LMFDB - Embedded newform 3420.2.bj.c.1189.7

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			1189.7
Root			$-2.10552 - 1.21562i$ of defining polynomial
Character	$\chi$	$=$	3420.1189
Dual form			3420.2.bj.c.2629.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.896156 + 2.04863i) q^{5} -0.663818i q^{7} +1.80905 q^{11} +(-1.99526 + 1.15197i) q^{13} +(-3.77643 - 2.18033i) q^{17} +(-4.21168 + 1.12329i) q^{19} +(1.81374 - 1.04716i) q^{23} +(-3.39381 + 3.67179i) q^{25} +(-0.974621 - 1.68809i) q^{29} -9.52527 q^{31} +(1.35992 - 0.594885i) q^{35} -2.97461i q^{37} +(0.247657 - 0.428954i) q^{41} +(-6.81715 - 3.93588i) q^{43} +(-5.69449 + 3.28772i) q^{47} +6.55935 q^{49} +(1.99575 - 1.15225i) q^{53} +(1.62119 + 3.70609i) q^{55} +(-3.88559 + 6.73003i) q^{59} +(-5.36021 - 9.28415i) q^{61} +(-4.14802 - 3.05522i) q^{65} +(-3.96984 + 2.29199i) q^{67} +(2.95914 - 5.12538i) q^{71} +(4.86313 + 2.80773i) q^{73} -1.20088i q^{77} +(-2.99810 + 5.19286i) q^{79} +6.20090i q^{83} +(1.08242 - 9.69045i) q^{85} +(6.65028 + 11.5186i) q^{89} +(0.764696 + 1.32449i) q^{91} +(-6.07552 - 7.62155i) q^{95} +(-8.80695 - 5.08470i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.896156	+	2.04863i	0.400773	+	0.916177i
$5$	0.896156	+	2.04863i	0.400773	+	0.916177i
$6$		0			0
$7$		−	0.663818i		−	0.250900i	−0.992100	−	0.125450i	$-0.959963\pi$
$7$		−	0.663818i		−	0.250900i	0.992100	−	0.125450i	$-0.0400374\pi$
$8$		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	−0.750487	−	0.660886i	$-0.770181\pi$
$13$	−1.99526	+	1.15197i	−0.553386	+	0.319498i	0.197100	+	0.980383i	$0.436847\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.77643	−	2.18033i	−0.915920	−	0.528807i	−0.0335887	−	0.999436i	$-0.510694\pi$
$17$	−3.77643	−	2.18033i	−0.915920	−	0.528807i	−0.882331	+	0.470629i	$0.844027\pi$
$18$		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	−0.298840	−	0.954303i	$-0.596600\pi$
$23$	1.81374	−	1.04716i	0.378191	−	0.218349i	0.677031	+	0.735955i	$0.263266\pi$
$24$		0			0
$25$	−3.39381	+	3.67179i	−0.678762	+	0.734359i
$26$		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
$35$	1.35992	−	0.594885i	0.229869	−	0.100554i
$36$		0			0
$37$		−	2.97461i		−	0.489023i	−0.969646	−	0.244511i	$-0.921372\pi$
$37$		−	2.97461i		−	0.489023i	0.969646	−	0.244511i	$-0.0786276\pi$
$38$		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	−0.119884	−	0.992788i	$-0.538252\pi$
$43$	−6.81715	−	3.93588i	−1.03960	−	0.600216i	−0.919721	+	0.392572i	$0.871585\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.69449	+	3.28772i	−0.830627	+	0.479563i	−0.854067	−	0.520163i	$-0.825871\pi$
$47$	−5.69449	+	3.28772i	−0.830627	+	0.479563i	0.0234403	+	0.999725i	$0.492538\pi$
$48$		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	−0.356629	−	0.934246i	$-0.616074\pi$
$53$	1.99575	−	1.15225i	0.274137	−	0.158273i	0.630766	+	0.775973i	$0.282741\pi$
$54$		0			0
$55$	1.62119	+	3.70609i	0.218602	+	0.499729i
$56$		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	−0.722495	−	0.691376i	$-0.757005\pi$
$67$	−3.96984	+	2.29199i	−0.484993	+	0.280011i	0.237502	+	0.971387i	$0.423671\pi$
$68$		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	0.756824	−	0.653618i	$-0.226750\pi$
$73$	4.86313	+	2.80773i	0.569187	+	0.328620i	−0.187638	+	0.982238i	$0.560083\pi$
$74$		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	$0.110535\pi$
$83$			6.20090i			0.680638i	−0.940310	+	0.340319i	$0.889465\pi$
$84$		0			0
$85$	1.08242	−	9.69045i	0.117404	−	1.05108i
$86$		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
$95$	−6.07552	−	7.62155i	−0.623335	−	0.781955i
$96$		0			0
$97$	−8.80695	−	5.08470i	−0.894211	−	0.516273i	−0.0188932	−	0.999822i	$-0.506014\pi$
$97$	−8.80695	−	5.08470i	−0.894211	−	0.516273i	−0.875317	+	0.483549i	$0.839348\pi$
$98$		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	$-0.647750\pi$
$103$		−	18.1501i		−	1.78839i	0.447681	−	0.894193i	$-0.352250\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	13.9698i		−	1.35051i	−0.737584	−	0.675256i	$-0.764033\pi$
$107$		−	13.9698i		−	1.35051i	0.737584	−	0.675256i	$-0.235967\pi$
$108$		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	$-0.828743\pi$
$113$		−	10.8946i		−	1.02487i	0.858725	−	0.512437i	$-0.171257\pi$
$114$		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	−0.367595	−	0.929986i	$-0.619819\pi$
$127$	2.86242	−	1.65262i	0.253998	−	0.146646i	0.621594	+	0.783340i	$0.286486\pi$
$128$		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	0.149197	−	0.988807i	$-0.452331\pi$
$137$	12.6426	−	7.29920i	1.08013	−	0.623613i	0.930931	+	0.365195i	$0.118998\pi$
$138$		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
$155$	−8.53613	−	19.5138i	−0.685638	−	1.56739i
$156$		0			0
$157$	−2.29893	−	1.32729i	−0.183474	−	0.105929i	0.405450	−	0.914117i	$-0.367115\pi$
$157$	−2.29893	−	1.32729i	−0.183474	−	0.105929i	−0.588924	+	0.808188i	$0.700448\pi$
$158$		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	$-0.717431\pi$
$163$		−	19.8052i		−	1.55127i	0.631184	−	0.775633i	$-0.282569\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.0776925	−	0.0448558i	0.00601203	−	0.00347105i	−0.496991	−	0.867756i	$-0.665562\pi$
$167$	0.0776925	−	0.0448558i	0.00601203	−	0.00347105i	0.503003	+	0.864285i	$0.332228\pi$
$168$		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	0.920541	−	0.390646i	$-0.127748\pi$
$173$	13.7120	+	7.91662i	1.04250	+	0.601889i	0.121962	+	0.992535i	$0.461082\pi$
$174$		0			0
$175$	2.43740	+	2.25287i	0.184250	+	0.170301i
$176$		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
$185$	6.09389	−	2.66571i	0.448032	−	0.195987i
$186$		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	−0.426461	−	0.904506i	$-0.640240\pi$
$193$	−19.7692	−	11.4137i	−1.42302	−	0.821579i	−0.996556	+	0.0829272i	$0.973573\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			10.4172i			0.742192i	0.928594	+	0.371096i	$0.121018\pi$
$197$			10.4172i			0.742192i	−0.928594	+	0.371096i	$0.878982\pi$
$198$		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
$205$	1.10071	+	0.122949i	0.0768769	+	0.00858710i
$206$		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
$215$	1.95396	−	17.4930i	0.133259	−	1.19301i
$216$		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	−0.327054	−	0.945006i	$-0.606056\pi$
$223$	−19.5472	−	11.2856i	−1.30898	−	0.755740i	−0.981926	+	0.189266i	$0.939389\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	11.4187i		−	0.757883i	−0.925421	−	0.378941i	$-0.876288\pi$
$227$		−	11.4187i		−	0.757883i	0.925421	−	0.378941i	$-0.123712\pi$
$228$		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	0.0667219	−	0.997772i	$-0.478746\pi$
$233$	−11.6621	−	6.73314i	−0.764013	−	0.441103i	−0.830735	+	0.556669i	$0.812079\pi$
$234$		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
$245$	5.87820	+	13.4377i	0.375544	+	0.858503i
$246$		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	−0.908595	−	0.417678i	$-0.862844\pi$
$257$	−16.0500	+	9.26649i	−1.00117	+	0.578028i	−0.0925780	+	0.995705i	$0.529511\pi$
$258$		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	0.184843	−	0.982768i	$-0.440822\pi$
$263$	−9.30609	−	5.37288i	−0.573838	−	0.331306i	−0.758681	+	0.651462i	$0.774156\pi$
$264$		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
$275$	−6.13958	+	6.64247i	−0.370231	+	0.400556i
$276$		0			0
$277$		−	5.94922i		−	0.357454i	−0.983899	−	0.178727i	$-0.942802\pi$
$277$		−	5.94922i		−	0.357454i	0.983899	−	0.178727i	$-0.0571979\pi$
$278$		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	$0.0500196\pi$
$283$	27.2029	+	15.7056i	1.61705	+	0.933603i	0.629368	+	0.777107i	$0.283314\pi$
$284$		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	$0.307186\pi$
$293$			28.1435i			1.64416i	−0.569372	+	0.822080i	$0.692814\pi$
$294$		0			0
$295$	−17.2695	−	1.92899i	−1.00547	−	0.112310i
$296$		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	0.985782	−	0.168028i	$-0.0537400\pi$
$307$	23.3588	+	13.4862i	1.33316	+	0.769698i	0.347374	+	0.937727i	$0.387073\pi$
$308$		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	−0.976878	−	0.213795i	$-0.931417\pi$
$313$	−22.6484	+	13.0761i	−1.28017	+	0.739104i	−0.303287	+	0.952899i	$0.598084\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.5314	+	13.0085i	−1.26549	+	0.730632i	−0.974131	−	0.225982i	$-0.927441\pi$
$317$	−22.5314	+	13.0085i	−1.26549	+	0.730632i	−0.291359	+	0.956614i	$0.594108\pi$
$318$		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
$325$	2.54176	−	11.2357i	0.140992	−	0.623247i
$326$		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	0.403700	−	0.914891i	$-0.367724\pi$
$337$	−3.42862	−	1.97951i	−0.186769	−	0.107831i	−0.590469	+	0.807060i	$0.701057\pi$
$338$		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	0.384153	−	0.923269i	$-0.374494\pi$
$347$	−4.16047	−	2.40205i	−0.223345	−	0.128949i	−0.607498	+	0.794321i	$0.707827\pi$
$348$		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	$0.159888\pi$
$353$			18.0910i			0.962889i	−0.876477	+	0.481444i	$0.840112\pi$
$354$		0			0
$355$	13.1519	+	1.46905i	0.698029	+	0.0779693i
$356$		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
$365$	−1.39389	+	12.4789i	−0.0729595	+	0.653178i
$366$		0			0
$367$	8.55319	−	4.93819i	0.446473	−	0.257771i	−0.259866	−	0.965645i	$-0.583679\pi$
$367$	8.55319	−	4.93819i	0.446473	−	0.257771i	0.706339	+	0.707873i	$0.250345\pi$
$368$		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	$-0.836591\pi$
$373$		−	18.9698i		−	0.982220i	0.871098	−	0.491110i	$-0.163409\pi$
$374$		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	0.812371	−	0.583140i	$-0.198176\pi$
$383$	13.9643	+	8.06230i	0.713543	+	0.411964i	−0.0988287	+	0.995104i	$0.531510\pi$
$384$		0			0
$385$	2.46017	−	1.07618i	0.125382	−	0.0548471i
$386$		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
$395$	−13.3250	−	1.48840i	−0.670455	−	0.0748894i
$396$		0			0
$397$	13.8674	+	8.00633i	0.695983	+	0.401826i	0.805850	−	0.592120i	$-0.201709\pi$
$397$	13.8674	+	8.00633i	0.695983	+	0.401826i	−0.109866	+	0.993946i	$0.535042\pi$
$398$		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
$415$	−12.7034	+	5.55698i	−0.623585	+	0.272781i
$416$		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	−0.996775	−	0.0802463i	$-0.974429\pi$
$433$	−29.6662	+	17.1278i	−1.42567	+	0.823109i	−0.428892	+	0.903356i	$0.641096\pi$
$434$		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	−0.987543	−	0.157352i	$-0.949704\pi$
$443$	−28.3099	+	16.3447i	−1.34504	+	0.776561i	−0.357500	+	0.933913i	$0.616371\pi$
$444$		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	$0.154244\pi$
$457$			19.9166i			0.931661i	−0.884874	+	0.465830i	$0.845756\pi$
$458$		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	$0.218590\pi$
$463$			27.2843i			1.26801i	−0.773329	+	0.634005i	$0.781410\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	39.5912i		−	1.83206i	−0.401107	−	0.916031i	$-0.631375\pi$
$467$		−	39.5912i		−	1.83206i	0.401107	−	0.916031i	$-0.368625\pi$
$468$		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
$475$	10.1692	−	19.2766i	0.466593	−	0.884472i
$476$		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
$485$	2.52428	−	22.5989i	0.114622	−	1.02616i
$486$		0			0
$487$		−	29.9289i		−	1.35621i	−0.734966	−	0.678104i	$-0.762802\pi$
$487$		−	29.9289i		−	1.35621i	0.734966	−	0.678104i	$-0.237198\pi$
$488$		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	−0.135036	−	0.990841i	$-0.543115\pi$
$503$	14.7022	−	8.48833i	0.655539	−	0.378476i	0.790575	+	0.612365i	$0.209782\pi$
$504$		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
$515$	37.1830	−	16.2654i	1.63848	−	0.716737i
$516$		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	−0.421155	−	0.906989i	$-0.638375\pi$
$523$	3.51597	−	2.02994i	0.153742	−	0.0887633i	0.574898	+	0.818225i	$0.305042\pi$
$524$		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
$535$	28.6190	−	12.5191i	1.23731	−	0.541249i
$536$		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
$545$	−40.9135	−	4.57001i	−1.75254	−	0.195758i
$546$		0			0
$547$	−29.6808	+	17.1362i	−1.26906	+	0.732692i	−0.974810	−	0.223036i	$-0.928403\pi$
$547$	−29.6808	+	17.1362i	−1.26906	+	0.732692i	−0.294250	+	0.955729i	$0.595070\pi$
$548$		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	0.491717	−	0.870755i	$-0.336369\pi$
$557$	35.2047	−	20.3255i	1.49167	−	0.861217i	0.999955	+	0.00953795i	$0.00303607\pi$
$558$		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	$-0.856221\pi$
$563$		−	20.7137i		−	0.872980i	0.899709	−	0.436490i	$-0.143779\pi$
$564$		0			0
$565$	22.3190	−	9.76323i	0.938967	−	0.410742i
$566$		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
$575$	−2.31052	+	10.2135i	−0.0963553	+	0.425934i
$576$		0			0
$577$		−	2.96818i		−	0.123567i	−0.998090	−	0.0617834i	$-0.980321\pi$
$577$		−	2.96818i		−	0.123567i	0.998090	−	0.0617834i	$-0.0196788\pi$
$578$		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	0.989527	−	0.144348i	$-0.0461085\pi$
$587$	32.9328	+	19.0138i	1.35928	+	0.784781i	0.369754	+	0.929130i	$0.379442\pi$
$588$		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	$-0.309442\pi$
$593$	38.0060	−	21.9428i	1.56072	−	0.901081i	0.997184	−	0.0749876i	$-0.0238917\pi$
$594$		0			0
$595$	−6.43270	−	0.718528i	−0.263715	−	0.0294568i
$596$		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
$605$	−6.92489	−	15.8305i	−0.281537	−	0.643600i
$606$		0			0
$607$		−	2.10357i		−	0.0853814i	−0.999088	−	0.0426907i	$-0.986407\pi$
$607$		−	2.10357i		−	0.0853814i	0.999088	−	0.0426907i	$-0.0135930\pi$
$608$		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	0.964520	−	0.264010i	$-0.0850450\pi$
$613$	30.1598	+	17.4127i	1.21814	+	0.703294i	0.253621	+	0.967304i	$0.418378\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−15.8782	+	9.16726i	−0.639231	+	0.369060i	−0.784318	−	0.620359i	$-0.786987\pi$
$617$	−15.8782	+	9.16726i	−0.639231	+	0.369060i	0.145087	+	0.989419i	$0.453654\pi$
$618$		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
$625$	−1.96412	−	24.9227i	−0.0785649	−	0.996909i
$626$		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	0.679367	−	0.733799i	$-0.262255\pi$
$643$	9.72615	+	5.61539i	0.383562	+	0.221450i	−0.295805	+	0.955248i	$0.595588\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			2.00223i			0.0787157i	0.999225	+	0.0393578i	$0.0125312\pi$
$647$			2.00223i			0.0787157i	−0.999225	+	0.0393578i	$0.987469\pi$
$648$		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	$0.0201895\pi$
$653$			3.23945i			0.126770i	−0.997989	+	0.0633848i	$0.979810\pi$
$654$		0			0
$655$	2.87393	+	0.321016i	0.112294	+	0.0125431i
$656$		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
$665$	−5.05933	+	4.03304i	−0.196192	+	0.156395i
$666$		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	$-0.687900\pi$
$673$		−	43.1041i		−	1.66154i	0.556616	−	0.830770i	$-0.312100\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	12.3727i		−	0.475522i	−0.971324	−	0.237761i	$-0.923587\pi$
$677$		−	12.3727i		−	0.475522i	0.971324	−	0.237761i	$-0.0764134\pi$
$678$		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	$-0.783742\pi$
$683$		−	32.8415i		−	1.25664i	0.777954	−	0.628322i	$-0.216258\pi$
$684$		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
$725$	9.50600	+	2.15046i	0.353044	+	0.0798660i
$726$		0			0
$727$	19.1410	+	11.0511i	0.709902	+	0.409862i	0.811025	−	0.585012i	$-0.198910\pi$
$727$	19.1410	+	11.0511i	0.709902	+	0.409862i	−0.101123	+	0.994874i	$0.532244\pi$
$728$		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	$0.114714\pi$
$733$			19.0945i			0.705271i	−0.935761	+	0.352635i	$0.885286\pi$
$734$		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	0.729368	−	0.684122i	$-0.239814\pi$
$743$	13.6722	+	7.89364i	0.501584	+	0.289590i	−0.227783	+	0.973712i	$0.573148\pi$
$744$		0			0
$745$	−17.0514	−	1.90463i	−0.624717	−	0.0697804i
$746$		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
$755$	1.45753	+	3.33196i	0.0530451	+	0.121262i
$756$		0			0
$757$	12.7465	+	7.35917i	0.463278	+	0.267473i	0.713421	−	0.700735i	$-0.247145\pi$
$757$	12.7465	+	7.35917i	0.463278	+	0.267473i	−0.250144	+	0.968209i	$0.580478\pi$
$758$		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	−0.816343	−	0.577567i	$-0.804002\pi$
$773$	−20.1384	+	11.6269i	−0.724327	+	0.418190i	0.0920165	+	0.995757i	$0.470669\pi$
$774$		0			0
$775$	32.3269	−	34.9748i	1.16122	−	1.25633i
$776$		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
$785$	0.658928	−	5.89912i	0.0235181	−	0.210549i
$786$		0			0
$787$			19.5711i			0.697636i	0.937191	+	0.348818i	$0.113417\pi$
$787$			19.5711i			0.697636i	−0.937191	+	0.348818i	$0.886583\pi$
$788$		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	$0.320057\pi$
$797$			47.6782i			1.68885i	−0.535676	+	0.844424i	$0.679943\pi$
$798$		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
$815$	40.5737	−	17.7486i	1.42123	−	0.621706i
$816$		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	−0.612277	−	0.790643i	$-0.709746\pi$
$823$	−6.70433	+	3.87075i	−0.233698	+	0.134926i	0.378579	+	0.925569i	$0.376413\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.0605	+	13.3140i	−0.801891	+	0.462972i	−0.844132	−	0.536136i	$-0.819884\pi$
$827$	−23.0605	+	13.3140i	−0.801891	+	0.462972i	0.0422411	+	0.999107i	$0.486550\pi$
$828$		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
$845$	−17.0933	−	1.90931i	−0.588028	−	0.0656823i
$846$		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	0.850684	−	0.525678i	$-0.176188\pi$
$853$	23.9717	+	13.8401i	0.820775	+	0.473875i	−0.0299085	+	0.999553i	$0.509522\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.2071	−	8.20245i	−0.485304	−	0.280190i	0.237320	−	0.971431i	$-0.423731\pi$
$857$	−14.2071	−	8.20245i	−0.485304	−	0.280190i	−0.722624	+	0.691241i	$0.757064\pi$
$858$		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	$0.102672\pi$
$863$			18.6243i			0.633979i	−0.948429	+	0.316990i	$0.897328\pi$
$864$		0			0
$865$	−3.93018	+	35.1854i	−0.133630	+	1.19634i
$866$		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	0.873413	−	0.486981i	$-0.161902\pi$
$877$	26.3087	+	15.1893i	0.888381	+	0.512907i	0.0149683	+	0.999888i	$0.495235\pi$
$878$		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	−0.860200	−	0.509957i	$-0.829661\pi$
$883$	−25.2183	+	14.5598i	−0.848664	+	0.489977i	0.0115356	+	0.999933i	$0.496328\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.3379	+	10.0100i	−0.582148	+	0.336104i	−0.761987	−	0.647593i	$-0.775776\pi$
$887$	−17.3379	+	10.0100i	−0.582148	+	0.336104i	0.179838	+	0.983696i	$0.442443\pi$
$888$		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
$895$	−12.1027	−	27.6670i	−0.404547	−	0.924805i
$896$		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	0.604042	−	0.796952i	$-0.293556\pi$
$907$	6.50159	+	3.75370i	0.215882	+	0.124639i	−0.388160	+	0.921592i	$0.626889\pi$
$908$		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
$925$	10.9222	+	10.0953i	0.359118	+	0.331930i
$926$		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
$935$	1.95815	−	17.5305i	0.0640383	−	0.573310i
$936$		0			0
$937$	11.7299	−	6.77228i	0.383200	−	0.221241i	−0.296010	−	0.955185i	$-0.595656\pi$
$937$	11.7299	−	6.77228i	0.383200	−	0.221241i	0.679210	+	0.733944i	$0.262323\pi$
$938$		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	0.647629	−	0.761956i	$-0.275761\pi$
$947$	9.58806	+	5.53567i	0.311570	+	0.179885i	−0.336059	+	0.941841i	$0.609094\pi$
$948$		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	0.600064	−	0.799952i	$-0.295142\pi$
$953$	6.40004	+	3.69507i	0.207318	+	0.119695i	−0.392747	+	0.919647i	$0.628475\pi$
$954$		0			0
$955$	−24.1075	−	55.1103i	−0.780099	−	1.78333i
$956$		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
$965$	5.66632	−	50.7283i	0.182405	−	1.63300i
$966$		0			0
$967$	−1.31785	−	0.760861i	−0.0423792	−	0.0244676i	0.478661	−	0.878000i	$-0.341122\pi$
$967$	−1.31785	−	0.760861i	−0.0423792	−	0.0244676i	−0.521040	+	0.853532i	$0.674456\pi$
$968$		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	$0.0667477\pi$
$977$			13.0130i			0.416321i	−0.978095	+	0.208161i	$0.933252\pi$
$978$		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	0.192019	−	0.981391i	$-0.438497\pi$
$983$	−17.6166	−	10.1709i	−0.561882	−	0.324402i	−0.753900	+	0.656989i	$0.771830\pi$
$984$		0			0
$985$	−21.3410	+	9.33541i	−0.679980	+	0.297451i
$986$		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	−0.547544	−	0.836777i	$-0.684437\pi$
$997$	−3.05162	+	1.76185i	−0.0966458	+	0.0557985i	0.450898	+	0.892575i	$0.351104\pi$
$998$		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.1189.7		20
3.2	odd	2		380.2.r.a.49.2	✓	20
5.4	even	2	inner	3420.2.bj.c.1189.1		20
15.2	even	4		1900.2.i.g.201.2		20
15.8	even	4		1900.2.i.g.201.9		20
15.14	odd	2		380.2.r.a.49.9	yes	20
19.7	even	3	inner	3420.2.bj.c.2629.1		20
57.26	odd	6		380.2.r.a.349.9	yes	20
95.64	even	6	inner	3420.2.bj.c.2629.7		20
285.83	even	12		1900.2.i.g.501.9		20
285.197	even	12		1900.2.i.g.501.2		20
285.254	odd	6		380.2.r.a.349.2	yes	20

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

\(f(q)\)	\(=\)	\(q+(0.896156 + 2.04863i) q^{5} -0.663818i q^{7} +1.80905 q^{11} +(-1.99526 + 1.15197i) q^{13} +(-3.77643 - 2.18033i) q^{17} +(-4.21168 + 1.12329i) q^{19} +(1.81374 - 1.04716i) q^{23} +(-3.39381 + 3.67179i) q^{25} +(-0.974621 - 1.68809i) q^{29} -9.52527 q^{31} +(1.35992 - 0.594885i) q^{35} -2.97461i q^{37} +(0.247657 - 0.428954i) q^{41} +(-6.81715 - 3.93588i) q^{43} +(-5.69449 + 3.28772i) q^{47} +6.55935 q^{49} +(1.99575 - 1.15225i) q^{53} +(1.62119 + 3.70609i) q^{55} +(-3.88559 + 6.73003i) q^{59} +(-5.36021 - 9.28415i) q^{61} +(-4.14802 - 3.05522i) q^{65} +(-3.96984 + 2.29199i) q^{67} +(2.95914 - 5.12538i) q^{71} +(4.86313 + 2.80773i) q^{73} -1.20088i q^{77} +(-2.99810 + 5.19286i) q^{79} +6.20090i q^{83} +(1.08242 - 9.69045i) q^{85} +(6.65028 + 11.5186i) q^{89} +(0.764696 + 1.32449i) q^{91} +(-6.07552 - 7.62155i) q^{95} +(-8.80695 - 5.08470i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) \) 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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