LMFDB - Embedded newform 414.2.j.a.17.1

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			17.1
Character	$\chi$	$=$	414.17
Dual form			414.2.j.a.341.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 - 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.75649 + 1.77149i) q^{5} +(-0.318197 - 0.0457498i) q^{7} +(-0.281733 - 0.959493i) q^{8} +O(q^{10})$	\(q+(-0.909632 - 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.75649 + 1.77149i) q^{5} +(-0.318197 - 0.0457498i) q^{7} +(-0.281733 - 0.959493i) q^{8} +(3.24329 - 0.466315i) q^{10} +(-0.811936 - 1.77789i) q^{11} +(-0.644154 - 4.48019i) q^{13} +(0.270437 + 0.173799i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(2.26722 - 2.61651i) q^{17} +(3.36493 - 2.91573i) q^{19} +(-3.14392 - 0.923137i) q^{20} +1.95452i q^{22} +(3.06858 - 3.68562i) q^{23} +(2.38298 - 5.21800i) q^{25} +(-1.27519 + 4.34291i) q^{26} +(-0.173799 - 0.270437i) q^{28} +(-5.05326 - 4.37867i) q^{29} +(-3.94021 + 1.15695i) q^{31} +(0.540641 - 0.841254i) q^{32} +(-3.14928 + 1.43823i) q^{34} +(0.958152 - 0.437573i) q^{35} +(0.995438 - 1.54893i) q^{37} +(-4.27209 + 1.25440i) q^{38} +(2.47632 + 2.14575i) q^{40} +(3.85817 + 6.00342i) q^{41} +(-2.34960 + 8.00199i) q^{43} +(0.811936 - 1.77789i) q^{44} +(-4.32234 + 2.07783i) q^{46} -8.46378i q^{47} +(-6.61729 - 1.94301i) q^{49} +(-4.33528 + 3.75654i) q^{50} +(2.96407 - 3.42072i) q^{52} +(0.630586 - 4.38582i) q^{53} +(5.38760 + 3.46240i) q^{55} +(0.0457498 + 0.318197i) q^{56} +(2.77764 + 6.08218i) q^{58} +(-5.67429 + 0.815840i) q^{59} +(-4.21542 - 14.3564i) q^{61} +(4.06476 + 0.584424i) q^{62} +(-0.841254 + 0.540641i) q^{64} +(9.71220 + 11.2085i) q^{65} +(-4.44836 - 2.03150i) q^{67} +3.46214 q^{68} -1.05334 q^{70} +(-1.27416 - 0.581887i) q^{71} +(-0.0883754 - 0.101991i) q^{73} +(-1.54893 + 0.995438i) q^{74} +(4.40713 + 0.633649i) q^{76} +(0.177017 + 0.602866i) q^{77} +(-9.24966 + 1.32990i) q^{79} +(-1.36117 - 2.98054i) q^{80} +(-1.01560 - 7.06365i) q^{82} +(13.3662 + 8.58993i) q^{83} +(-1.61445 + 11.2287i) q^{85} +(5.46142 - 6.30281i) q^{86} +(-1.47713 + 1.27994i) q^{88} +(15.1548 + 4.44986i) q^{89} +1.45505i q^{91} +(4.79490 - 0.0944928i) q^{92} +(-3.51598 + 7.69893i) q^{94} +(-4.11022 + 13.9981i) q^{95} +(2.80333 + 4.36207i) q^{97} +(5.21215 + 4.51635i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.75649	+	1.77149i	−1.23274	+	0.792233i	−0.984315	−	0.176418i	$-0.943549\pi$
$5$	−2.75649	+	1.77149i	−1.23274	+	0.792233i	−0.248424	+	0.968652i	$0.579912\pi$
$6$		0			0
$7$	−0.318197	−	0.0457498i	−0.120267	−	0.0172918i	0.0819184	−	0.996639i	$-0.473895\pi$
$7$	−0.318197	−	0.0457498i	−0.120267	−	0.0172918i	−0.202186	+	0.979347i	$0.564804\pi$
$8$	−0.281733	−	0.959493i	−0.0996075	−	0.339232i
$9$		0			0
$10$	3.24329	−	0.466315i	1.02562	−	0.147462i
$11$	−0.811936	−	1.77789i	−0.244808	−	0.536054i	0.746844	−	0.664999i	$-0.231568\pi$
$11$	−0.811936	−	1.77789i	−0.244808	−	0.536054i	−0.991652	+	0.128945i	$0.958841\pi$
$12$		0			0
$13$	−0.644154	−	4.48019i	−0.178656	−	1.24258i	−0.859876	−	0.510502i	$-0.829460\pi$
$13$	−0.644154	−	4.48019i	−0.178656	−	1.24258i	0.681220	−	0.732078i	$-0.261450\pi$
$14$	0.270437	+	0.173799i	0.0722774	+	0.0464498i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	2.26722	−	2.61651i	0.549882	−	0.634598i	−0.410974	−	0.911647i	$-0.634811\pi$
$17$	2.26722	−	2.61651i	0.549882	−	0.634598i	0.960856	+	0.277050i	$0.0893567\pi$
$18$		0			0
$19$	3.36493	−	2.91573i	0.771969	−	0.668915i	−0.177026	−	0.984206i	$-0.556648\pi$
$19$	3.36493	−	2.91573i	0.771969	−	0.668915i	0.948995	+	0.315292i	$0.102102\pi$
$20$	−3.14392	−	0.923137i	−0.703001	−	0.206420i
$21$		0			0
$22$			1.95452i			0.416704i
$23$	3.06858	−	3.68562i	0.639843	−	0.768506i
$23$	3.06858	−	3.68562i	0.639843	−	0.768506i
$24$		0			0
$25$	2.38298	−	5.21800i	0.476597	−	1.04360i
$26$	−1.27519	+	4.34291i	−0.250086	+	0.851716i
$27$		0			0
$28$	−0.173799	−	0.270437i	−0.0328450	−	0.0511078i
$29$	−5.05326	−	4.37867i	−0.938366	−	0.813099i	0.0441982	−	0.999023i	$-0.485927\pi$
$29$	−5.05326	−	4.37867i	−0.938366	−	0.813099i	−0.982564	+	0.185924i	$0.940472\pi$
$30$		0			0
$31$	−3.94021	+	1.15695i	−0.707683	+	0.207795i	−0.615717	−	0.787968i	$-0.711133\pi$
$31$	−3.94021	+	1.15695i	−0.707683	+	0.207795i	−0.0919664	+	0.995762i	$0.529315\pi$
$32$	0.540641	−	0.841254i	0.0955727	−	0.148714i
$33$		0			0
$34$	−3.14928	+	1.43823i	−0.540096	+	0.246654i
$35$	0.958152	−	0.437573i	0.161957	−	0.0739634i
$36$		0			0
$37$	0.995438	−	1.54893i	0.163649	−	0.254643i	−0.749738	−	0.661734i	$-0.769821\pi$
$37$	0.995438	−	1.54893i	0.163649	−	0.254643i	0.913387	+	0.407092i	$0.133457\pi$
$38$	−4.27209	+	1.25440i	−0.693024	+	0.203490i
$39$		0			0
$40$	2.47632	+	2.14575i	0.391541	+	0.339272i
$41$	3.85817	+	6.00342i	0.602544	+	0.937577i	0.999803	+	0.0198703i	$0.00632533\pi$
$41$	3.85817	+	6.00342i	0.602544	+	0.937577i	−0.397258	+	0.917707i	$0.630038\pi$
$42$		0			0
$43$	−2.34960	+	8.00199i	−0.358310	+	1.22029i	0.561350	+	0.827578i	$0.310282\pi$
$43$	−2.34960	+	8.00199i	−0.358310	+	1.22029i	−0.919661	+	0.392714i	$0.871536\pi$
$44$	0.811936	−	1.77789i	0.122404	−	0.268027i
$45$		0			0
$46$	−4.32234	+	2.07783i	−0.637294	+	0.306359i
$47$		−	8.46378i		−	1.23457i	−0.786740	−	0.617285i	$-0.788233\pi$
$47$		−	8.46378i		−	1.23457i	0.786740	−	0.617285i	$-0.211767\pi$
$48$		0			0
$49$	−6.61729	−	1.94301i	−0.945328	−	0.277573i
$50$	−4.33528	+	3.75654i	−0.613100	+	0.531255i
$51$		0			0
$52$	2.96407	−	3.42072i	0.411042	−	0.474368i
$53$	0.630586	−	4.38582i	0.0866177	−	0.602439i	−0.899566	−	0.436785i	$-0.856117\pi$
$53$	0.630586	−	4.38582i	0.0866177	−	0.602439i	0.986184	−	0.165655i	$-0.0529737\pi$
$54$		0			0
$55$	5.38760	+	3.46240i	0.726464	+	0.466870i
$56$	0.0457498	+	0.318197i	0.00611358	+	0.0425209i
$57$		0			0
$58$	2.77764	+	6.08218i	0.364722	+	0.798629i
$59$	−5.67429	+	0.815840i	−0.738730	+	0.106213i	−0.501400	−	0.865216i	$-0.667181\pi$
$59$	−5.67429	+	0.815840i	−0.738730	+	0.106213i	−0.237330	+	0.971429i	$0.576272\pi$
$60$		0			0
$61$	−4.21542	−	14.3564i	−0.539729	−	1.83815i	−0.545417	−	0.838165i	$-0.683629\pi$
$61$	−4.21542	−	14.3564i	−0.539729	−	1.83815i	0.00568827	−	0.999984i	$-0.498189\pi$
$62$	4.06476	+	0.584424i	0.516225	+	0.0742219i
$63$		0			0
$64$	−0.841254	+	0.540641i	−0.105157	+	0.0675801i
$65$	9.71220	+	11.2085i	1.20465	+	1.39024i
$66$		0			0
$67$	−4.44836	−	2.03150i	−0.543454	−	0.248187i	0.124720	−	0.992192i	$-0.460197\pi$
$67$	−4.44836	−	2.03150i	−0.543454	−	0.248187i	−0.668174	+	0.744005i	$0.732924\pi$
$68$	3.46214			0.419846
$69$		0			0
$70$	−1.05334			−0.125898
$71$	−1.27416	−	0.581887i	−0.151214	−	0.0690573i	0.338370	−	0.941013i	$-0.390124\pi$
$71$	−1.27416	−	0.581887i	−0.151214	−	0.0690573i	−0.489585	+	0.871956i	$0.662852\pi$
$72$		0			0
$73$	−0.0883754	−	0.101991i	−0.0103436	−	0.0119371i	0.750554	−	0.660809i	$-0.229787\pi$
$73$	−0.0883754	−	0.101991i	−0.0103436	−	0.0119371i	−0.760898	+	0.648872i	$0.775241\pi$
$74$	−1.54893	+	0.995438i	−0.180060	+	0.115717i
$75$		0			0
$76$	4.40713	+	0.633649i	0.505532	+	0.0726845i
$77$	0.177017	+	0.602866i	0.0201730	+	0.0687029i
$78$		0			0
$79$	−9.24966	+	1.32990i	−1.04067	+	0.149626i	−0.641398	−	0.767208i	$-0.721645\pi$
$79$	−9.24966	+	1.32990i	−1.04067	+	0.149626i	−0.399270	+	0.916833i	$0.630736\pi$
$80$	−1.36117	−	2.98054i	−0.152183	−	0.333234i
$81$		0			0
$82$	−1.01560	−	7.06365i	−0.112154	−	0.780049i
$83$	13.3662	+	8.58993i	1.46713	+	0.942868i	0.998221	+	0.0596214i	$0.0189894\pi$
$83$	13.3662	+	8.58993i	1.46713	+	0.942868i	0.468910	+	0.883246i	$0.344647\pi$
$84$		0			0
$85$	−1.61445	+	11.2287i	−0.175112	+	1.21793i
$86$	5.46142	−	6.30281i	0.588920	−	0.679650i
$87$		0			0
$88$	−1.47713	+	1.27994i	−0.157462	+	0.136442i
$89$	15.1548	+	4.44986i	1.60641	+	0.471684i	0.957320	−	0.289030i	$-0.0933328\pi$
$89$	15.1548	+	4.44986i	1.60641	+	0.471684i	0.649087	+	0.760714i	$0.275151\pi$
$90$		0			0
$91$			1.45505i			0.152531i
$92$	4.79490	−	0.0944928i	0.499903	−	0.00985156i
$93$		0			0
$94$	−3.51598	+	7.69893i	−0.362646	+	0.794084i
$95$	−4.11022	+	13.9981i	−0.421699	+	1.43618i
$96$		0			0
$97$	2.80333	+	4.36207i	0.284635	+	0.442901i	0.953901	−	0.300122i	$-0.0970275\pi$
$97$	2.80333	+	4.36207i	0.284635	+	0.442901i	−0.669266	+	0.743023i	$0.733391\pi$
$98$	5.21215	+	4.51635i	0.526506	+	0.456220i
$99$		0			0
$100$	5.50403	−	1.61613i	0.550403	−	0.161613i
$101$	−2.10333	+	3.27284i	−0.209289	+	0.325660i	−0.929989	−	0.367587i	$-0.880184\pi$
$101$	−2.10333	+	3.27284i	−0.209289	+	0.325660i	0.720700	+	0.693247i	$0.243820\pi$
$102$		0			0
$103$	4.58486	−	2.09383i	0.451759	−	0.206312i	−0.176524	−	0.984296i	$-0.556485\pi$
$103$	4.58486	−	2.09383i	0.451759	−	0.206312i	0.628283	+	0.777985i	$0.283758\pi$
$104$	−4.11723	+	1.88028i	−0.403728	+	0.184376i
$105$		0			0
$106$	−2.39554	+	3.72753i	−0.232675	+	0.362050i
$107$	−7.05111	+	2.07039i	−0.681657	+	0.200152i	−0.604187	−	0.796842i	$-0.706502\pi$
$107$	−7.05111	+	2.07039i	−0.681657	+	0.200152i	−0.0774692	+	0.996995i	$0.524684\pi$
$108$		0			0
$109$	10.3050	+	8.92932i	0.987039	+	0.855274i	0.989472	−	0.144723i	$-0.0462291\pi$
$109$	10.3050	+	8.92932i	0.987039	+	0.855274i	−0.00243337	+	0.999997i	$0.500775\pi$
$110$	−3.46240	−	5.38760i	−0.330127	−	0.513688i
$111$		0			0
$112$	0.0905683	−	0.308447i	0.00855790	−	0.0291455i
$113$	2.28720	−	5.00827i	0.215162	−	0.471138i	−0.771019	−	0.636812i	$-0.780253\pi$
$113$	2.28720	−	5.00827i	0.215162	−	0.471138i	0.986181	+	0.165674i	$0.0529800\pi$
$114$		0			0
$115$	−1.92947	+	15.5953i	−0.179924	+	1.45427i
$116$		−	6.68641i		−	0.620818i
$117$		0			0
$118$	5.50043	+	1.61507i	0.506355	+	0.148679i
$119$	−0.841128	+	0.728842i	−0.0771061	+	0.0668128i
$120$		0			0
$121$	4.70181	−	5.42618i	0.427437	−	0.493289i
$122$	−2.12938	+	14.8102i	−0.192785	+	1.34085i
$123$		0			0
$124$	−3.45466	−	2.22017i	−0.310237	−	0.199377i
$125$	0.343390	+	2.38833i	0.0307138	+	0.213619i
$126$		0			0
$127$	0.966609	+	2.11658i	0.0857727	+	0.187816i	0.947658	−	0.319287i	$-0.103444\pi$
$127$	0.966609	+	2.11658i	0.0857727	+	0.187816i	−0.861885	+	0.507103i	$0.830716\pi$
$128$	0.989821	−	0.142315i	0.0874887	−	0.0125790i
$129$		0			0
$130$	−4.17836	−	14.2302i	−0.366466	−	1.24807i
$131$	−20.1124	−	2.89172i	−1.75722	−	0.252651i	−0.813073	−	0.582162i	$-0.802207\pi$
$131$	−20.1124	−	2.89172i	−1.75722	−	0.252651i	−0.944152	+	0.329511i	$0.893116\pi$
$132$		0			0
$133$	−1.20411	+	0.773832i	−0.104409	+	0.0670998i
$134$	3.20246	+	3.69583i	0.276650	+	0.319271i
$135$		0			0
$136$	−3.14928	−	1.43823i	−0.270048	−	0.123327i
$137$	4.47423			0.382259			0.191130	−	0.981565i	$-0.438785\pi$
$137$	4.47423			0.382259			0.191130	+	0.981565i	$0.438785\pi$
$138$		0			0
$139$	−20.3866			−1.72917			−0.864583	−	0.502490i	$-0.832417\pi$
$139$	−20.3866			−1.72917			−0.864583	+	0.502490i	$0.832417\pi$
$140$	0.958152	+	0.437573i	0.0809786	+	0.0369817i
$141$		0			0
$142$	0.917288	+	1.05861i	0.0769771	+	0.0888363i
$143$	−7.44228	+	4.78286i	−0.622354	+	0.399963i
$144$		0			0
$145$	21.6860	+	3.11798i	1.80092	+	0.258934i
$146$	0.0380206	+	0.129486i	0.00314661	+	0.0107164i
$147$		0			0
$148$	1.82248	−	0.262033i	0.149807	−	0.0215390i
$149$	−2.82335	−	6.18227i	−0.231298	−	0.506471i	0.758023	−	0.652228i	$-0.226166\pi$
$149$	−2.82335	−	6.18227i	−0.231298	−	0.506471i	−0.989320	+	0.145757i	$0.953438\pi$
$150$		0			0
$151$	2.24099	+	15.5864i	0.182369	+	1.26840i	0.851142	+	0.524936i	$0.175911\pi$
$151$	2.24099	+	15.5864i	0.182369	+	1.26840i	−0.668773	+	0.743467i	$0.733180\pi$
$152$	−3.74563	−	2.40717i	−0.303811	−	0.195248i
$153$		0			0
$154$	0.0894188	−	0.621922i	0.00720557	−	0.0501159i
$155$	8.81162	−	10.1692i	0.707767	−	0.816806i
$156$		0			0
$157$	3.51530	−	3.04602i	0.280551	−	0.243099i	−0.503206	−	0.864167i	$-0.667846\pi$
$157$	3.51530	−	3.04602i	0.280551	−	0.243099i	0.783757	+	0.621068i	$0.213301\pi$
$158$	8.96625	+	2.63273i	0.713317	+	0.209449i
$159$		0			0
$160$			3.27664i			0.259041i
$161$	−1.14503	+	1.03237i	−0.0902410	+	0.0813620i
$162$		0			0
$163$	8.32023	−	18.2188i	0.651691	−	1.42700i	−0.238375	−	0.971173i	$-0.576615\pi$
$163$	8.32023	−	18.2188i	0.651691	−	1.42700i	0.890066	−	0.455831i	$-0.150658\pi$
$164$	−2.01052	+	6.84721i	−0.156995	+	0.534677i
$165$		0			0
$166$	−8.58993	−	13.3662i	−0.666708	−	1.03742i
$167$	−15.1802	−	13.1538i	−1.17468	−	1.01787i	−0.999444	−	0.0333426i	$-0.989385\pi$
$167$	−15.1802	−	13.1538i	−1.17468	−	1.01787i	−0.175239	−	0.984526i	$-0.556070\pi$
$168$		0			0
$169$	−7.18375	+	2.10934i	−0.552596	+	0.162257i
$170$	6.13314	−	9.54335i	0.470390	−	0.731942i
$171$		0			0
$172$	−7.58616	+	3.46448i	−0.578439	+	0.264164i
$173$	16.4514	−	7.51310i	1.25078	−	0.571211i	0.323728	−	0.946150i	$-0.395064\pi$
$173$	16.4514	−	7.51310i	1.25078	−	0.571211i	0.927049	+	0.374940i	$0.122337\pi$
$174$		0			0
$175$	−0.996981	+	1.55133i	−0.0753647	+	0.117270i
$176$	1.87535	−	0.550651i	0.141359	−	0.0415069i
$177$		0			0
$178$	−11.9368	−	10.3433i	−0.894699	−	0.775261i
$179$	−7.40178	−	11.5174i	−0.553235	−	0.860850i	0.446184	−	0.894941i	$-0.352783\pi$
$179$	−7.40178	−	11.5174i	−0.553235	−	0.860850i	−0.999419	+	0.0340912i	$0.989146\pi$
$180$		0			0
$181$	7.37361	−	25.1122i	0.548076	−	1.86657i	0.0513240	−	0.998682i	$-0.483656\pi$
$181$	7.37361	−	25.1122i	0.548076	−	1.86657i	0.496752	−	0.867893i	$-0.334526\pi$
$182$	0.604451	−	1.32356i	0.0448049	−	0.0981090i
$183$		0			0
$184$	−4.40085	−	1.90592i	−0.324435	−	0.140506i
$185$			6.03302i			0.443556i
$186$		0			0
$187$	−6.49271	−	1.90643i	−0.474794	−	0.139412i
$188$	6.39650	−	5.54260i	0.466513	−	0.404235i
$189$		0			0
$190$	9.55381	−	11.0257i	0.693106	−	0.799887i
$191$	−1.96401	+	13.6600i	−0.142111	+	0.988403i	0.786564	+	0.617508i	$0.211858\pi$
$191$	−1.96401	+	13.6600i	−0.142111	+	0.988403i	−0.928675	+	0.370894i	$0.879051\pi$
$192$		0			0
$193$	11.2893	+	7.25519i	0.812621	+	0.522240i	0.879712	−	0.475507i	$-0.157735\pi$
$193$	11.2893	+	7.25519i	0.812621	+	0.522240i	−0.0670907	+	0.997747i	$0.521372\pi$
$194$	−0.737931	−	5.13242i	−0.0529803	−	0.368486i
$195$		0			0
$196$	−2.86498	−	6.27342i	−0.204641	−	0.448101i
$197$	−15.0490	+	2.16372i	−1.07220	+	0.154159i	−0.655733	−	0.754993i	$-0.727640\pi$
$197$	−15.0490	+	2.16372i	−1.07220	+	0.154159i	−0.416465	+	0.909152i	$0.636731\pi$
$198$		0			0
$199$	−1.80314	−	6.14092i	−0.127821	−	0.435318i	0.870569	−	0.492047i	$-0.163751\pi$
$199$	−1.80314	−	6.14092i	−0.127821	−	0.435318i	−0.998390	+	0.0567287i	$0.981933\pi$
$200$	−5.67800	−	0.816374i	−0.401495	−	0.0577263i
$201$		0			0
$202$	3.27284	−	2.10333i	0.230276	−	0.147990i
$203$	1.40761	+	1.62447i	0.0987947	+	0.114015i
$204$		0			0
$205$	−21.2700	−	9.71367i	−1.48556	−	0.678432i
$206$	−5.04034			−0.351177
$207$		0			0
$208$	4.52626			0.313840
$209$	−7.91596	−	3.61510i	−0.547558	−	0.250062i
$210$		0			0
$211$	9.20465	+	10.6227i	0.633674	+	0.731299i	0.978243	−	0.207462i	$-0.0665204\pi$
$211$	9.20465	+	10.6227i	0.633674	+	0.731299i	−0.344569	+	0.938761i	$0.611975\pi$
$212$	3.72753	−	2.39554i	0.256008	−	0.164526i
$213$		0			0
$214$	7.27399	+	1.04584i	0.497240	+	0.0714923i
$215$	−7.69879	−	26.2197i	−0.525053	−	1.78817i
$216$		0			0
$217$	1.30669	−	0.187874i	0.0887042	−	0.0127537i
$218$	−5.66437	−	12.4032i	−0.383640	−	0.840054i
$219$		0			0
$220$	0.911420	+	6.33907i	0.0614479	+	0.427380i
$221$	−13.1829	−	8.47214i	−0.886778	−	0.569898i
$222$		0			0
$223$	−2.76424	+	19.2257i	−0.185107	+	1.28745i	0.659354	+	0.751833i	$0.270830\pi$
$223$	−2.76424	+	19.2257i	−0.185107	+	1.28745i	−0.844461	+	0.535617i	$0.820079\pi$
$224$	−0.210518	+	0.242950i	−0.0140658	+	0.0162328i
$225$		0			0
$226$	−4.16102	+	3.60554i	−0.276787	+	0.239837i
$227$	7.16080	+	2.10260i	0.475279	+	0.139555i	0.510594	−	0.859822i	$-0.329425\pi$
$227$	7.16080	+	2.10260i	0.475279	+	0.139555i	−0.0353153	+	0.999376i	$0.511244\pi$
$228$		0			0
$229$		−	1.01607i		−	0.0671439i	−0.999436	−	0.0335720i	$-0.989312\pi$
$229$		−	1.01607i		−	0.0671439i	0.999436	−	0.0335720i	$-0.0106883\pi$
$230$	8.23364	−	13.3845i	0.542910	−	0.882546i
$231$		0			0
$232$	−2.77764	+	6.08218i	−0.182361	+	0.399314i
$233$	0.466736	−	1.58956i	0.0305769	−	0.104135i	−0.942791	−	0.333385i	$-0.891809\pi$
$233$	0.466736	−	1.58956i	0.0305769	−	0.104135i	0.973368	+	0.229250i	$0.0736273\pi$
$234$		0			0
$235$	14.9935	+	23.3303i	0.978067	+	1.52190i
$236$	−4.33244	−	3.75408i	−0.282018	−	0.244370i
$237$		0			0
$238$	1.06789	−	0.313560i	0.0692210	−	0.0203251i
$239$	−6.34339	+	9.87051i	−0.410320	+	0.638470i	−0.983489	−	0.180967i	$-0.942077\pi$
$239$	−6.34339	+	9.87051i	−0.410320	+	0.638470i	0.573169	+	0.819437i	$0.305714\pi$
$240$		0			0
$241$	19.0146	−	8.68366i	1.22484	−	0.559364i	0.305257	−	0.952270i	$-0.401258\pi$
$241$	19.0146	−	8.68366i	1.22484	−	0.559364i	0.919578	+	0.392906i	$0.128530\pi$
$242$	−6.53103	+	2.98262i	−0.419831	+	0.191730i
$243$		0			0
$244$	8.08933	−	12.5872i	0.517866	−	0.805816i
$245$	21.6825	−	6.36656i	1.38524	−	0.406745i
$246$		0			0
$247$	−15.2306	−	13.1974i	−0.969097	−	0.839728i
$248$	2.22017	+	3.45466i	0.140981	+	0.219371i
$249$		0			0
$250$	0.679790	−	2.31515i	0.0429937	−	0.146423i
$251$	−6.47662	+	14.1818i	−0.408801	+	0.895149i	0.587501	+	0.809224i	$0.300112\pi$
$251$	−6.47662	+	14.1818i	−0.408801	+	0.895149i	−0.996302	+	0.0859254i	$0.972615\pi$
$252$		0			0
$253$	−9.04413	−	2.46311i	−0.568599	−	0.154854i
$254$		−	2.32685i		−	0.146000i
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	−1.42502	+	1.23478i	−0.0888901	+	0.0770237i	−0.698172	−	0.715930i	$-0.746003\pi$
$257$	−1.42502	+	1.23478i	−0.0888901	+	0.0770237i	0.609282	+	0.792953i	$0.291458\pi$
$258$		0			0
$259$	−0.387609	+	0.447325i	−0.0240848	+	0.0277954i
$260$	−2.11066	+	14.6800i	−0.130898	+	0.910414i
$261$		0			0
$262$	17.0936	+	10.9854i	1.05604	+	0.678679i
$263$	2.20329	+	15.3242i	0.135861	+	0.944933i	0.937713	+	0.347411i	$0.112939\pi$
$263$	2.20329	+	15.3242i	0.135861	+	0.944933i	−0.801852	+	0.597522i	$0.796152\pi$
$264$		0			0
$265$	6.03123	+	13.2065i	0.370495	+	0.811272i
$266$	1.41676	−	0.203699i	0.0868668	−	0.0124896i
$267$		0			0
$268$	−1.37775	−	4.69220i	−0.0841597	−	0.286622i
$269$	−17.5531	−	2.52375i	−1.07023	−	0.153876i	−0.415390	−	0.909643i	$-0.636355\pi$
$269$	−17.5531	−	2.52375i	−1.07023	−	0.153876i	−0.654840	+	0.755767i	$0.727264\pi$
$270$		0			0
$271$	3.57381	−	2.29675i	0.217094	−	0.139518i	−0.427575	−	0.903980i	$-0.640632\pi$
$271$	3.57381	−	2.29675i	0.217094	−	0.139518i	0.644668	+	0.764462i	$0.276996\pi$
$272$	2.26722	+	2.61651i	0.137470	+	0.158649i
$273$		0			0
$274$	−4.06990	−	1.85866i	−0.245872	−	0.112286i
$275$	−11.2119			−0.676101
$276$		0			0
$277$	−25.7548			−1.54746			−0.773729	−	0.633516i	$-0.781611\pi$
$277$	−25.7548			−1.54746			−0.773729	+	0.633516i	$0.781611\pi$
$278$	18.5443	+	8.46889i	1.11221	+	0.507930i
$279$		0			0
$280$	−0.689791	−	0.796061i	−0.0412229	−	0.0475738i
$281$	−20.8422	+	13.3945i	−1.24334	+	0.799046i	−0.985914	−	0.167252i	$-0.946511\pi$
$281$	−20.8422	+	13.3945i	−1.24334	+	0.799046i	−0.257426	+	0.966298i	$0.582874\pi$
$282$		0			0
$283$	8.62931	+	1.24071i	0.512959	+	0.0737524i	0.393934	−	0.919139i	$-0.371114\pi$
$283$	8.62931	+	1.24071i	0.512959	+	0.0737524i	0.119025	+	0.992891i	$0.462023\pi$
$284$	−0.394633	−	1.34400i	−0.0234172	−	0.0797516i
$285$		0			0
$286$	8.75660	−	1.25901i	0.517789	−	0.0744468i
$287$	−0.953001	−	2.08678i	−0.0562539	−	0.123179i
$288$		0			0
$289$	0.713506	+	4.96254i	0.0419709	+	0.291914i
$290$	−18.4310	−	11.8449i	−1.08231	−	0.695556i
$291$		0			0
$292$	0.0192058	−	0.133579i	0.00112393	−	0.00781714i
$293$	6.33986	−	7.31658i	0.370378	−	0.427439i	−0.539712	−	0.841850i	$-0.681467\pi$
$293$	6.33986	−	7.31658i	0.370378	−	0.427439i	0.910090	+	0.414411i	$0.136012\pi$
$294$		0			0
$295$	14.1959	−	12.3008i	0.826515	−	0.716179i
$296$	−1.76664	−	0.518731i	−0.102684	−	0.0301506i
$297$		0			0
$298$			6.79645i			0.393708i
$299$	−18.4889	−	11.3737i	−1.06924	−	0.657758i
$300$		0			0
$301$	1.11372	−	2.43872i	0.0641940	−	0.140565i
$302$	4.43635	−	15.1088i	0.255283	−	0.869415i
$303$		0			0
$304$	2.40717	+	3.74563i	0.138061	+	0.214827i
$305$	37.0519	+	32.1057i	2.12159	+	1.83837i
$306$		0			0
$307$	27.4295	−	8.05404i	1.56549	−	0.459668i	0.619803	−	0.784757i	$-0.287212\pi$
$307$	27.4295	−	8.05404i	1.56549	−	0.459668i	0.945684	+	0.325089i	$0.105394\pi$
$308$	−0.339694	+	0.528574i	−0.0193558	+	0.0301183i
$309$		0			0
$310$	−12.2398	+	5.58971i	−0.695171	+	0.317474i
$311$	22.2241	−	10.1494i	1.26021	−	0.575519i	0.330499	−	0.943806i	$-0.392783\pi$
$311$	22.2241	−	10.1494i	1.26021	−	0.575519i	0.929712	+	0.368287i	$0.120056\pi$
$312$		0			0
$313$	12.0618	−	18.7685i	0.681771	−	1.06086i	−0.312072	−	0.950059i	$-0.601023\pi$
$313$	12.0618	−	18.7685i	0.681771	−	1.06086i	0.993843	−	0.110798i	$-0.0353407\pi$
$314$	−4.46299	+	1.31045i	−0.251861	+	0.0739531i
$315$		0			0
$316$	−7.06231	−	6.11953i	−0.397286	−	0.344250i
$317$	2.62777	+	4.08889i	0.147590	+	0.229655i	0.907175	−	0.420753i	$-0.138234\pi$
$317$	2.62777	+	4.08889i	0.147590	+	0.229655i	−0.759585	+	0.650408i	$0.774598\pi$
$318$		0			0
$319$	−3.68188	+	12.5393i	−0.206146	+	0.702068i
$320$	1.36117	−	2.98054i	0.0760915	−	0.166617i
$321$		0			0
$322$	1.47042	−	0.463412i	0.0819431	−	0.0258250i
$323$		−	15.4150i		−	0.857713i
$324$		0			0
$325$	−24.9127	−	7.31501i	−1.38191	−	0.405764i
$326$	−15.1367	+	13.1160i	−0.838344	+	0.726429i
$327$		0			0
$328$	4.67327	−	5.39324i	0.258038	−	0.297792i
$329$	−0.387217	+	2.69315i	−0.0213479	+	0.148478i
$330$		0			0
$331$	−26.3889	−	16.9591i	−1.45047	−	0.932158i	−0.999209	−	0.0397634i	$-0.987340\pi$
$331$	−26.3889	−	16.9591i	−1.45047	−	0.932158i	−0.451257	−	0.892394i	$-0.649024\pi$
$332$	2.26116	+	15.7267i	0.124097	+	0.863115i
$333$		0			0
$334$	8.34417	+	18.2712i	0.456573	+	0.999755i
$335$	15.8606	−	2.28041i	0.866559	−	0.124592i
$336$		0			0
$337$	−4.84187	−	16.4899i	−0.263753	−	0.898262i	−0.979761	−	0.200169i	$-0.935851\pi$
$337$	−4.84187	−	16.4899i	−0.263753	−	0.898262i	0.716008	−	0.698092i	$-0.245967\pi$
$338$	7.41082	+	1.06551i	0.403095	+	0.0579563i
$339$		0			0
$340$	−9.54335	+	6.13314i	−0.517561	+	0.332616i
$341$	5.25613	+	6.06590i	0.284635	+	0.328487i
$342$		0			0
$343$	4.06364	+	1.85580i	0.219416	+	0.100204i
$344$	8.33981			0.449653
$345$		0			0
$346$	−18.0858			−0.972297
$347$	21.0415	+	9.60935i	1.12957	+	0.515857i	0.890426	−	0.455128i	$-0.150406\pi$
$347$	21.0415	+	9.60935i	1.12957	+	0.515857i	0.239143	+	0.970984i	$0.423134\pi$
$348$		0			0
$349$	15.5684	+	17.9669i	0.833358	+	0.961746i	0.999704	−	0.0243213i	$-0.00774248\pi$
$349$	15.5684	+	17.9669i	0.833358	+	0.961746i	−0.166347	+	0.986067i	$0.553197\pi$
$350$	1.55133	−	0.996981i	0.0829222	−	0.0532909i
$351$		0			0
$352$	−1.93462	−	0.278157i	−0.103116	−	0.0148258i
$353$	−6.12354	−	20.8549i	−0.325923	−	1.10999i	−0.945653	−	0.325177i	$-0.894576\pi$
$353$	−6.12354	−	20.8549i	−0.325923	−	1.10999i	0.619730	−	0.784815i	$-0.287242\pi$
$354$		0			0
$355$	4.54300	−	0.653185i	0.241117	−	0.0346674i
$356$	6.56132	+	14.3673i	0.347749	+	0.761464i
$357$		0			0
$358$	1.94840	+	13.5514i	0.102976	+	0.716214i
$359$	8.79203	+	5.65029i	0.464025	+	0.298211i	0.751686	−	0.659522i	$-0.229241\pi$
$359$	8.79203	+	5.65029i	0.464025	+	0.298211i	−0.287660	+	0.957732i	$0.592877\pi$
$360$		0			0
$361$	0.117305	−	0.815875i	0.00617395	−	0.0429408i
$362$	−17.1392	+	19.7797i	−0.900819	+	1.03960i
$363$		0			0
$364$	−1.09966	+	0.952857i	−0.0576376	+	0.0499433i
$365$	0.424281	+	0.124580i	0.0222079	+	0.00652082i
$366$		0			0
$367$			24.3686i			1.27203i	0.771677	+	0.636015i	$0.219418\pi$
$367$			24.3686i			1.27203i	−0.771677	+	0.636015i	$0.780582\pi$
$368$	3.21140	+	3.56186i	0.167406	+	0.185675i
$369$		0			0
$370$	2.50621	−	5.48783i	0.130291	−	0.285298i
$371$	−0.401301	+	1.36671i	−0.0208345	+	0.0709559i
$372$		0			0
$373$	15.0839	+	23.4710i	0.781015	+	1.21528i	0.972297	+	0.233749i	$0.0750992\pi$
$373$	15.0839	+	23.4710i	0.781015	+	1.21528i	−0.191282	+	0.981535i	$0.561264\pi$
$374$	5.11402	+	4.43132i	0.264440	+	0.229138i
$375$		0			0
$376$	−8.12094	+	2.38452i	−0.418805	+	0.122972i
$377$	−16.3622	+	25.4601i	−0.842696	+	1.31126i
$378$		0			0
$379$	−33.9031	+	15.4830i	−1.74149	+	0.795311i	−0.750578	+	0.660782i	$0.770225\pi$
$379$	−33.9031	+	15.4830i	−1.74149	+	0.795311i	−0.990910	+	0.134528i	$0.957048\pi$
$380$	−13.2707	+	6.06052i	−0.680772	+	0.310898i
$381$		0			0
$382$	7.46109	−	11.6097i	0.381743	−	0.594003i
$383$	30.9286	−	9.08146i	1.58038	−	0.464041i	0.630377	−	0.776289i	$-0.282900\pi$
$383$	30.9286	−	9.08146i	1.58038	−	0.464041i	0.950001	+	0.312248i	$0.101082\pi$
$384$		0			0
$385$	−1.55591	−	1.34821i	−0.0792968	−	0.0687110i
$386$	−7.25519	−	11.2893i	−0.369279	−	0.574610i
$387$		0			0
$388$	−1.46084	+	4.97516i	−0.0741629	+	0.252576i
$389$	0.968502	−	2.12072i	0.0491050	−	0.107525i	−0.883489	−	0.468451i	$-0.844812\pi$
$389$	0.968502	−	2.12072i	0.0491050	−	0.107525i	0.932594	+	0.360926i	$0.117539\pi$
$390$		0			0
$391$	−2.68633	−	16.3851i	−0.135854	−	0.828630i
$392$			6.89666i			0.348334i
$393$		0			0
$394$	14.5879	+	4.28340i	0.734928	+	0.215794i
$395$	23.1407	−	20.0515i	1.16433	−	1.00890i
$396$		0			0
$397$	4.04433	−	4.66740i	0.202979	−	0.234250i	−0.645129	−	0.764074i	$-0.723196\pi$
$397$	4.04433	−	4.66740i	0.202979	−	0.234250i	0.848108	+	0.529823i	$0.177742\pi$
$398$	−0.910840	+	6.33503i	−0.0456563	+	0.317546i
$399$		0			0
$400$	4.82576	+	3.10133i	0.241288	+	0.155066i
$401$	3.33329	+	23.1835i	0.166457	+	1.15773i	0.886136	+	0.463425i	$0.153380\pi$
$401$	3.33329	+	23.1835i	0.166457	+	1.15773i	−0.719680	+	0.694306i	$0.755711\pi$
$402$		0			0
$403$	7.72146	+	16.9076i	0.384633	+	0.842230i
$404$	−3.85083	+	0.553666i	−0.191586	+	0.0275459i
$405$		0			0
$406$	−0.605577	−	2.06241i	−0.0300543	−	0.102356i
$407$	−3.56206	−	0.512147i	−0.176565	−	0.0253862i
$408$		0			0
$409$	7.29465	−	4.68799i	0.360697	−	0.231806i	−0.347722	−	0.937598i	$-0.613045\pi$
$409$	7.29465	−	4.68799i	0.360697	−	0.231806i	0.708420	+	0.705792i	$0.249408\pi$
$410$	15.3126	+	17.6717i	0.756238	+	0.872745i
$411$		0			0
$412$	4.58486	+	2.09383i	0.225880	+	0.103156i
$413$	1.84287			0.0906816
$414$		0			0
$415$	−52.0607			−2.55556
$416$	−4.11723	−	1.88028i	−0.201864	−	0.0921881i
$417$		0			0
$418$	5.69885	+	6.57682i	0.278740	+	0.321683i
$419$	6.72203	−	4.31999i	0.328393	−	0.211045i	−0.366047	−	0.930597i	$-0.619289\pi$
$419$	6.72203	−	4.31999i	0.328393	−	0.211045i	0.694439	+	0.719551i	$0.255653\pi$
$420$		0			0
$421$	−6.20921	−	0.892749i	−0.302618	−	0.0435099i	−0.0106669	−	0.999943i	$-0.503395\pi$
$421$	−6.20921	−	0.892749i	−0.302618	−	0.0435099i	−0.291951	+	0.956433i	$0.594305\pi$
$422$	−3.96000	−	13.4865i	−0.192770	−	0.656514i
$423$		0			0
$424$	−4.38582	+	0.630586i	−0.212994	+	0.0306240i
$425$	−8.25023	−	18.0655i	−0.400195	−	0.876304i
$426$		0			0
$427$	0.684531	+	4.76102i	0.0331268	+	0.230402i
$428$	−6.18219	−	3.97305i	−0.298828	−	0.192045i
$429$		0			0
$430$	−3.88898	+	27.0485i	−0.187543	+	1.30439i
$431$	−9.92075	+	11.4492i	−0.477866	+	0.551487i	−0.942583	−	0.333973i	$-0.891611\pi$
$431$	−9.92075	+	11.4492i	−0.477866	+	0.551487i	0.464717	+	0.885459i	$0.346156\pi$
$432$		0			0
$433$	−8.36048	+	7.24440i	−0.401779	+	0.348143i	−0.832191	−	0.554489i	$-0.812914\pi$
$433$	−8.36048	+	7.24440i	−0.401779	+	0.348143i	0.430412	+	0.902633i	$0.358368\pi$
$434$	−1.26666	−	0.371924i	−0.0608015	−	0.0178529i
$435$		0			0
$436$			13.6355i			0.653020i
$437$	−0.420724	−	21.3490i	−0.0201260	−	1.02126i
$438$		0			0
$439$	10.4047	−	22.7831i	0.496589	−	1.08738i	−0.480974	−	0.876735i	$-0.659717\pi$
$439$	10.4047	−	22.7831i	0.496589	−	1.08738i	0.977563	−	0.210644i	$-0.0675560\pi$
$440$	1.80429	−	6.14484i	0.0860160	−	0.292944i
$441$		0			0
$442$	8.47214	+	13.1829i	0.402979	+	0.627047i
$443$	27.6388	+	23.9491i	1.31316	+	1.13786i	0.980867	+	0.194681i	$0.0623670\pi$
$443$	27.6388	+	23.9491i	1.31316	+	1.13786i	0.332291	+	0.943177i	$0.392178\pi$
$444$		0			0
$445$	−49.6569	+	14.5806i	−2.35396	+	0.691186i
$446$	10.5011	−	16.3400i	0.497242	−	0.773723i
$447$		0			0
$448$	0.292419	−	0.133543i	0.0138155	−	0.00630932i
$449$	−7.99541	+	3.65138i	−0.377327	+	0.172319i	−0.595045	−	0.803692i	$-0.702866\pi$
$449$	−7.99541	+	3.65138i	−0.377327	+	0.172319i	0.217718	+	0.976012i	$0.430139\pi$
$450$		0			0
$451$	7.54085	−	11.7338i	0.355085	−	0.552523i
$452$	5.28279	−	1.55117i	0.248482	−	0.0729608i
$453$		0			0
$454$	−5.64024	−	4.88730i	−0.264710	−	0.229372i
$455$	−2.57761	−	4.01084i	−0.120840	−	0.188031i
$456$		0			0
$457$	7.05141	−	24.0149i	0.329851	−	1.12337i	−0.612980	−	0.790098i	$-0.710029\pi$
$457$	7.05141	−	24.0149i	0.329851	−	1.12337i	0.942831	−	0.333271i	$-0.108152\pi$
$458$	−0.422091	+	0.924251i	−0.0197230	+	0.0431874i
$459$		0			0
$460$	−13.0497	+	8.75457i	−0.608445	+	0.408184i
$461$			12.6441i			0.588895i	0.955668	+	0.294448i	$0.0951357\pi$
$461$			12.6441i			0.588895i	−0.955668	+	0.294448i	$0.904864\pi$
$462$		0			0
$463$	35.7580	+	10.4995i	1.66182	+	0.487953i	0.971793	−	0.235834i	$-0.0757820\pi$
$463$	35.7580	+	10.4995i	1.66182	+	0.487953i	0.690023	+	0.723787i	$0.257600\pi$
$464$	5.05326	−	4.37867i	0.234591	−	0.203275i
$465$		0			0
$466$	−1.08488	+	1.25202i	−0.0502563	+	0.0579988i
$467$	1.72520	−	11.9990i	0.0798326	−	0.555248i	−0.910174	−	0.414226i	$-0.864052\pi$
$467$	1.72520	−	11.9990i	0.0798326	−	0.555248i	0.990007	−	0.141022i	$-0.0450387\pi$
$468$		0			0
$469$	1.32252	+	0.849929i	0.0610681	+	0.0392461i
$470$	−3.94679	−	27.4505i	−0.182052	−	1.26620i
$471$		0			0
$472$	2.38143	+	5.21459i	0.109614	+	0.240021i
$473$	16.1344	−	2.31978i	0.741860	−	0.106663i
$474$		0			0
$475$	−7.19572	−	24.5064i	−0.330162	−	1.12443i
$476$	−1.10164	−	0.158392i	−0.0504938	−	0.00725991i
$477$		0			0
$478$	9.87051	−	6.34339i	0.451467	−	0.290140i
$479$	15.0521	+	17.3711i	0.687750	+	0.793706i	0.987043	−	0.160455i	$-0.0512963\pi$
$479$	15.0521	+	17.3711i	0.687750	+	0.793706i	−0.299293	+	0.954161i	$0.596751\pi$
$480$		0			0
$481$	−7.58072	−	3.46200i	−0.345651	−	0.157854i
$482$	−20.9036			−0.952132
$483$		0			0
$484$	7.17986			0.326357
$485$	−15.4547	−	7.05792i	−0.701761	−	0.320484i
$486$		0			0
$487$	−16.3767	−	18.8998i	−0.742101	−	0.856430i	0.251677	−	0.967811i	$-0.419018\pi$
$487$	−16.3767	−	18.8998i	−0.742101	−	0.856430i	−0.993778	+	0.111382i	$0.964472\pi$
$488$	−12.5872	+	8.08933i	−0.569798	+	0.366187i
$489$		0			0
$490$	−22.3679	−	3.21601i	−1.01048	−	0.145285i
$491$	3.43115	+	11.6854i	0.154846	+	0.527356i	0.999974	−	0.00720759i	$-0.00229427\pi$
$491$	3.43115	+	11.6854i	0.154846	+	0.527356i	−0.845128	+	0.534563i	$0.820476\pi$
$492$		0			0
$493$	−22.9137	+	3.29449i	−1.03198	+	0.148376i
$494$	8.37183	+	18.3317i	0.376666	+	0.824784i
$495$		0			0
$496$	−0.584424	−	4.06476i	−0.0262414	−	0.182513i
$497$	0.378811	+	0.243447i	0.0169920	+	0.0109201i
$498$		0			0
$499$	1.48921	−	10.3577i	0.0666662	−	0.463674i	−0.928955	−	0.370193i	$-0.879292\pi$
$499$	1.48921	−	10.3577i	0.0666662	−	0.463674i	0.995621	−	0.0934807i	$-0.0297993\pi$
$500$	−1.58011	+	1.82354i	−0.0706646	+	0.0815513i
$501$		0			0
$502$	11.7827	−	10.2098i	0.525887	−	0.455684i
$503$	−10.2247	−	3.00224i	−0.455897	−	0.133863i	0.0457180	−	0.998954i	$-0.485442\pi$
$503$	−10.2247	−	3.00224i	−0.455897	−	0.133863i	−0.501615	+	0.865091i	$0.667261\pi$
$504$		0			0
$505$		−	12.7476i		−	0.567259i
$506$	7.20361	+	5.99759i	0.320240	+	0.266625i
$507$		0			0
$508$	−0.966609	+	2.11658i	−0.0428863	+	0.0939080i
$509$	6.80694	−	23.1823i	0.301712	−	1.02754i	−0.659495	−	0.751709i	$-0.729230\pi$
$509$	6.80694	−	23.1823i	0.301712	−	1.02754i	0.961207	−	0.275828i	$-0.0889522\pi$
$510$		0			0
$511$	0.0234547	+	0.0364963i	0.00103758	+	0.00161450i
$512$	0.755750	+	0.654861i	0.0333997	+	0.0289410i
$513$		0			0
$514$	1.80919	−	0.531226i	0.0797999	−	0.0234314i
$515$	−8.92890	+	13.8936i	−0.393454	+	0.612227i
$516$		0			0
$517$	−15.0477	+	6.87204i	−0.661796	+	0.302232i
$518$	0.538407	−	0.245882i	0.0236562	−	0.0108034i
$519$		0			0
$520$	8.01821	−	12.4766i	0.351622	−	0.547134i
$521$	17.9255	−	5.26341i	0.785332	−	0.230594i	0.135606	−	0.990763i	$-0.456702\pi$
$521$	17.9255	−	5.26341i	0.785332	−	0.230594i	0.649726	+	0.760168i	$0.274884\pi$
$522$		0			0
$523$	−11.6200	−	10.0688i	−0.508107	−	0.440277i	0.362698	−	0.931907i	$-0.381856\pi$
$523$	−11.6200	−	10.0688i	−0.508107	−	0.440277i	−0.870804	+	0.491630i	$0.836401\pi$
$524$	−10.9854	−	17.0936i	−0.479898	−	0.746736i
$525$		0			0
$526$	4.36173	−	14.8547i	0.190181	−	0.647696i
$527$	−5.90616	+	12.9327i	−0.257276	+	0.563356i
$528$		0			0
$529$	−4.16764	−	22.6193i	−0.181202	−	0.983446i
$530$		−	14.5186i		−	0.630646i
$531$		0			0
$532$	−1.37335	−	0.403251i	−0.0595421	−	0.0174831i
$533$	24.4112	−	21.1524i	1.05737	−	0.916214i
$534$		0			0
$535$	15.7686	−	18.1980i	0.681737	−	0.786767i
$536$	−0.695961	+	4.84051i	−0.0300609	+	0.209078i
$537$		0			0
$538$	14.9184	+	9.58750i	0.643180	+	0.413347i
$539$	1.91835	+	13.3424i	0.0826293	+	0.574699i
$540$		0			0
$541$	14.5059	+	31.7634i	0.623656	+	1.36562i	0.912830	+	0.408340i	$0.133892\pi$
$541$	14.5059	+	31.7634i	0.623656	+	1.36562i	−0.289173	+	0.957277i	$0.593380\pi$
$542$	−4.20496	+	0.604581i	−0.180618	+	0.0259690i
$543$		0			0
$544$	−0.975398	−	3.32190i	−0.0418199	−	0.142425i
$545$	−44.2238	−	6.35842i	−1.89434	−	0.272365i
$546$		0			0
$547$	1.04434	−	0.671154i	0.0446526	−	0.0286965i	−0.518124	−	0.855305i	$-0.673369\pi$
$547$	1.04434	−	0.671154i	0.0446526	−	0.0286965i	0.562777	+	0.826609i	$0.309733\pi$
$548$	2.93000	+	3.38140i	0.125163	+	0.144446i
$549$		0			0
$550$	10.1987	+	4.65758i	0.434873	+	0.198600i
$551$	−29.7709			−1.26828
$552$		0			0
$553$	3.00406			0.127746
$554$	23.4274	+	10.6989i	0.995336	+	0.454555i
$555$		0			0
$556$	−13.3504	−	15.4071i	−0.566182	−	0.653408i
$557$	−8.88697	+	5.71131i	−0.376553	+	0.241996i	−0.715203	−	0.698916i	$-0.753666\pi$
$557$	−8.88697	+	5.71131i	−0.376553	+	0.241996i	0.338650	+	0.940912i	$0.390030\pi$
$558$		0			0
$559$	37.3639	+	5.37212i	1.58033	+	0.227217i
$560$	0.296760	+	1.01067i	0.0125404	+	0.0427087i
$561$		0			0
$562$	24.5230	−	3.52587i	1.03444	−	0.148730i
$563$	0.332834	+	0.728804i	0.0140273	+	0.0307154i	0.916516	−	0.399998i	$-0.130989\pi$
$563$	0.332834	+	0.728804i	0.0140273	+	0.0307154i	−0.902489	+	0.430714i	$0.858262\pi$
$564$		0			0
$565$	2.56744	+	17.8570i	0.108013	+	0.751248i
$566$	−7.33409	−	4.71333i	−0.308275	−	0.198116i
$567$		0			0
$568$	−0.199346	+	1.38648i	−0.00836436	+	0.0581754i
$569$	16.9889	−	19.6063i	0.712213	−	0.821937i	−0.278135	−	0.960542i	$-0.589716\pi$
$569$	16.9889	−	19.6063i	0.712213	−	0.821937i	0.990348	+	0.138605i	$0.0442618\pi$
$570$		0			0
$571$	28.6994	−	24.8682i	1.20103	−	1.04070i	0.202925	−	0.979194i	$-0.434955\pi$
$571$	28.6994	−	24.8682i	1.20103	−	1.04070i	0.998107	−	0.0615055i	$-0.0195902\pi$
$572$	−8.48830	−	2.49239i	−0.354914	−	0.104212i
$573$		0			0
$574$			2.29409i			0.0957537i
$575$	−11.9192	−	24.7946i	−0.497066	−	1.03401i
$576$		0			0
$577$	6.10451	−	13.3670i	0.254134	−	0.556476i	−0.738966	−	0.673742i	$-0.764686\pi$
$577$	6.10451	−	13.3670i	0.254134	−	0.556476i	0.993101	+	0.117266i	$0.0374130\pi$
$578$	1.41249	−	4.81049i	0.0587517	−	0.200090i
$579$		0			0
$580$	11.8449	+	18.4310i	0.491833	+	0.765306i
$581$	−3.86010	−	3.34479i	−0.160144	−	0.138765i
$582$		0			0
$583$	−8.30951	+	2.43989i	−0.344145	+	0.101050i
$584$	−0.0729611	+	0.113530i	−0.00301915	+	0.00469789i
$585$		0			0
$586$	−8.80635	+	4.02173i	−0.363787	+	0.166136i
$587$	−9.01759	+	4.11820i	−0.372196	+	0.169976i	−0.592726	−	0.805404i	$-0.701948\pi$
$587$	−9.01759	+	4.11820i	−0.372196	+	0.169976i	0.220530	+	0.975380i	$0.429221\pi$
$588$		0			0
$589$	−9.88520	+	15.3817i	−0.407312	+	0.633790i
$590$	−18.0229	+	5.29201i	−0.741993	+	0.217869i
$591$		0			0
$592$	1.39150	+	1.20574i	0.0571903	+	0.0495557i
$593$	−0.367857	−	0.572397i	−0.0151061	−	0.0235055i	0.833618	−	0.552341i	$-0.186265\pi$
$593$	−0.367857	−	0.572397i	−0.0151061	−	0.0235055i	−0.848724	+	0.528835i	$0.822629\pi$
$594$		0			0
$595$	1.02743	−	3.49909i	0.0421204	−	0.143449i
$596$	2.82335	−	6.18227i	0.115649	−	0.253236i
$597$		0			0
$598$	12.0933	+	18.0265i	0.494532	+	0.737157i
$599$		−	25.3522i		−	1.03586i	−0.855422	−	0.517932i	$-0.826702\pi$
$599$		−	25.3522i		−	1.03586i	0.855422	−	0.517932i	$-0.173298\pi$
$600$		0			0
$601$	43.6164	+	12.8069i	1.77915	+	0.522405i	0.995151	−	0.0983590i	$-0.0313593\pi$
$601$	43.6164	+	12.8069i	1.77915	+	0.522405i	0.783997	+	0.620764i	$0.213178\pi$
$602$	−2.02616	+	1.75568i	−0.0825801	+	0.0715561i
$603$		0			0
$604$	−10.3119	+	11.9005i	−0.419584	+	0.484226i
$605$	−3.34808	+	23.2864i	−0.136119	+	0.946727i
$606$		0			0
$607$	−27.6236	−	17.7526i	−1.12121	−	0.720556i	−0.157500	−	0.987519i	$-0.550343\pi$
$607$	−27.6236	−	17.7526i	−1.12121	−	0.720556i	−0.963707	+	0.266963i	$0.913980\pi$
$608$	−0.633649	−	4.40713i	−0.0256979	−	0.178733i
$609$		0			0
$610$	−20.3664	−	44.5963i	−0.824613	−	1.80565i
$611$	−37.9193	+	5.45198i	−1.53405	+	0.220563i
$612$		0			0
$613$	11.3671	+	38.7129i	0.459114	+	1.56360i	0.785809	+	0.618470i	$0.212247\pi$
$613$	11.3671	+	38.7129i	0.459114	+	1.56360i	−0.326694	+	0.945130i	$0.605935\pi$
$614$	−28.2966	−	4.06843i	−1.14196	−	0.164189i
$615$		0			0
$616$	0.528574	−	0.339694i	0.0212968	−	0.0136867i
$617$	−12.3522	−	14.2552i	−0.497281	−	0.573892i	0.450516	−	0.892768i	$-0.351240\pi$
$617$	−12.3522	−	14.2552i	−0.497281	−	0.573892i	−0.947796	+	0.318876i	$0.896695\pi$
$618$		0			0
$619$	2.67911	+	1.22351i	0.107682	+	0.0491769i	0.468528	−	0.883449i	$-0.344785\pi$
$619$	2.67911	+	1.22351i	0.107682	+	0.0491769i	−0.360845	+	0.932626i	$0.617512\pi$
$620$	13.4557			0.540395
$621$		0			0
$622$	−24.4319			−0.979631
$623$	−4.61864	−	2.10926i	−0.185042	−	0.0845058i
$624$		0			0
$625$	13.6052	+	15.7013i	0.544210	+	0.628051i
$626$	−18.7685	+	12.0618i	−0.750139	+	0.482085i
$627$		0			0
$628$	4.60406	+	0.661964i	0.183722	+	0.0264152i
$629$	−1.79592	−	6.11635i	−0.0716081	−	0.243875i
$630$		0			0
$631$	22.6820	−	3.26119i	0.902958	−	0.129826i	0.324830	−	0.945772i	$-0.394693\pi$
$631$	22.6820	−	3.26119i	0.902958	−	0.129826i	0.578127	+	0.815947i	$0.303784\pi$
$632$	3.88196	+	8.50031i	0.154416	+	0.338124i
$633$		0			0
$634$	−0.691718	−	4.81100i	−0.0274716	−	0.191069i
$635$	−6.41394	−	4.12199i	−0.254529	−	0.163576i
$636$		0			0
$637$	−4.44251	+	30.8983i	−0.176019	+	1.22424i
$638$	8.55818	−	9.87667i	0.338822	−	0.391021i
$639$		0			0
$640$	−2.47632	+	2.14575i	−0.0978852	+	0.0848180i
$641$	13.2801	+	3.89940i	0.524533	+	0.154017i	0.533270	−	0.845945i	$-0.320963\pi$
$641$	13.2801	+	3.89940i	0.524533	+	0.154017i	−0.00873688	+	0.999962i	$0.502781\pi$
$642$		0			0
$643$			18.5664i			0.732189i	0.930578	+	0.366094i	$0.119305\pi$
$643$			18.5664i			0.732189i	−0.930578	+	0.366094i	$0.880695\pi$
$644$	−1.53005	−	0.189299i	−0.0602923	−	0.00745941i
$645$		0			0
$646$	−6.40362	+	14.0220i	−0.251947	+	0.551687i
$647$	−6.78893	+	23.1210i	−0.266901	+	0.908980i	0.711574	+	0.702611i	$0.247983\pi$
$647$	−6.78893	+	23.1210i	−0.266901	+	0.908980i	−0.978474	+	0.206368i	$0.933835\pi$
$648$		0			0
$649$	6.05763	+	9.42586i	0.237783	+	0.369997i
$650$	19.6226	+	17.0031i	0.769661	+	0.666915i
$651$		0			0
$652$	19.2174	−	5.64274i	0.752612	−	0.220987i
$653$	1.00238	−	1.55974i	0.0392263	−	0.0610373i	−0.821087	−	0.570804i	$-0.806632\pi$
$653$	1.00238	−	1.55974i	0.0392263	−	0.0610373i	0.860313	+	0.509766i	$0.170268\pi$
$654$		0			0
$655$	60.5621	−	27.6578i	2.36636	−	1.08068i
$656$	−6.49139	+	2.96452i	−0.253446	+	0.115745i
$657$		0			0
$658$	1.47100	−	2.28892i	0.0573455	−	0.0892314i
$659$	−7.33559	+	2.15392i	−0.285754	+	0.0839050i	−0.421469	−	0.906843i	$-0.638485\pi$
$659$	−7.33559	+	2.15392i	−0.285754	+	0.0839050i	0.135714	+	0.990748i	$0.456667\pi$
$660$		0			0
$661$	−9.49173	−	8.22463i	−0.369186	−	0.319901i	0.450433	−	0.892810i	$-0.351269\pi$
$661$	−9.49173	−	8.22463i	−0.369186	−	0.319901i	−0.819619	+	0.572909i	$0.805815\pi$
$662$	16.9591	+	26.3889i	0.659135	+	1.02563i
$663$		0			0
$664$	4.47629	−	15.2448i	0.173714	−	0.591614i
$665$	1.94827	−	4.26612i	0.0755507	−	0.165433i
$666$		0			0
$667$	−31.6444	+	5.18810i	−1.22528	+	0.200884i
$668$		−	20.0863i		−	0.777164i
$669$		0			0
$670$	−15.3747	−	4.51441i	−0.593975	−	0.174407i
$671$	−22.1015	+	19.1510i	−0.853217	+	0.739317i
$672$		0			0
$673$	31.9207	−	36.8384i	1.23045	−	1.42002i	0.356295	−	0.934374i	$-0.384040\pi$
$673$	31.9207	−	36.8384i	1.23045	−	1.42002i	0.874157	−	0.485644i	$-0.161415\pi$
$674$	−2.44583	+	17.0111i	−0.0942098	+	0.655244i
$675$		0			0
$676$	−6.29848	−	4.04779i	−0.242249	−	0.155684i
$677$	−4.48430	−	31.1890i	−0.172346	−	1.19869i	−0.873911	−	0.486086i	$-0.838424\pi$
$677$	−4.48430	−	31.1890i	−0.172346	−	1.19869i	0.701566	−	0.712605i	$-0.252485\pi$
$678$		0			0
$679$	−0.692448	−	1.51625i	−0.0265737	−	0.0581883i
$680$	11.2287	−	1.61445i	0.430602	−	0.0619113i
$681$		0			0
$682$	−2.26128	−	7.70121i	−0.0865889	−	0.294895i
$683$	17.4646	+	2.51103i	0.668264	+	0.0960819i	0.468093	−	0.883679i	$-0.344941\pi$
$683$	17.4646	+	2.51103i	0.668264	+	0.0960819i	0.200171	+	0.979761i	$0.435850\pi$
$684$		0			0
$685$	−12.3332	+	7.92604i	−0.471226	+	0.302838i
$686$	−2.92549	−	3.37620i	−0.111696	−	0.128904i
$687$		0			0
$688$	−7.58616	−	3.46448i	−0.289220	−	0.132082i
$689$	−20.0555			−0.764054
$690$		0			0
$691$	11.3619			0.432227			0.216114	−	0.976368i	$-0.430662\pi$
$691$	11.3619			0.432227			0.216114	+	0.976368i	$0.430662\pi$
$692$	16.4514	+	7.51310i	0.625388	+	0.285605i
$693$		0			0
$694$	−15.1482	−	17.4819i	−0.575017	−	0.663605i
$695$	56.1953	−	36.1145i	2.13161	−	1.36990i
$696$		0			0
$697$	24.4553	+	3.51615i	0.926312	+	0.133184i
$698$	−6.69780	−	22.8106i	−0.253516	−	0.863395i
$699$		0			0
$700$	−1.82530	+	0.262439i	−0.0689900	+	0.00991926i
$701$	−9.64503	−	21.1197i	−0.364288	−	0.797679i	−0.999675	−	0.0254854i	$-0.991887\pi$
$701$	−9.64503	−	21.1197i	−0.364288	−	0.797679i	0.635387	−	0.772194i	$-0.280840\pi$
$702$		0			0
$703$	−1.16669	−	8.11448i	−0.0440024	−	0.306044i
$704$	1.64424	+	1.05669i	0.0619698	+	0.0398256i
$705$		0			0
$706$	−3.09326	+	21.5141i	−0.116416	+	0.809692i
$707$	0.819004	−	0.945181i	0.0308018	−	0.0355472i
$708$		0			0
$709$	−15.7237	+	13.6247i	−0.590516	+	0.511685i	−0.898074	−	0.439844i	$-0.855034\pi$
$709$	−15.7237	+	13.6247i	−0.590516	+	0.511685i	0.307558	+	0.951529i	$0.400488\pi$
$710$	−4.40380	−	1.29307i	−0.165272	−	0.0485281i
$711$		0			0
$712$		−	15.7946i		−	0.591928i
$713$	−7.82677	+	18.0723i	−0.293115	+	0.676814i
$714$		0			0
$715$	12.0418	−	26.3678i	0.450336	−	0.986099i
$716$	3.85713	−	13.1362i	0.144148	−	0.490922i
$717$		0			0
$718$	−5.65029	−	8.79203i	−0.210867	−	0.328115i
$719$	0.386866	+	0.335222i	0.0144277	+	0.0125017i	0.662045	−	0.749464i	$-0.269689\pi$
$719$	0.386866	+	0.335222i	0.0144277	+	0.0125017i	−0.647617	+	0.761966i	$0.724234\pi$
$720$		0			0
$721$	−1.55468	+	0.456495i	−0.0578993	+	0.0170008i
$722$	−0.445631	+	0.693415i	−0.0165847	+	0.0258062i
$723$		0			0
$724$	23.8072	−	10.8724i	0.884788	−	0.404069i
$725$	−34.8897	+	15.9336i	−1.29577	+	0.591760i
$726$		0			0
$727$	−14.2658	+	22.1980i	−0.529088	+	0.823277i	−0.998207	−	0.0598581i	$-0.980935\pi$
$727$	−14.2658	+	22.1980i	−0.529088	+	0.823277i	0.469119	+	0.883135i	$0.344572\pi$
$728$	1.39611	−	0.409936i	0.0517434	−	0.0151932i
$729$		0			0
$730$	−0.334187	−	0.289575i	−0.0123688	−	0.0107176i
$731$	15.6103	+	24.2900i	0.577366	+	0.898399i
$732$		0			0
$733$	1.41812	−	4.82966i	0.0523793	−	0.178388i	−0.929149	−	0.369706i	$-0.879458\pi$
$733$	1.41812	−	4.82966i	0.0523793	−	0.178388i	0.981528	+	0.191319i	$0.0612764\pi$
$734$	10.1231	−	22.1664i	0.373650	−	0.818178i
$735$		0			0
$736$	−1.44154	−	4.57405i	−0.0531360	−	0.168602i
$737$			9.55815i			0.352079i
$738$		0			0
$739$	−29.3652	−	8.62241i	−1.08022	−	0.317181i	−0.307252	−	0.951628i	$-0.599409\pi$
$739$	−29.3652	−	8.62241i	−1.08022	−	0.317181i	−0.772966	+	0.634448i	$0.781228\pi$
$740$	−4.55945	+	3.95079i	−0.167609	+	0.145234i
$741$		0			0
$742$	0.932787	−	1.07649i	0.0342437	−	0.0395193i
$743$	4.22022	−	29.3523i	0.154825	−	1.07683i	−0.753163	−	0.657834i	$-0.771473\pi$
$743$	4.22022	−	29.3523i	0.154825	−	1.07683i	0.907988	−	0.418997i	$-0.137618\pi$
$744$		0			0
$745$	18.7343	+	12.0398i	0.686373	+	0.441105i
$746$	−3.97059	−	27.6161i	−0.145374	−	1.01110i
$747$		0			0
$748$	−2.81104	−	6.15531i	−0.102782	−	0.225060i
$749$	2.33836	−	0.336206i	0.0854419	−	0.0122847i
$750$		0			0
$751$	−5.66407	−	19.2901i	−0.206685	−	0.703904i	−0.995955	−	0.0898577i	$-0.971359\pi$
$751$	−5.66407	−	19.2901i	−0.206685	−	0.703904i	0.789270	−	0.614047i	$-0.210459\pi$
$752$	8.37763	+	1.20452i	0.305501	+	0.0439244i
$753$		0			0
$754$	25.4601	−	16.3622i	0.927201	−	0.595876i
$755$	−33.7883	−	38.9938i	−1.22968	−	1.41913i
$756$		0			0
$757$	−40.5483	−	18.5178i	−1.47375	−	0.673040i	−0.493312	−	0.869853i	$-0.664214\pi$
$757$	−40.5483	−	18.5178i	−1.47375	−	0.673040i	−0.980441	+	0.196812i	$0.936941\pi$
$758$	37.2713			1.35375
$759$		0			0
$760$	14.5891			0.529201
$761$	−48.2946	−	22.0554i	−1.75068	−	0.799509i	−0.988327	−	0.152347i	$-0.951317\pi$
$761$	−48.2946	−	22.0554i	−1.75068	−	0.799509i	−0.762353	−	0.647162i	$-0.775956\pi$
$762$		0			0
$763$	−2.87050	−	3.31274i	−0.103919	−	0.119929i
$764$	−11.6097	+	7.46109i	−0.420024	+	0.269933i
$765$		0			0
$766$	−31.9062	−	4.58742i	−1.15282	−	0.165750i
$767$	7.31023	+	24.8964i	0.263957	+	0.898956i
$768$		0			0
$769$	10.1866	−	1.46461i	0.367338	−	0.0528153i	0.0438258	−	0.999039i	$-0.486045\pi$
$769$	10.1866	−	1.46461i	0.367338	−	0.0528153i	0.323512	+	0.946224i	$0.395136\pi$
$770$	0.855244	+	1.87272i	0.0308209	+	0.0674883i
$771$		0			0
$772$	1.90981	+	13.2830i	0.0687356	+	0.478066i
$773$	45.0227	+	28.9344i	1.61936	+	1.04070i	0.956409	+	0.292030i	$0.0943307\pi$
$773$	45.0227	+	28.9344i	1.61936	+	1.04070i	0.662947	+	0.748667i	$0.269306\pi$
$774$		0			0
$775$	−3.35248	+	23.3170i	−0.120425	+	0.837573i
$776$	3.39558	−	3.91871i	0.121894	−	0.140674i
$777$		0			0
$778$	−1.76196	+	1.52675i	−0.0631693	+	0.0547365i
$779$	30.4868	+	8.95174i	1.09230	+	0.320729i
$780$		0			0
$781$			2.73776i			0.0979649i
$782$	−4.36304	+	16.0204i	−0.156022	+	0.572887i
$783$		0			0
$784$	2.86498	−	6.27342i	0.102321	−	0.224051i
$785$	−4.29388	+	14.6236i	−0.153255	+	0.521940i
$786$		0			0
$787$	−9.45527	−	14.7127i	−0.337044	−	0.524451i	0.630819	−	0.775930i	$-0.282719\pi$
$787$	−9.45527	−	14.7127i	−0.337044	−	0.524451i	−0.967863	+	0.251480i	$0.919083\pi$
$788$	−11.4902	−	9.95635i	−0.409323	−	0.354680i
$789$		0			0
$790$	−29.3792	+	8.62651i	−1.04527	+	0.306918i
$791$	−0.956907	+	1.48898i	−0.0340237	+	0.0529419i
$792$		0			0
$793$	−61.6040	+	28.1336i	−2.18762	+	0.999053i
$794$	−5.61776	+	2.56554i	−0.199367	+	0.0910478i
$795$		0			0
$796$	3.46019	−	5.38417i	0.122643	−	0.190837i
$797$	37.2471	−	10.9367i	1.31936	−	0.387399i	0.455098	−	0.890441i	$-0.349604\pi$
$797$	37.2471	−	10.9367i	1.31936	−	0.387399i	0.864262	+	0.503042i	$0.167786\pi$
$798$		0			0
$799$	−22.1456	−	19.1893i	−0.783455	−	0.678867i
$800$	−3.10133	−	4.82576i	−0.109648	−	0.170616i
$801$		0			0
$802$	6.59872	−	22.4732i	0.233009	−	0.793556i
$803$	−0.109573	+	0.239932i	−0.00386675	+	0.00846700i
$804$		0			0
$805$	1.32743	−	4.87411i	0.0467859	−	0.171790i
$806$		−	18.5873i		−	0.654711i
$807$		0			0
$808$	3.73284	+	1.09606i	0.131321	+	0.0385593i
$809$	−30.2251	+	26.1902i	−1.06266	+	0.920800i	−0.997028	−	0.0770442i	$-0.975452\pi$
$809$	−30.2251	+	26.1902i	−1.06266	+	0.920800i	−0.0656319	+	0.997844i	$0.520906\pi$
$810$		0			0
$811$	−7.33753	+	8.46796i	−0.257656	+	0.297350i	−0.869809	−	0.493389i	$-0.835758\pi$
$811$	−7.33753	+	8.46796i	−0.257656	+	0.297350i	0.612153	+	0.790739i	$0.290303\pi$
$812$	−0.305902	+	2.12760i	−0.0107351	+	0.0746640i
$813$		0			0
$814$	3.02741	+	1.94560i	0.106111	+	0.0681933i
$815$	9.33969	+	64.9590i	0.327155	+	2.27541i
$816$		0			0
$817$	15.4254	+	33.7770i	0.539667	+	1.18171i
$818$	−8.58291	+	1.23404i	−0.300094	+	0.0431470i
$819$		0			0
$820$	−6.58777	−	22.4359i	−0.230055	−	0.783495i
$821$	−8.16234	−	1.17357i	−0.284868	−	0.0409578i	−0.00160011	−	0.999999i	$-0.500509\pi$
$821$	−8.16234	−	1.17357i	−0.284868	−	0.0409578i	−0.283267	+	0.959041i	$0.591418\pi$
$822$		0			0
$823$	−44.7100	+	28.7333i	−1.55849	+	1.00158i	−0.575527	+	0.817783i	$0.695203\pi$
$823$	−44.7100	+	28.7333i	−1.55849	+	1.00158i	−0.982964	+	0.183799i	$0.941161\pi$
$824$	−3.30072	−	3.80924i	−0.114986	−	0.132701i
$825$		0			0
$826$	−1.67633	−	0.765555i	−0.0583270	−	0.0266371i
$827$	16.8003			0.584205			0.292103	−	0.956387i	$-0.405645\pi$
$827$	16.8003			0.584205			0.292103	+	0.956387i	$0.405645\pi$
$828$		0			0
$829$	−0.253715			−0.00881188			−0.00440594	−	0.999990i	$-0.501402\pi$
$829$	−0.253715			−0.00881188			−0.00440594	+	0.999990i	$0.501402\pi$
$830$	47.3561	+	21.6268i	1.64375	+	0.750677i
$831$		0			0
$832$	2.96407	+	3.42072i	0.102761	+	0.118592i
$833$	−20.0868	+	12.9090i	−0.695966	+	0.447270i
$834$		0			0
$835$	65.1459	+	9.36656i	2.25447	+	0.324143i
$836$	−2.45174	−	8.34987i	−0.0847953	−	0.288786i
$837$		0			0
$838$	−7.90916	+	1.13717i	−0.273217	+	0.0392827i
$839$	4.40134	+	9.63758i	0.151951	+	0.332726i	0.970265	−	0.242045i	$-0.0778182\pi$
$839$	4.40134	+	9.63758i	0.151951	+	0.332726i	−0.818314	+	0.574771i	$0.805091\pi$
$840$		0			0
$841$	2.23550	+	15.5483i	0.0770863	+	0.536147i
$842$	5.27723	+	3.39147i	0.181865	+	0.116878i
$843$		0			0
$844$	−2.00036	+	13.9128i	−0.0688553	+	0.478899i
$845$	16.0652	−	18.5403i	0.552661	−	0.637805i
$846$		0			0
$847$	−1.74435	+	1.51149i	−0.0599366	+	0.0519353i
$848$	4.25144	+	1.24834i	0.145995	+	0.0428680i
$849$		0			0
$850$			19.8602i			0.681199i
$851$	−2.65420	−	8.42183i	−0.0909848	−	0.288697i
$852$		0			0
$853$	−13.8476	+	30.3219i	−0.474132	+	1.03820i	0.509904	+	0.860231i	$0.329681\pi$
$853$	−13.8476	+	30.3219i	−0.474132	+	1.03820i	−0.984036	+	0.177972i	$0.943046\pi$
$854$	1.35513	−	4.61514i	0.0463715	−	0.157927i
$855$		0			0
$856$	3.97305	+	6.18219i	0.135796	+	0.211303i
$857$	−16.5134	−	14.3090i	−0.564089	−	0.488786i	0.325504	−	0.945541i	$-0.394466\pi$
$857$	−16.5134	−	14.3090i	−0.564089	−	0.488786i	−0.889592	+	0.456755i	$0.849012\pi$
$858$		0			0
$859$	23.2482	−	6.82630i	0.793220	−	0.232910i	0.140073	−	0.990141i	$-0.455266\pi$
$859$	23.2482	−	6.82630i	0.793220	−	0.232910i	0.653147	+	0.757231i	$0.273448\pi$
$860$	14.7739	−	22.9886i	0.503785	−	0.783905i
$861$		0			0
$862$	13.7804	−	6.29329i	0.469362	−	0.214350i
$863$	−1.46631	+	0.669640i	−0.0499136	+	0.0227948i	−0.440215	−	0.897892i	$-0.645098\pi$
$863$	−1.46631	+	0.669640i	−0.0499136	+	0.0227948i	0.390302	+	0.920687i	$0.372371\pi$
$864$		0			0
$865$	−32.0387	+	49.8532i	−1.08935	+	1.69506i
$866$	10.6144	−	3.11667i	0.360692	−	0.105909i
$867$		0			0
$868$	0.997689	+	0.864502i	0.0338638	+	0.0293431i
$869$	9.87455	+	15.3651i	0.334971	+	0.521225i
$870$		0			0
$871$	−6.23607	+	21.2381i	−0.211301	+	0.719626i
$872$	5.66437	−	12.4032i	0.191820	−	0.420027i
$873$		0			0
$874$	−8.48600	+	19.5945i	−0.287043	+	0.662795i
$875$		−	0.775670i		−	0.0262224i
$876$		0			0
$877$	−25.0774	−	7.36339i	−0.846804	−	0.248644i	−0.170583	−	0.985343i	$-0.554565\pi$
$877$	−25.0774	−	7.36339i	−0.846804	−	0.248644i	−0.676221	+	0.736699i	$0.736383\pi$
$878$	−18.9289	+	16.4020i	−0.638819	+	0.553540i
$879$		0			0
$880$	−4.19389	+	4.84001i	−0.141376	+	0.163157i
$881$	1.40603	−	9.77915i	0.0473703	−	0.329468i	−0.952332	−	0.305064i	$-0.901322\pi$
$881$	1.40603	−	9.77915i	0.0473703	−	0.329468i	0.999702	−	0.0244039i	$-0.00776876\pi$
$882$		0			0
$883$	37.9647	+	24.3984i	1.27761	+	0.821073i	0.990592	−	0.136851i	$-0.0436980\pi$
$883$	37.9647	+	24.3984i	1.27761	+	0.821073i	0.287023	+	0.957924i	$0.407334\pi$
$884$	−2.23015	−	15.5111i	−0.0750081	−	0.521693i
$885$		0			0
$886$	−15.1923	−	33.2665i	−0.510395	−	1.11761i
$887$	−32.8704	+	4.72605i	−1.10368	+	0.158685i	−0.669985	−	0.742375i	$-0.733700\pi$
$887$	−32.8704	+	4.72605i	−1.10368	+	0.158685i	−0.433695	+	0.901060i	$0.642790\pi$
$888$		0			0
$889$	−0.210739	−	0.717711i	−0.00706796	−	0.0240713i
$890$	51.2265	+	7.36526i	1.71712	+	0.246884i
$891$		0			0
$892$	−16.3400	+	10.5011i	−0.547105	+	0.351603i
$893$	−24.6781	−	28.4801i	−0.825821	−	0.953049i
$894$		0			0
$895$	40.8058	+	18.6354i	1.36399	+	0.622912i
$896$	−0.321469			−0.0107395
$897$		0			0
$898$	8.78972			0.293317
$899$	24.9768	+	11.4065i	0.833023	+	0.380429i
$900$		0			0
$901$	−10.0459	−	11.5936i	−0.334677	−	0.386238i
$902$	−11.7338	+	7.54085i	−0.390692	+	0.251083i
$903$		0			0
$904$	−5.44977	−	0.783559i	−0.181257	−	0.0260608i
$905$	24.1607	+	82.2837i	0.803128	+	2.73520i
$906$		0			0
$907$	−21.3179	+	3.06505i	−0.707849	+	0.101773i	−0.486830	−	0.873496i	$-0.661847\pi$
$907$	−21.3179	+	3.06505i	−0.707849	+	0.101773i	−0.221018	+	0.975270i	$0.570938\pi$
$908$	3.10029	+	6.78869i	0.102887	+	0.225290i
$909$		0			0
$910$	0.678513	+	4.71916i	0.0224925	+	0.156439i
$911$	42.2332	+	27.1416i	1.39925	+	0.899242i	0.999846	−	0.0175345i	$-0.00558169\pi$
$911$	42.2332	+	27.1416i	1.39925	+	0.899242i	0.399401	+	0.916776i	$0.369218\pi$
$912$		0			0
$913$	4.41947	−	30.7381i	0.146263	−	1.01728i
$914$	−16.3903	+	18.9155i	−0.542144	+	0.625668i
$915$		0			0
$916$	0.767896	−	0.665386i	0.0253720	−	0.0219850i
$917$	6.26740	+	1.84027i	0.206968	+	0.0607712i
$918$		0			0
$919$		−	16.2875i		−	0.537276i	−0.963241	−	0.268638i	$-0.913427\pi$
$919$		−	16.2875i		−	0.537276i	0.963241	−	0.268638i	$-0.0865735\pi$
$920$	15.5072	−	2.54240i	0.511257	−	0.0838205i
$921$		0			0
$922$	5.25256	−	11.5015i	0.172984	−	0.378782i
$923$	−1.78621	+	6.08328i	−0.0587939	+	0.200234i
$924$		0			0
$925$	−5.71022	−	8.88528i	−0.187751	−	0.292146i
$926$	−28.1650	−	24.4051i	−0.925559	−	0.802002i
$927$		0			0
$928$	−6.41557	+	1.88378i	−0.210601	+	0.0618381i
$929$	10.4485	−	16.2581i	0.342803	−	0.533412i	−0.626455	−	0.779457i	$-0.715495\pi$
$929$	10.4485	−	16.2581i	0.342803	−	0.533412i	0.969258	+	0.246046i	$0.0791313\pi$
$930$		0			0
$931$	−27.9321	+	12.7561i	−0.915436	+	0.418066i
$932$	1.50695	−	0.688203i	0.0493619	−	0.0225428i
$933$		0			0
$934$	−6.55386	+	10.1980i	−0.214449	+	0.333689i
$935$	21.2743	−	6.24670i	0.695744	−	0.204289i
$936$		0			0
$937$	27.6860	+	23.9900i	0.904462	+	0.783720i	0.976910	−	0.213652i	$-0.0685358\pi$
$937$	27.6860	+	23.9900i	0.904462	+	0.783720i	−0.0724483	+	0.997372i	$0.523081\pi$
$938$	−0.849929	−	1.32252i	−0.0277512	−	0.0431817i
$939$		0			0
$940$	−7.81323	+	26.6094i	−0.254839	+	0.867903i
$941$	−0.296287	+	0.648778i	−0.00965868	+	0.0211496i	−0.914400	−	0.404812i	$-0.867337\pi$
$941$	−0.296287	+	0.648778i	−0.00965868	+	0.0211496i	0.904741	+	0.425962i	$0.140064\pi$
$942$		0			0
$943$	33.9654	+	4.20223i	1.10607	+	0.136843i
$944$		−	5.73264i		−	0.186582i
$945$		0			0
$946$	−15.6400	−	4.59233i	−0.508501	−	0.149309i
$947$	5.76709	−	4.99721i	0.187405	−	0.162388i	−0.556105	−	0.831112i	$-0.687705\pi$
$947$	5.76709	−	4.99721i	0.187405	−	0.162388i	0.743510	+	0.668724i	$0.233159\pi$
$948$		0			0
$949$	−0.400010	+	0.461636i	−0.0129849	+	0.0149853i
$950$	−3.63486	+	25.2810i	−0.117930	+	0.820224i
$951$		0			0
$952$	0.936292	+	0.601718i	0.0303454	+	0.0195018i
$953$	−2.04473	−	14.2214i	−0.0662354	−	0.460677i	−0.995765	−	0.0919309i	$-0.970696\pi$
$953$	−2.04473	−	14.2214i	−0.0662354	−	0.460677i	0.929530	−	0.368747i	$-0.120213\pi$
$954$		0			0
$955$	−18.7847	−	41.1328i	−0.607860	−	1.33103i
$956$	−11.6137	+	1.66979i	−0.375613	+	0.0540050i
$957$		0			0
$958$	−6.47570	−	22.0542i	−0.209220	−	0.712539i
$959$	−1.42369	−	0.204695i	−0.0459732	−	0.00660995i
$960$		0			0
$961$	−11.8921	+	7.64260i	−0.383617	+	0.246535i
$962$	5.45750	+	6.29829i	0.175957	+	0.203065i
$963$		0			0
$964$	19.0146	+	8.68366i	0.612418	+	0.279682i
$965$	−43.9713			−1.41549
$966$		0			0
$967$	−3.30487			−0.106277			−0.0531387	−	0.998587i	$-0.516923\pi$
$967$	−3.30487			−0.106277			−0.0531387	+	0.998587i	$0.516923\pi$
$968$	−6.53103	−	2.98262i	−0.209915	−	0.0958651i
$969$		0			0
$970$	11.1261	+	12.8402i	0.357238	+	0.412275i
$971$	4.95666	−	3.18545i	0.159067	−	0.102226i	−0.458686	−	0.888598i	$-0.651680\pi$
$971$	4.95666	−	3.18545i	0.159067	−	0.102226i	0.617753	+	0.786372i	$0.288043\pi$
$972$		0			0
$973$	6.48695	+	0.932682i	0.207962	+	0.0299004i
$974$	7.04556	+	23.9950i	0.225754	+	0.768848i
$975$		0			0
$976$	14.8102	−	2.12938i	0.474063	−	0.0681599i
$977$	−2.51908	−	5.51601i	−0.0805924	−	0.176473i	0.865046	−	0.501692i	$-0.167289\pi$
$977$	−2.51908	−	5.51601i	−0.0805924	−	0.176473i	−0.945639	+	0.325220i	$0.894562\pi$
$978$		0			0
$979$	−4.39338	−	30.5566i	−0.140413	−	0.976593i
$980$	19.0106	+	12.2173i	0.607270	+	0.390269i
$981$		0			0
$982$	1.73322	−	12.0548i	0.0553092	−	0.384684i
$983$	30.5706	−	35.2803i	0.975049	−	1.12527i	−0.0170554	−	0.999855i	$-0.505429\pi$
$983$	30.5706	−	35.2803i	0.975049	−	1.12527i	0.992105	−	0.125412i	$-0.0400254\pi$
$984$		0			0
$985$	37.6494	−	32.6234i	1.19961	−	1.03947i
$986$	22.2116	+	6.52192i	0.707362	+	0.207700i
$987$		0			0
$988$		−	20.1529i		−	0.641150i
$989$	22.2824	+	33.2145i	0.708539	+	1.05616i
$990$		0			0
$991$	−3.47122	+	7.60092i	−0.110267	+	0.241451i	−0.956719	−	0.291014i	$-0.906007\pi$
$991$	−3.47122	+	7.60092i	−0.110267	+	0.241451i	0.846452	+	0.532466i	$0.178734\pi$
$992$	−1.15695	+	3.94021i	−0.0367332	+	0.125102i
$993$		0			0
$994$	−0.243447	−	0.378811i	−0.00772168	−	0.0120152i
$995$	15.8489	+	13.7331i	0.502443	+	0.435370i
$996$		0			0
$997$	−18.9141	+	5.55369i	−0.599017	+	0.175887i	−0.567163	−	0.823605i	$-0.691959\pi$
$997$	−18.9141	+	5.55369i	−0.599017	+	0.175887i	−0.0318536	+	0.999493i	$0.510141\pi$
$998$	−5.65737	+	8.80304i	−0.179081	+	0.278655i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.17.1	✓	80
3.2	odd	2	inner	414.2.j.a.17.8	yes	80
23.19	odd	22	inner	414.2.j.a.341.8	yes	80
69.65	even	22	inner	414.2.j.a.341.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.17.1	✓	80	1.1	even	1	trivial
414.2.j.a.17.8	yes	80	3.2	odd	2	inner
414.2.j.a.341.1	yes	80	69.65	even	22	inner
414.2.j.a.341.8	yes	80	23.19	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.909632 - 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.75649 + 1.77149i) q^{5} +(-0.318197 - 0.0457498i) q^{7} +(-0.281733 - 0.959493i) q^{8} +O(q^{10})\)	\(q+(-0.909632 - 0.415415i) q^{2} +(0.654861 + 0.755750i) q^{4} +(-2.75649 + 1.77149i) q^{5} +(-0.318197 - 0.0457498i) q^{7} +(-0.281733 - 0.959493i) q^{8} +(3.24329 - 0.466315i) q^{10} +(-0.811936 - 1.77789i) q^{11} +(-0.644154 - 4.48019i) q^{13} +(0.270437 + 0.173799i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(2.26722 - 2.61651i) q^{17} +(3.36493 - 2.91573i) q^{19} +(-3.14392 - 0.923137i) q^{20} +1.95452i q^{22} +(3.06858 - 3.68562i) q^{23} +(2.38298 - 5.21800i) q^{25} +(-1.27519 + 4.34291i) q^{26} +(-0.173799 - 0.270437i) q^{28} +(-5.05326 - 4.37867i) q^{29} +(-3.94021 + 1.15695i) q^{31} +(0.540641 - 0.841254i) q^{32} +(-3.14928 + 1.43823i) q^{34} +(0.958152 - 0.437573i) q^{35} +(0.995438 - 1.54893i) q^{37} +(-4.27209 + 1.25440i) q^{38} +(2.47632 + 2.14575i) q^{40} +(3.85817 + 6.00342i) q^{41} +(-2.34960 + 8.00199i) q^{43} +(0.811936 - 1.77789i) q^{44} +(-4.32234 + 2.07783i) q^{46} -8.46378i q^{47} +(-6.61729 - 1.94301i) q^{49} +(-4.33528 + 3.75654i) q^{50} +(2.96407 - 3.42072i) q^{52} +(0.630586 - 4.38582i) q^{53} +(5.38760 + 3.46240i) q^{55} +(0.0457498 + 0.318197i) q^{56} +(2.77764 + 6.08218i) q^{58} +(-5.67429 + 0.815840i) q^{59} +(-4.21542 - 14.3564i) q^{61} +(4.06476 + 0.584424i) q^{62} +(-0.841254 + 0.540641i) q^{64} +(9.71220 + 11.2085i) q^{65} +(-4.44836 - 2.03150i) q^{67} +3.46214 q^{68} -1.05334 q^{70} +(-1.27416 - 0.581887i) q^{71} +(-0.0883754 - 0.101991i) q^{73} +(-1.54893 + 0.995438i) q^{74} +(4.40713 + 0.633649i) q^{76} +(0.177017 + 0.602866i) q^{77} +(-9.24966 + 1.32990i) q^{79} +(-1.36117 - 2.98054i) q^{80} +(-1.01560 - 7.06365i) q^{82} +(13.3662 + 8.58993i) q^{83} +(-1.61445 + 11.2287i) q^{85} +(5.46142 - 6.30281i) q^{86} +(-1.47713 + 1.27994i) q^{88} +(15.1548 + 4.44986i) q^{89} +1.45505i q^{91} +(4.79490 - 0.0944928i) q^{92} +(-3.51598 + 7.69893i) q^{94} +(-4.11022 + 13.9981i) q^{95} +(2.80333 + 4.36207i) q^{97} +(5.21215 + 4.51635i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 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

Introduction

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