LMFDB - Embedded newform 945.2.cs.a.524.3

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			524.3
Character	$\chi$	$=$	945.524
Dual form			945.2.cs.a.734.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.306808 + 1.70466i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(0.459430 - 2.60556i) q^{7} +(-2.81174 + 1.04601i) q^{9} +O(q^{10})$	\(q+(0.306808 + 1.70466i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(0.459430 - 2.60556i) q^{7} +(-2.81174 + 1.04601i) q^{9} +(-0.890490 - 2.44660i) q^{11} +(3.25097 - 1.19632i) q^{12} +(0.146967 - 0.123320i) q^{13} +(-3.81650 - 0.659021i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(7.10570 - 4.10248i) q^{17} +(4.40419 + 0.776578i) q^{20} +(4.58255 - 0.0162334i) q^{21} +(-3.83022 - 3.21394i) q^{25} +(-2.64575 - 4.47214i) q^{27} -5.29150 q^{28} +(6.91142 - 8.23672i) q^{29} +(3.89741 - 2.26862i) q^{33} +(5.12348 + 2.95804i) q^{35} +(3.03674 + 5.17477i) q^{36} +(0.255310 + 0.212694i) q^{39} +(-4.50960 + 2.60362i) q^{44} +(-0.0475262 - 6.70804i) q^{45} +(7.67301 + 1.35296i) q^{47} +(-3.48533 - 5.98769i) q^{48} +(-6.57785 - 2.39414i) q^{49} +(9.17342 + 10.8541i) q^{51} +(-0.293934 - 0.246640i) q^{52} +5.82187 q^{55} +(0.0274394 + 7.74592i) q^{60} +(1.43363 + 7.80671i) q^{63} +(4.00000 + 6.92820i) q^{64} +(0.146725 + 0.403123i) q^{65} +(-10.5481 - 12.5707i) q^{68} +(8.45506 - 4.88153i) q^{71} +(7.52515 - 13.0339i) q^{73} +(4.30353 - 7.51529i) q^{75} +(-6.78387 + 1.19618i) q^{77} +(-9.32613 - 7.82555i) q^{79} -8.94427i q^{80} +(6.81174 - 5.88220i) q^{81} +(-10.9632 + 13.0654i) q^{83} +(-1.62348 - 9.02022i) q^{84} +(3.18590 + 18.0681i) q^{85} +(16.1613 + 9.25455i) q^{87} +(-0.253796 - 0.439588i) q^{91} +(-3.18582 + 1.15954i) q^{97} +(5.06298 + 5.94774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.722222\pi$
$3$	0.306808	+	1.70466i	0.177136	+	0.984186i
$3$	0.306808	+	1.70466i	0.177136	+	0.984186i
$4$	−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
$9$	−2.81174	+	1.04601i	−0.937246	+	0.348669i
$10$		0			0
$11$	−0.890490	−	2.44660i	−0.268493	−	0.737678i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−0.890490	−	2.44660i	−0.268493	−	0.737678i	0.730034	−	0.683411i	$-0.239504\pi$
$12$	3.25097	−	1.19632i	0.938475	−	0.345347i
$13$	0.146967	−	0.123320i	0.0407614	−	0.0342029i	−0.622179	−	0.782875i	$-0.713753\pi$
$13$	0.146967	−	0.123320i	0.0407614	−	0.0342029i	0.662941	+	0.748672i	$0.269308\pi$
$14$		0			0
$15$	−3.81650	−	0.659021i	−0.985417	−	0.170158i
$16$	−3.75877	+	1.36808i	−0.939693	+	0.342020i
$17$	7.10570	−	4.10248i	1.72339	−	0.994997i	0.811742	−	0.584016i	$-0.198519\pi$
$17$	7.10570	−	4.10248i	1.72339	−	0.994997i	0.911644	−	0.410982i	$-0.134814\pi$
$18$		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
$21$	4.58255	−	0.0162334i	0.999994	−	0.00354242i
$22$		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
$29$	6.91142	−	8.23672i	1.28342	−	1.52952i	0.597365	−	0.801970i	$-0.296214\pi$
$29$	6.91142	−	8.23672i	1.28342	−	1.52952i	0.686055	−	0.727550i	$-0.259341\pi$
$30$		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
$33$	3.89741	−	2.26862i	0.678453	−	0.394916i
$34$		0			0
$35$	5.12348	+	2.95804i	0.866025	+	0.500000i
$36$	3.03674	+	5.17477i	0.506123	+	0.862461i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$		0			0
$39$	0.255310	+	0.212694i	0.0408823	+	0.0340583i
$40$		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	$0.888889\pi$
$44$	−4.50960	+	2.60362i	−0.679847	+	0.392510i
$45$	−0.0475262	−	6.70804i	−0.00708479	−	0.999975i
$46$		0			0
$47$	7.67301	+	1.35296i	1.11922	+	0.197349i	0.702500	−	0.711684i	$-0.252067\pi$
$47$	7.67301	+	1.35296i	1.11922	+	0.197349i	0.416724	+	0.909033i	$0.363178\pi$
$48$	−3.48533	−	5.98769i	−0.503065	−	0.864249i
$49$	−6.57785	−	2.39414i	−0.939693	−	0.342020i
$50$		0			0
$51$	9.17342	+	10.8541i	1.28454	+	1.51988i
$52$	−0.293934	−	0.246640i	−0.0407614	−	0.0342029i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$		0			0
$55$	5.82187			0.785020
$56$		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	$0.611111\pi$
$60$	0.0274394	+	7.74592i	0.00354242	+	0.999994i
$61$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$61$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$62$		0			0
$63$	1.43363	+	7.80671i	0.180621	+	0.983553i
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	0.146725	+	0.403123i	0.0181990	+	0.0500012i
$66$		0			0
$67$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$67$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$68$	−10.5481	−	12.5707i	−1.27914	−	1.52442i
$69$		0			0
$70$		0			0
$71$	8.45506	−	4.88153i	1.00343	−	0.579331i	0.0941692	−	0.995556i	$-0.469981\pi$
$71$	8.45506	−	4.88153i	1.00343	−	0.579331i	0.909262	+	0.416225i	$0.136647\pi$
$72$		0			0
$73$	7.52515	−	13.0339i	0.880752	−	1.52551i	0.0302463	−	0.999542i	$-0.490371\pi$
$73$	7.52515	−	13.0339i	0.880752	−	1.52551i	0.850506	−	0.525965i	$-0.176296\pi$
$74$		0			0
$75$	4.30353	−	7.51529i	0.496929	−	0.867791i
$76$		0			0
$77$	−6.78387	+	1.19618i	−0.773094	+	0.136317i
$78$		0			0
$79$	−9.32613	−	7.82555i	−1.04927	−	0.880443i	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−9.32613	−	7.82555i	−1.04927	−	0.880443i	−0.993017	+	0.117973i	$0.962360\pi$
$80$		−	8.94427i		−	1.00000i
$81$	6.81174	−	5.88220i	0.756860	−	0.653577i
$82$		0			0
$83$	−10.9632	+	13.0654i	−1.20336	+	1.43411i	−0.332136	+	0.943231i	$0.607769\pi$
$83$	−10.9632	+	13.0654i	−1.20336	+	1.43411i	−0.871227	+	0.490881i	$0.836675\pi$
$84$	−1.62348	−	9.02022i	−0.177136	−	0.984186i
$85$	3.18590	+	18.0681i	0.345559	+	1.95976i
$86$		0			0
$87$	16.1613	+	9.25455i	1.73267	+	0.992191i
$88$		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
$91$	−0.253796	−	0.439588i	−0.0266051	−	0.0460814i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−3.18582	+	1.15954i	−0.323471	+	0.117734i	−0.498652	−	0.866802i	$-0.666171\pi$
$97$	−3.18582	+	1.15954i	−0.323471	+	0.117734i	0.175180	+	0.984536i	$0.443949\pi$
$98$		0			0
$99$	5.06298	+	5.94774i	0.508849	+	0.597770i
$100$	−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
$103$	15.1343	+	5.50842i	1.49122	+	0.542761i	0.953771	−	0.300533i	$-0.0971646\pi$
$103$	15.1343	+	5.50842i	1.49122	+	0.542761i	0.537452	+	0.843294i	$0.319387\pi$
$104$		0			0
$105$	−3.47053	+	9.64134i	−0.338689	+	0.940898i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−7.88953	+	6.76427i	−0.759170	+	0.650892i
$109$	−16.4069			−1.57149			−0.785747	−	0.618548i	$-0.787721\pi$
$109$	−16.4069			−1.57149			−0.785747	+	0.618548i	$0.787721\pi$
$110$		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
$116$	−18.6235	−	10.7523i	−1.72915	−	0.998323i
$117$	−0.284240	+	0.500473i	−0.0262780	+	0.0462687i
$118$		0			0
$119$	−7.42467	−	20.3991i	−0.680618	−	1.86998i
$120$		0			0
$121$	3.23361	−	2.71332i	0.293964	−	0.246666i
$122$		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	$0.944444\pi$
$132$	−5.82187	−	6.88852i	−0.506728	−	0.599569i
$133$		0			0
$134$		0			0
$135$	11.4203	−	2.13910i	0.982907	−	0.184104i
$136$		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
$141$	0.0478051	+	13.4950i	0.00402592	+	1.13648i
$142$		0			0
$143$	−0.432588	−	0.249755i	−0.0361748	−	0.0208855i
$144$	9.13765	−	7.77838i	0.761471	−	0.648199i
$145$	12.0214	+	20.8217i	0.998323	+	1.72915i
$146$		0			0
$147$	2.06306	−	11.9475i	0.170158	−	0.985417i
$148$		0			0
$149$	−12.9747	−	15.4627i	−1.06293	−	1.26675i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−12.9747	−	15.4627i	−1.06293	−	1.26675i	−0.100582	−	0.994929i	$-0.532070\pi$
$150$		0			0
$151$	−1.51705	+	0.552160i	−0.123455	+	0.0449341i	−0.403009	−	0.915196i	$-0.632036\pi$
$151$	−1.51705	+	0.552160i	−0.123455	+	0.0449341i	0.279554	+	0.960130i	$0.409814\pi$
$152$		0			0
$153$	−15.6881	+	18.9677i	−1.26831	+	1.53345i
$154$		0			0
$155$		0			0
$156$	0.330257	−	0.576730i	0.0264417	−	0.0461753i
$157$	−23.3401	−	8.49510i	−1.86274	−	0.677983i	−0.976788	−	0.214210i	$-0.931282\pi$
$157$	−23.3401	−	8.49510i	−1.86274	−	0.677983i	−0.885954	−	0.463772i	$-0.846496\pi$
$158$		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
$165$	1.78619	+	9.92431i	0.139055	+	0.772606i
$166$		0			0
$167$	−8.18939	+	22.5002i	−0.633714	+	1.74111i	0.0369115	+	0.999319i	$0.488248\pi$
$167$	−8.18939	+	22.5002i	−0.633714	+	1.74111i	−0.670625	+	0.741796i	$0.733974\pi$
$168$		0			0
$169$	−2.25103	+	12.7663i	−0.173157	+	0.982019i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.14105	+	14.1249i	0.390867	+	1.07390i	0.966607	+	0.256265i	$0.0824918\pi$
$173$	5.14105	+	14.1249i	0.390867	+	1.07390i	−0.575740	+	0.817633i	$0.695286\pi$
$174$		0			0
$175$	−10.1338	+	8.50328i	−0.766044	+	0.642788i
$176$	6.69429	+	7.97795i	0.504601	+	0.601360i
$177$		0			0
$178$		0			0
$179$	16.7377	−	9.66354i	1.25104	−	0.722287i	0.279722	−	0.960081i	$-0.409758\pi$
$179$	16.7377	−	9.66354i	1.25104	−	0.722287i	0.971316	+	0.237794i	$0.0764244\pi$
$180$	−13.1957	+	2.42328i	−0.983553	+	0.180621i
$181$		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
$187$	−16.3647	−	13.7316i	−1.19670	−	1.00415i
$188$		−	15.5828i		−	1.13649i
$189$	−12.8679	+	4.83902i	−0.936005	+	0.351987i
$190$		0			0
$191$	−3.80278	+	4.53198i	−0.275160	+	0.327923i	−0.885872	−	0.463930i	$-0.846439\pi$
$191$	−3.80278	+	4.53198i	−0.275160	+	0.327923i	0.610712	+	0.791853i	$0.290883\pi$
$192$	−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
$195$	−0.642171	+	0.373797i	−0.0459869	+	0.0267682i
$196$	−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
$203$	−18.2859	−	21.7923i	−1.28342	−	1.52952i
$204$	18.1926	−	21.8377i	1.27374	−	1.52895i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.383704	+	0.664595i	−0.0266051	+	0.0460814i
$209$		0			0
$210$		0			0
$211$	−20.1776	−	7.34403i	−1.38908	−	0.505584i	−0.464162	−	0.885750i	$-0.653645\pi$
$211$	−20.1776	−	7.34403i	−1.38908	−	0.505584i	−0.924918	+	0.380166i	$0.875867\pi$
$212$		0			0
$213$	10.9154	+	12.9153i	0.747913	+	0.884943i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$	24.5272	+	8.82891i	1.65740	+	0.596603i
$220$	−2.02191	−	11.4668i	−0.136317	−	0.773094i
$221$	0.538387	−	1.47921i	0.0362158	−	0.0995022i
$222$		0			0
$223$	2.02474	−	11.4829i	0.135587	−	0.768950i	−0.838863	−	0.544343i	$-0.816779\pi$
$223$	2.02474	−	11.4829i	0.135587	−	0.768950i	0.974449	−	0.224607i	$-0.0721099\pi$
$224$		0			0
$225$	14.1314	+	5.03031i	0.942092	+	0.335354i
$226$		0			0
$227$	10.2710	+	28.2195i	0.681713	+	1.87299i	0.418306	+	0.908306i	$0.362624\pi$
$227$	10.2710	+	28.2195i	0.681713	+	1.87299i	0.263407	+	0.964685i	$0.415154\pi$
$228$		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
$231$	−4.12043	−	11.1972i	−0.271104	−	0.736722i
$232$		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
$235$	−8.71103	+	15.0879i	−0.568245	+	0.984229i
$236$		0			0
$237$	10.4786	−	18.2988i	0.680657	−	1.18864i
$238$		0			0
$239$	−6.88969	+	1.21484i	−0.445657	+	0.0785813i	−0.391973	−	0.919977i	$-0.628207\pi$
$239$	−6.88969	+	1.21484i	−0.445657	+	0.0785813i	−0.0536837	+	0.998558i	$0.517096\pi$
$240$	15.2470	−	2.74417i	0.984186	−	0.177136i
$241$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$241$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$242$		0			0
$243$	12.1170	+	9.80700i	0.777309	+	0.629119i
$244$		0			0
$245$	10.0612	−	11.9905i	0.642788	−	0.766044i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−25.6356	−	14.6799i	−1.62459	−	0.930301i
$250$		0			0
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$	14.8783	−	5.53495i	0.937246	−	0.348669i
$253$		0			0
$254$		0			0
$255$	−29.8226	+	10.9743i	−1.86756	+	0.687238i
$256$	12.2567	−	10.2846i	0.766044	−	0.642788i
$257$	−4.27863	−	5.09908i	−0.266894	−	0.318072i	0.615907	−	0.787819i	$-0.288790\pi$
$257$	−4.27863	−	5.09908i	−0.266894	−	0.318072i	−0.882801	+	0.469747i	$0.844345\pi$
$258$		0			0
$259$		0			0
$260$	0.743040	−	0.428994i	0.0460814	−	0.0266051i
$261$	−10.8174	+	30.3889i	−0.669583	+	1.88102i
$262$		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			$\pi$
$272$	−21.0962	+	25.1415i	−1.27914	+	1.52442i
$273$	0.671482	−	0.567506i	0.0406400	−	0.0343470i
$274$		0			0
$275$	−4.45245	+	12.2330i	−0.268493	+	0.737678i
$276$		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
$281$	10.7638	+	29.5734i	0.642116	+	1.76420i	0.644974	+	0.764204i	$0.276868\pi$
$281$	10.7638	+	29.5734i	0.642116	+	1.76420i	−0.00285781	+	0.999996i	$0.500910\pi$
$282$		0			0
$283$	−25.6555	+	21.5275i	−1.52506	+	1.27968i	−0.701036	+	0.713126i	$0.747279\pi$
$283$	−25.6555	+	21.5275i	−1.52506	+	1.27968i	−0.824025	+	0.566553i	$0.808277\pi$
$284$	−12.5511	−	14.9579i	−0.744774	−	0.887587i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	25.1607	−	43.5796i	1.48004	−	2.56350i
$290$		0			0
$291$	−2.95407	−	5.07499i	−0.173170	−	0.297501i
$292$	−28.2853	−	10.2950i	−1.65527	−	0.602470i
$293$	8.19677	−	1.44531i	0.478860	−	0.0844360i	0.0709922	−	0.997477i	$-0.477383\pi$
$293$	8.19677	−	1.44531i	0.478860	−	0.0844360i	0.407868	+	0.913041i	$0.366272\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−8.58551	+	10.4555i	−0.498182	+	0.606689i
$298$		0			0
$299$		0			0
$300$	−16.2968	−	5.86627i	−0.940898	−	0.338689i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	15.3299	+	26.5522i	0.874926	+	1.51542i	0.856842	+	0.515579i	$0.172423\pi$
$307$	15.3299	+	26.5522i	0.874926	+	1.51542i	0.0180837	+	0.999836i	$0.494243\pi$
$308$	4.71203	+	12.9462i	0.268493	+	0.737678i
$309$	−4.74668	+	27.4888i	−0.270029	+	1.56378i
$310$		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
$313$	30.0514	−	10.9378i	1.69861	−	0.618242i	0.702941	−	0.711248i	$-0.251870\pi$
$313$	30.0514	−	10.9378i	1.69861	−	0.618242i	0.995666	+	0.0930055i	$0.0296474\pi$
$314$		0			0
$315$	−17.5000	−	2.95804i	−0.986013	−	0.166667i
$316$	−12.1744	+	21.0867i	−0.684863	+	1.18622i
$317$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$317$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$318$		0			0
$319$	−26.3065	−	9.57478i	−1.47288	−	0.536085i
$320$	−17.6168	+	3.10631i	−0.984808	+	0.173648i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−13.9514	−	11.3736i	−0.775075	−	0.631869i
$325$	−0.959261			−0.0532102
$326$		0			0
$327$	−5.03376	−	27.9682i	−0.278368	−	1.54664i
$328$		0			0
$329$	7.05042	−	19.3709i	0.388702	−	1.06795i
$330$		0			0
$331$	−5.82903	+	33.0580i	−0.320392	+	1.81703i	0.219860	+	0.975531i	$0.429440\pi$
$331$	−5.82903	+	33.0580i	−0.320392	+	1.81703i	−0.540252	+	0.841503i	$0.681671\pi$
$332$	29.5412	+	17.0556i	1.62129	+	0.936050i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−17.2025	+	6.33031i	−0.938475	+	0.345347i
$337$		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
$340$	34.4808	−	12.5500i	1.86998	−	0.680618i
$341$		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	$0.944444\pi$
$348$	12.6151	−	35.0456i	0.676243	−	1.87864i
$349$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$349$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$350$		0			0
$351$	−0.940343	−	0.330983i	−0.0501918	−	0.0176666i
$352$		0			0
$353$	22.5979	−	26.9311i	1.20276	−	1.43340i	0.330887	−	0.943670i	$-0.392652\pi$
$353$	22.5979	−	26.9311i	1.20276	−	1.43340i	0.871876	−	0.489726i	$-0.162903\pi$
$354$		0			0
$355$	3.79089	+	21.4992i	0.201200	+	1.14106i
$356$		0			0
$357$	32.4956	−	18.9152i	1.71985	−	1.00110i
$358$		0			0
$359$	21.8765	+	12.6304i	1.15460	+	0.666608i	0.950004	−	0.312239i	$-0.101079\pi$
$359$	21.8765	+	12.6304i	1.15460	+	0.666608i	0.204595	+	0.978847i	$0.434412\pi$
$360$		0			0
$361$	−9.50000	−	16.4545i	−0.500000	−	0.866025i
$362$		0			0
$363$	5.61739	+	4.67974i	0.294836	+	0.245623i
$364$	−0.777678	+	0.652549i	−0.0407614	+	0.0342029i
$365$	21.6321	+	25.7801i	1.13227	+	1.34939i
$366$		0			0
$367$	−6.92780	+	2.52151i	−0.361628	+	0.131622i	−0.516443	−	0.856322i	$-0.672744\pi$
$367$	−6.92780	+	2.52151i	−0.361628	+	0.131622i	0.154815	+	0.987944i	$0.450522\pi$
$368$		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
$377$		−	2.06285i		−	0.106242i
$378$		0			0
$379$	10.5600			0.542430			0.271215	−	0.962519i	$-0.412575\pi$
$379$	10.5600			0.542430			0.271215	+	0.962519i	$0.412575\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.22207	+	8.85257i	−0.164640	+	0.452345i	−0.994388	−	0.105793i	$-0.966262\pi$
$383$	−3.22207	+	8.85257i	−0.164640	+	0.452345i	0.829748	+	0.558138i	$0.188484\pi$
$384$		0			0
$385$	2.67474	−	15.1692i	0.136317	−	0.773094i
$386$		0			0
$387$		0			0
$388$	3.39028	+	5.87214i	0.172115	+	0.298113i
$389$	6.46352	+	17.7584i	0.327714	+	0.900386i	0.988689	+	0.149979i	$0.0479205\pi$
$389$	6.46352	+	17.7584i	0.327714	+	0.900386i	−0.660976	+	0.750407i	$0.729857\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$	23.5756	−	13.6114i	1.18622	−	0.684863i
$396$	9.95640	−	12.0378i	0.500328	−	0.604920i
$397$	0.115521	−	0.200088i	0.00579782	−	0.0100421i	−0.863112	−	0.505013i	$-0.831488\pi$
$397$	0.115521	−	0.200088i	0.00579782	−	0.0100421i	0.868910	+	0.494971i	$0.164821\pi$
$398$		0			0
$399$		0			0
$400$	18.7939	+	6.84040i	0.939693	+	0.342020i
$401$	29.1310	−	5.13658i	1.45473	−	0.256509i	0.610300	−	0.792170i	$-0.291049\pi$
$401$	29.1310	−	5.13658i	1.45473	−	0.256509i	0.844433	+	0.535662i	$0.179938\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	7.15028	+	18.8115i	0.355301	+	0.934752i
$406$		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
$412$	5.59340	−	31.7217i	0.275567	−	1.56282i
$413$		0			0
$414$		0			0
$415$	−19.0688	−	33.0281i	−0.936050	−	1.62129i
$416$		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	$0.277778\pi$
$420$	20.1950	+	3.48721i	0.985417	+	0.170158i
$421$	37.3547	−	13.5960i	1.82055	−	0.662628i	0.825372	−	0.564590i	$-0.190966\pi$
$421$	37.3547	−	13.5960i	1.82055	−	0.662628i	0.995183	−	0.0980380i	$-0.0312567\pi$
$422$		0			0
$423$	−22.9897	+	4.22186i	−1.11780	+	0.205274i
$424$		0			0
$425$	−40.4015	−	7.12388i	−1.95976	−	0.345559i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.293026	−	0.814042i	0.0141474	−	0.0393023i
$430$		0			0
$431$		−	39.9411i		−	1.92390i	−0.273231	−	0.961948i	$-0.588092\pi$
$431$		−	39.9411i		−	1.92390i	0.273231	−	0.961948i	$-0.411908\pi$
$432$	16.0630	+	13.1901i	0.772832	+	0.634611i
$433$	40.1484			1.92941			0.964703	−	0.263339i	$-0.0848238\pi$
$433$	40.1484			1.92941			0.964703	+	0.263339i	$0.0848238\pi$
$434$		0			0
$435$	−31.8056	+	26.8807i	−1.52496	+	1.28883i
$436$	5.69805	+	32.3152i	0.272887	+	1.54762i
$437$		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
$441$	20.9995	−	0.148781i	0.999975	−	0.00708479i
$442$		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
$447$	22.3778	−	26.8615i	1.05844	−	1.27051i
$448$	19.8895	−	7.23920i	0.939693	−	0.342020i
$449$	−24.6822	+	14.2503i	−1.16482	+	0.672511i	−0.952455	−	0.304679i	$-0.901451\pi$
$449$	−24.6822	+	14.2503i	−1.16482	+	0.672511i	−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−1.40669	−	2.41664i	−0.0660919	−	0.113544i
$454$		0			0
$455$	1.11777	−	0.197093i	0.0524018	−	0.00923985i
$456$		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
$459$	−37.1468	−	20.9235i	−1.73386	−	0.976627i
$460$		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	$0.444444\pi$
$464$	−14.7100	+	40.4153i	−0.682893	+	1.87623i
$465$		0			0
$466$		0			0
$467$	−13.1585	−	7.59708i	−0.608904	−	0.351551i	0.163632	−	0.986521i	$-0.447679\pi$
$467$	−13.1585	−	7.59708i	−0.608904	−	0.351551i	−0.772536	+	0.634970i	$0.781012\pi$
$468$	1.08445	+	0.386030i	0.0501289	+	0.0178443i
$469$		0			0
$470$		0			0
$471$	7.32034	−	42.3933i	0.337303	−	1.95338i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−37.5998	+	21.7083i	−1.72339	+	0.994997i
$477$		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
$484$	−6.46722	−	5.42664i	−0.293964	−	0.246666i
$485$		−	7.58090i		−	0.344231i
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.3672	−	36.7261i	0.603254	−	1.65743i	−0.141380	−	0.989955i	$-0.545154\pi$
$491$	13.3672	−	36.7261i	0.603254	−	1.65743i	0.744635	−	0.667472i	$-0.232624\pi$
$492$		0			0
$493$	15.3196	−	86.8816i	0.689959	−	3.91295i
$494$		0			0
$495$	−16.3696	+	6.08971i	−0.735757	+	0.273712i
$496$		0			0
$497$	−8.83460	−	24.2729i	−0.396286	−	1.08879i
$498$		0			0
$499$	18.8433	−	15.8114i	0.843542	−	0.707816i	−0.114816	−	0.993387i	$-0.536628\pi$
$499$	18.8433	−	15.8114i	0.843542	−	0.707816i	0.958358	+	0.285571i	$0.0921833\pi$
$500$	−14.3732	−	17.1293i	−0.642788	−	0.766044i
$501$	−40.8677	−	7.05690i	−1.82583	−	0.315279i
$502$		0			0
$503$	−1.39864	+	0.807506i	−0.0623624	+	0.0360049i	−0.530857	−	0.847461i	$-0.678130\pi$
$503$	−1.39864	+	0.807506i	−0.0623624	+	0.0360049i	0.468495	+	0.883466i	$0.344797\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−22.4528	+	0.0795375i	−0.997162	+	0.00353239i
$508$		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
$511$	−30.5034	−	25.5954i	−1.34939	−	1.13227i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−23.1488	+	27.5876i	−1.02006	+	1.21566i
$516$		0			0
$517$	−3.52259	−	19.9776i	−0.154923	−	0.878613i
$518$		0			0
$519$	−22.5009	+	13.0974i	−0.987679	+	0.574911i
$520$		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
$523$	21.9920	+	38.0913i	0.961644	+	1.66562i	0.718372	+	0.695659i	$0.244888\pi$
$523$	21.9920	+	38.0913i	0.961644	+	1.66562i	0.243272	+	0.969958i	$0.421779\pi$
$524$		0			0
$525$	−17.6043	−	14.6658i	−0.768317	−	0.640070i
$526$		0			0
$527$		0			0
$528$	−11.5458	+	13.8592i	−0.502468	+	0.603144i
$529$	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
$537$	21.6083	+	25.5673i	0.932468	+	1.10331i
$538$		0			0
$539$			18.2253i			0.785020i
$540$	−8.17944	−	21.7508i	−0.351987	−	0.936005i
$541$	34.3365			1.47624			0.738121	−	0.674668i	$-0.235713\pi$
$541$	34.3365			1.47624			0.738121	+	0.674668i	$0.235713\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	12.5477	−	34.4744i	0.537482	−	1.47672i
$546$		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
$553$	−24.6746	+	20.7045i	−1.04927	+	0.880443i
$554$		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
$561$	18.3869	−	32.1092i	0.776296	−	1.35565i
$562$		0			0
$563$	23.0436	−	4.06321i	0.971173	−	0.171244i	0.334515	−	0.942390i	$-0.391427\pi$
$563$	23.0436	−	4.06321i	0.971173	−	0.171244i	0.636658	+	0.771146i	$0.280316\pi$
$564$	26.5633	−	4.78092i	1.11852	−	0.201313i
$565$		0			0
$566$		0			0
$567$	−12.1969	−	20.4508i	−0.512221	−	0.858854i
$568$		0			0
$569$	9.08090	−	10.8222i	0.380691	−	0.453690i	−0.541341	−	0.840803i	$-0.682083\pi$
$569$	9.08090	−	10.8222i	0.380691	−	0.453690i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	−3.11345	−	17.6573i	−0.130294	−	0.738933i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−3.11345	−	17.6573i	−0.130294	−	0.738933i	0.847728	−	0.530431i	$-0.177970\pi$
$572$	−0.341685	+	0.938771i	−0.0142866	+	0.0392520i
$573$	−8.89221	−	5.09201i	−0.371478	−	0.212722i
$574$		0			0
$575$		0			0
$576$	−18.4939	−	15.2963i	−0.770579	−	0.637344i
$577$	−21.8961	−	37.9252i	−0.911547	−	1.57885i	−0.811880	−	0.583825i	$-0.801556\pi$
$577$	−21.8961	−	37.9252i	−0.911547	−	1.57885i	−0.0996670	−	0.995021i	$-0.531778\pi$
$578$		0			0
$579$		0			0
$580$	36.8357	−	30.9088i	1.52952	−	1.28342i
$581$	29.0058	+	34.5678i	1.20336	+	1.43411i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.834221	−	0.980001i	−0.0344908	−	0.0405180i
$586$		0			0
$587$	36.2124	+	6.38523i	1.49465	+	0.263546i	0.860414	−	0.509596i	$-0.170205\pi$
$587$	36.2124	+	6.38523i	1.49465	+	0.263546i	0.634232	+	0.773142i	$0.281316\pi$
$588$	−24.2486	+	0.0858990i	−0.999994	+	0.00354242i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	41.8642i		−	1.71916i	−0.511003	−	0.859579i	$-0.670726\pi$
$593$		−	41.8642i		−	1.71916i	0.511003	−	0.859579i	$-0.329274\pi$
$594$		0			0
$595$	48.5412			1.98999
$596$	−25.9494	+	30.9253i	−1.06293	+	1.26675i
$597$		0			0
$598$		0			0
$599$	−16.3241	+	44.8502i	−0.666987	+	1.83253i	−0.124975	+	0.992160i	$0.539885\pi$
$599$	−16.3241	+	44.8502i	−0.666987	+	1.83253i	−0.542012	+	0.840371i	$0.682337\pi$
$600$		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
$604$	1.61441	+	2.79624i	0.0656893	+	0.113777i
$605$	3.22827	+	8.86961i	0.131248	+	0.360601i
$606$		0			0
$607$	−30.5784	+	25.6584i	−1.24114	+	1.04144i	−0.243706	+	0.969849i	$0.578363\pi$
$607$	−30.5784	+	25.6584i	−1.24114	+	1.04144i	−0.997434	+	0.0715913i	$0.977192\pi$
$608$		0			0
$609$	31.5382	−	37.8573i	1.27799	−	1.53406i
$610$		0			0
$611$	1.29453	−	0.747397i	0.0523710	−	0.0302364i
$612$	42.8075	+	24.3122i	1.73039	+	0.982763i
$613$		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
$624$	−1.25063	−	0.450182i	−0.0500654	−	0.0180217i
$625$	4.34120	+	24.6202i	0.173648	+	0.984808i
$626$		0			0
$627$		0			0
$628$	−8.62615	+	48.9213i	−0.344221	+	1.95217i
$629$		0			0
$630$		0			0
$631$	25.1179	+	43.5055i	0.999928	+	1.73193i	0.510357	+	0.859962i	$0.329513\pi$
$631$	25.1179	+	43.5055i	0.999928	+	1.73193i	0.489570	+	0.871964i	$0.337154\pi$
$632$		0			0
$633$	6.32845	−	36.6491i	0.251533	−	1.45667i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.26197	+	0.459321i	−0.0500012	+	0.0181990i
$638$		0			0
$639$	−18.6673	+	22.5696i	−0.738467	+	0.892841i
$640$		0			0
$641$	38.6564	+	6.81617i	1.52684	+	0.269223i	0.873116	−	0.487513i	$-0.162096\pi$
$641$	38.6564	+	6.81617i	1.52684	+	0.269223i	0.653722	+	0.756735i	$0.273207\pi$
$642$		0			0
$643$	−42.2329	−	15.3715i	−1.66550	−	0.606194i	−0.674290	−	0.738467i	$-0.735550\pi$
$643$	−42.2329	−	15.3715i	−1.66550	−	0.606194i	−0.991213	+	0.132273i	$0.957772\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			50.1875i			1.97307i	0.163543	+	0.986536i	$0.447708\pi$
$647$			50.1875i			1.97307i	−0.163543	+	0.986536i	$0.552292\pi$
$648$		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
$657$	−7.52515	+	44.5194i	−0.293584	+	1.73687i
$658$		0			0
$659$	−12.7622	−	35.0638i	−0.497144	−	1.36589i	−0.894023	−	0.448022i	$-0.852129\pi$
$659$	−12.7622	−	35.0638i	−0.497144	−	1.36589i	0.396878	−	0.917871i	$-0.370093\pi$
$660$	18.9267	−	6.96479i	0.736722	−	0.271104i
$661$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$661$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$662$		0			0
$663$	2.68673	+	0.463935i	0.104344	+	0.0180177i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	47.1608	+	8.31572i	1.82471	+	0.321745i
$669$	20.1956	−	0.0715417i	0.780808	−	0.00276596i
$670$		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
$675$	−4.23935	+	25.6326i	−0.163173	+	0.986598i
$676$	25.9264			0.997169
$677$	−29.3197	+	34.9418i	−1.12685	+	1.34292i	−0.194690	+	0.980865i	$0.562370\pi$
$677$	−29.3197	+	34.9418i	−1.12685	+	1.34292i	−0.932156	+	0.362058i	$0.882074\pi$
$678$		0			0
$679$	1.55760	+	8.83357i	0.0597751	+	0.339001i
$680$		0			0
$681$	−44.9534	+	26.1666i	−1.72262	+	1.00271i
$682$		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	$0.888889\pi$
$692$	26.0352	−	15.0314i	0.989709	−	0.571409i
$693$	17.8233	−	10.4593i	0.677049	−	0.397317i
$694$		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
$701$			52.9359i			1.99936i	0.0253058	+	0.999680i	$0.491944\pi$
$701$			52.9359i			1.99936i	−0.0253058	+	0.999680i	$0.508056\pi$
$702$		0			0
$703$		0			0
$704$	13.3886	−	15.9559i	0.504601	−	0.601360i
$705$	−28.3924	−	10.2202i	−1.06932	−	0.384917i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−7.92032	+	44.9183i	−0.297454	+	1.68694i	0.359605	+	0.933105i	$0.382911\pi$
$709$	−7.92032	+	44.9183i	−0.297454	+	1.68694i	−0.657059	+	0.753839i	$0.728200\pi$
$710$		0			0
$711$	34.4082	+	12.2482i	1.29041	+	0.459343i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	0.855623	−	0.717953i	0.0319985	−	0.0268499i
$716$	−24.8464	−	29.6108i	−0.928554	−	1.10661i
$717$	−4.18470	−	11.3719i	−0.156280	−	0.424690i
$718$		0			0
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	9.35577	+	25.1489i	0.348669	+	0.937246i
$721$	21.3056	−	36.9024i	0.793463	−	1.37432i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−52.9446	+	9.33556i	−1.96631	+	0.346714i
$726$		0			0
$727$	−39.7818	−	33.3809i	−1.47543	−	1.23803i	−0.910909	−	0.412608i	$-0.864618\pi$
$727$	−39.7818	−	33.3809i	−1.47543	−	1.23803i	−0.564517	−	0.825421i	$-0.690938\pi$
$728$		0			0
$729$	−13.0000	+	23.6643i	−0.481481	+	0.876456i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	1.33817	+	7.58914i	0.0494264	+	0.280311i	0.999497	−	0.0317250i	$-0.0101001\pi$
$733$	1.33817	+	7.58914i	0.0494264	+	0.280311i	−0.950070	+	0.312036i	$0.898989\pi$
$734$		0			0
$735$	23.5266	+	13.4722i	0.867791	+	0.496929i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	25.8056	+	44.6967i	0.949276	+	1.64419i	0.746955	+	0.664875i	$0.231515\pi$
$739$	25.8056	+	44.6967i	0.949276	+	1.64419i	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
$745$	42.4132	−	15.4371i	1.55390	−	0.565573i
$746$		0			0
$747$	17.1590	−	48.2040i	0.627816	−	1.76369i
$748$	−21.3626	+	37.0011i	−0.781093	+	1.35289i
$749$		0			0
$750$		0			0
$751$	37.2224	+	13.5479i	1.35827	+	0.494368i	0.915518	−	0.402278i	$-0.131781\pi$
$751$	37.2224	+	13.5479i	1.35827	+	0.494368i	0.442748	+	0.896646i	$0.354004\pi$
$752$	−30.6921	+	5.41184i	−1.11922	+	0.197349i
$753$		0			0
$754$		0			0
$755$		−	3.60992i		−	0.131379i
$756$	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
$763$	−7.53781	+	42.7490i	−0.272887	+	1.54762i
$764$	10.2470	+	5.91608i	0.370722	+	0.214036i
$765$	−27.8573	−	47.4703i	−1.00718	−	1.71629i
$766$		0			0
$767$		0			0
$768$	21.2922	+	17.7381i	0.768317	+	0.640070i
$769$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$769$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$770$		0			0
$771$	7.37948	−	8.85805i	0.265765	−	0.319015i
$772$		0			0
$773$	−18.2767	+	10.5521i	−0.657367	+	0.379531i	−0.791273	−	0.611463i	$-0.790581\pi$
$773$	−18.2767	+	10.5521i	−0.657367	+	0.379531i	0.133906	+	0.990994i	$0.457248\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	0.959261	+	1.13501i	0.0343470	+	0.0406400i
$781$	−19.4723	−	16.3392i	−0.696773	−	0.584662i
$782$		0			0
$783$	−55.1216	−	9.11653i	−1.96989	−	0.325798i
$784$	28.0000			1.00000
$785$	35.7001	−	42.5457i	1.27419	−	1.51852i
$786$		0			0
$787$	−4.37961	−	24.8380i	−0.156116	−	0.885378i	−0.957758	−	0.287574i	$-0.907151\pi$
$787$	−4.37961	−	24.8380i	−0.156116	−	0.885378i	0.801642	−	0.597804i	$-0.203960\pi$
$788$		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
$797$	24.2467	+	28.8961i	0.858863	+	1.02355i	0.999439	+	0.0334835i	$0.0106601\pi$
$797$	24.2467	+	28.8961i	0.858863	+	1.02355i	−0.140576	+	0.990070i	$0.544895\pi$
$798$		0			0
$799$	60.0726	−	21.8647i	2.12522	−	0.773516i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−38.5899	−	6.80444i	−1.36181	−	0.240124i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$			45.5987i			1.60317i	0.597884	+	0.801583i	$0.296008\pi$
$809$			45.5987i			1.60317i	−0.597884	+	0.801583i	$0.703992\pi$
$810$		0			0
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−36.5718	+	43.5846i	−1.28342	+	1.52952i
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−49.3301	−	28.2482i	−1.72690	−	0.988886i
$817$		0			0
$818$		0			0
$819$	1.17342	+	0.970534i	0.0410027	+	0.0339132i
$820$		0			0
$821$	10.9812	+	30.1706i	0.383247	+	1.05296i	0.969981	+	0.243182i	$0.0781913\pi$
$821$	10.9812	+	30.1706i	0.383247	+	1.05296i	−0.586734	+	0.809780i	$0.699586\pi$
$822$		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
$825$	−22.2192	−	3.83673i	−0.773572	−	0.133578i
$826$		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
$832$	1.44226	+	0.524938i	0.0500012	+	0.0181990i
$833$	−56.5621	+	9.97343i	−1.95976	+	0.345559i
$834$		0			0
$835$	−41.0146	−	34.4154i	−1.41937	−	1.19099i
$836$		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
$841$	−15.0399	−	85.2955i	−0.518617	−	2.94122i
$842$		0			0
$843$	−47.1102	+	27.4220i	−1.62256	+	0.944465i
$844$	−7.45733	+	42.2926i	−0.256692	+	1.45577i
$845$	−25.1031	−	14.4933i	−0.863573	−	0.498584i
$846$		0			0
$847$	−5.58409	−	9.67193i	−0.191872	−	0.332332i
$848$		0			0
$849$	−44.5684	−	37.1291i	−1.52959	−	1.27427i
$850$		0			0
$851$		0			0
$852$	21.6473	−	25.9846i	0.741625	−	0.890219i
$853$	−52.6443	+	19.1609i	−1.80251	+	0.656058i	−0.804430	+	0.594048i	$0.797529\pi$
$853$	−52.6443	+	19.1609i	−1.80251	+	0.656058i	−0.998075	+	0.0620108i	$0.980249\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	39.2042	+	6.91277i	1.33919	+	0.236136i	0.796929	−	0.604073i	$-0.206457\pi$
$857$	39.2042	+	6.91277i	1.33919	+	0.236136i	0.542263	+	0.840209i	$0.317568\pi$
$858$		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
$865$	−33.6113			−1.14282
$866$		0			0
$867$	82.0079	+	29.5199i	2.78513	+	1.00255i
$868$		0			0
$869$	−10.8412	+	29.7859i	−0.367761	+	1.01042i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	7.74481	−	6.59273i	0.262122	−	0.223130i
$874$		0			0
$875$	−10.1171	−	27.7965i	−0.342020	−	0.939693i
$876$	8.87134	−	51.3755i	0.299735	−	1.73582i
$877$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$877$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$878$		0			0
$879$	4.97860	+	13.5293i	0.167924	+	0.456331i
$880$	−21.8831	+	7.96478i	−0.737678	+	0.268493i
$881$		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	$0.666667\pi$
$884$	−3.10045	−	0.546693i	−0.104279	−	0.0183873i
$885$		0			0
$886$		0			0
$887$	−22.9998	+	4.05549i	−0.772259	+	0.136170i	−0.545873	−	0.837868i	$-0.683802\pi$
$887$	−22.9998	+	4.05549i	−0.772259	+	0.136170i	−0.226385	+	0.974038i	$0.572691\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−20.4572	−	11.4276i	−0.685341	−	0.382838i
$892$	−23.3200			−0.780813
$893$		0			0
$894$		0			0
$895$	7.50449	+	42.5601i	0.250848	+	1.42263i
$896$		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	$0.888889\pi$
$908$	52.0144	−	30.0305i	1.72616	−	0.996598i
$909$		0			0
$910$		0			0
$911$	−58.7903	−	10.3663i	−1.94781	−	0.343451i	−0.999673	−	0.0255863i	$-0.991855\pi$
$911$	−58.7903	−	10.3663i	−1.94781	−	0.343451i	−0.948136	−	0.317865i	$-0.897034\pi$
$912$		0			0
$913$	41.7283	+	15.1879i	1.38101	+	0.502645i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−60.6113			−1.99938			−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−60.6113			−1.99938			−0.999691	+	0.0248659i	$0.992084\pi$
$920$		0			0
$921$	−40.5592	+	34.2788i	−1.33647	+	1.12952i
$922$		0			0
$923$	0.640626	−	1.76010i	0.0210864	−	0.0579345i
$924$	−20.6232	+	12.0044i	−0.678453	+	0.394916i
$925$		0			0
$926$		0			0
$927$	−48.3154	+	0.342313i	−1.58689	+	0.0112430i
$928$		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
$935$	41.3684	−	23.8841i	1.35289	−	0.781093i
$936$		0			0
$937$	−21.1518	+	36.6360i	−0.690999	+	1.19685i	0.280512	+	0.959851i	$0.409496\pi$
$937$	−21.1518	+	36.6360i	−0.690999	+	1.19685i	−0.971511	+	0.236995i	$0.923837\pi$
$938$		0			0
$939$	27.8653	+	47.8717i	0.909350	+	1.56223i
$940$	32.7428	+	11.9174i	1.06795	+	0.388702i
$941$		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
$945$	−0.326685	−	30.7391i	−0.0106271	−	0.999944i
$946$		0			0
$947$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$947$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$948$	−39.6808	−	14.2837i	−1.28877	−	0.463911i
$949$	−0.501397	−	2.84357i	−0.0162760	−	0.0923060i
$950$		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
$956$	4.78553	+	13.1481i	0.154775	+	0.425241i
$957$	8.25071	−	47.7813i	0.266708	−	1.54455i
$958$		0			0
$959$		0			0
$960$	−10.7002	−	29.0776i	−0.345347	−	0.938475i
$961$	−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	$0.5\pi$
$972$	15.1078	−	27.2719i	0.484583	−	0.874745i
$973$		0			0
$974$		0			0
$975$	−0.294309	−	1.63521i	−0.00942543	−	0.0523688i
$976$		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
$981$	46.1318	−	17.1617i	1.47288	−	0.547931i
$982$		0			0
$983$	4.59871	+	12.6348i	0.146676	+	0.402989i	0.991174	−	0.132570i	$-0.0423230\pi$
$983$	4.59871	+	12.6348i	0.146676	+	0.402989i	−0.844498	+	0.535559i	$0.820101\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	35.1839	+	6.07544i	1.11992	+	0.193383i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	8.50881	−	14.7377i	0.270291	−	0.468158i	−0.698645	−	0.715468i	$-0.746213\pi$
$991$	8.50881	−	14.7377i	0.270291	−	0.468158i	0.968936	+	0.247310i	$0.0795467\pi$
$992$		0			0
$993$	−58.1412	+	0.205961i	−1.84505	+	0.00653599i
$994$		0			0
$995$		0			0
$996$	−20.0106	+	55.5906i	−0.634060	+	1.76146i
$997$	−14.1873	−	11.9046i	−0.449318	−	0.377022i	0.389865	−	0.920872i	$-0.372522\pi$
$997$	−14.1873	−	11.9046i	−0.449318	−	0.377022i	−0.839183	+	0.543850i	$0.816966\pi$
$998$		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.524.3	yes	24
5.4	even	2	inner	945.2.cs.a.524.2	✓	24
7.6	odd	2	inner	945.2.cs.a.524.2	✓	24
27.5	odd	18	inner	945.2.cs.a.734.3	yes	24
35.34	odd	2	CM	945.2.cs.a.524.3	yes	24
135.59	odd	18	inner	945.2.cs.a.734.2	yes	24
189.167	even	18	inner	945.2.cs.a.734.2	yes	24
945.734	even	18	inner	945.2.cs.a.734.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
945.2.cs.a.524.2	✓	24	5.4	even	2	inner
945.2.cs.a.524.2	✓	24	7.6	odd	2	inner
945.2.cs.a.524.3	yes	24	1.1	even	1	trivial
945.2.cs.a.524.3	yes	24	35.34	odd	2	CM
945.2.cs.a.734.2	yes	24	135.59	odd	18	inner
945.2.cs.a.734.2	yes	24	189.167	even	18	inner
945.2.cs.a.734.3	yes	24	27.5	odd	18	inner
945.2.cs.a.734.3	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)

\(f(q)\)	\(=\)	\(q+(0.306808 + 1.70466i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(0.459430 - 2.60556i) q^{7} +(-2.81174 + 1.04601i) q^{9} +O(q^{10})\)	\(q+(0.306808 + 1.70466i) q^{3} +(-0.347296 - 1.96962i) q^{4} +(-0.764780 + 2.10122i) q^{5} +(0.459430 - 2.60556i) q^{7} +(-2.81174 + 1.04601i) q^{9} +(-0.890490 - 2.44660i) q^{11} +(3.25097 - 1.19632i) q^{12} +(0.146967 - 0.123320i) q^{13} +(-3.81650 - 0.659021i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(7.10570 - 4.10248i) q^{17} +(4.40419 + 0.776578i) q^{20} +(4.58255 - 0.0162334i) q^{21} +(-3.83022 - 3.21394i) q^{25} +(-2.64575 - 4.47214i) q^{27} -5.29150 q^{28} +(6.91142 - 8.23672i) q^{29} +(3.89741 - 2.26862i) q^{33} +(5.12348 + 2.95804i) q^{35} +(3.03674 + 5.17477i) q^{36} +(0.255310 + 0.212694i) q^{39} +(-4.50960 + 2.60362i) q^{44} +(-0.0475262 - 6.70804i) q^{45} +(7.67301 + 1.35296i) q^{47} +(-3.48533 - 5.98769i) q^{48} +(-6.57785 - 2.39414i) q^{49} +(9.17342 + 10.8541i) q^{51} +(-0.293934 - 0.246640i) q^{52} +5.82187 q^{55} +(0.0274394 + 7.74592i) q^{60} +(1.43363 + 7.80671i) q^{63} +(4.00000 + 6.92820i) q^{64} +(0.146725 + 0.403123i) q^{65} +(-10.5481 - 12.5707i) q^{68} +(8.45506 - 4.88153i) q^{71} +(7.52515 - 13.0339i) q^{73} +(4.30353 - 7.51529i) q^{75} +(-6.78387 + 1.19618i) q^{77} +(-9.32613 - 7.82555i) q^{79} -8.94427i q^{80} +(6.81174 - 5.88220i) q^{81} +(-10.9632 + 13.0654i) q^{83} +(-1.62348 - 9.02022i) q^{84} +(3.18590 + 18.0681i) q^{85} +(16.1613 + 9.25455i) q^{87} +(-0.253796 - 0.439588i) q^{91} +(-3.18582 + 1.15954i) q^{97} +(5.06298 + 5.94774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{9}+O(q^{10}) \) 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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