LMFDB - Embedded newform 2900.1.cr.a.1547.1

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			1547.1
Root			$-0.880596 + 0.473869i$ of defining polynomial
Character	$\chi$	$=$	2900.1547
Dual form			2900.1.cr.a.583.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.512899 + 0.858449i) q^{2} +(-0.473869 - 0.880596i) q^{4} +(-0.880596 - 0.473869i) q^{5} +(0.998993 + 0.0448648i) q^{8} +(0.936235 + 0.351375i) q^{9} +O(q^{10})$	\(q+(-0.512899 + 0.858449i) q^{2} +(-0.473869 - 0.880596i) q^{4} +(-0.880596 - 0.473869i) q^{5} +(0.998993 + 0.0448648i) q^{8} +(0.936235 + 0.351375i) q^{9} +(0.858449 - 0.512899i) q^{10} +(-1.61059 + 0.329770i) q^{13} +(-0.550897 + 0.834573i) q^{16} +(-0.105377 - 0.145039i) q^{17} +(-0.781831 + 0.623490i) q^{18} +1.00000i q^{20} +(0.550897 + 0.834573i) q^{25} +(0.542980 - 1.55175i) q^{26} +(-0.266037 + 0.963963i) q^{29} +(-0.433884 - 0.900969i) q^{32} +(0.178557 - 0.0160704i) q^{34} +(-0.134233 - 0.990950i) q^{36} +(1.29399 + 0.485644i) q^{37} +(-0.858449 - 0.512899i) q^{40} +(1.70672 + 0.869620i) q^{41} +(-0.657939 - 0.753071i) q^{45} +(0.781831 + 0.623490i) q^{49} +(-0.998993 + 0.0448648i) q^{50} +(1.05360 + 1.26201i) q^{52} +(-0.00905024 + 0.134233i) q^{53} +(-0.691063 - 0.722795i) q^{58} +(1.20884 - 1.58764i) q^{61} +(0.995974 + 0.0896393i) q^{64} +(1.57455 + 0.472814i) q^{65} +(-0.0777861 + 0.161524i) q^{68} +(0.919528 + 0.393025i) q^{72} +(0.135010 - 1.50008i) q^{73} +(-1.08059 + 0.861741i) q^{74} +(0.880596 - 0.473869i) q^{80} +(0.753071 + 0.657939i) q^{81} +(-1.62190 + 1.01911i) q^{82} +(0.0240652 + 0.177656i) q^{85} +(-0.802047 + 0.202098i) q^{89} +(0.983930 - 0.178557i) q^{90} +(0.939160 + 1.74525i) q^{97} +(-0.936235 + 0.351375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$	$1451$
$\chi(n)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{20}\right)$	$-1$

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 $

$2$	−0.512899	+	0.858449i	−0.512899	+	0.858449i
$2$	−0.512899	+	0.858449i	−0.512899	+	0.858449i
$3$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$3$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$4$	−0.473869	−	0.880596i	−0.473869	−	0.880596i
$5$	−0.880596	−	0.473869i	−0.880596	−	0.473869i
$5$	−0.880596	−	0.473869i	−0.880596	−	0.473869i
$6$		0			0
$7$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$7$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$8$	0.998993	+	0.0448648i	0.998993	+	0.0448648i
$9$	0.936235	+	0.351375i	0.936235	+	0.351375i
$10$	0.858449	−	0.512899i	0.858449	−	0.512899i
$11$		0			0		−0.910478	−	0.413559i	$-0.864286\pi$
$11$		0			0		0.910478	+	0.413559i	$0.135714\pi$
$12$		0			0
$13$	−1.61059	+	0.329770i	−1.61059	+	0.329770i	−0.919528	−	0.393025i	$-0.871429\pi$
$13$	−1.61059	+	0.329770i	−1.61059	+	0.329770i	−0.691063	+	0.722795i	$0.742857\pi$
$14$		0			0
$15$		0			0
$16$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$17$	−0.105377	−	0.145039i	−0.105377	−	0.145039i	0.753071	−	0.657939i	$-0.228571\pi$
$17$	−0.105377	−	0.145039i	−0.105377	−	0.145039i	−0.858449	+	0.512899i	$0.828571\pi$
$18$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$19$		0			0		0.569484	−	0.822002i	$-0.307143\pi$
$19$		0			0		−0.569484	+	0.822002i	$0.692857\pi$
$20$			1.00000i			1.00000i
$21$		0			0
$22$		0			0
$23$		0			0		0.767645	−	0.640876i	$-0.221429\pi$
$23$		0			0		−0.767645	+	0.640876i	$0.778571\pi$
$24$		0			0
$25$	0.550897	+	0.834573i	0.550897	+	0.834573i
$26$	0.542980	−	1.55175i	0.542980	−	1.55175i
$27$		0			0
$28$		0			0
$29$	−0.266037	+	0.963963i	−0.266037	+	0.963963i
$29$	−0.266037	+	0.963963i	−0.266037	+	0.963963i
$30$		0			0
$31$		0			0		0.372294	−	0.928115i	$-0.378571\pi$
$31$		0			0		−0.372294	+	0.928115i	$0.621429\pi$
$32$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$33$		0			0
$34$	0.178557	−	0.0160704i	0.178557	−	0.0160704i
$35$		0			0
$36$	−0.134233	−	0.990950i	−0.134233	−	0.990950i
$37$	1.29399	+	0.485644i	1.29399	+	0.485644i	0.900969	−	0.433884i	$-0.142857\pi$
$37$	1.29399	+	0.485644i	1.29399	+	0.485644i	0.393025	+	0.919528i	$0.371429\pi$
$38$		0			0
$39$		0			0
$40$	−0.858449	−	0.512899i	−0.858449	−	0.512899i
$41$	1.70672	+	0.869620i	1.70672	+	0.869620i	0.983930	+	0.178557i	$0.0571429\pi$
$41$	1.70672	+	0.869620i	1.70672	+	0.869620i	0.722795	+	0.691063i	$0.242857\pi$
$42$		0			0
$43$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$43$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$44$		0			0
$45$	−0.657939	−	0.753071i	−0.657939	−	0.753071i
$46$		0			0
$47$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$47$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$48$		0			0
$49$	0.781831	+	0.623490i	0.781831	+	0.623490i
$50$	−0.998993	+	0.0448648i	−0.998993	+	0.0448648i
$51$		0			0
$52$	1.05360	+	1.26201i	1.05360	+	1.26201i
$53$	−0.00905024	+	0.134233i	−0.00905024	+	0.134233i	0.990950	+	0.134233i	$0.0428571\pi$
$53$	−0.00905024	+	0.134233i	−0.00905024	+	0.134233i	−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$59$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$59$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$60$		0			0
$61$	1.20884	−	1.58764i	1.20884	−	1.58764i	0.550897	−	0.834573i	$-0.314286\pi$
$61$	1.20884	−	1.58764i	1.20884	−	1.58764i	0.657939	−	0.753071i	$-0.271429\pi$
$62$		0			0
$63$		0			0
$64$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$65$	1.57455	+	0.472814i	1.57455	+	0.472814i
$66$		0			0
$67$		0			0		−0.674671	−	0.738119i	$-0.735714\pi$
$67$		0			0		0.674671	+	0.738119i	$0.264286\pi$
$68$	−0.0777861	+	0.161524i	−0.0777861	+	0.161524i
$69$		0			0
$70$		0			0
$71$		0			0		0.998993	−	0.0448648i	$-0.0142857\pi$
$71$		0			0		−0.998993	+	0.0448648i	$0.985714\pi$
$72$	0.919528	+	0.393025i	0.919528	+	0.393025i
$73$	0.135010	−	1.50008i	0.135010	−	1.50008i	−0.587785	−	0.809017i	$-0.700000\pi$
$73$	0.135010	−	1.50008i	0.135010	−	1.50008i	0.722795	−	0.691063i	$-0.242857\pi$
$74$	−1.08059	+	0.861741i	−1.08059	+	0.861741i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.493508	−	0.869741i	$-0.335714\pi$
$79$		0			0		−0.493508	+	0.869741i	$0.664286\pi$
$80$	0.880596	−	0.473869i	0.880596	−	0.473869i
$81$	0.753071	+	0.657939i	0.753071	+	0.657939i
$82$	−1.62190	+	1.01911i	−1.62190	+	1.01911i
$83$		0			0		0.569484	−	0.822002i	$-0.307143\pi$
$83$		0			0		−0.569484	+	0.822002i	$0.692857\pi$
$84$		0			0
$85$	0.0240652	+	0.177656i	0.0240652	+	0.177656i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.802047	+	0.202098i	−0.802047	+	0.202098i	−0.623490	−	0.781831i	$-0.714286\pi$
$89$	−0.802047	+	0.202098i	−0.802047	+	0.202098i	−0.178557	+	0.983930i	$0.557143\pi$
$90$	0.983930	−	0.178557i	0.983930	−	0.178557i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.939160	+	1.74525i	0.939160	+	1.74525i	0.587785	+	0.809017i	$0.300000\pi$
$97$	0.939160	+	1.74525i	0.939160	+	1.74525i	0.351375	+	0.936235i	$0.385714\pi$
$98$	−0.936235	+	0.351375i	−0.936235	+	0.351375i
$99$		0			0
$100$	0.473869	−	0.880596i	0.473869	−	0.880596i
$101$	−0.968807	+	1.54185i	−0.968807	+	1.54185i	−0.134233	+	0.990950i	$0.542857\pi$
$101$	−0.968807	+	1.54185i	−0.968807	+	1.54185i	−0.834573	+	0.550897i	$0.814286\pi$
$102$		0			0
$103$		0			0		−0.738119	−	0.674671i	$-0.764286\pi$
$103$		0			0		0.738119	+	0.674671i	$0.235714\pi$
$104$	−1.62376	+	0.257179i	−1.62376	+	0.257179i
$105$		0			0
$106$	−0.110591	−	0.0766173i	−0.110591	−	0.0766173i
$107$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$107$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$108$		0			0
$109$	1.21709	+	1.27298i	1.21709	+	1.27298i	0.951057	+	0.309017i	$0.100000\pi$
$109$	1.21709	+	1.27298i	1.21709	+	1.27298i	0.266037	+	0.963963i	$0.414286\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.35341	+	1.29399i	−1.35341	+	1.29399i	−0.433884	+	0.900969i	$0.642857\pi$
$113$	−1.35341	+	1.29399i	−1.35341	+	1.29399i	−0.919528	+	0.393025i	$0.871429\pi$
$114$		0			0
$115$		0			0
$116$	0.974928	−	0.222521i	0.974928	−	0.222521i
$117$	−1.62376	−	0.257179i	−1.62376	−	0.257179i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.657939	+	0.753071i	0.657939	+	0.753071i
$122$	0.742901	+	1.85203i	0.742901	+	1.85203i
$123$		0			0
$124$		0			0
$125$	−0.0896393	−	0.995974i	−0.0896393	−	0.995974i
$126$		0			0
$127$		0			0		−0.351375	−	0.936235i	$-0.614286\pi$
$127$		0			0		0.351375	+	0.936235i	$0.385714\pi$
$128$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$129$		0			0
$130$	−1.21347	+	1.10916i	−1.21347	+	1.10916i
$131$		0			0		0.997735	−	0.0672690i	$-0.0214286\pi$
$131$		0			0		−0.997735	+	0.0672690i	$0.978571\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.0987640	−	0.149621i	−0.0987640	−	0.149621i
$137$	−0.186957	+	0.498146i	−0.186957	+	0.498146i	−0.995974	−	0.0896393i	$-0.971429\pi$
$137$	−0.186957	+	0.498146i	−0.186957	+	0.498146i	0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$139$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$145$	0.691063	−	0.722795i	0.691063	−	0.722795i
$146$	1.21850	+	0.885289i	1.21850	+	0.885289i
$147$		0			0
$148$	−0.185527	−	1.36962i	−0.185527	−	1.36962i
$149$	−0.708207	−	0.341054i	−0.708207	−	0.341054i	0.0448648	−	0.998993i	$-0.485714\pi$
$149$	−0.708207	−	0.341054i	−0.708207	−	0.341054i	−0.753071	+	0.657939i	$0.771429\pi$
$150$		0			0
$151$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$151$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$152$		0			0
$153$	−0.0476947	−	0.172818i	−0.0476947	−	0.172818i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.66915			1.66915			0.834573	−	0.550897i	$-0.185714\pi$
$157$	1.66915			1.66915			0.834573	+	0.550897i	$0.185714\pi$
$158$		0			0
$159$		0			0
$160$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$161$		0			0
$162$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$163$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$163$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$164$	−0.0429801	−	1.91502i	−0.0429801	−	1.91502i
$165$		0			0
$166$		0			0
$167$		0			0		−0.287599	−	0.957751i	$-0.592857\pi$
$167$		0			0		0.287599	+	0.957751i	$0.407143\pi$
$168$		0			0
$169$	1.56573	−	0.669223i	1.56573	−	0.669223i
$170$	−0.164852	−	0.0704610i	−0.164852	−	0.0704610i
$171$		0			0
$172$		0			0
$173$	−1.36795	+	0.697007i	−1.36795	+	0.697007i	−0.974928	−	0.222521i	$-0.928571\pi$
$173$	−1.36795	+	0.697007i	−1.36795	+	0.697007i	−0.393025	+	0.919528i	$0.628571\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.237878	−	0.792172i	0.237878	−	0.792172i
$179$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$179$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$180$	−0.351375	+	0.936235i	−0.351375	+	0.936235i
$181$	−0.522106	+	0.970235i	−0.522106	+	0.970235i	0.473869	+	0.880596i	$0.342857\pi$
$181$	−0.522106	+	0.970235i	−0.522106	+	0.970235i	−0.995974	+	0.0896393i	$0.971429\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.909354	−	1.04084i	−0.909354	−	1.04084i
$186$		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
$193$	−0.0808436	−	0.0389322i	−0.0808436	−	0.0389322i	0.393025	−	0.919528i	$-0.371429\pi$
$193$	−0.0808436	−	0.0389322i	−0.0808436	−	0.0389322i	−0.473869	+	0.880596i	$0.657143\pi$
$194$	−1.97990	−	0.0889176i	−1.97990	−	0.0889176i
$195$		0			0
$196$	0.178557	−	0.983930i	0.178557	−	0.983930i
$197$	1.25234	−	0.502351i	1.25234	−	0.502351i	0.351375	−	0.936235i	$-0.385714\pi$
$197$	1.25234	−	0.502351i	1.25234	−	0.502351i	0.900969	+	0.433884i	$0.142857\pi$
$198$		0			0
$199$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$199$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$200$	0.512899	+	0.858449i	0.512899	+	0.858449i
$201$		0			0
$202$	−0.826696	−	1.62248i	−0.826696	−	1.62248i
$203$		0			0
$204$		0			0
$205$	−1.09085	−	1.57455i	−1.09085	−	1.57455i
$206$		0			0
$207$		0			0
$208$	0.612052	−	1.52582i	0.612052	−	1.52582i
$209$		0			0
$210$		0			0
$211$		0			0		−0.979675	−	0.200589i	$-0.935714\pi$
$211$		0			0		0.979675	+	0.200589i	$0.0642857\pi$
$212$	0.122494	−	0.0556393i	0.122494	−	0.0556393i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−1.71703	+	0.391902i	−1.71703	+	0.391902i
$219$		0			0
$220$		0			0
$221$	0.217549	+	0.198849i	0.217549	+	0.198849i
$222$		0			0
$223$		0			0		−0.979675	−	0.200589i	$-0.935714\pi$
$223$		0			0		0.979675	+	0.200589i	$0.0642857\pi$
$224$		0			0
$225$	0.222521	+	0.974928i	0.222521	+	0.974928i
$226$	−0.416664	−	1.82552i	−0.416664	−	1.82552i
$227$		0			0		−0.244340	−	0.969690i	$-0.578571\pi$
$227$		0			0		0.244340	+	0.969690i	$0.421429\pi$
$228$		0			0
$229$	−1.05709	−	1.52582i	−1.05709	−	1.52582i	−0.834573	−	0.550897i	$-0.814286\pi$
$229$	−1.05709	−	1.52582i	−1.05709	−	1.52582i	−0.222521	−	0.974928i	$-0.571429\pi$
$230$		0			0
$231$		0			0
$232$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$233$	0.230935	−	1.45806i	0.230935	−	1.45806i	−0.550897	−	0.834573i	$-0.685714\pi$
$233$	0.230935	−	1.45806i	0.230935	−	1.45806i	0.781831	−	0.623490i	$-0.214286\pi$
$234$	1.05360	−	1.26201i	1.05360	−	1.26201i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$239$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$240$		0			0
$241$	0.699921	−	1.86493i	0.699921	−	1.86493i	0.266037	−	0.963963i	$-0.414286\pi$
$241$	0.699921	−	1.86493i	0.699921	−	1.86493i	0.433884	−	0.900969i	$-0.357143\pi$
$242$	−0.983930	+	0.178557i	−0.983930	+	0.178557i
$243$		0			0
$244$	−1.97090	−	0.312160i	−1.97090	−	0.312160i
$245$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.900969	+	0.433884i	0.900969	+	0.433884i
$251$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$251$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$257$	−0.376178	−	1.07505i	−0.376178	−	1.07505i	−0.963963	−	0.266037i	$-0.914286\pi$
$257$	−0.376178	−	1.07505i	−0.376178	−	1.07505i	0.587785	−	0.809017i	$-0.300000\pi$
$258$		0			0
$259$		0			0
$260$	−0.329770	−	1.61059i	−0.329770	−	1.61059i
$261$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$262$		0			0
$263$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$263$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$264$		0			0
$265$	0.0715785	−	0.113917i	0.0715785	−	0.113917i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.28394	−	1.17358i	1.28394	−	1.17358i	0.309017	−	0.951057i	$-0.400000\pi$
$269$	1.28394	−	1.17358i	1.28394	−	1.17358i	0.974928	−	0.222521i	$-0.0714286\pi$
$270$		0			0
$271$		0			0		−0.957751	−	0.287599i	$-0.907143\pi$
$271$		0			0		0.957751	+	0.287599i	$0.0928571\pi$
$272$	0.179098	−	0.00804330i	0.179098	−	0.00804330i
$273$		0			0
$274$	−0.331743	−	0.415992i	−0.331743	−	0.415992i
$275$		0			0
$276$		0			0
$277$	−0.444933	−	0.202098i	−0.444933	−	0.202098i	0.178557	−	0.983930i	$-0.442857\pi$
$277$	−0.444933	−	0.202098i	−0.444933	−	0.202098i	−0.623490	+	0.781831i	$0.714286\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.0160218	+	0.356754i	−0.0160218	+	0.356754i	0.974928	+	0.222521i	$0.0714286\pi$
$281$	−0.0160218	+	0.356754i	−0.0160218	+	0.356754i	−0.990950	+	0.134233i	$0.957143\pi$
$282$		0			0
$283$		0			0		0.957751	−	0.287599i	$-0.0928571\pi$
$283$		0			0		−0.957751	+	0.287599i	$0.907143\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0896393	−	0.995974i	−0.0896393	−	0.995974i
$289$	0.299085	−	0.920489i	0.299085	−	0.920489i
$290$	0.266037	+	0.963963i	0.266037	+	0.963963i
$291$		0			0
$292$	−1.38494	+	0.591952i	−1.38494	+	0.591952i
$293$	−1.30243	+	0.627218i	−1.30243	+	0.627218i	−0.951057	−	0.309017i	$-0.900000\pi$
$293$	−1.30243	+	0.627218i	−1.30243	+	0.627218i	−0.351375	+	0.936235i	$0.614286\pi$
$294$		0			0
$295$		0			0
$296$	1.27090	+	0.543210i	1.27090	+	0.543210i
$297$		0			0
$298$	0.656016	−	0.433033i	0.656016	−	0.433033i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.81683	+	0.825243i	−1.81683	+	0.825243i
$306$	0.172818	+	0.0476947i	0.172818	+	0.0476947i
$307$		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		0.200589	−	0.979675i	$-0.435714\pi$
$311$		0			0		−0.200589	+	0.979675i	$0.564286\pi$
$312$		0			0
$313$	−0.413778	+	1.64212i	−0.413778	+	1.64212i	0.309017	+	0.951057i	$0.400000\pi$
$313$	−0.413778	+	1.64212i	−0.413778	+	1.64212i	−0.722795	+	0.691063i	$0.757143\pi$
$314$	−0.856104	+	1.43288i	−0.856104	+	1.43288i
$315$		0			0
$316$		0			0
$317$	0.174913	+	0.409228i	0.174913	+	0.409228i	0.983930	−	0.178557i	$-0.0571429\pi$
$317$	0.174913	+	0.409228i	0.174913	+	0.409228i	−0.809017	+	0.587785i	$0.800000\pi$
$318$		0			0
$319$		0			0
$320$	−0.834573	−	0.550897i	−0.834573	−	0.550897i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.222521	−	0.974928i	0.222521	−	0.974928i
$325$	−1.16249	−	1.16249i	−1.16249	−	1.16249i
$326$		0			0
$327$		0			0
$328$	1.66599	+	0.945316i	1.66599	+	0.945316i
$329$		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
$333$	1.04084	+	0.909354i	1.04084	+	0.909354i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.478050	+	0.724216i	−0.478050	+	0.724216i	−0.990950	−	0.134233i	$-0.957143\pi$
$337$	−0.478050	+	0.724216i	−0.478050	+	0.724216i	0.512899	+	0.858449i	$0.328571\pi$
$338$	−0.228566	+	1.68734i	−0.228566	+	1.68734i
$339$		0			0
$340$	0.145039	−	0.105377i	0.145039	−	0.105377i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.103277	−	1.53181i	0.103277	−	1.53181i
$347$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$347$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$348$		0			0
$349$		−	1.71690i		−	1.71690i	−0.512899	−	0.858449i	$-0.671429\pi$
$349$		−	1.71690i		−	1.71690i	0.512899	−	0.858449i	$-0.328571\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.88349	+	0.126988i	1.88349	+	0.126988i	0.963963	−	0.266037i	$-0.0857143\pi$
$353$	1.88349	+	0.126988i	1.88349	+	0.126988i	0.919528	+	0.393025i	$0.128571\pi$
$354$		0			0
$355$		0			0
$356$	0.558031	+	0.610511i	0.558031	+	0.610511i
$357$		0			0
$358$		0			0
$359$		0			0		−0.200589	−	0.979675i	$-0.564286\pi$
$359$		0			0		0.200589	+	0.979675i	$0.435714\pi$
$360$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$361$	−0.351375	−	0.936235i	−0.351375	−	0.936235i
$362$	−0.565109	−	0.945834i	−0.565109	−	0.945834i
$363$		0			0
$364$		0			0
$365$	−0.829730	+	1.25699i	−0.829730	+	1.25699i
$366$		0			0
$367$		0			0		−0.178557	−	0.983930i	$-0.557143\pi$
$367$		0			0		0.178557	+	0.983930i	$0.442857\pi$
$368$		0			0
$369$	1.29233	+	1.41387i	1.29233	+	1.41387i
$370$	1.35991	−	0.246788i	1.35991	−	0.246788i
$371$		0			0
$372$		0			0
$373$	0.0445940	+	1.98692i	0.0445940	+	1.98692i	0.134233	+	0.990950i	$0.457143\pi$
$373$	0.0445940	+	1.98692i	0.0445940	+	1.98692i	−0.0896393	+	0.995974i	$0.528571\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.110591	−	1.64028i	0.110591	−	1.64028i
$378$		0			0
$379$		0			0		0.0672690	−	0.997735i	$-0.478571\pi$
$379$		0			0		−0.0672690	+	0.997735i	$0.521429\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.0672690	−	0.997735i	$-0.521429\pi$
$383$		0			0		0.0672690	+	0.997735i	$0.478571\pi$
$384$		0			0
$385$		0			0
$386$	0.0748860	−	0.0494318i	0.0748860	−	0.0494318i
$387$		0			0
$388$	1.09182	−	1.65404i	1.09182	−	1.65404i
$389$	−0.663432	+	0.338036i	−0.663432	+	0.338036i	−0.753071	−	0.657939i	$-0.771429\pi$
$389$	−0.663432	+	0.338036i	−0.663432	+	0.338036i	0.0896393	+	0.995974i	$0.471429\pi$
$390$		0			0
$391$		0			0
$392$	0.753071	+	0.657939i	0.753071	+	0.657939i
$393$		0			0
$394$	−0.211083	+	1.33273i	−0.211083	+	1.33273i
$395$		0			0
$396$		0			0
$397$	0.925460	+	0.525124i	0.925460	+	0.525124i	0.880596	−	0.473869i	$-0.157143\pi$
$397$	0.925460	+	0.525124i	0.925460	+	0.525124i	0.0448648	+	0.998993i	$0.485714\pi$
$398$		0			0
$399$		0			0
$400$	−1.00000			−1.00000
$401$	0.210891	−	0.923976i	0.210891	−	0.923976i	−0.753071	−	0.657939i	$-0.771429\pi$
$401$	0.210891	−	0.923976i	0.210891	−	0.923976i	0.963963	−	0.266037i	$-0.0857143\pi$
$402$		0			0
$403$		0			0
$404$	1.81683	+	0.122494i	1.81683	+	0.122494i
$405$	−0.351375	−	0.936235i	−0.351375	−	0.936235i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.401078	−	0.00900168i	−0.401078	−	0.00900168i	−0.178557	−	0.983930i	$-0.557143\pi$
$409$	−0.401078	−	0.00900168i	−0.401078	−	0.00900168i	−0.222521	+	0.974928i	$0.571429\pi$
$410$	1.91116	−	0.128854i	1.91116	−	0.128854i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.995921	+	1.30801i	0.995921	+	1.30801i
$417$		0			0
$418$		0			0
$419$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$419$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$420$		0			0
$421$	0.338036	+	0.842711i	0.338036	+	0.842711i	0.995974	+	0.0896393i	$0.0285714\pi$
$421$	0.338036	+	0.842711i	0.338036	+	0.842711i	−0.657939	+	0.753071i	$0.728571\pi$
$422$		0			0
$423$		0			0
$424$	−0.0150635	+	0.133692i	−0.0150635	+	0.133692i
$425$	0.0629940	−	0.167847i	0.0629940	−	0.167847i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$431$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$432$		0			0
$433$	−1.08097	+	0.462029i	−1.08097	+	0.462029i	−0.858449	−	0.512899i	$-0.828571\pi$
$433$	−1.08097	+	0.462029i	−1.08097	+	0.462029i	−0.222521	+	0.974928i	$0.571429\pi$
$434$		0			0
$435$		0			0
$436$	0.544238	−	1.67499i	0.544238	−	1.67499i
$437$		0			0
$438$		0			0
$439$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$439$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$440$		0			0
$441$	0.512899	+	0.858449i	0.512899	+	0.858449i
$442$	−0.282282	+	0.0847655i	−0.282282	+	0.0847655i
$443$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$443$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$444$		0			0
$445$	0.802047	+	0.202098i	0.802047	+	0.202098i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.64212	−	1.03181i	−1.64212	−	1.03181i	−0.951057	−	0.309017i	$-0.900000\pi$
$449$	−1.64212	−	1.03181i	−1.64212	−	1.03181i	−0.691063	−	0.722795i	$-0.742857\pi$
$450$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$451$		0			0
$452$	1.78082	+	0.578625i	1.78082	+	0.578625i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0739590	−	0.211363i	0.0739590	−	0.211363i	−0.900969	−	0.433884i	$-0.857143\pi$
$457$	0.0739590	−	0.211363i	0.0739590	−	0.211363i	0.974928	+	0.222521i	$0.0714286\pi$
$458$	1.85203	−	0.124867i	1.85203	−	0.124867i
$459$		0			0
$460$		0			0
$461$	−1.41781	−	1.07953i	−1.41781	−	1.07953i	−0.983930	−	0.178557i	$-0.942857\pi$
$461$	−1.41781	−	1.07953i	−1.41781	−	1.07953i	−0.433884	−	0.900969i	$-0.642857\pi$
$462$		0			0
$463$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$463$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$464$	−0.657939	−	0.753071i	−0.657939	−	0.753071i
$465$		0			0
$466$	1.13323	+	0.946085i	1.13323	+	0.946085i
$467$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$467$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$468$	0.542980	+	1.55175i	0.542980	+	1.55175i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.0556393	+	0.122494i	−0.0556393	+	0.122494i
$478$		0			0
$479$		0			0		0.928115	−	0.372294i	$-0.121429\pi$
$479$		0			0		−0.928115	+	0.372294i	$0.878571\pi$
$480$		0			0
$481$	−2.24424	−	0.355453i	−2.24424	−	0.355453i
$482$	1.24196	+	1.55737i	1.24196	+	1.55737i
$483$		0			0
$484$	0.351375	−	0.936235i	0.351375	−	0.936235i
$485$		−	1.98190i		−	1.98190i
$486$		0			0
$487$		0			0		−0.969690	−	0.244340i	$-0.921429\pi$
$487$		0			0		0.969690	+	0.244340i	$0.0785714\pi$
$488$	1.27885	−	1.53181i	1.27885	−	1.53181i
$489$		0			0
$490$	0.990950	+	0.134233i	0.990950	+	0.134233i
$491$		0			0		0.640876	−	0.767645i	$-0.278571\pi$
$491$		0			0		−0.640876	+	0.767645i	$0.721429\pi$
$492$		0			0
$493$	0.167847	−	0.0629940i	0.167847	−	0.0629940i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$499$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$500$	−0.834573	+	0.550897i	−0.834573	+	0.550897i
$501$		0			0
$502$		0			0
$503$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$503$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$504$		0			0
$505$	1.58376	−	0.898656i	1.58376	−	0.898656i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.224055	−	0.147897i	−0.224055	−	0.147897i	0.433884	−	0.900969i	$-0.357143\pi$
$509$	−0.224055	−	0.147897i	−0.224055	−	0.147897i	−0.657939	+	0.753071i	$0.728571\pi$
$510$		0			0
$511$		0			0
$512$	0.990950	+	0.134233i	0.990950	+	0.134233i
$513$		0			0
$514$	1.11582	+	0.228465i	1.11582	+	0.228465i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.55175	+	0.542980i	1.55175	+	0.542980i
$521$	−1.13321	+	1.55972i	−1.13321	+	1.55972i	−0.351375	+	0.936235i	$0.614286\pi$
$521$	−1.13321	+	1.55972i	−1.13321	+	1.55972i	−0.781831	+	0.623490i	$0.785714\pi$
$522$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$523$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$523$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.178557	−	0.983930i	0.178557	−	0.983930i
$530$	0.0610790	+	0.119874i	0.0610790	+	0.119874i
$531$		0			0
$532$		0			0
$533$	−3.03561	−	0.837775i	−3.03561	−	0.837775i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.348922	+	1.70413i	0.348922	+	1.70413i
$539$		0			0
$540$		0			0
$541$	−0.963963	+	0.733963i	−0.963963	+	0.733963i	−0.963963	−	0.266037i	$-0.914286\pi$
$541$	−0.963963	+	0.733963i	−0.963963	+	0.733963i			1.00000i	$0.5\pi$
$542$		0			0
$543$		0			0
$544$	−0.0849545	+	0.157872i	−0.0849545	+	0.157872i
$545$	−0.468542	−	1.69772i	−0.468542	−	1.69772i
$546$		0			0
$547$		0			0		0.287599	−	0.957751i	$-0.407143\pi$
$547$		0			0		−0.287599	+	0.957751i	$0.592857\pi$
$548$	0.527258	−	0.0714220i	0.527258	−	0.0714220i
$549$	1.68961	−	1.06165i	1.68961	−	1.06165i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.401697	−	0.278296i	0.401697	−	0.278296i
$555$		0			0
$556$		0			0
$557$	−0.0379977	−	0.0238755i	−0.0379977	−	0.0238755i	0.512899	−	0.858449i	$-0.328571\pi$
$557$	−0.0379977	−	0.0238755i	−0.0379977	−	0.0238755i	−0.550897	+	0.834573i	$0.685714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.298038	−	0.196733i	−0.298038	−	0.196733i
$563$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$563$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$564$		0			0
$565$	1.80499	−	0.498146i	1.80499	−	0.498146i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.0221467	−	0.0390306i	−0.0221467	−	0.0390306i	0.858449	−	0.512899i	$-0.171429\pi$
$569$	−0.0221467	−	0.0390306i	−0.0221467	−	0.0390306i	−0.880596	+	0.473869i	$0.842857\pi$
$570$		0			0
$571$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$571$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.900969	+	0.433884i	0.900969	+	0.433884i
$577$	−0.241880	−	1.78563i	−0.241880	−	1.78563i	−0.550897	−	0.834573i	$-0.685714\pi$
$577$	−0.241880	−	1.78563i	−0.241880	−	1.78563i	0.309017	−	0.951057i	$-0.400000\pi$
$578$	0.636792	+	0.728867i	0.636792	+	0.728867i
$579$		0			0
$580$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.202174	−	1.49251i	0.202174	−	1.49251i
$585$	1.30801	+	0.995921i	1.30801	+	0.995921i
$586$	0.129582	−	1.43977i	0.129582	−	1.43977i
$587$		0			0		0.0224381	−	0.999748i	$-0.492857\pi$
$587$		0			0		−0.0224381	+	0.999748i	$0.507143\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.11816	+	0.812393i	−1.11816	+	0.812393i
$593$	0.217142	−	1.92718i	0.217142	−	1.92718i	−0.134233	−	0.990950i	$-0.542857\pi$
$593$	0.217142	−	1.92718i	0.217142	−	1.92718i	0.351375	−	0.936235i	$-0.385714\pi$
$594$		0			0
$595$		0			0
$596$	0.0352660	+	0.785259i	0.0352660	+	0.785259i
$597$		0			0
$598$		0			0
$599$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$599$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$600$		0			0
$601$	−1.96296	+	0.221172i	−1.96296	+	0.221172i	−0.998993	−	0.0448648i	$-0.985714\pi$
$601$	−1.96296	+	0.221172i	−1.96296	+	0.221172i	−0.963963	+	0.266037i	$0.914286\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$606$		0			0
$607$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$607$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$608$		0			0
$609$		0			0
$610$	0.223422	−	1.98292i	0.223422	−	1.98292i
$611$		0			0
$612$	−0.129582	+	0.123893i	−0.129582	+	0.123893i
$613$	0.963963	−	0.733963i	0.963963	−	0.733963i		−	1.00000i	$-0.5\pi$
$613$	0.963963	−	0.733963i	0.963963	−	0.733963i	0.963963	+	0.266037i	$0.0857143\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.0896393	+	1.99597i	−0.0896393	+	1.99597i			1.00000i	$0.5\pi$
$617$	−0.0896393	+	1.99597i	−0.0896393	+	1.99597i	−0.0896393	+	0.995974i	$0.528571\pi$
$618$		0			0
$619$		0			0		−0.822002	−	0.569484i	$-0.807143\pi$
$619$		0			0		0.822002	+	0.569484i	$0.192857\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$626$	−1.19745	−	1.19745i	−1.19745	−	1.19745i
$627$		0			0
$628$	−0.790956	−	1.46984i	−0.790956	−	1.46984i
$629$	−0.0659201	−	0.238856i	−0.0659201	−	0.238856i
$630$		0			0
$631$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$631$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$632$		0			0
$633$		0			0
$634$	−0.441014	−	0.0597394i	−0.441014	−	0.0597394i
$635$		0			0
$636$		0			0
$637$	−1.46482	−	0.746362i	−1.46482	−	0.746362i
$638$		0			0
$639$		0			0
$640$	0.900969	−	0.433884i	0.900969	−	0.433884i
$641$	−0.0317322	+	1.41386i	−0.0317322	+	1.41386i	0.691063	+	0.722795i	$0.257143\pi$
$641$	−0.0317322	+	1.41386i	−0.0317322	+	1.41386i	−0.722795	+	0.691063i	$0.757143\pi$
$642$		0			0
$643$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$643$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.493508	−	0.869741i	$-0.335714\pi$
$647$		0			0		−0.493508	+	0.869741i	$0.664286\pi$
$648$	0.722795	+	0.691063i	0.722795	+	0.691063i
$649$		0			0
$650$	1.59417	−	0.401697i	1.59417	−	0.401697i
$651$		0			0
$652$		0			0
$653$	−0.246862	−	0.105514i	−0.246862	−	0.105514i	0.266037	−	0.963963i	$-0.414286\pi$
$653$	−0.246862	−	0.105514i	−0.246862	−	0.105514i	−0.512899	+	0.858449i	$0.671429\pi$
$654$		0			0
$655$		0			0
$656$	−1.66599	+	0.945316i	−1.66599	+	0.945316i
$657$	0.653491	−	1.35699i	0.653491	−	1.35699i
$658$		0			0
$659$		0			0		0.910478	−	0.413559i	$-0.135714\pi$
$659$		0			0		−0.910478	+	0.413559i	$0.864286\pi$
$660$		0			0
$661$	1.79468	+	0.161524i	1.79468	+	0.161524i	0.936235	−	0.351375i	$-0.114286\pi$
$661$	1.79468	+	0.161524i	1.79468	+	0.161524i	0.858449	+	0.512899i	$0.171429\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−1.31448	+	0.427100i	−1.31448	+	0.427100i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.25570	−	1.50409i	−1.25570	−	1.50409i	−0.781831	−	0.623490i	$-0.785714\pi$
$673$	−1.25570	−	1.50409i	−1.25570	−	1.50409i	−0.473869	−	0.880596i	$-0.657143\pi$
$674$	−0.376510	−	0.781831i	−0.376510	−	0.781831i
$675$		0			0
$676$	−1.33126	−	1.06165i	−1.33126	−	1.06165i
$677$	1.08059	−	1.13021i	1.08059	−	1.13021i	0.0896393	−	0.995974i	$-0.471429\pi$
$677$	1.08059	−	1.13021i	1.08059	−	1.13021i	0.990950	−	0.134233i	$-0.0428571\pi$
$678$		0			0
$679$		0			0
$680$	0.0160704	+	0.178557i	0.0160704	+	0.178557i
$681$		0			0
$682$		0			0
$683$		0			0		0.869741	−	0.493508i	$-0.164286\pi$
$683$		0			0		−0.869741	+	0.493508i	$0.835714\pi$
$684$		0			0
$685$	0.400690	−	0.350072i	0.400690	−	0.350072i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0296899	−	0.219179i	−0.0296899	−	0.219179i
$690$		0			0
$691$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$691$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$692$	1.26201	+	0.874324i	1.26201	+	0.874324i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.0537209	−	0.339181i	−0.0537209	−	0.339181i
$698$	1.47387	+	0.880596i	1.47387	+	0.880596i
$699$		0			0
$700$		0			0
$701$	1.79295	+	0.409228i	1.79295	+	0.409228i	0.983930	−	0.178557i	$-0.0571429\pi$
$701$	1.79295	+	0.409228i	1.79295	+	0.409228i	0.809017	+	0.587785i	$0.200000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.07505	+	1.55175i	−1.07505	+	1.55175i
$707$		0			0
$708$		0			0
$709$	−1.10068	+	1.66747i	−1.10068	+	1.66747i	−0.512899	+	0.858449i	$0.671429\pi$
$709$	−1.10068	+	1.66747i	−1.10068	+	1.66747i	−0.587785	+	0.809017i	$0.700000\pi$
$710$		0			0
$711$		0			0
$712$	−0.810306	+	0.165911i	−0.810306	+	0.165911i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.657939	−	0.753071i	$-0.271429\pi$
$719$		0			0		−0.657939	+	0.753071i	$0.728571\pi$
$720$	0.990950	−	0.134233i	0.990950	−	0.134233i
$721$		0			0
$722$	0.983930	+	0.178557i	0.983930	+	0.178557i
$723$		0			0
$724$	1.10179			1.10179
$725$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$726$		0			0
$727$		0			0		0.512899	−	0.858449i	$-0.328571\pi$
$727$		0			0		−0.512899	+	0.858449i	$0.671429\pi$
$728$		0			0
$729$	0.473869	+	0.880596i	0.473869	+	0.880596i
$730$	−0.653491	−	1.35699i	−0.653491	−	1.35699i
$731$		0			0
$732$		0			0
$733$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$733$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−1.87657	+	0.384229i	−1.87657	+	0.384229i
$739$		0			0		0.767645	−	0.640876i	$-0.221429\pi$
$739$		0			0		−0.767645	+	0.640876i	$0.778571\pi$
$740$	−0.485644	+	1.29399i	−0.485644	+	1.29399i
$741$		0			0
$742$		0			0
$743$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$743$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$744$		0			0
$745$	0.462029	+	0.635928i	0.462029	+	0.635928i
$746$	−1.72854	−	0.980810i	−1.72854	−	0.980810i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$751$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$752$		0			0
$753$		0			0
$754$	1.35137	+	0.936235i	1.35137	+	0.936235i
$755$		0			0
$756$		0			0
$757$	0.836496	+	1.73700i	0.836496	+	1.73700i	0.657939	+	0.753071i	$0.271429\pi$
$757$	0.836496	+	1.73700i	0.836496	+	1.73700i	0.178557	+	0.983930i	$0.442857\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.268196	+	1.97990i	0.268196	+	1.97990i	0.178557	+	0.983930i	$0.442857\pi$
$761$	0.268196	+	1.97990i	0.268196	+	1.97990i	0.0896393	+	0.995974i	$0.471429\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.0398932	+	0.174784i	−0.0398932	+	0.174784i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.0150635	+	0.223422i	0.0150635	+	0.223422i	0.998993	+	0.0448648i	$0.0142857\pi$
$769$	0.0150635	+	0.223422i	0.0150635	+	0.223422i	−0.983930	+	0.178557i	$0.942857\pi$
$770$		0			0
$771$		0			0
$772$	0.00402571	+	0.0896393i	0.00402571	+	0.0896393i
$773$	1.33232	−	1.39349i	1.33232	−	1.39349i	0.473869	−	0.880596i	$-0.342857\pi$
$773$	1.33232	−	1.39349i	1.33232	−	1.39349i	0.858449	−	0.512899i	$-0.171429\pi$
$774$		0			0
$775$		0			0
$776$	0.859914	+	1.78563i	0.859914	+	1.78563i
$777$		0			0
$778$	0.0500876	−	0.742901i	0.0500876	−	0.742901i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$785$	−1.46984	−	0.790956i	−1.46984	−	0.790956i
$786$		0			0
$787$		0			0		−0.605790	−	0.795625i	$-0.707143\pi$
$787$		0			0		0.605790	+	0.795625i	$0.292857\pi$
$788$	−1.03581	−	0.864760i	−1.03581	−	0.864760i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.42338	+	2.95568i	−1.42338	+	2.95568i
$794$	−0.925460	+	0.525124i	−0.925460	+	0.525124i
$795$		0			0
$796$		0			0
$797$	−0.871471	−	0.372484i	−0.871471	−	0.372484i	−0.0896393	−	0.995974i	$-0.528571\pi$
$797$	−0.871471	−	0.372484i	−0.871471	−	0.372484i	−0.781831	+	0.623490i	$0.785714\pi$
$798$		0			0
$799$		0			0
$800$	0.512899	−	0.858449i	0.512899	−	0.858449i
$801$	−0.821916	−	0.0926077i	−0.821916	−	0.0926077i
$802$	0.685020	+	0.654946i	0.685020	+	0.654946i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.03701	+	1.49683i	−1.03701	+	1.49683i
$809$	−0.0357045	+	1.59085i	−0.0357045	+	1.59085i	0.587785	+	0.809017i	$0.300000\pi$
$809$	−0.0357045	+	1.59085i	−0.0357045	+	1.59085i	−0.623490	+	0.781831i	$0.714286\pi$
$810$	0.983930	+	0.178557i	0.983930	+	0.178557i
$811$		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
$818$	0.213440	−	0.339688i	0.213440	−	0.339688i
$819$		0			0
$820$	−0.869620	+	1.70672i	−0.869620	+	1.70672i
$821$	−0.518733	−	1.87959i	−0.518733	−	1.87959i	−0.473869	−	0.880596i	$-0.657143\pi$
$821$	−0.518733	−	1.87959i	−0.518733	−	1.87959i	−0.0448648	−	0.998993i	$-0.514286\pi$
$822$		0			0
$823$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$823$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$827$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$828$		0			0
$829$	−0.568117	+	0.0899809i	−0.568117	+	0.0899809i	−0.433884	−	0.900969i	$-0.642857\pi$
$829$	−0.568117	+	0.0899809i	−0.568117	+	0.0899809i	−0.134233	+	0.990950i	$0.542857\pi$
$830$		0			0
$831$		0			0
$832$	−1.63367	+	0.184070i	−1.63367	+	0.184070i
$833$	0.00804330	−	0.179098i	0.00804330	−	0.179098i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.244340	−	0.969690i	$-0.578571\pi$
$839$		0			0		0.244340	+	0.969690i	$0.421429\pi$
$840$		0			0
$841$	−0.858449	−	0.512899i	−0.858449	−	0.512899i
$842$	−0.896802	−	0.142040i	−0.896802	−	0.142040i
$843$		0			0
$844$		0			0
$845$	−1.69589	−	0.152633i	−1.69589	−	0.152633i
$846$		0			0
$847$		0			0
$848$	−0.107042	−	0.0815018i	−0.107042	−	0.0815018i
$849$		0			0
$850$	0.111778	+	0.140166i	0.111778	+	0.140166i
$851$		0			0
$852$		0			0
$853$	−1.17439	+	1.61640i	−1.17439	+	1.61640i	−0.550897	+	0.834573i	$0.685714\pi$
$853$	−1.17439	+	1.61640i	−1.17439	+	1.61640i	−0.623490	+	0.781831i	$0.714286\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.158342	−	1.40532i	0.158342	−	1.40532i	−0.623490	−	0.781831i	$-0.714286\pi$
$857$	0.158342	−	1.40532i	0.158342	−	1.40532i	0.781831	−	0.623490i	$-0.214286\pi$
$858$		0			0
$859$		0			0		0.979675	−	0.200589i	$-0.0642857\pi$
$859$		0			0		−0.979675	+	0.200589i	$0.935714\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.0224381	−	0.999748i	$-0.492857\pi$
$863$		0			0		−0.0224381	+	0.999748i	$0.507143\pi$
$864$		0			0
$865$	1.53490	+	0.0344489i	1.53490	+	0.0344489i
$866$	0.157801	−	1.16493i	0.157801	−	1.16493i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.15876	+	1.32630i	1.15876	+	1.32630i
$873$	0.266037	+	1.96396i	0.266037	+	1.96396i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.19666	−	1.57166i	1.19666	−	1.57166i	0.473869	−	0.880596i	$-0.342857\pi$
$877$	1.19666	−	1.57166i	1.19666	−	1.57166i	0.722795	−	0.691063i	$-0.242857\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.525124	+	0.925460i	0.525124	+	0.925460i	0.998993	+	0.0448648i	$0.0142857\pi$
$881$	0.525124	+	0.925460i	0.525124	+	0.925460i	−0.473869	+	0.880596i	$0.657143\pi$
$882$	−1.00000			−1.00000
$883$		0			0		−0.493508	−	0.869741i	$-0.664286\pi$
$883$		0			0		0.493508	+	0.869741i	$0.335714\pi$
$884$	0.0720156	−	0.285801i	0.0720156	−	0.285801i
$885$		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
$890$	−0.584860	+	0.584860i	−0.584860	+	0.584860i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.72800	−	0.880460i	1.72800	−	0.880460i
$899$		0			0
$900$	0.753071	−	0.657939i	0.753071	−	0.657939i
$901$	0.0204228	−	0.0128325i	0.0204228	−	0.0128325i
$902$		0			0
$903$		0			0
$904$	−1.41010	+	1.23197i	−1.41010	+	1.23197i
$905$	0.919528	−	0.606975i	0.919528	−	0.606975i
$906$		0			0
$907$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$907$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$908$		0			0
$909$	−1.44880	+	1.10312i	−1.44880	+	1.10312i
$910$		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
$914$	0.143511	+	0.171898i	0.143511	+	0.171898i
$915$		0			0
$916$	−0.842711	+	1.65391i	−0.842711	+	1.65391i
$917$		0			0
$918$		0			0
$919$		0			0		−0.998993	−	0.0448648i	$-0.985714\pi$
$919$		0			0		0.998993	+	0.0448648i	$0.0142857\pi$
$920$		0			0
$921$		0			0
$922$	1.65391	−	0.663432i	1.65391	−	0.663432i
$923$		0			0
$924$		0			0
$925$	0.307552	+	1.34747i	0.307552	+	1.34747i
$926$		0			0
$927$		0			0
$928$	0.983930	−	0.178557i	0.983930	−	0.178557i
$929$	0.849696	−	1.16951i	0.849696	−	1.16951i	−0.134233	−	0.990950i	$-0.542857\pi$
$929$	0.849696	−	1.16951i	0.849696	−	1.16951i	0.983930	−	0.178557i	$-0.0571429\pi$
$930$		0			0
$931$		0			0
$932$	−1.39340	+	0.487571i	−1.39340	+	0.487571i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−1.61059	−	0.329770i	−1.61059	−	0.329770i
$937$	1.78394	−	0.810306i	1.78394	−	0.810306i	0.809017	−	0.587785i	$-0.200000\pi$
$937$	1.78394	−	0.810306i	1.78394	−	0.810306i	0.974928	−	0.222521i	$-0.0714286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.58745	+	1.04787i	1.58745	+	1.04787i	0.963963	+	0.266037i	$0.0857143\pi$
$941$	1.58745	+	1.04787i	1.58745	+	1.04787i	0.623490	+	0.781831i	$0.285714\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.880596	−	0.473869i	$-0.157143\pi$
$947$		0			0		−0.880596	+	0.473869i	$0.842857\pi$
$948$		0			0
$949$	0.277236	+	2.46054i	0.277236	+	2.46054i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.16039	+	0.348450i	1.16039	+	0.348450i	0.809017	−	0.587785i	$-0.200000\pi$
$953$	1.16039	+	0.348450i	1.16039	+	0.348450i	0.351375	+	0.936235i	$0.385714\pi$
$954$	−0.0766173	−	0.110591i	−0.0766173	−	0.110591i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.722795	−	0.691063i	−0.722795	−	0.691063i
$962$	1.45621	−	1.74426i	1.45621	−	1.74426i
$963$		0			0
$964$	−1.97392	+	0.267386i	−1.97392	+	0.267386i
$965$	0.0527418	+	0.0725928i	0.0527418	+	0.0725928i
$966$		0			0
$967$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$967$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$968$	0.623490	+	0.781831i	0.623490	+	0.781831i
$969$		0			0
$970$	1.70136	+	1.01651i	1.70136	+	1.01651i
$971$		0			0		0.928115	−	0.372294i	$-0.121429\pi$
$971$		0			0		−0.928115	+	0.372294i	$0.878571\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.659062	+	1.88349i	0.659062	+	1.88349i
$977$	0.348922	−	1.70413i	0.348922	−	1.70413i	−0.309017	−	0.951057i	$-0.600000\pi$
$977$	0.348922	−	1.70413i	0.348922	−	1.70413i	0.657939	−	0.753071i	$-0.271429\pi$
$978$		0			0
$979$		0			0
$980$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$981$	0.692192	+	1.61946i	0.692192	+	1.61946i
$982$		0			0
$983$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$983$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$984$		0			0
$985$	−1.34086	−	0.151078i	−1.34086	−	0.151078i
$986$	−0.0320114	+	0.176398i	−0.0320114	+	0.176398i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.0896393	−	0.995974i	$-0.528571\pi$
$991$		0			0		0.0896393	+	0.995974i	$0.471429\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.24572	+	0.0559455i	−1.24572	+	0.0559455i	−0.657939	−	0.753071i	$-0.728571\pi$
$997$	−1.24572	+	0.0559455i	−1.24572	+	0.0559455i	−0.587785	+	0.809017i	$0.700000\pi$
$998$		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.1547.1	yes	48
4.3	odd	2	CM	2900.1.cr.a.1547.1	yes	48
25.8	odd	20		2900.1.da.a.1083.1	yes	48
29.3	odd	28		2900.1.da.a.1047.1	yes	48
100.83	even	20		2900.1.da.a.1083.1	yes	48
116.3	even	28		2900.1.da.a.1047.1	yes	48
725.583	even	140	inner	2900.1.cr.a.583.1	✓	48
2900.583	odd	140	inner	2900.1.cr.a.583.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2900.1.cr.a.583.1	✓	48	725.583	even	140	inner
2900.1.cr.a.583.1	✓	48	2900.583	odd	140	inner
2900.1.cr.a.1547.1	yes	48	1.1	even	1	trivial
2900.1.cr.a.1547.1	yes	48	4.3	odd	2	CM
2900.1.da.a.1047.1	yes	48	29.3	odd	28
2900.1.da.a.1047.1	yes	48	116.3	even	28
2900.1.da.a.1083.1	yes	48	25.8	odd	20
2900.1.da.a.1083.1	yes	48	100.83	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)

\(f(q)\)	\(=\)	\(q+(-0.512899 + 0.858449i) q^{2} +(-0.473869 - 0.880596i) q^{4} +(-0.880596 - 0.473869i) q^{5} +(0.998993 + 0.0448648i) q^{8} +(0.936235 + 0.351375i) q^{9} +O(q^{10})\)	\(q+(-0.512899 + 0.858449i) q^{2} +(-0.473869 - 0.880596i) q^{4} +(-0.880596 - 0.473869i) q^{5} +(0.998993 + 0.0448648i) q^{8} +(0.936235 + 0.351375i) q^{9} +(0.858449 - 0.512899i) q^{10} +(-1.61059 + 0.329770i) q^{13} +(-0.550897 + 0.834573i) q^{16} +(-0.105377 - 0.145039i) q^{17} +(-0.781831 + 0.623490i) q^{18} +1.00000i q^{20} +(0.550897 + 0.834573i) q^{25} +(0.542980 - 1.55175i) q^{26} +(-0.266037 + 0.963963i) q^{29} +(-0.433884 - 0.900969i) q^{32} +(0.178557 - 0.0160704i) q^{34} +(-0.134233 - 0.990950i) q^{36} +(1.29399 + 0.485644i) q^{37} +(-0.858449 - 0.512899i) q^{40} +(1.70672 + 0.869620i) q^{41} +(-0.657939 - 0.753071i) q^{45} +(0.781831 + 0.623490i) q^{49} +(-0.998993 + 0.0448648i) q^{50} +(1.05360 + 1.26201i) q^{52} +(-0.00905024 + 0.134233i) q^{53} +(-0.691063 - 0.722795i) q^{58} +(1.20884 - 1.58764i) q^{61} +(0.995974 + 0.0896393i) q^{64} +(1.57455 + 0.472814i) q^{65} +(-0.0777861 + 0.161524i) q^{68} +(0.919528 + 0.393025i) q^{72} +(0.135010 - 1.50008i) q^{73} +(-1.08059 + 0.861741i) q^{74} +(0.880596 - 0.473869i) q^{80} +(0.753071 + 0.657939i) q^{81} +(-1.62190 + 1.01911i) q^{82} +(0.0240652 + 0.177656i) q^{85} +(-0.802047 + 0.202098i) q^{89} +(0.983930 - 0.178557i) q^{90} +(0.939160 + 1.74525i) q^{97} +(-0.936235 + 0.351375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 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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