LMFDB - Embedded newform 819.2.fm.f.622.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(370,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("819.370");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fm (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			622.6
Character	$\chi$	$=$	819.622
Dual form			819.2.fm.f.370.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.281068 - 1.04896i) q^{2} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-1.22381 + 2.34570i) q^{7} +(2.16598 - 2.16598i) q^{8} +O(q^{10})$	\(q+(0.281068 - 1.04896i) q^{2} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-1.22381 + 2.34570i) q^{7} +(2.16598 - 2.16598i) q^{8} +(0.788887 + 1.36639i) q^{10} +(-0.972198 - 0.260500i) q^{11} +(3.05530 + 1.91446i) q^{13} +(2.11656 + 1.94303i) q^{14} +(-0.842549 - 1.45934i) q^{16} +(-2.37035 + 4.10557i) q^{17} +(-0.391878 - 1.46251i) q^{19} +(-1.15173 + 0.308606i) q^{20} +(-0.546507 + 0.946578i) q^{22} +(0.337046 - 0.194594i) q^{23} +2.88914i q^{25} +(2.86693 - 2.66679i) q^{26} +(-1.83235 + 1.16499i) q^{28} +(4.30065 + 7.44895i) q^{29} +(-2.92542 + 2.92542i) q^{31} +(4.14997 - 1.11198i) q^{32} +(3.64034 + 3.64034i) q^{34} +(-1.15256 - 3.66710i) q^{35} +(9.77690 + 2.61971i) q^{37} -1.64425 q^{38} +4.45041i q^{40} +(8.64616 + 2.31673i) q^{41} +(-8.28885 - 4.78557i) q^{43} +(-0.584082 - 0.584082i) q^{44} +(-0.109388 - 0.408241i) q^{46} +(4.78928 + 4.78928i) q^{47} +(-4.00458 - 5.74137i) q^{49} +(3.03058 + 0.812042i) q^{50} +(1.38592 + 2.61440i) q^{52} -12.7329 q^{53} +(1.26640 - 0.731158i) q^{55} +(2.42998 + 7.73148i) q^{56} +(9.02241 - 2.41755i) q^{58} +(0.889636 - 0.238377i) q^{59} +(-8.36449 - 4.82924i) q^{61} +(2.24640 + 3.89088i) q^{62} -8.03588i q^{64} +(-5.10564 + 1.17203i) q^{65} +(1.71328 - 6.39405i) q^{67} +(-3.36939 + 1.94532i) q^{68} +(-4.17059 + 0.178284i) q^{70} +(2.56663 - 0.687727i) q^{71} +(2.46596 + 2.46596i) q^{73} +(5.49594 - 9.51925i) q^{74} +(0.321609 - 1.20026i) q^{76} +(1.80084 - 1.96168i) q^{77} +7.06532 q^{79} +(2.36483 + 0.633653i) q^{80} +(4.86031 - 8.41830i) q^{82} +(2.43414 - 2.43414i) q^{83} +(-1.78266 - 6.65299i) q^{85} +(-7.34959 + 7.34959i) q^{86} +(-2.67000 + 1.54152i) q^{88} +(2.79345 - 10.4253i) q^{89} +(-8.22984 + 4.82387i) q^{91} +0.319401 q^{92} +(6.36986 - 3.67764i) q^{94} +(1.90509 + 1.09990i) q^{95} +(-3.55710 - 13.2753i) q^{97} +(-7.14802 + 2.58692i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	$ 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$-1$

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 $

$2$	0.281068	−	1.04896i	0.198745	−	0.741726i	−0.792521	−	0.609845i	$-0.791232\pi$
$2$	0.281068	−	1.04896i	0.198745	−	0.741726i	0.991266	−	0.131881i	$-0.0421016\pi$
$3$		0			0
$3$		0			0
$4$	0.710736	+	0.410344i	0.355368	+	0.205172i
$5$	−1.02734	+	1.02734i	−0.459441	+	0.459441i	−0.898472	−	0.439031i	$-0.855322\pi$
$5$	−1.02734	+	1.02734i	−0.459441	+	0.459441i	0.439031	+	0.898472i	$0.355322\pi$
$6$		0			0
$7$	−1.22381	+	2.34570i	−0.462557	+	0.886590i
$7$	−1.22381	+	2.34570i	−0.462557	+	0.886590i
$8$	2.16598	−	2.16598i	0.765790	−	0.765790i
$9$		0			0
$10$	0.788887	+	1.36639i	0.249468	+	0.432091i
$11$	−0.972198	−	0.260500i	−0.293129	−	0.0785436i	0.109258	−	0.994013i	$-0.465153\pi$
$11$	−0.972198	−	0.260500i	−0.293129	−	0.0785436i	−0.402387	+	0.915470i	$0.631819\pi$
$12$		0			0
$13$	3.05530	+	1.91446i	0.847387	+	0.530975i
$13$	3.05530	+	1.91446i	0.847387	+	0.530975i
$14$	2.11656	+	1.94303i	0.565676	+	0.519295i
$15$		0			0
$16$	−0.842549	−	1.45934i	−0.210637	−	0.364834i
$17$	−2.37035	+	4.10557i	−0.574895	+	0.995747i	0.421159	+	0.906987i	$0.361624\pi$
$17$	−2.37035	+	4.10557i	−0.574895	+	0.995747i	−0.996053	+	0.0887595i	$0.971710\pi$
$18$		0			0
$19$	−0.391878	−	1.46251i	−0.0899030	−	0.335522i	0.906294	−	0.422647i	$-0.138899\pi$
$19$	−0.391878	−	1.46251i	−0.0899030	−	0.335522i	−0.996197	+	0.0871243i	$0.972232\pi$
$20$	−1.15173	+	0.308606i	−0.257535	+	0.0690064i
$21$		0			0
$22$	−0.546507	+	0.946578i	−0.116516	+	0.201811i
$23$	0.337046	−	0.194594i	0.0702790	−	0.0405756i	−0.464449	−	0.885600i	$-0.653748\pi$
$23$	0.337046	−	0.194594i	0.0702790	−	0.0405756i	0.534728	+	0.845024i	$0.320414\pi$
$24$		0			0
$25$			2.88914i			0.577827i
$26$	2.86693	−	2.66679i	0.562252	−	0.523000i
$27$		0			0
$28$	−1.83235	+	1.16499i	−0.346281	+	0.220162i
$29$	4.30065	+	7.44895i	0.798611	+	1.38324i	0.920521	+	0.390694i	$0.127765\pi$
$29$	4.30065	+	7.44895i	0.798611	+	1.38324i	−0.121909	+	0.992541i	$0.538902\pi$
$30$		0			0
$31$	−2.92542	+	2.92542i	−0.525420	+	0.525420i	−0.919203	−	0.393783i	$-0.871166\pi$
$31$	−2.92542	+	2.92542i	−0.525420	+	0.525420i	0.393783	+	0.919203i	$0.371166\pi$
$32$	4.14997	−	1.11198i	0.733618	−	0.196572i
$33$		0			0
$34$	3.64034	+	3.64034i	0.624313	+	0.624313i
$35$	−1.15256	−	3.66710i	−0.194818	−	0.619854i
$36$		0			0
$37$	9.77690	+	2.61971i	1.60731	+	0.430678i	0.947240	−	0.320524i	$-0.103859\pi$
$37$	9.77690	+	2.61971i	1.60731	+	0.430678i	0.660072	+	0.751202i	$0.270526\pi$
$38$	−1.64425			−0.266733
$39$		0			0
$40$			4.45041i			0.703671i
$41$	8.64616	+	2.31673i	1.35030	+	0.361813i	0.860247	−	0.509878i	$-0.170310\pi$
$41$	8.64616	+	2.31673i	1.35030	+	0.361813i	0.490056	+	0.871691i	$0.336976\pi$
$42$		0			0
$43$	−8.28885	−	4.78557i	−1.26404	−	0.729792i	−0.290184	−	0.956971i	$-0.593717\pi$
$43$	−8.28885	−	4.78557i	−1.26404	−	0.729792i	−0.973853	+	0.227179i	$0.927050\pi$
$44$	−0.584082	−	0.584082i	−0.0880537	−	0.0880537i
$45$		0			0
$46$	−0.109388	−	0.408241i	−0.0161284	−	0.0601919i
$47$	4.78928	+	4.78928i	0.698588	+	0.698588i	0.964106	−	0.265518i	$-0.0855430\pi$
$47$	4.78928	+	4.78928i	0.698588	+	0.698588i	−0.265518	+	0.964106i	$0.585543\pi$
$48$		0			0
$49$	−4.00458	−	5.74137i	−0.572082	−	0.820196i
$50$	3.03058	+	0.812042i	0.428589	+	0.114840i
$51$		0			0
$52$	1.38592	+	2.61440i	0.192193	+	0.362552i
$53$	−12.7329			−1.74900			−0.874498	−	0.485029i	$-0.838809\pi$
$53$	−12.7329			−1.74900			−0.874498	+	0.485029i	$0.838809\pi$
$54$		0			0
$55$	1.26640	−	0.731158i	0.170762	−	0.0985893i
$56$	2.42998	+	7.73148i	0.324720	+	1.03316i
$57$		0			0
$58$	9.02241	−	2.41755i	1.18470	−	0.317440i
$59$	0.889636	−	0.238377i	0.115821	−	0.0310341i	−0.200443	−	0.979705i	$-0.564238\pi$
$59$	0.889636	−	0.238377i	0.115821	−	0.0310341i	0.316264	+	0.948671i	$0.397572\pi$
$60$		0			0
$61$	−8.36449	−	4.82924i	−1.07096	−	0.618321i	−0.142519	−	0.989792i	$-0.545520\pi$
$61$	−8.36449	−	4.82924i	−1.07096	−	0.618321i	−0.928445	+	0.371471i	$0.878854\pi$
$62$	2.24640	+	3.89088i	0.285293	+	0.494142i
$63$		0			0
$64$		−	8.03588i		−	1.00449i
$65$	−5.10564	+	1.17203i	−0.633277	+	0.145373i
$66$		0			0
$67$	1.71328	−	6.39405i	0.209311	−	0.781158i	−0.778782	−	0.627295i	$-0.784162\pi$
$67$	1.71328	−	6.39405i	0.209311	−	0.781158i	0.988092	−	0.153863i	$-0.0491713\pi$
$68$	−3.36939	+	1.94532i	−0.408598	+	0.235904i
$69$		0			0
$70$	−4.17059	+	0.178284i	−0.498481	+	0.0213090i
$71$	2.56663	−	0.687727i	0.304603	−	0.0816182i	−0.103280	−	0.994652i	$-0.532934\pi$
$71$	2.56663	−	0.687727i	0.304603	−	0.0816182i	0.407883	+	0.913034i	$0.366267\pi$
$72$		0			0
$73$	2.46596	+	2.46596i	0.288619	+	0.288619i	0.836534	−	0.547915i	$-0.184578\pi$
$73$	2.46596	+	2.46596i	0.288619	+	0.288619i	−0.547915	+	0.836534i	$0.684578\pi$
$74$	5.49594	−	9.51925i	0.638890	−	1.10659i
$75$		0			0
$76$	0.321609	−	1.20026i	0.0368911	−	0.137680i
$77$	1.80084	−	1.96168i	0.205225	−	0.223554i
$78$		0			0
$79$	7.06532			0.794911			0.397455	−	0.917622i	$-0.369893\pi$
$79$	7.06532			0.794911			0.397455	+	0.917622i	$0.369893\pi$
$80$	2.36483	+	0.633653i	0.264396	+	0.0708446i
$81$		0			0
$82$	4.86031	−	8.41830i	0.536731	−	0.929646i
$83$	2.43414	−	2.43414i	0.267181	−	0.267181i	−0.560782	−	0.827963i	$-0.689499\pi$
$83$	2.43414	−	2.43414i	0.267181	−	0.267181i	0.827963	+	0.560782i	$0.189499\pi$
$84$		0			0
$85$	−1.78266	−	6.65299i	−0.193357	−	0.721618i
$86$	−7.34959	+	7.34959i	−0.792526	+	0.792526i
$87$		0			0
$88$	−2.67000	+	1.54152i	−0.284623	+	0.164327i
$89$	2.79345	−	10.4253i	0.296105	−	1.10508i	−0.644231	−	0.764831i	$-0.722822\pi$
$89$	2.79345	−	10.4253i	0.296105	−	1.10508i	0.940336	−	0.340248i	$-0.110511\pi$
$90$		0			0
$91$	−8.22984	+	4.82387i	−0.862722	+	0.505679i
$92$	0.319401			0.0332999
$93$		0			0
$94$	6.36986	−	3.67764i	0.657001	−	0.379320i
$95$	1.90509	+	1.09990i	0.195458	+	0.112848i
$96$		0			0
$97$	−3.55710	−	13.2753i	−0.361169	−	1.34790i	−0.872541	−	0.488541i	$-0.837529\pi$
$97$	−3.55710	−	13.2753i	−0.361169	−	1.34790i	0.511372	−	0.859359i	$-0.329137\pi$
$98$	−7.14802	+	2.58692i	−0.722059	+	0.261318i
$99$		0			0
$100$	−1.18554	+	2.05341i	−0.118554	+	0.205341i
$101$	1.97748	+	3.42510i	0.196767	+	0.340810i	0.947478	−	0.319820i	$-0.103622\pi$
$101$	1.97748	+	3.42510i	0.196767	+	0.340810i	−0.750711	+	0.660630i	$0.770289\pi$
$102$		0			0
$103$	12.7709			1.25835			0.629176	−	0.777263i	$-0.283393\pi$
$103$	12.7709			1.25835			0.629176	+	0.777263i	$0.283393\pi$
$104$	10.7644	−	2.47103i	1.05554	−	0.242305i
$105$		0			0
$106$	−3.57880	+	13.3563i	−0.347604	+	1.29728i
$107$	−1.79997	−	3.11764i	−0.174010	−	0.301394i	0.765808	−	0.643069i	$-0.222339\pi$
$107$	−1.79997	−	3.11764i	−0.174010	−	0.301394i	−0.939818	+	0.341675i	$0.889006\pi$
$108$		0			0
$109$	−0.0623175	−	0.0623175i	−0.00596893	−	0.00596893i	0.704116	−	0.710085i	$-0.251343\pi$
$109$	−0.0623175	−	0.0623175i	−0.00596893	−	0.00596893i	−0.710085	+	0.704116i	$0.751343\pi$
$110$	−0.411010	−	1.53391i	−0.0391882	−	0.146252i
$111$		0			0
$112$	4.45428	−	0.190411i	0.420890	−	0.0179922i
$113$	1.09268	−	1.89259i	0.102791	−	0.178039i	−0.810042	−	0.586371i	$-0.800556\pi$
$113$	1.09268	−	1.89259i	0.102791	−	0.178039i	0.912834	+	0.408332i	$0.133889\pi$
$114$		0			0
$115$	−0.146347	+	0.546176i	−0.0136470	+	0.0509312i
$116$			7.05898i			0.655410i
$117$		0			0
$118$		−	1.00019i		−	0.0920751i
$119$	−6.72955	−	10.5846i	−0.616897	−	0.970285i
$120$		0			0
$121$	−8.64897	−	4.99349i	−0.786270	−	0.453953i
$122$	−7.41666	+	7.41666i	−0.671473	+	0.671473i
$123$		0			0
$124$	−3.27962	+	0.878773i	−0.294519	+	0.0789161i
$125$	−8.10484	−	8.10484i	−0.724919	−	0.724919i
$126$		0			0
$127$	−12.3666	+	7.13987i	−1.09736	+	0.633561i	−0.935526	−	0.353257i	$-0.885074\pi$
$127$	−12.3666	+	7.13987i	−1.09736	+	0.633561i	−0.161834	+	0.986818i	$0.551741\pi$
$128$	−0.129367	−	0.0346639i	−0.0114346	−	0.00306389i
$129$		0			0
$130$	−0.205617	+	5.68503i	−0.0180338	+	0.498610i
$131$		−	17.8888i		−	1.56295i	−0.623934	−	0.781477i	$-0.714467\pi$
$131$		−	17.8888i		−	1.56295i	0.623934	−	0.781477i	$-0.285533\pi$
$132$		0			0
$133$	3.91018	+	0.870606i	0.339056	+	0.0754912i
$134$	−6.22555	−	3.59432i	−0.537805	−	0.310502i
$135$		0			0
$136$	3.75845	+	14.0267i	0.322284	+	1.20278i
$137$	0.654988	+	2.44445i	0.0559594	+	0.208843i	0.988245	−	0.152881i	$-0.0488550\pi$
$137$	0.654988	+	2.44445i	0.0559594	+	0.208843i	−0.932285	+	0.361724i	$0.882188\pi$
$138$		0			0
$139$	8.86338	+	5.11727i	0.751782	+	0.434041i	0.826337	−	0.563176i	$-0.190421\pi$
$139$	8.86338	+	5.11727i	0.751782	+	0.434041i	−0.0745556	+	0.997217i	$0.523754\pi$
$140$	0.685607	−	3.07929i	0.0579444	−	0.260247i
$141$		0			0
$142$		−	2.88559i		−	0.242153i
$143$	−2.47164	−	2.65714i	−0.206689	−	0.222201i
$144$		0			0
$145$	−12.0709	−	3.23438i	−1.00243	−	0.268601i
$146$	3.27979	−	1.89359i	0.271437	−	0.156714i
$147$		0			0
$148$	5.87381	+	5.87381i	0.482825	+	0.482825i
$149$	−8.14575	+	2.18265i	−0.667326	+	0.178809i	−0.576550	−	0.817062i	$-0.695601\pi$
$149$	−8.14575	+	2.18265i	−0.667326	+	0.178809i	−0.0907761	+	0.995871i	$0.528935\pi$
$150$		0			0
$151$	−0.453678	+	0.453678i	−0.0369198	+	0.0369198i	−0.725326	−	0.688406i	$-0.758311\pi$
$151$	−0.453678	+	0.453678i	−0.0369198	+	0.0369198i	0.688406	+	0.725326i	$0.258311\pi$
$152$	−4.01656	−	2.31896i	−0.325786	−	0.188093i
$153$		0			0
$154$	−1.55156	−	2.44037i	−0.125028	−	0.196651i
$155$		−	6.01081i		−	0.482800i
$156$		0			0
$157$			8.10530i			0.646874i	0.946250	+	0.323437i	$0.104838\pi$
$157$			8.10530i			0.646874i	−0.946250	+	0.323437i	$0.895162\pi$
$158$	1.98583	−	7.41123i	0.157984	−	0.589606i
$159$		0			0
$160$	−3.12105	+	5.40583i	−0.246741	+	0.427368i
$161$	0.0439771	+	1.02875i	0.00346588	+	0.0810771i
$162$		0			0
$163$	3.55525	+	13.2684i	0.278469	+	1.03926i	0.953481	+	0.301453i	$0.0974717\pi$
$163$	3.55525	+	13.2684i	0.278469	+	1.03926i	−0.675012	+	0.737807i	$0.735862\pi$
$164$	5.19448	+	5.19448i	0.405621	+	0.405621i
$165$		0			0
$166$	−1.86915	−	3.23746i	−0.145074	−	0.251276i
$167$	5.75214	−	21.4673i	0.445114	−	1.66119i	−0.270523	−	0.962714i	$-0.587196\pi$
$167$	5.75214	−	21.4673i	0.445114	−	1.66119i	0.715636	−	0.698473i	$-0.246137\pi$
$168$		0			0
$169$	5.66969	+	11.6985i	0.436130	+	0.899884i
$170$	−7.47975			−0.573671
$171$		0			0
$172$	−3.92745	−	6.80255i	−0.299466	−	0.518690i
$173$	−6.33728	+	10.9765i	−0.481815	+	0.834527i	−0.999782	−	0.0208728i	$-0.993355\pi$
$173$	−6.33728	+	10.9765i	−0.481815	+	0.834527i	0.517967	+	0.855400i	$0.326689\pi$
$174$		0			0
$175$	−6.77703	−	3.53575i	−0.512295	−	0.267278i
$176$	0.438968	+	1.63825i	0.0330884	+	0.123488i
$177$		0			0
$178$	−10.1505	−	5.86042i	−0.760816	−	0.439257i
$179$	−9.48849	+	5.47818i	−0.709203	+	0.409459i	−0.810766	−	0.585370i	$-0.800949\pi$
$179$	−9.48849	+	5.47818i	−0.709203	+	0.409459i	0.101563	+	0.994829i	$0.467616\pi$
$180$		0			0
$181$	4.38394			0.325856			0.162928	−	0.986638i	$-0.447906\pi$
$181$	4.38394			0.325856			0.162928	+	0.986638i	$0.447906\pi$
$182$	2.74689	+	9.98860i	0.203613	+	0.740404i
$183$		0			0
$184$	0.308549	−	1.15152i	0.0227466	−	0.0848913i
$185$	−12.7356	+	7.35288i	−0.936338	+	0.540595i
$186$		0			0
$187$	3.37395	−	3.37395i	0.246728	−	0.246728i
$188$	1.43866	+	5.36916i	0.104925	+	0.391586i
$189$		0			0
$190$	1.68921	−	1.68921i	0.122548	−	0.122548i
$191$	4.92507	−	8.53047i	0.356366	−	0.617243i	−0.630985	−	0.775795i	$-0.717349\pi$
$191$	4.92507	−	8.53047i	0.356366	−	0.617243i	0.987351	+	0.158552i	$0.0506824\pi$
$192$		0			0
$193$	12.2874	+	3.29240i	0.884465	+	0.236992i	0.672333	−	0.740249i	$-0.265292\pi$
$193$	12.2874	+	3.29240i	0.884465	+	0.236992i	0.212133	+	0.977241i	$0.431959\pi$
$194$	−14.9250			−1.07155
$195$		0			0
$196$	−0.490261	−	5.72385i	−0.0350187	−	0.408847i
$197$	0.404048	−	1.50793i	0.0287873	−	0.107436i	−0.950037	−	0.312136i	$-0.898955\pi$
$197$	0.404048	−	1.50793i	0.0287873	−	0.107436i	0.978825	+	0.204701i	$0.0656221\pi$
$198$		0			0
$199$	5.84499	−	10.1238i	0.414340	−	0.717659i	−0.581019	−	0.813890i	$-0.697346\pi$
$199$	5.84499	−	10.1238i	0.414340	−	0.717659i	0.995359	+	0.0962317i	$0.0306790\pi$
$200$	6.25781	+	6.25781i	0.442494	+	0.442494i
$201$		0			0
$202$	4.14860	−	1.11161i	0.291894	−	0.0782128i
$203$	−22.7362	+	0.971923i	−1.59577	+	0.0682156i
$204$		0			0
$205$	−11.2626	+	6.50249i	−0.786617	+	0.454153i
$206$	3.58948	−	13.3961i	0.250091	−	0.933351i
$207$		0			0
$208$	0.219604	−	6.07174i	0.0152268	−	0.420999i
$209$			1.52393i			0.105413i
$210$		0			0
$211$	−11.0809	−	19.1926i	−0.762838	−	1.32127i	−0.941382	−	0.337343i	$-0.890472\pi$
$211$	−11.0809	−	19.1926i	−0.762838	−	1.32127i	0.178544	−	0.983932i	$-0.442861\pi$
$212$	−9.04972	−	5.22486i	−0.621537	−	0.358845i
$213$		0			0
$214$	−3.77619	+	1.01183i	−0.258135	+	0.0691670i
$215$	13.4319	−	3.59907i	0.916048	−	0.245454i
$216$		0			0
$217$	−3.28198	−	10.4423i	−0.222795	−	0.708869i
$218$	−0.0828838	+	0.0478530i	−0.00561360	+	0.00324101i
$219$		0			0
$220$	1.20010			0.0809110
$221$	−15.1021	+	8.00580i	−1.01588	+	0.538528i
$222$		0			0
$223$	−13.2842	−	3.55949i	−0.889575	−	0.238361i	−0.215041	−	0.976605i	$-0.568989\pi$
$223$	−13.2842	−	3.55949i	−0.889575	−	0.238361i	−0.674534	+	0.738244i	$0.735655\pi$
$224$	−2.47041	+	11.0954i	−0.165061	+	0.741344i
$225$		0			0
$226$	−1.67813	−	1.67813i	−0.111627	−	0.111627i
$227$	1.04021	+	3.88213i	0.0690413	+	0.257666i	0.991816	−	0.127674i	$-0.0407510\pi$
$227$	1.04021	+	3.88213i	0.0690413	+	0.257666i	−0.922775	+	0.385339i	$0.874084\pi$
$228$		0			0
$229$	1.36272	+	1.36272i	0.0900509	+	0.0900509i	0.750697	−	0.660646i	$-0.229718\pi$
$229$	1.36272	+	1.36272i	0.0900509	+	0.0900509i	−0.660646	+	0.750697i	$0.729718\pi$
$230$	0.531783	+	0.307025i	0.0350647	+	0.0202446i
$231$		0			0
$232$	25.4494	+	6.81915i	1.67084	+	0.447699i
$233$			1.13013i			0.0740376i	0.999315	+	0.0370188i	$0.0117861\pi$
$233$			1.13013i			0.0740376i	−0.999315	+	0.0370188i	$0.988214\pi$
$234$		0			0
$235$	−9.84046			−0.641921
$236$	0.730113	+	0.195633i	0.0475263	+	0.0127346i
$237$		0			0
$238$	−12.9942	+	4.08405i	−0.842290	+	0.264729i
$239$	−3.62833	−	3.62833i	−0.234697	−	0.234697i	0.579953	−	0.814650i	$-0.303071\pi$
$239$	−3.62833	−	3.62833i	−0.234697	−	0.234697i	−0.814650	+	0.579953i	$0.803071\pi$
$240$		0			0
$241$	−9.46780	+	2.53689i	−0.609875	+	0.163415i	−0.550521	−	0.834822i	$-0.685571\pi$
$241$	−9.46780	+	2.53689i	−0.609875	+	0.163415i	−0.0593540	+	0.998237i	$0.518904\pi$
$242$	−7.66890	+	7.66890i	−0.492976	+	0.492976i
$243$		0			0
$244$	−3.96330	−	6.86463i	−0.253724	−	0.439463i
$245$	10.0124	+	1.78428i	0.639671	+	0.113994i
$246$		0			0
$247$	1.60261	−	5.21863i	0.101972	−	0.332054i
$248$			12.6728i			0.804723i
$249$		0			0
$250$	−10.7797	+	6.22363i	−0.681765	+	0.393617i
$251$	14.1820	−	24.5639i	0.895158	−	1.55046i	0.0615480	−	0.998104i	$-0.480396\pi$
$251$	14.1820	−	24.5639i	0.895158	−	1.55046i	0.833610	−	0.552354i	$-0.186270\pi$
$252$		0			0
$253$	−0.378367	+	0.101383i	−0.0237878	+	0.00637391i
$254$	4.01357	+	14.9789i	0.251834	+	0.939857i
$255$		0			0
$256$	7.96316	−	13.7926i	0.497698	−	0.862037i
$257$	3.32083	+	5.75185i	0.207148	+	0.358790i	0.950815	−	0.309760i	$-0.100249\pi$
$257$	3.32083	+	5.75185i	0.207148	+	0.358790i	−0.743667	+	0.668550i	$0.766915\pi$
$258$		0			0
$259$	−18.1101	+	19.7276i	−1.12531	+	1.22581i
$260$	−4.10970	−	1.26206i	−0.254873	−	0.0782698i
$261$		0			0
$262$	−18.7646	−	5.02797i	−1.15928	−	0.310629i
$263$	6.24723	+	10.8205i	0.385221	+	0.667222i	0.991800	−	0.127801i	$-0.0407920\pi$
$263$	6.24723	+	10.8205i	0.385221	+	0.667222i	−0.606579	+	0.795023i	$0.707459\pi$
$264$		0			0
$265$	13.0810	−	13.0810i	0.803561	−	0.803561i
$266$	2.01226	−	3.85692i	0.123379	−	0.236483i
$267$		0			0
$268$	3.84145	−	3.84145i	0.234654	−	0.234654i
$269$	−7.27737	−	4.20159i	−0.443709	−	0.256176i	0.261460	−	0.965214i	$-0.415796\pi$
$269$	−7.27737	−	4.20159i	−0.443709	−	0.256176i	−0.705170	+	0.709038i	$0.749129\pi$
$270$		0			0
$271$	0.0939748	−	0.350719i	0.00570857	−	0.0213047i	−0.963013	−	0.269456i	$-0.913156\pi$
$271$	0.0939748	−	0.350719i	0.00570857	−	0.0213047i	0.968721	+	0.248151i	$0.0798229\pi$
$272$	7.98855			0.484377
$273$		0			0
$274$	2.74822			0.166026
$275$	0.752619	−	2.80881i	0.0453846	−	0.169378i
$276$		0			0
$277$	13.5251	+	7.80875i	0.812647	+	0.469182i	0.847874	−	0.530197i	$-0.177882\pi$
$277$	13.5251	+	7.80875i	0.812647	+	0.469182i	−0.0352270	+	0.999379i	$0.511215\pi$
$278$	7.85901	−	7.85901i	0.471352	−	0.471352i
$279$		0			0
$280$	−10.4393	−	5.44645i	−0.623867	−	0.325488i
$281$	0.848694	−	0.848694i	0.0506289	−	0.0506289i	−0.681339	−	0.731968i	$-0.738602\pi$
$281$	0.848694	−	0.848694i	0.0506289	−	0.0506289i	0.731968	+	0.681339i	$0.238602\pi$
$282$		0			0
$283$	11.9723	+	20.7366i	0.711678	+	1.23266i	0.964227	+	0.265078i	$0.0853976\pi$
$283$	11.9723	+	20.7366i	0.711678	+	1.23266i	−0.252549	+	0.967584i	$0.581269\pi$
$284$	2.10640	+	0.564409i	0.124992	+	0.0334915i
$285$		0			0
$286$	−3.48193	+	1.84581i	−0.205891	+	0.109145i
$287$	−16.0156	+	17.4460i	−0.945371	+	1.02981i
$288$		0			0
$289$	−2.73713	−	4.74084i	−0.161007	−	0.278873i
$290$	−6.78546	+	11.7528i	−0.398456	+	0.690146i
$291$		0			0
$292$	0.740755	+	2.76454i	0.0433494	+	0.161782i
$293$	18.6502	−	4.99730i	1.08956	−	0.291946i	0.331051	−	0.943613i	$-0.392597\pi$
$293$	18.6502	−	4.99730i	1.08956	−	0.291946i	0.758505	+	0.651667i	$0.225930\pi$
$294$		0			0
$295$	−0.669066	+	1.15886i	−0.0389545	+	0.0674712i
$296$	26.8508	−	15.5023i	1.56067	−	0.901055i
$297$		0			0
$298$			9.15803i			0.530510i
$299$	1.40232	+	0.0507193i	0.0810982	+	0.00293317i
$300$		0			0
$301$	21.3695	−	13.5865i	1.23172	−	0.783112i
$302$	0.348375	+	0.603403i	0.0200467	+	0.0347220i
$303$		0			0
$304$	−1.80412	+	1.80412i	−0.103473	+	0.103473i
$305$	13.5545	−	3.63191i	0.776127	−	0.207963i
$306$		0			0
$307$	17.1942	+	17.1942i	0.981322	+	0.981322i	0.999829	−	0.0185063i	$-0.00589106\pi$
$307$	17.1942	+	17.1942i	0.981322	+	0.981322i	−0.0185063	+	0.999829i	$0.505891\pi$
$308$	2.08488	−	0.655273i	0.118797	−	0.0373377i
$309$		0			0
$310$	−6.30509	−	1.68944i	−0.358105	−	0.0959539i
$311$	−14.0638			−0.797487			−0.398744	−	0.917062i	$-0.630554\pi$
$311$	−14.0638			−0.797487			−0.398744	+	0.917062i	$0.630554\pi$
$312$		0			0
$313$			18.8063i			1.06300i	0.847060	+	0.531498i	$0.178371\pi$
$313$			18.8063i			1.06300i	−0.847060	+	0.531498i	$0.821629\pi$
$314$	8.50213	+	2.27814i	0.479803	+	0.128563i
$315$		0			0
$316$	5.02158	+	2.89921i	0.282486	+	0.163093i
$317$	1.67207	+	1.67207i	0.0939128	+	0.0939128i	0.752502	−	0.658590i	$-0.228847\pi$
$317$	1.67207	+	1.67207i	0.0939128	+	0.0939128i	−0.658590	+	0.752502i	$0.728847\pi$
$318$		0			0
$319$	−2.24064	−	8.36218i	−0.125452	−	0.468192i
$320$	8.25560	+	8.25560i	0.461502	+	0.461502i
$321$		0			0
$322$	1.09148	+	0.243019i	0.0608258	+	0.0135429i
$323$	6.93332	+	1.85778i	0.385780	+	0.103369i
$324$		0			0
$325$	−5.53113	+	8.82717i	−0.306812	+	0.489643i
$326$	14.9172			0.826190
$327$		0			0
$328$	23.7454	−	13.7094i	1.31112	−	0.756976i
$329$	−17.0954	+	5.37302i	−0.942497	+	0.296224i
$330$		0			0
$331$	−33.2290	+	8.90368i	−1.82643	+	0.489391i	−0.997545	−	0.0700274i	$-0.977691\pi$
$331$	−33.2290	+	8.90368i	−1.82643	+	0.489391i	−0.828886	+	0.559418i	$0.811025\pi$
$332$	2.72886	−	0.731196i	0.149766	−	0.0401296i
$333$		0			0
$334$	−20.9015	−	12.0675i	−1.14368	−	0.660304i
$335$	4.80875	+	8.32901i	0.262730	+	0.455062i
$336$		0			0
$337$			3.43766i			0.187261i	0.995607	+	0.0936305i	$0.0298472\pi$
$337$			3.43766i			0.187261i	−0.995607	+	0.0936305i	$0.970153\pi$
$338$	13.8648	−	2.65921i	0.754145	−	0.144642i
$339$		0			0
$340$	1.46301	−	5.46002i	0.0793428	−	0.296111i
$341$	3.60616	−	2.08201i	0.195284	−	0.112747i
$342$		0			0
$343$	18.3684	−	2.36717i	0.991798	−	0.127815i
$344$	−28.3189	+	7.58803i	−1.52685	+	0.409119i
$345$		0			0
$346$	9.73268	+	9.73268i	0.523232	+	0.523232i
$347$	9.46705	−	16.3974i	0.508218	−	0.880259i	−0.491737	−	0.870744i	$-0.663638\pi$
$347$	9.46705	−	16.3974i	0.508218	−	0.880259i	0.999955	−	0.00951518i	$-0.00302882\pi$
$348$		0			0
$349$	8.44404	−	31.5136i	0.451999	−	1.68688i	−0.244765	−	0.969582i	$-0.578711\pi$
$349$	8.44404	−	31.5136i	0.451999	−	1.68688i	0.696764	−	0.717300i	$-0.254623\pi$
$350$	−5.61366	+	6.11504i	−0.300063	+	0.326863i
$351$		0			0
$352$	−4.32426			−0.230484
$353$	−31.7685	−	8.51233i	−1.69086	−	0.453066i	−0.720251	−	0.693713i	$-0.755974\pi$
$353$	−31.7685	−	8.51233i	−1.69086	−	0.453066i	−0.970613	+	0.240647i	$0.922640\pi$
$354$		0			0
$355$	−1.93028	+	3.34334i	−0.102449	+	0.177446i
$356$	6.26336	−	6.26336i	0.331957	−	0.331957i
$357$		0			0
$358$	3.07948	+	11.4928i	0.162756	+	0.607412i
$359$	1.45164	−	1.45164i	0.0766146	−	0.0766146i	−0.667761	−	0.744376i	$-0.732747\pi$
$359$	1.45164	−	1.45164i	0.0766146	−	0.0766146i	0.744376	+	0.667761i	$0.232747\pi$
$360$		0			0
$361$	14.4691	−	8.35375i	0.761533	−	0.439671i
$362$	1.23218	−	4.59857i	0.0647622	−	0.241696i
$363$		0			0
$364$	−7.82869	+	0.0514311i	−0.410335	+	0.00269572i
$365$	−5.06677			−0.265207
$366$		0			0
$367$	0.400843	−	0.231427i	0.0209238	−	0.0120804i	−0.489502	−	0.872002i	$-0.662821\pi$
$367$	0.400843	−	0.231427i	0.0209238	−	0.0120804i	0.510425	+	0.859922i	$0.329488\pi$
$368$	−0.567956	−	0.327909i	−0.0296067	−	0.0170935i
$369$		0			0
$370$	4.13331	+	15.4257i	0.214881	+	0.801946i
$371$	15.5826	−	29.8675i	0.809010	−	1.55064i
$372$		0			0
$373$	5.17460	−	8.96266i	0.267930	−	0.464069i	−0.700397	−	0.713754i	$-0.746994\pi$
$373$	5.17460	−	8.96266i	0.267930	−	0.464069i	0.968327	+	0.249685i	$0.0803269\pi$
$374$	−2.59083	−	4.48744i	−0.133968	−	0.232040i
$375$		0			0
$376$	20.7470			1.06994
$377$	−1.12093	+	30.9922i	−0.0577309	+	1.59618i
$378$		0			0
$379$	3.99214	−	14.8989i	0.205062	−	0.765303i	−0.784368	−	0.620295i	$-0.787013\pi$
$379$	3.99214	−	14.8989i	0.205062	−	0.765303i	0.989431	−	0.145007i	$-0.0463206\pi$
$380$	0.902677	+	1.56348i	0.0463064	+	0.0802050i
$381$		0			0
$382$	−7.56383	−	7.56383i	−0.386999	−	0.386999i
$383$	8.40301	+	31.3605i	0.429374	+	1.60245i	0.754182	+	0.656665i	$0.228034\pi$
$383$	8.40301	+	31.3605i	0.429374	+	1.60245i	−0.324808	+	0.945780i	$0.605300\pi$
$384$		0			0
$385$	0.165238	+	3.86539i	0.00842128	+	0.196999i
$386$	6.90717	−	11.9636i	0.351566	−	0.608930i
$387$		0			0
$388$	2.91927	−	10.8948i	0.148203	−	0.553102i
$389$		−	37.3829i		−	1.89539i	−0.319179	−	0.947694i	$-0.603407\pi$
$389$		−	37.3829i		−	1.89539i	0.319179	−	0.947694i	$-0.396593\pi$
$390$		0			0
$391$			1.84502i			0.0933068i
$392$	−21.1095	−	3.76186i	−1.06619	−	0.190003i
$393$		0			0
$394$	−1.46819	−	0.847660i	−0.0739664	−	0.0427045i
$395$	−7.25850	+	7.25850i	−0.365215	+	0.365215i
$396$		0			0
$397$	34.9889	−	9.37524i	1.75604	−	0.470530i	0.770142	−	0.637873i	$-0.220185\pi$
$397$	34.9889	−	9.37524i	1.75604	−	0.470530i	0.985899	+	0.167343i	$0.0535187\pi$
$398$	−8.97663	−	8.97663i	−0.449958	−	0.449958i
$399$		0			0
$400$	4.21622	−	2.43424i	0.210811	−	0.121712i
$401$	33.6403	+	9.01390i	1.67992	+	0.450133i	0.967758	−	0.251883i	$-0.0810498\pi$
$401$	33.6403	+	9.01390i	1.67992	+	0.450133i	0.712161	+	0.702016i	$0.247716\pi$
$402$		0			0
$403$	−14.5386	+	3.33743i	−0.724220	+	0.166249i
$404$			3.24579i			0.161484i
$405$		0			0
$406$	−5.37089	+	24.1225i	−0.266553	+	1.19718i
$407$	−8.82265	−	5.09376i	−0.437323	−	0.252488i
$408$		0			0
$409$	−2.97572	−	11.1055i	−0.147140	−	0.549134i	−0.999651	−	0.0264241i	$-0.991588\pi$
$409$	−2.97572	−	11.1055i	−0.147140	−	0.549134i	0.852511	−	0.522709i	$-0.175079\pi$
$410$	3.65528	+	13.6417i	0.180521	+	0.673715i
$411$		0			0
$412$	9.07672	+	5.24044i	0.447178	+	0.258178i
$413$	−0.529585	+	2.37854i	−0.0260592	+	0.117040i
$414$		0			0
$415$			5.00138i			0.245508i
$416$	14.8082	+	4.54751i	0.726034	+	0.222960i
$417$		0			0
$418$	1.59854	+	0.428328i	0.0781872	+	0.0209502i
$419$	25.3323	−	14.6256i	1.23756	−	0.714507i	0.268967	−	0.963149i	$-0.413318\pi$
$419$	25.3323	−	14.6256i	1.23756	−	0.714507i	0.968595	+	0.248642i	$0.0799844\pi$
$420$		0			0
$421$	−8.84750	−	8.84750i	−0.431201	−	0.431201i	0.457836	−	0.889037i	$-0.348625\pi$
$421$	−8.84750	−	8.84750i	−0.431201	−	0.431201i	−0.889037	+	0.457836i	$0.848625\pi$
$422$	−23.2467	+	6.22894i	−1.13163	+	0.303220i
$423$		0			0
$424$	−27.5792	+	27.5792i	−1.33936	+	1.33936i
$425$	−11.8615	−	6.84826i	−0.575369	−	0.332190i
$426$		0			0
$427$	21.5645	−	13.7105i	1.04358	−	0.663497i
$428$		−	2.95443i		−	0.142808i
$429$		0			0
$430$		−	15.1011i		−	0.728239i
$431$	3.91058	−	14.5945i	0.188366	−	0.702992i	−0.805519	−	0.592570i	$-0.798113\pi$
$431$	3.91058	−	14.5945i	0.188366	−	0.702992i	0.993885	−	0.110422i	$-0.0352201\pi$
$432$		0			0
$433$	−16.6099	+	28.7692i	−0.798222	+	1.38256i	0.122550	+	0.992462i	$0.460893\pi$
$433$	−16.6099	+	28.7692i	−0.798222	+	1.38256i	−0.920773	+	0.390100i	$0.872441\pi$
$434$	−11.8760	+	0.507674i	−0.570066	+	0.0243691i
$435$		0			0
$436$	−0.0187197	−	0.0698628i	−0.000896511	−	0.00334582i
$437$	−0.416676	−	0.416676i	−0.0199323	−	0.0199323i
$438$		0			0
$439$	3.12262	+	5.40854i	0.149035	+	0.258135i	0.930871	−	0.365348i	$-0.119050\pi$
$439$	3.12262	+	5.40854i	0.149035	+	0.258135i	−0.781836	+	0.623484i	$0.785717\pi$
$440$	1.15933	−	4.32668i	0.0552689	−	0.206266i
$441$		0			0
$442$	4.15304	+	18.0916i	0.197540	+	0.860530i
$443$	17.0915			0.812043			0.406022	−	0.913863i	$-0.366916\pi$
$443$	17.0915			0.812043			0.406022	+	0.913863i	$0.366916\pi$
$444$		0			0
$445$	7.84051	+	13.5802i	0.371676	+	0.643762i
$446$	−7.46751	+	12.9341i	−0.353597	+	0.612448i
$447$		0			0
$448$	18.8497	+	9.83440i	0.890566	+	0.464632i
$449$	9.60577	+	35.8492i	0.453324	+	1.69183i	0.692968	+	0.720968i	$0.256303\pi$
$449$	9.60577	+	35.8492i	0.453324	+	1.69183i	−0.239644	+	0.970861i	$0.577031\pi$
$450$		0			0
$451$	−7.80227	−	4.50464i	−0.367395	−	0.212115i
$452$	1.55322	−	0.896753i	0.0730574	−	0.0421797i
$453$		0			0
$454$	4.36456			0.204839
$455$	3.49911	−	13.4106i	0.164041	−	0.628700i
$456$		0			0
$457$	2.07001	−	7.72540i	0.0968312	−	0.361379i	−0.900460	−	0.434940i	$-0.856770\pi$
$457$	2.07001	−	7.72540i	0.0968312	−	0.361379i	0.997291	+	0.0735609i	$0.0234363\pi$
$458$	1.81245	−	1.04642i	0.0846902	−	0.0488959i
$459$		0			0
$460$	−0.328134	+	0.328134i	−0.0152993	+	0.0152993i
$461$	2.87961	+	10.7469i	0.134117	+	0.500531i	1.00000		0.000284720i	$9.06291e-5\pi$
$461$	2.87961	+	10.7469i	0.134117	+	0.500531i	−0.865883	+	0.500247i	$0.833243\pi$
$462$		0			0
$463$	24.2312	−	24.2312i	1.12612	−	1.12612i	0.135316	−	0.990803i	$-0.456795\pi$
$463$	24.2312	−	24.2312i	1.12612	−	1.12612i	0.990803	−	0.135316i	$-0.0432049\pi$
$464$	7.24702	−	12.5522i	0.336435	−	0.582722i
$465$		0			0
$466$	1.18546	+	0.317644i	0.0549156	+	0.0147146i
$467$	10.5574			0.488538			0.244269	−	0.969707i	$-0.421452\pi$
$467$	10.5574			0.488538			0.244269	+	0.969707i	$0.421452\pi$
$468$		0			0
$469$	12.9018	+	11.8439i	0.595748	+	0.546902i
$470$	−2.76583	+	10.3222i	−0.127578	+	0.476129i
$471$		0			0
$472$	1.41061	−	2.44325i	0.0649287	−	0.112460i
$473$	6.81176	+	6.81176i	0.313205	+	0.313205i
$474$		0			0
$475$	4.22539	−	1.13219i	0.193874	−	0.0519484i
$476$	−0.439630	−	10.2843i	−0.0201504	−	0.471378i
$477$		0			0
$478$	−4.82578	+	2.78616i	−0.220726	+	0.127436i
$479$	2.28082	−	8.51215i	0.104214	−	0.388930i	−0.894041	−	0.447985i	$-0.852142\pi$
$479$	2.28082	−	8.51215i	0.104214	−	0.388930i	0.998255	+	0.0590545i	$0.0188086\pi$
$480$		0			0
$481$	24.8560	+	26.7215i	1.13334	+	1.21839i
$482$			10.6444i			0.484838i
$483$		0			0
$484$	−4.09809	−	7.09810i	−0.186277	−	0.322641i
$485$	17.2926	+	9.98389i	0.785217	+	0.453345i
$486$		0			0
$487$	19.8298	−	5.31338i	0.898574	−	0.240772i	0.220170	−	0.975461i	$-0.429339\pi$
$487$	19.8298	−	5.31338i	0.898574	−	0.240772i	0.678404	+	0.734689i	$0.262672\pi$
$488$	−28.5774	+	7.65728i	−1.29364	+	0.346629i
$489$		0			0
$490$	4.68581	−	10.0011i	0.211683	−	0.451804i
$491$	2.72329	−	1.57229i	0.122900	−	0.0709565i	−0.437290	−	0.899321i	$-0.644062\pi$
$491$	2.72329	−	1.57229i	0.122900	−	0.0709565i	0.560190	+	0.828364i	$0.310728\pi$
$492$		0			0
$493$	−40.7762			−1.83647
$494$	−5.02369	−	3.14786i	−0.226026	−	0.141629i
$495$		0			0
$496$	6.73398	+	1.80436i	0.302364	+	0.0810183i
$497$	−1.52787	+	6.86219i	−0.0685345	+	0.307811i
$498$		0			0
$499$	−10.7019	−	10.7019i	−0.479082	−	0.479082i	0.425756	−	0.904838i	$-0.360008\pi$
$499$	−10.7019	−	10.7019i	−0.479082	−	0.479082i	−0.904838	+	0.425756i	$0.860008\pi$
$500$	−2.43463	−	9.08617i	−0.108880	−	0.406346i
$501$		0			0
$502$	−21.7804	−	21.7804i	−0.972107	−	0.972107i
$503$	−22.4889	−	12.9840i	−1.00273	−	0.578926i	−0.0936745	−	0.995603i	$-0.529861\pi$
$503$	−22.4889	−	12.9840i	−1.00273	−	0.578926i	−0.909055	+	0.416677i	$0.863195\pi$
$504$		0			0
$505$	−5.55031	−	1.48720i	−0.246985	−	0.0661795i
$506$			0.425387i			0.0189108i
$507$		0			0
$508$	−11.7192			−0.519955
$509$	31.8249	+	8.52745i	1.41061	+	0.377973i	0.882144	−	0.470980i	$-0.156100\pi$
$509$	31.8249	+	8.52745i	1.41061	+	0.377973i	0.528469	+	0.848952i	$0.322766\pi$
$510$		0			0
$511$	−8.80225	+	2.76652i	−0.389389	+	0.122384i
$512$	−12.4191	−	12.4191i	−0.548851	−	0.548851i
$513$		0			0
$514$	6.96683	−	1.86676i	0.307294	−	0.0823391i
$515$	−13.1201	+	13.1201i	−0.578139	+	0.578139i
$516$		0			0
$517$	−3.40852	−	5.90373i	−0.149907	−	0.259646i
$518$	15.6033	+	24.5416i	0.685568	+	1.07829i
$519$		0			0
$520$	−8.52012	+	13.5973i	−0.373632	+	0.596282i
$521$			26.4544i			1.15899i	0.814976	+	0.579495i	$0.196750\pi$
$521$			26.4544i			1.15899i	−0.814976	+	0.579495i	$0.803250\pi$
$522$		0			0
$523$	−9.23888	+	5.33407i	−0.403988	+	0.233243i	−0.688203	−	0.725518i	$-0.741600\pi$
$523$	−9.23888	+	5.33407i	−0.403988	+	0.233243i	0.284215	+	0.958761i	$0.408267\pi$
$524$	7.34057	−	12.7142i	0.320674	−	0.555424i
$525$		0			0
$526$	13.1062	−	3.51179i	0.571456	−	0.153121i
$527$	−5.07623	−	18.9448i	−0.221124	−	0.825247i
$528$		0			0
$529$	−11.4243	+	19.7874i	−0.496707	+	0.860322i
$530$	−10.0448	−	17.3981i	−0.436318	−	0.755726i
$531$		0			0
$532$	2.42186	+	2.22329i	0.105001	+	0.0963919i
$533$	21.9813	+	23.6310i	0.952116	+	1.02357i
$534$		0			0
$535$	5.05207	+	1.35370i	0.218420	+	0.0585255i
$536$	−10.1385	−	17.5603i	−0.437915	−	0.758490i
$537$		0			0
$538$	−6.45273	+	6.45273i	−0.278197	+	0.278197i
$539$	2.39762	+	6.62494i	0.103273	+	0.285357i
$540$		0			0
$541$	3.42225	−	3.42225i	0.147134	−	0.147134i	−0.629702	−	0.776836i	$-0.716823\pi$
$541$	3.42225	−	3.42225i	0.147134	−	0.147134i	0.776836	+	0.629702i	$0.216823\pi$
$542$	−0.341476	−	0.197151i	−0.0146677	−	0.00846838i
$543$		0			0
$544$	−5.27157	+	19.6738i	−0.226017	+	0.843506i
$545$	0.128043			0.00548475
$546$		0			0
$547$	−19.6406			−0.839770			−0.419885	−	0.907577i	$-0.637930\pi$
$547$	−19.6406			−0.839770			−0.419885	+	0.907577i	$0.637930\pi$
$548$	−0.537540	+	2.00613i	−0.0229626	+	0.0856975i
$549$		0			0
$550$	−2.73479	−	1.57893i	−0.116612	−	0.0673259i
$551$	9.20882	−	9.20882i	0.392309	−	0.392309i
$552$		0			0
$553$	−8.64661	+	16.5731i	−0.367691	+	0.704759i
$554$	11.9925	−	11.9925i	0.509514	−	0.509514i
$555$		0			0
$556$	4.19968	+	7.27406i	0.178106	+	0.308489i
$557$	34.1973	+	9.16315i	1.44899	+	0.388255i	0.895672	−	0.444716i	$-0.146695\pi$
$557$	34.1973	+	9.16315i	1.44899	+	0.388255i	0.553316	+	0.832971i	$0.313362\pi$
$558$		0			0
$559$	−16.1631	−	30.4900i	−0.683627	−	1.28959i
$560$	−4.38045	+	4.77169i	−0.185108	+	0.201641i
$561$		0			0
$562$	−0.651705	−	1.12879i	−0.0274905	−	0.0476149i
$563$	−15.9428	+	27.6137i	−0.671908	+	1.16378i	0.305455	+	0.952207i	$0.401192\pi$
$563$	−15.9428	+	27.6137i	−0.671908	+	1.16378i	−0.977362	+	0.211572i	$0.932142\pi$
$564$		0			0
$565$	0.821772	+	3.06689i	0.0345722	+	0.129025i
$566$	25.1168	−	6.73003i	1.05574	−	0.282884i
$567$		0			0
$568$	4.06967	−	7.04888i	0.170760	−	0.295764i
$569$	−23.6253	+	13.6401i	−0.990426	+	0.571823i	−0.905402	−	0.424556i	$-0.860430\pi$
$569$	−23.6253	+	13.6401i	−0.990426	+	0.571823i	−0.0850245	+	0.996379i	$0.527097\pi$
$570$		0			0
$571$		−	33.0144i		−	1.38161i	−0.723042	−	0.690804i	$-0.757257\pi$
$571$		−	33.0144i		−	1.38161i	0.723042	−	0.690804i	$-0.242743\pi$
$572$	−0.666344	−	2.90275i	−0.0278612	−	0.121370i
$573$		0			0
$574$	13.7987	+	21.7032i	0.575946	+	0.905874i
$575$	0.562208	+	0.973772i	0.0234457	+	0.0406091i
$576$		0			0
$577$	−18.3031	+	18.3031i	−0.761967	+	0.761967i	−0.976678	−	0.214711i	$-0.931119\pi$
$577$	−18.3031	+	18.3031i	−0.761967	+	0.761967i	0.214711	+	0.976678i	$0.431119\pi$
$578$	−5.74226	+	1.53863i	−0.238847	+	0.0639988i
$579$		0			0
$580$	−7.25199	−	7.25199i	−0.301123	−	0.301123i
$581$	2.73082	+	8.68866i	0.113294	+	0.360467i
$582$		0			0
$583$	12.3789	+	3.31691i	0.512681	+	0.137373i
$584$	10.6824			0.442042
$585$		0			0
$586$		−	20.9678i		−	0.866174i
$587$	−30.3048	−	8.12014i	−1.25081	−	0.335154i	−0.428162	−	0.903702i	$-0.640839\pi$
$587$	−30.3048	−	8.12014i	−1.25081	−	0.335154i	−0.822650	+	0.568548i	$0.807505\pi$
$588$		0			0
$589$	5.42485	+	3.13204i	0.223527	+	0.129053i
$590$	1.02754	+	1.02754i	0.0423031	+	0.0423031i
$591$		0			0
$592$	−4.41447	−	16.4750i	−0.181434	−	0.677120i
$593$	14.5568	+	14.5568i	0.597777	+	0.597777i	0.939721	−	0.341943i	$-0.111085\pi$
$593$	14.5568	+	14.5568i	0.597777	+	0.597777i	−0.341943	+	0.939721i	$0.611085\pi$
$594$		0			0
$595$	17.7875	+	3.96041i	0.729217	+	0.162361i
$596$	−6.68512	−	1.79127i	−0.273833	−	0.0733733i
$597$		0			0
$598$	0.447349	−	1.45672i	0.0182934	−	0.0595696i
$599$	−17.9695			−0.734214			−0.367107	−	0.930179i	$-0.619652\pi$
$599$	−17.9695			−0.734214			−0.367107	+	0.930179i	$0.619652\pi$
$600$		0			0
$601$	−15.4598	+	8.92570i	−0.630617	+	0.364087i	−0.780991	−	0.624542i	$-0.785286\pi$
$601$	−15.4598	+	8.92570i	−0.630617	+	0.364087i	0.150374	+	0.988629i	$0.451952\pi$
$602$	−8.24539	−	26.2344i	−0.336057	−	1.06923i
$603$		0			0
$604$	−0.508609	+	0.136281i	−0.0206950	+	0.00554521i
$605$	14.0155	−	3.75543i	0.569810	−	0.152680i
$606$		0			0
$607$	22.2125	+	12.8244i	0.901578	+	0.520526i	0.877712	−	0.479189i	$-0.159069\pi$
$607$	22.2125	+	12.8244i	0.901578	+	0.520526i	0.0238664	+	0.999715i	$0.492402\pi$
$608$	−3.25256	−	5.63361i	−0.131909	−	0.228473i
$609$		0			0
$610$		−	15.2389i		−	0.617005i
$611$	5.46380	+	23.8015i	0.221042	+	0.962907i
$612$		0			0
$613$	0.916231	−	3.41942i	0.0370062	−	0.138109i	−0.944951	−	0.327211i	$-0.893891\pi$
$613$	0.916231	−	3.41942i	0.0370062	−	0.138109i	0.981957	+	0.189102i	$0.0605578\pi$
$614$	22.8687	−	13.2032i	0.922905	−	0.532839i
$615$		0			0
$616$	−0.348376	−	8.14954i	−0.0140365	−	0.328354i
$617$	5.87829	−	1.57508i	0.236651	−	0.0634105i	−0.138544	−	0.990356i	$-0.544242\pi$
$617$	5.87829	−	1.57508i	0.236651	−	0.0634105i	0.375195	+	0.926946i	$0.377576\pi$
$618$		0			0
$619$	−34.1674	−	34.1674i	−1.37331	−	1.37331i	−0.855496	−	0.517810i	$-0.826747\pi$
$619$	−34.1674	−	34.1674i	−1.37331	−	1.37331i	−0.517810	−	0.855496i	$-0.673253\pi$
$620$	2.46650	−	4.27210i	0.0990569	−	0.171572i
$621$		0			0
$622$	−3.95289	+	14.7524i	−0.158496	+	0.591517i
$623$	21.0359	+	19.3112i	0.842786	+	0.773685i
$624$		0			0
$625$	2.20722			0.0882889
$626$	19.7270	+	5.28584i	0.788451	+	0.211265i
$627$		0			0
$628$	−3.32596	+	5.76073i	−0.132720	+	0.229878i
$629$	−33.9301	+	33.9301i	−1.35288	+	1.35288i
$630$		0			0
$631$	2.80135	+	10.4548i	0.111520	+	0.416199i	0.999003	−	0.0446417i	$-0.0142146\pi$
$631$	2.80135	+	10.4548i	0.111520	+	0.416199i	−0.887483	+	0.460841i	$0.847548\pi$
$632$	15.3033	−	15.3033i	0.608734	−	0.608734i
$633$		0			0
$634$	2.22390	−	1.28397i	0.0883222	−	0.0509928i
$635$	5.36966	−	20.0398i	0.213088	−	0.795257i
$636$		0			0
$637$	−1.24355	−	25.2082i	−0.0492714	−	0.998785i
$638$	−9.40135			−0.372203
$639$		0			0
$640$	0.168516	−	0.0972930i	0.00666120	−	0.00384584i
$641$	−26.3470	−	15.2114i	−1.04064	−	0.600815i	−0.120627	−	0.992698i	$-0.538490\pi$
$641$	−26.3470	−	15.2114i	−1.04064	−	0.600815i	−0.920015	+	0.391883i	$0.871824\pi$
$642$		0			0
$643$	−5.55469	−	20.7304i	−0.219056	−	0.817527i	−0.984699	−	0.174262i	$-0.944246\pi$
$643$	−5.55469	−	20.7304i	−0.219056	−	0.817527i	0.765644	−	0.643265i	$-0.222421\pi$
$644$	−0.390886	+	0.749218i	−0.0154031	+	0.0295233i
$645$		0			0
$646$	3.89746	−	6.75060i	0.153344	−	0.265599i
$647$	−3.76958	−	6.52911i	−0.148198	−	0.256686i	0.782364	−	0.622822i	$-0.214014\pi$
$647$	−3.76958	−	6.52911i	−0.148198	−	0.256686i	−0.930561	+	0.366136i	$0.880681\pi$
$648$		0			0
$649$	−0.927000			−0.0363879
$650$	7.70471	+	8.28296i	0.302204	+	0.324884i
$651$		0			0
$652$	−2.91775	+	10.8892i	−0.114268	+	0.426454i
$653$	11.4217	+	19.7830i	0.446966	+	0.774167i	0.998187	−	0.0601918i	$-0.0191712\pi$
$653$	11.4217	+	19.7830i	0.446966	+	0.774167i	−0.551221	+	0.834359i	$0.685838\pi$
$654$		0			0
$655$	18.3779	+	18.3779i	0.718086	+	0.718086i
$656$	−3.90392	−	14.5696i	−0.152422	−	0.568848i
$657$		0			0
$658$	0.831126	+	19.4425i	0.0324007	+	0.757947i
$659$	−13.0916	+	22.6753i	−0.509975	+	0.883303i	0.489958	+	0.871746i	$0.337012\pi$
$659$	−13.0916	+	22.6753i	−0.509975	+	0.883303i	−0.999933	+	0.0115568i	$0.996321\pi$
$660$		0			0
$661$	4.50623	−	16.8175i	0.175272	−	0.654124i	−0.821233	−	0.570593i	$-0.806713\pi$
$661$	4.50623	−	16.8175i	0.175272	−	0.654124i	0.996505	−	0.0835312i	$-0.0266198\pi$
$662$			37.3584i			1.45197i
$663$		0			0
$664$		−	10.5446i		−	0.409209i
$665$	−4.91151	+	3.12269i	−0.190460	+	0.121093i
$666$		0			0
$667$	2.89904	+	1.67376i	0.112251	+	0.0648083i
$668$	12.8972	−	12.8972i	0.499008	−	0.499008i
$669$		0			0
$670$	10.0884	−	2.70317i	0.389748	−	0.104433i
$671$	6.87393	+	6.87393i	0.265365	+	0.265365i
$672$		0			0
$673$	13.2813	−	7.66796i	0.511957	−	0.295578i	−0.221681	−	0.975119i	$-0.571154\pi$
$673$	13.2813	−	7.66796i	0.511957	−	0.295578i	0.733638	+	0.679541i	$0.237821\pi$
$674$	3.60596	+	0.966213i	0.138896	+	0.0372172i
$675$		0			0
$676$	−0.770743	+	10.6411i	−0.0296440	+	0.409271i
$677$		−	4.31369i		−	0.165789i	−0.996558	−	0.0828943i	$-0.973584\pi$
$677$		−	4.31369i		−	0.165789i	0.996558	−	0.0828943i	$-0.0264164\pi$
$678$		0			0
$679$	35.4930	+	7.90254i	1.36210	+	0.303272i
$680$	−18.2714	−	10.5490i	−0.700678	−	0.404537i
$681$		0			0
$682$	−1.17037	−	4.36789i	−0.0448159	−	0.167255i
$683$	2.11067	+	7.87714i	0.0807627	+	0.301410i	0.994478	−	0.104944i	$-0.0334664\pi$
$683$	2.11067	+	7.87714i	0.0807627	+	0.301410i	−0.913715	+	0.406355i	$0.866800\pi$
$684$		0			0
$685$	−3.18418	−	1.83839i	−0.121661	−	0.0702412i
$686$	2.67969	−	19.9330i	0.102311	−	0.761045i
$687$		0			0
$688$			16.1283i			0.614886i
$689$	−38.9028	−	24.3766i	−1.48208	−	0.928674i
$690$		0			0
$691$	8.79665	+	2.35706i	0.334640	+	0.0896666i	0.422227	−	0.906490i	$-0.361249\pi$
$691$	8.79665	+	2.35706i	0.334640	+	0.0896666i	−0.0875862	+	0.996157i	$0.527915\pi$
$692$	−9.00827	+	5.20093i	−0.342443	+	0.197710i
$693$		0			0
$694$	−14.5393	−	14.5393i	−0.551905	−	0.551905i
$695$	−14.3629	+	3.84853i	−0.544816	+	0.145983i
$696$		0			0
$697$	−30.0059	+	30.0059i	−1.13656	+	1.13656i
$698$	−30.6831	−	17.7149i	−1.16137	−	0.670518i
$699$		0			0
$700$	−3.36581	−	5.29390i	−0.127216	−	0.200091i
$701$		−	42.0549i		−	1.58839i	−0.607663	−	0.794195i	$-0.707893\pi$
$701$		−	42.0549i		−	1.58839i	0.607663	−	0.794195i	$-0.292107\pi$
$702$		0			0
$703$		−	15.3254i		−	0.578009i
$704$	−2.09335	+	7.81247i	−0.0788959	+	0.294444i
$705$		0			0
$706$	−17.8582	+	30.9312i	−0.672101	+	1.16411i
$707$	−10.4543	+	0.446900i	−0.393175	+	0.0168074i
$708$		0			0
$709$	4.70279	+	17.5510i	0.176617	+	0.659143i	0.996271	+	0.0862837i	$0.0274991\pi$
$709$	4.70279	+	17.5510i	0.176617	+	0.659143i	−0.819654	+	0.572859i	$0.805834\pi$
$710$	2.96449	+	2.96449i	0.111255	+	0.111255i
$711$		0			0
$712$	−16.5304	−	28.6315i	−0.619504	−	1.07301i
$713$	−0.416733	+	1.55527i	−0.0156068	+	0.0582453i
$714$		0			0
$715$	5.26901	+	0.190570i	0.197050	+	0.00712693i
$716$	−8.99175			−0.336038
$717$		0			0
$718$	−1.11470	−	1.93072i	−0.0416003	−	0.0720538i
$719$	−22.3307	+	38.6778i	−0.832793	+	1.44244i	0.0630222	+	0.998012i	$0.479926\pi$
$719$	−22.3307	+	38.6778i	−0.832793	+	1.44244i	−0.895815	+	0.444427i	$0.853407\pi$
$720$		0			0
$721$	−15.6291	+	29.9566i	−0.582059	+	1.11564i
$722$	−4.69594	−	17.5255i	−0.174765	−	0.652231i
$723$		0			0
$724$	3.11583	+	1.79892i	0.115799	+	0.0668565i
$725$	−21.5210	+	12.4252i	−0.799271	+	0.461459i
$726$		0			0
$727$	−21.6855			−0.804272			−0.402136	−	0.915580i	$-0.631732\pi$
$727$	−21.6855			−0.804272			−0.402136	+	0.915580i	$0.631732\pi$
$728$	−7.37728	+	28.2741i	−0.273420	+	1.04791i
$729$		0			0
$730$	−1.42410	+	5.31483i	−0.0527085	+	0.196711i
$731$	39.2949	−	22.6869i	1.45338	−	0.839107i
$732$		0			0
$733$	−36.4440	+	36.4440i	−1.34609	+	1.34609i	−0.456223	+	0.889865i	$0.650798\pi$
$733$	−36.4440	+	36.4440i	−1.34609	+	1.34609i	−0.889865	+	0.456223i	$0.849202\pi$
$734$	−0.130093	−	0.485514i	−0.00480183	−	0.0179207i
$735$		0			0
$736$	1.18235	−	1.18235i	0.0435819	−	0.0435819i
$737$	−3.33130	+	5.76998i	−0.122710	+	0.212540i
$738$		0			0
$739$	−6.28312	−	1.68356i	−0.231128	−	0.0619307i	0.141396	−	0.989953i	$-0.454841\pi$
$739$	−6.28312	−	1.68356i	−0.231128	−	0.0619307i	−0.372524	+	0.928022i	$0.621508\pi$
$740$	−12.0688			−0.443659
$741$		0			0
$742$	−26.9500	−	24.7403i	−0.989364	−	0.908246i
$743$	−6.75798	+	25.2211i	−0.247926	+	0.925273i	0.723964	+	0.689838i	$0.242318\pi$
$743$	−6.75798	+	25.2211i	−0.247926	+	0.925273i	−0.971890	+	0.235435i	$0.924348\pi$
$744$		0			0
$745$	6.12615	−	10.6108i	0.224445	−	0.388750i
$746$	−7.94705	−	7.94705i	−0.290962	−	0.290962i
$747$		0			0
$748$	3.78247	−	1.01351i	0.138301	−	0.0370576i
$749$	9.51586	−	0.406783i	0.347702	−	0.0148635i
$750$		0			0
$751$	31.8018	−	18.3608i	1.16046	−	0.669993i	0.209048	−	0.977905i	$-0.432964\pi$
$751$	31.8018	−	18.3608i	1.16046	−	0.669993i	0.951415	+	0.307912i	$0.0996303\pi$
$752$	2.95397	−	11.0244i	0.107720	−	0.402017i
$753$		0			0
$754$	32.1945	+	9.88671i	1.17245	+	0.360053i
$755$		−	0.932165i		−	0.0339250i
$756$		0			0
$757$	25.3385	+	43.8875i	0.920943	+	1.59512i	0.797959	+	0.602711i	$0.205913\pi$
$757$	25.3385	+	43.8875i	0.920943	+	1.59512i	0.122984	+	0.992409i	$0.460754\pi$
$758$	−14.5062	−	8.37517i	−0.526890	−	0.304200i
$759$		0			0
$760$	6.50876	−	1.74402i	0.236097	−	0.0632621i
$761$	−25.8358	+	6.92269i	−0.936548	+	0.250947i	−0.694645	−	0.719353i	$-0.744438\pi$
$761$	−25.8358	+	6.92269i	−0.936548	+	0.250947i	−0.241903	+	0.970300i	$0.577772\pi$
$762$		0			0
$763$	0.222443	−	0.0699131i	0.00805296	−	0.00253102i
$764$	7.00085	−	4.04194i	0.253282	−	0.146232i
$765$		0			0
$766$	35.2576			1.27391
$767$	3.17447	+	0.974858i	0.114623	+	0.0352001i
$768$		0			0
$769$	−22.6180	−	6.06047i	−0.815626	−	0.218546i	−0.173193	−	0.984888i	$-0.555408\pi$
$769$	−22.6180	−	6.06047i	−0.815626	−	0.218546i	−0.642433	+	0.766342i	$0.722075\pi$
$770$	4.10108	+	0.913110i	0.147793	+	0.0329062i
$771$		0			0
$772$	7.38208	+	7.38208i	0.265687	+	0.265687i
$773$	−3.07578	−	11.4790i	−0.110628	−	0.412869i	0.888295	−	0.459274i	$-0.151890\pi$
$773$	−3.07578	−	11.4790i	−0.110628	−	0.412869i	−0.998923	+	0.0464045i	$0.985224\pi$
$774$		0			0
$775$	−8.45192	−	8.45192i	−0.303602	−	0.303602i
$776$	−36.4586	−	21.0494i	−1.30879	−	0.755628i
$777$		0			0
$778$	−39.2131	−	10.5071i	−1.40586	−	0.376699i
$779$		−	13.5530i		−	0.485585i
$780$		0			0
$781$	−2.67443			−0.0956986
$782$	1.93535	+	0.518576i	0.0692080	+	0.0185442i
$783$		0			0
$784$	−5.00455	+	10.6814i	−0.178734	+	0.381479i
$785$	−8.32692	−	8.32692i	−0.297201	−	0.297201i
$786$		0			0
$787$	1.37868	−	0.369415i	0.0491445	−	0.0131682i	−0.234163	−	0.972197i	$-0.575235\pi$
$787$	1.37868	−	0.369415i	0.0491445	−	0.0131682i	0.283308	+	0.959029i	$0.408568\pi$
$788$	0.905941	−	0.905941i	0.0322728	−	0.0322728i
$789$		0			0
$790$	5.57374	+	9.65400i	0.198305	+	0.343474i
$791$	3.10219	+	4.87927i	0.110301	+	0.173487i
$792$		0			0
$793$	−16.3106	−	30.7683i	−0.579208	−	1.09261i
$794$		−	39.3369i		−	1.39602i
$795$		0			0
$796$	8.30849	−	4.79691i	0.294487	−	0.170022i
$797$	15.8960	−	27.5327i	0.563065	−	0.975258i	−0.434161	−	0.900835i	$-0.642955\pi$
$797$	15.8960	−	27.5327i	0.563065	−	0.975258i	0.997227	−	0.0744227i	$-0.0237114\pi$
$798$		0			0
$799$	−31.0150	+	8.31044i	−1.09723	+	0.294002i
$800$	3.21266	+	11.9898i	0.113585	+	0.423904i
$801$		0			0
$802$	18.9104	−	32.7538i	0.667750	−	1.15658i
$803$	−1.75502	−	3.03978i	−0.0619333	−	0.107272i
$804$		0			0
$805$	−1.10206	−	1.01170i	−0.0388426	−	0.0356578i
$806$	−0.585506	+	16.1884i	−0.0206236	+	0.570213i
$807$		0			0
$808$	11.7019	+	3.13551i	0.411671	+	0.110307i
$809$	−7.21908	−	12.5038i	−0.253809	−	0.439611i	0.710762	−	0.703432i	$-0.248350\pi$
$809$	−7.21908	−	12.5038i	−0.253809	−	0.439611i	−0.964571	+	0.263822i	$0.915017\pi$
$810$		0			0
$811$	16.5212	−	16.5212i	0.580138	−	0.580138i	−0.354803	−	0.934941i	$-0.615452\pi$
$811$	16.5212	−	16.5212i	0.580138	−	0.580138i	0.934941	+	0.354803i	$0.115452\pi$
$812$	−16.5582	−	8.63886i	−0.581080	−	0.303164i
$813$		0			0
$814$	−7.82291	+	7.82291i	−0.274193	+	0.274193i
$815$	−17.2836	−	9.97871i	−0.605419	−	0.349539i
$816$		0			0
$817$	−3.75072	+	13.9979i	−0.131221	+	0.489723i
$818$	−12.4856			−0.436550
$819$		0			0
$820$	−10.6730			−0.372718
$821$	7.38477	−	27.5603i	0.257730	−	0.961862i	−0.708821	−	0.705388i	$-0.750773\pi$
$821$	7.38477	−	27.5603i	0.257730	−	0.961862i	0.966551	−	0.256474i	$-0.0825607\pi$
$822$		0			0
$823$	0.0527072	+	0.0304305i	0.00183726	+	0.00106074i	0.500918	−	0.865495i	$-0.332996\pi$
$823$	0.0527072	+	0.0304305i	0.00183726	+	0.00106074i	−0.499081	+	0.866555i	$0.666329\pi$
$824$	27.6614	−	27.6614i	0.963632	−	0.963632i
$825$		0			0
$826$	2.34614	+	1.22404i	0.0816328	+	0.0425900i
$827$	37.2665	−	37.2665i	1.29588	−	1.29588i	0.364798	−	0.931087i	$-0.381138\pi$
$827$	37.2665	−	37.2665i	1.29588	−	1.29588i	0.931087	−	0.364798i	$-0.118862\pi$
$828$		0			0
$829$	2.17299	+	3.76373i	0.0754711	+	0.130720i	0.901291	−	0.433214i	$-0.142621\pi$
$829$	2.17299	+	3.76373i	0.0754711	+	0.130720i	−0.825820	+	0.563934i	$0.809287\pi$
$830$	5.24624	+	1.40573i	0.182100	+	0.0487935i
$831$		0			0
$832$	15.3844	−	24.5520i	0.533357	−	0.851188i
$833$	33.0638	−	2.83200i	1.14559	−	0.0981228i
$834$		0			0
$835$	16.1448	+	27.9636i	0.558714	+	0.967722i
$836$	−0.625336	+	1.08311i	−0.0216277	+	0.0374603i
$837$		0			0
$838$	−8.22156	−	30.6833i	−0.284009	−	1.05994i
$839$	−46.4621	+	12.4495i	−1.60405	+	0.429804i	−0.946263	−	0.323399i	$-0.895174\pi$
$839$	−46.4621	+	12.4495i	−1.60405	+	0.429804i	−0.657788	+	0.753203i	$0.728508\pi$
$840$		0			0
$841$	−22.4912	+	38.9560i	−0.775560	+	1.34331i
$842$	−11.7674	+	6.79392i	−0.405532	+	0.234134i
$843$		0			0
$844$		−	18.1879i		−	0.626052i
$845$	−17.8431	−	6.19363i	−0.613820	−	0.213067i
$846$		0			0
$847$	22.2979	−	14.1768i	0.766165	−	0.487120i
$848$	10.7281	+	18.5816i	0.368404	+	0.638094i
$849$		0			0
$850$	−10.5174	+	10.5174i	−0.360745	+	0.360745i
$851$	3.80505	−	1.01956i	0.130435	−	0.0349500i
$852$		0			0
$853$	3.74166	+	3.74166i	0.128112	+	0.128112i	0.768255	−	0.640143i	$-0.221125\pi$
$853$	3.74166	+	3.74166i	0.128112	+	0.128112i	−0.640143	+	0.768255i	$0.721125\pi$
$854$	−8.32064	−	26.4738i	−0.284727	−	0.905915i
$855$		0			0
$856$	−10.6514	−	2.85405i	−0.364059	−	0.0975493i
$857$	−10.1411			−0.346413			−0.173207	−	0.984885i	$-0.555413\pi$
$857$	−10.1411			−0.346413			−0.173207	+	0.984885i	$0.555413\pi$
$858$		0			0
$859$			32.3015i			1.10211i	0.834468	+	0.551056i	$0.185775\pi$
$859$			32.3015i			1.10211i	−0.834468	+	0.551056i	$0.814225\pi$
$860$	11.0234	+	2.95371i	0.375894	+	0.100721i
$861$		0			0
$862$	−14.2099	−	8.20407i	−0.483990	−	0.279432i
$863$	−30.9883	−	30.9883i	−1.05486	−	1.05486i	−0.998405	−	0.0564495i	$-0.982022\pi$
$863$	−30.9883	−	30.9883i	−1.05486	−	1.05486i	−0.0564495	−	0.998405i	$-0.517978\pi$
$864$		0			0
$865$	−4.76606	−	17.7872i	−0.162051	−	0.604782i
$866$	25.5092	+	25.5092i	0.866839	+	0.866839i
$867$		0			0
$868$	1.95230	−	8.76845i	0.0662655	−	0.297621i
$869$	−6.86889	−	1.84051i	−0.233011	−	0.0624352i
$870$		0			0
$871$	17.4757	−	16.2557i	0.592143	−	0.550804i
$872$	−0.269957			−0.00914189
$873$		0			0
$874$	−0.554190	+	0.319962i	−0.0187458	+	0.0108229i
$875$	28.9303	−	9.09271i	0.978022	−	0.307390i
$876$		0			0
$877$	−17.0303	+	4.56327i	−0.575074	+	0.154091i	−0.534623	−	0.845091i	$-0.679546\pi$
$877$	−17.0303	+	4.56327i	−0.575074	+	0.154091i	−0.0404512	+	0.999182i	$0.512880\pi$
$878$	6.55100	−	1.75533i	0.221086	−	0.0592397i
$879$		0			0
$880$	−2.13401	−	1.23207i	−0.0719376	−	0.0415332i
$881$	−2.42023	−	4.19196i	−0.0815396	−	0.141231i	0.822372	−	0.568950i	$-0.192650\pi$
$881$	−2.42023	−	4.19196i	−0.0815396	−	0.141231i	−0.903911	+	0.427720i	$0.859317\pi$
$882$		0			0
$883$		−	23.3796i		−	0.786785i	−0.919371	−	0.393393i	$-0.871301\pi$
$883$		−	23.3796i		−	0.786785i	0.919371	−	0.393393i	$-0.128699\pi$
$884$	−14.0187	−	0.507031i	−0.471500	−	0.0170533i
$885$		0			0
$886$	4.80387	−	17.9283i	0.161389	−	0.602313i
$887$	43.5357	−	25.1353i	1.46178	−	0.843962i	0.462690	−	0.886520i	$-0.346884\pi$
$887$	43.5357	−	25.1353i	1.46178	−	0.843962i	0.999094	+	0.0425584i	$0.0135509\pi$
$888$		0			0
$889$	−1.61357	−	37.7462i	−0.0541174	−	1.26597i
$890$	16.4487	−	4.40743i	0.551363	−	0.147737i
$891$		0			0
$892$	−7.98094	−	7.98094i	−0.267222	−	0.267222i
$893$	5.12755	−	8.88117i	0.171587	−	0.297197i
$894$		0			0
$895$	4.11996	−	15.3759i	0.137715	−	0.513960i
$896$	0.239632	−	0.261035i	0.00800555	−	0.00872056i
$897$		0			0
$898$	40.3042			1.34497
$899$	−34.3725	−	9.21008i	−1.14639	−	0.307173i
$900$		0			0
$901$	30.1814	−	52.2757i	1.00549	−	1.74156i
$902$	−6.91815	+	6.91815i	−0.230349	+	0.230349i
$903$		0			0
$904$	−1.73257	−	6.46604i	−0.0576244	−	0.215057i
$905$	−4.50381	+	4.50381i	−0.149712	+	0.149712i
$906$		0			0
$907$	−31.7089	+	18.3071i	−1.05288	+	0.607878i	−0.923453	−	0.383712i	$-0.874646\pi$
$907$	−31.7089	+	18.3071i	−1.05288	+	0.607878i	−0.129422	+	0.991590i	$0.541312\pi$
$908$	−0.853689	+	3.18601i	−0.0283307	+	0.105732i
$909$		0			0
$910$	−13.0837	−	7.43971i	−0.433721	−	0.246624i
$911$	−40.8424			−1.35317			−0.676585	−	0.736365i	$-0.736541\pi$
$911$	−40.8424			−1.35317			−0.676585	+	0.736365i	$0.736541\pi$
$912$		0			0
$913$	−3.00056	+	1.73237i	−0.0993039	+	0.0573331i
$914$	−7.52181	−	4.34272i	−0.248799	−	0.143644i
$915$		0			0
$916$	0.409350	+	1.52772i	0.0135253	+	0.0504771i
$917$	41.9617	+	21.8925i	1.38570	+	0.722955i
$918$		0			0
$919$	12.1413	−	21.0293i	0.400504	−	0.693693i	−0.593283	−	0.804994i	$-0.702168\pi$
$919$	12.1413	−	21.0293i	0.400504	−	0.693693i	0.993787	+	0.111301i	$0.0355018\pi$
$920$	0.866021	+	1.49999i	0.0285519	+	0.0494533i
$921$		0			0
$922$	12.0824			0.397912
$923$	9.15845	+	2.81250i	0.301454	+	0.0925746i
$924$		0			0
$925$	−7.56871	+	28.2468i	−0.248858	+	0.928749i
$926$	−18.6069	−	32.2281i	−0.611461	−	1.05908i
$927$		0			0
$928$	26.1307	+	26.1307i	0.857781	+	0.857781i
$929$	−0.812091	−	3.03077i	−0.0266438	−	0.0994362i	0.951324	−	0.308194i	$-0.0997246\pi$
$929$	−0.812091	−	3.03077i	−0.0266438	−	0.0994362i	−0.977967	+	0.208758i	$0.933058\pi$
$930$		0			0
$931$	−6.82750	+	8.10665i	−0.223762	+	0.265685i
$932$	−0.463744	+	0.803228i	−0.0151904	+	0.0263106i
$933$		0			0
$934$	2.96734	−	11.0743i	0.0970944	−	0.362361i
$935$			6.93241i			0.226714i
$936$		0			0
$937$			39.6319i			1.29472i	0.762185	+	0.647359i	$0.224126\pi$
$937$			39.6319i			1.29472i	−0.762185	+	0.647359i	$0.775874\pi$
$938$	16.0501	−	10.2045i	0.524053	−	0.333188i
$939$		0			0
$940$	−6.99397	−	4.03797i	−0.228118	−	0.131704i
$941$	−9.63423	+	9.63423i	−0.314067	+	0.314067i	−0.846483	−	0.532416i	$-0.821284\pi$
$941$	−9.63423	+	9.63423i	−0.314067	+	0.314067i	0.532416	+	0.846483i	$0.321284\pi$
$942$		0			0
$943$	3.36498	−	0.901643i	0.109579	−	0.0293615i
$944$	−1.09743	−	1.09743i	−0.0357185	−	0.0357185i
$945$		0			0
$946$	9.05982	−	5.23069i	0.294560	−	0.170064i
$947$	−51.2831	−	13.7413i	−1.66648	−	0.446531i	−0.702319	−	0.711862i	$-0.747852\pi$
$947$	−51.2831	−	13.7413i	−1.66648	−	0.446531i	−0.964157	+	0.265331i	$0.914519\pi$
$948$		0			0
$949$	2.81326	+	12.2552i	0.0913224	+	0.397821i
$950$		−	4.75047i		−	0.154126i
$951$		0			0
$952$	−37.5020	−	8.34986i	−1.21545	−	0.270621i
$953$	28.0071	+	16.1699i	0.907238	+	0.523794i	0.879542	−	0.475822i	$-0.157849\pi$
$953$	28.0071	+	16.1699i	0.907238	+	0.523794i	0.0276968	+	0.999616i	$0.491183\pi$
$954$		0			0
$955$	3.70398	+	13.8234i	0.119858	+	0.447316i
$956$	−1.08992	−	4.06765i	−0.0352506	−	0.131557i
$957$		0			0
$958$	−8.28783	−	4.78498i	−0.267768	−	0.154596i
$959$	−6.53551	−	1.45514i	−0.211043	−	0.0469889i
$960$		0			0
$961$			13.8839i			0.447867i
$962$	35.0159	−	18.5624i	1.12896	−	0.598475i
$963$		0			0
$964$	−7.77010	−	2.08199i	−0.250258	−	0.0670565i
$965$	−16.0058	+	9.24094i	−0.515244	+	0.297476i
$966$		0			0
$967$	5.38328	+	5.38328i	0.173115	+	0.173115i	0.788346	−	0.615232i	$-0.210938\pi$
$967$	5.38328	+	5.38328i	0.173115	+	0.173115i	−0.615232	+	0.788346i	$0.710938\pi$
$968$	−29.5493	+	7.91771i	−0.949750	+	0.254485i
$969$		0			0
$970$	15.3331	−	15.3331i	0.492316	−	0.492316i
$971$	36.0969	+	20.8405i	1.15840	+	0.668804i	0.950921	−	0.309434i	$-0.100140\pi$
$971$	36.0969	+	20.8405i	1.15840	+	0.668804i	0.207483	+	0.978239i	$0.433473\pi$
$972$		0			0
$973$	−22.8507	+	14.5282i	−0.732558	+	0.465753i
$974$		−	22.2941i		−	0.714348i
$975$		0			0
$976$			16.2755i			0.520966i
$977$	2.38909	−	8.91619i	0.0764336	−	0.285254i	−0.917121	−	0.398609i	$-0.869493\pi$
$977$	2.38909	−	8.91619i	0.0764336	−	0.285254i	0.993555	+	0.113355i	$0.0361597\pi$
$978$		0			0
$979$	−5.43157	+	9.40776i	−0.173594	+	0.300673i
$980$	6.38402	+	5.37669i	0.203930	+	0.171752i
$981$		0			0
$982$	−0.883840	−	3.29853i	−0.0282045	−	0.105260i
$983$	23.8714	+	23.8714i	0.761380	+	0.761380i	0.976572	−	0.215192i	$-0.0690378\pi$
$983$	23.8714	+	23.8714i	0.761380	+	0.761380i	−0.215192	+	0.976572i	$0.569038\pi$
$984$		0			0
$985$	1.13406	+	1.96426i	0.0361343	+	0.0625864i
$986$	−11.4609	+	42.7726i	−0.364989	+	1.36216i
$987$		0			0
$988$	3.28047	−	3.05145i	0.104365	−	0.0970796i
$989$	−3.72497			−0.118447
$990$		0			0
$991$	−2.66281	−	4.61212i	−0.0845869	−	0.146509i	0.820628	−	0.571462i	$-0.193624\pi$
$991$	−2.66281	−	4.61212i	−0.0845869	−	0.146509i	−0.905215	+	0.424954i	$0.860290\pi$
$992$	−8.88738	+	15.3934i	−0.282175	+	0.488741i
$993$		0			0
$994$	6.76871	+	3.53141i	0.214691	+	0.112010i
$995$	4.39582	+	16.4054i	0.139357	+	0.520087i
$996$		0			0
$997$	28.6452	+	16.5383i	0.907203	+	0.523774i	0.879530	−	0.475843i	$-0.157857\pi$
$997$	28.6452	+	16.5383i	0.907203	+	0.523774i	0.0276726	+	0.999617i	$0.491190\pi$
$998$	−14.2338	+	8.21788i	−0.450563	+	0.260132i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fm.f.622.6		32
3.2	odd	2		273.2.by.c.76.3	✓	32
7.6	odd	2		819.2.fm.e.622.6		32
13.6	odd	12		819.2.fm.e.370.6		32
21.20	even	2		273.2.by.d.76.3	yes	32
39.32	even	12		273.2.by.d.97.3	yes	32
91.6	even	12	inner	819.2.fm.f.370.6		32
273.188	odd	12		273.2.by.c.97.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.3	✓	32	3.2	odd	2
273.2.by.c.97.3	yes	32	273.188	odd	12
273.2.by.d.76.3	yes	32	21.20	even	2
273.2.by.d.97.3	yes	32	39.32	even	12
819.2.fm.e.370.6		32	13.6	odd	12
819.2.fm.e.622.6		32	7.6	odd	2
819.2.fm.f.370.6		32	91.6	even	12	inner
819.2.fm.f.622.6		32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.281068 - 1.04896i) q^{2} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-1.22381 + 2.34570i) q^{7} +(2.16598 - 2.16598i) q^{8} +O(q^{10})\)	\(q+(0.281068 - 1.04896i) q^{2} +(0.710736 + 0.410344i) q^{4} +(-1.02734 + 1.02734i) q^{5} +(-1.22381 + 2.34570i) q^{7} +(2.16598 - 2.16598i) q^{8} +(0.788887 + 1.36639i) q^{10} +(-0.972198 - 0.260500i) q^{11} +(3.05530 + 1.91446i) q^{13} +(2.11656 + 1.94303i) q^{14} +(-0.842549 - 1.45934i) q^{16} +(-2.37035 + 4.10557i) q^{17} +(-0.391878 - 1.46251i) q^{19} +(-1.15173 + 0.308606i) q^{20} +(-0.546507 + 0.946578i) q^{22} +(0.337046 - 0.194594i) q^{23} +2.88914i q^{25} +(2.86693 - 2.66679i) q^{26} +(-1.83235 + 1.16499i) q^{28} +(4.30065 + 7.44895i) q^{29} +(-2.92542 + 2.92542i) q^{31} +(4.14997 - 1.11198i) q^{32} +(3.64034 + 3.64034i) q^{34} +(-1.15256 - 3.66710i) q^{35} +(9.77690 + 2.61971i) q^{37} -1.64425 q^{38} +4.45041i q^{40} +(8.64616 + 2.31673i) q^{41} +(-8.28885 - 4.78557i) q^{43} +(-0.584082 - 0.584082i) q^{44} +(-0.109388 - 0.408241i) q^{46} +(4.78928 + 4.78928i) q^{47} +(-4.00458 - 5.74137i) q^{49} +(3.03058 + 0.812042i) q^{50} +(1.38592 + 2.61440i) q^{52} -12.7329 q^{53} +(1.26640 - 0.731158i) q^{55} +(2.42998 + 7.73148i) q^{56} +(9.02241 - 2.41755i) q^{58} +(0.889636 - 0.238377i) q^{59} +(-8.36449 - 4.82924i) q^{61} +(2.24640 + 3.89088i) q^{62} -8.03588i q^{64} +(-5.10564 + 1.17203i) q^{65} +(1.71328 - 6.39405i) q^{67} +(-3.36939 + 1.94532i) q^{68} +(-4.17059 + 0.178284i) q^{70} +(2.56663 - 0.687727i) q^{71} +(2.46596 + 2.46596i) q^{73} +(5.49594 - 9.51925i) q^{74} +(0.321609 - 1.20026i) q^{76} +(1.80084 - 1.96168i) q^{77} +7.06532 q^{79} +(2.36483 + 0.633653i) q^{80} +(4.86031 - 8.41830i) q^{82} +(2.43414 - 2.43414i) q^{83} +(-1.78266 - 6.65299i) q^{85} +(-7.34959 + 7.34959i) q^{86} +(-2.67000 + 1.54152i) q^{88} +(2.79345 - 10.4253i) q^{89} +(-8.22984 + 4.82387i) q^{91} +0.319401 q^{92} +(6.36986 - 3.67764i) q^{94} +(1.90509 + 1.09990i) q^{95} +(-3.55710 - 13.2753i) q^{97} +(-7.14802 + 2.58692i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8	\( 32 q + 2 q^{2} + 6 q^{4} + 2 q^{5} - 2 q^{7} - 2 q^{8} - 2 q^{10} + 4 q^{11} - 6 q^{13} - 34 q^{14} + 14 q^{16} - 8 q^{17} - 2 q^{19} + 44 q^{20} - 4 q^{22} + 18 q^{23} - 28 q^{26} - 18 q^{28} + 18 q^{29} + 14 q^{31} + 8 q^{32} + 66 q^{34} + 20 q^{35} - 24 q^{37} + 24 q^{38} - 6 q^{43} + 20 q^{44} - 58 q^{46} - 28 q^{47} + 10 q^{49} - 70 q^{50} - 28 q^{52} + 80 q^{53} - 60 q^{55} + 120 q^{56} - 4 q^{58} - 42 q^{59} - 36 q^{61} + 52 q^{62} - 14 q^{65} + 26 q^{67} - 72 q^{68} + 68 q^{70} + 4 q^{71} - 12 q^{73} + 18 q^{74} + 48 q^{76} + 28 q^{77} - 4 q^{79} - 98 q^{80} - 20 q^{82} - 36 q^{83} - 10 q^{85} + 40 q^{86} + 96 q^{88} - 54 q^{89} - 54 q^{91} + 4 q^{92} - 60 q^{95} + 40 q^{97}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^4 + 2 * q^5 - 2 * q^7 - 2 * q^8 - 2 * q^10 + 4 * q^11 - 6 * q^13 - 34 * q^14 + 14 * q^16 - 8 * q^17 - 2 * q^19 + 44 * q^20 - 4 * q^22 + 18 * q^23 - 28 * q^26 - 18 * q^28 + 18 * q^29 + 14 * q^31 + 8 * q^32 + 66 * q^34 + 20 * q^35 - 24 * q^37 + 24 * q^38 - 6 * q^43 + 20 * q^44 - 58 * q^46 - 28 * q^47 + 10 * q^49 - 70 * q^50 - 28 * q^52 + 80 * q^53 - 60 * q^55 + 120 * q^56 - 4 * q^58 - 42 * q^59 - 36 * q^61 + 52 * q^62 - 14 * q^65 + 26 * q^67 - 72 * q^68 + 68 * q^70 + 4 * q^71 - 12 * q^73 + 18 * q^74 + 48 * q^76 + 28 * q^77 - 4 * q^79 - 98 * q^80 - 20 * q^82 - 36 * q^83 - 10 * q^85 + 40 * q^86 + 96 * q^88 - 54 * q^89 - 54 * q^91 + 4 * q^92 - 60 * q^95 + 40 * q^97

Introduction

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