LMFDB - Embedded newform 847.1.bb.a.482.1

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			482.1
Root			$-0.0285561 + 0.999592i$ of defining polynomial
Character	$\chi$	$=$	847.482
Dual form			847.1.bb.a.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0113419 + 0.397019i) q^{2} +(0.840874 + 0.0480829i) q^{4} +(0.198590 - 0.980083i) q^{7} +(-0.0626157 + 0.729021i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.0113419 + 0.397019i) q^{2} +(0.840874 + 0.0480829i) q^{4} +(0.198590 - 0.980083i) q^{7} +(-0.0626157 + 0.729021i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.564443 - 0.825472i) q^{11} +(0.386859 + 0.0899602i) q^{14} +(0.548032 + 0.0628808i) q^{16} +(0.374083 + 0.133472i) q^{18} +(0.334130 - 0.214732i) q^{22} +(-0.723442 + 1.58412i) q^{23} +(-0.466667 - 0.884433i) q^{25} +(0.214115 - 0.814577i) q^{28} +(-0.481972 + 0.913438i) q^{29} +(-0.135313 + 0.941124i) q^{32} +(0.305574 - 0.784860i) q^{36} +(0.587035 + 1.50779i) q^{37} +(-1.30118 + 1.50165i) q^{43} +(-0.434934 - 0.721258i) q^{44} +(-0.620719 - 0.305187i) q^{46} +(-0.921124 - 0.389270i) q^{49} +(0.356430 - 0.175245i) q^{50} +(1.78310 - 0.204591i) q^{53} +(0.702066 + 0.206145i) q^{56} +(-0.357186 - 0.201712i) q^{58} +(-0.870746 - 0.491733i) q^{63} +(0.171439 + 0.0296687i) q^{64} +(1.89088 - 0.555213i) q^{67} +(-0.456270 + 0.224333i) q^{71} +(0.673991 + 0.284831i) q^{72} +(-0.605278 + 0.215963i) q^{74} +(-0.921124 + 0.389270i) q^{77} +(-1.42616 + 0.602700i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.581424 - 0.533626i) q^{86} +(0.637130 - 0.359804i) q^{88} +(-0.684492 + 1.29726i) q^{92} +(0.164995 - 0.361288i) q^{98} +(-0.959493 + 0.281733i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{28}{55}\right)$

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 $

$2$	−0.0113419	+	0.397019i	−0.0113419	+	0.397019i	0.974012	+	0.226497i	$0.0727273\pi$
$2$	−0.0113419	+	0.397019i	−0.0113419	+	0.397019i	−0.985354	+	0.170522i	$0.945455\pi$
$3$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$3$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$4$	0.840874	+	0.0480829i	0.840874	+	0.0480829i
$5$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$5$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$6$		0			0
$7$	0.198590	−	0.980083i	0.198590	−	0.980083i
$7$	0.198590	−	0.980083i	0.198590	−	0.980083i
$8$	−0.0626157	+	0.729021i	−0.0626157	+	0.729021i
$9$	0.309017	−	0.951057i	0.309017	−	0.951057i
$10$		0			0
$11$	−0.564443	−	0.825472i	−0.564443	−	0.825472i
$11$	−0.564443	−	0.825472i	−0.564443	−	0.825472i
$12$		0			0
$13$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$13$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$14$	0.386859	+	0.0899602i	0.386859	+	0.0899602i
$15$		0			0
$16$	0.548032	+	0.0628808i	0.548032	+	0.0628808i
$17$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$17$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$18$	0.374083	+	0.133472i	0.374083	+	0.133472i
$19$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$19$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$20$		0			0
$21$		0			0
$22$	0.334130	−	0.214732i	0.334130	−	0.214732i
$23$	−0.723442	+	1.58412i	−0.723442	+	1.58412i	0.0855750	+	0.996332i	$0.472727\pi$
$23$	−0.723442	+	1.58412i	−0.723442	+	1.58412i	−0.809017	+	0.587785i	$0.800000\pi$
$24$		0			0
$25$	−0.466667	−	0.884433i	−0.466667	−	0.884433i
$26$		0			0
$27$		0			0
$28$	0.214115	−	0.814577i	0.214115	−	0.814577i
$29$	−0.481972	+	0.913438i	−0.481972	+	0.913438i	0.516397	+	0.856349i	$0.327273\pi$
$29$	−0.481972	+	0.913438i	−0.481972	+	0.913438i	−0.998369	+	0.0570888i	$0.981818\pi$
$30$		0			0
$31$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$31$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$32$	−0.135313	+	0.941124i	−0.135313	+	0.941124i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.305574	−	0.784860i	0.305574	−	0.784860i
$37$	0.587035	+	1.50779i	0.587035	+	1.50779i	0.841254	+	0.540641i	$0.181818\pi$
$37$	0.587035	+	1.50779i	0.587035	+	1.50779i	−0.254218	+	0.967147i	$0.581818\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$41$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$42$		0			0
$43$	−1.30118	+	1.50165i	−1.30118	+	1.50165i	−0.564443	+	0.825472i	$0.690909\pi$
$43$	−1.30118	+	1.50165i	−1.30118	+	1.50165i	−0.736741	+	0.676175i	$0.763636\pi$
$44$	−0.434934	−	0.721258i	−0.434934	−	0.721258i
$45$		0			0
$46$	−0.620719	−	0.305187i	−0.620719	−	0.305187i
$47$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$47$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$48$		0			0
$49$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$50$	0.356430	−	0.175245i	0.356430	−	0.175245i
$51$		0			0
$52$		0			0
$53$	1.78310	−	0.204591i	1.78310	−	0.204591i	0.841254	−	0.540641i	$-0.181818\pi$
$53$	1.78310	−	0.204591i	1.78310	−	0.204591i	0.941844	+	0.336049i	$0.109091\pi$
$54$		0			0
$55$		0			0
$56$	0.702066	+	0.206145i	0.702066	+	0.206145i
$57$		0			0
$58$	−0.357186	−	0.201712i	−0.357186	−	0.201712i
$59$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$59$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$60$		0			0
$61$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$61$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$62$		0			0
$63$	−0.870746	−	0.491733i	−0.870746	−	0.491733i
$64$	0.171439	+	0.0296687i	0.171439	+	0.0296687i
$65$		0			0
$66$		0			0
$67$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.897398	−	0.441221i	$-0.145455\pi$
$67$	1.89088	−	0.555213i	1.89088	−	0.555213i	0.993482	−	0.113991i	$-0.0363636\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−0.456270	+	0.224333i	−0.456270	+	0.224333i	−0.654861	−	0.755750i	$-0.727273\pi$
$71$	−0.456270	+	0.224333i	−0.456270	+	0.224333i	0.198590	+	0.980083i	$0.436364\pi$
$72$	0.673991	+	0.284831i	0.673991	+	0.284831i
$73$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$73$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$74$	−0.605278	+	0.215963i	−0.605278	+	0.215963i
$75$		0			0
$76$		0			0
$77$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$78$		0			0
$79$	−1.42616	+	0.602700i	−1.42616	+	0.602700i	−0.959493	−	0.281733i	$-0.909091\pi$
$79$	−1.42616	+	0.602700i	−1.42616	+	0.602700i	−0.466667	+	0.884433i	$0.654545\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$82$		0			0
$83$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$83$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$84$		0			0
$85$		0			0
$86$	−0.581424	−	0.533626i	−0.581424	−	0.533626i
$87$		0			0
$88$	0.637130	−	0.359804i	0.637130	−	0.359804i
$89$		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
$92$	−0.684492	+	1.29726i	−0.684492	+	1.29726i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$97$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$98$	0.164995	−	0.361288i	0.164995	−	0.361288i
$99$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$100$	−0.349882	−	0.766135i	−0.349882	−	0.766135i
$101$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$101$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$102$		0			0
$103$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$103$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$104$		0			0
$105$		0			0
$106$	0.0610029	+	0.710244i	0.0610029	+	0.710244i
$107$	−0.909079	−	0.211397i	−0.909079	−	0.211397i	−0.254218	−	0.967147i	$-0.581818\pi$
$107$	−0.909079	−	0.211397i	−0.909079	−	0.211397i	−0.654861	+	0.755750i	$0.727273\pi$
$108$		0			0
$109$	1.58466	−	1.01840i	1.58466	−	1.01840i	0.610648	−	0.791902i	$-0.290909\pi$
$109$	1.58466	−	1.01840i	1.58466	−	1.01840i	0.974012	−	0.226497i	$-0.0727273\pi$
$110$		0			0
$111$		0			0
$112$	0.170462	−	0.524629i	0.170462	−	0.524629i
$113$	−0.00488737	+	0.0569026i	−0.00488737	+	0.0569026i	−0.998369	−	0.0570888i	$-0.981818\pi$
$113$	−0.00488737	+	0.0569026i	−0.00488737	+	0.0569026i	0.993482	+	0.113991i	$0.0363636\pi$
$114$		0			0
$115$		0			0
$116$	−0.449198	+	0.744911i	−0.449198	+	0.744911i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.362808	+	0.931864i	−0.362808	+	0.931864i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.205103	−	0.340126i	0.205103	−	0.340126i
$127$	−1.09955	−	1.60804i	−1.09955	−	1.60804i	−0.736741	−	0.676175i	$-0.763636\pi$
$127$	−1.09955	−	1.60804i	−1.09955	−	1.60804i	−0.362808	−	0.931864i	$-0.618182\pi$
$128$	−0.202544	+	0.999592i	−0.202544	+	0.999592i
$129$		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
$134$	0.198984	+	0.757012i	0.198984	+	0.757012i
$135$		0			0
$136$		0			0
$137$	−1.98372	−	0.227611i	−1.98372	−	0.227611i	−0.998369	−	0.0570888i	$-0.981818\pi$
$137$	−1.98372	−	0.227611i	−1.98372	−	0.227611i	−0.985354	−	0.170522i	$-0.945455\pi$
$138$		0			0
$139$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$139$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$140$		0			0
$141$		0			0
$142$	−0.0838895	−	0.183692i	−0.0838895	−	0.183692i
$143$		0			0
$144$	0.229154	−	0.501778i	0.229154	−	0.501778i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	0.421124	+	1.29609i	0.421124	+	1.29609i
$149$	0.487841	−	1.85594i	0.487841	−	1.85594i	−0.0285561	−	0.999592i	$-0.509091\pi$
$149$	0.487841	−	1.85594i	0.487841	−	1.85594i	0.516397	−	0.856349i	$-0.327273\pi$
$150$		0			0
$151$	−0.170871	+	0.00977075i	−0.170871	+	0.00977075i	−0.142315	−	0.989821i	$-0.545455\pi$
$151$	−0.170871	+	0.00977075i	−0.170871	+	0.00977075i	−0.0285561	+	0.999592i	$0.509091\pi$
$152$		0			0
$153$		0			0
$154$	−0.144100	−	0.370119i	−0.144100	−	0.370119i
$155$		0			0
$156$		0			0
$157$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$157$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$158$	−0.223108	−	0.573048i	−0.223108	−	0.573048i
$159$		0			0
$160$		0			0
$161$	1.40890	+	1.02362i	1.40890	+	1.02362i
$162$	0.242538	−	0.314528i	0.242538	−	0.314528i
$163$	0.859717	−	0.363319i	0.859717	−	0.363319i	0.0855750	−	0.996332i	$-0.472727\pi$
$163$	0.859717	−	0.363319i	0.859717	−	0.363319i	0.774142	+	0.633012i	$0.218182\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$167$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$168$		0			0
$169$	−0.870746	+	0.491733i	−0.870746	+	0.491733i
$170$		0			0
$171$		0			0
$172$	−1.16634	+	1.20013i	−1.16634	+	1.20013i
$173$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$173$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$174$		0			0
$175$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$176$	−0.257427	−	0.487878i	−0.257427	−	0.487878i
$177$		0			0
$178$		0			0
$179$	−1.69623	−	0.957907i	−1.69623	−	0.957907i	−0.959493	−	0.281733i	$-0.909091\pi$
$179$	−1.69623	−	0.957907i	−1.69623	−	0.957907i	−0.736741	−	0.676175i	$-0.763636\pi$
$180$		0			0
$181$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$181$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$182$		0			0
$183$		0			0
$184$	−1.10956	−	0.626595i	−1.10956	−	0.626595i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.07906	−	1.11032i	1.07906	−	1.11032i	0.0855750	−	0.996332i	$-0.472727\pi$
$191$	1.07906	−	1.11032i	1.07906	−	1.11032i	0.993482	−	0.113991i	$-0.0363636\pi$
$192$		0			0
$193$	0.0526073	+	0.0222320i	0.0526073	+	0.0222320i	0.415415	−	0.909632i	$-0.363636\pi$
$193$	0.0526073	+	0.0222320i	0.0526073	+	0.0222320i	−0.362808	+	0.931864i	$0.618182\pi$
$194$		0			0
$195$		0			0
$196$	−0.755831	−	0.371617i	−0.755831	−	0.371617i
$197$	1.30759	+	1.50903i	1.30759	+	1.50903i	0.696938	+	0.717132i	$0.254545\pi$
$197$	1.30759	+	1.50903i	1.30759	+	1.50903i	0.610648	+	0.791902i	$0.290909\pi$
$198$	−0.100971	−	0.384132i	−0.100971	−	0.384132i
$199$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$199$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$200$	0.673991	−	0.284831i	0.673991	−	0.284831i
$201$		0			0
$202$		0			0
$203$	0.799530	+	0.653772i	0.799530	+	0.653772i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.28303	+	1.17755i	1.28303	+	1.17755i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.561729	+	0.459324i	−0.561729	+	0.459324i	−0.870746	−	0.491733i	$-0.836364\pi$
$211$	−0.561729	+	0.459324i	−0.561729	+	0.459324i	0.309017	+	0.951057i	$0.400000\pi$
$212$	1.50920	−	0.0862990i	1.50920	−	0.0862990i
$213$		0			0
$214$	0.0942394	−	0.358524i	0.0942394	−	0.358524i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.386351	+	0.640691i	0.386351	+	0.640691i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$223$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$224$	0.895507	+	0.319516i	0.895507	+	0.319516i
$225$	−0.985354	+	0.170522i	−0.985354	+	0.170522i
$226$	−0.0225360	−	0.00258576i	−0.0225360	−	0.00258576i
$227$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$227$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$228$		0			0
$229$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$229$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$230$		0			0
$231$		0			0
$232$	−0.635737	−	0.408563i	−0.635737	−	0.408563i
$233$	−0.0879554	+	0.270699i	−0.0879554	+	0.270699i	−0.985354	−	0.170522i	$-0.945455\pi$
$233$	−0.0879554	+	0.270699i	−0.0879554	+	0.270699i	0.897398	+	0.441221i	$0.145455\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.59434	−	1.15835i	1.59434	−	1.15835i	0.696938	−	0.717132i	$-0.254545\pi$
$239$	1.59434	−	1.15835i	1.59434	−	1.15835i	0.897398	−	0.441221i	$-0.145455\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−0.365853	−	0.154611i	−0.365853	−	0.154611i
$243$		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		0.309017	−	0.951057i	$-0.400000\pi$
$251$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$252$	−0.708544	−	0.455353i	−0.708544	−	0.455353i
$253$	1.71599	−	0.296963i	1.71599	−	0.296963i
$254$	0.650893	−	0.418303i	0.650893	−	0.418303i
$255$		0			0
$256$	−0.225094	−	0.0523433i	−0.225094	−	0.0523433i
$257$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$257$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$258$		0			0
$259$	1.59434	−	0.275911i	1.59434	−	0.275911i
$260$		0			0
$261$	0.719794	+	0.740650i	0.719794	+	0.740650i
$262$		0			0
$263$	−0.211212	−	0.462490i	−0.211212	−	0.462490i	0.774142	−	0.633012i	$-0.218182\pi$
$263$	−0.211212	−	0.462490i	−0.211212	−	0.462490i	−0.985354	+	0.170522i	$0.945455\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	1.61669	−	0.375945i	1.61669	−	0.375945i
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$		0			0
$271$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$271$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$272$		0			0
$273$		0			0
$274$	0.112865	−	0.784994i	0.112865	−	0.784994i
$275$	−0.466667	+	0.884433i	−0.466667	+	0.884433i
$276$		0			0
$277$	−1.02693	−	0.942503i	−1.02693	−	0.942503i	−0.0285561	−	0.999592i	$-0.509091\pi$
$277$	−1.02693	−	0.942503i	−1.02693	−	0.942503i	−0.998369	+	0.0570888i	$0.981818\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.38943	+	1.13613i	1.38943	+	1.13613i	0.974012	+	0.226497i	$0.0727273\pi$
$281$	1.38943	+	1.13613i	1.38943	+	1.13613i	0.415415	+	0.909632i	$0.363636\pi$
$282$		0			0
$283$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$283$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$284$	−0.394452	+	0.166697i	−0.394452	+	0.166697i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.853248	+	0.419514i	0.853248	+	0.419514i
$289$	0.941844	−	0.336049i	0.941844	−	0.336049i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$293$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$294$		0			0
$295$		0			0
$296$	−1.13597	+	0.333550i	−1.13597	+	0.333550i
$297$		0			0
$298$	0.731311	+	0.214732i	0.731311	+	0.214732i
$299$		0			0
$300$		0			0
$301$	1.21334	+	1.57348i	1.21334	+	1.57348i
$302$	−0.00194117	−	0.0679498i	−0.00194117	−	0.0679498i
$303$		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	$0.0909091\pi$
$308$	−0.793266	+	0.283037i	−0.793266	+	0.283037i
$309$		0			0
$310$		0			0
$311$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$311$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$312$		0			0
$313$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$313$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$314$		0			0
$315$		0			0
$316$	−1.22820	+	0.438221i	−1.22820	+	0.438221i
$317$	0.554623	+	0.272690i	0.554623	+	0.272690i	0.696938	−	0.717132i	$-0.254545\pi$
$317$	0.554623	+	0.272690i	0.554623	+	0.272690i	−0.142315	+	0.989821i	$0.545455\pi$
$318$		0			0
$319$	1.02606	−	0.117730i	1.02606	−	0.117730i
$320$		0			0
$321$		0			0
$322$	−0.422377	+	0.547749i	−0.422377	+	0.547749i
$323$		0			0
$324$	−0.652019	−	0.533153i	−0.652019	−	0.533153i
$325$		0			0
$326$	0.134494	+	0.345445i	0.134494	+	0.345445i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.173809	+	1.20886i	−0.173809	+	1.20886i	0.696938	+	0.717132i	$0.254545\pi$
$331$	−0.173809	+	1.20886i	−0.173809	+	1.20886i	−0.870746	+	0.491733i	$0.836364\pi$
$332$		0			0
$333$	1.61540	−	0.0923716i	1.61540	−	0.0923716i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.18956	−	0.276620i	1.18956	−	0.276620i	0.415415	−	0.909632i	$-0.363636\pi$
$337$	1.18956	−	0.276620i	1.18956	−	0.276620i	0.774142	+	0.633012i	$0.218182\pi$
$338$	−0.185351	−	0.351280i	−0.185351	−	0.351280i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$344$	−1.01326	−	1.04262i	−1.01326	−	1.04262i
$345$		0			0
$346$		0			0
$347$	−1.46388	−	0.167964i	−1.46388	−	0.167964i	−0.654861	−	0.755750i	$-0.727273\pi$
$347$	−1.46388	−	0.167964i	−1.46388	−	0.167964i	−0.809017	+	0.587785i	$0.800000\pi$
$348$		0			0
$349$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$349$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$350$	−0.100971	−	0.384132i	−0.100971	−	0.384132i
$351$		0			0
$352$	0.853248	−	0.419514i	0.853248	−	0.419514i
$353$		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
$358$	0.399546	−	0.662573i	0.399546	−	0.662573i
$359$	−1.21930	−	0.0697223i	−1.21930	−	0.0697223i	−0.564443	−	0.825472i	$-0.690909\pi$
$359$	−1.21930	−	0.0697223i	−1.21930	−	0.0697223i	−0.654861	+	0.755750i	$0.727273\pi$
$360$		0			0
$361$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$367$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$368$	−0.496080	+	0.822656i	−0.496080	+	0.822656i
$369$		0			0
$370$		0			0
$371$	0.153590	−	1.78821i	0.153590	−	1.78821i
$372$		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
$379$	0.170034	+	0.0195096i	0.170034	+	0.0195096i	0.198590	−	0.980083i	$-0.436364\pi$
$379$	0.170034	+	0.0195096i	0.170034	+	0.0195096i	−0.0285561	+	0.999592i	$0.509091\pi$
$380$		0			0
$381$		0			0
$382$	0.428581	+	0.440999i	0.428581	+	0.440999i
$383$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$383$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$384$		0			0
$385$		0			0
$386$	−0.00942321	+	0.0206339i	−0.00942321	+	0.0206339i
$387$	1.02606	+	1.70153i	1.02606	+	1.70153i
$388$		0			0
$389$	0.166702	−	0.0387649i	0.166702	−	0.0387649i	−0.142315	−	0.989821i	$-0.545455\pi$
$389$	0.166702	−	0.0387649i	0.166702	−	0.0387649i	0.309017	+	0.951057i	$0.400000\pi$
$390$		0			0
$391$		0			0
$392$	0.341463	−	0.647144i	0.341463	−	0.647144i
$393$		0			0
$394$	−0.613946	+	0.502021i	−0.613946	+	0.502021i
$395$		0			0
$396$	−0.820359	+	0.190766i	−0.820359	+	0.190766i
$397$		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
$400$	−0.200135	−	0.514042i	−0.200135	−	0.514042i
$401$	0.534591	−	0.490643i	0.534591	−	0.490643i	−0.362808	−	0.931864i	$-0.618182\pi$
$401$	0.534591	−	0.490643i	0.534591	−	0.490643i	0.897398	+	0.441221i	$0.145455\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.268628	+	0.310013i	−0.268628	+	0.310013i
$407$	0.913288	−	1.33564i	0.913288	−	1.33564i
$408$		0			0
$409$		0			0		−0.897398	−	0.441221i	$-0.854545\pi$
$409$		0			0		0.897398	+	0.441221i	$0.145455\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	−0.482063	+	0.496031i	−0.482063	+	0.496031i
$415$		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
$421$	−1.06344	−	0.600551i	−1.06344	−	0.600551i	−0.142315	−	0.989821i	$-0.545455\pi$
$421$	−1.06344	−	0.600551i	−1.06344	−	0.600551i	−0.921124	+	0.389270i	$0.872727\pi$
$422$	−0.175989	−	0.228227i	−0.175989	−	0.228227i
$423$		0			0
$424$	0.0375016	+	1.31273i	0.0375016	+	1.31273i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.754256	−	0.221470i	−0.754256	−	0.221470i
$429$		0			0
$430$		0			0
$431$	1.38479	−	0.158890i	1.38479	−	0.158890i	0.610648	−	0.791902i	$-0.290909\pi$
$431$	1.38479	−	0.158890i	1.38479	−	0.158890i	0.774142	+	0.633012i	$0.218182\pi$
$432$		0			0
$433$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$433$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$434$		0			0
$435$		0			0
$436$	1.38147	−	0.780150i	1.38147	−	0.780150i
$437$		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
$443$	−0.899779	+	1.16685i	−0.899779	+	1.16685i	0.0855750	+	0.996332i	$0.472727\pi$
$443$	−0.899779	+	1.16685i	−0.899779	+	1.16685i	−0.985354	+	0.170522i	$0.945455\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.0631240	−	0.162133i	0.0631240	−	0.162133i
$449$	−1.38779	−	1.27370i	−1.38779	−	1.27370i	−0.921124	−	0.389270i	$-0.872727\pi$
$449$	−1.38779	−	1.27370i	−1.38779	−	1.27370i	−0.466667	−	0.884433i	$-0.654545\pi$
$450$	−0.0565247	−	0.393138i	−0.0565247	−	0.393138i
$451$		0			0
$452$	−0.00684570	+	0.0476129i	−0.00684570	+	0.0476129i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	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
$463$	−0.468956	−	1.02687i	−0.468956	−	1.02687i	−0.985354	−	0.170522i	$-0.945455\pi$
$463$	−0.468956	−	1.02687i	−0.468956	−	1.02687i	0.516397	−	0.856349i	$-0.327273\pi$
$464$	−0.321574	+	0.470287i	−0.321574	+	0.470287i
$465$		0			0
$466$	−0.106475	−	0.0379902i	−0.106475	−	0.0379902i
$467$		0			0		0.985354	−	0.170522i	$-0.0545455\pi$
$467$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$468$		0			0
$469$	−0.168643	−	1.96348i	−0.168643	−	1.96348i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.97401	+	0.226497i	1.97401	+	0.226497i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.356430	−	1.75905i	0.356430	−	1.75905i
$478$	0.441805	+	0.646120i	0.441805	+	0.646120i
$479$		0			0		0.516397	−	0.856349i	$-0.327273\pi$
$479$		0			0		−0.516397	+	0.856349i	$0.672727\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.349882	+	0.766135i	−0.349882	+	0.766135i
$485$		0			0
$486$		0			0
$487$	−1.60749	+	1.16791i	−1.60749	+	1.16791i	−0.736741	+	0.676175i	$0.763636\pi$
$487$	−1.60749	+	1.16791i	−1.60749	+	1.16791i	−0.870746	+	0.491733i	$0.836364\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.164995	−	0.814282i	0.164995	−	0.814282i	−0.809017	−	0.587785i	$-0.800000\pi$
$491$	0.164995	−	0.814282i	0.164995	−	0.814282i	0.974012	−	0.226497i	$-0.0727273\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.129254	+	0.491733i	0.129254	+	0.491733i
$498$		0			0
$499$	0.0528883	+	0.615767i	0.0528883	+	0.615767i	0.974012	+	0.226497i	$0.0727273\pi$
$499$	0.0528883	+	0.615767i	0.0528883	+	0.615767i	−0.921124	+	0.389270i	$0.872727\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$503$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$504$	0.413006	−	0.604002i	0.413006	−	0.604002i
$505$		0			0
$506$	0.0984374	+	0.684647i	0.0984374	+	0.684647i
$507$		0			0
$508$	−0.847263	−	1.40503i	−0.847263	−	1.40503i
$509$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$509$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$510$		0			0
$511$		0			0
$512$	−0.235945	+	0.897626i	−0.235945	+	0.897626i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.0914590	+	0.636111i	0.0914590	+	0.636111i
$519$		0			0
$520$		0			0
$521$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$521$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$522$	−0.302216	+	0.277371i	−0.302216	+	0.277371i
$523$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$523$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$524$		0			0
$525$		0			0
$526$	0.186013	−	0.0786097i	0.186013	−	0.0786097i
$527$		0			0
$528$		0			0
$529$	−1.33120	−	1.53628i	−1.33120	−	1.53628i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.286363	+	1.41326i	0.286363	+	1.41326i
$537$		0			0
$538$		0			0
$539$	0.198590	+	0.980083i	0.198590	+	0.980083i
$540$		0			0
$541$	0.714988	+	0.123734i	0.714988	+	0.123734i	0.516397	−	0.856349i	$-0.327273\pi$
$541$	0.714988	+	0.123734i	0.714988	+	0.123734i	0.198590	+	0.980083i	$0.436364\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.247840	+	0.139962i	0.247840	+	0.139962i	0.610648	−	0.791902i	$-0.290909\pi$
$547$	0.247840	+	0.139962i	0.247840	+	0.139962i	−0.362808	+	0.931864i	$0.618182\pi$
$548$	−1.65712	−	0.286775i	−1.65712	−	0.286775i
$549$		0			0
$550$	−0.345844	−	0.195307i	−0.345844	−	0.195307i
$551$		0			0
$552$		0			0
$553$	0.307474	+	1.51745i	0.307474	+	1.51745i
$554$	0.385839	−	0.397019i	0.385839	−	0.397019i
$555$		0			0
$556$		0			0
$557$	−0.538151	+	0.303908i	−0.538151	+	0.303908i	−0.736741	−	0.676175i	$-0.763636\pi$
$557$	−0.538151	+	0.303908i	−0.538151	+	0.303908i	0.198590	+	0.980083i	$0.436364\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.466823	+	0.538743i	−0.466823	+	0.538743i
$563$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$563$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$568$	−0.134974	−	0.346678i	−0.134974	−	0.346678i
$569$	0.475177	−	1.22048i	0.475177	−	1.22048i	−0.466667	−	0.884433i	$-0.654545\pi$
$569$	0.475177	−	1.22048i	0.475177	−	1.22048i	0.941844	−	0.336049i	$-0.109091\pi$
$570$		0			0
$571$	0.284165	+	1.97641i	0.284165	+	1.97641i	0.198590	+	0.980083i	$0.436364\pi$
$571$	0.284165	+	1.97641i	0.284165	+	1.97641i	0.0855750	+	0.996332i	$0.472727\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.73865	−	0.0994197i	1.73865	−	0.0994197i
$576$	0.0811943	−	0.153880i	0.0811943	−	0.153880i
$577$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$577$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$578$	0.122736	+	0.377742i	0.122736	+	0.377742i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.17534	−	1.35642i	−1.17534	−	1.35642i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$587$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.226903	+	0.863229i	0.226903	+	0.863229i
$593$		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
$596$	0.499452	−	1.53716i	0.499452	−	1.53716i
$597$		0			0
$598$		0			0
$599$	−1.06324	−	1.55493i	−1.06324	−	1.55493i	−0.809017	−	0.587785i	$-0.800000\pi$
$599$	−1.06324	−	1.55493i	−1.06324	−	1.55493i	−0.254218	−	0.967147i	$-0.581818\pi$
$600$		0			0
$601$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$601$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$602$	−0.638463	+	0.463871i	−0.638463	+	0.463871i
$603$	0.0562756	−	1.96990i	0.0562756	−	1.96990i
$604$	−0.144151			−0.144151
$605$		0			0
$606$		0			0
$607$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$607$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.126093	+	1.46808i	−0.126093	+	1.46808i	0.610648	+	0.791902i	$0.290909\pi$
$613$	−0.126093	+	1.46808i	−0.126093	+	1.46808i	−0.736741	+	0.676175i	$0.763636\pi$
$614$		0			0
$615$		0			0
$616$	−0.226109	−	0.695893i	−0.226109	−	0.695893i
$617$	−0.949680	+	0.610322i	−0.949680	+	0.610322i	−0.921124	−	0.389270i	$-0.872727\pi$
$617$	−0.949680	+	0.610322i	−0.949680	+	0.610322i	−0.0285561	+	0.999592i	$0.509091\pi$
$618$		0			0
$619$		0			0		−0.974012	−	0.226497i	$-0.927273\pi$
$619$		0			0		0.974012	+	0.226497i	$0.0727273\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.706758	+	0.164350i	−0.706758	+	0.164350i	−0.564443	−	0.825472i	$-0.690909\pi$
$631$	−0.706758	+	0.164350i	−0.706758	+	0.164350i	−0.142315	+	0.989821i	$0.545455\pi$
$632$	−0.350081	−	1.07744i	−0.350081	−	1.07744i
$633$		0			0
$634$	−0.114553	+	0.217103i	−0.114553	+	0.217103i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.0351034	+	0.408702i	0.0351034	+	0.408702i
$639$	0.0723581	+	0.503262i	0.0723581	+	0.503262i
$640$		0			0
$641$	0.534591	−	1.37309i	0.534591	−	1.37309i	−0.362808	−	0.931864i	$-0.618182\pi$
$641$	0.534591	−	1.37309i	0.534591	−	1.37309i	0.897398	−	0.441221i	$-0.145455\pi$
$642$		0			0
$643$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$643$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$644$	1.13549	+	0.928482i	1.13549	+	0.928482i
$645$		0			0
$646$		0			0
$647$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$647$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$648$	0.479165	−	0.552986i	0.479165	−	0.552986i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.740383	−	0.264168i	0.740383	−	0.264168i
$653$	−1.69623	+	0.957907i	−1.69623	+	0.957907i	−0.736741	+	0.676175i	$0.763636\pi$
$653$	−1.69623	+	0.957907i	−1.69623	+	0.957907i	−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	$0.0909091\pi$
$662$	−0.477971	−	0.0827161i	−0.477971	−	0.0827161i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	0.0183516	+	0.642390i	0.0183516	+	0.642390i
$667$	−1.09831	−	1.42432i	−1.09831	−	1.42432i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.46388	+	0.167964i	−1.46388	+	0.167964i	−0.809017	−	0.587785i	$-0.800000\pi$
$673$	−1.46388	+	0.167964i	−1.46388	+	0.167964i	−0.654861	+	0.755750i	$0.727273\pi$
$674$	0.0963313	+	0.475414i	0.0963313	+	0.475414i
$675$		0			0
$676$	−0.755831	+	0.371617i	−0.755831	+	0.371617i
$677$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$677$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.475177	−	0.548384i	0.475177	−	0.548384i	−0.466667	−	0.884433i	$-0.654545\pi$
$683$	0.475177	−	0.548384i	0.475177	−	0.548384i	0.941844	+	0.336049i	$0.109091\pi$
$684$		0			0
$685$		0			0
$686$	−0.321326	−	0.233457i	−0.321326	−	0.233457i
$687$		0			0
$688$	−0.807516	+	0.741131i	−0.807516	+	0.741131i
$689$		0			0
$690$		0			0
$691$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$691$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$692$		0			0
$693$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$694$	0.0832882	−	0.579282i	0.0832882	−	0.579282i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.820359	+	0.190766i	−0.820359	+	0.190766i
$701$	−0.0798701	−	0.151371i	−0.0798701	−	0.151371i	0.841254	−	0.540641i	$-0.181818\pi$
$701$	−0.0798701	−	0.151371i	−0.0798701	−	0.151371i	−0.921124	+	0.389270i	$0.872727\pi$
$702$		0			0
$703$		0			0
$704$	−0.0722771	−	0.158265i	−0.0722771	−	0.158265i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.45190	−	0.251261i	1.45190	−	0.251261i	0.610648	−	0.791902i	$-0.290909\pi$
$709$	1.45190	−	0.251261i	1.45190	−	0.251261i	0.841254	+	0.540641i	$0.181818\pi$
$710$		0			0
$711$	0.132494	+	1.54260i	0.132494	+	1.54260i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.38026	−	0.887039i	−1.38026	−	0.887039i
$717$		0			0
$718$	0.0415103	−	0.483296i	0.0415103	−	0.483296i
$719$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$719$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$720$		0			0
$721$		0			0
$722$	−0.396533	−	0.0226746i	−0.396533	−	0.0226746i
$723$		0			0
$724$		0			0
$725$	1.03279			1.03279
$726$		0			0
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$733$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$734$		0			0
$735$		0			0
$736$	−1.39296	−	0.895200i	−1.39296	−	0.895200i
$737$	−1.52561	−	1.24748i	−1.52561	−	1.24748i
$738$		0			0
$739$	−0.157116	−	0.597730i	−0.157116	−	0.597730i	−0.998369	−	0.0570888i	$-0.981818\pi$
$739$	−0.157116	−	0.597730i	−0.157116	−	0.597730i	0.841254	−	0.540641i	$-0.181818\pi$
$740$		0			0
$741$		0			0
$742$	0.708212	+	0.0812598i	0.708212	+	0.0812598i
$743$	−0.608982	+	0.105389i	−0.608982	+	0.105389i	−0.466667	−	0.884433i	$-0.654545\pi$
$743$	−0.608982	+	0.105389i	−0.608982	+	0.105389i	−0.142315	+	0.989821i	$0.545455\pi$
$744$		0			0
$745$		0			0
$746$	−0.186261	+	0.272397i	−0.186261	+	0.272397i
$747$		0			0
$748$		0			0
$749$	−0.387721	+	0.848991i	−0.387721	+	0.848991i
$750$		0			0
$751$	0.931812	+	1.76598i	0.931812	+	1.76598i	0.516397	+	0.856349i	$0.327273\pi$
$751$	0.931812	+	1.76598i	0.931812	+	1.76598i	0.415415	+	0.909632i	$0.363636\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.873918	+	0.714599i	−0.873918	+	0.714599i	−0.959493	−	0.281733i	$-0.909091\pi$
$757$	−0.873918	+	0.714599i	−0.873918	+	0.714599i	0.0855750	+	0.996332i	$0.472727\pi$
$758$	−0.00967421	+	0.0672856i	−0.00967421	+	0.0672856i
$759$		0			0
$760$		0			0
$761$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$761$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$762$		0			0
$763$	−0.683417	−	1.75534i	−0.683417	−	1.75534i
$764$	0.960738	−	0.881757i	0.960738	−	0.881757i
$765$		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
$772$	0.0431671	+	0.0212238i	0.0431671	+	0.0212238i
$773$		0			0		0.941844	−	0.336049i	$-0.109091\pi$
$773$		0			0		−0.941844	+	0.336049i	$0.890909\pi$
$774$	−0.687179	+	0.388068i	−0.687179	+	0.388068i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.0134997	+	0.0666236i	0.0134997	+	0.0666236i
$779$		0			0
$780$		0			0
$781$	0.442719	+	0.250015i	0.442719	+	0.250015i
$782$		0			0
$783$		0			0
$784$	−0.480328	−	0.271254i	−0.480328	−	0.271254i
$785$		0			0
$786$		0			0
$787$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$787$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$788$	1.02696	+	1.33178i	1.02696	+	1.33178i
$789$		0			0
$790$		0			0
$791$	0.0547987	+	0.0160903i	0.0547987	+	0.0160903i
$792$	−0.145310	−	0.717132i	−0.145310	−	0.717132i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$797$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$798$		0			0
$799$		0			0
$800$	0.895507	−	0.319516i	0.895507	−	0.319516i
$801$		0			0
$802$	0.188731	+	0.217807i	0.188731	+	0.217807i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.43519	+	1.31720i	−1.43519	+	1.31720i	−0.564443	+	0.825472i	$0.690909\pi$
$809$	−1.43519	+	1.31720i	−1.43519	+	1.31720i	−0.870746	+	0.491733i	$0.836364\pi$
$810$		0			0
$811$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$811$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$812$	0.640868	+	0.588183i	0.640868	+	0.588183i
$813$		0			0
$814$	0.519917	+	0.377742i	0.519917	+	0.377742i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.63878	−	0.381082i	1.63878	−	0.381082i	0.696938	−	0.717132i	$-0.254545\pi$
$821$	1.63878	−	0.381082i	1.63878	−	0.381082i	0.941844	+	0.336049i	$0.109091\pi$
$822$		0			0
$823$	0.319151	+	0.529253i	0.319151	+	0.529253i	0.974012	−	0.226497i	$-0.0727273\pi$
$823$	0.319151	+	0.529253i	0.319151	+	0.529253i	−0.654861	+	0.755750i	$0.727273\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.08316	−	1.58407i	1.08316	−	1.58407i	0.309017	−	0.951057i	$-0.400000\pi$
$827$	1.08316	−	1.58407i	1.08316	−	1.58407i	0.774142	−	0.633012i	$-0.218182\pi$
$828$	1.02225	+	1.05187i	1.02225	+	1.05187i
$829$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$829$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$830$		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		0.0855750	−	0.996332i	$-0.472727\pi$
$839$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$840$		0			0
$841$	−0.0376288	−	0.0550304i	−0.0376288	−	0.0550304i
$842$	0.250492	−	0.415394i	0.250492	−	0.415394i
$843$		0			0
$844$	−0.494429	+	0.359224i	−0.494429	+	0.359224i
$845$		0			0
$846$		0			0
$847$	0.841254	+	0.540641i	0.841254	+	0.540641i
$848$	0.990060			0.990060
$849$		0			0
$850$		0			0
$851$	−2.81320	−	0.160864i	−2.81320	−	0.160864i
$852$		0			0
$853$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$853$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$854$		0			0
$855$		0			0
$856$	0.211036	−	0.649501i	0.211036	−	0.649501i
$857$		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
$862$	0.0473761	+	0.551590i	0.0473761	+	0.551590i
$863$	1.67154	+	0.191791i	1.67154	+	0.191791i	0.897398	−	0.441221i	$-0.145455\pi$
$863$	1.67154	+	0.191791i	1.67154	+	0.191791i	0.774142	+	0.633012i	$0.218182\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.30250	+	0.837065i	1.30250	+	0.837065i
$870$		0			0
$871$		0			0
$872$	0.643210	+	1.21902i	0.643210	+	1.21902i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.507607	−	0.0290260i	0.507607	−	0.0290260i	0.198590	−	0.980083i	$-0.436364\pi$
$877$	0.507607	−	0.0290260i	0.507607	−	0.0290260i	0.309017	+	0.951057i	$0.400000\pi$
$878$		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	$0.454545\pi$
$882$	−0.292620	−	0.268564i	−0.292620	−	0.268564i
$883$	0.103266	−	0.265236i	0.103266	−	0.265236i	−0.870746	−	0.491733i	$-0.836364\pi$
$883$	0.103266	−	0.265236i	0.103266	−	0.265236i	0.974012	+	0.226497i	$0.0727273\pi$
$884$		0			0
$885$		0			0
$886$	−0.453058	−	0.370464i	−0.453058	−	0.370464i
$887$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$887$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$888$		0			0
$889$	−1.79437	+	0.758307i	−1.79437	+	0.758307i
$890$		0			0
$891$	−0.0285561	+	0.999592i	−0.0285561	+	0.999592i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.939460	+	0.397019i	0.939460	+	0.397019i
$897$		0			0
$898$	0.521424	−	0.536533i	0.521424	−	0.536533i
$899$		0			0
$900$	−0.836757	+	0.0960090i	−0.836757	+	0.0960090i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.0411772	−	0.00712599i	−0.0411772	−	0.00712599i
$905$		0			0
$906$		0			0
$907$	0.00163090	+	0.0570888i	0.00163090	+	0.0570888i	1.00000			$0$
$907$	0.00163090	+	0.0570888i	0.00163090	+	0.0570888i	−0.998369	+	0.0570888i	$0.981818\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.89088	+	0.327230i	1.89088	+	0.327230i	0.993482	−	0.113991i	$-0.0363636\pi$
$911$	1.89088	+	0.327230i	1.89088	+	0.327230i	0.897398	+	0.441221i	$0.145455\pi$
$912$		0			0
$913$		0			0
$914$	0.616620	−	0.181056i	0.616620	−	0.181056i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.69694	+	0.717132i	1.69694	+	0.717132i	1.00000			$0$
$919$	1.69694	+	0.717132i	1.69694	+	0.717132i	0.696938	+	0.717132i	$0.254545\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.05959	−	1.22283i	1.05959	−	1.22283i
$926$	0.413006	−	0.174538i	0.413006	−	0.174538i
$927$		0			0
$928$	−0.794441	−	0.577195i	−0.794441	−	0.577195i
$929$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$929$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$930$		0			0
$931$		0			0
$932$	−0.0869754	+	0.223394i	−0.0869754	+	0.223394i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$937$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$938$	0.781451	−	0.0446850i	0.781451	−	0.0446850i
$939$		0			0
$940$		0			0
$941$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$941$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	−0.112313	+	0.781151i	−0.112313	+	0.781151i
$947$	−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
$953$	−0.0620945	−	0.722954i	−0.0620945	−	0.722954i	−0.959493	−	0.281733i	$-0.909091\pi$
$953$	−0.0620945	−	0.722954i	−0.0620945	−	0.722954i	0.897398	−	0.441221i	$-0.145455\pi$
$954$	0.694333	+	0.161460i	0.694333	+	0.161460i
$955$		0			0
$956$	1.39633	−	0.897368i	1.39633	−	0.897368i
$957$		0			0
$958$		0			0
$959$	−0.617026	+	1.89901i	−0.617026	+	1.89901i
$960$		0			0
$961$	0.198590	−	0.980083i	0.198590	−	0.980083i
$962$		0			0
$963$	−0.481972	+	0.799260i	−0.481972	+	0.799260i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.88369			1.88369			0.941844	−	0.336049i	$-0.109091\pi$
$967$	1.88369			1.88369			0.941844	+	0.336049i	$0.109091\pi$
$968$	−0.656631	−	0.322844i	−0.656631	−	0.322844i
$969$		0			0
$970$		0			0
$971$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$971$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$972$		0			0
$973$		0			0
$974$	−0.445450	−	0.651449i	−0.445450	−	0.651449i
$975$		0			0
$976$		0			0
$977$	0.377401	−	1.16152i	0.377401	−	1.16152i	−0.564443	−	0.825472i	$-0.690909\pi$
$977$	0.377401	−	1.16152i	0.377401	−	1.16152i	0.941844	−	0.336049i	$-0.109091\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−0.478868	−	1.82180i	−0.478868	−	1.82180i
$982$	0.321414	+	0.0747416i	0.321414	+	0.0747416i
$983$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$983$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.43745	−	3.14758i	−1.43745	−	3.14758i
$990$		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
$994$	−0.196693	+	0.0457391i	−0.196693	+	0.0457391i
$995$		0			0
$996$		0			0
$997$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$997$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$998$	−0.245071	+	0.0140137i	−0.245071	+	0.0140137i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.482.1	yes	40
7.6	odd	2	CM	847.1.bb.a.482.1	yes	40
121.60	even	55	inner	847.1.bb.a.181.1	✓	40
847.181	odd	110	inner	847.1.bb.a.181.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.181.1	✓	40	121.60	even	55	inner
847.1.bb.a.181.1	✓	40	847.181	odd	110	inner
847.1.bb.a.482.1	yes	40	1.1	even	1	trivial
847.1.bb.a.482.1	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)

\(f(q)\)	\(=\)	\(q+(-0.0113419 + 0.397019i) q^{2} +(0.840874 + 0.0480829i) q^{4} +(0.198590 - 0.980083i) q^{7} +(-0.0626157 + 0.729021i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.0113419 + 0.397019i) q^{2} +(0.840874 + 0.0480829i) q^{4} +(0.198590 - 0.980083i) q^{7} +(-0.0626157 + 0.729021i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.564443 - 0.825472i) q^{11} +(0.386859 + 0.0899602i) q^{14} +(0.548032 + 0.0628808i) q^{16} +(0.374083 + 0.133472i) q^{18} +(0.334130 - 0.214732i) q^{22} +(-0.723442 + 1.58412i) q^{23} +(-0.466667 - 0.884433i) q^{25} +(0.214115 - 0.814577i) q^{28} +(-0.481972 + 0.913438i) q^{29} +(-0.135313 + 0.941124i) q^{32} +(0.305574 - 0.784860i) q^{36} +(0.587035 + 1.50779i) q^{37} +(-1.30118 + 1.50165i) q^{43} +(-0.434934 - 0.721258i) q^{44} +(-0.620719 - 0.305187i) q^{46} +(-0.921124 - 0.389270i) q^{49} +(0.356430 - 0.175245i) q^{50} +(1.78310 - 0.204591i) q^{53} +(0.702066 + 0.206145i) q^{56} +(-0.357186 - 0.201712i) q^{58} +(-0.870746 - 0.491733i) q^{63} +(0.171439 + 0.0296687i) q^{64} +(1.89088 - 0.555213i) q^{67} +(-0.456270 + 0.224333i) q^{71} +(0.673991 + 0.284831i) q^{72} +(-0.605278 + 0.215963i) q^{74} +(-0.921124 + 0.389270i) q^{77} +(-1.42616 + 0.602700i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(-0.581424 - 0.533626i) q^{86} +(0.637130 - 0.359804i) q^{88} +(-0.684492 + 1.29726i) q^{92} +(0.164995 - 0.361288i) q^{98} +(-0.959493 + 0.281733i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9}+O(q^{10}) \) 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