LMFDB - Embedded newform 2900.1.da.a.1303.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2900,1,Mod(127,2900)]

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, 7, 125]))

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

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

chi := DirichletCharacter("2900.127");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2900 = 2^{2} \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2900.da (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:	$\Z[a_1, \ldots, a_{5}]$
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			1303.1
Root			$-0.998993 + 0.0448648i$ of defining polynomial
Character	$\chi$	$=$	2900.1303
Dual form			2900.1.da.a.1667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.936235 - 0.351375i) q^{2} +(0.753071 - 0.657939i) q^{4} +(-0.178557 - 0.983930i) q^{5} +(0.473869 - 0.880596i) q^{8} +(0.691063 + 0.722795i) q^{9} +O(q^{10})$	\(q+(0.936235 - 0.351375i) q^{2} +(0.753071 - 0.657939i) q^{4} +(-0.178557 - 0.983930i) q^{5} +(0.473869 - 0.880596i) q^{8} +(0.691063 + 0.722795i) q^{9} +(-0.512899 - 0.858449i) q^{10} +(1.20884 + 1.58764i) q^{13} +(0.134233 - 0.990950i) q^{16} +(0.568536 - 0.413066i) q^{17} +(0.900969 + 0.433884i) q^{18} +(-0.781831 - 0.623490i) q^{20} +(-0.936235 + 0.351375i) q^{25} +(1.68961 + 1.06165i) q^{26} +(-0.722795 - 0.691063i) q^{29} +(-0.222521 - 0.974928i) q^{32} +(0.387143 - 0.586496i) q^{34} +(0.995974 + 0.0896393i) q^{36} +(-1.43977 + 1.37656i) q^{37} +(-0.951057 - 0.309017i) q^{40} +(-1.65391 - 0.842711i) q^{41} +(0.587785 - 0.809017i) q^{45} +(0.433884 + 0.900969i) q^{49} +(-0.753071 + 0.657939i) q^{50} +(1.95491 + 0.400270i) q^{52} +(1.17358 - 1.28394i) q^{53} +(-0.919528 - 0.393025i) q^{58} +(-0.632555 - 0.757678i) q^{61} +(-0.550897 - 0.834573i) q^{64} +(1.34628 - 1.47289i) q^{65} +(0.156377 - 0.685130i) q^{68} +(0.963963 - 0.266037i) q^{72} +(-1.06209 - 1.60900i) q^{73} +(-0.864274 + 1.79468i) q^{74} +(-0.998993 + 0.0448648i) q^{80} +(-0.0448648 + 0.998993i) q^{81} +(-1.84456 - 0.207832i) q^{82} +(-0.507944 - 0.485644i) q^{85} +(-0.501059 + 1.10312i) q^{89} +(0.266037 - 0.963963i) q^{90} +(0.674913 + 0.772500i) q^{97} +(0.722795 + 0.691063i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 2 * q^9	$ 48 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} - 2 q^{13} + 2 q^{16} + 8 q^{18} - 2 q^{25} + 12 q^{26} - 8 q^{32} - 2 q^{36} + 2 q^{41} - 2 q^{50} - 2 q^{52} + 8 q^{53} - 2 q^{61} + 2 q^{64} - 8 q^{65} - 2 q^{72} + 10 q^{73} + 2 q^{81} + 2 q^{82} - 10 q^{85} + 2 q^{89} + 14 q^{97}+O(q^{100}) $ 48 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 2 * q^9 - 2 * q^13 + 2 * q^16 + 8 * q^18 - 2 * q^25 + 12 * q^26 - 8 * q^32 - 2 * q^36 + 2 * q^41 - 2 * q^50 - 2 * q^52 + 8 * q^53 - 2 * q^61 + 2 * q^64 - 8 * q^65 - 2 * q^72 + 10 * q^73 + 2 * q^81 + 2 * q^82 - 10 * q^85 + 2 * q^89 + 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$901$	$1277$	$1451$
$\chi(n)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{7}{20}\right)$	$-1$

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 $

$2$	0.936235	−	0.351375i	0.936235	−	0.351375i
$2$	0.936235	−	0.351375i	0.936235	−	0.351375i
$3$		0			0		−0.919528	−	0.393025i	$-0.871429\pi$
$3$		0			0		0.919528	+	0.393025i	$0.128571\pi$
$4$	0.753071	−	0.657939i	0.753071	−	0.657939i
$5$	−0.178557	−	0.983930i	−0.178557	−	0.983930i
$5$	−0.178557	−	0.983930i	−0.178557	−	0.983930i
$6$		0			0
$7$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$7$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$8$	0.473869	−	0.880596i	0.473869	−	0.880596i
$9$	0.691063	+	0.722795i	0.691063	+	0.722795i
$10$	−0.512899	−	0.858449i	−0.512899	−	0.858449i
$11$		0			0		0.999748	−	0.0224381i	$-0.00714286\pi$
$11$		0			0		−0.999748	+	0.0224381i	$0.992857\pi$
$12$		0			0
$13$	1.20884	+	1.58764i	1.20884	+	1.58764i	0.657939	+	0.753071i	$0.271429\pi$
$13$	1.20884	+	1.58764i	1.20884	+	1.58764i	0.550897	+	0.834573i	$0.314286\pi$
$14$		0			0
$15$		0			0
$16$	0.134233	−	0.990950i	0.134233	−	0.990950i
$17$	0.568536	−	0.413066i	0.568536	−	0.413066i	−0.266037	−	0.963963i	$-0.585714\pi$
$17$	0.568536	−	0.413066i	0.568536	−	0.413066i	0.834573	+	0.550897i	$0.185714\pi$
$18$	0.900969	+	0.433884i	0.900969	+	0.433884i
$19$		0			0		−0.928115	−	0.372294i	$-0.878571\pi$
$19$		0			0		0.928115	+	0.372294i	$0.121429\pi$
$20$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$21$		0			0
$22$		0			0
$23$		0			0		0.200589	−	0.979675i	$-0.435714\pi$
$23$		0			0		−0.200589	+	0.979675i	$0.564286\pi$
$24$		0			0
$25$	−0.936235	+	0.351375i	−0.936235	+	0.351375i
$26$	1.68961	+	1.06165i	1.68961	+	1.06165i
$27$		0			0
$28$		0			0
$29$	−0.722795	−	0.691063i	−0.722795	−	0.691063i
$29$	−0.722795	−	0.691063i	−0.722795	−	0.691063i
$30$		0			0
$31$		0			0		−0.493508	−	0.869741i	$-0.664286\pi$
$31$		0			0		0.493508	+	0.869741i	$0.335714\pi$
$32$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$33$		0			0
$34$	0.387143	−	0.586496i	0.387143	−	0.586496i
$35$		0			0
$36$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$37$	−1.43977	+	1.37656i	−1.43977	+	1.37656i	−0.657939	+	0.753071i	$0.728571\pi$
$37$	−1.43977	+	1.37656i	−1.43977	+	1.37656i	−0.781831	+	0.623490i	$0.785714\pi$
$38$		0			0
$39$		0			0
$40$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$41$	−1.65391	−	0.842711i	−1.65391	−	0.842711i	−0.995974	−	0.0896393i	$-0.971429\pi$
$41$	−1.65391	−	0.842711i	−1.65391	−	0.842711i	−0.657939	−	0.753071i	$-0.728571\pi$
$42$		0			0
$43$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$43$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$44$		0			0
$45$	0.587785	−	0.809017i	0.587785	−	0.809017i
$46$		0			0
$47$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$47$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$48$		0			0
$49$	0.433884	+	0.900969i	0.433884	+	0.900969i
$50$	−0.753071	+	0.657939i	−0.753071	+	0.657939i
$51$		0			0
$52$	1.95491	+	0.400270i	1.95491	+	0.400270i
$53$	1.17358	−	1.28394i	1.17358	−	1.28394i	0.222521	−	0.974928i	$-0.428571\pi$
$53$	1.17358	−	1.28394i	1.17358	−	1.28394i	0.951057	−	0.309017i	$-0.100000\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.919528	−	0.393025i	−0.919528	−	0.393025i
$59$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$59$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$60$		0			0
$61$	−0.632555	−	0.757678i	−0.632555	−	0.757678i	0.351375	−	0.936235i	$-0.385714\pi$
$61$	−0.632555	−	0.757678i	−0.632555	−	0.757678i	−0.983930	+	0.178557i	$0.942857\pi$
$62$		0			0
$63$		0			0
$64$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$65$	1.34628	−	1.47289i	1.34628	−	1.47289i
$66$		0			0
$67$		0			0		0.957751	−	0.287599i	$-0.0928571\pi$
$67$		0			0		−0.957751	+	0.287599i	$0.907143\pi$
$68$	0.156377	−	0.685130i	0.156377	−	0.685130i
$69$		0			0
$70$		0			0
$71$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$71$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$72$	0.963963	−	0.266037i	0.963963	−	0.266037i
$73$	−1.06209	−	1.60900i	−1.06209	−	1.60900i	−0.753071	−	0.657939i	$-0.771429\pi$
$73$	−1.06209	−	1.60900i	−1.06209	−	1.60900i	−0.309017	−	0.951057i	$-0.600000\pi$
$74$	−0.864274	+	1.79468i	−0.864274	+	1.79468i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.822002	−	0.569484i	$-0.192857\pi$
$79$		0			0		−0.822002	+	0.569484i	$0.807143\pi$
$80$	−0.998993	+	0.0448648i	−0.998993	+	0.0448648i
$81$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$82$	−1.84456	−	0.207832i	−1.84456	−	0.207832i
$83$		0			0		0.372294	−	0.928115i	$-0.378571\pi$
$83$		0			0		−0.372294	+	0.928115i	$0.621429\pi$
$84$		0			0
$85$	−0.507944	−	0.485644i	−0.507944	−	0.485644i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.501059	+	1.10312i	−0.501059	+	1.10312i	0.473869	+	0.880596i	$0.342857\pi$
$89$	−0.501059	+	1.10312i	−0.501059	+	1.10312i	−0.974928	+	0.222521i	$0.928571\pi$
$90$	0.266037	−	0.963963i	0.266037	−	0.963963i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.674913	+	0.772500i	0.674913	+	0.772500i	0.983930	−	0.178557i	$-0.0571429\pi$
$97$	0.674913	+	0.772500i	0.674913	+	0.772500i	−0.309017	+	0.951057i	$0.600000\pi$
$98$	0.722795	+	0.691063i	0.722795	+	0.691063i
$99$		0			0
$100$	−0.473869	+	0.880596i	−0.473869	+	0.880596i
$101$	−1.58124	+	0.178163i	−1.58124	+	0.178163i	−0.858449	−	0.512899i	$-0.828571\pi$
$101$	−1.58124	+	0.178163i	−1.58124	+	0.178163i	−0.722795	+	0.691063i	$0.757143\pi$
$102$		0			0
$103$		0			0		0.287599	−	0.957751i	$-0.407143\pi$
$103$		0			0		−0.287599	+	0.957751i	$0.592857\pi$
$104$	1.97090	−	0.312160i	1.97090	−	0.312160i
$105$		0			0
$106$	0.647598	−	1.61444i	0.647598	−	1.61444i
$107$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$107$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$108$		0			0
$109$	−1.57874	+	0.943250i	−1.57874	+	0.943250i	−0.587785	+	0.809017i	$0.700000\pi$
$109$	−1.57874	+	0.943250i	−1.57874	+	0.943250i	−0.990950	+	0.134233i	$0.957143\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.230465	−	0.137696i	0.230465	−	0.137696i	−0.393025	−	0.919528i	$-0.628571\pi$
$113$	0.230465	−	0.137696i	0.230465	−	0.137696i	0.623490	+	0.781831i	$0.285714\pi$
$114$		0			0
$115$		0			0
$116$	−0.998993	−	0.0448648i	−0.998993	−	0.0448648i
$117$	−0.312160	+	1.97090i	−0.312160	+	1.97090i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.998993	−	0.0448648i	0.998993	−	0.0448648i
$122$	−0.858449	−	0.487101i	−0.858449	−	0.487101i
$123$		0			0
$124$		0			0
$125$	0.512899	+	0.858449i	0.512899	+	0.858449i
$126$		0			0
$127$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$127$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$128$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$129$		0			0
$130$	0.742901	−	1.85203i	0.742901	−	1.85203i
$131$		0			0		−0.674671	−	0.738119i	$-0.735714\pi$
$131$		0			0		0.674671	+	0.738119i	$0.264286\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.0943324	−	0.696390i	−0.0943324	−	0.696390i
$137$	1.21709	+	1.27298i	1.21709	+	1.27298i	0.951057	+	0.309017i	$0.100000\pi$
$137$	1.21709	+	1.27298i	1.21709	+	1.27298i	0.266037	+	0.963963i	$0.414286\pi$
$138$		0			0
$139$		0			0		0.834573	−	0.550897i	$-0.185714\pi$
$139$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.809017	−	0.587785i	0.809017	−	0.587785i
$145$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$146$	−1.55972	−	1.13321i	−1.55972	−	1.13321i
$147$		0			0
$148$	−0.178557	+	1.98393i	−0.178557	+	1.98393i
$149$	0.0199667	−	0.0874800i	0.0199667	−	0.0874800i	−0.963963	−	0.266037i	$-0.914286\pi$
$149$	0.0199667	−	0.0874800i	0.0199667	−	0.0874800i	0.983930	+	0.178557i	$0.0571429\pi$
$150$		0			0
$151$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$151$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$152$		0			0
$153$	0.691456	+	0.125481i	0.691456	+	0.125481i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	1.44559i		−	1.44559i	−0.691063	−	0.722795i	$-0.742857\pi$
$157$		−	1.44559i		−	1.44559i	0.691063	−	0.722795i	$-0.257143\pi$
$158$		0			0
$159$		0			0
$160$	−0.919528	+	0.393025i	−0.919528	+	0.393025i
$161$		0			0
$162$	0.309017	+	0.951057i	0.309017	+	0.951057i
$163$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$163$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$164$	−1.79997	+	0.453552i	−1.79997	+	0.453552i
$165$		0			0
$166$		0			0
$167$		0			0		−0.0672690	−	0.997735i	$-0.521429\pi$
$167$		0			0		0.0672690	+	0.997735i	$0.478571\pi$
$168$		0			0
$169$	−0.793295	+	2.87444i	−0.793295	+	2.87444i
$170$	−0.646198	−	0.276198i	−0.646198	−	0.276198i
$171$		0			0
$172$		0			0
$173$	0.826696	+	1.62248i	0.826696	+	1.62248i	0.781831	+	0.623490i	$0.214286\pi$
$173$	0.826696	+	1.62248i	0.826696	+	1.62248i	0.0448648	+	0.998993i	$0.485714\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−0.0815018	+	1.20884i	−0.0815018	+	1.20884i
$179$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$179$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$180$	−0.0896393	−	0.995974i	−0.0896393	−	0.995974i
$181$	−1.04084	−	0.909354i	−1.04084	−	0.909354i	−0.0448648	−	0.998993i	$-0.514286\pi$
$181$	−1.04084	−	0.909354i	−1.04084	−	0.909354i	−0.995974	+	0.0896393i	$0.971429\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.61152	+	1.17084i	1.61152	+	1.17084i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$191$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$192$		0			0
$193$	1.91852	+	0.437890i	1.91852	+	0.437890i	0.998993	+	0.0448648i	$0.0142857\pi$
$193$	1.91852	+	0.437890i	1.91852	+	0.437890i	0.919528	+	0.393025i	$0.128571\pi$
$194$	0.903314	+	0.486094i	0.903314	+	0.486094i
$195$		0			0
$196$	0.919528	+	0.393025i	0.919528	+	0.393025i
$197$	0.811330	−	1.42986i	0.811330	−	1.42986i	−0.0896393	−	0.995974i	$-0.528571\pi$
$197$	0.811330	−	1.42986i	0.811330	−	1.42986i	0.900969	−	0.433884i	$-0.142857\pi$
$198$		0			0
$199$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$199$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$200$	−0.134233	+	0.990950i	−0.134233	+	0.990950i
$201$		0			0
$202$	−1.41781	+	0.722412i	−1.41781	+	0.722412i
$203$		0			0
$204$		0			0
$205$	−0.533850	+	1.77781i	−0.533850	+	1.77781i
$206$		0			0
$207$		0			0
$208$	1.73554	−	0.984781i	1.73554	−	0.984781i
$209$		0			0
$210$		0			0
$211$		0			0		−0.795625	−	0.605790i	$-0.792857\pi$
$211$		0			0		0.795625	+	0.605790i	$0.207143\pi$
$212$	0.0390306	−	1.73904i	0.0390306	−	1.73904i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.14663	+	1.43783i	−1.14663	+	1.43783i
$219$		0			0
$220$		0			0
$221$	1.34307	+	0.403305i	1.34307	+	0.403305i
$222$		0			0
$223$		0			0		0.605790	−	0.795625i	$-0.292857\pi$
$223$		0			0		−0.605790	+	0.795625i	$0.707143\pi$
$224$		0			0
$225$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$226$	0.167386	−	0.209896i	0.167386	−	0.209896i
$227$		0			0		0.413559	−	0.910478i	$-0.364286\pi$
$227$		0			0		−0.413559	+	0.910478i	$0.635714\pi$
$228$		0			0
$229$	−1.37012	+	0.549594i	−1.37012	+	0.549594i	−0.936235	−	0.351375i	$-0.885714\pi$
$229$	−1.37012	+	0.549594i	−1.37012	+	0.549594i	−0.433884	+	0.900969i	$0.642857\pi$
$230$		0			0
$231$		0			0
$232$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$233$	−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	$0.742857\pi$
$234$	0.400270	+	1.95491i	0.400270	+	1.95491i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$239$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$240$		0			0
$241$	1.35341	−	1.29399i	1.35341	−	1.29399i	0.433884	−	0.900969i	$-0.357143\pi$
$241$	1.35341	−	1.29399i	1.35341	−	1.29399i	0.919528	−	0.393025i	$-0.128571\pi$
$242$	0.919528	−	0.393025i	0.919528	−	0.393025i
$243$		0			0
$244$	−0.974865	−	0.154403i	−0.974865	−	0.154403i
$245$	0.809017	−	0.587785i	0.809017	−	0.587785i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.781831	+	0.623490i	0.781831	+	0.623490i
$251$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$251$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$257$	0.0715785	+	0.113917i	0.0715785	+	0.113917i	0.880596	−	0.473869i	$-0.157143\pi$
$257$	0.0715785	+	0.113917i	0.0715785	+	0.113917i	−0.809017	+	0.587785i	$0.800000\pi$
$258$		0			0
$259$		0			0
$260$	0.0447745	−	1.99497i	0.0447745	−	1.99497i
$261$		−	1.00000i		−	1.00000i
$262$		0			0
$263$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$263$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$264$		0			0
$265$	−1.47286	−	0.925460i	−1.47286	−	0.925460i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.83457	+	0.550897i	−1.83457	+	0.550897i	−0.834573	+	0.550897i	$0.814286\pi$
$269$	−1.83457	+	0.550897i	−1.83457	+	0.550897i	−1.00000			$\pi$
$270$		0			0
$271$		0			0		0.0672690	−	0.997735i	$-0.478571\pi$
$271$		0			0		−0.0672690	+	0.997735i	$0.521429\pi$
$272$	−0.333011	−	0.618838i	−0.333011	−	0.618838i
$273$		0			0
$274$	1.58678	+	0.764152i	1.58678	+	0.764152i
$275$		0			0
$276$		0			0
$277$	0.0439640	+	1.95886i	0.0439640	+	1.95886i	0.222521	+	0.974928i	$0.428571\pi$
$277$	0.0439640	+	1.95886i	0.0439640	+	1.95886i	−0.178557	+	0.983930i	$0.557143\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.623553	−	1.15876i	0.623553	−	1.15876i	−0.351375	−	0.936235i	$-0.614286\pi$
$281$	0.623553	−	1.15876i	0.623553	−	1.15876i	0.974928	−	0.222521i	$-0.0714286\pi$
$282$		0			0
$283$		0			0		0.997735	−	0.0672690i	$-0.0214286\pi$
$283$		0			0		−0.997735	+	0.0672690i	$0.978571\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.550897	−	0.834573i	0.550897	−	0.834573i
$289$	−0.156407	+	0.481371i	−0.156407	+	0.481371i
$290$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$291$		0			0
$292$	−1.85845	−	0.512899i	−1.85845	−	0.512899i
$293$	0.174784	−	0.0398932i	0.174784	−	0.0398932i	−0.134233	−	0.990950i	$-0.542857\pi$
$293$	0.174784	−	0.0398932i	0.174784	−	0.0398932i	0.309017	+	0.951057i	$0.400000\pi$
$294$		0			0
$295$		0			0
$296$	0.529932	+	1.92016i	0.529932	+	1.92016i
$297$		0			0
$298$	−0.0120447	−	0.0889176i	−0.0120447	−	0.0889176i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.632555	+	0.757678i	−0.632555	+	0.757678i
$306$	0.691456	−	0.125481i	0.691456	−	0.125481i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.605790	−	0.795625i	$-0.292857\pi$
$311$		0			0		−0.605790	+	0.795625i	$0.707143\pi$
$312$		0			0
$313$	−0.0926077	−	0.203882i	−0.0926077	−	0.203882i	0.858449	−	0.512899i	$-0.171429\pi$
$313$	−0.0926077	−	0.203882i	−0.0926077	−	0.203882i	−0.951057	+	0.309017i	$0.900000\pi$
$314$	−0.507944	−	1.35341i	−0.507944	−	1.35341i
$315$		0			0
$316$		0			0
$317$	−0.331743	+	1.20204i	−0.331743	+	1.20204i	0.587785	+	0.809017i	$0.300000\pi$
$317$	−0.331743	+	1.20204i	−0.331743	+	1.20204i	−0.919528	+	0.393025i	$0.871429\pi$
$318$		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
$325$	−1.68961	−	1.06165i	−1.68961	−	1.06165i
$326$		0			0
$327$		0			0
$328$	−1.52582	+	1.05709i	−1.52582	+	1.05709i
$329$		0			0
$330$		0			0
$331$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$331$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$332$		0			0
$333$	−1.98994	−	0.0893684i	−1.98994	−	0.0893684i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.93221	+	0.261736i	1.93221	+	0.261736i	0.995974	−	0.0896393i	$-0.0285714\pi$
$337$	1.93221	+	0.261736i	1.93221	+	0.261736i	0.936235	+	0.351375i	$0.114286\pi$
$338$	0.267295	+	2.96990i	0.267295	+	2.96990i
$339$		0			0
$340$	−0.702042	−	0.0315287i	−0.702042	−	0.0315287i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	1.34408	+	1.22854i	1.34408	+	1.22854i
$347$		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
$353$	−0.785406	−	0.717893i	−0.785406	−	0.717893i	0.178557	−	0.983930i	$-0.442857\pi$
$353$	−0.785406	−	0.717893i	−0.785406	−	0.717893i	−0.963963	+	0.266037i	$0.914286\pi$
$354$		0			0
$355$		0			0
$356$	0.348450	+	1.16039i	0.348450	+	1.16039i
$357$		0			0
$358$		0			0
$359$		0			0		−0.605790	−	0.795625i	$-0.707143\pi$
$359$		0			0		0.605790	+	0.795625i	$0.292857\pi$
$360$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$361$	0.722795	+	0.691063i	0.722795	+	0.691063i
$362$	−1.29399	−	0.485644i	−1.29399	−	0.485644i
$363$		0			0
$364$		0			0
$365$	−1.39349	+	1.33232i	−1.39349	+	1.33232i
$366$		0			0
$367$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$367$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$368$		0			0
$369$	−0.533850	−	1.77781i	−0.533850	−	1.77781i
$370$	1.92016	+	0.529932i	1.92016	+	0.529932i
$371$		0			0
$372$		0			0
$373$	−0.461258	−	1.83055i	−0.461258	−	1.83055i	−0.550897	−	0.834573i	$-0.685714\pi$
$373$	−0.461258	−	1.83055i	−0.461258	−	1.83055i	0.0896393	−	0.995974i	$-0.471429\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.223422	−	1.98292i	0.223422	−	1.98292i
$378$		0			0
$379$		0			0		−0.738119	−	0.674671i	$-0.764286\pi$
$379$		0			0		0.738119	+	0.674671i	$0.235714\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.674671	−	0.738119i	$-0.735714\pi$
$383$		0			0		0.674671	+	0.738119i	$0.264286\pi$
$384$		0			0
$385$		0			0
$386$	1.95005	−	0.264152i	1.95005	−	0.264152i
$387$		0			0
$388$	1.01651	+	0.137696i	1.01651	+	0.137696i
$389$	1.20227	−	0.612588i	1.20227	−	0.612588i	0.266037	−	0.963963i	$-0.414286\pi$
$389$	1.20227	−	0.612588i	1.20227	−	0.612588i	0.936235	+	0.351375i	$0.114286\pi$
$390$		0			0
$391$		0			0
$392$	0.998993	+	0.0448648i	0.998993	+	0.0448648i
$393$		0			0
$394$	0.257179	−	1.62376i	0.257179	−	1.62376i
$395$		0			0
$396$		0			0
$397$	−1.63367	+	1.13181i	−1.63367	+	1.13181i	−0.753071	+	0.657939i	$0.771429\pi$
$397$	−1.63367	+	1.13181i	−1.63367	+	1.13181i	−0.880596	+	0.473869i	$0.842857\pi$
$398$		0			0
$399$		0			0
$400$	0.222521	+	0.974928i	0.222521	+	0.974928i
$401$	0.490094	+	0.614559i	0.490094	+	0.614559i	0.963963	−	0.266037i	$-0.0857143\pi$
$401$	0.490094	+	0.614559i	0.490094	+	0.614559i	−0.473869	+	0.880596i	$0.657143\pi$
$402$		0			0
$403$		0			0
$404$	−1.07357	+	1.17453i	−1.07357	+	1.17453i
$405$	0.990950	−	0.134233i	0.990950	−	0.134233i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.0109651	+	0.0435159i	−0.0109651	+	0.0435159i	−0.974928	−	0.222521i	$-0.928571\pi$
$409$	−0.0109651	+	0.0435159i	−0.0109651	+	0.0435159i	0.963963	+	0.266037i	$0.0857143\pi$
$410$	0.124867	+	1.85203i	0.124867	+	1.85203i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	1.27885	−	1.53181i	1.27885	−	1.53181i
$417$		0			0
$418$		0			0
$419$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$419$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$420$		0			0
$421$	0.879438	−	1.54989i	0.879438	−	1.54989i	0.0448648	−	0.998993i	$-0.485714\pi$
$421$	0.879438	−	1.54989i	0.879438	−	1.54989i	0.834573	−	0.550897i	$-0.185714\pi$
$422$		0			0
$423$		0			0
$424$	−0.574515	−	1.64187i	−0.574515	−	1.64187i
$425$	−0.387143	+	0.586496i	−0.387143	+	0.586496i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$431$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$432$		0			0
$433$	1.13321	+	0.312745i	1.13321	+	0.312745i	0.781831	−	0.623490i	$-0.214286\pi$
$433$	1.13321	+	0.312745i	1.13321	+	0.312745i	0.351375	+	0.936235i	$0.385714\pi$
$434$		0			0
$435$		0			0
$436$	−0.568299	+	1.74905i	−0.568299	+	1.74905i
$437$		0			0
$438$		0			0
$439$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$439$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$440$		0			0
$441$	−0.351375	+	0.936235i	−0.351375	+	0.936235i
$442$	1.39914	−	0.0943324i	1.39914	−	0.0943324i
$443$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$443$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$444$		0			0
$445$	1.17486	+	0.296038i	1.17486	+	0.296038i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.0449178	+	0.398656i	0.0449178	+	0.398656i	0.995974	+	0.0896393i	$0.0285714\pi$
$449$	0.0449178	+	0.398656i	0.0449178	+	0.398656i	−0.951057	+	0.309017i	$0.900000\pi$
$450$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$451$		0			0
$452$	0.0829607	−	0.255327i	0.0829607	−	0.255327i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.351438	−	0.559311i	0.351438	−	0.559311i	−0.623490	−	0.781831i	$-0.714286\pi$
$457$	0.351438	−	0.559311i	0.351438	−	0.559311i	0.974928	+	0.222521i	$0.0714286\pi$
$458$	−1.08964	+	0.995974i	−1.08964	+	0.995974i
$459$		0			0
$460$		0			0
$461$	−0.697007	+	0.581903i	−0.697007	+	0.581903i	−0.919528	−	0.393025i	$-0.871429\pi$
$461$	−0.697007	+	0.581903i	−0.697007	+	0.581903i	0.222521	+	0.974928i	$0.428571\pi$
$462$		0			0
$463$		0			0		−0.891007	−	0.453990i	$-0.850000\pi$
$463$		0			0		0.891007	+	0.453990i	$0.150000\pi$
$464$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$465$		0			0
$466$	−1.11582	+	0.228465i	−1.11582	+	0.228465i
$467$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$467$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$468$	1.06165	+	1.68961i	1.06165	+	1.68961i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.73904	−	0.0390306i	1.73904	−	0.0390306i
$478$		0			0
$479$		0			0		−0.869741	−	0.493508i	$-0.835714\pi$
$479$		0			0		0.869741	+	0.493508i	$0.164286\pi$
$480$		0			0
$481$	−3.92594	−	0.621807i	−3.92594	−	0.621807i
$482$	0.812434	−	1.68704i	0.812434	−	1.68704i
$483$		0			0
$484$	0.722795	−	0.691063i	0.722795	−	0.691063i
$485$	0.639575	−	0.802002i	0.639575	−	0.802002i
$486$		0			0
$487$		0			0		0.910478	−	0.413559i	$-0.135714\pi$
$487$		0			0		−0.910478	+	0.413559i	$0.864286\pi$
$488$	−0.966956	+	0.197985i	−0.966956	+	0.197985i
$489$		0			0
$490$	0.550897	−	0.834573i	0.550897	−	0.834573i
$491$		0			0		−0.200589	−	0.979675i	$-0.564286\pi$
$491$		0			0		0.200589	+	0.979675i	$0.435714\pi$
$492$		0			0
$493$	−0.696390	−	0.0943324i	−0.696390	−	0.0943324i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$499$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$500$	0.951057	+	0.309017i	0.951057	+	0.309017i
$501$		0			0
$502$		0			0
$503$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$503$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$504$		0			0
$505$	0.457642	+	1.52402i	0.457642	+	1.52402i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.70136	−	0.230465i	−1.70136	−	0.230465i	−0.781831	−	0.623490i	$-0.785714\pi$
$509$	−1.70136	−	0.230465i	−1.70136	−	0.230465i	−0.919528	+	0.393025i	$0.871429\pi$
$510$		0			0
$511$		0			0
$512$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$513$		0			0
$514$	0.107042	+	0.0815018i	0.107042	+	0.0815018i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.659062	−	1.88349i	−0.659062	−	1.88349i
$521$	0.557066	−	0.766736i	0.557066	−	0.766736i	−0.433884	−	0.900969i	$-0.642857\pi$
$521$	0.557066	−	0.766736i	0.557066	−	0.766736i	0.990950	+	0.134233i	$0.0428571\pi$
$522$	−0.351375	−	0.936235i	−0.351375	−	0.936235i
$523$		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
$529$	−0.919528	−	0.393025i	−0.919528	−	0.393025i
$530$	−1.70413	−	0.348922i	−1.70413	−	0.348922i
$531$		0			0
$532$		0			0
$533$	−0.661384	−	3.64453i	−0.661384	−	3.64453i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.52402	+	1.16039i	−1.52402	+	1.16039i
$539$		0			0
$540$		0			0
$541$	−1.48875	−	1.24290i	−1.48875	−	1.24290i	−0.900969	−	0.433884i	$-0.857143\pi$
$541$	−1.48875	−	1.24290i	−1.48875	−	1.24290i	−0.587785	−	0.809017i	$-0.700000\pi$
$542$		0			0
$543$		0			0
$544$	−0.529221	−	0.462366i	−0.529221	−	0.462366i
$545$	1.20999	+	1.38494i	1.20999	+	1.38494i
$546$		0			0
$547$		0			0		0.0672690	−	0.997735i	$-0.478571\pi$
$547$		0			0		−0.0672690	+	0.997735i	$0.521429\pi$
$548$	1.75410	+	0.157872i	1.75410	+	0.157872i
$549$	0.110511	−	0.980810i	0.110511	−	0.980810i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.729454	+	1.81850i	0.729454	+	1.81850i
$555$		0			0
$556$		0			0
$557$	1.27369	−	0.143511i	1.27369	−	0.143511i	0.550897	−	0.834573i	$-0.314286\pi$
$557$	1.27369	−	0.143511i	1.27369	−	0.143511i	0.722795	+	0.691063i	$0.242857\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.176635	−	1.30397i	0.176635	−	1.30397i
$563$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$563$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$564$		0			0
$565$	−0.176635	−	0.202174i	−0.176635	−	0.202174i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.05360	+	0.729937i	1.05360	+	0.729937i	0.963963	−	0.266037i	$-0.0857143\pi$
$569$	1.05360	+	0.729937i	1.05360	+	0.729937i	0.0896393	+	0.995974i	$0.471429\pi$
$570$		0			0
$571$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$571$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.222521	−	0.974928i	0.222521	−	0.974928i
$577$	0.0398932	−	0.443250i	0.0398932	−	0.443250i	−0.951057	−	0.309017i	$-0.900000\pi$
$577$	0.0398932	−	0.443250i	0.0398932	−	0.443250i	0.990950	−	0.134233i	$-0.0428571\pi$
$578$	0.0227080	+	0.505633i	0.0227080	+	0.505633i
$579$		0			0
$580$	0.134233	+	0.990950i	0.134233	+	0.990950i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−1.92016	+	0.172818i	−1.92016	+	0.172818i
$585$	1.99497	−	0.0447745i	1.99497	−	0.0447745i
$586$	0.149621	−	0.0987640i	0.149621	−	0.0987640i
$587$		0			0		0.244340	−	0.969690i	$-0.421429\pi$
$587$		0			0		−0.244340	+	0.969690i	$0.578571\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.17084	+	1.61152i	1.17084	+	1.61152i
$593$	−0.378666	+	0.132501i	−0.378666	+	0.132501i	−0.512899	−	0.858449i	$-0.671429\pi$
$593$	−0.378666	+	0.132501i	−0.378666	+	0.132501i	0.134233	+	0.990950i	$0.457143\pi$
$594$		0			0
$595$		0			0
$596$	−0.0425201	−	0.0790155i	−0.0425201	−	0.0790155i
$597$		0			0
$598$		0			0
$599$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$599$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$600$		0			0
$601$	0.295312	+	0.103334i	0.295312	+	0.103334i	0.473869	−	0.880596i	$-0.342857\pi$
$601$	0.295312	+	0.103334i	0.295312	+	0.103334i	−0.178557	+	0.983930i	$0.557143\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$606$		0			0
$607$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$607$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$608$		0			0
$609$		0			0
$610$	−0.325991	+	0.931628i	−0.325991	+	0.931628i
$611$		0			0
$612$	0.603275	−	0.360440i	0.603275	−	0.360440i
$613$	−1.24290	+	1.48875i	−1.24290	+	1.48875i	−0.433884	+	0.900969i	$0.642857\pi$
$613$	−1.24290	+	1.48875i	−1.24290	+	1.48875i	−0.809017	+	0.587785i	$0.800000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.314473	−	0.169225i	−0.314473	−	0.169225i	0.309017	−	0.951057i	$-0.400000\pi$
$617$	−0.314473	−	0.169225i	−0.314473	−	0.169225i	−0.623490	+	0.781831i	$0.714286\pi$
$618$		0			0
$619$		0			0		0.372294	−	0.928115i	$-0.378571\pi$
$619$		0			0		−0.372294	+	0.928115i	$0.621429\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.753071	−	0.657939i	0.753071	−	0.657939i
$626$	−0.158342	−	0.158342i	−0.158342	−	0.158342i
$627$		0			0
$628$	−0.951109	−	1.08863i	−0.951109	−	1.08863i
$629$	−0.249951	+	1.37735i	−0.249951	+	1.37735i
$630$		0			0
$631$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$631$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$632$		0			0
$633$		0			0
$634$	0.111778	+	1.24196i	0.111778	+	1.24196i
$635$		0			0
$636$		0			0
$637$	−0.905924	+	1.77798i	−0.905924	+	1.77798i
$638$		0			0
$639$		0			0
$640$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$641$	−1.37135	−	0.345550i	−1.37135	−	0.345550i	−0.512899	−	0.858449i	$-0.671429\pi$
$641$	−1.37135	−	0.345550i	−1.37135	−	0.345550i	−0.858449	+	0.512899i	$0.828571\pi$
$642$		0			0
$643$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$643$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.569484	−	0.822002i	$-0.692857\pi$
$647$		0			0		0.569484	+	0.822002i	$0.307143\pi$
$648$	0.858449	+	0.512899i	0.858449	+	0.512899i
$649$		0			0
$650$	−1.95491	−	0.400270i	−1.95491	−	0.400270i
$651$		0			0
$652$		0			0
$653$	1.65503	−	0.456758i	1.65503	−	0.456758i	0.691063	−	0.722795i	$-0.257143\pi$
$653$	1.65503	−	0.456758i	1.65503	−	0.456758i	0.963963	+	0.266037i	$0.0857143\pi$
$654$		0			0
$655$		0			0
$656$	−1.05709	+	1.52582i	−1.05709	+	1.52582i
$657$	0.429004	−	1.87959i	0.429004	−	1.87959i
$658$		0			0
$659$		0			0		−0.999748	−	0.0224381i	$-0.992857\pi$
$659$		0			0		0.999748	+	0.0224381i	$0.00714286\pi$
$660$		0			0
$661$	0.245172	+	0.371420i	0.245172	+	0.371420i	0.936235	−	0.351375i	$-0.114286\pi$
$661$	0.245172	+	0.371420i	0.245172	+	0.371420i	−0.691063	+	0.722795i	$0.742857\pi$
$662$		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
$673$	1.95886	+	0.401078i	1.95886	+	0.401078i	0.983930	+	0.178557i	$0.0571429\pi$
$673$	1.95886	+	0.401078i	1.95886	+	0.401078i	0.974928	+	0.222521i	$0.0714286\pi$
$674$	1.90097	−	0.433884i	1.90097	−	0.433884i
$675$		0			0
$676$	1.29380	+	2.68660i	1.29380	+	2.68660i
$677$	0.445077	−	0.744934i	0.445077	−	0.744934i	−0.550897	−	0.834573i	$-0.685714\pi$
$677$	0.445077	−	0.744934i	0.445077	−	0.744934i	0.995974	+	0.0896393i	$0.0285714\pi$
$678$		0			0
$679$		0			0
$680$	−0.668355	+	0.217162i	−0.668355	+	0.217162i
$681$		0			0
$682$		0			0
$683$		0			0		−0.822002	−	0.569484i	$-0.807143\pi$
$683$		0			0		0.822002	+	0.569484i	$0.192857\pi$
$684$		0			0
$685$	1.03520	−	1.42483i	1.03520	−	1.42483i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.45711	+	0.311146i	3.45711	+	0.311146i
$690$		0			0
$691$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$691$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$692$	1.69006	+	0.677930i	1.69006	+	0.677930i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.28840	+	0.204063i	−1.28840	+	0.204063i
$698$	−0.387143	−	1.03154i	−0.387143	−	1.03154i
$699$		0			0
$700$		0			0
$701$	1.56209	−	1.24572i	1.56209	−	1.24572i	0.753071	−	0.657939i	$-0.228571\pi$
$701$	1.56209	−	1.24572i	1.56209	−	1.24572i	0.809017	−	0.587785i	$-0.200000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.987574	−	0.396144i	−0.987574	−	0.396144i
$707$		0			0
$708$		0			0
$709$	−0.0479366	+	0.353882i	−0.0479366	+	0.353882i	0.951057	+	0.309017i	$0.100000\pi$
$709$	−0.0479366	+	0.353882i	−0.0479366	+	0.353882i	−0.998993	+	0.0448648i	$0.985714\pi$
$710$		0			0
$711$		0			0
$712$	0.733963	+	0.963963i	0.733963	+	0.963963i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.998993	−	0.0448648i	$-0.985714\pi$
$719$		0			0		0.998993	+	0.0448648i	$0.0142857\pi$
$720$	−0.722795	−	0.691063i	−0.722795	−	0.691063i
$721$		0			0
$722$	0.919528	+	0.393025i	0.919528	+	0.393025i
$723$		0			0
$724$	−1.38213			−1.38213
$725$	0.919528	+	0.393025i	0.919528	+	0.393025i
$726$		0			0
$727$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$727$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$728$		0			0
$729$	−0.753071	+	0.657939i	−0.753071	+	0.657939i
$730$	−0.836496	+	1.73700i	−0.836496	+	1.73700i
$731$		0			0
$732$		0			0
$733$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$733$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−1.12449	−	1.47686i	−1.12449	−	1.47686i
$739$		0			0		−0.979675	−	0.200589i	$-0.935714\pi$
$739$		0			0		0.979675	+	0.200589i	$0.0642857\pi$
$740$	1.98393	−	0.178557i	1.98393	−	0.178557i
$741$		0			0
$742$		0			0
$743$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$743$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$744$		0			0
$745$	−0.0896393	−	0.00402571i	−0.0896393	−	0.00402571i
$746$	−1.07505	−	1.55175i	−1.07505	−	1.55175i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$751$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$752$		0			0
$753$		0			0
$754$	−0.487574	−	1.93499i	−0.487574	−	1.93499i
$755$		0			0
$756$		0			0
$757$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	−0.963963	−	0.266037i	$-0.914286\pi$
$757$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	0.753071	−	0.657939i	$-0.228571\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.355676	−	0.0320114i	−0.355676	−	0.0320114i	−0.0896393	−	0.995974i	$-0.528571\pi$
$761$	−0.355676	−	0.0320114i	−0.355676	−	0.0320114i	−0.266037	+	0.963963i	$0.585714\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		−	0.702750i		−	0.702750i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.487571	−	0.445659i	0.487571	−	0.445659i	−0.393025	−	0.919528i	$-0.628571\pi$
$769$	0.487571	−	0.445659i	0.487571	−	0.445659i	0.880596	+	0.473869i	$0.157143\pi$
$770$		0			0
$771$		0			0
$772$	1.73289	−	0.932507i	1.73289	−	0.932507i
$773$	−0.486094	+	0.813584i	−0.486094	+	0.813584i	−0.998993	−	0.0448648i	$-0.985714\pi$
$773$	−0.486094	+	0.813584i	−0.486094	+	0.813584i	0.512899	+	0.858449i	$0.328571\pi$
$774$		0			0
$775$		0			0
$776$	1.00008	−	0.228262i	1.00008	−	0.228262i
$777$		0			0
$778$	0.910361	−	0.995974i	0.910361	−	0.995974i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.951057	−	0.309017i	0.951057	−	0.309017i
$785$	−1.42236	+	0.258120i	−1.42236	+	0.258120i
$786$		0			0
$787$		0			0		−0.767645	−	0.640876i	$-0.778571\pi$
$787$		0			0		0.767645	+	0.640876i	$0.221429\pi$
$788$	−0.329770	−	1.61059i	−0.329770	−	1.61059i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.438269	−	1.92018i	0.438269	−	1.92018i
$794$	−1.13181	+	1.63367i	−1.13181	+	1.63367i
$795$		0			0
$796$		0			0
$797$	0.757723	−	0.209118i	0.757723	−	0.209118i	0.134233	−	0.990950i	$-0.457143\pi$
$797$	0.757723	−	0.209118i	0.757723	−	0.209118i	0.623490	+	0.781831i	$0.285714\pi$
$798$		0			0
$799$		0			0
$800$	0.550897	+	0.834573i	0.550897	+	0.834573i
$801$	−1.14359	+	0.400160i	−1.14359	+	0.400160i
$802$	0.674784	+	0.403165i	0.674784	+	0.403165i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.592412	+	1.47686i	−0.592412	+	1.47686i
$809$	0.473869	+	0.119404i	0.473869	+	0.119404i	0.473869	−	0.880596i	$-0.342857\pi$
$809$	0.473869	+	0.119404i	0.473869	+	0.119404i			1.00000i	$0.5\pi$
$810$	0.880596	−	0.473869i	0.880596	−	0.473869i
$811$		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
$818$	0.00502453	+	0.0445940i	0.00502453	+	0.0445940i
$819$		0			0
$820$	0.767660	+	1.69006i	0.767660	+	1.69006i
$821$	−0.279203	+	1.53853i	−0.279203	+	1.53853i	0.473869	+	0.880596i	$0.342857\pi$
$821$	−0.279203	+	1.53853i	−0.279203	+	1.53853i	−0.753071	+	0.657939i	$0.771429\pi$
$822$		0			0
$823$		0			0		−0.722795	−	0.691063i	$-0.757143\pi$
$823$		0			0		0.722795	+	0.691063i	$0.242857\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.834573	−	0.550897i	$-0.185714\pi$
$827$		0			0		−0.834573	+	0.550897i	$0.814286\pi$
$828$		0			0
$829$	−0.735420	+	0.116479i	−0.735420	+	0.116479i	−0.512899	−	0.858449i	$-0.671429\pi$
$829$	−0.735420	+	0.116479i	−0.735420	+	0.116479i	−0.222521	+	0.974928i	$0.571429\pi$
$830$		0			0
$831$		0			0
$832$	0.659062	−	1.88349i	0.659062	−	1.88349i
$833$	0.618838	+	0.333011i	0.618838	+	0.333011i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.910478	−	0.413559i	$-0.864286\pi$
$839$		0			0		0.910478	+	0.413559i	$0.135714\pi$
$840$		0			0
$841$	0.0448648	+	0.998993i	0.0448648	+	0.998993i
$842$	0.278768	−	1.76007i	0.278768	−	1.76007i
$843$		0			0
$844$		0			0
$845$	2.96990	+	0.267295i	2.96990	+	0.267295i
$846$		0			0
$847$		0			0
$848$	−1.11479	−	1.33530i	−1.11479	−	1.33530i
$849$		0			0
$850$	−0.156377	+	0.685130i	−0.156377	+	0.685130i
$851$		0			0
$852$		0			0
$853$	−0.288911	−	0.209906i	−0.288911	−	0.209906i	0.433884	−	0.900969i	$-0.357143\pi$
$853$	−0.288911	−	0.209906i	−0.288911	−	0.209906i	−0.722795	+	0.691063i	$0.757143\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.433884	−	0.900969i	$-0.357143\pi$
$857$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.900969	+	0.433884i	$0.142857\pi$
$858$		0			0
$859$		0			0		0.795625	−	0.605790i	$-0.207143\pi$
$859$		0			0		−0.795625	+	0.605790i	$0.792857\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.244340	−	0.969690i	$-0.421429\pi$
$863$		0			0		−0.244340	+	0.969690i	$0.578571\pi$
$864$		0			0
$865$	1.44880	−	1.10312i	1.44880	−	1.10312i
$866$	1.17084	−	0.105377i	1.17084	−	0.105377i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.0825089	+	1.83720i	0.0825089	+	1.83720i
$873$	−0.0919519	+	1.02167i	−0.0919519	+	1.02167i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.240172	−	0.200510i	0.240172	−	0.200510i	−0.512899	−	0.858449i	$-0.671429\pi$
$877$	0.240172	−	0.200510i	0.240172	−	0.200510i	0.753071	+	0.657939i	$0.228571\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.63367	−	1.13181i	−1.63367	−	1.13181i	−0.880596	−	0.473869i	$-0.842857\pi$
$881$	−1.63367	−	1.13181i	−1.63367	−	1.13181i	−0.753071	−	0.657939i	$-0.771429\pi$
$882$			1.00000i			1.00000i
$883$		0			0		0.569484	−	0.822002i	$-0.307143\pi$
$883$		0			0		−0.569484	+	0.822002i	$0.692857\pi$
$884$	1.27678	−	0.579940i	1.27678	−	0.579940i
$885$		0			0
$886$		0			0
$887$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$887$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$888$		0			0
$889$		0			0
$890$	1.20396	−	0.135654i	1.20396	−	0.135654i
$891$		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
$904$	−0.0120447	−	0.268196i	−0.0120447	−	0.268196i
$905$	−0.708891	+	1.18648i	−0.708891	+	1.18648i
$906$		0			0
$907$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$907$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$908$		0			0
$909$	−1.22151	−	1.01979i	−1.22151	−	1.01979i
$910$		0			0
$911$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$911$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$912$		0			0
$913$		0			0
$914$	0.132501	−	0.647133i	0.132501	−	0.647133i
$915$		0			0
$916$	−0.670198	+	1.31534i	−0.670198	+	1.31534i
$917$		0			0
$918$		0			0
$919$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$919$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$920$		0			0
$921$		0			0
$922$	−0.448096	+	0.789708i	−0.448096	+	0.789708i
$923$		0			0
$924$		0			0
$925$	0.864274	−	1.79468i	0.864274	−	1.79468i
$926$		0			0
$927$		0			0
$928$	−0.512899	+	0.858449i	−0.512899	+	0.858449i
$929$	−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
$932$	−0.964393	+	0.605968i	−0.964393	+	0.605968i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	1.58764	+	1.20884i	1.58764	+	1.20884i
$937$	−0.0448648	+	1.99899i	−0.0448648	+	1.99899i			1.00000i	$0.5\pi$
$937$	−0.0448648	+	1.99899i	−0.0448648	+	1.99899i	−0.0448648	+	0.998993i	$0.514286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.88490	+	0.255327i	1.88490	+	0.255327i	0.983930	−	0.178557i	$-0.0571429\pi$
$941$	1.88490	+	0.255327i	1.88490	+	0.255327i	0.900969	+	0.433884i	$0.142857\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$947$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$948$		0			0
$949$	1.27062	−	3.63123i	1.27062	−	3.63123i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.93499	−	0.130460i	−1.93499	−	0.130460i	−0.951057	−	0.309017i	$-0.900000\pi$
$953$	−1.93499	−	0.130460i	−1.93499	−	0.130460i	−0.983930	+	0.178557i	$0.942857\pi$
$954$	1.61444	−	0.647598i	1.61444	−	0.647598i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.512899	+	0.858449i	−0.512899	+	0.858449i
$962$	−3.89409	+	0.797317i	−3.89409	+	0.797317i
$963$		0			0
$964$	0.167847	−	1.86493i	0.167847	−	1.86493i
$965$	0.0882877	−	1.96588i	0.0882877	−	1.96588i
$966$		0			0
$967$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$967$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$968$	0.433884	−	0.900969i	0.433884	−	0.900969i
$969$		0			0
$970$	0.316989	−	0.975592i	0.316989	−	0.975592i
$971$		0			0		−0.869741	−	0.493508i	$-0.835714\pi$
$971$		0			0		0.869741	+	0.493508i	$0.164286\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.835731	+	0.525124i	−0.835731	+	0.525124i
$977$	−1.52402	−	1.16039i	−1.52402	−	1.16039i	−0.936235	−	0.351375i	$-0.885714\pi$
$977$	−1.52402	−	1.16039i	−1.52402	−	1.16039i	−0.587785	−	0.809017i	$-0.700000\pi$
$978$		0			0
$979$		0			0
$980$	0.222521	−	0.974928i	0.222521	−	0.974928i
$981$	−1.77278	−	0.489257i	−1.77278	−	0.489257i
$982$		0			0
$983$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$983$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$984$		0			0
$985$	−1.55175	−	0.542980i	−1.55175	−	0.542980i
$986$	−0.685130	+	0.156377i	−0.685130	+	0.156377i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$991$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.853882	+	1.58678i	0.853882	+	1.58678i	0.809017	+	0.587785i	$0.200000\pi$
$997$	0.853882	+	1.58678i	0.853882	+	1.58678i	0.0448648	+	0.998993i	$0.485714\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2900.1.da.a.1303.1	yes	48
4.3	odd	2	CM	2900.1.da.a.1303.1	yes	48
25.17	odd	20		2900.1.cr.a.1767.1	yes	48
29.14	odd	28		2900.1.cr.a.1203.1	✓	48
100.67	even	20		2900.1.cr.a.1767.1	yes	48
116.43	even	28		2900.1.cr.a.1203.1	✓	48
725.217	even	140	inner	2900.1.da.a.1667.1	yes	48
2900.1667	odd	140	inner	2900.1.da.a.1667.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2900.1.cr.a.1203.1	✓	48	29.14	odd	28
2900.1.cr.a.1203.1	✓	48	116.43	even	28
2900.1.cr.a.1767.1	yes	48	25.17	odd	20
2900.1.cr.a.1767.1	yes	48	100.67	even	20
2900.1.da.a.1303.1	yes	48	1.1	even	1	trivial
2900.1.da.a.1303.1	yes	48	4.3	odd	2	CM
2900.1.da.a.1667.1	yes	48	725.217	even	140	inner
2900.1.da.a.1667.1	yes	48	2900.1667	odd	140	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:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2900.da (of order \(140\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(0.936235 - 0.351375i) q^{2} +(0.753071 - 0.657939i) q^{4} +(-0.178557 - 0.983930i) q^{5} +(0.473869 - 0.880596i) q^{8} +(0.691063 + 0.722795i) q^{9} +O(q^{10})\)	\(q+(0.936235 - 0.351375i) q^{2} +(0.753071 - 0.657939i) q^{4} +(-0.178557 - 0.983930i) q^{5} +(0.473869 - 0.880596i) q^{8} +(0.691063 + 0.722795i) q^{9} +(-0.512899 - 0.858449i) q^{10} +(1.20884 + 1.58764i) q^{13} +(0.134233 - 0.990950i) q^{16} +(0.568536 - 0.413066i) q^{17} +(0.900969 + 0.433884i) q^{18} +(-0.781831 - 0.623490i) q^{20} +(-0.936235 + 0.351375i) q^{25} +(1.68961 + 1.06165i) q^{26} +(-0.722795 - 0.691063i) q^{29} +(-0.222521 - 0.974928i) q^{32} +(0.387143 - 0.586496i) q^{34} +(0.995974 + 0.0896393i) q^{36} +(-1.43977 + 1.37656i) q^{37} +(-0.951057 - 0.309017i) q^{40} +(-1.65391 - 0.842711i) q^{41} +(0.587785 - 0.809017i) q^{45} +(0.433884 + 0.900969i) q^{49} +(-0.753071 + 0.657939i) q^{50} +(1.95491 + 0.400270i) q^{52} +(1.17358 - 1.28394i) q^{53} +(-0.919528 - 0.393025i) q^{58} +(-0.632555 - 0.757678i) q^{61} +(-0.550897 - 0.834573i) q^{64} +(1.34628 - 1.47289i) q^{65} +(0.156377 - 0.685130i) q^{68} +(0.963963 - 0.266037i) q^{72} +(-1.06209 - 1.60900i) q^{73} +(-0.864274 + 1.79468i) q^{74} +(-0.998993 + 0.0448648i) q^{80} +(-0.0448648 + 0.998993i) q^{81} +(-1.84456 - 0.207832i) q^{82} +(-0.507944 - 0.485644i) q^{85} +(-0.501059 + 1.10312i) q^{89} +(0.266037 - 0.963963i) q^{90} +(0.674913 + 0.772500i) q^{97} +(0.722795 + 0.691063i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 2 * q^9	\( 48 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 2 q^{9} - 2 q^{13} + 2 q^{16} + 8 q^{18} - 2 q^{25} + 12 q^{26} - 8 q^{32} - 2 q^{36} + 2 q^{41} - 2 q^{50} - 2 q^{52} + 8 q^{53} - 2 q^{61} + 2 q^{64} - 8 q^{65} - 2 q^{72} + 10 q^{73} + 2 q^{81} + 2 q^{82} - 10 q^{85} + 2 q^{89} + 14 q^{97}+O(q^{100}) \) 48 * q + 2 * q^2 + 2 * q^4 + 2 * q^8 - 2 * q^9 - 2 * q^13 + 2 * q^16 + 8 * q^18 - 2 * q^25 + 12 * q^26 - 8 * q^32 - 2 * q^36 + 2 * q^41 - 2 * q^50 - 2 * q^52 + 8 * q^53 - 2 * q^61 + 2 * q^64 - 8 * q^65 - 2 * q^72 + 10 * q^73 + 2 * q^81 + 2 * q^82 - 10 * q^85 + 2 * q^89 + 14 * q^97

Introduction

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