LMFDB - Embedded newform 847.1.bb.a.454.1

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			454.1
Root			$-0.998369 + 0.0570888i$ of defining polynomial
Character	$\chi$	$=$	847.454
Dual form			847.1.bb.a.125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.83924 - 0.105172i) q^{2} +(2.37827 - 0.272881i) q^{4} +(-0.921124 + 0.389270i) q^{7} +(2.53025 - 0.437878i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.362808 - 0.931864i) q^{11} +(-1.65323 + 0.812838i) q^{14} +(2.27604 - 0.529269i) q^{16} +(-1.42616 + 1.16617i) q^{18} +(-0.765297 - 1.67577i) q^{22} +(-0.676337 + 0.780534i) q^{23} +(-0.564443 - 0.825472i) q^{25} +(-2.08446 + 1.17715i) q^{28} +(0.526814 - 0.770442i) q^{29} +(1.66667 - 0.489379i) q^{32} +(-1.76367 + 1.61868i) q^{36} +(-0.455331 - 0.417899i) q^{37} +(-0.277233 + 1.92820i) q^{43} +(-1.11714 - 2.11722i) q^{44} +(-1.16186 + 1.50672i) q^{46} +(0.696938 - 0.717132i) q^{49} +(-1.12496 - 1.45888i) q^{50} +(1.18956 + 0.276620i) q^{53} +(-2.16022 + 1.38829i) q^{56} +(0.887911 - 1.47243i) q^{58} +(0.516397 - 0.856349i) q^{63} +(0.813076 - 0.290105i) q^{64} +(1.58466 + 1.01840i) q^{67} +(-1.06344 - 1.37909i) q^{71} +(-1.78964 + 1.84150i) q^{72} +(-0.881416 - 0.720730i) q^{74} +(0.696938 + 0.717132i) q^{77} +(0.276810 + 0.284831i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.307107 + 3.57558i) q^{86} +(-1.32604 - 2.19899i) q^{88} +(-1.39552 + 2.04088i) q^{92} +(1.20642 - 1.39228i) q^{98} +(0.841254 + 0.540641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$122$	$365$
$\chi(n)$	$-1$	$e\left(\frac{54}{55}\right)$

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 $

$2$	1.83924	−	0.105172i	1.83924	−	0.105172i	0.897398	−	0.441221i	$-0.145455\pi$
$2$	1.83924	−	0.105172i	1.83924	−	0.105172i	0.941844	+	0.336049i	$0.109091\pi$
$3$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$3$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$4$	2.37827	−	0.272881i	2.37827	−	0.272881i
$5$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$5$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$6$		0			0
$7$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$7$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$8$	2.53025	−	0.437878i	2.53025	−	0.437878i
$9$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$10$		0			0
$11$	−0.362808	−	0.931864i	−0.362808	−	0.931864i
$11$	−0.362808	−	0.931864i	−0.362808	−	0.931864i
$12$		0			0
$13$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$13$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$14$	−1.65323	+	0.812838i	−1.65323	+	0.812838i
$15$		0			0
$16$	2.27604	−	0.529269i	2.27604	−	0.529269i
$17$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$17$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$18$	−1.42616	+	1.16617i	−1.42616	+	1.16617i
$19$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$19$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$20$		0			0
$21$		0			0
$22$	−0.765297	−	1.67577i	−0.765297	−	1.67577i
$23$	−0.676337	+	0.780534i	−0.676337	+	0.780534i	−0.985354	−	0.170522i	$-0.945455\pi$
$23$	−0.676337	+	0.780534i	−0.676337	+	0.780534i	0.309017	+	0.951057i	$0.400000\pi$
$24$		0			0
$25$	−0.564443	−	0.825472i	−0.564443	−	0.825472i
$26$		0			0
$27$		0			0
$28$	−2.08446	+	1.17715i	−2.08446	+	1.17715i
$29$	0.526814	−	0.770442i	0.526814	−	0.770442i	−0.466667	−	0.884433i	$-0.654545\pi$
$29$	0.526814	−	0.770442i	0.526814	−	0.770442i	0.993482	+	0.113991i	$0.0363636\pi$
$30$		0			0
$31$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$31$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$32$	1.66667	−	0.489379i	1.66667	−	0.489379i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−1.76367	+	1.61868i	−1.76367	+	1.61868i
$37$	−0.455331	−	0.417899i	−0.455331	−	0.417899i	0.415415	−	0.909632i	$-0.363636\pi$
$37$	−0.455331	−	0.417899i	−0.455331	−	0.417899i	−0.870746	+	0.491733i	$0.836364\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$41$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$42$		0			0
$43$	−0.277233	+	1.92820i	−0.277233	+	1.92820i	0.0855750	+	0.996332i	$0.472727\pi$
$43$	−0.277233	+	1.92820i	−0.277233	+	1.92820i	−0.362808	+	0.931864i	$0.618182\pi$
$44$	−1.11714	−	2.11722i	−1.11714	−	2.11722i
$45$		0			0
$46$	−1.16186	+	1.50672i	−1.16186	+	1.50672i
$47$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$47$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$48$		0			0
$49$	0.696938	−	0.717132i	0.696938	−	0.717132i
$50$	−1.12496	−	1.45888i	−1.12496	−	1.45888i
$51$		0			0
$52$		0			0
$53$	1.18956	+	0.276620i	1.18956	+	0.276620i	0.774142	−	0.633012i	$-0.218182\pi$
$53$	1.18956	+	0.276620i	1.18956	+	0.276620i	0.415415	+	0.909632i	$0.363636\pi$
$54$		0			0
$55$		0			0
$56$	−2.16022	+	1.38829i	−2.16022	+	1.38829i
$57$		0			0
$58$	0.887911	−	1.47243i	0.887911	−	1.47243i
$59$		0			0		−0.254218	−	0.967147i	$-0.581818\pi$
$59$		0			0		0.254218	+	0.967147i	$0.418182\pi$
$60$		0			0
$61$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$61$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$62$		0			0
$63$	0.516397	−	0.856349i	0.516397	−	0.856349i
$64$	0.813076	−	0.290105i	0.813076	−	0.290105i
$65$		0			0
$66$		0			0
$67$	1.58466	+	1.01840i	1.58466	+	1.01840i	0.974012	+	0.226497i	$0.0727273\pi$
$67$	1.58466	+	1.01840i	1.58466	+	1.01840i	0.610648	+	0.791902i	$0.290909\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.06344	−	1.37909i	−1.06344	−	1.37909i	−0.921124	−	0.389270i	$-0.872727\pi$
$71$	−1.06344	−	1.37909i	−1.06344	−	1.37909i	−0.142315	−	0.989821i	$-0.545455\pi$
$72$	−1.78964	+	1.84150i	−1.78964	+	1.84150i
$73$		0			0		−0.516397	−	0.856349i	$-0.672727\pi$
$73$		0			0		0.516397	+	0.856349i	$0.327273\pi$
$74$	−0.881416	−	0.720730i	−0.881416	−	0.720730i
$75$		0			0
$76$		0			0
$77$	0.696938	+	0.717132i	0.696938	+	0.717132i
$78$		0			0
$79$	0.276810	+	0.284831i	0.276810	+	0.284831i	0.841254	−	0.540641i	$-0.181818\pi$
$79$	0.276810	+	0.284831i	0.276810	+	0.284831i	−0.564443	+	0.825472i	$0.690909\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.309017	−	0.951057i
$82$		0			0
$83$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$83$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$84$		0			0
$85$		0			0
$86$	−0.307107	+	3.57558i	−0.307107	+	3.57558i
$87$		0			0
$88$	−1.32604	−	2.19899i	−1.32604	−	2.19899i
$89$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$89$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$90$		0			0
$91$		0			0
$92$	−1.39552	+	2.04088i	−1.39552	+	2.04088i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.466667	−	0.884433i	$-0.654545\pi$
$97$		0			0		0.466667	+	0.884433i	$0.345455\pi$
$98$	1.20642	−	1.39228i	1.20642	−	1.39228i
$99$	0.841254	+	0.540641i	0.841254	+	0.540641i
$100$	−1.56765	−	1.80917i	−1.56765	−	1.80917i
$101$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$101$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$102$		0			0
$103$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$103$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$104$		0			0
$105$		0			0
$106$	2.21698	+	0.383663i	2.21698	+	0.383663i
$107$	−1.01306	+	0.498089i	−1.01306	+	0.498089i	−0.870746	−	0.491733i	$-0.836364\pi$
$107$	−1.01306	+	0.498089i	−1.01306	+	0.498089i	−0.142315	+	0.989821i	$0.545455\pi$
$108$		0			0
$109$	0.643180	+	1.40837i	0.643180	+	1.40837i	0.897398	+	0.441221i	$0.145455\pi$
$109$	0.643180	+	1.40837i	0.643180	+	1.40837i	−0.254218	+	0.967147i	$0.581818\pi$
$110$		0			0
$111$		0			0
$112$	−1.89048	+	1.37351i	−1.89048	+	1.37351i
$113$	1.96749	−	0.340488i	1.96749	−	0.340488i	0.974012	−	0.226497i	$-0.0727273\pi$
$113$	1.96749	−	0.340488i	1.96749	−	0.340488i	0.993482	−	0.113991i	$-0.0363636\pi$
$114$		0			0
$115$		0			0
$116$	1.04267	−	1.97608i	1.04267	−	1.97608i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.736741	+	0.676175i	−0.736741	+	0.676175i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	0.859717	−	1.62934i	0.859717	−	1.62934i
$127$	−0.651166	−	1.67251i	−0.651166	−	1.67251i	−0.736741	−	0.676175i	$-0.763636\pi$
$127$	−0.651166	−	1.67251i	−0.651166	−	1.67251i	0.0855750	−	0.996332i	$-0.472727\pi$
$128$	−0.135088	+	0.0570888i	−0.135088	+	0.0570888i
$129$		0			0
$130$		0			0
$131$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$131$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$132$		0			0
$133$		0			0
$134$	3.02168	+	1.70642i	3.02168	+	1.70642i
$135$		0			0
$136$		0			0
$137$	1.93533	−	0.450041i	1.93533	−	0.450041i	0.941844	−	0.336049i	$-0.109091\pi$
$137$	1.93533	−	0.450041i	1.93533	−	0.450041i	0.993482	−	0.113991i	$-0.0363636\pi$
$138$		0			0
$139$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$139$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$140$		0			0
$141$		0			0
$142$	−2.10096	−	2.42464i	−2.10096	−	2.42464i
$143$		0			0
$144$	−1.53025	+	1.76601i	−1.53025	+	1.76601i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−1.19694	−	0.869626i	−1.19694	−	0.869626i
$149$	−1.46504	+	0.827344i	−1.46504	+	0.827344i	−0.998369	−	0.0570888i	$-0.981818\pi$
$149$	−1.46504	+	0.827344i	−1.46504	+	0.827344i	−0.466667	+	0.884433i	$0.654545\pi$
$150$		0			0
$151$	−1.95786	−	0.224644i	−1.95786	−	0.224644i	−0.959493	−	0.281733i	$-0.909091\pi$
$151$	−1.95786	−	0.224644i	−1.95786	−	0.224644i	−0.998369	+	0.0570888i	$0.981818\pi$
$152$		0			0
$153$		0			0
$154$	1.35726	+	1.24568i	1.35726	+	1.24568i
$155$		0			0
$156$		0			0
$157$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$157$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$158$	0.539078	+	0.494761i	0.539078	+	0.494761i
$159$		0			0
$160$		0			0
$161$	0.319151	−	0.982246i	0.319151	−	0.982246i
$162$	0.468333	−	1.78172i	0.468333	−	1.78172i
$163$	−0.786763	−	0.809560i	−0.786763	−	0.809560i	0.198590	−	0.980083i	$-0.436364\pi$
$163$	−0.786763	−	0.809560i	−0.786763	−	0.809560i	−0.985354	+	0.170522i	$0.945455\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$167$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$168$		0			0
$169$	0.516397	+	0.856349i	0.516397	+	0.856349i
$170$		0			0
$171$		0			0
$172$	−0.133166	+	4.66142i	−0.133166	+	4.66142i
$173$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$173$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$174$		0			0
$175$	0.841254	+	0.540641i	0.841254	+	0.540641i
$176$	−1.31897	−	1.92893i	−1.31897	−	1.92893i
$177$		0			0
$178$		0			0
$179$	0.926829	−	1.53697i	0.926829	−	1.53697i	0.0855750	−	0.996332i	$-0.472727\pi$
$179$	0.926829	−	1.53697i	0.926829	−	1.53697i	0.841254	−	0.540641i	$-0.181818\pi$
$180$		0			0
$181$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$181$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$182$		0			0
$183$		0			0
$184$	−1.36953	+	2.27110i	−1.36953	+	2.27110i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.0113419	+	0.397019i	−0.0113419	+	0.397019i	0.974012	+	0.226497i	$0.0727273\pi$
$191$	−0.0113419	+	0.397019i	−0.0113419	+	0.397019i	−0.985354	+	0.170522i	$0.945455\pi$
$192$		0			0
$193$	−1.39160	+	1.43192i	−1.39160	+	1.43192i	−0.654861	+	0.755750i	$0.727273\pi$
$193$	−1.39160	+	1.43192i	−1.39160	+	1.43192i	−0.736741	+	0.676175i	$0.763636\pi$
$194$		0			0
$195$		0			0
$196$	1.46181	−	1.89572i	1.46181	−	1.89572i
$197$	−0.282774	−	1.96674i	−0.282774	−	1.96674i	−0.254218	−	0.967147i	$-0.581818\pi$
$197$	−0.282774	−	1.96674i	−0.282774	−	1.96674i	−0.0285561	−	0.999592i	$-0.509091\pi$
$198$	1.60413	+	0.905894i	1.60413	+	0.905894i
$199$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$199$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$200$	−1.78964	−	1.84150i	−1.78964	−	1.84150i
$201$		0			0
$202$		0			0
$203$	−0.185351	+	0.914745i	−0.185351	+	0.914745i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.0883814	−	1.02901i	0.0883814	−	1.02901i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.292620	−	1.44413i	−0.292620	−	1.44413i	−0.809017	−	0.587785i	$-0.800000\pi$
$211$	−0.292620	−	1.44413i	−0.292620	−	1.44413i	0.516397	−	0.856349i	$-0.327273\pi$
$212$	2.90457	+	0.333269i	2.90457	+	0.333269i
$213$		0			0
$214$	−1.81088	+	1.02265i	−1.81088	+	1.02265i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.33108	+	2.52269i	1.33108	+	2.52269i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$223$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$224$	−1.34471	+	1.09956i	−1.34471	+	1.09956i
$225$	0.941844	+	0.336049i	0.941844	+	0.336049i
$226$	3.58289	−	0.833165i	3.58289	−	0.833165i
$227$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$227$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$228$		0			0
$229$		0			0		−0.870746	−	0.491733i	$-0.836364\pi$
$229$		0			0		0.870746	+	0.491733i	$0.163636\pi$
$230$		0			0
$231$		0			0
$232$	0.995615	−	2.18009i	0.995615	−	2.18009i
$233$	1.55249	−	1.12795i	1.55249	−	1.12795i	0.610648	−	0.791902i	$-0.290909\pi$
$233$	1.55249	−	1.12795i	1.55249	−	1.12795i	0.941844	−	0.336049i	$-0.109091\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.582092	+	1.79149i	0.582092	+	1.79149i	0.610648	+	0.791902i	$0.290909\pi$
$239$	0.582092	+	1.79149i	0.582092	+	1.79149i	−0.0285561	+	0.999592i	$0.509091\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−1.28393	+	1.32113i	−1.28393	+	1.32113i
$243$		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	$-0.200000\pi$
$251$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$252$	0.994452	−	2.17755i	0.994452	−	2.17755i
$253$	0.972732	+	0.347070i	0.972732	+	0.347070i
$254$	−1.37355	−	3.00766i	−1.37355	−	3.00766i
$255$		0			0
$256$	−1.01716	+	0.500105i	−1.01716	+	0.500105i
$257$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$257$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$258$		0			0
$259$	0.582092	+	0.207690i	0.582092	+	0.207690i
$260$		0			0
$261$	0.0266524	+	0.932954i	0.0266524	+	0.932954i
$262$		0			0
$263$	1.14043	+	1.31613i	1.14043	+	1.31613i	0.941844	+	0.336049i	$0.109091\pi$
$263$	1.14043	+	1.31613i	1.14043	+	1.31613i	0.198590	+	0.980083i	$0.436364\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	4.04665	+	1.98961i	4.04665	+	1.98961i
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$		0			0
$271$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$271$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$272$		0			0
$273$		0			0
$274$	3.51220	−	1.03128i	3.51220	−	1.03128i
$275$	−0.564443	+	0.825472i	−0.564443	+	0.825472i
$276$		0			0
$277$	−0.00488737	+	0.0569026i	−0.00488737	+	0.0569026i	−0.998369	−	0.0570888i	$-0.981818\pi$
$277$	−0.00488737	+	0.0569026i	−0.00488737	+	0.0569026i	0.993482	+	0.113991i	$0.0363636\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.242538	−	1.19697i	0.242538	−	1.19697i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	0.242538	−	1.19697i	0.242538	−	1.19697i	0.897398	−	0.441221i	$-0.145455\pi$
$282$		0			0
$283$		0			0		0.254218	−	0.967147i	$-0.418182\pi$
$283$		0			0		−0.254218	+	0.967147i	$0.581818\pi$
$284$	−2.90547	−	2.98966i	−2.90547	−	2.98966i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.06072	+	1.37556i	−1.06072	+	1.37556i
$289$	0.774142	+	0.633012i	0.774142	+	0.633012i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$293$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$294$		0			0
$295$		0			0
$296$	−1.33509	−	0.858011i	−1.33509	−	0.858011i
$297$		0			0
$298$	−2.60754	+	1.67577i	−2.60754	+	1.67577i
$299$		0			0
$300$		0			0
$301$	−0.495223	−	1.88403i	−0.495223	−	1.88403i
$302$	−3.62461	−	0.207263i	−3.62461	−	0.207263i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$307$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$308$	1.85320	+	1.51535i	1.85320	+	1.51535i
$309$		0			0
$310$		0			0
$311$		0			0		−0.921124	−	0.389270i	$-0.872727\pi$
$311$		0			0		0.921124	+	0.389270i	$0.127273\pi$
$312$		0			0
$313$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$313$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$314$		0			0
$315$		0			0
$316$	0.736055	+	0.601869i	0.736055	+	0.601869i
$317$	−0.988049	+	1.28132i	−0.988049	+	1.28132i	−0.0285561	+	0.999592i	$0.509091\pi$
$317$	−0.988049	+	1.28132i	−0.988049	+	1.28132i	−0.959493	+	0.281733i	$0.909091\pi$
$318$		0			0
$319$	−0.909079	−	0.211397i	−0.909079	−	0.211397i
$320$		0			0
$321$		0			0
$322$	0.483692	−	1.84016i	0.483692	−	1.84016i
$323$		0			0
$324$	0.475401	−	2.34620i	0.475401	−	2.34620i
$325$		0			0
$326$	−1.53219	−	1.40623i	−1.53219	−	1.40623i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.487841	−	0.143243i	0.487841	−	0.143243i	−0.0285561	−	0.999592i	$-0.509091\pi$
$331$	0.487841	−	0.143243i	0.487841	−	0.143243i	0.516397	+	0.856349i	$0.327273\pi$
$332$		0			0
$333$	0.614005	+	0.0704506i	0.614005	+	0.0704506i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.456270	−	0.224333i	−0.456270	−	0.224333i	0.198590	−	0.980083i	$-0.436364\pi$
$337$	−0.456270	−	0.224333i	−0.456270	−	0.224333i	−0.654861	+	0.755750i	$0.727273\pi$
$338$	1.03984	+	1.52072i	1.03984	+	1.52072i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.362808	+	0.931864i	−0.362808	+	0.931864i
$344$	0.142845	+	5.00022i	0.142845	+	5.00022i
$345$		0			0
$346$		0			0
$347$	0.166702	−	0.0387649i	0.166702	−	0.0387649i	−0.142315	−	0.989821i	$-0.545455\pi$
$347$	0.166702	−	0.0387649i	0.166702	−	0.0387649i	0.309017	+	0.951057i	$0.400000\pi$
$348$		0			0
$349$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$349$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$350$	1.60413	+	0.905894i	1.60413	+	0.905894i
$351$		0			0
$352$	−1.06072	−	1.37556i	−1.06072	−	1.37556i
$353$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$353$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	1.54302	−	2.92434i	1.54302	−	2.92434i
$359$	−0.505123	+	0.0579574i	−0.505123	+	0.0579574i	−0.362808	−	0.931864i	$-0.618182\pi$
$359$	−0.505123	+	0.0579574i	−0.505123	+	0.0579574i	−0.142315	+	0.989821i	$0.545455\pi$
$360$		0			0
$361$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$367$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$368$	−1.12625	+	2.13449i	−1.12625	+	2.13449i
$369$		0			0
$370$		0			0
$371$	−1.20341	+	0.208258i	−1.20341	+	0.208258i
$372$		0			0
$373$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	0.415415	+	0.909632i	$0.363636\pi$
$373$	−0.544078	+	1.19136i	−0.544078	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.91949	+	0.446359i	−1.91949	+	0.446359i	−0.921124	+	0.389270i	$0.872727\pi$
$379$	−1.91949	+	0.446359i	−1.91949	+	0.446359i	−0.998369	+	0.0570888i	$0.981818\pi$
$380$		0			0
$381$		0			0
$382$	0.0208946	+	0.731407i	0.0208946	+	0.731407i
$383$		0			0		0.362808	−	0.931864i	$-0.381818\pi$
$383$		0			0		−0.362808	+	0.931864i	$0.618182\pi$
$384$		0			0
$385$		0			0
$386$	−2.40890	+	2.78001i	−2.40890	+	2.78001i
$387$	−0.909079	−	1.72290i	−0.909079	−	1.72290i
$388$		0			0
$389$	−1.76851	−	0.869518i	−1.76851	−	0.869518i	−0.959493	−	0.281733i	$-0.909091\pi$
$389$	−1.76851	−	0.869518i	−1.76851	−	0.869518i	−0.809017	−	0.587785i	$-0.800000\pi$
$390$		0			0
$391$		0			0
$392$	1.44941	−	2.11970i	1.44941	−	2.11970i
$393$		0			0
$394$	−0.726936	−	3.58757i	−0.726936	−	3.58757i
$395$		0			0
$396$	2.14826	+	1.05623i	2.14826	+	1.05623i
$397$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$397$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$398$		0			0
$399$		0			0
$400$	−1.72159	−	1.58006i	−1.72159	−	1.58006i
$401$	−0.126093	−	1.46808i	−0.126093	−	1.46808i	−0.736741	−	0.676175i	$-0.763636\pi$
$401$	−0.126093	−	1.46808i	−0.126093	−	1.46808i	0.610648	−	0.791902i	$-0.290909\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.244701	+	1.70193i	−0.244701	+	1.70193i
$407$	−0.224227	+	0.575924i	−0.224227	+	0.575924i
$408$		0			0
$409$		0			0		0.610648	−	0.791902i	$-0.290909\pi$
$409$		0			0		−0.610648	+	0.791902i	$0.709091\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.0543326	−	1.90189i	0.0543326	−	1.90189i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$419$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$420$		0			0
$421$	−0.262555	+	0.435399i	−0.262555	+	0.435399i	−0.959493	−	0.281733i	$-0.909091\pi$
$421$	−0.262555	+	0.435399i	−0.262555	+	0.435399i	0.696938	+	0.717132i	$0.254545\pi$
$422$	−0.690080	−	2.62534i	−0.690080	−	2.62534i
$423$		0			0
$424$	3.13101	+	0.179037i	3.13101	+	0.179037i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−2.27341	+	1.46103i	−2.27341	+	1.46103i
$429$		0			0
$430$		0			0
$431$	−0.0556279	−	0.0129357i	−0.0556279	−	0.0129357i	0.198590	−	0.980083i	$-0.436364\pi$
$431$	−0.0556279	−	0.0129357i	−0.0556279	−	0.0129357i	−0.254218	+	0.967147i	$0.581818\pi$
$432$		0			0
$433$		0			0		0.0285561	−	0.999592i	$-0.490909\pi$
$433$		0			0		−0.0285561	+	0.999592i	$0.509091\pi$
$434$		0			0
$435$		0			0
$436$	1.91397	+	3.17397i	1.91397	+	3.17397i
$437$		0			0
$438$		0			0
$439$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$439$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$440$		0			0
$441$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$442$		0			0
$443$	−0.0435095	+	0.165527i	−0.0435095	+	0.165527i	−0.985354	−	0.170522i	$-0.945455\pi$
$443$	−0.0435095	+	0.165527i	−0.0435095	+	0.165527i	0.941844	+	0.336049i	$0.109091\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.636014	+	0.583729i	−0.636014	+	0.583729i
$449$	0.132494	−	1.54260i	0.132494	−	1.54260i	−0.564443	−	0.825472i	$-0.690909\pi$
$449$	0.132494	−	1.54260i	0.132494	−	1.54260i	0.696938	−	0.717132i	$-0.254545\pi$
$450$	1.76762	+	0.519021i	1.76762	+	0.519021i
$451$		0			0
$452$	4.58632	−	1.34667i	4.58632	−	1.34667i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$457$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$461$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$462$		0			0
$463$	0.475177	+	0.548384i	0.475177	+	0.548384i	0.941844	−	0.336049i	$-0.109091\pi$
$463$	0.475177	+	0.548384i	0.475177	+	0.548384i	−0.466667	+	0.884433i	$0.654545\pi$
$464$	0.791277	−	2.03238i	0.791277	−	2.03238i
$465$		0			0
$466$	2.73678	−	2.23786i	2.73678	−	2.23786i
$467$		0			0		−0.941844	−	0.336049i	$-0.890909\pi$
$467$		0			0		0.941844	+	0.336049i	$0.109091\pi$
$468$		0			0
$469$	−1.85610	−	0.321211i	−1.85610	−	0.321211i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.89740	−	0.441221i	1.89740	−	0.441221i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.12496	+	0.475414i	−1.12496	+	0.475414i
$478$	1.25902	+	3.23377i	1.25902	+	3.23377i
$479$		0			0		0.466667	−	0.884433i	$-0.345455\pi$
$479$		0			0		−0.466667	+	0.884433i	$0.654545\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.56765	+	1.80917i	−1.56765	+	1.80917i
$485$		0			0
$486$		0			0
$487$	0.601972	+	1.85268i	0.601972	+	1.85268i	0.516397	+	0.856349i	$0.327273\pi$
$487$	0.601972	+	1.85268i	0.601972	+	1.85268i	0.0855750	+	0.996332i	$0.472727\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.20642	−	0.509835i	1.20642	−	0.509835i	0.309017	−	0.951057i	$-0.400000\pi$
$491$	1.20642	−	0.509835i	1.20642	−	0.509835i	0.897398	+	0.441221i	$0.145455\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.51640	+	0.856349i	1.51640	+	0.856349i
$498$		0			0
$499$	1.59434	+	0.275911i	1.59434	+	0.275911i	0.897398	−	0.441221i	$-0.145455\pi$
$499$	1.59434	+	0.275911i	1.59434	+	0.275911i	0.696938	+	0.717132i	$0.254545\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.0285561	−	0.999592i	$-0.509091\pi$
$503$		0			0		0.0285561	+	0.999592i	$0.490909\pi$
$504$	0.931640	−	2.39290i	0.931640	−	2.39290i
$505$		0			0
$506$	1.82559	+	0.536042i	1.82559	+	0.536042i
$507$		0			0
$508$	−2.00505	−	3.79998i	−2.00505	−	3.79998i
$509$		0			0		−0.564443	−	0.825472i	$-0.690909\pi$
$509$		0			0		0.564443	+	0.825472i	$0.309091\pi$
$510$		0			0
$511$		0			0
$512$	−1.69051	+	0.954676i	−1.69051	+	0.954676i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.09245	+	0.320773i	1.09245	+	0.320773i
$519$		0			0
$520$		0			0
$521$		0			0		−0.736741	−	0.676175i	$-0.763636\pi$
$521$		0			0		0.736741	+	0.676175i	$0.236364\pi$
$522$	0.147141	+	1.71313i	0.147141	+	1.71313i
$523$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$523$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$524$		0			0
$525$		0			0
$526$	2.23596	+	2.30074i	2.23596	+	2.30074i
$527$		0			0
$528$		0			0
$529$	−0.00948747	−	0.0659868i	−0.00948747	−	0.0659868i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	4.45552	+	1.88292i	4.45552	+	1.88292i
$537$		0			0
$538$		0			0
$539$	−0.921124	−	0.389270i	−0.921124	−	0.389270i
$540$		0			0
$541$	−1.38779	+	0.495163i	−1.38779	+	0.495163i	−0.921124	−	0.389270i	$-0.872727\pi$
$541$	−1.38779	+	0.495163i	−1.38779	+	0.495163i	−0.466667	+	0.884433i	$0.654545\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.990959	+	1.64332i	−0.990959	+	1.64332i	−0.254218	+	0.967147i	$0.581818\pi$
$547$	−0.990959	+	1.64332i	−0.990959	+	1.64332i	−0.736741	+	0.676175i	$0.763636\pi$
$548$	4.47992	−	1.59843i	4.47992	−	1.59843i
$549$		0			0
$550$	−0.951332	+	1.57761i	−0.951332	+	1.57761i
$551$		0			0
$552$		0			0
$553$	−0.365853	−	0.154611i	−0.365853	−	0.154611i
$554$	−0.00300451	+	0.105172i	−0.00300451	+	0.105172i
$555$		0			0
$556$		0			0
$557$	−0.835549	−	1.38560i	−0.835549	−	1.38560i	−0.921124	−	0.389270i	$-0.872727\pi$
$557$	−0.835549	−	1.38560i	−0.835549	−	1.38560i	0.0855750	−	0.996332i	$-0.472727\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.320198	−	2.22703i	0.320198	−	2.22703i
$563$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$563$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.0855750	+	0.996332i	0.0855750	+	0.996332i
$568$	−3.29464	−	3.02380i	−3.29464	−	3.02380i
$569$	0.209698	−	0.192459i	0.209698	−	0.192459i	−0.564443	−	0.825472i	$-0.690909\pi$
$569$	0.209698	−	0.192459i	0.209698	−	0.192459i	0.774142	+	0.633012i	$0.218182\pi$
$570$		0			0
$571$	−1.90648	−	0.559792i	−1.90648	−	0.559792i	−0.985354	−	0.170522i	$-0.945455\pi$
$571$	−1.90648	−	0.559792i	−1.90648	−	0.559792i	−0.921124	−	0.389270i	$-0.872727\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.02606	+	0.117730i	1.02606	+	0.117730i
$576$	−0.487273	+	0.712614i	−0.487273	+	0.712614i
$577$		0			0		0.870746	−	0.491733i	$-0.163636\pi$
$577$		0			0		−0.870746	+	0.491733i	$0.836364\pi$
$578$	1.49041	+	1.08285i	1.49041	+	1.08285i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.173809	−	1.20886i	−0.173809	−	1.20886i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$587$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.25753	−	0.710160i	−1.25753	−	0.710160i
$593$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$593$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$594$		0			0
$595$		0			0
$596$	−3.25849	+	2.36743i	−3.25849	+	2.36743i
$597$		0			0
$598$		0			0
$599$	−0.561729	−	1.44279i	−0.561729	−	1.44279i	−0.870746	−	0.491733i	$-0.836364\pi$
$599$	−0.561729	−	1.44279i	−0.561729	−	1.44279i	0.309017	−	0.951057i	$-0.400000\pi$
$600$		0			0
$601$		0			0		0.993482	−	0.113991i	$-0.0363636\pi$
$601$		0			0		−0.993482	+	0.113991i	$0.963636\pi$
$602$	−1.10898	−	3.41310i	−1.10898	−	3.41310i
$603$	−1.88062	+	0.107538i	−1.88062	+	0.107538i
$604$	−4.71763			−4.71763
$605$		0			0
$606$		0			0
$607$		0			0		0.998369	−	0.0570888i	$-0.0181818\pi$
$607$		0			0		−0.998369	+	0.0570888i	$0.981818\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.168643	+	0.0291849i	−0.168643	+	0.0291849i	−0.254218	−	0.967147i	$-0.581818\pi$
$613$	−0.168643	+	0.0291849i	−0.168643	+	0.0291849i	0.0855750	+	0.996332i	$0.472727\pi$
$614$		0			0
$615$		0			0
$616$	2.07744	+	1.50935i	2.07744	+	1.50935i
$617$	−0.301432	−	0.660043i	−0.301432	−	0.660043i	0.696938	−	0.717132i	$-0.254545\pi$
$617$	−0.301432	−	0.660043i	−0.301432	−	0.660043i	−0.998369	+	0.0570888i	$0.981818\pi$
$618$		0			0
$619$		0			0		0.897398	−	0.441221i	$-0.145455\pi$
$619$		0			0		−0.897398	+	0.441221i	$0.854545\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.362808	+	0.931864i	−0.362808	+	0.931864i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−1.32230	−	0.650131i	−1.32230	−	0.650131i	−0.362808	−	0.931864i	$-0.618182\pi$
$631$	−1.32230	−	0.650131i	−1.32230	−	0.650131i	−0.959493	+	0.281733i	$0.909091\pi$
$632$	0.825121	+	0.599486i	0.825121	+	0.599486i
$633$		0			0
$634$	−1.68250	+	2.46058i	−1.68250	+	2.46058i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−1.69425	−	0.293202i	−1.69425	−	0.293202i
$639$	1.67095	+	0.490635i	1.67095	+	0.490635i
$640$		0			0
$641$	−0.126093	+	0.115727i	−0.126093	+	0.115727i	−0.736741	−	0.676175i	$-0.763636\pi$
$641$	−0.126093	+	0.115727i	−0.126093	+	0.115727i	0.610648	+	0.791902i	$0.290909\pi$
$642$		0			0
$643$		0			0		−0.0855750	−	0.996332i	$-0.527273\pi$
$643$		0			0		0.0855750	+	0.996332i	$0.472727\pi$
$644$	0.490992	−	2.42314i	0.490992	−	2.42314i
$645$		0			0
$646$		0			0
$647$		0			0		−0.696938	−	0.717132i	$-0.745455\pi$
$647$		0			0		0.696938	+	0.717132i	$0.254545\pi$
$648$	0.365445	−	2.54173i	0.365445	−	2.54173i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−2.09205	−	1.71066i	−2.09205	−	1.71066i
$653$	0.926829	+	1.53697i	0.926829	+	1.53697i	0.841254	+	0.540641i	$0.181818\pi$
$653$	0.926829	+	1.53697i	0.926829	+	1.53697i	0.0855750	+	0.996332i	$0.472727\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	0.415415	−	0.909632i	$-0.363636\pi$
$659$	−0.239446	−	0.153882i	−0.239446	−	0.153882i	−0.654861	+	0.755750i	$0.727273\pi$
$660$		0			0
$661$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$661$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$662$	0.882194	−	0.314766i	0.882194	−	0.314766i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.13671	+	0.0649997i	1.13671	+	0.0649997i
$667$	0.245052	+	0.932275i	0.245052	+	0.932275i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.166702	+	0.0387649i	0.166702	+	0.0387649i	0.309017	−	0.951057i	$-0.400000\pi$
$673$	0.166702	+	0.0387649i	0.166702	+	0.0387649i	−0.142315	+	0.989821i	$0.545455\pi$
$674$	−0.862785	−	0.364616i	−0.862785	−	0.364616i
$675$		0			0
$676$	1.46181	+	1.89572i	1.46181	+	1.89572i
$677$		0			0		0.696938	−	0.717132i	$-0.254545\pi$
$677$		0			0		−0.696938	+	0.717132i	$0.745455\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.209698	−	1.45848i	0.209698	−	1.45848i	−0.564443	−	0.825472i	$-0.690909\pi$
$683$	0.209698	−	1.45848i	0.209698	−	1.45848i	0.774142	−	0.633012i	$-0.218182\pi$
$684$		0			0
$685$		0			0
$686$	−0.569286	+	1.75208i	−0.569286	+	1.75208i
$687$		0			0
$688$	0.389543	+	4.53537i	0.389543	+	4.53537i
$689$		0			0
$690$		0			0
$691$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$691$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$692$		0			0
$693$	−0.985354	−	0.170522i	−0.985354	−	0.170522i
$694$	0.302529	−	0.0888305i	0.302529	−	0.0888305i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	2.14826	+	1.05623i	2.14826	+	1.05623i
$701$	1.11235	+	1.62676i	1.11235	+	1.62676i	0.696938	+	0.717132i	$0.254545\pi$
$701$	1.11235	+	1.62676i	1.11235	+	1.62676i	0.415415	+	0.909632i	$0.363636\pi$
$702$		0			0
$703$		0			0
$704$	−0.565329	−	0.652424i	−0.565329	−	0.652424i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.161197	+	0.0575149i	0.161197	+	0.0575149i	0.415415	−	0.909632i	$-0.363636\pi$
$709$	0.161197	+	0.0575149i	0.161197	+	0.0575149i	−0.254218	+	0.967147i	$0.581818\pi$
$710$		0			0
$711$	−0.391364	−	0.0677282i	−0.391364	−	0.0677282i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.78484	−	3.90825i	1.78484	−	3.90825i
$717$		0			0
$718$	−0.922948	+	0.159722i	−0.922948	+	0.159722i
$719$		0			0		0.921124	−	0.389270i	$-0.127273\pi$
$719$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$720$		0			0
$721$		0			0
$722$	−1.83024	+	0.210000i	−1.83024	+	0.210000i
$723$		0			0
$724$		0			0
$725$	−0.933335			−0.933335
$726$		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		0.921124	−	0.389270i	$-0.127273\pi$
$733$		0			0		−0.921124	+	0.389270i	$0.872727\pi$
$734$		0			0
$735$		0			0
$736$	−0.745254	+	1.63188i	−0.745254	+	1.63188i
$737$	0.374083	−	1.84617i	0.374083	−	1.84617i
$738$		0			0
$739$	1.40890	+	0.795641i	1.40890	+	0.795641i	0.993482	−	0.113991i	$-0.0363636\pi$
$739$	1.40890	+	0.795641i	1.40890	+	0.795641i	0.415415	+	0.909632i	$0.363636\pi$
$740$		0			0
$741$		0			0
$742$	−2.19146	+	0.509602i	−2.19146	+	0.509602i
$743$	−1.52394	−	0.543739i	−1.52394	−	0.543739i	−0.564443	−	0.825472i	$-0.690909\pi$
$743$	−1.52394	−	0.543739i	−1.52394	−	0.543739i	−0.959493	+	0.281733i	$0.909091\pi$
$744$		0			0
$745$		0			0
$746$	−0.875394	+	2.24843i	−0.875394	+	2.24843i
$747$		0			0
$748$		0			0
$749$	0.739263	−	0.853155i	0.739263	−	0.853155i
$750$		0			0
$751$	−1.12153	−	1.64018i	−1.12153	−	1.64018i	−0.654861	−	0.755750i	$-0.727273\pi$
$751$	−1.12153	−	1.64018i	−1.12153	−	1.64018i	−0.466667	−	0.884433i	$-0.654545\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.144100	−	0.711163i	−0.144100	−	0.711163i	−0.985354	−	0.170522i	$-0.945455\pi$
$757$	−0.144100	−	0.711163i	−0.144100	−	0.711163i	0.841254	−	0.540641i	$-0.181818\pi$
$758$	−3.48347	+	1.02284i	−3.48347	+	1.02284i
$759$		0			0
$760$		0			0
$761$		0			0		0.0855750	−	0.996332i	$-0.472727\pi$
$761$		0			0		−0.0855750	+	0.996332i	$0.527273\pi$
$762$		0			0
$763$	−1.14068	−	1.04691i	−1.14068	−	1.04691i
$764$	0.0813649	+	0.947314i	0.0813649	+	0.947314i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$769$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$770$		0			0
$771$		0			0
$772$	−2.91886	+	3.78525i	−2.91886	+	3.78525i
$773$		0			0		−0.774142	−	0.633012i	$-0.781818\pi$
$773$		0			0		0.774142	+	0.633012i	$0.218182\pi$
$774$	−1.85322	−	3.07322i	−1.85322	−	3.07322i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−3.34417	−	1.41326i	−3.34417	−	1.41326i
$779$		0			0
$780$		0			0
$781$	−0.899302	+	1.49133i	−0.899302	+	1.49133i
$782$		0			0
$783$		0			0
$784$	1.20670	−	2.00108i	1.20670	−	2.00108i
$785$		0			0
$786$		0			0
$787$		0			0		−0.998369	−	0.0570888i	$-0.981818\pi$
$787$		0			0		0.998369	+	0.0570888i	$0.0181818\pi$
$788$	−1.20920	−	4.60028i	−1.20920	−	4.60028i
$789$		0			0
$790$		0			0
$791$	−1.67976	+	1.07952i	−1.67976	+	1.07952i
$792$	2.36532	+	0.999592i	2.36532	+	0.999592i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.610648	−	0.791902i	$-0.709091\pi$
$797$		0			0		0.610648	+	0.791902i	$0.290909\pi$
$798$		0			0
$799$		0			0
$800$	−1.34471	−	1.09956i	−1.34471	−	1.09956i
$801$		0			0
$802$	−0.386316	−	2.68689i	−0.386316	−	2.68689i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.153590	+	1.78821i	0.153590	+	1.78821i	0.516397	+	0.856349i	$0.327273\pi$
$809$	0.153590	+	1.78821i	0.153590	+	1.78821i	−0.362808	+	0.931864i	$0.618182\pi$
$810$		0			0
$811$		0			0		0.736741	−	0.676175i	$-0.236364\pi$
$811$		0			0		−0.736741	+	0.676175i	$0.763636\pi$
$812$	−0.191199	+	2.22609i	−0.191199	+	2.22609i
$813$		0			0
$814$	−0.351838	+	1.08285i	−0.351838	+	1.08285i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.745586	+	0.366580i	0.745586	+	0.366580i	0.774142	−	0.633012i	$-0.218182\pi$
$821$	0.745586	+	0.366580i	0.745586	+	0.366580i	−0.0285561	+	0.999592i	$0.509091\pi$
$822$		0			0
$823$	0.755084	+	1.43104i	0.755084	+	1.43104i	0.897398	+	0.441221i	$0.145455\pi$
$823$	0.755084	+	1.43104i	0.755084	+	1.43104i	−0.142315	+	0.989821i	$0.545455\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.610427	+	1.56787i	−0.610427	+	1.56787i	0.198590	+	0.980083i	$0.436364\pi$
$827$	−0.610427	+	1.56787i	−0.610427	+	1.56787i	−0.809017	+	0.587785i	$0.800000\pi$
$828$	−0.0706015	−	2.47137i	−0.0706015	−	2.47137i
$829$		0			0		0.774142	−	0.633012i	$-0.218182\pi$
$829$		0			0		−0.774142	+	0.633012i	$0.781818\pi$
$830$		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		0.985354	−	0.170522i	$-0.0545455\pi$
$839$		0			0		−0.985354	+	0.170522i	$0.945455\pi$
$840$		0			0
$841$	0.0467610	+	0.120105i	0.0467610	+	0.120105i
$842$	−0.437111	+	0.828418i	−0.437111	+	0.828418i
$843$		0			0
$844$	−1.09001	−	3.35469i	−1.09001	−	3.35469i
$845$		0			0
$846$		0			0
$847$	0.415415	−	0.909632i	0.415415	−	0.909632i
$848$	2.85388			2.85388
$849$		0			0
$850$		0			0
$851$	0.634142	−	0.0727610i	0.634142	−	0.0727610i
$852$		0			0
$853$		0			0		−0.362808	−	0.931864i	$-0.618182\pi$
$853$		0			0		0.362808	+	0.931864i	$0.381818\pi$
$854$		0			0
$855$		0			0
$856$	−2.34520	+	1.70389i	−2.34520	+	1.70389i
$857$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$857$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$858$		0			0
$859$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$859$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$860$		0			0
$861$		0			0
$862$	−0.103674	−	0.0179414i	−0.103674	−	0.0179414i
$863$	0.809238	−	0.188180i	0.809238	−	0.188180i	0.198590	−	0.980083i	$-0.436364\pi$
$863$	0.809238	−	0.188180i	0.809238	−	0.188180i	0.610648	+	0.791902i	$0.290909\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.164995	−	0.361288i	0.164995	−	0.361288i
$870$		0			0
$871$		0			0
$872$	2.24410	+	3.28189i	2.24410	+	3.28189i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.73014	−	0.198515i	−1.73014	−	0.198515i	−0.809017	−	0.587785i	$-0.800000\pi$
$877$	−1.73014	−	0.198515i	−1.73014	−	0.198515i	−0.921124	+	0.389270i	$0.872727\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$881$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$882$	−0.157650	+	1.83549i	−0.157650	+	1.83549i
$883$	1.41380	−	1.29757i	1.41380	−	1.29757i	0.516397	−	0.856349i	$-0.327273\pi$
$883$	1.41380	−	1.29757i	1.41380	−	1.29757i	0.897398	−	0.441221i	$-0.145455\pi$
$884$		0			0
$885$		0			0
$886$	−0.0626157	+	0.309021i	−0.0626157	+	0.309021i
$887$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$887$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$888$		0			0
$889$	1.25086	+	1.28711i	1.25086	+	1.28711i
$890$		0			0
$891$	−0.998369	+	0.0570888i	−0.998369	+	0.0570888i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.102210	−	0.105172i	0.102210	−	0.105172i
$897$		0			0
$898$	0.0814510	−	2.85116i	0.0814510	−	2.85116i
$899$		0			0
$900$	2.33166	+	0.542205i	2.33166	+	0.542205i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	4.82917	−	1.72304i	4.82917	−	1.72304i
$905$		0			0
$906$		0			0
$907$	1.99348	+	0.113991i	1.99348	+	0.113991i	1.00000			$0$
$907$	1.99348	+	0.113991i	1.99348	+	0.113991i	0.993482	+	0.113991i	$0.0363636\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.58466	−	0.565405i	1.58466	−	0.565405i	0.610648	−	0.791902i	$-0.290909\pi$
$911$	1.58466	−	0.565405i	1.58466	−	0.565405i	0.974012	+	0.226497i	$0.0727273\pi$
$912$		0			0
$913$		0			0
$914$	−0.957827	−	0.615558i	−0.957827	−	0.615558i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.971444	−	0.999592i	0.971444	−	0.999592i	−0.0285561	−	0.999592i	$-0.509091\pi$
$919$	0.971444	−	0.999592i	0.971444	−	0.999592i	1.00000			$0$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.0879554	+	0.611743i	−0.0879554	+	0.611743i
$926$	0.931640	+	0.958635i	0.931640	+	0.958635i
$927$		0			0
$928$	0.500988	−	1.54188i	0.500988	−	1.54188i
$929$		0			0		0.198590	−	0.980083i	$-0.436364\pi$
$929$		0			0		−0.198590	+	0.980083i	$0.563636\pi$
$930$		0			0
$931$		0			0
$932$	3.38445	−	3.10622i	3.38445	−	3.10622i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.198590	−	0.980083i	$-0.563636\pi$
$937$		0			0		0.198590	+	0.980083i	$0.436364\pi$
$938$	−3.44760	−	0.395575i	−3.44760	−	0.395575i
$939$		0			0
$940$		0			0
$941$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$941$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	3.44337	−	1.01107i	3.44337	−	1.01107i
$947$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$947$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.45190	+	0.251261i	1.45190	+	0.251261i	0.841254	−	0.540641i	$-0.181818\pi$
$953$	1.45190	+	0.251261i	1.45190	+	0.251261i	0.610648	+	0.791902i	$0.290909\pi$
$954$	−2.01908	+	0.992716i	−2.01908	+	0.992716i
$955$		0			0
$956$	1.87324	+	4.10182i	1.87324	+	4.10182i
$957$		0			0
$958$		0			0
$959$	−1.60749	+	1.16791i	−1.60749	+	1.16791i
$960$		0			0
$961$	−0.921124	+	0.389270i	−0.921124	+	0.389270i
$962$		0			0
$963$	0.526814	−	0.998424i	0.526814	−	0.998424i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.54828			1.54828			0.774142	−	0.633012i	$-0.218182\pi$
$967$	1.54828			1.54828			0.774142	+	0.633012i	$0.218182\pi$
$968$	−1.56806	+	2.03350i	−1.56806	+	2.03350i
$969$		0			0
$970$		0			0
$971$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$971$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$972$		0			0
$973$		0			0
$974$	1.30202	+	3.34422i	1.30202	+	3.34422i
$975$		0			0
$976$		0			0
$977$	0.411334	−	0.298852i	0.411334	−	0.298852i	−0.362808	−	0.931864i	$-0.618182\pi$
$977$	0.411334	−	0.298852i	0.411334	−	0.298852i	0.774142	+	0.633012i	$0.218182\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−1.34816	−	0.761342i	−1.34816	−	0.761342i
$982$	2.16527	−	1.06459i	2.16527	−	1.06459i
$983$		0			0		−0.985354	−	0.170522i	$-0.945455\pi$
$983$		0			0		0.985354	+	0.170522i	$0.0545455\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.31752	−	1.52050i	−1.31752	−	1.52050i
$990$		0			0
$991$	0.186393	−	0.215109i	0.186393	−	0.215109i	−0.654861	−	0.755750i	$-0.727273\pi$
$991$	0.186393	−	0.215109i	0.186393	−	0.215109i	0.841254	+	0.540641i	$0.181818\pi$
$992$		0			0
$993$		0			0
$994$	2.87909	+	1.41555i	2.87909	+	1.41555i
$995$		0			0
$996$		0			0
$997$		0			0		0.564443	−	0.825472i	$-0.309091\pi$
$997$		0			0		−0.564443	+	0.825472i	$0.690909\pi$
$998$	2.96139	+	0.339788i	2.96139	+	0.339788i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.1.bb.a.454.1	yes	40
7.6	odd	2	CM	847.1.bb.a.454.1	yes	40
121.4	even	55	inner	847.1.bb.a.125.1	✓	40
847.125	odd	110	inner	847.1.bb.a.125.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.1.bb.a.125.1	✓	40	121.4	even	55	inner
847.1.bb.a.125.1	✓	40	847.125	odd	110	inner
847.1.bb.a.454.1	yes	40	1.1	even	1	trivial
847.1.bb.a.454.1	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)

\(f(q)\)	\(=\)	\(q+(1.83924 - 0.105172i) q^{2} +(2.37827 - 0.272881i) q^{4} +(-0.921124 + 0.389270i) q^{7} +(2.53025 - 0.437878i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.362808 - 0.931864i) q^{11} +(-1.65323 + 0.812838i) q^{14} +(2.27604 - 0.529269i) q^{16} +(-1.42616 + 1.16617i) q^{18} +(-0.765297 - 1.67577i) q^{22} +(-0.676337 + 0.780534i) q^{23} +(-0.564443 - 0.825472i) q^{25} +(-2.08446 + 1.17715i) q^{28} +(0.526814 - 0.770442i) q^{29} +(1.66667 - 0.489379i) q^{32} +(-1.76367 + 1.61868i) q^{36} +(-0.455331 - 0.417899i) q^{37} +(-0.277233 + 1.92820i) q^{43} +(-1.11714 - 2.11722i) q^{44} +(-1.16186 + 1.50672i) q^{46} +(0.696938 - 0.717132i) q^{49} +(-1.12496 - 1.45888i) q^{50} +(1.18956 + 0.276620i) q^{53} +(-2.16022 + 1.38829i) q^{56} +(0.887911 - 1.47243i) q^{58} +(0.516397 - 0.856349i) q^{63} +(0.813076 - 0.290105i) q^{64} +(1.58466 + 1.01840i) q^{67} +(-1.06344 - 1.37909i) q^{71} +(-1.78964 + 1.84150i) q^{72} +(-0.881416 - 0.720730i) q^{74} +(0.696938 + 0.717132i) q^{77} +(0.276810 + 0.284831i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-0.307107 + 3.57558i) q^{86} +(-1.32604 - 2.19899i) q^{88} +(-1.39552 + 2.04088i) q^{92} +(1.20642 - 1.39228i) q^{98} +(0.841254 + 0.540641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 2 q^{2} + 3 q^{4} + q^{7} - q^{8} - 10 q^{9} + q^{11} - 3 q^{14} - 3 q^{18} + 2 q^{22} - 9 q^{23} + q^{25} - 2 q^{28} + 2 q^{29} - 4 q^{32} + 3 q^{36} - 3 q^{37} + 2 q^{43} - 13 q^{44} - q^{46}+ \cdots - 4 q^{99}+O(q^{100}) \) 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

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