LMFDB - Embedded newform 912.2.f.h.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(113,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("912.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.f (of order $2$, degree $1$, not 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.20322144469993472.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 - 2x^6 + 22x^5 - 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			113.1
Root			$1.69830 + 0.340259i$ of defining polynomial
Character	$\chi$	$=$	912.113
Dual form			912.2.f.h.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69830 - 0.340259i) q^{3} +3.78858i q^{5} +4.37856 q^{7} +(2.76845 + 1.15572i) q^{9} +O(q^{10})$	\(q+(-1.69830 - 0.340259i) q^{3} +3.78858i q^{5} +4.37856 q^{7} +(2.76845 + 1.15572i) q^{9} +2.08929i q^{11} +5.19736i q^{13} +(1.28910 - 6.43415i) q^{15} -3.88236i q^{17} +(-1.35925 - 4.14155i) q^{19} +(-7.43610 - 1.48984i) q^{21} -2.20539i q^{23} -9.35336 q^{25} +(-4.30841 - 2.90476i) q^{27} +5.53689 q^{29} +6.99043i q^{31} +(0.710900 - 3.54824i) q^{33} +16.5885i q^{35} +4.69126i q^{37} +(1.76845 - 8.82667i) q^{39} +2.14029 q^{41} -3.56016 q^{43} +(-4.37856 + 10.4885i) q^{45} +7.44879i q^{47} +12.1718 q^{49} +(-1.32101 + 6.59342i) q^{51} +8.11509 q^{53} -7.91545 q^{55} +(0.899209 + 7.49609i) q^{57} -3.79842 q^{59} -3.12225 q^{61} +(12.1218 + 5.06040i) q^{63} -19.6906 q^{65} -8.92592i q^{67} +(-0.750404 + 3.74541i) q^{69} -9.65199 q^{71} -7.13314 q^{73} +(15.8848 + 3.18256i) q^{75} +9.14808i q^{77} +11.8618i q^{79} +(6.32860 + 6.39912i) q^{81} -2.29917i q^{83} +14.7087 q^{85} +(-9.40331 - 1.88398i) q^{87} -8.17891 q^{89} +22.7569i q^{91} +(2.37856 - 11.8718i) q^{93} +(15.6906 - 5.14962i) q^{95} +2.33687i q^{97} +(-2.41464 + 5.78409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q - q^3 + 2 * q^7 + 3 * q^9	$ 10 q - q^{3} + 2 q^{7} + 3 q^{9} + 10 q^{15} - 2 q^{19} - 5 q^{21} - 14 q^{25} - 10 q^{27} + 6 q^{29} + 10 q^{33} - 7 q^{39} + 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} + q^{51} + 26 q^{53} + 12 q^{55} - 11 q^{57} + 2 q^{59} - 4 q^{61} + 17 q^{63} - 32 q^{65} + 27 q^{69} + 8 q^{71} - 26 q^{73} + 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} - 4 q^{89} - 18 q^{93} - 8 q^{95} - 2 q^{99}+O(q^{100}) $ 10 * q - q^3 + 2 * q^7 + 3 * q^9 + 10 * q^15 - 2 * q^19 - 5 * q^21 - 14 * q^25 - 10 * q^27 + 6 * q^29 + 10 * q^33 - 7 * q^39 + 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 + q^51 + 26 * q^53 + 12 * q^55 - 11 * q^57 + 2 * q^59 - 4 * q^61 + 17 * q^63 - 32 * q^65 + 27 * q^69 + 8 * q^71 - 26 * q^73 + 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 - 4 * q^89 - 18 * q^93 - 8 * q^95 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.69830	−	0.340259i	−0.980514	−	0.196449i
$3$	−1.69830	−	0.340259i	−0.980514	−	0.196449i
$4$		0			0
$5$			3.78858i			1.69431i	0.531349	+	0.847153i	$0.321685\pi$
$5$			3.78858i			1.69431i	−0.531349	+	0.847153i	$0.678315\pi$
$6$		0			0
$7$	4.37856			1.65494			0.827469	−	0.561511i	$-0.189780\pi$
$7$	4.37856			1.65494			0.827469	+	0.561511i	$0.189780\pi$
$8$		0			0
$9$	2.76845	+	1.15572i	0.922816	+	0.385241i
$10$		0			0
$11$			2.08929i			0.629945i	0.949101	+	0.314972i	$0.101995\pi$
$11$			2.08929i			0.629945i	−0.949101	+	0.314972i	$0.898005\pi$
$12$		0			0
$13$			5.19736i			1.44149i	0.693202	+	0.720743i	$0.256199\pi$
$13$			5.19736i			1.44149i	−0.693202	+	0.720743i	$0.743801\pi$
$14$		0			0
$15$	1.28910	−	6.43415i	0.332844	−	1.66129i
$16$		0			0
$17$		−	3.88236i		−	0.941611i	−0.882237	−	0.470806i	$-0.843963\pi$
$17$		−	3.88236i		−	0.941611i	0.882237	−	0.470806i	$-0.156037\pi$
$18$		0			0
$19$	−1.35925	−	4.14155i	−0.311833	−	0.950137i
$19$	−1.35925	−	4.14155i	−0.311833	−	0.950137i
$20$		0			0
$21$	−7.43610	−	1.48984i	−1.62269	−	0.325111i
$22$		0			0
$23$		−	2.20539i		−	0.459855i	−0.973208	−	0.229928i	$-0.926151\pi$
$23$		−	2.20539i		−	0.459855i	0.973208	−	0.229928i	$-0.0738490\pi$
$24$		0			0
$25$	−9.35336			−1.87067
$26$		0			0
$27$	−4.30841	−	2.90476i	−0.829154	−	0.559021i
$28$		0			0
$29$	5.53689			1.02818			0.514088	−	0.857738i	$-0.328131\pi$
$29$	5.53689			1.02818			0.514088	+	0.857738i	$0.328131\pi$
$30$		0			0
$31$			6.99043i			1.25552i	0.778408	+	0.627759i	$0.216028\pi$
$31$			6.99043i			1.25552i	−0.778408	+	0.627759i	$0.783972\pi$
$32$		0			0
$33$	0.710900	−	3.54824i	0.123752	−	0.617670i
$34$		0			0
$35$			16.5885i			2.80397i
$36$		0			0
$37$			4.69126i			0.771238i	0.922658	+	0.385619i	$0.126012\pi$
$37$			4.69126i			0.771238i	−0.922658	+	0.385619i	$0.873988\pi$
$38$		0			0
$39$	1.76845	−	8.82667i	0.283178	−	1.41340i
$40$		0			0
$41$	2.14029			0.334258			0.167129	−	0.985935i	$-0.446550\pi$
$41$	2.14029			0.334258			0.167129	+	0.985935i	$0.446550\pi$
$42$		0			0
$43$	−3.56016			−0.542919			−0.271459	−	0.962450i	$-0.587506\pi$
$43$	−3.56016			−0.542919			−0.271459	+	0.962450i	$0.587506\pi$
$44$		0			0
$45$	−4.37856	+	10.4885i	−0.652717	+	1.56353i
$46$		0			0
$47$			7.44879i			1.08652i	0.839565	+	0.543259i	$0.182810\pi$
$47$			7.44879i			1.08652i	−0.839565	+	0.543259i	$0.817190\pi$
$48$		0			0
$49$	12.1718			1.73882
$50$		0			0
$51$	−1.32101	+	6.59342i	−0.184978	+	0.923263i
$52$		0			0
$53$	8.11509			1.11469			0.557347	−	0.830280i	$-0.311819\pi$
$53$	8.11509			1.11469			0.557347	+	0.830280i	$0.311819\pi$
$54$		0			0
$55$	−7.91545			−1.06732
$56$		0			0
$57$	0.899209	+	7.49609i	0.119103	+	0.992882i
$58$		0			0
$59$	−3.79842			−0.494512			−0.247256	−	0.968950i	$-0.579529\pi$
$59$	−3.79842			−0.494512			−0.247256	+	0.968950i	$0.579529\pi$
$60$		0			0
$61$	−3.12225			−0.399763			−0.199882	−	0.979820i	$-0.564056\pi$
$61$	−3.12225			−0.399763			−0.199882	+	0.979820i	$0.564056\pi$
$62$		0			0
$63$	12.1218	+	5.06040i	1.52720	+	0.637551i
$64$		0			0
$65$	−19.6906			−2.44232
$66$		0			0
$67$		−	8.92592i		−	1.09047i	−0.838282	−	0.545237i	$-0.816439\pi$
$67$		−	8.92592i		−	1.09047i	0.838282	−	0.545237i	$-0.183561\pi$
$68$		0			0
$69$	−0.750404	+	3.74541i	−0.0903380	+	0.450895i
$70$		0			0
$71$	−9.65199			−1.14548			−0.572740	−	0.819737i	$-0.694120\pi$
$71$	−9.65199			−1.14548			−0.572740	+	0.819737i	$0.694120\pi$
$72$		0			0
$73$	−7.13314			−0.834871			−0.417435	−	0.908707i	$-0.637071\pi$
$73$	−7.13314			−0.834871			−0.417435	+	0.908707i	$0.637071\pi$
$74$		0			0
$75$	15.8848	+	3.18256i	1.83422	+	0.367491i
$76$		0			0
$77$			9.14808i			1.04252i
$78$		0			0
$79$			11.8618i			1.33456i	0.744808	+	0.667279i	$0.232541\pi$
$79$			11.8618i			1.33456i	−0.744808	+	0.667279i	$0.767459\pi$
$80$		0			0
$81$	6.32860	+	6.39912i	0.703178	+	0.711014i
$82$		0			0
$83$		−	2.29917i		−	0.252367i	−0.992007	−	0.126183i	$-0.959727\pi$
$83$		−	2.29917i		−	0.252367i	0.992007	−	0.126183i	$-0.0402728\pi$
$84$		0			0
$85$	14.7087			1.59538
$86$		0			0
$87$	−9.40331	−	1.88398i	−1.00814	−	0.201984i
$88$		0			0
$89$	−8.17891			−0.866963			−0.433482	−	0.901162i	$-0.642715\pi$
$89$	−8.17891			−0.866963			−0.433482	+	0.901162i	$0.642715\pi$
$90$		0			0
$91$			22.7569i			2.38557i
$92$		0			0
$93$	2.37856	−	11.8718i	0.246645	−	1.23105i
$94$		0			0
$95$	15.6906	−	5.14962i	1.60982	−	0.528340i
$96$		0			0
$97$			2.33687i			0.237273i	0.992938	+	0.118637i	$0.0378523\pi$
$97$			2.33687i			0.237273i	−0.992938	+	0.118637i	$0.962148\pi$
$98$		0			0
$99$	−2.41464	+	5.78409i	−0.242681	+	0.581323i
$100$		0			0
$101$		−	14.8375i		−	1.47639i	−0.674590	−	0.738193i	$-0.735680\pi$
$101$		−	14.8375i		−	1.47639i	0.674590	−	0.738193i	$-0.264320\pi$
$102$		0			0
$103$		−	2.14361i		−	0.211216i	−0.994408	−	0.105608i	$-0.966321\pi$
$103$		−	2.14361i		−	0.211216i	0.994408	−	0.105608i	$-0.0336788\pi$
$104$		0			0
$105$	5.64440	−	28.1723i	0.550837	−	2.74933i
$106$		0			0
$107$	−1.50081			−0.145088			−0.0725442	−	0.997365i	$-0.523112\pi$
$107$	−1.50081			−0.145088			−0.0725442	+	0.997365i	$0.523112\pi$
$108$		0			0
$109$		−	7.34666i		−	0.703683i	−0.936060	−	0.351841i	$-0.885556\pi$
$109$		−	7.34666i		−	0.703683i	0.936060	−	0.351841i	$-0.114444\pi$
$110$		0			0
$111$	1.59624	−	7.96716i	0.151509	−	0.756210i
$112$		0			0
$113$	15.1589			1.42603			0.713016	−	0.701148i	$-0.247329\pi$
$113$	15.1589			1.42603			0.713016	+	0.701148i	$0.247329\pi$
$114$		0			0
$115$	8.35530			0.779135
$116$		0			0
$117$	−6.00671	+	14.3886i	−0.555320	+	1.33023i
$118$		0			0
$119$		−	16.9991i		−	1.55831i
$120$		0			0
$121$	6.63486			0.603169
$122$		0			0
$123$	−3.63486	−	0.728255i	−0.327745	−	0.0656645i
$124$		0			0
$125$		−	16.4930i		−	1.47518i
$126$		0			0
$127$			4.70440i			0.417448i	0.977975	+	0.208724i	$0.0669310\pi$
$127$			4.70440i			0.417448i	−0.977975	+	0.208724i	$0.933069\pi$
$128$		0			0
$129$	6.04621	+	1.21138i	0.532339	+	0.106656i
$130$		0			0
$131$			9.66646i			0.844562i	0.906465	+	0.422281i	$0.138770\pi$
$131$			9.66646i			0.844562i	−0.906465	+	0.422281i	$0.861230\pi$
$132$		0			0
$133$	−5.95154	−	18.1340i	−0.516064	−	1.57242i
$134$		0			0
$135$	11.0049	−	16.3228i	0.947152	−	1.40484i
$136$		0			0
$137$			5.78319i			0.494091i	0.969004	+	0.247046i	$0.0794597\pi$
$137$			5.78319i			0.494091i	−0.969004	+	0.247046i	$0.920540\pi$
$138$		0			0
$139$	16.7447			1.42027			0.710135	−	0.704065i	$-0.248634\pi$
$139$	16.7447			1.42027			0.710135	+	0.704065i	$0.248634\pi$
$140$		0			0
$141$	2.53452	−	12.6503i	0.213445	−	1.06535i
$142$		0			0
$143$	−10.8588			−0.908057
$144$		0			0
$145$			20.9770i			1.74204i
$146$		0			0
$147$	−20.6713	−	4.14155i	−1.70494	−	0.341589i
$148$		0			0
$149$			3.55639i			0.291351i	0.989332	+	0.145675i	$0.0465355\pi$
$149$			3.55639i			0.291351i	−0.989332	+	0.145675i	$0.953465\pi$
$150$		0			0
$151$		−	5.44183i		−	0.442850i	−0.975177	−	0.221425i	$-0.928929\pi$
$151$		−	5.44183i		−	0.442850i	0.975177	−	0.221425i	$-0.0710708\pi$
$152$		0			0
$153$	4.48694	−	10.7481i	0.362748	−	0.868934i
$154$		0			0
$155$	−26.4838			−2.12723
$156$		0			0
$157$	−24.3435			−1.94282			−0.971412	−	0.237400i	$-0.923705\pi$
$157$	−24.3435			−1.94282			−0.971412	+	0.237400i	$0.923705\pi$
$158$		0			0
$159$	−13.7819	−	2.76123i	−1.09297	−	0.218980i
$160$		0			0
$161$		−	9.65642i		−	0.761032i
$162$		0			0
$163$	−0.829289			−0.0649549			−0.0324775	−	0.999472i	$-0.510340\pi$
$163$	−0.829289			−0.0649549			−0.0324775	+	0.999472i	$0.510340\pi$
$164$		0			0
$165$	13.4428	+	2.69330i	1.04652	+	0.209673i
$166$		0			0
$167$	14.6706			1.13525			0.567624	−	0.823288i	$-0.307863\pi$
$167$	14.6706			1.13525			0.567624	+	0.823288i	$0.307863\pi$
$168$		0			0
$169$	−14.0125			−1.07788
$170$		0			0
$171$	1.02349	−	13.0366i	0.0782681	−	0.996932i
$172$		0			0
$173$	−9.47308			−0.720225			−0.360112	−	0.932909i	$-0.617262\pi$
$173$	−9.47308			−0.720225			−0.360112	+	0.932909i	$0.617262\pi$
$174$		0			0
$175$	−40.9542			−3.09585
$176$		0			0
$177$	6.45085	+	1.29245i	0.484876	+	0.0971462i
$178$		0			0
$179$	7.52601			0.562520			0.281260	−	0.959632i	$-0.409248\pi$
$179$	7.52601			0.562520			0.281260	+	0.959632i	$0.409248\pi$
$180$		0			0
$181$			7.98948i			0.593853i	0.954900	+	0.296927i	$0.0959617\pi$
$181$			7.98948i			0.593853i	−0.954900	+	0.296927i	$0.904038\pi$
$182$		0			0
$183$	5.30252	+	1.06237i	0.391973	+	0.0785330i
$184$		0			0
$185$	−17.7732			−1.30671
$186$		0			0
$187$	8.11139			0.593163
$188$		0			0
$189$	−18.8646	−	12.7186i	−1.37220	−	0.925145i
$190$		0			0
$191$		−	3.21982i		−	0.232978i	−0.993192	−	0.116489i	$-0.962836\pi$
$191$		−	3.21982i		−	0.232978i	0.993192	−	0.116489i	$-0.0371640\pi$
$192$		0			0
$193$		−	22.8270i		−	1.64312i	−0.570121	−	0.821561i	$-0.693104\pi$
$193$		−	22.8270i		−	1.64312i	0.570121	−	0.821561i	$-0.306896\pi$
$194$		0			0
$195$	33.4406	+	6.69991i	2.39473	+	0.479790i
$196$		0			0
$197$		−	6.13950i		−	0.437421i	−0.975790	−	0.218711i	$-0.929815\pi$
$197$		−	6.13950i		−	0.437421i	0.975790	−	0.218711i	$-0.0701850\pi$
$198$		0			0
$199$	−2.13406			−0.151279			−0.0756396	−	0.997135i	$-0.524100\pi$
$199$	−2.13406			−0.151279			−0.0756396	+	0.997135i	$0.524100\pi$
$200$		0			0
$201$	−3.03713	+	15.1589i	−0.214222	+	1.06923i
$202$		0			0
$203$	24.2436			1.70157
$204$		0			0
$205$			8.10868i			0.566335i
$206$		0			0
$207$	2.54882	−	6.10550i	0.177155	−	0.424362i
$208$		0			0
$209$	8.65291	−	2.83986i	0.598534	−	0.196437i
$210$		0			0
$211$		−	5.30342i		−	0.365102i	−0.983196	−	0.182551i	$-0.941565\pi$
$211$		−	5.30342i		−	0.365102i	0.983196	−	0.182551i	$-0.0584355\pi$
$212$		0			0
$213$	16.3920	+	3.28418i	1.12316	+	0.225028i
$214$		0			0
$215$		−	13.4879i		−	0.919870i
$216$		0			0
$217$			30.6080i			2.07781i
$218$		0			0
$219$	12.1142	+	2.42712i	0.818602	+	0.164009i
$220$		0			0
$221$	20.1780			1.35732
$222$		0			0
$223$		−	11.2136i		−	0.750921i	−0.926838	−	0.375461i	$-0.877485\pi$
$223$		−	11.2136i		−	0.750921i	0.926838	−	0.375461i	$-0.122515\pi$
$224$		0			0
$225$	−25.8943	−	10.8099i	−1.72629	−	0.720660i
$226$		0			0
$227$	−5.95961			−0.395553			−0.197777	−	0.980247i	$-0.563372\pi$
$227$	−5.95961			−0.395553			−0.197777	+	0.980247i	$0.563372\pi$
$228$		0			0
$229$	5.43893			0.359414			0.179707	−	0.983720i	$-0.442485\pi$
$229$	5.43893			0.359414			0.179707	+	0.983720i	$0.442485\pi$
$230$		0			0
$231$	3.11272	−	15.5362i	0.204802	−	1.02221i
$232$		0			0
$233$		−	11.0489i		−	0.723838i	−0.932210	−	0.361919i	$-0.882122\pi$
$233$		−	11.0489i		−	0.723838i	0.932210	−	0.361919i	$-0.117878\pi$
$234$		0			0
$235$	−28.2203			−1.84089
$236$		0			0
$237$	4.03609	−	20.1449i	0.262172	−	1.30855i
$238$		0			0
$239$		−	20.6947i		−	1.33863i	−0.742978	−	0.669316i	$-0.766587\pi$
$239$		−	20.6947i		−	1.33863i	0.742978	−	0.669316i	$-0.233413\pi$
$240$		0			0
$241$			22.4384i			1.44538i	0.691171	+	0.722692i	$0.257095\pi$
$241$			22.4384i			1.44538i	−0.691171	+	0.722692i	$0.742905\pi$
$242$		0			0
$243$	−8.57051	−	13.0210i	−0.549798	−	0.835297i
$244$		0			0
$245$			46.1137i			2.94610i
$246$		0			0
$247$	21.5251	−	7.06449i	1.36961	−	0.449503i
$248$		0			0
$249$	−0.782313	+	3.90468i	−0.0495771	+	0.247449i
$250$		0			0
$251$			4.99893i			0.315529i	0.987477	+	0.157765i	$0.0504287\pi$
$251$			4.99893i			0.315529i	−0.987477	+	0.157765i	$0.949571\pi$
$252$		0			0
$253$	4.60770			0.289684
$254$		0			0
$255$	−24.9797	−	5.00475i	−1.56429	−	0.313410i
$256$		0			0
$257$	29.9803			1.87012			0.935060	−	0.354488i	$-0.115345\pi$
$257$	29.9803			1.87012			0.935060	+	0.354488i	$0.115345\pi$
$258$		0			0
$259$			20.5409i			1.27635i
$260$		0			0
$261$	15.3286	+	6.39912i	0.948817	+	0.396096i
$262$		0			0
$263$		−	31.5922i		−	1.94806i	−0.226428	−	0.974028i	$-0.572705\pi$
$263$		−	31.5922i		−	1.94806i	0.226428	−	0.974028i	$-0.427295\pi$
$264$		0			0
$265$			30.7447i			1.88863i
$266$		0			0
$267$	13.8903	+	2.78295i	0.850070	+	0.170314i
$268$		0			0
$269$	−0.251090			−0.0153092			−0.00765460	−	0.999971i	$-0.502437\pi$
$269$	−0.251090			−0.0153092			−0.00765460	+	0.999971i	$0.502437\pi$
$270$		0			0
$271$	13.9991			0.850385			0.425193	−	0.905103i	$-0.360206\pi$
$271$	13.9991			0.850385			0.425193	+	0.905103i	$0.360206\pi$
$272$		0			0
$273$	7.74325	−	38.6481i	0.468643	−	2.33909i
$274$		0			0
$275$		−	19.5419i		−	1.17842i
$276$		0			0
$277$	25.5379			1.53443			0.767213	−	0.641392i	$-0.221643\pi$
$277$	25.5379			1.53443			0.767213	+	0.641392i	$0.221643\pi$
$278$		0			0
$279$	−8.07901	+	19.3526i	−0.483677	+	1.15861i
$280$		0			0
$281$	0.488305			0.0291298			0.0145649	−	0.999894i	$-0.495364\pi$
$281$	0.488305			0.0291298			0.0145649	+	0.999894i	$0.495364\pi$
$282$		0			0
$283$	3.15834			0.187744			0.0938719	−	0.995584i	$-0.470076\pi$
$283$	3.15834			0.187744			0.0938719	+	0.995584i	$0.470076\pi$
$284$		0			0
$285$	−28.3996	+	3.40673i	−1.68225	+	0.201797i
$286$		0			0
$287$	9.37140			0.553176
$288$		0			0
$289$	1.92726			0.113368
$290$		0			0
$291$	0.795141	−	3.96870i	0.0466120	−	0.232650i
$292$		0			0
$293$	−28.2797			−1.65212			−0.826059	−	0.563584i	$-0.809422\pi$
$293$	−28.2797			−1.65212			−0.826059	+	0.563584i	$0.809422\pi$
$294$		0			0
$295$		−	14.3906i		−	0.837854i
$296$		0			0
$297$	6.06888	−	9.00152i	0.352152	−	0.522321i
$298$		0			0
$299$	11.4622			0.662875
$300$		0			0
$301$	−15.5883			−0.898497
$302$		0			0
$303$	−5.04859	+	25.1985i	−0.290034	+	1.44762i
$304$		0			0
$305$		−	11.8289i		−	0.677321i
$306$		0			0
$307$			5.15796i			0.294381i	0.989108	+	0.147190i	$0.0470230\pi$
$307$			5.15796i			0.294381i	−0.989108	+	0.147190i	$0.952977\pi$
$308$		0			0
$309$	−0.729381	+	3.64049i	−0.0414931	+	0.207100i
$310$		0			0
$311$			20.2917i			1.15063i	0.817930	+	0.575317i	$0.195121\pi$
$311$			20.2917i			1.15063i	−0.817930	+	0.575317i	$0.804879\pi$
$312$		0			0
$313$	3.64769			0.206180			0.103090	−	0.994672i	$-0.467127\pi$
$313$	3.64769			0.206180			0.103090	+	0.994672i	$0.467127\pi$
$314$		0			0
$315$	−19.1718	+	45.9245i	−1.08021	+	2.58755i
$316$		0			0
$317$	16.2645			0.913506			0.456753	−	0.889594i	$-0.349012\pi$
$317$	16.2645			0.913506			0.456753	+	0.889594i	$0.349012\pi$
$318$		0			0
$319$			11.5682i			0.647694i
$320$		0			0
$321$	2.54882	+	0.510663i	0.142261	+	0.0285024i
$322$		0			0
$323$	−16.0790	+	5.27709i	−0.894660	+	0.293625i
$324$		0			0
$325$		−	48.6127i		−	2.69655i
$326$		0			0
$327$	−2.49977	+	12.4768i	−0.138238	+	0.689971i
$328$		0			0
$329$			32.6149i			1.79812i
$330$		0			0
$331$			18.5206i			1.01798i	0.860772	+	0.508991i	$0.169981\pi$
$331$			18.5206i			1.01798i	−0.860772	+	0.508991i	$0.830019\pi$
$332$		0			0
$333$	−5.42180	+	12.9875i	−0.297113	+	0.711711i
$334$		0			0
$335$	33.8166			1.84760
$336$		0			0
$337$		−	15.2301i		−	0.829638i	−0.909904	−	0.414819i	$-0.863845\pi$
$337$		−	15.2301i		−	0.829638i	0.909904	−	0.414819i	$-0.136155\pi$
$338$		0			0
$339$	−25.7444	−	5.15796i	−1.39824	−	0.280142i
$340$		0			0
$341$	−14.6050			−0.790907
$342$		0			0
$343$	22.6448			1.22271
$344$		0			0
$345$	−14.1898	−	2.84297i	−0.763953	−	0.153060i
$346$		0			0
$347$			7.17658i			0.385259i	0.981272	+	0.192629i	$0.0617015\pi$
$347$			7.17658i			0.385259i	−0.981272	+	0.192629i	$0.938298\pi$
$348$		0			0
$349$	30.2229			1.61779			0.808897	−	0.587951i	$-0.200065\pi$
$349$	30.2229			1.61779			0.808897	+	0.587951i	$0.200065\pi$
$350$		0			0
$351$	15.0971	−	22.3923i	0.805821	−	1.19521i
$352$		0			0
$353$		−	7.80023i		−	0.415164i	−0.978218	−	0.207582i	$-0.933441\pi$
$353$		−	7.80023i		−	0.415164i	0.978218	−	0.207582i	$-0.0665594\pi$
$354$		0			0
$355$		−	36.5674i		−	1.94079i
$356$		0			0
$357$	−5.78411	+	28.8697i	−0.306128	+	1.52794i
$358$		0			0
$359$			26.3956i			1.39311i	0.717504	+	0.696554i	$0.245284\pi$
$359$			26.3956i			1.39311i	−0.717504	+	0.696554i	$0.754716\pi$
$360$		0			0
$361$	−15.3049	+	11.2588i	−0.805521	+	0.592567i
$362$		0			0
$363$	−11.2680	−	2.25757i	−0.591416	−	0.118492i
$364$		0			0
$365$		−	27.0245i		−	1.41453i
$366$		0			0
$367$	6.46609			0.337527			0.168764	−	0.985657i	$-0.446023\pi$
$367$	6.46609			0.337527			0.168764	+	0.985657i	$0.446023\pi$
$368$		0			0
$369$	5.92529	+	2.47359i	0.308458	+	0.128770i
$370$		0			0
$371$	35.5324			1.84475
$372$		0			0
$373$		−	26.0952i		−	1.35116i	−0.737289	−	0.675578i	$-0.763894\pi$
$373$		−	26.0952i		−	1.35116i	0.737289	−	0.675578i	$-0.236106\pi$
$374$		0			0
$375$	−5.61191	+	28.0101i	−0.289798	+	1.44644i
$376$		0			0
$377$			28.7772i			1.48210i
$378$		0			0
$379$		−	15.7739i		−	0.810252i	−0.914261	−	0.405126i	$-0.867228\pi$
$379$		−	15.7739i		−	0.810252i	0.914261	−	0.405126i	$-0.132772\pi$
$380$		0			0
$381$	1.60071	−	7.98948i	0.0820071	−	0.409314i
$382$		0			0
$383$	6.78661			0.346780			0.173390	−	0.984853i	$-0.444528\pi$
$383$	6.78661			0.346780			0.173390	+	0.984853i	$0.444528\pi$
$384$		0			0
$385$	−34.6583			−1.76635
$386$		0			0
$387$	−9.85610	−	4.11456i	−0.501014	−	0.209155i
$388$		0			0
$389$			21.8113i			1.10588i	0.833222	+	0.552938i	$0.186493\pi$
$389$			21.8113i			1.10588i	−0.833222	+	0.552938i	$0.813507\pi$
$390$		0			0
$391$	−8.56212			−0.433005
$392$		0			0
$393$	3.28910	−	16.4165i	0.165913	−	0.828105i
$394$		0			0
$395$	−44.9394			−2.26115
$396$		0			0
$397$	1.55762			0.0781749			0.0390875	−	0.999236i	$-0.487555\pi$
$397$	1.55762			0.0781749			0.0390875	+	0.999236i	$0.487555\pi$
$398$		0			0
$399$	3.93724	+	32.8221i	0.197108	+	1.64316i
$400$		0			0
$401$	22.2545			1.11134			0.555668	−	0.831404i	$-0.312462\pi$
$401$	22.2545			1.11134			0.555668	+	0.831404i	$0.312462\pi$
$402$		0			0
$403$	−36.3317			−1.80981
$404$		0			0
$405$	−24.2436	+	23.9764i	−1.20467	+	1.19140i
$406$		0			0
$407$	−9.80140			−0.485838
$408$		0			0
$409$		−	26.6696i		−	1.31873i	−0.751824	−	0.659364i	$-0.770826\pi$
$409$		−	26.6696i		−	1.31873i	0.751824	−	0.659364i	$-0.229174\pi$
$410$		0			0
$411$	1.96778	−	9.82159i	0.0970635	−	0.484463i
$412$		0			0
$413$	−16.6316			−0.818387
$414$		0			0
$415$	8.71059			0.427586
$416$		0			0
$417$	−28.4376	−	5.69755i	−1.39260	−	0.279010i
$418$		0			0
$419$			29.2539i			1.42915i	0.699561	+	0.714573i	$0.253379\pi$
$419$			29.2539i			1.42915i	−0.699561	+	0.714573i	$0.746621\pi$
$420$		0			0
$421$			29.0331i			1.41499i	0.706719	+	0.707494i	$0.250174\pi$
$421$			29.0331i			1.41499i	−0.706719	+	0.707494i	$0.749826\pi$
$422$		0			0
$423$	−8.60875	+	20.6216i	−0.418572	+	1.00266i
$424$		0			0
$425$			36.3131i			1.76145i
$426$		0			0
$427$	−13.6710			−0.661584
$428$		0			0
$429$	18.4415	+	3.69480i	0.890363	+	0.178387i
$430$		0			0
$431$	6.77801			0.326485			0.163243	−	0.986586i	$-0.447805\pi$
$431$	6.77801			0.326485			0.163243	+	0.986586i	$0.447805\pi$
$432$		0			0
$433$		−	22.8270i		−	1.09699i	−0.836153	−	0.548497i	$-0.815200\pi$
$433$		−	22.8270i		−	1.09699i	0.836153	−	0.548497i	$-0.184800\pi$
$434$		0			0
$435$	7.13761	−	35.6252i	0.342222	−	1.70810i
$436$		0			0
$437$	−9.13373	+	2.99767i	−0.436926	+	0.143398i
$438$		0			0
$439$			13.7118i			0.654428i	0.944950	+	0.327214i	$0.106110\pi$
$439$			13.7118i			0.654428i	−0.944950	+	0.327214i	$0.893890\pi$
$440$		0			0
$441$	33.6969	+	14.0672i	1.60461	+	0.669866i
$442$		0			0
$443$		−	28.1301i		−	1.33650i	−0.743936	−	0.668251i	$-0.767043\pi$
$443$		−	28.1301i		−	1.33650i	0.743936	−	0.668251i	$-0.232957\pi$
$444$		0			0
$445$		−	30.9865i		−	1.46890i
$446$		0			0
$447$	1.21009	−	6.03981i	0.0572354	−	0.285673i
$448$		0			0
$449$	−19.6833			−0.928913			−0.464457	−	0.885596i	$-0.653750\pi$
$449$	−19.6833			−0.928913			−0.464457	+	0.885596i	$0.653750\pi$
$450$		0			0
$451$			4.47170i			0.210564i
$452$		0			0
$453$	−1.85163	+	9.24186i	−0.0869973	+	0.434220i
$454$		0			0
$455$	−86.2164			−4.04189
$456$		0			0
$457$	17.9793			0.841035			0.420517	−	0.907284i	$-0.361849\pi$
$457$	17.9793			0.841035			0.420517	+	0.907284i	$0.361849\pi$
$458$		0			0
$459$	−11.2773	+	16.7268i	−0.526380	+	0.780741i
$460$		0			0
$461$		−	30.4453i		−	1.41798i	−0.705219	−	0.708989i	$-0.749151\pi$
$461$		−	30.4453i		−	1.41798i	0.705219	−	0.708989i	$-0.250849\pi$
$462$		0			0
$463$	38.8667			1.80629			0.903144	−	0.429339i	$-0.141253\pi$
$463$	38.8667			1.80629			0.903144	+	0.429339i	$0.141253\pi$
$464$		0			0
$465$	44.9775	+	9.01136i	2.08578	+	0.417892i
$466$		0			0
$467$		−	25.7295i		−	1.19062i	−0.803497	−	0.595309i	$-0.797029\pi$
$467$		−	25.7295i		−	1.19062i	0.803497	−	0.595309i	$-0.202971\pi$
$468$		0			0
$469$		−	39.0827i		−	1.80467i
$470$		0			0
$471$	41.3426	+	8.28310i	1.90497	+	0.381665i
$472$		0			0
$473$		−	7.43820i		−	0.342009i
$474$		0			0
$475$	12.7135	+	38.7374i	0.583336	+	1.77739i
$476$		0			0
$477$	22.4662	+	9.37881i	1.02866	+	0.429426i
$478$		0			0
$479$			20.2882i			0.926990i	0.886100	+	0.463495i	$0.153405\pi$
$479$			20.2882i			0.926990i	−0.886100	+	0.463495i	$0.846595\pi$
$480$		0			0
$481$	−24.3821			−1.11173
$482$		0			0
$483$	−3.28568	+	16.3995i	−0.149504	+	0.746203i
$484$		0			0
$485$	−8.85342			−0.402013
$486$		0			0
$487$		−	36.9977i		−	1.67653i	−0.545266	−	0.838263i	$-0.683571\pi$
$487$		−	36.9977i		−	1.67653i	0.545266	−	0.838263i	$-0.316429\pi$
$488$		0			0
$489$	1.40838	+	0.282173i	0.0636892	+	0.0127603i
$490$		0			0
$491$			11.9893i			0.541069i	0.962710	+	0.270534i	$0.0872003\pi$
$491$			11.9893i			0.541069i	−0.962710	+	0.270534i	$0.912800\pi$
$492$		0			0
$493$		−	21.4962i		−	0.968142i
$494$		0			0
$495$	−21.9135	−	9.14808i	−0.984939	−	0.411176i
$496$		0			0
$497$	−42.2618			−1.89570
$498$		0			0
$499$	13.7799			0.616874			0.308437	−	0.951245i	$-0.400194\pi$
$499$	13.7799			0.616874			0.308437	+	0.951245i	$0.400194\pi$
$500$		0			0
$501$	−24.9151	−	4.99181i	−1.11313	−	0.223018i
$502$		0			0
$503$			11.2357i			0.500974i	0.968120	+	0.250487i	$0.0805908\pi$
$503$			11.2357i			0.500974i	−0.968120	+	0.250487i	$0.919409\pi$
$504$		0			0
$505$	56.2130			2.50145
$506$		0			0
$507$	23.7974	+	4.76788i	1.05688	+	0.211749i
$508$		0			0
$509$	−19.1301			−0.847928			−0.423964	−	0.905679i	$-0.639362\pi$
$509$	−19.1301			−0.847928			−0.423964	+	0.905679i	$0.639362\pi$
$510$		0			0
$511$	−31.2328			−1.38166
$512$		0			0
$513$	−6.17401	+	21.7918i	−0.272589	+	0.962131i
$514$		0			0
$515$	8.12123			0.357864
$516$		0			0
$517$	−15.5627			−0.684446
$518$		0			0
$519$	16.0881	+	3.22330i	0.706190	+	0.141487i
$520$		0			0
$521$	17.9117			0.784725			0.392362	−	0.919811i	$-0.371658\pi$
$521$	17.9117			0.784725			0.392362	+	0.919811i	$0.371658\pi$
$522$		0			0
$523$		−	0.792279i		−	0.0346439i	−0.999850	−	0.0173220i	$-0.994486\pi$
$523$		−	0.792279i		−	0.0346439i	0.999850	−	0.0173220i	$-0.00551403\pi$
$524$		0			0
$525$	69.5525	+	13.9350i	3.03552	+	0.608175i
$526$		0			0
$527$	27.1394			1.18221
$528$		0			0
$529$	18.1363			0.788533
$530$		0			0
$531$	−10.5157	−	4.38992i	−0.456343	−	0.190506i
$532$		0			0
$533$			11.1239i			0.481828i
$534$		0			0
$535$		−	5.68593i		−	0.245824i
$536$		0			0
$537$	−12.7814	−	2.56079i	−0.551559	−	0.110506i
$538$		0			0
$539$			25.4303i			1.09536i
$540$		0			0
$541$	18.9028			0.812693			0.406346	−	0.913719i	$-0.366803\pi$
$541$	18.9028			0.812693			0.406346	+	0.913719i	$0.366803\pi$
$542$		0			0
$543$	2.71849	−	13.5685i	0.116662	−	0.582282i
$544$		0			0
$545$	27.8334			1.19225
$546$		0			0
$547$		−	25.3992i		−	1.08599i	−0.839736	−	0.542995i	$-0.817290\pi$
$547$		−	25.3992i		−	1.08599i	0.839736	−	0.542995i	$-0.182710\pi$
$548$		0			0
$549$	−8.64379	−	3.60846i	−0.368908	−	0.154005i
$550$		0			0
$551$	−7.52601	−	22.9313i	−0.320619	−	0.976908i
$552$		0			0
$553$			51.9376i			2.20861i
$554$		0			0
$555$	30.1843	+	6.04750i	1.28125	+	0.256702i
$556$		0			0
$557$		−	13.0344i		−	0.552284i	−0.961117	−	0.276142i	$-0.910944\pi$
$557$		−	13.0344i		−	0.552284i	0.961117	−	0.276142i	$-0.0890561\pi$
$558$		0			0
$559$		−	18.5034i		−	0.782610i
$560$		0			0
$561$	−13.7756	−	2.75997i	−0.581605	−	0.116526i
$562$		0			0
$563$	47.3156			1.99412			0.997058	−	0.0766505i	$-0.0244226\pi$
$563$	47.3156			1.99412			0.997058	+	0.0766505i	$0.0244226\pi$
$564$		0			0
$565$			57.4309i			2.41613i
$566$		0			0
$567$	27.7101	+	28.0189i	1.16372	+	1.17668i
$568$		0			0
$569$	−27.2291			−1.14151			−0.570753	−	0.821122i	$-0.693348\pi$
$569$	−27.2291			−1.14151			−0.570753	+	0.821122i	$0.693348\pi$
$570$		0			0
$571$	2.71849			0.113765			0.0568827	−	0.998381i	$-0.481884\pi$
$571$	2.71849			0.113765			0.0568827	+	0.998381i	$0.481884\pi$
$572$		0			0
$573$	−1.09557	+	5.46823i	−0.0457683	+	0.228439i
$574$		0			0
$575$			20.6278i			0.860238i
$576$		0			0
$577$	−33.8063			−1.40737			−0.703687	−	0.710510i	$-0.748464\pi$
$577$	−33.8063			−1.40737			−0.703687	+	0.710510i	$0.748464\pi$
$578$		0			0
$579$	−7.76708	+	38.7670i	−0.322789	+	1.61110i
$580$		0			0
$581$		−	10.0670i		−	0.417651i
$582$		0			0
$583$			16.9548i			0.702196i
$584$		0			0
$585$	−54.5124	−	22.7569i	−2.25381	−	0.940883i
$586$		0			0
$587$		−	5.02687i		−	0.207481i	−0.994604	−	0.103741i	$-0.966919\pi$
$587$		−	5.02687i		−	0.207481i	0.994604	−	0.103741i	$-0.0330812\pi$
$588$		0			0
$589$	28.9512	−	9.50172i	1.19291	−	0.391511i
$590$		0			0
$591$	−2.08902	+	10.4267i	−0.0859308	+	0.428897i
$592$		0			0
$593$		−	23.4669i		−	0.963668i	−0.876262	−	0.481834i	$-0.839971\pi$
$593$		−	23.4669i		−	0.963668i	0.876262	−	0.481834i	$-0.160029\pi$
$594$		0			0
$595$	64.4027			2.64025
$596$		0			0
$597$	3.62427	+	0.726132i	0.148331	+	0.0297186i
$598$		0			0
$599$	−7.57506			−0.309509			−0.154754	−	0.987953i	$-0.549459\pi$
$599$	−7.57506			−0.309509			−0.154754	+	0.987953i	$0.549459\pi$
$600$		0			0
$601$		−	19.9766i		−	0.814862i	−0.913236	−	0.407431i	$-0.866425\pi$
$601$		−	19.9766i		−	0.814862i	0.913236	−	0.407431i	$-0.133575\pi$
$602$		0			0
$603$	10.3159	−	24.7109i	0.420096	−	1.00631i
$604$		0			0
$605$			25.1367i			1.02195i
$606$		0			0
$607$			7.31471i			0.296895i	0.988920	+	0.148447i	$0.0474276\pi$
$607$			7.31471i			0.296895i	−0.988920	+	0.148447i	$0.952572\pi$
$608$		0			0
$609$	−41.1729	−	8.24911i	−1.66841	−	0.334271i
$610$		0			0
$611$	−38.7140			−1.56620
$612$		0			0
$613$	8.50884			0.343669			0.171834	−	0.985126i	$-0.445031\pi$
$613$	8.50884			0.343669			0.171834	+	0.985126i	$0.445031\pi$
$614$		0			0
$615$	2.75905	−	13.7710i	0.111256	−	0.555299i
$616$		0			0
$617$		−	10.1156i		−	0.407240i	−0.979050	−	0.203620i	$-0.934729\pi$
$617$		−	10.1156i		−	0.407240i	0.979050	−	0.203620i	$-0.0652708\pi$
$618$		0			0
$619$	−24.1358			−0.970100			−0.485050	−	0.874487i	$-0.661199\pi$
$619$	−24.1358			−0.970100			−0.485050	+	0.874487i	$0.661199\pi$
$620$		0			0
$621$	−6.40612	+	9.50172i	−0.257069	+	0.381291i
$622$		0			0
$623$	−35.8118			−1.43477
$624$		0			0
$625$	15.7185			0.628740
$626$		0			0
$627$	−15.6615	+	1.87871i	−0.625461	+	0.0750284i
$628$		0			0
$629$	18.2132			0.726207
$630$		0			0
$631$	−16.7951			−0.668604			−0.334302	−	0.942466i	$-0.608501\pi$
$631$	−16.7951			−0.668604			−0.334302	+	0.942466i	$0.608501\pi$
$632$		0			0
$633$	−1.80454	+	9.00679i	−0.0717238	+	0.357988i
$634$		0			0
$635$	−17.8230			−0.707284
$636$		0			0
$637$			63.2609i			2.50649i
$638$		0			0
$639$	−26.7210	−	11.1550i	−1.05707	−	0.441286i
$640$		0			0
$641$	−14.6647			−0.579220			−0.289610	−	0.957145i	$-0.593526\pi$
$641$	−14.6647			−0.579220			−0.289610	+	0.957145i	$0.593526\pi$
$642$		0			0
$643$	−0.0884280			−0.00348726			−0.00174363	−	0.999998i	$-0.500555\pi$
$643$	−0.0884280			−0.00348726			−0.00174363	+	0.999998i	$0.500555\pi$
$644$		0			0
$645$	−4.58940	+	22.9066i	−0.180707	+	0.901946i
$646$		0			0
$647$			19.7860i			0.777869i	0.921265	+	0.388935i	$0.127157\pi$
$647$			19.7860i			0.777869i	−0.921265	+	0.388935i	$0.872843\pi$
$648$		0			0
$649$		−	7.93600i		−	0.311515i
$650$		0			0
$651$	10.4146	−	51.9815i	0.408182	−	2.03732i
$652$		0			0
$653$			7.35017i			0.287634i	0.989604	+	0.143817i	$0.0459377\pi$
$653$			7.35017i			0.287634i	−0.989604	+	0.143817i	$0.954062\pi$
$654$		0			0
$655$	−36.6222			−1.43095
$656$		0			0
$657$	−19.7477	−	8.24394i	−0.770432	−	0.321627i
$658$		0			0
$659$	−0.388398			−0.0151298			−0.00756492	−	0.999971i	$-0.502408\pi$
$659$	−0.388398			−0.0151298			−0.00756492	+	0.999971i	$0.502408\pi$
$660$		0			0
$661$		−	18.9377i		−	0.736593i	−0.929708	−	0.368296i	$-0.879941\pi$
$661$		−	18.9377i		−	0.736593i	0.929708	−	0.368296i	$-0.120059\pi$
$662$		0			0
$663$	−34.2683	−	6.86576i	−1.33087	−	0.266644i
$664$		0			0
$665$	68.7022	−	22.5479i	2.66416	−	0.874370i
$666$		0			0
$667$		−	12.2110i		−	0.472812i
$668$		0			0
$669$	−3.81554	+	19.0441i	−0.147517	+	0.736289i
$670$		0			0
$671$		−	6.52329i		−	0.251829i
$672$		0			0
$673$			14.7526i			0.568670i	0.958725	+	0.284335i	$0.0917728\pi$
$673$			14.7526i			0.568670i	−0.958725	+	0.284335i	$0.908227\pi$
$674$		0			0
$675$	40.2981	+	27.1692i	1.55107	+	1.04574i
$676$		0			0
$677$	33.1397			1.27366			0.636831	−	0.771003i	$-0.280245\pi$
$677$	33.1397			1.27366			0.636831	+	0.771003i	$0.280245\pi$
$678$		0			0
$679$			10.2321i			0.392672i
$680$		0			0
$681$	10.1212	+	2.02781i	0.387846	+	0.0777059i
$682$		0			0
$683$	8.62188			0.329907			0.164954	−	0.986301i	$-0.447253\pi$
$683$	8.62188			0.329907			0.164954	+	0.986301i	$0.447253\pi$
$684$		0			0
$685$	−21.9101			−0.837141
$686$		0			0
$687$	−9.23693	−	1.85064i	−0.352411	−	0.0706065i
$688$		0			0
$689$			42.1770i			1.60682i
$690$		0			0
$691$	−1.99941			−0.0760611			−0.0380305	−	0.999277i	$-0.512108\pi$
$691$	−1.99941			−0.0760611			−0.0380305	+	0.999277i	$0.512108\pi$
$692$		0			0
$693$	−10.5727	+	25.3260i	−0.401622	+	0.962054i
$694$		0			0
$695$			63.4388i			2.40637i
$696$		0			0
$697$		−	8.30940i		−	0.314741i
$698$		0			0
$699$	−3.75949	+	18.7644i	−0.142197	+	0.709733i
$700$		0			0
$701$		−	39.2719i		−	1.48328i	−0.670798	−	0.741640i	$-0.734048\pi$
$701$		−	39.2719i		−	1.48328i	0.670798	−	0.741640i	$-0.265952\pi$
$702$		0			0
$703$	19.4291	−	6.37658i	0.732782	−	0.240497i
$704$		0			0
$705$	47.9266	+	9.60223i	1.80502	+	0.361641i
$706$		0			0
$707$		−	64.9668i		−	2.44333i
$708$		0			0
$709$	−29.7805			−1.11843			−0.559215	−	0.829023i	$-0.688897\pi$
$709$	−29.7805			−1.11843			−0.559215	+	0.829023i	$0.688897\pi$
$710$		0			0
$711$	−13.7090	+	32.8388i	−0.514127	+	1.23155i
$712$		0			0
$713$	15.4166			0.577357
$714$		0			0
$715$		−	41.1394i		−	1.53853i
$716$		0			0
$717$	−7.04157	+	35.1459i	−0.262972	+	1.31255i
$718$		0			0
$719$			42.2808i			1.57681i	0.615157	+	0.788405i	$0.289093\pi$
$719$			42.2808i			1.57681i	−0.615157	+	0.788405i	$0.710907\pi$
$720$		0			0
$721$		−	9.38590i		−	0.349549i
$722$		0			0
$723$	7.63486	−	38.1071i	0.283944	−	1.41722i
$724$		0			0
$725$	−51.7886			−1.92338
$726$		0			0
$727$	−40.8893			−1.51650			−0.758251	−	0.651963i	$-0.773946\pi$
$727$	−40.8893			−1.51650			−0.758251	+	0.651963i	$0.773946\pi$
$728$		0			0
$729$	10.1248	+	25.0298i	0.374992	+	0.927028i
$730$		0			0
$731$			13.8218i			0.511218i
$732$		0			0
$733$	−21.9081			−0.809196			−0.404598	−	0.914495i	$-0.632588\pi$
$733$	−21.9081			−0.809196			−0.404598	+	0.914495i	$0.632588\pi$
$734$		0			0
$735$	15.6906	−	78.3149i	0.578757	−	2.88869i
$736$		0			0
$737$	18.6488			0.686939
$738$		0			0
$739$	26.8616			0.988120			0.494060	−	0.869428i	$-0.335512\pi$
$739$	26.8616			0.988120			0.494060	+	0.869428i	$0.335512\pi$
$740$		0			0
$741$	−38.9599	+	4.67351i	−1.43123	+	0.171686i
$742$		0			0
$743$	35.9547			1.31905			0.659524	−	0.751683i	$-0.270758\pi$
$743$	35.9547			1.31905			0.659524	+	0.751683i	$0.270758\pi$
$744$		0			0
$745$	−13.4737			−0.493637
$746$		0			0
$747$	2.65721	−	6.36513i	0.0972221	−	0.232888i
$748$		0			0
$749$	−6.57137			−0.240113
$750$		0			0
$751$			35.9744i			1.31272i	0.754446	+	0.656362i	$0.227906\pi$
$751$			35.9744i			1.31272i	−0.754446	+	0.656362i	$0.772094\pi$
$752$		0			0
$753$	1.70093	−	8.48968i	0.0619853	−	0.309381i
$754$		0			0
$755$	20.6168			0.750323
$756$		0			0
$757$	−42.4653			−1.54343			−0.771714	−	0.635969i	$-0.780601\pi$
$757$	−42.4653			−1.54343			−0.771714	+	0.635969i	$0.780601\pi$
$758$		0			0
$759$	−7.82526	−	1.56781i	−0.284039	−	0.0569080i
$760$		0			0
$761$			31.4689i			1.14075i	0.821385	+	0.570374i	$0.193202\pi$
$761$			31.4689i			1.14075i	−0.821385	+	0.570374i	$0.806798\pi$
$762$		0			0
$763$		−	32.1678i		−	1.16455i
$764$		0			0
$765$	40.7201	+	16.9991i	1.47224	+	0.614605i
$766$		0			0
$767$		−	19.7417i		−	0.712832i
$768$		0			0
$769$	−12.8669			−0.463991			−0.231995	−	0.972717i	$-0.574525\pi$
$769$	−12.8669			−0.463991			−0.231995	+	0.972717i	$0.574525\pi$
$770$		0			0
$771$	−50.9156	−	10.2011i	−1.83368	−	0.367383i
$772$		0			0
$773$	26.3617			0.948164			0.474082	−	0.880481i	$-0.342780\pi$
$773$	26.3617			0.948164			0.474082	+	0.880481i	$0.342780\pi$
$774$		0			0
$775$		−	65.3840i		−	2.34866i
$776$		0			0
$777$	6.98924	−	34.8847i	0.250738	−	1.25148i
$778$		0			0
$779$	−2.90919	−	8.86414i	−0.104232	−	0.317591i
$780$		0			0
$781$		−	20.1658i		−	0.721590i
$782$		0			0
$783$	−23.8552	−	16.0833i	−0.852516	−	0.574771i
$784$		0			0
$785$		−	92.2274i		−	3.29174i
$786$		0			0
$787$		−	45.4489i		−	1.62008i	−0.586376	−	0.810039i	$-0.699446\pi$
$787$		−	45.4489i		−	1.62008i	0.586376	−	0.810039i	$-0.300554\pi$
$788$		0			0
$789$	−10.7495	+	53.6530i	−0.382693	+	1.91010i
$790$		0			0
$791$	66.3742			2.36000
$792$		0			0
$793$		−	16.2274i		−	0.576253i
$794$		0			0
$795$	10.4612	−	52.2137i	0.371019	−	1.85183i
$796$		0			0
$797$	26.8209			0.950046			0.475023	−	0.879973i	$-0.342440\pi$
$797$	26.8209			0.950046			0.475023	+	0.879973i	$0.342440\pi$
$798$		0			0
$799$	28.9189			1.02308
$800$		0			0
$801$	−22.6429	−	9.45257i	−0.800047	−	0.333990i
$802$		0			0
$803$		−	14.9032i		−	0.525923i
$804$		0			0
$805$	36.5841			1.28942
$806$		0			0
$807$	0.426425	+	0.0854355i	0.0150109	+	0.00300747i
$808$		0			0
$809$		−	18.4443i		−	0.648465i	−0.945977	−	0.324233i	$-0.894894\pi$
$809$		−	18.4443i		−	0.648465i	0.945977	−	0.324233i	$-0.105106\pi$
$810$		0			0
$811$		−	0.492957i		−	0.0173101i	−0.999963	−	0.00865503i	$-0.997245\pi$
$811$		−	0.492957i		−	0.0173101i	0.999963	−	0.00865503i	$-0.00275501\pi$
$812$		0			0
$813$	−23.7747	−	4.76332i	−0.833815	−	0.167057i
$814$		0			0
$815$		−	3.14183i		−	0.110053i
$816$		0			0
$817$	4.83913	+	14.7446i	0.169300	+	0.515847i
$818$		0			0
$819$	−26.3007	+	63.0013i	−0.919021	+	2.20144i
$820$		0			0
$821$			19.7229i			0.688334i	0.938908	+	0.344167i	$0.111839\pi$
$821$			19.7229i			0.688334i	−0.938908	+	0.344167i	$0.888161\pi$
$822$		0			0
$823$	−29.8463			−1.04038			−0.520188	−	0.854052i	$-0.674138\pi$
$823$	−29.8463			−1.04038			−0.520188	+	0.854052i	$0.674138\pi$
$824$		0			0
$825$	−6.64930	+	33.1880i	−0.231499	+	1.15546i
$826$		0			0
$827$	23.5159			0.817727			0.408863	−	0.912596i	$-0.365925\pi$
$827$	23.5159			0.817727			0.408863	+	0.912596i	$0.365925\pi$
$828$		0			0
$829$		−	46.3842i		−	1.61099i	−0.592602	−	0.805495i	$-0.701899\pi$
$829$		−	46.3842i		−	1.61099i	0.592602	−	0.805495i	$-0.298101\pi$
$830$		0			0
$831$	−43.3711	−	8.68952i	−1.50453	−	0.301436i
$832$		0			0
$833$		−	47.2552i		−	1.63730i
$834$		0			0
$835$			55.5809i			1.92346i
$836$		0			0
$837$	20.3055	−	30.1176i	0.701860	−	1.04102i
$838$		0			0
$839$	−6.23202			−0.215153			−0.107577	−	0.994197i	$-0.534309\pi$
$839$	−6.23202			−0.215153			−0.107577	+	0.994197i	$0.534309\pi$
$840$		0			0
$841$	1.65721			0.0571450
$842$		0			0
$843$	−0.829289	−	0.166150i	−0.0285622	−	0.00572252i
$844$		0			0
$845$		−	53.0875i		−	1.82627i
$846$		0			0
$847$	29.0511			0.998208
$848$		0			0
$849$	−5.36381	−	1.07465i	−0.184085	−	0.0368820i
$850$		0			0
$851$	10.3460			0.354658
$852$		0			0
$853$	28.3217			0.969718			0.484859	−	0.874592i	$-0.338871\pi$
$853$	28.3217			0.969718			0.484859	+	0.874592i	$0.338871\pi$
$854$		0			0
$855$	49.3902	+	3.87757i	1.68911	+	0.132610i
$856$		0			0
$857$	−13.3135			−0.454782			−0.227391	−	0.973804i	$-0.573020\pi$
$857$	−13.3135			−0.454782			−0.227391	+	0.973804i	$0.573020\pi$
$858$		0			0
$859$	39.8553			1.35985			0.679923	−	0.733284i	$-0.262013\pi$
$859$	39.8553			1.35985			0.679923	+	0.733284i	$0.262013\pi$
$860$		0			0
$861$	−15.9155	−	3.18870i	−0.542397	−	0.108671i
$862$		0			0
$863$	−37.9090			−1.29044			−0.645219	−	0.763998i	$-0.723234\pi$
$863$	−37.9090			−1.29044			−0.645219	+	0.763998i	$0.723234\pi$
$864$		0			0
$865$		−	35.8895i		−	1.22028i
$866$		0			0
$867$	−3.27306	−	0.655767i	−0.111159	−	0.0222710i
$868$		0			0
$869$	−24.7828			−0.840698
$870$		0			0
$871$	46.3912			1.57191
$872$		0			0
$873$	−2.70078	+	6.46950i	−0.0914074	+	0.218959i
$874$		0			0
$875$		−	72.2157i		−	2.44134i
$876$		0			0
$877$			11.9662i			0.404069i	0.979378	+	0.202035i	$0.0647553\pi$
$877$			11.9662i			0.404069i	−0.979378	+	0.202035i	$0.935245\pi$
$878$		0			0
$879$	48.0274	+	9.62242i	1.61992	+	0.324556i
$880$		0			0
$881$		−	21.8993i		−	0.737807i	−0.929468	−	0.368904i	$-0.879733\pi$
$881$		−	21.8993i		−	0.737807i	0.929468	−	0.368904i	$-0.120267\pi$
$882$		0			0
$883$	−37.9075			−1.27569			−0.637845	−	0.770164i	$-0.720174\pi$
$883$	−37.9075			−1.27569			−0.637845	+	0.770164i	$0.720174\pi$
$884$		0			0
$885$	−4.89654	+	24.4396i	−0.164595	+	0.821528i
$886$		0			0
$887$	−51.1713			−1.71816			−0.859082	−	0.511839i	$-0.828965\pi$
$887$	−51.1713			−1.71816			−0.859082	+	0.511839i	$0.828965\pi$
$888$		0			0
$889$			20.5985i			0.690851i
$890$		0			0
$891$	−13.3696	+	13.2223i	−0.447900	+	0.442964i
$892$		0			0
$893$	30.8495	−	10.1247i	1.03234	−	0.338812i
$894$		0			0
$895$			28.5129i			0.953081i
$896$		0			0
$897$	−19.4662	−	3.90011i	−0.649959	−	0.130221i
$898$		0			0
$899$			38.7053i			1.29089i
$900$		0			0
$901$		−	31.5057i		−	1.04961i
$902$		0			0
$903$	26.4737	+	5.30408i	0.880989	+	0.176509i
$904$		0			0
$905$	−30.2688			−1.00617
$906$		0			0
$907$			30.7386i			1.02066i	0.859979	+	0.510330i	$0.170477\pi$
$907$			30.7386i			1.02066i	−0.859979	+	0.510330i	$0.829523\pi$
$908$		0			0
$909$	17.1480	−	41.0768i	0.568765	−	1.36243i
$910$		0			0
$911$	−9.91233			−0.328410			−0.164205	−	0.986426i	$-0.552506\pi$
$911$	−9.91233			−0.328410			−0.164205	+	0.986426i	$0.552506\pi$
$912$		0			0
$913$	4.80363			0.158977
$914$		0			0
$915$	−4.02489	+	20.0890i	−0.133059	+	0.664123i
$916$		0			0
$917$			42.3251i			1.39770i
$918$		0			0
$919$	−30.8078			−1.01626			−0.508128	−	0.861282i	$-0.669662\pi$
$919$	−30.8078			−1.01626			−0.508128	+	0.861282i	$0.669662\pi$
$920$		0			0
$921$	1.75504	−	8.75977i	0.0578307	−	0.288644i
$922$		0			0
$923$		−	50.1648i		−	1.65120i
$924$		0			0
$925$		−	43.8790i		−	1.44273i
$926$		0			0
$927$	2.47742	−	5.93446i	0.0813691	−	0.194913i
$928$		0			0
$929$			42.5968i			1.39756i	0.715339	+	0.698778i	$0.246272\pi$
$929$			42.5968i			1.39756i	−0.715339	+	0.698778i	$0.753728\pi$
$930$		0			0
$931$	−16.5444	−	50.4100i	−0.542222	−	1.65212i
$932$		0			0
$933$	6.90443	−	34.4613i	0.226041	−	1.12821i
$934$		0			0
$935$			30.7307i			1.00500i
$936$		0			0
$937$	16.8937			0.551893			0.275947	−	0.961173i	$-0.411009\pi$
$937$	16.8937			0.551893			0.275947	+	0.961173i	$0.411009\pi$
$938$		0			0
$939$	−6.19487	−	1.24116i	−0.202162	−	0.0405037i
$940$		0			0
$941$	30.2180			0.985077			0.492539	−	0.870291i	$-0.336069\pi$
$941$	30.2180			0.985077			0.492539	+	0.870291i	$0.336069\pi$
$942$		0			0
$943$		−	4.72018i		−	0.153710i
$944$		0			0
$945$	48.1856	−	71.4701i	1.56748	−	2.32492i
$946$		0			0
$947$			14.4370i			0.469139i	0.972099	+	0.234570i	$0.0753681\pi$
$947$			14.4370i			0.469139i	−0.972099	+	0.234570i	$0.924632\pi$
$948$		0			0
$949$		−	37.0735i		−	1.20346i
$950$		0			0
$951$	−27.6220	−	5.53415i	−0.895705	−	0.179457i
$952$		0			0
$953$	8.92691			0.289171			0.144585	−	0.989492i	$-0.453815\pi$
$953$	8.92691			0.289171			0.144585	+	0.989492i	$0.453815\pi$
$954$		0			0
$955$	12.1986			0.394737
$956$		0			0
$957$	3.93618	−	19.6463i	0.127239	−	0.635073i
$958$		0			0
$959$			25.3220i			0.817690i
$960$		0			0
$961$	−17.8661			−0.576325
$962$		0			0
$963$	−4.15491	−	1.73452i	−0.133890	−	0.0558941i
$964$		0			0
$965$	86.4818			2.78395
$966$		0			0
$967$	48.6345			1.56398			0.781991	−	0.623290i	$-0.214204\pi$
$967$	48.6345			1.56398			0.781991	+	0.623290i	$0.214204\pi$
$968$		0			0
$969$	29.1026	−	3.49105i	0.934909	−	0.112149i
$970$		0			0
$971$	9.18459			0.294747			0.147374	−	0.989081i	$-0.452918\pi$
$971$	9.18459			0.294747			0.147374	+	0.989081i	$0.452918\pi$
$972$		0			0
$973$	73.3178			2.35046
$974$		0			0
$975$	−16.5409	+	82.5590i	−0.529733	+	2.64400i
$976$		0			0
$977$	−25.5668			−0.817956			−0.408978	−	0.912544i	$-0.634115\pi$
$977$	−25.5668			−0.817956			−0.408978	+	0.912544i	$0.634115\pi$
$978$		0			0
$979$		−	17.0881i		−	0.546139i
$980$		0			0
$981$	8.49072	−	20.3388i	0.271088	−	0.649369i
$982$		0			0
$983$	29.1564			0.929945			0.464972	−	0.885325i	$-0.346064\pi$
$983$	29.1564			0.929945			0.464972	+	0.885325i	$0.346064\pi$
$984$		0			0
$985$	23.2600			0.741125
$986$		0			0
$987$	11.0975	−	55.3900i	0.353238	−	1.76308i
$988$		0			0
$989$			7.85153i			0.249664i
$990$		0			0
$991$			47.0795i			1.49553i	0.663963	+	0.747765i	$0.268873\pi$
$991$			47.0795i			1.49553i	−0.663963	+	0.747765i	$0.731127\pi$
$992$		0			0
$993$	6.30179	−	31.4535i	0.199981	−	0.998146i
$994$		0			0
$995$		−	8.08505i		−	0.256313i
$996$		0			0
$997$	−26.0219			−0.824121			−0.412061	−	0.911156i	$-0.635191\pi$
$997$	−26.0219			−0.824121			−0.412061	+	0.911156i	$0.635191\pi$
$998$		0			0
$999$	13.6270	−	20.2119i	0.431138	−	0.639475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.f.h.113.1		10
3.2	odd	2		912.2.f.i.113.9		10
4.3	odd	2		456.2.f.b.113.10	yes	10
12.11	even	2		456.2.f.a.113.2	yes	10
19.18	odd	2		912.2.f.i.113.10		10
57.56	even	2	inner	912.2.f.h.113.2		10
76.75	even	2		456.2.f.a.113.1	✓	10
228.227	odd	2		456.2.f.b.113.9	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.f.a.113.1	✓	10	76.75	even	2
456.2.f.a.113.2	yes	10	12.11	even	2
456.2.f.b.113.9	yes	10	228.227	odd	2
456.2.f.b.113.10	yes	10	4.3	odd	2
912.2.f.h.113.1		10	1.1	even	1	trivial
912.2.f.h.113.2		10	57.56	even	2	inner
912.2.f.i.113.9		10	3.2	odd	2
912.2.f.i.113.10		10	19.18	odd	2

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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.69830 - 0.340259i) q^{3} +3.78858i q^{5} +4.37856 q^{7} +(2.76845 + 1.15572i) q^{9} +O(q^{10})\)	\(q+(-1.69830 - 0.340259i) q^{3} +3.78858i q^{5} +4.37856 q^{7} +(2.76845 + 1.15572i) q^{9} +2.08929i q^{11} +5.19736i q^{13} +(1.28910 - 6.43415i) q^{15} -3.88236i q^{17} +(-1.35925 - 4.14155i) q^{19} +(-7.43610 - 1.48984i) q^{21} -2.20539i q^{23} -9.35336 q^{25} +(-4.30841 - 2.90476i) q^{27} +5.53689 q^{29} +6.99043i q^{31} +(0.710900 - 3.54824i) q^{33} +16.5885i q^{35} +4.69126i q^{37} +(1.76845 - 8.82667i) q^{39} +2.14029 q^{41} -3.56016 q^{43} +(-4.37856 + 10.4885i) q^{45} +7.44879i q^{47} +12.1718 q^{49} +(-1.32101 + 6.59342i) q^{51} +8.11509 q^{53} -7.91545 q^{55} +(0.899209 + 7.49609i) q^{57} -3.79842 q^{59} -3.12225 q^{61} +(12.1218 + 5.06040i) q^{63} -19.6906 q^{65} -8.92592i q^{67} +(-0.750404 + 3.74541i) q^{69} -9.65199 q^{71} -7.13314 q^{73} +(15.8848 + 3.18256i) q^{75} +9.14808i q^{77} +11.8618i q^{79} +(6.32860 + 6.39912i) q^{81} -2.29917i q^{83} +14.7087 q^{85} +(-9.40331 - 1.88398i) q^{87} -8.17891 q^{89} +22.7569i q^{91} +(2.37856 - 11.8718i) q^{93} +(15.6906 - 5.14962i) q^{95} +2.33687i q^{97} +(-2.41464 + 5.78409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q - q^3 + 2 * q^7 + 3 * q^9	\( 10 q - q^{3} + 2 q^{7} + 3 q^{9} + 10 q^{15} - 2 q^{19} - 5 q^{21} - 14 q^{25} - 10 q^{27} + 6 q^{29} + 10 q^{33} - 7 q^{39} + 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} + q^{51} + 26 q^{53} + 12 q^{55} - 11 q^{57} + 2 q^{59} - 4 q^{61} + 17 q^{63} - 32 q^{65} + 27 q^{69} + 8 q^{71} - 26 q^{73} + 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} - 4 q^{89} - 18 q^{93} - 8 q^{95} - 2 q^{99}+O(q^{100}) \) 10 * q - q^3 + 2 * q^7 + 3 * q^9 + 10 * q^15 - 2 * q^19 - 5 * q^21 - 14 * q^25 - 10 * q^27 + 6 * q^29 + 10 * q^33 - 7 * q^39 + 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 + q^51 + 26 * q^53 + 12 * q^55 - 11 * q^57 + 2 * q^59 - 4 * q^61 + 17 * q^63 - 32 * q^65 + 27 * q^69 + 8 * q^71 - 26 * q^73 + 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 - 4 * q^89 - 18 * q^93 - 8 * q^95 - 2 * q^99

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