Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(521,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, 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("1176.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.u (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: | \(9.39040727770\) |
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 | 1097.3 | ||
Root | \(0.247636 - 1.71426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1097 |
Dual form | 1176.2.u.b.521.3 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | \(0.362328\pi\) |
−0.995854 | + | 0.0909641i | \(0.971005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.17395 | − | 2.06735i | −0.724650 | − | 0.689117i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.43199 | + | 0.826762i | −0.431763 | + | 0.249278i | −0.700097 | − | 0.714048i | \(-0.746860\pi\) |
0.268335 | + | 0.963326i | \(0.413527\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.71177i | 1.58416i | 0.610418 | + | 0.792080i | \(0.291002\pi\) | ||||
−0.610418 | + | 0.792080i | \(0.708998\pi\) | |||||||
\(14\) | 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 | 0.172619 | − | 0.984989i | \(-0.444777\pi\) |
−0.766716 | + | 0.641987i | \(0.778110\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.249340 | − | 0.143957i | −0.0519910 | − | 0.0300170i | 0.473779 | − | 0.880644i | \(-0.342889\pi\) |
−0.525770 | + | 0.850627i | \(0.676223\pi\) | |||||||
\(24\) | 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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 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 | \(-0.608638\pi\) | ||||
−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 | ||||||||
\(45\) | 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 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 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 | 0.441954 | − | 0.897038i | \(-0.354285\pi\) |
−0.555880 | + | 0.831262i | \(0.687619\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | \(-0.620174\pi\) | ||
0.368631 | − | 0.929576i | \(-0.379826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.30170 | − | 1.90624i | 0.386434 | − | 0.223108i | −0.294180 | − | 0.955750i | \(-0.595046\pi\) |
0.680614 | + | 0.732642i | \(0.261713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.83154 | − | 0.409034i | 0.326958 | − | 0.0472312i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | ||||||||
\(81\) | 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 | \(0.446044\pi\) |
−0.937962 | + | 0.346738i | \(0.887289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 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 | \(-0.927672\pi\) | ||
0.974295 | − | 0.225274i | \(-0.0723278\pi\) | |||||||
\(98\) | 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 | 0.814617 | − | 0.579999i | \(-0.196947\pi\) |
−0.0949855 | + | 0.995479i | \(0.530280\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.6334 | − | 7.29389i | −1.22132 | − | 0.705127i | −0.256118 | − | 0.966646i | \(-0.582444\pi\) |
−0.965199 | + | 0.261518i | \(0.915777\pi\) | |||||||
\(108\) | 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 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 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 | \(-0.764532\pi\) | ||||
−0.738641 | + | 0.674099i | \(0.764532\pi\) | |||||||
\(128\) | 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 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | \(0.00729044\pi\) |
−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 | −0.778481 | − | 0.627668i | \(-0.784010\pi\) |
0.154335 | + | 0.988019i | \(0.450676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.92516 | − | 13.3269i | −0.152675 | − | 1.05690i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | ||||||||
\(165\) | 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 | −0.688657 | − | 0.725087i | \(-0.741799\pi\) |
0.972272 | + | 0.233851i | \(0.0751328\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.7863 | − | 2.42490i | 1.26174 | − | 0.182266i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.61465 | − | 1.50957i | 0.195428 | − | 0.112830i | −0.399093 | − | 0.916910i | \(-0.630675\pi\) |
0.594521 | + | 0.804080i | \(0.297342\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.762552i | 0.0566801i | 0.999598 | + | 0.0283400i | \(0.00902212\pi\) | ||||
−0.999598 | + | 0.0283400i | \(0.990978\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.05844 | + | 0.611089i | 0.0765859 | + | 0.0442169i | 0.537804 | − | 0.843070i | \(-0.319254\pi\) |
−0.461218 | + | 0.887287i | \(0.652587\pi\) | |||||||
\(192\) | 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 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 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 | \(-0.728214\pi\) | ||||
−0.657093 | + | 0.753809i | \(0.728214\pi\) | |||||||
\(212\) | 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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 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 | −0.0843986 | − | 0.996432i | \(-0.526897\pi\) |
−0.905135 | + | 0.425125i | \(0.860230\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | \(0.0588071\pi\) | ||||
−0.982983 | + | 0.183699i | \(0.941193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.1604 | + | 11.6396i | −1.29864 | + | 0.749773i | −0.980170 | − | 0.198158i | \(-0.936504\pi\) |
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7480 | − | 5.04952i | −0.946082 | − | 0.323927i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | −0.555419 | − | 0.831571i | \(-0.687442\pi\) |
0.997871 | + | 0.0652214i | \(0.0207753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.25577 | − | 4.47521i | 0.263425 | − | 0.277009i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.90698 | + | 1.10100i | −0.117590 | + | 0.0678904i | −0.557641 | − | 0.830082i | \(-0.688293\pi\) |
0.440052 | + | 0.897973i | \(0.354960\pi\) | |||||||
\(264\) | 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 | −0.144217 | − | 0.989546i | \(-0.546066\pi\) |
−0.929081 | + | 0.369877i | \(0.879400\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | 0 | ||||||||
\(288\) | 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 | \(-0.553751\pi\) | ||||
−0.168062 | + | 0.985776i | \(0.553751\pi\) | |||||||
\(294\) | 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 | 0 | ||||||||
\(302\) | 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 | 0.918012 | − | 0.396552i | \(-0.129793\pi\) |
0.115582 | + | 0.993298i | \(0.463127\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 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 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(333\) | 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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.183884 | + | 1.27293i | 0.00989996 | + | 0.0685325i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.5977 | − | 6.69596i | 0.622599 | − | 0.359458i | −0.155281 | − | 0.987870i | \(-0.549628\pi\) |
0.777880 | + | 0.628412i | \(0.216295\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 13.4025i | − | 0.717421i | −0.933449 | − | 0.358710i | \(-0.883217\pi\) | ||
0.933449 | − | 0.358710i | \(-0.116783\pi\) | |||||||
\(350\) | 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 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.4173 | + | 14.0974i | 1.28870 | + | 0.744030i | 0.978422 | − | 0.206616i | \(-0.0662452\pi\) |
0.310276 | + | 0.950647i | \(0.399579\pi\) | |||||||
\(360\) | 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 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | \(-0.319973\pi\) | ||||
0.535897 | + | 0.844283i | \(0.319973\pi\) | |||||||
\(380\) | 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 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | 0.544285 | − | 0.838901i | \(-0.316801\pi\) |
−0.454367 | + | 0.890815i | \(0.650134\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 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 | −0.998379 | − | 0.0569122i | \(-0.981874\pi\) |
−0.449902 | + | 0.893078i | \(0.648541\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.46394 | − | 17.0566i | −0.121537 | − | 0.841342i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 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 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.1904 | − | 2.33881i | 0.781679 | − | 0.112919i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.9148 | + | 8.61109i | −0.718423 | + | 0.414782i | −0.814172 | − | 0.580624i | \(-0.802809\pi\) |
0.0957491 | + | 0.995405i | \(0.469475\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.55093i | − | 0.0745329i | −0.999305 | − | 0.0372664i | \(-0.988135\pi\) | ||
0.999305 | − | 0.0372664i | \(-0.0118650\pi\) | |||||||
\(434\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.08964 | − | 1.78380i | −0.146793 | − | 0.0847510i | 0.424805 | − | 0.905285i | \(-0.360343\pi\) |
−0.571598 | + | 0.820534i | \(0.693676\pi\) | |||||||
\(444\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | \(-0.430368\pi\) | ||||
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 | ||||||||
\(465\) | −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 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 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 | 0 | ||||||||
\(484\) | 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 | \(-0.737114\pi\) | ||
0.677910 | − | 0.735145i | \(-0.262886\pi\) | |||||||
\(492\) | 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 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 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 | ||||||||
\(501\) | 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 | −0.851691 | − | 0.524044i | \(-0.824423\pi\) |
0.879681 | + | 0.475564i | \(0.157756\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 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 | \(0.0614755\pi\) |
−0.324486 | + | 0.945891i | \(0.605191\pi\) | |||||||
\(522\) | 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 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 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 | \(-0.351006\pi\) | ||||
0.451171 | + | 0.892437i | \(0.351006\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | 0.851987 | − | 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 | −0.604654 | − | 0.796488i | \(-0.706689\pi\) |
0.387452 | + | 0.921890i | \(0.373355\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −40.3148 | + | 5.82374i | −1.67543 | + | 0.242026i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 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 | −0.693232 | − | 0.720714i | \(-0.743814\pi\) |
0.970773 | + | 0.240000i | \(0.0771474\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.70432 | − | 11.7982i | −0.0697533 | − | 0.482867i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.68762 | + | 3.28375i | −0.232390 | + | 0.134170i | −0.611674 | − | 0.791110i | \(-0.709504\pi\) |
0.379284 | + | 0.925280i | \(0.376170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0499i | 0.409946i | 0.978768 | + | 0.204973i | \(0.0657106\pi\) | ||||
−0.978768 | + | 0.204973i | \(0.934289\pi\) | |||||||
\(602\) | 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 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 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 | \(-0.545841\pi\) | ||||
−0.143517 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(632\) | 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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 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 | \(0.0446788\pi\) | ||||
−0.990165 | + | 0.139902i | \(0.955321\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.2360 | − | 10.5285i | 0.709297 | − | 0.409513i | −0.101504 | − | 0.994835i | \(-0.532365\pi\) |
0.810801 | + | 0.585323i | \(0.199032\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.7303 | + | 74.2804i | 0.416730 | + | 2.88481i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | −0.913215 | − | 0.407477i | \(-0.866408\pi\) |
0.809493 | + | 0.587129i | \(0.199742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.4138 | + | 4.68238i | −1.24210 | + | 0.179429i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.9007 | + | 16.6858i | −1.10585 | + | 0.638465i | −0.937752 | − | 0.347305i | \(-0.887097\pi\) |
−0.168101 | + | 0.985770i | \(0.553764\pi\) | |||||||
\(684\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 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 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 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 | 0.291553 | − | 0.956555i | \(-0.405828\pi\) |
−0.682624 | + | 0.730770i | \(0.739161\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | \(0.210541\pi\) | ||||
−0.789113 | + | 0.614248i | \(0.789459\pi\) | |||||||
\(744\) | 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 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | ||||||||
\(753\) | 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 | −0.623950 | − | 0.781465i | \(-0.714473\pi\) |
0.988743 | + | 0.149624i | \(0.0478063\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | \(-0.954206\pi\) | ||
0.989669 | − | 0.143370i | \(-0.0457940\pi\) | |||||||
\(770\) | 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 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | \(-0.248662\pi\) | ||||
0.710074 | + | 0.704127i | \(0.248662\pi\) | |||||||
\(798\) | 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 | 0 | ||||||||
\(806\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | 0.874351 | − | 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 | \(-0.723152\pi\) | ||
0.645023 | − | 0.764163i | \(-0.276848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.57119 | − | 3.79388i | 0.228227 | − | 0.131767i | −0.381527 | − | 0.924358i | \(-0.624602\pi\) |
0.609754 | + | 0.792591i | \(0.291268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0183520 | − | 0.00265106i | 0.000636622 | − | 9.19643e-5i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 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 | \(0.00113625\pi\) | ||||
−0.999994 | + | 0.00356962i | \(0.998864\pi\) | |||||||
\(854\) | 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 | 0.162044 | − | 0.986783i | \(-0.448191\pi\) |
−0.773557 | + | 0.633726i | \(0.781525\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.8134 | + | 8.55253i | 0.504254 | + | 0.291131i | 0.730469 | − | 0.682946i | \(-0.239302\pi\) |
−0.226214 | + | 0.974078i | \(0.572635\pi\) | |||||||
\(864\) | 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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | \(-0.668968\pi\) | ||||
−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 | ||||||||
\(885\) | −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 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | \(-0.917794\pi\) | ||
0.966837 | − | 0.255396i | \(-0.0822058\pi\) | |||||||
\(912\) | 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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 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 | ||||||||
\(921\) | −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 | \(0.450015\pi\) |
−0.933563 | + | 0.358412i | \(0.883318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 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 | \(-0.769115\pi\) | ||
0.748270 | − | 0.663394i | \(-0.230885\pi\) | |||||||
\(938\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.1139 | + | 20.2730i | 1.14105 | + | 0.658785i | 0.946690 | − | 0.322145i | \(-0.104404\pi\) |
0.194359 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(948\) | 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 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 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 | \(-0.339131\pi\) | ||||
0.484145 | + | 0.874988i | \(0.339131\pi\) | |||||||
\(968\) | 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 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | −0.215565 | − | 0.976490i | \(-0.569159\pi\) |
0.737882 | + | 0.674929i | \(0.235826\pi\) | |||||||
\(998\) | 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 | 1176.2.u.b.1097.3 | 16 | ||
3.2 | odd | 2 | inner | 1176.2.u.b.1097.1 | 16 | ||
7.2 | even | 3 | 1176.2.k.a.881.5 | 16 | |||
7.3 | odd | 6 | inner | 1176.2.u.b.521.1 | 16 | ||
7.4 | even | 3 | 168.2.u.a.17.8 | yes | 16 | ||
7.5 | odd | 6 | 1176.2.k.a.881.12 | 16 | |||
7.6 | odd | 2 | 168.2.u.a.89.6 | yes | 16 | ||
21.2 | odd | 6 | 1176.2.k.a.881.11 | 16 | |||
21.5 | even | 6 | 1176.2.k.a.881.6 | 16 | |||
21.11 | odd | 6 | 168.2.u.a.17.6 | ✓ | 16 | ||
21.17 | even | 6 | inner | 1176.2.u.b.521.3 | 16 | ||
21.20 | even | 2 | 168.2.u.a.89.8 | yes | 16 | ||
28.11 | odd | 6 | 336.2.bc.f.17.1 | 16 | |||
28.19 | even | 6 | 2352.2.k.i.881.5 | 16 | |||
28.23 | odd | 6 | 2352.2.k.i.881.12 | 16 | |||
28.27 | even | 2 | 336.2.bc.f.257.3 | 16 | |||
84.11 | even | 6 | 336.2.bc.f.17.3 | 16 | |||
84.23 | even | 6 | 2352.2.k.i.881.6 | 16 | |||
84.47 | odd | 6 | 2352.2.k.i.881.11 | 16 | |||
84.83 | odd | 2 | 336.2.bc.f.257.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.6 | ✓ | 16 | 21.11 | odd | 6 | ||
168.2.u.a.17.8 | yes | 16 | 7.4 | even | 3 | ||
168.2.u.a.89.6 | yes | 16 | 7.6 | odd | 2 | ||
168.2.u.a.89.8 | yes | 16 | 21.20 | even | 2 | ||
336.2.bc.f.17.1 | 16 | 28.11 | odd | 6 | |||
336.2.bc.f.17.3 | 16 | 84.11 | even | 6 | |||
336.2.bc.f.257.1 | 16 | 84.83 | odd | 2 | |||
336.2.bc.f.257.3 | 16 | 28.27 | even | 2 | |||
1176.2.k.a.881.5 | 16 | 7.2 | even | 3 | |||
1176.2.k.a.881.6 | 16 | 21.5 | even | 6 | |||
1176.2.k.a.881.11 | 16 | 21.2 | odd | 6 | |||
1176.2.k.a.881.12 | 16 | 7.5 | odd | 6 | |||
1176.2.u.b.521.1 | 16 | 7.3 | odd | 6 | inner | ||
1176.2.u.b.521.3 | 16 | 21.17 | even | 6 | inner | ||
1176.2.u.b.1097.1 | 16 | 3.2 | odd | 2 | inner | ||
1176.2.u.b.1097.3 | 16 | 1.1 | even | 1 | trivial | ||
2352.2.k.i.881.5 | 16 | 28.19 | even | 6 | |||
2352.2.k.i.881.6 | 16 | 84.23 | even | 6 | |||
2352.2.k.i.881.11 | 16 | 84.47 | odd | 6 | |||
2352.2.k.i.881.12 | 16 | 28.23 | odd | 6 |