LMFDB - Embedded newform 1600.2.q.f.49.6

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			49.6
Root			$0.618969 - 1.27156i$ of defining polynomial
Character	$\chi$	$=$	1600.49
Dual form			1600.2.q.f.849.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.16859 + 2.16859i) q^{3} -3.30519 q^{7} +6.40553i q^{9} +O(q^{10})$	$q+(2.16859 + 2.16859i) q^{3} -3.30519 q^{7} +6.40553i q^{9} +(-2.01163 - 2.01163i) q^{11} +(-0.794042 - 0.794042i) q^{13} +4.61575i q^{17} +(-3.48786 + 3.48786i) q^{19} +(-7.16759 - 7.16759i) q^{21} -7.99801 q^{23} +(-7.38518 + 7.38518i) q^{27} +(1.95065 - 1.95065i) q^{29} +5.12695 q^{31} -8.72480i q^{33} +(-0.448156 + 0.448156i) q^{37} -3.44390i q^{39} -4.02230i q^{41} +(-4.97000 + 4.97000i) q^{43} +5.49112i q^{47} +3.92429 q^{49} +(-10.0096 + 10.0096i) q^{51} +(-3.35125 + 3.35125i) q^{53} -15.1274 q^{57} +(2.07673 + 2.07673i) q^{59} +(-0.557208 + 0.557208i) q^{61} -21.1715i q^{63} +(0.636094 + 0.636094i) q^{67} +(-17.3444 - 17.3444i) q^{69} -6.85258i q^{71} +10.5177 q^{73} +(6.64883 + 6.64883i) q^{77} -17.3005 q^{79} -12.8142 q^{81} +(9.48015 + 9.48015i) q^{83} +8.46030 q^{87} +7.62073i q^{89} +(2.62446 + 2.62446i) q^{91} +(11.1182 + 11.1182i) q^{93} +0.709082i q^{97} +(12.8856 - 12.8856i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

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

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
$7$	−3.30519			−1.24924			−0.624622	−	0.780927i	$-0.714747\pi$
$7$	−3.30519			−1.24924			−0.624622	+	0.780927i	$0.714747\pi$
$8$		0			0
$9$			6.40553i			2.13518i
$10$		0			0
$11$	−2.01163	−	2.01163i	−0.606530	−	0.606530i	0.335507	−	0.942038i	$-0.391092\pi$
$11$	−2.01163	−	2.01163i	−0.606530	−	0.606530i	−0.942038	+	0.335507i	$0.891092\pi$
$12$		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
$17$			4.61575i			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	−0.983122	−	0.182953i	$-0.941434\pi$
$19$	−3.48786	+	3.48786i	−0.800169	+	0.800169i	0.182953	+	0.983122i	$0.441434\pi$
$20$		0			0
$21$	−7.16759	−	7.16759i	−1.56410	−	1.56410i
$22$		0			0
$23$	−7.99801			−1.66770			−0.833850	−	0.551991i	$-0.813868\pi$
$23$	−7.99801			−1.66770			−0.833850	+	0.551991i	$0.813868\pi$
$24$		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	$-0.667552\pi$
$29$	1.95065	−	1.95065i	0.362227	−	0.362227i	0.864632	+	0.502406i	$0.167552\pi$
$30$		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	$-0.766591\pi$
$37$	−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	$-0.898301\pi$
$41$		−	4.02230i		−	0.628177i	0.949394	−	0.314089i	$-0.101699\pi$
$42$		0			0
$43$	−4.97000	+	4.97000i	−0.757918	+	0.757918i	−0.975943	−	0.218025i	$-0.930039\pi$
$43$	−4.97000	+	4.97000i	−0.757918	+	0.757918i	0.218025	+	0.975943i	$0.430039\pi$
$44$		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	$-0.855533\pi$
$53$	−3.35125	+	3.35125i	−0.460330	+	0.460330i	0.438434	+	0.898763i	$0.355533\pi$
$54$		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	0.829248	−	0.558881i	$-0.188769\pi$
$59$	2.07673	+	2.07673i	0.270367	+	0.270367i	−0.558881	+	0.829248i	$0.688769\pi$
$60$		0			0
$61$	−0.557208	+	0.557208i	−0.0713432	+	0.0713432i	−0.741878	−	0.670535i	$-0.766065\pi$
$61$	−0.557208	+	0.557208i	−0.0713432	+	0.0713432i	0.670535	+	0.741878i	$0.266065\pi$
$62$		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	$-0.232500\pi$
$67$	0.636094	+	0.636094i	0.0777112	+	0.0777112i	−0.667183	+	0.744894i	$0.732500\pi$
$68$		0			0
$69$	−17.3444	−	17.3444i	−2.08802	−	2.08802i
$70$		0			0
$71$		−	6.85258i		−	0.813252i	−0.913595	−	0.406626i	$-0.866705\pi$
$71$		−	6.85258i		−	0.813252i	0.913595	−	0.406626i	$-0.133295\pi$
$72$		0			0
$73$	10.5177			1.23101			0.615504	−	0.788134i	$-0.288953\pi$
$73$	10.5177			1.23101			0.615504	+	0.788134i	$0.288953\pi$
$74$		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	0.999141	+	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
$87$	8.46030			0.907040
$88$		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
$97$			0.709082i			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	0.943769	−	0.330605i	$-0.107253\pi$
$101$	6.16223	+	6.16223i	0.613164	+	0.613164i	−0.330605	+	0.943769i	$0.607253\pi$
$102$		0			0
$103$	15.9410			1.57072			0.785359	−	0.619040i	$-0.212478\pi$
$103$	15.9410			1.57072			0.785359	+	0.619040i	$0.212478\pi$
$104$		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	$-0.697162\pi$
$109$	2.43964	−	2.43964i	0.233675	−	0.233675i	0.814225	+	0.580550i	$0.197162\pi$
$110$		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	−0.178654	−	0.983912i	$-0.557174\pi$
$131$	9.21660	−	9.21660i	0.805258	−	0.805258i	0.983912	+	0.178654i	$0.0571743\pi$
$132$		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	$-0.453791\pi$
$137$	3.38639			0.289318			0.144659	+	0.989482i	$0.453791\pi$
$138$		0			0
$139$	−2.09626	−	2.09626i	−0.177802	−	0.177802i	0.612595	−	0.790397i	$-0.290126\pi$
$139$	−2.09626	−	2.09626i	−0.177802	−	0.177802i	−0.790397	+	0.612595i	$0.790126\pi$
$140$		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	0.800392	−	0.599477i	$-0.204625\pi$
$149$	2.45247	+	2.45247i	0.200915	+	0.200915i	−0.599477	+	0.800392i	$0.704625\pi$
$150$		0			0
$151$		−	1.11727i		−	0.0909222i	−0.998966	−	0.0454611i	$-0.985524\pi$
$151$		−	1.11727i		−	0.0909222i	0.998966	−	0.0454611i	$-0.0144757\pi$
$152$		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	0.949145	+	0.314839i	$0.101950\pi$
$157$	15.8377	+	15.8377i	1.26398	+	1.26398i	0.314839	+	0.949145i	$0.398050\pi$
$158$		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
$167$	−13.2304			−1.02380			−0.511901	−	0.859044i	$-0.671059\pi$
$167$	−13.2304			−1.02380			−0.511901	+	0.859044i	$0.671059\pi$
$168$		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
$177$			9.00712i			0.677017i
$178$		0			0
$179$	4.84732	−	4.84732i	0.362306	−	0.362306i	−0.502355	−	0.864661i	$-0.667533\pi$
$179$	4.84732	−	4.84732i	0.362306	−	0.362306i	0.864661	+	0.502355i	$0.167533\pi$
$180$		0			0
$181$	10.5742	+	10.5742i	0.785976	+	0.785976i	0.980832	−	0.194856i	$-0.0624240\pi$
$181$	10.5742	+	10.5742i	0.785976	+	0.785976i	−0.194856	+	0.980832i	$0.562424\pi$
$182$		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	$-0.783369\pi$
$197$	−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
$207$		−	51.2315i		−	3.56083i
$208$		0			0
$209$	14.0326			0.970653
$210$		0			0
$211$	2.51586	−	2.51586i	0.173199	−	0.173199i	−0.615184	−	0.788383i	$-0.710918\pi$
$211$	2.51586	−	2.51586i	0.173199	−	0.173199i	0.788383	+	0.615184i	$0.210918\pi$
$212$		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	$-0.0661340\pi$
$227$	11.6347	+	11.6347i	0.772220	+	0.772220i	−0.206275	+	0.978494i	$0.566134\pi$
$228$		0			0
$229$	1.60760	+	1.60760i	0.106233	+	0.106233i	0.758226	−	0.651992i	$-0.226067\pi$
$229$	1.60760	+	1.60760i	0.106233	+	0.106233i	−0.651992	+	0.758226i	$0.726067\pi$
$230$		0			0
$231$			28.8371i			1.89734i
$232$		0			0
$233$	−23.8100			−1.55985			−0.779924	−	0.625875i	$-0.784742\pi$
$233$	−23.8100			−1.55985			−0.779924	+	0.625875i	$0.784742\pi$
$234$		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	0.872915	−	0.487872i	$-0.162227\pi$
$251$	6.10023	+	6.10023i	0.385043	+	0.385043i	−0.487872	+	0.872915i	$0.662227\pi$
$252$		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	$-0.429306\pi$
$263$	7.14438			0.440542			0.220271	+	0.975439i	$0.429306\pi$
$264$		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	−0.419844	+	0.907596i	$0.637915\pi$
$269$	−21.7716	+	21.7716i	−1.32744	+	1.32744i	−0.907596	+	0.419844i	$0.862085\pi$
$270$		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	−0.265006	+	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	$-0.823542\pi$
$281$		−	17.6481i		−	1.05280i	0.850239	−	0.526398i	$-0.176458\pi$
$282$		0			0
$283$	−18.1525	+	18.1525i	−1.07906	+	1.07906i	−0.0824607	+	0.996594i	$0.526278\pi$
$283$	−18.1525	+	18.1525i	−1.07906	+	1.07906i	−0.996594	+	0.0824607i	$0.973722\pi$
$284$		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	$-0.758397\pi$
$293$	−0.638480	+	0.638480i	−0.0373004	+	0.0373004i	0.688211	+	0.725511i	$0.258397\pi$
$294$		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	$-0.308420\pi$
$307$	−4.52224	−	4.52224i	−0.258098	−	0.258098i	−0.824280	+	0.566182i	$0.808420\pi$
$308$		0			0
$309$	34.5695	+	34.5695i	1.96659	+	1.96659i
$310$		0			0
$311$		−	14.1014i		−	0.799620i	−0.916598	−	0.399810i	$-0.869076\pi$
$311$		−	14.1014i		−	0.799620i	0.916598	−	0.399810i	$-0.130924\pi$
$312$		0			0
$313$	−11.9204			−0.673779			−0.336889	−	0.941544i	$-0.609375\pi$
$313$	−11.9204			−0.673779			−0.336889	+	0.941544i	$0.609375\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	17.6516	+	17.6516i	0.991410	+	0.991410i	0.999963	−	0.00855359i	$-0.00272272\pi$
$317$	17.6516	+	17.6516i	0.991410	+	0.991410i	−0.00855359	+	0.999963i	$0.502723\pi$
$318$		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	0.856053	+	0.516888i	$0.172910\pi$
$331$	24.9785	+	24.9785i	1.37294	+	1.37294i	0.516888	+	0.856053i	$0.327090\pi$
$332$		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	$-0.520639\pi$
$347$	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	$-0.740684\pi$
$349$	0.773103	−	0.773103i	0.0413832	−	0.0413832i	0.727496	+	0.686112i	$0.240684\pi$
$350$		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	$-0.728520\pi$
$359$		−	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
$367$			0.909186i			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	−0.514946	+	0.857223i	$0.672188\pi$
$373$	−26.5010	+	26.5010i	−1.37217	+	1.37217i	−0.857223	+	0.514946i	$0.827812\pi$
$374$		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	0.738169	−	0.674616i	$-0.235691\pi$
$379$	1.23724	+	1.23724i	0.0635529	+	0.0635529i	−0.674616	+	0.738169i	$0.735691\pi$
$380$		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	0.161457	−	0.986880i	$-0.448381\pi$
$389$	−16.2799	−	16.2799i	−0.825423	−	0.825423i	−0.986880	+	0.161457i	$0.948381\pi$
$390$		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	0.986743	+	0.162292i	$0.0518887\pi$
$397$	22.8944	+	22.8944i	1.14903	+	1.14903i	0.162292	+	0.986743i	$0.448111\pi$
$398$		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	$0.0797006\pi$
$409$			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
$417$		−	9.09182i		−	0.445228i
$418$		0			0
$419$	14.4998	−	14.4998i	0.708362	−	0.708362i	−0.257829	−	0.966191i	$-0.583007\pi$
$419$	14.4998	−	14.4998i	0.708362	−	0.708362i	0.966191	+	0.257829i	$0.0830071\pi$
$420$		0			0
$421$	12.9983	+	12.9983i	0.633498	+	0.633498i	0.948944	−	0.315446i	$-0.102154\pi$
$421$	12.9983	+	12.9983i	0.633498	+	0.633498i	−0.315446	+	0.948944i	$0.602154\pi$
$422$		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	$0.0434458\pi$
$439$			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	−0.816503	−	0.577342i	$-0.804090\pi$
$443$	−5.03375	+	5.03375i	−0.239161	+	0.239161i	0.577342	+	0.816503i	$0.304090\pi$
$444$		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	$-0.433029\pi$
$457$	8.92927			0.417694			0.208847	+	0.977948i	$0.433029\pi$
$458$		0			0
$459$	−34.0881	−	34.0881i	−1.59110	−	1.59110i
$460$		0			0
$461$	−8.14776	+	8.14776i	−0.379479	+	0.379479i	−0.870914	−	0.491435i	$-0.836472\pi$
$461$	−8.14776	+	8.14776i	−0.379479	+	0.379479i	0.491435	+	0.870914i	$0.336472\pi$
$462$		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	$-0.0525065\pi$
$467$	17.7683	+	17.7683i	0.822219	+	0.822219i	−0.164207	+	0.986426i	$0.552506\pi$
$468$		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	$-0.715735\pi$
$487$	−27.6753			−1.25409			−0.627044	+	0.778984i	$0.715735\pi$
$488$		0			0
$489$		−	31.3188i		−	1.41629i
$490$		0			0
$491$	11.7995	+	11.7995i	0.532505	+	0.532505i	0.921317	−	0.388812i	$-0.127114\pi$
$491$	11.7995	+	11.7995i	0.532505	+	0.532505i	−0.388812	+	0.921317i	$0.627114\pi$
$492$		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	−0.129743	+	0.991548i	$0.541415\pi$
$499$	−25.0477	+	25.0477i	−1.12129	+	1.12129i	−0.991548	+	0.129743i	$0.958585\pi$
$500$		0			0
$501$	−28.6914	−	28.6914i	−1.28184	−	1.28184i
$502$		0			0
$503$	−22.8644			−1.01947			−0.509736	−	0.860331i	$-0.670257\pi$
$503$	−22.8644			−1.01947			−0.509736	+	0.860331i	$0.670257\pi$
$504$		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	$-0.569206\pi$
$509$	17.1633	−	17.1633i	0.760748	−	0.760748i	0.976458	+	0.215710i	$0.0692065\pi$
$510$		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	$0.0812077\pi$
$521$			11.5206i			0.504726i	−0.967633	+	0.252363i	$0.918792\pi$
$522$		0			0
$523$	25.4249	−	25.4249i	1.11175	−	1.11175i	0.118841	−	0.992913i	$-0.462082\pi$
$523$	25.4249	−	25.4249i	1.11175	−	1.11175i	0.992913	−	0.118841i	$-0.0379180\pi$
$524$		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	−0.341196	+	0.939992i	$0.610832\pi$
$541$	−29.7997	+	29.7997i	−1.28119	+	1.28119i	−0.939992	+	0.341196i	$0.889168\pi$
$542$		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	−0.970032	−	0.242979i	$-0.921875\pi$
$547$	−28.3699	−	28.3699i	−1.21301	−	1.21301i	−0.242979	−	0.970032i	$-0.578125\pi$
$548$		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	$-0.476263\pi$
$557$	−21.7769	−	21.7769i	−0.922718	−	0.922718i	−0.997221	+	0.0745028i	$0.976263\pi$
$558$		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
$567$	42.3534			1.77868
$568$		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	0.751710	−	0.659494i	$-0.229230\pi$
$571$	2.20354	+	2.20354i	0.0922153	+	0.0922153i	−0.659494	+	0.751710i	$0.729230\pi$
$572$		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	$-0.559123\pi$
$587$	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
$593$			18.1804i			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	$-0.989288\pi$
$599$		−	1.64695i		−	0.0672927i	0.999434	−	0.0336463i	$-0.0107120\pi$
$600$		0			0
$601$			12.7485i			0.520021i	0.965606	+	0.260011i	$0.0837261\pi$
$601$			12.7485i			0.520021i	−0.965606	+	0.260011i	$0.916274\pi$
$602$		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	$-0.826123\pi$
$613$	−8.29399	+	8.29399i	−0.334991	+	0.334991i	0.519487	+	0.854478i	$0.326123\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.3330			−0.818575			−0.409287	−	0.912406i	$-0.634223\pi$
$617$	−20.3330			−0.818575			−0.409287	+	0.912406i	$0.634223\pi$
$618$		0			0
$619$	12.5878	+	12.5878i	0.505946	+	0.505946i	0.913280	−	0.407333i	$-0.133541\pi$
$619$	12.5878	+	12.5878i	0.505946	+	0.505946i	−0.407333	+	0.913280i	$0.633541\pi$
$620$		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	$-0.859315\pi$
$631$		−	21.4887i		−	0.855453i	0.903908	−	0.427726i	$-0.140685\pi$
$632$		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	$-0.116043\pi$
$643$	14.6501	+	14.6501i	0.577743	+	0.577743i	−0.356538	+	0.934281i	$0.616043\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.2623			0.639337			0.319668	−	0.947530i	$-0.396429\pi$
$647$	16.2623			0.639337			0.319668	+	0.947530i	$0.396429\pi$
$648$		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
$657$			67.3717i			2.62842i
$658$		0			0
$659$	−7.04696	+	7.04696i	−0.274511	+	0.274511i	−0.830913	−	0.556402i	$-0.812181\pi$
$659$	−7.04696	+	7.04696i	−0.274511	+	0.274511i	0.556402	+	0.830913i	$0.312181\pi$
$660$		0			0
$661$	5.78655	+	5.78655i	0.225071	+	0.225071i	0.810630	−	0.585559i	$-0.199125\pi$
$661$	5.78655	+	5.78655i	0.225071	+	0.225071i	−0.585559	+	0.810630i	$0.699125\pi$
$662$		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	$-0.817305\pi$
$677$	−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	−0.342544	−	0.939502i	$-0.611289\pi$
$683$	15.6011	−	15.6011i	0.596958	−	0.596958i	0.939502	+	0.342544i	$0.111289\pi$
$684$		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	−0.157433	+	0.987530i	$0.550322\pi$
$691$	−30.0975	+	30.0975i	−1.14496	+	1.14496i	−0.987530	+	0.157433i	$0.949678\pi$
$692$		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	−0.369623	−	0.929182i	$-0.620513\pi$
$701$	14.8151	−	14.8151i	0.559559	−	0.559559i	0.929182	+	0.369623i	$0.120513\pi$
$702$		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	0.511377	−	0.859356i	$-0.329136\pi$
$709$	−9.26566	−	9.26566i	−0.347979	−	0.347979i	−0.859356	+	0.511377i	$0.829136\pi$
$710$		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	$-0.469202\pi$
$727$	5.20944			0.193208			0.0966038	+	0.995323i	$0.469202\pi$
$728$		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
$737$		−	2.55917i		−	0.0942684i
$738$		0			0
$739$	7.68017	−	7.68017i	0.282520	−	0.282520i	−0.551594	−	0.834113i	$-0.685980\pi$
$739$	7.68017	−	7.68017i	0.282520	−	0.282520i	0.834113	+	0.551594i	$0.185980\pi$
$740$		0			0
$741$	12.0118	+	12.0118i	0.441265	+	0.441265i
$742$		0			0
$743$	−34.9882			−1.28359			−0.641796	−	0.766876i	$-0.721810\pi$
$743$	−34.9882			−1.28359			−0.641796	+	0.766876i	$0.721810\pi$
$744$		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	$-0.942823\pi$
$757$	−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	$-0.662443\pi$
$761$		−	48.1426i		−	1.74517i	0.488466	−	0.872583i	$-0.337557\pi$
$762$		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	$-0.661393\pi$
$773$	10.8044	−	10.8044i	0.388607	−	0.388607i	0.874190	+	0.485583i	$0.161393\pi$
$774$		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	$-0.345704\pi$
$787$	−11.7496	−	11.7496i	−0.418826	−	0.418826i	−0.884799	+	0.465973i	$0.845704\pi$
$788$		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	$-0.119509\pi$
$797$	15.9126	+	15.9126i	0.563652	+	0.563652i	−0.366691	+	0.930343i	$0.619509\pi$
$798$		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	$-0.949041\pi$
$809$		−	9.06814i		−	0.318819i	0.987213	−	0.159409i	$-0.0509590\pi$
$810$		0			0
$811$	17.0825	+	17.0825i	0.599849	+	0.599849i	0.940272	−	0.340424i	$-0.110570\pi$
$811$	17.0825	+	17.0825i	0.599849	+	0.599849i	−0.340424	+	0.940272i	$0.610570\pi$
$812$		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	0.948082	−	0.318026i	$-0.103020\pi$
$821$	18.0531	+	18.0531i	0.630057	+	0.630057i	−0.318026	+	0.948082i	$0.603020\pi$
$822$		0			0
$823$	25.3535			0.883767			0.441884	−	0.897072i	$-0.354310\pi$
$823$	25.3535			0.883767			0.441884	+	0.897072i	$0.354310\pi$
$824$		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	−0.361555	+	0.932351i	$0.617754\pi$
$829$	−37.2546	+	37.2546i	−1.29391	+	1.29391i	−0.932351	+	0.361555i	$0.882246\pi$
$830$		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	$0.100349\pi$
$839$			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
$847$			9.60708i			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	$-0.822212\pi$
$853$	−9.29007	+	9.29007i	−0.318086	+	0.318086i	0.529946	+	0.848032i	$0.322212\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.3997			−0.355246			−0.177623	−	0.984099i	$-0.556841\pi$
$857$	−10.3997			−0.355246			−0.177623	+	0.984099i	$0.556841\pi$
$858$		0			0
$859$	15.3452	+	15.3452i	0.523571	+	0.523571i	0.918648	−	0.395077i	$-0.129282\pi$
$859$	15.3452	+	15.3452i	0.523571	+	0.523571i	−0.395077	+	0.918648i	$0.629282\pi$
$860$		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	$-0.293370\pi$
$877$	−5.68862	−	5.68862i	−0.192091	−	0.192091i	−0.796599	+	0.604508i	$0.793370\pi$
$878$		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
$887$	−12.7863			−0.429323			−0.214661	−	0.976689i	$-0.568865\pi$
$887$	−12.7863			−0.429323			−0.214661	+	0.976689i	$0.568865\pi$
$888$		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	$-0.771574\pi$
$907$	−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
$913$		−	38.1412i		−	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	$-0.870417\pi$
$919$		−	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
$927$			102.111i			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	$-0.726181\pi$
$937$	−39.9323			−1.30453			−0.652266	+	0.757991i	$0.726181\pi$
$938$		0			0
$939$	−25.8503	−	25.8503i	−0.843594	−	0.843594i
$940$		0			0
$941$	−21.6002	+	21.6002i	−0.704145	+	0.704145i	−0.965298	−	0.261153i	$-0.915897\pi$
$941$	−21.6002	+	21.6002i	−0.704145	+	0.704145i	0.261153	+	0.965298i	$0.415897\pi$
$942$		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	$-0.127845\pi$
$947$	16.2944	+	16.2944i	0.529498	+	0.529498i	−0.390925	+	0.920423i	$0.627845\pi$
$948$		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	$-0.562384\pi$
$953$	−12.0232			−0.389468			−0.194734	+	0.980856i	$0.562384\pi$
$954$		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	$-0.251110\pi$
$967$	43.8237			1.40927			0.704637	+	0.709568i	$0.251110\pi$
$968$		0			0
$969$		−	69.8244i		−	2.24308i
$970$		0			0
$971$	−35.9986	−	35.9986i	−1.15525	−	1.15525i	−0.985484	−	0.169766i	$-0.945699\pi$
$971$	−35.9986	−	35.9986i	−1.15525	−	1.15525i	−0.169766	−	0.985484i	$-0.554301\pi$
$972$		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	$-0.682451\pi$
$983$	−34.0060			−1.08462			−0.542312	+	0.840177i	$0.682451\pi$
$984$		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	$-0.704374\pi$
$997$	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.q.f.49.6		12
4.3	odd	2		400.2.q.f.149.1		12
5.2	odd	4		1600.2.l.g.1201.6		12
5.3	odd	4		1600.2.l.f.1201.1		12
5.4	even	2		1600.2.q.e.49.1		12
16.3	odd	4		400.2.q.e.349.6		12
16.13	even	4		1600.2.q.e.849.1		12
20.3	even	4		400.2.l.g.101.3	yes	12
20.7	even	4		400.2.l.f.101.4	✓	12
20.19	odd	2		400.2.q.e.149.6		12
80.3	even	4		400.2.l.g.301.3	yes	12
80.13	odd	4		1600.2.l.f.401.1		12
80.19	odd	4		400.2.q.f.349.1		12
80.29	even	4	inner	1600.2.q.f.849.6		12
80.67	even	4		400.2.l.f.301.4	yes	12
80.77	odd	4		1600.2.l.g.401.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.l.f.101.4	✓	12	20.7	even	4
400.2.l.f.301.4	yes	12	80.67	even	4
400.2.l.g.101.3	yes	12	20.3	even	4
400.2.l.g.301.3	yes	12	80.3	even	4
400.2.q.e.149.6		12	20.19	odd	2
400.2.q.e.349.6		12	16.3	odd	4
400.2.q.f.149.1		12	4.3	odd	2
400.2.q.f.349.1		12	80.19	odd	4
1600.2.l.f.401.1		12	80.13	odd	4
1600.2.l.f.1201.1		12	5.3	odd	4
1600.2.l.g.401.6		12	80.77	odd	4
1600.2.l.g.1201.6		12	5.2	odd	4
1600.2.q.e.49.1		12	5.4	even	2
1600.2.q.e.849.1		12	16.13	even	4
1600.2.q.f.49.6		12	1.1	even	1	trivial
1600.2.q.f.849.6		12	80.29	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
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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