LMFDB - Embedded newform 945.2.cs.a.524.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(104,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 9, 9]))

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

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

chi := DirichletCharacter("945.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.cs (of order $18$, degree $6$, 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{18}]$

Embedding invariants

Embedding label			524.4
Character	$\chi$	$=$	945.524
Dual form			945.2.cs.a.734.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62968 - 0.586627i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(-0.459430 + 2.60556i) q^{7} +(2.31174 - 1.91203i) q^{9} +O(q^{10})$	\(q+(1.62968 - 0.586627i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(-0.459430 + 2.60556i) q^{7} +(2.31174 - 1.91203i) q^{9} +(2.20957 + 6.07074i) q^{11} +(-1.72141 - 3.00612i) q^{12} +(-3.66210 + 3.07287i) q^{13} +(-0.0137197 + 3.87296i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-6.43317 + 3.71419i) q^{17} +(4.40419 + 0.776578i) q^{20} +(0.779764 + 4.51575i) q^{21} +(-3.83022 - 3.21394i) q^{25} +(2.64575 - 4.47214i) q^{27} +5.29150 q^{28} +(3.10864 - 3.70474i) q^{29} +(7.16215 + 8.59719i) q^{33} +(-5.12348 - 2.95804i) q^{35} +(-4.56883 - 3.88919i) q^{36} +(-4.16544 + 7.15609i) q^{39} +(11.1896 - 6.46034i) q^{44} +(2.24962 + 6.31975i) q^{45} +(13.0199 + 2.29576i) q^{47} +(-5.32305 + 4.43453i) q^{48} +(-6.57785 - 2.39414i) q^{49} +(-8.30518 + 9.82682i) q^{51} +(7.32420 + 6.14574i) q^{52} -14.4458 q^{55} +(7.63300 - 1.31804i) q^{60} +(3.91983 + 6.90181i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-3.65606 - 10.0449i) q^{65} +(9.54974 + 11.3809i) q^{68} +(12.0138 - 6.93616i) q^{71} +(5.68743 - 9.85092i) q^{73} +(-8.12743 - 2.99079i) q^{75} +(-16.8328 + 2.96807i) q^{77} +(8.15248 + 6.84074i) q^{79} -8.94427i q^{80} +(1.68826 - 8.84024i) q^{81} +(2.15477 - 2.56795i) q^{83} +(8.62348 - 3.10414i) q^{84} +(-2.88436 - 16.3580i) q^{85} +(2.89281 - 7.86116i) q^{87} +(-6.32405 - 10.9536i) q^{91} +(-9.22994 + 3.35942i) q^{97} +(16.7154 + 9.80919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{9}+O(q^{10}) $ 24 * q - 6 * q^9	$ 24 q - 6 q^{9} - 18 q^{11} - 24 q^{39} + 96 q^{64} - 180 q^{65} - 12 q^{79} + 102 q^{81} + 84 q^{84} + 60 q^{85} + 228 q^{99}+O(q^{100}) $ 24 * q - 6 * q^9 - 18 * q^11 - 24 * q^39 + 96 * q^64 - 180 * q^65 - 12 * q^79 + 102 * q^81 + 84 * q^84 + 60 * q^85 + 228 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$-1$

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			0		0.642788	−	0.766044i	$-0.277778\pi$
$2$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$3$	1.62968	−	0.586627i	0.940898	−	0.338689i
$3$	1.62968	−	0.586627i	0.940898	−	0.338689i
$4$	−0.347296	−	1.96962i	−0.173648	−	0.984808i
$5$	−0.764780	+	2.10122i	−0.342020	+	0.939693i
$5$	−0.764780	+	2.10122i	−0.342020	+	0.939693i
$6$		0			0
$7$	−0.459430	+	2.60556i	−0.173648	+	0.984808i
$7$	−0.459430	+	2.60556i	−0.173648	+	0.984808i
$8$		0			0
$9$	2.31174	−	1.91203i	0.770579	−	0.637344i
$10$		0			0
$11$	2.20957	+	6.07074i	0.666210	+	1.83040i	0.546259	+	0.837616i	$0.316051\pi$
$11$	2.20957	+	6.07074i	0.666210	+	1.83040i	0.119950	+	0.992780i	$0.461727\pi$
$12$	−1.72141	−	3.00612i	−0.496929	−	0.867791i
$13$	−3.66210	+	3.07287i	−1.01568	+	0.852260i	−0.989079	−	0.147386i	$-0.952914\pi$
$13$	−3.66210	+	3.07287i	−1.01568	+	0.852260i	−0.0266051	+	0.999646i	$0.508470\pi$
$14$		0			0
$15$	−0.0137197	+	3.87296i	−0.00354242	+	0.999994i
$16$	−3.75877	+	1.36808i	−0.939693	+	0.342020i
$17$	−6.43317	+	3.71419i	−1.56027	+	0.900823i	−0.563043	+	0.826428i	$0.690370\pi$
$17$	−6.43317	+	3.71419i	−1.56027	+	0.900823i	−0.997229	+	0.0743959i	$0.976297\pi$
$18$		0			0
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	4.40419	+	0.776578i	0.984808	+	0.173648i
$21$	0.779764	+	4.51575i	0.170158	+	0.985417i
$22$		0			0
$23$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$23$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$24$		0			0
$25$	−3.83022	−	3.21394i	−0.766044	−	0.642788i
$26$		0			0
$27$	2.64575	−	4.47214i	0.509175	−	0.860663i
$28$	5.29150			1.00000
$29$	3.10864	−	3.70474i	0.577260	−	0.687952i	−0.395844	−	0.918318i	$-0.629548\pi$
$29$	3.10864	−	3.70474i	0.577260	−	0.687952i	0.973104	+	0.230366i	$0.0739923\pi$
$30$		0			0
$31$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$31$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$32$		0			0
$33$	7.16215	+	8.59719i	1.24677	+	1.49658i
$34$		0			0
$35$	−5.12348	−	2.95804i	−0.866025	−	0.500000i
$36$	−4.56883	−	3.88919i	−0.761471	−	0.648199i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$	−4.16544	+	7.15609i	−0.667004	+	1.14589i
$40$		0			0
$41$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$41$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$42$		0			0
$43$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$43$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$44$	11.1896	−	6.46034i	1.68690	−	0.973933i
$45$	2.24962	+	6.31975i	0.335354	+	0.942092i
$46$		0			0
$47$	13.0199	+	2.29576i	1.89915	+	0.334872i	0.995608	−	0.0936230i	$-0.0298448\pi$
$47$	13.0199	+	2.29576i	1.89915	+	0.334872i	0.903544	+	0.428495i	$0.140956\pi$
$48$	−5.32305	+	4.43453i	−0.768317	+	0.640070i
$49$	−6.57785	−	2.39414i	−0.939693	−	0.342020i
$50$		0			0
$51$	−8.30518	+	9.82682i	−1.16296	+	1.37603i
$52$	7.32420	+	6.14574i	1.01568	+	0.852260i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	−14.4458			−1.94787
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$59$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$60$	7.63300	−	1.31804i	0.985417	−	0.170158i
$61$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$61$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$62$		0			0
$63$	3.91983	+	6.90181i	0.493852	+	0.869546i
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	−3.65606	−	10.0449i	−0.453478	−	1.24592i
$66$		0			0
$67$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$67$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$68$	9.54974	+	11.3809i	1.15808	+	1.38014i
$69$		0			0
$70$		0			0
$71$	12.0138	−	6.93616i	1.42577	−	0.823171i	0.428990	−	0.903309i	$-0.358869\pi$
$71$	12.0138	−	6.93616i	1.42577	−	0.823171i	0.996784	+	0.0801380i	$0.0255361\pi$
$72$		0			0
$73$	5.68743	−	9.85092i	0.665664	−	1.15296i	−0.313441	−	0.949608i	$-0.601482\pi$
$73$	5.68743	−	9.85092i	0.665664	−	1.15296i	0.979105	−	0.203355i	$-0.0651847\pi$
$74$		0			0
$75$	−8.12743	−	2.99079i	−0.938475	−	0.345347i
$76$		0			0
$77$	−16.8328	+	2.96807i	−1.91827	+	0.338243i
$78$		0			0
$79$	8.15248	+	6.84074i	0.917225	+	0.769644i	0.973480	−	0.228773i	$-0.0734713\pi$
$79$	8.15248	+	6.84074i	0.917225	+	0.769644i	−0.0562544	+	0.998416i	$0.517916\pi$
$80$		−	8.94427i		−	1.00000i
$81$	1.68826	−	8.84024i	0.187585	−	0.982248i
$82$		0			0
$83$	2.15477	−	2.56795i	0.236517	−	0.281870i	−0.634710	−	0.772750i	$-0.718880\pi$
$83$	2.15477	−	2.56795i	0.236517	−	0.281870i	0.871227	+	0.490881i	$0.163325\pi$
$84$	8.62348	−	3.10414i	0.940898	−	0.338689i
$85$	−2.88436	−	16.3580i	−0.312853	−	1.77428i
$86$		0			0
$87$	2.89281	−	7.86116i	0.310141	−	0.842805i
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−6.32405	−	10.9536i	−0.662941	−	1.14825i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.22994	+	3.35942i	−0.937159	+	0.341098i	−0.765043	−	0.643979i	$-0.777282\pi$
$97$	−9.22994	+	3.35942i	−0.937159	+	0.341098i	−0.172115	+	0.985077i	$0.555060\pi$
$98$		0			0
$99$	16.7154	+	9.80919i	1.67996	+	0.985860i
$100$	−5.00000	+	8.66025i	−0.500000	+	0.866025i
$101$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$101$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$102$		0			0
$103$	17.6205	+	6.41332i	1.73620	+	0.631923i	0.999040	−	0.0438001i	$-0.0139465\pi$
$103$	17.6205	+	6.41332i	1.73620	+	0.631923i	0.737155	+	0.675724i	$0.236169\pi$
$104$		0			0
$105$	−10.0849	−	1.81510i	−0.984186	−	0.177136i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−9.72725	−	3.65796i	−0.936005	−	0.351987i
$109$	−4.26636			−0.408644			−0.204322	−	0.978904i	$-0.565499\pi$
$109$	−4.26636			−0.408644			−0.204322	+	0.978904i	$0.565499\pi$
$110$		0			0
$111$		0			0
$112$	−1.83772	−	10.4222i	−0.173648	−	0.984808i
$113$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$113$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$114$		0			0
$115$		0			0
$116$	−8.37652	−	4.83619i	−0.777741	−	0.449029i
$117$	−2.59039	+	14.1057i	−0.239482	+	1.30407i
$118$		0			0
$119$	−6.72194	−	18.4684i	−0.616199	−	1.69299i
$120$		0			0
$121$	−23.5452	+	19.7567i	−2.14047	+	1.79607i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	9.68246	−	5.59017i	0.866025	−	0.500000i
$126$		0			0
$127$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$127$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$131$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$132$	14.4458	−	17.0925i	1.25734	−	1.48771i
$133$		0			0
$134$		0			0
$135$	7.37351	+	8.97950i	0.634611	+	0.772832i
$136$		0			0
$137$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$137$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$138$		0			0
$139$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$139$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$140$	−4.04684	+	11.1186i	−0.342020	+	0.939693i
$141$	22.5651	−	3.89647i	1.90033	−	0.328142i
$142$		0			0
$143$	−26.7462	−	15.4419i	−2.23663	−	1.29132i
$144$	−6.07348	+	10.3495i	−0.506123	+	0.862461i
$145$	5.40702	+	9.36524i	0.449029	+	0.777741i
$146$		0			0
$147$	−12.1243	−	0.0429495i	−0.999994	−	0.00354242i
$148$		0			0
$149$	15.6129	+	18.6067i	1.27906	+	1.52432i	0.716578	+	0.697507i	$0.245707\pi$
$149$	15.6129	+	18.6067i	1.27906	+	1.52432i	0.562478	+	0.826812i	$0.309848\pi$
$150$		0			0
$151$	−22.9577	+	8.35593i	−1.86827	+	0.679996i	−0.897000	+	0.442031i	$0.854258\pi$
$151$	−22.9577	+	8.35593i	−1.86827	+	0.679996i	−0.971274	+	0.237964i	$0.923520\pi$
$152$		0			0
$153$	−7.77014	+	20.8867i	−0.628179	+	1.68859i
$154$		0			0
$155$		0			0
$156$	15.5414	+	5.71903i	1.24431	+	0.457889i
$157$	7.13246	+	2.59600i	0.569232	+	0.207184i	0.610571	−	0.791962i	$-0.290940\pi$
$157$	7.13246	+	2.59600i	0.569232	+	0.207184i	−0.0413387	+	0.999145i	$0.513162\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$		0			0
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$	−23.5420	+	8.47428i	−1.83274	+	0.659721i
$166$		0			0
$167$	−4.69944	+	12.9116i	−0.363653	+	0.999129i	0.614074	+	0.789249i	$0.289530\pi$
$167$	−4.69944	+	12.9116i	−0.363653	+	0.999129i	−0.977727	+	0.209881i	$0.932692\pi$
$168$		0			0
$169$	1.71104	−	9.70381i	0.131619	−	0.746447i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.96495	−	24.6310i	−0.681593	−	1.87266i	−0.420221	−	0.907422i	$-0.638047\pi$
$173$	−8.96495	−	24.6310i	−0.681593	−	1.87266i	−0.261372	−	0.965238i	$-0.584175\pi$
$174$		0			0
$175$	10.1338	−	8.50328i	0.766044	−	0.642788i
$176$	−16.6105	−	19.7956i	−1.25206	−	1.49215i
$177$		0			0
$178$		0			0
$179$	−2.52023	+	1.45505i	−0.188371	+	0.108756i	−0.591220	−	0.806511i	$-0.701353\pi$
$179$	−2.52023	+	1.45505i	−0.188371	+	0.108756i	0.402849	+	0.915267i	$0.368020\pi$
$180$	11.6662	−	6.62572i	0.869546	−	0.493852i
$181$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$181$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−36.7624	−	30.8473i	−2.68833	−	2.25578i
$188$		−	26.4416i		−	1.92845i
$189$	10.4369	+	8.94829i	0.759170	+	0.650892i
$190$		0			0
$191$	3.80278	−	4.53198i	0.275160	−	0.327923i	−0.610712	−	0.791853i	$-0.709117\pi$
$191$	3.80278	−	4.53198i	0.275160	−	0.327923i	0.885872	+	0.463930i	$0.153561\pi$
$192$	10.5830	+	8.94427i	0.763763	+	0.645497i
$193$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$193$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$194$		0			0
$195$	−11.8508	−	14.2253i	−0.848657	−	1.01870i
$196$	−2.43107	+	13.7873i	−0.173648	+	0.984808i
$197$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$197$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.22469	+	9.80181i	0.577260	+	0.687952i
$204$	22.2394	+	12.9452i	1.55707	+	0.906345i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	9.56107	−	16.5603i	0.662941	−	1.14825i
$209$		0			0
$210$		0			0
$211$	12.6715	+	4.61204i	0.872340	+	0.317506i	0.739114	−	0.673580i	$-0.235244\pi$
$211$	12.6715	+	4.61204i	0.872340	+	0.317506i	0.133226	+	0.991086i	$0.457467\pi$
$212$		0			0
$213$	15.5097	−	18.3514i	1.06271	−	1.25741i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	3.48990	−	19.3903i	0.235826	−	1.31027i
$220$	5.01696	+	28.4526i	0.338243	+	1.91827i
$221$	12.1457	−	33.3700i	0.817008	−	2.24471i
$222$		0			0
$223$	0.269600	−	1.52898i	0.0180537	−	0.102388i	−0.974449	−	0.224607i	$-0.927890\pi$
$223$	0.269600	−	1.52898i	0.0180537	−	0.102388i	0.992503	+	0.122220i	$0.0390012\pi$
$224$		0			0
$225$	−14.9996	−	0.106272i	−0.999975	−	0.00708479i
$226$		0			0
$227$	8.41408	+	23.1175i	0.558462	+	1.53436i	0.821869	+	0.569677i	$0.192932\pi$
$227$	8.41408	+	23.1175i	0.558462	+	1.53436i	−0.263407	+	0.964685i	$0.584846\pi$
$228$		0			0
$229$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$229$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$230$		0			0
$231$	−25.6910	+	14.7116i	−1.69034	+	0.967952i
$232$		0			0
$233$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$233$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$234$		0			0
$235$	−14.7813	+	25.6019i	−0.964225	+	1.67009i
$236$		0			0
$237$	17.2989	+	6.36578i	1.12369	+	0.413502i
$238$		0			0
$239$	22.2413	−	3.92174i	1.43867	−	0.253677i	0.600737	−	0.799447i	$-0.294874\pi$
$239$	22.2413	−	3.92174i	1.43867	−	0.253677i	0.837935	+	0.545770i	$0.183763\pi$
$240$	−5.24695	−	14.5763i	−0.338689	−	0.940898i
$241$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$241$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$242$		0			0
$243$	−2.43459	−	15.3972i	−0.156179	−	0.987729i
$244$		0			0
$245$	10.0612	−	11.9905i	0.642788	−	0.766044i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	2.00516	−	5.44900i	0.127072	−	0.345316i
$250$		0			0
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$	12.2326	−	10.1175i	0.770579	−	0.637344i
$253$		0			0
$254$		0			0
$255$	−14.2966	−	24.9663i	−0.895291	−	1.56345i
$256$	12.2567	−	10.2846i	0.766044	−	0.642788i
$257$	9.68118	+	11.5376i	0.603895	+	0.719694i	0.978212	−	0.207606i	$-0.0665673\pi$
$257$	9.68118	+	11.5376i	0.603895	+	0.719694i	−0.374317	+	0.927301i	$0.622123\pi$
$258$		0			0
$259$		0			0
$260$	−18.5149	+	10.6896i	−1.14825	+	0.662941i
$261$	0.102790	−	14.5082i	0.00636255	−	0.898035i
$262$		0			0
$263$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$263$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	19.0995	−	22.7619i	1.15808	−	1.38014i
$273$	−16.7319	−	14.1410i	−1.01266	−	0.855853i
$274$		0			0
$275$	11.0478	−	30.3537i	0.666210	−	1.83040i
$276$		0			0
$277$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$277$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.4666	+	31.5041i	0.684037	+	1.87938i	0.344704	+	0.938711i	$0.387979\pi$
$281$	11.4666	+	31.5041i	0.684037	+	1.87938i	0.339333	+	0.940666i	$0.389799\pi$
$282$		0			0
$283$	−24.9516	+	20.9369i	−1.48322	+	1.24457i	−0.580558	+	0.814219i	$0.697165\pi$
$283$	−24.9516	+	20.9369i	−1.48322	+	1.24457i	−0.902662	+	0.430350i	$0.858390\pi$
$284$	−17.8339	−	21.2536i	−1.05825	−	1.26117i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	19.0904	−	33.0656i	1.12297	−	1.94503i
$290$		0			0
$291$	−13.0712	+	10.8893i	−0.766245	+	0.638344i
$292$	−21.3777	−	7.78086i	−1.25104	−	0.455341i
$293$	−32.4198	+	5.71649i	−1.89399	+	0.333961i	−0.994651	−	0.103296i	$-0.967061\pi$
$293$	−32.4198	+	5.71649i	−1.89399	+	0.333961i	−0.899336	+	0.437257i	$0.855950\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	32.9951	+	6.18017i	1.91457	+	0.358610i
$298$		0			0
$299$		0			0
$300$	−3.06808	+	17.0466i	−0.177136	+	0.984186i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−11.0180	−	19.0837i	−0.628830	−	1.08916i	−0.987787	−	0.155811i	$-0.950201\pi$
$307$	−11.0180	−	19.0837i	−0.628830	−	1.08916i	0.358957	−	0.933354i	$-0.383132\pi$
$308$	11.6919	+	32.1233i	0.666210	+	1.83040i
$309$	32.4780	+	0.115051i	1.84761	+	0.00654504i
$310$		0			0
$311$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$311$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$312$		0			0
$313$	2.70330	−	0.983921i	0.152800	−	0.0556145i	−0.264488	−	0.964389i	$-0.585203\pi$
$313$	2.70330	−	0.983921i	0.152800	−	0.0556145i	0.417288	+	0.908774i	$0.362981\pi$
$314$		0			0
$315$	−17.5000	+	2.95804i	−0.986013	+	0.166667i
$316$	10.6423	−	18.4330i	0.598676	−	1.03694i
$317$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$317$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$318$		0			0
$319$	29.3592	+	10.6859i	1.64380	+	0.598295i
$320$	−17.6168	+	3.10631i	−0.984808	+	0.173648i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−17.9982	−	0.255046i	−0.999900	−	0.0141692i
$325$	23.9027			1.32588
$326$		0			0
$327$	−6.95282	+	2.50276i	−0.384492	+	0.138403i
$328$		0			0
$329$	−11.9635	+	32.8694i	−0.659569	+	1.81215i
$330$		0			0
$331$	6.31148	−	35.7942i	0.346911	−	1.96743i	0.127051	−	0.991896i	$-0.459449\pi$
$331$	6.31148	−	35.7942i	0.346911	−	1.96743i	0.219860	−	0.975531i	$-0.429440\pi$
$332$	−5.80623	−	3.35223i	−0.318658	−	0.183977i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−9.10886	−	15.9069i	−0.496929	−	0.867791i
$337$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$337$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$338$		0			0
$339$		0			0
$340$	−31.2173	+	11.3622i	−1.69299	+	0.616199i
$341$		0			0
$342$		0			0
$343$	9.26013	−	16.0390i	0.500000	−	0.866025i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$347$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$348$	−16.4881	−	2.96756i	−0.883856	−	0.159078i
$349$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$349$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$350$		0			0
$351$	4.05327	+	24.5075i	0.216348	+	1.30811i
$352$		0			0
$353$	−3.91274	+	4.66303i	−0.208254	+	0.248188i	−0.860054	−	0.510204i	$-0.829570\pi$
$353$	−3.91274	+	4.66303i	−0.208254	+	0.248188i	0.651799	+	0.758392i	$0.274014\pi$
$354$		0			0
$355$	5.38647	+	30.5482i	0.285884	+	1.62133i
$356$		0			0
$357$	−21.7887	−	26.1544i	−1.15318	−	1.38424i
$358$		0			0
$359$	32.1235	+	18.5465i	1.69541	+	0.978847i	0.950004	+	0.312239i	$0.101079\pi$
$359$	32.1235	+	18.5465i	1.69541	+	0.978847i	0.745409	+	0.666608i	$0.232254\pi$
$360$		0			0
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$		0			0
$363$	−26.7813	+	46.0095i	−1.40566	+	2.41487i
$364$	−19.3780	+	16.2601i	−1.01568	+	0.852260i
$365$	16.3493	+	19.4843i	0.855761	+	1.01986i
$366$		0			0
$367$	−33.5913	+	12.2262i	−1.75345	+	0.638204i	−0.999818	−	0.0190919i	$-0.993923\pi$
$367$	−33.5913	+	12.2262i	−1.75345	+	0.638204i	−0.753633	+	0.657296i	$0.771700\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$373$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$374$		0			0
$375$	12.5000	−	14.7902i	0.645497	−	0.763763i
$376$		0			0
$377$			23.1196i			1.19072i
$378$		0			0
$379$	−35.0734			−1.80160			−0.900800	−	0.434234i	$-0.857019\pi$
$379$	−35.0734			−1.80160			−0.900800	+	0.434234i	$0.857019\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.47176	−	20.5285i	0.381789	−	1.04896i	−0.588813	−	0.808269i	$-0.700405\pi$
$383$	7.47176	−	20.5285i	0.381789	−	1.04896i	0.970603	−	0.240688i	$-0.0773730\pi$
$384$		0			0
$385$	6.63682	−	37.6393i	0.338243	−	1.91827i
$386$		0			0
$387$		0			0
$388$	9.82230	+	17.0127i	0.498652	+	0.863690i
$389$	2.66074	+	7.31033i	0.134905	+	0.370648i	0.988689	−	0.149979i	$-0.0479205\pi$
$389$	2.66074	+	7.31033i	0.134905	+	0.370648i	−0.853784	+	0.520627i	$0.825698\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−20.6087	+	11.8985i	−1.03694	+	0.598676i
$396$	13.5151	−	36.3296i	0.679161	−	1.82563i
$397$	17.3129	−	29.9868i	0.868910	−	1.50500i	0.00579782	−	0.999983i	$-0.498154\pi$
$397$	17.3129	−	29.9868i	0.868910	−	1.50500i	0.863112	−	0.505013i	$-0.168512\pi$
$398$		0			0
$399$		0			0
$400$	18.7939	+	6.84040i	0.939693	+	0.342020i
$401$	−29.1310	+	5.13658i	−1.45473	+	0.256509i	−0.844433	−	0.535662i	$-0.820062\pi$
$401$	−29.1310	+	5.13658i	−1.45473	+	0.256509i	−0.610300	+	0.792170i	$0.708951\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	17.2841	+	10.3082i	0.858854	+	0.512221i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$409$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$410$		0			0
$411$		0			0
$412$	6.51226	−	36.9329i	0.320836	−	1.81955i
$413$		0			0
$414$		0			0
$415$	3.74790	+	6.49156i	0.183977	+	0.318658i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$419$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$420$	−0.0725979	+	20.4938i	−0.00354242	+	0.999994i
$421$	15.9140	−	5.79221i	0.775600	−	0.282295i	0.0762630	−	0.997088i	$-0.475701\pi$
$421$	15.9140	−	5.79221i	0.775600	−	0.282295i	0.699337	+	0.714793i	$0.253479\pi$
$422$		0			0
$423$	34.4882	−	19.5873i	1.67688	−	0.952368i
$424$		0			0
$425$	36.5776	+	6.44962i	1.77428	+	0.312853i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−52.6466	−	9.47542i	−2.54180	−	0.457478i
$430$		0			0
$431$			37.8890i			1.82505i	0.409021	+	0.912525i	$0.365870\pi$
$431$			37.8890i			1.82505i	−0.409021	+	0.912525i	$0.634130\pi$
$432$	−3.82653	+	20.4293i	−0.184104	+	0.982907i
$433$	29.5653			1.42082			0.710410	−	0.703788i	$-0.248510\pi$
$433$	29.5653			1.42082			0.710410	+	0.703788i	$0.248510\pi$
$434$		0			0
$435$	14.3056	+	12.0905i	0.685903	+	0.579694i
$436$	1.48169	+	8.40310i	0.0709602	+	0.402435i
$437$		0			0
$438$		0			0
$439$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$439$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$440$		0			0
$441$	−19.7839	+	7.04243i	−0.942092	+	0.335354i
$442$		0			0
$443$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$443$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	36.3592	+	21.1641i	1.71973	+	1.00103i
$448$	−19.8895	+	7.23920i	−0.939693	+	0.342020i
$449$	11.1822	−	6.45603i	0.527719	−	0.304679i	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	11.1822	−	6.45603i	0.527719	−	0.304679i	0.740087	+	0.672511i	$0.234784\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−32.5120	+	27.0851i	−1.52755	+	1.27257i
$454$		0			0
$455$	27.8524	−	4.91112i	1.30574	−	0.230237i
$456$		0			0
$457$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$457$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$458$		0			0
$459$	−0.410194	+	38.5968i	−0.0191462	+	1.80155i
$460$		0			0
$461$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$461$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$462$		0			0
$463$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$463$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$464$	−6.61630	+	18.1781i	−0.307154	+	0.843898i
$465$		0			0
$466$		0			0
$467$	0.380337	+	0.219588i	0.0175999	+	0.0101613i	0.508774	−	0.860900i	$-0.330099\pi$
$467$	0.380337	+	0.219588i	0.0175999	+	0.0101613i	−0.491174	+	0.871061i	$0.663432\pi$
$468$	28.6825	+	0.203214i	1.32585	+	0.00939359i
$469$		0			0
$470$		0			0
$471$	13.1465	+	0.0465708i	0.605760	+	0.00214587i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−34.0411	+	19.6536i	−1.56027	+	0.900823i
$477$		0			0
$478$		0			0
$479$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$479$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	47.0903	+	39.5135i	2.14047	+	1.79607i
$485$		−	21.9633i		−	0.997304i
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.64669	+	15.5142i	−0.254832	+	0.700144i	0.744635	+	0.667472i	$0.232624\pi$
$491$	−5.64669	+	15.5142i	−0.254832	+	0.700144i	−0.999466	+	0.0326716i	$0.989598\pi$
$492$		0			0
$493$	−6.23832	+	35.3793i	−0.280960	+	1.59340i
$494$		0			0
$495$	−33.3948	+	27.6208i	−1.50099	+	1.24146i
$496$		0			0
$497$	12.5531	+	34.4893i	0.563082	+	1.54706i
$498$		0			0
$499$	−7.93548	+	6.65866i	−0.355241	+	0.298082i	−0.802890	−	0.596127i	$-0.796706\pi$
$499$	−7.93548	+	6.65866i	−0.355241	+	0.298082i	0.447650	+	0.894209i	$0.352261\pi$
$500$	−14.3732	−	17.1293i	−0.642788	−	0.766044i
$501$	−0.0843052	+	23.7986i	−0.00376648	+	1.06324i
$502$		0			0
$503$	34.3190	−	19.8141i	1.53021	−	0.883466i	0.530857	−	0.847461i	$-0.321870\pi$
$503$	34.3190	−	19.8141i	1.53021	−	0.883466i	0.999352	−	0.0360049i	$-0.0114632\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.90406	−	16.8179i	−0.128974	−	0.746908i
$508$		0			0
$509$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$509$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$510$		0			0
$511$	23.0542	+	19.3447i	1.01986	+	0.855761i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−26.9516	+	32.1196i	−1.18763	+	1.41536i
$516$		0			0
$517$	14.8314	+	84.1132i	0.652285	+	3.69929i
$518$		0			0
$519$	−29.0592	−	34.8817i	−1.27556	−	1.53113i
$520$		0			0
$521$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$521$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$522$		0			0
$523$	−12.8147	−	22.1957i	−0.560346	−	0.970548i	−0.997466	−	0.0711450i	$-0.977335\pi$
$523$	−12.8147	−	22.1957i	−0.560346	−	0.970548i	0.437120	−	0.899403i	$-0.355999\pi$
$524$		0			0
$525$	11.5267	−	19.8024i	0.503065	−	0.864249i
$526$		0			0
$527$		0			0
$528$	−38.6825	−	22.5165i	−1.68344	−	0.979903i
$529$	21.6129	−	7.86646i	0.939693	−	0.342020i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.25360	+	3.84971i	−0.140403	+	0.166127i
$538$		0			0
$539$		−	45.2224i		−	1.94787i
$540$	15.1254	−	17.6415i	0.650892	−	0.759170i
$541$	46.4770			1.99820			0.999102	−	0.0423705i	$-0.0134910\pi$
$541$	46.4770			1.99820			0.999102	+	0.0423705i	$0.0134910\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.26283	−	8.96455i	0.139764	−	0.383999i
$546$		0			0
$547$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$547$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−21.5694	+	18.0989i	−0.917225	+	0.769644i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$557$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$558$		0			0
$559$		0			0
$560$	23.3048	+	4.10927i	0.984808	+	0.173648i
$561$	−78.0069	−	28.7055i	−3.29345	−	1.21195i
$562$		0			0
$563$	−7.74803	+	1.36619i	−0.326541	+	0.0575779i	−0.334515	−	0.942390i	$-0.608573\pi$
$563$	−7.74803	+	1.36619i	−0.326541	+	0.0575779i	0.00797484	+	0.999968i	$0.497462\pi$
$564$	−15.5113	−	43.0914i	−0.653145	−	1.81447i
$565$		0			0
$566$		0			0
$567$	22.2581	+	8.46033i	0.934752	+	0.355301i
$568$		0			0
$569$	−1.48464	+	1.76932i	−0.0622392	+	0.0741738i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	−1.48464	+	1.76932i	−0.0622392	+	0.0741738i	0.734027	+	0.679121i	$0.237639\pi$
$570$		0			0
$571$	−7.32981	−	41.5694i	−0.306743	−	1.73963i	−0.615186	−	0.788382i	$-0.710919\pi$
$571$	−7.32981	−	41.5694i	−0.306743	−	1.73963i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	−21.1258	+	58.0427i	−0.883315	+	2.42689i
$573$	3.53875	−	9.61651i	0.147833	−	0.401735i
$574$		0			0
$575$		0			0
$576$	22.4939	+	8.36806i	0.937246	+	0.348669i
$577$	10.4244	+	18.0556i	0.433974	+	0.751664i	0.997211	−	0.0746307i	$-0.0237778\pi$
$577$	10.4244	+	18.0556i	0.433974	+	0.751664i	−0.563238	+	0.826295i	$0.690444\pi$
$578$		0			0
$579$		0			0
$580$	16.5681	−	13.9023i	0.687952	−	0.577260i
$581$	5.70099	+	6.79417i	0.236517	+	0.281870i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−27.6581	−	16.2308i	−1.14352	−	0.671059i
$586$		0			0
$587$	−45.0208	−	7.93838i	−1.85821	−	0.327652i	−0.871530	−	0.490342i	$-0.836872\pi$
$587$	−45.0208	−	7.93838i	−1.85821	−	0.327652i	−0.986677	+	0.162690i	$0.947983\pi$
$588$	4.12612	+	23.8951i	0.170158	+	0.985417i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	0.621055i		−	0.0255037i	−0.999919	−	0.0127518i	$-0.995941\pi$
$593$		−	0.621055i		−	0.0255037i	0.999919	−	0.0127518i	$-0.00405915\pi$
$594$		0			0
$595$	43.9469			1.80165
$596$	31.2257	−	37.2134i	1.27906	−	1.52432i
$597$		0			0
$598$		0			0
$599$	−0.823864	+	2.26355i	−0.0336622	+	0.0924860i	−0.955385	−	0.295363i	$-0.904559\pi$
$599$	−0.823864	+	2.26355i	−0.0336622	+	0.0924860i	0.921723	+	0.387849i	$0.126782\pi$
$600$		0			0
$601$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$601$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$602$		0			0
$603$		0			0
$604$	24.4311	+	42.3159i	0.994088	+	1.72181i
$605$	−23.5063	−	64.5831i	−0.955667	−	2.62567i
$606$		0			0
$607$	3.87654	−	3.25280i	0.157344	−	0.132027i	−0.560717	−	0.828008i	$-0.689474\pi$
$607$	3.87654	−	3.25280i	0.157344	−	0.132027i	0.718061	+	0.695980i	$0.245030\pi$
$608$		0			0
$609$	19.1537	+	11.1490i	0.776145	+	0.451781i
$610$		0			0
$611$	−54.7349	+	31.6012i	−2.21434	+	1.27845i
$612$	43.8372	+	8.05033i	1.77201	+	0.325415i
$613$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$613$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$617$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$618$		0			0
$619$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$619$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	5.86682	−	32.5968i	0.234861	−	1.30491i
$625$	4.34120	+	24.6202i	0.173648	+	0.984808i
$626$		0			0
$627$		0			0
$628$	2.63605	−	14.9498i	0.105190	−	0.596561i
$629$		0			0
$630$		0			0
$631$	19.0476	+	32.9915i	0.758275	+	1.31337i	0.943730	+	0.330718i	$0.107291\pi$
$631$	19.0476	+	32.9915i	0.758275	+	1.31337i	−0.185455	+	0.982653i	$0.559376\pi$
$632$		0			0
$633$	23.3560	+	0.0827373i	0.928319	+	0.00328851i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	31.4456	−	11.4453i	1.24592	−	0.453478i
$638$		0			0
$639$	14.5106	−	39.0053i	0.574029	−	1.54303i
$640$		0			0
$641$	−7.95317	−	1.40236i	−0.314131	−	0.0553898i	0.0143597	−	0.999897i	$-0.495429\pi$
$641$	−7.95317	−	1.40236i	−0.314131	−	0.0553898i	−0.328491	+	0.944507i	$0.606540\pi$
$642$		0			0
$643$	46.5449	+	16.9409i	1.83555	+	0.668086i	0.991213	+	0.132273i	$0.0422275\pi$
$643$	46.5449	+	16.9409i	1.83555	+	0.668086i	0.844337	+	0.535813i	$0.179995\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	32.2989i		−	1.26980i	−0.772594	−	0.634901i	$-0.781041\pi$
$647$		−	32.2989i		−	1.26980i	0.772594	−	0.634901i	$-0.218959\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$653$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.68743	−	33.6473i	−0.221888	−	1.31271i
$658$		0			0
$659$	−9.66213	−	26.5465i	−0.376383	−	1.03410i	−0.972844	−	0.231462i	$-0.925649\pi$
$659$	−9.66213	−	26.5465i	−0.376383	−	1.03410i	0.596461	−	0.802642i	$-0.296573\pi$
$660$	24.8671	+	43.4257i	0.967952	+	1.69034i
$661$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$661$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$	0.217887	−	61.5075i	0.00846202	−	2.38876i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	27.0630	+	4.77193i	1.04710	+	0.184632i
$669$	−0.457576	−	2.64990i	−0.0176909	−	0.102451i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$673$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$674$		0			0
$675$	−24.5070	+	8.62599i	−0.943274	+	0.332015i
$676$	−19.7070			−0.757962
$677$	−32.8096	+	39.1010i	−1.26098	+	1.50277i	−0.481347	+	0.876530i	$0.659852\pi$
$677$	−32.8096	+	39.1010i	−1.26098	+	1.50277i	−0.779629	+	0.626242i	$0.784592\pi$
$678$		0			0
$679$	−4.51266	−	25.5926i	−0.173180	−	0.982152i
$680$		0			0
$681$	27.2736	+	32.7383i	1.04513	+	1.25453i
$682$		0			0
$683$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$683$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$691$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$692$	−45.4001	+	26.2118i	−1.72585	+	0.996422i
$693$	−33.2379	+	39.0462i	−1.26260	+	1.48324i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−20.2676	−	17.0066i	−0.766044	−	0.642788i
$701$		−	10.5119i		−	0.397028i	−0.980098	−	0.198514i	$-0.936389\pi$
$701$		−	10.5119i		−	0.397028i	0.980098	−	0.198514i	$-0.0636115\pi$
$702$		0			0
$703$		0			0
$704$	−33.2210	+	39.5913i	−1.25206	+	1.49215i
$705$	−9.07003	+	50.3942i	−0.341597	+	1.89795i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	8.09396	−	45.9031i	0.303975	−	1.72393i	−0.324314	−	0.945949i	$-0.605134\pi$
$709$	8.09396	−	45.9031i	0.303975	−	1.72393i	0.628290	−	0.777980i	$-0.283755\pi$
$710$		0			0
$711$	31.9261	+	0.226195i	1.19732	+	0.00848299i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	52.9019	−	44.3899i	1.97842	−	1.66009i
$716$	3.74116	+	4.45855i	0.139814	+	0.166624i
$717$	33.9457	−	19.4386i	1.26773	−	0.725946i
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−17.1017	−	20.6768i	−0.637344	−	0.770579i
$721$	−24.8056	+	42.9646i	−0.923810	+	1.60009i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−23.8136	+	4.19898i	−0.884414	+	0.155946i
$726$		0			0
$727$	−41.1896	−	34.5622i	−1.52764	−	1.28184i	−0.812783	−	0.582566i	$-0.802049\pi$
$727$	−41.1896	−	34.5622i	−1.52764	−	1.28184i	−0.714854	−	0.699274i	$-0.753507\pi$
$728$		0			0
$729$	−13.0000	−	23.6643i	−0.481481	−	0.876456i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−7.39100	−	41.9164i	−0.272993	−	1.54822i	−0.745266	−	0.666767i	$-0.767678\pi$
$733$	−7.39100	−	41.9164i	−0.272993	−	1.54822i	0.472274	−	0.881452i	$-0.343433\pi$
$734$		0			0
$735$	9.36266	−	25.4429i	0.345347	−	0.938475i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−20.3056	−	35.1704i	−0.746955	−	1.29376i	−0.949276	−	0.314445i	$-0.898182\pi$
$739$	−20.3056	−	35.1704i	−0.746955	−	1.29376i	0.202321	−	0.979319i	$-0.435152\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$743$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$744$		0			0
$745$	−51.0371	+	18.5760i	−1.86985	+	0.680571i
$746$		0			0
$747$	0.0712494	−	10.0564i	0.00260688	−	0.367946i
$748$	−47.9899	+	83.1209i	−1.75468	+	3.03920i
$749$		0			0
$750$		0			0
$751$	−49.4384	−	17.9941i	−1.80403	−	0.656615i	−0.997892	−	0.0648920i	$-0.979330\pi$
$751$	−49.4384	−	17.9941i	−1.80403	−	0.656615i	−0.806142	−	0.591723i	$-0.798448\pi$
$752$	−52.0797	+	9.18306i	−1.89915	+	0.334872i
$753$		0			0
$754$		0			0
$755$		−	54.6296i		−	1.98818i
$756$	14.0000	−	23.6643i	0.509175	−	0.860663i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$761$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$762$		0			0
$763$	1.96009	−	11.1163i	0.0709602	−	0.402435i
$764$	−10.2470	−	5.91608i	−0.370722	−	0.214036i
$765$	−37.9449	−	32.3004i	−1.37190	−	1.16783i
$766$		0			0
$767$		0			0
$768$	13.9413	−	23.9508i	0.503065	−	0.864249i
$769$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$769$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$770$		0			0
$771$	22.5455	+	13.1234i	0.811957	+	0.472626i
$772$		0			0
$773$	14.6373	−	8.45084i	0.526467	−	0.303956i	−0.213110	−	0.977028i	$-0.568359\pi$
$773$	14.6373	−	8.45084i	0.526467	−	0.303956i	0.739576	+	0.673073i	$0.235026\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−23.9027	+	28.2820i	−0.855853	+	1.01266i
$781$	68.6529	+	57.6066i	2.45659	+	2.06133i
$782$		0			0
$783$	−8.34339	−	23.7041i	−0.298168	−	0.847115i
$784$	28.0000			1.00000
$785$	−10.9095	+	13.0015i	−0.389378	+	0.464042i
$786$		0			0
$787$	−7.09210	−	40.2213i	−0.252806	−	1.43373i	−0.801642	−	0.597804i	$-0.796040\pi$
$787$	−7.09210	−	40.2213i	−0.252806	−	1.43373i	0.548836	−	0.835930i	$-0.315071\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$	30.8057	+	36.7128i	1.09119	+	1.30043i	0.950618	+	0.310364i	$0.100451\pi$
$797$	30.8057	+	36.7128i	1.09119	+	1.30043i	0.140576	+	0.990070i	$0.455105\pi$
$798$		0			0
$799$	−92.2863	+	33.5895i	−3.26485	+	1.18831i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	72.3691	+	12.7606i	2.55385	+	0.450313i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$			31.2163i			1.09751i	0.835984	+	0.548753i	$0.184897\pi$
$809$			31.2163i			1.09751i	−0.835984	+	0.548753i	$0.815103\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	16.4494	−	19.6036i	0.577260	−	0.687952i
$813$		0			0
$814$		0			0
$815$		0			0
$816$	17.7734	−	48.2989i	0.622193	−	1.69080i
$817$		0			0
$818$		0			0
$819$	−35.5631	−	13.2300i	−1.24268	−	0.462294i
$820$		0			0
$821$	14.0813	+	38.6880i	0.491440	+	1.35022i	0.899363	+	0.437203i	$0.144031\pi$
$821$	14.0813	+	38.6880i	0.491440	+	1.35022i	−0.407923	+	0.913016i	$0.633747\pi$
$822$		0			0
$823$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$823$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$824$		0			0
$825$	0.198192	−	55.9479i	0.00690015	−	1.94785i
$826$		0			0
$827$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$827$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$	−35.9379	−	13.0803i	−1.24592	−	0.453478i
$833$	51.2087	−	9.02947i	1.77428	−	0.312853i
$834$		0			0
$835$	−23.5360	−	19.7491i	−0.814498	−	0.683445i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$839$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$840$		0			0
$841$	0.974388	+	5.52603i	0.0335996	+	0.190553i
$842$		0			0
$843$	37.1680	+	44.6151i	1.28013	+	1.53663i
$844$	4.68319	−	26.5597i	0.161202	−	0.914221i
$845$	19.0812	+	11.0166i	0.656414	+	0.378981i
$846$		0			0
$847$	−40.6599	−	70.4251i	−1.39709	−	2.41983i
$848$		0			0
$849$	−28.3811	+	48.7578i	−0.974037	+	1.67336i
$850$		0			0
$851$		0			0
$852$	−41.5316	−	24.1748i	−1.42285	−	0.828217i
$853$	−12.8652	+	4.68254i	−0.440495	+	0.160327i	−0.552741	−	0.833353i	$-0.686418\pi$
$853$	−12.8652	+	4.68254i	−0.440495	+	0.160327i	0.112245	+	0.993681i	$0.464196\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.3791	−	3.94604i	−0.764455	−	0.134794i	−0.222192	−	0.975003i	$-0.571321\pi$
$857$	−22.3791	−	3.94604i	−0.764455	−	0.134794i	−0.542263	+	0.840209i	$0.682432\pi$
$858$		0			0
$859$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$859$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	58.6113			1.99284
$866$		0			0
$867$	11.7142	−	65.0854i	0.397835	−	2.21042i
$868$		0			0
$869$	−23.5149	+	64.6066i	−0.797688	+	2.19163i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−14.9139	+	25.4141i	−0.504758	+	0.860136i
$874$		0			0
$875$	10.1171	+	27.7965i	0.342020	+	0.939693i
$876$	−39.4034	−	0.139584i	−1.33132	−	0.00471611i
$877$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$877$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$878$		0			0
$879$	−49.4806	+	28.3344i	−1.66894	+	0.955696i
$880$	54.2983	−	19.7630i	1.83040	−	0.666210i
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$		0			0
$883$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$883$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$884$	−69.9442	−	12.3331i	−2.35248	−	0.414806i
$885$		0			0
$886$		0			0
$887$	58.2334	−	10.2681i	1.95529	−	0.344770i	0.956734	−	0.290963i	$-0.0939758\pi$
$887$	58.2334	−	10.2681i	1.95529	−	0.344770i	0.998551	−	0.0538062i	$-0.0171353\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	57.3971	−	9.28410i	1.92287	−	0.311029i
$892$	−3.10512			−0.103967
$893$		0			0
$894$		0			0
$895$	−1.12996	−	6.40834i	−0.0377705	−	0.214207i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	5.00000	+	29.5804i	0.166667	+	0.986013i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$907$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$908$	42.6104	−	24.6011i	1.41408	−	0.816417i
$909$		0			0
$910$		0			0
$911$	50.7065	+	8.94092i	1.67998	+	0.296226i	0.930634	−	0.365951i	$-0.119256\pi$
$911$	50.7065	+	8.94092i	1.67998	+	0.296226i	0.749347	+	0.662177i	$0.230367\pi$
$912$		0			0
$913$	20.3505	+	7.40697i	0.673503	+	0.245135i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	31.6113			1.04276			0.521380	−	0.853325i	$-0.325417\pi$
$919$	31.6113			1.04276			0.521380	+	0.853325i	$0.325417\pi$
$920$		0			0
$921$	−29.1508	−	24.6370i	−0.960553	−	0.811816i
$922$		0			0
$923$	−22.6818	+	62.3177i	−0.746580	+	2.05121i
$924$	37.8986	+	45.4920i	1.24677	+	1.49658i
$925$		0			0
$926$		0			0
$927$	52.9964	−	18.8650i	1.74063	−	0.619607i
$928$		0			0
$929$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$929$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	92.9320	−	53.6543i	3.03920	−	1.75468i
$936$		0			0
$937$	25.4638	−	44.1045i	0.831864	−	1.44083i	−0.0646935	−	0.997905i	$-0.520607\pi$
$937$	25.4638	−	44.1045i	0.831864	−	1.44083i	0.896558	−	0.442926i	$-0.146060\pi$
$938$		0			0
$939$	3.82833	−	3.18931i	0.124933	−	0.104079i
$940$	55.5595	+	20.2220i	1.81215	+	0.659569i
$941$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$941$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−26.7842	+	15.0866i	−0.871290	+	0.490768i
$946$		0			0
$947$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$947$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$948$	6.53029	−	36.2830i	0.212094	−	1.17842i
$949$	9.44263	+	53.5518i	0.306521	+	1.73836i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$953$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$954$		0			0
$955$	6.61438	+	11.4564i	0.214036	+	0.370722i
$956$	−15.4487	−	42.4448i	−0.499645	−	1.37276i
$957$	54.1149	+	0.191699i	1.74929	+	0.00619674i
$958$		0			0
$959$		0			0
$960$	−26.8875	+	15.3968i	−0.867791	+	0.496929i
$961$	−29.1305	+	10.6026i	−0.939693	+	0.342020i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$967$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	−29.4810	+	10.1426i	−0.945603	+	0.325323i
$973$		0			0
$974$		0			0
$975$	38.9538	−	14.0219i	1.24752	−	0.449062i
$976$		0			0
$977$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$977$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$978$		0			0
$979$		0			0
$980$	−27.1109	−	15.6525i	−0.866025	−	0.500000i
$981$	−9.86271	+	8.15743i	−0.314892	+	0.260447i
$982$		0			0
$983$	−19.8310	−	54.4851i	−0.632509	−	1.73780i	−0.674068	−	0.738669i	$-0.735455\pi$
$983$	−19.8310	−	54.4851i	−0.632509	−	1.73780i	0.0415592	−	0.999136i	$-0.486767\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.214618	+	60.5849i	−0.00683137	+	1.92844i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	31.3255	−	54.2574i	0.995087	−	1.72354i	0.411807	−	0.911271i	$-0.364898\pi$
$991$	31.3255	−	54.2574i	0.995087	−	1.72354i	0.583280	−	0.812271i	$-0.301769\pi$
$992$		0			0
$993$	−10.7121	−	62.0357i	−0.339939	−	1.96864i
$994$		0			0
$995$		0			0
$996$	−11.4288	−	2.05698i	−0.362136	−	0.0651779i
$997$	14.1873	+	11.9046i	0.449318	+	0.377022i	0.839183	−	0.543850i	$-0.183034\pi$
$997$	14.1873	+	11.9046i	0.449318	+	0.377022i	−0.389865	+	0.920872i	$0.627478\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.cs.a.524.4	yes	24
5.4	even	2	inner	945.2.cs.a.524.1	✓	24
7.6	odd	2	inner	945.2.cs.a.524.1	✓	24
27.5	odd	18	inner	945.2.cs.a.734.4	yes	24
35.34	odd	2	CM	945.2.cs.a.524.4	yes	24
135.59	odd	18	inner	945.2.cs.a.734.1	yes	24
189.167	even	18	inner	945.2.cs.a.734.1	yes	24
945.734	even	18	inner	945.2.cs.a.734.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.a.524.1	✓	24	5.4	even	2	inner
945.2.cs.a.524.1	✓	24	7.6	odd	2	inner
945.2.cs.a.524.4	yes	24	1.1	even	1	trivial
945.2.cs.a.524.4	yes	24	35.34	odd	2	CM
945.2.cs.a.734.1	yes	24	135.59	odd	18	inner
945.2.cs.a.734.1	yes	24	189.167	even	18	inner
945.2.cs.a.734.4	yes	24	27.5	odd	18	inner
945.2.cs.a.734.4	yes	24	945.734	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.cs (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62968 - 0.586627i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(-0.459430 + 2.60556i) q^{7} +(2.31174 - 1.91203i) q^{9} +O(q^{10})\)	\(q+(1.62968 - 0.586627i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(-0.459430 + 2.60556i) q^{7} +(2.31174 - 1.91203i) q^{9} +(2.20957 + 6.07074i) q^{11} +(-1.72141 - 3.00612i) q^{12} +(-3.66210 + 3.07287i) q^{13} +(-0.0137197 + 3.87296i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(-6.43317 + 3.71419i) q^{17} +(4.40419 + 0.776578i) q^{20} +(0.779764 + 4.51575i) q^{21} +(-3.83022 - 3.21394i) q^{25} +(2.64575 - 4.47214i) q^{27} +5.29150 q^{28} +(3.10864 - 3.70474i) q^{29} +(7.16215 + 8.59719i) q^{33} +(-5.12348 - 2.95804i) q^{35} +(-4.56883 - 3.88919i) q^{36} +(-4.16544 + 7.15609i) q^{39} +(11.1896 - 6.46034i) q^{44} +(2.24962 + 6.31975i) q^{45} +(13.0199 + 2.29576i) q^{47} +(-5.32305 + 4.43453i) q^{48} +(-6.57785 - 2.39414i) q^{49} +(-8.30518 + 9.82682i) q^{51} +(7.32420 + 6.14574i) q^{52} -14.4458 q^{55} +(7.63300 - 1.31804i) q^{60} +(3.91983 + 6.90181i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-3.65606 - 10.0449i) q^{65} +(9.54974 + 11.3809i) q^{68} +(12.0138 - 6.93616i) q^{71} +(5.68743 - 9.85092i) q^{73} +(-8.12743 - 2.99079i) q^{75} +(-16.8328 + 2.96807i) q^{77} +(8.15248 + 6.84074i) q^{79} -8.94427i q^{80} +(1.68826 - 8.84024i) q^{81} +(2.15477 - 2.56795i) q^{83} +(8.62348 - 3.10414i) q^{84} +(-2.88436 - 16.3580i) q^{85} +(2.89281 - 7.86116i) q^{87} +(-6.32405 - 10.9536i) q^{91} +(-9.22994 + 3.35942i) q^{97} +(16.7154 + 9.80919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{9}+O(q^{10}) \) 24 * q - 6 * q^9	\( 24 q - 6 q^{9} - 18 q^{11} - 24 q^{39} + 96 q^{64} - 180 q^{65} - 12 q^{79} + 102 q^{81} + 84 q^{84} + 60 q^{85} + 228 q^{99}+O(q^{100}) \) 24 * q - 6 * q^9 - 18 * q^11 - 24 * q^39 + 96 * q^64 - 180 * q^65 - 12 * q^79 + 102 * q^81 + 84 * q^84 + 60 * q^85 + 228 * q^99

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