LMFDB - Embedded newform 2900.1.cr.a.1203.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2900,1,Mod(3,2900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2900, base_ring=CyclotomicField(140))

chi = DirichletCharacter(H, H._module([70, 49, 25]))

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

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

chi := DirichletCharacter("2900.3");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2900 = 2^{2} \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2900.cr (of order $140$, degree $48$, 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:	$1.44728853664$
Analytic rank:	$0$
Dimension:	$48$
Coefficient field:	$\Q(\zeta_{140})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} + x^{46} - x^{38} - x^{36} - x^{34} - x^{32} + x^{28} + x^{26} + x^{24} + x^{22} + x^{20} + \cdots + 1 $ x^48 + x^46 - x^38 - x^36 - x^34 - x^32 + x^28 + x^26 + x^24 + x^22 + x^20 - x^16 - x^14 - x^12 - x^10 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{140}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{140} - \cdots)$

Embedding invariants

Embedding label			1203.1
Root			$0.919528 + 0.393025i$ of defining polynomial
Character	$\chi$	$=$	2900.1203
Dual form			2900.1.cr.a.1767.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834573 + 0.550897i) q^{2} +(0.393025 - 0.919528i) q^{4} +(0.919528 - 0.393025i) q^{5} +(0.178557 + 0.983930i) q^{8} +(0.134233 - 0.990950i) q^{9} +O(q^{10})$	\(q+(-0.834573 + 0.550897i) q^{2} +(0.393025 - 0.919528i) q^{4} +(0.919528 - 0.393025i) q^{5} +(0.178557 + 0.983930i) q^{8} +(0.134233 - 0.990950i) q^{9} +(-0.550897 + 0.834573i) q^{10} +(-1.99497 - 0.0447745i) q^{13} +(-0.691063 - 0.722795i) q^{16} +(-0.413066 - 0.568536i) q^{17} +(0.433884 + 0.900969i) q^{18} -1.00000i q^{20} +(0.691063 - 0.722795i) q^{25} +(1.68961 - 1.06165i) q^{26} +(0.880596 + 0.473869i) q^{29} +(0.974928 + 0.222521i) q^{32} +(0.657939 + 0.246929i) q^{34} +(-0.858449 - 0.512899i) q^{36} +(0.267386 - 1.97392i) q^{37} +(0.550897 + 0.834573i) q^{40} +(0.842711 - 1.65391i) q^{41} +(-0.266037 - 0.963963i) q^{45} +(-0.433884 + 0.900969i) q^{49} +(-0.178557 + 0.983930i) q^{50} +(-0.825243 + 1.81683i) q^{52} +(-1.51290 - 0.858449i) q^{53} +(-0.995974 + 0.0896393i) q^{58} +(0.957099 - 0.241168i) q^{61} +(-0.936235 + 0.351375i) q^{64} +(-1.85203 + 0.742901i) q^{65} +(-0.685130 + 0.156377i) q^{68} +(0.998993 - 0.0448648i) q^{72} +(0.677425 + 1.80499i) q^{73} +(0.864274 + 1.79468i) q^{74} +(-0.919528 - 0.393025i) q^{80} +(-0.963963 - 0.266037i) q^{81} +(0.207832 + 1.84456i) q^{82} +(-0.603275 - 0.360440i) q^{85} +(0.243030 - 1.18696i) q^{89} +(0.753071 + 0.657939i) q^{90} +(0.403165 - 0.943250i) q^{97} +(-0.134233 - 0.990950i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 2 q^{9}+O(q^{10}) $ 48 * q - 2 * q^4 + 2 * q^9	$ 48 q - 2 q^{4} + 2 q^{9} + 2 q^{10} + 2 q^{13} + 2 q^{16} - 2 q^{25} + 12 q^{26} - 2 q^{36} + 6 q^{37} - 2 q^{40} + 2 q^{41} - 2 q^{52} - 48 q^{53} + 2 q^{58} - 2 q^{61} - 2 q^{64} - 8 q^{65} + 2 q^{81} + 2 q^{82} + 8 q^{89} + 2 q^{90} - 2 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 + 2 * q^9 + 2 * q^10 + 2 * q^13 + 2 * q^16 - 2 * q^25 + 12 * q^26 - 2 * q^36 + 6 * q^37 - 2 * q^40 + 2 * q^41 - 2 * q^52 - 48 * q^53 + 2 * q^58 - 2 * q^61 - 2 * q^64 - 8 * q^65 + 2 * q^81 + 2 * q^82 + 8 * q^89 + 2 * q^90 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$	$1451$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{7}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.834573	+	0.550897i	−0.834573	+	0.550897i
$2$	−0.834573	+	0.550897i	−0.834573	+	0.550897i
$3$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$3$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$4$	0.393025	−	0.919528i	0.393025	−	0.919528i
$5$	0.919528	−	0.393025i	0.919528	−	0.393025i
$5$	0.919528	−	0.393025i	0.919528	−	0.393025i
$6$		0			0
$7$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$7$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$8$	0.178557	+	0.983930i	0.178557	+	0.983930i
$9$	0.134233	−	0.990950i	0.134233	−	0.990950i
$10$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$11$		0			0		−0.795625	−	0.605790i	$-0.792857\pi$
$11$		0			0		0.795625	+	0.605790i	$0.207143\pi$
$12$		0			0
$13$	−1.99497	−	0.0447745i	−1.99497	−	0.0447745i	−0.995974	−	0.0896393i	$-0.971429\pi$
$13$	−1.99497	−	0.0447745i	−1.99497	−	0.0447745i	−0.998993	+	0.0448648i	$0.985714\pi$
$14$		0			0
$15$		0			0
$16$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$17$	−0.413066	−	0.568536i	−0.413066	−	0.568536i	0.550897	−	0.834573i	$-0.314286\pi$
$17$	−0.413066	−	0.568536i	−0.413066	−	0.568536i	−0.963963	+	0.266037i	$0.914286\pi$
$18$	0.433884	+	0.900969i	0.433884	+	0.900969i
$19$		0			0		−0.0672690	−	0.997735i	$-0.521429\pi$
$19$		0			0		0.0672690	+	0.997735i	$0.478571\pi$
$20$		−	1.00000i		−	1.00000i
$21$		0			0
$22$		0			0
$23$		0			0		−0.910478	−	0.413559i	$-0.864286\pi$
$23$		0			0		0.910478	+	0.413559i	$0.135714\pi$
$24$		0			0
$25$	0.691063	−	0.722795i	0.691063	−	0.722795i
$26$	1.68961	−	1.06165i	1.68961	−	1.06165i
$27$		0			0
$28$		0			0
$29$	0.880596	+	0.473869i	0.880596	+	0.473869i
$29$	0.880596	+	0.473869i	0.880596	+	0.473869i
$30$		0			0
$31$		0			0		−0.674671	−	0.738119i	$-0.735714\pi$
$31$		0			0		0.674671	+	0.738119i	$0.264286\pi$
$32$	0.974928	+	0.222521i	0.974928	+	0.222521i
$33$		0			0
$34$	0.657939	+	0.246929i	0.657939	+	0.246929i
$35$		0			0
$36$	−0.858449	−	0.512899i	−0.858449	−	0.512899i
$37$	0.267386	−	1.97392i	0.267386	−	1.97392i	0.0448648	−	0.998993i	$-0.485714\pi$
$37$	0.267386	−	1.97392i	0.267386	−	1.97392i	0.222521	−	0.974928i	$-0.428571\pi$
$38$		0			0
$39$		0			0
$40$	0.550897	+	0.834573i	0.550897	+	0.834573i
$41$	0.842711	−	1.65391i	0.842711	−	1.65391i	0.0896393	−	0.995974i	$-0.471429\pi$
$41$	0.842711	−	1.65391i	0.842711	−	1.65391i	0.753071	−	0.657939i	$-0.228571\pi$
$42$		0			0
$43$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$43$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$44$		0			0
$45$	−0.266037	−	0.963963i	−0.266037	−	0.963963i
$46$		0			0
$47$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$47$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$48$		0			0
$49$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$50$	−0.178557	+	0.983930i	−0.178557	+	0.983930i
$51$		0			0
$52$	−0.825243	+	1.81683i	−0.825243	+	1.81683i
$53$	−1.51290	−	0.858449i	−1.51290	−	0.858449i	−0.512899	−	0.858449i	$-0.671429\pi$
$53$	−1.51290	−	0.858449i	−1.51290	−	0.858449i	−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$59$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$59$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$60$		0			0
$61$	0.957099	−	0.241168i	0.957099	−	0.241168i	0.266037	−	0.963963i	$-0.414286\pi$
$61$	0.957099	−	0.241168i	0.957099	−	0.241168i	0.691063	+	0.722795i	$0.257143\pi$
$62$		0			0
$63$		0			0
$64$	−0.936235	+	0.351375i	−0.936235	+	0.351375i
$65$	−1.85203	+	0.742901i	−1.85203	+	0.742901i
$66$		0			0
$67$		0			0		−0.822002	−	0.569484i	$-0.807143\pi$
$67$		0			0		0.822002	+	0.569484i	$0.192857\pi$
$68$	−0.685130	+	0.156377i	−0.685130	+	0.156377i
$69$		0			0
$70$		0			0
$71$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$71$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$72$	0.998993	−	0.0448648i	0.998993	−	0.0448648i
$73$	0.677425	+	1.80499i	0.677425	+	1.80499i	0.587785	+	0.809017i	$0.300000\pi$
$73$	0.677425	+	1.80499i	0.677425	+	1.80499i	0.0896393	+	0.995974i	$0.471429\pi$
$74$	0.864274	+	1.79468i	0.864274	+	1.79468i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.287599	−	0.957751i	$-0.407143\pi$
$79$		0			0		−0.287599	+	0.957751i	$0.592857\pi$
$80$	−0.919528	−	0.393025i	−0.919528	−	0.393025i
$81$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$82$	0.207832	+	1.84456i	0.207832	+	1.84456i
$83$		0			0		−0.0672690	−	0.997735i	$-0.521429\pi$
$83$		0			0		0.0672690	+	0.997735i	$0.478571\pi$
$84$		0			0
$85$	−0.603275	−	0.360440i	−0.603275	−	0.360440i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.243030	−	1.18696i	0.243030	−	1.18696i	−0.657939	−	0.753071i	$-0.728571\pi$
$89$	0.243030	−	1.18696i	0.243030	−	1.18696i	0.900969	−	0.433884i	$-0.142857\pi$
$90$	0.753071	+	0.657939i	0.753071	+	0.657939i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.403165	−	0.943250i	0.403165	−	0.943250i	−0.587785	−	0.809017i	$-0.700000\pi$
$97$	0.403165	−	0.943250i	0.403165	−	0.943250i	0.990950	−	0.134233i	$-0.0428571\pi$
$98$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$99$		0			0
$100$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$101$	−1.58124	−	0.178163i	−1.58124	−	0.178163i	−0.722795	−	0.691063i	$-0.757143\pi$
$101$	−1.58124	−	0.178163i	−1.58124	−	0.178163i	−0.858449	+	0.512899i	$0.828571\pi$
$102$		0			0
$103$		0			0		−0.569484	−	0.822002i	$-0.692857\pi$
$103$		0			0		0.569484	+	0.822002i	$0.307143\pi$
$104$	−0.312160	−	1.97090i	−0.312160	−	1.97090i
$105$		0			0
$106$	1.73554	−	0.117013i	1.73554	−	0.117013i
$107$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$107$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$108$		0			0
$109$	−1.83165	+	0.164852i	−1.83165	+	0.164852i	−0.951057	−	0.309017i	$-0.900000\pi$
$109$	−1.83165	+	0.164852i	−1.83165	+	0.164852i	−0.880596	+	0.473869i	$0.842857\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.0240652	−	0.267386i	−0.0240652	−	0.267386i	−0.998993	−	0.0448648i	$-0.985714\pi$
$113$	−0.0240652	−	0.267386i	−0.0240652	−	0.267386i	0.974928	−	0.222521i	$-0.0714286\pi$
$114$		0			0
$115$		0			0
$116$	0.781831	−	0.623490i	0.781831	−	0.623490i
$117$	−0.312160	+	1.97090i	−0.312160	+	1.97090i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.266037	+	0.963963i	0.266037	+	0.963963i
$122$	−0.665911	+	0.728536i	−0.665911	+	0.728536i
$123$		0			0
$124$		0			0
$125$	0.351375	−	0.936235i	0.351375	−	0.936235i
$126$		0			0
$127$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$127$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$128$	0.587785	−	0.809017i	0.587785	−	0.809017i
$129$		0			0
$130$	1.13639	−	1.64028i	1.13639	−	1.64028i
$131$		0			0		−0.493508	−	0.869741i	$-0.664286\pi$
$131$		0			0		0.493508	+	0.869741i	$0.335714\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.485644	−	0.507944i	0.485644	−	0.507944i
$137$	1.74525	+	0.236410i	1.74525	+	0.236410i	0.936235	−	0.351375i	$-0.114286\pi$
$137$	1.74525	+	0.236410i	1.74525	+	0.236410i	0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$		0			0		−0.351375	−	0.936235i	$-0.614286\pi$
$139$		0			0		0.351375	+	0.936235i	$0.385714\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$145$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$146$	−1.55972	−	1.13321i	−1.55972	−	1.13321i
$147$		0			0
$148$	−1.70999	−	1.02167i	−1.70999	−	1.02167i
$149$	−0.0199667	−	0.0874800i	−0.0199667	−	0.0874800i	0.963963	−	0.266037i	$-0.0857143\pi$
$149$	−0.0199667	−	0.0874800i	−0.0199667	−	0.0874800i	−0.983930	+	0.178557i	$0.942857\pi$
$150$		0			0
$151$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$151$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$152$		0			0
$153$	−0.618838	+	0.333011i	−0.618838	+	0.333011i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.44559			1.44559			0.722795	−	0.691063i	$-0.242857\pi$
$157$	1.44559			1.44559			0.722795	+	0.691063i	$0.242857\pi$
$158$		0			0
$159$		0			0
$160$	0.983930	−	0.178557i	0.983930	−	0.178557i
$161$		0			0
$162$	0.951057	−	0.309017i	0.951057	−	0.309017i
$163$		0			0		0.722795	−	0.691063i	$-0.242857\pi$
$163$		0			0		−0.722795	+	0.691063i	$0.757143\pi$
$164$	−1.18961	−	1.42493i	−1.18961	−	1.42493i
$165$		0			0
$166$		0			0
$167$		0			0		0.372294	−	0.928115i	$-0.378571\pi$
$167$		0			0		−0.372294	+	0.928115i	$0.621429\pi$
$168$		0			0
$169$	2.97890	+	0.133782i	2.97890	+	0.133782i
$170$	0.702042	−	0.0315287i	0.702042	−	0.0315287i
$171$		0			0
$172$		0			0
$173$	−0.826696	−	1.62248i	−0.826696	−	1.62248i	−0.781831	−	0.623490i	$-0.785714\pi$
$173$	−0.826696	−	1.62248i	−0.826696	−	1.62248i	−0.0448648	−	0.998993i	$-0.514286\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.451064	+	1.12449i	0.451064	+	1.12449i
$179$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$179$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$180$	−0.990950	−	0.134233i	−0.990950	−	0.134233i
$181$	0.543210	+	1.27090i	0.543210	+	1.27090i	0.936235	+	0.351375i	$0.114286\pi$
$181$	0.543210	+	1.27090i	0.543210	+	1.27090i	−0.393025	+	0.919528i	$0.628571\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.529932	−	1.92016i	−0.529932	−	1.92016i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$191$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$192$		0			0
$193$	0.437890	+	1.91852i	0.437890	+	1.91852i	0.393025	+	0.919528i	$0.371429\pi$
$193$	0.437890	+	1.91852i	0.437890	+	1.91852i	0.0448648	+	0.998993i	$0.485714\pi$
$194$	0.183163	+	1.00931i	0.183163	+	1.00931i
$195$		0			0
$196$	0.657939	+	0.753071i	0.657939	+	0.753071i
$197$	1.21347	+	1.10916i	1.21347	+	1.10916i	0.990950	+	0.134233i	$0.0428571\pi$
$197$	1.21347	+	1.10916i	1.21347	+	1.10916i	0.222521	+	0.974928i	$0.428571\pi$
$198$		0			0
$199$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$199$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$200$	0.834573	+	0.550897i	0.834573	+	0.550897i
$201$		0			0
$202$	1.41781	−	0.722412i	1.41781	−	0.722412i
$203$		0			0
$204$		0			0
$205$	0.124867	−	1.85203i	0.124867	−	1.85203i
$206$		0			0
$207$		0			0
$208$	1.34628	+	1.47289i	1.34628	+	1.47289i
$209$		0			0
$210$		0			0
$211$		0			0		0.999748	−	0.0224381i	$-0.00714286\pi$
$211$		0			0		−0.999748	+	0.0224381i	$0.992857\pi$
$212$	−1.38397	+	1.05376i	−1.38397	+	1.05376i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.43783	−	1.14663i	1.43783	−	1.14663i
$219$		0			0
$220$		0			0
$221$	0.798597	+	1.15271i	0.798597	+	1.15271i
$222$		0			0
$223$		0			0		0.999748	−	0.0224381i	$-0.00714286\pi$
$223$		0			0		−0.999748	+	0.0224381i	$0.992857\pi$
$224$		0			0
$225$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$226$	0.167386	+	0.209896i	0.167386	+	0.209896i
$227$		0			0		−0.979675	−	0.200589i	$-0.935714\pi$
$227$		0			0		0.979675	+	0.200589i	$0.0642857\pi$
$228$		0			0
$229$	−0.0993051	+	1.47289i	−0.0993051	+	1.47289i	0.623490	+	0.781831i	$0.285714\pi$
$229$	−0.0993051	+	1.47289i	−0.0993051	+	1.47289i	−0.722795	+	0.691063i	$0.757143\pi$
$230$		0			0
$231$		0			0
$232$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$233$	−1.12495	−	0.178174i	−1.12495	−	0.178174i	−0.433884	−	0.900969i	$-0.642857\pi$
$233$	−1.12495	−	0.178174i	−1.12495	−	0.178174i	−0.691063	+	0.722795i	$0.742857\pi$
$234$	−0.825243	−	1.81683i	−0.825243	−	1.81683i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.512899	−	0.858449i	$-0.328571\pi$
$239$		0			0		−0.512899	+	0.858449i	$0.671429\pi$
$240$		0			0
$241$	−1.85552	−	0.251348i	−1.85552	−	0.251348i	−0.880596	−	0.473869i	$-0.842857\pi$
$241$	−1.85552	−	0.251348i	−1.85552	−	0.251348i	−0.974928	+	0.222521i	$0.928571\pi$
$242$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$243$		0			0
$244$	0.154403	−	0.974865i	0.154403	−	0.974865i
$245$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.222521	+	0.974928i	0.222521	+	0.974928i
$251$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$251$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$257$	−0.113917	−	0.0715785i	−0.113917	−	0.0715785i	0.473869	−	0.880596i	$-0.342857\pi$
$257$	−0.113917	−	0.0715785i	−0.113917	−	0.0715785i	−0.587785	+	0.809017i	$0.700000\pi$
$258$		0			0
$259$		0			0
$260$	−0.0447745	+	1.99497i	−0.0447745	+	1.99497i
$261$	0.587785	−	0.809017i	0.587785	−	0.809017i
$262$		0			0
$263$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$263$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$264$		0			0
$265$	−1.72854	−	0.194760i	−1.72854	−	0.194760i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.09085	−	1.57455i	1.09085	−	1.57455i	0.309017	−	0.951057i	$-0.400000\pi$
$269$	1.09085	−	1.57455i	1.09085	−	1.57455i	0.781831	−	0.623490i	$-0.214286\pi$
$270$		0			0
$271$		0			0		0.928115	−	0.372294i	$-0.121429\pi$
$271$		0			0		−0.928115	+	0.372294i	$0.878571\pi$
$272$	−0.125481	+	0.691456i	−0.125481	+	0.691456i
$273$		0			0
$274$	−1.58678	+	0.764152i	−1.58678	+	0.764152i
$275$		0			0
$276$		0			0
$277$	1.55891	+	1.18696i	1.55891	+	1.18696i	0.900969	+	0.433884i	$0.142857\pi$
$277$	1.55891	+	1.18696i	1.55891	+	1.18696i	0.657939	+	0.753071i	$0.271429\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.29473	−	0.234959i	1.29473	−	0.234959i	0.512899	−	0.858449i	$-0.328571\pi$
$281$	1.29473	−	0.234959i	1.29473	−	0.234959i	0.781831	+	0.623490i	$0.214286\pi$
$282$		0			0
$283$		0			0		−0.928115	−	0.372294i	$-0.878571\pi$
$283$		0			0		0.928115	+	0.372294i	$0.121429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.351375	−	0.936235i	0.351375	−	0.936235i
$289$	0.156407	−	0.481371i	0.156407	−	0.481371i
$290$	−0.880596	+	0.473869i	−0.880596	+	0.473869i
$291$		0			0
$292$	1.92598	+	0.0864961i	1.92598	+	0.0864961i
$293$	−0.0398932	+	0.174784i	−0.0398932	+	0.174784i	−0.990950	−	0.134233i	$-0.957143\pi$
$293$	−0.0398932	+	0.174784i	−0.0398932	+	0.174784i	0.951057	+	0.309017i	$0.100000\pi$
$294$		0			0
$295$		0			0
$296$	1.98994	−	0.0893684i	1.98994	−	0.0893684i
$297$		0			0
$298$	0.0648561	+	0.0620088i	0.0648561	+	0.0620088i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.785295	−	0.597925i	0.785295	−	0.597925i
$306$	0.333011	−	0.618838i	0.333011	−	0.618838i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.0224381	−	0.999748i	$-0.507143\pi$
$311$		0			0		0.0224381	+	0.999748i	$0.492857\pi$
$312$		0			0
$313$	0.219378	−	0.0449178i	0.219378	−	0.0449178i	−0.0896393	−	0.995974i	$-0.528571\pi$
$313$	0.219378	−	0.0449178i	0.219378	−	0.0449178i	0.309017	+	0.951057i	$0.400000\pi$
$314$	−1.20645	+	0.796371i	−1.20645	+	0.796371i
$315$		0			0
$316$		0			0
$317$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	0.753071	+	0.657939i	$0.228571\pi$
$317$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	−0.809017	+	0.587785i	$0.800000\pi$
$318$		0			0
$319$		0			0
$320$	−0.722795	+	0.691063i	−0.722795	+	0.691063i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$325$	−1.41101	+	1.41101i	−1.41101	+	1.41101i
$326$		0			0
$327$		0			0
$328$	1.77781	+	0.533850i	1.77781	+	0.533850i
$329$		0			0
$330$		0			0
$331$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$331$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$332$		0			0
$333$	−1.92016	−	0.529932i	−1.92016	−	0.529932i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.34747	+	1.40935i	1.34747	+	1.40935i	0.834573	+	0.550897i	$0.185714\pi$
$337$	1.34747	+	1.40935i	1.34747	+	1.40935i	0.512899	+	0.858449i	$0.328571\pi$
$338$	−2.55981	+	1.52941i	−2.55981	+	1.52941i
$339$		0			0
$340$	−0.568536	+	0.413066i	−0.568536	+	0.413066i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.58376	+	0.898656i	1.58376	+	0.898656i
$347$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$347$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$348$		0			0
$349$		−	1.10179i		−	1.10179i	−0.834573	−	0.550897i	$-0.814286\pi$
$349$		−	1.10179i		−	1.10179i	0.834573	−	0.550897i	$-0.185714\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.525124	−	0.925460i	0.525124	−	0.925460i	−0.473869	−	0.880596i	$-0.657143\pi$
$353$	0.525124	−	0.925460i	0.525124	−	0.925460i	0.998993	−	0.0448648i	$-0.0142857\pi$
$354$		0			0
$355$		0			0
$356$	−0.995921	−	0.689976i	−0.995921	−	0.689976i
$357$		0			0
$358$		0			0
$359$		0			0		0.0224381	−	0.999748i	$-0.492857\pi$
$359$		0			0		−0.0224381	+	0.999748i	$0.507143\pi$
$360$	0.900969	−	0.433884i	0.900969	−	0.433884i
$361$	−0.990950	+	0.134233i	−0.990950	+	0.134233i
$362$	−1.15348	−	0.761409i	−1.15348	−	0.761409i
$363$		0			0
$364$		0			0
$365$	1.33232	+	1.39349i	1.33232	+	1.39349i
$366$		0			0
$367$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$367$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$368$		0			0
$369$	−1.52582	−	1.05709i	−1.52582	−	1.05709i
$370$	1.50008	+	1.31058i	1.50008	+	1.31058i
$371$		0			0
$372$		0			0
$373$	1.20982	+	1.44913i	1.20982	+	1.44913i	0.858449	+	0.512899i	$0.171429\pi$
$373$	1.20982	+	1.44913i	1.20982	+	1.44913i	0.351375	+	0.936235i	$0.385714\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.73554	−	0.984781i	−1.73554	−	0.984781i
$378$		0			0
$379$		0			0		−0.869741	−	0.493508i	$-0.835714\pi$
$379$		0			0		0.869741	+	0.493508i	$0.164286\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.869741	−	0.493508i	$-0.164286\pi$
$383$		0			0		−0.869741	+	0.493508i	$0.835714\pi$
$384$		0			0
$385$		0			0
$386$	−1.42236	−	1.35991i	−1.42236	−	1.35991i
$387$		0			0
$388$	−0.708891	−	0.741442i	−0.708891	−	0.741442i
$389$	0.612588	+	1.20227i	0.612588	+	1.20227i	0.963963	+	0.266037i	$0.0857143\pi$
$389$	0.612588	+	1.20227i	0.612588	+	1.20227i	−0.351375	+	0.936235i	$0.614286\pi$
$390$		0			0
$391$		0			0
$392$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$393$		0			0
$394$	−1.62376	−	0.257179i	−1.62376	−	0.257179i
$395$		0			0
$396$		0			0
$397$	−1.90346	−	0.571582i	−1.90346	−	0.571582i	−0.983930	−	0.178557i	$-0.942857\pi$
$397$	−1.90346	−	0.571582i	−1.90346	−	0.571582i	−0.919528	−	0.393025i	$-0.871429\pi$
$398$		0			0
$399$		0			0
$400$	−1.00000			−1.00000
$401$	0.490094	−	0.614559i	0.490094	−	0.614559i	−0.473869	−	0.880596i	$-0.657143\pi$
$401$	0.490094	−	0.614559i	0.490094	−	0.614559i	0.963963	+	0.266037i	$0.0857143\pi$
$402$		0			0
$403$		0			0
$404$	−0.785295	+	1.38397i	−0.785295	+	1.38397i
$405$	−0.990950	+	0.134233i	−0.990950	+	0.134233i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.0344489	−	0.0287600i	−0.0344489	−	0.0287600i	0.623490	−	0.781831i	$-0.285714\pi$
$409$	−0.0344489	−	0.0287600i	−0.0344489	−	0.0287600i	−0.657939	+	0.753071i	$0.728571\pi$
$410$	0.916065	+	1.61444i	0.916065	+	1.61444i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−1.93499	−	0.487574i	−1.93499	−	0.487574i
$417$		0			0
$418$		0			0
$419$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$419$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$420$		0			0
$421$	−1.20227	+	1.31534i	−1.20227	+	1.31534i	−0.266037	+	0.963963i	$0.585714\pi$
$421$	−1.20227	+	1.31534i	−1.20227	+	1.31534i	−0.936235	+	0.351375i	$0.885714\pi$
$422$		0			0
$423$		0			0
$424$	0.574515	−	1.64187i	0.574515	−	1.64187i
$425$	−0.696390	−	0.0943324i	−0.696390	−	0.0943324i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$431$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$432$		0			0
$433$	1.17439	+	0.0527418i	1.17439	+	0.0527418i	0.623490	−	0.781831i	$-0.285714\pi$
$433$	1.17439	+	0.0527418i	1.17439	+	0.0527418i	0.550897	+	0.834573i	$0.314286\pi$
$434$		0			0
$435$		0			0
$436$	−0.568299	+	1.74905i	−0.568299	+	1.74905i
$437$		0			0
$438$		0			0
$439$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$439$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$440$		0			0
$441$	0.834573	+	0.550897i	0.834573	+	0.550897i
$442$	−1.30151	−	0.522073i	−1.30151	−	0.522073i
$443$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$443$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$444$		0			0
$445$	−0.243030	−	1.18696i	−0.243030	−	1.18696i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.0449178	+	0.398656i	−0.0449178	+	0.398656i	0.951057	+	0.309017i	$0.100000\pi$
$449$	−0.0449178	+	0.398656i	−0.0449178	+	0.398656i	−0.995974	+	0.0896393i	$0.971429\pi$
$450$	0.951057	+	0.309017i	0.951057	+	0.309017i
$451$		0			0
$452$	−0.255327	−	0.0829607i	−0.255327	−	0.0829607i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.559311	−	0.351438i	0.559311	−	0.351438i	−0.222521	−	0.974928i	$-0.571429\pi$
$457$	0.559311	−	0.351438i	0.559311	−	0.351438i	0.781831	+	0.623490i	$0.214286\pi$
$458$	−0.728536	−	1.28394i	−0.728536	−	1.28394i
$459$		0			0
$460$		0			0
$461$	0.221856	+	0.880460i	0.221856	+	0.880460i	0.974928	+	0.222521i	$0.0714286\pi$
$461$	0.221856	+	0.880460i	0.221856	+	0.880460i	−0.753071	+	0.657939i	$0.771429\pi$
$462$		0			0
$463$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$463$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$464$	−0.266037	−	0.963963i	−0.266037	−	0.963963i
$465$		0			0
$466$	1.03701	−	0.471030i	1.03701	−	0.471030i
$467$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$467$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$468$	1.68961	+	1.06165i	1.68961	+	1.06165i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.05376	+	1.38397i	−1.05376	+	1.38397i
$478$		0			0
$479$		0			0		−0.738119	−	0.674671i	$-0.764286\pi$
$479$		0			0		0.738119	+	0.674671i	$0.235714\pi$
$480$		0			0
$481$	−0.621807	+	3.92594i	−0.621807	+	3.92594i
$482$	1.68704	−	0.812434i	1.68704	−	0.812434i
$483$		0			0
$484$	0.990950	+	0.134233i	0.990950	+	0.134233i
$485$		−	1.02580i		−	1.02580i
$486$		0			0
$487$		0			0		−0.200589	−	0.979675i	$-0.564286\pi$
$487$		0			0		0.200589	+	0.979675i	$0.435714\pi$
$488$	0.408189	+	0.898656i	0.408189	+	0.898656i
$489$		0			0
$490$	−0.512899	−	0.858449i	−0.512899	−	0.858449i
$491$		0			0		−0.413559	−	0.910478i	$-0.635714\pi$
$491$		0			0		0.413559	+	0.910478i	$0.364286\pi$
$492$		0			0
$493$	−0.0943324	−	0.696390i	−0.0943324	−	0.696390i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$499$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$500$	−0.722795	−	0.691063i	−0.722795	−	0.691063i
$501$		0			0
$502$		0			0
$503$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$503$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$504$		0			0
$505$	−1.52402	+	0.457642i	−1.52402	+	0.457642i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.24096	+	1.18648i	−1.24096	+	1.18648i	−0.266037	+	0.963963i	$0.585714\pi$
$509$	−1.24096	+	1.18648i	−1.24096	+	1.18648i	−0.974928	+	0.222521i	$0.928571\pi$
$510$		0			0
$511$		0			0
$512$	−0.512899	−	0.858449i	−0.512899	−	0.858449i
$513$		0			0
$514$	0.134504	−	0.00301877i	0.134504	−	0.00301877i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−1.06165	−	1.68961i	−1.06165	−	1.68961i
$521$	−0.557066	+	0.766736i	−0.557066	+	0.766736i	−0.990950	−	0.134233i	$-0.957143\pi$
$521$	−0.557066	+	0.766736i	−0.557066	+	0.766736i	0.433884	+	0.900969i	$0.357143\pi$
$522$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$523$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$523$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.657939	+	0.753071i	0.657939	+	0.753071i
$530$	1.54989	−	0.789708i	1.54989	−	0.789708i
$531$		0			0
$532$		0			0
$533$	−1.75523	+	3.26177i	−1.75523	+	3.26177i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.0429801	+	1.91502i	−0.0429801	+	1.91502i
$539$		0			0
$540$		0			0
$541$	0.473869	−	1.88060i	0.473869	−	1.88060i		−	1.00000i	$-0.5\pi$
$541$	0.473869	−	1.88060i	0.473869	−	1.88060i	0.473869	−	0.880596i	$-0.342857\pi$
$542$		0			0
$543$		0			0
$544$	−0.276198	−	0.646198i	−0.276198	−	0.646198i
$545$	−1.61946	+	0.871471i	−1.61946	+	0.871471i
$546$		0			0
$547$		0			0		−0.372294	−	0.928115i	$-0.621429\pi$
$547$		0			0		0.372294	+	0.928115i	$0.378571\pi$
$548$	0.903314	−	1.51189i	0.903314	−	1.51189i
$549$	−0.110511	−	0.980810i	−0.110511	−	0.980810i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−1.95491	−	0.131804i	−1.95491	−	0.131804i
$555$		0			0
$556$		0			0
$557$	0.143511	−	1.27369i	0.143511	−	1.27369i	−0.691063	−	0.722795i	$-0.742857\pi$
$557$	0.143511	−	1.27369i	0.143511	−	1.27369i	0.834573	−	0.550897i	$-0.185714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.951109	+	0.909354i	−0.951109	+	0.909354i
$563$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$563$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$564$		0			0
$565$	−0.127218	−	0.236410i	−0.127218	−	0.236410i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.368631	+	1.22760i	0.368631	+	1.22760i	0.919528	+	0.393025i	$0.128571\pi$
$569$	0.368631	+	1.22760i	0.368631	+	1.22760i	−0.550897	+	0.834573i	$0.685714\pi$
$570$		0			0
$571$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$571$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.222521	+	0.974928i	0.222521	+	0.974928i
$577$	−0.382046	−	0.228262i	−0.382046	−	0.228262i	0.309017	−	0.951057i	$-0.400000\pi$
$577$	−0.382046	−	0.228262i	−0.382046	−	0.228262i	−0.691063	+	0.722795i	$0.742857\pi$
$578$	0.134653	+	0.487903i	0.134653	+	0.487903i
$579$		0			0
$580$	0.473869	−	0.880596i	0.473869	−	0.880596i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.65503	+	0.988832i	−1.65503	+	0.988832i
$585$	0.487574	+	1.93499i	0.487574	+	1.93499i
$586$	−0.0629940	−	0.167847i	−0.0629940	−	0.167847i
$587$		0			0		0.640876	−	0.767645i	$-0.278571\pi$
$587$		0			0		−0.640876	+	0.767645i	$0.721429\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.61152	+	1.17084i	−1.61152	+	1.17084i
$593$	0.132501	−	0.378666i	0.132501	−	0.378666i	−0.858449	−	0.512899i	$-0.828571\pi$
$593$	0.132501	−	0.378666i	0.132501	−	0.378666i	0.990950	+	0.134233i	$0.0428571\pi$
$594$		0			0
$595$		0			0
$596$	−0.0882877	−	0.0160218i	−0.0882877	−	0.0160218i
$597$		0			0
$598$		0			0
$599$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$599$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$600$		0			0
$601$	0.295312	−	0.103334i	0.295312	−	0.103334i	−0.178557	−	0.983930i	$-0.557143\pi$
$601$	0.295312	−	0.103334i	0.295312	−	0.103334i	0.473869	+	0.880596i	$0.342857\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.623490	+	0.781831i	0.623490	+	0.781831i
$606$		0			0
$607$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$607$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$608$		0			0
$609$		0			0
$610$	−0.325991	+	0.931628i	−0.325991	+	0.931628i
$611$		0			0
$612$	0.0629940	+	0.699921i	0.0629940	+	0.699921i
$613$	−0.473869	+	1.88060i	−0.473869	+	1.88060i			1.00000i	$0.5\pi$
$613$	−0.473869	+	1.88060i	−0.473869	+	1.88060i	−0.473869	+	0.880596i	$0.657143\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.351375	−	0.0637651i	0.351375	−	0.0637651i		−	1.00000i	$-0.5\pi$
$617$	0.351375	−	0.0637651i	0.351375	−	0.0637651i	0.351375	+	0.936235i	$0.385714\pi$
$618$		0			0
$619$		0			0		0.997735	−	0.0672690i	$-0.0214286\pi$
$619$		0			0		−0.997735	+	0.0672690i	$0.978571\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$626$	−0.158342	+	0.158342i	−0.158342	+	0.158342i
$627$		0			0
$628$	0.568153	−	1.32926i	0.568153	−	1.32926i
$629$	−1.23269	+	0.663341i	−1.23269	+	0.663341i
$630$		0			0
$631$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$631$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$632$		0			0
$633$		0			0
$634$	−0.639575	−	1.07047i	−0.639575	−	1.07047i
$635$		0			0
$636$		0			0
$637$	0.905924	−	1.77798i	0.905924	−	1.77798i
$638$		0			0
$639$		0			0
$640$	0.222521	−	0.974928i	0.222521	−	0.974928i
$641$	0.906335	−	1.08561i	0.906335	−	1.08561i	−0.0896393	−	0.995974i	$-0.528571\pi$
$641$	0.906335	−	1.08561i	0.906335	−	1.08561i	0.995974	−	0.0896393i	$-0.0285714\pi$
$642$		0			0
$643$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$643$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.287599	−	0.957751i	$-0.407143\pi$
$647$		0			0		−0.287599	+	0.957751i	$0.592857\pi$
$648$	0.0896393	−	0.995974i	0.0896393	−	0.995974i
$649$		0			0
$650$	0.400270	−	1.95491i	0.400270	−	1.95491i
$651$		0			0
$652$		0			0
$653$	−1.71517	+	0.0770283i	−1.71517	+	0.0770283i	−0.880596	−	0.473869i	$-0.842857\pi$
$653$	−1.71517	+	0.0770283i	−1.71517	+	0.0770283i	−0.834573	+	0.550897i	$0.814286\pi$
$654$		0			0
$655$		0			0
$656$	−1.77781	+	0.533850i	−1.77781	+	0.533850i
$657$	1.87959	−	0.429004i	1.87959	−	0.429004i
$658$		0			0
$659$		0			0		0.795625	−	0.605790i	$-0.207143\pi$
$659$		0			0		−0.795625	+	0.605790i	$0.792857\pi$
$660$		0			0
$661$	−0.416664	+	0.156377i	−0.416664	+	0.156377i	−0.550897	−	0.834573i	$-0.685714\pi$
$661$	−0.416664	+	0.156377i	−0.416664	+	0.156377i	0.134233	+	0.990950i	$0.457143\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.89446	−	0.615546i	1.89446	−	0.615546i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.826909	−	1.82050i	0.826909	−	1.82050i	0.393025	−	0.919528i	$-0.371429\pi$
$673$	0.826909	−	1.82050i	0.826909	−	1.82050i	0.433884	−	0.900969i	$-0.357143\pi$
$674$	−1.90097	−	0.433884i	−1.90097	−	0.433884i
$675$		0			0
$676$	1.29380	−	2.68660i	1.29380	−	2.68660i
$677$	−0.864274	−	0.0777861i	−0.864274	−	0.0777861i	−0.351375	−	0.936235i	$-0.614286\pi$
$677$	−0.864274	−	0.0777861i	−0.864274	−	0.0777861i	−0.512899	+	0.858449i	$0.671429\pi$
$678$		0			0
$679$		0			0
$680$	0.246929	−	0.657939i	0.246929	−	0.657939i
$681$		0			0
$682$		0			0
$683$		0			0		0.957751	−	0.287599i	$-0.0928571\pi$
$683$		0			0		−0.957751	+	0.287599i	$0.907143\pi$
$684$		0			0
$685$	1.69772	−	0.468542i	1.69772	−	0.468542i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.97975	+	1.78032i	2.97975	+	1.78032i
$690$		0			0
$691$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$691$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$692$	−1.81683	+	0.122494i	−1.81683	+	0.122494i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.28840	+	0.204063i	−1.28840	+	0.204063i
$698$	0.606975	+	0.919528i	0.606975	+	0.919528i
$699$		0			0
$700$		0			0
$701$	1.56209	+	1.24572i	1.56209	+	1.24572i	0.809017	+	0.587785i	$0.200000\pi$
$701$	1.56209	+	1.24572i	1.56209	+	1.24572i	0.753071	+	0.657939i	$0.228571\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.0715785	+	1.06165i	0.0715785	+	1.06165i
$707$		0			0
$708$		0			0
$709$	−0.246788	−	0.258120i	−0.246788	−	0.258120i	0.587785	−	0.809017i	$-0.300000\pi$
$709$	−0.246788	−	0.258120i	−0.246788	−	0.258120i	−0.834573	+	0.550897i	$0.814286\pi$
$710$		0			0
$711$		0			0
$712$	1.21128	+	0.0271855i	1.21128	+	0.0271855i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.266037	−	0.963963i	$-0.414286\pi$
$719$		0			0		−0.266037	+	0.963963i	$0.585714\pi$
$720$	−0.512899	+	0.858449i	−0.512899	+	0.858449i
$721$		0			0
$722$	0.753071	−	0.657939i	0.753071	−	0.657939i
$723$		0			0
$724$	1.38213			1.38213
$725$	0.951057	−	0.309017i	0.951057	−	0.309017i
$726$		0			0
$727$		0			0		0.834573	−	0.550897i	$-0.185714\pi$
$727$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$728$		0			0
$729$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$730$	−1.87959	−	0.429004i	−1.87959	−	0.429004i
$731$		0			0
$732$		0			0
$733$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$733$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	1.85576	+	0.0416502i	1.85576	+	0.0416502i
$739$		0			0		−0.910478	−	0.413559i	$-0.864286\pi$
$739$		0			0		0.910478	+	0.413559i	$0.135714\pi$
$740$	−1.97392	−	0.267386i	−1.97392	−	0.267386i
$741$		0			0
$742$		0			0
$743$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$743$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$744$		0			0
$745$	−0.0527418	−	0.0725928i	−0.0527418	−	0.0725928i
$746$	−1.80801	−	0.542920i	−1.80801	−	0.542920i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$751$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$752$		0			0
$753$		0			0
$754$	1.99095	−	0.134233i	1.99095	−	0.134233i
$755$		0			0
$756$		0			0
$757$	0.923976	+	0.210891i	0.923976	+	0.210891i	0.657939	−	0.753071i	$-0.271429\pi$
$757$	0.923976	+	0.210891i	0.923976	+	0.210891i	0.266037	+	0.963963i	$0.414286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.306564	+	0.183163i	0.306564	+	0.183163i	0.657939	−	0.753071i	$-0.271429\pi$
$761$	0.306564	+	0.183163i	0.306564	+	0.183163i	−0.351375	+	0.936235i	$0.614286\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.438157	+	0.549432i	−0.438157	+	0.549432i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−0.574515	+	0.325991i	−0.574515	+	0.325991i	−0.753071	−	0.657939i	$-0.771429\pi$
$769$	−0.574515	+	0.325991i	−0.574515	+	0.325991i	0.178557	+	0.983930i	$0.442857\pi$
$770$		0			0
$771$		0			0
$772$	1.93623	+	0.351375i	1.93623	+	0.351375i
$773$	−0.943922	−	0.0849545i	−0.943922	−	0.0849545i	−0.393025	−	0.919528i	$-0.628571\pi$
$773$	−0.943922	−	0.0849545i	−0.943922	−	0.0849545i	−0.550897	+	0.834573i	$0.685714\pi$
$774$		0			0
$775$		0			0
$776$	1.00008	+	0.228262i	1.00008	+	0.228262i
$777$		0			0
$778$	−1.17358	−	0.665911i	−1.17358	−	0.665911i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.951057	−	0.309017i	0.951057	−	0.309017i
$785$	1.32926	−	0.568153i	1.32926	−	0.568153i
$786$		0			0
$787$		0			0		−0.969690	−	0.244340i	$-0.921429\pi$
$787$		0			0		0.969690	+	0.244340i	$0.0785714\pi$
$788$	1.49683	−	0.679892i	1.49683	−	0.679892i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.92018	+	0.438269i	−1.92018	+	0.438269i
$794$	1.90346	−	0.571582i	1.90346	−	0.571582i
$795$		0			0
$796$		0			0
$797$	0.785259	−	0.0352660i	0.785259	−	0.0352660i	0.351375	−	0.936235i	$-0.385714\pi$
$797$	0.785259	−	0.0352660i	0.785259	−	0.0352660i	0.433884	+	0.900969i	$0.357143\pi$
$798$		0			0
$799$		0			0
$800$	0.834573	−	0.550897i	0.834573	−	0.550897i
$801$	−1.14359	−	0.400160i	−1.14359	−	0.400160i
$802$	−0.0704610	+	0.782886i	−0.0704610	+	0.782886i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.107042	−	1.58764i	−0.107042	−	1.58764i
$809$	0.313184	−	0.375133i	0.313184	−	0.375133i	−0.587785	−	0.809017i	$-0.700000\pi$
$809$	0.313184	−	0.375133i	0.313184	−	0.375133i	0.900969	+	0.433884i	$0.142857\pi$
$810$	0.753071	−	0.657939i	0.753071	−	0.657939i
$811$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$811$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	0.0445940	+	0.00502453i	0.0445940	+	0.00502453i
$819$		0			0
$820$	−1.65391	−	0.842711i	−1.65391	−	0.842711i
$821$	1.37695	−	0.740971i	1.37695	−	0.740971i	0.393025	−	0.919528i	$-0.371429\pi$
$821$	1.37695	−	0.740971i	1.37695	−	0.740971i	0.983930	+	0.178557i	$0.0571429\pi$
$822$		0			0
$823$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$823$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$827$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$828$		0			0
$829$	0.116479	+	0.735420i	0.116479	+	0.735420i	0.974928	+	0.222521i	$0.0714286\pi$
$829$	0.116479	+	0.735420i	0.116479	+	0.735420i	−0.858449	+	0.512899i	$0.828571\pi$
$830$		0			0
$831$		0			0
$832$	1.88349	−	0.659062i	1.88349	−	0.659062i
$833$	0.691456	−	0.125481i	0.691456	−	0.125481i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.979675	−	0.200589i	$-0.935714\pi$
$839$		0			0		0.979675	+	0.200589i	$0.0642857\pi$
$840$		0			0
$841$	0.550897	+	0.834573i	0.550897	+	0.834573i
$842$	0.278768	−	1.76007i	0.278768	−	1.76007i
$843$		0			0
$844$		0			0
$845$	2.79176	−	1.04776i	2.79176	−	1.04776i
$846$		0			0
$847$		0			0
$848$	0.425026	+	1.68676i	0.425026	+	1.68676i
$849$		0			0
$850$	0.633156	−	0.304912i	0.633156	−	0.304912i
$851$		0			0
$852$		0			0
$853$	0.209906	−	0.288911i	0.209906	−	0.288911i	−0.691063	−	0.722795i	$-0.742857\pi$
$853$	0.209906	−	0.288911i	0.209906	−	0.288911i	0.900969	+	0.433884i	$0.142857\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.467085	−	1.33485i	0.467085	−	1.33485i	−0.433884	−	0.900969i	$-0.642857\pi$
$857$	0.467085	−	1.33485i	0.467085	−	1.33485i	0.900969	−	0.433884i	$-0.142857\pi$
$858$		0			0
$859$		0			0		−0.999748	−	0.0224381i	$-0.992857\pi$
$859$		0			0		0.999748	+	0.0224381i	$0.00714286\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.640876	−	0.767645i	$-0.278571\pi$
$863$		0			0		−0.640876	+	0.767645i	$0.721429\pi$
$864$		0			0
$865$	−1.39785	−	1.16701i	−1.39785	−	1.16701i
$866$	−1.00917	+	0.602949i	−1.00917	+	0.602949i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.489257	−	1.77278i	−0.489257	−	1.77278i
$873$	−0.880596	−	0.526131i	−0.880596	−	0.526131i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.303386	+	0.0764465i	−0.303386	+	0.0764465i	−0.393025	−	0.919528i	$-0.628571\pi$
$877$	−0.303386	+	0.0764465i	−0.303386	+	0.0764465i	0.0896393	+	0.995974i	$0.471429\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.571582	+	1.90346i	0.571582	+	1.90346i	0.393025	+	0.919528i	$0.371429\pi$
$881$	0.571582	+	1.90346i	0.571582	+	1.90346i	0.178557	+	0.983930i	$0.442857\pi$
$882$	−1.00000			−1.00000
$883$		0			0		−0.287599	−	0.957751i	$-0.592857\pi$
$883$		0			0		0.287599	+	0.957751i	$0.407143\pi$
$884$	1.37381	−	0.281290i	1.37381	−	0.281290i
$885$		0			0
$886$		0			0
$887$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$887$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$888$		0			0
$889$		0			0
$890$	0.856716	+	0.856716i	0.856716	+	0.856716i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.182131	−	0.357453i	−0.182131	−	0.357453i
$899$		0			0
$900$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$901$	0.136868	+	1.21473i	0.136868	+	1.21473i
$902$		0			0
$903$		0			0
$904$	0.258792	−	0.0714220i	0.258792	−	0.0714220i
$905$	0.998993	+	0.955135i	0.998993	+	0.955135i
$906$		0			0
$907$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$907$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$908$		0			0
$909$	−0.388806	+	1.54302i	−0.388806	+	1.54302i
$910$		0			0
$911$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$911$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$912$		0			0
$913$		0			0
$914$	−0.273179	+	0.601423i	−0.273179	+	0.601423i
$915$		0			0
$916$	1.31534	+	0.670198i	1.31534	+	0.670198i
$917$		0			0
$918$		0			0
$919$		0			0		−0.178557	−	0.983930i	$-0.557143\pi$
$919$		0			0		0.178557	+	0.983930i	$0.442857\pi$
$920$		0			0
$921$		0			0
$922$	−0.670198	−	0.612588i	−0.670198	−	0.612588i
$923$		0			0
$924$		0			0
$925$	−1.24196	−	1.55737i	−1.24196	−	1.55737i
$926$		0			0
$927$		0			0
$928$	0.753071	+	0.657939i	0.753071	+	0.657939i
$929$	−0.105377	+	0.145039i	−0.105377	+	0.145039i	−0.858449	−	0.512899i	$-0.828571\pi$
$929$	−0.105377	+	0.145039i	−0.105377	+	0.145039i	0.753071	+	0.657939i	$0.228571\pi$
$930$		0			0
$931$		0			0
$932$	−0.605968	+	0.964393i	−0.605968	+	0.964393i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−1.99497	+	0.0447745i	−1.99497	+	0.0447745i
$937$	1.59085	−	1.21128i	1.59085	−	1.21128i	0.781831	−	0.623490i	$-0.214286\pi$
$937$	1.59085	−	1.21128i	1.59085	−	1.21128i	0.809017	−	0.587785i	$-0.200000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.37484	+	1.31448i	−1.37484	+	1.31448i	−0.473869	+	0.880596i	$0.657143\pi$
$941$	−1.37484	+	1.31448i	−1.37484	+	1.31448i	−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$947$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$948$		0			0
$949$	−1.27062	−	3.63123i	−1.27062	−	3.63123i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.79997	−	0.722019i	1.79997	−	0.722019i	0.809017	−	0.587785i	$-0.200000\pi$
$953$	1.79997	−	0.722019i	1.79997	−	0.722019i	0.990950	−	0.134233i	$-0.0428571\pi$
$954$	0.117013	−	1.73554i	0.117013	−	1.73554i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.0896393	+	0.995974i	−0.0896393	+	0.995974i
$962$	−1.64384	−	3.61903i	−1.64384	−	3.61903i
$963$		0			0
$964$	−0.960388	+	1.60742i	−0.960388	+	1.60742i
$965$	1.15668	+	1.59203i	1.15668	+	1.59203i
$966$		0			0
$967$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$967$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$968$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$969$		0			0
$970$	0.565109	+	0.856104i	0.565109	+	0.856104i
$971$		0			0		−0.738119	−	0.674671i	$-0.764286\pi$
$971$		0			0		0.738119	+	0.674671i	$0.235714\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.835731	−	0.525124i	−0.835731	−	0.525124i
$977$	−0.0429801	−	1.91502i	−0.0429801	−	1.91502i	−0.309017	−	0.951057i	$-0.600000\pi$
$977$	−0.0429801	−	1.91502i	−0.0429801	−	1.91502i	0.266037	−	0.963963i	$-0.414286\pi$
$978$		0			0
$979$		0			0
$980$	0.900969	+	0.433884i	0.900969	+	0.433884i
$981$	−0.0825089	+	1.83720i	−0.0825089	+	1.83720i
$982$		0			0
$983$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$983$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$984$		0			0
$985$	1.55175	+	0.542980i	1.55175	+	0.542980i
$986$	0.462366	+	0.529221i	0.462366	+	0.529221i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.351375	−	0.936235i	$-0.385714\pi$
$991$		0			0		−0.351375	+	0.936235i	$0.614286\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.321748	−	1.77298i	0.321748	−	1.77298i	−0.266037	−	0.963963i	$-0.585714\pi$
$997$	0.321748	−	1.77298i	0.321748	−	1.77298i	0.587785	−	0.809017i	$-0.300000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2900.1.cr.a.1203.1	✓	48
4.3	odd	2	CM	2900.1.cr.a.1203.1	✓	48
25.17	odd	20		2900.1.da.a.1667.1	yes	48
29.27	odd	28		2900.1.da.a.1303.1	yes	48
100.67	even	20		2900.1.da.a.1667.1	yes	48
116.27	even	28		2900.1.da.a.1303.1	yes	48
725.317	even	140	inner	2900.1.cr.a.1767.1	yes	48
2900.1767	odd	140	inner	2900.1.cr.a.1767.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2900.1.cr.a.1203.1	✓	48	1.1	even	1	trivial
2900.1.cr.a.1203.1	✓	48	4.3	odd	2	CM
2900.1.cr.a.1767.1	yes	48	725.317	even	140	inner
2900.1.cr.a.1767.1	yes	48	2900.1767	odd	140	inner
2900.1.da.a.1303.1	yes	48	29.27	odd	28
2900.1.da.a.1303.1	yes	48	116.27	even	28
2900.1.da.a.1667.1	yes	48	25.17	odd	20
2900.1.da.a.1667.1	yes	48	100.67	even	20

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:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2900.cr (of order \(140\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.834573 + 0.550897i) q^{2} +(0.393025 - 0.919528i) q^{4} +(0.919528 - 0.393025i) q^{5} +(0.178557 + 0.983930i) q^{8} +(0.134233 - 0.990950i) q^{9} +O(q^{10})\)	\(q+(-0.834573 + 0.550897i) q^{2} +(0.393025 - 0.919528i) q^{4} +(0.919528 - 0.393025i) q^{5} +(0.178557 + 0.983930i) q^{8} +(0.134233 - 0.990950i) q^{9} +(-0.550897 + 0.834573i) q^{10} +(-1.99497 - 0.0447745i) q^{13} +(-0.691063 - 0.722795i) q^{16} +(-0.413066 - 0.568536i) q^{17} +(0.433884 + 0.900969i) q^{18} -1.00000i q^{20} +(0.691063 - 0.722795i) q^{25} +(1.68961 - 1.06165i) q^{26} +(0.880596 + 0.473869i) q^{29} +(0.974928 + 0.222521i) q^{32} +(0.657939 + 0.246929i) q^{34} +(-0.858449 - 0.512899i) q^{36} +(0.267386 - 1.97392i) q^{37} +(0.550897 + 0.834573i) q^{40} +(0.842711 - 1.65391i) q^{41} +(-0.266037 - 0.963963i) q^{45} +(-0.433884 + 0.900969i) q^{49} +(-0.178557 + 0.983930i) q^{50} +(-0.825243 + 1.81683i) q^{52} +(-1.51290 - 0.858449i) q^{53} +(-0.995974 + 0.0896393i) q^{58} +(0.957099 - 0.241168i) q^{61} +(-0.936235 + 0.351375i) q^{64} +(-1.85203 + 0.742901i) q^{65} +(-0.685130 + 0.156377i) q^{68} +(0.998993 - 0.0448648i) q^{72} +(0.677425 + 1.80499i) q^{73} +(0.864274 + 1.79468i) q^{74} +(-0.919528 - 0.393025i) q^{80} +(-0.963963 - 0.266037i) q^{81} +(0.207832 + 1.84456i) q^{82} +(-0.603275 - 0.360440i) q^{85} +(0.243030 - 1.18696i) q^{89} +(0.753071 + 0.657939i) q^{90} +(0.403165 - 0.943250i) q^{97} +(-0.134233 - 0.990950i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 48 * q - 2 * q^4 + 2 * q^9	\( 48 q - 2 q^{4} + 2 q^{9} + 2 q^{10} + 2 q^{13} + 2 q^{16} - 2 q^{25} + 12 q^{26} - 2 q^{36} + 6 q^{37} - 2 q^{40} + 2 q^{41} - 2 q^{52} - 48 q^{53} + 2 q^{58} - 2 q^{61} - 2 q^{64} - 8 q^{65} + 2 q^{81} + 2 q^{82} + 8 q^{89} + 2 q^{90} - 2 q^{98}+O(q^{100}) \) 48 * q - 2 * q^4 + 2 * q^9 + 2 * q^10 + 2 * q^13 + 2 * q^16 - 2 * q^25 + 12 * q^26 - 2 * q^36 + 6 * q^37 - 2 * q^40 + 2 * q^41 - 2 * q^52 - 48 * q^53 + 2 * q^58 - 2 * q^61 - 2 * q^64 - 8 * q^65 + 2 * q^81 + 2 * q^82 + 8 * q^89 + 2 * q^90 - 2 * q^98

Introduction

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