LMFDB - Embedded newform 2900.1.cr.a.623.1

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			623.1
Root			$-0.0896393 + 0.995974i$ of defining polynomial
Character	$\chi$	$=$	2900.623
Dual form			2900.1.cr.a.1187.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998993 + 0.0448648i) q^{2} +(0.995974 + 0.0896393i) q^{4} +(-0.0896393 - 0.995974i) q^{5} +(0.990950 + 0.134233i) q^{8} +(0.473869 + 0.880596i) q^{9} +O(q^{10})$	\(q+(0.998993 + 0.0448648i) q^{2} +(0.995974 + 0.0896393i) q^{4} +(-0.0896393 - 0.995974i) q^{5} +(0.990950 + 0.134233i) q^{8} +(0.473869 + 0.880596i) q^{9} +(-0.0448648 - 0.998993i) q^{10} +(0.401697 - 0.278296i) q^{13} +(0.983930 + 0.178557i) q^{16} +(-0.506032 + 0.164420i) q^{17} +(0.433884 + 0.900969i) q^{18} -1.00000i q^{20} +(-0.983930 + 0.178557i) q^{25} +(0.413778 - 0.259994i) q^{26} +(0.722795 - 0.691063i) q^{29} +(0.974928 + 0.222521i) q^{32} +(-0.512899 + 0.141551i) q^{34} +(0.393025 + 0.919528i) q^{36} +(-0.713714 - 1.32630i) q^{37} +(0.0448648 - 0.998993i) q^{40} +(0.200510 + 1.26597i) q^{41} +(0.834573 - 0.550897i) q^{45} +(-0.433884 + 0.900969i) q^{49} +(-0.990950 + 0.134233i) q^{50} +(0.425026 - 0.241168i) q^{52} +(-0.0804722 + 0.393025i) q^{53} +(0.753071 - 0.657939i) q^{58} +(-1.81850 - 0.729454i) q^{61} +(0.963963 + 0.266037i) q^{64} +(-0.313184 - 0.375133i) q^{65} +(-0.518733 + 0.118398i) q^{68} +(0.351375 + 0.936235i) q^{72} +(0.293118 - 1.06209i) q^{73} +(-0.653491 - 1.35699i) q^{74} +(0.0896393 - 0.995974i) q^{80} +(-0.550897 + 0.834573i) q^{81} +(0.143511 + 1.27369i) q^{82} +(0.209118 + 0.489257i) q^{85} +(1.41387 - 1.29233i) q^{89} +(0.858449 - 0.512899i) q^{90} +(-1.83165 - 0.164852i) q^{97} +(-0.473869 + 0.880596i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} + 2 q^{9}+O(q^{10}) $ 48 * q - 2 * q^4 + 2 * q^9	$ 48 q - 2 q^{4} + 2 q^{9} + 2 q^{10} + 2 q^{13} + 2 q^{16} - 2 q^{25} + 12 q^{26} - 2 q^{36} + 6 q^{37} - 2 q^{40} + 2 q^{41} - 2 q^{52} - 48 q^{53} + 2 q^{58} - 2 q^{61} - 2 q^{64} - 8 q^{65} + 2 q^{81} + 2 q^{82} + 8 q^{89} + 2 q^{90} - 2 q^{98}+O(q^{100}) $ 48 * q - 2 * q^4 + 2 * q^9 + 2 * q^10 + 2 * q^13 + 2 * q^16 - 2 * q^25 + 12 * q^26 - 2 * q^36 + 6 * q^37 - 2 * q^40 + 2 * q^41 - 2 * q^52 - 48 * q^53 + 2 * q^58 - 2 * q^61 - 2 * q^64 - 8 * q^65 + 2 * q^81 + 2 * q^82 + 8 * q^89 + 2 * q^90 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$901$	$1277$	$1451$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{20}\right)$	$-1$

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 $

$2$	0.998993	+	0.0448648i	0.998993	+	0.0448648i
$2$	0.998993	+	0.0448648i	0.998993	+	0.0448648i
$3$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$3$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$4$	0.995974	+	0.0896393i	0.995974	+	0.0896393i
$5$	−0.0896393	−	0.995974i	−0.0896393	−	0.995974i
$5$	−0.0896393	−	0.995974i	−0.0896393	−	0.995974i
$6$		0			0
$7$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$7$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$8$	0.990950	+	0.134233i	0.990950	+	0.134233i
$9$	0.473869	+	0.880596i	0.473869	+	0.880596i
$10$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$11$		0			0		−0.287599	−	0.957751i	$-0.592857\pi$
$11$		0			0		0.287599	+	0.957751i	$0.407143\pi$
$12$		0			0
$13$	0.401697	−	0.278296i	0.401697	−	0.278296i	−0.351375	−	0.936235i	$-0.614286\pi$
$13$	0.401697	−	0.278296i	0.401697	−	0.278296i	0.753071	+	0.657939i	$0.228571\pi$
$14$		0			0
$15$		0			0
$16$	0.983930	+	0.178557i	0.983930	+	0.178557i
$17$	−0.506032	+	0.164420i	−0.506032	+	0.164420i	−0.550897	−	0.834573i	$-0.685714\pi$
$17$	−0.506032	+	0.164420i	−0.506032	+	0.164420i	0.0448648	+	0.998993i	$0.485714\pi$
$18$	0.433884	+	0.900969i	0.433884	+	0.900969i
$19$		0			0		−0.969690	−	0.244340i	$-0.921429\pi$
$19$		0			0		0.969690	+	0.244340i	$0.0785714\pi$
$20$		−	1.00000i		−	1.00000i
$21$		0			0
$22$		0			0
$23$		0			0		−0.493508	−	0.869741i	$-0.664286\pi$
$23$		0			0		0.493508	+	0.869741i	$0.335714\pi$
$24$		0			0
$25$	−0.983930	+	0.178557i	−0.983930	+	0.178557i
$26$	0.413778	−	0.259994i	0.413778	−	0.259994i
$27$		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		0.910478	−	0.413559i	$-0.135714\pi$
$31$		0			0		−0.910478	+	0.413559i	$0.864286\pi$
$32$	0.974928	+	0.222521i	0.974928	+	0.222521i
$33$		0			0
$34$	−0.512899	+	0.141551i	−0.512899	+	0.141551i
$35$		0			0
$36$	0.393025	+	0.919528i	0.393025	+	0.919528i
$37$	−0.713714	−	1.32630i	−0.713714	−	1.32630i	−0.936235	−	0.351375i	$-0.885714\pi$
$37$	−0.713714	−	1.32630i	−0.713714	−	1.32630i	0.222521	−	0.974928i	$-0.428571\pi$
$38$		0			0
$39$		0			0
$40$	0.0448648	−	0.998993i	0.0448648	−	0.998993i
$41$	0.200510	+	1.26597i	0.200510	+	1.26597i	0.858449	+	0.512899i	$0.171429\pi$
$41$	0.200510	+	1.26597i	0.200510	+	1.26597i	−0.657939	+	0.753071i	$0.728571\pi$
$42$		0			0
$43$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$43$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$44$		0			0
$45$	0.834573	−	0.550897i	0.834573	−	0.550897i
$46$		0			0
$47$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$47$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$48$		0			0
$49$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$50$	−0.990950	+	0.134233i	−0.990950	+	0.134233i
$51$		0			0
$52$	0.425026	−	0.241168i	0.425026	−	0.241168i
$53$	−0.0804722	+	0.393025i	−0.0804722	+	0.393025i	0.919528	+	0.393025i	$0.128571\pi$
$53$	−0.0804722	+	0.393025i	−0.0804722	+	0.393025i	−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	0.753071	−	0.657939i	0.753071	−	0.657939i
$59$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$59$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$60$		0			0
$61$	−1.81850	−	0.729454i	−1.81850	−	0.729454i	−0.983930	−	0.178557i	$-0.942857\pi$
$61$	−1.81850	−	0.729454i	−1.81850	−	0.729454i	−0.834573	−	0.550897i	$-0.814286\pi$
$62$		0			0
$63$		0			0
$64$	0.963963	+	0.266037i	0.963963	+	0.266037i
$65$	−0.313184	−	0.375133i	−0.313184	−	0.375133i
$66$		0			0
$67$		0			0		0.795625	−	0.605790i	$-0.207143\pi$
$67$		0			0		−0.795625	+	0.605790i	$0.792857\pi$
$68$	−0.518733	+	0.118398i	−0.518733	+	0.118398i
$69$		0			0
$70$		0			0
$71$		0			0		0.990950	−	0.134233i	$-0.0428571\pi$
$71$		0			0		−0.990950	+	0.134233i	$0.957143\pi$
$72$	0.351375	+	0.936235i	0.351375	+	0.936235i
$73$	0.293118	−	1.06209i	0.293118	−	1.06209i	−0.657939	−	0.753071i	$-0.728571\pi$
$73$	0.293118	−	1.06209i	0.293118	−	1.06209i	0.951057	−	0.309017i	$-0.100000\pi$
$74$	−0.653491	−	1.35699i	−0.653491	−	1.35699i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.999748	−	0.0224381i	$-0.00714286\pi$
$79$		0			0		−0.999748	+	0.0224381i	$0.992857\pi$
$80$	0.0896393	−	0.995974i	0.0896393	−	0.995974i
$81$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$82$	0.143511	+	1.27369i	0.143511	+	1.27369i
$83$		0			0		−0.969690	−	0.244340i	$-0.921429\pi$
$83$		0			0		0.969690	+	0.244340i	$0.0785714\pi$
$84$		0			0
$85$	0.209118	+	0.489257i	0.209118	+	0.489257i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.41387	−	1.29233i	1.41387	−	1.29233i	0.512899	−	0.858449i	$-0.328571\pi$
$89$	1.41387	−	1.29233i	1.41387	−	1.29233i	0.900969	−	0.433884i	$-0.142857\pi$
$90$	0.858449	−	0.512899i	0.858449	−	0.512899i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.83165	−	0.164852i	−1.83165	−	0.164852i	−0.880596	−	0.473869i	$-0.842857\pi$
$97$	−1.83165	−	0.164852i	−1.83165	−	0.164852i	−0.951057	+	0.309017i	$0.900000\pi$
$98$	−0.473869	+	0.880596i	−0.473869	+	0.880596i
$99$		0			0
$100$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$101$	0.571582	+	0.0644018i	0.571582	+	0.0644018i	0.393025	−	0.919528i	$-0.371429\pi$
$101$	0.571582	+	0.0644018i	0.571582	+	0.0644018i	0.178557	+	0.983930i	$0.442857\pi$
$102$		0			0
$103$		0			0		0.605790	−	0.795625i	$-0.292857\pi$
$103$		0			0		−0.605790	+	0.795625i	$0.707143\pi$
$104$	0.435418	−	0.221856i	0.435418	−	0.221856i
$105$		0			0
$106$	−0.0980242	+	0.389019i	−0.0980242	+	0.389019i
$107$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$107$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$108$		0			0
$109$	−0.135010	+	0.117954i	−0.135010	+	0.117954i	−0.722795	−	0.691063i	$-0.757143\pi$
$109$	−0.135010	+	0.117954i	−0.135010	+	0.117954i	0.587785	+	0.809017i	$0.300000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.623553	+	0.713714i	0.623553	+	0.713714i	0.974928	−	0.222521i	$-0.0714286\pi$
$113$	0.623553	+	0.713714i	0.623553	+	0.713714i	−0.351375	+	0.936235i	$0.614286\pi$
$114$		0			0
$115$		0			0
$116$	0.781831	−	0.623490i	0.781831	−	0.623490i
$117$	0.435418	+	0.221856i	0.435418	+	0.221856i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.834573	+	0.550897i	−0.834573	+	0.550897i
$122$	−1.78394	−	0.810306i	−1.78394	−	0.810306i
$123$		0			0
$124$		0			0
$125$	0.266037	+	0.963963i	0.266037	+	0.963963i
$126$		0			0
$127$		0			0		−0.880596	−	0.473869i	$-0.842857\pi$
$127$		0			0		0.880596	+	0.473869i	$0.157143\pi$
$128$	0.951057	+	0.309017i	0.951057	+	0.309017i
$129$		0			0
$130$	−0.296038	−	0.388806i	−0.296038	−	0.388806i
$131$		0			0		0.979675	−	0.200589i	$-0.0642857\pi$
$131$		0			0		−0.979675	+	0.200589i	$0.935714\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.523523	+	0.0950054i	−0.523523	+	0.0950054i
$137$	−1.27298	+	0.685020i	−1.27298	+	0.685020i	−0.963963	−	0.266037i	$-0.914286\pi$
$137$	−1.27298	+	0.685020i	−1.27298	+	0.685020i	−0.309017	+	0.951057i	$0.600000\pi$
$138$		0			0
$139$		0			0		0.266037	−	0.963963i	$-0.414286\pi$
$139$		0			0		−0.266037	+	0.963963i	$0.585714\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.309017	+	0.951057i	0.309017	+	0.951057i
$145$	−0.753071	−	0.657939i	−0.753071	−	0.657939i
$146$	0.340473	−	1.04787i	0.340473	−	1.04787i
$147$		0			0
$148$	−0.591952	−	1.38494i	−0.591952	−	1.38494i
$149$	0.416664	+	1.82552i	0.416664	+	1.82552i	0.550897	+	0.834573i	$0.314286\pi$
$149$	0.416664	+	1.82552i	0.416664	+	1.82552i	−0.134233	+	0.990950i	$0.542857\pi$
$150$		0			0
$151$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$151$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$152$		0			0
$153$	−0.384580	−	0.367696i	−0.384580	−	0.367696i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.357114			−0.357114			−0.178557	−	0.983930i	$-0.557143\pi$
$157$	−0.357114			−0.357114			−0.178557	+	0.983930i	$0.557143\pi$
$158$		0			0
$159$		0			0
$160$	0.134233	−	0.990950i	0.134233	−	0.990950i
$161$		0			0
$162$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$163$		0			0		0.178557	−	0.983930i	$-0.442857\pi$
$163$		0			0		−0.178557	+	0.983930i	$0.557143\pi$
$164$	0.0862221	+	1.27885i	0.0862221	+	1.27885i
$165$		0			0
$166$		0			0
$167$		0			0		−0.767645	−	0.640876i	$-0.778571\pi$
$167$		0			0		0.767645	+	0.640876i	$0.221429\pi$
$168$		0			0
$169$	−0.267463	+	0.712654i	−0.267463	+	0.712654i
$170$	0.186957	+	0.498146i	0.186957	+	0.498146i
$171$		0			0
$172$		0			0
$173$	0.154403	−	0.974865i	0.154403	−	0.974865i	−0.781831	−	0.623490i	$-0.785714\pi$
$173$	0.154403	−	0.974865i	0.154403	−	0.974865i	0.936235	−	0.351375i	$-0.114286\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	1.47042	−	1.22760i	1.47042	−	1.22760i
$179$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$179$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$180$	0.880596	−	0.473869i	0.880596	−	0.473869i
$181$	−1.95994	+	0.176398i	−1.95994	+	0.176398i	−0.995974	−	0.0896393i	$-0.971429\pi$
$181$	−1.95994	+	0.176398i	−1.95994	+	0.176398i	−0.963963	+	0.266037i	$0.914286\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.25699	+	0.829730i	−1.25699	+	0.829730i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$191$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$192$		0			0
$193$	0.0597394	+	0.261736i	0.0597394	+	0.261736i	0.995974	−	0.0896393i	$-0.0285714\pi$
$193$	0.0597394	+	0.261736i	0.0597394	+	0.261736i	−0.936235	+	0.351375i	$0.885714\pi$
$194$	−1.82241	−	0.246862i	−1.82241	−	0.246862i
$195$		0			0
$196$	−0.512899	+	0.858449i	−0.512899	+	0.858449i
$197$	−0.658075	+	1.44880i	−0.658075	+	1.44880i	0.222521	+	0.974928i	$0.428571\pi$
$197$	−0.658075	+	1.44880i	−0.658075	+	1.44880i	−0.880596	+	0.473869i	$0.842857\pi$
$198$		0			0
$199$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$199$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$200$	−0.998993	+	0.0448648i	−0.998993	+	0.0448648i
$201$		0			0
$202$	0.568117	+	0.0899809i	0.568117	+	0.0899809i
$203$		0			0
$204$		0			0
$205$	1.24290	−	0.313184i	1.24290	−	0.313184i
$206$		0			0
$207$		0			0
$208$	0.444933	−	0.202098i	0.444933	−	0.202098i
$209$		0			0
$210$		0			0
$211$		0			0		−0.822002	−	0.569484i	$-0.807143\pi$
$211$		0			0		0.822002	+	0.569484i	$0.192857\pi$
$212$	−0.115379	+	0.384229i	−0.115379	+	0.384229i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	−0.140166	+	0.111778i	−0.140166	+	0.111778i
$219$		0			0
$220$		0			0
$221$	−0.157514	+	0.206874i	−0.157514	+	0.206874i
$222$		0			0
$223$		0			0		−0.822002	−	0.569484i	$-0.807143\pi$
$223$		0			0		0.822002	+	0.569484i	$0.192857\pi$
$224$		0			0
$225$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$226$	0.590905	+	0.740971i	0.590905	+	0.740971i
$227$		0			0		−0.674671	−	0.738119i	$-0.735714\pi$
$227$		0			0		0.674671	+	0.738119i	$0.264286\pi$
$228$		0			0
$229$	0.802047	−	0.202098i	0.802047	−	0.202098i	0.178557	−	0.983930i	$-0.442857\pi$
$229$	0.802047	−	0.202098i	0.802047	−	0.202098i	0.623490	+	0.781831i	$0.285714\pi$
$230$		0			0
$231$		0			0
$232$	0.809017	−	0.587785i	0.809017	−	0.587785i
$233$	0.550046	−	1.07953i	0.550046	−	1.07953i	−0.433884	−	0.900969i	$-0.642857\pi$
$233$	0.550046	−	1.07953i	0.550046	−	1.07953i	0.983930	−	0.178557i	$-0.0571429\pi$
$234$	0.425026	+	0.241168i	0.425026	+	0.241168i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.919528	−	0.393025i	$-0.128571\pi$
$239$		0			0		−0.919528	+	0.393025i	$0.871429\pi$
$240$		0			0
$241$	−1.69772	+	0.913584i	−1.69772	+	0.913584i	−0.722795	+	0.691063i	$0.757143\pi$
$241$	−1.69772	+	0.913584i	−1.69772	+	0.913584i	−0.974928	+	0.222521i	$0.928571\pi$
$242$	−0.858449	+	0.512899i	−0.858449	+	0.512899i
$243$		0			0
$244$	−1.74579	−	0.889527i	−1.74579	−	0.889527i
$245$	0.936235	+	0.351375i	0.936235	+	0.351375i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.222521	+	0.974928i	0.222521	+	0.974928i
$251$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$251$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.936235	+	0.351375i	0.936235	+	0.351375i
$257$	−1.64212	−	1.03181i	−1.64212	−	1.03181i	−0.951057	−	0.309017i	$-0.900000\pi$
$257$	−1.64212	−	1.03181i	−1.64212	−	1.03181i	−0.691063	−	0.722795i	$-0.742857\pi$
$258$		0			0
$259$		0			0
$260$	−0.278296	−	0.401697i	−0.278296	−	0.401697i
$261$	0.951057	+	0.309017i	0.951057	+	0.309017i
$262$		0			0
$263$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$263$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$264$		0			0
$265$	0.398656	+	0.0449178i	0.398656	+	0.0449178i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.0271855	−	0.0357045i	−0.0271855	−	0.0357045i	0.781831	−	0.623490i	$-0.214286\pi$
$269$	−0.0271855	−	0.0357045i	−0.0271855	−	0.0357045i	−0.809017	+	0.587785i	$0.800000\pi$
$270$		0			0
$271$		0			0		−0.640876	−	0.767645i	$-0.721429\pi$
$271$		0			0		0.640876	+	0.767645i	$0.278571\pi$
$272$	−0.527258	+	0.0714220i	−0.527258	+	0.0714220i
$273$		0			0
$274$	−1.30243	+	0.627218i	−1.30243	+	0.627218i
$275$		0			0
$276$		0			0
$277$	0.388070	+	1.29233i	0.388070	+	1.29233i	0.900969	+	0.433884i	$0.142857\pi$
$277$	0.388070	+	1.29233i	0.388070	+	1.29233i	−0.512899	+	0.858449i	$0.671429\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.137696	+	1.01651i	−0.137696	+	1.01651i	0.781831	+	0.623490i	$0.214286\pi$
$281$	−0.137696	+	1.01651i	−0.137696	+	1.01651i	−0.919528	+	0.393025i	$0.871429\pi$
$282$		0			0
$283$		0			0		0.640876	−	0.767645i	$-0.278571\pi$
$283$		0			0		−0.640876	+	0.767645i	$0.721429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.266037	+	0.963963i	0.266037	+	0.963963i
$289$	−0.579982	+	0.421382i	−0.579982	+	0.421382i
$290$	−0.722795	−	0.691063i	−0.722795	−	0.691063i
$291$		0			0
$292$	0.387143	−	1.03154i	0.387143	−	1.03154i
$293$	0.292810	−	1.28289i	0.292810	−	1.28289i	−0.587785	−	0.809017i	$-0.700000\pi$
$293$	0.292810	−	1.28289i	0.292810	−	1.28289i	0.880596	−	0.473869i	$-0.157143\pi$
$294$		0			0
$295$		0			0
$296$	−0.529221	−	1.41010i	−0.529221	−	1.41010i
$297$		0			0
$298$	0.334342	+	1.84238i	0.334342	+	1.84238i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.563508	+	1.87657i	−0.563508	+	1.87657i
$306$	−0.367696	−	0.384580i	−0.367696	−	0.384580i
$307$		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		0.569484	−	0.822002i	$-0.307143\pi$
$311$		0			0		−0.569484	+	0.822002i	$0.692857\pi$
$312$		0			0
$313$	−0.151078	+	0.165286i	−0.151078	+	0.165286i	−0.809017	−	0.587785i	$-0.800000\pi$
$313$	−0.151078	+	0.165286i	−0.151078	+	0.165286i	0.657939	+	0.753071i	$0.271429\pi$
$314$	−0.356754	−	0.0160218i	−0.356754	−	0.0160218i
$315$		0			0
$316$		0			0
$317$	1.16747	+	0.438157i	1.16747	+	0.438157i	0.858449	−	0.512899i	$-0.171429\pi$
$317$	1.16747	+	0.438157i	1.16747	+	0.438157i	0.309017	+	0.951057i	$0.400000\pi$
$318$		0			0
$319$		0			0
$320$	0.178557	−	0.983930i	0.178557	−	0.983930i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$325$	−0.345550	+	0.345550i	−0.345550	+	0.345550i
$326$		0			0
$327$		0			0
$328$	0.0287600	+	1.28143i	0.0287600	+	1.28143i
$329$		0			0
$330$		0			0
$331$		0			0		0.453990	−	0.891007i	$-0.350000\pi$
$331$		0			0		−0.453990	+	0.891007i	$0.650000\pi$
$332$		0			0
$333$	0.829730	−	1.25699i	0.829730	−	1.25699i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.91852	−	0.348160i	−1.91852	−	0.348160i	−0.919528	−	0.393025i	$-0.871429\pi$
$337$	−1.91852	−	0.348160i	−1.91852	−	0.348160i	−0.998993	+	0.0448648i	$0.985714\pi$
$338$	−0.299167	+	0.699936i	−0.299167	+	0.699936i
$339$		0			0
$340$	0.164420	+	0.506032i	0.164420	+	0.506032i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.197985	−	0.966956i	0.197985	−	0.966956i
$347$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$347$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$348$		0			0
$349$		−	0.0897297i		−	0.0897297i	−0.998993	−	0.0448648i	$-0.985714\pi$
$349$		−	0.0897297i		−	0.0897297i	0.998993	−	0.0448648i	$-0.0142857\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.04244	+	0.213440i	1.04244	+	0.213440i	0.691063	−	0.722795i	$-0.257143\pi$
$353$	1.04244	+	0.213440i	1.04244	+	0.213440i	0.351375	+	0.936235i	$0.385714\pi$
$354$		0			0
$355$		0			0
$356$	1.52402	−	1.16039i	1.52402	−	1.16039i
$357$		0			0
$358$		0			0
$359$		0			0		−0.569484	−	0.822002i	$-0.692857\pi$
$359$		0			0		0.569484	+	0.822002i	$0.307143\pi$
$360$	0.900969	−	0.433884i	0.900969	−	0.433884i
$361$	0.880596	+	0.473869i	0.880596	+	0.473869i
$362$	−1.96588	+	0.0882877i	−1.96588	+	0.0882877i
$363$		0			0
$364$		0			0
$365$	−1.08409	−	0.196733i	−1.08409	−	0.196733i
$366$		0			0
$367$		0			0		−0.512899	−	0.858449i	$-0.671429\pi$
$367$		0			0		0.512899	+	0.858449i	$0.328571\pi$
$368$		0			0
$369$	−1.01979	+	0.776472i	−1.01979	+	0.776472i
$370$	−1.29295	+	0.772500i	−1.29295	+	0.772500i
$371$		0			0
$372$		0			0
$373$	−0.126988	−	1.88349i	−0.126988	−	1.88349i	−0.393025	−	0.919528i	$-0.628571\pi$
$373$	−0.126988	−	1.88349i	−0.126988	−	1.88349i	0.266037	−	0.963963i	$-0.414286\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.0980242	−	0.478749i	0.0980242	−	0.478749i
$378$		0			0
$379$		0			0		0.200589	−	0.979675i	$-0.435714\pi$
$379$		0			0		−0.200589	+	0.979675i	$0.564286\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.200589	−	0.979675i	$-0.564286\pi$
$383$		0			0		0.200589	+	0.979675i	$0.435714\pi$
$384$		0			0
$385$		0			0
$386$	0.0479366	+	0.264152i	0.0479366	+	0.264152i
$387$		0			0
$388$	−1.80950	−	0.328376i	−1.80950	−	0.328376i
$389$	0.284860	−	1.79854i	0.284860	−	1.79854i	−0.266037	−	0.963963i	$-0.585714\pi$
$389$	0.284860	−	1.79854i	0.284860	−	1.79854i	0.550897	−	0.834573i	$-0.314286\pi$
$390$		0			0
$391$		0			0
$392$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$393$		0			0
$394$	−0.722412	+	1.41781i	−0.722412	+	1.41781i
$395$		0			0
$396$		0			0
$397$	−0.0445940	−	1.98692i	−0.0445940	−	1.98692i	−0.134233	−	0.990950i	$-0.542857\pi$
$397$	−0.0445940	−	1.98692i	−0.0445940	−	1.98692i	0.0896393	−	0.995974i	$-0.471429\pi$
$398$		0			0
$399$		0			0
$400$	−1.00000			−1.00000
$401$	1.24196	−	1.55737i	1.24196	−	1.55737i	0.550897	−	0.834573i	$-0.314286\pi$
$401$	1.24196	−	1.55737i	1.24196	−	1.55737i	0.691063	−	0.722795i	$-0.257143\pi$
$402$		0			0
$403$		0			0
$404$	0.563508	+	0.115379i	0.563508	+	0.115379i
$405$	0.880596	+	0.473869i	0.880596	+	0.473869i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.13639	+	0.0766173i	1.13639	+	0.0766173i	0.623490	−	0.781831i	$-0.285714\pi$
$409$	1.13639	+	0.0766173i	1.13639	+	0.0766173i	0.512899	+	0.858449i	$0.328571\pi$
$410$	1.25570	−	0.257106i	1.25570	−	0.257106i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	0.453552	−	0.181933i	0.453552	−	0.181933i
$417$		0			0
$418$		0			0
$419$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$419$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$420$		0			0
$421$	1.79854	+	0.816934i	1.79854	+	0.816934i	0.963963	+	0.266037i	$0.0857143\pi$
$421$	1.79854	+	0.816934i	1.79854	+	0.816934i	0.834573	+	0.550897i	$0.185714\pi$
$422$		0			0
$423$		0			0
$424$	−0.132501	+	0.378666i	−0.132501	+	0.378666i
$425$	0.468542	−	0.252133i	0.468542	−	0.252133i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$431$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$432$		0			0
$433$	0.668355	−	1.78082i	0.668355	−	1.78082i	0.0448648	−	0.998993i	$-0.485714\pi$
$433$	0.668355	−	1.78082i	0.668355	−	1.78082i	0.623490	−	0.781831i	$-0.285714\pi$
$434$		0			0
$435$		0			0
$436$	−0.145039	+	0.105377i	−0.145039	+	0.105377i
$437$		0			0
$438$		0			0
$439$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$439$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$440$		0			0
$441$	−0.998993	+	0.0448648i	−0.998993	+	0.0448648i
$442$	−0.166637	+	0.199599i	−0.166637	+	0.199599i
$443$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$443$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$444$		0			0
$445$	−1.41387	−	1.29233i	−1.41387	−	1.29233i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.165286	−	1.46696i	0.165286	−	1.46696i	−0.587785	−	0.809017i	$-0.700000\pi$
$449$	0.165286	−	1.46696i	0.165286	−	1.46696i	0.753071	−	0.657939i	$-0.228571\pi$
$450$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$451$		0			0
$452$	0.557066	+	0.766736i	0.557066	+	0.766736i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.559311	−	0.351438i	0.559311	−	0.351438i	−0.222521	−	0.974928i	$-0.571429\pi$
$457$	0.559311	−	0.351438i	0.559311	−	0.351438i	0.781831	+	0.623490i	$0.214286\pi$
$458$	0.810306	−	0.165911i	0.810306	−	0.165911i
$459$		0			0
$460$		0			0
$461$	0.116479	−	0.290378i	0.116479	−	0.290378i	−0.858449	−	0.512899i	$-0.828571\pi$
$461$	0.116479	−	0.290378i	0.116479	−	0.290378i	0.974928	+	0.222521i	$0.0714286\pi$
$462$		0			0
$463$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$463$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$464$	0.834573	−	0.550897i	0.834573	−	0.550897i
$465$		0			0
$466$	0.597925	−	1.05376i	0.597925	−	1.05376i
$467$		0			0		−0.0896393	−	0.995974i	$-0.528571\pi$
$467$		0			0		0.0896393	+	0.995974i	$0.471429\pi$
$468$	0.413778	+	0.259994i	0.413778	+	0.259994i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.384229	+	0.115379i	−0.384229	+	0.115379i
$478$		0			0
$479$		0			0		0.413559	−	0.910478i	$-0.364286\pi$
$479$		0			0		−0.413559	+	0.910478i	$0.635714\pi$
$480$		0			0
$481$	−0.655801	−	0.334148i	−0.655801	−	0.334148i
$482$	−1.73700	+	0.836496i	−1.73700	+	0.836496i
$483$		0			0
$484$	−0.880596	+	0.473869i	−0.880596	+	0.473869i
$485$			1.83906i			1.83906i
$486$		0			0
$487$		0			0		−0.738119	−	0.674671i	$-0.764286\pi$
$487$		0			0		0.738119	+	0.674671i	$0.235714\pi$
$488$	−1.70413	−	0.966956i	−1.70413	−	0.966956i
$489$		0			0
$490$	0.919528	+	0.393025i	0.919528	+	0.393025i
$491$		0			0		−0.869741	−	0.493508i	$-0.835714\pi$
$491$		0			0		0.869741	+	0.493508i	$0.164286\pi$
$492$		0			0
$493$	−0.252133	+	0.468542i	−0.252133	+	0.468542i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$499$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$500$	0.178557	+	0.983930i	0.178557	+	0.983930i
$501$		0			0
$502$		0			0
$503$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$503$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$504$		0			0
$505$	0.0129063	−	0.575054i	0.0129063	−	0.575054i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.140355	+	0.773418i	−0.140355	+	0.773418i	0.834573	+	0.550897i	$0.185714\pi$
$509$	−0.140355	+	0.773418i	−0.140355	+	0.773418i	−0.974928	+	0.222521i	$0.928571\pi$
$510$		0			0
$511$		0			0
$512$	0.919528	+	0.393025i	0.919528	+	0.393025i
$513$		0			0
$514$	−1.59417	−	1.10445i	−1.59417	−	1.10445i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.259994	−	0.413778i	−0.259994	−	0.413778i
$521$	1.31448	+	0.427100i	1.31448	+	0.427100i	0.880596	−	0.473869i	$-0.157143\pi$
$521$	1.31448	+	0.427100i	1.31448	+	0.427100i	0.433884	+	0.900969i	$0.357143\pi$
$522$	0.936235	+	0.351375i	0.936235	+	0.351375i
$523$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$523$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.512899	+	0.858449i	−0.512899	+	0.858449i
$530$	0.396240	+	0.0627582i	0.396240	+	0.0627582i
$531$		0			0
$532$		0			0
$533$	0.432859	+	0.452735i	0.432859	+	0.452735i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.0255563	−	0.0368883i	−0.0255563	−	0.0368883i
$539$		0			0
$540$		0			0
$541$	−0.691063	−	1.72279i	−0.691063	−	1.72279i	−0.691063	−	0.722795i	$-0.742857\pi$
$541$	−0.691063	−	1.72279i	−0.691063	−	1.72279i		−	1.00000i	$-0.5\pi$
$542$		0			0
$543$		0			0
$544$	−0.529932	+	0.0476947i	−0.529932	+	0.0476947i
$545$	0.129582	+	0.123893i	0.129582	+	0.123893i
$546$		0			0
$547$		0			0		0.767645	−	0.640876i	$-0.221429\pi$
$547$		0			0		−0.767645	+	0.640876i	$0.778571\pi$
$548$	−1.32926	+	0.568153i	−1.32926	+	0.568153i
$549$	−0.219378	−	1.94703i	−0.219378	−	1.94703i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.329699	+	1.30844i	0.329699	+	1.30844i
$555$		0			0
$556$		0			0
$557$	−0.0150635	+	0.133692i	−0.0150635	+	0.133692i	−0.998993	−	0.0448648i	$-0.985714\pi$
$557$	−0.0150635	+	0.133692i	−0.0150635	+	0.133692i	0.983930	+	0.178557i	$0.0571429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.183163	+	1.00931i	−0.183163	+	1.00931i
$563$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$563$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$564$		0			0
$565$	0.654946	−	0.685020i	0.654946	−	0.685020i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.134504	−	0.00301877i	−0.134504	−	0.00301877i	−0.0448648	−	0.998993i	$-0.514286\pi$
$569$	−0.134504	−	0.00301877i	−0.134504	−	0.00301877i	−0.0896393	+	0.995974i	$0.528571\pi$
$570$		0			0
$571$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$571$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.222521	+	0.974928i	0.222521	+	0.974928i
$577$	0.174913	+	0.409228i	0.174913	+	0.409228i	0.983930	−	0.178557i	$-0.0571429\pi$
$577$	0.174913	+	0.409228i	0.174913	+	0.409228i	−0.809017	+	0.587785i	$0.800000\pi$
$578$	−0.598304	+	0.394937i	−0.598304	+	0.394937i
$579$		0			0
$580$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.433033	−	1.01313i	0.433033	−	1.01313i
$585$	0.181933	−	0.453552i	0.181933	−	0.453552i
$586$	0.350072	−	1.26846i	0.350072	−	1.26846i
$587$		0			0		0.0672690	−	0.997735i	$-0.478571\pi$
$587$		0			0		−0.0672690	+	0.997735i	$0.521429\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.465424	−	1.43243i	−0.465424	−	1.43243i
$593$	−0.487571	+	1.39340i	−0.487571	+	1.39340i	0.393025	+	0.919528i	$0.371429\pi$
$593$	−0.487571	+	1.39340i	−0.487571	+	1.39340i	−0.880596	+	0.473869i	$0.842857\pi$
$594$		0			0
$595$		0			0
$596$	0.251348	+	1.85552i	0.251348	+	1.85552i
$597$		0			0
$598$		0			0
$599$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$599$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$600$		0			0
$601$	−1.68201	+	0.588562i	−1.68201	+	0.588562i	−0.990950	−	0.134233i	$-0.957143\pi$
$601$	−1.68201	+	0.588562i	−1.68201	+	0.588562i	−0.691063	+	0.722795i	$0.742857\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.623490	+	0.781831i	0.623490	+	0.781831i
$606$		0			0
$607$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$607$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$608$		0			0
$609$		0			0
$610$	−0.647133	+	1.84940i	−0.647133	+	1.84940i
$611$		0			0
$612$	−0.350072	−	0.400690i	−0.350072	−	0.400690i
$613$	0.691063	+	1.72279i	0.691063	+	1.72279i	0.691063	+	0.722795i	$0.257143\pi$
$613$	0.691063	+	1.72279i	0.691063	+	1.72279i			1.00000i	$0.5\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.266037	−	1.96396i	0.266037	−	1.96396i		−	1.00000i	$-0.5\pi$
$617$	0.266037	−	1.96396i	0.266037	−	1.96396i	0.266037	−	0.963963i	$-0.414286\pi$
$618$		0			0
$619$		0			0		0.244340	−	0.969690i	$-0.421429\pi$
$619$		0			0		−0.244340	+	0.969690i	$0.578571\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.936235	−	0.351375i	0.936235	−	0.351375i
$626$	−0.158342	+	0.158342i	−0.158342	+	0.158342i
$627$		0			0
$628$	−0.355676	−	0.0320114i	−0.355676	−	0.0320114i
$629$	0.579233	+	0.553803i	0.579233	+	0.553803i
$630$		0			0
$631$		0			0		−0.0896393	−	0.995974i	$-0.528571\pi$
$631$		0			0		0.0896393	+	0.995974i	$0.471429\pi$
$632$		0			0
$633$		0			0
$634$	1.14663	+	0.490094i	1.14663	+	0.490094i
$635$		0			0
$636$		0			0
$637$	0.0764465	+	0.482664i	0.0764465	+	0.482664i
$638$		0			0
$639$		0			0
$640$	0.222521	−	0.974928i	0.222521	−	0.974928i
$641$	−0.0951327	+	1.41101i	−0.0951327	+	1.41101i	0.657939	+	0.753071i	$0.271429\pi$
$641$	−0.0951327	+	1.41101i	−0.0951327	+	1.41101i	−0.753071	+	0.657939i	$0.771429\pi$
$642$		0			0
$643$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$643$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.999748	−	0.0224381i	$-0.00714286\pi$
$647$		0			0		−0.999748	+	0.0224381i	$0.992857\pi$
$648$	−0.657939	+	0.753071i	−0.657939	+	0.753071i
$649$		0			0
$650$	−0.360705	+	0.329699i	−0.360705	+	0.329699i
$651$		0			0
$652$		0			0
$653$	0.276198	+	0.735927i	0.276198	+	0.735927i	0.998993	+	0.0448648i	$0.0142857\pi$
$653$	0.276198	+	0.735927i	0.276198	+	0.735927i	−0.722795	+	0.691063i	$0.757143\pi$
$654$		0			0
$655$		0			0
$656$	−0.0287600	+	1.28143i	−0.0287600	+	1.28143i
$657$	1.07417	−	0.245172i	1.07417	−	0.245172i
$658$		0			0
$659$		0			0		0.287599	−	0.957751i	$-0.407143\pi$
$659$		0			0		−0.287599	+	0.957751i	$0.592857\pi$
$660$		0			0
$661$	0.429004	+	0.118398i	0.429004	+	0.118398i	0.473869	−	0.880596i	$-0.342857\pi$
$661$	0.429004	+	0.118398i	0.429004	+	0.118398i	−0.0448648	+	0.998993i	$0.514286\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.885289	−	1.21850i	0.885289	−	1.21850i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.42986	−	0.811330i	1.42986	−	0.811330i	0.433884	−	0.900969i	$-0.357143\pi$
$673$	1.42986	−	0.811330i	1.42986	−	0.811330i	0.995974	+	0.0896393i	$0.0285714\pi$
$674$	−1.90097	−	0.433884i	−1.90097	−	0.433884i
$675$		0			0
$676$	−0.330268	+	0.685809i	−0.330268	+	0.685809i
$677$	0.653491	+	0.570938i	0.653491	+	0.570938i	0.919528	−	0.393025i	$-0.128571\pi$
$677$	0.653491	+	0.570938i	0.653491	+	0.570938i	−0.266037	+	0.963963i	$0.585714\pi$
$678$		0			0
$679$		0			0
$680$	0.141551	+	0.512899i	0.141551	+	0.512899i
$681$		0			0
$682$		0			0
$683$		0			0		0.0224381	−	0.999748i	$-0.492857\pi$
$683$		0			0		−0.0224381	+	0.999748i	$0.507143\pi$
$684$		0			0
$685$	0.796371	+	1.20645i	0.796371	+	1.20645i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.0770519	+	0.180272i	0.0770519	+	0.180272i
$690$		0			0
$691$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$691$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$692$	0.241168	−	0.957099i	0.241168	−	0.957099i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−0.309615	−	0.607654i	−0.309615	−	0.607654i
$698$	0.00402571	−	0.0896393i	0.00402571	−	0.0896393i
$699$		0			0
$700$		0			0
$701$	0.549432	+	0.438157i	0.549432	+	0.438157i	0.858449	−	0.512899i	$-0.171429\pi$
$701$	0.549432	+	0.438157i	0.549432	+	0.438157i	−0.309017	+	0.951057i	$0.600000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.03181	+	0.259994i	1.03181	+	0.259994i
$707$		0			0
$708$		0			0
$709$	1.95005	+	0.353882i	1.95005	+	0.353882i	0.998993	+	0.0448648i	$0.0142857\pi$
$709$	1.95005	+	0.353882i	1.95005	+	0.353882i	0.951057	+	0.309017i	$0.100000\pi$
$710$		0			0
$711$		0			0
$712$	1.57455	−	1.09085i	1.57455	−	1.09085i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.834573	−	0.550897i	$-0.814286\pi$
$719$		0			0		0.834573	+	0.550897i	$0.185714\pi$
$720$	0.919528	−	0.393025i	0.919528	−	0.393025i
$721$		0			0
$722$	0.858449	+	0.512899i	0.858449	+	0.512899i
$723$		0			0
$724$	−1.96786			−1.96786
$725$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$726$		0			0
$727$		0			0		−0.998993	−	0.0448648i	$-0.985714\pi$
$727$		0			0		0.998993	+	0.0448648i	$0.0142857\pi$
$728$		0			0
$729$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$730$	−1.07417	−	0.245172i	−1.07417	−	0.245172i
$731$		0			0
$732$		0			0
$733$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$733$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−1.05360	+	0.729937i	−1.05360	+	0.729937i
$739$		0			0		−0.493508	−	0.869741i	$-0.664286\pi$
$739$		0			0		0.493508	+	0.869741i	$0.335714\pi$
$740$	−1.32630	+	0.713714i	−1.32630	+	0.713714i
$741$		0			0
$742$		0			0
$743$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$743$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$744$		0			0
$745$	1.78082	−	0.578625i	1.78082	−	0.578625i
$746$	−0.0423578	−	1.88729i	−0.0423578	−	1.88729i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$751$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$752$		0			0
$753$		0			0
$754$	0.119404	−	0.473869i	0.119404	−	0.473869i
$755$		0			0
$756$		0			0
$757$	−1.34747	−	0.307552i	−1.34747	−	0.307552i	−0.512899	−	0.858449i	$-0.671429\pi$
$757$	−1.34747	−	0.307552i	−1.34747	−	0.307552i	−0.834573	+	0.550897i	$0.814286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.778936	−	1.82241i	−0.778936	−	1.82241i	−0.512899	−	0.858449i	$-0.671429\pi$
$761$	−0.778936	−	1.82241i	−0.778936	−	1.82241i	−0.266037	−	0.963963i	$-0.585714\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.331743	+	0.415992i	−0.331743	+	0.415992i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.132501	+	0.647133i	0.132501	+	0.647133i	0.990950	+	0.134233i	$0.0428571\pi$
$769$	0.132501	+	0.647133i	0.132501	+	0.647133i	−0.858449	+	0.512899i	$0.828571\pi$
$770$		0			0
$771$		0			0
$772$	0.0360371	+	0.266037i	0.0360371	+	0.266037i
$773$	−1.04084	−	0.909354i	−1.04084	−	0.909354i	−0.0448648	−	0.998993i	$-0.514286\pi$
$773$	−1.04084	−	0.909354i	−1.04084	−	0.909354i	−0.995974	+	0.0896393i	$0.971429\pi$
$774$		0			0
$775$		0			0
$776$	−1.79295	−	0.409228i	−1.79295	−	0.409228i
$777$		0			0
$778$	0.365264	−	1.78394i	0.365264	−	1.78394i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$785$	0.0320114	+	0.355676i	0.0320114	+	0.355676i
$786$		0			0
$787$		0			0		0.928115	−	0.372294i	$-0.121429\pi$
$787$		0			0		−0.928115	+	0.372294i	$0.878571\pi$
$788$	−0.785295	+	1.38397i	−0.785295	+	1.38397i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.933491	+	0.213063i	−0.933491	+	0.213063i
$794$	0.0445940	−	1.98692i	0.0445940	−	1.98692i
$795$		0			0
$796$		0			0
$797$	0.699921	+	1.86493i	0.699921	+	1.86493i	0.433884	+	0.900969i	$0.357143\pi$
$797$	0.699921	+	1.86493i	0.699921	+	1.86493i	0.266037	+	0.963963i	$0.414286\pi$
$798$		0			0
$799$		0			0
$800$	−0.998993	−	0.0448648i	−0.998993	−	0.0448648i
$801$	1.80801	+	0.632650i	1.80801	+	0.632650i
$802$	1.31058	−	1.50008i	1.31058	−	1.50008i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	0.557764	+	0.140544i	0.557764	+	0.140544i
$809$	−0.0500876	+	0.742901i	−0.0500876	+	0.742901i	0.900969	+	0.433884i	$0.142857\pi$
$809$	−0.0500876	+	0.742901i	−0.0500876	+	0.742901i	−0.951057	+	0.309017i	$0.900000\pi$
$810$	0.858449	+	0.512899i	0.858449	+	0.512899i
$811$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$811$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.13181	+	0.127524i	1.13181	+	0.127524i
$819$		0			0
$820$	1.26597	−	0.200510i	1.26597	−	0.200510i
$821$	1.13021	+	1.08059i	1.13021	+	1.08059i	0.995974	+	0.0896393i	$0.0285714\pi$
$821$	1.13021	+	1.08059i	1.13021	+	1.08059i	0.134233	+	0.990950i	$0.457143\pi$
$822$		0			0
$823$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$823$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$827$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$828$		0			0
$829$	1.36795	−	0.697007i	1.36795	−	0.697007i	0.393025	−	0.919528i	$-0.371429\pi$
$829$	1.36795	−	0.697007i	1.36795	−	0.697007i	0.974928	+	0.222521i	$0.0714286\pi$
$830$		0			0
$831$		0			0
$832$	0.461258	−	0.161401i	0.461258	−	0.161401i
$833$	0.0714220	−	0.527258i	0.0714220	−	0.527258i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.674671	−	0.738119i	$-0.735714\pi$
$839$		0			0		0.674671	+	0.738119i	$0.264286\pi$
$840$		0			0
$841$	0.0448648	−	0.998993i	0.0448648	−	0.998993i
$842$	1.76007	+	0.896802i	1.76007	+	0.896802i
$843$		0			0
$844$		0			0
$845$	0.733760	+	0.202505i	0.733760	+	0.202505i
$846$		0			0
$847$		0			0
$848$	−0.149356	+	0.372340i	−0.149356	+	0.372340i
$849$		0			0
$850$	0.479382	−	0.230858i	0.479382	−	0.230858i
$851$		0			0
$852$		0			0
$853$	1.88490	+	0.612441i	1.88490	+	0.612441i	0.983930	+	0.178557i	$0.0571429\pi$
$853$	1.88490	+	0.612441i	1.88490	+	0.612441i	0.900969	+	0.433884i	$0.142857\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.467085	−	1.33485i	0.467085	−	1.33485i	−0.433884	−	0.900969i	$-0.642857\pi$
$857$	0.467085	−	1.33485i	0.467085	−	1.33485i	0.900969	−	0.433884i	$-0.142857\pi$
$858$		0			0
$859$		0			0		0.822002	−	0.569484i	$-0.192857\pi$
$859$		0			0		−0.822002	+	0.569484i	$0.807143\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.0672690	−	0.997735i	$-0.478571\pi$
$863$		0			0		−0.0672690	+	0.997735i	$0.521429\pi$
$864$		0			0
$865$	−0.984781	−	0.0663956i	−0.984781	−	0.0663956i
$866$	0.747578	−	1.74905i	0.747578	−	1.74905i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.149621	+	0.0987640i	−0.149621	+	0.0987640i
$873$	−0.722795	−	1.69106i	−0.722795	−	1.69106i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.65391	−	0.663432i	−1.65391	−	0.663432i	−0.657939	−	0.753071i	$-0.728571\pi$
$877$	−1.65391	−	0.663432i	−1.65391	−	0.663432i	−0.995974	+	0.0896393i	$0.971429\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.98692	+	0.0445940i	1.98692	+	0.0445940i	0.995974	−	0.0896393i	$-0.0285714\pi$
$881$	1.98692	+	0.0445940i	1.98692	+	0.0445940i	0.990950	+	0.134233i	$0.0428571\pi$
$882$	−1.00000			−1.00000
$883$		0			0		−0.999748	−	0.0224381i	$-0.992857\pi$
$883$		0			0		0.999748	+	0.0224381i	$0.00714286\pi$
$884$	−0.175424	+	0.191921i	−0.175424	+	0.191921i
$885$		0			0
$886$		0			0
$887$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$887$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$888$		0			0
$889$		0			0
$890$	−1.35446	−	1.35446i	−1.35446	−	1.35446i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.230935	−	1.45806i	0.230935	−	1.45806i
$899$		0			0
$900$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$901$	−0.0238996	−	0.212115i	−0.0238996	−	0.212115i
$902$		0			0
$903$		0			0
$904$	0.522106	+	0.790956i	0.522106	+	0.790956i
$905$	0.351375	+	1.93623i	0.351375	+	1.93623i
$906$		0			0
$907$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$907$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$908$		0			0
$909$	0.214143	+	0.533850i	0.214143	+	0.533850i
$910$		0			0
$911$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$911$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$912$		0			0
$913$		0			0
$914$	0.574515	−	0.325991i	0.574515	−	0.325991i
$915$		0			0
$916$	0.816934	−	0.129390i	0.816934	−	0.129390i
$917$		0			0
$918$		0			0
$919$		0			0		−0.990950	−	0.134233i	$-0.957143\pi$
$919$		0			0		0.990950	+	0.134233i	$0.0428571\pi$
$920$		0			0
$921$		0			0
$922$	0.129390	−	0.284860i	0.129390	−	0.284860i
$923$		0			0
$924$		0			0
$925$	0.939065	+	1.17755i	0.939065	+	1.17755i
$926$		0			0
$927$		0			0
$928$	0.858449	−	0.512899i	0.858449	−	0.512899i
$929$	1.25147	+	0.406628i	1.25147	+	0.406628i	0.858449	−	0.512899i	$-0.171429\pi$
$929$	1.25147	+	0.406628i	1.25147	+	0.406628i	0.393025	+	0.919528i	$0.371429\pi$
$930$		0			0
$931$		0			0
$932$	0.644599	−	1.02587i	0.644599	−	1.02587i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.401697	+	0.278296i	0.401697	+	0.278296i
$937$	0.472814	−	1.57455i	0.472814	−	1.57455i	−0.309017	−	0.951057i	$-0.600000\pi$
$937$	0.472814	−	1.57455i	0.472814	−	1.57455i	0.781831	−	0.623490i	$-0.214286\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.209906	+	1.15668i	−0.209906	+	1.15668i	0.691063	+	0.722795i	$0.257143\pi$
$941$	−0.209906	+	1.15668i	−0.209906	+	1.15668i	−0.900969	+	0.433884i	$0.857143\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.0896393	−	0.995974i	$-0.471429\pi$
$947$		0			0		−0.0896393	+	0.995974i	$0.528571\pi$
$948$		0			0
$949$	−0.177831	−	0.508211i	−0.177831	−	0.508211i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.18961	−	1.42493i	−1.18961	−	1.42493i	−0.880596	−	0.473869i	$-0.842857\pi$
$953$	−1.18961	−	1.42493i	−1.18961	−	1.42493i	−0.309017	−	0.951057i	$-0.600000\pi$
$954$	−0.389019	+	0.0980242i	−0.389019	+	0.0980242i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.657939	−	0.753071i	0.657939	−	0.753071i
$962$	−0.640150	−	0.363233i	−0.640150	−	0.363233i
$963$		0			0
$964$	−1.77278	+	0.757723i	−1.77278	+	0.757723i
$965$	0.255327	−	0.0829607i	0.255327	−	0.0829607i
$966$		0			0
$967$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$967$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$968$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$969$		0			0
$970$	−0.0825089	+	1.83720i	−0.0825089	+	1.83720i
$971$		0			0		0.413559	−	0.910478i	$-0.364286\pi$
$971$		0			0		−0.413559	+	0.910478i	$0.635714\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.65903	−	1.04244i	−1.65903	−	1.04244i
$977$	−0.0255563	+	0.0368883i	−0.0255563	+	0.0368883i	−0.834573	−	0.550897i	$-0.814286\pi$
$977$	−0.0255563	+	0.0368883i	−0.0255563	+	0.0368883i	0.809017	+	0.587785i	$0.200000\pi$
$978$		0			0
$979$		0			0
$980$	0.900969	+	0.433884i	0.900969	+	0.433884i
$981$	−0.167847	−	0.0629940i	−0.167847	−	0.0629940i
$982$		0			0
$983$		0			0		−0.0896393	−	0.995974i	$-0.528571\pi$
$983$		0			0		0.0896393	+	0.995974i	$0.471429\pi$
$984$		0			0
$985$	1.50195	+	0.525556i	1.50195	+	0.525556i
$986$	−0.272900	+	0.456758i	−0.272900	+	0.456758i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.266037	−	0.963963i	$-0.585714\pi$
$991$		0			0		0.266037	+	0.963963i	$0.414286\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.78563	−	0.241880i	1.78563	−	0.241880i	0.834573	−	0.550897i	$-0.185714\pi$
$997$	1.78563	−	0.241880i	1.78563	−	0.241880i	0.951057	+	0.309017i	$0.100000\pi$
$998$		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.623.1	✓	48
4.3	odd	2	CM	2900.1.cr.a.623.1	✓	48
25.12	odd	20		2900.1.da.a.1087.1	yes	48
29.27	odd	28		2900.1.da.a.723.1	yes	48
100.87	even	20		2900.1.da.a.1087.1	yes	48
116.27	even	28		2900.1.da.a.723.1	yes	48
725.462	even	140	inner	2900.1.cr.a.1187.1	yes	48
2900.1187	odd	140	inner	2900.1.cr.a.1187.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2900.1.cr.a.623.1	✓	48	1.1	even	1	trivial
2900.1.cr.a.623.1	✓	48	4.3	odd	2	CM
2900.1.cr.a.1187.1	yes	48	725.462	even	140	inner
2900.1.cr.a.1187.1	yes	48	2900.1187	odd	140	inner
2900.1.da.a.723.1	yes	48	29.27	odd	28
2900.1.da.a.723.1	yes	48	116.27	even	28
2900.1.da.a.1087.1	yes	48	25.12	odd	20
2900.1.da.a.1087.1	yes	48	100.87	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)

\(f(q)\)	\(=\)	\(q+(0.998993 + 0.0448648i) q^{2} +(0.995974 + 0.0896393i) q^{4} +(-0.0896393 - 0.995974i) q^{5} +(0.990950 + 0.134233i) q^{8} +(0.473869 + 0.880596i) q^{9} +O(q^{10})\)	\(q+(0.998993 + 0.0448648i) q^{2} +(0.995974 + 0.0896393i) q^{4} +(-0.0896393 - 0.995974i) q^{5} +(0.990950 + 0.134233i) q^{8} +(0.473869 + 0.880596i) q^{9} +(-0.0448648 - 0.998993i) q^{10} +(0.401697 - 0.278296i) q^{13} +(0.983930 + 0.178557i) q^{16} +(-0.506032 + 0.164420i) q^{17} +(0.433884 + 0.900969i) q^{18} -1.00000i q^{20} +(-0.983930 + 0.178557i) q^{25} +(0.413778 - 0.259994i) q^{26} +(0.722795 - 0.691063i) q^{29} +(0.974928 + 0.222521i) q^{32} +(-0.512899 + 0.141551i) q^{34} +(0.393025 + 0.919528i) q^{36} +(-0.713714 - 1.32630i) q^{37} +(0.0448648 - 0.998993i) q^{40} +(0.200510 + 1.26597i) q^{41} +(0.834573 - 0.550897i) q^{45} +(-0.433884 + 0.900969i) q^{49} +(-0.990950 + 0.134233i) q^{50} +(0.425026 - 0.241168i) q^{52} +(-0.0804722 + 0.393025i) q^{53} +(0.753071 - 0.657939i) q^{58} +(-1.81850 - 0.729454i) q^{61} +(0.963963 + 0.266037i) q^{64} +(-0.313184 - 0.375133i) q^{65} +(-0.518733 + 0.118398i) q^{68} +(0.351375 + 0.936235i) q^{72} +(0.293118 - 1.06209i) q^{73} +(-0.653491 - 1.35699i) q^{74} +(0.0896393 - 0.995974i) q^{80} +(-0.550897 + 0.834573i) q^{81} +(0.143511 + 1.27369i) q^{82} +(0.209118 + 0.489257i) q^{85} +(1.41387 - 1.29233i) q^{89} +(0.858449 - 0.512899i) q^{90} +(-1.83165 - 0.164852i) q^{97} +(-0.473869 + 0.880596i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more