LMFDB - Embedded newform 414.2.j.a.107.4

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			107.4
Character	$\chi$	$=$	414.107
Dual form			414.2.j.a.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 - 0.142315i) q^{2} +(0.959493 + 0.281733i) q^{4} +(2.09328 + 2.41578i) q^{5} +(0.761188 - 1.18443i) q^{7} +(-0.909632 - 0.415415i) q^{8} +O(q^{10})$	\(q+(-0.989821 - 0.142315i) q^{2} +(0.959493 + 0.281733i) q^{4} +(2.09328 + 2.41578i) q^{5} +(0.761188 - 1.18443i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(-1.72817 - 2.68909i) q^{10} +(0.611710 + 4.25454i) q^{11} +(1.51536 - 0.973861i) q^{13} +(-0.922002 + 1.06405i) q^{14} +(0.841254 + 0.540641i) q^{16} +(-1.94380 + 0.570751i) q^{17} +(-0.0167231 + 0.0569538i) q^{19} +(1.32789 + 2.90767i) q^{20} -4.29829i q^{22} +(-2.58260 - 4.04106i) q^{23} +(-0.742571 + 5.16469i) q^{25} +(-1.63853 + 0.748291i) q^{26} +(1.06405 - 0.922002i) q^{28} +(2.29954 + 7.83150i) q^{29} +(-1.82540 + 3.99706i) q^{31} +(-0.755750 - 0.654861i) q^{32} +(2.00524 - 0.288310i) q^{34} +(4.45470 - 0.640489i) q^{35} +(4.96044 + 4.29825i) q^{37} +(0.0246583 - 0.0539941i) q^{38} +(-0.900567 - 3.06705i) q^{40} +(8.47079 - 7.33998i) q^{41} +(6.53347 - 2.98374i) q^{43} +(-0.611710 + 4.25454i) q^{44} +(1.98121 + 4.36747i) q^{46} -0.223550i q^{47} +(2.08443 + 4.56427i) q^{49} +(1.47002 - 5.00645i) q^{50} +(1.72834 - 0.507487i) q^{52} +(1.93957 + 1.24649i) q^{53} +(-8.99753 + 10.3837i) q^{55} +(-1.18443 + 0.761188i) q^{56} +(-1.16159 - 8.07905i) q^{58} +(-6.13821 - 9.55124i) q^{59} +(1.45253 + 0.663348i) q^{61} +(2.37566 - 3.69659i) q^{62} +(0.654861 + 0.755750i) q^{64} +(5.52470 + 1.62220i) q^{65} +(0.815293 + 0.117221i) q^{67} -2.02586 q^{68} -4.50051 q^{70} +(-10.6755 - 1.53490i) q^{71} +(-11.1441 - 3.27221i) q^{73} +(-4.29825 - 4.96044i) q^{74} +(-0.0320915 + 0.0499353i) q^{76} +(5.50483 + 2.51397i) q^{77} +(-8.97046 - 13.9583i) q^{79} +(0.454914 + 3.16399i) q^{80} +(-9.42916 + 6.05975i) q^{82} +(-1.33209 + 1.53731i) q^{83} +(-5.44772 - 3.50104i) q^{85} +(-6.89160 + 2.02356i) q^{86} +(1.21097 - 4.12418i) q^{88} +(2.08277 + 4.56064i) q^{89} -2.53613i q^{91} +(-1.33949 - 4.60497i) q^{92} +(-0.0318145 + 0.221275i) q^{94} +(-0.172594 + 0.0788209i) q^{95} +(-7.36577 + 6.38247i) q^{97} +(-1.41365 - 4.81446i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{17}{22}\right)$

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 $

$2$	−0.989821	−	0.142315i	−0.699909	−	0.100632i
$2$	−0.989821	−	0.142315i	−0.699909	−	0.100632i
$3$		0			0
$3$		0			0
$4$	0.959493	+	0.281733i	0.479746	+	0.140866i
$5$	2.09328	+	2.41578i	0.936144	+	1.08037i	0.996616	+	0.0821980i	$0.0261940\pi$
$5$	2.09328	+	2.41578i	0.936144	+	1.08037i	−0.0604719	+	0.998170i	$0.519261\pi$
$6$		0			0
$7$	0.761188	−	1.18443i	0.287702	−	0.447673i	−0.667077	−	0.744988i	$-0.732455\pi$
$7$	0.761188	−	1.18443i	0.287702	−	0.447673i	0.954779	+	0.297315i	$0.0960913\pi$
$8$	−0.909632	−	0.415415i	−0.321603	−	0.146871i
$9$		0			0
$10$	−1.72817	−	2.68909i	−0.546497	−	0.850366i
$11$	0.611710	+	4.25454i	0.184438	+	1.28279i	0.846114	+	0.533002i	$0.178936\pi$
$11$	0.611710	+	4.25454i	0.184438	+	1.28279i	−0.661677	+	0.749789i	$0.730155\pi$
$12$		0			0
$13$	1.51536	−	0.973861i	0.420285	−	0.270101i	−0.313359	−	0.949635i	$-0.601454\pi$
$13$	1.51536	−	0.973861i	0.420285	−	0.270101i	0.733644	+	0.679534i	$0.237818\pi$
$14$	−0.922002	+	1.06405i	−0.246415	+	0.284379i
$15$		0			0
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	−1.94380	+	0.570751i	−0.471440	+	0.138427i	−0.508818	−	0.860874i	$-0.669918\pi$
$17$	−1.94380	+	0.570751i	−0.471440	+	0.138427i	0.0373782	+	0.999301i	$0.488099\pi$
$18$		0			0
$19$	−0.0167231	+	0.0569538i	−0.00383655	+	0.0130661i	−0.961389	−	0.275193i	$-0.911258\pi$
$19$	−0.0167231	+	0.0569538i	−0.00383655	+	0.0130661i	0.957552	+	0.288259i	$0.0930764\pi$
$20$	1.32789	+	2.90767i	0.296924	+	0.650174i
$21$		0			0
$22$		−	4.29829i		−	0.916398i
$23$	−2.58260	−	4.04106i	−0.538510	−	0.842619i
$23$	−2.58260	−	4.04106i	−0.538510	−	0.842619i
$24$		0			0
$25$	−0.742571	+	5.16469i	−0.148514	+	1.03294i
$26$	−1.63853	+	0.748291i	−0.321342	+	0.146752i
$27$		0			0
$28$	1.06405	−	0.922002i	0.201086	−	0.174242i
$29$	2.29954	+	7.83150i	0.427013	+	1.45427i	0.839525	+	0.543321i	$0.182833\pi$
$29$	2.29954	+	7.83150i	0.427013	+	1.45427i	−0.412512	+	0.910952i	$0.635348\pi$
$30$		0			0
$31$	−1.82540	+	3.99706i	−0.327851	+	0.717893i	−0.999741	−	0.0227578i	$-0.992755\pi$
$31$	−1.82540	+	3.99706i	−0.327851	+	0.717893i	0.671890	+	0.740651i	$0.265483\pi$
$32$	−0.755750	−	0.654861i	−0.133599	−	0.115764i
$33$		0			0
$34$	2.00524	−	0.288310i	0.343896	−	0.0494447i
$35$	4.45470	−	0.640489i	0.752982	−	0.108262i
$36$		0			0
$37$	4.96044	+	4.29825i	0.815491	+	0.706627i	0.959119	−	0.283005i	$-0.0913312\pi$
$37$	4.96044	+	4.29825i	0.815491	+	0.706627i	−0.143627	+	0.989632i	$0.545877\pi$
$38$	0.0246583	−	0.0539941i	0.00400010	−	0.00875900i
$39$		0			0
$40$	−0.900567	−	3.06705i	−0.142392	−	0.484943i
$41$	8.47079	−	7.33998i	1.32292	−	1.14631i	0.344701	−	0.938712i	$-0.387980\pi$
$41$	8.47079	−	7.33998i	1.32292	−	1.14631i	0.978214	−	0.207600i	$-0.0665653\pi$
$42$		0			0
$43$	6.53347	−	2.98374i	0.996345	−	0.455016i	0.150596	−	0.988595i	$-0.451881\pi$
$43$	6.53347	−	2.98374i	0.996345	−	0.455016i	0.845750	+	0.533580i	$0.179154\pi$
$44$	−0.611710	+	4.25454i	−0.0922188	+	0.641396i
$45$		0			0
$46$	1.98121	+	4.36747i	0.292114	+	0.643948i
$47$		−	0.223550i		−	0.0326082i	−0.999867	−	0.0163041i	$-0.994810\pi$
$47$		−	0.223550i		−	0.0326082i	0.999867	−	0.0163041i	$-0.00518998\pi$
$48$		0			0
$49$	2.08443	+	4.56427i	0.297776	+	0.652039i
$50$	1.47002	−	5.00645i	0.207893	−	0.708018i
$51$		0			0
$52$	1.72834	−	0.507487i	0.239678	−	0.0703759i
$53$	1.93957	+	1.24649i	0.266421	+	0.171218i	0.667030	−	0.745031i	$-0.267565\pi$
$53$	1.93957	+	1.24649i	0.266421	+	0.171218i	−0.400609	+	0.916249i	$0.631202\pi$
$54$		0			0
$55$	−8.99753	+	10.3837i	−1.21323	+	1.40014i
$56$	−1.18443	+	0.761188i	−0.158276	+	0.101718i
$57$		0			0
$58$	−1.16159	−	8.07905i	−0.152524	−	1.06083i
$59$	−6.13821	−	9.55124i	−0.799127	−	1.24347i	−0.966269	−	0.257533i	$-0.917090\pi$
$59$	−6.13821	−	9.55124i	−0.799127	−	1.24347i	0.167143	−	0.985933i	$-0.446546\pi$
$60$		0			0
$61$	1.45253	+	0.663348i	0.185977	+	0.0849330i	0.506227	−	0.862400i	$-0.331040\pi$
$61$	1.45253	+	0.663348i	0.185977	+	0.0849330i	−0.320250	+	0.947333i	$0.603767\pi$
$62$	2.37566	−	3.69659i	0.301709	−	0.469468i
$63$		0			0
$64$	0.654861	+	0.755750i	0.0818576	+	0.0944687i
$65$	5.52470	+	1.62220i	0.685255	+	0.201209i
$66$		0			0
$67$	0.815293	+	0.117221i	0.0996039	+	0.0143209i	0.191937	−	0.981407i	$-0.438523\pi$
$67$	0.815293	+	0.117221i	0.0996039	+	0.0143209i	−0.0923326	+	0.995728i	$0.529432\pi$
$68$	−2.02586			−0.245672
$69$		0			0
$70$	−4.50051			−0.537914
$71$	−10.6755	−	1.53490i	−1.26694	−	0.182159i	−0.524119	−	0.851645i	$-0.675605\pi$
$71$	−10.6755	−	1.53490i	−1.26694	−	0.182159i	−0.742825	+	0.669486i	$0.766514\pi$
$72$		0			0
$73$	−11.1441	−	3.27221i	−1.30432	−	0.382984i	−0.445512	−	0.895276i	$-0.646978\pi$
$73$	−11.1441	−	3.27221i	−1.30432	−	0.382984i	−0.858811	+	0.512293i	$0.828796\pi$
$74$	−4.29825	−	4.96044i	−0.499661	−	0.576639i
$75$		0			0
$76$	−0.0320915	+	0.0499353i	−0.00368114	+	0.00572797i
$77$	5.50483	+	2.51397i	0.627334	+	0.286494i
$78$		0			0
$79$	−8.97046	−	13.9583i	−1.00926	−	1.57043i	−0.806527	−	0.591198i	$-0.798655\pi$
$79$	−8.97046	−	13.9583i	−1.00926	−	1.57043i	−0.202729	−	0.979235i	$-0.564981\pi$
$80$	0.454914	+	3.16399i	0.0508609	+	0.353745i
$81$		0			0
$82$	−9.42916	+	6.05975i	−1.04128	+	0.669188i
$83$	−1.33209	+	1.53731i	−0.146216	+	0.168742i	−0.824133	−	0.566396i	$-0.808337\pi$
$83$	−1.33209	+	1.53731i	−0.146216	+	0.168742i	0.677917	+	0.735138i	$0.262883\pi$
$84$		0			0
$85$	−5.44772	−	3.50104i	−0.590889	−	0.379741i
$86$	−6.89160	+	2.02356i	−0.743141	+	0.218206i
$87$		0			0
$88$	1.21097	−	4.12418i	0.129090	−	0.439639i
$89$	2.08277	+	4.56064i	0.220774	+	0.483427i	0.987316	−	0.158767i	$-0.0507518\pi$
$89$	2.08277	+	4.56064i	0.220774	+	0.483427i	−0.766543	+	0.642194i	$0.778025\pi$
$90$		0			0
$91$		−	2.53613i		−	0.265859i
$92$	−1.33949	−	4.60497i	−0.139652	−	0.480101i
$93$		0			0
$94$	−0.0318145	+	0.221275i	−0.00328142	+	0.0228228i
$95$	−0.172594	+	0.0788209i	−0.0177077	+	0.00808686i
$96$		0			0
$97$	−7.36577	+	6.38247i	−0.747880	+	0.648042i	−0.943021	−	0.332733i	$-0.892029\pi$
$97$	−7.36577	+	6.38247i	−0.747880	+	0.648042i	0.195141	+	0.980775i	$0.437484\pi$
$98$	−1.41365	−	4.81446i	−0.142801	−	0.486334i
$99$		0			0
$100$	−2.16755	+	4.74628i	−0.216755	+	0.474628i
$101$	−13.8249	−	11.9793i	−1.37563	−	1.19199i	−0.959169	−	0.282833i	$-0.908726\pi$
$101$	−13.8249	−	11.9793i	−1.37563	−	1.19199i	−0.416458	−	0.909155i	$-0.636729\pi$
$102$		0			0
$103$	15.8993	−	2.28598i	1.56661	−	0.225244i	0.696299	−	0.717752i	$-0.254829\pi$
$103$	15.8993	−	2.28598i	1.56661	−	0.225244i	0.870308	+	0.492508i	$0.163920\pi$
$104$	−1.78297	+	0.256353i	−0.174835	+	0.0251375i
$105$		0			0
$106$	−1.74244	−	1.50983i	−0.169240	−	0.146648i
$107$	2.43155	−	5.32435i	0.235067	−	0.514724i	−0.754932	−	0.655803i	$-0.772330\pi$
$107$	2.43155	−	5.32435i	0.235067	−	0.514724i	0.989998	+	0.141079i	$0.0450573\pi$
$108$		0			0
$109$	2.59644	+	8.84268i	0.248694	+	0.846975i	0.985326	+	0.170681i	$0.0545968\pi$
$109$	2.59644	+	8.84268i	0.248694	+	0.846975i	−0.736632	+	0.676294i	$0.763585\pi$
$110$	10.3837	−	8.99753i	0.990047	−	0.857880i
$111$		0			0
$112$	1.28070	−	0.584878i	0.121015	−	0.0552658i
$113$	2.65406	−	18.4594i	0.249673	−	1.73652i	−0.350427	−	0.936590i	$-0.613963\pi$
$113$	2.65406	−	18.4594i	0.249673	−	1.73652i	0.600100	−	0.799925i	$-0.295128\pi$
$114$		0			0
$115$	4.35617	−	14.6981i	0.406215	−	1.37060i
$116$			8.16213i			0.757834i
$117$		0			0
$118$	4.71645	+	10.3276i	0.434184	+	0.950731i
$119$	−0.803580	+	2.73674i	−0.0736641	+	0.250877i
$120$		0			0
$121$	−7.17247	+	2.10603i	−0.652043	+	0.191457i
$122$	−1.34334	−	0.863313i	−0.121620	−	0.0781607i
$123$		0			0
$124$	−2.87756	+	3.32088i	−0.258412	+	0.298223i
$125$	−0.585692	+	0.376402i	−0.0523859	+	0.0336664i
$126$		0			0
$127$	−1.95141	−	13.5723i	−0.173160	−	1.20435i	−0.872157	−	0.489227i	$-0.837279\pi$
$127$	−1.95141	−	13.5723i	−0.173160	−	1.20435i	0.698997	−	0.715124i	$-0.253630\pi$
$128$	−0.540641	−	0.841254i	−0.0477863	−	0.0743570i
$129$		0			0
$130$	−5.23761	−	2.39193i	−0.459368	−	0.209787i
$131$	2.16064	−	3.36202i	0.188776	−	0.293741i	−0.733946	−	0.679208i	$-0.762323\pi$
$131$	2.16064	−	3.36202i	0.188776	−	0.293741i	0.922722	+	0.385467i	$0.125960\pi$
$132$		0			0
$133$	0.0547284	+	0.0631599i	0.00474555	+	0.00547666i
$134$	−0.790312	−	0.232057i	−0.0682726	−	0.0200466i
$135$		0			0
$136$	2.00524	+	0.288310i	0.171948	+	0.0247224i
$137$	−12.1475			−1.03783			−0.518914	−	0.854826i	$-0.673664\pi$
$137$	−12.1475			−1.03783			−0.518914	+	0.854826i	$0.673664\pi$
$138$		0			0
$139$	−2.48973			−0.211176			−0.105588	−	0.994410i	$-0.533672\pi$
$139$	−2.48973			−0.211176			−0.105588	+	0.994410i	$0.533672\pi$
$140$	4.45470	+	0.640489i	0.376491	+	0.0541312i
$141$		0			0
$142$	10.3484	+	3.03855i	0.868415	+	0.254990i
$143$	5.07029	+	5.85142i	0.423999	+	0.489321i
$144$		0			0
$145$	−14.1056	+	21.9487i	−1.17140	+	1.82274i
$146$	10.5650	+	4.82488i	0.874367	+	0.399310i
$147$		0			0
$148$	3.54855	+	5.52165i	0.291689	+	0.453877i
$149$	1.13993	+	7.92840i	0.0933869	+	0.649520i	0.981721	+	0.190323i	$0.0609536\pi$
$149$	1.13993	+	7.92840i	0.0933869	+	0.649520i	−0.888335	+	0.459197i	$0.848137\pi$
$150$		0			0
$151$	19.1288	−	12.2933i	1.55668	−	1.00042i	0.573197	−	0.819418i	$-0.305703\pi$
$151$	19.1288	−	12.2933i	1.55668	−	1.00042i	0.983483	−	0.181000i	$-0.0579333\pi$
$152$	0.0388713	−	0.0448599i	0.00315288	−	0.00363862i
$153$		0			0
$154$	−5.09103	−	3.27180i	−0.410247	−	0.263649i
$155$	−13.4771	+	3.95722i	−1.08250	+	0.317852i
$156$		0			0
$157$	5.11443	−	17.4182i	0.408176	−	1.39012i	−0.457364	−	0.889280i	$-0.651206\pi$
$157$	5.11443	−	17.4182i	0.408176	−	1.39012i	0.865540	−	0.500840i	$-0.166976\pi$
$158$	6.89268	+	15.0929i	0.548352	+	1.20072i
$159$		0			0
$160$		−	3.19653i		−	0.252708i
$161$	−6.75220	−	0.0170872i	−0.532148	−	0.00134666i
$162$		0			0
$163$	0.147917	−	1.02879i	0.0115858	−	0.0805809i	−0.983208	−	0.182487i	$-0.941585\pi$
$163$	0.147917	−	1.02879i	0.0115858	−	0.0805809i	0.994794	+	0.101906i	$0.0324942\pi$
$164$	10.1956	−	4.65616i	0.796141	−	0.363585i
$165$		0			0
$166$	1.53731	−	1.33209i	0.119319	−	0.103390i
$167$	2.09591	+	7.13801i	0.162186	+	0.552356i	0.999980	+	0.00636857i	$0.00202719\pi$
$167$	2.09591	+	7.13801i	0.162186	+	0.552356i	−0.837793	+	0.545987i	$0.816155\pi$
$168$		0			0
$169$	−4.05249	+	8.87372i	−0.311730	+	0.682594i
$170$	4.89402	+	4.24070i	0.375354	+	0.325246i
$171$		0			0
$172$	7.10944	−	1.02218i	0.542090	−	0.0779407i
$173$	15.1180	−	2.17365i	1.14940	−	0.165259i	0.458832	−	0.888523i	$-0.348268\pi$
$173$	15.1180	−	2.17365i	1.14940	−	0.165259i	0.690572	+	0.723264i	$0.257359\pi$
$174$		0			0
$175$	5.55199	+	4.81083i	0.419691	+	0.363664i
$176$	−1.78557	+	3.90986i	−0.134593	+	0.294717i
$177$		0			0
$178$	−1.41253	−	4.81063i	−0.105873	−	0.360572i
$179$	−13.2117	+	11.4480i	−0.987489	+	0.855665i	−0.989529	−	0.144333i	$-0.953896\pi$
$179$	−13.2117	+	11.4480i	−0.987489	+	0.855665i	0.00203963	+	0.999998i	$0.499351\pi$
$180$		0			0
$181$	−9.74629	+	4.45098i	−0.724436	+	0.330839i	−0.743277	−	0.668984i	$-0.766730\pi$
$181$	−9.74629	+	4.45098i	−0.724436	+	0.330839i	0.0188413	+	0.999822i	$0.494002\pi$
$182$	−0.360929	+	2.51031i	−0.0267538	+	0.186077i
$183$		0			0
$184$	0.670503	+	4.74873i	0.0494301	+	0.350081i
$185$			20.9808i			1.54254i
$186$		0			0
$187$	−3.61732	−	7.92083i	−0.264525	−	0.579228i
$188$	0.0629814	−	0.214495i	0.00459339	−	0.0156437i
$189$		0			0
$190$	0.182054	−	0.0534560i	0.0132076	−	0.00387811i
$191$	−13.4931	−	8.67148i	−0.976325	−	0.627446i	−0.0478555	−	0.998854i	$-0.515239\pi$
$191$	−13.4931	−	8.67148i	−0.976325	−	0.627446i	−0.928470	+	0.371408i	$0.878875\pi$
$192$		0			0
$193$	0.166139	−	0.191734i	0.0119589	−	0.0138014i	−0.749739	−	0.661734i	$-0.769821\pi$
$193$	0.166139	−	0.191734i	0.0119589	−	0.0138014i	0.761698	+	0.647933i	$0.224366\pi$
$194$	8.19911	−	5.26925i	0.588662	−	0.378310i
$195$		0			0
$196$	0.714095	+	4.96664i	0.0510068	+	0.354760i
$197$	−3.12738	−	4.86629i	−0.222816	−	0.346709i	0.711790	−	0.702392i	$-0.247885\pi$
$197$	−3.12738	−	4.86629i	−0.222816	−	0.346709i	−0.934607	+	0.355683i	$0.884248\pi$
$198$		0			0
$199$	−5.88139	−	2.68594i	−0.416920	−	0.190401i	0.195899	−	0.980624i	$-0.437237\pi$
$199$	−5.88139	−	2.68594i	−0.416920	−	0.190401i	−0.612820	+	0.790223i	$0.709965\pi$
$200$	2.82096	−	4.38950i	0.199472	−	0.310384i
$201$		0			0
$202$	11.9793	+	13.8249i	0.842863	+	0.972716i
$203$	11.0263	+	3.23760i	0.773891	+	0.227235i
$204$		0			0
$205$	35.4635	+	5.09888i	2.47688	+	0.356121i
$206$	−16.0628			−1.11915
$207$		0			0
$208$	1.80131			0.124898
$209$	−0.252542	−	0.0363100i	−0.0174687	−	0.00251162i
$210$		0			0
$211$	7.31641	+	2.14829i	0.503682	+	0.147894i	0.523696	−	0.851905i	$-0.324553\pi$
$211$	7.31641	+	2.14829i	0.503682	+	0.147894i	−0.0200138	+	0.999800i	$0.506371\pi$
$212$	1.50983	+	1.74244i	0.103695	+	0.119671i
$213$		0			0
$214$	−3.16453	+	4.92411i	−0.216323	+	0.336605i
$215$	20.8844	+	9.53761i	1.42431	+	0.650459i
$216$		0			0
$217$	3.34477	+	5.20457i	0.227058	+	0.353309i
$218$	−1.31157	−	9.12218i	−0.0888308	−	0.617832i
$219$		0			0
$220$	−11.5585	+	7.42819i	−0.779273	+	0.500808i
$221$	−2.38972	+	2.75788i	−0.160750	+	0.185515i
$222$		0			0
$223$	−13.1618	−	8.45854i	−0.881376	−	0.566426i	0.0198366	−	0.999803i	$-0.493685\pi$
$223$	−13.1618	−	8.45854i	−0.881376	−	0.566426i	−0.901213	+	0.433377i	$0.857322\pi$
$224$	−1.35090	+	0.396661i	−0.0902611	+	0.0265031i
$225$		0			0
$226$	−5.25410	+	17.8938i	−0.349497	+	1.19028i
$227$	3.24522	+	7.10604i	0.215393	+	0.471644i	0.986228	−	0.165390i	$-0.0528882\pi$
$227$	3.24522	+	7.10604i	0.215393	+	0.471644i	−0.770835	+	0.637034i	$0.780161\pi$
$228$		0			0
$229$		−	16.8692i		−	1.11475i	−0.830261	−	0.557375i	$-0.811809\pi$
$229$		−	16.8692i		−	1.11475i	0.830261	−	0.557375i	$-0.188191\pi$
$230$	−6.40359	+	13.9285i	−0.422240	+	0.918419i
$231$		0			0
$232$	1.16159	−	8.07905i	0.0762622	−	0.530415i
$233$	18.7234	−	8.55067i	1.22661	−	0.560173i	0.306512	−	0.951867i	$-0.400838\pi$
$233$	18.7234	−	8.55067i	1.22661	−	0.560173i	0.920096	+	0.391694i	$0.128111\pi$
$234$		0			0
$235$	0.540048	−	0.467954i	0.0352288	−	0.0305260i
$236$	−3.19867	−	10.8937i	−0.208216	−	0.709118i
$237$		0			0
$238$	1.18488	−	2.59453i	0.0768044	−	0.168178i
$239$	3.92058	+	3.39720i	0.253601	+	0.219747i	0.772378	−	0.635163i	$-0.219067\pi$
$239$	3.92058	+	3.39720i	0.253601	+	0.219747i	−0.518777	+	0.854910i	$0.673612\pi$
$240$		0			0
$241$	12.3414	−	1.77442i	0.794978	−	0.114301i	0.267153	−	0.963654i	$-0.413917\pi$
$241$	12.3414	−	1.77442i	0.794978	−	0.114301i	0.527824	+	0.849353i	$0.323008\pi$
$242$	7.39918	−	1.06384i	0.475637	−	0.0683863i
$243$		0			0
$244$	1.20681	+	1.04570i	0.0772578	+	0.0669443i
$245$	−6.66296	+	14.5898i	−0.425681	+	0.932111i
$246$		0			0
$247$	0.0301235	+	0.102591i	0.00191671	+	0.00652773i
$248$	3.32088	−	2.87756i	0.210876	−	0.182725i
$249$		0			0
$250$	0.633298	−	0.289218i	0.0400533	−	0.0182917i
$251$	1.82978	−	12.7264i	0.115495	−	0.803284i	−0.846924	−	0.531714i	$-0.821548\pi$
$251$	1.82978	−	12.7264i	0.115495	−	0.803284i	0.962419	−	0.271570i	$-0.0875427\pi$
$252$		0			0
$253$	15.6130	−	13.4597i	0.981583	−	0.846207i
$254$			13.7119i			0.860362i
$255$		0			0
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	3.30430	−	11.2534i	0.206117	−	0.701969i	−0.789935	−	0.613191i	$-0.789886\pi$
$257$	3.30430	−	11.2534i	0.206117	−	0.701969i	0.996051	−	0.0887779i	$-0.0282961\pi$
$258$		0			0
$259$	8.86680	−	2.60353i	0.550956	−	0.161775i
$260$	4.84389	+	3.11298i	0.300405	+	0.193059i
$261$		0			0
$262$	−2.61711	+	3.02031i	−0.161686	+	0.186595i
$263$	−12.6567	+	8.13394i	−0.780443	+	0.501560i	−0.869180	−	0.494495i	$-0.835353\pi$
$263$	−12.6567	+	8.13394i	−0.780443	+	0.501560i	0.0887378	+	0.996055i	$0.471717\pi$
$264$		0			0
$265$	1.04884	+	7.29482i	0.0644295	+	0.448117i
$266$	−0.0451827	−	0.0703057i	−0.00277033	−	0.00431072i
$267$		0			0
$268$	0.749243	+	0.342168i	0.0457673	+	0.0209012i
$269$	−6.94788	+	10.8111i	−0.423619	+	0.659165i	−0.985814	−	0.167840i	$-0.946321\pi$
$269$	−6.94788	+	10.8111i	−0.423619	+	0.659165i	0.562195	+	0.827005i	$0.309957\pi$
$270$		0			0
$271$	11.5309	+	13.3073i	0.700450	+	0.808362i	0.988813	−	0.149159i	$-0.0476566\pi$
$271$	11.5309	+	13.3073i	0.700450	+	0.808362i	−0.288363	+	0.957521i	$0.593111\pi$
$272$	−1.94380	−	0.570751i	−0.117860	−	0.0346068i
$273$		0			0
$274$	12.0238	+	1.72877i	0.726386	+	0.104439i
$275$	−22.4276			−1.35244
$276$		0			0
$277$	−11.3655			−0.682885			−0.341442	−	0.939903i	$-0.610915\pi$
$277$	−11.3655			−0.682885			−0.341442	+	0.939903i	$0.610915\pi$
$278$	2.46439	+	0.354325i	0.147804	+	0.0212510i
$279$		0			0
$280$	−4.31821	−	1.26794i	−0.258062	−	0.0757739i
$281$	13.5937	+	15.6880i	0.810933	+	0.935866i	0.998927	−	0.0463039i	$-0.0147443\pi$
$281$	13.5937	+	15.6880i	0.810933	+	0.935866i	−0.187995	+	0.982170i	$0.560199\pi$
$282$		0			0
$283$	2.62562	−	4.08554i	0.156077	−	0.242860i	−0.754405	−	0.656409i	$-0.772075\pi$
$283$	2.62562	−	4.08554i	0.156077	−	0.242860i	0.910482	+	0.413549i	$0.135711\pi$
$284$	−9.81060	−	4.48035i	−0.582152	−	0.265860i
$285$		0			0
$286$	−4.18594	−	6.51344i	−0.247520	−	0.385148i
$287$	−2.24584	−	15.6202i	−0.132568	−	0.922030i
$288$		0			0
$289$	−10.8487	+	6.97205i	−0.638160	+	0.410120i
$290$	17.0856	−	19.7179i	1.00330	−	1.15787i
$291$		0			0
$292$	−9.77083	−	6.27933i	−0.571795	−	0.367470i
$293$	22.1230	−	6.49589i	1.29244	−	0.379494i	0.437966	−	0.898991i	$-0.355699\pi$
$293$	22.1230	−	6.49589i	1.29244	−	0.379494i	0.854472	+	0.519497i	$0.173881\pi$
$294$		0			0
$295$	10.2247	−	34.8220i	0.595303	−	2.02741i
$296$	−2.72662	−	5.97046i	−0.158482	−	0.347026i
$297$		0			0
$298$		−	8.00993i		−	0.464003i
$299$	−7.84900	−	3.60855i	−0.453919	−	0.208688i
$300$		0			0
$301$	1.43917	−	10.0096i	0.0829523	−	0.576946i
$302$	−20.6836	+	9.44589i	−1.19021	+	0.543550i
$303$		0			0
$304$	−0.0448599	+	0.0388713i	−0.00257289	+	0.00222942i
$305$	1.43805	+	4.89756i	0.0823427	+	0.280434i
$306$		0			0
$307$	−11.8942	+	26.0448i	−0.678841	+	1.48645i	0.185026	+	0.982734i	$0.440763\pi$
$307$	−11.8942	+	26.0448i	−0.678841	+	1.48645i	−0.863867	+	0.503720i	$0.831964\pi$
$308$	4.57358	+	3.96303i	0.260604	+	0.225815i
$309$		0			0
$310$	13.9031	−	1.99896i	0.789641	−	0.113533i
$311$	−22.8758	+	3.28905i	−1.29717	+	0.186505i	−0.756090	−	0.654467i	$-0.772893\pi$
$311$	−22.8758	+	3.28905i	−1.29717	+	0.186505i	−0.541079	+	0.840972i	$0.681984\pi$
$312$		0			0
$313$	−9.41020	−	8.15399i	−0.531896	−	0.460891i	0.347026	−	0.937855i	$-0.387191\pi$
$313$	−9.41020	−	8.15399i	−0.531896	−	0.460891i	−0.878922	+	0.476965i	$0.841737\pi$
$314$	−7.54124	+	16.5130i	−0.425577	+	0.931883i
$315$		0			0
$316$	−4.67458	−	15.9202i	−0.262966	−	0.895580i
$317$	−12.0880	+	10.4743i	−0.678928	+	0.588295i	−0.924545	−	0.381072i	$-0.875555\pi$
$317$	−12.0880	+	10.4743i	−0.678928	+	0.588295i	0.245617	+	0.969367i	$0.421009\pi$
$318$		0			0
$319$	−31.9128	+	14.5741i	−1.78677	+	0.815991i
$320$	−0.454914	+	3.16399i	−0.0254304	+	0.176873i
$321$		0			0
$322$	6.68104	+	0.977852i	0.372320	+	0.0544936i
$323$		−	0.120251i		−	0.00669096i
$324$		0			0
$325$	3.90443	+	8.54952i	0.216579	+	0.474242i
$326$	−0.292824	+	0.997266i	−0.0162180	+	0.0552334i
$327$		0			0
$328$	−10.7544	+	3.15779i	−0.593815	+	0.174360i
$329$	−0.264780	−	0.170164i	−0.0145978	−	0.00938144i
$330$		0			0
$331$	−11.3271	+	13.0722i	−0.622595	+	0.718513i	−0.976198	−	0.216883i	$-0.930411\pi$
$331$	−11.3271	+	13.0722i	−0.622595	+	0.718513i	0.353602	+	0.935396i	$0.384957\pi$
$332$	−1.71124	+	1.09975i	−0.0939166	+	0.0603565i
$333$		0			0
$334$	−1.05873	−	7.36364i	−0.0579312	−	0.402920i
$335$	1.42346	+	2.21494i	0.0777718	+	0.121015i
$336$		0			0
$337$	−22.9693	−	10.4897i	−1.25122	−	0.571412i	−0.324043	−	0.946042i	$-0.605042\pi$
$337$	−22.9693	−	10.4897i	−1.25122	−	0.571412i	−0.927174	+	0.374631i	$0.877770\pi$
$338$	5.27410	−	8.20667i	0.286873	−	0.446384i
$339$		0			0
$340$	−4.24070	−	4.89402i	−0.229984	−	0.265416i
$341$	−18.1222	−	5.32117i	−0.981375	−	0.288158i
$342$		0			0
$343$	16.7480	+	2.40799i	0.904305	+	0.130019i
$344$	−7.18255			−0.387257
$345$		0			0
$346$	−15.2735			−0.821109
$347$	−14.1623	−	2.03623i	−0.760270	−	0.109310i	−0.248734	−	0.968572i	$-0.580014\pi$
$347$	−14.1623	−	2.03623i	−0.760270	−	0.109310i	−0.511536	+	0.859262i	$0.670923\pi$
$348$		0			0
$349$	−21.2707	−	6.24564i	−1.13859	−	0.334322i	−0.342514	−	0.939513i	$-0.611279\pi$
$349$	−21.2707	−	6.24564i	−1.13859	−	0.334322i	−0.796080	+	0.605191i	$0.793097\pi$
$350$	−4.81083	−	5.55199i	−0.257149	−	0.296766i
$351$		0			0
$352$	2.32383	−	3.61595i	0.123861	−	0.192731i
$353$	31.5609	+	14.4134i	1.67982	+	0.767148i	0.999411	+	0.0343149i	$0.0109249\pi$
$353$	31.5609	+	14.4134i	1.67982	+	0.767148i	0.680409	+	0.732833i	$0.261802\pi$
$354$		0			0
$355$	−18.6388	−	29.0025i	−0.989243	−	1.53929i
$356$	0.713527	+	4.96269i	0.0378168	+	0.263022i
$357$		0			0
$358$	14.7065	−	9.45126i	0.777260	−	0.499515i
$359$	24.7144	−	28.5219i	1.30438	−	1.50533i	0.583974	−	0.811772i	$-0.301497\pi$
$359$	24.7144	−	28.5219i	1.30438	−	1.50533i	0.720401	−	0.693558i	$-0.243958\pi$
$360$		0			0
$361$	15.9809	+	10.2703i	0.841098	+	0.540541i
$362$	10.2805	−	3.01863i	0.540332	−	0.158656i
$363$		0			0
$364$	0.714510	−	2.43340i	0.0374505	−	0.127545i
$365$	−15.4229	−	33.7714i	−0.807271	−	1.76768i
$366$		0			0
$367$			35.0108i			1.82755i	0.406220	+	0.913775i	$0.366847\pi$
$367$			35.0108i			1.82755i	−0.406220	+	0.913775i	$0.633153\pi$
$368$	0.0121363	−	4.79582i	0.000632649	−	0.249999i
$369$		0			0
$370$	2.98587	−	20.7672i	0.155228	−	1.07964i
$371$	2.95276	−	1.34848i	0.153299	−	0.0700095i
$372$		0			0
$373$	21.4255	−	18.5653i	1.10937	−	0.961273i	0.109902	−	0.993942i	$-0.464946\pi$
$373$	21.4255	−	18.5653i	1.10937	−	0.961273i	0.999466	+	0.0326696i	$0.0104009\pi$
$374$	2.45325	+	8.35500i	0.126855	+	0.432027i
$375$		0			0
$376$	−0.0928662	+	0.203349i	−0.00478921	+	0.0104869i
$377$	11.1114	+	9.62810i	0.572267	+	0.495872i
$378$		0			0
$379$	−32.4797	+	4.66987i	−1.66837	+	0.239875i	−0.910790	−	0.412869i	$-0.864527\pi$
$379$	−32.4797	+	4.66987i	−1.66837	+	0.239875i	−0.757578	+	0.652745i	$0.773618\pi$
$380$	−0.187809	+	0.0270028i	−0.00963440	+	0.00138522i
$381$		0			0
$382$	12.1217	+	10.5035i	0.620198	+	0.537405i
$383$	13.7459	−	30.0992i	0.702381	−	1.53800i	−0.134680	−	0.990889i	$-0.543001\pi$
$383$	13.7459	−	30.0992i	0.702381	−	1.53800i	0.837061	−	0.547110i	$-0.184272\pi$
$384$		0			0
$385$	5.44997	+	18.5609i	0.277756	+	0.945951i
$386$	−0.191734	+	0.166139i	−0.00975903	+	0.00845625i
$387$		0			0
$388$	−8.86555	+	4.04876i	−0.450080	+	0.205545i
$389$	3.24429	−	22.5645i	0.164492	−	1.14407i	−0.725544	−	0.688176i	$-0.758412\pi$
$389$	3.24429	−	22.5645i	0.164492	−	1.14407i	0.890036	−	0.455891i	$-0.150679\pi$
$390$		0			0
$391$	7.32650	+	6.38098i	0.370517	+	0.322700i
$392$		−	5.01772i		−	0.253433i
$393$		0			0
$394$	2.40300	+	5.26183i	0.121061	+	0.265087i
$395$	14.9424	−	50.8893i	0.751836	−	2.56052i
$396$		0			0
$397$	−8.48991	+	2.49286i	−0.426096	+	0.125113i	−0.487748	−	0.872985i	$-0.662181\pi$
$397$	−8.48991	+	2.49286i	−0.426096	+	0.125113i	0.0616515	+	0.998098i	$0.480363\pi$
$398$	5.43927	+	3.49561i	0.272646	+	0.175219i
$399$		0			0
$400$	−3.41693	+	3.94335i	−0.170847	+	0.197168i
$401$	−3.83342	+	2.46359i	−0.191432	+	0.123026i	−0.632846	−	0.774278i	$-0.718113\pi$
$401$	−3.83342	+	2.46359i	−0.191432	+	0.123026i	0.441414	+	0.897304i	$0.354477\pi$
$402$		0			0
$403$	1.12645	+	7.83466i	0.0561126	+	0.390272i
$404$	−9.88991	−	15.3890i	−0.492042	−	0.765632i
$405$		0			0
$406$	−10.4533	−	4.77385i	−0.518787	−	0.236922i
$407$	−15.2527	+	23.7337i	−0.756048	+	1.17643i
$408$		0			0
$409$	24.2597	+	27.9972i	1.19957	+	1.38437i	0.903156	+	0.429313i	$0.141244\pi$
$409$	24.2597	+	27.9972i	1.19957	+	1.38437i	0.296411	+	0.955061i	$0.404210\pi$
$410$	−34.3769	−	10.0940i	−1.69775	−	0.498505i
$411$		0			0
$412$	15.8993	+	2.28598i	0.783304	+	0.112622i
$413$	−15.9851			−0.786576
$414$		0			0
$415$	−6.50224			−0.319183
$416$	−1.78297	−	0.256353i	−0.0874175	−	0.0125687i
$417$		0			0
$418$	0.244804	+	0.0718808i	0.0119737	+	0.00351581i
$419$	13.7628	+	15.8831i	0.672356	+	0.775940i	0.984743	−	0.174015i	$-0.0556741\pi$
$419$	13.7628	+	15.8831i	0.672356	+	0.775940i	−0.312387	+	0.949955i	$0.601129\pi$
$420$		0			0
$421$	−7.17175	+	11.1595i	−0.349530	+	0.543879i	−0.970853	−	0.239675i	$-0.922959\pi$
$421$	−7.17175	+	11.1595i	−0.349530	+	0.543879i	0.621323	+	0.783554i	$0.286595\pi$
$422$	−6.93620	−	3.16766i	−0.337649	−	0.154199i
$423$		0			0
$424$	−1.24649	−	1.93957i	−0.0605348	−	0.0941939i
$425$	−1.50434	−	10.4629i	−0.0729714	−	0.507527i
$426$		0			0
$427$	1.89134	−	1.21549i	0.0915283	−	0.0588217i
$428$	3.83310	−	4.42363i	0.185280	−	0.213824i
$429$		0			0
$430$	−19.3145	−	12.4127i	−0.931429	−	0.598593i
$431$	−4.14925	+	1.21833i	−0.199862	+	0.0586849i	−0.380132	−	0.924932i	$-0.624121\pi$
$431$	−4.14925	+	1.21833i	−0.199862	+	0.0586849i	0.180269	+	0.983617i	$0.442303\pi$
$432$		0			0
$433$	−1.92680	+	6.56206i	−0.0925959	+	0.315353i	−0.992747	−	0.120226i	$-0.961638\pi$
$433$	−1.92680	+	6.56206i	−0.0925959	+	0.315353i	0.900151	+	0.435579i	$0.143456\pi$
$434$	−2.57004	−	5.62760i	−0.123366	−	0.270134i
$435$		0			0
$436$			9.21599i			0.441366i
$437$	0.273343	−	0.0795099i	0.0130758	−	0.00380347i
$438$		0			0
$439$	0.650721	−	4.52587i	0.0310572	−	0.216008i	−0.968383	−	0.249469i	$-0.919744\pi$
$439$	0.650721	−	4.52587i	0.0310572	−	0.216008i	0.999440	+	0.0334612i	$0.0106530\pi$
$440$	12.4980	−	5.70764i	0.595818	−	0.272101i
$441$		0			0
$442$	2.75788	−	2.38972i	0.131179	−	0.113667i
$443$	−2.05792	−	7.00865i	−0.0977749	−	0.332991i	0.896050	−	0.443954i	$-0.146425\pi$
$443$	−2.05792	−	7.00865i	−0.0977749	−	0.332991i	−0.993825	+	0.110963i	$0.964606\pi$
$444$		0			0
$445$	−6.65765	+	14.5782i	−0.315603	+	0.691074i
$446$	11.8240	+	10.2456i	0.559883	+	0.485141i
$447$		0			0
$448$	1.39361	−	0.200370i	0.0658417	−	0.00946660i
$449$	12.2372	−	1.75944i	0.577507	−	0.0830330i	0.152629	−	0.988284i	$-0.451226\pi$
$449$	12.2372	−	1.75944i	0.577507	−	0.0830330i	0.424878	+	0.905251i	$0.360317\pi$
$450$		0			0
$451$	36.4099	+	31.5493i	1.71447	+	1.48560i
$452$	7.74717	−	16.9639i	0.364396	−	0.797917i
$453$		0			0
$454$	−2.20089	−	7.49555i	−0.103293	−	0.351784i
$455$	6.12672	−	5.30883i	0.287225	−	0.248882i
$456$		0			0
$457$	−24.2784	+	11.0876i	−1.13570	+	0.518655i	−0.892377	−	0.451292i	$-0.850963\pi$
$457$	−24.2784	+	11.0876i	−1.13570	+	0.518655i	−0.243319	+	0.969946i	$0.578236\pi$
$458$	−2.40074	+	16.6975i	−0.112179	+	0.780224i
$459$		0			0
$460$	8.32064	−	12.8754i	0.387952	−	0.600319i
$461$		−	14.4388i		−	0.672482i	−0.941776	−	0.336241i	$-0.890844\pi$
$461$		−	14.4388i		−	0.672482i	0.941776	−	0.336241i	$-0.109156\pi$
$462$		0			0
$463$	−2.27802	−	4.98817i	−0.105869	−	0.231820i	0.849283	−	0.527939i	$-0.177035\pi$
$463$	−2.27802	−	4.98817i	−0.105869	−	0.231820i	−0.955151	+	0.296119i	$0.904308\pi$
$464$	−2.29954	+	7.83150i	−0.106753	+	0.363568i
$465$		0			0
$466$	−19.7497	+	5.79902i	−0.914885	+	0.268635i
$467$	20.0609	+	12.8923i	0.928306	+	0.596586i	0.915056	−	0.403326i	$-0.132146\pi$
$467$	20.0609	+	12.8923i	0.928306	+	0.596586i	0.0132500	+	0.999912i	$0.495782\pi$
$468$		0			0
$469$	0.759432	−	0.876431i	0.0350673	−	0.0404698i
$470$	−0.601148	+	0.386334i	−0.0277289	+	0.0178203i
$471$		0			0
$472$	1.61578	+	11.2380i	0.0743725	+	0.517272i
$473$	16.6910	+	25.9717i	0.767454	+	1.19418i
$474$		0			0
$475$	−0.281731	−	0.128662i	−0.0129267	−	0.00590342i
$476$	−1.54206	+	2.39949i	−0.0706802	+	0.109981i
$477$		0			0
$478$	−3.39720	−	3.92058i	−0.155384	−	0.179323i
$479$	2.69705	+	0.791926i	0.123231	+	0.0361840i	0.342767	−	0.939421i	$-0.388636\pi$
$479$	2.69705	+	0.791926i	0.123231	+	0.0361840i	−0.219535	+	0.975605i	$0.570454\pi$
$480$		0			0
$481$	11.7027	+	1.68260i	0.533599	+	0.0767199i
$482$	−12.4683			−0.567915
$483$		0			0
$484$	−7.47527			−0.339785
$485$	−30.8373	−	4.43373i	−1.40025	−	0.201325i
$486$		0			0
$487$	2.89310	+	0.849491i	0.131099	+	0.0384941i	0.346624	−	0.938004i	$-0.387328\pi$
$487$	2.89310	+	0.849491i	0.131099	+	0.0384941i	−0.215525	+	0.976498i	$0.569146\pi$
$488$	−1.04570	−	1.20681i	−0.0473368	−	0.0546295i
$489$		0			0
$490$	8.67149	−	13.4931i	0.391738	−	0.609556i
$491$	11.2077	+	5.11839i	0.505797	+	0.230990i	0.651935	−	0.758274i	$-0.273957\pi$
$491$	11.2077	+	5.11839i	0.505797	+	0.230990i	−0.146139	+	0.989264i	$0.546685\pi$
$492$		0			0
$493$	−8.93967	−	13.9104i	−0.402622	−	0.626493i
$494$	−0.0152167	−	0.105834i	−0.000684630	−	0.00476170i
$495$		0			0
$496$	−3.69659	+	2.37566i	−0.165982	+	0.106670i
$497$	−9.94401	+	11.4760i	−0.446050	+	0.514769i
$498$		0			0
$499$	5.68259	+	3.65198i	0.254388	+	0.163485i	0.661619	−	0.749840i	$-0.269869\pi$
$499$	5.68259	+	3.65198i	0.254388	+	0.163485i	−0.407232	+	0.913325i	$0.633506\pi$
$500$	−0.668012	+	0.196146i	−0.0298744	+	0.00877192i
$501$		0			0
$502$	−3.62231	+	12.3365i	−0.161672	+	0.550603i
$503$	7.64114	+	16.7318i	0.340702	+	0.746032i	0.999983	−	0.00586407i	$-0.00186660\pi$
$503$	7.64114	+	16.7318i	0.340702	+	0.746032i	−0.659281	+	0.751896i	$0.729139\pi$
$504$		0			0
$505$		−	58.4739i		−	2.60206i
$506$	−17.3696	+	11.1008i	−0.772174	+	0.493490i
$507$		0			0
$508$	1.95141	−	13.5723i	0.0865798	−	0.602176i
$509$	21.4168	−	9.78073i	0.949283	−	0.433523i	0.120263	−	0.992742i	$-0.461626\pi$
$509$	21.4168	−	9.78073i	0.949283	−	0.433523i	0.829020	+	0.559219i	$0.188899\pi$
$510$		0			0
$511$	−12.3585	+	10.7087i	−0.546708	+	0.473725i
$512$	−0.281733	−	0.959493i	−0.0124509	−	0.0424040i
$513$		0			0
$514$	−4.87220	+	10.6686i	−0.214903	+	0.470573i
$515$	38.8042	+	33.6240i	1.70992	+	1.48165i
$516$		0			0
$517$	0.951103	−	0.136748i	0.0418295	−	0.00601417i
$518$	−9.14707	+	1.31515i	−0.401899	+	0.0577844i
$519$		0			0
$520$	−4.35156	−	3.77065i	−0.190829	−	0.165354i
$521$	−2.64240	+	5.78605i	−0.115766	+	0.253492i	−0.958641	−	0.284617i	$-0.908134\pi$
$521$	−2.64240	+	5.78605i	−0.115766	+	0.253492i	0.842876	+	0.538108i	$0.180861\pi$
$522$		0			0
$523$	−8.71575	−	29.6831i	−0.381113	−	1.29795i	−0.897279	−	0.441464i	$-0.854459\pi$
$523$	−8.71575	−	29.6831i	−0.381113	−	1.29795i	0.516166	−	0.856489i	$-0.327359\pi$
$524$	3.02031	−	2.61711i	0.131943	−	0.114329i
$525$		0			0
$526$	13.6854	−	6.24992i	0.596712	−	0.272509i
$527$	1.26688	−	8.81132i	0.0551860	−	0.383827i
$528$		0			0
$529$	−9.66031	+	20.8729i	−0.420013	+	0.907518i
$530$		−	7.36983i		−	0.320125i
$531$		0			0
$532$	0.0347173	+	0.0760203i	0.00150519	+	0.00329590i
$533$	5.68815	−	19.3721i	0.246381	−	0.839098i
$534$		0			0
$535$	17.9523	−	5.27128i	0.776148	−	0.227898i
$536$	−0.692921	−	0.445313i	−0.0299296	−	0.0192346i
$537$		0			0
$538$	8.41574	−	9.71228i	0.362828	−	0.418726i
$539$	−18.1438	+	11.6603i	−0.781509	+	0.502245i
$540$		0			0
$541$	−0.426802	−	2.96847i	−0.0183496	−	0.127624i	0.978588	−	0.205831i	$-0.0659897\pi$
$541$	−0.426802	−	2.96847i	−0.0183496	−	0.127624i	−0.996937	+	0.0782065i	$0.975081\pi$
$542$	−9.51966	−	14.8129i	−0.408905	−	0.636268i
$543$		0			0
$544$	1.84279	+	0.841572i	0.0790088	+	0.0360821i
$545$	−15.9268	+	24.7826i	−0.682231	+	1.06157i
$546$		0			0
$547$	26.5853	+	30.6811i	1.13671	+	1.31183i	0.943764	+	0.330619i	$0.107258\pi$
$547$	26.5853	+	30.6811i	1.13671	+	1.31183i	0.192942	+	0.981210i	$0.438197\pi$
$548$	−11.6554	−	3.42234i	−0.497895	−	0.146195i
$549$		0			0
$550$	22.1993	+	3.19178i	0.946583	+	0.136098i
$551$	−0.484489			−0.0206399
$552$		0			0
$553$	−23.3609			−0.993405
$554$	11.2498	+	1.61747i	0.477957	+	0.0687199i
$555$		0			0
$556$	−2.38888	−	0.701437i	−0.101311	−	0.0297476i
$557$	−1.97378	−	2.27786i	−0.0836317	−	0.0965161i	0.712391	−	0.701782i	$-0.247612\pi$
$557$	−1.97378	−	2.27786i	−0.0836317	−	0.0965161i	−0.796023	+	0.605266i	$0.793067\pi$
$558$		0			0
$559$	6.99480	−	10.8841i	0.295849	−	0.460350i
$560$	4.09381	+	1.86958i	0.172995	+	0.0790042i
$561$		0			0
$562$	−11.2227	−	17.4629i	−0.473402	−	0.736627i
$563$	3.67659	+	25.5712i	0.154950	+	1.07770i	0.907769	+	0.419471i	$0.137784\pi$
$563$	3.67659	+	25.5712i	0.154950	+	1.07770i	−0.752819	+	0.658228i	$0.771306\pi$
$564$		0			0
$565$	50.1495	−	32.2291i	2.10981	−	1.35589i
$566$	−3.18032	+	3.67029i	−0.133679	+	0.154274i
$567$		0			0
$568$	9.07312	+	5.83094i	0.380700	+	0.244661i
$569$	−19.6468	+	5.76881i	−0.823635	+	0.241841i	−0.666281	−	0.745701i	$-0.732115\pi$
$569$	−19.6468	+	5.76881i	−0.823635	+	0.241841i	−0.157355	+	0.987542i	$0.550297\pi$
$570$		0			0
$571$	−1.81675	+	6.18727i	−0.0760285	+	0.258929i	−0.988733	−	0.149691i	$-0.952172\pi$
$571$	−1.81675	+	6.18727i	−0.0760285	+	0.258929i	0.912704	+	0.408621i	$0.133990\pi$
$572$	3.21637	+	7.04287i	0.134483	+	0.294477i
$573$		0			0
$574$			15.7808i			0.658678i
$575$	22.7886	−	10.3376i	0.950350	−	0.431107i
$576$		0			0
$577$	4.97047	−	34.5704i	0.206923	−	1.43918i	−0.576195	−	0.817312i	$-0.695463\pi$
$577$	4.97047	−	34.5704i	0.206923	−	1.43918i	0.783119	−	0.621872i	$-0.213628\pi$
$578$	11.7305	−	5.35715i	0.487925	−	0.222828i
$579$		0			0
$580$	−19.7179	+	17.0856i	−0.818740	+	0.709442i
$581$	0.806872	+	2.74795i	0.0334747	+	0.114004i
$582$		0			0
$583$	−4.11677	+	9.01447i	−0.170499	+	0.373341i
$584$	8.77774	+	7.60595i	0.363225	+	0.314737i
$585$		0			0
$586$	−22.8223	+	3.28135i	−0.942779	+	0.135551i
$587$	−22.7888	+	3.27654i	−0.940596	+	0.135237i	−0.595523	−	0.803339i	$-0.703055\pi$
$587$	−22.7888	+	3.27654i	−0.940596	+	0.135237i	−0.345073	+	0.938576i	$0.612146\pi$
$588$		0			0
$589$	−0.197121	−	0.170806i	−0.00812224	−	0.00703796i
$590$	−15.0763	+	33.0124i	−0.620680	+	1.35910i
$591$		0			0
$592$	1.84918	+	6.29773i	0.0760009	+	0.258835i
$593$	−2.05705	+	1.78245i	−0.0844730	+	0.0731963i	−0.696074	−	0.717970i	$-0.745071\pi$
$593$	−2.05705	+	1.78245i	−0.0844730	+	0.0731963i	0.611601	+	0.791167i	$0.290526\pi$
$594$		0			0
$595$	−8.29348	+	3.78751i	−0.340000	+	0.155273i
$596$	−1.13993	+	7.92840i	−0.0466934	+	0.324760i
$597$		0			0
$598$	7.25556	+	4.68885i	0.296702	+	0.191741i
$599$			36.6970i			1.49940i	0.661777	+	0.749700i	$0.269802\pi$
$599$			36.6970i			1.49940i	−0.661777	+	0.749700i	$0.730198\pi$
$600$		0			0
$601$	14.5841	+	31.9347i	0.594898	+	1.30264i	0.932437	+	0.361333i	$0.117678\pi$
$601$	14.5841	+	31.9347i	0.594898	+	1.30264i	−0.337539	+	0.941311i	$0.609595\pi$
$602$	−2.84904	+	9.70294i	−0.116118	+	0.395462i
$603$		0			0
$604$	21.8174	−	6.40616i	0.887737	−	0.260663i
$605$	−20.1017	−	12.9186i	−0.817250	−	0.525215i
$606$		0			0
$607$	−19.8048	+	22.8559i	−0.803850	+	0.927693i	−0.998586	−	0.0531631i	$-0.983070\pi$
$607$	−19.8048	+	22.8559i	−0.803850	+	0.927693i	0.194736	+	0.980856i	$0.437615\pi$
$608$	0.0499353	−	0.0320915i	0.00202514	−	0.00130148i
$609$		0			0
$610$	−0.726421	−	5.05237i	−0.0294119	−	0.204564i
$611$	−0.217707	−	0.338759i	−0.00880749	−	0.0137047i
$612$		0			0
$613$	−29.5388	−	13.4899i	−1.19306	−	0.544852i	−0.282916	−	0.959145i	$-0.591302\pi$
$613$	−29.5388	−	13.4899i	−1.19306	−	0.544852i	−0.910144	+	0.414293i	$0.864029\pi$
$614$	15.4797	−	24.0869i	0.624711	−	0.972070i
$615$		0			0
$616$	−3.96303	−	4.57358i	−0.159675	−	0.184275i
$617$	−2.66921	−	0.783751i	−0.107458	−	0.0315526i	0.227561	−	0.973764i	$-0.426925\pi$
$617$	−2.66921	−	0.783751i	−0.107458	−	0.0315526i	−0.335020	+	0.942211i	$0.608743\pi$
$618$		0			0
$619$	−5.77427	−	0.830215i	−0.232088	−	0.0333692i	0.0252896	−	0.999680i	$-0.491949\pi$
$619$	−5.77427	−	0.830215i	−0.232088	−	0.0333692i	−0.257377	+	0.966311i	$0.582858\pi$
$620$	−14.0460			−0.564102
$621$		0			0
$622$	23.1111			0.926669
$623$	6.98715	+	1.00460i	0.279934	+	0.0402484i
$624$		0			0
$625$	22.8969	+	6.72314i	0.915876	+	0.268926i
$626$	8.15399	+	9.41020i	0.325899	+	0.376107i
$627$		0			0
$628$	9.81452	−	15.2717i	0.391642	−	0.609407i
$629$	−12.0953	−	5.52375i	−0.482272	−	0.220246i
$630$		0			0
$631$	13.8896	+	21.6126i	0.552936	+	0.860386i	0.999408	−	0.0344123i	$-0.0109559\pi$
$631$	13.8896	+	21.6126i	0.552936	+	0.860386i	−0.446471	+	0.894798i	$0.647320\pi$
$632$	2.36133	+	16.4234i	0.0939285	+	0.653287i
$633$		0			0
$634$	13.4556	−	8.64738i	0.534390	−	0.343431i
$635$	28.7029	−	33.1249i	1.13904	−	1.31452i
$636$		0			0
$637$	7.60363	+	4.88656i	0.301267	+	0.193613i
$638$	33.6620	−	9.88407i	1.33269	−	0.391314i
$639$		0			0
$640$	0.900567	−	3.06705i	0.0355980	−	0.121236i
$641$	−0.377769	−	0.827199i	−0.0149210	−	0.0326724i	0.902025	−	0.431684i	$-0.142081\pi$
$641$	−0.377769	−	0.827199i	−0.0149210	−	0.0326724i	−0.916946	+	0.399012i	$0.869353\pi$
$642$		0			0
$643$		−	22.8166i		−	0.899800i	−0.893079	−	0.449900i	$-0.851460\pi$
$643$		−	22.8166i		−	0.899800i	0.893079	−	0.449900i	$-0.148540\pi$
$644$	−6.47388	−	1.91871i	−0.255107	−	0.0756078i
$645$		0			0
$646$	−0.0171136	+	0.119027i	−0.000673324	+	0.00468307i
$647$	−18.2807	+	8.34851i	−0.718688	+	0.328214i	−0.740970	−	0.671538i	$-0.765634\pi$
$647$	−18.2807	+	8.34851i	−0.718688	+	0.328214i	0.0222821	+	0.999752i	$0.492907\pi$
$648$		0			0
$649$	36.8813	−	31.9578i	1.44772	−	1.25445i
$650$	−2.64797	−	9.01816i	−0.103862	−	0.353721i
$651$		0			0
$652$	0.431769	−	0.945442i	0.0169094	−	0.0370264i
$653$	−16.8177	−	14.5726i	−0.658127	−	0.570270i	0.260462	−	0.965484i	$-0.416125\pi$
$653$	−16.8177	−	14.5726i	−0.658127	−	0.570270i	−0.918589	+	0.395214i	$0.870670\pi$
$654$		0			0
$655$	12.6447	−	1.81803i	0.494069	−	0.0710365i
$656$	11.0944	−	1.59513i	0.433163	−	0.0622794i
$657$		0			0
$658$	0.237868	+	0.206114i	0.00927307	+	0.00803516i
$659$	−13.8092	+	30.2379i	−0.537930	+	1.17790i	0.424265	+	0.905538i	$0.360533\pi$
$659$	−13.8092	+	30.2379i	−0.537930	+	1.17790i	−0.962194	+	0.272363i	$0.912195\pi$
$660$		0			0
$661$	2.64227	+	8.99874i	0.102772	+	0.350010i	0.994784	−	0.102002i	$-0.0325247\pi$
$661$	2.64227	+	8.99874i	0.102772	+	0.350010i	−0.892012	+	0.452012i	$0.850706\pi$
$662$	13.0722	−	11.3271i	0.508066	−	0.440241i
$663$		0			0
$664$	1.85033	−	0.845019i	0.0718069	−	0.0327931i
$665$	−0.0380183	+	0.264423i	−0.00147429	+	0.0102539i
$666$		0			0
$667$	25.7088	−	29.5182i	0.995447	−	1.14295i
$668$			7.43936i			0.287837i
$669$		0			0
$670$	−1.09375	−	2.39498i	−0.0422552	−	0.0925260i
$671$	−1.93371	+	6.58562i	−0.0746501	+	0.254235i
$672$		0			0
$673$	−15.6942	+	4.60824i	−0.604968	+	0.177635i	−0.569850	−	0.821749i	$-0.692999\pi$
$673$	−15.6942	+	4.60824i	−0.604968	+	0.177635i	−0.0351176	+	0.999383i	$0.511181\pi$
$674$	21.2427	+	13.6518i	0.818237	+	0.525849i
$675$		0			0
$676$	−6.38835	+	7.37255i	−0.245706	+	0.283560i
$677$	−6.76875	+	4.35001i	−0.260144	+	0.167185i	−0.664211	−	0.747545i	$-0.731233\pi$
$677$	−6.76875	+	4.35001i	−0.260144	+	0.167185i	0.404067	+	0.914729i	$0.367596\pi$
$678$		0			0
$679$	1.95287	+	13.5825i	0.0749443	+	0.521249i
$680$	3.50104	+	5.44772i	0.134259	+	0.208911i
$681$		0			0
$682$	17.1805	+	7.84607i	0.657876	+	0.300442i
$683$	−7.15286	+	11.1301i	−0.273696	+	0.425880i	−0.950706	−	0.310094i	$-0.899639\pi$
$683$	−7.15286	+	11.1301i	−0.273696	+	0.425880i	0.677009	+	0.735974i	$0.263276\pi$
$684$		0			0
$685$	−25.4281	−	29.3456i	−0.971557	−	1.12124i
$686$	−16.2348	−	4.76696i	−0.619847	−	0.182004i
$687$		0			0
$688$	7.10944	+	1.02218i	0.271045	+	0.0389704i
$689$	4.15305			0.158219
$690$		0			0
$691$	−43.2933			−1.64695			−0.823477	−	0.567350i	$-0.807969\pi$
$691$	−43.2933			−1.64695			−0.823477	+	0.567350i	$0.807969\pi$
$692$	15.1180	+	2.17365i	0.574702	+	0.0826297i
$693$		0			0
$694$	13.7283	+	4.03100i	0.521120	+	0.153015i
$695$	−5.21170	−	6.01463i	−0.197691	−	0.228148i
$696$		0			0
$697$	−12.2762	+	19.1021i	−0.464994	+	0.723546i
$698$	20.1653	+	9.20921i	0.763270	+	0.348574i
$699$		0			0
$700$	3.97173	+	6.18013i	0.150117	+	0.233587i
$701$	−3.42315	−	23.8086i	−0.129291	−	0.899237i	−0.946456	−	0.322833i	$-0.895365\pi$
$701$	−3.42315	−	23.8086i	−0.129291	−	0.899237i	0.817165	−	0.576404i	$-0.195544\pi$
$702$		0			0
$703$	−0.327755	+	0.210636i	−0.0123615	+	0.00794427i
$704$	−2.81478	+	3.24843i	−0.106086	+	0.122430i
$705$		0			0
$706$	−29.1885	−	18.7583i	−1.09852	−	0.705977i
$707$	−24.7120	+	7.25611i	−0.929392	+	0.272894i
$708$		0			0
$709$	12.7576	−	43.4485i	0.479123	−	1.63174i	−0.265393	−	0.964140i	$-0.585502\pi$
$709$	12.7576	−	43.4485i	0.479123	−	1.63174i	0.744517	−	0.667604i	$-0.232680\pi$
$710$	14.3216	+	31.3599i	0.537479	+	1.17691i
$711$		0			0
$712$		−	5.01372i		−	0.187897i
$713$	20.8666	−	2.94629i	0.781461	−	0.110339i
$714$		0			0
$715$	−3.52219	+	24.4974i	−0.131722	+	0.916149i
$716$	−15.9018	+	7.26212i	−0.594279	+	0.271398i
$717$		0			0
$718$	−28.5219	+	24.7144i	−1.06443	+	0.922333i
$719$	3.28461	+	11.1864i	0.122495	+	0.417181i	0.997793	−	0.0664040i	$-0.0211526\pi$
$719$	3.28461	+	11.1864i	0.122495	+	0.417181i	−0.875297	+	0.483585i	$0.839334\pi$
$720$		0			0
$721$	9.39479	−	20.5717i	0.349880	−	0.766131i
$722$	−14.3566	−	12.4400i	−0.534297	−	0.462971i
$723$		0			0
$724$	−10.6055	+	1.52484i	−0.394150	+	0.0566701i
$725$	−42.1549	+	6.06096i	−1.56559	+	0.225098i
$726$		0			0
$727$	−18.2994	−	15.8565i	−0.678687	−	0.588086i	0.245790	−	0.969323i	$-0.420953\pi$
$727$	−18.2994	−	15.8565i	−0.678687	−	0.588086i	−0.924477	+	0.381238i	$0.875498\pi$
$728$	−1.05355	+	2.30694i	−0.0390470	+	0.0855010i
$729$		0			0
$730$	10.4597	+	35.6226i	0.387132	+	1.31845i
$731$	−10.9968	+	9.52877i	−0.406731	+	0.352434i
$732$		0			0
$733$	18.2074	−	8.31506i	0.672507	−	0.307124i	−0.0497364	−	0.998762i	$-0.515838\pi$
$733$	18.2074	−	8.31506i	0.672507	−	0.307124i	0.722244	+	0.691639i	$0.243111\pi$
$734$	4.98256	−	34.6545i	0.183910	−	1.27912i
$735$		0			0
$736$	−0.694529	+	4.74527i	−0.0256007	+	0.174913i
$737$			3.54040i			0.130412i
$738$		0			0
$739$	−0.965761	−	2.11472i	−0.0355261	−	0.0777913i	0.891037	−	0.453931i	$-0.149979\pi$
$739$	−0.965761	−	2.11472i	−0.0355261	−	0.0777913i	−0.926563	+	0.376139i	$0.877251\pi$
$740$	−5.91096	+	20.1309i	−0.217291	+	0.740026i
$741$		0			0
$742$	−3.11461	+	0.914532i	−0.114341	+	0.0335735i
$743$	15.3104	+	9.83940i	0.561684	+	0.360973i	0.790467	−	0.612505i	$-0.209838\pi$
$743$	15.3104	+	9.83940i	0.561684	+	0.360973i	−0.228782	+	0.973478i	$0.573474\pi$
$744$		0			0
$745$	−16.7670	+	19.3502i	−0.614297	+	0.708936i
$746$	−23.8495	+	15.3271i	−0.873192	+	0.561166i
$747$		0			0
$748$	−1.23924	−	8.61909i	−0.0453111	−	0.315145i
$749$	−4.45546	−	6.93283i	−0.162799	−	0.253320i
$750$		0			0
$751$	5.26722	+	2.40546i	0.192203	+	0.0877764i	0.509192	−	0.860653i	$-0.329944\pi$
$751$	5.26722	+	2.40546i	0.192203	+	0.0877764i	−0.316988	+	0.948429i	$0.602672\pi$
$752$	0.120860	−	0.188063i	0.00440733	−	0.00685794i
$753$		0			0
$754$	−9.62810	−	11.1114i	−0.350635	−	0.404654i
$755$	69.7399	+	20.4775i	2.53810	+	0.745252i
$756$		0			0
$757$	1.87780	+	0.269987i	0.0682499	+	0.00981286i	0.176355	−	0.984327i	$-0.443569\pi$
$757$	1.87780	+	0.269987i	0.0682499	+	0.00981286i	−0.108105	+	0.994139i	$0.534478\pi$
$758$	32.8137			1.19185
$759$		0			0
$760$	0.189740			0.00688260
$761$	−0.928675	−	0.133523i	−0.0336644	−	0.00484022i	0.125462	−	0.992098i	$-0.459959\pi$
$761$	−0.928675	−	0.133523i	−0.0336644	−	0.00484022i	−0.159126	+	0.987258i	$0.550868\pi$
$762$		0			0
$763$	12.4499	+	3.65563i	0.450717	+	0.132343i
$764$	−10.5035	−	12.1217i	−0.380003	−	0.438546i
$765$		0			0
$766$	−17.8895	+	27.8366i	−0.646375	+	1.00578i
$767$	−18.6032	−	8.49578i	−0.671722	−	0.306765i
$768$		0			0
$769$	−0.500315	−	0.778505i	−0.0180418	−	0.0280736i	0.832116	−	0.554602i	$-0.187130\pi$
$769$	−0.500315	−	0.778505i	−0.0180418	−	0.0280736i	−0.850157	+	0.526529i	$0.823493\pi$
$770$	−2.75301	−	19.1476i	−0.0992115	−	0.690031i
$771$		0			0
$772$	0.213427	−	0.137161i	0.00768140	−	0.00493654i
$773$	−23.5336	+	27.1592i	−0.846444	+	0.976849i	−0.999936	−	0.0113013i	$-0.996403\pi$
$773$	−23.5336	+	27.1592i	−0.846444	+	0.976849i	0.153492	+	0.988150i	$0.450948\pi$
$774$		0			0
$775$	−19.2881	−	12.3957i	−0.692849	−	0.445267i
$776$	9.35151	−	2.74585i	0.335700	−	0.0985703i
$777$		0			0
$778$	−6.42253	+	21.8731i	−0.230259	+	0.784190i
$779$	0.276381	+	0.605191i	0.00990239	+	0.0216832i
$780$		0			0
$781$		−	46.3580i		−	1.65882i
$782$	−6.34382	−	7.35870i	−0.226854	−	0.263147i
$783$		0			0
$784$	−0.714095	+	4.96664i	−0.0255034	+	0.177380i
$785$	52.7843	−	24.1058i	1.88395	−	0.860372i
$786$		0			0
$787$	−9.58029	+	8.30137i	−0.341500	+	0.295912i	−0.808678	−	0.588252i	$-0.799816\pi$
$787$	−9.58029	+	8.30137i	−0.341500	+	0.295912i	0.467177	+	0.884164i	$0.345271\pi$
$788$	−1.62970	−	5.55026i	−0.0580557	−	0.197720i
$789$		0			0
$790$	−22.0327	+	48.2448i	−0.783887	+	1.71647i
$791$	−19.8437	−	17.1946i	−0.705560	−	0.611371i
$792$		0			0
$793$	2.84711	−	0.409353i	0.101104	−	0.0145365i
$794$	8.75826	−	1.25925i	0.310819	−	0.0446891i
$795$		0			0
$796$	−4.88643	−	4.23412i	−0.173195	−	0.150074i
$797$	1.30941	−	2.86721i	0.0463817	−	0.101562i	−0.885023	−	0.465548i	$-0.845857\pi$
$797$	1.30941	−	2.86721i	0.0463817	−	0.101562i	0.931404	+	0.363986i	$0.118585\pi$
$798$		0			0
$799$	0.127592	+	0.434537i	0.00451386	+	0.0153728i
$800$	3.94335	−	3.41693i	0.139419	−	0.120807i
$801$		0			0
$802$	4.14501	−	1.89296i	0.146365	−	0.0668428i
$803$	7.10477	−	49.4148i	0.250722	−	1.74381i
$804$		0			0
$805$	−14.0930	−	16.3476i	−0.496713	−	0.576176i
$806$		−	7.91522i		−	0.278802i
$807$		0			0
$808$	7.59916	+	16.6398i	0.267338	+	0.585388i
$809$	−14.1074	+	48.0456i	−0.495991	+	1.68919i	0.207289	+	0.978280i	$0.433536\pi$
$809$	−14.1074	+	48.0456i	−0.495991	+	1.68919i	−0.703281	+	0.710912i	$0.748282\pi$
$810$		0			0
$811$	39.9506	−	11.7306i	1.40286	−	0.411915i	0.509192	−	0.860653i	$-0.329944\pi$
$811$	39.9506	−	11.7306i	1.40286	−	0.411915i	0.893663	+	0.448738i	$0.148126\pi$
$812$	9.66748	+	6.21291i	0.339262	+	0.218030i
$813$		0			0
$814$	18.4751	−	21.3214i	0.647552	−	0.747314i
$815$	2.79495	−	1.79621i	0.0979030	−	0.0629184i
$816$		0			0
$817$	0.0606749	+	0.422003i	0.00212275	+	0.0147640i
$818$	−20.0284	−	31.1648i	−0.700276	−	1.08965i
$819$		0			0
$820$	32.5905	+	14.8836i	1.13811	+	0.519757i
$821$	−11.7498	+	18.2830i	−0.410071	+	0.638083i	−0.983444	−	0.181212i	$-0.941998\pi$
$821$	−11.7498	+	18.2830i	−0.410071	+	0.638083i	0.573373	+	0.819294i	$0.305634\pi$
$822$		0			0
$823$	23.9420	+	27.6306i	0.834566	+	0.963141i	0.999733	−	0.0231248i	$-0.00736150\pi$
$823$	23.9420	+	27.6306i	0.834566	+	0.963141i	−0.165166	+	0.986266i	$0.552816\pi$
$824$	−15.4122	−	4.52542i	−0.536908	−	0.157650i
$825$		0			0
$826$	15.8224	+	2.27492i	0.550532	+	0.0791546i
$827$	52.6442			1.83062			0.915309	−	0.402752i	$-0.131946\pi$
$827$	52.6442			1.83062			0.915309	+	0.402752i	$0.131946\pi$
$828$		0			0
$829$	29.7388			1.03287			0.516436	−	0.856326i	$-0.327258\pi$
$829$	29.7388			1.03287			0.516436	+	0.856326i	$0.327258\pi$
$830$	6.43606	+	0.925366i	0.223399	+	0.0321199i
$831$		0			0
$832$	1.72834	+	0.507487i	0.0599195	+	0.0175940i
$833$	−6.65678	−	7.68234i	−0.230644	−	0.266177i
$834$		0			0
$835$	−12.8565	+	20.0051i	−0.444918	+	0.692306i
$836$	−0.232082	−	0.105988i	−0.00802673	−	0.00366568i
$837$		0			0
$838$	−11.3623	−	17.6801i	−0.392504	−	0.610748i
$839$	−6.76805	−	47.0728i	−0.233659	−	1.62513i	−0.682057	−	0.731299i	$-0.738914\pi$
$839$	−6.76805	−	47.0728i	−0.233659	−	1.62513i	0.448398	−	0.893834i	$-0.351995\pi$
$840$		0			0
$841$	−31.6482	+	20.3391i	−1.09132	+	0.701347i
$842$	8.68691	−	10.0252i	0.299371	−	0.345492i
$843$		0			0
$844$	6.41480	+	4.12254i	0.220806	+	0.141904i
$845$	−29.9199	+	8.78528i	−1.02928	+	0.302223i
$846$		0			0
$847$	−2.96515	+	10.0984i	−0.101884	+	0.346984i
$848$	0.957770	+	2.09722i	0.0328899	+	0.0720189i
$849$		0			0
$850$			10.5705i			0.362566i
$851$	4.55861	−	31.1461i	0.156267	−	1.06767i
$852$		0			0
$853$	2.03530	−	14.1559i	0.0696875	−	0.484687i	−0.924852	−	0.380327i	$-0.875811\pi$
$853$	2.03530	−	14.1559i	0.0696875	−	0.484687i	0.994540	−	0.104360i	$-0.0332795\pi$
$854$	−2.04507	+	0.933952i	−0.0699808	+	0.0319592i
$855$		0			0
$856$	−4.42363	+	3.83310i	−0.151196	+	0.131013i
$857$	−3.86923	−	13.1774i	−0.132170	−	0.450131i	0.866638	−	0.498938i	$-0.166276\pi$
$857$	−3.86923	−	13.1774i	−0.132170	−	0.450131i	−0.998808	+	0.0488067i	$0.984458\pi$
$858$		0			0
$859$	0.767765	−	1.68117i	0.0261958	−	0.0573608i	−0.896082	−	0.443889i	$-0.853598\pi$
$859$	0.767765	−	1.68117i	0.0261958	−	0.0573608i	0.922278	+	0.386528i	$0.126326\pi$
$860$	17.3514	+	15.0351i	0.591679	+	0.512692i
$861$		0			0
$862$	4.28041	−	0.615429i	0.145791	−	0.0209616i
$863$	33.1533	−	4.76673i	1.12855	−	0.162261i	0.447351	−	0.894358i	$-0.352367\pi$
$863$	33.1533	−	4.76673i	1.12855	−	0.162261i	0.681200	+	0.732097i	$0.261458\pi$
$864$		0			0
$865$	36.8974	+	31.9718i	1.25455	+	1.08707i
$866$	2.84106	−	6.22106i	0.0965432	−	0.211400i
$867$		0			0
$868$	1.74299	+	5.93608i	0.0591609	+	0.201484i
$869$	53.8988	−	46.7036i	1.82839	−	1.58431i
$870$		0			0
$871$	1.34962	−	0.616350i	0.0457301	−	0.0208842i
$872$	1.31157	−	9.12218i	0.0444154	−	0.308916i
$873$		0			0
$874$	−0.281876	+	0.0397998i	−0.00953460	+	0.00134625i
$875$			0.980225i			0.0331376i
$876$		0			0
$877$	2.60842	+	5.71164i	0.0880800	+	0.192868i	0.948546	−	0.316640i	$-0.102555\pi$
$877$	2.60842	+	5.71164i	0.0880800	+	0.192868i	−0.860466	+	0.509508i	$0.829827\pi$
$878$	−1.28820	+	4.38719i	−0.0434745	+	0.148061i
$879$		0			0
$880$	−13.1831	+	3.87089i	−0.444401	+	0.130488i
$881$	−27.6270	−	17.7548i	−0.930776	−	0.598174i	−0.0150110	−	0.999887i	$-0.504778\pi$
$881$	−27.6270	−	17.7548i	−0.930776	−	0.598174i	−0.915765	+	0.401714i	$0.868415\pi$
$882$		0			0
$883$	−5.04941	+	5.82733i	−0.169926	+	0.196105i	−0.834325	−	0.551273i	$-0.814142\pi$
$883$	−5.04941	+	5.82733i	−0.169926	+	0.196105i	0.664399	+	0.747378i	$0.268688\pi$
$884$	−3.06990	+	1.97291i	−0.103252	+	0.0663560i
$885$		0			0
$886$	1.03954	+	7.23018i	0.0349241	+	0.242903i
$887$	5.59634	+	8.70807i	0.187907	+	0.292388i	0.922407	−	0.386220i	$-0.126220\pi$
$887$	5.59634	+	8.70807i	0.187907	+	0.292388i	−0.734500	+	0.678609i	$0.762583\pi$
$888$		0			0
$889$	−17.5609	−	8.01980i	−0.588974	−	0.268975i
$890$	8.66458	−	13.4824i	0.290437	−	0.451929i
$891$		0			0
$892$	−10.2456	−	11.8240i	−0.343047	−	0.395897i
$893$	0.0127320	+	0.00373846i	0.000426061	+	0.000125103i
$894$		0			0
$895$	−55.3117	−	7.95262i	−1.84886	−	0.265827i
$896$	−1.40794			−0.0470358
$897$		0			0
$898$	−12.3630			−0.412558
$899$	−35.5005	−	5.10421i	−1.18401	−	0.170235i
$900$		0			0
$901$	−4.48157	−	1.31591i	−0.149303	−	0.0438392i
$902$	−31.5493	−	36.4099i	−1.05048	−	1.21232i
$903$		0			0
$904$	−10.0825	+	15.6887i	−0.335340	+	0.521800i
$905$	−31.1543	−	14.2277i	−1.03560	−	0.472944i
$906$		0			0
$907$	17.5520	+	27.3114i	0.582805	+	0.906862i	0.999998	−	0.00195613i	$-0.000622656\pi$
$907$	17.5520	+	27.3114i	0.582805	+	0.906862i	−0.417194	+	0.908818i	$0.636986\pi$
$908$	1.11176	+	7.73248i	0.0368951	+	0.256611i
$909$		0			0
$910$	−6.81988	+	4.38287i	−0.226077	+	0.145291i
$911$	−18.0337	+	20.8121i	−0.597485	+	0.689534i	−0.971270	−	0.237981i	$-0.923514\pi$
$911$	−18.0337	+	20.8121i	−0.597485	+	0.689534i	0.373785	+	0.927515i	$0.378060\pi$
$912$		0			0
$913$	−7.35541	−	4.72703i	−0.243428	−	0.156442i
$914$	25.6092	−	7.51954i	0.847077	−	0.248724i
$915$		0			0
$916$	4.75261	−	16.1859i	0.157031	−	0.534797i
$917$	−2.33743	−	5.11825i	−0.0771887	−	0.169020i
$918$		0			0
$919$		−	12.7876i		−	0.421826i	−0.977505	−	0.210913i	$-0.932356\pi$
$919$		−	12.7876i		−	0.421826i	0.977505	−	0.210913i	$-0.0676436\pi$
$920$	−10.0683	+	11.5602i	−0.331942	+	0.381129i
$921$		0			0
$922$	−2.05486	+	14.2918i	−0.0676731	+	0.470676i
$923$	−17.6719	+	8.07049i	−0.581678	+	0.265644i
$924$		0			0
$925$	−25.8826	+	22.4274i	−0.851015	+	0.737408i
$926$	1.54494	+	5.26159i	0.0507700	+	0.172907i
$927$		0			0
$928$	3.39067	−	7.42453i	0.111304	−	0.243722i
$929$	−7.63753	−	6.61796i	−0.250579	−	0.217128i	0.520509	−	0.853856i	$-0.325742\pi$
$929$	−7.63753	−	6.61796i	−0.250579	−	0.217128i	−0.771089	+	0.636728i	$0.780288\pi$
$930$		0			0
$931$	−0.294811	+	0.0423874i	−0.00966204	+	0.00138919i
$932$	20.3739	−	2.92933i	0.667370	−	0.0959533i
$933$		0			0
$934$	−18.0219	−	15.6161i	−0.589695	−	0.510974i
$935$	11.5629	−	25.3192i	0.378146	−	0.828025i
$936$		0			0
$937$	−6.85425	−	23.3434i	−0.223918	−	0.762596i	−0.992436	−	0.122767i	$-0.960823\pi$
$937$	−6.85425	−	23.3434i	−0.223918	−	0.762596i	0.768517	−	0.639829i	$-0.220995\pi$
$938$	−0.876431	+	0.759432i	−0.0286165	+	0.0247963i
$939$		0			0
$940$	0.650010	−	0.296850i	0.0212010	−	0.00968217i
$941$	6.14561	−	42.7436i	0.200341	−	1.39340i	−0.602933	−	0.797792i	$-0.706001\pi$
$941$	6.14561	−	42.7436i	0.200341	−	1.39340i	0.803274	−	0.595610i	$-0.203090\pi$
$942$		0			0
$943$	−51.5380	−	15.2747i	−1.67831	−	0.497412i
$944$		−	11.3536i		−	0.369528i
$945$		0			0
$946$	−12.8250	−	28.0827i	−0.416975	−	0.913049i
$947$	−10.0096	+	34.0897i	−0.325270	+	1.10777i	0.620845	+	0.783934i	$0.286790\pi$
$947$	−10.0096	+	34.0897i	−0.325270	+	1.10777i	−0.946114	+	0.323833i	$0.895028\pi$
$948$		0			0
$949$	−20.0740	+	5.89427i	−0.651631	+	0.191336i
$950$	0.260552	+	0.167447i	0.00845344	+	0.00543270i
$951$		0			0
$952$	1.86785	−	2.15561i	0.0605373	−	0.0698637i
$953$	2.88855	−	1.85636i	0.0935694	−	0.0601334i	−0.493019	−	0.870018i	$-0.664107\pi$
$953$	2.88855	−	1.85636i	0.0935694	−	0.0601334i	0.586589	+	0.809885i	$0.300470\pi$
$954$		0			0
$955$	−7.29648	−	50.7481i	−0.236108	−	1.64217i
$956$	2.80467	+	4.36415i	0.0907094	+	0.141147i
$957$		0			0
$958$	−2.55690	−	1.16770i	−0.0826096	−	0.0377265i
$959$	−9.24651	+	14.3878i	−0.298585	+	0.464608i
$960$		0			0
$961$	7.65627	+	8.83581i	0.246977	+	0.285026i
$962$	−11.3442	−	3.33095i	−0.365750	−	0.107394i
$963$		0			0
$964$	12.3414	+	1.77442i	0.397489	+	0.0571503i
$965$	0.810963			0.0261058
$966$		0			0
$967$	−48.3925			−1.55620			−0.778099	−	0.628141i	$-0.783816\pi$
$967$	−48.3925			−1.55620			−0.778099	+	0.628141i	$0.783816\pi$
$968$	7.39918	+	1.06384i	0.237819	+	0.0341932i
$969$		0			0
$970$	29.8924	+	8.77720i	0.959787	+	0.281819i
$971$	−37.5348	−	43.3174i	−1.20455	−	1.39012i	−0.899001	−	0.437946i	$-0.855706\pi$
$971$	−37.5348	−	43.3174i	−1.20455	−	1.39012i	−0.305547	−	0.952177i	$-0.598839\pi$
$972$		0			0
$973$	−1.89515	+	2.94891i	−0.0607557	+	0.0945378i
$974$	−2.74276	−	1.25258i	−0.0878836	−	0.0401351i
$975$		0			0
$976$	0.863313	+	1.34334i	0.0276340	+	0.0429993i
$977$	4.26489	+	29.6630i	0.136446	+	0.949003i	0.936897	+	0.349605i	$0.113684\pi$
$977$	4.26489	+	29.6630i	0.136446	+	0.949003i	−0.800451	+	0.599398i	$0.795407\pi$
$978$		0			0
$979$	−18.1294	+	11.6510i	−0.579417	+	0.372368i
$980$	−10.5035	+	12.1217i	−0.335522	+	0.387213i
$981$		0			0
$982$	−10.3652	−	6.66131i	−0.330767	−	0.212571i
$983$	−11.2540	+	3.30447i	−0.358947	+	0.105396i	−0.456233	−	0.889860i	$-0.650802\pi$
$983$	−11.2540	+	3.30447i	−0.358947	+	0.105396i	0.0972867	+	0.995256i	$0.468984\pi$
$984$		0			0
$985$	5.20939	−	17.7416i	0.165985	−	0.565293i
$986$	6.86902	+	15.0411i	0.218754	+	0.479005i
$987$		0			0
$988$			0.106922i			0.00340166i
$989$	−28.9308	−	18.6963i	−0.919947	−	0.594509i
$990$		0			0
$991$	−2.08049	+	14.4701i	−0.0660890	+	0.459659i	0.929725	+	0.368255i	$0.120045\pi$
$991$	−2.08049	+	14.4701i	−0.0660890	+	0.459659i	−0.995814	+	0.0914042i	$0.970864\pi$
$992$	3.99706	−	1.82540i	0.126907	−	0.0579564i
$993$		0			0
$994$	11.4760	−	9.94401i	0.363997	−	0.315405i
$995$	−5.82277	−	19.8305i	−0.184594	−	0.628670i
$996$		0			0
$997$	14.5982	−	31.9656i	0.462330	−	1.01236i	−0.524620	−	0.851336i	$-0.675793\pi$
$997$	14.5982	−	31.9656i	0.462330	−	1.01236i	0.986950	−	0.161025i	$-0.0514800\pi$
$998$	−5.10502	−	4.42353i	−0.161597	−	0.140024i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.107.4	yes	80
3.2	odd	2	inner	414.2.j.a.107.5	yes	80
23.20	odd	22	inner	414.2.j.a.89.5	yes	80
69.20	even	22	inner	414.2.j.a.89.4	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.89.4	✓	80	69.20	even	22	inner
414.2.j.a.89.5	yes	80	23.20	odd	22	inner
414.2.j.a.107.4	yes	80	1.1	even	1	trivial
414.2.j.a.107.5	yes	80	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.989821 - 0.142315i) q^{2} +(0.959493 + 0.281733i) q^{4} +(2.09328 + 2.41578i) q^{5} +(0.761188 - 1.18443i) q^{7} +(-0.909632 - 0.415415i) q^{8} +O(q^{10})\)	\(q+(-0.989821 - 0.142315i) q^{2} +(0.959493 + 0.281733i) q^{4} +(2.09328 + 2.41578i) q^{5} +(0.761188 - 1.18443i) q^{7} +(-0.909632 - 0.415415i) q^{8} +(-1.72817 - 2.68909i) q^{10} +(0.611710 + 4.25454i) q^{11} +(1.51536 - 0.973861i) q^{13} +(-0.922002 + 1.06405i) q^{14} +(0.841254 + 0.540641i) q^{16} +(-1.94380 + 0.570751i) q^{17} +(-0.0167231 + 0.0569538i) q^{19} +(1.32789 + 2.90767i) q^{20} -4.29829i q^{22} +(-2.58260 - 4.04106i) q^{23} +(-0.742571 + 5.16469i) q^{25} +(-1.63853 + 0.748291i) q^{26} +(1.06405 - 0.922002i) q^{28} +(2.29954 + 7.83150i) q^{29} +(-1.82540 + 3.99706i) q^{31} +(-0.755750 - 0.654861i) q^{32} +(2.00524 - 0.288310i) q^{34} +(4.45470 - 0.640489i) q^{35} +(4.96044 + 4.29825i) q^{37} +(0.0246583 - 0.0539941i) q^{38} +(-0.900567 - 3.06705i) q^{40} +(8.47079 - 7.33998i) q^{41} +(6.53347 - 2.98374i) q^{43} +(-0.611710 + 4.25454i) q^{44} +(1.98121 + 4.36747i) q^{46} -0.223550i q^{47} +(2.08443 + 4.56427i) q^{49} +(1.47002 - 5.00645i) q^{50} +(1.72834 - 0.507487i) q^{52} +(1.93957 + 1.24649i) q^{53} +(-8.99753 + 10.3837i) q^{55} +(-1.18443 + 0.761188i) q^{56} +(-1.16159 - 8.07905i) q^{58} +(-6.13821 - 9.55124i) q^{59} +(1.45253 + 0.663348i) q^{61} +(2.37566 - 3.69659i) q^{62} +(0.654861 + 0.755750i) q^{64} +(5.52470 + 1.62220i) q^{65} +(0.815293 + 0.117221i) q^{67} -2.02586 q^{68} -4.50051 q^{70} +(-10.6755 - 1.53490i) q^{71} +(-11.1441 - 3.27221i) q^{73} +(-4.29825 - 4.96044i) q^{74} +(-0.0320915 + 0.0499353i) q^{76} +(5.50483 + 2.51397i) q^{77} +(-8.97046 - 13.9583i) q^{79} +(0.454914 + 3.16399i) q^{80} +(-9.42916 + 6.05975i) q^{82} +(-1.33209 + 1.53731i) q^{83} +(-5.44772 - 3.50104i) q^{85} +(-6.89160 + 2.02356i) q^{86} +(1.21097 - 4.12418i) q^{88} +(2.08277 + 4.56064i) q^{89} -2.53613i q^{91} +(-1.33949 - 4.60497i) q^{92} +(-0.0318145 + 0.221275i) q^{94} +(-0.172594 + 0.0788209i) q^{95} +(-7.36577 + 6.38247i) q^{97} +(-1.41365 - 4.81446i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 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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