LMFDB - Embedded newform 3875.1.dk.a.929.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3875,1,Mod(154,3875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3875, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([31, 25]))

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

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

chi := DirichletCharacter("3875.154");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3875 = 5^{3} \cdot 31 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3875.dk (of order $50$, degree $20$, 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:	$1.93387692395$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{50})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{15} + x^{10} - x^{5} + 1 $ x^20 - x^15 + x^10 - x^5 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{50}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{50} + \cdots)$

Embedding invariants

Embedding label			929.1
Root			$-0.968583 + 0.248690i$ of defining polynomial
Character	$\chi$	$=$	3875.929
Dual form			3875.1.dk.a.2169.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30113 - 1.07639i) q^{2} +(0.346947 + 1.81876i) q^{4} +(-0.0627905 - 0.998027i) q^{5} +(-0.147338 + 0.202793i) q^{7} +(0.692757 - 1.26012i) q^{8} +(-0.968583 - 0.248690i) q^{9} +O(q^{10})$	\(q+(-1.30113 - 1.07639i) q^{2} +(0.346947 + 1.81876i) q^{4} +(-0.0627905 - 0.998027i) q^{5} +(-0.147338 + 0.202793i) q^{7} +(0.692757 - 1.26012i) q^{8} +(-0.968583 - 0.248690i) q^{9} +(-0.992567 + 1.36615i) q^{10} +(0.409991 - 0.105268i) q^{14} +(-0.536212 + 0.212301i) q^{16} +(0.992567 + 1.36615i) q^{18} +(1.44644 - 0.182728i) q^{19} +(1.79339 - 0.460464i) q^{20} +(-0.992115 + 0.125333i) q^{25} +(-0.419952 - 0.197614i) q^{28} +(0.187381 - 0.982287i) q^{31} +(-0.441408 - 0.143422i) q^{32} +(0.211645 + 0.134314i) q^{35} +(0.116260 - 1.84790i) q^{36} +(-2.07870 - 1.31918i) q^{38} +(-1.30113 - 0.612266i) q^{40} +(0.939097 - 1.47978i) q^{41} +(-0.187381 + 0.982287i) q^{45} +(-0.354691 - 0.645180i) q^{47} +(0.289600 + 0.891298i) q^{49} +(1.42578 + 0.904827i) q^{50} +(0.153475 + 0.326150i) q^{56} +(-0.124591 - 1.98031i) q^{59} +(-1.30113 + 1.07639i) q^{62} +(0.193142 - 0.159781i) q^{63} +(0.728969 + 1.14867i) q^{64} +(-1.63742 + 0.770513i) q^{67} +(-0.130804 - 0.402572i) q^{70} +(-1.75261 + 0.963507i) q^{71} +(-0.984371 + 1.04825i) q^{72} +(0.834178 + 2.56734i) q^{76} +(0.245551 + 0.521823i) q^{80} +(0.876307 + 0.481754i) q^{81} +(-2.81471 + 0.914555i) q^{82} +(1.30113 - 1.07639i) q^{90} +(-0.232966 + 1.22125i) q^{94} +(-0.273190 - 1.43211i) q^{95} +(-1.80608 - 0.849878i) q^{97} +(0.582576 - 1.47142i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} - 5 q^{4} + 5 q^{8}+O(q^{10}) $ 20 * q + 5 * q^2 - 5 * q^4 + 5 * q^8	$ 20 q + 5 q^{2} - 5 q^{4} + 5 q^{8} + 5 q^{14} - 5 q^{16} + 5 q^{19} - 5 q^{28} - 25 q^{32} - 5 q^{38} + 5 q^{40} + 5 q^{49} + 20 q^{50} - 20 q^{56} + 5 q^{62} - 20 q^{67} + 5 q^{72} - 15 q^{76} + 20 q^{80} - 5 q^{90} + 20 q^{94} - 5 q^{95} - 5 q^{98}+O(q^{100}) $ 20 * q + 5 * q^2 - 5 * q^4 + 5 * q^8 + 5 * q^14 - 5 * q^16 + 5 * q^19 - 5 * q^28 - 25 * q^32 - 5 * q^38 + 5 * q^40 + 5 * q^49 + 20 * q^50 - 20 * q^56 + 5 * q^62 - 20 * q^67 + 5 * q^72 - 15 * q^76 + 20 * q^80 - 5 * q^90 + 20 * q^94 - 5 * q^95 - 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3875\mathbb{Z}\right)^\times$.

$n$	$251$	$3752$
$\chi(n)$	$-1$	$e\left(\frac{11}{50}\right)$

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 $

$2$	−1.30113	−	1.07639i	−1.30113	−	1.07639i	−0.992115	−	0.125333i	$-0.960000\pi$
$2$	−1.30113	−	1.07639i	−1.30113	−	1.07639i	−0.309017	−	0.951057i	$-0.600000\pi$
$3$		0			0		0.125333	−	0.992115i	$-0.460000\pi$
$3$		0			0		−0.125333	+	0.992115i	$0.540000\pi$
$4$	0.346947	+	1.81876i	0.346947	+	1.81876i
$5$	−0.0627905	−	0.998027i	−0.0627905	−	0.998027i
$5$	−0.0627905	−	0.998027i	−0.0627905	−	0.998027i
$6$		0			0
$7$	−0.147338	+	0.202793i	−0.147338	+	0.202793i	−0.876307	−	0.481754i	$-0.840000\pi$
$7$	−0.147338	+	0.202793i	−0.147338	+	0.202793i	0.728969	+	0.684547i	$0.240000\pi$
$8$	0.692757	−	1.26012i	0.692757	−	1.26012i
$9$	−0.968583	−	0.248690i	−0.968583	−	0.248690i
$10$	−0.992567	+	1.36615i	−0.992567	+	1.36615i
$11$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$11$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$12$		0			0
$13$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$13$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$14$	0.409991	−	0.105268i	0.409991	−	0.105268i
$15$		0			0
$16$	−0.536212	+	0.212301i	−0.536212	+	0.212301i
$17$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$17$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$18$	0.992567	+	1.36615i	0.992567	+	1.36615i
$19$	1.44644	−	0.182728i	1.44644	−	0.182728i	0.637424	−	0.770513i	$-0.280000\pi$
$19$	1.44644	−	0.182728i	1.44644	−	0.182728i	0.809017	+	0.587785i	$0.200000\pi$
$20$	1.79339	−	0.460464i	1.79339	−	0.460464i
$21$		0			0
$22$		0			0
$23$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$23$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$24$		0			0
$25$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$26$		0			0
$27$		0			0
$28$	−0.419952	−	0.197614i	−0.419952	−	0.197614i
$29$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$29$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$30$		0			0
$31$	0.187381	−	0.982287i	0.187381	−	0.982287i
$31$	0.187381	−	0.982287i	0.187381	−	0.982287i
$32$	−0.441408	−	0.143422i	−0.441408	−	0.143422i
$33$		0			0
$34$		0			0
$35$	0.211645	+	0.134314i	0.211645	+	0.134314i
$36$	0.116260	−	1.84790i	0.116260	−	1.84790i
$37$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$37$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$38$	−2.07870	−	1.31918i	−2.07870	−	1.31918i
$39$		0			0
$40$	−1.30113	−	0.612266i	−1.30113	−	0.612266i
$41$	0.939097	−	1.47978i	0.939097	−	1.47978i	0.0627905	−	0.998027i	$-0.480000\pi$
$41$	0.939097	−	1.47978i	0.939097	−	1.47978i	0.876307	−	0.481754i	$-0.160000\pi$
$42$		0			0
$43$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$43$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$44$		0			0
$45$	−0.187381	+	0.982287i	−0.187381	+	0.982287i
$46$		0			0
$47$	−0.354691	−	0.645180i	−0.354691	−	0.645180i	0.637424	−	0.770513i	$-0.280000\pi$
$47$	−0.354691	−	0.645180i	−0.354691	−	0.645180i	−0.992115	+	0.125333i	$0.960000\pi$
$48$		0			0
$49$	0.289600	+	0.891298i	0.289600	+	0.891298i
$50$	1.42578	+	0.904827i	1.42578	+	0.904827i
$51$		0			0
$52$		0			0
$53$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$53$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$54$		0			0
$55$		0			0
$56$	0.153475	+	0.326150i	0.153475	+	0.326150i
$57$		0			0
$58$		0			0
$59$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	−0.187381	−	0.982287i	$-0.560000\pi$
$59$	−0.124591	−	1.98031i	−0.124591	−	1.98031i	0.0627905	−	0.998027i	$-0.480000\pi$
$60$		0			0
$61$		0			0		−0.535827	−	0.844328i	$-0.680000\pi$
$61$		0			0		0.535827	+	0.844328i	$0.320000\pi$
$62$	−1.30113	+	1.07639i	−1.30113	+	1.07639i
$63$	0.193142	−	0.159781i	0.193142	−	0.159781i
$64$	0.728969	+	1.14867i	0.728969	+	1.14867i
$65$		0			0
$66$		0			0
$67$	−1.63742	+	0.770513i	−1.63742	+	0.770513i	−0.637424	+	0.770513i	$0.720000\pi$
$67$	−1.63742	+	0.770513i	−1.63742	+	0.770513i	−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$	−0.130804	−	0.402572i	−0.130804	−	0.402572i
$71$	−1.75261	+	0.963507i	−1.75261	+	0.963507i	−0.876307	+	0.481754i	$0.840000\pi$
$71$	−1.75261	+	0.963507i	−1.75261	+	0.963507i	−0.876307	+	0.481754i	$0.840000\pi$
$72$	−0.984371	+	1.04825i	−0.984371	+	1.04825i
$73$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$73$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$74$		0			0
$75$		0			0
$76$	0.834178	+	2.56734i	0.834178	+	2.56734i
$77$		0			0
$78$		0			0
$79$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$79$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$80$	0.245551	+	0.521823i	0.245551	+	0.521823i
$81$	0.876307	+	0.481754i	0.876307	+	0.481754i
$82$	−2.81471	+	0.914555i	−2.81471	+	0.914555i
$83$		0			0		−0.125333	−	0.992115i	$-0.540000\pi$
$83$		0			0		0.125333	+	0.992115i	$0.460000\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$89$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$90$	1.30113	−	1.07639i	1.30113	−	1.07639i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.232966	+	1.22125i	−0.232966	+	1.22125i
$95$	−0.273190	−	1.43211i	−0.273190	−	1.43211i
$96$		0			0
$97$	−1.80608	−	0.849878i	−1.80608	−	0.849878i	−0.929776	−	0.368125i	$-0.880000\pi$
$97$	−1.80608	−	0.849878i	−1.80608	−	0.849878i	−0.876307	−	0.481754i	$-0.840000\pi$
$98$	0.582576	−	1.47142i	0.582576	−	1.47142i
$99$		0			0
$100$	−0.572163	−	1.76094i	−0.572163	−	1.76094i
$101$	0.866986	+	0.629902i	0.866986	+	0.629902i	0.929776	−	0.368125i	$-0.120000\pi$
$101$	0.866986	+	0.629902i	0.866986	+	0.629902i	−0.0627905	+	0.998027i	$0.520000\pi$
$102$		0			0
$103$	1.92978	−	0.368125i	1.92978	−	0.368125i	0.929776	−	0.368125i	$-0.120000\pi$
$103$	1.92978	−	0.368125i	1.92978	−	0.368125i	1.00000			$0$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.15475	−	1.58937i	−1.15475	−	1.58937i	−0.728969	−	0.684547i	$-0.760000\pi$
$107$	−1.15475	−	1.58937i	−1.15475	−	1.58937i	−0.425779	−	0.904827i	$-0.640000\pi$
$108$		0			0
$109$	−1.50441	+	0.595638i	−1.50441	+	0.595638i	−0.968583	−	0.248690i	$-0.920000\pi$
$109$	−1.50441	+	0.595638i	−1.50441	+	0.595638i	−0.535827	+	0.844328i	$0.680000\pi$
$110$		0			0
$111$		0			0
$112$	0.0359511	−	0.140020i	0.0359511	−	0.140020i
$113$	0.496398	−	0.0312307i	0.496398	−	0.0312307i	0.187381	−	0.982287i	$-0.440000\pi$
$113$	0.496398	−	0.0312307i	0.496398	−	0.0312307i	0.309017	+	0.951057i	$0.400000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.96948	+	2.71076i	−1.96948	+	2.71076i
$119$		0			0
$120$		0			0
$121$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$122$		0			0
$123$		0			0
$124$	1.85156			1.85156
$125$	0.187381	+	0.982287i	0.187381	+	0.982287i
$126$	−0.423289			−0.423289
$127$		0			0		−0.770513	−	0.637424i	$-0.780000\pi$
$127$		0			0		0.770513	+	0.637424i	$0.220000\pi$
$128$	0.229763	−	1.81876i	0.229763	−	1.81876i
$129$		0			0
$130$		0			0
$131$	0.929324	−	0.872693i	0.929324	−	0.872693i	−0.0627905	−	0.998027i	$-0.520000\pi$
$131$	0.929324	−	0.872693i	0.929324	−	0.872693i	0.992115	+	0.125333i	$0.0400000\pi$
$132$		0			0
$133$	−0.176060	+	0.320252i	−0.176060	+	0.320252i
$134$	2.95988	+	0.759967i	2.95988	+	0.759967i
$135$		0			0
$136$		0			0
$137$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$137$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$138$		0			0
$139$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$139$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$140$	−0.170855	+	0.431531i	−0.170855	+	0.431531i
$141$		0			0
$142$	3.31749	+	0.632845i	3.31749	+	0.632845i
$143$		0			0
$144$	0.572163	−	0.0722810i	0.572163	−	0.0722810i
$145$		0			0
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$149$	−0.866986	−	0.629902i	−0.866986	−	0.629902i	−0.929776	+	0.368125i	$0.880000\pi$
$150$		0			0
$151$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$151$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$152$	0.771772	−	1.94927i	0.771772	−	1.94927i
$153$		0			0
$154$		0			0
$155$	−0.992115	−	0.125333i	−0.992115	−	0.125333i
$156$		0			0
$157$	0.916350	+	0.297740i	0.916350	+	0.297740i	0.728969	−	0.684547i	$-0.240000\pi$
$157$	0.916350	+	0.297740i	0.916350	+	0.297740i	0.187381	+	0.982287i	$0.440000\pi$
$158$		0			0
$159$		0			0
$160$	−0.115423	+	0.449542i	−0.115423	+	0.449542i
$161$		0			0
$162$	−0.621636	−	1.57007i	−0.621636	−	1.57007i
$163$	−1.60601	−	1.01920i	−1.60601	−	1.01920i	−0.968583	−	0.248690i	$-0.920000\pi$
$163$	−1.60601	−	1.01920i	−1.60601	−	1.01920i	−0.637424	−	0.770513i	$-0.720000\pi$
$164$	3.01719	+	1.19459i	3.01719	+	1.19459i
$165$		0			0
$166$		0			0
$167$		0			0		−0.125333	−	0.992115i	$-0.540000\pi$
$167$		0			0		0.125333	+	0.992115i	$0.460000\pi$
$168$		0			0
$169$	−0.876307	−	0.481754i	−0.876307	−	0.481754i
$170$		0			0
$171$	−1.44644	−	0.182728i	−1.44644	−	0.182728i
$172$		0			0
$173$	−0.473036	−	1.84235i	−0.473036	−	1.84235i	−0.535827	−	0.844328i	$-0.680000\pi$
$173$	−0.473036	−	1.84235i	−0.473036	−	1.84235i	0.0627905	−	0.998027i	$-0.480000\pi$
$174$		0			0
$175$	0.120759	−	0.219661i	0.120759	−	0.219661i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$179$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$180$	−1.85156			−1.85156
$181$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$181$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.05037	−	0.868942i	1.05037	−	0.868942i
$189$		0			0
$190$	−1.18606	+	2.15743i	−1.18606	+	2.15743i
$191$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	0.968583	+	0.248690i	$0.0800000\pi$
$191$	0.0388067	+	0.616814i	0.0388067	+	0.616814i	−0.929776	+	0.368125i	$0.880000\pi$
$192$		0			0
$193$			1.17557i			1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$193$			1.17557i			1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$194$	1.43515	+	3.04985i	1.43515	+	3.04985i
$195$		0			0
$196$	−1.52058	+	0.835948i	−1.52058	+	0.835948i
$197$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$197$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$198$		0			0
$199$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$199$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$200$	−0.529359	+	1.33701i	−0.529359	+	1.33701i
$201$		0			0
$202$	−0.450043	−	1.75280i	−0.450043	−	1.75280i
$203$		0			0
$204$		0			0
$205$	−1.53583	−	0.844328i	−1.53583	−	0.844328i
$206$	−2.90714	−	1.59821i	−2.90714	−	1.59821i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.116762	+	0.0462295i	0.116762	+	0.0462295i	0.425779	−	0.904827i	$-0.360000\pi$
$211$	0.116762	+	0.0462295i	0.116762	+	0.0462295i	−0.309017	+	0.951057i	$0.600000\pi$
$212$		0			0
$213$		0			0
$214$	−0.208307	+	3.31094i	−0.208307	+	3.31094i
$215$		0			0
$216$		0			0
$217$	0.171593	+	0.182728i	0.171593	+	0.182728i
$218$	2.59857	+	0.844328i	2.59857	+	0.844328i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$223$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$224$	0.0941212	−	0.0683831i	0.0941212	−	0.0683831i
$225$	0.992115	+	0.125333i	0.992115	+	0.125333i
$226$	−0.679496	−	0.493683i	−0.679496	−	0.493683i
$227$	−1.68532	+	1.06954i	−1.68532	+	1.06954i	−0.809017	+	0.587785i	$0.800000\pi$
$227$	−1.68532	+	1.06954i	−1.68532	+	1.06954i	−0.876307	+	0.481754i	$0.840000\pi$
$228$		0			0
$229$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$229$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.946441	−	0.180543i	−0.946441	−	0.180543i	−0.309017	−	0.951057i	$-0.600000\pi$
$233$	−0.946441	−	0.180543i	−0.946441	−	0.180543i	−0.637424	+	0.770513i	$0.720000\pi$
$234$		0			0
$235$	−0.621636	+	0.394502i	−0.621636	+	0.394502i
$236$	3.55849	−	0.913666i	3.55849	−	0.913666i
$237$		0			0
$238$		0			0
$239$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$239$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$240$		0			0
$241$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$241$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$242$	−0.813516	+	1.47978i	−0.813516	+	1.47978i
$243$		0			0
$244$		0			0
$245$	0.871355	−	0.344994i	0.871355	−	0.344994i
$246$		0			0
$247$		0			0
$248$	−1.10799	−	0.916609i	−1.10799	−	0.916609i
$249$		0			0
$250$	0.813516	−	1.47978i	0.813516	−	1.47978i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	0.357613	+	0.295844i	0.357613	+	0.295844i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−1.26492	+	1.18784i	−1.26492	+	1.18784i
$257$	−0.292352	+	0.402389i	−0.292352	+	0.402389i	−0.929776	−	0.368125i	$-0.880000\pi$
$257$	−0.292352	+	0.402389i	−0.292352	+	0.402389i	0.637424	+	0.770513i	$0.280000\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−2.14853	+	0.135174i	−2.14853	+	0.135174i
$263$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$263$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$264$		0			0
$265$		0			0
$266$	0.573792	−	0.227180i	0.573792	−	0.227180i
$267$		0			0
$268$	−1.96948	−	2.71076i	−1.96948	−	2.71076i
$269$		0			0		0.992115	−	0.125333i	$-0.0400000\pi$
$269$		0			0		−0.992115	+	0.125333i	$0.960000\pi$
$270$		0			0
$271$		0			0		−0.728969	−	0.684547i	$-0.760000\pi$
$271$		0			0		0.728969	+	0.684547i	$0.240000\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.368125	−	0.929776i	$-0.380000\pi$
$277$		0			0		−0.368125	+	0.929776i	$0.620000\pi$
$278$		0			0
$279$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$280$	0.315870	−	0.173651i	0.315870	−	0.173651i
$281$	−0.303189	+	1.58937i	−0.303189	+	1.58937i	0.425779	+	0.904827i	$0.360000\pi$
$281$	−0.303189	+	1.58937i	−0.303189	+	1.58937i	−0.728969	+	0.684547i	$0.760000\pi$
$282$		0			0
$283$	−0.804733	−	0.856954i	−0.804733	−	0.856954i	0.187381	−	0.982287i	$-0.440000\pi$
$283$	−0.804733	−	0.856954i	−0.804733	−	0.856954i	−0.992115	+	0.125333i	$0.960000\pi$
$284$	−2.36046	−	2.85330i	−2.36046	−	2.85330i
$285$		0			0
$286$		0			0
$287$	0.161725	+	0.408471i	0.161725	+	0.408471i
$288$	0.391873	+	0.248690i	0.391873	+	0.248690i
$289$	0.929776	+	0.368125i	0.929776	+	0.368125i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.86842	−	0.607087i	1.86842	−	0.607087i	0.876307	−	0.481754i	$-0.160000\pi$
$293$	1.86842	−	0.607087i	1.86842	−	0.607087i	0.992115	−	0.125333i	$-0.0400000\pi$
$294$		0			0
$295$	−1.96858	+	0.248690i	−1.96858	+	0.248690i
$296$		0			0
$297$		0			0
$298$	0.450043	+	1.75280i	0.450043	+	1.75280i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.736806	+	0.405062i	−0.736806	+	0.405062i
$305$		0			0
$306$		0			0
$307$			0.497380i			0.497380i	0.968583	+	0.248690i	$0.0800000\pi$
$307$			0.497380i			0.497380i	−0.968583	+	0.248690i	$0.920000\pi$
$308$		0			0
$309$		0			0
$310$	1.15596	+	1.23098i	1.15596	+	1.23098i
$311$	0.574221	+	0.904827i	0.574221	+	0.904827i	1.00000			$0$
$311$	0.574221	+	0.904827i	0.574221	+	0.904827i	−0.425779	+	0.904827i	$0.640000\pi$
$312$		0			0
$313$		0			0		0.770513	−	0.637424i	$-0.220000\pi$
$313$		0			0		−0.770513	+	0.637424i	$0.780000\pi$
$314$	−0.871808	−	1.37375i	−0.871808	−	1.37375i
$315$	−0.171593	−	0.182728i	−0.171593	−	0.182728i
$316$		0			0
$317$	1.39436	−	0.656137i	1.39436	−	0.656137i	0.425779	−	0.904827i	$-0.360000\pi$
$317$	1.39436	−	0.656137i	1.39436	−	0.656137i	0.968583	+	0.248690i	$0.0800000\pi$
$318$		0			0
$319$		0			0
$320$	1.10063	−	0.799656i	1.10063	−	0.799656i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.572163	+	1.76094i	−0.572163	+	1.76094i
$325$		0			0
$326$	0.992567	+	3.05481i	0.992567	+	3.05481i
$327$		0			0
$328$	−1.21413	−	2.20850i	−1.21413	−	2.20850i
$329$	0.183098	+	0.0231306i	0.183098	+	0.0231306i
$330$		0			0
$331$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$331$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.871808	+	1.58581i	0.871808	+	1.58581i
$336$		0			0
$337$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$337$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$338$	0.621636	+	1.57007i	0.621636	+	1.57007i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	1.68532	+	1.79469i	1.68532	+	1.79469i
$343$	−0.461817	−	0.150053i	−0.461817	−	0.150053i
$344$		0			0
$345$		0			0
$346$	−1.36761	+	2.90632i	−1.36761	+	2.90632i
$347$		0			0		−0.904827	−	0.425779i	$-0.860000\pi$
$347$		0			0		0.904827	+	0.425779i	$0.140000\pi$
$348$		0			0
$349$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.728969	−	0.684547i	$-0.240000\pi$
$349$	1.60528	−	1.16630i	1.60528	−	1.16630i	0.876307	−	0.481754i	$-0.160000\pi$
$350$	−0.393565	+	0.155823i	−0.393565	+	0.155823i
$351$		0			0
$352$		0			0
$353$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$353$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$354$		0			0
$355$	1.07165	+	1.68866i	1.07165	+	1.68866i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.72897	+	0.684547i	−1.72897	+	0.684547i	−0.728969	+	0.684547i	$0.760000\pi$
$359$	−1.72897	+	0.684547i	−1.72897	+	0.684547i	−1.00000			$\pi$
$360$	1.10799	+	0.916609i	1.10799	+	0.916609i
$361$	1.09022	−	0.279921i	1.09022	−	0.279921i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.481754	−	0.876307i	$-0.340000\pi$
$367$		0			0		−0.481754	+	0.876307i	$0.660000\pi$
$368$		0			0
$369$	−1.27760	+	1.19975i	−1.27760	+	1.19975i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.193142	−	0.159781i	−0.193142	−	0.159781i	0.535827	−	0.844328i	$-0.320000\pi$
$373$	−0.193142	−	0.159781i	−0.193142	−	0.159781i	−0.728969	+	0.684547i	$0.760000\pi$
$374$		0			0
$375$		0			0
$376$	−1.05872			−1.05872
$377$		0			0
$378$		0			0
$379$	−0.273190	−	1.43211i	−0.273190	−	1.43211i	−0.809017	−	0.587785i	$-0.800000\pi$
$379$	−0.273190	−	1.43211i	−0.273190	−	1.43211i	0.535827	−	0.844328i	$-0.320000\pi$
$380$	2.50989	−	0.993736i	2.50989	−	0.993736i
$381$		0			0
$382$	0.613440	−	0.844328i	0.613440	−	0.844328i
$383$		0			0		0.481754	−	0.876307i	$-0.340000\pi$
$383$		0			0		−0.481754	+	0.876307i	$0.660000\pi$
$384$		0			0
$385$		0			0
$386$	1.26537	−	1.52957i	1.26537	−	1.52957i
$387$		0			0
$388$	0.919111	−	3.57970i	0.919111	−	3.57970i
$389$		0			0		0.968583	−	0.248690i	$-0.0800000\pi$
$389$		0			0		−0.968583	+	0.248690i	$0.920000\pi$
$390$		0			0
$391$		0			0
$392$	1.32376	+	0.252522i	1.32376	+	0.252522i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.946441	−	0.180543i	0.946441	−	0.180543i	0.309017	−	0.951057i	$-0.400000\pi$
$397$	0.946441	−	0.180543i	0.946441	−	0.180543i	0.637424	+	0.770513i	$0.280000\pi$
$398$		0			0
$399$		0			0
$400$	0.505375	−	0.277832i	0.505375	−	0.277832i
$401$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$401$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$402$		0			0
$403$		0			0
$404$	−0.844844	+	1.79538i	−0.844844	+	1.79538i
$405$	0.425779	−	0.904827i	0.425779	−	0.904827i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$409$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$410$	1.08949	+	2.75173i	1.08949	+	2.75173i
$411$		0			0
$412$	1.33906	+	3.38209i	1.33906	+	3.38209i
$413$	0.419952	+	0.266509i	0.419952	+	0.266509i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.11716	−	0.614163i	−1.11716	−	0.614163i	−0.187381	−	0.982287i	$-0.560000\pi$
$419$	−1.11716	−	0.614163i	−1.11716	−	0.614163i	−0.929776	+	0.368125i	$0.880000\pi$
$420$		0			0
$421$	1.84489	+	0.233064i	1.84489	+	0.233064i	0.968583	−	0.248690i	$-0.0800000\pi$
$421$	1.84489	+	0.233064i	1.84489	+	0.233064i	0.876307	+	0.481754i	$0.160000\pi$
$422$	−0.102162	−	0.185832i	−0.102162	−	0.185832i
$423$	0.183098	+	0.713118i	0.183098	+	0.713118i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	2.49006	−	2.65164i	2.49006	−	2.65164i
$429$		0			0
$430$		0			0
$431$	−0.159566	−	0.339095i	−0.159566	−	0.339095i	0.809017	−	0.587785i	$-0.200000\pi$
$431$	−0.159566	−	0.339095i	−0.159566	−	0.339095i	−0.968583	+	0.248690i	$0.920000\pi$
$432$		0			0
$433$		0			0		0.904827	−	0.425779i	$-0.140000\pi$
$433$		0			0		−0.904827	+	0.425779i	$0.860000\pi$
$434$	−0.0265786	−	0.422454i	−0.0265786	−	0.422454i
$435$		0			0
$436$	−1.60528	−	2.52951i	−1.60528	−	2.52951i
$437$		0			0
$438$		0			0
$439$	−0.683098	−	1.07639i	−0.683098	−	1.07639i	−0.992115	−	0.125333i	$-0.960000\pi$
$439$	−0.683098	−	1.07639i	−0.683098	−	1.07639i	0.309017	−	0.951057i	$-0.400000\pi$
$440$		0			0
$441$	−0.0588452	−	0.935317i	−0.0588452	−	0.935317i
$442$		0			0
$443$			1.80965i			1.80965i	0.425779	+	0.904827i	$0.360000\pi$
$443$			1.80965i			1.80965i	−0.425779	+	0.904827i	$0.640000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.340348	−	0.0214129i	−0.340348	−	0.0214129i
$449$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$449$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$450$	−1.15596	−	1.23098i	−1.15596	−	1.23098i
$451$		0			0
$452$	0.229025	+	0.891995i	0.229025	+	0.891995i
$453$		0			0
$454$	3.34407	+	0.422454i	3.34407	+	0.422454i
$455$		0			0
$456$		0			0
$457$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$457$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		−0.929776	−	0.368125i	$-0.880000\pi$
$461$		0			0		0.929776	+	0.368125i	$0.120000\pi$
$462$		0			0
$463$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$463$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$464$		0			0
$465$		0			0
$466$	1.03711	+	1.25365i	1.03711	+	1.25365i
$467$	1.30209	+	1.38658i	1.30209	+	1.38658i	0.876307	+	0.481754i	$0.160000\pi$
$467$	1.30209	+	1.38658i	1.30209	+	1.38658i	0.425779	+	0.904827i	$0.360000\pi$
$468$		0			0
$469$	0.0849998	−	0.445585i	0.0849998	−	0.445585i
$470$	1.23347	+	0.155823i	1.23347	+	0.155823i
$471$		0			0
$472$	−2.58174	−	1.21488i	−2.58174	−	1.21488i
$473$		0			0
$474$		0			0
$475$	−1.41213	+	0.362574i	−1.41213	+	0.362574i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.929776	−	0.368125i	$-0.880000\pi$
$479$	−1.35556	−	1.27295i	−1.35556	−	1.27295i	−0.425779	−	0.904827i	$-0.640000\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.72154	−	0.681604i	1.72154	−	0.681604i
$485$	−0.734796	+	1.85588i	−0.734796	+	1.85588i
$486$		0			0
$487$		0			0		0.248690	−	0.968583i	$-0.420000\pi$
$487$		0			0		−0.248690	+	0.968583i	$0.580000\pi$
$488$		0			0
$489$		0			0
$490$	−1.50510	−	0.489035i	−1.50510	−	0.489035i
$491$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$491$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.108065	+	0.566495i	0.108065	+	0.566495i
$497$	0.0628337	−	0.497380i	0.0628337	−	0.497380i
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	−1.72154	+	0.681604i	−1.72154	+	0.681604i
$501$		0			0
$502$		0			0
$503$	0.147338	−	1.16630i	0.147338	−	1.16630i	−0.728969	−	0.684547i	$-0.760000\pi$
$503$	0.147338	−	1.16630i	0.147338	−	1.16630i	0.876307	−	0.481754i	$-0.160000\pi$
$504$	−0.0675427	−	0.354071i	−0.0675427	−	0.354071i
$505$	0.574221	−	0.904827i	0.574221	−	0.904827i
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$509$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$510$		0			0
$511$		0			0
$512$	1.09480	−	0.0688792i	1.09480	−	0.0688792i
$513$		0			0
$514$	0.813516	−	0.208875i	0.813516	−	0.208875i
$515$	−0.488570	−	1.90285i	−0.488570	−	1.90285i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.27760	−	1.19975i	−1.27760	−	1.19975i	−0.968583	−	0.248690i	$-0.920000\pi$
$521$	−1.27760	−	1.19975i	−1.27760	−	1.19975i	−0.309017	−	0.951057i	$-0.600000\pi$
$522$		0			0
$523$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$523$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$524$	1.90965	+	1.38744i	1.90965	+	1.38744i
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.425779	−	0.904827i	0.425779	−	0.904827i
$530$		0			0
$531$	−0.371808	+	1.94908i	−0.371808	+	1.94908i
$532$	−0.643545	−	0.209100i	−0.643545	−	0.209100i
$533$		0			0
$534$		0			0
$535$	−1.51373	+	1.25227i	−1.51373	+	1.25227i
$536$	−0.163397	+	2.59713i	−0.163397	+	2.59713i
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.456288	−	0.718995i	0.456288	−	0.718995i	−0.535827	−	0.844328i	$-0.680000\pi$
$541$	0.456288	−	0.718995i	0.456288	−	0.718995i	0.992115	+	0.125333i	$0.0400000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.688925	+	1.46404i	0.688925	+	1.46404i
$546$		0			0
$547$	0.354691	+	0.645180i	0.354691	+	0.645180i	0.992115	−	0.125333i	$-0.0400000\pi$
$547$	0.354691	+	0.645180i	0.354691	+	0.645180i	−0.637424	+	0.770513i	$0.720000\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$	1.52794	−	0.718995i	1.52794	−	0.718995i
$559$		0			0
$560$	−0.142001	−	0.0270882i	−0.142001	−	0.0270882i
$561$		0			0
$562$	2.10528	−	1.74164i	2.10528	−	1.74164i
$563$	0.567290	−	0.469303i	0.567290	−	0.469303i	−0.309017	−	0.951057i	$-0.600000\pi$
$563$	0.567290	−	0.469303i	0.567290	−	0.469303i	0.876307	+	0.481754i	$0.160000\pi$
$564$		0			0
$565$	−0.0623382	−	0.493458i	−0.0623382	−	0.493458i
$566$	0.124648	+	1.98122i	0.124648	+	1.98122i
$567$	−0.226810	+	0.106729i	−0.226810	+	0.106729i
$568$			2.87598i			2.87598i
$569$		0			0		−0.425779	−	0.904827i	$-0.640000\pi$
$569$		0			0		0.425779	+	0.904827i	$0.360000\pi$
$570$		0			0
$571$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$571$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$572$		0			0
$573$		0			0
$574$	0.229248	−	0.705553i	0.229248	−	0.705553i
$575$		0			0
$576$	−0.420404	−	1.29387i	−0.420404	−	1.29387i
$577$	−0.496398	−	1.93334i	−0.496398	−	1.93334i	−0.309017	−	0.951057i	$-0.600000\pi$
$577$	−0.496398	−	1.93334i	−0.496398	−	1.93334i	−0.187381	−	0.982287i	$-0.560000\pi$
$578$	−0.813516	−	1.47978i	−0.813516	−	1.47978i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−3.08452	−	1.22125i	−3.08452	−	1.22125i
$587$		0			0		−0.844328	−	0.535827i	$-0.820000\pi$
$587$		0			0		0.844328	+	0.535827i	$0.180000\pi$
$588$		0			0
$589$	0.0915446	−	1.45506i	0.0915446	−	1.45506i
$590$	2.82907	+	1.79538i	2.82907	+	1.79538i
$591$		0			0
$592$		0			0
$593$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$593$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$594$		0			0
$595$		0			0
$596$	0.844844	−	1.79538i	0.844844	−	1.79538i
$597$		0			0
$598$		0			0
$599$	1.17950	−	0.856954i	1.17950	−	0.856954i	0.187381	−	0.982287i	$-0.440000\pi$
$599$	1.17950	−	0.856954i	1.17950	−	0.856954i	0.992115	+	0.125333i	$0.0400000\pi$
$600$		0			0
$601$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$601$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$602$		0			0
$603$	1.77760	−	0.339095i	1.77760	−	0.339095i
$604$		0			0
$605$	−0.968583	+	0.248690i	−0.968583	+	0.248690i
$606$		0			0
$607$	1.15475	+	1.58937i	1.15475	+	1.58937i	0.728969	+	0.684547i	$0.240000\pi$
$607$	1.15475	+	1.58937i	1.15475	+	1.58937i	0.425779	+	0.904827i	$0.360000\pi$
$608$	−0.664678	−	0.126794i	−0.664678	−	0.126794i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$613$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$614$	0.535374	−	0.647157i	0.535374	−	0.647157i
$615$		0			0
$616$		0			0
$617$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$617$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$618$		0			0
$619$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$619$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$620$	−0.116260	−	1.84790i	−0.116260	−	1.84790i
$621$		0			0
$622$	0.226810	−	1.79538i	0.226810	−	1.79538i
$623$		0			0
$624$		0			0
$625$	0.968583	−	0.248690i	0.968583	−	0.248690i
$626$		0			0
$627$		0			0
$628$	−0.223593	+	1.76992i	−0.223593	+	1.76992i
$629$		0			0
$630$	0.0265786	+	0.422454i	0.0265786	+	0.422454i
$631$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$631$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$632$		0			0
$633$		0			0
$634$	−2.52051	−	0.647157i	−2.52051	−	0.647157i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	1.93717	−	0.497380i	1.93717	−	0.497380i
$640$	−1.82960	−	0.115109i	−1.82960	−	0.115109i
$641$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$641$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$642$		0			0
$643$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$643$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.982287	−	0.187381i	$-0.0600000\pi$
$647$		0			0		−0.982287	+	0.187381i	$0.940000\pi$
$648$	1.21413	−	0.770513i	1.21413	−	0.770513i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	1.29649	−	3.27456i	1.29649	−	3.27456i
$653$	1.23879	+	0.582932i	1.23879	+	0.582932i	0.929776	−	0.368125i	$-0.120000\pi$
$653$	1.23879	+	0.582932i	1.23879	+	0.582932i	0.309017	+	0.951057i	$0.400000\pi$
$654$		0			0
$655$	−0.929324	−	0.872693i	−0.929324	−	0.872693i
$656$	−0.189396	+	0.992848i	−0.189396	+	0.992848i
$657$		0			0
$658$	−0.213337	−	0.227180i	−0.213337	−	0.227180i
$659$	0.0800484	+	0.0967619i	0.0800484	+	0.0967619i	0.809017	−	0.587785i	$-0.200000\pi$
$659$	0.0800484	+	0.0967619i	0.0800484	+	0.0967619i	−0.728969	+	0.684547i	$0.760000\pi$
$660$		0			0
$661$	0.101597	−	1.61484i	0.101597	−	1.61484i	−0.535827	−	0.844328i	$-0.680000\pi$
$661$	0.101597	−	1.61484i	0.101597	−	1.61484i	0.637424	−	0.770513i	$-0.280000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.330674	+	0.155604i	0.330674	+	0.155604i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	0.572615	−	3.00175i	0.572615	−	3.00175i
$671$		0			0
$672$		0			0
$673$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$673$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$674$		0			0
$675$		0			0
$676$	0.572163	−	1.76094i	0.572163	−	1.76094i
$677$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$677$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$678$		0			0
$679$	0.438454	−	0.241042i	0.438454	−	0.241042i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.80608	−	0.849878i	1.80608	−	0.849878i	0.876307	−	0.481754i	$-0.160000\pi$
$683$	1.80608	−	0.849878i	1.80608	−	0.849878i	0.929776	−	0.368125i	$-0.120000\pi$
$684$	−0.169500	−	2.69413i	−0.169500	−	2.69413i
$685$		0			0
$686$	0.439368	+	0.692334i	0.439368	+	0.692334i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.121636	+	1.93334i	0.121636	+	1.93334i	0.309017	+	0.951057i	$0.400000\pi$
$691$	0.121636	+	1.93334i	0.121636	+	1.93334i	−0.187381	+	0.982287i	$0.560000\pi$
$692$	3.18669	−	1.49954i	3.18669	−	1.49954i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−3.34407	−	0.210391i	−3.34407	−	0.210391i
$699$		0			0
$700$	0.441408	+	0.143422i	0.441408	+	0.143422i
$701$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.535827	+	0.844328i	$0.320000\pi$
$701$	0.598617	+	1.84235i	0.598617	+	1.84235i	0.0627905	+	0.998027i	$0.480000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.255480	+	0.0830105i	−0.255480	+	0.0830105i
$708$		0			0
$709$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$709$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$710$	0.423289	−	3.35068i	0.423289	−	3.35068i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	2.98646	+	0.970358i	2.98646	+	0.970358i
$719$		0			0		0.187381	−	0.982287i	$-0.440000\pi$
$719$		0			0		−0.187381	+	0.982287i	$0.560000\pi$
$720$	−0.108065	−	0.566495i	−0.108065	−	0.566495i
$721$	−0.209676	+	0.445585i	−0.209676	+	0.445585i
$722$	−1.71982	−	0.809287i	−1.71982	−	0.809287i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.52794	−	0.969661i	1.52794	−	0.969661i	0.535827	−	0.844328i	$-0.320000\pi$
$727$	1.52794	−	0.969661i	1.52794	−	0.969661i	0.992115	−	0.125333i	$-0.0400000\pi$
$728$		0			0
$729$	−0.728969	−	0.684547i	−0.728969	−	0.684547i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−1.51373	−	0.288760i	−1.51373	−	0.288760i	−0.637424	−	0.770513i	$-0.720000\pi$
$733$	−1.51373	−	0.288760i	−1.51373	−	0.288760i	−0.876307	+	0.481754i	$0.840000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	2.95372	−	0.185832i	2.95372	−	0.185832i
$739$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$739$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$743$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$744$		0			0
$745$	−0.574221	+	0.904827i	−0.574221	+	0.904827i
$746$	0.0793165	+	0.415792i	0.0793165	+	0.415792i
$747$		0			0
$748$		0			0
$749$	0.492453			0.492453
$750$		0			0
$751$	−0.125581			−0.125581			−0.0627905	−	0.998027i	$-0.520000\pi$
$751$	−0.125581			−0.125581			−0.0627905	+	0.998027i	$0.520000\pi$
$752$	0.327162	+	0.270652i	0.327162	+	0.270652i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$757$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$758$	−1.18606	+	2.15743i	−1.18606	+	2.15743i
$759$		0			0
$760$	−1.99389	−	0.647854i	−1.99389	−	0.647854i
$761$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$761$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$762$		0			0
$763$	0.100865	−	0.392845i	0.100865	−	0.392845i
$764$	−1.10838	+	0.284582i	−1.10838	+	0.284582i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	1.84489	−	0.233064i	1.84489	−	0.233064i	0.876307	−	0.481754i	$-0.160000\pi$
$769$	1.84489	−	0.233064i	1.84489	−	0.233064i	0.968583	+	0.248690i	$0.0800000\pi$
$770$		0			0
$771$		0			0
$772$	−2.13808	+	0.407861i	−2.13808	+	0.407861i
$773$		0			0		0.844328	−	0.535827i	$-0.180000\pi$
$773$		0			0		−0.844328	+	0.535827i	$0.820000\pi$
$774$		0			0
$775$	−0.0627905	+	0.998027i	−0.0627905	+	0.998027i
$776$	−2.32212	+	1.68712i	−2.32212	+	1.68712i
$777$		0			0
$778$		0			0
$779$	1.08795	−	2.31201i	1.08795	−	2.31201i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.344511	−	0.416442i	−0.344511	−	0.416442i
$785$	0.239615	−	0.933237i	0.239615	−	0.933237i
$786$		0			0
$787$		0			0		−0.368125	−	0.929776i	$-0.620000\pi$
$787$		0			0		0.368125	+	0.929776i	$0.380000\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.0668050	+	0.105268i	−0.0668050	+	0.105268i
$792$		0			0
$793$		0			0
$794$	−1.42578	−	0.783829i	−1.42578	−	0.783829i
$795$		0			0
$796$		0			0
$797$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$797$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$798$		0			0
$799$		0			0
$800$	0.455903	+	0.0869681i	0.455903	+	0.0869681i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	1.39436	−	0.656137i	1.39436	−	0.656137i
$809$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$809$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$810$	−1.52794	+	0.718995i	−1.52794	+	0.718995i
$811$	−0.456288	−	0.718995i	−0.456288	−	0.718995i	0.535827	−	0.844328i	$-0.320000\pi$
$811$	−0.456288	−	0.718995i	−0.456288	−	0.718995i	−0.992115	+	0.125333i	$0.960000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.916350	+	1.66683i	−0.916350	+	1.66683i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	1.00278	−	3.08624i	1.00278	−	3.08624i
$821$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$821$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$822$		0			0
$823$		0			0		−0.998027	−	0.0627905i	$-0.980000\pi$
$823$		0			0		0.998027	+	0.0627905i	$0.0200000\pi$
$824$	0.872985	−	2.68677i	0.872985	−	2.68677i
$825$		0			0
$826$	−0.259544	−	0.798795i	−0.259544	−	0.798795i
$827$		0			0		−0.248690	−	0.968583i	$-0.580000\pi$
$827$		0			0		0.248690	+	0.968583i	$0.420000\pi$
$828$		0			0
$829$		0			0		−0.992115	−	0.125333i	$-0.960000\pi$
$829$		0			0		0.992115	+	0.125333i	$0.0400000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.792491	+	2.00160i	0.792491	+	2.00160i
$839$	−0.00788530	+	0.125333i	−0.00788530	+	0.125333i	0.992115	+	0.125333i	$0.0400000\pi$
$839$	−0.00788530	+	0.125333i	−0.00788530	+	0.125333i	−1.00000			$\pi$
$840$		0			0
$841$	−0.637424	−	0.770513i	−0.637424	−	0.770513i
$842$	−2.14958	−	2.28907i	−2.14958	−	2.28907i
$843$		0			0
$844$	−0.0435700	+	0.228402i	−0.0435700	+	0.228402i
$845$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$846$	0.529359	−	1.12495i	0.529359	−	1.12495i
$847$	0.226810	+	0.106729i	0.226810	+	0.106729i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	0.946441	−	0.180543i	0.946441	−	0.180543i	0.309017	−	0.951057i	$-0.400000\pi$
$853$	0.946441	−	0.180543i	0.946441	−	0.180543i	0.637424	+	0.770513i	$0.280000\pi$
$854$		0			0
$855$	−0.0915446	+	1.45506i	−0.0915446	+	1.45506i
$856$	−2.80276	+	0.354071i	−2.80276	+	0.354071i
$857$	0.992567	+	1.36615i	0.992567	+	1.36615i	0.929776	+	0.368125i	$0.120000\pi$
$857$	0.992567	+	1.36615i	0.992567	+	1.36615i	0.0627905	+	0.998027i	$0.480000\pi$
$858$		0			0
$859$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$859$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$860$		0			0
$861$		0			0
$862$	−0.157382	+	0.612963i	−0.157382	+	0.612963i
$863$		0			0		0.998027	−	0.0627905i	$-0.0200000\pi$
$863$		0			0		−0.998027	+	0.0627905i	$0.980000\pi$
$864$		0			0
$865$	−1.80902	+	0.587785i	−1.80902	+	0.587785i
$866$		0			0
$867$		0			0
$868$	−0.272805	+	0.375484i	−0.272805	+	0.375484i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.291615	+	2.30837i	−0.291615	+	2.30837i
$873$	1.53799	+	1.27233i	1.53799	+	1.27233i
$874$		0			0
$875$	−0.226810	−	0.106729i	−0.226810	−	0.106729i
$876$		0			0
$877$	1.18738	+	0.982287i	1.18738	+	0.982287i	1.00000			$0$
$877$	1.18738	+	0.982287i	1.18738	+	0.982287i	0.187381	+	0.982287i	$0.440000\pi$
$878$	−0.269815	+	2.13580i	−0.269815	+	2.13580i
$879$		0			0
$880$		0			0
$881$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$881$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$882$	−0.930200	+	1.28031i	−0.930200	+	1.28031i
$883$		0			0		0.481754	−	0.876307i	$-0.340000\pi$
$883$		0			0		−0.481754	+	0.876307i	$0.660000\pi$
$884$		0			0
$885$		0			0
$886$	1.94789	−	2.35460i	1.94789	−	2.35460i
$887$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$887$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.630932	−	0.868403i	−0.630932	−	0.868403i
$894$		0			0
$895$		0			0
$896$	0.334980	+	0.314567i	0.334980	+	0.314567i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.116260	+	1.84790i	0.116260	+	1.84790i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.304529	−	0.647157i	0.304529	−	0.647157i
$905$		0			0
$906$		0			0
$907$	1.11803	+	0.363271i	1.11803	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$907$	1.11803	+	0.363271i	1.11803	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$908$	−2.52996	−	2.69413i	−2.52996	−	2.69413i
$909$	−0.683098	−	0.825723i	−0.683098	−	0.825723i
$910$		0			0
$911$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$911$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.0400517	+	0.317042i	0.0400517	+	0.317042i
$918$		0			0
$919$	−0.939097	−	0.516273i	−0.939097	−	0.516273i	−0.0627905	−	0.998027i	$-0.520000\pi$
$919$	−0.939097	−	0.516273i	−0.939097	−	0.516273i	−0.876307	+	0.481754i	$0.840000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.96070	−	0.123357i	−1.96070	−	0.123357i
$928$		0			0
$929$		0			0		0.876307	−	0.481754i	$-0.160000\pi$
$929$		0			0		−0.876307	+	0.481754i	$0.840000\pi$
$930$		0			0
$931$	0.581755	+	1.23629i	0.581755	+	1.23629i
$932$		−	1.78399i		−	1.78399i
$933$		0			0
$934$	−0.201684	−	3.20568i	−0.201684	−	3.20568i
$935$		0			0
$936$		0			0
$937$	1.39436	−	1.15352i	1.39436	−	1.15352i	0.425779	−	0.904827i	$-0.360000\pi$
$937$	1.39436	−	1.15352i	1.39436	−	1.15352i	0.968583	−	0.248690i	$-0.0800000\pi$
$938$	−0.590219	+	0.488271i	−0.590219	+	0.488271i
$939$		0			0
$940$	−0.933180	−	0.993736i	−0.933180	−	0.993736i
$941$		0			0		−0.0627905	−	0.998027i	$-0.520000\pi$
$941$		0			0		0.0627905	+	0.998027i	$0.480000\pi$
$942$		0			0
$943$		0			0
$944$	0.487230	+	1.03542i	0.487230	+	1.03542i
$945$		0			0
$946$		0			0
$947$		0			0		0.684547	−	0.728969i	$-0.260000\pi$
$947$		0			0		−0.684547	+	0.728969i	$0.740000\pi$
$948$		0			0
$949$		0			0
$950$	2.22764	+	1.04825i	2.22764	+	1.04825i
$951$		0			0
$952$		0			0
$953$		0			0		−0.481754	−	0.876307i	$-0.660000\pi$
$953$		0			0		0.481754	+	0.876307i	$0.340000\pi$
$954$		0			0
$955$	0.613161	−	0.0774602i	0.613161	−	0.0774602i
$956$		0			0
$957$		0			0
$958$	0.393565	+	3.11538i	0.393565	+	3.11538i
$959$		0			0
$960$		0			0
$961$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$962$		0			0
$963$	0.723208	+	1.82662i	0.723208	+	1.82662i
$964$		0			0
$965$	1.17325	−	0.0738147i	1.17325	−	0.0738147i
$966$		0			0
$967$		0			0		−0.684547	−	0.728969i	$-0.740000\pi$
$967$		0			0		0.684547	+	0.728969i	$0.260000\pi$
$968$	−1.36761	−	0.444363i	−1.36761	−	0.444363i
$969$		0			0
$970$	2.95372	−	1.62382i	2.95372	−	1.62382i
$971$	0.159566	−	0.339095i	0.159566	−	0.339095i	−0.809017	−	0.587785i	$-0.800000\pi$
$971$	0.159566	−	0.339095i	0.159566	−	0.339095i	0.968583	+	0.248690i	$0.0800000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.992567	−	0.629902i	0.992567	−	0.629902i	0.0627905	−	0.998027i	$-0.480000\pi$
$977$	0.992567	−	0.629902i	0.992567	−	0.629902i	0.929776	+	0.368125i	$0.120000\pi$
$978$		0			0
$979$		0			0
$980$	0.929776	+	1.46509i	0.929776	+	1.46509i
$981$	1.60528	−	0.202793i	1.60528	−	0.202793i
$982$		0			0
$983$		0			0		−0.982287	−	0.187381i	$-0.940000\pi$
$983$		0			0		0.982287	+	0.187381i	$0.0600000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.968583	−	0.248690i	$-0.920000\pi$
$991$		0			0		0.968583	+	0.248690i	$0.0800000\pi$
$992$	−0.223593	+	0.406715i	−0.223593	+	0.406715i
$993$		0			0
$994$	−0.617129	+	0.579523i	−0.617129	+	0.579523i
$995$		0			0
$996$		0			0
$997$	0.147338	−	1.16630i	0.147338	−	1.16630i	−0.728969	−	0.684547i	$-0.760000\pi$
$997$	0.147338	−	1.16630i	0.147338	−	1.16630i	0.876307	−	0.481754i	$-0.160000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3875.1.dk.a.929.1	✓	20
31.30	odd	2	CM	3875.1.dk.a.929.1	✓	20
125.44	even	50	inner	3875.1.dk.a.2169.1	yes	20
3875.2169	odd	50	inner	3875.1.dk.a.2169.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3875.1.dk.a.929.1	✓	20	1.1	even	1	trivial
3875.1.dk.a.929.1	✓	20	31.30	odd	2	CM
3875.1.dk.a.2169.1	yes	20	125.44	even	50	inner
3875.1.dk.a.2169.1	yes	20	3875.2169	odd	50	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:	\( N \)	\(=\)	\( 3875 = 5^{3} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3875.dk (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30113 - 1.07639i) q^{2} +(0.346947 + 1.81876i) q^{4} +(-0.0627905 - 0.998027i) q^{5} +(-0.147338 + 0.202793i) q^{7} +(0.692757 - 1.26012i) q^{8} +(-0.968583 - 0.248690i) q^{9} +O(q^{10})\)	\(q+(-1.30113 - 1.07639i) q^{2} +(0.346947 + 1.81876i) q^{4} +(-0.0627905 - 0.998027i) q^{5} +(-0.147338 + 0.202793i) q^{7} +(0.692757 - 1.26012i) q^{8} +(-0.968583 - 0.248690i) q^{9} +(-0.992567 + 1.36615i) q^{10} +(0.409991 - 0.105268i) q^{14} +(-0.536212 + 0.212301i) q^{16} +(0.992567 + 1.36615i) q^{18} +(1.44644 - 0.182728i) q^{19} +(1.79339 - 0.460464i) q^{20} +(-0.992115 + 0.125333i) q^{25} +(-0.419952 - 0.197614i) q^{28} +(0.187381 - 0.982287i) q^{31} +(-0.441408 - 0.143422i) q^{32} +(0.211645 + 0.134314i) q^{35} +(0.116260 - 1.84790i) q^{36} +(-2.07870 - 1.31918i) q^{38} +(-1.30113 - 0.612266i) q^{40} +(0.939097 - 1.47978i) q^{41} +(-0.187381 + 0.982287i) q^{45} +(-0.354691 - 0.645180i) q^{47} +(0.289600 + 0.891298i) q^{49} +(1.42578 + 0.904827i) q^{50} +(0.153475 + 0.326150i) q^{56} +(-0.124591 - 1.98031i) q^{59} +(-1.30113 + 1.07639i) q^{62} +(0.193142 - 0.159781i) q^{63} +(0.728969 + 1.14867i) q^{64} +(-1.63742 + 0.770513i) q^{67} +(-0.130804 - 0.402572i) q^{70} +(-1.75261 + 0.963507i) q^{71} +(-0.984371 + 1.04825i) q^{72} +(0.834178 + 2.56734i) q^{76} +(0.245551 + 0.521823i) q^{80} +(0.876307 + 0.481754i) q^{81} +(-2.81471 + 0.914555i) q^{82} +(1.30113 - 1.07639i) q^{90} +(-0.232966 + 1.22125i) q^{94} +(-0.273190 - 1.43211i) q^{95} +(-1.80608 - 0.849878i) q^{97} +(0.582576 - 1.47142i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} - 5 q^{4} + 5 q^{8}+O(q^{10}) \) 20 * q + 5 * q^2 - 5 * q^4 + 5 * q^8	\( 20 q + 5 q^{2} - 5 q^{4} + 5 q^{8} + 5 q^{14} - 5 q^{16} + 5 q^{19} - 5 q^{28} - 25 q^{32} - 5 q^{38} + 5 q^{40} + 5 q^{49} + 20 q^{50} - 20 q^{56} + 5 q^{62} - 20 q^{67} + 5 q^{72} - 15 q^{76} + 20 q^{80} - 5 q^{90} + 20 q^{94} - 5 q^{95} - 5 q^{98}+O(q^{100}) \) 20 * q + 5 * q^2 - 5 * q^4 + 5 * q^8 + 5 * q^14 - 5 * q^16 + 5 * q^19 - 5 * q^28 - 25 * q^32 - 5 * q^38 + 5 * q^40 + 5 * q^49 + 20 * q^50 - 20 * q^56 + 5 * q^62 - 20 * q^67 + 5 * q^72 - 15 * q^76 + 20 * q^80 - 5 * q^90 + 20 * q^94 - 5 * q^95 - 5 * q^98

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