LMFDB - Embedded newform 1600.2.l.g.401.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(401,1600)]

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, 3, 0]))

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

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

chi := DirichletCharacter("1600.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.l (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			401.6
Root			$0.618969 - 1.27156i$ of defining polynomial
Character	$\chi$	$=$	1600.401
Dual form			1600.2.l.g.1201.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16859 + 2.16859i) q^{3} +3.30519i q^{7} +6.40553i q^{9} +O(q^{10})$	$q+(2.16859 + 2.16859i) q^{3} +3.30519i q^{7} +6.40553i q^{9} +(-2.01163 + 2.01163i) q^{11} +(-0.794042 - 0.794042i) q^{13} -4.61575 q^{17} +(3.48786 + 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} -7.99801i q^{23} +(-7.38518 + 7.38518i) q^{27} +(-1.95065 - 1.95065i) q^{29} +5.12695 q^{31} -8.72480 q^{33} +(-0.448156 + 0.448156i) q^{37} -3.44390i q^{39} +4.02230i q^{41} +(4.97000 - 4.97000i) q^{43} -5.49112 q^{47} -3.92429 q^{49} +(-10.0096 - 10.0096i) q^{51} +(3.35125 - 3.35125i) q^{53} +15.1274i q^{57} +(-2.07673 + 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} -21.1715 q^{63} +(-0.636094 - 0.636094i) q^{67} +(17.3444 - 17.3444i) q^{69} +6.85258i q^{71} +10.5177i q^{73} +(-6.64883 - 6.64883i) q^{77} +17.3005 q^{79} -12.8142 q^{81} +(9.48015 + 9.48015i) q^{83} -8.46030i q^{87} +7.62073i q^{89} +(2.62446 - 2.62446i) q^{91} +(11.1182 + 11.1182i) q^{93} -0.709082 q^{97} +(-12.8856 - 12.8856i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{3}+O(q^{10}) $ 12 * q + 2 * q^3	$ 12 q + 2 q^{3} + 2 q^{11} + 4 q^{13} + 8 q^{17} + 14 q^{19} - 20 q^{21} - 10 q^{27} + 4 q^{31} - 28 q^{33} - 8 q^{37} + 8 q^{47} + 4 q^{49} - 10 q^{51} + 16 q^{53} - 20 q^{59} + 4 q^{61} - 8 q^{63} + 50 q^{67} + 8 q^{77} - 12 q^{79} - 8 q^{81} - 2 q^{83} + 44 q^{93} - 12 q^{99}+O(q^{100}) $ 12 * q + 2 * q^3 + 2 * q^11 + 4 * q^13 + 8 * q^17 + 14 * q^19 - 20 * q^21 - 10 * q^27 + 4 * q^31 - 28 * q^33 - 8 * q^37 + 8 * q^47 + 4 * q^49 - 10 * q^51 + 16 * q^53 - 20 * q^59 + 4 * q^61 - 8 * q^63 + 50 * q^67 + 8 * q^77 - 12 * q^79 - 8 * q^81 - 2 * q^83 + 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	0.954807	+	0.297227i	$0.0960617\pi$
$3$	2.16859	+	2.16859i	1.25203	+	1.25203i	0.297227	+	0.954807i	$0.403938\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			3.30519i			1.24924i	0.780927	+	0.624622i	$0.214747\pi$
$7$			3.30519i			1.24924i	−0.780927	+	0.624622i	$0.785253\pi$
$8$		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	$-0.299771\pi$
$13$	−0.794042	−	0.794042i	−0.220228	−	0.220228i	−0.808594	+	0.588367i	$0.799771\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.61575			−1.11948			−0.559741	−	0.828667i	$-0.689100\pi$
$17$	−4.61575			−1.11948			−0.559741	+	0.828667i	$0.689100\pi$
$18$		0			0
$19$	3.48786	+	3.48786i	0.800169	+	0.800169i	0.983122	−	0.182953i	$-0.0585655\pi$
$19$	3.48786	+	3.48786i	0.800169	+	0.800169i	−0.182953	+	0.983122i	$0.558566\pi$
$20$		0			0
$21$	−7.16759	+	7.16759i	−1.56410	+	1.56410i
$22$		0			0
$23$		−	7.99801i		−	1.66770i	−0.551991	−	0.833850i	$-0.686132\pi$
$23$		−	7.99801i		−	1.66770i	0.551991	−	0.833850i	$-0.313868\pi$
$24$		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	0.502406	−	0.864632i	$-0.332448\pi$
$29$	−1.95065	−	1.95065i	−0.362227	−	0.362227i	−0.864632	+	0.502406i	$0.832448\pi$
$30$		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
$33$	−8.72480			−1.51879
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−0.448156	+	0.448156i	−0.0736764	+	0.0736764i	−0.742985	−	0.669308i	$-0.766591\pi$
$37$	−0.448156	+	0.448156i	−0.0736764	+	0.0736764i	0.669308	+	0.742985i	$0.266591\pi$
$38$		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	−0.218025	−	0.975943i	$-0.569961\pi$
$43$	4.97000	−	4.97000i	0.757918	−	0.757918i	0.975943	+	0.218025i	$0.0699615\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.49112			−0.800962			−0.400481	−	0.916305i	$-0.631157\pi$
$47$	−5.49112			−0.800962			−0.400481	+	0.916305i	$0.631157\pi$
$48$		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	−0.438434	−	0.898763i	$-0.644467\pi$
$53$	3.35125	−	3.35125i	0.460330	−	0.460330i	0.898763	+	0.438434i	$0.144467\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			15.1274i			2.00368i
$58$		0			0
$59$	−2.07673	+	2.07673i	−0.270367	+	0.270367i	−0.829248	−	0.558881i	$-0.811231\pi$
$59$	−2.07673	+	2.07673i	−0.270367	+	0.270367i	0.558881	+	0.829248i	$0.311231\pi$
$60$		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
$63$	−21.1715			−2.66736
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−0.636094	−	0.636094i	−0.0777112	−	0.0777112i	0.667183	−	0.744894i	$-0.267500\pi$
$67$	−0.636094	−	0.636094i	−0.0777112	−	0.0777112i	−0.744894	+	0.667183i	$0.767500\pi$
$68$		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
$73$			10.5177i			1.23101i	0.788134	+	0.615504i	$0.211047\pi$
$73$			10.5177i			1.23101i	−0.788134	+	0.615504i	$0.788953\pi$
$74$		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	$-0.0738179\pi$
$79$	17.3005			1.94646			0.973230	+	0.229833i	$0.0738179\pi$
$80$		0			0
$81$	−12.8142			−1.42380
$82$		0			0
$83$	9.48015	+	9.48015i	1.04058	+	1.04058i	0.999141	+	0.0414412i	$0.0131949\pi$
$83$	9.48015	+	9.48015i	1.04058	+	1.04058i	0.0414412	+	0.999141i	$0.486805\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	8.46030i		−	0.907040i
$88$		0			0
$89$			7.62073i			0.807796i	0.914804	+	0.403898i	$0.132345\pi$
$89$			7.62073i			0.807796i	−0.914804	+	0.403898i	$0.867655\pi$
$90$		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
$97$	−0.709082			−0.0719964			−0.0359982	−	0.999352i	$-0.511461\pi$
$97$	−0.709082			−0.0719964			−0.0359982	+	0.999352i	$0.511461\pi$
$98$		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
$103$			15.9410i			1.57072i	0.619040	+	0.785359i	$0.287522\pi$
$103$			15.9410i			1.57072i	−0.619040	+	0.785359i	$0.712478\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.38717	+	3.38717i	−0.327450	+	0.327450i	−0.851616	−	0.524166i	$-0.824377\pi$
$107$	−3.38717	+	3.38717i	−0.327450	+	0.327450i	0.524166	+	0.851616i	$0.324377\pi$
$108$		0			0
$109$	−2.43964	−	2.43964i	−0.233675	−	0.233675i	0.580550	−	0.814225i	$-0.302838\pi$
$109$	−2.43964	−	2.43964i	−0.233675	−	0.233675i	−0.814225	+	0.580550i	$0.802838\pi$
$110$		0			0
$111$	−1.94373			−0.184491
$112$		0			0
$113$	−1.09801			−0.103292			−0.0516461	−	0.998665i	$-0.516447\pi$
$113$	−1.09801			−0.103292			−0.0516461	+	0.998665i	$0.516447\pi$
$114$		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
$127$	−1.51159			−0.134131			−0.0670657	−	0.997749i	$-0.521364\pi$
$127$	−1.51159			−0.134131			−0.0670657	+	0.997749i	$0.521364\pi$
$128$		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
$137$		−	3.38639i		−	0.289318i	−0.989482	−	0.144659i	$-0.953791\pi$
$137$		−	3.38639i		−	0.289318i	0.989482	−	0.144659i	$-0.0462086\pi$
$138$		0			0
$139$	2.09626	−	2.09626i	0.177802	−	0.177802i	−0.612595	−	0.790397i	$-0.709874\pi$
$139$	2.09626	−	2.09626i	0.177802	−	0.177802i	0.790397	+	0.612595i	$0.209874\pi$
$140$		0			0
$141$	−11.9080	−	11.9080i	−1.00283	−	1.00283i
$142$		0			0
$143$	3.19464			0.267149
$144$		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	−0.800392	−	0.599477i	$-0.795375\pi$
$149$	−2.45247	+	2.45247i	−0.200915	+	0.200915i	0.599477	+	0.800392i	$0.295375\pi$
$150$		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
$153$		−	29.5663i		−	2.39029i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−15.8377	−	15.8377i	−1.26398	−	1.26398i	−0.949145	−	0.314839i	$-0.898050\pi$
$157$	−15.8377	−	15.8377i	−1.26398	−	1.26398i	−0.314839	−	0.949145i	$-0.601950\pi$
$158$		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	$-0.380967\pi$
$163$	−7.22102	−	7.22102i	−0.565594	−	0.565594i	−0.930891	+	0.365297i	$0.880967\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			13.2304i			1.02380i	0.859044	+	0.511901i	$0.171059\pi$
$167$			13.2304i			1.02380i	−0.859044	+	0.511901i	$0.828941\pi$
$168$		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	$-0.467641\pi$
$173$	−11.7503	−	11.7503i	−0.893355	−	0.893355i	−0.994837	+	0.101482i	$0.967641\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.00712			−0.677017
$178$		0			0
$179$	−4.84732	−	4.84732i	−0.362306	−	0.362306i	0.502355	−	0.864661i	$-0.332467\pi$
$179$	−4.84732	−	4.84732i	−0.362306	−	0.362306i	−0.864661	+	0.502355i	$0.832467\pi$
$180$		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
$183$		−	2.41671i		−	0.178648i
$184$		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
$193$	20.8617			1.50166			0.750829	−	0.660496i	$-0.229654\pi$
$193$	20.8617			1.50166			0.750829	+	0.660496i	$0.229654\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.07707	+	2.07707i	−0.147985	+	0.147985i	−0.777217	−	0.629232i	$-0.783369\pi$
$197$	−2.07707	+	2.07707i	−0.147985	+	0.147985i	0.629232	+	0.777217i	$0.283369\pi$
$198$		0			0
$199$			23.2807i			1.65033i	0.564893	+	0.825164i	$0.308917\pi$
$199$			23.2807i			1.65033i	−0.564893	+	0.825164i	$0.691083\pi$
$200$		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
$207$	51.2315			3.56083
$208$		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
$217$			16.9456i			1.15034i
$218$		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
$223$	10.9088			0.730507			0.365253	−	0.930908i	$-0.380982\pi$
$223$	10.9088			0.730507			0.365253	+	0.930908i	$0.380982\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−11.6347	−	11.6347i	−0.772220	−	0.772220i	0.206275	−	0.978494i	$-0.433866\pi$
$227$	−11.6347	−	11.6347i	−0.772220	−	0.772220i	−0.978494	+	0.206275i	$0.933866\pi$
$228$		0			0
$229$	−1.60760	+	1.60760i	−0.106233	+	0.106233i	−0.758226	−	0.651992i	$-0.773933\pi$
$229$	−1.60760	+	1.60760i	−0.106233	+	0.106233i	0.651992	+	0.758226i	$0.273933\pi$
$230$		0			0
$231$		−	28.8371i		−	1.89734i
$232$		0			0
$233$		−	23.8100i		−	1.55985i	−0.625875	−	0.779924i	$-0.715258\pi$
$233$		−	23.8100i		−	1.55985i	0.625875	−	0.779924i	$-0.284742\pi$
$234$		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	$-0.497945\pi$
$239$	0.199630			0.0129130			0.00645649	+	0.999979i	$0.497945\pi$
$240$		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
$247$		−	5.53901i		−	0.352439i
$248$		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
$257$	19.8360			1.23733			0.618667	−	0.785653i	$-0.287673\pi$
$257$	19.8360			1.23733			0.618667	+	0.785653i	$0.287673\pi$
$258$		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
$263$			7.14438i			0.440542i	0.975439	+	0.220271i	$0.0706941\pi$
$263$			7.14438i			0.440542i	−0.975439	+	0.220271i	$0.929306\pi$
$264$		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	$0.137915\pi$
$269$	21.7716	+	21.7716i	1.32744	+	1.32744i	0.419844	+	0.907596i	$0.362085\pi$
$270$		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
$273$	11.3827			0.688915
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−20.4588	+	20.4588i	−1.22925	+	1.22925i	−0.265006	+	0.964247i	$0.585374\pi$
$277$	−20.4588	+	20.4588i	−1.22925	+	1.22925i	−0.964247	+	0.265006i	$0.914626\pi$
$278$		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	0.0824607	−	0.996594i	$-0.473722\pi$
$283$	18.1525	−	18.1525i	1.07906	−	1.07906i	0.996594	−	0.0824607i	$-0.0262779\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−13.2945			−0.784747
$288$		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	−0.688211	−	0.725511i	$-0.741603\pi$
$293$	0.638480	−	0.638480i	0.0373004	−	0.0373004i	0.725511	+	0.688211i	$0.241603\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	29.7126i		−	1.72410i
$298$		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
$303$	26.7266			1.53540
$304$		0			0
$305$		0			0
$306$		0			0
$307$	4.52224	+	4.52224i	0.258098	+	0.258098i	0.824280	−	0.566182i	$-0.191580\pi$
$307$	4.52224	+	4.52224i	0.258098	+	0.258098i	−0.566182	+	0.824280i	$0.691580\pi$
$308$		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
$313$		−	11.9204i		−	0.673779i	−0.941544	−	0.336889i	$-0.890625\pi$
$313$		−	11.9204i		−	0.673779i	0.941544	−	0.336889i	$-0.109375\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−17.6516	−	17.6516i	−0.991410	−	0.991410i	0.00855359	−	0.999963i	$-0.497277\pi$
$317$	−17.6516	−	17.6516i	−0.991410	−	0.991410i	−0.999963	+	0.00855359i	$0.997277\pi$
$318$		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
$327$		−	10.5811i		−	0.585138i
$328$		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
$337$	24.3167			1.32462			0.662308	−	0.749231i	$-0.269577\pi$
$337$	24.3167			1.32462			0.662308	+	0.749231i	$0.269577\pi$
$338$		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
$343$			10.1658i			0.548903i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	17.3818	−	17.3818i	0.933106	−	0.933106i	−0.0647931	−	0.997899i	$-0.520639\pi$
$347$	17.3818	−	17.3818i	0.933106	−	0.933106i	0.997899	+	0.0647931i	$0.0206387\pi$
$348$		0			0
$349$	−0.773103	−	0.773103i	−0.0413832	−	0.0413832i	0.686112	−	0.727496i	$-0.259316\pi$
$349$	−0.773103	−	0.773103i	−0.0413832	−	0.0413832i	−0.727496	+	0.686112i	$0.759316\pi$
$350$		0			0
$351$	11.7283			0.626010
$352$		0			0
$353$	−13.3720			−0.711720			−0.355860	−	0.934539i	$-0.615812\pi$
$353$	−13.3720			−0.711720			−0.355860	+	0.934539i	$0.615812\pi$
$354$		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	$-0.728520\pi$
$359$		−	28.5413i		−	1.50635i	0.657818	−	0.753177i	$-0.271480\pi$
$360$		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
$367$	−0.909186			−0.0474591			−0.0237296	−	0.999718i	$-0.507554\pi$
$367$	−0.909186			−0.0474591			−0.0237296	+	0.999718i	$0.507554\pi$
$368$		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	0.514946	−	0.857223i	$-0.327812\pi$
$373$	26.5010	−	26.5010i	1.37217	−	1.37217i	0.857223	−	0.514946i	$-0.172188\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			3.09780i			0.159545i
$378$		0			0
$379$	−1.23724	+	1.23724i	−0.0635529	+	0.0635529i	−0.738169	−	0.674616i	$-0.764309\pi$
$379$	−1.23724	+	1.23724i	−0.0635529	+	0.0635529i	0.674616	+	0.738169i	$0.264309\pi$
$380$		0			0
$381$	−3.27800	−	3.27800i	−0.167937	−	0.167937i
$382$		0			0
$383$	−15.7161			−0.803057			−0.401529	−	0.915846i	$-0.631521\pi$
$383$	−15.7161			−0.803057			−0.401529	+	0.915846i	$0.631521\pi$
$384$		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	−0.161457	−	0.986880i	$-0.551619\pi$
$389$	16.2799	−	16.2799i	0.825423	−	0.825423i	0.986880	+	0.161457i	$0.0516193\pi$
$390$		0			0
$391$			36.9168i			1.86696i
$392$		0			0
$393$			39.9740i			2.01642i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−22.8944	−	22.8944i	−1.14903	−	1.14903i	−0.986743	−	0.162292i	$-0.948111\pi$
$397$	−22.8944	−	22.8944i	−1.14903	−	1.14903i	−0.162292	−	0.986743i	$-0.551889\pi$
$398$		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
$407$		−	1.80305i		−	0.0893740i
$408$		0			0
$409$			10.0220i			0.495557i	0.968817	+	0.247779i	$0.0797006\pi$
$409$			10.0220i			0.495557i	−0.968817	+	0.247779i	$0.920299\pi$
$410$		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
$417$	9.09182			0.445228
$418$		0			0
$419$	−14.4998	−	14.4998i	−0.708362	−	0.708362i	0.257829	−	0.966191i	$-0.416993\pi$
$419$	−14.4998	−	14.4998i	−0.708362	−	0.708362i	−0.966191	+	0.257829i	$0.916993\pi$
$420$		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
$423$		−	35.1735i		−	1.71020i
$424$		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
$433$	14.5895			0.701128			0.350564	−	0.936539i	$-0.385990\pi$
$433$	14.5895			0.701128			0.350564	+	0.936539i	$0.385990\pi$
$434$		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	$0.0434458\pi$
$439$			5.70179i			0.272131i	−0.990700	+	0.136066i	$0.956554\pi$
$440$		0			0
$441$		−	25.1371i		−	1.19701i
$442$		0			0
$443$	5.03375	−	5.03375i	0.239161	−	0.239161i	−0.577342	−	0.816503i	$-0.695910\pi$
$443$	5.03375	−	5.03375i	0.239161	−	0.239161i	0.816503	+	0.577342i	$0.195910\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−10.6368			−0.503104
$448$		0			0
$449$	22.2502			1.05005			0.525025	−	0.851087i	$-0.324056\pi$
$449$	22.2502			1.05005			0.525025	+	0.851087i	$0.324056\pi$
$450$		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
$457$		−	8.92927i		−	0.417694i	−0.977948	−	0.208847i	$-0.933029\pi$
$457$		−	8.92927i		−	0.417694i	0.977948	−	0.208847i	$-0.0669710\pi$
$458$		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
$463$	−31.7058			−1.47349			−0.736747	−	0.676168i	$-0.763639\pi$
$463$	−31.7058			−1.47349			−0.736747	+	0.676168i	$0.763639\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.7683	−	17.7683i	−0.822219	−	0.822219i	0.164207	−	0.986426i	$-0.447494\pi$
$467$	−17.7683	−	17.7683i	−0.822219	−	0.822219i	−0.986426	+	0.164207i	$0.947494\pi$
$468$		0			0
$469$	2.10241	−	2.10241i	0.0970803	−	0.0970803i
$470$		0			0
$471$		−	68.6907i		−	3.16510i
$472$		0			0
$473$			19.9956i			0.919401i
$474$		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	$-0.442914\pi$
$479$	7.80806			0.356759			0.178380	+	0.983962i	$0.442914\pi$
$480$		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
$487$			27.6753i			1.25409i	0.778984	+	0.627044i	$0.215735\pi$
$487$			27.6753i			1.25409i	−0.778984	+	0.627044i	$0.784265\pi$
$488$		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
$497$	−22.6491			−1.01595
$498$		0			0
$499$	25.0477	+	25.0477i	1.12129	+	1.12129i	0.991548	+	0.129743i	$0.0414153\pi$
$499$	25.0477	+	25.0477i	1.12129	+	1.12129i	0.129743	+	0.991548i	$0.458585\pi$
$500$		0			0
$501$	−28.6914	+	28.6914i	−1.28184	+	1.28184i
$502$		0			0
$503$		−	22.8644i		−	1.01947i	−0.860331	−	0.509736i	$-0.829743\pi$
$503$		−	22.8644i		−	1.01947i	0.860331	−	0.509736i	$-0.170257\pi$
$504$		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	0.215710	−	0.976458i	$-0.430794\pi$
$509$	−17.1633	−	17.1633i	−0.760748	−	0.760748i	−0.976458	+	0.215710i	$0.930794\pi$
$510$		0			0
$511$	−34.7631			−1.53783
$512$		0			0
$513$	−51.5169			−2.27453
$514$		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	−0.118841	+	0.992913i	$0.537918\pi$
$523$	−25.4249	+	25.4249i	−1.11175	+	1.11175i	−0.992913	+	0.118841i	$0.962082\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−23.6647			−1.03085
$528$		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
$537$		−	21.0237i		−	0.907239i
$538$		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
$543$	45.8622			1.96814
$544$		0			0
$545$		0			0
$546$		0			0
$547$	28.3699	+	28.3699i	1.21301	+	1.21301i	0.970032	+	0.242979i	$0.0781246\pi$
$547$	28.3699	+	28.3699i	1.21301	+	1.21301i	0.242979	+	0.970032i	$0.421875\pi$
$548$		0			0
$549$	3.56921	−	3.56921i	0.152330	−	0.152330i
$550$		0			0
$551$		−	13.6072i		−	0.579685i
$552$		0			0
$553$			57.1815i			2.43161i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.7769	+	21.7769i	0.922718	+	0.922718i	0.997221	−	0.0745028i	$-0.0237370\pi$
$557$	21.7769	+	21.7769i	0.922718	+	0.922718i	−0.0745028	+	0.997221i	$0.523737\pi$
$558$		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	$-0.355329\pi$
$563$	−10.9022	−	10.9022i	−0.459473	−	0.459473i	−0.898482	+	0.439010i	$0.855329\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		−	42.3534i		−	1.77868i
$568$		0			0
$569$		−	31.1881i		−	1.30747i	−0.756723	−	0.653736i	$-0.773201\pi$
$569$		−	31.1881i		−	1.30747i	0.756723	−	0.653736i	$-0.226799\pi$
$570$		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
$577$	8.42524			0.350747			0.175374	−	0.984502i	$-0.443887\pi$
$577$	8.42524			0.350747			0.175374	+	0.984502i	$0.443887\pi$
$578$		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
$583$			13.4830i			0.558408i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.3370	−	19.3370i	0.798125	−	0.798125i	−0.184675	−	0.982800i	$-0.559123\pi$
$587$	19.3370	−	19.3370i	0.798125	−	0.798125i	0.982800	+	0.184675i	$0.0591231\pi$
$588$		0			0
$589$	17.8821	+	17.8821i	0.736818	+	0.736818i
$590$		0			0
$591$	−9.00862			−0.370565
$592$		0			0
$593$	18.1804			0.746580			0.373290	−	0.927715i	$-0.378230\pi$
$593$	18.1804			0.746580			0.373290	+	0.927715i	$0.378230\pi$
$594$		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	$-0.989288\pi$
$599$		−	1.64695i		−	0.0672927i	0.999434	−	0.0336463i	$-0.0107120\pi$
$600$		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
$607$	−15.6773			−0.636322			−0.318161	−	0.948037i	$-0.603065\pi$
$607$	−15.6773			−0.636322			−0.318161	+	0.948037i	$0.603065\pi$
$608$		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	−0.519487	−	0.854478i	$-0.673877\pi$
$613$	8.29399	−	8.29399i	0.334991	−	0.334991i	0.854478	+	0.519487i	$0.173877\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			20.3330i			0.818575i	0.912406	+	0.409287i	$0.134223\pi$
$617$			20.3330i			0.818575i	−0.912406	+	0.409287i	$0.865777\pi$
$618$		0			0
$619$	−12.5878	+	12.5878i	−0.505946	+	0.505946i	−0.913280	−	0.407333i	$-0.866459\pi$
$619$	−12.5878	+	12.5878i	−0.505946	+	0.505946i	0.407333	+	0.913280i	$0.366459\pi$
$620$		0			0
$621$	59.0667	+	59.0667i	2.37027	+	2.37027i
$622$		0			0
$623$	−25.1880			−1.00914
$624$		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
$633$			10.9117i			0.433702i
$634$		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	$-0.116043\pi$
$643$	14.6501	+	14.6501i	0.577743	+	0.577743i	−0.356538	+	0.934281i	$0.616043\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	16.2623i		−	0.639337i	−0.947530	−	0.319668i	$-0.896429\pi$
$647$		−	16.2623i		−	0.639337i	0.947530	−	0.319668i	$-0.103571\pi$
$648$		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	−0.953563	−	0.301194i	$-0.902615\pi$
$653$	−32.0639	−	32.0639i	−1.25476	−	1.25476i	−0.301194	−	0.953563i	$-0.597385\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−67.3717			−2.62842
$658$		0			0
$659$	7.04696	+	7.04696i	0.274511	+	0.274511i	0.830913	−	0.556402i	$-0.187819\pi$
$659$	7.04696	+	7.04696i	0.274511	+	0.274511i	−0.556402	+	0.830913i	$0.687819\pi$
$660$		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
$663$			15.8962i			0.617355i
$664$		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
$673$	−35.3380			−1.36218			−0.681090	−	0.732200i	$-0.738494\pi$
$673$	−35.3380			−1.36218			−0.681090	+	0.732200i	$0.738494\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.72259	+	7.72259i	−0.296803	+	0.296803i	−0.839760	−	0.542957i	$-0.817305\pi$
$677$	−7.72259	+	7.72259i	−0.296803	+	0.296803i	0.542957	+	0.839760i	$0.317305\pi$
$678$		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	−0.939502	−	0.342544i	$-0.888711\pi$
$683$	−15.6011	+	15.6011i	−0.596958	+	0.596958i	0.342544	+	0.939502i	$0.388711\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−6.97246			−0.266016
$688$		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
$697$		−	18.5659i		−	0.703234i
$698$		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
$703$	−3.12621			−0.117907
$704$		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	−0.511377	−	0.859356i	$-0.670864\pi$
$709$	9.26566	−	9.26566i	0.347979	−	0.347979i	0.859356	+	0.511377i	$0.170864\pi$
$710$		0			0
$711$			110.819i			4.15604i
$712$		0			0
$713$		−	41.0054i		−	1.53567i
$714$		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	$-0.775320\pi$
$719$	−40.8143			−1.52212			−0.761058	+	0.648684i	$0.775320\pi$
$720$		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
$727$		−	5.20944i		−	0.193208i	−0.995323	−	0.0966038i	$-0.969202\pi$
$727$		−	5.20944i		−	0.193208i	0.995323	−	0.0966038i	$-0.0307980\pi$
$728$		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	$-0.124536\pi$
$733$	14.7039	+	14.7039i	0.543099	+	0.543099i	−0.381337	+	0.924436i	$0.624536\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.55917			0.0942684
$738$		0			0
$739$	−7.68017	−	7.68017i	−0.282520	−	0.282520i	0.551594	−	0.834113i	$-0.314020\pi$
$739$	−7.68017	−	7.68017i	−0.282520	−	0.282520i	−0.834113	+	0.551594i	$0.814020\pi$
$740$		0			0
$741$	12.0118	−	12.0118i	0.441265	−	0.441265i
$742$		0			0
$743$		−	34.9882i		−	1.28359i	−0.766876	−	0.641796i	$-0.778190\pi$
$743$		−	34.9882i		−	1.28359i	0.766876	−	0.641796i	$-0.221810\pi$
$744$		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
$753$	26.4577			0.964174
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−22.1553	+	22.1553i	−0.805248	+	0.805248i	−0.983910	−	0.178663i	$-0.942823\pi$
$757$	−22.1553	+	22.1553i	−0.805248	+	0.805248i	0.178663	+	0.983910i	$0.442823\pi$
$758$		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
$767$	3.29802			0.119084
$768$		0			0
$769$	−41.1054			−1.48230			−0.741150	−	0.671339i	$-0.765719\pi$
$769$	−41.1054			−1.48230			−0.741150	+	0.671339i	$0.765719\pi$
$770$		0			0
$771$	43.0160	+	43.0160i	1.54918	+	1.54918i
$772$		0			0
$773$	−10.8044	+	10.8044i	−0.388607	+	0.388607i	−0.874190	−	0.485583i	$-0.838607\pi$
$773$	−10.8044	+	10.8044i	−0.388607	+	0.388607i	0.485583	+	0.874190i	$0.338607\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	6.42440i		−	0.230474i
$778$		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
$783$	28.8118			1.02965
$784$		0			0
$785$		0			0
$786$		0			0
$787$	11.7496	+	11.7496i	0.418826	+	0.418826i	0.884799	−	0.465973i	$-0.154296\pi$
$787$	11.7496	+	11.7496i	0.418826	+	0.418826i	−0.465973	+	0.884799i	$0.654296\pi$
$788$		0			0
$789$	−15.4932	+	15.4932i	−0.551573	+	0.551573i
$790$		0			0
$791$		−	3.62914i		−	0.129037i
$792$		0			0
$793$			0.884894i			0.0314235i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.9126	−	15.9126i	−0.563652	−	0.563652i	0.366691	−	0.930343i	$-0.380491\pi$
$797$	−15.9126	−	15.9126i	−0.563652	−	0.563652i	−0.930343	+	0.366691i	$0.880491\pi$
$798$		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
$807$			94.4274i			3.32400i
$808$		0			0
$809$		−	9.06814i		−	0.318819i	−0.987213	−	0.159409i	$-0.949041\pi$
$809$		−	9.06814i		−	0.318819i	0.987213	−	0.159409i	$-0.0509590\pi$
$810$		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
$817$	34.6693			1.21293
$818$		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
$823$			25.3535i			0.883767i	0.897072	+	0.441884i	$0.145690\pi$
$823$			25.3535i			0.883767i	−0.897072	+	0.441884i	$0.854310\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	15.3396	−	15.3396i	0.533410	−	0.533410i	−0.388176	−	0.921585i	$-0.626895\pi$
$827$	15.3396	−	15.3396i	0.533410	−	0.533410i	0.921585	+	0.388176i	$0.126895\pi$
$828$		0			0
$829$	37.2546	+	37.2546i	1.29391	+	1.29391i	0.932351	+	0.361555i	$0.117754\pi$
$829$	37.2546	+	37.2546i	1.29391	+	1.29391i	0.361555	+	0.932351i	$0.382246\pi$
$830$		0			0
$831$	−88.7335			−3.07813
$832$		0			0
$833$	18.1135			0.627596
$834$		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	$0.100349\pi$
$839$			17.9621i			0.620120i	−0.950717	+	0.310060i	$0.899651\pi$
$840$		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
$847$	−9.60708			−0.330103
$848$		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	−0.529946	−	0.848032i	$-0.677788\pi$
$853$	9.29007	−	9.29007i	0.318086	−	0.318086i	0.848032	+	0.529946i	$0.177788\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			10.3997i			0.355246i	0.984099	+	0.177623i	$0.0568407\pi$
$857$			10.3997i			0.355246i	−0.984099	+	0.177623i	$0.943159\pi$
$858$		0			0
$859$	−15.3452	+	15.3452i	−0.523571	+	0.523571i	−0.918648	−	0.395077i	$-0.870718\pi$
$859$	−15.3452	+	15.3452i	−0.523571	+	0.523571i	0.395077	+	0.918648i	$0.370718\pi$
$860$		0			0
$861$	−28.8302	−	28.8302i	−0.982530	−	0.982530i
$862$		0			0
$863$	8.81329			0.300008			0.150004	−	0.988685i	$-0.452071\pi$
$863$	8.81329			0.300008			0.150004	+	0.988685i	$0.452071\pi$
$864$		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
$873$		−	4.54205i		−	0.153725i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	5.68862	+	5.68862i	0.192091	+	0.192091i	0.796599	−	0.604508i	$-0.206630\pi$
$877$	5.68862	+	5.68862i	0.192091	+	0.192091i	−0.604508	+	0.796599i	$0.706630\pi$
$878$		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	$-0.402334\pi$
$883$	−19.3524	−	19.3524i	−0.651262	−	0.651262i	−0.953297	+	0.302035i	$0.902334\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$			12.7863i			0.429323i	0.976689	+	0.214661i	$0.0688648\pi$
$887$			12.7863i			0.429323i	−0.976689	+	0.214661i	$0.931135\pi$
$888$		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
$897$	−27.5443			−0.919678
$898$		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
$903$			71.2459i			2.37091i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−2.88449	+	2.88449i	−0.0957780	+	0.0957780i	−0.753372	−	0.657594i	$-0.771574\pi$
$907$	−2.88449	+	2.88449i	−0.0957780	+	0.0957780i	0.657594	+	0.753372i	$0.271574\pi$
$908$		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
$913$	−38.1412			−1.26229
$914$		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	$-0.870417\pi$
$919$		−	24.0062i		−	0.791893i	0.918274	−	0.395946i	$-0.129583\pi$
$920$		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
$927$	−102.111			−3.35376
$928$		0			0
$929$	15.1568			0.497279			0.248639	−	0.968596i	$-0.420017\pi$
$929$	15.1568			0.497279			0.248639	+	0.968596i	$0.420017\pi$
$930$		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
$937$			39.9323i			1.30453i	0.757991	+	0.652266i	$0.226181\pi$
$937$			39.9323i			1.30453i	−0.757991	+	0.652266i	$0.773819\pi$
$938$		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
$943$	32.1704			1.04761
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.2944	−	16.2944i	−0.529498	−	0.529498i	0.390925	−	0.920423i	$-0.372155\pi$
$947$	−16.2944	−	16.2944i	−0.529498	−	0.529498i	−0.920423	+	0.390925i	$0.872155\pi$
$948$		0			0
$949$	8.35152	−	8.35152i	0.271102	−	0.271102i
$950$		0			0
$951$		−	76.5578i		−	2.48256i
$952$		0			0
$953$		−	12.0232i		−	0.389468i	−0.980856	−	0.194734i	$-0.937616\pi$
$953$		−	12.0232i		−	0.389468i	0.980856	−	0.194734i	$-0.0623844\pi$
$954$		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
$967$		−	43.8237i		−	1.40927i	−0.709568	−	0.704637i	$-0.751110\pi$
$967$		−	43.8237i		−	1.40927i	0.709568	−	0.704637i	$-0.248890\pi$
$968$		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
$977$	−0.204913			−0.00655576			−0.00327788	−	0.999995i	$-0.501043\pi$
$977$	−0.204913			−0.00655576			−0.00327788	+	0.999995i	$0.501043\pi$
$978$		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
$983$		−	34.0060i		−	1.08462i	−0.840177	−	0.542312i	$-0.817549\pi$
$983$		−	34.0060i		−	1.08462i	0.840177	−	0.542312i	$-0.182451\pi$
$984$		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
$993$	108.336			3.43794
$994$		0			0
$995$		0			0
$996$		0			0
$997$	6.37875	−	6.37875i	0.202017	−	0.202017i	−0.598847	−	0.800864i	$-0.704374\pi$
$997$	6.37875	−	6.37875i	0.202017	−	0.202017i	0.800864	+	0.598847i	$0.204374\pi$
$998$		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.l.g.401.6		12
4.3	odd	2		400.2.l.f.301.4	yes	12
5.2	odd	4		1600.2.q.f.849.6		12
5.3	odd	4		1600.2.q.e.849.1		12
5.4	even	2		1600.2.l.f.401.1		12
16.5	even	4	inner	1600.2.l.g.1201.6		12
16.11	odd	4		400.2.l.f.101.4	✓	12
20.3	even	4		400.2.q.e.349.6		12
20.7	even	4		400.2.q.f.349.1		12
20.19	odd	2		400.2.l.g.301.3	yes	12
80.27	even	4		400.2.q.e.149.6		12
80.37	odd	4		1600.2.q.e.49.1		12
80.43	even	4		400.2.q.f.149.1		12
80.53	odd	4		1600.2.q.f.49.6		12
80.59	odd	4		400.2.l.g.101.3	yes	12
80.69	even	4		1600.2.l.f.1201.1		12

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

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.l (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.16859 + 2.16859i) q^{3} +3.30519i q^{7} +6.40553i q^{9} +O(q^{10})\)	\(q+(2.16859 + 2.16859i) q^{3} +3.30519i q^{7} +6.40553i q^{9} +(-2.01163 + 2.01163i) q^{11} +(-0.794042 - 0.794042i) q^{13} -4.61575 q^{17} +(3.48786 + 3.48786i) q^{19} +(-7.16759 + 7.16759i) q^{21} -7.99801i q^{23} +(-7.38518 + 7.38518i) q^{27} +(-1.95065 - 1.95065i) q^{29} +5.12695 q^{31} -8.72480 q^{33} +(-0.448156 + 0.448156i) q^{37} -3.44390i q^{39} +4.02230i q^{41} +(4.97000 - 4.97000i) q^{43} -5.49112 q^{47} -3.92429 q^{49} +(-10.0096 - 10.0096i) q^{51} +(3.35125 - 3.35125i) q^{53} +15.1274i q^{57} +(-2.07673 + 2.07673i) q^{59} +(-0.557208 - 0.557208i) q^{61} -21.1715 q^{63} +(-0.636094 - 0.636094i) q^{67} +(17.3444 - 17.3444i) q^{69} +6.85258i q^{71} +10.5177i q^{73} +(-6.64883 - 6.64883i) q^{77} +17.3005 q^{79} -12.8142 q^{81} +(9.48015 + 9.48015i) q^{83} -8.46030i q^{87} +7.62073i q^{89} +(2.62446 - 2.62446i) q^{91} +(11.1182 + 11.1182i) q^{93} -0.709082 q^{97} +(-12.8856 - 12.8856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{3}+O(q^{10}) \) 12 * q + 2 * q^3	\( 12 q + 2 q^{3} + 2 q^{11} + 4 q^{13} + 8 q^{17} + 14 q^{19} - 20 q^{21} - 10 q^{27} + 4 q^{31} - 28 q^{33} - 8 q^{37} + 8 q^{47} + 4 q^{49} - 10 q^{51} + 16 q^{53} - 20 q^{59} + 4 q^{61} - 8 q^{63} + 50 q^{67} + 8 q^{77} - 12 q^{79} - 8 q^{81} - 2 q^{83} + 44 q^{93} - 12 q^{99}+O(q^{100}) \) 12 * q + 2 * q^3 + 2 * q^11 + 4 * q^13 + 8 * q^17 + 14 * q^19 - 20 * q^21 - 10 * q^27 + 4 * q^31 - 28 * q^33 - 8 * q^37 + 8 * q^47 + 4 * q^49 - 10 * q^51 + 16 * q^53 - 20 * q^59 + 4 * q^61 - 8 * q^63 + 50 * q^67 + 8 * q^77 - 12 * q^79 - 8 * q^81 - 2 * q^83 + 44 * q^93 - 12 * q^99

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