LMFDB - Embedded newform 3420.2.bj.c.1189.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3420,2,Mod(1189,3420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("3420.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3420.bj (of order $6$, degree $2$, 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:	$27.3088374913$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1189.1
Root			$2.10552 + 1.21562i$ of defining polynomial
Character	$\chi$	$=$	3420.1189
Dual form			3420.2.bj.c.2629.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22225 + 0.248224i) q^{5} +0.663818i q^{7} +1.80905 q^{11} +(1.99526 - 1.15197i) q^{13} +(3.77643 + 2.18033i) q^{17} +(-4.21168 + 1.12329i) q^{19} +(-1.81374 + 1.04716i) q^{23} +(4.87677 - 1.10323i) q^{25} +(-0.974621 - 1.68809i) q^{29} -9.52527 q^{31} +(-0.164775 - 1.47517i) q^{35} +2.97461i q^{37} +(0.247657 - 0.428954i) q^{41} +(6.81715 + 3.93588i) q^{43} +(5.69449 - 3.28772i) q^{47} +6.55935 q^{49} +(-1.99575 + 1.15225i) q^{53} +(-4.02016 + 0.449050i) q^{55} +(-3.88559 + 6.73003i) q^{59} +(-5.36021 - 9.28415i) q^{61} +(-4.14802 + 3.05522i) q^{65} +(3.96984 - 2.29199i) q^{67} +(2.95914 - 5.12538i) q^{71} +(-4.86313 - 2.80773i) q^{73} +1.20088i q^{77} +(-2.99810 + 5.19286i) q^{79} -6.20090i q^{83} +(-8.93338 - 3.90782i) q^{85} +(6.65028 + 11.5186i) q^{89} +(0.764696 + 1.32449i) q^{91} +(9.08057 - 3.54166i) q^{95} +(8.80695 + 5.08470i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) $ 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times$.

$n$	$1711$	$1901$	$2737$	$3061$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.22225	+	0.248224i	−0.993819	+	0.111009i
$5$	−2.22225	+	0.248224i	−0.993819	+	0.111009i
$6$		0			0
$7$			0.663818i			0.250900i	0.992100	+	0.125450i	$0.0400374\pi$
$7$			0.663818i			0.250900i	−0.992100	+	0.125450i	$0.959963\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.80905			0.545450			0.272725	−	0.962092i	$-0.412075\pi$
$11$	1.80905			0.545450			0.272725	+	0.962092i	$0.412075\pi$
$12$		0			0
$13$	1.99526	−	1.15197i	0.553386	−	0.319498i	−0.197100	−	0.980383i	$-0.563153\pi$
$13$	1.99526	−	1.15197i	0.553386	−	0.319498i	0.750487	+	0.660886i	$0.229819\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.77643	+	2.18033i	0.915920	+	0.528807i	0.882331	−	0.470629i	$-0.155973\pi$
$17$	3.77643	+	2.18033i	0.915920	+	0.528807i	0.0335887	+	0.999436i	$0.489306\pi$
$18$		0			0
$19$	−4.21168	+	1.12329i	−0.966225	+	0.257699i
$19$	−4.21168	+	1.12329i	−0.966225	+	0.257699i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.81374	+	1.04716i	−0.378191	+	0.218349i	−0.677031	−	0.735955i	$-0.736734\pi$
$23$	−1.81374	+	1.04716i	−0.378191	+	0.218349i	0.298840	+	0.954303i	$0.403400\pi$
$24$		0			0
$25$	4.87677	−	1.10323i	0.975354	−	0.220646i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.974621	−	1.68809i	−0.180983	−	0.313471i	0.761233	−	0.648479i	$-0.224594\pi$
$29$	−0.974621	−	1.68809i	−0.180983	−	0.313471i	−0.942215	+	0.335008i	$0.891261\pi$
$30$		0			0
$31$	−9.52527			−1.71079			−0.855394	−	0.517977i	$-0.826685\pi$
$31$	−9.52527			−1.71079			−0.855394	+	0.517977i	$0.826685\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.164775	−	1.47517i	−0.0278521	−	0.249349i
$36$		0			0
$37$			2.97461i			0.489023i	0.969646	+	0.244511i	$0.0786276\pi$
$37$			2.97461i			0.489023i	−0.969646	+	0.244511i	$0.921372\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.247657	−	0.428954i	0.0386775	−	0.0669914i	−0.846039	−	0.533122i	$-0.821019\pi$
$41$	0.247657	−	0.428954i	0.0386775	−	0.0669914i	0.884716	+	0.466130i	$0.154352\pi$
$42$		0			0
$43$	6.81715	+	3.93588i	1.03960	+	0.600216i	0.919721	−	0.392572i	$-0.128415\pi$
$43$	6.81715	+	3.93588i	1.03960	+	0.600216i	0.119884	+	0.992788i	$0.461748\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.69449	−	3.28772i	0.830627	−	0.479563i	−0.0234403	−	0.999725i	$-0.507462\pi$
$47$	5.69449	−	3.28772i	0.830627	−	0.479563i	0.854067	+	0.520163i	$0.174129\pi$
$48$		0			0
$49$	6.55935			0.937049
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.99575	+	1.15225i	−0.274137	+	0.158273i	−0.630766	−	0.775973i	$-0.717259\pi$
$53$	−1.99575	+	1.15225i	−0.274137	+	0.158273i	0.356629	+	0.934246i	$0.383926\pi$
$54$		0			0
$55$	−4.02016	+	0.449050i	−0.542079	+	0.0605498i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.88559	+	6.73003i	−0.505860	+	0.876176i	0.494117	+	0.869396i	$0.335492\pi$
$59$	−3.88559	+	6.73003i	−0.505860	+	0.876176i	−0.999977	+	0.00678007i	$0.997842\pi$
$60$		0			0
$61$	−5.36021	−	9.28415i	−0.686304	−	1.18871i	−0.973025	−	0.230700i	$-0.925899\pi$
$61$	−5.36021	−	9.28415i	−0.686304	−	1.18871i	0.286721	−	0.958014i	$-0.407435\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.14802	+	3.05522i	−0.514499	+	0.378954i
$66$		0			0
$67$	3.96984	−	2.29199i	0.484993	−	0.280011i	−0.237502	−	0.971387i	$-0.576329\pi$
$67$	3.96984	−	2.29199i	0.484993	−	0.280011i	0.722495	+	0.691376i	$0.242995\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.95914	−	5.12538i	0.351185	−	0.608270i	−0.635272	−	0.772288i	$-0.719112\pi$
$71$	2.95914	−	5.12538i	0.351185	−	0.608270i	0.986457	+	0.164018i	$0.0524455\pi$
$72$		0			0
$73$	−4.86313	−	2.80773i	−0.569187	−	0.328620i	0.187638	−	0.982238i	$-0.439917\pi$
$73$	−4.86313	−	2.80773i	−0.569187	−	0.328620i	−0.756824	+	0.653618i	$0.773250\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			1.20088i			0.136853i
$78$		0			0
$79$	−2.99810	+	5.19286i	−0.337312	+	0.584242i	−0.983926	−	0.178575i	$-0.942851\pi$
$79$	−2.99810	+	5.19286i	−0.337312	+	0.584242i	0.646614	+	0.762817i	$0.276185\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	6.20090i		−	0.680638i	−0.940310	−	0.340319i	$-0.889465\pi$
$83$		−	6.20090i		−	0.680638i	0.940310	−	0.340319i	$-0.110535\pi$
$84$		0			0
$85$	−8.93338	−	3.90782i	−0.968961	−	0.423863i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.65028	+	11.5186i	0.704928	+	1.22097i	0.966717	+	0.255847i	$0.0823542\pi$
$89$	6.65028	+	11.5186i	0.704928	+	1.22097i	−0.261789	+	0.965125i	$0.584312\pi$
$90$		0			0
$91$	0.764696	+	1.32449i	0.0801619	+	0.138844i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9.08057	−	3.54166i	0.931646	−	0.363366i
$96$		0			0
$97$	8.80695	+	5.08470i	0.894211	+	0.516273i	0.875317	−	0.483549i	$-0.160652\pi$
$97$	8.80695	+	5.08470i	0.894211	+	0.516273i	0.0188932	+	0.999822i	$0.493986\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.48770	+	12.9691i	0.745054	+	1.29047i	0.950170	+	0.311733i	$0.100909\pi$
$101$	7.48770	+	12.9691i	0.745054	+	1.29047i	−0.205116	+	0.978738i	$0.565757\pi$
$102$		0			0
$103$			18.1501i			1.78839i	0.447681	+	0.894193i	$0.352250\pi$
$103$			18.1501i			1.78839i	−0.447681	+	0.894193i	$0.647750\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			13.9698i			1.35051i	0.737584	+	0.675256i	$0.235967\pi$
$107$			13.9698i			1.35051i	−0.737584	+	0.675256i	$0.764033\pi$
$108$		0			0
$109$	−9.20544	+	15.9443i	−0.881721	+	1.52719i	−0.0322945	+	0.999478i	$0.510281\pi$
$109$	−9.20544	+	15.9443i	−0.881721	+	1.52719i	−0.849426	+	0.527707i	$0.823052\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			10.8946i			1.02487i	0.858725	+	0.512437i	$0.171257\pi$
$113$			10.8946i			1.02487i	−0.858725	+	0.512437i	$0.828743\pi$
$114$		0			0
$115$	3.77065	−	2.77727i	0.351615	−	0.258982i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.44734	+	2.50687i	−0.132677	+	0.229804i
$120$		0			0
$121$	−7.72733			−0.702484
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.5635	+	3.66218i	−0.944832	+	0.327555i
$126$		0			0
$127$	−2.86242	+	1.65262i	−0.253998	+	0.146646i	−0.621594	−	0.783340i	$-0.713514\pi$
$127$	−2.86242	+	1.65262i	−0.253998	+	0.146646i	0.367595	+	0.929986i	$0.380181\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.646627	−	1.11999i	0.0564961	−	0.0978541i	−0.836394	−	0.548128i	$-0.815340\pi$
$131$	0.646627	−	1.11999i	0.0564961	−	0.0978541i	0.892890	+	0.450274i	$0.148674\pi$
$132$		0			0
$133$	−0.745658	−	2.79579i	−0.0646567	−	0.242426i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.6426	+	7.29920i	−1.08013	+	0.623613i	−0.930931	−	0.365195i	$-0.881002\pi$
$137$	−12.6426	+	7.29920i	−1.08013	+	0.623613i	−0.149197	+	0.988807i	$0.547669\pi$
$138$		0			0
$139$	−1.87915	−	3.25478i	−0.159387	−	0.276067i	0.775261	−	0.631641i	$-0.217618\pi$
$139$	−1.87915	−	3.25478i	−0.159387	−	0.276067i	−0.934648	+	0.355575i	$0.884285\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.60954	−	2.08397i	0.301844	−	0.174270i
$144$		0			0
$145$	2.58487	+	3.50944i	0.214662	+	0.291443i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.83653	+	6.64507i	−0.314301	+	0.544385i	−0.979289	−	0.202469i	$-0.935103\pi$
$149$	−3.83653	+	6.64507i	−0.314301	+	0.544385i	0.664988	+	0.746854i	$0.268437\pi$
$150$		0			0
$151$	1.62643			0.132357			0.0661785	−	0.997808i	$-0.478919\pi$
$151$	1.62643			0.132357			0.0661785	+	0.997808i	$0.478919\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	21.1675	−	2.36440i	1.70021	−	0.189913i
$156$		0			0
$157$	2.29893	+	1.32729i	0.183474	+	0.105929i	0.588924	−	0.808188i	$-0.299552\pi$
$157$	2.29893	+	1.32729i	0.183474	+	0.105929i	−0.405450	+	0.914117i	$0.632885\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.695126	−	1.20399i	−0.0547836	−	0.0948880i
$162$		0			0
$163$			19.8052i			1.55127i	0.631184	+	0.775633i	$0.282569\pi$
$163$			19.8052i			1.55127i	−0.631184	+	0.775633i	$0.717431\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.0776925	+	0.0448558i	−0.00601203	+	0.00347105i	−0.503003	−	0.864285i	$-0.667772\pi$
$167$	−0.0776925	+	0.0448558i	−0.00601203	+	0.00347105i	0.496991	+	0.867756i	$0.334438\pi$
$168$		0			0
$169$	−3.84595	+	6.66139i	−0.295842	+	0.512414i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−13.7120	−	7.91662i	−1.04250	−	0.601889i	−0.121962	−	0.992535i	$-0.538918\pi$
$173$	−13.7120	−	7.91662i	−1.04250	−	0.601889i	−0.920541	+	0.390646i	$0.872252\pi$
$174$		0			0
$175$	0.732343	+	3.23729i	0.0553599	+	0.244716i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.5051			−1.00942			−0.504709	−	0.863290i	$-0.668400\pi$
$179$	−13.5051			−1.00942			−0.504709	+	0.863290i	$0.668400\pi$
$180$		0			0
$181$	4.78591	+	8.28945i	0.355734	+	0.616150i	0.987243	−	0.159219i	$-0.0508975\pi$
$181$	4.78591	+	8.28945i	0.355734	+	0.616150i	−0.631509	+	0.775368i	$0.717564\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.738368	−	6.61032i	−0.0542859	−	0.486000i
$186$		0			0
$187$	6.83177	+	3.94432i	0.499588	+	0.288438i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−26.9010			−1.94649			−0.973243	−	0.229778i	$-0.926200\pi$
$191$	−26.9010			−1.94649			−0.973243	+	0.229778i	$0.926200\pi$
$192$		0			0
$193$	19.7692	+	11.4137i	1.42302	+	0.821579i	0.996556	−	0.0829272i	$-0.0264269\pi$
$193$	19.7692	+	11.4137i	1.42302	+	0.821579i	0.426461	+	0.904506i	$0.359760\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	10.4172i		−	0.742192i	−0.928594	−	0.371096i	$-0.878982\pi$
$197$		−	10.4172i		−	0.742192i	0.928594	−	0.371096i	$-0.121018\pi$
$198$		0			0
$199$	0.782081	+	1.35460i	0.0554403	+	0.0960254i	0.892414	−	0.451218i	$-0.149010\pi$
$199$	0.782081	+	1.35460i	0.0554403	+	0.0960254i	−0.836973	+	0.547244i	$0.815677\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.12059	−	0.646971i	0.0786498	−	0.0454085i
$204$		0			0
$205$	−0.443879	+	1.01472i	−0.0310018	+	0.0708709i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.61915	+	2.03208i	−0.527028	+	0.140562i
$210$		0			0
$211$	−10.4253	+	18.0571i	−0.717704	+	1.24310i	0.244203	+	0.969724i	$0.421474\pi$
$211$	−10.4253	+	18.0571i	−0.717704	+	1.24310i	−0.961907	+	0.273376i	$0.911860\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−16.1264	−	7.05433i	−1.09981	−	0.481101i
$216$		0			0
$217$		−	6.32305i		−	0.429236i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	10.0466			0.675810
$222$		0			0
$223$	19.5472	+	11.2856i	1.30898	+	0.755740i	0.981926	−	0.189266i	$-0.0606108\pi$
$223$	19.5472	+	11.2856i	1.30898	+	0.755740i	0.327054	+	0.945006i	$0.393944\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			11.4187i			0.757883i	0.925421	+	0.378941i	$0.123712\pi$
$227$			11.4187i			0.757883i	−0.925421	+	0.378941i	$0.876288\pi$
$228$		0			0
$229$	15.8237			1.04566			0.522829	−	0.852438i	$-0.324877\pi$
$229$	15.8237			1.04566			0.522829	+	0.852438i	$0.324877\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.6621	+	6.73314i	0.764013	+	0.441103i	0.830735	−	0.556669i	$-0.187921\pi$
$233$	11.6621	+	6.73314i	0.764013	+	0.441103i	−0.0667219	+	0.997772i	$0.521254\pi$
$234$		0			0
$235$	−11.8385	+	8.71963i	−0.772257	+	0.568806i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	19.7437			1.27711			0.638557	−	0.769574i	$-0.279532\pi$
$239$	19.7437			1.27711			0.638557	+	0.769574i	$0.279532\pi$
$240$		0			0
$241$	2.69793	+	4.67295i	0.173789	+	0.301011i	0.939742	−	0.341886i	$-0.111066\pi$
$241$	2.69793	+	4.67295i	0.173789	+	0.301011i	−0.765953	+	0.642897i	$0.777732\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−14.5765	+	1.62818i	−0.931258	+	0.104021i
$246$		0			0
$247$	−7.10942	+	7.09296i	−0.452361	+	0.451314i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.78646	−	3.09424i	−0.112760	−	0.195306i	0.804122	−	0.594464i	$-0.202636\pi$
$251$	−1.78646	−	3.09424i	−0.112760	−	0.195306i	−0.916882	+	0.399158i	$0.869303\pi$
$252$		0			0
$253$	−3.28115	+	1.89437i	−0.206284	+	0.119098i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	16.0500	−	9.26649i	1.00117	−	0.578028i	0.0925780	−	0.995705i	$-0.470489\pi$
$257$	16.0500	−	9.26649i	1.00117	−	0.578028i	0.908595	+	0.417678i	$0.137156\pi$
$258$		0			0
$259$	−1.97460			−0.122696
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.30609	+	5.37288i	0.573838	+	0.331306i	0.758681	−	0.651462i	$-0.225844\pi$
$263$	9.30609	+	5.37288i	0.573838	+	0.331306i	−0.184843	+	0.982768i	$0.559178\pi$
$264$		0			0
$265$	4.14904	−	3.05597i	0.254873	−	0.187727i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.05027	−	10.4794i	0.368892	−	0.638939i	−0.620501	−	0.784206i	$-0.713071\pi$
$269$	6.05027	−	10.4794i	0.368892	−	0.638939i	0.989393	+	0.145267i	$0.0464040\pi$
$270$		0			0
$271$	9.34472	−	16.1855i	0.567651	−	0.983201i	−0.429146	−	0.903235i	$-0.641185\pi$
$271$	9.34472	−	16.1855i	0.567651	−	0.983201i	0.996798	−	0.0799661i	$-0.0254812\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.82234	−	1.99580i	0.532007	−	0.120351i
$276$		0			0
$277$			5.94922i			0.357454i	0.983899	+	0.178727i	$0.0571979\pi$
$277$			5.94922i			0.357454i	−0.983899	+	0.178727i	$0.942802\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.78943	−	15.2237i	−0.524333	−	0.908172i	−0.999599	−	0.0283294i	$-0.990981\pi$
$281$	−8.78943	−	15.2237i	−0.524333	−	0.908172i	0.475265	−	0.879843i	$-0.342352\pi$
$282$		0			0
$283$	−27.2029	−	15.7056i	−1.61705	−	0.933603i	−0.987679	−	0.156495i	$-0.949980\pi$
$283$	−27.2029	−	15.7056i	−1.61705	−	0.933603i	−0.629368	−	0.777107i	$-0.716686\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.284748	+	0.164399i	0.0168081	+	0.00970418i
$288$		0			0
$289$	1.00764	+	1.74528i	0.0592727	+	0.102663i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	28.1435i		−	1.64416i	−0.569372	−	0.822080i	$-0.692814\pi$
$293$		−	28.1435i		−	1.64416i	0.569372	−	0.822080i	$-0.307186\pi$
$294$		0			0
$295$	6.96418	−	15.9203i	0.405470	−	0.926915i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.41259	+	4.17873i	−0.139524	+	0.241662i
$300$		0			0
$301$	−2.61271	+	4.52535i	−0.150594	+	0.260837i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	14.2163	+	19.3012i	0.814020	+	1.10518i
$306$		0			0
$307$	−23.3588	−	13.4862i	−1.33316	−	0.769698i	−0.347374	−	0.937727i	$-0.612927\pi$
$307$	−23.3588	−	13.4862i	−1.33316	−	0.769698i	−0.985782	+	0.168028i	$0.946260\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.99721			0.283366			0.141683	−	0.989912i	$-0.454749\pi$
$311$	4.99721			0.283366			0.141683	+	0.989912i	$0.454749\pi$
$312$		0			0
$313$	22.6484	−	13.0761i	1.28017	−	0.739104i	0.303287	−	0.952899i	$-0.401916\pi$
$313$	22.6484	−	13.0761i	1.28017	−	0.739104i	0.976878	+	0.213795i	$0.0685825\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.5314	−	13.0085i	1.26549	−	0.730632i	0.291359	−	0.956614i	$-0.405892\pi$
$317$	22.5314	−	13.0085i	1.26549	−	0.730632i	0.974131	+	0.225982i	$0.0725591\pi$
$318$		0			0
$319$	−1.76314	−	3.05385i	−0.0987169	−	0.170983i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−18.3543	−	4.94081i	−1.02126	−	0.274914i
$324$		0			0
$325$	8.45955	−	7.81910i	0.469252	−	0.433726i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.18245	+	3.78011i	0.120322	+	0.208404i
$330$		0			0
$331$	7.97402			0.438292			0.219146	−	0.975692i	$-0.429673\pi$
$331$	7.97402			0.438292			0.219146	+	0.975692i	$0.429673\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.25304	+	6.07877i	−0.450912	+	0.332119i
$336$		0			0
$337$	3.42862	+	1.97951i	0.186769	+	0.107831i	0.590469	−	0.807060i	$-0.298943\pi$
$337$	3.42862	+	1.97951i	0.186769	+	0.107831i	−0.403700	+	0.914891i	$0.632276\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−17.2317			−0.933150
$342$		0			0
$343$			9.00094i			0.486005i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.16047	+	2.40205i	0.223345	+	0.128949i	0.607498	−	0.794321i	$-0.292173\pi$
$347$	4.16047	+	2.40205i	0.223345	+	0.128949i	−0.384153	+	0.923269i	$0.625506\pi$
$348$		0			0
$349$	−9.02058			−0.482861			−0.241430	−	0.970418i	$-0.577617\pi$
$349$	−9.02058			−0.482861			−0.241430	+	0.970418i	$0.577617\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	18.0910i		−	0.962889i	−0.876477	−	0.481444i	$-0.840112\pi$
$353$		−	18.0910i		−	0.962889i	0.876477	−	0.481444i	$-0.159888\pi$
$354$		0			0
$355$	−5.30370	+	12.1244i	−0.281491	+	0.643495i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−17.4849	+	30.2848i	−0.922820	+	1.59837i	−0.127791	+	0.991801i	$0.540789\pi$
$359$	−17.4849	+	30.2848i	−0.922820	+	1.59837i	−0.795030	+	0.606571i	$0.792545\pi$
$360$		0			0
$361$	16.4765	−	9.46183i	0.867182	−	0.497991i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	11.5040	+	5.03233i	0.602149	+	0.263404i
$366$		0			0
$367$	−8.55319	+	4.93819i	−0.446473	+	0.257771i	−0.706339	−	0.707873i	$-0.749655\pi$
$367$	−8.55319	+	4.93819i	−0.446473	+	0.257771i	0.259866	+	0.965645i	$0.416321\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.764883	−	1.32482i	−0.0397107	−	0.0687810i
$372$		0			0
$373$			18.9698i			0.982220i	0.871098	+	0.491110i	$0.163409\pi$
$373$			18.9698i			0.982220i	−0.871098	+	0.491110i	$0.836591\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.88925	−	2.24546i	−0.200306	−	0.115647i
$378$		0			0
$379$	−8.93773			−0.459101			−0.229550	−	0.973297i	$-0.573726\pi$
$379$	−8.93773			−0.459101			−0.229550	+	0.973297i	$0.573726\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−13.9643	−	8.06230i	−0.713543	−	0.411964i	0.0988287	−	0.995104i	$-0.468490\pi$
$383$	−13.9643	−	8.06230i	−0.713543	−	0.411964i	−0.812371	+	0.583140i	$0.801824\pi$
$384$		0			0
$385$	−0.298087	−	2.66866i	−0.0151919	−	0.136007i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	10.0603	+	17.4249i	0.510075	+	0.883476i	0.999932	+	0.0116730i	$0.00371573\pi$
$389$	10.0603	+	17.4249i	0.510075	+	0.883476i	−0.489857	+	0.871803i	$0.662951\pi$
$390$		0			0
$391$	−9.13262			−0.461857
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.37353	−	12.2840i	0.270372	−	0.618076i
$396$		0			0
$397$	−13.8674	−	8.00633i	−0.695983	−	0.401826i	0.109866	−	0.993946i	$-0.464958\pi$
$397$	−13.8674	−	8.00633i	−0.695983	−	0.401826i	−0.805850	+	0.592120i	$0.798291\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.83602	+	11.8403i	−0.341375	+	0.591278i	−0.984688	−	0.174324i	$-0.944226\pi$
$401$	−6.83602	+	11.8403i	−0.341375	+	0.591278i	0.643313	+	0.765603i	$0.277559\pi$
$402$		0			0
$403$	−19.0054	+	10.9728i	−0.946727	+	0.546593i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5.38123i			0.266738i
$408$		0			0
$409$	3.03518	+	5.25709i	0.150080	+	0.259946i	0.931257	−	0.364364i	$-0.118713\pi$
$409$	3.03518	+	5.25709i	0.150080	+	0.259946i	−0.781177	+	0.624310i	$0.785380\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.46752	−	2.57932i	−0.219832	−	0.126920i
$414$		0			0
$415$	1.53921	+	13.7799i	0.0755569	+	0.676431i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−6.33985			−0.309722			−0.154861	−	0.987936i	$-0.549493\pi$
$419$	−6.33985			−0.309722			−0.154861	+	0.987936i	$0.549493\pi$
$420$		0			0
$421$	3.52768	−	6.11011i	0.171928	−	0.297789i	−0.767166	−	0.641449i	$-0.778334\pi$
$421$	3.52768	−	6.11011i	0.171928	−	0.297789i	0.939094	+	0.343660i	$0.111667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	20.8222	+	6.46668i	1.01002	+	0.313680i
$426$		0			0
$427$	6.16299	−	3.55820i	0.298248	−	0.172194i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.0390	−	22.5843i	−0.628069	−	1.08785i	−0.987939	−	0.154845i	$-0.950512\pi$
$431$	−13.0390	−	22.5843i	−0.628069	−	1.08785i	0.359870	−	0.933002i	$-0.382821\pi$
$432$		0			0
$433$	29.6662	−	17.1278i	1.42567	−	0.823109i	0.428892	−	0.903356i	$-0.358904\pi$
$433$	29.6662	−	17.1278i	1.42567	−	0.823109i	0.996775	+	0.0802463i	$0.0255707\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.46262	−	6.44766i	0.309149	−	0.308433i
$438$		0			0
$439$	3.13427	−	5.42872i	0.149591	−	0.259099i	−0.781485	−	0.623923i	$-0.785538\pi$
$439$	3.13427	−	5.42872i	0.149591	−	0.259099i	0.931076	+	0.364825i	$0.118871\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.3099	−	16.3447i	1.34504	−	0.776561i	0.357500	−	0.933913i	$-0.383629\pi$
$443$	28.3099	−	16.3447i	1.34504	−	0.776561i	0.987543	+	0.157352i	$0.0502958\pi$
$444$		0			0
$445$	−17.6378	−	23.9465i	−0.836110	−	1.13517i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−23.0822			−1.08932			−0.544659	−	0.838658i	$-0.683341\pi$
$449$	−23.0822			−1.08932			−0.544659	+	0.838658i	$0.683341\pi$
$450$		0			0
$451$	0.448025	−	0.776001i	0.0210967	−	0.0365405i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.02811	−	2.75353i	−0.0950794	−	0.129088i
$456$		0			0
$457$		−	19.9166i		−	0.931661i	−0.884874	−	0.465830i	$-0.845756\pi$
$457$		−	19.9166i		−	0.931661i	0.884874	−	0.465830i	$-0.154244\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	21.2586	−	36.8209i	0.990111	−	1.71492i	0.373562	−	0.927605i	$-0.378136\pi$
$461$	21.2586	−	36.8209i	0.990111	−	1.71492i	0.616548	−	0.787317i	$-0.288530\pi$
$462$		0			0
$463$		−	27.2843i		−	1.26801i	−0.773329	−	0.634005i	$-0.781410\pi$
$463$		−	27.2843i		−	1.26801i	0.773329	−	0.634005i	$-0.218590\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			39.5912i			1.83206i	0.401107	+	0.916031i	$0.368625\pi$
$467$			39.5912i			1.83206i	−0.401107	+	0.916031i	$0.631375\pi$
$468$		0			0
$469$	1.52146	+	2.63525i	0.0702547	+	0.121685i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.3326	+	7.12022i	0.567053	+	0.327388i
$474$		0			0
$475$	−19.3001	+	10.1244i	−0.885551	+	0.464541i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.7954	+	23.8943i	0.630326	+	1.09176i	0.987485	+	0.157713i	$0.0504121\pi$
$479$	13.7954	+	23.8943i	0.630326	+	1.09176i	−0.357159	+	0.934044i	$0.616255\pi$
$480$		0			0
$481$	3.42665	+	5.93513i	0.156242	+	0.270618i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−20.8334	−	9.11336i	−0.945995	−	0.413817i
$486$		0			0
$487$			29.9289i			1.35621i	0.734966	+	0.678104i	$0.237198\pi$
$487$			29.9289i			1.35621i	−0.734966	+	0.678104i	$0.762802\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.23550	−	12.5323i	0.326534	−	0.565573i	−0.655288	−	0.755379i	$-0.727453\pi$
$491$	7.23550	−	12.5323i	0.326534	−	0.565573i	0.981822	+	0.189806i	$0.0607860\pi$
$492$		0			0
$493$		−	8.49996i		−	0.382819i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.40232	+	1.96433i	0.152615	+	0.0881122i
$498$		0			0
$499$	−9.06799	+	15.7062i	−0.405939	+	0.703107i	−0.994430	−	0.105396i	$-0.966389\pi$
$499$	−9.06799	+	15.7062i	−0.405939	+	0.703107i	0.588491	+	0.808504i	$0.299722\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14.7022	+	8.48833i	−0.655539	+	0.378476i	−0.790575	−	0.612365i	$-0.790218\pi$
$503$	−14.7022	+	8.48833i	−0.655539	+	0.378476i	0.135036	+	0.990841i	$0.456885\pi$
$504$		0			0
$505$	−19.8587	−	26.9619i	−0.883703	−	1.19979i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	16.6888	+	28.9058i	0.739717	+	1.28123i	0.952623	+	0.304155i	$0.0983739\pi$
$509$	16.6888	+	28.9058i	0.739717	+	1.28123i	−0.212906	+	0.977073i	$0.568293\pi$
$510$		0			0
$511$	1.86382	−	3.22824i	0.0824507	−	0.142809i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.50529	−	40.3341i	−0.198527	−	1.77733i
$516$		0			0
$517$	10.3016	−	5.94765i	0.453065	−	0.261577i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.09359			−0.0479110			−0.0239555	−	0.999713i	$-0.507626\pi$
$521$	−1.09359			−0.0479110			−0.0239555	+	0.999713i	$0.507626\pi$
$522$		0			0
$523$	−3.51597	+	2.02994i	−0.153742	+	0.0887633i	−0.574898	−	0.818225i	$-0.694958\pi$
$523$	−3.51597	+	2.02994i	−0.153742	+	0.0887633i	0.421155	+	0.906989i	$0.361625\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−35.9715	−	20.7682i	−1.56695	−	0.904676i
$528$		0			0
$529$	−9.30690	+	16.1200i	−0.404648	+	0.700871i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	1.14117i		−	0.0494295i
$534$		0			0
$535$	−3.46763	−	31.0443i	−0.149919	−	1.34216i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	11.8662			0.511114
$540$		0			0
$541$	−6.65097	−	11.5198i	−0.285947	−	0.495275i	0.686891	−	0.726760i	$-0.258975\pi$
$541$	−6.65097	−	11.5198i	−0.285947	−	0.495275i	−0.972838	+	0.231485i	$0.925642\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.4990	−	37.7172i	0.706740	−	1.61563i
$546$		0			0
$547$	29.6808	−	17.1362i	1.26906	−	0.732692i	0.294250	−	0.955729i	$-0.404930\pi$
$547$	29.6808	−	17.1362i	1.26906	−	0.732692i	0.974810	+	0.223036i	$0.0715969\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.00100	+	6.01493i	0.255651	+	0.256244i
$552$		0			0
$553$	−3.44712	−	1.99019i	−0.146586	−	0.0846316i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−35.2047	+	20.3255i	−1.49167	+	0.861217i	−0.999955	−	0.00953795i	$-0.996964\pi$
$557$	−35.2047	+	20.3255i	−1.49167	+	0.861217i	−0.491717	+	0.870755i	$0.663631\pi$
$558$		0			0
$559$	18.1360			0.767071
$560$		0			0
$561$		0			0
$562$		0			0
$563$			20.7137i			0.872980i	0.899709	+	0.436490i	$0.143779\pi$
$563$			20.7137i			0.872980i	−0.899709	+	0.436490i	$0.856221\pi$
$564$		0			0
$565$	−2.70429	−	24.2104i	−0.113770	−	1.01854i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	34.0551			1.42766			0.713831	−	0.700318i	$-0.246958\pi$
$569$	34.0551			1.42766			0.713831	+	0.700318i	$0.246958\pi$
$570$		0			0
$571$	18.5413			0.775929			0.387965	−	0.921674i	$-0.373178\pi$
$571$	18.5413			0.775929			0.387965	+	0.921674i	$0.373178\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.68993	+	7.10774i	−0.320692	+	0.296413i
$576$		0			0
$577$			2.96818i			0.123567i	0.998090	+	0.0617834i	$0.0196788\pi$
$577$			2.96818i			0.123567i	−0.998090	+	0.0617834i	$0.980321\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.11627			0.170772
$582$		0			0
$583$	−3.61042	+	2.08448i	−0.149528	+	0.0863302i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−32.9328	−	19.0138i	−1.35928	−	0.784781i	−0.369754	−	0.929130i	$-0.620558\pi$
$587$	−32.9328	−	19.0138i	−1.35928	−	0.784781i	−0.989527	+	0.144348i	$0.953892\pi$
$588$		0			0
$589$	40.1174	−	10.6996i	1.65301	−	0.440869i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−38.0060	+	21.9428i	−1.56072	+	0.901081i	−0.563533	+	0.826093i	$0.690558\pi$
$593$	−38.0060	+	21.9428i	−1.56072	+	0.901081i	−0.997184	+	0.0749876i	$0.976108\pi$
$594$		0			0
$595$	2.59408	−	5.93014i	0.106347	−	0.243112i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.4883	+	30.2906i	0.714552	+	1.23764i	0.963132	+	0.269029i	$0.0867026\pi$
$599$	17.4883	+	30.2906i	0.714552	+	1.23764i	−0.248581	+	0.968611i	$0.579964\pi$
$600$		0			0
$601$	31.9988			1.30526			0.652630	−	0.757677i	$-0.273666\pi$
$601$	31.9988			1.30526			0.652630	+	0.757677i	$0.273666\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	17.1720	−	1.91810i	0.698143	−	0.0779820i
$606$		0			0
$607$			2.10357i			0.0853814i	0.999088	+	0.0426907i	$0.0135930\pi$
$607$			2.10357i			0.0853814i	−0.999088	+	0.0426907i	$0.986407\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.57467	−	13.1197i	0.306438	−	0.530767i
$612$		0			0
$613$	−30.1598	−	17.4127i	−1.21814	−	0.703294i	−0.253621	−	0.967304i	$-0.581622\pi$
$613$	−30.1598	−	17.4127i	−1.21814	−	0.703294i	−0.964520	+	0.264010i	$0.914955\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	15.8782	−	9.16726i	0.639231	−	0.369060i	−0.145087	−	0.989419i	$-0.546346\pi$
$617$	15.8782	−	9.16726i	0.639231	−	0.369060i	0.784318	+	0.620359i	$0.213013\pi$
$618$		0			0
$619$	−32.4325			−1.30357			−0.651786	−	0.758403i	$-0.725980\pi$
$619$	−32.4325			−1.30357			−0.651786	+	0.758403i	$0.725980\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.64628	+	4.41458i	−0.306342	+	0.176866i
$624$		0			0
$625$	22.5658	−	10.7604i	0.902631	−	0.430415i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.48562	+	11.2334i	−0.258598	+	0.447906i
$630$		0			0
$631$	−7.25551	−	12.5669i	−0.288837	−	0.500281i	0.684695	−	0.728830i	$-0.259935\pi$
$631$	−7.25551	−	12.5669i	−0.288837	−	0.500281i	−0.973532	+	0.228549i	$0.926602\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.95078	−	4.38304i	0.236150	−	0.173936i
$636$		0			0
$637$	13.0876	−	7.55614i	0.518550	−	0.299385i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−13.8849	+	24.0494i	−0.548421	+	0.949892i	0.449962	+	0.893048i	$0.351437\pi$
$641$	−13.8849	+	24.0494i	−0.548421	+	0.949892i	−0.998383	+	0.0568449i	$0.981896\pi$
$642$		0			0
$643$	−9.72615	−	5.61539i	−0.383562	−	0.221450i	0.295805	−	0.955248i	$-0.404412\pi$
$643$	−9.72615	−	5.61539i	−0.383562	−	0.221450i	−0.679367	+	0.733799i	$0.737745\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	2.00223i		−	0.0787157i	−0.999225	−	0.0393578i	$-0.987469\pi$
$647$		−	2.00223i		−	0.0787157i	0.999225	−	0.0393578i	$-0.0125312\pi$
$648$		0			0
$649$	−7.02923	+	12.1750i	−0.275921	+	0.477910i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	3.23945i		−	0.126770i	−0.997989	−	0.0633848i	$-0.979810\pi$
$653$		−	3.23945i		−	0.126770i	0.997989	−	0.0633848i	$-0.0201895\pi$
$654$		0			0
$655$	−1.15896	+	2.64941i	−0.0452842	+	0.103521i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.14745	+	5.45154i	0.122607	+	0.212362i	0.920795	−	0.390047i	$-0.127541\pi$
$659$	3.14745	+	5.45154i	0.122607	+	0.212362i	−0.798188	+	0.602409i	$0.794208\pi$
$660$		0			0
$661$	−0.196536	−	0.340410i	−0.00764435	−	0.0132404i	0.862178	−	0.506606i	$-0.169100\pi$
$661$	−0.196536	−	0.340410i	−0.00764435	−	0.0132404i	−0.869822	+	0.493365i	$0.835767\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.35102	+	6.02785i	0.0911685	+	0.233750i
$666$		0			0
$667$	3.53542	+	2.04117i	0.136892	+	0.0790346i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.69690	−	16.7955i	−0.374345	−	0.648384i
$672$		0			0
$673$			43.1041i			1.66154i	0.556616	+	0.830770i	$0.312100\pi$
$673$			43.1041i			1.66154i	−0.556616	+	0.830770i	$0.687900\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			12.3727i			0.475522i	0.971324	+	0.237761i	$0.0764134\pi$
$677$			12.3727i			0.475522i	−0.971324	+	0.237761i	$0.923587\pi$
$678$		0			0
$679$	−3.37532	+	5.84622i	−0.129533	+	0.224357i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			32.8415i			1.25664i	0.777954	+	0.628322i	$0.216258\pi$
$683$			32.8415i			1.25664i	−0.777954	+	0.628322i	$0.783742\pi$
$684$		0			0
$685$	26.2831	−	19.3588i	1.00423	−	0.739662i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.65470	+	4.59807i	−0.101136	+	0.175172i
$690$		0			0
$691$	−16.6704			−0.634171			−0.317085	−	0.948397i	$-0.602704\pi$
$691$	−16.6704			−0.634171			−0.317085	+	0.948397i	$0.602704\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.98384	+	6.76648i	0.189048	+	0.256667i
$696$		0			0
$697$	1.87052	−	1.07995i	0.0708510	−	0.0409059i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	15.9399	−	27.6087i	0.602041	−	1.04277i	−0.390470	−	0.920616i	$-0.627688\pi$
$701$	15.9399	−	27.6087i	0.602041	−	1.04277i	0.992512	−	0.122151i	$-0.0389791\pi$
$702$		0			0
$703$	−3.34134	−	12.5281i	−0.126021	−	0.472506i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.60911	+	4.97047i	−0.323779	+	0.186934i
$708$		0			0
$709$	−2.99202	−	5.18233i	−0.112368	−	0.194626i	0.804357	−	0.594147i	$-0.202510\pi$
$709$	−2.99202	−	5.18233i	−0.112368	−	0.194626i	−0.916724	+	0.399520i	$0.869177\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	17.2764	−	9.97451i	0.647004	−	0.373548i
$714$		0			0
$715$	−7.50399	+	5.52706i	−0.280633	+	0.206700i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.345920	−	0.599151i	0.0129006	−	0.0223446i	−0.859503	−	0.511131i	$-0.829227\pi$
$719$	0.345920	−	0.599151i	0.0129006	−	0.0223446i	0.872404	+	0.488786i	$0.162560\pi$
$720$		0			0
$721$	−12.0484			−0.448706
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.61535	−	7.15721i	−0.245688	−	0.265812i
$726$		0			0
$727$	−19.1410	−	11.0511i	−0.709902	−	0.409862i	0.101123	−	0.994874i	$-0.467756\pi$
$727$	−19.1410	−	11.0511i	−0.709902	−	0.409862i	−0.811025	+	0.585012i	$0.801090\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	17.1630	+	29.7272i	0.634796	+	1.09950i
$732$		0			0
$733$		−	19.0945i		−	0.705271i	−0.935761	−	0.352635i	$-0.885286\pi$
$733$		−	19.0945i		−	0.705271i	0.935761	−	0.352635i	$-0.114714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.18165	−	4.14633i	0.264540	−	0.152732i
$738$		0			0
$739$	6.05045	−	10.4797i	0.222569	−	0.385501i	−0.733018	−	0.680209i	$-0.761889\pi$
$739$	6.05045	−	10.4797i	0.222569	−	0.385501i	0.955587	+	0.294708i	$0.0952223\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13.6722	−	7.89364i	−0.501584	−	0.289590i	0.227783	−	0.973712i	$-0.426852\pi$
$743$	−13.6722	−	7.89364i	−0.501584	−	0.289590i	−0.729368	+	0.684122i	$0.760186\pi$
$744$		0			0
$745$	6.87626	−	15.7193i	0.251927	−	0.575911i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−9.27341			−0.338843
$750$		0			0
$751$	−17.5848	−	30.4578i	−0.641678	−	1.11142i	−0.985058	−	0.172223i	$-0.944905\pi$
$751$	−17.5848	−	30.4578i	−0.641678	−	1.11142i	0.343380	−	0.939197i	$-0.388428\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.61433	+	0.403718i	−0.131539	+	0.0146928i
$756$		0			0
$757$	−12.7465	−	7.35917i	−0.463278	−	0.267473i	0.250144	−	0.968209i	$-0.419522\pi$
$757$	−12.7465	−	7.35917i	−0.463278	−	0.267473i	−0.713421	+	0.700735i	$0.752855\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	39.9486			1.44814			0.724068	−	0.689728i	$-0.242270\pi$
$761$	39.9486			1.44814			0.724068	+	0.689728i	$0.242270\pi$
$762$		0			0
$763$	−10.5841	−	6.11074i	−0.383170	−	0.221224i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			17.9042i			0.646485i
$768$		0			0
$769$	24.9729	+	43.2544i	0.900547	+	1.55979i	0.826786	+	0.562516i	$0.190167\pi$
$769$	24.9729	+	43.2544i	0.900547	+	1.55979i	0.0737605	+	0.997276i	$0.476500\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	20.1384	−	11.6269i	0.724327	−	0.418190i	−0.0920165	−	0.995757i	$-0.529331\pi$
$773$	20.1384	−	11.6269i	0.724327	−	0.418190i	0.816343	+	0.577567i	$0.195998\pi$
$774$		0			0
$775$	−46.4525	+	10.5085i	−1.66862	+	0.377478i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.561213	+	2.08481i	−0.0201075	+	0.0746960i
$780$		0			0
$781$	5.35324	−	9.27208i	0.191554	−	0.331781i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.43825	−	2.37891i	−0.194100	−	0.0849070i
$786$		0			0
$787$		−	19.5711i		−	0.697636i	−0.937191	−	0.348818i	$-0.886583\pi$
$787$		−	19.5711i		−	0.697636i	0.937191	−	0.348818i	$-0.113417\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−7.23201			−0.257141
$792$		0			0
$793$	−21.3900	−	12.3495i	−0.759582	−	0.438545i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	47.6782i		−	1.68885i	−0.535676	−	0.844424i	$-0.679943\pi$
$797$		−	47.6782i		−	1.68885i	0.535676	−	0.844424i	$-0.320057\pi$
$798$		0			0
$799$	28.6732			1.01438
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.79767	−	5.07933i	−0.310463	−	0.179246i
$804$		0			0
$805$	1.84360	+	2.50303i	0.0649784	+	0.0882200i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−24.4485			−0.859565			−0.429782	−	0.902933i	$-0.641410\pi$
$809$	−24.4485			−0.859565			−0.429782	+	0.902933i	$0.641410\pi$
$810$		0			0
$811$	5.38004	+	9.31850i	0.188919	+	0.327217i	0.944890	−	0.327388i	$-0.106168\pi$
$811$	5.38004	+	9.31850i	0.188919	+	0.327217i	−0.755971	+	0.654605i	$0.772835\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.91613	−	44.0121i	−0.172204	−	1.54168i
$816$		0			0
$817$	−33.1327	−	8.91906i	−1.15917	−	0.312038i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.60434	−	6.24289i	−0.125792	−	0.217879i	0.796250	−	0.604968i	$-0.206814\pi$
$821$	−3.60434	−	6.24289i	−0.125792	−	0.217879i	−0.922042	+	0.387089i	$0.873481\pi$
$822$		0			0
$823$	6.70433	−	3.87075i	0.233698	−	0.134926i	−0.378579	−	0.925569i	$-0.623587\pi$
$823$	6.70433	−	3.87075i	0.233698	−	0.134926i	0.612277	+	0.790643i	$0.290254\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	23.0605	−	13.3140i	0.801891	−	0.462972i	−0.0422411	−	0.999107i	$-0.513450\pi$
$827$	23.0605	−	13.3140i	0.801891	−	0.462972i	0.844132	+	0.536136i	$0.180116\pi$
$828$		0			0
$829$	12.1093			0.420572			0.210286	−	0.977640i	$-0.432561\pi$
$829$	12.1093			0.420572			0.210286	+	0.977640i	$0.432561\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	24.7709	+	14.3015i	0.858262	+	0.495518i
$834$		0			0
$835$	0.161518	−	0.118966i	0.00558955	−	0.00411698i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.20591	−	2.08869i	0.0416325	−	0.0721096i	−0.844458	−	0.535621i	$-0.820077\pi$
$839$	1.20591	−	2.08869i	0.0416325	−	0.0721096i	0.886091	+	0.463512i	$0.153411\pi$
$840$		0			0
$841$	12.6002	−	21.8242i	0.434491	−	0.752560i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.89315	−	15.7579i	0.237131	−	0.542088i
$846$		0			0
$847$		−	5.12954i		−	0.176253i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.11490	−	5.39517i	−0.106777	−	0.184944i
$852$		0			0
$853$	−23.9717	−	13.8401i	−0.820775	−	0.473875i	0.0299085	−	0.999553i	$-0.490478\pi$
$853$	−23.9717	−	13.8401i	−0.820775	−	0.473875i	−0.850684	+	0.525678i	$0.823812\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.2071	+	8.20245i	0.485304	+	0.280190i	0.722624	−	0.691241i	$-0.242936\pi$
$857$	14.2071	+	8.20245i	0.485304	+	0.280190i	−0.237320	+	0.971431i	$0.576269\pi$
$858$		0			0
$859$	−17.4715	−	30.2616i	−0.596121	−	1.03251i	−0.993388	−	0.114808i	$-0.963375\pi$
$859$	−17.4715	−	30.2616i	−0.596121	−	1.03251i	0.397267	−	0.917703i	$-0.369959\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	18.6243i		−	0.633979i	−0.948429	−	0.316990i	$-0.897328\pi$
$863$		−	18.6243i		−	0.633979i	0.948429	−	0.316990i	$-0.102672\pi$
$864$		0			0
$865$	32.4365	+	14.1890i	1.10287	+	0.482442i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−5.42372	+	9.39416i	−0.183987	+	0.318675i
$870$		0			0
$871$	5.28058	−	9.14624i	0.178926	−	0.309908i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.43102	−	7.01228i	−0.0821835	−	0.237058i
$876$		0			0
$877$	−26.3087	−	15.1893i	−0.888381	−	0.512907i	−0.0149683	−	0.999888i	$-0.504765\pi$
$877$	−26.3087	−	15.1893i	−0.888381	−	0.512907i	−0.873413	+	0.486981i	$0.838098\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	26.3772			0.888670			0.444335	−	0.895861i	$-0.353440\pi$
$881$	26.3772			0.888670			0.444335	+	0.895861i	$0.353440\pi$
$882$		0			0
$883$	25.2183	−	14.5598i	0.848664	−	0.489977i	−0.0115356	−	0.999933i	$-0.503672\pi$
$883$	25.2183	−	14.5598i	0.848664	−	0.489977i	0.860200	+	0.509957i	$0.170339\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.3379	−	10.0100i	0.582148	−	0.336104i	−0.179838	−	0.983696i	$-0.557557\pi$
$887$	17.3379	−	10.0100i	0.582148	−	0.336104i	0.761987	+	0.647593i	$0.224224\pi$
$888$		0			0
$889$	−1.09704	−	1.90012i	−0.0367935	−	0.0637281i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−20.2903	+	20.2433i	−0.678990	+	0.677418i
$894$		0			0
$895$	30.0116	−	3.35228i	1.00318	−	0.112054i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	9.28352	+	16.0795i	0.309623	+	0.536283i
$900$		0			0
$901$	−10.0491			−0.334784
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.6931	−	17.2332i	−0.421934	−	0.572852i
$906$		0			0
$907$	−6.50159	−	3.75370i	−0.215882	−	0.124639i	0.388160	−	0.921592i	$-0.373111\pi$
$907$	−6.50159	−	3.75370i	−0.215882	−	0.124639i	−0.604042	+	0.796952i	$0.706444\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−38.3882			−1.27186			−0.635929	−	0.771748i	$-0.719383\pi$
$911$	−38.3882			−1.27186			−0.635929	+	0.771748i	$0.719383\pi$
$912$		0			0
$913$		−	11.2178i		−	0.371254i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.743471	+	0.429243i	0.0245516	+	0.0141749i
$918$		0			0
$919$	37.8811			1.24958			0.624791	−	0.780792i	$-0.285184\pi$
$919$	37.8811			1.24958			0.624791	+	0.780792i	$0.285184\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	13.6353i		−	0.448811i
$924$		0			0
$925$	3.28167	+	14.5065i	0.107901	+	0.476970i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.96821	−	10.3372i	0.195811	−	0.339154i	−0.751355	−	0.659898i	$-0.770600\pi$
$929$	5.96821	−	10.3372i	0.195811	−	0.339154i	0.947166	+	0.320744i	$0.103933\pi$
$930$		0			0
$931$	−27.6258	+	7.36802i	−0.905401	+	0.241477i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.1610	−	7.06946i	−0.528520	−	0.231196i
$936$		0			0
$937$	−11.7299	+	6.77228i	−0.383200	+	0.221241i	−0.679210	−	0.733944i	$-0.737677\pi$
$937$	−11.7299	+	6.77228i	−0.383200	+	0.221241i	0.296010	+	0.955185i	$0.404344\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.04614	+	12.2043i	0.229698	+	0.397848i	0.957718	−	0.287707i	$-0.0928929\pi$
$941$	7.04614	+	12.2043i	0.229698	+	0.397848i	−0.728021	+	0.685555i	$0.759560\pi$
$942$		0			0
$943$			1.03735i			0.0337807i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.58806	−	5.53567i	−0.311570	−	0.179885i	0.336059	−	0.941841i	$-0.390906\pi$
$947$	−9.58806	−	5.53567i	−0.311570	−	0.179885i	−0.647629	+	0.761956i	$0.724239\pi$
$948$		0			0
$949$	−12.9376			−0.419973
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.40004	−	3.69507i	−0.207318	−	0.119695i	0.392747	−	0.919647i	$-0.371525\pi$
$953$	−6.40004	−	3.69507i	−0.207318	−	0.119695i	−0.600064	+	0.799952i	$0.704858\pi$
$954$		0			0
$955$	59.7806	−	6.67745i	1.93446	−	0.216077i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.84534	−	8.39238i	−0.156464	−	0.271004i
$960$		0			0
$961$	59.7307			1.92680
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−46.7652	−	20.4570i	−1.50542	−	0.658534i
$966$		0			0
$967$	1.31785	+	0.760861i	0.0423792	+	0.0244676i	0.521040	−	0.853532i	$-0.325544\pi$
$967$	1.31785	+	0.760861i	0.0423792	+	0.0244676i	−0.478661	+	0.878000i	$0.658878\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−27.2897	+	47.2671i	−0.875768	+	1.51687i	−0.0198254	+	0.999803i	$0.506311\pi$
$971$	−27.2897	+	47.2671i	−0.875768	+	1.51687i	−0.855942	+	0.517071i	$0.827022\pi$
$972$		0			0
$973$	2.16058	−	1.24741i	0.0692651	−	0.0399902i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	13.0130i		−	0.416321i	−0.978095	−	0.208161i	$-0.933252\pi$
$977$		−	13.0130i		−	0.416321i	0.978095	−	0.208161i	$-0.0667477\pi$
$978$		0			0
$979$	12.0307	+	20.8378i	0.384503	+	0.665979i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	17.6166	+	10.1709i	0.561882	+	0.324402i	0.753900	−	0.656989i	$-0.228170\pi$
$983$	17.6166	+	10.1709i	0.561882	+	0.324402i	−0.192019	+	0.981391i	$0.561503\pi$
$984$		0			0
$985$	2.58579	+	23.1495i	0.0823900	+	0.737605i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.4860			−0.524225
$990$		0			0
$991$	−16.9449	+	29.3495i	−0.538274	+	0.932318i	0.460723	+	0.887544i	$0.347590\pi$
$991$	−16.9449	+	29.3495i	−0.538274	+	0.932318i	−0.998997	+	0.0447741i	$0.985743\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.07422	−	2.81614i	−0.0657573	−	0.0892775i
$996$		0			0
$997$	3.05162	−	1.76185i	0.0966458	−	0.0557985i	−0.450898	−	0.892575i	$-0.648896\pi$
$997$	3.05162	−	1.76185i	0.0966458	−	0.0557985i	0.547544	+	0.836777i	$0.315563\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3420.2.bj.c.1189.1		20
3.2	odd	2		380.2.r.a.49.9	yes	20
5.4	even	2	inner	3420.2.bj.c.1189.7		20
15.2	even	4		1900.2.i.g.201.9		20
15.8	even	4		1900.2.i.g.201.2		20
15.14	odd	2		380.2.r.a.49.2	✓	20
19.7	even	3	inner	3420.2.bj.c.2629.7		20
57.26	odd	6		380.2.r.a.349.2	yes	20
95.64	even	6	inner	3420.2.bj.c.2629.1		20
285.83	even	12		1900.2.i.g.501.2		20
285.197	even	12		1900.2.i.g.501.9		20
285.254	odd	6		380.2.r.a.349.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.2	✓	20	15.14	odd	2
380.2.r.a.49.9	yes	20	3.2	odd	2
380.2.r.a.349.2	yes	20	57.26	odd	6
380.2.r.a.349.9	yes	20	285.254	odd	6
1900.2.i.g.201.2		20	15.8	even	4
1900.2.i.g.201.9		20	15.2	even	4
1900.2.i.g.501.2		20	285.83	even	12
1900.2.i.g.501.9		20	285.197	even	12
3420.2.bj.c.1189.1		20	1.1	even	1	trivial
3420.2.bj.c.1189.7		20	5.4	even	2	inner
3420.2.bj.c.2629.1		20	95.64	even	6	inner
3420.2.bj.c.2629.7		20	19.7	even	3	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:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22225 + 0.248224i) q^{5} +0.663818i q^{7} +1.80905 q^{11} +(1.99526 - 1.15197i) q^{13} +(3.77643 + 2.18033i) q^{17} +(-4.21168 + 1.12329i) q^{19} +(-1.81374 + 1.04716i) q^{23} +(4.87677 - 1.10323i) q^{25} +(-0.974621 - 1.68809i) q^{29} -9.52527 q^{31} +(-0.164775 - 1.47517i) q^{35} +2.97461i q^{37} +(0.247657 - 0.428954i) q^{41} +(6.81715 + 3.93588i) q^{43} +(5.69449 - 3.28772i) q^{47} +6.55935 q^{49} +(-1.99575 + 1.15225i) q^{53} +(-4.02016 + 0.449050i) q^{55} +(-3.88559 + 6.73003i) q^{59} +(-5.36021 - 9.28415i) q^{61} +(-4.14802 + 3.05522i) q^{65} +(3.96984 - 2.29199i) q^{67} +(2.95914 - 5.12538i) q^{71} +(-4.86313 - 2.80773i) q^{73} +1.20088i q^{77} +(-2.99810 + 5.19286i) q^{79} -6.20090i q^{83} +(-8.93338 - 3.90782i) q^{85} +(6.65028 + 11.5186i) q^{89} +(0.764696 + 1.32449i) q^{91} +(9.08057 - 3.54166i) q^{95} +(8.80695 + 5.08470i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) \) 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

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