LMFDB - Embedded newform 1600.2.q.e.849.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(49,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1600.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.q (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.4767670494822400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 $ x^12 - 4x^11 + 7x^10 - 4x^9 - 8x^8 + 24x^7 - 38x^6 + 48x^5 - 32x^4 - 32x^3 + 112x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			849.1
Root			$0.618969 + 1.27156i$ of defining polynomial
Character	$\chi$	$=$	1600.849
Dual form			1600.2.q.e.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16859 + 2.16859i) q^{3} +3.30519 q^{7} -6.40553i q^{9} +O(q^{10})$	$q+(-2.16859 + 2.16859i) q^{3} +3.30519 q^{7} -6.40553i q^{9} +(-2.01163 + 2.01163i) q^{11} +(0.794042 - 0.794042i) q^{13} +4.61575i q^{17} +(-3.48786 - 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +7.99801 q^{23} +(7.38518 + 7.38518i) q^{27} +(1.95065 + 1.95065i) q^{29} +5.12695 q^{31} -8.72480i q^{33} +(0.448156 + 0.448156i) q^{37} +3.44390i q^{39} +4.02230i q^{41} +(4.97000 + 4.97000i) q^{43} +5.49112i q^{47} +3.92429 q^{49} +(-10.0096 - 10.0096i) q^{51} +(3.35125 + 3.35125i) q^{53} +15.1274 q^{57} +(2.07673 - 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} -21.1715i q^{63} +(-0.636094 + 0.636094i) q^{67} +(-17.3444 + 17.3444i) q^{69} +6.85258i q^{71} -10.5177 q^{73} +(-6.64883 + 6.64883i) q^{77} -17.3005 q^{79} -12.8142 q^{81} +(-9.48015 + 9.48015i) q^{83} -8.46030 q^{87} -7.62073i q^{89} +(2.62446 - 2.62446i) q^{91} +(-11.1182 + 11.1182i) q^{93} +0.709082i q^{97} +(12.8856 + 12.8856i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 12 q^{7}+O(q^{10}) $ 12 * q - 2 * q^3 + 12 * q^7	$ 12 q - 2 q^{3} + 12 q^{7} + 2 q^{11} - 4 q^{13} - 14 q^{19} - 20 q^{21} + 12 q^{23} + 10 q^{27} + 4 q^{31} + 8 q^{37} - 4 q^{49} - 10 q^{51} + 16 q^{53} + 16 q^{57} + 20 q^{59} + 4 q^{61} + 50 q^{67} - 40 q^{73} + 8 q^{77} + 12 q^{79} - 8 q^{81} + 2 q^{83} - 64 q^{87} - 44 q^{93} + 12 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 + 12 * q^7 + 2 * q^11 - 4 * q^13 - 14 * q^19 - 20 * q^21 + 12 * q^23 + 10 * q^27 + 4 * q^31 + 8 * q^37 - 4 * q^49 - 10 * q^51 + 16 * q^53 + 16 * q^57 + 20 * q^59 + 4 * q^61 + 50 * q^67 - 40 * q^73 + 8 * q^77 + 12 * q^79 - 8 * q^81 + 2 * q^83 - 64 * q^87 - 44 * q^93 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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
$2$		0			0
$3$	−2.16859	+	2.16859i	−1.25203	+	1.25203i	−0.297227	+	0.954807i	$0.596062\pi$
$3$	−2.16859	+	2.16859i	−1.25203	+	1.25203i	−0.954807	+	0.297227i	$0.903938\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.30519			1.24924			0.624622	−	0.780927i	$-0.285253\pi$
$7$	3.30519			1.24924			0.624622	+	0.780927i	$0.285253\pi$
$8$		0			0
$9$		−	6.40553i		−	2.13518i
$10$		0			0
$11$	−2.01163	+	2.01163i	−0.606530	+	0.606530i	−0.942038	−	0.335507i	$-0.891092\pi$
$11$	−2.01163	+	2.01163i	−0.606530	+	0.606530i	0.335507	+	0.942038i	$0.391092\pi$
$12$		0			0
$13$	0.794042	−	0.794042i	0.220228	−	0.220228i	−0.588367	−	0.808594i	$-0.700229\pi$
$13$	0.794042	−	0.794042i	0.220228	−	0.220228i	0.808594	+	0.588367i	$0.200229\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			4.61575i			1.11948i	0.828667	+	0.559741i	$0.189100\pi$
$17$			4.61575i			1.11948i	−0.828667	+	0.559741i	$0.810900\pi$
$18$		0			0
$19$	−3.48786	−	3.48786i	−0.800169	−	0.800169i	0.182953	−	0.983122i	$-0.441434\pi$
$19$	−3.48786	−	3.48786i	−0.800169	−	0.800169i	−0.983122	+	0.182953i	$0.941434\pi$
$20$		0			0
$21$	−7.16759	+	7.16759i	−1.56410	+	1.56410i
$22$		0			0
$23$	7.99801			1.66770			0.833850	−	0.551991i	$-0.186132\pi$
$23$	7.99801			1.66770			0.833850	+	0.551991i	$0.186132\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	7.38518	+	7.38518i	1.42128	+	1.42128i
$28$		0			0
$29$	1.95065	+	1.95065i	0.362227	+	0.362227i	0.864632	−	0.502406i	$-0.167552\pi$
$29$	1.95065	+	1.95065i	0.362227	+	0.362227i	−0.502406	+	0.864632i	$0.667552\pi$
$30$		0			0
$31$	5.12695			0.920828			0.460414	−	0.887704i	$-0.347701\pi$
$31$	5.12695			0.920828			0.460414	+	0.887704i	$0.347701\pi$
$32$		0			0
$33$		−	8.72480i		−	1.51879i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.448156	+	0.448156i	0.0736764	+	0.0736764i	0.742985	−	0.669308i	$-0.233409\pi$
$37$	0.448156	+	0.448156i	0.0736764	+	0.0736764i	−0.669308	+	0.742985i	$0.733409\pi$
$38$		0			0
$39$			3.44390i			0.551465i
$40$		0			0
$41$			4.02230i			0.628177i	0.949394	+	0.314089i	$0.101699\pi$
$41$			4.02230i			0.628177i	−0.949394	+	0.314089i	$0.898301\pi$
$42$		0			0
$43$	4.97000	+	4.97000i	0.757918	+	0.757918i	0.975943	−	0.218025i	$-0.0699615\pi$
$43$	4.97000	+	4.97000i	0.757918	+	0.757918i	−0.218025	+	0.975943i	$0.569961\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			5.49112i			0.800962i	0.916305	+	0.400481i	$0.131157\pi$
$47$			5.49112i			0.800962i	−0.916305	+	0.400481i	$0.868843\pi$
$48$		0			0
$49$	3.92429			0.560612
$50$		0			0
$51$	−10.0096	−	10.0096i	−1.40163	−	1.40163i
$52$		0			0
$53$	3.35125	+	3.35125i	0.460330	+	0.460330i	0.898763	−	0.438434i	$-0.144467\pi$
$53$	3.35125	+	3.35125i	0.460330	+	0.460330i	−0.438434	+	0.898763i	$0.644467\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	15.1274			2.00368
$58$		0			0
$59$	2.07673	−	2.07673i	0.270367	−	0.270367i	−0.558881	−	0.829248i	$-0.688769\pi$
$59$	2.07673	−	2.07673i	0.270367	−	0.270367i	0.829248	+	0.558881i	$0.188769\pi$
$60$		0			0
$61$	−0.557208	−	0.557208i	−0.0713432	−	0.0713432i	0.670535	−	0.741878i	$-0.266065\pi$
$61$	−0.557208	−	0.557208i	−0.0713432	−	0.0713432i	−0.741878	+	0.670535i	$0.766065\pi$
$62$		0			0
$63$		−	21.1715i		−	2.66736i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.636094	+	0.636094i	−0.0777112	+	0.0777112i	−0.744894	−	0.667183i	$-0.767500\pi$
$67$	−0.636094	+	0.636094i	−0.0777112	+	0.0777112i	0.667183	+	0.744894i	$0.267500\pi$
$68$		0			0
$69$	−17.3444	+	17.3444i	−2.08802	+	2.08802i
$70$		0			0
$71$			6.85258i			0.813252i	0.913595	+	0.406626i	$0.133295\pi$
$71$			6.85258i			0.813252i	−0.913595	+	0.406626i	$0.866705\pi$
$72$		0			0
$73$	−10.5177			−1.23101			−0.615504	−	0.788134i	$-0.711047\pi$
$73$	−10.5177			−1.23101			−0.615504	+	0.788134i	$0.711047\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.64883	+	6.64883i	−0.757705	+	0.757705i
$78$		0			0
$79$	−17.3005			−1.94646			−0.973230	−	0.229833i	$-0.926182\pi$
$79$	−17.3005			−1.94646			−0.973230	+	0.229833i	$0.926182\pi$
$80$		0			0
$81$	−12.8142			−1.42380
$82$		0			0
$83$	−9.48015	+	9.48015i	−1.04058	+	1.04058i	−0.0414412	+	0.999141i	$0.513195\pi$
$83$	−9.48015	+	9.48015i	−1.04058	+	1.04058i	−0.999141	+	0.0414412i	$0.986805\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−8.46030			−0.907040
$88$		0			0
$89$		−	7.62073i		−	0.807796i	−0.914804	−	0.403898i	$-0.867655\pi$
$89$		−	7.62073i		−	0.807796i	0.914804	−	0.403898i	$-0.132345\pi$
$90$		0			0
$91$	2.62446	−	2.62446i	0.275118	−	0.275118i
$92$		0			0
$93$	−11.1182	+	11.1182i	−1.15291	+	1.15291i
$94$		0			0
$95$		0			0
$96$		0			0
$97$			0.709082i			0.0719964i	0.999352	+	0.0359982i	$0.0114611\pi$
$97$			0.709082i			0.0719964i	−0.999352	+	0.0359982i	$0.988539\pi$
$98$		0			0
$99$	12.8856	+	12.8856i	1.29505	+	1.29505i
$100$		0			0
$101$	6.16223	−	6.16223i	0.613164	−	0.613164i	−0.330605	−	0.943769i	$-0.607253\pi$
$101$	6.16223	−	6.16223i	0.613164	−	0.613164i	0.943769	+	0.330605i	$0.107253\pi$
$102$		0			0
$103$	−15.9410			−1.57072			−0.785359	−	0.619040i	$-0.787522\pi$
$103$	−15.9410			−1.57072			−0.785359	+	0.619040i	$0.787522\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.38717	+	3.38717i	0.327450	+	0.327450i	0.851616	−	0.524166i	$-0.175623\pi$
$107$	3.38717	+	3.38717i	0.327450	+	0.327450i	−0.524166	+	0.851616i	$0.675623\pi$
$108$		0			0
$109$	2.43964	+	2.43964i	0.233675	+	0.233675i	0.814225	−	0.580550i	$-0.197162\pi$
$109$	2.43964	+	2.43964i	0.233675	+	0.233675i	−0.580550	+	0.814225i	$0.697162\pi$
$110$		0			0
$111$	−1.94373			−0.184491
$112$		0			0
$113$		−	1.09801i		−	0.103292i	−0.998665	−	0.0516461i	$-0.983553\pi$
$113$		−	1.09801i		−	0.103292i	0.998665	−	0.0516461i	$-0.0164468\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−5.08626	−	5.08626i	−0.470225	−	0.470225i
$118$		0			0
$119$			15.2559i			1.39851i
$120$		0			0
$121$			2.90666i			0.264242i
$122$		0			0
$123$	−8.72270	−	8.72270i	−0.786499	−	0.786499i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			1.51159i			0.134131i	0.997749	+	0.0670657i	$0.0213637\pi$
$127$			1.51159i			0.134131i	−0.997749	+	0.0670657i	$0.978636\pi$
$128$		0			0
$129$	−21.5557			−1.89788
$130$		0			0
$131$	9.21660	+	9.21660i	0.805258	+	0.805258i	0.983912	−	0.178654i	$-0.0571743\pi$
$131$	9.21660	+	9.21660i	0.805258	+	0.805258i	−0.178654	+	0.983912i	$0.557174\pi$
$132$		0			0
$133$	−11.5280	−	11.5280i	−0.999607	−	0.999607i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.38639			−0.289318			−0.144659	−	0.989482i	$-0.546209\pi$
$137$	−3.38639			−0.289318			−0.144659	+	0.989482i	$0.546209\pi$
$138$		0			0
$139$	−2.09626	+	2.09626i	−0.177802	+	0.177802i	−0.790397	−	0.612595i	$-0.790126\pi$
$139$	−2.09626	+	2.09626i	−0.177802	+	0.177802i	0.612595	+	0.790397i	$0.290126\pi$
$140$		0			0
$141$	−11.9080	−	11.9080i	−1.00283	−	1.00283i
$142$		0			0
$143$			3.19464i			0.267149i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−8.51015	+	8.51015i	−0.701906	+	0.701906i
$148$		0			0
$149$	2.45247	−	2.45247i	0.200915	−	0.200915i	−0.599477	−	0.800392i	$-0.704625\pi$
$149$	2.45247	−	2.45247i	0.200915	−	0.200915i	0.800392	+	0.599477i	$0.204625\pi$
$150$		0			0
$151$			1.11727i			0.0909222i	0.998966	+	0.0454611i	$0.0144757\pi$
$151$			1.11727i			0.0909222i	−0.998966	+	0.0454611i	$0.985524\pi$
$152$		0			0
$153$	29.5663			2.39029
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−15.8377	+	15.8377i	−1.26398	+	1.26398i	−0.314839	+	0.949145i	$0.601950\pi$
$157$	−15.8377	+	15.8377i	−1.26398	+	1.26398i	−0.949145	+	0.314839i	$0.898050\pi$
$158$		0			0
$159$	−14.5349			−1.15270
$160$		0			0
$161$	26.4349			2.08337
$162$		0			0
$163$	7.22102	−	7.22102i	0.565594	−	0.565594i	−0.365297	−	0.930891i	$-0.619033\pi$
$163$	7.22102	−	7.22102i	0.565594	−	0.565594i	0.930891	+	0.365297i	$0.119033\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.2304			1.02380			0.511901	−	0.859044i	$-0.328941\pi$
$167$	13.2304			1.02380			0.511901	+	0.859044i	$0.328941\pi$
$168$		0			0
$169$			11.7390i			0.903000i
$170$		0			0
$171$	−22.3416	+	22.3416i	−1.70850	+	1.70850i
$172$		0			0
$173$	11.7503	−	11.7503i	0.893355	−	0.893355i	−0.101482	−	0.994837i	$-0.532359\pi$
$173$	11.7503	−	11.7503i	0.893355	−	0.893355i	0.994837	+	0.101482i	$0.0323585\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			9.00712i			0.677017i
$178$		0			0
$179$	4.84732	+	4.84732i	0.362306	+	0.362306i	0.864661	−	0.502355i	$-0.167533\pi$
$179$	4.84732	+	4.84732i	0.362306	+	0.362306i	−0.502355	+	0.864661i	$0.667533\pi$
$180$		0			0
$181$	10.5742	−	10.5742i	0.785976	−	0.785976i	−0.194856	−	0.980832i	$-0.562424\pi$
$181$	10.5742	−	10.5742i	0.785976	−	0.785976i	0.980832	+	0.194856i	$0.0624240\pi$
$182$		0			0
$183$	2.41671			0.178648
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−9.28519	−	9.28519i	−0.679000	−	0.679000i
$188$		0			0
$189$	24.4094	+	24.4094i	1.77553	+	1.77553i
$190$		0			0
$191$	−7.94268			−0.574712			−0.287356	−	0.957824i	$-0.592776\pi$
$191$	−7.94268			−0.574712			−0.287356	+	0.957824i	$0.592776\pi$
$192$		0			0
$193$			20.8617i			1.50166i	0.660496	+	0.750829i	$0.270346\pi$
$193$			20.8617i			1.50166i	−0.660496	+	0.750829i	$0.729654\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.07707	+	2.07707i	0.147985	+	0.147985i	0.777217	−	0.629232i	$-0.216631\pi$
$197$	2.07707	+	2.07707i	0.147985	+	0.147985i	−0.629232	+	0.777217i	$0.716631\pi$
$198$		0			0
$199$		−	23.2807i		−	1.65033i	−0.564893	−	0.825164i	$-0.691083\pi$
$199$		−	23.2807i		−	1.65033i	0.564893	−	0.825164i	$-0.308917\pi$
$200$		0			0
$201$		−	2.75885i		−	0.194594i
$202$		0			0
$203$	6.44727	+	6.44727i	0.452510	+	0.452510i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	51.2315i		−	3.56083i
$208$		0			0
$209$	14.0326			0.970653
$210$		0			0
$211$	2.51586	+	2.51586i	0.173199	+	0.173199i	0.788383	−	0.615184i	$-0.210918\pi$
$211$	2.51586	+	2.51586i	0.173199	+	0.173199i	−0.615184	+	0.788383i	$0.710918\pi$
$212$		0			0
$213$	−14.8604	−	14.8604i	−1.01822	−	1.01822i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	16.9456			1.15034
$218$		0			0
$219$	22.8086	−	22.8086i	1.54126	−	1.54126i
$220$		0			0
$221$	3.66510	+	3.66510i	0.246541	+	0.246541i
$222$		0			0
$223$			10.9088i			0.730507i	0.930908	+	0.365253i	$0.119018\pi$
$223$			10.9088i			0.730507i	−0.930908	+	0.365253i	$0.880982\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.6347	+	11.6347i	−0.772220	+	0.772220i	−0.978494	−	0.206275i	$-0.933866\pi$
$227$	−11.6347	+	11.6347i	−0.772220	+	0.772220i	0.206275	+	0.978494i	$0.433866\pi$
$228$		0			0
$229$	1.60760	−	1.60760i	0.106233	−	0.106233i	−0.651992	−	0.758226i	$-0.726067\pi$
$229$	1.60760	−	1.60760i	0.106233	−	0.106233i	0.758226	+	0.651992i	$0.226067\pi$
$230$		0			0
$231$		−	28.8371i		−	1.89734i
$232$		0			0
$233$	23.8100			1.55985			0.779924	−	0.625875i	$-0.215258\pi$
$233$	23.8100			1.55985			0.779924	+	0.625875i	$0.215258\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	37.5177	−	37.5177i	2.43703	−	2.43703i
$238$		0			0
$239$	−0.199630			−0.0129130			−0.00645649	−	0.999979i	$-0.502055\pi$
$239$	−0.199630			−0.0129130			−0.00645649	+	0.999979i	$0.502055\pi$
$240$		0			0
$241$	−16.8755			−1.08705			−0.543525	−	0.839393i	$-0.682911\pi$
$241$	−16.8755			−1.08705			−0.543525	+	0.839393i	$0.682911\pi$
$242$		0			0
$243$	5.63317	−	5.63317i	0.361368	−	0.361368i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.53901			−0.352439
$248$		0			0
$249$		−	41.1171i		−	2.60569i
$250$		0			0
$251$	6.10023	−	6.10023i	0.385043	−	0.385043i	−0.487872	−	0.872915i	$-0.662227\pi$
$251$	6.10023	−	6.10023i	0.385043	−	0.385043i	0.872915	+	0.487872i	$0.162227\pi$
$252$		0			0
$253$	−16.0891	+	16.0891i	−1.01151	+	1.01151i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	19.8360i		−	1.23733i	−0.785653	−	0.618667i	$-0.787673\pi$
$257$		−	19.8360i		−	1.23733i	0.785653	−	0.618667i	$-0.212327\pi$
$258$		0			0
$259$	1.48124	+	1.48124i	0.0920399	+	0.0920399i
$260$		0			0
$261$	12.4949	−	12.4949i	0.773418	−	0.773418i
$262$		0			0
$263$	−7.14438			−0.440542			−0.220271	−	0.975439i	$-0.570694\pi$
$263$	−7.14438			−0.440542			−0.220271	+	0.975439i	$0.570694\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	16.5262	+	16.5262i	1.01139	+	1.01139i
$268$		0			0
$269$	−21.7716	−	21.7716i	−1.32744	−	1.32744i	−0.907596	−	0.419844i	$-0.862085\pi$
$269$	−21.7716	−	21.7716i	−1.32744	−	1.32744i	−0.419844	−	0.907596i	$-0.637915\pi$
$270$		0			0
$271$	4.71328			0.286312			0.143156	−	0.989700i	$-0.454275\pi$
$271$	4.71328			0.286312			0.143156	+	0.989700i	$0.454275\pi$
$272$		0			0
$273$			11.3827i			0.688915i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	20.4588	+	20.4588i	1.22925	+	1.22925i	0.964247	+	0.265006i	$0.0853739\pi$
$277$	20.4588	+	20.4588i	1.22925	+	1.22925i	0.265006	+	0.964247i	$0.414626\pi$
$278$		0			0
$279$		−	32.8409i		−	1.96613i
$280$		0			0
$281$			17.6481i			1.05280i	0.850239	+	0.526398i	$0.176458\pi$
$281$			17.6481i			1.05280i	−0.850239	+	0.526398i	$0.823542\pi$
$282$		0			0
$283$	18.1525	+	18.1525i	1.07906	+	1.07906i	0.996594	+	0.0824607i	$0.0262779\pi$
$283$	18.1525	+	18.1525i	1.07906	+	1.07906i	0.0824607	+	0.996594i	$0.473722\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			13.2945i			0.784747i
$288$		0			0
$289$	−4.30511			−0.253242
$290$		0			0
$291$	−1.53771	−	1.53771i	−0.0901419	−	0.0901419i
$292$		0			0
$293$	0.638480	+	0.638480i	0.0373004	+	0.0373004i	0.725511	−	0.688211i	$-0.241603\pi$
$293$	0.638480	+	0.638480i	0.0373004	+	0.0373004i	−0.688211	+	0.725511i	$0.741603\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−29.7126			−1.72410
$298$		0			0
$299$	6.35076	−	6.35076i	0.367274	−	0.367274i
$300$		0			0
$301$	16.4268	+	16.4268i	0.946825	+	0.946825i
$302$		0			0
$303$			26.7266i			1.53540i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	4.52224	−	4.52224i	0.258098	−	0.258098i	−0.566182	−	0.824280i	$-0.691580\pi$
$307$	4.52224	−	4.52224i	0.258098	−	0.258098i	0.824280	+	0.566182i	$0.191580\pi$
$308$		0			0
$309$	34.5695	−	34.5695i	1.96659	−	1.96659i
$310$		0			0
$311$			14.1014i			0.799620i	0.916598	+	0.399810i	$0.130924\pi$
$311$			14.1014i			0.799620i	−0.916598	+	0.399810i	$0.869076\pi$
$312$		0			0
$313$	11.9204			0.673779			0.336889	−	0.941544i	$-0.390625\pi$
$313$	11.9204			0.673779			0.336889	+	0.941544i	$0.390625\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.6516	+	17.6516i	−0.991410	+	0.991410i	−0.999963	−	0.00855359i	$-0.997277\pi$
$317$	−17.6516	+	17.6516i	−0.991410	+	0.991410i	0.00855359	+	0.999963i	$0.497277\pi$
$318$		0			0
$319$	−7.84798			−0.439403
$320$		0			0
$321$	−14.6907			−0.819958
$322$		0			0
$323$	16.0991	−	16.0991i	0.895775	−	0.895775i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−10.5811			−0.585138
$328$		0			0
$329$			18.1492i			1.00060i
$330$		0			0
$331$	24.9785	−	24.9785i	1.37294	−	1.37294i	0.516888	−	0.856053i	$-0.327090\pi$
$331$	24.9785	−	24.9785i	1.37294	−	1.37294i	0.856053	−	0.516888i	$-0.172910\pi$
$332$		0			0
$333$	2.87068	−	2.87068i	0.157312	−	0.157312i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	24.3167i		−	1.32462i	−0.749231	−	0.662308i	$-0.769577\pi$
$337$		−	24.3167i		−	1.32462i	0.749231	−	0.662308i	$-0.230423\pi$
$338$		0			0
$339$	2.38113	+	2.38113i	0.129325	+	0.129325i
$340$		0			0
$341$	−10.3136	+	10.3136i	−0.558510	+	0.558510i
$342$		0			0
$343$	−10.1658			−0.548903
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.3818	−	17.3818i	−0.933106	−	0.933106i	0.0647931	−	0.997899i	$-0.479361\pi$
$347$	−17.3818	−	17.3818i	−0.933106	−	0.933106i	−0.997899	+	0.0647931i	$0.979361\pi$
$348$		0			0
$349$	0.773103	+	0.773103i	0.0413832	+	0.0413832i	0.727496	−	0.686112i	$-0.240684\pi$
$349$	0.773103	+	0.773103i	0.0413832	+	0.0413832i	−0.686112	+	0.727496i	$0.740684\pi$
$350$		0			0
$351$	11.7283			0.626010
$352$		0			0
$353$		−	13.3720i		−	0.711720i	−0.934539	−	0.355860i	$-0.884188\pi$
$353$		−	13.3720i		−	0.711720i	0.934539	−	0.355860i	$-0.115812\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−33.0838	−	33.0838i	−1.75098	−	1.75098i
$358$		0			0
$359$			28.5413i			1.50635i	0.657818	+	0.753177i	$0.271480\pi$
$359$			28.5413i			1.50635i	−0.657818	+	0.753177i	$0.728520\pi$
$360$		0			0
$361$			5.33027i			0.280541i
$362$		0			0
$363$	−6.30335	−	6.30335i	−0.330840	−	0.330840i
$364$		0			0
$365$		0			0
$366$		0			0
$367$			0.909186i			0.0474591i	0.999718	+	0.0237296i	$0.00755406\pi$
$367$			0.909186i			0.0474591i	−0.999718	+	0.0237296i	$0.992446\pi$
$368$		0			0
$369$	25.7649			1.34127
$370$		0			0
$371$	11.0765	+	11.0765i	0.575064	+	0.575064i
$372$		0			0
$373$	26.5010	+	26.5010i	1.37217	+	1.37217i	0.857223	+	0.514946i	$0.172188\pi$
$373$	26.5010	+	26.5010i	1.37217	+	1.37217i	0.514946	+	0.857223i	$0.327812\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.09780			0.159545
$378$		0			0
$379$	1.23724	−	1.23724i	0.0635529	−	0.0635529i	−0.674616	−	0.738169i	$-0.735691\pi$
$379$	1.23724	−	1.23724i	0.0635529	−	0.0635529i	0.738169	+	0.674616i	$0.235691\pi$
$380$		0			0
$381$	−3.27800	−	3.27800i	−0.167937	−	0.167937i
$382$		0			0
$383$		−	15.7161i		−	0.803057i	−0.915846	−	0.401529i	$-0.868479\pi$
$383$		−	15.7161i		−	0.803057i	0.915846	−	0.401529i	$-0.131521\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	31.8355	−	31.8355i	1.61829	−	1.61829i
$388$		0			0
$389$	−16.2799	+	16.2799i	−0.825423	+	0.825423i	−0.986880	−	0.161457i	$-0.948381\pi$
$389$	−16.2799	+	16.2799i	−0.825423	+	0.825423i	0.161457	+	0.986880i	$0.448381\pi$
$390$		0			0
$391$			36.9168i			1.86696i
$392$		0			0
$393$	−39.9740			−2.01642
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−22.8944	+	22.8944i	−1.14903	+	1.14903i	−0.162292	+	0.986743i	$0.551889\pi$
$397$	−22.8944	+	22.8944i	−1.14903	+	1.14903i	−0.986743	+	0.162292i	$0.948111\pi$
$398$		0			0
$399$	49.9990			2.50308
$400$		0			0
$401$	15.8553			0.791778			0.395889	−	0.918298i	$-0.370437\pi$
$401$	15.8553			0.791778			0.395889	+	0.918298i	$0.370437\pi$
$402$		0			0
$403$	4.07102	−	4.07102i	0.202792	−	0.202792i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.80305			−0.0893740
$408$		0			0
$409$		−	10.0220i		−	0.495557i	−0.968817	−	0.247779i	$-0.920299\pi$
$409$		−	10.0220i		−	0.495557i	0.968817	−	0.247779i	$-0.0797006\pi$
$410$		0			0
$411$	7.34367	−	7.34367i	0.362236	−	0.362236i
$412$		0			0
$413$	6.86398	−	6.86398i	0.337754	−	0.337754i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	9.09182i		−	0.445228i
$418$		0			0
$419$	14.4998	+	14.4998i	0.708362	+	0.708362i	0.966191	−	0.257829i	$-0.0830071\pi$
$419$	14.4998	+	14.4998i	0.708362	+	0.708362i	−0.257829	+	0.966191i	$0.583007\pi$
$420$		0			0
$421$	12.9983	−	12.9983i	0.633498	−	0.633498i	−0.315446	−	0.948944i	$-0.602154\pi$
$421$	12.9983	−	12.9983i	0.633498	−	0.633498i	0.948944	+	0.315446i	$0.102154\pi$
$422$		0			0
$423$	35.1735			1.71020
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.84168	−	1.84168i	−0.0891251	−	0.0891251i
$428$		0			0
$429$	−6.92786	−	6.92786i	−0.334480	−	0.334480i
$430$		0			0
$431$	34.4404			1.65894			0.829469	−	0.558553i	$-0.188643\pi$
$431$	34.4404			1.65894			0.829469	+	0.558553i	$0.188643\pi$
$432$		0			0
$433$			14.5895i			0.701128i	0.936539	+	0.350564i	$0.114010\pi$
$433$			14.5895i			0.701128i	−0.936539	+	0.350564i	$0.885990\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−27.8959	−	27.8959i	−1.33444	−	1.33444i
$438$		0			0
$439$		−	5.70179i		−	0.272131i	−0.990700	−	0.136066i	$-0.956554\pi$
$439$		−	5.70179i		−	0.272131i	0.990700	−	0.136066i	$-0.0434458\pi$
$440$		0			0
$441$		−	25.1371i		−	1.19701i
$442$		0			0
$443$	5.03375	+	5.03375i	0.239161	+	0.239161i	0.816503	−	0.577342i	$-0.195910\pi$
$443$	5.03375	+	5.03375i	0.239161	+	0.239161i	−0.577342	+	0.816503i	$0.695910\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			10.6368i			0.503104i
$448$		0			0
$449$	−22.2502			−1.05005			−0.525025	−	0.851087i	$-0.675944\pi$
$449$	−22.2502			−1.05005			−0.525025	+	0.851087i	$0.675944\pi$
$450$		0			0
$451$	−8.09139	−	8.09139i	−0.381009	−	0.381009i
$452$		0			0
$453$	−2.42290	−	2.42290i	−0.113838	−	0.113838i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−8.92927			−0.417694			−0.208847	−	0.977948i	$-0.566971\pi$
$457$	−8.92927			−0.417694			−0.208847	+	0.977948i	$0.566971\pi$
$458$		0			0
$459$	−34.0881	+	34.0881i	−1.59110	+	1.59110i
$460$		0			0
$461$	−8.14776	−	8.14776i	−0.379479	−	0.379479i	0.491435	−	0.870914i	$-0.336472\pi$
$461$	−8.14776	−	8.14776i	−0.379479	−	0.379479i	−0.870914	+	0.491435i	$0.836472\pi$
$462$		0			0
$463$		−	31.7058i		−	1.47349i	−0.676168	−	0.736747i	$-0.736361\pi$
$463$		−	31.7058i		−	1.47349i	0.676168	−	0.736747i	$-0.263639\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.7683	+	17.7683i	−0.822219	+	0.822219i	−0.986426	−	0.164207i	$-0.947494\pi$
$467$	−17.7683	+	17.7683i	−0.822219	+	0.822219i	0.164207	+	0.986426i	$0.447494\pi$
$468$		0			0
$469$	−2.10241	+	2.10241i	−0.0970803	+	0.0970803i
$470$		0			0
$471$		−	68.6907i		−	3.16510i
$472$		0			0
$473$	−19.9956			−0.919401
$474$		0			0
$475$		0			0
$476$		0			0
$477$	21.4665	−	21.4665i	0.982885	−	0.982885i
$478$		0			0
$479$	−7.80806			−0.356759			−0.178380	−	0.983962i	$-0.557086\pi$
$479$	−7.80806			−0.356759			−0.178380	+	0.983962i	$0.557086\pi$
$480$		0			0
$481$	0.711710			0.0324512
$482$		0			0
$483$	−57.3264	+	57.3264i	−2.60844	+	2.60844i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	27.6753			1.25409			0.627044	−	0.778984i	$-0.284265\pi$
$487$	27.6753			1.25409			0.627044	+	0.778984i	$0.284265\pi$
$488$		0			0
$489$			31.3188i			1.41629i
$490$		0			0
$491$	11.7995	−	11.7995i	0.532505	−	0.532505i	−0.388812	−	0.921317i	$-0.627114\pi$
$491$	11.7995	−	11.7995i	0.532505	−	0.532505i	0.921317	+	0.388812i	$0.127114\pi$
$492$		0			0
$493$	−9.00370	+	9.00370i	−0.405506	+	0.405506i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			22.6491i			1.01595i
$498$		0			0
$499$	−25.0477	−	25.0477i	−1.12129	−	1.12129i	−0.991548	−	0.129743i	$-0.958585\pi$
$499$	−25.0477	−	25.0477i	−1.12129	−	1.12129i	−0.129743	−	0.991548i	$-0.541415\pi$
$500$		0			0
$501$	−28.6914	+	28.6914i	−1.28184	+	1.28184i
$502$		0			0
$503$	22.8644			1.01947			0.509736	−	0.860331i	$-0.329743\pi$
$503$	22.8644			1.01947			0.509736	+	0.860331i	$0.329743\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−25.4570	−	25.4570i	−1.13059	−	1.13059i
$508$		0			0
$509$	17.1633	+	17.1633i	0.760748	+	0.760748i	0.976458	−	0.215710i	$-0.0692065\pi$
$509$	17.1633	+	17.1633i	0.760748	+	0.760748i	−0.215710	+	0.976458i	$0.569206\pi$
$510$		0			0
$511$	−34.7631			−1.53783
$512$		0			0
$513$		−	51.5169i		−	2.27453i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−11.0461	−	11.0461i	−0.485808	−	0.485808i
$518$		0			0
$519$			50.9629i			2.23702i
$520$		0			0
$521$		−	11.5206i		−	0.504726i	−0.967633	−	0.252363i	$-0.918792\pi$
$521$		−	11.5206i		−	0.504726i	0.967633	−	0.252363i	$-0.0812077\pi$
$522$		0			0
$523$	−25.4249	−	25.4249i	−1.11175	−	1.11175i	−0.992913	−	0.118841i	$-0.962082\pi$
$523$	−25.4249	−	25.4249i	−1.11175	−	1.11175i	−0.118841	−	0.992913i	$-0.537918\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			23.6647i			1.03085i
$528$		0			0
$529$	40.9681			1.78122
$530$		0			0
$531$	−13.3025	−	13.3025i	−0.577281	−	0.577281i
$532$		0			0
$533$	3.19387	+	3.19387i	0.138342	+	0.138342i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−21.0237			−0.907239
$538$		0			0
$539$	−7.89423	+	7.89423i	−0.340028	+	0.340028i
$540$		0			0
$541$	−29.7997	−	29.7997i	−1.28119	−	1.28119i	−0.939992	−	0.341196i	$-0.889168\pi$
$541$	−29.7997	−	29.7997i	−1.28119	−	1.28119i	−0.341196	−	0.939992i	$-0.610832\pi$
$542$		0			0
$543$			45.8622i			1.96814i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	28.3699	−	28.3699i	1.21301	−	1.21301i	0.242979	−	0.970032i	$-0.421875\pi$
$547$	28.3699	−	28.3699i	1.21301	−	1.21301i	0.970032	−	0.242979i	$-0.0781246\pi$
$548$		0			0
$549$	−3.56921	+	3.56921i	−0.152330	+	0.152330i
$550$		0			0
$551$		−	13.6072i		−	0.579685i
$552$		0			0
$553$	−57.1815			−2.43161
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.7769	−	21.7769i	0.922718	−	0.922718i	−0.0745028	−	0.997221i	$-0.523737\pi$
$557$	21.7769	−	21.7769i	0.922718	−	0.922718i	0.997221	+	0.0745028i	$0.0237370\pi$
$558$		0			0
$559$	7.89278			0.333829
$560$		0			0
$561$	40.2715			1.70026
$562$		0			0
$563$	10.9022	−	10.9022i	0.459473	−	0.459473i	−0.439010	−	0.898482i	$-0.644671\pi$
$563$	10.9022	−	10.9022i	0.459473	−	0.459473i	0.898482	+	0.439010i	$0.144671\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−42.3534			−1.77868
$568$		0			0
$569$			31.1881i			1.30747i	0.756723	+	0.653736i	$0.226799\pi$
$569$			31.1881i			1.30747i	−0.756723	+	0.653736i	$0.773201\pi$
$570$		0			0
$571$	2.20354	−	2.20354i	0.0922153	−	0.0922153i	−0.659494	−	0.751710i	$-0.729230\pi$
$571$	2.20354	−	2.20354i	0.0922153	−	0.0922153i	0.751710	+	0.659494i	$0.229230\pi$
$572$		0			0
$573$	17.2244	−	17.2244i	0.719559	−	0.719559i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	8.42524i		−	0.350747i	−0.984502	−	0.175374i	$-0.943887\pi$
$577$		−	8.42524i		−	0.350747i	0.984502	−	0.175374i	$-0.0561134\pi$
$578$		0			0
$579$	−45.2404	−	45.2404i	−1.88013	−	1.88013i
$580$		0			0
$581$	−31.3337	+	31.3337i	−1.29994	+	1.29994i
$582$		0			0
$583$	−13.4830			−0.558408
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.3370	−	19.3370i	−0.798125	−	0.798125i	0.184675	−	0.982800i	$-0.440877\pi$
$587$	−19.3370	−	19.3370i	−0.798125	−	0.798125i	−0.982800	+	0.184675i	$0.940877\pi$
$588$		0			0
$589$	−17.8821	−	17.8821i	−0.736818	−	0.736818i
$590$		0			0
$591$	−9.00862			−0.370565
$592$		0			0
$593$			18.1804i			0.746580i	0.927715	+	0.373290i	$0.121770\pi$
$593$			18.1804i			0.746580i	−0.927715	+	0.373290i	$0.878230\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	50.4863	+	50.4863i	2.06627	+	2.06627i
$598$		0			0
$599$			1.64695i			0.0672927i	0.999434	+	0.0336463i	$0.0107120\pi$
$599$			1.64695i			0.0672927i	−0.999434	+	0.0336463i	$0.989288\pi$
$600$		0			0
$601$		−	12.7485i		−	0.520021i	−0.965606	−	0.260011i	$-0.916274\pi$
$601$		−	12.7485i		−	0.520021i	0.965606	−	0.260011i	$-0.0837261\pi$
$602$		0			0
$603$	4.07452	+	4.07452i	0.165927	+	0.165927i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			15.6773i			0.636322i	0.948037	+	0.318161i	$0.103065\pi$
$607$			15.6773i			0.636322i	−0.948037	+	0.318161i	$0.896935\pi$
$608$		0			0
$609$	−27.9629			−1.13311
$610$		0			0
$611$	4.36018	+	4.36018i	0.176394	+	0.176394i
$612$		0			0
$613$	8.29399	+	8.29399i	0.334991	+	0.334991i	0.854478	−	0.519487i	$-0.173877\pi$
$613$	8.29399	+	8.29399i	0.334991	+	0.334991i	−0.519487	+	0.854478i	$0.673877\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	20.3330			0.818575			0.409287	−	0.912406i	$-0.365777\pi$
$617$	20.3330			0.818575			0.409287	+	0.912406i	$0.365777\pi$
$618$		0			0
$619$	12.5878	−	12.5878i	0.505946	−	0.505946i	−0.407333	−	0.913280i	$-0.633541\pi$
$619$	12.5878	−	12.5878i	0.505946	−	0.505946i	0.913280	+	0.407333i	$0.133541\pi$
$620$		0			0
$621$	59.0667	+	59.0667i	2.37027	+	2.37027i
$622$		0			0
$623$		−	25.1880i		−	1.00914i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−30.4308	+	30.4308i	−1.21529	+	1.21529i
$628$		0			0
$629$	−2.06858	+	2.06858i	−0.0824795	+	0.0824795i
$630$		0			0
$631$			21.4887i			0.855453i	0.903908	+	0.427726i	$0.140685\pi$
$631$			21.4887i			0.855453i	−0.903908	+	0.427726i	$0.859315\pi$
$632$		0			0
$633$	−10.9117			−0.433702
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.11605	−	3.11605i	0.123462	−	0.123462i
$638$		0			0
$639$	43.8944			1.73644
$640$		0			0
$641$	26.1687			1.03360			0.516800	−	0.856106i	$-0.327123\pi$
$641$	26.1687			1.03360			0.516800	+	0.856106i	$0.327123\pi$
$642$		0			0
$643$	−14.6501	+	14.6501i	−0.577743	+	0.577743i	−0.934281	−	0.356538i	$-0.883957\pi$
$643$	−14.6501	+	14.6501i	−0.577743	+	0.577743i	0.356538	+	0.934281i	$0.383957\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.2623			−0.639337			−0.319668	−	0.947530i	$-0.603571\pi$
$647$	−16.2623			−0.639337			−0.319668	+	0.947530i	$0.603571\pi$
$648$		0			0
$649$			8.35522i			0.327971i
$650$		0			0
$651$	−36.7479	+	36.7479i	−1.44026	+	1.44026i
$652$		0			0
$653$	32.0639	−	32.0639i	1.25476	−	1.25476i	0.301194	−	0.953563i	$-0.402615\pi$
$653$	32.0639	−	32.0639i	1.25476	−	1.25476i	0.953563	−	0.301194i	$-0.0973851\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			67.3717i			2.62842i
$658$		0			0
$659$	−7.04696	−	7.04696i	−0.274511	−	0.274511i	0.556402	−	0.830913i	$-0.312181\pi$
$659$	−7.04696	−	7.04696i	−0.274511	−	0.274511i	−0.830913	+	0.556402i	$0.812181\pi$
$660$		0			0
$661$	5.78655	−	5.78655i	0.225071	−	0.225071i	−0.585559	−	0.810630i	$-0.699125\pi$
$661$	5.78655	−	5.78655i	0.225071	−	0.225071i	0.810630	+	0.585559i	$0.199125\pi$
$662$		0			0
$663$	−15.8962			−0.617355
$664$		0			0
$665$		0			0
$666$		0			0
$667$	15.6013	+	15.6013i	0.604085	+	0.604085i
$668$		0			0
$669$	−23.6567	−	23.6567i	−0.914619	−	0.914619i
$670$		0			0
$671$	2.24180			0.0865436
$672$		0			0
$673$		−	35.3380i		−	1.36218i	−0.732200	−	0.681090i	$-0.761506\pi$
$673$		−	35.3380i		−	1.36218i	0.732200	−	0.681090i	$-0.238494\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.72259	+	7.72259i	0.296803	+	0.296803i	0.839760	−	0.542957i	$-0.182695\pi$
$677$	7.72259	+	7.72259i	0.296803	+	0.296803i	−0.542957	+	0.839760i	$0.682695\pi$
$678$		0			0
$679$			2.34365i			0.0899411i
$680$		0			0
$681$		−	50.4615i		−	1.93369i
$682$		0			0
$683$	−15.6011	−	15.6011i	−0.596958	−	0.596958i	0.342544	−	0.939502i	$-0.388711\pi$
$683$	−15.6011	−	15.6011i	−0.596958	−	0.596958i	−0.939502	+	0.342544i	$0.888711\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			6.97246i			0.266016i
$688$		0			0
$689$	5.32207			0.202755
$690$		0			0
$691$	−30.0975	−	30.0975i	−1.14496	−	1.14496i	−0.987530	−	0.157433i	$-0.949678\pi$
$691$	−30.0975	−	30.0975i	−1.14496	−	1.14496i	−0.157433	−	0.987530i	$-0.550322\pi$
$692$		0			0
$693$	42.5893	+	42.5893i	1.61783	+	1.61783i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.5659			−0.703234
$698$		0			0
$699$	−51.6341	+	51.6341i	−1.95298	+	1.95298i
$700$		0			0
$701$	14.8151	+	14.8151i	0.559559	+	0.559559i	0.929182	−	0.369623i	$-0.120513\pi$
$701$	14.8151	+	14.8151i	0.559559	+	0.559559i	−0.369623	+	0.929182i	$0.620513\pi$
$702$		0			0
$703$		−	3.12621i		−	0.117907i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.3673	−	20.3673i	0.765992	−	0.765992i
$708$		0			0
$709$	−9.26566	+	9.26566i	−0.347979	+	0.347979i	−0.859356	−	0.511377i	$-0.829136\pi$
$709$	−9.26566	+	9.26566i	−0.347979	+	0.347979i	0.511377	+	0.859356i	$0.329136\pi$
$710$		0			0
$711$			110.819i			4.15604i
$712$		0			0
$713$	41.0054			1.53567
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.432914	−	0.432914i	0.0161675	−	0.0161675i
$718$		0			0
$719$	40.8143			1.52212			0.761058	−	0.648684i	$-0.224680\pi$
$719$	40.8143			1.52212			0.761058	+	0.648684i	$0.224680\pi$
$720$		0			0
$721$	−52.6882			−1.96221
$722$		0			0
$723$	36.5961	−	36.5961i	1.36102	−	1.36102i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−5.20944			−0.193208			−0.0966038	−	0.995323i	$-0.530798\pi$
$727$	−5.20944			−0.193208			−0.0966038	+	0.995323i	$0.530798\pi$
$728$		0			0
$729$		−	14.0106i		−	0.518911i
$730$		0			0
$731$	−22.9403	+	22.9403i	−0.848476	+	0.848476i
$732$		0			0
$733$	−14.7039	+	14.7039i	−0.543099	+	0.543099i	−0.924436	−	0.381337i	$-0.875464\pi$
$733$	−14.7039	+	14.7039i	−0.543099	+	0.543099i	0.381337	+	0.924436i	$0.375464\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	2.55917i		−	0.0942684i
$738$		0			0
$739$	7.68017	+	7.68017i	0.282520	+	0.282520i	0.834113	−	0.551594i	$-0.185980\pi$
$739$	7.68017	+	7.68017i	0.282520	+	0.282520i	−0.551594	+	0.834113i	$0.685980\pi$
$740$		0			0
$741$	12.0118	−	12.0118i	0.441265	−	0.441265i
$742$		0			0
$743$	34.9882			1.28359			0.641796	−	0.766876i	$-0.278190\pi$
$743$	34.9882			1.28359			0.641796	+	0.766876i	$0.278190\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	60.7254	+	60.7254i	2.22183	+	2.22183i
$748$		0			0
$749$	11.1953	+	11.1953i	0.409066	+	0.409066i
$750$		0			0
$751$	33.1447			1.20947			0.604733	−	0.796428i	$-0.293280\pi$
$751$	33.1447			1.20947			0.604733	+	0.796428i	$0.293280\pi$
$752$		0			0
$753$			26.4577i			0.964174i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	22.1553	+	22.1553i	0.805248	+	0.805248i	0.983910	−	0.178663i	$-0.0571771\pi$
$757$	22.1553	+	22.1553i	0.805248	+	0.805248i	−0.178663	+	0.983910i	$0.557177\pi$
$758$		0			0
$759$		−	69.7810i		−	2.53289i
$760$		0			0
$761$			48.1426i			1.74517i	0.488466	+	0.872583i	$0.337557\pi$
$761$			48.1426i			1.74517i	−0.488466	+	0.872583i	$0.662443\pi$
$762$		0			0
$763$	8.06347	+	8.06347i	0.291917	+	0.291917i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	3.29802i		−	0.119084i
$768$		0			0
$769$	41.1054			1.48230			0.741150	−	0.671339i	$-0.234281\pi$
$769$	41.1054			1.48230			0.741150	+	0.671339i	$0.234281\pi$
$770$		0			0
$771$	43.0160	+	43.0160i	1.54918	+	1.54918i
$772$		0			0
$773$	−10.8044	−	10.8044i	−0.388607	−	0.388607i	0.485583	−	0.874190i	$-0.338607\pi$
$773$	−10.8044	−	10.8044i	−0.388607	−	0.388607i	−0.874190	+	0.485583i	$0.838607\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−6.42440			−0.230474
$778$		0			0
$779$	14.0292	−	14.0292i	0.502648	−	0.502648i
$780$		0			0
$781$	−13.7849	−	13.7849i	−0.493262	−	0.493262i
$782$		0			0
$783$			28.8118i			1.02965i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	11.7496	−	11.7496i	0.418826	−	0.418826i	−0.465973	−	0.884799i	$-0.654296\pi$
$787$	11.7496	−	11.7496i	0.418826	−	0.418826i	0.884799	+	0.465973i	$0.154296\pi$
$788$		0			0
$789$	15.4932	−	15.4932i	0.551573	−	0.551573i
$790$		0			0
$791$		−	3.62914i		−	0.129037i
$792$		0			0
$793$	−0.884894			−0.0314235
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.9126	+	15.9126i	−0.563652	+	0.563652i	−0.930343	−	0.366691i	$-0.880491\pi$
$797$	−15.9126	+	15.9126i	−0.563652	+	0.563652i	0.366691	+	0.930343i	$0.380491\pi$
$798$		0			0
$799$	−25.3456			−0.896663
$800$		0			0
$801$	−48.8148			−1.72479
$802$		0			0
$803$	21.1578	−	21.1578i	0.746643	−	0.746643i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	94.4274			3.32400
$808$		0			0
$809$			9.06814i			0.318819i	0.987213	+	0.159409i	$0.0509590\pi$
$809$			9.06814i			0.318819i	−0.987213	+	0.159409i	$0.949041\pi$
$810$		0			0
$811$	17.0825	−	17.0825i	0.599849	−	0.599849i	−0.340424	−	0.940272i	$-0.610570\pi$
$811$	17.0825	−	17.0825i	0.599849	−	0.599849i	0.940272	+	0.340424i	$0.110570\pi$
$812$		0			0
$813$	−10.2212	+	10.2212i	−0.358472	+	0.358472i
$814$		0			0
$815$		0			0
$816$		0			0
$817$		−	34.6693i		−	1.21293i
$818$		0			0
$819$	−16.8111	−	16.8111i	−0.587426	−	0.587426i
$820$		0			0
$821$	18.0531	−	18.0531i	0.630057	−	0.630057i	−0.318026	−	0.948082i	$-0.603020\pi$
$821$	18.0531	−	18.0531i	0.630057	−	0.630057i	0.948082	+	0.318026i	$0.103020\pi$
$822$		0			0
$823$	−25.3535			−0.883767			−0.441884	−	0.897072i	$-0.645690\pi$
$823$	−25.3535			−0.883767			−0.441884	+	0.897072i	$0.645690\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.3396	−	15.3396i	−0.533410	−	0.533410i	0.388176	−	0.921585i	$-0.373105\pi$
$827$	−15.3396	−	15.3396i	−0.533410	−	0.533410i	−0.921585	+	0.388176i	$0.873105\pi$
$828$		0			0
$829$	−37.2546	−	37.2546i	−1.29391	−	1.29391i	−0.932351	−	0.361555i	$-0.882246\pi$
$829$	−37.2546	−	37.2546i	−1.29391	−	1.29391i	−0.361555	−	0.932351i	$-0.617754\pi$
$830$		0			0
$831$	−88.7335			−3.07813
$832$		0			0
$833$			18.1135i			0.627596i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	37.8635	+	37.8635i	1.30875	+	1.30875i
$838$		0			0
$839$		−	17.9621i		−	0.620120i	−0.950717	−	0.310060i	$-0.899651\pi$
$839$		−	17.9621i		−	0.620120i	0.950717	−	0.310060i	$-0.100349\pi$
$840$		0			0
$841$		−	21.3899i		−	0.737584i
$842$		0			0
$843$	−38.2713	−	38.2713i	−1.31813	−	1.31813i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			9.60708i			0.330103i
$848$		0			0
$849$	−78.7306			−2.70203
$850$		0			0
$851$	3.58436	+	3.58436i	0.122870	+	0.122870i
$852$		0			0
$853$	9.29007	+	9.29007i	0.318086	+	0.318086i	0.848032	−	0.529946i	$-0.177788\pi$
$853$	9.29007	+	9.29007i	0.318086	+	0.318086i	−0.529946	+	0.848032i	$0.677788\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.3997			0.355246			0.177623	−	0.984099i	$-0.443159\pi$
$857$	10.3997			0.355246			0.177623	+	0.984099i	$0.443159\pi$
$858$		0			0
$859$	15.3452	−	15.3452i	0.523571	−	0.523571i	−0.395077	−	0.918648i	$-0.629282\pi$
$859$	15.3452	−	15.3452i	0.523571	−	0.523571i	0.918648	+	0.395077i	$0.129282\pi$
$860$		0			0
$861$	−28.8302	−	28.8302i	−0.982530	−	0.982530i
$862$		0			0
$863$			8.81329i			0.300008i	0.988685	+	0.150004i	$0.0479286\pi$
$863$			8.81329i			0.300008i	−0.988685	+	0.150004i	$0.952071\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	9.33601	−	9.33601i	0.317067	−	0.317067i
$868$		0			0
$869$	34.8023	−	34.8023i	1.18059	−	1.18059i
$870$		0			0
$871$			1.01017i			0.0342283i
$872$		0			0
$873$	4.54205			0.153725
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.68862	−	5.68862i	0.192091	−	0.192091i	−0.604508	−	0.796599i	$-0.706630\pi$
$877$	5.68862	−	5.68862i	0.192091	−	0.192091i	0.796599	+	0.604508i	$0.206630\pi$
$878$		0			0
$879$	−2.76920			−0.0934028
$880$		0			0
$881$	−20.3573			−0.685856			−0.342928	−	0.939362i	$-0.611419\pi$
$881$	−20.3573			−0.685856			−0.342928	+	0.939362i	$0.611419\pi$
$882$		0			0
$883$	19.3524	−	19.3524i	0.651262	−	0.651262i	−0.302035	−	0.953297i	$-0.597666\pi$
$883$	19.3524	−	19.3524i	0.651262	−	0.651262i	0.953297	+	0.302035i	$0.0976660\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.7863			0.429323			0.214661	−	0.976689i	$-0.431135\pi$
$887$	12.7863			0.429323			0.214661	+	0.976689i	$0.431135\pi$
$888$		0			0
$889$			4.99608i			0.167563i
$890$		0			0
$891$	25.7775	−	25.7775i	0.863579	−	0.863579i
$892$		0			0
$893$	19.1522	−	19.1522i	0.640905	−	0.640905i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			27.5443i			0.919678i
$898$		0			0
$899$	10.0009	+	10.0009i	0.333548	+	0.333548i
$900$		0			0
$901$	−15.4685	+	15.4685i	−0.515331	+	0.515331i
$902$		0			0
$903$	−71.2459			−2.37091
$904$		0			0
$905$		0			0
$906$		0			0
$907$	2.88449	+	2.88449i	0.0957780	+	0.0957780i	0.753372	−	0.657594i	$-0.228426\pi$
$907$	2.88449	+	2.88449i	0.0957780	+	0.0957780i	−0.657594	+	0.753372i	$0.728426\pi$
$908$		0			0
$909$	−39.4723	−	39.4723i	−1.30921	−	1.30921i
$910$		0			0
$911$	−59.0271			−1.95565			−0.977827	−	0.209412i	$-0.932845\pi$
$911$	−59.0271			−1.95565			−0.977827	+	0.209412i	$0.932845\pi$
$912$		0			0
$913$		−	38.1412i		−	1.26229i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	30.4626	+	30.4626i	1.00596	+	1.00596i
$918$		0			0
$919$			24.0062i			0.791893i	0.918274	+	0.395946i	$0.129583\pi$
$919$			24.0062i			0.791893i	−0.918274	+	0.395946i	$0.870417\pi$
$920$		0			0
$921$			19.6137i			0.646294i
$922$		0			0
$923$	5.44124	+	5.44124i	0.179100	+	0.179100i
$924$		0			0
$925$		0			0
$926$		0			0
$927$			102.111i			3.35376i
$928$		0			0
$929$	−15.1568			−0.497279			−0.248639	−	0.968596i	$-0.579983\pi$
$929$	−15.1568			−0.497279			−0.248639	+	0.968596i	$0.579983\pi$
$930$		0			0
$931$	−13.6873	−	13.6873i	−0.448585	−	0.448585i
$932$		0			0
$933$	−30.5802	−	30.5802i	−1.00115	−	1.00115i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	39.9323			1.30453			0.652266	−	0.757991i	$-0.273819\pi$
$937$	39.9323			1.30453			0.652266	+	0.757991i	$0.273819\pi$
$938$		0			0
$939$	−25.8503	+	25.8503i	−0.843594	+	0.843594i
$940$		0			0
$941$	−21.6002	−	21.6002i	−0.704145	−	0.704145i	0.261153	−	0.965298i	$-0.415897\pi$
$941$	−21.6002	−	21.6002i	−0.704145	−	0.704145i	−0.965298	+	0.261153i	$0.915897\pi$
$942$		0			0
$943$			32.1704i			1.04761i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.2944	+	16.2944i	−0.529498	+	0.529498i	−0.920423	−	0.390925i	$-0.872155\pi$
$947$	−16.2944	+	16.2944i	−0.529498	+	0.529498i	0.390925	+	0.920423i	$0.372155\pi$
$948$		0			0
$949$	−8.35152	+	8.35152i	−0.271102	+	0.271102i
$950$		0			0
$951$		−	76.5578i		−	2.48256i
$952$		0			0
$953$	12.0232			0.389468			0.194734	−	0.980856i	$-0.437616\pi$
$953$	12.0232			0.389468			0.194734	+	0.980856i	$0.437616\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	17.0190	−	17.0190i	0.550147	−	0.550147i
$958$		0			0
$959$	−11.1927			−0.361430
$960$		0			0
$961$	−4.71434			−0.152076
$962$		0			0
$963$	21.6966	−	21.6966i	0.699164	−	0.699164i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−43.8237			−1.40927			−0.704637	−	0.709568i	$-0.748890\pi$
$967$	−43.8237			−1.40927			−0.704637	+	0.709568i	$0.748890\pi$
$968$		0			0
$969$			69.8244i			2.24308i
$970$		0			0
$971$	−35.9986	+	35.9986i	−1.15525	+	1.15525i	−0.169766	+	0.985484i	$0.554301\pi$
$971$	−35.9986	+	35.9986i	−1.15525	+	1.15525i	−0.985484	+	0.169766i	$0.945699\pi$
$972$		0			0
$973$	−6.92852	+	6.92852i	−0.222118	+	0.222118i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			0.204913i			0.00655576i	0.999995	+	0.00327788i	$0.00104338\pi$
$977$			0.204913i			0.00655576i	−0.999995	+	0.00327788i	$0.998957\pi$
$978$		0			0
$979$	15.3301	+	15.3301i	0.489953	+	0.489953i
$980$		0			0
$981$	15.6272	−	15.6272i	0.498937	−	0.498937i
$982$		0			0
$983$	34.0060			1.08462			0.542312	−	0.840177i	$-0.317549\pi$
$983$	34.0060			1.08462			0.542312	+	0.840177i	$0.317549\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−39.3581	−	39.3581i	−1.25278	−	1.25278i
$988$		0			0
$989$	39.7501	+	39.7501i	1.26398	+	1.26398i
$990$		0			0
$991$	−13.8223			−0.439079			−0.219539	−	0.975604i	$-0.570455\pi$
$991$	−13.8223			−0.439079			−0.219539	+	0.975604i	$0.570455\pi$
$992$		0			0
$993$			108.336i			3.43794i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−6.37875	−	6.37875i	−0.202017	−	0.202017i	0.598847	−	0.800864i	$-0.295626\pi$
$997$	−6.37875	−	6.37875i	−0.202017	−	0.202017i	−0.800864	+	0.598847i	$0.795626\pi$
$998$		0			0
$999$			6.61943i			0.209429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.q.e.849.1		12
4.3	odd	2		400.2.q.e.349.6		12
5.2	odd	4		1600.2.l.g.401.6		12
5.3	odd	4		1600.2.l.f.401.1		12
5.4	even	2		1600.2.q.f.849.6		12
16.5	even	4		1600.2.q.f.49.6		12
16.11	odd	4		400.2.q.f.149.1		12
20.3	even	4		400.2.l.g.301.3	yes	12
20.7	even	4		400.2.l.f.301.4	yes	12
20.19	odd	2		400.2.q.f.349.1		12
80.27	even	4		400.2.l.f.101.4	✓	12
80.37	odd	4		1600.2.l.g.1201.6		12
80.43	even	4		400.2.l.g.101.3	yes	12
80.53	odd	4		1600.2.l.f.1201.1		12
80.59	odd	4		400.2.q.e.149.6		12
80.69	even	4	inner	1600.2.q.e.49.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.4	✓	12	80.27	even	4
400.2.l.f.301.4	yes	12	20.7	even	4
400.2.l.g.101.3	yes	12	80.43	even	4
400.2.l.g.301.3	yes	12	20.3	even	4
400.2.q.e.149.6		12	80.59	odd	4
400.2.q.e.349.6		12	4.3	odd	2
400.2.q.f.149.1		12	16.11	odd	4
400.2.q.f.349.1		12	20.19	odd	2
1600.2.l.f.401.1		12	5.3	odd	4
1600.2.l.f.1201.1		12	80.53	odd	4
1600.2.l.g.401.6		12	5.2	odd	4
1600.2.l.g.1201.6		12	80.37	odd	4
1600.2.q.e.49.1		12	80.69	even	4	inner
1600.2.q.e.849.1		12	1.1	even	1	trivial
1600.2.q.f.49.6		12	16.5	even	4
1600.2.q.f.849.6		12	5.4	even	2

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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.16859 + 2.16859i) q^{3} +3.30519 q^{7} -6.40553i q^{9} +O(q^{10})\)	\(q+(-2.16859 + 2.16859i) q^{3} +3.30519 q^{7} -6.40553i q^{9} +(-2.01163 + 2.01163i) q^{11} +(0.794042 - 0.794042i) q^{13} +4.61575i q^{17} +(-3.48786 - 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} +7.99801 q^{23} +(7.38518 + 7.38518i) q^{27} +(1.95065 + 1.95065i) q^{29} +5.12695 q^{31} -8.72480i q^{33} +(0.448156 + 0.448156i) q^{37} +3.44390i q^{39} +4.02230i q^{41} +(4.97000 + 4.97000i) q^{43} +5.49112i q^{47} +3.92429 q^{49} +(-10.0096 - 10.0096i) q^{51} +(3.35125 + 3.35125i) q^{53} +15.1274 q^{57} +(2.07673 - 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} -21.1715i q^{63} +(-0.636094 + 0.636094i) q^{67} +(-17.3444 + 17.3444i) q^{69} +6.85258i q^{71} -10.5177 q^{73} +(-6.64883 + 6.64883i) q^{77} -17.3005 q^{79} -12.8142 q^{81} +(-9.48015 + 9.48015i) q^{83} -8.46030 q^{87} -7.62073i q^{89} +(2.62446 - 2.62446i) q^{91} +(-11.1182 + 11.1182i) q^{93} +0.709082i q^{97} +(12.8856 + 12.8856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 12 q^{7}+O(q^{10}) \) 12 * q - 2 * q^3 + 12 * q^7	\( 12 q - 2 q^{3} + 12 q^{7} + 2 q^{11} - 4 q^{13} - 14 q^{19} - 20 q^{21} + 12 q^{23} + 10 q^{27} + 4 q^{31} + 8 q^{37} - 4 q^{49} - 10 q^{51} + 16 q^{53} + 16 q^{57} + 20 q^{59} + 4 q^{61} + 50 q^{67} - 40 q^{73} + 8 q^{77} + 12 q^{79} - 8 q^{81} + 2 q^{83} - 64 q^{87} - 44 q^{93} + 12 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 + 12 * q^7 + 2 * q^11 - 4 * q^13 - 14 * q^19 - 20 * q^21 + 12 * q^23 + 10 * q^27 + 4 * q^31 + 8 * q^37 - 4 * q^49 - 10 * q^51 + 16 * q^53 + 16 * q^57 + 20 * q^59 + 4 * q^61 + 50 * q^67 - 40 * q^73 + 8 * q^77 + 12 * q^79 - 8 * q^81 + 2 * q^83 - 64 * q^87 - 44 * q^93 + 12 * q^99

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