LMFDB - Embedded newform 414.2.j.a.89.3

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			89.3
Character	$\chi$	$=$	414.89
Dual form			414.2.j.a.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.408438 + 0.471363i) q^{5} +(-2.27479 - 3.53964i) q^{7} +(-0.909632 + 0.415415i) q^{8} +O(q^{10})$	\(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.408438 + 0.471363i) q^{5} +(-2.27479 - 3.53964i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.337199 - 0.524692i) q^{10} +(-0.719483 + 5.00411i) q^{11} +(-2.56399 - 1.64778i) q^{13} +(2.75538 + 3.17987i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-7.54666 - 2.21590i) q^{17} +(1.77239 + 6.03620i) q^{19} +(-0.259095 + 0.567339i) q^{20} -5.05557i q^{22} +(-1.46111 - 4.56784i) q^{23} +(0.656213 + 4.56406i) q^{25} +(2.77240 + 1.26611i) q^{26} +(-3.17987 - 2.75538i) q^{28} +(-0.350823 + 1.19479i) q^{29} +(-4.37963 - 9.59005i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(7.78520 + 1.11934i) q^{34} +(2.59756 + 0.373473i) q^{35} +(-4.51237 + 3.90999i) q^{37} +(-2.61339 - 5.72252i) q^{38} +(0.175717 - 0.598438i) q^{40} +(-2.29479 - 1.98845i) q^{41} +(-2.41855 - 1.10452i) q^{43} +(0.719483 + 5.00411i) q^{44} +(2.09631 + 4.31341i) q^{46} -4.54818i q^{47} +(-4.44647 + 9.73641i) q^{49} +(-1.29907 - 4.42422i) q^{50} +(-2.92437 - 0.858671i) q^{52} +(-7.00945 + 4.50470i) q^{53} +(-2.06489 - 2.38301i) q^{55} +(3.53964 + 2.27479i) q^{56} +(0.177215 - 1.23256i) q^{58} +(1.30015 - 2.02307i) q^{59} +(-4.29810 + 1.96287i) q^{61} +(5.69986 + 8.86915i) q^{62} +(0.654861 - 0.755750i) q^{64} +(1.82393 - 0.535555i) q^{65} +(13.6633 - 1.96448i) q^{67} -7.86526 q^{68} -2.62427 q^{70} +(3.50036 - 0.503275i) q^{71} +(-2.66256 + 0.781797i) q^{73} +(3.90999 - 4.51237i) q^{74} +(3.40119 + 5.29235i) q^{76} +(19.3494 - 8.83658i) q^{77} +(2.10048 - 3.26841i) q^{79} +(-0.0887621 + 0.617354i) q^{80} +(2.55442 + 1.64162i) q^{82} +(-0.425150 - 0.490649i) q^{83} +(4.12684 - 2.65216i) q^{85} +(2.55112 + 0.749077i) q^{86} +(-1.42432 - 4.85078i) q^{88} +(5.96164 - 13.0542i) q^{89} +12.8239i q^{91} +(-2.68883 - 3.97117i) q^{92} +(0.647273 + 4.50188i) q^{94} +(-3.56915 - 1.62998i) q^{95} +(4.89137 + 4.23839i) q^{97} +(3.01558 - 10.2701i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$

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
$5$	−0.408438	+	0.471363i	−0.182659	+	0.210800i	−0.839693	−	0.543061i	$-0.817265\pi$
$5$	−0.408438	+	0.471363i	−0.182659	+	0.210800i	0.657034	+	0.753861i	$0.271811\pi$
$6$		0			0
$7$	−2.27479	−	3.53964i	−0.859788	−	1.33786i	−0.940034	−	0.341082i	$-0.889207\pi$
$7$	−2.27479	−	3.53964i	−0.859788	−	1.33786i	0.0802452	−	0.996775i	$-0.474430\pi$
$8$	−0.909632	+	0.415415i	−0.321603	+	0.146871i
$9$		0			0
$10$	0.337199	−	0.524692i	0.106632	−	0.165922i
$11$	−0.719483	+	5.00411i	−0.216932	+	1.50880i	0.532338	+	0.846532i	$0.321314\pi$
$11$	−0.719483	+	5.00411i	−0.216932	+	1.50880i	−0.749270	+	0.662265i	$0.769595\pi$
$12$		0			0
$13$	−2.56399	−	1.64778i	−0.711124	−	0.457011i	0.134415	−	0.990925i	$-0.457084\pi$
$13$	−2.56399	−	1.64778i	−0.711124	−	0.457011i	−0.845539	+	0.533914i	$0.820721\pi$
$14$	2.75538	+	3.17987i	0.736405	+	0.849857i
$15$		0			0
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−7.54666	−	2.21590i	−1.83033	−	0.537435i	−0.830525	−	0.556981i	$-0.811960\pi$
$17$	−7.54666	−	2.21590i	−1.83033	−	0.537435i	−0.999809	+	0.0195463i	$0.993778\pi$
$18$		0			0
$19$	1.77239	+	6.03620i	0.406614	+	1.38480i	0.867543	+	0.497362i	$0.165698\pi$
$19$	1.77239	+	6.03620i	0.406614	+	1.38480i	−0.460929	+	0.887437i	$0.652484\pi$
$20$	−0.259095	+	0.567339i	−0.0579354	+	0.126861i
$21$		0			0
$22$		−	5.05557i		−	1.07785i
$23$	−1.46111	−	4.56784i	−0.304663	−	0.952460i
$23$	−1.46111	−	4.56784i	−0.304663	−	0.952460i
$24$		0			0
$25$	0.656213	+	4.56406i	0.131243	+	0.912812i
$26$	2.77240	+	1.26611i	0.543712	+	0.248305i
$27$		0			0
$28$	−3.17987	−	2.75538i	−0.600939	−	0.520717i
$29$	−0.350823	+	1.19479i	−0.0651462	+	0.221868i	−0.985632	−	0.168909i	$-0.945975\pi$
$29$	−0.350823	+	1.19479i	−0.0651462	+	0.221868i	0.920485	+	0.390777i	$0.127794\pi$
$30$		0			0
$31$	−4.37963	−	9.59005i	−0.786605	−	1.72242i	−0.686123	−	0.727486i	$-0.740689\pi$
$31$	−4.37963	−	9.59005i	−0.786605	−	1.72242i	−0.100482	−	0.994939i	$-0.532038\pi$
$32$	−0.755750	+	0.654861i	−0.133599	+	0.115764i
$33$		0			0
$34$	7.78520	+	1.11934i	1.33515	+	0.191966i
$35$	2.59756	+	0.373473i	0.439068	+	0.0631284i
$36$		0			0
$37$	−4.51237	+	3.90999i	−0.741830	+	0.642799i	−0.941480	−	0.337068i	$-0.890565\pi$
$37$	−4.51237	+	3.90999i	−0.741830	+	0.642799i	0.199651	+	0.979867i	$0.436019\pi$
$38$	−2.61339	−	5.72252i	−0.423948	−	0.928316i
$39$		0			0
$40$	0.175717	−	0.598438i	0.0277833	−	0.0946213i
$41$	−2.29479	−	1.98845i	−0.358386	−	0.310543i	0.456994	−	0.889470i	$-0.348926\pi$
$41$	−2.29479	−	1.98845i	−0.358386	−	0.310543i	−0.815379	+	0.578927i	$0.803472\pi$
$42$		0			0
$43$	−2.41855	−	1.10452i	−0.368826	−	0.168437i	0.222376	−	0.974961i	$-0.428619\pi$
$43$	−2.41855	−	1.10452i	−0.368826	−	0.168437i	−0.591201	+	0.806524i	$0.701346\pi$
$44$	0.719483	+	5.00411i	0.108466	+	0.754398i
$45$		0			0
$46$	2.09631	+	4.31341i	0.309084	+	0.635977i
$47$		−	4.54818i		−	0.663420i	−0.943381	−	0.331710i	$-0.892375\pi$
$47$		−	4.54818i		−	0.663420i	0.943381	−	0.331710i	$-0.107625\pi$
$48$		0			0
$49$	−4.44647	+	9.73641i	−0.635210	+	1.39092i
$50$	−1.29907	−	4.42422i	−0.183716	−	0.625679i
$51$		0			0
$52$	−2.92437	−	0.858671i	−0.405536	−	0.119076i
$53$	−7.00945	+	4.50470i	−0.962821	+	0.618768i	−0.924778	−	0.380508i	$-0.875749\pi$
$53$	−7.00945	+	4.50470i	−0.962821	+	0.618768i	−0.0380439	+	0.999276i	$0.512113\pi$
$54$		0			0
$55$	−2.06489	−	2.38301i	−0.278429	−	0.321325i
$56$	3.53964	+	2.27479i	0.473004	+	0.303981i
$57$		0			0
$58$	0.177215	−	1.23256i	0.0232695	−	0.161843i
$59$	1.30015	−	2.02307i	0.169265	−	0.263381i	−0.746250	−	0.665666i	$-0.768147\pi$
$59$	1.30015	−	2.02307i	0.169265	−	0.263381i	0.915515	+	0.402285i	$0.131784\pi$
$60$		0			0
$61$	−4.29810	+	1.96287i	−0.550315	+	0.251320i	−0.671111	−	0.741357i	$-0.734183\pi$
$61$	−4.29810	+	1.96287i	−0.550315	+	0.251320i	0.120796	+	0.992677i	$0.461455\pi$
$62$	5.69986	+	8.86915i	0.723883	+	1.12638i
$63$		0			0
$64$	0.654861	−	0.755750i	0.0818576	−	0.0944687i
$65$	1.82393	−	0.535555i	0.226231	−	0.0664274i
$66$		0			0
$67$	13.6633	−	1.96448i	1.66924	−	0.240000i	0.758110	−	0.652127i	$-0.226123\pi$
$67$	13.6633	−	1.96448i	1.66924	−	0.240000i	0.911127	+	0.412127i	$0.135214\pi$
$68$	−7.86526			−0.953803
$69$		0			0
$70$	−2.62427			−0.313661
$71$	3.50036	−	0.503275i	0.415416	−	0.0597278i	0.0685618	−	0.997647i	$-0.478159\pi$
$71$	3.50036	−	0.503275i	0.415416	−	0.0597278i	0.346854	+	0.937919i	$0.387250\pi$
$72$		0			0
$73$	−2.66256	+	0.781797i	−0.311629	+	0.0915024i	−0.433807	−	0.901006i	$-0.642830\pi$
$73$	−2.66256	+	0.781797i	−0.311629	+	0.0915024i	0.122179	+	0.992508i	$0.461012\pi$
$74$	3.90999	−	4.51237i	0.454528	−	0.524553i
$75$		0			0
$76$	3.40119	+	5.29235i	0.390143	+	0.607074i
$77$	19.3494	−	8.83658i	2.20507	−	1.00702i
$78$		0			0
$79$	2.10048	−	3.26841i	0.236322	−	0.367725i	−0.702754	−	0.711433i	$-0.748047\pi$
$79$	2.10048	−	3.26841i	0.236322	−	0.367725i	0.939077	+	0.343708i	$0.111683\pi$
$80$	−0.0887621	+	0.617354i	−0.00992390	+	0.0690222i
$81$		0			0
$82$	2.55442	+	1.64162i	0.282088	+	0.181287i
$83$	−0.425150	−	0.490649i	−0.0466662	−	0.0538557i	0.731937	−	0.681373i	$-0.238617\pi$
$83$	−0.425150	−	0.490649i	−0.0466662	−	0.0538557i	−0.778603	+	0.627517i	$0.784071\pi$
$84$		0			0
$85$	4.12684	−	2.65216i	0.447618	−	0.287667i
$86$	2.55112	+	0.749077i	0.275095	+	0.0807751i
$87$		0			0
$88$	−1.42432	−	4.85078i	−0.151833	−	0.517095i
$89$	5.96164	−	13.0542i	0.631932	−	1.38374i	−0.274582	−	0.961564i	$-0.588540\pi$
$89$	5.96164	−	13.0542i	0.631932	−	1.38374i	0.906514	−	0.422175i	$-0.138733\pi$
$90$		0			0
$91$			12.8239i			1.34431i
$92$	−2.68883	−	3.97117i	−0.280330	−	0.414023i
$93$		0			0
$94$	0.647273	+	4.50188i	0.0667611	+	0.464334i
$95$	−3.56915	−	1.62998i	−0.366187	−	0.167232i
$96$		0			0
$97$	4.89137	+	4.23839i	0.496643	+	0.430344i	0.866823	−	0.498617i	$-0.166158\pi$
$97$	4.89137	+	4.23839i	0.496643	+	0.430344i	−0.370180	+	0.928960i	$0.620704\pi$
$98$	3.01558	−	10.2701i	0.304619	−	1.03744i
$99$		0			0
$100$	1.91548	+	4.19431i	0.191548	+	0.419431i
$101$	2.32566	−	2.01520i	0.231412	−	0.200520i	−0.531434	−	0.847100i	$-0.678347\pi$
$101$	2.32566	−	2.01520i	0.231412	−	0.200520i	0.762846	+	0.646580i	$0.223801\pi$
$102$		0			0
$103$	17.5778	+	2.52730i	1.73199	+	0.249022i	0.934918	−	0.354864i	$-0.115473\pi$
$103$	17.5778	+	2.52730i	1.73199	+	0.249022i	0.797071	+	0.603886i	$0.206382\pi$
$104$	3.01680	+	0.433751i	0.295822	+	0.0425327i
$105$		0			0
$106$	6.29701	−	5.45639i	0.611620	−	0.529972i
$107$	5.18621	+	11.3562i	0.501370	+	1.09785i	0.976022	+	0.217673i	$0.0698467\pi$
$107$	5.18621	+	11.3562i	0.501370	+	1.09785i	−0.474652	+	0.880174i	$0.657426\pi$
$108$		0			0
$109$	−1.60889	+	5.47938i	−0.154104	+	0.524830i	−0.999963	−	0.00857639i	$-0.997270\pi$
$109$	−1.60889	+	5.47938i	−0.154104	+	0.524830i	0.845859	+	0.533406i	$0.179088\pi$
$110$	2.38301	+	2.06489i	0.227211	+	0.196879i
$111$		0			0
$112$	−3.82734	−	1.74789i	−0.361650	−	0.165160i
$113$	1.07260	+	7.46008i	0.100901	+	0.701785i	0.975989	+	0.217820i	$0.0698946\pi$
$113$	1.07260	+	7.46008i	0.100901	+	0.701785i	−0.875087	+	0.483965i	$0.839196\pi$
$114$		0			0
$115$	2.74988	+	1.17697i	0.256428	+	0.109753i
$116$			1.24523i			0.115617i
$117$		0			0
$118$	−0.999002	+	2.18751i	−0.0919656	+	0.201376i
$119$	9.32356	+	31.7531i	0.854690	+	2.91081i
$120$		0			0
$121$	−13.9691	−	4.10169i	−1.26991	−	0.372881i
$122$	3.97500	−	2.55458i	0.359880	−	0.231281i
$123$		0			0
$124$	−6.90405	−	7.96770i	−0.620002	−	0.715521i
$125$	−5.04281	−	3.24082i	−0.451042	−	0.289867i
$126$		0			0
$127$	−1.12102	+	7.79687i	−0.0994745	+	0.691861i	0.877667	+	0.479271i	$0.159099\pi$
$127$	−1.12102	+	7.79687i	−0.0994745	+	0.691861i	−0.977142	+	0.212590i	$0.931810\pi$
$128$	−0.540641	+	0.841254i	−0.0477863	+	0.0743570i
$129$		0			0
$130$	−1.72915	+	0.789676i	−0.151656	+	0.0692592i
$131$	−4.64912	−	7.23417i	−0.406196	−	0.632053i	0.576540	−	0.817069i	$-0.304403\pi$
$131$	−4.64912	−	7.23417i	−0.406196	−	0.632053i	−0.982735	+	0.185016i	$0.940766\pi$
$132$		0			0
$133$	17.3342	−	20.0047i	1.50306	−	1.73463i
$134$	−13.2446	+	3.88898i	−1.14416	+	0.335957i
$135$		0			0
$136$	7.78520	−	1.11934i	0.667576	−	0.0959829i
$137$	−12.5429			−1.07162			−0.535808	−	0.844340i	$-0.679993\pi$
$137$	−12.5429			−1.07162			−0.535808	+	0.844340i	$0.679993\pi$
$138$		0			0
$139$	−0.983473			−0.0834171			−0.0417085	−	0.999130i	$-0.513280\pi$
$139$	−0.983473			−0.0834171			−0.0417085	+	0.999130i	$0.513280\pi$
$140$	2.59756	−	0.373473i	0.219534	−	0.0315642i
$141$		0			0
$142$	−3.39310	+	0.996305i	−0.284743	+	0.0836081i
$143$	10.0904	−	11.6450i	0.843803	−	0.973800i
$144$		0			0
$145$	−0.419891	−	0.653364i	−0.0348701	−	0.0542589i
$146$	2.52419	−	1.15276i	0.208904	−	0.0954031i
$147$		0			0
$148$	−3.22802	+	5.02290i	−0.265342	+	0.412879i
$149$	1.53705	−	10.6904i	0.125920	−	0.875793i	−0.824730	−	0.565527i	$-0.808673\pi$
$149$	1.53705	−	10.6904i	0.125920	−	0.875793i	0.950650	−	0.310266i	$-0.100418\pi$
$150$		0			0
$151$	−8.95467	−	5.75482i	−0.728721	−	0.468321i	0.122940	−	0.992414i	$-0.460768\pi$
$151$	−8.95467	−	5.75482i	−0.728721	−	0.468321i	−0.851661	+	0.524094i	$0.824404\pi$
$152$	−4.11975	−	4.75444i	−0.334156	−	0.385636i
$153$		0			0
$154$	−17.8949	+	11.5003i	−1.44201	+	0.926724i
$155$	6.30920	+	1.85255i	0.506767	+	0.148800i
$156$		0			0
$157$	4.07540	+	13.8795i	0.325252	+	1.10771i	0.946126	+	0.323798i	$0.104960\pi$
$157$	4.07540	+	13.8795i	0.325252	+	1.10771i	−0.620874	+	0.783910i	$0.713222\pi$
$158$	−1.61396	+	3.53407i	−0.128399	+	0.281155i
$159$		0			0
$160$		−	0.623702i		−	0.0493080i
$161$	−12.8448	+	15.5627i	−1.01231	+	1.22651i
$162$		0			0
$163$	−1.95491	−	13.5967i	−0.153120	−	1.06497i	−0.910949	−	0.412520i	$-0.864649\pi$
$163$	−1.95491	−	13.5967i	−0.153120	−	1.06497i	0.757829	−	0.652454i	$-0.226260\pi$
$164$	−2.76204	−	1.26138i	−0.215679	−	0.0984974i
$165$		0			0
$166$	0.490649	+	0.425150i	0.0380817	+	0.0329980i
$167$	0.226869	−	0.772645i	0.0175557	−	0.0597891i	−0.950249	−	0.311490i	$-0.899172\pi$
$167$	0.226869	−	0.772645i	0.0175557	−	0.0597891i	0.967805	+	0.251701i	$0.0809900\pi$
$168$		0			0
$169$	−1.54151	−	3.37544i	−0.118578	−	0.259649i
$170$	−3.70739	+	3.21247i	−0.284344	+	0.246385i
$171$		0			0
$172$	−2.63176	−	0.378390i	−0.200670	−	0.0288520i
$173$	−11.2721	−	1.62068i	−0.857003	−	0.123218i	−0.300213	−	0.953872i	$-0.597058\pi$
$173$	−11.2721	−	1.62068i	−0.857003	−	0.123218i	−0.556789	+	0.830654i	$0.687967\pi$
$174$		0			0
$175$	14.6624	−	12.7050i	1.10837	−	0.960409i
$176$	2.10016	+	4.59871i	0.158306	+	0.346641i
$177$		0			0
$178$	−4.04315	+	13.7697i	−0.303047	+	1.03208i
$179$	−0.0588099	−	0.0509591i	−0.00439566	−	0.00380886i	0.652660	−	0.757651i	$-0.273653\pi$
$179$	−0.0588099	−	0.0509591i	−0.00439566	−	0.00380886i	−0.657056	+	0.753842i	$0.728198\pi$
$180$		0			0
$181$	−8.38232	−	3.82808i	−0.623053	−	0.284539i	0.0787669	−	0.996893i	$-0.474902\pi$
$181$	−8.38232	−	3.82808i	−0.623053	−	0.284539i	−0.701820	+	0.712354i	$0.747629\pi$
$182$	−1.82504	−	12.6934i	−0.135281	−	0.940898i
$183$		0			0
$184$	3.22662	+	3.54809i	0.237870	+	0.261568i
$185$		−	3.72395i		−	0.273791i
$186$		0			0
$187$	16.5183	−	36.1700i	1.20794	−	2.64502i
$188$	−1.28137	−	4.36394i	−0.0934535	−	0.318273i
$189$		0			0
$190$	3.76479	+	1.10544i	0.273127	+	0.0801972i
$191$	9.37001	−	6.02174i	0.677990	−	0.435718i	−0.155808	−	0.987787i	$-0.549798\pi$
$191$	9.37001	−	6.02174i	0.677990	−	0.435718i	0.833798	+	0.552069i	$0.186162\pi$
$192$		0			0
$193$	−5.68621	−	6.56224i	−0.409302	−	0.472360i	0.513246	−	0.858242i	$-0.328443\pi$
$193$	−5.68621	−	6.56224i	−0.409302	−	0.472360i	−0.922548	+	0.385881i	$0.873897\pi$
$194$	−5.44477	−	3.49914i	−0.390911	−	0.251223i
$195$		0			0
$196$	−1.52329	+	10.5947i	−0.108807	+	0.756767i
$197$	−6.30332	+	9.80816i	−0.449093	+	0.698802i	−0.989809	−	0.142403i	$-0.954517\pi$
$197$	−6.30332	+	9.80816i	−0.449093	+	0.698802i	0.540716	+	0.841205i	$0.318153\pi$
$198$		0			0
$199$	−11.6216	+	5.30739i	−0.823830	+	0.376231i	−0.782296	−	0.622906i	$-0.785952\pi$
$199$	−11.6216	+	5.30739i	−0.823830	+	0.376231i	−0.0415340	+	0.999137i	$0.513224\pi$
$200$	−2.49289	−	3.87902i	−0.176274	−	0.274288i
$201$		0			0
$202$	−2.01520	+	2.32566i	−0.141789	+	0.163633i
$203$	5.02718	−	1.47611i	0.352839	−	0.103603i
$204$		0			0
$205$	1.87456	−	0.269521i	0.130925	−	0.0188241i
$206$	−17.7585			−1.23729
$207$		0			0
$208$	−3.04782			−0.211329
$209$	−31.4810	+	4.52629i	−2.17759	+	0.313090i
$210$		0			0
$211$	−17.7668	+	5.21680i	−1.22312	+	0.359139i	−0.828648	−	0.559770i	$-0.810889\pi$
$211$	−17.7668	+	5.21680i	−1.22312	+	0.359139i	−0.394469	+	0.918909i	$0.629071\pi$
$212$	−5.45639	+	6.29701i	−0.374747	+	0.432481i
$213$		0			0
$214$	−6.74958	−	10.5026i	−0.461392	−	0.717940i
$215$	1.50845	−	0.688888i	0.102876	−	0.0469818i
$216$		0			0
$217$	−23.9826	+	37.3176i	−1.62804	+	2.53329i
$218$	0.812718	−	5.65258i	0.0550442	−	0.382841i
$219$		0			0
$220$	−2.65262	−	1.70473i	−0.178839	−	0.114933i
$221$	15.6983	+	18.1168i	1.05598	+	1.21867i
$222$		0			0
$223$	−1.93780	+	1.24535i	−0.129765	+	0.0833947i	−0.603913	−	0.797050i	$-0.706392\pi$
$223$	−1.93780	+	1.24535i	−0.129765	+	0.0833947i	0.474148	+	0.880445i	$0.342756\pi$
$224$	4.03714	+	1.18541i	0.269743	+	0.0792036i
$225$		0			0
$226$	−2.12336	−	7.23150i	−0.141244	−	0.481032i
$227$	−7.61560	+	16.6758i	−0.505465	+	1.10681i	0.469189	+	0.883098i	$0.344546\pi$
$227$	−7.61560	+	16.6758i	−0.505465	+	1.10681i	−0.974654	+	0.223717i	$0.928181\pi$
$228$		0			0
$229$		−	2.42860i		−	0.160486i	−0.996775	−	0.0802432i	$-0.974430\pi$
$229$		−	2.42860i		−	0.160486i	0.996775	−	0.0802432i	$-0.0255697\pi$
$230$	−2.88939	−	0.773638i	−0.190521	−	0.0510122i
$231$		0			0
$232$	−0.177215	−	1.23256i	−0.0116348	−	0.0809215i
$233$	12.5735	+	5.74211i	0.823715	+	0.376178i	0.782252	−	0.622962i	$-0.214071\pi$
$233$	12.5735	+	5.74211i	0.823715	+	0.376178i	0.0414629	+	0.999140i	$0.486798\pi$
$234$		0			0
$235$	2.14384	+	1.85765i	0.139849	+	0.121180i
$236$	0.677518	−	2.30742i	0.0441027	−	0.150200i
$237$		0			0
$238$	−13.7476	−	30.1031i	−0.891125	−	1.95129i
$239$	−4.42019	+	3.83012i	−0.285918	+	0.247750i	−0.785997	−	0.618230i	$-0.787850\pi$
$239$	−4.42019	+	3.83012i	−0.285918	+	0.247750i	0.500079	+	0.865980i	$0.333304\pi$
$240$		0			0
$241$	−0.171127	−	0.0246044i	−0.0110233	−	0.00158491i	0.136801	−	0.990599i	$-0.456318\pi$
$241$	−0.171127	−	0.0246044i	−0.0110233	−	0.00158491i	−0.147824	+	0.989014i	$0.547227\pi$
$242$	14.4106	+	2.07193i	0.926349	+	0.133189i
$243$		0			0
$244$	−3.57099	+	3.09428i	−0.228609	+	0.198091i
$245$	−2.77327	−	6.07262i	−0.177178	−	0.387965i
$246$		0			0
$247$	5.40193	−	18.3973i	0.343716	−	1.17059i
$248$	7.96770	+	6.90405i	0.505950	+	0.438408i
$249$		0			0
$250$	5.45270	+	2.49016i	0.344859	+	0.157492i
$251$	0.334681	+	2.32776i	0.0211249	+	0.146927i	0.997654	−	0.0684589i	$-0.0218082\pi$
$251$	0.334681	+	2.32776i	0.0211249	+	0.146927i	−0.976529	+	0.215386i	$0.930899\pi$
$252$		0			0
$253$	23.9092	−	4.02508i	1.50316	−	0.253055i
$254$		−	7.87705i		−	0.494250i
$255$		0			0
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−3.01270	−	10.2603i	−0.187927	−	0.640020i	−0.998519	−	0.0544085i	$-0.982673\pi$
$257$	−3.01270	−	10.2603i	−0.187927	−	0.640020i	0.810592	−	0.585611i	$-0.199145\pi$
$258$		0			0
$259$	24.1046	+	7.07776i	1.49779	+	0.439791i
$260$	1.59917	−	1.02772i	0.0991761	−	0.0637366i
$261$		0			0
$262$	5.63133	+	6.49890i	0.347905	+	0.401503i
$263$	1.60826	+	1.03357i	0.0991695	+	0.0637324i	0.589286	−	0.807925i	$-0.299409\pi$
$263$	1.60826	+	1.03357i	0.0991695	+	0.0637324i	−0.490116	+	0.871657i	$0.663046\pi$
$264$		0			0
$265$	0.739578	−	5.14388i	0.0454319	−	0.315986i
$266$	−14.3108	+	22.2680i	−0.877448	+	1.36534i
$267$		0			0
$268$	12.5564	−	5.73430i	0.767002	−	0.350278i
$269$	0.611804	+	0.951986i	0.0373024	+	0.0580436i	0.859404	−	0.511297i	$-0.170835\pi$
$269$	0.611804	+	0.951986i	0.0373024	+	0.0580436i	−0.822102	+	0.569341i	$0.807198\pi$
$270$		0			0
$271$	2.06334	−	2.38122i	0.125339	−	0.144649i	−0.689611	−	0.724180i	$-0.742219\pi$
$271$	2.06334	−	2.38122i	0.125339	−	0.144649i	0.814951	+	0.579531i	$0.196764\pi$
$272$	−7.54666	+	2.21590i	−0.457584	+	0.134359i
$273$		0			0
$274$	12.4153	−	1.78505i	0.750034	−	0.107839i
$275$	−23.3112			−1.40572
$276$		0			0
$277$	−32.1339			−1.93074			−0.965370	−	0.260886i	$-0.915985\pi$
$277$	−32.1339			−1.93074			−0.965370	+	0.260886i	$0.915985\pi$
$278$	0.973462	−	0.139963i	0.0583844	−	0.00839441i
$279$		0			0
$280$	−2.51797	+	0.739343i	−0.150478	+	0.0441842i
$281$	14.8257	−	17.1098i	0.884429	−	1.02069i	−0.115197	−	0.993343i	$-0.536750\pi$
$281$	14.8257	−	17.1098i	0.884429	−	1.02069i	0.999626	−	0.0273428i	$-0.00870458\pi$
$282$		0			0
$283$	−12.7566	−	19.8497i	−0.758304	−	1.17994i	−0.978852	−	0.204568i	$-0.934421\pi$
$283$	−12.7566	−	19.8497i	−0.758304	−	1.17994i	0.220549	−	0.975376i	$-0.429215\pi$
$284$	3.21678	−	1.46905i	0.190881	−	0.0871723i
$285$		0			0
$286$	−8.33046	+	12.9624i	−0.492590	+	0.766485i
$287$	−1.81822	+	12.6460i	−0.107326	+	0.746470i
$288$		0			0
$289$	37.7406	+	24.2544i	2.22003	+	1.42673i
$290$	0.508601	+	0.586957i	0.0298661	+	0.0344673i
$291$		0			0
$292$	−2.33445	+	1.50026i	−0.136613	+	0.0877959i
$293$	−28.2589	−	8.29755i	−1.65090	−	0.484748i	−0.681826	−	0.731515i	$-0.738814\pi$
$293$	−28.2589	−	8.29755i	−1.65090	−	0.484748i	−0.969075	+	0.246767i	$0.920632\pi$
$294$		0			0
$295$	0.422570	+	1.43914i	0.0246030	+	0.0837900i
$296$	2.48033	−	5.43116i	0.144166	−	0.315680i
$297$		0			0
$298$			10.8003i			0.625647i
$299$	−3.78051	+	14.1195i	−0.218632	+	0.816551i
$300$		0			0
$301$	1.59210	+	11.0733i	0.0917673	+	0.638256i
$302$	9.68252	+	4.42186i	0.557167	+	0.254449i
$303$		0			0
$304$	4.75444	+	4.11975i	0.272686	+	0.236284i
$305$	0.830280	−	2.82767i	0.0475417	−	0.161912i
$306$		0			0
$307$	−0.354655	−	0.776587i	−0.0202413	−	0.0443222i	0.899241	−	0.437453i	$-0.144119\pi$
$307$	−0.354655	−	0.776587i	−0.0202413	−	0.0443222i	−0.919483	+	0.393131i	$0.871392\pi$
$308$	16.0761	−	13.9300i	0.916019	−	0.793735i
$309$		0			0
$310$	−6.50863	−	0.935799i	−0.369665	−	0.0531498i
$311$	18.0284	+	2.59210i	1.02230	+	0.146984i	0.633020	−	0.774136i	$-0.281815\pi$
$311$	18.0284	+	2.59210i	1.02230	+	0.146984i	0.389279	+	0.921120i	$0.372724\pi$
$312$		0			0
$313$	2.71766	−	2.35487i	0.153611	−	0.133105i	−0.574664	−	0.818389i	$-0.694867\pi$
$313$	2.71766	−	2.35487i	0.153611	−	0.133105i	0.728276	+	0.685284i	$0.240322\pi$
$314$	−6.00918	−	13.1583i	−0.339118	−	0.742564i
$315$		0			0
$316$	1.09458	−	3.72779i	0.0615748	−	0.209704i
$317$	15.6405	+	13.5526i	0.878459	+	0.761189i	0.972137	−	0.234414i	$-0.0753170\pi$
$317$	15.6405	+	13.5526i	0.878459	+	0.761189i	−0.0936781	+	0.995603i	$0.529862\pi$
$318$		0			0
$319$	−5.72647	−	2.61519i	−0.320621	−	0.146423i
$320$	0.0887621	+	0.617354i	0.00496195	+	0.0345111i
$321$		0			0
$322$	10.4992	−	17.2323i	0.585100	−	0.960316i
$323$		−	49.4806i		−	2.75317i
$324$		0			0
$325$	5.83804	−	12.7835i	0.323836	−	0.709102i
$326$	3.87002	+	13.1801i	0.214340	+	0.729976i
$327$		0			0
$328$	2.91344	+	0.855464i	0.160868	+	0.0472351i
$329$	−16.0989	+	10.3461i	−0.887561	+	0.570401i
$330$		0			0
$331$	−13.0486	−	15.0589i	−0.717215	−	0.827710i	0.273755	−	0.961800i	$-0.411734\pi$
$331$	−13.0486	−	15.0589i	−0.717215	−	0.827710i	−0.990969	+	0.134090i	$0.957189\pi$
$332$	−0.546160	−	0.350996i	−0.0299744	−	0.0192634i
$333$		0			0
$334$	−0.114601	+	0.797068i	−0.00627069	+	0.0436136i
$335$	−4.65462	+	7.24273i	−0.254309	+	0.395713i
$336$		0			0
$337$	−10.8330	+	4.94725i	−0.590109	+	0.269494i	−0.688009	−	0.725702i	$-0.741515\pi$
$337$	−10.8330	+	4.94725i	−0.590109	+	0.269494i	0.0978994	+	0.995196i	$0.468788\pi$
$338$	2.00619	+	3.12170i	0.109123	+	0.169798i
$339$		0			0
$340$	3.21247	−	3.70739i	0.174221	−	0.201061i
$341$	51.1408	−	15.0163i	2.76943	−	0.813177i
$342$		0			0
$343$	15.4249	−	2.21776i	0.832866	−	0.119748i
$344$	2.65882			0.143354
$345$		0			0
$346$	11.3880			0.612224
$347$	4.39964	−	0.632573i	0.236185	−	0.0339583i	−0.0232058	−	0.999731i	$-0.507387\pi$
$347$	4.39964	−	0.632573i	0.236185	−	0.0339583i	0.259391	+	0.965772i	$0.416478\pi$
$348$		0			0
$349$	19.3409	−	5.67899i	1.03529	−	0.303989i	0.280432	−	0.959874i	$-0.409522\pi$
$349$	19.3409	−	5.67899i	1.03529	−	0.303989i	0.754861	+	0.655885i	$0.227704\pi$
$350$	−12.7050	+	14.6624i	−0.679112	+	0.783737i
$351$		0			0
$352$	−2.73325	−	4.25302i	−0.145683	−	0.226687i
$353$	0.784723	−	0.358371i	0.0417666	−	0.0190742i	−0.394422	−	0.918929i	$-0.629055\pi$
$353$	0.784723	−	0.358371i	0.0417666	−	0.0190742i	0.436189	+	0.899855i	$0.356328\pi$
$354$		0			0
$355$	−1.19245	+	1.85549i	−0.0632889	+	0.0984794i
$356$	2.04237	−	14.2050i	0.108245	−	0.752862i
$357$		0			0
$358$	0.0654636	+	0.0420709i	0.00345986	+	0.00222352i
$359$	−0.00754198	−	0.00870390i	−0.000398050	−	0.000459374i	0.755551	−	0.655090i	$-0.227369\pi$
$359$	−0.00754198	−	0.00870390i	−0.000398050	−	0.000459374i	−0.755949	+	0.654631i	$0.772824\pi$
$360$		0			0
$361$	−17.3105	+	11.1248i	−0.911081	+	0.585516i
$362$	8.84180	+	2.59619i	0.464715	+	0.136453i
$363$		0			0
$364$	3.61292	+	12.3045i	0.189369	+	0.644930i
$365$	0.718979	−	1.57434i	0.0376331	−	0.0824050i
$366$		0			0
$367$			32.0251i			1.67169i	0.548962	+	0.835847i	$0.315023\pi$
$367$			32.0251i			1.67169i	−0.548962	+	0.835847i	$0.684977\pi$
$368$	−3.69872	−	3.05278i	−0.192809	−	0.159137i
$369$		0			0
$370$	0.529974	+	3.68605i	0.0275520	+	0.191629i
$371$	31.8900	+	14.5637i	1.65565	+	0.756108i
$372$		0			0
$373$	−7.71166	−	6.68219i	−0.399294	−	0.345991i	0.431950	−	0.901897i	$-0.357826\pi$
$373$	−7.71166	−	6.68219i	−0.399294	−	0.345991i	−0.831245	+	0.555907i	$0.812371\pi$
$374$	−11.2026	+	38.1527i	−0.579275	+	1.97283i
$375$		0			0
$376$	1.88938	+	4.13717i	0.0974374	+	0.213358i
$377$	2.86826	−	2.48536i	0.147723	−	0.128003i
$378$		0			0
$379$	−13.6267	−	1.95922i	−0.699956	−	0.100639i	−0.216856	−	0.976204i	$-0.569580\pi$
$379$	−13.6267	−	1.95922i	−0.699956	−	0.100639i	−0.483100	+	0.875565i	$0.660489\pi$
$380$	−3.88379	−	0.558405i	−0.199234	−	0.0286456i
$381$		0			0
$382$	−8.41766	+	7.29394i	−0.430685	+	0.373191i
$383$	−6.87263	−	15.0490i	−0.351175	−	0.768966i	−0.999968	−	0.00800131i	$-0.997453\pi$
$383$	−6.87263	−	15.0490i	−0.351175	−	0.768966i	0.648793	−	0.760965i	$-0.275274\pi$
$384$		0			0
$385$	−3.73780	+	12.7298i	−0.190496	+	0.648770i
$386$	6.56224	+	5.68621i	0.334009	+	0.289421i
$387$		0			0
$388$	5.88732	+	2.68865i	0.298884	+	0.136496i
$389$	2.82916	+	19.6773i	0.143444	+	0.997677i	0.926653	+	0.375918i	$0.122673\pi$
$389$	2.82916	+	19.6773i	0.143444	+	0.997677i	−0.783209	+	0.621759i	$0.786418\pi$
$390$		0			0
$391$	0.904631	+	37.7096i	0.0457492	+	1.90706i
$392$		−	10.7037i		−	0.540617i
$393$		0			0
$394$	4.84331	−	10.6054i	0.244003	−	0.534291i
$395$	0.682690	+	2.32503i	0.0343499	+	0.116985i
$396$		0			0
$397$	−10.2457	−	3.00842i	−0.514219	−	0.150988i	0.0143196	−	0.999897i	$-0.495442\pi$
$397$	−10.2457	−	3.00842i	−0.514219	−	0.150988i	−0.528539	+	0.848909i	$0.677260\pi$
$398$	10.7479	−	6.90729i	0.538746	−	0.346231i
$399$		0			0
$400$	3.01956	+	3.48476i	0.150978	+	0.174238i
$401$	−1.68016	−	1.07977i	−0.0839031	−	0.0539213i	0.498017	−	0.867167i	$-0.334062\pi$
$401$	−1.68016	−	1.07977i	−0.0839031	−	0.0539213i	−0.581920	+	0.813246i	$0.697698\pi$
$402$		0			0
$403$	−4.57294	+	31.8055i	−0.227794	+	1.58434i
$404$	1.66371	−	2.58878i	0.0827727	−	0.128797i
$405$		0			0
$406$	−4.76594	+	2.17653i	−0.236530	+	0.108019i
$407$	−16.3195	−	25.3936i	−0.808926	−	1.25871i
$408$		0			0
$409$	12.9551	−	14.9510i	0.640587	−	0.739277i	−0.338891	−	0.940826i	$-0.610052\pi$
$409$	12.9551	−	14.9510i	0.640587	−	0.739277i	0.979479	+	0.201548i	$0.0645973\pi$
$410$	−1.81712	+	0.533555i	−0.0897412	+	0.0263504i
$411$		0			0
$412$	17.5778	−	2.52730i	0.865994	−	0.124511i
$413$	−10.1185			−0.497898
$414$		0			0
$415$	0.404921			0.0198768
$416$	3.01680	−	0.433751i	0.147911	−	0.0212664i
$417$		0			0
$418$	30.5164	−	8.96043i	1.49261	−	0.438269i
$419$	4.06661	−	4.69312i	0.198667	−	0.229274i	−0.647671	−	0.761920i	$-0.724257\pi$
$419$	4.06661	−	4.69312i	0.198667	−	0.229274i	0.846338	+	0.532646i	$0.178802\pi$
$420$		0			0
$421$	−11.9640	−	18.6164i	−0.583090	−	0.907305i	0.416909	−	0.908948i	$-0.363113\pi$
$421$	−11.9640	−	18.6164i	−0.583090	−	0.907305i	−0.999999	+	0.00164286i	$0.999477\pi$
$422$	16.8435	−	7.69218i	0.819930	−	0.374450i
$423$		0			0
$424$	4.50470	−	7.00945i	0.218767	−	0.340409i
$425$	5.16129	−	35.8975i	0.250359	−	1.74129i
$426$		0			0
$427$	16.7251	+	10.7486i	0.809385	+	0.520160i
$428$	8.17555	+	9.43509i	0.395180	+	0.456062i
$429$		0			0
$430$	−1.39506	+	0.896552i	−0.0672759	+	0.0432356i
$431$	−12.2102	−	3.58525i	−0.588147	−	0.172696i	−0.0258995	−	0.999665i	$-0.508245\pi$
$431$	−12.2102	−	3.58525i	−0.588147	−	0.172696i	−0.562247	+	0.826969i	$0.690063\pi$
$432$		0			0
$433$	7.24704	+	24.6812i	0.348271	+	1.18610i	0.928402	+	0.371578i	$0.121183\pi$
$433$	7.24704	+	24.6812i	0.348271	+	1.18610i	−0.580131	+	0.814523i	$0.696999\pi$
$434$	18.4276	−	40.3509i	0.884554	−	1.93690i
$435$		0			0
$436$			5.71071i			0.273493i
$437$	24.9827	−	16.9155i	1.19509	−	0.809180i
$438$		0			0
$439$	3.35911	+	23.3631i	0.160321	+	1.11506i	0.898028	+	0.439938i	$0.145000\pi$
$439$	3.35911	+	23.3631i	0.160321	+	1.11506i	−0.737707	+	0.675121i	$0.764091\pi$
$440$	2.86822	+	1.30987i	0.136737	+	0.0624458i
$441$		0			0
$442$	−18.1168	−	15.6983i	−0.861727	−	0.746691i
$443$	8.09757	−	27.5778i	0.384727	−	1.31026i	−0.508658	−	0.860969i	$-0.669858\pi$
$443$	8.09757	−	27.5778i	0.384727	−	1.31026i	0.893385	−	0.449292i	$-0.148324\pi$
$444$		0			0
$445$	3.71829	+	8.14191i	0.176264	+	0.385963i
$446$	1.74084	−	1.50845i	0.0824314	−	0.0714272i
$447$		0			0
$448$	−4.16475	−	0.598800i	−0.196766	−	0.0282907i
$449$	−21.1887	−	3.04647i	−0.999956	−	0.143772i	−0.377153	−	0.926151i	$-0.623097\pi$
$449$	−21.1887	−	3.04647i	−0.999956	−	0.143772i	−0.622803	+	0.782379i	$0.714006\pi$
$450$		0			0
$451$	11.6015	−	10.0527i	0.546292	−	0.473364i
$452$	3.13090	+	6.85571i	0.147265	+	0.322465i
$453$		0			0
$454$	5.16487	−	17.5899i	0.242399	−	0.825536i
$455$	−6.04473	−	5.23779i	−0.283381	−	0.245551i
$456$		0			0
$457$	−8.91640	−	4.07198i	−0.417092	−	0.190479i	0.195804	−	0.980643i	$-0.437268\pi$
$457$	−8.91640	−	4.07198i	−0.417092	−	0.190479i	−0.612896	+	0.790164i	$0.709996\pi$
$458$	0.345626	+	2.40388i	0.0161500	+	0.112326i
$459$		0			0
$460$	2.97008	+	0.354560i	0.138481	+	0.0165314i
$461$			24.7633i			1.15334i	0.816976	+	0.576671i	$0.195649\pi$
$461$			24.7633i			1.15334i	−0.816976	+	0.576671i	$0.804351\pi$
$462$		0			0
$463$	−7.45039	+	16.3141i	−0.346249	+	0.758180i	0.653750	+	0.756711i	$0.273195\pi$
$463$	−7.45039	+	16.3141i	−0.346249	+	0.758180i	−0.999999	+	0.00146897i	$0.999532\pi$
$464$	0.350823	+	1.19479i	0.0162865	+	0.0554669i
$465$		0			0
$466$	−13.2627	−	3.89427i	−0.614381	−	0.180399i
$467$	0.00412835	−	0.00265313i	0.000191037	−	0.000122772i	−0.540545	−	0.841315i	$-0.681782\pi$
$467$	0.00412835	−	0.00265313i	0.000191037	−	0.000122772i	0.540736	+	0.841192i	$0.318146\pi$
$468$		0			0
$469$	−38.0346	−	43.8943i	−1.75628	−	2.02685i
$470$	−2.38639	−	1.53364i	−0.110076	−	0.0707415i
$471$		0			0
$472$	−0.342243	+	2.38035i	−0.0157530	+	0.109565i
$473$	7.26722	−	11.3080i	0.334147	−	0.519943i
$474$		0			0
$475$	−26.3865	+	12.0503i	−1.21070	+	0.552907i
$476$	17.8918	+	27.8402i	0.820069	+	1.27605i
$477$		0			0
$478$	3.83012	−	4.42019i	0.175185	−	0.202175i
$479$	−35.6438	+	10.4660i	−1.62861	+	0.478202i	−0.963313	−	0.268380i	$-0.913512\pi$
$479$	−35.6438	+	10.4660i	−1.62861	+	0.478202i	−0.665293	+	0.746582i	$0.731693\pi$
$480$		0			0
$481$	18.0125	−	2.58981i	0.821299	−	0.118085i
$482$	0.172887			0.00787479
$483$		0			0
$484$	−14.5588			−0.661763
$485$	−3.99564	+	0.574486i	−0.181433	+	0.0260861i
$486$		0			0
$487$	−3.53210	+	1.03712i	−0.160055	+	0.0469963i	−0.360778	−	0.932652i	$-0.617489\pi$
$487$	−3.53210	+	1.03712i	−0.160055	+	0.0469963i	0.200723	+	0.979648i	$0.435671\pi$
$488$	3.09428	−	3.57099i	0.140071	−	0.161651i
$489$		0			0
$490$	3.60927	+	5.61613i	0.163050	+	0.253711i
$491$	10.7450	−	4.90708i	0.484916	−	0.221454i	−0.157928	−	0.987451i	$-0.550482\pi$
$491$	10.7450	−	4.90708i	0.484916	−	0.221454i	0.642844	+	0.765997i	$0.277754\pi$
$492$		0			0
$493$	5.29508	−	8.23931i	0.238479	−	0.371080i
$494$	−2.72874	+	18.9788i	−0.122772	+	0.853896i
$495$		0			0
$496$	−8.86915	−	5.69986i	−0.398237	−	0.255931i
$497$	−9.74397	−	11.2451i	−0.437077	−	0.504414i
$498$		0			0
$499$	−34.4253	+	22.1238i	−1.54109	+	0.990398i	−0.553588	+	0.832790i	$0.686742\pi$
$499$	−34.4253	+	22.1238i	−1.54109	+	0.990398i	−0.987502	+	0.157608i	$0.949622\pi$
$500$	−5.75158	−	1.68882i	−0.257219	−	0.0755262i
$501$		0			0
$502$	−0.662549	−	2.25644i	−0.0295710	−	0.100710i
$503$	6.86148	−	15.0246i	0.305938	−	0.669912i	−0.692746	−	0.721181i	$-0.743599\pi$
$503$	6.86148	−	15.0246i	0.305938	−	0.669912i	0.998685	+	0.0512695i	$0.0163267\pi$
$504$		0			0
$505$			1.91931i			0.0854084i
$506$	−23.0930	+	7.38675i	−1.02661	+	0.328381i
$507$		0			0
$508$	1.12102	+	7.79687i	0.0497373	+	0.345930i
$509$	7.20103	+	3.28860i	0.319180	+	0.145765i	0.568562	−	0.822641i	$-0.307500\pi$
$509$	7.20103	+	3.28860i	0.319180	+	0.145765i	−0.249382	+	0.968405i	$0.580227\pi$
$510$		0			0
$511$	8.82402	+	7.64606i	0.390352	+	0.338242i
$512$	−0.281733	+	0.959493i	−0.0124509	+	0.0424040i
$513$		0			0
$514$	4.44222	+	9.72711i	0.195938	+	0.429045i
$515$	−8.37070	+	7.25325i	−0.368857	+	0.319617i
$516$		0			0
$517$	22.7596	+	3.27233i	1.00097	+	0.143917i
$518$	−24.8666	−	3.57527i	−1.09257	−	0.157088i
$519$		0			0
$520$	−1.43663	+	1.24485i	−0.0630004	+	0.0545901i
$521$	−1.34965	−	2.95532i	−0.0591292	−	0.129475i	0.877761	−	0.479099i	$-0.159037\pi$
$521$	−1.34965	−	2.95532i	−0.0591292	−	0.129475i	−0.936890	+	0.349624i	$0.886309\pi$
$522$		0			0
$523$	3.86183	−	13.1522i	0.168866	−	0.575105i	−0.830958	−	0.556335i	$-0.812207\pi$
$523$	3.86183	−	13.1522i	0.168866	−	0.575105i	0.999824	−	0.0187695i	$-0.00597486\pi$
$524$	−6.49890	−	5.63133i	−0.283906	−	0.246006i
$525$		0			0
$526$	−1.73898	−	0.794166i	−0.0758232	−	0.0346273i
$527$	11.8010	+	82.0777i	0.514059	+	3.57536i
$528$		0			0
$529$	−18.7303	+	13.3482i	−0.814361	+	0.580358i
$530$			5.19678i			0.225733i
$531$		0			0
$532$	10.9960	−	24.0779i	0.476738	−	1.04391i
$533$	2.60730	+	8.87966i	0.112935	+	0.384621i
$534$		0			0
$535$	−7.47114	−	2.19372i	−0.323006	−	0.0948430i
$536$	−11.6125	+	7.46289i	−0.501583	+	0.322348i
$537$		0			0
$538$	−0.741059	−	0.855227i	−0.0319493	−	0.0368715i
$539$	−45.5229	−	29.2558i	−1.96081	−	1.26014i
$540$		0			0
$541$	3.40564	−	23.6868i	0.146420	−	1.01837i	−0.775598	−	0.631227i	$-0.782552\pi$
$541$	3.40564	−	23.6868i	0.146420	−	1.01837i	0.922018	−	0.387147i	$-0.126539\pi$
$542$	−1.70346	+	2.65063i	−0.0731698	+	0.113854i
$543$		0			0
$544$	7.15449	−	3.26735i	0.306746	−	0.140086i
$545$	−1.92564	−	2.99636i	−0.0824855	−	0.128350i
$546$		0			0
$547$	9.35218	−	10.7930i	0.399870	−	0.461475i	−0.519730	−	0.854331i	$-0.673967\pi$
$547$	9.35218	−	10.7930i	0.399870	−	0.461475i	0.919600	+	0.392856i	$0.128513\pi$
$548$	−12.0349	+	3.53376i	−0.514104	+	0.150955i
$549$		0			0
$550$	23.0739	−	3.31753i	0.983876	−	0.141460i
$551$	−7.83381			−0.333731
$552$		0			0
$553$	−16.3471			−0.695150
$554$	31.8068	−	4.57313i	1.35134	−	0.194294i
$555$		0			0
$556$	−0.943635	+	0.277076i	−0.0400190	+	0.0117507i
$557$	−24.8928	+	28.7278i	−1.05474	+	1.21723i	−0.0793274	+	0.996849i	$0.525277\pi$
$557$	−24.8928	+	28.7278i	−1.05474	+	1.21723i	−0.975413	+	0.220386i	$0.929268\pi$
$558$		0			0
$559$	4.38115	+	6.81720i	0.185303	+	0.288337i
$560$	2.38712	−	1.09016i	0.100874	−	0.0460678i
$561$		0			0
$562$	−12.2398	+	19.0456i	−0.516307	+	0.803389i
$563$	−3.92403	+	27.2923i	−0.165378	+	1.15023i	0.722909	+	0.690943i	$0.242805\pi$
$563$	−3.92403	+	27.2923i	−0.165378	+	1.15023i	−0.888287	+	0.459288i	$0.848105\pi$
$564$		0			0
$565$	−3.95449	−	2.54140i	−0.166367	−	0.106917i
$566$	15.4517	+	17.8322i	0.649484	+	0.749544i
$567$		0			0
$568$	−2.97497	+	1.91190i	−0.124827	+	0.0802214i
$569$	35.9960	+	10.5694i	1.50903	+	0.443091i	0.928557	−	0.371190i	$-0.121050\pi$
$569$	35.9960	+	10.5694i	1.50903	+	0.443091i	0.580472	+	0.814280i	$0.302868\pi$
$570$		0			0
$571$	−1.96533	−	6.69329i	−0.0822463	−	0.280105i	0.908093	−	0.418768i	$-0.137538\pi$
$571$	−1.96533	−	6.69329i	−0.0822463	−	0.280105i	−0.990340	+	0.138662i	$0.955720\pi$
$572$	6.40092	−	14.0161i	0.267636	−	0.586041i
$573$		0			0
$574$		−	12.7760i		−	0.533262i
$575$	19.8891	−	9.66608i	0.829433	−	0.403103i
$576$		0			0
$577$	−0.547117	−	3.80528i	−0.0227768	−	0.158416i	0.975259	−	0.221066i	$-0.0709537\pi$
$577$	−0.547117	−	3.80528i	−0.0227768	−	0.158416i	−0.998036	+	0.0626505i	$0.980045\pi$
$578$	−40.8082	−	18.6365i	−1.69740	−	0.775175i
$579$		0			0
$580$	−0.586957	−	0.508601i	−0.0243721	−	0.0211185i
$581$	−0.769594	+	2.62100i	−0.0319281	+	0.108737i
$582$		0			0
$583$	−17.4988	−	38.3171i	−0.724728	−	1.58693i
$584$	2.09718	−	1.81721i	0.0867817	−	0.0751968i
$585$		0			0
$586$	29.1521	+	4.19144i	1.20426	+	0.173147i
$587$	40.5991	+	5.83727i	1.67570	+	0.240930i	0.913626	−	0.406555i	$-0.133270\pi$
$587$	40.5991	+	5.83727i	1.67570	+	0.240930i	0.762078	+	0.647485i	$0.224179\pi$
$588$		0			0
$589$	50.1251	−	43.4336i	2.06537	−	1.78965i
$590$	−0.623079	−	1.36435i	−0.0256518	−	0.0561695i
$591$		0			0
$592$	−1.68215	+	5.72887i	−0.0691359	+	0.235455i
$593$	−18.7556	−	16.2518i	−0.770200	−	0.667382i	0.178365	−	0.983964i	$-0.442919\pi$
$593$	−18.7556	−	16.2518i	−0.770200	−	0.667382i	−0.948565	+	0.316582i	$0.897465\pi$
$594$		0			0
$595$	−18.7753	−	8.57441i	−0.769714	−	0.351516i
$596$	−1.53705	−	10.6904i	−0.0629600	−	0.437897i
$597$		0			0
$598$	1.73262	−	14.5138i	0.0708519	−	0.593513i
$599$		−	25.4178i		−	1.03854i	−0.854610	−	0.519271i	$-0.826204\pi$
$599$		−	25.4178i		−	1.03854i	0.854610	−	0.519271i	$-0.173796\pi$
$600$		0			0
$601$	−10.1302	+	22.1821i	−0.413220	+	0.904825i	0.582537	+	0.812804i	$0.302060\pi$
$601$	−10.1302	+	22.1821i	−0.413220	+	0.904825i	−0.995757	+	0.0920212i	$0.970667\pi$
$602$	−3.15180	−	10.7340i	−0.128458	−	0.437487i
$603$		0			0
$604$	−10.2133	−	2.99889i	−0.415572	−	0.122023i
$605$	7.63888	−	4.90921i	0.310565	−	0.199588i
$606$		0			0
$607$	3.50898	+	4.04958i	0.142425	+	0.164367i	0.822480	−	0.568794i	$-0.192590\pi$
$607$	3.50898	+	4.04958i	0.142425	+	0.164367i	−0.680055	+	0.733161i	$0.738044\pi$
$608$	−5.29235	−	3.40119i	−0.214633	−	0.137936i
$609$		0			0
$610$	−0.419409	+	2.91705i	−0.0169814	+	0.118108i
$611$	−7.49438	+	11.6615i	−0.303190	+	0.471773i
$612$		0			0
$613$	21.4734	−	9.80659i	0.867304	−	0.396084i	0.0684823	−	0.997652i	$-0.478184\pi$
$613$	21.4734	−	9.80659i	0.867304	−	0.396084i	0.798822	+	0.601568i	$0.205457\pi$
$614$	0.461565	+	0.718210i	0.0186273	+	0.0289846i
$615$		0			0
$616$	−13.9300	+	16.0761i	−0.561255	+	0.647723i
$617$	−34.3200	+	10.0773i	−1.38167	+	0.405695i	−0.886350	−	0.463015i	$-0.846768\pi$
$617$	−34.3200	+	10.0773i	−1.38167	+	0.405695i	−0.495321	+	0.868710i	$0.664949\pi$
$618$		0			0
$619$	−2.37981	+	0.342165i	−0.0956526	+	0.0137528i	−0.189975	−	0.981789i	$-0.560841\pi$
$619$	−2.37981	+	0.342165i	−0.0956526	+	0.0137528i	0.0943223	+	0.995542i	$0.469932\pi$
$620$	6.57556			0.264081
$621$		0			0
$622$	−18.2138			−0.730308
$623$	−59.7684	+	8.59341i	−2.39457	+	0.344288i
$624$		0			0
$625$	−18.5338	+	5.44202i	−0.741353	+	0.217681i
$626$	−2.35487	+	2.71766i	−0.0941195	+	0.108620i
$627$		0			0
$628$	7.82064	+	12.1691i	0.312077	+	0.485602i
$629$	42.7175	−	19.5084i	1.70326	−	0.777852i
$630$		0			0
$631$	15.8682	−	24.6914i	0.631704	−	0.982951i	−0.366907	−	0.930258i	$-0.619583\pi$
$631$	15.8682	−	24.6914i	0.631704	−	0.982951i	0.998611	−	0.0526929i	$-0.0167805\pi$
$632$	−0.552916	+	3.84562i	−0.0219938	+	0.152970i
$633$		0			0
$634$	−17.4101	−	11.1888i	−0.691441	−	0.444362i
$635$	−3.21729	−	3.71295i	−0.127674	−	0.147344i
$636$		0			0
$637$	27.4442	−	17.6373i	1.08738	−	0.698815i
$638$	6.04036	+	1.77361i	0.239140	+	0.0702179i
$639$		0			0
$640$	−0.175717	−	0.598438i	−0.00694583	−	0.0236553i
$641$	−14.7347	+	32.2645i	−0.581986	+	1.27437i	0.358180	+	0.933653i	$0.383397\pi$
$641$	−14.7347	+	32.2645i	−0.581986	+	1.27437i	−0.940165	+	0.340718i	$0.889330\pi$
$642$		0			0
$643$			10.3489i			0.408119i	0.978958	+	0.204060i	$0.0654136\pi$
$643$			10.3489i			0.408119i	−0.978958	+	0.204060i	$0.934586\pi$
$644$	−7.93997	+	18.5511i	−0.312879	+	0.731014i
$645$		0			0
$646$	7.04182	+	48.9770i	0.277057	+	1.92697i
$647$	−0.453884	−	0.207282i	−0.0178440	−	0.00814909i	0.406473	−	0.913663i	$-0.366759\pi$
$647$	−0.453884	−	0.207282i	−0.0178440	−	0.00814909i	−0.424317	+	0.905514i	$0.639486\pi$
$648$		0			0
$649$	9.18824	+	7.96165i	0.360670	+	0.312522i
$650$	−3.95933	+	13.4842i	−0.155298	+	0.528895i
$651$		0			0
$652$	−5.70634	−	12.4952i	−0.223478	−	0.489348i
$653$	−7.85004	+	6.80210i	−0.307196	+	0.266187i	−0.794791	−	0.606883i	$-0.792420\pi$
$653$	−7.85004	+	6.80210i	−0.307196	+	0.266187i	0.487595	+	0.873070i	$0.337874\pi$
$654$		0			0
$655$	5.30880	+	0.763290i	0.207432	+	0.0298242i
$656$	−3.00553	−	0.432130i	−0.117346	−	0.0168719i
$657$		0			0
$658$	14.4626	−	12.5319i	0.563812	−	0.488546i
$659$	8.58637	+	18.8015i	0.334477	+	0.732404i	0.999901	−	0.0140624i	$-0.00447634\pi$
$659$	8.58637	+	18.8015i	0.334477	+	0.732404i	−0.665424	+	0.746466i	$0.731749\pi$
$660$		0			0
$661$	−0.113844	+	0.387717i	−0.00442801	+	0.0150804i	−0.961677	−	0.274184i	$-0.911592\pi$
$661$	−0.113844	+	0.387717i	−0.00442801	+	0.0150804i	0.957249	+	0.289264i	$0.0934106\pi$
$662$	15.0589	+	13.0486i	0.585279	+	0.507147i
$663$		0			0
$664$	0.590552	+	0.269696i	0.0229179	+	0.0104662i
$665$	2.34953	+	16.3413i	0.0911109	+	0.633690i
$666$		0			0
$667$	5.97022	−	0.143222i	0.231168	−	0.00554557i
$668$		−	0.805264i		−	0.0311566i
$669$		0			0
$670$	3.57650	−	7.83143i	0.138172	−	0.302555i
$671$	−6.73004	−	22.9204i	−0.259810	−	0.884833i
$672$		0			0
$673$	40.8846	+	12.0048i	1.57599	+	0.462752i	0.948737	−	0.316066i	$-0.102362\pi$
$673$	40.8846	+	12.0048i	1.57599	+	0.462752i	0.627250	+	0.778818i	$0.284180\pi$
$674$	10.0186	−	6.43859i	0.385903	−	0.248005i
$675$		0			0
$676$	−2.43004	−	2.80441i	−0.0934630	−	0.107862i
$677$	25.6993	+	16.5160i	0.987706	+	0.634760i	0.931531	−	0.363661i	$-0.118473\pi$
$677$	25.6993	+	16.5160i	0.987706	+	0.634760i	0.0561747	+	0.998421i	$0.482110\pi$
$678$		0			0
$679$	3.87556	−	26.9551i	0.148730	−	1.03444i
$680$	−2.65216	+	4.12684i	−0.101706	+	0.158257i
$681$		0			0
$682$	−48.4832	+	22.1415i	−1.85652	+	0.847843i
$683$	−20.4416	−	31.8078i	−0.782178	−	1.21709i	−0.971932	−	0.235261i	$-0.924406\pi$
$683$	−20.4416	−	31.8078i	−0.782178	−	1.21709i	0.189755	−	0.981832i	$-0.439231\pi$
$684$		0			0
$685$	5.12301	−	5.91227i	0.195740	−	0.225896i
$686$	−14.9523	+	4.39038i	−0.570880	+	0.167626i
$687$		0			0
$688$	−2.63176	+	0.378390i	−0.100335	+	0.0144260i
$689$	25.3949			0.967469
$690$		0			0
$691$	−7.09502			−0.269907			−0.134954	−	0.990852i	$-0.543089\pi$
$691$	−7.09502			−0.269907			−0.134954	+	0.990852i	$0.543089\pi$
$692$	−11.2721	+	1.62068i	−0.428501	+	0.0616092i
$693$		0			0
$694$	−4.26483	+	1.25227i	−0.161891	+	0.0475354i
$695$	0.401688	−	0.463572i	0.0152369	−	0.0175843i
$696$		0			0
$697$	12.9118	+	20.0911i	0.489069	+	0.761006i
$698$	−18.3358	+	8.37368i	−0.694020	+	0.316948i
$699$		0			0
$700$	10.4890	−	16.3212i	0.396448	−	0.616885i
$701$	−3.34367	+	23.2558i	−0.126289	+	0.878358i	0.823912	+	0.566718i	$0.191787\pi$
$701$	−3.34367	+	23.2558i	−0.126289	+	0.878358i	−0.950200	+	0.311639i	$0.899122\pi$
$702$		0			0
$703$	−31.5992	−	20.3076i	−1.19179	−	0.765914i
$704$	3.31069	+	3.82075i	0.124777	+	0.144000i
$705$		0			0
$706$	−0.725734	+	0.466401i	−0.0273134	+	0.0175532i
$707$	−12.4235	−	3.64786i	−0.467232	−	0.137192i
$708$		0			0
$709$	5.94161	+	20.2352i	0.223142	+	0.759951i	0.992619	+	0.121276i	$0.0386987\pi$
$709$	5.94161	+	20.2352i	0.223142	+	0.759951i	−0.769477	+	0.638674i	$0.779483\pi$
$710$	0.916252	−	2.00631i	0.0343863	−	0.0752955i
$711$		0			0
$712$			14.3510i			0.537828i
$713$	−37.4067	+	34.0176i	−1.40089	+	1.27397i
$714$		0			0
$715$	1.36769	+	9.51249i	0.0511487	+	0.355747i
$716$	−0.0707846	−	0.0323262i	−0.00264534	−	0.00120809i
$717$		0			0
$718$	0.00870390	+	0.00754198i	0.000324827	+	0.000281464i
$719$	9.50540	−	32.3724i	0.354492	−	1.20729i	−0.568570	−	0.822635i	$-0.692503\pi$
$719$	9.50540	−	32.3724i	0.354492	−	1.20729i	0.923061	−	0.384653i	$-0.125679\pi$
$720$		0			0
$721$	−31.0399	−	67.9680i	−1.15599	−	2.53126i
$722$	15.5511	−	13.4751i	0.578753	−	0.501492i
$723$		0			0
$724$	−9.12128	−	1.31144i	−0.338990	−	0.0487393i
$725$	−5.68333	−	0.817139i	−0.211073	−	0.0303478i
$726$		0			0
$727$	−16.6262	+	14.4067i	−0.616633	+	0.534315i	−0.906204	−	0.422841i	$-0.861033\pi$
$727$	−16.6262	+	14.4067i	−0.616633	+	0.534315i	0.289571	+	0.957157i	$0.406487\pi$
$728$	−5.32726	−	11.6651i	−0.197441	−	0.432336i
$729$		0			0
$730$	−0.487608	+	1.66064i	−0.0180472	+	0.0614631i
$731$	15.8045	+	13.6947i	0.584550	+	0.506516i
$732$		0			0
$733$	−25.4871	−	11.6396i	−0.941389	−	0.429918i	−0.115220	−	0.993340i	$-0.536757\pi$
$733$	−25.4871	−	11.6396i	−0.941389	−	0.429918i	−0.826169	+	0.563422i	$0.809485\pi$
$734$	−4.55764	−	31.6991i	−0.168226	−	1.17003i
$735$		0			0
$736$	4.09553	+	2.49532i	0.150963	+	0.0919787i
$737$			69.7861i			2.57060i
$738$		0			0
$739$	−14.1870	+	31.0651i	−0.521876	+	1.14275i	0.446849	+	0.894609i	$0.352546\pi$
$739$	−14.1870	+	31.0651i	−0.521876	+	1.14275i	−0.968725	+	0.248139i	$0.920181\pi$
$740$	−1.04916	−	3.57311i	−0.0385679	−	0.131350i
$741$		0			0
$742$	−33.6380	−	9.87701i	−1.23489	−	0.362597i
$743$	−8.04653	+	5.17119i	−0.295199	+	0.189713i	−0.679854	−	0.733348i	$-0.737957\pi$
$743$	−8.04653	+	5.17119i	−0.295199	+	0.189713i	0.384655	+	0.923060i	$0.374320\pi$
$744$		0			0
$745$	4.41127	+	5.09088i	0.161617	+	0.186515i
$746$	8.58414	+	5.51669i	0.314288	+	0.201980i
$747$		0			0
$748$	5.65892	−	39.3586i	0.206911	−	1.43909i
$749$	28.3994	−	44.1903i	1.03769	−	1.61468i
$750$		0			0
$751$	−21.0974	+	9.63487i	−0.769856	+	0.351581i	−0.761315	−	0.648382i	$-0.775446\pi$
$751$	−21.0974	+	9.63487i	−0.769856	+	0.351581i	−0.00854095	+	0.999964i	$0.502719\pi$
$752$	−2.45893	−	3.82617i	−0.0896679	−	0.139526i
$753$		0			0
$754$	−2.48536	+	2.86826i	−0.0905116	+	0.104456i
$755$	6.37004	−	1.87041i	0.231829	−	0.0680712i
$756$		0			0
$757$	7.45433	−	1.07177i	0.270932	−	0.0389542i	−0.00550958	−	0.999985i	$-0.501754\pi$
$757$	7.45433	−	1.07177i	0.270932	−	0.0389542i	0.276442	+	0.961031i	$0.410845\pi$
$758$	13.7668			0.500034
$759$		0			0
$760$	3.92373			0.142329
$761$	−27.6627	+	3.97729i	−1.00277	+	0.144177i	−0.624092	−	0.781351i	$-0.714531\pi$
$761$	−27.6627	+	3.97729i	−1.00277	+	0.144177i	−0.378679	+	0.925528i	$0.623622\pi$
$762$		0			0
$763$	23.0549	−	6.76953i	0.834644	−	0.245073i
$764$	7.29394	−	8.41766i	0.263886	−	0.304540i
$765$		0			0
$766$	8.94437	+	13.9177i	0.323173	+	0.502867i
$767$	−6.66714	+	3.04478i	−0.240736	+	0.109941i
$768$		0			0
$769$	−14.6499	+	22.7957i	−0.528288	+	0.822033i	−0.998156	−	0.0607043i	$-0.980665\pi$
$769$	−14.6499	+	22.7957i	−0.528288	+	0.822033i	0.469867	+	0.882737i	$0.344302\pi$
$770$	1.88812	−	13.1322i	0.0680431	−	0.473250i
$771$		0			0
$772$	−7.30468	−	4.69443i	−0.262901	−	0.168956i
$773$	15.9596	+	18.4184i	0.574028	+	0.662463i	0.966310	−	0.257382i	$-0.0828597\pi$
$773$	15.9596	+	18.4184i	0.574028	+	0.662463i	−0.392282	+	0.919845i	$0.628314\pi$
$774$		0			0
$775$	40.8956	−	26.2820i	1.46901	−	0.944078i
$776$	−6.21004	−	1.82343i	−0.222927	−	0.0654574i
$777$		0			0
$778$	−5.60073	−	19.0744i	−0.200796	−	0.683849i
$779$	7.93540	−	17.3761i	0.284315	−	0.622563i
$780$		0			0
$781$			17.8783i			0.639735i
$782$	−6.26206	−	37.1970i	−0.223931	−	1.33016i
$783$		0			0
$784$	1.52329	+	10.5947i	0.0544033	+	0.378383i
$785$	−8.20684	−	3.74794i	−0.292915	−	0.133770i
$786$		0			0
$787$	3.81262	+	3.30365i	0.135905	+	0.117762i	0.720161	−	0.693807i	$-0.244068\pi$
$787$	3.81262	+	3.30365i	0.135905	+	0.117762i	−0.584256	+	0.811570i	$0.698613\pi$
$788$	−3.28471	+	11.1867i	−0.117013	+	0.398510i
$789$		0			0
$790$	−1.00663	−	2.20421i	−0.0358142	−	0.0784221i
$791$	23.9660	−	20.7667i	0.852134	−	0.738378i
$792$		0			0
$793$	14.2547	+	2.04951i	0.506198	+	0.0727803i
$794$	10.5696	+	1.51968i	0.375101	+	0.0539314i
$795$		0			0
$796$	−9.65554	+	8.36657i	−0.342232	+	0.296545i
$797$	−17.5904	−	38.5176i	−0.623083	−	1.36436i	−0.913255	−	0.407387i	$-0.866440\pi$
$797$	−17.5904	−	38.5176i	−0.623083	−	1.36436i	0.290172	−	0.956974i	$-0.406287\pi$
$798$		0			0
$799$	−10.0783	+	34.3235i	−0.356545	+	1.21428i
$800$	−3.48476	−	3.01956i	−0.123205	−	0.106758i
$801$		0			0
$802$	1.81672	+	0.829670i	0.0641508	+	0.0292967i
$803$	−1.99654	−	13.8862i	−0.0704562	−	0.490034i
$804$		0			0
$805$	−2.08936	−	12.4109i	−0.0736402	−	0.437428i
$806$		−	32.1325i		−	1.13182i
$807$		0			0
$808$	−1.27835	+	2.79920i	−0.0449723	+	0.0984757i
$809$	13.6137	+	46.3640i	0.478632	+	1.63007i	0.745620	+	0.666371i	$0.232153\pi$
$809$	13.6137	+	46.3640i	0.478632	+	1.63007i	−0.266988	+	0.963700i	$0.586028\pi$
$810$		0			0
$811$	12.0333	+	3.53331i	0.422548	+	0.124071i	0.486092	−	0.873908i	$-0.338422\pi$
$811$	12.0333	+	3.53331i	0.422548	+	0.124071i	−0.0635439	+	0.997979i	$0.520240\pi$
$812$	4.40768	−	2.83264i	0.154679	−	0.0994062i
$813$		0			0
$814$	19.7673	+	22.8126i	0.692842	+	0.799582i
$815$	7.20742	+	4.63193i	0.252465	+	0.162249i
$816$		0			0
$817$	2.38046	−	16.5565i	0.0832819	−	0.579238i
$818$	−10.6955	+	16.6425i	−0.373958	+	0.581891i
$819$		0			0
$820$	1.72269	−	0.786727i	0.0601590	−	0.0274737i
$821$	−19.0415	−	29.6292i	−0.664554	−	1.03407i	−0.995892	−	0.0905541i	$-0.971136\pi$
$821$	−19.0415	−	29.6292i	−0.664554	−	1.03407i	0.331337	−	0.943512i	$-0.392500\pi$
$822$		0			0
$823$	5.54925	−	6.40418i	0.193435	−	0.223236i	−0.650744	−	0.759297i	$-0.725543\pi$
$823$	5.54925	−	6.40418i	0.193435	−	0.223236i	0.844179	+	0.536061i	$0.180088\pi$
$824$	−17.0392	+	5.00315i	−0.593588	+	0.174293i
$825$		0			0
$826$	10.0155	−	1.44001i	0.348484	−	0.0501044i
$827$	0.502499			0.0174736			0.00873680	−	0.999962i	$-0.497219\pi$
$827$	0.502499			0.0174736			0.00873680	+	0.999962i	$0.497219\pi$
$828$		0			0
$829$	−18.9103			−0.656783			−0.328391	−	0.944542i	$-0.606506\pi$
$829$	−18.9103			−0.656783			−0.328391	+	0.944542i	$0.606506\pi$
$830$	−0.400799	+	0.0576262i	−0.0139119	+	0.00200024i
$831$		0			0
$832$	−2.92437	+	0.858671i	−0.101384	+	0.0297691i
$833$	55.1309	−	63.6245i	1.91017	−	2.20446i
$834$		0			0
$835$	0.271534	+	0.422515i	0.00939683	+	0.0146217i
$836$	−28.9306	+	13.2122i	−1.00059	+	0.456953i
$837$		0			0
$838$	−3.35732	+	5.22409i	−0.115977	+	0.180463i
$839$	−3.87979	+	26.9845i	−0.133945	+	0.931610i	0.806396	+	0.591376i	$0.201415\pi$
$839$	−3.87979	+	26.9845i	−0.133945	+	0.931610i	−0.940341	+	0.340233i	$0.889494\pi$
$840$		0			0
$841$	23.0919	+	14.8403i	0.796272	+	0.511733i
$842$	14.4916	+	16.7242i	0.499414	+	0.576354i
$843$		0			0
$844$	−15.5774	+	10.0110i	−0.536195	+	0.344592i
$845$	2.22067	+	0.652046i	0.0763932	+	0.0224311i
$846$		0			0
$847$	17.2582	+	58.7759i	0.592997	+	2.01956i
$848$	−3.46130	+	7.57919i	−0.118861	+	0.260270i
$849$		0			0
$850$			36.2667i			1.24394i
$851$	24.4533	+	14.8989i	0.838248	+	0.510727i
$852$		0			0
$853$	−3.23268	−	22.4838i	−0.110685	−	0.769831i	−0.967256	−	0.253802i	$-0.918319\pi$
$853$	−3.23268	−	22.4838i	−0.110685	−	0.769831i	0.856571	−	0.516029i	$-0.172590\pi$
$854$	−18.0846	−	8.25894i	−0.618841	−	0.282615i
$855$		0			0
$856$	−9.43509	−	8.17555i	−0.322485	−	0.279434i
$857$	10.3579	−	35.2757i	0.353819	−	1.20500i	−0.569832	−	0.821761i	$-0.692992\pi$
$857$	10.3579	−	35.2757i	0.353819	−	1.20500i	0.923651	−	0.383235i	$-0.125190\pi$
$858$		0			0
$859$	5.33083	+	11.6729i	0.181886	+	0.398274i	0.978510	−	0.206201i	$-0.0661101\pi$
$859$	5.33083	+	11.6729i	0.181886	+	0.398274i	−0.796624	+	0.604475i	$0.793383\pi$
$860$	1.25327	−	1.08596i	0.0427361	−	0.0370311i
$861$		0			0
$862$	12.5962	+	1.81106i	0.429028	+	0.0616850i
$863$	5.33129	+	0.766523i	0.181479	+	0.0260927i	0.232455	−	0.972607i	$-0.425324\pi$
$863$	5.33129	+	0.766523i	0.181479	+	0.0260927i	−0.0509761	+	0.998700i	$0.516233\pi$
$864$		0			0
$865$	5.36789	−	4.65130i	0.182514	−	0.158149i
$866$	−10.6858	−	23.3986i	−0.363117	−	0.795116i
$867$		0			0
$868$	−12.4975	+	42.5627i	−0.424194	+	1.44467i
$869$	14.8442	+	12.8626i	0.503556	+	0.436333i
$870$		0			0
$871$	−38.2696	−	17.4771i	−1.29672	−	0.592190i
$872$	−0.812718	−	5.65258i	−0.0275221	−	0.191420i
$873$		0			0
$874$	−22.3211	+	20.2988i	−0.755023	+	0.686616i
$875$			25.2219i			0.852655i
$876$		0			0
$877$	13.0464	−	28.5676i	0.440545	−	0.964658i	−0.550953	−	0.834536i	$-0.685736\pi$
$877$	13.0464	−	28.5676i	0.440545	−	0.964658i	0.991498	−	0.130122i	$-0.0415369\pi$
$878$	−6.64983	−	22.6472i	−0.224421	−	0.764307i
$879$		0			0
$880$	−3.02544	−	0.888351i	−0.101988	−	0.0299463i
$881$	35.0021	−	22.4945i	1.17925	−	0.757858i	0.204002	−	0.978970i	$-0.434605\pi$
$881$	35.0021	−	22.4945i	1.17925	−	0.757858i	0.975248	+	0.221112i	$0.0709687\pi$
$882$		0			0
$883$	30.2693	+	34.9327i	1.01864	+	1.17558i	0.984360	+	0.176166i	$0.0563697\pi$
$883$	30.2693	+	34.9327i	1.01864	+	1.17558i	0.0342841	+	0.999412i	$0.489085\pi$
$884$	20.1665	+	12.9602i	0.678272	+	0.435899i
$885$		0			0
$886$	−4.09042	+	28.4495i	−0.137420	+	0.955780i
$887$	20.7234	−	32.2462i	0.695822	−	1.08272i	−0.296012	−	0.955184i	$-0.595657\pi$
$887$	20.7234	−	32.2462i	0.695822	−	1.08272i	0.991834	−	0.127536i	$-0.0407070\pi$
$888$		0			0
$889$	30.1482	−	13.7682i	1.01114	−	0.461771i
$890$	−4.83915	−	7.52987i	−0.162209	−	0.252402i
$891$		0			0
$892$	−1.50845	+	1.74084i	−0.0505067	+	0.0582878i
$893$	27.4537	−	8.06113i	0.918703	−	0.269756i
$894$		0			0
$895$	0.0480404	−	0.00690717i	0.00160581	−	0.000230881i
$896$	4.20757			0.140565
$897$		0			0
$898$	21.4066			0.714346
$899$	12.9946	−	1.86834i	0.433394	−	0.0623127i
$900$		0			0
$901$	62.8799	−	18.4632i	2.09483	−	0.615098i
$902$	−10.0527	+	11.6015i	−0.334719	+	0.386286i
$903$		0			0
$904$	−4.07470	−	6.34035i	−0.135522	−	0.210877i
$905$	5.22807	−	2.38758i	0.173787	−	0.0793659i
$906$		0			0
$907$	−13.1018	+	20.3868i	−0.435039	+	0.676934i	−0.987680	−	0.156485i	$-0.949984\pi$
$907$	−13.1018	+	20.3868i	−0.435039	+	0.676934i	0.552641	+	0.833419i	$0.313620\pi$
$908$	−2.60899	+	18.1459i	−0.0865824	+	0.602194i
$909$		0			0
$910$	6.72861	+	4.32422i	0.223051	+	0.143346i
$911$	−17.4320	−	20.1176i	−0.577547	−	0.666525i	0.389528	−	0.921015i	$-0.372638\pi$
$911$	−17.4320	−	20.1176i	−0.577547	−	0.666525i	−0.967076	+	0.254489i	$0.918093\pi$
$912$		0			0
$913$	2.76115	−	1.77448i	0.0913807	−	0.0587268i
$914$	9.40515	+	2.76160i	0.311095	+	0.0913456i
$915$		0			0
$916$	−0.684216	−	2.33023i	−0.0226071	−	0.0769928i
$917$	−15.0306	+	32.9124i	−0.496354	+	1.08686i
$918$		0			0
$919$		−	31.1605i		−	1.02789i	−0.857823	−	0.513946i	$-0.828183\pi$
$919$		−	31.1605i		−	1.02789i	0.857823	−	0.513946i	$-0.171817\pi$
$920$	−2.99031	+	0.0717357i	−0.0985876	+	0.00236506i
$921$		0			0
$922$	−3.52419	−	24.5113i	−0.116063	−	0.807235i
$923$	−9.80417	−	4.47742i	−0.322708	−	0.147376i
$924$		0			0
$925$	−20.8065	−	18.0290i	−0.684115	−	0.592789i
$926$	5.05282	−	17.2083i	0.166046	−	0.565501i
$927$		0			0
$928$	−0.517289	−	1.13270i	−0.0169808	−	0.0371829i
$929$	28.4770	−	24.6755i	0.934300	−	0.809576i	−0.0476211	−	0.998865i	$-0.515164\pi$
$929$	28.4770	−	24.6755i	0.934300	−	0.809576i	0.981921	+	0.189290i	$0.0606186\pi$
$930$		0			0
$931$	−66.6518	−	9.58308i	−2.18442	−	0.314073i
$932$	13.6819	+	1.96716i	0.448165	+	0.0644364i
$933$		0			0
$934$	−0.00370875	+	0.00321365i	−0.000121354	+	0.000105154i
$935$	10.3025	+	22.5593i	0.336928	+	0.737769i
$936$		0			0
$937$	11.1696	−	38.0402i	0.364895	−	1.24272i	−0.548674	−	0.836036i	$-0.684867\pi$
$937$	11.1696	−	38.0402i	0.364895	−	1.24272i	0.913569	−	0.406683i	$-0.133315\pi$
$938$	43.8943	+	38.0346i	1.43320	+	1.24187i
$939$		0			0
$940$	2.58036	+	1.17841i	0.0841620	+	0.0384355i
$941$	3.51417	+	24.4416i	0.114559	+	0.796774i	0.963389	+	0.268108i	$0.0863984\pi$
$941$	3.51417	+	24.4416i	0.114559	+	0.796774i	−0.848830	+	0.528666i	$0.822692\pi$
$942$		0			0
$943$	−5.72996	+	13.3876i	−0.186593	+	0.435959i
$944$		−	2.40483i		−	0.0782705i
$945$		0			0
$946$	−5.58395	+	12.2272i	−0.181550	+	0.397539i
$947$	−0.0938430	−	0.319600i	−0.00304949	−	0.0103856i	0.957954	−	0.286921i	$-0.0926318\pi$
$947$	−0.0938430	−	0.319600i	−0.00304949	−	0.0103856i	−0.961004	+	0.276536i	$0.910814\pi$
$948$		0			0
$949$	8.11500	+	2.38278i	0.263424	+	0.0773483i
$950$	24.4030	−	15.6829i	0.791738	−	0.508819i
$951$		0			0
$952$	−21.6717	−	25.0105i	−0.702385	−	0.810596i
$953$	−4.03008	−	2.58997i	−0.130547	−	0.0838975i	0.473737	−	0.880666i	$-0.342905\pi$
$953$	−4.03008	−	2.58997i	−0.130547	−	0.0838975i	−0.604284	+	0.796769i	$0.706541\pi$
$954$		0			0
$955$	−0.988646	+	6.87618i	−0.0319918	+	0.222508i
$956$	−3.16207	+	4.92028i	−0.102269	+	0.159133i
$957$		0			0
$958$	33.7915	−	15.4321i	1.09175	−	0.498588i
$959$	28.5325	+	44.3975i	0.921363	+	1.43367i
$960$		0			0
$961$	−52.4873	+	60.5735i	−1.69314	+	1.95399i
$962$	−17.4606	+	5.12689i	−0.562952	+	0.165298i
$963$		0			0
$964$	−0.171127	+	0.0246044i	−0.00551164	+	0.000792454i
$965$	5.41566			0.174336
$966$		0			0
$967$	26.6244			0.856182			0.428091	−	0.903736i	$-0.359186\pi$
$967$	26.6244			0.856182			0.428091	+	0.903736i	$0.359186\pi$
$968$	14.4106	−	2.07193i	0.463174	−	0.0665944i
$969$		0			0
$970$	3.87321	−	1.13728i	0.124361	−	0.0365158i
$971$	−26.5386	+	30.6272i	−0.851664	+	0.982873i	−0.999982	−	0.00606706i	$-0.998069\pi$
$971$	−26.5386	+	30.6272i	−0.851664	+	0.982873i	0.148318	+	0.988940i	$0.452614\pi$
$972$		0			0
$973$	2.23719	+	3.48114i	0.0717210	+	0.111600i
$974$	3.34855	−	1.52923i	0.107295	−	0.0489998i
$975$		0			0
$976$	−2.55458	+	3.97500i	−0.0817701	+	0.127237i
$977$	−2.24205	+	15.5938i	−0.0717296	+	0.498891i	0.922010	+	0.387167i	$0.126546\pi$
$977$	−2.24205	+	15.5938i	−0.0717296	+	0.498891i	−0.993739	+	0.111724i	$0.964363\pi$
$978$		0			0
$979$	61.0352	+	39.2249i	1.95069	+	1.25363i
$980$	−4.37179	−	5.04531i	−0.139652	−	0.161167i
$981$		0			0
$982$	−9.93729	+	6.38631i	−0.317112	+	0.203795i
$983$	−11.8780	−	3.48769i	−0.378848	−	0.111240i	0.0867635	−	0.996229i	$-0.472348\pi$
$983$	−11.8780	−	3.48769i	−0.378848	−	0.111240i	−0.465612	+	0.884989i	$0.654166\pi$
$984$		0			0
$985$	−2.04868	−	6.97717i	−0.0652765	−	0.222311i
$986$	−4.06861	+	8.90902i	−0.129571	+	0.283721i
$987$		0			0
$988$		−	19.1740i		−	0.610005i
$989$	−1.51148	+	12.6614i	−0.0480622	+	0.402608i
$990$		0			0
$991$	−0.709136	−	4.93215i	−0.0225264	−	0.156675i	0.975453	−	0.220206i	$-0.0706729\pi$
$991$	−0.709136	−	4.93215i	−0.0225264	−	0.156675i	−0.997980	+	0.0635310i	$0.979764\pi$
$992$	9.59005	+	4.37963i	0.304484	+	0.139053i
$993$		0			0
$994$	11.2451	+	9.74397i	0.356674	+	0.309060i
$995$	2.24498	−	7.64571i	0.0711707	−	0.242385i
$996$		0			0
$997$	12.8798	+	28.2029i	0.407908	+	0.893194i	0.996407	+	0.0846956i	$0.0269918\pi$
$997$	12.8798	+	28.2029i	0.407908	+	0.893194i	−0.588499	+	0.808498i	$0.700281\pi$
$998$	30.9264	−	26.7979i	0.978958	−	0.848272i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.j.a.89.3	✓	80
3.2	odd	2	inner	414.2.j.a.89.6	yes	80
23.15	odd	22	inner	414.2.j.a.107.6	yes	80
69.38	even	22	inner	414.2.j.a.107.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.j.a.89.3	✓	80	1.1	even	1	trivial
414.2.j.a.89.6	yes	80	3.2	odd	2	inner
414.2.j.a.107.3	yes	80	69.38	even	22	inner
414.2.j.a.107.6	yes	80	23.15	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)

\(f(q)\)	\(=\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.408438 + 0.471363i) q^{5} +(-2.27479 - 3.53964i) q^{7} +(-0.909632 + 0.415415i) q^{8} +O(q^{10})\)	\(q+(-0.989821 + 0.142315i) q^{2} +(0.959493 - 0.281733i) q^{4} +(-0.408438 + 0.471363i) q^{5} +(-2.27479 - 3.53964i) q^{7} +(-0.909632 + 0.415415i) q^{8} +(0.337199 - 0.524692i) q^{10} +(-0.719483 + 5.00411i) q^{11} +(-2.56399 - 1.64778i) q^{13} +(2.75538 + 3.17987i) q^{14} +(0.841254 - 0.540641i) q^{16} +(-7.54666 - 2.21590i) q^{17} +(1.77239 + 6.03620i) q^{19} +(-0.259095 + 0.567339i) q^{20} -5.05557i q^{22} +(-1.46111 - 4.56784i) q^{23} +(0.656213 + 4.56406i) q^{25} +(2.77240 + 1.26611i) q^{26} +(-3.17987 - 2.75538i) q^{28} +(-0.350823 + 1.19479i) q^{29} +(-4.37963 - 9.59005i) q^{31} +(-0.755750 + 0.654861i) q^{32} +(7.78520 + 1.11934i) q^{34} +(2.59756 + 0.373473i) q^{35} +(-4.51237 + 3.90999i) q^{37} +(-2.61339 - 5.72252i) q^{38} +(0.175717 - 0.598438i) q^{40} +(-2.29479 - 1.98845i) q^{41} +(-2.41855 - 1.10452i) q^{43} +(0.719483 + 5.00411i) q^{44} +(2.09631 + 4.31341i) q^{46} -4.54818i q^{47} +(-4.44647 + 9.73641i) q^{49} +(-1.29907 - 4.42422i) q^{50} +(-2.92437 - 0.858671i) q^{52} +(-7.00945 + 4.50470i) q^{53} +(-2.06489 - 2.38301i) q^{55} +(3.53964 + 2.27479i) q^{56} +(0.177215 - 1.23256i) q^{58} +(1.30015 - 2.02307i) q^{59} +(-4.29810 + 1.96287i) q^{61} +(5.69986 + 8.86915i) q^{62} +(0.654861 - 0.755750i) q^{64} +(1.82393 - 0.535555i) q^{65} +(13.6633 - 1.96448i) q^{67} -7.86526 q^{68} -2.62427 q^{70} +(3.50036 - 0.503275i) q^{71} +(-2.66256 + 0.781797i) q^{73} +(3.90999 - 4.51237i) q^{74} +(3.40119 + 5.29235i) q^{76} +(19.3494 - 8.83658i) q^{77} +(2.10048 - 3.26841i) q^{79} +(-0.0887621 + 0.617354i) q^{80} +(2.55442 + 1.64162i) q^{82} +(-0.425150 - 0.490649i) q^{83} +(4.12684 - 2.65216i) q^{85} +(2.55112 + 0.749077i) q^{86} +(-1.42432 - 4.85078i) q^{88} +(5.96164 - 13.0542i) q^{89} +12.8239i q^{91} +(-2.68883 - 3.97117i) q^{92} +(0.647273 + 4.50188i) q^{94} +(-3.56915 - 1.62998i) q^{95} +(4.89137 + 4.23839i) q^{97} +(3.01558 - 10.2701i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 8 q^{4}+O(q^{10}) \) 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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