | ||||||||
\(711\) | 19.8279 | − | 18.8556i | 0.743603 | − | 0.707140i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.73278 | −0.0648930 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.3584 | 0.910954 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.40653 | − | 9.73669i | 0.0525278 | − | 0.363623i | ||||
\(718\) | 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 | ||||||||
\(723\) | 37.4425 | − | 14.9608i | 1.39250 | − | 0.556400i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.94470 | + | 1.70012i | −0.109363 | + | 0.0631410i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.7975i | 1.47601i | 0.674797 | + | 0.738003i | \(0.264231\pi\) | ||||
−0.674797 | + | 0.738003i | \(0.735769\pi\) | |||||||
\(728\) | 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 | ||||||||
\(735\) | 22.8836 | − | 21.3108i | 0.844075 | − | 0.786060i | ||||
\(736\) | 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 | \(-0.987583\pi\) |
0.465846 | − | 0.884866i | \(-0.345750\pi\) | |||||||
\(740\) | 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 | ||||||||
\(747\) | 19.1392 | + | 5.64740i | 0.700265 | + | 0.206628i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.8104 | + | 31.8423i | −0.796934 | + | 1.16349i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.86021 | + | 10.1502i | −0.213842 | + | 0.370385i | −0.952914 | − | 0.303242i | \(-0.901931\pi\) |
0.739072 | + | 0.673627i | \(0.235264\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −36.6507 | − | 5.29443i | −1.33562 | − | 0.192940i | ||||
\(754\) | 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 | ||||||||
\(759\) | 0.816109 | + | 0.117892i | 0.0296229 | + | 0.00427922i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0633 | − | 17.4301i | 0.364793 | − | 0.631841i | −0.623950 | − | 0.781465i | \(-0.714473\pi\) |
0.988743 | + | 0.149624i | \(0.0478063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 41.2811 | − | 19.7705i | 1.49448 | − | 0.715739i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56.2975 | + | 16.6117i | 2.03544 | + | 0.600599i | ||||
\(766\) | 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 | \(0.0270182\pi\) |
−0.424780 | + | 0.905297i | \(0.639648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.60911 | + | 4.97047i | 0.309248 | + | 0.178545i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.91739 | − | 5.44687i | −0.212285 | − | 0.195405i | ||||
\(778\) | 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 | 0.0497122 | − | 0.998764i | \(-0.484170\pi\) |
0.889811 | + | 0.456330i | \(0.150836\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.54171 | − | 1.41516i | 0.126088 | − | 0.0503809i | ||||
\(790\) | 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 | ||||||||
\(795\) | −4.96519 | + | 34.3715i | −0.176097 | + | 1.21903i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.0924 | 1.42015 | 0.710074 | − | 0.704127i | \(-0.248662\pi\) | ||||
0.710074 | + | 0.704127i | \(0.248662\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.83098 | −0.100153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.5537 | + | 30.0065i | −1.11490 | + | 1.06023i | ||||
\(802\) | 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 | ||||||||
\(807\) | 9.42508 | + | 23.5881i | 0.331778 | + | 0.830341i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.0306 | − | 19.6476i | 1.19645 | − | 0.690773i | 0.236691 | − | 0.971585i | \(-0.423937\pi\) |
0.959763 | + | 0.280812i | \(0.0906039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.6789i | − | 0.831480i | −0.909484 | − | 0.415740i | \(-0.863523\pi\) | ||
0.909484 | − | 0.415740i | \(-0.136477\pi\) | |||||||
\(812\) | 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 | ||||||||
\(819\) | 42.3673 | + | 16.1352i | 1.48043 | + | 0.563811i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.4772 | − | 21.6374i | −1.30796 | − | 0.755152i | −0.326206 | − | 0.945299i | \(-0.605770\pi\) |
−0.981756 | + | 0.190146i | \(0.939104\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.484756 | + | 0.839623i | 0.0168975 | + | 0.0292674i | 0.874351 | − | 0.485295i | \(-0.161288\pi\) |
−0.857453 | + | 0.514562i | \(0.827954\pi\) | |||||||
\(824\) | 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 | ||||||||
\(831\) | −0.00688009 | − | 0.0172188i | −0.000238668 | − | 0.000597313i | ||||
\(832\) | 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 | ||||||||
\(837\) | −31.1368 | + | 2.91058i | −1.07624 | + | 0.100604i | ||||
\(838\) | 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 | ||||||||
\(843\) | −2.01009 | + | 13.9148i | −0.0692311 | + | 0.479252i | ||||
\(844\) | 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 | ||||||||
\(849\) | −6.21179 | + | 2.48204i | −0.213188 | + | 0.0851834i | ||||
\(850\) | 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 | \(0.00450398\pi\) |
−0.487696 | + | 0.873013i | \(0.662163\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.9227 | + | 10.3477i | 0.611513 | + | 0.353057i | 0.773557 | − | 0.633726i | \(-0.218475\pi\) |
−0.162044 | + | 0.986783i | \(0.551809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.29461 | − | 19.1673i | 0.146360 | − | 0.653219i | ||||
\(862\) | 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 | ||||||||
\(873\) | −3.76744 | + | 12.7679i | −0.127508 | + | 0.432129i | ||||
\(874\) | 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 | ||||||||
\(879\) | −9.86299 | − | 1.42477i | −0.332670 | − | 0.0480564i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0526 | −1.01250 | −0.506249 | − | 0.862387i | \(-0.668968\pi\) | ||||
−0.506249 | + | 0.862387i | \(0.668968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.8382 | −0.566649 | −0.283324 | − | 0.959024i | \(-0.591437\pi\) | ||||
−0.283324 | + | 0.959024i | \(0.591437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 43.2936 | + | 6.25405i | 1.45530 | + | 0.210228i | ||||
\(886\) | 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 | ||||||||
\(891\) | 14.8629 | + | 0.747604i | 0.497927 | + | 0.0250457i | ||||
\(892\) | 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 | ||||||||
\(903\) | −2.47012 | + | 11.0244i | −0.0822003 | + | 0.366869i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.70321 | + | 0.983349i | 0.0566166 | + | 0.0326876i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.22753 | − | 7.32230i | −0.140373 | − | 0.243133i | 0.787264 | − | 0.616616i | \(-0.211497\pi\) |
−0.927637 | + | 0.373483i | \(0.878163\pi\) | |||||||
\(908\) | 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 | ||||||||
\(915\) | −4.26210 | + | 1.70300i | −0.140901 | + | 0.0562995i | ||||
\(916\) | 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 | \(-0.434617\pi\) |
0.745838 | − | 0.666127i | \(-0.232049\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.91951 | − | 40.9778i | 0.195055 | − | 1.35026i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 89.4776 | 2.94519 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.89891 | 0.0953156 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.4346 | − | 18.3336i | −0.572628 | − | 0.602155i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.6879 | + | 41.0287i | −0.777176 | + | 1.34611i | 0.156388 | + | 0.987696i | \(0.450015\pi\) |
−0.933563 | + | 0.358412i | \(0.883318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.3086 | − | 13.1210i | −0.534492 | − | 0.430024i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.5975 | − | 34.0303i | −0.445161 | − | 1.11410i | ||||
\(934\) | 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 | 0.999874 | − | 0.0158745i | \(-0.00505322\pi\) |
−0.513685 | + | 0.857979i | \(0.671720\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.06876 | − | 0.617048i | −0.0348036 | − | 0.0200939i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.2251 | − | 30.4143i | −0.592861 | − | 0.989377i | ||||
\(946\) | 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 | \(-0.797276\pi\) | ||
0.803956 | − | 0.594688i | \(-0.202724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.72982 | − | 1.57606i | 0.0883348 | − | 0.0510001i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.18757 | − | 5.47483i | −0.0707142 | − | 0.176976i | ||||
\(958\) | 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 | ||||||||
\(963\) | 30.1581 | + | 31.7131i | 0.971830 | + | 1.02194i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −60.6536 | −1.95251 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.1106 | 0.968290 | 0.484145 | − | 0.874988i | \(-0.339131\pi\) | ||||
0.484145 | + | 0.874988i | \(0.339131\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.61752 | − | 38.8873i | 0.180461 | − | 1.24924i | ||||
\(970\) | 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 | ||||||||
\(975\) | −15.1745 | + | 6.06324i | −0.485972 | + | 0.194179i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.3918 | + | 27.9390i | −1.54819 | + | 0.893849i | −0.549912 | + | 0.835223i | \(0.685339\pi\) |
−0.998280 | + | 0.0586266i | \(0.981328\pi\) | |||||||
\(978\) | 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 | ||||||||
\(987\) | 1.25820 | + | 1.15816i | 0.0400490 | + | 0.0368645i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.614715 | + | 0.354906i | 0.0195468 | + | 0.0112853i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.7736 | + | 20.3924i | 0.374000 | + | 0.647787i | 0.990177 | − | 0.139821i | \(-0.0446528\pi\) |
−0.616177 | + | 0.787608i | \(0.711319\pi\) | |||||||
\(992\) | 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 | ||||||||
\(999\) | −7.43904 | + | 5.27500i | −0.235361 | + | 0.166894i |
(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 | 168.2.u.a.89.8 | yes | 16 | |
3.2 | odd | 2 | inner | 168.2.u.a.89.6 | yes | 16 | |
4.3 | odd | 2 | 336.2.bc.f.257.1 | 16 | |||
7.2 | even | 3 | 1176.2.k.a.881.6 | 16 | |||
7.3 | odd | 6 | inner | 168.2.u.a.17.6 | ✓ | 16 | |
7.4 | even | 3 | 1176.2.u.b.521.3 | 16 | |||
7.5 | odd | 6 | 1176.2.k.a.881.11 | 16 | |||
7.6 | odd | 2 | 1176.2.u.b.1097.1 | 16 | |||
12.11 | even | 2 | 336.2.bc.f.257.3 | 16 | |||
21.2 | odd | 6 | 1176.2.k.a.881.12 | 16 | |||
21.5 | even | 6 | 1176.2.k.a.881.5 | 16 | |||
21.11 | odd | 6 | 1176.2.u.b.521.1 | 16 | |||
21.17 | even | 6 | inner | 168.2.u.a.17.8 | yes | 16 | |
21.20 | even | 2 | 1176.2.u.b.1097.3 | 16 | |||
28.3 | even | 6 | 336.2.bc.f.17.3 | 16 | |||
28.19 | even | 6 | 2352.2.k.i.881.6 | 16 | |||
28.23 | odd | 6 | 2352.2.k.i.881.11 | 16 | |||
84.23 | even | 6 | 2352.2.k.i.881.5 | 16 | |||
84.47 | odd | 6 | 2352.2.k.i.881.12 | 16 | |||
84.59 | odd | 6 | 336.2.bc.f.17.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.6 | ✓ | 16 | 7.3 | odd | 6 | inner | |
168.2.u.a.17.8 | yes | 16 | 21.17 | even | 6 | inner | |
168.2.u.a.89.6 | yes | 16 | 3.2 | odd | 2 | inner | |
168.2.u.a.89.8 | yes | 16 | 1.1 | even | 1 | trivial | |
336.2.bc.f.17.1 | 16 | 84.59 | odd | 6 | |||
336.2.bc.f.17.3 | 16 | 28.3 | even | 6 | |||
336.2.bc.f.257.1 | 16 | 4.3 | odd | 2 | |||
336.2.bc.f.257.3 | 16 | 12.11 | even | 2 | |||
1176.2.k.a.881.5 | 16 | 21.5 | even | 6 | |||
1176.2.k.a.881.6 | 16 | 7.2 | even | 3 | |||
1176.2.k.a.881.11 | 16 | 7.5 | odd | 6 | |||
1176.2.k.a.881.12 | 16 | 21.2 | odd | 6 | |||
1176.2.u.b.521.1 | 16 | 21.11 | odd | 6 | |||
1176.2.u.b.521.3 | 16 | 7.4 | even | 3 | |||
1176.2.u.b.1097.1 | 16 | 7.6 | odd | 2 | |||
1176.2.u.b.1097.3 | 16 | 21.20 | even | 2 | |||
2352.2.k.i.881.5 | 16 | 84.23 | even | 6 | |||
2352.2.k.i.881.6 | 16 | 28.19 | even | 6 | |||
2352.2.k.i.881.11 | 16 | 28.23 | odd | 6 | |||
2352.2.k.i.881.12 | 16 | 84.47 | odd | 6 |