LMFDB - Embedded newform 405.2.r.a.368.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			368.10
Character	$\chi$	$=$	405.368
Dual form			405.2.r.a.197.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.639298 + 0.0559313i) q^{2} +(-1.56404 - 0.275783i) q^{4} +(1.26232 - 1.84568i) q^{5} +(3.52875 + 2.47086i) q^{7} +(-2.22421 - 0.595975i) q^{8} +O(q^{10})$	\(q+(0.639298 + 0.0559313i) q^{2} +(-1.56404 - 0.275783i) q^{4} +(1.26232 - 1.84568i) q^{5} +(3.52875 + 2.47086i) q^{7} +(-2.22421 - 0.595975i) q^{8} +(0.910229 - 1.10934i) q^{10} +(0.157893 - 0.433806i) q^{11} +(-0.462462 - 5.28596i) q^{13} +(2.11772 + 1.77698i) q^{14} +(1.59619 + 0.580964i) q^{16} +(4.93057 - 1.32114i) q^{17} +(1.03667 - 0.598524i) q^{19} +(-2.48333 + 2.53860i) q^{20} +(0.125204 - 0.268500i) q^{22} +(1.57814 + 2.25381i) q^{23} +(-1.81310 - 4.65968i) q^{25} -3.40517i q^{26} +(-4.83770 - 4.83770i) q^{28} +(0.00462297 - 0.00387914i) q^{29} +(-0.387533 + 2.19781i) q^{31} +(5.16180 + 2.40699i) q^{32} +(3.22599 - 0.568830i) q^{34} +(9.01483 - 3.39395i) q^{35} +(-1.94341 - 7.25290i) q^{37} +(0.696220 - 0.324653i) q^{38} +(-3.90764 + 3.35288i) q^{40} +(-3.02828 + 3.60897i) q^{41} +(0.806157 + 1.72881i) q^{43} +(-0.366587 + 0.634947i) q^{44} +(0.882840 + 1.52912i) q^{46} +(-6.47343 + 9.24502i) q^{47} +(3.95281 + 10.8602i) q^{49} +(-0.898490 - 3.08033i) q^{50} +(-0.734468 + 8.39501i) q^{52} +(-3.94023 + 3.94023i) q^{53} +(-0.601359 - 0.839022i) q^{55} +(-6.37611 - 7.59875i) q^{56} +(0.00317242 - 0.00222135i) q^{58} +(0.388624 - 0.141448i) q^{59} +(0.399307 + 2.26458i) q^{61} +(-0.370675 + 1.38338i) q^{62} +(0.223194 + 0.128861i) q^{64} +(-10.3400 - 5.81901i) q^{65} +(-5.84619 + 0.511475i) q^{67} +(-8.07597 + 0.706556i) q^{68} +(5.95299 - 1.66553i) q^{70} +(-0.648656 - 0.374502i) q^{71} +(-2.97508 + 11.1032i) q^{73} +(-0.836752 - 4.74546i) q^{74} +(-1.78647 + 0.650220i) q^{76} +(1.62904 - 1.14066i) q^{77} +(-1.01095 - 1.20481i) q^{79} +(3.08717 - 2.21269i) q^{80} +(-2.13783 + 2.13783i) q^{82} +(-0.930629 + 10.6371i) q^{83} +(3.78554 - 10.7680i) q^{85} +(0.418680 + 1.15031i) q^{86} +(-0.609724 + 0.870776i) q^{88} +(-6.36010 - 11.0160i) q^{89} +(11.4289 - 19.7955i) q^{91} +(-1.84671 - 3.96028i) q^{92} +(-4.65554 + 5.54825i) q^{94} +(0.203927 - 2.66890i) q^{95} +(-7.76434 + 3.62057i) q^{97} +(1.91959 + 7.16401i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.639298	+	0.0559313i	0.452052	+	0.0395494i	0.310909	−	0.950440i	$-0.399367\pi$
$2$	0.639298	+	0.0559313i	0.452052	+	0.0395494i	0.141143	+	0.989989i	$0.454922\pi$
$3$		0			0
$3$		0			0
$4$	−1.56404	−	0.275783i	−0.782021	−	0.137891i
$5$	1.26232	−	1.84568i	0.564526	−	0.825415i
$5$	1.26232	−	1.84568i	0.564526	−	0.825415i
$6$		0			0
$7$	3.52875	+	2.47086i	1.33374	+	0.933897i	0.999962	−	0.00875387i	$-0.00278648\pi$
$7$	3.52875	+	2.47086i	1.33374	+	0.933897i	0.333781	+	0.942651i	$0.391675\pi$
$8$	−2.22421	−	0.595975i	−0.786377	−	0.210709i
$9$		0			0
$10$	0.910229	−	1.10934i	0.287840	−	0.350804i
$11$	0.157893	−	0.433806i	0.0476064	−	0.130798i	−0.913611	−	0.406590i	$-0.866718\pi$
$11$	0.157893	−	0.433806i	0.0476064	−	0.130798i	0.961217	+	0.275792i	$0.0889401\pi$
$12$		0			0
$13$	−0.462462	−	5.28596i	−0.128264	−	1.46606i	−0.738720	−	0.674012i	$-0.764570\pi$
$13$	−0.462462	−	5.28596i	−0.128264	−	1.46606i	0.610457	−	0.792050i	$-0.290986\pi$
$14$	2.11772	+	1.77698i	0.565986	+	0.474918i
$15$		0			0
$16$	1.59619	+	0.580964i	0.399047	+	0.145241i
$17$	4.93057	−	1.32114i	1.19584	−	0.320424i	0.394647	−	0.918833i	$-0.370867\pi$
$17$	4.93057	−	1.32114i	1.19584	−	0.320424i	0.801191	+	0.598409i	$0.204200\pi$
$18$		0			0
$19$	1.03667	−	0.598524i	0.237829	−	0.137311i	−0.376349	−	0.926478i	$-0.622821\pi$
$19$	1.03667	−	0.598524i	0.237829	−	0.137311i	0.614179	+	0.789167i	$0.289487\pi$
$20$	−2.48333	+	2.53860i	−0.555289	+	0.567649i
$21$		0			0
$22$	0.125204	−	0.268500i	0.0266935	−	0.0572444i
$23$	1.57814	+	2.25381i	0.329064	+	0.469952i	0.949259	−	0.314496i	$-0.101835\pi$
$23$	1.57814	+	2.25381i	0.329064	+	0.469952i	−0.620195	+	0.784448i	$0.712946\pi$
$24$		0			0
$25$	−1.81310	−	4.65968i	−0.362621	−	0.931937i
$26$		−	3.40517i		−	0.667808i
$27$		0			0
$28$	−4.83770	−	4.83770i	−0.914239	−	0.914239i
$29$	0.00462297	−	0.00387914i	0.000858465	−	0.000720337i	−0.642358	−	0.766404i	$-0.722044\pi$
$29$	0.00462297	−	0.00387914i	0.000858465	−	0.000720337i	0.643217	+	0.765684i	$0.277599\pi$
$30$		0			0
$31$	−0.387533	+	2.19781i	−0.0696030	+	0.394738i	0.930026	+	0.367494i	$0.119784\pi$
$31$	−0.387533	+	2.19781i	−0.0696030	+	0.394738i	−0.999629	+	0.0272441i	$0.991327\pi$
$32$	5.16180	+	2.40699i	0.912486	+	0.425499i
$33$		0			0
$34$	3.22599	−	0.568830i	0.553253	−	0.0975535i
$35$	9.01483	−	3.39395i	1.52379	−	0.573683i
$36$		0			0
$37$	−1.94341	−	7.25290i	−0.319494	−	1.19237i	−0.919732	−	0.392547i	$-0.871594\pi$
$37$	−1.94341	−	7.25290i	−0.319494	−	1.19237i	0.600238	−	0.799822i	$-0.295073\pi$
$38$	0.696220	−	0.324653i	0.112942	−	0.0526656i
$39$		0			0
$40$	−3.90764	+	3.35288i	−0.617853	+	0.530137i
$41$	−3.02828	+	3.60897i	−0.472939	+	0.563626i	−0.948793	−	0.315898i	$-0.897694\pi$
$41$	−3.02828	+	3.60897i	−0.472939	+	0.563626i	0.475855	+	0.879524i	$0.342139\pi$
$42$		0			0
$43$	0.806157	+	1.72881i	0.122938	+	0.263641i	0.958139	−	0.286304i	$-0.0924266\pi$
$43$	0.806157	+	1.72881i	0.122938	+	0.263641i	−0.835201	+	0.549945i	$0.814649\pi$
$44$	−0.366587	+	0.634947i	−0.0552651	+	0.0957219i
$45$		0			0
$46$	0.882840	+	1.52912i	0.130168	+	0.225457i
$47$	−6.47343	+	9.24502i	−0.944247	+	1.34853i	−0.00695690	+	0.999976i	$0.502214\pi$
$47$	−6.47343	+	9.24502i	−0.944247	+	1.34853i	−0.937290	+	0.348549i	$0.886674\pi$
$48$		0			0
$49$	3.95281	+	10.8602i	0.564687	+	1.55146i
$50$	−0.898490	−	3.08033i	−0.127066	−	0.435625i
$51$		0			0
$52$	−0.734468	+	8.39501i	−0.101852	+	1.16418i
$53$	−3.94023	+	3.94023i	−0.541233	+	0.541233i	−0.923890	−	0.382657i	$-0.875009\pi$
$53$	−3.94023	+	3.94023i	−0.541233	+	0.541233i	0.382657	+	0.923890i	$0.375009\pi$
$54$		0			0
$55$	−0.601359	−	0.839022i	−0.0810872	−	0.113134i
$56$	−6.37611	−	7.59875i	−0.852044	−	1.01543i
$57$		0			0
$58$	0.00317242	−	0.00222135i	0.000416559	−	0.000291678i
$59$	0.388624	−	0.141448i	0.0505945	−	0.0184149i	−0.316599	−	0.948559i	$-0.602541\pi$
$59$	0.388624	−	0.141448i	0.0505945	−	0.0184149i	0.367193	+	0.930145i	$0.380319\pi$
$60$		0			0
$61$	0.399307	+	2.26458i	0.0511260	+	0.289950i	0.999641	−	0.0267812i	$-0.00852575\pi$
$61$	0.399307	+	2.26458i	0.0511260	+	0.289950i	−0.948515	+	0.316731i	$0.897415\pi$
$62$	−0.370675	+	1.38338i	−0.0470758	+	0.175689i
$63$		0			0
$64$	0.223194	+	0.128861i	0.0278993	+	0.0161077i
$65$	−10.3400	−	5.81901i	−1.28252	−	0.721759i
$66$		0			0
$67$	−5.84619	+	0.511475i	−0.714226	+	0.0624866i	−0.438476	−	0.898743i	$-0.644482\pi$
$67$	−5.84619	+	0.511475i	−0.714226	+	0.0624866i	−0.275750	+	0.961230i	$0.588926\pi$
$68$	−8.07597	+	0.706556i	−0.979355	+	0.0856824i
$69$		0			0
$70$	5.95299	−	1.66553i	0.711518	−	0.199069i
$71$	−0.648656	−	0.374502i	−0.0769813	−	0.0444452i	0.461015	−	0.887392i	$-0.347485\pi$
$71$	−0.648656	−	0.374502i	−0.0769813	−	0.0444452i	−0.537997	+	0.842947i	$0.680819\pi$
$72$		0			0
$73$	−2.97508	+	11.1032i	−0.348207	+	1.29953i	0.540614	+	0.841271i	$0.318192\pi$
$73$	−2.97508	+	11.1032i	−0.348207	+	1.29953i	−0.888821	+	0.458255i	$0.848475\pi$
$74$	−0.836752	−	4.74546i	−0.0972705	−	0.551648i
$75$		0			0
$76$	−1.78647	+	0.650220i	−0.204922	+	0.0745854i
$77$	1.62904	−	1.14066i	0.185646	−	0.129991i
$78$		0			0
$79$	−1.01095	−	1.20481i	−0.113741	−	0.135551i	0.706170	−	0.708043i	$-0.250422\pi$
$79$	−1.01095	−	1.20481i	−0.113741	−	0.135551i	−0.819911	+	0.572491i	$0.805977\pi$
$80$	3.08717	−	2.21269i	0.345156	−	0.247387i
$81$		0			0
$82$	−2.13783	+	2.13783i	−0.236084	+	0.236084i
$83$	−0.930629	+	10.6371i	−0.102150	+	1.16758i	0.756139	+	0.654411i	$0.227083\pi$
$83$	−0.930629	+	10.6371i	−0.102150	+	1.16758i	−0.858289	+	0.513167i	$0.828472\pi$
$84$		0			0
$85$	3.78554	−	10.7680i	0.410599	−	1.16795i
$86$	0.418680	+	1.15031i	0.0451474	+	0.124041i
$87$		0			0
$88$	−0.609724	+	0.870776i	−0.0649968	+	0.0928250i
$89$	−6.36010	−	11.0160i	−0.674169	−	1.16770i	−0.976711	−	0.214559i	$-0.931168\pi$
$89$	−6.36010	−	11.0160i	−0.674169	−	1.16770i	0.302542	−	0.953136i	$-0.402165\pi$
$90$		0			0
$91$	11.4289	−	19.7955i	1.19808	−	2.07513i
$92$	−1.84671	−	3.96028i	−0.192533	−	0.412888i
$93$		0			0
$94$	−4.65554	+	5.54825i	−0.480182	+	0.572259i
$95$	0.203927	−	2.66890i	0.0209224	−	0.273824i
$96$		0			0
$97$	−7.76434	+	3.62057i	−0.788349	+	0.367613i	−0.774729	−	0.632294i	$-0.782114\pi$
$97$	−7.76434	+	3.62057i	−0.788349	+	0.367613i	−0.0136208	+	0.999907i	$0.504336\pi$
$98$	1.91959	+	7.16401i	0.193908	+	0.723675i
$99$		0			0
$100$	1.55071	+	7.78797i	0.155071	+	0.778797i
$101$	15.4590	−	2.72585i	1.53823	−	0.271232i	0.660663	−	0.750682i	$-0.270275\pi$
$101$	15.4590	−	2.72585i	1.53823	−	0.271232i	0.877569	+	0.479450i	$0.159164\pi$
$102$		0			0
$103$	−12.6867	−	5.91592i	−1.25006	−	0.582912i	−0.318992	−	0.947758i	$-0.603344\pi$
$103$	−12.6867	−	5.91592i	−1.25006	−	0.582912i	−0.931068	+	0.364845i	$0.881122\pi$
$104$	−2.12169	+	12.0327i	−0.208049	+	1.17990i
$105$		0			0
$106$	−2.73936	+	2.29860i	−0.266071	+	0.223260i
$107$	−2.86472	−	2.86472i	−0.276943	−	0.276943i	0.554945	−	0.831887i	$-0.312739\pi$
$107$	−2.86472	−	2.86472i	−0.276943	−	0.276943i	−0.831887	+	0.554945i	$0.812739\pi$
$108$		0			0
$109$			6.64284i			0.636269i	0.948046	+	0.318134i	$0.103056\pi$
$109$			6.64284i			0.636269i	−0.948046	+	0.318134i	$0.896944\pi$
$110$	−0.337520	−	0.570019i	−0.0321812	−	0.0543492i
$111$		0			0
$112$	4.19706	+	5.99403i	0.396585	+	0.566382i
$113$	2.96857	−	6.36611i	0.279259	−	0.598874i	−0.715783	−	0.698322i	$-0.753930\pi$
$113$	2.96857	−	6.36611i	0.279259	−	0.598874i	0.995043	+	0.0994488i	$0.0317080\pi$
$114$		0			0
$115$	6.15193	−	0.0677124i	0.573671	−	0.00631422i
$116$	−0.00830033	+	0.00479220i	−0.000770666	+	0.000444944i
$117$		0			0
$118$	0.256358	−	0.0686908i	0.0235996	−	0.00632350i
$119$	20.6631	+	7.52076i	1.89418	+	0.689427i
$120$		0			0
$121$	8.26323	+	6.93367i	0.751203	+	0.630334i
$122$	0.128615	+	1.47008i	0.0116443	+	0.133094i
$123$		0			0
$124$	1.21224	−	3.33059i	0.108862	−	0.299096i
$125$	−10.8890	−	2.53559i	−0.973944	−	0.226790i
$126$		0			0
$127$	8.09882	+	2.17007i	0.718654	+	0.192563i	0.599571	−	0.800322i	$-0.295338\pi$
$127$	8.09882	+	2.17007i	0.718654	+	0.192563i	0.119083	+	0.992884i	$0.462005\pi$
$128$	−9.19534	−	6.43865i	−0.812761	−	0.569102i
$129$		0			0
$130$	−6.28487	−	4.29841i	−0.551219	−	0.376995i
$131$	11.2646	+	1.98625i	0.984193	+	0.173540i	0.642512	−	0.766276i	$-0.277892\pi$
$131$	11.2646	+	1.98625i	0.984193	+	0.173540i	0.341682	+	0.939816i	$0.389004\pi$
$132$		0			0
$133$	5.13704	+	0.449432i	0.445437	+	0.0389707i
$134$	−3.76606			−0.325338
$135$		0			0
$136$	−11.7540			−1.00790
$137$	−10.2700	−	0.898508i	−0.877424	−	0.0767647i	−0.360463	−	0.932773i	$-0.617381\pi$
$137$	−10.2700	−	0.898508i	−0.877424	−	0.0767647i	−0.516961	+	0.856009i	$0.672937\pi$
$138$		0			0
$139$	−1.70385	−	0.300434i	−0.144518	−	0.0254825i	0.100921	−	0.994894i	$-0.467821\pi$
$139$	−1.70385	−	0.300434i	−0.144518	−	0.0254825i	−0.245439	+	0.969412i	$0.578932\pi$
$140$	−15.0356	+	2.82215i	−1.27074	+	0.238515i
$141$		0			0
$142$	−0.393738	−	0.275698i	−0.0330417	−	0.0231361i
$143$	−2.36610	−	0.633995i	−0.197863	−	0.0530173i
$144$		0			0
$145$	−0.00132399	−	0.0134293i	−0.000109952	−	0.00111524i
$146$	−2.52298	+	6.93182i	−0.208803	+	0.573681i
$147$		0			0
$148$	1.03935	+	11.8798i	0.0854339	+	0.976513i
$149$	3.51771	+	2.95171i	0.288182	+	0.241813i	0.775405	−	0.631464i	$-0.217546\pi$
$149$	3.51771	+	2.95171i	0.288182	+	0.241813i	−0.487223	+	0.873277i	$0.661990\pi$
$150$		0			0
$151$	−4.16351	−	1.51539i	−0.338821	−	0.123321i	0.167005	−	0.985956i	$-0.446590\pi$
$151$	−4.16351	−	1.51539i	−0.338821	−	0.123321i	−0.505827	+	0.862635i	$0.668813\pi$
$152$	−2.66249	+	0.713411i	−0.215956	+	0.0578653i
$153$		0			0
$154$	1.10524	−	0.638110i	0.0890627	−	0.0514204i
$155$	3.56727	+	3.48960i	0.286530	+	0.280291i
$156$		0			0
$157$	0.351788	−	0.754412i	0.0280757	−	0.0602086i	−0.891770	−	0.452489i	$-0.850536\pi$
$157$	0.351788	−	0.754412i	0.0280757	−	0.0602086i	0.919846	+	0.392281i	$0.128314\pi$
$158$	−0.578913	−	0.826774i	−0.0460559	−	0.0657746i
$159$		0			0
$160$	10.9584	−	6.48867i	0.866336	−	0.512974i
$161$			11.8525i			0.934107i
$162$		0			0
$163$	−10.1572	−	10.1572i	−0.795571	−	0.795571i	0.186823	−	0.982394i	$-0.440181\pi$
$163$	−10.1572	−	10.1572i	−0.795571	−	0.795571i	−0.982394	+	0.186823i	$0.940181\pi$
$164$	5.73166	−	4.80943i	0.447567	−	0.375554i
$165$		0			0
$166$	−1.18990	+	6.74824i	−0.0923540	+	0.523765i
$167$	20.3353	+	9.48250i	1.57359	+	0.733778i	0.996555	−	0.0829395i	$-0.0264308\pi$
$167$	20.3353	+	9.48250i	1.57359	+	0.733778i	0.577038	+	0.816718i	$0.304209\pi$
$168$		0			0
$169$	−14.9250	+	2.63168i	−1.14808	+	0.202437i
$170$	3.02235	−	6.67221i	0.231804	−	0.511735i
$171$		0			0
$172$	−0.784088	−	2.92626i	−0.0597861	−	0.223125i
$173$	−2.09324	+	0.976093i	−0.159146	+	0.0742110i	−0.500559	−	0.865702i	$-0.666872\pi$
$173$	−2.09324	+	0.976093i	−0.159146	+	0.0742110i	0.341413	+	0.939913i	$0.389094\pi$
$174$		0			0
$175$	5.11543	−	20.9228i	0.386690	−	1.58161i
$176$	0.504052	−	0.600706i	0.0379943	−	0.0452799i
$177$		0			0
$178$	−3.44986	−	7.39824i	−0.258578	−	0.554522i
$179$	10.3891	−	17.9945i	0.776520	−	1.34497i	−0.157416	−	0.987532i	$-0.550316\pi$
$179$	10.3891	−	17.9945i	0.776520	−	1.34497i	0.933936	−	0.357440i	$-0.116350\pi$
$180$		0			0
$181$	1.61486	+	2.79701i	0.120031	+	0.207900i	0.919780	−	0.392435i	$-0.128367\pi$
$181$	1.61486	+	2.79701i	0.120031	+	0.207900i	−0.799748	+	0.600335i	$0.795034\pi$
$182$	8.41369	−	12.0160i	0.623664	−	0.890685i
$183$		0			0
$184$	−2.16689	−	5.95348i	−0.159745	−	0.438896i
$185$	−15.8398	−	5.56855i	−1.16456	−	0.409408i
$186$		0			0
$187$	0.205381	−	2.34751i	0.0150189	−	0.171667i
$188$	12.6743	−	12.6743i	0.924372	−	0.924372i
$189$		0			0
$190$	0.279645	−	1.69482i	0.0202876	−	0.122955i
$191$	−0.296698	−	0.353591i	−0.0214683	−	0.0255850i	0.755203	−	0.655490i	$-0.227538\pi$
$191$	−0.296698	−	0.353591i	−0.0214683	−	0.0255850i	−0.776672	+	0.629905i	$0.783094\pi$
$192$		0			0
$193$	−1.86360	+	1.30491i	−0.134145	+	0.0939292i	−0.638723	−	0.769437i	$-0.720537\pi$
$193$	−1.86360	+	1.30491i	−0.134145	+	0.0939292i	0.504578	+	0.863366i	$0.331648\pi$
$194$	−5.16623	+	1.88035i	−0.370914	+	0.135001i
$195$		0			0
$196$	−3.18729	−	18.0760i	−0.227663	−	1.29114i
$197$	−6.91110	+	25.7926i	−0.492396	+	1.83765i	0.0517571	+	0.998660i	$0.483518\pi$
$197$	−6.91110	+	25.7926i	−0.492396	+	1.83765i	−0.544153	+	0.838986i	$0.683149\pi$
$198$		0			0
$199$	20.6539	+	11.9246i	1.46412	+	0.845309i	0.999198	−	0.0400428i	$-0.0127494\pi$
$199$	20.6539	+	11.9246i	1.46412	+	0.845309i	0.464921	+	0.885352i	$0.346083\pi$
$200$	1.25566	+	11.4447i	0.0887889	+	0.809261i
$201$		0			0
$202$	10.0354	−	0.877983i	0.706088	−	0.0617747i
$203$	0.0258981	−	0.00226579i	0.00181769	−	0.000159027i
$204$		0			0
$205$	2.83836	+	10.1449i	0.198240	+	0.708552i
$206$	−7.77970	−	4.49161i	−0.542038	−	0.312946i
$207$		0			0
$208$	2.33278	−	8.70605i	0.161749	−	0.603656i
$209$	−0.0959604	−	0.544219i	−0.00663772	−	0.0376444i
$210$		0			0
$211$	20.3867	−	7.42015i	1.40348	−	0.510825i	0.474270	−	0.880379i	$-0.342712\pi$
$211$	20.3867	−	7.42015i	1.40348	−	0.510825i	0.929209	+	0.369555i	$0.120490\pi$
$212$	7.24934	−	5.07605i	0.497887	−	0.348624i
$213$		0			0
$214$	−1.67118	−	1.99163i	−0.114239	−	0.136145i
$215$	4.20846	+	0.694397i	0.287015	+	0.0473575i
$216$		0			0
$217$	−6.79799	+	6.79799i	−0.461477	+	0.461477i
$218$	−0.371543	+	4.24675i	−0.0251640	+	0.287626i
$219$		0			0
$220$	0.709163	+	1.47811i	0.0478118	+	0.0996542i
$221$	−9.26370	−	25.4518i	−0.623144	−	1.71207i
$222$		0			0
$223$	−6.30605	+	9.00598i	−0.422285	+	0.603085i	−0.972774	−	0.231757i	$-0.925552\pi$
$223$	−6.30605	+	9.00598i	−0.422285	+	0.603085i	0.550489	+	0.834842i	$0.314441\pi$
$224$	12.2674	+	21.2477i	0.819649	+	1.41967i
$225$		0			0
$226$	2.25386	−	3.90381i	0.149925	−	0.259677i
$227$	−4.18215	−	8.96865i	−0.277579	−	0.595270i	0.717252	−	0.696814i	$-0.245400\pi$
$227$	−4.18215	−	8.96865i	−0.277579	−	0.595270i	−0.994831	+	0.101544i	$0.967622\pi$
$228$		0			0
$229$	6.25137	−	7.45009i	0.413102	−	0.492316i	−0.518866	−	0.854855i	$-0.673646\pi$
$229$	6.25137	−	7.45009i	0.413102	−	0.492316i	0.931968	+	0.362540i	$0.118090\pi$
$230$	3.93670	+	0.300797i	0.259579	+	0.0198340i
$231$		0			0
$232$	−0.0125943	+	0.00587283i	−0.000826858	+	0.000385570i
$233$	2.61861	+	9.77279i	0.171551	+	0.640236i	0.997113	+	0.0759259i	$0.0241913\pi$
$233$	2.61861	+	9.77279i	0.171551	+	0.640236i	−0.825563	+	0.564311i	$0.809142\pi$
$234$		0			0
$235$	8.89186	+	23.6181i	0.580041	+	1.54067i
$236$	−0.646833	+	0.114054i	−0.0421053	+	0.00742429i
$237$		0			0
$238$	12.7892	+	5.96371i	0.829002	+	0.386570i
$239$	0.554723	−	3.14599i	0.0358821	−	0.203497i	−0.961596	−	0.274468i	$-0.911498\pi$
$239$	0.554723	−	3.14599i	0.0358821	−	0.203497i	0.997478	+	0.0709702i	$0.0226095\pi$
$240$		0			0
$241$	−15.5334	+	13.0341i	−1.00060	+	0.839600i	−0.987067	−	0.160309i	$-0.948751\pi$
$241$	−15.5334	+	13.0341i	−1.00060	+	0.839600i	−0.0135291	+	0.999908i	$0.504307\pi$
$242$	4.89485	+	4.89485i	0.314653	+	0.314653i
$243$		0			0
$244$		−	3.65203i		−	0.233797i
$245$	25.0343	+	6.41346i	1.59938	+	0.409741i
$246$		0			0
$247$	−3.64320	−	5.20303i	−0.231811	−	0.331061i
$248$	2.17179	−	4.65743i	0.137909	−	0.295747i
$249$		0			0
$250$	−6.81951	−	2.23003i	−0.431303	−	0.141040i
$251$	−12.3046	+	7.10409i	−0.776662	+	0.448406i	−0.835246	−	0.549876i	$-0.814675\pi$
$251$	−12.3046	+	7.10409i	−0.776662	+	0.448406i	0.0585840	+	0.998282i	$0.481341\pi$
$252$		0			0
$253$	1.22689	−	0.328745i	0.0771341	−	0.0206680i
$254$	5.05618	+	1.84030i	0.317253	+	0.115471i
$255$		0			0
$256$	−5.91329	−	4.96184i	−0.369581	−	0.310115i
$257$	−2.46595	−	28.1859i	−0.153822	−	1.75819i	−0.545522	−	0.838096i	$-0.683669\pi$
$257$	−2.46595	−	28.1859i	−0.153822	−	1.75819i	0.391701	−	0.920093i	$-0.371887\pi$
$258$		0			0
$259$	11.0631	−	30.3956i	0.687426	−	1.88869i
$260$	14.5674	+	11.9528i	0.903432	+	0.741279i
$261$		0			0
$262$	7.09034	+	1.89985i	0.438043	+	0.117373i
$263$	4.29988	+	3.01081i	0.265142	+	0.185655i	0.698586	−	0.715526i	$-0.253813\pi$
$263$	4.29988	+	3.01081i	0.265142	+	0.185655i	−0.433444	+	0.901181i	$0.642702\pi$
$264$		0			0
$265$	2.29860	+	12.2463i	0.141202	+	0.752282i
$266$	3.25896	+	0.574642i	0.199819	+	0.0352336i
$267$		0			0
$268$	9.28474	+	0.812310i	0.567156	+	0.0496197i
$269$	−11.2342			−0.684961			−0.342480	−	0.939525i	$-0.611267\pi$
$269$	−11.2342			−0.684961			−0.342480	+	0.939525i	$0.611267\pi$
$270$		0			0
$271$	−15.3871			−0.934699			−0.467349	−	0.884073i	$-0.654791\pi$
$271$	−15.3871			−0.934699			−0.467349	+	0.884073i	$0.654791\pi$
$272$	8.63764	+	0.755696i	0.523734	+	0.0458208i
$273$		0			0
$274$	−6.51532	−	1.14883i	−0.393605	−	0.0694032i
$275$	−2.30768	+	0.0508059i	−0.139158	+	0.00306371i
$276$		0			0
$277$	−13.4512	−	9.41860i	−0.808202	−	0.565909i	0.0948247	−	0.995494i	$-0.469771\pi$
$277$	−13.4512	−	9.41860i	−0.808202	−	0.565909i	−0.903026	+	0.429585i	$0.858660\pi$
$278$	−1.07246	−	0.287365i	−0.0643219	−	0.0172350i
$279$		0			0
$280$	−22.0736	+	2.17624i	−1.31915	+	0.130055i
$281$	3.30030	−	9.06751i	0.196880	−	0.540922i	−0.801490	−	0.598009i	$-0.795959\pi$
$281$	3.30030	−	9.06751i	0.196880	−	0.540922i	0.998369	+	0.0570865i	$0.0181811\pi$
$282$		0			0
$283$	−1.35265	−	15.4609i	−0.0804068	−	0.919054i	−0.924080	−	0.382198i	$-0.875167\pi$
$283$	−1.35265	−	15.4609i	−0.0804068	−	0.919054i	0.843674	−	0.536856i	$-0.180388\pi$
$284$	0.911245	+	0.764625i	0.0540724	+	0.0453721i
$285$		0			0
$286$	−1.47718	−	0.537651i	−0.0873477	−	0.0317920i
$287$	−19.6033	+	5.25269i	−1.15715	+	0.310057i
$288$		0			0
$289$	7.84266	−	4.52796i	0.461333	−	0.266351i
$290$	−9.53107e−5	−	0.00865934i	−5.59684e−6	−	0.000508494i
$291$		0			0
$292$	7.71521	−	16.5453i	0.451499	−	0.968242i
$293$	−5.53310	−	7.90208i	−0.323247	−	0.461645i	0.624335	−	0.781157i	$-0.285370\pi$
$293$	−5.53310	−	7.90208i	−0.323247	−	0.461645i	−0.947582	+	0.319512i	$0.896481\pi$
$294$		0			0
$295$	0.229500	−	0.895829i	0.0133620	−	0.0521572i
$296$			17.2902i			1.00497i
$297$		0			0
$298$	2.08377	+	2.08377i	0.120709	+	0.120709i
$299$	11.1837	−	9.38426i	0.646772	−	0.542706i
$300$		0			0
$301$	−1.42692	+	8.09244i	−0.0822460	+	0.466440i
$302$	−2.57696	−	1.20166i	−0.148288	−	0.0691476i
$303$		0			0
$304$	2.00245	−	0.353085i	0.114848	−	0.0202508i
$305$	4.68376	+	2.12163i	0.268191	+	0.121484i
$306$		0			0
$307$	−1.13471	−	4.23478i	−0.0647610	−	0.241692i	0.925956	−	0.377631i	$-0.123261\pi$
$307$	−1.13471	−	4.23478i	−0.0647610	−	0.241692i	−0.990717	+	0.135940i	$0.956595\pi$
$308$	−2.86246	+	1.33479i	−0.163104	+	0.0760566i
$309$		0			0
$310$	2.08537	+	2.43042i	0.118441	+	0.138038i
$311$	5.33012	−	6.35219i	0.302243	−	0.360199i	−0.593451	−	0.804870i	$-0.702235\pi$
$311$	5.33012	−	6.35219i	0.302243	−	0.360199i	0.895694	+	0.444671i	$0.146679\pi$
$312$		0			0
$313$	4.37462	+	9.38140i	0.247268	+	0.530268i	0.990293	−	0.138996i	$-0.0443874\pi$
$313$	4.37462	+	9.38140i	0.247268	+	0.530268i	−0.743025	+	0.669264i	$0.766610\pi$
$314$	0.267093	−	0.462618i	0.0150729	−	0.0261070i
$315$		0			0
$316$	1.24891	+	2.16317i	0.0702566	+	0.121688i
$317$	0.779004	−	1.11253i	0.0437532	−	0.0624861i	−0.796679	−	0.604402i	$-0.793412\pi$
$317$	0.779004	−	1.11253i	0.0437532	−	0.0624861i	0.840433	+	0.541916i	$0.182301\pi$
$318$		0			0
$319$	−0.000952860	−	0.00261796i	−5.33499e−5	−	0.000146578i
$320$	0.519580	−	0.249282i	0.0290454	−	0.0139353i
$321$		0			0
$322$	−0.662925	+	7.57727i	−0.0369434	+	0.422265i
$323$	4.32066	−	4.32066i	0.240408	−	0.240408i
$324$		0			0
$325$	−23.7924	+	11.7389i	−1.31977	+	0.651158i
$326$	−5.92535	−	7.06156i	−0.328175	−	0.391104i
$327$		0			0
$328$	8.88639	−	6.22232i	0.490669	−	0.343570i
$329$	−45.6863	+	16.6284i	−2.51877	+	0.916756i
$330$		0			0
$331$	1.24032	+	7.03423i	0.0681744	+	0.386636i	0.999734	+	0.0230485i	$0.00733722\pi$
$331$	1.24032	+	7.03423i	0.0681744	+	0.386636i	−0.931560	+	0.363588i	$0.881552\pi$
$332$	4.38908	−	16.3803i	0.240882	−	0.898985i
$333$		0			0
$334$	12.4699	+	7.19952i	0.682324	+	0.393940i
$335$	−6.43573	+	11.4359i	−0.351622	+	0.624808i
$336$		0			0
$337$	28.6457	−	2.50617i	1.56043	−	0.136520i	0.726023	−	0.687671i	$-0.241367\pi$
$337$	28.6457	−	2.50617i	1.56043	−	0.136520i	0.834406	+	0.551151i	$0.185811\pi$
$338$	−9.68871	+	0.847653i	−0.526997	+	0.0461062i
$339$		0			0
$340$	−8.89037	+	15.7976i	−0.482148	+	0.856744i
$341$	0.892235	+	0.515132i	0.0483172	+	0.0278960i
$342$		0			0
$343$	−5.08105	+	18.9628i	−0.274351	+	1.02389i
$344$	−0.762735	−	4.32568i	−0.0411239	−	0.233225i
$345$		0			0
$346$	−1.39280	+	0.506936i	−0.0748772	+	0.0272531i
$347$	−24.1565	+	16.9146i	−1.29679	+	0.908021i	−0.998914	−	0.0465844i	$-0.985166\pi$
$347$	−24.1565	+	16.9146i	−1.29679	+	0.908021i	−0.297874	+	0.954605i	$0.596277\pi$
$348$		0			0
$349$	−13.2402	−	15.7790i	−0.708730	−	0.844632i	0.284754	−	0.958601i	$-0.408088\pi$
$349$	−13.2402	−	15.7790i	−0.708730	−	0.844632i	−0.993484	+	0.113969i	$0.963644\pi$
$350$	4.44052	−	13.0898i	0.237356	−	0.699678i
$351$		0			0
$352$	1.85918	−	1.85918i	0.0990944	−	0.0990944i
$353$	−0.152839	+	1.74696i	−0.00813482	+	0.0929814i	−0.999177	−	0.0405701i	$-0.987083\pi$
$353$	−0.152839	+	1.74696i	−0.00813482	+	0.0929814i	0.991042	+	0.133552i	$0.0426382\pi$
$354$		0			0
$355$	−1.51002	+	0.724474i	−0.0801437	+	0.0384511i
$356$	6.90944	+	18.9835i	0.366199	+	1.00612i
$357$		0			0
$358$	7.64820	−	10.9228i	0.404220	−	0.577286i
$359$	−9.41628	−	16.3095i	−0.496972	−	0.860781i	0.503022	−	0.864274i	$-0.332222\pi$
$359$	−9.41628	−	16.3095i	−0.496972	−	0.860781i	−0.999994	+	0.00349274i	$0.998888\pi$
$360$		0			0
$361$	−8.78354	+	15.2135i	−0.462291	+	0.800712i
$362$	0.875933	+	1.87844i	0.0460380	+	0.0987288i
$363$		0			0
$364$	−23.3346	+	27.8091i	−1.22307	+	1.45759i
$365$	16.7374	+	19.5068i	0.876076	+	1.02103i
$366$		0			0
$367$	−24.3645	+	11.3614i	−1.27182	+	0.593058i	−0.937034	−	0.349237i	$-0.886441\pi$
$367$	−24.3645	+	11.3614i	−1.27182	+	0.593058i	−0.334783	+	0.942295i	$0.608663\pi$
$368$	1.20961	+	4.51434i	0.0630555	+	0.235326i
$369$		0			0
$370$	−9.81486	−	4.44590i	−0.510251	−	0.231131i
$371$	−23.6399	+	4.16835i	−1.22732	+	0.216410i
$372$		0			0
$373$	2.86161	+	1.33439i	0.148169	+	0.0690922i	0.495288	−	0.868729i	$-0.335062\pi$
$373$	2.86161	+	1.33439i	0.148169	+	0.0690922i	−0.347120	+	0.937821i	$0.612840\pi$
$374$	0.262599	−	1.48927i	0.0135786	−	0.0770083i
$375$		0			0
$376$	19.9081	−	16.7049i	1.02668	−	0.861487i
$377$	−0.0226429	−	0.0226429i	−0.00116617	−	0.00116617i
$378$		0			0
$379$			7.29800i			0.374873i	0.982277	+	0.187436i	$0.0600179\pi$
$379$			7.29800i			0.374873i	−0.982277	+	0.187436i	$0.939982\pi$
$380$	−1.05499	+	4.11804i	−0.0541197	+	0.211251i
$381$		0			0
$382$	−0.169902	−	0.242645i	−0.00869293	−	0.0124148i
$383$	7.76938	−	16.6615i	0.396997	−	0.851362i	−0.601620	−	0.798783i	$-0.705478\pi$
$383$	7.76938	−	16.6615i	0.396997	−	0.851362i	0.998617	−	0.0525799i	$-0.0167444\pi$
$384$		0			0
$385$	−0.0489420	−	4.44657i	−0.00249432	−	0.226618i
$386$	−1.26438	+	0.729990i	−0.0643552	+	0.0371555i
$387$		0			0
$388$	13.1423	−	3.52146i	0.667197	−	0.178775i
$389$	−19.7491	−	7.18808i	−1.00132	−	0.364450i	−0.211226	−	0.977437i	$-0.567746\pi$
$389$	−19.7491	−	7.18808i	−1.00132	−	0.364450i	−0.790093	+	0.612987i	$0.789968\pi$
$390$		0			0
$391$	10.7587	+	9.02763i	0.544091	+	0.456547i
$392$	−2.31943	−	26.5112i	−0.117149	−	1.33902i
$393$		0			0
$394$	−5.86086	+	16.1026i	−0.295266	+	0.811237i
$395$	−3.49984	+	0.345050i	−0.176096	+	0.0173614i
$396$		0			0
$397$	−32.7796	−	8.78326i	−1.64516	−	0.440819i	−0.686907	−	0.726745i	$-0.741032\pi$
$397$	−32.7796	−	8.78326i	−1.64516	−	0.440819i	−0.958252	+	0.285926i	$0.907699\pi$
$398$	12.5371	+	8.77854i	0.628426	+	0.440029i
$399$		0			0
$400$	−0.186940	−	8.49107i	−0.00934699	−	0.424554i
$401$	26.7887	+	4.72357i	1.33776	+	0.235884i	0.796332	−	0.604860i	$-0.206771\pi$
$401$	26.7887	+	4.72357i	1.33776	+	0.235884i	0.541433	+	0.840744i	$0.317882\pi$
$402$		0			0
$403$	11.7968	+	1.03208i	0.587638	+	0.0514117i
$404$	−24.9303			−1.24033
$405$		0			0
$406$	0.0166833			0.000827980
$407$	−3.45320	−	0.302116i	−0.171169	−	0.0149753i
$408$		0			0
$409$	−13.3695	−	2.35741i	−0.661081	−	0.116566i	−0.166965	−	0.985963i	$-0.553397\pi$
$409$	−13.3695	−	2.35741i	−0.661081	−	0.116566i	−0.494115	+	0.869396i	$0.664508\pi$
$410$	1.24714	+	6.64438i	0.0615917	+	0.328143i
$411$		0			0
$412$	18.2111	+	12.7515i	0.897195	+	0.628222i
$413$	1.72085	+	0.461102i	0.0846777	+	0.0226893i
$414$		0			0
$415$	18.4580	+	15.1451i	0.906070	+	0.743444i
$416$	10.3361	−	28.3982i	0.506769	−	1.39234i
$417$		0			0
$418$	−0.0309084	−	0.353285i	−0.00151178	−	0.0172797i
$419$	9.78730	+	8.21252i	0.478141	+	0.401208i	0.849754	−	0.527180i	$-0.176751\pi$
$419$	9.78730	+	8.21252i	0.478141	+	0.401208i	−0.371613	+	0.928388i	$0.621195\pi$
$420$		0			0
$421$	16.9246	+	6.16004i	0.824853	+	0.300222i	0.719745	−	0.694239i	$-0.244259\pi$
$421$	16.9246	+	6.16004i	0.824853	+	0.300222i	0.105108	+	0.994461i	$0.466481\pi$
$422$	13.4482	−	3.60343i	0.654648	−	0.175412i
$423$		0			0
$424$	11.1122	−	6.41562i	0.539656	−	0.311570i
$425$	−15.0957	−	20.5795i	−0.732251	−	0.998254i
$426$		0			0
$427$	−4.18641	+	8.97778i	−0.202595	+	0.434465i
$428$	3.69050	+	5.27058i	0.178387	+	0.254763i
$429$		0			0
$430$	2.65162	+	0.679311i	0.127873	+	0.0327593i
$431$			4.80209i			0.231309i	0.993290	+	0.115654i	$0.0368965\pi$
$431$			4.80209i			0.231309i	−0.993290	+	0.115654i	$0.963104\pi$
$432$		0			0
$433$	23.6615	+	23.6615i	1.13710	+	1.13710i	0.988968	+	0.148130i	$0.0473253\pi$
$433$	23.6615	+	23.6615i	1.13710	+	1.13710i	0.148130	+	0.988968i	$0.452675\pi$
$434$	−4.72616	+	3.96572i	−0.226863	+	0.190360i
$435$		0			0
$436$	1.83198	−	10.3897i	0.0877360	−	0.497576i
$437$	2.98497	+	1.39192i	0.142791	+	0.0665844i
$438$		0			0
$439$	0.531654	−	0.0937450i	0.0253745	−	0.00447420i	−0.160947	−	0.986963i	$-0.551455\pi$
$439$	0.531654	−	0.0937450i	0.0253745	−	0.00447420i	0.186321	+	0.982489i	$0.440344\pi$
$440$	0.837512	+	2.22455i	0.0399268	+	0.106051i
$441$		0			0
$442$	−4.49871	−	16.7894i	−0.213982	−	0.798591i
$443$	−4.71408	+	2.19821i	−0.223973	+	0.104440i	−0.531366	−	0.847142i	$-0.678321\pi$
$443$	−4.71408	+	2.19821i	−0.223973	+	0.104440i	0.307393	+	0.951583i	$0.400543\pi$
$444$		0			0
$445$	−28.3606	−	2.16699i	−1.34442	−	0.102725i
$446$	−4.53516	+	5.40479i	−0.214746	+	0.255924i
$447$		0			0
$448$	0.469199	+	1.00620i	0.0221676	+	0.0475385i
$449$	−6.99817	+	12.1212i	−0.330264	+	0.572034i	−0.982564	−	0.185927i	$-0.940471\pi$
$449$	−6.99817	+	12.1212i	−0.330264	+	0.572034i	0.652300	+	0.757961i	$0.273804\pi$
$450$		0			0
$451$	1.08745	+	1.88352i	0.0512060	+	0.0886914i
$452$	−6.39863	+	9.13819i	−0.300966	+	0.429824i
$453$		0			0
$454$	−2.17201	−	5.96755i	−0.101937	−	0.280071i
$455$	−22.1093	−	46.0825i	−1.03650	−	2.16038i
$456$		0			0
$457$	0.334574	−	3.82420i	0.0156507	−	0.178888i	−0.984346	−	0.176248i	$-0.943604\pi$
$457$	0.334574	−	3.82420i	0.0156507	−	0.178888i	0.999997	−	0.00264047i	$-0.000840488\pi$
$458$	4.41318	−	4.41318i	0.206214	−	0.206214i
$459$		0			0
$460$	−9.64056	−	1.59069i	−0.449493	−	0.0741664i
$461$	14.3235	+	17.0701i	0.667111	+	0.795032i	0.988388	−	0.151953i	$-0.0485563\pi$
$461$	14.3235	+	17.0701i	0.667111	+	0.795032i	−0.321276	+	0.946985i	$0.604112\pi$
$462$		0			0
$463$	−0.977400	+	0.684383i	−0.0454236	+	0.0318060i	−0.596068	−	0.802934i	$-0.703271\pi$
$463$	−0.977400	+	0.684383i	−0.0454236	+	0.0318060i	0.550644	+	0.834740i	$0.314382\pi$
$464$	0.00963277	−	0.00350604i	0.000447190	−	0.000162764i
$465$		0			0
$466$	1.12747	+	6.39418i	0.0522289	+	0.296205i
$467$	−0.233069	+	0.869824i	−0.0107851	+	0.0402506i	−0.971109	−	0.238638i	$-0.923299\pi$
$467$	−0.233069	+	0.869824i	−0.0107851	+	0.0402506i	0.960324	+	0.278888i	$0.0899659\pi$
$468$		0			0
$469$	−21.8935	−	12.6402i	−1.01095	−	0.583672i
$470$	4.36355	+	15.5963i	0.201276	+	0.719404i
$471$		0			0
$472$	−0.948680	+	0.0829988i	−0.0436665	+	0.00382033i
$473$	0.877255	−	0.0767499i	0.0403362	−	0.00352896i
$474$		0			0
$475$	−4.66853	−	3.74539i	−0.214207	−	0.171850i
$476$	−30.2439	−	17.4613i	−1.38623	−	0.800338i
$477$		0			0
$478$	0.530593	−	1.98020i	0.0242687	−	0.0905722i
$479$	5.10504	+	28.9521i	0.233255	+	1.32286i	0.846257	+	0.532775i	$0.178851\pi$
$479$	5.10504	+	28.9521i	0.233255	+	1.32286i	−0.613001	+	0.790082i	$0.710038\pi$
$480$		0			0
$481$	−37.4398	+	13.6270i	−1.70711	+	0.621336i
$482$	−10.6595	+	7.46386i	−0.485527	+	0.339969i
$483$		0			0
$484$	−11.0119	−	13.1234i	−0.500539	−	0.596519i
$485$	−3.11864	+	18.9008i	−0.141610	+	0.858243i
$486$		0			0
$487$	22.6006	−	22.6006i	1.02413	−	1.02413i	0.0244298	−	0.999702i	$-0.492223\pi$
$487$	22.6006	−	22.6006i	1.02413	−	1.02413i	0.999702	−	0.0244298i	$-0.00777702\pi$
$488$	0.461492	−	5.27488i	0.0208908	−	0.238783i
$489$		0			0
$490$	15.6456	+	5.50031i	0.706798	+	0.248479i
$491$	4.34237	+	11.9306i	0.195968	+	0.538419i	0.998289	−	0.0584746i	$-0.0186237\pi$
$491$	4.34237	+	11.9306i	0.195968	+	0.538419i	−0.802320	+	0.596894i	$0.796401\pi$
$492$		0			0
$493$	0.0176690	−	0.0252339i	0.000795772	−	0.00113648i
$494$	−2.03808	−	3.53005i	−0.0916974	−	0.158824i
$495$		0			0
$496$	−1.89542	+	3.28297i	−0.0851071	+	0.147410i
$497$	−1.36361	−	2.92426i	−0.0611661	−	0.131171i
$498$		0			0
$499$	−7.76871	+	9.25839i	−0.347775	+	0.414463i	−0.911369	−	0.411589i	$-0.864974\pi$
$499$	−7.76871	+	9.25839i	−0.347775	+	0.414463i	0.563594	+	0.826052i	$0.309418\pi$
$500$	16.3316	+	6.96878i	0.730372	+	0.311653i
$501$		0			0
$502$	−8.26367	+	3.85341i	−0.368825	+	0.171986i
$503$	−5.65132	−	21.0910i	−0.251980	−	0.940402i	−0.969746	−	0.244117i	$-0.921502\pi$
$503$	−5.65132	−	21.0910i	−0.251980	−	0.940402i	0.717766	−	0.696285i	$-0.245165\pi$
$504$		0			0
$505$	14.4832	−	31.9734i	0.644493	−	1.42280i
$506$	0.802737	−	0.141544i	0.0356860	−	0.00629241i
$507$		0			0
$508$	−12.0684	−	5.62760i	−0.535450	−	0.249684i
$509$	0.934268	−	5.29850i	0.0414107	−	0.234852i	−0.957077	−	0.289835i	$-0.906399\pi$
$509$	0.934268	−	5.29850i	0.0414107	−	0.234852i	0.998487	+	0.0549834i	$0.0175106\pi$
$510$		0			0
$511$	−37.9326	+	31.8293i	−1.67804	+	1.40804i
$512$	12.3723	+	12.3723i	0.546785	+	0.546785i
$513$		0			0
$514$		−	18.1571i		−	0.800876i
$515$	−26.9336	+	15.9479i	−1.18684	+	0.702749i
$516$		0			0
$517$	2.98844	+	4.26794i	0.131432	+	0.187704i
$518$	8.77266	−	18.8130i	0.385449	−	0.826597i
$519$		0			0
$520$	19.5303	+	19.1051i	0.856461	+	0.837813i
$521$	2.74885	−	1.58705i	0.120429	−	0.0695300i	−0.438575	−	0.898694i	$-0.644517\pi$
$521$	2.74885	−	1.58705i	0.120429	−	0.0695300i	0.559005	+	0.829165i	$0.311183\pi$
$522$		0			0
$523$	−11.6055	+	3.10969i	−0.507473	+	0.135977i	−0.503466	−	0.864015i	$-0.667942\pi$
$523$	−11.6055	+	3.10969i	−0.507473	+	0.135977i	−0.00400710	+	0.999992i	$0.501276\pi$
$524$	−17.0706	−	6.21317i	−0.745731	−	0.271424i
$525$		0			0
$526$	2.58051	+	2.16530i	0.112515	+	0.0944116i
$527$	0.992860	+	11.3484i	0.0432496	+	0.494346i
$528$		0			0
$529$	5.27731	−	14.4993i	0.229448	−	0.630404i
$530$	0.784539	+	7.95757i	0.0340782	+	0.345655i
$531$		0			0
$532$	−7.91060	−	2.11964i	−0.342968	−	0.0918980i
$533$	20.4773	+	14.3384i	0.886972	+	0.621064i
$534$		0			0
$535$	−8.90355	+	1.67118i	−0.384934	+	0.0722513i
$536$	13.3080	+	2.34655i	0.574817	+	0.101356i
$537$		0			0
$538$	−7.18199	−	0.628343i	−0.309638	−	0.0270898i
$539$	5.33536			0.229810
$540$		0			0
$541$	33.7781			1.45223			0.726116	−	0.687572i	$-0.241324\pi$
$541$	33.7781			1.45223			0.726116	+	0.687572i	$0.241324\pi$
$542$	−9.83692	−	0.860619i	−0.422532	−	0.0369668i
$543$		0			0
$544$	28.6306	+	5.04834i	1.22753	+	0.216446i
$545$	12.2606	+	8.38538i	0.525186	+	0.359190i
$546$		0			0
$547$	11.7446	+	8.22365i	0.502162	+	0.351618i	0.797049	−	0.603914i	$-0.206393\pi$
$547$	11.7446	+	8.22365i	0.502162	+	0.351618i	−0.294887	+	0.955532i	$0.595282\pi$
$548$	15.8149	+	4.23759i	0.675579	+	0.181021i
$549$		0			0
$550$	−1.47813	−	0.0965912i	−0.0630278	−	0.00411866i
$551$	0.00247076	−	0.00678836i	0.000105258	−	0.000289194i
$552$		0			0
$553$	−0.590495	−	6.74939i	−0.0251104	−	0.287013i
$554$	−8.07250	−	6.77363i	−0.342968	−	0.287784i
$555$		0			0
$556$	2.58203	+	0.939783i	0.109503	+	0.0398557i
$557$	9.77642	−	2.61958i	0.414240	−	0.110995i	−0.0456789	−	0.998956i	$-0.514545\pi$
$557$	9.77642	−	2.61958i	0.414240	−	0.110995i	0.459919	+	0.887961i	$0.347878\pi$
$558$		0			0
$559$	8.76560	−	5.06082i	0.370745	−	0.214050i
$560$	16.3611	−	0.180082i	0.691383	−	0.00760984i
$561$		0			0
$562$	2.61703	−	5.61224i	0.110393	−	0.236738i
$563$	16.1451	+	23.0577i	0.680437	+	0.971765i	0.999710	+	0.0241016i	$0.00767253\pi$
$563$	16.1451	+	23.0577i	0.680437	+	0.971765i	−0.319273	+	0.947663i	$0.603439\pi$
$564$		0			0
$565$	−8.00256	−	13.5151i	−0.336670	−	0.568585i
$566$		−	9.95976i		−	0.418640i
$567$		0			0
$568$	1.21955	+	1.21955i	0.0511713	+	0.0511713i
$569$	7.66040	−	6.42784i	0.321141	−	0.269469i	−0.467938	−	0.883761i	$-0.655003\pi$
$569$	7.66040	−	6.42784i	0.321141	−	0.269469i	0.789078	+	0.614292i	$0.210558\pi$
$570$		0			0
$571$	4.25288	−	24.1193i	0.177978	−	1.00936i	−0.756673	−	0.653794i	$-0.773176\pi$
$571$	4.25288	−	24.1193i	0.177978	−	1.00936i	0.934651	−	0.355568i	$-0.115712\pi$
$572$	3.52584	+	1.64413i	0.147423	+	0.0687444i
$573$		0			0
$574$	−12.8261	+	2.26159i	−0.535353	+	0.0943971i
$575$	7.64073	−	11.4400i	0.318640	−	0.477081i
$576$		0			0
$577$	−4.13963	−	15.4493i	−0.172335	−	0.643163i	−0.996990	−	0.0775272i	$-0.975298\pi$
$577$	−4.13963	−	15.4493i	−0.172335	−	0.643163i	0.824655	−	0.565636i	$-0.191369\pi$
$578$	5.26705	−	2.45606i	0.219080	−	0.102159i
$579$		0			0
$580$	−0.00163278	+	0.0213691i	−6.77973e−5	+	0.000887302i
$581$	−29.5668	+	35.2364i	−1.22664	+	1.46185i
$582$		0			0
$583$	1.08716	+	2.33143i	0.0450258	+	0.0965581i
$584$	13.2344	−	22.9227i	0.547643	−	0.948546i
$585$		0			0
$586$	−3.09532	−	5.36125i	−0.127867	−	0.221471i
$587$	11.3970	−	16.2765i	0.470403	−	0.671805i	−0.511913	−	0.859037i	$-0.671063\pi$
$587$	11.3970	−	16.2765i	0.470403	−	0.671805i	0.982316	+	0.187233i	$0.0599518\pi$
$588$		0			0
$589$	0.913697	+	2.51036i	0.0376482	+	0.103438i
$590$	0.196823	−	0.559865i	0.00810309	−	0.0230493i
$591$		0			0
$592$	1.11163	−	12.7060i	0.0456878	−	0.522214i
$593$	24.0438	−	24.0438i	0.987362	−	0.987362i	−0.0125593	−	0.999921i	$-0.503998\pi$
$593$	24.0438	−	24.0438i	0.987362	−	0.987362i	0.999921	+	0.0125593i	$0.00399784\pi$
$594$		0			0
$595$	39.9644	−	28.6440i	1.63838	−	1.17429i
$596$	−4.68781	−	5.58672i	−0.192020	−	0.228841i
$597$		0			0
$598$	7.67460	−	5.37382i	0.313838	−	0.219752i
$599$	32.8027	−	11.9392i	1.34028	−	0.487823i	0.430381	−	0.902647i	$-0.358379\pi$
$599$	32.8027	−	11.9392i	1.34028	−	0.487823i	0.909901	+	0.414825i	$0.136157\pi$
$600$		0			0
$601$	−4.52626	−	25.6697i	−0.184630	−	1.04709i	−0.926430	−	0.376467i	$-0.877139\pi$
$601$	−4.52626	−	25.6697i	−0.184630	−	1.04709i	0.741800	−	0.670621i	$-0.233972\pi$
$602$	−1.36484	+	5.09367i	−0.0556269	+	0.207602i
$603$		0			0
$604$	6.09398	+	3.51836i	0.247961	+	0.143160i
$605$	23.2282	−	6.49881i	0.944361	−	0.264214i
$606$		0			0
$607$	−3.56643	+	0.312022i	−0.144757	+	0.0126646i	−0.159304	−	0.987230i	$-0.550925\pi$
$607$	−3.56643	+	0.312022i	−0.144757	+	0.0126646i	0.0145470	+	0.999894i	$0.495369\pi$
$608$	6.79175	−	0.594201i	0.275442	−	0.0240980i
$609$		0			0
$610$	2.87565	+	1.61832i	0.116432	+	0.0655239i
$611$	51.8625	+	29.9428i	2.09813	+	1.21136i
$612$		0			0
$613$	4.71891	−	17.6112i	0.190595	−	0.711310i	−0.802768	−	0.596291i	$-0.796640\pi$
$613$	4.71891	−	17.6112i	0.190595	−	0.711310i	0.993363	−	0.115019i	$-0.0366928\pi$
$614$	−0.488558	−	2.77075i	−0.0197166	−	0.111818i
$615$		0			0
$616$	−4.30313	+	1.56621i	−0.173378	+	0.0631044i
$617$	−2.52278	+	1.76647i	−0.101563	+	0.0711153i	−0.623255	−	0.782019i	$-0.714190\pi$
$617$	−2.52278	+	1.76647i	−0.101563	+	0.0711153i	0.521692	+	0.853134i	$0.325301\pi$
$618$		0			0
$619$	22.9284	+	27.3250i	0.921572	+	1.09829i	0.994889	+	0.100978i	$0.0321970\pi$
$619$	22.9284	+	27.3250i	0.921572	+	1.09829i	−0.0733171	+	0.997309i	$0.523359\pi$
$620$	−4.61699	−	6.44168i	−0.185423	−	0.258704i
$621$		0			0
$622$	3.76282	−	3.76282i	0.150875	−	0.150875i
$623$	4.77580	−	54.5877i	0.191339	−	2.18701i
$624$		0			0
$625$	−18.4253	+	16.8970i	−0.737013	+	0.675879i
$626$	2.27197	+	6.24218i	0.0908062	+	0.249488i
$627$		0			0
$628$	−0.758266	+	1.08292i	−0.0302581	+	0.0432130i
$629$	−19.1642	−	33.1934i	−0.764127	−	1.32351i
$630$		0			0
$631$	0.459598	−	0.796047i	0.0182963	−	0.0316901i	−0.856732	−	0.515761i	$-0.827509\pi$
$631$	0.459598	−	0.796047i	0.0182963	−	0.0316901i	0.875029	+	0.484071i	$0.160842\pi$
$632$	1.53054	+	3.28225i	0.0608815	+	0.130561i
$633$		0			0
$634$	0.560241	−	0.667669i	0.0222500	−	0.0265165i
$635$	14.2286	−	12.2085i	0.564643	−	0.484481i
$636$		0			0
$637$	55.5788	−	25.9168i	2.20211	−	1.02686i
$638$	−0.000462735	−	0.00172695i	−1.83199e−5	−	6.83707e-5i
$639$		0			0
$640$	−23.4912	+	8.84408i	−0.928570	+	0.349593i
$641$	−28.1175	+	4.95787i	−1.11057	+	0.195824i	−0.698699	−	0.715416i	$-0.746237\pi$
$641$	−28.1175	+	4.95787i	−1.11057	+	0.195824i	−0.411875	+	0.911240i	$0.635126\pi$
$642$		0			0
$643$	34.3252	+	16.0061i	1.35365	+	0.631220i	0.957891	−	0.287133i	$-0.0927020\pi$
$643$	34.3252	+	16.0061i	1.35365	+	0.631220i	0.395764	+	0.918352i	$0.370480\pi$
$644$	3.26871	−	18.5378i	0.128805	−	0.730492i
$645$		0			0
$646$	3.00385	−	2.52053i	0.118185	−	0.0991688i
$647$	−30.2410	−	30.2410i	−1.18890	−	1.18890i	−0.977373	−	0.211525i	$-0.932157\pi$
$647$	−30.2410	−	30.2410i	−1.18890	−	1.18890i	−0.211525	−	0.977373i	$-0.567843\pi$
$648$		0			0
$649$		−	0.190921i		−	0.00749431i
$650$	−15.8670	+	6.17392i	−0.622355	+	0.242161i
$651$		0			0
$652$	13.0851	+	18.6874i	0.512451	+	0.731856i
$653$	−15.4696	+	33.1747i	−0.605374	+	1.29823i	0.329804	+	0.944049i	$0.393017\pi$
$653$	−15.4696	+	33.1747i	−0.605374	+	1.29823i	−0.935178	+	0.354178i	$0.884761\pi$
$654$		0			0
$655$	17.8855	−	18.2836i	0.698845	−	0.714400i
$656$	−6.93039	+	4.00126i	−0.270586	+	0.156223i
$657$		0			0
$658$	−30.1372	+	8.07523i	−1.17487	+	0.314805i
$659$	29.4659	+	10.7247i	1.14783	+	0.417776i	0.844735	−	0.535184i	$-0.179758\pi$
$659$	29.4659	+	10.7247i	1.14783	+	0.417776i	0.303095	+	0.952960i	$0.401980\pi$
$660$		0			0
$661$	3.28171	+	2.75368i	0.127644	+	0.107106i	0.704375	−	0.709828i	$-0.251227\pi$
$661$	3.28171	+	2.75368i	0.127644	+	0.107106i	−0.576731	+	0.816934i	$0.695672\pi$
$662$	0.399503	+	4.56634i	0.0155271	+	0.177476i
$663$		0			0
$664$	8.40938	−	23.1046i	0.326347	−	0.896632i
$665$	7.31409	−	8.91402i	0.283628	−	0.345671i
$666$		0			0
$667$	0.0160385	+	0.00429751i	0.000621014	+	0.000166400i
$668$	−29.1901	−	20.4392i	−1.12940	−	0.790815i
$669$		0			0
$670$	−4.75397	+	6.95096i	−0.183662	+	0.268539i
$671$	1.04544	+	0.184339i	0.0403587	+	0.00711633i
$672$		0			0
$673$	28.3733	+	2.48234i	1.09371	+	0.0956872i	0.619705	−	0.784835i	$-0.287252\pi$
$673$	28.3733	+	2.48234i	1.09371	+	0.0956872i	0.474005	+	0.880522i	$0.342808\pi$
$674$	18.4533			0.710793
$675$		0			0
$676$	24.0691			0.925735
$677$	−42.4749	−	3.71607i	−1.63244	−	0.142820i	−0.766255	−	0.642537i	$-0.777882\pi$
$677$	−42.4749	−	3.71607i	−1.63244	−	0.142820i	−0.866189	+	0.499717i	$0.833437\pi$
$678$		0			0
$679$	−36.3444	−	6.40849i	−1.39477	−	0.245935i
$680$	−14.8373	+	21.6941i	−0.568983	+	0.831933i
$681$		0			0
$682$	0.541592	+	0.379227i	0.0207386	+	0.0145213i
$683$	16.5292	+	4.42899i	0.632473	+	0.169471i	0.560792	−	0.827957i	$-0.310497\pi$
$683$	16.5292	+	4.42899i	0.632473	+	0.169471i	0.0716812	+	0.997428i	$0.477164\pi$
$684$		0			0
$685$	−14.6224	+	17.8210i	−0.558692	+	0.680904i
$686$	−4.30892	+	11.8386i	−0.164515	+	0.452002i
$687$		0			0
$688$	0.282400	+	3.22785i	0.0107664	+	0.123061i
$689$	22.6501	+	19.0057i	0.862901	+	0.724060i
$690$		0			0
$691$	−28.7479	−	10.4634i	−1.09362	−	0.398045i	−0.268660	−	0.963235i	$-0.586581\pi$
$691$	−28.7479	−	10.4634i	−1.09362	−	0.398045i	−0.824961	+	0.565190i	$0.808803\pi$
$692$	3.54310	−	0.949372i	0.134689	−	0.0360897i
$693$		0			0
$694$	−16.3892	+	9.46233i	−0.622127	+	0.359185i
$695$	−2.70530	+	2.76552i	−0.102618	+	0.104902i
$696$		0			0
$697$	−10.1632	+	21.7951i	−0.384959	+	0.825547i
$698$	−7.58187	−	10.8280i	−0.286978	−	0.409847i
$699$		0			0
$700$	−13.7709	+	31.3134i	−0.520491	+	1.18353i
$701$		−	33.1045i		−	1.25034i	−0.780488	−	0.625171i	$-0.785029\pi$
$701$		−	33.1045i		−	1.25034i	0.780488	−	0.625171i	$-0.214971\pi$
$702$		0			0
$703$	−6.35572	−	6.35572i	−0.239710	−	0.239710i
$704$	0.0911416	−	0.0764768i	0.00343503	−	0.00288233i
$705$		0			0
$706$	−0.195420	+	1.10828i	−0.00735472	+	0.0417107i
$707$	61.2863	+	28.5783i	2.30491	+	1.07480i
$708$		0			0
$709$	36.6991	−	6.47105i	1.37827	−	0.243025i	0.565083	−	0.825034i	$-0.308844\pi$
$709$	36.6991	−	6.47105i	1.37827	−	0.243025i	0.813182	+	0.582009i	$0.197733\pi$
$710$	−1.00587	+	0.378697i	−0.0377498	+	0.0142122i
$711$		0			0
$712$	7.58092	+	28.2924i	0.284107	+	1.06030i
$713$	−5.56503	+	2.59502i	−0.208412	+	0.0971841i
$714$		0			0
$715$	−4.15693	+	3.56677i	−0.155460	+	0.133390i
$716$	−21.2116	+	25.2790i	−0.792716	+	0.944722i
$717$		0			0
$718$	−5.10759	−	10.9533i	−0.190614	−	0.408772i
$719$	−21.5770	+	37.3725i	−0.804687	+	1.39376i	0.111816	+	0.993729i	$0.464333\pi$
$719$	−21.5770	+	37.3725i	−0.804687	+	1.39376i	−0.916502	+	0.400029i	$0.869000\pi$
$720$		0			0
$721$	−30.1509	−	52.2229i	−1.12288	−	1.94488i
$722$	−6.46621	+	9.23470i	−0.240647	+	0.343680i
$723$		0			0
$724$	−1.75433	−	4.82000i	−0.0651993	−	0.179134i
$725$	−0.0264575	−	0.0145083i	−0.000982606	−	0.000538826i
$726$		0			0
$727$	0.590839	−	6.75332i	0.0219130	−	0.250467i	−0.977335	−	0.211698i	$-0.932101\pi$
$727$	0.590839	−	6.75332i	0.0219130	−	0.250467i	0.999248	−	0.0387690i	$-0.0123436\pi$
$728$	−37.2180	+	37.2180i	−1.37939	+	1.37939i
$729$		0			0
$730$	9.60915	+	13.4068i	0.355651	+	0.496207i
$731$	6.25882	+	7.45897i	0.231491	+	0.275880i
$732$		0			0
$733$	−20.8024	+	14.5660i	−0.768353	+	0.538006i	−0.890760	−	0.454474i	$-0.849827\pi$
$733$	−20.8024	+	14.5660i	−0.768353	+	0.538006i	0.122408	+	0.992480i	$0.460938\pi$
$734$	−16.2116	+	5.90055i	−0.598382	+	0.217793i
$735$		0			0
$736$	2.72113	+	15.4323i	0.100302	+	0.568841i
$737$	−0.701189	+	2.61687i	−0.0258286	+	0.0963937i
$738$		0			0
$739$	−31.3022	−	18.0723i	−1.15147	−	0.664801i	−0.202224	−	0.979339i	$-0.564817\pi$
$739$	−31.3022	−	18.0723i	−1.15147	−	0.664801i	−0.949245	+	0.314538i	$0.898150\pi$
$740$	23.2384	+	13.0778i	0.854259	+	0.480749i
$741$		0			0
$742$	−15.3461	+	1.34261i	−0.563371	+	0.0492886i
$743$	−35.7603	+	3.12862i	−1.31192	+	0.114778i	−0.721554	−	0.692358i	$-0.756572\pi$
$743$	−35.7603	+	3.12862i	−1.31192	+	0.114778i	−0.590365	+	0.807136i	$0.701016\pi$
$744$		0			0
$745$	9.88838	−	2.76658i	0.362282	−	0.101360i
$746$	1.75479	+	1.01313i	0.0642473	+	0.0370932i
$747$		0			0
$748$	−0.968627	+	3.61497i	−0.0354165	+	0.132176i
$749$	−3.03056	−	17.1872i	−0.110734	−	0.628006i
$750$		0			0
$751$	20.6234	−	7.50630i	0.752558	−	0.273909i	0.0628763	−	0.998021i	$-0.479973\pi$
$751$	20.6234	−	7.50630i	0.752558	−	0.273909i	0.689682	+	0.724113i	$0.257750\pi$
$752$	−15.7038	+	10.9959i	−0.572660	+	0.400981i
$753$		0			0
$754$	−0.0132091	−	0.0157420i	−0.000481047	−	0.000573290i
$755$	−8.05261	+	5.77161i	−0.293065	+	0.210051i
$756$		0			0
$757$	−19.9998	+	19.9998i	−0.726906	+	0.726906i	−0.970002	−	0.243096i	$-0.921837\pi$
$757$	−19.9998	+	19.9998i	−0.726906	+	0.726906i	0.243096	+	0.970002i	$0.421837\pi$
$758$	−0.408186	+	4.66559i	−0.0148260	+	0.169462i
$759$		0			0
$760$	−2.04417	+	5.81466i	−0.0741500	+	0.210920i
$761$	−17.7365	−	48.7306i	−0.642947	−	1.76648i	−0.642264	−	0.766484i	$-0.722005\pi$
$761$	−17.7365	−	48.7306i	−0.642947	−	1.76648i	−0.000683402	−	1.00000i	$-0.500218\pi$
$762$		0			0
$763$	−16.4135	+	23.4409i	−0.594209	+	0.848619i
$764$	0.366534	+	0.634856i	0.0132607	+	0.0229683i
$765$		0			0
$766$	5.89884	−	10.2171i	0.213134	−	0.369159i
$767$	−0.927410	−	1.98884i	−0.0334868	−	0.0718127i
$768$		0			0
$769$	28.9226	−	34.4686i	1.04298	−	1.24297i	0.0736257	−	0.997286i	$-0.476543\pi$
$769$	28.9226	−	34.4686i	1.04298	−	1.24297i	0.969350	−	0.245684i	$-0.0790126\pi$
$770$	0.217414	−	2.84542i	0.00783506	−	0.102542i
$771$		0			0
$772$	3.27462	−	1.52698i	0.117856	−	0.0549572i
$773$	−6.21709	−	23.2025i	−0.223613	−	0.834536i	−0.982955	−	0.183844i	$-0.941146\pi$
$773$	−6.21709	−	23.2025i	−0.223613	−	0.834536i	0.759342	−	0.650691i	$-0.225521\pi$
$774$		0			0
$775$	10.9437	−	2.17907i	0.393111	−	0.0782746i
$776$	19.4273	−	3.42556i	0.697399	−	0.122970i
$777$		0			0
$778$	−12.2235	−	5.69992i	−0.438234	−	0.204352i
$779$	−0.979290	+	5.55383i	−0.0350867	+	0.198987i
$780$		0			0
$781$	−0.264879	+	0.222260i	−0.00947813	+	0.00795309i
$782$	6.37309	+	6.37309i	0.227901	+	0.227901i
$783$		0			0
$784$			19.6314i			0.701122i
$785$	−0.948338	−	1.60160i	−0.0338476	−	0.0571635i
$786$		0			0
$787$	−18.8846	−	26.9699i	−0.673162	−	0.961375i	−0.999868	−	0.0162488i	$-0.994828\pi$
$787$	−18.8846	−	26.9699i	−0.673162	−	0.961375i	0.326706	−	0.945126i	$-0.394061\pi$
$788$	17.9224	−	38.4347i	0.638460	−	1.36918i
$789$		0			0
$790$	−2.25674	+	0.0248392i	−0.0802911	+	0.000883739i
$791$	26.2051	−	15.1295i	0.931746	−	0.537944i
$792$		0			0
$793$	11.7858	−	3.15800i	0.418527	−	0.112144i
$794$	−20.4646	−	7.44852i	−0.726263	−	0.264338i
$795$		0			0
$796$	−29.0150	−	24.3465i	−1.02841	−	0.862939i
$797$	−4.05225	−	46.3175i	−0.143538	−	1.64065i	−0.636988	−	0.770874i	$-0.719820\pi$
$797$	−4.05225	−	46.3175i	−0.143538	−	1.64065i	0.493449	−	0.869774i	$-0.335736\pi$
$798$		0			0
$799$	−19.7037	+	54.1355i	−0.697068	+	1.91518i
$800$	1.85692	−	28.4165i	0.0656522	−	1.00467i
$801$		0			0
$802$	16.8618	+	4.51810i	0.595410	+	0.159540i
$803$	4.34687	+	3.04371i	0.153398	+	0.107410i
$804$		0			0
$805$	21.8760	+	14.9616i	0.771026	+	0.527328i
$806$	7.48391	+	1.31962i	0.263610	+	0.0464815i
$807$		0			0
$808$	−36.0087	−	3.15035i	−1.26678	−	0.110829i
$809$	14.6731			0.515879			0.257939	−	0.966161i	$-0.416957\pi$
$809$	14.6731			0.515879			0.257939	+	0.966161i	$0.416957\pi$
$810$		0			0
$811$	30.4369			1.06878			0.534392	−	0.845237i	$-0.320541\pi$
$811$	30.4369			1.06878			0.534392	+	0.845237i	$0.320541\pi$
$812$	−0.0411306	−	0.00359846i	−0.00144340	−	0.000126281i
$813$		0			0
$814$	−2.19073	−	0.386284i	−0.0767849	−	0.0135393i
$815$	−31.5685	+	5.92535i	−1.10580	+	0.207556i
$816$		0			0
$817$	1.87046	+	1.30971i	0.0654390	+	0.0458209i
$818$	−8.41525	−	2.25486i	−0.294232	−	0.0788393i
$819$		0			0
$820$	−1.64152	−	16.6499i	−0.0573242	−	0.581439i
$821$	−5.06906	+	13.9271i	−0.176911	+	0.486060i	−0.996177	−	0.0873536i	$-0.972159\pi$
$821$	−5.06906	+	13.9271i	−0.176911	+	0.486060i	0.819266	+	0.573414i	$0.194381\pi$
$822$		0			0
$823$	−1.04135	−	11.9027i	−0.0362993	−	0.414903i	−0.992505	−	0.122206i	$-0.961003\pi$
$823$	−1.04135	−	11.9027i	−0.0362993	−	0.414903i	0.956205	−	0.292696i	$-0.0945525\pi$
$824$	24.6922	+	20.7192i	0.860193	+	0.721788i
$825$		0			0
$826$	1.07435	+	0.391031i	0.0373813	+	0.0136057i
$827$	−5.37558	+	1.44038i	−0.186927	+	0.0500870i	−0.351068	−	0.936350i	$-0.614181\pi$
$827$	−5.37558	+	1.44038i	−0.186927	+	0.0500870i	0.164141	+	0.986437i	$0.447515\pi$
$828$		0			0
$829$	−34.1754	+	19.7312i	−1.18696	+	0.685293i	−0.957615	−	0.288052i	$-0.906992\pi$
$829$	−34.1754	+	19.7312i	−1.18696	+	0.685293i	−0.229347	+	0.973345i	$0.573659\pi$
$830$	10.9531	+	10.7146i	0.380188	+	0.371910i
$831$		0			0
$832$	0.577937	−	1.23939i	0.0200364	−	0.0429681i
$833$	33.8375	+	48.3250i	1.17240	+	1.67436i
$834$		0			0
$835$	43.1713	−	25.5626i	1.49401	−	0.884630i
$836$			0.877645i			0.0303540i
$837$		0			0
$838$	5.79766	+	5.79766i	0.200277	+	0.200277i
$839$	−34.4322	+	28.8921i	−1.18873	+	0.997464i	−0.188851	+	0.982006i	$0.560476\pi$
$839$	−34.4322	+	28.8921i	−1.18873	+	0.997464i	−0.999881	+	0.0154586i	$0.995079\pi$
$840$		0			0
$841$	−5.03579	+	28.5594i	−0.173648	+	0.984807i
$842$	10.4753	+	4.88471i	0.361003	+	0.168338i
$843$		0			0
$844$	−33.9320	+	5.98313i	−1.16799	+	0.205948i
$845$	−13.9829	+	30.8689i	−0.481025	+	1.06192i
$846$		0			0
$847$	12.0268	+	44.8845i	0.413244	+	1.54225i
$848$	−8.57848	+	4.00021i	−0.294586	+	0.137368i
$849$		0			0
$850$	−8.49962	−	14.0008i	−0.291535	−	0.480222i
$851$	13.2797	−	15.8261i	0.455222	−	0.542513i
$852$		0			0
$853$	−3.70943	−	7.95489i	−0.127008	−	0.272370i	0.832513	−	0.554005i	$-0.186901\pi$
$853$	−3.70943	−	7.95489i	−0.127008	−	0.272370i	−0.959522	+	0.281635i	$0.909123\pi$
$854$	−3.17850	+	5.50532i	−0.108766	+	0.188388i
$855$		0			0
$856$	4.66443	+	8.07903i	0.159427	+	0.276135i
$857$	19.8301	−	28.3204i	0.677385	−	0.967406i	−0.322399	−	0.946604i	$-0.604489\pi$
$857$	19.8301	−	28.3204i	0.677385	−	0.967406i	0.999784	−	0.0208017i	$-0.00662187\pi$
$858$		0			0
$859$	6.70299	+	18.4163i	0.228703	+	0.628357i	0.999967	−	0.00815913i	$-0.00259716\pi$
$859$	6.70299	+	18.4163i	0.228703	+	0.628357i	−0.771264	+	0.636516i	$0.780375\pi$
$860$	−6.39071	−	2.24669i	−0.217922	−	0.0766114i
$861$		0			0
$862$	−0.268587	+	3.06997i	−0.00914812	+	0.104563i
$863$	−29.8911	+	29.8911i	−1.01750	+	1.01750i	−0.0176605	+	0.999844i	$0.505622\pi$
$863$	−29.8911	+	29.8911i	−1.01750	+	1.01750i	−0.999844	+	0.0176605i	$0.994378\pi$
$864$		0			0
$865$	−0.840774	+	5.09560i	−0.0285872	+	0.173255i
$866$	13.8033	+	16.4501i	0.469055	+	0.558998i
$867$		0			0
$868$	12.5071	−	8.75757i	0.424519	−	0.297251i
$869$	−0.682275	+	0.248328i	−0.0231446	+	0.00842394i
$870$		0			0
$871$	5.40728	+	30.6662i	0.183219	+	1.03908i
$872$	3.95897	−	14.7751i	0.134068	−	0.500347i
$873$		0			0
$874$	1.83043	+	1.05680i	0.0619154	+	0.0357469i
$875$	−32.1596	−	35.8527i	−1.08719	−	1.21204i
$876$		0			0
$877$	−32.6921	+	2.86019i	−1.10393	+	0.0965817i	−0.624521	−	0.781008i	$-0.714706\pi$
$877$	−32.6921	+	2.86019i	−1.10393	+	0.0965817i	−0.479413	+	0.877590i	$0.659150\pi$
$878$	0.345129	−	0.0301948i	0.0116475	−	0.00101903i
$879$		0			0
$880$	−0.472439	−	1.68860i	−0.0159259	−	0.0569228i
$881$	10.5631	+	6.09860i	0.355879	+	0.205467i	0.667272	−	0.744814i	$-0.267462\pi$
$881$	10.5631	+	6.09860i	0.355879	+	0.205467i	−0.311392	+	0.950281i	$0.600795\pi$
$882$		0			0
$883$	9.21415	−	34.3877i	0.310081	−	1.15724i	−0.618402	−	0.785862i	$-0.712220\pi$
$883$	9.21415	−	34.3877i	0.310081	−	1.15724i	0.928483	−	0.371376i	$-0.121114\pi$
$884$	7.46965	+	42.3625i	0.251232	+	1.42480i
$885$		0			0
$886$	−3.13665	+	1.14165i	−0.105378	+	0.0383544i
$887$	−8.21054	+	5.74909i	−0.275683	+	0.193035i	−0.703239	−	0.710954i	$-0.748264\pi$
$887$	−8.21054	+	5.74909i	−0.275683	+	0.193035i	0.427556	+	0.903989i	$0.359375\pi$
$888$		0			0
$889$	23.2168	+	27.6687i	0.778666	+	0.927978i
$890$	−18.0096	−	2.97159i	−0.603684	−	0.0996080i
$891$		0			0
$892$	12.3466	−	12.3466i	0.413396	−	0.413396i
$893$	−1.17747	+	13.4586i	−0.0394027	+	0.450374i
$894$		0			0
$895$	−20.0978	−	41.8899i	−0.671795	−	1.40022i
$896$	−16.5391	−	45.4408i	−0.552532	−	1.51807i
$897$		0			0
$898$	−5.15187	+	7.35763i	−0.171920	+	0.245527i
$899$	0.00673405	+	0.0116637i	0.000224593	+	0.000389007i
$900$		0			0
$901$	−14.2220	+	24.6332i	−0.473803	+	0.820651i
$902$	0.589856	+	1.26495i	0.0196401	+	0.0421183i
$903$		0			0
$904$	−10.3968	+	12.3904i	−0.345791	+	0.412098i
$905$	7.20086	+	0.550206i	0.239365	+	0.0182895i
$906$		0			0
$907$	−16.0298	+	7.47482i	−0.532261	+	0.248197i	−0.670118	−	0.742255i	$-0.733756\pi$
$907$	−16.0298	+	7.47482i	−0.532261	+	0.248197i	0.137857	+	0.990452i	$0.455979\pi$
$908$	4.06766	+	15.1807i	0.134990	+	0.503790i
$909$		0			0
$910$	−11.5570	−	30.6970i	−0.383110	−	1.01760i
$911$	−15.2588	+	2.69054i	−0.505547	+	0.0891416i	−0.420604	−	0.907244i	$-0.638182\pi$
$911$	−15.2588	+	2.69054i	−0.505547	+	0.0891416i	−0.0849428	+	0.996386i	$0.527071\pi$
$912$		0			0
$913$	4.46752	+	2.08324i	0.147853	+	0.0689451i
$914$	0.427785	−	2.42609i	0.0141499	−	0.0802478i
$915$		0			0
$916$	−11.8320	+	9.92824i	−0.390941	+	0.328038i
$917$	34.8423	+	34.8423i	1.15059	+	1.15059i
$918$		0			0
$919$		−	18.6392i		−	0.614851i	−0.951572	−	0.307426i	$-0.900532\pi$
$919$		−	18.6392i		−	0.614851i	0.951572	−	0.307426i	$-0.0994676\pi$
$920$	−13.7235	−	3.51579i	−0.452452	−	0.115912i
$921$		0			0
$922$	8.20222	+	11.7140i	0.270126	+	0.385779i
$923$	−1.67962	+	3.60196i	−0.0552855	+	0.118560i
$924$		0			0
$925$	−30.2726	+	22.2059i	−0.995357	+	0.730126i
$926$	−0.663128	+	0.382857i	−0.0217917	+	0.0125815i
$927$		0			0
$928$	0.0331999	−	0.00889589i	0.00108984	−	0.000292022i
$929$	9.92982	+	3.61416i	0.325787	+	0.118577i	0.499736	−	0.866178i	$-0.333431\pi$
$929$	9.92982	+	3.61416i	0.325787	+	0.118577i	−0.173949	+	0.984755i	$0.555653\pi$
$930$		0			0
$931$	10.5979	+	8.89269i	0.347332	+	0.291446i
$932$	−1.40045	−	16.0072i	−0.0458733	−	0.524334i
$933$		0			0
$934$	−0.197650	+	0.543040i	−0.00646732	+	0.0177688i
$935$	−4.07351	−	3.34237i	−0.133218	−	0.109307i
$936$		0			0
$937$	−14.3508	−	3.84529i	−0.468820	−	0.125620i	0.0166719	−	0.999861i	$-0.494693\pi$
$937$	−14.3508	−	3.84529i	−0.468820	−	0.125620i	−0.485492	+	0.874241i	$0.661360\pi$
$938$	−13.2895	−	9.30540i	−0.433917	−	0.303832i
$939$		0			0
$940$	−7.39378	−	39.3919i	−0.241159	−	1.28482i
$941$	−16.9600	−	2.99051i	−0.552882	−	0.0974879i	−0.109774	−	0.993957i	$-0.535013\pi$
$941$	−16.9600	−	2.99051i	−0.552882	−	0.0974879i	−0.443107	+	0.896469i	$0.646124\pi$
$942$		0			0
$943$	−12.9130	−	1.12974i	−0.420504	−	0.0367894i
$944$	0.702492			0.0228642
$945$		0			0
$946$	0.565120			0.0183736
$947$	59.3613	+	5.19344i	1.92898	+	0.168764i	0.986304	−	0.164940i	$-0.0527431\pi$
$947$	59.3613	+	5.19344i	1.92898	+	0.168764i	0.942678	+	0.333704i	$0.108299\pi$
$948$		0			0
$949$	60.0667	+	10.5914i	1.94985	+	0.343811i
$950$	−2.77510	−	2.65554i	−0.0900360	−	0.0861569i
$951$		0			0
$952$	−41.4769	−	29.0424i	−1.34427	−	0.941271i
$953$	7.58847	+	2.03332i	0.245815	+	0.0658658i	0.379623	−	0.925141i	$-0.376054\pi$
$953$	7.58847	+	2.03332i	0.245815	+	0.0658658i	−0.133808	+	0.991007i	$0.542721\pi$
$954$		0			0
$955$	−1.02715	+	0.101267i	−0.0332377	+	0.00327691i
$956$	−1.73522	+	4.76748i	−0.0561211	+	0.154191i
$957$		0			0
$958$	1.64431	+	18.7946i	0.0531253	+	0.607225i
$959$	−34.0202	−	28.5463i	−1.09857	−	0.921808i
$960$		0			0
$961$	24.4503	+	8.89918i	0.788719	+	0.287070i
$962$	−24.6973	+	6.61763i	−0.796274	+	0.213361i
$963$		0			0
$964$	27.8895	−	16.1020i	0.898261	−	0.518611i
$965$	0.0559891	+	5.08682i	0.00180235	+	0.163751i
$966$		0			0
$967$	−13.1660	+	28.2347i	−0.423392	+	0.907966i	0.572710	+	0.819758i	$0.305892\pi$
$967$	−13.1660	+	28.2347i	−0.423392	+	0.907966i	−0.996102	+	0.0882085i	$0.971886\pi$
$968$	−14.2469	−	20.3466i	−0.457911	−	0.653965i
$969$		0			0
$970$	−3.05089	+	11.9088i	−0.0979581	+	0.382370i
$971$		−	46.4614i		−	1.49102i	−0.666496	−	0.745509i	$-0.732207\pi$
$971$		−	46.4614i		−	1.49102i	0.666496	−	0.745509i	$-0.267793\pi$
$972$		0			0
$973$	−5.27012	−	5.27012i	−0.168952	−	0.168952i
$974$	15.7126	−	13.1844i	0.503464	−	0.422456i
$975$		0			0
$976$	−0.678273	+	3.84668i	−0.0217110	+	0.123129i
$977$	−30.9924	−	14.4520i	−0.991534	−	0.462360i	−0.141985	−	0.989869i	$-0.545348\pi$
$977$	−30.9924	−	14.4520i	−0.991534	−	0.462360i	−0.849549	+	0.527509i	$0.823126\pi$
$978$		0			0
$979$	−5.78303	+	1.01970i	−0.184826	+	0.0325899i
$980$	−37.3860	−	16.9349i	−1.19425	−	0.540967i
$981$		0			0
$982$	2.10878	+	7.87006i	0.0672937	+	0.251144i
$983$	−32.2428	+	15.0350i	−1.02838	+	0.479543i	−0.862209	−	0.506553i	$-0.830919\pi$
$983$	−32.2428	+	15.0350i	−1.02838	+	0.479543i	−0.166175	+	0.986096i	$0.553142\pi$
$984$		0			0
$985$	38.8810	+	45.3142i	1.23885	+	1.44383i
$986$	0.0127071	−	0.0151438i	0.000404677	−	0.000482275i
$987$		0			0
$988$	4.26321	+	9.14249i	0.135631	+	0.290861i
$989$	−2.62418	+	4.54522i	−0.0834442	+	0.144530i
$990$		0			0
$991$	−2.77369	−	4.80418i	−0.0881092	−	0.152610i	0.818603	−	0.574360i	$-0.194749\pi$
$991$	−2.77369	−	4.80418i	−0.0881092	−	0.152610i	−0.906712	+	0.421751i	$0.861416\pi$
$992$	−7.29047	+	10.4119i	−0.231473	+	0.330577i
$993$		0			0
$994$	−0.708192	−	1.94574i	−0.0224625	−	0.0617152i
$995$	48.0808	−	23.0681i	1.52426	−	0.731307i
$996$		0			0
$997$	2.65905	−	30.3931i	0.0842129	−	0.962558i	−0.830117	−	0.557589i	$-0.811727\pi$
$997$	2.65905	−	30.3931i	0.0842129	−	0.962558i	0.914330	−	0.404969i	$-0.132718\pi$
$998$	−5.48435	+	5.48435i	−0.173604	+	0.173604i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.368.10		192
3.2	odd	2		135.2.q.a.113.7	yes	192
5.2	odd	4	inner	405.2.r.a.287.7		192
15.2	even	4		135.2.q.a.32.10	✓	192
15.8	even	4		675.2.ba.b.32.7		192
15.14	odd	2		675.2.ba.b.518.10		192
27.11	odd	18	inner	405.2.r.a.278.7		192
27.16	even	9		135.2.q.a.38.10	yes	192
135.43	odd	36		675.2.ba.b.632.10		192
135.92	even	36	inner	405.2.r.a.197.10		192
135.97	odd	36		135.2.q.a.92.7	yes	192
135.124	even	18		675.2.ba.b.443.7		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.10	✓	192	15.2	even	4
135.2.q.a.38.10	yes	192	27.16	even	9
135.2.q.a.92.7	yes	192	135.97	odd	36
135.2.q.a.113.7	yes	192	3.2	odd	2
405.2.r.a.197.10		192	135.92	even	36	inner
405.2.r.a.278.7		192	27.11	odd	18	inner
405.2.r.a.287.7		192	5.2	odd	4	inner
405.2.r.a.368.10		192	1.1	even	1	trivial
675.2.ba.b.32.7		192	15.8	even	4
675.2.ba.b.443.7		192	135.124	even	18
675.2.ba.b.518.10		192	15.14	odd	2
675.2.ba.b.632.10		192	135.43	odd	36

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.639298 + 0.0559313i) q^{2} +(-1.56404 - 0.275783i) q^{4} +(1.26232 - 1.84568i) q^{5} +(3.52875 + 2.47086i) q^{7} +(-2.22421 - 0.595975i) q^{8} +O(q^{10})\)	\(q+(0.639298 + 0.0559313i) q^{2} +(-1.56404 - 0.275783i) q^{4} +(1.26232 - 1.84568i) q^{5} +(3.52875 + 2.47086i) q^{7} +(-2.22421 - 0.595975i) q^{8} +(0.910229 - 1.10934i) q^{10} +(0.157893 - 0.433806i) q^{11} +(-0.462462 - 5.28596i) q^{13} +(2.11772 + 1.77698i) q^{14} +(1.59619 + 0.580964i) q^{16} +(4.93057 - 1.32114i) q^{17} +(1.03667 - 0.598524i) q^{19} +(-2.48333 + 2.53860i) q^{20} +(0.125204 - 0.268500i) q^{22} +(1.57814 + 2.25381i) q^{23} +(-1.81310 - 4.65968i) q^{25} -3.40517i q^{26} +(-4.83770 - 4.83770i) q^{28} +(0.00462297 - 0.00387914i) q^{29} +(-0.387533 + 2.19781i) q^{31} +(5.16180 + 2.40699i) q^{32} +(3.22599 - 0.568830i) q^{34} +(9.01483 - 3.39395i) q^{35} +(-1.94341 - 7.25290i) q^{37} +(0.696220 - 0.324653i) q^{38} +(-3.90764 + 3.35288i) q^{40} +(-3.02828 + 3.60897i) q^{41} +(0.806157 + 1.72881i) q^{43} +(-0.366587 + 0.634947i) q^{44} +(0.882840 + 1.52912i) q^{46} +(-6.47343 + 9.24502i) q^{47} +(3.95281 + 10.8602i) q^{49} +(-0.898490 - 3.08033i) q^{50} +(-0.734468 + 8.39501i) q^{52} +(-3.94023 + 3.94023i) q^{53} +(-0.601359 - 0.839022i) q^{55} +(-6.37611 - 7.59875i) q^{56} +(0.00317242 - 0.00222135i) q^{58} +(0.388624 - 0.141448i) q^{59} +(0.399307 + 2.26458i) q^{61} +(-0.370675 + 1.38338i) q^{62} +(0.223194 + 0.128861i) q^{64} +(-10.3400 - 5.81901i) q^{65} +(-5.84619 + 0.511475i) q^{67} +(-8.07597 + 0.706556i) q^{68} +(5.95299 - 1.66553i) q^{70} +(-0.648656 - 0.374502i) q^{71} +(-2.97508 + 11.1032i) q^{73} +(-0.836752 - 4.74546i) q^{74} +(-1.78647 + 0.650220i) q^{76} +(1.62904 - 1.14066i) q^{77} +(-1.01095 - 1.20481i) q^{79} +(3.08717 - 2.21269i) q^{80} +(-2.13783 + 2.13783i) q^{82} +(-0.930629 + 10.6371i) q^{83} +(3.78554 - 10.7680i) q^{85} +(0.418680 + 1.15031i) q^{86} +(-0.609724 + 0.870776i) q^{88} +(-6.36010 - 11.0160i) q^{89} +(11.4289 - 19.7955i) q^{91} +(-1.84671 - 3.96028i) q^{92} +(-4.65554 + 5.54825i) q^{94} +(0.203927 - 2.66890i) q^{95} +(-7.76434 + 3.62057i) q^{97} +(1.91959 + 7.16401i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

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