LMFDB - Embedded newform 414.2.j.a.17.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(17,414)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("414.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.j (of order $22$, degree $10$, 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:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	414.17
Dual form			414.2.j.a.341.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.08613 + 1.34067i) q^{5} +(2.86484 + 0.411901i) q^{7} +(0.281733 + 0.959493i) q^{8} +O(q^{10})$	\(q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.08613 + 1.34067i) q^{5} +(2.86484 + 0.411901i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-2.45454 + 0.352910i) q^{10} +(0.472602 + 1.03485i) q^{11} +(0.455270 + 3.16647i) q^{13} +(2.43484 + 1.56478i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-0.522787 + 0.603329i) q^{17} +(-0.243530 + 0.211020i) q^{19} +(-2.37933 - 0.698636i) q^{20} +1.13766i q^{22} +(2.48164 + 4.10384i) q^{23} +(0.477447 - 1.04546i) q^{25} +(-0.901271 + 3.06945i) q^{26} +(1.56478 + 2.43484i) q^{28} +(-5.18491 - 4.49275i) q^{29} +(4.09548 - 1.20254i) q^{31} +(-0.540641 + 0.841254i) q^{32} +(-0.726176 + 0.331633i) q^{34} +(-6.52864 + 2.98153i) q^{35} +(3.65447 - 5.68646i) q^{37} +(-0.309183 + 0.0907844i) q^{38} +(-1.87410 - 1.62391i) q^{40} +(3.17706 + 4.94360i) q^{41} +(2.80415 - 9.55005i) q^{43} +(-0.472602 + 1.03485i) q^{44} +(0.552579 + 4.76389i) q^{46} -5.22795i q^{47} +(1.32118 + 0.387933i) q^{49} +(0.868602 - 0.752648i) q^{50} +(-2.09492 + 2.41767i) q^{52} +(1.85223 - 12.8826i) q^{53} +(-2.37330 - 1.52523i) q^{55} +(0.411901 + 2.86484i) q^{56} +(-2.85000 - 6.24064i) q^{58} +(1.01042 - 0.145277i) q^{59} +(-1.27559 - 4.34427i) q^{61} +(4.22493 + 0.607454i) q^{62} +(-0.841254 + 0.540641i) q^{64} +(-5.19495 - 5.99529i) q^{65} +(-11.3241 - 5.17154i) q^{67} -0.798318 q^{68} -7.17723 q^{70} +(-0.297921 - 0.136056i) q^{71} +(10.8435 + 12.5140i) q^{73} +(5.68646 - 3.65447i) q^{74} +(-0.318956 - 0.0458590i) q^{76} +(0.927669 + 3.15935i) q^{77} +(-9.78336 + 1.40663i) q^{79} +(-1.03014 - 2.25569i) q^{80} +(0.836309 + 5.81665i) q^{82} +(5.29943 + 3.40574i) q^{83} +(0.281735 - 1.95951i) q^{85} +(6.51798 - 7.52215i) q^{86} +(-0.859787 + 0.745010i) q^{88} +(2.45350 + 0.720413i) q^{89} +9.25895i q^{91} +(-1.47635 + 4.56294i) q^{92} +(2.17177 - 4.75551i) q^{94} +(0.225126 - 0.766707i) q^{95} +(1.82885 + 2.84575i) q^{97} +(1.04063 + 0.901714i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 8 q^{4}+O(q^{10}) $ 80 * q + 8 * q^4	$ 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) $ 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (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 $

$2$	0.909632	+	0.415415i	0.643207	+	0.293743i
$2$	0.909632	+	0.415415i	0.643207	+	0.293743i
$3$		0			0
$3$		0			0
$4$	0.654861	+	0.755750i	0.327430	+	0.377875i
$5$	−2.08613	+	1.34067i	−0.932944	+	0.599567i	−0.916386	−	0.400296i	$-0.868907\pi$
$5$	−2.08613	+	1.34067i	−0.932944	+	0.599567i	−0.0165583	+	0.999863i	$0.505271\pi$
$6$		0			0
$7$	2.86484	+	0.411901i	1.08281	+	0.155684i	0.660542	−	0.750789i	$-0.270326\pi$
$7$	2.86484	+	0.411901i	1.08281	+	0.155684i	0.422264	+	0.906473i	$0.361235\pi$
$8$	0.281733	+	0.959493i	0.0996075	+	0.339232i
$9$		0			0
$10$	−2.45454	+	0.352910i	−0.776195	+	0.111600i
$11$	0.472602	+	1.03485i	0.142495	+	0.312020i	0.967401	−	0.253250i	$-0.0814994\pi$
$11$	0.472602	+	1.03485i	0.142495	+	0.312020i	−0.824906	+	0.565270i	$0.808772\pi$
$12$		0			0
$13$	0.455270	+	3.16647i	0.126269	+	0.878221i	0.950225	+	0.311566i	$0.100854\pi$
$13$	0.455270	+	3.16647i	0.126269	+	0.878221i	−0.823955	+	0.566655i	$0.808237\pi$
$14$	2.43484	+	1.56478i	0.650738	+	0.418204i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−0.522787	+	0.603329i	−0.126795	+	0.146329i	−0.815597	−	0.578620i	$-0.803591\pi$
$17$	−0.522787	+	0.603329i	−0.126795	+	0.146329i	0.688802	+	0.724949i	$0.258137\pi$
$18$		0			0
$19$	−0.243530	+	0.211020i	−0.0558696	+	0.0484112i	−0.682348	−	0.731027i	$-0.739041\pi$
$19$	−0.243530	+	0.211020i	−0.0558696	+	0.0484112i	0.626478	+	0.779439i	$0.284496\pi$
$20$	−2.37933	−	0.698636i	−0.532035	−	0.156220i
$21$		0			0
$22$			1.13766i			0.242550i
$23$	2.48164	+	4.10384i	0.517457	+	0.855709i
$23$	2.48164	+	4.10384i	0.517457	+	0.855709i
$24$		0			0
$25$	0.477447	−	1.04546i	0.0954894	−	0.209093i
$26$	−0.901271	+	3.06945i	−0.176754	+	0.601968i
$27$		0			0
$28$	1.56478	+	2.43484i	0.295715	+	0.460141i
$29$	−5.18491	−	4.49275i	−0.962813	−	0.834283i	0.0234058	−	0.999726i	$-0.492549\pi$
$29$	−5.18491	−	4.49275i	−0.962813	−	0.834283i	−0.986219	+	0.165443i	$0.947094\pi$
$30$		0			0
$31$	4.09548	−	1.20254i	0.735570	−	0.215983i	0.107572	−	0.994197i	$-0.465693\pi$
$31$	4.09548	−	1.20254i	0.735570	−	0.215983i	0.627999	+	0.778214i	$0.283874\pi$
$32$	−0.540641	+	0.841254i	−0.0955727	+	0.148714i
$33$		0			0
$34$	−0.726176	+	0.331633i	−0.124538	+	0.0568747i
$35$	−6.52864	+	2.98153i	−1.10354	+	0.503970i
$36$		0			0
$37$	3.65447	−	5.68646i	0.600791	−	0.934849i	−0.399049	−	0.916930i	$-0.630660\pi$
$37$	3.65447	−	5.68646i	0.600791	−	0.934849i	0.999839	−	0.0179188i	$-0.00570405\pi$
$38$	−0.309183	+	0.0907844i	−0.0501561	+	0.0147272i
$39$		0			0
$40$	−1.87410	−	1.62391i	−0.296320	−	0.256763i
$41$	3.17706	+	4.94360i	0.496173	+	0.772061i	0.995541	−	0.0943295i	$-0.0300707\pi$
$41$	3.17706	+	4.94360i	0.496173	+	0.772061i	−0.499368	+	0.866390i	$0.666434\pi$
$42$		0			0
$43$	2.80415	−	9.55005i	0.427628	−	1.45637i	−0.410985	−	0.911642i	$-0.634815\pi$
$43$	2.80415	−	9.55005i	0.427628	−	1.45637i	0.838614	−	0.544727i	$-0.183367\pi$
$44$	−0.472602	+	1.03485i	−0.0712474	+	0.156010i
$45$		0			0
$46$	0.552579	+	4.76389i	0.0814734	+	0.702397i
$47$		−	5.22795i		−	0.762575i	−0.924457	−	0.381287i	$-0.875481\pi$
$47$		−	5.22795i		−	0.762575i	0.924457	−	0.381287i	$-0.124519\pi$
$48$		0			0
$49$	1.32118	+	0.387933i	0.188740	+	0.0554190i
$50$	0.868602	−	0.752648i	0.122839	−	0.106440i
$51$		0			0
$52$	−2.09492	+	2.41767i	−0.290513	+	0.335270i
$53$	1.85223	−	12.8826i	0.254424	−	1.76956i	−0.316539	−	0.948580i	$-0.602521\pi$
$53$	1.85223	−	12.8826i	0.254424	−	1.76956i	0.570963	−	0.820976i	$-0.306570\pi$
$54$		0			0
$55$	−2.37330	−	1.52523i	−0.320016	−	0.205662i
$56$	0.411901	+	2.86484i	0.0550426	+	0.382830i
$57$		0			0
$58$	−2.85000	−	6.24064i	−0.374224	−	0.819436i
$59$	1.01042	−	0.145277i	0.131546	−	0.0189135i	−0.0762272	−	0.997090i	$-0.524287\pi$
$59$	1.01042	−	0.145277i	0.131546	−	0.0189135i	0.207773	+	0.978177i	$0.433378\pi$
$60$		0			0
$61$	−1.27559	−	4.34427i	−0.163323	−	0.556227i	−0.999964	−	0.00847537i	$-0.997302\pi$
$61$	−1.27559	−	4.34427i	−0.163323	−	0.556227i	0.836641	−	0.547751i	$-0.184516\pi$
$62$	4.22493	+	0.607454i	0.536567	+	0.0771467i
$63$		0			0
$64$	−0.841254	+	0.540641i	−0.105157	+	0.0675801i
$65$	−5.19495	−	5.99529i	−0.644354	−	0.743624i
$66$		0			0
$67$	−11.3241	−	5.17154i	−1.38346	−	0.631804i	−0.421959	−	0.906615i	$-0.638657\pi$
$67$	−11.3241	−	5.17154i	−1.38346	−	0.631804i	−0.961498	+	0.274811i	$0.911385\pi$
$68$	−0.798318			−0.0968103
$69$		0			0
$70$	−7.17723			−0.857843
$71$	−0.297921	−	0.136056i	−0.0353567	−	0.0161469i	0.397658	−	0.917534i	$-0.369823\pi$
$71$	−0.297921	−	0.136056i	−0.0353567	−	0.0161469i	−0.433015	+	0.901387i	$0.642550\pi$
$72$		0			0
$73$	10.8435	+	12.5140i	1.26913	+	1.46465i	0.821258	+	0.570557i	$0.193273\pi$
$73$	10.8435	+	12.5140i	1.26913	+	1.46465i	0.447872	+	0.894098i	$0.352182\pi$
$74$	5.68646	−	3.65447i	0.661038	−	0.424823i
$75$		0			0
$76$	−0.318956	−	0.0458590i	−0.0365868	−	0.00526038i
$77$	0.927669	+	3.15935i	0.105718	+	0.360041i
$78$		0			0
$79$	−9.78336	+	1.40663i	−1.10071	+	0.158259i	−0.668645	−	0.743582i	$-0.733125\pi$
$79$	−9.78336	+	1.40663i	−1.10071	+	0.158259i	−0.432069	+	0.901841i	$0.642216\pi$
$80$	−1.03014	−	2.25569i	−0.115173	−	0.252194i
$81$		0			0
$82$	0.836309	+	5.81665i	0.0923548	+	0.642342i
$83$	5.29943	+	3.40574i	0.581688	+	0.373828i	0.798146	−	0.602464i	$-0.205814\pi$
$83$	5.29943	+	3.40574i	0.581688	+	0.373828i	−0.216458	+	0.976292i	$0.569451\pi$
$84$		0			0
$85$	0.281735	−	1.95951i	0.0305584	−	0.212538i
$86$	6.51798	−	7.52215i	0.702851	−	0.811134i
$87$		0			0
$88$	−0.859787	+	0.745010i	−0.0916536	+	0.0794183i
$89$	2.45350	+	0.720413i	0.260071	+	0.0763636i	0.409169	−	0.912459i	$-0.365819\pi$
$89$	2.45350	+	0.720413i	0.260071	+	0.0763636i	−0.149098	+	0.988822i	$0.547637\pi$
$90$		0			0
$91$			9.25895i			0.970601i
$92$	−1.47635	+	4.56294i	−0.153920	+	0.475719i
$93$		0			0
$94$	2.17177	−	4.75551i	0.224001	−	0.490493i
$95$	0.225126	−	0.766707i	0.0230974	−	0.0786625i
$96$		0			0
$97$	1.82885	+	2.84575i	0.185692	+	0.288942i	0.921601	−	0.388138i	$-0.126882\pi$
$97$	1.82885	+	2.84575i	0.185692	+	0.288942i	−0.735910	+	0.677080i	$0.763245\pi$
$98$	1.04063	+	0.901714i	0.105120	+	0.0910869i
$99$		0			0
$100$	1.10277	−	0.323802i	0.110277	−	0.0323802i
$101$	6.36955	−	9.91121i	0.633794	−	0.986202i	−0.364689	−	0.931130i	$-0.618825\pi$
$101$	6.36955	−	9.91121i	0.633794	−	0.986202i	0.998482	−	0.0550727i	$-0.0175391\pi$
$102$		0			0
$103$	−14.0872	+	6.43341i	−1.38805	+	0.633903i	−0.962563	−	0.271059i	$-0.912626\pi$
$103$	−14.0872	+	6.43341i	−1.38805	+	0.633903i	−0.425492	+	0.904962i	$0.639899\pi$
$104$	−2.90994	+	1.32893i	−0.285343	+	0.130312i
$105$		0			0
$106$	7.03646	−	10.9489i	0.683441	−	1.06346i
$107$	−6.92132	+	2.03228i	−0.669110	+	0.196468i	−0.598606	−	0.801043i	$-0.704279\pi$
$107$	−6.92132	+	2.03228i	−0.669110	+	0.196468i	−0.0705032	+	0.997512i	$0.522460\pi$
$108$		0			0
$109$	−4.67618	−	4.05194i	−0.447897	−	0.388105i	0.401500	−	0.915859i	$-0.368489\pi$
$109$	−4.67618	−	4.05194i	−0.447897	−	0.388105i	−0.849397	+	0.527754i	$0.823034\pi$
$110$	−1.52523	−	2.37330i	−0.145425	−	0.226286i
$111$		0			0
$112$	−0.815418	+	2.77706i	−0.0770497	+	0.262407i
$113$	6.38987	−	13.9919i	0.601109	−	1.31624i	−0.327383	−	0.944892i	$-0.606167\pi$
$113$	6.38987	−	13.9919i	0.601109	−	1.31624i	0.928492	−	0.371353i	$-0.121106\pi$
$114$		0			0
$115$	−10.6789	−	5.23407i	−0.995813	−	0.488079i
$116$		−	6.86062i		−	0.636992i
$117$		0			0
$118$	0.979465	+	0.287597i	0.0901671	+	0.0264754i
$119$	−1.74621	+	1.51310i	−0.160075	+	0.138706i
$120$		0			0
$121$	6.35590	−	7.33510i	0.577809	−	0.666827i
$122$	0.644355	−	4.48159i	0.0583372	−	0.405744i
$123$		0			0
$124$	3.59079	+	2.30766i	0.322462	+	0.207234i
$125$	−1.35894	−	9.45165i	−0.121547	−	0.845381i
$126$		0			0
$127$	8.55696	+	18.7371i	0.759308	+	1.66265i	0.748879	+	0.662707i	$0.230592\pi$
$127$	8.55696	+	18.7371i	0.759308	+	1.66265i	0.0104288	+	0.999946i	$0.496680\pi$
$128$	−0.989821	+	0.142315i	−0.0874887	+	0.0125790i
$129$		0			0
$130$	−2.23496	−	7.61156i	−0.196019	−	0.667578i
$131$	14.0827	+	2.02479i	1.23042	+	0.176907i	0.726695	−	0.686960i	$-0.241055\pi$
$131$	14.0827	+	2.02479i	1.23042	+	0.176907i	0.503720	+	0.863867i	$0.331964\pi$
$132$		0			0
$133$	−0.784592	+	0.504227i	−0.0680328	+	0.0437220i
$134$	−8.15241	−	9.40839i	−0.704261	−	0.812761i
$135$		0			0
$136$	−0.726176	−	0.331633i	−0.0622691	−	0.0284373i
$137$	7.79517			0.665986			0.332993	−	0.942929i	$-0.391941\pi$
$137$	7.79517			0.665986			0.332993	+	0.942929i	$0.391941\pi$
$138$		0			0
$139$	−17.9088			−1.51900			−0.759502	−	0.650505i	$-0.774557\pi$
$139$	−17.9088			−1.51900			−0.759502	+	0.650505i	$0.774557\pi$
$140$	−6.52864	−	2.98153i	−0.551771	−	0.251985i
$141$		0			0
$142$	−0.214479	−	0.247522i	−0.0179987	−	0.0207716i
$143$	−3.06167	+	1.96762i	−0.256030	+	0.164540i
$144$		0			0
$145$	16.8397	+	2.42118i	1.39846	+	0.201068i
$146$	4.66504	+	15.8877i	0.386082	+	1.31487i
$147$		0			0
$148$	6.69071	−	0.961979i	0.549973	−	0.0790742i
$149$	6.74006	+	14.7587i	0.552167	+	1.20908i	0.955762	+	0.294140i	$0.0950332\pi$
$149$	6.74006	+	14.7587i	0.552167	+	1.20908i	−0.403595	+	0.914938i	$0.632240\pi$
$150$		0			0
$151$	−1.40499	−	9.77192i	−0.114336	−	0.795227i	−0.963617	−	0.267286i	$-0.913873\pi$
$151$	−1.40499	−	9.77192i	−0.114336	−	0.795227i	0.849281	−	0.527941i	$-0.177036\pi$
$152$	−0.271082	−	0.174214i	−0.0219877	−	0.0141306i
$153$		0			0
$154$	−0.468604	+	3.25921i	−0.0377612	+	0.262635i
$155$	−6.93148	+	7.99935i	−0.556750	+	0.642523i
$156$		0			0
$157$	7.63666	−	6.61721i	0.609472	−	0.528111i	−0.294528	−	0.955643i	$-0.595162\pi$
$157$	7.63666	−	6.61721i	0.609472	−	0.528111i	0.904000	+	0.427532i	$0.140617\pi$
$158$	−9.48360	−	2.78463i	−0.754474	−	0.221534i
$159$		0			0
$160$		−	2.47978i		−	0.196044i
$161$	5.41911	+	12.7790i	0.427085	+	1.00713i
$162$		0			0
$163$	−2.62309	+	5.74376i	−0.205456	+	0.449886i	−0.984108	−	0.177570i	$-0.943176\pi$
$163$	−2.62309	+	5.74376i	−0.205456	+	0.449886i	0.778652	+	0.627456i	$0.215904\pi$
$164$	−1.65559	+	5.63843i	−0.129280	+	0.440287i
$165$		0			0
$166$	3.40574	+	5.29943i	0.264336	+	0.411315i
$167$	−1.29577	−	1.12279i	−0.100270	−	0.0868843i	0.603283	−	0.797527i	$-0.293859\pi$
$167$	−1.29577	−	1.12279i	−0.100270	−	0.0868843i	−0.703553	+	0.710643i	$0.748404\pi$
$168$		0			0
$169$	2.65415	−	0.779329i	0.204165	−	0.0599484i
$170$	1.07028	−	1.66539i	0.0820870	−	0.127730i
$171$		0			0
$172$	9.05377	−	4.13472i	0.690344	−	0.315269i
$173$	−11.9662	+	5.46476i	−0.909770	+	0.415478i	−0.814627	−	0.579985i	$-0.803058\pi$
$173$	−11.9662	+	5.46476i	−0.909770	+	0.415478i	−0.0951433	+	0.995464i	$0.530331\pi$
$174$		0			0
$175$	1.79844	−	2.79842i	0.135949	−	0.211541i
$176$	−1.09158	+	0.320516i	−0.0822808	+	0.0241598i
$177$		0			0
$178$	1.93251	+	1.67453i	0.144848	+	0.125511i
$179$	4.27515	+	6.65227i	0.319540	+	0.497214i	0.963450	−	0.267887i	$-0.0863254\pi$
$179$	4.27515	+	6.65227i	0.319540	+	0.497214i	−0.643910	+	0.765101i	$0.722689\pi$
$180$		0			0
$181$	−4.73544	+	16.1274i	−0.351982	+	1.19874i	0.573263	+	0.819372i	$0.305677\pi$
$181$	−4.73544	+	16.1274i	−0.351982	+	1.19874i	−0.925245	+	0.379370i	$0.876141\pi$
$182$	−3.84630	+	8.42223i	−0.285107	+	0.624297i
$183$		0			0
$184$	−3.23845	+	3.53730i	−0.238741	+	0.260773i
$185$			16.7621i			1.23238i
$186$		0			0
$187$	−0.871427	−	0.255874i	−0.0637250	−	0.0187114i
$188$	3.95102	−	3.42358i	0.288158	−	0.249690i
$189$		0			0
$190$	0.523283	−	0.603901i	0.0379630	−	0.0438116i
$191$	−0.657122	+	4.57039i	−0.0475477	+	0.330702i	0.952139	+	0.305666i	$0.0988790\pi$
$191$	−0.657122	+	4.57039i	−0.0475477	+	0.330702i	−0.999687	+	0.0250357i	$0.992030\pi$
$192$		0			0
$193$	4.03913	+	2.59579i	0.290743	+	0.186849i	0.677879	−	0.735173i	$-0.262899\pi$
$193$	4.03913	+	2.59579i	0.290743	+	0.186849i	−0.387136	+	0.922023i	$0.626536\pi$
$194$	0.481416	+	3.34832i	0.0345636	+	0.240395i
$195$		0			0
$196$	0.572008	+	1.25252i	0.0408577	+	0.0894659i
$197$	−11.0542	+	1.58935i	−0.787577	+	0.113236i	−0.524356	−	0.851499i	$-0.675694\pi$
$197$	−11.0542	+	1.58935i	−0.787577	+	0.113236i	−0.263221	+	0.964736i	$0.584785\pi$
$198$		0			0
$199$	−5.11469	−	17.4190i	−0.362571	−	1.23480i	−0.915753	−	0.401742i	$-0.868405\pi$
$199$	−5.11469	−	17.4190i	−0.362571	−	1.23480i	0.553182	−	0.833060i	$-0.313413\pi$
$200$	1.13763	+	0.163566i	0.0804423	+	0.0115659i
$201$		0			0
$202$	9.91121	−	6.36955i	0.697350	−	0.448160i
$203$	−13.0034	−	15.0067i	−0.912656	−	1.05326i
$204$		0			0
$205$	−13.2555	−	6.05358i	−0.925804	−	0.422800i
$206$	−15.4867			−1.07901
$207$		0			0
$208$	−3.19903			−0.221813
$209$	−0.333467	−	0.152289i	−0.0230664	−	0.0105341i
$210$		0			0
$211$	2.03426	+	2.34766i	0.140044	+	0.161619i	0.821439	−	0.570297i	$-0.193172\pi$
$211$	2.03426	+	2.34766i	0.140044	+	0.161619i	−0.681395	+	0.731916i	$0.738626\pi$
$212$	10.9489	−	7.03646i	0.751977	−	0.483266i
$213$		0			0
$214$	−7.14010	−	1.02659i	−0.488087	−	0.0701763i
$215$	6.95368	+	23.6821i	0.474237	+	1.61510i
$216$		0			0
$217$	12.2282	−	1.75815i	0.830105	−	0.119351i
$218$	−2.57037	−	5.62833i	−0.174087	−	0.381198i
$219$		0			0
$220$	−0.401492	−	2.79244i	−0.0270686	−	0.188266i
$221$	−2.14843	−	1.38071i	−0.144519	−	0.0928768i
$222$		0			0
$223$	−2.79292	+	19.4252i	−0.187028	+	1.30081i	0.652624	+	0.757682i	$0.273668\pi$
$223$	−2.79292	+	19.4252i	−0.187028	+	1.30081i	−0.839651	+	0.543126i	$0.817241\pi$
$224$	−1.89536	+	2.18736i	−0.126639	+	0.146149i
$225$		0			0
$226$	11.6249	−	10.0730i	0.773274	−	0.670046i
$227$	−3.24347	−	0.952370i	−0.215277	−	0.0632110i	0.172316	−	0.985042i	$-0.444875\pi$
$227$	−3.24347	−	0.952370i	−0.215277	−	0.0632110i	−0.387593	+	0.921831i	$0.626693\pi$
$228$		0			0
$229$			2.13956i			0.141386i	0.997498	+	0.0706930i	$0.0225211\pi$
$229$			2.13956i			0.141386i	−0.997498	+	0.0706930i	$0.977479\pi$
$230$	−7.53957	−	9.19725i	−0.497144	−	0.606449i
$231$		0			0
$232$	2.85000	−	6.24064i	0.187112	−	0.409718i
$233$	6.39721	−	21.7869i	0.419095	−	1.42731i	−0.431798	−	0.901970i	$-0.642121\pi$
$233$	6.39721	−	21.7869i	0.419095	−	1.42731i	0.850894	−	0.525338i	$-0.176061\pi$
$234$		0			0
$235$	7.00896	+	10.9062i	0.457214	+	0.711439i
$236$	0.771481	+	0.668492i	0.0502191	+	0.0435151i
$237$		0			0
$238$	−2.21698	+	0.650963i	−0.143705	+	0.0421957i
$239$	−6.82769	+	10.6241i	−0.441647	+	0.687216i	−0.988704	−	0.149879i	$-0.952112\pi$
$239$	−6.82769	+	10.6241i	−0.441647	+	0.687216i	0.547058	+	0.837095i	$0.315748\pi$
$240$		0			0
$241$	2.46308	−	1.12485i	0.158661	−	0.0724580i	−0.334502	−	0.942395i	$-0.608568\pi$
$241$	2.46308	−	1.12485i	0.158661	−	0.0724580i	0.493163	+	0.869937i	$0.335841\pi$
$242$	8.82864	−	4.03190i	0.567526	−	0.259181i
$243$		0			0
$244$	2.44784	−	3.80892i	0.156707	−	0.243841i
$245$	−3.27624	+	0.961990i	−0.209311	+	0.0614593i
$246$		0			0
$247$	−0.779059	−	0.675059i	−0.0495703	−	0.0429530i
$248$	2.30766	+	3.59079i	0.146537	+	0.228015i
$249$		0			0
$250$	2.69022	−	9.16204i	0.170144	−	0.579459i
$251$	−6.66803	+	14.6010i	−0.420883	+	0.921604i	0.573837	+	0.818970i	$0.305454\pi$
$251$	−6.66803	+	14.6010i	−0.420883	+	0.921604i	−0.994719	+	0.102634i	$0.967273\pi$
$252$		0			0
$253$	−3.07404	+	4.50761i	−0.193263	+	0.283391i
$254$			20.5986i			1.29247i
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−14.2000	+	12.3043i	−0.885770	+	0.767524i	−0.973516	−	0.228619i	$-0.926579\pi$
$257$	−14.2000	+	12.3043i	−0.885770	+	0.767524i	0.0877464	+	0.996143i	$0.472033\pi$
$258$		0			0
$259$	12.8117	−	14.7855i	0.796081	−	0.918727i
$260$	1.12897	−	7.85216i	0.0700157	−	0.486970i
$261$		0			0
$262$	11.9690	+	7.69200i	0.739447	+	0.475213i
$263$	−3.72304	−	25.8943i	−0.229573	−	1.59671i	−0.699914	−	0.714227i	$-0.746778\pi$
$263$	−3.72304	−	25.8943i	−0.229573	−	1.59671i	0.470341	−	0.882485i	$-0.344131\pi$
$264$		0			0
$265$	13.4073	+	29.3579i	0.823604	+	1.80344i
$266$	−0.923154	+	0.132729i	−0.0566022	+	0.00813817i
$267$		0			0
$268$	−3.50731	−	11.9448i	−0.214243	−	0.729645i
$269$	19.3635	+	2.78405i	1.18061	+	0.169747i	0.704544	−	0.709661i	$-0.251152\pi$
$269$	19.3635	+	2.78405i	1.18061	+	0.169747i	0.476070	+	0.879407i	$0.342061\pi$
$270$		0			0
$271$	6.90572	−	4.43804i	0.419493	−	0.269592i	−0.313821	−	0.949482i	$-0.601609\pi$
$271$	6.90572	−	4.43804i	0.419493	−	0.269592i	0.733314	+	0.679891i	$0.237973\pi$
$272$	−0.522787	−	0.603329i	−0.0316986	−	0.0365822i
$273$		0			0
$274$	7.09073	+	3.23823i	0.428367	+	0.195629i
$275$	1.30754			0.0788478
$276$		0			0
$277$	−29.0606			−1.74608			−0.873040	−	0.487649i	$-0.837855\pi$
$277$	−29.0606			−1.74608			−0.873040	+	0.487649i	$0.837855\pi$
$278$	−16.2904	−	7.43959i	−0.977034	−	0.446197i
$279$		0			0
$280$	−4.70009	−	5.42419i	−0.280884	−	0.324157i
$281$	13.7994	−	8.86837i	0.823206	−	0.529042i	−0.0599062	−	0.998204i	$-0.519080\pi$
$281$	13.7994	−	8.86837i	0.823206	−	0.529042i	0.883112	+	0.469162i	$0.155444\pi$
$282$		0			0
$283$	15.3937	+	2.21328i	0.915061	+	0.131566i	0.583729	−	0.811948i	$-0.301593\pi$
$283$	15.3937	+	2.21328i	0.915061	+	0.131566i	0.331332	+	0.943514i	$0.392502\pi$
$284$	−0.0922725	−	0.314251i	−0.00547537	−	0.0186474i
$285$		0			0
$286$	−3.60237	+	0.517942i	−0.213013	+	0.0306266i
$287$	7.06548	+	15.4712i	0.417062	+	0.913239i
$288$		0			0
$289$	2.32865	+	16.1961i	0.136980	+	0.952714i
$290$	14.3121	+	9.19784i	0.840436	+	0.540116i
$291$		0			0
$292$	−2.35651	+	16.3899i	−0.137904	+	0.959145i
$293$	−11.9799	+	13.8256i	−0.699876	+	0.807700i	−0.988736	−	0.149672i	$-0.952178\pi$
$293$	−11.9799	+	13.8256i	−0.699876	+	0.807700i	0.288860	+	0.957371i	$0.406724\pi$
$294$		0			0
$295$	−1.91311	+	1.65772i	−0.111385	+	0.0965159i
$296$	6.48570	+	1.90437i	0.376974	+	0.110689i
$297$		0			0
$298$			16.2249i			0.939882i
$299$	−11.8649	+	9.72638i	−0.686163	+	0.562491i
$300$		0			0
$301$	11.9671	−	26.2043i	0.689772	−	1.51039i
$302$	2.78138	−	9.47250i	0.160050	−	0.545081i
$303$		0			0
$304$	−0.174214	−	0.271082i	−0.00999186	−	0.0155476i
$305$	8.48529	+	7.35254i	0.485866	+	0.421005i
$306$		0			0
$307$	−24.2207	+	7.11183i	−1.38235	+	0.405894i	−0.886585	−	0.462565i	$-0.846929\pi$
$307$	−24.2207	+	7.11183i	−1.38235	+	0.405894i	−0.495761	+	0.868459i	$0.665111\pi$
$308$	−1.78018	+	2.77002i	−0.101435	+	0.157837i
$309$		0			0
$310$	−9.62814	+	4.39703i	−0.546842	+	0.249734i
$311$	19.5777	−	8.94083i	1.11015	−	0.506988i	0.225969	−	0.974134i	$-0.427445\pi$
$311$	19.5777	−	8.94083i	1.11015	−	0.506988i	0.884180	+	0.467146i	$0.154718\pi$
$312$		0			0
$313$	−7.34457	+	11.4284i	−0.415140	+	0.645970i	−0.984351	−	0.176221i	$-0.943613\pi$
$313$	−7.34457	+	11.4284i	−0.415140	+	0.645970i	0.569211	+	0.822192i	$0.307249\pi$
$314$	9.69544	−	2.84684i	0.547145	−	0.160656i
$315$		0			0
$316$	−7.46980	−	6.47262i	−0.420209	−	0.364113i
$317$	−4.99255	−	7.76857i	−0.280410	−	0.436326i	0.672268	−	0.740308i	$-0.265320\pi$
$317$	−4.99255	−	7.76857i	−0.280410	−	0.436326i	−0.952678	+	0.303982i	$0.901684\pi$
$318$		0			0
$319$	2.19894	−	7.48890i	0.123117	−	0.419298i
$320$	1.03014	−	2.25569i	0.0575865	−	0.126097i
$321$		0			0
$322$	−0.379204	+	13.8754i	−0.0211322	+	0.773245i
$323$		−	0.257247i		−	0.0143136i
$324$		0			0
$325$	3.52779	+	1.03585i	0.195687	+	0.0574588i
$326$	−4.77208	+	4.13504i	−0.264301	+	0.229018i
$327$		0			0
$328$	−3.84827	+	4.44114i	−0.212485	+	0.245221i
$329$	2.15340	−	14.9772i	0.118721	−	0.825721i
$330$		0			0
$331$	11.0867	+	7.12499i	0.609380	+	0.391625i	0.808625	−	0.588325i	$-0.200212\pi$
$331$	11.0867	+	7.12499i	0.609380	+	0.391625i	−0.199244	+	0.979950i	$0.563849\pi$
$332$	0.896504	+	6.23532i	0.0492021	+	0.342208i
$333$		0			0
$334$	−0.712250	−	1.55961i	−0.0389726	−	0.0853381i
$335$	30.5568	−	4.39340i	1.66950	−	0.240037i
$336$		0			0
$337$	−7.59914	−	25.8803i	−0.413951	−	1.40979i	−0.857937	−	0.513755i	$-0.828254\pi$
$337$	−7.59914	−	25.8803i	−0.413951	−	1.40979i	0.443985	−	0.896034i	$-0.353564\pi$
$338$	2.73805	+	0.393672i	0.148930	+	0.0214129i
$339$		0			0
$340$	1.66539	−	1.07028i	0.0903186	−	0.0580443i
$341$	3.17998	+	3.66990i	0.172206	+	0.198736i
$342$		0			0
$343$	−14.8040	−	6.76078i	−0.799343	−	0.365048i
$344$	9.95322			0.536642
$345$		0			0
$346$	−13.1549			−0.707214
$347$	26.7003	+	12.1936i	1.43335	+	0.654588i	0.972503	−	0.232892i	$-0.0748189\pi$
$347$	26.7003	+	12.1936i	1.43335	+	0.654588i	0.460846	+	0.887480i	$0.347546\pi$
$348$		0			0
$349$	−9.77363	−	11.2794i	−0.523170	−	0.603771i	0.431252	−	0.902232i	$-0.358072\pi$
$349$	−9.77363	−	11.2794i	−0.523170	−	0.603771i	−0.954422	+	0.298461i	$0.903527\pi$
$350$	2.79842	−	1.79844i	0.149582	−	0.0961304i
$351$		0			0
$352$	−1.12608	−	0.161906i	−0.0600203	−	0.00862962i
$353$	−9.55703	−	32.5482i	−0.508669	−	1.73237i	−0.667072	−	0.744993i	$-0.732453\pi$
$353$	−9.55703	−	32.5482i	−0.508669	−	1.73237i	0.158403	−	0.987375i	$-0.449366\pi$
$354$		0			0
$355$	0.803907	−	0.115584i	0.0426670	−	0.00613458i
$356$	1.06225	+	2.32600i	0.0562991	+	0.123278i
$357$		0			0
$358$	1.12536	+	7.82708i	0.0594773	+	0.413674i
$359$	−18.5421	−	11.9163i	−0.978614	−	0.628917i	−0.0495246	−	0.998773i	$-0.515771\pi$
$359$	−18.5421	−	11.9163i	−0.978614	−	0.628917i	−0.929089	+	0.369856i	$0.879407\pi$
$360$		0			0
$361$	−2.68920	+	18.7038i	−0.141537	+	0.984412i
$362$	−11.0071	+	12.7028i	−0.578519	+	0.667647i
$363$		0			0
$364$	−6.99744	+	6.06332i	−0.366766	+	0.317804i
$365$	−39.3980	−	11.5683i	−2.06219	−	0.605512i
$366$		0			0
$367$		−	21.1712i		−	1.10513i	−0.833471	−	0.552564i	$-0.813650\pi$
$367$		−	21.1712i		−	1.10513i	0.833471	−	0.552564i	$-0.186350\pi$
$368$	−4.41524	+	1.87234i	−0.230160	+	0.0976024i
$369$		0			0
$370$	−6.96324	+	15.2474i	−0.362001	+	0.792673i
$371$	10.6127	−	36.1435i	0.550983	−	1.87648i
$372$		0			0
$373$	−5.99327	−	9.32571i	−0.310320	−	0.482867i	0.650705	−	0.759331i	$-0.274474\pi$
$373$	−5.99327	−	9.32571i	−0.310320	−	0.482867i	−0.961024	+	0.276464i	$0.910837\pi$
$374$	−0.686384	−	0.594755i	−0.0354921	−	0.0307540i
$375$		0			0
$376$	5.01618	−	1.47288i	0.258690	−	0.0759581i
$377$	11.8656	−	18.4633i	0.611111	−	0.950907i
$378$		0			0
$379$	17.7838	−	8.12159i	0.913493	−	0.417178i	0.0974967	−	0.995236i	$-0.468916\pi$
$379$	17.7838	−	8.12159i	0.913493	−	0.417178i	0.815996	+	0.578058i	$0.196189\pi$
$380$	0.726865	−	0.331948i	0.0372874	−	0.0170286i
$381$		0			0
$382$	−2.49635	+	3.88439i	−0.127724	+	0.198743i
$383$	−22.7421	+	6.67767i	−1.16207	+	0.341213i	−0.805235	−	0.592956i	$-0.797961\pi$
$383$	−22.7421	+	6.67767i	−1.16207	+	0.341213i	−0.356831	+	0.934169i	$0.616143\pi$
$384$		0			0
$385$	−6.17089	−	5.34710i	−0.314498	−	0.272514i
$386$	2.59579	+	4.03913i	0.132122	+	0.205586i
$387$		0			0
$388$	−0.953031	+	3.24573i	−0.0483828	+	0.164777i
$389$	1.53686	−	3.36526i	0.0779220	−	0.170625i	−0.866661	−	0.498897i	$-0.833739\pi$
$389$	1.53686	−	3.36526i	0.0779220	−	0.170625i	0.944584	+	0.328271i	$0.106466\pi$
$390$		0			0
$391$	−3.77333	−	0.648192i	−0.190826	−	0.0327805i
$392$			1.37696i			0.0695467i
$393$		0			0
$394$	−10.7155	−	3.14634i	−0.539837	−	0.158511i
$395$	18.5235	−	16.0507i	0.932018	−	0.807598i
$396$		0			0
$397$	19.9650	−	23.0408i	1.00201	−	1.15639i	0.0143345	−	0.999897i	$-0.495437\pi$
$397$	19.9650	−	23.0408i	1.00201	−	1.15639i	0.987680	−	0.156489i	$-0.0500175\pi$
$398$	2.58364	−	17.9696i	0.129506	−	0.900736i
$399$		0			0
$400$	0.966874	+	0.621372i	0.0483437	+	0.0310686i
$401$	−2.43025	−	16.9028i	−0.121361	−	0.844085i	−0.956017	−	0.293312i	$-0.905242\pi$
$401$	−2.43025	−	16.9028i	−0.121361	−	0.844085i	0.834656	−	0.550772i	$-0.185667\pi$
$402$		0			0
$403$	5.67236	+	12.4207i	0.282560	+	0.618721i
$404$	11.6616	−	1.67668i	0.580184	−	0.0834179i
$405$		0			0
$406$	−5.59427	−	19.0523i	−0.277639	−	0.945551i
$407$	7.61176	+	1.09441i	0.377301	+	0.0542477i
$408$		0			0
$409$	−18.5525	+	11.9230i	−0.917364	+	0.589554i	−0.911892	−	0.410431i	$-0.865378\pi$
$409$	−18.5525	+	11.9230i	−0.917364	+	0.589554i	−0.00547200	+	0.999985i	$0.501742\pi$
$410$	−9.54287	−	11.0131i	−0.471289	−	0.543896i
$411$		0			0
$412$	−14.0872	−	6.43341i	−0.694027	−	0.316952i
$413$	2.95454			0.145384
$414$		0			0
$415$	−15.6213			−0.766817
$416$	−2.90994	−	1.32893i	−0.142672	−	0.0651559i
$417$		0			0
$418$	−0.240069	−	0.277054i	−0.0117422	−	0.0135512i
$419$	4.93432	−	3.17109i	0.241057	−	0.154918i	−0.414535	−	0.910034i	$-0.636056\pi$
$419$	4.93432	−	3.17109i	0.241057	−	0.154918i	0.655592	+	0.755115i	$0.272419\pi$
$420$		0			0
$421$	32.3508	+	4.65135i	1.57668	+	0.226693i	0.874400	−	0.485206i	$-0.161255\pi$
$421$	32.3508	+	4.65135i	1.57668	+	0.226693i	0.702282	+	0.711898i	$0.252164\pi$
$422$	0.875173	+	2.98056i	0.0426027	+	0.145092i
$423$		0			0
$424$	12.8826	−	1.85223i	0.625632	−	0.0899524i
$425$	0.381155	+	0.834612i	0.0184887	+	0.0404846i
$426$		0			0
$427$	−1.86495	−	12.9710i	−0.0902515	−	0.627713i
$428$	−6.06840	−	3.89992i	−0.293327	−	0.188510i
$429$		0			0
$430$	−3.51259	+	24.4306i	−0.169392	+	1.17815i
$431$	−16.8828	+	19.4838i	−0.813216	+	0.938501i	−0.999028	−	0.0440844i	$-0.985963\pi$
$431$	−16.8828	+	19.4838i	−0.813216	+	0.938501i	0.185812	+	0.982585i	$0.440508\pi$
$432$		0			0
$433$	9.21266	−	7.98281i	0.442732	−	0.383630i	−0.404773	−	0.914417i	$-0.632649\pi$
$433$	9.21266	−	7.98281i	0.442732	−	0.383630i	0.847505	+	0.530788i	$0.178104\pi$
$434$	11.8535	+	3.48051i	0.568988	+	0.167070i
$435$		0			0
$436$		−	6.18748i		−	0.296326i
$437$	−1.47034	−	0.475733i	−0.0703360	−	0.0227574i
$438$		0			0
$439$	13.3515	−	29.2357i	0.637233	−	1.39534i	−0.265065	−	0.964231i	$-0.585393\pi$
$439$	13.3515	−	29.2357i	0.637233	−	1.39534i	0.902297	−	0.431114i	$-0.141879\pi$
$440$	0.794811	−	2.70688i	0.0378911	−	0.129045i
$441$		0			0
$442$	−1.38071	−	2.14843i	−0.0656738	−	0.102190i
$443$	−25.3700	−	21.9832i	−1.20537	−	1.04446i	−0.997804	−	0.0662335i	$-0.978902\pi$
$443$	−25.3700	−	21.9832i	−1.20537	−	1.04446i	−0.207562	−	0.978222i	$-0.566553\pi$
$444$		0			0
$445$	−6.08415	+	1.78647i	−0.288416	+	0.0846867i
$446$	−10.6101	+	16.5096i	−0.502401	+	0.781751i
$447$		0			0
$448$	−2.63275	+	1.20233i	−0.124386	+	0.0568050i
$449$	−4.60114	+	2.10127i	−0.217141	+	0.0991651i	−0.521016	−	0.853547i	$-0.674447\pi$
$449$	−4.60114	+	2.10127i	−0.217141	+	0.0991651i	0.303875	+	0.952712i	$0.401720\pi$
$450$		0			0
$451$	−3.61442	+	5.62414i	−0.170196	+	0.264830i
$452$	14.7588	−	4.33358i	0.694197	−	0.203835i
$453$		0			0
$454$	−2.55474	−	2.21369i	−0.119900	−	0.103894i
$455$	−12.4132	−	19.3153i	−0.581940	−	0.905517i
$456$		0			0
$457$	5.34745	−	18.2117i	0.250143	−	0.851909i	−0.734690	−	0.678403i	$-0.762672\pi$
$457$	5.34745	−	18.2117i	0.250143	−	0.851909i	0.984833	−	0.173506i	$-0.0555095\pi$
$458$	−0.888804	+	1.94621i	−0.0415311	+	0.0909404i
$459$		0			0
$460$	−3.03755	−	11.4982i	−0.141627	−	0.536105i
$461$			32.9957i			1.53676i	0.639991	+	0.768382i	$0.278938\pi$
$461$			32.9957i			1.53676i	−0.639991	+	0.768382i	$0.721062\pi$
$462$		0			0
$463$	−31.9865	−	9.39209i	−1.48654	−	0.436488i	−0.565105	−	0.825019i	$-0.691164\pi$
$463$	−31.9865	−	9.39209i	−1.48654	−	0.436488i	−0.921435	+	0.388531i	$0.872982\pi$
$464$	5.18491	−	4.49275i	0.240703	−	0.208571i
$465$		0			0
$466$	14.8697	−	17.1606i	0.688826	−	0.794948i
$467$	−1.87737	+	13.0574i	−0.0868745	+	0.604226i	0.899152	+	0.437637i	$0.144184\pi$
$467$	−1.87737	+	13.0574i	−0.0868745	+	0.604226i	−0.986026	+	0.166589i	$0.946725\pi$
$468$		0			0
$469$	−30.3115	−	19.4800i	−1.39965	−	0.899503i
$470$	1.84499	+	12.8322i	0.0851033	+	0.591906i
$471$		0			0
$472$	0.424062	+	0.928566i	0.0195190	+	0.0427407i
$473$	11.2081	−	1.61149i	0.515351	−	0.0740963i
$474$		0			0
$475$	0.104341	+	0.355352i	0.00478748	+	0.0163047i
$476$	−2.28705	−	0.328828i	−0.104827	−	0.0150718i
$477$		0			0
$478$	−10.6241	+	6.82769i	−0.485935	+	0.312291i
$479$	−0.0634607	−	0.0732375i	−0.00289959	−	0.00334631i	0.754298	−	0.656532i	$-0.227977\pi$
$479$	−0.0634607	−	0.0732375i	−0.00289959	−	0.00334631i	−0.757198	+	0.653186i	$0.773432\pi$
$480$		0			0
$481$	19.6698	+	8.98288i	0.896865	+	0.409584i
$482$	2.70778			0.123336
$483$		0			0
$484$	9.70573			0.441169
$485$	−7.63044	−	3.48470i	−0.346480	−	0.158232i
$486$		0			0
$487$	4.30356	+	4.96658i	0.195013	+	0.225057i	0.844832	−	0.535032i	$-0.179701\pi$
$487$	4.30356	+	4.96658i	0.195013	+	0.225057i	−0.649819	+	0.760089i	$0.725155\pi$
$488$	3.80892	−	2.44784i	0.172422	−	0.110809i
$489$		0			0
$490$	−3.37980	−	0.485941i	−0.152684	−	0.0219526i
$491$	9.65629	+	32.8863i	0.435782	+	1.48414i	0.826134	+	0.563473i	$0.190535\pi$
$491$	9.65629	+	32.8863i	0.435782	+	1.48414i	−0.390352	+	0.920666i	$0.627647\pi$
$492$		0			0
$493$	5.42121	−	0.779452i	0.244159	−	0.0351048i
$494$	−0.428228	−	0.937688i	−0.0192669	−	0.0421886i
$495$		0			0
$496$	0.607454	+	4.22493i	0.0272755	+	0.189705i
$497$	−0.797454	−	0.512492i	−0.0357707	−	0.0229884i
$498$		0			0
$499$	−0.725438	+	5.04553i	−0.0324751	+	0.225869i	−0.999595	−	0.0284509i	$-0.990943\pi$
$499$	−0.725438	+	5.04553i	−0.0324751	+	0.225869i	0.967120	+	0.254320i	$0.0818517\pi$
$500$	6.25316	−	7.21653i	0.279650	−	0.322733i
$501$		0			0
$502$	−12.1309	+	10.5115i	−0.541429	+	0.469151i
$503$	−28.7924	−	8.45422i	−1.28379	−	0.376955i	−0.432493	−	0.901637i	$-0.642366\pi$
$503$	−28.7924	−	8.45422i	−1.28379	−	0.376955i	−0.851298	+	0.524682i	$0.824184\pi$
$504$		0			0
$505$			29.2155i			1.30007i
$506$	−4.66878	+	2.82326i	−0.207552	+	0.125509i
$507$		0			0
$508$	−8.55696	+	18.7371i	−0.379654	+	0.831326i
$509$	−6.70807	+	22.8456i	−0.297330	+	1.01261i	0.666369	+	0.745622i	$0.267848\pi$
$509$	−6.70807	+	22.8456i	−0.297330	+	1.01261i	−0.963699	+	0.266991i	$0.913971\pi$
$510$		0			0
$511$	25.9102	+	40.3170i	1.14620	+	1.78352i
$512$	−0.755750	−	0.654861i	−0.0333997	−	0.0289410i
$513$		0			0
$514$	−18.0282	+	5.29354i	−0.795188	+	0.233488i
$515$	20.7626	−	32.3072i	0.914910	−	1.42363i
$516$		0			0
$517$	5.41016	−	2.47074i	0.237938	−	0.108663i
$518$	17.7961	−	8.12719i	0.781914	−	0.357088i
$519$		0			0
$520$	4.28885	−	6.67358i	0.188079	−	0.292656i
$521$	1.69403	−	0.497411i	0.0742167	−	0.0217920i	−0.244413	−	0.969671i	$-0.578595\pi$
$521$	1.69403	−	0.497411i	0.0742167	−	0.0217920i	0.318630	+	0.947879i	$0.396777\pi$
$522$		0			0
$523$	3.16834	+	2.74538i	0.138542	+	0.120047i	0.721375	−	0.692545i	$-0.243510\pi$
$523$	3.16834	+	2.74538i	0.138542	+	0.120047i	−0.582833	+	0.812592i	$0.698056\pi$
$524$	7.69200	+	11.9690i	0.336027	+	0.522868i
$525$		0			0
$526$	7.37029	−	25.1009i	0.321360	−	1.09445i
$527$	−1.41554	+	3.09960i	−0.0616618	+	0.135020i
$528$		0			0
$529$	−10.6830	+	20.3685i	−0.464477	+	0.885585i
$530$			32.2745i			1.40191i
$531$		0			0
$532$	−0.894868	−	0.262757i	−0.0387975	−	0.0113920i
$533$	−14.2073	+	12.3107i	−0.615388	+	0.533237i
$534$		0			0
$535$	11.7141	−	13.5188i	0.506446	−	0.584470i
$536$	1.77169	−	12.3224i	0.0765253	−	0.532245i
$537$		0			0
$538$	16.4571	+	10.5764i	0.709517	+	0.455979i
$539$	0.222937	+	1.55056i	0.00960259	+	0.0667875i
$540$		0			0
$541$	−16.6880	−	36.5416i	−0.717472	−	1.57104i	−0.817413	−	0.576052i	$-0.804593\pi$
$541$	−16.6880	−	36.5416i	−0.717472	−	1.57104i	0.0999412	−	0.994993i	$-0.468135\pi$
$542$	8.12530	−	1.16824i	0.349011	−	0.0501803i
$543$		0			0
$544$	−0.224912	−	0.765981i	−0.00964303	−	0.0328412i
$545$	15.1874	+	2.18362i	0.650558	+	0.0935361i
$546$		0			0
$547$	1.88937	−	1.21422i	0.0807836	−	0.0519164i	−0.499625	−	0.866242i	$-0.666529\pi$
$547$	1.88937	−	1.21422i	0.0807836	−	0.0519164i	0.580409	+	0.814325i	$0.302893\pi$
$548$	5.10475	+	5.89119i	0.218064	+	0.251659i
$549$		0			0
$550$	1.18938	+	0.543173i	0.0507154	+	0.0231610i
$551$	2.21074			0.0941806
$552$		0			0
$553$	−28.6071			−1.21650
$554$	−26.4344	−	12.0722i	−1.12309	−	0.512898i
$555$		0			0
$556$	−11.7278	−	13.5346i	−0.497368	−	0.573994i
$557$	14.0466	−	9.02721i	0.595174	−	0.382495i	−0.208097	−	0.978108i	$-0.566727\pi$
$557$	14.0466	−	9.02721i	0.595174	−	0.382495i	0.803272	+	0.595613i	$0.203091\pi$
$558$		0			0
$559$	31.5166	+	4.53140i	1.33301	+	0.191658i
$560$	−2.02206	−	6.88650i	−0.0854476	−	0.291008i
$561$		0			0
$562$	16.2365	−	2.33445i	0.684894	−	0.0984729i
$563$	−1.58149	−	3.46298i	−0.0666519	−	0.145947i	0.873374	−	0.487050i	$-0.161927\pi$
$563$	−1.58149	−	3.46298i	−0.0666519	−	0.145947i	−0.940026	+	0.341102i	$0.889200\pi$
$564$		0			0
$565$	5.42843	+	37.7555i	0.228376	+	1.58839i
$566$	13.0832	+	8.40805i	0.549927	+	0.353417i
$567$		0			0
$568$	0.0466107	−	0.324185i	0.00195574	−	0.0136025i
$569$	−15.6697	+	18.0838i	−0.656909	+	0.758114i	−0.982269	−	0.187477i	$-0.939969\pi$
$569$	−15.6697	+	18.0838i	−0.656909	+	0.758114i	0.325360	+	0.945590i	$0.394515\pi$
$570$		0			0
$571$	11.7955	−	10.2208i	0.493626	−	0.427729i	−0.372141	−	0.928176i	$-0.621376\pi$
$571$	11.7955	−	10.2208i	0.493626	−	0.427729i	0.865767	+	0.500447i	$0.166831\pi$
$572$	−3.49199	−	1.02534i	−0.146007	−	0.0428717i
$573$		0			0
$574$			17.0082i			0.709910i
$575$	5.47526	−	0.635093i	0.228334	−	0.0264852i
$576$		0			0
$577$	8.94508	−	19.5870i	0.372388	−	0.815417i	−0.626950	−	0.779059i	$-0.715697\pi$
$577$	8.94508	−	19.5870i	0.372388	−	0.815417i	0.999339	−	0.0363578i	$-0.0115756\pi$
$578$	−4.60990	+	15.6999i	−0.191747	+	0.653029i
$579$		0			0
$580$	9.19784	+	14.3121i	0.381919	+	0.594278i
$581$	13.7792	+	11.9397i	0.571656	+	0.495343i
$582$		0			0
$583$	14.2069	−	4.17153i	0.588391	−	0.172767i
$584$	−8.95215	+	13.9298i	−0.370443	+	0.576420i
$585$		0			0
$586$	−16.6407	+	7.59955i	−0.687421	+	0.313935i
$587$	−17.3263	+	7.91267i	−0.715134	+	0.326591i	−0.739541	−	0.673111i	$-0.764957\pi$
$587$	−17.3263	+	7.91267i	−0.715134	+	0.326591i	0.0244073	+	0.999702i	$0.492230\pi$
$588$		0			0
$589$	−0.743611	+	1.15708i	−0.0306400	+	0.0476767i
$590$	−2.42886	+	0.713178i	−0.0999946	+	0.0293611i
$591$		0			0
$592$	5.10850	+	4.42654i	0.209958	+	0.181930i
$593$	−1.78636	−	2.77963i	−0.0733570	−	0.114146i	0.802637	−	0.596468i	$-0.203430\pi$
$593$	−1.78636	−	2.77963i	−0.0733570	−	0.114146i	−0.875994	+	0.482322i	$0.839793\pi$
$594$		0			0
$595$	1.61425	−	5.49762i	0.0661777	−	0.225380i
$596$	−6.74006	+	14.7587i	−0.276084	+	0.604539i
$597$		0			0
$598$	−14.8331	+	3.91858i	−0.606572	+	0.160243i
$599$		−	3.47127i		−	0.141832i	−0.997482	−	0.0709161i	$-0.977408\pi$
$599$		−	3.47127i		−	0.141832i	0.997482	−	0.0709161i	$-0.0225923\pi$
$600$		0			0
$601$	8.89296	+	2.61121i	0.362751	+	0.106513i	0.458029	−	0.888937i	$-0.348556\pi$
$601$	8.89296	+	2.61121i	0.362751	+	0.106513i	−0.0952774	+	0.995451i	$0.530374\pi$
$602$	21.7713	−	18.8650i	0.887333	−	0.768878i
$603$		0			0
$604$	6.46505	−	7.46106i	0.263059	−	0.303586i
$605$	−3.42525	+	23.8231i	−0.139256	+	0.968548i
$606$		0			0
$607$	32.6403	+	20.9767i	1.32483	+	0.851417i	0.995679	−	0.0928604i	$-0.0296010\pi$
$607$	32.6403	+	20.9767i	1.32483	+	0.851417i	0.329151	+	0.944277i	$0.393237\pi$
$608$	−0.0458590	−	0.318956i	−0.00185983	−	0.0129354i
$609$		0			0
$610$	4.66413	+	10.2130i	0.188845	+	0.413513i
$611$	16.5541	−	2.38013i	0.669709	−	0.0962896i
$612$		0			0
$613$	−10.0707	−	34.2978i	−0.406753	−	1.38527i	−0.867365	−	0.497672i	$-0.834188\pi$
$613$	−10.0707	−	34.2978i	−0.406753	−	1.38527i	0.460613	−	0.887601i	$-0.347630\pi$
$614$	−24.9863	−	3.59248i	−1.00836	−	0.144981i
$615$		0			0
$616$	−2.77002	+	1.78018i	−0.111607	+	0.0717256i
$617$	4.19658	+	4.84311i	0.168948	+	0.194976i	0.833909	−	0.551901i	$-0.186098\pi$
$617$	4.19658	+	4.84311i	0.168948	+	0.194976i	−0.664961	+	0.746878i	$0.731552\pi$
$618$		0			0
$619$	17.8903	+	8.17024i	0.719073	+	0.328390i	0.741125	−	0.671367i	$-0.234293\pi$
$619$	17.8903	+	8.17024i	0.719073	+	0.328390i	−0.0220519	+	0.999757i	$0.507020\pi$
$620$	−10.5847			−0.425090
$621$		0			0
$622$	21.5227			0.862980
$623$	6.73214	+	3.07447i	0.269718	+	0.123176i
$624$		0			0
$625$	19.2697	+	22.2384i	0.770789	+	0.889538i
$626$	−11.4284	+	7.34457i	−0.456770	+	0.293548i
$627$		0			0
$628$	10.0019	+	1.43806i	0.399119	+	0.0573847i
$629$	1.52030	+	5.17766i	0.0606182	+	0.206447i
$630$		0			0
$631$	−10.8911	+	1.56591i	−0.433569	+	0.0623379i	−0.355644	−	0.934621i	$-0.615739\pi$
$631$	−10.8911	+	1.56591i	−0.433569	+	0.0623379i	−0.0779250	+	0.996959i	$0.524829\pi$
$632$	−4.10595	−	8.99077i	−0.163326	−	0.357634i
$633$		0			0
$634$	−1.31421	−	9.14052i	−0.0521939	−	0.363016i
$635$	−42.9713	−	27.6160i	−1.70526	−	1.09591i
$636$		0			0
$637$	−0.626886	+	4.36009i	−0.0248381	+	0.172753i
$638$	5.11123	−	5.89867i	0.202355	−	0.233531i
$639$		0			0
$640$	1.87410	−	1.62391i	0.0740801	−	0.0641908i
$641$	15.5465	+	4.56486i	0.614050	+	0.180301i	0.573945	−	0.818894i	$-0.305412\pi$
$641$	15.5465	+	4.56486i	0.614050	+	0.180301i	0.0401053	+	0.999195i	$0.487231\pi$
$642$		0			0
$643$			38.0723i			1.50142i	0.660630	+	0.750712i	$0.270289\pi$
$643$			38.0723i			1.50142i	−0.660630	+	0.750712i	$0.729711\pi$
$644$	−6.10898	+	12.4640i	−0.240727	+	0.491149i
$645$		0			0
$646$	0.106864	−	0.234000i	0.00420452	−	0.00920661i
$647$	−7.82346	+	26.6443i	−0.307572	+	1.04749i	0.650152	+	0.759805i	$0.274705\pi$
$647$	−7.82346	+	26.6443i	−0.307572	+	1.04749i	−0.957724	+	0.287690i	$0.907113\pi$
$648$		0			0
$649$	0.627869	+	0.976983i	0.0246460	+	0.0383499i
$650$	2.77868	+	2.40774i	0.108989	+	0.0944395i
$651$		0			0
$652$	−6.05860	+	1.77896i	−0.237273	+	0.0696696i
$653$	−13.1640	+	20.4835i	−0.515146	+	0.801582i	−0.997217	−	0.0745495i	$-0.976248\pi$
$653$	−13.1640	+	20.4835i	−0.515146	+	0.801582i	0.482072	+	0.876132i	$0.339884\pi$
$654$		0			0
$655$	−32.0930	+	14.6564i	−1.25398	+	0.572672i
$656$	−5.34542	+	2.44117i	−0.208704	+	0.0953118i
$657$		0			0
$658$	8.18056	−	12.7292i	0.318912	−	0.496236i
$659$	−24.3741	+	7.15688i	−0.949479	+	0.278792i	−0.719570	−	0.694420i	$-0.755661\pi$
$659$	−24.3741	+	7.15688i	−0.949479	+	0.278792i	−0.229909	+	0.973212i	$0.573843\pi$
$660$		0			0
$661$	−5.53578	−	4.79678i	−0.215317	−	0.186573i	0.540524	−	0.841329i	$-0.318226\pi$
$661$	−5.53578	−	4.79678i	−0.215317	−	0.186573i	−0.755841	+	0.654756i	$0.772772\pi$
$662$	7.12499	+	11.0867i	0.276921	+	0.430897i
$663$		0			0
$664$	−1.77476	+	6.04427i	−0.0688740	+	0.234563i
$665$	0.960756	−	2.10376i	0.0372565	−	0.0815804i
$666$		0			0
$667$	5.57046	−	32.4274i	0.215689	−	1.25559i
$668$		−	1.71455i		−	0.0663380i
$669$		0			0
$670$	29.6205	+	8.69737i	1.14434	+	0.336009i
$671$	3.89283	−	3.37316i	0.150281	−	0.130219i
$672$		0			0
$673$	−17.9276	+	20.6895i	−0.691058	+	0.797523i	−0.987515	−	0.157523i	$-0.949649\pi$
$673$	−17.9276	+	20.6895i	−0.691058	+	0.797523i	0.296457	+	0.955046i	$0.404195\pi$
$674$	3.83864	−	26.6983i	0.147859	−	1.02838i
$675$		0			0
$676$	2.32708	+	1.49552i	0.0895030	+	0.0575201i
$677$	5.40734	+	37.6089i	0.207821	+	1.44543i	0.780247	+	0.625471i	$0.215093\pi$
$677$	5.40734	+	37.6089i	0.207821	+	1.44543i	−0.572426	+	0.819956i	$0.693998\pi$
$678$		0			0
$679$	4.06720	+	8.90592i	0.156085	+	0.341778i
$680$	1.95951	−	0.281735i	0.0751436	−	0.0108040i
$681$		0			0
$682$	1.36808	+	4.65927i	0.0523867	+	0.178413i
$683$	8.75098	+	1.25820i	0.334847	+	0.0481437i	0.307688	−	0.951487i	$-0.400445\pi$
$683$	8.75098	+	1.25820i	0.334847	+	0.0481437i	0.0271593	+	0.999631i	$0.491354\pi$
$684$		0			0
$685$	−16.2617	+	10.4508i	−0.621328	+	0.399303i
$686$	−10.6577	−	12.2996i	−0.406913	−	0.469603i
$687$		0			0
$688$	9.05377	+	4.13472i	0.345172	+	0.157635i
$689$	41.6355			1.58619
$690$		0			0
$691$	13.5269			0.514586			0.257293	−	0.966333i	$-0.417169\pi$
$691$	13.5269			0.514586			0.257293	+	0.966333i	$0.417169\pi$
$692$	−11.9662	−	5.46476i	−0.454885	−	0.207739i
$693$		0			0
$694$	19.2220	+	22.1834i	0.729659	+	0.842071i
$695$	37.3600	−	24.0098i	1.41715	−	0.910745i
$696$		0			0
$697$	−4.64354	−	0.667641i	−0.175887	−	0.0252887i
$698$	−4.20479	−	14.3202i	−0.159153	−	0.542027i
$699$		0			0
$700$	3.29263	−	0.473409i	0.124450	−	0.0178932i
$701$	12.1056	+	26.5076i	0.457222	+	1.00118i	0.988112	+	0.153736i	$0.0491304\pi$
$701$	12.1056	+	26.5076i	0.457222	+	1.00118i	−0.530890	+	0.847441i	$0.678142\pi$
$702$		0			0
$703$	0.309984	+	2.15599i	0.0116913	+	0.0813146i
$704$	−0.957061	−	0.615066i	−0.0360706	−	0.0231812i
$705$		0			0
$706$	4.82765	−	33.5771i	0.181691	−	1.26369i
$707$	22.3302	−	25.7704i	0.839812	−	0.969195i
$708$		0			0
$709$	14.6795	−	12.7199i	0.551302	−	0.477706i	−0.334096	−	0.942539i	$-0.608431\pi$
$709$	14.6795	−	12.7199i	0.551302	−	0.477706i	0.885398	+	0.464833i	$0.153886\pi$
$710$	0.779275	+	0.228816i	0.0292457	+	0.00858731i
$711$		0			0
$712$			2.55708i			0.0958307i
$713$	15.0985	+	13.8229i	0.565444	+	0.517672i
$714$		0			0
$715$	3.74910	−	8.20939i	0.140208	−	0.307014i
$716$	−2.22782	+	7.58725i	−0.0832575	+	0.283549i
$717$		0			0
$718$	−11.9163	−	18.5421i	−0.444711	−	0.691984i
$719$	−26.8270	−	23.2457i	−1.00048	−	0.866919i	−0.00936641	−	0.999956i	$-0.502981\pi$
$719$	−26.8270	−	23.2457i	−1.00048	−	0.866919i	−0.991111	+	0.133038i	$0.957527\pi$
$720$		0			0
$721$	−43.0075	+	12.6281i	−1.60168	+	0.470297i
$722$	−10.2160	+	15.8965i	−0.380202	+	0.591605i
$723$		0			0
$724$	−15.2893	+	6.98241i	−0.568224	+	0.259499i
$725$	−7.17252	+	3.27558i	−0.266381	+	0.121652i
$726$		0			0
$727$	−6.58295	+	10.2433i	−0.244148	+	0.379902i	−0.941602	−	0.336728i	$-0.890680\pi$
$727$	−6.58295	+	10.2433i	−0.244148	+	0.379902i	0.697454	+	0.716630i	$0.254316\pi$
$728$	−8.88389	+	2.60855i	−0.329259	+	0.0966792i
$729$		0			0
$730$	−31.0320	−	26.8894i	−1.14855	−	0.995222i
$731$	4.29585	+	6.68447i	0.158888	+	0.247234i
$732$		0			0
$733$	−2.92987	+	9.97823i	−0.108217	+	0.368554i	−0.995740	−	0.0922107i	$-0.970607\pi$
$733$	−2.92987	+	9.97823i	−0.108217	+	0.368554i	0.887522	+	0.460765i	$0.152425\pi$
$734$	8.79483	−	19.2580i	0.324623	−	0.710826i
$735$		0			0
$736$	−4.79404	−	0.131018i	−0.176711	−	0.00482937i
$737$		−	14.1628i		−	0.521695i
$738$		0			0
$739$	−2.75994	−	0.810391i	−0.101526	−	0.0298107i	0.230575	−	0.973055i	$-0.425939\pi$
$739$	−2.75994	−	0.810391i	−0.101526	−	0.0298107i	−0.332101	+	0.943244i	$0.607757\pi$
$740$	−12.6680	+	10.9769i	−0.465684	+	0.403517i
$741$		0			0
$742$	24.6682	−	28.4686i	0.905598	−	1.04512i
$743$	−3.29841	+	22.9410i	−0.121007	+	0.841622i	0.835412	+	0.549624i	$0.185229\pi$
$743$	−3.29841	+	22.9410i	−0.121007	+	0.841622i	−0.956419	+	0.291998i	$0.905680\pi$
$744$		0			0
$745$	−33.8472	−	21.7522i	−1.24006	−	0.796941i
$746$	−1.57763	−	10.9727i	−0.0577611	−	0.401737i
$747$		0			0
$748$	−0.377286	−	0.826142i	−0.0137950	−	0.0302067i
$749$	−20.6656	+	2.97126i	−0.755103	+	0.108567i
$750$		0			0
$751$	10.4854	+	35.7099i	0.382617	+	1.30307i	0.895671	+	0.444717i	$0.146696\pi$
$751$	10.4854	+	35.7099i	0.382617	+	1.30307i	−0.513055	+	0.858356i	$0.671486\pi$
$752$	5.17474	+	0.744015i	0.188703	+	0.0271314i
$753$		0			0
$754$	18.4633	−	11.8656i	0.672393	−	0.432120i
$755$	16.0319	+	18.5018i	0.583461	+	0.673350i
$756$		0			0
$757$	−21.9929	−	10.0438i	−0.799345	−	0.365049i	−0.0265043	−	0.999649i	$-0.508438\pi$
$757$	−21.9929	−	10.0438i	−0.799345	−	0.365049i	−0.772841	+	0.634600i	$0.781165\pi$
$758$	19.5505			0.710108
$759$		0			0
$760$	0.799076			0.0289855
$761$	23.6934	+	10.8204i	0.858885	+	0.392240i	0.795648	−	0.605759i	$-0.207130\pi$
$761$	23.6934	+	10.8204i	0.858885	+	0.392240i	0.0632370	+	0.997999i	$0.479858\pi$
$762$		0			0
$763$	−11.7275	−	13.5343i	−0.424564	−	0.489973i
$764$	−3.88439	+	2.49635i	−0.140532	+	0.0903147i
$765$		0			0
$766$	−23.4609	−	3.37317i	−0.847677	−	0.121878i
$767$	0.920031	+	3.13334i	0.0332204	+	0.113138i
$768$		0			0
$769$	−8.28594	+	1.19134i	−0.298799	+	0.0429608i	−0.290084	−	0.957001i	$-0.593683\pi$
$769$	−8.28594	+	1.19134i	−0.298799	+	0.0429608i	−0.00871495	+	0.999962i	$0.502774\pi$
$770$	−3.39197	−	7.42738i	−0.122238	−	0.267664i
$771$		0			0
$772$	0.683299	+	4.75245i	0.0245925	+	0.171044i
$773$	−35.3548	−	22.7212i	−1.27162	−	0.817223i	−0.281794	−	0.959475i	$-0.590929\pi$
$773$	−35.3548	−	22.7212i	−1.27162	−	0.817223i	−0.989831	+	0.142252i	$0.954566\pi$
$774$		0			0
$775$	0.698162	−	4.85582i	0.0250787	−	0.174426i
$776$	−2.21523	+	2.55651i	−0.0795221	+	0.0917734i
$777$		0			0
$778$	2.79596	−	2.42271i	0.100240	−	0.0868585i
$779$	−1.81691	−	0.533492i	−0.0650974	−	0.0191143i
$780$		0			0
$781$		−	0.372605i		−	0.0133328i
$782$	−3.16307	−	2.15712i	−0.113111	−	0.0771383i
$783$		0			0
$784$	−0.572008	+	1.25252i	−0.0204289	+	0.0447329i
$785$	−7.05954	+	24.0426i	−0.251966	+	0.858117i
$786$		0			0
$787$	28.3464	+	44.1079i	1.01044	+	1.57228i	0.804711	+	0.593666i	$0.202320\pi$
$787$	28.3464	+	44.1079i	1.01044	+	1.57228i	0.205729	+	0.978609i	$0.434044\pi$
$788$	−8.44009	−	7.31338i	−0.300666	−	0.260528i
$789$		0			0
$790$	23.5173	−	6.90529i	0.836707	−	0.245679i
$791$	24.0692	−	37.4524i	0.855803	−	1.33166i
$792$		0			0
$793$	13.1753	−	6.01694i	0.467867	−	0.213668i
$794$	27.7323	−	12.6649i	0.984183	−	0.449461i
$795$		0			0
$796$	9.81502	−	15.2725i	0.347884	−	0.541318i
$797$	−37.8287	+	11.1075i	−1.33996	+	0.393449i	−0.871656	−	0.490118i	$-0.836954\pi$
$797$	−37.8287	+	11.1075i	−1.33996	+	0.393449i	−0.468306	+	0.883566i	$0.655136\pi$
$798$		0			0
$799$	3.15417	+	2.73311i	0.111587	+	0.0966903i
$800$	0.621372	+	0.966874i	0.0219688	+	0.0341841i
$801$		0			0
$802$	4.81103	−	16.3849i	0.169884	−	0.578570i
$803$	−7.82553	+	17.1355i	−0.276157	+	0.604699i
$804$		0			0
$805$	−28.4374	−	19.3934i	−1.00229	−	0.683528i
$806$			13.6547i			0.480966i
$807$		0			0
$808$	11.3042	+	3.31923i	0.397682	+	0.116770i
$809$	−5.29528	+	4.58839i	−0.186172	+	0.161319i	−0.742960	−	0.669335i	$-0.766579\pi$
$809$	−5.29528	+	4.58839i	−0.186172	+	0.161319i	0.556788	+	0.830655i	$0.312034\pi$
$810$		0			0
$811$	2.40680	−	2.77759i	0.0845141	−	0.0975345i	−0.711917	−	0.702263i	$-0.752173\pi$
$811$	2.40680	−	2.77759i	0.0845141	−	0.0975345i	0.796432	+	0.604729i	$0.206718\pi$
$812$	2.82590	−	19.6546i	0.0991696	−	0.689740i
$813$		0			0
$814$	6.46927	+	4.15755i	0.226748	+	0.145722i
$815$	−2.22841	−	15.4989i	−0.0780576	−	0.542903i
$816$		0			0
$817$	1.33236	+	2.91745i	0.0466132	+	0.102069i
$818$	−21.8290	+	3.13853i	−0.763232	+	0.109736i
$819$		0			0
$820$	−4.10551	−	13.9821i	−0.143371	−	0.488276i
$821$	19.3902	+	2.78790i	0.676724	+	0.0972982i	0.472104	−	0.881543i	$-0.343495\pi$
$821$	19.3902	+	2.78790i	0.676724	+	0.0972982i	0.204621	+	0.978841i	$0.434404\pi$
$822$		0			0
$823$	5.30214	−	3.40748i	0.184821	−	0.118777i	−0.444959	−	0.895551i	$-0.646782\pi$
$823$	5.30214	−	3.40748i	0.184821	−	0.118777i	0.629780	+	0.776774i	$0.283145\pi$
$824$	−10.1416	−	11.7041i	−0.353301	−	0.407731i
$825$		0			0
$826$	2.68755	+	1.22736i	0.0935117	+	0.0427054i
$827$	−8.82393			−0.306838			−0.153419	−	0.988161i	$-0.549028\pi$
$827$	−8.82393			−0.306838			−0.153419	+	0.988161i	$0.549028\pi$
$828$		0			0
$829$	−40.4237			−1.40397			−0.701986	−	0.712191i	$-0.747703\pi$
$829$	−40.4237			−1.40397			−0.701986	+	0.712191i	$0.747703\pi$
$830$	−14.2096	−	6.48930i	−0.493222	−	0.225247i
$831$		0			0
$832$	−2.09492	−	2.41767i	−0.0726283	−	0.0838175i
$833$	−0.924747	+	0.594299i	−0.0320406	+	0.0205912i
$834$		0			0
$835$	4.20844	+	0.605082i	0.145639	+	0.0209397i
$836$	−0.103282	−	0.351746i	−0.00357208	−	0.0121654i
$837$		0			0
$838$	5.80573	−	0.834739i	0.200556	−	0.0288356i
$839$	−6.61383	−	14.4823i	−0.228335	−	0.499983i	0.760438	−	0.649410i	$-0.224984\pi$
$839$	−6.61383	−	14.4823i	−0.228335	−	0.499983i	−0.988773	+	0.149427i	$0.952257\pi$
$840$		0			0
$841$	2.57136	+	17.8842i	0.0886674	+	0.616696i
$842$	27.4951	+	17.6700i	0.947544	+	0.608949i
$843$		0			0
$844$	−0.442086	+	3.07478i	−0.0152172	+	0.105838i
$845$	−4.49207	+	5.18412i	−0.154532	+	0.178339i
$846$		0			0
$847$	21.2300	−	18.3959i	0.729470	−	0.632089i
$848$	12.4878	+	3.66676i	0.428834	+	0.125917i
$849$		0			0
$850$			0.917527i			0.0314709i
$851$	32.4054	+	0.885615i	1.11084	+	0.0303585i
$852$		0			0
$853$	14.9303	−	32.6928i	0.511204	−	1.11938i	−0.461459	−	0.887161i	$-0.652674\pi$
$853$	14.9303	−	32.6928i	0.511204	−	1.11938i	0.972663	−	0.232220i	$-0.0745988\pi$
$854$	3.69194	−	12.5736i	0.126336	−	0.430260i
$855$		0			0
$856$	−3.89992	−	6.06840i	−0.133297	−	0.207414i
$857$	−34.1758	−	29.6135i	−1.16742	−	1.01158i	−0.999668	−	0.0257481i	$-0.991803\pi$
$857$	−34.1758	−	29.6135i	−1.16742	−	1.01158i	−0.167754	−	0.985829i	$-0.553651\pi$
$858$		0			0
$859$	3.10935	−	0.912987i	0.106090	−	0.0311507i	−0.228257	−	0.973601i	$-0.573303\pi$
$859$	3.10935	−	0.912987i	0.106090	−	0.0311507i	0.334346	+	0.942450i	$0.391484\pi$
$860$	−13.3440	+	20.7637i	−0.455027	+	0.708036i
$861$		0			0
$862$	−23.4510	+	10.7097i	−0.798744	+	0.364774i
$863$	17.7932	−	8.12590i	0.605689	−	0.276609i	−0.0888717	−	0.996043i	$-0.528326\pi$
$863$	17.7932	−	8.12590i	0.605689	−	0.276609i	0.694561	+	0.719434i	$0.255599\pi$
$864$		0			0
$865$	17.6365	−	27.4429i	0.599658	−	0.933086i
$866$	11.6963	−	3.43435i	0.397457	−	0.116704i
$867$		0			0
$868$	9.33650	+	8.09012i	0.316901	+	0.274597i
$869$	−6.07929	−	9.45956i	−0.206226	−	0.320894i
$870$		0			0
$871$	11.2200	−	38.2118i	0.380175	−	1.29476i
$872$	2.57037	−	5.62833i	0.0870437	−	0.190599i
$873$		0			0
$874$	−1.13984	−	1.04354i	−0.0385558	−	0.0352984i
$875$		−	27.6372i		−	0.934307i
$876$		0			0
$877$	−22.4469	−	6.59101i	−0.757978	−	0.222562i	−0.120165	−	0.992754i	$-0.538342\pi$
$877$	−22.4469	−	6.59101i	−0.757978	−	0.222562i	−0.637813	+	0.770191i	$0.720161\pi$
$878$	24.2899	−	21.0473i	0.819745	−	0.710313i
$879$		0			0
$880$	1.84746	−	2.13209i	0.0622779	−	0.0718726i
$881$	0.652920	−	4.54116i	0.0219974	−	0.152995i	−0.975862	−	0.218387i	$-0.929921\pi$
$881$	0.652920	−	4.54116i	0.0219974	−	0.152995i	0.997860	+	0.0653915i	$0.0208296\pi$
$882$		0			0
$883$	−37.7867	−	24.2841i	−1.27162	−	0.817224i	−0.281794	−	0.959475i	$-0.590929\pi$
$883$	−37.7867	−	24.2841i	−1.27162	−	0.817224i	−0.989831	+	0.142251i	$0.954566\pi$
$884$	−0.363450	−	2.52785i	−0.0122241	−	0.0850208i
$885$		0			0
$886$	−13.9452	−	30.5357i	−0.468498	−	1.02587i
$887$	−17.0744	+	2.45493i	−0.573302	+	0.0824283i	−0.422867	−	0.906192i	$-0.638976\pi$
$887$	−17.0744	+	2.45493i	−0.573302	+	0.0824283i	−0.150434	+	0.988620i	$0.548067\pi$
$888$		0			0
$889$	16.7965	+	57.2035i	0.563335	+	1.91854i
$890$	−6.27646	−	0.902419i	−0.210388	−	0.0302492i
$891$		0			0
$892$	−16.5096	+	10.6101i	−0.552781	+	0.355251i
$893$	1.10320	+	1.27316i	0.0369172	+	0.0426047i
$894$		0			0
$895$	−17.8370	−	8.14589i	−0.596226	−	0.272287i
$896$	−2.89430			−0.0966917
$897$		0			0
$898$	−5.05824			−0.168796
$899$	−26.6374	−	12.1649i	−0.888408	−	0.405722i
$900$		0			0
$901$	6.80410	+	7.85234i	0.226677	+	0.261600i
$902$	−5.62414	+	3.61442i	−0.187263	+	0.120347i
$903$		0			0
$904$	15.2253	+	2.18907i	0.506387	+	0.0728075i
$905$	−11.7429	−	39.9925i	−0.390346	−	1.32940i
$906$		0			0
$907$	−38.5453	+	5.54198i	−1.27988	+	0.184018i	−0.748510	−	0.663124i	$-0.769230\pi$
$907$	−38.5453	+	5.54198i	−1.27988	+	0.184018i	−0.531366	+	0.847142i	$0.678321\pi$
$908$	−1.40427	−	3.07492i	−0.0466023	−	0.102045i
$909$		0			0
$910$	−3.26757	−	22.7265i	−0.108319	−	0.753375i
$911$	12.1095	+	7.78228i	0.401205	+	0.257839i	0.725647	−	0.688067i	$-0.241540\pi$
$911$	12.1095	+	7.78228i	0.401205	+	0.257839i	−0.324443	+	0.945905i	$0.605177\pi$
$912$		0			0
$913$	−1.01992	+	7.09368i	−0.0337544	+	0.234767i
$914$	12.4296	−	14.3446i	0.411136	−	0.474476i
$915$		0			0
$916$	−1.61697	+	1.40111i	−0.0534262	+	0.0462941i
$917$	39.5108	+	11.6014i	1.30476	+	0.383112i
$918$		0			0
$919$		−	36.2635i		−	1.19622i	−0.801413	−	0.598111i	$-0.795918\pi$
$919$		−	36.2635i		−	1.19622i	0.801413	−	0.598111i	$-0.204082\pi$
$920$	2.01345	−	11.7209i	0.0663816	−	0.386428i
$921$		0			0
$922$	−13.7069	+	30.0140i	−0.451413	+	0.988457i
$923$	0.295183	−	1.00530i	0.00971606	−	0.0330898i
$924$		0			0
$925$	−4.20017	−	6.53559i	−0.138101	−	0.214889i
$926$	−25.1944	−	21.8310i	−0.827938	−	0.717412i
$927$		0			0
$928$	6.58271	−	1.93286i	0.216088	−	0.0634492i
$929$	22.9891	−	35.7717i	0.754247	−	1.17363i	−0.225666	−	0.974205i	$-0.572456\pi$
$929$	22.9891	−	35.7717i	0.754247	−	1.17363i	0.979913	−	0.199426i	$-0.0639078\pi$
$930$		0			0
$931$	−0.403608	+	0.184322i	−0.0132277	+	0.00604089i
$932$	20.6547	−	9.43270i	0.676568	−	0.308978i
$933$		0			0
$934$	−7.13197	+	11.0976i	−0.233365	+	0.363123i
$935$	2.16095	−	0.634512i	0.0706706	−	0.0207508i
$936$		0			0
$937$	3.90051	+	3.37981i	0.127424	+	0.110413i	0.716242	−	0.697852i	$-0.245861\pi$
$937$	3.90051	+	3.37981i	0.127424	+	0.110413i	−0.588818	+	0.808266i	$0.700406\pi$
$938$	−19.4800	−	30.3115i	−0.636045	−	0.989705i
$939$		0			0
$940$	−3.65243	+	12.4390i	−0.119129	+	0.405717i
$941$	14.8781	−	32.5784i	0.485011	−	1.06203i	−0.496044	−	0.868297i	$-0.665215\pi$
$941$	14.8781	−	32.5784i	0.485011	−	1.06203i	0.981055	−	0.193728i	$-0.0620581\pi$
$942$		0			0
$943$	−12.4034	+	25.3063i	−0.403911	+	0.824088i
$944$			1.02082i			0.0332247i
$945$		0			0
$946$	10.8647	+	3.19017i	0.353243	+	0.103721i
$947$	22.1060	−	19.1550i	0.718349	−	0.622453i	−0.217003	−	0.976171i	$-0.569628\pi$
$947$	22.1060	−	19.1550i	0.718349	−	0.622453i	0.935352	+	0.353718i	$0.115083\pi$
$948$		0			0
$949$	−34.6885	+	40.0327i	−1.12604	+	1.29952i
$950$	−0.0527069	+	0.366584i	−0.00171004	+	0.0118936i
$951$		0			0
$952$	−1.94378	−	1.24919i	−0.0629981	−	0.0404864i
$953$	−0.964103	−	6.70548i	−0.0312304	−	0.217212i	0.968230	−	0.250062i	$-0.0804509\pi$
$953$	−0.964103	−	6.70548i	−0.0312304	−	0.217212i	−0.999460	+	0.0328496i	$0.989542\pi$
$954$		0			0
$955$	−4.75655	−	10.4154i	−0.153918	−	0.337034i
$956$	−12.5003	+	1.79728i	−0.404290	+	0.0581281i
$957$		0			0
$958$	−0.0273019	−	0.0929817i	−0.000882084	−	0.00300410i
$959$	22.3319	+	3.21084i	0.721134	+	0.103683i
$960$		0			0
$961$	−10.7520	+	6.90989i	−0.346839	+	0.222900i
$962$	14.1606	+	16.3422i	0.456557	+	0.526895i
$963$		0			0
$964$	2.46308	+	1.12485i	0.0793305	+	0.0362290i
$965$	−11.9062			−0.383275
$966$		0			0
$967$	14.5890			0.469150			0.234575	−	0.972098i	$-0.424630\pi$
$967$	14.5890			0.469150			0.234575	+	0.972098i	$0.424630\pi$
$968$	8.82864	+	4.03190i	0.283763	+	0.129590i
$969$		0			0
$970$	−5.49329	−	6.33960i	−0.176379	−	0.203552i
$971$	−50.5770	+	32.5039i	−1.62309	+	1.04310i	−0.669145	+	0.743132i	$0.733340\pi$
$971$	−50.5770	+	32.5039i	−1.62309	+	1.04310i	−0.953949	+	0.299968i	$0.903024\pi$
$972$		0			0
$973$	−51.3058	−	7.37666i	−1.64479	−	0.236485i
$974$	1.85147	+	6.30552i	0.0593249	+	0.202042i
$975$		0			0
$976$	4.48159	−	0.644355i	0.143452	−	0.0206253i
$977$	3.39453	+	7.43298i	0.108601	+	0.237802i	0.956128	−	0.292950i	$-0.0946369\pi$
$977$	3.39453	+	7.43298i	0.108601	+	0.237802i	−0.847527	+	0.530752i	$0.821910\pi$
$978$		0			0
$979$	0.414007	+	2.87948i	0.0132317	+	0.0920286i
$980$	−2.87250	−	1.84605i	−0.0917587	−	0.0589698i
$981$		0			0
$982$	−4.87780	+	33.9258i	−0.155657	+	1.08262i
$983$	29.1719	−	33.6662i	0.930439	−	1.07378i	−0.0666684	−	0.997775i	$-0.521237\pi$
$983$	29.1719	−	33.6662i	0.930439	−	1.07378i	0.997107	−	0.0760084i	$-0.0242176\pi$
$984$		0			0
$985$	20.9296	−	18.1356i	0.666872	−	0.577848i
$986$	5.25510	+	1.54304i	0.167357	+	0.0491403i
$987$		0			0
$988$		−	1.03084i		−	0.0327955i
$989$	46.1507	−	12.1920i	1.46751	−	0.387682i
$990$		0			0
$991$	−8.27760	+	18.1254i	−0.262947	+	0.575773i	−0.994347	−	0.106175i	$-0.966140\pi$
$991$	−8.27760	+	18.1254i	−0.262947	+	0.575773i	0.731401	+	0.681948i	$0.238867\pi$
$992$	−1.20254	+	4.09548i	−0.0381807	+	0.130032i
$993$		0			0
$994$	−0.512492	−	0.797454i	−0.0162553	−	0.0252937i
$995$	34.0231	+	29.4812i	1.07861	+	0.934617i
$996$		0			0
$997$	−16.6396	+	4.88583i	−0.526982	+	0.154736i	−0.534392	−	0.845237i	$-0.679459\pi$
$997$	−16.6396	+	4.88583i	−0.526982	+	0.154736i	0.00741012	+	0.999973i	$0.497641\pi$
$998$	−2.75587	+	4.28822i	−0.0872356	+	0.135741i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.17.6	yes	80
3.2	odd	2	inner	414.2.j.a.17.3	✓	80
23.19	odd	22	inner	414.2.j.a.341.3	yes	80
69.65	even	22	inner	414.2.j.a.341.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.17.3	✓	80	3.2	odd	2	inner
414.2.j.a.17.6	yes	80	1.1	even	1	trivial
414.2.j.a.341.3	yes	80	23.19	odd	22	inner
414.2.j.a.341.6	yes	80	69.65	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.08613 + 1.34067i) q^{5} +(2.86484 + 0.411901i) q^{7} +(0.281733 + 0.959493i) q^{8} +O(q^{10})\)	\(q+(0.909632 + 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.08613 + 1.34067i) q^{5} +(2.86484 + 0.411901i) q^{7} +(0.281733 + 0.959493i) q^{8} +(-2.45454 + 0.352910i) q^{10} +(0.472602 + 1.03485i) q^{11} +(0.455270 + 3.16647i) q^{13} +(2.43484 + 1.56478i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(-0.522787 + 0.603329i) q^{17} +(-0.243530 + 0.211020i) q^{19} +(-2.37933 - 0.698636i) q^{20} +1.13766i q^{22} +(2.48164 + 4.10384i) q^{23} +(0.477447 - 1.04546i) q^{25} +(-0.901271 + 3.06945i) q^{26} +(1.56478 + 2.43484i) q^{28} +(-5.18491 - 4.49275i) q^{29} +(4.09548 - 1.20254i) q^{31} +(-0.540641 + 0.841254i) q^{32} +(-0.726176 + 0.331633i) q^{34} +(-6.52864 + 2.98153i) q^{35} +(3.65447 - 5.68646i) q^{37} +(-0.309183 + 0.0907844i) q^{38} +(-1.87410 - 1.62391i) q^{40} +(3.17706 + 4.94360i) q^{41} +(2.80415 - 9.55005i) q^{43} +(-0.472602 + 1.03485i) q^{44} +(0.552579 + 4.76389i) q^{46} -5.22795i q^{47} +(1.32118 + 0.387933i) q^{49} +(0.868602 - 0.752648i) q^{50} +(-2.09492 + 2.41767i) q^{52} +(1.85223 - 12.8826i) q^{53} +(-2.37330 - 1.52523i) q^{55} +(0.411901 + 2.86484i) q^{56} +(-2.85000 - 6.24064i) q^{58} +(1.01042 - 0.145277i) q^{59} +(-1.27559 - 4.34427i) q^{61} +(4.22493 + 0.607454i) q^{62} +(-0.841254 + 0.540641i) q^{64} +(-5.19495 - 5.99529i) q^{65} +(-11.3241 - 5.17154i) q^{67} -0.798318 q^{68} -7.17723 q^{70} +(-0.297921 - 0.136056i) q^{71} +(10.8435 + 12.5140i) q^{73} +(5.68646 - 3.65447i) q^{74} +(-0.318956 - 0.0458590i) q^{76} +(0.927669 + 3.15935i) q^{77} +(-9.78336 + 1.40663i) q^{79} +(-1.03014 - 2.25569i) q^{80} +(0.836309 + 5.81665i) q^{82} +(5.29943 + 3.40574i) q^{83} +(0.281735 - 1.95951i) q^{85} +(6.51798 - 7.52215i) q^{86} +(-0.859787 + 0.745010i) q^{88} +(2.45350 + 0.720413i) q^{89} +9.25895i q^{91} +(-1.47635 + 4.56294i) q^{92} +(2.17177 - 4.75551i) q^{94} +(0.225126 - 0.766707i) q^{95} +(1.82885 + 2.84575i) q^{97} +(1.04063 + 0.901714i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 80 * q + 8 * q^4	\( 80 q + 8 q^{4} - 16 q^{13} - 8 q^{16} + 24 q^{25} - 16 q^{31} + 88 q^{37} + 88 q^{43} + 8 q^{46} + 8 q^{49} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 176 q^{61} + 8 q^{64} - 88 q^{67} - 176 q^{70} - 56 q^{73} - 176 q^{79} - 88 q^{82} - 88 q^{85} + 16 q^{94}+O(q^{100}) \) 80 * q + 8 * q^4 - 16 * q^13 - 8 * q^16 + 24 * q^25 - 16 * q^31 + 88 * q^37 + 88 * q^43 + 8 * q^46 + 8 * q^49 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 176 * q^61 + 8 * q^64 - 88 * q^67 - 176 * q^70 - 56 * q^73 - 176 * q^79 - 88 * q^82 - 88 * q^85 + 16 * q^94

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