LMFDB - Embedded newform 945.2.cs.a.209.4

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			209.4
Character	$\chi$	$=$	945.209
Dual form			945.2.cs.a.104.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.62968 - 0.586627i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(-2.02676 - 1.70066i) q^{7} +(2.31174 - 1.91203i) q^{9} +O(q^{10})$	\(q+(1.62968 - 0.586627i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(-2.02676 - 1.70066i) q^{7} +(2.31174 - 1.91203i) q^{9} +(4.46437 + 0.787188i) q^{11} +(-1.74267 + 2.99385i) q^{12} +(-6.63961 - 2.41662i) q^{13} +(3.36094 - 1.92460i) q^{15} +(0.694593 - 3.93923i) q^{16} +(5.90187 - 3.40745i) q^{17} +(-2.87463 + 3.42585i) q^{20} +(-4.30063 - 1.58258i) q^{21} +(4.69846 - 1.71010i) q^{25} +(2.64575 - 4.47214i) q^{27} +5.29150 q^{28} +(1.65407 + 4.54453i) q^{29} +(7.73729 - 1.33605i) q^{33} +(-5.12348 - 2.95804i) q^{35} +(-1.08373 + 5.90132i) q^{36} +(-12.2381 - 0.0433527i) q^{39} +(-7.85180 + 4.53324i) q^{44} +(4.34825 - 5.10810i) q^{45} +(6.27240 - 7.47515i) q^{47} +(-1.17889 - 6.82717i) q^{48} +(1.21554 + 6.89365i) q^{49} +(7.61929 - 9.01526i) q^{51} +(13.2792 - 4.83324i) q^{52} +10.1366 q^{55} +(-2.67504 + 7.26940i) q^{60} +(-7.93705 - 0.0562338i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-15.5594 - 2.74354i) q^{65} +(-4.66166 + 12.8078i) q^{68} +(1.16957 - 0.675254i) q^{71} +(-8.36548 + 14.4894i) q^{73} +(6.65382 - 5.54317i) q^{75} +(-7.70948 - 9.18780i) q^{77} +(-6.58720 + 2.39754i) q^{79} -8.94427i q^{80} +(1.68826 - 8.84024i) q^{81} +(4.73160 + 13.0000i) q^{83} +(8.62348 - 3.10414i) q^{84} +(11.6734 - 9.79516i) q^{85} +(5.36156 + 6.43582i) q^{87} +(9.34707 + 16.1896i) q^{91} +(1.71484 - 9.72536i) q^{97} +(11.8256 - 6.71624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$-1$

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		−0.342020	−	0.939693i	$-0.611111\pi$
$2$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$3$	1.62968	−	0.586627i	0.940898	−	0.338689i
$3$	1.62968	−	0.586627i	0.940898	−	0.338689i
$4$	−1.53209	+	1.28558i	−0.766044	+	0.642788i
$5$	2.20210	−	0.388289i	0.984808	−	0.173648i
$5$	2.20210	−	0.388289i	0.984808	−	0.173648i
$6$		0			0
$7$	−2.02676	−	1.70066i	−0.766044	−	0.642788i
$7$	−2.02676	−	1.70066i	−0.766044	−	0.642788i
$8$		0			0
$9$	2.31174	−	1.91203i	0.770579	−	0.637344i
$10$		0			0
$11$	4.46437	+	0.787188i	1.34606	+	0.237346i	0.799798	−	0.600270i	$-0.204940\pi$
$11$	4.46437	+	0.787188i	1.34606	+	0.237346i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−1.74267	+	2.99385i	−0.503065	+	0.864249i
$13$	−6.63961	−	2.41662i	−1.84150	−	0.670250i	−0.989079	−	0.147386i	$-0.952914\pi$
$13$	−6.63961	−	2.41662i	−1.84150	−	0.670250i	−0.852416	−	0.522864i	$-0.824864\pi$
$14$		0			0
$15$	3.36094	−	1.92460i	0.867791	−	0.496929i
$16$	0.694593	−	3.93923i	0.173648	−	0.984808i
$17$	5.90187	−	3.40745i	1.43141	−	0.826428i	0.434186	−	0.900823i	$-0.357036\pi$
$17$	5.90187	−	3.40745i	1.43141	−	0.826428i	0.997229	+	0.0743959i	$0.0237028\pi$
$18$		0			0
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−2.87463	+	3.42585i	−0.642788	+	0.766044i
$21$	−4.30063	−	1.58258i	−0.938475	−	0.345347i
$22$		0			0
$23$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$23$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$24$		0			0
$25$	4.69846	−	1.71010i	0.939693	−	0.342020i
$26$		0			0
$27$	2.64575	−	4.47214i	0.509175	−	0.860663i
$28$	5.29150			1.00000
$29$	1.65407	+	4.54453i	0.307154	+	0.843898i	0.993208	+	0.116348i	$0.0371189\pi$
$29$	1.65407	+	4.54453i	0.307154	+	0.843898i	−0.686055	+	0.727550i	$0.740659\pi$
$30$		0			0
$31$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$31$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$32$		0			0
$33$	7.73729	−	1.33605i	1.34689	−	0.232576i
$34$		0			0
$35$	−5.12348	−	2.95804i	−0.866025	−	0.500000i
$36$	−1.08373	+	5.90132i	−0.180621	+	0.983553i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$	−12.2381	−	0.0433527i	−1.95967	−	0.00694200i
$40$		0			0
$41$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$41$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$42$		0			0
$43$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$43$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$44$	−7.85180	+	4.53324i	−1.18370	+	0.683411i
$45$	4.34825	−	5.10810i	0.648199	−	0.761471i
$46$		0			0
$47$	6.27240	−	7.47515i	0.914923	−	1.09036i	−0.0806848	−	0.996740i	$-0.525711\pi$
$47$	6.27240	−	7.47515i	0.914923	−	1.09036i	0.995608	−	0.0936230i	$-0.0298448\pi$
$48$	−1.17889	−	6.82717i	−0.170158	−	0.985417i
$49$	1.21554	+	6.89365i	0.173648	+	0.984808i
$50$		0			0
$51$	7.61929	−	9.01526i	1.06691	−	1.26239i
$52$	13.2792	−	4.83324i	1.84150	−	0.670250i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	10.1366			1.36682
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$59$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$60$	−2.67504	+	7.26940i	−0.345347	+	0.938475i
$61$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$61$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$62$		0			0
$63$	−7.93705	−	0.0562338i	−0.999975	−	0.00708479i
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	−15.5594	−	2.74354i	−1.92991	−	0.340295i
$66$		0			0
$67$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$67$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$68$	−4.66166	+	12.8078i	−0.565310	+	1.55318i
$69$		0			0
$70$		0			0
$71$	1.16957	−	0.675254i	0.138803	−	0.0801380i	−0.428990	−	0.903309i	$-0.641131\pi$
$71$	1.16957	−	0.675254i	0.138803	−	0.0801380i	0.567793	+	0.823171i	$0.307797\pi$
$72$		0			0
$73$	−8.36548	+	14.4894i	−0.979105	+	1.69586i	−0.313441	+	0.949608i	$0.601482\pi$
$73$	−8.36548	+	14.4894i	−0.979105	+	1.69586i	−0.665664	+	0.746252i	$0.731851\pi$
$74$		0			0
$75$	6.65382	−	5.54317i	0.768317	−	0.640070i
$76$		0			0
$77$	−7.70948	−	9.18780i	−0.878576	−	1.04705i
$78$		0			0
$79$	−6.58720	+	2.39754i	−0.741117	+	0.269745i	−0.684863	−	0.728672i	$-0.740138\pi$
$79$	−6.58720	+	2.39754i	−0.741117	+	0.269745i	−0.0562544	+	0.998416i	$0.517916\pi$
$80$		−	8.94427i		−	1.00000i
$81$	1.68826	−	8.84024i	0.187585	−	0.982248i
$82$		0			0
$83$	4.73160	+	13.0000i	0.519360	+	1.42693i	0.871227	+	0.490881i	$0.163325\pi$
$83$	4.73160	+	13.0000i	0.519360	+	1.42693i	−0.351866	+	0.936050i	$0.614453\pi$
$84$	8.62348	−	3.10414i	0.940898	−	0.338689i
$85$	11.6734	−	9.79516i	1.26616	−	1.06243i
$86$		0			0
$87$	5.36156	+	6.43582i	0.574820	+	0.689993i
$88$		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
$91$	9.34707	+	16.1896i	0.979839	+	1.69713i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.71484	−	9.72536i	0.174116	−	0.987461i	−0.765043	−	0.643979i	$-0.777282\pi$
$97$	1.71484	−	9.72536i	0.174116	−	0.987461i	0.939159	−	0.343482i	$-0.111606\pi$
$98$		0			0
$99$	11.8256	−	6.71624i	1.18851	−	0.675008i
$100$	−5.00000	+	8.66025i	−0.500000	+	0.866025i
$101$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$101$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$102$		0			0
$103$	−3.25613	−	18.4664i	−0.320836	−	1.81955i	−0.537452	−	0.843294i	$-0.680613\pi$
$103$	−3.25613	−	18.4664i	−0.320836	−	1.81955i	0.216616	−	0.976257i	$-0.430498\pi$
$104$		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	$0.5\pi$
$108$	1.69574	+	10.2530i	0.163173	+	0.986598i
$109$	−15.5685			−1.49119			−0.745595	−	0.666400i	$-0.767834\pi$
$109$	−15.5685			−1.49119			−0.745595	+	0.666400i	$0.767834\pi$
$110$		0			0
$111$		0			0
$112$	−8.10705	+	6.80262i	−0.766044	+	0.642788i
$113$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$113$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$114$		0			0
$115$		0			0
$116$	−8.37652	−	4.83619i	−0.777741	−	0.449029i
$117$	−19.9697	+	7.10855i	−1.84620	+	0.657186i
$118$		0			0
$119$	−17.7566	−	3.13097i	−1.62774	−	0.287015i
$120$		0			0
$121$	8.97428	+	3.26637i	0.815844	+	0.296943i
$122$		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		−0.642788	−	0.766044i	$-0.722222\pi$
$131$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$132$	−10.1366	+	11.9938i	−0.882280	+	1.04393i
$133$		0			0
$134$		0			0
$135$	4.08972	−	10.8754i	0.351987	−	0.936005i
$136$		0			0
$137$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$137$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$138$		0			0
$139$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$139$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$140$	11.6524	−	2.05463i	0.984808	−	0.173648i
$141$	5.83690	−	15.8617i	0.491555	−	1.33579i
$142$		0			0
$143$	−27.7393	−	16.0153i	−2.31968	−	1.33927i
$144$	−5.92622	−	10.4346i	−0.493852	−	0.869546i
$145$	5.40702	+	9.36524i	0.449029	+	0.777741i
$146$		0			0
$147$	6.02494	+	10.5214i	0.496929	+	0.867791i
$148$		0			0
$149$	−3.42640	+	9.41395i	−0.280701	+	0.771221i	0.716578	+	0.697507i	$0.245707\pi$
$149$	−3.42640	+	9.41395i	−0.280701	+	0.771221i	−0.997279	+	0.0737137i	$0.976515\pi$
$150$		0			0
$151$	−1.71990	+	9.75405i	−0.139964	+	0.793773i	0.831310	+	0.555809i	$0.187591\pi$
$151$	−1.71990	+	9.75405i	−0.139964	+	0.793773i	−0.971274	+	0.237964i	$0.923520\pi$
$152$		0			0
$153$	7.12843	−	19.1617i	0.576299	−	1.54913i
$154$		0			0
$155$		0			0
$156$	18.8056	−	15.6666i	1.50565	−	1.25433i
$157$	4.25060	+	24.1063i	0.339235	+	1.92390i	0.380573	+	0.924751i	$0.375727\pi$
$157$	4.25060	+	24.1063i	0.339235	+	1.92390i	−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
$165$	16.5195	−	5.94642i	1.28604	−	0.462928i
$166$		0			0
$167$	−25.4357	+	4.48500i	−1.96827	+	0.347060i	−0.977727	+	0.209881i	$0.932692\pi$
$167$	−25.4357	+	4.48500i	−1.96827	+	0.347060i	−0.990546	+	0.137179i	$0.956196\pi$
$168$		0			0
$169$	28.2857	+	23.7346i	2.17583	+	1.82574i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	25.8135	+	4.55162i	1.96257	+	0.346054i	0.995961	+	0.0897890i	$0.0286193\pi$
$173$	25.8135	+	4.55162i	1.96257	+	0.346054i	0.966607	+	0.256265i	$0.0824918\pi$
$174$		0			0
$175$	−12.4310	−	4.52450i	−0.939693	−	0.342020i
$176$	6.20183	−	17.0394i	0.467481	−	1.28439i
$177$		0			0
$178$		0			0
$179$	−18.6895	+	10.7904i	−1.39692	+	0.806511i	−0.994068	−	0.108756i	$-0.965313\pi$
$179$	−18.6895	+	10.7904i	−1.39692	+	0.806511i	−0.402849	+	0.915267i	$0.631980\pi$
$180$	−0.0950524	+	13.4161i	−0.00708479	+	0.999975i
$181$		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
$187$	29.0304	−	10.5662i	2.12291	−	0.772678i
$188$			19.5162i			1.42337i
$189$	−12.9679	+	4.56445i	−0.943274	+	0.332015i
$190$		0			0
$191$	2.02342	+	5.55930i	0.146409	+	0.402257i	0.991121	−	0.132966i	$-0.0424500\pi$
$191$	2.02342	+	5.55930i	0.146409	+	0.402257i	−0.844711	+	0.535222i	$0.820228\pi$
$192$	10.5830	+	8.94427i	0.763763	+	0.645497i
$193$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$193$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$194$		0			0
$195$	−26.9663	+	4.65646i	−1.93110	+	0.333456i
$196$	−10.7246	−	8.99903i	−0.766044	−	0.642788i
$197$		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
$203$	4.37627	−	12.0237i	0.307154	−	0.843898i
$204$	−0.0836275	+	23.6073i	−0.00585510	+	1.65284i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−14.1314	+	24.4764i	−0.979839	+	1.69713i
$209$		0			0
$210$		0			0
$211$	5.04055	+	28.5864i	0.347006	+	1.96797i	0.213780	+	0.976882i	$0.431422\pi$
$211$	5.04055	+	28.5864i	0.347006	+	1.96797i	0.133226	+	0.991086i	$0.457467\pi$
$212$		0			0
$213$	1.50991	−	1.78656i	0.103458	−	0.122413i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−5.13319	+	28.5206i	−0.346869	+	1.92724i
$220$	−15.5302	+	13.0314i	−1.04705	+	0.878576i
$221$	−47.4206	+	8.36153i	−3.18986	+	0.562458i
$222$		0			0
$223$	−20.3816	−	17.1022i	−1.36486	−	1.14525i	−0.974449	−	0.224607i	$-0.927890\pi$
$223$	−20.3816	−	17.1022i	−1.36486	−	1.14525i	−0.390406	−	0.920643i	$-0.627665\pi$
$224$		0			0
$225$	7.59185	−	12.9369i	0.506123	−	0.862461i
$226$		0			0
$227$	−2.72684	−	0.480816i	−0.180987	−	0.0319129i	0.0824200	−	0.996598i	$-0.473735\pi$
$227$	−2.72684	−	0.480816i	−0.180987	−	0.0319129i	−0.263407	+	0.964685i	$0.584846\pi$
$228$		0			0
$229$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$229$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$230$		0			0
$231$	−17.9538	−	10.4506i	−1.18127	−	0.687600i
$232$		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
$235$	10.9099	−	18.8965i	0.711684	−	1.23267i
$236$		0			0
$237$	−9.32858	+	7.77146i	−0.605957	+	0.504811i
$238$		0			0
$239$	−14.5170	−	17.3007i	−0.939026	−	1.11909i	−0.992710	−	0.120530i	$-0.961541\pi$
$239$	−14.5170	−	17.3007i	−0.939026	−	1.11909i	0.0536837	−	0.998558i	$-0.482904\pi$
$240$	−5.24695	−	14.5763i	−0.338689	−	0.940898i
$241$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$241$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$242$		0			0
$243$	−2.43459	−	15.3972i	−0.156179	−	0.987729i
$244$		0			0
$245$	5.35346	+	14.7085i	0.342020	+	0.939693i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	15.3371	+	18.4101i	0.971951	+	1.16670i
$250$		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
$255$	13.2779	−	22.8110i	0.831493	−	1.42848i
$256$	−15.0351	−	5.47232i	−0.939693	−	0.342020i
$257$	−10.9594	+	30.1108i	−0.683631	+	1.87826i	−0.309314	+	0.950960i	$0.600099\pi$
$257$	−10.9594	+	30.1108i	−0.683631	+	1.87826i	−0.374317	+	0.927301i	$0.622123\pi$
$258$		0			0
$259$		0			0
$260$	27.3654	−	15.7994i	1.69713	−	0.979839i
$261$	12.5131	+	7.34312i	0.774540	+	0.454528i
$262$		0			0
$263$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$263$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$264$		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			$\pi$
$272$	−9.32333	−	25.6156i	−0.565310	−	1.55318i
$273$	24.7300	+	20.9007i	1.49673	+	1.26497i
$274$		0			0
$275$	22.3218	−	3.93594i	1.34606	−	0.237346i
$276$		0			0
$277$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$277$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.4266	+	2.89645i	0.979929	+	0.172788i	0.640596	−	0.767878i	$-0.278687\pi$
$281$	16.4266	+	2.89645i	0.979929	+	0.172788i	0.339333	+	0.940666i	$0.389799\pi$
$282$		0			0
$283$	−22.1641	−	8.06706i	−1.31752	−	0.479537i	−0.414855	−	0.909887i	$-0.636168\pi$
$283$	−22.1641	−	8.06706i	−1.31752	−	0.479537i	−0.902662	+	0.430350i	$0.858390\pi$
$284$	−0.923802	+	2.53813i	−0.0548176	+	0.150610i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	14.7214	−	25.4982i	0.865965	−	1.49990i
$290$		0			0
$291$	−2.91051	−	16.8552i	−0.170617	−	0.988071i
$292$	−5.81060	−	32.9535i	−0.340040	−	1.92846i
$293$	21.1605	+	25.2182i	1.23621	+	1.47326i	0.828344	+	0.560220i	$0.189283\pi$
$293$	21.1605	+	25.2182i	1.23621	+	1.47326i	0.407868	+	0.913041i	$0.366272\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	15.3320	−	17.8825i	0.889654	−	1.03765i
$298$		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
$307$	17.3074	+	29.9773i	0.987787	+	1.71090i	0.628830	+	0.777543i	$0.283534\pi$
$307$	17.3074	+	29.9773i	0.987787	+	1.71090i	0.358957	+	0.933354i	$0.383132\pi$
$308$	23.6232	+	4.16541i	1.34606	+	0.237346i
$309$	−16.1394	−	28.1843i	−0.918136	−	1.60335i
$310$		0			0
$311$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$311$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$312$		0			0
$313$	−0.499550	+	2.83309i	−0.0282362	+	0.160136i	−0.995666	−	0.0930055i	$-0.970353\pi$
$313$	−0.499550	+	2.83309i	−0.0282362	+	0.160136i	0.967429	+	0.253141i	$0.0814637\pi$
$314$		0			0
$315$	−17.5000	+	2.95804i	−0.986013	+	0.166667i
$316$	7.00995	−	12.1416i	0.394340	−	0.683018i
$317$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$317$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$318$		0			0
$319$	3.80699	+	21.5905i	0.213151	+	1.20884i
$320$	11.4985	+	13.7034i	0.642788	+	0.766044i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	8.77822	+	15.7144i	0.487679	+	0.873023i
$325$	−35.3286			−1.95968
$326$		0			0
$327$	−25.3717	+	9.13289i	−1.40306	+	0.505050i
$328$		0			0
$329$	−25.4253	+	4.48317i	−1.40174	+	0.247165i
$330$		0			0
$331$	−12.7840	−	10.7271i	−0.702673	−	0.589612i	0.219860	−	0.975531i	$-0.429440\pi$
$331$	−12.7840	−	10.7271i	−0.702673	−	0.589612i	−0.922533	+	0.385919i	$0.873884\pi$
$332$	−23.9617	−	13.8343i	−1.31507	−	0.759254i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−9.22133	+	15.8419i	−0.503065	+	0.864249i
$337$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$337$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$338$		0			0
$339$		0			0
$340$	−5.29230	+	30.0141i	−0.287015	+	1.62774i
$341$		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		−0.642788	−	0.766044i	$-0.722222\pi$
$347$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$348$	−16.4881	−	2.96756i	−0.883856	−	0.159078i
$349$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$349$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$350$		0			0
$351$	−28.3742	+	23.2994i	−1.51450	+	1.24363i
$352$		0			0
$353$	−2.08193	−	5.72005i	−0.110810	−	0.304447i	0.871876	−	0.489726i	$-0.162903\pi$
$353$	−2.08193	−	5.72005i	−0.110810	−	0.304447i	−0.982686	+	0.185279i	$0.940681\pi$
$354$		0			0
$355$	2.31332	−	1.94111i	0.122778	−	0.103023i
$356$		0			0
$357$	−30.7743	+	5.31401i	−1.62875	+	0.281247i
$358$		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
$363$	16.5414	+	0.0585968i	0.868197	+	0.00307553i
$364$	−35.1335	−	12.7875i	−1.84150	−	0.670250i
$365$	−12.7955	+	35.1554i	−0.669747	+	1.84012i
$366$		0			0
$367$	−1.03002	+	5.84153i	−0.0537666	+	0.304925i	−0.999818	−	0.0190919i	$-0.993923\pi$
$367$	−1.03002	+	5.84153i	−0.0537666	+	0.304925i	0.946051	+	0.324017i	$0.105034\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$373$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$374$		0			0
$375$	12.5000	−	14.7902i	0.645497	−	0.763763i
$376$		0			0
$377$		−	34.1712i		−	1.75990i
$378$		0			0
$379$	2.89457			0.148684			0.0743421	−	0.997233i	$-0.476314\pi$
$379$	2.89457			0.148684			0.0743421	+	0.997233i	$0.476314\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−16.9416	+	2.98725i	−0.865673	+	0.152641i	−0.588813	−	0.808269i	$-0.700405\pi$
$383$	−16.9416	+	2.98725i	−0.865673	+	0.152641i	−0.276859	+	0.960910i	$0.589294\pi$
$384$		0			0
$385$	−20.5445	−	17.2389i	−1.04705	−	0.878576i
$386$		0			0
$387$		0			0
$388$	9.87539	+	17.1047i	0.501347	+	0.868359i
$389$	36.8123	+	6.49100i	1.86646	+	0.329107i	0.988689	−	0.149979i	$-0.0479205\pi$
$389$	36.8123	+	6.49100i	1.86646	+	0.329107i	0.877768	+	0.479085i	$0.159032\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−13.5747	+	7.83736i	−0.683018	+	0.394340i
$396$	−9.48360	+	25.4925i	−0.476569	+	1.28105i
$397$	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
$400$	−3.47296	−	19.6962i	−0.173648	−	0.984808i
$401$	19.0139	+	22.6599i	0.949510	+	1.13158i	0.991190	+	0.132450i	$0.0422845\pi$
$401$	19.0139	+	22.6599i	0.949510	+	1.13158i	−0.0416801	+	0.999131i	$0.513271\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	0.285150	−	20.1226i	0.0141692	−	0.999900i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$409$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$410$		0			0
$411$		0			0
$412$	28.7287	+	24.1062i	1.41536	+	1.18763i
$413$		0			0
$414$		0			0
$415$	15.4672	+	26.7899i	0.759254	+	1.31507i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$419$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$420$	17.7844	−	10.1840i	0.867791	−	0.496929i
$421$	7.09160	−	40.2184i	0.345623	−	1.96013i	0.0762630	−	0.997088i	$-0.475701\pi$
$421$	7.09160	−	40.2184i	0.345623	−	1.96013i	0.269360	−	0.963039i	$-0.413188\pi$
$422$		0			0
$423$	0.207402	−	29.2736i	0.0100843	−	1.42333i
$424$		0			0
$425$	21.9027	−	26.1026i	1.06243	−	1.26616i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−54.6013	−	9.82724i	−2.63617	−	0.474464i
$430$		0			0
$431$		−	4.23679i		−	0.204079i	−0.994780	−	0.102040i	$-0.967463\pi$
$431$		−	4.23679i		−	0.204079i	0.994780	−	0.102040i	$-0.0325368\pi$
$432$	−15.7791	−	13.5285i	−0.759170	−	0.650892i
$433$	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
$436$	23.8523	−	20.0144i	1.14232	−	0.958518i
$437$		0			0
$438$		0			0
$439$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$439$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$440$		0			0
$441$	15.9909	+	13.6122i	0.761471	+	0.648199i
$442$		0			0
$443$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$443$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−0.0614676	+	17.3518i	−0.00290732	+	0.820711i
$448$	3.67544	−	20.8445i	0.173648	−	0.984808i
$449$	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
$453$	2.91909	+	16.9050i	0.137151	+	0.794264i
$454$		0			0
$455$	26.8694	+	32.0217i	1.25966	+	1.50120i
$456$		0			0
$457$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$457$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$458$		0			0
$459$	0.376318	−	35.4092i	0.0175650	−	1.65276i
$460$		0			0
$461$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$461$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$462$		0			0
$463$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$463$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$464$	19.0509	−	3.35918i	0.884414	−	0.155946i
$465$		0			0
$466$		0			0
$467$	−32.6038	−	18.8238i	−1.50872	−	0.871061i	−0.999948	−	0.0101613i	$-0.996765\pi$
$467$	−32.6038	−	18.8238i	−1.50872	−	0.871061i	−0.508774	−	0.860900i	$-0.669901\pi$
$468$	21.4567	−	36.5635i	0.991838	−	1.69015i
$469$		0			0
$470$		0			0
$471$	21.0686	+	36.7922i	0.970788	+	1.69530i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	31.2298	−	18.0305i	1.43141	−	0.826428i
$477$		0			0
$478$		0			0
$479$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$479$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−17.9486	+	6.53274i	−0.815844	+	0.296943i
$485$		−	22.0820i		−	1.00269i
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	26.9464	−	4.75137i	1.21607	−	0.214427i	0.471439	−	0.881899i	$-0.343735\pi$
$491$	26.9464	−	4.75137i	1.21607	−	0.214427i	0.744635	+	0.667472i	$0.232624\pi$
$492$		0			0
$493$	25.2474	+	21.1851i	1.13709	+	0.954128i
$494$		0			0
$495$	23.4332	−	19.3816i	1.05324	−	0.871136i
$496$		0			0
$497$	−3.51883	−	0.620464i	−0.157841	−	0.0278316i
$498$		0			0
$499$	−40.2340	−	14.6440i	−1.80112	−	0.655555i	−0.998233	−	0.0594285i	$-0.981072\pi$
$499$	−40.2340	−	14.6440i	−1.80112	−	0.655555i	−0.802890	−	0.596127i	$-0.796706\pi$
$500$	−7.64780	+	21.0122i	−0.342020	+	0.939693i
$501$	−38.8211	+	22.2304i	−1.73440	+	0.993181i
$502$		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
$507$	60.0201	+	22.0866i	2.66559	+	0.980902i
$508$		0			0
$509$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$509$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$510$		0			0
$511$	41.5964	−	15.1398i	1.84012	−	0.669747i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−14.3406	−	39.4005i	−0.631923	−	1.73620i
$516$		0			0
$517$	33.8866	−	28.4342i	1.49033	−	1.25054i
$518$		0			0
$519$	44.7380	−	7.72521i	1.96378	−	0.339099i
$520$		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
$523$	−9.99657	−	17.3146i	−0.437120	−	0.757113i	0.560346	−	0.828258i	$-0.310668\pi$
$523$	−9.99657	−	17.3146i	−0.437120	−	0.757113i	−0.997466	+	0.0711450i	$0.977335\pi$
$524$		0			0
$525$	−22.9127	−	0.0811669i	−0.999994	−	0.00354242i
$526$		0			0
$527$		0			0
$528$	0.111257	−	31.4070i	0.00484185	−	1.36681i
$529$	−3.99391	+	22.6506i	−0.173648	+	0.984808i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−24.1280	+	28.5487i	−1.04120	+	1.23197i
$538$		0			0
$539$			31.7327i			1.36682i
$540$	7.71532	+	21.9197i	0.332015	+	0.943274i
$541$	−24.9455			−1.07249			−0.536245	−	0.844062i	$-0.680158\pi$
$541$	−24.9455			−1.07249			−0.536245	+	0.844062i	$0.680158\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−34.2833	+	6.04507i	−1.46853	+	0.258942i
$546$		0			0
$547$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$547$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	17.4281	+	6.34330i	0.741117	+	0.269745i
$554$		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
$560$	−15.2111	+	18.1279i	−0.642788	+	0.766044i
$561$	41.1120	−	34.2496i	1.73575	−	1.44602i
$562$		0			0
$563$	−28.5799	−	34.0602i	−1.20450	−	1.43547i	−0.869985	−	0.493078i	$-0.835872\pi$
$563$	−28.5799	−	34.0602i	−1.20450	−	1.43547i	−0.334515	−	0.942390i	$-0.608573\pi$
$564$	11.4487	+	31.8053i	0.482079	+	1.33924i
$565$		0			0
$566$		0			0
$567$	−18.4559	+	15.0459i	−0.775075	+	0.631869i
$568$		0			0
$569$	−13.7193	−	37.6935i	−0.575143	−	1.58019i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	−13.7193	−	37.6935i	−0.575143	−	1.58019i	0.221123	−	0.975246i	$-0.429028\pi$
$570$		0			0
$571$	31.0355	−	26.0419i	1.29879	−	1.08982i	0.308443	−	0.951243i	$-0.400192\pi$
$571$	31.0355	−	26.0419i	1.29879	−	1.08982i	0.990352	−	0.138575i	$-0.0442523\pi$
$572$	63.0879	−	11.1241i	2.63784	−	0.465122i
$573$	6.55877	+	7.87290i	0.273996	+	0.328895i
$574$		0			0
$575$		0			0
$576$	22.4939	+	8.36806i	0.937246	+	0.348669i
$577$	13.5294	+	23.4337i	0.563238	+	0.975556i	0.997211	+	0.0746307i	$0.0237778\pi$
$577$	13.5294	+	23.4337i	0.563238	+	0.975556i	−0.433974	+	0.900926i	$0.642889\pi$
$578$		0			0
$579$		0			0
$580$	−20.3238	−	7.39724i	−0.843898	−	0.307154i
$581$	12.5186	−	34.3947i	0.519360	−	1.42693i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−41.2150	+	23.4077i	−1.70403	+	0.967791i
$586$		0			0
$587$	29.3852	−	35.0200i	1.21286	−	1.44543i	0.352445	−	0.935833i	$-0.385350\pi$
$587$	29.3852	−	35.0200i	1.21286	−	1.44543i	0.860414	−	0.509596i	$-0.170205\pi$
$588$	−22.7568	−	8.37421i	−0.938475	−	0.345347i
$589$		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
$595$	−40.3175			−1.65286
$596$	−6.85279	−	18.8279i	−0.280701	−	0.771221i
$597$		0			0
$598$		0			0
$599$	40.5103	−	7.14306i	1.65521	−	0.291858i	0.733484	−	0.679706i	$-0.237893\pi$
$599$	40.5103	−	7.14306i	1.65521	−	0.291858i	0.921723	+	0.387849i	$0.126782\pi$
$600$		0			0
$601$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$601$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$602$		0			0
$603$		0			0
$604$	−9.90452	−	17.1551i	−0.403009	−	0.698032i
$605$	21.0305	+	3.70825i	0.855013	+	0.150762i
$606$		0			0
$607$	−4.75528	−	1.73078i	−0.193011	−	0.0702502i	0.243706	−	0.969849i	$-0.421637\pi$
$607$	−4.75528	−	1.73078i	−0.193011	−	0.0702502i	−0.436717	+	0.899599i	$0.643859\pi$
$608$		0			0
$609$	0.0785077	−	22.1621i	0.00318129	−	0.898052i
$610$		0			0
$611$	−59.7108	+	34.4741i	−2.41564	+	1.39467i
$612$	13.7124	+	38.5216i	0.554292	+	1.55714i
$613$		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		−0.642788	−	0.766044i	$-0.722222\pi$
$617$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$618$		0			0
$619$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$619$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−8.67128	+	48.1786i	−0.347129	+	1.92869i
$625$	19.1511	−	16.0697i	0.766044	−	0.642788i
$626$		0			0
$627$		0			0
$628$	−37.5028	−	31.4686i	−1.49653	−	1.25573i
$629$		0			0
$630$		0			0
$631$	4.65857	+	8.06888i	0.185455	+	0.321217i	0.943730	−	0.330718i	$-0.107291\pi$
$631$	4.65857	+	8.06888i	0.185455	+	0.321217i	−0.758275	+	0.651935i	$0.773958\pi$
$632$		0			0
$633$	24.9840	+	43.6298i	0.993027	+	1.73413i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	8.58865	−	48.7086i	0.340295	−	1.92991i
$638$		0			0
$639$	1.41264	−	3.79728i	0.0558833	−	0.150218i
$640$		0			0
$641$	5.19106	−	6.18647i	0.205035	−	0.244351i	−0.653722	−	0.756735i	$-0.726793\pi$
$641$	5.19106	−	6.18647i	0.205035	−	0.244351i	0.858756	+	0.512384i	$0.171238\pi$
$642$		0			0
$643$	2.66297	+	15.1025i	0.105017	+	0.595584i	0.991213	+	0.132273i	$0.0422275\pi$
$643$	2.66297	+	15.1025i	0.105017	+	0.595584i	−0.886196	+	0.463311i	$0.846661\pi$
$644$		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		0.984808	−	0.173648i	$-0.0555556\pi$
$653$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	8.36548	+	49.4908i	0.326368	+	1.93082i
$658$		0			0
$659$	22.6529	+	3.99431i	0.882430	+	0.155596i	0.596461	−	0.802642i	$-0.296573\pi$
$659$	22.6529	+	3.99431i	0.882430	+	0.155596i	0.285970	+	0.958239i	$0.407684\pi$
$660$	−17.6648	+	30.3475i	−0.687600	+	1.18127i
$661$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$661$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$662$		0			0
$663$	−72.3755	+	41.4449i	−2.81083	+	1.60959i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	33.2039	−	39.5709i	1.28470	−	1.53104i
$669$	−43.2483	−	15.9148i	−1.67207	−	0.615302i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$673$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$674$		0			0
$675$	4.78316	−	25.5367i	0.184104	−	0.982907i
$676$	−73.8488			−2.84034
$677$	5.72792	+	15.7373i	0.220142	+	0.604835i	0.999771	−	0.0214069i	$-0.00681454\pi$
$677$	5.72792	+	15.7373i	0.220142	+	0.604835i	−0.779629	+	0.626242i	$0.784592\pi$
$678$		0			0
$679$	−20.0151	+	16.7946i	−0.768108	+	0.644519i
$680$		0			0
$681$	−4.72595	+	0.816062i	−0.181099	+	0.0312716i
$682$		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		0.173648	−	0.984808i	$-0.444444\pi$
$691$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$692$	−45.4001	+	26.2118i	−1.72585	+	0.996422i
$693$	−35.3897	−	6.49900i	−1.34434	−	0.246877i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	24.8619	−	9.04900i	0.939693	−	0.342020i
$701$			50.2017i			1.89609i	0.318131	+	0.948047i	$0.396945\pi$
$701$			50.2017i			1.89609i	−0.318131	+	0.948047i	$0.603055\pi$
$702$		0			0
$703$		0			0
$704$	12.4037	+	34.0788i	0.467481	+	1.28439i
$705$	6.69449	−	37.1954i	0.252129	−	1.40086i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	35.7063	+	29.9612i	1.34098	+	1.12521i	0.981373	+	0.192110i	$0.0615331\pi$
$709$	35.7063	+	29.9612i	1.34098	+	1.12521i	0.359605	+	0.933105i	$0.382911\pi$
$710$		0			0
$711$	−10.6437	+	18.1374i	−0.399170	+	0.680207i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−67.3032	−	24.4964i	−2.51700	−	0.916112i
$716$	14.7621	−	40.5585i	0.551686	−	1.51574i
$717$	−33.8071	−	19.6786i	−1.26255	−	0.734910i
$718$		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
$725$	15.5432	+	18.5237i	0.577260	+	0.687952i
$726$		0			0
$727$	−28.6062	+	10.4118i	−1.06095	+	0.386152i	−0.812783	−	0.582566i	$-0.802049\pi$
$727$	−28.6062	+	10.4118i	−1.06095	+	0.386152i	−0.248162	+	0.968719i	$0.579826\pi$
$728$		0			0
$729$	−13.0000	−	23.6643i	−0.481481	−	0.876456i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−32.6052	+	27.3590i	−1.20430	+	1.01053i	−0.204804	+	0.978803i	$0.565656\pi$
$733$	−32.6052	+	27.3590i	−1.20430	+	1.01053i	−0.999497	+	0.0317250i	$0.989900\pi$
$734$		0			0
$735$	17.3529	+	20.8297i	0.640070	+	0.768317i
$736$		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		0.342020	−	0.939693i	$-0.388889\pi$
$743$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$744$		0			0
$745$	−3.88992	+	22.0609i	−0.142516	+	0.808247i
$746$		0			0
$747$	35.7946	+	21.0055i	1.30965	+	0.768552i
$748$	−30.8935	+	53.5092i	−1.12958	+	1.95649i
$749$		0			0
$750$		0			0
$751$	9.13585	+	51.8120i	0.333372	+	1.89065i	0.442748	+	0.896646i	$0.354004\pi$
$751$	9.13585	+	51.8120i	0.333372	+	1.89065i	−0.109376	+	0.994000i	$0.534885\pi$
$752$	−25.0896	−	29.9006i	−0.914923	−	1.09036i
$753$		0			0
$754$		0			0
$755$			22.1472i			0.806018i
$756$	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		0.984808	−	0.173648i	$-0.0555556\pi$
$761$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$762$		0			0
$763$	31.5536	+	26.4766i	1.14232	+	0.958518i
$764$	−10.2470	−	5.91608i	−0.370722	−	0.214036i
$765$	8.25722	−	44.9638i	0.298540	−	1.62567i
$766$		0			0
$767$		0			0
$768$	−27.7126	−	0.0981703i	−0.999994	−	0.00354242i
$769$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$769$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$770$		0			0
$771$	−0.196606	+	55.5002i	−0.00708059	+	1.99879i
$772$		0			0
$773$	−47.0498	+	27.1642i	−1.69226	+	0.977028i	−0.739576	+	0.673073i	$0.764974\pi$
$773$	−47.0498	+	27.1642i	−1.69226	+	0.977028i	−0.952686	+	0.303956i	$0.901693\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	35.3286	−	41.8014i	1.26497	−	1.49673i
$781$	5.75296	−	2.09391i	0.205857	−	0.0749259i
$782$		0			0
$783$	24.7000	+	4.62645i	0.882707	+	0.165336i
$784$	28.0000			1.00000
$785$	18.7205	+	51.4341i	0.668162	+	1.83576i
$786$		0			0
$787$	−9.87831	+	8.28889i	−0.352124	+	0.295467i	−0.801642	−	0.597804i	$-0.796040\pi$
$787$	−9.87831	+	8.28889i	−0.352124	+	0.295467i	0.449518	+	0.893271i	$0.351596\pi$
$788$		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
$797$	−17.0380	+	46.8115i	−0.603516	+	1.65815i	0.140576	+	0.990070i	$0.455105\pi$
$797$	−17.0380	+	46.8115i	−0.603516	+	1.65815i	−0.744092	+	0.668077i	$0.767118\pi$
$798$		0			0
$799$	11.5477	−	65.4902i	0.408528	−	2.31688i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−48.7525	+	58.1009i	−1.72044	+	2.05034i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	56.7926i		−	1.99672i	−0.0572419	−	0.998360i	$-0.518231\pi$
$809$		−	56.7926i		−	1.99672i	0.0572419	−	0.998360i	$-0.481769\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	8.75254	+	24.0474i	0.307154	+	0.843898i
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−30.2209	−	36.2761i	−1.05794	−	1.26992i
$817$		0			0
$818$		0			0
$819$	52.5630	+	19.5542i	1.83670	+	0.683279i
$820$		0			0
$821$	−13.7241	−	2.41994i	−0.478976	−	0.0844563i	−0.0710524	−	0.997473i	$-0.522636\pi$
$821$	−13.7241	−	2.41994i	−0.478976	−	0.0844563i	−0.407923	+	0.913016i	$0.633747\pi$
$822$		0			0
$823$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$823$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$824$		0			0
$825$	34.0686	−	19.5089i	1.18612	−	0.679214i
$826$		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
$832$	−9.81560	−	55.6670i	−0.340295	−	1.92991i
$833$	30.6637	+	36.5436i	1.06243	+	1.26616i
$834$		0			0
$835$	−54.2704	+	19.7528i	−1.87810	+	0.683574i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$839$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$840$		0			0
$841$	4.29849	−	3.60686i	0.148224	−	0.124374i
$842$		0			0
$843$	28.4693	−	4.91599i	0.980535	−	0.169316i
$844$	−44.4725	−	37.3169i	−1.53081	−	1.28450i
$845$	71.5038	+	41.2828i	2.45981	+	1.42017i
$846$		0			0
$847$	−12.6338	−	21.8823i	−0.434101	−	0.751886i
$848$		0			0
$849$	−40.8528	−	0.144718i	−1.40206	−	0.00496672i
$850$		0			0
$851$		0			0
$852$	−0.0165725	+	4.67827i	−0.000567764	+	0.160275i
$853$	2.37739	−	13.4828i	0.0814003	−	0.461644i	−0.916675	−	0.399633i	$-0.869138\pi$
$853$	2.37739	−	13.4828i	0.0814003	−	0.461644i	0.998075	−	0.0620108i	$-0.0197513\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−37.3410	+	44.5013i	−1.27554	+	1.52013i	−0.542263	+	0.840209i	$0.682432\pi$
$857$	−37.3410	+	44.5013i	−1.27554	+	1.52013i	−0.733281	+	0.679925i	$0.762012\pi$
$858$		0			0
$859$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$859$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$860$		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
$867$	9.03329	−	50.1900i	0.306787	−	1.70454i
$868$		0			0
$869$	−31.2950	+	5.51815i	−1.06161	+	0.187190i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−14.6309	−	25.7613i	−0.495182	−	0.871889i
$874$		0			0
$875$	−29.1310	−	5.13658i	−0.984808	−	0.173648i
$876$	−28.8009	−	50.2952i	−0.973091	−	1.69932i
$877$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$877$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$878$		0			0
$879$	49.2786	+	28.6843i	1.66213	+	0.967496i
$880$	7.04083	−	39.9305i	0.237346	−	1.34606i
$881$		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	$0.666667\pi$
$884$	61.9032	−	73.7734i	2.08203	−	2.48127i
$885$		0			0
$886$		0			0
$887$	−38.0091	−	45.2975i	−1.27622	−	1.52094i	−0.730349	−	0.683074i	$-0.760642\pi$
$887$	−38.0091	−	45.2975i	−1.27622	−	1.52094i	−0.545873	−	0.837868i	$-0.683802\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	14.4960	−	38.1371i	0.485633	−	1.27764i
$892$	53.2127			1.78169
$893$		0			0
$894$		0			0
$895$	−36.9663	+	31.0184i	−1.23565	+	1.03683i
$896$		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		0.173648	−	0.984808i	$-0.444444\pi$
$907$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$908$	4.79589	−	2.76891i	0.159157	−	0.0918895i
$909$		0			0
$910$		0			0
$911$	−0.992804	+	1.18318i	−0.0328931	+	0.0392004i	−0.782240	−	0.622977i	$-0.785923\pi$
$911$	−0.992804	+	1.18318i	−0.0328931	+	0.0392004i	0.749347	+	0.662177i	$0.230367\pi$
$912$		0			0
$913$	10.8902	+	61.7612i	0.360412	+	2.04400i
$914$		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
$921$	45.7911	+	38.7006i	1.50887	+	1.27523i
$922$		0			0
$923$	−9.39735	+	1.65701i	−0.309318	+	0.0545410i
$924$	40.9419	−	7.06971i	1.34689	−	0.232576i
$925$		0			0
$926$		0			0
$927$	−42.8357	−	36.4637i	−1.40691	−	1.19763i
$928$		0			0
$929$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$929$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	59.8251	−	34.5400i	1.95649	−	1.12958i
$936$		0			0
$937$	−27.4440	+	47.5345i	−0.896558	+	1.55288i	−0.0646935	+	0.997905i	$0.520607\pi$
$937$	−27.4440	+	47.5345i	−0.896558	+	1.55288i	−0.831864	+	0.554979i	$0.812726\pi$
$938$		0			0
$939$	0.847857	+	4.91009i	0.0276688	+	0.160235i
$940$	7.57794	+	42.9766i	0.247165	+	1.40174i
$941$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$941$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−26.7842	+	15.0866i	−0.871290	+	0.490768i
$946$		0			0
$947$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$947$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$948$	4.30142	−	23.8992i	0.139704	−	0.776209i
$949$	90.5589	−	75.9879i	2.93967	−	2.46667i
$950$		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
$956$	44.4826	+	7.84349i	1.43867	+	0.253677i
$957$	18.8698	+	32.9524i	0.609973	+	1.06520i
$958$		0			0
$959$		0			0
$960$	26.7778	+	15.5869i	0.864249	+	0.503065i
$961$	5.38309	−	30.5290i	0.173648	−	0.984808i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$967$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	23.5242	+	20.4600i	0.754540	+	0.656254i
$973$		0			0
$974$		0			0
$975$	−57.5745	+	20.7247i	−1.84386	+	0.663722i
$976$		0			0
$977$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$977$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$978$		0			0
$979$		0			0
$980$	−27.1109	−	15.6525i	−0.866025	−	0.500000i
$981$	−35.9902	+	29.7674i	−1.14908	+	0.950401i
$982$		0			0
$983$	−8.18662	−	1.44352i	−0.261113	−	0.0460412i	0.0415592	−	0.999136i	$-0.486767\pi$
$983$	−8.18662	−	1.44352i	−0.261113	−	0.0460412i	−0.302672	+	0.953095i	$0.597879\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−38.8053	+	22.2213i	−1.23519	+	0.707313i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−18.3618	+	31.8035i	−0.583280	+	1.01027i	0.411807	+	0.911271i	$0.364898\pi$
$991$	−18.3618	+	31.8035i	−0.583280	+	1.01027i	−0.995087	+	0.0990001i	$0.968436\pi$
$992$		0			0
$993$	−27.1267	−	9.98227i	−0.860839	−	0.316778i
$994$		0			0
$995$		0			0
$996$	−47.1655	−	8.48893i	−1.49450	−	0.268982i
$997$	−17.4034	+	6.33430i	−0.551170	+	0.200609i	−0.602566	−	0.798069i	$-0.705855\pi$
$997$	−17.4034	+	6.33430i	−0.551170	+	0.200609i	0.0513964	+	0.998678i	$0.483633\pi$
$998$		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.209.4	yes	24
5.4	even	2	inner	945.2.cs.a.209.1	yes	24
7.6	odd	2	inner	945.2.cs.a.209.1	yes	24
27.23	odd	18	inner	945.2.cs.a.104.4	yes	24
35.34	odd	2	CM	945.2.cs.a.209.4	yes	24
135.104	odd	18	inner	945.2.cs.a.104.1	✓	24
189.104	even	18	inner	945.2.cs.a.104.1	✓	24
945.104	even	18	inner	945.2.cs.a.104.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.a.104.1	✓	24	135.104	odd	18	inner
945.2.cs.a.104.1	✓	24	189.104	even	18	inner
945.2.cs.a.104.4	yes	24	27.23	odd	18	inner
945.2.cs.a.104.4	yes	24	945.104	even	18	inner
945.2.cs.a.209.1	yes	24	5.4	even	2	inner
945.2.cs.a.209.1	yes	24	7.6	odd	2	inner
945.2.cs.a.209.4	yes	24	1.1	even	1	trivial
945.2.cs.a.209.4	yes	24	35.34	odd	2	CM

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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)

\(f(q)\)	\(=\)	\(q+(1.62968 - 0.586627i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(-2.02676 - 1.70066i) q^{7} +(2.31174 - 1.91203i) q^{9} +O(q^{10})\)	\(q+(1.62968 - 0.586627i) q^{3} +(-1.53209 + 1.28558i) q^{4} +(2.20210 - 0.388289i) q^{5} +(-2.02676 - 1.70066i) q^{7} +(2.31174 - 1.91203i) q^{9} +(4.46437 + 0.787188i) q^{11} +(-1.74267 + 2.99385i) q^{12} +(-6.63961 - 2.41662i) q^{13} +(3.36094 - 1.92460i) q^{15} +(0.694593 - 3.93923i) q^{16} +(5.90187 - 3.40745i) q^{17} +(-2.87463 + 3.42585i) q^{20} +(-4.30063 - 1.58258i) q^{21} +(4.69846 - 1.71010i) q^{25} +(2.64575 - 4.47214i) q^{27} +5.29150 q^{28} +(1.65407 + 4.54453i) q^{29} +(7.73729 - 1.33605i) q^{33} +(-5.12348 - 2.95804i) q^{35} +(-1.08373 + 5.90132i) q^{36} +(-12.2381 - 0.0433527i) q^{39} +(-7.85180 + 4.53324i) q^{44} +(4.34825 - 5.10810i) q^{45} +(6.27240 - 7.47515i) q^{47} +(-1.17889 - 6.82717i) q^{48} +(1.21554 + 6.89365i) q^{49} +(7.61929 - 9.01526i) q^{51} +(13.2792 - 4.83324i) q^{52} +10.1366 q^{55} +(-2.67504 + 7.26940i) q^{60} +(-7.93705 - 0.0562338i) q^{63} +(4.00000 + 6.92820i) q^{64} +(-15.5594 - 2.74354i) q^{65} +(-4.66166 + 12.8078i) q^{68} +(1.16957 - 0.675254i) q^{71} +(-8.36548 + 14.4894i) q^{73} +(6.65382 - 5.54317i) q^{75} +(-7.70948 - 9.18780i) q^{77} +(-6.58720 + 2.39754i) q^{79} -8.94427i q^{80} +(1.68826 - 8.84024i) q^{81} +(4.73160 + 13.0000i) q^{83} +(8.62348 - 3.10414i) q^{84} +(11.6734 - 9.79516i) q^{85} +(5.36156 + 6.43582i) q^{87} +(9.34707 + 16.1896i) q^{91} +(1.71484 - 9.72536i) q^{97} +(11.8256 - 6.71624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{9}+O(q^{10}) \) 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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