LMFDB - Embedded newform 3460.1.bd.a.587.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3460,1,Mod(7,3460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3460, base_ring=CyclotomicField(172))

chi = DirichletCharacter(H, H._module([86, 43, 95]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3460.7");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3460 = 2^{2} \cdot 5 \cdot 173 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3460.bd (of order $172$, degree $84$, 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:	$1.72676494371$
Analytic rank:	$0$
Dimension:	$84$
Coefficient field:	$\Q(\zeta_{172})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{84} - x^{82} + x^{80} - x^{78} + x^{76} - x^{74} + x^{72} - x^{70} + x^{68} - x^{66} + x^{64} + \cdots + 1 $ x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{172}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{172} - \cdots)$

Embedding invariants

Embedding label			587.1
Root			$-0.217430 - 0.976076i$ of defining polynomial
Character	$\chi$	$=$	3460.587
Dual form			3460.1.bd.a.2623.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.551768 - 0.833998i) q^{2} +(-0.391105 - 0.920346i) q^{4} +(0.768647 + 0.639673i) q^{5} +(-0.983366 - 0.181637i) q^{8} +(-0.989343 - 0.145601i) q^{9} +O(q^{10})$	\(q+(0.551768 - 0.833998i) q^{2} +(-0.391105 - 0.920346i) q^{4} +(0.768647 + 0.639673i) q^{5} +(-0.983366 - 0.181637i) q^{8} +(-0.989343 - 0.145601i) q^{9} +(0.957601 - 0.288099i) q^{10} +(0.393753 + 1.93335i) q^{13} +(-0.694074 + 0.719903i) q^{16} +(1.90278 + 0.497452i) q^{17} +(-0.667319 + 0.744772i) q^{18} +(0.288099 - 0.957601i) q^{20} +(0.181637 + 0.983366i) q^{25} +(1.82967 + 0.738371i) q^{26} +(0.636770 + 0.824645i) q^{29} +(0.217430 + 0.976076i) q^{32} +(1.46477 - 1.31244i) q^{34} +(0.252933 + 0.967484i) q^{36} +(1.28045 - 0.463104i) q^{37} +(-0.639673 - 0.768647i) q^{40} +(-1.09204 - 0.666463i) q^{41} +(-0.667319 - 0.744772i) q^{45} +(-0.457242 - 0.889342i) q^{49} +(0.920346 + 0.391105i) q^{50} +(1.62535 - 1.11853i) q^{52} +(-0.947008 - 1.68739i) q^{53} +(1.03910 - 0.0760524i) q^{58} +(0.412142 - 0.703919i) q^{61} +(0.934016 + 0.357231i) q^{64} +(-0.934054 + 1.73794i) q^{65} +(-0.286358 - 1.94577i) q^{68} +(0.946440 + 0.322880i) q^{72} +(0.364429 + 0.162786i) q^{73} +(0.320282 - 1.32342i) q^{74} +(-0.994001 + 0.109371i) q^{80} +(0.957601 + 0.288099i) q^{81} +(-1.15838 + 0.543027i) q^{82} +(1.14436 + 1.59952i) q^{85} +(-1.35494 - 0.301825i) q^{89} +(-0.989343 + 0.145601i) q^{90} +(-1.77750 - 0.0649611i) q^{97} +(-0.994001 - 0.109371i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2 q^{4} + 2 q^{9}+O(q^{10}) $ 84 * q + 2 * q^4 + 2 * q^9	$ 84 q + 2 q^{4} + 2 q^{9} - 2 q^{10} + 2 q^{13} - 2 q^{16} + 2 q^{25} + 2 q^{26} - 2 q^{36} - 2 q^{37} + 2 q^{40} - 2 q^{49} - 2 q^{52} + 4 q^{58} - 2 q^{61} + 2 q^{64} - 2 q^{65} + 2 q^{73} + 2 q^{74} - 2 q^{81} + 4 q^{82} + 4 q^{89} + 2 q^{90}+O(q^{100}) $ 84 * q + 2 * q^4 + 2 * q^9 - 2 * q^10 + 2 * q^13 - 2 * q^16 + 2 * q^25 + 2 * q^26 - 2 * q^36 - 2 * q^37 + 2 * q^40 - 2 * q^49 - 2 * q^52 + 4 * q^58 - 2 * q^61 + 2 * q^64 - 2 * q^65 + 2 * q^73 + 2 * q^74 - 2 * q^81 + 4 * q^82 + 4 * q^89 + 2 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3460\mathbb{Z}\right)^\times$.

$n$	$521$	$1731$	$2077$
$\chi(n)$	$e\left(\frac{75}{172}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.551768	−	0.833998i	0.551768	−	0.833998i
$2$	0.551768	−	0.833998i	0.551768	−	0.833998i
$3$		0			0		0.0729953	−	0.997332i	$-0.476744\pi$
$3$		0			0		−0.0729953	+	0.997332i	$0.523256\pi$
$4$	−0.391105	−	0.920346i	−0.391105	−	0.920346i
$5$	0.768647	+	0.639673i	0.768647	+	0.639673i
$5$	0.768647	+	0.639673i	0.768647	+	0.639673i
$6$		0			0
$7$		0			0		0.520940	−	0.853593i	$-0.325581\pi$
$7$		0			0		−0.520940	+	0.853593i	$0.674419\pi$
$8$	−0.983366	−	0.181637i	−0.983366	−	0.181637i
$9$	−0.989343	−	0.145601i	−0.989343	−	0.145601i
$10$	0.957601	−	0.288099i	0.957601	−	0.288099i
$11$		0			0		−0.995833	−	0.0911985i	$-0.970930\pi$
$11$		0			0		0.995833	+	0.0911985i	$0.0290698\pi$
$12$		0			0
$13$	0.393753	+	1.93335i	0.393753	+	1.93335i	0.357231	+	0.934016i	$0.383721\pi$
$13$	0.393753	+	1.93335i	0.393753	+	1.93335i	0.0365220	+	0.999333i	$0.488372\pi$
$14$		0			0
$15$		0			0
$16$	−0.694074	+	0.719903i	−0.694074	+	0.719903i
$17$	1.90278	+	0.497452i	1.90278	+	0.497452i	0.997332	+	0.0729953i	$0.0232558\pi$
$17$	1.90278	+	0.497452i	1.90278	+	0.497452i	0.905448	+	0.424457i	$0.139535\pi$
$18$	−0.667319	+	0.744772i	−0.667319	+	0.744772i
$19$		0			0		0.940385	−	0.340112i	$-0.110465\pi$
$19$		0			0		−0.940385	+	0.340112i	$0.889535\pi$
$20$	0.288099	−	0.957601i	0.288099	−	0.957601i
$21$		0			0
$22$		0			0
$23$		0			0		−0.0911985	−	0.995833i	$-0.529070\pi$
$23$		0			0		0.0911985	+	0.995833i	$0.470930\pi$
$24$		0			0
$25$	0.181637	+	0.983366i	0.181637	+	0.983366i
$26$	1.82967	+	0.738371i	1.82967	+	0.738371i
$27$		0			0
$28$		0			0
$29$	0.636770	+	0.824645i	0.636770	+	0.824645i	0.994001	−	0.109371i	$-0.0348837\pi$
$29$	0.636770	+	0.824645i	0.636770	+	0.824645i	−0.357231	+	0.934016i	$0.616279\pi$
$30$		0			0
$31$		0			0		−0.0729953	−	0.997332i	$-0.523256\pi$
$31$		0			0		0.0729953	+	0.997332i	$0.476744\pi$
$32$	0.217430	+	0.976076i	0.217430	+	0.976076i
$33$		0			0
$34$	1.46477	−	1.31244i	1.46477	−	1.31244i
$35$		0			0
$36$	0.252933	+	0.967484i	0.252933	+	0.967484i
$37$	1.28045	−	0.463104i	1.28045	−	0.463104i	0.391105	−	0.920346i	$-0.372093\pi$
$37$	1.28045	−	0.463104i	1.28045	−	0.463104i	0.889342	+	0.457242i	$0.151163\pi$
$38$		0			0
$39$		0			0
$40$	−0.639673	−	0.768647i	−0.639673	−	0.768647i
$41$	−1.09204	−	0.666463i	−1.09204	−	0.666463i	−0.145601	−	0.989343i	$-0.546512\pi$
$41$	−1.09204	−	0.666463i	−1.09204	−	0.666463i	−0.946440	+	0.322880i	$0.895349\pi$
$42$		0			0
$43$		0			0		−0.374230	−	0.927336i	$-0.622093\pi$
$43$		0			0		0.374230	+	0.927336i	$0.377907\pi$
$44$		0			0
$45$	−0.667319	−	0.744772i	−0.667319	−	0.744772i
$46$		0			0
$47$		0			0		−0.880843	−	0.473409i	$-0.843023\pi$
$47$		0			0		0.880843	+	0.473409i	$0.156977\pi$
$48$		0			0
$49$	−0.457242	−	0.889342i	−0.457242	−	0.889342i
$50$	0.920346	+	0.391105i	0.920346	+	0.391105i
$51$		0			0
$52$	1.62535	−	1.11853i	1.62535	−	1.11853i
$53$	−0.947008	−	1.68739i	−0.947008	−	1.68739i	−0.694074	−	0.719903i	$-0.744186\pi$
$53$	−0.947008	−	1.68739i	−0.947008	−	1.68739i	−0.252933	−	0.967484i	$-0.581395\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	1.03910	−	0.0760524i	1.03910	−	0.0760524i
$59$		0			0		0.305541	−	0.952179i	$-0.401163\pi$
$59$		0			0		−0.305541	+	0.952179i	$0.598837\pi$
$60$		0			0
$61$	0.412142	−	0.703919i	0.412142	−	0.703919i	−0.581859	−	0.813290i	$-0.697674\pi$
$61$	0.412142	−	0.703919i	0.412142	−	0.703919i	0.994001	+	0.109371i	$0.0348837\pi$
$62$		0			0
$63$		0			0
$64$	0.934016	+	0.357231i	0.934016	+	0.357231i
$65$	−0.934054	+	1.73794i	−0.934054	+	1.73794i
$66$		0			0
$67$		0			0		0.756836	−	0.653605i	$-0.226744\pi$
$67$		0			0		−0.756836	+	0.653605i	$0.773256\pi$
$68$	−0.286358	−	1.94577i	−0.286358	−	1.94577i
$69$		0			0
$70$		0			0
$71$		0			0		0.127507	−	0.991838i	$-0.459302\pi$
$71$		0			0		−0.127507	+	0.991838i	$0.540698\pi$
$72$	0.946440	+	0.322880i	0.946440	+	0.322880i
$73$	0.364429	+	0.162786i	0.364429	+	0.162786i	0.581859	−	0.813290i	$-0.302326\pi$
$73$	0.364429	+	0.162786i	0.364429	+	0.162786i	−0.217430	+	0.976076i	$0.569767\pi$
$74$	0.320282	−	1.32342i	0.320282	−	1.32342i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.473409	−	0.880843i	$-0.656977\pi$
$79$		0			0		0.473409	+	0.880843i	$0.343023\pi$
$80$	−0.994001	+	0.109371i	−0.994001	+	0.109371i
$81$	0.957601	+	0.288099i	0.957601	+	0.288099i
$82$	−1.15838	+	0.543027i	−1.15838	+	0.543027i
$83$		0			0		−0.732460	−	0.680810i	$-0.761628\pi$
$83$		0			0		0.732460	+	0.680810i	$0.238372\pi$
$84$		0			0
$85$	1.14436	+	1.59952i	1.14436	+	1.59952i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.35494	−	0.301825i	−1.35494	−	0.301825i	−0.520940	−	0.853593i	$-0.674419\pi$
$89$	−1.35494	−	0.301825i	−1.35494	−	0.301825i	−0.833998	+	0.551768i	$0.813953\pi$
$90$	−0.989343	+	0.145601i	−0.989343	+	0.145601i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.77750	−	0.0649611i	−1.77750	−	0.0649611i	−0.872049	−	0.489418i	$-0.837209\pi$
$97$	−1.77750	−	0.0649611i	−1.77750	−	0.0649611i	−0.905448	+	0.424457i	$0.860465\pi$
$98$	−0.994001	−	0.109371i	−0.994001	−	0.109371i
$99$		0			0
$100$	0.833998	−	0.551768i	0.833998	−	0.551768i
$101$	0.817767	+	1.66465i	0.817767	+	1.66465i	0.744772	+	0.667319i	$0.232558\pi$
$101$	0.817767	+	1.66465i	0.817767	+	1.66465i	0.0729953	+	0.997332i	$0.476744\pi$
$102$		0			0
$103$		0			0		−0.934016	−	0.357231i	$-0.883721\pi$
$103$		0			0		0.934016	+	0.357231i	$0.116279\pi$
$104$	−0.0360357	−	1.97271i	−0.0360357	−	1.97271i
$105$		0			0
$106$	−1.92981	−	0.141244i	−1.92981	−	0.141244i
$107$		0			0		0.999333	−	0.0365220i	$-0.0116279\pi$
$107$		0			0		−0.999333	+	0.0365220i	$0.988372\pi$
$108$		0			0
$109$	−0.436660	+	1.14169i	−0.436660	+	1.14169i	0.520940	+	0.853593i	$0.325581\pi$
$109$	−0.436660	+	1.14169i	−0.436660	+	1.14169i	−0.957601	+	0.288099i	$0.906977\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.13617	−	0.364581i	1.13617	−	0.364581i	0.322880	−	0.946440i	$-0.395349\pi$
$113$	1.13617	−	0.364581i	1.13617	−	0.364581i	0.813290	+	0.581859i	$0.197674\pi$
$114$		0			0
$115$		0			0
$116$	0.509915	−	0.908571i	0.509915	−	0.908571i
$117$	−0.108059	−	1.97008i	−0.108059	−	1.97008i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.983366	+	0.181637i	0.983366	+	0.181637i
$122$	−0.359660	−	0.732125i	−0.359660	−	0.732125i
$123$		0			0
$124$		0			0
$125$	−0.489418	+	0.872049i	−0.489418	+	0.872049i
$126$		0			0
$127$		0			0		0.957601	−	0.288099i	$-0.0930233\pi$
$127$		0			0		−0.957601	+	0.288099i	$0.906977\pi$
$128$	0.813290	−	0.581859i	0.813290	−	0.581859i
$129$		0			0
$130$	0.934054	+	1.73794i	0.934054	+	1.73794i
$131$		0			0		−0.913050	−	0.407849i	$-0.866279\pi$
$131$		0			0		0.913050	+	0.407849i	$0.133721\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−1.78077	−	0.834792i	−1.78077	−	0.834792i
$137$	−0.587010	−	0.343693i	−0.587010	−	0.343693i	0.181637	−	0.983366i	$-0.441860\pi$
$137$	−0.587010	−	0.343693i	−0.587010	−	0.343693i	−0.768647	+	0.639673i	$0.779070\pi$
$138$		0			0
$139$		0			0		−0.667319	−	0.744772i	$-0.732558\pi$
$139$		0			0		0.667319	+	0.744772i	$0.267442\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.791496	−	0.611174i	0.791496	−	0.611174i
$145$	−0.0380516	+	1.04119i	−0.0380516	+	1.04119i
$146$	0.336843	−	0.214113i	0.336843	−	0.214113i
$147$		0			0
$148$	−0.927005	−	0.997332i	−0.927005	−	0.997332i
$149$	1.78084	+	0.465573i	1.78084	+	0.465573i	0.989343	−	0.145601i	$-0.0465116\pi$
$149$	1.78084	+	0.465573i	1.78084	+	0.465573i	0.791496	+	0.611174i	$0.209302\pi$
$150$		0			0
$151$		0			0		0.994001	−	0.109371i	$-0.0348837\pi$
$151$		0			0		−0.994001	+	0.109371i	$0.965116\pi$
$152$		0			0
$153$	−1.81007	−	0.769198i	−1.81007	−	0.769198i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.0111608	−	0.610980i	−0.0111608	−	0.610980i	−0.957601	−	0.288099i	$-0.906977\pi$
$157$	−0.0111608	−	0.610980i	−0.0111608	−	0.610980i	0.946440	−	0.322880i	$-0.104651\pi$
$158$		0			0
$159$		0			0
$160$	−0.457242	+	0.889342i	−0.457242	+	0.889342i
$161$		0			0
$162$	0.768647	−	0.639673i	0.768647	−	0.639673i
$163$		0			0		0.566908	−	0.823781i	$-0.308140\pi$
$163$		0			0		−0.566908	+	0.823781i	$0.691860\pi$
$164$	−0.186274	+	1.26571i	−0.186274	+	1.26571i
$165$		0			0
$166$		0			0
$167$		0			0		0.991838	−	0.127507i	$-0.0406977\pi$
$167$		0			0		−0.991838	+	0.127507i	$0.959302\pi$
$168$		0			0
$169$	−2.66245	+	1.13142i	−2.66245	+	1.13142i
$170$	1.96542	−	0.0718290i	1.96542	−	0.0718290i
$171$		0			0
$172$		0			0
$173$	−0.719903	−	0.694074i	−0.719903	−	0.694074i
$173$	−0.719903	−	0.694074i	−0.719903	−	0.694074i
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.999333	+	0.963478i	−0.999333	+	0.963478i
$179$		0			0		0.611174	−	0.791496i	$-0.290698\pi$
$179$		0			0		−0.611174	+	0.791496i	$0.709302\pi$
$180$	−0.424457	+	0.905448i	−0.424457	+	0.905448i
$181$	−0.998713	−	1.45124i	−0.998713	−	1.45124i	−0.889342	−	0.457242i	$-0.848837\pi$
$181$	−0.998713	−	1.45124i	−0.998713	−	1.45124i	−0.109371	−	0.994001i	$-0.534884\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.28045	+	0.463104i	1.28045	+	0.463104i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.998499	−	0.0547678i	$-0.0174419\pi$
$191$		0			0		−0.998499	+	0.0547678i	$0.982558\pi$
$192$		0			0
$193$	0.113891	−	0.268007i	0.113891	−	0.268007i	−0.853593	−	0.520940i	$-0.825581\pi$
$193$	0.113891	−	0.268007i	0.113891	−	0.268007i	0.967484	+	0.252933i	$0.0813953\pi$
$194$	−1.03494	+	1.44659i	−1.03494	+	1.44659i
$195$		0			0
$196$	−0.639673	+	0.768647i	−0.639673	+	0.768647i
$197$	0.445565	+	0.761003i	0.445565	+	0.761003i	0.997332	−	0.0729953i	$-0.0232558\pi$
$197$	0.445565	+	0.761003i	0.445565	+	0.761003i	−0.551768	+	0.833998i	$0.686047\pi$
$198$		0			0
$199$		0			0		0.374230	−	0.927336i	$-0.377907\pi$
$199$		0			0		−0.374230	+	0.927336i	$0.622093\pi$
$200$		−	1.00000i		−	1.00000i
$201$		0			0
$202$	1.83953	+	0.236484i	1.83953	+	0.236484i
$203$		0			0
$204$		0			0
$205$	−0.413076	−	1.21082i	−0.413076	−	1.21082i
$206$		0			0
$207$		0			0
$208$	−1.66512	−	1.05842i	−1.66512	−	1.05842i
$209$		0			0
$210$		0			0
$211$		0			0		0.853593	−	0.520940i	$-0.174419\pi$
$211$		0			0		−0.853593	+	0.520940i	$0.825581\pi$
$212$	−1.18260	+	1.53152i	−1.18260	+	1.53152i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.711234	+	0.994123i	0.711234	+	0.994123i
$219$		0			0
$220$		0			0
$221$	−0.212523	+	3.87461i	−0.212523	+	3.87461i
$222$		0			0
$223$		0			0		−0.813290	−	0.581859i	$-0.802326\pi$
$223$		0			0		0.813290	+	0.581859i	$0.197674\pi$
$224$		0			0
$225$	−0.0365220	−	0.999333i	−0.0365220	−	0.999333i
$226$	0.322842	−	1.14873i	0.322842	−	1.14873i
$227$		0			0		−0.999833	−	0.0182641i	$-0.994186\pi$
$227$		0			0		0.999833	+	0.0182641i	$0.00581395\pi$
$228$		0			0
$229$	0.632247	+	0.566496i	0.632247	+	0.566496i	0.920346	−	0.391105i	$-0.127907\pi$
$229$	0.632247	+	0.566496i	0.632247	+	0.566496i	−0.288099	+	0.957601i	$0.593023\pi$
$230$		0			0
$231$		0			0
$232$	−0.476392	−	0.926588i	−0.476392	−	0.926588i
$233$	−0.0334676	−	0.104298i	−0.0334676	−	0.104298i	0.934016	−	0.357231i	$-0.116279\pi$
$233$	−0.0334676	−	0.104298i	−0.0334676	−	0.104298i	−0.967484	+	0.252933i	$0.918605\pi$
$234$	−1.70266	−	0.996904i	−1.70266	−	0.996904i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.680810	−	0.732460i	$-0.261628\pi$
$239$		0			0		−0.680810	+	0.732460i	$0.738372\pi$
$240$		0			0
$241$	−1.07098	+	1.44061i	−1.07098	+	1.44061i	−0.181637	+	0.983366i	$0.558140\pi$
$241$	−1.07098	+	1.44061i	−1.07098	+	1.44061i	−0.889342	+	0.457242i	$0.848837\pi$
$242$	0.694074	−	0.719903i	0.694074	−	0.719903i
$243$		0			0
$244$	−0.809039	−	0.104008i	−0.809039	−	0.104008i
$245$	0.217430	−	0.976076i	0.217430	−	0.976076i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.457242	+	0.889342i	0.457242	+	0.889342i
$251$		0			0		0.946440	−	0.322880i	$-0.104651\pi$
$251$		0			0		−0.946440	+	0.322880i	$0.895349\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.0365220	−	0.999333i	−0.0365220	−	0.999333i
$257$	−1.03287	−	1.62492i	−1.03287	−	1.62492i	−0.744772	−	0.667319i	$-0.767442\pi$
$257$	−1.03287	−	1.62492i	−1.03287	−	1.62492i	−0.288099	−	0.957601i	$-0.593023\pi$
$258$		0			0
$259$		0			0
$260$	1.96482	+	0.179938i	1.96482	+	0.179938i
$261$	−0.509915	−	0.908571i	−0.509915	−	0.908571i
$262$		0			0
$263$		0			0		0.680810	−	0.732460i	$-0.261628\pi$
$263$		0			0		−0.680810	+	0.732460i	$0.738372\pi$
$264$		0			0
$265$	0.351461	−	1.90278i	0.351461	−	1.90278i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.253943	−	1.72551i	−0.253943	−	1.72551i	−0.611174	−	0.791496i	$-0.709302\pi$
$269$	−0.253943	−	1.72551i	−0.253943	−	1.72551i	0.357231	−	0.934016i	$-0.383721\pi$
$270$		0			0
$271$		0			0		−0.625528	−	0.780202i	$-0.715116\pi$
$271$		0			0		0.625528	+	0.780202i	$0.284884\pi$
$272$	−1.67879	+	1.02455i	−1.67879	+	1.02455i
$273$		0			0
$274$	−0.610532	+	0.299927i	−0.610532	+	0.299927i
$275$		0			0
$276$		0			0
$277$	0.105099	+	0.101328i	0.105099	+	0.101328i	0.744772	−	0.667319i	$-0.232558\pi$
$277$	0.105099	+	0.101328i	0.105099	+	0.101328i	−0.639673	+	0.768647i	$0.720930\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.210076	+	0.144570i	0.210076	+	0.144570i	0.667319	−	0.744772i	$-0.267442\pi$
$281$	0.210076	+	0.144570i	0.210076	+	0.144570i	−0.457242	+	0.889342i	$0.651163\pi$
$282$		0			0
$283$		0			0		−0.768647	−	0.639673i	$-0.779070\pi$
$283$		0			0		0.768647	+	0.639673i	$0.220930\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0729953	−	0.997332i	−0.0729953	−	0.997332i
$289$	2.50107	+	1.40367i	2.50107	+	1.40367i
$290$	0.847351	+	0.606228i	0.847351	+	0.606228i
$291$		0			0
$292$	0.00728980	−	0.399067i	0.00728980	−	0.399067i
$293$	1.67015	−	0.937334i	1.67015	−	0.937334i	0.694074	−	0.719903i	$-0.255814\pi$
$293$	1.67015	−	0.937334i	1.67015	−	0.937334i	0.976076	−	0.217430i	$-0.0697674\pi$
$294$		0			0
$295$		0			0
$296$	−1.34326	+	0.222824i	−1.34326	+	0.222824i
$297$		0			0
$298$	1.37090	−	1.22833i	1.37090	−	1.22833i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.767070	−	0.277429i	0.767070	−	0.277429i
$306$	−1.64025	+	1.08518i	−1.64025	+	1.08518i
$307$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$307$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.976076	−	0.217430i	$-0.0697674\pi$
$311$		0			0		−0.976076	+	0.217430i	$0.930233\pi$
$312$		0			0
$313$	−1.70266	−	0.282442i	−1.70266	−	0.282442i	−0.768647	−	0.639673i	$-0.779070\pi$
$313$	−1.70266	−	0.282442i	−1.70266	−	0.282442i	−0.934016	+	0.357231i	$0.883721\pi$
$314$	−0.515714	−	0.327811i	−0.515714	−	0.327811i
$315$		0			0
$316$		0			0
$317$	0.252933	−	1.96748i	0.252933	−	1.96748i		−	1.00000i	$-0.5\pi$
$317$	0.252933	−	1.96748i	0.252933	−	1.96748i	0.252933	−	0.967484i	$-0.418605\pi$
$318$		0			0
$319$		0			0
$320$	0.489418	+	0.872049i	0.489418	+	0.872049i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.109371	−	0.994001i	−0.109371	−	0.994001i
$325$	−1.82967	+	0.738371i	−1.82967	+	0.738371i
$326$		0			0
$327$		0			0
$328$	0.952821	+	0.853732i	0.952821	+	0.853732i
$329$		0			0
$330$		0			0
$331$		0			0		−0.639673	−	0.768647i	$-0.720930\pi$
$331$		0			0		0.639673	+	0.768647i	$0.279070\pi$
$332$		0			0
$333$	−1.33423	+	0.271734i	−1.33423	+	0.271734i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0217933	−	0.0293148i	−0.0217933	−	0.0293148i	0.791496	−	0.611174i	$-0.209302\pi$
$337$	−0.0217933	−	0.0293148i	−0.0217933	−	0.0293148i	−0.813290	+	0.581859i	$0.802326\pi$
$338$	−0.525454	+	2.84476i	−0.525454	+	2.84476i
$339$		0			0
$340$	1.02455	−	1.67879i	1.02455	−	1.67879i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.976076	+	0.217430i	−0.976076	+	0.217430i
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$		0			0
$349$	−1.28091	−	1.48322i	−1.28091	−	1.48322i	−0.791496	−	0.611174i	$-0.790698\pi$
$349$	−1.28091	−	1.48322i	−1.28091	−	1.48322i	−0.489418	−	0.872049i	$-0.662791\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.42379	−	0.868926i	−1.42379	−	0.868926i	−0.424457	−	0.905448i	$-0.639535\pi$
$353$	−1.42379	−	0.868926i	−1.42379	−	0.868926i	−0.999333	+	0.0365220i	$0.988372\pi$
$354$		0			0
$355$		0			0
$356$	0.252139	+	1.36506i	0.252139	+	1.36506i
$357$		0			0
$358$		0			0
$359$		0			0		−0.833998	−	0.551768i	$-0.813953\pi$
$359$		0			0		0.833998	+	0.551768i	$0.186047\pi$
$360$	0.520940	+	0.853593i	0.520940	+	0.853593i
$361$	0.768647	−	0.639673i	0.768647	−	0.639673i
$362$	−1.76139	+	0.0321755i	−1.76139	+	0.0321755i
$363$		0			0
$364$		0			0
$365$	0.175987	+	0.358240i	0.175987	+	0.358240i
$366$		0			0
$367$		0			0		−0.163646	−	0.986519i	$-0.552326\pi$
$367$		0			0		0.163646	+	0.986519i	$0.447674\pi$
$368$		0			0
$369$	0.983366	+	0.818363i	0.983366	+	0.818363i
$370$	1.09274	−	0.812364i	1.09274	−	0.812364i
$371$		0			0
$372$		0			0
$373$	−0.763496	−	0.170076i	−0.763496	−	0.170076i	−0.181637	−	0.983366i	$-0.558140\pi$
$373$	−0.763496	−	0.170076i	−0.763496	−	0.170076i	−0.581859	+	0.813290i	$0.697674\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.34360	+	1.55581i	−1.34360	+	1.55581i
$378$		0			0
$379$		0			0		−0.581859	−	0.813290i	$-0.697674\pi$
$379$		0			0		0.581859	+	0.813290i	$0.302326\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.340112	−	0.940385i	$-0.610465\pi$
$383$		0			0		0.340112	+	0.940385i	$0.389535\pi$
$384$		0			0
$385$		0			0
$386$	−0.160676	−	0.242862i	−0.160676	−	0.242862i
$387$		0			0
$388$	0.635401	+	1.66132i	0.635401	+	1.66132i
$389$	0.530302	+	0.225354i	0.530302	+	0.225354i	0.639673	−	0.768647i	$-0.279070\pi$
$389$	0.530302	+	0.225354i	0.530302	+	0.225354i	−0.109371	+	0.994001i	$0.534884\pi$
$390$		0			0
$391$		0			0
$392$	0.288099	+	0.957601i	0.288099	+	0.957601i
$393$		0			0
$394$	0.880523	+	0.0482968i	0.880523	+	0.0482968i
$395$		0			0
$396$		0			0
$397$	−1.70925	+	0.839675i	−1.70925	+	0.839675i	−0.719903	+	0.694074i	$0.755814\pi$
$397$	−1.70925	+	0.839675i	−1.70925	+	0.839675i	−0.989343	+	0.145601i	$0.953488\pi$
$398$		0			0
$399$		0			0
$400$	−0.833998	−	0.551768i	−0.833998	−	0.551768i
$401$	1.48061	+	0.162913i	1.48061	+	0.162913i	0.813290	−	0.581859i	$-0.197674\pi$
$401$	1.48061	+	0.162913i	1.48061	+	0.162913i	0.667319	+	0.744772i	$0.267442\pi$
$402$		0			0
$403$		0			0
$404$	1.21222	−	1.40368i	1.21222	−	1.40368i
$405$	0.551768	+	0.833998i	0.551768	+	0.833998i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.0863484	−	0.942872i	−0.0863484	−	0.942872i	−0.920346	−	0.391105i	$-0.872093\pi$
$409$	−0.0863484	−	0.942872i	−0.0863484	−	0.942872i	0.833998	−	0.551768i	$-0.186047\pi$
$410$	−1.23775	−	0.323589i	−1.23775	−	0.323589i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−1.80148	+	0.804701i	−1.80148	+	0.804701i
$417$		0			0
$418$		0			0
$419$		0			0		0.934016	−	0.357231i	$-0.116279\pi$
$419$		0			0		−0.934016	+	0.357231i	$0.883721\pi$
$420$		0			0
$421$	−1.14293	+	0.916348i	−1.14293	+	0.916348i	−0.997332	−	0.0729953i	$-0.976744\pi$
$421$	−1.14293	+	0.916348i	−1.14293	+	0.916348i	−0.145601	+	0.989343i	$0.546512\pi$
$422$		0			0
$423$		0			0
$424$	0.624763	+	1.83133i	0.624763	+	1.83133i
$425$	−0.143562	+	1.96148i	−0.143562	+	1.96148i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.872049	−	0.489418i	$-0.162791\pi$
$431$		0			0		−0.872049	+	0.489418i	$0.837209\pi$
$432$		0			0
$433$	1.10059	+	1.66355i	1.10059	+	1.66355i	0.611174	+	0.791496i	$0.290698\pi$
$433$	1.10059	+	1.66355i	1.10059	+	1.66355i	0.489418	+	0.872049i	$0.337209\pi$
$434$		0			0
$435$		0			0
$436$	1.22153	−	0.0446426i	1.22153	−	0.0446426i
$437$		0			0
$438$		0			0
$439$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$439$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$440$		0			0
$441$	0.322880	+	0.946440i	0.322880	+	0.946440i
$442$	3.11415	+	2.31513i	3.11415	+	2.31513i
$443$		0			0		0.0365220	−	0.999333i	$-0.488372\pi$
$443$		0			0		−0.0365220	+	0.999333i	$0.511628\pi$
$444$		0			0
$445$	−0.848400	−	1.09871i	−0.848400	−	1.09871i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.166537	−	0.0743904i	0.166537	−	0.0743904i	−0.322880	−	0.946440i	$-0.604651\pi$
$449$	0.166537	−	0.0743904i	0.166537	−	0.0743904i	0.489418	+	0.872049i	$0.337209\pi$
$450$	−0.853593	−	0.520940i	−0.853593	−	0.520940i
$451$		0			0
$452$	−0.779902	−	0.903081i	−0.779902	−	0.903081i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.447565	−	0.797476i	0.447565	−	0.797476i	−0.551768	−	0.833998i	$-0.686047\pi$
$457$	0.447565	−	0.797476i	0.447565	−	0.797476i	0.999333	+	0.0365220i	$0.0116279\pi$
$458$	0.821310	−	0.214719i	0.821310	−	0.214719i
$459$		0			0
$460$		0			0
$461$	−0.353680	+	0.409541i	−0.353680	+	0.409541i	−0.905448	−	0.424457i	$-0.860465\pi$
$461$	−0.353680	+	0.409541i	−0.353680	+	0.409541i	0.551768	+	0.833998i	$0.313953\pi$
$462$		0			0
$463$		0			0		0.998499	−	0.0547678i	$-0.0174419\pi$
$463$		0			0		−0.998499	+	0.0547678i	$0.982558\pi$
$464$	−1.03563	−	0.113952i	−1.03563	−	0.113952i
$465$		0			0
$466$	−0.105450	−	0.0296361i	−0.105450	−	0.0296361i
$467$		0			0		−0.566908	−	0.823781i	$-0.691860\pi$
$467$		0			0		0.566908	+	0.823781i	$0.308140\pi$
$468$	−1.77089	+	0.869958i	−1.77089	+	0.869958i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.691230	+	1.80729i	0.691230	+	1.80729i
$478$		0			0
$479$		0			0		−0.551768	−	0.833998i	$-0.686047\pi$
$479$		0			0		0.551768	+	0.833998i	$0.313953\pi$
$480$		0			0
$481$	1.39952	+	2.29320i	1.39952	+	2.29320i
$482$	0.610532	+	1.68808i	0.610532	+	1.68808i
$483$		0			0
$484$	−0.217430	−	0.976076i	−0.217430	−	0.976076i
$485$	−1.32471	−	1.18695i	−1.32471	−	1.18695i
$486$		0			0
$487$		0			0		0.976076	−	0.217430i	$-0.0697674\pi$
$487$		0			0		−0.976076	+	0.217430i	$0.930233\pi$
$488$	−0.533144	+	0.617349i	−0.533144	+	0.617349i
$489$		0			0
$490$	−0.694074	−	0.719903i	−0.694074	−	0.719903i
$491$		0			0		0.802527	−	0.596616i	$-0.203488\pi$
$491$		0			0		−0.802527	+	0.596616i	$0.796512\pi$
$492$		0			0
$493$	0.801412	+	1.88588i	0.801412	+	1.88588i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.927336	−	0.374230i	$-0.122093\pi$
$499$		0			0		−0.927336	+	0.374230i	$0.877907\pi$
$500$	0.994001	+	0.109371i	0.994001	+	0.109371i
$501$		0			0
$502$		0			0
$503$		0			0		0.999833	−	0.0182641i	$-0.00581395\pi$
$503$		0			0		−0.999833	+	0.0182641i	$0.994186\pi$
$504$		0			0
$505$	−0.436258	+	1.80263i	−0.436258	+	1.80263i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.0918840	−	0.497452i	−0.0918840	−	0.497452i	−0.997332	−	0.0729953i	$-0.976744\pi$
$509$	−0.0918840	−	0.497452i	−0.0918840	−	0.497452i	0.905448	−	0.424457i	$-0.139535\pi$
$510$		0			0
$511$		0			0
$512$	−0.853593	−	0.520940i	−0.853593	−	0.520940i
$513$		0			0
$514$	−1.92508	−	0.0351657i	−1.92508	−	0.0351657i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.23419	−	1.53937i	1.23419	−	1.53937i
$521$	−0.387935	−	1.90478i	−0.387935	−	1.90478i	−0.424457	−	0.905448i	$-0.639535\pi$
$521$	−0.387935	−	1.90478i	−0.387935	−	1.90478i	0.0365220	−	0.999333i	$-0.488372\pi$
$522$	−1.03910	−	0.0760524i	−1.03910	−	0.0760524i
$523$		0			0		0.374230	−	0.927336i	$-0.377907\pi$
$523$		0			0		−0.374230	+	0.927336i	$0.622093\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.983366	+	0.181637i	−0.983366	+	0.181637i
$530$	−1.39299	−	1.34301i	−1.39299	−	1.34301i
$531$		0			0
$532$		0			0
$533$	0.858511	−	2.37372i	0.858511	−	2.37372i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.57919	−	0.740294i	−1.57919	−	0.740294i
$539$		0			0
$540$		0			0
$541$	0.107056	+	0.972964i	0.107056	+	0.972964i	0.920346	+	0.391105i	$0.127907\pi$
$541$	0.107056	+	0.972964i	0.107056	+	0.972964i	−0.813290	+	0.581859i	$0.802326\pi$
$542$		0			0
$543$		0			0
$544$	−0.0718290	+	1.96542i	−0.0718290	+	1.96542i
$545$	−1.06595	+	0.598239i	−1.06595	+	0.598239i
$546$		0			0
$547$		0			0		0.145601	−	0.989343i	$-0.453488\pi$
$547$		0			0		−0.145601	+	0.989343i	$0.546512\pi$
$548$	−0.0867337	+	0.674672i	−0.0867337	+	0.674672i
$549$	−0.510241	+	0.636409i	−0.510241	+	0.636409i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.142498	−	0.0317428i	0.142498	−	0.0317428i
$555$		0			0
$556$		0			0
$557$	−1.77486	−	0.429537i	−1.77486	−	0.429537i	−0.791496	−	0.611174i	$-0.790698\pi$
$557$	−1.77486	−	0.429537i	−1.77486	−	0.429537i	−0.983366	+	0.181637i	$0.941860\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.236484	−	0.0954343i	0.236484	−	0.0954343i
$563$		0			0		0.457242	−	0.889342i	$-0.348837\pi$
$563$		0			0		−0.457242	+	0.889342i	$0.651163\pi$
$564$		0			0
$565$	1.10653	+	0.446543i	1.10653	+	0.446543i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.97008	+	0.326801i	−1.97008	+	0.326801i	−0.976076	+	0.217430i	$0.930233\pi$
$569$	−1.97008	+	0.326801i	−1.97008	+	0.326801i	−0.994001	+	0.109371i	$0.965116\pi$
$570$		0			0
$571$		0			0		0.181637	−	0.983366i	$-0.441860\pi$
$571$		0			0		−0.181637	+	0.983366i	$0.558140\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.872049	−	0.489418i	−0.872049	−	0.489418i
$577$	0.00533187	+	0.0728492i	0.00533187	+	0.0728492i	0.999333	−	0.0365220i	$-0.0116279\pi$
$577$	0.00533187	+	0.0728492i	0.00533187	+	0.0728492i	−0.994001	+	0.109371i	$0.965116\pi$
$578$	2.55066	−	1.31139i	2.55066	−	1.31139i
$579$		0			0
$580$	0.973133	−	0.372192i	0.973133	−	0.372192i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.328799	−	0.226272i	−0.328799	−	0.226272i
$585$	1.17715	−	1.58342i	1.17715	−	1.58342i
$586$	0.139801	−	1.91009i	0.139801	−	1.91009i
$587$		0			0		0.989343	−	0.145601i	$-0.0465116\pi$
$587$		0			0		−0.989343	+	0.145601i	$0.953488\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.555335	+	1.24323i	−0.555335	+	1.24323i
$593$	1.22901	−	0.750054i	1.22901	−	0.750054i	0.252933	−	0.967484i	$-0.418605\pi$
$593$	1.22901	−	0.750054i	1.22901	−	0.750054i	0.976076	+	0.217430i	$0.0697674\pi$
$594$		0			0
$595$		0			0
$596$	−0.268007	−	1.82108i	−0.268007	−	1.82108i
$597$		0			0
$598$		0			0
$599$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$599$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$600$		0			0
$601$	−0.574066	+	1.58725i	−0.574066	+	1.58725i	0.217430	+	0.976076i	$0.430233\pi$
$601$	−0.574066	+	1.58725i	−0.574066	+	1.58725i	−0.791496	+	0.611174i	$0.790698\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.639673	+	0.768647i	0.639673	+	0.768647i
$606$		0			0
$607$		0			0		0.270561	−	0.962703i	$-0.412791\pi$
$607$		0			0		−0.270561	+	0.962703i	$0.587209\pi$
$608$		0			0
$609$		0			0
$610$	0.191869	−	0.792811i	0.191869	−	0.792811i
$611$		0			0
$612$			1.96673i			1.96673i
$613$	1.63480	+	0.491839i	1.63480	+	0.491839i	0.967484	−	0.252933i	$-0.0813953\pi$
$613$	1.63480	+	0.491839i	1.63480	+	0.491839i	0.667319	+	0.744772i	$0.267442\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.198060	+	1.80003i	−0.198060	+	1.80003i	0.322880	+	0.946440i	$0.395349\pi$
$617$	−0.198060	+	1.80003i	−0.198060	+	1.80003i	−0.520940	+	0.853593i	$0.674419\pi$
$618$		0			0
$619$		0			0		−0.357231	−	0.934016i	$-0.616279\pi$
$619$		0			0		0.357231	+	0.934016i	$0.383721\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.934016	+	0.357231i	−0.934016	+	0.357231i
$626$	−1.17503	+	1.26417i	−1.17503	+	1.26417i
$627$		0			0
$628$	−0.557948	+	0.249229i	−0.557948	+	0.249229i
$629$	2.66678	−	0.244224i	2.66678	−	0.244224i
$630$		0			0
$631$		0			0		−0.862965	−	0.505263i	$-0.831395\pi$
$631$		0			0		0.862965	+	0.505263i	$0.168605\pi$
$632$		0			0
$633$		0			0
$634$	−1.50132	−	1.29654i	−1.50132	−	1.29654i
$635$		0			0
$636$		0			0
$637$	1.53937	−	1.23419i	1.53937	−	1.23419i
$638$		0			0
$639$		0			0
$640$	0.997332	+	0.0729953i	0.997332	+	0.0729953i
$641$	0.611174	+	0.208504i	0.611174	+	0.208504i	0.611174	−	0.791496i	$-0.290698\pi$
$641$	0.611174	+	0.208504i	0.611174	+	0.208504i			1.00000i	$0.5\pi$
$642$		0			0
$643$		0			0		−0.952179	−	0.305541i	$-0.901163\pi$
$643$		0			0		0.952179	+	0.305541i	$0.0988372\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.581859	−	0.813290i	$-0.697674\pi$
$647$		0			0		0.581859	+	0.813290i	$0.302326\pi$
$648$	−0.889342	−	0.457242i	−0.889342	−	0.457242i
$649$		0			0
$650$	−0.393753	+	1.93335i	−0.393753	+	1.93335i
$651$		0			0
$652$		0			0
$653$	1.20932	−	1.56612i	1.20932	−	1.56612i	0.489418	−	0.872049i	$-0.337209\pi$
$653$	1.20932	−	1.56612i	1.20932	−	1.56612i	0.719903	−	0.694074i	$-0.244186\pi$
$654$		0			0
$655$		0			0
$656$	1.23775	−	0.323589i	1.23775	−	0.323589i
$657$	−0.336843	−	0.214113i	−0.336843	−	0.214113i
$658$		0			0
$659$		0			0		0.813290	−	0.581859i	$-0.197674\pi$
$659$		0			0		−0.813290	+	0.581859i	$0.802326\pi$
$660$		0			0
$661$	−1.43597	+	0.105099i	−1.43597	+	0.105099i	−0.768647	−	0.639673i	$-0.779070\pi$
$661$	−1.43597	+	0.105099i	−1.43597	+	0.105099i	−0.667319	+	0.744772i	$0.732558\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.509559	+	1.26268i	−0.509559	+	1.26268i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.828604	−	1.76757i	0.828604	−	1.76757i	0.217430	−	0.976076i	$-0.430233\pi$
$673$	0.828604	−	1.76757i	0.828604	−	1.76757i	0.611174	−	0.791496i	$-0.290698\pi$
$674$	−0.0364733	+	0.00200056i	−0.0364733	+	0.00200056i
$675$		0			0
$676$	2.08259	+	2.00787i	2.08259	+	2.00787i
$677$	0.182123	−	1.98868i	0.182123	−	1.98868i	0.0365220	−	0.999333i	$-0.488372\pi$
$677$	0.182123	−	1.98868i	0.182123	−	1.98868i	0.145601	−	0.989343i	$-0.453488\pi$
$678$		0			0
$679$		0			0
$680$	−0.834792	−	1.78077i	−0.834792	−	1.78077i
$681$		0			0
$682$		0			0
$683$		0			0		0.802527	−	0.596616i	$-0.203488\pi$
$683$		0			0		−0.802527	+	0.596616i	$0.796512\pi$
$684$		0			0
$685$	−0.231353	−	0.639673i	−0.231353	−	0.639673i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.88942	−	2.49531i	2.88942	−	2.49531i
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$	−0.357231	+	0.934016i	−0.357231	+	0.934016i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.74638	−	1.81137i	−1.74638	−	1.81137i
$698$	−1.94377	+	0.249885i	−1.94377	+	0.249885i
$699$		0			0
$700$		0			0
$701$	0.288099	−	1.95760i	0.288099	−	1.95760i		−	1.00000i	$-0.5\pi$
$701$	0.288099	−	1.95760i	0.288099	−	1.95760i	0.288099	−	0.957601i	$-0.406977\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.51028	+	0.707992i	−1.51028	+	0.707992i
$707$		0			0
$708$		0			0
$709$	0.764803	+	1.30625i	0.764803	+	1.30625i	0.946440	+	0.322880i	$0.104651\pi$
$709$	0.764803	+	1.30625i	0.764803	+	1.30625i	−0.181637	+	0.983366i	$0.558140\pi$
$710$		0			0
$711$		0			0
$712$	1.27758	+	0.542911i	1.27758	+	0.542911i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.843936	−	0.536444i	$-0.180233\pi$
$719$		0			0		−0.843936	+	0.536444i	$0.819767\pi$
$720$	0.999333	+	0.0365220i	0.999333	+	0.0365220i
$721$		0			0
$722$	−0.109371	−	0.994001i	−0.109371	−	0.994001i
$723$		0			0
$724$	−0.945045	+	1.48675i	−0.945045	+	1.48675i
$725$	−0.695267	+	0.775964i	−0.695267	+	0.775964i
$726$		0			0
$727$		0			0		0.536444	−	0.843936i	$-0.319767\pi$
$727$		0			0		−0.536444	+	0.843936i	$0.680233\pi$
$728$		0			0
$729$	−0.905448	−	0.424457i	−0.905448	−	0.424457i
$730$	0.395876	+	0.0508925i	0.395876	+	0.0508925i
$731$		0			0
$732$		0			0
$733$	1.56002	−	0.377542i	1.56002	−	0.377542i	0.639673	−	0.768647i	$-0.279070\pi$
$733$	1.56002	−	0.377542i	1.56002	−	0.377542i	0.920346	+	0.391105i	$0.127907\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	1.22510	−	0.368578i	1.22510	−	0.368578i
$739$		0			0		−0.288099	−	0.957601i	$-0.593023\pi$
$739$		0			0		0.288099	+	0.957601i	$0.406977\pi$
$740$	−0.0745729	−	1.35958i	−0.0745729	−	1.35958i
$741$		0			0
$742$		0			0
$743$		0			0		−0.440923	−	0.897545i	$-0.645349\pi$
$743$		0			0		0.440923	+	0.897545i	$0.354651\pi$
$744$		0			0
$745$	1.07102	+	1.49702i	1.07102	+	1.49702i
$746$	−0.563115	+	0.542911i	−0.563115	+	0.542911i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.952179	−	0.305541i	$-0.901163\pi$
$751$		0			0		0.952179	+	0.305541i	$0.0988372\pi$
$752$		0			0
$753$		0			0
$754$	0.556185	+	1.97900i	0.556185	+	1.97900i
$755$		0			0
$756$		0			0
$757$	−0.427627	+	0.0789867i	−0.427627	+	0.0789867i	−0.391105	−	0.920346i	$-0.627907\pi$
$757$	−0.427627	+	0.0789867i	−0.427627	+	0.0789867i	−0.0365220	+	0.999333i	$0.511628\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.0184563	+	1.01036i	0.0184563	+	1.01036i	0.872049	+	0.489418i	$0.162791\pi$
$761$	0.0184563	+	1.01036i	0.0184563	+	1.01036i	−0.853593	+	0.520940i	$0.825581\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.899273	−	1.74910i	−0.899273	−	1.74910i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−1.52091	+	0.223832i	−1.52091	+	0.223832i	−0.853593	−	0.520940i	$-0.825581\pi$
$769$	−1.52091	+	0.223832i	−1.52091	+	0.223832i	−0.667319	+	0.744772i	$0.732558\pi$
$770$		0			0
$771$		0			0
$772$	−0.291202			−0.291202
$773$	1.75434	−	0.942872i	1.75434	−	0.942872i	0.833998	−	0.551768i	$-0.186047\pi$
$773$	1.75434	−	0.942872i	1.75434	−	0.942872i	0.920346	−	0.391105i	$-0.127907\pi$
$774$		0			0
$775$		0			0
$776$	1.73613	+	0.386740i	1.73613	+	0.386740i
$777$		0			0
$778$	0.480548	−	0.317928i	0.480548	−	0.317928i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.957601	+	0.288099i	0.957601	+	0.288099i
$785$	0.382248	−	0.476767i	0.382248	−	0.476767i
$786$		0			0
$787$		0			0		0.440923	−	0.897545i	$-0.354651\pi$
$787$		0			0		−0.440923	+	0.897545i	$0.645349\pi$
$788$	0.526123	−	0.707705i	0.526123	−	0.707705i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.52320	+	0.519644i	1.52320	+	0.519644i
$794$	−0.242820	+	1.88881i	−0.242820	+	1.88881i
$795$		0			0
$796$		0			0
$797$	−0.0940235	−	0.638879i	−0.0940235	−	0.638879i	−0.983366	−	0.181637i	$-0.941860\pi$
$797$	−0.0940235	−	0.638879i	−0.0940235	−	0.638879i	0.889342	−	0.457242i	$-0.151163\pi$
$798$		0			0
$799$		0			0
$800$	−0.920346	+	0.391105i	−0.920346	+	0.391105i
$801$	1.29655	+	0.495889i	1.29655	+	0.495889i
$802$	0.952821	−	1.14493i	0.952821	−	1.14493i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.501803	−	1.78550i	−0.501803	−	1.78550i
$809$	−1.33375	+	1.48855i	−1.33375	+	1.48855i	−0.639673	+	0.768647i	$0.720930\pi$
$809$	−1.33375	+	1.48855i	−1.33375	+	1.48855i	−0.694074	+	0.719903i	$0.744186\pi$
$810$	1.00000			1.00000
$811$		0			0		−0.694074	−	0.719903i	$-0.744186\pi$
$811$		0			0		0.694074	+	0.719903i	$0.255814\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.833998	−	0.448232i	−0.833998	−	0.448232i
$819$		0			0
$820$	−0.952821	+	0.853732i	−0.952821	+	0.853732i
$821$	−0.143739	−	0.447945i	−0.143739	−	0.447945i	0.853593	−	0.520940i	$-0.174419\pi$
$821$	−0.143739	−	0.447945i	−0.143739	−	0.447945i	−0.997332	+	0.0729953i	$0.976744\pi$
$822$		0			0
$823$		0			0		0.934016	−	0.357231i	$-0.116279\pi$
$823$		0			0		−0.934016	+	0.357231i	$0.883721\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.235221	−	0.971942i	$-0.424419\pi$
$827$		0			0		−0.235221	+	0.971942i	$0.575581\pi$
$828$		0			0
$829$	−0.337574	−	1.29124i	−0.337574	−	1.29124i	−0.889342	−	0.457242i	$-0.848837\pi$
$829$	−0.337574	−	1.29124i	−0.337574	−	1.29124i	0.551768	−	0.833998i	$-0.313953\pi$
$830$		0			0
$831$		0			0
$832$	−0.322880	+	1.94644i	−0.322880	+	1.94644i
$833$	−0.427627	−	1.91968i	−0.427627	−	1.91968i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.927336	−	0.374230i	$-0.877907\pi$
$839$		0			0		0.927336	+	0.374230i	$0.122093\pi$
$840$		0			0
$841$	−0.0216297	+	0.0827347i	−0.0216297	+	0.0827347i
$842$	0.133598	+	1.45882i	0.133598	+	1.45882i
$843$		0			0
$844$		0			0
$845$	−2.77022	−	0.833436i	−2.77022	−	0.833436i
$846$		0			0
$847$		0			0
$848$	1.87205	+	0.489418i	1.87205	+	0.489418i
$849$		0			0
$850$	1.55666	+	1.20201i	1.55666	+	1.20201i
$851$		0			0
$852$		0			0
$853$	−1.49821	+	0.511117i	−1.49821	+	0.511117i	−0.946440	−	0.322880i	$-0.895349\pi$
$853$	−1.49821	+	0.511117i	−1.49821	+	0.511117i	−0.551768	+	0.833998i	$0.686047\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.96542	+	0.363031i	1.96542	+	0.363031i	0.989343	+	0.145601i	$0.0465116\pi$
$857$	1.96542	+	0.363031i	1.96542	+	0.363031i	0.976076	+	0.217430i	$0.0697674\pi$
$858$		0			0
$859$		0			0		−0.791496	−	0.611174i	$-0.790698\pi$
$859$		0			0		0.791496	+	0.611174i	$0.209302\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.551768	−	0.833998i	$-0.313953\pi$
$863$		0			0		−0.551768	+	0.833998i	$0.686047\pi$
$864$		0			0
$865$	−0.109371	−	0.994001i	−0.109371	−	0.994001i
$866$	1.99466			1.99466
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.636770	−	1.04339i	0.636770	−	1.04339i
$873$	1.74910	+	0.323075i	1.74910	+	0.323075i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.89162	−	0.645330i	1.89162	−	0.645330i	0.934016	−	0.357231i	$-0.116279\pi$
$877$	1.89162	−	0.645330i	1.89162	−	0.645330i	0.957601	−	0.288099i	$-0.0930233\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.252139	+	0.261522i	−0.252139	+	0.261522i	−0.833998	−	0.551768i	$-0.813953\pi$
$881$	−0.252139	+	0.261522i	−0.252139	+	0.261522i	0.581859	+	0.813290i	$0.302326\pi$
$882$	0.967484	+	0.252933i	0.967484	+	0.252933i
$883$		0			0		0.667319	−	0.744772i	$-0.267442\pi$
$883$		0			0		−0.667319	+	0.744772i	$0.732558\pi$
$884$	3.64910	−	1.31978i	3.64910	−	1.31978i
$885$		0			0
$886$		0			0
$887$		0			0		0.625528	−	0.780202i	$-0.284884\pi$
$887$		0			0		−0.625528	+	0.780202i	$0.715116\pi$
$888$		0			0
$889$		0			0
$890$	−1.38445	+	0.101328i	−1.38445	+	0.101328i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.0298486	−	0.179938i	0.0298486	−	0.179938i
$899$		0			0
$900$	−0.905448	+	0.424457i	−0.905448	+	0.424457i
$901$	−0.962553	−	3.68182i	−0.962553	−	3.68182i
$902$		0			0
$903$		0			0
$904$	−1.18349	+	0.152146i	−1.18349	+	0.152146i
$905$	0.160663	−	1.75434i	0.160663	−	1.75434i
$906$		0			0
$907$		0			0		0.934016	−	0.357231i	$-0.116279\pi$
$907$		0			0		−0.934016	+	0.357231i	$0.883721\pi$
$908$		0			0
$909$	−0.566678	−	1.76598i	−0.566678	−	1.76598i
$910$		0			0
$911$		0			0		−0.880843	−	0.473409i	$-0.843023\pi$
$911$		0			0		0.880843	+	0.473409i	$0.156977\pi$
$912$		0			0
$913$		0			0
$914$	−0.418141	−	0.813290i	−0.418141	−	0.813290i
$915$		0			0
$916$	0.274098	−	0.803445i	0.274098	−	0.803445i
$917$		0			0
$918$		0			0
$919$		0			0		−0.694074	−	0.719903i	$-0.744186\pi$
$919$		0			0		0.694074	+	0.719903i	$0.255814\pi$
$920$		0			0
$921$		0			0
$922$	0.146407	+	0.520940i	0.146407	+	0.520940i
$923$		0			0
$924$		0			0
$925$	0.687977	+	1.17503i	0.687977	+	1.17503i
$926$		0			0
$927$		0			0
$928$	−0.666463	+	0.800839i	−0.666463	+	0.800839i
$929$	1.69141	+	0.646908i	1.69141	+	0.646908i	0.997332	−	0.0729953i	$-0.0232558\pi$
$929$	1.69141	+	0.646908i	1.69141	+	0.646908i	0.694074	+	0.719903i	$0.255814\pi$
$930$		0			0
$931$		0			0
$932$	−0.0829005	+	0.0715930i	−0.0829005	+	0.0715930i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.251577	+	1.95693i	−0.251577	+	1.95693i
$937$	−1.40976	−	0.480945i	−1.40976	−	0.480945i	−0.489418	−	0.872049i	$-0.662791\pi$
$937$	−1.40976	−	0.480945i	−1.40976	−	0.480945i	−0.920346	+	0.391105i	$0.872093\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.320282	−	0.344580i	−0.320282	−	0.344580i	0.551768	−	0.833998i	$-0.313953\pi$
$941$	−0.320282	−	0.344580i	−0.320282	−	0.344580i	−0.872049	+	0.489418i	$0.837209\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.905448	−	0.424457i	$-0.139535\pi$
$947$		0			0		−0.905448	+	0.424457i	$0.860465\pi$
$948$		0			0
$949$	−0.171228	+	0.768665i	−0.171228	+	0.768665i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.911504	−	0.256172i	−0.911504	−	0.256172i	−0.217430	−	0.976076i	$-0.569767\pi$
$953$	−0.911504	−	0.256172i	−0.911504	−	0.256172i	−0.694074	+	0.719903i	$0.744186\pi$
$954$	1.88867	+	0.420720i	1.88867	+	0.420720i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.989343	+	0.145601i	−0.989343	+	0.145601i
$962$	2.68474	+	0.0981175i	2.68474	+	0.0981175i
$963$		0			0
$964$	1.74472	+	0.422243i	1.74472	+	0.422243i
$965$	0.258979	−	0.133150i	0.258979	−	0.133150i
$966$		0			0
$967$		0			0		−0.611174	−	0.791496i	$-0.709302\pi$
$967$		0			0		0.611174	+	0.791496i	$0.290698\pi$
$968$	−0.934016	−	0.357231i	−0.934016	−	0.357231i
$969$		0			0
$970$	−1.72085	+	0.449889i	−1.72085	+	0.449889i
$971$		0			0		−0.997332	−	0.0729953i	$-0.976744\pi$
$971$		0			0		0.997332	+	0.0729953i	$0.0232558\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.220696	+	0.785274i	0.220696	+	0.785274i
$977$	−0.145740	−	0.557462i	−0.145740	−	0.557462i	−0.999333	−	0.0365220i	$-0.988372\pi$
$977$	−0.145740	−	0.557462i	−0.145740	−	0.557462i	0.853593	−	0.520940i	$-0.174419\pi$
$978$		0			0
$979$		0			0
$980$	−0.983366	+	0.181637i	−0.983366	+	0.181637i
$981$	0.598239	−	1.06595i	0.598239	−	1.06595i
$982$		0			0
$983$		0			0		−0.625528	−	0.780202i	$-0.715116\pi$
$983$		0			0		0.625528	+	0.780202i	$0.284884\pi$
$984$		0			0
$985$	−0.144311	+	0.869958i	−0.144311	+	0.869958i
$986$	2.01501	+	0.372192i	2.01501	+	0.372192i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.288099	−	0.957601i	$-0.593023\pi$
$991$		0			0		0.288099	+	0.957601i	$0.406977\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.60133	+	0.387541i	−1.60133	+	0.387541i	−0.934016	−	0.357231i	$-0.883721\pi$
$997$	−1.60133	+	0.387541i	−1.60133	+	0.387541i	−0.667319	+	0.744772i	$0.732558\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3460.1.bd.a.587.1	✓	84
4.3	odd	2	CM	3460.1.bd.a.587.1	✓	84
5.3	odd	4		3460.1.bm.a.2663.1	yes	84
20.3	even	4		3460.1.bm.a.2663.1	yes	84
173.28	odd	172		3460.1.bm.a.547.1	yes	84
692.547	even	172		3460.1.bm.a.547.1	yes	84
865.28	even	172	inner	3460.1.bd.a.2623.1	yes	84
3460.2623	odd	172	inner	3460.1.bd.a.2623.1	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3460.1.bd.a.587.1	✓	84	1.1	even	1	trivial
3460.1.bd.a.587.1	✓	84	4.3	odd	2	CM
3460.1.bd.a.2623.1	yes	84	865.28	even	172	inner
3460.1.bd.a.2623.1	yes	84	3460.2623	odd	172	inner
3460.1.bm.a.547.1	yes	84	173.28	odd	172
3460.1.bm.a.547.1	yes	84	692.547	even	172
3460.1.bm.a.2663.1	yes	84	5.3	odd	4
3460.1.bm.a.2663.1	yes	84	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3460 = 2^{2} \cdot 5 \cdot 173 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3460.bd (of order \(172\), degree \(84\), minimal)

\(f(q)\)	\(=\)	\(q+(0.551768 - 0.833998i) q^{2} +(-0.391105 - 0.920346i) q^{4} +(0.768647 + 0.639673i) q^{5} +(-0.983366 - 0.181637i) q^{8} +(-0.989343 - 0.145601i) q^{9} +O(q^{10})\)	\(q+(0.551768 - 0.833998i) q^{2} +(-0.391105 - 0.920346i) q^{4} +(0.768647 + 0.639673i) q^{5} +(-0.983366 - 0.181637i) q^{8} +(-0.989343 - 0.145601i) q^{9} +(0.957601 - 0.288099i) q^{10} +(0.393753 + 1.93335i) q^{13} +(-0.694074 + 0.719903i) q^{16} +(1.90278 + 0.497452i) q^{17} +(-0.667319 + 0.744772i) q^{18} +(0.288099 - 0.957601i) q^{20} +(0.181637 + 0.983366i) q^{25} +(1.82967 + 0.738371i) q^{26} +(0.636770 + 0.824645i) q^{29} +(0.217430 + 0.976076i) q^{32} +(1.46477 - 1.31244i) q^{34} +(0.252933 + 0.967484i) q^{36} +(1.28045 - 0.463104i) q^{37} +(-0.639673 - 0.768647i) q^{40} +(-1.09204 - 0.666463i) q^{41} +(-0.667319 - 0.744772i) q^{45} +(-0.457242 - 0.889342i) q^{49} +(0.920346 + 0.391105i) q^{50} +(1.62535 - 1.11853i) q^{52} +(-0.947008 - 1.68739i) q^{53} +(1.03910 - 0.0760524i) q^{58} +(0.412142 - 0.703919i) q^{61} +(0.934016 + 0.357231i) q^{64} +(-0.934054 + 1.73794i) q^{65} +(-0.286358 - 1.94577i) q^{68} +(0.946440 + 0.322880i) q^{72} +(0.364429 + 0.162786i) q^{73} +(0.320282 - 1.32342i) q^{74} +(-0.994001 + 0.109371i) q^{80} +(0.957601 + 0.288099i) q^{81} +(-1.15838 + 0.543027i) q^{82} +(1.14436 + 1.59952i) q^{85} +(-1.35494 - 0.301825i) q^{89} +(-0.989343 + 0.145601i) q^{90} +(-1.77750 - 0.0649611i) q^{97} +(-0.994001 - 0.109371i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2 q^{4} + 2 q^{9}+O(q^{10}) \) 84 * q + 2 * q^4 + 2 * q^9	\( 84 q + 2 q^{4} + 2 q^{9} - 2 q^{10} + 2 q^{13} - 2 q^{16} + 2 q^{25} + 2 q^{26} - 2 q^{36} - 2 q^{37} + 2 q^{40} - 2 q^{49} - 2 q^{52} + 4 q^{58} - 2 q^{61} + 2 q^{64} - 2 q^{65} + 2 q^{73} + 2 q^{74} - 2 q^{81} + 4 q^{82} + 4 q^{89} + 2 q^{90}+O(q^{100}) \) 84 * q + 2 * q^4 + 2 * q^9 - 2 * q^10 + 2 * q^13 - 2 * q^16 + 2 * q^25 + 2 * q^26 - 2 * q^36 - 2 * q^37 + 2 * q^40 - 2 * q^49 - 2 * q^52 + 4 * q^58 - 2 * q^61 + 2 * q^64 - 2 * q^65 + 2 * q^73 + 2 * q^74 - 2 * q^81 + 4 * q^82 + 4 * q^89 + 2 * q^90

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