LMFDB - Embedded newform 847.1.bb.a.587.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,1,Mod(20,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([55, 76]))

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

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

chi := DirichletCharacter("847.20");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	847.bb (of order $110$, degree $40$, 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:	$0.422708065700$
Analytic rank:	$0$
Dimension:	$40$
Coefficient field:	$\Q(\zeta_{55})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{39} + x^{35} - x^{34} + x^{30} - x^{28} + x^{25} - x^{23} + x^{20} - x^{17} + x^{15} + \cdots + 1 $ x^40 - x^39 + x^35 - x^34 + x^30 - x^28 + x^25 - x^23 + x^20 - x^17 + x^15 - x^12 + x^10 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{55}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{55} - \cdots)$

Embedding invariants

Embedding label			587.1
Root			$0.941844 + 0.336049i$ of defining polynomial
Character	$\chi$	$=$	847.587
Dual form			847.1.bb.a.531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38779 - 0.495163i) q^{2} +(0.906636 + 0.741353i) q^{4} +(-0.736741 + 0.676175i) q^{7} +(-0.130228 - 0.215960i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.38779 - 0.495163i) q^{2} +(0.906636 + 0.741353i) q^{4} +(-0.736741 + 0.676175i) q^{7} +(-0.130228 - 0.215960i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.610648 - 0.791902i) q^{11} +(1.35726 - 0.573583i) q^{14} +(-0.158785 - 0.783633i) q^{16} +(0.831697 + 1.21632i) q^{18} +(-1.23957 + 0.796625i) q^{22} +(0.825414 - 1.80741i) q^{23} +(0.897398 + 0.441221i) q^{25} +(-1.16924 + 0.0668596i) q^{28} +(1.74815 - 0.859509i) q^{29} +(-0.203556 + 1.41576i) q^{32} +(-0.297728 - 1.13267i) q^{36} +(-0.157116 + 0.597730i) q^{37} +(-0.260098 + 0.300169i) q^{43} +(1.14071 - 0.265262i) q^{44} +(-2.04046 + 2.09959i) q^{46} +(0.0855750 - 0.996332i) q^{49} +(-1.02693 - 1.05668i) q^{50} +(0.276810 - 1.36611i) q^{53} +(0.241971 + 0.0710492i) q^{56} +(-2.85167 + 0.327199i) q^{58} +(0.993482 - 0.113991i) q^{63} +(0.610398 - 1.15683i) q^{64} +(0.895528 - 0.262951i) q^{67} +(-1.39160 - 1.43192i) q^{71} +(-0.0215809 + 0.251261i) q^{72} +(0.514017 - 0.751726i) q^{74} +(0.0855750 + 0.996332i) q^{77} +(-0.0620945 - 0.722954i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.509595 - 0.287781i) q^{86} +(-0.250543 - 0.0287471i) q^{88} +(2.08828 - 1.02674i) q^{92} +(-0.612107 + 1.34033i) q^{98} +(-0.959493 + 0.281733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	$ 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{6}{55}\right)$

Coefficient data

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

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

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

$2$	−1.38779	−	0.495163i	−1.38779	−	0.495163i	−0.466667	−	0.884433i	$-0.654545\pi$
$2$	−1.38779	−	0.495163i	−1.38779	−	0.495163i	−0.921124	+	0.389270i	$0.872727\pi$
$3$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$3$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$4$	0.906636	+	0.741353i	0.906636	+	0.741353i
$5$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$5$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$6$		0			0
$7$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$7$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$8$	−0.130228	−	0.215960i	−0.130228	−	0.215960i
$9$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$10$		0			0
$11$	0.610648	−	0.791902i	0.610648	−	0.791902i
$11$	0.610648	−	0.791902i	0.610648	−	0.791902i
$12$		0			0
$13$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$13$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$14$	1.35726	−	0.573583i	1.35726	−	0.573583i
$15$		0			0
$16$	−0.158785	−	0.783633i	−0.158785	−	0.783633i
$17$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$17$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$18$	0.831697	+	1.21632i	0.831697	+	1.21632i
$19$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$19$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$20$		0			0
$21$		0			0
$22$	−1.23957	+	0.796625i	−1.23957	+	0.796625i
$23$	0.825414	−	1.80741i	0.825414	−	1.80741i	0.309017	−	0.951057i	$-0.400000\pi$
$23$	0.825414	−	1.80741i	0.825414	−	1.80741i	0.516397	−	0.856349i	$-0.327273\pi$
$24$		0			0
$25$	0.897398	+	0.441221i	0.897398	+	0.441221i
$26$		0			0
$27$		0			0
$28$	−1.16924	+	0.0668596i	−1.16924	+	0.0668596i
$29$	1.74815	−	0.859509i	1.74815	−	0.859509i	0.774142	−	0.633012i	$-0.218182\pi$
$29$	1.74815	−	0.859509i	1.74815	−	0.859509i	0.974012	−	0.226497i	$-0.0727273\pi$
$30$		0			0
$31$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$31$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$32$	−0.203556	+	1.41576i	−0.203556	+	1.41576i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.297728	−	1.13267i	−0.297728	−	1.13267i
$37$	−0.157116	+	0.597730i	−0.157116	+	0.597730i	0.841254	+	0.540641i	$0.181818\pi$
$37$	−0.157116	+	0.597730i	−0.157116	+	0.597730i	−0.998369	+	0.0570888i	$0.981818\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$41$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$42$		0			0
$43$	−0.260098	+	0.300169i	−0.260098	+	0.300169i	−0.870746	−	0.491733i	$-0.836364\pi$
$43$	−0.260098	+	0.300169i	−0.260098	+	0.300169i	0.610648	+	0.791902i	$0.290909\pi$
$44$	1.14071	−	0.265262i	1.14071	−	0.265262i
$45$		0			0
$46$	−2.04046	+	2.09959i	−2.04046	+	2.09959i
$47$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$47$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$48$		0			0
$49$	0.0855750	−	0.996332i	0.0855750	−	0.996332i
$50$	−1.02693	−	1.05668i	−1.02693	−	1.05668i
$51$		0			0
$52$		0			0
$53$	0.276810	−	1.36611i	0.276810	−	1.36611i	−0.564443	−	0.825472i	$-0.690909\pi$
$53$	0.276810	−	1.36611i	0.276810	−	1.36611i	0.841254	−	0.540641i	$-0.181818\pi$
$54$		0			0
$55$		0			0
$56$	0.241971	+	0.0710492i	0.241971	+	0.0710492i
$57$		0			0
$58$	−2.85167	+	0.327199i	−2.85167	+	0.327199i
$59$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$59$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$60$		0			0
$61$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$61$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$62$		0			0
$63$	0.993482	−	0.113991i	0.993482	−	0.113991i
$64$	0.610398	−	1.15683i	0.610398	−	1.15683i
$65$		0			0
$66$		0			0
$67$	0.895528	−	0.262951i	0.895528	−	0.262951i	0.198590	−	0.980083i	$-0.436364\pi$
$67$	0.895528	−	0.262951i	0.895528	−	0.262951i	0.696938	+	0.717132i	$0.254545\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.39160	−	1.43192i	−1.39160	−	1.43192i	−0.736741	−	0.676175i	$-0.763636\pi$
$71$	−1.39160	−	1.43192i	−1.39160	−	1.43192i	−0.654861	−	0.755750i	$-0.727273\pi$
$72$	−0.0215809	+	0.251261i	−0.0215809	+	0.251261i
$73$		0			0		−0.993482	−	0.113991i	$-0.963636\pi$
$73$		0			0		0.993482	+	0.113991i	$0.0363636\pi$
$74$	0.514017	−	0.751726i	0.514017	−	0.751726i
$75$		0			0
$76$		0			0
$77$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$78$		0			0
$79$	−0.0620945	−	0.722954i	−0.0620945	−	0.722954i	−0.959493	−	0.281733i	$-0.909091\pi$
$79$	−0.0620945	−	0.722954i	−0.0620945	−	0.722954i	0.897398	−	0.441221i	$-0.145455\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.309017	+	0.951057i
$82$		0			0
$83$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$83$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$84$		0			0
$85$		0			0
$86$	0.509595	−	0.287781i	0.509595	−	0.287781i
$87$		0			0
$88$	−0.250543	−	0.0287471i	−0.250543	−	0.0287471i
$89$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$89$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$90$		0			0
$91$		0			0
$92$	2.08828	−	1.02674i	2.08828	−	1.02674i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		0.974012	−	0.226497i	$-0.0727273\pi$
$97$		0			0		−0.974012	+	0.226497i	$0.927273\pi$
$98$	−0.612107	+	1.34033i	−0.612107	+	1.34033i
$99$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$100$	0.486513	+	1.06532i	0.486513	+	1.06532i
$101$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$101$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$102$		0			0
$103$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$103$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$104$		0			0
$105$		0			0
$106$	−1.06060	+	1.75881i	−1.06060	+	1.75881i
$107$	−1.65323	+	0.698661i	−1.65323	+	0.698661i	−0.998369	−	0.0570888i	$-0.981818\pi$
$107$	−1.65323	+	0.698661i	−1.65323	+	0.698661i	−0.654861	+	0.755750i	$0.727273\pi$
$108$		0			0
$109$	−0.949680	+	0.610322i	−0.949680	+	0.610322i	−0.921124	−	0.389270i	$-0.872727\pi$
$109$	−0.949680	+	0.610322i	−0.949680	+	0.610322i	−0.0285561	+	0.999592i	$0.509091\pi$
$110$		0			0
$111$		0			0
$112$	0.646856	+	0.469968i	0.646856	+	0.469968i
$113$	0.972732	+	1.61310i	0.972732	+	1.61310i	0.774142	+	0.633012i	$0.218182\pi$
$113$	0.972732	+	1.61310i	0.972732	+	1.61310i	0.198590	+	0.980083i	$0.436364\pi$
$114$		0			0
$115$		0			0
$116$	2.22214	+	0.516736i	2.22214	+	0.516736i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.254218	−	0.967147i	−0.254218	−	0.967147i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.43519	−	0.333739i	−1.43519	−	0.333739i
$127$	−1.12496	+	1.45888i	−1.12496	+	1.45888i	−0.254218	+	0.967147i	$0.581818\pi$
$127$	−1.12496	+	1.45888i	−1.12496	+	1.45888i	−0.870746	+	0.491733i	$0.836364\pi$
$128$	−0.366150	+	0.336049i	−0.366150	+	0.336049i
$129$		0			0
$130$		0			0
$131$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$131$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$132$		0			0
$133$		0			0
$134$	−1.37301	−	0.0785115i	−1.37301	−	0.0785115i
$135$		0			0
$136$		0			0
$137$	0.307474	+	1.51745i	0.307474	+	1.51745i	0.774142	+	0.633012i	$0.218182\pi$
$137$	0.307474	+	1.51745i	0.307474	+	1.51745i	−0.466667	+	0.884433i	$0.654545\pi$
$138$		0			0
$139$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$139$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$140$		0			0
$141$		0			0
$142$	1.22222	+	2.67628i	1.22222	+	2.67628i
$143$		0			0
$144$	−0.332148	+	0.727303i	−0.332148	+	0.727303i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.585575	+	0.425445i	−0.585575	+	0.425445i
$149$	1.91586	−	0.109553i	1.91586	−	0.109553i	0.941844	−	0.336049i	$-0.109091\pi$
$149$	1.91586	−	0.109553i	1.91586	−	0.109553i	0.974012	+	0.226497i	$0.0727273\pi$
$150$		0			0
$151$	0.799530	−	0.653772i	0.799530	−	0.653772i	−0.142315	−	0.989821i	$-0.545455\pi$
$151$	0.799530	−	0.653772i	0.799530	−	0.653772i	0.941844	+	0.336049i	$0.109091\pi$
$152$		0			0
$153$		0			0
$154$	0.374586	−	1.42507i	0.374586	−	1.42507i
$155$		0			0
$156$		0			0
$157$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$157$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$158$	−0.271806	+	1.03406i	−0.271806	+	1.03406i
$159$		0			0
$160$		0			0
$161$	0.614005	+	1.88971i	0.614005	+	1.88971i
$162$	0.0420768	−	1.47288i	0.0420768	−	1.47288i
$163$	0.153590	+	1.78821i	0.153590	+	1.78821i	0.516397	+	0.856349i	$0.327273\pi$
$163$	0.153590	+	1.78821i	0.153590	+	1.78821i	−0.362808	+	0.931864i	$0.618182\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$167$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$168$		0			0
$169$	0.993482	+	0.113991i	0.993482	+	0.113991i
$170$		0			0
$171$		0			0
$172$	−0.458346	+	0.0793198i	−0.458346	+	0.0793198i
$173$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$173$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$174$		0			0
$175$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$176$	−0.717522	−	0.352782i	−0.717522	−	0.352782i
$177$		0			0
$178$		0			0
$179$	−1.83024	+	0.210000i	−1.83024	+	0.210000i	−0.959493	−	0.281733i	$-0.909091\pi$
$179$	−1.83024	+	0.210000i	−1.83024	+	0.210000i	−0.870746	+	0.491733i	$0.836364\pi$
$180$		0			0
$181$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$181$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$182$		0			0
$183$		0			0
$184$	−0.497819	+	0.0571194i	−0.497819	+	0.0571194i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.714988	−	0.123734i	0.714988	−	0.123734i	0.198590	−	0.980083i	$-0.436364\pi$
$191$	0.714988	−	0.123734i	0.714988	−	0.123734i	0.516397	+	0.856349i	$0.327273\pi$
$192$		0			0
$193$	0.161197	−	1.87678i	0.161197	−	1.87678i	−0.254218	−	0.967147i	$-0.581818\pi$
$193$	0.161197	−	1.87678i	0.161197	−	1.87678i	0.415415	−	0.909632i	$-0.363636\pi$
$194$		0			0
$195$		0			0
$196$	0.816218	−	0.839869i	0.816218	−	0.839869i
$197$	−1.01391	−	1.17011i	−1.01391	−	1.17011i	−0.985354	−	0.170522i	$-0.945455\pi$
$197$	−1.01391	−	1.17011i	−1.01391	−	1.17011i	−0.0285561	−	0.999592i	$-0.509091\pi$
$198$	1.47108	+	0.0841194i	1.47108	+	0.0841194i
$199$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$199$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$200$	−0.0215809	−	0.251261i	−0.0215809	−	0.251261i
$201$		0			0
$202$		0			0
$203$	−0.706758	+	1.81529i	−0.706758	+	1.81529i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.73014	+	0.977055i	−1.73014	+	0.977055i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.184465	+	0.473794i	0.184465	+	0.473794i	0.993482	−	0.113991i	$-0.0363636\pi$
$211$	0.184465	+	0.473794i	0.184465	+	0.473794i	−0.809017	+	0.587785i	$0.800000\pi$
$212$	1.26374	−	1.03335i	1.26374	−	1.03335i
$213$		0			0
$214$	2.64029	−	0.150977i	2.64029	−	0.150977i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.62017	−	0.376753i	1.62017	−	0.376753i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$223$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$224$	−0.807335	−	1.18069i	−0.807335	−	1.18069i
$225$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$226$	−0.551204	−	2.72030i	−0.551204	−	2.72030i
$227$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$227$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$228$		0			0
$229$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$229$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$230$		0			0
$231$		0			0
$232$	−0.413279	−	0.265598i	−0.413279	−	0.265598i
$233$	0.230270	+	0.167301i	0.230270	+	0.167301i	0.696938	−	0.717132i	$-0.254545\pi$
$233$	0.230270	+	0.167301i	0.230270	+	0.167301i	−0.466667	+	0.884433i	$0.654545\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.288416	+	0.887654i	−0.288416	+	0.887654i	0.696938	+	0.717132i	$0.254545\pi$
$239$	−0.288416	+	0.887654i	−0.288416	+	0.887654i	−0.985354	+	0.170522i	$0.945455\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−0.126093	+	1.46808i	−0.126093	+	1.46808i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$251$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$252$	0.985234	+	0.633172i	0.985234	+	0.633172i
$253$	−0.927251	−	1.75734i	−0.927251	−	1.75734i
$254$	2.28360	−	1.46758i	2.28360	−	1.46758i
$255$		0			0
$256$	−0.530286	+	0.224101i	−0.530286	+	0.224101i
$257$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$257$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$258$		0			0
$259$	−0.288416	−	0.546610i	−0.288416	−	0.546610i
$260$		0			0
$261$	−1.91949	−	0.332181i	−1.91949	−	0.332181i
$262$		0			0
$263$	−0.829475	−	1.81630i	−0.829475	−	1.81630i	−0.466667	−	0.884433i	$-0.654545\pi$
$263$	−0.829475	−	1.81630i	−0.829475	−	1.81630i	−0.362808	−	0.931864i	$-0.618182\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.00686	+	0.425501i	1.00686	+	0.425501i
$269$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$269$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$270$		0			0
$271$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$271$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$272$		0			0
$273$		0			0
$274$	0.324673	−	2.25815i	0.324673	−	2.25815i
$275$	0.897398	−	0.441221i	0.897398	−	0.441221i
$276$		0			0
$277$	1.71599	−	0.969062i	1.71599	−	0.969062i	0.774142	−	0.633012i	$-0.218182\pi$
$277$	1.71599	−	0.969062i	1.71599	−	0.969062i	0.941844	−	0.336049i	$-0.109091\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.505709	+	1.29890i	−0.505709	+	1.29890i	0.415415	+	0.909632i	$0.363636\pi$
$281$	−0.505709	+	1.29890i	−0.505709	+	1.29890i	−0.921124	+	0.389270i	$0.872727\pi$
$282$		0			0
$283$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$283$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$284$	−0.200115	−	2.32990i	−0.200115	−	2.32990i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.996844	−	1.02573i	0.996844	−	1.02573i
$289$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$293$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$294$		0			0
$295$		0			0
$296$	0.149546	−	0.0439108i	0.149546	−	0.0439108i
$297$		0			0
$298$	−2.71305	−	0.796625i	−2.71305	−	0.796625i
$299$		0			0
$300$		0			0
$301$	−0.0113419	−	0.397019i	−0.0113419	−	0.397019i
$302$	−1.43330	+	0.511402i	−1.43330	+	0.511402i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$307$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$308$	−0.661048	+	0.966751i	−0.661048	+	0.966751i
$309$		0			0
$310$		0			0
$311$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$311$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$312$		0			0
$313$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$313$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$314$		0			0
$315$		0			0
$316$	0.479666	−	0.701490i	0.479666	−	0.701490i
$317$	−1.12767	+	1.16034i	−1.12767	+	1.16034i	−0.142315	+	0.989821i	$0.545455\pi$
$317$	−1.12767	+	1.16034i	−1.12767	+	1.16034i	−0.985354	+	0.170522i	$0.945455\pi$
$318$		0			0
$319$	0.386859	−	1.90922i	0.386859	−	1.90922i
$320$		0			0
$321$		0			0
$322$	0.0836051	−	2.92656i	0.0836051	−	2.92656i
$323$		0			0
$324$	−0.424902	+	1.09135i	−0.424902	+	1.09135i
$325$		0			0
$326$	0.672306	−	2.55772i	0.672306	−	2.55772i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.00812790	−	0.0565308i	0.00812790	−	0.0565308i	−0.985354	−	0.170522i	$-0.945455\pi$
$331$	0.00812790	−	0.0565308i	0.00812790	−	0.0565308i	0.993482	+	0.113991i	$0.0363636\pi$
$332$		0			0
$333$	0.478446	−	0.391223i	0.478446	−	0.391223i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0526073	+	0.0222320i	0.0526073	+	0.0222320i	0.415415	−	0.909632i	$-0.363636\pi$
$337$	0.0526073	+	0.0222320i	0.0526073	+	0.0222320i	−0.362808	+	0.931864i	$0.618182\pi$
$338$	−1.32230	−	0.650131i	−1.32230	−	0.650131i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.610648	+	0.791902i	0.610648	+	0.791902i
$344$	0.0986967	+	0.0170801i	0.0986967	+	0.0170801i
$345$		0			0
$346$		0			0
$347$	−0.345844	−	1.70681i	−0.345844	−	1.70681i	−0.654861	−	0.755750i	$-0.727273\pi$
$347$	−0.345844	−	1.70681i	−0.345844	−	1.70681i	0.309017	−	0.951057i	$-0.400000\pi$
$348$		0			0
$349$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$349$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$350$	1.47108	+	0.0841194i	1.47108	+	0.0841194i
$351$		0			0
$352$	0.996844	+	1.02573i	0.996844	+	1.02573i
$353$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$353$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	2.64397	+	0.614830i	2.64397	+	0.614830i
$359$	−0.0442129	−	0.0361527i	−0.0442129	−	0.0361527i	0.610648	−	0.791902i	$-0.290909\pi$
$359$	−0.0442129	−	0.0361527i	−0.0442129	−	0.0361527i	−0.654861	+	0.755750i	$0.727273\pi$
$360$		0			0
$361$	0.941844	+	0.336049i	0.941844	+	0.336049i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$367$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$368$	−1.54740	−	0.359834i	−1.54740	−	0.359834i
$369$		0			0
$370$		0			0
$371$	0.719794	+	1.19364i	0.719794	+	1.19364i
$372$		0			0
$373$	0.698939	+	0.449181i	0.698939	+	0.449181i	0.841254	−	0.540641i	$-0.181818\pi$
$373$	0.698939	+	0.449181i	0.698939	+	0.449181i	−0.142315	+	0.989821i	$0.545455\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.205103	+	1.01222i	0.205103	+	1.01222i	0.941844	+	0.336049i	$0.109091\pi$
$379$	0.205103	+	1.01222i	0.205103	+	1.01222i	−0.736741	+	0.676175i	$0.763636\pi$
$380$		0			0
$381$		0			0
$382$	−1.05352	−	0.182319i	−1.05352	−	0.182319i
$383$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$383$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$384$		0			0
$385$		0			0
$386$	−1.15302	+	2.52476i	−1.15302	+	2.52476i
$387$	0.386859	−	0.0899602i	0.386859	−	0.0899602i
$388$		0			0
$389$	−0.951332	−	0.402036i	−0.951332	−	0.402036i	−0.142315	−	0.989821i	$-0.545455\pi$
$389$	−0.951332	−	0.402036i	−0.951332	−	0.402036i	−0.809017	+	0.587785i	$0.800000\pi$
$390$		0			0
$391$		0			0
$392$	−0.226312	+	0.111270i	−0.226312	+	0.111270i
$393$		0			0
$394$	0.827698	+	2.12592i	0.827698	+	2.12592i
$395$		0			0
$396$	−1.07877	−	0.455894i	−1.07877	−	0.455894i
$397$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$397$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$398$		0			0
$399$		0			0
$400$	0.203262	−	0.773290i	0.203262	−	0.773290i
$401$	0.442719	+	0.250015i	0.442719	+	0.250015i	0.696938	−	0.717132i	$-0.254545\pi$
$401$	0.442719	+	0.250015i	0.442719	+	0.250015i	−0.254218	+	0.967147i	$0.581818\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	1.87970	−	2.16929i	1.87970	−	2.16929i
$407$	0.377401	+	0.489423i	0.377401	+	0.489423i
$408$		0			0
$409$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$409$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	2.88488	−	0.499247i	2.88488	−	0.499247i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$419$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$420$		0			0
$421$	−0.0567398	+	0.00651029i	−0.0567398	+	0.00651029i	−0.142315	−	0.989821i	$-0.545455\pi$
$421$	−0.0567398	+	0.00651029i	−0.0567398	+	0.00651029i	0.0855750	+	0.996332i	$0.472727\pi$
$422$	−0.0213934	−	0.748867i	−0.0213934	−	0.748867i
$423$		0			0
$424$	−0.331074	+	0.118127i	−0.331074	+	0.118127i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−2.01683	−	0.592195i	−2.01683	−	0.592195i
$429$		0			0
$430$		0			0
$431$	−0.391364	+	1.93146i	−0.391364	+	1.93146i	−0.0285561	+	0.999592i	$0.509091\pi$
$431$	−0.391364	+	1.93146i	−0.391364	+	1.93146i	−0.362808	+	0.931864i	$0.618182\pi$
$432$		0			0
$433$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$433$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$434$		0			0
$435$		0			0
$436$	−1.31348	−	0.150708i	−1.31348	−	0.150708i
$437$		0			0
$438$		0			0
$439$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$439$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$440$		0			0
$441$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$442$		0			0
$443$	0.0497301	−	1.74078i	0.0497301	−	1.74078i	−0.466667	−	0.884433i	$-0.654545\pi$
$443$	0.0497301	−	1.74078i	0.0497301	−	1.74078i	0.516397	−	0.856349i	$-0.327273\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.332516	+	1.26502i	0.332516	+	1.26502i
$449$	0.982973	−	0.555111i	0.982973	−	0.555111i	0.0855750	−	0.996332i	$-0.472727\pi$
$449$	0.982973	−	0.555111i	0.982973	−	0.555111i	0.897398	+	0.441221i	$0.145455\pi$
$450$	0.209698	+	1.45848i	0.209698	+	1.45848i
$451$		0			0
$452$	−0.313958	+	2.18363i	−0.313958	+	2.18363i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$461$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$462$		0			0
$463$	0.507345	+	1.11093i	0.507345	+	1.11093i	0.974012	+	0.226497i	$0.0727273\pi$
$463$	0.507345	+	1.11093i	0.507345	+	1.11093i	−0.466667	+	0.884433i	$0.654545\pi$
$464$	−0.951119	−	1.23343i	−0.951119	−	1.23343i
$465$		0			0
$466$	−0.236726	−	0.346200i	−0.236726	−	0.346200i
$467$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$467$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$468$		0			0
$469$	−0.481972	+	0.799260i	−0.481972	+	0.799260i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.0788763	+	0.389270i	0.0788763	+	0.389270i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.02693	+	0.942503i	−1.02693	+	0.942503i
$478$	0.839795	−	1.08907i	0.839795	−	1.08907i
$479$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$479$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.486513	−	1.06532i	0.486513	−	1.06532i
$485$		0			0
$486$		0			0
$487$	0.122736	−	0.377742i	0.122736	−	0.377742i	−0.870746	−	0.491733i	$-0.836364\pi$
$487$	0.122736	−	0.377742i	0.122736	−	0.377742i	0.993482	+	0.113991i	$0.0363636\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.612107	+	0.561786i	−0.612107	+	0.561786i	−0.921124	−	0.389270i	$-0.872727\pi$
$491$	−0.612107	+	0.561786i	−0.612107	+	0.561786i	0.309017	+	0.951057i	$0.400000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.99348	+	0.113991i	1.99348	+	0.113991i
$498$		0			0
$499$	−0.835549	+	1.38560i	−0.835549	+	1.38560i	0.0855750	+	0.996332i	$0.472727\pi$
$499$	−0.835549	+	1.38560i	−0.835549	+	1.38560i	−0.921124	+	0.389270i	$0.872727\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$503$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$504$	−0.153997	−	0.199707i	−0.153997	−	0.199707i
$505$		0			0
$506$	0.416663	+	2.89796i	0.416663	+	2.89796i
$507$		0			0
$508$	−2.10148	+	0.488678i	−2.10148	+	0.488678i
$509$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$509$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$510$		0			0
$511$		0			0
$512$	1.34307	−	0.0767994i	1.34307	−	0.0767994i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.129601	+	0.901393i	0.129601	+	0.901393i
$519$		0			0
$520$		0			0
$521$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$521$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$522$	2.49937	+	1.41146i	2.49937	+	1.41146i
$523$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$523$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$524$		0			0
$525$		0			0
$526$	0.251775	+	2.93137i	0.251775	+	2.93137i
$527$		0			0
$528$		0			0
$529$	−1.93055	−	2.22797i	−1.93055	−	2.22797i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.173410	−	0.159154i	−0.173410	−	0.159154i
$537$		0			0
$538$		0			0
$539$	−0.736741	−	0.676175i	−0.736741	−	0.676175i
$540$		0			0
$541$	0.237271	−	0.449678i	0.237271	−	0.449678i	−0.736741	−	0.676175i	$-0.763636\pi$
$541$	0.237271	−	0.449678i	0.237271	−	0.449678i	0.974012	+	0.226497i	$0.0727273\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.282774	+	0.0324453i	−0.282774	+	0.0324453i	−0.254218	−	0.967147i	$-0.581818\pi$
$547$	−0.282774	+	0.0324453i	−0.282774	+	0.0324453i	−0.0285561	+	0.999592i	$0.509091\pi$
$548$	−0.846195	+	1.60372i	−0.846195	+	1.60372i
$549$		0			0
$550$	−1.46388	+	0.167964i	−1.46388	+	0.167964i
$551$		0			0
$552$		0			0
$553$	0.534591	+	0.490643i	0.534591	+	0.490643i
$554$	−2.86127	+	0.495163i	−2.86127	+	0.495163i
$555$		0			0
$556$		0			0
$557$	−1.60749	−	0.184442i	−1.60749	−	0.184442i	−0.736741	−	0.676175i	$-0.763636\pi$
$557$	−1.60749	−	0.184442i	−1.60749	−	0.184442i	−0.870746	+	0.491733i	$0.836364\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.34499	−	1.55220i	1.34499	−	1.55220i
$563$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$563$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.870746	−	0.491733i	−0.870746	−	0.491733i
$568$	−0.128012	+	0.487007i	−0.128012	+	0.487007i
$569$	0.332955	+	1.26669i	0.332955	+	1.26669i	0.897398	+	0.441221i	$0.145455\pi$
$569$	0.332955	+	1.26669i	0.332955	+	1.26669i	−0.564443	+	0.825472i	$0.690909\pi$
$570$		0			0
$571$	−0.220344	−	1.53252i	−0.220344	−	1.53252i	−0.736741	−	0.676175i	$-0.763636\pi$
$571$	−0.220344	−	1.53252i	−0.220344	−	1.53252i	0.516397	−	0.856349i	$-0.327273\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.53819	−	1.25777i	1.53819	−	1.25777i
$576$	−1.17379	+	0.577115i	−1.17379	+	0.577115i
$577$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$577$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$578$	1.19207	−	0.866091i	1.19207	−	0.866091i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.912794	−	1.05342i	−0.912794	−	1.05342i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$587$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.493348	+	0.0282107i	0.493348	+	0.0282107i
$593$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$593$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$594$		0			0
$595$		0			0
$596$	1.81820	+	1.32100i	1.81820	+	1.32100i
$597$		0			0
$598$		0			0
$599$	−0.689352	+	0.893968i	−0.689352	+	0.893968i	−0.998369	−	0.0570888i	$-0.981818\pi$
$599$	−0.689352	+	0.893968i	−0.689352	+	0.893968i	0.309017	+	0.951057i	$0.400000\pi$
$600$		0			0
$601$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$601$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$602$	−0.180849	+	0.556595i	−0.180849	+	0.556595i
$603$	−0.879056	−	0.313647i	−0.879056	−	0.313647i
$604$	1.20956			1.20956
$605$		0			0
$606$		0			0
$607$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$607$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.899302	−	1.49133i	−0.899302	−	1.49133i	−0.870746	−	0.491733i	$-0.836364\pi$
$613$	−0.899302	−	1.49133i	−0.899302	−	1.49133i	−0.0285561	−	0.999592i	$-0.509091\pi$
$614$		0			0
$615$		0			0
$616$	0.204023	−	0.148232i	0.204023	−	0.148232i
$617$	1.02742	−	0.660282i	1.02742	−	0.660282i	0.0855750	−	0.996332i	$-0.472727\pi$
$617$	1.02742	−	0.660282i	1.02742	−	0.660282i	0.941844	+	0.336049i	$0.109091\pi$
$618$		0			0
$619$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$619$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.610648	+	0.791902i	0.610648	+	0.791902i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.468333	+	0.197919i	0.468333	+	0.197919i	0.610648	−	0.791902i	$-0.290909\pi$
$631$	0.468333	+	0.197919i	0.468333	+	0.197919i	−0.142315	+	0.989821i	$0.545455\pi$
$632$	−0.148042	+	0.107559i	−0.148042	+	0.107559i
$633$		0			0
$634$	2.13953	−	1.05193i	2.13953	−	1.05193i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.48226	+	2.45805i	−1.48226	+	2.45805i
$639$	0.284165	+	1.97641i	0.284165	+	1.97641i
$640$		0			0
$641$	0.442719	+	1.68428i	0.442719	+	1.68428i	0.696938	+	0.717132i	$0.254545\pi$
$641$	0.442719	+	1.68428i	0.442719	+	1.68428i	−0.254218	+	0.967147i	$0.581818\pi$
$642$		0			0
$643$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$643$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$644$	−0.844265	+	2.16848i	−0.844265	+	2.16848i
$645$		0			0
$646$		0			0
$647$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$647$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$648$	0.165147	−	0.190590i	0.165147	−	0.190590i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.18645	+	1.73512i	−1.18645	+	1.73512i
$653$	−1.83024	−	0.210000i	−1.83024	−	0.210000i	−0.870746	−	0.491733i	$-0.836364\pi$
$653$	−1.83024	−	0.210000i	−1.83024	−	0.210000i	−0.959493	+	0.281733i	$0.909091\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$659$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$660$		0			0
$661$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$661$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$662$	−0.0392718	+	0.0744283i	−0.0392718	+	0.0744283i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−0.857702	+	0.306027i	−0.857702	+	0.306027i
$667$	−0.110531	−	3.86907i	−0.110531	−	3.86907i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.345844	+	1.70681i	−0.345844	+	1.70681i	0.309017	+	0.951057i	$0.400000\pi$
$673$	−0.345844	+	1.70681i	−0.345844	+	1.70681i	−0.654861	+	0.755750i	$0.727273\pi$
$674$	−0.0619995	−	0.0569026i	−0.0619995	−	0.0569026i
$675$		0			0
$676$	0.816218	+	0.839869i	0.816218	+	0.839869i
$677$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$677$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.332955	−	0.384251i	0.332955	−	0.384251i	−0.564443	−	0.825472i	$-0.690909\pi$
$683$	0.332955	−	0.384251i	0.332955	−	0.384251i	0.897398	+	0.441221i	$0.145455\pi$
$684$		0			0
$685$		0			0
$686$	−0.455331	−	1.40136i	−0.455331	−	1.40136i
$687$		0			0
$688$	0.276522	+	0.156159i	0.276522	+	0.156159i
$689$		0			0
$690$		0			0
$691$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$691$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$692$		0			0
$693$	0.516397	−	0.856349i	0.516397	−	0.856349i
$694$	−0.365188	+	2.53994i	−0.365188	+	2.53994i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−1.07877	−	0.455894i	−1.07877	−	0.455894i
$701$	0.926829	+	0.455691i	0.926829	+	0.455691i	0.841254	−	0.540641i	$-0.181818\pi$
$701$	0.926829	+	0.455691i	0.926829	+	0.455691i	0.0855750	+	0.996332i	$0.472727\pi$
$702$		0			0
$703$		0			0
$704$	−0.543360	−	1.18979i	−0.543360	−	1.18979i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.812697	+	1.54023i	0.812697	+	1.54023i	0.841254	+	0.540641i	$0.181818\pi$
$709$	0.812697	+	1.54023i	0.812697	+	1.54023i	−0.0285561	+	0.999592i	$0.509091\pi$
$710$		0			0
$711$	−0.374706	+	0.621380i	−0.374706	+	0.621380i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.81504	−	1.16646i	−1.81504	−	1.16646i
$717$		0			0
$718$	0.0434567	+	0.0720649i	0.0434567	+	0.0720649i
$719$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$719$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$720$		0			0
$721$		0			0
$722$	−1.14068	−	0.932733i	−1.14068	−	0.932733i
$723$		0			0
$724$		0			0
$725$	1.94802			1.94802
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	0.309017	−	0.951057i	0.309017	−	0.951057i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$733$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$734$		0			0
$735$		0			0
$736$	2.39084	+	1.53650i	2.39084	+	1.53650i
$737$	0.338621	−	0.869741i	0.338621	−	0.869741i
$738$		0			0
$739$	1.61540	+	0.0923716i	1.61540	+	0.0923716i	0.841254	−	0.540641i	$-0.181818\pi$
$739$	1.61540	+	0.0923716i	1.61540	+	0.0923716i	0.774142	+	0.633012i	$0.218182\pi$
$740$		0			0
$741$		0			0
$742$	−0.407875	−	2.01294i	−0.407875	−	2.01294i
$743$	0.755084	+	1.43104i	0.755084	+	1.43104i	0.897398	+	0.441221i	$0.145455\pi$
$743$	0.755084	+	1.43104i	0.755084	+	1.43104i	−0.142315	+	0.989821i	$0.545455\pi$
$744$		0			0
$745$		0			0
$746$	−0.747563	−	0.969457i	−0.747563	−	0.969457i
$747$		0			0
$748$		0			0
$749$	0.745586	−	1.63260i	0.745586	−	1.63260i
$750$		0			0
$751$	1.38943	+	0.683135i	1.38943	+	0.683135i	0.974012	−	0.226497i	$-0.0727273\pi$
$751$	1.38943	+	0.683135i	1.38943	+	0.683135i	0.415415	+	0.909632i	$0.363636\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.443096	−	1.13808i	−0.443096	−	1.13808i	−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−0.443096	−	1.13808i	−0.443096	−	1.13808i	0.516397	−	0.856349i	$-0.327273\pi$
$758$	0.216575	−	1.50632i	0.216575	−	1.50632i
$759$		0			0
$760$		0			0
$761$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$761$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$762$		0			0
$763$	0.286984	−	1.09180i	0.286984	−	1.09180i
$764$	0.739964	+	0.417877i	0.739964	+	0.417877i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$769$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$770$		0			0
$771$		0			0
$772$	1.53750	−	1.58205i	1.53750	−	1.58205i
$773$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$773$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$774$	−0.581424	−	0.0667122i	−0.581424	−	0.0667122i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	1.12118	+	1.02901i	1.12118	+	1.02901i
$779$		0			0
$780$		0			0
$781$	−1.98372	+	0.227611i	−1.98372	+	0.227611i
$782$		0			0
$783$		0			0
$784$	−0.794346	+	0.0911427i	−0.794346	+	0.0911427i
$785$		0			0
$786$		0			0
$787$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$787$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$788$	−0.0517799	−	1.81253i	−0.0517799	−	1.81253i
$789$		0			0
$790$		0			0
$791$	−1.80739	−	0.530696i	−1.80739	−	0.530696i
$792$	0.185796	+	0.170522i	0.185796	+	0.170522i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$797$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$798$		0			0
$799$		0			0
$800$	−0.807335	+	1.18069i	−0.807335	+	1.18069i
$801$		0			0
$802$	−0.490604	−	0.566187i	−0.490604	−	0.566187i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.60413	+	0.905894i	1.60413	+	0.905894i	0.993482	+	0.113991i	$0.0363636\pi$
$809$	1.60413	+	0.905894i	1.60413	+	0.905894i	0.610648	+	0.791902i	$0.290909\pi$
$810$		0			0
$811$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$811$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$812$	−1.98654	+	1.12185i	−1.98654	+	1.12185i
$813$		0			0
$814$	−0.281410	−	0.866091i	−0.281410	−	0.866091i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.54980	−	0.654950i	−1.54980	−	0.654950i	−0.564443	−	0.825472i	$-0.690909\pi$
$821$	−1.54980	−	0.654950i	−1.54980	−	0.654950i	−0.985354	+	0.170522i	$0.945455\pi$
$822$		0			0
$823$	−1.57598	+	0.366479i	−1.57598	+	0.366479i	−0.921124	−	0.389270i	$-0.872727\pi$
$823$	−1.57598	+	0.366479i	−1.57598	+	0.366479i	−0.654861	+	0.755750i	$0.727273\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.17182	−	1.51965i	−1.17182	−	1.51965i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	−1.17182	−	1.51965i	−1.17182	−	1.51965i	−0.362808	−	0.931864i	$-0.618182\pi$
$828$	−2.29295	−	0.396811i	−2.29295	−	0.396811i
$829$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$829$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$839$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$840$		0			0
$841$	1.70664	−	2.21321i	1.70664	−	2.21321i
$842$	0.0819667	+	0.0190605i	0.0819667	+	0.0190605i
$843$		0			0
$844$	−0.184006	+	0.566312i	−0.184006	+	0.566312i
$845$		0			0
$846$		0			0
$847$	0.841254	+	0.540641i	0.841254	+	0.540641i
$848$	−1.11448			−1.11448
$849$		0			0
$850$		0			0
$851$	0.950654	+	0.777346i	0.950654	+	0.777346i
$852$		0			0
$853$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$853$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$854$		0			0
$855$		0			0
$856$	0.366180	+	0.266045i	0.366180	+	0.266045i
$857$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$857$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$858$		0			0
$859$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$859$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$860$		0			0
$861$		0			0
$862$	1.49952	−	2.48667i	1.49952	−	2.48667i
$863$	0.334130	+	1.64900i	0.334130	+	1.64900i	0.696938	+	0.717132i	$0.254545\pi$
$863$	0.334130	+	1.64900i	0.334130	+	1.64900i	−0.362808	+	0.931864i	$0.618182\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.610427	−	0.392297i	−0.610427	−	0.392297i
$870$		0			0
$871$		0			0
$872$	0.255480	+	0.125611i	0.255480	+	0.125611i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.54576	+	1.26396i	−1.54576	+	1.26396i	−0.736741	+	0.676175i	$0.763636\pi$
$877$	−1.54576	+	1.26396i	−1.54576	+	1.26396i	−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$881$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$882$	1.28303	−	0.724560i	1.28303	−	0.724560i
$883$	0.0723581	+	0.275279i	0.0723581	+	0.275279i	0.993482	−	0.113991i	$-0.0363636\pi$
$883$	0.0723581	+	0.275279i	0.0723581	+	0.275279i	−0.921124	+	0.389270i	$0.872727\pi$
$884$		0			0
$885$		0			0
$886$	−0.930986	+	2.39122i	−0.930986	+	2.39122i
$887$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$887$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$888$		0			0
$889$	−0.157650	−	1.83549i	−0.157650	−	1.83549i
$890$		0			0
$891$	0.941844	+	0.336049i	0.941844	+	0.336049i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.0425296	−	0.495163i	0.0425296	−	0.495163i
$897$		0			0
$898$	−1.63903	+	0.283646i	−1.63903	+	0.283646i
$899$		0			0
$900$	0.232579	−	1.14782i	0.232579	−	1.14782i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.221686	−	0.420142i	0.221686	−	0.420142i
$905$		0			0
$906$		0			0
$907$	1.77414	−	0.633012i	1.77414	−	0.633012i	0.774142	−	0.633012i	$-0.218182\pi$
$907$	1.77414	−	0.633012i	1.77414	−	0.633012i	1.00000			$0$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	0.895528	−	1.69721i	0.895528	−	1.69721i	0.198590	−	0.980083i	$-0.436364\pi$
$911$	0.895528	−	1.69721i	0.895528	−	1.69721i	0.696938	−	0.717132i	$-0.254545\pi$
$912$		0			0
$913$		0			0
$914$	0.873774	−	0.256563i	0.873774	−	0.256563i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.0146462	−	0.170522i	0.0146462	−	0.170522i	−0.985354	−	0.170522i	$-0.945455\pi$
$919$	0.0146462	−	0.170522i	0.0146462	−	0.170522i	1.00000			$0$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.404726	+	0.467079i	−0.404726	+	0.467079i
$926$	−0.153997	−	1.79296i	−0.153997	−	1.79296i
$927$		0			0
$928$	0.861014	+	2.64993i	0.861014	+	2.64993i
$929$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$929$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$930$		0			0
$931$		0			0
$932$	0.0847422	+	0.322393i	0.0847422	+	0.322393i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$937$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$938$	1.06464	−	0.870552i	1.06464	−	0.870552i
$939$		0			0
$940$		0			0
$941$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$941$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.0832882	−	0.579282i	0.0832882	−	0.579282i
$947$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	−0.959493	−	0.281733i	$-0.909091\pi$
$947$	−0.544078	−	1.19136i	−0.544078	−	1.19136i	0.415415	−	0.909632i	$-0.363636\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.262555	+	0.435399i	−0.262555	+	0.435399i	−0.959493	−	0.281733i	$-0.909091\pi$
$953$	−0.262555	+	0.435399i	−0.262555	+	0.435399i	0.696938	+	0.717132i	$0.254545\pi$
$954$	1.89185	−	0.799503i	1.89185	−	0.799503i
$955$		0			0
$956$	−0.919553	+	0.590961i	−0.919553	+	0.590961i
$957$		0			0
$958$		0			0
$959$	−1.25259	−	0.910058i	−1.25259	−	0.910058i
$960$		0			0
$961$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$962$		0			0
$963$	1.74815	+	0.406516i	1.74815	+	0.406516i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.12889			−1.12889			−0.564443	−	0.825472i	$-0.690909\pi$
$967$	−1.12889			−1.12889			−0.564443	+	0.825472i	$0.690909\pi$
$968$	−0.175758	+	0.180851i	−0.175758	+	0.180851i
$969$		0			0
$970$		0			0
$971$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$971$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$972$		0			0
$973$		0			0
$974$	−0.357375	+	0.463452i	−0.357375	+	0.463452i
$975$		0			0
$976$		0			0
$977$	0.0462047	+	0.0335697i	0.0462047	+	0.0335697i	0.610648	−	0.791902i	$-0.290909\pi$
$977$	0.0462047	+	0.0335697i	0.0462047	+	0.0335697i	−0.564443	+	0.825472i	$0.690909\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.12705	+	0.0644468i	1.12705	+	0.0644468i
$982$	1.12765	−	0.476550i	1.12765	−	0.476550i
$983$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$983$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.327839	+	0.717867i	0.327839	+	0.717867i
$990$		0			0
$991$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$991$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$992$		0			0
$993$		0			0
$994$	−2.71009	−	1.14529i	−2.71009	−	1.14529i
$995$		0			0
$996$		0			0
$997$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$997$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$998$	1.84567	−	1.50919i	1.84567	−	1.50919i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.587.1	yes	40
7.6	odd	2	CM	847.1.bb.a.587.1	yes	40
121.47	even	55	inner	847.1.bb.a.531.1	✓	40
847.531	odd	110	inner	847.1.bb.a.531.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.531.1	✓	40	121.47	even	55	inner
847.1.bb.a.531.1	✓	40	847.531	odd	110	inner
847.1.bb.a.587.1	yes	40	1.1	even	1	trivial
847.1.bb.a.587.1	yes	40	7.6	odd	2	CM

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	847.bb (of order \(110\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38779 - 0.495163i) q^{2} +(0.906636 + 0.741353i) q^{4} +(-0.736741 + 0.676175i) q^{7} +(-0.130228 - 0.215960i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.38779 - 0.495163i) q^{2} +(0.906636 + 0.741353i) q^{4} +(-0.736741 + 0.676175i) q^{7} +(-0.130228 - 0.215960i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.610648 - 0.791902i) q^{11} +(1.35726 - 0.573583i) q^{14} +(-0.158785 - 0.783633i) q^{16} +(0.831697 + 1.21632i) q^{18} +(-1.23957 + 0.796625i) q^{22} +(0.825414 - 1.80741i) q^{23} +(0.897398 + 0.441221i) q^{25} +(-1.16924 + 0.0668596i) q^{28} +(1.74815 - 0.859509i) q^{29} +(-0.203556 + 1.41576i) q^{32} +(-0.297728 - 1.13267i) q^{36} +(-0.157116 + 0.597730i) q^{37} +(-0.260098 + 0.300169i) q^{43} +(1.14071 - 0.265262i) q^{44} +(-2.04046 + 2.09959i) q^{46} +(0.0855750 - 0.996332i) q^{49} +(-1.02693 - 1.05668i) q^{50} +(0.276810 - 1.36611i) q^{53} +(0.241971 + 0.0710492i) q^{56} +(-2.85167 + 0.327199i) q^{58} +(0.993482 - 0.113991i) q^{63} +(0.610398 - 1.15683i) q^{64} +(0.895528 - 0.262951i) q^{67} +(-1.39160 - 1.43192i) q^{71} +(-0.0215809 + 0.251261i) q^{72} +(0.514017 - 0.751726i) q^{74} +(0.0855750 + 0.996332i) q^{77} +(-0.0620945 - 0.722954i) q^{79} +(0.309017 + 0.951057i) q^{81} +(0.509595 - 0.287781i) q^{86} +(-0.250543 - 0.0287471i) q^{88} +(2.08828 - 1.02674i) q^{92} +(-0.612107 + 1.34033i) q^{98} +(-0.959493 + 0.281733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46} + q^{49} + 2 q^{50} - 3 q^{53} - 7 q^{56} - 12 q^{58} + q^{63} - 9 q^{64} + 2 q^{67} - 3 q^{71} - q^{72} + 4 q^{74} + q^{77} - 3 q^{79} - 10 q^{81} - q^{86} - 12 q^{88} - 4 q^{92} - 9 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q + 2 * q^2 + 3 * q^4 + q^7 - q^8 - 10 * q^9 + q^11 - 3 * q^14 - 3 * q^18 + 2 * q^22 - 9 * q^23 + q^25 - 2 * q^28 + 2 * q^29 - 4 * q^32 + 3 * q^36 - 3 * q^37 + 2 * q^43 - 13 * q^44 - q^46 + q^49 + 2 * q^50 - 3 * q^53 - 7 * q^56 - 12 * q^58 + q^63 - 9 * q^64 + 2 * q^67 - 3 * q^71 - q^72 + 4 * q^74 + q^77 - 3 * q^79 - 10 * q^81 - q^86 - 12 * q^88 - 4 * q^92 - 9 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more