LMFDB - Embedded newform 2940.2.q.i.961.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(361,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,1,0,-1,0,0,0,-1,0,-6,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2940.961
Dual form			2940.2.q.i.361.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} +4.00000 q^{13} -1.00000 q^{15} +(3.00000 + 5.19615i) q^{17} +(1.00000 - 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +6.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(3.00000 - 5.19615i) q^{33} +(-1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{51} +(6.00000 + 10.3923i) q^{53} +6.00000 q^{55} +2.00000 q^{57} +(7.00000 - 12.1244i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +6.00000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(0.500000 - 0.866025i) q^{75} +(8.00000 - 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -6.00000 q^{85} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +(5.00000 - 8.66025i) q^{93} +(1.00000 + 1.73205i) q^{95} +16.0000 q^{97} +6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{5} - q^{9} - 6 q^{11} + 8 q^{13} - 2 q^{15} + 6 q^{17} + 2 q^{19} - q^{25} - 2 q^{27} + 12 q^{29} - 10 q^{31} + 6 q^{33} - 2 q^{37} + 4 q^{39} + 12 q^{41} - 8 q^{43} - q^{45} - 6 q^{51}+ \cdots + 12 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^5 - q^9 - 6 * q^11 + 8 * q^13 - 2 * q^15 + 6 * q^17 + 2 * q^19 - q^25 - 2 * q^27 + 12 * q^29 - 10 * q^31 + 6 * q^33 - 2 * q^37 + 4 * q^39 + 12 * q^41 - 8 * q^43 - q^45 - 6 * q^51 + 12 * q^53 + 12 * q^55 + 4 * q^57 + 14 * q^61 - 4 * q^65 + 4 * q^67 + 12 * q^71 - 4 * q^73 + q^75 + 16 * q^79 - q^81 + 24 * q^83 - 12 * q^85 + 6 * q^87 + 6 * q^89 + 10 * q^93 + 2 * q^95 + 32 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$		0			0
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−5.00000	−	8.66025i	−0.898027	−	1.55543i	−0.0680129	−	0.997684i	$-0.521666\pi$
$32$		0			0
$33$	3.00000	−	5.19615i	0.522233	−	0.904534i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$		0			0
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$		0			0
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$		0			0
$55$	6.00000			0.809040
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	0.724923	−	0.688830i	$-0.241875\pi$
$73$	−2.00000	−	3.46410i	−0.234082	−	0.405442i	−0.959006	+	0.283387i	$0.908542\pi$
$74$		0			0
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$		0			0
$87$	3.00000	+	5.19615i	0.321634	+	0.557086i
$88$		0			0
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.00000	−	8.66025i	0.518476	−	0.898027i
$94$		0			0
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	16.0000			1.62455			0.812277	−	0.583272i	$-0.198228\pi$
$97$	16.0000			1.62455			0.812277	+	0.583272i	$0.198228\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		0			0
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$		0			0
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	22.0000			1.86602			0.933008	−	0.359856i	$-0.117174\pi$
$139$	22.0000			1.86602			0.933008	+	0.359856i	$0.117174\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−12.0000	−	20.7846i	−1.00349	−	1.73810i
$144$		0			0
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		0			0
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	0.935857	−	0.352381i	$-0.114628\pi$
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	−0.773099	+	0.634285i	$0.781294\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$		0			0
$155$	10.0000			0.803219
$156$		0			0
$157$	4.00000	+	6.92820i	0.319235	+	0.552931i	0.980329	−	0.197372i	$-0.0632408\pi$
$157$	4.00000	+	6.92820i	0.319235	+	0.552931i	−0.661094	+	0.750303i	$0.729907\pi$
$158$		0			0
$159$	−6.00000	+	10.3923i	−0.475831	+	0.824163i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$		0			0
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$		0			0
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$		0			0
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$		0			0
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$		0			0
$187$	18.0000	−	31.1769i	1.31629	−	2.27988i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.773272	−	0.634074i	$-0.781381\pi$
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.162488	−	0.986710i	$-0.551952\pi$
$194$		0			0
$195$	−4.00000			−0.286446
$196$		0			0
$197$	−24.0000			−1.70993			−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000			−1.70993			−0.854965	+	0.518686i	$0.826421\pi$
$198$		0			0
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$		0			0
$201$	−2.00000	+	3.46410i	−0.141069	+	0.244339i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$		0			0
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$		0			0
$215$	2.00000	−	3.46410i	0.136399	−	0.236250i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$		0			0
$221$	12.0000	+	20.7846i	0.807207	+	1.39812i
$222$		0			0
$223$	4.00000			0.267860			0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000			0.267860			0.133930	+	0.990991i	$0.457240\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	−0.142166	−	0.989843i	$-0.545407\pi$
$233$	12.0000	−	20.7846i	0.786146	−	1.36165i	0.928312	−	0.371802i	$-0.121260\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	16.0000			1.03931
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$		0			0
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−3.00000	−	5.19615i	−0.187867	−	0.325396i
$256$		0			0
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	6.00000			0.367194
$268$		0			0
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$		0			0
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	1.00000	−	1.73205i	0.0607457	−	0.105215i	0.894799	+	0.446469i	$0.147319\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.00000	+	5.19615i	−0.180907	+	0.313340i
$276$		0			0
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	0.150210	−	0.988654i	$-0.452005\pi$
$278$		0			0
$279$	10.0000			0.598684
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$		0			0
$285$	−1.00000	+	1.73205i	−0.0592349	+	0.102598i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	8.00000	+	13.8564i	0.468968	+	0.812277i
$292$		0			0
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.00000	+	5.19615i	0.174078	+	0.301511i
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$		0			0
$305$	7.00000	+	12.1244i	0.400819	+	0.694239i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	−16.0000			−0.910208
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	−0.646872	−	0.762598i	$-0.723923\pi$
$317$	6.00000	−	10.3923i	0.336994	−	0.583690i	0.983866	+	0.178908i	$0.0572566\pi$
$318$		0			0
$319$	−18.0000	−	31.1769i	−1.00781	−	1.74557i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	−2.00000	−	3.46410i	−0.110940	−	0.192154i
$326$		0			0
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$		0			0
$333$	−1.00000	−	1.73205i	−0.0547997	−	0.0949158i
$334$		0			0
$335$	−4.00000			−0.218543
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−30.0000	+	51.9615i	−1.62459	+	2.81387i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$		0			0
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	0.920677	+	0.390324i	$0.127637\pi$
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	−0.122308	+	0.992492i	$0.539030\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	−0.133263	−	0.991081i	$-0.542545\pi$
$359$	15.0000	−	25.9808i	0.791670	−	1.37121i	0.924932	−	0.380131i	$-0.124121\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$		0			0
$363$	−25.0000			−1.31216
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	0.809093	−	0.587680i	$-0.199959\pi$
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	−0.913493	+	0.406855i	$0.866625\pi$
$368$		0			0
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$		0			0
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	24.0000			1.23606
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	4.00000	+	6.92820i	0.204926	+	0.354943i
$382$		0			0
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$		0			0
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	0.542445	−	0.840091i	$-0.317499\pi$
$389$	−9.00000	−	15.5885i	−0.456318	−	0.790366i	−0.998763	+	0.0497253i	$0.984165\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−12.0000			−0.605320
$394$		0			0
$395$	8.00000	+	13.8564i	0.402524	+	0.697191i
$396$		0			0
$397$	−2.00000	+	3.46410i	−0.100377	+	0.173858i	−0.911840	−	0.410546i	$-0.865338\pi$
$397$	−2.00000	+	3.46410i	−0.100377	+	0.173858i	0.811463	+	0.584404i	$0.198672\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		0			0
$403$	−20.0000	−	34.6410i	−0.996271	−	1.72559i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	12.0000			0.594818
$408$		0			0
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$		0			0
$411$	−6.00000	+	10.3923i	−0.295958	+	0.512615i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	11.0000	+	19.0526i	0.538672	+	0.933008i
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.00000	−	5.19615i	0.145521	−	0.252050i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	12.0000	−	20.7846i	0.579365	−	1.00349i
$430$		0			0
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		0			0
$433$	−8.00000			−0.384455			−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000			−0.384455			−0.192228	+	0.981350i	$0.561571\pi$
$434$		0			0
$435$	−6.00000			−0.287678
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	−0.960323	−	0.278889i	$-0.910034\pi$
$439$	−5.00000	+	8.66025i	−0.238637	+	0.413331i	0.721686	+	0.692220i	$0.243367\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$		0			0
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$		0			0
$447$	−18.0000			−0.851371
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	−18.0000	−	31.1769i	−0.847587	−	1.46806i
$452$		0			0
$453$	−2.00000	+	3.46410i	−0.0939682	+	0.162758i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	−0.127469	−	0.991843i	$-0.540685\pi$
$457$	17.0000	−	29.4449i	0.795226	−	1.37737i	0.922695	−	0.385530i	$-0.125981\pi$
$458$		0			0
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$		0			0
$461$	−18.0000			−0.838344			−0.419172	−	0.907907i	$-0.637680\pi$
$461$	−18.0000			−0.838344			−0.419172	+	0.907907i	$0.637680\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$		0			0
$465$	5.00000	+	8.66025i	0.231869	+	0.401610i
$466$		0			0
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−4.00000	+	6.92820i	−0.184310	+	0.319235i
$472$		0			0
$473$	12.0000	+	20.7846i	0.551761	+	0.955677i
$474$		0			0
$475$	−2.00000			−0.0917663
$476$		0			0
$477$	−12.0000			−0.549442
$478$		0			0
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−8.00000	+	13.8564i	−0.363261	+	0.629187i
$486$		0			0
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$		0			0
$489$	−20.0000			−0.904431
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$		0			0
$493$	18.0000	+	31.1769i	0.810679	+	1.40414i
$494$		0			0
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$		0			0
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.00000	+	1.73205i	−0.0441511	+	0.0764719i
$514$		0			0
$515$	−8.00000	−	13.8564i	−0.352522	−	0.610586i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	6.00000			0.263371
$520$		0			0
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$		0			0
$523$	16.0000	−	27.7128i	0.699631	−	1.21180i	−0.268963	−	0.963150i	$-0.586681\pi$
$523$	16.0000	−	27.7128i	0.699631	−	1.21180i	0.968594	−	0.248646i	$-0.0799857\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	30.0000	−	51.9615i	1.30682	−	2.26348i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.0000			1.03956
$534$		0			0
$535$		0			0
$536$		0			0
$537$	3.00000	−	5.19615i	0.129460	−	0.224231i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	0.0911008	+	0.995842i	$0.470961\pi$
$541$	−19.0000	+	32.9090i	−0.816874	+	1.41487i	−0.907975	+	0.419025i	$0.862372\pi$
$542$		0			0
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$		0			0
$545$	2.00000			0.0856706
$546$		0			0
$547$	−28.0000			−1.19719			−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000			−1.19719			−0.598597	+	0.801050i	$0.704275\pi$
$548$		0			0
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$		0			0
$551$	6.00000	−	10.3923i	0.255609	−	0.442727i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.00000	−	1.73205i	0.0424476	−	0.0735215i
$556$		0			0
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	0.710457	−	0.703740i	$-0.248488\pi$
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	−0.964686	+	0.263404i	$0.915155\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$	36.0000			1.51992
$562$		0			0
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	−0.358954	−	0.933355i	$-0.616866\pi$
$569$	15.0000	−	25.9808i	0.628833	−	1.08917i	0.987786	−	0.155815i	$-0.0498003\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$		0			0
$573$	−18.0000			−0.751961
$574$		0			0
$575$		0			0
$576$		0			0
$577$	16.0000	+	27.7128i	0.666089	+	1.15370i	0.978989	+	0.203913i	$0.0653661\pi$
$577$	16.0000	+	27.7128i	0.666089	+	1.15370i	−0.312900	+	0.949786i	$0.601301\pi$
$578$		0			0
$579$	13.0000	−	22.5167i	0.540262	−	0.935760i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	36.0000	−	62.3538i	1.49097	−	2.58243i
$584$		0			0
$585$	−2.00000	−	3.46410i	−0.0826898	−	0.143223i
$586$		0			0
$587$	−36.0000			−1.48588			−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000			−1.48588			−0.742940	+	0.669359i	$0.766569\pi$
$588$		0			0
$589$	−20.0000			−0.824086
$590$		0			0
$591$	−12.0000	−	20.7846i	−0.493614	−	0.854965i
$592$		0			0
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.00000	−	8.66025i	0.204636	−	0.354441i
$598$		0			0
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	0.990752	+	0.135686i	$0.0433238\pi$
$599$	15.0000	+	25.9808i	0.612883	+	1.06155i	−0.377869	+	0.925859i	$0.623343\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	−4.00000			−0.162893
$604$		0			0
$605$	−12.5000	−	21.6506i	−0.508197	−	0.880223i
$606$		0			0
$607$	−2.00000	+	3.46410i	−0.0811775	+	0.140604i	−0.903756	−	0.428048i	$-0.859201\pi$
$607$	−2.00000	+	3.46410i	−0.0811775	+	0.140604i	0.822578	+	0.568652i	$0.192535\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$		0			0
$615$	−6.00000			−0.241943
$616$		0			0
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$		0			0
$619$	1.00000	+	1.73205i	0.0401934	+	0.0696170i	0.885422	−	0.464787i	$-0.153869\pi$
$619$	1.00000	+	1.73205i	0.0401934	+	0.0696170i	−0.845229	+	0.534404i	$0.820536\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$		0			0
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	10.0000	+	17.3205i	0.397464	+	0.688428i
$634$		0			0
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$		0			0
$643$	−32.0000			−1.26196			−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000			−1.26196			−0.630978	+	0.775800i	$0.717346\pi$
$644$		0			0
$645$	4.00000			0.157500
$646$		0			0
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.758654	+	0.651494i	$0.225858\pi$
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.184884	+	0.982760i	$0.440809\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.0000	+	41.5692i	−0.939193	+	1.62673i	−0.172211	+	0.985060i	$0.555091\pi$
$653$	−24.0000	+	41.5692i	−0.939193	+	1.62673i	−0.766982	+	0.641669i	$0.778242\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$		0			0
$657$	4.00000			0.156055
$658$		0			0
$659$	42.0000			1.63609			0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000			1.63609			0.818044	+	0.575156i	$0.195059\pi$
$660$		0			0
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	0.752252	−	0.658876i	$-0.228968\pi$
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	−0.946729	+	0.322031i	$0.895634\pi$
$662$		0			0
$663$	−12.0000	+	20.7846i	−0.466041	+	0.807207i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$	2.00000	+	3.46410i	0.0773245	+	0.133930i
$670$		0			0
$671$	−84.0000			−3.24278
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$		0			0
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$		0			0
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−6.00000	+	10.3923i	−0.229920	+	0.398234i
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	14.0000			0.534133
$688$		0			0
$689$	24.0000	+	41.5692i	0.914327	+	1.58366i
$690$		0			0
$691$	−17.0000	+	29.4449i	−0.646710	+	1.12014i	0.337193	+	0.941435i	$0.390522\pi$
$691$	−17.0000	+	29.4449i	−0.646710	+	1.12014i	−0.983904	+	0.178700i	$0.942811\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.0000	+	19.0526i	−0.417254	+	0.722705i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$		0			0
$699$	24.0000			0.907763
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	2.00000	+	3.46410i	0.0754314	+	0.130651i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	0.249952	+	0.968258i	$0.419585\pi$
$709$	−19.0000	+	32.9090i	−0.713560	+	1.23592i	−0.963512	+	0.267664i	$0.913748\pi$
$710$		0			0
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	24.0000			0.897549
$716$		0			0
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$		0			0
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$		0			0
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$		0			0
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	10.0000	−	17.3205i	0.369358	−	0.639748i	−0.620107	−	0.784517i	$-0.712911\pi$
$733$	10.0000	−	17.3205i	0.369358	−	0.639748i	0.989465	+	0.144770i	$0.0462441\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		0			0
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	0.783028	−	0.621987i	$-0.213674\pi$
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	−0.930170	+	0.367129i	$0.880341\pi$
$740$		0			0
$741$	8.00000			0.293887
$742$		0			0
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$		0			0
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$		0			0
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$		0			0
$753$	−12.0000	−	20.7846i	−0.437304	−	0.757433i
$754$		0			0
$755$	−4.00000			−0.145575
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	10.0000			0.360609			0.180305	−	0.983611i	$-0.442292\pi$
$769$	10.0000			0.360609			0.180305	+	0.983611i	$0.442292\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$		0			0
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	0.657542	−	0.753418i	$-0.271596\pi$
$773$	−9.00000	−	15.5885i	−0.323708	−	0.560678i	−0.981250	+	0.192740i	$0.938263\pi$
$774$		0			0
$775$	−5.00000	+	8.66025i	−0.179605	+	0.311086i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	−18.0000	−	31.1769i	−0.644091	−	1.11560i
$782$		0			0
$783$	−6.00000			−0.214423
$784$		0			0
$785$	−8.00000			−0.285532
$786$		0			0
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	0.687481	−	0.726202i	$-0.258716\pi$
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	−0.972650	+	0.232275i	$0.925383\pi$
$788$		0			0
$789$	−6.00000	+	10.3923i	−0.213606	+	0.369976i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	28.0000	−	48.4974i	0.994309	−	1.72219i
$794$		0			0
$795$	−6.00000	−	10.3923i	−0.212798	−	0.368577i
$796$		0			0
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$		0			0
$803$	−12.0000	+	20.7846i	−0.423471	+	0.733473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.00000	+	5.19615i	−0.105605	+	0.182913i
$808$		0			0
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$		0			0
$811$	46.0000			1.61528			0.807639	−	0.589677i	$-0.200745\pi$
$811$	46.0000			1.61528			0.807639	+	0.589677i	$0.200745\pi$
$812$		0			0
$813$	2.00000			0.0701431
$814$		0			0
$815$	−10.0000	−	17.3205i	−0.350285	−	0.606711i
$816$		0			0
$817$	−4.00000	+	6.92820i	−0.139942	+	0.242387i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$		0			0
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$		0			0
$829$	13.0000	+	22.5167i	0.451509	+	0.782036i	0.998480	−	0.0551154i	$-0.0175527\pi$
$829$	13.0000	+	22.5167i	0.451509	+	0.782036i	−0.546971	+	0.837151i	$0.684219\pi$
$830$		0			0
$831$	13.0000	−	22.5167i	0.450965	−	0.781094i
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.00000	+	8.66025i	0.172825	+	0.299342i
$838$		0			0
$839$	12.0000			0.414286			0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000			0.414286			0.207143	+	0.978311i	$0.433583\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$	3.00000	+	5.19615i	0.103325	+	0.178965i
$844$		0			0
$845$	−1.50000	+	2.59808i	−0.0516016	+	0.0893765i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	4.00000			0.136957			0.0684787	−	0.997653i	$-0.478185\pi$
$853$	4.00000			0.136957			0.0684787	+	0.997653i	$0.478185\pi$
$854$		0			0
$855$	−2.00000			−0.0683986
$856$		0			0
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	−0.721544	−	0.692369i	$-0.756567\pi$
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	0.960381	+	0.278691i	$0.0899005\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$		0			0
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$		0			0
$867$	−19.0000			−0.645274
$868$		0			0
$869$	−96.0000			−3.25658
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$		0			0
$873$	−8.00000	+	13.8564i	−0.270759	+	0.468968i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$		0			0
$879$	9.00000	+	15.5885i	0.303562	+	0.525786i
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	6.00000			0.200558
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.0000	−	51.9615i	−1.00056	−	1.73301i
$900$		0			0
$901$	−36.0000	+	62.3538i	−1.19933	+	2.07731i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.00000	−	1.73205i	0.0332411	−	0.0575753i
$906$		0			0
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	0.650868	−	0.759191i	$-0.274405\pi$
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	−0.982913	+	0.184073i	$0.941072\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	−36.0000	−	62.3538i	−1.19143	−	2.06361i
$914$		0			0
$915$	−7.00000	+	12.1244i	−0.231413	+	0.400819i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	8.00000	+	13.8564i	0.263609	+	0.456584i
$922$		0			0
$923$	24.0000			0.789970
$924$		0			0
$925$	2.00000			0.0657596
$926$		0			0
$927$	−8.00000	−	13.8564i	−0.262754	−	0.455104i
$928$		0			0
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$		0			0
$935$	18.0000	+	31.1769i	0.588663	+	1.01959i
$936$		0			0
$937$	−20.0000			−0.653372			−0.326686	−	0.945133i	$-0.605932\pi$
$937$	−20.0000			−0.653372			−0.326686	+	0.945133i	$0.605932\pi$
$938$		0			0
$939$	8.00000			0.261070
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$		0			0
$949$	−8.00000	−	13.8564i	−0.259691	−	0.449798i
$950$		0			0
$951$	12.0000			0.389127
$952$		0			0
$953$	48.0000			1.55487			0.777436	−	0.628962i	$-0.216520\pi$
$953$	48.0000			1.55487			0.777436	+	0.628962i	$0.216520\pi$
$954$		0			0
$955$	−9.00000	−	15.5885i	−0.291233	−	0.504431i
$956$		0			0
$957$	18.0000	−	31.1769i	0.581857	−	1.00781i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−34.5000	+	59.7558i	−1.11290	+	1.92760i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	26.0000			0.836970
$966$		0			0
$967$	56.0000			1.80084			0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000			1.80084			0.900419	+	0.435023i	$0.143260\pi$
$968$		0			0
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.00000	−	3.46410i	0.0640513	−	0.110940i
$976$		0			0
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	−0.938738	−	0.344631i	$-0.888004\pi$
$977$	−24.0000	−	41.5692i	−0.767828	−	1.32992i	0.170910	−	0.985287i	$-0.445329\pi$
$978$		0			0
$979$	−36.0000			−1.15056
$980$		0			0
$981$	2.00000			0.0638551
$982$		0			0
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$	12.0000	−	20.7846i	0.382352	−	0.662253i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	0.986447	+	0.164080i	$0.0524655\pi$
$991$	20.0000	+	34.6410i	0.635321	+	1.10041i	−0.351126	+	0.936328i	$0.614201\pi$
$992$		0			0
$993$	4.00000			0.126936
$994$		0			0
$995$	10.0000			0.317021
$996$		0			0
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	0.554554	−	0.832148i	$-0.312889\pi$
$997$	−14.0000	−	24.2487i	−0.443384	−	0.767964i	−0.997938	+	0.0641836i	$0.979556\pi$
$998$		0			0
$999$	1.00000	−	1.73205i	0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.q.i.961.1		2
7.2	even	3		2940.2.a.f.1.1		1
7.3	odd	6		2940.2.q.e.361.1		2
7.4	even	3	inner	2940.2.q.i.361.1		2
7.5	odd	6		420.2.a.c.1.1	✓	1
7.6	odd	2		2940.2.q.e.961.1		2
21.2	odd	6		8820.2.a.b.1.1		1
21.5	even	6		1260.2.a.i.1.1		1
28.19	even	6		1680.2.a.a.1.1		1
35.12	even	12		2100.2.k.j.1849.1		2
35.19	odd	6		2100.2.a.d.1.1		1
35.33	even	12		2100.2.k.j.1849.2		2
56.5	odd	6		6720.2.a.x.1.1		1
56.19	even	6		6720.2.a.ch.1.1		1
84.47	odd	6		5040.2.a.bc.1.1		1
105.47	odd	12		6300.2.k.a.6049.2		2
105.68	odd	12		6300.2.k.a.6049.1		2
105.89	even	6		6300.2.a.a.1.1		1
140.19	even	6		8400.2.a.cj.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.a.c.1.1	✓	1	7.5	odd	6
1260.2.a.i.1.1		1	21.5	even	6
1680.2.a.a.1.1		1	28.19	even	6
2100.2.a.d.1.1		1	35.19	odd	6
2100.2.k.j.1849.1		2	35.12	even	12
2100.2.k.j.1849.2		2	35.33	even	12
2940.2.a.f.1.1		1	7.2	even	3
2940.2.q.e.361.1		2	7.3	odd	6
2940.2.q.e.961.1		2	7.6	odd	2
2940.2.q.i.361.1		2	7.4	even	3	inner
2940.2.q.i.961.1		2	1.1	even	1	trivial
5040.2.a.bc.1.1		1	84.47	odd	6
6300.2.a.a.1.1		1	105.89	even	6
6300.2.k.a.6049.1		2	105.68	odd	12
6300.2.k.a.6049.2		2	105.47	odd	12
6720.2.a.x.1.1		1	56.5	odd	6
6720.2.a.ch.1.1		1	56.19	even	6
8400.2.a.cj.1.1		1	140.19	even	6
8820.2.a.b.1.1		1	21.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} +4.00000 q^{13} -1.00000 q^{15} +(3.00000 + 5.19615i) q^{17} +(1.00000 - 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} +6.00000 q^{29} +(-5.00000 - 8.66025i) q^{31} +(3.00000 - 5.19615i) q^{33} +(-1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-3.00000 + 5.19615i) q^{51} +(6.00000 + 10.3923i) q^{53} +6.00000 q^{55} +2.00000 q^{57} +(7.00000 - 12.1244i) q^{61} +(-2.00000 + 3.46410i) q^{65} +(2.00000 + 3.46410i) q^{67} +6.00000 q^{71} +(-2.00000 - 3.46410i) q^{73} +(0.500000 - 0.866025i) q^{75} +(8.00000 - 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} -6.00000 q^{85} +(3.00000 + 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{89} +(5.00000 - 8.66025i) q^{93} +(1.00000 + 1.73205i) q^{95} +16.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{5} - q^{9} - 6 q^{11} + 8 q^{13} - 2 q^{15} + 6 q^{17} + 2 q^{19} - q^{25} - 2 q^{27} + 12 q^{29} - 10 q^{31} + 6 q^{33} - 2 q^{37} + 4 q^{39} + 12 q^{41} - 8 q^{43} - q^{45} - 6 q^{51}+ \cdots + 12 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^5 - q^9 - 6 * q^11 + 8 * q^13 - 2 * q^15 + 6 * q^17 + 2 * q^19 - q^25 - 2 * q^27 + 12 * q^29 - 10 * q^31 + 6 * q^33 - 2 * q^37 + 4 * q^39 + 12 * q^41 - 8 * q^43 - q^45 - 6 * q^51 + 12 * q^53 + 12 * q^55 + 4 * q^57 + 14 * q^61 - 4 * q^65 + 4 * q^67 + 12 * q^71 - 4 * q^73 + q^75 + 16 * q^79 - q^81 + 24 * q^83 - 12 * q^85 + 6 * q^87 + 6 * q^89 + 10 * q^93 + 2 * q^95 + 32 * q^97 + 12 * q^99

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